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examples/MoDeNaModels/twoTankFortran/src/twoTanksMacroscopicProblemFortran.f90 create mode 100644 examples/MoDeNaModels/twoTankFortran/twoTankFortran.py create mode 100644 examples/multicomponentDiffusion/README.md create mode 100644 examples/twoTanks/README.md create mode 100644 examples/twoTanksAutoInit/README.md create mode 100644 examples/twoTanksChained/README.md create mode 100644 examples/twoTanksFortran/README.md diff --git a/applications/PUfoam/MoDeNaModels/CFD_tool_0D/.gitignore b/applications/PUfoam/MoDeNaModels/CFD_tool_0D/.gitignore new file mode 100644 index 000000000..0c39074ec --- /dev/null +++ b/applications/PUfoam/MoDeNaModels/CFD_tool_0D/.gitignore @@ -0,0 +1,5 @@ +QmomKinetics +Makefile +cmake_install.cmake +CMakeCache.txt +CMakeFiles/ \ No newline at end of file diff --git a/applications/PUfoam/MoDeNaModels/CFD_tool_0D/QmomKinetics.py b/applications/PUfoam/MoDeNaModels/CFD_tool_0D/QmomKinetics.py new file mode 100644 index 000000000..bb4b28a24 --- /dev/null +++ b/applications/PUfoam/MoDeNaModels/CFD_tool_0D/QmomKinetics.py @@ -0,0 +1,46 @@ +'''@cond + + ooo ooooo oooooooooo. ooooo ooo + `88. .888' `888' `Y8b `888b. `8' + 888b d'888 .ooooo. 888 888 .ooooo. 8 `88b. 8 .oooo. + 8 Y88. .P 888 d88' `88b 888 888 d88' `88b 8 `88b. 8 `P )88b + 8 `888' 888 888 888 888 888 888ooo888 8 `88b.8 .oP"888 + 8 Y 888 888 888 888 d88' 888 .o 8 `888 d8( 888 + o8o o888o `Y8bod8P' o888bood8P' `Y8bod8P' o8o `8 `Y888""8o + +Copyright + 2014-2015 MoDeNa Consortium, All rights reserved. + +License + This file is part of Modena. + + Modena is free software; you can redistribute it and/or modify it under + the terms of the GNU General Public License as published by the Free + Software Foundation, either version 3 of the License, or (at your option) + any later version. + + Modena is distributed in the hope that it will be useful, but WITHOUT ANY + WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS + FOR A PARTICULAR PURPOSE. See the GNU General Public License + for more details. + + You should have received a copy of the GNU General Public License along + with Modena. If not, see . +@endcond''' + +""" +@file +Backward mapping Firetask for QmomKinetics model. +Contains path to the detailed model executable. + +@author Mohsen Karimi +@copyright 2014-2015, MoDeNa Project. GNU Public License. +@ingroup app_foaming +""" +import os +from modena.Strategy import BackwardMappingScriptTask + +# Source code in src/twoTanksMacroscopicProblem.C +m = BackwardMappingScriptTask( + script=os.path.dirname(os.path.abspath(__file__))+'/src/QmomKinetics' +) diff --git a/applications/PUfoam/MoDeNaModels/CFD_tool_0D/README.md b/applications/PUfoam/MoDeNaModels/CFD_tool_0D/README.md new file mode 100644 index 000000000..4cabdd382 --- /dev/null +++ b/applications/PUfoam/MoDeNaModels/CFD_tool_0D/README.md @@ -0,0 +1,65 @@ +# README +@ingroup app_foaming +@brief This is a 0D example of the CFD code with the calls to the database using the MoDeNa interface. + +## Description +This is a zero dimensional prototype of the application of MoDeNa interface library to connect different +modeling scales. The first prototype shows the successful connections of nano, meso and macro sclaes for the simulation of foaming process. +The macro-scale code builds the RHS of 20 ODEs within the `QmomKinetics( const state_type &y , state_type &dydt , double t )` function including: +- dydt[0] : XW, conversion of the blowing reaction +- dydt[1] : XOH, conversion of the gelling reaction +- dydt[2] : T, temperature of the foam, K +- dydt[3] : L_l, weight fraction of the blowing agent in the liquid +- dydt[4] : L_g, weight fraction of the blowing agent in the gas +- dydt[5] : CO2_l, weight fraction of CO2 in the liquid +- dydt[6] : CO2_g, weight fraction of CO2 in the gas +- dydt[7] : m0, moment of order zero of the BSD +- dydt[8] : m1, moment of order one of the BSD +- dydt[9] : m2, moment of order two of the BSD +- dydt[10]: m3, moment of order three of the BSD +- dydt[11]: EG_NCO, Concentration of NCO end groups +- dydt[12]: EG_OH, Concentration of OH end groups +- dydt[13]: H2O, Water concentration +- dydt[14]: CO2, CO2 Concentration +- dydt[15]: PENTANE, Cylcopentane concentration +- dydt[16]: POLYMER, Dummy concentration of polymer +- dydt[17]: POLYMERBLOW, Second dummy concentration of polymer +- dydt[18]: UREA, Concentration of urea end groups +- dydt[19]: R_1_temp, Temperature + +Throughout the computation of RHSs the inputs of the surrogate models are set and the outputs are retirieved using modena library. +It should be remembred that the surrogate models should be initialized on the local machine before running this code. +The `write_kinetics(y, t)` function appends the results into the different text files that can be later plotted. +This function also computes the density of the foam based on the moments of BSD and converts the moments based +on the unit volume of the foam. +The `main(int argc, char **argv)` function starts with the initialization of the solution. Then, a 'stepper' has been +used to solve the ODEs. Further details on the integration method can be found [here.](http://headmyshoulder.github.io/odeint-v2/doc/boost_numeric_odeint/odeint_in_detail/steppers.html) + + +## How to run independently? + +1. Get Boost C++ Library + * Skip this step if you have boost at /usr/local/ (I have used boost_1_57_0) + * If not, get boost: + \verbatim sudo apt-get install libboost-dev + \endverbatim +2. Compile the project: + * \verbatim cmake . \endverbatim +3. Make the executatble from the main code + * \verbatim make \endverbatim +4. Set the environmental variable for the shared libraries by: + * \verbatim export LD_LIBRARY_PATH=$LD_LIBRARY_PATH:./eigen \endverbatim +5. Run the executable by: + * \verbatim ./QmomKinetics \endverbatim +6. Plot the results by software your choice. + +### Note: + In modifications of the solver are required, + first run the cleanupScript.sh (./cleanupScript) to remove the old results + then compile the modified code (make), + run the executable (./QmomKinetics) and plot the results (gnuplot gnuplot_script.gnu). + +------------- + +@authors Mohsen Karimi, Daniele Marchisio, Pavel Ferkl +@copyright 2014-2015, MoDeNa Project. GNU Public License. \ No newline at end of file diff --git a/applications/PUfoam/MoDeNaModels/CFD_tool_0D/__init__.py b/applications/PUfoam/MoDeNaModels/CFD_tool_0D/__init__.py new file mode 100644 index 000000000..dfc2471ce --- /dev/null +++ b/applications/PUfoam/MoDeNaModels/CFD_tool_0D/__init__.py @@ -0,0 +1,40 @@ +''' + + ooo ooooo oooooooooo. ooooo ooo + `88. .888' `888' `Y8b `888b. `8' + 888b d'888 .ooooo. 888 888 .ooooo. 8 `88b. 8 .oooo. + 8 Y88. .P 888 d88' `88b 888 888 d88' `88b 8 `88b. 8 `P )88b + 8 `888' 888 888 888 888 888 888ooo888 8 `88b.8 .oP"888 + 8 Y 888 888 888 888 d88' 888 .o 8 `888 d8( 888 + o8o o888o `Y8bod8P' o888bood8P' `Y8bod8P' o8o `8 `Y888""8o + +Copyright + 2014-2015 MoDeNa Consortium, All rights reserved. + +License + This file is part of Modena. + + Modena is free software; you can redistribute it and/or modify it under + the terms of the GNU General Public License as published by the Free + Software Foundation, either version 3 of the License, or (at your option) + any later version. + + Modena is distributed in the hope that it will be useful, but WITHOUT ANY + WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS + FOR A PARTICULAR PURPOSE. See the GNU General Public License + for more details. + + You should have received a copy of the GNU General Public License along + with Modena. If not, see . + +Description + Python library of FireTasks + +Authors + Henrik Rusche + +Contributors +''' + +from QmomKinetics import m + diff --git a/applications/PUfoam/MoDeNaModels/CFD_tool_0D/cleanupScript.sh b/applications/PUfoam/MoDeNaModels/CFD_tool_0D/cleanupScript.sh new file mode 100755 index 000000000..302aaf1c3 --- /dev/null +++ b/applications/PUfoam/MoDeNaModels/CFD_tool_0D/cleanupScript.sh @@ -0,0 +1,7 @@ +#!/bin/bash + +# delete everything but the good stuff! +ls > list +egrep -v 'CMakeCache.txt|CMakeFiles|cmake_install.cmake|Makefile|CMakeLists.txt|cleanupScript.sh|coalescence.h|eigen|experimentalInputs.h|getBoost.sh|gnuplot_script.gnu|growth.h|initializeMoments.h|liquidBA.h|partialPressure.h|README|readParameters.h|results|testingKinetics|pda.h|QmomKinetics|QmomKinetics.cpp|write_kinetics.h|momentsConverter.h|plot_cfd.vsz|inputsQmom.in' list > list2 +mv list2 list +rm -rf $(. +@endcond +@file + This is a macro-scale modeling tool for the foaming process. The code utilizes + the MoDeNa interface library to connect different models including nano, and + meso scale models. The code returns the evolution of foam properties such as + density, temperature and bubble/cell size distribution. +@brief macor-scale tool for the foaming process. +@authors Mohsen Karimi, Daniele Marchisio, Pavel Ferkl +@copyright 2014-2015, MoDeNa Project. GNU Public License. +@ingroup app_foaming +*/ + +#include +#include +#include +#include +#include +#include +#include "modena.h" + +extern "C"{void dsteqr_(char &, int *, double *, double *, double *, int *, double *, int *); } + +#include "experimentalInputs.h" +#include "readParameters.h" +#include "initializeMoments.h" +#include "pda.h" +#include "growth.h" +#include "coalescence.h" +#include "liquidBA.h" + +using namespace std; +using namespace boost::numeric::odeint; +/** +@typedef +typedef vector to state_type +typedef runge_kutta_cash_karp54< state_type > error_stepper_type +typedef controlled_runge_kutta< error_stepper_type > controlled_stepper_type +*/ +typedef std::vector< double > state_type; +typedef runge_kutta_cash_karp54< state_type > error_stepper_type; +typedef controlled_runge_kutta< error_stepper_type > controlled_stepper_type; +/** +@var controlled_stepper +@sa http://headmyshoulder.github.io/odeint-v2/doc/boost_numeric_odeint/concepts/controlled_stepper.html +*/ +controlled_stepper_type controlled_stepper; + +#include "partialPressure.h" +/** +@var dpdt[2]: global double array +@brief This is used to compute the partial pressures. + +@var pOld[2]: global double array variable +@brief This is to hold the old pressure values during the partial pressure calculations. +*/ +double dpdt[2] = {}; +double pOld[2] = {}; + +#include "modenaCalls.h" +#include "momentsConverter.h" +#include "write_kinetics.h" +/** +@fn QmomKinetics(const state_type &y , state_type &dydt , double t) +@brief This is to calculate the RHD of all the ODEs. +@param [in] const state_type &y - vector to hold the results. +@param [in] state_type &dydt - vector to hold the RHDs of ODEs. +@param [in] double t - time +@return void. +*/ +void QmomKinetics( const state_type &y , state_type &dydt , double t ) +{ + // dydt[0] : XW + // dydt[1] : XOH + // dydt[2] : T + // dydt[3] : L_l + // dydt[4] : L_g + // dydt[5] : CO2_l + // dydt[6] : CO2_g + // dydt[7] : m0 + // dydt[8] : m1 + // dydt[9] : m2 + // dydt[10]: m3 + // ---simpleKinetics--- + // dydt[11]: EG_NCO + // dydt[12]: EG_OH + // dydt[13]: H2O + // dydt[14]: CO2 + // dydt[15]: PENTANE + // dydt[16]: POLYMER + // dydt[17]: POLYMERBLOW + // dydt[18]: UREA + // dydt[19]: R_1_temp + + int nNodes = 2; + int mOrder[6] = {0, 1, 2, 3, 4, 5}; + double mom[2*nNodes], we[nNodes], vi[nNodes], sgBA[2*nNodes], sgCO2[2*nNodes], sc[2*nNodes]; + double L_l, L_g, CO2_l, CO2_g, T, Lm, c1; + double rhoPolySurrgate; + double beta0 = 0.0; + double XW, XOH; + // simpleKinetics variables + double EG_XNCO, EG_NCO, EG_OH, EG_XOH, H2O, XH2O, CO2, PENTANE, POLYMER, POLYMERBLOW, UREA, R_1_temp; + double init_EG_NCO = 5.0; + double init_EG_OH = 5.0; + double init_H2O = 0.2; + + XW = y[0]; + XOH = y[1]; + T = y[2]; + L_l = y[3]; + L_g = y[4]; + CO2_l = y[5]; + CO2_g = y[6]; + mom[0] = y[7]; + mom[1] = y[8]; + mom[2] = y[9]; + mom[3] = y[10]; + // EG_NCO = y[11]; + // EG_OH = y[12]; + // H2O = y[13]; + // CO2 = y[14]; + // PENTANE = y[15]; + // POLYMER = y[16]; + // POLYMERBLOW = y[17]; + // UREA = y[18]; + // R_1_temp = y[19]; + + // EG_XNCO = 1.0 - (y[11]/init_EG_NCO); + // EG_XOH = 1.0 - (y[12]/init_EG_OH); + // XH2O = 1.0 - (y[13]/init_H2O); + + // Calling the simpleKinetics model + // if (kinMod == 3) + // { + // // inputs argPos + // modena_model_t *kinetics = modena_model_new("simpleKinetics"); + // modena_inputs_t *inputs_kinetics = modena_inputs_new (kinetics); + // modena_outputs_t *outputs_kinetics = modena_outputs_new (kinetics); + // size_t EG_NCO_Pos = modena_model_inputs_argPos(kinetics, "'EG_NCO'"); + // size_t EG_OH_Pos = modena_model_inputs_argPos(kinetics, "'EG_OH'"); + // size_t H2O_Pos = modena_model_inputs_argPos(kinetics, "'H2O'"); + // size_t CO2_Pos = modena_model_inputs_argPos(kinetics, "'CO2'"); + // size_t PENTANE_Pos = modena_model_inputs_argPos(kinetics, "'PENTANE'"); + // size_t POLYMER_Pos = modena_model_inputs_argPos(kinetics, "'POLYMER'"); + // size_t POLYMERBLOW_Pos = modena_model_inputs_argPos(kinetics, "'POLMERBLOW'"); + // size_t UREA_Pos = modena_model_inputs_argPos(kinetics, "'UREA'"); + // size_t R_1_temp_Pos = modena_model_inputs_argPos(kinetics, "'R_1_temp'"); + + // // outputs argPos + // size_t source_EG_NCO_Pos = modena_model_outputs_argPos(kinetics, "source_EG_NCO"); + // size_t source_EG_OH_Pos = modena_model_outputs_argPos(kinetics, "source_EG_OH"); + // size_t source_H2O_Pos = modena_model_outputs_argPos(kinetics, "source_H2O"); + // size_t source_CO2_Pos = modena_model_outputs_argPos(kinetics, "source_CO2"); + // size_t source_PENTANE_Pos = modena_model_outputs_argPos(kinetics, "source_PENTANE"); + // size_t source_POLYMER_Pos = modena_model_outputs_argPos(kinetics, "source_POLYMER"); + // size_t source_POLYMERBLOW_Pos = modena_model_outputs_argPos(kinetics, "source_POLMERBLOW"); + // size_t source_UREA_Pos = modena_model_outputs_argPos(kinetics, "source_UREA"); + // size_t source_R_1_temp_Pos = modena_model_outputs_argPos(kinetics, "source_R_1_temp"); + + // modena_model_argPos_check(kinetics); + + // // set input vector + // modena_inputs_set(inputs_kinetics, EG_NCO_Pos, EG_NCO); + // modena_inputs_set(inputs_kinetics, EG_OH_Pos, EG_OH); + // modena_inputs_set(inputs_kinetics, H2O_Pos, H2O); + // modena_inputs_set(inputs_kinetics, CO2_Pos, CO2); + // modena_inputs_set(inputs_kinetics, PENTANE_Pos, PENTANE); + // modena_inputs_set(inputs_kinetics, POLYMER_Pos, POLYMER); + // modena_inputs_set(inputs_kinetics, POLYMERBLOW_Pos, POLYMERBLOW); + // modena_inputs_set(inputs_kinetics, UREA_Pos, UREA); + // modena_inputs_set(inputs_kinetics, R_1_temp_Pos, R_1_temp); + + + // // call the model + // int ret_kinetics = modena_model_call(kinetics, inputs_kinetics, outputs_kinetics); + + // // terminate, if requested + // if(ret_kinetics != 0) + // { + // modena_inputs_destroy (inputs_kinetics); + // modena_outputs_destroy (outputs_kinetics); + // modena_model_destroy (kinetics); + // //return ret_kinetics; + // } + + // // get the source terms for simpleKinetics + // dydt[11] = modena_outputs_get(outputs_kinetics, source_EG_NCO_Pos); + // dydt[12] = modena_outputs_get(outputs_kinetics, source_EG_OH_Pos); + // dydt[13] = modena_outputs_get(outputs_kinetics, source_H2O_Pos); + // dydt[14] = modena_outputs_get(outputs_kinetics, source_CO2_Pos); + // dydt[15] = modena_outputs_get(outputs_kinetics, source_PENTANE_Pos); + // dydt[16] = modena_outputs_get(outputs_kinetics, source_POLYMER_Pos); + // dydt[17] = modena_outputs_get(outputs_kinetics, source_POLYMERBLOW_Pos); + // dydt[18] = modena_outputs_get(outputs_kinetics, source_UREA_Pos); + // dydt[19] = modena_outputs_get(outputs_kinetics, source_R_1_temp_Pos); + // } + + // Check for negative sources + // for (int i = 11; i < 20; i++) + // { + // if(dydt[i] < 0.0) + // { + // dydt[i] = 0.0; + // } + // } + + switch (denMod) + { + case 1: + { + // Calling the model for density reaction mixture + // size_t T_denpos = modena_model_inputs_argPos(density_reaction_mixturemodel, "T"); + // size_t XOH_denpos = modena_model_inputs_argPos(density_reaction_mixturemodel, "XOH"); + // modena_model_argPos_check(density_reaction_mixturemodel); + + // // set input vector + // modena_inputs_set(inputs_den, T_denpos, T); + // modena_inputs_set(inputs_den, XOH_denpos, EG_XOH); + + // // call the model + // int ret_den = modena_model_call (density_reaction_mixturemodel, inputs_den, outputs_den); + + // if(ret_den != 0) + // { + // modena_inputs_destroy (inputs_den); + // modena_outputs_destroy (outputs_den); + // modena_model_destroy (density_reaction_mixturemodel); + // exit(ret_den); + // } + + // rhoPolySurrgate = modena_outputs_get(outputs_den, 0); + // break; + } + case 2: + rhoPolySurrgate = rhoPoly; + break; + } + + // ODEs + dydt[0] = A_W*exp(-E_W/(RR*y[2]))*(1-y[0]); + if(dydt[0] < 0.0) + { + dydt[0] = 0.0; + } + if(W_0 < 0.0) + { + dydt[0] = 0.0; + } + + double Rx; + switch (kinMod) { + case 1: + Rx=1; + case 2: + if (y[1]<0.5) { + Rx=1; + } else if (y[1]<0.87) { + Rx=-2.027*y[1]+2.013; + } else { + Rx=3.461*y[1]-2.761; + } + } + + dydt[1] = Rx*A_OH*exp(-E_OH/(RR*y[2]))*OH_0*(1-y[1])*(NCO_0/OH_0 - 2.0*y[0]*W_0/OH_0 - y[1]); + if(dydt[1] < 0.0) + { + dydt[1] = 0.0; + } + if (dilution) { + dydt[0]=dydt[0]/(1+y[3]*rhoPolySurrgate/rhoBL); + dydt[1]=dydt[1]/(1+y[3]*rhoPolySurrgate/rhoBL); + } + double dT=1e-4; + double dLdT=(min(LMax(T),L0)-min(LMax(T+dT),L0))/dT; + C_TOT = C_Poly + CO2_g*C_CO2 + L_g*C_BG + L_l*C_BL + dLdT*lambda; + // this implementation of evaporation heat assumes that concentration of + // physical blowing agent in liquid is always in equilibrium + dydt[2] = (-DH_OH*OH_0)/(rhoPolySurrgate*C_TOT)*dydt[1]+(-DH_W*W_0)/(rhoPolySurrgate*C_TOT)*dydt[0]; + + Lm = LMax(T); + + // bubble radius for bblgr1 and bblgr2 model + double R = bubbleRadius(mom[0], mom[1]); + + // partial pressure within bubbles due to the evaporation of physical blowing agent + double p_1 = partialPressureBA(y); + + // partial pressure within bubbles due to the generation of CO2 + double p_2 = partialPressureCO2(y); + + double c_1 = L_l*rhoPolySurrgate*1000.0/M_B; + double c_2 = CO2_l*rhoPolySurrgate*1000.0/M_CO2; + double KH1 = (rhoPolySurrgate*Lm)/((M_B/1000.0)*Pr); + double KH2 = (rhoPolySurrgate*CO2_D)/((M_CO2/1000.0)*Pr); + + size_t Tbblgr1pos = modena_model_inputs_argPos(bblgr1, "T"); + size_t Rbblgr1pos = modena_model_inputs_argPos(bblgr1, "R"); + size_t KH1bblgr1pos = modena_model_inputs_argPos(bblgr1, "kH"); + size_t c_1bblgr1pos = modena_model_inputs_argPos(bblgr1, "c"); + size_t p_1bblgr1pos = modena_model_inputs_argPos(bblgr1, "p"); + modena_model_argPos_check(bblgr1); + size_t Tbblgr2pos = modena_model_inputs_argPos(bblgr2, "T"); + size_t Rbblgr2pos = modena_model_inputs_argPos(bblgr2, "R"); + size_t KH2bblgr2pos = modena_model_inputs_argPos(bblgr2, "kH"); + size_t c_2bblgr2pos = modena_model_inputs_argPos(bblgr2, "c"); + size_t p_2bblgr2pos = modena_model_inputs_argPos(bblgr2, "p"); + modena_model_argPos_check(bblgr2); + + // set input vector + modena_inputs_set(inputs_bblgr1, Tbblgr1pos, T); + modena_inputs_set(inputs_bblgr1, Rbblgr1pos, R); + modena_inputs_set(inputs_bblgr1, KH1bblgr1pos, KH1); + modena_inputs_set(inputs_bblgr1, c_1bblgr1pos, c_1); + modena_inputs_set(inputs_bblgr1, p_1bblgr1pos, p_1); + // set input vector + modena_inputs_set(inputs_bblgr2, Tbblgr2pos, T); + modena_inputs_set(inputs_bblgr2, Rbblgr2pos, R); + modena_inputs_set(inputs_bblgr2, KH2bblgr2pos, KH2); + modena_inputs_set(inputs_bblgr2, c_2bblgr2pos, c_2); + modena_inputs_set(inputs_bblgr2, p_2bblgr2pos, p_2); + + // call the bblgr1 model + int ret_bblgr1 = modena_model_call (bblgr1, inputs_bblgr1, outputs_bblgr1); + // terminate, if requested + if(ret_bblgr1 != 0) + { + modena_inputs_destroy (inputs_bblgr1); + modena_outputs_destroy (outputs_bblgr1); + modena_model_destroy (bblgr1); + // return ret_bblgr1; + } + // call the bblgr2 model + int ret_bblgr2 = modena_model_call (bblgr2, inputs_bblgr2, outputs_bblgr2); + // terminate, if requested + if(ret_bblgr2 != 0) + { + modena_inputs_destroy (inputs_bblgr2); + modena_outputs_destroy (outputs_bblgr2); + modena_model_destroy (bblgr2); + // return ret_bblgr2; + } + + double G1, G2, dVdt_1, dVdt_2; + G1 = modena_outputs_get(outputs_bblgr1, 0); + G2 = modena_outputs_get(outputs_bblgr2, 0); + // double mpar=0.0; + // double mpar2=1.0; + // G1=G1*pow(R,mpar)*mpar2; //for testing + // G2=G2*pow(R,mpar)*mpar2; + dVdt_1 = (G1*RR*T)/(p_1); + if (dVdt_1 < 0.0 || G1 < 0.0 || L0<1e-8 || y[1]>0.5) //hardcoded gel point + { + dVdt_1 = 0.0; + } + dVdt_2 = (G2*RR*T)/(p_2); + if (dVdt_2 < 0.0 || G2 < 0.0 || W_0<1e-8 || y[1]>0.5) //hardcoded gel point + { + dVdt_2 = 0.0; + } + + // call the surrogate model for rheology + // double shearRate = 0.3; + + // size_t temp_rheopos = modena_model_inputs_argPos(rheologymodel, "temp"); + // size_t conv_rheopos = modena_model_inputs_argPos(rheologymodel, "conv"); + // size_t shear_rheopos = modena_model_inputs_argPos(rheologymodel, "shear"); + + // modena_model_argPos_check(rheologymodel); + + // // set input vector + // modena_inputs_set(inputs_rheo, temp_rheopos, T); + // modena_inputs_set(inputs_rheo, conv_rheopos, EG_XOH); + // modena_inputs_set(inputs_rheo, shear_rheopos, shearRate); + + // // call the model + // int ret_rheo = modena_model_call (rheologymodel, inputs_rheo, outputs_rheo); + + // // terminate, if requested + // if(ret_rheo != 0) + // { + // modena_inputs_destroy (inputs_rheo); + // modena_outputs_destroy (outputs_rheo); + // modena_model_destroy (rheologymodel); + // } + + // double mu_app = modena_outputs_get(outputs_rheo, 0); + + // Gelling point representation + if(y[1] > 0.5) + { + beta0 = 0.0; + } + else + { + beta0 = beta0; + } + + PDA(we, vi, mom, nNodes); + growthSource(sgBA, sgCO2, we, vi, nNodes, mOrder, CO2_l, L_l, T, dVdt_2, dVdt_1); + coalescenceSource(sc, we, vi, nNodes, mOrder, beta0); + + dydt[3] = -sgBA[1]*(p_1/(RR*y[2]))*(M_B/1000.0)*(1.0/rhoPolySurrgate); + dydt[4] = sgBA[1]*(p_1/(RR*y[2]))*(M_B/1000.0)*(1.0/rhoPolySurrgate); + dydt[6] = sgCO2[1]*(p_2/(RR*y[2]))*(M_CO2/1000.0)*(1.0/rhoPolySurrgate); + dydt[5] = -sgCO2[1]*(p_2/(RR*y[2]))*(M_CO2/1000.0)*(1.0/rhoPolySurrgate) + W_0*dydt[0]*(M_CO2/1000.0)*(1.0/rhoPolySurrgate); + + dydt[7] = sgBA[0] + sgCO2[0] + sc[0]; + dydt[8] = sgBA[1] + sgCO2[1] + sc[1]; + dydt[9] = sgBA[2] + sgCO2[2] + sc[2]; + dydt[10] = sgBA[3] + sgCO2[3] + sc[3]; +} +/** +@fn main(int argc, char **argv) +@brief main function, initializes the state_type variables and performs the integration. + +*/ +int main(int argc, char **argv) +{ + readParams(); + // initial conditions + state_type y(11); + y[0] = 0.0; + y[1] = 0.0; + y[2] = Temp0; + y[3] = L0; + y[4] = 1.0e-14; + y[5] = 0.0; + y[6] = 1.0e-14; + + // moments initialization + int nOfmom = 4; + double momz[nOfmom]; + double pBA, pCO2, bubble_radius; + mom_init(momz, init_size, nOfmom, sig, NN); + + y[7] = momz[0]; + y[8] = momz[1]; + y[9] = momz[2]; + y[10] = momz[3]; + double R = bubbleRadius(y[7], y[8]); + air_g=y[8]/(1+y[8])*M_air*1e-3*(Pr+2*surfaceTension/R)/(RR*Temp0*rhoPoly); + + // initialize simpleKinetics variables + // y[11] = 5.0; + // y[12] = 5.0; + // y[13] = 0.2; + // y[14] = 0.0; + // y[15] = 0.0; + // y[16] = 0.0; + // y[17] = 0.0; + // y[18] = 0.0; + // y[19] = 300.0; + + + runge_kutta4< state_type > stepper; + + for( double t=0.0 ; t stepper; + integrate_const( stepper , harmonic_oscillator , x , 0.0 , 10.0 , 0.01 ); +] + +[ integrate_const_loop + const double dt = 0.01; + for( double t=0.0 ; t<10.0 ; t+= dt ) + stepper.do_step( harmonic_oscillator , x , t , dt ); + ] + + [ define_adapt_stepper + typedef runge_kutta_cash_karp54< state_type > error_stepper_type; + ] + + [integrate_adapt_make_controlled + integrate_adaptive( make_controlled< error_stepper_type >( 1.0e-10 , 1.0e-6 ) , + harmonic_oscillator , x , 0.0 , 10.0 , 0.01 ); + ] +[ integrate_const with abs and rel error +integrate_const( make_dense_output( 1.0e-6 , 1.0e-6 , runge_kutta_dopri5< state_type >() ) , sys , inout , t_start , t_end , dt ); +irst two parameters are the absolute and the relative error tolerances +] +[ using adaptive integrate +double abs_err = 1.0e-12; + double rel_err = 1.0e-10; + integrate_adaptive( make_controlled< error_stepper_type >(abs_err , rel_err), kinetics, y, 0.0, 300.0, 0.01, write_kinetics ); + +] + +*/ diff --git a/applications/PUfoam/MoDeNaModels/CFD_tool_0D/src/coalescence.h b/applications/PUfoam/MoDeNaModels/CFD_tool_0D/src/coalescence.h new file mode 100644 index 000000000..146b2c55a --- /dev/null +++ b/applications/PUfoam/MoDeNaModels/CFD_tool_0D/src/coalescence.h @@ -0,0 +1,87 @@ +/** @file coalescence.h + @brief Source term due to bubble coalescence + @fn void coalescenceSource(double *sc, double *we, double *vi, int &nNodes, int *mOrder, double &beta0) + @param double *sc - source due to coalescence + @param double *we - weights of quadrature approximation + @param double *vi - nodes of quadrature approximation + @param int &nNodes - number of nodes + @param int *mOrder - order of moments + @param double &beta0 - coalescence constant + @return void. +*/ + +void coalescenceSource(double *, double *, double *, int &, int *, double &); + +void coalescenceSource(double *sc, double *we, double *vi, int &nNodes, int *mOrder, double &beta0) +{ + + + int counter = 0; + double k; // To hold the moment order + int i, j; + +// coalescence kernel beta0*(v(i) + v(j)) + + while(counter<2*nNodes) + { + sc[counter] = 0.0; + k = static_cast(mOrder[counter]); + + if(counter == 0) + { + for(i=0;i \brief \b DCOPY +* +* =========== DOCUMENTATION =========== +* +* Online html documentation available at +* http://www.netlib.org/lapack/explore-html/ +* +* Definition: +* =========== +* +* SUBROUTINE DCOPY(N,DX,INCX,DY,INCY) +* +* .. Scalar Arguments .. +* INTEGER INCX,INCY,N +* .. +* .. Array Arguments .. +* DOUBLE PRECISION DX(*),DY(*) +* .. +* +* +*> \par Purpose: +* ============= +*> +*> \verbatim +*> +*> DCOPY copies a vector, x, to a vector, y. +*> uses unrolled loops for increments equal to one. +*> \endverbatim +* +* Authors: +* ======== +* +*> \author Univ. of Tennessee +*> \author Univ. of California Berkeley +*> \author Univ. of Colorado Denver +*> \author NAG Ltd. +* +*> \date November 2011 +* +*> \ingroup double_blas_level1 +* +*> \par Further Details: +* ===================== +*> +*> \verbatim +*> +*> jack dongarra, linpack, 3/11/78. +*> modified 12/3/93, array(1) declarations changed to array(*) +*> \endverbatim +*> +* ===================================================================== + SUBROUTINE DCOPY(N,DX,INCX,DY,INCY) +* +* -- Reference BLAS level1 routine (version 3.4.0) -- +* -- Reference BLAS is a software package provided by Univ. of Tennessee, -- +* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- +* November 2011 +* +* .. Scalar Arguments .. + INTEGER INCX,INCY,N +* .. +* .. Array Arguments .. + DOUBLE PRECISION DX(*),DY(*) +* .. +* +* ===================================================================== +* +* .. Local Scalars .. + INTEGER I,IX,IY,M,MP1 +* .. +* .. Intrinsic Functions .. + INTRINSIC MOD +* .. + IF (N.LE.0) RETURN + IF (INCX.EQ.1 .AND. INCY.EQ.1) THEN +* +* code for both increments equal to 1 +* +* +* clean-up loop +* + M = MOD(N,7) + IF (M.NE.0) THEN + DO I = 1,M + DY(I) = DX(I) + END DO + IF (N.LT.7) RETURN + END IF + MP1 = M + 1 + DO I = MP1,N,7 + DY(I) = DX(I) + DY(I+1) = DX(I+1) + DY(I+2) = DX(I+2) + DY(I+3) = DX(I+3) + DY(I+4) = DX(I+4) + DY(I+5) = DX(I+5) + DY(I+6) = DX(I+6) + END DO + ELSE +* +* code for unequal increments or equal increments +* not equal to 1 +* + IX = 1 + IY = 1 + IF (INCX.LT.0) IX = (-N+1)*INCX + 1 + IF (INCY.LT.0) IY = (-N+1)*INCY + 1 + DO I = 1,N + DY(IY) = DX(IX) + IX = IX + INCX + IY = IY + INCY + END DO + END IF + RETURN + END + diff --git a/applications/PUfoam/MoDeNaModels/CFD_tool_0D/src/eigen/src/dgemm.f b/applications/PUfoam/MoDeNaModels/CFD_tool_0D/src/eigen/src/dgemm.f new file mode 100644 index 000000000..7ac8c46bf --- /dev/null +++ b/applications/PUfoam/MoDeNaModels/CFD_tool_0D/src/eigen/src/dgemm.f @@ -0,0 +1,316 @@ + SUBROUTINE DGEMM(TRANSA,TRANSB,M,N,K,ALPHA,A,LDA,B,LDB,BETA,C,LDC) +* .. Scalar Arguments .. + DOUBLE PRECISION ALPHA,BETA + INTEGER K,LDA,LDB,LDC,M,N + CHARACTER TRANSA,TRANSB +* .. +* .. Array Arguments .. + DOUBLE PRECISION A(LDA,*),B(LDB,*),C(LDC,*) +* .. +* +* Purpose +* ======= +* +* DGEMM performs one of the matrix-matrix operations +* +* C := alpha*op( A )*op( B ) + beta*C, +* +* where op( X ) is one of +* +* op( X ) = X or op( X ) = X**T, +* +* alpha and beta are scalars, and A, B and C are matrices, with op( A ) +* an m by k matrix, op( B ) a k by n matrix and C an m by n matrix. +* +* Arguments +* ========== +* +* TRANSA - CHARACTER*1. +* On entry, TRANSA specifies the form of op( A ) to be used in +* the matrix multiplication as follows: +* +* TRANSA = 'N' or 'n', op( A ) = A. +* +* TRANSA = 'T' or 't', op( A ) = A**T. +* +* TRANSA = 'C' or 'c', op( A ) = A**T. +* +* Unchanged on exit. +* +* TRANSB - CHARACTER*1. +* On entry, TRANSB specifies the form of op( B ) to be used in +* the matrix multiplication as follows: +* +* TRANSB = 'N' or 'n', op( B ) = B. +* +* TRANSB = 'T' or 't', op( B ) = B**T. +* +* TRANSB = 'C' or 'c', op( B ) = B**T. +* +* Unchanged on exit. +* +* M - INTEGER. +* On entry, M specifies the number of rows of the matrix +* op( A ) and of the matrix C. M must be at least zero. +* Unchanged on exit. +* +* N - INTEGER. +* On entry, N specifies the number of columns of the matrix +* op( B ) and the number of columns of the matrix C. N must be +* at least zero. +* Unchanged on exit. +* +* K - INTEGER. +* On entry, K specifies the number of columns of the matrix +* op( A ) and the number of rows of the matrix op( B ). K must +* be at least zero. +* Unchanged on exit. +* +* ALPHA - DOUBLE PRECISION. +* On entry, ALPHA specifies the scalar alpha. +* Unchanged on exit. +* +* A - DOUBLE PRECISION array of DIMENSION ( LDA, ka ), where ka is +* k when TRANSA = 'N' or 'n', and is m otherwise. +* Before entry with TRANSA = 'N' or 'n', the leading m by k +* part of the array A must contain the matrix A, otherwise +* the leading k by m part of the array A must contain the +* matrix A. +* Unchanged on exit. +* +* LDA - INTEGER. +* On entry, LDA specifies the first dimension of A as declared +* in the calling (sub) program. When TRANSA = 'N' or 'n' then +* LDA must be at least max( 1, m ), otherwise LDA must be at +* least max( 1, k ). +* Unchanged on exit. +* +* B - DOUBLE PRECISION array of DIMENSION ( LDB, kb ), where kb is +* n when TRANSB = 'N' or 'n', and is k otherwise. +* Before entry with TRANSB = 'N' or 'n', the leading k by n +* part of the array B must contain the matrix B, otherwise +* the leading n by k part of the array B must contain the +* matrix B. +* Unchanged on exit. +* +* LDB - INTEGER. +* On entry, LDB specifies the first dimension of B as declared +* in the calling (sub) program. When TRANSB = 'N' or 'n' then +* LDB must be at least max( 1, k ), otherwise LDB must be at +* least max( 1, n ). +* Unchanged on exit. +* +* BETA - DOUBLE PRECISION. +* On entry, BETA specifies the scalar beta. When BETA is +* supplied as zero then C need not be set on input. +* Unchanged on exit. +* +* C - DOUBLE PRECISION array of DIMENSION ( LDC, n ). +* Before entry, the leading m by n part of the array C must +* contain the matrix C, except when beta is zero, in which +* case C need not be set on entry. +* On exit, the array C is overwritten by the m by n matrix +* ( alpha*op( A )*op( B ) + beta*C ). +* +* LDC - INTEGER. +* On entry, LDC specifies the first dimension of C as declared +* in the calling (sub) program. LDC must be at least +* max( 1, m ). +* Unchanged on exit. +* +* Further Details +* =============== +* +* Level 3 Blas routine. +* +* -- Written on 8-February-1989. +* Jack Dongarra, Argonne National Laboratory. +* Iain Duff, AERE Harwell. +* Jeremy Du Croz, Numerical Algorithms Group Ltd. +* Sven Hammarling, Numerical Algorithms Group Ltd. +* +* ===================================================================== +* +* .. External Functions .. + LOGICAL LSAME + EXTERNAL LSAME +* .. +* .. External Subroutines .. + EXTERNAL XERBLA +* .. +* .. Intrinsic Functions .. + INTRINSIC MAX +* .. +* .. Local Scalars .. + DOUBLE PRECISION TEMP + INTEGER I,INFO,J,L,NCOLA,NROWA,NROWB + LOGICAL NOTA,NOTB +* .. +* .. Parameters .. + DOUBLE PRECISION ONE,ZERO + PARAMETER (ONE=1.0D+0,ZERO=0.0D+0) +* .. +* +* Set NOTA and NOTB as true if A and B respectively are not +* transposed and set NROWA, NCOLA and NROWB as the number of rows +* and columns of A and the number of rows of B respectively. +* + NOTA = LSAME(TRANSA,'N') + NOTB = LSAME(TRANSB,'N') + IF (NOTA) THEN + NROWA = M + NCOLA = K + ELSE + NROWA = K + NCOLA = M + END IF + IF (NOTB) THEN + NROWB = K + ELSE + NROWB = N + END IF +* +* Test the input parameters. +* + INFO = 0 + IF ((.NOT.NOTA) .AND. (.NOT.LSAME(TRANSA,'C')) .AND. + + (.NOT.LSAME(TRANSA,'T'))) THEN + INFO = 1 + ELSE IF ((.NOT.NOTB) .AND. (.NOT.LSAME(TRANSB,'C')) .AND. + + (.NOT.LSAME(TRANSB,'T'))) THEN + INFO = 2 + ELSE IF (M.LT.0) THEN + INFO = 3 + ELSE IF (N.LT.0) THEN + INFO = 4 + ELSE IF (K.LT.0) THEN + INFO = 5 + ELSE IF (LDA.LT.MAX(1,NROWA)) THEN + INFO = 8 + ELSE IF (LDB.LT.MAX(1,NROWB)) THEN + INFO = 10 + ELSE IF (LDC.LT.MAX(1,M)) THEN + INFO = 13 + END IF + IF (INFO.NE.0) THEN + CALL XERBLA('DGEMM ',INFO) + RETURN + END IF +* +* Quick return if possible. +* + IF ((M.EQ.0) .OR. (N.EQ.0) .OR. + + (((ALPHA.EQ.ZERO).OR. (K.EQ.0)).AND. (BETA.EQ.ONE))) RETURN +* +* And if alpha.eq.zero. +* + IF (ALPHA.EQ.ZERO) THEN + IF (BETA.EQ.ZERO) THEN + DO 20 J = 1,N + DO 10 I = 1,M + C(I,J) = ZERO + 10 CONTINUE + 20 CONTINUE + ELSE + DO 40 J = 1,N + DO 30 I = 1,M + C(I,J) = BETA*C(I,J) + 30 CONTINUE + 40 CONTINUE + END IF + RETURN + END IF +* +* Start the operations. +* + IF (NOTB) THEN + IF (NOTA) THEN +* +* Form C := alpha*A*B + beta*C. +* + DO 90 J = 1,N + IF (BETA.EQ.ZERO) THEN + DO 50 I = 1,M + C(I,J) = ZERO + 50 CONTINUE + ELSE IF (BETA.NE.ONE) THEN + DO 60 I = 1,M + C(I,J) = BETA*C(I,J) + 60 CONTINUE + END IF + DO 80 L = 1,K + IF (B(L,J).NE.ZERO) THEN + TEMP = ALPHA*B(L,J) + DO 70 I = 1,M + C(I,J) = C(I,J) + TEMP*A(I,L) + 70 CONTINUE + END IF + 80 CONTINUE + 90 CONTINUE + ELSE +* +* Form C := alpha*A**T*B + beta*C +* + DO 120 J = 1,N + DO 110 I = 1,M + TEMP = ZERO + DO 100 L = 1,K + TEMP = TEMP + A(L,I)*B(L,J) + 100 CONTINUE + IF (BETA.EQ.ZERO) THEN + C(I,J) = ALPHA*TEMP + ELSE + C(I,J) = ALPHA*TEMP + BETA*C(I,J) + END IF + 110 CONTINUE + 120 CONTINUE + END IF + ELSE + IF (NOTA) THEN +* +* Form C := alpha*A*B**T + beta*C +* + DO 170 J = 1,N + IF (BETA.EQ.ZERO) THEN + DO 130 I = 1,M + C(I,J) = ZERO + 130 CONTINUE + ELSE IF (BETA.NE.ONE) THEN + DO 140 I = 1,M + C(I,J) = BETA*C(I,J) + 140 CONTINUE + END IF + DO 160 L = 1,K + IF (B(J,L).NE.ZERO) THEN + TEMP = ALPHA*B(J,L) + DO 150 I = 1,M + C(I,J) = C(I,J) + TEMP*A(I,L) + 150 CONTINUE + END IF + 160 CONTINUE + 170 CONTINUE + ELSE +* +* Form C := alpha*A**T*B**T + beta*C +* + DO 200 J = 1,N + DO 190 I = 1,M + TEMP = ZERO + DO 180 L = 1,K + TEMP = TEMP + A(L,I)*B(J,L) + 180 CONTINUE + IF (BETA.EQ.ZERO) THEN + C(I,J) = ALPHA*TEMP + ELSE + C(I,J) = ALPHA*TEMP + BETA*C(I,J) + END IF + 190 CONTINUE + 200 CONTINUE + END IF + END IF +* + RETURN +* +* End of DGEMM . +* + END diff --git a/applications/PUfoam/MoDeNaModels/CFD_tool_0D/src/eigen/src/dger.f b/applications/PUfoam/MoDeNaModels/CFD_tool_0D/src/eigen/src/dger.f new file mode 100644 index 000000000..1d95257e0 --- /dev/null +++ b/applications/PUfoam/MoDeNaModels/CFD_tool_0D/src/eigen/src/dger.f @@ -0,0 +1,162 @@ + SUBROUTINE DGER(M,N,ALPHA,X,INCX,Y,INCY,A,LDA) +* .. Scalar Arguments .. + DOUBLE PRECISION ALPHA + INTEGER INCX,INCY,LDA,M,N +* .. +* .. Array Arguments .. + DOUBLE PRECISION A(LDA,*),X(*),Y(*) +* .. +* +* Purpose +* ======= +* +* DGER performs the rank 1 operation +* +* A := alpha*x*y**T + A, +* +* where alpha is a scalar, x is an m element vector, y is an n element +* vector and A is an m by n matrix. +* +* Arguments +* ========== +* +* M - INTEGER. +* On entry, M specifies the number of rows of the matrix A. +* M must be at least zero. +* Unchanged on exit. +* +* N - INTEGER. +* On entry, N specifies the number of columns of the matrix A. +* N must be at least zero. +* Unchanged on exit. +* +* ALPHA - DOUBLE PRECISION. +* On entry, ALPHA specifies the scalar alpha. +* Unchanged on exit. +* +* X - DOUBLE PRECISION array of dimension at least +* ( 1 + ( m - 1 )*abs( INCX ) ). +* Before entry, the incremented array X must contain the m +* element vector x. +* Unchanged on exit. +* +* INCX - INTEGER. +* On entry, INCX specifies the increment for the elements of +* X. INCX must not be zero. +* Unchanged on exit. +* +* Y - DOUBLE PRECISION array of dimension at least +* ( 1 + ( n - 1 )*abs( INCY ) ). +* Before entry, the incremented array Y must contain the n +* element vector y. +* Unchanged on exit. +* +* INCY - INTEGER. +* On entry, INCY specifies the increment for the elements of +* Y. INCY must not be zero. +* Unchanged on exit. +* +* A - DOUBLE PRECISION array of DIMENSION ( LDA, n ). +* Before entry, the leading m by n part of the array A must +* contain the matrix of coefficients. On exit, A is +* overwritten by the updated matrix. +* +* LDA - INTEGER. +* On entry, LDA specifies the first dimension of A as declared +* in the calling (sub) program. LDA must be at least +* max( 1, m ). +* Unchanged on exit. +* +* Further Details +* =============== +* +* Level 2 Blas routine. +* +* -- Written on 22-October-1986. +* Jack Dongarra, Argonne National Lab. +* Jeremy Du Croz, Nag Central Office. +* Sven Hammarling, Nag Central Office. +* Richard Hanson, Sandia National Labs. +* +* ===================================================================== +* +* .. Parameters .. + DOUBLE PRECISION ZERO + PARAMETER (ZERO=0.0D+0) +* .. +* .. Local Scalars .. + DOUBLE PRECISION TEMP + INTEGER I,INFO,IX,J,JY,KX +* .. +* .. External Subroutines .. + EXTERNAL XERBLA +* .. +* .. Intrinsic Functions .. + INTRINSIC MAX +* .. +* +* Test the input parameters. +* + INFO = 0 + IF (M.LT.0) THEN + INFO = 1 + ELSE IF (N.LT.0) THEN + INFO = 2 + ELSE IF (INCX.EQ.0) THEN + INFO = 5 + ELSE IF (INCY.EQ.0) THEN + INFO = 7 + ELSE IF (LDA.LT.MAX(1,M)) THEN + INFO = 9 + END IF + IF (INFO.NE.0) THEN + CALL XERBLA('DGER ',INFO) + RETURN + END IF +* +* Quick return if possible. +* + IF ((M.EQ.0) .OR. (N.EQ.0) .OR. (ALPHA.EQ.ZERO)) RETURN +* +* Start the operations. In this version the elements of A are +* accessed sequentially with one pass through A. +* + IF (INCY.GT.0) THEN + JY = 1 + ELSE + JY = 1 - (N-1)*INCY + END IF + IF (INCX.EQ.1) THEN + DO 20 J = 1,N + IF (Y(JY).NE.ZERO) THEN + TEMP = ALPHA*Y(JY) + DO 10 I = 1,M + A(I,J) = A(I,J) + X(I)*TEMP + 10 CONTINUE + END IF + JY = JY + INCY + 20 CONTINUE + ELSE + IF (INCX.GT.0) THEN + KX = 1 + ELSE + KX = 1 - (M-1)*INCX + END IF + DO 40 J = 1,N + IF (Y(JY).NE.ZERO) THEN + TEMP = ALPHA*Y(JY) + IX = KX + DO 30 I = 1,M + A(I,J) = A(I,J) + X(IX)*TEMP + IX = IX + INCX + 30 CONTINUE + END IF + JY = JY + INCY + 40 CONTINUE + END IF +* + RETURN +* +* End of DGER . +* + END diff --git a/applications/PUfoam/MoDeNaModels/CFD_tool_0D/src/eigen/src/dgesv.f b/applications/PUfoam/MoDeNaModels/CFD_tool_0D/src/eigen/src/dgesv.f new file mode 100644 index 000000000..8d47f839d --- /dev/null +++ b/applications/PUfoam/MoDeNaModels/CFD_tool_0D/src/eigen/src/dgesv.f @@ -0,0 +1,179 @@ +*> \brief DGESV computes the solution to system of linear equations A * X = B for GE matrices +* +* =========== DOCUMENTATION =========== +* +* Online html documentation available at +* http://www.netlib.org/lapack/explore-html/ +* +*> \htmlonly +*> Download DGESV + dependencies +*> +*> [TGZ] +*> +*> [ZIP] +*> +*> [TXT] +*> \endhtmlonly +* +* Definition: +* =========== +* +* SUBROUTINE DGESV( N, NRHS, A, LDA, IPIV, B, LDB, INFO ) +* +* .. Scalar Arguments .. +* INTEGER INFO, LDA, LDB, N, NRHS +* .. +* .. Array Arguments .. +* INTEGER IPIV( * ) +* DOUBLE PRECISION A( LDA, * ), B( LDB, * ) +* .. +* +* +*> \par Purpose: +* ============= +*> +*> \verbatim +*> +*> DGESV computes the solution to a real system of linear equations +*> A * X = B, +*> where A is an N-by-N matrix and X and B are N-by-NRHS matrices. +*> +*> The LU decomposition with partial pivoting and row interchanges is +*> used to factor A as +*> A = P * L * U, +*> where P is a permutation matrix, L is unit lower triangular, and U is +*> upper triangular. The factored form of A is then used to solve the +*> system of equations A * X = B. +*> \endverbatim +* +* Arguments: +* ========== +* +*> \param[in] N +*> \verbatim +*> N is INTEGER +*> The number of linear equations, i.e., the order of the +*> matrix A. N >= 0. +*> \endverbatim +*> +*> \param[in] NRHS +*> \verbatim +*> NRHS is INTEGER +*> The number of right hand sides, i.e., the number of columns +*> of the matrix B. NRHS >= 0. +*> \endverbatim +*> +*> \param[in,out] A +*> \verbatim +*> A is DOUBLE PRECISION array, dimension (LDA,N) +*> On entry, the N-by-N coefficient matrix A. +*> On exit, the factors L and U from the factorization +*> A = P*L*U; the unit diagonal elements of L are not stored. +*> \endverbatim +*> +*> \param[in] LDA +*> \verbatim +*> LDA is INTEGER +*> The leading dimension of the array A. LDA >= max(1,N). +*> \endverbatim +*> +*> \param[out] IPIV +*> \verbatim +*> IPIV is INTEGER array, dimension (N) +*> The pivot indices that define the permutation matrix P; +*> row i of the matrix was interchanged with row IPIV(i). +*> \endverbatim +*> +*> \param[in,out] B +*> \verbatim +*> B is DOUBLE PRECISION array, dimension (LDB,NRHS) +*> On entry, the N-by-NRHS matrix of right hand side matrix B. +*> On exit, if INFO = 0, the N-by-NRHS solution matrix X. +*> \endverbatim +*> +*> \param[in] LDB +*> \verbatim +*> LDB is INTEGER +*> The leading dimension of the array B. LDB >= max(1,N). +*> \endverbatim +*> +*> \param[out] INFO +*> \verbatim +*> INFO is INTEGER +*> = 0: successful exit +*> < 0: if INFO = -i, the i-th argument had an illegal value +*> > 0: if INFO = i, U(i,i) is exactly zero. The factorization +*> has been completed, but the factor U is exactly +*> singular, so the solution could not be computed. +*> \endverbatim +* +* Authors: +* ======== +* +*> \author Univ. of Tennessee +*> \author Univ. of California Berkeley +*> \author Univ. of Colorado Denver +*> \author NAG Ltd. +* +*> \date November 2011 +* +*> \ingroup doubleGEsolve +* +* ===================================================================== + SUBROUTINE DGESV( N, NRHS, A, LDA, IPIV, B, LDB, INFO ) +* +* -- LAPACK driver routine (version 3.4.0) -- +* -- LAPACK is a software package provided by Univ. of Tennessee, -- +* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- +* November 2011 +* +* .. Scalar Arguments .. + INTEGER INFO, LDA, LDB, N, NRHS +* .. +* .. Array Arguments .. + INTEGER IPIV( * ) + DOUBLE PRECISION A( LDA, * ), B( LDB, * ) +* .. +* +* ===================================================================== +* +* .. External Subroutines .. + EXTERNAL DGETRF, DGETRS, XERBLA +* .. +* .. Intrinsic Functions .. + INTRINSIC MAX +* .. +* .. Executable Statements .. +* +* Test the input parameters. +* + INFO = 0 + IF( N.LT.0 ) THEN + INFO = -1 + ELSE IF( NRHS.LT.0 ) THEN + INFO = -2 + ELSE IF( LDA.LT.MAX( 1, N ) ) THEN + INFO = -4 + ELSE IF( LDB.LT.MAX( 1, N ) ) THEN + INFO = -7 + END IF + IF( INFO.NE.0 ) THEN + CALL XERBLA( 'DGESV ', -INFO ) + RETURN + END IF +* +* Compute the LU factorization of A. +* + CALL DGETRF( N, N, A, LDA, IPIV, INFO ) + IF( INFO.EQ.0 ) THEN +* +* Solve the system A*X = B, overwriting B with X. +* + CALL DGETRS( 'No transpose', N, NRHS, A, LDA, IPIV, B, LDB, + $ INFO ) + END IF + RETURN +* +* End of DGESV +* + END diff --git a/applications/PUfoam/MoDeNaModels/CFD_tool_0D/src/eigen/src/dgetf2.f b/applications/PUfoam/MoDeNaModels/CFD_tool_0D/src/eigen/src/dgetf2.f new file mode 100644 index 000000000..649d0671d --- /dev/null +++ b/applications/PUfoam/MoDeNaModels/CFD_tool_0D/src/eigen/src/dgetf2.f @@ -0,0 +1,213 @@ +*> \brief \b DGETF2 computes the LU factorization of a general m-by-n matrix using partial pivoting with row interchanges (unblocked algorithm). +* +* =========== DOCUMENTATION =========== +* +* Online html documentation available at +* http://www.netlib.org/lapack/explore-html/ +* +*> \htmlonly +*> Download DGETF2 + dependencies +*> +*> [TGZ] +*> +*> [ZIP] +*> +*> [TXT] +*> \endhtmlonly +* +* Definition: +* =========== +* +* SUBROUTINE DGETF2( M, N, A, LDA, IPIV, INFO ) +* +* .. Scalar Arguments .. +* INTEGER INFO, LDA, M, N +* .. +* .. Array Arguments .. +* INTEGER IPIV( * ) +* DOUBLE PRECISION A( LDA, * ) +* .. +* +* +*> \par Purpose: +* ============= +*> +*> \verbatim +*> +*> DGETF2 computes an LU factorization of a general m-by-n matrix A +*> using partial pivoting with row interchanges. +*> +*> The factorization has the form +*> A = P * L * U +*> where P is a permutation matrix, L is lower triangular with unit +*> diagonal elements (lower trapezoidal if m > n), and U is upper +*> triangular (upper trapezoidal if m < n). +*> +*> This is the right-looking Level 2 BLAS version of the algorithm. +*> \endverbatim +* +* Arguments: +* ========== +* +*> \param[in] M +*> \verbatim +*> M is INTEGER +*> The number of rows of the matrix A. M >= 0. +*> \endverbatim +*> +*> \param[in] N +*> \verbatim +*> N is INTEGER +*> The number of columns of the matrix A. N >= 0. +*> \endverbatim +*> +*> \param[in,out] A +*> \verbatim +*> A is DOUBLE PRECISION array, dimension (LDA,N) +*> On entry, the m by n matrix to be factored. +*> On exit, the factors L and U from the factorization +*> A = P*L*U; the unit diagonal elements of L are not stored. +*> \endverbatim +*> +*> \param[in] LDA +*> \verbatim +*> LDA is INTEGER +*> The leading dimension of the array A. LDA >= max(1,M). +*> \endverbatim +*> +*> \param[out] IPIV +*> \verbatim +*> IPIV is INTEGER array, dimension (min(M,N)) +*> The pivot indices; for 1 <= i <= min(M,N), row i of the +*> matrix was interchanged with row IPIV(i). +*> \endverbatim +*> +*> \param[out] INFO +*> \verbatim +*> INFO is INTEGER +*> = 0: successful exit +*> < 0: if INFO = -k, the k-th argument had an illegal value +*> > 0: if INFO = k, U(k,k) is exactly zero. The factorization +*> has been completed, but the factor U is exactly +*> singular, and division by zero will occur if it is used +*> to solve a system of equations. +*> \endverbatim +* +* Authors: +* ======== +* +*> \author Univ. of Tennessee +*> \author Univ. of California Berkeley +*> \author Univ. of Colorado Denver +*> \author NAG Ltd. +* +*> \date September 2012 +* +*> \ingroup doubleGEcomputational +* +* ===================================================================== + SUBROUTINE DGETF2( M, N, A, LDA, IPIV, INFO ) +* +* -- LAPACK computational routine (version 3.4.2) -- +* -- LAPACK is a software package provided by Univ. of Tennessee, -- +* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- +* September 2012 +* +* .. Scalar Arguments .. + INTEGER INFO, LDA, M, N +* .. +* .. Array Arguments .. + INTEGER IPIV( * ) + DOUBLE PRECISION A( LDA, * ) +* .. +* +* ===================================================================== +* +* .. Parameters .. + DOUBLE PRECISION ONE, ZERO + PARAMETER ( ONE = 1.0D+0, ZERO = 0.0D+0 ) +* .. +* .. Local Scalars .. + DOUBLE PRECISION SFMIN + INTEGER I, J, JP +* .. +* .. External Functions .. + DOUBLE PRECISION DLAMCH + INTEGER IDAMAX + EXTERNAL DLAMCH, IDAMAX +* .. +* .. External Subroutines .. + EXTERNAL DGER, DSCAL, DSWAP, XERBLA +* .. +* .. Intrinsic Functions .. + INTRINSIC MAX, MIN +* .. +* .. Executable Statements .. +* +* Test the input parameters. +* + INFO = 0 + IF( M.LT.0 ) THEN + INFO = -1 + ELSE IF( N.LT.0 ) THEN + INFO = -2 + ELSE IF( LDA.LT.MAX( 1, M ) ) THEN + INFO = -4 + END IF + IF( INFO.NE.0 ) THEN + CALL XERBLA( 'DGETF2', -INFO ) + RETURN + END IF +* +* Quick return if possible +* + IF( M.EQ.0 .OR. N.EQ.0 ) + $ RETURN +* +* Compute machine safe minimum +* + SFMIN = DLAMCH('S') +* + DO 10 J = 1, MIN( M, N ) +* +* Find pivot and test for singularity. +* + JP = J - 1 + IDAMAX( M-J+1, A( J, J ), 1 ) + IPIV( J ) = JP + IF( A( JP, J ).NE.ZERO ) THEN +* +* Apply the interchange to columns 1:N. +* + IF( JP.NE.J ) + $ CALL DSWAP( N, A( J, 1 ), LDA, A( JP, 1 ), LDA ) +* +* Compute elements J+1:M of J-th column. +* + IF( J.LT.M ) THEN + IF( ABS(A( J, J )) .GE. SFMIN ) THEN + CALL DSCAL( M-J, ONE / A( J, J ), A( J+1, J ), 1 ) + ELSE + DO 20 I = 1, M-J + A( J+I, J ) = A( J+I, J ) / A( J, J ) + 20 CONTINUE + END IF + END IF +* + ELSE IF( INFO.EQ.0 ) THEN +* + INFO = J + END IF +* + IF( J.LT.MIN( M, N ) ) THEN +* +* Update trailing submatrix. +* + CALL DGER( M-J, N-J, -ONE, A( J+1, J ), 1, A( J, J+1 ), LDA, + $ A( J+1, J+1 ), LDA ) + END IF + 10 CONTINUE + RETURN +* +* End of DGETF2 +* + END diff --git a/applications/PUfoam/MoDeNaModels/CFD_tool_0D/src/eigen/src/dgetrf.f b/applications/PUfoam/MoDeNaModels/CFD_tool_0D/src/eigen/src/dgetrf.f new file mode 100644 index 000000000..45bb97f30 --- /dev/null +++ b/applications/PUfoam/MoDeNaModels/CFD_tool_0D/src/eigen/src/dgetrf.f @@ -0,0 +1,225 @@ +*> \brief \b DGETRF +* +* =========== DOCUMENTATION =========== +* +* Online html documentation available at +* http://www.netlib.org/lapack/explore-html/ +* +*> \htmlonly +*> Download DGETRF + dependencies +*> +*> [TGZ] +*> +*> [ZIP] +*> +*> [TXT] +*> \endhtmlonly +* +* Definition: +* =========== +* +* SUBROUTINE DGETRF( M, N, A, LDA, IPIV, INFO ) +* +* .. Scalar Arguments .. +* INTEGER INFO, LDA, M, N +* .. +* .. Array Arguments .. +* INTEGER IPIV( * ) +* DOUBLE PRECISION A( LDA, * ) +* .. +* +* +*> \par Purpose: +* ============= +*> +*> \verbatim +*> +*> DGETRF computes an LU factorization of a general M-by-N matrix A +*> using partial pivoting with row interchanges. +*> +*> The factorization has the form +*> A = P * L * U +*> where P is a permutation matrix, L is lower triangular with unit +*> diagonal elements (lower trapezoidal if m > n), and U is upper +*> triangular (upper trapezoidal if m < n). +*> +*> This is the right-looking Level 3 BLAS version of the algorithm. +*> \endverbatim +* +* Arguments: +* ========== +* +*> \param[in] M +*> \verbatim +*> M is INTEGER +*> The number of rows of the matrix A. M >= 0. +*> \endverbatim +*> +*> \param[in] N +*> \verbatim +*> N is INTEGER +*> The number of columns of the matrix A. N >= 0. +*> \endverbatim +*> +*> \param[in,out] A +*> \verbatim +*> A is DOUBLE PRECISION array, dimension (LDA,N) +*> On entry, the M-by-N matrix to be factored. +*> On exit, the factors L and U from the factorization +*> A = P*L*U; the unit diagonal elements of L are not stored. +*> \endverbatim +*> +*> \param[in] LDA +*> \verbatim +*> LDA is INTEGER +*> The leading dimension of the array A. LDA >= max(1,M). +*> \endverbatim +*> +*> \param[out] IPIV +*> \verbatim +*> IPIV is INTEGER array, dimension (min(M,N)) +*> The pivot indices; for 1 <= i <= min(M,N), row i of the +*> matrix was interchanged with row IPIV(i). +*> \endverbatim +*> +*> \param[out] INFO +*> \verbatim +*> INFO is INTEGER +*> = 0: successful exit +*> < 0: if INFO = -i, the i-th argument had an illegal value +*> > 0: if INFO = i, U(i,i) is exactly zero. The factorization +*> has been completed, but the factor U is exactly +*> singular, and division by zero will occur if it is used +*> to solve a system of equations. +*> \endverbatim +* +* Authors: +* ======== +* +*> \author Univ. of Tennessee +*> \author Univ. of California Berkeley +*> \author Univ. of Colorado Denver +*> \author NAG Ltd. +* +*> \date November 2011 +* +*> \ingroup doubleGEcomputational +* +* ===================================================================== + SUBROUTINE DGETRF( M, N, A, LDA, IPIV, INFO ) +* +* -- LAPACK computational routine (version 3.4.0) -- +* -- LAPACK is a software package provided by Univ. of Tennessee, -- +* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- +* November 2011 +* +* .. Scalar Arguments .. + INTEGER INFO, LDA, M, N +* .. +* .. Array Arguments .. + INTEGER IPIV( * ) + DOUBLE PRECISION A( LDA, * ) +* .. +* +* ===================================================================== +* +* .. Parameters .. + DOUBLE PRECISION ONE + PARAMETER ( ONE = 1.0D+0 ) +* .. +* .. Local Scalars .. + INTEGER I, IINFO, J, JB, NB +* .. +* .. External Subroutines .. + EXTERNAL DGEMM, DGETF2, DLASWP, DTRSM, XERBLA +* .. +* .. External Functions .. + INTEGER ILAENV + EXTERNAL ILAENV +* .. +* .. Intrinsic Functions .. + INTRINSIC MAX, MIN +* .. +* .. Executable Statements .. +* +* Test the input parameters. +* + INFO = 0 + IF( M.LT.0 ) THEN + INFO = -1 + ELSE IF( N.LT.0 ) THEN + INFO = -2 + ELSE IF( LDA.LT.MAX( 1, M ) ) THEN + INFO = -4 + END IF + IF( INFO.NE.0 ) THEN + CALL XERBLA( 'DGETRF', -INFO ) + RETURN + END IF +* +* Quick return if possible +* + IF( M.EQ.0 .OR. N.EQ.0 ) + $ RETURN +* +* Determine the block size for this environment. +* + NB = ILAENV( 1, 'DGETRF', ' ', M, N, -1, -1 ) + IF( NB.LE.1 .OR. NB.GE.MIN( M, N ) ) THEN +* +* Use unblocked code. +* + CALL DGETF2( M, N, A, LDA, IPIV, INFO ) + ELSE +* +* Use blocked code. +* + DO 20 J = 1, MIN( M, N ), NB + JB = MIN( MIN( M, N )-J+1, NB ) +* +* Factor diagonal and subdiagonal blocks and test for exact +* singularity. +* + CALL DGETF2( M-J+1, JB, A( J, J ), LDA, IPIV( J ), IINFO ) +* +* Adjust INFO and the pivot indices. +* + IF( INFO.EQ.0 .AND. IINFO.GT.0 ) + $ INFO = IINFO + J - 1 + DO 10 I = J, MIN( M, J+JB-1 ) + IPIV( I ) = J - 1 + IPIV( I ) + 10 CONTINUE +* +* Apply interchanges to columns 1:J-1. +* + CALL DLASWP( J-1, A, LDA, J, J+JB-1, IPIV, 1 ) +* + IF( J+JB.LE.N ) THEN +* +* Apply interchanges to columns J+JB:N. +* + CALL DLASWP( N-J-JB+1, A( 1, J+JB ), LDA, J, J+JB-1, + $ IPIV, 1 ) +* +* Compute block row of U. +* + CALL DTRSM( 'Left', 'Lower', 'No transpose', 'Unit', JB, + $ N-J-JB+1, ONE, A( J, J ), LDA, A( J, J+JB ), + $ LDA ) + IF( J+JB.LE.M ) THEN +* +* Update trailing submatrix. +* + CALL DGEMM( 'No transpose', 'No transpose', M-J-JB+1, + $ N-J-JB+1, JB, -ONE, A( J+JB, J ), LDA, + $ A( J, J+JB ), LDA, ONE, A( J+JB, J+JB ), + $ LDA ) + END IF + END IF + 20 CONTINUE + END IF + RETURN +* +* End of DGETRF +* + END diff --git a/applications/PUfoam/MoDeNaModels/CFD_tool_0D/src/eigen/src/dgetrs.f b/applications/PUfoam/MoDeNaModels/CFD_tool_0D/src/eigen/src/dgetrs.f new file mode 100644 index 000000000..02e9832af --- /dev/null +++ b/applications/PUfoam/MoDeNaModels/CFD_tool_0D/src/eigen/src/dgetrs.f @@ -0,0 +1,225 @@ +*> \brief \b DGETRS +* +* =========== DOCUMENTATION =========== +* +* Online html documentation available at +* http://www.netlib.org/lapack/explore-html/ +* +*> \htmlonly +*> Download DGETRS + dependencies +*> +*> [TGZ] +*> +*> [ZIP] +*> +*> [TXT] +*> \endhtmlonly +* +* Definition: +* =========== +* +* SUBROUTINE DGETRS( TRANS, N, NRHS, A, LDA, IPIV, B, LDB, INFO ) +* +* .. Scalar Arguments .. +* CHARACTER TRANS +* INTEGER INFO, LDA, LDB, N, NRHS +* .. +* .. Array Arguments .. +* INTEGER IPIV( * ) +* DOUBLE PRECISION A( LDA, * ), B( LDB, * ) +* .. +* +* +*> \par Purpose: +* ============= +*> +*> \verbatim +*> +*> DGETRS solves a system of linear equations +*> A * X = B or A**T * X = B +*> with a general N-by-N matrix A using the LU factorization computed +*> by DGETRF. +*> \endverbatim +* +* Arguments: +* ========== +* +*> \param[in] TRANS +*> \verbatim +*> TRANS is CHARACTER*1 +*> Specifies the form of the system of equations: +*> = 'N': A * X = B (No transpose) +*> = 'T': A**T* X = B (Transpose) +*> = 'C': A**T* X = B (Conjugate transpose = Transpose) +*> \endverbatim +*> +*> \param[in] N +*> \verbatim +*> N is INTEGER +*> The order of the matrix A. N >= 0. +*> \endverbatim +*> +*> \param[in] NRHS +*> \verbatim +*> NRHS is INTEGER +*> The number of right hand sides, i.e., the number of columns +*> of the matrix B. NRHS >= 0. +*> \endverbatim +*> +*> \param[in] A +*> \verbatim +*> A is DOUBLE PRECISION array, dimension (LDA,N) +*> The factors L and U from the factorization A = P*L*U +*> as computed by DGETRF. +*> \endverbatim +*> +*> \param[in] LDA +*> \verbatim +*> LDA is INTEGER +*> The leading dimension of the array A. LDA >= max(1,N). +*> \endverbatim +*> +*> \param[in] IPIV +*> \verbatim +*> IPIV is INTEGER array, dimension (N) +*> The pivot indices from DGETRF; for 1<=i<=N, row i of the +*> matrix was interchanged with row IPIV(i). +*> \endverbatim +*> +*> \param[in,out] B +*> \verbatim +*> B is DOUBLE PRECISION array, dimension (LDB,NRHS) +*> On entry, the right hand side matrix B. +*> On exit, the solution matrix X. +*> \endverbatim +*> +*> \param[in] LDB +*> \verbatim +*> LDB is INTEGER +*> The leading dimension of the array B. LDB >= max(1,N). +*> \endverbatim +*> +*> \param[out] INFO +*> \verbatim +*> INFO is INTEGER +*> = 0: successful exit +*> < 0: if INFO = -i, the i-th argument had an illegal value +*> \endverbatim +* +* Authors: +* ======== +* +*> \author Univ. of Tennessee +*> \author Univ. of California Berkeley +*> \author Univ. of Colorado Denver +*> \author NAG Ltd. +* +*> \date November 2011 +* +*> \ingroup doubleGEcomputational +* +* ===================================================================== + SUBROUTINE DGETRS( TRANS, N, NRHS, A, LDA, IPIV, B, LDB, INFO ) +* +* -- LAPACK computational routine (version 3.4.0) -- +* -- LAPACK is a software package provided by Univ. of Tennessee, -- +* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- +* November 2011 +* +* .. Scalar Arguments .. + CHARACTER TRANS + INTEGER INFO, LDA, LDB, N, NRHS +* .. +* .. Array Arguments .. + INTEGER IPIV( * ) + DOUBLE PRECISION A( LDA, * ), B( LDB, * ) +* .. +* +* ===================================================================== +* +* .. Parameters .. + DOUBLE PRECISION ONE + PARAMETER ( ONE = 1.0D+0 ) +* .. +* .. Local Scalars .. + LOGICAL NOTRAN +* .. +* .. External Functions .. + LOGICAL LSAME + EXTERNAL LSAME +* .. +* .. External Subroutines .. + EXTERNAL DLASWP, DTRSM, XERBLA +* .. +* .. Intrinsic Functions .. + INTRINSIC MAX +* .. +* .. Executable Statements .. +* +* Test the input parameters. +* + INFO = 0 + NOTRAN = LSAME( TRANS, 'N' ) + IF( .NOT.NOTRAN .AND. .NOT.LSAME( TRANS, 'T' ) .AND. .NOT. + $ LSAME( TRANS, 'C' ) ) THEN + INFO = -1 + ELSE IF( N.LT.0 ) THEN + INFO = -2 + ELSE IF( NRHS.LT.0 ) THEN + INFO = -3 + ELSE IF( LDA.LT.MAX( 1, N ) ) THEN + INFO = -5 + ELSE IF( LDB.LT.MAX( 1, N ) ) THEN + INFO = -8 + END IF + IF( INFO.NE.0 ) THEN + CALL XERBLA( 'DGETRS', -INFO ) + RETURN + END IF +* +* Quick return if possible +* + IF( N.EQ.0 .OR. NRHS.EQ.0 ) + $ RETURN +* + IF( NOTRAN ) THEN +* +* Solve A * X = B. +* +* Apply row interchanges to the right hand sides. +* + CALL DLASWP( NRHS, B, LDB, 1, N, IPIV, 1 ) +* +* Solve L*X = B, overwriting B with X. +* + CALL DTRSM( 'Left', 'Lower', 'No transpose', 'Unit', N, NRHS, + $ ONE, A, LDA, B, LDB ) +* +* Solve U*X = B, overwriting B with X. +* + CALL DTRSM( 'Left', 'Upper', 'No transpose', 'Non-unit', N, + $ NRHS, ONE, A, LDA, B, LDB ) + ELSE +* +* Solve A**T * X = B. +* +* Solve U**T *X = B, overwriting B with X. +* + CALL DTRSM( 'Left', 'Upper', 'Transpose', 'Non-unit', N, NRHS, + $ ONE, A, LDA, B, LDB ) +* +* Solve L**T *X = B, overwriting B with X. +* + CALL DTRSM( 'Left', 'Lower', 'Transpose', 'Unit', N, NRHS, ONE, + $ A, LDA, B, LDB ) +* +* Apply row interchanges to the solution vectors. +* + CALL DLASWP( NRHS, B, LDB, 1, N, IPIV, -1 ) + END IF +* + RETURN +* +* End of DGETRS +* + END diff --git a/applications/PUfoam/MoDeNaModels/CFD_tool_0D/src/eigen/src/disnan.f b/applications/PUfoam/MoDeNaModels/CFD_tool_0D/src/eigen/src/disnan.f new file mode 100644 index 000000000..f6a02bf1f --- /dev/null +++ b/applications/PUfoam/MoDeNaModels/CFD_tool_0D/src/eigen/src/disnan.f @@ -0,0 +1,80 @@ +*> \brief \b DISNAN +* +* =========== DOCUMENTATION =========== +* +* Online html documentation available at +* http://www.netlib.org/lapack/explore-html/ +* +*> \htmlonly +*> Download DISNAN + dependencies +*> +*> [TGZ] +*> +*> [ZIP] +*> +*> [TXT] +*> \endhtmlonly +* +* Definition: +* =========== +* +* LOGICAL FUNCTION DISNAN( DIN ) +* +* .. Scalar Arguments .. +* DOUBLE PRECISION DIN +* .. +* +* +*> \par Purpose: +* ============= +*> +*> \verbatim +*> +*> DISNAN returns .TRUE. if its argument is NaN, and .FALSE. +*> otherwise. To be replaced by the Fortran 2003 intrinsic in the +*> future. +*> \endverbatim +* +* Arguments: +* ========== +* +*> \param[in] DIN +*> \verbatim +*> DIN is DOUBLE PRECISION +*> Input to test for NaN. +*> \endverbatim +* +* Authors: +* ======== +* +*> \author Univ. of Tennessee +*> \author Univ. of California Berkeley +*> \author Univ. of Colorado Denver +*> \author NAG Ltd. +* +*> \date November 2011 +* +*> \ingroup auxOTHERauxiliary +* +* ===================================================================== + LOGICAL FUNCTION DISNAN( DIN ) +* +* -- LAPACK auxiliary routine (version 3.4.0) -- +* -- LAPACK is a software package provided by Univ. of Tennessee, -- +* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- +* November 2011 +* +* .. Scalar Arguments .. + DOUBLE PRECISION DIN +* .. +* +* ===================================================================== +* +* .. External Functions .. + LOGICAL DLAISNAN + EXTERNAL DLAISNAN +* .. +* .. Executable Statements .. + DISNAN = DLAISNAN(DIN,DIN) + RETURN + END diff --git a/applications/PUfoam/MoDeNaModels/CFD_tool_0D/src/eigen/src/dlae2.f b/applications/PUfoam/MoDeNaModels/CFD_tool_0D/src/eigen/src/dlae2.f new file mode 100644 index 000000000..099334283 --- /dev/null +++ b/applications/PUfoam/MoDeNaModels/CFD_tool_0D/src/eigen/src/dlae2.f @@ -0,0 +1,185 @@ +*> \brief \b DLAE2 +* +* =========== DOCUMENTATION =========== +* +* Online html documentation available at +* http://www.netlib.org/lapack/explore-html/ +* +*> \htmlonly +*> Download DLAE2 + dependencies +*> +*> [TGZ] +*> +*> [ZIP] +*> +*> [TXT] +*> \endhtmlonly +* +* Definition: +* =========== +* +* SUBROUTINE DLAE2( A, B, C, RT1, RT2 ) +* +* .. Scalar Arguments .. +* DOUBLE PRECISION A, B, C, RT1, RT2 +* .. +* +* +*> \par Purpose: +* ============= +*> +*> \verbatim +*> +*> DLAE2 computes the eigenvalues of a 2-by-2 symmetric matrix +*> [ A B ] +*> [ B C ]. +*> On return, RT1 is the eigenvalue of larger absolute value, and RT2 +*> is the eigenvalue of smaller absolute value. +*> \endverbatim +* +* Arguments: +* ========== +* +*> \param[in] A +*> \verbatim +*> A is DOUBLE PRECISION +*> The (1,1) element of the 2-by-2 matrix. +*> \endverbatim +*> +*> \param[in] B +*> \verbatim +*> B is DOUBLE PRECISION +*> The (1,2) and (2,1) elements of the 2-by-2 matrix. +*> \endverbatim +*> +*> \param[in] C +*> \verbatim +*> C is DOUBLE PRECISION +*> The (2,2) element of the 2-by-2 matrix. +*> \endverbatim +*> +*> \param[out] RT1 +*> \verbatim +*> RT1 is DOUBLE PRECISION +*> The eigenvalue of larger absolute value. +*> \endverbatim +*> +*> \param[out] RT2 +*> \verbatim +*> RT2 is DOUBLE PRECISION +*> The eigenvalue of smaller absolute value. +*> \endverbatim +* +* Authors: +* ======== +* +*> \author Univ. of Tennessee +*> \author Univ. of California Berkeley +*> \author Univ. of Colorado Denver +*> \author NAG Ltd. +* +*> \date November 2011 +* +*> \ingroup auxOTHERauxiliary +* +*> \par Further Details: +* ===================== +*> +*> \verbatim +*> +*> RT1 is accurate to a few ulps barring over/underflow. +*> +*> RT2 may be inaccurate if there is massive cancellation in the +*> determinant A*C-B*B; higher precision or correctly rounded or +*> correctly truncated arithmetic would be needed to compute RT2 +*> accurately in all cases. +*> +*> Overflow is possible only if RT1 is within a factor of 5 of overflow. +*> Underflow is harmless if the input data is 0 or exceeds +*> underflow_threshold / macheps. +*> \endverbatim +*> +* ===================================================================== + SUBROUTINE DLAE2( A, B, C, RT1, RT2 ) +* +* -- LAPACK auxiliary routine (version 3.4.0) -- +* -- LAPACK is a software package provided by Univ. of Tennessee, -- +* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- +* November 2011 +* +* .. Scalar Arguments .. + DOUBLE PRECISION A, B, C, RT1, RT2 +* .. +* +* ===================================================================== +* +* .. Parameters .. + DOUBLE PRECISION ONE + PARAMETER ( ONE = 1.0D0 ) + DOUBLE PRECISION TWO + PARAMETER ( TWO = 2.0D0 ) + DOUBLE PRECISION ZERO + PARAMETER ( ZERO = 0.0D0 ) + DOUBLE PRECISION HALF + PARAMETER ( HALF = 0.5D0 ) +* .. +* .. Local Scalars .. + DOUBLE PRECISION AB, ACMN, ACMX, ADF, DF, RT, SM, TB +* .. +* .. Intrinsic Functions .. + INTRINSIC ABS, SQRT +* .. +* .. Executable Statements .. +* +* Compute the eigenvalues +* + SM = A + C + DF = A - C + ADF = ABS( DF ) + TB = B + B + AB = ABS( TB ) + IF( ABS( A ).GT.ABS( C ) ) THEN + ACMX = A + ACMN = C + ELSE + ACMX = C + ACMN = A + END IF + IF( ADF.GT.AB ) THEN + RT = ADF*SQRT( ONE+( AB / ADF )**2 ) + ELSE IF( ADF.LT.AB ) THEN + RT = AB*SQRT( ONE+( ADF / AB )**2 ) + ELSE +* +* Includes case AB=ADF=0 +* + RT = AB*SQRT( TWO ) + END IF + IF( SM.LT.ZERO ) THEN + RT1 = HALF*( SM-RT ) +* +* Order of execution important. +* To get fully accurate smaller eigenvalue, +* next line needs to be executed in higher precision. +* + RT2 = ( ACMX / RT1 )*ACMN - ( B / RT1 )*B + ELSE IF( SM.GT.ZERO ) THEN + RT1 = HALF*( SM+RT ) +* +* Order of execution important. +* To get fully accurate smaller eigenvalue, +* next line needs to be executed in higher precision. +* + RT2 = ( ACMX / RT1 )*ACMN - ( B / RT1 )*B + ELSE +* +* Includes case RT1 = RT2 = 0 +* + RT1 = HALF*RT + RT2 = -HALF*RT + END IF + RETURN +* +* End of DLAE2 +* + END diff --git a/applications/PUfoam/MoDeNaModels/CFD_tool_0D/src/eigen/src/dlaebz.f b/applications/PUfoam/MoDeNaModels/CFD_tool_0D/src/eigen/src/dlaebz.f new file mode 100644 index 000000000..80eb29101 --- /dev/null +++ b/applications/PUfoam/MoDeNaModels/CFD_tool_0D/src/eigen/src/dlaebz.f @@ -0,0 +1,649 @@ +*> \brief \b DLAEBZ +* +* =========== DOCUMENTATION =========== +* +* Online html documentation available at +* http://www.netlib.org/lapack/explore-html/ +* +*> \htmlonly +*> Download DLAEBZ + dependencies +*> +*> [TGZ] +*> +*> [ZIP] +*> +*> [TXT] +*> \endhtmlonly +* +* Definition: +* =========== +* +* SUBROUTINE DLAEBZ( IJOB, NITMAX, N, MMAX, MINP, NBMIN, ABSTOL, +* RELTOL, PIVMIN, D, E, E2, NVAL, AB, C, MOUT, +* NAB, WORK, IWORK, INFO ) +* +* .. Scalar Arguments .. +* INTEGER IJOB, INFO, MINP, MMAX, MOUT, N, NBMIN, NITMAX +* DOUBLE PRECISION ABSTOL, PIVMIN, RELTOL +* .. +* .. Array Arguments .. +* INTEGER IWORK( * ), NAB( MMAX, * ), NVAL( * ) +* DOUBLE PRECISION AB( MMAX, * ), C( * ), D( * ), E( * ), E2( * ), +* $ WORK( * ) +* .. +* +* +*> \par Purpose: +* ============= +*> +*> \verbatim +*> +*> DLAEBZ contains the iteration loops which compute and use the +*> function N(w), which is the count of eigenvalues of a symmetric +*> tridiagonal matrix T less than or equal to its argument w. It +*> performs a choice of two types of loops: +*> +*> IJOB=1, followed by +*> IJOB=2: It takes as input a list of intervals and returns a list of +*> sufficiently small intervals whose union contains the same +*> eigenvalues as the union of the original intervals. +*> The input intervals are (AB(j,1),AB(j,2)], j=1,...,MINP. +*> The output interval (AB(j,1),AB(j,2)] will contain +*> eigenvalues NAB(j,1)+1,...,NAB(j,2), where 1 <= j <= MOUT. +*> +*> IJOB=3: It performs a binary search in each input interval +*> (AB(j,1),AB(j,2)] for a point w(j) such that +*> N(w(j))=NVAL(j), and uses C(j) as the starting point of +*> the search. If such a w(j) is found, then on output +*> AB(j,1)=AB(j,2)=w. If no such w(j) is found, then on output +*> (AB(j,1),AB(j,2)] will be a small interval containing the +*> point where N(w) jumps through NVAL(j), unless that point +*> lies outside the initial interval. +*> +*> Note that the intervals are in all cases half-open intervals, +*> i.e., of the form (a,b] , which includes b but not a . +*> +*> To avoid underflow, the matrix should be scaled so that its largest +*> element is no greater than overflow**(1/2) * underflow**(1/4) +*> in absolute value. To assure the most accurate computation +*> of small eigenvalues, the matrix should be scaled to be +*> not much smaller than that, either. +*> +*> See W. Kahan "Accurate Eigenvalues of a Symmetric Tridiagonal +*> Matrix", Report CS41, Computer Science Dept., Stanford +*> University, July 21, 1966 +*> +*> Note: the arguments are, in general, *not* checked for unreasonable +*> values. +*> \endverbatim +* +* Arguments: +* ========== +* +*> \param[in] IJOB +*> \verbatim +*> IJOB is INTEGER +*> Specifies what is to be done: +*> = 1: Compute NAB for the initial intervals. +*> = 2: Perform bisection iteration to find eigenvalues of T. +*> = 3: Perform bisection iteration to invert N(w), i.e., +*> to find a point which has a specified number of +*> eigenvalues of T to its left. +*> Other values will cause DLAEBZ to return with INFO=-1. +*> \endverbatim +*> +*> \param[in] NITMAX +*> \verbatim +*> NITMAX is INTEGER +*> The maximum number of "levels" of bisection to be +*> performed, i.e., an interval of width W will not be made +*> smaller than 2^(-NITMAX) * W. If not all intervals +*> have converged after NITMAX iterations, then INFO is set +*> to the number of non-converged intervals. +*> \endverbatim +*> +*> \param[in] N +*> \verbatim +*> N is INTEGER +*> The dimension n of the tridiagonal matrix T. It must be at +*> least 1. +*> \endverbatim +*> +*> \param[in] MMAX +*> \verbatim +*> MMAX is INTEGER +*> The maximum number of intervals. If more than MMAX intervals +*> are generated, then DLAEBZ will quit with INFO=MMAX+1. +*> \endverbatim +*> +*> \param[in] MINP +*> \verbatim +*> MINP is INTEGER +*> The initial number of intervals. It may not be greater than +*> MMAX. +*> \endverbatim +*> +*> \param[in] NBMIN +*> \verbatim +*> NBMIN is INTEGER +*> The smallest number of intervals that should be processed +*> using a vector loop. If zero, then only the scalar loop +*> will be used. +*> \endverbatim +*> +*> \param[in] ABSTOL +*> \verbatim +*> ABSTOL is DOUBLE PRECISION +*> The minimum (absolute) width of an interval. When an +*> interval is narrower than ABSTOL, or than RELTOL times the +*> larger (in magnitude) endpoint, then it is considered to be +*> sufficiently small, i.e., converged. This must be at least +*> zero. +*> \endverbatim +*> +*> \param[in] RELTOL +*> \verbatim +*> RELTOL is DOUBLE PRECISION +*> The minimum relative width of an interval. When an interval +*> is narrower than ABSTOL, or than RELTOL times the larger (in +*> magnitude) endpoint, then it is considered to be +*> sufficiently small, i.e., converged. Note: this should +*> always be at least radix*machine epsilon. +*> \endverbatim +*> +*> \param[in] PIVMIN +*> \verbatim +*> PIVMIN is DOUBLE PRECISION +*> The minimum absolute value of a "pivot" in the Sturm +*> sequence loop. +*> This must be at least max |e(j)**2|*safe_min and at +*> least safe_min, where safe_min is at least +*> the smallest number that can divide one without overflow. +*> \endverbatim +*> +*> \param[in] D +*> \verbatim +*> D is DOUBLE PRECISION array, dimension (N) +*> The diagonal elements of the tridiagonal matrix T. +*> \endverbatim +*> +*> \param[in] E +*> \verbatim +*> E is DOUBLE PRECISION array, dimension (N) +*> The offdiagonal elements of the tridiagonal matrix T in +*> positions 1 through N-1. E(N) is arbitrary. +*> \endverbatim +*> +*> \param[in] E2 +*> \verbatim +*> E2 is DOUBLE PRECISION array, dimension (N) +*> The squares of the offdiagonal elements of the tridiagonal +*> matrix T. E2(N) is ignored. +*> \endverbatim +*> +*> \param[in,out] NVAL +*> \verbatim +*> NVAL is INTEGER array, dimension (MINP) +*> If IJOB=1 or 2, not referenced. +*> If IJOB=3, the desired values of N(w). The elements of NVAL +*> will be reordered to correspond with the intervals in AB. +*> Thus, NVAL(j) on output will not, in general be the same as +*> NVAL(j) on input, but it will correspond with the interval +*> (AB(j,1),AB(j,2)] on output. +*> \endverbatim +*> +*> \param[in,out] AB +*> \verbatim +*> AB is DOUBLE PRECISION array, dimension (MMAX,2) +*> The endpoints of the intervals. AB(j,1) is a(j), the left +*> endpoint of the j-th interval, and AB(j,2) is b(j), the +*> right endpoint of the j-th interval. The input intervals +*> will, in general, be modified, split, and reordered by the +*> calculation. +*> \endverbatim +*> +*> \param[in,out] C +*> \verbatim +*> C is DOUBLE PRECISION array, dimension (MMAX) +*> If IJOB=1, ignored. +*> If IJOB=2, workspace. +*> If IJOB=3, then on input C(j) should be initialized to the +*> first search point in the binary search. +*> \endverbatim +*> +*> \param[out] MOUT +*> \verbatim +*> MOUT is INTEGER +*> If IJOB=1, the number of eigenvalues in the intervals. +*> If IJOB=2 or 3, the number of intervals output. +*> If IJOB=3, MOUT will equal MINP. +*> \endverbatim +*> +*> \param[in,out] NAB +*> \verbatim +*> NAB is INTEGER array, dimension (MMAX,2) +*> If IJOB=1, then on output NAB(i,j) will be set to N(AB(i,j)). +*> If IJOB=2, then on input, NAB(i,j) should be set. It must +*> satisfy the condition: +*> N(AB(i,1)) <= NAB(i,1) <= NAB(i,2) <= N(AB(i,2)), +*> which means that in interval i only eigenvalues +*> NAB(i,1)+1,...,NAB(i,2) will be considered. Usually, +*> NAB(i,j)=N(AB(i,j)), from a previous call to DLAEBZ with +*> IJOB=1. +*> On output, NAB(i,j) will contain +*> max(na(k),min(nb(k),N(AB(i,j)))), where k is the index of +*> the input interval that the output interval +*> (AB(j,1),AB(j,2)] came from, and na(k) and nb(k) are the +*> the input values of NAB(k,1) and NAB(k,2). +*> If IJOB=3, then on output, NAB(i,j) contains N(AB(i,j)), +*> unless N(w) > NVAL(i) for all search points w , in which +*> case NAB(i,1) will not be modified, i.e., the output +*> value will be the same as the input value (modulo +*> reorderings -- see NVAL and AB), or unless N(w) < NVAL(i) +*> for all search points w , in which case NAB(i,2) will +*> not be modified. Normally, NAB should be set to some +*> distinctive value(s) before DLAEBZ is called. +*> \endverbatim +*> +*> \param[out] WORK +*> \verbatim +*> WORK is DOUBLE PRECISION array, dimension (MMAX) +*> Workspace. +*> \endverbatim +*> +*> \param[out] IWORK +*> \verbatim +*> IWORK is INTEGER array, dimension (MMAX) +*> Workspace. +*> \endverbatim +*> +*> \param[out] INFO +*> \verbatim +*> INFO is INTEGER +*> = 0: All intervals converged. +*> = 1--MMAX: The last INFO intervals did not converge. +*> = MMAX+1: More than MMAX intervals were generated. +*> \endverbatim +* +* Authors: +* ======== +* +*> \author Univ. of Tennessee +*> \author Univ. of California Berkeley +*> \author Univ. of Colorado Denver +*> \author NAG Ltd. +* +*> \date November 2011 +* +*> \ingroup auxOTHERauxiliary +* +*> \par Further Details: +* ===================== +*> +*> \verbatim +*> +*> This routine is intended to be called only by other LAPACK +*> routines, thus the interface is less user-friendly. It is intended +*> for two purposes: +*> +*> (a) finding eigenvalues. In this case, DLAEBZ should have one or +*> more initial intervals set up in AB, and DLAEBZ should be called +*> with IJOB=1. This sets up NAB, and also counts the eigenvalues. +*> Intervals with no eigenvalues would usually be thrown out at +*> this point. Also, if not all the eigenvalues in an interval i +*> are desired, NAB(i,1) can be increased or NAB(i,2) decreased. +*> For example, set NAB(i,1)=NAB(i,2)-1 to get the largest +*> eigenvalue. DLAEBZ is then called with IJOB=2 and MMAX +*> no smaller than the value of MOUT returned by the call with +*> IJOB=1. After this (IJOB=2) call, eigenvalues NAB(i,1)+1 +*> through NAB(i,2) are approximately AB(i,1) (or AB(i,2)) to the +*> tolerance specified by ABSTOL and RELTOL. +*> +*> (b) finding an interval (a',b'] containing eigenvalues w(f),...,w(l). +*> In this case, start with a Gershgorin interval (a,b). Set up +*> AB to contain 2 search intervals, both initially (a,b). One +*> NVAL element should contain f-1 and the other should contain l +*> , while C should contain a and b, resp. NAB(i,1) should be -1 +*> and NAB(i,2) should be N+1, to flag an error if the desired +*> interval does not lie in (a,b). DLAEBZ is then called with +*> IJOB=3. On exit, if w(f-1) < w(f), then one of the intervals -- +*> j -- will have AB(j,1)=AB(j,2) and NAB(j,1)=NAB(j,2)=f-1, while +*> if, to the specified tolerance, w(f-k)=...=w(f+r), k > 0 and r +*> >= 0, then the interval will have N(AB(j,1))=NAB(j,1)=f-k and +*> N(AB(j,2))=NAB(j,2)=f+r. The cases w(l) < w(l+1) and +*> w(l-r)=...=w(l+k) are handled similarly. +*> \endverbatim +*> +* ===================================================================== + SUBROUTINE DLAEBZ( IJOB, NITMAX, N, MMAX, MINP, NBMIN, ABSTOL, + $ RELTOL, PIVMIN, D, E, E2, NVAL, AB, C, MOUT, + $ NAB, WORK, IWORK, INFO ) +* +* -- LAPACK auxiliary routine (version 3.4.0) -- +* -- LAPACK is a software package provided by Univ. of Tennessee, -- +* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- +* November 2011 +* +* .. Scalar Arguments .. + INTEGER IJOB, INFO, MINP, MMAX, MOUT, N, NBMIN, NITMAX + DOUBLE PRECISION ABSTOL, PIVMIN, RELTOL +* .. +* .. Array Arguments .. + INTEGER IWORK( * ), NAB( MMAX, * ), NVAL( * ) + DOUBLE PRECISION AB( MMAX, * ), C( * ), D( * ), E( * ), E2( * ), + $ WORK( * ) +* .. +* +* ===================================================================== +* +* .. Parameters .. + DOUBLE PRECISION ZERO, TWO, HALF + PARAMETER ( ZERO = 0.0D0, TWO = 2.0D0, + $ HALF = 1.0D0 / TWO ) +* .. +* .. Local Scalars .. + INTEGER ITMP1, ITMP2, J, JI, JIT, JP, KF, KFNEW, KL, + $ KLNEW + DOUBLE PRECISION TMP1, TMP2 +* .. +* .. Intrinsic Functions .. + INTRINSIC ABS, MAX, MIN +* .. +* .. Executable Statements .. +* +* Check for Errors +* + INFO = 0 + IF( IJOB.LT.1 .OR. IJOB.GT.3 ) THEN + INFO = -1 + RETURN + END IF +* +* Initialize NAB +* + IF( IJOB.EQ.1 ) THEN +* +* Compute the number of eigenvalues in the initial intervals. +* + MOUT = 0 + DO 30 JI = 1, MINP + DO 20 JP = 1, 2 + TMP1 = D( 1 ) - AB( JI, JP ) + IF( ABS( TMP1 ).LT.PIVMIN ) + $ TMP1 = -PIVMIN + NAB( JI, JP ) = 0 + IF( TMP1.LE.ZERO ) + $ NAB( JI, JP ) = 1 +* + DO 10 J = 2, N + TMP1 = D( J ) - E2( J-1 ) / TMP1 - AB( JI, JP ) + IF( ABS( TMP1 ).LT.PIVMIN ) + $ TMP1 = -PIVMIN + IF( TMP1.LE.ZERO ) + $ NAB( JI, JP ) = NAB( JI, JP ) + 1 + 10 CONTINUE + 20 CONTINUE + MOUT = MOUT + NAB( JI, 2 ) - NAB( JI, 1 ) + 30 CONTINUE + RETURN + END IF +* +* Initialize for loop +* +* KF and KL have the following meaning: +* Intervals 1,...,KF-1 have converged. +* Intervals KF,...,KL still need to be refined. +* + KF = 1 + KL = MINP +* +* If IJOB=2, initialize C. +* If IJOB=3, use the user-supplied starting point. +* + IF( IJOB.EQ.2 ) THEN + DO 40 JI = 1, MINP + C( JI ) = HALF*( AB( JI, 1 )+AB( JI, 2 ) ) + 40 CONTINUE + END IF +* +* Iteration loop +* + DO 130 JIT = 1, NITMAX +* +* Loop over intervals +* + IF( KL-KF+1.GE.NBMIN .AND. NBMIN.GT.0 ) THEN +* +* Begin of Parallel Version of the loop +* + DO 60 JI = KF, KL +* +* Compute N(c), the number of eigenvalues less than c +* + WORK( JI ) = D( 1 ) - C( JI ) + IWORK( JI ) = 0 + IF( WORK( JI ).LE.PIVMIN ) THEN + IWORK( JI ) = 1 + WORK( JI ) = MIN( WORK( JI ), -PIVMIN ) + END IF +* + DO 50 J = 2, N + WORK( JI ) = D( J ) - E2( J-1 ) / WORK( JI ) - C( JI ) + IF( WORK( JI ).LE.PIVMIN ) THEN + IWORK( JI ) = IWORK( JI ) + 1 + WORK( JI ) = MIN( WORK( JI ), -PIVMIN ) + END IF + 50 CONTINUE + 60 CONTINUE +* + IF( IJOB.LE.2 ) THEN +* +* IJOB=2: Choose all intervals containing eigenvalues. +* + KLNEW = KL + DO 70 JI = KF, KL +* +* Insure that N(w) is monotone +* + IWORK( JI ) = MIN( NAB( JI, 2 ), + $ MAX( NAB( JI, 1 ), IWORK( JI ) ) ) +* +* Update the Queue -- add intervals if both halves +* contain eigenvalues. +* + IF( IWORK( JI ).EQ.NAB( JI, 2 ) ) THEN +* +* No eigenvalue in the upper interval: +* just use the lower interval. +* + AB( JI, 2 ) = C( JI ) +* + ELSE IF( IWORK( JI ).EQ.NAB( JI, 1 ) ) THEN +* +* No eigenvalue in the lower interval: +* just use the upper interval. +* + AB( JI, 1 ) = C( JI ) + ELSE + KLNEW = KLNEW + 1 + IF( KLNEW.LE.MMAX ) THEN +* +* Eigenvalue in both intervals -- add upper to +* queue. +* + AB( KLNEW, 2 ) = AB( JI, 2 ) + NAB( KLNEW, 2 ) = NAB( JI, 2 ) + AB( KLNEW, 1 ) = C( JI ) + NAB( KLNEW, 1 ) = IWORK( JI ) + AB( JI, 2 ) = C( JI ) + NAB( JI, 2 ) = IWORK( JI ) + ELSE + INFO = MMAX + 1 + END IF + END IF + 70 CONTINUE + IF( INFO.NE.0 ) + $ RETURN + KL = KLNEW + ELSE +* +* IJOB=3: Binary search. Keep only the interval containing +* w s.t. N(w) = NVAL +* + DO 80 JI = KF, KL + IF( IWORK( JI ).LE.NVAL( JI ) ) THEN + AB( JI, 1 ) = C( JI ) + NAB( JI, 1 ) = IWORK( JI ) + END IF + IF( IWORK( JI ).GE.NVAL( JI ) ) THEN + AB( JI, 2 ) = C( JI ) + NAB( JI, 2 ) = IWORK( JI ) + END IF + 80 CONTINUE + END IF +* + ELSE +* +* End of Parallel Version of the loop +* +* Begin of Serial Version of the loop +* + KLNEW = KL + DO 100 JI = KF, KL +* +* Compute N(w), the number of eigenvalues less than w +* + TMP1 = C( JI ) + TMP2 = D( 1 ) - TMP1 + ITMP1 = 0 + IF( TMP2.LE.PIVMIN ) THEN + ITMP1 = 1 + TMP2 = MIN( TMP2, -PIVMIN ) + END IF +* + DO 90 J = 2, N + TMP2 = D( J ) - E2( J-1 ) / TMP2 - TMP1 + IF( TMP2.LE.PIVMIN ) THEN + ITMP1 = ITMP1 + 1 + TMP2 = MIN( TMP2, -PIVMIN ) + END IF + 90 CONTINUE +* + IF( IJOB.LE.2 ) THEN +* +* IJOB=2: Choose all intervals containing eigenvalues. +* +* Insure that N(w) is monotone +* + ITMP1 = MIN( NAB( JI, 2 ), + $ MAX( NAB( JI, 1 ), ITMP1 ) ) +* +* Update the Queue -- add intervals if both halves +* contain eigenvalues. +* + IF( ITMP1.EQ.NAB( JI, 2 ) ) THEN +* +* No eigenvalue in the upper interval: +* just use the lower interval. +* + AB( JI, 2 ) = TMP1 +* + ELSE IF( ITMP1.EQ.NAB( JI, 1 ) ) THEN +* +* No eigenvalue in the lower interval: +* just use the upper interval. +* + AB( JI, 1 ) = TMP1 + ELSE IF( KLNEW.LT.MMAX ) THEN +* +* Eigenvalue in both intervals -- add upper to queue. +* + KLNEW = KLNEW + 1 + AB( KLNEW, 2 ) = AB( JI, 2 ) + NAB( KLNEW, 2 ) = NAB( JI, 2 ) + AB( KLNEW, 1 ) = TMP1 + NAB( KLNEW, 1 ) = ITMP1 + AB( JI, 2 ) = TMP1 + NAB( JI, 2 ) = ITMP1 + ELSE + INFO = MMAX + 1 + RETURN + END IF + ELSE +* +* IJOB=3: Binary search. Keep only the interval +* containing w s.t. N(w) = NVAL +* + IF( ITMP1.LE.NVAL( JI ) ) THEN + AB( JI, 1 ) = TMP1 + NAB( JI, 1 ) = ITMP1 + END IF + IF( ITMP1.GE.NVAL( JI ) ) THEN + AB( JI, 2 ) = TMP1 + NAB( JI, 2 ) = ITMP1 + END IF + END IF + 100 CONTINUE + KL = KLNEW +* + END IF +* +* Check for convergence +* + KFNEW = KF + DO 110 JI = KF, KL + TMP1 = ABS( AB( JI, 2 )-AB( JI, 1 ) ) + TMP2 = MAX( ABS( AB( JI, 2 ) ), ABS( AB( JI, 1 ) ) ) + IF( TMP1.LT.MAX( ABSTOL, PIVMIN, RELTOL*TMP2 ) .OR. + $ NAB( JI, 1 ).GE.NAB( JI, 2 ) ) THEN +* +* Converged -- Swap with position KFNEW, +* then increment KFNEW +* + IF( JI.GT.KFNEW ) THEN + TMP1 = AB( JI, 1 ) + TMP2 = AB( JI, 2 ) + ITMP1 = NAB( JI, 1 ) + ITMP2 = NAB( JI, 2 ) + AB( JI, 1 ) = AB( KFNEW, 1 ) + AB( JI, 2 ) = AB( KFNEW, 2 ) + NAB( JI, 1 ) = NAB( KFNEW, 1 ) + NAB( JI, 2 ) = NAB( KFNEW, 2 ) + AB( KFNEW, 1 ) = TMP1 + AB( KFNEW, 2 ) = TMP2 + NAB( KFNEW, 1 ) = ITMP1 + NAB( KFNEW, 2 ) = ITMP2 + IF( IJOB.EQ.3 ) THEN + ITMP1 = NVAL( JI ) + NVAL( JI ) = NVAL( KFNEW ) + NVAL( KFNEW ) = ITMP1 + END IF + END IF + KFNEW = KFNEW + 1 + END IF + 110 CONTINUE + KF = KFNEW +* +* Choose Midpoints +* + DO 120 JI = KF, KL + C( JI ) = HALF*( AB( JI, 1 )+AB( JI, 2 ) ) + 120 CONTINUE +* +* If no more intervals to refine, quit. +* + IF( KF.GT.KL ) + $ GO TO 140 + 130 CONTINUE +* +* Converged +* + 140 CONTINUE + INFO = MAX( KL+1-KF, 0 ) + MOUT = KL +* + RETURN +* +* End of DLAEBZ +* + END diff --git a/applications/PUfoam/MoDeNaModels/CFD_tool_0D/src/eigen/src/dlaev2.f b/applications/PUfoam/MoDeNaModels/CFD_tool_0D/src/eigen/src/dlaev2.f new file mode 100644 index 000000000..98230d053 --- /dev/null +++ b/applications/PUfoam/MoDeNaModels/CFD_tool_0D/src/eigen/src/dlaev2.f @@ -0,0 +1,238 @@ +*> \brief \b DLAEV2 +* +* =========== DOCUMENTATION =========== +* +* Online html documentation available at +* http://www.netlib.org/lapack/explore-html/ +* +*> \htmlonly +*> Download DLAEV2 + dependencies +*> +*> [TGZ] +*> +*> [ZIP] +*> +*> [TXT] +*> \endhtmlonly +* +* Definition: +* =========== +* +* SUBROUTINE DLAEV2( A, B, C, RT1, RT2, CS1, SN1 ) +* +* .. Scalar Arguments .. +* DOUBLE PRECISION A, B, C, CS1, RT1, RT2, SN1 +* .. +* +* +*> \par Purpose: +* ============= +*> +*> \verbatim +*> +*> DLAEV2 computes the eigendecomposition of a 2-by-2 symmetric matrix +*> [ A B ] +*> [ B C ]. +*> On return, RT1 is the eigenvalue of larger absolute value, RT2 is the +*> eigenvalue of smaller absolute value, and (CS1,SN1) is the unit right +*> eigenvector for RT1, giving the decomposition +*> +*> [ CS1 SN1 ] [ A B ] [ CS1 -SN1 ] = [ RT1 0 ] +*> [-SN1 CS1 ] [ B C ] [ SN1 CS1 ] [ 0 RT2 ]. +*> \endverbatim +* +* Arguments: +* ========== +* +*> \param[in] A +*> \verbatim +*> A is DOUBLE PRECISION +*> The (1,1) element of the 2-by-2 matrix. +*> \endverbatim +*> +*> \param[in] B +*> \verbatim +*> B is DOUBLE PRECISION +*> The (1,2) element and the conjugate of the (2,1) element of +*> the 2-by-2 matrix. +*> \endverbatim +*> +*> \param[in] C +*> \verbatim +*> C is DOUBLE PRECISION +*> The (2,2) element of the 2-by-2 matrix. +*> \endverbatim +*> +*> \param[out] RT1 +*> \verbatim +*> RT1 is DOUBLE PRECISION +*> The eigenvalue of larger absolute value. +*> \endverbatim +*> +*> \param[out] RT2 +*> \verbatim +*> RT2 is DOUBLE PRECISION +*> The eigenvalue of smaller absolute value. +*> \endverbatim +*> +*> \param[out] CS1 +*> \verbatim +*> CS1 is DOUBLE PRECISION +*> \endverbatim +*> +*> \param[out] SN1 +*> \verbatim +*> SN1 is DOUBLE PRECISION +*> The vector (CS1, SN1) is a unit right eigenvector for RT1. +*> \endverbatim +* +* Authors: +* ======== +* +*> \author Univ. of Tennessee +*> \author Univ. of California Berkeley +*> \author Univ. of Colorado Denver +*> \author NAG Ltd. +* +*> \date November 2011 +* +*> \ingroup auxOTHERauxiliary +* +*> \par Further Details: +* ===================== +*> +*> \verbatim +*> +*> RT1 is accurate to a few ulps barring over/underflow. +*> +*> RT2 may be inaccurate if there is massive cancellation in the +*> determinant A*C-B*B; higher precision or correctly rounded or +*> correctly truncated arithmetic would be needed to compute RT2 +*> accurately in all cases. +*> +*> CS1 and SN1 are accurate to a few ulps barring over/underflow. +*> +*> Overflow is possible only if RT1 is within a factor of 5 of overflow. +*> Underflow is harmless if the input data is 0 or exceeds +*> underflow_threshold / macheps. +*> \endverbatim +*> +* ===================================================================== + SUBROUTINE DLAEV2( A, B, C, RT1, RT2, CS1, SN1 ) +* +* -- LAPACK auxiliary routine (version 3.4.0) -- +* -- LAPACK is a software package provided by Univ. of Tennessee, -- +* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- +* November 2011 +* +* .. Scalar Arguments .. + DOUBLE PRECISION A, B, C, CS1, RT1, RT2, SN1 +* .. +* +* ===================================================================== +* +* .. Parameters .. + DOUBLE PRECISION ONE + PARAMETER ( ONE = 1.0D0 ) + DOUBLE PRECISION TWO + PARAMETER ( TWO = 2.0D0 ) + DOUBLE PRECISION ZERO + PARAMETER ( ZERO = 0.0D0 ) + DOUBLE PRECISION HALF + PARAMETER ( HALF = 0.5D0 ) +* .. +* .. Local Scalars .. + INTEGER SGN1, SGN2 + DOUBLE PRECISION AB, ACMN, ACMX, ACS, ADF, CS, CT, DF, RT, SM, + $ TB, TN +* .. +* .. Intrinsic Functions .. + INTRINSIC ABS, SQRT +* .. +* .. Executable Statements .. +* +* Compute the eigenvalues +* + SM = A + C + DF = A - C + ADF = ABS( DF ) + TB = B + B + AB = ABS( TB ) + IF( ABS( A ).GT.ABS( C ) ) THEN + ACMX = A + ACMN = C + ELSE + ACMX = C + ACMN = A + END IF + IF( ADF.GT.AB ) THEN + RT = ADF*SQRT( ONE+( AB / ADF )**2 ) + ELSE IF( ADF.LT.AB ) THEN + RT = AB*SQRT( ONE+( ADF / AB )**2 ) + ELSE +* +* Includes case AB=ADF=0 +* + RT = AB*SQRT( TWO ) + END IF + IF( SM.LT.ZERO ) THEN + RT1 = HALF*( SM-RT ) + SGN1 = -1 +* +* Order of execution important. +* To get fully accurate smaller eigenvalue, +* next line needs to be executed in higher precision. +* + RT2 = ( ACMX / RT1 )*ACMN - ( B / RT1 )*B + ELSE IF( SM.GT.ZERO ) THEN + RT1 = HALF*( SM+RT ) + SGN1 = 1 +* +* Order of execution important. +* To get fully accurate smaller eigenvalue, +* next line needs to be executed in higher precision. +* + RT2 = ( ACMX / RT1 )*ACMN - ( B / RT1 )*B + ELSE +* +* Includes case RT1 = RT2 = 0 +* + RT1 = HALF*RT + RT2 = -HALF*RT + SGN1 = 1 + END IF +* +* Compute the eigenvector +* + IF( DF.GE.ZERO ) THEN + CS = DF + RT + SGN2 = 1 + ELSE + CS = DF - RT + SGN2 = -1 + END IF + ACS = ABS( CS ) + IF( ACS.GT.AB ) THEN + CT = -TB / CS + SN1 = ONE / SQRT( ONE+CT*CT ) + CS1 = CT*SN1 + ELSE + IF( AB.EQ.ZERO ) THEN + CS1 = ONE + SN1 = ZERO + ELSE + TN = -CS / TB + CS1 = ONE / SQRT( ONE+TN*TN ) + SN1 = TN*CS1 + END IF + END IF + IF( SGN1.EQ.SGN2 ) THEN + TN = CS1 + CS1 = -SN1 + SN1 = TN + END IF + RETURN +* +* End of DLAEV2 +* + END diff --git a/applications/PUfoam/MoDeNaModels/CFD_tool_0D/src/eigen/src/dlaisnan.f b/applications/PUfoam/MoDeNaModels/CFD_tool_0D/src/eigen/src/dlaisnan.f new file mode 100644 index 000000000..c3cd27803 --- /dev/null +++ b/applications/PUfoam/MoDeNaModels/CFD_tool_0D/src/eigen/src/dlaisnan.f @@ -0,0 +1,91 @@ +*> \brief \b DLAISNAN +* +* =========== DOCUMENTATION =========== +* +* Online html documentation available at +* http://www.netlib.org/lapack/explore-html/ +* +*> \htmlonly +*> Download DLAISNAN + dependencies +*> +*> [TGZ] +*> +*> [ZIP] +*> +*> [TXT] +*> \endhtmlonly +* +* Definition: +* =========== +* +* LOGICAL FUNCTION DLAISNAN( DIN1, DIN2 ) +* +* .. Scalar Arguments .. +* DOUBLE PRECISION DIN1, DIN2 +* .. +* +* +*> \par Purpose: +* ============= +*> +*> \verbatim +*> +*> This routine is not for general use. It exists solely to avoid +*> over-optimization in DISNAN. +*> +*> DLAISNAN checks for NaNs by comparing its two arguments for +*> inequality. NaN is the only floating-point value where NaN != NaN +*> returns .TRUE. To check for NaNs, pass the same variable as both +*> arguments. +*> +*> A compiler must assume that the two arguments are +*> not the same variable, and the test will not be optimized away. +*> Interprocedural or whole-program optimization may delete this +*> test. The ISNAN functions will be replaced by the correct +*> Fortran 03 intrinsic once the intrinsic is widely available. +*> \endverbatim +* +* Arguments: +* ========== +* +*> \param[in] DIN1 +*> \verbatim +*> DIN1 is DOUBLE PRECISION +*> \endverbatim +*> +*> \param[in] DIN2 +*> \verbatim +*> DIN2 is DOUBLE PRECISION +*> Two numbers to compare for inequality. +*> \endverbatim +* +* Authors: +* ======== +* +*> \author Univ. of Tennessee +*> \author Univ. of California Berkeley +*> \author Univ. of Colorado Denver +*> \author NAG Ltd. +* +*> \date November 2011 +* +*> \ingroup auxOTHERauxiliary +* +* ===================================================================== + LOGICAL FUNCTION DLAISNAN( DIN1, DIN2 ) +* +* -- LAPACK auxiliary routine (version 3.4.0) -- +* -- LAPACK is a software package provided by Univ. of Tennessee, -- +* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- +* November 2011 +* +* .. Scalar Arguments .. + DOUBLE PRECISION DIN1, DIN2 +* .. +* +* ===================================================================== +* +* .. Executable Statements .. + DLAISNAN = (DIN1.NE.DIN2) + RETURN + END diff --git a/applications/PUfoam/MoDeNaModels/CFD_tool_0D/src/eigen/src/dlamch.f b/applications/PUfoam/MoDeNaModels/CFD_tool_0D/src/eigen/src/dlamch.f new file mode 100644 index 000000000..25c2c8e6e --- /dev/null +++ b/applications/PUfoam/MoDeNaModels/CFD_tool_0D/src/eigen/src/dlamch.f @@ -0,0 +1,193 @@ +*> \brief \b DLAMCH +* +* =========== DOCUMENTATION =========== +* +* Online html documentation available at +* http://www.netlib.org/lapack/explore-html/ +* +* Definition: +* =========== +* +* DOUBLE PRECISION FUNCTION DLAMCH( CMACH ) +* +* +*> \par Purpose: +* ============= +*> +*> \verbatim +*> +*> DLAMCH determines double precision machine parameters. +*> \endverbatim +* +* Arguments: +* ========== +* +*> \param[in] CMACH +*> \verbatim +*> Specifies the value to be returned by DLAMCH: +*> = 'E' or 'e', DLAMCH := eps +*> = 'S' or 's , DLAMCH := sfmin +*> = 'B' or 'b', DLAMCH := base +*> = 'P' or 'p', DLAMCH := eps*base +*> = 'N' or 'n', DLAMCH := t +*> = 'R' or 'r', DLAMCH := rnd +*> = 'M' or 'm', DLAMCH := emin +*> = 'U' or 'u', DLAMCH := rmin +*> = 'L' or 'l', DLAMCH := emax +*> = 'O' or 'o', DLAMCH := rmax +*> where +*> eps = relative machine precision +*> sfmin = safe minimum, such that 1/sfmin does not overflow +*> base = base of the machine +*> prec = eps*base +*> t = number of (base) digits in the mantissa +*> rnd = 1.0 when rounding occurs in addition, 0.0 otherwise +*> emin = minimum exponent before (gradual) underflow +*> rmin = underflow threshold - base**(emin-1) +*> emax = largest exponent before overflow +*> rmax = overflow threshold - (base**emax)*(1-eps) +*> \endverbatim +* +* Authors: +* ======== +* +*> \author Univ. of Tennessee +*> \author Univ. of California Berkeley +*> \author Univ. of Colorado Denver +*> \author NAG Ltd. +* +*> \date November 2011 +* +*> \ingroup auxOTHERauxiliary +* +* ===================================================================== + DOUBLE PRECISION FUNCTION DLAMCH( CMACH ) +* +* -- LAPACK auxiliary routine (version 3.4.0) -- +* -- LAPACK is a software package provided by Univ. of Tennessee, -- +* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- +* November 2011 +* +* .. Scalar Arguments .. + CHARACTER CMACH +* .. +* +* .. Scalar Arguments .. + DOUBLE PRECISION A, B +* .. +* +* ===================================================================== +* +* .. Parameters .. + DOUBLE PRECISION ONE, ZERO + PARAMETER ( ONE = 1.0D+0, ZERO = 0.0D+0 ) +* .. +* .. Local Scalars .. + DOUBLE PRECISION RND, EPS, SFMIN, SMALL, RMACH +* .. +* .. External Functions .. + LOGICAL LSAME + EXTERNAL LSAME +* .. +* .. Intrinsic Functions .. + INTRINSIC DIGITS, EPSILON, HUGE, MAXEXPONENT, + $ MINEXPONENT, RADIX, TINY +* .. +* .. Executable Statements .. +* +* +* Assume rounding, not chopping. Always. +* + RND = ONE +* + IF( ONE.EQ.RND ) THEN + EPS = EPSILON(ZERO) * 0.5 + ELSE + EPS = EPSILON(ZERO) + END IF +* + IF( LSAME( CMACH, 'E' ) ) THEN + RMACH = EPS + ELSE IF( LSAME( CMACH, 'S' ) ) THEN + SFMIN = TINY(ZERO) + SMALL = ONE / HUGE(ZERO) + IF( SMALL.GE.SFMIN ) THEN +* +* Use SMALL plus a bit, to avoid the possibility of rounding +* causing overflow when computing 1/sfmin. +* + SFMIN = SMALL*( ONE+EPS ) + END IF + RMACH = SFMIN + ELSE IF( LSAME( CMACH, 'B' ) ) THEN + RMACH = RADIX(ZERO) + ELSE IF( LSAME( CMACH, 'P' ) ) THEN + RMACH = EPS * RADIX(ZERO) + ELSE IF( LSAME( CMACH, 'N' ) ) THEN + RMACH = DIGITS(ZERO) + ELSE IF( LSAME( CMACH, 'R' ) ) THEN + RMACH = RND + ELSE IF( LSAME( CMACH, 'M' ) ) THEN + RMACH = MINEXPONENT(ZERO) + ELSE IF( LSAME( CMACH, 'U' ) ) THEN + RMACH = tiny(zero) + ELSE IF( LSAME( CMACH, 'L' ) ) THEN + RMACH = MAXEXPONENT(ZERO) + ELSE IF( LSAME( CMACH, 'O' ) ) THEN + RMACH = HUGE(ZERO) + ELSE + RMACH = ZERO + END IF +* + DLAMCH = RMACH + RETURN +* +* End of DLAMCH +* + END +************************************************************************ +*> \brief \b DLAMC3 +*> \details +*> \b Purpose: +*> \verbatim +*> DLAMC3 is intended to force A and B to be stored prior to doing +*> the addition of A and B , for use in situations where optimizers +*> might hold one of these in a register. +*> \endverbatim +*> \author LAPACK is a software package provided by Univ. of Tennessee, Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd.. +*> \date November 2011 +*> \ingroup auxOTHERauxiliary +*> +*> \param[in] A +*> \verbatim +*> A is a DOUBLE PRECISION +*> \endverbatim +*> +*> \param[in] B +*> \verbatim +*> B is a DOUBLE PRECISION +*> The values A and B. +*> \endverbatim +*> + DOUBLE PRECISION FUNCTION DLAMC3( A, B ) +* +* -- LAPACK auxiliary routine (version 3.4.0) -- +* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. +* November 2010 +* +* .. Scalar Arguments .. + DOUBLE PRECISION A, B +* .. +* ===================================================================== +* +* .. Executable Statements .. +* + DLAMC3 = A + B +* + RETURN +* +* End of DLAMC3 +* + END +* +************************************************************************ diff --git a/applications/PUfoam/MoDeNaModels/CFD_tool_0D/src/eigen/src/dlaneg.f b/applications/PUfoam/MoDeNaModels/CFD_tool_0D/src/eigen/src/dlaneg.f new file mode 100644 index 000000000..0d9980368 --- /dev/null +++ b/applications/PUfoam/MoDeNaModels/CFD_tool_0D/src/eigen/src/dlaneg.f @@ -0,0 +1,227 @@ +*> \brief \b DLANEG +* +* =========== DOCUMENTATION =========== +* +* Online html documentation available at +* http://www.netlib.org/lapack/explore-html/ +* +*> \htmlonly +*> Download DLANEG + dependencies +*> +*> [TGZ] +*> +*> [ZIP] +*> +*> [TXT] +*> \endhtmlonly +* +* Definition: +* =========== +* +* INTEGER FUNCTION DLANEG( N, D, LLD, SIGMA, PIVMIN, R ) +* +* .. Scalar Arguments .. +* INTEGER N, R +* DOUBLE PRECISION PIVMIN, SIGMA +* .. +* .. Array Arguments .. +* DOUBLE PRECISION D( * ), LLD( * ) +* .. +* +* +*> \par Purpose: +* ============= +*> +*> \verbatim +*> +*> DLANEG computes the Sturm count, the number of negative pivots +*> encountered while factoring tridiagonal T - sigma I = L D L^T. +*> This implementation works directly on the factors without forming +*> the tridiagonal matrix T. The Sturm count is also the number of +*> eigenvalues of T less than sigma. +*> +*> This routine is called from DLARRB. +*> +*> The current routine does not use the PIVMIN parameter but rather +*> requires IEEE-754 propagation of Infinities and NaNs. This +*> routine also has no input range restrictions but does require +*> default exception handling such that x/0 produces Inf when x is +*> non-zero, and Inf/Inf produces NaN. For more information, see: +*> +*> Marques, Riedy, and Voemel, "Benefits of IEEE-754 Features in +*> Modern Symmetric Tridiagonal Eigensolvers," SIAM Journal on +*> Scientific Computing, v28, n5, 2006. DOI 10.1137/050641624 +*> (Tech report version in LAWN 172 with the same title.) +*> \endverbatim +* +* Arguments: +* ========== +* +*> \param[in] N +*> \verbatim +*> N is INTEGER +*> The order of the matrix. +*> \endverbatim +*> +*> \param[in] D +*> \verbatim +*> D is DOUBLE PRECISION array, dimension (N) +*> The N diagonal elements of the diagonal matrix D. +*> \endverbatim +*> +*> \param[in] LLD +*> \verbatim +*> LLD is DOUBLE PRECISION array, dimension (N-1) +*> The (N-1) elements L(i)*L(i)*D(i). +*> \endverbatim +*> +*> \param[in] SIGMA +*> \verbatim +*> SIGMA is DOUBLE PRECISION +*> Shift amount in T - sigma I = L D L^T. +*> \endverbatim +*> +*> \param[in] PIVMIN +*> \verbatim +*> PIVMIN is DOUBLE PRECISION +*> The minimum pivot in the Sturm sequence. May be used +*> when zero pivots are encountered on non-IEEE-754 +*> architectures. +*> \endverbatim +*> +*> \param[in] R +*> \verbatim +*> R is INTEGER +*> The twist index for the twisted factorization that is used +*> for the negcount. +*> \endverbatim +* +* Authors: +* ======== +* +*> \author Univ. of Tennessee +*> \author Univ. of California Berkeley +*> \author Univ. of Colorado Denver +*> \author NAG Ltd. +* +*> \date November 2011 +* +*> \ingroup auxOTHERauxiliary +* +*> \par Contributors: +* ================== +*> +*> Osni Marques, LBNL/NERSC, USA \n +*> Christof Voemel, University of California, Berkeley, USA \n +*> Jason Riedy, University of California, Berkeley, USA \n +*> +* ===================================================================== + INTEGER FUNCTION DLANEG( N, D, LLD, SIGMA, PIVMIN, R ) +* +* -- LAPACK auxiliary routine (version 3.4.0) -- +* -- LAPACK is a software package provided by Univ. of Tennessee, -- +* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- +* November 2011 +* +* .. Scalar Arguments .. + INTEGER N, R + DOUBLE PRECISION PIVMIN, SIGMA +* .. +* .. Array Arguments .. + DOUBLE PRECISION D( * ), LLD( * ) +* .. +* +* ===================================================================== +* +* .. Parameters .. + DOUBLE PRECISION ZERO, ONE + PARAMETER ( ZERO = 0.0D0, ONE = 1.0D0 ) +* Some architectures propagate Infinities and NaNs very slowly, so +* the code computes counts in BLKLEN chunks. Then a NaN can +* propagate at most BLKLEN columns before being detected. This is +* not a general tuning parameter; it needs only to be just large +* enough that the overhead is tiny in common cases. + INTEGER BLKLEN + PARAMETER ( BLKLEN = 128 ) +* .. +* .. Local Scalars .. + INTEGER BJ, J, NEG1, NEG2, NEGCNT + DOUBLE PRECISION BSAV, DMINUS, DPLUS, GAMMA, P, T, TMP + LOGICAL SAWNAN +* .. +* .. Intrinsic Functions .. + INTRINSIC MIN, MAX +* .. +* .. External Functions .. + LOGICAL DISNAN + EXTERNAL DISNAN +* .. +* .. Executable Statements .. + + NEGCNT = 0 + +* I) upper part: L D L^T - SIGMA I = L+ D+ L+^T + T = -SIGMA + DO 210 BJ = 1, R-1, BLKLEN + NEG1 = 0 + BSAV = T + DO 21 J = BJ, MIN(BJ+BLKLEN-1, R-1) + DPLUS = D( J ) + T + IF( DPLUS.LT.ZERO ) NEG1 = NEG1 + 1 + TMP = T / DPLUS + T = TMP * LLD( J ) - SIGMA + 21 CONTINUE + SAWNAN = DISNAN( T ) +* Run a slower version of the above loop if a NaN is detected. +* A NaN should occur only with a zero pivot after an infinite +* pivot. In that case, substituting 1 for T/DPLUS is the +* correct limit. + IF( SAWNAN ) THEN + NEG1 = 0 + T = BSAV + DO 22 J = BJ, MIN(BJ+BLKLEN-1, R-1) + DPLUS = D( J ) + T + IF( DPLUS.LT.ZERO ) NEG1 = NEG1 + 1 + TMP = T / DPLUS + IF (DISNAN(TMP)) TMP = ONE + T = TMP * LLD(J) - SIGMA + 22 CONTINUE + END IF + NEGCNT = NEGCNT + NEG1 + 210 CONTINUE +* +* II) lower part: L D L^T - SIGMA I = U- D- U-^T + P = D( N ) - SIGMA + DO 230 BJ = N-1, R, -BLKLEN + NEG2 = 0 + BSAV = P + DO 23 J = BJ, MAX(BJ-BLKLEN+1, R), -1 + DMINUS = LLD( J ) + P + IF( DMINUS.LT.ZERO ) NEG2 = NEG2 + 1 + TMP = P / DMINUS + P = TMP * D( J ) - SIGMA + 23 CONTINUE + SAWNAN = DISNAN( P ) +* As above, run a slower version that substitutes 1 for Inf/Inf. +* + IF( SAWNAN ) THEN + NEG2 = 0 + P = BSAV + DO 24 J = BJ, MAX(BJ-BLKLEN+1, R), -1 + DMINUS = LLD( J ) + P + IF( DMINUS.LT.ZERO ) NEG2 = NEG2 + 1 + TMP = P / DMINUS + IF (DISNAN(TMP)) TMP = ONE + P = TMP * D(J) - SIGMA + 24 CONTINUE + END IF + NEGCNT = NEGCNT + NEG2 + 230 CONTINUE +* +* III) Twist index +* T was shifted by SIGMA initially. + GAMMA = (T + SIGMA) + P + IF( GAMMA.LT.ZERO ) NEGCNT = NEGCNT+1 + + DLANEG = NEGCNT + END diff --git a/applications/PUfoam/MoDeNaModels/CFD_tool_0D/src/eigen/src/dlanst.f b/applications/PUfoam/MoDeNaModels/CFD_tool_0D/src/eigen/src/dlanst.f new file mode 100644 index 000000000..b4eb093e8 --- /dev/null +++ b/applications/PUfoam/MoDeNaModels/CFD_tool_0D/src/eigen/src/dlanst.f @@ -0,0 +1,183 @@ +*> \brief \b DLANST +* +* =========== DOCUMENTATION =========== +* +* Online html documentation available at +* http://www.netlib.org/lapack/explore-html/ +* +*> \htmlonly +*> Download DLANST + dependencies +*> +*> [TGZ] +*> +*> [ZIP] +*> +*> [TXT] +*> \endhtmlonly +* +* Definition: +* =========== +* +* DOUBLE PRECISION FUNCTION DLANST( NORM, N, D, E ) +* +* .. Scalar Arguments .. +* CHARACTER NORM +* INTEGER N +* .. +* .. Array Arguments .. +* DOUBLE PRECISION D( * ), E( * ) +* .. +* +* +*> \par Purpose: +* ============= +*> +*> \verbatim +*> +*> DLANST returns the value of the one norm, or the Frobenius norm, or +*> the infinity norm, or the element of largest absolute value of a +*> real symmetric tridiagonal matrix A. +*> \endverbatim +*> +*> \return DLANST +*> \verbatim +*> +*> DLANST = ( max(abs(A(i,j))), NORM = 'M' or 'm' +*> ( +*> ( norm1(A), NORM = '1', 'O' or 'o' +*> ( +*> ( normI(A), NORM = 'I' or 'i' +*> ( +*> ( normF(A), NORM = 'F', 'f', 'E' or 'e' +*> +*> where norm1 denotes the one norm of a matrix (maximum column sum), +*> normI denotes the infinity norm of a matrix (maximum row sum) and +*> normF denotes the Frobenius norm of a matrix (square root of sum of +*> squares). Note that max(abs(A(i,j))) is not a consistent matrix norm. +*> \endverbatim +* +* Arguments: +* ========== +* +*> \param[in] NORM +*> \verbatim +*> NORM is CHARACTER*1 +*> Specifies the value to be returned in DLANST as described +*> above. +*> \endverbatim +*> +*> \param[in] N +*> \verbatim +*> N is INTEGER +*> The order of the matrix A. N >= 0. When N = 0, DLANST is +*> set to zero. +*> \endverbatim +*> +*> \param[in] D +*> \verbatim +*> D is DOUBLE PRECISION array, dimension (N) +*> The diagonal elements of A. +*> \endverbatim +*> +*> \param[in] E +*> \verbatim +*> E is DOUBLE PRECISION array, dimension (N-1) +*> The (n-1) sub-diagonal or super-diagonal elements of A. +*> \endverbatim +* +* Authors: +* ======== +* +*> \author Univ. of Tennessee +*> \author Univ. of California Berkeley +*> \author Univ. of Colorado Denver +*> \author NAG Ltd. +* +*> \date November 2011 +* +*> \ingroup auxOTHERauxiliary +* +* ===================================================================== + DOUBLE PRECISION FUNCTION DLANST( NORM, N, D, E ) +* +* -- LAPACK auxiliary routine (version 3.4.0) -- +* -- LAPACK is a software package provided by Univ. of Tennessee, -- +* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- +* November 2011 +* +* .. Scalar Arguments .. + CHARACTER NORM + INTEGER N +* .. +* .. Array Arguments .. + DOUBLE PRECISION D( * ), E( * ) +* .. +* +* ===================================================================== +* +* .. Parameters .. + DOUBLE PRECISION ONE, ZERO + PARAMETER ( ONE = 1.0D+0, ZERO = 0.0D+0 ) +* .. +* .. Local Scalars .. + INTEGER I + DOUBLE PRECISION ANORM, SCALE, SUM +* .. +* .. External Functions .. + LOGICAL LSAME + EXTERNAL LSAME +* .. +* .. External Subroutines .. + EXTERNAL DLASSQ +* .. +* .. Intrinsic Functions .. + INTRINSIC ABS, MAX, SQRT +* .. +* .. Executable Statements .. +* + IF( N.LE.0 ) THEN + ANORM = ZERO + ELSE IF( LSAME( NORM, 'M' ) ) THEN +* +* Find max(abs(A(i,j))). +* + ANORM = ABS( D( N ) ) + DO 10 I = 1, N - 1 + ANORM = MAX( ANORM, ABS( D( I ) ) ) + ANORM = MAX( ANORM, ABS( E( I ) ) ) + 10 CONTINUE + ELSE IF( LSAME( NORM, 'O' ) .OR. NORM.EQ.'1' .OR. + $ LSAME( NORM, 'I' ) ) THEN +* +* Find norm1(A). +* + IF( N.EQ.1 ) THEN + ANORM = ABS( D( 1 ) ) + ELSE + ANORM = MAX( ABS( D( 1 ) )+ABS( E( 1 ) ), + $ ABS( E( N-1 ) )+ABS( D( N ) ) ) + DO 20 I = 2, N - 1 + ANORM = MAX( ANORM, ABS( D( I ) )+ABS( E( I ) )+ + $ ABS( E( I-1 ) ) ) + 20 CONTINUE + END IF + ELSE IF( ( LSAME( NORM, 'F' ) ) .OR. ( LSAME( NORM, 'E' ) ) ) THEN +* +* Find normF(A). +* + SCALE = ZERO + SUM = ONE + IF( N.GT.1 ) THEN + CALL DLASSQ( N-1, E, 1, SCALE, SUM ) + SUM = 2*SUM + END IF + CALL DLASSQ( N, D, 1, SCALE, SUM ) + ANORM = SCALE*SQRT( SUM ) + END IF +* + DLANST = ANORM + RETURN +* +* End of DLANST +* + END diff --git a/applications/PUfoam/MoDeNaModels/CFD_tool_0D/src/eigen/src/dlapy2.f b/applications/PUfoam/MoDeNaModels/CFD_tool_0D/src/eigen/src/dlapy2.f new file mode 100644 index 000000000..e6a62bf4a --- /dev/null +++ b/applications/PUfoam/MoDeNaModels/CFD_tool_0D/src/eigen/src/dlapy2.f @@ -0,0 +1,104 @@ +*> \brief \b DLAPY2 +* +* =========== DOCUMENTATION =========== +* +* Online html documentation available at +* http://www.netlib.org/lapack/explore-html/ +* +*> \htmlonly +*> Download DLAPY2 + dependencies +*> +*> [TGZ] +*> +*> [ZIP] +*> +*> [TXT] +*> \endhtmlonly +* +* Definition: +* =========== +* +* DOUBLE PRECISION FUNCTION DLAPY2( X, Y ) +* +* .. Scalar Arguments .. +* DOUBLE PRECISION X, Y +* .. +* +* +*> \par Purpose: +* ============= +*> +*> \verbatim +*> +*> DLAPY2 returns sqrt(x**2+y**2), taking care not to cause unnecessary +*> overflow. +*> \endverbatim +* +* Arguments: +* ========== +* +*> \param[in] X +*> \verbatim +*> X is DOUBLE PRECISION +*> \endverbatim +*> +*> \param[in] Y +*> \verbatim +*> Y is DOUBLE PRECISION +*> X and Y specify the values x and y. +*> \endverbatim +* +* Authors: +* ======== +* +*> \author Univ. of Tennessee +*> \author Univ. of California Berkeley +*> \author Univ. of Colorado Denver +*> \author NAG Ltd. +* +*> \date November 2011 +* +*> \ingroup auxOTHERauxiliary +* +* ===================================================================== + DOUBLE PRECISION FUNCTION DLAPY2( X, Y ) +* +* -- LAPACK auxiliary routine (version 3.4.0) -- +* -- LAPACK is a software package provided by Univ. of Tennessee, -- +* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- +* November 2011 +* +* .. Scalar Arguments .. + DOUBLE PRECISION X, Y +* .. +* +* ===================================================================== +* +* .. Parameters .. + DOUBLE PRECISION ZERO + PARAMETER ( ZERO = 0.0D0 ) + DOUBLE PRECISION ONE + PARAMETER ( ONE = 1.0D0 ) +* .. +* .. Local Scalars .. + DOUBLE PRECISION W, XABS, YABS, Z +* .. +* .. Intrinsic Functions .. + INTRINSIC ABS, MAX, MIN, SQRT +* .. +* .. Executable Statements .. +* + XABS = ABS( X ) + YABS = ABS( Y ) + W = MAX( XABS, YABS ) + Z = MIN( XABS, YABS ) + IF( Z.EQ.ZERO ) THEN + DLAPY2 = W + ELSE + DLAPY2 = W*SQRT( ONE+( Z / W )**2 ) + END IF + RETURN +* +* End of DLAPY2 +* + END diff --git a/applications/PUfoam/MoDeNaModels/CFD_tool_0D/src/eigen/src/dlar1v.f b/applications/PUfoam/MoDeNaModels/CFD_tool_0D/src/eigen/src/dlar1v.f new file mode 100644 index 000000000..2aa46910e --- /dev/null +++ b/applications/PUfoam/MoDeNaModels/CFD_tool_0D/src/eigen/src/dlar1v.f @@ -0,0 +1,486 @@ +*> \brief \b DLAR1V +* +* =========== DOCUMENTATION =========== +* +* Online html documentation available at +* http://www.netlib.org/lapack/explore-html/ +* +*> \htmlonly +*> Download DLAR1V + dependencies +*> +*> [TGZ] +*> +*> [ZIP] +*> +*> [TXT] +*> \endhtmlonly +* +* Definition: +* =========== +* +* SUBROUTINE DLAR1V( N, B1, BN, LAMBDA, D, L, LD, LLD, +* PIVMIN, GAPTOL, Z, WANTNC, NEGCNT, ZTZ, MINGMA, +* R, ISUPPZ, NRMINV, RESID, RQCORR, WORK ) +* +* .. Scalar Arguments .. +* LOGICAL WANTNC +* INTEGER B1, BN, N, NEGCNT, R +* DOUBLE PRECISION GAPTOL, LAMBDA, MINGMA, NRMINV, PIVMIN, RESID, +* $ RQCORR, ZTZ +* .. +* .. Array Arguments .. +* INTEGER ISUPPZ( * ) +* DOUBLE PRECISION D( * ), L( * ), LD( * ), LLD( * ), +* $ WORK( * ) +* DOUBLE PRECISION Z( * ) +* .. +* +* +*> \par Purpose: +* ============= +*> +*> \verbatim +*> +*> DLAR1V computes the (scaled) r-th column of the inverse of +*> the sumbmatrix in rows B1 through BN of the tridiagonal matrix +*> L D L**T - sigma I. When sigma is close to an eigenvalue, the +*> computed vector is an accurate eigenvector. Usually, r corresponds +*> to the index where the eigenvector is largest in magnitude. +*> The following steps accomplish this computation : +*> (a) Stationary qd transform, L D L**T - sigma I = L(+) D(+) L(+)**T, +*> (b) Progressive qd transform, L D L**T - sigma I = U(-) D(-) U(-)**T, +*> (c) Computation of the diagonal elements of the inverse of +*> L D L**T - sigma I by combining the above transforms, and choosing +*> r as the index where the diagonal of the inverse is (one of the) +*> largest in magnitude. +*> (d) Computation of the (scaled) r-th column of the inverse using the +*> twisted factorization obtained by combining the top part of the +*> the stationary and the bottom part of the progressive transform. +*> \endverbatim +* +* Arguments: +* ========== +* +*> \param[in] N +*> \verbatim +*> N is INTEGER +*> The order of the matrix L D L**T. +*> \endverbatim +*> +*> \param[in] B1 +*> \verbatim +*> B1 is INTEGER +*> First index of the submatrix of L D L**T. +*> \endverbatim +*> +*> \param[in] BN +*> \verbatim +*> BN is INTEGER +*> Last index of the submatrix of L D L**T. +*> \endverbatim +*> +*> \param[in] LAMBDA +*> \verbatim +*> LAMBDA is DOUBLE PRECISION +*> The shift. In order to compute an accurate eigenvector, +*> LAMBDA should be a good approximation to an eigenvalue +*> of L D L**T. +*> \endverbatim +*> +*> \param[in] L +*> \verbatim +*> L is DOUBLE PRECISION array, dimension (N-1) +*> The (n-1) subdiagonal elements of the unit bidiagonal matrix +*> L, in elements 1 to N-1. +*> \endverbatim +*> +*> \param[in] D +*> \verbatim +*> D is DOUBLE PRECISION array, dimension (N) +*> The n diagonal elements of the diagonal matrix D. +*> \endverbatim +*> +*> \param[in] LD +*> \verbatim +*> LD is DOUBLE PRECISION array, dimension (N-1) +*> The n-1 elements L(i)*D(i). +*> \endverbatim +*> +*> \param[in] LLD +*> \verbatim +*> LLD is DOUBLE PRECISION array, dimension (N-1) +*> The n-1 elements L(i)*L(i)*D(i). +*> \endverbatim +*> +*> \param[in] PIVMIN +*> \verbatim +*> PIVMIN is DOUBLE PRECISION +*> The minimum pivot in the Sturm sequence. +*> \endverbatim +*> +*> \param[in] GAPTOL +*> \verbatim +*> GAPTOL is DOUBLE PRECISION +*> Tolerance that indicates when eigenvector entries are negligible +*> w.r.t. their contribution to the residual. +*> \endverbatim +*> +*> \param[in,out] Z +*> \verbatim +*> Z is DOUBLE PRECISION array, dimension (N) +*> On input, all entries of Z must be set to 0. +*> On output, Z contains the (scaled) r-th column of the +*> inverse. The scaling is such that Z(R) equals 1. +*> \endverbatim +*> +*> \param[in] WANTNC +*> \verbatim +*> WANTNC is LOGICAL +*> Specifies whether NEGCNT has to be computed. +*> \endverbatim +*> +*> \param[out] NEGCNT +*> \verbatim +*> NEGCNT is INTEGER +*> If WANTNC is .TRUE. then NEGCNT = the number of pivots < pivmin +*> in the matrix factorization L D L**T, and NEGCNT = -1 otherwise. +*> \endverbatim +*> +*> \param[out] ZTZ +*> \verbatim +*> ZTZ is DOUBLE PRECISION +*> The square of the 2-norm of Z. +*> \endverbatim +*> +*> \param[out] MINGMA +*> \verbatim +*> MINGMA is DOUBLE PRECISION +*> The reciprocal of the largest (in magnitude) diagonal +*> element of the inverse of L D L**T - sigma I. +*> \endverbatim +*> +*> \param[in,out] R +*> \verbatim +*> R is INTEGER +*> The twist index for the twisted factorization used to +*> compute Z. +*> On input, 0 <= R <= N. If R is input as 0, R is set to +*> the index where (L D L**T - sigma I)^{-1} is largest +*> in magnitude. If 1 <= R <= N, R is unchanged. +*> On output, R contains the twist index used to compute Z. +*> Ideally, R designates the position of the maximum entry in the +*> eigenvector. +*> \endverbatim +*> +*> \param[out] ISUPPZ +*> \verbatim +*> ISUPPZ is INTEGER array, dimension (2) +*> The support of the vector in Z, i.e., the vector Z is +*> nonzero only in elements ISUPPZ(1) through ISUPPZ( 2 ). +*> \endverbatim +*> +*> \param[out] NRMINV +*> \verbatim +*> NRMINV is DOUBLE PRECISION +*> NRMINV = 1/SQRT( ZTZ ) +*> \endverbatim +*> +*> \param[out] RESID +*> \verbatim +*> RESID is DOUBLE PRECISION +*> The residual of the FP vector. +*> RESID = ABS( MINGMA )/SQRT( ZTZ ) +*> \endverbatim +*> +*> \param[out] RQCORR +*> \verbatim +*> RQCORR is DOUBLE PRECISION +*> The Rayleigh Quotient correction to LAMBDA. +*> RQCORR = MINGMA*TMP +*> \endverbatim +*> +*> \param[out] WORK +*> \verbatim +*> WORK is DOUBLE PRECISION array, dimension (4*N) +*> \endverbatim +* +* Authors: +* ======== +* +*> \author Univ. of Tennessee +*> \author Univ. of California Berkeley +*> \author Univ. of Colorado Denver +*> \author NAG Ltd. +* +*> \date November 2011 +* +*> \ingroup doubleOTHERauxiliary +* +*> \par Contributors: +* ================== +*> +*> Beresford Parlett, University of California, Berkeley, USA \n +*> Jim Demmel, University of California, Berkeley, USA \n +*> Inderjit Dhillon, University of Texas, Austin, USA \n +*> Osni Marques, LBNL/NERSC, USA \n +*> Christof Voemel, University of California, Berkeley, USA +* +* ===================================================================== + SUBROUTINE DLAR1V( N, B1, BN, LAMBDA, D, L, LD, LLD, + $ PIVMIN, GAPTOL, Z, WANTNC, NEGCNT, ZTZ, MINGMA, + $ R, ISUPPZ, NRMINV, RESID, RQCORR, WORK ) +* +* -- LAPACK auxiliary routine (version 3.4.0) -- +* -- LAPACK is a software package provided by Univ. of Tennessee, -- +* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- +* November 2011 +* +* .. Scalar Arguments .. + LOGICAL WANTNC + INTEGER B1, BN, N, NEGCNT, R + DOUBLE PRECISION GAPTOL, LAMBDA, MINGMA, NRMINV, PIVMIN, RESID, + $ RQCORR, ZTZ +* .. +* .. Array Arguments .. + INTEGER ISUPPZ( * ) + DOUBLE PRECISION D( * ), L( * ), LD( * ), LLD( * ), + $ WORK( * ) + DOUBLE PRECISION Z( * ) +* .. +* +* ===================================================================== +* +* .. Parameters .. + DOUBLE PRECISION ZERO, ONE + PARAMETER ( ZERO = 0.0D0, ONE = 1.0D0 ) + +* .. +* .. Local Scalars .. + LOGICAL SAWNAN1, SAWNAN2 + INTEGER I, INDLPL, INDP, INDS, INDUMN, NEG1, NEG2, R1, + $ R2 + DOUBLE PRECISION DMINUS, DPLUS, EPS, S, TMP +* .. +* .. External Functions .. + LOGICAL DISNAN + DOUBLE PRECISION DLAMCH + EXTERNAL DISNAN, DLAMCH +* .. +* .. Intrinsic Functions .. + INTRINSIC ABS +* .. +* .. Executable Statements .. +* + EPS = DLAMCH( 'Precision' ) + + + IF( R.EQ.0 ) THEN + R1 = B1 + R2 = BN + ELSE + R1 = R + R2 = R + END IF + +* Storage for LPLUS + INDLPL = 0 +* Storage for UMINUS + INDUMN = N + INDS = 2*N + 1 + INDP = 3*N + 1 + + IF( B1.EQ.1 ) THEN + WORK( INDS ) = ZERO + ELSE + WORK( INDS+B1-1 ) = LLD( B1-1 ) + END IF + +* +* Compute the stationary transform (using the differential form) +* until the index R2. +* + SAWNAN1 = .FALSE. + NEG1 = 0 + S = WORK( INDS+B1-1 ) - LAMBDA + DO 50 I = B1, R1 - 1 + DPLUS = D( I ) + S + WORK( INDLPL+I ) = LD( I ) / DPLUS + IF(DPLUS.LT.ZERO) NEG1 = NEG1 + 1 + WORK( INDS+I ) = S*WORK( INDLPL+I )*L( I ) + S = WORK( INDS+I ) - LAMBDA + 50 CONTINUE + SAWNAN1 = DISNAN( S ) + IF( SAWNAN1 ) GOTO 60 + DO 51 I = R1, R2 - 1 + DPLUS = D( I ) + S + WORK( INDLPL+I ) = LD( I ) / DPLUS + WORK( INDS+I ) = S*WORK( INDLPL+I )*L( I ) + S = WORK( INDS+I ) - LAMBDA + 51 CONTINUE + SAWNAN1 = DISNAN( S ) +* + 60 CONTINUE + IF( SAWNAN1 ) THEN +* Runs a slower version of the above loop if a NaN is detected + NEG1 = 0 + S = WORK( INDS+B1-1 ) - LAMBDA + DO 70 I = B1, R1 - 1 + DPLUS = D( I ) + S + IF(ABS(DPLUS).LT.PIVMIN) DPLUS = -PIVMIN + WORK( INDLPL+I ) = LD( I ) / DPLUS + IF(DPLUS.LT.ZERO) NEG1 = NEG1 + 1 + WORK( INDS+I ) = S*WORK( INDLPL+I )*L( I ) + IF( WORK( INDLPL+I ).EQ.ZERO ) + $ WORK( INDS+I ) = LLD( I ) + S = WORK( INDS+I ) - LAMBDA + 70 CONTINUE + DO 71 I = R1, R2 - 1 + DPLUS = D( I ) + S + IF(ABS(DPLUS).LT.PIVMIN) DPLUS = -PIVMIN + WORK( INDLPL+I ) = LD( I ) / DPLUS + WORK( INDS+I ) = S*WORK( INDLPL+I )*L( I ) + IF( WORK( INDLPL+I ).EQ.ZERO ) + $ WORK( INDS+I ) = LLD( I ) + S = WORK( INDS+I ) - LAMBDA + 71 CONTINUE + END IF +* +* Compute the progressive transform (using the differential form) +* until the index R1 +* + SAWNAN2 = .FALSE. + NEG2 = 0 + WORK( INDP+BN-1 ) = D( BN ) - LAMBDA + DO 80 I = BN - 1, R1, -1 + DMINUS = LLD( I ) + WORK( INDP+I ) + TMP = D( I ) / DMINUS + IF(DMINUS.LT.ZERO) NEG2 = NEG2 + 1 + WORK( INDUMN+I ) = L( I )*TMP + WORK( INDP+I-1 ) = WORK( INDP+I )*TMP - LAMBDA + 80 CONTINUE + TMP = WORK( INDP+R1-1 ) + SAWNAN2 = DISNAN( TMP ) + + IF( SAWNAN2 ) THEN +* Runs a slower version of the above loop if a NaN is detected + NEG2 = 0 + DO 100 I = BN-1, R1, -1 + DMINUS = LLD( I ) + WORK( INDP+I ) + IF(ABS(DMINUS).LT.PIVMIN) DMINUS = -PIVMIN + TMP = D( I ) / DMINUS + IF(DMINUS.LT.ZERO) NEG2 = NEG2 + 1 + WORK( INDUMN+I ) = L( I )*TMP + WORK( INDP+I-1 ) = WORK( INDP+I )*TMP - LAMBDA + IF( TMP.EQ.ZERO ) + $ WORK( INDP+I-1 ) = D( I ) - LAMBDA + 100 CONTINUE + END IF +* +* Find the index (from R1 to R2) of the largest (in magnitude) +* diagonal element of the inverse +* + MINGMA = WORK( INDS+R1-1 ) + WORK( INDP+R1-1 ) + IF( MINGMA.LT.ZERO ) NEG1 = NEG1 + 1 + IF( WANTNC ) THEN + NEGCNT = NEG1 + NEG2 + ELSE + NEGCNT = -1 + ENDIF + IF( ABS(MINGMA).EQ.ZERO ) + $ MINGMA = EPS*WORK( INDS+R1-1 ) + R = R1 + DO 110 I = R1, R2 - 1 + TMP = WORK( INDS+I ) + WORK( INDP+I ) + IF( TMP.EQ.ZERO ) + $ TMP = EPS*WORK( INDS+I ) + IF( ABS( TMP ).LE.ABS( MINGMA ) ) THEN + MINGMA = TMP + R = I + 1 + END IF + 110 CONTINUE +* +* Compute the FP vector: solve N^T v = e_r +* + ISUPPZ( 1 ) = B1 + ISUPPZ( 2 ) = BN + Z( R ) = ONE + ZTZ = ONE +* +* Compute the FP vector upwards from R +* + IF( .NOT.SAWNAN1 .AND. .NOT.SAWNAN2 ) THEN + DO 210 I = R-1, B1, -1 + Z( I ) = -( WORK( INDLPL+I )*Z( I+1 ) ) + IF( (ABS(Z(I))+ABS(Z(I+1)))* ABS(LD(I)).LT.GAPTOL ) + $ THEN + Z( I ) = ZERO + ISUPPZ( 1 ) = I + 1 + GOTO 220 + ENDIF + ZTZ = ZTZ + Z( I )*Z( I ) + 210 CONTINUE + 220 CONTINUE + ELSE +* Run slower loop if NaN occurred. + DO 230 I = R - 1, B1, -1 + IF( Z( I+1 ).EQ.ZERO ) THEN + Z( I ) = -( LD( I+1 ) / LD( I ) )*Z( I+2 ) + ELSE + Z( I ) = -( WORK( INDLPL+I )*Z( I+1 ) ) + END IF + IF( (ABS(Z(I))+ABS(Z(I+1)))* ABS(LD(I)).LT.GAPTOL ) + $ THEN + Z( I ) = ZERO + ISUPPZ( 1 ) = I + 1 + GO TO 240 + END IF + ZTZ = ZTZ + Z( I )*Z( I ) + 230 CONTINUE + 240 CONTINUE + ENDIF + +* Compute the FP vector downwards from R in blocks of size BLKSIZ + IF( .NOT.SAWNAN1 .AND. .NOT.SAWNAN2 ) THEN + DO 250 I = R, BN-1 + Z( I+1 ) = -( WORK( INDUMN+I )*Z( I ) ) + IF( (ABS(Z(I))+ABS(Z(I+1)))* ABS(LD(I)).LT.GAPTOL ) + $ THEN + Z( I+1 ) = ZERO + ISUPPZ( 2 ) = I + GO TO 260 + END IF + ZTZ = ZTZ + Z( I+1 )*Z( I+1 ) + 250 CONTINUE + 260 CONTINUE + ELSE +* Run slower loop if NaN occurred. + DO 270 I = R, BN - 1 + IF( Z( I ).EQ.ZERO ) THEN + Z( I+1 ) = -( LD( I-1 ) / LD( I ) )*Z( I-1 ) + ELSE + Z( I+1 ) = -( WORK( INDUMN+I )*Z( I ) ) + END IF + IF( (ABS(Z(I))+ABS(Z(I+1)))* ABS(LD(I)).LT.GAPTOL ) + $ THEN + Z( I+1 ) = ZERO + ISUPPZ( 2 ) = I + GO TO 280 + END IF + ZTZ = ZTZ + Z( I+1 )*Z( I+1 ) + 270 CONTINUE + 280 CONTINUE + END IF +* +* Compute quantities for convergence test +* + TMP = ONE / ZTZ + NRMINV = SQRT( TMP ) + RESID = ABS( MINGMA )*NRMINV + RQCORR = MINGMA*TMP +* +* + RETURN +* +* End of DLAR1V +* + END diff --git a/applications/PUfoam/MoDeNaModels/CFD_tool_0D/src/eigen/src/dlarnv.f b/applications/PUfoam/MoDeNaModels/CFD_tool_0D/src/eigen/src/dlarnv.f new file mode 100644 index 000000000..8195ae9c7 --- /dev/null +++ b/applications/PUfoam/MoDeNaModels/CFD_tool_0D/src/eigen/src/dlarnv.f @@ -0,0 +1,178 @@ +*> \brief \b DLARNV +* +* =========== DOCUMENTATION =========== +* +* Online html documentation available at +* http://www.netlib.org/lapack/explore-html/ +* +*> \htmlonly +*> Download DLARNV + dependencies +*> +*> [TGZ] +*> +*> [ZIP] +*> +*> [TXT] +*> \endhtmlonly +* +* Definition: +* =========== +* +* SUBROUTINE DLARNV( IDIST, ISEED, N, X ) +* +* .. Scalar Arguments .. +* INTEGER IDIST, N +* .. +* .. Array Arguments .. +* INTEGER ISEED( 4 ) +* DOUBLE PRECISION X( * ) +* .. +* +* +*> \par Purpose: +* ============= +*> +*> \verbatim +*> +*> DLARNV returns a vector of n random real numbers from a uniform or +*> normal distribution. +*> \endverbatim +* +* Arguments: +* ========== +* +*> \param[in] IDIST +*> \verbatim +*> IDIST is INTEGER +*> Specifies the distribution of the random numbers: +*> = 1: uniform (0,1) +*> = 2: uniform (-1,1) +*> = 3: normal (0,1) +*> \endverbatim +*> +*> \param[in,out] ISEED +*> \verbatim +*> ISEED is INTEGER array, dimension (4) +*> On entry, the seed of the random number generator; the array +*> elements must be between 0 and 4095, and ISEED(4) must be +*> odd. +*> On exit, the seed is updated. +*> \endverbatim +*> +*> \param[in] N +*> \verbatim +*> N is INTEGER +*> The number of random numbers to be generated. +*> \endverbatim +*> +*> \param[out] X +*> \verbatim +*> X is DOUBLE PRECISION array, dimension (N) +*> The generated random numbers. +*> \endverbatim +* +* Authors: +* ======== +* +*> \author Univ. of Tennessee +*> \author Univ. of California Berkeley +*> \author Univ. of Colorado Denver +*> \author NAG Ltd. +* +*> \date November 2011 +* +*> \ingroup auxOTHERauxiliary +* +*> \par Further Details: +* ===================== +*> +*> \verbatim +*> +*> This routine calls the auxiliary routine DLARUV to generate random +*> real numbers from a uniform (0,1) distribution, in batches of up to +*> 128 using vectorisable code. The Box-Muller method is used to +*> transform numbers from a uniform to a normal distribution. +*> \endverbatim +*> +* ===================================================================== + SUBROUTINE DLARNV( IDIST, ISEED, N, X ) +* +* -- LAPACK auxiliary routine (version 3.4.0) -- +* -- LAPACK is a software package provided by Univ. of Tennessee, -- +* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- +* November 2011 +* +* .. Scalar Arguments .. + INTEGER IDIST, N +* .. +* .. Array Arguments .. + INTEGER ISEED( 4 ) + DOUBLE PRECISION X( * ) +* .. +* +* ===================================================================== +* +* .. Parameters .. + DOUBLE PRECISION ONE, TWO + PARAMETER ( ONE = 1.0D+0, TWO = 2.0D+0 ) + INTEGER LV + PARAMETER ( LV = 128 ) + DOUBLE PRECISION TWOPI + PARAMETER ( TWOPI = 6.2831853071795864769252867663D+0 ) +* .. +* .. Local Scalars .. + INTEGER I, IL, IL2, IV +* .. +* .. Local Arrays .. + DOUBLE PRECISION U( LV ) +* .. +* .. Intrinsic Functions .. + INTRINSIC COS, LOG, MIN, SQRT +* .. +* .. External Subroutines .. + EXTERNAL DLARUV +* .. +* .. Executable Statements .. +* + DO 40 IV = 1, N, LV / 2 + IL = MIN( LV / 2, N-IV+1 ) + IF( IDIST.EQ.3 ) THEN + IL2 = 2*IL + ELSE + IL2 = IL + END IF +* +* Call DLARUV to generate IL2 numbers from a uniform (0,1) +* distribution (IL2 <= LV) +* + CALL DLARUV( ISEED, IL2, U ) +* + IF( IDIST.EQ.1 ) THEN +* +* Copy generated numbers +* + DO 10 I = 1, IL + X( IV+I-1 ) = U( I ) + 10 CONTINUE + ELSE IF( IDIST.EQ.2 ) THEN +* +* Convert generated numbers to uniform (-1,1) distribution +* + DO 20 I = 1, IL + X( IV+I-1 ) = TWO*U( I ) - ONE + 20 CONTINUE + ELSE IF( IDIST.EQ.3 ) THEN +* +* Convert generated numbers to normal (0,1) distribution +* + DO 30 I = 1, IL + X( IV+I-1 ) = SQRT( -TWO*LOG( U( 2*I-1 ) ) )* + $ COS( TWOPI*U( 2*I ) ) + 30 CONTINUE + END IF + 40 CONTINUE + RETURN +* +* End of DLARNV +* + END diff --git a/applications/PUfoam/MoDeNaModels/CFD_tool_0D/src/eigen/src/dlarra.f b/applications/PUfoam/MoDeNaModels/CFD_tool_0D/src/eigen/src/dlarra.f new file mode 100644 index 000000000..08b846b4a --- /dev/null +++ b/applications/PUfoam/MoDeNaModels/CFD_tool_0D/src/eigen/src/dlarra.f @@ -0,0 +1,204 @@ +*> \brief \b DLARRA +* +* =========== DOCUMENTATION =========== +* +* Online html documentation available at +* http://www.netlib.org/lapack/explore-html/ +* +*> \htmlonly +*> Download DLARRA + dependencies +*> +*> [TGZ] +*> +*> [ZIP] +*> +*> [TXT] +*> \endhtmlonly +* +* Definition: +* =========== +* +* SUBROUTINE DLARRA( N, D, E, E2, SPLTOL, TNRM, +* NSPLIT, ISPLIT, INFO ) +* +* .. Scalar Arguments .. +* INTEGER INFO, N, NSPLIT +* DOUBLE PRECISION SPLTOL, TNRM +* .. +* .. Array Arguments .. +* INTEGER ISPLIT( * ) +* DOUBLE PRECISION D( * ), E( * ), E2( * ) +* .. +* +* +*> \par Purpose: +* ============= +*> +*> \verbatim +*> +*> Compute the splitting points with threshold SPLTOL. +*> DLARRA sets any "small" off-diagonal elements to zero. +*> \endverbatim +* +* Arguments: +* ========== +* +*> \param[in] N +*> \verbatim +*> N is INTEGER +*> The order of the matrix. N > 0. +*> \endverbatim +*> +*> \param[in] D +*> \verbatim +*> D is DOUBLE PRECISION array, dimension (N) +*> On entry, the N diagonal elements of the tridiagonal +*> matrix T. +*> \endverbatim +*> +*> \param[in,out] E +*> \verbatim +*> E is DOUBLE PRECISION array, dimension (N) +*> On entry, the first (N-1) entries contain the subdiagonal +*> elements of the tridiagonal matrix T; E(N) need not be set. +*> On exit, the entries E( ISPLIT( I ) ), 1 <= I <= NSPLIT, +*> are set to zero, the other entries of E are untouched. +*> \endverbatim +*> +*> \param[in,out] E2 +*> \verbatim +*> E2 is DOUBLE PRECISION array, dimension (N) +*> On entry, the first (N-1) entries contain the SQUARES of the +*> subdiagonal elements of the tridiagonal matrix T; +*> E2(N) need not be set. +*> On exit, the entries E2( ISPLIT( I ) ), +*> 1 <= I <= NSPLIT, have been set to zero +*> \endverbatim +*> +*> \param[in] SPLTOL +*> \verbatim +*> SPLTOL is DOUBLE PRECISION +*> The threshold for splitting. Two criteria can be used: +*> SPLTOL<0 : criterion based on absolute off-diagonal value +*> SPLTOL>0 : criterion that preserves relative accuracy +*> \endverbatim +*> +*> \param[in] TNRM +*> \verbatim +*> TNRM is DOUBLE PRECISION +*> The norm of the matrix. +*> \endverbatim +*> +*> \param[out] NSPLIT +*> \verbatim +*> NSPLIT is INTEGER +*> The number of blocks T splits into. 1 <= NSPLIT <= N. +*> \endverbatim +*> +*> \param[out] ISPLIT +*> \verbatim +*> ISPLIT is INTEGER array, dimension (N) +*> The splitting points, at which T breaks up into blocks. +*> The first block consists of rows/columns 1 to ISPLIT(1), +*> the second of rows/columns ISPLIT(1)+1 through ISPLIT(2), +*> etc., and the NSPLIT-th consists of rows/columns +*> ISPLIT(NSPLIT-1)+1 through ISPLIT(NSPLIT)=N. +*> \endverbatim +*> +*> \param[out] INFO +*> \verbatim +*> INFO is INTEGER +*> = 0: successful exit +*> \endverbatim +* +* Authors: +* ======== +* +*> \author Univ. of Tennessee +*> \author Univ. of California Berkeley +*> \author Univ. of Colorado Denver +*> \author NAG Ltd. +* +*> \date November 2011 +* +*> \ingroup auxOTHERauxiliary +* +*> \par Contributors: +* ================== +*> +*> Beresford Parlett, University of California, Berkeley, USA \n +*> Jim Demmel, University of California, Berkeley, USA \n +*> Inderjit Dhillon, University of Texas, Austin, USA \n +*> Osni Marques, LBNL/NERSC, USA \n +*> Christof Voemel, University of California, Berkeley, USA +* +* ===================================================================== + SUBROUTINE DLARRA( N, D, E, E2, SPLTOL, TNRM, + $ NSPLIT, ISPLIT, INFO ) +* +* -- LAPACK auxiliary routine (version 3.4.0) -- +* -- LAPACK is a software package provided by Univ. of Tennessee, -- +* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- +* November 2011 +* +* .. Scalar Arguments .. + INTEGER INFO, N, NSPLIT + DOUBLE PRECISION SPLTOL, TNRM +* .. +* .. Array Arguments .. + INTEGER ISPLIT( * ) + DOUBLE PRECISION D( * ), E( * ), E2( * ) +* .. +* +* ===================================================================== +* +* .. Parameters .. + DOUBLE PRECISION ZERO + PARAMETER ( ZERO = 0.0D0 ) +* .. +* .. Local Scalars .. + INTEGER I + DOUBLE PRECISION EABS, TMP1 + +* .. +* .. Intrinsic Functions .. + INTRINSIC ABS +* .. +* .. Executable Statements .. +* + INFO = 0 + +* Compute splitting points + NSPLIT = 1 + IF(SPLTOL.LT.ZERO) THEN +* Criterion based on absolute off-diagonal value + TMP1 = ABS(SPLTOL)* TNRM + DO 9 I = 1, N-1 + EABS = ABS( E(I) ) + IF( EABS .LE. TMP1) THEN + E(I) = ZERO + E2(I) = ZERO + ISPLIT( NSPLIT ) = I + NSPLIT = NSPLIT + 1 + END IF + 9 CONTINUE + ELSE +* Criterion that guarantees relative accuracy + DO 10 I = 1, N-1 + EABS = ABS( E(I) ) + IF( EABS .LE. SPLTOL * SQRT(ABS(D(I)))*SQRT(ABS(D(I+1))) ) + $ THEN + E(I) = ZERO + E2(I) = ZERO + ISPLIT( NSPLIT ) = I + NSPLIT = NSPLIT + 1 + END IF + 10 CONTINUE + ENDIF + ISPLIT( NSPLIT ) = N + + RETURN +* +* End of DLARRA +* + END diff --git a/applications/PUfoam/MoDeNaModels/CFD_tool_0D/src/eigen/src/dlarrb.f b/applications/PUfoam/MoDeNaModels/CFD_tool_0D/src/eigen/src/dlarrb.f new file mode 100644 index 000000000..b6018b399 --- /dev/null +++ b/applications/PUfoam/MoDeNaModels/CFD_tool_0D/src/eigen/src/dlarrb.f @@ -0,0 +1,401 @@ +*> \brief \b DLARRB +* +* =========== DOCUMENTATION =========== +* +* Online html documentation available at +* http://www.netlib.org/lapack/explore-html/ +* +*> \htmlonly +*> Download DLARRB + dependencies +*> +*> [TGZ] +*> +*> [ZIP] +*> +*> [TXT] +*> \endhtmlonly +* +* Definition: +* =========== +* +* SUBROUTINE DLARRB( N, D, LLD, IFIRST, ILAST, RTOL1, +* RTOL2, OFFSET, W, WGAP, WERR, WORK, IWORK, +* PIVMIN, SPDIAM, TWIST, INFO ) +* +* .. Scalar Arguments .. +* INTEGER IFIRST, ILAST, INFO, N, OFFSET, TWIST +* DOUBLE PRECISION PIVMIN, RTOL1, RTOL2, SPDIAM +* .. +* .. Array Arguments .. +* INTEGER IWORK( * ) +* DOUBLE PRECISION D( * ), LLD( * ), W( * ), +* $ WERR( * ), WGAP( * ), WORK( * ) +* .. +* +* +*> \par Purpose: +* ============= +*> +*> \verbatim +*> +*> Given the relatively robust representation(RRR) L D L^T, DLARRB +*> does "limited" bisection to refine the eigenvalues of L D L^T, +*> W( IFIRST-OFFSET ) through W( ILAST-OFFSET ), to more accuracy. Initial +*> guesses for these eigenvalues are input in W, the corresponding estimate +*> of the error in these guesses and their gaps are input in WERR +*> and WGAP, respectively. During bisection, intervals +*> [left, right] are maintained by storing their mid-points and +*> semi-widths in the arrays W and WERR respectively. +*> \endverbatim +* +* Arguments: +* ========== +* +*> \param[in] N +*> \verbatim +*> N is INTEGER +*> The order of the matrix. +*> \endverbatim +*> +*> \param[in] D +*> \verbatim +*> D is DOUBLE PRECISION array, dimension (N) +*> The N diagonal elements of the diagonal matrix D. +*> \endverbatim +*> +*> \param[in] LLD +*> \verbatim +*> LLD is DOUBLE PRECISION array, dimension (N-1) +*> The (N-1) elements L(i)*L(i)*D(i). +*> \endverbatim +*> +*> \param[in] IFIRST +*> \verbatim +*> IFIRST is INTEGER +*> The index of the first eigenvalue to be computed. +*> \endverbatim +*> +*> \param[in] ILAST +*> \verbatim +*> ILAST is INTEGER +*> The index of the last eigenvalue to be computed. +*> \endverbatim +*> +*> \param[in] RTOL1 +*> \verbatim +*> RTOL1 is DOUBLE PRECISION +*> \endverbatim +*> +*> \param[in] RTOL2 +*> \verbatim +*> RTOL2 is DOUBLE PRECISION +*> Tolerance for the convergence of the bisection intervals. +*> An interval [LEFT,RIGHT] has converged if +*> RIGHT-LEFT.LT.MAX( RTOL1*GAP, RTOL2*MAX(|LEFT|,|RIGHT|) ) +*> where GAP is the (estimated) distance to the nearest +*> eigenvalue. +*> \endverbatim +*> +*> \param[in] OFFSET +*> \verbatim +*> OFFSET is INTEGER +*> Offset for the arrays W, WGAP and WERR, i.e., the IFIRST-OFFSET +*> through ILAST-OFFSET elements of these arrays are to be used. +*> \endverbatim +*> +*> \param[in,out] W +*> \verbatim +*> W is DOUBLE PRECISION array, dimension (N) +*> On input, W( IFIRST-OFFSET ) through W( ILAST-OFFSET ) are +*> estimates of the eigenvalues of L D L^T indexed IFIRST throug +*> ILAST. +*> On output, these estimates are refined. +*> \endverbatim +*> +*> \param[in,out] WGAP +*> \verbatim +*> WGAP is DOUBLE PRECISION array, dimension (N-1) +*> On input, the (estimated) gaps between consecutive +*> eigenvalues of L D L^T, i.e., WGAP(I-OFFSET) is the gap between +*> eigenvalues I and I+1. Note that if IFIRST.EQ.ILAST +*> then WGAP(IFIRST-OFFSET) must be set to ZERO. +*> On output, these gaps are refined. +*> \endverbatim +*> +*> \param[in,out] WERR +*> \verbatim +*> WERR is DOUBLE PRECISION array, dimension (N) +*> On input, WERR( IFIRST-OFFSET ) through WERR( ILAST-OFFSET ) are +*> the errors in the estimates of the corresponding elements in W. +*> On output, these errors are refined. +*> \endverbatim +*> +*> \param[out] WORK +*> \verbatim +*> WORK is DOUBLE PRECISION array, dimension (2*N) +*> Workspace. +*> \endverbatim +*> +*> \param[out] IWORK +*> \verbatim +*> IWORK is INTEGER array, dimension (2*N) +*> Workspace. +*> \endverbatim +*> +*> \param[in] PIVMIN +*> \verbatim +*> PIVMIN is DOUBLE PRECISION +*> The minimum pivot in the Sturm sequence. +*> \endverbatim +*> +*> \param[in] SPDIAM +*> \verbatim +*> SPDIAM is DOUBLE PRECISION +*> The spectral diameter of the matrix. +*> \endverbatim +*> +*> \param[in] TWIST +*> \verbatim +*> TWIST is INTEGER +*> The twist index for the twisted factorization that is used +*> for the negcount. +*> TWIST = N: Compute negcount from L D L^T - LAMBDA I = L+ D+ L+^T +*> TWIST = 1: Compute negcount from L D L^T - LAMBDA I = U- D- U-^T +*> TWIST = R: Compute negcount from L D L^T - LAMBDA I = N(r) D(r) N(r) +*> \endverbatim +*> +*> \param[out] INFO +*> \verbatim +*> INFO is INTEGER +*> Error flag. +*> \endverbatim +* +* Authors: +* ======== +* +*> \author Univ. of Tennessee +*> \author Univ. of California Berkeley +*> \author Univ. of Colorado Denver +*> \author NAG Ltd. +* +*> \date November 2011 +* +*> \ingroup auxOTHERauxiliary +* +*> \par Contributors: +* ================== +*> +*> Beresford Parlett, University of California, Berkeley, USA \n +*> Jim Demmel, University of California, Berkeley, USA \n +*> Inderjit Dhillon, University of Texas, Austin, USA \n +*> Osni Marques, LBNL/NERSC, USA \n +*> Christof Voemel, University of California, Berkeley, USA +* +* ===================================================================== + SUBROUTINE DLARRB( N, D, LLD, IFIRST, ILAST, RTOL1, + $ RTOL2, OFFSET, W, WGAP, WERR, WORK, IWORK, + $ PIVMIN, SPDIAM, TWIST, INFO ) +* +* -- LAPACK auxiliary routine (version 3.4.0) -- +* -- LAPACK is a software package provided by Univ. of Tennessee, -- +* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- +* November 2011 +* +* .. Scalar Arguments .. + INTEGER IFIRST, ILAST, INFO, N, OFFSET, TWIST + DOUBLE PRECISION PIVMIN, RTOL1, RTOL2, SPDIAM +* .. +* .. Array Arguments .. + INTEGER IWORK( * ) + DOUBLE PRECISION D( * ), LLD( * ), W( * ), + $ WERR( * ), WGAP( * ), WORK( * ) +* .. +* +* ===================================================================== +* +* .. Parameters .. + DOUBLE PRECISION ZERO, TWO, HALF + PARAMETER ( ZERO = 0.0D0, TWO = 2.0D0, + $ HALF = 0.5D0 ) + INTEGER MAXITR +* .. +* .. Local Scalars .. + INTEGER I, I1, II, IP, ITER, K, NEGCNT, NEXT, NINT, + $ OLNINT, PREV, R + DOUBLE PRECISION BACK, CVRGD, GAP, LEFT, LGAP, MID, MNWDTH, + $ RGAP, RIGHT, TMP, WIDTH +* .. +* .. External Functions .. + INTEGER DLANEG + EXTERNAL DLANEG +* +* .. +* .. Intrinsic Functions .. + INTRINSIC ABS, MAX, MIN +* .. +* .. Executable Statements .. +* + INFO = 0 +* + MAXITR = INT( ( LOG( SPDIAM+PIVMIN )-LOG( PIVMIN ) ) / + $ LOG( TWO ) ) + 2 + MNWDTH = TWO * PIVMIN +* + R = TWIST + IF((R.LT.1).OR.(R.GT.N)) R = N +* +* Initialize unconverged intervals in [ WORK(2*I-1), WORK(2*I) ]. +* The Sturm Count, Count( WORK(2*I-1) ) is arranged to be I-1, while +* Count( WORK(2*I) ) is stored in IWORK( 2*I ). The integer IWORK( 2*I-1 ) +* for an unconverged interval is set to the index of the next unconverged +* interval, and is -1 or 0 for a converged interval. Thus a linked +* list of unconverged intervals is set up. +* + I1 = IFIRST +* The number of unconverged intervals + NINT = 0 +* The last unconverged interval found + PREV = 0 + + RGAP = WGAP( I1-OFFSET ) + DO 75 I = I1, ILAST + K = 2*I + II = I - OFFSET + LEFT = W( II ) - WERR( II ) + RIGHT = W( II ) + WERR( II ) + LGAP = RGAP + RGAP = WGAP( II ) + GAP = MIN( LGAP, RGAP ) + +* Make sure that [LEFT,RIGHT] contains the desired eigenvalue +* Compute negcount from dstqds facto L+D+L+^T = L D L^T - LEFT +* +* Do while( NEGCNT(LEFT).GT.I-1 ) +* + BACK = WERR( II ) + 20 CONTINUE + NEGCNT = DLANEG( N, D, LLD, LEFT, PIVMIN, R ) + IF( NEGCNT.GT.I-1 ) THEN + LEFT = LEFT - BACK + BACK = TWO*BACK + GO TO 20 + END IF +* +* Do while( NEGCNT(RIGHT).LT.I ) +* Compute negcount from dstqds facto L+D+L+^T = L D L^T - RIGHT +* + BACK = WERR( II ) + 50 CONTINUE + + NEGCNT = DLANEG( N, D, LLD, RIGHT, PIVMIN, R ) + IF( NEGCNT.LT.I ) THEN + RIGHT = RIGHT + BACK + BACK = TWO*BACK + GO TO 50 + END IF + WIDTH = HALF*ABS( LEFT - RIGHT ) + TMP = MAX( ABS( LEFT ), ABS( RIGHT ) ) + CVRGD = MAX(RTOL1*GAP,RTOL2*TMP) + IF( WIDTH.LE.CVRGD .OR. WIDTH.LE.MNWDTH ) THEN +* This interval has already converged and does not need refinement. +* (Note that the gaps might change through refining the +* eigenvalues, however, they can only get bigger.) +* Remove it from the list. + IWORK( K-1 ) = -1 +* Make sure that I1 always points to the first unconverged interval + IF((I.EQ.I1).AND.(I.LT.ILAST)) I1 = I + 1 + IF((PREV.GE.I1).AND.(I.LE.ILAST)) IWORK( 2*PREV-1 ) = I + 1 + ELSE +* unconverged interval found + PREV = I + NINT = NINT + 1 + IWORK( K-1 ) = I + 1 + IWORK( K ) = NEGCNT + END IF + WORK( K-1 ) = LEFT + WORK( K ) = RIGHT + 75 CONTINUE + +* +* Do while( NINT.GT.0 ), i.e. there are still unconverged intervals +* and while (ITER.LT.MAXITR) +* + ITER = 0 + 80 CONTINUE + PREV = I1 - 1 + I = I1 + OLNINT = NINT + + DO 100 IP = 1, OLNINT + K = 2*I + II = I - OFFSET + RGAP = WGAP( II ) + LGAP = RGAP + IF(II.GT.1) LGAP = WGAP( II-1 ) + GAP = MIN( LGAP, RGAP ) + NEXT = IWORK( K-1 ) + LEFT = WORK( K-1 ) + RIGHT = WORK( K ) + MID = HALF*( LEFT + RIGHT ) + +* semiwidth of interval + WIDTH = RIGHT - MID + TMP = MAX( ABS( LEFT ), ABS( RIGHT ) ) + CVRGD = MAX(RTOL1*GAP,RTOL2*TMP) + IF( ( WIDTH.LE.CVRGD ) .OR. ( WIDTH.LE.MNWDTH ).OR. + $ ( ITER.EQ.MAXITR ) )THEN +* reduce number of unconverged intervals + NINT = NINT - 1 +* Mark interval as converged. + IWORK( K-1 ) = 0 + IF( I1.EQ.I ) THEN + I1 = NEXT + ELSE +* Prev holds the last unconverged interval previously examined + IF(PREV.GE.I1) IWORK( 2*PREV-1 ) = NEXT + END IF + I = NEXT + GO TO 100 + END IF + PREV = I +* +* Perform one bisection step +* + NEGCNT = DLANEG( N, D, LLD, MID, PIVMIN, R ) + IF( NEGCNT.LE.I-1 ) THEN + WORK( K-1 ) = MID + ELSE + WORK( K ) = MID + END IF + I = NEXT + 100 CONTINUE + ITER = ITER + 1 +* do another loop if there are still unconverged intervals +* However, in the last iteration, all intervals are accepted +* since this is the best we can do. + IF( ( NINT.GT.0 ).AND.(ITER.LE.MAXITR) ) GO TO 80 +* +* +* At this point, all the intervals have converged + DO 110 I = IFIRST, ILAST + K = 2*I + II = I - OFFSET +* All intervals marked by '0' have been refined. + IF( IWORK( K-1 ).EQ.0 ) THEN + W( II ) = HALF*( WORK( K-1 )+WORK( K ) ) + WERR( II ) = WORK( K ) - W( II ) + END IF + 110 CONTINUE +* + DO 111 I = IFIRST+1, ILAST + K = 2*I + II = I - OFFSET + WGAP( II-1 ) = MAX( ZERO, + $ W(II) - WERR (II) - W( II-1 ) - WERR( II-1 )) + 111 CONTINUE + + RETURN +* +* End of DLARRB +* + END diff --git a/applications/PUfoam/MoDeNaModels/CFD_tool_0D/src/eigen/src/dlarrc.f b/applications/PUfoam/MoDeNaModels/CFD_tool_0D/src/eigen/src/dlarrc.f new file mode 100644 index 000000000..9c2201f31 --- /dev/null +++ b/applications/PUfoam/MoDeNaModels/CFD_tool_0D/src/eigen/src/dlarrc.f @@ -0,0 +1,243 @@ +*> \brief \b DLARRC +* +* =========== DOCUMENTATION =========== +* +* Online html documentation available at +* http://www.netlib.org/lapack/explore-html/ +* +*> \htmlonly +*> Download DLARRC + dependencies +*> +*> [TGZ] +*> +*> [ZIP] +*> +*> [TXT] +*> \endhtmlonly +* +* Definition: +* =========== +* +* SUBROUTINE DLARRC( JOBT, N, VL, VU, D, E, PIVMIN, +* EIGCNT, LCNT, RCNT, INFO ) +* +* .. Scalar Arguments .. +* CHARACTER JOBT +* INTEGER EIGCNT, INFO, LCNT, N, RCNT +* DOUBLE PRECISION PIVMIN, VL, VU +* .. +* .. Array Arguments .. +* DOUBLE PRECISION D( * ), E( * ) +* .. +* +* +*> \par Purpose: +* ============= +*> +*> \verbatim +*> +*> Find the number of eigenvalues of the symmetric tridiagonal matrix T +*> that are in the interval (VL,VU] if JOBT = 'T', and of L D L^T +*> if JOBT = 'L'. +*> \endverbatim +* +* Arguments: +* ========== +* +*> \param[in] JOBT +*> \verbatim +*> JOBT is CHARACTER*1 +*> = 'T': Compute Sturm count for matrix T. +*> = 'L': Compute Sturm count for matrix L D L^T. +*> \endverbatim +*> +*> \param[in] N +*> \verbatim +*> N is INTEGER +*> The order of the matrix. N > 0. +*> \endverbatim +*> +*> \param[in] VL +*> \verbatim +*> VL is DOUBLE PRECISION +*> \endverbatim +*> +*> \param[in] VU +*> \verbatim +*> VU is DOUBLE PRECISION +*> The lower and upper bounds for the eigenvalues. +*> \endverbatim +*> +*> \param[in] D +*> \verbatim +*> D is DOUBLE PRECISION array, dimension (N) +*> JOBT = 'T': The N diagonal elements of the tridiagonal matrix T. +*> JOBT = 'L': The N diagonal elements of the diagonal matrix D. +*> \endverbatim +*> +*> \param[in] E +*> \verbatim +*> E is DOUBLE PRECISION array, dimension (N) +*> JOBT = 'T': The N-1 offdiagonal elements of the matrix T. +*> JOBT = 'L': The N-1 offdiagonal elements of the matrix L. +*> \endverbatim +*> +*> \param[in] PIVMIN +*> \verbatim +*> PIVMIN is DOUBLE PRECISION +*> The minimum pivot in the Sturm sequence for T. +*> \endverbatim +*> +*> \param[out] EIGCNT +*> \verbatim +*> EIGCNT is INTEGER +*> The number of eigenvalues of the symmetric tridiagonal matrix T +*> that are in the interval (VL,VU] +*> \endverbatim +*> +*> \param[out] LCNT +*> \verbatim +*> LCNT is INTEGER +*> \endverbatim +*> +*> \param[out] RCNT +*> \verbatim +*> RCNT is INTEGER +*> The left and right negcounts of the interval. +*> \endverbatim +*> +*> \param[out] INFO +*> \verbatim +*> INFO is INTEGER +*> \endverbatim +* +* Authors: +* ======== +* +*> \author Univ. of Tennessee +*> \author Univ. of California Berkeley +*> \author Univ. of Colorado Denver +*> \author NAG Ltd. +* +*> \date November 2011 +* +*> \ingroup auxOTHERauxiliary +* +*> \par Contributors: +* ================== +*> +*> Beresford Parlett, University of California, Berkeley, USA \n +*> Jim Demmel, University of California, Berkeley, USA \n +*> Inderjit Dhillon, University of Texas, Austin, USA \n +*> Osni Marques, LBNL/NERSC, USA \n +*> Christof Voemel, University of California, Berkeley, USA +* +* ===================================================================== + SUBROUTINE DLARRC( JOBT, N, VL, VU, D, E, PIVMIN, + $ EIGCNT, LCNT, RCNT, INFO ) +* +* -- LAPACK auxiliary routine (version 3.4.0) -- +* -- LAPACK is a software package provided by Univ. of Tennessee, -- +* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- +* November 2011 +* +* .. Scalar Arguments .. + CHARACTER JOBT + INTEGER EIGCNT, INFO, LCNT, N, RCNT + DOUBLE PRECISION PIVMIN, VL, VU +* .. +* .. Array Arguments .. + DOUBLE PRECISION D( * ), E( * ) +* .. +* +* ===================================================================== +* +* .. Parameters .. + DOUBLE PRECISION ZERO + PARAMETER ( ZERO = 0.0D0 ) +* .. +* .. Local Scalars .. + INTEGER I + LOGICAL MATT + DOUBLE PRECISION LPIVOT, RPIVOT, SL, SU, TMP, TMP2 + +* .. +* .. External Functions .. + LOGICAL LSAME + EXTERNAL LSAME +* .. +* .. Executable Statements .. +* + INFO = 0 + LCNT = 0 + RCNT = 0 + EIGCNT = 0 + MATT = LSAME( JOBT, 'T' ) + + + IF (MATT) THEN +* Sturm sequence count on T + LPIVOT = D( 1 ) - VL + RPIVOT = D( 1 ) - VU + IF( LPIVOT.LE.ZERO ) THEN + LCNT = LCNT + 1 + ENDIF + IF( RPIVOT.LE.ZERO ) THEN + RCNT = RCNT + 1 + ENDIF + DO 10 I = 1, N-1 + TMP = E(I)**2 + LPIVOT = ( D( I+1 )-VL ) - TMP/LPIVOT + RPIVOT = ( D( I+1 )-VU ) - TMP/RPIVOT + IF( LPIVOT.LE.ZERO ) THEN + LCNT = LCNT + 1 + ENDIF + IF( RPIVOT.LE.ZERO ) THEN + RCNT = RCNT + 1 + ENDIF + 10 CONTINUE + ELSE +* Sturm sequence count on L D L^T + SL = -VL + SU = -VU + DO 20 I = 1, N - 1 + LPIVOT = D( I ) + SL + RPIVOT = D( I ) + SU + IF( LPIVOT.LE.ZERO ) THEN + LCNT = LCNT + 1 + ENDIF + IF( RPIVOT.LE.ZERO ) THEN + RCNT = RCNT + 1 + ENDIF + TMP = E(I) * D(I) * E(I) +* + TMP2 = TMP / LPIVOT + IF( TMP2.EQ.ZERO ) THEN + SL = TMP - VL + ELSE + SL = SL*TMP2 - VL + END IF +* + TMP2 = TMP / RPIVOT + IF( TMP2.EQ.ZERO ) THEN + SU = TMP - VU + ELSE + SU = SU*TMP2 - VU + END IF + 20 CONTINUE + LPIVOT = D( N ) + SL + RPIVOT = D( N ) + SU + IF( LPIVOT.LE.ZERO ) THEN + LCNT = LCNT + 1 + ENDIF + IF( RPIVOT.LE.ZERO ) THEN + RCNT = RCNT + 1 + ENDIF + ENDIF + EIGCNT = RCNT - LCNT + + RETURN +* +* end of DLARRC +* + END diff --git a/applications/PUfoam/MoDeNaModels/CFD_tool_0D/src/eigen/src/dlarrd.f b/applications/PUfoam/MoDeNaModels/CFD_tool_0D/src/eigen/src/dlarrd.f new file mode 100644 index 000000000..a4be90c51 --- /dev/null +++ b/applications/PUfoam/MoDeNaModels/CFD_tool_0D/src/eigen/src/dlarrd.f @@ -0,0 +1,855 @@ +*> \brief \b DLARRD +* +* =========== DOCUMENTATION =========== +* +* Online html documentation available at +* http://www.netlib.org/lapack/explore-html/ +* +*> \htmlonly +*> Download DLARRD + dependencies +*> +*> [TGZ] +*> +*> [ZIP] +*> +*> [TXT] +*> \endhtmlonly +* +* Definition: +* =========== +* +* SUBROUTINE DLARRD( RANGE, ORDER, N, VL, VU, IL, IU, GERS, +* RELTOL, D, E, E2, PIVMIN, NSPLIT, ISPLIT, +* M, W, WERR, WL, WU, IBLOCK, INDEXW, +* WORK, IWORK, INFO ) +* +* .. Scalar Arguments .. +* CHARACTER ORDER, RANGE +* INTEGER IL, INFO, IU, M, N, NSPLIT +* DOUBLE PRECISION PIVMIN, RELTOL, VL, VU, WL, WU +* .. +* .. Array Arguments .. +* INTEGER IBLOCK( * ), INDEXW( * ), +* $ ISPLIT( * ), IWORK( * ) +* DOUBLE PRECISION D( * ), E( * ), E2( * ), +* $ GERS( * ), W( * ), WERR( * ), WORK( * ) +* .. +* +* +*> \par Purpose: +* ============= +*> +*> \verbatim +*> +*> DLARRD computes the eigenvalues of a symmetric tridiagonal +*> matrix T to suitable accuracy. This is an auxiliary code to be +*> called from DSTEMR. +*> The user may ask for all eigenvalues, all eigenvalues +*> in the half-open interval (VL, VU], or the IL-th through IU-th +*> eigenvalues. +*> +*> To avoid overflow, the matrix must be scaled so that its +*> largest element is no greater than overflow**(1/2) * underflow**(1/4) in absolute value, and for greatest +*> accuracy, it should not be much smaller than that. +*> +*> See W. Kahan "Accurate Eigenvalues of a Symmetric Tridiagonal +*> Matrix", Report CS41, Computer Science Dept., Stanford +*> University, July 21, 1966. +*> \endverbatim +* +* Arguments: +* ========== +* +*> \param[in] RANGE +*> \verbatim +*> RANGE is CHARACTER*1 +*> = 'A': ("All") all eigenvalues will be found. +*> = 'V': ("Value") all eigenvalues in the half-open interval +*> (VL, VU] will be found. +*> = 'I': ("Index") the IL-th through IU-th eigenvalues (of the +*> entire matrix) will be found. +*> \endverbatim +*> +*> \param[in] ORDER +*> \verbatim +*> ORDER is CHARACTER*1 +*> = 'B': ("By Block") the eigenvalues will be grouped by +*> split-off block (see IBLOCK, ISPLIT) and +*> ordered from smallest to largest within +*> the block. +*> = 'E': ("Entire matrix") +*> the eigenvalues for the entire matrix +*> will be ordered from smallest to +*> largest. +*> \endverbatim +*> +*> \param[in] N +*> \verbatim +*> N is INTEGER +*> The order of the tridiagonal matrix T. N >= 0. +*> \endverbatim +*> +*> \param[in] VL +*> \verbatim +*> VL is DOUBLE PRECISION +*> \endverbatim +*> +*> \param[in] VU +*> \verbatim +*> VU is DOUBLE PRECISION +*> If RANGE='V', the lower and upper bounds of the interval to +*> be searched for eigenvalues. Eigenvalues less than or equal +*> to VL, or greater than VU, will not be returned. VL < VU. +*> Not referenced if RANGE = 'A' or 'I'. +*> \endverbatim +*> +*> \param[in] IL +*> \verbatim +*> IL is INTEGER +*> \endverbatim +*> +*> \param[in] IU +*> \verbatim +*> IU is INTEGER +*> If RANGE='I', the indices (in ascending order) of the +*> smallest and largest eigenvalues to be returned. +*> 1 <= IL <= IU <= N, if N > 0; IL = 1 and IU = 0 if N = 0. +*> Not referenced if RANGE = 'A' or 'V'. +*> \endverbatim +*> +*> \param[in] GERS +*> \verbatim +*> GERS is DOUBLE PRECISION array, dimension (2*N) +*> The N Gerschgorin intervals (the i-th Gerschgorin interval +*> is (GERS(2*i-1), GERS(2*i)). +*> \endverbatim +*> +*> \param[in] RELTOL +*> \verbatim +*> RELTOL is DOUBLE PRECISION +*> The minimum relative width of an interval. When an interval +*> is narrower than RELTOL times the larger (in +*> magnitude) endpoint, then it is considered to be +*> sufficiently small, i.e., converged. Note: this should +*> always be at least radix*machine epsilon. +*> \endverbatim +*> +*> \param[in] D +*> \verbatim +*> D is DOUBLE PRECISION array, dimension (N) +*> The n diagonal elements of the tridiagonal matrix T. +*> \endverbatim +*> +*> \param[in] E +*> \verbatim +*> E is DOUBLE PRECISION array, dimension (N-1) +*> The (n-1) off-diagonal elements of the tridiagonal matrix T. +*> \endverbatim +*> +*> \param[in] E2 +*> \verbatim +*> E2 is DOUBLE PRECISION array, dimension (N-1) +*> The (n-1) squared off-diagonal elements of the tridiagonal matrix T. +*> \endverbatim +*> +*> \param[in] PIVMIN +*> \verbatim +*> PIVMIN is DOUBLE PRECISION +*> The minimum pivot allowed in the Sturm sequence for T. +*> \endverbatim +*> +*> \param[in] NSPLIT +*> \verbatim +*> NSPLIT is INTEGER +*> The number of diagonal blocks in the matrix T. +*> 1 <= NSPLIT <= N. +*> \endverbatim +*> +*> \param[in] ISPLIT +*> \verbatim +*> ISPLIT is INTEGER array, dimension (N) +*> The splitting points, at which T breaks up into submatrices. +*> The first submatrix consists of rows/columns 1 to ISPLIT(1), +*> the second of rows/columns ISPLIT(1)+1 through ISPLIT(2), +*> etc., and the NSPLIT-th consists of rows/columns +*> ISPLIT(NSPLIT-1)+1 through ISPLIT(NSPLIT)=N. +*> (Only the first NSPLIT elements will actually be used, but +*> since the user cannot know a priori what value NSPLIT will +*> have, N words must be reserved for ISPLIT.) +*> \endverbatim +*> +*> \param[out] M +*> \verbatim +*> M is INTEGER +*> The actual number of eigenvalues found. 0 <= M <= N. +*> (See also the description of INFO=2,3.) +*> \endverbatim +*> +*> \param[out] W +*> \verbatim +*> W is DOUBLE PRECISION array, dimension (N) +*> On exit, the first M elements of W will contain the +*> eigenvalue approximations. DLARRD computes an interval +*> I_j = (a_j, b_j] that includes eigenvalue j. The eigenvalue +*> approximation is given as the interval midpoint +*> W(j)= ( a_j + b_j)/2. The corresponding error is bounded by +*> WERR(j) = abs( a_j - b_j)/2 +*> \endverbatim +*> +*> \param[out] WERR +*> \verbatim +*> WERR is DOUBLE PRECISION array, dimension (N) +*> The error bound on the corresponding eigenvalue approximation +*> in W. +*> \endverbatim +*> +*> \param[out] WL +*> \verbatim +*> WL is DOUBLE PRECISION +*> \endverbatim +*> +*> \param[out] WU +*> \verbatim +*> WU is DOUBLE PRECISION +*> The interval (WL, WU] contains all the wanted eigenvalues. +*> If RANGE='V', then WL=VL and WU=VU. +*> If RANGE='A', then WL and WU are the global Gerschgorin bounds +*> on the spectrum. +*> If RANGE='I', then WL and WU are computed by DLAEBZ from the +*> index range specified. +*> \endverbatim +*> +*> \param[out] IBLOCK +*> \verbatim +*> IBLOCK is INTEGER array, dimension (N) +*> At each row/column j where E(j) is zero or small, the +*> matrix T is considered to split into a block diagonal +*> matrix. On exit, if INFO = 0, IBLOCK(i) specifies to which +*> block (from 1 to the number of blocks) the eigenvalue W(i) +*> belongs. (DLARRD may use the remaining N-M elements as +*> workspace.) +*> \endverbatim +*> +*> \param[out] INDEXW +*> \verbatim +*> INDEXW is INTEGER array, dimension (N) +*> The indices of the eigenvalues within each block (submatrix); +*> for example, INDEXW(i)= j and IBLOCK(i)=k imply that the +*> i-th eigenvalue W(i) is the j-th eigenvalue in block k. +*> \endverbatim +*> +*> \param[out] WORK +*> \verbatim +*> WORK is DOUBLE PRECISION array, dimension (4*N) +*> \endverbatim +*> +*> \param[out] IWORK +*> \verbatim +*> IWORK is INTEGER array, dimension (3*N) +*> \endverbatim +*> +*> \param[out] INFO +*> \verbatim +*> INFO is INTEGER +*> = 0: successful exit +*> < 0: if INFO = -i, the i-th argument had an illegal value +*> > 0: some or all of the eigenvalues failed to converge or +*> were not computed: +*> =1 or 3: Bisection failed to converge for some +*> eigenvalues; these eigenvalues are flagged by a +*> negative block number. The effect is that the +*> eigenvalues may not be as accurate as the +*> absolute and relative tolerances. This is +*> generally caused by unexpectedly inaccurate +*> arithmetic. +*> =2 or 3: RANGE='I' only: Not all of the eigenvalues +*> IL:IU were found. +*> Effect: M < IU+1-IL +*> Cause: non-monotonic arithmetic, causing the +*> Sturm sequence to be non-monotonic. +*> Cure: recalculate, using RANGE='A', and pick +*> out eigenvalues IL:IU. In some cases, +*> increasing the PARAMETER "FUDGE" may +*> make things work. +*> = 4: RANGE='I', and the Gershgorin interval +*> initially used was too small. No eigenvalues +*> were computed. +*> Probable cause: your machine has sloppy +*> floating-point arithmetic. +*> Cure: Increase the PARAMETER "FUDGE", +*> recompile, and try again. +*> \endverbatim +* +*> \par Internal Parameters: +* ========================= +*> +*> \verbatim +*> FUDGE DOUBLE PRECISION, default = 2 +*> A "fudge factor" to widen the Gershgorin intervals. Ideally, +*> a value of 1 should work, but on machines with sloppy +*> arithmetic, this needs to be larger. The default for +*> publicly released versions should be large enough to handle +*> the worst machine around. Note that this has no effect +*> on accuracy of the solution. +*> \endverbatim +*> +*> \par Contributors: +* ================== +*> +*> W. Kahan, University of California, Berkeley, USA \n +*> Beresford Parlett, University of California, Berkeley, USA \n +*> Jim Demmel, University of California, Berkeley, USA \n +*> Inderjit Dhillon, University of Texas, Austin, USA \n +*> Osni Marques, LBNL/NERSC, USA \n +*> Christof Voemel, University of California, Berkeley, USA \n +* +* Authors: +* ======== +* +*> \author Univ. of Tennessee +*> \author Univ. of California Berkeley +*> \author Univ. of Colorado Denver +*> \author NAG Ltd. +* +*> \date November 2011 +* +*> \ingroup auxOTHERauxiliary +* +* ===================================================================== + SUBROUTINE DLARRD( RANGE, ORDER, N, VL, VU, IL, IU, GERS, + $ RELTOL, D, E, E2, PIVMIN, NSPLIT, ISPLIT, + $ M, W, WERR, WL, WU, IBLOCK, INDEXW, + $ WORK, IWORK, INFO ) +* +* -- LAPACK auxiliary routine (version 3.4.0) -- +* -- LAPACK is a software package provided by Univ. of Tennessee, -- +* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- +* November 2011 +* +* .. Scalar Arguments .. + CHARACTER ORDER, RANGE + INTEGER IL, INFO, IU, M, N, NSPLIT + DOUBLE PRECISION PIVMIN, RELTOL, VL, VU, WL, WU +* .. +* .. Array Arguments .. + INTEGER IBLOCK( * ), INDEXW( * ), + $ ISPLIT( * ), IWORK( * ) + DOUBLE PRECISION D( * ), E( * ), E2( * ), + $ GERS( * ), W( * ), WERR( * ), WORK( * ) +* .. +* +* ===================================================================== +* +* .. Parameters .. + DOUBLE PRECISION ZERO, ONE, TWO, HALF, FUDGE + PARAMETER ( ZERO = 0.0D0, ONE = 1.0D0, + $ TWO = 2.0D0, HALF = ONE/TWO, + $ FUDGE = TWO ) + INTEGER ALLRNG, VALRNG, INDRNG + PARAMETER ( ALLRNG = 1, VALRNG = 2, INDRNG = 3 ) +* .. +* .. Local Scalars .. + LOGICAL NCNVRG, TOOFEW + INTEGER I, IB, IBEGIN, IDISCL, IDISCU, IE, IEND, IINFO, + $ IM, IN, IOFF, IOUT, IRANGE, ITMAX, ITMP1, + $ ITMP2, IW, IWOFF, J, JBLK, JDISC, JE, JEE, NB, + $ NWL, NWU + DOUBLE PRECISION ATOLI, EPS, GL, GU, RTOLI, TMP1, TMP2, + $ TNORM, UFLOW, WKILL, WLU, WUL + +* .. +* .. Local Arrays .. + INTEGER IDUMMA( 1 ) +* .. +* .. External Functions .. + LOGICAL LSAME + INTEGER ILAENV + DOUBLE PRECISION DLAMCH + EXTERNAL LSAME, ILAENV, DLAMCH +* .. +* .. External Subroutines .. + EXTERNAL DLAEBZ +* .. +* .. Intrinsic Functions .. + INTRINSIC ABS, INT, LOG, MAX, MIN +* .. +* .. Executable Statements .. +* + INFO = 0 +* +* Decode RANGE +* + IF( LSAME( RANGE, 'A' ) ) THEN + IRANGE = ALLRNG + ELSE IF( LSAME( RANGE, 'V' ) ) THEN + IRANGE = VALRNG + ELSE IF( LSAME( RANGE, 'I' ) ) THEN + IRANGE = INDRNG + ELSE + IRANGE = 0 + END IF +* +* Check for Errors +* + IF( IRANGE.LE.0 ) THEN + INFO = -1 + ELSE IF( .NOT.(LSAME(ORDER,'B').OR.LSAME(ORDER,'E')) ) THEN + INFO = -2 + ELSE IF( N.LT.0 ) THEN + INFO = -3 + ELSE IF( IRANGE.EQ.VALRNG ) THEN + IF( VL.GE.VU ) + $ INFO = -5 + ELSE IF( IRANGE.EQ.INDRNG .AND. + $ ( IL.LT.1 .OR. IL.GT.MAX( 1, N ) ) ) THEN + INFO = -6 + ELSE IF( IRANGE.EQ.INDRNG .AND. + $ ( IU.LT.MIN( N, IL ) .OR. IU.GT.N ) ) THEN + INFO = -7 + END IF +* + IF( INFO.NE.0 ) THEN + RETURN + END IF + +* Initialize error flags + INFO = 0 + NCNVRG = .FALSE. + TOOFEW = .FALSE. + +* Quick return if possible + M = 0 + IF( N.EQ.0 ) RETURN + +* Simplification: + IF( IRANGE.EQ.INDRNG .AND. IL.EQ.1 .AND. IU.EQ.N ) IRANGE = 1 + +* Get machine constants + EPS = DLAMCH( 'P' ) + UFLOW = DLAMCH( 'U' ) + + +* Special Case when N=1 +* Treat case of 1x1 matrix for quick return + IF( N.EQ.1 ) THEN + IF( (IRANGE.EQ.ALLRNG).OR. + $ ((IRANGE.EQ.VALRNG).AND.(D(1).GT.VL).AND.(D(1).LE.VU)).OR. + $ ((IRANGE.EQ.INDRNG).AND.(IL.EQ.1).AND.(IU.EQ.1)) ) THEN + M = 1 + W(1) = D(1) +* The computation error of the eigenvalue is zero + WERR(1) = ZERO + IBLOCK( 1 ) = 1 + INDEXW( 1 ) = 1 + ENDIF + RETURN + END IF + +* NB is the minimum vector length for vector bisection, or 0 +* if only scalar is to be done. + NB = ILAENV( 1, 'DSTEBZ', ' ', N, -1, -1, -1 ) + IF( NB.LE.1 ) NB = 0 + +* Find global spectral radius + GL = D(1) + GU = D(1) + DO 5 I = 1,N + GL = MIN( GL, GERS( 2*I - 1)) + GU = MAX( GU, GERS(2*I) ) + 5 CONTINUE +* Compute global Gerschgorin bounds and spectral diameter + TNORM = MAX( ABS( GL ), ABS( GU ) ) + GL = GL - FUDGE*TNORM*EPS*N - FUDGE*TWO*PIVMIN + GU = GU + FUDGE*TNORM*EPS*N + FUDGE*TWO*PIVMIN +* [JAN/28/2009] remove the line below since SPDIAM variable not use +* SPDIAM = GU - GL +* Input arguments for DLAEBZ: +* The relative tolerance. An interval (a,b] lies within +* "relative tolerance" if b-a < RELTOL*max(|a|,|b|), + RTOLI = RELTOL +* Set the absolute tolerance for interval convergence to zero to force +* interval convergence based on relative size of the interval. +* This is dangerous because intervals might not converge when RELTOL is +* small. But at least a very small number should be selected so that for +* strongly graded matrices, the code can get relatively accurate +* eigenvalues. + ATOLI = FUDGE*TWO*UFLOW + FUDGE*TWO*PIVMIN + + IF( IRANGE.EQ.INDRNG ) THEN + +* RANGE='I': Compute an interval containing eigenvalues +* IL through IU. The initial interval [GL,GU] from the global +* Gerschgorin bounds GL and GU is refined by DLAEBZ. + ITMAX = INT( ( LOG( TNORM+PIVMIN )-LOG( PIVMIN ) ) / + $ LOG( TWO ) ) + 2 + WORK( N+1 ) = GL + WORK( N+2 ) = GL + WORK( N+3 ) = GU + WORK( N+4 ) = GU + WORK( N+5 ) = GL + WORK( N+6 ) = GU + IWORK( 1 ) = -1 + IWORK( 2 ) = -1 + IWORK( 3 ) = N + 1 + IWORK( 4 ) = N + 1 + IWORK( 5 ) = IL - 1 + IWORK( 6 ) = IU +* + CALL DLAEBZ( 3, ITMAX, N, 2, 2, NB, ATOLI, RTOLI, PIVMIN, + $ D, E, E2, IWORK( 5 ), WORK( N+1 ), WORK( N+5 ), IOUT, + $ IWORK, W, IBLOCK, IINFO ) + IF( IINFO .NE. 0 ) THEN + INFO = IINFO + RETURN + END IF +* On exit, output intervals may not be ordered by ascending negcount + IF( IWORK( 6 ).EQ.IU ) THEN + WL = WORK( N+1 ) + WLU = WORK( N+3 ) + NWL = IWORK( 1 ) + WU = WORK( N+4 ) + WUL = WORK( N+2 ) + NWU = IWORK( 4 ) + ELSE + WL = WORK( N+2 ) + WLU = WORK( N+4 ) + NWL = IWORK( 2 ) + WU = WORK( N+3 ) + WUL = WORK( N+1 ) + NWU = IWORK( 3 ) + END IF +* On exit, the interval [WL, WLU] contains a value with negcount NWL, +* and [WUL, WU] contains a value with negcount NWU. + IF( NWL.LT.0 .OR. NWL.GE.N .OR. NWU.LT.1 .OR. NWU.GT.N ) THEN + INFO = 4 + RETURN + END IF + + ELSEIF( IRANGE.EQ.VALRNG ) THEN + WL = VL + WU = VU + + ELSEIF( IRANGE.EQ.ALLRNG ) THEN + WL = GL + WU = GU + ENDIF + + + +* Find Eigenvalues -- Loop Over blocks and recompute NWL and NWU. +* NWL accumulates the number of eigenvalues .le. WL, +* NWU accumulates the number of eigenvalues .le. WU + M = 0 + IEND = 0 + INFO = 0 + NWL = 0 + NWU = 0 +* + DO 70 JBLK = 1, NSPLIT + IOFF = IEND + IBEGIN = IOFF + 1 + IEND = ISPLIT( JBLK ) + IN = IEND - IOFF +* + IF( IN.EQ.1 ) THEN +* 1x1 block + IF( WL.GE.D( IBEGIN )-PIVMIN ) + $ NWL = NWL + 1 + IF( WU.GE.D( IBEGIN )-PIVMIN ) + $ NWU = NWU + 1 + IF( IRANGE.EQ.ALLRNG .OR. + $ ( WL.LT.D( IBEGIN )-PIVMIN + $ .AND. WU.GE. D( IBEGIN )-PIVMIN ) ) THEN + M = M + 1 + W( M ) = D( IBEGIN ) + WERR(M) = ZERO +* The gap for a single block doesn't matter for the later +* algorithm and is assigned an arbitrary large value + IBLOCK( M ) = JBLK + INDEXW( M ) = 1 + END IF + +* Disabled 2x2 case because of a failure on the following matrix +* RANGE = 'I', IL = IU = 4 +* Original Tridiagonal, d = [ +* -0.150102010615740E+00 +* -0.849897989384260E+00 +* -0.128208148052635E-15 +* 0.128257718286320E-15 +* ]; +* e = [ +* -0.357171383266986E+00 +* -0.180411241501588E-15 +* -0.175152352710251E-15 +* ]; +* +* ELSE IF( IN.EQ.2 ) THEN +** 2x2 block +* DISC = SQRT( (HALF*(D(IBEGIN)-D(IEND)))**2 + E(IBEGIN)**2 ) +* TMP1 = HALF*(D(IBEGIN)+D(IEND)) +* L1 = TMP1 - DISC +* IF( WL.GE. L1-PIVMIN ) +* $ NWL = NWL + 1 +* IF( WU.GE. L1-PIVMIN ) +* $ NWU = NWU + 1 +* IF( IRANGE.EQ.ALLRNG .OR. ( WL.LT.L1-PIVMIN .AND. WU.GE. +* $ L1-PIVMIN ) ) THEN +* M = M + 1 +* W( M ) = L1 +** The uncertainty of eigenvalues of a 2x2 matrix is very small +* WERR( M ) = EPS * ABS( W( M ) ) * TWO +* IBLOCK( M ) = JBLK +* INDEXW( M ) = 1 +* ENDIF +* L2 = TMP1 + DISC +* IF( WL.GE. L2-PIVMIN ) +* $ NWL = NWL + 1 +* IF( WU.GE. L2-PIVMIN ) +* $ NWU = NWU + 1 +* IF( IRANGE.EQ.ALLRNG .OR. ( WL.LT.L2-PIVMIN .AND. WU.GE. +* $ L2-PIVMIN ) ) THEN +* M = M + 1 +* W( M ) = L2 +** The uncertainty of eigenvalues of a 2x2 matrix is very small +* WERR( M ) = EPS * ABS( W( M ) ) * TWO +* IBLOCK( M ) = JBLK +* INDEXW( M ) = 2 +* ENDIF + ELSE +* General Case - block of size IN >= 2 +* Compute local Gerschgorin interval and use it as the initial +* interval for DLAEBZ + GU = D( IBEGIN ) + GL = D( IBEGIN ) + TMP1 = ZERO + + DO 40 J = IBEGIN, IEND + GL = MIN( GL, GERS( 2*J - 1)) + GU = MAX( GU, GERS(2*J) ) + 40 CONTINUE +* [JAN/28/2009] +* change SPDIAM by TNORM in lines 2 and 3 thereafter +* line 1: remove computation of SPDIAM (not useful anymore) +* SPDIAM = GU - GL +* GL = GL - FUDGE*SPDIAM*EPS*IN - FUDGE*PIVMIN +* GU = GU + FUDGE*SPDIAM*EPS*IN + FUDGE*PIVMIN + GL = GL - FUDGE*TNORM*EPS*IN - FUDGE*PIVMIN + GU = GU + FUDGE*TNORM*EPS*IN + FUDGE*PIVMIN +* + IF( IRANGE.GT.1 ) THEN + IF( GU.LT.WL ) THEN +* the local block contains none of the wanted eigenvalues + NWL = NWL + IN + NWU = NWU + IN + GO TO 70 + END IF +* refine search interval if possible, only range (WL,WU] matters + GL = MAX( GL, WL ) + GU = MIN( GU, WU ) + IF( GL.GE.GU ) + $ GO TO 70 + END IF + +* Find negcount of initial interval boundaries GL and GU + WORK( N+1 ) = GL + WORK( N+IN+1 ) = GU + CALL DLAEBZ( 1, 0, IN, IN, 1, NB, ATOLI, RTOLI, PIVMIN, + $ D( IBEGIN ), E( IBEGIN ), E2( IBEGIN ), + $ IDUMMA, WORK( N+1 ), WORK( N+2*IN+1 ), IM, + $ IWORK, W( M+1 ), IBLOCK( M+1 ), IINFO ) + IF( IINFO .NE. 0 ) THEN + INFO = IINFO + RETURN + END IF +* + NWL = NWL + IWORK( 1 ) + NWU = NWU + IWORK( IN+1 ) + IWOFF = M - IWORK( 1 ) + +* Compute Eigenvalues + ITMAX = INT( ( LOG( GU-GL+PIVMIN )-LOG( PIVMIN ) ) / + $ LOG( TWO ) ) + 2 + CALL DLAEBZ( 2, ITMAX, IN, IN, 1, NB, ATOLI, RTOLI, PIVMIN, + $ D( IBEGIN ), E( IBEGIN ), E2( IBEGIN ), + $ IDUMMA, WORK( N+1 ), WORK( N+2*IN+1 ), IOUT, + $ IWORK, W( M+1 ), IBLOCK( M+1 ), IINFO ) + IF( IINFO .NE. 0 ) THEN + INFO = IINFO + RETURN + END IF +* +* Copy eigenvalues into W and IBLOCK +* Use -JBLK for block number for unconverged eigenvalues. +* Loop over the number of output intervals from DLAEBZ + DO 60 J = 1, IOUT +* eigenvalue approximation is middle point of interval + TMP1 = HALF*( WORK( J+N )+WORK( J+IN+N ) ) +* semi length of error interval + TMP2 = HALF*ABS( WORK( J+N )-WORK( J+IN+N ) ) + IF( J.GT.IOUT-IINFO ) THEN +* Flag non-convergence. + NCNVRG = .TRUE. + IB = -JBLK + ELSE + IB = JBLK + END IF + DO 50 JE = IWORK( J ) + 1 + IWOFF, + $ IWORK( J+IN ) + IWOFF + W( JE ) = TMP1 + WERR( JE ) = TMP2 + INDEXW( JE ) = JE - IWOFF + IBLOCK( JE ) = IB + 50 CONTINUE + 60 CONTINUE +* + M = M + IM + END IF + 70 CONTINUE + +* If RANGE='I', then (WL,WU) contains eigenvalues NWL+1,...,NWU +* If NWL+1 < IL or NWU > IU, discard extra eigenvalues. + IF( IRANGE.EQ.INDRNG ) THEN + IDISCL = IL - 1 - NWL + IDISCU = NWU - IU +* + IF( IDISCL.GT.0 ) THEN + IM = 0 + DO 80 JE = 1, M +* Remove some of the smallest eigenvalues from the left so that +* at the end IDISCL =0. Move all eigenvalues up to the left. + IF( W( JE ).LE.WLU .AND. IDISCL.GT.0 ) THEN + IDISCL = IDISCL - 1 + ELSE + IM = IM + 1 + W( IM ) = W( JE ) + WERR( IM ) = WERR( JE ) + INDEXW( IM ) = INDEXW( JE ) + IBLOCK( IM ) = IBLOCK( JE ) + END IF + 80 CONTINUE + M = IM + END IF + IF( IDISCU.GT.0 ) THEN +* Remove some of the largest eigenvalues from the right so that +* at the end IDISCU =0. Move all eigenvalues up to the left. + IM=M+1 + DO 81 JE = M, 1, -1 + IF( W( JE ).GE.WUL .AND. IDISCU.GT.0 ) THEN + IDISCU = IDISCU - 1 + ELSE + IM = IM - 1 + W( IM ) = W( JE ) + WERR( IM ) = WERR( JE ) + INDEXW( IM ) = INDEXW( JE ) + IBLOCK( IM ) = IBLOCK( JE ) + END IF + 81 CONTINUE + JEE = 0 + DO 82 JE = IM, M + JEE = JEE + 1 + W( JEE ) = W( JE ) + WERR( JEE ) = WERR( JE ) + INDEXW( JEE ) = INDEXW( JE ) + IBLOCK( JEE ) = IBLOCK( JE ) + 82 CONTINUE + M = M-IM+1 + END IF + + IF( IDISCL.GT.0 .OR. IDISCU.GT.0 ) THEN +* Code to deal with effects of bad arithmetic. (If N(w) is +* monotone non-decreasing, this should never happen.) +* Some low eigenvalues to be discarded are not in (WL,WLU], +* or high eigenvalues to be discarded are not in (WUL,WU] +* so just kill off the smallest IDISCL/largest IDISCU +* eigenvalues, by marking the corresponding IBLOCK = 0 + IF( IDISCL.GT.0 ) THEN + WKILL = WU + DO 100 JDISC = 1, IDISCL + IW = 0 + DO 90 JE = 1, M + IF( IBLOCK( JE ).NE.0 .AND. + $ ( W( JE ).LT.WKILL .OR. IW.EQ.0 ) ) THEN + IW = JE + WKILL = W( JE ) + END IF + 90 CONTINUE + IBLOCK( IW ) = 0 + 100 CONTINUE + END IF + IF( IDISCU.GT.0 ) THEN + WKILL = WL + DO 120 JDISC = 1, IDISCU + IW = 0 + DO 110 JE = 1, M + IF( IBLOCK( JE ).NE.0 .AND. + $ ( W( JE ).GE.WKILL .OR. IW.EQ.0 ) ) THEN + IW = JE + WKILL = W( JE ) + END IF + 110 CONTINUE + IBLOCK( IW ) = 0 + 120 CONTINUE + END IF +* Now erase all eigenvalues with IBLOCK set to zero + IM = 0 + DO 130 JE = 1, M + IF( IBLOCK( JE ).NE.0 ) THEN + IM = IM + 1 + W( IM ) = W( JE ) + WERR( IM ) = WERR( JE ) + INDEXW( IM ) = INDEXW( JE ) + IBLOCK( IM ) = IBLOCK( JE ) + END IF + 130 CONTINUE + M = IM + END IF + IF( IDISCL.LT.0 .OR. IDISCU.LT.0 ) THEN + TOOFEW = .TRUE. + END IF + END IF +* + IF(( IRANGE.EQ.ALLRNG .AND. M.NE.N ).OR. + $ ( IRANGE.EQ.INDRNG .AND. M.NE.IU-IL+1 ) ) THEN + TOOFEW = .TRUE. + END IF + +* If ORDER='B', do nothing the eigenvalues are already sorted by +* block. +* If ORDER='E', sort the eigenvalues from smallest to largest + + IF( LSAME(ORDER,'E') .AND. NSPLIT.GT.1 ) THEN + DO 150 JE = 1, M - 1 + IE = 0 + TMP1 = W( JE ) + DO 140 J = JE + 1, M + IF( W( J ).LT.TMP1 ) THEN + IE = J + TMP1 = W( J ) + END IF + 140 CONTINUE + IF( IE.NE.0 ) THEN + TMP2 = WERR( IE ) + ITMP1 = IBLOCK( IE ) + ITMP2 = INDEXW( IE ) + W( IE ) = W( JE ) + WERR( IE ) = WERR( JE ) + IBLOCK( IE ) = IBLOCK( JE ) + INDEXW( IE ) = INDEXW( JE ) + W( JE ) = TMP1 + WERR( JE ) = TMP2 + IBLOCK( JE ) = ITMP1 + INDEXW( JE ) = ITMP2 + END IF + 150 CONTINUE + END IF +* + INFO = 0 + IF( NCNVRG ) + $ INFO = INFO + 1 + IF( TOOFEW ) + $ INFO = INFO + 2 + RETURN +* +* End of DLARRD +* + END diff --git a/applications/PUfoam/MoDeNaModels/CFD_tool_0D/src/eigen/src/dlarre.f b/applications/PUfoam/MoDeNaModels/CFD_tool_0D/src/eigen/src/dlarre.f new file mode 100644 index 000000000..109328a7e --- /dev/null +++ b/applications/PUfoam/MoDeNaModels/CFD_tool_0D/src/eigen/src/dlarre.f @@ -0,0 +1,891 @@ +*> \brief \b DLARRE +* +* =========== DOCUMENTATION =========== +* +* Online html documentation available at +* http://www.netlib.org/lapack/explore-html/ +* +*> \htmlonly +*> Download DLARRE + dependencies +*> +*> [TGZ] +*> +*> [ZIP] +*> +*> [TXT] +*> \endhtmlonly +* +* Definition: +* =========== +* +* SUBROUTINE DLARRE( RANGE, N, VL, VU, IL, IU, D, E, E2, +* RTOL1, RTOL2, SPLTOL, NSPLIT, ISPLIT, M, +* W, WERR, WGAP, IBLOCK, INDEXW, GERS, PIVMIN, +* WORK, IWORK, INFO ) +* +* .. Scalar Arguments .. +* CHARACTER RANGE +* INTEGER IL, INFO, IU, M, N, NSPLIT +* DOUBLE PRECISION PIVMIN, RTOL1, RTOL2, SPLTOL, VL, VU +* .. +* .. Array Arguments .. +* INTEGER IBLOCK( * ), ISPLIT( * ), IWORK( * ), +* $ INDEXW( * ) +* DOUBLE PRECISION D( * ), E( * ), E2( * ), GERS( * ), +* $ W( * ),WERR( * ), WGAP( * ), WORK( * ) +* .. +* +* +*> \par Purpose: +* ============= +*> +*> \verbatim +*> +*> To find the desired eigenvalues of a given real symmetric +*> tridiagonal matrix T, DLARRE sets any "small" off-diagonal +*> elements to zero, and for each unreduced block T_i, it finds +*> (a) a suitable shift at one end of the block's spectrum, +*> (b) the base representation, T_i - sigma_i I = L_i D_i L_i^T, and +*> (c) eigenvalues of each L_i D_i L_i^T. +*> The representations and eigenvalues found are then used by +*> DSTEMR to compute the eigenvectors of T. +*> The accuracy varies depending on whether bisection is used to +*> find a few eigenvalues or the dqds algorithm (subroutine DLASQ2) to +*> conpute all and then discard any unwanted one. +*> As an added benefit, DLARRE also outputs the n +*> Gerschgorin intervals for the matrices L_i D_i L_i^T. +*> \endverbatim +* +* Arguments: +* ========== +* +*> \param[in] RANGE +*> \verbatim +*> RANGE is CHARACTER*1 +*> = 'A': ("All") all eigenvalues will be found. +*> = 'V': ("Value") all eigenvalues in the half-open interval +*> (VL, VU] will be found. +*> = 'I': ("Index") the IL-th through IU-th eigenvalues (of the +*> entire matrix) will be found. +*> \endverbatim +*> +*> \param[in] N +*> \verbatim +*> N is INTEGER +*> The order of the matrix. N > 0. +*> \endverbatim +*> +*> \param[in,out] VL +*> \verbatim +*> VL is DOUBLE PRECISION +*> \endverbatim +*> +*> \param[in,out] VU +*> \verbatim +*> VU is DOUBLE PRECISION +*> If RANGE='V', the lower and upper bounds for the eigenvalues. +*> Eigenvalues less than or equal to VL, or greater than VU, +*> will not be returned. VL < VU. +*> If RANGE='I' or ='A', DLARRE computes bounds on the desired +*> part of the spectrum. +*> \endverbatim +*> +*> \param[in] IL +*> \verbatim +*> IL is INTEGER +*> \endverbatim +*> +*> \param[in] IU +*> \verbatim +*> IU is INTEGER +*> If RANGE='I', the indices (in ascending order) of the +*> smallest and largest eigenvalues to be returned. +*> 1 <= IL <= IU <= N. +*> \endverbatim +*> +*> \param[in,out] D +*> \verbatim +*> D is DOUBLE PRECISION array, dimension (N) +*> On entry, the N diagonal elements of the tridiagonal +*> matrix T. +*> On exit, the N diagonal elements of the diagonal +*> matrices D_i. +*> \endverbatim +*> +*> \param[in,out] E +*> \verbatim +*> E is DOUBLE PRECISION array, dimension (N) +*> On entry, the first (N-1) entries contain the subdiagonal +*> elements of the tridiagonal matrix T; E(N) need not be set. +*> On exit, E contains the subdiagonal elements of the unit +*> bidiagonal matrices L_i. The entries E( ISPLIT( I ) ), +*> 1 <= I <= NSPLIT, contain the base points sigma_i on output. +*> \endverbatim +*> +*> \param[in,out] E2 +*> \verbatim +*> E2 is DOUBLE PRECISION array, dimension (N) +*> On entry, the first (N-1) entries contain the SQUARES of the +*> subdiagonal elements of the tridiagonal matrix T; +*> E2(N) need not be set. +*> On exit, the entries E2( ISPLIT( I ) ), +*> 1 <= I <= NSPLIT, have been set to zero +*> \endverbatim +*> +*> \param[in] RTOL1 +*> \verbatim +*> RTOL1 is DOUBLE PRECISION +*> \endverbatim +*> +*> \param[in] RTOL2 +*> \verbatim +*> RTOL2 is DOUBLE PRECISION +*> Parameters for bisection. +*> An interval [LEFT,RIGHT] has converged if +*> RIGHT-LEFT.LT.MAX( RTOL1*GAP, RTOL2*MAX(|LEFT|,|RIGHT|) ) +*> \endverbatim +*> +*> \param[in] SPLTOL +*> \verbatim +*> SPLTOL is DOUBLE PRECISION +*> The threshold for splitting. +*> \endverbatim +*> +*> \param[out] NSPLIT +*> \verbatim +*> NSPLIT is INTEGER +*> The number of blocks T splits into. 1 <= NSPLIT <= N. +*> \endverbatim +*> +*> \param[out] ISPLIT +*> \verbatim +*> ISPLIT is INTEGER array, dimension (N) +*> The splitting points, at which T breaks up into blocks. +*> The first block consists of rows/columns 1 to ISPLIT(1), +*> the second of rows/columns ISPLIT(1)+1 through ISPLIT(2), +*> etc., and the NSPLIT-th consists of rows/columns +*> ISPLIT(NSPLIT-1)+1 through ISPLIT(NSPLIT)=N. +*> \endverbatim +*> +*> \param[out] M +*> \verbatim +*> M is INTEGER +*> The total number of eigenvalues (of all L_i D_i L_i^T) +*> found. +*> \endverbatim +*> +*> \param[out] W +*> \verbatim +*> W is DOUBLE PRECISION array, dimension (N) +*> The first M elements contain the eigenvalues. The +*> eigenvalues of each of the blocks, L_i D_i L_i^T, are +*> sorted in ascending order ( DLARRE may use the +*> remaining N-M elements as workspace). +*> \endverbatim +*> +*> \param[out] WERR +*> \verbatim +*> WERR is DOUBLE PRECISION array, dimension (N) +*> The error bound on the corresponding eigenvalue in W. +*> \endverbatim +*> +*> \param[out] WGAP +*> \verbatim +*> WGAP is DOUBLE PRECISION array, dimension (N) +*> The separation from the right neighbor eigenvalue in W. +*> The gap is only with respect to the eigenvalues of the same block +*> as each block has its own representation tree. +*> Exception: at the right end of a block we store the left gap +*> \endverbatim +*> +*> \param[out] IBLOCK +*> \verbatim +*> IBLOCK is INTEGER array, dimension (N) +*> The indices of the blocks (submatrices) associated with the +*> corresponding eigenvalues in W; IBLOCK(i)=1 if eigenvalue +*> W(i) belongs to the first block from the top, =2 if W(i) +*> belongs to the second block, etc. +*> \endverbatim +*> +*> \param[out] INDEXW +*> \verbatim +*> INDEXW is INTEGER array, dimension (N) +*> The indices of the eigenvalues within each block (submatrix); +*> for example, INDEXW(i)= 10 and IBLOCK(i)=2 imply that the +*> i-th eigenvalue W(i) is the 10-th eigenvalue in block 2 +*> \endverbatim +*> +*> \param[out] GERS +*> \verbatim +*> GERS is DOUBLE PRECISION array, dimension (2*N) +*> The N Gerschgorin intervals (the i-th Gerschgorin interval +*> is (GERS(2*i-1), GERS(2*i)). +*> \endverbatim +*> +*> \param[out] PIVMIN +*> \verbatim +*> PIVMIN is DOUBLE PRECISION +*> The minimum pivot in the Sturm sequence for T. +*> \endverbatim +*> +*> \param[out] WORK +*> \verbatim +*> WORK is DOUBLE PRECISION array, dimension (6*N) +*> Workspace. +*> \endverbatim +*> +*> \param[out] IWORK +*> \verbatim +*> IWORK is INTEGER array, dimension (5*N) +*> Workspace. +*> \endverbatim +*> +*> \param[out] INFO +*> \verbatim +*> INFO is INTEGER +*> = 0: successful exit +*> > 0: A problem occured in DLARRE. +*> < 0: One of the called subroutines signaled an internal problem. +*> Needs inspection of the corresponding parameter IINFO +*> for further information. +*> +*> =-1: Problem in DLARRD. +*> = 2: No base representation could be found in MAXTRY iterations. +*> Increasing MAXTRY and recompilation might be a remedy. +*> =-3: Problem in DLARRB when computing the refined root +*> representation for DLASQ2. +*> =-4: Problem in DLARRB when preforming bisection on the +*> desired part of the spectrum. +*> =-5: Problem in DLASQ2. +*> =-6: Problem in DLASQ2. +*> \endverbatim +* +* Authors: +* ======== +* +*> \author Univ. of Tennessee +*> \author Univ. of California Berkeley +*> \author Univ. of Colorado Denver +*> \author NAG Ltd. +* +*> \date November 2011 +* +*> \ingroup auxOTHERauxiliary +* +*> \par Further Details: +* ===================== +*> +*> \verbatim +*> +*> The base representations are required to suffer very little +*> element growth and consequently define all their eigenvalues to +*> high relative accuracy. +*> \endverbatim +* +*> \par Contributors: +* ================== +*> +*> Beresford Parlett, University of California, Berkeley, USA \n +*> Jim Demmel, University of California, Berkeley, USA \n +*> Inderjit Dhillon, University of Texas, Austin, USA \n +*> Osni Marques, LBNL/NERSC, USA \n +*> Christof Voemel, University of California, Berkeley, USA \n +*> +* ===================================================================== + SUBROUTINE DLARRE( RANGE, N, VL, VU, IL, IU, D, E, E2, + $ RTOL1, RTOL2, SPLTOL, NSPLIT, ISPLIT, M, + $ W, WERR, WGAP, IBLOCK, INDEXW, GERS, PIVMIN, + $ WORK, IWORK, INFO ) +* +* -- LAPACK auxiliary routine (version 3.4.0) -- +* -- LAPACK is a software package provided by Univ. of Tennessee, -- +* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- +* November 2011 +* +* .. Scalar Arguments .. + CHARACTER RANGE + INTEGER IL, INFO, IU, M, N, NSPLIT + DOUBLE PRECISION PIVMIN, RTOL1, RTOL2, SPLTOL, VL, VU +* .. +* .. Array Arguments .. + INTEGER IBLOCK( * ), ISPLIT( * ), IWORK( * ), + $ INDEXW( * ) + DOUBLE PRECISION D( * ), E( * ), E2( * ), GERS( * ), + $ W( * ),WERR( * ), WGAP( * ), WORK( * ) +* .. +* +* ===================================================================== +* +* .. Parameters .. + DOUBLE PRECISION FAC, FOUR, FOURTH, FUDGE, HALF, HNDRD, + $ MAXGROWTH, ONE, PERT, TWO, ZERO + PARAMETER ( ZERO = 0.0D0, ONE = 1.0D0, + $ TWO = 2.0D0, FOUR=4.0D0, + $ HNDRD = 100.0D0, + $ PERT = 8.0D0, + $ HALF = ONE/TWO, FOURTH = ONE/FOUR, FAC= HALF, + $ MAXGROWTH = 64.0D0, FUDGE = 2.0D0 ) + INTEGER MAXTRY, ALLRNG, INDRNG, VALRNG + PARAMETER ( MAXTRY = 6, ALLRNG = 1, INDRNG = 2, + $ VALRNG = 3 ) +* .. +* .. Local Scalars .. + LOGICAL FORCEB, NOREP, USEDQD + INTEGER CNT, CNT1, CNT2, I, IBEGIN, IDUM, IEND, IINFO, + $ IN, INDL, INDU, IRANGE, J, JBLK, MB, MM, + $ WBEGIN, WEND + DOUBLE PRECISION AVGAP, BSRTOL, CLWDTH, DMAX, DPIVOT, EABS, + $ EMAX, EOLD, EPS, GL, GU, ISLEFT, ISRGHT, RTL, + $ RTOL, S1, S2, SAFMIN, SGNDEF, SIGMA, SPDIAM, + $ TAU, TMP, TMP1 + + +* .. +* .. Local Arrays .. + INTEGER ISEED( 4 ) +* .. +* .. External Functions .. + LOGICAL LSAME + DOUBLE PRECISION DLAMCH + EXTERNAL DLAMCH, LSAME + +* .. +* .. External Subroutines .. + EXTERNAL DCOPY, DLARNV, DLARRA, DLARRB, DLARRC, DLARRD, + $ DLASQ2 +* .. +* .. Intrinsic Functions .. + INTRINSIC ABS, MAX, MIN + +* .. +* .. Executable Statements .. +* + + INFO = 0 + +* +* Decode RANGE +* + IF( LSAME( RANGE, 'A' ) ) THEN + IRANGE = ALLRNG + ELSE IF( LSAME( RANGE, 'V' ) ) THEN + IRANGE = VALRNG + ELSE IF( LSAME( RANGE, 'I' ) ) THEN + IRANGE = INDRNG + END IF + + M = 0 + +* Get machine constants + SAFMIN = DLAMCH( 'S' ) + EPS = DLAMCH( 'P' ) + +* Set parameters + RTL = SQRT(EPS) + BSRTOL = SQRT(EPS) + +* Treat case of 1x1 matrix for quick return + IF( N.EQ.1 ) THEN + IF( (IRANGE.EQ.ALLRNG).OR. + $ ((IRANGE.EQ.VALRNG).AND.(D(1).GT.VL).AND.(D(1).LE.VU)).OR. + $ ((IRANGE.EQ.INDRNG).AND.(IL.EQ.1).AND.(IU.EQ.1)) ) THEN + M = 1 + W(1) = D(1) +* The computation error of the eigenvalue is zero + WERR(1) = ZERO + WGAP(1) = ZERO + IBLOCK( 1 ) = 1 + INDEXW( 1 ) = 1 + GERS(1) = D( 1 ) + GERS(2) = D( 1 ) + ENDIF +* store the shift for the initial RRR, which is zero in this case + E(1) = ZERO + RETURN + END IF + +* General case: tridiagonal matrix of order > 1 +* +* Init WERR, WGAP. Compute Gerschgorin intervals and spectral diameter. +* Compute maximum off-diagonal entry and pivmin. + GL = D(1) + GU = D(1) + EOLD = ZERO + EMAX = ZERO + E(N) = ZERO + DO 5 I = 1,N + WERR(I) = ZERO + WGAP(I) = ZERO + EABS = ABS( E(I) ) + IF( EABS .GE. EMAX ) THEN + EMAX = EABS + END IF + TMP1 = EABS + EOLD + GERS( 2*I-1) = D(I) - TMP1 + GL = MIN( GL, GERS( 2*I - 1)) + GERS( 2*I ) = D(I) + TMP1 + GU = MAX( GU, GERS(2*I) ) + EOLD = EABS + 5 CONTINUE +* The minimum pivot allowed in the Sturm sequence for T + PIVMIN = SAFMIN * MAX( ONE, EMAX**2 ) +* Compute spectral diameter. The Gerschgorin bounds give an +* estimate that is wrong by at most a factor of SQRT(2) + SPDIAM = GU - GL + +* Compute splitting points + CALL DLARRA( N, D, E, E2, SPLTOL, SPDIAM, + $ NSPLIT, ISPLIT, IINFO ) + +* Can force use of bisection instead of faster DQDS. +* Option left in the code for future multisection work. + FORCEB = .FALSE. + +* Initialize USEDQD, DQDS should be used for ALLRNG unless someone +* explicitly wants bisection. + USEDQD = (( IRANGE.EQ.ALLRNG ) .AND. (.NOT.FORCEB)) + + IF( (IRANGE.EQ.ALLRNG) .AND. (.NOT. FORCEB) ) THEN +* Set interval [VL,VU] that contains all eigenvalues + VL = GL + VU = GU + ELSE +* We call DLARRD to find crude approximations to the eigenvalues +* in the desired range. In case IRANGE = INDRNG, we also obtain the +* interval (VL,VU] that contains all the wanted eigenvalues. +* An interval [LEFT,RIGHT] has converged if +* RIGHT-LEFT.LT.RTOL*MAX(ABS(LEFT),ABS(RIGHT)) +* DLARRD needs a WORK of size 4*N, IWORK of size 3*N + CALL DLARRD( RANGE, 'B', N, VL, VU, IL, IU, GERS, + $ BSRTOL, D, E, E2, PIVMIN, NSPLIT, ISPLIT, + $ MM, W, WERR, VL, VU, IBLOCK, INDEXW, + $ WORK, IWORK, IINFO ) + IF( IINFO.NE.0 ) THEN + INFO = -1 + RETURN + ENDIF +* Make sure that the entries M+1 to N in W, WERR, IBLOCK, INDEXW are 0 + DO 14 I = MM+1,N + W( I ) = ZERO + WERR( I ) = ZERO + IBLOCK( I ) = 0 + INDEXW( I ) = 0 + 14 CONTINUE + END IF + + +*** +* Loop over unreduced blocks + IBEGIN = 1 + WBEGIN = 1 + DO 170 JBLK = 1, NSPLIT + IEND = ISPLIT( JBLK ) + IN = IEND - IBEGIN + 1 + +* 1 X 1 block + IF( IN.EQ.1 ) THEN + IF( (IRANGE.EQ.ALLRNG).OR.( (IRANGE.EQ.VALRNG).AND. + $ ( D( IBEGIN ).GT.VL ).AND.( D( IBEGIN ).LE.VU ) ) + $ .OR. ( (IRANGE.EQ.INDRNG).AND.(IBLOCK(WBEGIN).EQ.JBLK)) + $ ) THEN + M = M + 1 + W( M ) = D( IBEGIN ) + WERR(M) = ZERO +* The gap for a single block doesn't matter for the later +* algorithm and is assigned an arbitrary large value + WGAP(M) = ZERO + IBLOCK( M ) = JBLK + INDEXW( M ) = 1 + WBEGIN = WBEGIN + 1 + ENDIF +* E( IEND ) holds the shift for the initial RRR + E( IEND ) = ZERO + IBEGIN = IEND + 1 + GO TO 170 + END IF +* +* Blocks of size larger than 1x1 +* +* E( IEND ) will hold the shift for the initial RRR, for now set it =0 + E( IEND ) = ZERO +* +* Find local outer bounds GL,GU for the block + GL = D(IBEGIN) + GU = D(IBEGIN) + DO 15 I = IBEGIN , IEND + GL = MIN( GERS( 2*I-1 ), GL ) + GU = MAX( GERS( 2*I ), GU ) + 15 CONTINUE + SPDIAM = GU - GL + + IF(.NOT. ((IRANGE.EQ.ALLRNG).AND.(.NOT.FORCEB)) ) THEN +* Count the number of eigenvalues in the current block. + MB = 0 + DO 20 I = WBEGIN,MM + IF( IBLOCK(I).EQ.JBLK ) THEN + MB = MB+1 + ELSE + GOTO 21 + ENDIF + 20 CONTINUE + 21 CONTINUE + + IF( MB.EQ.0) THEN +* No eigenvalue in the current block lies in the desired range +* E( IEND ) holds the shift for the initial RRR + E( IEND ) = ZERO + IBEGIN = IEND + 1 + GO TO 170 + ELSE + +* Decide whether dqds or bisection is more efficient + USEDQD = ( (MB .GT. FAC*IN) .AND. (.NOT.FORCEB) ) + WEND = WBEGIN + MB - 1 +* Calculate gaps for the current block +* In later stages, when representations for individual +* eigenvalues are different, we use SIGMA = E( IEND ). + SIGMA = ZERO + DO 30 I = WBEGIN, WEND - 1 + WGAP( I ) = MAX( ZERO, + $ W(I+1)-WERR(I+1) - (W(I)+WERR(I)) ) + 30 CONTINUE + WGAP( WEND ) = MAX( ZERO, + $ VU - SIGMA - (W( WEND )+WERR( WEND ))) +* Find local index of the first and last desired evalue. + INDL = INDEXW(WBEGIN) + INDU = INDEXW( WEND ) + ENDIF + ENDIF + IF(( (IRANGE.EQ.ALLRNG) .AND. (.NOT. FORCEB) ).OR.USEDQD) THEN +* Case of DQDS +* Find approximations to the extremal eigenvalues of the block + CALL DLARRK( IN, 1, GL, GU, D(IBEGIN), + $ E2(IBEGIN), PIVMIN, RTL, TMP, TMP1, IINFO ) + IF( IINFO.NE.0 ) THEN + INFO = -1 + RETURN + ENDIF + ISLEFT = MAX(GL, TMP - TMP1 + $ - HNDRD * EPS* ABS(TMP - TMP1)) + + CALL DLARRK( IN, IN, GL, GU, D(IBEGIN), + $ E2(IBEGIN), PIVMIN, RTL, TMP, TMP1, IINFO ) + IF( IINFO.NE.0 ) THEN + INFO = -1 + RETURN + ENDIF + ISRGHT = MIN(GU, TMP + TMP1 + $ + HNDRD * EPS * ABS(TMP + TMP1)) +* Improve the estimate of the spectral diameter + SPDIAM = ISRGHT - ISLEFT + ELSE +* Case of bisection +* Find approximations to the wanted extremal eigenvalues + ISLEFT = MAX(GL, W(WBEGIN) - WERR(WBEGIN) + $ - HNDRD * EPS*ABS(W(WBEGIN)- WERR(WBEGIN) )) + ISRGHT = MIN(GU,W(WEND) + WERR(WEND) + $ + HNDRD * EPS * ABS(W(WEND)+ WERR(WEND))) + ENDIF + + +* Decide whether the base representation for the current block +* L_JBLK D_JBLK L_JBLK^T = T_JBLK - sigma_JBLK I +* should be on the left or the right end of the current block. +* The strategy is to shift to the end which is "more populated" +* Furthermore, decide whether to use DQDS for the computation of +* the eigenvalue approximations at the end of DLARRE or bisection. +* dqds is chosen if all eigenvalues are desired or the number of +* eigenvalues to be computed is large compared to the blocksize. + IF( ( IRANGE.EQ.ALLRNG ) .AND. (.NOT.FORCEB) ) THEN +* If all the eigenvalues have to be computed, we use dqd + USEDQD = .TRUE. +* INDL is the local index of the first eigenvalue to compute + INDL = 1 + INDU = IN +* MB = number of eigenvalues to compute + MB = IN + WEND = WBEGIN + MB - 1 +* Define 1/4 and 3/4 points of the spectrum + S1 = ISLEFT + FOURTH * SPDIAM + S2 = ISRGHT - FOURTH * SPDIAM + ELSE +* DLARRD has computed IBLOCK and INDEXW for each eigenvalue +* approximation. +* choose sigma + IF( USEDQD ) THEN + S1 = ISLEFT + FOURTH * SPDIAM + S2 = ISRGHT - FOURTH * SPDIAM + ELSE + TMP = MIN(ISRGHT,VU) - MAX(ISLEFT,VL) + S1 = MAX(ISLEFT,VL) + FOURTH * TMP + S2 = MIN(ISRGHT,VU) - FOURTH * TMP + ENDIF + ENDIF + +* Compute the negcount at the 1/4 and 3/4 points + IF(MB.GT.1) THEN + CALL DLARRC( 'T', IN, S1, S2, D(IBEGIN), + $ E(IBEGIN), PIVMIN, CNT, CNT1, CNT2, IINFO) + ENDIF + + IF(MB.EQ.1) THEN + SIGMA = GL + SGNDEF = ONE + ELSEIF( CNT1 - INDL .GE. INDU - CNT2 ) THEN + IF( ( IRANGE.EQ.ALLRNG ) .AND. (.NOT.FORCEB) ) THEN + SIGMA = MAX(ISLEFT,GL) + ELSEIF( USEDQD ) THEN +* use Gerschgorin bound as shift to get pos def matrix +* for dqds + SIGMA = ISLEFT + ELSE +* use approximation of the first desired eigenvalue of the +* block as shift + SIGMA = MAX(ISLEFT,VL) + ENDIF + SGNDEF = ONE + ELSE + IF( ( IRANGE.EQ.ALLRNG ) .AND. (.NOT.FORCEB) ) THEN + SIGMA = MIN(ISRGHT,GU) + ELSEIF( USEDQD ) THEN +* use Gerschgorin bound as shift to get neg def matrix +* for dqds + SIGMA = ISRGHT + ELSE +* use approximation of the first desired eigenvalue of the +* block as shift + SIGMA = MIN(ISRGHT,VU) + ENDIF + SGNDEF = -ONE + ENDIF + + +* An initial SIGMA has been chosen that will be used for computing +* T - SIGMA I = L D L^T +* Define the increment TAU of the shift in case the initial shift +* needs to be refined to obtain a factorization with not too much +* element growth. + IF( USEDQD ) THEN +* The initial SIGMA was to the outer end of the spectrum +* the matrix is definite and we need not retreat. + TAU = SPDIAM*EPS*N + TWO*PIVMIN + TAU = MAX( TAU,TWO*EPS*ABS(SIGMA) ) + ELSE + IF(MB.GT.1) THEN + CLWDTH = W(WEND) + WERR(WEND) - W(WBEGIN) - WERR(WBEGIN) + AVGAP = ABS(CLWDTH / DBLE(WEND-WBEGIN)) + IF( SGNDEF.EQ.ONE ) THEN + TAU = HALF*MAX(WGAP(WBEGIN),AVGAP) + TAU = MAX(TAU,WERR(WBEGIN)) + ELSE + TAU = HALF*MAX(WGAP(WEND-1),AVGAP) + TAU = MAX(TAU,WERR(WEND)) + ENDIF + ELSE + TAU = WERR(WBEGIN) + ENDIF + ENDIF +* + DO 80 IDUM = 1, MAXTRY +* Compute L D L^T factorization of tridiagonal matrix T - sigma I. +* Store D in WORK(1:IN), L in WORK(IN+1:2*IN), and reciprocals of +* pivots in WORK(2*IN+1:3*IN) + DPIVOT = D( IBEGIN ) - SIGMA + WORK( 1 ) = DPIVOT + DMAX = ABS( WORK(1) ) + J = IBEGIN + DO 70 I = 1, IN - 1 + WORK( 2*IN+I ) = ONE / WORK( I ) + TMP = E( J )*WORK( 2*IN+I ) + WORK( IN+I ) = TMP + DPIVOT = ( D( J+1 )-SIGMA ) - TMP*E( J ) + WORK( I+1 ) = DPIVOT + DMAX = MAX( DMAX, ABS(DPIVOT) ) + J = J + 1 + 70 CONTINUE +* check for element growth + IF( DMAX .GT. MAXGROWTH*SPDIAM ) THEN + NOREP = .TRUE. + ELSE + NOREP = .FALSE. + ENDIF + IF( USEDQD .AND. .NOT.NOREP ) THEN +* Ensure the definiteness of the representation +* All entries of D (of L D L^T) must have the same sign + DO 71 I = 1, IN + TMP = SGNDEF*WORK( I ) + IF( TMP.LT.ZERO ) NOREP = .TRUE. + 71 CONTINUE + ENDIF + IF(NOREP) THEN +* Note that in the case of IRANGE=ALLRNG, we use the Gerschgorin +* shift which makes the matrix definite. So we should end up +* here really only in the case of IRANGE = VALRNG or INDRNG. + IF( IDUM.EQ.MAXTRY-1 ) THEN + IF( SGNDEF.EQ.ONE ) THEN +* The fudged Gerschgorin shift should succeed + SIGMA = + $ GL - FUDGE*SPDIAM*EPS*N - FUDGE*TWO*PIVMIN + ELSE + SIGMA = + $ GU + FUDGE*SPDIAM*EPS*N + FUDGE*TWO*PIVMIN + END IF + ELSE + SIGMA = SIGMA - SGNDEF * TAU + TAU = TWO * TAU + END IF + ELSE +* an initial RRR is found + GO TO 83 + END IF + 80 CONTINUE +* if the program reaches this point, no base representation could be +* found in MAXTRY iterations. + INFO = 2 + RETURN + + 83 CONTINUE +* At this point, we have found an initial base representation +* T - SIGMA I = L D L^T with not too much element growth. +* Store the shift. + E( IEND ) = SIGMA +* Store D and L. + CALL DCOPY( IN, WORK, 1, D( IBEGIN ), 1 ) + CALL DCOPY( IN-1, WORK( IN+1 ), 1, E( IBEGIN ), 1 ) + + + IF(MB.GT.1 ) THEN +* +* Perturb each entry of the base representation by a small +* (but random) relative amount to overcome difficulties with +* glued matrices. +* + DO 122 I = 1, 4 + ISEED( I ) = 1 + 122 CONTINUE + + CALL DLARNV(2, ISEED, 2*IN-1, WORK(1)) + DO 125 I = 1,IN-1 + D(IBEGIN+I-1) = D(IBEGIN+I-1)*(ONE+EPS*PERT*WORK(I)) + E(IBEGIN+I-1) = E(IBEGIN+I-1)*(ONE+EPS*PERT*WORK(IN+I)) + 125 CONTINUE + D(IEND) = D(IEND)*(ONE+EPS*FOUR*WORK(IN)) +* + ENDIF +* +* Don't update the Gerschgorin intervals because keeping track +* of the updates would be too much work in DLARRV. +* We update W instead and use it to locate the proper Gerschgorin +* intervals. + +* Compute the required eigenvalues of L D L' by bisection or dqds + IF ( .NOT.USEDQD ) THEN +* If DLARRD has been used, shift the eigenvalue approximations +* according to their representation. This is necessary for +* a uniform DLARRV since dqds computes eigenvalues of the +* shifted representation. In DLARRV, W will always hold the +* UNshifted eigenvalue approximation. + DO 134 J=WBEGIN,WEND + W(J) = W(J) - SIGMA + WERR(J) = WERR(J) + ABS(W(J)) * EPS + 134 CONTINUE +* call DLARRB to reduce eigenvalue error of the approximations +* from DLARRD + DO 135 I = IBEGIN, IEND-1 + WORK( I ) = D( I ) * E( I )**2 + 135 CONTINUE +* use bisection to find EV from INDL to INDU + CALL DLARRB(IN, D(IBEGIN), WORK(IBEGIN), + $ INDL, INDU, RTOL1, RTOL2, INDL-1, + $ W(WBEGIN), WGAP(WBEGIN), WERR(WBEGIN), + $ WORK( 2*N+1 ), IWORK, PIVMIN, SPDIAM, + $ IN, IINFO ) + IF( IINFO .NE. 0 ) THEN + INFO = -4 + RETURN + END IF +* DLARRB computes all gaps correctly except for the last one +* Record distance to VU/GU + WGAP( WEND ) = MAX( ZERO, + $ ( VU-SIGMA ) - ( W( WEND ) + WERR( WEND ) ) ) + DO 138 I = INDL, INDU + M = M + 1 + IBLOCK(M) = JBLK + INDEXW(M) = I + 138 CONTINUE + ELSE +* Call dqds to get all eigs (and then possibly delete unwanted +* eigenvalues). +* Note that dqds finds the eigenvalues of the L D L^T representation +* of T to high relative accuracy. High relative accuracy +* might be lost when the shift of the RRR is subtracted to obtain +* the eigenvalues of T. However, T is not guaranteed to define its +* eigenvalues to high relative accuracy anyway. +* Set RTOL to the order of the tolerance used in DLASQ2 +* This is an ESTIMATED error, the worst case bound is 4*N*EPS +* which is usually too large and requires unnecessary work to be +* done by bisection when computing the eigenvectors + RTOL = LOG(DBLE(IN)) * FOUR * EPS + J = IBEGIN + DO 140 I = 1, IN - 1 + WORK( 2*I-1 ) = ABS( D( J ) ) + WORK( 2*I ) = E( J )*E( J )*WORK( 2*I-1 ) + J = J + 1 + 140 CONTINUE + WORK( 2*IN-1 ) = ABS( D( IEND ) ) + WORK( 2*IN ) = ZERO + CALL DLASQ2( IN, WORK, IINFO ) + IF( IINFO .NE. 0 ) THEN +* If IINFO = -5 then an index is part of a tight cluster +* and should be changed. The index is in IWORK(1) and the +* gap is in WORK(N+1) + INFO = -5 + RETURN + ELSE +* Test that all eigenvalues are positive as expected + DO 149 I = 1, IN + IF( WORK( I ).LT.ZERO ) THEN + INFO = -6 + RETURN + ENDIF + 149 CONTINUE + END IF + IF( SGNDEF.GT.ZERO ) THEN + DO 150 I = INDL, INDU + M = M + 1 + W( M ) = WORK( IN-I+1 ) + IBLOCK( M ) = JBLK + INDEXW( M ) = I + 150 CONTINUE + ELSE + DO 160 I = INDL, INDU + M = M + 1 + W( M ) = -WORK( I ) + IBLOCK( M ) = JBLK + INDEXW( M ) = I + 160 CONTINUE + END IF + + DO 165 I = M - MB + 1, M +* the value of RTOL below should be the tolerance in DLASQ2 + WERR( I ) = RTOL * ABS( W(I) ) + 165 CONTINUE + DO 166 I = M - MB + 1, M - 1 +* compute the right gap between the intervals + WGAP( I ) = MAX( ZERO, + $ W(I+1)-WERR(I+1) - (W(I)+WERR(I)) ) + 166 CONTINUE + WGAP( M ) = MAX( ZERO, + $ ( VU-SIGMA ) - ( W( M ) + WERR( M ) ) ) + END IF +* proceed with next block + IBEGIN = IEND + 1 + WBEGIN = WEND + 1 + 170 CONTINUE +* + + RETURN +* +* end of DLARRE +* + END diff --git a/applications/PUfoam/MoDeNaModels/CFD_tool_0D/src/eigen/src/dlarrf.f b/applications/PUfoam/MoDeNaModels/CFD_tool_0D/src/eigen/src/dlarrf.f new file mode 100644 index 000000000..1c11f9298 --- /dev/null +++ b/applications/PUfoam/MoDeNaModels/CFD_tool_0D/src/eigen/src/dlarrf.f @@ -0,0 +1,488 @@ +*> \brief \b DLARRF +* +* =========== DOCUMENTATION =========== +* +* Online html documentation available at +* http://www.netlib.org/lapack/explore-html/ +* +*> \htmlonly +*> Download DLARRF + dependencies +*> +*> [TGZ] +*> +*> [ZIP] +*> +*> [TXT] +*> \endhtmlonly +* +* Definition: +* =========== +* +* SUBROUTINE DLARRF( N, D, L, LD, CLSTRT, CLEND, +* W, WGAP, WERR, +* SPDIAM, CLGAPL, CLGAPR, PIVMIN, SIGMA, +* DPLUS, LPLUS, WORK, INFO ) +* +* .. Scalar Arguments .. +* INTEGER CLSTRT, CLEND, INFO, N +* DOUBLE PRECISION CLGAPL, CLGAPR, PIVMIN, SIGMA, SPDIAM +* .. +* .. Array Arguments .. +* DOUBLE PRECISION D( * ), DPLUS( * ), L( * ), LD( * ), +* $ LPLUS( * ), W( * ), WGAP( * ), WERR( * ), WORK( * ) +* .. +* +* +*> \par Purpose: +* ============= +*> +*> \verbatim +*> +*> Given the initial representation L D L^T and its cluster of close +*> eigenvalues (in a relative measure), W( CLSTRT ), W( CLSTRT+1 ), ... +*> W( CLEND ), DLARRF finds a new relatively robust representation +*> L D L^T - SIGMA I = L(+) D(+) L(+)^T such that at least one of the +*> eigenvalues of L(+) D(+) L(+)^T is relatively isolated. +*> \endverbatim +* +* Arguments: +* ========== +* +*> \param[in] N +*> \verbatim +*> N is INTEGER +*> The order of the matrix (subblock, if the matrix splitted). +*> \endverbatim +*> +*> \param[in] D +*> \verbatim +*> D is DOUBLE PRECISION array, dimension (N) +*> The N diagonal elements of the diagonal matrix D. +*> \endverbatim +*> +*> \param[in] L +*> \verbatim +*> L is DOUBLE PRECISION array, dimension (N-1) +*> The (N-1) subdiagonal elements of the unit bidiagonal +*> matrix L. +*> \endverbatim +*> +*> \param[in] LD +*> \verbatim +*> LD is DOUBLE PRECISION array, dimension (N-1) +*> The (N-1) elements L(i)*D(i). +*> \endverbatim +*> +*> \param[in] CLSTRT +*> \verbatim +*> CLSTRT is INTEGER +*> The index of the first eigenvalue in the cluster. +*> \endverbatim +*> +*> \param[in] CLEND +*> \verbatim +*> CLEND is INTEGER +*> The index of the last eigenvalue in the cluster. +*> \endverbatim +*> +*> \param[in] W +*> \verbatim +*> W is DOUBLE PRECISION array, dimension +*> dimension is >= (CLEND-CLSTRT+1) +*> The eigenvalue APPROXIMATIONS of L D L^T in ascending order. +*> W( CLSTRT ) through W( CLEND ) form the cluster of relatively +*> close eigenalues. +*> \endverbatim +*> +*> \param[in,out] WGAP +*> \verbatim +*> WGAP is DOUBLE PRECISION array, dimension +*> dimension is >= (CLEND-CLSTRT+1) +*> The separation from the right neighbor eigenvalue in W. +*> \endverbatim +*> +*> \param[in] WERR +*> \verbatim +*> WERR is DOUBLE PRECISION array, dimension +*> dimension is >= (CLEND-CLSTRT+1) +*> WERR contain the semiwidth of the uncertainty +*> interval of the corresponding eigenvalue APPROXIMATION in W +*> \endverbatim +*> +*> \param[in] SPDIAM +*> \verbatim +*> SPDIAM is DOUBLE PRECISION +*> estimate of the spectral diameter obtained from the +*> Gerschgorin intervals +*> \endverbatim +*> +*> \param[in] CLGAPL +*> \verbatim +*> CLGAPL is DOUBLE PRECISION +*> \endverbatim +*> +*> \param[in] CLGAPR +*> \verbatim +*> CLGAPR is DOUBLE PRECISION +*> absolute gap on each end of the cluster. +*> Set by the calling routine to protect against shifts too close +*> to eigenvalues outside the cluster. +*> \endverbatim +*> +*> \param[in] PIVMIN +*> \verbatim +*> PIVMIN is DOUBLE PRECISION +*> The minimum pivot allowed in the Sturm sequence. +*> \endverbatim +*> +*> \param[out] SIGMA +*> \verbatim +*> SIGMA is DOUBLE PRECISION +*> The shift used to form L(+) D(+) L(+)^T. +*> \endverbatim +*> +*> \param[out] DPLUS +*> \verbatim +*> DPLUS is DOUBLE PRECISION array, dimension (N) +*> The N diagonal elements of the diagonal matrix D(+). +*> \endverbatim +*> +*> \param[out] LPLUS +*> \verbatim +*> LPLUS is DOUBLE PRECISION array, dimension (N-1) +*> The first (N-1) elements of LPLUS contain the subdiagonal +*> elements of the unit bidiagonal matrix L(+). +*> \endverbatim +*> +*> \param[out] WORK +*> \verbatim +*> WORK is DOUBLE PRECISION array, dimension (2*N) +*> Workspace. +*> \endverbatim +*> +*> \param[out] INFO +*> \verbatim +*> INFO is INTEGER +*> Signals processing OK (=0) or failure (=1) +*> \endverbatim +* +* Authors: +* ======== +* +*> \author Univ. of Tennessee +*> \author Univ. of California Berkeley +*> \author Univ. of Colorado Denver +*> \author NAG Ltd. +* +*> \date November 2011 +* +*> \ingroup auxOTHERauxiliary +* +*> \par Contributors: +* ================== +*> +*> Beresford Parlett, University of California, Berkeley, USA \n +*> Jim Demmel, University of California, Berkeley, USA \n +*> Inderjit Dhillon, University of Texas, Austin, USA \n +*> Osni Marques, LBNL/NERSC, USA \n +*> Christof Voemel, University of California, Berkeley, USA +* +* ===================================================================== + SUBROUTINE DLARRF( N, D, L, LD, CLSTRT, CLEND, + $ W, WGAP, WERR, + $ SPDIAM, CLGAPL, CLGAPR, PIVMIN, SIGMA, + $ DPLUS, LPLUS, WORK, INFO ) +* +* -- LAPACK auxiliary routine (version 3.4.0) -- +* -- LAPACK is a software package provided by Univ. of Tennessee, -- +* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- +* November 2011 +* +* .. Scalar Arguments .. + INTEGER CLSTRT, CLEND, INFO, N + DOUBLE PRECISION CLGAPL, CLGAPR, PIVMIN, SIGMA, SPDIAM +* .. +* .. Array Arguments .. + DOUBLE PRECISION D( * ), DPLUS( * ), L( * ), LD( * ), + $ LPLUS( * ), W( * ), WGAP( * ), WERR( * ), WORK( * ) +* .. +* +* ===================================================================== +* +* .. Parameters .. + DOUBLE PRECISION FOUR, MAXGROWTH1, MAXGROWTH2, ONE, QUART, TWO, + $ ZERO + PARAMETER ( ZERO = 0.0D0, ONE = 1.0D0, TWO = 2.0D0, + $ FOUR = 4.0D0, QUART = 0.25D0, + $ MAXGROWTH1 = 8.D0, + $ MAXGROWTH2 = 8.D0 ) +* .. +* .. Local Scalars .. + LOGICAL DORRR1, FORCER, NOFAIL, SAWNAN1, SAWNAN2, TRYRRR1 + INTEGER I, INDX, KTRY, KTRYMAX, SLEFT, SRIGHT, SHIFT + PARAMETER ( KTRYMAX = 1, SLEFT = 1, SRIGHT = 2 ) + DOUBLE PRECISION AVGAP, BESTSHIFT, CLWDTH, EPS, FACT, FAIL, + $ FAIL2, GROWTHBOUND, LDELTA, LDMAX, LSIGMA, + $ MAX1, MAX2, MINGAP, OLDP, PROD, RDELTA, RDMAX, + $ RRR1, RRR2, RSIGMA, S, SMLGROWTH, TMP, ZNM2 +* .. +* .. External Functions .. + LOGICAL DISNAN + DOUBLE PRECISION DLAMCH + EXTERNAL DISNAN, DLAMCH +* .. +* .. External Subroutines .. + EXTERNAL DCOPY +* .. +* .. Intrinsic Functions .. + INTRINSIC ABS +* .. +* .. Executable Statements .. +* + INFO = 0 + FACT = DBLE(2**KTRYMAX) + EPS = DLAMCH( 'Precision' ) + SHIFT = 0 + FORCER = .FALSE. + + +* Note that we cannot guarantee that for any of the shifts tried, +* the factorization has a small or even moderate element growth. +* There could be Ritz values at both ends of the cluster and despite +* backing off, there are examples where all factorizations tried +* (in IEEE mode, allowing zero pivots & infinities) have INFINITE +* element growth. +* For this reason, we should use PIVMIN in this subroutine so that at +* least the L D L^T factorization exists. It can be checked afterwards +* whether the element growth caused bad residuals/orthogonality. + +* Decide whether the code should accept the best among all +* representations despite large element growth or signal INFO=1 + NOFAIL = .TRUE. +* + +* Compute the average gap length of the cluster + CLWDTH = ABS(W(CLEND)-W(CLSTRT)) + WERR(CLEND) + WERR(CLSTRT) + AVGAP = CLWDTH / DBLE(CLEND-CLSTRT) + MINGAP = MIN(CLGAPL, CLGAPR) +* Initial values for shifts to both ends of cluster + LSIGMA = MIN(W( CLSTRT ),W( CLEND )) - WERR( CLSTRT ) + RSIGMA = MAX(W( CLSTRT ),W( CLEND )) + WERR( CLEND ) + +* Use a small fudge to make sure that we really shift to the outside + LSIGMA = LSIGMA - ABS(LSIGMA)* FOUR * EPS + RSIGMA = RSIGMA + ABS(RSIGMA)* FOUR * EPS + +* Compute upper bounds for how much to back off the initial shifts + LDMAX = QUART * MINGAP + TWO * PIVMIN + RDMAX = QUART * MINGAP + TWO * PIVMIN + + LDELTA = MAX(AVGAP,WGAP( CLSTRT ))/FACT + RDELTA = MAX(AVGAP,WGAP( CLEND-1 ))/FACT +* +* Initialize the record of the best representation found +* + S = DLAMCH( 'S' ) + SMLGROWTH = ONE / S + FAIL = DBLE(N-1)*MINGAP/(SPDIAM*EPS) + FAIL2 = DBLE(N-1)*MINGAP/(SPDIAM*SQRT(EPS)) + BESTSHIFT = LSIGMA +* +* while (KTRY <= KTRYMAX) + KTRY = 0 + GROWTHBOUND = MAXGROWTH1*SPDIAM + + 5 CONTINUE + SAWNAN1 = .FALSE. + SAWNAN2 = .FALSE. +* Ensure that we do not back off too much of the initial shifts + LDELTA = MIN(LDMAX,LDELTA) + RDELTA = MIN(RDMAX,RDELTA) + +* Compute the element growth when shifting to both ends of the cluster +* accept the shift if there is no element growth at one of the two ends + +* Left end + S = -LSIGMA + DPLUS( 1 ) = D( 1 ) + S + IF(ABS(DPLUS(1)).LT.PIVMIN) THEN + DPLUS(1) = -PIVMIN +* Need to set SAWNAN1 because refined RRR test should not be used +* in this case + SAWNAN1 = .TRUE. + ENDIF + MAX1 = ABS( DPLUS( 1 ) ) + DO 6 I = 1, N - 1 + LPLUS( I ) = LD( I ) / DPLUS( I ) + S = S*LPLUS( I )*L( I ) - LSIGMA + DPLUS( I+1 ) = D( I+1 ) + S + IF(ABS(DPLUS(I+1)).LT.PIVMIN) THEN + DPLUS(I+1) = -PIVMIN +* Need to set SAWNAN1 because refined RRR test should not be used +* in this case + SAWNAN1 = .TRUE. + ENDIF + MAX1 = MAX( MAX1,ABS(DPLUS(I+1)) ) + 6 CONTINUE + SAWNAN1 = SAWNAN1 .OR. DISNAN( MAX1 ) + + IF( FORCER .OR. + $ (MAX1.LE.GROWTHBOUND .AND. .NOT.SAWNAN1 ) ) THEN + SIGMA = LSIGMA + SHIFT = SLEFT + GOTO 100 + ENDIF + +* Right end + S = -RSIGMA + WORK( 1 ) = D( 1 ) + S + IF(ABS(WORK(1)).LT.PIVMIN) THEN + WORK(1) = -PIVMIN +* Need to set SAWNAN2 because refined RRR test should not be used +* in this case + SAWNAN2 = .TRUE. + ENDIF + MAX2 = ABS( WORK( 1 ) ) + DO 7 I = 1, N - 1 + WORK( N+I ) = LD( I ) / WORK( I ) + S = S*WORK( N+I )*L( I ) - RSIGMA + WORK( I+1 ) = D( I+1 ) + S + IF(ABS(WORK(I+1)).LT.PIVMIN) THEN + WORK(I+1) = -PIVMIN +* Need to set SAWNAN2 because refined RRR test should not be used +* in this case + SAWNAN2 = .TRUE. + ENDIF + MAX2 = MAX( MAX2,ABS(WORK(I+1)) ) + 7 CONTINUE + SAWNAN2 = SAWNAN2 .OR. DISNAN( MAX2 ) + + IF( FORCER .OR. + $ (MAX2.LE.GROWTHBOUND .AND. .NOT.SAWNAN2 ) ) THEN + SIGMA = RSIGMA + SHIFT = SRIGHT + GOTO 100 + ENDIF +* If we are at this point, both shifts led to too much element growth + +* Record the better of the two shifts (provided it didn't lead to NaN) + IF(SAWNAN1.AND.SAWNAN2) THEN +* both MAX1 and MAX2 are NaN + GOTO 50 + ELSE + IF( .NOT.SAWNAN1 ) THEN + INDX = 1 + IF(MAX1.LE.SMLGROWTH) THEN + SMLGROWTH = MAX1 + BESTSHIFT = LSIGMA + ENDIF + ENDIF + IF( .NOT.SAWNAN2 ) THEN + IF(SAWNAN1 .OR. MAX2.LE.MAX1) INDX = 2 + IF(MAX2.LE.SMLGROWTH) THEN + SMLGROWTH = MAX2 + BESTSHIFT = RSIGMA + ENDIF + ENDIF + ENDIF + +* If we are here, both the left and the right shift led to +* element growth. If the element growth is moderate, then +* we may still accept the representation, if it passes a +* refined test for RRR. This test supposes that no NaN occurred. +* Moreover, we use the refined RRR test only for isolated clusters. + IF((CLWDTH.LT.MINGAP/DBLE(128)) .AND. + $ (MIN(MAX1,MAX2).LT.FAIL2) + $ .AND.(.NOT.SAWNAN1).AND.(.NOT.SAWNAN2)) THEN + DORRR1 = .TRUE. + ELSE + DORRR1 = .FALSE. + ENDIF + TRYRRR1 = .TRUE. + IF( TRYRRR1 .AND. DORRR1 ) THEN + IF(INDX.EQ.1) THEN + TMP = ABS( DPLUS( N ) ) + ZNM2 = ONE + PROD = ONE + OLDP = ONE + DO 15 I = N-1, 1, -1 + IF( PROD .LE. EPS ) THEN + PROD = + $ ((DPLUS(I+1)*WORK(N+I+1))/(DPLUS(I)*WORK(N+I)))*OLDP + ELSE + PROD = PROD*ABS(WORK(N+I)) + END IF + OLDP = PROD + ZNM2 = ZNM2 + PROD**2 + TMP = MAX( TMP, ABS( DPLUS( I ) * PROD )) + 15 CONTINUE + RRR1 = TMP/( SPDIAM * SQRT( ZNM2 ) ) + IF (RRR1.LE.MAXGROWTH2) THEN + SIGMA = LSIGMA + SHIFT = SLEFT + GOTO 100 + ENDIF + ELSE IF(INDX.EQ.2) THEN + TMP = ABS( WORK( N ) ) + ZNM2 = ONE + PROD = ONE + OLDP = ONE + DO 16 I = N-1, 1, -1 + IF( PROD .LE. EPS ) THEN + PROD = ((WORK(I+1)*LPLUS(I+1))/(WORK(I)*LPLUS(I)))*OLDP + ELSE + PROD = PROD*ABS(LPLUS(I)) + END IF + OLDP = PROD + ZNM2 = ZNM2 + PROD**2 + TMP = MAX( TMP, ABS( WORK( I ) * PROD )) + 16 CONTINUE + RRR2 = TMP/( SPDIAM * SQRT( ZNM2 ) ) + IF (RRR2.LE.MAXGROWTH2) THEN + SIGMA = RSIGMA + SHIFT = SRIGHT + GOTO 100 + ENDIF + END IF + ENDIF + + 50 CONTINUE + + IF (KTRY.LT.KTRYMAX) THEN +* If we are here, both shifts failed also the RRR test. +* Back off to the outside + LSIGMA = MAX( LSIGMA - LDELTA, + $ LSIGMA - LDMAX) + RSIGMA = MIN( RSIGMA + RDELTA, + $ RSIGMA + RDMAX ) + LDELTA = TWO * LDELTA + RDELTA = TWO * RDELTA + KTRY = KTRY + 1 + GOTO 5 + ELSE +* None of the representations investigated satisfied our +* criteria. Take the best one we found. + IF((SMLGROWTH.LT.FAIL).OR.NOFAIL) THEN + LSIGMA = BESTSHIFT + RSIGMA = BESTSHIFT + FORCER = .TRUE. + GOTO 5 + ELSE + INFO = 1 + RETURN + ENDIF + END IF + + 100 CONTINUE + IF (SHIFT.EQ.SLEFT) THEN + ELSEIF (SHIFT.EQ.SRIGHT) THEN +* store new L and D back into DPLUS, LPLUS + CALL DCOPY( N, WORK, 1, DPLUS, 1 ) + CALL DCOPY( N-1, WORK(N+1), 1, LPLUS, 1 ) + ENDIF + + RETURN +* +* End of DLARRF +* + END diff --git a/applications/PUfoam/MoDeNaModels/CFD_tool_0D/src/eigen/src/dlarrj.f b/applications/PUfoam/MoDeNaModels/CFD_tool_0D/src/eigen/src/dlarrj.f new file mode 100644 index 000000000..3b4ec34c5 --- /dev/null +++ b/applications/PUfoam/MoDeNaModels/CFD_tool_0D/src/eigen/src/dlarrj.f @@ -0,0 +1,373 @@ +*> \brief \b DLARRJ +* +* =========== DOCUMENTATION =========== +* +* Online html documentation available at +* http://www.netlib.org/lapack/explore-html/ +* +*> \htmlonly +*> Download DLARRJ + dependencies +*> +*> [TGZ] +*> +*> [ZIP] +*> +*> [TXT] +*> \endhtmlonly +* +* Definition: +* =========== +* +* SUBROUTINE DLARRJ( N, D, E2, IFIRST, ILAST, +* RTOL, OFFSET, W, WERR, WORK, IWORK, +* PIVMIN, SPDIAM, INFO ) +* +* .. Scalar Arguments .. +* INTEGER IFIRST, ILAST, INFO, N, OFFSET +* DOUBLE PRECISION PIVMIN, RTOL, SPDIAM +* .. +* .. Array Arguments .. +* INTEGER IWORK( * ) +* DOUBLE PRECISION D( * ), E2( * ), W( * ), +* $ WERR( * ), WORK( * ) +* .. +* +* +*> \par Purpose: +* ============= +*> +*> \verbatim +*> +*> Given the initial eigenvalue approximations of T, DLARRJ +*> does bisection to refine the eigenvalues of T, +*> W( IFIRST-OFFSET ) through W( ILAST-OFFSET ), to more accuracy. Initial +*> guesses for these eigenvalues are input in W, the corresponding estimate +*> of the error in these guesses in WERR. During bisection, intervals +*> [left, right] are maintained by storing their mid-points and +*> semi-widths in the arrays W and WERR respectively. +*> \endverbatim +* +* Arguments: +* ========== +* +*> \param[in] N +*> \verbatim +*> N is INTEGER +*> The order of the matrix. +*> \endverbatim +*> +*> \param[in] D +*> \verbatim +*> D is DOUBLE PRECISION array, dimension (N) +*> The N diagonal elements of T. +*> \endverbatim +*> +*> \param[in] E2 +*> \verbatim +*> E2 is DOUBLE PRECISION array, dimension (N-1) +*> The Squares of the (N-1) subdiagonal elements of T. +*> \endverbatim +*> +*> \param[in] IFIRST +*> \verbatim +*> IFIRST is INTEGER +*> The index of the first eigenvalue to be computed. +*> \endverbatim +*> +*> \param[in] ILAST +*> \verbatim +*> ILAST is INTEGER +*> The index of the last eigenvalue to be computed. +*> \endverbatim +*> +*> \param[in] RTOL +*> \verbatim +*> RTOL is DOUBLE PRECISION +*> Tolerance for the convergence of the bisection intervals. +*> An interval [LEFT,RIGHT] has converged if +*> RIGHT-LEFT.LT.RTOL*MAX(|LEFT|,|RIGHT|). +*> \endverbatim +*> +*> \param[in] OFFSET +*> \verbatim +*> OFFSET is INTEGER +*> Offset for the arrays W and WERR, i.e., the IFIRST-OFFSET +*> through ILAST-OFFSET elements of these arrays are to be used. +*> \endverbatim +*> +*> \param[in,out] W +*> \verbatim +*> W is DOUBLE PRECISION array, dimension (N) +*> On input, W( IFIRST-OFFSET ) through W( ILAST-OFFSET ) are +*> estimates of the eigenvalues of L D L^T indexed IFIRST through +*> ILAST. +*> On output, these estimates are refined. +*> \endverbatim +*> +*> \param[in,out] WERR +*> \verbatim +*> WERR is DOUBLE PRECISION array, dimension (N) +*> On input, WERR( IFIRST-OFFSET ) through WERR( ILAST-OFFSET ) are +*> the errors in the estimates of the corresponding elements in W. +*> On output, these errors are refined. +*> \endverbatim +*> +*> \param[out] WORK +*> \verbatim +*> WORK is DOUBLE PRECISION array, dimension (2*N) +*> Workspace. +*> \endverbatim +*> +*> \param[out] IWORK +*> \verbatim +*> IWORK is INTEGER array, dimension (2*N) +*> Workspace. +*> \endverbatim +*> +*> \param[in] PIVMIN +*> \verbatim +*> PIVMIN is DOUBLE PRECISION +*> The minimum pivot in the Sturm sequence for T. +*> \endverbatim +*> +*> \param[in] SPDIAM +*> \verbatim +*> SPDIAM is DOUBLE PRECISION +*> The spectral diameter of T. +*> \endverbatim +*> +*> \param[out] INFO +*> \verbatim +*> INFO is INTEGER +*> Error flag. +*> \endverbatim +* +* Authors: +* ======== +* +*> \author Univ. of Tennessee +*> \author Univ. of California Berkeley +*> \author Univ. of Colorado Denver +*> \author NAG Ltd. +* +*> \date November 2011 +* +*> \ingroup auxOTHERauxiliary +* +*> \par Contributors: +* ================== +*> +*> Beresford Parlett, University of California, Berkeley, USA \n +*> Jim Demmel, University of California, Berkeley, USA \n +*> Inderjit Dhillon, University of Texas, Austin, USA \n +*> Osni Marques, LBNL/NERSC, USA \n +*> Christof Voemel, University of California, Berkeley, USA +* +* ===================================================================== + SUBROUTINE DLARRJ( N, D, E2, IFIRST, ILAST, + $ RTOL, OFFSET, W, WERR, WORK, IWORK, + $ PIVMIN, SPDIAM, INFO ) +* +* -- LAPACK auxiliary routine (version 3.4.0) -- +* -- LAPACK is a software package provided by Univ. of Tennessee, -- +* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- +* November 2011 +* +* .. Scalar Arguments .. + INTEGER IFIRST, ILAST, INFO, N, OFFSET + DOUBLE PRECISION PIVMIN, RTOL, SPDIAM +* .. +* .. Array Arguments .. + INTEGER IWORK( * ) + DOUBLE PRECISION D( * ), E2( * ), W( * ), + $ WERR( * ), WORK( * ) +* .. +* +* ===================================================================== +* +* .. Parameters .. + DOUBLE PRECISION ZERO, ONE, TWO, HALF + PARAMETER ( ZERO = 0.0D0, ONE = 1.0D0, TWO = 2.0D0, + $ HALF = 0.5D0 ) + INTEGER MAXITR +* .. +* .. Local Scalars .. + INTEGER CNT, I, I1, I2, II, ITER, J, K, NEXT, NINT, + $ OLNINT, P, PREV, SAVI1 + DOUBLE PRECISION DPLUS, FAC, LEFT, MID, RIGHT, S, TMP, WIDTH +* +* .. +* .. Intrinsic Functions .. + INTRINSIC ABS, MAX +* .. +* .. Executable Statements .. +* + INFO = 0 +* + MAXITR = INT( ( LOG( SPDIAM+PIVMIN )-LOG( PIVMIN ) ) / + $ LOG( TWO ) ) + 2 +* +* Initialize unconverged intervals in [ WORK(2*I-1), WORK(2*I) ]. +* The Sturm Count, Count( WORK(2*I-1) ) is arranged to be I-1, while +* Count( WORK(2*I) ) is stored in IWORK( 2*I ). The integer IWORK( 2*I-1 ) +* for an unconverged interval is set to the index of the next unconverged +* interval, and is -1 or 0 for a converged interval. Thus a linked +* list of unconverged intervals is set up. +* + + I1 = IFIRST + I2 = ILAST +* The number of unconverged intervals + NINT = 0 +* The last unconverged interval found + PREV = 0 + DO 75 I = I1, I2 + K = 2*I + II = I - OFFSET + LEFT = W( II ) - WERR( II ) + MID = W(II) + RIGHT = W( II ) + WERR( II ) + WIDTH = RIGHT - MID + TMP = MAX( ABS( LEFT ), ABS( RIGHT ) ) + +* The following test prevents the test of converged intervals + IF( WIDTH.LT.RTOL*TMP ) THEN +* This interval has already converged and does not need refinement. +* (Note that the gaps might change through refining the +* eigenvalues, however, they can only get bigger.) +* Remove it from the list. + IWORK( K-1 ) = -1 +* Make sure that I1 always points to the first unconverged interval + IF((I.EQ.I1).AND.(I.LT.I2)) I1 = I + 1 + IF((PREV.GE.I1).AND.(I.LE.I2)) IWORK( 2*PREV-1 ) = I + 1 + ELSE +* unconverged interval found + PREV = I +* Make sure that [LEFT,RIGHT] contains the desired eigenvalue +* +* Do while( CNT(LEFT).GT.I-1 ) +* + FAC = ONE + 20 CONTINUE + CNT = 0 + S = LEFT + DPLUS = D( 1 ) - S + IF( DPLUS.LT.ZERO ) CNT = CNT + 1 + DO 30 J = 2, N + DPLUS = D( J ) - S - E2( J-1 )/DPLUS + IF( DPLUS.LT.ZERO ) CNT = CNT + 1 + 30 CONTINUE + IF( CNT.GT.I-1 ) THEN + LEFT = LEFT - WERR( II )*FAC + FAC = TWO*FAC + GO TO 20 + END IF +* +* Do while( CNT(RIGHT).LT.I ) +* + FAC = ONE + 50 CONTINUE + CNT = 0 + S = RIGHT + DPLUS = D( 1 ) - S + IF( DPLUS.LT.ZERO ) CNT = CNT + 1 + DO 60 J = 2, N + DPLUS = D( J ) - S - E2( J-1 )/DPLUS + IF( DPLUS.LT.ZERO ) CNT = CNT + 1 + 60 CONTINUE + IF( CNT.LT.I ) THEN + RIGHT = RIGHT + WERR( II )*FAC + FAC = TWO*FAC + GO TO 50 + END IF + NINT = NINT + 1 + IWORK( K-1 ) = I + 1 + IWORK( K ) = CNT + END IF + WORK( K-1 ) = LEFT + WORK( K ) = RIGHT + 75 CONTINUE + + + SAVI1 = I1 +* +* Do while( NINT.GT.0 ), i.e. there are still unconverged intervals +* and while (ITER.LT.MAXITR) +* + ITER = 0 + 80 CONTINUE + PREV = I1 - 1 + I = I1 + OLNINT = NINT + + DO 100 P = 1, OLNINT + K = 2*I + II = I - OFFSET + NEXT = IWORK( K-1 ) + LEFT = WORK( K-1 ) + RIGHT = WORK( K ) + MID = HALF*( LEFT + RIGHT ) + +* semiwidth of interval + WIDTH = RIGHT - MID + TMP = MAX( ABS( LEFT ), ABS( RIGHT ) ) + + IF( ( WIDTH.LT.RTOL*TMP ) .OR. + $ (ITER.EQ.MAXITR) )THEN +* reduce number of unconverged intervals + NINT = NINT - 1 +* Mark interval as converged. + IWORK( K-1 ) = 0 + IF( I1.EQ.I ) THEN + I1 = NEXT + ELSE +* Prev holds the last unconverged interval previously examined + IF(PREV.GE.I1) IWORK( 2*PREV-1 ) = NEXT + END IF + I = NEXT + GO TO 100 + END IF + PREV = I +* +* Perform one bisection step +* + CNT = 0 + S = MID + DPLUS = D( 1 ) - S + IF( DPLUS.LT.ZERO ) CNT = CNT + 1 + DO 90 J = 2, N + DPLUS = D( J ) - S - E2( J-1 )/DPLUS + IF( DPLUS.LT.ZERO ) CNT = CNT + 1 + 90 CONTINUE + IF( CNT.LE.I-1 ) THEN + WORK( K-1 ) = MID + ELSE + WORK( K ) = MID + END IF + I = NEXT + + 100 CONTINUE + ITER = ITER + 1 +* do another loop if there are still unconverged intervals +* However, in the last iteration, all intervals are accepted +* since this is the best we can do. + IF( ( NINT.GT.0 ).AND.(ITER.LE.MAXITR) ) GO TO 80 +* +* +* At this point, all the intervals have converged + DO 110 I = SAVI1, ILAST + K = 2*I + II = I - OFFSET +* All intervals marked by '0' have been refined. + IF( IWORK( K-1 ).EQ.0 ) THEN + W( II ) = HALF*( WORK( K-1 )+WORK( K ) ) + WERR( II ) = WORK( K ) - W( II ) + END IF + 110 CONTINUE +* + + RETURN +* +* End of DLARRJ +* + END diff --git a/applications/PUfoam/MoDeNaModels/CFD_tool_0D/src/eigen/src/dlarrk.f b/applications/PUfoam/MoDeNaModels/CFD_tool_0D/src/eigen/src/dlarrk.f new file mode 100644 index 000000000..e4db3b942 --- /dev/null +++ b/applications/PUfoam/MoDeNaModels/CFD_tool_0D/src/eigen/src/dlarrk.f @@ -0,0 +1,249 @@ +*> \brief \b DLARRK +* +* =========== DOCUMENTATION =========== +* +* Online html documentation available at +* http://www.netlib.org/lapack/explore-html/ +* +*> \htmlonly +*> Download DLARRK + dependencies +*> +*> [TGZ] +*> +*> [ZIP] +*> +*> [TXT] +*> \endhtmlonly +* +* Definition: +* =========== +* +* SUBROUTINE DLARRK( N, IW, GL, GU, +* D, E2, PIVMIN, RELTOL, W, WERR, INFO) +* +* .. Scalar Arguments .. +* INTEGER INFO, IW, N +* DOUBLE PRECISION PIVMIN, RELTOL, GL, GU, W, WERR +* .. +* .. Array Arguments .. +* DOUBLE PRECISION D( * ), E2( * ) +* .. +* +* +*> \par Purpose: +* ============= +*> +*> \verbatim +*> +*> DLARRK computes one eigenvalue of a symmetric tridiagonal +*> matrix T to suitable accuracy. This is an auxiliary code to be +*> called from DSTEMR. +*> +*> To avoid overflow, the matrix must be scaled so that its +*> largest element is no greater than overflow**(1/2) * underflow**(1/4) in absolute value, and for greatest +*> accuracy, it should not be much smaller than that. +*> +*> See W. Kahan "Accurate Eigenvalues of a Symmetric Tridiagonal +*> Matrix", Report CS41, Computer Science Dept., Stanford +*> University, July 21, 1966. +*> \endverbatim +* +* Arguments: +* ========== +* +*> \param[in] N +*> \verbatim +*> N is INTEGER +*> The order of the tridiagonal matrix T. N >= 0. +*> \endverbatim +*> +*> \param[in] IW +*> \verbatim +*> IW is INTEGER +*> The index of the eigenvalues to be returned. +*> \endverbatim +*> +*> \param[in] GL +*> \verbatim +*> GL is DOUBLE PRECISION +*> \endverbatim +*> +*> \param[in] GU +*> \verbatim +*> GU is DOUBLE PRECISION +*> An upper and a lower bound on the eigenvalue. +*> \endverbatim +*> +*> \param[in] D +*> \verbatim +*> D is DOUBLE PRECISION array, dimension (N) +*> The n diagonal elements of the tridiagonal matrix T. +*> \endverbatim +*> +*> \param[in] E2 +*> \verbatim +*> E2 is DOUBLE PRECISION array, dimension (N-1) +*> The (n-1) squared off-diagonal elements of the tridiagonal matrix T. +*> \endverbatim +*> +*> \param[in] PIVMIN +*> \verbatim +*> PIVMIN is DOUBLE PRECISION +*> The minimum pivot allowed in the Sturm sequence for T. +*> \endverbatim +*> +*> \param[in] RELTOL +*> \verbatim +*> RELTOL is DOUBLE PRECISION +*> The minimum relative width of an interval. When an interval +*> is narrower than RELTOL times the larger (in +*> magnitude) endpoint, then it is considered to be +*> sufficiently small, i.e., converged. Note: this should +*> always be at least radix*machine epsilon. +*> \endverbatim +*> +*> \param[out] W +*> \verbatim +*> W is DOUBLE PRECISION +*> \endverbatim +*> +*> \param[out] WERR +*> \verbatim +*> WERR is DOUBLE PRECISION +*> The error bound on the corresponding eigenvalue approximation +*> in W. +*> \endverbatim +*> +*> \param[out] INFO +*> \verbatim +*> INFO is INTEGER +*> = 0: Eigenvalue converged +*> = -1: Eigenvalue did NOT converge +*> \endverbatim +* +*> \par Internal Parameters: +* ========================= +*> +*> \verbatim +*> FUDGE DOUBLE PRECISION, default = 2 +*> A "fudge factor" to widen the Gershgorin intervals. +*> \endverbatim +* +* Authors: +* ======== +* +*> \author Univ. of Tennessee +*> \author Univ. of California Berkeley +*> \author Univ. of Colorado Denver +*> \author NAG Ltd. +* +*> \date November 2011 +* +*> \ingroup auxOTHERauxiliary +* +* ===================================================================== + SUBROUTINE DLARRK( N, IW, GL, GU, + $ D, E2, PIVMIN, RELTOL, W, WERR, INFO) +* +* -- LAPACK auxiliary routine (version 3.4.0) -- +* -- LAPACK is a software package provided by Univ. of Tennessee, -- +* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- +* November 2011 +* +* .. Scalar Arguments .. + INTEGER INFO, IW, N + DOUBLE PRECISION PIVMIN, RELTOL, GL, GU, W, WERR +* .. +* .. Array Arguments .. + DOUBLE PRECISION D( * ), E2( * ) +* .. +* +* ===================================================================== +* +* .. Parameters .. + DOUBLE PRECISION FUDGE, HALF, TWO, ZERO + PARAMETER ( HALF = 0.5D0, TWO = 2.0D0, + $ FUDGE = TWO, ZERO = 0.0D0 ) +* .. +* .. Local Scalars .. + INTEGER I, IT, ITMAX, NEGCNT + DOUBLE PRECISION ATOLI, EPS, LEFT, MID, RIGHT, RTOLI, TMP1, + $ TMP2, TNORM +* .. +* .. External Functions .. + DOUBLE PRECISION DLAMCH + EXTERNAL DLAMCH +* .. +* .. Intrinsic Functions .. + INTRINSIC ABS, INT, LOG, MAX +* .. +* .. Executable Statements .. +* +* Get machine constants + EPS = DLAMCH( 'P' ) + + TNORM = MAX( ABS( GL ), ABS( GU ) ) + RTOLI = RELTOL + ATOLI = FUDGE*TWO*PIVMIN + + ITMAX = INT( ( LOG( TNORM+PIVMIN )-LOG( PIVMIN ) ) / + $ LOG( TWO ) ) + 2 + + INFO = -1 + + LEFT = GL - FUDGE*TNORM*EPS*N - FUDGE*TWO*PIVMIN + RIGHT = GU + FUDGE*TNORM*EPS*N + FUDGE*TWO*PIVMIN + IT = 0 + + 10 CONTINUE +* +* Check if interval converged or maximum number of iterations reached +* + TMP1 = ABS( RIGHT - LEFT ) + TMP2 = MAX( ABS(RIGHT), ABS(LEFT) ) + IF( TMP1.LT.MAX( ATOLI, PIVMIN, RTOLI*TMP2 ) ) THEN + INFO = 0 + GOTO 30 + ENDIF + IF(IT.GT.ITMAX) + $ GOTO 30 + +* +* Count number of negative pivots for mid-point +* + IT = IT + 1 + MID = HALF * (LEFT + RIGHT) + NEGCNT = 0 + TMP1 = D( 1 ) - MID + IF( ABS( TMP1 ).LT.PIVMIN ) + $ TMP1 = -PIVMIN + IF( TMP1.LE.ZERO ) + $ NEGCNT = NEGCNT + 1 +* + DO 20 I = 2, N + TMP1 = D( I ) - E2( I-1 ) / TMP1 - MID + IF( ABS( TMP1 ).LT.PIVMIN ) + $ TMP1 = -PIVMIN + IF( TMP1.LE.ZERO ) + $ NEGCNT = NEGCNT + 1 + 20 CONTINUE + + IF(NEGCNT.GE.IW) THEN + RIGHT = MID + ELSE + LEFT = MID + ENDIF + GOTO 10 + + 30 CONTINUE +* +* Converged or maximum number of iterations reached +* + W = HALF * (LEFT + RIGHT) + WERR = HALF * ABS( RIGHT - LEFT ) + + RETURN +* +* End of DLARRK +* + END diff --git a/applications/PUfoam/MoDeNaModels/CFD_tool_0D/src/eigen/src/dlarrr.f b/applications/PUfoam/MoDeNaModels/CFD_tool_0D/src/eigen/src/dlarrr.f new file mode 100644 index 000000000..df343fe4b --- /dev/null +++ b/applications/PUfoam/MoDeNaModels/CFD_tool_0D/src/eigen/src/dlarrr.f @@ -0,0 +1,204 @@ +*> \brief \b DLARRR +* +* =========== DOCUMENTATION =========== +* +* Online html documentation available at +* http://www.netlib.org/lapack/explore-html/ +* +*> \htmlonly +*> Download DLARRR + dependencies +*> +*> [TGZ] +*> +*> [ZIP] +*> +*> [TXT] +*> \endhtmlonly +* +* Definition: +* =========== +* +* SUBROUTINE DLARRR( N, D, E, INFO ) +* +* .. Scalar Arguments .. +* INTEGER N, INFO +* .. +* .. Array Arguments .. +* DOUBLE PRECISION D( * ), E( * ) +* .. +* +* +* +*> \par Purpose: +* ============= +*> +*> \verbatim +*> +*> Perform tests to decide whether the symmetric tridiagonal matrix T +*> warrants expensive computations which guarantee high relative accuracy +*> in the eigenvalues. +*> \endverbatim +* +* Arguments: +* ========== +* +*> \param[in] N +*> \verbatim +*> N is INTEGER +*> The order of the matrix. N > 0. +*> \endverbatim +*> +*> \param[in] D +*> \verbatim +*> D is DOUBLE PRECISION array, dimension (N) +*> The N diagonal elements of the tridiagonal matrix T. +*> \endverbatim +*> +*> \param[in,out] E +*> \verbatim +*> E is DOUBLE PRECISION array, dimension (N) +*> On entry, the first (N-1) entries contain the subdiagonal +*> elements of the tridiagonal matrix T; E(N) is set to ZERO. +*> \endverbatim +*> +*> \param[out] INFO +*> \verbatim +*> INFO is INTEGER +*> INFO = 0(default) : the matrix warrants computations preserving +*> relative accuracy. +*> INFO = 1 : the matrix warrants computations guaranteeing +*> only absolute accuracy. +*> \endverbatim +* +* Authors: +* ======== +* +*> \author Univ. of Tennessee +*> \author Univ. of California Berkeley +*> \author Univ. of Colorado Denver +*> \author NAG Ltd. +* +*> \date November 2011 +* +*> \ingroup auxOTHERauxiliary +* +*> \par Contributors: +* ================== +*> +*> Beresford Parlett, University of California, Berkeley, USA \n +*> Jim Demmel, University of California, Berkeley, USA \n +*> Inderjit Dhillon, University of Texas, Austin, USA \n +*> Osni Marques, LBNL/NERSC, USA \n +*> Christof Voemel, University of California, Berkeley, USA +* +* ===================================================================== + SUBROUTINE DLARRR( N, D, E, INFO ) +* +* -- LAPACK auxiliary routine (version 3.4.0) -- +* -- LAPACK is a software package provided by Univ. of Tennessee, -- +* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- +* November 2011 +* +* .. Scalar Arguments .. + INTEGER N, INFO +* .. +* .. Array Arguments .. + DOUBLE PRECISION D( * ), E( * ) +* .. +* +* +* ===================================================================== +* +* .. Parameters .. + DOUBLE PRECISION ZERO, RELCOND + PARAMETER ( ZERO = 0.0D0, + $ RELCOND = 0.999D0 ) +* .. +* .. Local Scalars .. + INTEGER I + LOGICAL YESREL + DOUBLE PRECISION EPS, SAFMIN, SMLNUM, RMIN, TMP, TMP2, + $ OFFDIG, OFFDIG2 + +* .. +* .. External Functions .. + DOUBLE PRECISION DLAMCH + EXTERNAL DLAMCH +* .. +* .. Intrinsic Functions .. + INTRINSIC ABS +* .. +* .. Executable Statements .. +* +* As a default, do NOT go for relative-accuracy preserving computations. + INFO = 1 + + SAFMIN = DLAMCH( 'Safe minimum' ) + EPS = DLAMCH( 'Precision' ) + SMLNUM = SAFMIN / EPS + RMIN = SQRT( SMLNUM ) + +* Tests for relative accuracy +* +* Test for scaled diagonal dominance +* Scale the diagonal entries to one and check whether the sum of the +* off-diagonals is less than one +* +* The sdd relative error bounds have a 1/(1- 2*x) factor in them, +* x = max(OFFDIG + OFFDIG2), so when x is close to 1/2, no relative +* accuracy is promised. In the notation of the code fragment below, +* 1/(1 - (OFFDIG + OFFDIG2)) is the condition number. +* We don't think it is worth going into "sdd mode" unless the relative +* condition number is reasonable, not 1/macheps. +* The threshold should be compatible with other thresholds used in the +* code. We set OFFDIG + OFFDIG2 <= .999 =: RELCOND, it corresponds +* to losing at most 3 decimal digits: 1 / (1 - (OFFDIG + OFFDIG2)) <= 1000 +* instead of the current OFFDIG + OFFDIG2 < 1 +* + YESREL = .TRUE. + OFFDIG = ZERO + TMP = SQRT(ABS(D(1))) + IF (TMP.LT.RMIN) YESREL = .FALSE. + IF(.NOT.YESREL) GOTO 11 + DO 10 I = 2, N + TMP2 = SQRT(ABS(D(I))) + IF (TMP2.LT.RMIN) YESREL = .FALSE. + IF(.NOT.YESREL) GOTO 11 + OFFDIG2 = ABS(E(I-1))/(TMP*TMP2) + IF(OFFDIG+OFFDIG2.GE.RELCOND) YESREL = .FALSE. + IF(.NOT.YESREL) GOTO 11 + TMP = TMP2 + OFFDIG = OFFDIG2 + 10 CONTINUE + 11 CONTINUE + + IF( YESREL ) THEN + INFO = 0 + RETURN + ELSE + ENDIF +* + +* +* *** MORE TO BE IMPLEMENTED *** +* + +* +* Test if the lower bidiagonal matrix L from T = L D L^T +* (zero shift facto) is well conditioned +* + +* +* Test if the upper bidiagonal matrix U from T = U D U^T +* (zero shift facto) is well conditioned. +* In this case, the matrix needs to be flipped and, at the end +* of the eigenvector computation, the flip needs to be applied +* to the computed eigenvectors (and the support) +* + +* + RETURN +* +* END OF DLARRR +* + END diff --git a/applications/PUfoam/MoDeNaModels/CFD_tool_0D/src/eigen/src/dlarrv.f b/applications/PUfoam/MoDeNaModels/CFD_tool_0D/src/eigen/src/dlarrv.f new file mode 100644 index 000000000..c5826356a --- /dev/null +++ b/applications/PUfoam/MoDeNaModels/CFD_tool_0D/src/eigen/src/dlarrv.f @@ -0,0 +1,1028 @@ +*> \brief \b DLARRV +* +* =========== DOCUMENTATION =========== +* +* Online html documentation available at +* http://www.netlib.org/lapack/explore-html/ +* +*> \htmlonly +*> Download DLARRV + dependencies +*> +*> [TGZ] +*> +*> [ZIP] +*> +*> [TXT] +*> \endhtmlonly +* +* Definition: +* =========== +* +* SUBROUTINE DLARRV( N, VL, VU, D, L, PIVMIN, +* ISPLIT, M, DOL, DOU, MINRGP, +* RTOL1, RTOL2, W, WERR, WGAP, +* IBLOCK, INDEXW, GERS, Z, LDZ, ISUPPZ, +* WORK, IWORK, INFO ) +* +* .. Scalar Arguments .. +* INTEGER DOL, DOU, INFO, LDZ, M, N +* DOUBLE PRECISION MINRGP, PIVMIN, RTOL1, RTOL2, VL, VU +* .. +* .. Array Arguments .. +* INTEGER IBLOCK( * ), INDEXW( * ), ISPLIT( * ), +* $ ISUPPZ( * ), IWORK( * ) +* DOUBLE PRECISION D( * ), GERS( * ), L( * ), W( * ), WERR( * ), +* $ WGAP( * ), WORK( * ) +* DOUBLE PRECISION Z( LDZ, * ) +* .. +* +* +*> \par Purpose: +* ============= +*> +*> \verbatim +*> +*> DLARRV computes the eigenvectors of the tridiagonal matrix +*> T = L D L**T given L, D and APPROXIMATIONS to the eigenvalues of L D L**T. +*> The input eigenvalues should have been computed by DLARRE. +*> \endverbatim +* +* Arguments: +* ========== +* +*> \param[in] N +*> \verbatim +*> N is INTEGER +*> The order of the matrix. N >= 0. +*> \endverbatim +*> +*> \param[in] VL +*> \verbatim +*> VL is DOUBLE PRECISION +*> \endverbatim +*> +*> \param[in] VU +*> \verbatim +*> VU is DOUBLE PRECISION +*> Lower and upper bounds of the interval that contains the desired +*> eigenvalues. VL < VU. Needed to compute gaps on the left or right +*> end of the extremal eigenvalues in the desired RANGE. +*> \endverbatim +*> +*> \param[in,out] D +*> \verbatim +*> D is DOUBLE PRECISION array, dimension (N) +*> On entry, the N diagonal elements of the diagonal matrix D. +*> On exit, D may be overwritten. +*> \endverbatim +*> +*> \param[in,out] L +*> \verbatim +*> L is DOUBLE PRECISION array, dimension (N) +*> On entry, the (N-1) subdiagonal elements of the unit +*> bidiagonal matrix L are in elements 1 to N-1 of L +*> (if the matrix is not splitted.) At the end of each block +*> is stored the corresponding shift as given by DLARRE. +*> On exit, L is overwritten. +*> \endverbatim +*> +*> \param[in] PIVMIN +*> \verbatim +*> PIVMIN is DOUBLE PRECISION +*> The minimum pivot allowed in the Sturm sequence. +*> \endverbatim +*> +*> \param[in] ISPLIT +*> \verbatim +*> ISPLIT is INTEGER array, dimension (N) +*> The splitting points, at which T breaks up into blocks. +*> The first block consists of rows/columns 1 to +*> ISPLIT( 1 ), the second of rows/columns ISPLIT( 1 )+1 +*> through ISPLIT( 2 ), etc. +*> \endverbatim +*> +*> \param[in] M +*> \verbatim +*> M is INTEGER +*> The total number of input eigenvalues. 0 <= M <= N. +*> \endverbatim +*> +*> \param[in] DOL +*> \verbatim +*> DOL is INTEGER +*> \endverbatim +*> +*> \param[in] DOU +*> \verbatim +*> DOU is INTEGER +*> If the user wants to compute only selected eigenvectors from all +*> the eigenvalues supplied, he can specify an index range DOL:DOU. +*> Or else the setting DOL=1, DOU=M should be applied. +*> Note that DOL and DOU refer to the order in which the eigenvalues +*> are stored in W. +*> If the user wants to compute only selected eigenpairs, then +*> the columns DOL-1 to DOU+1 of the eigenvector space Z contain the +*> computed eigenvectors. All other columns of Z are set to zero. +*> \endverbatim +*> +*> \param[in] MINRGP +*> \verbatim +*> MINRGP is DOUBLE PRECISION +*> \endverbatim +*> +*> \param[in] RTOL1 +*> \verbatim +*> RTOL1 is DOUBLE PRECISION +*> \endverbatim +*> +*> \param[in] RTOL2 +*> \verbatim +*> RTOL2 is DOUBLE PRECISION +*> Parameters for bisection. +*> An interval [LEFT,RIGHT] has converged if +*> RIGHT-LEFT.LT.MAX( RTOL1*GAP, RTOL2*MAX(|LEFT|,|RIGHT|) ) +*> \endverbatim +*> +*> \param[in,out] W +*> \verbatim +*> W is DOUBLE PRECISION array, dimension (N) +*> The first M elements of W contain the APPROXIMATE eigenvalues for +*> which eigenvectors are to be computed. The eigenvalues +*> should be grouped by split-off block and ordered from +*> smallest to largest within the block ( The output array +*> W from DLARRE is expected here ). Furthermore, they are with +*> respect to the shift of the corresponding root representation +*> for their block. On exit, W holds the eigenvalues of the +*> UNshifted matrix. +*> \endverbatim +*> +*> \param[in,out] WERR +*> \verbatim +*> WERR is DOUBLE PRECISION array, dimension (N) +*> The first M elements contain the semiwidth of the uncertainty +*> interval of the corresponding eigenvalue in W +*> \endverbatim +*> +*> \param[in,out] WGAP +*> \verbatim +*> WGAP is DOUBLE PRECISION array, dimension (N) +*> The separation from the right neighbor eigenvalue in W. +*> \endverbatim +*> +*> \param[in] IBLOCK +*> \verbatim +*> IBLOCK is INTEGER array, dimension (N) +*> The indices of the blocks (submatrices) associated with the +*> corresponding eigenvalues in W; IBLOCK(i)=1 if eigenvalue +*> W(i) belongs to the first block from the top, =2 if W(i) +*> belongs to the second block, etc. +*> \endverbatim +*> +*> \param[in] INDEXW +*> \verbatim +*> INDEXW is INTEGER array, dimension (N) +*> The indices of the eigenvalues within each block (submatrix); +*> for example, INDEXW(i)= 10 and IBLOCK(i)=2 imply that the +*> i-th eigenvalue W(i) is the 10-th eigenvalue in the second block. +*> \endverbatim +*> +*> \param[in] GERS +*> \verbatim +*> GERS is DOUBLE PRECISION array, dimension (2*N) +*> The N Gerschgorin intervals (the i-th Gerschgorin interval +*> is (GERS(2*i-1), GERS(2*i)). The Gerschgorin intervals should +*> be computed from the original UNshifted matrix. +*> \endverbatim +*> +*> \param[out] Z +*> \verbatim +*> Z is DOUBLE PRECISION array, dimension (LDZ, max(1,M) ) +*> If INFO = 0, the first M columns of Z contain the +*> orthonormal eigenvectors of the matrix T +*> corresponding to the input eigenvalues, with the i-th +*> column of Z holding the eigenvector associated with W(i). +*> Note: the user must ensure that at least max(1,M) columns are +*> supplied in the array Z. +*> \endverbatim +*> +*> \param[in] LDZ +*> \verbatim +*> LDZ is INTEGER +*> The leading dimension of the array Z. LDZ >= 1, and if +*> JOBZ = 'V', LDZ >= max(1,N). +*> \endverbatim +*> +*> \param[out] ISUPPZ +*> \verbatim +*> ISUPPZ is INTEGER array, dimension ( 2*max(1,M) ) +*> The support of the eigenvectors in Z, i.e., the indices +*> indicating the nonzero elements in Z. The I-th eigenvector +*> is nonzero only in elements ISUPPZ( 2*I-1 ) through +*> ISUPPZ( 2*I ). +*> \endverbatim +*> +*> \param[out] WORK +*> \verbatim +*> WORK is DOUBLE PRECISION array, dimension (12*N) +*> \endverbatim +*> +*> \param[out] IWORK +*> \verbatim +*> IWORK is INTEGER array, dimension (7*N) +*> \endverbatim +*> +*> \param[out] INFO +*> \verbatim +*> INFO is INTEGER +*> = 0: successful exit +*> +*> > 0: A problem occured in DLARRV. +*> < 0: One of the called subroutines signaled an internal problem. +*> Needs inspection of the corresponding parameter IINFO +*> for further information. +*> +*> =-1: Problem in DLARRB when refining a child's eigenvalues. +*> =-2: Problem in DLARRF when computing the RRR of a child. +*> When a child is inside a tight cluster, it can be difficult +*> to find an RRR. A partial remedy from the user's point of +*> view is to make the parameter MINRGP smaller and recompile. +*> However, as the orthogonality of the computed vectors is +*> proportional to 1/MINRGP, the user should be aware that +*> he might be trading in precision when he decreases MINRGP. +*> =-3: Problem in DLARRB when refining a single eigenvalue +*> after the Rayleigh correction was rejected. +*> = 5: The Rayleigh Quotient Iteration failed to converge to +*> full accuracy in MAXITR steps. +*> \endverbatim +* +* Authors: +* ======== +* +*> \author Univ. of Tennessee +*> \author Univ. of California Berkeley +*> \author Univ. of Colorado Denver +*> \author NAG Ltd. +* +*> \date November 2011 +* +*> \ingroup doubleOTHERauxiliary +* +*> \par Contributors: +* ================== +*> +*> Beresford Parlett, University of California, Berkeley, USA \n +*> Jim Demmel, University of California, Berkeley, USA \n +*> Inderjit Dhillon, University of Texas, Austin, USA \n +*> Osni Marques, LBNL/NERSC, USA \n +*> Christof Voemel, University of California, Berkeley, USA +* +* ===================================================================== + SUBROUTINE DLARRV( N, VL, VU, D, L, PIVMIN, + $ ISPLIT, M, DOL, DOU, MINRGP, + $ RTOL1, RTOL2, W, WERR, WGAP, + $ IBLOCK, INDEXW, GERS, Z, LDZ, ISUPPZ, + $ WORK, IWORK, INFO ) +* +* -- LAPACK auxiliary routine (version 3.4.0) -- +* -- LAPACK is a software package provided by Univ. of Tennessee, -- +* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- +* November 2011 +* +* .. Scalar Arguments .. + INTEGER DOL, DOU, INFO, LDZ, M, N + DOUBLE PRECISION MINRGP, PIVMIN, RTOL1, RTOL2, VL, VU +* .. +* .. Array Arguments .. + INTEGER IBLOCK( * ), INDEXW( * ), ISPLIT( * ), + $ ISUPPZ( * ), IWORK( * ) + DOUBLE PRECISION D( * ), GERS( * ), L( * ), W( * ), WERR( * ), + $ WGAP( * ), WORK( * ) + DOUBLE PRECISION Z( LDZ, * ) +* .. +* +* ===================================================================== +* +* .. Parameters .. + INTEGER MAXITR + PARAMETER ( MAXITR = 10 ) + DOUBLE PRECISION ZERO, ONE, TWO, THREE, FOUR, HALF + PARAMETER ( ZERO = 0.0D0, ONE = 1.0D0, + $ TWO = 2.0D0, THREE = 3.0D0, + $ FOUR = 4.0D0, HALF = 0.5D0) +* .. +* .. Local Scalars .. + LOGICAL ESKIP, NEEDBS, STP2II, TRYRQC, USEDBS, USEDRQ + INTEGER DONE, I, IBEGIN, IDONE, IEND, II, IINDC1, + $ IINDC2, IINDR, IINDWK, IINFO, IM, IN, INDEIG, + $ INDLD, INDLLD, INDWRK, ISUPMN, ISUPMX, ITER, + $ ITMP1, J, JBLK, K, MINIWSIZE, MINWSIZE, NCLUS, + $ NDEPTH, NEGCNT, NEWCLS, NEWFST, NEWFTT, NEWLST, + $ NEWSIZ, OFFSET, OLDCLS, OLDFST, OLDIEN, OLDLST, + $ OLDNCL, P, PARITY, Q, WBEGIN, WEND, WINDEX, + $ WINDMN, WINDPL, ZFROM, ZTO, ZUSEDL, ZUSEDU, + $ ZUSEDW + DOUBLE PRECISION BSTRES, BSTW, EPS, FUDGE, GAP, GAPTOL, GL, GU, + $ LAMBDA, LEFT, LGAP, MINGMA, NRMINV, RESID, + $ RGAP, RIGHT, RQCORR, RQTOL, SAVGAP, SGNDEF, + $ SIGMA, SPDIAM, SSIGMA, TAU, TMP, TOL, ZTZ +* .. +* .. External Functions .. + DOUBLE PRECISION DLAMCH + EXTERNAL DLAMCH +* .. +* .. External Subroutines .. + EXTERNAL DCOPY, DLAR1V, DLARRB, DLARRF, DLASET, + $ DSCAL +* .. +* .. Intrinsic Functions .. + INTRINSIC ABS, DBLE, MAX, MIN +* .. +* .. Executable Statements .. +* .. + +* The first N entries of WORK are reserved for the eigenvalues + INDLD = N+1 + INDLLD= 2*N+1 + INDWRK= 3*N+1 + MINWSIZE = 12 * N + + DO 5 I= 1,MINWSIZE + WORK( I ) = ZERO + 5 CONTINUE + +* IWORK(IINDR+1:IINDR+N) hold the twist indices R for the +* factorization used to compute the FP vector + IINDR = 0 +* IWORK(IINDC1+1:IINC2+N) are used to store the clusters of the current +* layer and the one above. + IINDC1 = N + IINDC2 = 2*N + IINDWK = 3*N + 1 + + MINIWSIZE = 7 * N + DO 10 I= 1,MINIWSIZE + IWORK( I ) = 0 + 10 CONTINUE + + ZUSEDL = 1 + IF(DOL.GT.1) THEN +* Set lower bound for use of Z + ZUSEDL = DOL-1 + ENDIF + ZUSEDU = M + IF(DOU.LT.M) THEN +* Set lower bound for use of Z + ZUSEDU = DOU+1 + ENDIF +* The width of the part of Z that is used + ZUSEDW = ZUSEDU - ZUSEDL + 1 + + + CALL DLASET( 'Full', N, ZUSEDW, ZERO, ZERO, + $ Z(1,ZUSEDL), LDZ ) + + EPS = DLAMCH( 'Precision' ) + RQTOL = TWO * EPS +* +* Set expert flags for standard code. + TRYRQC = .TRUE. + + IF((DOL.EQ.1).AND.(DOU.EQ.M)) THEN + ELSE +* Only selected eigenpairs are computed. Since the other evalues +* are not refined by RQ iteration, bisection has to compute to full +* accuracy. + RTOL1 = FOUR * EPS + RTOL2 = FOUR * EPS + ENDIF + +* The entries WBEGIN:WEND in W, WERR, WGAP correspond to the +* desired eigenvalues. The support of the nonzero eigenvector +* entries is contained in the interval IBEGIN:IEND. +* Remark that if k eigenpairs are desired, then the eigenvectors +* are stored in k contiguous columns of Z. + +* DONE is the number of eigenvectors already computed + DONE = 0 + IBEGIN = 1 + WBEGIN = 1 + DO 170 JBLK = 1, IBLOCK( M ) + IEND = ISPLIT( JBLK ) + SIGMA = L( IEND ) +* Find the eigenvectors of the submatrix indexed IBEGIN +* through IEND. + WEND = WBEGIN - 1 + 15 CONTINUE + IF( WEND.LT.M ) THEN + IF( IBLOCK( WEND+1 ).EQ.JBLK ) THEN + WEND = WEND + 1 + GO TO 15 + END IF + END IF + IF( WEND.LT.WBEGIN ) THEN + IBEGIN = IEND + 1 + GO TO 170 + ELSEIF( (WEND.LT.DOL).OR.(WBEGIN.GT.DOU) ) THEN + IBEGIN = IEND + 1 + WBEGIN = WEND + 1 + GO TO 170 + END IF + +* Find local spectral diameter of the block + GL = GERS( 2*IBEGIN-1 ) + GU = GERS( 2*IBEGIN ) + DO 20 I = IBEGIN+1 , IEND + GL = MIN( GERS( 2*I-1 ), GL ) + GU = MAX( GERS( 2*I ), GU ) + 20 CONTINUE + SPDIAM = GU - GL + +* OLDIEN is the last index of the previous block + OLDIEN = IBEGIN - 1 +* Calculate the size of the current block + IN = IEND - IBEGIN + 1 +* The number of eigenvalues in the current block + IM = WEND - WBEGIN + 1 + +* This is for a 1x1 block + IF( IBEGIN.EQ.IEND ) THEN + DONE = DONE+1 + Z( IBEGIN, WBEGIN ) = ONE + ISUPPZ( 2*WBEGIN-1 ) = IBEGIN + ISUPPZ( 2*WBEGIN ) = IBEGIN + W( WBEGIN ) = W( WBEGIN ) + SIGMA + WORK( WBEGIN ) = W( WBEGIN ) + IBEGIN = IEND + 1 + WBEGIN = WBEGIN + 1 + GO TO 170 + END IF + +* The desired (shifted) eigenvalues are stored in W(WBEGIN:WEND) +* Note that these can be approximations, in this case, the corresp. +* entries of WERR give the size of the uncertainty interval. +* The eigenvalue approximations will be refined when necessary as +* high relative accuracy is required for the computation of the +* corresponding eigenvectors. + CALL DCOPY( IM, W( WBEGIN ), 1, + $ WORK( WBEGIN ), 1 ) + +* We store in W the eigenvalue approximations w.r.t. the original +* matrix T. + DO 30 I=1,IM + W(WBEGIN+I-1) = W(WBEGIN+I-1)+SIGMA + 30 CONTINUE + + +* NDEPTH is the current depth of the representation tree + NDEPTH = 0 +* PARITY is either 1 or 0 + PARITY = 1 +* NCLUS is the number of clusters for the next level of the +* representation tree, we start with NCLUS = 1 for the root + NCLUS = 1 + IWORK( IINDC1+1 ) = 1 + IWORK( IINDC1+2 ) = IM + +* IDONE is the number of eigenvectors already computed in the current +* block + IDONE = 0 +* loop while( IDONE.LT.IM ) +* generate the representation tree for the current block and +* compute the eigenvectors + 40 CONTINUE + IF( IDONE.LT.IM ) THEN +* This is a crude protection against infinitely deep trees + IF( NDEPTH.GT.M ) THEN + INFO = -2 + RETURN + ENDIF +* breadth first processing of the current level of the representation +* tree: OLDNCL = number of clusters on current level + OLDNCL = NCLUS +* reset NCLUS to count the number of child clusters + NCLUS = 0 +* + PARITY = 1 - PARITY + IF( PARITY.EQ.0 ) THEN + OLDCLS = IINDC1 + NEWCLS = IINDC2 + ELSE + OLDCLS = IINDC2 + NEWCLS = IINDC1 + END IF +* Process the clusters on the current level + DO 150 I = 1, OLDNCL + J = OLDCLS + 2*I +* OLDFST, OLDLST = first, last index of current cluster. +* cluster indices start with 1 and are relative +* to WBEGIN when accessing W, WGAP, WERR, Z + OLDFST = IWORK( J-1 ) + OLDLST = IWORK( J ) + IF( NDEPTH.GT.0 ) THEN +* Retrieve relatively robust representation (RRR) of cluster +* that has been computed at the previous level +* The RRR is stored in Z and overwritten once the eigenvectors +* have been computed or when the cluster is refined + + IF((DOL.EQ.1).AND.(DOU.EQ.M)) THEN +* Get representation from location of the leftmost evalue +* of the cluster + J = WBEGIN + OLDFST - 1 + ELSE + IF(WBEGIN+OLDFST-1.LT.DOL) THEN +* Get representation from the left end of Z array + J = DOL - 1 + ELSEIF(WBEGIN+OLDFST-1.GT.DOU) THEN +* Get representation from the right end of Z array + J = DOU + ELSE + J = WBEGIN + OLDFST - 1 + ENDIF + ENDIF + CALL DCOPY( IN, Z( IBEGIN, J ), 1, D( IBEGIN ), 1 ) + CALL DCOPY( IN-1, Z( IBEGIN, J+1 ), 1, L( IBEGIN ), + $ 1 ) + SIGMA = Z( IEND, J+1 ) + +* Set the corresponding entries in Z to zero + CALL DLASET( 'Full', IN, 2, ZERO, ZERO, + $ Z( IBEGIN, J), LDZ ) + END IF + +* Compute DL and DLL of current RRR + DO 50 J = IBEGIN, IEND-1 + TMP = D( J )*L( J ) + WORK( INDLD-1+J ) = TMP + WORK( INDLLD-1+J ) = TMP*L( J ) + 50 CONTINUE + + IF( NDEPTH.GT.0 ) THEN +* P and Q are index of the first and last eigenvalue to compute +* within the current block + P = INDEXW( WBEGIN-1+OLDFST ) + Q = INDEXW( WBEGIN-1+OLDLST ) +* Offset for the arrays WORK, WGAP and WERR, i.e., the P-OFFSET +* through the Q-OFFSET elements of these arrays are to be used. +* OFFSET = P-OLDFST + OFFSET = INDEXW( WBEGIN ) - 1 +* perform limited bisection (if necessary) to get approximate +* eigenvalues to the precision needed. + CALL DLARRB( IN, D( IBEGIN ), + $ WORK(INDLLD+IBEGIN-1), + $ P, Q, RTOL1, RTOL2, OFFSET, + $ WORK(WBEGIN),WGAP(WBEGIN),WERR(WBEGIN), + $ WORK( INDWRK ), IWORK( IINDWK ), + $ PIVMIN, SPDIAM, IN, IINFO ) + IF( IINFO.NE.0 ) THEN + INFO = -1 + RETURN + ENDIF +* We also recompute the extremal gaps. W holds all eigenvalues +* of the unshifted matrix and must be used for computation +* of WGAP, the entries of WORK might stem from RRRs with +* different shifts. The gaps from WBEGIN-1+OLDFST to +* WBEGIN-1+OLDLST are correctly computed in DLARRB. +* However, we only allow the gaps to become greater since +* this is what should happen when we decrease WERR + IF( OLDFST.GT.1) THEN + WGAP( WBEGIN+OLDFST-2 ) = + $ MAX(WGAP(WBEGIN+OLDFST-2), + $ W(WBEGIN+OLDFST-1)-WERR(WBEGIN+OLDFST-1) + $ - W(WBEGIN+OLDFST-2)-WERR(WBEGIN+OLDFST-2) ) + ENDIF + IF( WBEGIN + OLDLST -1 .LT. WEND ) THEN + WGAP( WBEGIN+OLDLST-1 ) = + $ MAX(WGAP(WBEGIN+OLDLST-1), + $ W(WBEGIN+OLDLST)-WERR(WBEGIN+OLDLST) + $ - W(WBEGIN+OLDLST-1)-WERR(WBEGIN+OLDLST-1) ) + ENDIF +* Each time the eigenvalues in WORK get refined, we store +* the newly found approximation with all shifts applied in W + DO 53 J=OLDFST,OLDLST + W(WBEGIN+J-1) = WORK(WBEGIN+J-1)+SIGMA + 53 CONTINUE + END IF + +* Process the current node. + NEWFST = OLDFST + DO 140 J = OLDFST, OLDLST + IF( J.EQ.OLDLST ) THEN +* we are at the right end of the cluster, this is also the +* boundary of the child cluster + NEWLST = J + ELSE IF ( WGAP( WBEGIN + J -1).GE. + $ MINRGP* ABS( WORK(WBEGIN + J -1) ) ) THEN +* the right relative gap is big enough, the child cluster +* (NEWFST,..,NEWLST) is well separated from the following + NEWLST = J + ELSE +* inside a child cluster, the relative gap is not +* big enough. + GOTO 140 + END IF + +* Compute size of child cluster found + NEWSIZ = NEWLST - NEWFST + 1 + +* NEWFTT is the place in Z where the new RRR or the computed +* eigenvector is to be stored + IF((DOL.EQ.1).AND.(DOU.EQ.M)) THEN +* Store representation at location of the leftmost evalue +* of the cluster + NEWFTT = WBEGIN + NEWFST - 1 + ELSE + IF(WBEGIN+NEWFST-1.LT.DOL) THEN +* Store representation at the left end of Z array + NEWFTT = DOL - 1 + ELSEIF(WBEGIN+NEWFST-1.GT.DOU) THEN +* Store representation at the right end of Z array + NEWFTT = DOU + ELSE + NEWFTT = WBEGIN + NEWFST - 1 + ENDIF + ENDIF + + IF( NEWSIZ.GT.1) THEN +* +* Current child is not a singleton but a cluster. +* Compute and store new representation of child. +* +* +* Compute left and right cluster gap. +* +* LGAP and RGAP are not computed from WORK because +* the eigenvalue approximations may stem from RRRs +* different shifts. However, W hold all eigenvalues +* of the unshifted matrix. Still, the entries in WGAP +* have to be computed from WORK since the entries +* in W might be of the same order so that gaps are not +* exhibited correctly for very close eigenvalues. + IF( NEWFST.EQ.1 ) THEN + LGAP = MAX( ZERO, + $ W(WBEGIN)-WERR(WBEGIN) - VL ) + ELSE + LGAP = WGAP( WBEGIN+NEWFST-2 ) + ENDIF + RGAP = WGAP( WBEGIN+NEWLST-1 ) +* +* Compute left- and rightmost eigenvalue of child +* to high precision in order to shift as close +* as possible and obtain as large relative gaps +* as possible +* + DO 55 K =1,2 + IF(K.EQ.1) THEN + P = INDEXW( WBEGIN-1+NEWFST ) + ELSE + P = INDEXW( WBEGIN-1+NEWLST ) + ENDIF + OFFSET = INDEXW( WBEGIN ) - 1 + CALL DLARRB( IN, D(IBEGIN), + $ WORK( INDLLD+IBEGIN-1 ),P,P, + $ RQTOL, RQTOL, OFFSET, + $ WORK(WBEGIN),WGAP(WBEGIN), + $ WERR(WBEGIN),WORK( INDWRK ), + $ IWORK( IINDWK ), PIVMIN, SPDIAM, + $ IN, IINFO ) + 55 CONTINUE +* + IF((WBEGIN+NEWLST-1.LT.DOL).OR. + $ (WBEGIN+NEWFST-1.GT.DOU)) THEN +* if the cluster contains no desired eigenvalues +* skip the computation of that branch of the rep. tree +* +* We could skip before the refinement of the extremal +* eigenvalues of the child, but then the representation +* tree could be different from the one when nothing is +* skipped. For this reason we skip at this place. + IDONE = IDONE + NEWLST - NEWFST + 1 + GOTO 139 + ENDIF +* +* Compute RRR of child cluster. +* Note that the new RRR is stored in Z +* +* DLARRF needs LWORK = 2*N + CALL DLARRF( IN, D( IBEGIN ), L( IBEGIN ), + $ WORK(INDLD+IBEGIN-1), + $ NEWFST, NEWLST, WORK(WBEGIN), + $ WGAP(WBEGIN), WERR(WBEGIN), + $ SPDIAM, LGAP, RGAP, PIVMIN, TAU, + $ Z(IBEGIN, NEWFTT),Z(IBEGIN, NEWFTT+1), + $ WORK( INDWRK ), IINFO ) + IF( IINFO.EQ.0 ) THEN +* a new RRR for the cluster was found by DLARRF +* update shift and store it + SSIGMA = SIGMA + TAU + Z( IEND, NEWFTT+1 ) = SSIGMA +* WORK() are the midpoints and WERR() the semi-width +* Note that the entries in W are unchanged. + DO 116 K = NEWFST, NEWLST + FUDGE = + $ THREE*EPS*ABS(WORK(WBEGIN+K-1)) + WORK( WBEGIN + K - 1 ) = + $ WORK( WBEGIN + K - 1) - TAU + FUDGE = FUDGE + + $ FOUR*EPS*ABS(WORK(WBEGIN+K-1)) +* Fudge errors + WERR( WBEGIN + K - 1 ) = + $ WERR( WBEGIN + K - 1 ) + FUDGE +* Gaps are not fudged. Provided that WERR is small +* when eigenvalues are close, a zero gap indicates +* that a new representation is needed for resolving +* the cluster. A fudge could lead to a wrong decision +* of judging eigenvalues 'separated' which in +* reality are not. This could have a negative impact +* on the orthogonality of the computed eigenvectors. + 116 CONTINUE + + NCLUS = NCLUS + 1 + K = NEWCLS + 2*NCLUS + IWORK( K-1 ) = NEWFST + IWORK( K ) = NEWLST + ELSE + INFO = -2 + RETURN + ENDIF + ELSE +* +* Compute eigenvector of singleton +* + ITER = 0 +* + TOL = FOUR * LOG(DBLE(IN)) * EPS +* + K = NEWFST + WINDEX = WBEGIN + K - 1 + WINDMN = MAX(WINDEX - 1,1) + WINDPL = MIN(WINDEX + 1,M) + LAMBDA = WORK( WINDEX ) + DONE = DONE + 1 +* Check if eigenvector computation is to be skipped + IF((WINDEX.LT.DOL).OR. + $ (WINDEX.GT.DOU)) THEN + ESKIP = .TRUE. + GOTO 125 + ELSE + ESKIP = .FALSE. + ENDIF + LEFT = WORK( WINDEX ) - WERR( WINDEX ) + RIGHT = WORK( WINDEX ) + WERR( WINDEX ) + INDEIG = INDEXW( WINDEX ) +* Note that since we compute the eigenpairs for a child, +* all eigenvalue approximations are w.r.t the same shift. +* In this case, the entries in WORK should be used for +* computing the gaps since they exhibit even very small +* differences in the eigenvalues, as opposed to the +* entries in W which might "look" the same. + + IF( K .EQ. 1) THEN +* In the case RANGE='I' and with not much initial +* accuracy in LAMBDA and VL, the formula +* LGAP = MAX( ZERO, (SIGMA - VL) + LAMBDA ) +* can lead to an overestimation of the left gap and +* thus to inadequately early RQI 'convergence'. +* Prevent this by forcing a small left gap. + LGAP = EPS*MAX(ABS(LEFT),ABS(RIGHT)) + ELSE + LGAP = WGAP(WINDMN) + ENDIF + IF( K .EQ. IM) THEN +* In the case RANGE='I' and with not much initial +* accuracy in LAMBDA and VU, the formula +* can lead to an overestimation of the right gap and +* thus to inadequately early RQI 'convergence'. +* Prevent this by forcing a small right gap. + RGAP = EPS*MAX(ABS(LEFT),ABS(RIGHT)) + ELSE + RGAP = WGAP(WINDEX) + ENDIF + GAP = MIN( LGAP, RGAP ) + IF(( K .EQ. 1).OR.(K .EQ. IM)) THEN +* The eigenvector support can become wrong +* because significant entries could be cut off due to a +* large GAPTOL parameter in LAR1V. Prevent this. + GAPTOL = ZERO + ELSE + GAPTOL = GAP * EPS + ENDIF + ISUPMN = IN + ISUPMX = 1 +* Update WGAP so that it holds the minimum gap +* to the left or the right. This is crucial in the +* case where bisection is used to ensure that the +* eigenvalue is refined up to the required precision. +* The correct value is restored afterwards. + SAVGAP = WGAP(WINDEX) + WGAP(WINDEX) = GAP +* We want to use the Rayleigh Quotient Correction +* as often as possible since it converges quadratically +* when we are close enough to the desired eigenvalue. +* However, the Rayleigh Quotient can have the wrong sign +* and lead us away from the desired eigenvalue. In this +* case, the best we can do is to use bisection. + USEDBS = .FALSE. + USEDRQ = .FALSE. +* Bisection is initially turned off unless it is forced + NEEDBS = .NOT.TRYRQC + 120 CONTINUE +* Check if bisection should be used to refine eigenvalue + IF(NEEDBS) THEN +* Take the bisection as new iterate + USEDBS = .TRUE. + ITMP1 = IWORK( IINDR+WINDEX ) + OFFSET = INDEXW( WBEGIN ) - 1 + CALL DLARRB( IN, D(IBEGIN), + $ WORK(INDLLD+IBEGIN-1),INDEIG,INDEIG, + $ ZERO, TWO*EPS, OFFSET, + $ WORK(WBEGIN),WGAP(WBEGIN), + $ WERR(WBEGIN),WORK( INDWRK ), + $ IWORK( IINDWK ), PIVMIN, SPDIAM, + $ ITMP1, IINFO ) + IF( IINFO.NE.0 ) THEN + INFO = -3 + RETURN + ENDIF + LAMBDA = WORK( WINDEX ) +* Reset twist index from inaccurate LAMBDA to +* force computation of true MINGMA + IWORK( IINDR+WINDEX ) = 0 + ENDIF +* Given LAMBDA, compute the eigenvector. + CALL DLAR1V( IN, 1, IN, LAMBDA, D( IBEGIN ), + $ L( IBEGIN ), WORK(INDLD+IBEGIN-1), + $ WORK(INDLLD+IBEGIN-1), + $ PIVMIN, GAPTOL, Z( IBEGIN, WINDEX ), + $ .NOT.USEDBS, NEGCNT, ZTZ, MINGMA, + $ IWORK( IINDR+WINDEX ), ISUPPZ( 2*WINDEX-1 ), + $ NRMINV, RESID, RQCORR, WORK( INDWRK ) ) + IF(ITER .EQ. 0) THEN + BSTRES = RESID + BSTW = LAMBDA + ELSEIF(RESID.LT.BSTRES) THEN + BSTRES = RESID + BSTW = LAMBDA + ENDIF + ISUPMN = MIN(ISUPMN,ISUPPZ( 2*WINDEX-1 )) + ISUPMX = MAX(ISUPMX,ISUPPZ( 2*WINDEX )) + ITER = ITER + 1 + +* sin alpha <= |resid|/gap +* Note that both the residual and the gap are +* proportional to the matrix, so ||T|| doesn't play +* a role in the quotient + +* +* Convergence test for Rayleigh-Quotient iteration +* (omitted when Bisection has been used) +* + IF( RESID.GT.TOL*GAP .AND. ABS( RQCORR ).GT. + $ RQTOL*ABS( LAMBDA ) .AND. .NOT. USEDBS) + $ THEN +* We need to check that the RQCORR update doesn't +* move the eigenvalue away from the desired one and +* towards a neighbor. -> protection with bisection + IF(INDEIG.LE.NEGCNT) THEN +* The wanted eigenvalue lies to the left + SGNDEF = -ONE + ELSE +* The wanted eigenvalue lies to the right + SGNDEF = ONE + ENDIF +* We only use the RQCORR if it improves the +* the iterate reasonably. + IF( ( RQCORR*SGNDEF.GE.ZERO ) + $ .AND.( LAMBDA + RQCORR.LE. RIGHT) + $ .AND.( LAMBDA + RQCORR.GE. LEFT) + $ ) THEN + USEDRQ = .TRUE. +* Store new midpoint of bisection interval in WORK + IF(SGNDEF.EQ.ONE) THEN +* The current LAMBDA is on the left of the true +* eigenvalue + LEFT = LAMBDA +* We prefer to assume that the error estimate +* is correct. We could make the interval not +* as a bracket but to be modified if the RQCORR +* chooses to. In this case, the RIGHT side should +* be modified as follows: +* RIGHT = MAX(RIGHT, LAMBDA + RQCORR) + ELSE +* The current LAMBDA is on the right of the true +* eigenvalue + RIGHT = LAMBDA +* See comment about assuming the error estimate is +* correct above. +* LEFT = MIN(LEFT, LAMBDA + RQCORR) + ENDIF + WORK( WINDEX ) = + $ HALF * (RIGHT + LEFT) +* Take RQCORR since it has the correct sign and +* improves the iterate reasonably + LAMBDA = LAMBDA + RQCORR +* Update width of error interval + WERR( WINDEX ) = + $ HALF * (RIGHT-LEFT) + ELSE + NEEDBS = .TRUE. + ENDIF + IF(RIGHT-LEFT.LT.RQTOL*ABS(LAMBDA)) THEN +* The eigenvalue is computed to bisection accuracy +* compute eigenvector and stop + USEDBS = .TRUE. + GOTO 120 + ELSEIF( ITER.LT.MAXITR ) THEN + GOTO 120 + ELSEIF( ITER.EQ.MAXITR ) THEN + NEEDBS = .TRUE. + GOTO 120 + ELSE + INFO = 5 + RETURN + END IF + ELSE + STP2II = .FALSE. + IF(USEDRQ .AND. USEDBS .AND. + $ BSTRES.LE.RESID) THEN + LAMBDA = BSTW + STP2II = .TRUE. + ENDIF + IF (STP2II) THEN +* improve error angle by second step + CALL DLAR1V( IN, 1, IN, LAMBDA, + $ D( IBEGIN ), L( IBEGIN ), + $ WORK(INDLD+IBEGIN-1), + $ WORK(INDLLD+IBEGIN-1), + $ PIVMIN, GAPTOL, Z( IBEGIN, WINDEX ), + $ .NOT.USEDBS, NEGCNT, ZTZ, MINGMA, + $ IWORK( IINDR+WINDEX ), + $ ISUPPZ( 2*WINDEX-1 ), + $ NRMINV, RESID, RQCORR, WORK( INDWRK ) ) + ENDIF + WORK( WINDEX ) = LAMBDA + END IF +* +* Compute FP-vector support w.r.t. whole matrix +* + ISUPPZ( 2*WINDEX-1 ) = ISUPPZ( 2*WINDEX-1 )+OLDIEN + ISUPPZ( 2*WINDEX ) = ISUPPZ( 2*WINDEX )+OLDIEN + ZFROM = ISUPPZ( 2*WINDEX-1 ) + ZTO = ISUPPZ( 2*WINDEX ) + ISUPMN = ISUPMN + OLDIEN + ISUPMX = ISUPMX + OLDIEN +* Ensure vector is ok if support in the RQI has changed + IF(ISUPMN.LT.ZFROM) THEN + DO 122 II = ISUPMN,ZFROM-1 + Z( II, WINDEX ) = ZERO + 122 CONTINUE + ENDIF + IF(ISUPMX.GT.ZTO) THEN + DO 123 II = ZTO+1,ISUPMX + Z( II, WINDEX ) = ZERO + 123 CONTINUE + ENDIF + CALL DSCAL( ZTO-ZFROM+1, NRMINV, + $ Z( ZFROM, WINDEX ), 1 ) + 125 CONTINUE +* Update W + W( WINDEX ) = LAMBDA+SIGMA +* Recompute the gaps on the left and right +* But only allow them to become larger and not +* smaller (which can only happen through "bad" +* cancellation and doesn't reflect the theory +* where the initial gaps are underestimated due +* to WERR being too crude.) + IF(.NOT.ESKIP) THEN + IF( K.GT.1) THEN + WGAP( WINDMN ) = MAX( WGAP(WINDMN), + $ W(WINDEX)-WERR(WINDEX) + $ - W(WINDMN)-WERR(WINDMN) ) + ENDIF + IF( WINDEX.LT.WEND ) THEN + WGAP( WINDEX ) = MAX( SAVGAP, + $ W( WINDPL )-WERR( WINDPL ) + $ - W( WINDEX )-WERR( WINDEX) ) + ENDIF + ENDIF + IDONE = IDONE + 1 + ENDIF +* here ends the code for the current child +* + 139 CONTINUE +* Proceed to any remaining child nodes + NEWFST = J + 1 + 140 CONTINUE + 150 CONTINUE + NDEPTH = NDEPTH + 1 + GO TO 40 + END IF + IBEGIN = IEND + 1 + WBEGIN = WEND + 1 + 170 CONTINUE +* + + RETURN +* +* End of DLARRV +* + END diff --git a/applications/PUfoam/MoDeNaModels/CFD_tool_0D/src/eigen/src/dlartg.f b/applications/PUfoam/MoDeNaModels/CFD_tool_0D/src/eigen/src/dlartg.f new file mode 100644 index 000000000..aa68c3776 --- /dev/null +++ b/applications/PUfoam/MoDeNaModels/CFD_tool_0D/src/eigen/src/dlartg.f @@ -0,0 +1,204 @@ +*> \brief \b DLARTG +* +* =========== DOCUMENTATION =========== +* +* Online html documentation available at +* http://www.netlib.org/lapack/explore-html/ +* +*> \htmlonly +*> Download DLARTG + dependencies +*> +*> [TGZ] +*> +*> [ZIP] +*> +*> [TXT] +*> \endhtmlonly +* +* Definition: +* =========== +* +* SUBROUTINE DLARTG( F, G, CS, SN, R ) +* +* .. Scalar Arguments .. +* DOUBLE PRECISION CS, F, G, R, SN +* .. +* +* +*> \par Purpose: +* ============= +*> +*> \verbatim +*> +*> DLARTG generate a plane rotation so that +*> +*> [ CS SN ] . [ F ] = [ R ] where CS**2 + SN**2 = 1. +*> [ -SN CS ] [ G ] [ 0 ] +*> +*> This is a slower, more accurate version of the BLAS1 routine DROTG, +*> with the following other differences: +*> F and G are unchanged on return. +*> If G=0, then CS=1 and SN=0. +*> If F=0 and (G .ne. 0), then CS=0 and SN=1 without doing any +*> floating point operations (saves work in DBDSQR when +*> there are zeros on the diagonal). +*> +*> If F exceeds G in magnitude, CS will be positive. +*> \endverbatim +* +* Arguments: +* ========== +* +*> \param[in] F +*> \verbatim +*> F is DOUBLE PRECISION +*> The first component of vector to be rotated. +*> \endverbatim +*> +*> \param[in] G +*> \verbatim +*> G is DOUBLE PRECISION +*> The second component of vector to be rotated. +*> \endverbatim +*> +*> \param[out] CS +*> \verbatim +*> CS is DOUBLE PRECISION +*> The cosine of the rotation. +*> \endverbatim +*> +*> \param[out] SN +*> \verbatim +*> SN is DOUBLE PRECISION +*> The sine of the rotation. +*> \endverbatim +*> +*> \param[out] R +*> \verbatim +*> R is DOUBLE PRECISION +*> The nonzero component of the rotated vector. +*> +*> This version has a few statements commented out for thread safety +*> (machine parameters are computed on each entry). 10 feb 03, SJH. +*> \endverbatim +* +* Authors: +* ======== +* +*> \author Univ. of Tennessee +*> \author Univ. of California Berkeley +*> \author Univ. of Colorado Denver +*> \author NAG Ltd. +* +*> \date November 2011 +* +*> \ingroup auxOTHERauxiliary +* +* ===================================================================== + SUBROUTINE DLARTG( F, G, CS, SN, R ) +* +* -- LAPACK auxiliary routine (version 3.4.0) -- +* -- LAPACK is a software package provided by Univ. of Tennessee, -- +* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- +* November 2011 +* +* .. Scalar Arguments .. + DOUBLE PRECISION CS, F, G, R, SN +* .. +* +* ===================================================================== +* +* .. Parameters .. + DOUBLE PRECISION ZERO + PARAMETER ( ZERO = 0.0D0 ) + DOUBLE PRECISION ONE + PARAMETER ( ONE = 1.0D0 ) + DOUBLE PRECISION TWO + PARAMETER ( TWO = 2.0D0 ) +* .. +* .. Local Scalars .. +* LOGICAL FIRST + INTEGER COUNT, I + DOUBLE PRECISION EPS, F1, G1, SAFMIN, SAFMN2, SAFMX2, SCALE +* .. +* .. External Functions .. + DOUBLE PRECISION DLAMCH + EXTERNAL DLAMCH +* .. +* .. Intrinsic Functions .. + INTRINSIC ABS, INT, LOG, MAX, SQRT +* .. +* .. Save statement .. +* SAVE FIRST, SAFMX2, SAFMIN, SAFMN2 +* .. +* .. Data statements .. +* DATA FIRST / .TRUE. / +* .. +* .. Executable Statements .. +* +* IF( FIRST ) THEN + SAFMIN = DLAMCH( 'S' ) + EPS = DLAMCH( 'E' ) + SAFMN2 = DLAMCH( 'B' )**INT( LOG( SAFMIN / EPS ) / + $ LOG( DLAMCH( 'B' ) ) / TWO ) + SAFMX2 = ONE / SAFMN2 +* FIRST = .FALSE. +* END IF + IF( G.EQ.ZERO ) THEN + CS = ONE + SN = ZERO + R = F + ELSE IF( F.EQ.ZERO ) THEN + CS = ZERO + SN = ONE + R = G + ELSE + F1 = F + G1 = G + SCALE = MAX( ABS( F1 ), ABS( G1 ) ) + IF( SCALE.GE.SAFMX2 ) THEN + COUNT = 0 + 10 CONTINUE + COUNT = COUNT + 1 + F1 = F1*SAFMN2 + G1 = G1*SAFMN2 + SCALE = MAX( ABS( F1 ), ABS( G1 ) ) + IF( SCALE.GE.SAFMX2 ) + $ GO TO 10 + R = SQRT( F1**2+G1**2 ) + CS = F1 / R + SN = G1 / R + DO 20 I = 1, COUNT + R = R*SAFMX2 + 20 CONTINUE + ELSE IF( SCALE.LE.SAFMN2 ) THEN + COUNT = 0 + 30 CONTINUE + COUNT = COUNT + 1 + F1 = F1*SAFMX2 + G1 = G1*SAFMX2 + SCALE = MAX( ABS( F1 ), ABS( G1 ) ) + IF( SCALE.LE.SAFMN2 ) + $ GO TO 30 + R = SQRT( F1**2+G1**2 ) + CS = F1 / R + SN = G1 / R + DO 40 I = 1, COUNT + R = R*SAFMN2 + 40 CONTINUE + ELSE + R = SQRT( F1**2+G1**2 ) + CS = F1 / R + SN = G1 / R + END IF + IF( ABS( F ).GT.ABS( G ) .AND. CS.LT.ZERO ) THEN + CS = -CS + SN = -SN + R = -R + END IF + END IF + RETURN +* +* End of DLARTG +* + END diff --git a/applications/PUfoam/MoDeNaModels/CFD_tool_0D/src/eigen/src/dlaruv.f b/applications/PUfoam/MoDeNaModels/CFD_tool_0D/src/eigen/src/dlaruv.f new file mode 100644 index 000000000..70755a255 --- /dev/null +++ b/applications/PUfoam/MoDeNaModels/CFD_tool_0D/src/eigen/src/dlaruv.f @@ -0,0 +1,446 @@ +*> \brief \b DLARUV +* +* =========== DOCUMENTATION =========== +* +* Online html documentation available at +* http://www.netlib.org/lapack/explore-html/ +* +*> \htmlonly +*> Download DLARUV + dependencies +*> +*> [TGZ] +*> +*> [ZIP] +*> +*> [TXT] +*> \endhtmlonly +* +* Definition: +* =========== +* +* SUBROUTINE DLARUV( ISEED, N, X ) +* +* .. Scalar Arguments .. +* INTEGER N +* .. +* .. Array Arguments .. +* INTEGER ISEED( 4 ) +* DOUBLE PRECISION X( N ) +* .. +* +* +*> \par Purpose: +* ============= +*> +*> \verbatim +*> +*> DLARUV returns a vector of n random real numbers from a uniform (0,1) +*> distribution (n <= 128). +*> +*> This is an auxiliary routine called by DLARNV and ZLARNV. +*> \endverbatim +* +* Arguments: +* ========== +* +*> \param[in,out] ISEED +*> \verbatim +*> ISEED is INTEGER array, dimension (4) +*> On entry, the seed of the random number generator; the array +*> elements must be between 0 and 4095, and ISEED(4) must be +*> odd. +*> On exit, the seed is updated. +*> \endverbatim +*> +*> \param[in] N +*> \verbatim +*> N is INTEGER +*> The number of random numbers to be generated. N <= 128. +*> \endverbatim +*> +*> \param[out] X +*> \verbatim +*> X is DOUBLE PRECISION array, dimension (N) +*> The generated random numbers. +*> \endverbatim +* +* Authors: +* ======== +* +*> \author Univ. of Tennessee +*> \author Univ. of California Berkeley +*> \author Univ. of Colorado Denver +*> \author NAG Ltd. +* +*> \date November 2011 +* +*> \ingroup auxOTHERauxiliary +* +*> \par Further Details: +* ===================== +*> +*> \verbatim +*> +*> This routine uses a multiplicative congruential method with modulus +*> 2**48 and multiplier 33952834046453 (see G.S.Fishman, +*> 'Multiplicative congruential random number generators with modulus +*> 2**b: an exhaustive analysis for b = 32 and a partial analysis for +*> b = 48', Math. Comp. 189, pp 331-344, 1990). +*> +*> 48-bit integers are stored in 4 integer array elements with 12 bits +*> per element. Hence the routine is portable across machines with +*> integers of 32 bits or more. +*> \endverbatim +*> +* ===================================================================== + SUBROUTINE DLARUV( ISEED, N, X ) +* +* -- LAPACK auxiliary routine (version 3.4.0) -- +* -- LAPACK is a software package provided by Univ. of Tennessee, -- +* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- +* November 2011 +* +* .. Scalar Arguments .. + INTEGER N +* .. +* .. Array Arguments .. + INTEGER ISEED( 4 ) + DOUBLE PRECISION X( N ) +* .. +* +* ===================================================================== +* +* .. Parameters .. + DOUBLE PRECISION ONE + PARAMETER ( ONE = 1.0D0 ) + INTEGER LV, IPW2 + DOUBLE PRECISION R + PARAMETER ( LV = 128, IPW2 = 4096, R = ONE / IPW2 ) +* .. +* .. Local Scalars .. + INTEGER I, I1, I2, I3, I4, IT1, IT2, IT3, IT4, J +* .. +* .. Local Arrays .. + INTEGER MM( LV, 4 ) +* .. +* .. Intrinsic Functions .. + INTRINSIC DBLE, MIN, MOD +* .. +* .. Data statements .. + DATA ( MM( 1, J ), J = 1, 4 ) / 494, 322, 2508, + $ 2549 / + DATA ( MM( 2, J ), J = 1, 4 ) / 2637, 789, 3754, + $ 1145 / + DATA ( MM( 3, J ), J = 1, 4 ) / 255, 1440, 1766, + $ 2253 / + DATA ( MM( 4, J ), J = 1, 4 ) / 2008, 752, 3572, + $ 305 / + DATA ( MM( 5, J ), J = 1, 4 ) / 1253, 2859, 2893, + $ 3301 / + DATA ( MM( 6, J ), J = 1, 4 ) / 3344, 123, 307, + $ 1065 / + DATA ( MM( 7, J ), J = 1, 4 ) / 4084, 1848, 1297, + $ 3133 / + DATA ( MM( 8, J ), J = 1, 4 ) / 1739, 643, 3966, + $ 2913 / + DATA ( MM( 9, J ), J = 1, 4 ) / 3143, 2405, 758, + $ 3285 / + DATA ( MM( 10, J ), J = 1, 4 ) / 3468, 2638, 2598, + $ 1241 / + DATA ( MM( 11, J ), J = 1, 4 ) / 688, 2344, 3406, + $ 1197 / + DATA ( MM( 12, J ), J = 1, 4 ) / 1657, 46, 2922, + $ 3729 / + DATA ( MM( 13, J ), J = 1, 4 ) / 1238, 3814, 1038, + $ 2501 / + DATA ( MM( 14, J ), J = 1, 4 ) / 3166, 913, 2934, + $ 1673 / + DATA ( MM( 15, J ), J = 1, 4 ) / 1292, 3649, 2091, + $ 541 / + DATA ( MM( 16, J ), J = 1, 4 ) / 3422, 339, 2451, + $ 2753 / + DATA ( MM( 17, J ), J = 1, 4 ) / 1270, 3808, 1580, + $ 949 / + DATA ( MM( 18, J ), J = 1, 4 ) / 2016, 822, 1958, + $ 2361 / + DATA ( MM( 19, J ), J = 1, 4 ) / 154, 2832, 2055, + $ 1165 / + DATA ( MM( 20, J ), J = 1, 4 ) / 2862, 3078, 1507, + $ 4081 / + DATA ( MM( 21, J ), J = 1, 4 ) / 697, 3633, 1078, + $ 2725 / + DATA ( MM( 22, J ), J = 1, 4 ) / 1706, 2970, 3273, + $ 3305 / + DATA ( MM( 23, J ), J = 1, 4 ) / 491, 637, 17, + $ 3069 / + DATA ( MM( 24, J ), J = 1, 4 ) / 931, 2249, 854, + $ 3617 / + DATA ( MM( 25, J ), J = 1, 4 ) / 1444, 2081, 2916, + $ 3733 / + DATA ( MM( 26, J ), J = 1, 4 ) / 444, 4019, 3971, + $ 409 / + DATA ( MM( 27, J ), J = 1, 4 ) / 3577, 1478, 2889, + $ 2157 / + DATA ( MM( 28, J ), J = 1, 4 ) / 3944, 242, 3831, + $ 1361 / + DATA ( MM( 29, J ), J = 1, 4 ) / 2184, 481, 2621, + $ 3973 / + DATA ( MM( 30, J ), J = 1, 4 ) / 1661, 2075, 1541, + $ 1865 / + DATA ( MM( 31, J ), J = 1, 4 ) / 3482, 4058, 893, + $ 2525 / + DATA ( MM( 32, J ), J = 1, 4 ) / 657, 622, 736, + $ 1409 / + DATA ( MM( 33, J ), J = 1, 4 ) / 3023, 3376, 3992, + $ 3445 / + DATA ( MM( 34, J ), J = 1, 4 ) / 3618, 812, 787, + $ 3577 / + DATA ( MM( 35, J ), J = 1, 4 ) / 1267, 234, 2125, + $ 77 / + DATA ( MM( 36, J ), J = 1, 4 ) / 1828, 641, 2364, + $ 3761 / + DATA ( MM( 37, J ), J = 1, 4 ) / 164, 4005, 2460, + $ 2149 / + DATA ( MM( 38, J ), J = 1, 4 ) / 3798, 1122, 257, + $ 1449 / + DATA ( MM( 39, J ), J = 1, 4 ) / 3087, 3135, 1574, + $ 3005 / + DATA ( MM( 40, J ), J = 1, 4 ) / 2400, 2640, 3912, + $ 225 / + DATA ( MM( 41, J ), J = 1, 4 ) / 2870, 2302, 1216, + $ 85 / + DATA ( MM( 42, J ), J = 1, 4 ) / 3876, 40, 3248, + $ 3673 / + DATA ( MM( 43, J ), J = 1, 4 ) / 1905, 1832, 3401, + $ 3117 / + DATA ( MM( 44, J ), J = 1, 4 ) / 1593, 2247, 2124, + $ 3089 / + DATA ( MM( 45, J ), J = 1, 4 ) / 1797, 2034, 2762, + $ 1349 / + DATA ( MM( 46, J ), J = 1, 4 ) / 1234, 2637, 149, + $ 2057 / + DATA ( MM( 47, J ), J = 1, 4 ) / 3460, 1287, 2245, + $ 413 / + DATA ( MM( 48, J ), J = 1, 4 ) / 328, 1691, 166, + $ 65 / + DATA ( MM( 49, J ), J = 1, 4 ) / 2861, 496, 466, + $ 1845 / + DATA ( MM( 50, J ), J = 1, 4 ) / 1950, 1597, 4018, + $ 697 / + DATA ( MM( 51, J ), J = 1, 4 ) / 617, 2394, 1399, + $ 3085 / + DATA ( MM( 52, J ), J = 1, 4 ) / 2070, 2584, 190, + $ 3441 / + DATA ( MM( 53, J ), J = 1, 4 ) / 3331, 1843, 2879, + $ 1573 / + DATA ( MM( 54, J ), J = 1, 4 ) / 769, 336, 153, + $ 3689 / + DATA ( MM( 55, J ), J = 1, 4 ) / 1558, 1472, 2320, + $ 2941 / + DATA ( MM( 56, J ), J = 1, 4 ) / 2412, 2407, 18, + $ 929 / + DATA ( MM( 57, J ), J = 1, 4 ) / 2800, 433, 712, + $ 533 / + DATA ( MM( 58, J ), J = 1, 4 ) / 189, 2096, 2159, + $ 2841 / + DATA ( MM( 59, J ), J = 1, 4 ) / 287, 1761, 2318, + $ 4077 / + DATA ( MM( 60, J ), J = 1, 4 ) / 2045, 2810, 2091, + $ 721 / + DATA ( MM( 61, J ), J = 1, 4 ) / 1227, 566, 3443, + $ 2821 / + DATA ( MM( 62, J ), J = 1, 4 ) / 2838, 442, 1510, + $ 2249 / + DATA ( MM( 63, J ), J = 1, 4 ) / 209, 41, 449, + $ 2397 / + DATA ( MM( 64, J ), J = 1, 4 ) / 2770, 1238, 1956, + $ 2817 / + DATA ( MM( 65, J ), J = 1, 4 ) / 3654, 1086, 2201, + $ 245 / + DATA ( MM( 66, J ), J = 1, 4 ) / 3993, 603, 3137, + $ 1913 / + DATA ( MM( 67, J ), J = 1, 4 ) / 192, 840, 3399, + $ 1997 / + DATA ( MM( 68, J ), J = 1, 4 ) / 2253, 3168, 1321, + $ 3121 / + DATA ( MM( 69, J ), J = 1, 4 ) / 3491, 1499, 2271, + $ 997 / + DATA ( MM( 70, J ), J = 1, 4 ) / 2889, 1084, 3667, + $ 1833 / + DATA ( MM( 71, J ), J = 1, 4 ) / 2857, 3438, 2703, + $ 2877 / + DATA ( MM( 72, J ), J = 1, 4 ) / 2094, 2408, 629, + $ 1633 / + DATA ( MM( 73, J ), J = 1, 4 ) / 1818, 1589, 2365, + $ 981 / + DATA ( MM( 74, J ), J = 1, 4 ) / 688, 2391, 2431, + $ 2009 / + DATA ( MM( 75, J ), J = 1, 4 ) / 1407, 288, 1113, + $ 941 / + DATA ( MM( 76, J ), J = 1, 4 ) / 634, 26, 3922, + $ 2449 / + DATA ( MM( 77, J ), J = 1, 4 ) / 3231, 512, 2554, + $ 197 / + DATA ( MM( 78, J ), J = 1, 4 ) / 815, 1456, 184, + $ 2441 / + DATA ( MM( 79, J ), J = 1, 4 ) / 3524, 171, 2099, + $ 285 / + DATA ( MM( 80, J ), J = 1, 4 ) / 1914, 1677, 3228, + $ 1473 / + DATA ( MM( 81, J ), J = 1, 4 ) / 516, 2657, 4012, + $ 2741 / + DATA ( MM( 82, J ), J = 1, 4 ) / 164, 2270, 1921, + $ 3129 / + DATA ( MM( 83, J ), J = 1, 4 ) / 303, 2587, 3452, + $ 909 / + DATA ( MM( 84, J ), J = 1, 4 ) / 2144, 2961, 3901, + $ 2801 / + DATA ( MM( 85, J ), J = 1, 4 ) / 3480, 1970, 572, + $ 421 / + DATA ( MM( 86, J ), J = 1, 4 ) / 119, 1817, 3309, + $ 4073 / + DATA ( MM( 87, J ), J = 1, 4 ) / 3357, 676, 3171, + $ 2813 / + DATA ( MM( 88, J ), J = 1, 4 ) / 837, 1410, 817, + $ 2337 / + DATA ( MM( 89, J ), J = 1, 4 ) / 2826, 3723, 3039, + $ 1429 / + DATA ( MM( 90, J ), J = 1, 4 ) / 2332, 2803, 1696, + $ 1177 / + DATA ( MM( 91, J ), J = 1, 4 ) / 2089, 3185, 1256, + $ 1901 / + DATA ( MM( 92, J ), J = 1, 4 ) / 3780, 184, 3715, + $ 81 / + DATA ( MM( 93, J ), J = 1, 4 ) / 1700, 663, 2077, + $ 1669 / + DATA ( MM( 94, J ), J = 1, 4 ) / 3712, 499, 3019, + $ 2633 / + DATA ( MM( 95, J ), J = 1, 4 ) / 150, 3784, 1497, + $ 2269 / + DATA ( MM( 96, J ), J = 1, 4 ) / 2000, 1631, 1101, + $ 129 / + DATA ( MM( 97, J ), J = 1, 4 ) / 3375, 1925, 717, + $ 1141 / + DATA ( MM( 98, J ), J = 1, 4 ) / 1621, 3912, 51, + $ 249 / + DATA ( MM( 99, J ), J = 1, 4 ) / 3090, 1398, 981, + $ 3917 / + DATA ( MM( 100, J ), J = 1, 4 ) / 3765, 1349, 1978, + $ 2481 / + DATA ( MM( 101, J ), J = 1, 4 ) / 1149, 1441, 1813, + $ 3941 / + DATA ( MM( 102, J ), J = 1, 4 ) / 3146, 2224, 3881, + $ 2217 / + DATA ( MM( 103, J ), J = 1, 4 ) / 33, 2411, 76, + $ 2749 / + DATA ( MM( 104, J ), J = 1, 4 ) / 3082, 1907, 3846, + $ 3041 / + DATA ( MM( 105, J ), J = 1, 4 ) / 2741, 3192, 3694, + $ 1877 / + DATA ( MM( 106, J ), J = 1, 4 ) / 359, 2786, 1682, + $ 345 / + DATA ( MM( 107, J ), J = 1, 4 ) / 3316, 382, 124, + $ 2861 / + DATA ( MM( 108, J ), J = 1, 4 ) / 1749, 37, 1660, + $ 1809 / + DATA ( MM( 109, J ), J = 1, 4 ) / 185, 759, 3997, + $ 3141 / + DATA ( MM( 110, J ), J = 1, 4 ) / 2784, 2948, 479, + $ 2825 / + DATA ( MM( 111, J ), J = 1, 4 ) / 2202, 1862, 1141, + $ 157 / + DATA ( MM( 112, J ), J = 1, 4 ) / 2199, 3802, 886, + $ 2881 / + DATA ( MM( 113, J ), J = 1, 4 ) / 1364, 2423, 3514, + $ 3637 / + DATA ( MM( 114, J ), J = 1, 4 ) / 1244, 2051, 1301, + $ 1465 / + DATA ( MM( 115, J ), J = 1, 4 ) / 2020, 2295, 3604, + $ 2829 / + DATA ( MM( 116, J ), J = 1, 4 ) / 3160, 1332, 1888, + $ 2161 / + DATA ( MM( 117, J ), J = 1, 4 ) / 2785, 1832, 1836, + $ 3365 / + DATA ( MM( 118, J ), J = 1, 4 ) / 2772, 2405, 1990, + $ 361 / + DATA ( MM( 119, J ), J = 1, 4 ) / 1217, 3638, 2058, + $ 2685 / + DATA ( MM( 120, J ), J = 1, 4 ) / 1822, 3661, 692, + $ 3745 / + DATA ( MM( 121, J ), J = 1, 4 ) / 1245, 327, 1194, + $ 2325 / + DATA ( MM( 122, J ), J = 1, 4 ) / 2252, 3660, 20, + $ 3609 / + DATA ( MM( 123, J ), J = 1, 4 ) / 3904, 716, 3285, + $ 3821 / + DATA ( MM( 124, J ), J = 1, 4 ) / 2774, 1842, 2046, + $ 3537 / + DATA ( MM( 125, J ), J = 1, 4 ) / 997, 3987, 2107, + $ 517 / + DATA ( MM( 126, J ), J = 1, 4 ) / 2573, 1368, 3508, + $ 3017 / + DATA ( MM( 127, J ), J = 1, 4 ) / 1148, 1848, 3525, + $ 2141 / + DATA ( MM( 128, J ), J = 1, 4 ) / 545, 2366, 3801, + $ 1537 / +* .. +* .. Executable Statements .. +* + I1 = ISEED( 1 ) + I2 = ISEED( 2 ) + I3 = ISEED( 3 ) + I4 = ISEED( 4 ) +* + DO 10 I = 1, MIN( N, LV ) +* + 20 CONTINUE +* +* Multiply the seed by i-th power of the multiplier modulo 2**48 +* + IT4 = I4*MM( I, 4 ) + IT3 = IT4 / IPW2 + IT4 = IT4 - IPW2*IT3 + IT3 = IT3 + I3*MM( I, 4 ) + I4*MM( I, 3 ) + IT2 = IT3 / IPW2 + IT3 = IT3 - IPW2*IT2 + IT2 = IT2 + I2*MM( I, 4 ) + I3*MM( I, 3 ) + I4*MM( I, 2 ) + IT1 = IT2 / IPW2 + IT2 = IT2 - IPW2*IT1 + IT1 = IT1 + I1*MM( I, 4 ) + I2*MM( I, 3 ) + I3*MM( I, 2 ) + + $ I4*MM( I, 1 ) + IT1 = MOD( IT1, IPW2 ) +* +* Convert 48-bit integer to a real number in the interval (0,1) +* + X( I ) = R*( DBLE( IT1 )+R*( DBLE( IT2 )+R*( DBLE( IT3 )+R* + $ DBLE( IT4 ) ) ) ) +* + IF (X( I ).EQ.1.0D0) THEN +* If a real number has n bits of precision, and the first +* n bits of the 48-bit integer above happen to be all 1 (which +* will occur about once every 2**n calls), then X( I ) will +* be rounded to exactly 1.0. +* Since X( I ) is not supposed to return exactly 0.0 or 1.0, +* the statistically correct thing to do in this situation is +* simply to iterate again. +* N.B. the case X( I ) = 0.0 should not be possible. + I1 = I1 + 2 + I2 = I2 + 2 + I3 = I3 + 2 + I4 = I4 + 2 + GOTO 20 + END IF +* + 10 CONTINUE +* +* Return final value of seed +* + ISEED( 1 ) = IT1 + ISEED( 2 ) = IT2 + ISEED( 3 ) = IT3 + ISEED( 4 ) = IT4 + RETURN +* +* End of DLARUV +* + END diff --git a/applications/PUfoam/MoDeNaModels/CFD_tool_0D/src/eigen/src/dlascl.f b/applications/PUfoam/MoDeNaModels/CFD_tool_0D/src/eigen/src/dlascl.f new file mode 100644 index 000000000..5b4d3b24e --- /dev/null +++ b/applications/PUfoam/MoDeNaModels/CFD_tool_0D/src/eigen/src/dlascl.f @@ -0,0 +1,364 @@ +*> \brief \b DLASCL +* +* =========== DOCUMENTATION =========== +* +* Online html documentation available at +* http://www.netlib.org/lapack/explore-html/ +* +*> \htmlonly +*> Download DLASCL + dependencies +*> +*> [TGZ] +*> +*> [ZIP] +*> +*> [TXT] +*> \endhtmlonly +* +* Definition: +* =========== +* +* SUBROUTINE DLASCL( TYPE, KL, KU, CFROM, CTO, M, N, A, LDA, INFO ) +* +* .. Scalar Arguments .. +* CHARACTER TYPE +* INTEGER INFO, KL, KU, LDA, M, N +* DOUBLE PRECISION CFROM, CTO +* .. +* .. Array Arguments .. +* DOUBLE PRECISION A( LDA, * ) +* .. +* +* +*> \par Purpose: +* ============= +*> +*> \verbatim +*> +*> DLASCL multiplies the M by N real matrix A by the real scalar +*> CTO/CFROM. This is done without over/underflow as long as the final +*> result CTO*A(I,J)/CFROM does not over/underflow. TYPE specifies that +*> A may be full, upper triangular, lower triangular, upper Hessenberg, +*> or banded. +*> \endverbatim +* +* Arguments: +* ========== +* +*> \param[in] TYPE +*> \verbatim +*> TYPE is CHARACTER*1 +*> TYPE indices the storage type of the input matrix. +*> = 'G': A is a full matrix. +*> = 'L': A is a lower triangular matrix. +*> = 'U': A is an upper triangular matrix. +*> = 'H': A is an upper Hessenberg matrix. +*> = 'B': A is a symmetric band matrix with lower bandwidth KL +*> and upper bandwidth KU and with the only the lower +*> half stored. +*> = 'Q': A is a symmetric band matrix with lower bandwidth KL +*> and upper bandwidth KU and with the only the upper +*> half stored. +*> = 'Z': A is a band matrix with lower bandwidth KL and upper +*> bandwidth KU. See DGBTRF for storage details. +*> \endverbatim +*> +*> \param[in] KL +*> \verbatim +*> KL is INTEGER +*> The lower bandwidth of A. Referenced only if TYPE = 'B', +*> 'Q' or 'Z'. +*> \endverbatim +*> +*> \param[in] KU +*> \verbatim +*> KU is INTEGER +*> The upper bandwidth of A. Referenced only if TYPE = 'B', +*> 'Q' or 'Z'. +*> \endverbatim +*> +*> \param[in] CFROM +*> \verbatim +*> CFROM is DOUBLE PRECISION +*> \endverbatim +*> +*> \param[in] CTO +*> \verbatim +*> CTO is DOUBLE PRECISION +*> +*> The matrix A is multiplied by CTO/CFROM. A(I,J) is computed +*> without over/underflow if the final result CTO*A(I,J)/CFROM +*> can be represented without over/underflow. CFROM must be +*> nonzero. +*> \endverbatim +*> +*> \param[in] M +*> \verbatim +*> M is INTEGER +*> The number of rows of the matrix A. M >= 0. +*> \endverbatim +*> +*> \param[in] N +*> \verbatim +*> N is INTEGER +*> The number of columns of the matrix A. N >= 0. +*> \endverbatim +*> +*> \param[in,out] A +*> \verbatim +*> A is DOUBLE PRECISION array, dimension (LDA,N) +*> The matrix to be multiplied by CTO/CFROM. See TYPE for the +*> storage type. +*> \endverbatim +*> +*> \param[in] LDA +*> \verbatim +*> LDA is INTEGER +*> The leading dimension of the array A. LDA >= max(1,M). +*> \endverbatim +*> +*> \param[out] INFO +*> \verbatim +*> INFO is INTEGER +*> 0 - successful exit +*> <0 - if INFO = -i, the i-th argument had an illegal value. +*> \endverbatim +* +* Authors: +* ======== +* +*> \author Univ. of Tennessee +*> \author Univ. of California Berkeley +*> \author Univ. of Colorado Denver +*> \author NAG Ltd. +* +*> \date November 2011 +* +*> \ingroup auxOTHERauxiliary +* +* ===================================================================== + SUBROUTINE DLASCL( TYPE, KL, KU, CFROM, CTO, M, N, A, LDA, INFO ) +* +* -- LAPACK auxiliary routine (version 3.4.0) -- +* -- LAPACK is a software package provided by Univ. of Tennessee, -- +* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- +* November 2011 +* +* .. Scalar Arguments .. + CHARACTER TYPE + INTEGER INFO, KL, KU, LDA, M, N + DOUBLE PRECISION CFROM, CTO +* .. +* .. Array Arguments .. + DOUBLE PRECISION A( LDA, * ) +* .. +* +* ===================================================================== +* +* .. Parameters .. + DOUBLE PRECISION ZERO, ONE + PARAMETER ( ZERO = 0.0D0, ONE = 1.0D0 ) +* .. +* .. Local Scalars .. + LOGICAL DONE + INTEGER I, ITYPE, J, K1, K2, K3, K4 + DOUBLE PRECISION BIGNUM, CFROM1, CFROMC, CTO1, CTOC, MUL, SMLNUM +* .. +* .. External Functions .. + LOGICAL LSAME, DISNAN + DOUBLE PRECISION DLAMCH + EXTERNAL LSAME, DLAMCH, DISNAN +* .. +* .. Intrinsic Functions .. + INTRINSIC ABS, MAX, MIN +* .. +* .. External Subroutines .. + EXTERNAL XERBLA +* .. +* .. Executable Statements .. +* +* Test the input arguments +* + INFO = 0 +* + IF( LSAME( TYPE, 'G' ) ) THEN + ITYPE = 0 + ELSE IF( LSAME( TYPE, 'L' ) ) THEN + ITYPE = 1 + ELSE IF( LSAME( TYPE, 'U' ) ) THEN + ITYPE = 2 + ELSE IF( LSAME( TYPE, 'H' ) ) THEN + ITYPE = 3 + ELSE IF( LSAME( TYPE, 'B' ) ) THEN + ITYPE = 4 + ELSE IF( LSAME( TYPE, 'Q' ) ) THEN + ITYPE = 5 + ELSE IF( LSAME( TYPE, 'Z' ) ) THEN + ITYPE = 6 + ELSE + ITYPE = -1 + END IF +* + IF( ITYPE.EQ.-1 ) THEN + INFO = -1 + ELSE IF( CFROM.EQ.ZERO .OR. DISNAN(CFROM) ) THEN + INFO = -4 + ELSE IF( DISNAN(CTO) ) THEN + INFO = -5 + ELSE IF( M.LT.0 ) THEN + INFO = -6 + ELSE IF( N.LT.0 .OR. ( ITYPE.EQ.4 .AND. N.NE.M ) .OR. + $ ( ITYPE.EQ.5 .AND. N.NE.M ) ) THEN + INFO = -7 + ELSE IF( ITYPE.LE.3 .AND. LDA.LT.MAX( 1, M ) ) THEN + INFO = -9 + ELSE IF( ITYPE.GE.4 ) THEN + IF( KL.LT.0 .OR. KL.GT.MAX( M-1, 0 ) ) THEN + INFO = -2 + ELSE IF( KU.LT.0 .OR. KU.GT.MAX( N-1, 0 ) .OR. + $ ( ( ITYPE.EQ.4 .OR. ITYPE.EQ.5 ) .AND. KL.NE.KU ) ) + $ THEN + INFO = -3 + ELSE IF( ( ITYPE.EQ.4 .AND. LDA.LT.KL+1 ) .OR. + $ ( ITYPE.EQ.5 .AND. LDA.LT.KU+1 ) .OR. + $ ( ITYPE.EQ.6 .AND. LDA.LT.2*KL+KU+1 ) ) THEN + INFO = -9 + END IF + END IF +* + IF( INFO.NE.0 ) THEN + CALL XERBLA( 'DLASCL', -INFO ) + RETURN + END IF +* +* Quick return if possible +* + IF( N.EQ.0 .OR. M.EQ.0 ) + $ RETURN +* +* Get machine parameters +* + SMLNUM = DLAMCH( 'S' ) + BIGNUM = ONE / SMLNUM +* + CFROMC = CFROM + CTOC = CTO +* + 10 CONTINUE + CFROM1 = CFROMC*SMLNUM + IF( CFROM1.EQ.CFROMC ) THEN +! CFROMC is an inf. Multiply by a correctly signed zero for +! finite CTOC, or a NaN if CTOC is infinite. + MUL = CTOC / CFROMC + DONE = .TRUE. + CTO1 = CTOC + ELSE + CTO1 = CTOC / BIGNUM + IF( CTO1.EQ.CTOC ) THEN +! CTOC is either 0 or an inf. In both cases, CTOC itself +! serves as the correct multiplication factor. + MUL = CTOC + DONE = .TRUE. + CFROMC = ONE + ELSE IF( ABS( CFROM1 ).GT.ABS( CTOC ) .AND. CTOC.NE.ZERO ) THEN + MUL = SMLNUM + DONE = .FALSE. + CFROMC = CFROM1 + ELSE IF( ABS( CTO1 ).GT.ABS( CFROMC ) ) THEN + MUL = BIGNUM + DONE = .FALSE. + CTOC = CTO1 + ELSE + MUL = CTOC / CFROMC + DONE = .TRUE. + END IF + END IF +* + IF( ITYPE.EQ.0 ) THEN +* +* Full matrix +* + DO 30 J = 1, N + DO 20 I = 1, M + A( I, J ) = A( I, J )*MUL + 20 CONTINUE + 30 CONTINUE +* + ELSE IF( ITYPE.EQ.1 ) THEN +* +* Lower triangular matrix +* + DO 50 J = 1, N + DO 40 I = J, M + A( I, J ) = A( I, J )*MUL + 40 CONTINUE + 50 CONTINUE +* + ELSE IF( ITYPE.EQ.2 ) THEN +* +* Upper triangular matrix +* + DO 70 J = 1, N + DO 60 I = 1, MIN( J, M ) + A( I, J ) = A( I, J )*MUL + 60 CONTINUE + 70 CONTINUE +* + ELSE IF( ITYPE.EQ.3 ) THEN +* +* Upper Hessenberg matrix +* + DO 90 J = 1, N + DO 80 I = 1, MIN( J+1, M ) + A( I, J ) = A( I, J )*MUL + 80 CONTINUE + 90 CONTINUE +* + ELSE IF( ITYPE.EQ.4 ) THEN +* +* Lower half of a symmetric band matrix +* + K3 = KL + 1 + K4 = N + 1 + DO 110 J = 1, N + DO 100 I = 1, MIN( K3, K4-J ) + A( I, J ) = A( I, J )*MUL + 100 CONTINUE + 110 CONTINUE +* + ELSE IF( ITYPE.EQ.5 ) THEN +* +* Upper half of a symmetric band matrix +* + K1 = KU + 2 + K3 = KU + 1 + DO 130 J = 1, N + DO 120 I = MAX( K1-J, 1 ), K3 + A( I, J ) = A( I, J )*MUL + 120 CONTINUE + 130 CONTINUE +* + ELSE IF( ITYPE.EQ.6 ) THEN +* +* Band matrix +* + K1 = KL + KU + 2 + K2 = KL + 1 + K3 = 2*KL + KU + 1 + K4 = KL + KU + 1 + M + DO 150 J = 1, N + DO 140 I = MAX( K1-J, K2 ), MIN( K3, K4-J ) + A( I, J ) = A( I, J )*MUL + 140 CONTINUE + 150 CONTINUE +* + END IF +* + IF( .NOT.DONE ) + $ GO TO 10 +* + RETURN +* +* End of DLASCL +* + END diff --git a/applications/PUfoam/MoDeNaModels/CFD_tool_0D/src/eigen/src/dlaset.f b/applications/PUfoam/MoDeNaModels/CFD_tool_0D/src/eigen/src/dlaset.f new file mode 100644 index 000000000..166a8da97 --- /dev/null +++ b/applications/PUfoam/MoDeNaModels/CFD_tool_0D/src/eigen/src/dlaset.f @@ -0,0 +1,184 @@ +*> \brief \b DLASET +* +* =========== DOCUMENTATION =========== +* +* Online html documentation available at +* http://www.netlib.org/lapack/explore-html/ +* +*> \htmlonly +*> Download DLASET + dependencies +*> +*> [TGZ] +*> +*> [ZIP] +*> +*> [TXT] +*> \endhtmlonly +* +* Definition: +* =========== +* +* SUBROUTINE DLASET( UPLO, M, N, ALPHA, BETA, A, LDA ) +* +* .. Scalar Arguments .. +* CHARACTER UPLO +* INTEGER LDA, M, N +* DOUBLE PRECISION ALPHA, BETA +* .. +* .. Array Arguments .. +* DOUBLE PRECISION A( LDA, * ) +* .. +* +* +*> \par Purpose: +* ============= +*> +*> \verbatim +*> +*> DLASET initializes an m-by-n matrix A to BETA on the diagonal and +*> ALPHA on the offdiagonals. +*> \endverbatim +* +* Arguments: +* ========== +* +*> \param[in] UPLO +*> \verbatim +*> UPLO is CHARACTER*1 +*> Specifies the part of the matrix A to be set. +*> = 'U': Upper triangular part is set; the strictly lower +*> triangular part of A is not changed. +*> = 'L': Lower triangular part is set; the strictly upper +*> triangular part of A is not changed. +*> Otherwise: All of the matrix A is set. +*> \endverbatim +*> +*> \param[in] M +*> \verbatim +*> M is INTEGER +*> The number of rows of the matrix A. M >= 0. +*> \endverbatim +*> +*> \param[in] N +*> \verbatim +*> N is INTEGER +*> The number of columns of the matrix A. N >= 0. +*> \endverbatim +*> +*> \param[in] ALPHA +*> \verbatim +*> ALPHA is DOUBLE PRECISION +*> The constant to which the offdiagonal elements are to be set. +*> \endverbatim +*> +*> \param[in] BETA +*> \verbatim +*> BETA is DOUBLE PRECISION +*> The constant to which the diagonal elements are to be set. +*> \endverbatim +*> +*> \param[in,out] A +*> \verbatim +*> A is DOUBLE PRECISION array, dimension (LDA,N) +*> On exit, the leading m-by-n submatrix of A is set as follows: +*> +*> if UPLO = 'U', A(i,j) = ALPHA, 1<=i<=j-1, 1<=j<=n, +*> if UPLO = 'L', A(i,j) = ALPHA, j+1<=i<=m, 1<=j<=n, +*> otherwise, A(i,j) = ALPHA, 1<=i<=m, 1<=j<=n, i.ne.j, +*> +*> and, for all UPLO, A(i,i) = BETA, 1<=i<=min(m,n). +*> \endverbatim +*> +*> \param[in] LDA +*> \verbatim +*> LDA is INTEGER +*> The leading dimension of the array A. LDA >= max(1,M). +*> \endverbatim +* +* Authors: +* ======== +* +*> \author Univ. of Tennessee +*> \author Univ. of California Berkeley +*> \author Univ. of Colorado Denver +*> \author NAG Ltd. +* +*> \date November 2011 +* +*> \ingroup auxOTHERauxiliary +* +* ===================================================================== + SUBROUTINE DLASET( UPLO, M, N, ALPHA, BETA, A, LDA ) +* +* -- LAPACK auxiliary routine (version 3.4.0) -- +* -- LAPACK is a software package provided by Univ. of Tennessee, -- +* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- +* November 2011 +* +* .. Scalar Arguments .. + CHARACTER UPLO + INTEGER LDA, M, N + DOUBLE PRECISION ALPHA, BETA +* .. +* .. Array Arguments .. + DOUBLE PRECISION A( LDA, * ) +* .. +* +* ===================================================================== +* +* .. Local Scalars .. + INTEGER I, J +* .. +* .. External Functions .. + LOGICAL LSAME + EXTERNAL LSAME +* .. +* .. Intrinsic Functions .. + INTRINSIC MIN +* .. +* .. Executable Statements .. +* + IF( LSAME( UPLO, 'U' ) ) THEN +* +* Set the strictly upper triangular or trapezoidal part of the +* array to ALPHA. +* + DO 20 J = 2, N + DO 10 I = 1, MIN( J-1, M ) + A( I, J ) = ALPHA + 10 CONTINUE + 20 CONTINUE +* + ELSE IF( LSAME( UPLO, 'L' ) ) THEN +* +* Set the strictly lower triangular or trapezoidal part of the +* array to ALPHA. +* + DO 40 J = 1, MIN( M, N ) + DO 30 I = J + 1, M + A( I, J ) = ALPHA + 30 CONTINUE + 40 CONTINUE +* + ELSE +* +* Set the leading m-by-n submatrix to ALPHA. +* + DO 60 J = 1, N + DO 50 I = 1, M + A( I, J ) = ALPHA + 50 CONTINUE + 60 CONTINUE + END IF +* +* Set the first min(M,N) diagonal elements to BETA. +* + DO 70 I = 1, MIN( M, N ) + A( I, I ) = BETA + 70 CONTINUE +* + RETURN +* +* End of DLASET +* + END diff --git a/applications/PUfoam/MoDeNaModels/CFD_tool_0D/src/eigen/src/dlasq2.f b/applications/PUfoam/MoDeNaModels/CFD_tool_0D/src/eigen/src/dlasq2.f new file mode 100644 index 000000000..94feaba7b --- /dev/null +++ b/applications/PUfoam/MoDeNaModels/CFD_tool_0D/src/eigen/src/dlasq2.f @@ -0,0 +1,582 @@ +*> \brief \b DLASQ2 +* +* =========== DOCUMENTATION =========== +* +* Online html documentation available at +* http://www.netlib.org/lapack/explore-html/ +* +*> \htmlonly +*> Download DLASQ2 + dependencies +*> +*> [TGZ] +*> +*> [ZIP] +*> +*> [TXT] +*> \endhtmlonly +* +* Definition: +* =========== +* +* SUBROUTINE DLASQ2( N, Z, INFO ) +* +* .. Scalar Arguments .. +* INTEGER INFO, N +* .. +* .. Array Arguments .. +* DOUBLE PRECISION Z( * ) +* .. +* +* +*> \par Purpose: +* ============= +*> +*> \verbatim +*> +*> DLASQ2 computes all the eigenvalues of the symmetric positive +*> definite tridiagonal matrix associated with the qd array Z to high +*> relative accuracy are computed to high relative accuracy, in the +*> absence of denormalization, underflow and overflow. +*> +*> To see the relation of Z to the tridiagonal matrix, let L be a +*> unit lower bidiagonal matrix with subdiagonals Z(2,4,6,,..) and +*> let U be an upper bidiagonal matrix with 1's above and diagonal +*> Z(1,3,5,,..). The tridiagonal is L*U or, if you prefer, the +*> symmetric tridiagonal to which it is similar. +*> +*> Note : DLASQ2 defines a logical variable, IEEE, which is true +*> on machines which follow ieee-754 floating-point standard in their +*> handling of infinities and NaNs, and false otherwise. This variable +*> is passed to DLASQ3. +*> \endverbatim +* +* Arguments: +* ========== +* +*> \param[in] N +*> \verbatim +*> N is INTEGER +*> The number of rows and columns in the matrix. N >= 0. +*> \endverbatim +*> +*> \param[in,out] Z +*> \verbatim +*> Z is DOUBLE PRECISION array, dimension ( 4*N ) +*> On entry Z holds the qd array. On exit, entries 1 to N hold +*> the eigenvalues in decreasing order, Z( 2*N+1 ) holds the +*> trace, and Z( 2*N+2 ) holds the sum of the eigenvalues. If +*> N > 2, then Z( 2*N+3 ) holds the iteration count, Z( 2*N+4 ) +*> holds NDIVS/NIN^2, and Z( 2*N+5 ) holds the percentage of +*> shifts that failed. +*> \endverbatim +*> +*> \param[out] INFO +*> \verbatim +*> INFO is INTEGER +*> = 0: successful exit +*> < 0: if the i-th argument is a scalar and had an illegal +*> value, then INFO = -i, if the i-th argument is an +*> array and the j-entry had an illegal value, then +*> INFO = -(i*100+j) +*> > 0: the algorithm failed +*> = 1, a split was marked by a positive value in E +*> = 2, current block of Z not diagonalized after 100*N +*> iterations (in inner while loop). On exit Z holds +*> a qd array with the same eigenvalues as the given Z. +*> = 3, termination criterion of outer while loop not met +*> (program created more than N unreduced blocks) +*> \endverbatim +* +* Authors: +* ======== +* +*> \author Univ. of Tennessee +*> \author Univ. of California Berkeley +*> \author Univ. of Colorado Denver +*> \author NAG Ltd. +* +*> \date November 2011 +* +*> \ingroup auxOTHERcomputational +* +*> \par Further Details: +* ===================== +*> +*> \verbatim +*> +*> Local Variables: I0:N0 defines a current unreduced segment of Z. +*> The shifts are accumulated in SIGMA. Iteration count is in ITER. +*> Ping-pong is controlled by PP (alternates between 0 and 1). +*> \endverbatim +*> +* ===================================================================== + SUBROUTINE DLASQ2( N, Z, INFO ) +* +* -- LAPACK computational routine (version 3.4.0) -- +* -- LAPACK is a software package provided by Univ. of Tennessee, -- +* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- +* November 2011 +* +* .. Scalar Arguments .. + INTEGER INFO, N +* .. +* .. Array Arguments .. + DOUBLE PRECISION Z( * ) +* .. +* +* ===================================================================== +* +* .. Parameters .. + DOUBLE PRECISION CBIAS + PARAMETER ( CBIAS = 1.50D0 ) + DOUBLE PRECISION ZERO, HALF, ONE, TWO, FOUR, HUNDRD + PARAMETER ( ZERO = 0.0D0, HALF = 0.5D0, ONE = 1.0D0, + $ TWO = 2.0D0, FOUR = 4.0D0, HUNDRD = 100.0D0 ) +* .. +* .. Local Scalars .. + LOGICAL IEEE + INTEGER I0, I1, I4, IINFO, IPN4, ITER, IWHILA, IWHILB, + $ K, KMIN, N0, N1, NBIG, NDIV, NFAIL, PP, SPLT, + $ TTYPE + DOUBLE PRECISION D, DEE, DEEMIN, DESIG, DMIN, DMIN1, DMIN2, DN, + $ DN1, DN2, E, EMAX, EMIN, EPS, G, OLDEMN, QMAX, + $ QMIN, S, SAFMIN, SIGMA, T, TAU, TEMP, TOL, + $ TOL2, TRACE, ZMAX, TEMPE, TEMPQ +* .. +* .. External Subroutines .. + EXTERNAL DLASQ3, DLASRT, XERBLA +* .. +* .. External Functions .. + INTEGER ILAENV + DOUBLE PRECISION DLAMCH + EXTERNAL DLAMCH, ILAENV +* .. +* .. Intrinsic Functions .. + INTRINSIC ABS, DBLE, MAX, MIN, SQRT +* .. +* .. Executable Statements .. +* +* Test the input arguments. +* (in case DLASQ2 is not called by DLASQ1) +* + INFO = 0 + EPS = DLAMCH( 'Precision' ) + SAFMIN = DLAMCH( 'Safe minimum' ) + TOL = EPS*HUNDRD + TOL2 = TOL**2 +* + IF( N.LT.0 ) THEN + INFO = -1 + CALL XERBLA( 'DLASQ2', 1 ) + RETURN + ELSE IF( N.EQ.0 ) THEN + RETURN + ELSE IF( N.EQ.1 ) THEN +* +* 1-by-1 case. +* + IF( Z( 1 ).LT.ZERO ) THEN + INFO = -201 + CALL XERBLA( 'DLASQ2', 2 ) + END IF + RETURN + ELSE IF( N.EQ.2 ) THEN +* +* 2-by-2 case. +* + IF( Z( 2 ).LT.ZERO .OR. Z( 3 ).LT.ZERO ) THEN + INFO = -2 + CALL XERBLA( 'DLASQ2', 2 ) + RETURN + ELSE IF( Z( 3 ).GT.Z( 1 ) ) THEN + D = Z( 3 ) + Z( 3 ) = Z( 1 ) + Z( 1 ) = D + END IF + Z( 5 ) = Z( 1 ) + Z( 2 ) + Z( 3 ) + IF( Z( 2 ).GT.Z( 3 )*TOL2 ) THEN + T = HALF*( ( Z( 1 )-Z( 3 ) )+Z( 2 ) ) + S = Z( 3 )*( Z( 2 ) / T ) + IF( S.LE.T ) THEN + S = Z( 3 )*( Z( 2 ) / ( T*( ONE+SQRT( ONE+S / T ) ) ) ) + ELSE + S = Z( 3 )*( Z( 2 ) / ( T+SQRT( T )*SQRT( T+S ) ) ) + END IF + T = Z( 1 ) + ( S+Z( 2 ) ) + Z( 3 ) = Z( 3 )*( Z( 1 ) / T ) + Z( 1 ) = T + END IF + Z( 2 ) = Z( 3 ) + Z( 6 ) = Z( 2 ) + Z( 1 ) + RETURN + END IF +* +* Check for negative data and compute sums of q's and e's. +* + Z( 2*N ) = ZERO + EMIN = Z( 2 ) + QMAX = ZERO + ZMAX = ZERO + D = ZERO + E = ZERO +* + DO 10 K = 1, 2*( N-1 ), 2 + IF( Z( K ).LT.ZERO ) THEN + INFO = -( 200+K ) + CALL XERBLA( 'DLASQ2', 2 ) + RETURN + ELSE IF( Z( K+1 ).LT.ZERO ) THEN + INFO = -( 200+K+1 ) + CALL XERBLA( 'DLASQ2', 2 ) + RETURN + END IF + D = D + Z( K ) + E = E + Z( K+1 ) + QMAX = MAX( QMAX, Z( K ) ) + EMIN = MIN( EMIN, Z( K+1 ) ) + ZMAX = MAX( QMAX, ZMAX, Z( K+1 ) ) + 10 CONTINUE + IF( Z( 2*N-1 ).LT.ZERO ) THEN + INFO = -( 200+2*N-1 ) + CALL XERBLA( 'DLASQ2', 2 ) + RETURN + END IF + D = D + Z( 2*N-1 ) + QMAX = MAX( QMAX, Z( 2*N-1 ) ) + ZMAX = MAX( QMAX, ZMAX ) +* +* Check for diagonality. +* + IF( E.EQ.ZERO ) THEN + DO 20 K = 2, N + Z( K ) = Z( 2*K-1 ) + 20 CONTINUE + CALL DLASRT( 'D', N, Z, IINFO ) + Z( 2*N-1 ) = D + RETURN + END IF +* + TRACE = D + E +* +* Check for zero data. +* + IF( TRACE.EQ.ZERO ) THEN + Z( 2*N-1 ) = ZERO + RETURN + END IF +* +* Check whether the machine is IEEE conformable. +* + IEEE = ILAENV( 10, 'DLASQ2', 'N', 1, 2, 3, 4 ).EQ.1 .AND. + $ ILAENV( 11, 'DLASQ2', 'N', 1, 2, 3, 4 ).EQ.1 +* +* Rearrange data for locality: Z=(q1,qq1,e1,ee1,q2,qq2,e2,ee2,...). +* + DO 30 K = 2*N, 2, -2 + Z( 2*K ) = ZERO + Z( 2*K-1 ) = Z( K ) + Z( 2*K-2 ) = ZERO + Z( 2*K-3 ) = Z( K-1 ) + 30 CONTINUE +* + I0 = 1 + N0 = N +* +* Reverse the qd-array, if warranted. +* + IF( CBIAS*Z( 4*I0-3 ).LT.Z( 4*N0-3 ) ) THEN + IPN4 = 4*( I0+N0 ) + DO 40 I4 = 4*I0, 2*( I0+N0-1 ), 4 + TEMP = Z( I4-3 ) + Z( I4-3 ) = Z( IPN4-I4-3 ) + Z( IPN4-I4-3 ) = TEMP + TEMP = Z( I4-1 ) + Z( I4-1 ) = Z( IPN4-I4-5 ) + Z( IPN4-I4-5 ) = TEMP + 40 CONTINUE + END IF +* +* Initial split checking via dqd and Li's test. +* + PP = 0 +* + DO 80 K = 1, 2 +* + D = Z( 4*N0+PP-3 ) + DO 50 I4 = 4*( N0-1 ) + PP, 4*I0 + PP, -4 + IF( Z( I4-1 ).LE.TOL2*D ) THEN + Z( I4-1 ) = -ZERO + D = Z( I4-3 ) + ELSE + D = Z( I4-3 )*( D / ( D+Z( I4-1 ) ) ) + END IF + 50 CONTINUE +* +* dqd maps Z to ZZ plus Li's test. +* + EMIN = Z( 4*I0+PP+1 ) + D = Z( 4*I0+PP-3 ) + DO 60 I4 = 4*I0 + PP, 4*( N0-1 ) + PP, 4 + Z( I4-2*PP-2 ) = D + Z( I4-1 ) + IF( Z( I4-1 ).LE.TOL2*D ) THEN + Z( I4-1 ) = -ZERO + Z( I4-2*PP-2 ) = D + Z( I4-2*PP ) = ZERO + D = Z( I4+1 ) + ELSE IF( SAFMIN*Z( I4+1 ).LT.Z( I4-2*PP-2 ) .AND. + $ SAFMIN*Z( I4-2*PP-2 ).LT.Z( I4+1 ) ) THEN + TEMP = Z( I4+1 ) / Z( I4-2*PP-2 ) + Z( I4-2*PP ) = Z( I4-1 )*TEMP + D = D*TEMP + ELSE + Z( I4-2*PP ) = Z( I4+1 )*( Z( I4-1 ) / Z( I4-2*PP-2 ) ) + D = Z( I4+1 )*( D / Z( I4-2*PP-2 ) ) + END IF + EMIN = MIN( EMIN, Z( I4-2*PP ) ) + 60 CONTINUE + Z( 4*N0-PP-2 ) = D +* +* Now find qmax. +* + QMAX = Z( 4*I0-PP-2 ) + DO 70 I4 = 4*I0 - PP + 2, 4*N0 - PP - 2, 4 + QMAX = MAX( QMAX, Z( I4 ) ) + 70 CONTINUE +* +* Prepare for the next iteration on K. +* + PP = 1 - PP + 80 CONTINUE +* +* Initialise variables to pass to DLASQ3. +* + TTYPE = 0 + DMIN1 = ZERO + DMIN2 = ZERO + DN = ZERO + DN1 = ZERO + DN2 = ZERO + G = ZERO + TAU = ZERO +* + ITER = 2 + NFAIL = 0 + NDIV = 2*( N0-I0 ) +* + DO 160 IWHILA = 1, N + 1 + IF( N0.LT.1 ) + $ GO TO 170 +* +* While array unfinished do +* +* E(N0) holds the value of SIGMA when submatrix in I0:N0 +* splits from the rest of the array, but is negated. +* + DESIG = ZERO + IF( N0.EQ.N ) THEN + SIGMA = ZERO + ELSE + SIGMA = -Z( 4*N0-1 ) + END IF + IF( SIGMA.LT.ZERO ) THEN + INFO = 1 + RETURN + END IF +* +* Find last unreduced submatrix's top index I0, find QMAX and +* EMIN. Find Gershgorin-type bound if Q's much greater than E's. +* + EMAX = ZERO + IF( N0.GT.I0 ) THEN + EMIN = ABS( Z( 4*N0-5 ) ) + ELSE + EMIN = ZERO + END IF + QMIN = Z( 4*N0-3 ) + QMAX = QMIN + DO 90 I4 = 4*N0, 8, -4 + IF( Z( I4-5 ).LE.ZERO ) + $ GO TO 100 + IF( QMIN.GE.FOUR*EMAX ) THEN + QMIN = MIN( QMIN, Z( I4-3 ) ) + EMAX = MAX( EMAX, Z( I4-5 ) ) + END IF + QMAX = MAX( QMAX, Z( I4-7 )+Z( I4-5 ) ) + EMIN = MIN( EMIN, Z( I4-5 ) ) + 90 CONTINUE + I4 = 4 +* + 100 CONTINUE + I0 = I4 / 4 + PP = 0 +* + IF( N0-I0.GT.1 ) THEN + DEE = Z( 4*I0-3 ) + DEEMIN = DEE + KMIN = I0 + DO 110 I4 = 4*I0+1, 4*N0-3, 4 + DEE = Z( I4 )*( DEE /( DEE+Z( I4-2 ) ) ) + IF( DEE.LE.DEEMIN ) THEN + DEEMIN = DEE + KMIN = ( I4+3 )/4 + END IF + 110 CONTINUE + IF( (KMIN-I0)*2.LT.N0-KMIN .AND. + $ DEEMIN.LE.HALF*Z(4*N0-3) ) THEN + IPN4 = 4*( I0+N0 ) + PP = 2 + DO 120 I4 = 4*I0, 2*( I0+N0-1 ), 4 + TEMP = Z( I4-3 ) + Z( I4-3 ) = Z( IPN4-I4-3 ) + Z( IPN4-I4-3 ) = TEMP + TEMP = Z( I4-2 ) + Z( I4-2 ) = Z( IPN4-I4-2 ) + Z( IPN4-I4-2 ) = TEMP + TEMP = Z( I4-1 ) + Z( I4-1 ) = Z( IPN4-I4-5 ) + Z( IPN4-I4-5 ) = TEMP + TEMP = Z( I4 ) + Z( I4 ) = Z( IPN4-I4-4 ) + Z( IPN4-I4-4 ) = TEMP + 120 CONTINUE + END IF + END IF +* +* Put -(initial shift) into DMIN. +* + DMIN = -MAX( ZERO, QMIN-TWO*SQRT( QMIN )*SQRT( EMAX ) ) +* +* Now I0:N0 is unreduced. +* PP = 0 for ping, PP = 1 for pong. +* PP = 2 indicates that flipping was applied to the Z array and +* and that the tests for deflation upon entry in DLASQ3 +* should not be performed. +* + NBIG = 100*( N0-I0+1 ) + DO 140 IWHILB = 1, NBIG + IF( I0.GT.N0 ) + $ GO TO 150 +* +* While submatrix unfinished take a good dqds step. +* + CALL DLASQ3( I0, N0, Z, PP, DMIN, SIGMA, DESIG, QMAX, NFAIL, + $ ITER, NDIV, IEEE, TTYPE, DMIN1, DMIN2, DN, DN1, + $ DN2, G, TAU ) +* + PP = 1 - PP +* +* When EMIN is very small check for splits. +* + IF( PP.EQ.0 .AND. N0-I0.GE.3 ) THEN + IF( Z( 4*N0 ).LE.TOL2*QMAX .OR. + $ Z( 4*N0-1 ).LE.TOL2*SIGMA ) THEN + SPLT = I0 - 1 + QMAX = Z( 4*I0-3 ) + EMIN = Z( 4*I0-1 ) + OLDEMN = Z( 4*I0 ) + DO 130 I4 = 4*I0, 4*( N0-3 ), 4 + IF( Z( I4 ).LE.TOL2*Z( I4-3 ) .OR. + $ Z( I4-1 ).LE.TOL2*SIGMA ) THEN + Z( I4-1 ) = -SIGMA + SPLT = I4 / 4 + QMAX = ZERO + EMIN = Z( I4+3 ) + OLDEMN = Z( I4+4 ) + ELSE + QMAX = MAX( QMAX, Z( I4+1 ) ) + EMIN = MIN( EMIN, Z( I4-1 ) ) + OLDEMN = MIN( OLDEMN, Z( I4 ) ) + END IF + 130 CONTINUE + Z( 4*N0-1 ) = EMIN + Z( 4*N0 ) = OLDEMN + I0 = SPLT + 1 + END IF + END IF +* + 140 CONTINUE +* + INFO = 2 +* +* Maximum number of iterations exceeded, restore the shift +* SIGMA and place the new d's and e's in a qd array. +* This might need to be done for several blocks +* + I1 = I0 + N1 = N0 + 145 CONTINUE + TEMPQ = Z( 4*I0-3 ) + Z( 4*I0-3 ) = Z( 4*I0-3 ) + SIGMA + DO K = I0+1, N0 + TEMPE = Z( 4*K-5 ) + Z( 4*K-5 ) = Z( 4*K-5 ) * (TEMPQ / Z( 4*K-7 )) + TEMPQ = Z( 4*K-3 ) + Z( 4*K-3 ) = Z( 4*K-3 ) + SIGMA + TEMPE - Z( 4*K-5 ) + END DO +* +* Prepare to do this on the previous block if there is one +* + IF( I1.GT.1 ) THEN + N1 = I1-1 + DO WHILE( ( I1.GE.2 ) .AND. ( Z(4*I1-5).GE.ZERO ) ) + I1 = I1 - 1 + END DO + SIGMA = -Z(4*N1-1) + GO TO 145 + END IF + + DO K = 1, N + Z( 2*K-1 ) = Z( 4*K-3 ) +* +* Only the block 1..N0 is unfinished. The rest of the e's +* must be essentially zero, although sometimes other data +* has been stored in them. +* + IF( K.LT.N0 ) THEN + Z( 2*K ) = Z( 4*K-1 ) + ELSE + Z( 2*K ) = 0 + END IF + END DO + RETURN +* +* end IWHILB +* + 150 CONTINUE +* + 160 CONTINUE +* + INFO = 3 + RETURN +* +* end IWHILA +* + 170 CONTINUE +* +* Move q's to the front. +* + DO 180 K = 2, N + Z( K ) = Z( 4*K-3 ) + 180 CONTINUE +* +* Sort and compute sum of eigenvalues. +* + CALL DLASRT( 'D', N, Z, IINFO ) +* + E = ZERO + DO 190 K = N, 1, -1 + E = E + Z( K ) + 190 CONTINUE +* +* Store trace, sum(eigenvalues) and information on performance. +* + Z( 2*N+1 ) = TRACE + Z( 2*N+2 ) = E + Z( 2*N+3 ) = DBLE( ITER ) + Z( 2*N+4 ) = DBLE( NDIV ) / DBLE( N**2 ) + Z( 2*N+5 ) = HUNDRD*NFAIL / DBLE( ITER ) + RETURN +* +* End of DLASQ2 +* + END diff --git a/applications/PUfoam/MoDeNaModels/CFD_tool_0D/src/eigen/src/dlasq3.f b/applications/PUfoam/MoDeNaModels/CFD_tool_0D/src/eigen/src/dlasq3.f new file mode 100644 index 000000000..a1ce68bf1 --- /dev/null +++ b/applications/PUfoam/MoDeNaModels/CFD_tool_0D/src/eigen/src/dlasq3.f @@ -0,0 +1,421 @@ +*> \brief \b DLASQ3 +* +* =========== DOCUMENTATION =========== +* +* Online html documentation available at +* http://www.netlib.org/lapack/explore-html/ +* +*> \htmlonly +*> Download DLASQ3 + dependencies +*> +*> [TGZ] +*> +*> [ZIP] +*> +*> [TXT] +*> \endhtmlonly +* +* Definition: +* =========== +* +* SUBROUTINE DLASQ3( I0, N0, Z, PP, DMIN, SIGMA, DESIG, QMAX, NFAIL, +* ITER, NDIV, IEEE, TTYPE, DMIN1, DMIN2, DN, DN1, +* DN2, G, TAU ) +* +* .. Scalar Arguments .. +* LOGICAL IEEE +* INTEGER I0, ITER, N0, NDIV, NFAIL, PP +* DOUBLE PRECISION DESIG, DMIN, DMIN1, DMIN2, DN, DN1, DN2, G, +* $ QMAX, SIGMA, TAU +* .. +* .. Array Arguments .. +* DOUBLE PRECISION Z( * ) +* .. +* +* +*> \par Purpose: +* ============= +*> +*> \verbatim +*> +*> DLASQ3 checks for deflation, computes a shift (TAU) and calls dqds. +*> In case of failure it changes shifts, and tries again until output +*> is positive. +*> \endverbatim +* +* Arguments: +* ========== +* +*> \param[in] I0 +*> \verbatim +*> I0 is INTEGER +*> First index. +*> \endverbatim +*> +*> \param[in,out] N0 +*> \verbatim +*> N0 is INTEGER +*> Last index. +*> \endverbatim +*> +*> \param[in] Z +*> \verbatim +*> Z is DOUBLE PRECISION array, dimension ( 4*N ) +*> Z holds the qd array. +*> \endverbatim +*> +*> \param[in,out] PP +*> \verbatim +*> PP is INTEGER +*> PP=0 for ping, PP=1 for pong. +*> PP=2 indicates that flipping was applied to the Z array +*> and that the initial tests for deflation should not be +*> performed. +*> \endverbatim +*> +*> \param[out] DMIN +*> \verbatim +*> DMIN is DOUBLE PRECISION +*> Minimum value of d. +*> \endverbatim +*> +*> \param[out] SIGMA +*> \verbatim +*> SIGMA is DOUBLE PRECISION +*> Sum of shifts used in current segment. +*> \endverbatim +*> +*> \param[in,out] DESIG +*> \verbatim +*> DESIG is DOUBLE PRECISION +*> Lower order part of SIGMA +*> \endverbatim +*> +*> \param[in] QMAX +*> \verbatim +*> QMAX is DOUBLE PRECISION +*> Maximum value of q. +*> \endverbatim +*> +*> \param[out] NFAIL +*> \verbatim +*> NFAIL is INTEGER +*> Number of times shift was too big. +*> \endverbatim +*> +*> \param[out] ITER +*> \verbatim +*> ITER is INTEGER +*> Number of iterations. +*> \endverbatim +*> +*> \param[out] NDIV +*> \verbatim +*> NDIV is INTEGER +*> Number of divisions. +*> \endverbatim +*> +*> \param[in] IEEE +*> \verbatim +*> IEEE is LOGICAL +*> Flag for IEEE or non IEEE arithmetic (passed to DLASQ5). +*> \endverbatim +*> +*> \param[in,out] TTYPE +*> \verbatim +*> TTYPE is INTEGER +*> Shift type. +*> \endverbatim +*> +*> \param[in,out] DMIN1 +*> \verbatim +*> DMIN1 is DOUBLE PRECISION +*> \endverbatim +*> +*> \param[in,out] DMIN2 +*> \verbatim +*> DMIN2 is DOUBLE PRECISION +*> \endverbatim +*> +*> \param[in,out] DN +*> \verbatim +*> DN is DOUBLE PRECISION +*> \endverbatim +*> +*> \param[in,out] DN1 +*> \verbatim +*> DN1 is DOUBLE PRECISION +*> \endverbatim +*> +*> \param[in,out] DN2 +*> \verbatim +*> DN2 is DOUBLE PRECISION +*> \endverbatim +*> +*> \param[in,out] G +*> \verbatim +*> G is DOUBLE PRECISION +*> \endverbatim +*> +*> \param[in,out] TAU +*> \verbatim +*> TAU is DOUBLE PRECISION +*> +*> These are passed as arguments in order to save their values +*> between calls to DLASQ3. +*> \endverbatim +* +* Authors: +* ======== +* +*> \author Univ. of Tennessee +*> \author Univ. of California Berkeley +*> \author Univ. of Colorado Denver +*> \author NAG Ltd. +* +*> \date November 2011 +* +*> \ingroup auxOTHERcomputational +* +* ===================================================================== + SUBROUTINE DLASQ3( I0, N0, Z, PP, DMIN, SIGMA, DESIG, QMAX, NFAIL, + $ ITER, NDIV, IEEE, TTYPE, DMIN1, DMIN2, DN, DN1, + $ DN2, G, TAU ) +* +* -- LAPACK computational routine (version 3.4.0) -- +* -- LAPACK is a software package provided by Univ. of Tennessee, -- +* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- +* November 2011 +* +* .. Scalar Arguments .. + LOGICAL IEEE + INTEGER I0, ITER, N0, NDIV, NFAIL, PP + DOUBLE PRECISION DESIG, DMIN, DMIN1, DMIN2, DN, DN1, DN2, G, + $ QMAX, SIGMA, TAU +* .. +* .. Array Arguments .. + DOUBLE PRECISION Z( * ) +* .. +* +* ===================================================================== +* +* .. Parameters .. + DOUBLE PRECISION CBIAS + PARAMETER ( CBIAS = 1.50D0 ) + DOUBLE PRECISION ZERO, QURTR, HALF, ONE, TWO, HUNDRD + PARAMETER ( ZERO = 0.0D0, QURTR = 0.250D0, HALF = 0.5D0, + $ ONE = 1.0D0, TWO = 2.0D0, HUNDRD = 100.0D0 ) +* .. +* .. Local Scalars .. + INTEGER IPN4, J4, N0IN, NN, TTYPE + DOUBLE PRECISION EPS, S, T, TEMP, TOL, TOL2 +* .. +* .. External Subroutines .. + EXTERNAL DLASQ4, DLASQ5, DLASQ6 +* .. +* .. External Function .. + DOUBLE PRECISION DLAMCH + LOGICAL DISNAN + EXTERNAL DISNAN, DLAMCH +* .. +* .. Intrinsic Functions .. + INTRINSIC ABS, MAX, MIN, SQRT +* .. +* .. Executable Statements .. +* + N0IN = N0 + EPS = DLAMCH( 'Precision' ) + TOL = EPS*HUNDRD + TOL2 = TOL**2 +* +* Check for deflation. +* + 10 CONTINUE +* + IF( N0.LT.I0 ) + $ RETURN + IF( N0.EQ.I0 ) + $ GO TO 20 + NN = 4*N0 + PP + IF( N0.EQ.( I0+1 ) ) + $ GO TO 40 +* +* Check whether E(N0-1) is negligible, 1 eigenvalue. +* + IF( Z( NN-5 ).GT.TOL2*( SIGMA+Z( NN-3 ) ) .AND. + $ Z( NN-2*PP-4 ).GT.TOL2*Z( NN-7 ) ) + $ GO TO 30 +* + 20 CONTINUE +* + Z( 4*N0-3 ) = Z( 4*N0+PP-3 ) + SIGMA + N0 = N0 - 1 + GO TO 10 +* +* Check whether E(N0-2) is negligible, 2 eigenvalues. +* + 30 CONTINUE +* + IF( Z( NN-9 ).GT.TOL2*SIGMA .AND. + $ Z( NN-2*PP-8 ).GT.TOL2*Z( NN-11 ) ) + $ GO TO 50 +* + 40 CONTINUE +* + IF( Z( NN-3 ).GT.Z( NN-7 ) ) THEN + S = Z( NN-3 ) + Z( NN-3 ) = Z( NN-7 ) + Z( NN-7 ) = S + END IF + IF( Z( NN-5 ).GT.Z( NN-3 )*TOL2 ) THEN + T = HALF*( ( Z( NN-7 )-Z( NN-3 ) )+Z( NN-5 ) ) + S = Z( NN-3 )*( Z( NN-5 ) / T ) + IF( S.LE.T ) THEN + S = Z( NN-3 )*( Z( NN-5 ) / + $ ( T*( ONE+SQRT( ONE+S / T ) ) ) ) + ELSE + S = Z( NN-3 )*( Z( NN-5 ) / ( T+SQRT( T )*SQRT( T+S ) ) ) + END IF + T = Z( NN-7 ) + ( S+Z( NN-5 ) ) + Z( NN-3 ) = Z( NN-3 )*( Z( NN-7 ) / T ) + Z( NN-7 ) = T + END IF + Z( 4*N0-7 ) = Z( NN-7 ) + SIGMA + Z( 4*N0-3 ) = Z( NN-3 ) + SIGMA + N0 = N0 - 2 + GO TO 10 +* + 50 CONTINUE + IF( PP.EQ.2 ) + $ PP = 0 +* +* Reverse the qd-array, if warranted. +* + IF( DMIN.LE.ZERO .OR. N0.LT.N0IN ) THEN + IF( CBIAS*Z( 4*I0+PP-3 ).LT.Z( 4*N0+PP-3 ) ) THEN + IPN4 = 4*( I0+N0 ) + DO 60 J4 = 4*I0, 2*( I0+N0-1 ), 4 + TEMP = Z( J4-3 ) + Z( J4-3 ) = Z( IPN4-J4-3 ) + Z( IPN4-J4-3 ) = TEMP + TEMP = Z( J4-2 ) + Z( J4-2 ) = Z( IPN4-J4-2 ) + Z( IPN4-J4-2 ) = TEMP + TEMP = Z( J4-1 ) + Z( J4-1 ) = Z( IPN4-J4-5 ) + Z( IPN4-J4-5 ) = TEMP + TEMP = Z( J4 ) + Z( J4 ) = Z( IPN4-J4-4 ) + Z( IPN4-J4-4 ) = TEMP + 60 CONTINUE + IF( N0-I0.LE.4 ) THEN + Z( 4*N0+PP-1 ) = Z( 4*I0+PP-1 ) + Z( 4*N0-PP ) = Z( 4*I0-PP ) + END IF + DMIN2 = MIN( DMIN2, Z( 4*N0+PP-1 ) ) + Z( 4*N0+PP-1 ) = MIN( Z( 4*N0+PP-1 ), Z( 4*I0+PP-1 ), + $ Z( 4*I0+PP+3 ) ) + Z( 4*N0-PP ) = MIN( Z( 4*N0-PP ), Z( 4*I0-PP ), + $ Z( 4*I0-PP+4 ) ) + QMAX = MAX( QMAX, Z( 4*I0+PP-3 ), Z( 4*I0+PP+1 ) ) + DMIN = -ZERO + END IF + END IF +* +* Choose a shift. +* + CALL DLASQ4( I0, N0, Z, PP, N0IN, DMIN, DMIN1, DMIN2, DN, DN1, + $ DN2, TAU, TTYPE, G ) +* +* Call dqds until DMIN > 0. +* + 70 CONTINUE +* + CALL DLASQ5( I0, N0, Z, PP, TAU, DMIN, DMIN1, DMIN2, DN, + $ DN1, DN2, IEEE ) +* + NDIV = NDIV + ( N0-I0+2 ) + ITER = ITER + 1 +* +* Check status. +* + IF( DMIN.GE.ZERO .AND. DMIN1.GT.ZERO ) THEN +* +* Success. +* + GO TO 90 +* + ELSE IF( DMIN.LT.ZERO .AND. DMIN1.GT.ZERO .AND. + $ Z( 4*( N0-1 )-PP ).LT.TOL*( SIGMA+DN1 ) .AND. + $ ABS( DN ).LT.TOL*SIGMA ) THEN +* +* Convergence hidden by negative DN. +* + Z( 4*( N0-1 )-PP+2 ) = ZERO + DMIN = ZERO + GO TO 90 + ELSE IF( DMIN.LT.ZERO ) THEN +* +* TAU too big. Select new TAU and try again. +* + NFAIL = NFAIL + 1 + IF( TTYPE.LT.-22 ) THEN +* +* Failed twice. Play it safe. +* + TAU = ZERO + ELSE IF( DMIN1.GT.ZERO ) THEN +* +* Late failure. Gives excellent shift. +* + TAU = ( TAU+DMIN )*( ONE-TWO*EPS ) + TTYPE = TTYPE - 11 + ELSE +* +* Early failure. Divide by 4. +* + TAU = QURTR*TAU + TTYPE = TTYPE - 12 + END IF + GO TO 70 + ELSE IF( DISNAN( DMIN ) ) THEN +* +* NaN. +* + IF( TAU.EQ.ZERO ) THEN + GO TO 80 + ELSE + TAU = ZERO + GO TO 70 + END IF + ELSE +* +* Possible underflow. Play it safe. +* + GO TO 80 + END IF +* +* Risk of underflow. +* + 80 CONTINUE + CALL DLASQ6( I0, N0, Z, PP, DMIN, DMIN1, DMIN2, DN, DN1, DN2 ) + NDIV = NDIV + ( N0-I0+2 ) + ITER = ITER + 1 + TAU = ZERO +* + 90 CONTINUE + IF( TAU.LT.SIGMA ) THEN + DESIG = DESIG + TAU + T = SIGMA + DESIG + DESIG = DESIG - ( T-SIGMA ) + ELSE + T = SIGMA + TAU + DESIG = SIGMA - ( T-TAU ) + DESIG + END IF + SIGMA = T +* + RETURN +* +* End of DLASQ3 +* + END diff --git a/applications/PUfoam/MoDeNaModels/CFD_tool_0D/src/eigen/src/dlasq4.f b/applications/PUfoam/MoDeNaModels/CFD_tool_0D/src/eigen/src/dlasq4.f new file mode 100644 index 000000000..dc6fb719c --- /dev/null +++ b/applications/PUfoam/MoDeNaModels/CFD_tool_0D/src/eigen/src/dlasq4.f @@ -0,0 +1,425 @@ +*> \brief \b DLASQ4 +* +* =========== DOCUMENTATION =========== +* +* Online html documentation available at +* http://www.netlib.org/lapack/explore-html/ +* +*> \htmlonly +*> Download DLASQ4 + dependencies +*> +*> [TGZ] +*> +*> [ZIP] +*> +*> [TXT] +*> \endhtmlonly +* +* Definition: +* =========== +* +* SUBROUTINE DLASQ4( I0, N0, Z, PP, N0IN, DMIN, DMIN1, DMIN2, DN, +* DN1, DN2, TAU, TTYPE, G ) +* +* .. Scalar Arguments .. +* INTEGER I0, N0, N0IN, PP, TTYPE +* DOUBLE PRECISION DMIN, DMIN1, DMIN2, DN, DN1, DN2, G, TAU +* .. +* .. Array Arguments .. +* DOUBLE PRECISION Z( * ) +* .. +* +* +*> \par Purpose: +* ============= +*> +*> \verbatim +*> +*> DLASQ4 computes an approximation TAU to the smallest eigenvalue +*> using values of d from the previous transform. +*> \endverbatim +* +* Arguments: +* ========== +* +*> \param[in] I0 +*> \verbatim +*> I0 is INTEGER +*> First index. +*> \endverbatim +*> +*> \param[in] N0 +*> \verbatim +*> N0 is INTEGER +*> Last index. +*> \endverbatim +*> +*> \param[in] Z +*> \verbatim +*> Z is DOUBLE PRECISION array, dimension ( 4*N ) +*> Z holds the qd array. +*> \endverbatim +*> +*> \param[in] PP +*> \verbatim +*> PP is INTEGER +*> PP=0 for ping, PP=1 for pong. +*> \endverbatim +*> +*> \param[in] N0IN +*> \verbatim +*> N0IN is INTEGER +*> The value of N0 at start of EIGTEST. +*> \endverbatim +*> +*> \param[in] DMIN +*> \verbatim +*> DMIN is DOUBLE PRECISION +*> Minimum value of d. +*> \endverbatim +*> +*> \param[in] DMIN1 +*> \verbatim +*> DMIN1 is DOUBLE PRECISION +*> Minimum value of d, excluding D( N0 ). +*> \endverbatim +*> +*> \param[in] DMIN2 +*> \verbatim +*> DMIN2 is DOUBLE PRECISION +*> Minimum value of d, excluding D( N0 ) and D( N0-1 ). +*> \endverbatim +*> +*> \param[in] DN +*> \verbatim +*> DN is DOUBLE PRECISION +*> d(N) +*> \endverbatim +*> +*> \param[in] DN1 +*> \verbatim +*> DN1 is DOUBLE PRECISION +*> d(N-1) +*> \endverbatim +*> +*> \param[in] DN2 +*> \verbatim +*> DN2 is DOUBLE PRECISION +*> d(N-2) +*> \endverbatim +*> +*> \param[out] TAU +*> \verbatim +*> TAU is DOUBLE PRECISION +*> This is the shift. +*> \endverbatim +*> +*> \param[out] TTYPE +*> \verbatim +*> TTYPE is INTEGER +*> Shift type. +*> \endverbatim +*> +*> \param[in,out] G +*> \verbatim +*> G is REAL +*> G is passed as an argument in order to save its value between +*> calls to DLASQ4. +*> \endverbatim +* +* Authors: +* ======== +* +*> \author Univ. of Tennessee +*> \author Univ. of California Berkeley +*> \author Univ. of Colorado Denver +*> \author NAG Ltd. +* +*> \date November 2011 +* +*> \ingroup auxOTHERcomputational +* +*> \par Further Details: +* ===================== +*> +*> \verbatim +*> +*> CNST1 = 9/16 +*> \endverbatim +*> +* ===================================================================== + SUBROUTINE DLASQ4( I0, N0, Z, PP, N0IN, DMIN, DMIN1, DMIN2, DN, + $ DN1, DN2, TAU, TTYPE, G ) +* +* -- LAPACK computational routine (version 3.4.0) -- +* -- LAPACK is a software package provided by Univ. of Tennessee, -- +* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- +* November 2011 +* +* .. Scalar Arguments .. + INTEGER I0, N0, N0IN, PP, TTYPE + DOUBLE PRECISION DMIN, DMIN1, DMIN2, DN, DN1, DN2, G, TAU +* .. +* .. Array Arguments .. + DOUBLE PRECISION Z( * ) +* .. +* +* ===================================================================== +* +* .. Parameters .. + DOUBLE PRECISION CNST1, CNST2, CNST3 + PARAMETER ( CNST1 = 0.5630D0, CNST2 = 1.010D0, + $ CNST3 = 1.050D0 ) + DOUBLE PRECISION QURTR, THIRD, HALF, ZERO, ONE, TWO, HUNDRD + PARAMETER ( QURTR = 0.250D0, THIRD = 0.3330D0, + $ HALF = 0.50D0, ZERO = 0.0D0, ONE = 1.0D0, + $ TWO = 2.0D0, HUNDRD = 100.0D0 ) +* .. +* .. Local Scalars .. + INTEGER I4, NN, NP + DOUBLE PRECISION A2, B1, B2, GAM, GAP1, GAP2, S +* .. +* .. Intrinsic Functions .. + INTRINSIC MAX, MIN, SQRT +* .. +* .. Executable Statements .. +* +* A negative DMIN forces the shift to take that absolute value +* TTYPE records the type of shift. +* + IF( DMIN.LE.ZERO ) THEN + TAU = -DMIN + TTYPE = -1 + RETURN + END IF +* + NN = 4*N0 + PP + IF( N0IN.EQ.N0 ) THEN +* +* No eigenvalues deflated. +* + IF( DMIN.EQ.DN .OR. DMIN.EQ.DN1 ) THEN +* + B1 = SQRT( Z( NN-3 ) )*SQRT( Z( NN-5 ) ) + B2 = SQRT( Z( NN-7 ) )*SQRT( Z( NN-9 ) ) + A2 = Z( NN-7 ) + Z( NN-5 ) +* +* Cases 2 and 3. +* + IF( DMIN.EQ.DN .AND. DMIN1.EQ.DN1 ) THEN + GAP2 = DMIN2 - A2 - DMIN2*QURTR + IF( GAP2.GT.ZERO .AND. GAP2.GT.B2 ) THEN + GAP1 = A2 - DN - ( B2 / GAP2 )*B2 + ELSE + GAP1 = A2 - DN - ( B1+B2 ) + END IF + IF( GAP1.GT.ZERO .AND. GAP1.GT.B1 ) THEN + S = MAX( DN-( B1 / GAP1 )*B1, HALF*DMIN ) + TTYPE = -2 + ELSE + S = ZERO + IF( DN.GT.B1 ) + $ S = DN - B1 + IF( A2.GT.( B1+B2 ) ) + $ S = MIN( S, A2-( B1+B2 ) ) + S = MAX( S, THIRD*DMIN ) + TTYPE = -3 + END IF + ELSE +* +* Case 4. +* + TTYPE = -4 + S = QURTR*DMIN + IF( DMIN.EQ.DN ) THEN + GAM = DN + A2 = ZERO + IF( Z( NN-5 ) .GT. Z( NN-7 ) ) + $ RETURN + B2 = Z( NN-5 ) / Z( NN-7 ) + NP = NN - 9 + ELSE + NP = NN - 2*PP + B2 = Z( NP-2 ) + GAM = DN1 + IF( Z( NP-4 ) .GT. Z( NP-2 ) ) + $ RETURN + A2 = Z( NP-4 ) / Z( NP-2 ) + IF( Z( NN-9 ) .GT. Z( NN-11 ) ) + $ RETURN + B2 = Z( NN-9 ) / Z( NN-11 ) + NP = NN - 13 + END IF +* +* Approximate contribution to norm squared from I < NN-1. +* + A2 = A2 + B2 + DO 10 I4 = NP, 4*I0 - 1 + PP, -4 + IF( B2.EQ.ZERO ) + $ GO TO 20 + B1 = B2 + IF( Z( I4 ) .GT. Z( I4-2 ) ) + $ RETURN + B2 = B2*( Z( I4 ) / Z( I4-2 ) ) + A2 = A2 + B2 + IF( HUNDRD*MAX( B2, B1 ).LT.A2 .OR. CNST1.LT.A2 ) + $ GO TO 20 + 10 CONTINUE + 20 CONTINUE + A2 = CNST3*A2 +* +* Rayleigh quotient residual bound. +* + IF( A2.LT.CNST1 ) + $ S = GAM*( ONE-SQRT( A2 ) ) / ( ONE+A2 ) + END IF + ELSE IF( DMIN.EQ.DN2 ) THEN +* +* Case 5. +* + TTYPE = -5 + S = QURTR*DMIN +* +* Compute contribution to norm squared from I > NN-2. +* + NP = NN - 2*PP + B1 = Z( NP-2 ) + B2 = Z( NP-6 ) + GAM = DN2 + IF( Z( NP-8 ).GT.B2 .OR. Z( NP-4 ).GT.B1 ) + $ RETURN + A2 = ( Z( NP-8 ) / B2 )*( ONE+Z( NP-4 ) / B1 ) +* +* Approximate contribution to norm squared from I < NN-2. +* + IF( N0-I0.GT.2 ) THEN + B2 = Z( NN-13 ) / Z( NN-15 ) + A2 = A2 + B2 + DO 30 I4 = NN - 17, 4*I0 - 1 + PP, -4 + IF( B2.EQ.ZERO ) + $ GO TO 40 + B1 = B2 + IF( Z( I4 ) .GT. Z( I4-2 ) ) + $ RETURN + B2 = B2*( Z( I4 ) / Z( I4-2 ) ) + A2 = A2 + B2 + IF( HUNDRD*MAX( B2, B1 ).LT.A2 .OR. CNST1.LT.A2 ) + $ GO TO 40 + 30 CONTINUE + 40 CONTINUE + A2 = CNST3*A2 + END IF +* + IF( A2.LT.CNST1 ) + $ S = GAM*( ONE-SQRT( A2 ) ) / ( ONE+A2 ) + ELSE +* +* Case 6, no information to guide us. +* + IF( TTYPE.EQ.-6 ) THEN + G = G + THIRD*( ONE-G ) + ELSE IF( TTYPE.EQ.-18 ) THEN + G = QURTR*THIRD + ELSE + G = QURTR + END IF + S = G*DMIN + TTYPE = -6 + END IF +* + ELSE IF( N0IN.EQ.( N0+1 ) ) THEN +* +* One eigenvalue just deflated. Use DMIN1, DN1 for DMIN and DN. +* + IF( DMIN1.EQ.DN1 .AND. DMIN2.EQ.DN2 ) THEN +* +* Cases 7 and 8. +* + TTYPE = -7 + S = THIRD*DMIN1 + IF( Z( NN-5 ).GT.Z( NN-7 ) ) + $ RETURN + B1 = Z( NN-5 ) / Z( NN-7 ) + B2 = B1 + IF( B2.EQ.ZERO ) + $ GO TO 60 + DO 50 I4 = 4*N0 - 9 + PP, 4*I0 - 1 + PP, -4 + A2 = B1 + IF( Z( I4 ).GT.Z( I4-2 ) ) + $ RETURN + B1 = B1*( Z( I4 ) / Z( I4-2 ) ) + B2 = B2 + B1 + IF( HUNDRD*MAX( B1, A2 ).LT.B2 ) + $ GO TO 60 + 50 CONTINUE + 60 CONTINUE + B2 = SQRT( CNST3*B2 ) + A2 = DMIN1 / ( ONE+B2**2 ) + GAP2 = HALF*DMIN2 - A2 + IF( GAP2.GT.ZERO .AND. GAP2.GT.B2*A2 ) THEN + S = MAX( S, A2*( ONE-CNST2*A2*( B2 / GAP2 )*B2 ) ) + ELSE + S = MAX( S, A2*( ONE-CNST2*B2 ) ) + TTYPE = -8 + END IF + ELSE +* +* Case 9. +* + S = QURTR*DMIN1 + IF( DMIN1.EQ.DN1 ) + $ S = HALF*DMIN1 + TTYPE = -9 + END IF +* + ELSE IF( N0IN.EQ.( N0+2 ) ) THEN +* +* Two eigenvalues deflated. Use DMIN2, DN2 for DMIN and DN. +* +* Cases 10 and 11. +* + IF( DMIN2.EQ.DN2 .AND. TWO*Z( NN-5 ).LT.Z( NN-7 ) ) THEN + TTYPE = -10 + S = THIRD*DMIN2 + IF( Z( NN-5 ).GT.Z( NN-7 ) ) + $ RETURN + B1 = Z( NN-5 ) / Z( NN-7 ) + B2 = B1 + IF( B2.EQ.ZERO ) + $ GO TO 80 + DO 70 I4 = 4*N0 - 9 + PP, 4*I0 - 1 + PP, -4 + IF( Z( I4 ).GT.Z( I4-2 ) ) + $ RETURN + B1 = B1*( Z( I4 ) / Z( I4-2 ) ) + B2 = B2 + B1 + IF( HUNDRD*B1.LT.B2 ) + $ GO TO 80 + 70 CONTINUE + 80 CONTINUE + B2 = SQRT( CNST3*B2 ) + A2 = DMIN2 / ( ONE+B2**2 ) + GAP2 = Z( NN-7 ) + Z( NN-9 ) - + $ SQRT( Z( NN-11 ) )*SQRT( Z( NN-9 ) ) - A2 + IF( GAP2.GT.ZERO .AND. GAP2.GT.B2*A2 ) THEN + S = MAX( S, A2*( ONE-CNST2*A2*( B2 / GAP2 )*B2 ) ) + ELSE + S = MAX( S, A2*( ONE-CNST2*B2 ) ) + END IF + ELSE + S = QURTR*DMIN2 + TTYPE = -11 + END IF + ELSE IF( N0IN.GT.( N0+2 ) ) THEN +* +* Case 12, more than two eigenvalues deflated. No information. +* + S = ZERO + TTYPE = -12 + END IF +* + TAU = S + RETURN +* +* End of DLASQ4 +* + END diff --git a/applications/PUfoam/MoDeNaModels/CFD_tool_0D/src/eigen/src/dlasq5.f b/applications/PUfoam/MoDeNaModels/CFD_tool_0D/src/eigen/src/dlasq5.f new file mode 100644 index 000000000..d78dd867b --- /dev/null +++ b/applications/PUfoam/MoDeNaModels/CFD_tool_0D/src/eigen/src/dlasq5.f @@ -0,0 +1,281 @@ +*> \brief \b DLASQ5 +* +* =========== DOCUMENTATION =========== +* +* Online html documentation available at +* http://www.netlib.org/lapack/explore-html/ +* +*> \htmlonly +*> Download DLASQ5 + dependencies +*> +*> [TGZ] +*> +*> [ZIP] +*> +*> [TXT] +*> \endhtmlonly +* +* Definition: +* =========== +* +* SUBROUTINE DLASQ5( I0, N0, Z, PP, TAU, DMIN, DMIN1, DMIN2, DN, +* DNM1, DNM2, IEEE ) +* +* .. Scalar Arguments .. +* LOGICAL IEEE +* INTEGER I0, N0, PP +* DOUBLE PRECISION DMIN, DMIN1, DMIN2, DN, DNM1, DNM2, TAU +* .. +* .. Array Arguments .. +* DOUBLE PRECISION Z( * ) +* .. +* +* +*> \par Purpose: +* ============= +*> +*> \verbatim +*> +*> DLASQ5 computes one dqds transform in ping-pong form, one +*> version for IEEE machines another for non IEEE machines. +*> \endverbatim +* +* Arguments: +* ========== +* +*> \param[in] I0 +*> \verbatim +*> I0 is INTEGER +*> First index. +*> \endverbatim +*> +*> \param[in] N0 +*> \verbatim +*> N0 is INTEGER +*> Last index. +*> \endverbatim +*> +*> \param[in] Z +*> \verbatim +*> Z is DOUBLE PRECISION array, dimension ( 4*N ) +*> Z holds the qd array. EMIN is stored in Z(4*N0) to avoid +*> an extra argument. +*> \endverbatim +*> +*> \param[in] PP +*> \verbatim +*> PP is INTEGER +*> PP=0 for ping, PP=1 for pong. +*> \endverbatim +*> +*> \param[in] TAU +*> \verbatim +*> TAU is DOUBLE PRECISION +*> This is the shift. +*> \endverbatim +*> +*> \param[out] DMIN +*> \verbatim +*> DMIN is DOUBLE PRECISION +*> Minimum value of d. +*> \endverbatim +*> +*> \param[out] DMIN1 +*> \verbatim +*> DMIN1 is DOUBLE PRECISION +*> Minimum value of d, excluding D( N0 ). +*> \endverbatim +*> +*> \param[out] DMIN2 +*> \verbatim +*> DMIN2 is DOUBLE PRECISION +*> Minimum value of d, excluding D( N0 ) and D( N0-1 ). +*> \endverbatim +*> +*> \param[out] DN +*> \verbatim +*> DN is DOUBLE PRECISION +*> d(N0), the last value of d. +*> \endverbatim +*> +*> \param[out] DNM1 +*> \verbatim +*> DNM1 is DOUBLE PRECISION +*> d(N0-1). +*> \endverbatim +*> +*> \param[out] DNM2 +*> \verbatim +*> DNM2 is DOUBLE PRECISION +*> d(N0-2). +*> \endverbatim +*> +*> \param[in] IEEE +*> \verbatim +*> IEEE is LOGICAL +*> Flag for IEEE or non IEEE arithmetic. +*> \endverbatim +* +* Authors: +* ======== +* +*> \author Univ. of Tennessee +*> \author Univ. of California Berkeley +*> \author Univ. of Colorado Denver +*> \author NAG Ltd. +* +*> \date November 2011 +* +*> \ingroup auxOTHERcomputational +* +* ===================================================================== + SUBROUTINE DLASQ5( I0, N0, Z, PP, TAU, DMIN, DMIN1, DMIN2, DN, + $ DNM1, DNM2, IEEE ) +* +* -- LAPACK computational routine (version 3.4.0) -- +* -- LAPACK is a software package provided by Univ. of Tennessee, -- +* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- +* November 2011 +* +* .. Scalar Arguments .. + LOGICAL IEEE + INTEGER I0, N0, PP + DOUBLE PRECISION DMIN, DMIN1, DMIN2, DN, DNM1, DNM2, TAU +* .. +* .. Array Arguments .. + DOUBLE PRECISION Z( * ) +* .. +* +* ===================================================================== +* +* .. Parameter .. + DOUBLE PRECISION ZERO + PARAMETER ( ZERO = 0.0D0 ) +* .. +* .. Local Scalars .. + INTEGER J4, J4P2 + DOUBLE PRECISION D, EMIN, TEMP +* .. +* .. Intrinsic Functions .. + INTRINSIC MIN +* .. +* .. Executable Statements .. +* + IF( ( N0-I0-1 ).LE.0 ) + $ RETURN +* + J4 = 4*I0 + PP - 3 + EMIN = Z( J4+4 ) + D = Z( J4 ) - TAU + DMIN = D + DMIN1 = -Z( J4 ) +* + IF( IEEE ) THEN +* +* Code for IEEE arithmetic. +* + IF( PP.EQ.0 ) THEN + DO 10 J4 = 4*I0, 4*( N0-3 ), 4 + Z( J4-2 ) = D + Z( J4-1 ) + TEMP = Z( J4+1 ) / Z( J4-2 ) + D = D*TEMP - TAU + DMIN = MIN( DMIN, D ) + Z( J4 ) = Z( J4-1 )*TEMP + EMIN = MIN( Z( J4 ), EMIN ) + 10 CONTINUE + ELSE + DO 20 J4 = 4*I0, 4*( N0-3 ), 4 + Z( J4-3 ) = D + Z( J4 ) + TEMP = Z( J4+2 ) / Z( J4-3 ) + D = D*TEMP - TAU + DMIN = MIN( DMIN, D ) + Z( J4-1 ) = Z( J4 )*TEMP + EMIN = MIN( Z( J4-1 ), EMIN ) + 20 CONTINUE + END IF +* +* Unroll last two steps. +* + DNM2 = D + DMIN2 = DMIN + J4 = 4*( N0-2 ) - PP + J4P2 = J4 + 2*PP - 1 + Z( J4-2 ) = DNM2 + Z( J4P2 ) + Z( J4 ) = Z( J4P2+2 )*( Z( J4P2 ) / Z( J4-2 ) ) + DNM1 = Z( J4P2+2 )*( DNM2 / Z( J4-2 ) ) - TAU + DMIN = MIN( DMIN, DNM1 ) +* + DMIN1 = DMIN + J4 = J4 + 4 + J4P2 = J4 + 2*PP - 1 + Z( J4-2 ) = DNM1 + Z( J4P2 ) + Z( J4 ) = Z( J4P2+2 )*( Z( J4P2 ) / Z( J4-2 ) ) + DN = Z( J4P2+2 )*( DNM1 / Z( J4-2 ) ) - TAU + DMIN = MIN( DMIN, DN ) +* + ELSE +* +* Code for non IEEE arithmetic. +* + IF( PP.EQ.0 ) THEN + DO 30 J4 = 4*I0, 4*( N0-3 ), 4 + Z( J4-2 ) = D + Z( J4-1 ) + IF( D.LT.ZERO ) THEN + RETURN + ELSE + Z( J4 ) = Z( J4+1 )*( Z( J4-1 ) / Z( J4-2 ) ) + D = Z( J4+1 )*( D / Z( J4-2 ) ) - TAU + END IF + DMIN = MIN( DMIN, D ) + EMIN = MIN( EMIN, Z( J4 ) ) + 30 CONTINUE + ELSE + DO 40 J4 = 4*I0, 4*( N0-3 ), 4 + Z( J4-3 ) = D + Z( J4 ) + IF( D.LT.ZERO ) THEN + RETURN + ELSE + Z( J4-1 ) = Z( J4+2 )*( Z( J4 ) / Z( J4-3 ) ) + D = Z( J4+2 )*( D / Z( J4-3 ) ) - TAU + END IF + DMIN = MIN( DMIN, D ) + EMIN = MIN( EMIN, Z( J4-1 ) ) + 40 CONTINUE + END IF +* +* Unroll last two steps. +* + DNM2 = D + DMIN2 = DMIN + J4 = 4*( N0-2 ) - PP + J4P2 = J4 + 2*PP - 1 + Z( J4-2 ) = DNM2 + Z( J4P2 ) + IF( DNM2.LT.ZERO ) THEN + RETURN + ELSE + Z( J4 ) = Z( J4P2+2 )*( Z( J4P2 ) / Z( J4-2 ) ) + DNM1 = Z( J4P2+2 )*( DNM2 / Z( J4-2 ) ) - TAU + END IF + DMIN = MIN( DMIN, DNM1 ) +* + DMIN1 = DMIN + J4 = J4 + 4 + J4P2 = J4 + 2*PP - 1 + Z( J4-2 ) = DNM1 + Z( J4P2 ) + IF( DNM1.LT.ZERO ) THEN + RETURN + ELSE + Z( J4 ) = Z( J4P2+2 )*( Z( J4P2 ) / Z( J4-2 ) ) + DN = Z( J4P2+2 )*( DNM1 / Z( J4-2 ) ) - TAU + END IF + DMIN = MIN( DMIN, DN ) +* + END IF +* + Z( J4+2 ) = DN + Z( 4*N0-PP ) = EMIN + RETURN +* +* End of DLASQ5 +* + END diff --git a/applications/PUfoam/MoDeNaModels/CFD_tool_0D/src/eigen/src/dlasq6.f b/applications/PUfoam/MoDeNaModels/CFD_tool_0D/src/eigen/src/dlasq6.f new file mode 100644 index 000000000..e069fa6f7 --- /dev/null +++ b/applications/PUfoam/MoDeNaModels/CFD_tool_0D/src/eigen/src/dlasq6.f @@ -0,0 +1,254 @@ +*> \brief \b DLASQ6 +* +* =========== DOCUMENTATION =========== +* +* Online html documentation available at +* http://www.netlib.org/lapack/explore-html/ +* +*> \htmlonly +*> Download DLASQ6 + dependencies +*> +*> [TGZ] +*> +*> [ZIP] +*> +*> [TXT] +*> \endhtmlonly +* +* Definition: +* =========== +* +* SUBROUTINE DLASQ6( I0, N0, Z, PP, DMIN, DMIN1, DMIN2, DN, +* DNM1, DNM2 ) +* +* .. Scalar Arguments .. +* INTEGER I0, N0, PP +* DOUBLE PRECISION DMIN, DMIN1, DMIN2, DN, DNM1, DNM2 +* .. +* .. Array Arguments .. +* DOUBLE PRECISION Z( * ) +* .. +* +* +*> \par Purpose: +* ============= +*> +*> \verbatim +*> +*> DLASQ6 computes one dqd (shift equal to zero) transform in +*> ping-pong form, with protection against underflow and overflow. +*> \endverbatim +* +* Arguments: +* ========== +* +*> \param[in] I0 +*> \verbatim +*> I0 is INTEGER +*> First index. +*> \endverbatim +*> +*> \param[in] N0 +*> \verbatim +*> N0 is INTEGER +*> Last index. +*> \endverbatim +*> +*> \param[in] Z +*> \verbatim +*> Z is DOUBLE PRECISION array, dimension ( 4*N ) +*> Z holds the qd array. EMIN is stored in Z(4*N0) to avoid +*> an extra argument. +*> \endverbatim +*> +*> \param[in] PP +*> \verbatim +*> PP is INTEGER +*> PP=0 for ping, PP=1 for pong. +*> \endverbatim +*> +*> \param[out] DMIN +*> \verbatim +*> DMIN is DOUBLE PRECISION +*> Minimum value of d. +*> \endverbatim +*> +*> \param[out] DMIN1 +*> \verbatim +*> DMIN1 is DOUBLE PRECISION +*> Minimum value of d, excluding D( N0 ). +*> \endverbatim +*> +*> \param[out] DMIN2 +*> \verbatim +*> DMIN2 is DOUBLE PRECISION +*> Minimum value of d, excluding D( N0 ) and D( N0-1 ). +*> \endverbatim +*> +*> \param[out] DN +*> \verbatim +*> DN is DOUBLE PRECISION +*> d(N0), the last value of d. +*> \endverbatim +*> +*> \param[out] DNM1 +*> \verbatim +*> DNM1 is DOUBLE PRECISION +*> d(N0-1). +*> \endverbatim +*> +*> \param[out] DNM2 +*> \verbatim +*> DNM2 is DOUBLE PRECISION +*> d(N0-2). +*> \endverbatim +* +* Authors: +* ======== +* +*> \author Univ. of Tennessee +*> \author Univ. of California Berkeley +*> \author Univ. of Colorado Denver +*> \author NAG Ltd. +* +*> \date November 2011 +* +*> \ingroup auxOTHERcomputational +* +* ===================================================================== + SUBROUTINE DLASQ6( I0, N0, Z, PP, DMIN, DMIN1, DMIN2, DN, + $ DNM1, DNM2 ) +* +* -- LAPACK computational routine (version 3.4.0) -- +* -- LAPACK is a software package provided by Univ. of Tennessee, -- +* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- +* November 2011 +* +* .. Scalar Arguments .. + INTEGER I0, N0, PP + DOUBLE PRECISION DMIN, DMIN1, DMIN2, DN, DNM1, DNM2 +* .. +* .. Array Arguments .. + DOUBLE PRECISION Z( * ) +* .. +* +* ===================================================================== +* +* .. Parameter .. + DOUBLE PRECISION ZERO + PARAMETER ( ZERO = 0.0D0 ) +* .. +* .. Local Scalars .. + INTEGER J4, J4P2 + DOUBLE PRECISION D, EMIN, SAFMIN, TEMP +* .. +* .. External Function .. + DOUBLE PRECISION DLAMCH + EXTERNAL DLAMCH +* .. +* .. Intrinsic Functions .. + INTRINSIC MIN +* .. +* .. Executable Statements .. +* + IF( ( N0-I0-1 ).LE.0 ) + $ RETURN +* + SAFMIN = DLAMCH( 'Safe minimum' ) + J4 = 4*I0 + PP - 3 + EMIN = Z( J4+4 ) + D = Z( J4 ) + DMIN = D +* + IF( PP.EQ.0 ) THEN + DO 10 J4 = 4*I0, 4*( N0-3 ), 4 + Z( J4-2 ) = D + Z( J4-1 ) + IF( Z( J4-2 ).EQ.ZERO ) THEN + Z( J4 ) = ZERO + D = Z( J4+1 ) + DMIN = D + EMIN = ZERO + ELSE IF( SAFMIN*Z( J4+1 ).LT.Z( J4-2 ) .AND. + $ SAFMIN*Z( J4-2 ).LT.Z( J4+1 ) ) THEN + TEMP = Z( J4+1 ) / Z( J4-2 ) + Z( J4 ) = Z( J4-1 )*TEMP + D = D*TEMP + ELSE + Z( J4 ) = Z( J4+1 )*( Z( J4-1 ) / Z( J4-2 ) ) + D = Z( J4+1 )*( D / Z( J4-2 ) ) + END IF + DMIN = MIN( DMIN, D ) + EMIN = MIN( EMIN, Z( J4 ) ) + 10 CONTINUE + ELSE + DO 20 J4 = 4*I0, 4*( N0-3 ), 4 + Z( J4-3 ) = D + Z( J4 ) + IF( Z( J4-3 ).EQ.ZERO ) THEN + Z( J4-1 ) = ZERO + D = Z( J4+2 ) + DMIN = D + EMIN = ZERO + ELSE IF( SAFMIN*Z( J4+2 ).LT.Z( J4-3 ) .AND. + $ SAFMIN*Z( J4-3 ).LT.Z( J4+2 ) ) THEN + TEMP = Z( J4+2 ) / Z( J4-3 ) + Z( J4-1 ) = Z( J4 )*TEMP + D = D*TEMP + ELSE + Z( J4-1 ) = Z( J4+2 )*( Z( J4 ) / Z( J4-3 ) ) + D = Z( J4+2 )*( D / Z( J4-3 ) ) + END IF + DMIN = MIN( DMIN, D ) + EMIN = MIN( EMIN, Z( J4-1 ) ) + 20 CONTINUE + END IF +* +* Unroll last two steps. +* + DNM2 = D + DMIN2 = DMIN + J4 = 4*( N0-2 ) - PP + J4P2 = J4 + 2*PP - 1 + Z( J4-2 ) = DNM2 + Z( J4P2 ) + IF( Z( J4-2 ).EQ.ZERO ) THEN + Z( J4 ) = ZERO + DNM1 = Z( J4P2+2 ) + DMIN = DNM1 + EMIN = ZERO + ELSE IF( SAFMIN*Z( J4P2+2 ).LT.Z( J4-2 ) .AND. + $ SAFMIN*Z( J4-2 ).LT.Z( J4P2+2 ) ) THEN + TEMP = Z( J4P2+2 ) / Z( J4-2 ) + Z( J4 ) = Z( J4P2 )*TEMP + DNM1 = DNM2*TEMP + ELSE + Z( J4 ) = Z( J4P2+2 )*( Z( J4P2 ) / Z( J4-2 ) ) + DNM1 = Z( J4P2+2 )*( DNM2 / Z( J4-2 ) ) + END IF + DMIN = MIN( DMIN, DNM1 ) +* + DMIN1 = DMIN + J4 = J4 + 4 + J4P2 = J4 + 2*PP - 1 + Z( J4-2 ) = DNM1 + Z( J4P2 ) + IF( Z( J4-2 ).EQ.ZERO ) THEN + Z( J4 ) = ZERO + DN = Z( J4P2+2 ) + DMIN = DN + EMIN = ZERO + ELSE IF( SAFMIN*Z( J4P2+2 ).LT.Z( J4-2 ) .AND. + $ SAFMIN*Z( J4-2 ).LT.Z( J4P2+2 ) ) THEN + TEMP = Z( J4P2+2 ) / Z( J4-2 ) + Z( J4 ) = Z( J4P2 )*TEMP + DN = DNM1*TEMP + ELSE + Z( J4 ) = Z( J4P2+2 )*( Z( J4P2 ) / Z( J4-2 ) ) + DN = Z( J4P2+2 )*( DNM1 / Z( J4-2 ) ) + END IF + DMIN = MIN( DMIN, DN ) +* + Z( J4+2 ) = DN + Z( 4*N0-PP ) = EMIN + RETURN +* +* End of DLASQ6 +* + END diff --git a/applications/PUfoam/MoDeNaModels/CFD_tool_0D/src/eigen/src/dlasr.f b/applications/PUfoam/MoDeNaModels/CFD_tool_0D/src/eigen/src/dlasr.f new file mode 100644 index 000000000..bbe6217dd --- /dev/null +++ b/applications/PUfoam/MoDeNaModels/CFD_tool_0D/src/eigen/src/dlasr.f @@ -0,0 +1,436 @@ +*> \brief \b DLASR +* +* =========== DOCUMENTATION =========== +* +* Online html documentation available at +* http://www.netlib.org/lapack/explore-html/ +* +*> \htmlonly +*> Download DLASR + dependencies +*> +*> [TGZ] +*> +*> [ZIP] +*> +*> [TXT] +*> \endhtmlonly +* +* Definition: +* =========== +* +* SUBROUTINE DLASR( SIDE, PIVOT, DIRECT, M, N, C, S, A, LDA ) +* +* .. Scalar Arguments .. +* CHARACTER DIRECT, PIVOT, SIDE +* INTEGER LDA, M, N +* .. +* .. Array Arguments .. +* DOUBLE PRECISION A( LDA, * ), C( * ), S( * ) +* .. +* +* +*> \par Purpose: +* ============= +*> +*> \verbatim +*> +*> DLASR applies a sequence of plane rotations to a real matrix A, +*> from either the left or the right. +*> +*> When SIDE = 'L', the transformation takes the form +*> +*> A := P*A +*> +*> and when SIDE = 'R', the transformation takes the form +*> +*> A := A*P**T +*> +*> where P is an orthogonal matrix consisting of a sequence of z plane +*> rotations, with z = M when SIDE = 'L' and z = N when SIDE = 'R', +*> and P**T is the transpose of P. +*> +*> When DIRECT = 'F' (Forward sequence), then +*> +*> P = P(z-1) * ... * P(2) * P(1) +*> +*> and when DIRECT = 'B' (Backward sequence), then +*> +*> P = P(1) * P(2) * ... * P(z-1) +*> +*> where P(k) is a plane rotation matrix defined by the 2-by-2 rotation +*> +*> R(k) = ( c(k) s(k) ) +*> = ( -s(k) c(k) ). +*> +*> When PIVOT = 'V' (Variable pivot), the rotation is performed +*> for the plane (k,k+1), i.e., P(k) has the form +*> +*> P(k) = ( 1 ) +*> ( ... ) +*> ( 1 ) +*> ( c(k) s(k) ) +*> ( -s(k) c(k) ) +*> ( 1 ) +*> ( ... ) +*> ( 1 ) +*> +*> where R(k) appears as a rank-2 modification to the identity matrix in +*> rows and columns k and k+1. +*> +*> When PIVOT = 'T' (Top pivot), the rotation is performed for the +*> plane (1,k+1), so P(k) has the form +*> +*> P(k) = ( c(k) s(k) ) +*> ( 1 ) +*> ( ... ) +*> ( 1 ) +*> ( -s(k) c(k) ) +*> ( 1 ) +*> ( ... ) +*> ( 1 ) +*> +*> where R(k) appears in rows and columns 1 and k+1. +*> +*> Similarly, when PIVOT = 'B' (Bottom pivot), the rotation is +*> performed for the plane (k,z), giving P(k) the form +*> +*> P(k) = ( 1 ) +*> ( ... ) +*> ( 1 ) +*> ( c(k) s(k) ) +*> ( 1 ) +*> ( ... ) +*> ( 1 ) +*> ( -s(k) c(k) ) +*> +*> where R(k) appears in rows and columns k and z. The rotations are +*> performed without ever forming P(k) explicitly. +*> \endverbatim +* +* Arguments: +* ========== +* +*> \param[in] SIDE +*> \verbatim +*> SIDE is CHARACTER*1 +*> Specifies whether the plane rotation matrix P is applied to +*> A on the left or the right. +*> = 'L': Left, compute A := P*A +*> = 'R': Right, compute A:= A*P**T +*> \endverbatim +*> +*> \param[in] PIVOT +*> \verbatim +*> PIVOT is CHARACTER*1 +*> Specifies the plane for which P(k) is a plane rotation +*> matrix. +*> = 'V': Variable pivot, the plane (k,k+1) +*> = 'T': Top pivot, the plane (1,k+1) +*> = 'B': Bottom pivot, the plane (k,z) +*> \endverbatim +*> +*> \param[in] DIRECT +*> \verbatim +*> DIRECT is CHARACTER*1 +*> Specifies whether P is a forward or backward sequence of +*> plane rotations. +*> = 'F': Forward, P = P(z-1)*...*P(2)*P(1) +*> = 'B': Backward, P = P(1)*P(2)*...*P(z-1) +*> \endverbatim +*> +*> \param[in] M +*> \verbatim +*> M is INTEGER +*> The number of rows of the matrix A. If m <= 1, an immediate +*> return is effected. +*> \endverbatim +*> +*> \param[in] N +*> \verbatim +*> N is INTEGER +*> The number of columns of the matrix A. If n <= 1, an +*> immediate return is effected. +*> \endverbatim +*> +*> \param[in] C +*> \verbatim +*> C is DOUBLE PRECISION array, dimension +*> (M-1) if SIDE = 'L' +*> (N-1) if SIDE = 'R' +*> The cosines c(k) of the plane rotations. +*> \endverbatim +*> +*> \param[in] S +*> \verbatim +*> S is DOUBLE PRECISION array, dimension +*> (M-1) if SIDE = 'L' +*> (N-1) if SIDE = 'R' +*> The sines s(k) of the plane rotations. The 2-by-2 plane +*> rotation part of the matrix P(k), R(k), has the form +*> R(k) = ( c(k) s(k) ) +*> ( -s(k) c(k) ). +*> \endverbatim +*> +*> \param[in,out] A +*> \verbatim +*> A is DOUBLE PRECISION array, dimension (LDA,N) +*> The M-by-N matrix A. On exit, A is overwritten by P*A if +*> SIDE = 'R' or by A*P**T if SIDE = 'L'. +*> \endverbatim +*> +*> \param[in] LDA +*> \verbatim +*> LDA is INTEGER +*> The leading dimension of the array A. LDA >= max(1,M). +*> \endverbatim +* +* Authors: +* ======== +* +*> \author Univ. of Tennessee +*> \author Univ. of California Berkeley +*> \author Univ. of Colorado Denver +*> \author NAG Ltd. +* +*> \date November 2011 +* +*> \ingroup auxOTHERauxiliary +* +* ===================================================================== + SUBROUTINE DLASR( SIDE, PIVOT, DIRECT, M, N, C, S, A, LDA ) +* +* -- LAPACK auxiliary routine (version 3.4.0) -- +* -- LAPACK is a software package provided by Univ. of Tennessee, -- +* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- +* November 2011 +* +* .. Scalar Arguments .. + CHARACTER DIRECT, PIVOT, SIDE + INTEGER LDA, M, N +* .. +* .. Array Arguments .. + DOUBLE PRECISION A( LDA, * ), C( * ), S( * ) +* .. +* +* ===================================================================== +* +* .. Parameters .. + DOUBLE PRECISION ONE, ZERO + PARAMETER ( ONE = 1.0D+0, ZERO = 0.0D+0 ) +* .. +* .. Local Scalars .. + INTEGER I, INFO, J + DOUBLE PRECISION CTEMP, STEMP, TEMP +* .. +* .. External Functions .. + LOGICAL LSAME + EXTERNAL LSAME +* .. +* .. External Subroutines .. + EXTERNAL XERBLA +* .. +* .. Intrinsic Functions .. + INTRINSIC MAX +* .. +* .. Executable Statements .. +* +* Test the input parameters +* + INFO = 0 + IF( .NOT.( LSAME( SIDE, 'L' ) .OR. LSAME( SIDE, 'R' ) ) ) THEN + INFO = 1 + ELSE IF( .NOT.( LSAME( PIVOT, 'V' ) .OR. LSAME( PIVOT, + $ 'T' ) .OR. LSAME( PIVOT, 'B' ) ) ) THEN + INFO = 2 + ELSE IF( .NOT.( LSAME( DIRECT, 'F' ) .OR. LSAME( DIRECT, 'B' ) ) ) + $ THEN + INFO = 3 + ELSE IF( M.LT.0 ) THEN + INFO = 4 + ELSE IF( N.LT.0 ) THEN + INFO = 5 + ELSE IF( LDA.LT.MAX( 1, M ) ) THEN + INFO = 9 + END IF + IF( INFO.NE.0 ) THEN + CALL XERBLA( 'DLASR ', INFO ) + RETURN + END IF +* +* Quick return if possible +* + IF( ( M.EQ.0 ) .OR. ( N.EQ.0 ) ) + $ RETURN + IF( LSAME( SIDE, 'L' ) ) THEN +* +* Form P * A +* + IF( LSAME( PIVOT, 'V' ) ) THEN + IF( LSAME( DIRECT, 'F' ) ) THEN + DO 20 J = 1, M - 1 + CTEMP = C( J ) + STEMP = S( J ) + IF( ( CTEMP.NE.ONE ) .OR. ( STEMP.NE.ZERO ) ) THEN + DO 10 I = 1, N + TEMP = A( J+1, I ) + A( J+1, I ) = CTEMP*TEMP - STEMP*A( J, I ) + A( J, I ) = STEMP*TEMP + CTEMP*A( J, I ) + 10 CONTINUE + END IF + 20 CONTINUE + ELSE IF( LSAME( DIRECT, 'B' ) ) THEN + DO 40 J = M - 1, 1, -1 + CTEMP = C( J ) + STEMP = S( J ) + IF( ( CTEMP.NE.ONE ) .OR. ( STEMP.NE.ZERO ) ) THEN + DO 30 I = 1, N + TEMP = A( J+1, I ) + A( J+1, I ) = CTEMP*TEMP - STEMP*A( J, I ) + A( J, I ) = STEMP*TEMP + CTEMP*A( J, I ) + 30 CONTINUE + END IF + 40 CONTINUE + END IF + ELSE IF( LSAME( PIVOT, 'T' ) ) THEN + IF( LSAME( DIRECT, 'F' ) ) THEN + DO 60 J = 2, M + CTEMP = C( J-1 ) + STEMP = S( J-1 ) + IF( ( CTEMP.NE.ONE ) .OR. ( STEMP.NE.ZERO ) ) THEN + DO 50 I = 1, N + TEMP = A( J, I ) + A( J, I ) = CTEMP*TEMP - STEMP*A( 1, I ) + A( 1, I ) = STEMP*TEMP + CTEMP*A( 1, I ) + 50 CONTINUE + END IF + 60 CONTINUE + ELSE IF( LSAME( DIRECT, 'B' ) ) THEN + DO 80 J = M, 2, -1 + CTEMP = C( J-1 ) + STEMP = S( J-1 ) + IF( ( CTEMP.NE.ONE ) .OR. ( STEMP.NE.ZERO ) ) THEN + DO 70 I = 1, N + TEMP = A( J, I ) + A( J, I ) = CTEMP*TEMP - STEMP*A( 1, I ) + A( 1, I ) = STEMP*TEMP + CTEMP*A( 1, I ) + 70 CONTINUE + END IF + 80 CONTINUE + END IF + ELSE IF( LSAME( PIVOT, 'B' ) ) THEN + IF( LSAME( DIRECT, 'F' ) ) THEN + DO 100 J = 1, M - 1 + CTEMP = C( J ) + STEMP = S( J ) + IF( ( CTEMP.NE.ONE ) .OR. ( STEMP.NE.ZERO ) ) THEN + DO 90 I = 1, N + TEMP = A( J, I ) + A( J, I ) = STEMP*A( M, I ) + CTEMP*TEMP + A( M, I ) = CTEMP*A( M, I ) - STEMP*TEMP + 90 CONTINUE + END IF + 100 CONTINUE + ELSE IF( LSAME( DIRECT, 'B' ) ) THEN + DO 120 J = M - 1, 1, -1 + CTEMP = C( J ) + STEMP = S( J ) + IF( ( CTEMP.NE.ONE ) .OR. ( STEMP.NE.ZERO ) ) THEN + DO 110 I = 1, N + TEMP = A( J, I ) + A( J, I ) = STEMP*A( M, I ) + CTEMP*TEMP + A( M, I ) = CTEMP*A( M, I ) - STEMP*TEMP + 110 CONTINUE + END IF + 120 CONTINUE + END IF + END IF + ELSE IF( LSAME( SIDE, 'R' ) ) THEN +* +* Form A * P**T +* + IF( LSAME( PIVOT, 'V' ) ) THEN + IF( LSAME( DIRECT, 'F' ) ) THEN + DO 140 J = 1, N - 1 + CTEMP = C( J ) + STEMP = S( J ) + IF( ( CTEMP.NE.ONE ) .OR. ( STEMP.NE.ZERO ) ) THEN + DO 130 I = 1, M + TEMP = A( I, J+1 ) + A( I, J+1 ) = CTEMP*TEMP - STEMP*A( I, J ) + A( I, J ) = STEMP*TEMP + CTEMP*A( I, J ) + 130 CONTINUE + END IF + 140 CONTINUE + ELSE IF( LSAME( DIRECT, 'B' ) ) THEN + DO 160 J = N - 1, 1, -1 + CTEMP = C( J ) + STEMP = S( J ) + IF( ( CTEMP.NE.ONE ) .OR. ( STEMP.NE.ZERO ) ) THEN + DO 150 I = 1, M + TEMP = A( I, J+1 ) + A( I, J+1 ) = CTEMP*TEMP - STEMP*A( I, J ) + A( I, J ) = STEMP*TEMP + CTEMP*A( I, J ) + 150 CONTINUE + END IF + 160 CONTINUE + END IF + ELSE IF( LSAME( PIVOT, 'T' ) ) THEN + IF( LSAME( DIRECT, 'F' ) ) THEN + DO 180 J = 2, N + CTEMP = C( J-1 ) + STEMP = S( J-1 ) + IF( ( CTEMP.NE.ONE ) .OR. ( STEMP.NE.ZERO ) ) THEN + DO 170 I = 1, M + TEMP = A( I, J ) + A( I, J ) = CTEMP*TEMP - STEMP*A( I, 1 ) + A( I, 1 ) = STEMP*TEMP + CTEMP*A( I, 1 ) + 170 CONTINUE + END IF + 180 CONTINUE + ELSE IF( LSAME( DIRECT, 'B' ) ) THEN + DO 200 J = N, 2, -1 + CTEMP = C( J-1 ) + STEMP = S( J-1 ) + IF( ( CTEMP.NE.ONE ) .OR. ( STEMP.NE.ZERO ) ) THEN + DO 190 I = 1, M + TEMP = A( I, J ) + A( I, J ) = CTEMP*TEMP - STEMP*A( I, 1 ) + A( I, 1 ) = STEMP*TEMP + CTEMP*A( I, 1 ) + 190 CONTINUE + END IF + 200 CONTINUE + END IF + ELSE IF( LSAME( PIVOT, 'B' ) ) THEN + IF( LSAME( DIRECT, 'F' ) ) THEN + DO 220 J = 1, N - 1 + CTEMP = C( J ) + STEMP = S( J ) + IF( ( CTEMP.NE.ONE ) .OR. ( STEMP.NE.ZERO ) ) THEN + DO 210 I = 1, M + TEMP = A( I, J ) + A( I, J ) = STEMP*A( I, N ) + CTEMP*TEMP + A( I, N ) = CTEMP*A( I, N ) - STEMP*TEMP + 210 CONTINUE + END IF + 220 CONTINUE + ELSE IF( LSAME( DIRECT, 'B' ) ) THEN + DO 240 J = N - 1, 1, -1 + CTEMP = C( J ) + STEMP = S( J ) + IF( ( CTEMP.NE.ONE ) .OR. ( STEMP.NE.ZERO ) ) THEN + DO 230 I = 1, M + TEMP = A( I, J ) + A( I, J ) = STEMP*A( I, N ) + CTEMP*TEMP + A( I, N ) = CTEMP*A( I, N ) - STEMP*TEMP + 230 CONTINUE + END IF + 240 CONTINUE + END IF + END IF + END IF +* + RETURN +* +* End of DLASR +* + END diff --git a/applications/PUfoam/MoDeNaModels/CFD_tool_0D/src/eigen/src/dlasrt.f b/applications/PUfoam/MoDeNaModels/CFD_tool_0D/src/eigen/src/dlasrt.f new file mode 100644 index 000000000..fe8f526a2 --- /dev/null +++ b/applications/PUfoam/MoDeNaModels/CFD_tool_0D/src/eigen/src/dlasrt.f @@ -0,0 +1,303 @@ +*> \brief \b DLASRT +* +* =========== DOCUMENTATION =========== +* +* Online html documentation available at +* http://www.netlib.org/lapack/explore-html/ +* +*> \htmlonly +*> Download DLASRT + dependencies +*> +*> [TGZ] +*> +*> [ZIP] +*> +*> [TXT] +*> \endhtmlonly +* +* Definition: +* =========== +* +* SUBROUTINE DLASRT( ID, N, D, INFO ) +* +* .. Scalar Arguments .. +* CHARACTER ID +* INTEGER INFO, N +* .. +* .. Array Arguments .. +* DOUBLE PRECISION D( * ) +* .. +* +* +*> \par Purpose: +* ============= +*> +*> \verbatim +*> +*> Sort the numbers in D in increasing order (if ID = 'I') or +*> in decreasing order (if ID = 'D' ). +*> +*> Use Quick Sort, reverting to Insertion sort on arrays of +*> size <= 20. Dimension of STACK limits N to about 2**32. +*> \endverbatim +* +* Arguments: +* ========== +* +*> \param[in] ID +*> \verbatim +*> ID is CHARACTER*1 +*> = 'I': sort D in increasing order; +*> = 'D': sort D in decreasing order. +*> \endverbatim +*> +*> \param[in] N +*> \verbatim +*> N is INTEGER +*> The length of the array D. +*> \endverbatim +*> +*> \param[in,out] D +*> \verbatim +*> D is DOUBLE PRECISION array, dimension (N) +*> On entry, the array to be sorted. +*> On exit, D has been sorted into increasing order +*> (D(1) <= ... <= D(N) ) or into decreasing order +*> (D(1) >= ... >= D(N) ), depending on ID. +*> \endverbatim +*> +*> \param[out] INFO +*> \verbatim +*> INFO is INTEGER +*> = 0: successful exit +*> < 0: if INFO = -i, the i-th argument had an illegal value +*> \endverbatim +* +* Authors: +* ======== +* +*> \author Univ. of Tennessee +*> \author Univ. of California Berkeley +*> \author Univ. of Colorado Denver +*> \author NAG Ltd. +* +*> \date November 2011 +* +*> \ingroup auxOTHERcomputational +* +* ===================================================================== + SUBROUTINE DLASRT( ID, N, D, INFO ) +* +* -- LAPACK computational routine (version 3.4.0) -- +* -- LAPACK is a software package provided by Univ. of Tennessee, -- +* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- +* November 2011 +* +* .. Scalar Arguments .. + CHARACTER ID + INTEGER INFO, N +* .. +* .. Array Arguments .. + DOUBLE PRECISION D( * ) +* .. +* +* ===================================================================== +* +* .. Parameters .. + INTEGER SELECT + PARAMETER ( SELECT = 20 ) +* .. +* .. Local Scalars .. + INTEGER DIR, ENDD, I, J, START, STKPNT + DOUBLE PRECISION D1, D2, D3, DMNMX, TMP +* .. +* .. Local Arrays .. + INTEGER STACK( 2, 32 ) +* .. +* .. External Functions .. + LOGICAL LSAME + EXTERNAL LSAME +* .. +* .. External Subroutines .. + EXTERNAL XERBLA +* .. +* .. Executable Statements .. +* +* Test the input paramters. +* + INFO = 0 + DIR = -1 + IF( LSAME( ID, 'D' ) ) THEN + DIR = 0 + ELSE IF( LSAME( ID, 'I' ) ) THEN + DIR = 1 + END IF + IF( DIR.EQ.-1 ) THEN + INFO = -1 + ELSE IF( N.LT.0 ) THEN + INFO = -2 + END IF + IF( INFO.NE.0 ) THEN + CALL XERBLA( 'DLASRT', -INFO ) + RETURN + END IF +* +* Quick return if possible +* + IF( N.LE.1 ) + $ RETURN +* + STKPNT = 1 + STACK( 1, 1 ) = 1 + STACK( 2, 1 ) = N + 10 CONTINUE + START = STACK( 1, STKPNT ) + ENDD = STACK( 2, STKPNT ) + STKPNT = STKPNT - 1 + IF( ENDD-START.LE.SELECT .AND. ENDD-START.GT.0 ) THEN +* +* Do Insertion sort on D( START:ENDD ) +* + IF( DIR.EQ.0 ) THEN +* +* Sort into decreasing order +* + DO 30 I = START + 1, ENDD + DO 20 J = I, START + 1, -1 + IF( D( J ).GT.D( J-1 ) ) THEN + DMNMX = D( J ) + D( J ) = D( J-1 ) + D( J-1 ) = DMNMX + ELSE + GO TO 30 + END IF + 20 CONTINUE + 30 CONTINUE +* + ELSE +* +* Sort into increasing order +* + DO 50 I = START + 1, ENDD + DO 40 J = I, START + 1, -1 + IF( D( J ).LT.D( J-1 ) ) THEN + DMNMX = D( J ) + D( J ) = D( J-1 ) + D( J-1 ) = DMNMX + ELSE + GO TO 50 + END IF + 40 CONTINUE + 50 CONTINUE +* + END IF +* + ELSE IF( ENDD-START.GT.SELECT ) THEN +* +* Partition D( START:ENDD ) and stack parts, largest one first +* +* Choose partition entry as median of 3 +* + D1 = D( START ) + D2 = D( ENDD ) + I = ( START+ENDD ) / 2 + D3 = D( I ) + IF( D1.LT.D2 ) THEN + IF( D3.LT.D1 ) THEN + DMNMX = D1 + ELSE IF( D3.LT.D2 ) THEN + DMNMX = D3 + ELSE + DMNMX = D2 + END IF + ELSE + IF( D3.LT.D2 ) THEN + DMNMX = D2 + ELSE IF( D3.LT.D1 ) THEN + DMNMX = D3 + ELSE + DMNMX = D1 + END IF + END IF +* + IF( DIR.EQ.0 ) THEN +* +* Sort into decreasing order +* + I = START - 1 + J = ENDD + 1 + 60 CONTINUE + 70 CONTINUE + J = J - 1 + IF( D( J ).LT.DMNMX ) + $ GO TO 70 + 80 CONTINUE + I = I + 1 + IF( D( I ).GT.DMNMX ) + $ GO TO 80 + IF( I.LT.J ) THEN + TMP = D( I ) + D( I ) = D( J ) + D( J ) = TMP + GO TO 60 + END IF + IF( J-START.GT.ENDD-J-1 ) THEN + STKPNT = STKPNT + 1 + STACK( 1, STKPNT ) = START + STACK( 2, STKPNT ) = J + STKPNT = STKPNT + 1 + STACK( 1, STKPNT ) = J + 1 + STACK( 2, STKPNT ) = ENDD + ELSE + STKPNT = STKPNT + 1 + STACK( 1, STKPNT ) = J + 1 + STACK( 2, STKPNT ) = ENDD + STKPNT = STKPNT + 1 + STACK( 1, STKPNT ) = START + STACK( 2, STKPNT ) = J + END IF + ELSE +* +* Sort into increasing order +* + I = START - 1 + J = ENDD + 1 + 90 CONTINUE + 100 CONTINUE + J = J - 1 + IF( D( J ).GT.DMNMX ) + $ GO TO 100 + 110 CONTINUE + I = I + 1 + IF( D( I ).LT.DMNMX ) + $ GO TO 110 + IF( I.LT.J ) THEN + TMP = D( I ) + D( I ) = D( J ) + D( J ) = TMP + GO TO 90 + END IF + IF( J-START.GT.ENDD-J-1 ) THEN + STKPNT = STKPNT + 1 + STACK( 1, STKPNT ) = START + STACK( 2, STKPNT ) = J + STKPNT = STKPNT + 1 + STACK( 1, STKPNT ) = J + 1 + STACK( 2, STKPNT ) = ENDD + ELSE + STKPNT = STKPNT + 1 + STACK( 1, STKPNT ) = J + 1 + STACK( 2, STKPNT ) = ENDD + STKPNT = STKPNT + 1 + STACK( 1, STKPNT ) = START + STACK( 2, STKPNT ) = J + END IF + END IF + END IF + IF( STKPNT.GT.0 ) + $ GO TO 10 + RETURN +* +* End of DLASRT +* + END diff --git a/applications/PUfoam/MoDeNaModels/CFD_tool_0D/src/eigen/src/dlassq.f b/applications/PUfoam/MoDeNaModels/CFD_tool_0D/src/eigen/src/dlassq.f new file mode 100644 index 000000000..51d5a22d2 --- /dev/null +++ b/applications/PUfoam/MoDeNaModels/CFD_tool_0D/src/eigen/src/dlassq.f @@ -0,0 +1,151 @@ +*> \brief \b DLASSQ +* +* =========== DOCUMENTATION =========== +* +* Online html documentation available at +* http://www.netlib.org/lapack/explore-html/ +* +*> \htmlonly +*> Download DLASSQ + dependencies +*> +*> [TGZ] +*> +*> [ZIP] +*> +*> [TXT] +*> \endhtmlonly +* +* Definition: +* =========== +* +* SUBROUTINE DLASSQ( N, X, INCX, SCALE, SUMSQ ) +* +* .. Scalar Arguments .. +* INTEGER INCX, N +* DOUBLE PRECISION SCALE, SUMSQ +* .. +* .. Array Arguments .. +* DOUBLE PRECISION X( * ) +* .. +* +* +*> \par Purpose: +* ============= +*> +*> \verbatim +*> +*> DLASSQ returns the values scl and smsq such that +*> +*> ( scl**2 )*smsq = x( 1 )**2 +...+ x( n )**2 + ( scale**2 )*sumsq, +*> +*> where x( i ) = X( 1 + ( i - 1 )*INCX ). The value of sumsq is +*> assumed to be non-negative and scl returns the value +*> +*> scl = max( scale, abs( x( i ) ) ). +*> +*> scale and sumsq must be supplied in SCALE and SUMSQ and +*> scl and smsq are overwritten on SCALE and SUMSQ respectively. +*> +*> The routine makes only one pass through the vector x. +*> \endverbatim +* +* Arguments: +* ========== +* +*> \param[in] N +*> \verbatim +*> N is INTEGER +*> The number of elements to be used from the vector X. +*> \endverbatim +*> +*> \param[in] X +*> \verbatim +*> X is DOUBLE PRECISION array, dimension (N) +*> The vector for which a scaled sum of squares is computed. +*> x( i ) = X( 1 + ( i - 1 )*INCX ), 1 <= i <= n. +*> \endverbatim +*> +*> \param[in] INCX +*> \verbatim +*> INCX is INTEGER +*> The increment between successive values of the vector X. +*> INCX > 0. +*> \endverbatim +*> +*> \param[in,out] SCALE +*> \verbatim +*> SCALE is DOUBLE PRECISION +*> On entry, the value scale in the equation above. +*> On exit, SCALE is overwritten with scl , the scaling factor +*> for the sum of squares. +*> \endverbatim +*> +*> \param[in,out] SUMSQ +*> \verbatim +*> SUMSQ is DOUBLE PRECISION +*> On entry, the value sumsq in the equation above. +*> On exit, SUMSQ is overwritten with smsq , the basic sum of +*> squares from which scl has been factored out. +*> \endverbatim +* +* Authors: +* ======== +* +*> \author Univ. of Tennessee +*> \author Univ. of California Berkeley +*> \author Univ. of Colorado Denver +*> \author NAG Ltd. +* +*> \date November 2011 +* +*> \ingroup auxOTHERauxiliary +* +* ===================================================================== + SUBROUTINE DLASSQ( N, X, INCX, SCALE, SUMSQ ) +* +* -- LAPACK auxiliary routine (version 3.4.0) -- +* -- LAPACK is a software package provided by Univ. of Tennessee, -- +* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- +* November 2011 +* +* .. Scalar Arguments .. + INTEGER INCX, N + DOUBLE PRECISION SCALE, SUMSQ +* .. +* .. Array Arguments .. + DOUBLE PRECISION X( * ) +* .. +* +* ===================================================================== +* +* .. Parameters .. + DOUBLE PRECISION ZERO + PARAMETER ( ZERO = 0.0D+0 ) +* .. +* .. Local Scalars .. + INTEGER IX + DOUBLE PRECISION ABSXI +* .. +* .. Intrinsic Functions .. + INTRINSIC ABS +* .. +* .. Executable Statements .. +* + IF( N.GT.0 ) THEN + DO 10 IX = 1, 1 + ( N-1 )*INCX, INCX + IF( X( IX ).NE.ZERO ) THEN + ABSXI = ABS( X( IX ) ) + IF( SCALE.LT.ABSXI ) THEN + SUMSQ = 1 + SUMSQ*( SCALE / ABSXI )**2 + SCALE = ABSXI + ELSE + SUMSQ = SUMSQ + ( ABSXI / SCALE )**2 + END IF + END IF + 10 CONTINUE + END IF + RETURN +* +* End of DLASSQ +* + END diff --git a/applications/PUfoam/MoDeNaModels/CFD_tool_0D/src/eigen/src/dlaswp.f b/applications/PUfoam/MoDeNaModels/CFD_tool_0D/src/eigen/src/dlaswp.f new file mode 100644 index 000000000..937e12b2f --- /dev/null +++ b/applications/PUfoam/MoDeNaModels/CFD_tool_0D/src/eigen/src/dlaswp.f @@ -0,0 +1,191 @@ +*> \brief \b DLASWP performs a series of row interchanges on a general rectangular matrix. +* +* =========== DOCUMENTATION =========== +* +* Online html documentation available at +* http://www.netlib.org/lapack/explore-html/ +* +*> \htmlonly +*> Download DLASWP + dependencies +*> +*> [TGZ] +*> +*> [ZIP] +*> +*> [TXT] +*> \endhtmlonly +* +* Definition: +* =========== +* +* SUBROUTINE DLASWP( N, A, LDA, K1, K2, IPIV, INCX ) +* +* .. Scalar Arguments .. +* INTEGER INCX, K1, K2, LDA, N +* .. +* .. Array Arguments .. +* INTEGER IPIV( * ) +* DOUBLE PRECISION A( LDA, * ) +* .. +* +* +*> \par Purpose: +* ============= +*> +*> \verbatim +*> +*> DLASWP performs a series of row interchanges on the matrix A. +*> One row interchange is initiated for each of rows K1 through K2 of A. +*> \endverbatim +* +* Arguments: +* ========== +* +*> \param[in] N +*> \verbatim +*> N is INTEGER +*> The number of columns of the matrix A. +*> \endverbatim +*> +*> \param[in,out] A +*> \verbatim +*> A is DOUBLE PRECISION array, dimension (LDA,N) +*> On entry, the matrix of column dimension N to which the row +*> interchanges will be applied. +*> On exit, the permuted matrix. +*> \endverbatim +*> +*> \param[in] LDA +*> \verbatim +*> LDA is INTEGER +*> The leading dimension of the array A. +*> \endverbatim +*> +*> \param[in] K1 +*> \verbatim +*> K1 is INTEGER +*> The first element of IPIV for which a row interchange will +*> be done. +*> \endverbatim +*> +*> \param[in] K2 +*> \verbatim +*> K2 is INTEGER +*> The last element of IPIV for which a row interchange will +*> be done. +*> \endverbatim +*> +*> \param[in] IPIV +*> \verbatim +*> IPIV is INTEGER array, dimension (K2*abs(INCX)) +*> The vector of pivot indices. Only the elements in positions +*> K1 through K2 of IPIV are accessed. +*> IPIV(K) = L implies rows K and L are to be interchanged. +*> \endverbatim +*> +*> \param[in] INCX +*> \verbatim +*> INCX is INTEGER +*> The increment between successive values of IPIV. If IPIV +*> is negative, the pivots are applied in reverse order. +*> \endverbatim +* +* Authors: +* ======== +* +*> \author Univ. of Tennessee +*> \author Univ. of California Berkeley +*> \author Univ. of Colorado Denver +*> \author NAG Ltd. +* +*> \date September 2012 +* +*> \ingroup doubleOTHERauxiliary +* +*> \par Further Details: +* ===================== +*> +*> \verbatim +*> +*> Modified by +*> R. C. Whaley, Computer Science Dept., Univ. of Tenn., Knoxville, USA +*> \endverbatim +*> +* ===================================================================== + SUBROUTINE DLASWP( N, A, LDA, K1, K2, IPIV, INCX ) +* +* -- LAPACK auxiliary routine (version 3.4.2) -- +* -- LAPACK is a software package provided by Univ. of Tennessee, -- +* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- +* September 2012 +* +* .. Scalar Arguments .. + INTEGER INCX, K1, K2, LDA, N +* .. +* .. Array Arguments .. + INTEGER IPIV( * ) + DOUBLE PRECISION A( LDA, * ) +* .. +* +* ===================================================================== +* +* .. Local Scalars .. + INTEGER I, I1, I2, INC, IP, IX, IX0, J, K, N32 + DOUBLE PRECISION TEMP +* .. +* .. Executable Statements .. +* +* Interchange row I with row IPIV(I) for each of rows K1 through K2. +* + IF( INCX.GT.0 ) THEN + IX0 = K1 + I1 = K1 + I2 = K2 + INC = 1 + ELSE IF( INCX.LT.0 ) THEN + IX0 = 1 + ( 1-K2 )*INCX + I1 = K2 + I2 = K1 + INC = -1 + ELSE + RETURN + END IF +* + N32 = ( N / 32 )*32 + IF( N32.NE.0 ) THEN + DO 30 J = 1, N32, 32 + IX = IX0 + DO 20 I = I1, I2, INC + IP = IPIV( IX ) + IF( IP.NE.I ) THEN + DO 10 K = J, J + 31 + TEMP = A( I, K ) + A( I, K ) = A( IP, K ) + A( IP, K ) = TEMP + 10 CONTINUE + END IF + IX = IX + INCX + 20 CONTINUE + 30 CONTINUE + END IF + IF( N32.NE.N ) THEN + N32 = N32 + 1 + IX = IX0 + DO 50 I = I1, I2, INC + IP = IPIV( IX ) + IF( IP.NE.I ) THEN + DO 40 K = N32, N + TEMP = A( I, K ) + A( I, K ) = A( IP, K ) + A( IP, K ) = TEMP + 40 CONTINUE + END IF + IX = IX + INCX + 50 CONTINUE + END IF +* + RETURN +* +* End of DLASWP +* + END diff --git a/applications/PUfoam/MoDeNaModels/CFD_tool_0D/src/eigen/src/dscal.f b/applications/PUfoam/MoDeNaModels/CFD_tool_0D/src/eigen/src/dscal.f new file mode 100644 index 000000000..32dc5e54d --- /dev/null +++ b/applications/PUfoam/MoDeNaModels/CFD_tool_0D/src/eigen/src/dscal.f @@ -0,0 +1,111 @@ +*> \brief \b DSCAL +* +* =========== DOCUMENTATION =========== +* +* Online html documentation available at +* http://www.netlib.org/lapack/explore-html/ +* +* Definition: +* =========== +* +* SUBROUTINE DSCAL(N,DA,DX,INCX) +* +* .. Scalar Arguments .. +* DOUBLE PRECISION DA +* INTEGER INCX,N +* .. +* .. Array Arguments .. +* DOUBLE PRECISION DX(*) +* .. +* +* +*> \par Purpose: +* ============= +*> +*> \verbatim +*> +*> DSCAL scales a vector by a constant. +*> uses unrolled loops for increment equal to one. +*> \endverbatim +* +* Authors: +* ======== +* +*> \author Univ. of Tennessee +*> \author Univ. of California Berkeley +*> \author Univ. of Colorado Denver +*> \author NAG Ltd. +* +*> \date November 2011 +* +*> \ingroup double_blas_level1 +* +*> \par Further Details: +* ===================== +*> +*> \verbatim +*> +*> jack dongarra, linpack, 3/11/78. +*> modified 3/93 to return if incx .le. 0. +*> modified 12/3/93, array(1) declarations changed to array(*) +*> \endverbatim +*> +* ===================================================================== + SUBROUTINE DSCAL(N,DA,DX,INCX) +* +* -- Reference BLAS level1 routine (version 3.4.0) -- +* -- Reference BLAS is a software package provided by Univ. of Tennessee, -- +* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- +* November 2011 +* +* .. Scalar Arguments .. + DOUBLE PRECISION DA + INTEGER INCX,N +* .. +* .. Array Arguments .. + DOUBLE PRECISION DX(*) +* .. +* +* ===================================================================== +* +* .. Local Scalars .. + INTEGER I,M,MP1,NINCX +* .. +* .. Intrinsic Functions .. + INTRINSIC MOD +* .. + IF (N.LE.0 .OR. INCX.LE.0) RETURN + IF (INCX.EQ.1) THEN +* +* code for increment equal to 1 +* +* +* clean-up loop +* + M = MOD(N,5) + IF (M.NE.0) THEN + DO I = 1,M + DX(I) = DA*DX(I) + END DO + IF (N.LT.5) RETURN + END IF + MP1 = M + 1 + DO I = MP1,N,5 + DX(I) = DA*DX(I) + DX(I+1) = DA*DX(I+1) + DX(I+2) = DA*DX(I+2) + DX(I+3) = DA*DX(I+3) + DX(I+4) = DA*DX(I+4) + END DO + ELSE +* +* code for increment not equal to 1 +* + NINCX = N*INCX + DO I = 1,NINCX,INCX + DX(I) = DA*DX(I) + END DO + END IF + RETURN + END + diff --git a/applications/PUfoam/MoDeNaModels/CFD_tool_0D/src/eigen/src/dstegr.f b/applications/PUfoam/MoDeNaModels/CFD_tool_0D/src/eigen/src/dstegr.f new file mode 100644 index 000000000..298e1c766 --- /dev/null +++ b/applications/PUfoam/MoDeNaModels/CFD_tool_0D/src/eigen/src/dstegr.f @@ -0,0 +1,293 @@ +*> \brief \b DSTEGR +* +* =========== DOCUMENTATION =========== +* +* Online html documentation available at +* http://www.netlib.org/lapack/explore-html/ +* +*> \htmlonly +*> Download DSTEGR + dependencies +*> +*> [TGZ] +*> +*> [ZIP] +*> +*> [TXT] +*> \endhtmlonly +* +* Definition: +* =========== +* +* SUBROUTINE DSTEGR( JOBZ, RANGE, N, D, E, VL, VU, IL, IU, +* ABSTOL, M, W, Z, LDZ, ISUPPZ, WORK, LWORK, IWORK, +* LIWORK, INFO ) +* +* .. Scalar Arguments .. +* CHARACTER JOBZ, RANGE +* INTEGER IL, INFO, IU, LDZ, LIWORK, LWORK, M, N +* DOUBLE PRECISION ABSTOL, VL, VU +* .. +* .. Array Arguments .. +* INTEGER ISUPPZ( * ), IWORK( * ) +* DOUBLE PRECISION D( * ), E( * ), W( * ), WORK( * ) +* DOUBLE PRECISION Z( LDZ, * ) +* .. +* +* +*> \par Purpose: +* ============= +*> +*> \verbatim +*> +*> DSTEGR computes selected eigenvalues and, optionally, eigenvectors +*> of a real symmetric tridiagonal matrix T. Any such unreduced matrix has +*> a well defined set of pairwise different real eigenvalues, the corresponding +*> real eigenvectors are pairwise orthogonal. +*> +*> The spectrum may be computed either completely or partially by specifying +*> either an interval (VL,VU] or a range of indices IL:IU for the desired +*> eigenvalues. +*> +*> DSTEGR is a compatability wrapper around the improved DSTEMR routine. +*> See DSTEMR for further details. +*> +*> One important change is that the ABSTOL parameter no longer provides any +*> benefit and hence is no longer used. +*> +*> Note : DSTEGR and DSTEMR work only on machines which follow +*> IEEE-754 floating-point standard in their handling of infinities and +*> NaNs. Normal execution may create these exceptiona values and hence +*> may abort due to a floating point exception in environments which +*> do not conform to the IEEE-754 standard. +*> \endverbatim +* +* Arguments: +* ========== +* +*> \param[in] JOBZ +*> \verbatim +*> JOBZ is CHARACTER*1 +*> = 'N': Compute eigenvalues only; +*> = 'V': Compute eigenvalues and eigenvectors. +*> \endverbatim +*> +*> \param[in] RANGE +*> \verbatim +*> RANGE is CHARACTER*1 +*> = 'A': all eigenvalues will be found. +*> = 'V': all eigenvalues in the half-open interval (VL,VU] +*> will be found. +*> = 'I': the IL-th through IU-th eigenvalues will be found. +*> \endverbatim +*> +*> \param[in] N +*> \verbatim +*> N is INTEGER +*> The order of the matrix. N >= 0. +*> \endverbatim +*> +*> \param[in,out] D +*> \verbatim +*> D is DOUBLE PRECISION array, dimension (N) +*> On entry, the N diagonal elements of the tridiagonal matrix +*> T. On exit, D is overwritten. +*> \endverbatim +*> +*> \param[in,out] E +*> \verbatim +*> E is DOUBLE PRECISION array, dimension (N) +*> On entry, the (N-1) subdiagonal elements of the tridiagonal +*> matrix T in elements 1 to N-1 of E. E(N) need not be set on +*> input, but is used internally as workspace. +*> On exit, E is overwritten. +*> \endverbatim +*> +*> \param[in] VL +*> \verbatim +*> VL is DOUBLE PRECISION +*> \endverbatim +*> +*> \param[in] VU +*> \verbatim +*> VU is DOUBLE PRECISION +*> +*> If RANGE='V', the lower and upper bounds of the interval to +*> be searched for eigenvalues. VL < VU. +*> Not referenced if RANGE = 'A' or 'I'. +*> \endverbatim +*> +*> \param[in] IL +*> \verbatim +*> IL is INTEGER +*> \endverbatim +*> +*> \param[in] IU +*> \verbatim +*> IU is INTEGER +*> +*> If RANGE='I', the indices (in ascending order) of the +*> smallest and largest eigenvalues to be returned. +*> 1 <= IL <= IU <= N, if N > 0. +*> Not referenced if RANGE = 'A' or 'V'. +*> \endverbatim +*> +*> \param[in] ABSTOL +*> \verbatim +*> ABSTOL is DOUBLE PRECISION +*> Unused. Was the absolute error tolerance for the +*> eigenvalues/eigenvectors in previous versions. +*> \endverbatim +*> +*> \param[out] M +*> \verbatim +*> M is INTEGER +*> The total number of eigenvalues found. 0 <= M <= N. +*> If RANGE = 'A', M = N, and if RANGE = 'I', M = IU-IL+1. +*> \endverbatim +*> +*> \param[out] W +*> \verbatim +*> W is DOUBLE PRECISION array, dimension (N) +*> The first M elements contain the selected eigenvalues in +*> ascending order. +*> \endverbatim +*> +*> \param[out] Z +*> \verbatim +*> Z is DOUBLE PRECISION array, dimension (LDZ, max(1,M) ) +*> If JOBZ = 'V', and if INFO = 0, then the first M columns of Z +*> contain the orthonormal eigenvectors of the matrix T +*> corresponding to the selected eigenvalues, with the i-th +*> column of Z holding the eigenvector associated with W(i). +*> If JOBZ = 'N', then Z is not referenced. +*> Note: the user must ensure that at least max(1,M) columns are +*> supplied in the array Z; if RANGE = 'V', the exact value of M +*> is not known in advance and an upper bound must be used. +*> Supplying N columns is always safe. +*> \endverbatim +*> +*> \param[in] LDZ +*> \verbatim +*> LDZ is INTEGER +*> The leading dimension of the array Z. LDZ >= 1, and if +*> JOBZ = 'V', then LDZ >= max(1,N). +*> \endverbatim +*> +*> \param[out] ISUPPZ +*> \verbatim +*> ISUPPZ is INTEGER ARRAY, dimension ( 2*max(1,M) ) +*> The support of the eigenvectors in Z, i.e., the indices +*> indicating the nonzero elements in Z. The i-th computed eigenvector +*> is nonzero only in elements ISUPPZ( 2*i-1 ) through +*> ISUPPZ( 2*i ). This is relevant in the case when the matrix +*> is split. ISUPPZ is only accessed when JOBZ is 'V' and N > 0. +*> \endverbatim +*> +*> \param[out] WORK +*> \verbatim +*> WORK is DOUBLE PRECISION array, dimension (LWORK) +*> On exit, if INFO = 0, WORK(1) returns the optimal +*> (and minimal) LWORK. +*> \endverbatim +*> +*> \param[in] LWORK +*> \verbatim +*> LWORK is INTEGER +*> The dimension of the array WORK. LWORK >= max(1,18*N) +*> if JOBZ = 'V', and LWORK >= max(1,12*N) if JOBZ = 'N'. +*> If LWORK = -1, then a workspace query is assumed; the routine +*> only calculates the optimal size of the WORK array, returns +*> this value as the first entry of the WORK array, and no error +*> message related to LWORK is issued by XERBLA. +*> \endverbatim +*> +*> \param[out] IWORK +*> \verbatim +*> IWORK is INTEGER array, dimension (LIWORK) +*> On exit, if INFO = 0, IWORK(1) returns the optimal LIWORK. +*> \endverbatim +*> +*> \param[in] LIWORK +*> \verbatim +*> LIWORK is INTEGER +*> The dimension of the array IWORK. LIWORK >= max(1,10*N) +*> if the eigenvectors are desired, and LIWORK >= max(1,8*N) +*> if only the eigenvalues are to be computed. +*> If LIWORK = -1, then a workspace query is assumed; the +*> routine only calculates the optimal size of the IWORK array, +*> returns this value as the first entry of the IWORK array, and +*> no error message related to LIWORK is issued by XERBLA. +*> \endverbatim +*> +*> \param[out] INFO +*> \verbatim +*> INFO is INTEGER +*> On exit, INFO +*> = 0: successful exit +*> < 0: if INFO = -i, the i-th argument had an illegal value +*> > 0: if INFO = 1X, internal error in DLARRE, +*> if INFO = 2X, internal error in DLARRV. +*> Here, the digit X = ABS( IINFO ) < 10, where IINFO is +*> the nonzero error code returned by DLARRE or +*> DLARRV, respectively. +*> \endverbatim +* +* Authors: +* ======== +* +*> \author Univ. of Tennessee +*> \author Univ. of California Berkeley +*> \author Univ. of Colorado Denver +*> \author NAG Ltd. +* +*> \date November 2011 +* +*> \ingroup doubleOTHERcomputational +* +*> \par Contributors: +* ================== +*> +*> Inderjit Dhillon, IBM Almaden, USA \n +*> Osni Marques, LBNL/NERSC, USA \n +*> Christof Voemel, LBNL/NERSC, USA \n +* +* ===================================================================== + SUBROUTINE DSTEGR( JOBZ, RANGE, N, D, E, VL, VU, IL, IU, + $ ABSTOL, M, W, Z, LDZ, ISUPPZ, WORK, LWORK, IWORK, + $ LIWORK, INFO ) +* +* -- LAPACK computational routine (version 3.4.0) -- +* -- LAPACK is a software package provided by Univ. of Tennessee, -- +* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- +* November 2011 +* +* .. Scalar Arguments .. + CHARACTER JOBZ, RANGE + INTEGER IL, INFO, IU, LDZ, LIWORK, LWORK, M, N + DOUBLE PRECISION ABSTOL, VL, VU +* .. +* .. Array Arguments .. + INTEGER ISUPPZ( * ), IWORK( * ) + DOUBLE PRECISION D( * ), E( * ), W( * ), WORK( * ) + DOUBLE PRECISION Z( LDZ, * ) +* .. +* +* ===================================================================== +* +* .. Local Scalars .. + LOGICAL TRYRAC +* .. +* .. External Subroutines .. + EXTERNAL DSTEMR +* .. +* .. Executable Statements .. + INFO = 0 + TRYRAC = .FALSE. + + CALL DSTEMR( JOBZ, RANGE, N, D, E, VL, VU, IL, IU, + $ M, W, Z, LDZ, N, ISUPPZ, TRYRAC, WORK, LWORK, + $ IWORK, LIWORK, INFO ) +* +* End of DSTEGR +* + END diff --git a/applications/PUfoam/MoDeNaModels/CFD_tool_0D/src/eigen/src/dstemr.f b/applications/PUfoam/MoDeNaModels/CFD_tool_0D/src/eigen/src/dstemr.f new file mode 100644 index 000000000..24e0a4b47 --- /dev/null +++ b/applications/PUfoam/MoDeNaModels/CFD_tool_0D/src/eigen/src/dstemr.f @@ -0,0 +1,764 @@ +*> \brief \b DSTEMR +* +* =========== DOCUMENTATION =========== +* +* Online html documentation available at +* http://www.netlib.org/lapack/explore-html/ +* +*> \htmlonly +*> Download DSTEMR + dependencies +*> +*> [TGZ] +*> +*> [ZIP] +*> +*> [TXT] +*> \endhtmlonly +* +* Definition: +* =========== +* +* SUBROUTINE DSTEMR( JOBZ, RANGE, N, D, E, VL, VU, IL, IU, +* M, W, Z, LDZ, NZC, ISUPPZ, TRYRAC, WORK, LWORK, +* IWORK, LIWORK, INFO ) +* +* .. Scalar Arguments .. +* CHARACTER JOBZ, RANGE +* LOGICAL TRYRAC +* INTEGER IL, INFO, IU, LDZ, NZC, LIWORK, LWORK, M, N +* DOUBLE PRECISION VL, VU +* .. +* .. Array Arguments .. +* INTEGER ISUPPZ( * ), IWORK( * ) +* DOUBLE PRECISION D( * ), E( * ), W( * ), WORK( * ) +* DOUBLE PRECISION Z( LDZ, * ) +* .. +* +* +*> \par Purpose: +* ============= +*> +*> \verbatim +*> +*> DSTEMR computes selected eigenvalues and, optionally, eigenvectors +*> of a real symmetric tridiagonal matrix T. Any such unreduced matrix has +*> a well defined set of pairwise different real eigenvalues, the corresponding +*> real eigenvectors are pairwise orthogonal. +*> +*> The spectrum may be computed either completely or partially by specifying +*> either an interval (VL,VU] or a range of indices IL:IU for the desired +*> eigenvalues. +*> +*> Depending on the number of desired eigenvalues, these are computed either +*> by bisection or the dqds algorithm. Numerically orthogonal eigenvectors are +*> computed by the use of various suitable L D L^T factorizations near clusters +*> of close eigenvalues (referred to as RRRs, Relatively Robust +*> Representations). An informal sketch of the algorithm follows. +*> +*> For each unreduced block (submatrix) of T, +*> (a) Compute T - sigma I = L D L^T, so that L and D +*> define all the wanted eigenvalues to high relative accuracy. +*> This means that small relative changes in the entries of D and L +*> cause only small relative changes in the eigenvalues and +*> eigenvectors. The standard (unfactored) representation of the +*> tridiagonal matrix T does not have this property in general. +*> (b) Compute the eigenvalues to suitable accuracy. +*> If the eigenvectors are desired, the algorithm attains full +*> accuracy of the computed eigenvalues only right before +*> the corresponding vectors have to be computed, see steps c) and d). +*> (c) For each cluster of close eigenvalues, select a new +*> shift close to the cluster, find a new factorization, and refine +*> the shifted eigenvalues to suitable accuracy. +*> (d) For each eigenvalue with a large enough relative separation compute +*> the corresponding eigenvector by forming a rank revealing twisted +*> factorization. Go back to (c) for any clusters that remain. +*> +*> For more details, see: +*> - Inderjit S. Dhillon and Beresford N. Parlett: "Multiple representations +*> to compute orthogonal eigenvectors of symmetric tridiagonal matrices," +*> Linear Algebra and its Applications, 387(1), pp. 1-28, August 2004. +*> - Inderjit Dhillon and Beresford Parlett: "Orthogonal Eigenvectors and +*> Relative Gaps," SIAM Journal on Matrix Analysis and Applications, Vol. 25, +*> 2004. Also LAPACK Working Note 154. +*> - Inderjit Dhillon: "A new O(n^2) algorithm for the symmetric +*> tridiagonal eigenvalue/eigenvector problem", +*> Computer Science Division Technical Report No. UCB/CSD-97-971, +*> UC Berkeley, May 1997. +*> +*> Further Details +*> 1.DSTEMR works only on machines which follow IEEE-754 +*> floating-point standard in their handling of infinities and NaNs. +*> This permits the use of efficient inner loops avoiding a check for +*> zero divisors. +*> \endverbatim +* +* Arguments: +* ========== +* +*> \param[in] JOBZ +*> \verbatim +*> JOBZ is CHARACTER*1 +*> = 'N': Compute eigenvalues only; +*> = 'V': Compute eigenvalues and eigenvectors. +*> \endverbatim +*> +*> \param[in] RANGE +*> \verbatim +*> RANGE is CHARACTER*1 +*> = 'A': all eigenvalues will be found. +*> = 'V': all eigenvalues in the half-open interval (VL,VU] +*> will be found. +*> = 'I': the IL-th through IU-th eigenvalues will be found. +*> \endverbatim +*> +*> \param[in] N +*> \verbatim +*> N is INTEGER +*> The order of the matrix. N >= 0. +*> \endverbatim +*> +*> \param[in,out] D +*> \verbatim +*> D is DOUBLE PRECISION array, dimension (N) +*> On entry, the N diagonal elements of the tridiagonal matrix +*> T. On exit, D is overwritten. +*> \endverbatim +*> +*> \param[in,out] E +*> \verbatim +*> E is DOUBLE PRECISION array, dimension (N) +*> On entry, the (N-1) subdiagonal elements of the tridiagonal +*> matrix T in elements 1 to N-1 of E. E(N) need not be set on +*> input, but is used internally as workspace. +*> On exit, E is overwritten. +*> \endverbatim +*> +*> \param[in] VL +*> \verbatim +*> VL is DOUBLE PRECISION +*> \endverbatim +*> +*> \param[in] VU +*> \verbatim +*> VU is DOUBLE PRECISION +*> +*> If RANGE='V', the lower and upper bounds of the interval to +*> be searched for eigenvalues. VL < VU. +*> Not referenced if RANGE = 'A' or 'I'. +*> \endverbatim +*> +*> \param[in] IL +*> \verbatim +*> IL is INTEGER +*> \endverbatim +*> +*> \param[in] IU +*> \verbatim +*> IU is INTEGER +*> +*> If RANGE='I', the indices (in ascending order) of the +*> smallest and largest eigenvalues to be returned. +*> 1 <= IL <= IU <= N, if N > 0. +*> Not referenced if RANGE = 'A' or 'V'. +*> \endverbatim +*> +*> \param[out] M +*> \verbatim +*> M is INTEGER +*> The total number of eigenvalues found. 0 <= M <= N. +*> If RANGE = 'A', M = N, and if RANGE = 'I', M = IU-IL+1. +*> \endverbatim +*> +*> \param[out] W +*> \verbatim +*> W is DOUBLE PRECISION array, dimension (N) +*> The first M elements contain the selected eigenvalues in +*> ascending order. +*> \endverbatim +*> +*> \param[out] Z +*> \verbatim +*> Z is DOUBLE PRECISION array, dimension (LDZ, max(1,M) ) +*> If JOBZ = 'V', and if INFO = 0, then the first M columns of Z +*> contain the orthonormal eigenvectors of the matrix T +*> corresponding to the selected eigenvalues, with the i-th +*> column of Z holding the eigenvector associated with W(i). +*> If JOBZ = 'N', then Z is not referenced. +*> Note: the user must ensure that at least max(1,M) columns are +*> supplied in the array Z; if RANGE = 'V', the exact value of M +*> is not known in advance and can be computed with a workspace +*> query by setting NZC = -1, see below. +*> \endverbatim +*> +*> \param[in] LDZ +*> \verbatim +*> LDZ is INTEGER +*> The leading dimension of the array Z. LDZ >= 1, and if +*> JOBZ = 'V', then LDZ >= max(1,N). +*> \endverbatim +*> +*> \param[in] NZC +*> \verbatim +*> NZC is INTEGER +*> The number of eigenvectors to be held in the array Z. +*> If RANGE = 'A', then NZC >= max(1,N). +*> If RANGE = 'V', then NZC >= the number of eigenvalues in (VL,VU]. +*> If RANGE = 'I', then NZC >= IU-IL+1. +*> If NZC = -1, then a workspace query is assumed; the +*> routine calculates the number of columns of the array Z that +*> are needed to hold the eigenvectors. +*> This value is returned as the first entry of the Z array, and +*> no error message related to NZC is issued by XERBLA. +*> \endverbatim +*> +*> \param[out] ISUPPZ +*> \verbatim +*> ISUPPZ is INTEGER ARRAY, dimension ( 2*max(1,M) ) +*> The support of the eigenvectors in Z, i.e., the indices +*> indicating the nonzero elements in Z. The i-th computed eigenvector +*> is nonzero only in elements ISUPPZ( 2*i-1 ) through +*> ISUPPZ( 2*i ). This is relevant in the case when the matrix +*> is split. ISUPPZ is only accessed when JOBZ is 'V' and N > 0. +*> \endverbatim +*> +*> \param[in,out] TRYRAC +*> \verbatim +*> TRYRAC is LOGICAL +*> If TRYRAC.EQ..TRUE., indicates that the code should check whether +*> the tridiagonal matrix defines its eigenvalues to high relative +*> accuracy. If so, the code uses relative-accuracy preserving +*> algorithms that might be (a bit) slower depending on the matrix. +*> If the matrix does not define its eigenvalues to high relative +*> accuracy, the code can uses possibly faster algorithms. +*> If TRYRAC.EQ..FALSE., the code is not required to guarantee +*> relatively accurate eigenvalues and can use the fastest possible +*> techniques. +*> On exit, a .TRUE. TRYRAC will be set to .FALSE. if the matrix +*> does not define its eigenvalues to high relative accuracy. +*> \endverbatim +*> +*> \param[out] WORK +*> \verbatim +*> WORK is DOUBLE PRECISION array, dimension (LWORK) +*> On exit, if INFO = 0, WORK(1) returns the optimal +*> (and minimal) LWORK. +*> \endverbatim +*> +*> \param[in] LWORK +*> \verbatim +*> LWORK is INTEGER +*> The dimension of the array WORK. LWORK >= max(1,18*N) +*> if JOBZ = 'V', and LWORK >= max(1,12*N) if JOBZ = 'N'. +*> If LWORK = -1, then a workspace query is assumed; the routine +*> only calculates the optimal size of the WORK array, returns +*> this value as the first entry of the WORK array, and no error +*> message related to LWORK is issued by XERBLA. +*> \endverbatim +*> +*> \param[out] IWORK +*> \verbatim +*> IWORK is INTEGER array, dimension (LIWORK) +*> On exit, if INFO = 0, IWORK(1) returns the optimal LIWORK. +*> \endverbatim +*> +*> \param[in] LIWORK +*> \verbatim +*> LIWORK is INTEGER +*> The dimension of the array IWORK. LIWORK >= max(1,10*N) +*> if the eigenvectors are desired, and LIWORK >= max(1,8*N) +*> if only the eigenvalues are to be computed. +*> If LIWORK = -1, then a workspace query is assumed; the +*> routine only calculates the optimal size of the IWORK array, +*> returns this value as the first entry of the IWORK array, and +*> no error message related to LIWORK is issued by XERBLA. +*> \endverbatim +*> +*> \param[out] INFO +*> \verbatim +*> INFO is INTEGER +*> On exit, INFO +*> = 0: successful exit +*> < 0: if INFO = -i, the i-th argument had an illegal value +*> > 0: if INFO = 1X, internal error in DLARRE, +*> if INFO = 2X, internal error in DLARRV. +*> Here, the digit X = ABS( IINFO ) < 10, where IINFO is +*> the nonzero error code returned by DLARRE or +*> DLARRV, respectively. +*> \endverbatim +* +* Authors: +* ======== +* +*> \author Univ. of Tennessee +*> \author Univ. of California Berkeley +*> \author Univ. of Colorado Denver +*> \author NAG Ltd. +* +*> \date November 2011 +* +*> \ingroup doubleOTHERcomputational +* +*> \par Contributors: +* ================== +*> +*> Beresford Parlett, University of California, Berkeley, USA \n +*> Jim Demmel, University of California, Berkeley, USA \n +*> Inderjit Dhillon, University of Texas, Austin, USA \n +*> Osni Marques, LBNL/NERSC, USA \n +*> Christof Voemel, University of California, Berkeley, USA +* +* ===================================================================== + SUBROUTINE DSTEMR( JOBZ, RANGE, N, D, E, VL, VU, IL, IU, + $ M, W, Z, LDZ, NZC, ISUPPZ, TRYRAC, WORK, LWORK, + $ IWORK, LIWORK, INFO ) +* +* -- LAPACK computational routine (version 3.4.0) -- +* -- LAPACK is a software package provided by Univ. of Tennessee, -- +* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- +* November 2011 +* +* .. Scalar Arguments .. + CHARACTER JOBZ, RANGE + LOGICAL TRYRAC + INTEGER IL, INFO, IU, LDZ, NZC, LIWORK, LWORK, M, N + DOUBLE PRECISION VL, VU +* .. +* .. Array Arguments .. + INTEGER ISUPPZ( * ), IWORK( * ) + DOUBLE PRECISION D( * ), E( * ), W( * ), WORK( * ) + DOUBLE PRECISION Z( LDZ, * ) +* .. +* +* ===================================================================== +* +* .. Parameters .. + DOUBLE PRECISION ZERO, ONE, FOUR, MINRGP + PARAMETER ( ZERO = 0.0D0, ONE = 1.0D0, + $ FOUR = 4.0D0, + $ MINRGP = 1.0D-3 ) +* .. +* .. Local Scalars .. + LOGICAL ALLEIG, INDEIG, LQUERY, VALEIG, WANTZ, ZQUERY + INTEGER I, IBEGIN, IEND, IFIRST, IIL, IINDBL, IINDW, + $ IINDWK, IINFO, IINSPL, IIU, ILAST, IN, INDD, + $ INDE2, INDERR, INDGP, INDGRS, INDWRK, ITMP, + $ ITMP2, J, JBLK, JJ, LIWMIN, LWMIN, NSPLIT, + $ NZCMIN, OFFSET, WBEGIN, WEND + DOUBLE PRECISION BIGNUM, CS, EPS, PIVMIN, R1, R2, RMAX, RMIN, + $ RTOL1, RTOL2, SAFMIN, SCALE, SMLNUM, SN, + $ THRESH, TMP, TNRM, WL, WU +* .. +* .. +* .. External Functions .. + LOGICAL LSAME + DOUBLE PRECISION DLAMCH, DLANST + EXTERNAL LSAME, DLAMCH, DLANST +* .. +* .. External Subroutines .. + EXTERNAL DCOPY, DLAE2, DLAEV2, DLARRC, DLARRE, DLARRJ, + $ DLARRR, DLARRV, DLASRT, DSCAL, DSWAP, XERBLA +* .. +* .. Intrinsic Functions .. + INTRINSIC MAX, MIN, SQRT + + +* .. +* .. Executable Statements .. +* +* Test the input parameters. +* + WANTZ = LSAME( JOBZ, 'V' ) + ALLEIG = LSAME( RANGE, 'A' ) + VALEIG = LSAME( RANGE, 'V' ) + INDEIG = LSAME( RANGE, 'I' ) +* + LQUERY = ( ( LWORK.EQ.-1 ).OR.( LIWORK.EQ.-1 ) ) + ZQUERY = ( NZC.EQ.-1 ) + +* DSTEMR needs WORK of size 6*N, IWORK of size 3*N. +* In addition, DLARRE needs WORK of size 6*N, IWORK of size 5*N. +* Furthermore, DLARRV needs WORK of size 12*N, IWORK of size 7*N. + IF( WANTZ ) THEN + LWMIN = 18*N + LIWMIN = 10*N + ELSE +* need less workspace if only the eigenvalues are wanted + LWMIN = 12*N + LIWMIN = 8*N + ENDIF + + WL = ZERO + WU = ZERO + IIL = 0 + IIU = 0 + + IF( VALEIG ) THEN +* We do not reference VL, VU in the cases RANGE = 'I','A' +* The interval (WL, WU] contains all the wanted eigenvalues. +* It is either given by the user or computed in DLARRE. + WL = VL + WU = VU + ELSEIF( INDEIG ) THEN +* We do not reference IL, IU in the cases RANGE = 'V','A' + IIL = IL + IIU = IU + ENDIF +* + INFO = 0 + IF( .NOT.( WANTZ .OR. LSAME( JOBZ, 'N' ) ) ) THEN + INFO = -1 + ELSE IF( .NOT.( ALLEIG .OR. VALEIG .OR. INDEIG ) ) THEN + INFO = -2 + ELSE IF( N.LT.0 ) THEN + INFO = -3 + ELSE IF( VALEIG .AND. N.GT.0 .AND. WU.LE.WL ) THEN + INFO = -7 + ELSE IF( INDEIG .AND. ( IIL.LT.1 .OR. IIL.GT.N ) ) THEN + INFO = -8 + ELSE IF( INDEIG .AND. ( IIU.LT.IIL .OR. IIU.GT.N ) ) THEN + INFO = -9 + ELSE IF( LDZ.LT.1 .OR. ( WANTZ .AND. LDZ.LT.N ) ) THEN + INFO = -13 + ELSE IF( LWORK.LT.LWMIN .AND. .NOT.LQUERY ) THEN + INFO = -17 + ELSE IF( LIWORK.LT.LIWMIN .AND. .NOT.LQUERY ) THEN + INFO = -19 + END IF +* +* Get machine constants. +* + SAFMIN = DLAMCH( 'Safe minimum' ) + EPS = DLAMCH( 'Precision' ) + SMLNUM = SAFMIN / EPS + BIGNUM = ONE / SMLNUM + RMIN = SQRT( SMLNUM ) + RMAX = MIN( SQRT( BIGNUM ), ONE / SQRT( SQRT( SAFMIN ) ) ) +* + IF( INFO.EQ.0 ) THEN + WORK( 1 ) = LWMIN + IWORK( 1 ) = LIWMIN +* + IF( WANTZ .AND. ALLEIG ) THEN + NZCMIN = N + ELSE IF( WANTZ .AND. VALEIG ) THEN + CALL DLARRC( 'T', N, VL, VU, D, E, SAFMIN, + $ NZCMIN, ITMP, ITMP2, INFO ) + ELSE IF( WANTZ .AND. INDEIG ) THEN + NZCMIN = IIU-IIL+1 + ELSE +* WANTZ .EQ. FALSE. + NZCMIN = 0 + ENDIF + IF( ZQUERY .AND. INFO.EQ.0 ) THEN + Z( 1,1 ) = NZCMIN + ELSE IF( NZC.LT.NZCMIN .AND. .NOT.ZQUERY ) THEN + INFO = -14 + END IF + END IF + + IF( INFO.NE.0 ) THEN +* + CALL XERBLA( 'DSTEMR', -INFO ) +* + RETURN + ELSE IF( LQUERY .OR. ZQUERY ) THEN + RETURN + END IF +* +* Handle N = 0, 1, and 2 cases immediately +* + M = 0 + IF( N.EQ.0 ) + $ RETURN +* + IF( N.EQ.1 ) THEN + IF( ALLEIG .OR. INDEIG ) THEN + M = 1 + W( 1 ) = D( 1 ) + ELSE + IF( WL.LT.D( 1 ) .AND. WU.GE.D( 1 ) ) THEN + M = 1 + W( 1 ) = D( 1 ) + END IF + END IF + IF( WANTZ.AND.(.NOT.ZQUERY) ) THEN + Z( 1, 1 ) = ONE + ISUPPZ(1) = 1 + ISUPPZ(2) = 1 + END IF + RETURN + END IF +* + IF( N.EQ.2 ) THEN + IF( .NOT.WANTZ ) THEN + CALL DLAE2( D(1), E(1), D(2), R1, R2 ) + ELSE IF( WANTZ.AND.(.NOT.ZQUERY) ) THEN + CALL DLAEV2( D(1), E(1), D(2), R1, R2, CS, SN ) + END IF + IF( ALLEIG.OR. + $ (VALEIG.AND.(R2.GT.WL).AND. + $ (R2.LE.WU)).OR. + $ (INDEIG.AND.(IIL.EQ.1)) ) THEN + M = M+1 + W( M ) = R2 + IF( WANTZ.AND.(.NOT.ZQUERY) ) THEN + Z( 1, M ) = -SN + Z( 2, M ) = CS +* Note: At most one of SN and CS can be zero. + IF (SN.NE.ZERO) THEN + IF (CS.NE.ZERO) THEN + ISUPPZ(2*M-1) = 1 + ISUPPZ(2*M) = 2 + ELSE + ISUPPZ(2*M-1) = 1 + ISUPPZ(2*M) = 1 + END IF + ELSE + ISUPPZ(2*M-1) = 2 + ISUPPZ(2*M) = 2 + END IF + ENDIF + ENDIF + IF( ALLEIG.OR. + $ (VALEIG.AND.(R1.GT.WL).AND. + $ (R1.LE.WU)).OR. + $ (INDEIG.AND.(IIU.EQ.2)) ) THEN + M = M+1 + W( M ) = R1 + IF( WANTZ.AND.(.NOT.ZQUERY) ) THEN + Z( 1, M ) = CS + Z( 2, M ) = SN +* Note: At most one of SN and CS can be zero. + IF (SN.NE.ZERO) THEN + IF (CS.NE.ZERO) THEN + ISUPPZ(2*M-1) = 1 + ISUPPZ(2*M) = 2 + ELSE + ISUPPZ(2*M-1) = 1 + ISUPPZ(2*M) = 1 + END IF + ELSE + ISUPPZ(2*M-1) = 2 + ISUPPZ(2*M) = 2 + END IF + ENDIF + ENDIF + RETURN + END IF + +* Continue with general N + + INDGRS = 1 + INDERR = 2*N + 1 + INDGP = 3*N + 1 + INDD = 4*N + 1 + INDE2 = 5*N + 1 + INDWRK = 6*N + 1 +* + IINSPL = 1 + IINDBL = N + 1 + IINDW = 2*N + 1 + IINDWK = 3*N + 1 +* +* Scale matrix to allowable range, if necessary. +* The allowable range is related to the PIVMIN parameter; see the +* comments in DLARRD. The preference for scaling small values +* up is heuristic; we expect users' matrices not to be close to the +* RMAX threshold. +* + SCALE = ONE + TNRM = DLANST( 'M', N, D, E ) + IF( TNRM.GT.ZERO .AND. TNRM.LT.RMIN ) THEN + SCALE = RMIN / TNRM + ELSE IF( TNRM.GT.RMAX ) THEN + SCALE = RMAX / TNRM + END IF + IF( SCALE.NE.ONE ) THEN + CALL DSCAL( N, SCALE, D, 1 ) + CALL DSCAL( N-1, SCALE, E, 1 ) + TNRM = TNRM*SCALE + IF( VALEIG ) THEN +* If eigenvalues in interval have to be found, +* scale (WL, WU] accordingly + WL = WL*SCALE + WU = WU*SCALE + ENDIF + END IF +* +* Compute the desired eigenvalues of the tridiagonal after splitting +* into smaller subblocks if the corresponding off-diagonal elements +* are small +* THRESH is the splitting parameter for DLARRE +* A negative THRESH forces the old splitting criterion based on the +* size of the off-diagonal. A positive THRESH switches to splitting +* which preserves relative accuracy. +* + IF( TRYRAC ) THEN +* Test whether the matrix warrants the more expensive relative approach. + CALL DLARRR( N, D, E, IINFO ) + ELSE +* The user does not care about relative accurately eigenvalues + IINFO = -1 + ENDIF +* Set the splitting criterion + IF (IINFO.EQ.0) THEN + THRESH = EPS + ELSE + THRESH = -EPS +* relative accuracy is desired but T does not guarantee it + TRYRAC = .FALSE. + ENDIF +* + IF( TRYRAC ) THEN +* Copy original diagonal, needed to guarantee relative accuracy + CALL DCOPY(N,D,1,WORK(INDD),1) + ENDIF +* Store the squares of the offdiagonal values of T + DO 5 J = 1, N-1 + WORK( INDE2+J-1 ) = E(J)**2 + 5 CONTINUE + +* Set the tolerance parameters for bisection + IF( .NOT.WANTZ ) THEN +* DLARRE computes the eigenvalues to full precision. + RTOL1 = FOUR * EPS + RTOL2 = FOUR * EPS + ELSE +* DLARRE computes the eigenvalues to less than full precision. +* DLARRV will refine the eigenvalue approximations, and we can +* need less accurate initial bisection in DLARRE. +* Note: these settings do only affect the subset case and DLARRE + RTOL1 = SQRT(EPS) + RTOL2 = MAX( SQRT(EPS)*5.0D-3, FOUR * EPS ) + ENDIF + CALL DLARRE( RANGE, N, WL, WU, IIL, IIU, D, E, + $ WORK(INDE2), RTOL1, RTOL2, THRESH, NSPLIT, + $ IWORK( IINSPL ), M, W, WORK( INDERR ), + $ WORK( INDGP ), IWORK( IINDBL ), + $ IWORK( IINDW ), WORK( INDGRS ), PIVMIN, + $ WORK( INDWRK ), IWORK( IINDWK ), IINFO ) + IF( IINFO.NE.0 ) THEN + INFO = 10 + ABS( IINFO ) + RETURN + END IF +* Note that if RANGE .NE. 'V', DLARRE computes bounds on the desired +* part of the spectrum. All desired eigenvalues are contained in +* (WL,WU] + + + IF( WANTZ ) THEN +* +* Compute the desired eigenvectors corresponding to the computed +* eigenvalues +* + CALL DLARRV( N, WL, WU, D, E, + $ PIVMIN, IWORK( IINSPL ), M, + $ 1, M, MINRGP, RTOL1, RTOL2, + $ W, WORK( INDERR ), WORK( INDGP ), IWORK( IINDBL ), + $ IWORK( IINDW ), WORK( INDGRS ), Z, LDZ, + $ ISUPPZ, WORK( INDWRK ), IWORK( IINDWK ), IINFO ) + IF( IINFO.NE.0 ) THEN + INFO = 20 + ABS( IINFO ) + RETURN + END IF + ELSE +* DLARRE computes eigenvalues of the (shifted) root representation +* DLARRV returns the eigenvalues of the unshifted matrix. +* However, if the eigenvectors are not desired by the user, we need +* to apply the corresponding shifts from DLARRE to obtain the +* eigenvalues of the original matrix. + DO 20 J = 1, M + ITMP = IWORK( IINDBL+J-1 ) + W( J ) = W( J ) + E( IWORK( IINSPL+ITMP-1 ) ) + 20 CONTINUE + END IF +* + + IF ( TRYRAC ) THEN +* Refine computed eigenvalues so that they are relatively accurate +* with respect to the original matrix T. + IBEGIN = 1 + WBEGIN = 1 + DO 39 JBLK = 1, IWORK( IINDBL+M-1 ) + IEND = IWORK( IINSPL+JBLK-1 ) + IN = IEND - IBEGIN + 1 + WEND = WBEGIN - 1 +* check if any eigenvalues have to be refined in this block + 36 CONTINUE + IF( WEND.LT.M ) THEN + IF( IWORK( IINDBL+WEND ).EQ.JBLK ) THEN + WEND = WEND + 1 + GO TO 36 + END IF + END IF + IF( WEND.LT.WBEGIN ) THEN + IBEGIN = IEND + 1 + GO TO 39 + END IF + + OFFSET = IWORK(IINDW+WBEGIN-1)-1 + IFIRST = IWORK(IINDW+WBEGIN-1) + ILAST = IWORK(IINDW+WEND-1) + RTOL2 = FOUR * EPS + CALL DLARRJ( IN, + $ WORK(INDD+IBEGIN-1), WORK(INDE2+IBEGIN-1), + $ IFIRST, ILAST, RTOL2, OFFSET, W(WBEGIN), + $ WORK( INDERR+WBEGIN-1 ), + $ WORK( INDWRK ), IWORK( IINDWK ), PIVMIN, + $ TNRM, IINFO ) + IBEGIN = IEND + 1 + WBEGIN = WEND + 1 + 39 CONTINUE + ENDIF +* +* If matrix was scaled, then rescale eigenvalues appropriately. +* + IF( SCALE.NE.ONE ) THEN + CALL DSCAL( M, ONE / SCALE, W, 1 ) + END IF +* +* If eigenvalues are not in increasing order, then sort them, +* possibly along with eigenvectors. +* + IF( NSPLIT.GT.1 ) THEN + IF( .NOT. WANTZ ) THEN + CALL DLASRT( 'I', M, W, IINFO ) + IF( IINFO.NE.0 ) THEN + INFO = 3 + RETURN + END IF + ELSE + DO 60 J = 1, M - 1 + I = 0 + TMP = W( J ) + DO 50 JJ = J + 1, M + IF( W( JJ ).LT.TMP ) THEN + I = JJ + TMP = W( JJ ) + END IF + 50 CONTINUE + IF( I.NE.0 ) THEN + W( I ) = W( J ) + W( J ) = TMP + IF( WANTZ ) THEN + CALL DSWAP( N, Z( 1, I ), 1, Z( 1, J ), 1 ) + ITMP = ISUPPZ( 2*I-1 ) + ISUPPZ( 2*I-1 ) = ISUPPZ( 2*J-1 ) + ISUPPZ( 2*J-1 ) = ITMP + ITMP = ISUPPZ( 2*I ) + ISUPPZ( 2*I ) = ISUPPZ( 2*J ) + ISUPPZ( 2*J ) = ITMP + END IF + END IF + 60 CONTINUE + END IF + ENDIF +* +* + WORK( 1 ) = LWMIN + IWORK( 1 ) = LIWMIN + RETURN +* +* End of DSTEMR +* + END diff --git a/applications/PUfoam/MoDeNaModels/CFD_tool_0D/src/eigen/src/dsteqr.f b/applications/PUfoam/MoDeNaModels/CFD_tool_0D/src/eigen/src/dsteqr.f new file mode 100644 index 000000000..9e165bb6b --- /dev/null +++ b/applications/PUfoam/MoDeNaModels/CFD_tool_0D/src/eigen/src/dsteqr.f @@ -0,0 +1,572 @@ +*> \brief \b DSTEQR +* +* =========== DOCUMENTATION =========== +* +* Online html documentation available at +* http://www.netlib.org/lapack/explore-html/ +* +*> \htmlonly +*> Download DSTEQR + dependencies +*> +*> [TGZ] +*> +*> [ZIP] +*> +*> [TXT] +*> \endhtmlonly +* +* Definition: +* =========== +* +* SUBROUTINE DSTEQR( COMPZ, N, D, E, Z, LDZ, WORK, INFO ) +* +* .. Scalar Arguments .. +* CHARACTER COMPZ +* INTEGER INFO, LDZ, N +* .. +* .. Array Arguments .. +* DOUBLE PRECISION D( * ), E( * ), WORK( * ), Z( LDZ, * ) +* .. +* +* +*> \par Purpose: +* ============= +*> +*> \verbatim +*> +*> DSTEQR computes all eigenvalues and, optionally, eigenvectors of a +*> symmetric tridiagonal matrix using the implicit QL or QR method. +*> The eigenvectors of a full or band symmetric matrix can also be found +*> if DSYTRD or DSPTRD or DSBTRD has been used to reduce this matrix to +*> tridiagonal form. +*> \endverbatim +* +* Arguments: +* ========== +* +*> \param[in] COMPZ +*> \verbatim +*> COMPZ is CHARACTER*1 +*> = 'N': Compute eigenvalues only. +*> = 'V': Compute eigenvalues and eigenvectors of the original +*> symmetric matrix. On entry, Z must contain the +*> orthogonal matrix used to reduce the original matrix +*> to tridiagonal form. +*> = 'I': Compute eigenvalues and eigenvectors of the +*> tridiagonal matrix. Z is initialized to the identity +*> matrix. +*> \endverbatim +*> +*> \param[in] N +*> \verbatim +*> N is INTEGER +*> The order of the matrix. N >= 0. +*> \endverbatim +*> +*> \param[in,out] D +*> \verbatim +*> D is DOUBLE PRECISION array, dimension (N) +*> On entry, the diagonal elements of the tridiagonal matrix. +*> On exit, if INFO = 0, the eigenvalues in ascending order. +*> \endverbatim +*> +*> \param[in,out] E +*> \verbatim +*> E is DOUBLE PRECISION array, dimension (N-1) +*> On entry, the (n-1) subdiagonal elements of the tridiagonal +*> matrix. +*> On exit, E has been destroyed. +*> \endverbatim +*> +*> \param[in,out] Z +*> \verbatim +*> Z is DOUBLE PRECISION array, dimension (LDZ, N) +*> On entry, if COMPZ = 'V', then Z contains the orthogonal +*> matrix used in the reduction to tridiagonal form. +*> On exit, if INFO = 0, then if COMPZ = 'V', Z contains the +*> orthonormal eigenvectors of the original symmetric matrix, +*> and if COMPZ = 'I', Z contains the orthonormal eigenvectors +*> of the symmetric tridiagonal matrix. +*> If COMPZ = 'N', then Z is not referenced. +*> \endverbatim +*> +*> \param[in] LDZ +*> \verbatim +*> LDZ is INTEGER +*> The leading dimension of the array Z. LDZ >= 1, and if +*> eigenvectors are desired, then LDZ >= max(1,N). +*> \endverbatim +*> +*> \param[out] WORK +*> \verbatim +*> WORK is DOUBLE PRECISION array, dimension (max(1,2*N-2)) +*> If COMPZ = 'N', then WORK is not referenced. +*> \endverbatim +*> +*> \param[out] INFO +*> \verbatim +*> INFO is INTEGER +*> = 0: successful exit +*> < 0: if INFO = -i, the i-th argument had an illegal value +*> > 0: the algorithm has failed to find all the eigenvalues in +*> a total of 30*N iterations; if INFO = i, then i +*> elements of E have not converged to zero; on exit, D +*> and E contain the elements of a symmetric tridiagonal +*> matrix which is orthogonally similar to the original +*> matrix. +*> \endverbatim +* +* Authors: +* ======== +* +*> \author Univ. of Tennessee +*> \author Univ. of California Berkeley +*> \author Univ. of Colorado Denver +*> \author NAG Ltd. +* +*> \date November 2011 +* +*> \ingroup auxOTHERcomputational +* +* ===================================================================== + SUBROUTINE DSTEQR( COMPZ, N, D, E, Z, LDZ, WORK, INFO ) +* +* -- LAPACK computational routine (version 3.4.0) -- +* -- LAPACK is a software package provided by Univ. of Tennessee, -- +* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- +* November 2011 +* +* .. Scalar Arguments .. + CHARACTER COMPZ + INTEGER INFO, LDZ, N +* .. +* .. Array Arguments .. + DOUBLE PRECISION D( * ), E( * ), WORK( * ), Z( LDZ, * ) +* .. +* +* ===================================================================== +* +* .. Parameters .. + DOUBLE PRECISION ZERO, ONE, TWO, THREE + PARAMETER ( ZERO = 0.0D0, ONE = 1.0D0, TWO = 2.0D0, + $ THREE = 3.0D0 ) + INTEGER MAXIT + PARAMETER ( MAXIT = 30 ) +* .. +* .. Local Scalars .. + INTEGER I, ICOMPZ, II, ISCALE, J, JTOT, K, L, L1, LEND, + $ LENDM1, LENDP1, LENDSV, LM1, LSV, M, MM, MM1, + $ NM1, NMAXIT + DOUBLE PRECISION ANORM, B, C, EPS, EPS2, F, G, P, R, RT1, RT2, + $ S, SAFMAX, SAFMIN, SSFMAX, SSFMIN, TST +* .. +* .. External Functions .. + LOGICAL LSAME + DOUBLE PRECISION DLAMCH, DLANST, DLAPY2 + EXTERNAL LSAME, DLAMCH, DLANST, DLAPY2 +* .. +* .. External Subroutines .. + EXTERNAL DLAE2, DLAEV2, DLARTG, DLASCL, DLASET, DLASR, + $ DLASRT, DSWAP, XERBLA +* .. +* .. Intrinsic Functions .. + INTRINSIC ABS, MAX, SIGN, SQRT +* .. +* .. Executable Statements .. +* +* Test the input parameters. +* + INFO = 0 +* + IF( LSAME( COMPZ, 'N' ) ) THEN + ICOMPZ = 0 + ELSE IF( LSAME( COMPZ, 'V' ) ) THEN + ICOMPZ = 1 + ELSE IF( LSAME( COMPZ, 'I' ) ) THEN + ICOMPZ = 2 + ELSE + ICOMPZ = -1 + END IF + IF( ICOMPZ.LT.0 ) THEN + INFO = -1 + ELSE IF( N.LT.0 ) THEN + INFO = -2 + ELSE IF( ( LDZ.LT.1 ) .OR. ( ICOMPZ.GT.0 .AND. LDZ.LT.MAX( 1, + $ N ) ) ) THEN + INFO = -6 + END IF + IF( INFO.NE.0 ) THEN + CALL XERBLA( 'DSTEQR', -INFO ) + RETURN + END IF +* +* Quick return if possible +* + IF( N.EQ.0 ) + $ RETURN +* + IF( N.EQ.1 ) THEN + IF( ICOMPZ.EQ.2 ) + $ Z( 1, 1 ) = ONE + RETURN + END IF +* +* Determine the unit roundoff and over/underflow thresholds. +* + EPS = DLAMCH( 'E' ) + EPS2 = EPS**2 + SAFMIN = DLAMCH( 'S' ) + SAFMAX = ONE / SAFMIN + SSFMAX = SQRT( SAFMAX ) / THREE + SSFMIN = SQRT( SAFMIN ) / EPS2 +* +* Compute the eigenvalues and eigenvectors of the tridiagonal +* matrix. +* + IF( ICOMPZ.EQ.2 ) + $ CALL DLASET( 'Full', N, N, ZERO, ONE, Z, LDZ ) +* + NMAXIT = N*MAXIT + JTOT = 0 +* +* Determine where the matrix splits and choose QL or QR iteration +* for each block, according to whether top or bottom diagonal +* element is smaller. +* + L1 = 1 + NM1 = N - 1 +* + 10 CONTINUE + IF( L1.GT.N ) + $ GO TO 160 + IF( L1.GT.1 ) + $ E( L1-1 ) = ZERO + IF( L1.LE.NM1 ) THEN + DO 20 M = L1, NM1 + TST = ABS( E( M ) ) + IF( TST.EQ.ZERO ) + $ GO TO 30 + IF( TST.LE.( SQRT( ABS( D( M ) ) )*SQRT( ABS( D( M+ + $ 1 ) ) ) )*EPS ) THEN + E( M ) = ZERO + GO TO 30 + END IF + 20 CONTINUE + END IF + M = N +* + 30 CONTINUE + L = L1 + LSV = L + LEND = M + LENDSV = LEND + L1 = M + 1 + IF( LEND.EQ.L ) + $ GO TO 10 +* +* Scale submatrix in rows and columns L to LEND +* + ANORM = DLANST( 'M', LEND-L+1, D( L ), E( L ) ) + ISCALE = 0 + IF( ANORM.EQ.ZERO ) + $ GO TO 10 + IF( ANORM.GT.SSFMAX ) THEN + ISCALE = 1 + CALL DLASCL( 'G', 0, 0, ANORM, SSFMAX, LEND-L+1, 1, D( L ), N, + $ INFO ) + CALL DLASCL( 'G', 0, 0, ANORM, SSFMAX, LEND-L, 1, E( L ), N, + $ INFO ) + ELSE IF( ANORM.LT.SSFMIN ) THEN + ISCALE = 2 + CALL DLASCL( 'G', 0, 0, ANORM, SSFMIN, LEND-L+1, 1, D( L ), N, + $ INFO ) + CALL DLASCL( 'G', 0, 0, ANORM, SSFMIN, LEND-L, 1, E( L ), N, + $ INFO ) + END IF +* +* Choose between QL and QR iteration +* + IF( ABS( D( LEND ) ).LT.ABS( D( L ) ) ) THEN + LEND = LSV + L = LENDSV + END IF +* + IF( LEND.GT.L ) THEN +* +* QL Iteration +* +* Look for small subdiagonal element. +* + 40 CONTINUE + IF( L.NE.LEND ) THEN + LENDM1 = LEND - 1 + DO 50 M = L, LENDM1 + TST = ABS( E( M ) )**2 + IF( TST.LE.( EPS2*ABS( D( M ) ) )*ABS( D( M+1 ) )+ + $ SAFMIN )GO TO 60 + 50 CONTINUE + END IF +* + M = LEND +* + 60 CONTINUE + IF( M.LT.LEND ) + $ E( M ) = ZERO + P = D( L ) + IF( M.EQ.L ) + $ GO TO 80 +* +* If remaining matrix is 2-by-2, use DLAE2 or SLAEV2 +* to compute its eigensystem. +* + IF( M.EQ.L+1 ) THEN + IF( ICOMPZ.GT.0 ) THEN + CALL DLAEV2( D( L ), E( L ), D( L+1 ), RT1, RT2, C, S ) + WORK( L ) = C + WORK( N-1+L ) = S + CALL DLASR( 'R', 'V', 'B', N, 2, WORK( L ), + $ WORK( N-1+L ), Z( 1, L ), LDZ ) + ELSE + CALL DLAE2( D( L ), E( L ), D( L+1 ), RT1, RT2 ) + END IF + D( L ) = RT1 + D( L+1 ) = RT2 + E( L ) = ZERO + L = L + 2 + IF( L.LE.LEND ) + $ GO TO 40 + GO TO 140 + END IF +* + IF( JTOT.EQ.NMAXIT ) + $ GO TO 140 + JTOT = JTOT + 1 +* +* Form shift. +* + G = ( D( L+1 )-P ) / ( TWO*E( L ) ) + R = DLAPY2( G, ONE ) + G = D( M ) - P + ( E( L ) / ( G+SIGN( R, G ) ) ) +* + S = ONE + C = ONE + P = ZERO +* +* Inner loop +* + MM1 = M - 1 + DO 70 I = MM1, L, -1 + F = S*E( I ) + B = C*E( I ) + CALL DLARTG( G, F, C, S, R ) + IF( I.NE.M-1 ) + $ E( I+1 ) = R + G = D( I+1 ) - P + R = ( D( I )-G )*S + TWO*C*B + P = S*R + D( I+1 ) = G + P + G = C*R - B +* +* If eigenvectors are desired, then save rotations. +* + IF( ICOMPZ.GT.0 ) THEN + WORK( I ) = C + WORK( N-1+I ) = -S + END IF +* + 70 CONTINUE +* +* If eigenvectors are desired, then apply saved rotations. +* + IF( ICOMPZ.GT.0 ) THEN + MM = M - L + 1 + CALL DLASR( 'R', 'V', 'B', N, MM, WORK( L ), WORK( N-1+L ), + $ Z( 1, L ), LDZ ) + END IF +* + D( L ) = D( L ) - P + E( L ) = G + GO TO 40 +* +* Eigenvalue found. +* + 80 CONTINUE + D( L ) = P +* + L = L + 1 + IF( L.LE.LEND ) + $ GO TO 40 + GO TO 140 +* + ELSE +* +* QR Iteration +* +* Look for small superdiagonal element. +* + 90 CONTINUE + IF( L.NE.LEND ) THEN + LENDP1 = LEND + 1 + DO 100 M = L, LENDP1, -1 + TST = ABS( E( M-1 ) )**2 + IF( TST.LE.( EPS2*ABS( D( M ) ) )*ABS( D( M-1 ) )+ + $ SAFMIN )GO TO 110 + 100 CONTINUE + END IF +* + M = LEND +* + 110 CONTINUE + IF( M.GT.LEND ) + $ E( M-1 ) = ZERO + P = D( L ) + IF( M.EQ.L ) + $ GO TO 130 +* +* If remaining matrix is 2-by-2, use DLAE2 or SLAEV2 +* to compute its eigensystem. +* + IF( M.EQ.L-1 ) THEN + IF( ICOMPZ.GT.0 ) THEN + CALL DLAEV2( D( L-1 ), E( L-1 ), D( L ), RT1, RT2, C, S ) + WORK( M ) = C + WORK( N-1+M ) = S + CALL DLASR( 'R', 'V', 'F', N, 2, WORK( M ), + $ WORK( N-1+M ), Z( 1, L-1 ), LDZ ) + ELSE + CALL DLAE2( D( L-1 ), E( L-1 ), D( L ), RT1, RT2 ) + END IF + D( L-1 ) = RT1 + D( L ) = RT2 + E( L-1 ) = ZERO + L = L - 2 + IF( L.GE.LEND ) + $ GO TO 90 + GO TO 140 + END IF +* + IF( JTOT.EQ.NMAXIT ) + $ GO TO 140 + JTOT = JTOT + 1 +* +* Form shift. +* + G = ( D( L-1 )-P ) / ( TWO*E( L-1 ) ) + R = DLAPY2( G, ONE ) + G = D( M ) - P + ( E( L-1 ) / ( G+SIGN( R, G ) ) ) +* + S = ONE + C = ONE + P = ZERO +* +* Inner loop +* + LM1 = L - 1 + DO 120 I = M, LM1 + F = S*E( I ) + B = C*E( I ) + CALL DLARTG( G, F, C, S, R ) + IF( I.NE.M ) + $ E( I-1 ) = R + G = D( I ) - P + R = ( D( I+1 )-G )*S + TWO*C*B + P = S*R + D( I ) = G + P + G = C*R - B +* +* If eigenvectors are desired, then save rotations. +* + IF( ICOMPZ.GT.0 ) THEN + WORK( I ) = C + WORK( N-1+I ) = S + END IF +* + 120 CONTINUE +* +* If eigenvectors are desired, then apply saved rotations. +* + IF( ICOMPZ.GT.0 ) THEN + MM = L - M + 1 + CALL DLASR( 'R', 'V', 'F', N, MM, WORK( M ), WORK( N-1+M ), + $ Z( 1, M ), LDZ ) + END IF +* + D( L ) = D( L ) - P + E( LM1 ) = G + GO TO 90 +* +* Eigenvalue found. +* + 130 CONTINUE + D( L ) = P +* + L = L - 1 + IF( L.GE.LEND ) + $ GO TO 90 + GO TO 140 +* + END IF +* +* Undo scaling if necessary +* + 140 CONTINUE + IF( ISCALE.EQ.1 ) THEN + CALL DLASCL( 'G', 0, 0, SSFMAX, ANORM, LENDSV-LSV+1, 1, + $ D( LSV ), N, INFO ) + CALL DLASCL( 'G', 0, 0, SSFMAX, ANORM, LENDSV-LSV, 1, E( LSV ), + $ N, INFO ) + ELSE IF( ISCALE.EQ.2 ) THEN + CALL DLASCL( 'G', 0, 0, SSFMIN, ANORM, LENDSV-LSV+1, 1, + $ D( LSV ), N, INFO ) + CALL DLASCL( 'G', 0, 0, SSFMIN, ANORM, LENDSV-LSV, 1, E( LSV ), + $ N, INFO ) + END IF +* +* Check for no convergence to an eigenvalue after a total +* of N*MAXIT iterations. +* + IF( JTOT.LT.NMAXIT ) + $ GO TO 10 + DO 150 I = 1, N - 1 + IF( E( I ).NE.ZERO ) + $ INFO = INFO + 1 + 150 CONTINUE + GO TO 190 +* +* Order eigenvalues and eigenvectors. +* + 160 CONTINUE + IF( ICOMPZ.EQ.0 ) THEN +* +* Use Quick Sort +* + CALL DLASRT( 'I', N, D, INFO ) +* + ELSE +* +* Use Selection Sort to minimize swaps of eigenvectors +* + DO 180 II = 2, N + I = II - 1 + K = I + P = D( I ) + DO 170 J = II, N + IF( D( J ).LT.P ) THEN + K = J + P = D( J ) + END IF + 170 CONTINUE + IF( K.NE.I ) THEN + D( K ) = D( I ) + D( I ) = P + CALL DSWAP( N, Z( 1, I ), 1, Z( 1, K ), 1 ) + END IF + 180 CONTINUE + END IF +* + 190 CONTINUE + RETURN +* +* End of DSTEQR +* + END diff --git a/applications/PUfoam/MoDeNaModels/CFD_tool_0D/src/eigen/src/dswap.f b/applications/PUfoam/MoDeNaModels/CFD_tool_0D/src/eigen/src/dswap.f new file mode 100644 index 000000000..e5ec80690 --- /dev/null +++ b/applications/PUfoam/MoDeNaModels/CFD_tool_0D/src/eigen/src/dswap.f @@ -0,0 +1,123 @@ +*> \brief \b DSWAP +* +* =========== DOCUMENTATION =========== +* +* Online html documentation available at +* http://www.netlib.org/lapack/explore-html/ +* +* Definition: +* =========== +* +* SUBROUTINE DSWAP(N,DX,INCX,DY,INCY) +* +* .. Scalar Arguments .. +* INTEGER INCX,INCY,N +* .. +* .. Array Arguments .. +* DOUBLE PRECISION DX(*),DY(*) +* .. +* +* +*> \par Purpose: +* ============= +*> +*> \verbatim +*> +*> interchanges two vectors. +*> uses unrolled loops for increments equal one. +*> \endverbatim +* +* Authors: +* ======== +* +*> \author Univ. of Tennessee +*> \author Univ. of California Berkeley +*> \author Univ. of Colorado Denver +*> \author NAG Ltd. +* +*> \date November 2011 +* +*> \ingroup double_blas_level1 +* +*> \par Further Details: +* ===================== +*> +*> \verbatim +*> +*> jack dongarra, linpack, 3/11/78. +*> modified 12/3/93, array(1) declarations changed to array(*) +*> \endverbatim +*> +* ===================================================================== + SUBROUTINE DSWAP(N,DX,INCX,DY,INCY) +* +* -- Reference BLAS level1 routine (version 3.4.0) -- +* -- Reference BLAS is a software package provided by Univ. of Tennessee, -- +* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- +* November 2011 +* +* .. Scalar Arguments .. + INTEGER INCX,INCY,N +* .. +* .. Array Arguments .. + DOUBLE PRECISION DX(*),DY(*) +* .. +* +* ===================================================================== +* +* .. Local Scalars .. + DOUBLE PRECISION DTEMP + INTEGER I,IX,IY,M,MP1 +* .. +* .. Intrinsic Functions .. + INTRINSIC MOD +* .. + IF (N.LE.0) RETURN + IF (INCX.EQ.1 .AND. INCY.EQ.1) THEN +* +* code for both increments equal to 1 +* +* +* clean-up loop +* + M = MOD(N,3) + IF (M.NE.0) THEN + DO I = 1,M + DTEMP = DX(I) + DX(I) = DY(I) + DY(I) = DTEMP + END DO + IF (N.LT.3) RETURN + END IF + MP1 = M + 1 + DO I = MP1,N,3 + DTEMP = DX(I) + DX(I) = DY(I) + DY(I) = DTEMP + DTEMP = DX(I+1) + DX(I+1) = DY(I+1) + DY(I+1) = DTEMP + DTEMP = DX(I+2) + DX(I+2) = DY(I+2) + DY(I+2) = DTEMP + END DO + ELSE +* +* code for unequal increments or equal increments not equal +* to 1 +* + IX = 1 + IY = 1 + IF (INCX.LT.0) IX = (-N+1)*INCX + 1 + IF (INCY.LT.0) IY = (-N+1)*INCY + 1 + DO I = 1,N + DTEMP = DX(IX) + DX(IX) = DY(IY) + DY(IY) = DTEMP + IX = IX + INCX + IY = IY + INCY + END DO + END IF + RETURN + END + diff --git a/applications/PUfoam/MoDeNaModels/CFD_tool_0D/src/eigen/src/dtrsm.f b/applications/PUfoam/MoDeNaModels/CFD_tool_0D/src/eigen/src/dtrsm.f new file mode 100644 index 000000000..dec5c8d02 --- /dev/null +++ b/applications/PUfoam/MoDeNaModels/CFD_tool_0D/src/eigen/src/dtrsm.f @@ -0,0 +1,376 @@ + SUBROUTINE DTRSM(SIDE,UPLO,TRANSA,DIAG,M,N,ALPHA,A,LDA,B,LDB) +* .. Scalar Arguments .. + DOUBLE PRECISION ALPHA + INTEGER LDA,LDB,M,N + CHARACTER DIAG,SIDE,TRANSA,UPLO +* .. +* .. Array Arguments .. + DOUBLE PRECISION A(LDA,*),B(LDB,*) +* .. +* +* Purpose +* ======= +* +* DTRSM solves one of the matrix equations +* +* op( A )*X = alpha*B, or X*op( A ) = alpha*B, +* +* where alpha is a scalar, X and B are m by n matrices, A is a unit, or +* non-unit, upper or lower triangular matrix and op( A ) is one of +* +* op( A ) = A or op( A ) = A**T. +* +* The matrix X is overwritten on B. +* +* Arguments +* ========== +* +* SIDE - CHARACTER*1. +* On entry, SIDE specifies whether op( A ) appears on the left +* or right of X as follows: +* +* SIDE = 'L' or 'l' op( A )*X = alpha*B. +* +* SIDE = 'R' or 'r' X*op( A ) = alpha*B. +* +* Unchanged on exit. +* +* UPLO - CHARACTER*1. +* On entry, UPLO specifies whether the matrix A is an upper or +* lower triangular matrix as follows: +* +* UPLO = 'U' or 'u' A is an upper triangular matrix. +* +* UPLO = 'L' or 'l' A is a lower triangular matrix. +* +* Unchanged on exit. +* +* TRANSA - CHARACTER*1. +* On entry, TRANSA specifies the form of op( A ) to be used in +* the matrix multiplication as follows: +* +* TRANSA = 'N' or 'n' op( A ) = A. +* +* TRANSA = 'T' or 't' op( A ) = A**T. +* +* TRANSA = 'C' or 'c' op( A ) = A**T. +* +* Unchanged on exit. +* +* DIAG - CHARACTER*1. +* On entry, DIAG specifies whether or not A is unit triangular +* as follows: +* +* DIAG = 'U' or 'u' A is assumed to be unit triangular. +* +* DIAG = 'N' or 'n' A is not assumed to be unit +* triangular. +* +* Unchanged on exit. +* +* M - INTEGER. +* On entry, M specifies the number of rows of B. M must be at +* least zero. +* Unchanged on exit. +* +* N - INTEGER. +* On entry, N specifies the number of columns of B. N must be +* at least zero. +* Unchanged on exit. +* +* ALPHA - DOUBLE PRECISION. +* On entry, ALPHA specifies the scalar alpha. When alpha is +* zero then A is not referenced and B need not be set before +* entry. +* Unchanged on exit. +* +* A - DOUBLE PRECISION array of DIMENSION ( LDA, k ), where k is m +* when SIDE = 'L' or 'l' and is n when SIDE = 'R' or 'r'. +* Before entry with UPLO = 'U' or 'u', the leading k by k +* upper triangular part of the array A must contain the upper +* triangular matrix and the strictly lower triangular part of +* A is not referenced. +* Before entry with UPLO = 'L' or 'l', the leading k by k +* lower triangular part of the array A must contain the lower +* triangular matrix and the strictly upper triangular part of +* A is not referenced. +* Note that when DIAG = 'U' or 'u', the diagonal elements of +* A are not referenced either, but are assumed to be unity. +* Unchanged on exit. +* +* LDA - INTEGER. +* On entry, LDA specifies the first dimension of A as declared +* in the calling (sub) program. When SIDE = 'L' or 'l' then +* LDA must be at least max( 1, m ), when SIDE = 'R' or 'r' +* then LDA must be at least max( 1, n ). +* Unchanged on exit. +* +* B - DOUBLE PRECISION array of DIMENSION ( LDB, n ). +* Before entry, the leading m by n part of the array B must +* contain the right-hand side matrix B, and on exit is +* overwritten by the solution matrix X. +* +* LDB - INTEGER. +* On entry, LDB specifies the first dimension of B as declared +* in the calling (sub) program. LDB must be at least +* max( 1, m ). +* Unchanged on exit. +* +* Further Details +* =============== +* +* Level 3 Blas routine. +* +* +* -- Written on 8-February-1989. +* Jack Dongarra, Argonne National Laboratory. +* Iain Duff, AERE Harwell. +* Jeremy Du Croz, Numerical Algorithms Group Ltd. +* Sven Hammarling, Numerical Algorithms Group Ltd. +* +* ===================================================================== +* +* .. External Functions .. + LOGICAL LSAME + EXTERNAL LSAME +* .. +* .. External Subroutines .. + EXTERNAL XERBLA +* .. +* .. Intrinsic Functions .. + INTRINSIC MAX +* .. +* .. Local Scalars .. + DOUBLE PRECISION TEMP + INTEGER I,INFO,J,K,NROWA + LOGICAL LSIDE,NOUNIT,UPPER +* .. +* .. Parameters .. + DOUBLE PRECISION ONE,ZERO + PARAMETER (ONE=1.0D+0,ZERO=0.0D+0) +* .. +* +* Test the input parameters. +* + LSIDE = LSAME(SIDE,'L') + IF (LSIDE) THEN + NROWA = M + ELSE + NROWA = N + END IF + NOUNIT = LSAME(DIAG,'N') + UPPER = LSAME(UPLO,'U') +* + INFO = 0 + IF ((.NOT.LSIDE) .AND. (.NOT.LSAME(SIDE,'R'))) THEN + INFO = 1 + ELSE IF ((.NOT.UPPER) .AND. (.NOT.LSAME(UPLO,'L'))) THEN + INFO = 2 + ELSE IF ((.NOT.LSAME(TRANSA,'N')) .AND. + + (.NOT.LSAME(TRANSA,'T')) .AND. + + (.NOT.LSAME(TRANSA,'C'))) THEN + INFO = 3 + ELSE IF ((.NOT.LSAME(DIAG,'U')) .AND. (.NOT.LSAME(DIAG,'N'))) THEN + INFO = 4 + ELSE IF (M.LT.0) THEN + INFO = 5 + ELSE IF (N.LT.0) THEN + INFO = 6 + ELSE IF (LDA.LT.MAX(1,NROWA)) THEN + INFO = 9 + ELSE IF (LDB.LT.MAX(1,M)) THEN + INFO = 11 + END IF + IF (INFO.NE.0) THEN + CALL XERBLA('DTRSM ',INFO) + RETURN + END IF +* +* Quick return if possible. +* + IF (M.EQ.0 .OR. N.EQ.0) RETURN +* +* And when alpha.eq.zero. +* + IF (ALPHA.EQ.ZERO) THEN + DO 20 J = 1,N + DO 10 I = 1,M + B(I,J) = ZERO + 10 CONTINUE + 20 CONTINUE + RETURN + END IF +* +* Start the operations. +* + IF (LSIDE) THEN + IF (LSAME(TRANSA,'N')) THEN +* +* Form B := alpha*inv( A )*B. +* + IF (UPPER) THEN + DO 60 J = 1,N + IF (ALPHA.NE.ONE) THEN + DO 30 I = 1,M + B(I,J) = ALPHA*B(I,J) + 30 CONTINUE + END IF + DO 50 K = M,1,-1 + IF (B(K,J).NE.ZERO) THEN + IF (NOUNIT) B(K,J) = B(K,J)/A(K,K) + DO 40 I = 1,K - 1 + B(I,J) = B(I,J) - B(K,J)*A(I,K) + 40 CONTINUE + END IF + 50 CONTINUE + 60 CONTINUE + ELSE + DO 100 J = 1,N + IF (ALPHA.NE.ONE) THEN + DO 70 I = 1,M + B(I,J) = ALPHA*B(I,J) + 70 CONTINUE + END IF + DO 90 K = 1,M + IF (B(K,J).NE.ZERO) THEN + IF (NOUNIT) B(K,J) = B(K,J)/A(K,K) + DO 80 I = K + 1,M + B(I,J) = B(I,J) - B(K,J)*A(I,K) + 80 CONTINUE + END IF + 90 CONTINUE + 100 CONTINUE + END IF + ELSE +* +* Form B := alpha*inv( A**T )*B. +* + IF (UPPER) THEN + DO 130 J = 1,N + DO 120 I = 1,M + TEMP = ALPHA*B(I,J) + DO 110 K = 1,I - 1 + TEMP = TEMP - A(K,I)*B(K,J) + 110 CONTINUE + IF (NOUNIT) TEMP = TEMP/A(I,I) + B(I,J) = TEMP + 120 CONTINUE + 130 CONTINUE + ELSE + DO 160 J = 1,N + DO 150 I = M,1,-1 + TEMP = ALPHA*B(I,J) + DO 140 K = I + 1,M + TEMP = TEMP - A(K,I)*B(K,J) + 140 CONTINUE + IF (NOUNIT) TEMP = TEMP/A(I,I) + B(I,J) = TEMP + 150 CONTINUE + 160 CONTINUE + END IF + END IF + ELSE + IF (LSAME(TRANSA,'N')) THEN +* +* Form B := alpha*B*inv( A ). +* + IF (UPPER) THEN + DO 210 J = 1,N + IF (ALPHA.NE.ONE) THEN + DO 170 I = 1,M + B(I,J) = ALPHA*B(I,J) + 170 CONTINUE + END IF + DO 190 K = 1,J - 1 + IF (A(K,J).NE.ZERO) THEN + DO 180 I = 1,M + B(I,J) = B(I,J) - A(K,J)*B(I,K) + 180 CONTINUE + END IF + 190 CONTINUE + IF (NOUNIT) THEN + TEMP = ONE/A(J,J) + DO 200 I = 1,M + B(I,J) = TEMP*B(I,J) + 200 CONTINUE + END IF + 210 CONTINUE + ELSE + DO 260 J = N,1,-1 + IF (ALPHA.NE.ONE) THEN + DO 220 I = 1,M + B(I,J) = ALPHA*B(I,J) + 220 CONTINUE + END IF + DO 240 K = J + 1,N + IF (A(K,J).NE.ZERO) THEN + DO 230 I = 1,M + B(I,J) = B(I,J) - A(K,J)*B(I,K) + 230 CONTINUE + END IF + 240 CONTINUE + IF (NOUNIT) THEN + TEMP = ONE/A(J,J) + DO 250 I = 1,M + B(I,J) = TEMP*B(I,J) + 250 CONTINUE + END IF + 260 CONTINUE + END IF + ELSE +* +* Form B := alpha*B*inv( A**T ). +* + IF (UPPER) THEN + DO 310 K = N,1,-1 + IF (NOUNIT) THEN + TEMP = ONE/A(K,K) + DO 270 I = 1,M + B(I,K) = TEMP*B(I,K) + 270 CONTINUE + END IF + DO 290 J = 1,K - 1 + IF (A(J,K).NE.ZERO) THEN + TEMP = A(J,K) + DO 280 I = 1,M + B(I,J) = B(I,J) - TEMP*B(I,K) + 280 CONTINUE + END IF + 290 CONTINUE + IF (ALPHA.NE.ONE) THEN + DO 300 I = 1,M + B(I,K) = ALPHA*B(I,K) + 300 CONTINUE + END IF + 310 CONTINUE + ELSE + DO 360 K = 1,N + IF (NOUNIT) THEN + TEMP = ONE/A(K,K) + DO 320 I = 1,M + B(I,K) = TEMP*B(I,K) + 320 CONTINUE + END IF + DO 340 J = K + 1,N + IF (A(J,K).NE.ZERO) THEN + TEMP = A(J,K) + DO 330 I = 1,M + B(I,J) = B(I,J) - TEMP*B(I,K) + 330 CONTINUE + END IF + 340 CONTINUE + IF (ALPHA.NE.ONE) THEN + DO 350 I = 1,M + B(I,K) = ALPHA*B(I,K) + 350 CONTINUE + END IF + 360 CONTINUE + END IF + END IF + END IF +* + RETURN +* +* End of DTRSM . +* + END diff --git a/applications/PUfoam/MoDeNaModels/CFD_tool_0D/src/eigen/src/idamax.f b/applications/PUfoam/MoDeNaModels/CFD_tool_0D/src/eigen/src/idamax.f new file mode 100644 index 000000000..2cc0f9a5f --- /dev/null +++ b/applications/PUfoam/MoDeNaModels/CFD_tool_0D/src/eigen/src/idamax.f @@ -0,0 +1,61 @@ + INTEGER FUNCTION IDAMAX(N,DX,INCX) +* .. Scalar Arguments .. + INTEGER INCX,N +* .. +* .. Array Arguments .. + DOUBLE PRECISION DX(*) +* .. +* +* Purpose +* ======= +* +* IDAMAX finds the index of element having max. absolute value. +* +* Further Details +* =============== +* +* jack dongarra, linpack, 3/11/78. +* modified 3/93 to return if incx .le. 0. +* modified 12/3/93, array(1) declarations changed to array(*) +* +* ===================================================================== +* +* .. Local Scalars .. + DOUBLE PRECISION DMAX + INTEGER I,IX +* .. +* .. Intrinsic Functions .. + INTRINSIC DABS +* .. + IDAMAX = 0 + IF (N.LT.1 .OR. INCX.LE.0) RETURN + IDAMAX = 1 + IF (N.EQ.1) RETURN + IF (INCX.EQ.1) THEN +* +* code for increment equal to 1 +* + DMAX = DABS(DX(1)) + DO I = 2,N + IF (DABS(DX(I)).GT.DMAX) THEN + IDAMAX = I + DMAX = DABS(DX(I)) + END IF + END DO + ELSE +* +* code for increment not equal to 1 +* + IX = 1 + DMAX = DABS(DX(1)) + IX = IX + INCX + DO I = 2,N + IF (DABS(DX(IX)).GT.DMAX) THEN + IDAMAX = I + DMAX = DABS(DX(IX)) + END IF + IX = IX + INCX + END DO + END IF + RETURN + END diff --git a/applications/PUfoam/MoDeNaModels/CFD_tool_0D/src/eigen/src/ieeeck.f b/applications/PUfoam/MoDeNaModels/CFD_tool_0D/src/eigen/src/ieeeck.f new file mode 100644 index 000000000..132e43677 --- /dev/null +++ b/applications/PUfoam/MoDeNaModels/CFD_tool_0D/src/eigen/src/ieeeck.f @@ -0,0 +1,203 @@ +*> \brief \b IEEECK +* +* =========== DOCUMENTATION =========== +* +* Online html documentation available at +* http://www.netlib.org/lapack/explore-html/ +* +*> \htmlonly +*> Download IEEECK + dependencies +*> +*> [TGZ] +*> +*> [ZIP] +*> +*> [TXT] +*> \endhtmlonly +* +* Definition: +* =========== +* +* INTEGER FUNCTION IEEECK( ISPEC, ZERO, ONE ) +* +* .. Scalar Arguments .. +* INTEGER ISPEC +* REAL ONE, ZERO +* .. +* +* +*> \par Purpose: +* ============= +*> +*> \verbatim +*> +*> IEEECK is called from the ILAENV to verify that Infinity and +*> possibly NaN arithmetic is safe (i.e. will not trap). +*> \endverbatim +* +* Arguments: +* ========== +* +*> \param[in] ISPEC +*> \verbatim +*> ISPEC is INTEGER +*> Specifies whether to test just for inifinity arithmetic +*> or whether to test for infinity and NaN arithmetic. +*> = 0: Verify infinity arithmetic only. +*> = 1: Verify infinity and NaN arithmetic. +*> \endverbatim +*> +*> \param[in] ZERO +*> \verbatim +*> ZERO is REAL +*> Must contain the value 0.0 +*> This is passed to prevent the compiler from optimizing +*> away this code. +*> \endverbatim +*> +*> \param[in] ONE +*> \verbatim +*> ONE is REAL +*> Must contain the value 1.0 +*> This is passed to prevent the compiler from optimizing +*> away this code. +*> +*> RETURN VALUE: INTEGER +*> = 0: Arithmetic failed to produce the correct answers +*> = 1: Arithmetic produced the correct answers +*> \endverbatim +* +* Authors: +* ======== +* +*> \author Univ. of Tennessee +*> \author Univ. of California Berkeley +*> \author Univ. of Colorado Denver +*> \author NAG Ltd. +* +*> \date November 2011 +* +*> \ingroup auxOTHERauxiliary +* +* ===================================================================== + INTEGER FUNCTION IEEECK( ISPEC, ZERO, ONE ) +* +* -- LAPACK auxiliary routine (version 3.4.0) -- +* -- LAPACK is a software package provided by Univ. of Tennessee, -- +* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- +* November 2011 +* +* .. Scalar Arguments .. + INTEGER ISPEC + REAL ONE, ZERO +* .. +* +* ===================================================================== +* +* .. Local Scalars .. + REAL NAN1, NAN2, NAN3, NAN4, NAN5, NAN6, NEGINF, + $ NEGZRO, NEWZRO, POSINF +* .. +* .. Executable Statements .. + IEEECK = 1 +* + POSINF = ONE / ZERO + IF( POSINF.LE.ONE ) THEN + IEEECK = 0 + RETURN + END IF +* + NEGINF = -ONE / ZERO + IF( NEGINF.GE.ZERO ) THEN + IEEECK = 0 + RETURN + END IF +* + NEGZRO = ONE / ( NEGINF+ONE ) + IF( NEGZRO.NE.ZERO ) THEN + IEEECK = 0 + RETURN + END IF +* + NEGINF = ONE / NEGZRO + IF( NEGINF.GE.ZERO ) THEN + IEEECK = 0 + RETURN + END IF +* + NEWZRO = NEGZRO + ZERO + IF( NEWZRO.NE.ZERO ) THEN + IEEECK = 0 + RETURN + END IF +* + POSINF = ONE / NEWZRO + IF( POSINF.LE.ONE ) THEN + IEEECK = 0 + RETURN + END IF +* + NEGINF = NEGINF*POSINF + IF( NEGINF.GE.ZERO ) THEN + IEEECK = 0 + RETURN + END IF +* + POSINF = POSINF*POSINF + IF( POSINF.LE.ONE ) THEN + IEEECK = 0 + RETURN + END IF +* +* +* +* +* Return if we were only asked to check infinity arithmetic +* + IF( ISPEC.EQ.0 ) + $ RETURN +* + NAN1 = POSINF + NEGINF +* + NAN2 = POSINF / NEGINF +* + NAN3 = POSINF / POSINF +* + NAN4 = POSINF*ZERO +* + NAN5 = NEGINF*NEGZRO +* + NAN6 = NAN5*ZERO +* + IF( NAN1.EQ.NAN1 ) THEN + IEEECK = 0 + RETURN + END IF +* + IF( NAN2.EQ.NAN2 ) THEN + IEEECK = 0 + RETURN + END IF +* + IF( NAN3.EQ.NAN3 ) THEN + IEEECK = 0 + RETURN + END IF +* + IF( NAN4.EQ.NAN4 ) THEN + IEEECK = 0 + RETURN + END IF +* + IF( NAN5.EQ.NAN5 ) THEN + IEEECK = 0 + RETURN + END IF +* + IF( NAN6.EQ.NAN6 ) THEN + IEEECK = 0 + RETURN + END IF +* + RETURN + END diff --git a/applications/PUfoam/MoDeNaModels/CFD_tool_0D/src/eigen/src/ilaenv.f b/applications/PUfoam/MoDeNaModels/CFD_tool_0D/src/eigen/src/ilaenv.f new file mode 100644 index 000000000..867464de3 --- /dev/null +++ b/applications/PUfoam/MoDeNaModels/CFD_tool_0D/src/eigen/src/ilaenv.f @@ -0,0 +1,624 @@ +*> \brief \b ILAENV +* +* =========== DOCUMENTATION =========== +* +* Online html documentation available at +* http://www.netlib.org/lapack/explore-html/ +* +*> \htmlonly +*> Download ILAENV + dependencies +*> +*> [TGZ] +*> +*> [ZIP] +*> +*> [TXT] +*> \endhtmlonly +* +* Definition: +* =========== +* +* INTEGER FUNCTION ILAENV( ISPEC, NAME, OPTS, N1, N2, N3, N4 ) +* +* .. Scalar Arguments .. +* CHARACTER*( * ) NAME, OPTS +* INTEGER ISPEC, N1, N2, N3, N4 +* .. +* +* +*> \par Purpose: +* ============= +*> +*> \verbatim +*> +*> ILAENV is called from the LAPACK routines to choose problem-dependent +*> parameters for the local environment. See ISPEC for a description of +*> the parameters. +*> +*> ILAENV returns an INTEGER +*> if ILAENV >= 0: ILAENV returns the value of the parameter specified by ISPEC +*> if ILAENV < 0: if ILAENV = -k, the k-th argument had an illegal value. +*> +*> This version provides a set of parameters which should give good, +*> but not optimal, performance on many of the currently available +*> computers. Users are encouraged to modify this subroutine to set +*> the tuning parameters for their particular machine using the option +*> and problem size information in the arguments. +*> +*> This routine will not function correctly if it is converted to all +*> lower case. Converting it to all upper case is allowed. +*> \endverbatim +* +* Arguments: +* ========== +* +*> \param[in] ISPEC +*> \verbatim +*> ISPEC is INTEGER +*> Specifies the parameter to be returned as the value of +*> ILAENV. +*> = 1: the optimal blocksize; if this value is 1, an unblocked +*> algorithm will give the best performance. +*> = 2: the minimum block size for which the block routine +*> should be used; if the usable block size is less than +*> this value, an unblocked routine should be used. +*> = 3: the crossover point (in a block routine, for N less +*> than this value, an unblocked routine should be used) +*> = 4: the number of shifts, used in the nonsymmetric +*> eigenvalue routines (DEPRECATED) +*> = 5: the minimum column dimension for blocking to be used; +*> rectangular blocks must have dimension at least k by m, +*> where k is given by ILAENV(2,...) and m by ILAENV(5,...) +*> = 6: the crossover point for the SVD (when reducing an m by n +*> matrix to bidiagonal form, if max(m,n)/min(m,n) exceeds +*> this value, a QR factorization is used first to reduce +*> the matrix to a triangular form.) +*> = 7: the number of processors +*> = 8: the crossover point for the multishift QR method +*> for nonsymmetric eigenvalue problems (DEPRECATED) +*> = 9: maximum size of the subproblems at the bottom of the +*> computation tree in the divide-and-conquer algorithm +*> (used by xGELSD and xGESDD) +*> =10: ieee NaN arithmetic can be trusted not to trap +*> =11: infinity arithmetic can be trusted not to trap +*> 12 <= ISPEC <= 16: +*> xHSEQR or one of its subroutines, +*> see IPARMQ for detailed explanation +*> \endverbatim +*> +*> \param[in] NAME +*> \verbatim +*> NAME is CHARACTER*(*) +*> The name of the calling subroutine, in either upper case or +*> lower case. +*> \endverbatim +*> +*> \param[in] OPTS +*> \verbatim +*> OPTS is CHARACTER*(*) +*> The character options to the subroutine NAME, concatenated +*> into a single character string. For example, UPLO = 'U', +*> TRANS = 'T', and DIAG = 'N' for a triangular routine would +*> be specified as OPTS = 'UTN'. +*> \endverbatim +*> +*> \param[in] N1 +*> \verbatim +*> N1 is INTEGER +*> \endverbatim +*> +*> \param[in] N2 +*> \verbatim +*> N2 is INTEGER +*> \endverbatim +*> +*> \param[in] N3 +*> \verbatim +*> N3 is INTEGER +*> \endverbatim +*> +*> \param[in] N4 +*> \verbatim +*> N4 is INTEGER +*> Problem dimensions for the subroutine NAME; these may not all +*> be required. +*> \endverbatim +* +* Authors: +* ======== +* +*> \author Univ. of Tennessee +*> \author Univ. of California Berkeley +*> \author Univ. of Colorado Denver +*> \author NAG Ltd. +* +*> \date November 2011 +* +*> \ingroup auxOTHERauxiliary +* +*> \par Further Details: +* ===================== +*> +*> \verbatim +*> +*> The following conventions have been used when calling ILAENV from the +*> LAPACK routines: +*> 1) OPTS is a concatenation of all of the character options to +*> subroutine NAME, in the same order that they appear in the +*> argument list for NAME, even if they are not used in determining +*> the value of the parameter specified by ISPEC. +*> 2) The problem dimensions N1, N2, N3, N4 are specified in the order +*> that they appear in the argument list for NAME. N1 is used +*> first, N2 second, and so on, and unused problem dimensions are +*> passed a value of -1. +*> 3) The parameter value returned by ILAENV is checked for validity in +*> the calling subroutine. For example, ILAENV is used to retrieve +*> the optimal blocksize for STRTRI as follows: +*> +*> NB = ILAENV( 1, 'STRTRI', UPLO // DIAG, N, -1, -1, -1 ) +*> IF( NB.LE.1 ) NB = MAX( 1, N ) +*> \endverbatim +*> +* ===================================================================== + INTEGER FUNCTION ILAENV( ISPEC, NAME, OPTS, N1, N2, N3, N4 ) +* +* -- LAPACK auxiliary routine (version 3.4.0) -- +* -- LAPACK is a software package provided by Univ. of Tennessee, -- +* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- +* November 2011 +* +* .. Scalar Arguments .. + CHARACTER*( * ) NAME, OPTS + INTEGER ISPEC, N1, N2, N3, N4 +* .. +* +* ===================================================================== +* +* .. Local Scalars .. + INTEGER I, IC, IZ, NB, NBMIN, NX + LOGICAL CNAME, SNAME + CHARACTER C1*1, C2*2, C4*2, C3*3, SUBNAM*6 +* .. +* .. Intrinsic Functions .. + INTRINSIC CHAR, ICHAR, INT, MIN, REAL +* .. +* .. External Functions .. + INTEGER IEEECK, IPARMQ + EXTERNAL IEEECK, IPARMQ +* .. +* .. Executable Statements .. +* + GO TO ( 10, 10, 10, 80, 90, 100, 110, 120, + $ 130, 140, 150, 160, 160, 160, 160, 160 )ISPEC +* +* Invalid value for ISPEC +* + ILAENV = -1 + RETURN +* + 10 CONTINUE +* +* Convert NAME to upper case if the first character is lower case. +* + ILAENV = 1 + SUBNAM = NAME + IC = ICHAR( SUBNAM( 1: 1 ) ) + IZ = ICHAR( 'Z' ) + IF( IZ.EQ.90 .OR. IZ.EQ.122 ) THEN +* +* ASCII character set +* + IF( IC.GE.97 .AND. IC.LE.122 ) THEN + SUBNAM( 1: 1 ) = CHAR( IC-32 ) + DO 20 I = 2, 6 + IC = ICHAR( SUBNAM( I: I ) ) + IF( IC.GE.97 .AND. IC.LE.122 ) + $ SUBNAM( I: I ) = CHAR( IC-32 ) + 20 CONTINUE + END IF +* + ELSE IF( IZ.EQ.233 .OR. IZ.EQ.169 ) THEN +* +* EBCDIC character set +* + IF( ( IC.GE.129 .AND. IC.LE.137 ) .OR. + $ ( IC.GE.145 .AND. IC.LE.153 ) .OR. + $ ( IC.GE.162 .AND. IC.LE.169 ) ) THEN + SUBNAM( 1: 1 ) = CHAR( IC+64 ) + DO 30 I = 2, 6 + IC = ICHAR( SUBNAM( I: I ) ) + IF( ( IC.GE.129 .AND. IC.LE.137 ) .OR. + $ ( IC.GE.145 .AND. IC.LE.153 ) .OR. + $ ( IC.GE.162 .AND. IC.LE.169 ) )SUBNAM( I: + $ I ) = CHAR( IC+64 ) + 30 CONTINUE + END IF +* + ELSE IF( IZ.EQ.218 .OR. IZ.EQ.250 ) THEN +* +* Prime machines: ASCII+128 +* + IF( IC.GE.225 .AND. IC.LE.250 ) THEN + SUBNAM( 1: 1 ) = CHAR( IC-32 ) + DO 40 I = 2, 6 + IC = ICHAR( SUBNAM( I: I ) ) + IF( IC.GE.225 .AND. IC.LE.250 ) + $ SUBNAM( I: I ) = CHAR( IC-32 ) + 40 CONTINUE + END IF + END IF +* + C1 = SUBNAM( 1: 1 ) + SNAME = C1.EQ.'S' .OR. C1.EQ.'D' + CNAME = C1.EQ.'C' .OR. C1.EQ.'Z' + IF( .NOT.( CNAME .OR. SNAME ) ) + $ RETURN + C2 = SUBNAM( 2: 3 ) + C3 = SUBNAM( 4: 6 ) + C4 = C3( 2: 3 ) +* + GO TO ( 50, 60, 70 )ISPEC +* + 50 CONTINUE +* +* ISPEC = 1: block size +* +* In these examples, separate code is provided for setting NB for +* real and complex. We assume that NB will take the same value in +* single or double precision. +* + NB = 1 +* + IF( C2.EQ.'GE' ) THEN + IF( C3.EQ.'TRF' ) THEN + IF( SNAME ) THEN + NB = 64 + ELSE + NB = 64 + END IF + ELSE IF( C3.EQ.'QRF' .OR. C3.EQ.'RQF' .OR. C3.EQ.'LQF' .OR. + $ C3.EQ.'QLF' ) THEN + IF( SNAME ) THEN + NB = 32 + ELSE + NB = 32 + END IF + ELSE IF( C3.EQ.'HRD' ) THEN + IF( SNAME ) THEN + NB = 32 + ELSE + NB = 32 + END IF + ELSE IF( C3.EQ.'BRD' ) THEN + IF( SNAME ) THEN + NB = 32 + ELSE + NB = 32 + END IF + ELSE IF( C3.EQ.'TRI' ) THEN + IF( SNAME ) THEN + NB = 64 + ELSE + NB = 64 + END IF + END IF + ELSE IF( C2.EQ.'PO' ) THEN + IF( C3.EQ.'TRF' ) THEN + IF( SNAME ) THEN + NB = 64 + ELSE + NB = 64 + END IF + END IF + ELSE IF( C2.EQ.'SY' ) THEN + IF( C3.EQ.'TRF' ) THEN + IF( SNAME ) THEN + NB = 64 + ELSE + NB = 64 + END IF + ELSE IF( SNAME .AND. C3.EQ.'TRD' ) THEN + NB = 32 + ELSE IF( SNAME .AND. C3.EQ.'GST' ) THEN + NB = 64 + END IF + ELSE IF( CNAME .AND. C2.EQ.'HE' ) THEN + IF( C3.EQ.'TRF' ) THEN + NB = 64 + ELSE IF( C3.EQ.'TRD' ) THEN + NB = 32 + ELSE IF( C3.EQ.'GST' ) THEN + NB = 64 + END IF + ELSE IF( SNAME .AND. C2.EQ.'OR' ) THEN + IF( C3( 1: 1 ).EQ.'G' ) THEN + IF( C4.EQ.'QR' .OR. C4.EQ.'RQ' .OR. C4.EQ.'LQ' .OR. C4.EQ. + $ 'QL' .OR. C4.EQ.'HR' .OR. C4.EQ.'TR' .OR. C4.EQ.'BR' ) + $ THEN + NB = 32 + END IF + ELSE IF( C3( 1: 1 ).EQ.'M' ) THEN + IF( C4.EQ.'QR' .OR. C4.EQ.'RQ' .OR. C4.EQ.'LQ' .OR. C4.EQ. + $ 'QL' .OR. C4.EQ.'HR' .OR. C4.EQ.'TR' .OR. C4.EQ.'BR' ) + $ THEN + NB = 32 + END IF + END IF + ELSE IF( CNAME .AND. C2.EQ.'UN' ) THEN + IF( C3( 1: 1 ).EQ.'G' ) THEN + IF( C4.EQ.'QR' .OR. C4.EQ.'RQ' .OR. C4.EQ.'LQ' .OR. C4.EQ. + $ 'QL' .OR. C4.EQ.'HR' .OR. C4.EQ.'TR' .OR. C4.EQ.'BR' ) + $ THEN + NB = 32 + END IF + ELSE IF( C3( 1: 1 ).EQ.'M' ) THEN + IF( C4.EQ.'QR' .OR. C4.EQ.'RQ' .OR. C4.EQ.'LQ' .OR. C4.EQ. + $ 'QL' .OR. C4.EQ.'HR' .OR. C4.EQ.'TR' .OR. C4.EQ.'BR' ) + $ THEN + NB = 32 + END IF + END IF + ELSE IF( C2.EQ.'GB' ) THEN + IF( C3.EQ.'TRF' ) THEN + IF( SNAME ) THEN + IF( N4.LE.64 ) THEN + NB = 1 + ELSE + NB = 32 + END IF + ELSE + IF( N4.LE.64 ) THEN + NB = 1 + ELSE + NB = 32 + END IF + END IF + END IF + ELSE IF( C2.EQ.'PB' ) THEN + IF( C3.EQ.'TRF' ) THEN + IF( SNAME ) THEN + IF( N2.LE.64 ) THEN + NB = 1 + ELSE + NB = 32 + END IF + ELSE + IF( N2.LE.64 ) THEN + NB = 1 + ELSE + NB = 32 + END IF + END IF + END IF + ELSE IF( C2.EQ.'TR' ) THEN + IF( C3.EQ.'TRI' ) THEN + IF( SNAME ) THEN + NB = 64 + ELSE + NB = 64 + END IF + END IF + ELSE IF( C2.EQ.'LA' ) THEN + IF( C3.EQ.'UUM' ) THEN + IF( SNAME ) THEN + NB = 64 + ELSE + NB = 64 + END IF + END IF + ELSE IF( SNAME .AND. C2.EQ.'ST' ) THEN + IF( C3.EQ.'EBZ' ) THEN + NB = 1 + END IF + END IF + ILAENV = NB + RETURN +* + 60 CONTINUE +* +* ISPEC = 2: minimum block size +* + NBMIN = 2 + IF( C2.EQ.'GE' ) THEN + IF( C3.EQ.'QRF' .OR. C3.EQ.'RQF' .OR. C3.EQ.'LQF' .OR. C3.EQ. + $ 'QLF' ) THEN + IF( SNAME ) THEN + NBMIN = 2 + ELSE + NBMIN = 2 + END IF + ELSE IF( C3.EQ.'HRD' ) THEN + IF( SNAME ) THEN + NBMIN = 2 + ELSE + NBMIN = 2 + END IF + ELSE IF( C3.EQ.'BRD' ) THEN + IF( SNAME ) THEN + NBMIN = 2 + ELSE + NBMIN = 2 + END IF + ELSE IF( C3.EQ.'TRI' ) THEN + IF( SNAME ) THEN + NBMIN = 2 + ELSE + NBMIN = 2 + END IF + END IF + ELSE IF( C2.EQ.'SY' ) THEN + IF( C3.EQ.'TRF' ) THEN + IF( SNAME ) THEN + NBMIN = 8 + ELSE + NBMIN = 8 + END IF + ELSE IF( SNAME .AND. C3.EQ.'TRD' ) THEN + NBMIN = 2 + END IF + ELSE IF( CNAME .AND. C2.EQ.'HE' ) THEN + IF( C3.EQ.'TRD' ) THEN + NBMIN = 2 + END IF + ELSE IF( SNAME .AND. C2.EQ.'OR' ) THEN + IF( C3( 1: 1 ).EQ.'G' ) THEN + IF( C4.EQ.'QR' .OR. C4.EQ.'RQ' .OR. C4.EQ.'LQ' .OR. C4.EQ. + $ 'QL' .OR. C4.EQ.'HR' .OR. C4.EQ.'TR' .OR. C4.EQ.'BR' ) + $ THEN + NBMIN = 2 + END IF + ELSE IF( C3( 1: 1 ).EQ.'M' ) THEN + IF( C4.EQ.'QR' .OR. C4.EQ.'RQ' .OR. C4.EQ.'LQ' .OR. C4.EQ. + $ 'QL' .OR. C4.EQ.'HR' .OR. C4.EQ.'TR' .OR. C4.EQ.'BR' ) + $ THEN + NBMIN = 2 + END IF + END IF + ELSE IF( CNAME .AND. C2.EQ.'UN' ) THEN + IF( C3( 1: 1 ).EQ.'G' ) THEN + IF( C4.EQ.'QR' .OR. C4.EQ.'RQ' .OR. C4.EQ.'LQ' .OR. C4.EQ. + $ 'QL' .OR. C4.EQ.'HR' .OR. C4.EQ.'TR' .OR. C4.EQ.'BR' ) + $ THEN + NBMIN = 2 + END IF + ELSE IF( C3( 1: 1 ).EQ.'M' ) THEN + IF( C4.EQ.'QR' .OR. C4.EQ.'RQ' .OR. C4.EQ.'LQ' .OR. C4.EQ. + $ 'QL' .OR. C4.EQ.'HR' .OR. C4.EQ.'TR' .OR. C4.EQ.'BR' ) + $ THEN + NBMIN = 2 + END IF + END IF + END IF + ILAENV = NBMIN + RETURN +* + 70 CONTINUE +* +* ISPEC = 3: crossover point +* + NX = 0 + IF( C2.EQ.'GE' ) THEN + IF( C3.EQ.'QRF' .OR. C3.EQ.'RQF' .OR. C3.EQ.'LQF' .OR. C3.EQ. + $ 'QLF' ) THEN + IF( SNAME ) THEN + NX = 128 + ELSE + NX = 128 + END IF + ELSE IF( C3.EQ.'HRD' ) THEN + IF( SNAME ) THEN + NX = 128 + ELSE + NX = 128 + END IF + ELSE IF( C3.EQ.'BRD' ) THEN + IF( SNAME ) THEN + NX = 128 + ELSE + NX = 128 + END IF + END IF + ELSE IF( C2.EQ.'SY' ) THEN + IF( SNAME .AND. C3.EQ.'TRD' ) THEN + NX = 32 + END IF + ELSE IF( CNAME .AND. C2.EQ.'HE' ) THEN + IF( C3.EQ.'TRD' ) THEN + NX = 32 + END IF + ELSE IF( SNAME .AND. C2.EQ.'OR' ) THEN + IF( C3( 1: 1 ).EQ.'G' ) THEN + IF( C4.EQ.'QR' .OR. C4.EQ.'RQ' .OR. C4.EQ.'LQ' .OR. C4.EQ. + $ 'QL' .OR. C4.EQ.'HR' .OR. C4.EQ.'TR' .OR. C4.EQ.'BR' ) + $ THEN + NX = 128 + END IF + END IF + ELSE IF( CNAME .AND. C2.EQ.'UN' ) THEN + IF( C3( 1: 1 ).EQ.'G' ) THEN + IF( C4.EQ.'QR' .OR. C4.EQ.'RQ' .OR. C4.EQ.'LQ' .OR. C4.EQ. + $ 'QL' .OR. C4.EQ.'HR' .OR. C4.EQ.'TR' .OR. C4.EQ.'BR' ) + $ THEN + NX = 128 + END IF + END IF + END IF + ILAENV = NX + RETURN +* + 80 CONTINUE +* +* ISPEC = 4: number of shifts (used by xHSEQR) +* + ILAENV = 6 + RETURN +* + 90 CONTINUE +* +* ISPEC = 5: minimum column dimension (not used) +* + ILAENV = 2 + RETURN +* + 100 CONTINUE +* +* ISPEC = 6: crossover point for SVD (used by xGELSS and xGESVD) +* + ILAENV = INT( REAL( MIN( N1, N2 ) )*1.6E0 ) + RETURN +* + 110 CONTINUE +* +* ISPEC = 7: number of processors (not used) +* + ILAENV = 1 + RETURN +* + 120 CONTINUE +* +* ISPEC = 8: crossover point for multishift (used by xHSEQR) +* + ILAENV = 50 + RETURN +* + 130 CONTINUE +* +* ISPEC = 9: maximum size of the subproblems at the bottom of the +* computation tree in the divide-and-conquer algorithm +* (used by xGELSD and xGESDD) +* + ILAENV = 25 + RETURN +* + 140 CONTINUE +* +* ISPEC = 10: ieee NaN arithmetic can be trusted not to trap +* +* ILAENV = 0 + ILAENV = 1 + IF( ILAENV.EQ.1 ) THEN + ILAENV = IEEECK( 1, 0.0, 1.0 ) + END IF + RETURN +* + 150 CONTINUE +* +* ISPEC = 11: infinity arithmetic can be trusted not to trap +* +* ILAENV = 0 + ILAENV = 1 + IF( ILAENV.EQ.1 ) THEN + ILAENV = IEEECK( 0, 0.0, 1.0 ) + END IF + RETURN +* + 160 CONTINUE +* +* 12 <= ISPEC <= 16: xHSEQR or one of its subroutines. +* + ILAENV = IPARMQ( ISPEC, NAME, OPTS, N1, N2, N3, N4 ) + RETURN +* +* End of ILAENV +* + END diff --git a/applications/PUfoam/MoDeNaModels/CFD_tool_0D/src/eigen/src/iparmq.f b/applications/PUfoam/MoDeNaModels/CFD_tool_0D/src/eigen/src/iparmq.f new file mode 100644 index 000000000..bd5bd7a0d --- /dev/null +++ b/applications/PUfoam/MoDeNaModels/CFD_tool_0D/src/eigen/src/iparmq.f @@ -0,0 +1,322 @@ +*> \brief \b IPARMQ +* +* =========== DOCUMENTATION =========== +* +* Online html documentation available at +* http://www.netlib.org/lapack/explore-html/ +* +*> \htmlonly +*> Download IPARMQ + dependencies +*> +*> [TGZ] +*> +*> [ZIP] +*> +*> [TXT] +*> \endhtmlonly +* +* Definition: +* =========== +* +* INTEGER FUNCTION IPARMQ( ISPEC, NAME, OPTS, N, ILO, IHI, LWORK ) +* +* .. Scalar Arguments .. +* INTEGER IHI, ILO, ISPEC, LWORK, N +* CHARACTER NAME*( * ), OPTS*( * ) +* +* +*> \par Purpose: +* ============= +*> +*> \verbatim +*> +*> This program sets problem and machine dependent parameters +*> useful for xHSEQR and its subroutines. It is called whenever +*> ILAENV is called with 12 <= ISPEC <= 16 +*> \endverbatim +* +* Arguments: +* ========== +* +*> \param[in] ISPEC +*> \verbatim +*> ISPEC is integer scalar +*> ISPEC specifies which tunable parameter IPARMQ should +*> return. +*> +*> ISPEC=12: (INMIN) Matrices of order nmin or less +*> are sent directly to xLAHQR, the implicit +*> double shift QR algorithm. NMIN must be +*> at least 11. +*> +*> ISPEC=13: (INWIN) Size of the deflation window. +*> This is best set greater than or equal to +*> the number of simultaneous shifts NS. +*> Larger matrices benefit from larger deflation +*> windows. +*> +*> ISPEC=14: (INIBL) Determines when to stop nibbling and +*> invest in an (expensive) multi-shift QR sweep. +*> If the aggressive early deflation subroutine +*> finds LD converged eigenvalues from an order +*> NW deflation window and LD.GT.(NW*NIBBLE)/100, +*> then the next QR sweep is skipped and early +*> deflation is applied immediately to the +*> remaining active diagonal block. Setting +*> IPARMQ(ISPEC=14) = 0 causes TTQRE to skip a +*> multi-shift QR sweep whenever early deflation +*> finds a converged eigenvalue. Setting +*> IPARMQ(ISPEC=14) greater than or equal to 100 +*> prevents TTQRE from skipping a multi-shift +*> QR sweep. +*> +*> ISPEC=15: (NSHFTS) The number of simultaneous shifts in +*> a multi-shift QR iteration. +*> +*> ISPEC=16: (IACC22) IPARMQ is set to 0, 1 or 2 with the +*> following meanings. +*> 0: During the multi-shift QR sweep, +*> xLAQR5 does not accumulate reflections and +*> does not use matrix-matrix multiply to +*> update the far-from-diagonal matrix +*> entries. +*> 1: During the multi-shift QR sweep, +*> xLAQR5 and/or xLAQRaccumulates reflections and uses +*> matrix-matrix multiply to update the +*> far-from-diagonal matrix entries. +*> 2: During the multi-shift QR sweep. +*> xLAQR5 accumulates reflections and takes +*> advantage of 2-by-2 block structure during +*> matrix-matrix multiplies. +*> (If xTRMM is slower than xGEMM, then +*> IPARMQ(ISPEC=16)=1 may be more efficient than +*> IPARMQ(ISPEC=16)=2 despite the greater level of +*> arithmetic work implied by the latter choice.) +*> \endverbatim +*> +*> \param[in] NAME +*> \verbatim +*> NAME is character string +*> Name of the calling subroutine +*> \endverbatim +*> +*> \param[in] OPTS +*> \verbatim +*> OPTS is character string +*> This is a concatenation of the string arguments to +*> TTQRE. +*> \endverbatim +*> +*> \param[in] N +*> \verbatim +*> N is integer scalar +*> N is the order of the Hessenberg matrix H. +*> \endverbatim +*> +*> \param[in] ILO +*> \verbatim +*> ILO is INTEGER +*> \endverbatim +*> +*> \param[in] IHI +*> \verbatim +*> IHI is INTEGER +*> It is assumed that H is already upper triangular +*> in rows and columns 1:ILO-1 and IHI+1:N. +*> \endverbatim +*> +*> \param[in] LWORK +*> \verbatim +*> LWORK is integer scalar +*> The amount of workspace available. +*> \endverbatim +* +* Authors: +* ======== +* +*> \author Univ. of Tennessee +*> \author Univ. of California Berkeley +*> \author Univ. of Colorado Denver +*> \author NAG Ltd. +* +*> \date November 2011 +* +*> \ingroup auxOTHERauxiliary +* +*> \par Further Details: +* ===================== +*> +*> \verbatim +*> +*> Little is known about how best to choose these parameters. +*> It is possible to use different values of the parameters +*> for each of CHSEQR, DHSEQR, SHSEQR and ZHSEQR. +*> +*> It is probably best to choose different parameters for +*> different matrices and different parameters at different +*> times during the iteration, but this has not been +*> implemented --- yet. +*> +*> +*> The best choices of most of the parameters depend +*> in an ill-understood way on the relative execution +*> rate of xLAQR3 and xLAQR5 and on the nature of each +*> particular eigenvalue problem. Experiment may be the +*> only practical way to determine which choices are most +*> effective. +*> +*> Following is a list of default values supplied by IPARMQ. +*> These defaults may be adjusted in order to attain better +*> performance in any particular computational environment. +*> +*> IPARMQ(ISPEC=12) The xLAHQR vs xLAQR0 crossover point. +*> Default: 75. (Must be at least 11.) +*> +*> IPARMQ(ISPEC=13) Recommended deflation window size. +*> This depends on ILO, IHI and NS, the +*> number of simultaneous shifts returned +*> by IPARMQ(ISPEC=15). The default for +*> (IHI-ILO+1).LE.500 is NS. The default +*> for (IHI-ILO+1).GT.500 is 3*NS/2. +*> +*> IPARMQ(ISPEC=14) Nibble crossover point. Default: 14. +*> +*> IPARMQ(ISPEC=15) Number of simultaneous shifts, NS. +*> a multi-shift QR iteration. +*> +*> If IHI-ILO+1 is ... +*> +*> greater than ...but less ... the +*> or equal to ... than default is +*> +*> 0 30 NS = 2+ +*> 30 60 NS = 4+ +*> 60 150 NS = 10 +*> 150 590 NS = ** +*> 590 3000 NS = 64 +*> 3000 6000 NS = 128 +*> 6000 infinity NS = 256 +*> +*> (+) By default matrices of this order are +*> passed to the implicit double shift routine +*> xLAHQR. See IPARMQ(ISPEC=12) above. These +*> values of NS are used only in case of a rare +*> xLAHQR failure. +*> +*> (**) The asterisks (**) indicate an ad-hoc +*> function increasing from 10 to 64. +*> +*> IPARMQ(ISPEC=16) Select structured matrix multiply. +*> (See ISPEC=16 above for details.) +*> Default: 3. +*> \endverbatim +*> +* ===================================================================== + INTEGER FUNCTION IPARMQ( ISPEC, NAME, OPTS, N, ILO, IHI, LWORK ) +* +* -- LAPACK auxiliary routine (version 3.4.0) -- +* -- LAPACK is a software package provided by Univ. of Tennessee, -- +* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- +* November 2011 +* +* .. Scalar Arguments .. + INTEGER IHI, ILO, ISPEC, LWORK, N + CHARACTER NAME*( * ), OPTS*( * ) +* +* ================================================================ +* .. Parameters .. + INTEGER INMIN, INWIN, INIBL, ISHFTS, IACC22 + PARAMETER ( INMIN = 12, INWIN = 13, INIBL = 14, + $ ISHFTS = 15, IACC22 = 16 ) + INTEGER NMIN, K22MIN, KACMIN, NIBBLE, KNWSWP + PARAMETER ( NMIN = 75, K22MIN = 14, KACMIN = 14, + $ NIBBLE = 14, KNWSWP = 500 ) + REAL TWO + PARAMETER ( TWO = 2.0 ) +* .. +* .. Local Scalars .. + INTEGER NH, NS +* .. +* .. Intrinsic Functions .. + INTRINSIC LOG, MAX, MOD, NINT, REAL +* .. +* .. Executable Statements .. + IF( ( ISPEC.EQ.ISHFTS ) .OR. ( ISPEC.EQ.INWIN ) .OR. + $ ( ISPEC.EQ.IACC22 ) ) THEN +* +* ==== Set the number simultaneous shifts ==== +* + NH = IHI - ILO + 1 + NS = 2 + IF( NH.GE.30 ) + $ NS = 4 + IF( NH.GE.60 ) + $ NS = 10 + IF( NH.GE.150 ) + $ NS = MAX( 10, NH / NINT( LOG( REAL( NH ) ) / LOG( TWO ) ) ) + IF( NH.GE.590 ) + $ NS = 64 + IF( NH.GE.3000 ) + $ NS = 128 + IF( NH.GE.6000 ) + $ NS = 256 + NS = MAX( 2, NS-MOD( NS, 2 ) ) + END IF +* + IF( ISPEC.EQ.INMIN ) THEN +* +* +* ===== Matrices of order smaller than NMIN get sent +* . to xLAHQR, the classic double shift algorithm. +* . This must be at least 11. ==== +* + IPARMQ = NMIN +* + ELSE IF( ISPEC.EQ.INIBL ) THEN +* +* ==== INIBL: skip a multi-shift qr iteration and +* . whenever aggressive early deflation finds +* . at least (NIBBLE*(window size)/100) deflations. ==== +* + IPARMQ = NIBBLE +* + ELSE IF( ISPEC.EQ.ISHFTS ) THEN +* +* ==== NSHFTS: The number of simultaneous shifts ===== +* + IPARMQ = NS +* + ELSE IF( ISPEC.EQ.INWIN ) THEN +* +* ==== NW: deflation window size. ==== +* + IF( NH.LE.KNWSWP ) THEN + IPARMQ = NS + ELSE + IPARMQ = 3*NS / 2 + END IF +* + ELSE IF( ISPEC.EQ.IACC22 ) THEN +* +* ==== IACC22: Whether to accumulate reflections +* . before updating the far-from-diagonal elements +* . and whether to use 2-by-2 block structure while +* . doing it. A small amount of work could be saved +* . by making this choice dependent also upon the +* . NH=IHI-ILO+1. +* + IPARMQ = 0 + IF( NS.GE.KACMIN ) + $ IPARMQ = 1 + IF( NS.GE.K22MIN ) + $ IPARMQ = 2 +* + ELSE +* ===== invalid value of ispec ===== + IPARMQ = -1 +* + END IF +* +* ==== End of IPARMQ ==== +* + END diff --git a/applications/PUfoam/MoDeNaModels/CFD_tool_0D/src/eigen/src/lsame.f b/applications/PUfoam/MoDeNaModels/CFD_tool_0D/src/eigen/src/lsame.f new file mode 100644 index 000000000..315304c3d --- /dev/null +++ b/applications/PUfoam/MoDeNaModels/CFD_tool_0D/src/eigen/src/lsame.f @@ -0,0 +1,125 @@ +*> \brief \b LSAME +* +* =========== DOCUMENTATION =========== +* +* Online html documentation available at +* http://www.netlib.org/lapack/explore-html/ +* +* Definition: +* =========== +* +* LOGICAL FUNCTION LSAME( CA, CB ) +* +* .. Scalar Arguments .. +* CHARACTER CA, CB +* .. +* +* +*> \par Purpose: +* ============= +*> +*> \verbatim +*> +*> LSAME returns .TRUE. if CA is the same letter as CB regardless of +*> case. +*> \endverbatim +* +* Arguments: +* ========== +* +*> \param[in] CA +*> \verbatim +*> \endverbatim +*> +*> \param[in] CB +*> \verbatim +*> CA and CB specify the single characters to be compared. +*> \endverbatim +* +* Authors: +* ======== +* +*> \author Univ. of Tennessee +*> \author Univ. of California Berkeley +*> \author Univ. of Colorado Denver +*> \author NAG Ltd. +* +*> \date November 2011 +* +*> \ingroup auxOTHERauxiliary +* +* ===================================================================== + LOGICAL FUNCTION LSAME( CA, CB ) +* +* -- LAPACK auxiliary routine (version 3.4.0) -- +* -- LAPACK is a software package provided by Univ. of Tennessee, -- +* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- +* November 2011 +* +* .. Scalar Arguments .. + CHARACTER CA, CB +* .. +* +* ===================================================================== +* +* .. Intrinsic Functions .. + INTRINSIC ICHAR +* .. +* .. Local Scalars .. + INTEGER INTA, INTB, ZCODE +* .. +* .. Executable Statements .. +* +* Test if the characters are equal +* + LSAME = CA.EQ.CB + IF( LSAME ) + $ RETURN +* +* Now test for equivalence if both characters are alphabetic. +* + ZCODE = ICHAR( 'Z' ) +* +* Use 'Z' rather than 'A' so that ASCII can be detected on Prime +* machines, on which ICHAR returns a value with bit 8 set. +* ICHAR('A') on Prime machines returns 193 which is the same as +* ICHAR('A') on an EBCDIC machine. +* + INTA = ICHAR( CA ) + INTB = ICHAR( CB ) +* + IF( ZCODE.EQ.90 .OR. ZCODE.EQ.122 ) THEN +* +* ASCII is assumed - ZCODE is the ASCII code of either lower or +* upper case 'Z'. +* + IF( INTA.GE.97 .AND. INTA.LE.122 ) INTA = INTA - 32 + IF( INTB.GE.97 .AND. INTB.LE.122 ) INTB = INTB - 32 +* + ELSE IF( ZCODE.EQ.233 .OR. ZCODE.EQ.169 ) THEN +* +* EBCDIC is assumed - ZCODE is the EBCDIC code of either lower or +* upper case 'Z'. +* + IF( INTA.GE.129 .AND. INTA.LE.137 .OR. + $ INTA.GE.145 .AND. INTA.LE.153 .OR. + $ INTA.GE.162 .AND. INTA.LE.169 ) INTA = INTA + 64 + IF( INTB.GE.129 .AND. INTB.LE.137 .OR. + $ INTB.GE.145 .AND. INTB.LE.153 .OR. + $ INTB.GE.162 .AND. INTB.LE.169 ) INTB = INTB + 64 +* + ELSE IF( ZCODE.EQ.218 .OR. ZCODE.EQ.250 ) THEN +* +* ASCII is assumed, on Prime machines - ZCODE is the ASCII code +* plus 128 of either lower or upper case 'Z'. +* + IF( INTA.GE.225 .AND. INTA.LE.250 ) INTA = INTA - 32 + IF( INTB.GE.225 .AND. INTB.LE.250 ) INTB = INTB - 32 + END IF + LSAME = INTA.EQ.INTB +* +* RETURN +* +* End of LSAME +* + END diff --git a/applications/PUfoam/MoDeNaModels/CFD_tool_0D/src/eigen/src/vandermonde.f b/applications/PUfoam/MoDeNaModels/CFD_tool_0D/src/eigen/src/vandermonde.f new file mode 100644 index 000000000..60848966f --- /dev/null +++ b/applications/PUfoam/MoDeNaModels/CFD_tool_0D/src/eigen/src/vandermonde.f @@ -0,0 +1,15 @@ + subroutine vandermonde(a,mc,n1,cc,ipiv,info) + + integer n1,cc,info,ipiv(n1) + double precision a(n1,n1), mc(cc,n1) + double precision mmc(n1,cc) + + a=transpose(a) + mmc=transpose(mc) + + + call dgesv(n1,cc,a,n1,ipiv,mmc,n1,info) + + mc = transpose(mmc) + + end subroutine diff --git a/applications/PUfoam/MoDeNaModels/CFD_tool_0D/src/eigen/src/xerbla.f b/applications/PUfoam/MoDeNaModels/CFD_tool_0D/src/eigen/src/xerbla.f new file mode 100644 index 000000000..3e93bc4e0 --- /dev/null +++ b/applications/PUfoam/MoDeNaModels/CFD_tool_0D/src/eigen/src/xerbla.f @@ -0,0 +1,99 @@ +*> \brief \b XERBLA +* +* =========== DOCUMENTATION =========== +* +* Online html documentation available at +* http://www.netlib.org/lapack/explore-html/ +* +*> \htmlonly +*> Download XERBLA + dependencies +*> +*> [TGZ] +*> +*> [ZIP] +*> +*> [TXT] +*> \endhtmlonly +* +* Definition: +* =========== +* +* SUBROUTINE XERBLA( SRNAME, INFO ) +* +* .. Scalar Arguments .. +* CHARACTER*(*) SRNAME +* INTEGER INFO +* .. +* +* +*> \par Purpose: +* ============= +*> +*> \verbatim +*> +*> XERBLA is an error handler for the LAPACK routines. +*> It is called by an LAPACK routine if an input parameter has an +*> invalid value. A message is printed and execution stops. +*> +*> Installers may consider modifying the STOP statement in order to +*> call system-specific exception-handling facilities. +*> \endverbatim +* +* Arguments: +* ========== +* +*> \param[in] SRNAME +*> \verbatim +*> SRNAME is CHARACTER*(*) +*> The name of the routine which called XERBLA. +*> \endverbatim +*> +*> \param[in] INFO +*> \verbatim +*> INFO is INTEGER +*> The position of the invalid parameter in the parameter list +*> of the calling routine. +*> \endverbatim +* +* Authors: +* ======== +* +*> \author Univ. of Tennessee +*> \author Univ. of California Berkeley +*> \author Univ. of Colorado Denver +*> \author NAG Ltd. +* +*> \date November 2011 +* +*> \ingroup auxOTHERauxiliary +* +* ===================================================================== + SUBROUTINE XERBLA( SRNAME, INFO ) +* +* -- LAPACK auxiliary routine (version 3.4.0) -- +* -- LAPACK is a software package provided by Univ. of Tennessee, -- +* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- +* November 2011 +* +* .. Scalar Arguments .. + CHARACTER*(*) SRNAME + INTEGER INFO +* .. +* +* ===================================================================== +* +* .. Intrinsic Functions .. + INTRINSIC LEN_TRIM +* .. +* .. Executable Statements .. +* + WRITE( *, FMT = 9999 )SRNAME( 1:LEN_TRIM( SRNAME ) ), INFO +* + STOP +* + 9999 FORMAT( ' ** On entry to ', A, ' parameter number ', I2, ' had ', + $ 'an illegal value' ) +* +* End of XERBLA +* + END diff --git a/applications/PUfoam/MoDeNaModels/CFD_tool_0D/src/experimentalInputs.h b/applications/PUfoam/MoDeNaModels/CFD_tool_0D/src/experimentalInputs.h new file mode 100644 index 000000000..fb7562ee1 --- /dev/null +++ b/applications/PUfoam/MoDeNaModels/CFD_tool_0D/src/experimentalInputs.h @@ -0,0 +1,135 @@ +/** @file experimentalInputs.h + @brief All the experimental data required for the source terms calculations + @var double Pr + @brief initial/final pressure of the mixture, Pa + @var double Temp0 + @brief initial temperature, K + @var double A_OH + @brief pre-exponential factor for the gelling reaction, 1/s + @var double E_OH + @brief activation energy for the gelling reaction, J/mol + @var double OH_0 + @brief Initial concentration of polyol OH groups in the mixutre, mol/m3 + @var double NCO_0 + @brief Initial concentration of isocianate NCO groups in the mixutre, mol/m3 + @var double W_0 + @brief Initial concentration of water in the mixture, mol/m3 + @var double A_W + @brief pre-exponential factor for the blowing reaction, 1/s + @var double E_W + @brief activation energy for the blowing reaction, J/mol + @var double RR + @brief ideal gas constant, J/mol K + @var double rhoPoly + @brief density of the liquid polymer, kg/m3 + @var double rhoBL + @brief density of the blowing agent, kg/m3 + @var double DH_OH + @brief Reaction heat for the gelling reaction, J/mol + @var double DH_W + @brief Reaction heat for the blowing reaction, J/mol + @var double C_Poy + @brief Polyurethane specific heat, J/kg K + @var double C_CO2 + @brief CO2 specific heat, J/kg K + @var double C_BG + @brief Specific heat of the physical blowing agent in gas phase, J/kg K + @var double C_BL + @brief Specific heat of the physical blowing agent in liquid phase, J/kg K + @var double lambda + @brief Latent heat of blowing agent, J/kg + @var double C_TOT + @brief Total specifc heat of the mixture + @var int phBL + @brief type of physical blowing agent 1 = pentane, 2 = R-11 + @var int denMod + @brief density mode, 1 = modena, 2 = constant + @var int kinMod + @brief kinetics model, 1 = Baser, 2 = Baser with R(x) + @sa http://onlinelibrary.wiley.com/doi/10.1002/pen.760340804/abstract + @var bool dilution + @brief use dilution effect + @var double M_CO2 + @brief Molecular mass of carbon dioxide, kg/kmol + @var double M_B + @brief Molecular mass of blowing agent, kg/kmol + @var double M_NCO + @brief Molecular weight of NCO, kg/kmol + @var double M_air + @brief Molecular weight of air, kg/kmol + @var double CO2_D + @brief Weight fraction of dissolved CO2 in the mixture, - + @var double L0 + @brief Initial weight fraction of blowing agent in the liquid, - + @var double CO2_0 + @brief Initial weight fraction of CO2 in the liquid, - + @var double surfaceTension + @brief required for the computation of partial pressure + @var double sig + @brief correlated to variance of initial distribution + @var double init_size + @brief initial mean bubble diameter, m + @var double NN + @brief correlated to number of initial bubbles in m^3 + @var double air_g + @brief air weight fraction + @var double abs_err + @brief absolute error + @var double rel_err + @brief relative error + @var double dt + @brief time step, s + @var double tend + @brief end time, s +*/ + double Pr = 101325.0; + double Temp0 = 297; +/* Inputs for gelling reaction, XOH */ + double A_OH = 1965.0; + double E_OH = 5.487e4; + double OH_0 = 3765.0; + double NCO_0 = 3765.0; + double W_0 = -1.0; +/* Inputs for blowing reaction, XW */ + double A_W = 1.385e3; + double E_W = 3.266e4; +/* Constants */ + double RR = 8.3145; + double rhoPoly = 1100.0; + double rhoBL = 1467.0; +/* Inputs for enthalpy */ + double DH_OH = -7.49e4; + double DH_W = -8.6e4; + double C_Poly = 1800.0; + double C_CO2 = 836.6; + double C_BG = 593.0; + double C_BL = 870.0; + double lambda = 2.0e5; + double C_TOT; +// physical blowing agent (used for solubility model) + int phBL = 2; +// density model used + int denMod = 2; +// kinetics model used + int kinMod = 2; + bool dilution= true; +/* Inputs for weight fraction of gaseous CO2 in the mixture */ + double M_CO2 = 44.0; + double M_B = 137.37; + double M_NCO = 615.0; + double M_air = 29.0; + double CO2_D = 4.4e-4; + double L0 = 0.155; + double CO2_0 = 0.0; +// Other physical properties + double surfaceTension = 25e-3; +// initial bubble size distribution + double sig = 1e-1; + double init_size= 2.0e-6; + double NN = 0.138e12; + double air_g; +// integration parameters + double abs_err = 1e-6; + double rel_err = 1e-6; + double dt = 1e0; + double tend = 200.0; diff --git a/applications/PUfoam/MoDeNaModels/CFD_tool_0D/src/growth.h b/applications/PUfoam/MoDeNaModels/CFD_tool_0D/src/growth.h new file mode 100644 index 000000000..33e1a9dd9 --- /dev/null +++ b/applications/PUfoam/MoDeNaModels/CFD_tool_0D/src/growth.h @@ -0,0 +1,78 @@ +/** @file growth.h + @brief Source terms due to the bubble growth + @fn void growthSource(double *sgBA, double *sgCO2, double *we, double *vi, int &nNodes, int *mOrder, double &CO2_l, double &L_l, double &tmp, double &dVdt_2, double &dVdt_1) + @param double *sgBA - source terms due to blowing agent + @param double *sgCO2 - source terms due to CO2 + @param double *we - weights of quadrature approximation + @param double *vi - nodes of quadrature approximation + @param int &nNodes - number of nodes + @param int *mOrder - order of moments + @param double &CO2_l - weight fraction of CO2 in liquid + @param double &L_l - weight fraction of blowing agent in liquid + @param double &tmp - temperature + @param double &dVdt_2 - growth rate due to generation of CO2 + @param double &dVdt_1 - growth rate due to evaporation of blowing agent + @return void +*/ + +void growthSource(double *, double *, double *, double *, int &, int *, double &, double &, double &, double &, double &); // function prototype + +void growthSource(double *sgBA, double *sgCO2, double *we, double *vi, int &nNodes, int *mOrder, double &CO2_l, double &L_l, double &tmp, double &dVdt_2, double &dVdt_1) +{ + + int i; + int counter = 0; + double k; + + while(counter<2*nNodes) + { + sgBA[counter] = 0.0; + sgCO2[counter] = 0.0; + + // using static_cast to convert moment order from int to double + k = static_cast(mOrder[counter]); + + if(counter == 0) + { + sgBA[counter] = 0.0; + sgCO2[counter] = 0.0; + } + else if(counter == 1) + { + for(i=0;i 0.0) + { + sgBA[counter] += dVdt_1*we[i]; + sgCO2[counter] += dVdt_2*we[i]; + + } + else + { + sgBA[counter] = sgBA[counter]; + sgCO2[counter] = sgCO2[counter]; + } + + } + + } + else + { + for(i=0;i 0.0) + { + sgBA[counter] += k*dVdt_1*we[i]*(pow(vi[i], (k-1))); + sgCO2[counter] += k*dVdt_2*we[i]*(pow(vi[i], (k-1))); + } + else + { + sgBA[counter] = sgBA[counter]; + sgCO2[counter] = sgCO2[counter]; + } + } + } + + counter++; + } // end of while +} diff --git a/applications/PUfoam/MoDeNaModels/CFD_tool_0D/src/initializeMoments.h b/applications/PUfoam/MoDeNaModels/CFD_tool_0D/src/initializeMoments.h new file mode 100644 index 000000000..adf276161 --- /dev/null +++ b/applications/PUfoam/MoDeNaModels/CFD_tool_0D/src/initializeMoments.h @@ -0,0 +1,30 @@ +/** @file initializeMoments.h + @brief Initialize the moments + @fn void mom_init(double *momz, double &size_0, int &n, double &sigma, double &NN) + @param double &size_0 - initial bubble diameter + @param int &n - number of moments + @param double &sigma - correlated to variance of initial distribution + @param double &NN - correlated to number of initial bubbles per unit volume + @return void +*/ +void mom_init(double *, double &, int &, double &, double &); + +void mom_init(double *momz, double &size_0, int &n, double &sigma, double &NN) +{ + int i; + double v_0 = (M_PI/6.0)*(pow(size_0,3)); + double mu = log(v_0); + + for(i=0;i T0) + { + double tempDummy = pow((tm-T0),2.0); + lMax = (aa + hh*exp((-tempDummy/(2.0*ww*ww)))); + break; + } + else + { + lMax=aa+hh; + break; + } + case 2: + aa = 1e-7; // - + hh = 4.2934; // - + T0 = 203.3556; // K + ww = 40.016; // 1/K + // double T_in = 300; // K + if (tm > T0) + { + double tempDummy = pow((tm-T0),2.0); + lMax = (aa + hh*exp((-tempDummy/(2.0*ww*ww)))); + break; + } + else + { + lMax=aa+hh; + break; + } + } + return lMax; +} diff --git a/applications/PUfoam/MoDeNaModels/CFD_tool_0D/src/modenaCalls.h b/applications/PUfoam/MoDeNaModels/CFD_tool_0D/src/modenaCalls.h new file mode 100644 index 000000000..4b117dd58 --- /dev/null +++ b/applications/PUfoam/MoDeNaModels/CFD_tool_0D/src/modenaCalls.h @@ -0,0 +1,40 @@ +/** @file modenaCalls.h + @brief instantiates the surrogate models, allocates memory and fetches arg positions +*/ +#ifndef MODENACALLS_H +#define MODENACALLS_H +/* +instantiate the surrogate models: + - bubbleGrowth1, + - bubbleGrowth2, + - density_reaction_mixture, + - rheology, + - simpleKinetics +*/ + +modena_model_t *bblgr1 = modena_model_new("bubbleGrowth1"); +modena_model_t *bblgr2 = modena_model_new("bubbleGrowth2"); +// modena_model_t *density_reaction_mixturemodel = modena_model_new("density_reaction_mixtureSM"); +// modena_model_t *rheologymodel = modena_model_new("rheology"); +// modena_model_t *kinetics = modena_model_new("simpleKinetics"); +/* allocate memory and fetch arg positions: + - bubbleGrowth1, + - bubbleGrowth2, + - density_reaction_mixture, + - rheology. +*/ +modena_inputs_t *inputs_bblgr1 = modena_inputs_new (bblgr1); +modena_outputs_t *outputs_bblgr1 = modena_outputs_new (bblgr1); + +modena_inputs_t *inputs_bblgr2 = modena_inputs_new (bblgr2); +modena_outputs_t *outputs_bblgr2 = modena_outputs_new (bblgr2); + +// modena_inputs_t *inputs_den = modena_inputs_new (density_reaction_mixturemodel); +// modena_outputs_t *outputs_den = modena_outputs_new (density_reaction_mixturemodel); + +// modena_inputs_t *inputs_rheo = modena_inputs_new (rheologymodel); +// modena_outputs_t *outputs_rheo = modena_outputs_new (rheologymodel); + +// modena_inputs_t *inputs_kinetics = modena_inputs_new (kinetics); +// modena_outputs_t *outputs_kinetics = modena_outputs_new (kinetics); +#endif \ No newline at end of file diff --git a/applications/PUfoam/MoDeNaModels/CFD_tool_0D/src/momentsConverter.h b/applications/PUfoam/MoDeNaModels/CFD_tool_0D/src/momentsConverter.h new file mode 100644 index 000000000..640dd9d37 --- /dev/null +++ b/applications/PUfoam/MoDeNaModels/CFD_tool_0D/src/momentsConverter.h @@ -0,0 +1,29 @@ +/** @file momentsConverter.h + @brief Converts moments based on the unit volume of foam + @fn void momentsConverter(const state_type &y , const double t) + @param const state_type &y - vector of all the variables + @param const double t - time +*/ +void momentsConverter(const state_type &y , const double t); + +void momentsConverter(const state_type &y , const double t) +{ + double kappa = 1.0 - (y[8]/(1.0+y[8])); + double M[4] = {}; + M[0] = kappa*y[7]; + M[1] = kappa*y[8]; + M[2] = kappa*y[9]; + M[3] = kappa*y[10]; + + ofstream MM[4]; + MM[0].open("../results/M0.txt", std::ios::app); + MM[1].open("../results/M1.txt", std::ios::app); + MM[2].open("../results/M2.txt", std::ios::app); + MM[3].open("../results/M3.txt", std::ios::app); + + for (int i = 0; i < 4; i++) + { + MM[i] << t << '\t' << M[i] << '\n'; + MM[i].close(); + } +} diff --git a/applications/PUfoam/MoDeNaModels/CFD_tool_0D/src/partialPressure.h b/applications/PUfoam/MoDeNaModels/CFD_tool_0D/src/partialPressure.h new file mode 100644 index 000000000..838093136 --- /dev/null +++ b/applications/PUfoam/MoDeNaModels/CFD_tool_0D/src/partialPressure.h @@ -0,0 +1,100 @@ +/** @file partialPressure.h + @brief functions related to the calculations of partial pressures + @fn void ddtpartialPressure(const state_type &y , const double t , const double dt , double *dpdt , double *pOld, const double p_1, const double p_2, const double R) + @brief time derivative of partial pressure + @param const state_type &y - vector of all the variables + @param const double t - time + @param double *dpdt - time derivative of pressure + @param double *pOld - pressure values at the previous time step + @param const double p_1 - partial pressure of blowing agent + @param const double p_2 - partial pressure of CO2 + @param const double R - bubble radius + @return void + @fn double bubbleRadius (const double m0, const double m1) + @brief radius of bubbles based on the moments + @param const double m0 - moment of order zero + @param const double m1 - moment of order one + @return bubble radius + @fn double partialPressureBA(const state_type &y) + @brief partial pressure of the physical blowing agent + @param const state_type &y vector of all the variables + @return partial pressure of the physical blowing agent + @fn double partialPressureCO2(const state_type &y) + @brief partial pressure of CO2 + @param const state_type &y - vector of all the variables + @return partial pressure of CO2 +*/ +void ddtpartialPressure(const state_type &y , const double t , const double dt , double *dpdt , double *pOld, const double p_1, const double p_2, const double R); +double bubbleRadius (const double m0, const double m1); +double partialPressureBA(const state_type &y); +double partialPressureCO2(const state_type &y); + +void ddtpartialPressure(const state_type &y , const double t , const double dt , double *dpdt , double *pOld, const double p_1, const double p_2, const double R) +{ + // dp1dt: + dpdt[0] = (p_1 - pOld[0])/(dt); + pOld[0] = p_1; + + // dp2dt: + dpdt[1] = (p_2 - pOld[1])/(dt); + pOld[1] = p_2; +} + +double bubbleRadius (const double m0, const double m1) +{ + double R; + R = pow((3.0*m1/(4.0*M_PI*m0)), 1.0/3.0); + if (isnan(R)) { + R=init_size; + } + return R; +} + +double partialPressureBA(const state_type &y) +{ + double L_g = y[4]; + double CO2_g = y[6]; + double m0 = y[7]; + double m1 = y[8]; + double PENTANE = y[15]; + double CO2 = y[14]; + + double R = bubbleRadius(m0, m1); + + double p_1; + if (L_g == 0.0) + { + p_1 = 0.0; + } + else + { + p_1 = ((L_g/M_B)/(L_g/M_B + CO2_g/M_CO2 + air_g/M_air)) * (Pr + 2*surfaceTension/R); + } + + return p_1; +} + +double partialPressureCO2(const state_type &y) +{ + double L_g = y[4]; + double CO2_g = y[6]; + double m0 = y[7]; + double m1 = y[8]; + double PENTANE = y[15]; + double CO2 = y[14]; + + double R = bubbleRadius(m0, m1); + + double p_2; + + if (CO2_g == 0.0) + { + p_2 = 0.0; + } + else + { + p_2 = ((CO2_g/M_CO2)/(L_g/M_B + CO2_g/M_CO2 + air_g/M_air)) * (Pr + 2*surfaceTension/R); + } + + return p_2; +} \ No newline at end of file diff --git a/applications/PUfoam/MoDeNaModels/CFD_tool_0D/src/pda.h b/applications/PUfoam/MoDeNaModels/CFD_tool_0D/src/pda.h new file mode 100644 index 000000000..c63ee8817 --- /dev/null +++ b/applications/PUfoam/MoDeNaModels/CFD_tool_0D/src/pda.h @@ -0,0 +1,131 @@ +/** @file pda.h + @brief Product Difference Algorithm + @param double *we - weights of quadrature approximation + @param double *vi - nodes of quadrature approximation + @param double *mom - moments + @param int &n - number of nodes + @return void +*/ +void PDA(double *, double *, double *, int &); + +void PDA(double *we, double *vi, double *mom, int &n) +{ + +// Construct P Matrix + int i,j; + + double p[2*n+1][2*n+1]; + + for(i=0;i<2*n+1;i++) + { + for(j=0;j<2*n+1;j++) + { + p[i][j] = 0.0; + } + } + + double norm_mom[2*n]; + +// Normalize the moments + for(i=0;i<2*n;i++) + { + norm_mom[i] = mom[i]/(fmax(mom[0],1.0e-10)); + } +// First column of P matrix + p[0][0] = 1.0; + p[0][1] = 1.0; +// Second column of P matrix + for(i=1;i<2*n;i++) + { + p[i][1] = pow(-1,double (i))*norm_mom[i]; + } + +// Recursion method for calculation of P + for(j=2;j<2*n+1;j++) + { + for(i=0;i<2*n+2-j;i++) + { + p[i][j] = p[0][j-1]*p[i+1][j-2] - p[0][j-2]*p[i+1][j-1]; + } + } + +// Computing zeta + double zeta[2*n]; + for(i=0;i<2*n;i++) + { + zeta[i] = 0.0; + } + + for(i=1;i<2*n;i++) + { + if(p[0][i]*p[0][i-1]>0) + { + zeta[i] = p[0][i+1]/(p[0][i]*p[0][i-1]); + } + else + { + zeta[i] = 0.0; + } + } + +// Coefficients of Jacobi matrix + double aa[n]; + double bb[n-1], cc[n-1]; + + for(i=0;i> Pr; // initial/final pressure of the mixture, Pa + inputs >> Temp0; // initial temperature, K +/* Inputs for gelling reaction, XOH */ + inputs >> A_OH; // m3/mol s + inputs >> E_OH; // J/mol + inputs >> OH_0; // Initial concentration of polyol OH groups in the mixutre, mol/m3 + inputs >> NCO_0; // Initial concentration of isocianate NCO groups in the mixutre, mol/m3 + inputs >> W_0; // Initial concentration of water in the mixture, mol/m3 +/* Inputs for blowing reaction, XW */ + inputs >> A_W; // 1/s + inputs >> E_W; // J/mol +/* Constants */ + inputs >> RR; // J/mol K + inputs >> rhoPoly; // kg/m3 Density of the liquid polymer + inputs >> rhoBL; // kg/m3 Density of the blowing agent +/* Inputs for enthalpy */ + inputs >> DH_OH; // Reaction heat for the gelling reaction, J/mol + inputs >> DH_W; // Reaction heat for the blowing reaction, J/mol + inputs >> C_Poly; // Polyurethane specific heat, J/kg K + inputs >> C_CO2; // CO2 specific heat, J/kg K + inputs >> C_BG; // Physical blowing agent in gas phase specific heat, J/kg K + inputs >> C_BL; // Physical blowing agent in liquid phase specific heat, J/kg K + inputs >> lambda; // Latent heat of blowing agent, J/kg +// physical blowing agent (used for solubility model) + inputs >> phBL; // 1=pentane, 2=R-11 +// density model used + inputs >> denMod; // 1=modena, 2=rhoPoly +// kinetics model used + inputs >> kinMod; // 1=Baser, 2=Baser with R(x) + inputs >> dilution; // use dilution effect +/* Inputs for weight fraction of gaseous CO2 in the mixture */ + inputs >> M_CO2; // Molecular mass of carbon dioxide, kg/kmol + inputs >> M_B; // Molecular mass of blowing agent, kg/kmol + inputs >> M_NCO; // Molecular weight of NCO, kg/kmol + inputs >> M_air; // Molecular weight of air, kg/kmol + inputs >> CO2_D; // Weight fraction of dissolved CO2 in the mixture, - + inputs >> L0; // Initial weight fraction of blowing agent in the liquid, - + inputs >> CO2_0; // Initial weight fraction of CO2 in the liquid, - +// Other physical properties + inputs >> surfaceTension; // required for partial pressure +// initial bubble size distribution + inputs >> sig; // correlated to variance of initial distribution + inputs >> init_size; // initial mean bubble diameter, m + inputs >> NN; // correlated to number of initial bubbles in m^3 +// integration parameters + inputs >> abs_err;// absolute error + inputs >> rel_err;// relative error + inputs >> dt; // time step, s + inputs >> tend; // end time, s + inputs.close(); + if (W_0<1e-8) { + W_0=-1.0; + } +} diff --git a/applications/PUfoam/MoDeNaModels/CFD_tool_0D/src/write_kinetics.h b/applications/PUfoam/MoDeNaModels/CFD_tool_0D/src/write_kinetics.h new file mode 100644 index 000000000..3a3bfa061 --- /dev/null +++ b/applications/PUfoam/MoDeNaModels/CFD_tool_0D/src/write_kinetics.h @@ -0,0 +1,127 @@ +/** @file write_kinetics.h + @brief write the results into text files + @fn void write_kinetics( const state_type &y , const double t ) + @param const state_type &y - vector of all the variables + @param const double t - time + @return void +*/ +void write_kinetics( const state_type &y , const double t ); + +void write_kinetics( const state_type &y , const double t ) +{ +// write_kinetics - write the results into text files +// @param - const state_type &y - vector of all the variables +// @param - const double t - time + int n; + n = y.size(); + + ofstream out[n]; + out[0].open("../results/XW1.txt", std::ios::app); + out[1].open("../results/XOH1.txt", std::ios::app); + out[2].open("../results/T1.txt", std::ios::app); + out[3].open("../results/L_l1.txt", std::ios::app); + out[4].open("../results/L_g1.txt", std::ios::app); + out[5].open("../results/CO2_l1.txt", std::ios::app); + out[6].open("../results/CO2_g1.txt", std::ios::app); + out[7].open("../results/m01.txt", std::ios::app); + out[8].open("../results/m11.txt", std::ios::app); + out[9].open("../results/m21.txt", std::ios::app); + out[10].open("../results/m31.txt", std::ios::app); + // out[11].open("../results/EG_XNCO1.txt", std::ios::app); + // out[12].open("../results/EG_XOH1.txt", std::ios::app); + // out[13].open("../results/XH2O1.txt", std::ios::app); + // out[14].open("../results/CO21.txt", std::ios::app); + // out[15].open("../results/PENTANE1.txt", std::ios::app); + // out[16].open("../results/POLYMER1.txt", std::ios::app); + // out[17].open("../results/POLYMERBLOW1.txt", std::ios::app); + // out[18].open("../results/UREA1.txt", std::ios::app); + // out[19].open("../results/R_1_temp1.txt", std::ios::app); + + for (int i = 0; i < n; i++) + { + if(i == 11) + { + out[i] << t << '\t' << (1.0-y[i]/5.0) << '\n'; + } + else if (i == 12) + { + out[i] << t << '\t' << (1.0-y[i]/5.0) << '\n'; + } + else if (i == 13) + { + out[i] << t << '\t' << (1.0-y[i]/0.2) << '\n'; + } + else + { + out[i] << t << '\t' << y[i] << '\n'; + } + out[i].close(); + } + + double rhoPolySurrgate; + switch (denMod) { + case 1: { + // // Calling the model for density reaction mixture + // size_t T_denpos = modena_model_inputs_argPos(density_reaction_mixturemodel, "T"); + // size_t XOH_denpos = modena_model_inputs_argPos(density_reaction_mixturemodel, "XOH"); + // modena_model_argPos_check(density_reaction_mixturemodel); + // // set input vector + // double EG_XOH; + // double init_EG_OH = 5.0; + // EG_XOH = 1.0 - (y[12]/init_EG_OH); + // modena_inputs_set(inputs_den, T_denpos, y[2]); + // modena_inputs_set(inputs_den, XOH_denpos, EG_XOH); + // // call the model + // int ret_den = modena_model_call (density_reaction_mixturemodel, inputs_den, outputs_den); + // // terminate, if requested + // if(ret_den != 0) + // { + // modena_inputs_destroy (inputs_den); + // modena_outputs_destroy (outputs_den); + // modena_model_destroy (density_reaction_mixturemodel); + // exit(ret_den); + // //return ret_den; + // } + // rhoPolySurrgate = modena_outputs_get(outputs_den, 0); + } + case 2: + rhoPolySurrgate = rhoPoly; + } + + double p1,p2; + p1 = partialPressureBA(y); + p2 = partialPressureCO2(y); + double rho_bubble = ((p1+p2)/(RR*y[2]))*(y[6]*M_CO2 + y[4]*M_B)/(fmax((1000.0*(y[6] + y[4])),1.0e-8)); + // double rho_foam = (rho_bubble*(y[8]/(1.0+y[8])) + (1.0+L0)*rhoPolySurrgate*(1.0 - (y[8]/(1.0+y[8])))); + double rho_foam = (rho_bubble*(y[8]/(1.0+y[8])) + rhoPolySurrgate*(1.0 - (y[8]/(1.0+y[8])))); + + ofstream rho_bubbleout; + rho_bubbleout.open("../results/rho_bubble.txt", std::ios::app); + rho_bubbleout << t << '\t' << rho_bubble << '\n'; + rho_bubbleout.close(); + + ofstream rho_foamout; + rho_foamout.open("../results/rho_foam.txt", std::ios::app); + rho_foamout << t << '\t' << rho_foam << '\n'; + rho_foamout.close(); + + ofstream R_bubble; + double R = bubbleRadius(y[7], y[8]); + R_bubble.open("../results/R_bubble.txt", std::ios::app); + R_bubble << t << '\t' << R << '\n'; + R_bubble.close(); + + momentsConverter(y,t); + + double p_1 = partialPressureBA(y); + ofstream p1out; + p1out.open("../results/p_1.txt", std::ios::app); + p1out << t << '\t' << p_1 << '\n'; + p1out.close(); + + double p_2 = partialPressureCO2(y); + ofstream p2out; + p2out.open("../results/p_2.txt", std::ios::app); + p2out << t << '\t' << p_2 << '\n'; + p2out.close(); +} diff --git a/applications/PUfoam/MoDeNaModels/FoamConstruction/.gitignore b/applications/PUfoam/MoDeNaModels/FoamConstruction/.gitignore new file mode 100644 index 000000000..a1f190d0f --- /dev/null +++ b/applications/PUfoam/MoDeNaModels/FoamConstruction/.gitignore @@ -0,0 +1,16 @@ +*.geo +*.txt +*.cmf +*.ply +*.stl +*.vtk +*.prj +*.rco +*.rst +*.sco +*.stcell +*.stedge +*.stface +*.stver +*.json +*.out diff --git a/applications/PUfoam/MoDeNaModels/FoamConstruction/FoamGeometryConstruction_Periodic.py b/applications/PUfoam/MoDeNaModels/FoamConstruction/FoamGeometryConstruction_Periodic.py new file mode 100644 index 000000000..c22a6dbb2 --- /dev/null +++ b/applications/PUfoam/MoDeNaModels/FoamConstruction/FoamGeometryConstruction_Periodic.py @@ -0,0 +1,282 @@ +__author__ = 'Mohammad Marvi-Mashhadi (IMDEA Materials)' +import os +import os.path +import numpy as np +mypath=os.getcwd() +def main(MU,SIGMA,NumOfCells,filenameOut,packing,tesselation,geometry, + statistics,hypermesh,deleteFiles,dx,dy,dz): + #####To create input file for SpherePack + if packing: + myfile=os.path.join(mypath,'Project01.prj') + f=open(myfile,'w') + f.write('{0:34s}\n'.format('# RANDOM COORDINATES: 0 OR FILE: 1')) + f.write('{0}\n'.format('0')) + f.write('{0}\n'.format('# NUMBER OF SPHERES')) + f.write('{0:d}\n'.format(NumOfCells)) + f.write('{0}\n'.format('# LENGTH IN X-, Y- AND Z-DIRECTION')) + f.write('{0:f}\n'.format(dx)) + f.write('{0:f}\n'.format(dy)) + f.write('{0:f}\n'.format(dz)) + f.write('{0}\n'.format('# EPSILON')) + f.write('{0}\n'.format('0.0001')) + f.write('{0}\n'.format('# NTAU')) + f.write('{0}\n'.format('963800000')) + f.write('{0}\n'.format('# NOMINAL DENSITY')) + f.write('{0}\n'.format('0.25')) + f.write('{0}\n'.format('# MAX. AND MINIM. DIAMETER')) + f.write('{0}\n'.format('3.0')) + f.write('{0}\n'.format('1.0')) + f.write('{0}\n'.format('# MAX. NUMBER OF STEPS')) + f.write('{0}\n'.format('50000000')) + f.write('{0}\n'.format('# DISTRIBUTION')) + f.write('{0}\n'.format('3')) + f.write('{0}\n'.format('# DISTRIBUTION PARAMETERS')) + f.write('{0:f}\n'.format(MU)) + f.write('{0:f}\n'.format(SIGMA)) + f.write('{0}\n'.format('0.4')) + f.write('{0}\n'.format('-3.3')) + f.write('{0}\n'.format('3')) + f.write('{0}\n'.format('0.10')) + f.write('{0}\n'.format('0.20')) + f.write('{0}\n'.format('0.70')) + f.write('{0}\n'.format('0.902113')) + f.write('{0}\n'.format('3.000000')) + f.write('{0}\n'.format('1.000000')) + f.close() + ########################################################### + os.chdir(mypath) + command1='wine SpherePackFB.exe' + os.system(command1) + if tesselation: + myfile12=os.path.join(mypath,'Project01.rco') + CentersRads=np.loadtxt(myfile12,usecols = (0,1,2,3)) + Centers=CentersRads[:,:3] #All centers of spheres + Rads=CentersRads[:,3] #All radii of spheres + Rads=Rads/2 + MaxCenters=np.amax(Centers, axis=0) + L2=int(0.5+MaxCenters[0]) + print (L2) + X=L2+Centers[:,0] + Y=L2+Centers[:,1] + Z=L2+Centers[:,2] + Centers27=np.array([X,X+L2,X-L2,X+L2,X,X+L2,X,X-L2,X-L2,X-L2,X+L2,X,X,X-L2,X+L2,X+L2,X,X,X-L2,X,X,X-L2,X+L2,X+L2,X-L2,X-L2,X+L2,Y,Y+L2,Y-L2,Y+L2,Y+L2,Y,Y-L2,Y,Y-L2,Y+L2,Y-L2,Y-L2,Y+L2,Y,Y,Y,Y+L2,Y,Y,Y-L2,Y,Y+L2,Y-L2,Y+L2,Y-L2,Y+L2,Y-L2,Z,Z+L2,Z-L2,Z,Z+L2,Z+L2,Z-L2,Z-L2,Z,Z,Z,Z+L2,Z-L2,Z+L2,Z-L2,Z,Z,Z+L2,Z,Z,Z-L2,Z+L2,Z+L2,Z-L2,Z+L2,Z-L2,Z-L2]) + # Creation of input .txt files for neper + myfile3=os.path.join(mypath,'Centers.txt') + ff=open(myfile3,'w') + for i in range(0,27): + for j in range(0,NumOfCells): + ff.write('{0:f}\t{1:f}\t{2:f}\n'.format(Centers27[i,j],Centers27[i+27,j],Centers27[i+54,j])) + ff.close() + #mypath4=r'/home/mohammad/' + myfile4=os.path.join(mypath,'Rads.txt') + fff=open(myfile4,'w') + for i in range(0,27): + for j in range(0,NumOfCells): + fff.write('{0:f}\n'.format(Rads[j])) + fff.close() + commandTessellation="neper -T -n {0:d} -domain 'cube({1:d},{2:d},{3:d})' -morpho @Centers.txt -weight @Rads.txt -o RVE27 -format geo -statcell vol -statedge length -statface area -statver x".format((27*NumOfCells),3*dx,3*dy,3*dz) + os.system(commandTessellation) + ################################################################ + ######Extraction of middle Representative volume element######## + ################################################################ + if geometry: + myfile12=os.path.join(mypath,'RVE27.stver') + verX=np.loadtxt(myfile12) + NumOfNodes=len(verX) + myfile12=os.path.join(mypath,'RVE27.stedge') + EdgesLength=np.loadtxt(myfile12) + NumOfEdges=len(EdgesLength) + myfile12=os.path.join(mypath,'RVE27.stface') + SurfacesArea=np.loadtxt(myfile12) + NumOfSurfaces=len(SurfacesArea) + myfile12=os.path.join(mypath,'RVE27.stcell') + CellVolumes=np.loadtxt(myfile12) + NumOfVolumes=len(CellVolumes) + #### Reading the GEO file + myfile12=os.path.join(mypath,'RVE27.geo') + text_file = open(myfile12, "r") + lines = text_file.readlines() + #### Extraction of Nodes + t=0 + Nodes=list(range(NumOfNodes)) + for i in range(0,NumOfNodes): + currentline = lines[i].split("{") + a=currentline[1].split("}") + b=a[0].split(",") + c=np.array(b) + Nodes[t]=np.absolute(c.astype(np.float)) + t=t+1 + ##### Extraction of Edges + Edges=list(range(NumOfEdges)) + r=0 + t=0 + for i in range(NumOfNodes,NumOfNodes+NumOfEdges): + currentline = lines[i].split("{") + a=currentline[1].split("}") + b=a[0].split(",") + c=np.array(b) + Edges[t]=np.absolute(c.astype(np.float)) + t=t+1 + #### Extraction of Faces + Faces=list(range(NumOfSurfaces)) + r=0 + t=0 + for i in range(0,NumOfSurfaces): + j=NumOfNodes+NumOfEdges+(2*i) + currentline = lines[j].split("{") + a=currentline[1].split("}") + b=a[0].split(",") + c=np.array(b) + Faces[t]=np.absolute(c.astype(np.float)) + t=t+1 + #### Extraction of volumes + Volumes=list(range(NumOfVolumes)) + #print NumOfNodes+NumOfEdges+(2*NumOfSurfaces) + a=list(lines[NumOfNodes+NumOfEdges+(2*NumOfSurfaces)]) + a[0:21]='' + o=len(a) + a[o-3:]='' + lines[NumOfNodes+NumOfEdges+(2*NumOfSurfaces)]="".join(a) + currentline=lines[NumOfNodes+NumOfEdges+(2*NumOfSurfaces)].split(",") + c=np.array(currentline) + Volumes[0]=np.absolute(c.astype(np.float)) + t=1 + for i in range(1,NumOfVolumes): + j=NumOfNodes+NumOfEdges+(2*NumOfSurfaces)+i + currentline = lines[j].split(" = {") + a=currentline[2].split("}") + b=a[0].split(",") + c=np.array(b) + Volumes[t]=np.absolute(c.astype(np.float)) + t=t+1 + ##################################################### + MAX0=list(range(0,NumOfCells)) + for i in range(NumOfCells): + MAX0[i]=max(Volumes[i]) + MaxIndexOfFaces=max(MAX0) + MAX1=list(range(0,int(MaxIndexOfFaces))) + for i in range(int(MaxIndexOfFaces)): + MAX1[i]=max(Faces[i]) + MaxIndexOfEdges=max(MAX1) + MAX2=list(range(0,int(MaxIndexOfEdges))) + for i in range(int(MaxIndexOfEdges)): + MAX2[i]=max(Edges[i]) + MaxIndexOfNodes=max(MAX2) + text_file.close() + #################################################### + # Making GEO file containing Periodic RVE + myfile13=os.path.join(mypath,filenameOut+".geo") + text_GEO = open(myfile13, "w") + for i in range(int(MaxIndexOfNodes)): + text_GEO.write('{0}'.format(lines[i])) + for i in range(int(NumOfNodes),int(NumOfNodes+MaxIndexOfEdges)): + text_GEO.write('{0}'.format(lines[i])) + j=int(NumOfNodes+NumOfEdges) + for i in range(int(NumOfNodes+NumOfEdges),int(NumOfNodes+NumOfEdges+MaxIndexOfFaces)): + text_GEO.write('{0}{1}'.format(lines[j],lines[j+1])) + j=2+j + text_GEO.write('{0}{1}{2}\n'.format(' Surface Loop (1) = {',lines[int(NumOfNodes+NumOfEdges+(2*NumOfSurfaces))],'};')) + NumOfCells=NumOfVolumes/27 + j=int(NumOfNodes+NumOfEdges+(2*NumOfSurfaces)+1) + for i in range(int(NumOfCells-1)): + text_GEO.write('{0}'.format(lines[j])) + j+=1 + text_GEO.write('{0}{1}{2}{3}{4}'.format('Volume (',NumOfCells,') = {',NumOfCells,'};')) + text_GEO.close() + #################################################### + # Creating periodic domain - not working yet + # minDomain=[4,4,4] + # maxDomain=[8,8,8] + # def inDomain(point): + # inDomain=1 + # for i,pos in enumerate(point): + # if (posmaxDomain[i]): + # inDomain=0 + # return inDomain + # return inDomain + # NodesInDomain=[] + # NodeIndex=[] + # NodeIndexNew=range(len(Nodes)) + # for i,point in enumerate(Nodes): + # if (inDomain(point)): + # NodesInDomain.append(point) + # NodeIndex.append(i) + # NodeIndexNew[i]=len(NodeIndex)-1 + # EdgesInDomain=[] + # for i,index in enumerate(Edges): + # if (index[0] in NodeIndex or index[1] in NodeIndex): + # EdgesInDomain.append([NodeIndexNew[int(index[0])],NodeIndexNew[int(index[1])]]) + # geofile=open('PeriodicRVEdomain.geo','w') + # for i,pos in enumerate(NodesInDomain): + # geofile.write('Point ({0}) = {{{1},{2},{3}}};\n'.format(i,pos[0],pos[1],pos[2])) + # for i,index in enumerate(EdgesInDomain): + # geofile.write('Line ({0}) = {{{1},{2}}};\n'.format(i,index[0],index[1])) + # geofile.close() + # End of Geometry construction + ################################################################ + ######Statistical info for Periodic RVE######################### + ################################################################ + if statistics: + myfile14=os.path.join(mypath,'EdgeLengths_PeriodicRVE.txt') + EdgesLengthsOfMiddleRVE= open(myfile14, "w") + for i in range(int(MaxIndexOfEdges)): + EdgesLengthsOfMiddleRVE.write('{0}\n'.format(EdgesLength[i])) + EdgesLengthsOfMiddleRVE.close() + myfile15=os.path.join(mypath,'FaceAreas_PeriodicRVE.txt') + AreaOfFaceOfMiddleRVE= open(myfile15, "w") + for i in range(int(MaxIndexOfFaces)): + AreaOfFaceOfMiddleRVE.write('{0}\n'.format(SurfacesArea[i])) + AreaOfFaceOfMiddleRVE.close() + myfile16=os.path.join(mypath,'CellVolumes_PeriodicRVE.txt') + VolumeOfCellOfMiddleRVE= open(myfile16, "w") + for i in range(int(NumOfCells)): + VolumeOfCellOfMiddleRVE.write('{0}\n'.format(CellVolumes[i])) + VolumeOfCellOfMiddleRVE.close() + ################################################################ + ######Creation of input for HyperMesh########################### + ################################################################ + if hypermesh: + myfile17=os.path.join(mypath,'HyperMeshInput.cmf') + HyperMeshInput= open(myfile17, "w") + HyperMeshInput.write('{0}\n'.format('*cleanuptoleranceset(0.001)')) + HyperMeshInput.write('{0}\n'.format('*toleranceset(0.001)')) + for i in range(int(MaxIndexOfNodes)): + HyperMeshInput.write('{0}{1}{2}{3}{4}{5}{6}\n'.format('*createnode(',Nodes[i][0],',',Nodes[i][1],',',Nodes[i][2],',0,0,0)')) + for i in range(int(MaxIndexOfEdges)): + HyperMeshInput.write('{0}\n{1}{2}{3}{4}\n'.format('*linecreatefromnodes(1,0,150,5,179)','*createlist(nodes,1) ',int(Edges[i][0]),' ',int(Edges[i][1]))) + for i in range(int(MaxIndexOfFaces)): + HyperMeshInput.write('{0}\n'.format('*surfacemode(4)')) + HyperMeshInput.write('{0}'.format('*createmark(lines,1) ')) + for j in range(len(Faces[i])): + HyperMeshInput.write('{0}\t'.format(int(Faces[i][j]))) + HyperMeshInput.write('\n{0}\n{1}\n'.format('*createplane(1,1,0,0,0,0,0)','*splinesurface(lines,1,1,1,1)')) + HyperMeshInput.write('{0}\n'.format('*createmark(lines,1) "all"')) + HyperMeshInput.write('{0}\n'.format('*deletemark(lines,1)')) + HyperMeshInput.write('{0}\n'.format('*settopologyedgedisplay(2,0)')) + HyperMeshInput.write('{0}\n'.format('*plot()')) + HyperMeshInput.write('{0}\n'.format('*settopologyedgedisplay(3,0)')) + HyperMeshInput.write('{0}\n'.format('*plot()')) + HyperMeshInput.write('{0}\n'.format('*settopologyedgedisplay(1,0)')) + HyperMeshInput.write('{0}\n'.format('*plot()')) + Tol=0.001 + for i in range(NumOfCells): + HyperMeshInput.write('{0}\n'.format('*createmark(surfaces,1) "displayed"')) + HyperMeshInput.write('{0}{1}{2}{3}{4}\n'.format('*selfstitchcombine(1,82,',Tol,',',Tol,')')) + Tol=0.0001+Tol + HyperMeshInput.close() + ################################################################ + ######Removing unrequired files################################# + ################################################################ + if deleteFiles: + os.chdir(mypath) + os.remove('Project01.prj') + os.remove('Project01.rco') + os.remove('Project01.rst') + os.remove('Project01.sco') + os.remove('Rads.txt') + os.remove('Centers.txt') + os.remove('RVE27.geo') + os.remove('RVE27.stcell') + os.remove('RVE27.stedge') + os.remove('RVE27.stface') + os.remove('RVE27.stver') diff --git a/applications/PUfoam/MoDeNaModels/FoamConstruction/README.md b/applications/PUfoam/MoDeNaModels/FoamConstruction/README.md new file mode 100644 index 000000000..f58c3360d --- /dev/null +++ b/applications/PUfoam/MoDeNaModels/FoamConstruction/README.md @@ -0,0 +1,77 @@ +Foam Construction +============================ +## Installation +The code depends on several third-party applications: +- `wine` to have ability of running windows executable files (i.e. file.exe). +- `neper` for tessellation +- `gmsh`, `vtk`, `meshconv` and `binvox` for mesh manipulation + +To install all of these on Ubuntu, do: +``` +sudo add-apt-repository ppa:ubuntu-wine/ppa +sudo apt-get update +sudo apt-get install wine1.7 libmatheval-dev gmsh gsl-bin libgsl0-dev \ + python-vtk +``` +Then download and install `neper` from http://neper.sourceforge.net/downloads.html +(follow its README for instructions), +download `meshconv` from http://www.cs.princeton.edu/~min/meshconv/, download +`binvox` from http://www.cs.princeton.edu/~min/binvox/ and copy `meshconv` and + `binvox` to `$PATH` + +## Files +The folder `FoamConstruction` contains following files: +- `SpherePackFB.exe` - packing algorithm +- `FoamGeometryConstruction_Periodic.py` - tessellation, creation of RVE +- `periodicBox.py` - creation of the box with periodic boundary conditions +- `vtkconv.py` - conversion from binary vtk to ascii vtk +- `run` - main executable script + +All files must be in one directory. + +## Inputs +The code is controlled by the `input.json` file, which must be located in the +root of `FoamConstruction` folder. Default input file can be found +in `example_inputs` directory. Following inputs can be adjusted: +- `MU` - mean of cell size distribution +- `SIGMA` - standard deviation of cell size distribution +- `NumOfCells` - number of cells in RVE (representative volume element) +- `porosity` - desired porosity of voxelized foam +- `filename` - name of the output file with RVE +- `deleteFiles` - delete some redundant output files after execution +- `packing` - call packing algorithm, which creates seeds and radii for +tessellation +- `tesselation` - call tessellation program, which creates foam with desired +cell size distribution based on results of packing +- `geometry` - limits the foam to RVE +- `statistics` - compute and save cell volumes, face surfaces, etc. +- `hypermesh` - create input for `Hypermesh` +- `moveToPeriodicBox` - move RVE to box with periodic boundary conditions +- `renderBox` - show the box with periodic boundary conditions +- `binarizeBox` - voxelize the box with periodic boundary conditions + +## Execution +Prepare `input.json`, then: +``` +./run +``` + +## Outputs +Several output files are created: +- `PeriodicRVE.geo` which is the periodic geometry of foam in .GEO +format. +- `CellVolumes_PeriodicRVE.txt` containing the volumes of all the +cells in RVE. +- `FaceAreas_PeriodicRVE.txt` containing the areas of all the faces +in RVE. +- `EdgeLengths_PeriodicRVE.txt` containing the lengths of all the +edges in RVE. +- `HyperMeshinput.cmf` which is a input file for `Hypermesh` to +recreate the geometry. +- `PeriodicRVEBox.stl` - surface mesh of the box with periodic boundary +conditions +- `PeriodicRVEBox-ascii.vtk` - voxelized verion of the box with periodic +boundary conditions + +Generally, `.geo` files can be viewed with `gmsh`, `.stl`, `.ply` and `.vtk` +files can be viewed with `paraview`. diff --git a/applications/PUfoam/MoDeNaModels/FoamConstruction/SpherePackFB.exe b/applications/PUfoam/MoDeNaModels/FoamConstruction/SpherePackFB.exe new file mode 100755 index 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b/applications/PUfoam/MoDeNaModels/FoamConstruction/example_inputs/input.json @@ -0,0 +1,16 @@ +{ + "MU": 0.15, + "SIGMA": 0.01, + "NumOfCells": 27, + "porosity": 0.94, + "filename": "PeriodicRVE", + "deleteFiles": 1, + "packing": 1, + "tesselation": 1, + "geometry": 1, + "statistics": 0, + "hypermesh": 0, + "moveToPeriodicBox": 1, + "renderBox": 0, + "binarizeBox": 1 +} diff --git a/applications/PUfoam/MoDeNaModels/FoamConstruction/periodicBox.py b/applications/PUfoam/MoDeNaModels/FoamConstruction/periodicBox.py new file mode 100644 index 000000000..d60d7e195 --- /dev/null +++ b/applications/PUfoam/MoDeNaModels/FoamConstruction/periodicBox.py @@ -0,0 +1,172 @@ +# -*- coding: utf-8 -*- +""" +Created on Thu Dec 3 12:25:27 2015 +Takes the representative volume element and moves it into a box with +periodic boundary conditions +@author: Pavel Ferkl +""" +import vtk +def main(filenameIn,filenameOut,xmin,ymin,zmin,dx,dy,dz,render): + # print vtk.VTK_MAJOR_VERSION # Check the version + # Read the file and create polydata + reader = vtk.vtkSTLReader() + reader.SetFileName(filenameIn) + # Define planes for clipping + Origins=[ + [xmin,ymin,zmin], + [xmin,ymin,zmin], + [xmin,ymin,zmin], + [xmin+dx,ymin+dy,zmin+dz], + [xmin+dx,ymin+dy,zmin+dz], + [xmin+dx,ymin+dy,zmin+dz], + ] + Normals=[ + [[-1,0,0],[0,-1,0],[0,0,-1],[-1,0,0],[0,-1,0],[0,0,-1]], + [[+1,0,0],[0,-1,0],[0,0,-1],[-1,0,0],[0,-1,0],[0,0,-1]], + [[+1,0,0],[0,-1,0],[0,0,-1],[+1,0,0],[0,-1,0],[0,0,-1]], + [[-1,0,0],[0,+1,0],[0,0,-1],[-1,0,0],[0,-1,0],[0,0,-1]], + [[+1,0,0],[0,+1,0],[0,0,-1],[-1,0,0],[0,-1,0],[0,0,-1]], + [[+1,0,0],[0,+1,0],[0,0,-1],[+1,0,0],[0,-1,0],[0,0,-1]], + [[-1,0,0],[0,+1,0],[0,0,-1],[-1,0,0],[0,+1,0],[0,0,-1]], + [[+1,0,0],[0,+1,0],[0,0,-1],[-1,0,0],[0,+1,0],[0,0,-1]], + [[+1,0,0],[0,+1,0],[0,0,-1],[+1,0,0],[0,+1,0],[0,0,-1]], + + [[-1,0,0],[0,-1,0],[0,0,+1],[-1,0,0],[0,-1,0],[0,0,-1]], + [[+1,0,0],[0,-1,0],[0,0,+1],[-1,0,0],[0,-1,0],[0,0,-1]], + [[+1,0,0],[0,-1,0],[0,0,+1],[+1,0,0],[0,-1,0],[0,0,-1]], + [[-1,0,0],[0,+1,0],[0,0,+1],[-1,0,0],[0,-1,0],[0,0,-1]], + [[+1,0,0],[0,+1,0],[0,0,+1],[-1,0,0],[0,-1,0],[0,0,-1]], + [[+1,0,0],[0,+1,0],[0,0,+1],[+1,0,0],[0,-1,0],[0,0,-1]], + [[-1,0,0],[0,+1,0],[0,0,+1],[-1,0,0],[0,+1,0],[0,0,-1]], + [[+1,0,0],[0,+1,0],[0,0,+1],[-1,0,0],[0,+1,0],[0,0,-1]], + [[+1,0,0],[0,+1,0],[0,0,+1],[+1,0,0],[0,+1,0],[0,0,-1]], + + [[-1,0,0],[0,-1,0],[0,0,+1],[-1,0,0],[0,-1,0],[0,0,+1]], + [[+1,0,0],[0,-1,0],[0,0,+1],[-1,0,0],[0,-1,0],[0,0,+1]], + [[+1,0,0],[0,-1,0],[0,0,+1],[+1,0,0],[0,-1,0],[0,0,+1]], + [[-1,0,0],[0,+1,0],[0,0,+1],[-1,0,0],[0,-1,0],[0,0,+1]], + [[+1,0,0],[0,+1,0],[0,0,+1],[-1,0,0],[0,-1,0],[0,0,+1]], + [[+1,0,0],[0,+1,0],[0,0,+1],[+1,0,0],[0,-1,0],[0,0,+1]], + [[-1,0,0],[0,+1,0],[0,0,+1],[-1,0,0],[0,+1,0],[0,0,+1]], + [[+1,0,0],[0,+1,0],[0,0,+1],[-1,0,0],[0,+1,0],[0,0,+1]], + [[+1,0,0],[0,+1,0],[0,0,+1],[+1,0,0],[0,+1,0],[0,0,+1]], + ] + # Define directions for moving clipped regions + Direction=[ + [dx,dy,dz], + [0,dy,dz], + [-dx,dy,dz], + [dx,0,dz], + [0,0,dz], + [-dx,0,dz], + [dx,-dy,dz], + [0,-dy,dz], + [-dx,-dy,dz], + [dx,dy,0], + [0,dy,0], + [-dx,dy,0], + [dx,0,0], + [0,0,0], + [-dx,0,0], + [dx,-dy,0], + [0,-dy,0], + [-dx,-dy,0], + [dx,dy,-dz], + [0,dy,-dz], + [-dx,dy,-dz], + [dx,0,-dz], + [0,0,-dz], + [-dx,0,-dz], + [dx,-dy,-dz], + [0,-dy,-dz], + [-dx,-dy,-dz], + ] + regions=[] + n=27 + for j in xrange(n): + polydata=reader + # Clip it with all 6 planes + for i in xrange(6): + plane=vtk.vtkPlane() + plane.SetOrigin(Origins[i]) + plane.SetNormal(Normals[j][i]) + clipper = vtk.vtkClipPolyData() + clipper.SetInputConnection(polydata.GetOutputPort()) + clipper.SetClipFunction(plane) + polydata=clipper + polydata.Update() + # Move it if not empty + if polydata.GetOutput().GetLength()>0: + transform = vtk.vtkTransform() + transform.Translate(Direction[j]) + transformFilter = vtk.vtkTransformPolyDataFilter() + transformFilter.SetTransform(transform) + transformFilter.SetInputConnection(polydata.GetOutputPort()) + transformFilter.Update() + regions.append(vtk.vtkPolyData()) + regions[j].ShallowCopy(transformFilter.GetOutput()) + else: + regions.append(vtk.vtkPolyData()) + regions[j].ShallowCopy(polydata.GetOutput()) + # Append the all regions + appendFilter = vtk.vtkAppendPolyData() + if vtk.VTK_MAJOR_VERSION <= 5: + for j in xrange(n): + appendFilter.AddInputConnection(regions[j].GetProducerPort()) + else: + for j in xrange(n): + appendFilter.AddInputData(regions[j]) + appendFilter.Update() + # Remove any duplicate points + cleanFilter = vtk.vtkCleanPolyData() + cleanFilter.SetInputConnection(appendFilter.GetOutputPort()) + cleanFilter.Update() + # One more rotation - not needed + # transform = vtk.vtkTransform() + # transform.Translate(-6,-6,-6) + # transformFilter = vtk.vtkTransformPolyDataFilter() + # transformFilter.SetTransform(transform) + # transformFilter.SetInputConnection(cleanFilter.GetOutputPort()) + # transformFilter.Update() + # transform = vtk.vtkTransform() + # transform.RotateWXYZ(90,1,0,0) + # transform.RotateWXYZ(-90,0,1,0) + # transformFilter2 = vtk.vtkTransformPolyDataFilter() + # transformFilter2.SetTransform(transform) + # transformFilter2.SetInputConnection(transformFilter.GetOutputPort()) + # transformFilter2.Update() + # transform = vtk.vtkTransform() + # transform.Translate(6,6,6) + # transformFilter = vtk.vtkTransformPolyDataFilter() + # transformFilter.SetTransform(transform) + # transformFilter.SetInputConnection(transformFilter2.GetOutputPort()) + # transformFilter.Update() + # Final data to be saved and displayed + finalData=cleanFilter + # Write the stl file to disk + stlWriter = vtk.vtkSTLWriter() + stlWriter.SetFileName(filenameOut) + stlWriter.SetInputConnection(finalData.GetOutputPort()) + stlWriter.Write() + if render: + # Create mappper and actor for rendering + mapper = vtk.vtkPolyDataMapper() + if vtk.VTK_MAJOR_VERSION <= 5: + mapper.SetInput(finalData.GetOutput()) + else: + mapper.SetInputConnection(finalData.GetOutputPort()) + actor = vtk.vtkActor() + actor.SetMapper(mapper) + # Create a rendering window and renderer + ren = vtk.vtkRenderer() + renWin = vtk.vtkRenderWindow() + renWin.AddRenderer(ren) + # Create a renderwindowinteractor + iren = vtk.vtkRenderWindowInteractor() + iren.SetRenderWindow(renWin) + # Assign actor to the renderer + ren.AddActor(actor) + # Enable user interface interactor + iren.Initialize() + renWin.Render() + iren.Start() diff --git a/applications/PUfoam/MoDeNaModels/FoamConstruction/run b/applications/PUfoam/MoDeNaModels/FoamConstruction/run new file mode 100755 index 000000000..5ea03049d --- /dev/null +++ b/applications/PUfoam/MoDeNaModels/FoamConstruction/run @@ -0,0 +1,113 @@ +#!/usr/bin/env python +""" +@author: Pavel Ferkl +""" +from __future__ import division +import os +from blessings import Terminal +import json +from scipy.optimize import newton as newton +from scipy.optimize import minimize_scalar as minimize_scalar +import FoamGeometryConstruction_Periodic +import periodicBox +import vtkconv +dx=dy=dz=4 # size of RVE +########## Read input file +with open('input.json') as data_file: + data = json.load(data_file) +locals().update(data) # Creates variables from dictionary +########## Create terminal for colour output +term = Terminal() +########## Function for finding size of box, which would give desired porosity +def porOpt(vx): + vx=int(vx) + vy=vx + vz=vx + if os.path.isfile(filename+'.vtk'): + os.remove(filename+'.vtk') + if not os.path.isfile(filename+'.ply'): + raise SystemError(".ply file is missing. Nothing to binarize.") + os.system("binvox -e -d {0:d} -rotz -rotx -rotz -rotz -t vtk ".format(vx)+ + filename+".ply >binvox.out") + with open('binvox.out') as data_file: + for line in data_file: + if "counted" in line: + solidVoxel,totalVoxel=\ + [int(s) for s in line.split() if s.isdigit()] + eps=1-solidVoxel/totalVoxel + print "porosity: {0:f}".format(eps) + return (eps-porosity)**2 +########## Create periodic RVE of foam +print( + term.yellow + + "Create periodic RVE of foam" + + term.normal +) +FoamGeometryConstruction_Periodic.main(MU,SIGMA,NumOfCells,filename,packing,\ + tesselation,geometry,statistics,hypermesh,deleteFiles,dx,dy,dz) +if moveToPeriodicBox: + ########## Convert .geo to .stl + print( + term.yellow + + "Convert .geo to .stl" + + term.normal + ) + os.system("gmsh -n -2 -format stl "+filename+".geo >gmsh.out") + if deleteFiles: + os.remove("gmsh.out") + ########## Move to periodic box + print( + term.yellow + + "Move to periodic box" + + term.normal + ) + filenameIn = filename+".stl" + filename = filename+"Box" + filenameOut = filename+".stl" + xmin=dx + ymin=dy + zmin=dz + periodicBox.main(filenameIn,filenameOut,xmin,ymin,zmin,dx,dy,dz,renderBox) + if deleteFiles: + os.remove(filenameIn) + ########## Convert .stl to .ply + print( + term.yellow + + "Convert .stl to .ply" + + term.normal + ) + os.system("meshconv "+filename+".stl -c ply") +if binarizeBox: + ########## Binarize and save as .vtk + if deleteFiles and os.path.isfile(filename+'.stl'): + os.remove(filename+'.stl') + print( + term.yellow + + "Binarize and save as .vtk" + + term.normal + ) + # Find the size of box, which would give desired porosity + # This method is not optimal, since the solver doesn't know that the + # function takes only integer arguments + res=minimize_scalar(porOpt,bracket=[100,120],method='Brent',tol=1e-2) + vx=res.x + vx=int(vx) + vy=vx + vz=vx + print 'box size: {0:d}'.format(vx) + porOpt(vx) # Call it with the optimized box size + if deleteFiles: + os.remove("binvox.out") + os.remove(filename+".ply") + ########## Convert binary .vtk to ascii .vtk + print( + term.yellow + + "Convert binary .vtk to ascii .vtk" + + term.normal + ) + filenameIn = filename+".vtk" + filename = filename+"-ascii" + filenameOut = filename+".vtk" + vtkconv.main(filenameIn,filenameOut,dx,dy,dz,vx,vy,vz) + if deleteFiles: + os.remove(filenameIn) diff --git a/applications/PUfoam/MoDeNaModels/FoamConstruction/vtkconv.py b/applications/PUfoam/MoDeNaModels/FoamConstruction/vtkconv.py new file mode 100644 index 000000000..141754ac2 --- /dev/null +++ b/applications/PUfoam/MoDeNaModels/FoamConstruction/vtkconv.py @@ -0,0 +1,23 @@ +# -*- coding: utf-8 -*- +""" +Created on Tue Nov 24 11:32:34 2015 +Reads binary vtk file and creates ascii vtk file +@author: Pavel Ferkl +""" +from __future__ import division +import vtk +def main(filenameIn,filenameOut,dx,dy,dz,vx,vy,vz): + r = vtk.vtkDataSetReader() + r.SetFileName(filenameIn) + r.Update() + data = vtk.vtkImageData() + 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zzxK!UHyZ&MnHib?rWa;5*57OiT2Fw#`4tlo_#b3{$IQ&a&i;FU%s|Fp_xQiyV_^cV z*1ySEe%(a>+Kz*r@poMTLH7849&F4^py$26UdzVJ2Kdci0PKuR?4Zr-FJrJX0-66N zV+R8ME@NZ*4KpLiUpRhi2XZwgw%;&=WFUb59@oK6*VMw$4xXEvkU`$m&G6USXOOeD zb|Cy?BL&@T#jK313IEt4e;o)Ds&lgfS=g9F*hPT?!mI)u!ayMaiwFxqh(nkez%0Nj jD#A. + +Description + Python library of FireTasks + +Authors + Henrik Rusche + +Contributors +''' + +from modena.Strategy import BackwardMappingScriptTask + + +__author__ = 'Henrik Rusche' +__copyright__ = 'Copyright 2014, MoDeNa Project' +__version__ = '0.2' +__maintainer__ = 'Henrik Rusche' +__email__ = 'h.rusche@wikki.co.uk.' +__date__ = 'Sep 4, 2014' + + +# Source code in src/twoTanksMacroscopicProblem.C +m = BackwardMappingScriptTask( + script='../src/MacroscopicProblem' +) + diff --git a/applications/PUfoam/MoDeNaModels/PolymerDensity/ExampleOfUsage/README.md b/applications/PUfoam/MoDeNaModels/PolymerDensity/ExampleOfUsage/README.md new file mode 100644 index 000000000..935104871 --- /dev/null +++ b/applications/PUfoam/MoDeNaModels/PolymerDensity/ExampleOfUsage/README.md @@ -0,0 +1,42 @@ + +Example simulation with Density model: + +A simple macroscopic code calls the density model for different temperatures. + + +How to run? +----------- + +# Make sure PYTHONPATH and LD\_LIBRARY\_PATH are set +# TODO: +# Make this easier to use +``` +export PKG_CONFIG_PATH=${PKG_CONFIG_PATH:-}:${HOME}/lib/pkgconfig:/usr/local/lib/pkgconfig +export PYTHONPATH=${PYTHONPATH:-}:${HOME}/lib/python2.7/site-packages +export LD_LIBRARY_PATH=${LD_LIBRARY_PATH:-}:${HOME}/lib/python2.7/site-packages:${HOME}/lib:/usr/local/lib +``` + +# Compile project specific sources (only locally) +``` +cd src +cmake . +make +``` + +#Compile detailed model code +``` +cd src/ +cmake . +make +``` + +# Initialise the model in the database +``` +./initModel +``` + +# Start the workflow +``` +./workflow +``` + diff --git a/applications/PUfoam/MoDeNaModels/PolymerDensity/ExampleOfUsage/initModels b/applications/PUfoam/MoDeNaModels/PolymerDensity/ExampleOfUsage/initModels new file mode 100755 index 000000000..4497f6fda --- /dev/null +++ b/applications/PUfoam/MoDeNaModels/PolymerDensity/ExampleOfUsage/initModels @@ -0,0 +1,62 @@ +#!/usr/bin/python +''' + + ooo ooooo oooooooooo. ooooo ooo + `88. .888' `888' `Y8b `888b. `8' + 888b d'888 .ooooo. 888 888 .ooooo. 8 `88b. 8 .oooo. + 8 Y88. .P 888 d88' `88b 888 888 d88' `88b 8 `88b. 8 `P )88b + 8 `888' 888 888 888 888 888 888ooo888 8 `88b.8 .oP"888 + 8 Y 888 888 888 888 d88' 888 .o 8 `888 d8( 888 + o8o o888o `Y8bod8P' o888bood8P' `Y8bod8P' o8o `8 `Y888""8o + +Copyright + 2014-2015 MoDeNa Consortium, All rights reserved. + +License + This file is part of Modena. + + Modena is free software; you can redistribute it and/or modify it under + the terms of the GNU General Public License as published by the Free + Software Foundation, either version 3 of the License, or (at your option) + any later version. + + Modena is distributed in the hope that it will be useful, but WITHOUT ANY + WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS + FOR A PARTICULAR PURPOSE. See the GNU General Public License for more + details. + + You should have received a copy of the GNU General Public License along + with Modena. If not, see . + +Description + Initialisation script for the flowRate model. The script calculates a few + data points and fits the surrogate model. Then the model is inserted into + the database. + +Authors + Henrik Rusche + +Contributors +''' + +from modena import SurrogateModel +from modena.Strategy import Workflow2 +#import flowRate +import modDensity +from fireworks import LaunchPad +from fireworks.core.rocket_launcher import rapidfire +from fireworks.utilities.fw_serializers import load_object + + +# set up the LaunchPad and reset it +launchpad = LaunchPad() +launchpad.reset('', require_password=False) + +initWfs = Workflow2([]) +for m in SurrogateModel.get_instances(): + initWfs.addNoLink(m.initialisationStrategy().workflow(m)) + +# store workflow and launch it locally +launchpad.add_wf(initWfs) +rapidfire(launchpad) + diff --git a/applications/PUfoam/MoDeNaModels/PolymerDensity/ExampleOfUsage/modDensity.py b/applications/PUfoam/MoDeNaModels/PolymerDensity/ExampleOfUsage/modDensity.py new file mode 100644 index 000000000..700b150e7 --- /dev/null +++ b/applications/PUfoam/MoDeNaModels/PolymerDensity/ExampleOfUsage/modDensity.py @@ -0,0 +1,208 @@ +'''@cond + + ooo ooooo oooooooooo. ooooo ooo + `88. .888' `888' `Y8b `888b. `8' + 888b d'888 .ooooo. 888 888 .ooooo. 8 `88b. 8 .oooo. + 8 Y88. .P 888 d88' `88b 888 888 d88' `88b 8 `88b. 8 `P )88b + 8 `888' 888 888 888 888 888 888ooo888 8 `88b.8 .oP"888 + 8 Y 888 888 888 888 d88' 888 .o 8 `888 d8( 888 + o8o o888o `Y8bod8P' o888bood8P' `Y8bod8P' o8o `8 `Y888""8o + +Copyright + 2014-2015 MoDeNa Consortium, All rights reserved. + +License + This file is part of Modena. + + Modena is free software; you can redistribute it and/or modify it under + the terms of the GNU General Public License as published by the Free + Software Foundation, either version 3 of the License, or (at your option) + any later version. + + Modena is distributed in the hope that it will be useful, but WITHOUT ANY + WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS + FOR A PARTICULAR PURPOSE. See the GNU General Public License + for more details. + + You should have received a copy of the GNU General Public License along + with Modena. If not, see . +@endcond''' + +""" +@file +Python library of FireTasks +This is the Density python module. Basically, it contains the following: + +The FireTask which controls the call of the detailed model. This detailed model is called +at the very beginning of the simulation in order to generate initial data points +which can be used to fit the parameters of the surrogate model and during a running simulation +as soon as the Density model is called with input parameters which lie outside the range +the parameters of the surrogate model was so far fitted for. This FireTask is stored in the class +"DensityExactSim" and a more detailed description of the detailed model can be found +in the description of this class. + +Furthermore, this module contains the code of the surrogate model function as well as the +definitions of its input and output values and its fittable parameters. Care should be +taken to set reasonable bounds for these variables. + +Also, this module contains the backward mapping model. This model consits of the +surrogate model function, an initialisation strategy, the out of bounds strategy and the +parameter fitting strategy. The initialisation strategy defines the initial data points where the +detailed model will be evaluated at simulation start for an initial fit of the surrogate model parameters. +The out of bounds strategy determines, how many new points and where to place these new +points, once the Density model is called for input values outside of the +fitted range. The parameter fitting strategy defines tolerances and maximal iterations +which are passed to the numerical solver which performs the actual fitting of the +surrogate model parameters. + +@author Jonas Mairhofer +@copyright 2014-2015, MoDeNa Project. GNU Public License. +@ingroup app_foaming +""" + + +import os +import modena +from modena import ForwardMappingModel,BackwardMappingModel,SurrogateModel,CFunction,IndexSet +import modena.Strategy as Strategy +from fireworks.user_objects.firetasks.script_task import FireTaskBase, ScriptTask +from fireworks import Firework, Workflow, FWAction +from fireworks.utilities.fw_utilities import explicit_serialize +from blessings import Terminal +from jinja2 import Template + +# Create terminal for colour output +term = Terminal() + + +__author__ = 'Henrik Rusche' +__copyright__ = 'Copyright 2014, MoDeNa Project' +__version__ = '0.2' +__maintainer__ = 'Henrik Rusche' +__email__ = 'h.rusche@wikki.co.uk.' +__date__ = 'Sep 4, 2014' + + +# ********************************* Class ********************************** # +@explicit_serialize +class DensityExactSim(FireTaskBase): + """ + This FireTask controls the execution of the detailed model of the Density model. + The detailed model uses the PC-SAFT equation of state. A + detailed description of PC-SAFT model can be found in Deliverable 1.3 on the MoDeNa website. + + In order to start the detailed model, the input values for the model are first written to the + file "in.txt". The detailed model code picks them up from this file and performs the according + calculation. Once it is done, the output value is written to the file "out.txt". This FireTask + then reads in the calculated density from "out.txt" and inserts this value into the + database. + """ + + def run_task(self, fw_spec): + print( + term.yellow + + "Performing exact simulation (microscopic code recipe)" + + term.normal + ) + + # Write input for detailed model + ff = open('in.txt', 'w') + Tstr = str(self['point']['T']) + ff.write('%s \n' %(Tstr)) + + + ##TODO INPUT SHOULD COME FROM IndexSet + + ff.write('2 \n') #number of components in system + ff.write('air \n') #component 1 + ff.write('pu \n') #component 2 + ff.write('0. \n') #molar feed (initial) composition component 1 + ff.write('0. \n') #molar feed (initial) composition component 2 + ff.close() + + #create output file for detailed code + fff = open('out.txt', 'w+') + fff.close() + + # Execute detailed model + os.system('../src/PCSAFT_Density') + + # Analyse output + f = open('out.txt', 'r') + self['point']['rho'] = float(f.readline()) + f.close() + + return FWAction(mod_spec=[{'_push': self['point']}]) + + + + + + +f = CFunction( + Ccode= ''' +#include "modena.h" +#include "math.h" + +void surroDensity +( + const double* parameters, + const double* inherited_inputs, + const double* inputs, + double *outputs +) +{ + + const double T = inputs[0]; + + const double P0 = parameters[0]; + const double P1 = parameters[1]; + const double P2 = parameters[2]; + + // const double expo = 1.0 + (1.0 - T/P2); + // const double pwr = pow(P1,expo); + + // outputs[0] = P0 / pwr; + + + outputs[0] = P0 + T*P1 + P2*T*T; +} +''', + # These are global bounds for the function + inputs={ + 'T': { 'min': 270.0, 'max': 300.0, 'argPos': 0 }, #check if boundaries reasonable, from this range, the random values for the DOE are chosen! + }, + outputs={ + 'rho': { 'min': 9e99, 'max': -9e99, 'argPos': 0 }, + }, + parameters={ + 'param0': { 'min': -1E10, 'max': 1E10, 'argPos': 0 }, #check if boundaries are reasonable!!! + 'param1': { 'min': -1E10, 'max': 1E10, 'argPos': 1 }, + 'param2': { 'min': -1E10, 'max': 1E10, 'argPos': 2 }, + }, +) + +m = BackwardMappingModel( + _id= 'Density', + surrogateFunction= f, + exactTask= DensityExactSim(), + substituteModels= [ ], + initialisationStrategy= Strategy.InitialPoints( + initialPoints= + { + 'T': [270.0, 290.0, 300.0], + }, + ), + outOfBoundsStrategy= Strategy.ExtendSpaceStochasticSampling( + nNewPoints= 4 + ), + parameterFittingStrategy= Strategy.NonLinFitWithErrorContol( + testDataPercentage= 0.2, + maxError= 300.0, + improveErrorStrategy= Strategy.StochasticSampling( + nNewPoints= 2 + ), + maxIterations= 5 # Currently not used + ), +) + diff --git a/applications/PUfoam/MoDeNaModels/PolymerDensity/ExampleOfUsage/src/.gitignore b/applications/PUfoam/MoDeNaModels/PolymerDensity/ExampleOfUsage/src/.gitignore new file mode 100644 index 000000000..0c66e77c1 --- /dev/null +++ b/applications/PUfoam/MoDeNaModels/PolymerDensity/ExampleOfUsage/src/.gitignore @@ -0,0 +1,20 @@ +# Backups +*~ +*bak + +# Various intermediate files from automake +CMakeFiles/ +Makefile +libmodena.pc +CMakeCache.txt +cmake_install.cmake +install_manifest.txt + +# Intermediate files generated by SWIG +*_wrap.c + +# locate results (executables and libraries) +*.l[ao] + +flowRateExact +twoTanksMacroscopicProblem diff --git a/applications/PUfoam/MoDeNaModels/PolymerDensity/ExampleOfUsage/src/CMakeLists.txt b/applications/PUfoam/MoDeNaModels/PolymerDensity/ExampleOfUsage/src/CMakeLists.txt new file mode 100644 index 000000000..c2e39aabe --- /dev/null +++ b/applications/PUfoam/MoDeNaModels/PolymerDensity/ExampleOfUsage/src/CMakeLists.txt @@ -0,0 +1,47 @@ +cmake_minimum_required (VERSION 2.8) + +# I am specifying two projects in the same Cmake file (not sure if good idea) +project (PCSAFT_Density C CXX Fortran) +project (MacroscopicProblem C) + +if( CMAKE_VERSION VERSION_GREATER "3.0" ) + cmake_policy(SET CMP0042 OLD) + cmake_policy(SET CMP0026 OLD) + cmake_policy(SET CMP0028 OLD) +endif() + +set(CMAKE_BUILD_TYPE Release) + +add_custom_target(debug + COMMAND ${CMAKE_COMMAND} -DCMAKE_BUILD_TYPE=Debug ${CMAKE_SOURCE_DIR} + COMMAND ${CMAKE_COMMAND} --build ${CMAKE_BINARY_DIR} --target all + COMMENT "Switch CMAKE_BUILD_TYPE to Debug" + ) + +add_custom_target(release + COMMAND ${CMAKE_COMMAND} -DCMAKE_BUILD_TYPE=Release ${CMAKE_SOURCE_DIR} + COMMAND ${CMAKE_COMMAND} --build ${CMAKE_BINARY_DIR} --target all + COMMENT "Switch CMAKE_BUILD_TYPE to Release" + ) + +find_package(MODENA REQUIRED) + +include(CheckCInline) +check_c_inline(C_INLINE) + +# ---------------------------------------------------------------------------- +# NOTE: +# This will look through **all** subdirectories and find **any** FORTRAN file +# it will then attempt to to compile and link all the files together. +# ------> FRAGILE <------ +file(GLOB FORTRANFILES ${CMAKE_CURRENT_SOURCE_DIR}/*/*.f90) +add_executable(PCSAFT_Density ${FORTRANFILES}) +set_target_properties(PCSAFT_Density PROPERTIES COMPILE_FLAGS "-fdefault-real-8") +target_link_libraries(PCSAFT_Density MODENA::modena) + +# ---------------------------------------------------------------------------- +# Compile C project +add_executable(MacroscopicProblem MacroscopicProblem.C) +target_link_libraries(MacroscopicProblem MODENA::modena) + + diff --git a/applications/PUfoam/MoDeNaModels/PolymerDensity/ExampleOfUsage/src/MacroscopicProblem.C b/applications/PUfoam/MoDeNaModels/PolymerDensity/ExampleOfUsage/src/MacroscopicProblem.C new file mode 100644 index 000000000..b1fc312a4 --- /dev/null +++ b/applications/PUfoam/MoDeNaModels/PolymerDensity/ExampleOfUsage/src/MacroscopicProblem.C @@ -0,0 +1,108 @@ +/* + + ooo ooooo oooooooooo. ooooo ooo + `88. .888' `888' `Y8b `888b. `8' + 888b d'888 .ooooo. 888 888 .ooooo. 8 `88b. 8 .oooo. + 8 Y88. .P 888 d88' `88b 888 888 d88' `88b 8 `88b. 8 `P )88b + 8 `888' 888 888 888 888 888 888ooo888 8 `88b.8 .oP"888 + 8 Y 888 888 888 888 d88' 888 .o 8 `888 d8( 888 + o8o o888o `Y8bod8P' o888bood8P' `Y8bod8P' o8o `8 `Y888""8o + +Copyright + 2014-2015 MoDeNa Consortium, All rights reserved. + +License + This file is part of Modena. + + Modena is free software; you can redistribute it and/or modify it under + the terms of the GNU General Public License as published by the Free + Software Foundation, either version 3 of the License, or (at your option) + any later version. + + Modena is distributed in the hope that it will be useful, but WITHOUT ANY + WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS + FOR A PARTICULAR PURPOSE. See the GNU General Public License + for more details. + + You should have received a copy of the GNU General Public License along + with Modena. If not, see . + +Description + Solving the two tank problem the MoDeNa way. + + A prototypical macros-scopic code embeds a micro-scale model (flowRate) + through the MoDeNa interface library. + +Authors + Henrik Rusche + +Contributors +*/ + +#include +#include +#include "modena.h" + +using namespace std; + +int +main(int argc, char *argv[]) +{ + double T = 270; + double Tend = 290.0; + + // Instantiate index set + //modena_index_set_t *indexSet = modena_index_set_new("species"); + + + // Instantiate a model + modena_model_t *model = modena_model_new("Density"); //muss das FunctionModule genau so heißen?? + if(modena_error_occurred()) + { + return modena_error(); + } + + // Allocate memory and fetch arg positions + modena_inputs_t *inputs = modena_inputs_new(model); //How many inputs and outputs is defined in the function module!! + modena_outputs_t *outputs = modena_outputs_new(model); + + + size_t Tpos = modena_model_inputs_argPos(model, "T"); + + modena_model_argPos_check(model); + + + while(T < Tend) + { + // Set input vector + modena_inputs_set(inputs, Tpos, T); + + // Call the model + int ret = modena_model_call(model, inputs, outputs); + + // Terminate, if requested + if(modena_error_occurred()) + { + modena_inputs_destroy(inputs); + modena_outputs_destroy(outputs); + modena_model_destroy(model); + + return modena_error(); + } + + // Fetch result + double rho = modena_outputs_get(outputs, 0); + + cout << "T = " << T; + + + T = T + 10.0; + } + + + modena_inputs_destroy(inputs); + modena_outputs_destroy(outputs); + modena_model_destroy(model); + + return 0; +} diff --git a/applications/PUfoam/MoDeNaModels/PolymerDensity/ExampleOfUsage/src/srcDetailedCode/Numeric_subroutines.f90 b/applications/PUfoam/MoDeNaModels/PolymerDensity/ExampleOfUsage/src/srcDetailedCode/Numeric_subroutines.f90 new file mode 100644 index 000000000..7a243184b --- /dev/null +++ b/applications/PUfoam/MoDeNaModels/PolymerDensity/ExampleOfUsage/src/srcDetailedCode/Numeric_subroutines.f90 @@ -0,0 +1,1667 @@ +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! + SUBROUTINE bicub_derivative ( ya, x1a, x2a, y1a, y2a, y12a, i_max, k_max ) +! + USE DFT_MODULE, ONLY: NDFT, r_grid + IMPLICIT NONE +! +! ---------------------------------------------------------------------- + REAL, INTENT(IN) :: ya(r_grid,NDFT) + REAL, INTENT(IN) :: x1a(r_grid) + REAL, INTENT(IN) :: x2a(NDFT) + REAL, INTENT(OUT) :: y1a(r_grid,NDFT) + REAL, INTENT(OUT) :: y2a(r_grid,NDFT) + REAL, INTENT(OUT) :: y12a(r_grid,NDFT) + INTEGER, INTENT(IN) :: i_max + INTEGER, INTENT(IN) :: k_max +! +! ---------------------------------------------------------------------- + INTEGER :: i, k +! ---------------------------------------------------------------------- + + +DO i = 2, i_max-1 + DO k = 2, k_max-1 + y1a(i,k) = (ya(i+1,k)-ya(i-1,k)) / (x1a(i+1)-x1a(i-1)) + y2a(i,k) = (ya(i,k+1)-ya(i,k-1)) / (x2a(k+1)-x2a(k-1)) + y12a(i,k)= (ya(i+1,k+1)-ya(i+1,k-1)-ya(i-1,k+1)+ya(i-1,k-1)) & + /((x1a(i+1)-x1a(i-1))*(x2a(k+1)-x2a(k-1))) + END DO +END DO + +i = 1 +DO k = 1, k_max + y1a(i,k) = 0.0 + y2a(i,k) = 0.0 + y12a(i,k)= 0.0 +END DO + +k = 1 +DO i = 1, i_max + y1a(i,k) = 0.0 + y2a(i,k) = 0.0 + y12a(i,k)= 0.0 +END DO + + +i = i_max +DO k = 2, k_max-1 + y1a(i,k) = (ya(i,k)-ya(i-1,k)) / (x1a(i)-x1a(i-1)) + y2a(i,k) = (ya(i,k+1)-ya(i,k-1)) / (x2a(k+1)-x2a(k-1)) + y12a(i,k)= (ya(i,k+1)-ya(i,k-1)-ya(i-1,k+1)+ya(i-1,k-1)) & + /((x1a(i)-x1a(i-1))*(x2a(k+1)-x2a(k-1))) +END DO + + +k = k_max +DO i = 2, i_max-1 + y1a(i,k) = (ya(i+1,k)-ya(i-1,k)) / (x1a(i+1)-x1a(i-1)) + y2a(i,k) = (ya(i,k)-ya(i,k-1)) / (x2a(k)-x2a(k-1)) + y12a(i,k)= (ya(i+1,k)-ya(i+1,k-1)-ya(i-1,k)+ya(i-1,k-1)) & + /((x1a(i+1)-x1a(i-1))*(x2a(k)-x2a(k-1))) +END DO + +k = k_max +i = i_max +y1a(i,k) = (ya(i,k)-ya(i-1,k)) / (x1a(i)-x1a(i-1)) +y2a(i,k) = (ya(i,k)-ya(i,k-1)) / (x2a(k)-x2a(k-1)) +y12a(i,k)= (ya(i,k)-ya(i,k-1)-ya(i-1,k)+ya(i-1,k-1)) & + /((x1a(i)-x1a(i-1))*(x2a(k)-x2a(k-1))) + +END SUBROUTINE bicub_derivative + + +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! + SUBROUTINE bicub_c ( ya, x1a, x2a, y1a, y2a, y12a, c_bicub, i_max, k_max ) +! + USE DFT_MODULE, ONLY: NDFT, r_grid + IMPLICIT NONE +! +! ---------------------------------------------------------------------- + REAL, INTENT(IN) :: ya(r_grid,NDFT) + REAL, INTENT(IN) :: x1a(r_grid) + REAL, INTENT(IN) :: x2a(NDFT) + REAL, INTENT(IN) :: y1a(r_grid,NDFT) + REAL, INTENT(IN) :: y2a(r_grid,NDFT) + REAL, INTENT(IN) :: y12a(r_grid,NDFT) + REAL, INTENT(OUT) :: c_bicub(r_grid,NDFT,4,4) + INTEGER, INTENT(IN) :: i_max + INTEGER, INTENT(IN) :: k_max +! +! ---------------------------------------------------------------------- + INTEGER :: i, k, m, n + REAL :: y(4),y1(4),y2(4),y12(4),x1l,x1u,x2l,x2u + REAL :: c(4,4) +! ---------------------------------------------------------------------- + +DO i = 1, i_max-1 + DO k = 1, k_max-1 + y(1)=ya(i,k) + y(2)=ya(i+1,k) + y(3)=ya(i+1,k+1) + y(4)=ya(i,k+1) + + y1(1)=y1a(i,k) + y1(2)=y1a(i+1,k) + y1(3)=y1a(i+1,k+1) + y1(4)=y1a(i,k+1) + + y2(1)=y2a(i,k) + y2(2)=y2a(i+1,k) + y2(3)=y2a(i+1,k+1) + y2(4)=y2a(i,k+1) + + y12(1)=y12a(i,k) + y12(2)=y12a(i+1,k) + y12(3)=y12a(i+1,k+1) + y12(4)=y12a(i,k+1) + + x1l=x1a(i) + x1u=x1a(i+1) + x2l=x2a(k) + x2u=x2a(k+1) + + CALL bcucof(y,y1,y2,y12,x1u-x1l,x2u-x2l,c) + DO m=1,4 + DO n=1,4 + c_bicub(i,k,m,n)=c(m,n) + END DO + END DO + + END DO +END DO + +END SUBROUTINE bicub_c + +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! + SUBROUTINE bcucof(y,y1,y2,y12,d1,d2,c) +! + IMPLICIT NONE +! +! ---------------------------------------------------------------------- + REAL, INTENT(IN) :: y(4) + REAL, INTENT(IN) :: y1(4) + REAL, INTENT(IN) :: y2(4) + REAL, INTENT(IN) :: y12(4) + REAL, INTENT(IN) :: d1 + REAL, INTENT(IN) :: d2 + REAL, INTENT(OUT) :: c(4,4) +! +! ---------------------------------------------------------------------- + INTEGER :: i,j,k,l + REAL :: d1d2,xx,cl(16),wt(16,16),x(16) + SAVE wt + DATA wt/1,0,-3,2,4*0,-3,0,9,-6,2,0,-6,4,8*0,3,0,-9,6,-2,0,6,-4,10* & + 0,9,-6,2*0,-6,4,2*0,3,-2,6*0,-9,6,2*0,6,-4,4*0,1,0,-3,2,-2,0,6,-4, & + 1,0,-3,2,8*0,-1,0,3,-2,1,0,-3,2,10*0,-3,2,2*0,3,-2,6*0,3,-2,2*0, & + -6,4,2*0,3,-2,0,1,-2,1,5*0,-3,6,-3,0,2,-4,2,9*0,3,-6,3,0,-2,4,-2, & + 10*0,-3,3,2*0,2,-2,2*0,-1,1,6*0,3,-3,2*0,-2,2,5*0,1,-2,1,0,-2,4, & + -2,0,1,-2,1,9*0,-1,2,-1,0,1,-2,1,10*0,1,-1,2*0,-1,1,6*0,-1,1,2*0, & + 2,-2,2*0,-1,1/ +! ---------------------------------------------------------------------- + +d1d2 = d1 * d2 +DO i = 1, 4 + x(i) = y(i) + x(i+4) = y1(i)*d1 + x(i+8) = y2(i)*d2 + x(i+12) = y12(i)*d1d2 +END DO +DO i = 1, 16 + xx = 0.0 + DO k = 1, 16 + xx = xx + wt(i,k) * x(k) + END DO + cl(i) = xx +END DO +l = 0 +DO i = 1, 4 + DO j = 1, 4 + l = l + 1 + c(i,j) = cl(l) + END DO +END DO + +END SUBROUTINE bcucof + + +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! + SUBROUTINE BI_CUB_SPLINE ( rho_rdf, xg, ya, x1a, x2a, y1a, y2a, y12a, & + c_bicub, rdf, dg_drho, dg_dr, i_max, ih, k ) +! + USE DFT_MODULE, ONLY: NDFT, r_grid + IMPLICIT NONE +! +! ---------------------------------------------------------------------- + REAL, INTENT(IN OUT) :: rho_rdf + REAL, INTENT(IN OUT) :: xg + REAL, INTENT(IN) :: ya(r_grid,NDFT) + REAL, INTENT(IN) :: x1a(r_grid) + REAL, INTENT(IN) :: x2a(NDFT) + REAL, INTENT(IN) :: y1a(r_grid,NDFT) + REAL, INTENT(IN) :: y2a(r_grid,NDFT) + REAL, INTENT(IN) :: y12a(r_grid,NDFT) + REAL, INTENT(IN) :: c_bicub(r_grid,NDFT,4,4) + REAL, INTENT(OUT) :: rdf + REAL, INTENT(OUT) :: dg_drho + REAL, INTENT(OUT) :: dg_dr + INTEGER, INTENT(IN OUT) :: i_max + !INTEGER, INTENT(IN OUT) :: k_max + INTEGER, INTENT(OUT) :: ih + INTEGER, INTENT(IN) :: k +! +! ---------------------------------------------------------------------- + INTEGER :: m, n + + REAL :: y(4),y1(4),y2(4),y12(4),x1l,x1u,x2l,x2u + REAL :: c(4,4) +! ---------------------------------------------------------------------- + +IF ( rho_rdf < x1a(1) ) THEN + dg_drho = 0.0 + dg_dr = 0.0 + rdf = 1.0 + RETURN +END IF +IF ( x1a(ih) <= rho_rdf .AND. rho_rdf < x1a(ih+1) ) GO TO 10 +IF ( ih > 2 ) THEN + IF ( x1a(ih-1) <= rho_rdf .AND. rho_rdf < x1a(ih) ) THEN + ih = ih - 1 + GO TO 10 + END IF +END IF +! write (*,*) 'in ',ih +CALL hunt ( x1a, i_max, rho_rdf, ih ) +! write (*,*) 'out',ih +10 CONTINUE +IF ( x2a(k) /= xg ) THEN +! write (*,*) 'error bi-cubic-spline',k,x2a(k),xg +! DO k=1,NDFT +! write (*,*) k,x2a(k) +! ENDDO +! stop +END IF + + + +y(1) = ya(ih,k) +y(2) = ya(ih+1,k) +y(3) = ya(ih+1,k+1) +y(4) = ya(ih,k+1) + +y1(1) = y1a(ih,k) +y1(2) = y1a(ih+1,k) +y1(3) = y1a(ih+1,k+1) +y1(4) = y1a(ih,k+1) + +y2(1) = y2a(ih,k) +y2(2) = y2a(ih+1,k) +y2(3) = y2a(ih+1,k+1) +y2(4) = y2a(ih,k+1) + +y12(1) = y12a(ih,k) +y12(2) = y12a(ih+1,k) +y12(3) = y12a(ih+1,k+1) +y12(4) = y12a(ih,k+1) + +x1l = x1a(ih) +x1u = x1a(ih+1) +x2l = x2a(k) +x2u = x2a(k+1) + +DO m = 1, 4 + DO n = 1, 4 + c(m,n) = c_bicub( ih, k, m, n ) + END DO +END DO +CALL bcuint ( x1l, x1u, x2l, x2u, rho_rdf, xg, c, rdf, dg_drho, dg_dr ) + +END SUBROUTINE BI_CUB_SPLINE + +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! SUBROUTINE hunt +! +! Given an array xx(1:n), and given a value x, returns a value jlo +! such that x is between xx(jlo) and xx(jlo+1). xx(1:n) must be +! monotonic, either increasing or decreasing. jlo=0 or jlo=n is +! returned to indicate that x is out of range. jlo on input is taken +! as the initial guess for jlo on output. +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! + SUBROUTINE hunt ( xx, n, x, jlo ) +! + IMPLICIT NONE +! +! ---------------------------------------------------------------------- + INTEGER, INTENT(IN) :: n + INTEGER, INTENT(OUT) :: jlo + REAL, INTENT(IN) :: xx(n) + REAL :: x +! +! ---------------------------------------------------------------------- + INTEGER :: inc,jhi,jm + LOGICAL :: ascnd +! ---------------------------------------------------------------------- + +ascnd = xx(n) >= xx(1) +IF( jlo <= 0 .OR. jlo > n ) THEN + jlo = 0 + jhi = n + 1 + GO TO 3 +END IF +inc = 1 +IF( x >= xx(jlo) .EQV. ascnd ) THEN +1 jhi = jlo + inc + IF ( jhi > n ) THEN + jhi = n + 1 + ELSE IF ( x >= xx(jhi) .EQV. ascnd ) THEN + jlo = jhi + inc = inc + inc + GO TO 1 + END IF +ELSE + jhi = jlo +2 jlo = jhi - inc + IF ( jlo < 1 ) THEN + jlo = 0 + ELSE IF ( x < xx(jlo) .EQV. ascnd ) THEN + jhi = jlo + inc = inc + inc + GO TO 2 + END IF +END IF +3 IF (jhi-jlo == 1 ) THEN + IF ( x == xx(n)) jlo = n - 1 + IF ( x == xx(1) ) jlo = 1 + RETURN +END IF +jm = ( jhi + jlo ) / 2 +IF ( x >= xx(jm) .EQV. ascnd ) THEN + jlo = jm +ELSE + jhi = jm +END IF +GO TO 3 +END SUBROUTINE hunt + + + +!********************************************************************** +! +!********************************************************************** +! + !SUBROUTINE bcuint ( y, y1, y2, y12, x1l, x1u, x2l, x2u, x1, x2, c, ansy, ansy1, ansy2 ) + SUBROUTINE bcuint ( x1l, x1u, x2l, x2u, x1, x2, c, ansy, ansy1, ansy2 ) +! + IMPLICIT NONE +! +! ---------------------------------------------------------------------- + !REAL, INTENT(IN OUT) :: y(4) + !REAL, INTENT(IN OUT) :: y1(4) + !REAL, INTENT(IN OUT) :: y2(4) + !REAL, INTENT(IN OUT) :: y12(4) + REAL, INTENT(IN OUT) :: x1l + REAL, INTENT(IN OUT) :: x1u + REAL, INTENT(IN OUT) :: x2l + REAL, INTENT(IN OUT) :: x2u + REAL, INTENT(IN OUT) :: x1 + REAL, INTENT(IN OUT) :: x2 + REAL, INTENT(IN) :: c(4,4) + REAL, INTENT(OUT) :: ansy + REAL, INTENT(OUT) :: ansy1 + REAL, INTENT(OUT) :: ansy2 +! +! ---------------------------------------------------------------------- + !U USES bcucof + INTEGER :: i + REAL :: t, u +! ---------------------------------------------------------------------- + +! call bcucof ( y, y1, y2, y12, x1u-x1l, x2u-x2l, c ) + +IF ( x1u == x1l .OR. x2u == x2l ) PAUSE 'bad input in bcuint' +t = (x1-x1l) / (x1u-x1l) +u = (x2-x2l) / (x2u-x2l) +ansy = 0.0 +ansy2 = 0.0 +ansy1 = 0.0 +DO i = 4, 1, -1 + ansy = t *ansy + ( (c(i,4)*u + c(i,3))*u+c(i,2) )*u + c(i,1) + ansy2 = t *ansy2 + ( 3.*c(i,4)*u+2.*c(i,3) )*u + c(i,2) + ansy1 = u *ansy1 + ( 3.*c(4,i)*t+2.*c(3,i) )*t + c(2,i) +END DO +ansy1 = ansy1 / (x1u-x1l) +ansy2 = ansy2 / (x2u-x2l) + +END SUBROUTINE bcuint + + +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! SUBROUTINE spline +! +! Given arrays x(1:n) and y(1:n) containing a tabulated function, +! i.e., yi = f(xi), with x1 < x2 < .. . < xN, and given values yp1 and +! ypn for the first derivative of the interpolating function at points 1 +! and n, respectively, this routine returns an array y2(1:n) of length n +! which contains the second derivatives of the interpolating function at +! the tabulated points xi. If yp1 and/or ypn are equal to 1 1030 or +! larger, the routine is signaled to set the corresponding boundary +! condition for a natural spline, with zero second derivative on that +! boundary. +! Parameter: NMAX is the largest anticipated value of n. +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! + SUBROUTINE spline ( x, y, n, yp1, ypn, y2 ) +! + IMPLICIT NONE +! +! ---------------------------------------------------------------------- + INTEGER, INTENT(IN) :: n + REAL, INTENT(IN) :: x(n) + REAL, INTENT(IN) :: y(n) + REAL, INTENT(IN) :: yp1 + REAL, INTENT(IN) :: ypn + REAL, INTENT(OUT) :: y2(n) +! +! ---------------------------------------------------------------------- + INTEGER, PARAMETER :: NMAX = 500 + INTEGER :: i, k + REAL :: p, qn, sig, un, u(NMAX) +! ---------------------------------------------------------------------- + + IF ( yp1 > 0.99E30 ) THEN + y2(1) = 0.0 + u(1) = 0.0 + ELSE + y2(1) = -0.5 + u(1) = ( 3.0/(x(2)-x(1)) ) * ( (y(2)-y(1))/(x(2)-x(1))-yp1 ) + END IF + DO i = 2, n-1 + IF ( (x(i+1)-x(i)) == 0.0 .OR. (x(i)-x(i-1)) == 0.0 .OR. (x(i+1)-x(i-1)) == 0.0 ) THEN + write (*,*) 'error in spline-interpolation' + stop + END IF + sig = (x(i)-x(i-1)) / (x(i+1)-x(i-1)) + p = sig*y2(i-1) + 2.0 + y2(i) = (sig-1.0) / p + u(i) = ( 6.0 * ((y(i+1)-y(i))/(x(i+1)-x(i))-(y(i)-y(i-1))/(x(i)-x(i-1))) / (x(i+1)-x(i-1)) & + - sig * u(i-1) ) / p + END DO + IF ( ypn > 0.99E30 ) THEN + qn = 0.0 + un = 0.0 + ELSE + qn = 0.5 + un = (3.0/(x(n)-x(n-1))) * (ypn-(y(n)-y(n-1))/(x(n)-x(n-1))) + END IF + y2(n) = (un-qn*u(n-1)) / (qn*y2(n-1)+1.0) + DO k = n-1, 1, -1 + y2(k) = y2(k) * y2(k+1) + u(k) + END DO + +END SUBROUTINE spline + +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! SUBROUTINE splint_integral +! +! Given the arrays xa(1:n) and ya(1:n) of length n, which tabulate a +! function (with the in order), and given the array y2a(1:n), which is +! the output from spline above, and given a value of x, this routine +! returns a cubic-spline interpolated value y. +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! + SUBROUTINE splint_integral ( xa, ya, y2a, n, xlo, xhi, integral ) +! + IMPLICIT NONE +! +! ---------------------------------------------------------------------- + INTEGER, INTENT(IN) :: n + REAL, INTENT(IN) :: xa(n) + REAL, INTENT(IN) :: ya(n) + REAL, INTENT(IN) :: y2a(n) + REAL, INTENT(IN) :: xlo + REAL, INTENT(IN) :: xhi + REAL, INTENT(OUT) :: integral +! +! ---------------------------------------------------------------------- + INTEGER :: k, khi_l, klo_l, khi_h, klo_h + REAL :: xl, xh, h, INT, x0, x1, y0, y1, y20, y21 +! ---------------------------------------------------------------------- + + integral = 0.0 + klo_l = 1 + khi_l = n +1 IF ( khi_l-klo_l > 1 ) THEN + k = ( khi_l + klo_l ) / 2 + IF ( xa(k) > xlo ) THEN + khi_l = k + ELSE + klo_l = k + END IF + GO TO 1 + END IF + + klo_h = 1 + khi_h = n +2 IF ( khi_h-klo_h > 1 ) THEN + k = ( khi_h + klo_h ) / 2 + IF ( xa(k) > xhi ) THEN + khi_h = k + ELSE + klo_h = k + END IF + GO TO 2 + END IF + + ! integration in spline pieces, the lower interval, bracketed + ! by xa(klo_L) and xa(khi_L) is in steps shifted upward. + + ! first: determine upper integration bound + xl = xlo +3 CONTINUE + IF ( khi_h > khi_l ) THEN + xh = xa(khi_l) + ELSE IF ( khi_h == khi_l ) THEN + xh = xhi + ELSE + WRITE (*,*) 'error in spline-integration' + PAUSE + END IF + + h = xa(khi_l) - xa(klo_l) + IF ( h == 0.0 ) PAUSE 'bad xa input in splint' + x0 = xa(klo_l) + x1 = xa(khi_l) + y0 = ya(klo_l) + y1 = ya(khi_l) + y20= y2a(klo_l) + y21= y2a(khi_l) + ! int = -xL/h * ( (x1-.5*xL)*y0 + (0.5*xL-x0)*y1 & + ! +y20/6.*(x1**3-1.5*xL*x1*x1+xL*xL*x1-.25*xL**3) & + ! -y20/6.*h*h*(x1-.5*xL) & + ! +y21/6.*(.25*xL**3-xL*xL*x0+1.5*xL*x0*x0-x0**3) & + ! -y21/6.*h*h*(.5*xL-x0) ) + ! int = int + xH/h * ( (x1-.5*xH)*y0 + (0.5*xH-x0)*y1 & + ! +y20/6.*(x1**3-1.5*xH*x1*x1+xH*xH*x1-.25*xH**3) & + ! -y20/6.*h*h*(x1-.5*xH) & + ! +y21/6.*(.25*xH**3-xH*xH*x0+1.5*xH*x0*x0-x0**3) & + ! -y21/6.*h*h*(.5*xH-x0) ) + INT = -1.0/h * ( xl*((x1-.5*xl)*y0 + (0.5*xl-x0)*y1) & + -y20/24.*(x1-xl)**4 + y20/6.*(0.5*xl*xl-x1*xl)*h*h & + +y21/24.*(xl-x0)**4 - y21/6.*(0.5*xl*xl-x0*xl)*h*h ) + INT = INT + 1.0/h * ( xh*((x1-.5*xh)*y0 + (0.5*xh-x0)*y1) & + -y20/24.*(x1-xh)**4 + y20/6.*(0.5*xh*xh-x1*xh)*h*h & + +y21/24.*(xh-x0)**4 - y21/6.*(0.5*xh*xh-x0*xh)*h*h ) + + integral = integral + INT + ! write (*,*) integral,x1,xH + klo_l = klo_l + 1 + khi_l = khi_l + 1 + xl = x1 + IF (khi_h /= (khi_l-1)) GO TO 3 ! the -1 in (khi_L-1) because khi_L was already counted up + +END SUBROUTINE splint_integral + + + + +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! + REAL FUNCTION praxis( t0, machep, h0, n, prin, x, f, fmin ) + + IMPLICIT NONE + +! ---------------------------------------------------------------------- + REAL, INTENT(IN OUT) :: t0 + REAL, INTENT(IN) :: machep + REAL, INTENT(IN) :: h0 + INTEGER :: n + INTEGER, INTENT(IN OUT) :: prin + REAL, INTENT(IN OUT) :: x(n) + REAL :: f + REAL, INTENT(IN OUT) :: fmin +! ---------------------------------------------------------------------- + +EXTERNAL f + +! PRAXIS RETURNS THE MINIMUM OF THE FUNCTION F(X,N) OF N VARIABLES +! USING THE PRINCIPAL AXIS METHOD. THE GRADIENT OF THE FUNCTION IS +! NOT REQUIRED. + +! FOR A DESCRIPTION OF THE ALGORITHM, SEE CHAPTER SEVEN OF +! "ALGORITHMS FOR FINDING ZEROS AND EXTREMA OF FUNCTIONS WITHOUT +! CALCULATING DERIVATIVES" BY RICHARD P BRENT. + +! THE PARAMETERS ARE: +! T0 IS A TOLERANCE. PRAXIS ATTEMPTS TO RETURN PRAXIS=F(X) +! SUCH THAT IF X0 IS THE TRUE LOCAL MINIMUM NEAR X, THEN +! NORM(X-X0) < T0 + SQUAREROOT(MACHEP)*NORM(X). +! MACHEP IS THE MACHINE PRECISION, THE SMALLEST NUMBER SUCH THAT +! 1 + MACHEP > 1. MACHEP SHOULD BE 16.**-13 (ABOUT +! 2.22D-16) FOR REAL*8 ARITHMETIC ON THE IBM 360. +! H0 IS THE MAXIMUM STEP SIZE. H0 SHOULD BE SET TO ABOUT THE +! MAXIMUM DISTANCE FROM THE INITIAL GUESS TO THE MINIMUM. +! (IF H0 IS SET TOO LARGE OR TOO SMALL, THE INITIAL RATE OF +! CONVERGENCE MAY BE SLOW.) +! N (AT LEAST TWO) IS THE NUMBER OF VARIABLES UPON WHICH +! THE FUNCTION DEPENDS. +! PRIN CONTROLS THE PRINTING OF INTERMEDIATE RESULTS. +! IF PRIN=0, NOTHING IS PRINTED. +! IF PRIN=1, F IS PRINTED AFTER EVERY N+1 OR N+2 LINEAR +! MINIMIZATIONS. FINAL X IS PRINTED, BUT INTERMEDIATE X IS +! PRINTED ONLY IF N IS AT MOST 4. +! IF PRIN=2, THE SCALE FACTORS AND THE PRINCIPAL VALUES OF +! THE APPROXIMATING QUADRATIC FORM ARE ALSO PRINTED. +! IF PRIN=3, X IS ALSO PRINTED AFTER EVERY FEW LINEAR +! MINIMIZATIONS. +! IF PRIN=4, THE PRINCIPAL VECTORS OF THE APPROXIMATING +! QUADRATIC FORM ARE ALSO PRINTED. +! X IS AN ARRAY CONTAINING ON ENTRY A GUESS OF THE POINT OF +! MINIMUM, ON RETURN THE ESTIMATED POINT OF MINIMUM. +! F(X,N) IS THE FUNCTION TO BE MINIMIZED. F SHOULD BE A REAL*8 +! FUNCTION DECLARED EXTERNAL IN THE CALLING PROGRAM. +! FMIN IS AN ESTIMATE OF THE MINIMUM, USED ONLY IN PRINTING +! INTERMEDIATE RESULTS. +! THE APPROXIMATING QUADRATIC FORM IS +! Q(X') = F(X,N) + (1/2) * (X'-X)-TRANSPOSE * A * (X'-X) +! WHERE X IS THE BEST ESTIMATE OF THE MINIMUM AND A IS +! INVERSE(V-TRANSPOSE) * D * INVERSE(V) +! (V(*,*) IS THE MATRIX OF SEARCH DIRECTIONS; D(*) IS THE ARRAY +! OF SECOND DIFFERENCES). IF F HAS CONTINUOUS SECOND DERIVATIVES +! NEAR X0, A WILL TEND TO THE HESSIAN OF F AT X0 AS X APPROACHES X0. + +! IT IS ASSUMED THAT ON FLOATING-POINT UNDERFLOW THE RESULT IS SET +! TO ZERO. +! THE USER SHOULD OBSERVE THE COMMENT ON HEURISTIC NUMBERS AFTER +! THE INITIALIZATION OF MACHINE DEPENDENT NUMBERS. + + LOGICAL :: illc + INTEGER :: nl,nf,kl,kt,ktm,idim,i,j,k,k2,km1,klmk,ii,im1 + REAL :: s,sl,dn,dmin,fx,f1,lds,ldt,t,h,sf,df,qf1,qd0, qd1,qa,qb,qc + REAL :: m2,m4,small,vsmall,large,vlarge,scbd,ldfac,t2, dni,value + REAL :: random + +!.....IF N>20 OR IF N<20 AND YOU NEED MORE SPACE, CHANGE '20' TO THE +! LARGEST VALUE OF N IN THE NEXT CARD, IN THE CARD 'IDIM=20', AND +! IN THE DIMENSION STATEMENTS IN SUBROUTINES MINFIT,MIN,FLIN,QUAD. + + REAL :: d(20),y(20),z(20),q0(20),q1(20),v(20,20) + COMMON /global/ fx,ldt,dmin,nf,nl /q/ v,q0,q1,qa,qb,qc,qd0,qd1,qf1 + +! --------------------------------- +! introduced by Joachim........ + idim = n +! --------------------------------- + + + +!.....INITIALIZATION..... +! MACHINE DEPENDENT NUMBERS: + +small = machep*machep +vsmall = small*small +large = 1.d0/small +vlarge = 1.d0/vsmall +m2 = SQRT(machep) +m4 = SQRT(m2) + +! HEURISTIC NUMBERS: +! IF THE AXES MAY BE BADLY SCALED (WHICH IS TO BE AVOIDED IF +! POSSIBLE), THEN SET SCBD=10. OTHERWISE SET SCBD=1. +! IF THE PROBLEM IS KNOWN TO BE ILL-CONDITIONED, SET ILLC=TRUE. +! OTHERWISE SET ILLC=FALSE. +! KTM IS THE NUMBER OF ITERATIONS WITHOUT IMPROVEMENT BEFORE THE +! ALGORITHM TERMINATES. KTM=4 IS VERY CAUTIOUS; USUALLY KTM=1 +! IS SATISFACTORY. + +scbd = 1.0 +illc = .false. +ktm = 1 + +ldfac = 0.01 +IF (illc) ldfac = 0.1 +kt = 0 +nl = 0 +nf = 1 +fx = f(x,n) +qf1 = fx +t = small+ABS(t0) +t2 = t +dmin = small +h = h0 +IF (h < 100*t) h = 100*t +ldt = h +!.....THE FIRST SET OF SEARCH DIRECTIONS V IS THE IDENTITY MATRIX..... +DO i = 1,n + DO j = 1,n + v(i,j) = 0.0 + END DO + v(i,i) = 1.0 +END DO +d(1) = 0.0 +qd0 = 0.0 +DO i = 1,n + q0(i) = x(i) + q1(i) = x(i) +END DO +IF (prin > 0) CALL PRINT(n,x,prin,fmin) + +!.....THE MAIN LOOP STARTS HERE..... +40 sf=d(1) +d(1)=0.d0 +s=0.d0 + +!.....MINIMIZE ALONG THE FIRST DIRECTION V(*,1). +! FX MUST BE PASSED TO MIN BY VALUE. +value=fx +CALL MIN(n,1,2,d(1),s,value,.false.,f,x,t,machep,h) +IF (s > 0.d0) GO TO 50 +DO i=1,n + v(i,1)=-v(i,1) +END DO +50 IF (sf > 0.9D0*d(1).AND.0.9D0*sf < d(1)) GO TO 70 +DO i=2,n + d(i)=0.d0 +END DO + +!.....THE INNER LOOP STARTS HERE..... +70 DO k=2,n + DO i=1,n + y(i)=x(i) + END DO + sf=fx + IF (kt > 0) illc=.true. + 80 kl=k + df=0.d0 + +!.....A RANDOM STEP FOLLOWS (TO AVOID RESOLUTION VALLEYS). +! PRAXIS ASSUMES THAT RANDOM RETURNS A RANDOM NUMBER UNIFORMLY +! DISTRIBUTED IN (0,1). + + IF(.NOT.illc) GO TO 95 + DO i=1,n + s=(0.1D0*ldt+t2*(10**kt))*(random(n)-0.5D0) + z(i)=s + DO j=1,n + x(j)=x(j)+s*v(j,i) + END DO + END DO + fx=f(x,n) + nf=nf+1 + +!.....MINIMIZE ALONG THE "NON-CONJUGATE" DIRECTIONS V(*,K),...,V(*,N) + + 95 DO k2=k,n + sl=fx + s=0.d0 + value=fx + CALL MIN(n,k2,2,d(k2),s,value,.false.,f,x,t,machep,h) + IF (illc) GO TO 97 + s=sl-fx + GO TO 99 + 97 s=d(k2)*((s+z(k2))**2) + 99 IF (df > s) CYCLE + df=s + kl=k2 + END DO + IF (illc.OR.(df >= ABS((100*machep)*fx))) GO TO 110 + +!.....IF THERE WAS NOT MUCH IMPROVEMENT ON THE FIRST TRY, SET +! ILLC=TRUE AND START THE INNER LOOP AGAIN..... + + illc=.true. + GO TO 80 + 110 IF (k == 2.AND.prin > 1) CALL vcprnt(1,d,n) + +!.....MINIMIZE ALONG THE "CONJUGATE" DIRECTIONS V(*,1),...,V(*,K-1) + + km1=k-1 + DO k2=1,km1 + s=0 + value=fx + CALL MIN(n,k2,2,d(k2),s,value,.false.,f,x,t,machep,h) + END DO + f1=fx + fx=sf + lds=0 + DO i=1,n + sl=x(i) + x(i)=y(i) + sl=sl-y(i) + y(i)=sl + lds=lds+sl*sl + END DO + lds=SQRT(lds) + IF (lds <= small) GO TO 160 + +!.....DISCARD DIRECTION V(*,KL). +! IF NO RANDOM STEP WAS TAKEN, V(*,KL) IS THE "NON-CONJUGATE" +! DIRECTION ALONG WHICH THE GREATEST IMPROVEMENT WAS MADE..... + + klmk=kl-k + IF (klmk < 1) GO TO 141 + DO ii=1,klmk + i=kl-ii + DO j=1,n + v(j,i+1)=v(j,i) + END DO + d(i+1)=d(i) + END DO + 141 d(k)=0 + DO i=1,n + v(i,k)=y(i)/lds + END DO + +!.....MINIMIZE ALONG THE NEW "CONJUGATE" DIRECTION V(*,K), WHICH IS +! THE NORMALIZED VECTOR: (NEW X) - (0LD X)..... + + value=f1 + CALL MIN(n,k,4,d(k),lds,value,.true.,f,x,t,machep,h) + IF (lds > 0.d0) GO TO 160 + lds=-lds + DO i=1,n + v(i,k)=-v(i,k) + END DO + 160 ldt=ldfac*ldt + IF (ldt < lds) ldt=lds + IF (prin > 0) CALL PRINT(n,x,prin,fmin) + t2=0.d0 + DO i=1,n + t2=t2+x(i)**2 + END DO + t2=m2*SQRT(t2)+t + +!.....SEE WHETHER THE LENGTH OF THE STEP TAKEN SINCE STARTING THE +! INNER LOOP EXCEEDS HALF THE TOLERANCE..... + + IF (ldt > (0.5*t2)) kt=-1 + kt=kt+1 + IF (kt > ktm) GO TO 400 +END DO +!.....THE INNER LOOP ENDS HERE. + +! TRY QUADRATIC EXTRAPOLATION IN CASE WE ARE IN A CURVED VALLEY. + +CALL quad(n,f,x,t,machep,h) +dn=0.d0 +DO i=1,n + d(i)=1.d0/SQRT(d(i)) + IF (dn < d(i)) dn=d(i) +END DO +IF (prin > 3) CALL maprnt(1,v,idim,n) +DO j=1,n + s=d(j)/dn + DO i=1,n + v(i,j)=s*v(i,j) + END DO +END DO + +!.....SCALE THE AXES TO TRY TO REDUCE THE CONDITION NUMBER..... + +IF (scbd <= 1.d0) GO TO 200 +s=vlarge +DO i=1,n + sl=0.d0 + DO j=1,n + sl=sl+v(i,j)*v(i,j) + END DO + z(i)=SQRT(sl) + IF (z(i) < m4) z(i)=m4 + IF (s > z(i)) s=z(i) +END DO +DO i=1,n + sl=s/z(i) + z(i)=1.d0/sl + IF (z(i) <= scbd) GO TO 189 + sl=1.d0/scbd + z(i)=scbd + 189 DO j=1,n + v(i,j)=sl*v(i,j) + END DO +END DO + +!.....CALCULATE A NEW SET OF ORTHOGONAL DIRECTIONS BEFORE REPEATING +! THE MAIN LOOP. +! FIRST TRANSPOSE V FOR MINFIT: + +200 DO i=2,n + im1=i-1 + DO j=1,im1 + s=v(i,j) + v(i,j)=v(j,i) + v(j,i)=s + END DO +END DO + +!.....CALL MINFIT TO FIND THE SINGULAR VALUE DECOMPOSITION OF V. +! THIS GIVES THE PRINCIPAL VALUES AND PRINCIPAL DIRECTIONS OF THE +! APPROXIMATING QUADRATIC FORM WITHOUT SQUARING THE CONDITION +! NUMBER..... + +CALL minfit(idim,n,machep,vsmall,v,d) + +!.....UNSCALE THE AXES..... + +IF (scbd <= 1.d0) GO TO 250 +DO i=1,n + s=z(i) + DO j=1,n + v(i,j)=s*v(i,j) + END DO +END DO +DO i=1,n + s=0.d0 + DO j=1,n + s=s+v(j,i)**2 + END DO + s=SQRT(s) + d(i)=s*d(i) + s=1/s + DO j=1,n + v(j,i)=s*v(j,i) + END DO +END DO + +250 DO i=1,n + dni=dn*d(i) + IF (dni > large) GO TO 265 + IF (dni < small) GO TO 260 + d(i)=1/(dni*dni) + CYCLE + 260 d(i)=vlarge + CYCLE + 265 d(i)=vsmall +END DO + +!.....SORT THE EIGENVALUES AND EIGENVECTORS..... + +CALL sort(idim,n,d,v) +dmin=d(n) +IF (dmin < small) dmin=small +illc=.false. +IF (m2*d(1) > dmin) illc=.true. +IF (prin > 1.AND.scbd > 1.d0) CALL vcprnt(2,z,n) +IF (prin > 1) CALL vcprnt(3,d,n) +IF (prin > 3) CALL maprnt(2,v,idim,n) +!.....THE MAIN LOOP ENDS HERE..... + +GO TO 40 + +!.....RETURN..... + +400 IF (prin > 0) CALL vcprnt(4,x,n) +praxis=fx + +END FUNCTION praxis + + +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! + SUBROUTINE minfit(m,n,machep,tol,ab,q) + + IMPLICIT NONE + + INTEGER, INTENT(IN OUT) :: m + INTEGER, INTENT(IN) :: n + REAL, INTENT(IN) :: machep + REAL, INTENT(IN OUT) :: tol + REAL, INTENT(IN OUT) :: ab(m,n) + REAL, INTENT(OUT) :: q(n) + INTEGER :: i,j,k,l, kk,kt,l2,ll2,ii,lp1 +! IMPLICIT REAL (A-H,O-Z) + + +REAL :: x,eps,e(20),g,s, f,h,y,c,z,temp +!...AN IMPROVED VERSION OF MINFIT (SEE GOLUB AND REINSCH, 1969) +! RESTRICTED TO M=N,P=0. +! THE SINGULAR VALUES OF THE ARRAY AB ARE RETURNED IN Q AND AB IS +! OVERWRITTEN WITH THE ORTHOGONAL MATRIX V SUCH THAT U.DIAG(Q) = AB.V, +! WHERE U IS ANOTHER ORTHOGONAL MATRIX. + +!...HOUSEHOLDER'S REDUCTION TO BIDIAGONAL FORM... +IF (n == 1) GO TO 200 +eps = machep +g = 0.d0 +x = 0.d0 +DO i=1,n + e(i) = g + s = 0.d0 + l = i + 1 + DO j=i,n + s = s + ab(j,i)**2 + END DO + g = 0.d0 + IF (s < tol) GO TO 4 + f = ab(i,i) + g = SQRT(s) + IF (f >= 0.d0) g = -g + h = f*g - s + ab(i,i)=f-g + IF (l > n) GO TO 4 + DO j=l,n + f = 0.d0 + DO k=i,n + f = f + ab(k,i)*ab(k,j) + END DO + f = f/h + DO k=i,n + ab(k,j) = ab(k,j) + f*ab(k,i) + END DO + END DO + 4 q(i) = g + s = 0.d0 + IF (i == n) GO TO 6 + DO j=l,n + s = s + ab(i,j)*ab(i,j) + END DO + 6 g = 0.d0 + IF (s < tol) GO TO 10 + IF (i == n) GO TO 16 + f = ab(i,i+1) + 16 g = SQRT(s) + IF (f >= 0.d0) g = -g + h = f*g - s + IF (i == n) GO TO 10 + ab(i,i+1) = f - g + DO j=l,n + e(j) = ab(i,j)/h + END DO + DO j=l,n + s = 0.d0 + DO k=l,n + s = s + ab(j,k)*ab(i,k) + END DO + DO k=l,n + ab(j,k) = ab(j,k) + s*e(k) + END DO + END DO + 10 y = ABS(q(i)) + ABS(e(i)) + IF (y > x) x = y +END DO +!...ACCUMULATION OF RIGHT-HAND TRANSFORMATIONS... +ab(n,n) = 1.d0 +g = e(n) +l = n +DO ii=2,n + i = n - ii + 1 + IF (g == 0.d0) GO TO 23 + h = ab(i,i+1)*g + DO j=l,n + ab(j,i) = ab(i,j)/h + END DO + DO j=l,n + s = 0.d0 + DO k=l,n + s = s + ab(i,k)*ab(k,j) + END DO + DO k=l,n + ab(k,j) = ab(k,j) + s*ab(k,i) + END DO + END DO + 23 DO j=l,n + ab(i,j) = 0.d0 + ab(j,i) = 0.d0 + END DO + ab(i,i) = 1.d0 + g = e(i) + l = i +END DO +!...DIAGONALIZATION OF THE BIDIAGONAL FORM... +eps = eps*x +DO kk=1,n + k = n - kk + 1 + kt = 0 + 101 kt = kt + 1 + IF (kt <= 30) GO TO 102 + e(k) = 0.d0 + WRITE (6,1000) + 1000 FORMAT (' QR FAILED') + 102 DO ll2=1,k + l2 = k - ll2 + 1 + l = l2 + IF (ABS(e(l)) <= eps) GO TO 120 + IF (l == 1) CYCLE + IF (ABS(q(l-1)) <= eps) EXIT + END DO +!...CANCELLATION OF E(L) IF L>1... + c = 0.d0 + s = 1.d0 + DO i=l,k + f = s*e(i) + e(i) = c*e(i) + IF (ABS(f) <= eps) GO TO 120 + g = q(i) +!...Q(I) = H = SQRT(G*G + F*F)... + IF (ABS(f) < ABS(g)) GO TO 113 + IF (f == 0.0) THEN + GO TO 111 + ELSE + GO TO 112 + END IF + 111 h = 0.d0 + GO TO 114 + 112 h = ABS(f)*SQRT(1 + (g/f)**2) + GO TO 114 + 113 h = ABS(g)*SQRT(1 + (f/g)**2) + 114 q(i) = h + IF (h /= 0.d0) GO TO 115 + g = 1.d0 + h = 1.d0 + 115 c = g/h + s = -f/h + END DO +!...TEST FOR CONVERGENCE... + 120 z = q(k) + IF (l == k) GO TO 140 +!...SHIFT FROM BOTTOM 2*2 MINOR... + x = q(l) + y = q(k-1) + g = e(k-1) + h = e(k) + f = ((y - z)*(y + z) + (g - h)*(g + h))/(2*h*y) + g = SQRT(f*f + 1.0D0) + temp = f - g + IF (f >= 0.d0) temp = f + g + f = ((x - z)*(x + z) + h*(y/temp - h))/x +!...NEXT QR TRANSFORMATION... + c = 1.d0 + s = 1.d0 + lp1 = l + 1 + IF (lp1 > k) GO TO 133 + DO i=lp1,k + g = e(i) + y = q(i) + h = s*g + g = g*c + IF (ABS(f) < ABS(h)) GO TO 123 + IF (f == 0.0) THEN + GO TO 121 + ELSE + GO TO 122 + END IF + 121 z = 0.d0 + GO TO 124 + 122 z = ABS(f)*SQRT(1 + (h/f)**2) + GO TO 124 + 123 z = ABS(h)*SQRT(1 + (f/h)**2) + 124 e(i-1) = z + IF (z /= 0.d0) GO TO 125 + f = 1.d0 + z = 1.d0 + 125 c = f/z + s = h/z + f = x*c + g*s + g = -x*s + g*c + h = y*s + y = y*c + DO j=1,n + x = ab(j,i-1) + z = ab(j,i) + ab(j,i-1) = x*c + z*s + ab(j,i) = -x*s + z*c + END DO + IF (ABS(f) < ABS(h)) GO TO 129 + IF (f == 0.0) THEN + GO TO 127 + ELSE + GO TO 128 + END IF + 127 z = 0.d0 + GO TO 130 + 128 z = ABS(f)*SQRT(1 + (h/f)**2) + GO TO 130 + 129 z = ABS(h)*SQRT(1 + (f/h)**2) + 130 q(i-1) = z + IF (z /= 0.d0) GO TO 131 + f = 1.d0 + z = 1.d0 + 131 c = f/z + s = h/z + f = c*g + s*y + x = -s*g + c*y + END DO + 133 e(l) = 0.d0 + e(k) = f + q(k) = x + GO TO 101 +!...CONVERGENCE: Q(K) IS MADE NON-NEGATIVE... + 140 IF (z >= 0.d0) CYCLE + q(k) = -z + DO j=1,n + ab(j,k) = -ab(j,k) + END DO +END DO +RETURN +200 q(1) = ab(1,1) +ab(1,1) = 1.d0 + +END SUBROUTINE minfit + + + + +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! + SUBROUTINE MIN(n,j,nits,d2,x1,f1,fk,f,x,t,machep,h) + + IMPLICIT NONE + + INTEGER, INTENT(IN) :: n + INTEGER :: j + INTEGER :: nits + REAL, INTENT(IN OUT) :: d2 + REAL, INTENT(IN OUT) :: x1 + REAL, INTENT(IN OUT) :: f1 + LOGICAL :: fk + REAL :: f + REAL, INTENT(IN OUT) :: x(n) + REAL, INTENT(IN) :: t + REAL, INTENT(IN) :: machep + REAL, INTENT(IN) :: h + + INTEGER :: i,k + EXTERNAL f + + + REAL :: flin ! function + REAL :: small,sf1,sx1,s,temp, xm,x2,f2,d1 + REAL :: fm,f0,t2 +!---------------------------------------------- + INTEGER :: nf,nl + REAL :: fx,ldt,dmin + REAL :: v(20,20),q0(20),q1(20),qa,qb,qc,qd0,qd1,qf1 + COMMON /global/ fx,ldt,dmin,nf,nl /q/ v,q0,q1,qa,qb,qc,qd0,qd1,qf1 +!---------------------------------------------- +!...THE SUBROUTINE MIN MINIMIZES F FROM X IN THE DIRECTION V(*,J) UNLESS +! J IS LESS THAN 1, WHEN A QUADRATIC SEARCH IS MADE IN THE PLANE +! DEFINED BY Q0,Q1,X. +! D2 IS EITHER ZERO OR AN APPROXIMATION TO HALF F". +! ON ENTRY, X1 IS AN ESTIMATE OF THE DISTANCE FROM X TO THE MINIMUM +! ALONG V(*,J) (OR, IF J=0, A CURVE). ON RETURN, X1 IS THE DISTANCE +! FOUND. +! IF FK=.TRUE., THEN F1 IS FLIN(X1). OTHERWISE X1 AND F1 ARE IGNORED +! ON ENTRY UNLESS FINAL FX IS GREATER THAN F1. +! NITS CONTROLS THE NUMBER OF TIMES AN ATTEMPT WILL BE MADE TO HALVE +! THE INTERVAL. + LOGICAL :: dz + REAL :: m2,m4 + +small = machep**2 +m2 = SQRT(machep) +m4 = SQRT(m2) +sf1 = f1 +sx1 = x1 +k = 0 +xm = 0.d0 +fm = fx +f0 = fx +dz = d2 < machep +!...FIND THE STEP SIZE... +s = 0.d0 +DO i=1,n + s = s + x(i)**2 +END DO +s = SQRT(s) +temp = d2 +IF (dz) temp = dmin +t2 = m4*SQRT(ABS(fx)/temp + s*ldt) + m2*ldt +s = m4*s + t +IF (dz.AND.t2 > s) t2 = s +t2 = DMAX1(t2,small) +t2 = DMIN1(t2,.01D0*h) +IF (.NOT.fk.OR.f1 > fm) GO TO 2 +xm = x1 +fm = f1 +2 IF (fk.AND.ABS(x1) >= t2) GO TO 3 +temp=1.d0 +IF (x1 < 0.d0) temp=-1.d0 +x1=temp*t2 +f1 = flin(n,j,x1,f,x,nf) +3 IF (f1 > fm) GO TO 4 +xm = x1 +fm = f1 +4 IF (.NOT.dz) GO TO 6 +!...EVALUATE FLIN AT ANOTHER POINT AND ESTIMATE THE SECOND DERIVATIVE... +x2 = -x1 +IF (f0 >= f1) x2 = 2.d0*x1 +f2 = flin(n,j,x2,f,x,nf) +IF (f2 > fm) GO TO 5 +xm = x2 +fm = f2 +5 d2 = (x2*(f1 - f0)-x1*(f2 - f0))/((x1*x2)*(x1 - x2)) +!...ESTIMATE THE FIRST DERIVATIVE AT 0... +6 d1 = (f1 - f0)/x1 - x1*d2 +dz = .true. +!...PREDICT THE MINIMUM... +IF (d2 > small) GO TO 7 +x2 = h +IF (d1 >= 0.d0) x2 = -x2 +GO TO 8 +7 x2 = (-.5D0*d1)/d2 +8 IF (ABS(x2) <= h) GO TO 11 +IF (x2 > 0.0) THEN + GO TO 10 +END IF +x2 = -h +GO TO 11 +10 x2 = h +!...EVALUATE F AT THE PREDICTED MINIMUM... +11 f2 = flin(n,j,x2,f,x,nf) +IF (k >= nits.OR.f2 <= f0) GO TO 12 +!...NO SUCCESS, SO TRY AGAIN... +k = k + 1 +IF (f0 < f1.AND.(x1*x2) > 0.d0) GO TO 4 +x2 = 0.5D0*x2 +GO TO 11 +!...INCREMENT THE ONE-DIMENSIONAL SEARCH COUNTER... +12 nl = nl + 1 +IF (f2 <= fm) GO TO 13 +x2 = xm +GO TO 14 +13 fm = f2 +!...GET A NEW ESTIMATE OF THE SECOND DERIVATIVE... +14 IF (ABS(x2*(x2 - x1)) <= small) GO TO 15 +d2 = (x2*(f1-f0) - x1*(fm-f0))/((x1*x2)*(x1 - x2)) +GO TO 16 +15 IF (k > 0) d2 = 0.d0 +16 IF (d2 <= small) d2 = small +x1 = x2 +fx = fm +IF (sf1 >= fx) GO TO 17 +fx = sf1 +x1 = sx1 +!...UPDATE X FOR LINEAR BUT NOT PARABOLIC SEARCH... +17 IF (j == 0) RETURN +DO i=1,n + x(i) = x(i) + x1*v(i,j) +END DO + +END SUBROUTINE MIN + + +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! + SUBROUTINE vcprnt(option,v,n) + + IMPLICIT NONE + INTEGER :: option + REAL, INTENT(IN OUT) :: v(n) + INTEGER :: n + + INTEGER :: i + +SELECT CASE ( option ) + CASE ( 1) + GO TO 1 + CASE ( 2) + GO TO 2 + CASE ( 3) + GO TO 3 + CASE ( 4) + GO TO 4 +END SELECT + +1 WRITE (6,101) (v(i),i=1,n) +RETURN +2 WRITE (6,102) (v(i),i=1,n) +RETURN +3 WRITE (6,103) (v(i),i=1,n) +RETURN +4 WRITE (6,104) (v(i),i=1,n) +RETURN +101 FORMAT (/' THE SECOND DIFFERENCE ARRAY D(*) IS:'/ (e32.14,4E25.14)) +102 FORMAT (/' THE SCALE FACTORS ARE:'/(e32.14,4E25.14)) +103 FORMAT (/' THE APPROXIMATING QUADR. FORM HAS PRINCIPAL VALUES:'/ & + (e32.14,4E25.14)) +104 FORMAT (/' X IS:',e26.14/(e32.14)) +END SUBROUTINE vcprnt + + +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! + SUBROUTINE PRINT(n,x,prin,fmin) + + IMPLICIT NONE + INTEGER :: n + REAL, INTENT(IN OUT) :: x(n) + INTEGER, INTENT(IN OUT) :: prin + REAL, INTENT(IN OUT) :: fmin + + INTEGER :: i + REAL :: ln +!---------------------------------------------- +INTEGER :: nf,nl +REAL :: fx,ldt,dmin +COMMON /global/ fx,ldt,dmin,nf,nl +!---------------------------------------------- +WRITE (6,101) nl,nf,fx + +IF (fx <= fmin) GO TO 1 +ln = LOG10(fx-fmin) +WRITE (6,102) fmin,ln +GO TO 2 +1 WRITE (6,103) fmin +2 IF (n > 4.AND.prin <= 2) RETURN +WRITE (6,104) (x(i),i=1,n) +RETURN +101 FORMAT (/' AFTER',i6, & + ' LINEAR SEARCHES, THE FUNCTION HAS BEEN EVALUATED',i6, & + ' TIMES. THE SMALLEST VALUE FOUND IS F(X) = ',e21.14) +102 FORMAT (' LOG (F(X)-',e21.14,') = ',e21.14) +103 FORMAT (' LOG (F(X)-',e21.14,') IS UNDEFINED.') +104 FORMAT (' X IS:',e26.14/(e32.14)) +END SUBROUTINE PRINT + + +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! + SUBROUTINE maprnt(option,v,m,n) + + IMPLICIT NONE + INTEGER :: option + REAL, INTENT(IN OUT) :: v(m,n) + INTEGER, INTENT(IN OUT) :: m + INTEGER, INTENT(IN) :: n + INTEGER :: i,j + + INTEGER :: low,upp +!...THE SUBROUTINE MAPRNT PRINTS THE COLUMNS OF THE NXN MATRIX V +! WITH A HEADING AS SPECIFIED BY OPTION. +! M IS THE ROW DIMENSION OF V AS DECLARED IN THE CALLING PROGRAM... +low = 1 +upp = 5 +SELECT CASE ( option ) + CASE ( 1) + GO TO 1 + CASE ( 2) + GO TO 2 +END SELECT +1 WRITE (6,101) +101 FORMAT (/' THE NEW DIRECTIONS ARE:') +GO TO 3 +2 WRITE (6,102) +102 FORMAT (' AND THE PRINCIPAL AXES:') +3 IF (n < upp) upp = n +DO i=1,n + WRITE (6,104) (v(i,j),j=low,upp) +END DO +low = low + 5 +IF (n < low) RETURN +upp = upp + 5 +WRITE (6,103) +GO TO 3 +103 FORMAT (' ') +104 FORMAT (e32.14,4E25.14) +END SUBROUTINE maprnt + + +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! + REAL FUNCTION random(naught) + + IMPLICIT NONE + INTEGER, INTENT(IN OUT) :: naught + + REAL :: ran1,ran3(127),half + INTEGER :: i,j,ran2,q,r + LOGICAL :: init + DATA init/.false./ + SAVE init,ran2,ran1,ran3 + +IF (init) GO TO 3 +r = MOD(naught,8190) + 1 +ran2 = 128 +DO i=1,127 + ran2 = ran2 - 1 + ran1 = -2.d0**55 + DO j=1,7 + r = MOD(1756*r,8191) + q = r/32 + ran1 = (ran1 + q)*(1.0D0/256) + END DO + ran3(ran2) = ran1 +END DO +init = .true. +3 IF (ran2 == 1) ran2 = 128 +ran2 = ran2 - 1 +ran1 = ran1 + ran3(ran2) +half = .5D0 +IF (ran1 >= 0.d0) half = -half +ran1 = ran1 + half +ran3(ran2) = ran1 +random = ran1 + .5D0 + +END FUNCTION random + + + +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! + REAL FUNCTION flin (n,j,l,f,x,nf) + IMPLICIT NONE + + INTEGER, INTENT(IN) :: n + INTEGER, INTENT(IN OUT) :: j + REAL, INTENT(IN) :: l + REAL :: f + REAL, INTENT(IN) :: x(n) + INTEGER, INTENT(OUT) :: nf + + INTEGER :: i + REAL :: t(20) + + EXTERNAL f + +!...FLIN IS THE FUNCTION OF ONE REAL VARIABLE L THAT IS MINIMIZED +! BY THE SUBROUTINE MIN... +!---------------------------------------------- + REAL :: v(20,20),q0(20),q1(20),qa,qb,qc,qd0,qd1,qf1 + COMMON /q/ v,q0,q1,qa,qb,qc,qd0,qd1,qf1 +!---------------------------------------------- +IF (j == 0) GO TO 2 +!...THE SEARCH IS LINEAR... +DO i=1,n + t(i) = x(i) + l*v(i,j) +END DO +GO TO 4 +!...THE SEARCH IS ALONG A PARABOLIC SPACE CURVE... +2 qa = (l*(l - qd1))/(qd0*(qd0 + qd1)) +qb = ((l + qd0)*(qd1 - l))/(qd0*qd1) +qc = (l*(l + qd0))/(qd1*(qd0 + qd1)) +DO i=1,n + t(i) = (qa*q0(i) + qb*x(i)) + qc*q1(i) +END DO +!...THE FUNCTION EVALUATION COUNTER NF IS INCREMENTED... +4 nf = nf + 1 +flin = f(t,n) + +END FUNCTION flin + + +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! + SUBROUTINE sort(m,n,d,v) + IMPLICIT NONE +! + INTEGER, INTENT(IN OUT) :: m + INTEGER, INTENT(IN) :: n + REAL, INTENT(IN OUT) :: d(n) + REAL, INTENT(IN OUT) :: v(m,n) + + INTEGER :: i,j,k,nm1,ip1 + REAL :: s +!...SORTS THE ELEMENTS OF D(N) INTO DESCENDING ORDER AND MOVES THE +! CORRESPONDING COLUMNS OF V(N,N). +! M IS THE ROW DIMENSION OF V AS DECLARED IN THE CALLING PROGRAM. +IF (n == 1) RETURN +nm1 = n - 1 +DO i = 1,nm1 + k=i + s = d(i) + ip1 = i + 1 + DO j = ip1,n + IF (d(j) <= s) CYCLE + k = j + s = d(j) + END DO + IF (k <= i) CYCLE + d(k) = d(i) + d(i) = s + DO j = 1,n + s = v(j,i) + v(j,i) = v(j,k) + v(j,k) = s + END DO +END DO +END SUBROUTINE sort + + +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! + SUBROUTINE quad(n,f,x,t,machep,h) + IMPLICIT NONE + + INTEGER, INTENT(IN) :: n + REAL :: f + REAL, INTENT(IN OUT) :: x(n) + REAL, INTENT(IN OUT) :: t + REAL :: machep + REAL, INTENT(IN OUT) :: h +! IMPLICIT REAL (A-H,O-Z) + EXTERNAL f + +!...QUAD LOOKS FOR THE MINIMUM OF F ALONG A CURVE DEFINED BY Q0,Q1,X... + INTEGER :: i + REAL :: l + REAL :: s,value +!---------------------------------------------- + INTEGER :: nf,nl + REAL :: fx,ldt,dmin + +REAL :: v(20,20),q0(20),q1(20),qa,qb,qc,qd0,qd1,qf1 +COMMON /global/ fx,ldt,dmin,nf,nl /q/ v,q0,q1,qa,qb,qc,qd0,qd1,qf1 +!---------------------------------------------- +s = fx +fx = qf1 +qf1 = s +qd1 = 0.d0 +DO i=1,n + s = x(i) + l = q1(i) + x(i) = l + q1(i) = s + qd1 = qd1 + (s-l)**2 +END DO +qd1 = SQRT(qd1) +l = qd1 +s = 0.d0 +IF (qd0 <= 0.d0 .OR. qd1 <= 0.d0 .OR. nl < 3*n*n) GO TO 2 +value=qf1 +CALL MIN(n,0,2,s,l,value,.true.,f,x,t,machep,h) +qa = (l*(l-qd1))/(qd0*(qd0+qd1)) +qb = ((l+qd0)*(qd1-l))/(qd0*qd1) +qc = (l*(l+qd0))/(qd1*(qd0+qd1)) +GO TO 3 +2 fx = qf1 +qa = 0.d0 +qb = qa +qc = 1.d0 +3 qd0 = qd1 +DO i=1,n + s = q0(i) + q0(i) = x(i) + x(i) = (qa*s + qb*x(i)) + qc*q1(i) +END DO +END SUBROUTINE quad + diff --git a/applications/PUfoam/MoDeNaModels/PolymerDensity/ExampleOfUsage/src/srcDetailedCode/VLE_main.f90 b/applications/PUfoam/MoDeNaModels/PolymerDensity/ExampleOfUsage/src/srcDetailedCode/VLE_main.f90 new file mode 100644 index 000000000..cebd3d769 --- /dev/null +++ b/applications/PUfoam/MoDeNaModels/PolymerDensity/ExampleOfUsage/src/srcDetailedCode/VLE_main.f90 @@ -0,0 +1,125 @@ +SUBROUTINE VLE_MIX(rhob,density,chemPot_total,compID) + + USE parameters, ONLY: PI, RGAS, KBOL + USE basic_variables + USE EOS_VARIABLES, ONLY: fres, eta, eta_start, dhs, mseg, uij, sig_ij, rho, x, z3t + USE DFT_MODULE + USE EOS_NUMERICAL_DERIVATIVES + IMPLICIT NONE + + +! --------------------------------------------------------------------- +! Variables +! --------------------------------------------------------------------- + + +!passed + REAL :: chemPot_total(nc) + REAL :: rhob(2,0:nc),density(np) + INTEGER :: compID + +!local + REAL, DIMENSION(nc) :: dhs_star + REAL :: w(np,nc), lnphi(np,nc) + INTEGER :: converg + CHARACTER(LEN=4) :: char_ncomp + REAL :: Polymer_density + INTEGER :: i + CHARACTER (LEN=50) :: filename + + + ! --------------------------------------------------------------------- + ! prepare for phase equilibrium calculation for given T + ! --------------------------------------------------------------------- + + dhs(1:ncomp) = parame(1:ncomp,2) * ( 1.0 - 0.12*EXP( -3.0*parame(1:ncomp,3)/t ) ) ! needed for rdf_matrix + dhs_star(1:ncomp) = dhs(1:ncomp)/parame(1:ncomp,2) + + nphas = 2 + outp = 0 ! output to terminal + + CALL START_VAR (converg) ! gets starting values, sets "val_init" + + IF ( converg /= 1 ) THEN + WRITE (*,*) 'no VLE found' + RETURN + END IF + + ! rhob(phase,0): molecular density + rhob(1,0) = dense(1) / ( PI/6.0* SUM( xi(1,1:ncomp) * parame(1:ncomp,1) * dhs(1:ncomp)**3 ) ) + rhob(2,0) = dense(2) / ( PI/6.0* SUM( xi(2,1:ncomp) * parame(1:ncomp,1) * dhs(1:ncomp)**3 ) ) + ! rhob(phase,i): molecular component density (with i=(1,...ncomp) ) in units (1/A^3) + rhob(1,1:ncomp) = rhob(1,0)*xi(1,1:ncomp) + rhob(2,1:ncomp) = rhob(2,0)*xi(2,1:ncomp) + + ! get density in SI-units (kg/m**3) + CALL SI_DENS ( density, w ) + + ! calculate residual chemical potentials + ensemble_flag = 'tv' ! this flag is for: mu_res=mu_res(T,rho) + densta(1) = dense(1) ! Index 1 is for liquid density (here: packing fraction eta) + densta(2) = dense(2) ! Index 2 is for vapour density (here: packing fraction eta) + CALL fugacity (lnphi) + chemPot_total(1:ncomp) = lnphi(1,1:ncomp)! + LOG( rhob(1,1:ncomp) ) ! my0 = mu_res(T,rho_bulk_L) + ln(rho_bulk_l) + +! WRITE(*,*) '--------------------------------------------------' +! WRITE(*,*)'RESULT OF PHASE EQUILIBRIUM CALCULATION' +! WRITE (char_ncomp,'(I3)') ncomp +! WRITE (*,*) 'T = ',t, 'K, and p =', p/1.E5,' bar' +! WRITE(*,*)' ' +! WRITE(*,'(t15,4(a12,1x),10x,a)') (compna(i),i=1,ncomp) +! +! write(*,*)'Mass fraction:' +! WRITE(*,'(2x,a,'//char_ncomp//'(g13.6,1x))') 'PHASE I w', (w(1,i),i=1,ncomp) +! WRITE(*,'(2x,a,'//char_ncomp//'(g13.6,1x))') 'PHASE II w', (w(2,i),i=1,ncomp) +! +! write(*,*)'Molar composition:' +! WRITE(*,'(2x,a,'//char_ncomp//'(g13.6,1x))') 'PHASE I x', (EXP(lnx(1,i)),i=1,ncomp) +! WRITE(*,'(2x,a,'//char_ncomp//'(g13.6,1x))') 'PHASE II x', (EXP(lnx(2,i)),i=1,ncomp) +! WRITE(*,*)' ' +! !!WRITE(*,'(2x,a,'//char_ncomp//'(g13.6,1x))') 'PHASE I density', (rhob(1,i),i=1,ncomp) +! !! WRITE(*,'(2x,a,'//char_ncomp//'(g13.6,1x))') 'PHASE II density', (rhob(2,i),i=1,ncomp) +! !!WRITE(*,*)' ' +! WRITE(*,'(2x,a,'//char_ncomp//'(g13.6,1x))') 'PHASE I chemPot', (lnphi(1,i) + LOG(rhob(1,i)),i=1,ncomp) +! WRITE(*,'(2x,a,'//char_ncomp//'(g13.6,1x))') 'PHASE II chemPot', (lnphi(2,i) + LOG(rhob(2,i)),i=1,ncomp) +! WRITE(*,*)' ' +! !!WRITE(*,*)'Phase densities ' +! WRITE(*,'(2x,a,2(g13.6,1x))') 'SI-DENSITY [kg/m3] ', density(1),density(2) +! !!WRITE(*,'(2x,a,2(g13.6,1x))') 'NUMBER-DENSITY ', rhob(1,0),rhob(2,0) +! +! WRITE(*,*) + + + write(*,*)' ' + write(*,*)'--------------------------------------------' + write(*,*)'Output detailed model:' + write(*,*)'T /K:',t,'p/bar:',p/1.E5 + write(*,*)'Liquid density /kg/m3:', max(density(1),density(2)) + write(*,*)'--------------------------------------------' + write(*,*)' ' + + + !write liquid phase density in kg/m3 to out.txt + Polymer_density = max(density(1),density(2)) !* w(1,1) + + filename='./out.txt' + CALL file_open(filename,78) + write(78,*) Polymer_density + !write(*,*)'Polymer_density [kg/m3]:',Polymer_density + + + + + +! WRITE (*,*) ' ' +! WRITE (*,*) 'temperature ',t, 'K, and p=', p/1.E5,' bar' +! WRITE (*,*) 'x1_liquid ',xi(1,1),' x1_vapor', xi(2,1) +! WRITE (*,*) 'densities ',rhob(1,0), rhob(2,0) +! WRITE (*,*) 'dense ',dense(1), dense(2) +! WRITE (*,*) 'density [kg/m3] ',density(1), density(2) +! write (*,*) 'chemical potentials comp1' , lnphi(1,1) + LOG( rhob(1,1) ), lnphi(2,1) + LOG( rhob(2,1) ) +! write (*,*) 'chemical potentials comp2' ,lnphi(1,2) + LOG( rhob(1,2) ), lnphi(2,2) + LOG( rhob(2,2) ) +! + + +END SUBROUTINE VLE_MIX diff --git a/applications/PUfoam/MoDeNaModels/PolymerDensity/ExampleOfUsage/src/srcDetailedCode/VLE_subroutines.f90 b/applications/PUfoam/MoDeNaModels/PolymerDensity/ExampleOfUsage/src/srcDetailedCode/VLE_subroutines.f90 new file mode 100644 index 000000000..3f54b25ea --- /dev/null +++ b/applications/PUfoam/MoDeNaModels/PolymerDensity/ExampleOfUsage/src/srcDetailedCode/VLE_subroutines.f90 @@ -0,0 +1,7156 @@ +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! SUBROUTINE start_var +! +! This subroutine generates a converged solution for binary systems +! or performes a flash calculation for mixtues. This routine is a +! fairly weak point of the program. +! +! IF a polymer is considered, starting values for mole fractions +! are determined from the SUBROUTINGE POLY_STA_VAR (see below). The +! polymer needs to be placed as component 1 (first line) in INPUT +! file. +! +! A phase equilib. iteration is started at the end of this routine. +! If no solution is found (converg=0), the program will stop within +! this routine. +! +! Currently, this routine assumes two-phase equilibrium and derives +! starting values (xi,density) only for two phases. +! +! Prerequisites are: +! SUBROUTINE INPUT needs to be called prior to this routine, because +! all pure comp. parameters as well as (T,P,kij) need to be in place. +! Also, the variable to be iterated "it(i)" and the variables to be +! calculated through the summation relation "sum_rel(i)" have to be +! defined. +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! + SUBROUTINE start_var(converg) +! + USE BASIC_VARIABLES + USE STARTING_VALUES + IMPLICIT NONE +! +! ---------------------------------------------------------------------- + INTEGER, INTENT(IN OUT) :: converg +! +! ---------------------------------------------------------------------- + INTEGER :: ph, i, k + INTEGER :: ncompsav, n_unkwsav, ph_split + LOGICAL :: lle_check, flashcase, renormalize + REAL :: den1, den2, x_1, x_2 + CHARACTER (LEN=50) :: filename +! ---------------------------------------------------------------------- + +converg = 0 + +! CALL RACHFORD_RICE (converg) +! CALL Heidemann_Khalil + +! ---------------------------------------------------------------------- +! This first condition (eos >= 4) is for LJ models, not for PC-SAFT +! ---------------------------------------------------------------------- + +IF (eos >= 4) THEN + + ncomp = 2 ! set number of components to 2 + n_unkw = ncomp ! number of quantities to be iterated + it(1) = 'x11' ! iteration of mol fraction of comp.1 phase 1 + it(2) = 'x21' ! iteration of mol fraction of comp.1 phase 2 + sum_rel(1) = 'x12' ! summation relation: x12 = 1 - sum(x1j) + sum_rel(2) = 'x22' ! summation relation: x22 = 1 - sum(x2j) + + filename = 'LJ_START_VAL.INC' + CALL file_open(filename,84) + READ (84,*) den1,den2 + READ (84,*) x_1,x_2 + CLOSE (84) + + xi(1,1) = x_1 + xi(2,1) = x_2 + xi(1,2) = 1.0 - xi(1,1) + xi(2,2) = 1.0 - xi(2,1) + lnx(1,1) = LOG(xi(1,1)) + lnx(2,1) = LOG(xi(2,1)) + lnx(1,2) = LOG(xi(1,2)) + lnx(2,2) = LOG(xi(2,2)) + + val_init(1) = den1 + val_init(2) = den2 + val_init(3) = t + val_init(4) = p + DO ph = 1,nphas + DO k = 1,ncomp + val_init(4+k+(ph-1)*ncomp) = LOG(xi(ph,k)) + END DO + END DO + + CALL objective_ctrl (converg) + IF (converg == 1) WRITE (*,*) t, p/1.0E5, xi(1,1), xi(2,1) + IF (converg == 0) WRITE (*,*) ' weak starting values' + + +! ---------------------------------------------------------------------- +! ELSE: PC-SAFT equation of state +! ---------------------------------------------------------------------- + +ELSE + + renormalize = .false. ! for renormalization group theory (RGT) + IF (num == 2) renormalize = .true. + IF (num == 2) num = 0 ! if RGT: initial phase equilibr. is for non-renormalized model + + flashcase = .false. ! .true. when a specific feed conc. xif is given + IF (xif(1) /= 0.0) flashcase = .true. + + lle_check = .true. + +! ---------------------------------------------------------------------- +! IF: non-polymeric system +! ---------------------------------------------------------------------- + IF (mm(1) < 1.0E8) THEN + + DO i=1,ncomp ! setting mole-fractions for the case that + ! anything goes wrong in the coming routines + xi(1,i) = 1.0 / REAL(ncomp) + xi(2,i) = 1.0 / REAL(ncomp) + END DO + + + ! ------------------------------------------------------------------ + ! determine an initial conc. (phase 1) that will phase split + ! ------------------------------------------------------------------ + IF( ncomp == 2 .AND. .NOT.flashcase ) THEN + CALL vle_min( lle_check ) + WRITE(*,*)' INITIAL FEED-COMPOSITION',(xi(1,i), i=1,ncomp),converg + END IF + + ! ------------------------------------------------------------------ + ! perform a phase stability test + ! ------------------------------------------------------------------ + ph_split = 0 + CALL phase_stability ( .false., flashcase, ph_split ) + write (*,*) 'stability analysis I indicates phase-split is:',ph_split + + + ! ------------------------------------------------------------------ + ! determine species i, for which x(i) is calc from summation relation + ! ------------------------------------------------------------------ + CALL select_sum_rel (1,0,1) ! synthax (m,n,o): phase m + ! exclude comp. n + ! assign it(o) and higher + CALL select_sum_rel (2,0,2) ! for ncomp>=3, the quantities + ! to be iterated will be overwritten + + ! ------------------------------------------------------------------ + ! if 2 phases (VLE) + ! ------------------------------------------------------------------ + IF (ph_split == 1) THEN + + ! --- perform tangent plane minimization ------------------------ + CALL tangent_plane + ph_split = 0 + + ! --- determine, for which substance summation relation is used -- + IF (flashcase) THEN + CALL determine_flash_it2 + ELSE + CALL select_sum_rel (1,0,1) + CALL select_sum_rel (2,0,2) + END IF + + ! --- do full phase equilibr. calculation ------------------------ + n_unkw = ncomp ! number of quantities to be iterated + CALL objective_ctrl (converg) + IF (converg == 1 ) write (*,*) ' converged (maybe a VLE)',dense(1),dense(2) + + END IF + + ! ------------------------------------------------------------------ + ! test for LLE + ! ------------------------------------------------------------------ + ph_split = 0 + + IF (lle_check) CALL phase_stability (lle_check,flashcase,ph_split) + IF (lle_check) write (*,*) 'stability analysis II, phase-split is:',ph_split + + + ! ------------------------------------------------------------------ + ! if two phases (LLE) + ! ------------------------------------------------------------------ + IF (ph_split == 1) THEN + + write (*,*) ' LLE-stability test indicates 2 phases (VLE or LLE)' + + ! --- perform tangent plane minimization ------------------------ + IF (flashcase) CALL select_sum_rel (1,0,1) + IF (flashcase) CALL select_sum_rel (2,0,2) + + CALL tangent_plane + + ! --- determine, for which substance summation relation ---------- + IF (flashcase) THEN + CALL determine_flash_it2 + ELSE + CALL select_sum_rel (1,0,1) + CALL select_sum_rel (2,0,2) + END IF + + ! --- do full phase equilibr. calculation ------------------------ + n_unkw = ncomp ! number of quantities to be iterated + val_conv(2) = 0.0 + CALL objective_ctrl (converg) + IF (converg == 1 ) write (*,*) ' converged (maybe an LLE)',dense(1),dense(2) + + END IF + + ! ------------------------------------------------------------------ + ! equilibr. calc. converged: set initial var. for further calc. + ! ------------------------------------------------------------------ + IF (converg == 1) THEN + val_init = val_conv + DO ph = 1,nphas + DO i = 1,ncomp + xi(ph,i) = EXP( val_conv(4+i+(ph-1)*ncomp) ) + END DO + END DO + dense(1:2) = val_conv(1:2) + ELSE + WRITE (*,*) ' NO SOLUTION FOUND FOR THE STARTING VALUES' + STOP + END IF + + + ! --------------------------------------------------------------------- + ! ELSE: for systems with polymers + ! --------------------------------------------------------------------- + + ELSE + + ncompsav = ncomp + ncomp = 2 ! set number of components to 2 + n_unkwsav = n_unkw + + CALL poly_sta_var(converg) + + IF (converg == 1) THEN + val_init = val_conv + ELSE + WRITE (*,*) ' NO SOLUTION FOUND FOR THE STARTING VALUES' + STOP + END IF + + ncomp = ncompsav + n_unkw = n_unkwsav ! number of quantities to be iterated + + END IF + +! --- for RGT: set flag back to num=2 indicating an RGT calculation ---- + IF (renormalize) num = 2 + +END IF + +END SUBROUTINE start_var + + + + +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! SUBROUTINE objective_ctrl +! +! This subroutine controls the iso-fugacity iteration. It uses +! the variables defined in the array "val_init". If successfull, +! the converged values are written to "val_conv", and the flag +! converg is set to 1. +! See also above desciption for subroutine PHASE_EQUILIB +! This routine calls SUBROUTINE HYBRID, which is a solver (modified +! POWELL HYBRID METHOD). HYBRID is freely available for non-commercial +! applications. HYBRID requires three definitions: +! 1.the number of equations to be solved (=No. of variables to be +! iterated). The appropriate parameter is: "n_unkw" +! 2.the equations to be iterated, they are here gathered in the SUB- +! ROUTINE OBJEC_FCT (see below). Since HYBRID is a root finder, +! these objective functions are iterated to be zero (essentially, +! OBJEC_FCT contains the iso-fugacity relation. +! 3.an array of variables is required, containing the quatities to be +! iterated. This array is termed "y(i)" +! +! INPUT VARIABLES: +! val_init(i) array containing (densities,T,P,lnx's) serving as +! starting values for the phase equilibrium calculation +! it(i) contains the information, which variable is deter- +! mined iteratively. For syntax refer e.g.to SUB BINMIX. +! sum_rel(i) indicates, which mole fraction is determined from the +! summation relation sum(xi)=1 +! +! OUTPUT VARIABLES: +! val_conv(i) array containing the converged system variables +! analogous to "val_init" +! converg 0 if no convergence achieved, 1 if converged solution +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! + SUBROUTINE objective_ctrl (converg) +! + USE BASIC_VARIABLES + USE Solve_NonLin + IMPLICIT NONE +! +! ---------------------------------------------------------------------- + INTEGER, INTENT(OUT) :: converg +! +! ---------------------------------------------------------------------- + INTERFACE + SUBROUTINE objec_fct ( iter_no, y, residu, dummy ) + INTEGER, INTENT(IN) :: iter_no + REAL, INTENT(IN) :: y(iter_no) + REAL, INTENT(OUT) :: residu(iter_no) + INTEGER, INTENT(IN OUT) :: dummy + END SUBROUTINE objec_fct + END INTERFACE +! + INTEGER :: info,k,posn,i + INTEGER, PARAMETER :: mxr = nc*(nc+1)/2 + REAL, ALLOCATABLE :: y(:),diag(:),residu(:) + REAL :: x_init, x_solut, r_diff1, r_diff2, totres + REAL :: r_thrash, x_thrash + CHARACTER (LEN=2) :: compon + LOGICAL :: convergence +! ---------------------------------------------------------------------- + +info=1 + +ALLOCATE( y(n_unkw), diag(n_unkw), residu(n_unkw) ) + +IF (num == 0) acc_a = 1.E-7 +IF (num == 0) step_a = 2.E-8 +IF (num == 1) acc_a = 1.E-7 +IF (num == 1) step_a = 2.E-8 +IF (num == 2) acc_a = 5.E-7 +IF (num == 2) step_a = 1.E-7 + +posn = 0 +DO i = 1,n_unkw + posn = posn + 1 + IF (it(i) == 't') y(posn) = val_init(3) + IF (it(i) == 'p') y(posn) = val_init(4) + IF (it(i) == 'lnp') y(posn) = LOG( val_init(4) ) + IF (it(i) == 'fls') y(posn) = alpha + IF (it(i)(1:1) == 'x' .AND. it(i)(2:2) == '1') compon = it(i)(3:3) + IF (it(i)(1:1) == 'x' .AND. it(i)(2:2) == '1') READ(compon,*) k + IF (it(i)(1:1) == 'x' .AND. it(i)(2:2) == '1') y(posn) = val_init(4+k) + IF (it(i)(1:1) == 'x' .AND. it(i)(2:2) == '2') compon = it(i)(3:3) + IF (it(i)(1:1) == 'x' .AND. it(i)(2:2) == '2') READ(compon,*) k + IF (it(i)(1:1) == 'x' .AND. it(i)(2:2) == '2') y(posn) = val_init(4+ncomp+k) + IF (it(i)(1:1) == 'x' .AND. it(i)(2:2) == '3') compon = it(i)(3:3) + IF (it(i)(1:1) == 'x' .AND. it(i)(2:2) == '3') READ(compon,*) k + IF (it(i)(1:1) == 'x' .AND. it(i)(2:2) == '3') y(posn) = val_init(4+ncomp+ncomp+k) +END DO + +CALL init_vars + +x_init = 0.0 +DO i = 1,ncomp + IF (lnx(1,i) /= 0.0 .AND. lnx(2,i) /= 0.0) THEN + x_init = x_init + ABS( 1.0 - lnx(2,i)/lnx(1,i) ) + ELSE + x_init = x_init + ABS( 1.0 - EXP(lnx(2,i))/EXP(lnx(1,i)) ) + END IF +END DO + +CALL hbrd (objec_fct, n_unkw, y, residu, step_a, acc_a, info, diag) + +x_solut = 0.0 +DO i = 1,ncomp + IF ( lnx(1,i) /= 0.0 .AND. lnx(2,i) /= 0.0 ) THEN + x_solut = x_solut + ABS( 1.0 - lnx(2,i)/lnx(1,i) ) + ELSE + IF (lnx(1,i) < 1E300 .AND. lnx(1,i) > -1.E300 ) & + x_solut = x_solut + ABS( 1.0 - EXP(lnx(2,i))/EXP(lnx(1,i)) ) + END IF +END DO +r_diff1 = ABS( 1.0 - dense(1)/dense(2) ) +IF ( val_conv(2) > 0.0 ) THEN + r_diff2 = ABS( 1.0 - val_conv(1)/val_conv(2) ) +ELSE + r_diff2 = 0.0 +END IF + +totres = SUM( ABS( residu(1:n_unkw) ) ) + +r_thrash = 0.0005 +x_thrash = 0.0005 +if (num > 0 ) r_thrash = r_thrash * 10.0 +if (num > 0 ) x_thrash = x_thrash * 100.0 + +convergence = .true. + +IF ( info >= 2 ) convergence = .false. +IF ( ABS( 1.0- dense(1)/dense(2) ) < r_thrash .AND. x_solut < x_thrash ) THEN + IF ( x_init > 0.050 ) convergence = .false. + IF ( ( ABS( 1.0- dense(1)/dense(2) ) + x_solut ) < 1.E-7 ) convergence = .false. +ENDIF +IF ( r_diff2 /= 0.0 .AND. r_diff2 > (4.0*r_diff1) .AND. bindiag == 1 ) convergence = .false. +IF ( ncomp == 1 .AND. totres > 100.0*acc_a ) convergence = .false. +IF ( totres > 1000.0*acc_a ) convergence = .false. +IF ( ncomp == 1 .AND. r_diff1 < 1.d-5 ) convergence = .false. + +IF ( convergence ) THEN + converg = 1 + ! write (*,*) residu(1),residu(2) + CALL converged + IF (num <= 1) CALL enthalpy_etc +ELSE + converg = 0 +END IF + +DEALLOCATE( y, diag, residu ) + +END SUBROUTINE objective_ctrl + + + +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! SUBROUTINE objec_fct +! +! This subroutine contains the equations to be solved numerically +! (iso-fugacity: fi'-fi''=0) as well as other dependent equations, +! which can be solved analytically, namely the summation relation +! xi=1-sum(xj) or the condition of equal charge for electrolyte +! solutions. +! This subroutine is required and controlled by the solver HBRD ! +! HBRD varies the variables "y(i)" and eveluates the result of +! these changes from this routine. +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! + SUBROUTINE objec_fct ( iter_no, y, residu, dummy ) +! + USE BASIC_VARIABLES + USE EOS_VARIABLES, ONLY: density_error + IMPLICIT NONE +! +! ---------------------------------------------------------------------- + INTEGER, INTENT(IN) :: iter_no + REAL, INTENT(IN) :: y(iter_no) + REAL, INTENT(OUT) :: residu(iter_no) + INTEGER, INTENT(IN OUT) :: dummy +! +! ---------------------------------------------------------------------- + INTEGER :: i, ph,k,posn, skip,phase + REAL :: lnphi(np,nc),isofugacity + CHARACTER (LEN=2) :: compon +! ---------------------------------------------------------------------- + + +posn = 0 +DO i = 1,n_unkw + posn = posn + 1 + IF (it(i) == 't') t = y(posn) + IF (it(i) == 'p') p = y(posn) + IF (it(i) == 'lnp') p = EXP( y(posn) ) + IF (it(i) == 'fls') alpha = y(posn) + IF (it(i)(1:1) == 'x' .AND. it(i)(2:2) == '1') compon = it(i)(3:3) + IF (it(i)(1:1) == 'x' .AND. it(i)(2:2) == '1') READ(compon,*) k + IF (it(i)(1:1) == 'x' .AND. it(i)(2:2) == '1') lnx(1,k) = y(posn) + IF (it(i)(1:1) == 'x' .AND. it(i)(2:2) == '2') compon = it(i)(3:3) + IF (it(i)(1:1) == 'x' .AND. it(i)(2:2) == '2') READ(compon,*) k + IF (it(i)(1:1) == 'x' .AND. it(i)(2:2) == '2') lnx(2,k) = y(posn) + IF (it(i)(1:1) == 'x' .AND. it(i)(2:2) == '3') compon = it(i)(3:3) + IF (it(i)(1:1) == 'x' .AND. it(i)(2:2) == '3') READ(compon,*) k + IF (it(i)(1:1) == 'x' .AND. it(i)(2:2) == '3') lnx(3,k) = y(posn) +END DO + +DO k = 1,ncomp + IF (lnx(1,k) > 0.0) lnx(1,k) = 0.0 + IF (lnx(2,k) > 0.0) lnx(2,k) = 0.0 +END DO + +IF (p < 1.E-100) p = 1.E-12 +!IF ( IsNaN( p ) ) p = 1000.0 ! rebounce for the case of NaN-solver output +!IF ( IsNaN( t ) ) t = 300.0 ! rebounce for the case of NaN-solver output +!IF ( IsNaN( alpha ) ) alpha = 0.5 ! rebounce for the case of NaN-solver output +IF ( p /= p ) p = 1000.0 ! rebounce for the case of NaN-solver output +IF ( t /= t ) t = 300.0 ! rebounce for the case of NaN-solver output +IF ( alpha /= alpha ) alpha = 0.5 ! rebounce for the case of NaN-solver output + +! --- setting of mole fractions ---------------------------------------- +DO ph = 1, nphas + DO i = 1, ncomp + IF ( lnx(ph,i) < -300.0 ) THEN + xi(ph,i) = 0.0 + ELSE + xi(ph,i) = EXP( lnx(ph,i) ) + END IF + END DO +END DO + +IF (ncomp > 1) CALL x_summation + +CALL fugacity (lnphi) + +phase = 2 +DO i = 1,n_unkw + skip = 0 !for ions/polymers, the isofug-eq. is not always solved + IF (n_unkw < (ncomp*(nphas-1))) skip = ncomp*(nphas-1) - n_unkw + IF ((i+skip-ncomp*(phase-2)) > ncomp) phase = phase + 1 + residu(i) = isofugacity((i+skip-ncomp*(phase-2)),phase,lnphi) + if ( density_error(phase) /= 0.0 ) residu(i) = residu(i) + SIGN( density_error(phase), residu(i) ) * 0.001 +END DO + +END SUBROUTINE objec_fct + + + +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! REAL FUNCTION isofugacity +! +! calculates the deviation from the condition of equal fugacities in +! logarithmic form. +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! + REAL FUNCTION isofugacity (i,phase,lnphi) +! + USE BASIC_VARIABLES + IMPLICIT NONE +! +! ---------------------------------------------------------------------- + INTEGER, INTENT(IN) :: i + INTEGER, INTENT(IN) :: phase + REAL, INTENT(IN) :: lnphi(np,nc) +! +! ---------------------------------------------------------------------- + INTEGER :: p1, p2 +! ---------------------------------------------------------------------- + + +! p1=1 +p1 = phase-1 +p2 = phase + +isofugacity = scaling(i) *( lnphi(p2,i)+lnx(p2,i)-lnx(p1,i)-lnphi(p1,i) ) +! write (*,'(a, 4G18.8)') ' t, p ',t,p,dense(1),dense(2) +! write (*,'(a,i3,i3,3G18.8)') ' phi_V',i,p2,lnx(p2,i),lnphi(p2,i),dense(p2) +! write (*,'(a,i3,i3,3G18.8)') ' phi_L',i,p1,lnx(p1,i),lnphi(p1,i),dense(p1) +! write (*,*) ' ISOFUGACITY',i,ISOFUGACITY, scaling(i) +! write (*,'(a,i3,4G18.8)') ' ISOFUGACITY',i,ISOFUGACITY, lnphi(p2,i)+lnx(p2,i), -lnx(p1,i)-lnphi(p1,i) +! pause + +END FUNCTION isofugacity + + + + + + + + + + + + + + + + + +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! + SUBROUTINE vle_min(lle_check) +! + USE PARAMETERS, ONLY: RGAS + USE BASIC_VARIABLES + USE STARTING_VALUES + IMPLICIT NONE +! +! ---------------------------------------------------------------------- + LOGICAL, INTENT(OUT) :: lle_check + + INTEGER :: i,j,k,phasen(0:40),steps + REAL :: lnphi(np,nc) + REAL :: vlemin(0:40),llemin(0:40),xval(0:40) + REAL :: start_xv(0:40),start_xl(0:40),x_sav,dg_dx2 +! ---------------------------------------------------------------------- + + + +j = 0 +k = 0 +nphas = 2 + +steps = 40 + +x_sav = xi(1,1) +sum_rel(1) = 'x12' ! summation relation +sum_rel(2) = 'x22' ! summation relation + +DO i = 0, steps + densta(1) = 0.45 + densta(2) = 1.d-6 + xi(1,1) = 1.0 - REAL(i) / REAL(steps) + IF ( xi(1,1) <= 1.E-50 ) xi(1,1) = 1.E-50 + xi(2,1) = xi(1,1) + lnx(1,1) = LOG(xi(1,1)) + lnx(2,1) = LOG(xi(2,1)) + + CALL x_summation + CALL fugacity (lnphi) + CALL enthalpy_etc !!KANN DAS RAUS???? + + + + + xval(i) = xi(1,1) + llemin(i)= gibbs(1) +(xi(1,1)*lnx(1,1)+xi(1,2)*lnx(1,2))*RGAS*t + + IF ( ABS(1.0-dense(1)/dense(2)) > 0.0001 ) THEN + vlemin(i)= gibbs(1) +(xi(1,1)*lnx(1,1)+xi(1,2)*lnx(1,2))*RGAS*t & + - ( gibbs(2) +(xi(2,1)*lnx(2,1)+xi(2,2)*lnx(2,2))*RGAS*t ) + phasen(i) = 2 + ELSE + phasen(i) = 1 + END IF + + IF (i > 0 .AND. phasen(i) == 2) THEN + IF (phasen(i-1) == 2 .AND. ABS(vlemin(i)+vlemin(i-1)) < & + ABS(vlemin(i))+ABS(vlemin(i-1))) THEN + j = j + 1 + start_xv(j)=xval(i-1) + (xval(i)-xval(i-1)) & + * ABS(vlemin(i-1))/ABS(vlemin(i)-vlemin(i-1)) + END IF + END IF + +END DO + + +DO i=2,steps-2 + dg_dx2 = (-llemin(i-2)+16.0*llemin(i-1)-30.0*llemin(i) & + +16.0*llemin(i+1)-llemin(i+2)) / (12.0*((xval(i)-xval(i-1))**2)) + IF (dg_dx2 < 0.0) THEN + k = k + 1 + start_xl(k)=xval(i) + END IF +END DO + + +IF (start_xl(1) == 0.0 .AND. start_xv(1) /= 0.0) THEN + xi(1,1) = start_xv(1) + xi(1,2) = 1.0-xi(1,1) + lle_check=.false. + ! write (*,*) 'VLE is likely', xi(1,1),xi(1,2) +ELSE IF (start_xl(1) /= 0.0 .AND. start_xv(1) == 0.0) THEN + xi(1,1) = start_xl(1) + xi(1,2) = 1.0-xi(1,1) + ! write (*,*) 'LLE is likely', xi(1,1),xi(1,2) + lle_check=.true. +ELSE IF (start_xl(1) /= 0.0 .AND. start_xv(1) /= 0.0) THEN + xi(1,1) = start_xv(1) + xi(1,2) = 1.0-xi(1,1) + ! write(*,*) 'starting with VLE and check for LLE' + lle_check=.true. +ELSE + xi(1,1) = x_sav + xi(1,2) = 1.0 - xi(1,1) +END IF + + +CALL x_summation + +END SUBROUTINE vle_min + + +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! SUBROUTINE phase_stability +! +! the index 'LLE_check' is for the starting density (which determines +! whether a liquid or vapor phase is found) of the trial phase. The +! feed-point exits either as a vapor or as a liquid. If it can exist as +! both (feedphases=2), then both states are tested. +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! + SUBROUTINE phase_stability ( lle_check, flashcase, ph_split ) +! + USE BASIC_VARIABLES + USE STARTING_VALUES + USE EOS_VARIABLES, ONLY: dhs, PI, x, eta, eta_start, z3t, fres + USE EOS_NUMERICAL_DERIVATIVES + IMPLICIT NONE +! +! ---------------------------------------------------------------------- + LOGICAL :: lle_check + LOGICAL, INTENT(IN OUT) :: flashcase + INTEGER, INTENT(OUT) :: ph_split +! ---------------------------------------------------------------------- + + INTERFACE + REAL FUNCTION F_STABILITY ( optpara, n ) + INTEGER, INTENT(IN) :: n + REAL, INTENT(IN OUT) :: optpara(n) + END FUNCTION + END INTERFACE + +!INTERFACE +! SUBROUTINE F_STABILITY (fmin, optpara, n) +! REAL, INTENT(IN OUT) :: fmin +! REAL, INTENT(IN) :: optpara(:) +! INTEGER, INTENT(IN) :: n +! END SUBROUTINE F_STABILITY +! +! SUBROUTINE stability_grad (g, optpara, n) +! REAL, INTENT(IN OUT) :: g(:) +! REAL, INTENT(IN) :: optpara(:) +! INTEGER, INTENT(IN) :: n +! END SUBROUTINE stability_grad +! +! SUBROUTINE stability_hessian (hessian, g, fmin, optpara, n) +! REAL, INTENT(IN OUT) :: hessian(:,:) +! REAL, INTENT(IN OUT) :: g(:) +! REAL, INTENT(IN OUT) :: fmin +! REAL, INTENT(IN) :: optpara(:) +! INTEGER, INTENT(IN) :: n +! END SUBROUTINE stability_hessian +!END INTERFACE + + INTEGER :: n, PRIN + REAL :: fmin, t0, h0, MACHEP, PRAXIS + REAL, ALLOCATABLE :: optpara(:) + + INTEGER :: i, feedphases, trial + REAL :: rhoi(nc),rho_start + REAL :: feeddens, rho_phas(np) + REAL :: fden + REAL :: dens + REAL :: rhot + REAL :: lnphi(np,nc) + REAL :: w(np,nc), mean_mass +! ---------------------------------------------------------------------- + +n = ncomp +ALLOCATE( optpara(n) ) + +IF (lle_check) WRITE (*,*) ' stability test starting with dense phase' + +DO i = 1, ncomp ! setting feed-phase x's + IF (.NOT.flashcase) xif(i) = xi(1,i) + IF (flashcase) xi(1,i) = xif(i) + xi(2,i) = xif(i) ! feed is tested for both: V and L density +END DO + +densta(1) = 0.45 +densta(2) = 1.d-6 + +CALL dens_calc(rho_phas) +IF ( ABS(1.0-dense(1)/dense(2)) > 0.0005 ) THEN + feedphases=2 ! feed-composition can exist both, in V and L +ELSE + feedphases=1 ! feed-composition can exist either in V or L +END IF +densta(1) = dense(1) +feeddens = dense(2) +!write (*,*) 'feedphases',dense(1), dense(2),feedphases + +10 CONTINUE ! IF FeedPhases=2 THEN there is a second cycle + + trial = 1 + + ! -------------------------------------------------------------------- + ! setting trial-phase mole-fractions + ! if there is no phase-split then further trial-phases are + ! considered (loop: 20 CONTINUE) + ! -------------------------------------------------------------------- + DO i = 1, ncomp + w(2,i) = 1.0 / REAL(ncomp) + END DO + mean_mass = 1.0 / SUM( w(2,1:ncomp)/mm(1:ncomp) ) + xi(2,1:ncomp) = w(2,1:ncomp)/mm(1:ncomp) * mean_mass + + 20 CONTINUE + + DO i = 1, ncomp + rhoif(i) = rho_phas(1) * xif(i) + rhoi(i) = rhoif(i) + END DO + + !write (*,'(a,6G16.8)') 'startval',rho_phas(2),xi(2,1:ncomp) + + ! -------------------------------------------------------------------- + ! calc Helmholtz energy density and derivative (numerical) to rhoif(i). + ! The derivative is taken around the "feed-point" not the trial phase + ! -------------------------------------------------------------------- + + rhot = SUM( rhoi(1:ncomp) ) + x(1:ncomp) = rhoi(1:ncomp) / rhot + CALL PERTURBATION_PARAMETER + xi(1,1:ncomp) = x(1:ncomp) + eta = rhot * z3t + eta_start = eta + densta(1) = eta_start + ensemble_flag = 'tv' + CALL FUGACITY (lnphi) + ensemble_flag = 'tp' + + call fden_calc ( fden, rhoi ) + fdenf = fden + + grad_fd(1:ncomp) = lnphi(1,1:ncomp) + LOG( rhoi(1:ncomp) ) + + + ! -------------------------------------------------------------------- + ! starting values for iteration (optpara) + ! -------------------------------------------------------------------- + rho_start = 1.E-5 + IF (lle_check) THEN + densta(2) = 0.45 + CALL dens_calc(rho_phas) + rho_start = rho_phas(2)*0.45/dense(2) + END IF + DO i = 1,ncomp + rhoi(i) = xi(2,i)*rho_start + optpara(i) = LOG( rhoi(i) ) + END DO + + ! -------------------------------------------------------------------- + ! minimizing the objective fct. Phase split for values of fmin < 0.0 + ! -------------------------------------------------------------------- + t0 = 5.E-5 + h0 = 0.5 + PRIN = 0 + MACHEP = 1.E-15 + + fmin = PRAXIS( t0, MACHEP, h0, n, PRIN, optpara, F_STABILITY, fmin ) + + + ! -------------------------------------------------------------------- + ! updating the ln(x) valus from optpara. The optimal optpara-vector is + ! not necessarily the one that was last evaluated. At the very end, + ! cg_decent writes the best values to optpara + ! -------------------------------------------------------------------- + fmin = F_STABILITY( optpara, n ) + + + + ! IF ( n == 2 ) THEN + ! CALL Newton_Opt_2D ( stability_hessian, F_stability, optpara, n, 1.E-8, 1.E-8, g, fmin) + ! ELSE + ! CALL cg_descent (1.d-5, optpara, n, F_STABILITY, stability_grad, STATUS, & + ! gnorm, fmin, iter, nfunc, ngrad, d, g, xtemp, gtemp) + ! ENDIF + ! CALL F_STABILITY (fmin, optpara, n) + + + ! -------------------------------------------------------------------- + ! determine instability & non-trivial solution + ! -------------------------------------------------------------------- + ph_split = 0 + IF (fmin < -1.E-7 .AND. & + ABS( 1.0 - maxval(EXP(optpara),mask=optpara /= 0.0) /maxval(rhoif) ) > 0.0005) THEN + ph_split = 1 + END IF + + IF (ph_split == 1) THEN + + ! ------------------------------------------------------------------ + ! here, there should be IF FeedPhases=2 THEN GOTO 10 + ! and test for another phase (while saving optpara) + ! ------------------------------------------------------------------ + + rhoi2(1:ncomp) = EXP( optpara(1:ncomp) ) + dens = PI/6.0 * SUM( rhoi2(1:ncomp) * parame(1:ncomp,1) * dhs(1:ncomp)**3 ) + rhot = SUM( rhoi2(1:ncomp) ) + xi(2,1:ncomp) = rhoi2(1:ncomp) / rhot + + ELSE + + IF (trial <= ncomp + ncomp) THEN + ! ---------------------------------------------------------------- + ! setting trial-phase x's + ! ---------------------------------------------------------------- + IF (trial <= ncomp) THEN + DO i=1,ncomp + w(2,i) = 1.0 / REAL(ncomp-1) * 0.05 + END DO + w(2,trial) = 0.95 + ELSE + DO i=1,ncomp + w(2,i) = 1.0 / REAL(ncomp-1) * 0.00001 + END DO + w(2,trial-ncomp) = 0.99999 + END IF + mean_mass = 1.0 / SUM( w(2,1:ncomp)/mm(1:ncomp) ) + xi(2,1:ncomp) = w(2,1:ncomp)/mm(1:ncomp) * mean_mass + trial = trial + 1 + GO TO 20 + END IF + ! IF (.NOT.LLE_check) write (*,*) 'no phase split detected' + ! IF (.NOT.LLE_check) pause + IF (feedphases > 1 .AND. .NOT.lle_check .AND. densta(1) > 0.2) THEN + densta(1) = feeddens ! this will be the lower-valued density (vapor) + CALL dens_calc(rho_phas) + ! WRITE (*,*) 'try feed as vapor-phase' + GO TO 10 + END IF + + END IF + +DEALLOCATE( optpara ) + +END SUBROUTINE phase_stability + + +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! SUBROUTINE select_sum_rel +! +! This subroutine determines which component of a phase "ph" is calculated +! from the summation relation x_i = 1 - sum(x_j). The other components are, +! by default, said to be iterated during the phase equilibrium calculation. +! +! Note that for flash calculations not all of these mole fractions are in +! fact iterated - this is raken care of in "determine_flash_it". +! +! ph phase +! excl exclude comp. n +! startindex assign it(startindex) for quantities to be iterated +! (further it(startindex+1) is assigned, for a ternary +! mixture, etc.) +! +! sum_index indicates the component, with the largest mole +! fraction. If ph=1 and sum_index=2, we define +! sum_rel(ph=1)='x12', so that this component is +! calculated from the summation relation. +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! + SUBROUTINE select_sum_rel (ph,excl,startindex) +! + USE BASIC_VARIABLES + IMPLICIT NONE +! +! ---------------------------------------------------------------------- + INTEGER, INTENT(IN) :: ph + INTEGER, INTENT(IN) :: excl + INTEGER, INTENT(IN) :: startindex +! ---------------------------------------------------------------------- + INTEGER :: i,j, sum_index + REAL :: xmax(np) + ! CHARACTER :: compNo*2,phasNo*2 +! ---------------------------------------------------------------------- + +xmax(ph) = 0.0 +DO i = 1, ncomp + + IF ( xi(ph,i) > xmax(ph) ) THEN + xmax(ph) = xi(ph,i) + sum_index = i + + IF (ph == 1 .AND. i == 1) sum_rel(1) = 'x11' + IF (ph == 1 .AND. i == 2) sum_rel(1) = 'x12' + IF (ph == 1 .AND. i == 3) sum_rel(1) = 'x13' + IF (ph == 1 .AND. i == 4) sum_rel(1) = 'x14' + IF (ph == 1 .AND. i == 5) sum_rel(1) = 'x15' + + IF (ph == 2 .AND. i == 1) sum_rel(2) = 'x21' + IF (ph == 2 .AND. i == 2) sum_rel(2) = 'x22' + IF (ph == 2 .AND. i == 3) sum_rel(2) = 'x23' + IF (ph == 2 .AND. i == 4) sum_rel(2) = 'x24' + IF (ph == 2 .AND. i == 5) sum_rel(2) = 'x25' + + IF (ph == 3 .AND. i == 1) sum_rel(3) = 'x31' + IF (ph == 3 .AND. i == 2) sum_rel(3) = 'x32' + IF (ph == 3 .AND. i == 3) sum_rel(3) = 'x33' + IF (ph == 3 .AND. i == 4) sum_rel(3) = 'x34' + IF (ph == 3 .AND. i == 5) sum_rel(3) = 'x35' +! write (*,*) ph,i,xi(ph,i),sum_rel(ph) + END IF + +END DO + +j = 0 +DO i = 1, ncomp + + IF ( i /= sum_index .AND. i /= excl ) THEN + IF (ph == 1 .AND. i == 1) it(startindex+j) = 'x11' + IF (ph == 1 .AND. i == 2) it(startindex+j) = 'x12' + IF (ph == 1 .AND. i == 3) it(startindex+j) = 'x13' + IF (ph == 1 .AND. i == 4) it(startindex+j) = 'x14' + IF (ph == 1 .AND. i == 5) it(startindex+j) = 'x15' + + IF (ph == 2 .AND. i == 1) it(startindex+j) = 'x21' + IF (ph == 2 .AND. i == 2) it(startindex+j) = 'x22' + IF (ph == 2 .AND. i == 3) it(startindex+j) = 'x23' + IF (ph == 2 .AND. i == 4) it(startindex+j) = 'x24' + IF (ph == 2 .AND. i == 5) it(startindex+j) = 'x25' + + IF (ph == 3 .AND. i == 1) it(startindex+j) = 'x31' + IF (ph == 3 .AND. i == 2) it(startindex+j) = 'x32' + IF (ph == 3 .AND. i == 3) it(startindex+j) = 'x33' + IF (ph == 3 .AND. i == 4) it(startindex+j) = 'x34' + IF (ph == 3 .AND. i == 5) it(startindex+j) = 'x35' +! write (*,*) 'iter ',it(startindex+j) + j = j + 1 + END IF + +END DO + +END SUBROUTINE select_sum_rel + + + + +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! + SUBROUTINE tangent_plane +! + USE BASIC_VARIABLES + USE STARTING_VALUES + IMPLICIT NONE +! +! ---------------------------------------------------------------------- +!!$ INTERFACE +!!$ SUBROUTINE tangent_value (fmin, optpara, n) +!!$ INTEGER, INTENT(IN) :: n +!!$ REAL, INTENT(IN OUT) :: fmin +!!$ REAL, INTENT(IN) :: optpara(:) +!!$ END SUBROUTINE tangent_value +!!$ +!!$ SUBROUTINE tangent_grad (g, optpara, n) +!!$ INTEGER, INTENT(IN) :: n +!!$ REAL, INTENT(IN OUT) :: g(:) +!!$ REAL, INTENT(IN) :: optpara(:) +!!$ END SUBROUTINE tangent_grad +!!$ END INTERFACE + +! +! ---------------------------------------------------------------------- + INTERFACE + REAL FUNCTION PRAXIS( t0, MACHEP, h0, n, PRIN, optpara, TANGENT_VALUE, fmin ) + REAL, INTENT(IN OUT) :: t0 + REAL, INTENT(IN) :: machep + REAL, INTENT(IN) :: h0 + INTEGER :: n + INTEGER, INTENT(IN OUT) :: prin + REAL, INTENT(IN OUT) :: optpara(n) + REAL, EXTERNAL :: TANGENT_VALUE + REAL, INTENT(IN OUT) :: fmin + END FUNCTION + + REAL FUNCTION TANGENT_VALUE2 ( optpara, n ) + INTEGER, INTENT(IN) :: n + REAL, INTENT(IN) :: optpara(n) + END FUNCTION + END INTERFACE +! +! ---------------------------------------------------------------------- + INTEGER :: n + INTEGER :: i, k, ph + INTEGER :: small_i, min_ph, other_ph + INTEGER :: PRIN + REAL :: fmin , t0, h0, MACHEP + REAL :: lnphi(np,nc) + REAL, ALLOCATABLE :: optpara(:) + +! INTEGER :: STATUS, iter, nfunc, ngrad +! REAL :: gnorm +! REAL, ALLOCATABLE :: d(:), g(:), xtemp(:), gtemp(:) +! ---------------------------------------------------------------------- + +n = ncomp +t0 = 1.E-4 +h0 = 0.1 +PRIN = 0 +MACHEP = 1.E-15 + +ALLOCATE( optpara(n) ) +!ALLOCATE( d(n) ) +!ALLOCATE( g(n) ) +!ALLOCATE( xtemp(n) ) +!ALLOCATE( gtemp(n) ) + +DO i = 1,ncomp + rhoi1(i) = rhoif(i) + lnx(1,i) = LOG(xi(1,i)) + lnx(2,i) = LOG(xi(2,i)) +END DO + +DO i = 1,ncomp + optpara(i) = LOG( xi(2,i) * 0.001 ) +END DO + +! CALL cg_descent (1.d-4, optpara, n, tangent_value, tangent_grad, STATUS, & +! gnorm, fmin, iter, nfunc, ngrad, d, g, xtemp, gtemp) +! +! updating the ln(x) valus from optpara. The optimal optpara-vector is not necessarily +! the one that was last evaluated. At the very end, cg_decent writes the best values to optpara +! CALL tangent_value (fmin, optpara, n) + + + +fmin = PRAXIS( t0, MACHEP, h0, n, PRIN, optpara, TANGENT_VALUE2, fmin ) + +! The optimal optpara-vector is not necessarily the one that was last evaluated. +! TANGENT_VALUE is reexecuted with the optimal vector optpara, in order to update the ln(x) values +fmin = TANGENT_VALUE2( optpara, n ) + + +! ---------------------------------------------------------------------- +! If one component is a polymer (indicated by a low component-density) +! then get an estimate of the polymer-lean composition, by solving for +! xi_p1 = ( xi_p2 * phii_p2) / phii_p1 (phase equilibrium condition, +! with p1 for phase 1) +! ---------------------------------------------------------------------- +IF ( MINVAL( lnx(1,1:ncomp) ) < MINVAL( lnx(2,1:ncomp) ) ) THEN + min_ph = 1 + other_ph = 2 +ELSE + min_ph = 2 + other_ph = 1 +ENDIF +small_i = MINLOC( lnx(min_ph,1:ncomp), 1 ) +! --- if one component is a polymer ------------------------------------ +IF ( MINVAL( lnx(min_ph,1:ncomp) ) < -20.0 ) THEN + CALL FUGACITY ( lnphi ) + lnx(min_ph,small_i) = lnx(other_ph,small_i)+lnphi(other_ph,small_i) - lnphi(min_ph,small_i) + optpara(small_i) = lnx(2,small_i) + LOG( SUM( EXP( optpara(1:ncomp) ) ) ) +END IF + +! ---------------------------------------------------------------------- +! caution: these initial values are for a flashcase overwritten in +! SUBROUTINE determine_flash_it2, because in that case, the lnx-values +! treated as ln(mole_number). +! ---------------------------------------------------------------------- +val_init(1) = dense(1) +val_init(2) = dense(2) +val_init(3) = t +val_init(4) = p +DO ph = 1,nphas + DO k = 1,ncomp + val_init(4+k+(ph-1)*ncomp) = lnx(ph,k) + END DO +END DO +!alpha = optpara(1) + + +!DEALLOCATE( optpara, d, g, xtemp, gtemp ) +DEALLOCATE( optpara ) + +END SUBROUTINE tangent_plane + + +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! + SUBROUTINE determine_flash_it2 +! + USE BASIC_VARIABLES + IMPLICIT NONE +! +! ---------------------------------------------------------------------- + INTEGER :: i, k, ph + REAL :: n_phase1, n_phase2, max_x_diff +! ---------------------------------------------------------------------- + + IF ( MINVAL( lnx(1,1:ncomp) ) < MINVAL( lnx(2,1:ncomp) ) ) THEN + it(1) = 'x11' + it(2) = 'x12' + IF (ncomp >= 3) it(3) = 'x13' + IF (ncomp >= 4) it(4) = 'x14' + IF (ncomp >= 5) it(5) = 'x15' + sum_rel(1) = 'nfl' + ELSE + it(1) = 'x21' + it(2) = 'x22' + IF (ncomp >= 3) it(3) = 'x23' + IF (ncomp >= 4) it(4) = 'x24' + IF (ncomp >= 5) it(5) = 'x25' + sum_rel(2) = 'nfl' + ENDIF + max_x_diff = 0.0 + DO i = 1,ncomp + IF ( ABS( EXP( lnx(1,i) ) - EXP( lnx(2,i) ) ) > max_x_diff ) THEN + max_x_diff = ABS( EXP( lnx(1,i) ) - EXP( lnx(2,i) ) ) + n_phase1 = ( xif(i) - EXP( lnx(2,i) ) ) / ( EXP( lnx(1,i) ) - EXP( lnx(2,i) ) ) + n_phase2 = 1.0 - n_phase1 + END IF + END DO + lnx(1,1:ncomp) = lnx(1,1:ncomp) + LOG( n_phase1 ) ! these x's are treated as mole numbers + lnx(2,1:ncomp) = lnx(2,1:ncomp) + LOG( n_phase2 ) ! these x's are treated as mole numbers + + + val_init(1) = dense(1) + val_init(2) = dense(2) + val_init(3) = t + val_init(4) = p + DO ph = 1,nphas + DO k = 1,ncomp + val_init(4+k+(ph-1)*ncomp) = lnx(ph,k) ! - LOG( SUM( EXP( lnx(ph,1:ncomp) ) ) ) + ! write (*,*) ph,k, lnx(ph,k) + END DO + END DO + +END SUBROUTINE determine_flash_it2 + +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! SUBROUTINE poly_sta_var +! +! This subroutine generates starting values for mole fractons of +! polymer-solvent systems. +! The determination of these starting values follows a two-step +! procedure. Fist, the equilibrium concentration of the polymer-rich +! phase is estimated with the assumption of zero concentration +! of polymer in the polymer-lean-phase. This is achieved in the +! SUBROUTINE POLYMER_FREE. (Only one equation has to be iterated +! for this case). Once this is achieved, the rigorous calculation +! is triggered. If it converges, fine! If no solution is obtained, +! the pressure is somewhat reduced, the procedure is repeated and +! a calculation is started to approach the originally specified +! pressure. +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! + SUBROUTINE poly_sta_var (converg) +! + USE BASIC_VARIABLES + IMPLICIT NONE +! +! ---------------------------------------------------------------------- + INTEGER, INTENT(IN OUT) :: converg +! +! ---------------------------------------------------------------------- + INTEGER :: k,ph,sol + REAL :: p_spec,solution(10,4+nc*np) +! ---------------------------------------------------------------------- + + p_spec = p + + find_equilibrium: DO + + CALL polymer_free(p_spec,sol,solution) + + WRITE (*,*) ' ' + WRITE (*,*) ' GENERATING STARTING VALUES' + + val_init(1) = solution(1,1) ! approx.solutions for next iteration + val_init(2) = solution(1,2) ! approx.solutions for next iteration + val_init(3) = solution(1,3) ! approx.solutions for next iteration + val_init(4) = solution(1,4) ! approx.solutions for next iteration + DO ph = 1,nphas + DO k = 1,ncomp + val_init(4+k+(ph-1)*ncomp) = solution(1,4+k+(ph-1)*ncomp) + END DO + END DO + val_init(7) = -10000.0 ! start.val. for lnx(2,1) for iterat. + + IF (p /= p_spec) & + WRITE (*,*) ' INITIAL EQUILIBRIUM CALC. FAILD. NEXT STEP STARTS' + + IF (p == p_spec) THEN + n_unkw = ncomp ! number of quantities to be iterated + it(1)='x11' ! iteration of mol fraction of comp.1 phase 1 + it(2)='x21' ! iteration of mol fraction of comp.1 phase 2 + CALL objective_ctrl (converg) + ELSE + outp = 0 ! output to terminal + running ='p' ! Pressure is running var. in PHASE_EQUILIB + CALL phase_equilib(p_spec,5.0,converg) + END IF + + IF (converg == 1) EXIT find_equilibrium + p = p * 0.9 + IF ( p < (0.7*p_spec) ) WRITE (*,*) ' NO SOLUTION FOUND' + IF ( p < (0.7*p_spec) ) STOP + + END DO find_equilibrium + + WRITE (*,*) ' FINISHED: POLY_STA_VAR' + +END SUBROUTINE poly_sta_var + + +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! SUBROUTINE x_summation +! +! This subroutine solves the summation relation: xi=1-sum(xj) +! The variable "sum_rel(i)" contains the information, which mole +! fraction is the one to be calculated here. Consider the example +! sum_rel(1)='x12'. The fist letter 'x' of this variable indicates, +! that this subroutine needs to be executed and that the mole +! fraction of a component has to be calculated. The second letter +! of the string points to phase 1, the third letter to component 2. +! If the fist letter is 'e', not 'x', then the subroutine +! NEUTR_CHARGE is called. This is the case of electrolyte solutions, +! neutral charges have to be enforced in all phases (see below). +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! + SUBROUTINE x_summation +! + USE BASIC_VARIABLES + IMPLICIT NONE +! +! ---------------------------------------------------------------------- + INTEGER :: i, j, comp_i, ph_i + REAL :: sum_x + CHARACTER (LEN=2) :: phasno + CHARACTER (LEN=2) :: compno + LOGICAL :: flashcase2 +! ---------------------------------------------------------------------- + +DO j = 1, nphas + IF (sum_rel(j)(1:3) == 'nfl') THEN + CALL new_flash (j) + RETURN + END IF +END DO + + + +flashcase2 = .false. + +DO j = 1, nphas + + IF (sum_rel(j)(1:1) == 'x') THEN + + phasno = sum_rel(j)(2:2) + READ(phasno,*) ph_i + compno = sum_rel(j)(3:3) + READ(compno,*) comp_i + IF ( sum_rel(nphas+j)(1:1) == 'e' ) CALL neutr_charge(nphas+j) + + sum_x = 0.0 + DO i = 1, ncomp + IF ( i /= comp_i ) sum_x = sum_x + xi(ph_i,i) + END DO + xi(ph_i,comp_i) = 1.0 - sum_x + IF ( xi(ph_i,comp_i ) < 0.0 ) xi(ph_i,comp_i) = 0.0 + IF ( xi(ph_i,comp_i ) /= 0.0 ) THEN + lnx(ph_i,comp_i) = LOG( xi(ph_i,comp_i) ) + ELSE + lnx(ph_i,comp_i) = -100000.0 + END IF + ! write (*,*) 'sum_x',ph_i,comp_i,lnx(ph_i,comp_i),xi(ph_i,comp_i) + + ELSE IF ( sum_rel(j)(1:2) == 'fl' ) THEN + + flashcase2 = .true. + ! ------------------------------------------------------------------ + ! This case is true when all molefractions of one phase are + ! determined from a component balance. What is needed to + ! calculate all molefractions of that phase are all mole- + ! fractions of the other phase (nphas=2, so far) and the + ! phase fraction alpha. + ! Alpha is calculated (in FLASH_ALPHA) from the mole fraction + ! of component {sum_rel(j)(3:3)}. IF sum_rel(2)='fl3', then + ! the alpha is determined from the molefraction of comp. 3 and + ! the molefraction of phase 2 is then completely determined ELSE + ! ------------------------------------------------------------------ + + ELSE + WRITE (*,*) 'summation relation not defined' + STOP + END IF + +END DO + +IF ( it(1) == 'fls' ) CALL flash_sum +IF ( flashcase2 ) CALL flash_alpha + +END SUBROUTINE x_summation + + + +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! SUBROUTINE FUGACITY +! +! This subroutine serves as an interface to the eos-subroutines. +! (1) case 1, when ensemble_flag = 'tp' +! The subroutine gives the residual chemical potential: +! mu_i^res(T,p,x)/kT = ln( phi_i ) +! and in addition, the densities that satisfy the specified p +! (2) case 2, when ensemble_flag = 'tv' +! The subroutine gives the residual chemical potential: +! --> mu_i^res(T,rho,x)/kT +! and in addition the resulting pressure for the given density. +! The term "residual" means difference of the property and the same +! property for an ideal gas mixture. +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! + SUBROUTINE FUGACITY (ln_phi) +! + USE BASIC_VARIABLES + USE EOS_VARIABLES, ONLY: phas, x, eta, eta_start, lnphi, fres, rho, pges, KBOL + IMPLICIT NONE +! +! ---------------------------------------------------------------------- + REAL, INTENT(OUT) :: ln_phi(np,nc) +! +! --- local variables -------------------------------------------------- + INTEGER :: ph +! ---------------------------------------------------------------------- +! +IF (eos < 2) THEN + + DO ph = 1,nphas + + phas = ph + eta_start = densta(ph) + x(1:ncomp) = xi(ph,1:ncomp) + + IF (p < 1.E-100) THEN + WRITE(*,*) ' FUGACITY: PRESSURE TOO LOW', p + p = 1.E-6 + END IF + + IF (num == 0) CALL PHI_EOS + IF (num == 1) CALL PHI_NUMERICAL + !!IF (num == 2) CALL PHI_CRITICAL_RENORM + IF (num == 2) write(*,*) 'CRITICAL RENORM NOT INCLUDED YET' + + dense(ph) = eta + ln_phi(ph,1:ncomp) = lnphi(1:ncomp) + ! gibbs(ph) = fres + sum( xi(ph,1:ncomp)*( log( xi(ph,1:ncomp)*rho) - 1.0 ) ) & + ! + (pges * 1.d-30) / (KBOL*t*rho) ! includes ideal gas contribution + + ! f_res(ph) = fres + ! write (*,'(i3,4G20.11)') ph,eta,lnphi(1),lnphi(2) + ! DO i = 1,ncomp + ! DO j=1,NINT(parame(i,12)) + ! mxx(ph,i,j) = mx(i,j) + ! END DO + ! END DO + + END DO + +ELSE + +! IF (eos == 2) CALL srk_eos (ln_phi) +! IF (eos == 3) CALL pr_eos (ln_phi) +! dense(1) = 0.01 +! dense(2) = 0.3 +! IF (eos == 4.OR.eos == 5.OR.eos == 6.OR.eos == 8) CALL lj_fugacity(ln_phi) +! IF (eos == 7) CALL sw_fugacity(ln_phi) +! IF (eos == 9) CALL lj_bh_fug(ln_phi) + +END IF + +END SUBROUTINE FUGACITY + + +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! SUBROUTINE enthalpy_etc +! +! This subroutine serves as an interface to the EOS-routines. The +! residual enthalpy h_res, residual entropy s_res, residual Gibbs +! enthalpy g_res, and residual heat capacity at constant pressure +! (cp_res) corresponding to converged conditions are calculated. +! The conditions in (T,P,xi,rho) need to be converged equilibrium +! conditions !! +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! + SUBROUTINE enthalpy_etc +! + USE BASIC_VARIABLES + USE EOS_VARIABLES + IMPLICIT NONE +! + INTEGER :: ph +! ------------------------------------------------------------------ + +IF (eos <= 1) THEN + + DO ph=1,nphas + + phas = ph + eta = dense(ph) +! eta_start = dense(ph) + x(1:ncomp) = xi(ph,1:ncomp) + + IF(num == 0) THEN + CALL H_EOS + ELSE + IF(num == 1) CALL H_numerical + IF(num == 2) write (*,*) 'enthalpy_etc: incorporate H_EOS_RN' + IF(num == 2) stop +! IF(num == 2) CALL H_EOS_rn + END IF + enthal(ph) = h_res + entrop(ph) = s_res + ! gibbs(ph) = h_res - t * s_res ! already defined in eos.f90 (including ideal gas) + cpres(ph) = cp_res + + END DO + IF (nphas == 2) h_lv = enthal(2)-enthal(1) + +ENDIF + +END SUBROUTINE enthalpy_etc + + +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! SUBROUTINE dens_calc +! +! This subroutine serves as an interface to the EOS-routines. The +! densities corresponding to given (P,T,xi) are calculated. +! (Note: the more common interface is SUBROUTINE FUGACITY. +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! + SUBROUTINE dens_calc(rho_phas) +! + USE BASIC_VARIABLES + USE EOS_VARIABLES + IMPLICIT NONE +! +! +!------------------------------------------------------------------ + REAL, INTENT(OUT) :: rho_phas(np) +! + INTEGER :: ph +!------------------------------------------------------------------ + + +DO ph = 1, nphas + + IF (eos < 2) THEN + + phas = ph + eta = densta(ph) + eta_start = densta(ph) + x(1:ncomp) = xi(ph,1:ncomp) + + CALL PERTURBATION_PARAMETER + CALL DENSITY_ITERATION + + dense(ph)= eta + rho_phas(ph) = eta/z3t + + ELSE + write (*,*) ' SUBROUTINE DENS_CALC not available for cubic EOS' + stop + END IF + +END DO + +END SUBROUTINE dens_calc + + +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! + SUBROUTINE fden_calc (fden, rhoi) +! + USE BASIC_VARIABLES + USE EOS_VARIABLES + IMPLICIT NONE +! +! ---------------------------------------------------------------------- + REAL, INTENT(OUT) :: fden + REAL, INTENT(IN OUT) :: rhoi(nc) +! ---------------------------------------------------------------------- + REAL :: rhot, fden_id +! ---------------------------------------------------------------------- + + +IF (eos < 2) THEN + + rhot = SUM( rhoi(1:ncomp) ) + x(1:ncomp) = rhoi(1:ncomp) / rhot + + CALL PERTURBATION_PARAMETER + eta = rhot * z3t + eta_start = eta + + IF (num == 0) THEN + CALL F_EOS + ELSE IF(num == 1) THEN + CALL F_NUMERICAL + ELSE + write (*,*) 'deactivated this line when making a transition to f90' + stop + ! CALL F_EOS_rn + END IF + + fden_id = SUM( rhoi(1:ncomp) * ( LOG( rhoi(1:ncomp) ) - 1.0 ) ) + + fden = fres * rhot + fden_id + +ELSE + write (*,*) ' SUBROUTINE FDEN_CALC not available for cubic EOS' + stop +END IF + +END SUBROUTINE fden_calc + + + + +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! SUBROUTINE polymer_free +! +! This subroutine performes a phase equilibrium calculation assuming +! the polymer-lean hase to be polymer-free (x_poly=0). Only the +! equality of the solvent-fugacities has to be ensured (only one +! equation to be iterated). This procedure delivers very good +! appoximations for the polymer-rich phase up-to fairly close to the +! mixture critical point. Both, liquid-liquid and vapor-liquid +! equilibria can be calculated. +! See also comments to SUBROUTINE POLY_STA_VAR. +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! + SUBROUTINE polymer_free (p_spec,sol,solution) +! + USE BASIC_VARIABLES + IMPLICIT NONE +! +! ---------------------------------------------------------------------- + REAL, INTENT(IN OUT) :: p_spec + INTEGER, INTENT(OUT) :: sol + REAL, INTENT(OUT) :: solution(10,4+nc*np) +! +! ---------------------------------------------------------------------- + INTEGER :: k,j,ph, converg + REAL :: grid(10) +! ---------------------------------------------------------------------- + + sol = 0 + + grid(1)=0.98 + grid(2)=0.9 + grid(3)=0.7 + grid(4)=0.5 + grid(5)=0.3 + grid(6)=0.2 + grid(7)=0.1 + grid(8)=0.05 + + DO WHILE ( sol == 0 ) + + DO j = 1,8 + ! Phase 2 is solvent-phase + ! starting value for xi(1,1) of polymer-phase 1: w_polymer=0.95 to 0.05 + ! from simple approximate equation + xi(1,1) = grid(j) / ( (1.0-grid(j)) * mm(1) / mm(2) ) !xi(1,1) Phase 1 Komponente 1 + IF ( mm(1) < 5000.0 ) xi(1,1) = xi(1,1) * 0.8 + xi(1,2) = 1.0 - xi(1,1) !xi(1,2) Phase 1 Komponente 2 + lnx(1,1) = LOG(xi(1,1)) + lnx(1,2) = LOG(xi(1,2)) + lnx(2,1) = -1.E10 !ln(xi) Phase 2 Komponente 1 + lnx(2,2) = 0.0 !ln(xi) Phase 2 Komponente 2 + + + + val_init(1) = 0.45 ! starting density targeting at a liquid phase + val_init(2) = 0.0001 ! starting density targeting at a vapor phase + ! val_init(2) = 0.45 + val_init(3) = t + val_init(4) = p + DO ph = 1,nphas + DO k = 1,ncomp + val_init(4+k+(ph-1)*ncomp) = lnx(ph,k) + END DO + END DO + + + + + n_unkw = ncomp-1 ! number of quantities to be iterated + it(1) = 'x11' ! iteration of mol fraction of comp.1 phase 1 + it(2) = ' ' + sum_rel(1) = 'x12' ! summation relation: x12 = 1 - sum(x1j) + sum_rel(2) = 'x22' + + CALL objective_ctrl (converg) + + IF (converg == 1 .AND. ABS(dense(1)/dense(2)-1.0) > 1.d-3 .AND. dense(1) > 0.1) THEN + IF (sol == 0) THEN + sol = sol + 1 + DO k = 1,4+ncomp*nphas + solution(sol,k) = val_conv(k) + END DO + ELSE IF (ABS(solution(sol,5)/lnx(1,1)-1.0) > 1.d-2) THEN + sol = sol + 1 + DO k = 1,4+ncomp*nphas + solution(sol,k) = val_conv(k) + END DO + END IF + END IF + + END DO + + + + + + IF (sol == 0) THEN + WRITE (*,*) ' no initial solution found' + p = p*0.9 + IF (p < (0.7*p_spec)) WRITE (*,*) ' NO SOLUTION FOUND' + IF (p < (0.7*p_spec)) STOP + ELSE IF (sol > 1) THEN + ! write (*,*) ' ' + ! write (*,*) ' ',sol,' solutions found:' + ! write (*,*) ' lnx(1,1), dichte_1, dichte_2' + ! DO k = 1,sol + ! write (*,*) solution(k,5),solution(k,1),solution(k,2) + ! END DO + END IF + END DO + + n_unkw = ncomp ! number of quantities to be iterated + it(1) = 'x11' ! iteration of mol fraction of comp.1 phase 1 + it(2) = 'x21' ! iteration of mol fraction of comp.1 phase 2 + sum_rel(1) = 'x12' ! summation relation: x12 = 1 - sum(x1j) + sum_rel(2) = 'x22' ! summation relation: x22 = 1 - sum(x2j) + + + END SUBROUTINE polymer_free + + + + + +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! SUBROUTINE phase_equilib +! +! This subroutine varies a predefined "running variable" and +! organizes phase equilibrium calculations. For an isotherm +! calculation e.g., the running variable is often the pressure. The +! code is designed to deliver only converged solutions. In order to +! enforce convergence, a step-width adjustment (reduction) is +! implemented. + +! VARIABLE LIST: +! running defines the running variable. For example: if you want +! to calculate the vapor pressure curve of a component +! starting from 100�C to 200�C, then running is 't'. The +! temperature is step-wise increased until the end- +! -temperature of 200�C is reached. +! (in this example end_x=200+273.15) +! end_x end point for running variable +! steps No. of calculation steps towards the end point of calc. +! converg 0 if no convergence achieved, 1 if converged solution +! +! PREREQUISITES: +! prior to execution of this routine, the follwing variables have to +! be defined: "val_init" an array containing the starting values for +! this iteration, "it(i)" provides the information, which variable is +! determined iteratively, "sum_rel(i)" indicates, which mole fraction +! is determined from the summation relation sum(xi)=1. Furthermore, +! the number of phases and the variables provided by the subroutine +! INPUT are required. +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! + SUBROUTINE phase_equilib (end_x,steps,converg) +! + USE BASIC_VARIABLES + IMPLICIT NONE +! +! ---------------------------------------------------------------------- + REAL, INTENT(IN) :: end_x + REAL, INTENT(IN) :: steps + INTEGER, INTENT(OUT) :: converg +! +! ---------------------------------------------------------------------- + INTEGER :: k, count1,count2,runindex,maxiter + REAL :: delta_x,delta_org,val_org,runvar + CHARACTER (LEN=2) :: compon + LOGICAL :: continue_cycle +! ---------------------------------------------------------------------- + +IF (running(1:2) == 'd1') runindex = 1 +IF (running(1:2) == 'd2') runindex = 2 +IF (running(1:1) == 't') runindex = 3 +IF (running(1:1) == 'p') runindex = 4 +IF (running(1:2) == 'x1') compon = running(3:3) +IF (running(1:2) == 'x1') READ(compon,*) k +IF (running(1:2) == 'x1') runindex = 4+k +IF (running(1:2) == 'x2') compon = running(3:3) +IF (running(1:2) == 'x2') READ(compon,*) k +IF (running(1:2) == 'x2') runindex = 4+ncomp+k +IF (running(1:2) == 'l1') compon = running(3:3) +IF (running(1:2) == 'l1') READ(compon,*) k +IF (running(1:2) == 'l1') runindex = 4+k +IF (running(1:2) == 'l2') compon = running(3:3) +IF (running(1:2) == 'l2') READ(compon,*) k +IF (running(1:2) == 'l2') runindex = 4+ncomp+k + +maxiter = 200 +IF ( ncomp >= 3 ) maxiter = 1000 +count1 = 0 +count2 = 0 +delta_x = ( end_x - val_init(runindex) ) / steps !J: calc increment in running var = (phi_end - phi_init)/steps +delta_org = ( end_x - val_init(runindex) ) / steps +val_org = val_init(runindex) +IF ( running(1:1) == 'x' ) THEN + delta_x = ( end_x - EXP(val_init(runindex)) ) / steps + delta_org = ( end_x - EXP(val_init(runindex)) ) / steps + val_org = EXP(val_init(runindex)) +END IF + +continue_cycle = .true. + +DO WHILE ( continue_cycle ) + + count1 = count1 + 1 + count2 = count2 + 1 + ! val_org = val_init(runindex) + + + CALL objective_ctrl (converg) + + IF (converg == 1) THEN + val_init( 1:(4+ncomp*nphas) ) = val_conv( 1:(4+ncomp*nphas) ) + IF (outp == 1 .AND. (ABS(delta_x) > 0.1*ABS(delta_org) .OR. count2 == 2)) CALL output + ELSE + delta_x = delta_x / 2.0 + IF (num == 2) delta_x = delta_x / 2.0 + val_init(runindex) = val_org + IF (running(1:1) == 'x') val_init(runindex) = LOG(val_org) + continue_cycle = .true. + count2 = 0 + END IF + runvar = val_init(runindex) + IF (running(1:1) == 'x') runvar = EXP(val_init(runindex)) + + IF ( end_x == 0.0 .AND. running(1:1) /= 'x' ) THEN + IF ( ABS(runvar-end_x) < 1.E-8 ) continue_cycle = .false. + ELSE IF ( ABS((runvar-end_x)/end_x) < 1.E-8 ) THEN + ! IF(delta_org.NE.0.0) WRITE (*,*)' FINISHED ITERATION',count1 + continue_cycle = .false. + ELSE IF ( count1 == maxiter ) THEN + WRITE (*,*) ' MAX. NO OF ITERATIONS',count1 + converg = 0 + continue_cycle = .false. + ELSE IF ( ABS(delta_x) < 1.E-5*ABS(delta_org) ) THEN + ! WRITE (*,*) ' CLOSEST APPROACH REACHED',count1 + converg = 0 + continue_cycle = .false. + ELSE + continue_cycle = .true. + val_org = runvar + IF (ABS(runvar+delta_x-end_x) > ABS(runvar-end_x)) delta_x = end_x - runvar ! if end-point passed + val_init(runindex) = runvar + delta_x + IF (running(1:1) == 'x') val_init(runindex) = LOG(runvar+delta_x) + END IF + + IF (ABS(delta_x) < ABS(delta_org) .AND. count2 >= 5) THEN + delta_x = delta_x * 2.0 + count2 = 0 + END IF + +END DO ! continue_cycle + +END SUBROUTINE phase_equilib + +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! + SUBROUTINE new_flash (ph_it) +! + USE BASIC_VARIABLES + IMPLICIT NONE +! +! ---------------------------------------------------------------------- + INTEGER, INTENT(IN) :: ph_it +! +! ---------------------------------------------------------------------- + INTEGER :: i, ph_cal + REAL, DIMENSION(nc) :: ni_1, ni_2 +! ---------------------------------------------------------------------- + + ph_cal = 3 - ph_it ! for two phases only + + DO i = 1, ncomp + IF ( lnx(ph_it,i) < -300.0 ) THEN + ni_2(i) = 0.0 + ELSE + ni_2(i) = EXP( lnx(ph_it,i) ) + END IF + END DO + + DO i = 1, ncomp + ni_1(i) = xif(i)-ni_2(i) + IF ( ni_2(i) > xif(i) ) THEN + ni_2(i) = xif(i) + ni_1(i) = xif(i) * 1.E-20 + ENDIF + END DO + + xi(ph_it,1:ncomp) = ni_2(1:ncomp) / SUM( ni_2(1:ncomp) ) + DO i = 1, ncomp + IF ( xi(ph_it,i) >= 1.E-300 ) lnx(ph_it,i) = LOG( xi(ph_it,i) ) + END DO + xi(ph_cal,1:ncomp) = ni_1(1:ncomp) / SUM( ni_1(1:ncomp) ) + lnx(ph_cal,1:ncomp) = LOG( xi(ph_cal,1:ncomp) ) + +END SUBROUTINE new_flash + + +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! SUBROUTINE PHI_EOS +! +! This subroutine gives the residual chemical potential: +! --> mu_i^res(T,p,x)/kT = ln( phi_i ) when ensemble_flag = 'tp' +! The required input for this case (T, p, x(nc)) and as a starting value +! eta_start +! +! or it gives +! +! --> mu_i^res(T,rho,x)/kT when ensemble_flag = 'tv' +! The required input for this case (T, eta_start, x(nc)). Note that +! eta_start is the specified density (packing fraction) in this case. +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! + SUBROUTINE PHI_EOS +! + USE PARAMETERS + USE EOS_VARIABLES + USE EOS_CONSTANTS + IMPLICIT NONE +! +! --- local variables--------------------------------------------------- + INTEGER :: i, j, k, ki, l, m + REAL :: z0, z1, z2, z3, z0_rk, z1_rk, z2_rk, z3_rk + REAL :: zms, m_mean + REAL, DIMENSION(nc) :: mhs, mdsp, mhc, myres + REAL, DIMENSION(nc) :: m_rk + REAL :: gij_rk(nc,nc) + REAL :: zres, zges + REAL :: dpdz, dpdz2 + + REAL :: I1, I2, I1_rk, I2_rk + REAL :: ord1_rk, ord2_rk + REAL :: c1_con, c2_con, c1_rk + REAL :: zmr, nmr, zmr_rk, nmr_rk, um_rk + REAL, DIMENSION(nc,0:6) :: ap_rk, bp_rk + + LOGICAL :: assoc + REAL :: ass_s2, m_hbon(nc) + + REAL :: fdd_rk, fqq_rk, fdq_rk + REAL, DIMENSION(nc) :: my_dd, my_qq, my_dq +! ---------------------------------------------------------------------- + +! ---------------------------------------------------------------------- +! obtain parameters and density independent expressions +! ---------------------------------------------------------------------- +CALL PERTURBATION_PARAMETER + + +! ---------------------------------------------------------------------- +! density iteration: (pTx)-ensemble OR p calc.: (pvx)-ensemble +! ---------------------------------------------------------------------- +IF (ensemble_flag == 'tp') THEN + CALL DENSITY_ITERATION +ELSEIF (ensemble_flag == 'tv') THEN + eta = eta_start + CALL P_EOS +ELSE + write (*,*) 'PHI_EOS: define ensemble, ensemble_flag == (pv) or (pt)' + stop +END IF + + +! --- Eq.(A.8) --------------------------------------------------------- +rho = eta / z3t +z0 = z0t * rho +z1 = z1t * rho +z2 = z2t * rho +z3 = z3t * rho + +m_mean = z0t / (PI/6.0) +zms = 1.0 - eta + +! ---------------------------------------------------------------------- +! compressibility factor z = p/(kT*rho) +! ---------------------------------------------------------------------- +zges = (p * 1.d-30) / (KBOL*t*rho) +IF ( ensemble_flag == 'tv' ) zges = (pges * 1.d-30) / (KBOL*t*rho) +zres = zges - 1.0 + + + +! ====================================================================== +! calculate the derivatives of f to mole fraction x ( d(f)/d(x) ) +! ====================================================================== + +DO k = 1, ncomp + + z0_rk = PI/6.0 * mseg(k) + z1_rk = PI/6.0 * mseg(k) * dhs(k) + z2_rk = PI/6.0 * mseg(k) * dhs(k)*dhs(k) + z3_rk = PI/6.0 * mseg(k) * dhs(k)**3 + +! --- derivative d(m_mean)/d(x) ---------------------------------------- + m_rk(k) = ( mseg(k) - m_mean ) / rho + ! lij(1,2)= -0.050 + ! lij(2,1)=lij(1,2) + ! r_m2dx(k)=0.0 + ! m_mean2=0.0 + ! DO i =1,ncomp + ! r_m2dx(k)=r_m2dx(k)+2.0*x(i)*(mseg(i)+mseg(k))/2.0*(1.0-lij(i,k)) + ! DO j =1,ncomp + ! m_mean2=m_mean2+x(i)*x(j)*(mseg(i)+mseg(j))/2.0*(1.0-lij(i,j)) + ! ENDDO + ! ENDDO + + ! -------------------------------------------------------------------- + ! d(f)/d(x) : hard sphere contribution + ! -------------------------------------------------------------------- + mhs(k) = 6.0/PI* ( 3.0*(z1_rk*z2+z1*z2_rk)/zms + 3.0*z1*z2*z3_rk/zms/zms & + + 3.0*z2*z2*z2_rk/z3/zms/zms + z2**3 *z3_rk*(3.0*z3-1.0)/z3/z3/zms**3 & + + ((3.0*z2*z2*z2_rk*z3-2.0*z2**3 *z3_rk)/z3**3 -z0_rk) *LOG(zms) & + + (z0-z2**3 /z3/z3)*z3_rk/zms ) + + ! -------------------------------------------------------------------- + ! d(f)/d(x) : chain term + ! -------------------------------------------------------------------- + DO i = 1, ncomp + DO j = 1, ncomp + gij(i,j) = 1.0/zms + 3.0*dij_ab(i,j)*z2/zms/zms + 2.0*(dij_ab(i,j)*z2)**2 /zms**3 + gij_rk(i,j) = z3_rk/zms/zms & + + 3.0*dij_ab(i,j)*(z2_rk+2.0*z2*z3_rk/zms)/zms/zms & + + dij_ab(i,j)**2 *z2/zms**3 *(4.0*z2_rk+6.0*z2*z3_rk/zms) + END DO + END DO + + mhc(k) = 0.0 + DO i = 1, ncomp + mhc(k) = mhc(k) + x(i)*rho * (1.0-mseg(i)) / gij(i,i) * gij_rk(i,i) + END DO + mhc(k) = mhc(k) + ( 1.0-mseg(k)) * LOG( gij(k,k) ) + + + ! -------------------------------------------------------------------- + ! PC-SAFT: d(f)/d(x) : dispersion contribution + ! -------------------------------------------------------------------- + IF (eos == 1) THEN + + ! --- derivatives of apar, bpar to rho_k --------------------------- + DO m = 0, 6 + ap_rk(k,m) = m_rk(k)/m_mean**2 * ( ap(m,2) + (3.0 -4.0/m_mean) *ap(m,3) ) + bp_rk(k,m) = m_rk(k)/m_mean**2 * ( bp(m,2) + (3.0 -4.0/m_mean) *bp(m,3) ) + END DO + + I1 = 0.0 + I2 = 0.0 + I1_rk = 0.0 + I2_rk = 0.0 + DO m = 0, 6 + I1 = I1 + apar(m)*eta**REAL(m) + I2 = I2 + bpar(m)*eta**REAL(m) + I1_rk = I1_rk + apar(m)*REAL(m)*eta**REAL(m-1)*z3_rk + ap_rk(k,m)*eta**REAL(m) + I2_rk = I2_rk + bpar(m)*REAL(m)*eta**REAL(m-1)*z3_rk + bp_rk(k,m)*eta**REAL(m) + END DO + + ord1_rk = 0.0 + ord2_rk = 0.0 + DO i = 1,ncomp + ord1_rk = ord1_rk + 2.0*mseg(k)*rho*x(i)*mseg(i)*sig_ij(i,k)**3 *uij(i,k)/t + ord2_rk = ord2_rk + 2.0*mseg(k)*rho*x(i)*mseg(i)*sig_ij(i,k)**3 *(uij(i,k)/t)**2 + END DO + + c1_con= 1.0/ ( 1.0 + m_mean*(8.0*z3-2.0*z3*z3)/zms**4 & + + (1.0 - m_mean)*(20.0*z3-27.0*z3*z3 +12.0*z3**3 -2.0*z3**4 ) & + /(zms*(2.0-z3))**2 ) + c2_con= - c1_con*c1_con *( m_mean*(-4.0*z3*z3+20.0*z3+8.0)/zms**5 & + + (1.0 - m_mean) *(2.0*z3**3 +12.0*z3*z3-48.0*z3+40.0) & + /(zms*(2.0-z3))**3 ) + c1_rk= c2_con*z3_rk - c1_con*c1_con*m_rk(k) * ( (8.0*z3-2.0*z3*z3)/zms**4 & + - (-2.0*z3**4 +12.0*z3**3 -27.0*z3*z3+20.0*z3) / (zms*(2.0-z3))**2 ) + + mdsp(k) = -2.0*PI* ( order1*rho*rho*I1_rk + ord1_rk*I1 ) & + - PI* c1_con*m_mean * ( order2*rho*rho*I2_rk + ord2_rk*I2 ) & + - PI* ( c1_con*m_rk(k) + c1_rk*m_mean ) * order2*rho*rho*I2 + + ! -------------------------------------------------------------------- + ! SAFT: d(f)/d(x) : dispersion contribution + ! -------------------------------------------------------------------- + ELSE + + zmr = 0.0 + nmr = 0.0 + zmr_rk = 0.0 + nmr_rk = 0.0 + DO i = 1, ncomp + DO j = 1, ncomp + zmr = zmr + x(i)*x(j)*mseg(i)*mseg(j)*vij(i,j)*uij(i,j) + nmr = nmr + x(i)*x(j)*mseg(i)*mseg(j)*vij(i,j) + END DO + zmr_rk = zmr_rk + 2.0*mseg(k) * x(i)*mseg(i)*vij(k,i)*uij(k,i) + nmr_rk = nmr_rk + 2.0*mseg(k) * x(i)*mseg(i)*vij(k,i) + END DO + + um_rk = 1.0/nmr**2 * ( nmr*zmr_rk - zmr*nmr_rk ) + + mdsp(k) = 0.0 + DO i = 1,4 + DO j = 1,9 + mdsp(k) = mdsp(k) + dnm(i,j)*(um/t)**REAL(i)*(eta/tau)**REAL(j) & + * ( 1.0 + z3_rk*rho/eta*REAL(j) + um_rk*rho/um*REAL(i) ) + END DO + END DO + + END IF + ! --- end of dispersion contribution------------------------------------ + + + ! -------------------------------------------------------------------- + ! TPT-1-association according to Chapman et al. + ! -------------------------------------------------------------------- + m_hbon(k) = 0.0 + assoc = .false. + DO i = 1,ncomp + IF (nhb_typ(i) /= 0) assoc = .true. + END DO + IF (assoc) THEN + + ass_s2 = 0.0 + DO l = 1, nhb_typ(k) + ass_s2 = ass_s2 + nhb_no(k,l) * LOG(mx(k,l)) + END DO + + m_hbon(k)=ass_s2 + DO i = 1, ncomp + DO ki = 1, nhb_typ(i) + DO j = 1, ncomp + DO l = 1, nhb_typ(j) + m_hbon(k)= m_hbon(k) - rho*rho/2.0*x(i)*x(j) *mx(i,ki)*mx(j,l) *nhb_no(i,ki)*nhb_no(j,l) & + * gij_rk(i,j) * ass_d(i,j,ki,l) + END DO + END DO + END DO + END DO + + END IF + ! --- end of TPT-1-association accord. to Chapman -------------------- + + + ! -------------------------------------------------------------------- + ! polar terms + ! -------------------------------------------------------------------- + CALL PHI_POLAR ( k, z3_rk, fdd_rk, fqq_rk, fdq_rk ) + my_dd(k) = fdd_rk + my_qq(k) = fqq_rk + my_dq(k) = fdq_rk + + + ! -------------------------------------------------------------------- + ! d(f)/d(x) : summation of all contributions + ! -------------------------------------------------------------------- + myres(k) = mhs(k) +mhc(k) +mdsp(k) +m_hbon(k) +my_dd(k) +my_qq(k) +my_dq(k) + +END DO + + +! ---------------------------------------------------------------------- +! finally calculate +! mu_i^res(T,p,x)/kT = ln( phi_i ) when ensemble_flag = 'tp' +! mu_i^res(T,rho,x)/kT when ensemble_flag = 'tv' +! ---------------------------------------------------------------------- + +DO k = 1, ncomp + ! write (*,*) k,myres(k) +LOG(rho*x(k)),rho + IF (ensemble_flag == 'tp' ) lnphi(k) = myres(k) - LOG(zges) + IF (ensemble_flag == 'tv' ) lnphi(k) = myres(k) + ! write (*,*) 'in',k,EXP(lnphi(k)),LOG(zges),eta +END DO +!write (*,'(5G18.10)') lnphi(1),rho + +dpdz = pgesdz +dpdz2 = pgesd2 + +END SUBROUTINE PHI_EOS + + +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! + SUBROUTINE PHI_NUMERICAL +! + USE EOS_VARIABLES + USE EOS_CONSTANTS + USE DFT_MODULE, ONLY: z_ges, fres_temp + IMPLICIT NONE +! +!-----local variables------------------------------------------------- + INTEGER :: k + REAL :: zres, zges + REAL :: fres1, fres2, fres3, fres4, fres5 + REAL :: delta_rho + REAL, DIMENSION(nc) :: myres + REAL, DIMENSION(nc) :: rhoi, rhoi_0 + REAL :: tfr_1, tfr_2, tfr_3, tfr_4, tfr_5 +!----------------------------------------------------------------------- + + +!----------------------------------------------------------------------- +! density iteration or pressure calculation +!----------------------------------------------------------------------- + +IF (ensemble_flag == 'tp') THEN + CALL DENSITY_ITERATION +ELSEIF (ensemble_flag == 'tv') THEN + eta = eta_start + CALL P_NUMERICAL +ELSE + write (*,*) 'PHI_EOS: define ensemble, ensemble_flag == (tv) or (tp)' + stop +END IF + +!----------------------------------------------------------------------- +! compressibility factor z = p/(kT*rho) +!----------------------------------------------------------------------- + +zges = (p * 1.E-30) / (kbol*t*eta/z3t) +IF ( ensemble_flag == 'tv' ) zges = (pges * 1.E-30) / (kbol*t*eta/z3t) +zres = zges - 1.0 +z_ges = zges + +rhoi_0(1:ncomp) = x(1:ncomp) * eta/z3t +rhoi(1:ncomp) = rhoi_0(1:ncomp) + + +!----------------------------------------------------------------------- +! derivative to rho_k (keeping other rho_i's constant +!----------------------------------------------------------------------- + +DO k = 1, ncomp + + IF ( rhoi_0(k) > 1.d-9 ) THEN + delta_rho = 1.E-13 * 10.0**(0.5*(15.0+LOG10(rhoi_0(k)))) + ELSE + delta_rho = 1.E-10 + END IF + + rhoi(k) = rhoi_0(k) + delta_rho + eta = PI/6.0 * SUM( rhoi(1:ncomp)*mseg(1:ncomp)*dhs(1:ncomp)**3 ) + x(1:ncomp) = rhoi(1:ncomp) / SUM( rhoi(1:ncomp) ) + rho = SUM( rhoi(1:ncomp) ) + CALL F_NUMERICAL + fres1 = fres*rho + tfr_1 = tfr*rho + + rhoi(k) = rhoi_0(k) + 0.5 * delta_rho + eta = PI/6.0 * SUM( rhoi(1:ncomp)*mseg(1:ncomp)*dhs(1:ncomp)**3 ) + x(1:ncomp) = rhoi(1:ncomp) / SUM( rhoi(1:ncomp) ) + rho = SUM( rhoi(1:ncomp) ) + CALL F_NUMERICAL + fres2 = fres*rho + tfr_2 = tfr*rho + + IF ( rhoi_0(k) > 1.E-9 ) THEN + rhoi(k) = rhoi_0(k) - 0.5 * delta_rho + eta = PI/6.0 * SUM( rhoi(1:ncomp)*mseg(1:ncomp)*dhs(1:ncomp)**3 ) + x(1:ncomp) = rhoi(1:ncomp) / SUM( rhoi(1:ncomp) ) + rho = SUM( rhoi(1:ncomp) ) + CALL F_NUMERICAL + fres4 = fres*rho + tfr_4 = tfr*rho + + rhoi(k) = rhoi_0(k) - delta_rho + eta = PI/6.0 * SUM( rhoi(1:ncomp)*mseg(1:ncomp)*dhs(1:ncomp)**3 ) + x(1:ncomp) = rhoi(1:ncomp) / SUM( rhoi(1:ncomp) ) + rho = SUM( rhoi(1:ncomp) ) + CALL F_NUMERICAL + fres5 = fres*rho + tfr_5 = tfr*rho + END IF + + rhoi(k) = rhoi_0(k) + eta = PI/6.0 * SUM( rhoi(1:ncomp)*mseg(1:ncomp)*dhs(1:ncomp)**3 ) + x(1:ncomp) = rhoi(1:ncomp) / SUM( rhoi(1:ncomp) ) + rho = SUM( rhoi(1:ncomp) ) + CALL F_NUMERICAL + fres3 = fres*rho + tfr_3 = tfr*rho + + IF ( rhoi_0(k) > 1.E-9 ) THEN + myres(k) = ( fres5 - 8.0*fres4 + 8.0*fres2 - fres1 ) / ( 6.0*delta_rho ) + ELSE + myres(k) = ( -3.0*fres3 + 4.0*fres2 - fres1 ) / delta_rho + END IF + +END DO + + +!----------------------------------------------------------------------- +! residual Helmholtz energy +!----------------------------------------------------------------------- + +fres_temp = fres + +!----------------------------------------------------------------------- +! residual chemical potential +!----------------------------------------------------------------------- + +DO k = 1, ncomp + IF (ensemble_flag == 'tp') lnphi(k) = myres(k) - LOG(zges) + IF (ensemble_flag == 'tv' .AND. eta >= 0.0) lnphi(k) = myres(k) !+LOG(rho) + ! write (*,*) 'in',k,EXP(lnphi(k)),LOG(zges),eta + ! IF (DFT.GE.98) write (*,*) dft + ! write (*,*) 'lnphi',k,LNPHI(k),x(k),MYRES(k), -LOG(ZGES) + ! pause + ! write (*,*) k, myres(k), fres, ZRES +END DO + +END SUBROUTINE PHI_NUMERICAL + + +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW + +! SUBROUTINE H_EOS (phas,h_res,s_res,cp_res,X,T,P,PARAME, +! 1 KIJ,lij,NCOMP,ETA_START,ETA,eos,tfr) +! IMPLICIT NONE +! INTEGER nc +! PARAMETER (nc=20) +! INTEGER phas,ncomp,eos,i +! REAL kij(nc,nc),lij(nc,nc),x(nc),t,p,parame(nc,25) +! REAL eta_start,eta,tfr,h_res,cp_res,s_res + + +! i=1 + +! IF (i.EQ.1) THEN +! CALL H_EOS_1(phas,h_res,s_res,cp_res,X,T,P,PARAME, +! 1 KIJ,lij,NCOMP,ETA_START,ETA,eos,tfr) +! ELSE +! CALL H_EOS_NUM (phas,h_res,s_res,cp_res,X,T,P,PARAME, +! 1 KIJ,lij,NCOMP,ETA_START,ETA,eos,tfr) +! ENDIF + +! RETURN +! END + + +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! + SUBROUTINE H_EOS +! + USE PARAMETERS, ONLY: RGAS + USE EOS_CONSTANTS + USE EOS_VARIABLES + IMPLICIT NONE +! +! ---------------------------------------------------------------------- + REAL :: zges, df_dt, dfdr, ddfdrdr + REAL :: cv_res, df_dt2, df_drdt + REAL :: fact, dist, t_tmp, rho_0 + REAL :: fdr1, fdr2, fdr3, fdr4 + + INTEGER :: i, m + REAL :: dhsdt(nc), dhsdt2(nc) + REAL :: z0, z1, z2, z3, z1tdt, z2tdt, z3tdt + REAL :: z1dt, z2dt, z3dt, zms, gii + REAL :: fhsdt, fhsdt2 + REAL :: fchdt, fchdt2 + REAL :: fdspdt, fdspdt2 + REAL :: fhbdt, fhbdt2 + REAL :: sumseg, I1, I2, I1dt, I2dt, I1dt2, I2dt2 + REAL :: c1_con, c2_con, c3_con, c1_dt, c1_dt2 + REAL :: z1tdt2, z2tdt2, z3tdt2 + REAL :: z1dt2, z2dt2, z3dt2 + + INTEGER :: j, k, l, no, ass_cnt, max_eval + LOGICAL :: assoc + REAL :: dij, dijdt, dijdt2 + REAL :: gij1dt, gij2dt, gij3dt + REAL :: gij1dt2, gij2dt2, gij3dt2 + REAL, DIMENSION(nc,nc) :: gijdt, gijdt2, kap_hb + REAL, DIMENSION(nc,nc,nsite,nsite) :: ass_d_dt, ass_d_dt2, eps_hb, delta, deltadt, deltadt2 + REAL, DIMENSION(nc,nsite) :: mxdt, mxdt2, mx_itr, mx_itrdt, mx_itrdt2 + REAL :: attenu, tol, suma, sumdt, sumdt2, err_sum + + INTEGER :: dipole + REAL :: fdddt, fdddt2 + REAL, DIMENSION(nc) :: my2dd, my0 + REAL, DIMENSION(nc,nc) :: idd2, idd2dt, idd2dt2, idd4, idd4dt, idd4dt2 + REAL, DIMENSION(nc,nc,nc) :: idd3, idd3dt, idd3dt2 + REAL :: factor2, factor3 + REAL :: fdd2, fdd3, fdd2dt, fdd3dt, fdd2dt2, fdd3dt2 + REAL :: eij, xijmt, xijkmt + + INTEGER :: qudpole + REAL :: fqqdt, fqqdt2 + REAL, DIMENSION(nc) :: qq2 + REAL, DIMENSION(nc,nc) :: iqq2, iqq2dt, iqq2dt2, iqq4, iqq4dt, iqq4dt2 + REAL, DIMENSION(nc,nc,nc) :: iqq3, iqq3dt, iqq3dt2 + REAL :: fqq2, fqq2dt, fqq2dt2, fqq3, fqq3dt, fqq3dt2 + + INTEGER :: dip_quad + REAL :: fdqdt, fdqdt2 + REAL, DIMENSION(nc) :: myfac, q_fac + REAL, DIMENSION(nc,nc) :: idq2, idq2dt, idq2dt2, idq4, idq4dt, idq4dt2 + REAL, DIMENSION(nc,nc,nc) :: idq3, idq3dt, idq3dt2 + REAL :: fdq2, fdq2dt, fdq2dt2, fdq3, fdq3dt, fdq3dt2 +! ---------------------------------------------------------------------- + + +! ---------------------------------------------------------------------- +! Initializing +! ---------------------------------------------------------------------- +CALL PERTURBATION_PARAMETER + +rho = eta/z3t +z0 = z0t*rho +z1 = z1t*rho +z2 = z2t*rho +z3 = z3t*rho + +sumseg = z0t / (PI/6.0) +zms = 1.0 - z3 + + +! ---------------------------------------------------------------------- +! first and second derivative of f to density (dfdr,ddfdrdr) +! ---------------------------------------------------------------------- +CALL P_EOS + +zges = (pges * 1.E-30)/(kbol*t*rho) + +dfdr = pges/(eta*rho*(kbol*t)/1.E-30) +ddfdrdr = pgesdz/(eta*rho*(kbol*t)/1.E-30) - dfdr*2.0/eta - 1.0/eta**2 + + +! ---------------------------------------------------------------------- +! Helmholtz Energy f/kT = fres +! ---------------------------------------------------------------------- +CALL F_EOS + + +! ---------------------------------------------------------------------- +! derivative of some auxilliary properties to temperature +! ---------------------------------------------------------------------- +DO i = 1,ncomp + dhsdt(i)=parame(i,2) *(-3.0*parame(i,3)/t/t)*0.12*EXP(-3.0*parame(i,3)/t) + dhsdt2(i) = dhsdt(i)*3.0*parame(i,3)/t/t & + + 6.0*parame(i,2)*parame(i,3)/t**3 *0.12*EXP(-3.0*parame(i,3)/t) +END DO + +z1tdt = 0.0 +z2tdt = 0.0 +z3tdt = 0.0 +DO i = 1,ncomp + z1tdt = z1tdt + x(i) * mseg(i) * dhsdt(i) + z2tdt = z2tdt + x(i) * mseg(i) * 2.0*dhs(i)*dhsdt(i) + z3tdt = z3tdt + x(i) * mseg(i) * 3.0*dhs(i)*dhs(i)*dhsdt(i) +END DO +z1dt = PI / 6.0*z1tdt *rho +z2dt = PI / 6.0*z2tdt *rho +z3dt = PI / 6.0*z3tdt *rho + + +z1tdt2 = 0.0 +z2tdt2 = 0.0 +z3tdt2 = 0.0 +DO i = 1,ncomp + z1tdt2 = z1tdt2 + x(i)*mseg(i)*dhsdt2(i) + z2tdt2 = z2tdt2 + x(i)*mseg(i)*2.0 *( dhsdt(i)*dhsdt(i) +dhs(i)*dhsdt2(i) ) + z3tdt2 = z3tdt2 + x(i)*mseg(i)*3.0 *( 2.0*dhs(i)*dhsdt(i)* & + dhsdt(i) +dhs(i)*dhs(i)*dhsdt2(i) ) +END DO +z1dt2 = PI / 6.0*z1tdt2 *rho +z2dt2 = PI / 6.0*z2tdt2 *rho +z3dt2 = PI / 6.0*z3tdt2 *rho + + +! ---------------------------------------------------------------------- +! 1st & 2nd derivative of f/kT hard spheres to temp. (fhsdt) +! ---------------------------------------------------------------------- +fhsdt = 6.0/PI/rho*( 3.0*(z1dt*z2+z1*z2dt)/zms + 3.0*z1*z2*z3dt/zms/zms & + + 3.0*z2*z2*z2dt/z3/zms/zms & + + z2**3 *(2.0*z3*z3dt-z3dt*zms)/(z3*z3*zms**3 ) & + + (3.0*z2*z2*z2dt*z3-2.0*z2**3 *z3dt)/z3**3 *LOG(zms) & + + (z0-z2**3 /z3/z3)*z3dt/zms ) + +fhsdt2= 6.0/PI/rho*( 3.0*(z1dt2*z2+2.0*z1dt*z2dt+z1*z2dt2)/zms & + + 6.0*(z1dt*z2+z1*z2dt)*z3dt/zms/zms & + + 3.0*z1*z2*z3dt2/zms/zms + 6.0*z1*z2*z3dt*z3dt/zms**3 & + + 3.0*z2*(2.0*z2dt*z2dt+z2*z2dt2)/z3/zms/zms & + - z2*z2*(6.0*z2dt*z3dt+z2*z3dt2)/(z3*z3*zms*zms) & + + 2.0*z2**3 *z3dt*z3dt/(z3**3 *zms*zms) & + - 4.0*z2**3 *z3dt*z3dt/(z3*z3 *zms**3 ) & + + (12.0*z2*z2*z2dt*z3dt+2.0*z2**3 *z3dt2)/(z3*zms**3 ) & + + 6.0*z2**3 *z3dt*z3dt/(z3*zms**4 ) & + - 2.0*(3.0*z2*z2*z2dt/z3/z3-2.0*z2**3 *z3dt/z3**3 ) *z3dt/zms & + -(z2**3 /z3/z3-z0)*(z3dt2/zms+z3dt*z3dt/zms/zms) & + + ( (6.0*z2*z2dt*z2dt+3.0*z2*z2*z2dt2)/z3/z3 & + - (12.0*z2*z2*z2dt*z3dt+2.0*z2**3 *z3dt2)/z3**3 & + + 6.0*z2**3 *z3dt*z3dt/z3**4 )* LOG(zms) ) + + +! ---------------------------------------------------------------------- +! 1st & 2nd derivative of f/kT of chain term to T (fchdt) +! ---------------------------------------------------------------------- +fchdt = 0.0 +fchdt2 = 0.0 +DO i = 1, ncomp + DO j = 1, ncomp + dij=dhs(i)*dhs(j)/(dhs(i)+dhs(j)) + dijdt =(dhsdt(i)*dhs(j) + dhs(i)*dhsdt(j)) / (dhs(i)+dhs(j)) & + - dhs(i)*dhs(j)/(dhs(i)+dhs(j))**2 *(dhsdt(i)+dhsdt(j)) + dijdt2=(dhsdt2(i)*dhs(j) + 2.0*dhsdt(i)*dhsdt(j) & + + dhs(i)*dhsdt2(j)) / (dhs(i)+dhs(j)) & + - 2.0*(dhsdt(i)*dhs(j) + dhs(i)*dhsdt(j)) & + / (dhs(i)+dhs(j))**2 *(dhsdt(i)+dhsdt(j)) & + + 2.0* dhs(i)*dhs(j) / (dhs(i)+dhs(j))**3 & + * (dhsdt(i)+dhsdt(j))**2 & + - dhs(i)*dhs(j)/(dhs(i)+dhs(j))**2 *(dhsdt2(i)+dhsdt2(j)) + gij1dt = z3dt/zms/zms + gij2dt = 3.0*( z2dt*dij+z2*dijdt )/zms/zms +6.0*z2*dij*z3dt/zms**3 + gij3dt = 4.0*(dij*z2)* (dijdt*z2 + dij*z2dt) /zms**3 & + + 6.0*(dij*z2)**2 * z3dt /zms**4 + gij1dt2 = z3dt2/zms/zms +2.0*z3dt*z3dt/zms**3 + gij2dt2 = 3.0*( z2dt2*dij+2.0*z2dt*dijdt+z2*dijdt2 )/zms/zms & + + 6.0*( z2dt*dij+z2*dijdt )/zms**3 * z3dt & + + 6.0*(z2dt*dij*z3dt+z2*dijdt*z3dt+z2*dij*z3dt2) /zms**3 & + + 18.0*z2*dij*z3dt*z3dt/zms**4 + gij3dt2 = 4.0*(dijdt*z2+dij*z2dt)**2 /zms**3 & + + 4.0*(dij*z2)* (dijdt2*z2+2.0*dijdt*z2dt+dij*z2dt2) /zms**3 & + + 24.0*(dij*z2) *(dijdt*z2+dij*z2dt)/zms**4 *z3dt & + + 6.0*(dij*z2)**2 * z3dt2 /zms**4 & + + 24.0*(dij*z2)**2 * z3dt*z3dt /zms**5 + gijdt(i,j) = gij1dt + gij2dt + gij3dt + gijdt2(i,j) = gij1dt2 + gij2dt2 + gij3dt2 + END DO +END DO + +DO i = 1, ncomp + gii = 1.0/zms + 3.0*dhs(i)/2.0*z2/zms/zms + 2.0*dhs(i)*dhs(i)/4.0*z2*z2/zms**3 + fchdt = fchdt + x(i) * (1.0-mseg(i)) * gijdt(i,i) / gii + fchdt2= fchdt2+ x(i) * (1.0-mseg(i)) & + * (gijdt2(i,i) / gii - (gijdt(i,i)/gii)**2 ) +END DO + + +! ---------------------------------------------------------------------- +! 1st & 2nd derivative of f/kT dispersion term to T (fdspdt) +! ---------------------------------------------------------------------- +I1 = 0.0 +I2 = 0.0 +I1dt = 0.0 +I2dt = 0.0 +I1dt2= 0.0 +I2dt2= 0.0 +DO m = 0, 6 + I1 = I1 + apar(m)*z3**REAL(m) + I2 = I2 + bpar(m)*z3**REAL(m) + I1dt = I1dt + apar(m)*z3dt*REAL(m)*z3**REAL(m-1) + I2dt = I2dt + bpar(m)*z3dt*REAL(m)*z3**REAL(m-1) + I1dt2= I1dt2+ apar(m)*z3dt2*REAL(m)*z3**REAL(m-1) & + + apar(m)*z3dt*z3dt *REAL(m)*REAL(m-1)*z3**REAL(m-2) + I2dt2= I2dt2+ bpar(m)*z3dt2*REAL(m)*z3**REAL(m-1) & + + bpar(m)*z3dt*z3dt *REAL(m)*REAL(m-1)*z3**REAL(m-2) +END DO + +c1_con= 1.0/ ( 1.0 + sumseg*(8.0*z3-2.0*z3**2 )/zms**4 & + + (1.0 - sumseg)*(20.0*z3-27.0*z3**2 +12.0*z3**3 -2.0*z3**4 ) & + /(zms*(2.0-z3))**2 ) +c2_con= - c1_con*c1_con *(sumseg*(-4.0*z3**2 +20.0*z3+8.0)/zms**5 & + + (1.0 - sumseg) *(2.0*z3**3 +12.0*z3**2 -48.0*z3+40.0) & + /(zms*(2.0-z3))**3 ) +c3_con= 2.0 * c2_con*c2_con/c1_con - c1_con*c1_con & + *( sumseg*(-12.0*z3**2 +72.0*z3+60.0)/zms**6 + (1.0 - sumseg) & + *(-6.0*z3**4 -48.0*z3**3 +288.0*z3**2 -480.0*z3+264.0) & + /(zms*(2.0-z3))**4 ) +c1_dt = c2_con*z3dt +c1_dt2 = c3_con*z3dt*z3dt + c2_con*z3dt2 + +fdspdt = - 2.0*PI*rho*(I1dt-I1/t)*order1 & + - PI*rho*sumseg*(c1_dt*I2+c1_con*I2dt-2.0*c1_con*I2/t)*order2 + +fdspdt2 = - 2.0*PI*rho*(I1dt2-2.0*I1dt/t+2.0*I1/t/t)*order1 & + - PI*rho*sumseg*order2*( c1_dt2*I2 +2.0*c1_dt*I2dt -4.0*c1_dt*I2/t & + + 6.0*c1_con*I2/t/t -4.0*c1_con*I2dt/t +c1_con*I2dt2) + + +! ---------------------------------------------------------------------- +! 1st & 2nd derivative of f/kT association term to T (fhbdt) +! ---------------------------------------------------------------------- +fhbdt = 0.0 +fhbdt2 = 0.0 +assoc = .false. +DO i = 1,ncomp + IF ( nhb_typ(i) /= 0 ) assoc = .true. +END DO +IF (assoc) THEN + + DO i = 1,ncomp + IF ( nhb_typ(i) /= 0 ) THEN + kap_hb(i,i) = parame(i,13) + no = 0 + DO j = 1,nhb_typ(i) + DO k = 1,nhb_typ(i) + eps_hb(i,i,j,k) = parame(i,(14+no)) + no = no + 1 + END DO + END DO + DO j = 1,nhb_typ(i) + no = no + 1 + END DO + ELSE + kap_hb(i,i) = 0.0 + DO k = 1,nsite + DO l = 1,nsite + eps_hb(i,i,k,l) = 0.0 + END DO + END DO + END IF + END DO + + DO i = 1,ncomp + DO j = 1,ncomp + IF ( i /= j .AND. (nhb_typ(i) /= 0 .AND. nhb_typ(j) /= 0) ) THEN + kap_hb(i,j)= (kap_hb(i,i)*kap_hb(j,j))**0.5 & + *((parame(i,2)*parame(j,2))**3 )**0.5 & + /(0.5*(parame(i,2)+parame(j,2)))**3 + ! kap_hb(i,j)= kap_hb(i,j)*(1.0-k_kij) + DO k = 1,nhb_typ(i) + DO l = 1,nhb_typ(j) + IF (k /= l) THEN + eps_hb(i,j,k,l)=(eps_hb(i,i,k,l)+eps_hb(j,j,l,k))/2.0 + ! eps_hb(i,j,k,l)=eps_hb(i,j,k,l)*(1.0-eps_kij) + END IF + END DO + END DO + END IF + END DO + END DO + IF (nhb_typ(1) == 3) THEN + eps_hb(1,2,3,1)=0.5*(eps_hb(1,1,3,1)+eps_hb(2,2,1,2)) + eps_hb(2,1,1,3) = eps_hb(1,2,3,1) + END IF + IF (nhb_typ(2) == 3) THEN + eps_hb(2,1,3,1)=0.5*(eps_hb(2,2,3,1)+eps_hb(1,1,1,2)) + eps_hb(1,2,1,3) = eps_hb(2,1,3,1) + END IF + + DO i = 1, ncomp + DO k = 1, nhb_typ(i) + DO j = 1, ncomp + DO l = 1, nhb_typ(j) + ! ass_d(i,j,k,l)=kap_hb(i,j) *sig_ij(i,j)**3 *(EXP(eps_hb(i,j,k,l)/t)-1.0) + ass_d_dt(i,j,k,l)= - kap_hb(i,j) *sig_ij(i,j)**3 * eps_hb(i,j,k,l)/t/t*EXP(eps_hb(i,j,k,l)/t) + ass_d_dt2(i,j,k,l)= - kap_hb(i,j) *sig_ij(i,j)**3 & + * eps_hb(i,j,k,l)/t/t*EXP(eps_hb(i,j,k,l)/t) & + * (-2.0/t - eps_hb(i,j,k,l)/t/t) + END DO + END DO + END DO + END DO + + DO i = 1, ncomp + DO k = 1, nhb_typ(i) + DO j = 1, ncomp + DO l = 1, nhb_typ(j) + delta(i,j,k,l)=gij(i,j)*ass_d(i,j,k,l) + deltadt(i,j,k,l) = gijdt(i,j)*ass_d(i,j,k,l) + gij(i,j)*ass_d_dt(i,j,k,l) + deltadt2(i,j,k,l)= gijdt2(i,j)*ass_d(i,j,k,l) & + + 2.0*gijdt(i,j)*ass_d_dt(i,j,k,l) +gij(i,j)*ass_d_dt2(i,j,k,l) + END DO + END DO + END DO + END DO + + +! ------ constants for iteration --------------------------------------- + attenu = 0.7 + tol = 1.E-10 + IF (eta < 0.2) tol = 1.E-11 + IF (eta < 0.01) tol = 1.E-12 + max_eval = 200 + +! ------ initialize mxdt(i,j) ------------------------------------------ + DO i = 1, ncomp + DO k = 1, nhb_typ(i) + mxdt(i,k) = 0.0 + mxdt2(i,k) = 0.0 + END DO + END DO + + +! ------ iterate over all components and all sites --------------------- + DO ass_cnt = 1, max_eval + + DO i = 1, ncomp + DO k = 1, nhb_typ(i) + suma = 0.0 + sumdt = 0.0 + sumdt2= 0.0 + DO j = 1, ncomp + DO l = 1, nhb_typ(j) + suma = suma + x(j)*nhb_no(j,l)* mx(j,l) *delta(i,j,k,l) + sumdt = sumdt + x(j)*nhb_no(j,l)*( mx(j,l) *deltadt(i,j,k,l) & + + mxdt(j,l)*delta(i,j,k,l) ) + sumdt2 = sumdt2 + x(j)*nhb_no(j,l)*( mx(j,l)*deltadt2(i,j,k,l) & + + 2.0*mxdt(j,l)*deltadt(i,j,k,l) + mxdt2(j,l)*delta(i,j,k,l) ) + END DO + END DO + mx_itr(i,k) = 1.0 / (1.0 + suma * rho) + mx_itrdt(i,k)= - mx_itr(i,k)**2 * sumdt*rho + mx_itrdt2(i,k)= +2.0*mx_itr(i,k)**3 * (sumdt*rho)**2 - mx_itr(i,k)**2 *sumdt2*rho + END DO + END DO + + err_sum = 0.0 + DO i = 1, ncomp + DO k = 1, nhb_typ(i) + err_sum = err_sum + ABS(mx_itr(i,k) - mx(i,k)) & + + ABS(mx_itrdt(i,k) - mxdt(i,k)) + ABS(mx_itrdt2(i,k) - mxdt2(i,k)) + mx(i,k) = mx_itr(i,k) * attenu + mx(i,k) * (1.0 - attenu) + mxdt(i,k)=mx_itrdt(i,k)*attenu +mxdt(i,k)* (1.0 - attenu) + mxdt2(i,k)=mx_itrdt2(i,k)*attenu +mxdt2(i,k)* (1.0 - attenu) + END DO + END DO + IF(err_sum <= tol) GO TO 10 + + END DO + WRITE(6,*) 'CAL_PCSAFT: max_eval violated err_sum = ',err_sum,tol + STOP + 10 CONTINUE + + DO i = 1, ncomp + DO k = 1, nhb_typ(i) + ! fhb = fhb + x(i)* nhb_no(i,k)* ( 0.5 * ( 1.0 - mx(i,k) ) + LOG(mx(i,k)) ) + fhbdt = fhbdt + x(i)*nhb_no(i,k) *mxdt(i,k)*(1.0/mx(i,k)-0.5) + fhbdt2= fhbdt2 + x(i)*nhb_no(i,k) *(mxdt2(i,k)*(1.0/mx(i,k)-0.5) & + -(mxdt(i,k)/mx(i,k))**2 ) + END DO + END DO + +END IF + + +! ---------------------------------------------------------------------- +! derivatives of f/kT of dipole-dipole term to temp. (fdddt) +! ---------------------------------------------------------------------- +fdddt = 0.0 +fdddt2 = 0.0 +dipole = 0 +DO i = 1,ncomp + my2dd(i) = 0.0 + IF ( parame(i,6) /= 0.0 .AND. uij(i,i) /= 0.0 ) THEN + dipole = 1 + my2dd(i) = (parame(i,6))**2 *1.E-49 / (uij(i,i)*kbol*mseg(i)*sig_ij(i,i)**3 *1.E-30) + END IF + my0(i) = my2dd(i) ! needed for dipole-quadrupole-term +END DO + +IF (dipole == 1) THEN + DO i = 1,ncomp + DO j = 1,ncomp + idd2(i,j) =0.0 + idd4(i,j) =0.0 + idd2dt(i,j) =0.0 + idd4dt(i,j) =0.0 + idd2dt2(i,j)=0.0 + idd4dt2(i,j)=0.0 + DO m=0,4 + idd2(i,j) = idd2(i,j) +ddp2(i,j,m)*z3**REAL(m) + idd4(i,j) = idd4(i,j) +ddp4(i,j,m)*z3**REAL(m) + idd2dt(i,j)= idd2dt(i,j) +ddp2(i,j,m)*z3dt*REAL(m)*z3**REAL(m-1) + idd4dt(i,j)= idd4dt(i,j) +ddp4(i,j,m)*z3dt*REAL(m)*z3**REAL(m-1) + idd2dt2(i,j)=idd2dt2(i,j)+ddp2(i,j,m)*z3dt2*REAL(m)*z3**REAL(m-1) & + + ddp2(i,j,m)*z3dt**2 *REAL(m)*REAL(m-1)*z3**REAL(m-2) + idd4dt2(i,j)=idd4dt2(i,j)+ddp4(i,j,m)*z3dt2*REAL(m)*z3**REAL(m-1) & + + ddp4(i,j,m)*z3dt**2 *REAL(m)*REAL(m-1)*z3**REAL(m-2) + END DO + DO k = 1,ncomp + idd3(i,j,k) =0.0 + idd3dt(i,j,k) =0.0 + idd3dt2(i,j,k)=0.0 + DO m = 0, 4 + idd3(i,j,k) = idd3(i,j,k) +ddp3(i,j,k,m)*z3**REAL(m) + idd3dt(i,j,k) = idd3dt(i,j,k)+ddp3(i,j,k,m)*z3dt*REAL(m) *z3**REAL(m-1) + idd3dt2(i,j,k)= idd3dt2(i,j,k)+ddp3(i,j,k,m)*z3dt2*REAL(m) & + *z3**REAL(m-1) +ddp3(i,j,k,m)*z3dt**2 *REAL(m)*REAL(m-1) *z3**REAL(m-2) + END DO + END DO + END DO + END DO + + + factor2= -PI *rho + factor3= -4.0/3.0*PI**2 * rho**2 + + fdd2 = 0.0 + fdd3 = 0.0 + fdd2dt= 0.0 + fdd3dt= 0.0 + fdd2dt2= 0.0 + fdd3dt2= 0.0 + DO i = 1, ncomp + DO j = 1, ncomp + xijmt = x(i)*parame(i,3)*parame(i,2)**3 *x(j)*parame(j,3)*parame(j,2)**3 & + / ((parame(i,2)+parame(j,2))/2.0)**3 *my2dd(i)*my2dd(j) + eij = (parame(i,3)*parame(j,3))**0.5 + fdd2 = fdd2 +factor2* xijmt/t/t*(idd2(i,j)+eij/t*idd4(i,j)) + fdd2dt= fdd2dt+ factor2* xijmt/t/t*(idd2dt(i,j)-2.0*idd2(i,j)/t & + +eij/t*idd4dt(i,j)-3.0*eij/t/t*idd4(i,j)) + fdd2dt2=fdd2dt2+factor2*xijmt/t/t*(idd2dt2(i,j)-4.0*idd2dt(i,j)/t & + +6.0*idd2(i,j)/t/t+eij/t*idd4dt2(i,j) & + -6.0*eij/t/t*idd4dt(i,j)+12.0*eij/t**3 *idd4(i,j)) + DO k = 1, ncomp + xijkmt=x(i)*parame(i,3)*parame(i,2)**3 & + *x(j)*parame(j,3)*parame(j,2)**3 & + *x(k)*parame(k,3)*parame(k,2)**3 & + /((parame(i,2)+parame(j,2))/2.0) /((parame(i,2)+parame(k,2))/2.0) & + /((parame(j,2)+parame(k,2))/2.0) *my2dd(i)*my2dd(j)*my2dd(k) + fdd3 =fdd3 +factor3*xijkmt/t**3 *idd3(i,j,k) + fdd3dt =fdd3dt +factor3*xijkmt/t**3 * (idd3dt(i,j,k)-3.0*idd3(i,j,k)/t) + fdd3dt2=fdd3dt2+factor3*xijkmt/t**3 & + *( idd3dt2(i,j,k)-6.0*idd3dt(i,j,k)/t+12.0*idd3(i,j,k)/t/t ) + END DO + END DO + END DO + + IF ( fdd2 < -1.E-100 .AND. fdd3 /= 0.0 ) THEN + fdddt = fdd2* (fdd2*fdd2dt - 2.0*fdd3*fdd2dt+fdd2*fdd3dt) / (fdd2-fdd3)**2 + fdddt2 = ( 2.0*fdd2*fdd2dt*fdd2dt +fdd2*fdd2*fdd2dt2 & + -2.0*fdd2dt**2 *fdd3 -2.0*fdd2*fdd2dt2*fdd3 +fdd2*fdd2*fdd3dt2 ) & + /(fdd2-fdd3)**2 + fdddt * 2.0*(fdd3dt-fdd2dt)/(fdd2-fdd3) + END IF +END IF + + +! ---------------------------------------------------------------------- +! derivatives f/kT of quadrupole-quadrup. term to T (fqqdt) +! ---------------------------------------------------------------------- +fqqdt = 0.0 +fqqdt2 = 0.0 +qudpole = 0 +DO i = 1, ncomp + qq2(i) = (parame(i,7))**2 *1.E-69 / (uij(i,i)*kbol*mseg(i)*sig_ij(i,i)**5 *1.E-50) + IF (qq2(i) /= 0.0) qudpole = 1 +END DO + +IF (qudpole == 1) THEN + + DO i = 1,ncomp + DO j = 1,ncomp + iqq2(i,j) = 0.0 + iqq4(i,j) = 0.0 + iqq2dt(i,j) = 0.0 + iqq4dt(i,j) = 0.0 + iqq2dt2(i,j)= 0.0 + iqq4dt2(i,j)= 0.0 + DO m = 0, 4 + iqq2(i,j) = iqq2(i,j) + qqp2(i,j,m)*z3**REAL(m) + iqq4(i,j) = iqq4(i,j) + qqp4(i,j,m)*z3**REAL(m) + iqq2dt(i,j) = iqq2dt(i,j)+ qqp2(i,j,m)*z3dt*REAL(m)*z3**REAL(m-1) + iqq4dt(i,j) = iqq4dt(i,j)+ qqp4(i,j,m)*z3dt*REAL(m)*z3**REAL(m-1) + iqq2dt2(i,j)= iqq2dt2(i,j)+qqp2(i,j,m)*z3dt2*REAL(m)*z3**REAL(m-1) & + + qqp2(i,j,m)*z3dt**2 *REAL(m)*REAL(m-1)*z3**REAL(m-2) + iqq4dt2(i,j)= iqq4dt2(i,j)+qqp4(i,j,m)*z3dt2*REAL(m)*z3**REAL(m-1) & + + qqp4(i,j,m)*z3dt**2 *REAL(m)*REAL(m-1)*z3**REAL(m-2) + END DO + DO k = 1,ncomp + iqq3(i,j,k) =0.0 + iqq3dt(i,j,k) =0.0 + iqq3dt2(i,j,k)=0.0 + DO m = 0, 4 + iqq3(i,j,k) = iqq3(i,j,k) + qqp3(i,j,k,m)*z3**REAL(m) + iqq3dt(i,j,k) = iqq3dt(i,j,k)+ qqp3(i,j,k,m)*z3dt*REAL(m) * z3**REAL(m-1) + iqq3dt2(i,j,k)= iqq3dt2(i,j,k)+qqp3(i,j,k,m)*z3dt2*REAL(m) * z3**REAL(m-1) & + + qqp3(i,j,k,m)*z3dt**2 *REAL(m)*REAL(m-1)*z3**REAL(m-2) + END DO + END DO + END DO + END DO + + factor2 = -9.0/16.0 * PI *rho + factor3 = 9.0/16.0 * PI**2 * rho**2 + + fqq2 = 0.0 + fqq3 = 0.0 + fqq2dt = 0.0 + fqq3dt = 0.0 + fqq2dt2= 0.0 + fqq3dt2= 0.0 + DO i = 1,ncomp + DO j = 1,ncomp + xijmt = x(i)*uij(i,i)*qq2(i)*sig_ij(i,i)**5 & + * x(j)*uij(j,j)*qq2(j)*sig_ij(j,j)**5 /sig_ij(i,j)**7.0 + eij = (parame(i,3)*parame(j,3))**0.5 + fqq2 = fqq2 +factor2* xijmt/t/t*(iqq2(i,j)+eij/t*iqq4(i,j)) + fqq2dt= fqq2dt +factor2* xijmt/t/t*(iqq2dt(i,j)-2.0*iqq2(i,j)/t & + + eij/t*iqq4dt(i,j)-3.0*eij/t/t*iqq4(i,j)) + fqq2dt2=fqq2dt2+factor2*xijmt/t/t*(iqq2dt2(i,j)-4.0*iqq2dt(i,j)/t & + + 6.0*iqq2(i,j)/t/t+eij/t*iqq4dt2(i,j) & + - 6.0*eij/t/t*iqq4dt(i,j)+12.0*eij/t**3 *iqq4(i,j)) + DO k = 1,ncomp + xijkmt = x(i)*uij(i,i)*qq2(i)*sig_ij(i,i)**5 /sig_ij(i,j)**3 & + * x(j)*uij(j,j)*qq2(j)*sig_ij(j,j)**5 /sig_ij(i,k)**3 & + * x(k)*uij(k,k)*qq2(k)*sig_ij(k,k)**5 /sig_ij(j,k)**3 + fqq3 = fqq3 +factor3*xijkmt/t**3 *iqq3(i,j,k) + fqq3dt = fqq3dt +factor3*xijkmt/t**3 *(iqq3dt(i,j,k)-3.0*iqq3(i,j,k)/t) + fqq3dt2= fqq3dt2+factor3*xijkmt/t**3 & + * ( iqq3dt2(i,j,k)-6.0*iqq3dt(i,j,k)/t+12.0*iqq3(i,j,k)/t/t ) + END DO + END DO + END DO + + IF ( fqq2 /= 0.0 .AND. fqq3 /= 0.0 ) THEN + fqqdt = fqq2* (fqq2*fqq2dt - 2.0*fqq3*fqq2dt+fqq2*fqq3dt) / (fqq2-fqq3)**2 + fqqdt2 = ( 2.0*fqq2*fqq2dt*fqq2dt +fqq2*fqq2*fqq2dt2 & + - 2.0*fqq2dt**2 *fqq3 -2.0*fqq2*fqq2dt2*fqq3 +fqq2*fqq2*fqq3dt2 ) & + / (fqq2-fqq3)**2 + fqqdt * 2.0*(fqq3dt-fqq2dt)/(fqq2-fqq3) + END IF + +END IF + + +! ---------------------------------------------------------------------- +! derivatives f/kT of dipole-quadruppole term to T (fdqdt) +! ---------------------------------------------------------------------- +fdqdt = 0.0 +fdqdt2= 0.0 +dip_quad = 0 +DO i = 1,ncomp + DO j = 1,ncomp + IF (parame(i,6) /= 0.0 .AND. parame(j,7) /= 0.0) dip_quad = 1 + END DO + myfac(i) = parame(i,3)*parame(i,2)**4 *my0(i) + q_fac(i) = parame(i,3)*parame(i,2)**4 *qq2(i) +END DO + +IF (dip_quad == 1) THEN + + DO i = 1,ncomp + DO j = 1,ncomp + idq2(i,j) = 0.0 + idq4(i,j) = 0.0 + idq2dt(i,j) = 0.0 + idq4dt(i,j) = 0.0 + idq2dt2(i,j)= 0.0 + idq4dt2(i,j)= 0.0 + IF ( myfac(i) /= 0.0 .AND. q_fac(j) /= 0.0 ) THEN + DO m = 0, 4 + idq2(i,j) = idq2(i,j) + dqp2(i,j,m)*z3**REAL(m) + idq4(i,j) = idq4(i,j) + dqp4(i,j,m)*z3**REAL(m) + idq2dt(i,j) = idq2dt(i,j)+ dqp2(i,j,m)*z3dt*REAL(m)*z3**REAL(m-1) + idq4dt(i,j) = idq4dt(i,j)+ dqp4(i,j,m)*z3dt*REAL(m)*z3**REAL(m-1) + idq2dt2(i,j)= idq2dt2(i,j)+dqp2(i,j,m)*z3dt2*REAL(m)*z3**REAL(m-1) & + + dqp2(i,j,m)*z3dt**2 *REAL(m)*REAL(m-1)*z3**REAL(m-2) + idq4dt2(i,j)= idq4dt2(i,j)+dqp4(i,j,m)*z3dt2*REAL(m)*z3**REAL(m-1) & + + dqp4(i,j,m)*z3dt**2 *REAL(m)*REAL(m-1)*z3**REAL(m-2) + END DO + + DO k = 1,ncomp + idq3(i,j,k) = 0.0 + idq3dt(i,j,k) = 0.0 + idq3dt2(i,j,k)= 0.0 + IF ( myfac(k) /= 0.0 .OR. q_fac(k) /= 0.0 ) THEN + DO m = 0, 4 + idq3(i,j,k) = idq3(i,j,k) + dqp3(i,j,k,m)*z3**REAL(m) + idq3dt(i,j,k)= idq3dt(i,j,k)+ dqp3(i,j,k,m)*z3dt*REAL(m) *z3**REAL(m-1) + idq3dt2(i,j,k)= idq3dt2(i,j,k)+dqp3(i,j,k,m)*z3dt2*REAL(m) *z3**REAL(m-1) & + + dqp3(i,j,k,m)*z3dt**2 *REAL(m)*REAL(m-1)*z3**REAL(m-2) + END DO + END IF + END DO + END IF + END DO + END DO + + factor2= -9.0/4.0 * PI * rho + factor3= PI**2 * rho**2 + + fdq2 = 0.0 + fdq3 = 0.0 + fdq2dt= 0.0 + fdq3dt= 0.0 + fdq2dt2=0.0 + fdq3dt2=0.0 + DO i = 1,ncomp + DO j = 1,ncomp + IF ( myfac(i) /= 0.0 .AND. q_fac(j) /= 0.0 ) THEN + xijmt = x(i)*myfac(i) * x(j)*q_fac(j) /sig_ij(i,j)**5 + eij = (parame(i,3)*parame(j,3))**0.5 + fdq2 = fdq2 + factor2* xijmt/t/t*(idq2(i,j)+eij/t*idq4(i,j)) + fdq2dt= fdq2dt+ factor2* xijmt/t/t*(idq2dt(i,j)-2.0*idq2(i,j)/t & + + eij/t*idq4dt(i,j)-3.0*eij/t/t*idq4(i,j)) + fdq2dt2 = fdq2dt2+factor2*xijmt/t/t*(idq2dt2(i,j)-4.0*idq2dt(i,j)/t & + + 6.0*idq2(i,j)/t/t+eij/t*idq4dt2(i,j) & + - 6.0*eij/t/t*idq4dt(i,j)+12.0*eij/t**3 *idq4(i,j)) + DO k = 1,ncomp + IF ( myfac(k) /= 0.0 .OR. q_fac(k) /= 0.0 ) THEN + xijkmt= x(i)*x(j)*x(k)/(sig_ij(i,j)*sig_ij(i,k)*sig_ij(j,k))**2 & + * ( myfac(i)*q_fac(j)*myfac(k) & + + myfac(i)*q_fac(j)*q_fac(k)*1.193735 ) + + fdq3 =fdq3 + factor3*xijkmt/t**3 *idq3(i,j,k) + fdq3dt=fdq3dt+ factor3*xijkmt/t**3 * (idq3dt(i,j,k)-3.0*idq3(i,j,k)/t) + fdq3dt2=fdq3dt2+factor3*xijkmt/t**3 & + *( idq3dt2(i,j,k)-6.0*idq3dt(i,j,k)/t+12.0*idq3(i,j,k)/t/t ) + END IF + END DO + END IF + END DO + END DO + + IF (fdq2 /= 0.0 .AND. fdq3 /= 0.0) THEN + fdqdt = fdq2* (fdq2*fdq2dt - 2.0*fdq3*fdq2dt+fdq2*fdq3dt) / (fdq2-fdq3)**2 + fdqdt2 = ( 2.0*fdq2*fdq2dt*fdq2dt +fdq2*fdq2*fdq2dt2 & + - 2.0*fdq2dt**2 *fdq3 -2.0*fdq2*fdq2dt2*fdq3 +fdq2*fdq2*fdq3dt2 ) & + / (fdq2-fdq3)**2 + fdqdt * 2.0*(fdq3dt-fdq2dt)/(fdq2-fdq3) + END IF + +END IF +! ---------------------------------------------------------------------- + + + + +! ---------------------------------------------------------------------- +! total derivative of fres/kT to temperature +! ---------------------------------------------------------------------- + +df_dt = fhsdt + fchdt + fdspdt + fhbdt + fdddt + fqqdt + fdqdt + + + +! ---------------------------------------------------------------------- +! second derivative of fres/kT to T +! ---------------------------------------------------------------------- + +df_dt2 = fhsdt2 +fchdt2 +fdspdt2 +fhbdt2 +fdddt2 +fqqdt2 +fdqdt2 + + + +! ---------------------------------------------------------------------- +! ------ derivatives of fres/kt to density and to T -------------------- +! ---------------------------------------------------------------------- + +! ---------------------------------------------------------------------- +! the analytic derivative of fres/kT to (density and T) (df_drdt) +! is still missing. A numerical differentiation is implemented. +! ---------------------------------------------------------------------- +fact = 1.0 +dist = t * 100.E-5 * fact +t_tmp = t +rho_0 = rho + + +t = t_tmp - 2.0*dist +CALL PERTURBATION_PARAMETER +eta = z3t*rho_0 +CALL P_EOS +fdr1 = pges / (eta*rho_0*(kbol*t)/1.E-30) +t = t_tmp - dist +CALL PERTURBATION_PARAMETER +eta = z3t*rho_0 +CALL P_EOS +fdr2 = pges / (eta*rho_0*(kbol*t)/1.E-30) + +t = t_tmp + dist +CALL PERTURBATION_PARAMETER +eta = z3t*rho_0 +CALL P_EOS +fdr3 = pges / (eta*rho_0*(kbol*t)/1.E-30) + +t = t_tmp + 2.0*dist +CALL PERTURBATION_PARAMETER +eta = z3t*rho_0 +CALL P_EOS +fdr4 = pges / (eta*rho_0*(kbol*t)/1.E-30) + +t = t_tmp +CALL PERTURBATION_PARAMETER +eta = z3t*rho_0 +CALL P_EOS + + +df_drdt = (-fdr4+8.0*fdr3-8.0*fdr2+fdr1)/(12.0*dist) + + + + + +! ---------------------------------------------------------------------- +! thermodynamic properties +! ---------------------------------------------------------------------- + +s_res = ( - df_dt *t - fres )*RGAS + RGAS * LOG(zges) +h_res = ( - t*df_dt + zges-1.0 ) * RGAS *t +cv_res = - ( t*df_dt2 + 2.0*df_dt ) * RGAS*t +cp_res = cv_res - RGAS + RGAS*(zges +eta*t*df_drdt)**2 & + / (1.0 + 2.0*eta*dfdr +eta**2 *ddfdrdr) + +! write (*,*) 'df_... ', df_dt,df_dt2 +! write (*,*) 'kreuz ', zges,eta*t*df_drdt,eta*dfdr, eta**2 *ddfdrdr +! write (*,*) 'h,cv,cp', h_res,cv_res,cp_res + + +END SUBROUTINE H_EOS + + + +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! SUBROUTINE H_EOS_num +! +! This subroutine calculates enthalpies and heat capacities (cp) by +! taking numerical derivatieves. +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! + SUBROUTINE H_EOS_num +! + USE PARAMETERS, ONLY: RGAS + USE EOS_VARIABLES + IMPLICIT NONE +! +!--------------------------------------------------------------------- + REAL :: dist, fact, rho_0 + REAL :: fres1, fres2, fres3, fres4, fres5 + REAL :: f_1, f_2, f_3, f_4 + REAL :: cv_res, t_tmp, zges + REAL :: df_dt, df_dtdt, df_drdt, dfdr, ddfdrdr + +!----------------------------------------------------------------------- + + +CALL PERTURBATION_PARAMETER +rho_0 = eta/z3t + + +fact = 1.0 +dist = t * 100.E-5 * fact + +t_tmp = t + +t = t_tmp - 2.0*dist +CALL PERTURBATION_PARAMETER +eta = z3t*rho_0 +CALL F_EOS +fres1 = fres +t = t_tmp - dist +CALL PERTURBATION_PARAMETER +eta = z3t*rho_0 +CALL F_EOS +fres2 = fres +t = t_tmp + dist +CALL PERTURBATION_PARAMETER +eta = z3t*rho_0 +CALL F_EOS +fres3 = fres +t = t_tmp + 2.0*dist +CALL PERTURBATION_PARAMETER +eta = z3t*rho_0 +CALL F_EOS +fres4 = fres +t = t_tmp +CALL PERTURBATION_PARAMETER +eta = z3t*rho_0 +CALL F_EOS +fres5 = fres +! *(KBOL*T)/1.E-30 + +zges = (p * 1.E-30)/(kbol*t*rho_0) + + +df_dt = (-fres4+8.0*fres3-8.0*fres2+fres1)/(12.0*dist) +df_dtdt = (-fres4+16.0*fres3-3.d1*fres5+16.0*fres2-fres1) & + /(12.0*(dist**2 )) + + +s_res = (- df_dt -fres/t)*RGAS*t + RGAS * LOG(zges) +h_res = ( - t*df_dt + zges-1.0 ) * RGAS*t +cv_res = -( t*df_dtdt + 2.0*df_dt ) * RGAS*t + + + +t = t_tmp - 2.0*dist +CALL PERTURBATION_PARAMETER +eta = z3t*rho_0 +CALL P_EOS +f_1 = pges/(eta*rho_0*(kbol*t)/1.E-30) + +t = t_tmp - dist +CALL PERTURBATION_PARAMETER +eta = z3t*rho_0 +CALL P_EOS +f_2 = pges/(eta*rho_0*(kbol*t)/1.E-30) + +t = t_tmp + dist +CALL PERTURBATION_PARAMETER +eta = z3t*rho_0 +CALL P_EOS +f_3 = pges/(eta*rho_0*(kbol*t)/1.E-30) + +t = t_tmp + 2.0*dist +CALL PERTURBATION_PARAMETER +eta = z3t*rho_0 +CALL P_EOS +f_4 = pges/(eta*rho_0*(kbol*t)/1.E-30) + +t = t_tmp +CALL PERTURBATION_PARAMETER +eta = z3t*rho_0 +CALL P_EOS + +dfdr = pges / (eta*rho_0*(kbol*t)/1.E-30) +ddfdrdr = pgesdz/(eta*rho_0*(kbol*t)/1.E-30) - dfdr*2.0/eta - 1.0/eta**2 + +df_drdt = ( -f_4 +8.0*f_3 -8.0*f_2 +f_1) / (12.0*dist) + +cp_res = cv_res - RGAS +RGAS*(zges+eta*t*df_drdt)**2 & + * 1.0/(1.0 + 2.0*eta*dfdr + eta**2 *ddfdrdr) + +! write (*,*) 'n',df_dt,df_dtdt +! write (*,*) 'kreuz ', zges,eta*t*df_drdt,eta*dfdr, eta**2 *ddfdrdr +! write (*,*) 'h, cv', h_res, cv_res +! write (*,*) h_res - t*s_res +! write (*,*) cv_res,cp_res,eta +! pause + +END SUBROUTINE H_EOS_num + + +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! SUBROUTINE DENSITY_ITERATION +! +! iterates the density until the calculated pressure 'pges' is equal to +! the specified pressure 'p'. A Newton-scheme is used for determining +! the root to the objective function f(eta) = (pges / p ) - 1.0. +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! + SUBROUTINE DENSITY_ITERATION +! + USE BASIC_VARIABLES, ONLY: num + USE EOS_VARIABLES + IMPLICIT NONE +! +! ---------------------------------------------------------------------- + INTEGER :: i, start, max_i + REAL :: eta_iteration + REAL :: error, dydx, acc_i, delta_eta +! ---------------------------------------------------------------------- + + +IF ( densav(phas) /= 0.0 .AND. eta_start == denold(phas) ) THEN + denold(phas) = eta_start + eta_start = densav(phas) +ELSE + denold(phas) = eta_start + densav(phas) = eta_start +END IF + + +acc_i = 1.d-9 +max_i = 30 +density_error(:) = 0.0 + +i = 0 +eta_iteration = eta_start + +! ---------------------------------------------------------------------- +! iterate density until p_calc = p +! ---------------------------------------------------------------------- +iterate_density: DO + + i = i + 1 + eta = eta_iteration + + IF ( num == 0 ) THEN + CALL P_EOS + ELSE IF ( num == 1 ) THEN + CALL P_NUMERICAL + ELSE IF ( num == 2 ) THEN + WRITE(*,*) 'CRITICAL RENORM NOT INCLUDED YET' + !!CALL F_EOS_RN + ELSE + write (*,*) 'define calculation option (num)' + END IF + + error = (pges / p ) - 1.0 + + ! --- instable region correction ------------------------------------- + IF ( pgesdz < 0.0 .AND. i < max_i ) THEN + IF ( error > 0.0 .AND. pgesd2 > 0.0 ) THEN ! no liquid density + CALL PRESSURE_SPINODAL + eta_iteration = eta + error = (pges / p ) - 1.0 + IF ( ((pges/p ) -1.0) > 0.0 ) eta_iteration = 0.001 ! no solution possible + IF ( ((pges/p ) -1.0) <=0.0 ) eta_iteration = eta_iteration * 1.1 ! no solution found so far + ELSE IF ( error < 0.0 .AND. pgesd2 < 0.0 ) THEN ! no vapor density + CALL PRESSURE_SPINODAL + eta_iteration = eta + error = (pges / p ) - 1.0 + IF ( ((pges/p ) -1.0) < 0.0 ) eta_iteration = 0.5 ! no solution possible + IF ( ((pges/p ) -1.0) >=0.0 ) eta_iteration = eta_iteration * 0.9 ! no solution found so far + ELSE + eta_iteration = (eta_iteration + eta_start) / 2.0 + IF (eta_iteration == eta_start) eta_iteration = eta_iteration + 0.2 + END IF + CYCLE iterate_density + END IF + + + dydx = pgesdz/p + delta_eta = error/ dydx + IF ( delta_eta > 0.05 ) delta_eta = 0.05 + IF ( delta_eta < -0.05 ) delta_eta = -0.05 + + eta_iteration = eta_iteration - delta_eta + + IF (eta_iteration > 0.9) eta_iteration = 0.6 + IF (eta_iteration <= 0.0) eta_iteration = 1.E-16 + start = 1 + + IF ( ABS(error*p/pgesdz) < 1.d-12 ) start = 0 + IF ( ABS(error) < acc_i ) start = 0 + IF ( i > max_i ) THEN + start = 0 + density_error(phas) = ABS( error ) + ! write (*,*) 'density iteration failed' + END IF + + IF (start /= 1) EXIT iterate_density + +END DO iterate_density + +eta = eta_iteration + +IF ((eta > 0.3 .AND. densav(phas) > 0.3) .OR. & + (eta < 0.1 .AND. densav(phas) < 0.1)) densav(phas) = eta + +END SUBROUTINE DENSITY_ITERATION + + + + +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! SUBROUTINE F_EOS +! +! calculates the Helmholtz energy f/kT. The input to the subroutine is +! (T,eta,x), where eta is the packing fraction. +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! + SUBROUTINE F_EOS +! + USE PARAMETERS, ONLY: nc, nsite + USE EOS_VARIABLES + USE EOS_CONSTANTS + IMPLICIT NONE +! +! --- local variables -------------------------------------------------- + INTEGER :: i, j, k, l, m, n + REAL :: z0, z1, z2, z3 + REAL :: zms, m_mean ! ,lij(nc,nc) + REAL :: I1,I2, c1_con + REAL :: fhs, fdsp, fhc + + LOGICAL :: assoc + INTEGER :: ass_cnt,max_eval + REAL :: delta(nc,nc,nsite,nsite) + REAL :: mx_itr(nc,nsite), err_sum, sum, attenu, tol, fhb + REAL :: ass_s1, ass_s2 + + REAL :: fdd, fqq, fdq +! ---------------------------------------------------------------------- + + +! ---------------------------------------------------------------------- +! abbreviations +! ---------------------------------------------------------------------- +rho = eta/z3t +z0 = z0t*rho +z1 = z1t*rho +z2 = z2t*rho +z3 = z3t*rho + +m_mean = z0t / ( PI / 6.0 ) +zms = 1.0 - eta + +! m_mean2 = 0.0 +! lij(1,2) = -0.05 +! lij(2,1) = lij(1,2) +! DO i = 1, ncomp +! DO j = 1, ncomp +! m_mean2 = m_mean2 + x(i)*x(j)*(mseg(i)+mseg(j))/2.0*(1.0-lij(i,j)) +! ENDDO +! ENDDO + + +! ---------------------------------------------------------------------- +! radial distr. function at contact, gij +! ---------------------------------------------------------------------- +DO i = 1, ncomp + DO j=1,ncomp + gij(i,j) = 1.0/zms + 3.0*dij_ab(i,j)*z2/zms/zms + 2.0*(dij_ab(i,j)*z2)**2 /zms**3 + END DO +END DO + + +! ---------------------------------------------------------------------- +! Helmholtz energy : hard sphere contribution +! ---------------------------------------------------------------------- +fhs= m_mean*( 3.0*z1*z2/zms + z2**3 /z3/zms/zms + (z2**3 /z3/z3-z0)*LOG(zms) )/z0 + + +! ---------------------------------------------------------------------- +! Helmholtz energy : chain term +! ---------------------------------------------------------------------- +fhc = 0.0 +DO i = 1, ncomp + fhc = fhc + x(i) *(1.0- mseg(i)) *LOG(gij(i,i)) +END DO + + +! ---------------------------------------------------------------------- +! Helmholtz energy : PC-SAFT dispersion contribution +! ---------------------------------------------------------------------- +IF (eos == 1) THEN + + I1 = 0.0 + I2 = 0.0 + DO m = 0, 6 + I1 = I1 + apar(m)*eta**REAL(m) + I2 = I2 + bpar(m)*eta**REAL(m) + END DO + + c1_con= 1.0/ ( 1.0 + m_mean*(8.0*eta-2.0*eta**2 )/zms**4 & + + (1.0 - m_mean)*(20.0*eta-27.0*eta**2 & + + 12.0*eta**3 -2.0*eta**4 ) /(zms*(2.0-eta))**2 ) + + fdsp = -2.0*PI*rho*I1*order1 - PI*rho*c1_con*m_mean*I2*order2 + +! ---------------------------------------------------------------------- +! Helmholtz energy : SAFT (Chen, Kreglewski) dispersion contribution +! ---------------------------------------------------------------------- +ELSE + + fdsp = 0.0 + DO n = 1,4 + DO m = 1,9 + fdsp = fdsp + dnm(n,m) * (um/t)**REAL(n) *(eta/tau)**REAL(m) + END DO + END DO + fdsp = m_mean * fdsp + +END IF + + +! ---------------------------------------------------------------------- +! TPT-1-association according to Chapman et al. +! ---------------------------------------------------------------------- +fhb = 0.0 +assoc = .false. +DO i = 1, ncomp + IF (nhb_typ(i) /= 0) assoc = .true. +END DO +IF (assoc) THEN + + DO i = 1, ncomp + DO k = 1, nhb_typ(i) + IF (mx(i,k) == 0.0) mx(i,k) = 1.0 ! Initialize mx(i,j) + DO j = 1, ncomp + DO l = 1, nhb_typ(j) + delta(i,j,k,l) = gij(i,j) * ass_d(i,j,k,l) + END DO + END DO + END DO + END DO + + +! --- constants for iteration ------------------------------------------ + attenu = 0.70 + tol = 1.d-10 + IF (eta < 0.2) tol = 1.d-12 + IF (eta < 0.01) tol = 1.d-13 + max_eval = 200 + +! --- iterate over all components and all sites ------------------------ + ass_cnt = 0 + iterate_TPT1: DO + + ass_cnt = ass_cnt + 1 + + DO i = 1, ncomp + DO k = 1, nhb_typ(i) + sum = 0.0 + DO j = 1, ncomp + DO l = 1, nhb_typ(j) + sum = sum + x(j)* mx(j,l)*nhb_no(j,l) *delta(i,j,k,l) +! if (ass_cnt == 1) write (*,*) j,l,x(j), mx(j,l) + END DO + END DO + mx_itr(i,k) = 1.0 / (1.0 + sum * rho) +! if (ass_cnt == 1) write (*,*) 'B',ass_cnt,sum, rho + END DO + END DO + + err_sum = 0.0 + DO i = 1, ncomp + DO k = 1, nhb_typ(i) + err_sum = err_sum + ABS(mx_itr(i,k) - mx(i,k)) ! / ABS(mx_itr(i,k)) + mx(i,k) = mx_itr(i,k) * attenu + mx(i,k) * (1.0 - attenu) + END DO + END DO + + IF ( err_sum <= tol .OR. ass_cnt >= max_eval ) THEN + IF (ass_cnt >= max_eval) WRITE(*,'(a,2G15.7)') 'F_EOS: Max_eval violated (mx) Err_Sum = ',err_sum,tol + EXIT iterate_TPT1 + END IF + + END DO iterate_TPT1 + + DO i = 1, ncomp + ass_s1 = 0.0 + ass_s2 = 0.0 + DO k = 1, nhb_typ(i) + ass_s1 = ass_s1 + nhb_no(i,k) * ( 1.0 - mx(i,k) ) + ass_s2 = ass_s2 + nhb_no(i,k) * LOG( mx(i,k) ) + END DO + fhb = fhb + x(i) * ( ass_s2 + ass_s1 / 2.0 ) + END DO + +END IF +! --- TPT-1-association accord. to Chapman ----------------------------- + + +! ---------------------------------------------------------------------- +! polar terms +! ---------------------------------------------------------------------- + CALL F_POLAR ( fdd, fqq, fdq ) + + +! ---------------------------------------------------------------------- +! resid. Helmholtz energy f/kT +! ---------------------------------------------------------------------- +fres = fhs + fhc + fdsp + fhb + fdd + fqq + fdq + +tfr= fres + +END SUBROUTINE F_EOS + + +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! + SUBROUTINE F_NUMERICAL +! + USE EOS_VARIABLES + USE EOS_CONSTANTS + USE EOS_NUMERICAL_DERIVATIVES, ONLY: ideal_gas, hard_sphere, chain_term, & + disp_term, hb_term, LC_term, branch_term, & + II_term, ID_term, subtract1, subtract2 + IMPLICIT NONE +! +!--------------------------------------------------------------------- + +!-----local variables------------------------------------------------- + INTEGER :: i, j + REAL :: m_mean2 + REAL :: fid, fhs, fdsp, fhc + REAL :: fhb, fdd, fqq, fdq + REAL :: fhend, fcc + REAL :: fbr, flc + REAL :: fref + + REAL :: eps_kij, k_kij +!--------------------------------------------------------------------- + +eps_kij = 0.0 +k_kij = 0.0 + +fid = 0.0 +fhs = 0.0 +fhc = 0.0 +fdsp= 0.0 +fhb = 0.0 +fdd = 0.0 +fqq = 0.0 +fdq = 0.0 +fcc = 0.0 +fbr = 0.0 +flc = 0.0 + + +CALL PERTURBATION_PARAMETER + +! ---------------------------------------------------------------------- +! overwrite the standard mixing rules by those published by Tang & Gross +! using an additional lij parameter +! WARNING : the lij parameter is set to lij = - lji in 'para_input' +! ---------------------------------------------------------------------- +order1 = 0.0 +order2 = 0.0 +DO i = 1, ncomp + DO j = 1, ncomp + order1 = order1 + x(i)*x(j)* mseg(i)*mseg(j) * sig_ij(i,j)**3 * uij(i,j)/t + order2 = order2 + x(i)*x(j)* mseg(i)*mseg(j) * sig_ij(i,j)**3 * (uij(i,j)/t)**2 + END DO +END DO +DO i = 1, ncomp + DO j = 1, ncomp + order1 = order1 + x(i)*mseg(i)/t*( x(j)*mseg(j) & + *sig_ij(i,j)*(uij(i,i)*uij(j,j))**(1.0/6.0) )**3 *lij(i,j) + END DO +END DO + + +! ---------------------------------------------------------------------- +! a non-standard mixing rule scaling the hard-sphere term +! WARNING : the lij parameter is set to lij = - lji in 'para_input' +! (uses an additional lij parameter) +! ---------------------------------------------------------------------- +m_mean2 = 0.0 +DO i = 1, ncomp + DO j = 1, ncomp + m_mean2 = m_mean2 + x(i)*x(j)*(mseg(i)+mseg(j))/2.0 + END DO +END DO +DO i = 1, ncomp + DO j = 1, ncomp + ! m_mean2=m_mean2+x(i)*(x(j)*((mseg(i)+mseg(j))*0.5)**(1.0/3.0) *lij(i,j) )**3 + END DO +END DO + +! --- ideal gas contribution ------------------------------------------- +IF ( ideal_gas == 'yes' ) CALL F_IDEAL_GAS ( fid ) +! ---------------------------------------------------------------------- + +! --- hard-sphere contribution ----------------------------------------- +IF ( hard_sphere == 'CSBM' ) CALL F_HARD_SPHERE ( m_mean2, fhs ) +! ---------------------------------------------------------------------- + +! -- chain term -------------------------------------------------------- +IF ( chain_term == 'TPT1' ) CALL F_CHAIN_TPT1 ( fhc ) +IF ( chain_term == 'TPT2' ) CALL F_CHAIN_TPT_D ( fhc ) +IF ( chain_term == 'HuLiu' ) CALL F_CHAIN_HU_LIU ( fhc ) +IF ( chain_term == 'HuLiu_rc' ) CALL F_CHAIN_HU_LIU_RC ( fhs, fhc ) +!!IF ( chain_term == 'SPT' ) CALL F_SPT ( fhs, fhc ) +IF ( chain_term == 'SPT' ) WRITE(*,*) 'SPT NOT INCLUDED YET' +! ---------------------------------------------------------------------- + +! --- dispersive attraction -------------------------------------------- +IF ( disp_term == 'PC-SAFT') CALL F_DISP_PCSAFT ( fdsp ) +IF ( disp_term == 'CK') CALL F_DISP_CKSAFT ( fdsp ) +IF ( disp_term(1:2) == 'PT') CALL F_pert_theory ( fdsp ) +! ---------------------------------------------------------------------- + +! --- H-bonding contribution / Association ----------------------------- +IF ( hb_term == 'TPT1_Chap') CALL F_ASSOCIATION( eps_kij, k_kij, fhb ) +! ---------------------------------------------------------------------- + +! --- polar terms ------------------------------------------------------ + CALL F_POLAR ( fdd, fqq, fdq ) +! ---------------------------------------------------------------------- + +! --- ion-dipole term -------------------------------------------------- +IF ( ID_term == 'TBH') CALL F_ION_DIPOLE_TBH ( fhend ) +! ---------------------------------------------------------------------- + +! --- ion-ion term ----------------------------------------------------- +IF ( II_term == 'primMSA') CALL F_ION_ION_PrimMSA ( fcc ) +IF ( II_term == 'nprMSA') CALL F_ION_ION_nonPrimMSA ( fdd, fqq, fdq, fcc ) +! ---------------------------------------------------------------------- + +! --- liquid-crystal term ---------------------------------------------- +IF ( LC_term == 'MSaupe') CALL F_LC_MayerSaupe ( flc ) + +!!IF ( LC_term == 'OVL') fref = fhs + fhc +IF ( LC_term == 'OVL') WRITE(*,*) 'OVL NOT INCLUDED YET' +!IF ( LC_term == 'OVL') CALL F_LC_OVL ( fref, flc ) +!! IF ( LC_term == 'SPT') fref = fhs + fhc +IF ( LC_term == 'SPT') WRITE(*,*) 'SPT NOT INCLUDED YET' +!!IF ( LC_term == 'SPT') CALL F_LC_SPT( fref, flc ) +! ---------------------------------------------------------------------- + +! ====================================================================== +! SUBTRACT TERMS (local density approximation) FOR DFT +! ====================================================================== + +!IF ( subtract1 == '1PT') CALL F_subtract_local_pert_theory ( subtract1, fdsp ) +!IF ( subtract1 == '2PT') CALL F_subtract_local_pert_theory ( subtract1, fdsp ) +!IF ( subtract2 =='ITTpolar') CALL F_local_ITT_polar ( fdd ) +! ---------------------------------------------------------------------- + +! ---------------------------------------------------------------------- +! residual Helmholtz energy F/(NkT) +! ---------------------------------------------------------------------- +fres = fid + fhs + fhc + fdsp + fhb + fdd + fqq + fdq + fcc + flc + +tfr = 0.0 + +END SUBROUTINE F_NUMERICAL + + + +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! SUBROUTINE P_EOS +! +! calculates the pressure in units (Pa). +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! + SUBROUTINE P_EOS +! +! ---------------------------------------------------------------------- + USE PARAMETERS, ONLY: nc, nsite + USE EOS_VARIABLES + USE EOS_CONSTANTS + IMPLICIT NONE +! +! --- local variables -------------------------------------------------- + INTEGER :: i, j, k, l, m, n + INTEGER :: ass_cnt,max_eval + LOGICAL :: assoc + REAL :: z0, z1, z2, z3 + REAL :: zms, m_mean + REAL :: zges, zgesdz, zgesd2, zgesd3 + REAL :: zhs, zhsdz, zhsd2, zhsd3 + REAL :: zhc, zhcdz, zhcd2, zhcd3 + REAL, DIMENSION(nc,nc) :: dgijdz, dgijd2, dgijd3, dgijd4 + REAL :: zdsp, zdspdz, zdspd2, zdspd3 + REAL :: c1_con, c2_con, c3_con, c4_con, c5_con + REAL :: I2, edI1dz, edI2dz, edI1d2, edI2d2 + REAL :: edI1d3, edI2d3, edI1d4, edI2d4 + REAL :: fdspdz,fdspd2 + REAL :: zhb, zhbdz, zhbd2, zhbd3 + REAL, DIMENSION(nc,nc,nsite,nsite) :: delta, dq_dz, dq_d2, dq_d3, dq_d4 + REAL, DIMENSION(nc,nsite) :: mx_itr, dmx_dz, ndmxdz, dmx_d2, ndmxd2 + REAL, DIMENSION(nc,nsite) :: dmx_d3, ndmxd3, dmx_d4, ndmxd4 + REAL :: err_sum, sum0, sum1, sum2, sum3, sum4, attenu, tol + REAL :: sum_d1, sum_d2, sum_d3, sum_d4 + REAL :: zdd, zddz, zddz2, zddz3 + REAL :: zqq, zqqz, zqqz2, zqqz3 + REAL :: zdq, zdqz, zdqz2, zdqz3 +! ---------------------------------------------------------------------- + + +! ---------------------------------------------------------------------- +! abbreviations +! ---------------------------------------------------------------------- +rho = eta/z3t +z0 = z0t*rho +z1 = z1t*rho +z2 = z2t*rho +z3 = z3t*rho + +m_mean = z0t/(PI/6.0) +zms = 1.0 -eta + +! m_mean2=0.0 +! lij(1,2)= -0.050 +! lij(2,1)=lij(1,2) +! DO i =1,ncomp +! DO j =1,ncomp +! m_mean2=m_mean2+x(i)*x(j) * (mseg(i)+mseg(j))/2.0*(1.0-lij(i,j)) +! ENDDO +! ENDDO + + +! ---------------------------------------------------------------------- +! radial distr. function at contact, gij , and derivatives +! dgijdz=d(gij)/d(eta) and dgijd2 = dd(gij)/d(eta)**2 +! ---------------------------------------------------------------------- +DO i = 1, ncomp + DO j=1,ncomp + ! j=i + gij(i,j) = 1.0/zms + 3.0*dij_ab(i,j)*z2/zms/zms + 2.0*(dij_ab(i,j)*z2)**2 /zms**3 + dgijdz(i,j)= 1.0/zms/zms + 3.0*dij_ab(i,j)*z2*(1.0+z3)/z3/zms**3 & + + (dij_ab(i,j)*z2/zms/zms)**2 *(4.0+2.0*z3)/z3 + dgijd2(i,j) = 2.0/zms**3 & + + 6.0*dij_ab(i,j)*z2/z3/zms**4 *(2.0+z3) & + + (2.0*dij_ab(i,j)*z2/z3)**2 /zms**5 *(1.0+4.0*z3+z3*z3) + dgijd3(i,j) = 6.0/zms**4 & + + 18.0*dij_ab(i,j)*z2/z3/zms**5 *(3.0+z3) & + + 12.0*(dij_ab(i,j)*z2/z3/zms**3 )**2 *(3.0+6.0*z3+z3*z3) + dgijd4(i,j) = 24.0/zms**5 & + + 72.0*dij_ab(i,j)*z2/z3/zms**6 *(4.0+z3) & + + 48.0*(dij_ab(i,j)*z2/z3)**2 /zms**7 *(6.0+8.0*z3+z3*z3) + END DO +END DO + + +! ---------------------------------------------------------------------- +! p : hard sphere contribution +! ---------------------------------------------------------------------- +zhs = m_mean* ( z3/zms + 3.0*z1*z2/z0/zms/zms + z2**3 /z0*(3.0-z3)/zms**3 ) +zhsdz = m_mean*( 1.0/zms/zms + 3.0*z1*z2/z0/z3*(1.0+z3)/zms**3 & + + 6.0*z2**3 /z0/z3/zms**4 ) +zhsd2 = m_mean*( 2.0/zms**3 + 6.0*z1*z2/z0/z3*(2.0+z3)/zms**4 & + + 6.0*z2**3 /z0/z3/z3*(1.0+3.0*z3)/zms**5 ) +zhsd3 = m_mean*( 6.0/zms**4 + 18.0*z1*z2/z0/z3*(3.0+z3)/zms**5 & + + 24.0*z2**3 /z0/z3/z3*(2.0+3.0*z3)/zms**6 ) + + +! ---------------------------------------------------------------------- +! p : chain term +! ---------------------------------------------------------------------- +zhc = 0.0 +zhcdz = 0.0 +zhcd2 = 0.0 +zhcd3 = 0.0 +DO i= 1, ncomp + zhc = zhc + x(i)*(1.0-mseg(i))*eta/gij(i,i)* dgijdz(i,i) + zhcdz = zhcdz + x(i)*(1.0-mseg(i)) *(-eta*(dgijdz(i,i)/gij(i,i))**2 & + + dgijdz(i,i)/gij(i,i) + eta/gij(i,i)*dgijd2(i,i)) + zhcd2 = zhcd2 + x(i)*(1.0-mseg(i)) & + *( 2.0*eta*(dgijdz(i,i)/gij(i,i))**3 & + -2.0*(dgijdz(i,i)/gij(i,i))**2 & + -3.0*eta/gij(i,i)**2 *dgijdz(i,i)*dgijd2(i,i) & + +2.0/gij(i,i)*dgijd2(i,i) +eta/gij(i,i)*dgijd3(i,i) ) + zhcd3 = zhcd3 + x(i)*(1.0-mseg(i)) *( 6.0*(dgijdz(i,i)/gij(i,i))**3 & + -6.0*eta*(dgijdz(i,i)/gij(i,i))**4 & + +12.0*eta/gij(i,i)**3 *dgijdz(i,i)**2 *dgijd2(i,i) & + -9.0/gij(i,i)**2 *dgijdz(i,i)*dgijd2(i,i) +3.0/gij(i,i)*dgijd3(i,i) & + -3.0*eta*(dgijd2(i,i)/gij(i,i))**2 & + -4.0*eta/gij(i,i)**2 *dgijdz(i,i)*dgijd3(i,i) & + +eta/gij(i,i)*dgijd4(i,i) ) +END DO + +! ---------------------------------------------------------------------- +! p : PC-SAFT dispersion contribution +! note: edI1dz is equal to d(eta*I1)/d(eta), analogous for edI2dz +! ---------------------------------------------------------------------- +IF (eos == 1) THEN + + I2 = 0.0 + edI1dz = 0.0 + edI2dz = 0.0 + edI1d2 = 0.0 + edI2d2 = 0.0 + edI1d3 = 0.0 + edI2d3 = 0.0 + edI1d4 = 0.0 + edI2d4 = 0.0 + DO m=0,6 + I2 = I2 + bpar(m)*z3**REAL(m) + edI1dz= edI1dz+apar(m)*REAL(m+1)*z3**REAL(m) + edI2dz= edI2dz+bpar(m)*REAL(m+1)*z3**REAL(m) + edI1d2= edI1d2+apar(m)*REAL((m+1)*m)*z3**REAL(m-1) + edI2d2= edI2d2+bpar(m)*REAL((m+1)*m)*z3**REAL(m-1) + edI1d3= edI1d3+apar(m)*REAL((m+1)*m*(m-1))*z3**REAL(m-2) + edI2d3= edI2d3+bpar(m)*REAL((m+1)*m*(m-1))*z3**REAL(m-2) + edI1d4= edI1d4+apar(m)*REAL((m+1)*m*(m-1)*(m-2))*z3**REAL(m-3) + edI2d4= edI2d4+bpar(m)*REAL((m+1)*m*(m-1)*(m-2))*z3**REAL(m-3) + END DO + + c1_con= 1.0/ ( 1.0 + m_mean*(8.0*eta-2.0*eta**2 )/zms**4 & + + (1.0 - m_mean)*(20.0*eta-27.0*eta**2 & + + 12.0*eta**3 -2.0*eta**4 ) /(zms*(2.0-eta))**2 ) + c2_con= - c1_con*c1_con & + *(m_mean*(-4.0*eta**2 +20.0*eta+8.0)/zms**5 + (1.0 - m_mean) & + *(2.0*eta**3 +12.0*eta**2 -48.0*eta+40.0) & + /(zms*(2.0-eta))**3 ) + c3_con= 2.0 * c2_con*c2_con/c1_con - c1_con*c1_con & + *( m_mean*(-12.0*eta**2 +72.0*eta+60.0)/zms**6 & + + (1.0 - m_mean) & + *(-6.0*eta**4 -48.0*eta**3 +288.0*eta**2 & + -480.0*eta+264.0) /(zms*(2.0-eta))**4 ) + c4_con= 6.0*c2_con*c3_con/c1_con -6.0*c2_con**3 /c1_con**2 & + - c1_con*c1_con & + *( m_mean*(-48.0*eta**2 +336.0*eta+432.0)/zms**7 & + + (1.0 - m_mean) & + *(24.0*eta**5 +240.0*eta**4 -1920.0*eta**3 & + +4800.0*eta**2 -5280.0*eta+2208.0) /(zms*(2.0-eta))**5 ) + c5_con= 6.0*c3_con**2 /c1_con - 36.0*c2_con**2 /c1_con**2 *c3_con & + + 8.0*c2_con/c1_con*c4_con+24.0*c2_con**4 /c1_con**3 & + - c1_con*c1_con & + *( m_mean*(-240.0*eta**2 +1920.0*eta+3360.0)/zms**8 & + + (1.0 - m_mean) & + *(-120.0*eta**6 -1440.0*eta**5 +14400.0*eta**4 & + -48000.0*eta**3 +79200.0*eta**2 -66240.0*eta+22560.0) & + /(zms*(2.0-eta))**6 ) + + zdsp = - 2.0*PI*rho*edI1dz*order1 & + - PI*rho*order2*m_mean*(c2_con*I2*eta + c1_con*edI2dz) + zdspdz= zdsp/eta - 2.0*PI*rho*edI1d2*order1 & + - PI*rho*order2*m_mean*(c3_con*I2*eta & + + 2.0*c2_con*edI2dz + c1_con*edI2d2) + zdspd2= -2.0*zdsp/eta/eta +2.0*zdspdz/eta & + - 2.0*PI*rho*edI1d3*order1 - PI*rho*order2*m_mean*(c4_con*I2*eta & + + 3.0*c3_con*edI2dz +3.0*c2_con*edI2d2 +c1_con*edI2d3) + zdspd3= 6.0*zdsp/eta**3 -6.0*zdspdz/eta/eta & + + 3.0*zdspd2/eta - 2.0*PI*rho*edI1d4*order1 & + - PI*rho*order2*m_mean*(c5_con*I2*eta & + + 4.0*c4_con*edI2dz +6.0*c3_con*edI2d2 & + + 4.0*c2_con*edI2d3 + c1_con*edI2d4) + + +! ---------------------------------------------------------------------- +! p : SAFT (Chen & Kreglewski) dispersion contribution +! ---------------------------------------------------------------------- +ELSE + + fdspdz = 0.0 + fdspd2 = 0.0 + DO n = 1,4 + DO m = 1,9 + fdspdz = fdspdz + m_mean/tau * dnm(n,m) * (um/t)**REAL(n) *REAL(m)*(eta/tau)**REAL(m-1) + END DO + DO m= 2,9 + fdspd2= fdspd2 + m_mean/tau * dnm(n,m)*(um/t)**REAL(n) *REAL(m)*REAL(m-1) & + * (eta/tau)**REAL(m-2) * 1.0/tau + END DO + END DO + zdsp = eta * fdspdz + zdspdz = (2.0*fdspdz + eta*fdspd2) - zdsp/z3 + +END IF +! --- end of dispersion contribution ----------------------------------- + + +! ---------------------------------------------------------------------- +! p: TPT-1-association accord. to Chapman et al. +! ---------------------------------------------------------------------- +zhb = 0.0 +zhbdz = 0.0 +zhbd2 = 0.0 +zhbd3 = 0.0 +assoc = .false. +DO i = 1,ncomp + IF (nhb_typ(i) /= 0) assoc = .true. +END DO +IF (assoc) THEN + + DO j = 1, ncomp + DO i = 1, nhb_typ(j) + DO k = 1, ncomp + DO l = 1, nhb_typ(k) + delta(j,k,i,l) = gij(j,k) * ass_d(j,k,i,l) + dq_dz(j,k,i,l) = dgijdz(j,k) * ass_d(j,k,i,l) + dq_d2(j,k,i,l) = dgijd2(j,k) * ass_d(j,k,i,l) + dq_d3(j,k,i,l) = dgijd3(j,k) * ass_d(j,k,i,l) + dq_d4(j,k,i,l) = dgijd4(j,k) * ass_d(j,k,i,l) + END DO + END DO + END DO + END DO + +! --- constants for iteration ------------------------------------------ + attenu = 0.7 + tol = 1.d-10 + IF ( eta < 0.2 ) tol = 1.d-12 + IF ( eta < 0.01 ) tol = 1.d-13 + IF ( eta < 1.E-6) tol = 1.d-15 + max_eval = 1000 + +! --- initialize mx(i,j) ----------------------------------------------- + DO i = 1, ncomp + DO j = 1, nhb_typ(i) + mx(i,j) = 1.0 + dmx_dz(i,j) = 0.0 + dmx_d2(i,j) = 0.0 + dmx_d3(i,j) = 0.0 + dmx_d4(i,j) = 0.0 + END DO + END DO + +! --- iterate over all components and all sites ------------------------ + ass_cnt = 0 + err_sum = tol + 1.0 + DO WHILE ( err_sum > tol .AND. ass_cnt <= max_eval) + ass_cnt = ass_cnt + 1 + DO i = 1, ncomp + DO j = 1, nhb_typ(i) + sum0 = 0.0 + sum1 = 0.0 + sum2 = 0.0 + sum3 = 0.0 + sum4 = 0.0 + DO k = 1, ncomp + DO l = 1, nhb_typ(k) + sum0 =sum0 +x(k)*nhb_no(k,l)* mx(k,l)* delta(i,k,j,l) + sum1 =sum1 +x(k)*nhb_no(k,l)*( mx(k,l)* dq_dz(i,k,j,l) & + + dmx_dz(k,l)* delta(i,k,j,l)) + sum2 =sum2 +x(k)*nhb_no(k,l)*( mx(k,l)* dq_d2(i,k,j,l) & + + 2.0*dmx_dz(k,l)* dq_dz(i,k,j,l) & + + dmx_d2(k,l)* delta(i,k,j,l)) + sum3 =sum3 +x(k)*nhb_no(k,l)*( mx(k,l)* dq_d3(i,k,j,l) & + + 3.0*dmx_dz(k,l)* dq_d2(i,k,j,l) & + + 3.0*dmx_d2(k,l)* dq_dz(i,k,j,l) & + + dmx_d3(k,l)* delta(i,k,j,l)) + sum4 =sum4 + x(k)*nhb_no(k,l)*( mx(k,l)* dq_d4(i,k,j,l) & + + 4.0*dmx_dz(k,l)* dq_d3(i,k,j,l) & + + 6.0*dmx_d2(k,l)* dq_d2(i,k,j,l) & + + 4.0*dmx_d3(k,l)* dq_dz(i,k,j,l) & + + dmx_d4(k,l)* delta(i,k,j,l)) + END DO + END DO + mx_itr(i,j)= 1.0 / (1.0 + sum0 * rho) + ndmxdz(i,j)= -(mx_itr(i,j)*mx_itr(i,j))* (sum0/z3t +sum1*rho) + ndmxd2(i,j)= + 2.0/mx_itr(i,j)*ndmxdz(i,j)*ndmxdz(i,j) & + - (mx_itr(i,j)*mx_itr(i,j)) * (2.0/z3t*sum1 + rho*sum2) + ndmxd3(i,j)= - 6.0/mx_itr(i,j)**2 *ndmxdz(i,j)**3 & + + 6.0/mx_itr(i,j)*ndmxdz(i,j)*ndmxd2(i,j) - mx_itr(i,j)*mx_itr(i,j) & + * (3.0/z3t*sum2 + rho*sum3) + ndmxd4(i,j)= 24.0/mx_itr(i,j)**3 *ndmxdz(i,j)**4 & + -36.0/mx_itr(i,j)**2 *ndmxdz(i,j)**2 *ndmxd2(i,j) & + +6.0/mx_itr(i,j)*ndmxd2(i,j)**2 & + +8.0/mx_itr(i,j)*ndmxdz(i,j)*ndmxd3(i,j) - mx_itr(i,j)**2 & + *(4.0/z3t*sum3 + rho*sum4) + END DO + END DO + + err_sum = 0.0 + DO i = 1, ncomp + DO j = 1, nhb_typ(i) + err_sum = err_sum + ABS(mx_itr(i,j) - mx(i,j)) & + + ABS(ndmxdz(i,j) - dmx_dz(i,j)) + ABS(ndmxd2(i,j) - dmx_d2(i,j)) + mx(i,j) = mx_itr(i,j)*attenu + mx(i,j) * (1.0-attenu) + dmx_dz(i,j) = ndmxdz(i,j)*attenu + dmx_dz(i,j) * (1.0-attenu) + dmx_d2(i,j) = ndmxd2(i,j)*attenu + dmx_d2(i,j) * (1.0-attenu) + dmx_d3(i,j) = ndmxd3(i,j)*attenu + dmx_d3(i,j) * (1.0-attenu) + dmx_d4(i,j) = ndmxd4(i,j)*attenu + dmx_d4(i,j) * (1.0-attenu) + END DO + END DO + END DO + + IF ( ass_cnt >= max_eval .AND. err_sum > SQRT(tol) ) THEN + WRITE (*,'(a,2G15.7)') 'P_EOS: Max_eval violated (mx) Err_Sum= ',err_sum,tol + ! stop + END IF + + + ! --- calculate the hydrogen-bonding contribution -------------------- + DO i = 1, ncomp + sum_d1 = 0.0 + sum_d2 = 0.0 + sum_d3 = 0.0 + sum_d4 = 0.0 + DO j = 1, nhb_typ(i) + sum_d1= sum_d1 +nhb_no(i,j)* dmx_dz(i,j)*(1.0/mx(i,j)-0.5) + sum_d2= sum_d2 +nhb_no(i,j)*(dmx_d2(i,j)*(1.0/mx(i,j)-0.5) & + -(dmx_dz(i,j)/mx(i,j))**2 ) + sum_d3= sum_d3 +nhb_no(i,j)*(dmx_d3(i,j)*(1.0/mx(i,j)-0.5) & + -3.0/mx(i,j)**2 *dmx_dz(i,j)*dmx_d2(i,j) + 2.0*(dmx_dz(i,j)/mx(i,j))**3 ) + sum_d4= sum_d4 +nhb_no(i,j)*(dmx_d4(i,j)*(1.0/mx(i,j)-0.5) & + -4.0/mx(i,j)**2 *dmx_dz(i,j)*dmx_d3(i,j) & + + 12.0/mx(i,j)**3 *dmx_dz(i,j)**2 *dmx_d2(i,j) & + - 3.0/mx(i,j)**2 *dmx_d2(i,j)**2 - 6.0*(dmx_dz(i,j)/mx(i,j))**4 ) + END DO + zhb = zhb + x(i) * eta * sum_d1 + zhbdz = zhbdz + x(i) * eta * sum_d2 + zhbd2 = zhbd2 + x(i) * eta * sum_d3 + zhbd3 = zhbd3 + x(i) * eta * sum_d4 + END DO + zhbdz = zhbdz + zhb/eta + zhbd2 = zhbd2 + 2.0/eta*zhbdz-2.0/eta**2 *zhb + zhbd3 = zhbd3 - 6.0/eta**2 *zhbdz+3.0/eta*zhbd2 + 6.0/eta**3 *zhb +END IF +! --- TPT-1-association accord. to Chapman ----------------------------- + + +! ---------------------------------------------------------------------- +! p: polar terms +! ---------------------------------------------------------------------- +CALL P_POLAR ( zdd, zddz, zddz2, zddz3, zqq, zqqz, zqqz2, zqqz3, zdq, zdqz, zdqz2, zdqz3 ) + + +! ---------------------------------------------------------------------- +! compressibility factor z and total p +! as well as derivatives d(z)/d(eta) and d(p)/d(eta) with unit [Pa] +! ---------------------------------------------------------------------- +zges = 1.0 + zhs + zhc + zdsp + zhb + zdd + zqq + zdq +zgesdz = zhsdz + zhcdz + zdspdz + zhbdz + zddz + zqqz + zdqz +zgesd2 = zhsd2 + zhcd2 + zdspd2 + zhbd2 + zddz2 +zqqz2+zdqz2 +zgesd3 = zhsd3 + zhcd3 + zdspd3 + zhbd3 + zddz3 +zqqz3+zdqz3 + +pges = zges *rho *(kbol*t)/1.d-30 +pgesdz = ( zgesdz*rho + zges*rho/z3 )*(kbol*t)/1.d-30 +pgesd2 = ( zgesd2*rho + 2.0*zgesdz*rho/z3 )*(kbol*t)/1.d-30 +pgesd3 = ( zgesd3*rho + 3.0*zgesd2*rho/z3 )*(kbol*t)/1.d-30 + +END SUBROUTINE P_EOS + + + + +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! + SUBROUTINE PHI_POLAR ( k, z3_rk, fdd_rk, fqq_rk, fdq_rk ) +! + USE EOS_VARIABLES, ONLY: ncomp, parame, dd_term, qq_term, dq_term + IMPLICIT NONE +! +! ---------------------------------------------------------------------- + INTEGER, INTENT(IN) :: k + REAL, INTENT(IN) :: z3_rk + REAL, INTENT(OUT) :: fdd_rk, fqq_rk, fdq_rk +! +! --- local variables--------------------------------------------------- + INTEGER :: dipole + INTEGER :: quadrupole + INTEGER :: dipole_quad +! ---------------------------------------------------------------------- + + fdd_rk = 0.0 + fqq_rk = 0.0 + fdq_rk = 0.0 + + dipole = 0 + quadrupole = 0 + dipole_quad = 0 + IF ( SUM( parame(1:ncomp,6) ) /= 0.0 ) dipole = 1 + IF ( SUM( parame(1:ncomp,7) ) /= 0.0 ) quadrupole = 1 + IF ( dipole == 1 .AND. quadrupole == 1 ) dipole_quad = 1 + + ! -------------------------------------------------------------------- + ! dipole-dipole term + ! -------------------------------------------------------------------- + IF (dipole == 1) THEN + + IF (dd_term == 'GV') CALL PHI_DD_GROSS_VRABEC( k, z3_rk, fdd_rk ) + ! IF (dd_term == 'SF') CALL PHI_DD_SAAGER_FISCHER( k ) + + IF (dd_term /= 'GV' .AND. dd_term /= 'SF') write (*,*) 'specify dipole term !' + + ENDIF + + ! -------------------------------------------------------------------- + ! quadrupole-quadrupole term + ! -------------------------------------------------------------------- + IF (quadrupole == 1) THEN + + !IF (qq_term == 'SF') CALL PHI_QQ_SAAGER_FISCHER( k ) + IF (qq_term == 'JG') CALL PHI_QQ_GROSS( k, z3_rk, fqq_rk ) + + IF (qq_term /= 'JG' .AND. qq_term /= 'SF') write (*,*) 'specify quadrupole term !' + + ENDIF + + ! -------------------------------------------------------------------- + ! dipole-quadrupole cross term + ! -------------------------------------------------------------------- + IF (dipole_quad == 1) THEN + + IF (dq_term == 'VG') CALL PHI_DQ_VRABEC_GROSS( k, z3_rk, fdq_rk ) + + IF (dq_term /= 'VG' ) write (*,*) 'specify DQ-cross term !' + + ENDIF + +END SUBROUTINE PHI_POLAR + + +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! + SUBROUTINE PHI_DD_GROSS_VRABEC( k, z3_rk, fdd_rk ) +! + USE PARAMETERS, ONLY: PI, KBOL + USE EOS_VARIABLES, ONLY: nc, ncomp, uij, parame, mseg, sig_ij, rho, eta, x, t + USE EOS_CONSTANTS, ONLY: ddp2, ddp3, ddp4 + IMPLICIT NONE +! +! ---------------------------------------------------------------------- + INTEGER, INTENT(IN) :: k + REAL, INTENT(IN) :: z3_rk + REAL, INTENT(IN OUT) :: fdd_rk +! +! --- local variables--------------------------------------------------- + INTEGER :: i, j, l, m + + REAL :: factor2, factor3, z3 + REAL :: xijfa, xijkfa, xijfa_x, xijkf_x, eij + REAL :: fdd2, fdd3, fdd2x, fdd3x + REAL, DIMENSION(nc) :: my2dd + REAL, DIMENSION(nc,nc) :: Idd2, Idd4, Idd2x, Idd4x + REAL, DIMENSION(nc,nc,nc) :: Idd3, Idd3x +! ---------------------------------------------------------------------- + + + fdd_rk = 0.0 + z3 = eta + DO i = 1, ncomp + IF ( uij(i,i) == 0.0 ) write (*,*) 'PHI_DD_GROSS_VRABEC: do not use dimensionless units' + IF ( uij(i,i) == 0.0 ) stop + my2dd(i) = (parame(i,6))**2 *1.E-49 / (uij(i,i)*KBOL*mseg(i)*sig_ij(i,i)**3 *1.E-30) + END DO + + DO i = 1, ncomp + DO j = 1, ncomp + Idd2(i,j) = 0.0 + Idd4(i,j) = 0.0 + Idd2x(i,j) = 0.0 + Idd4x(i,j) = 0.0 + IF (parame(i,6) /= 0.0 .AND. parame(j,6) /= 0.0) THEN + DO m=0,4 + Idd2(i,j) =Idd2(i,j) + ddp2(i,j,m)*z3**m + Idd4(i,j) =Idd4(i,j) + ddp4(i,j,m)*z3**m + Idd2x(i,j) =Idd2x(i,j)+ ddp2(i,j,m)*REAL(m)*z3**(m-1)*z3_rk + Idd4x(i,j) =Idd4x(i,j)+ ddp4(i,j,m)*REAL(m)*z3**(m-1)*z3_rk + END DO + DO l = 1, ncomp + Idd3(i,j,l) = 0.0 + Idd3x(i,j,l) = 0.0 + IF (parame(l,6) /= 0.0) THEN + DO m=0,4 + Idd3(i,j,l) =Idd3(i,j,l) +ddp3(i,j,l,m)*z3**m + Idd3x(i,j,l)=Idd3x(i,j,l)+ddp3(i,j,l,m)*REAL(m)*z3**(m-1)*z3_rk + END DO + END IF + END DO + END IF + END DO + END DO + + factor2= -PI + factor3= -4.0/3.0*PI**2 + + fdd2 = 0.0 + fdd3 = 0.0 + fdd2x = 0.0 + fdd3x = 0.0 + DO i = 1, ncomp + xijfa_x = 2.0*x(i)*rho*uij(i,i)*my2dd(i)*sig_ij(i,i)**3 /t & + *uij(k,k)*my2dd(k)*sig_ij(k,k)**3 /t/sig_ij(i,k)**3 + eij = (parame(i,3)*parame(k,3))**0.5 + fdd2x = fdd2x + factor2*xijfa_x*( Idd2(i,k) + eij/t*Idd4(i,k) ) + DO j = 1, ncomp + IF (parame(i,6) /= 0.0 .AND. parame(j,6) /= 0.0) THEN + xijfa =x(i)*rho*uij(i,i)*my2dd(i)*sig_ij(i,i)**3 /t & + *x(j)*rho*uij(j,j)*my2dd(j)*sig_ij(j,j)**3 /t/sig_ij(i,j)**3 + eij = (parame(i,3)*parame(j,3))**0.5 + fdd2= fdd2 +factor2*xijfa*(Idd2(i,j) +eij/t*Idd4(i,j) ) + fdd2x =fdd2x +factor2*xijfa*(Idd2x(i,j)+eij/t*Idd4x(i,j)) + !--------------------- + xijkf_x=x(i)*rho*uij(i,i)*my2dd(i)*sig_ij(i,i)**3 /t/sig_ij(i,j) & + *x(j)*rho*uij(j,j)*my2dd(j)*sig_ij(j,j)**3 /t/sig_ij(i,k) & + *3.0* uij(k,k)*my2dd(k)*sig_ij(k,k)**3 /t/sig_ij(j,k) + fdd3x=fdd3x+factor3*xijkf_x*Idd3(i,j,k) + DO l=1,ncomp + IF (parame(l,6) /= 0.0) THEN + xijkfa= x(i)*rho*uij(i,i)/t*my2dd(i)*sig_ij(i,i)**3 & + *x(j)*rho*uij(j,j)/t*my2dd(j)*sig_ij(j,j)**3 & + *x(l)*rho*uij(l,l)/t*my2dd(l)*sig_ij(l,l)**3 & + /sig_ij(i,j)/sig_ij(i,l)/sig_ij(j,l) + fdd3 =fdd3 + factor3 * xijkfa *Idd3(i,j,l) + fdd3x =fdd3x + factor3 * xijkfa *Idd3x(i,j,l) + END IF + END DO + END IF + END DO + END DO + + IF (fdd2 < -1.E-50 .AND. fdd3 /= 0.0 .AND. fdd2x /= 0.0 .AND. fdd3x /= 0.0)THEN + + fdd_rk = fdd2* (fdd2*fdd2x - 2.0*fdd3*fdd2x+fdd2*fdd3x) / (fdd2-fdd3)**2 + + END IF + +END SUBROUTINE PHI_DD_GROSS_VRABEC + + + +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! + SUBROUTINE PHI_QQ_GROSS( k, z3_rk, fqq_rk ) +! + USE PARAMETERS, ONLY: PI, KBOL + USE EOS_VARIABLES, ONLY: nc, ncomp, uij, parame, mseg, sig_ij, rho, eta, x, t + USE EOS_CONSTANTS, ONLY: qqp2, qqp3, qqp4 + IMPLICIT NONE +! +! ---------------------------------------------------------------------- + INTEGER, INTENT(IN) :: k + REAL, INTENT(IN) :: z3_rk + REAL, INTENT(IN OUT) :: fqq_rk +! +! --- local variables--------------------------------------------------- + INTEGER :: i, j, l, m + + REAL :: factor2, factor3, z3 + REAL :: xijfa, xijkfa, xijfa_x, xijkf_x, eij + REAL :: fqq2, fqq3, fqq2x, fqq3x + REAL, DIMENSION(nc) :: qq2 + REAL, DIMENSION(nc,nc) :: Iqq2, Iqq4, Iqq2x, Iqq4x + REAL, DIMENSION(nc,nc,nc) :: Iqq3, Iqq3x +! ---------------------------------------------------------------------- + + + fqq_rk = 0.0 + z3 = eta + DO i = 1, ncomp + IF ( uij(i,i) == 0.0 ) write (*,*) 'PHI_QQ_GROSS: do not use dimensionless units' + qq2(i) = (parame(i,7))**2 *1.E-69 / (uij(i,i)*kbol*mseg(i)*sig_ij(i,i)**5 *1.E-50) + END DO + + DO i = 1, ncomp + DO j = 1, ncomp + Iqq2(i,j) = 0.0 + Iqq4(i,j) = 0.0 + Iqq2x(i,j) = 0.0 + Iqq4x(i,j) = 0.0 + IF (parame(i,7) /= 0.0 .AND. parame(j,7) /= 0.0) THEN + DO m = 0, 4 + Iqq2(i,j) = Iqq2(i,j) + qqp2(i,j,m) * z3**m + Iqq4(i,j) = Iqq4(i,j) + qqp4(i,j,m) * z3**m + Iqq2x(i,j) = Iqq2x(i,j) + qqp2(i,j,m) * REAL(m)*z3**(m-1)*z3_rk + Iqq4x(i,j) = Iqq4x(i,j) + qqp4(i,j,m) * REAL(m)*z3**(m-1)*z3_rk + END DO + DO l = 1, ncomp + Iqq3(i,j,l) = 0.0 + Iqq3x(i,j,l) = 0.0 + IF (parame(l,7) /= 0.0) THEN + DO m = 0, 4 + Iqq3(i,j,l) = Iqq3(i,j,l) + qqp3(i,j,l,m)*z3**m + Iqq3x(i,j,l) = Iqq3x(i,j,l) + qqp3(i,j,l,m)*REAL(m) *z3**(m-1)*z3_rk + END DO + END IF + END DO + END IF + END DO + END DO + + factor2= -9.0/16.0*PI + factor3= 9.0/16.0*PI**2 + + fqq2 = 0.0 + fqq3 = 0.0 + fqq2x = 0.0 + fqq3x = 0.0 + DO i = 1, ncomp + xijfa_x = 2.0*x(i)*rho*uij(i,i)*qq2(i)*sig_ij(i,i)**5 /t & + *uij(k,k)*qq2(k)*sig_ij(k,k)**5 /t/sig_ij(i,k)**7.0 + eij = (parame(i,3)*parame(k,3))**0.5 + fqq2x =fqq2x +factor2*xijfa_x*(Iqq2(i,k)+eij/t*Iqq4(i,k)) + DO j=1,ncomp + IF (parame(i,7) /= 0.0 .AND. parame(j,7) /= 0.0) THEN + xijfa =x(i)*rho*uij(i,i)*qq2(i)*sig_ij(i,i)**5 /t & + *x(j)*rho*uij(j,j)*qq2(j)*sig_ij(j,j)**5 /t/sig_ij(i,j)**7.0 + eij = (parame(i,3)*parame(j,3))**0.5 + fqq2= fqq2 +factor2*xijfa*(Iqq2(i,j) +eij/t*Iqq4(i,j) ) + fqq2x =fqq2x +factor2*xijfa*(Iqq2x(i,j)+eij/t*Iqq4x(i,j)) + ! ------------------ + xijkf_x=x(i)*rho*uij(i,i)*qq2(i)*sig_ij(i,i)**5 /t/sig_ij(i,j)**3 & + *x(j)*rho*uij(j,j)*qq2(j)*sig_ij(j,j)**5 /t/sig_ij(i,k)**3 & + *3.0* uij(k,k)*qq2(k)*sig_ij(k,k)**5 /t/sig_ij(j,k)**3 + fqq3x = fqq3x + factor3*xijkf_x*Iqq3(i,j,k) + DO l = 1, ncomp + IF (parame(l,7) /= 0.0) THEN + xijkfa=x(i)*rho*uij(i,i)*qq2(i)*sig_ij(i,i)**5 /t/sig_ij(i,j)**3 & + *x(j)*rho*uij(j,j)*qq2(j)*sig_ij(j,j)**5 /t/sig_ij(i,l)**3 & + *x(l)*rho*uij(l,l)*qq2(l)*sig_ij(l,l)**5 /t/sig_ij(j,l)**3 + fqq3 =fqq3 + factor3 * xijkfa *Iqq3(i,j,l) + fqq3x =fqq3x + factor3 * xijkfa *Iqq3x(i,j,l) + END IF + END DO + END IF + END DO + END DO + + IF (fqq2 < -1.E-50 .AND. fqq3 /= 0.0 .AND. fqq2x /= 0.0 .AND. fqq3x /= 0.0) THEN + fqq_rk = fqq2* (fqq2*fqq2x - 2.0*fqq3*fqq2x+fqq2*fqq3x) / (fqq2-fqq3)**2 + END IF + +END SUBROUTINE PHI_QQ_GROSS + +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! + SUBROUTINE PHI_DQ_VRABEC_GROSS( k, z3_rk, fdq_rk ) +! + USE PARAMETERS, ONLY: PI, KBOL + USE EOS_VARIABLES, ONLY: nc, ncomp, uij, parame, mseg, sig_ij, rho, eta, x, t + USE EOS_CONSTANTS, ONLY: dqp2, dqp3, dqp4 + IMPLICIT NONE +! +! ---------------------------------------------------------------------- + INTEGER, INTENT(IN) :: k + REAL, INTENT(IN) :: z3_rk + REAL, INTENT(IN OUT) :: fdq_rk +! +! --- local variables--------------------------------------------------- + INTEGER :: i, j, l, m + + REAL :: factor2, factor3, z3 + REAL :: xijfa, xijkfa, xijfa_x, xijkf_x, eij + REAL :: fdq2, fdq3, fdq2x, fdq3x + REAL, DIMENSION(nc) :: my2dd, myfac, qq2, q_fac + REAL, DIMENSION(nc,nc) :: Idq2, Idq4, Idq2x, Idq4x + REAL, DIMENSION(nc,nc,nc) :: Idq3, Idq3x +! ---------------------------------------------------------------------- + + fdq_rk = 0.0 + z3 = eta + DO i=1,ncomp + my2dd(i) = (parame(i,6))**2 *1.E-49 / (uij(i,i)*KBOL*mseg(i)*sig_ij(i,i)**3 *1.E-30) + myfac(i) = parame(i,3)/t*parame(i,2)**4 *my2dd(i) + qq2(i) = (parame(i,7))**2 *1.E-69 / (uij(i,i)*kbol*mseg(i)*sig_ij(i,i)**5 *1.E-50) + q_fac(i) = parame(i,3)/t*parame(i,2)**4 *qq2(i) + END DO + + DO i = 1, ncomp + DO j = 1, ncomp + Idq2(i,j) = 0.0 + Idq4(i,j) = 0.0 + Idq2x(i,j) = 0.0 + Idq4x(i,j) = 0.0 + DO m = 0, 4 + Idq2(i,j) = Idq2(i,j) + dqp2(i,j,m)*z3**m + Idq4(i,j) = Idq4(i,j) + dqp4(i,j,m)*z3**m + Idq2x(i,j) = Idq2x(i,j) + dqp2(i,j,m)*REAL(m)*z3**(m-1) *z3_rk + Idq4x(i,j) = Idq4x(i,j) + dqp4(i,j,m)*REAL(m)*z3**(m-1) *z3_rk + END DO + DO l = 1, ncomp + Idq3(i,j,l) = 0.0 + Idq3x(i,j,l) = 0.0 + DO m = 0, 4 + Idq3(i,j,l) =Idq3(i,j,l) +dqp3(i,j,l,m)*z3**m + Idq3x(i,j,l)=Idq3x(i,j,l)+dqp3(i,j,l,m)*REAL(m)*z3**(m-1)*z3_rk + END DO + END DO + END DO + END DO + + factor2= -9.0/4.0*PI + factor3= PI**2 + + fdq2 = 0.0 + fdq3 = 0.0 + fdq2x = 0.0 + fdq3x = 0.0 + DO i = 1, ncomp + xijfa_x = x(i)*rho*( myfac(i)*q_fac(k) + myfac(k)*q_fac(i) ) / sig_ij(i,k)**5 + eij = (parame(i,3)*parame(k,3))**0.5 + fdq2x =fdq2x +factor2*xijfa_x*(Idq2(i,k)+eij/t*Idq4(i,k)) + DO j=1,ncomp + xijfa =x(i)*rho*myfac(i) * x(j)*rho*q_fac(j) /sig_ij(i,j)**5 + eij = (parame(i,3)*parame(j,3))**0.5 + fdq2= fdq2 +factor2*xijfa*(Idq2(i,j) +eij/t*Idq4(i,j) ) + fdq2x =fdq2x +factor2*xijfa*(Idq2x(i,j) +eij/t*Idq4x(i,j)) + !--------------------- + xijkf_x=x(i)*rho*x(j)*rho/(sig_ij(i,j)*sig_ij(i,k)*sig_ij(j,k))**2 & + *( myfac(i)*q_fac(j)*myfac(k) + myfac(i)*q_fac(k)*myfac(j) & + + myfac(k)*q_fac(i)*myfac(j) +myfac(i)*q_fac(j)*q_fac(k)*1.1937350 & + +myfac(i)*q_fac(k)*q_fac(j)*1.193735 & + +myfac(k)*q_fac(i)*q_fac(j)*1.193735 ) + fdq3x = fdq3x + factor3*xijkf_x*Idq3(i,j,k) + DO l = 1, ncomp + xijkfa=x(i)*rho*x(j)*rho*x(l)*rho/(sig_ij(i,j)*sig_ij(i,l)*sig_ij(j,l))**2 & + *( myfac(i)*q_fac(j)*myfac(l) & + +myfac(i)*q_fac(j)*q_fac(l)*1.193735 ) + fdq3 =fdq3 + factor3 * xijkfa *Idq3(i,j,l) + fdq3x =fdq3x + factor3 * xijkfa *Idq3x(i,j,l) + END DO + END DO + END DO + + IF (fdq2 < -1.E-50 .AND. fdq3 /= 0.0 .AND. fdq2x /= 0.0 .AND. fdq3x /= 0.0)THEN + + fdq_rk = fdq2* (fdq2*fdq2x - 2.0*fdq3*fdq2x+fdq2*fdq3x) / (fdq2-fdq3)**2 + + END IF + +END SUBROUTINE PHI_DQ_VRABEC_GROSS + + + +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! + SUBROUTINE P_NUMERICAL +! + USE EOS_VARIABLES + IMPLICIT NONE +! +!-----local variables------------------------------------------------- + REAL :: dzetdv, eta_0, dist, fact + REAL :: fres1, fres2, fres3, fres4, fres5 + REAL :: df_dr, df_drdr, pideal, dpiddz + REAL :: tfr_1, tfr_2, tfr_3, tfr_4, tfr_5 +!----------------------------------------------------------------------- + + +IF (eta > 0.1) THEN + fact = 1.0 +ELSE IF (eta <= 0.1 .AND. eta > 0.01) THEN + fact = 10.0 +ELSE + fact = 10.0 +END IF +dist = eta*3.d-3 *fact +! dist = eta*4.d-3 *fact +!***************************** +! fuer MC simulation: neues dist: +! dist = eta*5.d-3*fact + +eta_0 = eta +eta = eta_0 - 2.0*dist +CALL F_NUMERICAL +fres1 = fres +tfr_1 = tfr +eta = eta_0 - dist +CALL F_NUMERICAL +fres2 = fres +tfr_2 = tfr +eta = eta_0 + dist +CALL F_NUMERICAL +fres3 = fres +tfr_3 = tfr +eta = eta_0 + 2.0*dist +CALL F_NUMERICAL +fres4 = fres +tfr_4 = tfr +eta = eta_0 +CALL F_NUMERICAL +fres5 = fres +tfr_5 = tfr + +!--------------------------------------------------------- +! ptfr = (-tfr_4+8.0*tfr_3-8.0*tfr_2+tfr_1)/(12.0*dist) +! & *dzetdv*(KBOL*T)/1.E-30 +! ztfr =ptfr /( rho * (KBOL*t) / 1.E-30) +! ptfrdz = (-tfr_4+16.0*tfr_3-3.d1*tfr_5+16.0*tfr_2-tfr_1) +! & /(12.0*(dist**2 ))* dzetdv*(KBOL*T)/1.E-30 +! & + (-tfr_4+8.0*tfr_3-8.0*tfr_2+tfr_1) +! & /(12.0*dist) * 2.0 *eta*6.0/PI/D +! & *(KBOL*T)/1.E-30 +! ztfrdz=ptfrdz/( rho*(kbol*T)/1.E-30 ) - ztfr/eta +! write (*,*) eta,ztfr,ztfrdz + +! dtfr_dr = (-tfr_4+8.0*tfr_3-8.0*tfr_2+tfr_1)/(12.0*dist) +! write (*,*) eta,dtfr_dr +! stop +!--------------------------------------------------------- + +df_dr = (-fres4+8.0*fres3-8.0*fres2+fres1) / (12.0*dist) +df_drdr = (-fres4+16.0*fres3-3.d1*fres5+16.0*fres2-fres1) & + /(12.0*(dist**2 )) + + +dzetdv = eta*rho + +pges = (-fres4+8.0*fres3-8.0*fres2+fres1) & + /(12.0*dist) *dzetdv*(kbol*t)/1.E-30 + +dpiddz = 1.0/z3t*(kbol*t)/1.E-30 +pgesdz = (-fres4+16.0*fres3-3.d1*fres5+16.0*fres2-fres1) & + /(12.0*(dist**2 ))* dzetdv*(kbol*t)/1.E-30 & + + (-fres4+8.0*fres3-8.0*fres2+fres1) /(12.0*dist) * 2.0 *rho & + *(kbol*t)/1.E-30 + dpiddz + +pgesd2 = (fres4-2.0*fres3+2.0*fres2-fres1) /(2.0*dist**3 ) & + * dzetdv*(kbol*t)/1.E-30 & + + (-fres4+16.0*fres3-3.d1*fres5+16.0*fres2-fres1) /(12.0*(dist**2 )) & + * 4.0 *rho *(kbol*t)/1.E-30 + (-fres4+8.0*fres3-8.0*fres2+fres1) & + /(12.0*dist) * 2.0 /z3t *(kbol*t)/1.E-30 +pgesd3 = (fres4-4.0*fres3+6.0*fres5-4.0*fres2+fres1) /(dist**4 ) & + * dzetdv*(kbol*t)/1.E-30 + (fres4-2.0*fres3+2.0*fres2-fres1) & + /(2.0*dist**3 ) * 6.0 *rho *(kbol*t)/1.E-30 & + + (-fres4+16.0*fres3-3.d1*fres5+16.0*fres2-fres1) & + /(12.0*dist**2 )* 6.0 /z3t *(kbol*t)/1.E-30 + +!------------------p ideal------------------------------------ +pideal = rho * (kbol*t) / 1.E-30 + +!------------------p summation, p comes out in Pa ------------ +pges = pideal + pges + +END SUBROUTINE P_NUMERICAL + + +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! + SUBROUTINE H_numerical +! + USE PARAMETERS, ONLY: RGAS + USE EOS_VARIABLES + IMPLICIT NONE +! +!--------------------------------------------------------------------- + REAL :: dist, fact, rho_0 + REAL :: fres1,fres2,fres3,fres4,fres5 + REAL :: f_1, f_2, f_3, f_4 + REAL :: cv_res, t_tmp, zges + REAL :: f_dt, f_dtdt, f_dr, f_drdr, f_drdt +!----------------------------------------------------------------------- + + +CALL PERTURBATION_PARAMETER +rho_0 = eta/z3t + + +fact = 1.0 +dist = t * 100.E-5 * fact + +t_tmp = t + +t = t_tmp - 2.0*dist +CALL PERTURBATION_PARAMETER +eta = z3t*rho_0 +CALL F_NUMERICAL +fres1 = fres +t = t_tmp - dist +CALL PERTURBATION_PARAMETER +eta = z3t*rho_0 +CALL F_NUMERICAL +fres2 = fres +t = t_tmp + dist +CALL PERTURBATION_PARAMETER +eta = z3t*rho_0 +CALL F_NUMERICAL +fres3 = fres +t = t_tmp + 2.0*dist +CALL PERTURBATION_PARAMETER +eta = z3t*rho_0 +CALL F_NUMERICAL +fres4 = fres +t = t_tmp +CALL PERTURBATION_PARAMETER +eta = z3t*rho_0 +CALL F_NUMERICAL +fres5 = fres +! *(KBOL*T)/1.E-30 + +zges = (p * 1.E-30)/(kbol*t*rho_0) + + +f_dt = (-fres4+8.0*fres3-8.0*fres2+fres1)/(12.0*dist) +f_dtdt = (-fres4+16.0*fres3-3.d1*fres5+16.0*fres2-fres1) /(12.0*(dist**2 )) + +s_res = (- f_dt -fres/t)*RGAS*t + RGAS * LOG(zges) +h_res = ( - t*f_dt + zges-1.0 ) * RGAS*t +cv_res = -( t*f_dtdt + 2.0*f_dt ) * RGAS*t + + + +t = t_tmp - 2.0*dist +CALL PERTURBATION_PARAMETER +eta = z3t*rho_0 +CALL P_NUMERICAL +f_1 = pges/(eta*rho_0*(KBOL*T)/1.E-30) + +t = t_tmp - dist +CALL PERTURBATION_PARAMETER +eta = z3t*rho_0 +CALL P_NUMERICAL +f_2 = pges/(eta*rho_0*(KBOL*T)/1.E-30) + +t = t_tmp + dist +CALL PERTURBATION_PARAMETER +eta = z3t*rho_0 +CALL P_NUMERICAL +f_3 = pges/(eta*rho_0*(KBOL*T)/1.E-30) + +t = t_tmp + 2.0*dist +CALL PERTURBATION_PARAMETER +eta = z3t*rho_0 +CALL P_NUMERICAL +f_4 = pges/(eta*rho_0*(KBOL*T)/1.E-30) + +t = t_tmp +CALL PERTURBATION_PARAMETER +eta = z3t*rho_0 +CALL P_NUMERICAL + +f_dr = pges / (eta*rho_0*(KBOL*T)/1.E-30) +f_drdr = pgesdz/ (eta*rho_0*(KBOL*T)/1.E-30) - f_dr*2.0/eta - 1.0/eta**2 + +f_drdt = ( - f_4 + 8.0*f_3 - 8.0*f_2 + f_1 ) / ( 12.0*dist ) + +cp_res = cv_res - RGAS + RGAS*( zges + eta*t*f_drdt)**2 / (1.0 + 2.0*eta*f_dr + eta**2 *f_drdr) +! write (*,*) cv_res,cp_res,eta + + +END SUBROUTINE H_numerical + + + + + + + + + + + +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! + SUBROUTINE F_POLAR ( fdd, fqq, fdq ) +! + USE EOS_VARIABLES, ONLY: ncomp, parame, dd_term, qq_term, dq_term + IMPLICIT NONE +! +! ---------------------------------------------------------------------- + REAL, INTENT(OUT) :: fdd, fqq, fdq +! +! --- local variables--------------------------------------------------- + INTEGER :: dipole + INTEGER :: quadrupole + INTEGER :: dipole_quad +! ---------------------------------------------------------------------- + + fdd = 0.0 + fqq = 0.0 + fdq = 0.0 + + dipole = 0 + quadrupole = 0 + dipole_quad = 0 + IF ( SUM( parame(1:ncomp,6) ) /= 0.0 ) dipole = 1 + IF ( SUM( parame(1:ncomp,7) ) /= 0.0 ) quadrupole = 1 + IF ( dipole == 1 .AND. quadrupole == 1 ) dipole_quad = 1 + + ! -------------------------------------------------------------------- + ! dipole-dipole term + ! -------------------------------------------------------------------- + IF (dipole == 1) THEN + + IF (dd_term == 'GV') CALL F_DD_GROSS_VRABEC( fdd ) + ! IF (dd_term == 'SF') CALL F_DD_SAAGER_FISCHER( k ) + IF (dd_term /= 'GV' .AND. dd_term /= 'SF') write (*,*) 'specify dipole term !' + + ENDIF + + ! -------------------------------------------------------------------- + ! quadrupole-quadrupole term + ! -------------------------------------------------------------------- + IF (quadrupole == 1) THEN + + !IF (qq_term == 'SF') CALL F_QQ_SAAGER_FISCHER( k ) + IF (qq_term == 'JG') CALL F_QQ_GROSS( fqq ) + IF (qq_term /= 'JG' .AND. qq_term /= 'SF') write (*,*) 'specify quadrupole term !' + + ENDIF + + ! -------------------------------------------------------------------- + ! dipole-quadrupole cross term + ! -------------------------------------------------------------------- + IF (dipole_quad == 1) THEN + + IF (dq_term == 'VG') CALL F_DQ_VRABEC_GROSS( fdq ) + IF (dq_term /= 'VG' ) write (*,*) 'specify DQ-cross term !' + + ENDIF + +END SUBROUTINE F_POLAR + + + +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! SUBROUTINE PRESSURE_SPINODAL +! +! iterates the density until the derivative of pressure 'pges' to +! density is equal to zero. A Newton-scheme is used for determining +! the root to the objective function. +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! + SUBROUTINE PRESSURE_SPINODAL +! + USE BASIC_VARIABLES, ONLY: num + USE EOS_VARIABLES + IMPLICIT NONE +! +! ---------------------------------------------------------------------- + INTEGER :: i, max_i + REAL :: eta_iteration + REAL :: error, acc_i, delta_eta +! ---------------------------------------------------------------------- + +acc_i = 1.d-6 +max_i = 30 + +i = 0 +eta_iteration = eta_start + +! ---------------------------------------------------------------------- +! iterate density until p_calc = p +! ---------------------------------------------------------------------- + +error = acc_i + 1.0 +DO WHILE ( ABS(error) > acc_i .AND. i < max_i ) + + i = i + 1 + eta = eta_iteration + + IF ( num == 0 ) THEN + CALL P_EOS + ELSE IF ( num == 1 ) THEN + CALL P_NUMERICAL + ELSE IF ( num == 2 ) THEN + WRITE(*,*) 'CRITICAL RENORM NOT INCLUDED YET' + !!CALL F_EOS_RN + ELSE + write (*,*) 'define calculation option (num)' + END IF + + error = pgesdz + + delta_eta = error/ pgesd2 + IF ( delta_eta > 0.02 ) delta_eta = 0.02 + IF ( delta_eta < -0.02 ) delta_eta = -0.02 + + eta_iteration = eta_iteration - delta_eta + ! write (*,'(a,i3,3G18.10)') 'iter',i, error, eta_iteration, pgesdz + + IF (eta_iteration > 0.9) eta_iteration = 0.5 + IF (eta_iteration <= 0.0) eta_iteration = 1.E-16 + +END DO + +eta = eta_iteration + +END SUBROUTINE PRESSURE_SPINODAL + + +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! + SUBROUTINE F_IDEAL_GAS ( fid ) +! + USE EOS_VARIABLES, ONLY: nc, ncomp, t, x, rho, PI, KBOL, NAv + IMPLICIT NONE +! +!--------------------------------------------------------------------- + REAL, INTENT(IN OUT) :: fid +!--------------------------------------------------------------------- + INTEGER :: i + REAL, DIMENSION(nc) :: rhoi +!---------------------------------------------------------------------- + + !h_Planck = 6.62606896E-34 ! Js + DO i = 1, ncomp + rhoi(i) = x(i) * rho + ! debroglie(i) = h_Planck *1d10 & ! in units Angstrom + ! *SQRT( 1.0 / (2.0*PI *1.0 / NAv / 1000.0 * KBOL*T) ) + ! ! *SQRT( 1.0 / (2.0*PI *mm(i) /NAv/1000.0 * KBOL*T) ) + ! fid = fid + x(i) * ( LOG(rhoi(i)*debroglie(i)**3) - 1.0 ) + fid = fid + x(i) * ( LOG(rhoi(i)) - 1.0 ) + END DO + + END SUBROUTINE F_IDEAL_GAS + +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! + SUBROUTINE F_HARD_SPHERE ( m_mean2, fhs ) +! + USE EOS_VARIABLES, ONLY: z0t, z1t, z2t, z3t, eta, rho + IMPLICIT NONE +! +!--------------------------------------------------------------------- + REAL, INTENT(IN) :: m_mean2 + REAL, INTENT(IN OUT) :: fhs +!--------------------------------------------------------------------- + REAL :: z0, z1, z2, z3, zms +!---------------------------------------------------------------------- + + rho = eta / z3t + z0 = z0t * rho + z1 = z1t * rho + z2 = z2t * rho + z3 = z3t * rho + zms = 1.0 - z3 + + fhs= m_mean2*( 3.0*z1*z2/zms + z2**3 /z3/zms/zms + (z2**3 /z3/z3-z0)*LOG(zms) )/z0 + + + END SUBROUTINE F_HARD_SPHERE + +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! + SUBROUTINE F_CHAIN_TPT1 ( fhc ) +! + USE EOS_VARIABLES, ONLY: nc, ncomp, mseg, x, z0t, z1t, z2t, z3t, & + rho, eta, dij_ab, gij + IMPLICIT NONE +! +!--------------------------------------------------------------------- + REAL, INTENT(IN OUT) :: fhc +!--------------------------------------------------------------------- + INTEGER :: i, j + REAL :: z0, z1, z2, z3, zms +!--------------------------------------------------------------------- + + rho = eta / z3t + z0 = z0t * rho + z1 = z1t * rho + z2 = z2t * rho + z3 = z3t * rho + zms = 1.0 - z3 + + DO i = 1, ncomp + DO j = 1, ncomp + gij(i,j) = 1.0/zms + 3.0*dij_ab(i,j)*z2/zms/zms + 2.0*(dij_ab(i,j)*z2)**2 / zms**3 + END DO + END DO + + fhc = 0.0 + DO i = 1, ncomp + fhc = fhc + x(i) *(1.0- mseg(i)) *LOG(gij(i,i)) + END DO + + END SUBROUTINE F_CHAIN_TPT1 + + +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! + SUBROUTINE F_CHAIN_TPT_D ( fhc ) +! + USE EOS_VARIABLES, ONLY: nc, ncomp, mseg, x, z0t, z1t, z2t, z3t, rho, eta, & + dhs, mseg, dij_ab, gij + IMPLICIT NONE +! +!--------------------------------------------------------------------- + REAL, INTENT(OUT) :: fhc +!--------------------------------------------------------------------- + INTEGER :: i, j + REAL, DIMENSION(nc) :: gij_hd + REAL :: z0, z1, z2, z3, zms +!--------------------------------------------------------------------- + + rho = eta / z3t + z0 = z0t * rho + z1 = z1t * rho + z2 = z2t * rho + z3 = z3t * rho + zms = 1.0 - z3 + + DO i = 1, ncomp + DO j = 1, ncomp + gij(i,j) = 1.0/zms + 3.0*dij_ab(i,j)*z2/zms/zms + 2.0*(dij_ab(i,j)*z2)**2 / zms**3 + END DO + END DO + + DO i = 1, ncomp + gij_hd(i) = 1.0/(2.0*zms) + 3.0*dij_ab(i,i)*z2 / zms**2 + END DO + + fhc = 0.0 + DO i = 1, ncomp + IF ( mseg(i) >= 2.0 ) THEN + fhc = fhc - x(i) * ( mseg(i)/2.0 * LOG( gij(i,i) ) + ( mseg(i)/2.0 - 1.0 ) * LOG( gij_hd(i)) ) + ELSE + fhc = fhc + x(i) * ( 1.0 - mseg(i) ) * LOG( gij(i,i) ) + END IF + END DO + + END SUBROUTINE F_CHAIN_TPT_D + + +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! + SUBROUTINE F_CHAIN_HU_LIU ( fhc ) +! + USE EOS_VARIABLES, ONLY: nc, ncomp, mseg, x, rho, eta + IMPLICIT NONE +! +! This subroutine calculates the hard chain contribution of the TPT-Liu-Hu Eos. +!--------------------------------------------------------------------- + REAL, INTENT(OUT) :: fhc +!--------------------------------------------------------------------- + REAL :: a2, b2, c2, a3, b3, c3 + REAL :: a20, b20, c20, a30, b30, c30 + REAL :: sum1, sum2, am, bm, cm + REAL :: zms +!--------------------------------------------------------------------- + + zms = 1.0 - eta + + sum1 = SUM( x(1:ncomp)*(mseg(1:ncomp)-1.0) ) + sum2 = SUM( x(1:ncomp)/mseg(1:ncomp)*(mseg(1:ncomp)-1.0)*(mseg(1:ncomp)-2.0) ) + + a2 = 0.45696 + a3 = -0.74745 + b2 = 2.10386 + b3 = 3.49695 + c2 = 1.75503 + c3 = 4.83207 + a20 = - a2 + b2 - 3.0*c2 + b20 = - a2 - b2 + c2 + c20 = c2 + a30 = - a3 + b3 - 3.0*c3 + b30 = - a3 - b3 + c3 + c30 = c3 + am = (3.0 + a20) * sum1 + a30 * sum2 + bm = (1.0 + b20) * sum1 + b30 * sum2 + cm = (1.0 + c20) * sum1 + c30 * sum2 + + fhc = - ( (am*eta - bm) / (2.0*zms) + bm/2.0/zms**2 - cm *LOG(ZMS) ) + + + END SUBROUTINE F_CHAIN_HU_LIU + +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! + SUBROUTINE F_CHAIN_HU_LIU_RC ( fhs, fhc ) +! + USE EOS_VARIABLES, ONLY: mseg, chiR, eta + IMPLICIT NONE +! +! This subroutine calculates the hard chain contribution of the TPT-Liu-Hu Eos. +!--------------------------------------------------------------------- + REAL, INTENT(IN) :: fhs + REAL, INTENT(OUT) :: fhc +!--------------------------------------------------------------------- + REAL :: a2, b2, c2, a3, b3, c3 + REAL :: para1,para2,para3,para4 + REAL :: aLH,bLH,cLH +!--------------------------------------------------------------------- + +! This routine is only for pure components + + a2 = 0.45696 + b2 = 2.10386 + c2 = 1.75503 + + para1 = -0.74745 + para2 = 0.299154629727814 + para3 = 1.087271036653154 + para4 = -0.708979110326831 + a3 = para1 + para2*chiR(1) + para3*chiR(1)**2 + para4*chiR(1)**3 + b3 = 3.49695 - (3.49695 + 0.317719074806190)*chiR(1) + c3 = 4.83207 - (4.83207 - 3.480163780334421)*chiR(1) + + aLH = mseg(1)*(1.0 + ((mseg(1)-1.0)/mseg(1))*a2 + ((mseg(1)-1.0)/mseg(1))*((mseg(1)-2.0)/mseg(1))*a3 ) + bLH = mseg(1)*(1.0 + ((mseg(1)-1.0)/mseg(1))*b2 + ((mseg(1)-1.0)/mseg(1))*((mseg(1)-2.0)/mseg(1))*b3 ) + cLH = mseg(1)*(1.0 + ((mseg(1)-1.0)/mseg(1))*c2 + ((mseg(1)-1.0)/mseg(1))*((mseg(1)-2.0)/mseg(1))*c3 ) + + fhc = ((3.0 + aLH - bLH + 3.0*cLH)*eta - (1.0 + aLH + bLH - cLH)) / (2.0*(1.0-eta)) + & + (1.0 + aLH + bLH - cLH) / ( 2.0*(1.0-eta)**2 ) + (cLH - 1.0)*LOG(1.0-eta) + + fhc = fhc - fhs + + END SUBROUTINE F_CHAIN_HU_LIU_RC + + + + +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! + SUBROUTINE F_DISP_PCSAFT ( fdsp ) +! + USE EOS_VARIABLES, ONLY: PI, rho, eta, z0t, apar, bpar, order1, order2 + IMPLICIT NONE +! +!--------------------------------------------------------------------- + REAL, INTENT(IN OUT) :: fdsp +!--------------------------------------------------------------------- + INTEGER :: m + REAL :: I1, I2, c1_con, z3, zms, m_mean +!--------------------------------------------------------------------- + + z3 = eta + zms = 1.0 - eta + m_mean = z0t / ( PI / 6.0 ) + + I1 = 0.0 + I2 = 0.0 + DO m = 0, 6 + I1 = I1 + apar(m) * z3**m + I2 = I2 + bpar(m) * z3**m + END DO + + c1_con= 1.0/ ( 1.0 + m_mean*(8.0*z3-2.0*z3**2 )/zms**4 & + + (1.0-m_mean)*( 20.0*z3-27.0*z3**2 +12.0*z3**3 -2.0*z3**4 )/(zms*(2.0-z3))**2 ) + + fdsp = -2.0*PI*rho*I1*order1 - PI*rho*c1_con*m_mean*I2*order2 + + END SUBROUTINE F_DISP_PCSAFT + +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! + SUBROUTINE F_DISP_CKSAFT ( fdsp ) +! + USE EOS_VARIABLES, ONLY: nc, ncomp, PI, TAU, t, rho, eta, x, z0t, mseg, vij, uij, parame, um + USE EOS_CONSTANTS, ONLY: DNM + IMPLICIT NONE +! +!--------------------------------------------------------------------- + REAL, INTENT(IN OUT) :: fdsp +!--------------------------------------------------------------------- + INTEGER :: i, j, n, m + REAL :: zmr, nmr, m_mean +!--------------------------------------------------------------------- + + m_mean = z0t / ( PI / 6.0 ) + + DO i = 1, ncomp + DO j = 1, ncomp + vij(i,j)=(0.5*((parame(i,2)*(1.0-0.12 *EXP(-3.0*parame(i,3)/t))**3 )**(1.0/3.0) & + +(parame(j,2)*(1.0-0.12 *EXP(-3.0*parame(j,3)/t))**3 )**(1.0/3.0)))**3 + END DO + END DO + zmr = 0.0 + nmr = 0.0 + DO i = 1, ncomp + DO j = 1, ncomp + zmr = zmr + x(i)*x(j)*mseg(i)*mseg(j)*vij(i,j)*uij(i,j) + nmr = nmr + x(i)*x(j)*mseg(i)*mseg(j)*vij(i,j) + END DO + END DO + um = zmr / nmr + fdsp = 0.0 + DO n = 1, 4 + DO m = 1, 9 + fdsp = fdsp + DNM(n,m) * (um/t)**n *(eta/TAU)**m + END DO + END DO + fdsp = m_mean * fdsp + + + END SUBROUTINE F_DISP_CKSAFT + +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! + SUBROUTINE F_ASSOCIATION ( eps_kij, k_kij, fhb ) +! + USE EOS_VARIABLES, ONLY: nc, nsite, ncomp, t, z0t, z1t, z2t, z3t, rho, eta, x, & + parame, sig_ij, dij_ab, gij, nhb_typ, mx, nhb_no + IMPLICIT NONE +! +!--------------------------------------------------------------------- + REAL, INTENT(IN) :: eps_kij, k_kij + REAL, INTENT(IN OUT) :: fhb +!--------------------------------------------------------------------- + LOGICAL :: assoc + INTEGER :: i, j, k, l, no, ass_cnt, max_eval + REAL, DIMENSION(nc,nc) :: kap_hb + REAL, DIMENSION(nc,nc,nsite,nsite) :: eps_hb + REAL, DIMENSION(nc,nsite,nc,nsite) :: delta + REAL, DIMENSION(nc,nsite) :: mx_itr + REAL :: err_sum, sum0, amix, tol, ass_s1, ass_s2 + REAL :: z0, z1, z2, z3, zms +!--------------------------------------------------------------------- + + assoc = .false. + DO i = 1,ncomp + IF (NINT(parame(i,12)) /= 0) assoc = .true. + END DO + IF (assoc) THEN + + rho = eta / z3t + z0 = z0t * rho + z1 = z1t * rho + z2 = z2t * rho + z3 = z3t * rho + zms = 1.0 - z3 + + DO i = 1, ncomp + DO j = 1, ncomp + gij(i,j) = 1.0/zms + 3.0*dij_ab(i,j)*z2/zms/zms + 2.0*(dij_ab(i,j)*z2)**2 / zms**3 + END DO + END DO + + + DO i = 1, ncomp + IF ( NINT(parame(i,12)) /= 0 ) THEN + nhb_typ(i) = NINT( parame(i,12) ) + kap_hb(i,i) = parame(i,13) + no = 0 + DO k = 1,nhb_typ(i) + DO l = 1,nhb_typ(i) + eps_hb(i,i,k,l) = parame(i,(14+no)) + no = no + 1 + END DO + END DO + DO k = 1,nhb_typ(i) + nhb_no(i,k) = parame(i,(14+no)) + no = no + 1 + END DO + ELSE + nhb_typ(i) = 0 + kap_hb(i,i)= 0.0 + DO k = 1,nsite + DO l = 1,nsite + eps_hb(i,i,k,l) = 0.0 + END DO + END DO + END IF + END DO + + DO i = 1,ncomp + DO j = 1,ncomp + IF ( i /= j .AND. (nhb_typ(i) /= 0.AND.nhb_typ(j) /= 0) ) THEN + ! kap_hb(i,j)= (kap_hb(i,i)+kap_hb(j,j))/2.0 + ! kap_hb(i,j)= ( ( kap_hb(i,i)**(1.0/3.0) + kap_hb(j,j)**(1.0/3.0) )/2.0 )**3 + kap_hb(i,j) = (kap_hb(i,i)*kap_hb(j,j))**0.5 & + *((parame(i,2)*parame(j,2))**3 )**0.5 & + / (0.5*(parame(i,2)+parame(j,2)))**3 + kap_hb(i,j)= kap_hb(i,j)*(1.0-k_kij) + DO k = 1,nhb_typ(i) + DO l = 1,nhb_typ(j) + IF ( k /= l .AND. nhb_typ(i) >= 2 .AND. nhb_typ(j) >= 2 ) THEN + eps_hb(i,j,k,l) = (eps_hb(i,i,k,l)+eps_hb(j,j,l,k))/2.0 + ! eps_hb(i,j,k,l) = (eps_hb(i,i,k,l)*eps_hb(j,j,l,k))**0.5 + eps_hb(i,j,k,l) = eps_hb(i,j,k,l)*(1.0-eps_kij) + ELSE IF ( nhb_typ(i) == 1 .AND. l > k ) THEN + eps_hb(i,j,k,l) = (eps_hb(i,i,k,k)+eps_hb(j,j,l,k))/2.0 + eps_hb(j,i,l,k) = (eps_hb(i,i,k,k)+eps_hb(j,j,l,k))/2.0 + eps_hb(i,j,k,l) = eps_hb(i,j,k,l)*(1.0-eps_kij) + eps_hb(j,i,l,k) = eps_hb(j,i,l,k)*(1.0-eps_kij) + END IF + END DO + END DO + END IF + END DO + END DO + +!-----setting the self-association to zero for ionic compounds------ + DO i = 1,ncomp + IF ( parame(i,10) /= 0) kap_hb(i,i)=0.0 + DO j = 1,ncomp + IF ( parame(i,10) /= 0 .AND. parame(j,10) /= 0 ) kap_hb(i,j) = 0.0 + END DO + END DO + ! kap_hb(1,2)=0.050 + ! kap_hb(2,1)=0.050 + ! eps_hb(2,1,1,1)=465.0 + ! eps_hb(1,2,1,1)=465.0 + ! nhb_typ(1) = 1 + ! nhb_typ(2) = 1 + ! nhb_no(1,1)= 1.0 + ! nhb_no(2,1)= 1.0 + + + DO i = 1, ncomp + DO k = 1, nhb_typ(i) + DO j = 1, ncomp + DO l = 1, nhb_typ(j) + delta(i,k,j,l)=gij(i,j)*kap_hb(i,j)*(EXP(eps_hb(i,j,k,l)/t)-1.0) *sig_ij(i,j)**3 +!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! +! IF ((i+j).EQ.3) delta(i,k,j,l)=94.0 +!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! + END DO + END DO + IF ( mx(i,k) == 0.0 ) mx(i,k) = 1.0 + END DO + END DO + +!------constants for Iteration --------------------------------------- + amix = 0.7 + tol = 1.E-10 + IF (eta < 0.2) tol = 1.E-11 + IF (eta < 0.01) tol = 1.E-14 + max_eval = 200 + +! --- Iterate over all components and all sites ------------------------ + ass_cnt = 0 + iterate_TPT1: DO + + ass_cnt = ass_cnt + 1 + + DO i = 1, ncomp + DO k = 1, nhb_typ(i) + sum0 = 0.0 + DO j = 1, ncomp + DO l = 1, nhb_typ(j) + sum0 = sum0 + x(j)* mx(j,l)*nhb_no(j,l) *delta(i,k,j,l) + END DO + END DO + mx_itr(i,k) = 1.0 / (1.0 + sum0*rho) + END DO + END DO + + err_sum = 0.0 + DO i = 1, ncomp + DO k = 1, nhb_typ(i) + err_sum = err_sum + ABS( mx_itr(i,k) - mx(i,k) ) ! / ABS(mx_itr(i,k)) + mx(i,k) = mx_itr(i,k) * amix + mx(i,k) * (1.0 - amix) + IF ( mx(i,k) <= 0.0 ) mx(i,k)=1.E-50 + IF ( mx(i,k) > 1.0 ) mx(i,k)=1.0 + END DO + END DO + + IF ( err_sum <= tol .OR. ass_cnt >= max_eval ) THEN + IF ( ass_cnt >= max_eval ) WRITE(*,*) 'F_NUMERICAL: Max_eval violated = ',err_sum,tol + EXIT iterate_TPT1 + END IF + + END DO iterate_TPT1 + + DO i = 1, ncomp + ass_s1 = 0.0 + ass_s2 = 0.0 + DO k = 1, nhb_typ(i) + ass_s1 = ass_s1 + nhb_no(i,k) * ( 1.0 - mx(i,k) ) + ass_s2 = ass_s2 + nhb_no(i,k) * LOG(mx(i,k)) + END DO + fhb = fhb + x(i) * ( ass_s2 + ass_s1/2.0 ) + END DO + + END IF + + END SUBROUTINE F_ASSOCIATION + + +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! + SUBROUTINE F_ION_DIPOLE_TBH ( fhend ) +! + USE EOS_VARIABLES, ONLY: nc, PI, KBOL, NAv, ncomp, t, rho, eta, x, z0t, parame, uij, sig_ij + IMPLICIT NONE +! +!--------------------------------------------------------------------- + REAL, INTENT(IN OUT) :: fhend +!--------------------------------------------------------------------- + INTEGER :: i, dipole, ions + REAL :: m_mean + REAL :: fh32, fh2, fh52, fh3 + REAL :: e_elem, eps_cc0, rho_sol, dielec + REAL :: polabil, ydd, kappa, x_dipol, x_ions + REAL, DIMENSION(nc) :: my2dd, z_ii, e_cd, x_dd, x_ii + REAL :: sig_c, sig_d, sig_cd, r_s + REAL :: I0cc, I1cc, I2cc, Icd, Idd + REAL :: Iccc, Iccd, Icdd, Iddd +!--------------------------------------------------------------------- + +m_mean = z0t / ( PI / 6.0 ) + +!----------------Dieletric Constant of Water-------------------------- +e_elem = 1.602189246E-19 ! in Unit [Coulomb] +eps_cc0 = 8.854187818E-22 ! in Unit [Coulomb**2 /(J*Angstrom)] +! Correlation of M. Uematsu and E. U. Frank +! (Static Dieletric Constant of Water and Steam) +! valid range of conditions 273,15 K <=T<= 823,15 K +! and density <= 1150 kg/m3 (i.e. 0 <= p <= 500 MPa) +rho_sol = rho * 18.015 * 1.E27/ NAv +rho_sol = rho_sol/1000.0 +dielec = 1.0+(7.62571/(t/293.15))*rho_sol +(2.44E2/(t/293.15)-1.41E2 & + + 2.78E1*(t/293.15))*rho_sol**2 & + + (-9.63E1/(t/293.15)+4.18E1*(t/293.15) & + - 1.02E1*(t/293.15)**2 )*rho_sol**3 +(-4.52E1/(t/293.15)**2 & + + 8.46E1/(t/293.15)-3.59E1)*rho_sol**4 + + +! !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! + +dielec = 1.0 + +! !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! + + +!----------------Dipole-Ion Term----------------------------------- +dipole = 0 +ions = 0 +fhend = 0.0 +DO i = 1, ncomp + IF ( parame(i,6) /= 0.0 .AND. uij(i,i) /= 0.0 .AND. x(i) > 0.0 ) THEN + my2dd(i) = (parame(i,6))**2 *1.E-49 / (uij(i,i)*KBOL*sig_ij(i,i)**3 *1.E-30) + dipole = 1 + ELSE + my2dd(i) = 0.0 + END IF + + z_ii(i) = parame(i,10) + IF ( z_ii(i) /= 0.0 .AND. uij(i,i) /= 0.0 .AND. x(i) > 0.0 ) THEN + e_cd(i) = ( parame(i,10)*e_elem* 1.E5 / SQRT(1.11265005) )**2 & + / ( uij(i,i)*kbol*sig_ij(i,i)*1.E-10 ) + ions = 1 + ELSE + e_cd(i) = 0.0 + END IF +END DO + + +IF ( dipole == 1 .AND. ions == 1 ) THEN + + ydd = 0.0 + kappa = 0.0 + x_dipol = 0.0 + x_ions = 0.0 + polabil = 0.0 + DO i = 1, ncomp + ydd = ydd + x(i)*(parame(i,6))**2 *1.E-49/ (kbol*t*1.E-30) + kappa = kappa + x(i) & + *(parame(i,10)*e_elem* 1.E5/SQRT(1.11265005))**2 /(KBOL*t*1.E-10) + IF (parame(i,10) /= 0.0) THEN + x_ions = x_ions + x(i) + ELSE + polabil = polabil + 4.0*PI*x(i)*rho*1.4573 *1.E-30 & + / (sig_ij(3,3)**3 *1.E-30) + END IF + IF (parame(i,6) /= 0.0) x_dipol= x_dipol+ x(i) + END DO + ydd = ydd * 4.0/9.0 * PI * rho + kappa = SQRT( 4.0 * PI * rho * kappa ) + + fh2 = 0.0 + sig_c = 0.0 + sig_d = 0.0 + DO i=1,ncomp + x_ii(i) = 0.0 + x_dd(i) = 0.0 + IF(parame(i,10) /= 0.0 .AND. x_ions /= 0.0) x_ii(i) = x(i)/x_ions + IF(parame(i,6) /= 0.0 .AND. x_dipol /= 0.0) x_dd(i) = x(i)/x_dipol + sig_c = sig_c + x_ii(i)*parame(i,2) + sig_d = sig_d + x_dd(i)*parame(i,2) + END DO + sig_cd = 0.5 * (sig_c + sig_d) + + r_s = 0.0 + ! DO i=1,ncomp + ! r_s=r_s + rho * x(i) * dhs(i)**3 + ! END DO + r_s = eta*6.0 / PI / m_mean + + I0cc = - (1.0 + 0.97743 * r_s + 0.05257*r_s*r_s) & + /(1.0 + 1.43613 * r_s + 0.41580*r_s*r_s) + ! I1cc = - (10.0 - 2.0*z3 + z3*z3) /20.0/(1.0 + 2.0*z3) + I1cc = - (10.0 - 2.0*r_s*pi/6.0 + r_s*r_s*pi/6.0*pi/6.0) & + /20.0/(1.0 + 2.0*r_s*pi/6.0) +!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! + ! I2cc = + (z3-4.0)*(z3*z3+2.0) /24.0/(1.0+2.0*z3) + ! relation of Stell and Lebowitz + I2cc = -0.33331+0.7418*r_s - 1.2047*r_s*r_s & + + 1.6139*r_s**3 - 1.5487*r_s**4 + 0.6626*r_s**5 +!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! + Icd = (1.0 + 0.79576 *r_s + 0.104556 *r_s*r_s) & + /(1.0 + 0.486704*r_s - 0.0222903*r_s*r_s) + Idd = (1.0 + 0.18158*r_s - 0.11467*r_s*r_s) & + /3.0/(1.0 - 0.49303*r_s + 0.06293*r_s*r_s) + Iccc= 3.0*(1.0 - 1.05560*r_s + 0.26591*r_s*r_s) & + /2.0/(1.0 + 0.53892*r_s - 0.94236*r_s*r_s) + Iccd= 11.0*(1.0 + 2.25642 *r_s + 0.05679 *r_s*r_s) & + /6.0/(1.0 + 2.64178 *r_s + 0.79783 *r_s*r_s) + Icdd= 0.94685*(1.0 + 2.97323 *r_s + 3.11931 *r_s*r_s) & + /(1.0 + 2.70186 *r_s + 1.22989 *r_s*r_s) + Iddd= 5.0*(1.0 + 1.12754*r_s + 0.56192*r_s*r_s) & + /24.0/(1.0 - 0.05495*r_s + 0.13332*r_s*r_s) + + IF ( sig_c <= 0.0 ) WRITE (*,*) 'error in Henderson ion term' + + fh32= - kappa**3 /(12.0*pi*rho) + fh2 = - 3.0* kappa**2 * ydd*Icd /(8.0*pi*rho) / sig_cd & + - kappa**4 *sig_c/(16.0*pi*rho)*I0cc + IF (sig_d /= 0.0) fh2 = fh2 - 27.0* ydd * ydd*Idd & + /(8.0*pi*rho) / sig_d**3 + fh52= (3.0*kappa**3 * ydd + kappa**5 *sig_c**2 *I1cc) & + /(8.0*pi*rho) + fh3 = - kappa**6 * sig_c**3 /(8.0*pi*rho) *(I2cc-Iccc/6.0) & + + kappa**4 * ydd *sig_c/(16.0*pi*rho) & + *( (6.0+5.0/3.0*sig_d/sig_c)*I0cc + 3.0*sig_d/sig_c*Iccd ) & + + 3.0*kappa**2 * ydd*ydd /(8.0*pi*rho) / sig_cd & + *( (2.0-3.21555*sig_d/sig_cd)*Icd +3.0*sig_d/sig_cd*Icdd ) + IF (sig_d /= 0.0) fh3 = fh3 + 27.0*ydd**3 & + /(16.0*pi*rho)/sig_d**3 *Iddd + + fhend = ( fh32 + (fh32*fh32*fh3-2.0*fh32*fh2*fh52+fh2**3 ) & + /(fh2*fh2-fh32*fh52) ) & + / ( 1.0 + (fh32*fh3-fh2*fh52) /(fh2*fh2-fh32*fh52) & + - (fh2*fh3-fh52*fh52) /(fh2*fh2-fh32*fh52) ) +!---------- +! fH32= - kappa**3 /(12.0*PI*rho) +! fH2 = - 3.0* kappa**2 * ydd*Icd /(8.0*PI*rho) / sig_cd +! fH52= (3.0*kappa**3 * ydd)/(8.0*PI*rho) +! fH3 = + kappa**4 * ydd *sig_c/(16.0*PI*rho) & +! *( (6.0+5.0/3.0*sig_d/sig_c)*0.0*I0cc + 3.0*sig_d/sig_c*Iccd) & +! + 3.0*kappa**2 * ydd*ydd /(8.0*PI*rho) / sig_cd & +! *( (2.0-3.215550*sig_d/sig_cd)*Icd +3.0*sig_d/sig_cd*Icdd ) + +! fHcd = ( + (fH32*fH32*fH3-2.0*fH32*fH2*fH52+fH2**3 ) & +! /(fH2*fH2-fH32*fH52) ) & +! / ( 1.0 + (fH32*fH3-fH2*fH52) /(fH2*fH2-fH32*fH52) & +! - (fH2*fH3-fH52*fH52) /(fH2*fH2-fH32*fH52) ) + +END IF + + END SUBROUTINE F_ION_DIPOLE_TBH + + +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! + SUBROUTINE F_ION_ION_PrimMSA ( fcc ) +! + USE EOS_VARIABLES, ONLY: nc, PI, KBOL, NAv, ncomp, t, rho, x, parame, mx + IMPLICIT NONE +! +!--------------------------------------------------------------------- + REAL, INTENT(IN OUT) :: fcc +!--------------------------------------------------------------------- + INTEGER :: i, j, cc_it, ions + REAL :: e_elem, eps_cc0, rho_sol, dielec + REAL :: x_ions + REAL :: cc_sig1, cc_sig2, cc_sig3 + REAL, DIMENSION(nc) :: z_ii, x_ii, sigm_i, my2dd + REAL :: alpha_2, kappa, ii_par + REAL :: cc_omeg, p_n, q2_i, cc_q2, cc_gam + REAL :: cc_error(2), cc_delt + REAL :: rhs, lambda, lam_s +!--------------------------------------------------------------------- + +!----------------Dieletric Constant of Water-------------------------- +e_elem = 1.602189246E-19 ! in Unit [Coulomb] +eps_cc0 = 8.854187818E-22 ! in Unit [Coulomb**2 /(J*Angstrom)] +! Correlation of M. Uematsu and E. U. Frank +! (Static Dieletric Constant of Water and Steam) +! valid range of conditions 273,15 K <=T<= 823,15 K +! and density <= 1150 kg/m3 (i.e. 0 <= p <= 500 MPa) +rho_sol = rho * 18.015 * 1.E27/ NAv +rho_sol = rho_sol/1000.0 +dielec = 1.0+(7.62571/(t/293.15))*rho_sol +(2.44E2/(t/293.15)-1.41E2 & + +2.78E1*(t/293.15))*rho_sol**2 & + +(-9.63E1/(t/293.15)+4.18E1*(t/293.15) & + -1.02E1*(t/293.15)**2 )*rho_sol**3 +(-4.52E1/(t/293.15)**2 & + +8.46E1/(t/293.15)-3.59E1)*rho_sol**4 + + +! !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! + +dielec = 1.0 + +! !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! + + +!----------------Ion-Ion: primitive MSA ------------------------------- +! the (dipole moment)**2 [my**2] corresponds to an attraction from +! point charges of [ SUM(xi * zi**2 * e_elem**2) * 3 * di**2 ] + +! parame(ion,6))**2 * 1.E-49 / (kbol*T) +! = (e_elem* 1.E5/SQRT(1.112650050))**2 +! *x(i)*zi**2 *3.0*sig_ij(1,1)**2 *1.E-20 + +! parame(ion,6))**2 = (e_elem* 1.E5/SQRT(1.112650050))**2 /1.E-49 +! *x(i)*zi**2 *3.0*sig_ij(i,i)**2 *1.E-20 + +! with the units +! my**2 [=] D**2 = 1.E-49 J*m3 +! e_elem **2 [=] C**2 = 1.E5 / SQRT(1.112650050) J*m + + +ions = 0 +x_ions = 0.0 +fcc = 0.0 +DO i = 1, ncomp + z_ii(i) = parame(i,10) + IF (z_ii(i) /= 0.0) THEN + sigm_i(i) = parame(i,2) + ELSE + sigm_i(i) = 0.0 + END IF + IF (z_ii(i) /= 0.0) ions = 1 + IF (z_ii(i) /= 0.0) x_ions = x_ions + x(i) +END DO + +IF (ions == 1 .AND. x_ions > 0.0) THEN + + cc_sig1 = 0.0 + cc_sig2 = 0.0 + cc_sig3 = 0.0 + DO i=1,ncomp + IF (z_ii(i) /= 0.0) THEN + x_ii(i) = x(i)/x_ions + ELSE + x_ii(i) =0.0 + END IF + cc_sig1 = cc_sig1 +x_ii(i)*sigm_i(i) + cc_sig2 = cc_sig2 +x_ii(i)*sigm_i(i)**2 + cc_sig3 = cc_sig3 +x_ii(i)*sigm_i(i)**3 + END DO + + + ! alpha_2 = 4.0*PI*e_elem**2 /eps_cc0/dielec/kbol/T + alpha_2 = e_elem**2 /eps_cc0 / dielec / KBOL/t + kappa = 0.0 + DO i = 1, ncomp + kappa = kappa + x(i)*z_ii(i)*z_ii(i)*mx(i,1) + END DO + kappa = SQRT( rho * alpha_2 * kappa ) + ii_par= kappa * cc_sig1 + + ! Temporaer: nach der Arbeit von Krienke verifiziert + ! noch nicht fuer Mischungen mit unterschiedl. Ladung erweitert + ! ii_par = DSQRT( e_elem**2 /eps_cc0/dielec/kbol/T & + ! *rho*(x(1)*Z_ii(1)**2 + x(2)*Z_ii(2)**2 ) )*cc_sig1 + + + cc_gam = kappa/2.0 + + ! noch offen !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! + cc_delt = 0.0 + DO i = 1, ncomp + cc_delt = cc_delt + x(i)*mx(i,1)*rho*sigm_i(i)**3 + END DO + cc_delt= 1.0 - PI/6.0*cc_delt + + cc_it = 0 + 13 CONTINUE + j = 0 + cc_it = cc_it + 1 + 131 CONTINUE + j = j + 1 + cc_omeg = 0.0 + DO i = 1, ncomp + cc_omeg = cc_omeg +x(i)*mx(i,1)*sigm_i(i)**3 /(1.0+cc_gam*sigm_i(i)) + END DO + cc_omeg = 1.0 + PI/2.0 / cc_delt * rho * cc_omeg + p_n = 0.0 + DO i = 1, ncomp + p_n = p_n + x(i)*mx(i,1)*rho / cc_omeg*sigm_i(i)*z_ii(i) / (1.0+cc_gam*sigm_i(i)) + END DO + q2_i = 0.0 + cc_q2= 0.0 + DO i = 1, ncomp + q2_i = q2_i + rho*x(i)*mx(i,1)*( (z_ii(i)-pi/2.0/cc_delt*sigm_i(i)**2 *p_n) & + /(1.0+cc_gam*sigm_i(i)) )**2 + cc_q2 = cc_q2 + x(i)*mx(i,1)*rho*z_ii(i)**2 / (1.0+cc_gam*sigm_i(i)) + END DO + q2_i = q2_i*alpha_2 / 4.0 + + cc_error(j) = cc_gam - SQRT(q2_i) + IF (j == 1) cc_gam = cc_gam*1.000001 + IF (j == 2) cc_gam = cc_gam - cc_error(2)* (cc_gam-cc_gam/1.000001)/(cc_error(2)-cc_error(1)) + + IF ( j == 1 .AND. ABS(cc_error(1)) > 1.E-15 ) GO TO 131 + IF ( cc_it >= 10 ) THEN + WRITE (*,*) ' cc error' + STOP + END IF + IF ( j /= 1 ) GO TO 13 + + fcc= - alpha_2 / PI/4.0 /rho* (cc_gam*cc_q2 & + + pi/2.0/cc_delt *cc_omeg*p_n**2 ) + cc_gam**3 /pi/3.0/rho + ! Restricted Primitive Model + ! fcc=-(3.0*ii_par*ii_par+6.0*ii_par+2.0 & + ! -2.0*(1.0+2.0*ii_par)**1.50) & + ! /(12.0*PI*rho *cc_sig1**3 ) + + ! fcc = x_ions * fcc + + my2dd(3) = (parame(3,6))**2 *1.E-19 /(KBOL*t) + my2dd(3) = (1.84)**2 *1.E-19 /(kbol*t) + + rhs = 12.0 * PI * rho * x(3) * my2dd(3) + lam_s = 1.0 + 12 CONTINUE + lambda = (rhs/((lam_s+2.0)**2 ) + 16.0/((1.0+lam_s)**4 ) )**0.5 + IF ( ABS(lam_s-lambda) > 1.E-10 )THEN + lam_s = ( lambda + lam_s ) / 2.0 + GO TO 12 + END IF + + ! f_cd = -(ii_par*ii_par)/(4.0*PI*rho*m_mean *cc_sig1**3 ) & + ! *(dielec-1.0)/(1.0 + parame(3,2)/cc_sig1/lambda) + ! write (*,*) ' ',f_cd,fcc,x_ions + ! f_cd = f_cd/(1.0 - fcc/f_cd) + ! fcc = 0.0 + +END IF + + +END SUBROUTINE F_ION_ION_PrimMSA + + +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! + SUBROUTINE F_ION_ION_nonPrimMSA ( fdd, fqq, fdq, fcc ) +! + USE EOS_VARIABLES, ONLY: nc, ncomp, t, eta, x, parame, mseg + IMPLICIT NONE +! +!--------------------------------------------------------------------- + REAL, INTENT(IN OUT) :: fdd, fqq, fdq, fcc +!--------------------------------------------------------------------- + INTEGER :: dipole + !REAL :: A_MSA !, A_CC, A_CD, A_DD, U_MSA, chempot + REAL, DIMENSION(nc) :: x_export, msegm +!--------------------------------------------------------------------- + + dipole = 0 + IF ( SUM( parame(1:ncomp,6) ) > 1.E-5 ) dipole = 1 + + IF ( dipole /= 0 ) THEN ! alternatively ions and dipoles = 1 + fdd = 0.0 + fqq = 0.0 + fdq = 0.0 + fcc = 0.0 + msegm(:) = mseg(:) ! the entries of the vector mseg and x are changed + x_export(:) = x(:) ! in SEMIRESTRICTED because the ions should be positioned first + ! that is why dummy vectors msegm and x_export are defined + !CALL SEMIRESTRICTED (A_MSA,A_CC,A_CD,A_DD,U_MSA, & + ! chempot,ncomp,parame,t,eta,x_export,msegm,0) + !fdd = A_MSA + write (*,*) 'why are individual contrib. A_CC,A_CD,A_DD not used' + stop + END IF + + END SUBROUTINE F_ION_ION_nonPrimMSA + + +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! + SUBROUTINE F_LC_MayerSaupe ( flc ) +! + USE EOS_VARIABLES, ONLY: nc, PI, KBOL, NAv, ncomp, phas, t, rho, eta, & + x, mseg, parame, E_lc, S_lc, dhs + IMPLICIT NONE +! +!--------------------------------------------------------------------- + REAL, INTENT(IN OUT) :: flc +!--------------------------------------------------------------------- + INTEGER :: i, j, k + INTEGER :: liq_crystal, count_lc, steps_lc + REAL :: alpha_lc, tolerance, deltay + REAL :: integrand1, integrand2, accel_lc + REAL :: error_lc, u_term, sphase + REAL, DIMENSION(nc) :: z_lc, S_lc1, S_lc2, sumu + REAL, DIMENSION(nc,nc) :: u_lc, klc +!--------------------------------------------------------------------- +INTEGER :: stabil +COMMON /stabil / stabil +!--------------------------------------------------------------------- + + + klc(1,2) = 0.0 + klc(2,1) = klc(1,2) + + alpha_lc = 1.0 + accel_lc = 4.0 + IF ( eta < 0.35 ) accel_lc = 1.3 + IF ( eta < 0.15 ) accel_lc = 1.0 + + liq_crystal = 0 + DO i = 1, ncomp + DO j = 1, ncomp + E_lc(i,j) = (E_lc(i,i)*E_lc(j,j))**0.5 *(1.0-klc(i,j)) !combining rule + ! E_LC(i,j)= ( E_LC(i,i)+E_LC(j,j) ) * 0.5 !combining rule + ! S_LC(i,j)= ( S_LC(i,i)+S_LC(j,j) ) * 0.5 !combining rule + IF (E_lc(i,j) /= 0.0) liq_crystal = 1 + END DO + END DO + ! S_LC(1,2) = 0.0 + ! S_LC(2,1) = S_LC(1,2) + ! E_LC(1,2) = 60.0 + ! E_LC(2,1) = E_LC(1,2) + + IF ( liq_crystal == 1 .AND. phas == 1 .AND. stabil == 0 ) THEN + + count_lc = 0 + tolerance = 1.E-6 + + steps_lc = 200 + deltay = 1.0 / REAL(steps_lc) + + ! --- dimensionless function U_LC repres. anisotr. intermolecular interactions in l.c. + + DO i = 1, ncomp + DO j = 1, ncomp + u_lc(i,j) = 2.0/3.0*pi*mseg(i)*mseg(j) *(0.5*(dhs(i)+dhs(j)))**3 & ! sig_ij(i,j)**3 + *(E_lc(i,j)/t+S_lc(i,j))*rho + END DO + END DO + + + DO i=1,ncomp + ! S_lc2(i) = 0.0 !for isotropic + S_lc2(i) = 0.5 !for nematic + S_lc1(i) = S_lc2(i) + END DO + + 1 CONTINUE + + DO i = 1, ncomp + IF (S_lc2(i) <= 0.3) S_lc1(i) = S_lc2(i) + IF (S_lc2(i) > 0.3) S_lc1(i) = S_lc1(i) + (S_lc2(i)-S_lc1(i))*accel_lc + END DO + + count_lc = count_lc + 1 + + ! --- single-particle orientation partition function Z_LC in liquid crystals + + DO i = 1, ncomp + sumu(i) = 0.0 + DO j = 1, ncomp + sumu(i) = sumu(i) + x(j)*u_lc(i,j)*S_lc1(j) + END DO + END DO + + DO i = 1, ncomp + z_lc(i) = 0.0 + integrand1 = EXP(-0.5*sumu(i)) !eq. for Z_LC with y=0 + DO k = 1, steps_lc + integrand2 = EXP(0.5*sumu(i)*(3.0*(deltay*REAL(k)) **2 -1.0)) + z_lc(i) = z_lc(i) + (integrand1 + integrand2)/2.0*deltay + integrand1 = integrand2 + END DO !k-index integration + END DO !i-index Z_LC(i) calculation + + ! --- order parameter S_lc in liquid crystals ----------------------- + + error_lc = 0.0 + DO i = 1, ncomp + S_lc2(i) = 0.0 + integrand1 = -1.0/z_lc(i)*0.5*EXP(-0.5*sumu(i)) !for S_lc with y=0 + DO k = 1, steps_lc + integrand2 = 1.0/z_lc(i)*0.5*(3.0*(deltay*REAL(k)) & + **2 -1.0)*EXP(0.5*sumu(i)*(3.0 *(deltay*REAL(k))**2 -1.0)) + S_lc2(i) = S_lc2(i) + (integrand1 + integrand2)/2.0*deltay + integrand1 = integrand2 + END DO !k-index integration + error_lc = error_lc + ABS(S_lc2(i)-S_lc1(i)) + END DO !i-index Z_LC(i) calculation + + sphase = 0.0 + DO i = 1, ncomp + sphase = sphase + S_lc2(i) + END DO + IF (sphase < 1.E-4) THEN + error_lc = 0.0 + DO i = 1, ncomp + S_lc2(i)= 0.0 + z_lc(i) = 1.0 + END DO + END IF + + + ! write (*,*) count_LC,S_lc2(1)-S_lc1(1),S_lc2(2)-S_lc1(2) + IF (error_lc > tolerance .AND. count_lc < 400) GO TO 1 + ! write (*,*) 'done',eta,S_lc2(1),S_lc2(2) + + IF (count_lc == 400) WRITE (*,*) 'LC iteration not converg.' + + ! --- the anisotropic contribution to the Helmholtz energy ---------- + + u_term = 0.0 + DO i = 1, ncomp + DO j = 1, ncomp + u_term = u_term + 0.5*x(i)*x(j)*S_lc2(i) *S_lc2(j)*u_lc(i,j) + END DO + END DO + + flc = 0.0 + DO i = 1, ncomp + IF (z_lc(i) /= 0.0) flc = flc - x(i) * LOG(z_lc(i)) + END DO + flc = flc + u_term + ! pause + + END IF + ! write (*,'(i2,i2,4(f15.8))') phas,stabil,flc,eta,S_lc2(1),x(1) + + + END SUBROUTINE F_LC_MayerSaupe + + + +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! + SUBROUTINE P_POLAR ( zdd, zddz, zddz2, zddz3, zqq, zqqz, zqqz2, zqqz3, zdq, zdqz, zdqz2, zdqz3 ) +! + USE EOS_VARIABLES, ONLY: ncomp, parame, dd_term, qq_term, dq_term + IMPLICIT NONE +! +! ---------------------------------------------------------------------- + REAL, INTENT(OUT) :: zdd, zddz, zddz2, zddz3 + REAL, INTENT(OUT) :: zqq, zqqz, zqqz2, zqqz3 + REAL, INTENT(OUT) :: zdq, zdqz, zdqz2, zdqz3 +! +! --- local variables--------------------------------------------------- + INTEGER :: dipole + INTEGER :: quadrupole + INTEGER :: dipole_quad +! ---------------------------------------------------------------------- + + zdd = 0.0 + zddz = 0.0 + zddz2 = 0.0 + zddz3 = 0.0 + zqq = 0.0 + zqqz = 0.0 + zqqz2 = 0.0 + zqqz3 = 0.0 + zdq = 0.0 + zdqz = 0.0 + zdqz2 = 0.0 + zdqz3 = 0.0 + + dipole = 0 + quadrupole = 0 + dipole_quad = 0 + IF ( SUM( parame(1:ncomp,6) ) /= 0.0 ) dipole = 1 + IF ( SUM( parame(1:ncomp,7) ) /= 0.0 ) quadrupole = 1 + IF ( dipole == 1 .AND. quadrupole == 1 ) dipole_quad = 1 + + ! -------------------------------------------------------------------- + ! dipole-dipole term + ! -------------------------------------------------------------------- + IF (dipole == 1) THEN + + IF (dd_term == 'GV') CALL P_DD_GROSS_VRABEC( zdd, zddz, zddz2, zddz3 ) + ! IF (dd_term == 'SF') CALL F_DD_SAAGER_FISCHER( k ) + IF (dd_term /= 'GV' .AND. dd_term /= 'SF') write (*,*) 'specify dipole term !' + + ENDIF + + ! -------------------------------------------------------------------- + ! quadrupole-quadrupole term + ! -------------------------------------------------------------------- + IF (quadrupole == 1) THEN + + !IF (qq_term == 'SF') CALL F_QQ_SAAGER_FISCHER( k ) + IF (qq_term == 'JG') CALL P_QQ_GROSS( zqq, zqqz, zqqz2, zqqz3 ) + IF (qq_term /= 'JG' .AND. qq_term /= 'SF') write (*,*) 'specify quadrupole term !' + + ENDIF + + ! -------------------------------------------------------------------- + ! dipole-quadrupole cross term + ! -------------------------------------------------------------------- + IF (dipole_quad == 1) THEN + + IF (dq_term == 'VG') CALL P_DQ_VRABEC_GROSS( zdq, zdqz, zdqz2, zdqz3 ) + IF (dq_term /= 'VG' ) write (*,*) 'specify DQ-cross term !' + + ENDIF + +END SUBROUTINE P_POLAR + + +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! + SUBROUTINE P_DD_GROSS_VRABEC( zdd, zddz, zddz2, zddz3 ) +! + USE PARAMETERS, ONLY: PI, KBOL + USE EOS_VARIABLES, ONLY: nc, ncomp, uij, parame, mseg, sig_ij, rho, eta, x, t + USE EOS_CONSTANTS, ONLY: ddp2, ddp3, ddp4 + IMPLICIT NONE +! +! ---------------------------------------------------------------------- + REAL, INTENT(IN OUT) :: zdd, zddz, zddz2, zddz3 +! ---------------------------------------------------------------------- + INTEGER :: i, j, k, m + REAL :: factor2, factor3, z3 + REAL :: xijfa, xijkfa, eij + REAL :: fdddr, fddd2, fddd3, fddd4 + REAL :: fdd2, fdd2z, fdd2z2, fdd2z3, fdd2z4 + REAL :: fdd3, fdd3z, fdd3z2, fdd3z3, fdd3z4 + REAL, DIMENSION(nc) :: my2dd + REAL, DIMENSION(nc,nc) :: Idd2, Idd2z, Idd2z2, Idd2z3, Idd2z4 + REAL, DIMENSION(nc,nc) :: Idd4, Idd4z, Idd4z2, Idd4z3, Idd4z4 + REAL, DIMENSION(nc,nc,nc) :: Idd3, Idd3z, Idd3z2, Idd3z3, Idd3z4 +! ---------------------------------------------------------------------- + + + zdd = 0.0 + zddz = 0.0 + zddz2 = 0.0 + zddz3 = 0.0 + z3 = eta + DO i = 1, ncomp + my2dd(i) = (parame(i,6))**2 *1.E-49 / (uij(i,i)*KBOL*mseg(i)*sig_ij(i,i)**3 *1.E-30) + END DO + + DO i = 1, ncomp + DO j = 1, ncomp + Idd2(i,j) = 0.0 + Idd4(i,j) = 0.0 + Idd2z(i,j) = 0.0 + Idd4z(i,j) = 0.0 + Idd2z2(i,j) = 0.0 + Idd4z2(i,j) = 0.0 + Idd2z3(i,j) = 0.0 + Idd4z3(i,j) = 0.0 + Idd2z4(i,j) = 0.0 + Idd4z4(i,j) = 0.0 + ! IF (paramei,6).NE.0.0 .AND. parame(j,6).NE.0.0) THEN + DO m = 0, 4 + Idd2(i,j) =Idd2(i,j) + ddp2(i,j,m) *z3**(m+1) + Idd4(i,j) =Idd4(i,j) + ddp4(i,j,m) *z3**(m+1) + Idd2z(i,j) =Idd2z(i,j) +ddp2(i,j,m)*REAL(m+1) *z3**m + Idd4z(i,j) =Idd4z(i,j) +ddp4(i,j,m)*REAL(m+1) *z3**m + Idd2z2(i,j)=Idd2z2(i,j)+ddp2(i,j,m)*REAL((m+1)*m) *z3**(m-1) + Idd4z2(i,j)=Idd4z2(i,j)+ddp4(i,j,m)*REAL((m+1)*m) *z3**(m-1) + Idd2z3(i,j)=Idd2z3(i,j)+ddp2(i,j,m)*REAL((m+1)*m*(m-1)) *z3**(m-2) + Idd4z3(i,j)=Idd4z3(i,j)+ddp4(i,j,m)*REAL((m+1)*m*(m-1)) *z3**(m-2) + Idd2z4(i,j)=Idd2z4(i,j)+ddp2(i,j,m)*REAL((m+1)*m*(m-1)*(m-2)) *z3**(m-3) + Idd4z4(i,j)=Idd4z4(i,j)+ddp4(i,j,m)*REAL((m+1)*m*(m-1)*(m-2)) *z3**(m-3) + END DO + DO k = 1, ncomp + Idd3(i,j,k) = 0.0 + Idd3z(i,j,k) = 0.0 + Idd3z2(i,j,k) = 0.0 + Idd3z3(i,j,k) = 0.0 + Idd3z4(i,j,k) = 0.0 + ! IF (parame(k,6).NE.0.0) THEN + DO m = 0, 4 + Idd3(i,j,k) =Idd3(i,j,k) +ddp3(i,j,k,m)*z3**(m+2) + Idd3z(i,j,k) =Idd3z(i,j,k) +ddp3(i,j,k,m)*REAL(m+2)*z3**(m+1) + Idd3z2(i,j,k)=Idd3z2(i,j,k)+ddp3(i,j,k,m)*REAL((m+2)*(m+1))*z3**m + Idd3z3(i,j,k)=Idd3z3(i,j,k)+ddp3(i,j,k,m)*REAL((m+2)*(m+1)*m)*z3**(m-1) + Idd3z4(i,j,k)=Idd3z4(i,j,k)+ddp3(i,j,k,m)*REAL((m+2)*(m+1)*m*(m-1)) *z3**(m-2) + END DO + ! ENDIF + END DO + ! ENDIF + END DO + END DO + + factor2= -PI *rho/z3 + factor3= -4.0/3.0*PI**2 * (rho/z3)**2 + + fdd2 = 0.0 + fdd2z = 0.0 + fdd2z2 = 0.0 + fdd2z3 = 0.0 + fdd2z4 = 0.0 + fdd3 = 0.0 + fdd3z = 0.0 + fdd3z2 = 0.0 + fdd3z3 = 0.0 + fdd3z4 = 0.0 + DO i = 1, ncomp + DO j = 1, ncomp + ! IF (parame(i,6).NE.0.0 .AND. parame(j,6).NE.0.0) THEN + xijfa = x(i)*parame(i,3)/t*parame(i,2)**3 *x(j)*parame(j,3)/t*parame(j,2)**3 & + / ((parame(i,2)+parame(j,2))/2.0)**3 *my2dd(i)*my2dd(j) + eij = (parame(i,3)*parame(j,3))**0.5 + fdd2 = fdd2 +factor2*xijfa*(Idd2(i,j) +eij/t*Idd4(i,j)) + fdd2z = fdd2z +factor2*xijfa*(Idd2z(i,j) +eij/t*Idd4z(i,j)) + fdd2z2 = fdd2z2+factor2*xijfa*(Idd2z2(i,j)+eij/t*Idd4z2(i,j)) + fdd2z3 = fdd2z3+factor2*xijfa*(Idd2z3(i,j)+eij/t*Idd4z3(i,j)) + fdd2z4 = fdd2z4+factor2*xijfa*(Idd2z4(i,j)+eij/t*Idd4z4(i,j)) + DO k = 1, ncomp + ! IF (parame(k,6).NE.0.0) THEN + xijkfa= x(i)*parame(i,3)/t*parame(i,2)**3 *x(j)*parame(j,3)/t*parame(j,2)**3 & + *x(k)*parame(k,3)/t*parame(k,2)**3 /((parame(i,2)+parame(j,2))/2.0) & + /((parame(i,2)+parame(k,2))/2.0) /((parame(j,2)+parame(k,2))/2.0) & + *my2dd(i)*my2dd(j)*my2dd(k) + fdd3 = fdd3 + factor3 * xijkfa*Idd3(i,j,k) + fdd3z = fdd3z + factor3 * xijkfa*Idd3z(i,j,k) + fdd3z2 = fdd3z2 + factor3 * xijkfa*Idd3z2(i,j,k) + fdd3z3 = fdd3z3 + factor3 * xijkfa*Idd3z3(i,j,k) + fdd3z4 = fdd3z4 + factor3 * xijkfa*Idd3z4(i,j,k) + ! ENDIF + END DO + ! ENDIF + END DO + END DO + IF (fdd2 < -1.E-50 .AND. fdd3 /= 0.0 .AND. fdd2z /= 0.0 .AND. fdd3z /= 0.0) THEN + + fdddr= fdd2* (fdd2*fdd2z - 2.0*fdd3*fdd2z+fdd2*fdd3z) / (fdd2-fdd3)**2 + fddd2=(2.0*fdd2*fdd2z*fdd2z +fdd2*fdd2*fdd2z2 & + -2.0*fdd2z**2 *fdd3-2.0*fdd2*fdd2z2*fdd3+fdd2*fdd2*fdd3z2) & + /(fdd2-fdd3)**2 + fdddr * 2.0*(fdd3z-fdd2z)/(fdd2-fdd3) + fddd3=(2.0*fdd2z**3 +6.0*fdd2*fdd2z*fdd2z2+fdd2*fdd2*fdd2z3 & + -6.0*fdd2z*fdd2z2*fdd3-2.0*fdd2z**2 *fdd3z & + -2.0*fdd2*fdd2z3*fdd3 -2.0*fdd2*fdd2z2*fdd3z & + +2.0*fdd2*fdd2z*fdd3z2+fdd2*fdd2*fdd3z3) /(fdd2-fdd3)**2 & + + 2.0/(fdd2-fdd3)* ( 2.0*fddd2*(fdd3z-fdd2z) & + + fdddr*(fdd3z2-fdd2z2) & + - fdddr/(fdd2-fdd3)*(fdd3z-fdd2z)**2 ) + fddd4=( 12.0*fdd2z**2 *fdd2z2+6.0*fdd2*fdd2z2**2 & + +8.0*fdd2*fdd2z*fdd2z3+fdd2*fdd2*fdd2z4-6.0*fdd2z2**2 *fdd3 & + -12.0*fdd2z*fdd2z2*fdd3z -8.0*fdd2z*fdd2z3*fdd3 & + -2.0*fdd2*fdd2z4*fdd3-4.0*fdd2*fdd2z3*fdd3z & + +4.0*fdd2*fdd2z*fdd3z3+fdd2**2 *fdd3z4 ) /(fdd2-fdd3)**2 & + + 6.0/(fdd2-fdd3)* ( fddd3*(fdd3z-fdd2z) & + -fddd2/(fdd2-fdd3)*(fdd3z-fdd2z)**2 & + - fdddr/(fdd2-fdd3)*(fdd3z-fdd2z)*(fdd3z2-fdd2z2) & + + fddd2*(fdd3z2-fdd2z2) +1.0/3.0*fdddr*(fdd3z3-fdd2z3) ) + zdd = fdddr*eta + zddz = fddd2*eta + fdddr + zddz2 = fddd3*eta + 2.0* fddd2 + zddz3 = fddd4*eta + 3.0* fddd3 + + END IF + + +END SUBROUTINE P_DD_GROSS_VRABEC + + + +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! + SUBROUTINE P_QQ_GROSS( zqq, zqqz, zqqz2, zqqz3 ) +! + USE PARAMETERS, ONLY: PI, KBOL + USE EOS_VARIABLES, ONLY: nc, ncomp, uij, parame, mseg, sig_ij, rho, eta, x, t + USE EOS_CONSTANTS, ONLY: qqp2, qqp3, qqp4 + IMPLICIT NONE +! +! ---------------------------------------------------------------------- + REAL, INTENT(IN OUT) :: zqq, zqqz, zqqz2, zqqz3 +! ---------------------------------------------------------------------- + INTEGER :: i, j, k, m + REAL :: factor2, factor3, z3 + REAL :: xijfa, xijkfa, eij + REAL :: fqqdr, fqqd2, fqqd3, fqqd4 + REAL :: fqq2, fqq2z, fqq2z2, fqq2z3, fqq2z4 + REAL :: fqq3, fqq3z, fqq3z2, fqq3z3, fqq3z4 + REAL, DIMENSION(nc) :: qq2 + REAL, DIMENSION(nc,nc) :: Iqq2, Iqq2z, Iqq2z2, Iqq2z3, Iqq2z4 + REAL, DIMENSION(nc,nc) :: Iqq4, Iqq4z, Iqq4z2, Iqq4z3, Iqq4z4 + REAL, DIMENSION(nc,nc,nc) :: Iqq3, Iqq3z, Iqq3z2, Iqq3z3, Iqq3z4 +! ---------------------------------------------------------------------- + + zqq = 0.0 + zqqz = 0.0 + zqqz2 = 0.0 + zqqz3 = 0.0 + z3 = eta + DO i=1,ncomp + qq2(i) = (parame(i,7))**2 *1.E-69 / (uij(i,i)*kbol*mseg(i)*sig_ij(i,i)**5 *1.E-50) + END DO + + DO i = 1, ncomp + DO j = 1, ncomp + Iqq2(i,j) = 0.0 + Iqq4(i,j) = 0.0 + Iqq2z(i,j) = 0.0 + Iqq4z(i,j) = 0.0 + Iqq2z2(i,j) = 0.0 + Iqq4z2(i,j) = 0.0 + Iqq2z3(i,j) = 0.0 + Iqq4z3(i,j) = 0.0 + Iqq2z4(i,j) = 0.0 + Iqq4z4(i,j) = 0.0 + IF (parame(i,7) /= 0.0 .AND. parame(j,7) /= 0.0) THEN + DO m = 0, 4 + Iqq2(i,j) =Iqq2(i,j) + qqp2(i,j,m)*z3**(m+1) + Iqq4(i,j) =Iqq4(i,j) + qqp4(i,j,m)*z3**(m+1) + Iqq2z(i,j) =Iqq2z(i,j) +qqp2(i,j,m)*REAL(m+1)*z3**m + Iqq4z(i,j) =Iqq4z(i,j) +qqp4(i,j,m)*REAL(m+1)*z3**m + Iqq2z2(i,j)=Iqq2z2(i,j)+qqp2(i,j,m)*REAL((m+1)*m)*z3**(m-1) + Iqq4z2(i,j)=Iqq4z2(i,j)+qqp4(i,j,m)*REAL((m+1)*m)*z3**(m-1) + Iqq2z3(i,j)=Iqq2z3(i,j)+qqp2(i,j,m)*REAL((m+1)*m*(m-1)) *z3**(m-2) + Iqq4z3(i,j)=Iqq4z3(i,j)+qqp4(i,j,m)*REAL((m+1)*m*(m-1)) *z3**(m-2) + Iqq2z4(i,j)=Iqq2z4(i,j)+qqp2(i,j,m)*REAL((m+1)*m*(m-1)*(m-2)) *z3**(m-3) + Iqq4z4(i,j)=Iqq4z4(i,j)+qqp4(i,j,m)*REAL((m+1)*m*(m-1)*(m-2)) *z3**(m-3) + END DO + DO k=1,ncomp + Iqq3(i,j,k) = 0.0 + Iqq3z(i,j,k) = 0.0 + Iqq3z2(i,j,k) = 0.0 + Iqq3z3(i,j,k) = 0.0 + Iqq3z4(i,j,k) = 0.0 + IF (parame(k,7) /= 0.0) THEN + DO m=0,4 + Iqq3(i,j,k) =Iqq3(i,j,k) + qqp3(i,j,k,m)*z3**(m+2) + Iqq3z(i,j,k)=Iqq3z(i,j,k)+qqp3(i,j,k,m)*REAL(m+2)*z3**(m+1) + Iqq3z2(i,j,k)=Iqq3z2(i,j,k)+qqp3(i,j,k,m)*REAL((m+2)*(m+1)) *z3**m + Iqq3z3(i,j,k)=Iqq3z3(i,j,k)+qqp3(i,j,k,m)*REAL((m+2)*(m+1)*m) *z3**(m-1) + Iqq3z4(i,j,k)=Iqq3z4(i,j,k)+qqp3(i,j,k,m) *REAL((m+2)*(m+1)*m*(m-1)) *z3**(m-2) + END DO + END IF + END DO + + END IF + END DO + END DO + + factor2= -9.0/16.0*PI *rho/z3 + factor3= 9.0/16.0*PI**2 * (rho/z3)**2 + + fqq2 = 0.0 + fqq2z = 0.0 + fqq2z2 = 0.0 + fqq2z3 = 0.0 + fqq2z4 = 0.0 + fqq3 = 0.0 + fqq3z = 0.0 + fqq3z2 = 0.0 + fqq3z3 = 0.0 + fqq3z4 = 0.0 + DO i = 1, ncomp + DO j = 1, ncomp + IF (parame(i,7) /= 0.0 .AND. parame(j,7) /= 0.0) THEN + xijfa =x(i)*uij(i,i)*qq2(i)*sig_ij(i,i)**5 /t & + *x(j)*uij(j,j)*qq2(j)*sig_ij(j,j)**5 /t/sig_ij(i,j)**7.0 + eij = (parame(i,3)*parame(j,3))**0.5 + fqq2= fqq2 +factor2*xijfa*(Iqq2(i,j) +eij/t*Iqq4(i,j) ) + fqq2z =fqq2z +factor2*xijfa*(Iqq2z(i,j) +eij/t*Iqq4z(i,j) ) + fqq2z2=fqq2z2+factor2*xijfa*(Iqq2z2(i,j)+eij/t*Iqq4z2(i,j)) + fqq2z3=fqq2z3+factor2*xijfa*(Iqq2z3(i,j)+eij/t*Iqq4z3(i,j)) + fqq2z4=fqq2z4+factor2*xijfa*(Iqq2z4(i,j)+eij/t*Iqq4z4(i,j)) + DO k = 1, ncomp + IF (parame(k,7) /= 0.0) THEN + xijkfa=x(i)*uij(i,i)*qq2(i)*sig_ij(i,i)**5 /t/sig_ij(i,j)**3 & + *x(j)*uij(j,j)*qq2(j)*sig_ij(j,j)**5 /t/sig_ij(i,k)**3 & + *x(k)*uij(k,k)*qq2(k)*sig_ij(k,k)**5 /t/sig_ij(j,k)**3 + fqq3 = fqq3 + factor3 * xijkfa*Iqq3(i,j,k) + fqq3z = fqq3z + factor3 * xijkfa*Iqq3z(i,j,k) + fqq3z2 = fqq3z2 + factor3 * xijkfa*Iqq3z2(i,j,k) + fqq3z3 = fqq3z3 + factor3 * xijkfa*Iqq3z3(i,j,k) + fqq3z4 = fqq3z4 + factor3 * xijkfa*Iqq3z4(i,j,k) + END IF + END DO + END IF + END DO + END DO + IF (fqq2 < -1.E-50 .AND. fqq3 /= 0.0 .AND. fqq2z /= 0.0 .AND. fqq3z /= 0.0) THEN + fqqdr = fqq2* (fqq2*fqq2z - 2.0*fqq3*fqq2z+fqq2*fqq3z) /(fqq2-fqq3)**2 + fqqd2= (2.0*fqq2*fqq2z*fqq2z +fqq2*fqq2*fqq2z2 & + -2.0*fqq2z**2 *fqq3-2.0*fqq2*fqq2z2*fqq3+fqq2*fqq2*fqq3z2) & + /(fqq2-fqq3)**2 + fqqdr * 2.0*(fqq3z-fqq2z)/(fqq2-fqq3) + fqqd3=(2.0*fqq2z**3 +6.0*fqq2*fqq2z*fqq2z2+fqq2*fqq2*fqq2z3 & + -6.0*fqq2z*fqq2z2*fqq3-2.0*fqq2z**2 *fqq3z & + -2.0*fqq2*fqq2z3*fqq3 -2.0*fqq2*fqq2z2*fqq3z & + +2.0*fqq2*fqq2z*fqq3z2+fqq2*fqq2*fqq3z3) /(fqq2-fqq3)**2 & + + 2.0/(fqq2-fqq3)* ( 2.0*fqqd2*(fqq3z-fqq2z) & + + fqqdr*(fqq3z2-fqq2z2) - fqqdr/(fqq2-fqq3)*(fqq3z-fqq2z)**2 ) + fqqd4=( 12.0*fqq2z**2 *fqq2z2+6.0*fqq2*fqq2z2**2 & + +8.0*fqq2*fqq2z*fqq2z3+fqq2*fqq2*fqq2z4-6.0*fqq2z2**2 *fqq3 & + -12.0*fqq2z*fqq2z2*fqq3z -8.0*fqq2z*fqq2z3*fqq3 & + -2.0*fqq2*fqq2z4*fqq3-4.0*fqq2*fqq2z3*fqq3z & + +4.0*fqq2*fqq2z*fqq3z3+fqq2**2 *fqq3z4 ) /(fqq2-fqq3)**2 & + + 6.0/(fqq2-fqq3)* ( fqqd3*(fqq3z-fqq2z) & + -fqqd2/(fqq2-fqq3)*(fqq3z-fqq2z)**2 & + - fqqdr/(fqq2-fqq3)*(fqq3z-fqq2z)*(fqq3z2-fqq2z2) & + + fqqd2*(fqq3z2-fqq2z2) +1.0/3.0*fqqdr*(fqq3z3-fqq2z3) ) + zqq = fqqdr*eta + zqqz = fqqd2*eta + fqqdr + zqqz2 = fqqd3*eta + 2.0* fqqd2 + zqqz3 = fqqd4*eta + 3.0* fqqd3 + END IF + + +END SUBROUTINE P_QQ_GROSS + +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! + SUBROUTINE P_DQ_VRABEC_GROSS( zdq, zdqz, zdqz2, zdqz3 ) +! + USE PARAMETERS, ONLY: PI, KBOL + USE EOS_VARIABLES, ONLY: nc, ncomp, uij, parame, mseg, sig_ij, rho, eta, x, t + USE EOS_CONSTANTS, ONLY: dqp2, dqp3, dqp4 + IMPLICIT NONE +! +! ---------------------------------------------------------------------- + REAL, INTENT(IN OUT) :: zdq, zdqz, zdqz2, zdqz3 +! ---------------------------------------------------------------------- + INTEGER :: i, j, k, m + REAL :: factor2, factor3, z3 + REAL :: xijfa, xijkfa, eij + REAL :: fdqdr, fdqd2, fdqd3, fdqd4 + REAL :: fdq2, fdq2z, fdq2z2, fdq2z3, fdq2z4 + REAL :: fdq3, fdq3z, fdq3z2, fdq3z3, fdq3z4 + REAL, DIMENSION(nc) :: my2dd, myfac, qq2, q_fac + REAL, DIMENSION(nc,nc) :: Idq2, Idq2z, Idq2z2, Idq2z3, Idq2z4 + REAL, DIMENSION(nc,nc) :: Idq4, Idq4z, Idq4z2, Idq4z3, Idq4z4 + REAL, DIMENSION(nc,nc,nc) :: Idq3, Idq3z, Idq3z2, Idq3z3, Idq3z4 +! ---------------------------------------------------------------------- + + zdq = 0.0 + zdqz = 0.0 + zdqz2 = 0.0 + zdqz3 = 0.0 + z3 = eta + DO i = 1, ncomp + my2dd(i) = (parame(i,6))**2 *1.E-49 / (uij(i,i)*KBOL*mseg(i)*sig_ij(i,i)**3 *1.E-30) + myfac(i) = parame(i,3)/t*parame(i,2)**4 *my2dd(i) + qq2(i) = (parame(i,7))**2 *1.E-69 / (uij(i,i)*kbol*mseg(i)*sig_ij(i,i)**5 *1.E-50) + q_fac(i) = parame(i,3)/t*parame(i,2)**4 *qq2(i) + END DO + + + DO i = 1, ncomp + DO j = 1, ncomp + Idq2(i,j) = 0.0 + Idq4(i,j) = 0.0 + Idq2z(i,j) = 0.0 + Idq4z(i,j) = 0.0 + Idq2z2(i,j) = 0.0 + Idq4z2(i,j) = 0.0 + Idq2z3(i,j) = 0.0 + Idq4z3(i,j) = 0.0 + Idq2z4(i,j) = 0.0 + Idq4z4(i,j) = 0.0 + IF (myfac(i) /= 0.0 .AND. q_fac(j) /= 0.0) THEN + DO m = 0, 4 + Idq2(i,j) =Idq2(i,j) + dqp2(i,j,m)*z3**(m+1) + Idq4(i,j) =Idq4(i,j) + dqp4(i,j,m)*z3**(m+1) + Idq2z(i,j) =Idq2z(i,j) +dqp2(i,j,m)*REAL(m+1)*z3**m + Idq4z(i,j) =Idq4z(i,j) +dqp4(i,j,m)*REAL(m+1)*z3**m + Idq2z2(i,j)=Idq2z2(i,j)+dqp2(i,j,m)*REAL((m+1)*m)*z3**(m-1) + Idq4z2(i,j)=Idq4z2(i,j)+dqp4(i,j,m)*REAL((m+1)*m)*z3**(m-1) + Idq2z3(i,j)=Idq2z3(i,j)+dqp2(i,j,m)*REAL((m+1)*m*(m-1)) *z3**(m-2) + Idq4z3(i,j)=Idq4z3(i,j)+dqp4(i,j,m)*REAL((m+1)*m*(m-1)) *z3**(m-2) + Idq2z4(i,j)=Idq2z4(i,j)+dqp2(i,j,m)*REAL((m+1)*m*(m-1)*(m-2)) *z3**(m-3) + Idq4z4(i,j)=Idq4z4(i,j)+dqp4(i,j,m)*REAL((m+1)*m*(m-1)*(m-2)) *z3**(m-3) + END DO + DO k = 1, ncomp + Idq3(i,j,k) = 0.0 + Idq3z(i,j,k) = 0.0 + Idq3z2(i,j,k) = 0.0 + Idq3z3(i,j,k) = 0.0 + Idq3z4(i,j,k) = 0.0 + IF (myfac(k) /= 0.0.OR.q_fac(k) /= 0.0) THEN + DO m = 0, 4 + Idq3(i,j,k) =Idq3(i,j,k) + dqp3(i,j,k,m)*z3**(m+2) + Idq3z(i,j,k)=Idq3z(i,j,k)+dqp3(i,j,k,m)*REAL(m+2)*z3**(m+1) + Idq3z2(i,j,k)=Idq3z2(i,j,k)+dqp3(i,j,k,m)*REAL((m+2)*(m+1)) *z3**m + Idq3z3(i,j,k)=Idq3z3(i,j,k)+dqp3(i,j,k,m)*REAL((m+2)*(m+1)*m) *z3**(m-1) + Idq3z4(i,j,k)=Idq3z4(i,j,k)+dqp3(i,j,k,m) & + *REAL((m+2)*(m+1)*m*(m-1)) *z3**(m-2) + END DO + END IF + END DO + + END IF + END DO + END DO + + factor2= -9.0/4.0*PI *rho/z3 + factor3= PI**2 * (rho/z3)**2 + + fdq2 = 0.0 + fdq2z = 0.0 + fdq2z2 = 0.0 + fdq2z3 = 0.0 + fdq2z4 = 0.0 + fdq3 = 0.0 + fdq3z = 0.0 + fdq3z2 = 0.0 + fdq3z3 = 0.0 + fdq3z4 = 0.0 + DO i = 1, ncomp + DO j = 1, ncomp + IF (myfac(i) /= 0.0 .AND. q_fac(j) /= 0.0) THEN + xijfa =x(i)*myfac(i) * x(j)*q_fac(j) /sig_ij(i,j)**5 + eij = (parame(i,3)*parame(j,3))**0.5 + fdq2= fdq2 +factor2*xijfa*(Idq2(i,j) +eij/t*Idq4(i,j) ) + fdq2z =fdq2z +factor2*xijfa*(Idq2z(i,j) +eij/t*Idq4z(i,j) ) + fdq2z2=fdq2z2+factor2*xijfa*(Idq2z2(i,j)+eij/t*Idq4z2(i,j)) + fdq2z3=fdq2z3+factor2*xijfa*(Idq2z3(i,j)+eij/t*Idq4z3(i,j)) + fdq2z4=fdq2z4+factor2*xijfa*(Idq2z4(i,j)+eij/t*Idq4z4(i,j)) + DO k = 1, ncomp + IF (myfac(k) /= 0.0.OR.q_fac(k) /= 0.0) THEN + xijkfa=x(i)*x(j)*x(k)/(sig_ij(i,j)*sig_ij(i,k)*sig_ij(j,k))**2 & + *( myfac(i)*q_fac(j)*myfac(k) + myfac(i)*q_fac(j)*q_fac(k)*1.193735 ) + fdq3 =fdq3 + factor3 * xijkfa*Idq3(i,j,k) + fdq3z =fdq3z + factor3 * xijkfa*Idq3z(i,j,k) + fdq3z2=fdq3z2 + factor3 * xijkfa*Idq3z2(i,j,k) + fdq3z3=fdq3z3 + factor3 * xijkfa*Idq3z3(i,j,k) + fdq3z4=fdq3z4 + factor3 * xijkfa*Idq3z4(i,j,k) + END IF + END DO + END IF + END DO + END DO + IF (fdq2 < -1.E-50 .AND. fdq3 /= 0.0 .AND. fdq2z /= 0.0 .AND. fdq3z /= 0.0) THEN + fdqdr = fdq2* (fdq2*fdq2z - 2.0*fdq3*fdq2z+fdq2*fdq3z) /(fdq2-fdq3)**2 + fdqd2= (2.0*fdq2*fdq2z*fdq2z +fdq2*fdq2*fdq2z2 & + -2.0*fdq2z**2 *fdq3-2.0*fdq2*fdq2z2*fdq3+fdq2*fdq2*fdq3z2) & + /(fdq2-fdq3)**2 + fdqdr * 2.0*(fdq3z-fdq2z)/(fdq2-fdq3) + fdqd3=(2.0*fdq2z**3 +6.0*fdq2*fdq2z*fdq2z2+fdq2*fdq2*fdq2z3 & + -6.0*fdq2z*fdq2z2*fdq3-2.0*fdq2z**2 *fdq3z & + -2.0*fdq2*fdq2z3*fdq3 -2.0*fdq2*fdq2z2*fdq3z & + +2.0*fdq2*fdq2z*fdq3z2+fdq2*fdq2*fdq3z3) /(fdq2-fdq3)**2 & + + 2.0/(fdq2-fdq3)* ( 2.0*fdqd2*(fdq3z-fdq2z) & + + fdqdr*(fdq3z2-fdq2z2) - fdqdr/(fdq2-fdq3)*(fdq3z-fdq2z)**2 ) + fdqd4=( 12.0*fdq2z**2 *fdq2z2+6.0*fdq2*fdq2z2**2 & + +8.0*fdq2*fdq2z*fdq2z3+fdq2*fdq2*fdq2z4-6.0*fdq2z2**2 *fdq3 & + -12.0*fdq2z*fdq2z2*fdq3z -8.0*fdq2z*fdq2z3*fdq3 & + -2.0*fdq2*fdq2z4*fdq3-4.0*fdq2*fdq2z3*fdq3z & + +4.0*fdq2*fdq2z*fdq3z3+fdq2**2 *fdq3z4 ) /(fdq2-fdq3)**2 & + + 6.0/(fdq2-fdq3)* ( fdqd3*(fdq3z-fdq2z) & + -fdqd2/(fdq2-fdq3)*(fdq3z-fdq2z)**2 & + - fdqdr/(fdq2-fdq3)*(fdq3z-fdq2z)*(fdq3z2-fdq2z2) & + + fdqd2*(fdq3z2-fdq2z2) +1.0/3.0*fdqdr*(fdq3z3-fdq2z3) ) + zdq = fdqdr*eta + zdqz = fdqd2*eta + fdqdr + zdqz2 = fdqd3*eta + 2.0* fdqd2 + zdqz3 = fdqd4*eta + 3.0* fdqd3 + END IF + + +END SUBROUTINE P_DQ_VRABEC_GROSS + + + +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! + SUBROUTINE F_pert_theory ( fdsp ) +! + USE EOS_VARIABLES, ONLY: nc, PI, ncomp, t, p, rho, eta, & + x, z0t, mseg, parame, order1, order2 + USE EOS_NUMERICAL_DERIVATIVES, ONLY: disp_term + USE DFT_MODULE + IMPLICIT NONE +! +!--------------------------------------------------------------------- + REAL, INTENT(IN OUT) :: fdsp +!--------------------------------------------------------------------- + REAL :: I1, I2 + REAL :: z3, zms, c1_con, m_mean +!--------------------------------------------------------------------- + + ! caution: positive sign of correlation integral is used here ! + ! (the Helmholtz energy terms are written with a negative sign, while I1 and I2 are positive) + + IF (disp_term == 'PT1') THEN + + CALL f_dft ( I1, I2) + c1_con = 0.0 + I2 = 0.0 + fdsp = + ( - 2.0*PI*rho*I1*order1 ) + + ELSEIF (disp_term == 'PT2') THEN + + CALL f_dft ( I1, I2) + z3 = eta + zms = 1.0 - z3 + m_mean = z0t / ( PI / 6.0 ) + c1_con = 1.0/ ( 1.0 + m_mean*(8.0*z3-2.0*z3**2 )/zms**4 & + + (1.0 - m_mean)*( 20.0*z3 -27.0*z3**2 +12.0*z3**3 -2.0*z3**4 ) & + /(zms*(2.0-z3))**2 ) + fdsp = + ( - 2.0*PI*rho*I1*order1 - PI*rho*c1_con*m_mean*I2*order2 ) + + ELSEIF (disp_term == 'PT_MIX') THEN + + CALL f_pert_theory_mix ( fdsp ) + + ELSEIF (disp_term == 'PT_MF') THEN + + ! mean field theory + I1 = - ( - 8.0/9.0 - 4.0/9.0*(rc**(-9) -3.0*rc**(-3) ) - tau_cut/3.0*(rc**3 -1.0) ) + fdsp = + ( - 2.0*PI*rho*I1*order1 ) + write (*,*) 'caution: not thoroughly checked and tested' + + ELSE + write (*,*) 'define the type of perturbation theory' + stop + END IF + + ! I1 = I1 + 4.0/9.0*(2.5**-9 -3.0*2.5**-3 ) + ! fdsp = + ( - 2.0*PI*rho*I1*order1 - PI*rho*c1_con*m_mean*I2*order2 ) + + END SUBROUTINE F_pert_theory + + + + +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! + SUBROUTINE f_pert_theory_mix ( fdsp ) +! + USE EOS_VARIABLES, ONLY: nc, PI, ncomp, t, rho, eta, x, parame, mseg, dhs, sig_ij, uij + USE DFT_MODULE + IMPLICIT NONE +! +! ---------------------------------------------------------------------- + REAL, INTENT(IN OUT) :: fdsp +! +! ---------------------------------------------------------------------- + INTEGER :: k, ih + INTEGER :: l, m + REAL :: z3 + REAL :: ua, ua_c, rm + REAL, DIMENSION(nc,nc) :: I1 + REAL :: int10, int11 + REAL :: d_ij, dzr_local + REAL :: rad, xg, rdf + REAL :: dg_dz3, dg_dr + ! REAL :: intgrid(0:5000),intgri2(0:5000), utri(5000),I1_spline +! ---------------------------------------------------------------------- + +! -----constants-------------------------------------------------------- + ua_c = 4.0 * ( rc**(-12) - rc**(-6) ) + rm = 2.0**(1.0/6.0) + + I1(:,:) = 0.0 + + DO l = 1, ncomp + DO m = 1, ncomp + + rad = rc + + int10 = rc * rc * ua_c + ! intgrid(0)= int10 + + k = 0 + ih = 85 + + DO WHILE ( rad /= 1.0 ) + + dzr_local = dzr + IF ( rad - dzr_local <= 1.0 ) dzr_local = rad - 1.0 + + rad = rad - dzr_local + + k = k + 1 + + d_ij = 0.5*(dhs(l)+dhs(m)) / sig_ij(l,m) ! dimensionless effective hs-diameter d(T)/sig + xg = rad / d_ij + z3 = eta + rdf = 1.0 + dg_dz3 = 0.0 + IF ( rad <= rg ) THEN + IF ( l == 1 .AND. m == 1 ) CALL BI_CUB_SPLINE (z3,xg,ya_11,x1a_11,x2a_11,y1a_11,y2a_11,y12a_11, & + c_bicub_11,rdf,dg_dz3,dg_dr,den_step,ih,k) + IF ( l /= m ) CALL BI_CUB_SPLINE (z3,xg,ya_12,x1a_12,x2a_12,y1a_12,y2a_12,y12a_12, & + c_bicub_12,rdf,dg_dz3,dg_dr,den_step,ih,k) + IF ( l == 2 .AND. m == 2 ) CALL BI_CUB_SPLINE (z3,xg,ya_22,x1a_22,x2a_22,y1a_22,y2a_22,y12a_22, & + c_bicub_22,rdf,dg_dz3,dg_dr,den_step,ih,k) + END IF + + ua = 4.0 * ( rad**(-12) - rad**(-6) ) + + int11 = rdf * rad * rad * ua + I1(l,m) = I1(l,m) + dzr_local * ( int11 + int10 ) / 2.0 + + int10 = int11 + ! intgrid(k)= int11 + + END DO + + ! stepno = k + ! CALL SPLINE_PARA (dzr,intgrid,utri,stepno) + ! CALL SPLINE_INT (I1_spline,dzr,intgrid,utri,stepno) + + + ! caution: 1st order integral is in F_EOS.f defined with negative sign + ! --------------------------------------------------------------- + ! cut-off corrections + ! --------------------------------------------------------------- + ! I1(l,m) = I1(l,m) + ( 4.0/9.0 * rc**-9 - 4.0/3.0 * rc**-3 ) + ! I2(l,m) = I2(l,m) + 16.0/21.0 * rc**-21 - 32.0/15.0 * rc**-15 + 16.0/9.0 * rc**-9 + + END DO + END DO + + + fdsp = 0.0 + DO l = 1, ncomp + DO m = 1, ncomp + fdsp = fdsp + 2.0*PI*rho*x(l)*x(m)* mseg(l)*mseg(m)*sig_ij(l,m)**3 * uij(l,m)/t *I1(l,m) + ! ( 2.0*PI*rho*I1*order1 - PI*rho*c1_con*m_mean*I2*order2 ) + END DO + END DO + + +!!$ IF (disp_term == 'PT1') THEN +!!$ c1_con = 0.0 +!!$ I2 = 0.0 +!!$ ELSEIF (disp_term == 'PT2') THEN +!!$ zms = 1.0 - z3 +!!$ c1_con = 1.0/ ( 1.0 + m_mean*(8.0*z3-2.0*z3**2 )/zms**4 & +!!$ + (1.0 - m_mean)*( 20.0*z3 -27.0*z3**2 +12.0*z3**3 -2.0*z3**4 ) & +!!$ /(zms*(2.0-z3))**2 ) +!!$ ELSE +!!$ write (*,*) 'define the type of perturbation theory' +!!$ stop +!!$ END IF + + +END SUBROUTINE f_pert_theory_mix + + +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! + SUBROUTINE mu_pert_theory_mix ( mu_dsp ) +! + USE EOS_VARIABLES, ONLY: nc, PI, ncomp, t, rho, eta, x, parame, mseg, dhs, sig_ij, uij + USE DFT_MODULE + IMPLICIT NONE +! +! ---------------------------------------------------------------------- + REAL, INTENT(IN OUT) :: mu_dsp(nc) +! +! ---------------------------------------------------------------------- + INTEGER :: k, ih + INTEGER :: l, m + REAL :: z3 + REAL :: ua, ua_c, rm + REAL, DIMENSION(nc,nc) :: I1, I2 + REAL :: int1_0, int1_1, int2_0, int2_1 + REAL :: d_ij, dzr_local + REAL :: rad, xg, rdf + REAL :: dg_dz3, dg_dr + REAL :: term1(nc), term2 + ! REAL :: intgrid(0:5000),intgri2(0:5000), utri(5000),I1_spline +! ---------------------------------------------------------------------- + +! -----constants-------------------------------------------------------- + ua_c = 4.0 * ( rc**(-12) - rc**(-6) ) + rm = 2.0**(1.0/6.0) + + I1(:,:) = 0.0 + I2(:,:) = 0.0 + + DO l = 1, ncomp + + term1(l) = 0.0 + + DO m = 1, ncomp + + rad = rc + + int1_0 = rc * rc * ua_c + int2_0 = 0.0 + + k = 0 + ih = 85 + + DO WHILE ( rad /= 1.0 ) + + dzr_local = dzr + IF ( rad - dzr_local <= 1.0 ) dzr_local = rad - 1.0 + + rad = rad - dzr_local + k = k + 1 + + d_ij = 0.5*(dhs(l)+dhs(m)) / sig_ij(l,m) ! dimensionless effective hs-diameter d(T)/sig + xg = rad / d_ij + z3 = eta + rdf = 1.0 + dg_dz3 = 0.0 + IF ( rad <= rg ) THEN + IF ( l == 1 .AND. m == 1 ) CALL BI_CUB_SPLINE (z3,xg,ya_11,x1a_11,x2a_11,y1a_11,y2a_11,y12a_11, & + c_bicub_11,rdf,dg_dz3,dg_dr,den_step,ih,k) + IF ( l /= m ) CALL BI_CUB_SPLINE (z3,xg,ya_12,x1a_12,x2a_12,y1a_12,y2a_12,y12a_12, & + c_bicub_12,rdf,dg_dz3,dg_dr,den_step,ih,k) + IF ( l == 2 .AND. m == 2 ) CALL BI_CUB_SPLINE (z3,xg,ya_22,x1a_22,x2a_22,y1a_22,y2a_22,y12a_22, & + c_bicub_22,rdf,dg_dz3,dg_dr,den_step,ih,k) + END IF + + ua = 4.0 * ( rad**(-12) - rad**(-6) ) + + int1_1 = rdf * rad * rad * ua + int2_1 = dg_dz3 * rad * rad * ua + I1(l,m) = I1(l,m) + dzr_local * ( int1_1 + int1_0 ) / 2.0 + I2(l,m) = I2(l,m) + dzr_local * ( int2_1 + int2_0 ) / 2.0 + + int1_0 = int1_1 + int2_0 = int2_1 + + term1(l) = term1(l) +4.0*PI*rho*x(m)* mseg(l)*mseg(m) *sig_ij(l,m)**3 *uij(l,m)/t* dzr_local*(int1_1+int1_0)/2.0 + + END DO + + END DO + END DO + + + ! DO l = 1, ncomp + ! term1(l) = 0.0 + ! DO m = 1, ncomp + ! term1(l) = term1(l) + 4.0*PI*rho*x(m)* mseg(l)*mseg(m) * sig_ij(l,m)**3 * uij(l,m)/t *I1(l,m) + ! END DO + ! END DO + + term2 = 0.0 + DO l = 1, ncomp + DO m = 1, ncomp + term2 = term2 + 2.0*PI*rho*x(l) * rho*x(m)* mseg(l)*mseg(m) * sig_ij(l,m)**3 * uij(l,m)/t *I2(l,m) + END DO + END DO + + DO l = 1, ncomp + mu_dsp(l) = term1(l) + term2 * PI/ 6.0 * mseg(l)*dhs(l)**3 + END DO + +END SUBROUTINE mu_pert_theory_mix + + +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! + SUBROUTINE F_DD_GROSS_VRABEC( fdd ) +! + USE PARAMETERS, ONLY: PI, KBOL + USE EOS_VARIABLES, ONLY: nc, ncomp, uij, parame, mseg, sig_ij, rho, eta, x, t + USE EOS_CONSTANTS, ONLY: ddp2, ddp3, ddp4 + IMPLICIT NONE +! +! ---------------------------------------------------------------------- + REAL, INTENT(IN OUT) :: fdd +! ---------------------------------------------------------------------- + INTEGER :: i, j, k, m + INTEGER :: ddit, ddmax + REAL :: factor2, factor3 + REAL :: xijfa, xijkfa, xijf_j, xijkf_j, eij + REAL :: fdd2, fdd3 + REAL, DIMENSION(nc) :: my2dd, my0, alph_tst, z1dd, z2dd, dderror + REAL, DIMENSION(nc) :: fdd2m, fdd3m, fdd2m2, fdd3m2, fddm, fddm2 + REAL, DIMENSION(nc,nc) :: Idd2, Idd4 + REAL, DIMENSION(nc,nc,nc) :: Idd3 +! ---------------------------------------------------------------------- + + fdd = 0.0 + ddit = 0 + ddmax = 0 ! value assigned, if polarizable compound is present + fddm(:) = 0.0 + DO i = 1, ncomp + IF ( uij(i,i) == 0.0 ) write (*,*) 'F_DD_GROSS_VRABEC: do not use dimensionless units' + IF ( uij(i,i) == 0.0 ) stop + my2dd(i) = (parame(i,6))**2 *1.E-49 /(uij(i,i)*kbol* mseg(i)*sig_ij(i,i)**3 *1.E-30) + alph_tst(i) = parame(i,11) / (mseg(i)*sig_ij(i,i)**3 ) * t/parame(i,3) + IF ( alph_Tst(i) /= 0.0 ) ddmax = 25 ! set maximum number of polarizable RGT-iterations + z1dd(i) = my2dd(i) + 3.0*alph_tst(i) + z2dd(i) = 3.0*alph_tst(i) + my0(i) = my2dd(i) + END DO + + DO i = 1, ncomp + DO j = 1, ncomp + Idd2(i,j) = 0.0 + Idd4(i,j) = 0.0 + ! IF (parame(i,6).NE.0.0 .AND. parame(j,6).NE.0.0) THEN + DO m = 0, 4 + Idd2(i,j) = Idd2(i,j) + ddp2(i,j,m)*eta**m + Idd4(i,j) = Idd4(i,j) + ddp4(i,j,m)*eta**m + END DO + DO k = 1, ncomp + Idd3(i,j,k) = 0.0 + ! IF (parame(k,6).NE.0.0) THEN + DO m = 0, 4 + Idd3(i,j,k) = Idd3(i,j,k) + ddp3(i,j,k,m)*eta**m + END DO + ! ENDIF + END DO + ! ENDIF + END DO + END DO + + factor2 = -PI *rho + factor3 = -4.0/3.0*PI**2 * rho**2 + +9 CONTINUE + + fdd2m(:) = 0.0 + fdd2m2(:) = 0.0 + fdd3m(:) = 0.0 + fdd3m2(:) = 0.0 + fdd2 = 0.0 + fdd3 = 0.0 + DO i = 1, ncomp + DO j = 1, ncomp + ! IF (parame(i,6).NE.0.0 .AND. parame(j,6).NE.0.0) THEN + xijfa =x(i)*parame(i,3)/t*parame(i,2)**3 * x(j)*parame(j,3)/t*parame(j,2)**3 & + /((parame(i,2)+parame(j,2))/2.0)**3 * (z1dd(i)*z1dd(j)-z2dd(i)*z2dd(j)) ! * (1.0-lij(i,j)) + eij = (parame(i,3)*parame(j,3))**0.5 + fdd2= fdd2 + factor2 * xijfa * ( Idd2(i,j) + eij/t*Idd4(i,j) ) + xijf_j = parame(i,3)/t*parame(i,2)**3 *x(j)*parame(j,3)/t*parame(j,2)**3 & + /((parame(i,2)+parame(j,2))/2.0)**3 ! * (1.0-lij(i,j)) + fdd2m(i)=fdd2m(i)+4.0*SQRT(my2dd(i))*z1dd(j)*factor2* xijf_j *(Idd2(i,j)+eij/t*Idd4(i,j)) + fdd2m2(i)=fdd2m2(i) + 4.0*z1dd(j)*factor2* xijf_j *(Idd2(i,j)+eij/t*Idd4(i,j)) + IF (j == i) fdd2m2(i) =fdd2m2(i) +8.0*factor2* xijf_j*my2dd(i) *(Idd2(i,j)+eij/t*Idd4(i,j)) + DO k = 1, ncomp + ! IF (parame(k,6).NE.0.0) THEN + xijkfa = x(i)*parame(i,3)/t*parame(i,2)**3 *x(j)*parame(j,3)/t*parame(j,2)**3 & + *x(k)*parame(k,3)/t*parame(k,2)**3 / ((parame(i,2)+parame(j,2))/2.0) & + /((parame(i,2)+parame(k,2))/2.0) / ((parame(j,2)+parame(k,2))/2.0) & + *(z1dd(i)*z1dd(j)*z1dd(k)-z2dd(i)*z2dd(j)*z2dd(k)) + ! *(1.0-lij(i,j))*(1.0-lij(i,k))*(1.0-lij(j,k)) + fdd3 = fdd3 + factor3 * xijkfa * Idd3(i,j,k) + xijkf_j = parame(i,3)/t*parame(i,2)**3 *x(j)*parame(j,3)/t*parame(j,2)**3 & + *x(k)*parame(k,3)/t*parame(k,2)**3 /((parame(i,2)+parame(j,2))/2.0) & + /((parame(i,2)+parame(k,2))/2.0) /((parame(j,2)+parame(k,2))/2.0) + ! *(1.0-lij(i,j))*(1.0-lij(i,k))*(1.0-lij(j,k)) + fdd3m(i)=fdd3m(i)+6.0*factor3*SQRT(my2dd(i))*z1dd(j)*z1dd(k) *xijkf_j*Idd3(i,j,k) + fdd3m2(i)=fdd3m2(i)+6.0*factor3*z1dd(j)*z1dd(k) *xijkf_j*Idd3(i,j,k) + IF(j == i) fdd3m2(i) =fdd3m2(i)+24.0*factor3*my2dd(i)*z1dd(k) *xijkf_j*Idd3(i,j,k) + ! ENDIF + END DO + ! ENDIF + END DO + END DO + + IF (fdd2 < -1.E-50 .AND. fdd3 /= 0.0) THEN + fdd = fdd2 / ( 1.0 - fdd3/fdd2 ) + IF ( ddmax /= 0 ) THEN + DO i = 1, ncomp + ddit = ddit + 1 + fddm(i) =fdd2*(fdd2*fdd2m(i) -2.0*fdd3*fdd2m(i)+fdd2*fdd3m(i)) /(fdd2-fdd3)**2 + fddm2(i) = fdd2m(i) * (fdd2*fdd2m(i)-2.0*fdd3*fdd2m(i) +fdd2*fdd3m(i)) / (fdd2-fdd3)**2 & + + fdd2*(fdd2*fdd2m2(i) -2.0*fdd3*fdd2m2(i)+fdd2m(i)**2 & + -fdd2m(i)*fdd3m(i) +fdd2*fdd3m2(i)) / (fdd2-fdd3)**2 & + - 2.0*fdd2*(fdd2*fdd2m(i) -2.0*fdd3*fdd2m(i) +fdd2*fdd3m(i)) /(fdd2-fdd3)**3 & + *(fdd2m(i)-fdd3m(i)) + dderror(i)= SQRT( my2dd(i) ) - SQRT( my0(i) ) + alph_Tst(i)*fddm(i) + my2dd(i) = ( SQRT( my2dd(i) ) - dderror(i) / (1.0+alph_Tst(i)*fddm2(i)) )**2 + z1dd(i) = my2dd(i) + 3.0 * alph_Tst(i) + ENDDO + DO i = 1, ncomp + IF (ABS(dderror(i)) > 1.E-11 .AND. ddit < ddmax) GOTO 9 + ENDDO + fdd = fdd + SUM( 0.5*x(1:ncomp)*alph_Tst(1:ncomp)*fddm(1:ncomp)**2 ) + ENDIF + END IF + + +END SUBROUTINE F_DD_GROSS_VRABEC + + + +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! + SUBROUTINE F_QQ_GROSS( fqq ) +! + USE PARAMETERS, ONLY: PI, KBOL + USE EOS_VARIABLES, ONLY: nc, ncomp, uij, parame, mseg, sig_ij, rho, eta, x, t + USE EOS_CONSTANTS, ONLY: qqp2, qqp3, qqp4 + IMPLICIT NONE +! +! ---------------------------------------------------------------------- + REAL, INTENT(IN OUT) :: fqq +! ---------------------------------------------------------------------- + INTEGER :: i, j, k, m + REAL :: factor2, factor3 + REAL :: xijfa, xijkfa, eij + REAL :: fqq2, fqq3 + REAL, DIMENSION(nc) :: qq2 + REAL, DIMENSION(nc,nc) :: Iqq2, Iqq4 + REAL, DIMENSION(nc,nc,nc) :: Iqq3 +! ---------------------------------------------------------------------- + + + fqq = 0.0 + DO i = 1, ncomp + qq2(i) = (parame(i,7))**2 *1.E-69 / (uij(i,i)*kbol*mseg(i)*sig_ij(i,i)**5 *1.E-50) + END DO + + DO i = 1, ncomp + DO j = 1, ncomp + Iqq2(i,j) = 0.0 + Iqq4(i,j) = 0.0 + IF (parame(i,7) /= 0.0 .AND. parame(j,7) /= 0.0) THEN + DO m = 0, 4 + Iqq2(i,j) = Iqq2(i,j) + qqp2(i,j,m)*eta**m + Iqq4(i,j) = Iqq4(i,j) + qqp4(i,j,m)*eta**m + END DO + DO k = 1, ncomp + Iqq3(i,j,k) = 0.0 + IF (parame(k,7) /= 0.0) THEN + DO m = 0, 4 + Iqq3(i,j,k) = Iqq3(i,j,k) + qqp3(i,j,k,m)*eta**m + END DO + END IF + END DO + END IF + END DO + END DO + + factor2 = -9.0/16.0*PI *rho + factor3 = 9.0/16.0*PI**2 * rho**2 + + fqq2 = 0.0 + fqq3 = 0.0 + DO i = 1, ncomp + DO j = 1, ncomp + IF (parame(i,7) /= 0.0 .AND. parame(j,7) /= 0.0) THEN + xijfa=x(i)*uij(i,i)*qq2(i)*sig_ij(i,i)**5 /t & + *x(j)*uij(j,j)*qq2(j)*sig_ij(j,j)**5 /t/sig_ij(i,j)**7.0 + eij = (parame(i,3)*parame(j,3))**0.5 + fqq2= fqq2 +factor2* xijfa * (Iqq2(i,j)+eij/t*Iqq4(i,j)) + DO k = 1, ncomp + IF (parame(k,7) /= 0.0) THEN + xijkfa=x(i)*uij(i,i)*qq2(i)*sig_ij(i,i)**5 /t/sig_ij(i,j)**3 & + *x(j)*uij(j,j)*qq2(j)*sig_ij(j,j)**5 /t/sig_ij(i,k)**3 & + *x(k)*uij(k,k)*qq2(k)*sig_ij(k,k)**5 /t/sig_ij(j,k)**3 + fqq3 = fqq3 + factor3 * xijkfa * Iqq3(i,j,k) + END IF + END DO + END IF + END DO + END DO + + IF ( fqq2 < -1.E-50 .AND. fqq3 /= 0.0 ) THEN + fqq = fqq2 / ( 1.0 - fqq3/fqq2 ) + END IF + + + +END SUBROUTINE F_QQ_GROSS + +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! + SUBROUTINE F_DQ_VRABEC_GROSS( fdq ) +! + USE PARAMETERS, ONLY: PI, KBOL + USE EOS_VARIABLES, ONLY: nc, ncomp, uij, parame, mseg, sig_ij, rho, eta, x, t + USE EOS_CONSTANTS, ONLY: dqp2, dqp3, dqp4 + IMPLICIT NONE +! +! ---------------------------------------------------------------------- + REAL, INTENT(IN OUT) :: fdq +! ---------------------------------------------------------------------- + INTEGER :: i, j, k, m + REAL :: factor2, factor3 + REAL :: xijfa, xijkfa, eij + REAL :: fdq2, fdq3 + REAL, DIMENSION(nc) :: my2dd, myfac, qq2, q_fac + REAL, DIMENSION(nc,nc) :: Idq2, Idq4 + REAL, DIMENSION(nc,nc,nc) :: Idq3 +! ---------------------------------------------------------------------- + + + fdq = 0.0 + DO i = 1, ncomp + my2dd(i) = (parame(i,6))**2 *1.E-49 /(uij(i,i)*kbol* mseg(i)*sig_ij(i,i)**3 *1.E-30) + myfac(i) = parame(i,3)/t*parame(i,2)**4 *my2dd(i) + ! myfac(i)=parame(i,3)/T*parame(i,2)**4 *my2dd_renormalized(i) + qq2(i) = (parame(i,7))**2 *1.E-69 / (uij(i,i)*kbol*mseg(i)*sig_ij(i,i)**5 *1.E-50) + q_fac(i) = parame(i,3)/t*parame(i,2)**4 *qq2(i) + END DO + + DO i = 1, ncomp + DO j = 1, ncomp + Idq2(i,j) = 0.0 + Idq4(i,j) = 0.0 + IF (myfac(i) /= 0.0 .AND. q_fac(j) /= 0.0) THEN + DO m = 0, 4 + Idq2(i,j) = Idq2(i,j) + dqp2(i,j,m)*eta**m + Idq4(i,j) = Idq4(i,j) + dqp4(i,j,m)*eta**m + END DO + DO k = 1, ncomp + Idq3(i,j,k) = 0.0 + IF (myfac(k) /= 0.0 .OR. q_fac(k) /= 0.0) THEN + DO m = 0, 4 + Idq3(i,j,k) = Idq3(i,j,k) + dqp3(i,j,k,m)*eta**m + END DO + END IF + END DO + END IF + END DO + END DO + + factor2 = -9.0/4.0 * PI *rho + factor3 = PI**2 * rho**2 + + fdq2 = 0.0 + fdq3 = 0.0 + DO i = 1, ncomp + DO j = 1, ncomp + IF (myfac(i) /= 0.0 .AND. q_fac(j) /= 0.0) THEN + xijfa = x(i)*myfac(i) * x(j)*q_fac(j) /sig_ij(i,j)**5 + eij = (parame(i,3)*parame(j,3))**0.5 + fdq2 = fdq2 +factor2* xijfa*(Idq2(i,j)+eij/t*Idq4(i,j)) + DO k = 1, ncomp + IF (myfac(k) /= 0.0 .OR. q_fac(k) /= 0.0) THEN + xijkfa=x(i)*x(j)*x(k)/(sig_ij(i,j)*sig_ij(i,k)*sig_ij(j,k))**2 & + *( myfac(i)*q_fac(j)*myfac(k) + myfac(i)*q_fac(j)*q_fac(k)*1.1937350 ) + fdq3 = fdq3 + factor3*xijkfa*Idq3(i,j,k) + END IF + END DO + END IF + END DO + END DO + + IF (fdq2 < -1.E-50 .AND. fdq3 /= 0.0) THEN + fdq = fdq2 / ( 1.0 - fdq3/fdq2 ) + END IF + +END SUBROUTINE F_DQ_VRABEC_GROSS + + +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! + SUBROUTINE f_dft ( I1_dft, I2_dft ) +! + USE EOS_VARIABLES, ONLY: nc, PI, ncomp, t, rho, eta, x, mseg, parame + USE DFT_MODULE + IMPLICIT NONE +! +! ---------------------------------------------------------------------- + REAL, INTENT(OUT) :: I1_dft + REAL, INTENT(OUT) :: I2_dft +! +! ---------------------------------------------------------------------- + INTEGER :: k,ih + ! REAL :: z3 + REAL :: ua, ua_c, ua_2, ua_c_2, rm + REAL :: int10, int11, int20, int21 + REAL :: dg_drho + REAL :: rad, xg, rdf, rho_st, msegm + REAL :: sig_ij + REAL :: dg_dr, dzr_org !,rdf_d + ! REAL :: intgrid(0:NDFT),intgri2(0:NDFT) +! ---------------------------------------------------------------------- + +! -----constants-------------------------------------------------------- +msegm = parame(1,1) +rho_st = rho * parame(1,2)**3 + +ua_c = 4.0 * ( rc**(-12) - rc**(-6) ) +ua_c_2 = ua_c * ua_c +rm = 2.0**(1.0/6.0) + +int10 = rc*rc* ua_c +int20 = rc*rc* ua_c_2 +! intgrid(0)= int10 +! intgri2(0)= int20 + + +sig_ij = parame(1,2) + + +I1_dft = 0.0 +I2_dft = 0.0 +rad = rc +!dzr = dzp / 2.0 ! this line is obsolete. dzr is defined in DFT-nMF2 (dimensionless) +dzr_org= dzr +k = 0 +ih = 85 + +DO WHILE ( rad-dzr+1.E-9 >= 1.0 ) + + rad = rad - dzr + ! IF (rad <= 8.0) dzr = dzp + ! IF (rad <= rg) dzr = dzp/2.0 + k = k + 1 + xg = rad / dhs_st + ua = 4.0 * ( rad**(-12) - rad**(-6) ) + ua_2 = ua * ua + rdf = 1.0 + dg_drho = 0.0 + IF ( rad <= rg ) THEN + CALL BI_CUB_SPLINE (rho_st,xg,ya,x1a,x2a,y1a,y2a,y12a, & + c_bicub,rdf,dg_drho,dg_dr,den_step,ih,k) + END IF + + int11 = rdf*rad*rad* ua + int21 = rdf*rad*rad* ua_2 + I1_dft= I1_dft + dzr*(int11+int10)/2.0 + I2_dft= I2_dft + dzr*(int21+int20)/2.0 + int10 = int11 + int20 = int21 + +END DO + +dzr = dzr_org + +! stepno = k +! CALL SPLINE_PARA (dzr,intgrid,utri,stepno) +! CALL SPLINE_INT (I1,dzr,intgrid,utri,stepno) + +! caution: 1st order integral is in F_EOS.f defined with negative sign +I1_dft= - I1_dft - ( 4.0/9.0 * rc**(-9) - 4.0/3.0 * rc**(-3) ) + +! CALL SPLINE_PARA (dzr,intgri2,utri,stepno) +! CALL SPLINE_INT (I2,dzr,intgri2,utri,stepno) + +I2_dft = I2_dft + 16.0/21.0 * rc**(-21) - 32.0/15.0 * rc**(-15) + 16.0/9.0 * rc**(-9) + + +END SUBROUTINE f_dft + + + + +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! + REAL FUNCTION TANGENT_VALUE2 ( optpara, n ) +! SUBROUTINE TANGENT_VALUE ( fmin, optpara, n ) +! + USE BASIC_VARIABLES + USE STARTING_VALUES + IMPLICIT NONE +! +! ---------------------------------------------------------------------- + INTEGER, INTENT(IN) :: n + REAL, INTENT(IN) :: optpara(n) + !REAL, INTENT(IN) :: optpara(:) + !REAL, INTENT(IN OUT) :: fmin +! +! ---------------------------------------------------------------------- + INTEGER :: i + REAL :: lnphi(np,nc),ph_frac, gibbs_full(np),xlnx1,xlnx2 + REAL, DIMENSION(nc) :: ni_1, ni_2 +! ---------------------------------------------------------------------- + + + ! --- setting of mole fractions --------------------------------------- + DO i = 1, ncomp + IF ( optpara(i) < -300.0 ) THEN + ni_2(i) = 0.0 + ELSE + ni_2(i) = EXP( optpara(i) ) + END IF + END DO + + DO i = 1, ncomp + ni_1(i) = xif(i) - ni_2(i) + IF ( ni_2(i) > xif(i) ) THEN + ni_2(i) = xif(i) + ni_1(i) = xif(i) * 1.E-20 + ENDIF + END DO + + xi(2,1:ncomp) = ni_2(1:ncomp) / SUM( ni_2(1:ncomp) ) + lnx(2,1:ncomp) = optpara(1:ncomp) - LOG( SUM( ni_2(1:ncomp) ) ) + + ph_frac = SUM( ni_1(1:ncomp) ) + xi(1,1:ncomp) = ni_1(1:ncomp) / ph_frac + lnx(1,1:ncomp) = LOG( ni_1(1:ncomp) ) - LOG( ph_frac ) + ! write (*,'(a,4G18.8)') 'FF',(xif(i),i=1,ncomp) + ! write (*,'(a,4G18.8)') 'AA',(xi(1,i),i=1,ncomp) + ! write (*,'(a,3G18.8)') 'BB',(xi(2,i),i=1,ncomp) + + CALL fugacity (lnphi) + !CALL enthalpy_etc + + gibbs(1) = SUM( xi(1,1:ncomp) * lnphi(1,1:ncomp) ) ! dimensionless g/RT + gibbs(2) = SUM( xi(2,1:ncomp) * lnphi(2,1:ncomp) ) + + xlnx1 = SUM( xi(1,1:ncomp)*lnx(1,1:ncomp) ) ! dimensionless s/RT + xlnx2 = SUM( xi(2,1:ncomp)*lnx(2,1:ncomp) ) + + gibbs_full(1) = gibbs(1) + xlnx1 + gibbs_full(2) = gibbs(2) + xlnx2 + + TANGENT_VALUE2 = gibbs_full(1)*ph_frac + gibbs_full(2)*(1.0-ph_frac) + !fmin = gibbs_full(1)*ph_frac + gibbs_full(2)*(1.0-ph_frac) + !write (*,'(a,4G18.8)') 'TP',TANGENT_VALUE2,(lnx(1,i),i=1,ncomp) + !write (*,'(a,4G18.8)') 'al',ph_frac,(lnx(2,i), i=1,ncomp) + !write (*,*) ' ' + !pause + +END FUNCTION TANGENT_VALUE2 + + + + + + + + diff --git a/applications/PUfoam/MoDeNaModels/PolymerDensity/ExampleOfUsage/src/srcDetailedCode/getting_started_subroutines.f90 b/applications/PUfoam/MoDeNaModels/PolymerDensity/ExampleOfUsage/src/srcDetailedCode/getting_started_subroutines.f90 new file mode 100644 index 000000000..a53ec5cb0 --- /dev/null +++ b/applications/PUfoam/MoDeNaModels/PolymerDensity/ExampleOfUsage/src/srcDetailedCode/getting_started_subroutines.f90 @@ -0,0 +1,4097 @@ +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! SUBROUTINE eos_const +! +! This subroutine provides the constants of the PC-SAFT EOS. +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! + SUBROUTINE eos_const (ap,bp,dnm) +! + IMPLICIT NONE +! +! ---------------------------------------------------------------------- + REAL, INTENT(OUT) :: ap(0:6,3) + REAL, INTENT(OUT) :: bp(0:6,3) + REAL, INTENT(OUT) :: dnm(4,9) +! ---------------------------------------------------------------------- + + +! --- dispersion term constants ---------------------------------------- +ap(0,1) = 0.91056314451539 +ap(0,2) = -0.30840169182720 +ap(0,3) = -0.09061483509767 +ap(1,1) = 0.63612814494991 +ap(1,2) = 0.18605311591713 +ap(1,3) = 0.45278428063920 +ap(2,1) = 2.68613478913903 +ap(2,2) = -2.50300472586548 +ap(2,3) = 0.59627007280101 +ap(3,1) = -26.5473624914884 +ap(3,2) = 21.4197936296668 +ap(3,3) = -1.72418291311787 +ap(4,1) = 97.7592087835073 +ap(4,2) = -65.2558853303492 +ap(4,3) = -4.13021125311661 +ap(5,1) = -159.591540865600 +ap(5,2) = 83.3186804808856 +ap(5,3) = 13.7766318697211 +ap(6,1) = 91.2977740839123 +ap(6,2) = -33.7469229297323 +ap(6,3) = -8.67284703679646 + +bp(0,1) = 0.72409469413165 +bp(0,2) = -0.57554980753450 +bp(0,3) = 0.09768831158356 +bp(1,1) = 1.11913959304690 *2.0 +bp(1,2) = 0.34975477607218 *2.0 +bp(1,3) = -0.12787874908050 *2.0 +bp(2,1) = -1.33419498282114 *3.0 +bp(2,2) = 1.29752244631769 *3.0 +bp(2,3) = -3.05195205099107 *3.0 +bp(3,1) = -5.25089420371162 *4.0 +bp(3,2) = -4.30386791194303 *4.0 +bp(3,3) = 5.16051899359931 *4.0 +bp(4,1) = 5.37112827253230 *5.0 +bp(4,2) = 38.5344528930499 *5.0 +bp(4,3) = -7.76088601041257 *5.0 +bp(5,1) = 34.4252230677698 *6.0 +bp(5,2) = -26.9710769414608 *6.0 +bp(5,3) = 15.6044623461691 *6.0 +bp(6,1) = -50.8003365888685 *7.0 +bp(6,2) = -23.6010990650801 *7.0 +bp(6,3) = -4.23812936930675 *7.0 + + +! square-well fluid +! ap(1,1)= 0.79152347258784 +! ap(1,2)= -0.62269805320654 +! ap(1,3)= -0.06798823934067 +! ap(2,1)= 1.07120982251709 +! ap(2,2)= 0.48628215731716 +! ap(2,3)= 0.02837828512515 +! ap(3,1)= 0.92084839459226 +! ap(3,2)= 1.11652038059747 +! ap(3,3)= 0.09713202077943 +! ap(4,1)= -7.84708350369249 +! ap(4,2)= -2.04200599876547 +! ap(4,3)= 0.06475764015088 +! ap(5,1)= 25.90284137818050 +! ap(5,2)= 9.27791640100603 +! ap(5,3)= 0.07729792971827 +! ap(6,1)= -57.1528726997640 +! ap(6,2)= -16.8377999920957 +! ap(6,3)= 0.24883598436184 +! ap(7,1)= 42.02314637860930 +! ap(7,2)= 7.62432635016420 +! ap(7,3)= -0.72472024688888 + +! bp(1,1)= 0.79152347258784 +! bp(1,2)= -0.62269805320654 +! bp(1,3)= -0.06798823934067 +! bp(2,1)= 1.07120982251709 *2.0 +! bp(2,2)= 0.48628215731716 *2.0 +! bp(2,3)= 0.02837828512515 *2.0 +! bp(3,1)= 0.92084839459226 *3.0 +! bp(3,2)= 1.11652038059747 *3.0 +! bp(3,3)= 0.09713202077943 *3.0 +! bp(4,1)= -7.84708350369249 *4.0 +! bp(4,2)= -2.04200599876547 *4.0 +! bp(4,3)= 0.06475764015088 *4.0 +! bp(5,1)= 25.90284137818050 *5.0 +! bp(5,2)= 9.27791640100603 *5.0 +! bp(5,3)= 0.07729792971827 *5.0 +! bp(6,1)= -57.1528726997640 *6.0 +! bp(6,2)= -16.8377999920957 *6.0 +! bp(6,3)= 0.24883598436184 *6.0 +! bp(7,1)= 42.02314637860930 *7.0 +! bp(7,2)= 7.62432635016420 *7.0 +! bp(7,3)= -0.72472024688888 *7.0 + + +dnm(1,1) = -8.8043 +dnm(1,2) = +4.1646270 +dnm(1,3) = -48.203555 +dnm(1,4) = +140.43620 +dnm(1,5) = -195.23339 +dnm(1,6) = +113.51500 +dnm(2,1) = +2.9396 +dnm(2,2) = -6.0865383 +dnm(2,3) = +40.137956 +dnm(2,4) = -76.230797 +dnm(2,5) = -133.70055 +dnm(2,6) = +860.25349 +dnm(2,7) = -1535.3224 +dnm(2,8) = +1221.4261 +dnm(2,9) = -409.10539 +dnm(3,1) = -2.8225 +dnm(3,2) = +4.7600148 +dnm(3,3) = +11.257177 +dnm(3,4) = -66.382743 +dnm(3,5) = +69.248785 +dnm(4,1) = +0.3400 +dnm(4,2) = -3.1875014 +dnm(4,3) = +12.231796 +dnm(4,4) = -12.110681 + +END SUBROUTINE eos_const + + + +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! SUBROUTINE dq_const +! +! This subr. provides the constants of the dipole-quadrupole term. +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! + SUBROUTINE dq_const ( dqp2,dqp3,dqp4 ) +! + USE PARAMETERS, ONLY: nc + USE EOS_VARIABLES, ONLY: ncomp, parame + IMPLICIT NONE +! +! ---------------------------------------------------------------------- + REAL, INTENT(OUT) :: dqp2(nc,nc,0:8) + REAL, INTENT(OUT) :: dqp3(nc,nc,nc,0:8) + REAL, INTENT(OUT) :: dqp4(nc,nc,0:8) +! +! ---------------------------------------------------------------------- + INTEGER :: i, j, k + REAL :: mdq(nc) + REAL :: mf1, mf2, msegij +! ---------------------------------------------------------------------- + +DO i=1,ncomp + mdq(i) = parame(i,1) + IF (mdq(i) > 2.0) mdq(i) = 2.0 +END DO + + +DO i=1,ncomp + DO j=1,ncomp + + msegij=(mdq(i)*mdq(j))**0.5 + mf1 = (msegij-1.0)/msegij + mf2 = mf1*(msegij-2.0)/msegij + + dqp2(i,j,0) = 0.697094963 + mf1*(-0.673459279) + mf2*0.670340770 + dqp2(i,j,1) = -0.633554144 + mf1*(-1.425899106) + mf2*(-4.338471826) + dqp2(i,j,2) = 2.945509028 + mf1 * 4.19441392 + mf2*7.234168360 + dqp2(i,j,3) = -1.467027314 + mf1 * 1.0266216 + dqp2(i,j,4) = 0.0 + + dqp4(i,j,0) = -0.484038322 + mf1 * 0.67651011 + mf2*(-1.167560146) + dqp4(i,j,1) = 1.970405465 + mf1*(-3.013867512) + mf2*2.13488432 + dqp4(i,j,2) = -2.118572671 + mf1 * 0.46742656 + dqp4(i,j,3) = 0.0 + dqp4(i,j,4) = 0.0 + + + DO k=1,ncomp + msegij=(mdq(i)*mdq(j)*mdq(k))**(1.0/3.0) + mf1 = (msegij-1.0)/msegij + mf2 = (msegij-2.0)/msegij + dqp3(i,j,k,0) = 0.795009692 + mf1*(-2.099579397) + dqp3(i,j,k,1) = 3.386863396 + mf1*(-5.941376392) + dqp3(i,j,k,2) = 0.475106328 + mf1*(-0.178820384) + dqp3(i,j,k,3) = 0.0 + dqp3(i,j,k,4) = 0.0 + END DO + + END DO +END DO + +END SUBROUTINE dq_const + + +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! SUBROUTINE dd_const +! +! This subroutine provides the constants of the dipole-term. +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! + SUBROUTINE dd_const ( ddp2,ddp3,ddp4 ) +! + USE PARAMETERS, ONLY: nc, PI + USE EOS_VARIABLES, ONLY: ncomp, parame + IMPLICIT NONE +! +! ---------------------------------------------------------------------- + REAL, INTENT(OUT) :: ddp2(nc,nc,0:8) + REAL, INTENT(OUT) :: ddp3(nc,nc,nc,0:8) + REAL, INTENT(OUT) :: ddp4(nc,nc,0:8) +! +! ---------------------------------------------------------------------- + INTEGER :: i, j, k + REAL :: pardd(nc) + REAL :: mf1,mf2,msegij,sin2t +! ---------------------------------------------------------------------- + +sin2t = SIN( 0.0 * PI / 180.0 ) +sin2t = sin2t*sin2t + +DO i = 1, ncomp + pardd(i) = parame(i,1) + IF (pardd(i) > 2.0) pardd(i) = 2.0 +END DO + +DO i=1,ncomp + DO j=1,ncomp +! IF (parame(i,6).NE.0.0.AND.parame(j,6).NE.0.0) THEN + + msegij=(pardd(i)*pardd(j))**0.5 + mf1 = (msegij-1.0)/msegij + mf2 = mf1*(msegij-2.0)/msegij + + ddp2(i,j,0) = 0.30435038064 + mf1*(0.95346405973+0.201436*sin2t) & + + mf2*(-1.16100802773-1.74114*sin2t) + ddp2(i,j,1) = -0.13585877707 + mf1*(-1.83963831920+1.31649*sin2t) & + + mf2*4.52586067320 + ddp2(i,j,2) = 1.44933285154 + mf1 * 2.01311801180 + mf2*0.97512223853 + ddp2(i,j,3) = 0.35569769252 + mf1*(-7.37249576667) + mf2*(-12.2810377713) + ddp2(i,j,4) = -2.06533084541 + mf1 * 8.23741345333 + mf2*5.93975747420 + + ddp4(i,j,0) = 0.21879385627 + mf1*(-0.58731641193) + mf2*3.48695755800 + ddp4(i,j,1) = -1.18964307357 + mf1 * 1.24891317047 + mf2*(-14.9159739347) + ddp4(i,j,2) = 1.16268885692 + mf1*(-0.50852797392) + mf2*15.3720218600 + ddp4(i,j,3) = 0.0 + ddp4(i,j,4) = 0.0 + + DO k=1,ncomp +! IF (parame(k,6).NE.0.0) THEN + msegij=(pardd(i)*pardd(j)*pardd(k))**(1.0/3.0) + mf1 = (msegij-1.0)/msegij + mf2 = mf1*(msegij-2.0)/msegij + ddp3(i,j,k,0) = -0.06467735252 + mf1*(-0.95208758351+0.28503*sin2t) & + + mf2*(-0.62609792333+2.2195*sin2t) + ddp3(i,j,k,1) = 0.19758818347 + mf1 * 2.99242575222 + mf2*1.29246858189 + ddp3(i,j,k,2) = -0.80875619458 + mf1*(-2.38026356489) + mf2*1.65427830900 + ddp3(i,j,k,3) = 0.69028490492 + mf1*(-0.27012609786) + mf2*(-3.43967436378) + ddp3(i,j,k,4) = 0.0 + +! ENDIF + END DO + +! ENDIF + END DO +END DO + +END SUBROUTINE dd_const + + +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! SUBROUTINE qq_const +! +! This subroutine provides the constants of the quadrupole-term. +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! + SUBROUTINE qq_const ( qqp2,qqp3,qqp4 ) +! + USE PARAMETERS, ONLY: nc + USE EOS_VARIABLES, ONLY: ncomp, parame + IMPLICIT NONE +! +! ---------------------------------------------------------------------- + REAL, INTENT(OUT) :: qqp2(nc,nc,0:8) + REAL, INTENT(OUT) :: qqp3(nc,nc,nc,0:8) + REAL, INTENT(OUT) :: qqp4(nc,nc,0:8) +! +! ---------------------------------------------------------------------- + INTEGER :: i, j, k + REAL :: mqq(nc) + REAL :: mf1, mf2, msegij +! ---------------------------------------------------------------------- + +DO i = 1,ncomp + mqq(i) = parame(i,1) + IF (mqq(i) > 2.0) mqq(i) = 2.0 +END DO + +DO i = 1,ncomp + DO j = 1,ncomp + IF (parame(i,7) /= 0.0 .AND. parame(j,7) /= 0.0) THEN + + msegij=(mqq(i)*mqq(j))**0.5 +! msegij=(parame(i,1)*parame(j,1))**0.50 + mf1 = (msegij-1.0)/msegij + mf2 = mf1*(msegij-2.0)/msegij + + qqp2(i,j,0) = 1.237830788 + mf1 * 1.285410878 + mf2*1.794295401 + qqp2(i,j,1) = 2.435503144 + mf1*(-11.46561451) + mf2*0.769510293 + qqp2(i,j,2) = 1.633090469 + mf1 *22.08689285 + mf2*7.264792255 + qqp2(i,j,3) = -1.611815241 + mf1 * 7.46913832 + mf2*94.48669892 + qqp2(i,j,4) = 6.977118504 + mf1*(-17.19777208) + mf2*(-77.1484579) + + qqp4(i,j,0) = 0.454271755 + mf1*(-0.813734006) + mf2*6.868267516 + qqp4(i,j,1) = -4.501626435 + mf1 * 10.06402986 + mf2*(-5.173223765) + qqp4(i,j,2) = 3.585886783 + mf1*(-10.87663092) + mf2*(-17.2402066) + qqp4(i,j,3) = 0.0 + qqp4(i,j,4) = 0.0 + + DO k = 1,ncomp + IF (parame(k,7) /= 0.0) THEN + msegij=(mqq(i)*mqq(j)*mqq(k))**(1.0/3.0) +! msegij=(parame(i,1)*parame(j,1)*parame(k,1))**(1.0/3.0) + mf1 = (msegij-1.0)/msegij + mf2 = mf1*(msegij-2.0)/msegij + qqp3(i,j,k,0) = -0.500043713 + mf1 * 2.000209381 + mf2*3.135827145 + qqp3(i,j,k,1) = 6.531869153 + mf1*(-6.78386584) + mf2*7.247588801 + qqp3(i,j,k,2) = -16.01477983 + mf1 * 20.38324603 + mf2*3.075947834 + qqp3(i,j,k,3) = 14.42597018 + mf1*(-10.89598394) + qqp3(i,j,k,4) = 0.0 + END IF + END DO + + END IF + END DO +END DO + +END SUBROUTINE qq_const + + + + + + + +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! + SUBROUTINE SET_DEFAULT_EOS_NUMERICAL +! + USE EOS_NUMERICAL_DERIVATIVES + IMPLICIT NONE +! +! ---------------------------------------------------------------------- + + ideal_gas = 'no' ! ( yes, no ) + hard_sphere = 'CSBM' ! ( CSBM, no ) + chain_term = 'TPT1' ! ( TPT1, HuLiu, no ) + disp_term = 'PC-SAFT' ! ( PC-SAFT, CK, PT1, PT2, PT_MF, PT_MIX, no ) + hb_term = 'TPT1_Chap' ! ( TPT1_Chap, no ) + LC_term = 'no' ! ( MSaupe, OVL, no ) + branch_term = 'no' ! ( TPT2, no ) + II_term = 'no' + ID_term = 'no' + + subtract1 = 'no' ! (1PT, 2PT, no) + subtract2 = 'no' ! (ITTpolar, no) + +END SUBROUTINE SET_DEFAULT_EOS_NUMERICAL + + + + + + + + + +! SUBROUTINE READ_INPUT +! ! +! USE BASIC_VARIABLES +! IMPLICIT NONE +! ! +! ! ---------------------------------------------------------------------- +! INTEGER :: i +! REAL :: reading2,reading3,sumfeed +! CHARACTER (LEN=4) :: uoutp, uinp +! CHARACTER (LEN=1) :: uoutt, uint +! CHARACTER (LEN=50) :: filename +! CHARACTER (LEN=30) :: reading1 +! ! ---------------------------------------------------------------------- +! +! filename='./input_file/INPUT.INP' +! CALL file_open(filename,30) +! READ (30,*) eos, pol !J: specify by numbers! eos(1=pcsaft, 2=SRK,...) pol (=polar) yes(1) no(0) +! READ (30,*) t, uint, p, uinp !J: t: value of temp, uint: unit of temp, p: value of pressure, uinp: unit of pressure +! +! ncomp = 0 +! i = 0 +! sumfeed = 0.0 +! read_loop: DO +! READ (30,*) reading1,reading2,reading3 +! IF (reading1 == 'end') EXIT read_loop +! ncomp = ncomp + 1 +! i = i + 1 +! compna(i)= reading1 ! comp.name +! mm(i) = reading2 ! molec.mass (mandatory only for polymers) +! xif(i) = reading3 !J: molefractions +! sumfeed = sumfeed + xif(i) +! ENDDO read_loop +! +! CLOSE (30) +! +! IF (sumfeed /= 0.0 .AND. sumfeed /= 1.0) THEN !J: in case mole fractions dont sum up to 1?? +! xif(1:ncomp) = xif(1:ncomp)/sumfeed +! END IF +! +! uoutt = uint +! uoutp = uinp +! IF (uint == 'C') THEN !J: unit stuff +! u_in_t = 273.15 +! ELSE +! u_in_t = 0.0 +! END IF +! IF (uinp == 'bar') THEN +! u_in_p = 1.E5 +! ELSE IF (uinp == 'mbar') THEN +! u_in_p = 1.E2 +! ELSE IF (uinp == 'MPa') THEN +! u_in_p = 1.E6 +! ELSE IF (uinp == 'kPa') THEN +! u_in_p = 1.E3 +! ELSE +! u_in_p = 1.E0 +! END IF +! +! IF (uoutt == 'C') THEN +! u_out_t = 273.15 +! ELSE +! u_out_t = 0.0 +! END IF +! IF (uoutp == 'bar') THEN +! u_out_p = 1.E5 +! ELSE IF (uoutp == 'mbar') THEN +! u_out_p = 1.E2 +! ELSE IF (uoutp == 'MPa') THEN +! u_out_p = 1.E6 +! ELSE IF (uoutp == 'kPa') THEN +! u_out_p = 1.E3 +! ELSE +! u_out_p = 1.0 +! END IF +! +! t = t + u_in_t !J: calculate temp in Kelvin +! p = p * u_in_p !J: calculate pressure in Pascal +! +! CALL para_input ! retriev pure comp. parameters +! +! +! END SUBROUTINE READ_INPUT + + + + + +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! SUBROUTINE file_open +! +! This subroutine opens files for reading. Beforehand, it checks +! whether this file is available. +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! + SUBROUTINE file_open(filename,file_number) +! +! ---------------------------------------------------------------------- + CHARACTER (LEN=50) :: filename + INTEGER :: file_number + LOGICAL :: filefound +! ---------------------------------------------------------------------- + +INQUIRE (FILE=filename, EXIST = filefound) +IF (filefound) THEN + OPEN (file_number, FILE = filename) +ELSE + write (*,*) ' FOLLOWING FILE CAN NOT BE OPENED', filename + stop +END IF + +END SUBROUTINE file_open + + + +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! SUBROUTINE para_input +! +! This subroutine provides pure component parameters and kij parameters. +! The following syntax applies: +! +! compna(i) component name +! parame(i,k) pure comp. parameter: +! parame(i,1): segment number [/] +! parame(i,2): segment diameter "sigma" [Angstrom] +! parame(i,3): segment energy param. epsilon/k [K] +! parame(i,4): model parameter; not used for PC-SAFT (=0) +! it is 10K most of the time for SAFT [K] +! parame(i,5): Param. for T-dependent segment diameter [/] +! parame(i,6): dipolar moment [debye] +! parame(i,7): quadrupolar moment [debye] +! parame(i,8): number of segments that are part of a branching 4-mer [/] +! parame(i,9): +! parame(i,10): ionic charge number (positiv or negativ) [/] +! parame(i,11): polarizability [A**3] +! parame(i,12): number of association sites [/] +! parame(i,13): (=kap_hb, see below) [/] +! parame(i,14 to 25): (=eps_hb, see below) [K] +! nhb_typ(i) number of different types of association sites (comp. i) +! nhb_no(i,k) number of association sites of type k +! eps_hb depth of association potential [K] +! kap_hb effective width of assoc. potential (angle-averg.) +! mm molec. mass +! scaling param. for roughly scaling the set of objective functions +! +! As opposed to low-molec mass compounds, the molecular mass of a +! polymer is not obtained from this routine. Rather, it is a +! user-specification given in the file INPUT.INP +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! + SUBROUTINE para_input +! + USE BASIC_VARIABLES + IMPLICIT NONE +! +!---------------------------------------------------------------------- + INTEGER :: i +!---------------------------------------------------------------------- + +IF (eos == 1) THEN + CALL pcsaft_par +ELSE IF (eos == 4 .OR. eos == 5 .OR. eos == 6 .OR. eos == 8) THEN + ! CALL lj_par + write (*,*) 'deactivated this line when making a transition to f90' + stop +ELSE IF (eos == 7) THEN + ! CALL sw_par + write (*,*) 'deactivated this line when making a transition to f90' + stop +ELSE IF (eos == 10) THEN + i = 1 + IF (compna(i) == 'LC_generic' .AND. ncomp == 1 ) THEN + mm(i) = 1.0 + parame(i,1) = 7.0 + parame(i,2) = 1.0 + parame(i,3) = 0.0 + ELSE + write (*,*) 'PARA_INPUT: define the component !' + stop + ENDIF +ELSE + !CALL saft_par +END IF + +DO i = 1, ncomp + IF ( mm(i) >= 1.0 .AND. mm(i) < 45.0 ) THEN + scaling(i) = 10000.0 + ELSE IF( mm(i) >= 45.0 .AND. mm(i) < 90.0 ) THEN + scaling(i) = 1000.0 + ELSE IF( mm(i) >= 90.0 .AND. mm(i) < 150.0 ) THEN + scaling(i) = 100.0 + ELSE IF( mm(i) >= 150.0 .AND. mm(i) < 250.0 ) THEN + scaling(i) = 10.0 + ELSE + scaling(i) = 1.0 + END IF + IF (parame(i,10) /= 0.0) scaling(i) = scaling(i) / 1.E4 ! Electrolytes +END DO + +END SUBROUTINE para_input + + + + +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! SUBROUTINE pcsaft_par +! +! pure component parameters and kij parameters +! (as described in SUBROUTINE para_input) +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! + SUBROUTINE pcsaft_par +! + USE BASIC_VARIABLES + IMPLICIT NONE +! +!---------------------------------------------------------------------- + INTEGER :: i, j, k, no + INTEGER, DIMENSION(nc) :: nhb_typ + INTEGER, DIMENSION(nc,nsite) :: nhb_no + REAL, DIMENSION(nc,nc,nsite,nsite) :: eps_hb + REAL, DIMENSION(nc,nc) :: kap_hb +!---------------------------------------------------------------------- + + +DO i = 1, ncomp + parame(i,4) = 0.0 ! T correct. required for SAFT, not PC-SAFT + parame(i,5) = 0.12 ! Param. for T-dependent segment diameter + parame(i,6) = 0.0 ! dipolar moment + parame(i,7) = 0.0 ! quadrupolar moment + parame(i,8) = 0.0 ! number of segments that are part of a branching 4-mer + parame(i,9) = 0.0 + parame(i,10)= 0.0 ! ionic charge number + parame(i,11)= 0.0 ! polarizability + lli(i) = 0.0 + phi_criti(i)= 0.0 + chap(i) = 0.0 + + nhb_typ(i) = 0 + kap_hb(i,i) = 0.0 + ! irgendwann sollten nhb_typ und kap_hb durch parame(i,12) und (i,13) + ! ersetzt werden. + + IF (compna(i) == '14-butandiol') THEN + mm(i) = 90.12 + parame(i,1) = 4.35923557 + parame(i,2) = 3.02947364 + parame(i,3) = 197.11998863 + + ELSE IF (compna(i) == 'air') THEN + mm(i) = 28.899 !n2 and o2 according to mole fractions + parame(i,1) = 1.18938 !n2 and o2 according to mole fractions (weighted artihm. avg) + parame(i,2) = 3.28694 !n2 and o2 according to mole fractions (weighted artihm. avg) + parame(i,3) = 95.672 !n2 and o2 according to mole fractions (weighted artihm. avg) + + + Else IF(compna(i) == 'mdi') THEN + mm(i) = 2.50252E+02 + parame(i,1) = mm(i)*0.030769 + parame(i,2) = 2.886003 + parame(i,3) = 283.052778 + + Else IF(compna(i) == 'po') THEN + mm(i) = 90.12 + parame(i,1) = 4.35923557 + parame(i,2) = 3.02947364 + parame(i,3) = 197.11998863 + Else IF(compna(i) == 'pu') THEN +! mm(i) = 2042.22 !pu n = 5 +! parame(i,1) = mm(i)*0.008845 +! parame(i,2) = 5.680270 +! parame(i,3) = 497.997594 + mm(i) = 340.37 !pu n = 0 + parame(i,1) = mm(i)*0.043312 + parame(i,2) = 3.008359 + parame(i,3) = 273.445205 +! mm(i) = 680.74 !pu n = 1 +! parame(i,1) = mm(i)*0.024106 +! parame(i,2) = 3.744327 +! parame(i,3) = 321.486386 +! mm(i) = 1021.11 !pu n = 2 +! parame(i,1) = mm(i)*0.015076 +! parame(i,2) = 4.537837 +! parame(i,3) = 400.036950 + + + + + Else IF(compna(i) == 'tpg') THEN + mm(i) = 192.25 + parame(i,1) = mm(i)*0.01239 + parame(i,2) = 4.549 + parame(i,3) = 148.678 + parame(i,6) = 0.41 + + nhb_typ(i) = 2 ! no. of different association sites + nhb_no(i,1) = 2 ! no. of sites of type 1 + nhb_no(i,2) = 2 ! no. of sites of type 2 + + eps_hb(i,i,1,2)= 5597.844 + eps_hb(i,i,2,1)= 5597.844 + eps_hb(i,i,1,1)= 0.0 + eps_hb(i,i,2,2)= 0.0 + kap_hb(i,i) = 0.03 + + + + + + ELSE IF (compna(i) == 'ps') THEN + parame(i,1) = mm(i)*1.9E-2 + parame(i,2) = 4.10705961 + parame(i,3) = 267.0 + ELSE IF (compna(i) == 'pg2') THEN !Polyglycerol 2 + mm(i) = 2000.0 + parame(i,1) = mm(i)*2.37E-2 ! from figure 5 PCSAFT paper + parame(i,2) = 3.8 ! from figure 5 PCSAFT paper + parame(i,3) = 270.0 ! starting value for iteration + ! this is the extra parameter + parame(i,8) = mm(i)*2.37E-2 + + nhb_typ(i) = 2 ! no. of different association sites + nhb_no(i,1) = 27 ! no. of sites of type 1 + nhb_no(i,2) = 27 ! no. of sites of type 2 + eps_hb(i,i,1,2)= 2544.6 ! taken from butanol (same M/OH) + eps_hb(i,i,2,1)= 2544.6 + eps_hb(i,i,1,1)= 0.0 + eps_hb(i,i,2,2)= 0.0 + kap_hb(i,i)= .00489087833 ! taken from butanol (same M/OH) + ELSE IF (compna(i) == 'peva') THEN + parame(i,1) = mm(i)*2.63E-2 + ! -- 0 Gew.% VA------------- + ! parame(i,2) = 4.021767 + ! parame(i,3) = 249.5 + ! -- 7.5 Gew.% VA------------- + ! parame(i,2) = 4.011 + ! parame(i,3) = 248.1864 + ! parame(i,3) = 247.6286 + ! ---12.7 Gew.% VA------------ + ! parame(i,2) = 4.0028 + ! parame(i,3) = 247.2075 + ! parame(i,3) = 246.24454 + ! ---27.3 Gew.% VA------------ + ! parame(i,2) = 3.9762 + ! parame(i,3) = 244.114 + ! parame(i,3) = 241.9345 + ! ---31.8 Gew.% VA------------ + parame(i,2) = 3.9666 + parame(i,3) = 243.0436 + ! parame(i,3) = 240.46 + ! ---42.7 Gew.% VA------------ + ! parame(i,2) = 3.9400 + ! parame(i,3) = 240.184 + ! parame(i,3) = 236.62 + ! --------------- + ELSE IF (compna(i) == 'pp') THEN + parame(i,1) = mm(i)*2.2E-2 + parame(i,2) = 4.2 + parame(i,3) = 220.0 + + parame(i,1) = mm(i)*0.0230487701 + parame(i,2) = 4.1 + parame(i,3) = 217.0 + ELSE IF (compna(i) == 'pe') THEN + parame(i,1) = mm(i)*2.622E-2 + parame(i,2) = 4.021767 + parame(i,3) = 252.0 + ! HDPE: extrapolated from pure comp. param. of n-alkane series! + ! parame(i,1) = mm(i)*2.4346E-2 + ! parame(i,2) = 4.07182 + ! parame(i,3) = 269.67 + !! parame(i,3) = 252.5 + ELSE IF (compna(i) == 'ldpe') THEN + parame(i,1) = mm(i)*2.63E-2 + parame(i,2) = 4.021767 + parame(i,3) = 249.5 + ELSE IF (compna(i) == 'pba') THEN + parame(i,1) = mm(i)*2.5872E-2 + parame(i,2) = 3.95 + parame(i,3) = 229.0 + ELSE IF (compna(i) == 'dextran') THEN + parame(i,1) = mm(i)*2.E-2 + parame(i,2) = 4.0 + parame(i,3) = 300.0 + ELSE IF (compna(i) == 'glycol-ethers') THEN + ! mm(i) = 218.0 + ! parame(i,1) = 7.4044 + ! parame(i,2) = 3.61576 + ! parame(i,3) = 244.0034598 + mm(i) = 222.0 + parame(i,1) = 7.994 + parame(i,2) = 3.445377778 + parame(i,3) = 234.916506 + ELSE IF (compna(i) == 'LJ') THEN + mm(i) = 1.0 + parame(i,1) = 1.0 + parame(i,2) = 1.0 + parame(i,3) = 1.0 + ELSE IF (compna(i) == 'LJ1205') THEN + mm(i) = 1.0 + parame(i,1) = 1.0 + parame(i,2) = 1.0 + parame(i,3) = 140.0 + ELSE IF (compna(i) == 'adamantane') THEN + mm(i) = 136.235000000000 + parame(i,1) = 4.81897145432221 + parame(i,2) = 3.47128575274660 + parame(i,3) = 266.936967922521 + ELSE IF (compna(i) == 'methane') THEN + mm(i) = 16.043 + parame(i,1) = 1.0 + parame(i,2) = 3.70388767 + parame(i,3) = 150.033987 + ! LLi(i) = 1.185*parame(i,2) + ! phi_criti(i)= 11.141 + ! chap(i) = 0.787 + lli(i) = 1.398*parame(i,2) + phi_criti(i)= 16.01197 + chap(i) = 0.6 + IF (pol == 2) parame(i,11)= 2.593 + ! --- adjusted to Tc, Pc und omega --- + ! mm(i) = 16.0430000000000 + ! parame(i,1) = 1.03353666429362 + ! parame(i,2) = 3.64824920605089 + ! parame(i,3) = 147.903953522994 + lli(i) = 2.254442763775*parame(i,2) + phi_criti(i)= 42.060975627454 + chap(i) = 0.704895924 + lli(i) = 1.935801125833*parame(i,2) + phi_criti(i)= 26.363325937261 + chap(i) = 0.700112854298 + lli(i) = 2.610103087662*parame(i,2) + phi_criti(i)= 38.192854403173 + chap(i) = 0.812100472735 + ! 2.122960316503 34.937141524804 0.734513223627 + ! 2.082897379591 33.036391564859 0.877578492999 + ELSE IF (compna(i) == 'ethane') THEN + mm(i) = 30.070 + parame(i,1) =mm(i)* .0534364758 + parame(i,2) = 3.5205923 + parame(i,3) = 191.423815 + lli(i) = 1.40*parame(i,2) + phi_criti(i)= 15.38 + chap(i) = 0.520 + IF (pol == 2) parame(i,11)= 4.3 + ! --- adjusted to Tc, Pc und omega --- + ! mm(i) = 30.069 + ! parame(i,1) = 1.74034548122 + ! parame(i,2) = 3.4697441893134 + ! parame(i,3) = 181.90770083591 + IF (pol >= 1) mm(i) = 30.0700000000000 + IF (pol >= 1) parame(i,1) = mm(i)* 5.341907666260094E-002 + IF (pol >= 1) parame(i,2) = 3.52104466654628 + IF (pol >= 1) parame(i,3) = 191.449300423694 + IF (pol >= 1) parame(i,7) = 0.650000000000000 + IF (pol >= 1) lli(i) = 0.0 + IF (pol >= 1) phi_criti(i)= 0.0 + IF (pol >= 1) chap(i) = 0.0 + ELSE IF (compna(i) == 'propane') THEN + mm(i) = 44.096 + parame(i,1) = mm(i)* .0453970622 + parame(i,2) = 3.61835302 + parame(i,3) = 208.110116 + lli(i) = 1.8*parame(i,2) + phi_criti(i)= 21.0 + chap(i) = 1.0 + lli(i) = 1.63*parame(i,2) + phi_criti(i)= 20.37 + chap(i) = 0.397 + IF (pol == 2) parame(i,11)= 6.29 + ELSE IF (compna(i) == 'butane_debug') THEN + mm(i) = 58.123 + parame(i,1) = 2.3374 + parame(i,2) = 3.6655 + parame(i,3) = 214.805 + ELSE IF (compna(i) == 'butane') THEN + mm(i) = 58.123 + parame(i,1) = mm(i)* .0401146927 + parame(i,2) = 3.70860139 + parame(i,3) = 222.877405 + lli(i) = 1.75*parame(i,2) + phi_criti(i)= 23.43 + chap(i) = 0.304 + ! LLi(i) = 1.942079633622*parame(i,2) + ! phi_criti(i)= 24.527323443155 + ! chap(i) = 0.734064026277 + ! LLi(i) = 1.515115760477*parame(i,2) + ! phi_criti(i)= 17.682929717796 + ! chap(i) = 0.335848717079 + IF (pol == 2) parame(i,11)= 8.2 + ! --- adjusted to Tc, Pc und omega --- + ! mm(i) = 58.1230000000 + ! parame(i,1) = 2.45352304112 + ! parame(i,2) = 3.74239117802 + ! parame(i,3) = 214.185157925 + ELSE IF (compna(i) == 'pentane') THEN + mm(i) = 72.146 + parame(i,1) = mm(i)* .03727896 + parame(i,2) = 3.77293174 + parame(i,3) = 231.197015 + IF (pol == 2) parame(i,11)= 9.99 + ELSE IF (compna(i) == 'hexane') THEN + mm(i) = 86.177 + parame(i,1) = mm(i)* .0354812325 + parame(i,2) = 3.79829291 + parame(i,3) = 236.769054 + lli(i) = 2.24*parame(i,2) + phi_criti(i)= 33.25 + chap(i) = 0.205 + IF (pol == 2) parame(i,11)= 11.9 + ELSE IF (compna(i) == 'heptane') THEN + mm(i) = 100.203 + parame(i,1) = mm(i)* .034762384 + parame(i,2) = 3.80487025 + parame(i,3) = 238.400913 + lli(i) = 2.35*parame(i,2) + phi_criti(i)= 38.10 + chap(i) = 0.173 + IF (pol == 2) parame(i,11)= 13.61 + ELSE IF (compna(i) == 'octane') THEN + mm(i) = 114.231 + parame(i,1) = mm(i)* .0334228038 + parame(i,2) = 3.83732677 + parame(i,3) = 242.775853 + ! LLi(i) = 2.0*parame(i,2) + ! phi_criti(i)= 18.75 + ! chap(i) = 1.0 + lli(i) = 2.63*parame(i,2) + phi_criti(i)= 42.06 + chap(i) = 0.155 + IF (pol == 2) parame(i,11)= 15.9 + ELSE IF (compna(i) == 'nonane') THEN + mm(i) = 128.25 + parame(i,1) = mm(i)* .0328062594 + parame(i,2) = 3.84483643 + parame(i,3) = 244.508457 + ELSE IF (compna(i) == 'decane') THEN + mm(i) = 142.285 + parame(i,1) = mm(i)* .03277373 + parame(i,2) = 3.8384498 + parame(i,3) = 243.866074 + lli(i) = 1.845*parame(i,2) + phi_criti(i)= 21.27 + chap(i) = 1.0 + lli(i) = 2.68*parame(i,2) + phi_criti(i)= 45.0 + chap(i) = 0.15 + IF (pol == 2) parame(i,11)= 19.1 + ! --- adjusted to Tc, Pc und omega --- + ! parame(i,1) = 4.794137228322 + ! parame(i,2) = 4.030446690586 + ! parame(i,3) = 236.5884493386 + ELSE IF (compna(i) == 'dodecane') THEN + mm(i) = 170.338 + parame(i,1) = mm(i)* .0311484156 + parame(i,2) = 3.89589236 + parame(i,3) = 249.214532 + ELSE IF (compna(i) == 'hexadecane') THEN + mm(i) = 226.446 + parame(i,1) = mm(i)* .0293593045 + parame(i,2) = 3.95516743 + parame(i,3) = 254.700131 + ELSE IF (compna(i) == 'octadecane') THEN + mm(i) = 254.5 + parame(i,1) = 7.3271 + parame(i,2) = 3.9668 + parame(i,3) = 256.20 + IF (pol == 2) parame(i,11)= 30.2 + ! --- adjusted to Tc, Pc und omega --- + ! mm(i) = 226.446000000000 + ! parame(i,1) = 6.66976520488694 + ! parame(i,2) = 4.25025597912511 + ! parame(i,3) = 249.582941976119 + ELSE IF (compna(i) == 'eicosane') THEN + mm(i) = 282.553 + parame(i,1) = mm(i)* .0282572812 + parame(i,2) = 3.98692612 + parame(i,3) = 257.747939 + ELSE IF (compna(i) == 'triacontane') THEN + ! mm(i) = 422.822 ! polyethylene parameters + ! parame(i,1) = mm(i)*2.622E-2 + ! parame(i,2) = 4.021767 + ! parame(i,3) = 252.0 + mm(i) = 422.822 ! param. by extrapolation of n-alkanes + parame(i,1) = mm(i)* 0.026922527 + parame(i,2) = 4.007608009 + parame(i,3) = 262.28622 + ELSE IF (compna(i) == 'octaeicosane') THEN + mm(i) = 395.0 ! param. by extrapolation of n-alkanes (sloppy!!) + parame(i,1) = mm(i)* 0.026922527 + parame(i,2) = 4.007608009 + parame(i,3) = 262.28622 + ELSE IF (compna(i) == 'tetracontane') THEN + ! mm(i) = 563.1 ! polyethylene parameters + ! parame(i,1) = mm(i)*2.622E-2 + ! parame(i,2) = 4.021767 + ! parame(i,3) = 252.0 + mm(i) = 563.1 ! param. by extrapolation of n-alkanes + parame(i,1) = mm(i)*0.026287593 + parame(i,2) = 4.023277 + parame(i,3) = 264.10466 + ELSE IF (compna(i) == 'isobutane') THEN + mm(i) = 58.123 + parame(i,1) = mm(i)* .0389105395 + parame(i,2) = 3.75735249 + parame(i,3) = 216.528584 + ELSE IF (compna(i) == 'isopentane') THEN + mm(i) = 72.15 + parame(i,1) = 2.5620 + parame(i,2) = 3.8296 + parame(i,3) = 230.75 + ELSE IF (compna(i) == '2-methylpentane') THEN + mm(i) = 86.177 + parame(i,1) = mm(i)* .0340166994 + parame(i,2) = 3.85354665 + parame(i,3) = 235.5801 + ELSE IF (compna(i) == '23-dimethylbutane') THEN + mm(i) = 86.177 + parame(i,1) = mm(i)* .0311599207 + parame(i,2) = 3.9544545 + parame(i,3) = 246.068188 + ELSE IF (compna(i) == 'ethylene') THEN + mm(i) = 28.05 + parame(i,1) = mm(i)* .0567939013 + parame(i,2) = 3.44499904 + parame(i,3) = 176.468725 + IF (pol == 2) parame(i,11)= 4.252 +! eigener 3-ter Anlauf. + IF (pol >= 1) parame(i,1) = mm(i)* 5.574644443117726E-002 + IF (pol >= 1) parame(i,2) = 3.43281482228714 + IF (pol >= 1) parame(i,3) = 178.627308564610 + IF (pol >= 1) parame(i,7) = 1.56885870200446 + IF (pol == 2) parame(i,11)= 4.252 + ELSE IF (compna(i) == 'propylene') THEN + mm(i) = 42.081 + parame(i,1) = mm(i)* .0465710324 + parame(i,2) = 3.53559831 + parame(i,3) = 207.189309 + ! --- adjusted to Tc, Pc und omega --- + ! mm(i) = 42.081 + ! parame(i,1) = 2.086735327675 + ! parame(i,2) = 3.536779407969 + ! parame(i,3) = 198.3529810625 + ELSE IF (compna(i) == '1-butene') THEN + mm(i) = 56.107 + parame(i,1) = mm(i)* .0407524782 + parame(i,2) = 3.64305136 + parame(i,3) = 222.002756 + IF (pol == 2) parame(i,11)= 7.97 + ELSE IF (compna(i) == '1-pentene') THEN + mm(i) = 70.134 + parame(i,1) = 2.6006 + parame(i,2) = 3.7399 + parame(i,3) = 231.99 + ELSE IF (compna(i) == '1-hexene') THEN + mm(i) = 84.616 + parame(i,1) = mm(i)* .0352836857 + parame(i,2) = 3.77529612 + parame(i,3) = 236.810973 + ELSE IF (compna(i) == '1-octene') THEN + mm(i) = 112.215 + parame(i,1) = mm(i)* .033345175 + parame(i,2) = 3.81329011 + parame(i,3) = 243.017587 + ELSE IF (compna(i) == 'cyclopentane') THEN + mm(i) = 70.13 + parame(i,1) = mm(i)* .0337262571 + parame(i,2) = 3.71139254 + parame(i,3) = 265.828755 + ELSE IF (compna(i) == 'cyclohexane') THEN + mm(i) = 84.147 + parame(i,1) = mm(i)* .0300695505 + parame(i,2) = 3.84990887 + parame(i,3) = 278.108786 + IF (pol == 2) parame(i,11)= 10.87 + ELSE IF (compna(i) == 'toluene') THEN + mm(i) = 92.141 + parame(i,1) = mm(i)* .0305499338 + parame(i,2) = 3.71689689 + parame(i,3) = 285.68996 + IF (pol == 2) parame(i,11)= 11.8 + ! --- adjusted to Tc, Pc und omega --- + ! mm(i) = 92.141 + ! parame(i,1) = 3.002119827762 + ! parame(i,2) = 3.803702734224 + ! parame(i,3) = 271.9428642880 + ELSE IF (compna(i) == 'm-xylene') THEN + mm(i) = 106.167 + parame(i,1) = mm(i)* .030011086 + parame(i,2) = 3.75625585 + parame(i,3) = 283.977525 + ELSE IF (compna(i) == 'o-xylene') THEN + mm(i) = 106.167 + parame(i,1) = mm(i)* .0295409161 + parame(i,2) = 3.76000631 + parame(i,3) = 291.049123 + ELSE IF (compna(i) == 'thf') THEN + mm(i) = 72.1057000000000 + ! parame(i,1) = mm(i)* 0.34311391E-01 + parame(i,1) = 2.47404685540709 + parame(i,2) = 3.51369375633677 + parame(i,3) = 274.181927093696 + parame(i,6) = 1.63100000000000 + ELSE IF (compna(i) == 'co2') THEN + mm(i) = 44.01 + parame(i,1) = mm(i)* .0470968503 + parame(i,2) = 2.7851954 + parame(i,3) = 169.207418 + IF (pol >= 1) parame(i,1) = mm(i)* 3.438191426159075E-002 + IF (pol >= 1) parame(i,2) = 3.18693935424469 + IF (pol >= 1) parame(i,3) = 163.333232725156 + IF (pol >= 1) parame(i,7) = 4.400000000000 + IF (pol >= 1) lli(i) = 1.472215*parame(i,2) + IF (pol >= 1) phi_criti(i)= 17.706567 + IF (pol >= 1) chap(i) = 0.5 + IF (pol == 2) parame(i,11)= 2.911 + ELSE IF (compna(i) == 'co') THEN + IF (pol /= 1) write (*,*) 'parameters for co missing' + IF (pol /= 1) stop + IF (pol >= 1) mm(i) = 28.01 + IF (pol >= 1) parame(i,1) = mm(i)* 5.126059746332587E-002 ! 1.43580933494776 + IF (pol >= 1) parame(i,2) = 3.13556624711756 + IF (pol >= 1) parame(i,3) = 87.7191028693595 + IF (pol >= 1) parame(i,6) = 0.1098 + ELSE IF (compna(i) == 'n2') THEN + mm(i) = 28.01 + parame(i,1) = mm(i)* .0430301713 + parame(i,2) = 3.3129702 + parame(i,3) = 90.9606924 + IF (pol >= 1) parame(i,1) = mm(i)* 3.971157114787596E-002 + IF (pol >= 1) parame(i,2) = 3.42116853868336 + IF (pol >= 1) parame(i,3) = 92.3972606842862 + IF (pol >= 1) parame(i,7) = 1.52000000000000 + IF (pol >= 1) lli(i) = 1.5188*parame(i,2) + IF (pol >= 1) phi_criti(i)= 19.9247 + IF (pol >= 1) chap(i) = 0.375 + ! better RGT-results came later, with: 1.5822 21.201 0.3972 + ELSE IF (compna(i) == 'o2') THEN + mm(i) = 32.05 + parame(i,1) = mm(i)* .0353671563 + parame(i,2) = 3.19465166 + parame(i,3) = 114.430197 + ELSE IF (compna(i) == 'hydrogen') THEN + mm(i) = 2.016 + parame(i,1) = mm(i)* .258951975 + parame(i,2) = 4.43304935 + parame(i,3) = 29.6509579 + + mm(i) = 2.016 + parame(i,1) = 1.0 + parame(i,2) = 2.915 + parame(i,3) = 38.0 + + ! mm(i) = 2.016 ! Ghosh et al. 2003 + ! parame(i,1) = 1.0 + ! parame(i,2) = 2.986 + ! parame(i,3) = 19.2775 + ELSE IF (compna(i) == 'argon') THEN + ! mm(i) = 39.948 ! adjusted m !! + ! parame(i,1) = 0.9285 + ! parame(i,2) = 3.4784 + ! parame(i,3) = 122.23 + mm(i) = 39.948 ! enforced m=1 !! + parame(i,1) = 1.0 + parame(i,2) = 3.3658 + parame(i,3) = 118.34 + IF (pol == 2) parame(i,11)= 1.6411 + ELSE IF (compna(i) == 'xenon') THEN + mm(i) = 131.29 + parame(i,1) = 1.0 + parame(i,2) = 3.93143 + parame(i,3) = 227.749 + ELSE IF (compna(i) == 'chlorine') THEN ! Cl2 + mm(i) = 70.906 + parame(i,1) = 1.5514 + parame(i,2) = 3.3672 + parame(i,3) = 265.67 + ELSE IF (compna(i) == 'SF6') THEN + mm(i) = 146.056 ! adjusted m !! + parame(i,1) = 2.48191 + parame(i,2) = 3.32727 + parame(i,3) = 161.639 + ! mm(i) = 146.056 ! enforced m=1 !! + ! parame(i,1) = 1.0 + ! parame(i,2) = 4.55222 + ! parame(i,3) = 263.1356 + ELSE IF (compna(i) == 'benzene') THEN + mm(i) = 78.114 + parame(i,1) = mm(i)* .0315590546 + parame(i,2) = 3.64778975 + parame(i,3) = 287.354574 + IF (pol >= 1) mm(i) = 78.114 ! PCP-SAFT with m=2 in QQ term + IF (pol >= 1) parame(i,1) = mm(i)* 2.932783311E-2 ! = 2.29091435590515 + IF (pol >= 1) parame(i,2) = 3.7563854 + IF (pol >= 1) parame(i,3) = 294.06253 + IF (pol >= 1) parame(i,7) = 5.5907 + ELSE IF (compna(i) == 'ethylbenzene') THEN + mm(i) = 106.167 + parame(i,1) = mm(i)* .0290120497 + parame(i,2) = 3.79741116 + parame(i,3) = 287.348098 + IF (pol == 2) parame(i,11)= 13.3 + ELSE IF (compna(i) == 'propylbenzene') THEN + mm(i) = 120.194 + parame(i,1) = mm(i)* .0278171627 + parame(i,2) = 3.8437772 + parame(i,3) = 288.128269 + ELSE IF (compna(i) == 'n-butylbenzene') THEN + mm(i) = 134.221 + parame(i,1) = mm(i)* .0280642225 + parame(i,2) = 3.87267961 + parame(i,3) = 283.072331 + ELSE IF (compna(i) == 'tetralin') THEN + mm(i) = 132.205 + parame(i,1) = mm(i)* .0250640795 + parame(i,2) = 3.87498866 + parame(i,3) = 325.065688 + ELSE IF (compna(i) == 'methylcyclohexane') THEN + mm(i) = 98.182 + parame(i,1) = mm(i)* .0271259953 + parame(i,2) = 3.99931892 + parame(i,3) = 282.334148 + IF (pol == 2) parame(i,11)= 13.1 + ELSE IF (compna(i) == 'methylcyclopentane') THEN + mm(i) = 84.156 + parame(i,1) = mm(i)* .0310459009 + parame(i,2) = 3.82534693 + parame(i,3) = 265.122799 + ELSE IF (compna(i) == 'acetone') THEN + mm(i) = 58.0800000000000 ! PC-SAFT + parame(i,1) = mm(i)* 4.870380408159182E-002 ! =2.82871694105885 + parame(i,2) = 3.24969003020675 + parame(i,3) = 250.262241927379 + lli(i) = 2.0021*parame(i,2) + phi_criti(i)= 21.336 + chap(i) = 0.24931 + IF (pol >= 1) mm(i) = 58.0800000000000 ! PCP-SAFT + IF (pol >= 1) parame(i,1) = mm(i)* 4.725811736856114E-002 ! =2.74475145676603 + IF (pol >= 1) parame(i,2) = 3.27423145271184 + IF (pol >= 1) parame(i,3) = 232.990879135326 + IF (pol >= 1) parame(i,6) = 2.88000000000000 + IF (pol >= 1) lli(i) = 2.0641*parame(i,2) + IF (pol >= 1) phi_criti(i)= 28.1783 + IF (pol >= 1) chap(i) = 0.22695 + IF (pol >= 2) mm(i) = 58.0800000000000 ! PCIP-SAFT + IF (pol >= 2) parame(i,1) = mm(i)* 4.902301475689938E-002 ! =2.84725669708072 + IF (pol >= 2) parame(i,2) = 3.23880349104868 + IF (pol >= 2) parame(i,3) = 220.884202656054 + IF (pol >= 2) parame(i,6) = 2.88000000000000 + IF (pol == 2) parame(i,11)= 6.40000000000000 + ELSE IF (compna(i) == 'butanone') THEN + mm(i) = 72.1066 ! PC-SAFT + parame(i,1) = mm(i)* 4.264192830122321E-002 ! =3.07476446724498 + parame(i,2) = 3.39324011060028 + parame(i,3) = 252.267273608975 + IF (pol >= 1) mm(i) = 72.1066 ! PCP-SAFT + IF (pol >= 1) parame(i,1) = mm(i)* 4.137668924230600E-002 ! =2.98353238051926 + IF (pol >= 1) parame(i,2) = 3.42393701353423 + IF (pol >= 1) parame(i,3) = 244.994381354681 + IF (pol >= 1) parame(i,6) = 2.78000000000000 + IF (pol >= 2) mm(i) = 72.1066 ! PCIP-SAFT + IF (pol >= 2) parame(i,1) = mm(i)* 4.254697075199448E-002 ! =3.06791740122577 + IF (pol >= 2) parame(i,2) = 3.39138375903252 + IF (pol >= 2) parame(i,3) = 236.527763837528 + IF (pol >= 2) parame(i,6) = 2.78000000000000 + IF (pol == 2) parame(i,11)= 8.13000000000000 + ELSE IF (compna(i) == '2-pentanone') THEN + ! mm(i) = 86.134 ! PC-SAFT + ! parame(i,1) = mm(i)* 3.982654501296355E-002 ! =3.43041962814660 + ! parame(i,2) = 3.46877976946838 + ! parame(i,3) = 249.834724442656 + ! mm(i) = 86.134 ! PCP-SAFT + ! parame(i,1) = mm(i)* 3.893594769994072E-002 ! =3.35370891918669 + ! parame(i,2) = 3.49417356096593 + ! parame(i,3) = 246.656329096835 + ! parame(i,6) = 2.70000000000000 + mm(i) = 86.134 ! PCIP-SAFT + parame(i,1) = mm(i)* 3.973160761515879E-002 ! =3.42224229032409 + parame(i,2) = 3.46827593107280 + parame(i,3) = 240.904278156822 + parame(i,6) = 2.70000000000000 + IF (pol == 2) parame(i,11)= 9.93000000000000 + ELSE IF (compna(i) == '3-pentanone') THEN + mm(i) = 86.134 ! PC-SAFT + parame(i,1) = 3.36439508013322 + parame(i,2) = 3.48770251979329 + parame(i,3) = 252.695415552376 + IF (pol >= 1) mm(i) = 86.134 ! PCP-SAFT + IF (pol >= 1) parame(i,1) = 3.27863398611842 + IF (pol >= 1) parame(i,2) = 3.51592571835030 + IF (pol >= 1) parame(i,3) = 248.690775540981 + IF (pol >= 1) parame(i,6) = 2.82000000000000 + IF (pol == 2) mm(i) = 86.134 ! PCIP-SAFT + IF (pol == 2) parame(i,1) = 3.34821857026283 + IF (pol == 2) parame(i,2) = 3.48903345340516 + IF (pol == 2) parame(i,3) = 242.314578558329 + IF (pol == 2) parame(i,6) = 2.82000000000000 + IF (pol == 2) parame(i,11)= 9.93000000000000 + ELSE IF (compna(i) == 'cyclohexanone') THEN ! from DIPPR + ! IF (pol.GE.1) mm(i) = 98.1430 ! PCP-SAFT + ! IF (pol.GE.1) parame(i,1) = 3.084202 + ! IF (pol.GE.1) parame(i,2) = 3.613681 + ! IF (pol.GE.1) parame(i,3) = 286.15865 + ! IF (pol.GE.1) parame(i,6) = 3.087862 + IF (pol >= 1) mm(i) = 98.1500000000000 + IF (pol >= 1) parame(i,1) = 2.72291913132818 + IF (pol >= 1) parame(i,2) = 3.79018433908522 + IF (pol >= 1) parame(i,3) = 314.772193827344 + IF (pol >= 1) parame(i,6) = 3.24600000000000 + IF (pol /= 1) WRITE (*,*) 'no non-polar param. for cyclohexanone' + IF (pol /= 1) STOP + ELSE IF (compna(i) == 'propanal') THEN + mm(i) = 58.08 ! PC-SAFT + parame(i,1) = 2.67564746980910 + parame(i,2) = 3.26295953984941 + parame(i,3) = 251.888982765626 + IF (pol >= 1) mm(i) = 58.08 ! PCP-SAFT + IF (pol >= 1) parame(i,1) = 2.60007872084995 + IF (pol >= 1) parame(i,2) = 3.28720732189761 + IF (pol >= 1) parame(i,3) = 235.205188090107 + IF (pol >= 1) parame(i,6) = 2.72000000000000 + IF (pol >= 2) mm(i) = 58.08 ! PCIP-SAFT + IF (pol >= 2) parame(i,1) = 2.72471167411028 + IF (pol >= 2) parame(i,2) = 3.24781643022922 + IF (pol >= 2) parame(i,3) = 221.642071811094 + IF (pol >= 2) parame(i,6) = 2.72000000000000 + IF (pol >= 2) parame(i,11)= 6.50000000000000 + ELSE IF (compna(i) == 'butanal') THEN + mm(i) = 72.1066000000000 ! PC-SAFT + parame(i,1) = 2.96824823599784 + parame(i,2) = 3.44068916025889 + parame(i,3) = 253.929404992884 + IF (pol >= 1) mm(i) = 72.1066000000000 ! PCP-SAFT + IF (pol >= 1) parame(i,1) = 2.86783706423953 + IF (pol >= 1) parame(i,2) = 3.47737904036296 + IF (pol >= 1) parame(i,3) = 247.543312127310 + IF (pol >= 1) parame(i,6) = 2.72000000000000 + ELSE IF (compna(i) == 'dmso') THEN + mm(i) = 78.1300000000000 ! PC-SAFT + parame(i,1) = 2.92225114054231 + parame(i,2) = 3.27780791606297 + parame(i,3) = 355.688793038512 + IF (pol >= 1) mm(i) = 78.1300000000000 ! PCP-SAFT + IF (pol >= 1) parame(i,1) = 3.02433694138348 + IF (pol >= 1) parame(i,2) = 3.24270742566613 + IF (pol >= 1) parame(i,3) = 309.357476696679 + IF (pol >= 1) parame(i,6) = 3.96000000000000 + IF (pol >= 2) mm(i) = 78.1300000000000 ! PCIP-SAFT + IF (pol >= 2) parame(i,1) = 3.19078234633277 + IF (pol >= 2) parame(i,2) = 3.19778269816832 + IF (pol >= 2) parame(i,3) = 286.337981216861 + IF (pol >= 2) parame(i,6) = 3.96000000000000 + IF (pol >= 2) parame(i,11)= 7.97000000000000 + ELSE IF (compna(i) == 'acetone_JC') THEN ! Jog-Chapman + ! mm(i) = 58.0800000000000 ! Dominik et al.2005 + ! parame(i,1) = 2.221 + ! parame(i,2) = 3.607908 + ! parame(i,3) = 259.99 + ! parame(i,6) = 2.7 + ! parame(i,8) = 0.2258 + ! mm(i) = 58.0800000000000 + ! parame(i,1) = mm(i)* 3.556617369195472E-002 + ! parame(i,2) = 3.58780367502515 + ! parame(i,3) = 273.025100470307 + ! parame(i,6) = 2.70000000000000 + ! parame(i,8) = 0.229800000000000 + + mm(i) = 58.08 ! Tumakaka Sadowski 2004 + parame(i,1) = mm(i)* 3.766E-2 + parame(i,2) = 3.6028 + parame(i,3) = 245.49 + parame(i,6) = 2.72 + parame(i,8) = 0.2969 + ! mm(i) = 58.0800000000000 ! no adjust. DD-param. + ! parame(i,1) = 1.87041620247774 + ! parame(i,2) = 3.79783535570774 + ! parame(i,3) = 208.885730881588 + ! parame(i,6) = 2.88000000000000 + ! parame(i,8) = 1.0/parame(i,1) + WRITE (*,*) 'caution: parame(i,8) is now used for branching' + STOP + kij(1,2) = -0.005 + kij(2,1)=kij(1,2) + ELSE IF (compna(i) == 'acetone_SF') THEN ! Saager-Fischer + mm(i) = 58.08 + parame(i,1) = mm(i)* 4.603296414764944E-002 + parame(i,2) = 3.29454924451643 + parame(i,3) = 221.052649057645 + parame(i,6) = 2.70000000000000 + parame(i,8) = 0.625410000000000 + mm(i) = 58.08 ! form as expected from me - no DD-param adjusted.dat + parame(i,1) = mm(i)* 4.364264724158790E-002 ! =2.53476495179143 + parame(i,2) = 3.37098670735567 + parame(i,3) = 254.366379701851 + parame(i,6) = 2.88000000000000 + ! mm(i) = 58.08 ! form as expected but w/ sumseg/1.5 - no DD-param adjusted.dat + ! parame(i,1) = mm(i)* 4.694644361257521E-002 ! =2.72664944501837 + ! parame(i,2) = 3.27842292595463 + ! parame(i,3) = 238.398883501772 + ! parame(i,6) = 2.88000000000000 + ! mm(i) = 58.08 ! form as expected but w/ sumseg/1.5 and fdd*sumseg- no DD-param adjusted.dat + ! parame(i,1) = mm(i)* 4.458214655521766E-002 ! =2.58933107192704 + ! parame(i,2) = 3.32050824493493 + ! parame(i,3) = 218.285994651271 + ! parame(i,6) = 2.88000000000000 + WRITE (*,*) 'caution: parame(i,8) is now used for branching' + STOP + kij(1,2) = 0.035 + kij(2,1)=kij(1,2) + ELSE IF (compna(i) == 'ethylacetate_JC') THEN ! Jog-Chapman + ! mm(i) = 88.11 + ! parame(i,1) = 2.7481 + ! parame(i,2) = 3.6511 + ! parame(i,3) = 236.99 + ! parame(i,6) = 1.84 + ! parame(i,8) = 0.5458 + mm(i) = 88.1060000000000 + parame(i,1) = mm(i)* 0.03117 ! 2.74626402 + parame(i,2) = 3.6493 + parame(i,3) = 236.75 + parame(i,6) = 1.8 + parame(i,8) = 0.5462 + ELSE IF (compna(i) == 'ethylacetate_SF') THEN ! Saager-Fischer + mm(i) = 88.106 + parame(i,1) = mm(i)* 3.564165384763394E-002 + parame(i,2) = 3.447379322 + parame(i,3) = 226.0930487 + parame(i,6) = 1.8 + parame(i,8) = 0.849967000000000 + WRITE (*,*) 'caution: parame(i,8) is now used for branching' + STOP + ELSE IF (compna(i) == '12po_JC') THEN ! Jog-Chapman + mm(i) = 58.08 + parame(i,1) = 2.0105 + parame(i,2) = 3.6095 + parame(i,3) = 258.82 + parame(i,6) = 2.0 + parame(i,8) = 0.3979 + WRITE (*,*) 'caution: parame(i,8) is now used for branching' + STOP + ELSE IF (compna(i) == '12po_SF') THEN ! Saager-Fischer + mm(i) = 58.08 + parame(i,1) = 2.1341 + parame(i,2) = 3.4739 + parame(i,3) = 252.95 + parame(i,6) = 2.0 + parame(i,8) = 0.916 + WRITE (*,*) 'caution: parame(i,8) is now used for branching' + STOP + ELSE IF (compna(i) == 'acrylonitrile') THEN + IF (pol >= 2) mm(i) = 53.06 ! PCIP-SAFT + IF (pol >= 2) parame(i,1) = 2.168 + IF (pol >= 2) parame(i,2) = 3.575 + IF (pol >= 2) parame(i,3) = 214.83 + IF (pol >= 2) parame(i,6) = 3.91 + IF (pol == 2) parame(i,11)= 8.04 + IF (pol >= 2) mm(i) = 53.0000000000000 ! second parameter set ?? + IF (pol >= 2) parame(i,1) = 2.45403467006041 + IF (pol >= 2) parame(i,2) = 3.41276825781723 + IF (pol >= 2) parame(i,3) = 195.194353082408 + IF (pol >= 2) parame(i,6) = 3.91000000000000 + IF (pol == 2) parame(i,11)= 8.04000000000000 + ELSE IF (compna(i) == 'butyronitrile') THEN + ! mm(i) = 69.11 + ! parame(i,1) = 2.860 + ! parame(i,2) = 3.478 + ! parame(i,3) = 253.21 + ! parame(i,6) = 4.07 + mm(i) = 69.11 + parame(i,1) = 2.989 + parame(i,2) = 3.441 + parame(i,3) = 234.04 + parame(i,6) = 4.07 + IF (pol == 2) parame(i,11)= 8.4 + ELSE IF (compna(i) == 'propionitrile') THEN + mm(i) = 55.079 ! PC-SAFT + parame(i,1) = 2.66211021227108 + parame(i,2) = 3.34032231132738 + parame(i,3) = 294.078737359580 + IF (pol >= 1) mm(i) = 55.079 ! PCP-SAFT + IF (pol >= 1) parame(i,1) = 2.50958981615666 + IF (pol >= 1) parame(i,2) = 3.39806320429568 + IF (pol >= 1) parame(i,3) = 239.152759066148 + IF (pol >= 1) parame(i,6) = 4.05000000000000 + IF (pol >= 2) mm(i) = 55.079 ! PCIP-SAFT + IF (pol >= 2) parame(i,1) = 2.54684827683436 + IF (pol >= 2) parame(i,2) = 3.41240089912190 + IF (pol >= 2) parame(i,3) = 218.299491580335 + IF (pol >= 2) parame(i,6) = 4.05000000000000 + IF (pol == 2) parame(i,11)= 6.24000000000000 + ! IF (pol.GE.2) mm(i) = 55.079 ! PCIP-SAFT my_DD adjusted + ! IF (pol.GE.2) parame(i,1) = 2.61175151088002 + ! IF (pol.GE.2) parame(i,2) = 3.37194293181453 + ! IF (pol.GE.2) parame(i,3) = 233.346110749402 + ! IF (pol.GE.2) parame(i,6) = 3.74682245835235 + ! IF (pol.EQ.2) parame(i,11)= 6.24000000000000 + ELSE IF (compna(i) == 'nitromethane') THEN + mm(i) = 61.04 ! PC-SAFT + parame(i,1) = mm(i)* 4.233767489308791E-002 ! =2.58429167547409 + parame(i,2) = 3.10839592337018 + parame(i,3) = 310.694151426943 + IF (pol >= 1) mm(i) = 61.04 ! PCP-SAFT + IF (pol >= 1) parame(i,1) = mm(i)* 4.191475020685036E-002 ! =2.55847635262615 + IF (pol >= 1) parame(i,2) = 3.10129282495975 + IF (pol >= 1) parame(i,3) = 256.456941430554 + IF (pol >= 1) parame(i,6) = 3.46000000000000 + IF (pol >= 2) mm(i) = 61.04 ! PCIP-SAFT + IF (pol >= 2) parame(i,1) = mm(i)* 4.394323357988009E-002 ! =2.68229497771588 + IF (pol >= 2) parame(i,2) = 3.10654492320028 + IF (pol >= 2) parame(i,3) = 225.973607468282 + IF (pol >= 2) parame(i,6) = 3.46000000000000 + IF (pol >= 2) parame(i,11)= 7.37000000000000 + ELSE IF (compna(i) == 'nitroethane') THEN + mm(i) = 75.067 ! PC-SAFT + parame(i,1) = mm(i)* 4.019977215251163E-002 ! =3.01767629617259 + parame(i,2) = 3.21364231060938 + parame(i,3) = 286.571650044235 + IF (pol >= 1) mm(i) = 75.067 ! PCP-SAFT + IF (pol >= 1) parame(i,1) = mm(i)* 3.928506808347654E-002 ! =2.94901220582233 + IF (pol >= 1) parame(i,2) = 3.23117331990738 + IF (pol >= 1) parame(i,3) = 265.961000131109 + IF (pol >= 1) parame(i,6) = 3.23000000000000 + IF (pol >= 2) mm(i) = 75.067 ! PCIP-SAFT + IF (pol >= 2) parame(i,1) = mm(i)* 4.117677400894779E-002 ! =3.09101689452968 + IF (pol >= 2) parame(i,2) = 3.19364569858756 + IF (pol >= 2) parame(i,3) = 246.676040248662 + IF (pol >= 2) parame(i,6) = 3.23000000000000 + IF (pol >= 2) parame(i,11)= 9.63000000000000 + ELSE IF (compna(i) == 'acetonitrile') THEN + mm(i) = 41.052 ! PC-SAFT + parame(i,1) = mm(i)* 5.673187410405271E-002 ! =2.32895689571957 + parame(i,2) = 3.18980108373791 + parame(i,3) = 311.307486044181 + IF (pol >= 1) mm(i) = 41.052 ! PCP-SAFT + IF (pol >= 1) parame(i,1) = mm(i)* 5.254832931037250E-002 ! =2.15721401484941 + IF (pol >= 1) parame(i,2) = 3.27301469369132 + IF (pol >= 1) parame(i,3) = 216.888948676921 + IF (pol >= 1) parame(i,6) = 3.92520000000000 + IF (pol >= 2) mm(i) = 41.052 ! PCIP-SAFT + IF (pol >= 2) parame(i,1) = mm(i)* 5.125846581157176E-002 ! =2.10426253849664 + IF (pol >= 2) parame(i,2) = 3.39403305120647 + IF (pol >= 2) parame(i,3) = 199.070191065791 + IF (pol >= 2) parame(i,6) = 3.92520000000000 + IF (pol >= 2) parame(i,11)= 4.40000000000000 + ! IF (pol >= 2) mm(i) = 41.052 ! PCIP-SAFT my_DD adjusted + ! IF (pol >= 2) parame(i,1) = mm(i)* 5.755347845863738E-002 ! =2.36268539768398 + ! IF (pol >= 2) parame(i,2) = 3.18554306395900 + ! IF (pol >= 2) parame(i,3) = 225.143934506015 + ! IF (pol >= 2) parame(i,6) = 3.43151866932598 + ! IF (pol >= 2) parame(i,11)= 4.40000000000000 + ! mm(i) = 41.053 ! PCP-SAFT dipole and quadrupole + ! parame(i,1) = 1.79993 + ! parame(i,2) = 3.47366 + ! parame(i,3) = 211.001 + ! parame(i,6) = 3.93800 + ! parame(i,7) = 2.44000 + ! parame(i,11)= 0.0 + ELSE IF (compna(i) == 'dmf') THEN + mm(i) = 73.09 ! PC-SAFT + parame(i,1) = 2.388 + parame(i,2) = 3.658 + parame(i,3) = 363.77 + IF (pol >= 1) mm(i) = 73.09 ! PCP-SAFT + IF (pol >= 1) parame(i,1) = 2.269 + IF (pol >= 1) parame(i,2) = 3.714 + IF (pol >= 1) parame(i,3) = 331.56 + IF (pol >= 1) parame(i,6) = 3.82 + IF (pol >= 2) mm(i) = 73.09 ! PCIP-SAFT + IF (pol >= 2) parame(i,1) = 2.375 + IF (pol >= 2) parame(i,2) = 3.667 + IF (pol >= 2) parame(i,3) = 308.42 + IF (pol >= 2) parame(i,6) = 3.82 + IF (pol >= 2) parame(i,11)= 7.81 + ELSE IF (compna(i) == 'chloroform') THEN + mm(i) = 119.377 ! PCIP-SAFT + parame(i,1) = 2.5957 + parame(i,2) = 3.4299 + parame(i,3) = 264.664 + parame(i,6) = 1.04 + IF (pol == 2) parame(i,11)= 8.23 + ELSE IF (compna(i) == 'dimethyl-ether') THEN + mm(i) = 46.069 ! PC-SAFT + parame(i,1) = mm(i)* 0.049107715 ! =2.26234331 + parame(i,2) = 3.276640534 + parame(i,3) = 212.9343244 + IF (pol >= 1) mm(i) = 46.0690000000000 ! PCP-SAFT + IF (pol >= 1) parame(i,1) = mm(i)* 0.048170452 ! =2.219164566 + IF (pol >= 1) parame(i,2) = 3.296939638 + IF (pol >= 1) parame(i,3) = 212.1048888 + IF (pol >= 1) parame(i,6) = 1.30000000000000 + IF (pol >= 2) mm(i) = 46.0690000000000 ! PCIP-SAFT + IF (pol >= 2) parame(i,1) = mm(i)* 4.939183716945787E-002 ! =2.27543254655976 + IF (pol >= 2) parame(i,2) = 3.26584718800835 + IF (pol >= 2) parame(i,3) = 206.904551967059 + IF (pol >= 2) parame(i,6) = 1.30000000000000 + IF (pol == 2) parame(i,11)= 5.29000000000000 + ELSE IF (compna(i) == 'methyl-ethyl-ether') THEN + mm(i) = 60.096 + parame(i,1) = mm(i)* .0442404671 + parame(i,2) = 3.37282595 + parame(i,3) = 216.010217 + IF (pol >= 1) mm(i) = 60.096 ! PCP-SAFT + IF (pol >= 1) parame(i,1) = mm(i)* 4.3971676124088D-002 ! =2.64252184835325 + IF (pol >= 1) parame(i,2) = 3.37938465390 + IF (pol >= 1) parame(i,3) = 215.787173860 + IF (pol >= 1) parame(i,6) = 1.17000000000 + IF (pol >= 2) mm(i) = 60.096 ! PICP-SAFT + IF (pol >= 2) parame(i,1) = mm(i)* 4.4580196137984D-002 ! =2.67909146710834 + IF (pol >= 2) parame(i,2) = 3.36105342286 + IF (pol >= 2) parame(i,3) = 212.871911999 + IF (pol >= 2) parame(i,6) = 1.17000000000 + IF (pol >= 2) parame(i,11) = 7.93000000000 + ELSE IF (compna(i) == 'diethyl-ether') THEN + mm(i) = 74.123 ! PC-SAFT + parame(i,1) = mm(i)* .0409704089 + parame(i,2) = 3.48569553 + parame(i,3) = 217.64113 + IF (pol >= 1) mm(i) = 74.123 ! PCP-SAFT + IF (pol >= 1) parame(i,1) = mm(i)* 4.0103121403686E-2 ! =2.97256367 + IF (pol >= 1) parame(i,2) = 3.51268687697978 + IF (pol >= 1) parame(i,3) = 219.527376572135 + IF (pol >= 1) parame(i,6) = 1.15000000000000 + IF (pol >= 2) mm(i) = 74.123 ! PCIP-SAFT + IF (pol >= 2) parame(i,1) = mm(i)* 4.04144179873E-2 ! =2.9956379 + IF (pol >= 2) parame(i,2) = 3.501724569 + IF (pol >= 2) parame(i,3) = 217.8941822 + IF (pol >= 2) parame(i,6) = 1.15 + IF (pol == 2) parame(i,11)= 8.73 + ELSE IF (compna(i) == 'vinylacetate') THEN + mm(i) = 86.092 + parame(i,1) = mm(i)* .0374329292 + parame(i,2) = 3.35278602 + parame(i,3) = 240.492049 + ELSE IF (compna(i) == 'chloromethane') THEN ! R40 + mm(i) = 50.488 ! PC-SAFT + parame(i,1) = mm(i)* 0.039418879 ! 1.9902 + parame(i,2) = 3.1974 + parame(i,3) = 237.27 + IF (pol >= 1) mm(i) = 50.488 ! PCP-SAFT + IF (pol >= 1) parame(i,1) = mm(i)* 0.035790801 ! 1.8070 + IF (pol >= 1) parame(i,2) = 3.3034 + IF (pol >= 1) parame(i,3) = 229.97 + IF (pol >= 1) parame(i,6) = 1.8963 + IF (pol >= 1) lli(i) = 1.67703*parame(i,2) + IF (pol >= 1) phi_criti(i)= 20.75417 + IF (pol >= 1) chap(i) = 0.5 + IF (pol >= 2) mm(i) = 50.488 ! PCIP-SAFT + IF (pol >= 2) parame(i,1) = mm(i)* 3.68559992E-2 ! 1.86078 + IF (pol >= 2) parame(i,2) = 3.275186 + IF (pol >= 2) parame(i,3) = 216.4621 + IF (pol >= 2) parame(i,6) = 1.8963 + IF (pol == 2) parame(i,11)= 4.72 + ELSE IF (compna(i) == 'fluoromethane') THEN ! R41 + IF (pol /= 1) write (*,*) 'non-polar parameters missing for fluoromethane' + IF (pol /= 1) stop + IF (pol >= 1) mm(i) = 34.0329000000000 + IF (pol >= 1) parame(i,1) = 1.94494757526896 + IF (pol >= 1) parame(i,2) = 2.96858005012635 + IF (pol >= 1) parame(i,3) = 168.938697391009 + IF (pol >= 1) parame(i,6) = 1.57823038894029 + ELSE IF (compna(i) == 'dichloromethane') THEN ! R30 + mm(i) = 84.932 ! PC-SAFT + parame(i,1) = 2.3117 + parame(i,2) = 3.3161 + parame(i,3) = 270.98 + IF (pol >= 1) mm(i) = 84.932 ! PCP-SAFT + IF (pol >= 1) parame(i,1) = 2.2687 + IF (pol >= 1) parame(i,2) = 3.3373 + IF (pol >= 1) parame(i,3) = 269.08 + IF (pol >= 1) parame(i,6) = 1.6 + IF (pol >= 2) mm(i) = 84.932 ! PCIP-SAFT + IF (pol >= 2) parame(i,1) = 2.3435 + IF (pol >= 2) parame(i,2) = 3.2987 + IF (pol >= 2) parame(i,3) = 260.66 + IF (pol >= 2) parame(i,6) = 1.6 + IF (pol == 2) parame(i,11)= 6.48 + ELSE IF (compna(i) == 'difluoromethane') THEN ! R32 + IF (pol /= 1) write (*,*) 'non-polar parameters missing for difluoromethane' + IF (pol /= 1) stop + IF (pol >= 1) mm(i) = 52.0236 ! PCP-SAFT + IF (pol >= 1) parame(i,1) = mm(i)* 4.814700934384165E-002 ! 2.50478075530028 + IF (pol >= 1) parame(i,2) = 2.79365980535456 + IF (pol >= 1) parame(i,3) = 160.893555378523 + IF (pol >= 1) parame(i,6) = 1.97850000000000 + ELSE IF (compna(i) == 'trifluoromethane') THEN ! R23 + IF (pol /= 1) write (*,*) 'non-polar parameters missing for trifluoromethane' + IF (pol /= 1) stop + IF (pol >= 1) mm(i) = 70.0138000000000 + IF (pol >= 1) parame(i,1) = 2.66039274225485 + IF (pol >= 1) parame(i,2) = 2.82905884530501 + IF (pol >= 1) parame(i,3) = 149.527709542333 + IF (pol >= 1) parame(i,6) = 1.339963415253999E-002 + ELSE IF (compna(i) == 'tetrachloromethane') THEN ! R10 + mm(i) = 153.822 + parame(i,1) = mm(i)* .0150432213 + parame(i,2) = 3.81801454 + parame(i,3) = 292.838632 + ELSE IF (compna(i) == 'trichlorofluoromethane') THEN ! R11 + IF (pol /= 1) write (*,*) 'non-polar parameters missing for trichlorofluoromethane' + IF (pol /= 1) stop + IF (pol >= 1) mm(i) = 137.368000000000 + IF (pol >= 1) parame(i,1) = 2.28793359008803 + IF (pol >= 1) parame(i,2) = 3.69013104930876 + IF (pol >= 1) parame(i,3) = 248.603173885090 + IF (pol >= 1) parame(i,6) = 0.23225538492979 + ELSE IF (compna(i) == 'chlorodifluoromethane') THEN ! R22 ( CHClF2 or CHF2Cl) + IF (pol /= 1) write (*,*) 'non-polar parameters missing for chlorodifluoromethane' + IF (pol /= 1) stop + IF (pol >= 1) mm(i) = 86.4684000000000 + IF (pol >= 1) parame(i,1) = 2.47218586047893 + IF (pol >= 1) parame(i,2) = 3.13845692489930 + IF (pol >= 1) parame(i,3) = 187.666355083434 + IF (pol >= 1) parame(i,6) = 1.04954264812860 + ELSE IF (compna(i) == 'chloroethane') THEN + mm(i) = 64.514 + parame(i,1) = mm(i)* .0350926868 + parame(i,2) = 3.41602397 + parame(i,3) = 245.42626 + ELSE IF (compna(i) == '11difluoroethane') THEN + ! mm(i) = 66.0500000000000 ! PC-SAFT + ! parame(i,1) = mm(i)* 4.109944338817734E-002 + ! parame(i,2) = 3.10257444633546 + ! parame(i,3) = 192.177159144029 + ! mm(i) = 66.05 ! PC-SAFT assoc + ! parame(i,1)= 2.984947188 + ! parame(i,2)= 2.978630027 + ! parame(i,3)= 137.8192282 + ! nhb_typ(i) = 2 + ! nhb_no(i,1)= 1 + ! nhb_no(i,2)= 1 + ! eps_hb(i,i,1,2)= 823.3478288 + ! eps_hb(i,i,2,1)= 823.3478288 + ! eps_hb(i,i,1,1)= 0.0 + ! eps_hb(i,i,2,2)= 0.0 + ! kap_hb(i,i) = 0.96345994 + IF (pol >= 1) mm(i) = 66.0500000000000 ! PCP-SAFT + IF (pol >= 1) parame(i,1) = mm(i)* 3.949665745363346E-002 ! =2.60875422481249 + IF (pol >= 1) parame(i,2) = 3.13758353925036 + IF (pol >= 1) parame(i,3) = 179.517952627836 + IF (pol >= 1) parame(i,6) = 2.27000000000000 + IF (pol >= 1) lli(i) = 2.03907*parame(i,2) + IF (pol >= 1) phi_criti(i)= 26.5 + IF (pol >= 1) chap(i) = 0.4 + IF (pol >= 2) mm(i) = 66.0500000000000 ! PCIP-SAFT + IF (pol >= 2) parame(i,1) = mm(i)* 4.093647666154238E-002 ! =2.70385428349487 + IF (pol >= 2) parame(i,2) = 3.10437129415885 + IF (pol >= 2) parame(i,3) = 170.464400902455 + IF (pol >= 2) parame(i,6) = 2.27000000000000 + IF (pol == 2) parame(i,11)= 5.01000000000000 + ELSE IF (compna(i) == '1-chlorobutane') THEN + mm(i) = 92.568 + parame(i,1) = mm(i)* .0308793201 + parame(i,2) = 3.64240187 + parame(i,3) = 258.655298 + ELSE IF (compna(i) == 'chlorobenzene') THEN + ! mm(i) = 112.558 + ! parame(i,1) = mm(i)* .0235308686 + ! parame(i,2) = 3.75328494 + ! parame(i,3) = 315.039018 + mm(i) = 112.558 ! PCIP-SAFT + parame(i,1) = mm(i)* 0.023824167 ! =2.6816 + parame(i,2) = 3.7352 + parame(i,3) = 308.82 + parame(i,6) = 1.69 + IF (pol == 2) parame(i,11)= 14.1 + ELSE IF (compna(i) == 'styrene') THEN + mm(i) = 104.150 + parame(i,1) = mm(i)* 2.9124104853E-2 + parame(i,2) = 3.760233548 + parame(i,3) = 298.51287564 + ELSE IF (compna(i) == 'methylmethanoate') THEN + mm(i) = 60.053 + parame(i,1) = mm(i)* .0446000264 + parame(i,2) = 3.08753499 + parame(i,3) = 242.626755 + IF (pol >= 1) mm(i) = 60.053 ! PCP-SAFT + IF (pol >= 1) parame(i,1) = mm(i)* 4.366991153963102E-002 ! =2.62250919768946 + IF (pol >= 1) parame(i,2) = 3.10946396964 + IF (pol >= 1) parame(i,3) = 239.051951942 + IF (pol >= 1) parame(i,6) = 1.77 + IF (pol >= 2) mm(i) = 60.053 ! PCIP-SAFT + IF (pol >= 2) parame(i,1) = mm(i)* 4.492572388931002E-2 ! 2.69792449 + IF (pol >= 2) parame(i,2) = 3.078467837 + IF (pol >= 2) parame(i,3) = 232.1842551 + IF (pol >= 2) parame(i,6) = 1.77 + IF (pol == 2) parame(i,11)= 5.05 + ELSE IF (compna(i) == 'ethylmethanoate') THEN + mm(i) = 74.079 ! PC-SAFT + parame(i,1) = mm(i)* .03898009 + parame(i,2) = 3.31087192 + parame(i,3) = 246.465646 + IF (pol >= 1) mm(i) = 74.079 ! PCP-SAFT + IF (pol >= 1) parame(i,1) = mm(i)* 3.825407152074255E-002 ! =2.83382336418509 + IF (pol >= 1) parame(i,2) = 3.33160046679 + IF (pol >= 1) parame(i,3) = 244.495680932 + IF (pol >= 1) parame(i,6) = 1.93000000000 + ELSE IF (compna(i) == 'propylmethanoate') THEN + mm(i) = 88.106 + parame(i,1) = mm(i)* .0364206062 + parame(i,2) = 3.41679642 + parame(i,3) = 246.457732 + IF (pol >= 1) mm(i) = 88.106 + IF (pol >= 1) parame(i,1) = mm(i)* 3.60050739149E-2 ! =3.17226304235232 + IF (pol >= 1) parame(i,2) = 3.42957609309 + IF (pol >= 1) parame(i,3) = 245.637644107 + IF (pol >= 1) parame(i,6) = 1.89 + ELSE IF (compna(i) == 'methylacetate') THEN + mm(i) = 74.079 ! PC-SAFT + parame(i,1) = mm(i)* 4.286817177E-2 ! =3.175631296 + parame(i,2) = 3.18722021277843 + parame(i,3) = 234.106931032456 + IF (pol >= 1) mm(i) = 74.079 ! PCP-SAFT + IF (pol >= 1) parame(i,1) = mm(i)* 4.228922065E-2 ! =3.132743176 + IF (pol >= 1) parame(i,2) = 3.2011401688 + IF (pol >= 1) parame(i,3) = 233.17562886 + IF (pol >= 1) parame(i,6) = 1.72 + IF (pol >= 2) mm(i) = 74.079 ! PCIP-SAFT + IF (pol >= 2) parame(i,1) = mm(i)* 4.298900538E-2 ! =3.18458252 + IF (pol >= 2) parame(i,2) = 3.180642322 + IF (pol >= 2) parame(i,3) = 229.3132680 + IF (pol >= 2) parame(i,6) = 1.72 + IF (pol == 2) parame(i,11)= 6.94 + ELSE IF (compna(i) == 'ethylacetate') THEN + mm(i) = 88.106 ! PC-SAFT + parame(i,1) = mm(i)* .0401464427 ! =3.537142481 + parame(i,2) = 3.30789258 + parame(i,3) = 230.800689 + IF (pol >= 1) mm(i) = 88.106 ! PCP-SAFT + IF (pol >= 1) parame(i,1) = mm(i)* 0.039792575 ! =3.505964572 + IF (pol >= 1) parame(i,2) = 3.317655188 + IF (pol >= 1) parame(i,3) = 230.2434769 + IF (pol >= 1) parame(i,6) = 1.78 + IF (pol >= 2) mm(i) = 88.106 ! PCIP-SAFT + IF (pol >= 2) parame(i,1) = mm(i)* 0.040270267 ! =3.548052143 + IF (pol >= 2) parame(i,2) = 3.302097562 + IF (pol >= 2) parame(i,3) = 227.5026191 + IF (pol >= 2) parame(i,6) = 1.78 + IF (pol == 2) parame(i,11)= 8.62 + ELSE IF (compna(i) == 'ethyl-propanoate') THEN + mm(i) = 102.133 + parame(i,1) = mm(i)* .0375692464 + parame(i,2) = 3.40306071 + parame(i,3) = 232.778374 + ELSE IF (compna(i) == 'propyl-ethanoate') THEN + mm(i) = 102.133 + parame(i,1) = mm(i)* .0370721275 + parame(i,2) = 3.42272266 + parame(i,3) = 235.758378 + IF (pol >= 1) mm(i) = 102.133 ! PCP-SAFT + IF (pol >= 1) parame(i,1) = mm(i)* 3.687149995200072E-2 ! =3.76579690459769 + IF (pol >= 1) parame(i,2) = 3.4289353421006 + IF (pol >= 1) parame(i,3) = 235.41679442910 + IF (pol >= 1) parame(i,6) = 1.78 + ! IF (pol.EQ.2) parame(i,11)= 10.41 + ELSE IF (compna(i) == 'nbutyl-ethanoate') THEN + mm(i) = 116.16 ! PC-SAFT + parame(i,1) = mm(i)* .03427004 + parame(i,2) = 3.54269638 + parame(i,3) = 242.515768 + IF (pol >= 1) mm(i) = 116.16 ! PCP-SAFT + IF (pol >= 1) parame(i,1) = mm(i)* 3.411585209773470E-002 ! =3.96289737967286 + IF (pol >= 1) parame(i,2) = 3.54821589228130 + IF (pol >= 1) parame(i,3) = 242.274388267447 + IF (pol >= 1) parame(i,6) = 1.87000000000000 + IF (pol >= 2) mm(i) = 116.16 ! PCIP-SAFT + IF (pol >= 2) parame(i,1) = mm(i)* 3.442139015733717E-002 ! =3.99838868067629 + IF (pol >= 2) parame(i,2) = 3.53576054452119 + IF (pol >= 2) parame(i,3) = 240.154409609249 + IF (pol >= 2) parame(i,6) = 1.87000000000000 + IF (pol == 2) parame(i,11)= 14.2000000000000 + ELSE IF (compna(i) == 'methyl-octanoate') THEN + mm(i) = 158.24 ! PC-SAFT + parame(i,1) = 5.2074 + parame(i,2) = 3.6069 + parame(i,3) = 244.12 + ELSE IF (compna(i) == 'methyl-decanoate') THEN + mm(i) = 186.2912 ! PC-SAFT + parame(i,1) = 5.8402 + parame(i,2) = 3.6871 + parame(i,3) = 248.27 + + mm(i) = 186.2912 ! PC-SAFT from GC-method Tim + parame(i,1) = 7.716 + parame(i,2) = 3.337303029 + parame(i,3) = 204.250907 + + mm(i) = 186.2912 ! PC-SAFT from GC-method (tightly fit) Tim + parame(i,1) = 7.728 + parame(i,2) = 3.334023322 + parame(i,3) = 206.9099379 + + ! mm(i) = 186.2912 ! PC-SAFT from fit to DIPPR + ! parame(i,1) = 6.285005 + ! parame(i,2) = 3.594888 + ! parame(i,3) = 236.781461 + ! ! parame(i,6) = 2.08056 + + ! mm(i) = 186.291000000000 + ! parame(i,1) = 6.28500485898895 + ! parame(i,2) = 3.59488828061149 + ! parame(i,3) = 236.781461491921 + ! parame(i,6) = 2.08055996894836 + ! parame(i,8) = 1.00000000000000 + mm(i) = 186.291000000000 + parame(i,1) = 6.14436331493372 + parame(i,2) = 3.61977264863944 + parame(i,3) = 242.071887817656 + + ELSE IF (compna(i) == 'methyl-dodecanoate') THEN + mm(i) = 214.344 ! PC-SAFT + parame(i,1) = 6.5153 + parame(i,2) = 3.7406 + parame(i,3) = 250.7 + ELSE IF (compna(i) == 'methyl-tetradecanoate') THEN + mm(i) = 242.398 ! PC-SAFT + parame(i,1) = 7.1197 + parame(i,2) = 3.7968 + parame(i,3) = 253.77 + ELSE IF (compna(i) == 'methyl-hexadecanoate') THEN + mm(i) = 270.451 ! PC-SAFT + parame(i,1) = 7.891 + parame(i,2) = 3.814 + parame(i,3) = 253.71 + ELSE IF (compna(i) == 'methyl-octadecanoate') THEN + mm(i) = 298.504 ! PC-SAFT + parame(i,1) = 8.8759 + parame(i,2) = 3.7932 + parame(i,3) = 250.81 + ELSE IF (compna(i) == 'CH2F2') THEN + mm(i) = 52.02 + parame(i,1) = 3.110084171 + parame(i,2) = 2.8145230485 + parame(i,3) = 158.98060151 + ELSE IF (compna(i) == 'naphthalene') THEN + ! mm(i) = 128.174000000 + ! parame(i,1) = mm(i)* 2.4877834216412E-2 + ! parame(i,2) = 3.82355815011 + ! parame(i,3) = 341.560675334 + + mm(i) = 128.17400000000 + parame(i,1) = mm(i)* 2.6400924157729E-2 + parame(i,2) = 3.8102186020014 + parame(i,3) = 328.96792935903 + ELSE IF (compna(i) == 'h2s') THEN + mm(i) = 34.0820000000000 ! PC-SAFT + parame(i,1) = mm(i)* 4.838886696385162E-002 ! = 1.64918936386199 + parame(i,2) = 3.05478289838459 + parame(i,3) = 229.838873939562 + nhb_typ(i) = 2 + nhb_no(i,1) = 1 + nhb_no(i,2) = 1 + eps_hb(i,i,1,2)= 536.634834731413 + eps_hb(i,i,2,1)= 536.634834731413 + eps_hb(i,i,1,1)= 0.0 + eps_hb(i,i,2,2)= 0.0 + kap_hb(i,i) = 1.000000000000000E-003 +! PC-SAFT from Xiaohua + mm(i) = 34.082 ! PC-SAFT + parame(i,1) = 1.63677 + parame(i,2) = 3.06565 + parame(i,3) = 230.2121 + nhb_typ(i) = 2 + nhb_no(i,1) = 1 + nhb_no(i,2) = 1 + eps_hb(i,i,1,2)= 275.1088 + eps_hb(i,i,2,1)= 275.1088 + eps_hb(i,i,1,1)= 0.0 + eps_hb(i,i,2,2)= 0.0 + kap_hb(i,i) = 1.E-2 + ! IF (pol.GE.1) mm(i) = 34.082 ! PCP-SAFT with quadrupole + ! IF (pol.GE.1) parame(i,1) = mm(i)* 3.03171032558E-2 ! =1.03326751316478 + ! IF (pol.GE.1) parame(i,2) = 3.6868189914018 + ! IF (pol.GE.1) parame(i,3) = 246.862831266172 + ! IF (pol.GE.1) nhb_typ(i) = 2 + ! IF (pol.GE.1) nhb_no(i,1) = 1 + ! IF (pol.GE.1) nhb_no(i,2) = 1 + ! IF (pol.GE.1) eps_hb(i,i,1,2)= 987.4927232 + ! IF (pol.GE.1) eps_hb(i,i,2,1)= 987.4927232 + ! IF (pol.GE.1) eps_hb(i,i,1,1)= 0.0 + ! IF (pol.GE.1) eps_hb(i,i,2,2)= 0.0 + ! IF (pol.GE.1) kap_hb(i,i) = 5.5480659623d-4 + ! IF (pol.GE.1) parame(i,6) = 0.97833 + ! IF (pol.GE.1) parame(i,7) = 3.8623 + ! IF (pol.GE.1) LLi(i) = 1.2737*parame(i,2) + ! IF (pol.GE.1) phi_criti(i)= 14.316 + ! IF (pol.GE.1) chap(i) = 0.4473 + IF (pol >= 1) mm(i) = 34.0820000000000 ! PCP-SAFT no quadrupoLE + IF (pol >= 1) parame(i,1) = mm(i)* 4.646468487062725E-002 ! 1.58360938976072 + IF (pol >= 1) parame(i,2) = 3.10111012646306 + IF (pol >= 1) parame(i,3) = 230.243457544889 + IF (pol >= 1) nhb_typ(i) = 2 + IF (pol >= 1) nhb_no(i,1) = 1 + IF (pol >= 1) nhb_no(i,2) = 1 + IF (pol >= 1) eps_hb(i,i,1,2)= 584.367708701411 + IF (pol >= 1) eps_hb(i,i,2,1)= 584.367708701411 + IF (pol >= 1) eps_hb(i,i,1,1)= 0.0 + IF (pol >= 1) eps_hb(i,i,2,2)= 0.0 + IF (pol >= 1) kap_hb(i,i) = 1.000000000000000E-003 + IF (pol >= 1) parame(i,6) = 0.978330000000000 + + IF (pol >= 1) lli(i) = 1.2737*parame(i,2) + IF (pol >= 1) phi_criti(i)= 14.316 + IF (pol >= 1) chap(i) = 0.4473 + + + IF (pol == 2) parame(i,7) = 0.0 + IF (pol == 2) mm(i) = 34.0820000000000 ! PCIP-SAFT + IF (pol == 2) parame(i,1) = mm(i)* 4.806418212963168E-002 ! 1.63812345534211 + IF (pol == 2) parame(i,2) = 3.06556006883749 + IF (pol == 2) parame(i,3) = 221.746622243054 + IF (pol == 2) nhb_typ(i) = 2 + IF (pol == 2) nhb_no(i,1) = 1 + IF (pol == 2) nhb_no(i,2) = 1 + IF (pol == 2) eps_hb(i,i,1,2)= 672.164783984789 + IF (pol == 2) eps_hb(i,i,2,1)= 672.164783984789 + IF (pol == 2) eps_hb(i,i,1,1)= 0.0 + IF (pol == 2) eps_hb(i,i,2,2)= 0.0 + IF (pol == 2) kap_hb(i,i) = 1.000000000000000E-003 + IF (pol == 2) parame(i,6) = 0.978330000000000 + IF (pol == 2) parame(i,11) = 3.60200000000000 + IF (pol == 2) parame(i,7) = 0.0 + + IF (pol >= 1)mm(i) = 34.0820000000000 !PCP-SAFT D&Q + IF (pol >= 1)parame(i,1) = mm(i)* 3.974667896078737E-002 ! = 1.35464631234155 + IF (pol >= 1)parame(i,2) = 3.30857082333438 + IF (pol >= 1)parame(i,3) = 234.248947273191 + IF (pol >= 1)nhb_typ(i) = 2 + IF (pol >= 1)nhb_no(i,1) = 1 + IF (pol >= 1)nhb_no(i,2) = 1 + IF (pol >= 1)eps_hb(i,i,1,2)= 780.770936834770 + IF (pol >= 1)eps_hb(i,i,2,1)= 780.770936834770 + IF (pol >= 1)eps_hb(i,i,1,1)= 0.0 + IF (pol >= 1)eps_hb(i,i,2,2)= 0.0 + IF (pol >= 1)kap_hb(i,i) = 1.000000000000000E-003 + IF (pol >= 1)parame(i,6) = 0.978330000000000 + IF (pol >= 1)parame(i,7) = 2.93750500000000 + + ELSE IF (compna(i) == 'methanol') THEN + mm(i) = 32.042 ! PC-SAFT + parame(i,1) = mm(i)* .0476100379 + parame(i,2) = 3.23000005 + parame(i,3) = 188.904644 + nhb_typ(i) = 2 + nhb_no(i,1) = 1 ! no. of sites of type 1 + nhb_no(i,2) = 1 ! no. of sites of type 2 + eps_hb(i,i,1,2)= 2899.49055 + eps_hb(i,i,2,1)= 2899.49055 + eps_hb(i,i,1,1)= 0.0 + eps_hb(i,i,2,2)= 0.0 + kap_hb(i,i) = .0351760892 + IF (pol >= 1) mm(i) = 32.042 ! PCP-SAFT + IF (pol >= 1) parame(i,1) = mm(i)* 7.213091821E-2 ! =2.31121888139672 + IF (pol >= 1) parame(i,2) = 2.8270129502 + IF (pol >= 1) parame(i,3) = 176.3760515 + IF (pol >= 1) nhb_typ(i) = 2 + IF (pol >= 1) nhb_no(i,1) = 1 + IF (pol >= 1) nhb_no(i,2) = 1 + IF (pol >= 1) eps_hb(i,i,1,2)= 2332.5845803 + IF (pol >= 1) eps_hb(i,i,2,1)= 2332.5845803 + IF (pol >= 1) eps_hb(i,i,1,1)= 0.0 + IF (pol >= 1) eps_hb(i,i,2,2)= 0.0 + IF (pol >= 1) kap_hb(i,i) = 8.9248658086E-2 + IF (pol >= 1) parame(i,6) = 1.7 + IF (pol >= 1) lli(i) = 1.75*parame(i,2) + IF (pol >= 1) phi_criti(i)= 23.43 + IF (pol >= 1) chap(i) = 0.304 + IF (pol == 2) mm(i) = 32.042 ! PCIP-SAFT + IF (pol == 2) parame(i,1) = 2.0693 + IF (pol == 2) parame(i,2) = 2.9547 + IF (pol == 2) parame(i,3) = 174.51 + IF (pol == 2) nhb_typ(i) = 2 + IF (pol == 2) nhb_no(i,1) = 1 + IF (pol == 2) nhb_no(i,2) = 1 + IF (pol == 2) eps_hb(i,i,1,2)= 2418.5 + IF (pol == 2) eps_hb(i,i,2,1)= 2418.5 + IF (pol == 2) eps_hb(i,i,1,1)= 0.0 + IF (pol == 2) eps_hb(i,i,2,2)= 0.0 + IF (pol == 2) kap_hb(i,i) = 0.06319 + IF (pol == 2) parame(i,6) = 1.7 + IF (pol == 2) parame(i,11)= 3.29 + ! mm(i) = 32.0420000000000 ! PCP-SAFT with adjusted QQ + ! parame(i,1) = mm(i)* 6.241807629559099E-002 + ! ! parame(i,1) = 2.00000000066333 + ! parame(i,2) = 2.97610169698593 + ! parame(i,3) = 163.268505098639 + ! nhb_typ(i) = 2 + ! nhb_no(i,1) = 1 + ! nhb_no(i,2) = 1 + ! eps_hb(i,i,1,2)= 2449.55621933612 + ! eps_hb(i,i,2,1)= 2449.55621933612 + ! eps_hb(i,i,1,1)= 0.0 + ! eps_hb(i,i,2,2)= 0.0 + ! kap_hb(i,i) = 8.431015160393653E-002 + ! parame(i,6) = 1.72000000000000 + ! parame(i,7) = 1.59810028824523 + ELSE IF (compna(i) == 'ethanol') THEN + mm(i) = 46.069 + parame(i,1) = mm(i)* .0517195521 + parame(i,2) = 3.17705595 + parame(i,3) = 198.236542 + nhb_typ(i) = 2 + nhb_no(i,1) = 1 ! no. of sites of type 1 + nhb_no(i,2) = 1 ! no. of sites of type 2 + eps_hb(i,i,1,2)= 2653.38367 + eps_hb(i,i,2,1)= 2653.38367 + eps_hb(i,i,1,1)= 0.0 + eps_hb(i,i,2,2)= 0.0 + kap_hb(i,i) = .0323840159 + IF (pol >= 1) mm(i) = 46.0690000000000 + IF (pol >= 1) parame(i,1) = mm(i)* 4.753626908781145E-002 ! =2.18994838060639 + IF (pol >= 1) parame(i,2) = 3.30120000000000 + IF (pol >= 1) parame(i,3) = 209.824555801706 + IF (pol >= 1) nhb_typ(i) = 2 + IF (pol >= 1) nhb_no(i,1) = 1 + IF (pol >= 1) nhb_no(i,2) = 1 + IF (pol >= 1) eps_hb(i,i,1,2)= 2584.53116785767 + IF (pol >= 1) eps_hb(i,i,2,1)= 2584.53116785767 + IF (pol >= 1) eps_hb(i,i,1,1)= 0.0 + IF (pol >= 1) eps_hb(i,i,2,2)= 0.0 + IF (pol >= 1) kap_hb(i,i) = 2.349382956935725E-002 + IF (pol >= 1) parame(i,6) = 1.69000000000000 + ! mm(i) = 46.0690000000000 + ! parame(i,1) = mm(i)* 5.117957752785066E-002 ! =2.357791957 + ! parame(i,2) = 3.24027031244304 + ! parame(i,3) = 175.657110615456 + ! nhb_typ(i) = 2 + ! nhb_no(i,1) = 1 + ! nhb_no(i,2) = 1 + ! eps_hb(i,i,1,2)= 2273.62670516146 + ! eps_hb(i,i,2,1)= 2273.62670516146 + ! eps_hb(i,i,1,1)= 0.0 + ! eps_hb(i,i,2,2)= 0.0 + ! kap_hb(i,i) = 7.030279197039477E-002 + ! parame(i,6) = 1.69000000000000 + ! parame(i,7) = 3.63701294195013 + IF (pol == 2) mm(i) = 46.0690000000000 + IF (pol == 2) parame(i,1) = mm(i)* 4.733436280008321E-002 ! =2.18064676 + IF (pol == 2) parame(i,2) = 3.31260000000000 + IF (pol == 2) parame(i,3) = 207.594119926613 + IF (pol == 2) nhb_typ(i) = 2 + IF (pol == 2) nhb_no(i,1) = 1 + IF (pol == 2) nhb_no(i,2) = 1 + IF (pol == 2) eps_hb(i,i,1,2)= 2589.68311382661 + IF (pol == 2) eps_hb(i,i,2,1)= 2589.68311382661 + IF (pol == 2) eps_hb(i,i,1,1)= 0.0 + IF (pol == 2) eps_hb(i,i,2,2)= 0.0 + IF (pol == 2) kap_hb(i,i) = 2.132561218631547E-002 + IF (pol == 2) parame(i,6) = 1.69000000000000 + IF (pol == 2) parame(i,7) = 0.0 + IF (pol == 2) parame(i,11)= 5.11000000000000 + ELSE IF (compna(i) == '1-propanol') THEN + mm(i) = 60.096 + parame(i,1) = mm(i)* .0499154461 + parame(i,2) = 3.25221234 + parame(i,3) = 233.396705 + nhb_typ(i) = 2 + nhb_no(i,1) = 1 ! no. of sites of type 1 + nhb_no(i,2) = 1 ! no. of sites of type 2 + eps_hb(i,i,1,2)= 2276.77867 + eps_hb(i,i,2,1)= 2276.77867 + eps_hb(i,i,1,1)= 0.0 + eps_hb(i,i,2,2)= 0.0 + kap_hb(i,i) = .0152683094 + ELSE IF (compna(i) == '1-butanol') THEN + mm(i) = 74.123 + parame(i,1) = mm(i)* .0341065046 + parame(i,2) = 3.72361538 + parame(i,3) = 269.798048 + nhb_typ(i) = 2 + nhb_no(i,1) = 1 ! no. of sites of type 1 + nhb_no(i,2) = 1 ! no. of sites of type 2 + eps_hb(i,i,1,2)= 2661.37119 + eps_hb(i,i,2,1)= 2661.37119 + eps_hb(i,i,1,1)= 0.0 + eps_hb(i,i,2,2)= 0.0 + kap_hb(i,i) = .00489087833 + mm(i) = 74.1230000000000 + parame(i,1) = mm(i)* 3.329202420547412E-002 ! =2.46770471018236 + parame(i,2) = 3.76179376417092 + parame(i,3) = 270.237284242002 + nhb_typ(i) = 2 + nhb_no(i,1) = 1 + nhb_no(i,2) = 1 + eps_hb(i,i,1,2)= 2669.28754983370 + eps_hb(i,i,2,1)= 2669.28754983370 + eps_hb(i,i,1,1)= 0.0 + eps_hb(i,i,2,2)= 0.0 + kap_hb(i,i) = 4.855584122733399E-003 + parame(i,6) = 1.66000000000000 + ELSE IF (compna(i) == '1-pentanol') THEN + mm(i) = 88.15 ! PC-SAFT + parame(i,1) = mm(i)* .041134139 + parame(i,2) = 3.45079143 + parame(i,3) = 247.278748 + nhb_typ(i) = 2 + nhb_no(i,1) = 1 ! no. of sites of type 1 + nhb_no(i,2) = 1 ! no. of sites of type 2 + eps_hb(i,i,1,2)= 2252.09237 + eps_hb(i,i,2,1)= 2252.09237 + eps_hb(i,i,1,1)= 0.0 + eps_hb(i,i,2,2)= 0.0 + kap_hb(i,i) = .0103189939 + IF (pol >= 1) mm(i) = 88.1500000000000 ! PCP-SAFT + IF (pol >= 1) parame(i,1) = mm(i)* 4.138903382168521E-002 ! =3.64844333138155 + IF (pol >= 1) parame(i,2) = 3.44250118689142 + IF (pol >= 1) parame(i,3) = 246.078034174947 + IF (pol >= 1) nhb_typ(i) = 2 + IF (pol >= 1) nhb_no(i,1) = 1 + IF (pol >= 1) nhb_no(i,2) = 1 + IF (pol >= 1) eps_hb(i,i,1,2)= 2236.72830142446 + IF (pol >= 1) eps_hb(i,i,2,1)= 2236.72830142446 + IF (pol >= 1) eps_hb(i,i,1,1)= 0.0 + IF (pol >= 1) eps_hb(i,i,2,2)= 0.0 + IF (pol >= 1) kap_hb(i,i) = 1.040067895187016E-002 + IF (pol >= 1) parame(i,6) = 1.70000000000000 + IF (pol == 2) mm(i) = 88.1500000000000 ! PCIP-SAFT + IF (pol == 2) parame(i,1) = mm(i)* 4.161521814399406E-002 ! =3.66838147939308 + IF (pol == 2) parame(i,2) = 3.43496654431777 + IF (pol == 2) parame(i,3) = 244.177313808431 + IF (pol == 2) nhb_typ(i) = 2 + IF (pol == 2) nhb_no(i,1) = 1 + IF (pol == 2) nhb_no(i,2) = 1 + IF (pol == 2) eps_hb(i,i,1,2)= 2241.27880639096 + IF (pol == 2) eps_hb(i,i,2,1)= 2241.27880639096 + IF (pol == 2) eps_hb(i,i,1,1)= 0.0 + IF (pol == 2) eps_hb(i,i,2,2)= 0.0 + IF (pol == 2) kap_hb(i,i) = 1.049516309928397E-002 + IF (pol == 2) parame(i,6) = 1.70000000000000 + IF (pol == 2) parame(i,11)= 10.8000000000000 + ELSE IF (compna(i) == '1-octanol') THEN + mm(i) = 130.23 + parame(i,1) = mm(i)* .0334446084 + parame(i,2) = 3.714535 + parame(i,3) = 262.740637 + nhb_typ(i) = 2 + nhb_no(i,1) = 1 ! no. of sites of type 1 + nhb_no(i,2) = 1 ! no. of sites of type 2 + eps_hb(i,i,1,2)= 2754.77272 + eps_hb(i,i,2,1)= 2754.77272 + eps_hb(i,i,1,1)= 0.0 + eps_hb(i,i,2,2)= 0.0 + kap_hb(i,i) = .00219656803 + ELSE IF (compna(i) == '1-nonanol') THEN + mm(i) = 144.257 + parame(i,1) = mm(i)* .0324692669 + parame(i,2) = 3.72924286 + parame(i,3) = 263.636673 + nhb_typ(i) = 2 + nhb_no(i,1) = 1 ! no. of sites of type 1 + nhb_no(i,2) = 1 ! no. of sites of type 2 + eps_hb(i,i,1,2)= 2941.9231 + eps_hb(i,i,2,1)= 2941.9231 + eps_hb(i,i,1,1)= 0.0 + eps_hb(i,i,2,2)= 0.0 + kap_hb(i,i) = .00142696883 + ELSE IF (compna(i) == '2-propanol') THEN + mm(i) = 60.096 + parame(i,1) = mm(i)* .0514663133 + parame(i,2) = 3.20845858 + parame(i,3) = 208.420809 + nhb_typ(i) = 2 + nhb_no(i,1) = 1 ! no. of sites of type 1 + nhb_no(i,2) = 1 ! no. of sites of type 2 + eps_hb(i,i,1,2)= 2253.91064 + eps_hb(i,i,2,1)= 2253.91064 + eps_hb(i,i,1,1)= 0.0 + eps_hb(i,i,2,2)= 0.0 + kap_hb(i,i) = .0246746934 + ELSE IF (compna(i) == '2-methyl-2-butanol') THEN + mm(i) = 88.15 + parame(i,1) = mm(i)* .0289135026 + parame(i,2) = 3.90526707 + parame(i,3) = 266.011828 + nhb_typ(i) = 2 + nhb_no(i,1) = 1 ! no. of sites of type 1 + nhb_no(i,2) = 1 ! no. of sites of type 2 + eps_hb(i,i,1,2)= 2618.80124 + eps_hb(i,i,2,1)= 2618.80124 + eps_hb(i,i,1,1)= 0.0 + eps_hb(i,i,2,2)= 0.0 + kap_hb(i,i) = .00186263367 + ELSE IF (compna(i) == 'acetic-acid') THEN + mm(i) = 60.053 + parame(i,1) = mm(i)* .0227076949 + parame(i,2) = 3.79651163 + parame(i,3) = 199.225066 + nhb_typ(i) = 2 + nhb_no(i,1) = 1 ! no. of sites of type 1 + nhb_no(i,2) = 1 ! no. of sites of type 2 + eps_hb(i,i,1,2)= 3092.40109 + eps_hb(i,i,2,1)= 3092.40109 + eps_hb(i,i,1,1)= 0.0 + eps_hb(i,i,2,2)= 0.0 + kap_hb(i,i) = .0870093874 + + + mm(i) = 60.053 + parame(i,1) = mm(i)* .0181797646 + parame(i,2) = 4.13711044 + parame(i,3) = 207.552969 + nhb_typ(i) = 2 + nhb_no(i,1) = 1 ! no. of sites of type 1 + nhb_no(i,2) = 1 ! no. of sites of type 2 + eps_hb(i,i,1,2)= 3198.84362 + eps_hb(i,i,2,1)= 3198.84362 + eps_hb(i,i,1,1)= 0.0 + eps_hb(i,i,2,2)= 0.0 + kap_hb(i,i) = .0586552968 + +! mit gesetztem Dipol-Moment + mm(i) = 60.0530000000000 + parame(i,1) = mm(i)* 1.736420143637533E-002 + parame(i,2) = 4.25220708070687 + parame(i,3) = 190.957247854820 + parame(i,6) = 3.50000000000000 + nhb_typ(i) = 2 + nhb_no(i,1) = 1 ! no. of sites of type 1 + nhb_no(i,2) = 1 ! no. of sites of type 2 + eps_hb(i,i,1,2)= 3096.36190957945 + eps_hb(i,i,2,1)= 3096.36190957945 + eps_hb(i,i,1,1)= 0.0 + eps_hb(i,i,2,2)= 0.0 + kap_hb(i,i) = 6.154307094782551E-002 + + ELSE IF (compna(i) == 'propionic-acid') THEN + mm(i) = 74.0800000000000 + parame(i,1) = mm(i)* 2.359519915877884E-002 + parame(i,2) = 3.99339224153844 + parame(i,3) = 295.947729838532 + nhb_typ(i) = 2 + nhb_no(i,1) = 1 ! no. of sites of type 1 + nhb_no(i,2) = 1 ! no. of sites of type 2 + eps_hb(i,i,1,2)= 2668.97826430874 + eps_hb(i,i,2,1)= 2668.97826430874 + eps_hb(i,i,1,1)= 0.0 + eps_hb(i,i,2,2)= 0.0 + kap_hb(i,i) = 3.660242292423115E-002 + ELSE IF (compna(i) == 'acrylic-acid') THEN + mm(i) = 72.0636 + parame(i,1) = mm(i)* .0430585424 + parame(i,2) = 3.0545415 + parame(i,3) = 164.115604 + nhb_typ(i) = 2 + nhb_no(i,1) = 1 ! no. of sites of type 1 + nhb_no(i,2) = 1 ! no. of sites of type 2 + eps_hb(i,i,1,2)= 3065.40667 + eps_hb(i,i,2,1)= 3065.40667 + eps_hb(i,i,1,1)= 0.0 + eps_hb(i,i,2,2)= 0.0 + kap_hb(i,i) = .336261669 + ELSE IF (compna(i) == 'caproic-acid') THEN + mm(i) = 116.16 + parame(i,1) = 5.87151 + parame(i,2) = 3.0694697 + parame(i,3) = 241.4569 + nhb_typ(i) = 1 + eps_hb(i,i,1,1)= 2871.37 + kap_hb(i,i) = 3.411613D-3 + ELSE IF (compna(i) == 'aniline') THEN + mm(i) = 93.13 + parame(i,1) = mm(i)* .0285695992 + parame(i,2) = 3.70214085 + parame(i,3) = 335.471062 + nhb_typ(i) = 2 + nhb_no(i,1) = 1 ! no. of sites of type 1 + nhb_no(i,2) = 1 ! no. of sites of type 2 + eps_hb(i,i,1,2)= 1351.64234 + eps_hb(i,i,2,1)= 1351.64234 + eps_hb(i,i,1,1)= 0.0 + eps_hb(i,i,2,2)= 0.0 + kap_hb(i,i) = .0748830615 + + mm(i) = 93.1300000000000 + parame(i,1) = mm(i)* 2.834372610192228E-002 ! =2.63965121187202 + parame(i,2) = 3.71326867619433 + parame(i,3) = 332.253796842009 + nhb_typ(i) = 2 + nhb_no(i,1) = 1 + nhb_no(i,2) = 1 + eps_hb(i,i,1,2)= 1392.14266886674 + eps_hb(i,i,2,1)= 1392.14266886674 + eps_hb(i,i,1,1)= 0.0 + eps_hb(i,i,2,2)= 0.0 + kap_hb(i,i) = 7.424612087328866E-002 + parame(i,6) = 1.55000000000000 + IF (pol == 2) parame(i,11)= 12.1000000000000 + ELSE IF (compna(i) == 'HF') THEN + ! mm(i) = 20.006 ! PC-SAFT + ! parame(i,1) = 0.87731 + ! parame(i,2) = 3.0006 + ! parame(i,3) = 112.24 + ! nhb_typ(i) = 2 + ! nhb_no(i,1) = 1 + ! nhb_no(i,2) = 1 + ! eps_hb(i,i,1,2)= 2208.22 + ! eps_hb(i,i,2,1)= 2208.22 + ! eps_hb(i,i,1,1)= 0.0 + ! eps_hb(i,i,2,2)= 0.0 + ! kap_hb(i,i) = 0.71265 + mm(i) = 20.0060000000000 ! PCP-SAFT + parame(i,1) = 1.00030000000000 + parame(i,2) = 3.17603622195029 + parame(i,3) = 331.133373208282 + nhb_typ(i) = 2 + nhb_no(i,1) = 1 + nhb_no(i,2) = 1 + eps_hb(i,i,1,2)= 348.251433080979 + eps_hb(i,i,2,1)= 348.251433080979 + eps_hb(i,i,1,1)= 0.0 + eps_hb(i,i,2,2)= 0.0 + kap_hb(i,i) = 2.868887975449893E-002 + parame(i,6) = 1.82600000000000 + ELSE IF (compna(i) == 'HCl') THEN + ! mm(i) = 36.4610000000000 + ! parame(i,1) = mm(i)* 3.922046741026943E-002 + ! parame(i,2) = 3.08731180727493 + ! parame(i,3) = 203.898845304388 + ! nhb_typ(i) = 2 + ! nhb_no(i,1) = 1 + ! nhb_no(i,2) = 1 + ! eps_hb(i,i,1,2)= 245.462773177367 + ! eps_hb(i,i,2,1)= 245.462773177367 + ! eps_hb(i,i,1,1)= 0.0 + ! eps_hb(i,i,2,2)= 0.0 + ! kap_hb(i,i) = 0.256454187330899 + mm(i) = 36.461 ! PCIP-SAFT + parame(i,1) = 1.6335 + parame(i,2) = 2.9066 + parame(i,3) = 190.17 + parame(i,6) = 1.1086 + IF (pol == 2) parame(i,11)= 2.63 + ELSE IF (compna(i) == 'gen') THEN + mm(i) = 302.0 + parame(i,1) = 8.7563 + parame(i,2) = 3.604243 + parame(i,3) = 255.6434 + nhb_typ(i) = 2 + nhb_no(i,1) = 1 ! no. of sites of type 1 + nhb_no(i,2) = 1 ! no. of sites of type 2 + eps_hb(i,i,1,2)= 0.0 + eps_hb(i,i,2,1)= 0.0 + eps_hb(i,i,1,1)= 0.0 + eps_hb(i,i,2,2)= 0.0 + kap_hb(i,i) = 0.02 + ELSE IF (compna(i) == 'h2o') THEN + mm(i) = 18.015 + parame(i,1) = mm(i)* .05915 + parame(i,2) = 3.00068335 + parame(i,3) = 366.512135 + nhb_typ(i) = 2 + nhb_no(i,1) = 1 ! no. of sites of type 1 + nhb_no(i,2) = 1 ! no. of sites of type 2 + eps_hb(i,i,1,2)= 2500.6706 + eps_hb(i,i,2,1)= 2500.6706 + eps_hb(i,i,1,1)= 0.0 + eps_hb(i,i,2,2)= 0.0 + kap_hb(i,i) = .0348679836 + + ! mm(i) = 18.015 + ! parame(i,1) = 1.706 + ! parame(i,2) = 2.429 + ! parame(i,3) = 242.19 + ! nhb_typ(i) = 2 + ! nhb_no(i,1) = 1 ! no. of sites of type 1 + ! nhb_no(i,2) = 1 ! no. of sites of type 2 + ! eps_hb(i,i,1,2)= 2644.2 + ! eps_hb(i,i,2,1)= 2644.2 + ! eps_hb(i,i,1,1)= 0.0 + ! eps_hb(i,i,2,2)= 0.0 + ! kap_hb(i,i) = 0.153 + + ! mm(i) = 18.015 + ! parame(i,1) = mm(i)* .0588185709 + ! parame(i,2) = 3.02483704 + ! parame(i,3) = 382.086672 + !c! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! + ! nhb_typ(i) = 2 + ! nhb_no(i,1) = 1 ! no. of sites of type 1 + ! nhb_no(i,2) = 2 ! no. of sites of type 2 + !c! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! + ! eps_hb(i,i,1,2)= 2442.49782 + ! eps_hb(i,i,2,1)= 2442.49782 + ! eps_hb(i,i,1,1)=0.0 + ! eps_hb(i,i,2,2)=0.0 + ! kap_hb(i,i) = .0303754635 + + ! mit gefittetem Dipol-Moment - Haarlem-night + ! mm(i) = 18.015 + ! parame(i,1) = mm(i)* 7.0037160952278E-2 + ! parame(i,2) = 2.79276650240763 + ! parame(i,3) = 270.970053834558 + ! nhb_typ(i) = 2 + ! nhb_no(i,1) = 1 ! no. of sites of type 1 + ! nhb_no(i,2) = 1 ! no. of sites of type 2 + ! eps_hb(i,i,1,2)= 1427.8287 + ! eps_hb(i,i,2,1)= 1427.8287 + ! eps_hb(i,i,1,1)=0.0 + ! eps_hb(i,i,2,2)=0.0 + ! kap_hb(i,i) = 4.335167238E-2 + ! parame(i,6) = 3.968686856378 + + IF (pol >= 1) mm(i) = 18.015 ! PCP-SAFT + IF (pol >= 1) parame(i,1) = 0.922688825223317 + IF (pol >= 1) parame(i,2) = 3.17562052023944 + IF (pol >= 1) parame(i,3) = 388.462197714696 + IF (pol >= 1) nhb_typ(i) = 2 + IF (pol >= 1) nhb_no(i,1) = 1 + IF (pol >= 1) nhb_no(i,2) = 1 + IF (pol >= 1) eps_hb(i,i,1,2)= 2000.67247409031 + IF (pol >= 1) eps_hb(i,i,2,1)= 2000.67247409031 + IF (pol >= 1) eps_hb(i,i,1,1)= 0.0 + IF (pol >= 1) eps_hb(i,i,2,2)= 0.0 + IF (pol >= 1) kap_hb(i,i) = 2.040614952751225E-003 + IF (pol >= 1) parame(i,6) = 1.85500000000000 + IF (pol >= 1) parame(i,7) = 2.00000000000000 + ! IF (pol.EQ.2) mm(i) = 18.015 ! PCIP-SAFT - DQ with my=my_RPT + ! IF (pol.EQ.2) parame(i,1) = 1.0 + ! IF (pol.EQ.2) parame(i,2) = 3.14540664928026 + ! IF (pol.EQ.2) parame(i,3) = 320.283823615925 + ! IF (pol.EQ.2) nhb_typ(i) = 2 + ! IF (pol.EQ.2) nhb_no(i,1) = 2 + ! IF (pol.EQ.2) nhb_no(i,2) = 2 + ! IF (pol.EQ.2) eps_hb(i,i,1,2)= 1335.72887678032 + ! IF (pol.EQ.2) eps_hb(i,i,2,1)= 1335.72887678032 + ! IF (pol.EQ.2) eps_hb(i,i,1,1)= 0.0 + ! IF (pol.EQ.2) eps_hb(i,i,2,2)= 0.0 + ! IF (pol.EQ.2) kap_hb(i,i) = 4.162619960844732E-003 + ! IF (pol.EQ.2) parame(i,6) = 1.85500000000000 + ! IF (pol.EQ.2) parame(i,7) = 2.00000000000000 + ! IF (pol.EQ.2) parame(i,11)= 1.45000000000000 + ! mm(i) = 18.0150000000000 + ! parame(i,1) = 1.0 + ! parame(i,2) = 3.11505069470915 + ! parame(i,3) = 320.991387913502 + ! nhb_typ(i) = 2 + ! nhb_no(i,1) = 1 + ! nhb_no(i,2) = 1 + ! eps_hb(i,i,1,2)= 2037.76329812542 + ! eps_hb(i,i,2,1)= 2037.76329812542 + ! eps_hb(i,i,1,1)= 0.0 + ! eps_hb(i,i,2,2)= 0.0 + ! kap_hb(i,i) = 3.763148982832804E-003 + ! parame(i,6) = 1.85500000000000 + ! parame(i,7) = 2.00000000000000 + ! IF (pol.EQ.2) parame(i,11)= 1.45000000000000 + IF (pol == 2) mm(i) = 18.015 ! PCIP-SAFT - DQ with my=my_0 + IF (pol == 2) parame(i,1) = 1.0 + IF (pol == 2) parame(i,2) = 3.11574491885322 + IF (pol == 2) parame(i,3) = 322.699984283499 + IF (pol == 2) nhb_typ(i) = 2 + IF (pol == 2) nhb_no(i,1) = 1 + IF (pol == 2) nhb_no(i,2) = 1 + IF (pol == 2) eps_hb(i,i,1,2)= 2033.87777692450 + IF (pol == 2) eps_hb(i,i,2,1)= 2033.87777692450 + IF (pol == 2) eps_hb(i,i,1,1)= 0.0 + IF (pol == 2) eps_hb(i,i,2,2)= 0.0 + IF (pol == 2) kap_hb(i,i) = 3.815764667176484E-003 + IF (pol == 2) parame(i,6) = 1.85500000000000 + IF (pol == 2) parame(i,7) = 2.00000000000000 + IF (pol == 2) parame(i,11)= 1.45000000000000 + ! mm(i) = 18.015 ! Dortmund + ! parame(i,1) = 0.11065254*mm(i) + ! parame(i,2) = 2.36393615 + ! parame(i,3) = 300.288589 + ! nhb_typ(i) = 2 + ! nhb_no(i,1) = 1 + ! nhb_no(i,2) = 1 + ! eps_hb(i,i,1,2)= 1193.45585 + ! eps_hb(i,i,2,1)= 1193.45585 + ! eps_hb(i,i,1,1)= 0.0 + ! eps_hb(i,i,2,2)= 0.0 + ! kap_hb(i,i) = 0.091203519 + ! parame(i,6) = 1.8546 + ! parame(i,7) = 0.0 + ! parame(i,11)= 0.0 + ELSE IF (compna(i) == 'MBBA') THEN + mm(i) = 267.37 + parame(i,1) = 12.194 + parame(i,2) = 3.064 + parame(i,3) = 270.7 + e_lc(i,i) = 13.7 !Hino & Prausnitz + s_lc(i,i) = 0.176 !Hino & Prausnitz + ELSE IF (compna(i) == 'PCH5') THEN + mm(i) = 255.41 + parame(i,1) = 11.6 + parame(i,2) = 3.2 + parame(i,3) = 270.7 + ! E_LC(i,i) = 16.7 !Hino & Prausnitz + ! S_LC(i,i) = 0.176 !Hino & Prausnitz + e_lc(i,i) = 8.95 + s_lc(i,i) = 0.2 + + ! mm(i) = 255.41 + ! parame(i,1) = 11.6 + ! parame(i,2) = 3.2 + ! parame(i,3) = 290.7 + ! E_LC(i,i) = 7.18 + ! S_LC(i,i) = 0.2 + + ELSE IF (compna(i) == 'Li') THEN + mm(i) = 6.9 + parame(i,1) = 1.0 + parame(i,2) = 1.4 + parame(i,3) = 96.83 + parame(i,10)= 1.0 +! the self-association is set to zero in routine F_EXPL for ions + ! nhb_typ(i) = 1 + ! nhb_no(i,1) = 3 ! no. of sites of type 1 + ! eps_hb(i,i,1,1)= 2000.0 + ! kap_hb(i,i) = 0.008 + ELSE IF (compna(i) == 'Na') THEN + mm(i) = 23.0 + parame(i,1) = 1.0 + parame(i,2) = 1.9 + parame(i,3) = 147.38 + parame(i,10)= 1.0 +! the self-association is set to zero in routine F_EXPL for ions + nhb_typ(i) = 1 + nhb_no(i,1) = 3 ! no. of sites of type 1 + eps_hb(i,i,1,1)= 8946.28257 ! 25C, 3 sites, dG-ref-1 + kap_hb(i,i) = 0.001648933 + ELSE IF (compna(i) == 'Ka') THEN + mm(i) = 39.1 + parame(i,1) = 1.0 + parame(i,2) = 2.66 + parame(i,3) = 221.44 + parame(i,10)= 1.0 + ! the self-association is set to zero in routine F_EXPL for ions + nhb_typ(i) = 1 + nhb_no(i,1) = 3 ! no. of sites of type 1 + eps_hb(i,i,1,1)= 3118.336216 ! 25C, 3 sites, dG-ref-1 + kap_hb(i,i) = 0.00200559 + ELSE IF (compna(i) == 'Cs') THEN + mm(i) = 132.9 + parame(i,1) = 1.0 + parame(i,2) = 3.38 + parame(i,3) = 523.28 + parame(i,10)= 1.0 + ! the self-association is set to zero in routine F_EXPL for ions + ! nhb_typ(i) = 1 + ! nhb_no(i,1) = 3 ! no. of sites of type 1 + ! eps_hb(i,i,1,1)= 2000.0 + ! kap_hb(i,i) = 0.00200559 + ELSE IF (compna(i) == 'Cl') THEN + mm(i) = 35.5 + parame(i,1) = 1.0 + parame(i,2) = 3.62 + parame(i,3) = 225.44 + parame(i,10)= -1.0 +! the self-association is set to zero in routine F_EXPL for ions + nhb_typ(i) = 1 + nhb_no(i,1) = 4 ! no. of sites of type 1 + eps_hb(i,i,1,1)= 6744.12509 ! 25C, 3 sites, dG-ref-1 + kap_hb(i,i) = 0.00155252 + ELSE IF (compna(i) == 'Br') THEN + mm(i) = 79.9 + parame(i,1) = 1.0 + parame(i,2) = 3.9 + parame(i,3) = 330.82 + parame(i,10)= -1.0 +! the self-association is set to zero in routine F_EXPL for ions + nhb_typ(i) = 1 + nhb_no(i,1) = 4 ! no. of sites of type 1 + eps_hb(i,i,1,1)= 4516.033227 ! 25C, 3 sites, dG-ref-1 + kap_hb(i,i) = 0.00200559 + ELSE IF (compna(i) == 'Io') THEN + mm(i) = 126.9 + parame(i,1) = 1.0 + parame(i,2) = 4.4 + parame(i,3) = 380.60 + parame(i,10)= -1.0 +! the self-association is set to zero in routine F_EXPL for ions + nhb_typ(i) = 1 + nhb_no(i,1) = 4 ! no. of sites of type 1 + eps_hb(i,i,1,1)= 1631.203342 ! 25C, 3 sites, dG-ref-1 + kap_hb(i,i) = 0.00200559 + ELSE IF (compna(i) == 'OH') THEN + mm(i) = 17.0 + parame(i,1) = 1.0 + parame(i,2) = 3.06 + parame(i,3) = 217.26 + parame(i,10)= -1.0 + ! the self-association is set to zero in routine F_EXPL for ions + nhb_typ(i) = 1 + nhb_no(i,1) = 4 ! no. of sites of type 1 + eps_hb(i,i,1,1)= 14118.68089 ! 25C, 3 sites, dG-ref-1 + kap_hb(i,i) = 0.00200559 + ELSE IF (compna(i) == 'NO3') THEN + mm(i) = 62.0 + parame(i,1) = 1.0 + parame(i,2) = 4.12 + parame(i,3) = 239.48 + parame(i,10)= -1.0 + ! the self-association is set to zero in routine F_EXPL for ions + ! nhb_typ(i) = 1 + ! nhb_no(i,1) = 4 ! no. of sites of type 1 + ! eps_hb(i,i,1,1)= 2000.0 + ! kap_hb(i,i) = 0.00200559 + ELSE IF (compna(i) == 'bf4') THEN + mm(i) = 86.8 + parame(i,1) = 1.0 + parame(i,2) = 4.51 ! *0.85 + parame(i,3) = 164.7 + parame(i,10)= -1.0 + ELSE IF (compna(i) == 'pf6') THEN + mm(i) = 145.0 + parame(i,1) = 1.0 + parame(i,2) = 5.06 + parame(i,3) = 224.9 + parame(i,10)= -1.0 + ELSE IF (compna(i) == 'emim') THEN + mm(i) = 111.16 + parame(i,1) = 3.11 + parame(i,2) = 4.0 + parame(i,3) = 250.0 + parame(i,10)= 1.0 + ELSE IF (compna(i) == 'bmim') THEN + mm(i) = 139.21 + ! parame(i,1) = 2.81 + ! parame(i,2) = 3.5 + parame(i,1) = 3.81 + parame(i,2) = 4.0 + parame(i,3) = 250.0 + parame(i,6) = 0.0 + parame(i,10)= 1.0 + ELSE IF (compna(i) == 'hmim') THEN + mm(i) = 167.27 + parame(i,1) = 4.53 + parame(i,2) = 4.0 + parame(i,3) = 250.0 + parame(i,10)= 1.0 + ELSE IF (compna(i) == 'omim') THEN + mm(i) = 195.32 + parame(i,1) = 5.30 + parame(i,2) = 4.0 + parame(i,3) = 250.0 + parame(i,10)= 1.0 + ELSE IF (compna(i) == 'sw') THEN + parame(i,1) = 1.0 + parame(i,2) = 1.0 + parame(i,3) = 100.0 + parame(i,4) = 0.0 + parame(i,5) = 0.0 + mm(i) = 1.0 + parame(i,6) = 0.1175015839*2.0 + ! use Temp. in Kelvin in the input-file. For dimensionless quantities + ! (P*=P*sig**3/epsilon, T*=T*kBol/epsilon, rho*=rho*sig**3) calculate + ! P* = P *1E5 * (1.e-10)^3 / (100*8.31441/6.022045E+23) + ! T* = (T+273.15)/100 + ! for rho* go to utilities.f (subroutine SI_DENS) and write + ! density(ph) = dense(ph)*6.0/PI + ELSE IF (compna(i) == 'c8-sim') THEN + mm(i) = 114.231 + parame(i,1) = mm(i)* 4.095944E-2 ! =4.67883774717337 + parame(i,2) = 3.501769 + parame(i,3) = 163.8606 + ! mm(i) = 114.231000000000 + ! parame(i,1) = mm(i)* 3.547001476437745E-002 ! =4.05177525654960 + ! parame(i,2) = 3.70988567055814 + ! parame(i,3) = 192.787548176343 + ELSE IF (compna(i) == 'argon_ge') THEN + mm(i) = 39.948 + parame(i,1) = mm(i)*0.030327 + parame(i,2) = 3.149910 + parame(i,3) = 100.188975 + ELSE IF (compna(i) == 'argon_ge2') THEN + mm(i) = 39.948 + parame(i,1) = mm(i)*0.030327 + parame(i,2) = 3.149910 + parame(i,3) = 0.8*100.188975 + ELSE + WRITE (*,*) ' pure component parameters missing for ',compna(i) + STOP + END IF + + IF (pol == 2.AND.parame(i,11) == 0.0) THEN + WRITE (*,*) ' polarizability missing for comp. ',compna(i) + STOP + END IF + + IF (nhb_typ(i) /= 0) THEN + parame(i,12) = DBLE(nhb_typ(i)) + parame(i,13) = kap_hb(i,i) + no = 0 + DO j=1,nhb_typ(i) + DO k=1,nhb_typ(i) + parame(i,(14+no))=eps_hb(i,i,j,k) + no=no+1 + END DO + END DO + DO j=1,nhb_typ(i) + parame(i,(14+no))=DBLE(nhb_no(i,j)) + no=no+1 + END DO + ELSE + DO k=12,25 + parame(i,k)=0.0 + END DO + END IF + +END DO + + +DO i = 1,ncomp + DO j = 1,ncomp + IF (compna(i) == 'ps'.AND.compna(j) == 'cyclohexane')THEN + kij(i,j) = 0.0075 + ELSE IF(compna(i) == 'peva'.AND.compna(j) == 'ethylene')THEN +! -- 0 Gew.% VA------------- + ! kij(i,j) = 0.039 +! -- 7.5 Gew.% VA------------- + ! kij(i,j) = 0.0377325 + ! kij(i,j) = 0.0374867 +! ---12.7 Gew.% VA------------ + ! kij(i,j) = 0.036854 + ! kij(i,j) = 0.0366508 +! ---27.3 Gew.% VA------------ + ! kij(i,j) = 0.034386 + ! kij(i,j) = 0.0352375 +! ---31.8 Gew.% VA------------ + kij(i,j) = 0.033626 + ! kij(i,j) = 0.0350795 +! ---42.7 Gew.% VA------------ + ! kij(i,j) = 0.031784 + ! kij(i,j) = 0.035239 + ELSE IF(compna(i) == 'gen'.AND.compna(j) == 'h2o')THEN + kij(i,j) = - 0.2 + ELSE IF(compna(i) == 'peva'.AND.compna(j) == 'vinylacetate')THEN + kij(i,j) = 0.019 + ELSE IF(compna(i) == 'ps'.AND.compna(j) == 'co2') THEN + IF ( pol == 0 ) kij(i,j) = 0.195 + IF ( pol == 1 ) kij(i,j) = 0.06 + ELSE IF(compna(i) == 'ps'.AND.compna(j) == 'acetone') THEN + kij(i,j) = 0.021 + ELSE IF(compna(i) == 'ps'.AND.compna(j) == 'hexane') THEN + kij(i,j) = 0.012 + ELSE IF(compna(i) == 'ps'.AND.compna(j) == 'pentane')THEN + kij(i,j) = 0.005 + ELSE IF(compna(i) == 'ps'.AND.compna(j) == 'methylcyclohexane') THEN + kij(i,j) = 0.0073 + ELSE IF(compna(i) == 'ps'.AND.compna(j) == 'ethylbenzene')THEN + kij(i,j) = 0.008 + ELSE IF(compna(i) == 'pe'.AND.compna(j) == 'co2') THEN + ! kij(i,j) = 0.181 + kij(i,j) = 0.088 + ELSE IF(compna(i) == 'pe'.AND.compna(j) == 'propane') THEN + kij(i,j) = 0.0206 + ELSE IF(compna(i) == 'pe'.AND.compna(j) == 'butane') THEN + kij(i,j) = 0.01 + ELSE IF(compna(i) == 'methane'.AND.compna(j) == 'argon') THEN + kij(i,j) = 0.01 + ELSE IF(compna(i) == 'methane'.AND.compna(j) == 'butane') THEN + kij(i,j) = 0.026 + ELSE IF(compna(i) == 'pe'.AND.compna(j) == 'pentane') THEN + ! kij(i,j) = -0.0195 + ELSE IF(compna(i) == 'pe'.AND.compna(j) == 'hexane') THEN + ! kij(i,j) = 0.008 + kij(i,j) = 0.004 + ELSE IF(compna(i) == 'pe'.AND.compna(j) == 'ethylene') THEN + kij(i,j) = 0.0404 + ! kij(i,j) = 0.0423 + ! kij(i,j) = 0.044 + ELSE IF(compna(i) == 'pe'.AND.compna(j) == 'cyclohexane') THEN + kij(i,j) = -0.1 + ELSE IF(compna(i) == 'ldpe'.AND.compna(j) == 'cyclopentane')THEN + kij(i,j) = -0.016 + ELSE IF(compna(i) == 'pp'.AND.compna(j) == 'propane') THEN + kij(i,j) = 0.0242 + ELSE IF(compna(i) == 'pp'.AND.compna(j) == 'pentane') THEN + kij(i,j) = 0.0137583176 + ELSE IF(compna(i) == 'pp'.AND.compna(j) == 'co2') THEN + kij(i,j) = 0.1767 ! without quadrupol-term + kij(i,j) = 0.063 ! with quadrupol-term + ELSE IF(compna(i) == 'pba'.AND.compna(j) == 'ethylene') THEN + kij(i,j) = 0.026 + ELSE IF(compna(i) == 'decane'.AND.compna(j) == 'ethane') THEN + kij(i,j) = 0.017 + ELSE IF(compna(i) == 'n2'.AND.compna(j) == 'co2') THEN + ! kij(i,j) = -0.04 + ELSE IF(compna(i) == 'methane'.AND.compna(j) == 'co2') THEN + kij(i,j) = 0.051875 ! PC-SAFT + IF (pol == 1) kij(i,j) = -0.0353125 ! PCP-SAFT + ELSE IF(compna(i) == 'methane'.AND.compna(j) == 'co') THEN + ! IF (pol == 1) kij(i,j) = -0.003 ! PCP-SAFT + IF (pol == 1) kij(i,j) = 0.018 ! PCP-SAFT + ELSE IF(compna(i) == 'ethane'.AND.compna(j) == 'co2') THEN + kij(i,j) = 0.095 + kij(i,j) = 0.021 + ! kij(i,j) = 0.024 + ELSE IF(compna(i) == 'propane'.AND.compna(j) == 'co2') THEN + kij(i,j) = 0.042 + ELSE IF(compna(i) == 'argon_ge'.AND.compna(j) == 'argon_ge2') THEN + read (*,*) kij(i,j) + ELSE IF(compna(i) == 'butane'.AND.compna(j) == 'co2') THEN + ! kij(i,j) = 0.115 + ! kij(i,j) = 0.048 + kij(i,j) = 0.036 + ELSE IF(compna(i) == 'pentane'.AND.compna(j) == 'co2') THEN + kij(i,j) = 0.143 ! without quadrupol-term + kij(i,j) = 0.0 ! with quadrupol-term + ELSE IF(compna(i) == 'hexane'.AND.compna(j) == 'co2') THEN + ! kij(i,j) = 0.125 ! without quadrupol-term + kij(i,j) = 0.0495 + ELSE IF(compna(i) == 'heptane'.AND.compna(j) == 'co2') THEN + kij(i,j) = 0.11 ! without quadrupol-term + ! kij(i,j) = 0.05 + ! kij(i,j) = 0.039 ! with quadrupol-term + ELSE IF(compna(i) == 'decane'.AND.compna(j) == 'co2') THEN + ! kij(i,j) = 0.128 ! without quadrupol-term + kij(i,j) = 0.053 ! with quadrupol-term + ELSE IF(compna(i) == 'dodecane'.AND.compna(j) == 'co2') THEN + kij(i,j) = 0.12 ! without quadrupol-term + kij(i,j) = 0.0508 ! with quadrupol-term + ELSE IF(compna(i) == 'benzene'.AND.compna(j) == 'co2') THEN + ! kij(i,j) = 0.087968750000 ! without quadrupol-term + ! kij(i,j) = 0.008203125 ! only co2 quadrupol + kij(i,j) = 0.042 ! both quadrupol + ! kij(i,j) = 0.003 ! both quadrupol + ELSE IF(compna(i) == 'toluene'.AND.compna(j) == 'co2') THEN + ! kij(i,j) = 0.110784912 ! without quadrupol-term + kij(i,j) = 0.0305 ! with quadrupol-term + ELSE IF(compna(i) == 'cyclohexane'.AND.compna(j) == 'co2') THEN + kij(i,j) = 0.13 + lij(i,j) = - 0.00 + ! kij(i,j) = 0.045 + ELSE IF(compna(i) == 'chloromethane'.AND.compna(j) == 'co2')THEN + ! kij(i,j) = 0.04 ! PC-SAFT + kij(i,j) = 0.025 ! PCP-SAFT + ! kij(i,j) = 0.083 ! PCIP-SAFT + ELSE IF(compna(i) == 'acetone'.AND.compna(j) == 'n2')THEN + kij(i,j) = 0.035211 ! PCP-SAFT + lij(i,j) = + 0.013225 ! PCP-SAFT + kij(i,j) = 0.023 ! PCP-SAFT + lij(i,j) = + 0.013225 ! PCP-SAFT + !kij(i,j) = 1.722238535635467E-002 ! PCP-SAFT + !lij(i,j) = 2.815974678394451E-003 ! PCP-SAFT + !kij(i,j) = 1.931522058164026E-002 ! PCP-SAFT + !lij(i,j) = 0.0 ! PCP-SAFT + !kij(i,j) = 1.641053794134795E-002 ! PCP-SAFT + !lij(i,j) = -5.850421759950764E-003 ! PCP-SAFT + if ( num == 0 ) write (*,*) 'calculation with lij only possible with num=1' + if ( num == 0 ) stop + ELSE IF(compna(i) == 'acetone'.AND.compna(j) == 'co2')THEN + kij(i,j) = 0.015 ! PC-SAFT + IF (pol == 1) kij(i,j) = -0.02 ! PCP-SAFT + IF (pol == 2) kij(i,j) = -0.005 ! PCIP-SAFT where DQ with my=my_vacuum + ! IF (pol.EQ.2) kij(i,j) = 0.0 ! PCIP-SAFT where DQ with my=my_RPT + ELSE IF(compna(i) == 'methanol'.AND.compna(j) == 'co2')THEN + ! kij(i,j) = 0.0288 ! PC-SAFT + ! kij(i,j) = - 0.035 ! PCP-SAFT for co2 and PC-SAFT methanol + ! kij(i,j) = - 0.035 ! PCP-SAFT + ! lij(i,j) = 0.3 ! PCP-SAFT + ELSE IF(compna(i) == 'dimethyl-ether'.AND.compna(j) == 'co2')THEN + kij(i,j) = 0.00896894 ! PC-SAFT + ! kij(i,j) = - 0.015 ! PCP-SAFT + ELSE IF(compna(i) == 'dimethyl-ether'.AND.compna(j) == 'h2o')THEN + ! kij(i,j) = -0.134 ! PC-SAFT + ELSE IF(compna(i) == 'dichloromethane'.AND.compna(j) == 'co2')THEN + ! kij(i,j) = 0.06881725 ! PC-SAFT + ! kij(i,j) = 0.05839145 ! PCP-SAFT + kij(i,j) = -0.00944346 ! PCP-SAFT co2 dichloromethane PC-SAFT + ! kij(i,j) = 0.06 ! PCIP-SAFT + ELSE IF(compna(i) == 'h2s'.AND.compna(j) == 'methane')THEN + ! kij(i,j) = 0.0414 ! PC-SAFT + kij(i,j) = 0.0152 ! PCP-SAFT Dipole momnet (d with Q) + ELSE IF(compna(i) == 'butane'.AND.compna(j) == 'h2s')THEN + kij(i,j) = -0.002 ! PCP-SAFT + ELSE IF(compna(i) == 'methanol'.AND.compna(j) == 'h2s')THEN + kij(i,j) = 0.0 ! PCP-SAFT + lij(i,j) = 0.0 ! PCP-SAFT + ELSE IF(compna(i) == 'co2'.AND.compna(j) == 'hydrogen') THEN + ! lij(i,j) = -0.08 !!!!! Lij not kij !!!! + ELSE IF(compna(i) == 'hexane'.AND.compna(j) == 'n2') THEN + kij(i,j) = 0.11 + ELSE IF(compna(i) == 'propane'.AND.compna(j) == 'n2') THEN + kij(i,j) = 0.0251171875 + ELSE IF(compna(i) == 'co2'.AND.compna(j) == 'hexadecane') THEN + ! kij(i,j) = 0.1194 ! PC-SAFT ohne QQ + kij(i,j) = 0.0588 + ELSE IF(compna(i) == 'ethane'.AND.compna(j) == 'acetone') THEN + ! kij(i,j) = 0.065 ! no DD + kij(i,j) = 0.038 ! DD non-polarizable + ! kij(i,j) = 0.025 ! DD polarizable + ELSE IF(compna(i) == 'butane'.AND.compna(j) == 'acetone') THEN + ! kij(i,j) = 0.065 ! no DD + kij(i,j) = 0.037 ! DD non-polarizable + ! kij(i,j) = 0.025 ! DD polarizable + ELSE IF(compna(i) == 'pentane'.AND.compna(j) == 'acetone') THEN + ! kij(i,j) = 0.072 ! no DD + ! kij(i,j) = 0.041 ! DD non-polarizable + kij(i,j) = 0.039 ! DD polarizable + ! kij(i,j) = 0.035 ! DD polarizable + ELSE IF(compna(i) == 'hexane'.AND.compna(j) == 'acetone') THEN + ! kij(i,j) = 0.063 + kij(i,j) = 0.038 ! PCP-SAFT + ! kij(i,j) = 0.036 ! PCIP-SAFT + ELSE IF(compna(i) == 'heptane'.AND.compna(j) == 'acetone') THEN + kij(i,j) = 0.035 ! PCP-SAFT + ELSE IF(compna(i) == 'decane'.AND.compna(j) == 'acetone') THEN + ! kij(i,j) = 0.059 ! no DD + ! kij(i,j) = 0.03281250 ! DD non-polarizable + kij(i,j) = 0.028 ! DD polarizable + ELSE IF(compna(i) == 'hexadecane'.AND.compna(j) == 'acetone') THEN + ! kij(i,j) = 0.07 ! no DD + ! kij(i,j) = 0.0415 ! DD non-polarizable + kij(i,j) = 0.035 ! DD polarizable + ELSE IF(compna(i) == 'hexane'.AND.compna(j) == 'butanone')THEN + kij(i,j) = 0.027 ! PCP-SAFT + ! kij(i,j) = 0.033 ! PCP-SAFT with lij + ! lij(i,j) = 0.13 ! PCP-SAFT + ! kij(i,j) = 0.042 ! PC-SAFT + ELSE IF(compna(i) == 'heptane'.AND.compna(j) == 'butanone')THEN + kij(i,j) = 0.042 ! no DD + ! kij(i,j) = 0.027 ! DD non-polarizable + ELSE IF(compna(i) == 'heptane'.AND.compna(j) == '2-pentanone')THEN + kij(i,j) = 0.041 ! no DD + ! kij(i,j) = 0.031 ! DD non-polarizable + ELSE IF(compna(i) == 'hexane'.AND.compna(j) == '3-pentanone')THEN + kij(i,j) = 0.0 + ELSE IF(compna(i) == 'pentane'.AND.compna(j) == 'propanal')THEN + ! kij(i,j) = 0.055 ! no DD + kij(i,j) = 0.027 ! DD non-polarizable + ! kij(i,j) = 0.026 ! DD polarizable 22 + ELSE IF(compna(i) == 'cyclohexane'.AND.compna(j) == 'propanal')THEN + ! kij(i,j) = 0.06 ! no DD + kij(i,j) = 0.036 ! DD non-polarizable + kij(i,j) = 0.035 ! DD polarizable 22 + ELSE IF(compna(i) == 'heptane'.AND.compna(j) == 'butanal')THEN + kij(i,j) = 0.041 ! no DD + ! kij(i,j) = 0.025 ! DD non-polarizable + ELSE IF(compna(i) == 'hexane'.AND.compna(j) == 'thf')THEN + kij(i,j) = 0.012 ! PCP-SAFT + ELSE IF(compna(i) == 'octane'.AND.compna(j) == 'thf')THEN + kij(i,j) = 0.012 ! PCP-SAFT + ELSE IF(compna(i) == 'decane'.AND.compna(j) == 'thf')THEN + kij(i,j) = 0.012 ! PCP-SAFT + ELSE IF(compna(i) == 'toluene'.AND.compna(j) == 'dmso')THEN + ! kij(i,j) = 0.025 ! no DD + kij(i,j) = - 0.0105 ! DD non-polarizable + ! kij(i,j) = - 0.019 ! DD polarizable + ELSE IF(compna(i) == 'hexane'.AND.compna(j) == 'acrylonitrile')THEN + kij(i,j) = - 0.05 ! DD polarizable + ELSE IF(compna(i) == 'heptane' .AND. compna(j) == 'butyronitrile')THEN + kij(i,j) = - 0.002 ! DD polarizable 11 + kij(i,j) = 0.002 ! DD polarizable 22 + ELSE IF(compna(i) == '1-butene'.AND.compna(j) == 'dmf')THEN + ! kij(i,j) = 0.04 ! no DD + ! kij(i,j) = 0.004 ! DD non-polarizable + kij(i,j) = 0.005 ! DD polarizable 22 + ELSE IF(compna(i) == 'cyclohexane'.AND.compna(j) == 'dmf')THEN + kij(i,j) = 0.0135 ! DD polarizable 11 + kij(i,j) = 0.022 ! DD polarizable 22 + ELSE IF(compna(i) == 'ethylene'.AND.compna(j) == 'dmf')THEN + ! kij(i,j) = - 0.0215 ! DD polarizable 11 + kij(i,j) = - 0.01 ! DD polarizable 22 + ELSE IF(compna(i) == 'nbutyl-ethanoate'.AND.compna(j) == 'dmf')THEN + ! kij(i,j) = 0.016 ! no DD + ! kij(i,j) = -0.01 ! DD non-polarizable + kij(i,j) = - 0.015 ! DD polarizable 22 + ELSE IF(compna(i) == 'methylacetate' .AND. compna(j) == 'cyclohexane')THEN + kij(i,j) = 0.066 ! PC-SAFT + ! kij(i,j) = 0.061 ! PCP-SAFT + ! kij(i,j) = 0.0625 ! PCIP-SAFT + ELSE IF(compna(i) == 'methylacetate'.AND.compna(j) == 'decane')THEN + kij(i,j) = 0.0625 ! PCIP-SAFT + ELSE IF(compna(i) == 'methylacetate' .AND. compna(j) == 'methanol')THEN + ! kij(i,j) = -0.07 ! PCIP-SAFT + ELSE IF(compna(i) == 'pentane' .AND. compna(j) == 'propionitrile')THEN + kij(i,j) = 0.0498 + IF (pol >= 1) kij(i,j) = -0.01 + IF (pol >= 2) kij(i,j) = -0.027 + ELSE IF(compna(i) == 'hexane' .AND. compna(j) == 'propionitrile')THEN + kij(i,j) = 0.05 + IF (pol >= 1) kij(i,j) = 0.0 + IF (pol >= 2) kij(i,j) = -0.03 + ELSE IF(compna(i) == 'octane' .AND. compna(j) == 'propionitrile')THEN + kij(i,j) = 0.0 ! DD polarizable 22 + ELSE IF(compna(i) == 'cyclohexane' .AND. compna(j) == 'nitromethane')THEN + kij(i,j) = 0.14 ! no DD + ! kij(i,j) = 0.07 ! DD non-polarizable + ! kij(i,j) = 0.055 ! DD polarizable 22 + ELSE IF(compna(i) == 'cyclohexane' .AND. compna(j) == 'nitroethane')THEN + ! kij(i,j) = 0.06 ! no DD + kij(i,j) = 0.03 ! DD polarizable 22 + ELSE IF(compna(i) == 'acetone' .AND. compna(j) == 'nitromethane')THEN + ! kij(i,j) = - 0.017 ! no DD + kij(i,j) = - 0.021 ! DD non-polarizable + ! kij(i,j) = - 0.023 ! DD polarizable 22 + ELSE IF(compna(i) == 'acetone' .AND. compna(j) == 'h2o')THEN + kij(i,j) = - 0.2 ! PCP-SAFT (no cross-association) + ELSE IF(compna(i) == 'methylcyclohexane' .AND. compna(j) == 'acetonitrile')THEN + ! kij(i,j) = 0.09 ! no DD + ! kij(i,j) = 0.033 ! DD non-polarizable + ! kij(i,j) = 0.025 ! DD polarizable 22 + kij(i,j) = 0.04 ! DD polarizable 22 und my angepasst + ELSE IF(compna(i) == 'ethylacetate' .AND. compna(j) == 'acetonitrile')THEN + kij(i,j) = 0.007 ! no DD + ! kij(i,j) = -0.045 ! DD polarizable 22 + ELSE IF(compna(i) == 'dimethyl-ether' .AND. compna(j) == 'propane')THEN + ! kij(i,j) = 0.03 ! no DD + kij(i,j) = 0.0225 ! DD non-polarizable + ELSE IF(compna(i) == 'benzene' .AND. compna(j) == 'pentane')THEN + ! kij(i,j) = 0.012968750 ! ohne QQ + ! kij(i,j) = 0.004921875 ! mit QQ=5.6D (gefittet) + ! kij(i,j) = -0.006406250 ! mit QQ=7.45D (Literatur) + ELSE IF(compna(i) == 'benzene' .AND. compna(j) == 'heptane')THEN + kij(i,j) = 0.01328125 + ! kij(i,j) = 0.0038 + ELSE IF(compna(i) == 'benzene' .AND. compna(j) == '1-hexene')THEN + kij(i,j) = 0.0067 + ELSE IF(compna(i) == 'ethylene' .AND. compna(j) == 'co2') THEN + kij(i,j) = 0.04 + kij(i,j) = -0.029 + ELSE IF(compna(i) == 'ethylene' .AND. compna(j) == 'vinylacetate') THEN + kij(i,j) = - 0.013847 + ELSE IF(compna(i) == 'triacontane' .AND. compna(j) == 'ethylene') THEN + kij(i,j) = 0.028 + ELSE IF(compna(i) == 'triacontane' .AND. compna(j) == 'methane')THEN + ! kij(i,j) = 0.061953125 ! polyethylene parameters + kij(i,j) = 0.039609375 ! param. by extrapolation of n-alkanes + ELSE IF(compna(i) == 'tetracontane' .AND. compna(j) == 'methane')THEN + ! kij(i,j) = 0.06515625 ! polyethylene parameters + kij(i,j) = 0.04453125 ! param. by extrapolation of n-alkanes + ! --- kij and lij adjusted ------- + ! kij(i,j) = 0.045786119 ! param. by extrapolation of n-alkanes + ! lij(i,j) = +8.53466437d-4 ! param. by extrapolation of n-alkanes + ELSE IF(compna(i) == 'eicosane' .AND. compna(j) == 'methane')THEN + kij(i,j) = 0.0360134457445 + ELSE IF(compna(i) == 'tetracontane' .AND. compna(j) == 'methane')THEN + kij(i,j) = 0.0360134457445 ! assumed equal to eicosane-C1 + ELSE IF(compna(i) == 'chlorobenzene' .AND. compna(j) == 'cyclohexane') THEN + kij(i,j) = 0.013 + ELSE IF(compna(i) == 'chloroethane' .AND. compna(j) == 'butane')THEN + kij(i,j) = 0.025 + ELSE IF(compna(i) == 'tetrachloromethane' .AND. compna(j) == '2-methylpentane') THEN + kij(i,j) = 0.0070105 + ELSE IF(compna(i) == 'tetrachloromethane' .AND. compna(j) == 'hexane') THEN + kij(i,j) = 0.004 + ELSE IF(compna(i) == 'hydrogen' .AND. compna(j) == 'hexane') THEN + kij(i,j) = 0.1501 + ELSE IF(compna(i) == 'ethanol' .AND. compna(j) == 'co2') THEN + ! kij(i,j) = -0.08 + ELSE IF(compna(i) == 'ethanol' .AND. compna(j) == 'propane') THEN + kij(i,j) = - 0.07 + ELSE IF(compna(i) == 'ethanol' .AND. compna(j) == 'ethane') THEN + kij(i,j) = 0.0 + ELSE IF(compna(i) == 'ethanol' .AND. compna(j) == 'butane') THEN + kij(i,j) = 0.028 + kij(i,j) = 0.016 + ELSE IF(compna(i) == 'ethanol' .AND. compna(j) == 'cyclohexane')THEN + kij(i,j) = 0.037 + ELSE IF(compna(i) == 'ethanol' .AND. compna(j) == '2-methylpentane') THEN + kij(i,j) = 0.028 + ELSE IF(compna(i) == 'ethanol' .AND. compna(j) == '1-octanol')THEN + kij(i,j) = 0.06 + ELSE IF(compna(i) == 'methanol' .AND. compna(j) == 'cyclohexane') THEN + kij(i,j) = 0.0508 + ! kij(i,j) = 0.03 + ELSE IF(compna(i) == 'methanol' .AND. compna(j) == 'heptane')THEN + kij(i,j) = 0.034 + ELSE IF(compna(i) == 'methanol' .AND. compna(j) == 'decane')THEN + ! kij(i,j) = 0.042 ! PC-SAFT + ! kij(i,j) = 0.011 ! PCP-SAFT + kij(i,j) = 0.000 ! PCIP-SAFT + ELSE IF(compna(i) == 'methanol' .AND. compna(j) == 'isobutane') THEN + kij(i,j) = 0.051 + ELSE IF(compna(i) == 'methanol' .AND. compna(j) == '1-octanol') THEN + kij(i,j) = 0.02 + ELSE IF(compna(i) == '1-butanol' .AND. compna(j) == 'butane') THEN + kij(i,j) = 0.015 + ELSE IF(compna(i) == '1-nonanol' .AND. compna(j) == 'co2') THEN + kij(i,j) = 0.076 + kij(i,j) = 0.01443 + ELSE IF(compna(i) == '1-propanol' .AND. compna(j) == 'ethylbenzene') THEN + kij(i,j) = 0.0251757813 + ELSE IF(compna(i) == 'decane'.AND.compna(j) == 'ethanol') THEN + kij(i,j) = 0.085 + ELSE IF(compna(i) == 'hexane'.AND.compna(j) == '1-chlorobutane') THEN + kij(i,j) = 0.017 + ELSE IF(compna(i) == 'aniline'.AND.compna(j) == 'methylcyclopentane') THEN + kij(i,j) = 0.0153 + ELSE IF(compna(i) == 'heptane'.AND.compna(j) == 'nbutyl-ethanoate')THEN + kij(i,j) = 0.027 + ELSE IF(compna(i) == '1-hexene'.AND.compna(j) == 'ethyl-ethanoate')THEN + kij(i,j) = 0.026 + ELSE IF(compna(i) == 'co2'.AND.compna(j) == '1-butanol')THEN + ! kij(i,j) = 0.075 + kij(i,j) = 0.0 + ELSE IF(compna(i) == 'acrylic-acid'.AND.compna(j) == 'co2')THEN + kij(i,j) = -0.1 + ELSE IF(compna(i) == 'bmim'.AND.compna(j) == 'hydrogen')THEN + lij(i,j) = 0.55 !!!!! Lij not kij !!!! + ELSE IF(compna(i) == 'bf4'.AND.compna(j) == 'hydrogen')THEN + lij(i,j) = 0.55 !!!!! Lij not kij !!!! + ELSE IF(compna(i) == 'h2o'.AND.compna(j) == 'butane')THEN !K.R.Hall FPE 2007 254 112-125 kij=0.1850 + kij(i,j) = -0.07 + ELSE IF(compna(i) == 'h2o'.AND.compna(j) == '1-butanol')THEN + kij(i,j) = -0.12 + ELSE IF(compna(i) == 'h2o'.AND.compna(j) == 'aniline')THEN + kij(i,j) = 0.0 + ELSE IF(compna(i) == 'h2o'.AND.compna(j) == 'methanol') THEN + kij(i,j) = -0.02 + ELSE IF(compna(i) == 'h2o'.AND.compna(j) == 'ethanol') THEN + kij(i,j) = -0.027 + ELSE IF(compna(i) == 'h2o'.AND.compna(j) == 'styrene') THEN + kij(i,j) = 0.1 + ELSE IF(compna(i) == 'h2o'.AND.compna(j) == 'propyl-ethanoate') THEN + kij(i,j) = -0.205 + ELSE IF(compna(i) == 'h2o'.AND.compna(j) == 'ethyl-propanoate') THEN + kij(i,j) = 0.0 + ELSE IF(compna(i) == 'h2o'.AND.compna(j) == '1-pentanol') THEN + kij(i,j) = 0.0165 + ! kij(i,j) = 0.0294 + ! kij(i,j) = -0.082 + ELSE IF(compna(i) == 'h2o'.AND.compna(j) == 'methane') THEN + ! kij(i,j) = +0.06 + kij(i,j) = -0.08 + ELSE IF(compna(i) == 'h2o'.AND.compna(j) == 'propane') THEN + kij(i,j) = 0.02 + ELSE IF(compna(i) == 'h2o'.AND.compna(j) == 'hexane') THEN + kij(i,j) = -0.02 + ELSE IF(compna(i) == 'h2o'.AND.compna(j) == 'acetic-acid') THEN + kij(i,j) = -0.0 + ELSE IF(compna(i) == 'h2o'.AND.compna(j) == 'co2') THEN + if (pol == 0) kij(i,j) = 0.0030625 ! for T=50C, according to X.Tang + stop ! very T-dependent + ELSE IF(compna(i) == 'toluene'.AND.compna(j) == 'acetic-acid') THEN + kij(i,j) = -0.1 + ELSE IF(compna(i) == 'caproic-acid'.AND.compna(j) == 'cyclohexane') THEN + kij(i,j) = 0.041531 + ELSE IF(compna(i) == '1-octanol'.AND.compna(j) == 'h2o')THEN + kij(i,j) = 0.07 + ELSE IF(compna(i) == 'acetone'.AND.compna(j) == 'benzene')THEN + kij(i,j) = 0.02132466 ! PC-SAFT + ! kij(i,j) = 0.01495148 ! PCP-SAFT + ! kij(i,j) = -0.00735575 ! PCP-SAFT but non-polar benzene + ELSE IF(compna(i) == '1-propanol'.AND.compna(j) == 'benzene')THEN + kij(i,j) = 0.02017 + ELSE IF(compna(i) == '2-propanol'.AND.compna(j) == 'benzene')THEN + kij(i,j) = 0.021386 + ELSE IF(compna(i) == '1-pentanol'.AND.compna(j) == 'benzene')THEN + kij(i,j) = 0.0129638671875 + ELSE IF(compna(i) == 'CH2F2' .AND. compna(j) == 'co2') THEN + kij(i,j) = 2.2548828125E-2 + ELSE IF(compna(i) == 'dmso' .AND. compna(j) == 'co2') THEN + kij(i,j) = -0.00 + ELSE IF(compna(i) == 'dmf'.AND.compna(j) == 'h2o')THEN + kij(i,j) = -0.0 + ELSE IF(compna(i) == 'decane'.AND.compna(j) == 'h2o')THEN + kij(i,j) = 0.11 + ELSE IF(compna(i) == '11difluoroethane'.AND.compna(j) == 'HF')THEN + kij(i,j) = 0.032 ! association: eps_kij = 0.16 + ELSE IF(compna(i) == '11difluoroethane'.AND.compna(j) == 'co2')THEN + kij(i,j) = -0.004 ! PCP-SAFT (taken from simulation) + ELSE IF(compna(i) == 'difluoromethane'.AND.compna(j) == 'HF')THEN + kij(i,j) = -0.02 + ELSE IF(compna(i) == 'naphthalene'.AND.compna(j) == 'co2')THEN + kij(i,j) = 0.137 ! angepasst an SVLE-Linie (tradition.CO2-Parameter) + kij(i,j) = 0.09 ! angepasst an SVLE-Linie (tradition.CO2-Parameter) + ELSE IF(compna(i) == 'pg2'.AND.compna(j) == 'methanol')THEN + kij(i,j) = 0.03 + ELSE IF(compna(i) == 'pg2'.AND.compna(j) == 'co2')THEN + ! kij(i,j) = 0.05 + ELSE IF(compna(i) == 'PCH5'.AND.compna(j) == 'co2')THEN + ! kij(i,j) = -0.047 + kij(i,j) = +0.055 + ! kij(i,j) = +0.036 + ELSE + END IF + kij(j,i) = kij(i,j) + lij(j,i) = -lij(i,j) + + END DO +END DO + +END SUBROUTINE pcsaft_par + + +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! SUBROUTINE init_vars +! +! This subroutine writes variables from an array "val_init" to the +! system-variables. Those variables +! include some specifications but also some starting values for a +! phase equilibrium calculation. (val_init stands for 'initial value') + +! The array comprises the following elements +! element 0 density of third phase +! element 1 density of first phase +! element 2 density of second phase +! element 3 temperature [K] +! element 4 pressure [Pa] +! element 5,..(5+NCOMP) mole-fraction of comp. i in log. from (phase 1) +! element ... mole-fraction of comp. i in log. from (phase 2) +! element ... mole-fraction of comp. i in log. from (phase 3) +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! + SUBROUTINE init_vars +! + USE BASIC_VARIABLES + IMPLICIT NONE +! + INTEGER :: i, ph +! ---------------------------------------------------------------------- + +densta(3)=val_init(0) +densta(1)=val_init(1) +densta(2)=val_init(2) +t = val_init(3) +p = val_init(4) +DO ph = 1,nphas + DO i = 1,ncomp + lnx(ph,i) = val_init(4+i+(ph-1)*ncomp) + END DO +END DO + +END SUBROUTINE init_vars + + +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! SUBROUTINE converged +! +! Once a converged solution for an equilibrium calculation is found, +! this subroutine writes variables to an array "val_conv". +! (= short for converged values) +! The array comprises the following elements +! element 0 density of third phase +! element 1 density of first phase +! element 2 density of second phase +! element 3 temperature [K] +! element 4 pressure [Pa] +! element 5,..(4+NCOMP) mole-fraction of comp. i in log. from (phase 1) +! element ... mole-fraction of comp. i in log. from (phase 2) +! element ... mole-fraction of comp. i in log. from (phase 3) +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! + SUBROUTINE converged +! + USE BASIC_VARIABLES + IMPLICIT NONE +! + INTEGER :: i, ph +! ---------------------------------------------------------------------- + +val_conv(0) = dense(3) +val_conv(1) = dense(1) +val_conv(2) = dense(2) +val_conv(3) = t +val_conv(4) = p +DO ph = 1,nphas + DO i = 1,ncomp + val_conv(4+i+(ph-1)*ncomp) = lnx(ph,i) + END DO +END DO + +END SUBROUTINE converged + +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! SUBROUTINE PERTURBATION_PARAMETER +! +! calculates density-independent parameters of the equation of state. +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! + SUBROUTINE PERTURBATION_PARAMETER +! + USE PARAMETERS, ONLY: PI, KBOL, RGAS, NAV, TAU + USE EOS_VARIABLES + USE EOS_CONSTANTS + IMPLICIT NONE +! +! --- local variables -------------------------------------------------- + INTEGER :: i, j, k, l, m, no + LOGICAL :: assoc, qudpole, dipole + REAL :: m_mean + REAL, DIMENSION(nc) :: v00, v0, d00, u + REAL, DIMENSION(nc,nc,nsite,nsite) :: eps_hb + REAL, DIMENSION(nc,nc) :: kap_hb + REAL :: zmr, nmr + REAL :: eps_kij, k_kij +! ---------------------------------------------------------------------- + +! ---------------------------------------------------------------------- +! pure component parameters +! ---------------------------------------------------------------------- +DO i = 1, ncomp + u(i) = parame(i,3) * (1.0 + parame(i,4)/t) + mseg(i) = parame(i,1) + IF (eos == 0) THEN + v00(i) = parame(i,2) + v0(i) = v00(i)*(1.0-0.12*EXP(-3.0*parame(i,3)/t))**3 + d00(i) = (1.d30/1.d6 *tau *v00(i)*6.0/PI /NAV)**(1.0/3.0) + dhs(i) = d00(i)*(1.0-0.12*EXP(-3.0*parame(i,3)/t)) + ELSE + dhs(i) = parame(i,2)*(1.0-0.12*EXP(-3.0*parame(i,3)/t)) + d00(i) = parame(i,2) + END IF +END DO + + +! ---------------------------------------------------------------------- +! combination rules +! ---------------------------------------------------------------------- +DO i = 1, ncomp + DO j = 1, ncomp + sig_ij(i,j) = 0.5 * ( d00(i) + d00(j) ) + uij(i,j) = ( 1.0 - kij(i,j) ) * ( u(i)*u(j) )**0.5 + vij(i,j) = ( 0.5*( v0(i)**(1.0/3.0) + v0(j)**(1.0/3.0) ) )**3 + END DO +END DO + + +! ---------------------------------------------------------------------- +! abbreviations +! ---------------------------------------------------------------------- +z0t = PI / 6.0 * SUM( x(1:ncomp) * mseg(1:ncomp) ) +z1t = PI / 6.0 * SUM( x(1:ncomp) * mseg(1:ncomp) * dhs(1:ncomp) ) +z2t = PI / 6.0 * SUM( x(1:ncomp) * mseg(1:ncomp) * dhs(1:ncomp)**2 ) +z3t = PI / 6.0 * SUM( x(1:ncomp) * mseg(1:ncomp) * dhs(1:ncomp)**3 ) + +m_mean = z0t/(PI/6.0) + +DO i = 1, ncomp + DO j = 1, ncomp + dij_ab(i,j) = dhs(i)*dhs(j) / ( dhs(i) + dhs(j) ) + END DO +END DO + +! ---------------------------------------------------------------------- +! dispersion term parameters for chain molecules +! ---------------------------------------------------------------------- +DO m = 0, 6 + apar(m) = ap(m,1) + (1.0-1.0/m_mean)*ap(m,2) & + + (1.0-1.0/m_mean)*(1.0-2.0/m_mean)*ap(m,3) + bpar(m) = bp(m,1) + (1.0-1.0/m_mean)*bp(m,2) & + + (1.0-1.0/m_mean)*(1.0-2.0/m_mean)*bp(m,3) +END DO + + +! ---------------------------------------------------------------------- +! van der Waals mixing rules for perturbation terms +! ---------------------------------------------------------------------- +order1 = 0.0 +order2 = 0.0 +DO i = 1, ncomp + DO j = 1, ncomp + order1 = order1 + x(i)*x(j)* mseg(i)*mseg(j)*sig_ij(i,j)**3 * uij(i,j)/t + order2 = order2 + x(i)*x(j)* mseg(i)*mseg(j)*sig_ij(i,j)**3 * (uij(i,j)/t)**2 + END DO +END DO + + +! ---------------------------------------------------------------------- +! SAFT parameters +! ---------------------------------------------------------------------- +IF (eos == 0) THEN + zmr = 0.0 + nmr = 0.0 + DO i = 1, ncomp + DO j = 1, ncomp + zmr = zmr + x(i)*x(j)*mseg(i)*mseg(j)*vij(i,j)*uij(i,j) + nmr = nmr + x(i)*x(j)*mseg(i)*mseg(j)*vij(i,j) + END DO + END DO + um = zmr / nmr +END IF + + + +! ---------------------------------------------------------------------- +! association and polar parameters +! ---------------------------------------------------------------------- +assoc = .false. +qudpole = .false. +dipole = .false. +DO i = 1, ncomp + IF (NINT(parame(i,12)) /= 0) assoc = .true. + IF (parame(i,7) /= 0.0) qudpole = .true. + IF (parame(i,6) /= 0.0) dipole = .true. +END DO + +! --- dipole and quadrupole constants ---------------------------------- +IF (qudpole) CALL qq_const ( qqp2, qqp3, qqp4 ) +IF (dipole) CALL dd_const ( ddp2, ddp3, ddp4 ) +IF (dipole .AND. qudpole) CALL dq_const ( dqp2, dqp3, dqp4 ) + + +! --- TPT-1-association parameters ------------------------------------- +IF (assoc) THEN + + eps_kij = 0.0 + k_kij = 0.0 + + DO i = 1, ncomp + IF (NINT(parame(i,12)) /= 0) THEN + nhb_typ(i) = NINT(parame(i,12)) + kap_hb(i,i) = parame(i,13) + no = 0 + DO j = 1, nhb_typ(i) + DO k = 1, nhb_typ(i) + eps_hb(i,i,j,k) = parame(i,(14+no)) + no=no+1 + END DO + END DO + DO j = 1, nhb_typ(i) + nhb_no(i,j) = parame(i,(14+no)) + no=no+1 + END DO + ELSE + nhb_typ(i) = 0 + kap_hb(i,i)= 0.0 + DO k = 1, nsite + DO l = 1, nsite + eps_hb(i,i,k,l) = 0.0 + END DO + END DO + END IF + END DO + + DO i = 1, ncomp + DO j = 1, ncomp + IF (i /= j .AND. (nhb_typ(i) /= 0 .AND. nhb_typ(j) /= 0)) THEN + kap_hb(i,j)= (kap_hb(i,i)*kap_hb(j,j))**0.5 & + *((parame(i,2)*parame(j,2))**3 )**0.5 & + /(0.5*(parame(i,2)+parame(j,2)))**3 + kap_hb(i,j)= kap_hb(i,j)*(1.0-k_kij) + DO k = 1, nhb_typ(i) + DO l = 1, nhb_typ(j) + IF (k /= l) THEN + eps_hb(i,j,k,l) = (eps_hb(i,i,k,l)+eps_hb(j,j,l,k))/2.0 + eps_hb(i,j,k,l) = eps_hb(i,j,k,l)*(1.0-eps_kij) + END IF + END DO + END DO + END IF + END DO + END DO + IF (nhb_typ(1) == 3) THEN +! write(*,*)'eps_hb manuell eingegeben' + eps_hb(1,2,3,1) = 0.5*(eps_hb(1,1,3,1)+eps_hb(2,2,1,2)) + eps_hb(2,1,1,3) = eps_hb(1,2,3,1) + END IF + IF (nhb_typ(2) == 3) THEN + eps_hb(2,1,3,1) = 0.5*(eps_hb(2,2,3,1)+eps_hb(1,1,1,2)) + eps_hb(1,2,1,3) = eps_hb(2,1,3,1) + END IF + + DO i = 1, ncomp + DO k = 1, nhb_typ(i) + DO j = 1, ncomp + DO l = 1, nhb_typ(j) + ass_d(i,j,k,l) = kap_hb(i,j) *sig_ij(i,j)**3 *(EXP(eps_hb(i,j,k,l)/t)-1.0) + END DO + END DO + END DO + END DO + +END IF + +END SUBROUTINE PERTURBATION_PARAMETER + + + + +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! SUBROUTINE OUTPUT +! +! The purpose of this subroutine is obvious. +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! + SUBROUTINE OUTPUT +! + USE BASIC_VARIABLES + IMPLICIT NONE +! +! ---------------------------------------------------------------------- + INTEGER :: i + CHARACTER (LEN=4) :: t_ind + CHARACTER (LEN=4) :: p_ind + CHARACTER (LEN=4) :: char_ncomp + REAL :: density(np),w(np,nc) +! ---------------------------------------------------------------------- + + CALL si_dens (density,w) + + IF (u_in_p == 1.E5) THEN + p_ind = ' bar' + ELSE IF (u_in_p == 1.E2) THEN + p_ind = 'mbar' + ELSE IF (u_in_p == 1.E6) THEN + p_ind = ' MPa' + ELSE IF (u_in_p == 1.E3) THEN + p_ind = ' kPa' + ELSE + p_ind = ' Pa' + END IF + IF (u_in_t == 273.15) THEN + t_ind = ' C' + ELSE + t_ind = ' K' + END IF + + WRITE(*,*) '--------------------------------------------------' + WRITE (char_ncomp,'(I3)') ncomp + WRITE(*,'(t2,a,f7.2,2a,f9.4,a)') ' T =',t-u_out_t,t_ind & + ,' P =',p/u_out_p,p_ind + WRITE(*,'(t15,4(a12,1x),10x,a)') (compna(i),i=1,ncomp) + WRITE(*,'(2x,a,'//char_ncomp//'(g13.6,1x))') 'PHASE I w', (w(1,i),i=1,ncomp) + WRITE(*,'(2x,a,'//char_ncomp//'(g13.6,1x))') 'PHASE II w', (w(2,i),i=1,ncomp) + WRITE(*,'(2x,a,'//char_ncomp//'(g13.6,1x))') 'PHASE I x', (EXP(lnx(1,i)),i=1,ncomp) + WRITE(*,'(2x,a,'//char_ncomp//'(g13.6,1x))') 'PHASE II x', (EXP(lnx(2,i)),i=1,ncomp) + WRITE(*,'(2x,a,2(g13.6,1x))') 'DENSITY ', density(1),density(2) + + !-----output to files-------------------------------------------------- + IF (ncomp == 1) THEN + WRITE (40,'(7(2x,f18.8))') t-u_out_t, p/u_out_p, & + density(1), density(2),h_lv,cpres(1),cpres(2) + ! & ,(enthal(2)-enthal(1))/mm(1) + ! WRITE (40,'(4(2x,f15.8))') t, p, 0.3107*dense(1) + ! & /0.1617*(0.689+0.311*(T/1.328)**0.3674),0.3107 + ! & *dense(2)/0.1617*(0.689+0.311*(T/1.328)**0.3674) + ELSE IF (ncomp == 2) THEN + WRITE (40,'(12(2x,G15.8))') 1.0-xi(1,1),1.0-xi(2,1), & + w(1,1),w(2,1),t-u_out_t, p/u_out_p, density(1),density(2) & + ,enthal(1),enthal(2),cpres(1),cpres(2) + ELSE IF (ncomp == 3) THEN + WRITE (40,'(10(2x,f15.8))') xi(1,1),xi(1,2),xi(1,3),xi(2,1),xi(2,2), & + xi(2,3),t-u_out_t, p/u_out_p, density(1),density(2) + END IF + + END SUBROUTINE OUTPUT + + + +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! SUBROUTINE neutr_charge +! +! This subroutine is called for electrolye solutions, where a +! neutral overall-charge has to be enforced in all phases. The basic +! philosophy is similar to the above described routine X_SUMMATION. +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! + SUBROUTINE neutr_charge(i) +! + USE BASIC_VARIABLES + IMPLICIT NONE +! +! ---------------------------------------------------------------------- + INTEGER, INTENT(IN) :: i +! +! ---------------------------------------------------------------------- + INTEGER :: comp_e, ph_e + REAL :: sum_c + CHARACTER (LEN=2) :: phasno + CHARACTER (LEN=2) :: compno +! ---------------------------------------------------------------------- + +phasno = sum_rel(i)(2:2) +READ(phasno,*) ph_e +compno = sum_rel(i)(3:3) +READ(compno,*) comp_e + +sum_c = 0.0 +write (*,*) 'there must be an error in neutr_charge' +stop +! there is an error in the following passage. The index i is an +! argument to this subroutine - I guess it is INTENT(IN), so the +! index in the following loop can not be i. +! +! I have commented the loop until I check the code. +!DO i=1,ncomp +! IF ( comp_e /= i .AND. parame(i,10) /= 0.0) & +! sum_c = sum_c + xi(ph_e,i)*parame(i,10) +!END DO + +xi(ph_e,comp_e) = - sum_c +IF (xi(ph_e,comp_e) < 0.0) xi(ph_e,comp_e)=0.0 +IF (xi(ph_e,comp_e) /= 0.0) THEN + lnx(ph_e,comp_e) = LOG(xi(ph_e,comp_e)) +ELSE + lnx(ph_e,comp_e) = -100000.0 +END IF + +! xi(2,1) = xi(2,2) +! IF (xi(2,1).NE.0.0) lnx(2,1) = LOG(xi(2,1)) + +END SUBROUTINE neutr_charge + + +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! + SUBROUTINE flash_sum +! + USE BASIC_VARIABLES + IMPLICIT NONE +! + INTEGER :: i, j, ph_i, phase1, phase2 +! ---------------------------------------------------------------------- + +phase1=0 +phase2=0 +DO j=1,ncomp + IF (it(j)(2:2) == '1') phase1=phase1+1 + IF (it(j)(2:2) == '2') phase2=phase2+1 +END DO + +IF (phase1 == ncomp-1) THEN + ph_i = 1 +ELSE IF (phase2 == ncomp-1) THEN + ph_i = 2 +ELSE + WRITE (*,*) ' FLASH_SUM: undefined flash-case' + STOP +END IF + + + +IF (ph_i == 1) THEN + DO i=1,ncomp + IF (alpha > DMIN1(1.0,xif(i)/xi(1,i), & + (xif(i)-1.0)/(xi(1,i)-1.0),alpha)) THEN + WRITE (*,*) ' FLASH_SUM: exeeded 1st alpha-bound' + alpha=DMIN1(1.0,xif(i)/xi(1,i),(xif(i)-1.0)/(xi(1,i)-1.0)) + END IF + END DO + DO i=1,ncomp + xi(2,i) = ( xif(i) - alpha*xi(1,i) ) / (1.0-alpha) + IF (xi(2,i) > 0.0) THEN + lnx(2,i) = LOG(xi(2,i)) + ELSE + xi(2,i) = 0.0 + lnx(2,i) = -100000.0 + END IF + END DO +ELSE IF (ph_i == 2) THEN + DO i=1,ncomp + IF (alpha > DMAX1(0.0,(xif(i)-xi(2,i))/(1.0-xi(2,i)), & + 1.0-xif(i)/xi(2,i),alpha)) THEN + WRITE (*,*) ' FLASH_SUM: exeeded 2nd alpha-bound' + WRITE (*,*) 0.0,(xif(i)-xi(2,i))/(1.0-xi(2,i)), 1.0-xif(i)/xi(2,i) + alpha=DMAX1(0.0,(xif(i)-xi(2,i))/(1.0-xi(2,i)), 1.0-xif(i)/xi(2,i)) + END IF + END DO + DO i=1,ncomp + xi(1,i) = ( xif(i) - (1.0-alpha)*xi(2,i) ) / alpha +! write (*,*) 'x1,i',xi(1,i),xi(2,i),alpha + IF (xi(1,i) > 0.0) THEN + lnx(1,i) = LOG(xi(1,i)) + ELSE + xi(1,i) = 0.0 + lnx(1,i) = -100000.0 + END IF + END DO +END IF + +! pause + +RETURN +END SUBROUTINE flash_sum + +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! SUBROUTINE flash_alpha +! +! This subroutine calculates all molefractions of one phase +! from a component balance. What is needed for this calculation +! are all molefractions of the other phase (nphas=2, so far) +! and the phase fraction alpha. +! Alpha is calculated from the mole fraction +! of component {sum_rel(j)(3:3)}. If for example sum_rel(2)='fl3', +! then the alpha is determined from the molefraction of comp. 3 and +! all molefractions of one phase are calculated using that alpha-value. +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! + SUBROUTINE flash_alpha +! + USE BASIC_VARIABLES + IMPLICIT NONE +! +! ---------------------------------------------------------------------- + INTEGER :: i, j, comp_i, phase1, phase2 + CHARACTER (LEN=2) :: compno +! ---------------------------------------------------------------------- + + +! ---------------------------------------------------------------------- +! first calculate the phase fraction alpha from a known composition +! of component sum_rel(j)(3:3). +! ---------------------------------------------------------------------- + +DO j = 1, nphas + IF ( sum_rel(j)(1:2) == 'fl' ) THEN + compno = sum_rel(j)(3:3) + READ(compno,*) comp_i + IF ( (xi(1,comp_i)-xi(2,comp_i)) /= 0.0 ) THEN + alpha = (xif(comp_i)-xi(2,comp_i)) / (xi(1,comp_i)-xi(2,comp_i)) + write (*,*) 'flsh',(xif(comp_i)-xi(2,comp_i)),(xi(1,comp_i)-xi(2,comp_i)) + ELSE + alpha = 0.5 + WRITE (*,*) 'FLASH_ALPHA:error in calc. of phase fraction',comp_i + END IF + ! IF (alpha <= 0.0 .OR. alpha >= 1.0) WRITE(*,*) 'FLASH_ALPHA: error',alpha + IF (alpha > 1.0) alpha = 1.0 + IF (alpha < 0.0) alpha = 0.0 + END IF +END DO + +! ---------------------------------------------------------------------- +! determine which phase is fully determined by iterated molefractions (+ summation relation) +! ---------------------------------------------------------------------- +phase1 = 0 +phase2 = 0 +DO i = 1, ncomp + IF ( it(i)(2:2) == '1' ) phase1 = phase1 + 1 + IF ( it(i)(2:2) == '2' ) phase2 = phase2 + 1 +END DO +DO i = 1, ncomp + IF ( sum_rel(i)(2:2) == '1' ) phase1 = phase1 + 1 + IF ( sum_rel(i)(2:2) == '2' ) phase2 = phase2 + 1 +END DO + + +IF ( phase1 == ncomp ) THEN + ! -------------------------------------------------------------------- + ! phase 1 is defined by iterated molefractions + summation relation + ! phase 2 is determined from componennt balance (using alpha) + ! -------------------------------------------------------------------- + IF ( alpha == 1.0 ) alpha = 1.0 - 1.0E-10 + DO i=1,ncomp + xi(2,i) = ( xif(i) - alpha*xi(1,i) ) / (1.0-alpha) + IF ( xi(2,i) < 0.0 ) xi(2,i) = 0.0 + IF ( xi(2,i) > 1.0 ) xi(2,i) = 1.0 + IF ( xi(2,i) /= 0.0 ) THEN + lnx(2,i) = LOG( xi(2,i) ) + ELSE + lnx(2,i) = -100000.0 + END IF + write (*,*) 'fl_cal ph=2',i,lnx(2,i),xi(2,i) + END DO +ELSE IF ( phase2 == ncomp ) THEN + ! -------------------------------------------------------------------- + ! phase 2 is defined by iterated molefractions + summation relation + ! phase 1 is determined from componennt balance (using alpha) + ! -------------------------------------------------------------------- + DO i = 1, ncomp + xi(1,i) = ( xif(i) - (1.0-alpha)*xi(2,i) ) /alpha + IF ( xi(1,i) < 0.0 ) xi(1,i) = 0.0 + IF ( xi(1,i) > 1.0 ) xi(1,i) = 1.0 + IF ( xi(1,i) /= 0.0 ) THEN + lnx(1,i) = LOG( xi(1,i) ) + ELSE + lnx(1,i) = -100000.0 + END IF + write (*,*) 'fl_cal ph=1',i,lnx(1,i),xi(1,i),alpha + END DO +ELSE + WRITE (*,*) ' FLASH_ALPHA: undefined flash-case' + STOP +END IF + +END SUBROUTINE flash_alpha + + +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! SUBROUTINE SI_DENS (density,w) +! +! This subroutine calculates the (macroskopic) fluid-density in +! units [kg/m3] from the dimensionless density (eta=zeta3). +! Further, mass fractions are calculated from mole fractions. +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! + SUBROUTINE SI_DENS (density,w) +! + USE PARAMETERS, ONLY: pi, nav, tau + USE BASIC_VARIABLES + IMPLICIT NONE +! +! ---------------------------------------------------------------------- + REAL, INTENT(OUT) :: density(np) + REAL, INTENT(OUT) :: w(np,nc) +! +! ---------------------------------------------------------------------- + INTEGER :: i, ph + REAL :: mm_mean, rho, z3t + REAL :: dhs(nc), d00(nc), t_p, pcon, l_st +! ---------------------------------------------------------------------- + + +DO i = 1,ncomp + IF (eos == 1) THEN + dhs(i) = parame(i,2) * ( 1.0 - 0.12 *EXP( -3.0*parame(i,3)/t ) ) + ELSE IF (eos == 0) THEN + d00(i) = ( 1.E30/1.E6*tau*parame(i,2)*6.0/pi/nav )**(1.0/3.0) + dhs(i) = d00(i) * ( 1.0 - 0.12 *EXP( -3.0*parame(i,3)/t ) ) + ELSE IF (eos == 4) THEN + dhs(i) = ( 0.1617/0.3107 / ( 0.689+0.311*(t/parame(i,3)/1.328)**0.3674 ) & + / ( pi/6.0 ) )**(1.0/3.0) * parame(i,2) + ELSE IF (eos == 5.OR.eos == 6) THEN + l_st = parame(1,25) + IF (ncomp /= 1) write (*,*) ' ERROR for EOS = 5' + t_p =((34.037352+17.733741*l_st) /(1.0+0.53237307*l_st+12.860239*l_st**2 ))**0.5 + IF (l_st == 0.0) t_p = t_p/4.0 + IF (eos == 5 .AND. l_st /= 0.0) t_p = t_p/4.0*parame(1,1)**2 + t_p = t/parame(i,3)/t_p + pcon =0.5256+3.2088804*l_st**2 -3.1499114*l_st**2.5 +0.43049357*l_st**4 + dhs(i) = ( pcon/(0.67793+0.32207*(t_p)**0.3674) /(pi/6.0) )**(1.0/3.0) *parame(i,2) + ELSE IF (eos == 8) THEN + dhs(i) = parame(i,2)*(1.0+0.2977*t/parame(i,3)) & + /(1.0+0.33163*t/parame(i,3) +1.0477E-3*(t/parame(i,3))**2 ) + ELSE + write (*,*) 'define EOS in subroutine: SI_DENS' + stop + END IF +END DO + +DO ph = 1,nphas + mm_mean = 0.0 + z3t = 0.0 + DO i = 1, ncomp + mm_mean = mm_mean + xi(ph,i)*mm(i) + z3t = z3t + xi(ph,i) * parame(i,1) * dhs(i)**3 + END DO + z3t = pi/6.0 * z3t + rho = dense(ph)/z3t + density(ph) = rho * mm_mean * 1.E27 /nav + DO i = 1, ncomp + w(ph,i) = xi(ph,i) * mm(i)/mm_mean + END DO +! write (*,*) density(ph),rho,mm_mean,1.d27 /NAV +END DO + +END SUBROUTINE SI_DENS + + + +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! + REAL FUNCTION F_STABILITY ( optpara, n ) +! + USE BASIC_VARIABLES + USE STARTING_VALUES + USE EOS_VARIABLES, ONLY: dhs, PI + IMPLICIT NONE +! +! ---------------------------------------------------------------------- + INTEGER, INTENT(IN) :: n + REAL, INTENT(IN OUT) :: optpara(n) +! +! ---------------------------------------------------------------------- + INTEGER :: i, stabil + REAL :: rhoi(nc),gradterm + REAL :: fden,punish + REAL :: dens +! ---------------------------------------------------------------------- + +COMMON /stabil / stabil + +punish = 0.0 +stabil = 1 + +DO i = 1, n + IF ( optpara(i) < 0.5 ) rhoi(i) = EXP(optpara(i) ) + IF ( optpara(i) >= 0.5) rhoi(i) = EXP(0.5) +END DO + +dens = PI/6.0 * SUM( rhoi(1:ncomp) * parame(1:ncomp,1) * dhs(1:ncomp)**3 ) + +IF (dens > 0.65) THEN + punish = punish + (dens-0.65)*10000.0 + rhoi(1:n) = rhoi(1:n)*0.65/dens +END IF + +CALL fden_calc (fden, rhoi) + +gradterm = sum( grad_fd(1:n) * ( rhoi(1:n) - rhoif(1:n) ) ) + +f_stability = fden - fdenf - gradterm + punish + +! write (*,'(5G16.8)') F_STABILITY,(rhoi(i),i=1,n) +! pause + +stabil = 0 + +END FUNCTION F_STABILITY + + + + +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! SUBROUTINE p_calc (pges_transfer, zges) +! +! This subroutine serves as an iterface to the EOS-routines. The +! system pressure corresponding to given (desity,T,xi) is calculated. +! (Note: the more common interface is SUBROUTINE FUGACITY. This +! routine is only used for one-phase systems, e.g. calculation of +! virial coefficients) +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! + SUBROUTINE p_calc (pges_transfer, zges) +! + USE BASIC_VARIABLES + USE EOS_VARIABLES + IMPLICIT NONE +! +! ---------------------------------------------------------------------- + REAL, INTENT(IN OUT) :: pges_transfer + REAL, INTENT(OUT) :: zges +! ---------------------------------------------------------------------- + +IF (nphas /= 1 ) THEN + write (*,*) 'P_CALC: can only be called for single phases' + stop +ENDIF + +IF (eos < 2) THEN + + phas = 1 + eta = dense(1) + x(1:ncomp) = xi(1,1:ncomp) + + CALL PERTURBATION_PARAMETER + IF (num == 0) CALL P_EOS + IF(num == 1) CALL P_NUMERICAL + !! IF(num == 2) CALL F_EOS_RN + + pges_transfer = pges + rho = eta/z3t + zges = (pges * 1.E-30) / (kbol*t*rho) + +ELSE + write (*,*) ' SUBROUTINE P_CALC not available for cubic EOS' + stop +END IF + +END SUBROUTINE p_calc + + + +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! +SUBROUTINE ONLY_ONE_TERM_EOS_NUMERICAL ( only_term, type_of_term ) +! + USE EOS_NUMERICAL_DERIVATIVES + IMPLICIT NONE +! + character (LEN=9) :: only_term, type_of_term +! ---------------------------------------------------------------------- + + save_eos_terms(1) = ideal_gas + save_eos_terms(2) = hard_sphere + save_eos_terms(3) = chain_term + save_eos_terms(4) = disp_term + save_eos_terms(5) = hb_term + save_eos_terms(6) = LC_term + save_eos_terms(7) = branch_term + save_eos_terms(8) = II_term + save_eos_terms(9) = ID_term + + ideal_gas = 'no' + hard_sphere = 'no' + chain_term = 'no' + disp_term = 'no' + hb_term = 'no' + LC_term = 'no' + branch_term = 'no' + II_term = 'no' + ID_term = 'no' + + IF ( only_term == 'ideal_gas' ) ideal_gas = trim( adjustl( type_of_term ) ) + IF ( only_term == 'hard_sphere' ) hard_sphere = trim( adjustl( type_of_term ) ) + IF ( only_term == 'chain_term' ) chain_term = trim( adjustl( type_of_term ) ) + IF ( only_term == 'disp_term' ) disp_term = trim( adjustl( type_of_term ) ) + IF ( only_term == 'hb_term' ) hb_term = trim( adjustl( type_of_term ) ) + IF ( only_term == 'LC_term' ) LC_term = trim( adjustl( type_of_term ) ) + IF ( only_term == 'branch_term' ) branch_term = trim( adjustl( type_of_term ) ) + IF ( only_term == 'II_term' ) II_term = trim( adjustl( type_of_term ) ) + IF ( only_term == 'ID_term' ) ID_term = trim( adjustl( type_of_term ) ) + +END SUBROUTINE ONLY_ONE_TERM_EOS_NUMERICAL + + +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! +SUBROUTINE RESTORE_PREVIOUS_EOS_NUMERICAL +! + USE EOS_NUMERICAL_DERIVATIVES + IMPLICIT NONE +! +! ---------------------------------------------------------------------- + ideal_gas = trim( adjustl( save_eos_terms(1) ) ) + hard_sphere = trim( adjustl( save_eos_terms(2) ) ) + chain_term = trim( adjustl( save_eos_terms(3) ) ) + disp_term = trim( adjustl( save_eos_terms(4) ) ) + hb_term = trim( adjustl( save_eos_terms(5) ) ) + LC_term = trim( adjustl( save_eos_terms(6) ) ) + branch_term = trim( adjustl( save_eos_terms(7) ) ) + II_term = trim( adjustl( save_eos_terms(8) ) ) + ID_term = trim( adjustl( save_eos_terms(9) ) ) + +END SUBROUTINE RESTORE_PREVIOUS_EOS_NUMERICAL + + + + diff --git a/applications/PUfoam/MoDeNaModels/PolymerDensity/ExampleOfUsage/src/srcDetailedCode/main.f90 b/applications/PUfoam/MoDeNaModels/PolymerDensity/ExampleOfUsage/src/srcDetailedCode/main.f90 new file mode 100644 index 000000000..44cc5cb21 --- /dev/null +++ b/applications/PUfoam/MoDeNaModels/PolymerDensity/ExampleOfUsage/src/srcDetailedCode/main.f90 @@ -0,0 +1,132 @@ + +! +!THIS CODE WAS WRITTEN AT +!UNIVERSITY OF STUTTGART, +!INSTITUTE OF TECHNICAL THERMODYNAMICS AND THERMAL PROCESS ENGINEERING +!BY +!JOACHIM GROSS +! +! +! +! + + + + + + +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! This program calculates densities of a liquid phase which is in equilibrium with a gas phase +! using the PC-SAFT equation of state. +! The input parameters are read from the file "in.txt" which has to +! be in the same directory as the executable. +! +! The input file must have the following format: +! Line1: Value of temperature in Kelvin +! Line2: Number of components present in the system (ncomp) +! Line3 Name of component 1 +! ... +! Line3+ncomp Name of component ncomp +! Line3+ncomp+1 Molar (overall) fraction of component 1 +! ... +! Line3+2ncomp Molar (overall) fraction of component ncomp +! +! For a binary system, these molar fractions are only treated as an initial guess and may be set to e.g. 0. +! +! So far, pressure is set to 1bar in all calculaions +! +! +!If you would like to use this code in your work, please cite the +!following publications: +! +!Gross, Joachim, and Gabriele Sadowski. "Perturbed-chain SAFT: An equation of state based on a perturbation theory for chain molecules." Industrial & engineering chemistry research 40.4 (2001): 1244-1260. +!Gross, Joachim, and Gabriele Sadowski. "Application of the perturbed-chain SAFT equation of state to associating systems." Industrial & engineering chemistry research 41.22 (2002): 5510-5515. +!Gross, Joachim, and Jadran Vrabec. "An equation‐of‐state contribution for polar components: Dipolar molecules." AIChE journal 52.3 (2006): 1194-1204. +! +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW + + + + + + +PROGRAM PC_SAFT +! +! ---------------------------------------------------------------------- + USE BASIC_VARIABLES + USE EOS_CONSTANTS + USE DFT_MODULE + USE EOS_VARIABLES!, ONLY: dd_term, qq_term, dq_term + IMPLICIT NONE + +! ---------------------------------------------------------------------- +!Variables +! ---------------------------------------------------------------------- + + REAL :: tc,pc,chemPot_total(nc) + REAL :: rhob(2,0:nc),density(np) + CHARACTER (LEN=50) :: filename + INTEGER :: compID,i + REAL :: cif(nc) + +! ---------------------------------------------------------------------- +!Read information from inputfile "in.txt" +! ---------------------------------------------------------------------- + + filename='./in.txt' + CALL file_open(filename,77) + READ (77,*) t + READ (77,*) ncomp ! read number of components in the system + Do i = 1,ncomp ! read component names + READ (77,*) compna(i) + End Do + Do i = 1,ncomp ! read component overall molar concentrations + READ (77,*) xif(i) + End Do + + + + !calculate molar fractions from molar concentrations + !xif(1:ncomp) = cif(1:ncomp) / sum(cif(1:ncomp)) + + + +! ---------------------------------------------------------------------- +!General simulation set up +! ---------------------------------------------------------------------- + + num = 1 ! (num=0: using analytical derivatives of EOS) + ! (num=1: using numerical derivatives of EOS) + ! (num=2: White's renormalization group theory) + IF ( num /= 0 ) CALL SET_DEFAULT_EOS_NUMERICAL + + + eos = 1 + pol = 1 + + p = 1.000e05 + + CALL para_input ! retriev pure comp. parameters + + ensemble_flag = 'tp' ! this specifies, whether the eos-subroutines + ! are executed for constant 'tp' or for constant 'tv' + + +! ---------------------------------------------------------------------- +!Start phase equilibrium calculation +! ---------------------------------------------------------------------- + + CALL EOS_CONST (ap, bp, dnm) + + dd_term = 'GV' ! dipole-dipole term of Gross & Vrabec (2006) + qq_term = 'JG' ! quadrupole-quadrupole term of Gross (2005) + dq_term = 'VG' ! dipole-quadrupole term of Vrabec & Gross (2008) + + + + CALL VLE_MIX(rhob,density,chemPot_total,compID) + + +END PROGRAM PC_SAFT + + diff --git a/applications/PUfoam/MoDeNaModels/PolymerDensity/ExampleOfUsage/src/srcDetailedCode/module_solve_nonlinear.f90 b/applications/PUfoam/MoDeNaModels/PolymerDensity/ExampleOfUsage/src/srcDetailedCode/module_solve_nonlinear.f90 new file mode 100644 index 000000000..595a8ba80 --- /dev/null +++ b/applications/PUfoam/MoDeNaModels/PolymerDensity/ExampleOfUsage/src/srcDetailedCode/module_solve_nonlinear.f90 @@ -0,0 +1,1645 @@ + +MODULE Solve_NonLin + +! Corrections to FUNCTION Enorm - 28 November 2003 + +IMPLICIT NONE +INTEGER, PARAMETER :: dp = SELECTED_REAL_KIND(14, 60) +PRIVATE +PUBLIC :: hbrd, hybrd + + +CONTAINS + + +SUBROUTINE hbrd(fcn, n, x, fvec, epsfcn, tol, info, diag) + +! Code converted using TO_F90 by Alan Miller +! Date: 2003-07-15 Time: 13:27:42 + +INTEGER, INTENT(IN) :: n +REAL (dp), INTENT(IN OUT) :: x(n) +REAL (dp), INTENT(IN OUT) :: fvec(n) +REAL (dp), INTENT(IN) :: epsfcn +REAL (dp), INTENT(IN) :: tol +INTEGER, INTENT(OUT) :: info +REAL (dp), INTENT(OUT) :: diag(n) + +! EXTERNAL fcn +INTERFACE + SUBROUTINE FCN(N, X, FVEC, IFLAG) + IMPLICIT NONE + INTEGER, PARAMETER :: dp = SELECTED_REAL_KIND(14, 60) + INTEGER, INTENT(IN) :: n + REAL (dp), INTENT(IN) :: x(n) + REAL (dp), INTENT(OUT) :: fvec(n) + INTEGER, INTENT(IN OUT) :: iflag + END SUBROUTINE FCN +END INTERFACE + +! ********** + +! SUBROUTINE HBRD + +! THE PURPOSE OF HBRD IS TO FIND A ZERO OF A SYSTEM OF N NONLINEAR +! FUNCTIONS IN N VARIABLES BY A MODIFICATION OF THE POWELL HYBRID METHOD. +! THIS IS DONE BY USING THE MORE GENERAL NONLINEAR EQUATION SOLVER HYBRD. +! THE USER MUST PROVIDE A SUBROUTINE WHICH CALCULATES THE FUNCTIONS. +! THE JACOBIAN IS THEN CALCULATED BY A FORWARD-DIFFERENCE APPROXIMATION. + +! THE SUBROUTINE STATEMENT IS + +! SUBROUTINE HBRD(N, X, FVEC, EPSFCN, TOL, INFO, WA, LWA) + +! WHERE + +! FCN IS THE NAME OF THE USER-SUPPLIED SUBROUTINE WHICH CALCULATES +! THE FUNCTIONS. FCN MUST BE DECLARED IN AN EXTERNAL STATEMENT +! IN THE USER CALLING PROGRAM, AND SHOULD BE WRITTEN AS FOLLOWS. + +! SUBROUTINE FCN(N, X, FVEC, IFLAG) +! INTEGER N,IFLAG +! REAL X(N),FVEC(N) +! ---------- +! CALCULATE THE FUNCTIONS AT X AND RETURN THIS VECTOR IN FVEC. +! --------- +! RETURN +! END + +! THE VALUE OF IFLAG NOT BE CHANGED BY FCN UNLESS +! THE USER WANTS TO TERMINATE THE EXECUTION OF HBRD. +! IN THIS CASE SET IFLAG TO A NEGATIVE INTEGER. + +! N IS A POSITIVE INTEGER INPUT VARIABLE SET TO THE NUMBER +! OF FUNCTIONS AND VARIABLES. + +! X IS AN ARRAY OF LENGTH N. ON INPUT X MUST CONTAIN AN INITIAL +! ESTIMATE OF THE SOLUTION VECTOR. ON OUTPUT X CONTAINS THE +! FINAL ESTIMATE OF THE SOLUTION VECTOR. + +! FVEC IS AN OUTPUT ARRAY OF LENGTH N WHICH CONTAINS +! THE FUNCTIONS EVALUATED AT THE OUTPUT X. + +! EPSFCN IS AN INPUT VARIABLE USED IN DETERMINING A SUITABLE STEP LENGTH +! FOR THE FORWARD-DIFFERENCE APPROXIMATION. THIS APPROXIMATION ASSUMES +! THAT THE RELATIVE ERRORS IN THE FUNCTIONS ARE OF THE ORDER OF EPSFCN. +! IF EPSFCN IS LESS THAN THE MACHINE PRECISION, IT IS ASSUMED THAT THE +! RELATIVE ERRORS IN THE FUNCTIONS ARE OF THE ORDER OF THE MACHINE +! PRECISION. + +! TOL IS A NONNEGATIVE INPUT VARIABLE. TERMINATION OCCURS WHEN THE +! ALGORITHM ESTIMATES THAT THE RELATIVE ERROR BETWEEN X AND THE SOLUTION +! IS AT MOST TOL. + +! INFO IS AN INTEGER OUTPUT VARIABLE. IF THE USER HAS TERMINATED +! EXECUTION, INFO IS SET TO THE (NEGATIVE) VALUE OF IFLAG. +! SEE DESCRIPTION OF FCN. OTHERWISE, INFO IS SET AS FOLLOWS. + +! INFO = 0 IMPROPER INPUT PARAMETERS. + +! INFO = 1 ALGORITHM ESTIMATES THAT THE RELATIVE ERROR +! BETWEEN X AND THE SOLUTION IS AT MOST TOL. + +! INFO = 2 NUMBER OF CALLS TO FCN HAS REACHED OR EXCEEDED 200*(N+1). + +! INFO = 3 TOL IS TOO SMALL. NO FURTHER IMPROVEMENT IN +! THE APPROXIMATE SOLUTION X IS POSSIBLE. + +! INFO = 4 ITERATION IS NOT MAKING GOOD PROGRESS. + +! SUBPROGRAMS CALLED + +! USER-SUPPLIED ...... FCN + +! MINPACK-SUPPLIED ... HYBRD + +! ARGONNE NATIONAL LABORATORY. MINPACK PROJECT. MARCH 1980. +! BURTON S. GARBOW, KENNETH E. HILLSTROM, JORGE J. MORE + +! Reference: +! Powell, M.J.D. 'A hybrid method for nonlinear equations' in Numerical Methods +! for Nonlinear Algebraic Equations', P.Rabinowitz (editor), Gordon and +! Breach, London 1970. +! ********** +INTEGER :: maxfev, ml, mode, mu, nfev, nprint +REAL (dp) :: xtol +REAL (dp), PARAMETER :: factor = 1.0_dp, zero = 0.0_dp + +info = 0 + +! CHECK THE INPUT PARAMETERS FOR ERRORS. + + +IF (n <= 0 .OR. epsfcn < zero .OR. tol < zero) GO TO 20 + +! CALL HYBRD. + +maxfev = 200*(n + 1) +xtol = tol +ml = n - 1 +mu = n - 1 +mode = 2 +nprint = 0 +CALL hybrd(fcn, n, x, fvec, xtol, maxfev, ml, mu, epsfcn, diag, mode, & + factor, nprint, info, nfev) +IF (info == 5) info = 4 +20 RETURN + +! LAST CARD OF SUBROUTINE HBRD. + +END SUBROUTINE hbrd + + + +SUBROUTINE hybrd(fcn, n, x, fvec, xtol, maxfev, ml, mu, epsfcn, diag, mode, & + factor, nprint, info, nfev) + +INTEGER, INTENT(IN) :: n +REAL (dp), INTENT(IN OUT) :: x(n) +REAL (dp), INTENT(IN OUT) :: fvec(n) +REAL (dp), INTENT(IN) :: xtol +INTEGER, INTENT(IN OUT) :: maxfev +INTEGER, INTENT(IN OUT) :: ml +INTEGER, INTENT(IN) :: mu +REAL (dp), INTENT(IN) :: epsfcn +REAL (dp), INTENT(OUT) :: diag(n) +INTEGER, INTENT(IN) :: mode +REAL (dp), INTENT(IN) :: factor +INTEGER, INTENT(IN OUT) :: nprint +INTEGER, INTENT(OUT) :: info +INTEGER, INTENT(OUT) :: nfev + +! EXTERNAL fcn +INTERFACE + SUBROUTINE FCN(N, X, FVEC, IFLAG) + IMPLICIT NONE + INTEGER, PARAMETER :: dp = SELECTED_REAL_KIND(14, 60) + INTEGER, INTENT(IN) :: n + REAL (dp), INTENT(IN) :: x(n) + REAL (dp), INTENT(OUT) :: fvec(n) + INTEGER, INTENT(IN OUT) :: iflag + END SUBROUTINE FCN +END INTERFACE + +! ********** + +! SUBROUTINE HYBRD + +! THE PURPOSE OF HYBRD IS TO FIND A ZERO OF A SYSTEM OF N NONLINEAR +! FUNCTIONS IN N VARIABLES BY A MODIFICATION OF THE POWELL HYBRID METHOD. +! THE USER MUST PROVIDE A SUBROUTINE WHICH CALCULATES THE FUNCTIONS. +! THE JACOBIAN IS THEN CALCULATED BY A FORWARD-DIFFERENCE APPROXIMATION. + +! THE SUBROUTINE STATEMENT IS + +! SUBROUTINE HYBRD(FCN, N, X, FVEC, XTOL, MAXFEV, ML, MU, EPSFCN, +! DIAG, MODE, FACTOR, NPRINT, INFO, NFEV, FJAC, +! LDFJAC, R, LR, QTF, WA1, WA2, WA3, WA4) + +! WHERE + +! FCN IS THE NAME OF THE USER-SUPPLIED SUBROUTINE WHICH CALCULATES +! THE FUNCTIONS. FCN MUST BE DECLARED IN AN EXTERNAL STATEMENT IN +! THE USER CALLING PROGRAM, AND SHOULD BE WRITTEN AS FOLLOWS. + +! SUBROUTINE FCN(N, X, FVEC, IFLAG) +! INTEGER N, IFLAG +! REAL X(N), FVEC(N) +! ---------- +! CALCULATE THE FUNCTIONS AT X AND +! RETURN THIS VECTOR IN FVEC. +! --------- +! RETURN +! END + +! THE VALUE OF IFLAG SHOULD NOT BE CHANGED BY FCN UNLESS +! THE USER WANTS TO TERMINATE EXECUTION OF HYBRD. +! IN THIS CASE SET IFLAG TO A NEGATIVE INTEGER. + +! N IS A POSITIVE INTEGER INPUT VARIABLE SET TO THE NUMBER +! OF FUNCTIONS AND VARIABLES. + +! X IS AN ARRAY OF LENGTH N. ON INPUT X MUST CONTAIN AN INITIAL +! ESTIMATE OF THE SOLUTION VECTOR. ON OUTPUT X CONTAINS THE FINAL +! ESTIMATE OF THE SOLUTION VECTOR. + +! FVEC IS AN OUTPUT ARRAY OF LENGTH N WHICH CONTAINS +! THE FUNCTIONS EVALUATED AT THE OUTPUT X. + +! XTOL IS A NONNEGATIVE INPUT VARIABLE. TERMINATION OCCURS WHEN THE +! RELATIVE ERROR BETWEEN TWO CONSECUTIVE ITERATES IS AT MOST XTOL. + +! MAXFEV IS A POSITIVE INTEGER INPUT VARIABLE. TERMINATION OCCURS WHEN +! THE NUMBER OF CALLS TO FCN IS AT LEAST MAXFEV BY THE END OF AN +! ITERATION. + +! ML IS A NONNEGATIVE INTEGER INPUT VARIABLE WHICH SPECIFIES THE +! NUMBER OF SUBDIAGONALS WITHIN THE BAND OF THE JACOBIAN MATRIX. +! IF THE JACOBIAN IS NOT BANDED, SET ML TO AT LEAST N - 1. + +! MU IS A NONNEGATIVE INTEGER INPUT VARIABLE WHICH SPECIFIES THE NUMBER +! OF SUPERDIAGONALS WITHIN THE BAND OF THE JACOBIAN MATRIX. +! IF THE JACOBIAN IS NOT BANDED, SET MU TO AT LEAST N - 1. + +! EPSFCN IS AN INPUT VARIABLE USED IN DETERMINING A SUITABLE STEP LENGTH +! FOR THE FORWARD-DIFFERENCE APPROXIMATION. THIS APPROXIMATION +! ASSUMES THAT THE RELATIVE ERRORS IN THE FUNCTIONS ARE OF THE ORDER +! OF EPSFCN. IF EPSFCN IS LESS THAN THE MACHINE PRECISION, +! IT IS ASSUMED THAT THE RELATIVE ERRORS IN THE FUNCTIONS ARE OF THE +! ORDER OF THE MACHINE PRECISION. + +! DIAG IS AN ARRAY OF LENGTH N. IF MODE = 1 (SEE BELOW), +! DIAG IS INTERNALLY SET. IF MODE = 2, DIAG MUST CONTAIN POSITIVE +! ENTRIES THAT SERVE AS MULTIPLICATIVE SCALE FACTORS FOR THE +! VARIABLES. + +! MODE IS AN INTEGER INPUT VARIABLE. IF MODE = 1, THE VARIABLES WILL BE +! SCALED INTERNALLY. IF MODE = 2, THE SCALING IS SPECIFIED BY THE +! INPUT DIAG. OTHER VALUES OF MODE ARE EQUIVALENT TO MODE = 1. + +! FACTOR IS A POSITIVE INPUT VARIABLE USED IN DETERMINING THE +! INITIAL STEP BOUND. THIS BOUND IS SET TO THE PRODUCT OF +! FACTOR AND THE EUCLIDEAN NORM OF DIAG*X IF NONZERO, OR ELSE +! TO FACTOR ITSELF. IN MOST CASES FACTOR SHOULD LIE IN THE +! INTERVAL (.1,100.). 100. IS A GENERALLY RECOMMENDED VALUE. + +! NPRINT IS AN INTEGER INPUT VARIABLE THAT ENABLES CONTROLLED +! PRINTING OF ITERATES IF IT IS POSITIVE. IN THIS CASE, +! FCN IS CALLED WITH IFLAG = 0 AT THE BEGINNING OF THE FIRST +! ITERATION AND EVERY NPRINT ITERATIONS THEREAFTER AND +! IMMEDIATELY PRIOR TO RETURN, WITH X AND FVEC AVAILABLE +! FOR PRINTING. IF NPRINT IS NOT POSITIVE, NO SPECIAL CALLS +! OF FCN WITH IFLAG = 0 ARE MADE. + +! INFO IS AN INTEGER OUTPUT VARIABLE. IF THE USER HAS +! TERMINATED EXECUTION, INFO IS SET TO THE (NEGATIVE) +! VALUE OF IFLAG. SEE DESCRIPTION OF FCN. OTHERWISE, +! INFO IS SET AS FOLLOWS. + +! INFO = 0 IMPROPER INPUT PARAMETERS. + +! INFO = 1 RELATIVE ERROR BETWEEN TWO CONSECUTIVE ITERATES +! IS AT MOST XTOL. + +! INFO = 2 NUMBER OF CALLS TO FCN HAS REACHED OR EXCEEDED MAXFEV. + +! INFO = 3 XTOL IS TOO SMALL. NO FURTHER IMPROVEMENT IN +! THE APPROXIMATE SOLUTION X IS POSSIBLE. + +! INFO = 4 ITERATION IS NOT MAKING GOOD PROGRESS, AS +! MEASURED BY THE IMPROVEMENT FROM THE LAST +! FIVE JACOBIAN EVALUATIONS. + +! INFO = 5 ITERATION IS NOT MAKING GOOD PROGRESS, AS MEASURED BY +! THE IMPROVEMENT FROM THE LAST TEN ITERATIONS. + +! NFEV IS AN INTEGER OUTPUT VARIABLE SET TO THE NUMBER OF CALLS TO FCN. + +! FJAC IS AN OUTPUT N BY N ARRAY WHICH CONTAINS THE ORTHOGONAL MATRIX Q +! PRODUCED BY THE QR FACTORIZATION OF THE FINAL APPROXIMATE JACOBIAN. + +! LDFJAC IS A POSITIVE INTEGER INPUT VARIABLE NOT LESS THAN N +! WHICH SPECIFIES THE LEADING DIMENSION OF THE ARRAY FJAC. + +! R IS AN OUTPUT ARRAY OF LENGTH LR WHICH CONTAINS THE +! UPPER TRIANGULAR MATRIX PRODUCED BY THE QR FACTORIZATION +! OF THE FINAL APPROXIMATE JACOBIAN, STORED ROWWISE. + +! LR IS A POSITIVE INTEGER INPUT VARIABLE NOT LESS THAN (N*(N+1))/2. + +! QTF IS AN OUTPUT ARRAY OF LENGTH N WHICH CONTAINS +! THE VECTOR (Q TRANSPOSE)*FVEC. + +! WA1, WA2, WA3, AND WA4 ARE WORK ARRAYS OF LENGTH N. + +! SUBPROGRAMS CALLED + +! USER-SUPPLIED ...... FCN + +! MINPACK-SUPPLIED ... DOGLEG,SPMPAR,ENORM,FDJAC1, +! QFORM,QRFAC,R1MPYQ,R1UPDT + +! FORTRAN-SUPPLIED ... ABS,MAX,MIN,MIN,MOD + +! ARGONNE NATIONAL LABORATORY. MINPACK PROJECT. MARCH 1980. +! BURTON S. GARBOW, KENNETH E. HILLSTROM, JORGE J. MORE + +! ********** + +INTEGER :: i, iflag, iter, j, jm1, l, lr, msum, ncfail, ncsuc, nslow1, & + nslow2 +INTEGER :: iwa(1) +LOGICAL :: jeval, sing +REAL (dp) :: actred, delta, epsmch, fnorm, fnorm1, pnorm, prered, & + ratio, sum, temp, xnorm +REAL (dp), PARAMETER :: one = 1.0_dp, p1 = 0.1_dp, p5 = 0.5_dp, & + p001 = 0.001_dp, p0001 = 0.0001_dp, zero = 0.0_dp + +! The following were workspace arguments +REAL (dp) :: fjac(n,n), r(n*(n+1)/2), qtf(n), wa1(n), wa2(n), & + wa3(n), wa4(n) + +! EPSMCH IS THE MACHINE PRECISION. + +epsmch = EPSILON(1.0_dp) + +info = 0 +iflag = 0 +nfev = 0 +lr = n*(n+1)/2 + +! CHECK THE INPUT PARAMETERS FOR ERRORS. + +IF (n > 0 .AND. xtol >= zero .AND. maxfev > 0 .AND. ml >= 0 .AND. mu >= & + 0 .AND. factor > zero ) THEN +IF (mode == 2) THEN + diag(1:n) = one +END IF + +! EVALUATE THE FUNCTION AT THE STARTING POINT AND CALCULATE ITS NORM. + +iflag = 1 +CALL fcn(n, x, fvec, iflag) +nfev = 1 +IF (iflag >= 0) THEN + fnorm = enorm(n, fvec) + +! DETERMINE THE NUMBER OF CALLS TO FCN NEEDED TO COMPUTE THE JACOBIAN MATRIX. + + msum = MIN(ml+mu+1,n) + +! INITIALIZE ITERATION COUNTER AND MONITORS. + + iter = 1 + ncsuc = 0 + ncfail = 0 + nslow1 = 0 + nslow2 = 0 + +! BEGINNING OF THE OUTER LOOP. + + 20 jeval = .true. + +! CALCULATE THE JACOBIAN MATRIX. + + iflag = 2 + CALL fdjac1(fcn, n, x, fvec, fjac, n, iflag, ml, mu, epsfcn, wa1, wa2) + nfev = nfev + msum + IF (iflag >= 0) THEN + +! COMPUTE THE QR FACTORIZATION OF THE JACOBIAN. + + CALL qrfac(n, n, fjac, n, .false., iwa, 1, wa1, wa2, wa3) + +! ON THE FIRST ITERATION AND IF MODE IS 1, SCALE ACCORDING +! TO THE NORMS OF THE COLUMNS OF THE INITIAL JACOBIAN. + + IF (iter == 1) THEN + IF (mode /= 2) THEN + DO j = 1, n + diag(j) = wa2(j) + IF (wa2(j) == zero) diag(j) = one + END DO + END IF + +! ON THE FIRST ITERATION, CALCULATE THE NORM OF THE SCALED X +! AND INITIALIZE THE STEP BOUND DELTA. + + wa3(1:n) = diag(1:n) * x(1:n) + xnorm = enorm(n, wa3) + delta = factor * xnorm + IF (delta == zero) delta = factor + END IF + +! FORM (Q TRANSPOSE)*FVEC AND STORE IN QTF. + + qtf(1:n) = fvec(1:n) + DO j = 1, n + IF (fjac(j,j) /= zero) THEN + sum = zero + DO i = j, n + sum = sum + fjac(i,j) * qtf(i) + END DO + temp = -sum / fjac(j,j) + DO i = j, n + qtf(i) = qtf(i) + fjac(i,j) * temp + END DO + END IF + END DO + +! COPY THE TRIANGULAR FACTOR OF THE QR FACTORIZATION INTO R. + + sing = .false. + DO j = 1, n + l = j + jm1 = j - 1 + IF (jm1 >= 1) THEN + DO i = 1, jm1 + r(l) = fjac(i,j) + l = l + n - i + END DO + END IF + r(l) = wa1(j) + IF (wa1(j) == zero) sing = .true. + END DO + +! ACCUMULATE THE ORTHOGONAL FACTOR IN FJAC. + + CALL qform(n, n, fjac, n, wa1) + +! RESCALE IF NECESSARY. + + IF (mode /= 2) THEN + DO j = 1, n + diag(j) = MAX(diag(j), wa2(j)) + END DO + END IF + +! BEGINNING OF THE INNER LOOP. + +! IF REQUESTED, CALL FCN TO ENABLE PRINTING OF ITERATES. + + 120 IF (nprint > 0) THEN + iflag = 0 + IF (MOD(iter-1, nprint) == 0) CALL fcn(n, x, fvec, iflag) + IF (iflag < 0) GO TO 190 + END IF + +! DETERMINE THE DIRECTION P. + + CALL dogleg(n, r, lr, diag, qtf, delta, wa1, wa2, wa3) + +! STORE THE DIRECTION P AND X + P. CALCULATE THE NORM OF P. + + DO j = 1, n + wa1(j) = -wa1(j) + wa2(j) = x(j) + wa1(j) + wa3(j) = diag(j) * wa1(j) + END DO + pnorm = enorm(n, wa3) + +! ON THE FIRST ITERATION, ADJUST THE INITIAL STEP BOUND. + + IF (iter == 1) delta = MIN(delta, pnorm) + +! EVALUATE THE FUNCTION AT X + P AND CALCULATE ITS NORM. + + iflag = 1 + CALL fcn(n, wa2, wa4, iflag) + nfev = nfev + 1 + IF (iflag >= 0) THEN + fnorm1 = enorm(n, wa4) + +! COMPUTE THE SCALED ACTUAL REDUCTION. + + actred = -one + IF (fnorm1 < fnorm) actred = one - (fnorm1/fnorm) ** 2 + +! COMPUTE THE SCALED PREDICTED REDUCTION. + + l = 1 + DO i = 1, n + sum = zero + DO j = i, n + sum = sum + r(l) * wa1(j) + l = l + 1 + END DO + wa3(i) = qtf(i) + sum + END DO + temp = enorm(n, wa3) + prered = zero + IF (temp < fnorm) prered = one - (temp/fnorm) ** 2 + +! COMPUTE THE RATIO OF THE ACTUAL TO THE PREDICTED REDUCTION. + + ratio = zero + IF (prered > zero) ratio = actred / prered + +! UPDATE THE STEP BOUND. + + IF (ratio < p1) THEN + ncsuc = 0 + ncfail = ncfail + 1 + delta = p5 * delta + ELSE + ncfail = 0 + ncsuc = ncsuc + 1 + IF (ratio >= p5 .OR. ncsuc > 1) delta = MAX(delta,pnorm/p5) + IF (ABS(ratio-one) <= p1) delta = pnorm / p5 + END IF + +! TEST FOR SUCCESSFUL ITERATION. + + IF (ratio >= p0001) THEN + +! SUCCESSFUL ITERATION. UPDATE X, FVEC, AND THEIR NORMS. + + DO j = 1, n + x(j) = wa2(j) + wa2(j) = diag(j) * x(j) + fvec(j) = wa4(j) + END DO + xnorm = enorm(n, wa2) + fnorm = fnorm1 + iter = iter + 1 + END IF + +! DETERMINE THE PROGRESS OF THE ITERATION. + + nslow1 = nslow1 + 1 + IF (actred >= p001) nslow1 = 0 + IF (jeval) nslow2 = nslow2 + 1 + IF (actred >= p1) nslow2 = 0 + +! TEST FOR CONVERGENCE. + + IF (delta <= xtol*xnorm .OR. fnorm == zero) info = 1 + IF (info == 0) THEN + +! TESTS FOR TERMINATION AND STRINGENT TOLERANCES. + + IF (nfev >= maxfev) info = 2 + IF (p1*MAX(p1*delta, pnorm) <= epsmch*xnorm) info = 3 + IF (nslow2 == 5) info = 4 + IF (nslow1 == 10) info = 5 + IF (info == 0) THEN + +! CRITERION FOR RECALCULATING JACOBIAN APPROXIMATION +! BY FORWARD DIFFERENCES. + + IF (ncfail /= 2) THEN + +! CALCULATE THE RANK ONE MODIFICATION TO THE JACOBIAN +! AND UPDATE QTF IF NECESSARY. + + DO j = 1, n + sum = zero + DO i = 1, n + sum = sum + fjac(i,j) * wa4(i) + END DO + wa2(j) = (sum-wa3(j)) / pnorm + wa1(j) = diag(j) * ((diag(j)*wa1(j))/pnorm) + IF (ratio >= p0001) qtf(j) = sum + END DO + +! COMPUTE THE QR FACTORIZATION OF THE UPDATED JACOBIAN. + + CALL r1updt(n, n, r, lr, wa1, wa2, wa3, sing) + CALL r1mpyq(n, n, fjac, n, wa2, wa3) + CALL r1mpyq(1, n, qtf, 1, wa2, wa3) + +! END OF THE INNER LOOP. + + jeval = .false. + GO TO 120 + END IF + +! END OF THE OUTER LOOP. + + GO TO 20 + END IF + END IF + END IF + END IF +END IF +END IF + +! TERMINATION, EITHER NORMAL OR USER IMPOSED. + +190 IF (iflag < 0) info = iflag +iflag = 0 +IF (nprint > 0) CALL fcn(n, x, fvec, iflag) +RETURN + +! LAST CARD OF SUBROUTINE HYBRD. + +END SUBROUTINE hybrd + + + +SUBROUTINE dogleg(n, r, lr, diag, qtb, delta, x, wa1, wa2) + +INTEGER, INTENT(IN) :: n +INTEGER, INTENT(IN) :: lr +REAL (dp), INTENT(IN) :: r(lr) +REAL (dp), INTENT(IN) :: diag(n) +REAL (dp), INTENT(IN) :: qtb(n) +REAL (dp), INTENT(IN) :: delta +REAL (dp), INTENT(IN OUT) :: x(n) +REAL (dp), INTENT(OUT) :: wa1(n) +REAL (dp), INTENT(OUT) :: wa2(n) + + +! ********** + +! SUBROUTINE DOGLEG + +! GIVEN AN M BY N MATRIX A, AN N BY N NONSINGULAR DIAGONAL +! MATRIX D, AN M-VECTOR B, AND A POSITIVE NUMBER DELTA, THE +! PROBLEM IS TO DETERMINE THE CONVEX COMBINATION X OF THE +! GAUSS-NEWTON AND SCALED GRADIENT DIRECTIONS THAT MINIMIZES +! (A*X - B) IN THE LEAST SQUARES SENSE, SUBJECT TO THE +! RESTRICTION THAT THE EUCLIDEAN NORM OF D*X BE AT MOST DELTA. + +! THIS SUBROUTINE COMPLETES THE SOLUTION OF THE PROBLEM +! IF IT IS PROVIDED WITH THE NECESSARY INFORMATION FROM THE +! QR FACTORIZATION OF A. THAT IS, IF A = Q*R, WHERE Q HAS +! ORTHOGONAL COLUMNS AND R IS AN UPPER TRIANGULAR MATRIX, +! THEN DOGLEG EXPECTS THE FULL UPPER TRIANGLE OF R AND +! THE FIRST N COMPONENTS OF (Q TRANSPOSE)*B. + +! THE SUBROUTINE STATEMENT IS + +! SUBROUTINE DOGLEG(N,R,LR,DIAG,QTB,DELTA,X,WA1,WA2) + +! WHERE + +! N IS A POSITIVE INTEGER INPUT VARIABLE SET TO THE ORDER OF R. + +! R IS AN INPUT ARRAY OF LENGTH LR WHICH MUST CONTAIN THE UPPER +! TRIANGULAR MATRIX R STORED BY ROWS. + +! LR IS A POSITIVE INTEGER INPUT VARIABLE NOT LESS THAN +! (N*(N+1))/2. + +! DIAG IS AN INPUT ARRAY OF LENGTH N WHICH MUST CONTAIN THE +! DIAGONAL ELEMENTS OF THE MATRIX D. + +! QTB IS AN INPUT ARRAY OF LENGTH N WHICH MUST CONTAIN THE FIRST +! N ELEMENTS OF THE VECTOR (Q TRANSPOSE)*B. + +! DELTA IS A POSITIVE INPUT VARIABLE WHICH SPECIFIES AN UPPER +! BOUND ON THE EUCLIDEAN NORM OF D*X. + +! X IS AN OUTPUT ARRAY OF LENGTH N WHICH CONTAINS THE DESIRED +! CONVEX COMBINATION OF THE GAUSS-NEWTON DIRECTION AND THE +! SCALED GRADIENT DIRECTION. + +! WA1 AND WA2 ARE WORK ARRAYS OF LENGTH N. + +! SUBPROGRAMS CALLED + +! MINPACK-SUPPLIED ... SPMPAR,ENORM + +! FORTRAN-SUPPLIED ... ABS,MAX,MIN,SQRT + +! ARGONNE NATIONAL LABORATORY. MINPACK PROJECT. MARCH 1980. +! BURTON S. GARBOW, KENNETH E. HILLSTROM, JORGE J. MORE + +! ********** +INTEGER :: i, j, jj, jp1, k, l +REAL (dp) :: alpha, bnorm, epsmch, gnorm, qnorm, sgnorm, sum, temp + +! EPSMCH IS THE MACHINE PRECISION. + +epsmch = EPSILON(1.0_dp) + +! FIRST, CALCULATE THE GAUSS-NEWTON DIRECTION. + +jj = (n*(n+1)) / 2 + 1 +DO k = 1, n + j = n - k + 1 + jp1 = j + 1 + jj = jj - k + l = jj + 1 + sum = 0.0 + IF (n >= jp1) THEN + DO i = jp1, n + sum = sum + r(l) * x(i) + l = l + 1 + END DO + END IF + temp = r(jj) + IF (temp == 0.0) THEN + l = j + DO i = 1, j + temp = MAX(temp,ABS(r(l))) + l = l + n - i + END DO + temp = epsmch * temp + IF (temp == 0.0) temp = epsmch + END IF + x(j) = (qtb(j)-sum) / temp +END DO + +! TEST WHETHER THE GAUSS-NEWTON DIRECTION IS ACCEPTABLE. + +DO j = 1, n + wa1(j) = 0.0 + wa2(j) = diag(j) * x(j) +END DO +qnorm = enorm(n, wa2) +IF (qnorm > delta) THEN + +! THE GAUSS-NEWTON DIRECTION IS NOT ACCEPTABLE. +! NEXT, CALCULATE THE SCALED GRADIENT DIRECTION. + + l = 1 + DO j = 1, n + temp = qtb(j) + DO i = j, n + wa1(i) = wa1(i) + r(l) * temp + l = l + 1 + END DO + wa1(j) = wa1(j) / diag(j) + END DO + +! CALCULATE THE NORM OF THE SCALED GRADIENT AND TEST FOR +! THE SPECIAL CASE IN WHICH THE SCALED GRADIENT IS ZERO. + + gnorm = enorm(n, wa1) + sgnorm = 0.0 + alpha = delta / qnorm + IF (gnorm /= 0.0) THEN + +! CALCULATE THE POINT ALONG THE SCALED GRADIENT +! AT WHICH THE QUADRATIC IS MINIMIZED. + + DO j = 1, n + wa1(j) = (wa1(j)/gnorm) / diag(j) + END DO + l = 1 + DO j = 1, n + sum = 0.0 + DO i = j, n + sum = sum + r(l) * wa1(i) + l = l + 1 + END DO + wa2(j) = sum + END DO + temp = enorm(n, wa2) + sgnorm = (gnorm/temp) / temp + +! TEST WHETHER THE SCALED GRADIENT DIRECTION IS ACCEPTABLE. + + alpha = 0.0 + IF (sgnorm < delta) THEN + +! THE SCALED GRADIENT DIRECTION IS NOT ACCEPTABLE. +! FINALLY, CALCULATE THE POINT ALONG THE DOGLEG +! AT WHICH THE QUADRATIC IS MINIMIZED. + + bnorm = enorm(n, qtb) + temp = (bnorm/gnorm) * (bnorm/qnorm) * (sgnorm/delta) + temp = temp - (delta/qnorm) * (sgnorm/delta) ** 2 + SQRT(( & + temp-(delta/qnorm))**2+(1.0-(delta/qnorm)**2)*(1.0-( sgnorm/delta)**2)) + alpha = ((delta/qnorm)*(1.0-(sgnorm/delta)**2)) / temp + END IF + END IF + +! FORM APPROPRIATE CONVEX COMBINATION OF THE GAUSS-NEWTON +! DIRECTION AND THE SCALED GRADIENT DIRECTION. + + temp = (1.0-alpha) * MIN(sgnorm,delta) + DO j = 1, n + x(j) = temp * wa1(j) + alpha * x(j) + END DO +END IF +RETURN +END SUBROUTINE dogleg + + +SUBROUTINE fdjac1(fcn, n, x, fvec, fjac, ldfjac, iflag, ml, mu, epsfcn, & + wa1, wa2) + +INTEGER, INTENT(IN) :: n +REAL (dp), INTENT(IN OUT) :: x(n) +REAL (dp), INTENT(IN) :: fvec(n) +INTEGER, INTENT(IN) :: ldfjac +REAL (dp), INTENT(OUT) :: fjac(ldfjac,n) +INTEGER, INTENT(IN OUT) :: iflag +INTEGER, INTENT(IN) :: ml +INTEGER, INTENT(IN) :: mu +REAL (dp), INTENT(IN) :: epsfcn +REAL (dp), INTENT(IN OUT) :: wa1(n) +REAL (dp), INTENT(OUT) :: wa2(n) + +! EXTERNAL fcn +INTERFACE + SUBROUTINE FCN(N, X, FVEC, IFLAG) + IMPLICIT NONE + INTEGER, PARAMETER :: dp = SELECTED_REAL_KIND(14, 60) + INTEGER, INTENT(IN) :: n + REAL (dp), INTENT(IN) :: x(n) + REAL (dp), INTENT(OUT) :: fvec(n) + INTEGER, INTENT(IN OUT) :: iflag + END SUBROUTINE FCN +END INTERFACE + +! ********** + +! SUBROUTINE FDJAC1 + +! THIS SUBROUTINE COMPUTES A FORWARD-DIFFERENCE APPROXIMATION TO THE N BY N +! JACOBIAN MATRIX ASSOCIATED WITH A SPECIFIED PROBLEM OF N FUNCTIONS IN N +! VARIABLES. IF THE JACOBIAN HAS A BANDED FORM, THEN FUNCTION EVALUATIONS +! ARE SAVED BY ONLY APPROXIMATING THE NONZERO TERMS. + +! THE SUBROUTINE STATEMENT IS + +! SUBROUTINE FDJAC1(FCN,N,X,FVEC,FJAC,LDFJAC,IFLAG,ML,MU,EPSFCN, +! WA1,WA2) + +! WHERE + +! FCN IS THE NAME OF THE USER-SUPPLIED SUBROUTINE WHICH CALCULATES +! THE FUNCTIONS. FCN MUST BE DECLARED IN AN EXTERNAL STATEMENT IN +! THE USER CALLING PROGRAM, AND SHOULD BE WRITTEN AS FOLLOWS. + +! SUBROUTINE FCN(N,X,FVEC,IFLAG) +! INTEGER N,IFLAG +! REAL X(N),FVEC(N) +! ---------- +! CALCULATE THE FUNCTIONS AT X AND +! RETURN THIS VECTOR IN FVEC. +! ---------- +! RETURN +! END + +! THE VALUE OF IFLAG SHOULD NOT BE CHANGED BY FCN UNLESS +! THE USER WANTS TO TERMINATE EXECUTION OF FDJAC1. +! IN THIS CASE SET IFLAG TO A NEGATIVE INTEGER. + +! N IS A POSITIVE INTEGER INPUT VARIABLE SET TO THE NUMBER +! OF FUNCTIONS AND VARIABLES. + +! X IS AN INPUT ARRAY OF LENGTH N. + +! FVEC IS AN INPUT ARRAY OF LENGTH N WHICH MUST CONTAIN THE +! FUNCTIONS EVALUATED AT X. + +! FJAC IS AN OUTPUT N BY N ARRAY WHICH CONTAINS THE +! APPROXIMATION TO THE JACOBIAN MATRIX EVALUATED AT X. + +! LDFJAC IS A POSITIVE INTEGER INPUT VARIABLE NOT LESS THAN N +! WHICH SPECIFIES THE LEADING DIMENSION OF THE ARRAY FJAC. + +! IFLAG IS AN INTEGER VARIABLE WHICH CAN BE USED TO TERMINATE +! THE EXECUTION OF FDJAC1. SEE DESCRIPTION OF FCN. + +! ML IS A NONNEGATIVE INTEGER INPUT VARIABLE WHICH SPECIFIES +! THE NUMBER OF SUBDIAGONALS WITHIN THE BAND OF THE +! JACOBIAN MATRIX. IF THE JACOBIAN IS NOT BANDED, SET +! ML TO AT LEAST N - 1. + +! EPSFCN IS AN INPUT VARIABLE USED IN DETERMINING A SUITABLE +! STEP LENGTH FOR THE FORWARD-DIFFERENCE APPROXIMATION. THIS +! APPROXIMATION ASSUMES THAT THE RELATIVE ERRORS IN THE +! FUNCTIONS ARE OF THE ORDER OF EPSFCN. IF EPSFCN IS LESS +! THAN THE MACHINE PRECISION, IT IS ASSUMED THAT THE RELATIVE +! ERRORS IN THE FUNCTIONS ARE OF THE ORDER OF THE MACHINE PRECISION. + +! MU IS A NONNEGATIVE INTEGER INPUT VARIABLE WHICH SPECIFIES +! THE NUMBER OF SUPERDIAGONALS WITHIN THE BAND OF THE +! JACOBIAN MATRIX. IF THE JACOBIAN IS NOT BANDED, SET +! MU TO AT LEAST N - 1. + +! WA1 AND WA2 ARE WORK ARRAYS OF LENGTH N. IF ML + MU + 1 IS AT +! LEAST N, THEN THE JACOBIAN IS CONSIDERED DENSE, AND WA2 IS +! NOT REFERENCED. + +! SUBPROGRAMS CALLED + +! MINPACK-SUPPLIED ... SPMPAR + +! FORTRAN-SUPPLIED ... ABS,MAX,SQRT + +! ARGONNE NATIONAL LABORATORY. MINPACK PROJECT. MARCH 1980. +! BURTON S. GARBOW, KENNETH E. HILLSTROM, JORGE J. MORE + +! ********** +INTEGER :: i, j, k, msum +REAL (dp) :: eps, epsmch, h, temp +REAL (dp), PARAMETER :: zero = 0.0_dp + +! EPSMCH IS THE MACHINE PRECISION. + +epsmch = EPSILON(1.0_dp) + +eps = SQRT(MAX(epsfcn, epsmch)) +msum = ml + mu + 1 +IF (msum >= n) THEN + +! COMPUTATION OF DENSE APPROXIMATE JACOBIAN. + + DO j = 1, n + temp = x(j) + h = eps * ABS(temp) + IF (h == zero) h = eps + x(j) = temp + h + CALL fcn(n, x, wa1, iflag) + IF (iflag < 0) EXIT + x(j) = temp + DO i = 1, n + fjac(i,j) = (wa1(i)-fvec(i)) / h + END DO + END DO +ELSE + +! COMPUTATION OF BANDED APPROXIMATE JACOBIAN. + + DO k = 1, msum + DO j = k, n, msum + wa2(j) = x(j) + h = eps * ABS(wa2(j)) + IF (h == zero) h = eps + x(j) = wa2(j) + h + END DO + CALL fcn(n, x, wa1, iflag) + IF (iflag < 0) EXIT + DO j = k, n, msum + x(j) = wa2(j) + h = eps * ABS(wa2(j)) + IF (h == zero) h = eps + DO i = 1, n + fjac(i,j) = zero + IF (i >= j-mu .AND. i <= j+ml) fjac(i,j) = (wa1(i)-fvec(i)) / h + END DO + END DO + END DO +END IF +RETURN + +! LAST CARD OF SUBROUTINE FDJAC1. + +END SUBROUTINE fdjac1 + + + +SUBROUTINE qform(m, n, q, ldq, wa) + +INTEGER, INTENT(IN) :: m +INTEGER, INTENT(IN) :: n +INTEGER, INTENT(IN) :: ldq +REAL (dp), INTENT(OUT) :: q(ldq,m) +REAL (dp), INTENT(OUT) :: wa(m) + + +! ********** + +! SUBROUTINE QFORM + +! THIS SUBROUTINE PROCEEDS FROM THE COMPUTED QR FACTORIZATION OF AN M BY N +! MATRIX A TO ACCUMULATE THE M BY M ORTHOGONAL MATRIX Q FROM ITS FACTORED FORM. + +! THE SUBROUTINE STATEMENT IS + +! SUBROUTINE QFORM(M,N,Q,LDQ,WA) + +! WHERE + +! M IS A POSITIVE INTEGER INPUT VARIABLE SET TO THE NUMBER +! OF ROWS OF A AND THE ORDER OF Q. + +! N IS A POSITIVE INTEGER INPUT VARIABLE SET TO THE NUMBER OF COLUMNS OF A. + +! Q IS AN M BY M ARRAY. ON INPUT THE FULL LOWER TRAPEZOID IN +! THE FIRST MIN(M,N) COLUMNS OF Q CONTAINS THE FACTORED FORM. +! ON OUTPUT Q HAS BEEN ACCUMULATED INTO A SQUARE MATRIX. + +! LDQ IS A POSITIVE INTEGER INPUT VARIABLE NOT LESS THAN M +! WHICH SPECIFIES THE LEADING DIMENSION OF THE ARRAY Q. + +! WA IS A WORK ARRAY OF LENGTH M. + +! SUBPROGRAMS CALLED + +! FORTRAN-SUPPLIED ... MIN + +! ARGONNE NATIONAL LABORATORY. MINPACK PROJECT. MARCH 1980. +! BURTON S. GARBOW, KENNETH E. HILLSTROM, JORGE J. MORE + +! ********** +INTEGER :: i, j, jm1, k, l, minmn, np1 +REAL (dp) :: sum, temp +REAL (dp), PARAMETER :: one = 1.0_dp, zero = 0.0_dp + +! ZERO OUT UPPER TRIANGLE OF Q IN THE FIRST MIN(M,N) COLUMNS. + +minmn = MIN(m,n) +IF (minmn >= 2) THEN + DO j = 2, minmn + jm1 = j - 1 + DO i = 1, jm1 + q(i,j) = zero + END DO + END DO +END IF + +! INITIALIZE REMAINING COLUMNS TO THOSE OF THE IDENTITY MATRIX. + +np1 = n + 1 +IF (m >= np1) THEN + DO j = np1, m + DO i = 1, m + q(i,j) = zero + END DO + q(j,j) = one + END DO +END IF + +! ACCUMULATE Q FROM ITS FACTORED FORM. + +DO l = 1, minmn + k = minmn - l + 1 + DO i = k, m + wa(i) = q(i,k) + q(i,k) = zero + END DO + q(k,k) = one + IF (wa(k) /= zero) THEN + DO j = k, m + sum = zero + DO i = k, m + sum = sum + q(i,j) * wa(i) + END DO + temp = sum / wa(k) + DO i = k, m + q(i,j) = q(i,j) - temp * wa(i) + END DO + END DO + END IF +END DO +RETURN + +! LAST CARD OF SUBROUTINE QFORM. + +END SUBROUTINE qform + + +SUBROUTINE qrfac(m, n, a, lda, pivot, ipvt, lipvt, rdiag, acnorm, wa) + +INTEGER, INTENT(IN) :: m +INTEGER, INTENT(IN) :: n +INTEGER, INTENT(IN) :: lda +REAL (dp), INTENT(IN OUT) :: a(lda,n) +LOGICAL, INTENT(IN) :: pivot +INTEGER, INTENT(IN) :: lipvt +INTEGER, INTENT(OUT) :: ipvt(lipvt) +REAL (dp), INTENT(OUT) :: rdiag(n) +REAL (dp), INTENT(OUT) :: acnorm(n) +REAL (dp), INTENT(OUT) :: wa(n) + + +! ********** + +! SUBROUTINE QRFAC + +! THIS SUBROUTINE USES HOUSEHOLDER TRANSFORMATIONS WITH COLUMN PIVOTING +! (OPTIONAL) TO COMPUTE A QR FACTORIZATION OF THE M BY N MATRIX A. +! THAT IS, QRFAC DETERMINES AN ORTHOGONAL MATRIX Q, A PERMUTATION MATRIX P, +! AND AN UPPER TRAPEZOIDAL MATRIX R WITH DIAGONAL ELEMENTS OF NONINCREASING +! MAGNITUDE, SUCH THAT A*P = Q*R. THE HOUSEHOLDER TRANSFORMATION FOR +! COLUMN K, K = 1,2,...,MIN(M,N), IS OF THE FORM + +! T +! I - (1/U(K))*U*U + +! WHERE U HAS ZEROS IN THE FIRST K-1 POSITIONS. THE FORM OF THIS +! TRANSFORMATION AND THE METHOD OF PIVOTING FIRST APPEARED IN THE +! CORRESPONDING LINPACK SUBROUTINE. + +! THE SUBROUTINE STATEMENT IS + +! SUBROUTINE QRFAC(M,N,A,LDA,PIVOT,IPVT,LIPVT,RDIAG,ACNORM,WA) + +! WHERE + +! M IS A POSITIVE INTEGER INPUT VARIABLE SET TO THE NUMBER OF ROWS OF A. + +! N IS A POSITIVE INTEGER INPUT VARIABLE SET TO THE NUMBER +! OF COLUMNS OF A. + +! A IS AN M BY N ARRAY. ON INPUT A CONTAINS THE MATRIX FOR WHICH THE +! QR FACTORIZATION IS TO BE COMPUTED. ON OUTPUT THE STRICT UPPER +! TRAPEZOIDAL PART OF A CONTAINS THE STRICT UPPER TRAPEZOIDAL PART OF R, +! AND THE LOWER TRAPEZOIDAL PART OF A CONTAINS A FACTORED FORM OF Q +! (THE NON-TRIVIAL ELEMENTS OF THE U VECTORS DESCRIBED ABOVE). + +! LDA IS A POSITIVE INTEGER INPUT VARIABLE NOT LESS THAN M +! WHICH SPECIFIES THE LEADING DIMENSION OF THE ARRAY A. + +! PIVOT IS A LOGICAL INPUT VARIABLE. IF PIVOT IS SET TRUE, +! THEN COLUMN PIVOTING IS ENFORCED. IF PIVOT IS SET FALSE, +! THEN NO COLUMN PIVOTING IS DONE. + +! IPVT IS AN INTEGER OUTPUT ARRAY OF LENGTH LIPVT. IPVT DEFINES THE +! PERMUTATION MATRIX P SUCH THAT A*P = Q*R. +! COLUMN J OF P IS COLUMN IPVT(J) OF THE IDENTITY MATRIX. +! IF PIVOT IS FALSE, IPVT IS NOT REFERENCED. + +! LIPVT IS A POSITIVE INTEGER INPUT VARIABLE. IF PIVOT IS FALSE, +! THEN LIPVT MAY BE AS SMALL AS 1. IF PIVOT IS TRUE, THEN +! LIPVT MUST BE AT LEAST N. + +! RDIAG IS AN OUTPUT ARRAY OF LENGTH N WHICH CONTAINS THE +! DIAGONAL ELEMENTS OF R. + +! ACNORM IS AN OUTPUT ARRAY OF LENGTH N WHICH CONTAINS THE NORMS OF +! THE CORRESPONDING COLUMNS OF THE INPUT MATRIX A. +! IF THIS INFORMATION IS NOT NEEDED, THEN ACNORM CAN COINCIDE WITH RDIAG. + +! WA IS A WORK ARRAY OF LENGTH N. IF PIVOT IS FALSE, THEN WA +! CAN COINCIDE WITH RDIAG. + +! SUBPROGRAMS CALLED + +! MINPACK-SUPPLIED ... SPMPAR,ENORM + +! FORTRAN-SUPPLIED ... MAX,SQRT,MIN + +! ARGONNE NATIONAL LABORATORY. MINPACK PROJECT. MARCH 1980. +! BURTON S. GARBOW, KENNETH E. HILLSTROM, JORGE J. MORE + +! ********** +INTEGER :: i, j, jp1, k, kmax, minmn +REAL (dp) :: ajnorm, epsmch, sum, temp +REAL (dp), PARAMETER :: one = 1.0_dp, p05 = 0.05_dp, zero = 0.0_dp + +! EPSMCH IS THE MACHINE PRECISION. + +epsmch = EPSILON(1.0_dp) + +! COMPUTE THE INITIAL COLUMN NORMS AND INITIALIZE SEVERAL ARRAYS. + +DO j = 1, n + acnorm(j) = enorm(m, a(1:,j)) + rdiag(j) = acnorm(j) + wa(j) = rdiag(j) + IF (pivot) ipvt(j) = j +END DO + +! REDUCE A TO R WITH HOUSEHOLDER TRANSFORMATIONS. + +minmn = MIN(m,n) +DO j = 1, minmn + IF (pivot) THEN + +! BRING THE COLUMN OF LARGEST NORM INTO THE PIVOT POSITION. + + kmax = j + DO k = j, n + IF (rdiag(k) > rdiag(kmax)) kmax = k + END DO + IF (kmax /= j) THEN + DO i = 1, m + temp = a(i,j) + a(i,j) = a(i,kmax) + a(i,kmax) = temp + END DO + rdiag(kmax) = rdiag(j) + wa(kmax) = wa(j) + k = ipvt(j) + ipvt(j) = ipvt(kmax) + ipvt(kmax) = k + END IF + END IF + +! COMPUTE THE HOUSEHOLDER TRANSFORMATION TO REDUCE THE +! J-TH COLUMN OF A TO A MULTIPLE OF THE J-TH UNIT VECTOR. + + ajnorm = enorm(m-j+1, a(j:,j)) + IF (ajnorm /= zero) THEN + IF (a(j,j) < zero) ajnorm = -ajnorm + DO i = j, m + a(i,j) = a(i,j) / ajnorm + END DO + a(j,j) = a(j,j) + one + +! APPLY THE TRANSFORMATION TO THE REMAINING COLUMNS AND UPDATE THE NORMS. + + jp1 = j + 1 + IF (n >= jp1) THEN + DO k = jp1, n + sum = zero + DO i = j, m + sum = sum + a(i,j) * a(i,k) + END DO + temp = sum / a(j,j) + DO i = j, m + a(i,k) = a(i,k) - temp * a(i,j) + END DO + IF (.NOT.(.NOT.pivot.OR.rdiag(k) == zero)) THEN + temp = a(j,k) / rdiag(k) + rdiag(k) = rdiag(k) * SQRT(MAX(zero,one-temp**2)) + IF (p05*(rdiag(k)/wa(k))**2 <= epsmch) THEN + rdiag(k) = enorm(m-j, a(jp1:,k)) + wa(k) = rdiag(k) + END IF + END IF + END DO + END IF + END IF + rdiag(j) = -ajnorm +END DO +RETURN + +! LAST CARD OF SUBROUTINE QRFAC. + +END SUBROUTINE qrfac + + + +SUBROUTINE r1mpyq(m, n, a, lda, v, w) + +INTEGER, INTENT(IN) :: m +INTEGER, INTENT(IN) :: n +INTEGER, INTENT(IN) :: lda +REAL (dp), INTENT(IN OUT) :: a(lda,n) +REAL (dp), INTENT(IN) :: v(n) +REAL (dp), INTENT(IN) :: w(n) + + +! ********** + +! SUBROUTINE R1MPYQ + +! GIVEN AN M BY N MATRIX A, THIS SUBROUTINE COMPUTES A*Q WHERE +! Q IS THE PRODUCT OF 2*(N - 1) TRANSFORMATIONS + +! GV(N-1)*...*GV(1)*GW(1)*...*GW(N-1) + +! AND GV(I), GW(I) ARE GIVENS ROTATIONS IN THE (I,N) PLANE WHICH +! ELIMINATE ELEMENTS IN THE I-TH AND N-TH PLANES, RESPECTIVELY. +! Q ITSELF IS NOT GIVEN, RATHER THE INFORMATION TO RECOVER THE +! GV, GW ROTATIONS IS SUPPLIED. + +! THE SUBROUTINE STATEMENT IS + +! SUBROUTINE R1MPYQ(M, N, A, LDA, V, W) + +! WHERE + +! M IS A POSITIVE INTEGER INPUT VARIABLE SET TO THE NUMBER OF ROWS OF A. + +! N IS A POSITIVE INTEGER INPUT VARIABLE SET TO THE NUMBER OF COLUMNS OF A. + +! A IS AN M BY N ARRAY. ON INPUT A MUST CONTAIN THE MATRIX TO BE +! POSTMULTIPLIED BY THE ORTHOGONAL MATRIX Q DESCRIBED ABOVE. +! ON OUTPUT A*Q HAS REPLACED A. + +! LDA IS A POSITIVE INTEGER INPUT VARIABLE NOT LESS THAN M +! WHICH SPECIFIES THE LEADING DIMENSION OF THE ARRAY A. + +! V IS AN INPUT ARRAY OF LENGTH N. V(I) MUST CONTAIN THE INFORMATION +! NECESSARY TO RECOVER THE GIVENS ROTATION GV(I) DESCRIBED ABOVE. + +! W IS AN INPUT ARRAY OF LENGTH N. W(I) MUST CONTAIN THE INFORMATION +! NECESSARY TO RECOVER THE GIVENS ROTATION GW(I) DESCRIBED ABOVE. + +! SUBROUTINES CALLED + +! FORTRAN-SUPPLIED ... ABS, SQRT + +! ARGONNE NATIONAL LABORATORY. MINPACK PROJECT. MARCH 1980. +! BURTON S. GARBOW, KENNETH E. HILLSTROM, JORGE J. MORE + +! ********** +INTEGER :: i, j, nmj, nm1 +REAL (dp) :: COS, SIN, temp +REAL (dp), PARAMETER :: one = 1.0_dp + +! APPLY THE FIRST SET OF GIVENS ROTATIONS TO A. + +nm1 = n - 1 +IF (nm1 >= 1) THEN + DO nmj = 1, nm1 + j = n - nmj + IF (ABS(v(j)) > one) COS = one / v(j) + IF (ABS(v(j)) > one) SIN = SQRT(one-COS**2) + IF (ABS(v(j)) <= one) SIN = v(j) + IF (ABS(v(j)) <= one) COS = SQRT(one-SIN**2) + DO i = 1, m + temp = COS * a(i,j) - SIN * a(i,n) + a(i,n) = SIN * a(i,j) + COS * a(i,n) + a(i,j) = temp + END DO + END DO + +! APPLY THE SECOND SET OF GIVENS ROTATIONS TO A. + + DO j = 1, nm1 + IF (ABS(w(j)) > one) COS = one / w(j) + IF (ABS(w(j)) > one) SIN = SQRT(one-COS**2) + IF (ABS(w(j)) <= one) SIN = w(j) + IF (ABS(w(j)) <= one) COS = SQRT(one-SIN**2) + DO i = 1, m + temp = COS * a(i,j) + SIN * a(i,n) + a(i,n) = -SIN * a(i,j) + COS * a(i,n) + a(i,j) = temp + END DO + END DO +END IF +RETURN + +! LAST CARD OF SUBROUTINE R1MPYQ. + +END SUBROUTINE r1mpyq + + + +SUBROUTINE r1updt(m, n, s, ls, u, v, w, sing) + +INTEGER, INTENT(IN) :: m +INTEGER, INTENT(IN) :: n +INTEGER, INTENT(IN) :: ls +REAL (dp), INTENT(IN OUT) :: s(ls) +REAL (dp), INTENT(IN) :: u(m) +REAL (dp), INTENT(IN OUT) :: v(n) +REAL (dp), INTENT(OUT) :: w(m) +LOGICAL, INTENT(OUT) :: sing + + +! ********** + +! SUBROUTINE R1UPDT + +! GIVEN AN M BY N LOWER TRAPEZOIDAL MATRIX S, AN M-VECTOR U, +! AND AN N-VECTOR V, THE PROBLEM IS TO DETERMINE AN +! ORTHOGONAL MATRIX Q SUCH THAT + +! T +! (S + U*V )*Q + +! IS AGAIN LOWER TRAPEZOIDAL. + +! THIS SUBROUTINE DETERMINES Q AS THE PRODUCT OF 2*(N - 1) TRANSFORMATIONS + +! GV(N-1)*...*GV(1)*GW(1)*...*GW(N-1) + +! WHERE GV(I), GW(I) ARE GIVENS ROTATIONS IN THE (I,N) PLANE +! WHICH ELIMINATE ELEMENTS IN THE I-TH AND N-TH PLANES, RESPECTIVELY. +! Q ITSELF IS NOT ACCUMULATED, RATHER THE INFORMATION TO RECOVER THE GV, +! GW ROTATIONS IS RETURNED. + +! THE SUBROUTINE STATEMENT IS + +! SUBROUTINE R1UPDT(M,N,S,LS,U,V,W,SING) + +! WHERE + +! M IS A POSITIVE INTEGER INPUT VARIABLE SET TO THE NUMBER OF ROWS OF S. + +! N IS A POSITIVE INTEGER INPUT VARIABLE SET TO THE NUMBER +! OF COLUMNS OF S. N MUST NOT EXCEED M. + +! S IS AN ARRAY OF LENGTH LS. ON INPUT S MUST CONTAIN THE LOWER +! TRAPEZOIDAL MATRIX S STORED BY COLUMNS. ON OUTPUT S CONTAINS +! THE LOWER TRAPEZOIDAL MATRIX PRODUCED AS DESCRIBED ABOVE. + +! LS IS A POSITIVE INTEGER INPUT VARIABLE NOT LESS THAN +! (N*(2*M-N+1))/2. + +! U IS AN INPUT ARRAY OF LENGTH M WHICH MUST CONTAIN THE VECTOR U. + +! V IS AN ARRAY OF LENGTH N. ON INPUT V MUST CONTAIN THE VECTOR V. +! ON OUTPUT V(I) CONTAINS THE INFORMATION NECESSARY TO +! RECOVER THE GIVENS ROTATION GV(I) DESCRIBED ABOVE. + +! W IS AN OUTPUT ARRAY OF LENGTH M. W(I) CONTAINS INFORMATION +! NECESSARY TO RECOVER THE GIVENS ROTATION GW(I) DESCRIBED ABOVE. + +! SING IS A LOGICAL OUTPUT VARIABLE. SING IS SET TRUE IF ANY OF THE +! DIAGONAL ELEMENTS OF THE OUTPUT S ARE ZERO. OTHERWISE SING IS +! SET FALSE. + +! SUBPROGRAMS CALLED + +! MINPACK-SUPPLIED ... SPMPAR + +! FORTRAN-SUPPLIED ... ABS,SQRT + +! ARGONNE NATIONAL LABORATORY. MINPACK PROJECT. MARCH 1980. +! BURTON S. GARBOW, KENNETH E. HILLSTROM, JORGE J. MORE, JOHN L. NAZARETH + +! ********** +INTEGER :: i, j, jj, l, nmj, nm1 +REAL (dp) :: COS, cotan, giant, SIN, TAN, tau, temp +REAL (dp), PARAMETER :: one = 1.0_dp, p5 = 0.5_dp, p25 = 0.25_dp, zero = 0.0_dp + +! GIANT IS THE LARGEST MAGNITUDE. + +giant = HUGE(1.0_dp) + +! INITIALIZE THE DIAGONAL ELEMENT POINTER. + +jj = (n*(2*m-n+1)) / 2 - (m-n) + +! MOVE THE NONTRIVIAL PART OF THE LAST COLUMN OF S INTO W. + +l = jj +DO i = n, m + w(i) = s(l) + l = l + 1 +END DO + +! ROTATE THE VECTOR V INTO A MULTIPLE OF THE N-TH UNIT VECTOR +! IN SUCH A WAY THAT A SPIKE IS INTRODUCED INTO W. + +nm1 = n - 1 +IF (nm1 >= 1) THEN + DO nmj = 1, nm1 + j = n - nmj + jj = jj - (m-j+1) + w(j) = zero + IF (v(j) /= zero) THEN + +! DETERMINE A GIVENS ROTATION WHICH ELIMINATES THE J-TH ELEMENT OF V. + + IF (ABS(v(n)) < ABS(v(j))) THEN + cotan = v(n) / v(j) + SIN = p5 / SQRT(p25+p25*cotan**2) + COS = SIN * cotan + tau = one + IF (ABS(COS)*giant > one) tau = one / COS + ELSE + TAN = v(j) / v(n) + COS = p5 / SQRT(p25+p25*TAN**2) + SIN = COS * TAN + tau = SIN + END IF + +! APPLY THE TRANSFORMATION TO V AND STORE THE INFORMATION +! NECESSARY TO RECOVER THE GIVENS ROTATION. + + v(n) = SIN * v(j) + COS * v(n) + v(j) = tau + +! APPLY THE TRANSFORMATION TO S AND EXTEND THE SPIKE IN W. + + l = jj + DO i = j, m + temp = COS * s(l) - SIN * w(i) + w(i) = SIN * s(l) + COS * w(i) + s(l) = temp + l = l + 1 + END DO + END IF + END DO +END IF + +! ADD THE SPIKE FROM THE RANK 1 UPDATE TO W. + +DO i = 1, m + w(i) = w(i) + v(n) * u(i) +END DO + +! ELIMINATE THE SPIKE. + +sing = .false. +IF (nm1 >= 1) THEN + DO j = 1, nm1 + IF (w(j) /= zero) THEN + +! DETERMINE A GIVENS ROTATION WHICH ELIMINATES THE +! J-TH ELEMENT OF THE SPIKE. + + IF (ABS(s(jj)) < ABS(w(j))) THEN + cotan = s(jj) / w(j) + SIN = p5 / SQRT(p25 + p25*cotan**2) + COS = SIN * cotan + tau = one + IF (ABS(COS)*giant > one) tau = one / COS + ELSE + TAN = w(j) / s(jj) + COS = p5 / SQRT(p25+p25*TAN**2) + SIN = COS * TAN + tau = SIN + END IF + +! APPLY THE TRANSFORMATION TO S AND REDUCE THE SPIKE IN W. + + l = jj + DO i = j, m + temp = COS * s(l) + SIN * w(i) + w(i) = -SIN * s(l) + COS * w(i) + s(l) = temp + l = l + 1 + END DO + +! STORE THE INFORMATION NECESSARY TO RECOVER THE GIVENS ROTATION. + + w(j) = tau + END IF + +! TEST FOR ZERO DIAGONAL ELEMENTS IN THE OUTPUT S. + + IF (s(jj) == zero) sing = .true. + jj = jj + (m-j+1) + END DO +END IF + +! MOVE W BACK INTO THE LAST COLUMN OF THE OUTPUT S. + +l = jj +DO i = n, m + s(l) = w(i) + l = l + 1 +END DO +IF (s(jj) == zero) sing = .true. +RETURN + +! LAST CARD OF SUBROUTINE R1UPDT. + +END SUBROUTINE r1updt + + +FUNCTION enorm(n, x) RESULT(fn_val) + +INTEGER, INTENT(IN) :: n +REAL (dp), INTENT(IN) :: x(n) +REAL (dp) :: fn_val + +! ********** + +! FUNCTION ENORM + +! GIVEN AN N-VECTOR X, THIS FUNCTION CALCULATES THE EUCLIDEAN NORM OF X. + +! THE EUCLIDEAN NORM IS COMPUTED BY ACCUMULATING THE SUM OF SQUARES IN THREE +! DIFFERENT SUMS. THE SUMS OF SQUARES FOR THE SMALL AND LARGE COMPONENTS +! ARE SCALED SO THAT NO OVERFLOWS OCCUR. NON-DESTRUCTIVE UNDERFLOWS ARE +! PERMITTED. UNDERFLOWS AND OVERFLOWS DO NOT OCCUR IN THE COMPUTATION OF THE UNSCALED +! SUM OF SQUARES FOR THE INTERMEDIATE COMPONENTS. +! THE DEFINITIONS OF SMALL, INTERMEDIATE AND LARGE COMPONENTS DEPEND ON +! TWO CONSTANTS, RDWARF AND RGIANT. THE MAIN RESTRICTIONS ON THESE CONSTANTS +! ARE THAT RDWARF**2 NOT UNDERFLOW AND RGIANT**2 NOT OVERFLOW. +! THE CONSTANTS GIVEN HERE ARE SUITABLE FOR EVERY KNOWN COMPUTER. + +! THE FUNCTION STATEMENT IS + +! REAL FUNCTION ENORM(N, X) + +! WHERE + +! N IS A POSITIVE INTEGER INPUT VARIABLE. + +! X IS AN INPUT ARRAY OF LENGTH N. + +! SUBPROGRAMS CALLED + +! FORTRAN-SUPPLIED ... ABS,SQRT + +! ARGONNE NATIONAL LABORATORY. MINPACK PROJECT. MARCH 1980. +! BURTON S. GARBOW, KENNETH E. HILLSTROM, JORGE J. MORE + +! ********** +INTEGER :: i +REAL (dp) :: agiant, floatn, s1, s2, s3, xabs, x1max, x3max +REAL (dp), PARAMETER :: rdwarf = 1.0D-100, rgiant = 1.0D+100 + +s1 = 0.0_dp +s2 = 0.0_dp +s3 = 0.0_dp +x1max = 0.0_dp +x3max = 0.0_dp +floatn = n +agiant = rgiant / floatn +DO i = 1, n + xabs = ABS(x(i)) + IF (xabs <= rdwarf .OR. xabs >= agiant) THEN + IF (xabs > rdwarf) THEN + +! SUM FOR LARGE COMPONENTS. + + IF (xabs > x1max) THEN + s1 = 1.0_dp + s1 * (x1max/xabs) ** 2 + x1max = xabs + ELSE + s1 = s1 + (xabs/x1max) ** 2 + END IF + ELSE + +! SUM FOR SMALL COMPONENTS. + + IF (xabs > x3max) THEN + s3 = 1.0_dp + s3 * (x3max/xabs) ** 2 + x3max = xabs + ELSE + IF (xabs /= 0.0_dp) s3 = s3 + (xabs/x3max) ** 2 + END IF + END IF + ELSE + +! SUM FOR INTERMEDIATE COMPONENTS. + + s2 = s2 + xabs ** 2 + END IF +END DO + +! CALCULATION OF NORM. + +IF (s1 /= 0.0_dp) THEN + fn_val = x1max * SQRT(s1 + (s2/x1max)/x1max) +ELSE + IF (s2 /= 0.0_dp) THEN + IF (s2 >= x3max) fn_val = SQRT(s2*(1.0_dp + (x3max/s2)*(x3max*s3))) + IF (s2 < x3max) fn_val = SQRT(x3max*((s2/x3max) + (x3max*s3))) + ELSE + fn_val = x3max * SQRT(s3) + END IF +END IF +RETURN +END FUNCTION enorm + +END MODULE Solve_NonLin diff --git a/applications/PUfoam/MoDeNaModels/PolymerDensity/ExampleOfUsage/src/srcDetailedCode/modules.f90 b/applications/PUfoam/MoDeNaModels/PolymerDensity/ExampleOfUsage/src/srcDetailedCode/modules.f90 new file mode 100644 index 000000000..4147cd131 --- /dev/null +++ b/applications/PUfoam/MoDeNaModels/PolymerDensity/ExampleOfUsage/src/srcDetailedCode/modules.f90 @@ -0,0 +1,368 @@ +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! This module contains parameters and variables .... +! ................ +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW + +Module PARAMETERS + + implicit none + save + + integer, parameter :: nc = 6 + integer, parameter :: np = 3 + integer, parameter :: nsite = 5 + + real, parameter :: PI = 3.141592653589793 + real, parameter :: RGAS = 8.31441 + real, parameter :: NAv = 6.022045E23 + real, parameter :: KBOL = RGAS / NAv + real, parameter :: TAU = PI / 3.0 / SQRT(2.0) + +End Module PARAMETERS + + +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! This module contains parameters and variables .... +! ................ +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW + +Module BASIC_VARIABLES + + use PARAMETERS, only: nc, np, nsite + implicit none + save + +! ---------------------------------------------------------------------- +! basic quantities defining the mixture +! ---------------------------------------------------------------------- + integer :: ncomp + integer :: nphas + + real :: t + !real :: tc + real :: p + real, dimension(np) :: dense + !real, dimension(np) :: rhob + + real, dimension(np, nc) :: xi + real, dimension(np, nc) :: lnx + real, dimension(nc) :: xiF + + real, dimension(nc) :: mm + real, dimension(np, nc, nsite) :: mxx + + real :: alpha + + +! ---------------------------------------------------------------------- +! pure component parameters +! ---------------------------------------------------------------------- + real, dimension(nc, 25) :: parame = 0.0 + real, dimension(nc) :: chiR + character*30, dimension(nc) :: compna + real, dimension(nc, nc) :: kij, lij + real, dimension(nc, nc) :: E_LC, S_LC + real, dimension(nc) :: LLi, phi_criti, chap + + +! ---------------------------------------------------------------------- +! thermodynamic quantities +! ---------------------------------------------------------------------- + real, dimension(np) :: densta + real, dimension(0:nc*np+6) :: val_init, val_conv + + real :: h_lv + real, dimension(np) :: cpres, enthal, entrop, gibbs, f_res + + real, dimension(np) :: dp_dz, dp_dz2 + + +! ---------------------------------------------------------------------- +! choice of EOS-model and solution method +! ---------------------------------------------------------------------- + integer :: eos, pol + integer :: num + character (LEN=2) :: ensemble_flag + character (LEN=10) :: RGT_variant + + +! ---------------------------------------------------------------------- +! for input/output +! ---------------------------------------------------------------------- + integer :: outp, bindiag + real :: u_in_T, u_out_T, u_in_P, u_out_P + + +! ---------------------------------------------------------------------- +! quantities defining the numerical procedure +! ---------------------------------------------------------------------- + integer :: n_unkw + + real :: step_a, acc_a !, acc_i + real, dimension(nc) :: scaling + real, dimension(3500) :: plv_kon + real, dimension(2, 3500) :: d_kond + + character*3, dimension(10) :: it, sum_rel + character*3 :: running + + +End Module BASIC_VARIABLES + + + + +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! This module contains parameters and variables .... +! ................ +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW + +Module EOS_VARIABLES + + use PARAMETERS, only: nc, nsite, PI, KBOL, TAU, NAv + use BASIC_VARIABLES, only: ncomp, eos, t, p, parame, E_LC, S_LC, chiR, & + LLi, phi_criti, chap, kij, lij, ensemble_flag + implicit none + save + +! ---------------------------------------------------------------------- +! basic quantities defining the mixture (single phase) +! ---------------------------------------------------------------------- + real :: x(nc) + real :: eta_start + real :: eta + real :: rho + +! ---------------------------------------------------------------------- +! thermodynamic quantities +! ---------------------------------------------------------------------- + real :: fres + real :: lnphi(nc) + real :: pges + real :: pgesdz + real :: pgesd2 + real :: pgesd3 + + real :: h_res + real :: cp_res + real :: s_res + +! ---------------------------------------------------------------------- +! quantities of fluid theory +! ---------------------------------------------------------------------- + real :: gij(nc,nc) + real :: mx(nc,nsite) + + real :: mseg(nc) + real :: dhs(nc) + real :: uij(nc,nc) + real :: sig_ij(nc,nc) + real :: vij(nc,nc) + + real :: um + real :: order1 + real :: order2 + real :: apar(0:6) + real :: bpar(0:6) + + real :: z0t + real :: z1t + real :: z2t + real :: z3t + + integer :: nhb_typ(nc) + real :: ass_d(nc,nc,nsite,nsite) + real :: nhb_no(nc,nsite) + real :: dij_ab(nc,nc) + +! ---------------------------------------------------------------------- +! auxilliary quantities +! ---------------------------------------------------------------------- + real :: tfr + integer :: phas + + character (LEN = 2) :: dd_term, qq_term, dq_term + + real :: densav(3), denold(3) + real :: density_error(3) + + real :: alpha_nematic + real :: alpha_test(2) + +End Module EOS_VARIABLES + + + +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! This module contains parameters and variables .... +! ................ +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW + +Module EOS_CONSTANTS + + use PARAMETERS, only: nc + implicit none + save + + real, dimension(0:6,3) :: ap, bp + real, dimension(4,9) :: dnm + + real, dimension(28) :: c_dd, n_dd, m_dd, k_dd, o_dd + real, dimension(nc,nc,0:8) :: qqp2, qqp4, ddp2, ddp4, dqp2, dqp4 + real, dimension(nc,nc,nc,0:8) :: qqp3, ddp3, dqp3 + +End Module EOS_CONSTANTS + +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! This module contains parameters and variables .... +! ................ +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW + +Module EOS_NUMERICAL_DERIVATIVES + + use EOS_VARIABLES, only: dd_term, qq_term, dq_term + + implicit none + save + + character (LEN=9) :: ideal_gas ! (yes, no) + character (LEN=9) :: hard_sphere ! (CSBM, no) + character (LEN=9) :: chain_term ! (TPT1, no) + character (LEN=9) :: disp_term ! (PC-SAFT, CK, no) + character (LEN=9) :: hb_term ! (TPT1_Chap, no) + character (LEN=9) :: LC_term ! (MSaupe, no) + character (LEN=9) :: branch_term ! (TPT2, no) + character (LEN=9) :: II_term ! (......., no) + character (LEN=9) :: ID_term ! (......., no) + + character (LEN=9) :: subtract1 ! (1PT, 2PT, no) + character (LEN=9) :: subtract2 ! (ITTpolar, no) + + character (LEN=9) :: save_eos_terms(10) + +End Module EOS_NUMERICAL_DERIVATIVES + + +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! Module STARTING_VALUES +! +! This module contains parameters and variables for a phase stability +! analyis as part of a flash calculation. +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW + + Module STARTING_VALUES + + use PARAMETERS, only: nc + implicit none + save + + REAL, DIMENSION(nc) :: rhoif, rhoi1, rhoi2, grad_fd + REAL :: fdenf + + End Module STARTING_VALUES + + + + + +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! Module DFT_MODULE +! +! This module contains parameters and variables for DFT calculations. +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! + Module DFT_MODULE + + use PARAMETERS, only: nc + implicit none + save + + INTEGER, PARAMETER :: NDFT = 4000 + !!integer :: discret + REAL :: box_l_no_unit + INTEGER, PARAMETER :: r_grid = 200 + INTEGER :: kmax, den_step + LOGICAL :: shift, WCA, MFT + REAL :: rc, rg, dzr, tau_cut,dzp + REAL :: d_hs, dhs_st, z3t_st + REAL :: z_ges + REAL, DIMENSION(r_grid) :: x1a + REAL, DIMENSION(NDFT) :: x2a + REAL, DIMENSION(r_grid,NDFT) :: ya, y1a, y2a, y12a + REAL, DIMENSION(r_grid,NDFT,4,4) :: c_bicub + REAL :: fres_temp + + REAL, DIMENSION(r_grid) :: x1a_11 + REAL, DIMENSION(NDFT) :: x2a_11 + REAL, DIMENSION(r_grid,NDFT) :: ya_11, y1a_11, y2a_11, y12a_11 + REAL, DIMENSION(r_grid,NDFT,4,4) :: c_bicub_11 + REAL, DIMENSION(r_grid) :: x1a_12 + REAL, DIMENSION(NDFT) :: x2a_12 + REAL, DIMENSION(r_grid,NDFT) :: ya_12, y1a_12, y2a_12, y12a_12 + REAL, DIMENSION(r_grid,NDFT,4,4) :: c_bicub_12 + REAL, DIMENSION(r_grid) :: x1a_22 + REAL, DIMENSION(NDFT) :: x2a_22 + REAL, DIMENSION(r_grid,NDFT) :: ya_22, y1a_22, y2a_22, y12a_22 + REAL, DIMENSION(r_grid,NDFT,4,4) :: c_bicub_22 + + End Module DFT_MODULE + + +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! This module ........... +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +Module rdf_variables + + implicit none + save + + real, dimension(0:20) :: fac(0:20) + +End Module rdf_variables + + +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! This module contains the variavles that are needed in the core DFT_FCN +! They are not passed directly to DFT_FCN because the nonlinear solver +! needs a certain calling structure: fcn(x,fvec,n) +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +Module DFT_FCN_MODULE + +use PARAMETERS, only: nc +use DFT_MODULE, only: ndft + implicit none + +INTEGER :: irc(nc),irc_j,ih,fa(nc) + REAL, DIMENSION(-NDFT:NDFT) :: zp + REAL, DIMENSION(-NDFT:NDFT) :: f_tot + REAL, DIMENSION(-NDFT:NDFT,2) :: dF_drho_tot + REAL :: rhob_dft(2,0:nc) + REAL :: my0(nc) + +End Module DFT_FCN_MODULE + + + + + + + + +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! Module Module_Heidemann_Khalil +! +! This module .... +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! + Module Module_Heidemann_Khalil + + implicit none + save + + real :: error_condition2 + + End Module + + + + diff --git a/applications/PUfoam/MoDeNaModels/PolymerDensity/ExampleOfUsage/workflow b/applications/PUfoam/MoDeNaModels/PolymerDensity/ExampleOfUsage/workflow new file mode 100755 index 000000000..ed3dee6c5 --- /dev/null +++ b/applications/PUfoam/MoDeNaModels/PolymerDensity/ExampleOfUsage/workflow @@ -0,0 +1,57 @@ +#!/usr/bin/python +''' + + ooo ooooo oooooooooo. ooooo ooo + `88. .888' `888' `Y8b `888b. `8' + 888b d'888 .ooooo. 888 888 .ooooo. 8 `88b. 8 .oooo. + 8 Y88. .P 888 d88' `88b 888 888 d88' `88b 8 `88b. 8 `P )88b + 8 `888' 888 888 888 888 888 888ooo888 8 `88b.8 .oP"888 + 8 Y 888 888 888 888 d88' 888 .o 8 `888 d8( 888 + o8o o888o `Y8bod8P' o888bood8P' `Y8bod8P' o8o `8 `Y888""8o + +Copyright + 2014-2015 MoDeNa Consortium, All rights reserved. + +License + This file is part of Modena. + + Modena is free software; you can redistribute it and/or modify it under + the terms of the GNU General Public License as published by the Free + Software Foundation, either version 3 of the License, or (at your option) + any later version. + + Modena is distributed in the hope that it will be useful, but WITHOUT ANY + WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS + FOR A PARTICULAR PURPOSE. See the GNU General Public License for more + details. + + You should have received a copy of the GNU General Public License along + with Modena. If not, see . + +Description + A simple workflow + +Authors + Henrik Rusche + +Contributors +''' + +from fireworks import Firework, Workflow, LaunchPad +from fireworks.core.rocket_launcher import rapidfire +import Density +from modulefinder import ModuleFinder + + +# set up the LaunchPad and reset it +launchpad = LaunchPad() +launchpad.reset('', require_password=False) + +# create the individual FireWorks and Workflow +# Source code in src/twoTanksMacroscopicProblem.C +wf = Workflow([Firework(Density.m)], {}, name="simulation") + +# store workflow and launch it locally +launchpad.add_wf(wf) +rapidfire(launchpad) + diff --git a/applications/PUfoam/MoDeNaModels/PolymerDensity/PolymerDensity.py b/applications/PUfoam/MoDeNaModels/PolymerDensity/PolymerDensity.py new file mode 100644 index 000000000..ef894deec --- /dev/null +++ b/applications/PUfoam/MoDeNaModels/PolymerDensity/PolymerDensity.py @@ -0,0 +1,176 @@ + +''' + + ooo ooooo oooooooooo. ooooo ooo + `88. .888' `888' `Y8b `888b. `8' + 888b d'888 .ooooo. 888 888 .ooooo. 8 `88b. 8 .oooo. + 8 Y88. .P 888 d88' `88b 888 888 d88' `88b 8 `88b. 8 `P )88b + 8 `888' 888 888 888 888 888 888ooo888 8 `88b.8 .oP"888 + 8 Y 888 888 888 888 d88' 888 .o 8 `888 d8( 888 + o8o o888o `Y8bod8P' o888bood8P' `Y8bod8P' o8o `8 `Y888""8o + +Copyright + 2014-2015 MoDeNa Consortium, All rights reserved. + +License + This file is part of Modena. + + Modena is free software; you can redistribute it and/or modify it under + the terms of the GNU General Public License as published by the Free + Software Foundation, either version 3 of the License, or (at your option) + any later version. + + Modena is distributed in the hope that it will be useful, but WITHOUT ANY + WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS + FOR A PARTICULAR PURPOSE. See the GNU General Public License + for more details. + + You should have received a copy of the GNU General Public License along + with Modena. If not, see . + +Description + Python library of FireTasks + +Authors + Henrik Rusche + +Contributors +''' + +import os +import modena +from modena import ForwardMappingModel,BackwardMappingModel,SurrogateModel,CFunction,IndexSet +import modena.Strategy as Strategy +from fireworks.user_objects.firetasks.script_task import FireTaskBase, ScriptTask +from fireworks import Firework, Workflow, FWAction +from fireworks.utilities.fw_utilities import explicit_serialize +from blessings import Terminal +from jinja2 import Template + +# Create terminal for colour output +term = Terminal() + + +__author__ = 'Henrik Rusche' +__copyright__ = 'Copyright 2014, MoDeNa Project' +__version__ = '0.2' +__maintainer__ = 'Henrik Rusche' +__email__ = 'h.rusche@wikki.co.uk.' +__date__ = 'Sep 4, 2014' + + +# ********************************* Class ********************************** # +@explicit_serialize +class DensityExactSim(FireTaskBase): + """ + A FireTask that starts a microscopic code and updates the database. + """ + + def run_task(self, fw_spec): + print( + term.yellow + + "Performing exact simulation (microscopic code recipe)" + + term.normal + ) + + # Write input for detailed model + ff = open('in.txt', 'w') + Tstr = str(self['point']['T']) + ff.write('%s \n' %(Tstr)) + + + ##TODO INPUT SHOULD COME FROM IndexSet + + ff.write('2 \n') #number of components in system + ff.write('air \n') #component 1 + ff.write('pu \n') #component 2 + ff.write('0. \n') #molar feed (initial) composition component 1 + ff.write('0. \n') #molar feed (initial) composition component 2 + ff.close() + + #create output file for detailed code + fff = open('out.txt', 'w+') + fff.close() + + # Execute detailed model + os.system('../src/PCSAFT_Density') + + # Analyse output + f = open('out.txt', 'r') + self['point']['rho'] = float(f.readline()) + f.close() + + return FWAction(mod_spec=[{'_push': self['point']}]) + + + + + + +f = CFunction( + Ccode= ''' +#include "modena.h" +#include "math.h" + +void surroDensity +( + const double* parameters, + const double* inherited_inputs, + const double* inputs, + double *outputs +) +{ + + const double T = inputs[0]; + + const double P0 = parameters[0]; + const double P1 = parameters[1]; + const double P2 = parameters[2]; + + // const double expo = 1.0 + (1.0 - T/P2); + // const double pwr = pow(P1,expo); + + // outputs[0] = P0 / pwr; + + + outputs[0] = P0 + T*P1 + P2*T*T; +} +''', + # These are global bounds for the function + inputs={ + 'T': { 'min': 270.0, 'max': 300.0, 'argPos': 0 }, #check if boundaries reasonable, from this range, the random values for the DOE are chosen! + }, + outputs={ + 'rho': { 'min': 9e99, 'max': -9e99, 'argPos': 0 }, + }, + parameters={ + 'param0': { 'min': -1E10, 'max': 1E10, 'argPos': 0 }, #check if boundaries are reasonable!!! + 'param1': { 'min': -1E10, 'max': 1E10, 'argPos': 1 }, + 'param2': { 'min': -1E10, 'max': 1E10, 'argPos': 2 }, + }, +) + +m = BackwardMappingModel( + _id= 'PolymerDensity', + surrogateFunction= f, + exactTask= DensityExactSim(), + substituteModels= [ ], + initialisationStrategy= Strategy.InitialPoints( + initialPoints= + { + 'T': [270.0, 290.0, 300.0], + }, + ), + outOfBoundsStrategy= Strategy.ExtendSpaceStochasticSampling( + nNewPoints= 4 + ), + parameterFittingStrategy= Strategy.NonLinFitWithErrorContol( + testDataPercentage= 0.2, + maxError= 300.0, + improveErrorStrategy= Strategy.StochasticSampling( + nNewPoints= 2 + ), + maxIterations= 5 # Currently not used + ), +) + diff --git a/applications/PUfoam/MoDeNaModels/PolymerDensity/README.md b/applications/PUfoam/MoDeNaModels/PolymerDensity/README.md new file mode 100644 index 000000000..e69de29bb diff --git a/applications/PUfoam/MoDeNaModels/PolymerDensity/__init__.py b/applications/PUfoam/MoDeNaModels/PolymerDensity/__init__.py new file mode 100644 index 000000000..2c66c26e0 --- /dev/null +++ b/applications/PUfoam/MoDeNaModels/PolymerDensity/__init__.py @@ -0,0 +1,38 @@ +''' + + ooo ooooo oooooooooo. ooooo ooo + `88. .888' `888' `Y8b `888b. `8' + 888b d'888 .ooooo. 888 888 .ooooo. 8 `88b. 8 .oooo. + 8 Y88. .P 888 d88' `88b 888 888 d88' `88b 8 `88b. 8 `P )88b + 8 `888' 888 888 888 888 888 888ooo888 8 `88b.8 .oP"888 + 8 Y 888 888 888 888 d88' 888 .o 8 `888 d8( 888 + o8o o888o `Y8bod8P' o888bood8P' `Y8bod8P' o8o `8 `Y888""8o + +Copyright + 2014-2015 MoDeNa Consortium, All rights reserved. + +License + This file is part of Modena. + + Modena is free software; you can redistribute it and/or modify it under + the terms of the GNU General Public License as published by the Free + Software Foundation, either version 3 of the License, or (at your option) + any later version. + + Modena is distributed in the hope that it will be useful, but WITHOUT ANY + WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS + FOR A PARTICULAR PURPOSE. See the GNU General Public License + for more details. + + You should have received a copy of the GNU General Public License along + with Modena. If not, see . + +Description + Python library of FireTasks + +Authors + Henrik Rusche + +Contributors +''' + diff --git a/applications/PUfoam/MoDeNaModels/PolymerDensity/initModels b/applications/PUfoam/MoDeNaModels/PolymerDensity/initModels new file mode 100755 index 000000000..4497f6fda --- /dev/null +++ b/applications/PUfoam/MoDeNaModels/PolymerDensity/initModels @@ -0,0 +1,62 @@ +#!/usr/bin/python +''' + + ooo ooooo oooooooooo. ooooo ooo + `88. .888' `888' `Y8b `888b. `8' + 888b d'888 .ooooo. 888 888 .ooooo. 8 `88b. 8 .oooo. + 8 Y88. .P 888 d88' `88b 888 888 d88' `88b 8 `88b. 8 `P )88b + 8 `888' 888 888 888 888 888 888ooo888 8 `88b.8 .oP"888 + 8 Y 888 888 888 888 d88' 888 .o 8 `888 d8( 888 + o8o o888o `Y8bod8P' o888bood8P' `Y8bod8P' o8o `8 `Y888""8o + +Copyright + 2014-2015 MoDeNa Consortium, All rights reserved. + +License + This file is part of Modena. + + Modena is free software; you can redistribute it and/or modify it under + the terms of the GNU General Public License as published by the Free + Software Foundation, either version 3 of the License, or (at your option) + any later version. + + Modena is distributed in the hope that it will be useful, but WITHOUT ANY + WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS + FOR A PARTICULAR PURPOSE. See the GNU General Public License for more + details. + + You should have received a copy of the GNU General Public License along + with Modena. If not, see . + +Description + Initialisation script for the flowRate model. The script calculates a few + data points and fits the surrogate model. Then the model is inserted into + the database. + +Authors + Henrik Rusche + +Contributors +''' + +from modena import SurrogateModel +from modena.Strategy import Workflow2 +#import flowRate +import modDensity +from fireworks import LaunchPad +from fireworks.core.rocket_launcher import rapidfire +from fireworks.utilities.fw_serializers import load_object + + +# set up the LaunchPad and reset it +launchpad = LaunchPad() +launchpad.reset('', require_password=False) + +initWfs = Workflow2([]) +for m in SurrogateModel.get_instances(): + initWfs.addNoLink(m.initialisationStrategy().workflow(m)) + +# store workflow and launch it locally +launchpad.add_wf(initWfs) +rapidfire(launchpad) + diff --git a/applications/PUfoam/MoDeNaModels/PolymerDensity/src/CMakeLists.txt b/applications/PUfoam/MoDeNaModels/PolymerDensity/src/CMakeLists.txt new file mode 100644 index 000000000..13afbae49 --- /dev/null +++ b/applications/PUfoam/MoDeNaModels/PolymerDensity/src/CMakeLists.txt @@ -0,0 +1,40 @@ +cmake_minimum_required (VERSION 2.8) + +# I am specifying two projects in the same Cmake file (not sure if good idea) +project (PCSAFT_Density C CXX Fortran) + +if( CMAKE_VERSION VERSION_GREATER "3.0" ) + cmake_policy(SET CMP0042 OLD) + cmake_policy(SET CMP0026 OLD) + cmake_policy(SET CMP0028 OLD) +endif() + +set(CMAKE_BUILD_TYPE Release) + +add_custom_target(debug + COMMAND ${CMAKE_COMMAND} -DCMAKE_BUILD_TYPE=Debug ${CMAKE_SOURCE_DIR} + COMMAND ${CMAKE_COMMAND} --build ${CMAKE_BINARY_DIR} --target all + COMMENT "Switch CMAKE_BUILD_TYPE to Debug" + ) + +add_custom_target(release + COMMAND ${CMAKE_COMMAND} -DCMAKE_BUILD_TYPE=Release ${CMAKE_SOURCE_DIR} + COMMAND ${CMAKE_COMMAND} --build ${CMAKE_BINARY_DIR} --target all + COMMENT "Switch CMAKE_BUILD_TYPE to Release" + ) + +find_package(MODENA REQUIRED) + +include(CheckCInline) +check_c_inline(C_INLINE) + +# ---------------------------------------------------------------------------- +# NOTE: +# This will look through **all** subdirectories and find **any** FORTRAN file +# it will then attempt to to compile and link all the files together. +# ------> FRAGILE <------ +file(GLOB FORTRANFILES ${CMAKE_CURRENT_SOURCE_DIR}/*/*.f90) +add_executable(PCSAFT_Density ${FORTRANFILES}) +set_target_properties(PCSAFT_Density PROPERTIES COMPILE_FLAGS "-fdefault-real-8") +target_link_libraries(PCSAFT_Density MODENA::modena) + diff --git a/applications/PUfoam/MoDeNaModels/PolymerDensity/src/DetailedModelCode/Numeric_subroutines.f90 b/applications/PUfoam/MoDeNaModels/PolymerDensity/src/DetailedModelCode/Numeric_subroutines.f90 new file mode 100644 index 000000000..63f65c284 --- /dev/null +++ b/applications/PUfoam/MoDeNaModels/PolymerDensity/src/DetailedModelCode/Numeric_subroutines.f90 @@ -0,0 +1,1672 @@ +!>WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +!! This file contains subroutines for subtasks like spline interpolations, +!! spline integration and function minimization +!!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW + + + + + + SUBROUTINE bicub_derivative ( ya, x1a, x2a, y1a, y2a, y12a, i_max, k_max ) +! + USE DFT_MODULE, ONLY: NDFT, r_grid + IMPLICIT NONE +! +! ---------------------------------------------------------------------- + REAL, INTENT(IN) :: ya(r_grid,NDFT) + REAL, INTENT(IN) :: x1a(r_grid) + REAL, INTENT(IN) :: x2a(NDFT) + REAL, INTENT(OUT) :: y1a(r_grid,NDFT) + REAL, INTENT(OUT) :: y2a(r_grid,NDFT) + REAL, INTENT(OUT) :: y12a(r_grid,NDFT) + INTEGER, INTENT(IN) :: i_max + INTEGER, INTENT(IN) :: k_max +! +! ---------------------------------------------------------------------- + INTEGER :: i, k +! ---------------------------------------------------------------------- + + +DO i = 2, i_max-1 + DO k = 2, k_max-1 + y1a(i,k) = (ya(i+1,k)-ya(i-1,k)) / (x1a(i+1)-x1a(i-1)) + y2a(i,k) = (ya(i,k+1)-ya(i,k-1)) / (x2a(k+1)-x2a(k-1)) + y12a(i,k)= (ya(i+1,k+1)-ya(i+1,k-1)-ya(i-1,k+1)+ya(i-1,k-1)) & + /((x1a(i+1)-x1a(i-1))*(x2a(k+1)-x2a(k-1))) + END DO +END DO + +i = 1 +DO k = 1, k_max + y1a(i,k) = 0.0 + y2a(i,k) = 0.0 + y12a(i,k)= 0.0 +END DO + +k = 1 +DO i = 1, i_max + y1a(i,k) = 0.0 + y2a(i,k) = 0.0 + y12a(i,k)= 0.0 +END DO + + +i = i_max +DO k = 2, k_max-1 + y1a(i,k) = (ya(i,k)-ya(i-1,k)) / (x1a(i)-x1a(i-1)) + y2a(i,k) = (ya(i,k+1)-ya(i,k-1)) / (x2a(k+1)-x2a(k-1)) + y12a(i,k)= (ya(i,k+1)-ya(i,k-1)-ya(i-1,k+1)+ya(i-1,k-1)) & + /((x1a(i)-x1a(i-1))*(x2a(k+1)-x2a(k-1))) +END DO + + +k = k_max +DO i = 2, i_max-1 + y1a(i,k) = (ya(i+1,k)-ya(i-1,k)) / (x1a(i+1)-x1a(i-1)) + y2a(i,k) = (ya(i,k)-ya(i,k-1)) / (x2a(k)-x2a(k-1)) + y12a(i,k)= (ya(i+1,k)-ya(i+1,k-1)-ya(i-1,k)+ya(i-1,k-1)) & + /((x1a(i+1)-x1a(i-1))*(x2a(k)-x2a(k-1))) +END DO + +k = k_max +i = i_max +y1a(i,k) = (ya(i,k)-ya(i-1,k)) / (x1a(i)-x1a(i-1)) +y2a(i,k) = (ya(i,k)-ya(i,k-1)) / (x2a(k)-x2a(k-1)) +y12a(i,k)= (ya(i,k)-ya(i,k-1)-ya(i-1,k)+ya(i-1,k-1)) & + /((x1a(i)-x1a(i-1))*(x2a(k)-x2a(k-1))) + +END SUBROUTINE bicub_derivative + + +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! + SUBROUTINE bicub_c ( ya, x1a, x2a, y1a, y2a, y12a, c_bicub, i_max, k_max ) +! + USE DFT_MODULE, ONLY: NDFT, r_grid + IMPLICIT NONE +! +! ---------------------------------------------------------------------- + REAL, INTENT(IN) :: ya(r_grid,NDFT) + REAL, INTENT(IN) :: x1a(r_grid) + REAL, INTENT(IN) :: x2a(NDFT) + REAL, INTENT(IN) :: y1a(r_grid,NDFT) + REAL, INTENT(IN) :: y2a(r_grid,NDFT) + REAL, INTENT(IN) :: y12a(r_grid,NDFT) + REAL, INTENT(OUT) :: c_bicub(r_grid,NDFT,4,4) + INTEGER, INTENT(IN) :: i_max + INTEGER, INTENT(IN) :: k_max +! +! ---------------------------------------------------------------------- + INTEGER :: i, k, m, n + REAL :: y(4),y1(4),y2(4),y12(4),x1l,x1u,x2l,x2u + REAL :: c(4,4) +! ---------------------------------------------------------------------- + +DO i = 1, i_max-1 + DO k = 1, k_max-1 + y(1)=ya(i,k) + y(2)=ya(i+1,k) + y(3)=ya(i+1,k+1) + y(4)=ya(i,k+1) + + y1(1)=y1a(i,k) + y1(2)=y1a(i+1,k) + y1(3)=y1a(i+1,k+1) + y1(4)=y1a(i,k+1) + + y2(1)=y2a(i,k) + y2(2)=y2a(i+1,k) + y2(3)=y2a(i+1,k+1) + y2(4)=y2a(i,k+1) + + y12(1)=y12a(i,k) + y12(2)=y12a(i+1,k) + y12(3)=y12a(i+1,k+1) + y12(4)=y12a(i,k+1) + + x1l=x1a(i) + x1u=x1a(i+1) + x2l=x2a(k) + x2u=x2a(k+1) + + CALL bcucof(y,y1,y2,y12,x1u-x1l,x2u-x2l,c) + DO m=1,4 + DO n=1,4 + c_bicub(i,k,m,n)=c(m,n) + END DO + END DO + + END DO +END DO + +END SUBROUTINE bicub_c + +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! + SUBROUTINE bcucof(y,y1,y2,y12,d1,d2,c) +! + IMPLICIT NONE +! +! ---------------------------------------------------------------------- + REAL, INTENT(IN) :: y(4) + REAL, INTENT(IN) :: y1(4) + REAL, INTENT(IN) :: y2(4) + REAL, INTENT(IN) :: y12(4) + REAL, INTENT(IN) :: d1 + REAL, INTENT(IN) :: d2 + REAL, INTENT(OUT) :: c(4,4) +! +! ---------------------------------------------------------------------- + INTEGER :: i,j,k,l + REAL :: d1d2,xx,cl(16),wt(16,16),x(16) + SAVE wt + DATA wt/1,0,-3,2,4*0,-3,0,9,-6,2,0,-6,4,8*0,3,0,-9,6,-2,0,6,-4,10* & + 0,9,-6,2*0,-6,4,2*0,3,-2,6*0,-9,6,2*0,6,-4,4*0,1,0,-3,2,-2,0,6,-4, & + 1,0,-3,2,8*0,-1,0,3,-2,1,0,-3,2,10*0,-3,2,2*0,3,-2,6*0,3,-2,2*0, & + -6,4,2*0,3,-2,0,1,-2,1,5*0,-3,6,-3,0,2,-4,2,9*0,3,-6,3,0,-2,4,-2, & + 10*0,-3,3,2*0,2,-2,2*0,-1,1,6*0,3,-3,2*0,-2,2,5*0,1,-2,1,0,-2,4, & + -2,0,1,-2,1,9*0,-1,2,-1,0,1,-2,1,10*0,1,-1,2*0,-1,1,6*0,-1,1,2*0, & + 2,-2,2*0,-1,1/ +! ---------------------------------------------------------------------- + +d1d2 = d1 * d2 +DO i = 1, 4 + x(i) = y(i) + x(i+4) = y1(i)*d1 + x(i+8) = y2(i)*d2 + x(i+12) = y12(i)*d1d2 +END DO +DO i = 1, 16 + xx = 0.0 + DO k = 1, 16 + xx = xx + wt(i,k) * x(k) + END DO + cl(i) = xx +END DO +l = 0 +DO i = 1, 4 + DO j = 1, 4 + l = l + 1 + c(i,j) = cl(l) + END DO +END DO + +END SUBROUTINE bcucof + + +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! + SUBROUTINE BI_CUB_SPLINE ( rho_rdf, xg, ya, x1a, x2a, y1a, y2a, y12a, & + c_bicub, rdf, dg_drho, dg_dr, i_max, ih, k ) +! + USE DFT_MODULE, ONLY: NDFT, r_grid + IMPLICIT NONE +! +! ---------------------------------------------------------------------- + REAL, INTENT(IN OUT) :: rho_rdf + REAL, INTENT(IN OUT) :: xg + REAL, INTENT(IN) :: ya(r_grid,NDFT) + REAL, INTENT(IN) :: x1a(r_grid) + REAL, INTENT(IN) :: x2a(NDFT) + REAL, INTENT(IN) :: y1a(r_grid,NDFT) + REAL, INTENT(IN) :: y2a(r_grid,NDFT) + REAL, INTENT(IN) :: y12a(r_grid,NDFT) + REAL, INTENT(IN) :: c_bicub(r_grid,NDFT,4,4) + REAL, INTENT(OUT) :: rdf + REAL, INTENT(OUT) :: dg_drho + REAL, INTENT(OUT) :: dg_dr + INTEGER, INTENT(IN OUT) :: i_max + !INTEGER, INTENT(IN OUT) :: k_max + INTEGER, INTENT(OUT) :: ih + INTEGER, INTENT(IN) :: k +! +! ---------------------------------------------------------------------- + INTEGER :: m, n + + REAL :: y(4),y1(4),y2(4),y12(4),x1l,x1u,x2l,x2u + REAL :: c(4,4) +! ---------------------------------------------------------------------- + +IF ( rho_rdf < x1a(1) ) THEN + dg_drho = 0.0 + dg_dr = 0.0 + rdf = 1.0 + RETURN +END IF +IF ( x1a(ih) <= rho_rdf .AND. rho_rdf < x1a(ih+1) ) GO TO 10 +IF ( ih > 2 ) THEN + IF ( x1a(ih-1) <= rho_rdf .AND. rho_rdf < x1a(ih) ) THEN + ih = ih - 1 + GO TO 10 + END IF +END IF +! write (*,*) 'in ',ih +CALL hunt ( x1a, i_max, rho_rdf, ih ) +! write (*,*) 'out',ih +10 CONTINUE +IF ( x2a(k) /= xg ) THEN +! write (*,*) 'error bi-cubic-spline',k,x2a(k),xg +! DO k=1,NDFT +! write (*,*) k,x2a(k) +! ENDDO +! stop +END IF + + + +y(1) = ya(ih,k) +y(2) = ya(ih+1,k) +y(3) = ya(ih+1,k+1) +y(4) = ya(ih,k+1) + +y1(1) = y1a(ih,k) +y1(2) = y1a(ih+1,k) +y1(3) = y1a(ih+1,k+1) +y1(4) = y1a(ih,k+1) + +y2(1) = y2a(ih,k) +y2(2) = y2a(ih+1,k) +y2(3) = y2a(ih+1,k+1) +y2(4) = y2a(ih,k+1) + +y12(1) = y12a(ih,k) +y12(2) = y12a(ih+1,k) +y12(3) = y12a(ih+1,k+1) +y12(4) = y12a(ih,k+1) + +x1l = x1a(ih) +x1u = x1a(ih+1) +x2l = x2a(k) +x2u = x2a(k+1) + +DO m = 1, 4 + DO n = 1, 4 + c(m,n) = c_bicub( ih, k, m, n ) + END DO +END DO +CALL bcuint ( x1l, x1u, x2l, x2u, rho_rdf, xg, c, rdf, dg_drho, dg_dr ) + +END SUBROUTINE BI_CUB_SPLINE + +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! SUBROUTINE hunt +! +! Given an array xx(1:n), and given a value x, returns a value jlo +! such that x is between xx(jlo) and xx(jlo+1). xx(1:n) must be +! monotonic, either increasing or decreasing. jlo=0 or jlo=n is +! returned to indicate that x is out of range. jlo on input is taken +! as the initial guess for jlo on output. +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! + SUBROUTINE hunt ( xx, n, x, jlo ) +! + IMPLICIT NONE +! +! ---------------------------------------------------------------------- + INTEGER, INTENT(IN) :: n + INTEGER, INTENT(OUT) :: jlo + REAL, INTENT(IN) :: xx(n) + REAL :: x +! +! ---------------------------------------------------------------------- + INTEGER :: inc,jhi,jm + LOGICAL :: ascnd +! ---------------------------------------------------------------------- + +ascnd = xx(n) >= xx(1) +IF( jlo <= 0 .OR. jlo > n ) THEN + jlo = 0 + jhi = n + 1 + GO TO 3 +END IF +inc = 1 +IF( x >= xx(jlo) .EQV. ascnd ) THEN +1 jhi = jlo + inc + IF ( jhi > n ) THEN + jhi = n + 1 + ELSE IF ( x >= xx(jhi) .EQV. ascnd ) THEN + jlo = jhi + inc = inc + inc + GO TO 1 + END IF +ELSE + jhi = jlo +2 jlo = jhi - inc + IF ( jlo < 1 ) THEN + jlo = 0 + ELSE IF ( x < xx(jlo) .EQV. ascnd ) THEN + jhi = jlo + inc = inc + inc + GO TO 2 + END IF +END IF +3 IF (jhi-jlo == 1 ) THEN + IF ( x == xx(n)) jlo = n - 1 + IF ( x == xx(1) ) jlo = 1 + RETURN +END IF +jm = ( jhi + jlo ) / 2 +IF ( x >= xx(jm) .EQV. ascnd ) THEN + jlo = jm +ELSE + jhi = jm +END IF +GO TO 3 +END SUBROUTINE hunt + + + +!********************************************************************** +! +!********************************************************************** +! + !SUBROUTINE bcuint ( y, y1, y2, y12, x1l, x1u, x2l, x2u, x1, x2, c, ansy, ansy1, ansy2 ) + SUBROUTINE bcuint ( x1l, x1u, x2l, x2u, x1, x2, c, ansy, ansy1, ansy2 ) +! + IMPLICIT NONE +! +! ---------------------------------------------------------------------- + !REAL, INTENT(IN OUT) :: y(4) + !REAL, INTENT(IN OUT) :: y1(4) + !REAL, INTENT(IN OUT) :: y2(4) + !REAL, INTENT(IN OUT) :: y12(4) + REAL, INTENT(IN OUT) :: x1l + REAL, INTENT(IN OUT) :: x1u + REAL, INTENT(IN OUT) :: x2l + REAL, INTENT(IN OUT) :: x2u + REAL, INTENT(IN OUT) :: x1 + REAL, INTENT(IN OUT) :: x2 + REAL, INTENT(IN) :: c(4,4) + REAL, INTENT(OUT) :: ansy + REAL, INTENT(OUT) :: ansy1 + REAL, INTENT(OUT) :: ansy2 +! +! ---------------------------------------------------------------------- + !U USES bcucof + INTEGER :: i + REAL :: t, u +! ---------------------------------------------------------------------- + +! call bcucof ( y, y1, y2, y12, x1u-x1l, x2u-x2l, c ) + +IF ( x1u == x1l .OR. x2u == x2l ) PAUSE 'bad input in bcuint' +t = (x1-x1l) / (x1u-x1l) +u = (x2-x2l) / (x2u-x2l) +ansy = 0.0 +ansy2 = 0.0 +ansy1 = 0.0 +DO i = 4, 1, -1 + ansy = t *ansy + ( (c(i,4)*u + c(i,3))*u+c(i,2) )*u + c(i,1) + ansy2 = t *ansy2 + ( 3.*c(i,4)*u+2.*c(i,3) )*u + c(i,2) + ansy1 = u *ansy1 + ( 3.*c(4,i)*t+2.*c(3,i) )*t + c(2,i) +END DO +ansy1 = ansy1 / (x1u-x1l) +ansy2 = ansy2 / (x2u-x2l) + +END SUBROUTINE bcuint + + +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! SUBROUTINE spline +! +! Given arrays x(1:n) and y(1:n) containing a tabulated function, +! i.e., yi = f(xi), with x1 < x2 < .. . < xN, and given values yp1 and +! ypn for the first derivative of the interpolating function at points 1 +! and n, respectively, this routine returns an array y2(1:n) of length n +! which contains the second derivatives of the interpolating function at +! the tabulated points xi. If yp1 and/or ypn are equal to 1 1030 or +! larger, the routine is signaled to set the corresponding boundary +! condition for a natural spline, with zero second derivative on that +! boundary. +! Parameter: NMAX is the largest anticipated value of n. +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! + SUBROUTINE spline ( x, y, n, yp1, ypn, y2 ) +! + IMPLICIT NONE +! +! ---------------------------------------------------------------------- + INTEGER, INTENT(IN) :: n + REAL, INTENT(IN) :: x(n) + REAL, INTENT(IN) :: y(n) + REAL, INTENT(IN) :: yp1 + REAL, INTENT(IN) :: ypn + REAL, INTENT(OUT) :: y2(n) +! +! ---------------------------------------------------------------------- + INTEGER, PARAMETER :: NMAX = 500 + INTEGER :: i, k + REAL :: p, qn, sig, un, u(NMAX) +! ---------------------------------------------------------------------- + + IF ( yp1 > 0.99E30 ) THEN + y2(1) = 0.0 + u(1) = 0.0 + ELSE + y2(1) = -0.5 + u(1) = ( 3.0/(x(2)-x(1)) ) * ( (y(2)-y(1))/(x(2)-x(1))-yp1 ) + END IF + DO i = 2, n-1 + IF ( (x(i+1)-x(i)) == 0.0 .OR. (x(i)-x(i-1)) == 0.0 .OR. (x(i+1)-x(i-1)) == 0.0 ) THEN + write (*,*) 'error in spline-interpolation' + stop + END IF + sig = (x(i)-x(i-1)) / (x(i+1)-x(i-1)) + p = sig*y2(i-1) + 2.0 + y2(i) = (sig-1.0) / p + u(i) = ( 6.0 * ((y(i+1)-y(i))/(x(i+1)-x(i))-(y(i)-y(i-1))/(x(i)-x(i-1))) / (x(i+1)-x(i-1)) & + - sig * u(i-1) ) / p + END DO + IF ( ypn > 0.99E30 ) THEN + qn = 0.0 + un = 0.0 + ELSE + qn = 0.5 + un = (3.0/(x(n)-x(n-1))) * (ypn-(y(n)-y(n-1))/(x(n)-x(n-1))) + END IF + y2(n) = (un-qn*u(n-1)) / (qn*y2(n-1)+1.0) + DO k = n-1, 1, -1 + y2(k) = y2(k) * y2(k+1) + u(k) + END DO + +END SUBROUTINE spline + +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! SUBROUTINE splint_integral +! +! Given the arrays xa(1:n) and ya(1:n) of length n, which tabulate a +! function (with the in order), and given the array y2a(1:n), which is +! the output from spline above, and given a value of x, this routine +! returns a cubic-spline interpolated value y. +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! + SUBROUTINE splint_integral ( xa, ya, y2a, n, xlo, xhi, integral ) +! + IMPLICIT NONE +! +! ---------------------------------------------------------------------- + INTEGER, INTENT(IN) :: n + REAL, INTENT(IN) :: xa(n) + REAL, INTENT(IN) :: ya(n) + REAL, INTENT(IN) :: y2a(n) + REAL, INTENT(IN) :: xlo + REAL, INTENT(IN) :: xhi + REAL, INTENT(OUT) :: integral +! +! ---------------------------------------------------------------------- + INTEGER :: k, khi_l, klo_l, khi_h, klo_h + REAL :: xl, xh, h, INT, x0, x1, y0, y1, y20, y21 +! ---------------------------------------------------------------------- + + integral = 0.0 + klo_l = 1 + khi_l = n +1 IF ( khi_l-klo_l > 1 ) THEN + k = ( khi_l + klo_l ) / 2 + IF ( xa(k) > xlo ) THEN + khi_l = k + ELSE + klo_l = k + END IF + GO TO 1 + END IF + + klo_h = 1 + khi_h = n +2 IF ( khi_h-klo_h > 1 ) THEN + k = ( khi_h + klo_h ) / 2 + IF ( xa(k) > xhi ) THEN + khi_h = k + ELSE + klo_h = k + END IF + GO TO 2 + END IF + + ! integration in spline pieces, the lower interval, bracketed + ! by xa(klo_L) and xa(khi_L) is in steps shifted upward. + + ! first: determine upper integration bound + xl = xlo +3 CONTINUE + IF ( khi_h > khi_l ) THEN + xh = xa(khi_l) + ELSE IF ( khi_h == khi_l ) THEN + xh = xhi + ELSE + WRITE (*,*) 'error in spline-integration' + PAUSE + END IF + + h = xa(khi_l) - xa(klo_l) + IF ( h == 0.0 ) PAUSE 'bad xa input in splint' + x0 = xa(klo_l) + x1 = xa(khi_l) + y0 = ya(klo_l) + y1 = ya(khi_l) + y20= y2a(klo_l) + y21= y2a(khi_l) + ! int = -xL/h * ( (x1-.5*xL)*y0 + (0.5*xL-x0)*y1 & + ! +y20/6.*(x1**3-1.5*xL*x1*x1+xL*xL*x1-.25*xL**3) & + ! -y20/6.*h*h*(x1-.5*xL) & + ! +y21/6.*(.25*xL**3-xL*xL*x0+1.5*xL*x0*x0-x0**3) & + ! -y21/6.*h*h*(.5*xL-x0) ) + ! int = int + xH/h * ( (x1-.5*xH)*y0 + (0.5*xH-x0)*y1 & + ! +y20/6.*(x1**3-1.5*xH*x1*x1+xH*xH*x1-.25*xH**3) & + ! -y20/6.*h*h*(x1-.5*xH) & + ! +y21/6.*(.25*xH**3-xH*xH*x0+1.5*xH*x0*x0-x0**3) & + ! -y21/6.*h*h*(.5*xH-x0) ) + INT = -1.0/h * ( xl*((x1-.5*xl)*y0 + (0.5*xl-x0)*y1) & + -y20/24.*(x1-xl)**4 + y20/6.*(0.5*xl*xl-x1*xl)*h*h & + +y21/24.*(xl-x0)**4 - y21/6.*(0.5*xl*xl-x0*xl)*h*h ) + INT = INT + 1.0/h * ( xh*((x1-.5*xh)*y0 + (0.5*xh-x0)*y1) & + -y20/24.*(x1-xh)**4 + y20/6.*(0.5*xh*xh-x1*xh)*h*h & + +y21/24.*(xh-x0)**4 - y21/6.*(0.5*xh*xh-x0*xh)*h*h ) + + integral = integral + INT + ! write (*,*) integral,x1,xH + klo_l = klo_l + 1 + khi_l = khi_l + 1 + xl = x1 + IF (khi_h /= (khi_l-1)) GO TO 3 ! the -1 in (khi_L-1) because khi_L was already counted up + +END SUBROUTINE splint_integral + + + + +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! + REAL FUNCTION praxis( t0, machep, h0, n, prin, x, f, fmin ) + + IMPLICIT NONE + +! ---------------------------------------------------------------------- + REAL, INTENT(IN OUT) :: t0 + REAL, INTENT(IN) :: machep + REAL, INTENT(IN) :: h0 + INTEGER :: n + INTEGER, INTENT(IN OUT) :: prin + REAL, INTENT(IN OUT) :: x(n) + REAL :: f + REAL, INTENT(IN OUT) :: fmin +! ---------------------------------------------------------------------- + +EXTERNAL f + +! PRAXIS RETURNS THE MINIMUM OF THE FUNCTION F(X,N) OF N VARIABLES +! USING THE PRINCIPAL AXIS METHOD. THE GRADIENT OF THE FUNCTION IS +! NOT REQUIRED. + +! FOR A DESCRIPTION OF THE ALGORITHM, SEE CHAPTER SEVEN OF +! "ALGORITHMS FOR FINDING ZEROS AND EXTREMA OF FUNCTIONS WITHOUT +! CALCULATING DERIVATIVES" BY RICHARD P BRENT. + +! THE PARAMETERS ARE: +! T0 IS A TOLERANCE. PRAXIS ATTEMPTS TO RETURN PRAXIS=F(X) +! SUCH THAT IF X0 IS THE TRUE LOCAL MINIMUM NEAR X, THEN +! NORM(X-X0) < T0 + SQUAREROOT(MACHEP)*NORM(X). +! MACHEP IS THE MACHINE PRECISION, THE SMALLEST NUMBER SUCH THAT +! 1 + MACHEP > 1. MACHEP SHOULD BE 16.**-13 (ABOUT +! 2.22D-16) FOR REAL*8 ARITHMETIC ON THE IBM 360. +! H0 IS THE MAXIMUM STEP SIZE. H0 SHOULD BE SET TO ABOUT THE +! MAXIMUM DISTANCE FROM THE INITIAL GUESS TO THE MINIMUM. +! (IF H0 IS SET TOO LARGE OR TOO SMALL, THE INITIAL RATE OF +! CONVERGENCE MAY BE SLOW.) +! N (AT LEAST TWO) IS THE NUMBER OF VARIABLES UPON WHICH +! THE FUNCTION DEPENDS. +! PRIN CONTROLS THE PRINTING OF INTERMEDIATE RESULTS. +! IF PRIN=0, NOTHING IS PRINTED. +! IF PRIN=1, F IS PRINTED AFTER EVERY N+1 OR N+2 LINEAR +! MINIMIZATIONS. FINAL X IS PRINTED, BUT INTERMEDIATE X IS +! PRINTED ONLY IF N IS AT MOST 4. +! IF PRIN=2, THE SCALE FACTORS AND THE PRINCIPAL VALUES OF +! THE APPROXIMATING QUADRATIC FORM ARE ALSO PRINTED. +! IF PRIN=3, X IS ALSO PRINTED AFTER EVERY FEW LINEAR +! MINIMIZATIONS. +! IF PRIN=4, THE PRINCIPAL VECTORS OF THE APPROXIMATING +! QUADRATIC FORM ARE ALSO PRINTED. +! X IS AN ARRAY CONTAINING ON ENTRY A GUESS OF THE POINT OF +! MINIMUM, ON RETURN THE ESTIMATED POINT OF MINIMUM. +! F(X,N) IS THE FUNCTION TO BE MINIMIZED. F SHOULD BE A REAL*8 +! FUNCTION DECLARED EXTERNAL IN THE CALLING PROGRAM. +! FMIN IS AN ESTIMATE OF THE MINIMUM, USED ONLY IN PRINTING +! INTERMEDIATE RESULTS. +! THE APPROXIMATING QUADRATIC FORM IS +! Q(X') = F(X,N) + (1/2) * (X'-X)-TRANSPOSE * A * (X'-X) +! WHERE X IS THE BEST ESTIMATE OF THE MINIMUM AND A IS +! INVERSE(V-TRANSPOSE) * D * INVERSE(V) +! (V(*,*) IS THE MATRIX OF SEARCH DIRECTIONS; D(*) IS THE ARRAY +! OF SECOND DIFFERENCES). IF F HAS CONTINUOUS SECOND DERIVATIVES +! NEAR X0, A WILL TEND TO THE HESSIAN OF F AT X0 AS X APPROACHES X0. + +! IT IS ASSUMED THAT ON FLOATING-POINT UNDERFLOW THE RESULT IS SET +! TO ZERO. +! THE USER SHOULD OBSERVE THE COMMENT ON HEURISTIC NUMBERS AFTER +! THE INITIALIZATION OF MACHINE DEPENDENT NUMBERS. + + LOGICAL :: illc + INTEGER :: nl,nf,kl,kt,ktm,idim,i,j,k,k2,km1,klmk,ii,im1 + REAL :: s,sl,dn,dmin,fx,f1,lds,ldt,t,h,sf,df,qf1,qd0, qd1,qa,qb,qc + REAL :: m2,m4,small,vsmall,large,vlarge,scbd,ldfac,t2, dni,value + REAL :: random + +!.....IF N>20 OR IF N<20 AND YOU NEED MORE SPACE, CHANGE '20' TO THE +! LARGEST VALUE OF N IN THE NEXT CARD, IN THE CARD 'IDIM=20', AND +! IN THE DIMENSION STATEMENTS IN SUBROUTINES MINFIT,MIN,FLIN,QUAD. + + REAL :: d(20),y(20),z(20),q0(20),q1(20),v(20,20) + COMMON /global/ fx,ldt,dmin,nf,nl /q/ v,q0,q1,qa,qb,qc,qd0,qd1,qf1 + +! --------------------------------- +! introduced by Joachim........ + idim = n +! --------------------------------- + + + +!.....INITIALIZATION..... +! MACHINE DEPENDENT NUMBERS: + +small = machep*machep +vsmall = small*small +large = 1.d0/small +vlarge = 1.d0/vsmall +m2 = SQRT(machep) +m4 = SQRT(m2) + +! HEURISTIC NUMBERS: +! IF THE AXES MAY BE BADLY SCALED (WHICH IS TO BE AVOIDED IF +! POSSIBLE), THEN SET SCBD=10. OTHERWISE SET SCBD=1. +! IF THE PROBLEM IS KNOWN TO BE ILL-CONDITIONED, SET ILLC=TRUE. +! OTHERWISE SET ILLC=FALSE. +! KTM IS THE NUMBER OF ITERATIONS WITHOUT IMPROVEMENT BEFORE THE +! ALGORITHM TERMINATES. KTM=4 IS VERY CAUTIOUS; USUALLY KTM=1 +! IS SATISFACTORY. + +scbd = 1.0 +illc = .false. +ktm = 1 + +ldfac = 0.01 +IF (illc) ldfac = 0.1 +kt = 0 +nl = 0 +nf = 1 +fx = f(x,n) +qf1 = fx +t = small+ABS(t0) +t2 = t +dmin = small +h = h0 +IF (h < 100*t) h = 100*t +ldt = h +!.....THE FIRST SET OF SEARCH DIRECTIONS V IS THE IDENTITY MATRIX..... +DO i = 1,n + DO j = 1,n + v(i,j) = 0.0 + END DO + v(i,i) = 1.0 +END DO +d(1) = 0.0 +qd0 = 0.0 +DO i = 1,n + q0(i) = x(i) + q1(i) = x(i) +END DO +IF (prin > 0) CALL PRINT(n,x,prin,fmin) + +!.....THE MAIN LOOP STARTS HERE..... +40 sf=d(1) +d(1)=0.d0 +s=0.d0 + +!.....MINIMIZE ALONG THE FIRST DIRECTION V(*,1). +! FX MUST BE PASSED TO MIN BY VALUE. +value=fx +CALL MIN(n,1,2,d(1),s,value,.false.,f,x,t,machep,h) +IF (s > 0.d0) GO TO 50 +DO i=1,n + v(i,1)=-v(i,1) +END DO +50 IF (sf > 0.9D0*d(1).AND.0.9D0*sf < d(1)) GO TO 70 +DO i=2,n + d(i)=0.d0 +END DO + +!.....THE INNER LOOP STARTS HERE..... +70 DO k=2,n + DO i=1,n + y(i)=x(i) + END DO + sf=fx + IF (kt > 0) illc=.true. + 80 kl=k + df=0.d0 + +!.....A RANDOM STEP FOLLOWS (TO AVOID RESOLUTION VALLEYS). +! PRAXIS ASSUMES THAT RANDOM RETURNS A RANDOM NUMBER UNIFORMLY +! DISTRIBUTED IN (0,1). + + IF(.NOT.illc) GO TO 95 + DO i=1,n + s=(0.1D0*ldt+t2*(10**kt))*(random(n)-0.5D0) + z(i)=s + DO j=1,n + x(j)=x(j)+s*v(j,i) + END DO + END DO + fx=f(x,n) + nf=nf+1 + +!.....MINIMIZE ALONG THE "NON-CONJUGATE" DIRECTIONS V(*,K),...,V(*,N) + + 95 DO k2=k,n + sl=fx + s=0.d0 + value=fx + CALL MIN(n,k2,2,d(k2),s,value,.false.,f,x,t,machep,h) + IF (illc) GO TO 97 + s=sl-fx + GO TO 99 + 97 s=d(k2)*((s+z(k2))**2) + 99 IF (df > s) CYCLE + df=s + kl=k2 + END DO + IF (illc.OR.(df >= ABS((100*machep)*fx))) GO TO 110 + +!.....IF THERE WAS NOT MUCH IMPROVEMENT ON THE FIRST TRY, SET +! ILLC=TRUE AND START THE INNER LOOP AGAIN..... + + illc=.true. + GO TO 80 + 110 IF (k == 2.AND.prin > 1) CALL vcprnt(1,d,n) + +!.....MINIMIZE ALONG THE "CONJUGATE" DIRECTIONS V(*,1),...,V(*,K-1) + + km1=k-1 + DO k2=1,km1 + s=0 + value=fx + CALL MIN(n,k2,2,d(k2),s,value,.false.,f,x,t,machep,h) + END DO + f1=fx + fx=sf + lds=0 + DO i=1,n + sl=x(i) + x(i)=y(i) + sl=sl-y(i) + y(i)=sl + lds=lds+sl*sl + END DO + lds=SQRT(lds) + IF (lds <= small) GO TO 160 + +!.....DISCARD DIRECTION V(*,KL). +! IF NO RANDOM STEP WAS TAKEN, V(*,KL) IS THE "NON-CONJUGATE" +! DIRECTION ALONG WHICH THE GREATEST IMPROVEMENT WAS MADE..... + + klmk=kl-k + IF (klmk < 1) GO TO 141 + DO ii=1,klmk + i=kl-ii + DO j=1,n + v(j,i+1)=v(j,i) + END DO + d(i+1)=d(i) + END DO + 141 d(k)=0 + DO i=1,n + v(i,k)=y(i)/lds + END DO + +!.....MINIMIZE ALONG THE NEW "CONJUGATE" DIRECTION V(*,K), WHICH IS +! THE NORMALIZED VECTOR: (NEW X) - (0LD X)..... + + value=f1 + CALL MIN(n,k,4,d(k),lds,value,.true.,f,x,t,machep,h) + IF (lds > 0.d0) GO TO 160 + lds=-lds + DO i=1,n + v(i,k)=-v(i,k) + END DO + 160 ldt=ldfac*ldt + IF (ldt < lds) ldt=lds + IF (prin > 0) CALL PRINT(n,x,prin,fmin) + t2=0.d0 + DO i=1,n + t2=t2+x(i)**2 + END DO + t2=m2*SQRT(t2)+t + +!.....SEE WHETHER THE LENGTH OF THE STEP TAKEN SINCE STARTING THE +! INNER LOOP EXCEEDS HALF THE TOLERANCE..... + + IF (ldt > (0.5*t2)) kt=-1 + kt=kt+1 + IF (kt > ktm) GO TO 400 +END DO +!.....THE INNER LOOP ENDS HERE. + +! TRY QUADRATIC EXTRAPOLATION IN CASE WE ARE IN A CURVED VALLEY. + +CALL quad(n,f,x,t,machep,h) +dn=0.d0 +DO i=1,n + d(i)=1.d0/SQRT(d(i)) + IF (dn < d(i)) dn=d(i) +END DO +IF (prin > 3) CALL maprnt(1,v,idim,n) +DO j=1,n + s=d(j)/dn + DO i=1,n + v(i,j)=s*v(i,j) + END DO +END DO + +!.....SCALE THE AXES TO TRY TO REDUCE THE CONDITION NUMBER..... + +IF (scbd <= 1.d0) GO TO 200 +s=vlarge +DO i=1,n + sl=0.d0 + DO j=1,n + sl=sl+v(i,j)*v(i,j) + END DO + z(i)=SQRT(sl) + IF (z(i) < m4) z(i)=m4 + IF (s > z(i)) s=z(i) +END DO +DO i=1,n + sl=s/z(i) + z(i)=1.d0/sl + IF (z(i) <= scbd) GO TO 189 + sl=1.d0/scbd + z(i)=scbd + 189 DO j=1,n + v(i,j)=sl*v(i,j) + END DO +END DO + +!.....CALCULATE A NEW SET OF ORTHOGONAL DIRECTIONS BEFORE REPEATING +! THE MAIN LOOP. +! FIRST TRANSPOSE V FOR MINFIT: + +200 DO i=2,n + im1=i-1 + DO j=1,im1 + s=v(i,j) + v(i,j)=v(j,i) + v(j,i)=s + END DO +END DO + +!.....CALL MINFIT TO FIND THE SINGULAR VALUE DECOMPOSITION OF V. +! THIS GIVES THE PRINCIPAL VALUES AND PRINCIPAL DIRECTIONS OF THE +! APPROXIMATING QUADRATIC FORM WITHOUT SQUARING THE CONDITION +! NUMBER..... + +CALL minfit(idim,n,machep,vsmall,v,d) + +!.....UNSCALE THE AXES..... + +IF (scbd <= 1.d0) GO TO 250 +DO i=1,n + s=z(i) + DO j=1,n + v(i,j)=s*v(i,j) + END DO +END DO +DO i=1,n + s=0.d0 + DO j=1,n + s=s+v(j,i)**2 + END DO + s=SQRT(s) + d(i)=s*d(i) + s=1/s + DO j=1,n + v(j,i)=s*v(j,i) + END DO +END DO + +250 DO i=1,n + dni=dn*d(i) + IF (dni > large) GO TO 265 + IF (dni < small) GO TO 260 + d(i)=1/(dni*dni) + CYCLE + 260 d(i)=vlarge + CYCLE + 265 d(i)=vsmall +END DO + +!.....SORT THE EIGENVALUES AND EIGENVECTORS..... + +CALL sort(idim,n,d,v) +dmin=d(n) +IF (dmin < small) dmin=small +illc=.false. +IF (m2*d(1) > dmin) illc=.true. +IF (prin > 1.AND.scbd > 1.d0) CALL vcprnt(2,z,n) +IF (prin > 1) CALL vcprnt(3,d,n) +IF (prin > 3) CALL maprnt(2,v,idim,n) +!.....THE MAIN LOOP ENDS HERE..... + +GO TO 40 + +!.....RETURN..... + +400 IF (prin > 0) CALL vcprnt(4,x,n) +praxis=fx + +END FUNCTION praxis + + +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! + SUBROUTINE minfit(m,n,machep,tol,ab,q) + + IMPLICIT NONE + + INTEGER, INTENT(IN OUT) :: m + INTEGER, INTENT(IN) :: n + REAL, INTENT(IN) :: machep + REAL, INTENT(IN OUT) :: tol + REAL, INTENT(IN OUT) :: ab(m,n) + REAL, INTENT(OUT) :: q(n) + INTEGER :: i,j,k,l, kk,kt,l2,ll2,ii,lp1 +! IMPLICIT REAL (A-H,O-Z) + + +REAL :: x,eps,e(20),g,s, f,h,y,c,z,temp +!...AN IMPROVED VERSION OF MINFIT (SEE GOLUB AND REINSCH, 1969) +! RESTRICTED TO M=N,P=0. +! THE SINGULAR VALUES OF THE ARRAY AB ARE RETURNED IN Q AND AB IS +! OVERWRITTEN WITH THE ORTHOGONAL MATRIX V SUCH THAT U.DIAG(Q) = AB.V, +! WHERE U IS ANOTHER ORTHOGONAL MATRIX. + +!...HOUSEHOLDER'S REDUCTION TO BIDIAGONAL FORM... +IF (n == 1) GO TO 200 +eps = machep +g = 0.d0 +x = 0.d0 +DO i=1,n + e(i) = g + s = 0.d0 + l = i + 1 + DO j=i,n + s = s + ab(j,i)**2 + END DO + g = 0.d0 + IF (s < tol) GO TO 4 + f = ab(i,i) + g = SQRT(s) + IF (f >= 0.d0) g = -g + h = f*g - s + ab(i,i)=f-g + IF (l > n) GO TO 4 + DO j=l,n + f = 0.d0 + DO k=i,n + f = f + ab(k,i)*ab(k,j) + END DO + f = f/h + DO k=i,n + ab(k,j) = ab(k,j) + f*ab(k,i) + END DO + END DO + 4 q(i) = g + s = 0.d0 + IF (i == n) GO TO 6 + DO j=l,n + s = s + ab(i,j)*ab(i,j) + END DO + 6 g = 0.d0 + IF (s < tol) GO TO 10 + IF (i == n) GO TO 16 + f = ab(i,i+1) + 16 g = SQRT(s) + IF (f >= 0.d0) g = -g + h = f*g - s + IF (i == n) GO TO 10 + ab(i,i+1) = f - g + DO j=l,n + e(j) = ab(i,j)/h + END DO + DO j=l,n + s = 0.d0 + DO k=l,n + s = s + ab(j,k)*ab(i,k) + END DO + DO k=l,n + ab(j,k) = ab(j,k) + s*e(k) + END DO + END DO + 10 y = ABS(q(i)) + ABS(e(i)) + IF (y > x) x = y +END DO +!...ACCUMULATION OF RIGHT-HAND TRANSFORMATIONS... +ab(n,n) = 1.d0 +g = e(n) +l = n +DO ii=2,n + i = n - ii + 1 + IF (g == 0.d0) GO TO 23 + h = ab(i,i+1)*g + DO j=l,n + ab(j,i) = ab(i,j)/h + END DO + DO j=l,n + s = 0.d0 + DO k=l,n + s = s + ab(i,k)*ab(k,j) + END DO + DO k=l,n + ab(k,j) = ab(k,j) + s*ab(k,i) + END DO + END DO + 23 DO j=l,n + ab(i,j) = 0.d0 + ab(j,i) = 0.d0 + END DO + ab(i,i) = 1.d0 + g = e(i) + l = i +END DO +!...DIAGONALIZATION OF THE BIDIAGONAL FORM... +eps = eps*x +DO kk=1,n + k = n - kk + 1 + kt = 0 + 101 kt = kt + 1 + IF (kt <= 30) GO TO 102 + e(k) = 0.d0 + WRITE (6,1000) + 1000 FORMAT (' QR FAILED') + 102 DO ll2=1,k + l2 = k - ll2 + 1 + l = l2 + IF (ABS(e(l)) <= eps) GO TO 120 + IF (l == 1) CYCLE + IF (ABS(q(l-1)) <= eps) EXIT + END DO +!...CANCELLATION OF E(L) IF L>1... + c = 0.d0 + s = 1.d0 + DO i=l,k + f = s*e(i) + e(i) = c*e(i) + IF (ABS(f) <= eps) GO TO 120 + g = q(i) +!...Q(I) = H = SQRT(G*G + F*F)... + IF (ABS(f) < ABS(g)) GO TO 113 + IF (f == 0.0) THEN + GO TO 111 + ELSE + GO TO 112 + END IF + 111 h = 0.d0 + GO TO 114 + 112 h = ABS(f)*SQRT(1 + (g/f)**2) + GO TO 114 + 113 h = ABS(g)*SQRT(1 + (f/g)**2) + 114 q(i) = h + IF (h /= 0.d0) GO TO 115 + g = 1.d0 + h = 1.d0 + 115 c = g/h + s = -f/h + END DO +!...TEST FOR CONVERGENCE... + 120 z = q(k) + IF (l == k) GO TO 140 +!...SHIFT FROM BOTTOM 2*2 MINOR... + x = q(l) + y = q(k-1) + g = e(k-1) + h = e(k) + f = ((y - z)*(y + z) + (g - h)*(g + h))/(2*h*y) + g = SQRT(f*f + 1.0D0) + temp = f - g + IF (f >= 0.d0) temp = f + g + f = ((x - z)*(x + z) + h*(y/temp - h))/x +!...NEXT QR TRANSFORMATION... + c = 1.d0 + s = 1.d0 + lp1 = l + 1 + IF (lp1 > k) GO TO 133 + DO i=lp1,k + g = e(i) + y = q(i) + h = s*g + g = g*c + IF (ABS(f) < ABS(h)) GO TO 123 + IF (f == 0.0) THEN + GO TO 121 + ELSE + GO TO 122 + END IF + 121 z = 0.d0 + GO TO 124 + 122 z = ABS(f)*SQRT(1 + (h/f)**2) + GO TO 124 + 123 z = ABS(h)*SQRT(1 + (f/h)**2) + 124 e(i-1) = z + IF (z /= 0.d0) GO TO 125 + f = 1.d0 + z = 1.d0 + 125 c = f/z + s = h/z + f = x*c + g*s + g = -x*s + g*c + h = y*s + y = y*c + DO j=1,n + x = ab(j,i-1) + z = ab(j,i) + ab(j,i-1) = x*c + z*s + ab(j,i) = -x*s + z*c + END DO + IF (ABS(f) < ABS(h)) GO TO 129 + IF (f == 0.0) THEN + GO TO 127 + ELSE + GO TO 128 + END IF + 127 z = 0.d0 + GO TO 130 + 128 z = ABS(f)*SQRT(1 + (h/f)**2) + GO TO 130 + 129 z = ABS(h)*SQRT(1 + (f/h)**2) + 130 q(i-1) = z + IF (z /= 0.d0) GO TO 131 + f = 1.d0 + z = 1.d0 + 131 c = f/z + s = h/z + f = c*g + s*y + x = -s*g + c*y + END DO + 133 e(l) = 0.d0 + e(k) = f + q(k) = x + GO TO 101 +!...CONVERGENCE: Q(K) IS MADE NON-NEGATIVE... + 140 IF (z >= 0.d0) CYCLE + q(k) = -z + DO j=1,n + ab(j,k) = -ab(j,k) + END DO +END DO +RETURN +200 q(1) = ab(1,1) +ab(1,1) = 1.d0 + +END SUBROUTINE minfit + + + + +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! + SUBROUTINE MIN(n,j,nits,d2,x1,f1,fk,f,x,t,machep,h) + + IMPLICIT NONE + + INTEGER, INTENT(IN) :: n + INTEGER :: j + INTEGER :: nits + REAL, INTENT(IN OUT) :: d2 + REAL, INTENT(IN OUT) :: x1 + REAL, INTENT(IN OUT) :: f1 + LOGICAL :: fk + REAL :: f + REAL, INTENT(IN OUT) :: x(n) + REAL, INTENT(IN) :: t + REAL, INTENT(IN) :: machep + REAL, INTENT(IN) :: h + + INTEGER :: i,k + EXTERNAL f + + + REAL :: flin ! function + REAL :: small,sf1,sx1,s,temp, xm,x2,f2,d1 + REAL :: fm,f0,t2 +!---------------------------------------------- + INTEGER :: nf,nl + REAL :: fx,ldt,dmin + REAL :: v(20,20),q0(20),q1(20),qa,qb,qc,qd0,qd1,qf1 + COMMON /global/ fx,ldt,dmin,nf,nl /q/ v,q0,q1,qa,qb,qc,qd0,qd1,qf1 +!---------------------------------------------- +!...THE SUBROUTINE MIN MINIMIZES F FROM X IN THE DIRECTION V(*,J) UNLESS +! J IS LESS THAN 1, WHEN A QUADRATIC SEARCH IS MADE IN THE PLANE +! DEFINED BY Q0,Q1,X. +! D2 IS EITHER ZERO OR AN APPROXIMATION TO HALF F". +! ON ENTRY, X1 IS AN ESTIMATE OF THE DISTANCE FROM X TO THE MINIMUM +! ALONG V(*,J) (OR, IF J=0, A CURVE). ON RETURN, X1 IS THE DISTANCE +! FOUND. +! IF FK=.TRUE., THEN F1 IS FLIN(X1). OTHERWISE X1 AND F1 ARE IGNORED +! ON ENTRY UNLESS FINAL FX IS GREATER THAN F1. +! NITS CONTROLS THE NUMBER OF TIMES AN ATTEMPT WILL BE MADE TO HALVE +! THE INTERVAL. + LOGICAL :: dz + REAL :: m2,m4 + +small = machep**2 +m2 = SQRT(machep) +m4 = SQRT(m2) +sf1 = f1 +sx1 = x1 +k = 0 +xm = 0.d0 +fm = fx +f0 = fx +dz = d2 < machep +!...FIND THE STEP SIZE... +s = 0.d0 +DO i=1,n + s = s + x(i)**2 +END DO +s = SQRT(s) +temp = d2 +IF (dz) temp = dmin +t2 = m4*SQRT(ABS(fx)/temp + s*ldt) + m2*ldt +s = m4*s + t +IF (dz.AND.t2 > s) t2 = s +t2 = DMAX1(t2,small) +t2 = DMIN1(t2,.01D0*h) +IF (.NOT.fk.OR.f1 > fm) GO TO 2 +xm = x1 +fm = f1 +2 IF (fk.AND.ABS(x1) >= t2) GO TO 3 +temp=1.d0 +IF (x1 < 0.d0) temp=-1.d0 +x1=temp*t2 +f1 = flin(n,j,x1,f,x,nf) +3 IF (f1 > fm) GO TO 4 +xm = x1 +fm = f1 +4 IF (.NOT.dz) GO TO 6 +!...EVALUATE FLIN AT ANOTHER POINT AND ESTIMATE THE SECOND DERIVATIVE... +x2 = -x1 +IF (f0 >= f1) x2 = 2.d0*x1 +f2 = flin(n,j,x2,f,x,nf) +IF (f2 > fm) GO TO 5 +xm = x2 +fm = f2 +5 d2 = (x2*(f1 - f0)-x1*(f2 - f0))/((x1*x2)*(x1 - x2)) +!...ESTIMATE THE FIRST DERIVATIVE AT 0... +6 d1 = (f1 - f0)/x1 - x1*d2 +dz = .true. +!...PREDICT THE MINIMUM... +IF (d2 > small) GO TO 7 +x2 = h +IF (d1 >= 0.d0) x2 = -x2 +GO TO 8 +7 x2 = (-.5D0*d1)/d2 +8 IF (ABS(x2) <= h) GO TO 11 +IF (x2 > 0.0) THEN + GO TO 10 +END IF +x2 = -h +GO TO 11 +10 x2 = h +!...EVALUATE F AT THE PREDICTED MINIMUM... +11 f2 = flin(n,j,x2,f,x,nf) +IF (k >= nits.OR.f2 <= f0) GO TO 12 +!...NO SUCCESS, SO TRY AGAIN... +k = k + 1 +IF (f0 < f1.AND.(x1*x2) > 0.d0) GO TO 4 +x2 = 0.5D0*x2 +GO TO 11 +!...INCREMENT THE ONE-DIMENSIONAL SEARCH COUNTER... +12 nl = nl + 1 +IF (f2 <= fm) GO TO 13 +x2 = xm +GO TO 14 +13 fm = f2 +!...GET A NEW ESTIMATE OF THE SECOND DERIVATIVE... +14 IF (ABS(x2*(x2 - x1)) <= small) GO TO 15 +d2 = (x2*(f1-f0) - x1*(fm-f0))/((x1*x2)*(x1 - x2)) +GO TO 16 +15 IF (k > 0) d2 = 0.d0 +16 IF (d2 <= small) d2 = small +x1 = x2 +fx = fm +IF (sf1 >= fx) GO TO 17 +fx = sf1 +x1 = sx1 +!...UPDATE X FOR LINEAR BUT NOT PARABOLIC SEARCH... +17 IF (j == 0) RETURN +DO i=1,n + x(i) = x(i) + x1*v(i,j) +END DO + +END SUBROUTINE MIN + + +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! + SUBROUTINE vcprnt(option,v,n) + + IMPLICIT NONE + INTEGER :: option + REAL, INTENT(IN OUT) :: v(n) + INTEGER :: n + + INTEGER :: i + +SELECT CASE ( option ) + CASE ( 1) + GO TO 1 + CASE ( 2) + GO TO 2 + CASE ( 3) + GO TO 3 + CASE ( 4) + GO TO 4 +END SELECT + +1 WRITE (6,101) (v(i),i=1,n) +RETURN +2 WRITE (6,102) (v(i),i=1,n) +RETURN +3 WRITE (6,103) (v(i),i=1,n) +RETURN +4 WRITE (6,104) (v(i),i=1,n) +RETURN +101 FORMAT (/' THE SECOND DIFFERENCE ARRAY D(*) IS:'/ (e32.14,4E25.14)) +102 FORMAT (/' THE SCALE FACTORS ARE:'/(e32.14,4E25.14)) +103 FORMAT (/' THE APPROXIMATING QUADR. FORM HAS PRINCIPAL VALUES:'/ & + (e32.14,4E25.14)) +104 FORMAT (/' X IS:',e26.14/(e32.14)) +END SUBROUTINE vcprnt + + +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! + SUBROUTINE PRINT(n,x,prin,fmin) + + IMPLICIT NONE + INTEGER :: n + REAL, INTENT(IN OUT) :: x(n) + INTEGER, INTENT(IN OUT) :: prin + REAL, INTENT(IN OUT) :: fmin + + INTEGER :: i + REAL :: ln +!---------------------------------------------- +INTEGER :: nf,nl +REAL :: fx,ldt,dmin +COMMON /global/ fx,ldt,dmin,nf,nl +!---------------------------------------------- +WRITE (6,101) nl,nf,fx + +IF (fx <= fmin) GO TO 1 +ln = LOG10(fx-fmin) +WRITE (6,102) fmin,ln +GO TO 2 +1 WRITE (6,103) fmin +2 IF (n > 4.AND.prin <= 2) RETURN +WRITE (6,104) (x(i),i=1,n) +RETURN +101 FORMAT (/' AFTER',i6, & + ' LINEAR SEARCHES, THE FUNCTION HAS BEEN EVALUATED',i6, & + ' TIMES. THE SMALLEST VALUE FOUND IS F(X) = ',e21.14) +102 FORMAT (' LOG (F(X)-',e21.14,') = ',e21.14) +103 FORMAT (' LOG (F(X)-',e21.14,') IS UNDEFINED.') +104 FORMAT (' X IS:',e26.14/(e32.14)) +END SUBROUTINE PRINT + + +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! + SUBROUTINE maprnt(option,v,m,n) + + IMPLICIT NONE + INTEGER :: option + REAL, INTENT(IN OUT) :: v(m,n) + INTEGER, INTENT(IN OUT) :: m + INTEGER, INTENT(IN) :: n + INTEGER :: i,j + + INTEGER :: low,upp +!...THE SUBROUTINE MAPRNT PRINTS THE COLUMNS OF THE NXN MATRIX V +! WITH A HEADING AS SPECIFIED BY OPTION. +! M IS THE ROW DIMENSION OF V AS DECLARED IN THE CALLING PROGRAM... +low = 1 +upp = 5 +SELECT CASE ( option ) + CASE ( 1) + GO TO 1 + CASE ( 2) + GO TO 2 +END SELECT +1 WRITE (6,101) +101 FORMAT (/' THE NEW DIRECTIONS ARE:') +GO TO 3 +2 WRITE (6,102) +102 FORMAT (' AND THE PRINCIPAL AXES:') +3 IF (n < upp) upp = n +DO i=1,n + WRITE (6,104) (v(i,j),j=low,upp) +END DO +low = low + 5 +IF (n < low) RETURN +upp = upp + 5 +WRITE (6,103) +GO TO 3 +103 FORMAT (' ') +104 FORMAT (e32.14,4E25.14) +END SUBROUTINE maprnt + + +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! + REAL FUNCTION random(naught) + + IMPLICIT NONE + INTEGER, INTENT(IN OUT) :: naught + + REAL :: ran1,ran3(127),half + INTEGER :: i,j,ran2,q,r + LOGICAL :: init + DATA init/.false./ + SAVE init,ran2,ran1,ran3 + +IF (init) GO TO 3 +r = MOD(naught,8190) + 1 +ran2 = 128 +DO i=1,127 + ran2 = ran2 - 1 + ran1 = -2.d0**55 + DO j=1,7 + r = MOD(1756*r,8191) + q = r/32 + ran1 = (ran1 + q)*(1.0D0/256) + END DO + ran3(ran2) = ran1 +END DO +init = .true. +3 IF (ran2 == 1) ran2 = 128 +ran2 = ran2 - 1 +ran1 = ran1 + ran3(ran2) +half = .5D0 +IF (ran1 >= 0.d0) half = -half +ran1 = ran1 + half +ran3(ran2) = ran1 +random = ran1 + .5D0 + +END FUNCTION random + + + +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! + REAL FUNCTION flin (n,j,l,f,x,nf) + IMPLICIT NONE + + INTEGER, INTENT(IN) :: n + INTEGER, INTENT(IN OUT) :: j + REAL, INTENT(IN) :: l + REAL :: f + REAL, INTENT(IN) :: x(n) + INTEGER, INTENT(OUT) :: nf + + INTEGER :: i + REAL :: t(20) + + EXTERNAL f + +!...FLIN IS THE FUNCTION OF ONE REAL VARIABLE L THAT IS MINIMIZED +! BY THE SUBROUTINE MIN... +!---------------------------------------------- + REAL :: v(20,20),q0(20),q1(20),qa,qb,qc,qd0,qd1,qf1 + COMMON /q/ v,q0,q1,qa,qb,qc,qd0,qd1,qf1 +!---------------------------------------------- +IF (j == 0) GO TO 2 +!...THE SEARCH IS LINEAR... +DO i=1,n + t(i) = x(i) + l*v(i,j) +END DO +GO TO 4 +!...THE SEARCH IS ALONG A PARABOLIC SPACE CURVE... +2 qa = (l*(l - qd1))/(qd0*(qd0 + qd1)) +qb = ((l + qd0)*(qd1 - l))/(qd0*qd1) +qc = (l*(l + qd0))/(qd1*(qd0 + qd1)) +DO i=1,n + t(i) = (qa*q0(i) + qb*x(i)) + qc*q1(i) +END DO +!...THE FUNCTION EVALUATION COUNTER NF IS INCREMENTED... +4 nf = nf + 1 +flin = f(t,n) + +END FUNCTION flin + + +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! + SUBROUTINE sort(m,n,d,v) + IMPLICIT NONE +! + INTEGER, INTENT(IN OUT) :: m + INTEGER, INTENT(IN) :: n + REAL, INTENT(IN OUT) :: d(n) + REAL, INTENT(IN OUT) :: v(m,n) + + INTEGER :: i,j,k,nm1,ip1 + REAL :: s +!...SORTS THE ELEMENTS OF D(N) INTO DESCENDING ORDER AND MOVES THE +! CORRESPONDING COLUMNS OF V(N,N). +! M IS THE ROW DIMENSION OF V AS DECLARED IN THE CALLING PROGRAM. +IF (n == 1) RETURN +nm1 = n - 1 +DO i = 1,nm1 + k=i + s = d(i) + ip1 = i + 1 + DO j = ip1,n + IF (d(j) <= s) CYCLE + k = j + s = d(j) + END DO + IF (k <= i) CYCLE + d(k) = d(i) + d(i) = s + DO j = 1,n + s = v(j,i) + v(j,i) = v(j,k) + v(j,k) = s + END DO +END DO +END SUBROUTINE sort + + +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! + SUBROUTINE quad(n,f,x,t,machep,h) + IMPLICIT NONE + + INTEGER, INTENT(IN) :: n + REAL :: f + REAL, INTENT(IN OUT) :: x(n) + REAL, INTENT(IN OUT) :: t + REAL :: machep + REAL, INTENT(IN OUT) :: h +! IMPLICIT REAL (A-H,O-Z) + EXTERNAL f + +!...QUAD LOOKS FOR THE MINIMUM OF F ALONG A CURVE DEFINED BY Q0,Q1,X... + INTEGER :: i + REAL :: l + REAL :: s,value +!---------------------------------------------- + INTEGER :: nf,nl + REAL :: fx,ldt,dmin + +REAL :: v(20,20),q0(20),q1(20),qa,qb,qc,qd0,qd1,qf1 +COMMON /global/ fx,ldt,dmin,nf,nl /q/ v,q0,q1,qa,qb,qc,qd0,qd1,qf1 +!---------------------------------------------- +s = fx +fx = qf1 +qf1 = s +qd1 = 0.d0 +DO i=1,n + s = x(i) + l = q1(i) + x(i) = l + q1(i) = s + qd1 = qd1 + (s-l)**2 +END DO +qd1 = SQRT(qd1) +l = qd1 +s = 0.d0 +IF (qd0 <= 0.d0 .OR. qd1 <= 0.d0 .OR. nl < 3*n*n) GO TO 2 +value=qf1 +CALL MIN(n,0,2,s,l,value,.true.,f,x,t,machep,h) +qa = (l*(l-qd1))/(qd0*(qd0+qd1)) +qb = ((l+qd0)*(qd1-l))/(qd0*qd1) +qc = (l*(l+qd0))/(qd1*(qd0+qd1)) +GO TO 3 +2 fx = qf1 +qa = 0.d0 +qb = qa +qc = 1.d0 +3 qd0 = qd1 +DO i=1,n + s = q0(i) + q0(i) = x(i) + x(i) = (qa*s + qb*x(i)) + qc*q1(i) +END DO +END SUBROUTINE quad + diff --git a/applications/PUfoam/MoDeNaModels/PolymerDensity/src/DetailedModelCode/VLE_main.f90 b/applications/PUfoam/MoDeNaModels/PolymerDensity/src/DetailedModelCode/VLE_main.f90 new file mode 100644 index 000000000..24a45a65c --- /dev/null +++ b/applications/PUfoam/MoDeNaModels/PolymerDensity/src/DetailedModelCode/VLE_main.f90 @@ -0,0 +1,131 @@ +!> This file contains the subroutine which starts the phase equilibrium calculation. +!! It also prints the calculated density to the outputfile "out.txt". + + +SUBROUTINE VLE_MIX(rhob,density,chemPot_total,compID) + + USE parameters, ONLY: PI, RGAS, KBOL + USE basic_variables + USE EOS_VARIABLES, ONLY: fres, eta, eta_start, dhs, mseg, uij, sig_ij, rho, x, z3t + USE DFT_MODULE + USE EOS_NUMERICAL_DERIVATIVES + IMPLICIT NONE + + +!> --------------------------------------------------------------------- +!! Variables +!! --------------------------------------------------------------------- + + +!passed + REAL :: chemPot_total(nc) + REAL :: rhob(2,0:nc),density(np) + INTEGER :: compID + +!local + REAL, DIMENSION(nc) :: dhs_star + REAL :: w(np,nc), lnphi(np,nc) + INTEGER :: converg + CHARACTER(LEN=4) :: char_ncomp + REAL :: Polymer_density + INTEGER :: i + CHARACTER (LEN=50) :: filename + + + !> --------------------------------------------------------------------- + !! prepare for phase equilibrium calculation for given T + !! --------------------------------------------------------------------- + + dhs(1:ncomp) = parame(1:ncomp,2) * ( 1.0 - 0.12*EXP( -3.0*parame(1:ncomp,3)/t ) ) ! needed for rdf_matrix + dhs_star(1:ncomp) = dhs(1:ncomp)/parame(1:ncomp,2) + + nphas = 2 + outp = 0 ! output to terminal + + CALL START_VAR (converg) ! gets starting values, sets "val_init" + + IF ( converg /= 1 ) THEN + WRITE (*,*) 'no VLE found' + RETURN + END IF + + ! rhob(phase,0): molecular density + rhob(1,0) = dense(1) / ( PI/6.0* SUM( xi(1,1:ncomp) * parame(1:ncomp,1) * dhs(1:ncomp)**3 ) ) + rhob(2,0) = dense(2) / ( PI/6.0* SUM( xi(2,1:ncomp) * parame(1:ncomp,1) * dhs(1:ncomp)**3 ) ) + ! rhob(phase,i): molecular component density (with i=(1,...ncomp) ) in units (1/A^3) + rhob(1,1:ncomp) = rhob(1,0)*xi(1,1:ncomp) + rhob(2,1:ncomp) = rhob(2,0)*xi(2,1:ncomp) + + ! get density in SI-units (kg/m**3) + CALL SI_DENS ( density, w ) + + ! calculate residual chemical potentials + ensemble_flag = 'tv' ! this flag is for: mu_res=mu_res(T,rho) + densta(1) = dense(1) ! Index 1 is for liquid density (here: packing fraction eta) + densta(2) = dense(2) ! Index 2 is for vapour density (here: packing fraction eta) + CALL fugacity (lnphi) + chemPot_total(1:ncomp) = lnphi(1,1:ncomp)! + LOG( rhob(1,1:ncomp) ) ! my0 = mu_res(T,rho_bulk_L) + ln(rho_bulk_l) + +! WRITE(*,*) '--------------------------------------------------' +! WRITE(*,*)'RESULT OF PHASE EQUILIBRIUM CALCULATION' +! WRITE (char_ncomp,'(I3)') ncomp +! WRITE (*,*) 'T = ',t, 'K, and p =', p/1.E5,' bar' +! WRITE(*,*)' ' +! WRITE(*,'(t15,4(a12,1x),10x,a)') (compna(i),i=1,ncomp) +! +! write(*,*)'Mass fraction:' +! WRITE(*,'(2x,a,'//char_ncomp//'(g13.6,1x))') 'PHASE I w', (w(1,i),i=1,ncomp) +! WRITE(*,'(2x,a,'//char_ncomp//'(g13.6,1x))') 'PHASE II w', (w(2,i),i=1,ncomp) +! +! write(*,*)'Molar composition:' +! WRITE(*,'(2x,a,'//char_ncomp//'(g13.6,1x))') 'PHASE I x', (EXP(lnx(1,i)),i=1,ncomp) +! WRITE(*,'(2x,a,'//char_ncomp//'(g13.6,1x))') 'PHASE II x', (EXP(lnx(2,i)),i=1,ncomp) +! WRITE(*,*)' ' +! !!WRITE(*,'(2x,a,'//char_ncomp//'(g13.6,1x))') 'PHASE I density', (rhob(1,i),i=1,ncomp) +! !! WRITE(*,'(2x,a,'//char_ncomp//'(g13.6,1x))') 'PHASE II density', (rhob(2,i),i=1,ncomp) +! !!WRITE(*,*)' ' +! WRITE(*,'(2x,a,'//char_ncomp//'(g13.6,1x))') 'PHASE I chemPot', (lnphi(1,i) + LOG(rhob(1,i)),i=1,ncomp) +! WRITE(*,'(2x,a,'//char_ncomp//'(g13.6,1x))') 'PHASE II chemPot', (lnphi(2,i) + LOG(rhob(2,i)),i=1,ncomp) +! WRITE(*,*)' ' +! !!WRITE(*,*)'Phase densities ' +! WRITE(*,'(2x,a,2(g13.6,1x))') 'SI-DENSITY [kg/m3] ', density(1),density(2) +! !!WRITE(*,'(2x,a,2(g13.6,1x))') 'NUMBER-DENSITY ', rhob(1,0),rhob(2,0) +! +! WRITE(*,*) + + + write(*,*)' ' + write(*,*)'--------------------------------------------' + write(*,*)'Output detailed model:' + write(*,*)'T /K:',t,'p/bar:',p/1.E5 + write(*,*)'Liquid density /kg/m3:', max(density(1),density(2)) + write(*,*)'--------------------------------------------' + write(*,*)' ' + + + + !>write liquid phase density in kg/m3 to out.txt + + Polymer_density = max(density(1),density(2)) !* w(1,1) + + filename='./out.txt' + CALL file_open(filename,78) + write(78,*) Polymer_density + !write(*,*)'Polymer_density [kg/m3]:',Polymer_density + + + + + +! WRITE (*,*) ' ' +! WRITE (*,*) 'temperature ',t, 'K, and p=', p/1.E5,' bar' +! WRITE (*,*) 'x1_liquid ',xi(1,1),' x1_vapor', xi(2,1) +! WRITE (*,*) 'densities ',rhob(1,0), rhob(2,0) +! WRITE (*,*) 'dense ',dense(1), dense(2) +! WRITE (*,*) 'density [kg/m3] ',density(1), density(2) +! write (*,*) 'chemical potentials comp1' , lnphi(1,1) + LOG( rhob(1,1) ), lnphi(2,1) + LOG( rhob(2,1) ) +! write (*,*) 'chemical potentials comp2' ,lnphi(1,2) + LOG( rhob(1,2) ), lnphi(2,2) + LOG( rhob(2,2) ) +! + + +END SUBROUTINE VLE_MIX diff --git a/applications/PUfoam/MoDeNaModels/PolymerDensity/src/DetailedModelCode/VLE_subroutines.f90 b/applications/PUfoam/MoDeNaModels/PolymerDensity/src/DetailedModelCode/VLE_subroutines.f90 new file mode 100644 index 000000000..6d821cb27 --- /dev/null +++ b/applications/PUfoam/MoDeNaModels/PolymerDensity/src/DetailedModelCode/VLE_subroutines.f90 @@ -0,0 +1,7163 @@ +!> This file contains the subroutines which perform and control the +!! phase equilibrium calculation. + + + + + +!>WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +!! SUBROUTINE start_var +!! +!! This subroutine generates a converged solution for binary systems +!! or performes a flash calculation for mixtues. This routine is a +!! fairly weak point of the program. +!! +!! IF a polymer is considered, starting values for mole fractions +!! are determined from the SUBROUTINGE POLY_STA_VAR (see below). The +!! polymer needs to be placed as component 1 (first line) in INPUT +!! file. +!! +!! A phase equilib. iteration is started at the end of this routine. +!! If no solution is found (converg=0), the program will stop within +!! this routine. +!! +!! Currently, this routine assumes two-phase equilibrium and derives +!! starting values (xi,density) only for two phases. +!! +!! Prerequisites are: +!! SUBROUTINE INPUT needs to be called prior to this routine, because +!! all pure comp. parameters as well as (T,P,kij) need to be in place. +!! Also, the variable to be iterated "it(i)" and the variables to be +!! calculated through the summation relation "sum_rel(i)" have to be +!! defined. +!!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW + + SUBROUTINE start_var(converg) +! + USE BASIC_VARIABLES + USE STARTING_VALUES + IMPLICIT NONE +! +! ---------------------------------------------------------------------- + INTEGER, INTENT(IN OUT) :: converg +! +! ---------------------------------------------------------------------- + INTEGER :: ph, i, k + INTEGER :: ncompsav, n_unkwsav, ph_split + LOGICAL :: lle_check, flashcase, renormalize + REAL :: den1, den2, x_1, x_2 + CHARACTER (LEN=50) :: filename +! ---------------------------------------------------------------------- + +converg = 0 + +! CALL RACHFORD_RICE (converg) +! CALL Heidemann_Khalil + +! ---------------------------------------------------------------------- +! This first condition (eos >= 4) is for LJ models, not for PC-SAFT +! ---------------------------------------------------------------------- + +IF (eos >= 4) THEN + + ncomp = 2 ! set number of components to 2 + n_unkw = ncomp ! number of quantities to be iterated + it(1) = 'x11' ! iteration of mol fraction of comp.1 phase 1 + it(2) = 'x21' ! iteration of mol fraction of comp.1 phase 2 + sum_rel(1) = 'x12' ! summation relation: x12 = 1 - sum(x1j) + sum_rel(2) = 'x22' ! summation relation: x22 = 1 - sum(x2j) + + filename = 'LJ_START_VAL.INC' + CALL file_open(filename,84) + READ (84,*) den1,den2 + READ (84,*) x_1,x_2 + CLOSE (84) + + xi(1,1) = x_1 + xi(2,1) = x_2 + xi(1,2) = 1.0 - xi(1,1) + xi(2,2) = 1.0 - xi(2,1) + lnx(1,1) = LOG(xi(1,1)) + lnx(2,1) = LOG(xi(2,1)) + lnx(1,2) = LOG(xi(1,2)) + lnx(2,2) = LOG(xi(2,2)) + + val_init(1) = den1 + val_init(2) = den2 + val_init(3) = t + val_init(4) = p + DO ph = 1,nphas + DO k = 1,ncomp + val_init(4+k+(ph-1)*ncomp) = LOG(xi(ph,k)) + END DO + END DO + + CALL objective_ctrl (converg) + IF (converg == 1) WRITE (*,*) t, p/1.0E5, xi(1,1), xi(2,1) + IF (converg == 0) WRITE (*,*) ' weak starting values' + + +! ---------------------------------------------------------------------- +! ELSE: PC-SAFT equation of state +! ---------------------------------------------------------------------- + +ELSE + + renormalize = .false. ! for renormalization group theory (RGT) + IF (num == 2) renormalize = .true. + IF (num == 2) num = 0 ! if RGT: initial phase equilibr. is for non-renormalized model + + flashcase = .false. ! .true. when a specific feed conc. xif is given + IF (xif(1) /= 0.0) flashcase = .true. + + lle_check = .true. + +! ---------------------------------------------------------------------- +! IF: non-polymeric system +! ---------------------------------------------------------------------- + IF (mm(1) < 1.0E8) THEN + + DO i=1,ncomp ! setting mole-fractions for the case that + ! anything goes wrong in the coming routines + xi(1,i) = 1.0 / REAL(ncomp) + xi(2,i) = 1.0 / REAL(ncomp) + END DO + + + ! ------------------------------------------------------------------ + ! determine an initial conc. (phase 1) that will phase split + ! ------------------------------------------------------------------ + IF( ncomp == 2 .AND. .NOT.flashcase ) THEN + CALL vle_min( lle_check ) + WRITE(*,*)' INITIAL FEED-COMPOSITION',(xi(1,i), i=1,ncomp),converg + END IF + + ! ------------------------------------------------------------------ + ! perform a phase stability test + ! ------------------------------------------------------------------ + ph_split = 0 + CALL phase_stability ( .false., flashcase, ph_split ) + write (*,*) 'stability analysis I indicates phase-split is:',ph_split + + + ! ------------------------------------------------------------------ + ! determine species i, for which x(i) is calc from summation relation + ! ------------------------------------------------------------------ + CALL select_sum_rel (1,0,1) ! synthax (m,n,o): phase m + ! exclude comp. n + ! assign it(o) and higher + CALL select_sum_rel (2,0,2) ! for ncomp>=3, the quantities + ! to be iterated will be overwritten + + ! ------------------------------------------------------------------ + ! if 2 phases (VLE) + ! ------------------------------------------------------------------ + IF (ph_split == 1) THEN + + ! --- perform tangent plane minimization ------------------------ + CALL tangent_plane + ph_split = 0 + + ! --- determine, for which substance summation relation is used -- + IF (flashcase) THEN + CALL determine_flash_it2 + ELSE + CALL select_sum_rel (1,0,1) + CALL select_sum_rel (2,0,2) + END IF + + ! --- do full phase equilibr. calculation ------------------------ + n_unkw = ncomp ! number of quantities to be iterated + CALL objective_ctrl (converg) + IF (converg == 1 ) write (*,*) ' converged (maybe a VLE)',dense(1),dense(2) + + END IF + + ! ------------------------------------------------------------------ + ! test for LLE + ! ------------------------------------------------------------------ + ph_split = 0 + + IF (lle_check) CALL phase_stability (lle_check,flashcase,ph_split) + IF (lle_check) write (*,*) 'stability analysis II, phase-split is:',ph_split + + + ! ------------------------------------------------------------------ + ! if two phases (LLE) + ! ------------------------------------------------------------------ + IF (ph_split == 1) THEN + + write (*,*) ' LLE-stability test indicates 2 phases (VLE or LLE)' + + ! --- perform tangent plane minimization ------------------------ + IF (flashcase) CALL select_sum_rel (1,0,1) + IF (flashcase) CALL select_sum_rel (2,0,2) + + CALL tangent_plane + + ! --- determine, for which substance summation relation ---------- + IF (flashcase) THEN + CALL determine_flash_it2 + ELSE + CALL select_sum_rel (1,0,1) + CALL select_sum_rel (2,0,2) + END IF + + ! --- do full phase equilibr. calculation ------------------------ + n_unkw = ncomp ! number of quantities to be iterated + val_conv(2) = 0.0 + CALL objective_ctrl (converg) + IF (converg == 1 ) write (*,*) ' converged (maybe an LLE)',dense(1),dense(2) + + END IF + + ! ------------------------------------------------------------------ + ! equilibr. calc. converged: set initial var. for further calc. + ! ------------------------------------------------------------------ + IF (converg == 1) THEN + val_init = val_conv + DO ph = 1,nphas + DO i = 1,ncomp + xi(ph,i) = EXP( val_conv(4+i+(ph-1)*ncomp) ) + END DO + END DO + dense(1:2) = val_conv(1:2) + ELSE + WRITE (*,*) ' NO SOLUTION FOUND FOR THE STARTING VALUES' + STOP + END IF + + + ! --------------------------------------------------------------------- + ! ELSE: for systems with polymers + ! --------------------------------------------------------------------- + + ELSE + + ncompsav = ncomp + ncomp = 2 ! set number of components to 2 + n_unkwsav = n_unkw + + CALL poly_sta_var(converg) + + IF (converg == 1) THEN + val_init = val_conv + ELSE + WRITE (*,*) ' NO SOLUTION FOUND FOR THE STARTING VALUES' + STOP + END IF + + ncomp = ncompsav + n_unkw = n_unkwsav ! number of quantities to be iterated + + END IF + +! --- for RGT: set flag back to num=2 indicating an RGT calculation ---- + IF (renormalize) num = 2 + +END IF + +END SUBROUTINE start_var + + + + +!>WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +!! SUBROUTINE objective_ctrl +!! +!! This subroutine controls the iso-fugacity iteration. It uses +!! the variables defined in the array "val_init". If successfull, +!! the converged values are written to "val_conv", and the flag +!! converg is set to 1. +!! See also above desciption for subroutine PHASE_EQUILIB +!! This routine calls SUBROUTINE HYBRID, which is a solver (modified +!! POWELL HYBRID METHOD). HYBRID is freely available for non-commercial +!! applications. HYBRID requires three definitions: +!! 1.the number of equations to be solved (=No. of variables to be +!! iterated). The appropriate parameter is: "n_unkw" +!! 2.the equations to be iterated, they are here gathered in the SUB- +!! ROUTINE OBJEC_FCT (see below). Since HYBRID is a root finder, +!! these objective functions are iterated to be zero (essentially, +!! OBJEC_FCT contains the iso-fugacity relation. +!! 3.an array of variables is required, containing the quatities to be +!! iterated. This array is termed "y(i)" +!! +!! INPUT VARIABLES: +!! val_init(i) array containing (densities,T,P,lnx's) serving as +!! starting values for the phase equilibrium calculation +!! it(i) contains the information, which variable is deter- +!! mined iteratively. For syntax refer e.g.to SUB BINMIX. +!! sum_rel(i) indicates, which mole fraction is determined from the +!! summation relation sum(xi)=1 +!! +!! OUTPUT VARIABLES: +!! val_conv(i) array containing the converged system variables +!! analogous to "val_init" +!! converg 0 if no convergence achieved, 1 if converged solution +!!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! + SUBROUTINE objective_ctrl (converg) +! + USE BASIC_VARIABLES + USE Solve_NonLin + IMPLICIT NONE +! +! ---------------------------------------------------------------------- + INTEGER, INTENT(OUT) :: converg +! +! ---------------------------------------------------------------------- + INTERFACE + SUBROUTINE objec_fct ( iter_no, y, residu, dummy ) + INTEGER, INTENT(IN) :: iter_no + REAL, INTENT(IN) :: y(iter_no) + REAL, INTENT(OUT) :: residu(iter_no) + INTEGER, INTENT(IN OUT) :: dummy + END SUBROUTINE objec_fct + END INTERFACE +! + INTEGER :: info,k,posn,i + INTEGER, PARAMETER :: mxr = nc*(nc+1)/2 + REAL, ALLOCATABLE :: y(:),diag(:),residu(:) + REAL :: x_init, x_solut, r_diff1, r_diff2, totres + REAL :: r_thrash, x_thrash + CHARACTER (LEN=2) :: compon + LOGICAL :: convergence +! ---------------------------------------------------------------------- + +info=1 + +ALLOCATE( y(n_unkw), diag(n_unkw), residu(n_unkw) ) + +IF (num == 0) acc_a = 1.E-7 +IF (num == 0) step_a = 2.E-8 +IF (num == 1) acc_a = 1.E-7 +IF (num == 1) step_a = 2.E-8 +IF (num == 2) acc_a = 5.E-7 +IF (num == 2) step_a = 1.E-7 + +posn = 0 +DO i = 1,n_unkw + posn = posn + 1 + IF (it(i) == 't') y(posn) = val_init(3) + IF (it(i) == 'p') y(posn) = val_init(4) + IF (it(i) == 'lnp') y(posn) = LOG( val_init(4) ) + IF (it(i) == 'fls') y(posn) = alpha + IF (it(i)(1:1) == 'x' .AND. it(i)(2:2) == '1') compon = it(i)(3:3) + IF (it(i)(1:1) == 'x' .AND. it(i)(2:2) == '1') READ(compon,*) k + IF (it(i)(1:1) == 'x' .AND. it(i)(2:2) == '1') y(posn) = val_init(4+k) + IF (it(i)(1:1) == 'x' .AND. it(i)(2:2) == '2') compon = it(i)(3:3) + IF (it(i)(1:1) == 'x' .AND. it(i)(2:2) == '2') READ(compon,*) k + IF (it(i)(1:1) == 'x' .AND. it(i)(2:2) == '2') y(posn) = val_init(4+ncomp+k) + IF (it(i)(1:1) == 'x' .AND. it(i)(2:2) == '3') compon = it(i)(3:3) + IF (it(i)(1:1) == 'x' .AND. it(i)(2:2) == '3') READ(compon,*) k + IF (it(i)(1:1) == 'x' .AND. it(i)(2:2) == '3') y(posn) = val_init(4+ncomp+ncomp+k) +END DO + +CALL init_vars + +x_init = 0.0 +DO i = 1,ncomp + IF (lnx(1,i) /= 0.0 .AND. lnx(2,i) /= 0.0) THEN + x_init = x_init + ABS( 1.0 - lnx(2,i)/lnx(1,i) ) + ELSE + x_init = x_init + ABS( 1.0 - EXP(lnx(2,i))/EXP(lnx(1,i)) ) + END IF +END DO + +CALL hbrd (objec_fct, n_unkw, y, residu, step_a, acc_a, info, diag) + +x_solut = 0.0 +DO i = 1,ncomp + IF ( lnx(1,i) /= 0.0 .AND. lnx(2,i) /= 0.0 ) THEN + x_solut = x_solut + ABS( 1.0 - lnx(2,i)/lnx(1,i) ) + ELSE + IF (lnx(1,i) < 1E300 .AND. lnx(1,i) > -1.E300 ) & + x_solut = x_solut + ABS( 1.0 - EXP(lnx(2,i))/EXP(lnx(1,i)) ) + END IF +END DO +r_diff1 = ABS( 1.0 - dense(1)/dense(2) ) +IF ( val_conv(2) > 0.0 ) THEN + r_diff2 = ABS( 1.0 - val_conv(1)/val_conv(2) ) +ELSE + r_diff2 = 0.0 +END IF + +totres = SUM( ABS( residu(1:n_unkw) ) ) + +r_thrash = 0.0005 +x_thrash = 0.0005 +if (num > 0 ) r_thrash = r_thrash * 10.0 +if (num > 0 ) x_thrash = x_thrash * 100.0 + +convergence = .true. + +IF ( info >= 2 ) convergence = .false. +IF ( ABS( 1.0- dense(1)/dense(2) ) < r_thrash .AND. x_solut < x_thrash ) THEN + IF ( x_init > 0.050 ) convergence = .false. + IF ( ( ABS( 1.0- dense(1)/dense(2) ) + x_solut ) < 1.E-7 ) convergence = .false. +ENDIF +IF ( r_diff2 /= 0.0 .AND. r_diff2 > (4.0*r_diff1) .AND. bindiag == 1 ) convergence = .false. +IF ( ncomp == 1 .AND. totres > 100.0*acc_a ) convergence = .false. +IF ( totres > 1000.0*acc_a ) convergence = .false. +IF ( ncomp == 1 .AND. r_diff1 < 1.d-5 ) convergence = .false. + +IF ( convergence ) THEN + converg = 1 + ! write (*,*) residu(1),residu(2) + CALL converged + IF (num <= 1) CALL enthalpy_etc +ELSE + converg = 0 +END IF + +DEALLOCATE( y, diag, residu ) + +END SUBROUTINE objective_ctrl + + + +!>WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +!! SUBROUTINE objec_fct +!! +!! This subroutine contains the equations to be solved numerically +!! (iso-fugacity: fi'-fi''=0) as well as other dependent equations, +!! which can be solved analytically, namely the summation relation +!! xi=1-sum(xj) or the condition of equal charge for electrolyte +!! solutions. +!! This subroutine is required and controlled by the solver HBRD ! +!! HBRD varies the variables "y(i)" and eveluates the result of +!! these changes from this routine. +!!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +!! + SUBROUTINE objec_fct ( iter_no, y, residu, dummy ) +! + USE BASIC_VARIABLES + USE EOS_VARIABLES, ONLY: density_error + IMPLICIT NONE +! +! ---------------------------------------------------------------------- + INTEGER, INTENT(IN) :: iter_no + REAL, INTENT(IN) :: y(iter_no) + REAL, INTENT(OUT) :: residu(iter_no) + INTEGER, INTENT(IN OUT) :: dummy +! +! ---------------------------------------------------------------------- + INTEGER :: i, ph,k,posn, skip,phase + REAL :: lnphi(np,nc),isofugacity + CHARACTER (LEN=2) :: compon +! ---------------------------------------------------------------------- + + +posn = 0 +DO i = 1,n_unkw + posn = posn + 1 + IF (it(i) == 't') t = y(posn) + IF (it(i) == 'p') p = y(posn) + IF (it(i) == 'lnp') p = EXP( y(posn) ) + IF (it(i) == 'fls') alpha = y(posn) + IF (it(i)(1:1) == 'x' .AND. it(i)(2:2) == '1') compon = it(i)(3:3) + IF (it(i)(1:1) == 'x' .AND. it(i)(2:2) == '1') READ(compon,*) k + IF (it(i)(1:1) == 'x' .AND. it(i)(2:2) == '1') lnx(1,k) = y(posn) + IF (it(i)(1:1) == 'x' .AND. it(i)(2:2) == '2') compon = it(i)(3:3) + IF (it(i)(1:1) == 'x' .AND. it(i)(2:2) == '2') READ(compon,*) k + IF (it(i)(1:1) == 'x' .AND. it(i)(2:2) == '2') lnx(2,k) = y(posn) + IF (it(i)(1:1) == 'x' .AND. it(i)(2:2) == '3') compon = it(i)(3:3) + IF (it(i)(1:1) == 'x' .AND. it(i)(2:2) == '3') READ(compon,*) k + IF (it(i)(1:1) == 'x' .AND. it(i)(2:2) == '3') lnx(3,k) = y(posn) +END DO + +DO k = 1,ncomp + IF (lnx(1,k) > 0.0) lnx(1,k) = 0.0 + IF (lnx(2,k) > 0.0) lnx(2,k) = 0.0 +END DO + +IF (p < 1.E-100) p = 1.E-12 +!IF ( IsNaN( p ) ) p = 1000.0 ! rebounce for the case of NaN-solver output +!IF ( IsNaN( t ) ) t = 300.0 ! rebounce for the case of NaN-solver output +!IF ( IsNaN( alpha ) ) alpha = 0.5 ! rebounce for the case of NaN-solver output +IF ( p /= p ) p = 1000.0 ! rebounce for the case of NaN-solver output +IF ( t /= t ) t = 300.0 ! rebounce for the case of NaN-solver output +IF ( alpha /= alpha ) alpha = 0.5 ! rebounce for the case of NaN-solver output + +! --- setting of mole fractions ---------------------------------------- +DO ph = 1, nphas + DO i = 1, ncomp + IF ( lnx(ph,i) < -300.0 ) THEN + xi(ph,i) = 0.0 + ELSE + xi(ph,i) = EXP( lnx(ph,i) ) + END IF + END DO +END DO + +IF (ncomp > 1) CALL x_summation + +CALL fugacity (lnphi) + +phase = 2 +DO i = 1,n_unkw + skip = 0 !for ions/polymers, the isofug-eq. is not always solved + IF (n_unkw < (ncomp*(nphas-1))) skip = ncomp*(nphas-1) - n_unkw + IF ((i+skip-ncomp*(phase-2)) > ncomp) phase = phase + 1 + residu(i) = isofugacity((i+skip-ncomp*(phase-2)),phase,lnphi) + if ( density_error(phase) /= 0.0 ) residu(i) = residu(i) + SIGN( density_error(phase), residu(i) ) * 0.001 +END DO + +END SUBROUTINE objec_fct + + + +!>WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +!! REAL FUNCTION isofugacity +!! +!! calculates the deviation from the condition of equal fugacities in +!! logarithmic form. +!!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +!! + REAL FUNCTION isofugacity (i,phase,lnphi) +! + USE BASIC_VARIABLES + IMPLICIT NONE +! +! ---------------------------------------------------------------------- + INTEGER, INTENT(IN) :: i + INTEGER, INTENT(IN) :: phase + REAL, INTENT(IN) :: lnphi(np,nc) +! +! ---------------------------------------------------------------------- + INTEGER :: p1, p2 +! ---------------------------------------------------------------------- + + +! p1=1 +p1 = phase-1 +p2 = phase + +isofugacity = scaling(i) *( lnphi(p2,i)+lnx(p2,i)-lnx(p1,i)-lnphi(p1,i) ) +! write (*,'(a, 4G18.8)') ' t, p ',t,p,dense(1),dense(2) +! write (*,'(a,i3,i3,3G18.8)') ' phi_V',i,p2,lnx(p2,i),lnphi(p2,i),dense(p2) +! write (*,'(a,i3,i3,3G18.8)') ' phi_L',i,p1,lnx(p1,i),lnphi(p1,i),dense(p1) +! write (*,*) ' ISOFUGACITY',i,ISOFUGACITY, scaling(i) +! write (*,'(a,i3,4G18.8)') ' ISOFUGACITY',i,ISOFUGACITY, lnphi(p2,i)+lnx(p2,i), -lnx(p1,i)-lnphi(p1,i) +! pause + +END FUNCTION isofugacity + + + + + + + + + + + + + + + + + +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! + SUBROUTINE vle_min(lle_check) +! + USE PARAMETERS, ONLY: RGAS + USE BASIC_VARIABLES + USE STARTING_VALUES + IMPLICIT NONE +! +! ---------------------------------------------------------------------- + LOGICAL, INTENT(OUT) :: lle_check + + INTEGER :: i,j,k,phasen(0:40),steps + REAL :: lnphi(np,nc) + REAL :: vlemin(0:40),llemin(0:40),xval(0:40) + REAL :: start_xv(0:40),start_xl(0:40),x_sav,dg_dx2 +! ---------------------------------------------------------------------- + + + +j = 0 +k = 0 +nphas = 2 + +steps = 40 + +x_sav = xi(1,1) +sum_rel(1) = 'x12' ! summation relation +sum_rel(2) = 'x22' ! summation relation + +DO i = 0, steps + densta(1) = 0.45 + densta(2) = 1.d-6 + xi(1,1) = 1.0 - REAL(i) / REAL(steps) + IF ( xi(1,1) <= 1.E-50 ) xi(1,1) = 1.E-50 + xi(2,1) = xi(1,1) + lnx(1,1) = LOG(xi(1,1)) + lnx(2,1) = LOG(xi(2,1)) + + CALL x_summation + CALL fugacity (lnphi) + CALL enthalpy_etc !!KANN DAS RAUS???? + + + + + xval(i) = xi(1,1) + llemin(i)= gibbs(1) +(xi(1,1)*lnx(1,1)+xi(1,2)*lnx(1,2))*RGAS*t + + IF ( ABS(1.0-dense(1)/dense(2)) > 0.0001 ) THEN + vlemin(i)= gibbs(1) +(xi(1,1)*lnx(1,1)+xi(1,2)*lnx(1,2))*RGAS*t & + - ( gibbs(2) +(xi(2,1)*lnx(2,1)+xi(2,2)*lnx(2,2))*RGAS*t ) + phasen(i) = 2 + ELSE + phasen(i) = 1 + END IF + + IF (i > 0 .AND. phasen(i) == 2) THEN + IF (phasen(i-1) == 2 .AND. ABS(vlemin(i)+vlemin(i-1)) < & + ABS(vlemin(i))+ABS(vlemin(i-1))) THEN + j = j + 1 + start_xv(j)=xval(i-1) + (xval(i)-xval(i-1)) & + * ABS(vlemin(i-1))/ABS(vlemin(i)-vlemin(i-1)) + END IF + END IF + +END DO + + +DO i=2,steps-2 + dg_dx2 = (-llemin(i-2)+16.0*llemin(i-1)-30.0*llemin(i) & + +16.0*llemin(i+1)-llemin(i+2)) / (12.0*((xval(i)-xval(i-1))**2)) + IF (dg_dx2 < 0.0) THEN + k = k + 1 + start_xl(k)=xval(i) + END IF +END DO + + +IF (start_xl(1) == 0.0 .AND. start_xv(1) /= 0.0) THEN + xi(1,1) = start_xv(1) + xi(1,2) = 1.0-xi(1,1) + lle_check=.false. + ! write (*,*) 'VLE is likely', xi(1,1),xi(1,2) +ELSE IF (start_xl(1) /= 0.0 .AND. start_xv(1) == 0.0) THEN + xi(1,1) = start_xl(1) + xi(1,2) = 1.0-xi(1,1) + ! write (*,*) 'LLE is likely', xi(1,1),xi(1,2) + lle_check=.true. +ELSE IF (start_xl(1) /= 0.0 .AND. start_xv(1) /= 0.0) THEN + xi(1,1) = start_xv(1) + xi(1,2) = 1.0-xi(1,1) + ! write(*,*) 'starting with VLE and check for LLE' + lle_check=.true. +ELSE + xi(1,1) = x_sav + xi(1,2) = 1.0 - xi(1,1) +END IF + + +CALL x_summation + +END SUBROUTINE vle_min + + +!>WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +!! SUBROUTINE phase_stability +!! +!! the index 'LLE_check' is for the starting density (which determines +!! whether a liquid or vapor phase is found) of the trial phase. The +!! feed-point exits either as a vapor or as a liquid. If it can exist as +!! both (feedphases=2), then both states are tested. +!!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +!! + SUBROUTINE phase_stability ( lle_check, flashcase, ph_split ) +! + USE BASIC_VARIABLES + USE STARTING_VALUES + USE EOS_VARIABLES, ONLY: dhs, PI, x, eta, eta_start, z3t, fres + USE EOS_NUMERICAL_DERIVATIVES + IMPLICIT NONE +! +! ---------------------------------------------------------------------- + LOGICAL :: lle_check + LOGICAL, INTENT(IN OUT) :: flashcase + INTEGER, INTENT(OUT) :: ph_split +! ---------------------------------------------------------------------- + + INTERFACE + REAL FUNCTION F_STABILITY ( optpara, n ) + INTEGER, INTENT(IN) :: n + REAL, INTENT(IN OUT) :: optpara(n) + END FUNCTION + END INTERFACE + +!INTERFACE +! SUBROUTINE F_STABILITY (fmin, optpara, n) +! REAL, INTENT(IN OUT) :: fmin +! REAL, INTENT(IN) :: optpara(:) +! INTEGER, INTENT(IN) :: n +! END SUBROUTINE F_STABILITY +! +! SUBROUTINE stability_grad (g, optpara, n) +! REAL, INTENT(IN OUT) :: g(:) +! REAL, INTENT(IN) :: optpara(:) +! INTEGER, INTENT(IN) :: n +! END SUBROUTINE stability_grad +! +! SUBROUTINE stability_hessian (hessian, g, fmin, optpara, n) +! REAL, INTENT(IN OUT) :: hessian(:,:) +! REAL, INTENT(IN OUT) :: g(:) +! REAL, INTENT(IN OUT) :: fmin +! REAL, INTENT(IN) :: optpara(:) +! INTEGER, INTENT(IN) :: n +! END SUBROUTINE stability_hessian +!END INTERFACE + + INTEGER :: n, PRIN + REAL :: fmin, t0, h0, MACHEP, PRAXIS + REAL, ALLOCATABLE :: optpara(:) + + INTEGER :: i, feedphases, trial + REAL :: rhoi(nc),rho_start + REAL :: feeddens, rho_phas(np) + REAL :: fden + REAL :: dens + REAL :: rhot + REAL :: lnphi(np,nc) + REAL :: w(np,nc), mean_mass +! ---------------------------------------------------------------------- + +n = ncomp +ALLOCATE( optpara(n) ) + +IF (lle_check) WRITE (*,*) ' stability test starting with dense phase' + +DO i = 1, ncomp ! setting feed-phase x's + IF (.NOT.flashcase) xif(i) = xi(1,i) + IF (flashcase) xi(1,i) = xif(i) + xi(2,i) = xif(i) ! feed is tested for both: V and L density +END DO + +densta(1) = 0.45 +densta(2) = 1.d-6 + +CALL dens_calc(rho_phas) +IF ( ABS(1.0-dense(1)/dense(2)) > 0.0005 ) THEN + feedphases=2 ! feed-composition can exist both, in V and L +ELSE + feedphases=1 ! feed-composition can exist either in V or L +END IF +densta(1) = dense(1) +feeddens = dense(2) +!write (*,*) 'feedphases',dense(1), dense(2),feedphases + +10 CONTINUE ! IF FeedPhases=2 THEN there is a second cycle + + trial = 1 + + ! -------------------------------------------------------------------- + ! setting trial-phase mole-fractions + ! if there is no phase-split then further trial-phases are + ! considered (loop: 20 CONTINUE) + ! -------------------------------------------------------------------- + DO i = 1, ncomp + w(2,i) = 1.0 / REAL(ncomp) + END DO + mean_mass = 1.0 / SUM( w(2,1:ncomp)/mm(1:ncomp) ) + xi(2,1:ncomp) = w(2,1:ncomp)/mm(1:ncomp) * mean_mass + + 20 CONTINUE + + DO i = 1, ncomp + rhoif(i) = rho_phas(1) * xif(i) + rhoi(i) = rhoif(i) + END DO + + !write (*,'(a,6G16.8)') 'startval',rho_phas(2),xi(2,1:ncomp) + + ! -------------------------------------------------------------------- + ! calc Helmholtz energy density and derivative (numerical) to rhoif(i). + ! The derivative is taken around the "feed-point" not the trial phase + ! -------------------------------------------------------------------- + + rhot = SUM( rhoi(1:ncomp) ) + x(1:ncomp) = rhoi(1:ncomp) / rhot + CALL PERTURBATION_PARAMETER + xi(1,1:ncomp) = x(1:ncomp) + eta = rhot * z3t + eta_start = eta + densta(1) = eta_start + ensemble_flag = 'tv' + CALL FUGACITY (lnphi) + ensemble_flag = 'tp' + + call fden_calc ( fden, rhoi ) + fdenf = fden + + grad_fd(1:ncomp) = lnphi(1,1:ncomp) + LOG( rhoi(1:ncomp) ) + + + ! -------------------------------------------------------------------- + ! starting values for iteration (optpara) + ! -------------------------------------------------------------------- + rho_start = 1.E-5 + IF (lle_check) THEN + densta(2) = 0.45 + CALL dens_calc(rho_phas) + rho_start = rho_phas(2)*0.45/dense(2) + END IF + DO i = 1,ncomp + rhoi(i) = xi(2,i)*rho_start + optpara(i) = LOG( rhoi(i) ) + END DO + + ! -------------------------------------------------------------------- + ! minimizing the objective fct. Phase split for values of fmin < 0.0 + ! -------------------------------------------------------------------- + t0 = 5.E-5 + h0 = 0.5 + PRIN = 0 + MACHEP = 1.E-15 + + fmin = PRAXIS( t0, MACHEP, h0, n, PRIN, optpara, F_STABILITY, fmin ) + + + ! -------------------------------------------------------------------- + ! updating the ln(x) valus from optpara. The optimal optpara-vector is + ! not necessarily the one that was last evaluated. At the very end, + ! cg_decent writes the best values to optpara + ! -------------------------------------------------------------------- + fmin = F_STABILITY( optpara, n ) + + + + ! IF ( n == 2 ) THEN + ! CALL Newton_Opt_2D ( stability_hessian, F_stability, optpara, n, 1.E-8, 1.E-8, g, fmin) + ! ELSE + ! CALL cg_descent (1.d-5, optpara, n, F_STABILITY, stability_grad, STATUS, & + ! gnorm, fmin, iter, nfunc, ngrad, d, g, xtemp, gtemp) + ! ENDIF + ! CALL F_STABILITY (fmin, optpara, n) + + + ! -------------------------------------------------------------------- + ! determine instability & non-trivial solution + ! -------------------------------------------------------------------- + ph_split = 0 + IF (fmin < -1.E-7 .AND. & + ABS( 1.0 - maxval(EXP(optpara),mask=optpara /= 0.0) /maxval(rhoif) ) > 0.0005) THEN + ph_split = 1 + END IF + + IF (ph_split == 1) THEN + + ! ------------------------------------------------------------------ + ! here, there should be IF FeedPhases=2 THEN GOTO 10 + ! and test for another phase (while saving optpara) + ! ------------------------------------------------------------------ + + rhoi2(1:ncomp) = EXP( optpara(1:ncomp) ) + dens = PI/6.0 * SUM( rhoi2(1:ncomp) * parame(1:ncomp,1) * dhs(1:ncomp)**3 ) + rhot = SUM( rhoi2(1:ncomp) ) + xi(2,1:ncomp) = rhoi2(1:ncomp) / rhot + + ELSE + + IF (trial <= ncomp + ncomp) THEN + ! ---------------------------------------------------------------- + ! setting trial-phase x's + ! ---------------------------------------------------------------- + IF (trial <= ncomp) THEN + DO i=1,ncomp + w(2,i) = 1.0 / REAL(ncomp-1) * 0.05 + END DO + w(2,trial) = 0.95 + ELSE + DO i=1,ncomp + w(2,i) = 1.0 / REAL(ncomp-1) * 0.00001 + END DO + w(2,trial-ncomp) = 0.99999 + END IF + mean_mass = 1.0 / SUM( w(2,1:ncomp)/mm(1:ncomp) ) + xi(2,1:ncomp) = w(2,1:ncomp)/mm(1:ncomp) * mean_mass + trial = trial + 1 + GO TO 20 + END IF + ! IF (.NOT.LLE_check) write (*,*) 'no phase split detected' + ! IF (.NOT.LLE_check) pause + IF (feedphases > 1 .AND. .NOT.lle_check .AND. densta(1) > 0.2) THEN + densta(1) = feeddens ! this will be the lower-valued density (vapor) + CALL dens_calc(rho_phas) + ! WRITE (*,*) 'try feed as vapor-phase' + GO TO 10 + END IF + + END IF + +DEALLOCATE( optpara ) + +END SUBROUTINE phase_stability + + +!>WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +!! SUBROUTINE select_sum_rel +!! +!! This subroutine determines which component of a phase "ph" is calculated +!! from the summation relation x_i = 1 - sum(x_j). The other components are, +!! by default, said to be iterated during the phase equilibrium calculation. +!! +!! Note that for flash calculations not all of these mole fractions are in +!! fact iterated - this is raken care of in "determine_flash_it". +!! +!! ph phase +!! excl exclude comp. n +!! startindex assign it(startindex) for quantities to be iterated +!! (further it(startindex+1) is assigned, for a ternary +!! mixture, etc.) +!! +!! sum_index indicates the component, with the largest mole +!! fraction. If ph=1 and sum_index=2, we define +!! sum_rel(ph=1)='x12', so that this component is +!! calculated from the summation relation. +!!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! + SUBROUTINE select_sum_rel (ph,excl,startindex) +! + USE BASIC_VARIABLES + IMPLICIT NONE +! +! ---------------------------------------------------------------------- + INTEGER, INTENT(IN) :: ph + INTEGER, INTENT(IN) :: excl + INTEGER, INTENT(IN) :: startindex +! ---------------------------------------------------------------------- + INTEGER :: i,j, sum_index + REAL :: xmax(np) + ! CHARACTER :: compNo*2,phasNo*2 +! ---------------------------------------------------------------------- + +xmax(ph) = 0.0 +DO i = 1, ncomp + + IF ( xi(ph,i) > xmax(ph) ) THEN + xmax(ph) = xi(ph,i) + sum_index = i + + IF (ph == 1 .AND. i == 1) sum_rel(1) = 'x11' + IF (ph == 1 .AND. i == 2) sum_rel(1) = 'x12' + IF (ph == 1 .AND. i == 3) sum_rel(1) = 'x13' + IF (ph == 1 .AND. i == 4) sum_rel(1) = 'x14' + IF (ph == 1 .AND. i == 5) sum_rel(1) = 'x15' + + IF (ph == 2 .AND. i == 1) sum_rel(2) = 'x21' + IF (ph == 2 .AND. i == 2) sum_rel(2) = 'x22' + IF (ph == 2 .AND. i == 3) sum_rel(2) = 'x23' + IF (ph == 2 .AND. i == 4) sum_rel(2) = 'x24' + IF (ph == 2 .AND. i == 5) sum_rel(2) = 'x25' + + IF (ph == 3 .AND. i == 1) sum_rel(3) = 'x31' + IF (ph == 3 .AND. i == 2) sum_rel(3) = 'x32' + IF (ph == 3 .AND. i == 3) sum_rel(3) = 'x33' + IF (ph == 3 .AND. i == 4) sum_rel(3) = 'x34' + IF (ph == 3 .AND. i == 5) sum_rel(3) = 'x35' +! write (*,*) ph,i,xi(ph,i),sum_rel(ph) + END IF + +END DO + +j = 0 +DO i = 1, ncomp + + IF ( i /= sum_index .AND. i /= excl ) THEN + IF (ph == 1 .AND. i == 1) it(startindex+j) = 'x11' + IF (ph == 1 .AND. i == 2) it(startindex+j) = 'x12' + IF (ph == 1 .AND. i == 3) it(startindex+j) = 'x13' + IF (ph == 1 .AND. i == 4) it(startindex+j) = 'x14' + IF (ph == 1 .AND. i == 5) it(startindex+j) = 'x15' + + IF (ph == 2 .AND. i == 1) it(startindex+j) = 'x21' + IF (ph == 2 .AND. i == 2) it(startindex+j) = 'x22' + IF (ph == 2 .AND. i == 3) it(startindex+j) = 'x23' + IF (ph == 2 .AND. i == 4) it(startindex+j) = 'x24' + IF (ph == 2 .AND. i == 5) it(startindex+j) = 'x25' + + IF (ph == 3 .AND. i == 1) it(startindex+j) = 'x31' + IF (ph == 3 .AND. i == 2) it(startindex+j) = 'x32' + IF (ph == 3 .AND. i == 3) it(startindex+j) = 'x33' + IF (ph == 3 .AND. i == 4) it(startindex+j) = 'x34' + IF (ph == 3 .AND. i == 5) it(startindex+j) = 'x35' +! write (*,*) 'iter ',it(startindex+j) + j = j + 1 + END IF + +END DO + +END SUBROUTINE select_sum_rel + + + + +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! + SUBROUTINE tangent_plane +! + USE BASIC_VARIABLES + USE STARTING_VALUES + IMPLICIT NONE +! +! ---------------------------------------------------------------------- +!!$ INTERFACE +!!$ SUBROUTINE tangent_value (fmin, optpara, n) +!!$ INTEGER, INTENT(IN) :: n +!!$ REAL, INTENT(IN OUT) :: fmin +!!$ REAL, INTENT(IN) :: optpara(:) +!!$ END SUBROUTINE tangent_value +!!$ +!!$ SUBROUTINE tangent_grad (g, optpara, n) +!!$ INTEGER, INTENT(IN) :: n +!!$ REAL, INTENT(IN OUT) :: g(:) +!!$ REAL, INTENT(IN) :: optpara(:) +!!$ END SUBROUTINE tangent_grad +!!$ END INTERFACE + +! +! ---------------------------------------------------------------------- + INTERFACE + REAL FUNCTION PRAXIS( t0, MACHEP, h0, n, PRIN, optpara, TANGENT_VALUE, fmin ) + REAL, INTENT(IN OUT) :: t0 + REAL, INTENT(IN) :: machep + REAL, INTENT(IN) :: h0 + INTEGER :: n + INTEGER, INTENT(IN OUT) :: prin + REAL, INTENT(IN OUT) :: optpara(n) + REAL, EXTERNAL :: TANGENT_VALUE + REAL, INTENT(IN OUT) :: fmin + END FUNCTION + + REAL FUNCTION TANGENT_VALUE2 ( optpara, n ) + INTEGER, INTENT(IN) :: n + REAL, INTENT(IN) :: optpara(n) + END FUNCTION + END INTERFACE +! +! ---------------------------------------------------------------------- + INTEGER :: n + INTEGER :: i, k, ph + INTEGER :: small_i, min_ph, other_ph + INTEGER :: PRIN + REAL :: fmin , t0, h0, MACHEP + REAL :: lnphi(np,nc) + REAL, ALLOCATABLE :: optpara(:) + +! INTEGER :: STATUS, iter, nfunc, ngrad +! REAL :: gnorm +! REAL, ALLOCATABLE :: d(:), g(:), xtemp(:), gtemp(:) +! ---------------------------------------------------------------------- + +n = ncomp +t0 = 1.E-4 +h0 = 0.1 +PRIN = 0 +MACHEP = 1.E-15 + +ALLOCATE( optpara(n) ) +!ALLOCATE( d(n) ) +!ALLOCATE( g(n) ) +!ALLOCATE( xtemp(n) ) +!ALLOCATE( gtemp(n) ) + +DO i = 1,ncomp + rhoi1(i) = rhoif(i) + lnx(1,i) = LOG(xi(1,i)) + lnx(2,i) = LOG(xi(2,i)) +END DO + +DO i = 1,ncomp + optpara(i) = LOG( xi(2,i) * 0.001 ) +END DO + +! CALL cg_descent (1.d-4, optpara, n, tangent_value, tangent_grad, STATUS, & +! gnorm, fmin, iter, nfunc, ngrad, d, g, xtemp, gtemp) +! +! updating the ln(x) valus from optpara. The optimal optpara-vector is not necessarily +! the one that was last evaluated. At the very end, cg_decent writes the best values to optpara +! CALL tangent_value (fmin, optpara, n) + + + +fmin = PRAXIS( t0, MACHEP, h0, n, PRIN, optpara, TANGENT_VALUE2, fmin ) + +! The optimal optpara-vector is not necessarily the one that was last evaluated. +! TANGENT_VALUE is reexecuted with the optimal vector optpara, in order to update the ln(x) values +fmin = TANGENT_VALUE2( optpara, n ) + + +! ---------------------------------------------------------------------- +! If one component is a polymer (indicated by a low component-density) +! then get an estimate of the polymer-lean composition, by solving for +! xi_p1 = ( xi_p2 * phii_p2) / phii_p1 (phase equilibrium condition, +! with p1 for phase 1) +! ---------------------------------------------------------------------- +IF ( MINVAL( lnx(1,1:ncomp) ) < MINVAL( lnx(2,1:ncomp) ) ) THEN + min_ph = 1 + other_ph = 2 +ELSE + min_ph = 2 + other_ph = 1 +ENDIF +small_i = MINLOC( lnx(min_ph,1:ncomp), 1 ) +! --- if one component is a polymer ------------------------------------ +IF ( MINVAL( lnx(min_ph,1:ncomp) ) < -20.0 ) THEN + CALL FUGACITY ( lnphi ) + lnx(min_ph,small_i) = lnx(other_ph,small_i)+lnphi(other_ph,small_i) - lnphi(min_ph,small_i) + optpara(small_i) = lnx(2,small_i) + LOG( SUM( EXP( optpara(1:ncomp) ) ) ) +END IF + +! ---------------------------------------------------------------------- +! caution: these initial values are for a flashcase overwritten in +! SUBROUTINE determine_flash_it2, because in that case, the lnx-values +! treated as ln(mole_number). +! ---------------------------------------------------------------------- +val_init(1) = dense(1) +val_init(2) = dense(2) +val_init(3) = t +val_init(4) = p +DO ph = 1,nphas + DO k = 1,ncomp + val_init(4+k+(ph-1)*ncomp) = lnx(ph,k) + END DO +END DO +!alpha = optpara(1) + + +!DEALLOCATE( optpara, d, g, xtemp, gtemp ) +DEALLOCATE( optpara ) + +END SUBROUTINE tangent_plane + + +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! + SUBROUTINE determine_flash_it2 +! + USE BASIC_VARIABLES + IMPLICIT NONE +! +! ---------------------------------------------------------------------- + INTEGER :: i, k, ph + REAL :: n_phase1, n_phase2, max_x_diff +! ---------------------------------------------------------------------- + + IF ( MINVAL( lnx(1,1:ncomp) ) < MINVAL( lnx(2,1:ncomp) ) ) THEN + it(1) = 'x11' + it(2) = 'x12' + IF (ncomp >= 3) it(3) = 'x13' + IF (ncomp >= 4) it(4) = 'x14' + IF (ncomp >= 5) it(5) = 'x15' + sum_rel(1) = 'nfl' + ELSE + it(1) = 'x21' + it(2) = 'x22' + IF (ncomp >= 3) it(3) = 'x23' + IF (ncomp >= 4) it(4) = 'x24' + IF (ncomp >= 5) it(5) = 'x25' + sum_rel(2) = 'nfl' + ENDIF + max_x_diff = 0.0 + DO i = 1,ncomp + IF ( ABS( EXP( lnx(1,i) ) - EXP( lnx(2,i) ) ) > max_x_diff ) THEN + max_x_diff = ABS( EXP( lnx(1,i) ) - EXP( lnx(2,i) ) ) + n_phase1 = ( xif(i) - EXP( lnx(2,i) ) ) / ( EXP( lnx(1,i) ) - EXP( lnx(2,i) ) ) + n_phase2 = 1.0 - n_phase1 + END IF + END DO + lnx(1,1:ncomp) = lnx(1,1:ncomp) + LOG( n_phase1 ) ! these x's are treated as mole numbers + lnx(2,1:ncomp) = lnx(2,1:ncomp) + LOG( n_phase2 ) ! these x's are treated as mole numbers + + + val_init(1) = dense(1) + val_init(2) = dense(2) + val_init(3) = t + val_init(4) = p + DO ph = 1,nphas + DO k = 1,ncomp + val_init(4+k+(ph-1)*ncomp) = lnx(ph,k) ! - LOG( SUM( EXP( lnx(ph,1:ncomp) ) ) ) + ! write (*,*) ph,k, lnx(ph,k) + END DO + END DO + +END SUBROUTINE determine_flash_it2 + +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! SUBROUTINE poly_sta_var +! +! This subroutine generates starting values for mole fractons of +! polymer-solvent systems. +! The determination of these starting values follows a two-step +! procedure. Fist, the equilibrium concentration of the polymer-rich +! phase is estimated with the assumption of zero concentration +! of polymer in the polymer-lean-phase. This is achieved in the +! SUBROUTINE POLYMER_FREE. (Only one equation has to be iterated +! for this case). Once this is achieved, the rigorous calculation +! is triggered. If it converges, fine! If no solution is obtained, +! the pressure is somewhat reduced, the procedure is repeated and +! a calculation is started to approach the originally specified +! pressure. +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! + SUBROUTINE poly_sta_var (converg) +! + USE BASIC_VARIABLES + IMPLICIT NONE +! +! ---------------------------------------------------------------------- + INTEGER, INTENT(IN OUT) :: converg +! +! ---------------------------------------------------------------------- + INTEGER :: k,ph,sol + REAL :: p_spec,solution(10,4+nc*np) +! ---------------------------------------------------------------------- + + p_spec = p + + find_equilibrium: DO + + CALL polymer_free(p_spec,sol,solution) + + WRITE (*,*) ' ' + WRITE (*,*) ' GENERATING STARTING VALUES' + + val_init(1) = solution(1,1) ! approx.solutions for next iteration + val_init(2) = solution(1,2) ! approx.solutions for next iteration + val_init(3) = solution(1,3) ! approx.solutions for next iteration + val_init(4) = solution(1,4) ! approx.solutions for next iteration + DO ph = 1,nphas + DO k = 1,ncomp + val_init(4+k+(ph-1)*ncomp) = solution(1,4+k+(ph-1)*ncomp) + END DO + END DO + val_init(7) = -10000.0 ! start.val. for lnx(2,1) for iterat. + + IF (p /= p_spec) & + WRITE (*,*) ' INITIAL EQUILIBRIUM CALC. FAILD. NEXT STEP STARTS' + + IF (p == p_spec) THEN + n_unkw = ncomp ! number of quantities to be iterated + it(1)='x11' ! iteration of mol fraction of comp.1 phase 1 + it(2)='x21' ! iteration of mol fraction of comp.1 phase 2 + CALL objective_ctrl (converg) + ELSE + outp = 0 ! output to terminal + running ='p' ! Pressure is running var. in PHASE_EQUILIB + CALL phase_equilib(p_spec,5.0,converg) + END IF + + IF (converg == 1) EXIT find_equilibrium + p = p * 0.9 + IF ( p < (0.7*p_spec) ) WRITE (*,*) ' NO SOLUTION FOUND' + IF ( p < (0.7*p_spec) ) STOP + + END DO find_equilibrium + + WRITE (*,*) ' FINISHED: POLY_STA_VAR' + +END SUBROUTINE poly_sta_var + + +!>WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +!! SUBROUTINE x_summation +!! +!! This subroutine solves the summation relation: xi=1-sum(xj) +!! The variable "sum_rel(i)" contains the information, which mole +!! fraction is the one to be calculated here. Consider the example +!! sum_rel(1)='x12'. The fist letter 'x' of this variable indicates, +!! that this subroutine needs to be executed and that the mole +!! fraction of a component has to be calculated. The second letter +!! of the string points to phase 1, the third letter to component 2. +!! If the fist letter is 'e', not 'x', then the subroutine +!! NEUTR_CHARGE is called. This is the case of electrolyte solutions, +!! neutral charges have to be enforced in all phases (see below). +!!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +!! + SUBROUTINE x_summation +! + USE BASIC_VARIABLES + IMPLICIT NONE +! +! ---------------------------------------------------------------------- + INTEGER :: i, j, comp_i, ph_i + REAL :: sum_x + CHARACTER (LEN=2) :: phasno + CHARACTER (LEN=2) :: compno + LOGICAL :: flashcase2 +! ---------------------------------------------------------------------- + +DO j = 1, nphas + IF (sum_rel(j)(1:3) == 'nfl') THEN + CALL new_flash (j) + RETURN + END IF +END DO + + + +flashcase2 = .false. + +DO j = 1, nphas + + IF (sum_rel(j)(1:1) == 'x') THEN + + phasno = sum_rel(j)(2:2) + READ(phasno,*) ph_i + compno = sum_rel(j)(3:3) + READ(compno,*) comp_i + IF ( sum_rel(nphas+j)(1:1) == 'e' ) CALL neutr_charge(nphas+j) + + sum_x = 0.0 + DO i = 1, ncomp + IF ( i /= comp_i ) sum_x = sum_x + xi(ph_i,i) + END DO + xi(ph_i,comp_i) = 1.0 - sum_x + IF ( xi(ph_i,comp_i ) < 0.0 ) xi(ph_i,comp_i) = 0.0 + IF ( xi(ph_i,comp_i ) /= 0.0 ) THEN + lnx(ph_i,comp_i) = LOG( xi(ph_i,comp_i) ) + ELSE + lnx(ph_i,comp_i) = -100000.0 + END IF + ! write (*,*) 'sum_x',ph_i,comp_i,lnx(ph_i,comp_i),xi(ph_i,comp_i) + + ELSE IF ( sum_rel(j)(1:2) == 'fl' ) THEN + + flashcase2 = .true. + ! ------------------------------------------------------------------ + ! This case is true when all molefractions of one phase are + ! determined from a component balance. What is needed to + ! calculate all molefractions of that phase are all mole- + ! fractions of the other phase (nphas=2, so far) and the + ! phase fraction alpha. + ! Alpha is calculated (in FLASH_ALPHA) from the mole fraction + ! of component {sum_rel(j)(3:3)}. IF sum_rel(2)='fl3', then + ! the alpha is determined from the molefraction of comp. 3 and + ! the molefraction of phase 2 is then completely determined ELSE + ! ------------------------------------------------------------------ + + ELSE + WRITE (*,*) 'summation relation not defined' + STOP + END IF + +END DO + +IF ( it(1) == 'fls' ) CALL flash_sum +IF ( flashcase2 ) CALL flash_alpha + +END SUBROUTINE x_summation + + + +!>WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +!! SUBROUTINE FUGACITY +!! +!! This subroutine serves as an interface to the eos-subroutines. +!! (1) case 1, when ensemble_flag = 'tp' +!! The subroutine gives the residual chemical potential: +!! mu_i^res(T,p,x)/kT = ln( phi_i ) +!! and in addition, the densities that satisfy the specified p +!! (2) case 2, when ensemble_flag = 'tv' +!! The subroutine gives the residual chemical potential: +!! --> mu_i^res(T,rho,x)/kT +!! and in addition the resulting pressure for the given density. +!! The term "residual" means difference of the property and the same +!! property for an ideal gas mixture. +!!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +!! + SUBROUTINE FUGACITY (ln_phi) +! + USE BASIC_VARIABLES + USE EOS_VARIABLES, ONLY: phas, x, eta, eta_start, lnphi, fres, rho, pges, KBOL + IMPLICIT NONE +! +! ---------------------------------------------------------------------- + REAL, INTENT(OUT) :: ln_phi(np,nc) +! +! --- local variables -------------------------------------------------- + INTEGER :: ph +! ---------------------------------------------------------------------- +! +IF (eos < 2) THEN + + DO ph = 1,nphas + + phas = ph + eta_start = densta(ph) + x(1:ncomp) = xi(ph,1:ncomp) + + IF (p < 1.E-100) THEN + WRITE(*,*) ' FUGACITY: PRESSURE TOO LOW', p + p = 1.E-6 + END IF + + IF (num == 0) CALL PHI_EOS + IF (num == 1) CALL PHI_NUMERICAL + !!IF (num == 2) CALL PHI_CRITICAL_RENORM + IF (num == 2) write(*,*) 'CRITICAL RENORM NOT INCLUDED YET' + + dense(ph) = eta + ln_phi(ph,1:ncomp) = lnphi(1:ncomp) + ! gibbs(ph) = fres + sum( xi(ph,1:ncomp)*( log( xi(ph,1:ncomp)*rho) - 1.0 ) ) & + ! + (pges * 1.d-30) / (KBOL*t*rho) ! includes ideal gas contribution + + ! f_res(ph) = fres + ! write (*,'(i3,4G20.11)') ph,eta,lnphi(1),lnphi(2) + ! DO i = 1,ncomp + ! DO j=1,NINT(parame(i,12)) + ! mxx(ph,i,j) = mx(i,j) + ! END DO + ! END DO + + END DO + +ELSE + +! IF (eos == 2) CALL srk_eos (ln_phi) +! IF (eos == 3) CALL pr_eos (ln_phi) +! dense(1) = 0.01 +! dense(2) = 0.3 +! IF (eos == 4.OR.eos == 5.OR.eos == 6.OR.eos == 8) CALL lj_fugacity(ln_phi) +! IF (eos == 7) CALL sw_fugacity(ln_phi) +! IF (eos == 9) CALL lj_bh_fug(ln_phi) + +END IF + +END SUBROUTINE FUGACITY + + +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! SUBROUTINE enthalpy_etc +! +! This subroutine serves as an interface to the EOS-routines. The +! residual enthalpy h_res, residual entropy s_res, residual Gibbs +! enthalpy g_res, and residual heat capacity at constant pressure +! (cp_res) corresponding to converged conditions are calculated. +! The conditions in (T,P,xi,rho) need to be converged equilibrium +! conditions !! +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! + SUBROUTINE enthalpy_etc +! + USE BASIC_VARIABLES + USE EOS_VARIABLES + IMPLICIT NONE +! + INTEGER :: ph +! ------------------------------------------------------------------ + +IF (eos <= 1) THEN + + DO ph=1,nphas + + phas = ph + eta = dense(ph) +! eta_start = dense(ph) + x(1:ncomp) = xi(ph,1:ncomp) + + IF(num == 0) THEN + CALL H_EOS + ELSE + IF(num == 1) CALL H_numerical + IF(num == 2) write (*,*) 'enthalpy_etc: incorporate H_EOS_RN' + IF(num == 2) stop +! IF(num == 2) CALL H_EOS_rn + END IF + enthal(ph) = h_res + entrop(ph) = s_res + ! gibbs(ph) = h_res - t * s_res ! already defined in eos.f90 (including ideal gas) + cpres(ph) = cp_res + + END DO + IF (nphas == 2) h_lv = enthal(2)-enthal(1) + +ENDIF + +END SUBROUTINE enthalpy_etc + + +!>WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +!! SUBROUTINE dens_calc +!! +!! This subroutine serves as an interface to the EOS-routines. The +!! densities corresponding to given (P,T,xi) are calculated. +!! (Note: the more common interface is SUBROUTINE FUGACITY. +!!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +!! + SUBROUTINE dens_calc(rho_phas) +! + USE BASIC_VARIABLES + USE EOS_VARIABLES + IMPLICIT NONE +! +! +!------------------------------------------------------------------ + REAL, INTENT(OUT) :: rho_phas(np) +! + INTEGER :: ph +!------------------------------------------------------------------ + + +DO ph = 1, nphas + + IF (eos < 2) THEN + + phas = ph + eta = densta(ph) + eta_start = densta(ph) + x(1:ncomp) = xi(ph,1:ncomp) + + CALL PERTURBATION_PARAMETER + CALL DENSITY_ITERATION + + dense(ph)= eta + rho_phas(ph) = eta/z3t + + ELSE + write (*,*) ' SUBROUTINE DENS_CALC not available for cubic EOS' + stop + END IF + +END DO + +END SUBROUTINE dens_calc + + +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! + SUBROUTINE fden_calc (fden, rhoi) +! + USE BASIC_VARIABLES + USE EOS_VARIABLES + IMPLICIT NONE +! +! ---------------------------------------------------------------------- + REAL, INTENT(OUT) :: fden + REAL, INTENT(IN OUT) :: rhoi(nc) +! ---------------------------------------------------------------------- + REAL :: rhot, fden_id +! ---------------------------------------------------------------------- + + +IF (eos < 2) THEN + + rhot = SUM( rhoi(1:ncomp) ) + x(1:ncomp) = rhoi(1:ncomp) / rhot + + CALL PERTURBATION_PARAMETER + eta = rhot * z3t + eta_start = eta + + IF (num == 0) THEN + CALL F_EOS + ELSE IF(num == 1) THEN + CALL F_NUMERICAL + ELSE + write (*,*) 'deactivated this line when making a transition to f90' + stop + ! CALL F_EOS_rn + END IF + + fden_id = SUM( rhoi(1:ncomp) * ( LOG( rhoi(1:ncomp) ) - 1.0 ) ) + + fden = fres * rhot + fden_id + +ELSE + write (*,*) ' SUBROUTINE FDEN_CALC not available for cubic EOS' + stop +END IF + +END SUBROUTINE fden_calc + + + + +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! SUBROUTINE polymer_free +! +! This subroutine performes a phase equilibrium calculation assuming +! the polymer-lean hase to be polymer-free (x_poly=0). Only the +! equality of the solvent-fugacities has to be ensured (only one +! equation to be iterated). This procedure delivers very good +! appoximations for the polymer-rich phase up-to fairly close to the +! mixture critical point. Both, liquid-liquid and vapor-liquid +! equilibria can be calculated. +! See also comments to SUBROUTINE POLY_STA_VAR. +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! + SUBROUTINE polymer_free (p_spec,sol,solution) +! + USE BASIC_VARIABLES + IMPLICIT NONE +! +! ---------------------------------------------------------------------- + REAL, INTENT(IN OUT) :: p_spec + INTEGER, INTENT(OUT) :: sol + REAL, INTENT(OUT) :: solution(10,4+nc*np) +! +! ---------------------------------------------------------------------- + INTEGER :: k,j,ph, converg + REAL :: grid(10) +! ---------------------------------------------------------------------- + + sol = 0 + + grid(1)=0.98 + grid(2)=0.9 + grid(3)=0.7 + grid(4)=0.5 + grid(5)=0.3 + grid(6)=0.2 + grid(7)=0.1 + grid(8)=0.05 + + DO WHILE ( sol == 0 ) + + DO j = 1,8 + ! Phase 2 is solvent-phase + ! starting value for xi(1,1) of polymer-phase 1: w_polymer=0.95 to 0.05 + ! from simple approximate equation + xi(1,1) = grid(j) / ( (1.0-grid(j)) * mm(1) / mm(2) ) !xi(1,1) Phase 1 Komponente 1 + IF ( mm(1) < 5000.0 ) xi(1,1) = xi(1,1) * 0.8 + xi(1,2) = 1.0 - xi(1,1) !xi(1,2) Phase 1 Komponente 2 + lnx(1,1) = LOG(xi(1,1)) + lnx(1,2) = LOG(xi(1,2)) + lnx(2,1) = -1.E10 !ln(xi) Phase 2 Komponente 1 + lnx(2,2) = 0.0 !ln(xi) Phase 2 Komponente 2 + + + + val_init(1) = 0.45 ! starting density targeting at a liquid phase + val_init(2) = 0.0001 ! starting density targeting at a vapor phase + ! val_init(2) = 0.45 + val_init(3) = t + val_init(4) = p + DO ph = 1,nphas + DO k = 1,ncomp + val_init(4+k+(ph-1)*ncomp) = lnx(ph,k) + END DO + END DO + + + + + n_unkw = ncomp-1 ! number of quantities to be iterated + it(1) = 'x11' ! iteration of mol fraction of comp.1 phase 1 + it(2) = ' ' + sum_rel(1) = 'x12' ! summation relation: x12 = 1 - sum(x1j) + sum_rel(2) = 'x22' + + CALL objective_ctrl (converg) + + IF (converg == 1 .AND. ABS(dense(1)/dense(2)-1.0) > 1.d-3 .AND. dense(1) > 0.1) THEN + IF (sol == 0) THEN + sol = sol + 1 + DO k = 1,4+ncomp*nphas + solution(sol,k) = val_conv(k) + END DO + ELSE IF (ABS(solution(sol,5)/lnx(1,1)-1.0) > 1.d-2) THEN + sol = sol + 1 + DO k = 1,4+ncomp*nphas + solution(sol,k) = val_conv(k) + END DO + END IF + END IF + + END DO + + + + + + IF (sol == 0) THEN + WRITE (*,*) ' no initial solution found' + p = p*0.9 + IF (p < (0.7*p_spec)) WRITE (*,*) ' NO SOLUTION FOUND' + IF (p < (0.7*p_spec)) STOP + ELSE IF (sol > 1) THEN + ! write (*,*) ' ' + ! write (*,*) ' ',sol,' solutions found:' + ! write (*,*) ' lnx(1,1), dichte_1, dichte_2' + ! DO k = 1,sol + ! write (*,*) solution(k,5),solution(k,1),solution(k,2) + ! END DO + END IF + END DO + + n_unkw = ncomp ! number of quantities to be iterated + it(1) = 'x11' ! iteration of mol fraction of comp.1 phase 1 + it(2) = 'x21' ! iteration of mol fraction of comp.1 phase 2 + sum_rel(1) = 'x12' ! summation relation: x12 = 1 - sum(x1j) + sum_rel(2) = 'x22' ! summation relation: x22 = 1 - sum(x2j) + + + END SUBROUTINE polymer_free + + + + + +!>WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +!! SUBROUTINE phase_equilib +!! +!! This subroutine varies a predefined "running variable" and +!! organizes phase equilibrium calculations. For an isotherm +!! calculation e.g., the running variable is often the pressure. The +!! code is designed to deliver only converged solutions. In order to +!! enforce convergence, a step-width adjustment (reduction) is +!! implemented. +!! +!! VARIABLE LIST: +!! running defines the running variable. For example: if you want +!! to calculate the vapor pressure curve of a component +!! starting from 100�C to 200�C, then running is 't'. The +!! temperature is step-wise increased until the end- +!! -temperature of 200�C is reached. +!! (in this example end_x=200+273.15) +!! end_x end point for running variable +!! steps No. of calculation steps towards the end point of calc. +!! converg 0 if no convergence achieved, 1 if converged solution +!! +!! PREREQUISITES: +!! prior to execution of this routine, the follwing variables have to +!! be defined: "val_init" an array containing the starting values for +!! this iteration, "it(i)" provides the information, which variable is +!! determined iteratively, "sum_rel(i)" indicates, which mole fraction +!! is determined from the summation relation sum(xi)=1. Furthermore, +!! the number of phases and the variables provided by the subroutine +!! INPUT are required. +!!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +!! + SUBROUTINE phase_equilib (end_x,steps,converg) +! + USE BASIC_VARIABLES + IMPLICIT NONE +! +! ---------------------------------------------------------------------- + REAL, INTENT(IN) :: end_x + REAL, INTENT(IN) :: steps + INTEGER, INTENT(OUT) :: converg +! +! ---------------------------------------------------------------------- + INTEGER :: k, count1,count2,runindex,maxiter + REAL :: delta_x,delta_org,val_org,runvar + CHARACTER (LEN=2) :: compon + LOGICAL :: continue_cycle +! ---------------------------------------------------------------------- + +IF (running(1:2) == 'd1') runindex = 1 +IF (running(1:2) == 'd2') runindex = 2 +IF (running(1:1) == 't') runindex = 3 +IF (running(1:1) == 'p') runindex = 4 +IF (running(1:2) == 'x1') compon = running(3:3) +IF (running(1:2) == 'x1') READ(compon,*) k +IF (running(1:2) == 'x1') runindex = 4+k +IF (running(1:2) == 'x2') compon = running(3:3) +IF (running(1:2) == 'x2') READ(compon,*) k +IF (running(1:2) == 'x2') runindex = 4+ncomp+k +IF (running(1:2) == 'l1') compon = running(3:3) +IF (running(1:2) == 'l1') READ(compon,*) k +IF (running(1:2) == 'l1') runindex = 4+k +IF (running(1:2) == 'l2') compon = running(3:3) +IF (running(1:2) == 'l2') READ(compon,*) k +IF (running(1:2) == 'l2') runindex = 4+ncomp+k + +maxiter = 200 +IF ( ncomp >= 3 ) maxiter = 1000 +count1 = 0 +count2 = 0 +delta_x = ( end_x - val_init(runindex) ) / steps !J: calc increment in running var = (phi_end - phi_init)/steps +delta_org = ( end_x - val_init(runindex) ) / steps +val_org = val_init(runindex) +IF ( running(1:1) == 'x' ) THEN + delta_x = ( end_x - EXP(val_init(runindex)) ) / steps + delta_org = ( end_x - EXP(val_init(runindex)) ) / steps + val_org = EXP(val_init(runindex)) +END IF + +continue_cycle = .true. + +DO WHILE ( continue_cycle ) + + count1 = count1 + 1 + count2 = count2 + 1 + ! val_org = val_init(runindex) + + + CALL objective_ctrl (converg) + + IF (converg == 1) THEN + val_init( 1:(4+ncomp*nphas) ) = val_conv( 1:(4+ncomp*nphas) ) + IF (outp == 1 .AND. (ABS(delta_x) > 0.1*ABS(delta_org) .OR. count2 == 2)) CALL output + ELSE + delta_x = delta_x / 2.0 + IF (num == 2) delta_x = delta_x / 2.0 + val_init(runindex) = val_org + IF (running(1:1) == 'x') val_init(runindex) = LOG(val_org) + continue_cycle = .true. + count2 = 0 + END IF + runvar = val_init(runindex) + IF (running(1:1) == 'x') runvar = EXP(val_init(runindex)) + + IF ( end_x == 0.0 .AND. running(1:1) /= 'x' ) THEN + IF ( ABS(runvar-end_x) < 1.E-8 ) continue_cycle = .false. + ELSE IF ( ABS((runvar-end_x)/end_x) < 1.E-8 ) THEN + ! IF(delta_org.NE.0.0) WRITE (*,*)' FINISHED ITERATION',count1 + continue_cycle = .false. + ELSE IF ( count1 == maxiter ) THEN + WRITE (*,*) ' MAX. NO OF ITERATIONS',count1 + converg = 0 + continue_cycle = .false. + ELSE IF ( ABS(delta_x) < 1.E-5*ABS(delta_org) ) THEN + ! WRITE (*,*) ' CLOSEST APPROACH REACHED',count1 + converg = 0 + continue_cycle = .false. + ELSE + continue_cycle = .true. + val_org = runvar + IF (ABS(runvar+delta_x-end_x) > ABS(runvar-end_x)) delta_x = end_x - runvar ! if end-point passed + val_init(runindex) = runvar + delta_x + IF (running(1:1) == 'x') val_init(runindex) = LOG(runvar+delta_x) + END IF + + IF (ABS(delta_x) < ABS(delta_org) .AND. count2 >= 5) THEN + delta_x = delta_x * 2.0 + count2 = 0 + END IF + +END DO ! continue_cycle + +END SUBROUTINE phase_equilib + +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! + SUBROUTINE new_flash (ph_it) +! + USE BASIC_VARIABLES + IMPLICIT NONE +! +! ---------------------------------------------------------------------- + INTEGER, INTENT(IN) :: ph_it +! +! ---------------------------------------------------------------------- + INTEGER :: i, ph_cal + REAL, DIMENSION(nc) :: ni_1, ni_2 +! ---------------------------------------------------------------------- + + ph_cal = 3 - ph_it ! for two phases only + + DO i = 1, ncomp + IF ( lnx(ph_it,i) < -300.0 ) THEN + ni_2(i) = 0.0 + ELSE + ni_2(i) = EXP( lnx(ph_it,i) ) + END IF + END DO + + DO i = 1, ncomp + ni_1(i) = xif(i)-ni_2(i) + IF ( ni_2(i) > xif(i) ) THEN + ni_2(i) = xif(i) + ni_1(i) = xif(i) * 1.E-20 + ENDIF + END DO + + xi(ph_it,1:ncomp) = ni_2(1:ncomp) / SUM( ni_2(1:ncomp) ) + DO i = 1, ncomp + IF ( xi(ph_it,i) >= 1.E-300 ) lnx(ph_it,i) = LOG( xi(ph_it,i) ) + END DO + xi(ph_cal,1:ncomp) = ni_1(1:ncomp) / SUM( ni_1(1:ncomp) ) + lnx(ph_cal,1:ncomp) = LOG( xi(ph_cal,1:ncomp) ) + +END SUBROUTINE new_flash + + +!>WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +!! SUBROUTINE PHI_EOS +!! +!! This subroutine gives the residual chemical potential: +!! --> mu_i^res(T,p,x)/kT = ln( phi_i ) when ensemble_flag = 'tp' +!! The required input for this case (T, p, x(nc)) and as a starting value +!! eta_start +!! +!! or it gives +!! +!! --> mu_i^res(T,rho,x)/kT when ensemble_flag = 'tv' +!! The required input for this case (T, eta_start, x(nc)). Note that +!! eta_start is the specified density (packing fraction) in this case. +!!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +!! + SUBROUTINE PHI_EOS +! + USE PARAMETERS + USE EOS_VARIABLES + USE EOS_CONSTANTS + IMPLICIT NONE +! +! --- local variables--------------------------------------------------- + INTEGER :: i, j, k, ki, l, m + REAL :: z0, z1, z2, z3, z0_rk, z1_rk, z2_rk, z3_rk + REAL :: zms, m_mean + REAL, DIMENSION(nc) :: mhs, mdsp, mhc, myres + REAL, DIMENSION(nc) :: m_rk + REAL :: gij_rk(nc,nc) + REAL :: zres, zges + REAL :: dpdz, dpdz2 + + REAL :: I1, I2, I1_rk, I2_rk + REAL :: ord1_rk, ord2_rk + REAL :: c1_con, c2_con, c1_rk + REAL :: zmr, nmr, zmr_rk, nmr_rk, um_rk + REAL, DIMENSION(nc,0:6) :: ap_rk, bp_rk + + LOGICAL :: assoc + REAL :: ass_s2, m_hbon(nc) + + REAL :: fdd_rk, fqq_rk, fdq_rk + REAL, DIMENSION(nc) :: my_dd, my_qq, my_dq +! ---------------------------------------------------------------------- + +! ---------------------------------------------------------------------- +! obtain parameters and density independent expressions +! ---------------------------------------------------------------------- +CALL PERTURBATION_PARAMETER + + +! ---------------------------------------------------------------------- +! density iteration: (pTx)-ensemble OR p calc.: (pvx)-ensemble +! ---------------------------------------------------------------------- +IF (ensemble_flag == 'tp') THEN + CALL DENSITY_ITERATION +ELSEIF (ensemble_flag == 'tv') THEN + eta = eta_start + CALL P_EOS +ELSE + write (*,*) 'PHI_EOS: define ensemble, ensemble_flag == (pv) or (pt)' + stop +END IF + + +! --- Eq.(A.8) --------------------------------------------------------- +rho = eta / z3t +z0 = z0t * rho +z1 = z1t * rho +z2 = z2t * rho +z3 = z3t * rho + +m_mean = z0t / (PI/6.0) +zms = 1.0 - eta + +! ---------------------------------------------------------------------- +! compressibility factor z = p/(kT*rho) +! ---------------------------------------------------------------------- +zges = (p * 1.d-30) / (KBOL*t*rho) +IF ( ensemble_flag == 'tv' ) zges = (pges * 1.d-30) / (KBOL*t*rho) +zres = zges - 1.0 + + + +! ====================================================================== +! calculate the derivatives of f to mole fraction x ( d(f)/d(x) ) +! ====================================================================== + +DO k = 1, ncomp + + z0_rk = PI/6.0 * mseg(k) + z1_rk = PI/6.0 * mseg(k) * dhs(k) + z2_rk = PI/6.0 * mseg(k) * dhs(k)*dhs(k) + z3_rk = PI/6.0 * mseg(k) * dhs(k)**3 + +! --- derivative d(m_mean)/d(x) ---------------------------------------- + m_rk(k) = ( mseg(k) - m_mean ) / rho + ! lij(1,2)= -0.050 + ! lij(2,1)=lij(1,2) + ! r_m2dx(k)=0.0 + ! m_mean2=0.0 + ! DO i =1,ncomp + ! r_m2dx(k)=r_m2dx(k)+2.0*x(i)*(mseg(i)+mseg(k))/2.0*(1.0-lij(i,k)) + ! DO j =1,ncomp + ! m_mean2=m_mean2+x(i)*x(j)*(mseg(i)+mseg(j))/2.0*(1.0-lij(i,j)) + ! ENDDO + ! ENDDO + + ! -------------------------------------------------------------------- + ! d(f)/d(x) : hard sphere contribution + ! -------------------------------------------------------------------- + mhs(k) = 6.0/PI* ( 3.0*(z1_rk*z2+z1*z2_rk)/zms + 3.0*z1*z2*z3_rk/zms/zms & + + 3.0*z2*z2*z2_rk/z3/zms/zms + z2**3 *z3_rk*(3.0*z3-1.0)/z3/z3/zms**3 & + + ((3.0*z2*z2*z2_rk*z3-2.0*z2**3 *z3_rk)/z3**3 -z0_rk) *LOG(zms) & + + (z0-z2**3 /z3/z3)*z3_rk/zms ) + + ! -------------------------------------------------------------------- + ! d(f)/d(x) : chain term + ! -------------------------------------------------------------------- + DO i = 1, ncomp + DO j = 1, ncomp + gij(i,j) = 1.0/zms + 3.0*dij_ab(i,j)*z2/zms/zms + 2.0*(dij_ab(i,j)*z2)**2 /zms**3 + gij_rk(i,j) = z3_rk/zms/zms & + + 3.0*dij_ab(i,j)*(z2_rk+2.0*z2*z3_rk/zms)/zms/zms & + + dij_ab(i,j)**2 *z2/zms**3 *(4.0*z2_rk+6.0*z2*z3_rk/zms) + END DO + END DO + + mhc(k) = 0.0 + DO i = 1, ncomp + mhc(k) = mhc(k) + x(i)*rho * (1.0-mseg(i)) / gij(i,i) * gij_rk(i,i) + END DO + mhc(k) = mhc(k) + ( 1.0-mseg(k)) * LOG( gij(k,k) ) + + + ! -------------------------------------------------------------------- + ! PC-SAFT: d(f)/d(x) : dispersion contribution + ! -------------------------------------------------------------------- + IF (eos == 1) THEN + + ! --- derivatives of apar, bpar to rho_k --------------------------- + DO m = 0, 6 + ap_rk(k,m) = m_rk(k)/m_mean**2 * ( ap(m,2) + (3.0 -4.0/m_mean) *ap(m,3) ) + bp_rk(k,m) = m_rk(k)/m_mean**2 * ( bp(m,2) + (3.0 -4.0/m_mean) *bp(m,3) ) + END DO + + I1 = 0.0 + I2 = 0.0 + I1_rk = 0.0 + I2_rk = 0.0 + DO m = 0, 6 + I1 = I1 + apar(m)*eta**REAL(m) + I2 = I2 + bpar(m)*eta**REAL(m) + I1_rk = I1_rk + apar(m)*REAL(m)*eta**REAL(m-1)*z3_rk + ap_rk(k,m)*eta**REAL(m) + I2_rk = I2_rk + bpar(m)*REAL(m)*eta**REAL(m-1)*z3_rk + bp_rk(k,m)*eta**REAL(m) + END DO + + ord1_rk = 0.0 + ord2_rk = 0.0 + DO i = 1,ncomp + ord1_rk = ord1_rk + 2.0*mseg(k)*rho*x(i)*mseg(i)*sig_ij(i,k)**3 *uij(i,k)/t + ord2_rk = ord2_rk + 2.0*mseg(k)*rho*x(i)*mseg(i)*sig_ij(i,k)**3 *(uij(i,k)/t)**2 + END DO + + c1_con= 1.0/ ( 1.0 + m_mean*(8.0*z3-2.0*z3*z3)/zms**4 & + + (1.0 - m_mean)*(20.0*z3-27.0*z3*z3 +12.0*z3**3 -2.0*z3**4 ) & + /(zms*(2.0-z3))**2 ) + c2_con= - c1_con*c1_con *( m_mean*(-4.0*z3*z3+20.0*z3+8.0)/zms**5 & + + (1.0 - m_mean) *(2.0*z3**3 +12.0*z3*z3-48.0*z3+40.0) & + /(zms*(2.0-z3))**3 ) + c1_rk= c2_con*z3_rk - c1_con*c1_con*m_rk(k) * ( (8.0*z3-2.0*z3*z3)/zms**4 & + - (-2.0*z3**4 +12.0*z3**3 -27.0*z3*z3+20.0*z3) / (zms*(2.0-z3))**2 ) + + mdsp(k) = -2.0*PI* ( order1*rho*rho*I1_rk + ord1_rk*I1 ) & + - PI* c1_con*m_mean * ( order2*rho*rho*I2_rk + ord2_rk*I2 ) & + - PI* ( c1_con*m_rk(k) + c1_rk*m_mean ) * order2*rho*rho*I2 + + ! -------------------------------------------------------------------- + ! SAFT: d(f)/d(x) : dispersion contribution + ! -------------------------------------------------------------------- + ELSE + + zmr = 0.0 + nmr = 0.0 + zmr_rk = 0.0 + nmr_rk = 0.0 + DO i = 1, ncomp + DO j = 1, ncomp + zmr = zmr + x(i)*x(j)*mseg(i)*mseg(j)*vij(i,j)*uij(i,j) + nmr = nmr + x(i)*x(j)*mseg(i)*mseg(j)*vij(i,j) + END DO + zmr_rk = zmr_rk + 2.0*mseg(k) * x(i)*mseg(i)*vij(k,i)*uij(k,i) + nmr_rk = nmr_rk + 2.0*mseg(k) * x(i)*mseg(i)*vij(k,i) + END DO + + um_rk = 1.0/nmr**2 * ( nmr*zmr_rk - zmr*nmr_rk ) + + mdsp(k) = 0.0 + DO i = 1,4 + DO j = 1,9 + mdsp(k) = mdsp(k) + dnm(i,j)*(um/t)**REAL(i)*(eta/tau)**REAL(j) & + * ( 1.0 + z3_rk*rho/eta*REAL(j) + um_rk*rho/um*REAL(i) ) + END DO + END DO + + END IF + ! --- end of dispersion contribution------------------------------------ + + + ! -------------------------------------------------------------------- + ! TPT-1-association according to Chapman et al. + ! -------------------------------------------------------------------- + m_hbon(k) = 0.0 + assoc = .false. + DO i = 1,ncomp + IF (nhb_typ(i) /= 0) assoc = .true. + END DO + IF (assoc) THEN + + ass_s2 = 0.0 + DO l = 1, nhb_typ(k) + ass_s2 = ass_s2 + nhb_no(k,l) * LOG(mx(k,l)) + END DO + + m_hbon(k)=ass_s2 + DO i = 1, ncomp + DO ki = 1, nhb_typ(i) + DO j = 1, ncomp + DO l = 1, nhb_typ(j) + m_hbon(k)= m_hbon(k) - rho*rho/2.0*x(i)*x(j) *mx(i,ki)*mx(j,l) *nhb_no(i,ki)*nhb_no(j,l) & + * gij_rk(i,j) * ass_d(i,j,ki,l) + END DO + END DO + END DO + END DO + + END IF + ! --- end of TPT-1-association accord. to Chapman -------------------- + + + ! -------------------------------------------------------------------- + ! polar terms + ! -------------------------------------------------------------------- + CALL PHI_POLAR ( k, z3_rk, fdd_rk, fqq_rk, fdq_rk ) + my_dd(k) = fdd_rk + my_qq(k) = fqq_rk + my_dq(k) = fdq_rk + + + ! -------------------------------------------------------------------- + ! d(f)/d(x) : summation of all contributions + ! -------------------------------------------------------------------- + myres(k) = mhs(k) +mhc(k) +mdsp(k) +m_hbon(k) +my_dd(k) +my_qq(k) +my_dq(k) + +END DO + + +! ---------------------------------------------------------------------- +! finally calculate +! mu_i^res(T,p,x)/kT = ln( phi_i ) when ensemble_flag = 'tp' +! mu_i^res(T,rho,x)/kT when ensemble_flag = 'tv' +! ---------------------------------------------------------------------- + +DO k = 1, ncomp + ! write (*,*) k,myres(k) +LOG(rho*x(k)),rho + IF (ensemble_flag == 'tp' ) lnphi(k) = myres(k) - LOG(zges) + IF (ensemble_flag == 'tv' ) lnphi(k) = myres(k) + ! write (*,*) 'in',k,EXP(lnphi(k)),LOG(zges),eta +END DO +!write (*,'(5G18.10)') lnphi(1),rho + +dpdz = pgesdz +dpdz2 = pgesd2 + +END SUBROUTINE PHI_EOS + + +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! + SUBROUTINE PHI_NUMERICAL +! + USE EOS_VARIABLES + USE EOS_CONSTANTS + USE DFT_MODULE, ONLY: z_ges, fres_temp + IMPLICIT NONE +! +!-----local variables------------------------------------------------- + INTEGER :: k + REAL :: zres, zges + REAL :: fres1, fres2, fres3, fres4, fres5 + REAL :: delta_rho + REAL, DIMENSION(nc) :: myres + REAL, DIMENSION(nc) :: rhoi, rhoi_0 + REAL :: tfr_1, tfr_2, tfr_3, tfr_4, tfr_5 +!----------------------------------------------------------------------- + + +!----------------------------------------------------------------------- +! density iteration or pressure calculation +!----------------------------------------------------------------------- + +IF (ensemble_flag == 'tp') THEN + CALL DENSITY_ITERATION +ELSEIF (ensemble_flag == 'tv') THEN + eta = eta_start + CALL P_NUMERICAL +ELSE + write (*,*) 'PHI_EOS: define ensemble, ensemble_flag == (tv) or (tp)' + stop +END IF + +!----------------------------------------------------------------------- +! compressibility factor z = p/(kT*rho) +!----------------------------------------------------------------------- + +zges = (p * 1.E-30) / (kbol*t*eta/z3t) +IF ( ensemble_flag == 'tv' ) zges = (pges * 1.E-30) / (kbol*t*eta/z3t) +zres = zges - 1.0 +z_ges = zges + +rhoi_0(1:ncomp) = x(1:ncomp) * eta/z3t +rhoi(1:ncomp) = rhoi_0(1:ncomp) + + +!----------------------------------------------------------------------- +! derivative to rho_k (keeping other rho_i's constant +!----------------------------------------------------------------------- + +DO k = 1, ncomp + + IF ( rhoi_0(k) > 1.d-9 ) THEN + delta_rho = 1.E-13 * 10.0**(0.5*(15.0+LOG10(rhoi_0(k)))) + ELSE + delta_rho = 1.E-10 + END IF + + rhoi(k) = rhoi_0(k) + delta_rho + eta = PI/6.0 * SUM( rhoi(1:ncomp)*mseg(1:ncomp)*dhs(1:ncomp)**3 ) + x(1:ncomp) = rhoi(1:ncomp) / SUM( rhoi(1:ncomp) ) + rho = SUM( rhoi(1:ncomp) ) + CALL F_NUMERICAL + fres1 = fres*rho + tfr_1 = tfr*rho + + rhoi(k) = rhoi_0(k) + 0.5 * delta_rho + eta = PI/6.0 * SUM( rhoi(1:ncomp)*mseg(1:ncomp)*dhs(1:ncomp)**3 ) + x(1:ncomp) = rhoi(1:ncomp) / SUM( rhoi(1:ncomp) ) + rho = SUM( rhoi(1:ncomp) ) + CALL F_NUMERICAL + fres2 = fres*rho + tfr_2 = tfr*rho + + IF ( rhoi_0(k) > 1.E-9 ) THEN + rhoi(k) = rhoi_0(k) - 0.5 * delta_rho + eta = PI/6.0 * SUM( rhoi(1:ncomp)*mseg(1:ncomp)*dhs(1:ncomp)**3 ) + x(1:ncomp) = rhoi(1:ncomp) / SUM( rhoi(1:ncomp) ) + rho = SUM( rhoi(1:ncomp) ) + CALL F_NUMERICAL + fres4 = fres*rho + tfr_4 = tfr*rho + + rhoi(k) = rhoi_0(k) - delta_rho + eta = PI/6.0 * SUM( rhoi(1:ncomp)*mseg(1:ncomp)*dhs(1:ncomp)**3 ) + x(1:ncomp) = rhoi(1:ncomp) / SUM( rhoi(1:ncomp) ) + rho = SUM( rhoi(1:ncomp) ) + CALL F_NUMERICAL + fres5 = fres*rho + tfr_5 = tfr*rho + END IF + + rhoi(k) = rhoi_0(k) + eta = PI/6.0 * SUM( rhoi(1:ncomp)*mseg(1:ncomp)*dhs(1:ncomp)**3 ) + x(1:ncomp) = rhoi(1:ncomp) / SUM( rhoi(1:ncomp) ) + rho = SUM( rhoi(1:ncomp) ) + CALL F_NUMERICAL + fres3 = fres*rho + tfr_3 = tfr*rho + + IF ( rhoi_0(k) > 1.E-9 ) THEN + myres(k) = ( fres5 - 8.0*fres4 + 8.0*fres2 - fres1 ) / ( 6.0*delta_rho ) + ELSE + myres(k) = ( -3.0*fres3 + 4.0*fres2 - fres1 ) / delta_rho + END IF + +END DO + + +!----------------------------------------------------------------------- +! residual Helmholtz energy +!----------------------------------------------------------------------- + +fres_temp = fres + +!----------------------------------------------------------------------- +! residual chemical potential +!----------------------------------------------------------------------- + +DO k = 1, ncomp + IF (ensemble_flag == 'tp') lnphi(k) = myres(k) - LOG(zges) + IF (ensemble_flag == 'tv' .AND. eta >= 0.0) lnphi(k) = myres(k) !+LOG(rho) + ! write (*,*) 'in',k,EXP(lnphi(k)),LOG(zges),eta + ! IF (DFT.GE.98) write (*,*) dft + ! write (*,*) 'lnphi',k,LNPHI(k),x(k),MYRES(k), -LOG(ZGES) + ! pause + ! write (*,*) k, myres(k), fres, ZRES +END DO + +END SUBROUTINE PHI_NUMERICAL + + +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW + +! SUBROUTINE H_EOS (phas,h_res,s_res,cp_res,X,T,P,PARAME, +! 1 KIJ,lij,NCOMP,ETA_START,ETA,eos,tfr) +! IMPLICIT NONE +! INTEGER nc +! PARAMETER (nc=20) +! INTEGER phas,ncomp,eos,i +! REAL kij(nc,nc),lij(nc,nc),x(nc),t,p,parame(nc,25) +! REAL eta_start,eta,tfr,h_res,cp_res,s_res + + +! i=1 + +! IF (i.EQ.1) THEN +! CALL H_EOS_1(phas,h_res,s_res,cp_res,X,T,P,PARAME, +! 1 KIJ,lij,NCOMP,ETA_START,ETA,eos,tfr) +! ELSE +! CALL H_EOS_NUM (phas,h_res,s_res,cp_res,X,T,P,PARAME, +! 1 KIJ,lij,NCOMP,ETA_START,ETA,eos,tfr) +! ENDIF + +! RETURN +! END + + +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! + SUBROUTINE H_EOS +! + USE PARAMETERS, ONLY: RGAS + USE EOS_CONSTANTS + USE EOS_VARIABLES + IMPLICIT NONE +! +! ---------------------------------------------------------------------- + REAL :: zges, df_dt, dfdr, ddfdrdr + REAL :: cv_res, df_dt2, df_drdt + REAL :: fact, dist, t_tmp, rho_0 + REAL :: fdr1, fdr2, fdr3, fdr4 + + INTEGER :: i, m + REAL :: dhsdt(nc), dhsdt2(nc) + REAL :: z0, z1, z2, z3, z1tdt, z2tdt, z3tdt + REAL :: z1dt, z2dt, z3dt, zms, gii + REAL :: fhsdt, fhsdt2 + REAL :: fchdt, fchdt2 + REAL :: fdspdt, fdspdt2 + REAL :: fhbdt, fhbdt2 + REAL :: sumseg, I1, I2, I1dt, I2dt, I1dt2, I2dt2 + REAL :: c1_con, c2_con, c3_con, c1_dt, c1_dt2 + REAL :: z1tdt2, z2tdt2, z3tdt2 + REAL :: z1dt2, z2dt2, z3dt2 + + INTEGER :: j, k, l, no, ass_cnt, max_eval + LOGICAL :: assoc + REAL :: dij, dijdt, dijdt2 + REAL :: gij1dt, gij2dt, gij3dt + REAL :: gij1dt2, gij2dt2, gij3dt2 + REAL, DIMENSION(nc,nc) :: gijdt, gijdt2, kap_hb + REAL, DIMENSION(nc,nc,nsite,nsite) :: ass_d_dt, ass_d_dt2, eps_hb, delta, deltadt, deltadt2 + REAL, DIMENSION(nc,nsite) :: mxdt, mxdt2, mx_itr, mx_itrdt, mx_itrdt2 + REAL :: attenu, tol, suma, sumdt, sumdt2, err_sum + + INTEGER :: dipole + REAL :: fdddt, fdddt2 + REAL, DIMENSION(nc) :: my2dd, my0 + REAL, DIMENSION(nc,nc) :: idd2, idd2dt, idd2dt2, idd4, idd4dt, idd4dt2 + REAL, DIMENSION(nc,nc,nc) :: idd3, idd3dt, idd3dt2 + REAL :: factor2, factor3 + REAL :: fdd2, fdd3, fdd2dt, fdd3dt, fdd2dt2, fdd3dt2 + REAL :: eij, xijmt, xijkmt + + INTEGER :: qudpole + REAL :: fqqdt, fqqdt2 + REAL, DIMENSION(nc) :: qq2 + REAL, DIMENSION(nc,nc) :: iqq2, iqq2dt, iqq2dt2, iqq4, iqq4dt, iqq4dt2 + REAL, DIMENSION(nc,nc,nc) :: iqq3, iqq3dt, iqq3dt2 + REAL :: fqq2, fqq2dt, fqq2dt2, fqq3, fqq3dt, fqq3dt2 + + INTEGER :: dip_quad + REAL :: fdqdt, fdqdt2 + REAL, DIMENSION(nc) :: myfac, q_fac + REAL, DIMENSION(nc,nc) :: idq2, idq2dt, idq2dt2, idq4, idq4dt, idq4dt2 + REAL, DIMENSION(nc,nc,nc) :: idq3, idq3dt, idq3dt2 + REAL :: fdq2, fdq2dt, fdq2dt2, fdq3, fdq3dt, fdq3dt2 +! ---------------------------------------------------------------------- + + +! ---------------------------------------------------------------------- +! Initializing +! ---------------------------------------------------------------------- +CALL PERTURBATION_PARAMETER + +rho = eta/z3t +z0 = z0t*rho +z1 = z1t*rho +z2 = z2t*rho +z3 = z3t*rho + +sumseg = z0t / (PI/6.0) +zms = 1.0 - z3 + + +! ---------------------------------------------------------------------- +! first and second derivative of f to density (dfdr,ddfdrdr) +! ---------------------------------------------------------------------- +CALL P_EOS + +zges = (pges * 1.E-30)/(kbol*t*rho) + +dfdr = pges/(eta*rho*(kbol*t)/1.E-30) +ddfdrdr = pgesdz/(eta*rho*(kbol*t)/1.E-30) - dfdr*2.0/eta - 1.0/eta**2 + + +! ---------------------------------------------------------------------- +! Helmholtz Energy f/kT = fres +! ---------------------------------------------------------------------- +CALL F_EOS + + +! ---------------------------------------------------------------------- +! derivative of some auxilliary properties to temperature +! ---------------------------------------------------------------------- +DO i = 1,ncomp + dhsdt(i)=parame(i,2) *(-3.0*parame(i,3)/t/t)*0.12*EXP(-3.0*parame(i,3)/t) + dhsdt2(i) = dhsdt(i)*3.0*parame(i,3)/t/t & + + 6.0*parame(i,2)*parame(i,3)/t**3 *0.12*EXP(-3.0*parame(i,3)/t) +END DO + +z1tdt = 0.0 +z2tdt = 0.0 +z3tdt = 0.0 +DO i = 1,ncomp + z1tdt = z1tdt + x(i) * mseg(i) * dhsdt(i) + z2tdt = z2tdt + x(i) * mseg(i) * 2.0*dhs(i)*dhsdt(i) + z3tdt = z3tdt + x(i) * mseg(i) * 3.0*dhs(i)*dhs(i)*dhsdt(i) +END DO +z1dt = PI / 6.0*z1tdt *rho +z2dt = PI / 6.0*z2tdt *rho +z3dt = PI / 6.0*z3tdt *rho + + +z1tdt2 = 0.0 +z2tdt2 = 0.0 +z3tdt2 = 0.0 +DO i = 1,ncomp + z1tdt2 = z1tdt2 + x(i)*mseg(i)*dhsdt2(i) + z2tdt2 = z2tdt2 + x(i)*mseg(i)*2.0 *( dhsdt(i)*dhsdt(i) +dhs(i)*dhsdt2(i) ) + z3tdt2 = z3tdt2 + x(i)*mseg(i)*3.0 *( 2.0*dhs(i)*dhsdt(i)* & + dhsdt(i) +dhs(i)*dhs(i)*dhsdt2(i) ) +END DO +z1dt2 = PI / 6.0*z1tdt2 *rho +z2dt2 = PI / 6.0*z2tdt2 *rho +z3dt2 = PI / 6.0*z3tdt2 *rho + + +! ---------------------------------------------------------------------- +! 1st & 2nd derivative of f/kT hard spheres to temp. (fhsdt) +! ---------------------------------------------------------------------- +fhsdt = 6.0/PI/rho*( 3.0*(z1dt*z2+z1*z2dt)/zms + 3.0*z1*z2*z3dt/zms/zms & + + 3.0*z2*z2*z2dt/z3/zms/zms & + + z2**3 *(2.0*z3*z3dt-z3dt*zms)/(z3*z3*zms**3 ) & + + (3.0*z2*z2*z2dt*z3-2.0*z2**3 *z3dt)/z3**3 *LOG(zms) & + + (z0-z2**3 /z3/z3)*z3dt/zms ) + +fhsdt2= 6.0/PI/rho*( 3.0*(z1dt2*z2+2.0*z1dt*z2dt+z1*z2dt2)/zms & + + 6.0*(z1dt*z2+z1*z2dt)*z3dt/zms/zms & + + 3.0*z1*z2*z3dt2/zms/zms + 6.0*z1*z2*z3dt*z3dt/zms**3 & + + 3.0*z2*(2.0*z2dt*z2dt+z2*z2dt2)/z3/zms/zms & + - z2*z2*(6.0*z2dt*z3dt+z2*z3dt2)/(z3*z3*zms*zms) & + + 2.0*z2**3 *z3dt*z3dt/(z3**3 *zms*zms) & + - 4.0*z2**3 *z3dt*z3dt/(z3*z3 *zms**3 ) & + + (12.0*z2*z2*z2dt*z3dt+2.0*z2**3 *z3dt2)/(z3*zms**3 ) & + + 6.0*z2**3 *z3dt*z3dt/(z3*zms**4 ) & + - 2.0*(3.0*z2*z2*z2dt/z3/z3-2.0*z2**3 *z3dt/z3**3 ) *z3dt/zms & + -(z2**3 /z3/z3-z0)*(z3dt2/zms+z3dt*z3dt/zms/zms) & + + ( (6.0*z2*z2dt*z2dt+3.0*z2*z2*z2dt2)/z3/z3 & + - (12.0*z2*z2*z2dt*z3dt+2.0*z2**3 *z3dt2)/z3**3 & + + 6.0*z2**3 *z3dt*z3dt/z3**4 )* LOG(zms) ) + + +! ---------------------------------------------------------------------- +! 1st & 2nd derivative of f/kT of chain term to T (fchdt) +! ---------------------------------------------------------------------- +fchdt = 0.0 +fchdt2 = 0.0 +DO i = 1, ncomp + DO j = 1, ncomp + dij=dhs(i)*dhs(j)/(dhs(i)+dhs(j)) + dijdt =(dhsdt(i)*dhs(j) + dhs(i)*dhsdt(j)) / (dhs(i)+dhs(j)) & + - dhs(i)*dhs(j)/(dhs(i)+dhs(j))**2 *(dhsdt(i)+dhsdt(j)) + dijdt2=(dhsdt2(i)*dhs(j) + 2.0*dhsdt(i)*dhsdt(j) & + + dhs(i)*dhsdt2(j)) / (dhs(i)+dhs(j)) & + - 2.0*(dhsdt(i)*dhs(j) + dhs(i)*dhsdt(j)) & + / (dhs(i)+dhs(j))**2 *(dhsdt(i)+dhsdt(j)) & + + 2.0* dhs(i)*dhs(j) / (dhs(i)+dhs(j))**3 & + * (dhsdt(i)+dhsdt(j))**2 & + - dhs(i)*dhs(j)/(dhs(i)+dhs(j))**2 *(dhsdt2(i)+dhsdt2(j)) + gij1dt = z3dt/zms/zms + gij2dt = 3.0*( z2dt*dij+z2*dijdt )/zms/zms +6.0*z2*dij*z3dt/zms**3 + gij3dt = 4.0*(dij*z2)* (dijdt*z2 + dij*z2dt) /zms**3 & + + 6.0*(dij*z2)**2 * z3dt /zms**4 + gij1dt2 = z3dt2/zms/zms +2.0*z3dt*z3dt/zms**3 + gij2dt2 = 3.0*( z2dt2*dij+2.0*z2dt*dijdt+z2*dijdt2 )/zms/zms & + + 6.0*( z2dt*dij+z2*dijdt )/zms**3 * z3dt & + + 6.0*(z2dt*dij*z3dt+z2*dijdt*z3dt+z2*dij*z3dt2) /zms**3 & + + 18.0*z2*dij*z3dt*z3dt/zms**4 + gij3dt2 = 4.0*(dijdt*z2+dij*z2dt)**2 /zms**3 & + + 4.0*(dij*z2)* (dijdt2*z2+2.0*dijdt*z2dt+dij*z2dt2) /zms**3 & + + 24.0*(dij*z2) *(dijdt*z2+dij*z2dt)/zms**4 *z3dt & + + 6.0*(dij*z2)**2 * z3dt2 /zms**4 & + + 24.0*(dij*z2)**2 * z3dt*z3dt /zms**5 + gijdt(i,j) = gij1dt + gij2dt + gij3dt + gijdt2(i,j) = gij1dt2 + gij2dt2 + gij3dt2 + END DO +END DO + +DO i = 1, ncomp + gii = 1.0/zms + 3.0*dhs(i)/2.0*z2/zms/zms + 2.0*dhs(i)*dhs(i)/4.0*z2*z2/zms**3 + fchdt = fchdt + x(i) * (1.0-mseg(i)) * gijdt(i,i) / gii + fchdt2= fchdt2+ x(i) * (1.0-mseg(i)) & + * (gijdt2(i,i) / gii - (gijdt(i,i)/gii)**2 ) +END DO + + +! ---------------------------------------------------------------------- +! 1st & 2nd derivative of f/kT dispersion term to T (fdspdt) +! ---------------------------------------------------------------------- +I1 = 0.0 +I2 = 0.0 +I1dt = 0.0 +I2dt = 0.0 +I1dt2= 0.0 +I2dt2= 0.0 +DO m = 0, 6 + I1 = I1 + apar(m)*z3**REAL(m) + I2 = I2 + bpar(m)*z3**REAL(m) + I1dt = I1dt + apar(m)*z3dt*REAL(m)*z3**REAL(m-1) + I2dt = I2dt + bpar(m)*z3dt*REAL(m)*z3**REAL(m-1) + I1dt2= I1dt2+ apar(m)*z3dt2*REAL(m)*z3**REAL(m-1) & + + apar(m)*z3dt*z3dt *REAL(m)*REAL(m-1)*z3**REAL(m-2) + I2dt2= I2dt2+ bpar(m)*z3dt2*REAL(m)*z3**REAL(m-1) & + + bpar(m)*z3dt*z3dt *REAL(m)*REAL(m-1)*z3**REAL(m-2) +END DO + +c1_con= 1.0/ ( 1.0 + sumseg*(8.0*z3-2.0*z3**2 )/zms**4 & + + (1.0 - sumseg)*(20.0*z3-27.0*z3**2 +12.0*z3**3 -2.0*z3**4 ) & + /(zms*(2.0-z3))**2 ) +c2_con= - c1_con*c1_con *(sumseg*(-4.0*z3**2 +20.0*z3+8.0)/zms**5 & + + (1.0 - sumseg) *(2.0*z3**3 +12.0*z3**2 -48.0*z3+40.0) & + /(zms*(2.0-z3))**3 ) +c3_con= 2.0 * c2_con*c2_con/c1_con - c1_con*c1_con & + *( sumseg*(-12.0*z3**2 +72.0*z3+60.0)/zms**6 + (1.0 - sumseg) & + *(-6.0*z3**4 -48.0*z3**3 +288.0*z3**2 -480.0*z3+264.0) & + /(zms*(2.0-z3))**4 ) +c1_dt = c2_con*z3dt +c1_dt2 = c3_con*z3dt*z3dt + c2_con*z3dt2 + +fdspdt = - 2.0*PI*rho*(I1dt-I1/t)*order1 & + - PI*rho*sumseg*(c1_dt*I2+c1_con*I2dt-2.0*c1_con*I2/t)*order2 + +fdspdt2 = - 2.0*PI*rho*(I1dt2-2.0*I1dt/t+2.0*I1/t/t)*order1 & + - PI*rho*sumseg*order2*( c1_dt2*I2 +2.0*c1_dt*I2dt -4.0*c1_dt*I2/t & + + 6.0*c1_con*I2/t/t -4.0*c1_con*I2dt/t +c1_con*I2dt2) + + +! ---------------------------------------------------------------------- +! 1st & 2nd derivative of f/kT association term to T (fhbdt) +! ---------------------------------------------------------------------- +fhbdt = 0.0 +fhbdt2 = 0.0 +assoc = .false. +DO i = 1,ncomp + IF ( nhb_typ(i) /= 0 ) assoc = .true. +END DO +IF (assoc) THEN + + DO i = 1,ncomp + IF ( nhb_typ(i) /= 0 ) THEN + kap_hb(i,i) = parame(i,13) + no = 0 + DO j = 1,nhb_typ(i) + DO k = 1,nhb_typ(i) + eps_hb(i,i,j,k) = parame(i,(14+no)) + no = no + 1 + END DO + END DO + DO j = 1,nhb_typ(i) + no = no + 1 + END DO + ELSE + kap_hb(i,i) = 0.0 + DO k = 1,nsite + DO l = 1,nsite + eps_hb(i,i,k,l) = 0.0 + END DO + END DO + END IF + END DO + + DO i = 1,ncomp + DO j = 1,ncomp + IF ( i /= j .AND. (nhb_typ(i) /= 0 .AND. nhb_typ(j) /= 0) ) THEN + kap_hb(i,j)= (kap_hb(i,i)*kap_hb(j,j))**0.5 & + *((parame(i,2)*parame(j,2))**3 )**0.5 & + /(0.5*(parame(i,2)+parame(j,2)))**3 + ! kap_hb(i,j)= kap_hb(i,j)*(1.0-k_kij) + DO k = 1,nhb_typ(i) + DO l = 1,nhb_typ(j) + IF (k /= l) THEN + eps_hb(i,j,k,l)=(eps_hb(i,i,k,l)+eps_hb(j,j,l,k))/2.0 + ! eps_hb(i,j,k,l)=eps_hb(i,j,k,l)*(1.0-eps_kij) + END IF + END DO + END DO + END IF + END DO + END DO + IF (nhb_typ(1) == 3) THEN + eps_hb(1,2,3,1)=0.5*(eps_hb(1,1,3,1)+eps_hb(2,2,1,2)) + eps_hb(2,1,1,3) = eps_hb(1,2,3,1) + END IF + IF (nhb_typ(2) == 3) THEN + eps_hb(2,1,3,1)=0.5*(eps_hb(2,2,3,1)+eps_hb(1,1,1,2)) + eps_hb(1,2,1,3) = eps_hb(2,1,3,1) + END IF + + DO i = 1, ncomp + DO k = 1, nhb_typ(i) + DO j = 1, ncomp + DO l = 1, nhb_typ(j) + ! ass_d(i,j,k,l)=kap_hb(i,j) *sig_ij(i,j)**3 *(EXP(eps_hb(i,j,k,l)/t)-1.0) + ass_d_dt(i,j,k,l)= - kap_hb(i,j) *sig_ij(i,j)**3 * eps_hb(i,j,k,l)/t/t*EXP(eps_hb(i,j,k,l)/t) + ass_d_dt2(i,j,k,l)= - kap_hb(i,j) *sig_ij(i,j)**3 & + * eps_hb(i,j,k,l)/t/t*EXP(eps_hb(i,j,k,l)/t) & + * (-2.0/t - eps_hb(i,j,k,l)/t/t) + END DO + END DO + END DO + END DO + + DO i = 1, ncomp + DO k = 1, nhb_typ(i) + DO j = 1, ncomp + DO l = 1, nhb_typ(j) + delta(i,j,k,l)=gij(i,j)*ass_d(i,j,k,l) + deltadt(i,j,k,l) = gijdt(i,j)*ass_d(i,j,k,l) + gij(i,j)*ass_d_dt(i,j,k,l) + deltadt2(i,j,k,l)= gijdt2(i,j)*ass_d(i,j,k,l) & + + 2.0*gijdt(i,j)*ass_d_dt(i,j,k,l) +gij(i,j)*ass_d_dt2(i,j,k,l) + END DO + END DO + END DO + END DO + + +! ------ constants for iteration --------------------------------------- + attenu = 0.7 + tol = 1.E-10 + IF (eta < 0.2) tol = 1.E-11 + IF (eta < 0.01) tol = 1.E-12 + max_eval = 200 + +! ------ initialize mxdt(i,j) ------------------------------------------ + DO i = 1, ncomp + DO k = 1, nhb_typ(i) + mxdt(i,k) = 0.0 + mxdt2(i,k) = 0.0 + END DO + END DO + + +! ------ iterate over all components and all sites --------------------- + DO ass_cnt = 1, max_eval + + DO i = 1, ncomp + DO k = 1, nhb_typ(i) + suma = 0.0 + sumdt = 0.0 + sumdt2= 0.0 + DO j = 1, ncomp + DO l = 1, nhb_typ(j) + suma = suma + x(j)*nhb_no(j,l)* mx(j,l) *delta(i,j,k,l) + sumdt = sumdt + x(j)*nhb_no(j,l)*( mx(j,l) *deltadt(i,j,k,l) & + + mxdt(j,l)*delta(i,j,k,l) ) + sumdt2 = sumdt2 + x(j)*nhb_no(j,l)*( mx(j,l)*deltadt2(i,j,k,l) & + + 2.0*mxdt(j,l)*deltadt(i,j,k,l) + mxdt2(j,l)*delta(i,j,k,l) ) + END DO + END DO + mx_itr(i,k) = 1.0 / (1.0 + suma * rho) + mx_itrdt(i,k)= - mx_itr(i,k)**2 * sumdt*rho + mx_itrdt2(i,k)= +2.0*mx_itr(i,k)**3 * (sumdt*rho)**2 - mx_itr(i,k)**2 *sumdt2*rho + END DO + END DO + + err_sum = 0.0 + DO i = 1, ncomp + DO k = 1, nhb_typ(i) + err_sum = err_sum + ABS(mx_itr(i,k) - mx(i,k)) & + + ABS(mx_itrdt(i,k) - mxdt(i,k)) + ABS(mx_itrdt2(i,k) - mxdt2(i,k)) + mx(i,k) = mx_itr(i,k) * attenu + mx(i,k) * (1.0 - attenu) + mxdt(i,k)=mx_itrdt(i,k)*attenu +mxdt(i,k)* (1.0 - attenu) + mxdt2(i,k)=mx_itrdt2(i,k)*attenu +mxdt2(i,k)* (1.0 - attenu) + END DO + END DO + IF(err_sum <= tol) GO TO 10 + + END DO + WRITE(6,*) 'CAL_PCSAFT: max_eval violated err_sum = ',err_sum,tol + STOP + 10 CONTINUE + + DO i = 1, ncomp + DO k = 1, nhb_typ(i) + ! fhb = fhb + x(i)* nhb_no(i,k)* ( 0.5 * ( 1.0 - mx(i,k) ) + LOG(mx(i,k)) ) + fhbdt = fhbdt + x(i)*nhb_no(i,k) *mxdt(i,k)*(1.0/mx(i,k)-0.5) + fhbdt2= fhbdt2 + x(i)*nhb_no(i,k) *(mxdt2(i,k)*(1.0/mx(i,k)-0.5) & + -(mxdt(i,k)/mx(i,k))**2 ) + END DO + END DO + +END IF + + +! ---------------------------------------------------------------------- +! derivatives of f/kT of dipole-dipole term to temp. (fdddt) +! ---------------------------------------------------------------------- +fdddt = 0.0 +fdddt2 = 0.0 +dipole = 0 +DO i = 1,ncomp + my2dd(i) = 0.0 + IF ( parame(i,6) /= 0.0 .AND. uij(i,i) /= 0.0 ) THEN + dipole = 1 + my2dd(i) = (parame(i,6))**2 *1.E-49 / (uij(i,i)*kbol*mseg(i)*sig_ij(i,i)**3 *1.E-30) + END IF + my0(i) = my2dd(i) ! needed for dipole-quadrupole-term +END DO + +IF (dipole == 1) THEN + DO i = 1,ncomp + DO j = 1,ncomp + idd2(i,j) =0.0 + idd4(i,j) =0.0 + idd2dt(i,j) =0.0 + idd4dt(i,j) =0.0 + idd2dt2(i,j)=0.0 + idd4dt2(i,j)=0.0 + DO m=0,4 + idd2(i,j) = idd2(i,j) +ddp2(i,j,m)*z3**REAL(m) + idd4(i,j) = idd4(i,j) +ddp4(i,j,m)*z3**REAL(m) + idd2dt(i,j)= idd2dt(i,j) +ddp2(i,j,m)*z3dt*REAL(m)*z3**REAL(m-1) + idd4dt(i,j)= idd4dt(i,j) +ddp4(i,j,m)*z3dt*REAL(m)*z3**REAL(m-1) + idd2dt2(i,j)=idd2dt2(i,j)+ddp2(i,j,m)*z3dt2*REAL(m)*z3**REAL(m-1) & + + ddp2(i,j,m)*z3dt**2 *REAL(m)*REAL(m-1)*z3**REAL(m-2) + idd4dt2(i,j)=idd4dt2(i,j)+ddp4(i,j,m)*z3dt2*REAL(m)*z3**REAL(m-1) & + + ddp4(i,j,m)*z3dt**2 *REAL(m)*REAL(m-1)*z3**REAL(m-2) + END DO + DO k = 1,ncomp + idd3(i,j,k) =0.0 + idd3dt(i,j,k) =0.0 + idd3dt2(i,j,k)=0.0 + DO m = 0, 4 + idd3(i,j,k) = idd3(i,j,k) +ddp3(i,j,k,m)*z3**REAL(m) + idd3dt(i,j,k) = idd3dt(i,j,k)+ddp3(i,j,k,m)*z3dt*REAL(m) *z3**REAL(m-1) + idd3dt2(i,j,k)= idd3dt2(i,j,k)+ddp3(i,j,k,m)*z3dt2*REAL(m) & + *z3**REAL(m-1) +ddp3(i,j,k,m)*z3dt**2 *REAL(m)*REAL(m-1) *z3**REAL(m-2) + END DO + END DO + END DO + END DO + + + factor2= -PI *rho + factor3= -4.0/3.0*PI**2 * rho**2 + + fdd2 = 0.0 + fdd3 = 0.0 + fdd2dt= 0.0 + fdd3dt= 0.0 + fdd2dt2= 0.0 + fdd3dt2= 0.0 + DO i = 1, ncomp + DO j = 1, ncomp + xijmt = x(i)*parame(i,3)*parame(i,2)**3 *x(j)*parame(j,3)*parame(j,2)**3 & + / ((parame(i,2)+parame(j,2))/2.0)**3 *my2dd(i)*my2dd(j) + eij = (parame(i,3)*parame(j,3))**0.5 + fdd2 = fdd2 +factor2* xijmt/t/t*(idd2(i,j)+eij/t*idd4(i,j)) + fdd2dt= fdd2dt+ factor2* xijmt/t/t*(idd2dt(i,j)-2.0*idd2(i,j)/t & + +eij/t*idd4dt(i,j)-3.0*eij/t/t*idd4(i,j)) + fdd2dt2=fdd2dt2+factor2*xijmt/t/t*(idd2dt2(i,j)-4.0*idd2dt(i,j)/t & + +6.0*idd2(i,j)/t/t+eij/t*idd4dt2(i,j) & + -6.0*eij/t/t*idd4dt(i,j)+12.0*eij/t**3 *idd4(i,j)) + DO k = 1, ncomp + xijkmt=x(i)*parame(i,3)*parame(i,2)**3 & + *x(j)*parame(j,3)*parame(j,2)**3 & + *x(k)*parame(k,3)*parame(k,2)**3 & + /((parame(i,2)+parame(j,2))/2.0) /((parame(i,2)+parame(k,2))/2.0) & + /((parame(j,2)+parame(k,2))/2.0) *my2dd(i)*my2dd(j)*my2dd(k) + fdd3 =fdd3 +factor3*xijkmt/t**3 *idd3(i,j,k) + fdd3dt =fdd3dt +factor3*xijkmt/t**3 * (idd3dt(i,j,k)-3.0*idd3(i,j,k)/t) + fdd3dt2=fdd3dt2+factor3*xijkmt/t**3 & + *( idd3dt2(i,j,k)-6.0*idd3dt(i,j,k)/t+12.0*idd3(i,j,k)/t/t ) + END DO + END DO + END DO + + IF ( fdd2 < -1.E-100 .AND. fdd3 /= 0.0 ) THEN + fdddt = fdd2* (fdd2*fdd2dt - 2.0*fdd3*fdd2dt+fdd2*fdd3dt) / (fdd2-fdd3)**2 + fdddt2 = ( 2.0*fdd2*fdd2dt*fdd2dt +fdd2*fdd2*fdd2dt2 & + -2.0*fdd2dt**2 *fdd3 -2.0*fdd2*fdd2dt2*fdd3 +fdd2*fdd2*fdd3dt2 ) & + /(fdd2-fdd3)**2 + fdddt * 2.0*(fdd3dt-fdd2dt)/(fdd2-fdd3) + END IF +END IF + + +! ---------------------------------------------------------------------- +! derivatives f/kT of quadrupole-quadrup. term to T (fqqdt) +! ---------------------------------------------------------------------- +fqqdt = 0.0 +fqqdt2 = 0.0 +qudpole = 0 +DO i = 1, ncomp + qq2(i) = (parame(i,7))**2 *1.E-69 / (uij(i,i)*kbol*mseg(i)*sig_ij(i,i)**5 *1.E-50) + IF (qq2(i) /= 0.0) qudpole = 1 +END DO + +IF (qudpole == 1) THEN + + DO i = 1,ncomp + DO j = 1,ncomp + iqq2(i,j) = 0.0 + iqq4(i,j) = 0.0 + iqq2dt(i,j) = 0.0 + iqq4dt(i,j) = 0.0 + iqq2dt2(i,j)= 0.0 + iqq4dt2(i,j)= 0.0 + DO m = 0, 4 + iqq2(i,j) = iqq2(i,j) + qqp2(i,j,m)*z3**REAL(m) + iqq4(i,j) = iqq4(i,j) + qqp4(i,j,m)*z3**REAL(m) + iqq2dt(i,j) = iqq2dt(i,j)+ qqp2(i,j,m)*z3dt*REAL(m)*z3**REAL(m-1) + iqq4dt(i,j) = iqq4dt(i,j)+ qqp4(i,j,m)*z3dt*REAL(m)*z3**REAL(m-1) + iqq2dt2(i,j)= iqq2dt2(i,j)+qqp2(i,j,m)*z3dt2*REAL(m)*z3**REAL(m-1) & + + qqp2(i,j,m)*z3dt**2 *REAL(m)*REAL(m-1)*z3**REAL(m-2) + iqq4dt2(i,j)= iqq4dt2(i,j)+qqp4(i,j,m)*z3dt2*REAL(m)*z3**REAL(m-1) & + + qqp4(i,j,m)*z3dt**2 *REAL(m)*REAL(m-1)*z3**REAL(m-2) + END DO + DO k = 1,ncomp + iqq3(i,j,k) =0.0 + iqq3dt(i,j,k) =0.0 + iqq3dt2(i,j,k)=0.0 + DO m = 0, 4 + iqq3(i,j,k) = iqq3(i,j,k) + qqp3(i,j,k,m)*z3**REAL(m) + iqq3dt(i,j,k) = iqq3dt(i,j,k)+ qqp3(i,j,k,m)*z3dt*REAL(m) * z3**REAL(m-1) + iqq3dt2(i,j,k)= iqq3dt2(i,j,k)+qqp3(i,j,k,m)*z3dt2*REAL(m) * z3**REAL(m-1) & + + qqp3(i,j,k,m)*z3dt**2 *REAL(m)*REAL(m-1)*z3**REAL(m-2) + END DO + END DO + END DO + END DO + + factor2 = -9.0/16.0 * PI *rho + factor3 = 9.0/16.0 * PI**2 * rho**2 + + fqq2 = 0.0 + fqq3 = 0.0 + fqq2dt = 0.0 + fqq3dt = 0.0 + fqq2dt2= 0.0 + fqq3dt2= 0.0 + DO i = 1,ncomp + DO j = 1,ncomp + xijmt = x(i)*uij(i,i)*qq2(i)*sig_ij(i,i)**5 & + * x(j)*uij(j,j)*qq2(j)*sig_ij(j,j)**5 /sig_ij(i,j)**7.0 + eij = (parame(i,3)*parame(j,3))**0.5 + fqq2 = fqq2 +factor2* xijmt/t/t*(iqq2(i,j)+eij/t*iqq4(i,j)) + fqq2dt= fqq2dt +factor2* xijmt/t/t*(iqq2dt(i,j)-2.0*iqq2(i,j)/t & + + eij/t*iqq4dt(i,j)-3.0*eij/t/t*iqq4(i,j)) + fqq2dt2=fqq2dt2+factor2*xijmt/t/t*(iqq2dt2(i,j)-4.0*iqq2dt(i,j)/t & + + 6.0*iqq2(i,j)/t/t+eij/t*iqq4dt2(i,j) & + - 6.0*eij/t/t*iqq4dt(i,j)+12.0*eij/t**3 *iqq4(i,j)) + DO k = 1,ncomp + xijkmt = x(i)*uij(i,i)*qq2(i)*sig_ij(i,i)**5 /sig_ij(i,j)**3 & + * x(j)*uij(j,j)*qq2(j)*sig_ij(j,j)**5 /sig_ij(i,k)**3 & + * x(k)*uij(k,k)*qq2(k)*sig_ij(k,k)**5 /sig_ij(j,k)**3 + fqq3 = fqq3 +factor3*xijkmt/t**3 *iqq3(i,j,k) + fqq3dt = fqq3dt +factor3*xijkmt/t**3 *(iqq3dt(i,j,k)-3.0*iqq3(i,j,k)/t) + fqq3dt2= fqq3dt2+factor3*xijkmt/t**3 & + * ( iqq3dt2(i,j,k)-6.0*iqq3dt(i,j,k)/t+12.0*iqq3(i,j,k)/t/t ) + END DO + END DO + END DO + + IF ( fqq2 /= 0.0 .AND. fqq3 /= 0.0 ) THEN + fqqdt = fqq2* (fqq2*fqq2dt - 2.0*fqq3*fqq2dt+fqq2*fqq3dt) / (fqq2-fqq3)**2 + fqqdt2 = ( 2.0*fqq2*fqq2dt*fqq2dt +fqq2*fqq2*fqq2dt2 & + - 2.0*fqq2dt**2 *fqq3 -2.0*fqq2*fqq2dt2*fqq3 +fqq2*fqq2*fqq3dt2 ) & + / (fqq2-fqq3)**2 + fqqdt * 2.0*(fqq3dt-fqq2dt)/(fqq2-fqq3) + END IF + +END IF + + +! ---------------------------------------------------------------------- +! derivatives f/kT of dipole-quadruppole term to T (fdqdt) +! ---------------------------------------------------------------------- +fdqdt = 0.0 +fdqdt2= 0.0 +dip_quad = 0 +DO i = 1,ncomp + DO j = 1,ncomp + IF (parame(i,6) /= 0.0 .AND. parame(j,7) /= 0.0) dip_quad = 1 + END DO + myfac(i) = parame(i,3)*parame(i,2)**4 *my0(i) + q_fac(i) = parame(i,3)*parame(i,2)**4 *qq2(i) +END DO + +IF (dip_quad == 1) THEN + + DO i = 1,ncomp + DO j = 1,ncomp + idq2(i,j) = 0.0 + idq4(i,j) = 0.0 + idq2dt(i,j) = 0.0 + idq4dt(i,j) = 0.0 + idq2dt2(i,j)= 0.0 + idq4dt2(i,j)= 0.0 + IF ( myfac(i) /= 0.0 .AND. q_fac(j) /= 0.0 ) THEN + DO m = 0, 4 + idq2(i,j) = idq2(i,j) + dqp2(i,j,m)*z3**REAL(m) + idq4(i,j) = idq4(i,j) + dqp4(i,j,m)*z3**REAL(m) + idq2dt(i,j) = idq2dt(i,j)+ dqp2(i,j,m)*z3dt*REAL(m)*z3**REAL(m-1) + idq4dt(i,j) = idq4dt(i,j)+ dqp4(i,j,m)*z3dt*REAL(m)*z3**REAL(m-1) + idq2dt2(i,j)= idq2dt2(i,j)+dqp2(i,j,m)*z3dt2*REAL(m)*z3**REAL(m-1) & + + dqp2(i,j,m)*z3dt**2 *REAL(m)*REAL(m-1)*z3**REAL(m-2) + idq4dt2(i,j)= idq4dt2(i,j)+dqp4(i,j,m)*z3dt2*REAL(m)*z3**REAL(m-1) & + + dqp4(i,j,m)*z3dt**2 *REAL(m)*REAL(m-1)*z3**REAL(m-2) + END DO + + DO k = 1,ncomp + idq3(i,j,k) = 0.0 + idq3dt(i,j,k) = 0.0 + idq3dt2(i,j,k)= 0.0 + IF ( myfac(k) /= 0.0 .OR. q_fac(k) /= 0.0 ) THEN + DO m = 0, 4 + idq3(i,j,k) = idq3(i,j,k) + dqp3(i,j,k,m)*z3**REAL(m) + idq3dt(i,j,k)= idq3dt(i,j,k)+ dqp3(i,j,k,m)*z3dt*REAL(m) *z3**REAL(m-1) + idq3dt2(i,j,k)= idq3dt2(i,j,k)+dqp3(i,j,k,m)*z3dt2*REAL(m) *z3**REAL(m-1) & + + dqp3(i,j,k,m)*z3dt**2 *REAL(m)*REAL(m-1)*z3**REAL(m-2) + END DO + END IF + END DO + END IF + END DO + END DO + + factor2= -9.0/4.0 * PI * rho + factor3= PI**2 * rho**2 + + fdq2 = 0.0 + fdq3 = 0.0 + fdq2dt= 0.0 + fdq3dt= 0.0 + fdq2dt2=0.0 + fdq3dt2=0.0 + DO i = 1,ncomp + DO j = 1,ncomp + IF ( myfac(i) /= 0.0 .AND. q_fac(j) /= 0.0 ) THEN + xijmt = x(i)*myfac(i) * x(j)*q_fac(j) /sig_ij(i,j)**5 + eij = (parame(i,3)*parame(j,3))**0.5 + fdq2 = fdq2 + factor2* xijmt/t/t*(idq2(i,j)+eij/t*idq4(i,j)) + fdq2dt= fdq2dt+ factor2* xijmt/t/t*(idq2dt(i,j)-2.0*idq2(i,j)/t & + + eij/t*idq4dt(i,j)-3.0*eij/t/t*idq4(i,j)) + fdq2dt2 = fdq2dt2+factor2*xijmt/t/t*(idq2dt2(i,j)-4.0*idq2dt(i,j)/t & + + 6.0*idq2(i,j)/t/t+eij/t*idq4dt2(i,j) & + - 6.0*eij/t/t*idq4dt(i,j)+12.0*eij/t**3 *idq4(i,j)) + DO k = 1,ncomp + IF ( myfac(k) /= 0.0 .OR. q_fac(k) /= 0.0 ) THEN + xijkmt= x(i)*x(j)*x(k)/(sig_ij(i,j)*sig_ij(i,k)*sig_ij(j,k))**2 & + * ( myfac(i)*q_fac(j)*myfac(k) & + + myfac(i)*q_fac(j)*q_fac(k)*1.193735 ) + + fdq3 =fdq3 + factor3*xijkmt/t**3 *idq3(i,j,k) + fdq3dt=fdq3dt+ factor3*xijkmt/t**3 * (idq3dt(i,j,k)-3.0*idq3(i,j,k)/t) + fdq3dt2=fdq3dt2+factor3*xijkmt/t**3 & + *( idq3dt2(i,j,k)-6.0*idq3dt(i,j,k)/t+12.0*idq3(i,j,k)/t/t ) + END IF + END DO + END IF + END DO + END DO + + IF (fdq2 /= 0.0 .AND. fdq3 /= 0.0) THEN + fdqdt = fdq2* (fdq2*fdq2dt - 2.0*fdq3*fdq2dt+fdq2*fdq3dt) / (fdq2-fdq3)**2 + fdqdt2 = ( 2.0*fdq2*fdq2dt*fdq2dt +fdq2*fdq2*fdq2dt2 & + - 2.0*fdq2dt**2 *fdq3 -2.0*fdq2*fdq2dt2*fdq3 +fdq2*fdq2*fdq3dt2 ) & + / (fdq2-fdq3)**2 + fdqdt * 2.0*(fdq3dt-fdq2dt)/(fdq2-fdq3) + END IF + +END IF +! ---------------------------------------------------------------------- + + + + +! ---------------------------------------------------------------------- +! total derivative of fres/kT to temperature +! ---------------------------------------------------------------------- + +df_dt = fhsdt + fchdt + fdspdt + fhbdt + fdddt + fqqdt + fdqdt + + + +! ---------------------------------------------------------------------- +! second derivative of fres/kT to T +! ---------------------------------------------------------------------- + +df_dt2 = fhsdt2 +fchdt2 +fdspdt2 +fhbdt2 +fdddt2 +fqqdt2 +fdqdt2 + + + +! ---------------------------------------------------------------------- +! ------ derivatives of fres/kt to density and to T -------------------- +! ---------------------------------------------------------------------- + +! ---------------------------------------------------------------------- +! the analytic derivative of fres/kT to (density and T) (df_drdt) +! is still missing. A numerical differentiation is implemented. +! ---------------------------------------------------------------------- +fact = 1.0 +dist = t * 100.E-5 * fact +t_tmp = t +rho_0 = rho + + +t = t_tmp - 2.0*dist +CALL PERTURBATION_PARAMETER +eta = z3t*rho_0 +CALL P_EOS +fdr1 = pges / (eta*rho_0*(kbol*t)/1.E-30) +t = t_tmp - dist +CALL PERTURBATION_PARAMETER +eta = z3t*rho_0 +CALL P_EOS +fdr2 = pges / (eta*rho_0*(kbol*t)/1.E-30) + +t = t_tmp + dist +CALL PERTURBATION_PARAMETER +eta = z3t*rho_0 +CALL P_EOS +fdr3 = pges / (eta*rho_0*(kbol*t)/1.E-30) + +t = t_tmp + 2.0*dist +CALL PERTURBATION_PARAMETER +eta = z3t*rho_0 +CALL P_EOS +fdr4 = pges / (eta*rho_0*(kbol*t)/1.E-30) + +t = t_tmp +CALL PERTURBATION_PARAMETER +eta = z3t*rho_0 +CALL P_EOS + + +df_drdt = (-fdr4+8.0*fdr3-8.0*fdr2+fdr1)/(12.0*dist) + + + + + +! ---------------------------------------------------------------------- +! thermodynamic properties +! ---------------------------------------------------------------------- + +s_res = ( - df_dt *t - fres )*RGAS + RGAS * LOG(zges) +h_res = ( - t*df_dt + zges-1.0 ) * RGAS *t +cv_res = - ( t*df_dt2 + 2.0*df_dt ) * RGAS*t +cp_res = cv_res - RGAS + RGAS*(zges +eta*t*df_drdt)**2 & + / (1.0 + 2.0*eta*dfdr +eta**2 *ddfdrdr) + +! write (*,*) 'df_... ', df_dt,df_dt2 +! write (*,*) 'kreuz ', zges,eta*t*df_drdt,eta*dfdr, eta**2 *ddfdrdr +! write (*,*) 'h,cv,cp', h_res,cv_res,cp_res + + +END SUBROUTINE H_EOS + + + +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! SUBROUTINE H_EOS_num +! +! This subroutine calculates enthalpies and heat capacities (cp) by +! taking numerical derivatieves. +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! + SUBROUTINE H_EOS_num +! + USE PARAMETERS, ONLY: RGAS + USE EOS_VARIABLES + IMPLICIT NONE +! +!--------------------------------------------------------------------- + REAL :: dist, fact, rho_0 + REAL :: fres1, fres2, fres3, fres4, fres5 + REAL :: f_1, f_2, f_3, f_4 + REAL :: cv_res, t_tmp, zges + REAL :: df_dt, df_dtdt, df_drdt, dfdr, ddfdrdr + +!----------------------------------------------------------------------- + + +CALL PERTURBATION_PARAMETER +rho_0 = eta/z3t + + +fact = 1.0 +dist = t * 100.E-5 * fact + +t_tmp = t + +t = t_tmp - 2.0*dist +CALL PERTURBATION_PARAMETER +eta = z3t*rho_0 +CALL F_EOS +fres1 = fres +t = t_tmp - dist +CALL PERTURBATION_PARAMETER +eta = z3t*rho_0 +CALL F_EOS +fres2 = fres +t = t_tmp + dist +CALL PERTURBATION_PARAMETER +eta = z3t*rho_0 +CALL F_EOS +fres3 = fres +t = t_tmp + 2.0*dist +CALL PERTURBATION_PARAMETER +eta = z3t*rho_0 +CALL F_EOS +fres4 = fres +t = t_tmp +CALL PERTURBATION_PARAMETER +eta = z3t*rho_0 +CALL F_EOS +fres5 = fres +! *(KBOL*T)/1.E-30 + +zges = (p * 1.E-30)/(kbol*t*rho_0) + + +df_dt = (-fres4+8.0*fres3-8.0*fres2+fres1)/(12.0*dist) +df_dtdt = (-fres4+16.0*fres3-3.d1*fres5+16.0*fres2-fres1) & + /(12.0*(dist**2 )) + + +s_res = (- df_dt -fres/t)*RGAS*t + RGAS * LOG(zges) +h_res = ( - t*df_dt + zges-1.0 ) * RGAS*t +cv_res = -( t*df_dtdt + 2.0*df_dt ) * RGAS*t + + + +t = t_tmp - 2.0*dist +CALL PERTURBATION_PARAMETER +eta = z3t*rho_0 +CALL P_EOS +f_1 = pges/(eta*rho_0*(kbol*t)/1.E-30) + +t = t_tmp - dist +CALL PERTURBATION_PARAMETER +eta = z3t*rho_0 +CALL P_EOS +f_2 = pges/(eta*rho_0*(kbol*t)/1.E-30) + +t = t_tmp + dist +CALL PERTURBATION_PARAMETER +eta = z3t*rho_0 +CALL P_EOS +f_3 = pges/(eta*rho_0*(kbol*t)/1.E-30) + +t = t_tmp + 2.0*dist +CALL PERTURBATION_PARAMETER +eta = z3t*rho_0 +CALL P_EOS +f_4 = pges/(eta*rho_0*(kbol*t)/1.E-30) + +t = t_tmp +CALL PERTURBATION_PARAMETER +eta = z3t*rho_0 +CALL P_EOS + +dfdr = pges / (eta*rho_0*(kbol*t)/1.E-30) +ddfdrdr = pgesdz/(eta*rho_0*(kbol*t)/1.E-30) - dfdr*2.0/eta - 1.0/eta**2 + +df_drdt = ( -f_4 +8.0*f_3 -8.0*f_2 +f_1) / (12.0*dist) + +cp_res = cv_res - RGAS +RGAS*(zges+eta*t*df_drdt)**2 & + * 1.0/(1.0 + 2.0*eta*dfdr + eta**2 *ddfdrdr) + +! write (*,*) 'n',df_dt,df_dtdt +! write (*,*) 'kreuz ', zges,eta*t*df_drdt,eta*dfdr, eta**2 *ddfdrdr +! write (*,*) 'h, cv', h_res, cv_res +! write (*,*) h_res - t*s_res +! write (*,*) cv_res,cp_res,eta +! pause + +END SUBROUTINE H_EOS_num + + +!>WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +!! SUBROUTINE DENSITY_ITERATION +!! +!! iterates the density until the calculated pressure 'pges' is equal to +!! the specified pressure 'p'. A Newton-scheme is used for determining +!! the root to the objective function f(eta) = (pges / p ) - 1.0. +!!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +!! + SUBROUTINE DENSITY_ITERATION +! + USE BASIC_VARIABLES, ONLY: num + USE EOS_VARIABLES + IMPLICIT NONE +! +! ---------------------------------------------------------------------- + INTEGER :: i, start, max_i + REAL :: eta_iteration + REAL :: error, dydx, acc_i, delta_eta +! ---------------------------------------------------------------------- + + +IF ( densav(phas) /= 0.0 .AND. eta_start == denold(phas) ) THEN + denold(phas) = eta_start + eta_start = densav(phas) +ELSE + denold(phas) = eta_start + densav(phas) = eta_start +END IF + + +acc_i = 1.d-9 +max_i = 30 +density_error(:) = 0.0 + +i = 0 +eta_iteration = eta_start + +! ---------------------------------------------------------------------- +! iterate density until p_calc = p +! ---------------------------------------------------------------------- +iterate_density: DO + + i = i + 1 + eta = eta_iteration + + IF ( num == 0 ) THEN + CALL P_EOS + ELSE IF ( num == 1 ) THEN + CALL P_NUMERICAL + ELSE IF ( num == 2 ) THEN + WRITE(*,*) 'CRITICAL RENORM NOT INCLUDED YET' + !!CALL F_EOS_RN + ELSE + write (*,*) 'define calculation option (num)' + END IF + + error = (pges / p ) - 1.0 + + ! --- instable region correction ------------------------------------- + IF ( pgesdz < 0.0 .AND. i < max_i ) THEN + IF ( error > 0.0 .AND. pgesd2 > 0.0 ) THEN ! no liquid density + CALL PRESSURE_SPINODAL + eta_iteration = eta + error = (pges / p ) - 1.0 + IF ( ((pges/p ) -1.0) > 0.0 ) eta_iteration = 0.001 ! no solution possible + IF ( ((pges/p ) -1.0) <=0.0 ) eta_iteration = eta_iteration * 1.1 ! no solution found so far + ELSE IF ( error < 0.0 .AND. pgesd2 < 0.0 ) THEN ! no vapor density + CALL PRESSURE_SPINODAL + eta_iteration = eta + error = (pges / p ) - 1.0 + IF ( ((pges/p ) -1.0) < 0.0 ) eta_iteration = 0.5 ! no solution possible + IF ( ((pges/p ) -1.0) >=0.0 ) eta_iteration = eta_iteration * 0.9 ! no solution found so far + ELSE + eta_iteration = (eta_iteration + eta_start) / 2.0 + IF (eta_iteration == eta_start) eta_iteration = eta_iteration + 0.2 + END IF + CYCLE iterate_density + END IF + + + dydx = pgesdz/p + delta_eta = error/ dydx + IF ( delta_eta > 0.05 ) delta_eta = 0.05 + IF ( delta_eta < -0.05 ) delta_eta = -0.05 + + eta_iteration = eta_iteration - delta_eta + + IF (eta_iteration > 0.9) eta_iteration = 0.6 + IF (eta_iteration <= 0.0) eta_iteration = 1.E-16 + start = 1 + + IF ( ABS(error*p/pgesdz) < 1.d-12 ) start = 0 + IF ( ABS(error) < acc_i ) start = 0 + IF ( i > max_i ) THEN + start = 0 + density_error(phas) = ABS( error ) + ! write (*,*) 'density iteration failed' + END IF + + IF (start /= 1) EXIT iterate_density + +END DO iterate_density + +eta = eta_iteration + +IF ((eta > 0.3 .AND. densav(phas) > 0.3) .OR. & + (eta < 0.1 .AND. densav(phas) < 0.1)) densav(phas) = eta + +END SUBROUTINE DENSITY_ITERATION + + + + +!>WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +!! SUBROUTINE F_EOS +!! +!! calculates the Helmholtz energy f/kT. The input to the subroutine is +!! (T,eta,x), where eta is the packing fraction. +!!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +!! + SUBROUTINE F_EOS +! + USE PARAMETERS, ONLY: nc, nsite + USE EOS_VARIABLES + USE EOS_CONSTANTS + IMPLICIT NONE +! +! --- local variables -------------------------------------------------- + INTEGER :: i, j, k, l, m, n + REAL :: z0, z1, z2, z3 + REAL :: zms, m_mean ! ,lij(nc,nc) + REAL :: I1,I2, c1_con + REAL :: fhs, fdsp, fhc + + LOGICAL :: assoc + INTEGER :: ass_cnt,max_eval + REAL :: delta(nc,nc,nsite,nsite) + REAL :: mx_itr(nc,nsite), err_sum, sum, attenu, tol, fhb + REAL :: ass_s1, ass_s2 + + REAL :: fdd, fqq, fdq +! ---------------------------------------------------------------------- + + +! ---------------------------------------------------------------------- +! abbreviations +! ---------------------------------------------------------------------- +rho = eta/z3t +z0 = z0t*rho +z1 = z1t*rho +z2 = z2t*rho +z3 = z3t*rho + +m_mean = z0t / ( PI / 6.0 ) +zms = 1.0 - eta + +! m_mean2 = 0.0 +! lij(1,2) = -0.05 +! lij(2,1) = lij(1,2) +! DO i = 1, ncomp +! DO j = 1, ncomp +! m_mean2 = m_mean2 + x(i)*x(j)*(mseg(i)+mseg(j))/2.0*(1.0-lij(i,j)) +! ENDDO +! ENDDO + + +! ---------------------------------------------------------------------- +! radial distr. function at contact, gij +! ---------------------------------------------------------------------- +DO i = 1, ncomp + DO j=1,ncomp + gij(i,j) = 1.0/zms + 3.0*dij_ab(i,j)*z2/zms/zms + 2.0*(dij_ab(i,j)*z2)**2 /zms**3 + END DO +END DO + + +! ---------------------------------------------------------------------- +! Helmholtz energy : hard sphere contribution +! ---------------------------------------------------------------------- +fhs= m_mean*( 3.0*z1*z2/zms + z2**3 /z3/zms/zms + (z2**3 /z3/z3-z0)*LOG(zms) )/z0 + + +! ---------------------------------------------------------------------- +! Helmholtz energy : chain term +! ---------------------------------------------------------------------- +fhc = 0.0 +DO i = 1, ncomp + fhc = fhc + x(i) *(1.0- mseg(i)) *LOG(gij(i,i)) +END DO + + +! ---------------------------------------------------------------------- +! Helmholtz energy : PC-SAFT dispersion contribution +! ---------------------------------------------------------------------- +IF (eos == 1) THEN + + I1 = 0.0 + I2 = 0.0 + DO m = 0, 6 + I1 = I1 + apar(m)*eta**REAL(m) + I2 = I2 + bpar(m)*eta**REAL(m) + END DO + + c1_con= 1.0/ ( 1.0 + m_mean*(8.0*eta-2.0*eta**2 )/zms**4 & + + (1.0 - m_mean)*(20.0*eta-27.0*eta**2 & + + 12.0*eta**3 -2.0*eta**4 ) /(zms*(2.0-eta))**2 ) + + fdsp = -2.0*PI*rho*I1*order1 - PI*rho*c1_con*m_mean*I2*order2 + +! ---------------------------------------------------------------------- +! Helmholtz energy : SAFT (Chen, Kreglewski) dispersion contribution +! ---------------------------------------------------------------------- +ELSE + + fdsp = 0.0 + DO n = 1,4 + DO m = 1,9 + fdsp = fdsp + dnm(n,m) * (um/t)**REAL(n) *(eta/tau)**REAL(m) + END DO + END DO + fdsp = m_mean * fdsp + +END IF + + +! ---------------------------------------------------------------------- +! TPT-1-association according to Chapman et al. +! ---------------------------------------------------------------------- +fhb = 0.0 +assoc = .false. +DO i = 1, ncomp + IF (nhb_typ(i) /= 0) assoc = .true. +END DO +IF (assoc) THEN + + DO i = 1, ncomp + DO k = 1, nhb_typ(i) + IF (mx(i,k) == 0.0) mx(i,k) = 1.0 ! Initialize mx(i,j) + DO j = 1, ncomp + DO l = 1, nhb_typ(j) + delta(i,j,k,l) = gij(i,j) * ass_d(i,j,k,l) + END DO + END DO + END DO + END DO + + +! --- constants for iteration ------------------------------------------ + attenu = 0.70 + tol = 1.d-10 + IF (eta < 0.2) tol = 1.d-12 + IF (eta < 0.01) tol = 1.d-13 + max_eval = 200 + +! --- iterate over all components and all sites ------------------------ + ass_cnt = 0 + iterate_TPT1: DO + + ass_cnt = ass_cnt + 1 + + DO i = 1, ncomp + DO k = 1, nhb_typ(i) + sum = 0.0 + DO j = 1, ncomp + DO l = 1, nhb_typ(j) + sum = sum + x(j)* mx(j,l)*nhb_no(j,l) *delta(i,j,k,l) +! if (ass_cnt == 1) write (*,*) j,l,x(j), mx(j,l) + END DO + END DO + mx_itr(i,k) = 1.0 / (1.0 + sum * rho) +! if (ass_cnt == 1) write (*,*) 'B',ass_cnt,sum, rho + END DO + END DO + + err_sum = 0.0 + DO i = 1, ncomp + DO k = 1, nhb_typ(i) + err_sum = err_sum + ABS(mx_itr(i,k) - mx(i,k)) ! / ABS(mx_itr(i,k)) + mx(i,k) = mx_itr(i,k) * attenu + mx(i,k) * (1.0 - attenu) + END DO + END DO + + IF ( err_sum <= tol .OR. ass_cnt >= max_eval ) THEN + IF (ass_cnt >= max_eval) WRITE(*,'(a,2G15.7)') 'F_EOS: Max_eval violated (mx) Err_Sum = ',err_sum,tol + EXIT iterate_TPT1 + END IF + + END DO iterate_TPT1 + + DO i = 1, ncomp + ass_s1 = 0.0 + ass_s2 = 0.0 + DO k = 1, nhb_typ(i) + ass_s1 = ass_s1 + nhb_no(i,k) * ( 1.0 - mx(i,k) ) + ass_s2 = ass_s2 + nhb_no(i,k) * LOG( mx(i,k) ) + END DO + fhb = fhb + x(i) * ( ass_s2 + ass_s1 / 2.0 ) + END DO + +END IF +! --- TPT-1-association accord. to Chapman ----------------------------- + + +! ---------------------------------------------------------------------- +! polar terms +! ---------------------------------------------------------------------- + CALL F_POLAR ( fdd, fqq, fdq ) + + +! ---------------------------------------------------------------------- +! resid. Helmholtz energy f/kT +! ---------------------------------------------------------------------- +fres = fhs + fhc + fdsp + fhb + fdd + fqq + fdq + +tfr= fres + +END SUBROUTINE F_EOS + + +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! + SUBROUTINE F_NUMERICAL +! + USE EOS_VARIABLES + USE EOS_CONSTANTS + USE EOS_NUMERICAL_DERIVATIVES, ONLY: ideal_gas, hard_sphere, chain_term, & + disp_term, hb_term, LC_term, branch_term, & + II_term, ID_term, subtract1, subtract2 + IMPLICIT NONE +! +!--------------------------------------------------------------------- + +!-----local variables------------------------------------------------- + INTEGER :: i, j + REAL :: m_mean2 + REAL :: fid, fhs, fdsp, fhc + REAL :: fhb, fdd, fqq, fdq + REAL :: fhend, fcc + REAL :: fbr, flc + REAL :: fref + + REAL :: eps_kij, k_kij +!--------------------------------------------------------------------- + +eps_kij = 0.0 +k_kij = 0.0 + +fid = 0.0 +fhs = 0.0 +fhc = 0.0 +fdsp= 0.0 +fhb = 0.0 +fdd = 0.0 +fqq = 0.0 +fdq = 0.0 +fcc = 0.0 +fbr = 0.0 +flc = 0.0 + + +CALL PERTURBATION_PARAMETER + +! ---------------------------------------------------------------------- +! overwrite the standard mixing rules by those published by Tang & Gross +! using an additional lij parameter +! WARNING : the lij parameter is set to lij = - lji in 'para_input' +! ---------------------------------------------------------------------- +order1 = 0.0 +order2 = 0.0 +DO i = 1, ncomp + DO j = 1, ncomp + order1 = order1 + x(i)*x(j)* mseg(i)*mseg(j) * sig_ij(i,j)**3 * uij(i,j)/t + order2 = order2 + x(i)*x(j)* mseg(i)*mseg(j) * sig_ij(i,j)**3 * (uij(i,j)/t)**2 + END DO +END DO +DO i = 1, ncomp + DO j = 1, ncomp + order1 = order1 + x(i)*mseg(i)/t*( x(j)*mseg(j) & + *sig_ij(i,j)*(uij(i,i)*uij(j,j))**(1.0/6.0) )**3 *lij(i,j) + END DO +END DO + + +! ---------------------------------------------------------------------- +! a non-standard mixing rule scaling the hard-sphere term +! WARNING : the lij parameter is set to lij = - lji in 'para_input' +! (uses an additional lij parameter) +! ---------------------------------------------------------------------- +m_mean2 = 0.0 +DO i = 1, ncomp + DO j = 1, ncomp + m_mean2 = m_mean2 + x(i)*x(j)*(mseg(i)+mseg(j))/2.0 + END DO +END DO +DO i = 1, ncomp + DO j = 1, ncomp + ! m_mean2=m_mean2+x(i)*(x(j)*((mseg(i)+mseg(j))*0.5)**(1.0/3.0) *lij(i,j) )**3 + END DO +END DO + +! --- ideal gas contribution ------------------------------------------- +IF ( ideal_gas == 'yes' ) CALL F_IDEAL_GAS ( fid ) +! ---------------------------------------------------------------------- + +! --- hard-sphere contribution ----------------------------------------- +IF ( hard_sphere == 'CSBM' ) CALL F_HARD_SPHERE ( m_mean2, fhs ) +! ---------------------------------------------------------------------- + +! -- chain term -------------------------------------------------------- +IF ( chain_term == 'TPT1' ) CALL F_CHAIN_TPT1 ( fhc ) +IF ( chain_term == 'TPT2' ) CALL F_CHAIN_TPT_D ( fhc ) +IF ( chain_term == 'HuLiu' ) CALL F_CHAIN_HU_LIU ( fhc ) +IF ( chain_term == 'HuLiu_rc' ) CALL F_CHAIN_HU_LIU_RC ( fhs, fhc ) +!!IF ( chain_term == 'SPT' ) CALL F_SPT ( fhs, fhc ) +IF ( chain_term == 'SPT' ) WRITE(*,*) 'SPT NOT INCLUDED YET' +! ---------------------------------------------------------------------- + +! --- dispersive attraction -------------------------------------------- +IF ( disp_term == 'PC-SAFT') CALL F_DISP_PCSAFT ( fdsp ) +IF ( disp_term == 'CK') CALL F_DISP_CKSAFT ( fdsp ) +IF ( disp_term(1:2) == 'PT') CALL F_pert_theory ( fdsp ) +! ---------------------------------------------------------------------- + +! --- H-bonding contribution / Association ----------------------------- +IF ( hb_term == 'TPT1_Chap') CALL F_ASSOCIATION( eps_kij, k_kij, fhb ) +! ---------------------------------------------------------------------- + +! --- polar terms ------------------------------------------------------ + CALL F_POLAR ( fdd, fqq, fdq ) +! ---------------------------------------------------------------------- + +! --- ion-dipole term -------------------------------------------------- +IF ( ID_term == 'TBH') CALL F_ION_DIPOLE_TBH ( fhend ) +! ---------------------------------------------------------------------- + +! --- ion-ion term ----------------------------------------------------- +IF ( II_term == 'primMSA') CALL F_ION_ION_PrimMSA ( fcc ) +IF ( II_term == 'nprMSA') CALL F_ION_ION_nonPrimMSA ( fdd, fqq, fdq, fcc ) +! ---------------------------------------------------------------------- + +! --- liquid-crystal term ---------------------------------------------- +IF ( LC_term == 'MSaupe') CALL F_LC_MayerSaupe ( flc ) + +!!IF ( LC_term == 'OVL') fref = fhs + fhc +IF ( LC_term == 'OVL') WRITE(*,*) 'OVL NOT INCLUDED YET' +!IF ( LC_term == 'OVL') CALL F_LC_OVL ( fref, flc ) +!! IF ( LC_term == 'SPT') fref = fhs + fhc +IF ( LC_term == 'SPT') WRITE(*,*) 'SPT NOT INCLUDED YET' +!!IF ( LC_term == 'SPT') CALL F_LC_SPT( fref, flc ) +! ---------------------------------------------------------------------- + +! ====================================================================== +! SUBTRACT TERMS (local density approximation) FOR DFT +! ====================================================================== + +!IF ( subtract1 == '1PT') CALL F_subtract_local_pert_theory ( subtract1, fdsp ) +!IF ( subtract1 == '2PT') CALL F_subtract_local_pert_theory ( subtract1, fdsp ) +!IF ( subtract2 =='ITTpolar') CALL F_local_ITT_polar ( fdd ) +! ---------------------------------------------------------------------- + +! ---------------------------------------------------------------------- +! residual Helmholtz energy F/(NkT) +! ---------------------------------------------------------------------- +fres = fid + fhs + fhc + fdsp + fhb + fdd + fqq + fdq + fcc + flc + +tfr = 0.0 + +END SUBROUTINE F_NUMERICAL + + + +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! SUBROUTINE P_EOS +! +! calculates the pressure in units (Pa). +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! + SUBROUTINE P_EOS +! +! ---------------------------------------------------------------------- + USE PARAMETERS, ONLY: nc, nsite + USE EOS_VARIABLES + USE EOS_CONSTANTS + IMPLICIT NONE +! +! --- local variables -------------------------------------------------- + INTEGER :: i, j, k, l, m, n + INTEGER :: ass_cnt,max_eval + LOGICAL :: assoc + REAL :: z0, z1, z2, z3 + REAL :: zms, m_mean + REAL :: zges, zgesdz, zgesd2, zgesd3 + REAL :: zhs, zhsdz, zhsd2, zhsd3 + REAL :: zhc, zhcdz, zhcd2, zhcd3 + REAL, DIMENSION(nc,nc) :: dgijdz, dgijd2, dgijd3, dgijd4 + REAL :: zdsp, zdspdz, zdspd2, zdspd3 + REAL :: c1_con, c2_con, c3_con, c4_con, c5_con + REAL :: I2, edI1dz, edI2dz, edI1d2, edI2d2 + REAL :: edI1d3, edI2d3, edI1d4, edI2d4 + REAL :: fdspdz,fdspd2 + REAL :: zhb, zhbdz, zhbd2, zhbd3 + REAL, DIMENSION(nc,nc,nsite,nsite) :: delta, dq_dz, dq_d2, dq_d3, dq_d4 + REAL, DIMENSION(nc,nsite) :: mx_itr, dmx_dz, ndmxdz, dmx_d2, ndmxd2 + REAL, DIMENSION(nc,nsite) :: dmx_d3, ndmxd3, dmx_d4, ndmxd4 + REAL :: err_sum, sum0, sum1, sum2, sum3, sum4, attenu, tol + REAL :: sum_d1, sum_d2, sum_d3, sum_d4 + REAL :: zdd, zddz, zddz2, zddz3 + REAL :: zqq, zqqz, zqqz2, zqqz3 + REAL :: zdq, zdqz, zdqz2, zdqz3 +! ---------------------------------------------------------------------- + + +! ---------------------------------------------------------------------- +! abbreviations +! ---------------------------------------------------------------------- +rho = eta/z3t +z0 = z0t*rho +z1 = z1t*rho +z2 = z2t*rho +z3 = z3t*rho + +m_mean = z0t/(PI/6.0) +zms = 1.0 -eta + +! m_mean2=0.0 +! lij(1,2)= -0.050 +! lij(2,1)=lij(1,2) +! DO i =1,ncomp +! DO j =1,ncomp +! m_mean2=m_mean2+x(i)*x(j) * (mseg(i)+mseg(j))/2.0*(1.0-lij(i,j)) +! ENDDO +! ENDDO + + +! ---------------------------------------------------------------------- +! radial distr. function at contact, gij , and derivatives +! dgijdz=d(gij)/d(eta) and dgijd2 = dd(gij)/d(eta)**2 +! ---------------------------------------------------------------------- +DO i = 1, ncomp + DO j=1,ncomp + ! j=i + gij(i,j) = 1.0/zms + 3.0*dij_ab(i,j)*z2/zms/zms + 2.0*(dij_ab(i,j)*z2)**2 /zms**3 + dgijdz(i,j)= 1.0/zms/zms + 3.0*dij_ab(i,j)*z2*(1.0+z3)/z3/zms**3 & + + (dij_ab(i,j)*z2/zms/zms)**2 *(4.0+2.0*z3)/z3 + dgijd2(i,j) = 2.0/zms**3 & + + 6.0*dij_ab(i,j)*z2/z3/zms**4 *(2.0+z3) & + + (2.0*dij_ab(i,j)*z2/z3)**2 /zms**5 *(1.0+4.0*z3+z3*z3) + dgijd3(i,j) = 6.0/zms**4 & + + 18.0*dij_ab(i,j)*z2/z3/zms**5 *(3.0+z3) & + + 12.0*(dij_ab(i,j)*z2/z3/zms**3 )**2 *(3.0+6.0*z3+z3*z3) + dgijd4(i,j) = 24.0/zms**5 & + + 72.0*dij_ab(i,j)*z2/z3/zms**6 *(4.0+z3) & + + 48.0*(dij_ab(i,j)*z2/z3)**2 /zms**7 *(6.0+8.0*z3+z3*z3) + END DO +END DO + + +! ---------------------------------------------------------------------- +! p : hard sphere contribution +! ---------------------------------------------------------------------- +zhs = m_mean* ( z3/zms + 3.0*z1*z2/z0/zms/zms + z2**3 /z0*(3.0-z3)/zms**3 ) +zhsdz = m_mean*( 1.0/zms/zms + 3.0*z1*z2/z0/z3*(1.0+z3)/zms**3 & + + 6.0*z2**3 /z0/z3/zms**4 ) +zhsd2 = m_mean*( 2.0/zms**3 + 6.0*z1*z2/z0/z3*(2.0+z3)/zms**4 & + + 6.0*z2**3 /z0/z3/z3*(1.0+3.0*z3)/zms**5 ) +zhsd3 = m_mean*( 6.0/zms**4 + 18.0*z1*z2/z0/z3*(3.0+z3)/zms**5 & + + 24.0*z2**3 /z0/z3/z3*(2.0+3.0*z3)/zms**6 ) + + +! ---------------------------------------------------------------------- +! p : chain term +! ---------------------------------------------------------------------- +zhc = 0.0 +zhcdz = 0.0 +zhcd2 = 0.0 +zhcd3 = 0.0 +DO i= 1, ncomp + zhc = zhc + x(i)*(1.0-mseg(i))*eta/gij(i,i)* dgijdz(i,i) + zhcdz = zhcdz + x(i)*(1.0-mseg(i)) *(-eta*(dgijdz(i,i)/gij(i,i))**2 & + + dgijdz(i,i)/gij(i,i) + eta/gij(i,i)*dgijd2(i,i)) + zhcd2 = zhcd2 + x(i)*(1.0-mseg(i)) & + *( 2.0*eta*(dgijdz(i,i)/gij(i,i))**3 & + -2.0*(dgijdz(i,i)/gij(i,i))**2 & + -3.0*eta/gij(i,i)**2 *dgijdz(i,i)*dgijd2(i,i) & + +2.0/gij(i,i)*dgijd2(i,i) +eta/gij(i,i)*dgijd3(i,i) ) + zhcd3 = zhcd3 + x(i)*(1.0-mseg(i)) *( 6.0*(dgijdz(i,i)/gij(i,i))**3 & + -6.0*eta*(dgijdz(i,i)/gij(i,i))**4 & + +12.0*eta/gij(i,i)**3 *dgijdz(i,i)**2 *dgijd2(i,i) & + -9.0/gij(i,i)**2 *dgijdz(i,i)*dgijd2(i,i) +3.0/gij(i,i)*dgijd3(i,i) & + -3.0*eta*(dgijd2(i,i)/gij(i,i))**2 & + -4.0*eta/gij(i,i)**2 *dgijdz(i,i)*dgijd3(i,i) & + +eta/gij(i,i)*dgijd4(i,i) ) +END DO + +! ---------------------------------------------------------------------- +! p : PC-SAFT dispersion contribution +! note: edI1dz is equal to d(eta*I1)/d(eta), analogous for edI2dz +! ---------------------------------------------------------------------- +IF (eos == 1) THEN + + I2 = 0.0 + edI1dz = 0.0 + edI2dz = 0.0 + edI1d2 = 0.0 + edI2d2 = 0.0 + edI1d3 = 0.0 + edI2d3 = 0.0 + edI1d4 = 0.0 + edI2d4 = 0.0 + DO m=0,6 + I2 = I2 + bpar(m)*z3**REAL(m) + edI1dz= edI1dz+apar(m)*REAL(m+1)*z3**REAL(m) + edI2dz= edI2dz+bpar(m)*REAL(m+1)*z3**REAL(m) + edI1d2= edI1d2+apar(m)*REAL((m+1)*m)*z3**REAL(m-1) + edI2d2= edI2d2+bpar(m)*REAL((m+1)*m)*z3**REAL(m-1) + edI1d3= edI1d3+apar(m)*REAL((m+1)*m*(m-1))*z3**REAL(m-2) + edI2d3= edI2d3+bpar(m)*REAL((m+1)*m*(m-1))*z3**REAL(m-2) + edI1d4= edI1d4+apar(m)*REAL((m+1)*m*(m-1)*(m-2))*z3**REAL(m-3) + edI2d4= edI2d4+bpar(m)*REAL((m+1)*m*(m-1)*(m-2))*z3**REAL(m-3) + END DO + + c1_con= 1.0/ ( 1.0 + m_mean*(8.0*eta-2.0*eta**2 )/zms**4 & + + (1.0 - m_mean)*(20.0*eta-27.0*eta**2 & + + 12.0*eta**3 -2.0*eta**4 ) /(zms*(2.0-eta))**2 ) + c2_con= - c1_con*c1_con & + *(m_mean*(-4.0*eta**2 +20.0*eta+8.0)/zms**5 + (1.0 - m_mean) & + *(2.0*eta**3 +12.0*eta**2 -48.0*eta+40.0) & + /(zms*(2.0-eta))**3 ) + c3_con= 2.0 * c2_con*c2_con/c1_con - c1_con*c1_con & + *( m_mean*(-12.0*eta**2 +72.0*eta+60.0)/zms**6 & + + (1.0 - m_mean) & + *(-6.0*eta**4 -48.0*eta**3 +288.0*eta**2 & + -480.0*eta+264.0) /(zms*(2.0-eta))**4 ) + c4_con= 6.0*c2_con*c3_con/c1_con -6.0*c2_con**3 /c1_con**2 & + - c1_con*c1_con & + *( m_mean*(-48.0*eta**2 +336.0*eta+432.0)/zms**7 & + + (1.0 - m_mean) & + *(24.0*eta**5 +240.0*eta**4 -1920.0*eta**3 & + +4800.0*eta**2 -5280.0*eta+2208.0) /(zms*(2.0-eta))**5 ) + c5_con= 6.0*c3_con**2 /c1_con - 36.0*c2_con**2 /c1_con**2 *c3_con & + + 8.0*c2_con/c1_con*c4_con+24.0*c2_con**4 /c1_con**3 & + - c1_con*c1_con & + *( m_mean*(-240.0*eta**2 +1920.0*eta+3360.0)/zms**8 & + + (1.0 - m_mean) & + *(-120.0*eta**6 -1440.0*eta**5 +14400.0*eta**4 & + -48000.0*eta**3 +79200.0*eta**2 -66240.0*eta+22560.0) & + /(zms*(2.0-eta))**6 ) + + zdsp = - 2.0*PI*rho*edI1dz*order1 & + - PI*rho*order2*m_mean*(c2_con*I2*eta + c1_con*edI2dz) + zdspdz= zdsp/eta - 2.0*PI*rho*edI1d2*order1 & + - PI*rho*order2*m_mean*(c3_con*I2*eta & + + 2.0*c2_con*edI2dz + c1_con*edI2d2) + zdspd2= -2.0*zdsp/eta/eta +2.0*zdspdz/eta & + - 2.0*PI*rho*edI1d3*order1 - PI*rho*order2*m_mean*(c4_con*I2*eta & + + 3.0*c3_con*edI2dz +3.0*c2_con*edI2d2 +c1_con*edI2d3) + zdspd3= 6.0*zdsp/eta**3 -6.0*zdspdz/eta/eta & + + 3.0*zdspd2/eta - 2.0*PI*rho*edI1d4*order1 & + - PI*rho*order2*m_mean*(c5_con*I2*eta & + + 4.0*c4_con*edI2dz +6.0*c3_con*edI2d2 & + + 4.0*c2_con*edI2d3 + c1_con*edI2d4) + + +! ---------------------------------------------------------------------- +! p : SAFT (Chen & Kreglewski) dispersion contribution +! ---------------------------------------------------------------------- +ELSE + + fdspdz = 0.0 + fdspd2 = 0.0 + DO n = 1,4 + DO m = 1,9 + fdspdz = fdspdz + m_mean/tau * dnm(n,m) * (um/t)**REAL(n) *REAL(m)*(eta/tau)**REAL(m-1) + END DO + DO m= 2,9 + fdspd2= fdspd2 + m_mean/tau * dnm(n,m)*(um/t)**REAL(n) *REAL(m)*REAL(m-1) & + * (eta/tau)**REAL(m-2) * 1.0/tau + END DO + END DO + zdsp = eta * fdspdz + zdspdz = (2.0*fdspdz + eta*fdspd2) - zdsp/z3 + +END IF +! --- end of dispersion contribution ----------------------------------- + + +! ---------------------------------------------------------------------- +! p: TPT-1-association accord. to Chapman et al. +! ---------------------------------------------------------------------- +zhb = 0.0 +zhbdz = 0.0 +zhbd2 = 0.0 +zhbd3 = 0.0 +assoc = .false. +DO i = 1,ncomp + IF (nhb_typ(i) /= 0) assoc = .true. +END DO +IF (assoc) THEN + + DO j = 1, ncomp + DO i = 1, nhb_typ(j) + DO k = 1, ncomp + DO l = 1, nhb_typ(k) + delta(j,k,i,l) = gij(j,k) * ass_d(j,k,i,l) + dq_dz(j,k,i,l) = dgijdz(j,k) * ass_d(j,k,i,l) + dq_d2(j,k,i,l) = dgijd2(j,k) * ass_d(j,k,i,l) + dq_d3(j,k,i,l) = dgijd3(j,k) * ass_d(j,k,i,l) + dq_d4(j,k,i,l) = dgijd4(j,k) * ass_d(j,k,i,l) + END DO + END DO + END DO + END DO + +! --- constants for iteration ------------------------------------------ + attenu = 0.7 + tol = 1.d-10 + IF ( eta < 0.2 ) tol = 1.d-12 + IF ( eta < 0.01 ) tol = 1.d-13 + IF ( eta < 1.E-6) tol = 1.d-15 + max_eval = 1000 + +! --- initialize mx(i,j) ----------------------------------------------- + DO i = 1, ncomp + DO j = 1, nhb_typ(i) + mx(i,j) = 1.0 + dmx_dz(i,j) = 0.0 + dmx_d2(i,j) = 0.0 + dmx_d3(i,j) = 0.0 + dmx_d4(i,j) = 0.0 + END DO + END DO + +! --- iterate over all components and all sites ------------------------ + ass_cnt = 0 + err_sum = tol + 1.0 + DO WHILE ( err_sum > tol .AND. ass_cnt <= max_eval) + ass_cnt = ass_cnt + 1 + DO i = 1, ncomp + DO j = 1, nhb_typ(i) + sum0 = 0.0 + sum1 = 0.0 + sum2 = 0.0 + sum3 = 0.0 + sum4 = 0.0 + DO k = 1, ncomp + DO l = 1, nhb_typ(k) + sum0 =sum0 +x(k)*nhb_no(k,l)* mx(k,l)* delta(i,k,j,l) + sum1 =sum1 +x(k)*nhb_no(k,l)*( mx(k,l)* dq_dz(i,k,j,l) & + + dmx_dz(k,l)* delta(i,k,j,l)) + sum2 =sum2 +x(k)*nhb_no(k,l)*( mx(k,l)* dq_d2(i,k,j,l) & + + 2.0*dmx_dz(k,l)* dq_dz(i,k,j,l) & + + dmx_d2(k,l)* delta(i,k,j,l)) + sum3 =sum3 +x(k)*nhb_no(k,l)*( mx(k,l)* dq_d3(i,k,j,l) & + + 3.0*dmx_dz(k,l)* dq_d2(i,k,j,l) & + + 3.0*dmx_d2(k,l)* dq_dz(i,k,j,l) & + + dmx_d3(k,l)* delta(i,k,j,l)) + sum4 =sum4 + x(k)*nhb_no(k,l)*( mx(k,l)* dq_d4(i,k,j,l) & + + 4.0*dmx_dz(k,l)* dq_d3(i,k,j,l) & + + 6.0*dmx_d2(k,l)* dq_d2(i,k,j,l) & + + 4.0*dmx_d3(k,l)* dq_dz(i,k,j,l) & + + dmx_d4(k,l)* delta(i,k,j,l)) + END DO + END DO + mx_itr(i,j)= 1.0 / (1.0 + sum0 * rho) + ndmxdz(i,j)= -(mx_itr(i,j)*mx_itr(i,j))* (sum0/z3t +sum1*rho) + ndmxd2(i,j)= + 2.0/mx_itr(i,j)*ndmxdz(i,j)*ndmxdz(i,j) & + - (mx_itr(i,j)*mx_itr(i,j)) * (2.0/z3t*sum1 + rho*sum2) + ndmxd3(i,j)= - 6.0/mx_itr(i,j)**2 *ndmxdz(i,j)**3 & + + 6.0/mx_itr(i,j)*ndmxdz(i,j)*ndmxd2(i,j) - mx_itr(i,j)*mx_itr(i,j) & + * (3.0/z3t*sum2 + rho*sum3) + ndmxd4(i,j)= 24.0/mx_itr(i,j)**3 *ndmxdz(i,j)**4 & + -36.0/mx_itr(i,j)**2 *ndmxdz(i,j)**2 *ndmxd2(i,j) & + +6.0/mx_itr(i,j)*ndmxd2(i,j)**2 & + +8.0/mx_itr(i,j)*ndmxdz(i,j)*ndmxd3(i,j) - mx_itr(i,j)**2 & + *(4.0/z3t*sum3 + rho*sum4) + END DO + END DO + + err_sum = 0.0 + DO i = 1, ncomp + DO j = 1, nhb_typ(i) + err_sum = err_sum + ABS(mx_itr(i,j) - mx(i,j)) & + + ABS(ndmxdz(i,j) - dmx_dz(i,j)) + ABS(ndmxd2(i,j) - dmx_d2(i,j)) + mx(i,j) = mx_itr(i,j)*attenu + mx(i,j) * (1.0-attenu) + dmx_dz(i,j) = ndmxdz(i,j)*attenu + dmx_dz(i,j) * (1.0-attenu) + dmx_d2(i,j) = ndmxd2(i,j)*attenu + dmx_d2(i,j) * (1.0-attenu) + dmx_d3(i,j) = ndmxd3(i,j)*attenu + dmx_d3(i,j) * (1.0-attenu) + dmx_d4(i,j) = ndmxd4(i,j)*attenu + dmx_d4(i,j) * (1.0-attenu) + END DO + END DO + END DO + + IF ( ass_cnt >= max_eval .AND. err_sum > SQRT(tol) ) THEN + WRITE (*,'(a,2G15.7)') 'P_EOS: Max_eval violated (mx) Err_Sum= ',err_sum,tol + ! stop + END IF + + + ! --- calculate the hydrogen-bonding contribution -------------------- + DO i = 1, ncomp + sum_d1 = 0.0 + sum_d2 = 0.0 + sum_d3 = 0.0 + sum_d4 = 0.0 + DO j = 1, nhb_typ(i) + sum_d1= sum_d1 +nhb_no(i,j)* dmx_dz(i,j)*(1.0/mx(i,j)-0.5) + sum_d2= sum_d2 +nhb_no(i,j)*(dmx_d2(i,j)*(1.0/mx(i,j)-0.5) & + -(dmx_dz(i,j)/mx(i,j))**2 ) + sum_d3= sum_d3 +nhb_no(i,j)*(dmx_d3(i,j)*(1.0/mx(i,j)-0.5) & + -3.0/mx(i,j)**2 *dmx_dz(i,j)*dmx_d2(i,j) + 2.0*(dmx_dz(i,j)/mx(i,j))**3 ) + sum_d4= sum_d4 +nhb_no(i,j)*(dmx_d4(i,j)*(1.0/mx(i,j)-0.5) & + -4.0/mx(i,j)**2 *dmx_dz(i,j)*dmx_d3(i,j) & + + 12.0/mx(i,j)**3 *dmx_dz(i,j)**2 *dmx_d2(i,j) & + - 3.0/mx(i,j)**2 *dmx_d2(i,j)**2 - 6.0*(dmx_dz(i,j)/mx(i,j))**4 ) + END DO + zhb = zhb + x(i) * eta * sum_d1 + zhbdz = zhbdz + x(i) * eta * sum_d2 + zhbd2 = zhbd2 + x(i) * eta * sum_d3 + zhbd3 = zhbd3 + x(i) * eta * sum_d4 + END DO + zhbdz = zhbdz + zhb/eta + zhbd2 = zhbd2 + 2.0/eta*zhbdz-2.0/eta**2 *zhb + zhbd3 = zhbd3 - 6.0/eta**2 *zhbdz+3.0/eta*zhbd2 + 6.0/eta**3 *zhb +END IF +! --- TPT-1-association accord. to Chapman ----------------------------- + + +! ---------------------------------------------------------------------- +! p: polar terms +! ---------------------------------------------------------------------- +CALL P_POLAR ( zdd, zddz, zddz2, zddz3, zqq, zqqz, zqqz2, zqqz3, zdq, zdqz, zdqz2, zdqz3 ) + + +! ---------------------------------------------------------------------- +! compressibility factor z and total p +! as well as derivatives d(z)/d(eta) and d(p)/d(eta) with unit [Pa] +! ---------------------------------------------------------------------- +zges = 1.0 + zhs + zhc + zdsp + zhb + zdd + zqq + zdq +zgesdz = zhsdz + zhcdz + zdspdz + zhbdz + zddz + zqqz + zdqz +zgesd2 = zhsd2 + zhcd2 + zdspd2 + zhbd2 + zddz2 +zqqz2+zdqz2 +zgesd3 = zhsd3 + zhcd3 + zdspd3 + zhbd3 + zddz3 +zqqz3+zdqz3 + +pges = zges *rho *(kbol*t)/1.d-30 +pgesdz = ( zgesdz*rho + zges*rho/z3 )*(kbol*t)/1.d-30 +pgesd2 = ( zgesd2*rho + 2.0*zgesdz*rho/z3 )*(kbol*t)/1.d-30 +pgesd3 = ( zgesd3*rho + 3.0*zgesd2*rho/z3 )*(kbol*t)/1.d-30 + +END SUBROUTINE P_EOS + + + + +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! + SUBROUTINE PHI_POLAR ( k, z3_rk, fdd_rk, fqq_rk, fdq_rk ) +! + USE EOS_VARIABLES, ONLY: ncomp, parame, dd_term, qq_term, dq_term + IMPLICIT NONE +! +! ---------------------------------------------------------------------- + INTEGER, INTENT(IN) :: k + REAL, INTENT(IN) :: z3_rk + REAL, INTENT(OUT) :: fdd_rk, fqq_rk, fdq_rk +! +! --- local variables--------------------------------------------------- + INTEGER :: dipole + INTEGER :: quadrupole + INTEGER :: dipole_quad +! ---------------------------------------------------------------------- + + fdd_rk = 0.0 + fqq_rk = 0.0 + fdq_rk = 0.0 + + dipole = 0 + quadrupole = 0 + dipole_quad = 0 + IF ( SUM( parame(1:ncomp,6) ) /= 0.0 ) dipole = 1 + IF ( SUM( parame(1:ncomp,7) ) /= 0.0 ) quadrupole = 1 + IF ( dipole == 1 .AND. quadrupole == 1 ) dipole_quad = 1 + + ! -------------------------------------------------------------------- + ! dipole-dipole term + ! -------------------------------------------------------------------- + IF (dipole == 1) THEN + + IF (dd_term == 'GV') CALL PHI_DD_GROSS_VRABEC( k, z3_rk, fdd_rk ) + ! IF (dd_term == 'SF') CALL PHI_DD_SAAGER_FISCHER( k ) + + IF (dd_term /= 'GV' .AND. dd_term /= 'SF') write (*,*) 'specify dipole term !' + + ENDIF + + ! -------------------------------------------------------------------- + ! quadrupole-quadrupole term + ! -------------------------------------------------------------------- + IF (quadrupole == 1) THEN + + !IF (qq_term == 'SF') CALL PHI_QQ_SAAGER_FISCHER( k ) + IF (qq_term == 'JG') CALL PHI_QQ_GROSS( k, z3_rk, fqq_rk ) + + IF (qq_term /= 'JG' .AND. qq_term /= 'SF') write (*,*) 'specify quadrupole term !' + + ENDIF + + ! -------------------------------------------------------------------- + ! dipole-quadrupole cross term + ! -------------------------------------------------------------------- + IF (dipole_quad == 1) THEN + + IF (dq_term == 'VG') CALL PHI_DQ_VRABEC_GROSS( k, z3_rk, fdq_rk ) + + IF (dq_term /= 'VG' ) write (*,*) 'specify DQ-cross term !' + + ENDIF + +END SUBROUTINE PHI_POLAR + + +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! + SUBROUTINE PHI_DD_GROSS_VRABEC( k, z3_rk, fdd_rk ) +! + USE PARAMETERS, ONLY: PI, KBOL + USE EOS_VARIABLES, ONLY: nc, ncomp, uij, parame, mseg, sig_ij, rho, eta, x, t + USE EOS_CONSTANTS, ONLY: ddp2, ddp3, ddp4 + IMPLICIT NONE +! +! ---------------------------------------------------------------------- + INTEGER, INTENT(IN) :: k + REAL, INTENT(IN) :: z3_rk + REAL, INTENT(IN OUT) :: fdd_rk +! +! --- local variables--------------------------------------------------- + INTEGER :: i, j, l, m + + REAL :: factor2, factor3, z3 + REAL :: xijfa, xijkfa, xijfa_x, xijkf_x, eij + REAL :: fdd2, fdd3, fdd2x, fdd3x + REAL, DIMENSION(nc) :: my2dd + REAL, DIMENSION(nc,nc) :: Idd2, Idd4, Idd2x, Idd4x + REAL, DIMENSION(nc,nc,nc) :: Idd3, Idd3x +! ---------------------------------------------------------------------- + + + fdd_rk = 0.0 + z3 = eta + DO i = 1, ncomp + IF ( uij(i,i) == 0.0 ) write (*,*) 'PHI_DD_GROSS_VRABEC: do not use dimensionless units' + IF ( uij(i,i) == 0.0 ) stop + my2dd(i) = (parame(i,6))**2 *1.E-49 / (uij(i,i)*KBOL*mseg(i)*sig_ij(i,i)**3 *1.E-30) + END DO + + DO i = 1, ncomp + DO j = 1, ncomp + Idd2(i,j) = 0.0 + Idd4(i,j) = 0.0 + Idd2x(i,j) = 0.0 + Idd4x(i,j) = 0.0 + IF (parame(i,6) /= 0.0 .AND. parame(j,6) /= 0.0) THEN + DO m=0,4 + Idd2(i,j) =Idd2(i,j) + ddp2(i,j,m)*z3**m + Idd4(i,j) =Idd4(i,j) + ddp4(i,j,m)*z3**m + Idd2x(i,j) =Idd2x(i,j)+ ddp2(i,j,m)*REAL(m)*z3**(m-1)*z3_rk + Idd4x(i,j) =Idd4x(i,j)+ ddp4(i,j,m)*REAL(m)*z3**(m-1)*z3_rk + END DO + DO l = 1, ncomp + Idd3(i,j,l) = 0.0 + Idd3x(i,j,l) = 0.0 + IF (parame(l,6) /= 0.0) THEN + DO m=0,4 + Idd3(i,j,l) =Idd3(i,j,l) +ddp3(i,j,l,m)*z3**m + Idd3x(i,j,l)=Idd3x(i,j,l)+ddp3(i,j,l,m)*REAL(m)*z3**(m-1)*z3_rk + END DO + END IF + END DO + END IF + END DO + END DO + + factor2= -PI + factor3= -4.0/3.0*PI**2 + + fdd2 = 0.0 + fdd3 = 0.0 + fdd2x = 0.0 + fdd3x = 0.0 + DO i = 1, ncomp + xijfa_x = 2.0*x(i)*rho*uij(i,i)*my2dd(i)*sig_ij(i,i)**3 /t & + *uij(k,k)*my2dd(k)*sig_ij(k,k)**3 /t/sig_ij(i,k)**3 + eij = (parame(i,3)*parame(k,3))**0.5 + fdd2x = fdd2x + factor2*xijfa_x*( Idd2(i,k) + eij/t*Idd4(i,k) ) + DO j = 1, ncomp + IF (parame(i,6) /= 0.0 .AND. parame(j,6) /= 0.0) THEN + xijfa =x(i)*rho*uij(i,i)*my2dd(i)*sig_ij(i,i)**3 /t & + *x(j)*rho*uij(j,j)*my2dd(j)*sig_ij(j,j)**3 /t/sig_ij(i,j)**3 + eij = (parame(i,3)*parame(j,3))**0.5 + fdd2= fdd2 +factor2*xijfa*(Idd2(i,j) +eij/t*Idd4(i,j) ) + fdd2x =fdd2x +factor2*xijfa*(Idd2x(i,j)+eij/t*Idd4x(i,j)) + !--------------------- + xijkf_x=x(i)*rho*uij(i,i)*my2dd(i)*sig_ij(i,i)**3 /t/sig_ij(i,j) & + *x(j)*rho*uij(j,j)*my2dd(j)*sig_ij(j,j)**3 /t/sig_ij(i,k) & + *3.0* uij(k,k)*my2dd(k)*sig_ij(k,k)**3 /t/sig_ij(j,k) + fdd3x=fdd3x+factor3*xijkf_x*Idd3(i,j,k) + DO l=1,ncomp + IF (parame(l,6) /= 0.0) THEN + xijkfa= x(i)*rho*uij(i,i)/t*my2dd(i)*sig_ij(i,i)**3 & + *x(j)*rho*uij(j,j)/t*my2dd(j)*sig_ij(j,j)**3 & + *x(l)*rho*uij(l,l)/t*my2dd(l)*sig_ij(l,l)**3 & + /sig_ij(i,j)/sig_ij(i,l)/sig_ij(j,l) + fdd3 =fdd3 + factor3 * xijkfa *Idd3(i,j,l) + fdd3x =fdd3x + factor3 * xijkfa *Idd3x(i,j,l) + END IF + END DO + END IF + END DO + END DO + + IF (fdd2 < -1.E-50 .AND. fdd3 /= 0.0 .AND. fdd2x /= 0.0 .AND. fdd3x /= 0.0)THEN + + fdd_rk = fdd2* (fdd2*fdd2x - 2.0*fdd3*fdd2x+fdd2*fdd3x) / (fdd2-fdd3)**2 + + END IF + +END SUBROUTINE PHI_DD_GROSS_VRABEC + + + +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! + SUBROUTINE PHI_QQ_GROSS( k, z3_rk, fqq_rk ) +! + USE PARAMETERS, ONLY: PI, KBOL + USE EOS_VARIABLES, ONLY: nc, ncomp, uij, parame, mseg, sig_ij, rho, eta, x, t + USE EOS_CONSTANTS, ONLY: qqp2, qqp3, qqp4 + IMPLICIT NONE +! +! ---------------------------------------------------------------------- + INTEGER, INTENT(IN) :: k + REAL, INTENT(IN) :: z3_rk + REAL, INTENT(IN OUT) :: fqq_rk +! +! --- local variables--------------------------------------------------- + INTEGER :: i, j, l, m + + REAL :: factor2, factor3, z3 + REAL :: xijfa, xijkfa, xijfa_x, xijkf_x, eij + REAL :: fqq2, fqq3, fqq2x, fqq3x + REAL, DIMENSION(nc) :: qq2 + REAL, DIMENSION(nc,nc) :: Iqq2, Iqq4, Iqq2x, Iqq4x + REAL, DIMENSION(nc,nc,nc) :: Iqq3, Iqq3x +! ---------------------------------------------------------------------- + + + fqq_rk = 0.0 + z3 = eta + DO i = 1, ncomp + IF ( uij(i,i) == 0.0 ) write (*,*) 'PHI_QQ_GROSS: do not use dimensionless units' + qq2(i) = (parame(i,7))**2 *1.E-69 / (uij(i,i)*kbol*mseg(i)*sig_ij(i,i)**5 *1.E-50) + END DO + + DO i = 1, ncomp + DO j = 1, ncomp + Iqq2(i,j) = 0.0 + Iqq4(i,j) = 0.0 + Iqq2x(i,j) = 0.0 + Iqq4x(i,j) = 0.0 + IF (parame(i,7) /= 0.0 .AND. parame(j,7) /= 0.0) THEN + DO m = 0, 4 + Iqq2(i,j) = Iqq2(i,j) + qqp2(i,j,m) * z3**m + Iqq4(i,j) = Iqq4(i,j) + qqp4(i,j,m) * z3**m + Iqq2x(i,j) = Iqq2x(i,j) + qqp2(i,j,m) * REAL(m)*z3**(m-1)*z3_rk + Iqq4x(i,j) = Iqq4x(i,j) + qqp4(i,j,m) * REAL(m)*z3**(m-1)*z3_rk + END DO + DO l = 1, ncomp + Iqq3(i,j,l) = 0.0 + Iqq3x(i,j,l) = 0.0 + IF (parame(l,7) /= 0.0) THEN + DO m = 0, 4 + Iqq3(i,j,l) = Iqq3(i,j,l) + qqp3(i,j,l,m)*z3**m + Iqq3x(i,j,l) = Iqq3x(i,j,l) + qqp3(i,j,l,m)*REAL(m) *z3**(m-1)*z3_rk + END DO + END IF + END DO + END IF + END DO + END DO + + factor2= -9.0/16.0*PI + factor3= 9.0/16.0*PI**2 + + fqq2 = 0.0 + fqq3 = 0.0 + fqq2x = 0.0 + fqq3x = 0.0 + DO i = 1, ncomp + xijfa_x = 2.0*x(i)*rho*uij(i,i)*qq2(i)*sig_ij(i,i)**5 /t & + *uij(k,k)*qq2(k)*sig_ij(k,k)**5 /t/sig_ij(i,k)**7.0 + eij = (parame(i,3)*parame(k,3))**0.5 + fqq2x =fqq2x +factor2*xijfa_x*(Iqq2(i,k)+eij/t*Iqq4(i,k)) + DO j=1,ncomp + IF (parame(i,7) /= 0.0 .AND. parame(j,7) /= 0.0) THEN + xijfa =x(i)*rho*uij(i,i)*qq2(i)*sig_ij(i,i)**5 /t & + *x(j)*rho*uij(j,j)*qq2(j)*sig_ij(j,j)**5 /t/sig_ij(i,j)**7.0 + eij = (parame(i,3)*parame(j,3))**0.5 + fqq2= fqq2 +factor2*xijfa*(Iqq2(i,j) +eij/t*Iqq4(i,j) ) + fqq2x =fqq2x +factor2*xijfa*(Iqq2x(i,j)+eij/t*Iqq4x(i,j)) + ! ------------------ + xijkf_x=x(i)*rho*uij(i,i)*qq2(i)*sig_ij(i,i)**5 /t/sig_ij(i,j)**3 & + *x(j)*rho*uij(j,j)*qq2(j)*sig_ij(j,j)**5 /t/sig_ij(i,k)**3 & + *3.0* uij(k,k)*qq2(k)*sig_ij(k,k)**5 /t/sig_ij(j,k)**3 + fqq3x = fqq3x + factor3*xijkf_x*Iqq3(i,j,k) + DO l = 1, ncomp + IF (parame(l,7) /= 0.0) THEN + xijkfa=x(i)*rho*uij(i,i)*qq2(i)*sig_ij(i,i)**5 /t/sig_ij(i,j)**3 & + *x(j)*rho*uij(j,j)*qq2(j)*sig_ij(j,j)**5 /t/sig_ij(i,l)**3 & + *x(l)*rho*uij(l,l)*qq2(l)*sig_ij(l,l)**5 /t/sig_ij(j,l)**3 + fqq3 =fqq3 + factor3 * xijkfa *Iqq3(i,j,l) + fqq3x =fqq3x + factor3 * xijkfa *Iqq3x(i,j,l) + END IF + END DO + END IF + END DO + END DO + + IF (fqq2 < -1.E-50 .AND. fqq3 /= 0.0 .AND. fqq2x /= 0.0 .AND. fqq3x /= 0.0) THEN + fqq_rk = fqq2* (fqq2*fqq2x - 2.0*fqq3*fqq2x+fqq2*fqq3x) / (fqq2-fqq3)**2 + END IF + +END SUBROUTINE PHI_QQ_GROSS + +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! + SUBROUTINE PHI_DQ_VRABEC_GROSS( k, z3_rk, fdq_rk ) +! + USE PARAMETERS, ONLY: PI, KBOL + USE EOS_VARIABLES, ONLY: nc, ncomp, uij, parame, mseg, sig_ij, rho, eta, x, t + USE EOS_CONSTANTS, ONLY: dqp2, dqp3, dqp4 + IMPLICIT NONE +! +! ---------------------------------------------------------------------- + INTEGER, INTENT(IN) :: k + REAL, INTENT(IN) :: z3_rk + REAL, INTENT(IN OUT) :: fdq_rk +! +! --- local variables--------------------------------------------------- + INTEGER :: i, j, l, m + + REAL :: factor2, factor3, z3 + REAL :: xijfa, xijkfa, xijfa_x, xijkf_x, eij + REAL :: fdq2, fdq3, fdq2x, fdq3x + REAL, DIMENSION(nc) :: my2dd, myfac, qq2, q_fac + REAL, DIMENSION(nc,nc) :: Idq2, Idq4, Idq2x, Idq4x + REAL, DIMENSION(nc,nc,nc) :: Idq3, Idq3x +! ---------------------------------------------------------------------- + + fdq_rk = 0.0 + z3 = eta + DO i=1,ncomp + my2dd(i) = (parame(i,6))**2 *1.E-49 / (uij(i,i)*KBOL*mseg(i)*sig_ij(i,i)**3 *1.E-30) + myfac(i) = parame(i,3)/t*parame(i,2)**4 *my2dd(i) + qq2(i) = (parame(i,7))**2 *1.E-69 / (uij(i,i)*kbol*mseg(i)*sig_ij(i,i)**5 *1.E-50) + q_fac(i) = parame(i,3)/t*parame(i,2)**4 *qq2(i) + END DO + + DO i = 1, ncomp + DO j = 1, ncomp + Idq2(i,j) = 0.0 + Idq4(i,j) = 0.0 + Idq2x(i,j) = 0.0 + Idq4x(i,j) = 0.0 + DO m = 0, 4 + Idq2(i,j) = Idq2(i,j) + dqp2(i,j,m)*z3**m + Idq4(i,j) = Idq4(i,j) + dqp4(i,j,m)*z3**m + Idq2x(i,j) = Idq2x(i,j) + dqp2(i,j,m)*REAL(m)*z3**(m-1) *z3_rk + Idq4x(i,j) = Idq4x(i,j) + dqp4(i,j,m)*REAL(m)*z3**(m-1) *z3_rk + END DO + DO l = 1, ncomp + Idq3(i,j,l) = 0.0 + Idq3x(i,j,l) = 0.0 + DO m = 0, 4 + Idq3(i,j,l) =Idq3(i,j,l) +dqp3(i,j,l,m)*z3**m + Idq3x(i,j,l)=Idq3x(i,j,l)+dqp3(i,j,l,m)*REAL(m)*z3**(m-1)*z3_rk + END DO + END DO + END DO + END DO + + factor2= -9.0/4.0*PI + factor3= PI**2 + + fdq2 = 0.0 + fdq3 = 0.0 + fdq2x = 0.0 + fdq3x = 0.0 + DO i = 1, ncomp + xijfa_x = x(i)*rho*( myfac(i)*q_fac(k) + myfac(k)*q_fac(i) ) / sig_ij(i,k)**5 + eij = (parame(i,3)*parame(k,3))**0.5 + fdq2x =fdq2x +factor2*xijfa_x*(Idq2(i,k)+eij/t*Idq4(i,k)) + DO j=1,ncomp + xijfa =x(i)*rho*myfac(i) * x(j)*rho*q_fac(j) /sig_ij(i,j)**5 + eij = (parame(i,3)*parame(j,3))**0.5 + fdq2= fdq2 +factor2*xijfa*(Idq2(i,j) +eij/t*Idq4(i,j) ) + fdq2x =fdq2x +factor2*xijfa*(Idq2x(i,j) +eij/t*Idq4x(i,j)) + !--------------------- + xijkf_x=x(i)*rho*x(j)*rho/(sig_ij(i,j)*sig_ij(i,k)*sig_ij(j,k))**2 & + *( myfac(i)*q_fac(j)*myfac(k) + myfac(i)*q_fac(k)*myfac(j) & + + myfac(k)*q_fac(i)*myfac(j) +myfac(i)*q_fac(j)*q_fac(k)*1.1937350 & + +myfac(i)*q_fac(k)*q_fac(j)*1.193735 & + +myfac(k)*q_fac(i)*q_fac(j)*1.193735 ) + fdq3x = fdq3x + factor3*xijkf_x*Idq3(i,j,k) + DO l = 1, ncomp + xijkfa=x(i)*rho*x(j)*rho*x(l)*rho/(sig_ij(i,j)*sig_ij(i,l)*sig_ij(j,l))**2 & + *( myfac(i)*q_fac(j)*myfac(l) & + +myfac(i)*q_fac(j)*q_fac(l)*1.193735 ) + fdq3 =fdq3 + factor3 * xijkfa *Idq3(i,j,l) + fdq3x =fdq3x + factor3 * xijkfa *Idq3x(i,j,l) + END DO + END DO + END DO + + IF (fdq2 < -1.E-50 .AND. fdq3 /= 0.0 .AND. fdq2x /= 0.0 .AND. fdq3x /= 0.0)THEN + + fdq_rk = fdq2* (fdq2*fdq2x - 2.0*fdq3*fdq2x+fdq2*fdq3x) / (fdq2-fdq3)**2 + + END IF + +END SUBROUTINE PHI_DQ_VRABEC_GROSS + + + +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! + SUBROUTINE P_NUMERICAL +! + USE EOS_VARIABLES + IMPLICIT NONE +! +!-----local variables------------------------------------------------- + REAL :: dzetdv, eta_0, dist, fact + REAL :: fres1, fres2, fres3, fres4, fres5 + REAL :: df_dr, df_drdr, pideal, dpiddz + REAL :: tfr_1, tfr_2, tfr_3, tfr_4, tfr_5 +!----------------------------------------------------------------------- + + +IF (eta > 0.1) THEN + fact = 1.0 +ELSE IF (eta <= 0.1 .AND. eta > 0.01) THEN + fact = 10.0 +ELSE + fact = 10.0 +END IF +dist = eta*3.d-3 *fact +! dist = eta*4.d-3 *fact +!***************************** +! fuer MC simulation: neues dist: +! dist = eta*5.d-3*fact + +eta_0 = eta +eta = eta_0 - 2.0*dist +CALL F_NUMERICAL +fres1 = fres +tfr_1 = tfr +eta = eta_0 - dist +CALL F_NUMERICAL +fres2 = fres +tfr_2 = tfr +eta = eta_0 + dist +CALL F_NUMERICAL +fres3 = fres +tfr_3 = tfr +eta = eta_0 + 2.0*dist +CALL F_NUMERICAL +fres4 = fres +tfr_4 = tfr +eta = eta_0 +CALL F_NUMERICAL +fres5 = fres +tfr_5 = tfr + +!--------------------------------------------------------- +! ptfr = (-tfr_4+8.0*tfr_3-8.0*tfr_2+tfr_1)/(12.0*dist) +! & *dzetdv*(KBOL*T)/1.E-30 +! ztfr =ptfr /( rho * (KBOL*t) / 1.E-30) +! ptfrdz = (-tfr_4+16.0*tfr_3-3.d1*tfr_5+16.0*tfr_2-tfr_1) +! & /(12.0*(dist**2 ))* dzetdv*(KBOL*T)/1.E-30 +! & + (-tfr_4+8.0*tfr_3-8.0*tfr_2+tfr_1) +! & /(12.0*dist) * 2.0 *eta*6.0/PI/D +! & *(KBOL*T)/1.E-30 +! ztfrdz=ptfrdz/( rho*(kbol*T)/1.E-30 ) - ztfr/eta +! write (*,*) eta,ztfr,ztfrdz + +! dtfr_dr = (-tfr_4+8.0*tfr_3-8.0*tfr_2+tfr_1)/(12.0*dist) +! write (*,*) eta,dtfr_dr +! stop +!--------------------------------------------------------- + +df_dr = (-fres4+8.0*fres3-8.0*fres2+fres1) / (12.0*dist) +df_drdr = (-fres4+16.0*fres3-3.d1*fres5+16.0*fres2-fres1) & + /(12.0*(dist**2 )) + + +dzetdv = eta*rho + +pges = (-fres4+8.0*fres3-8.0*fres2+fres1) & + /(12.0*dist) *dzetdv*(kbol*t)/1.E-30 + +dpiddz = 1.0/z3t*(kbol*t)/1.E-30 +pgesdz = (-fres4+16.0*fres3-3.d1*fres5+16.0*fres2-fres1) & + /(12.0*(dist**2 ))* dzetdv*(kbol*t)/1.E-30 & + + (-fres4+8.0*fres3-8.0*fres2+fres1) /(12.0*dist) * 2.0 *rho & + *(kbol*t)/1.E-30 + dpiddz + +pgesd2 = (fres4-2.0*fres3+2.0*fres2-fres1) /(2.0*dist**3 ) & + * dzetdv*(kbol*t)/1.E-30 & + + (-fres4+16.0*fres3-3.d1*fres5+16.0*fres2-fres1) /(12.0*(dist**2 )) & + * 4.0 *rho *(kbol*t)/1.E-30 + (-fres4+8.0*fres3-8.0*fres2+fres1) & + /(12.0*dist) * 2.0 /z3t *(kbol*t)/1.E-30 +pgesd3 = (fres4-4.0*fres3+6.0*fres5-4.0*fres2+fres1) /(dist**4 ) & + * dzetdv*(kbol*t)/1.E-30 + (fres4-2.0*fres3+2.0*fres2-fres1) & + /(2.0*dist**3 ) * 6.0 *rho *(kbol*t)/1.E-30 & + + (-fres4+16.0*fres3-3.d1*fres5+16.0*fres2-fres1) & + /(12.0*dist**2 )* 6.0 /z3t *(kbol*t)/1.E-30 + +!------------------p ideal------------------------------------ +pideal = rho * (kbol*t) / 1.E-30 + +!------------------p summation, p comes out in Pa ------------ +pges = pideal + pges + +END SUBROUTINE P_NUMERICAL + + +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! + SUBROUTINE H_numerical +! + USE PARAMETERS, ONLY: RGAS + USE EOS_VARIABLES + IMPLICIT NONE +! +!--------------------------------------------------------------------- + REAL :: dist, fact, rho_0 + REAL :: fres1,fres2,fres3,fres4,fres5 + REAL :: f_1, f_2, f_3, f_4 + REAL :: cv_res, t_tmp, zges + REAL :: f_dt, f_dtdt, f_dr, f_drdr, f_drdt +!----------------------------------------------------------------------- + + +CALL PERTURBATION_PARAMETER +rho_0 = eta/z3t + + +fact = 1.0 +dist = t * 100.E-5 * fact + +t_tmp = t + +t = t_tmp - 2.0*dist +CALL PERTURBATION_PARAMETER +eta = z3t*rho_0 +CALL F_NUMERICAL +fres1 = fres +t = t_tmp - dist +CALL PERTURBATION_PARAMETER +eta = z3t*rho_0 +CALL F_NUMERICAL +fres2 = fres +t = t_tmp + dist +CALL PERTURBATION_PARAMETER +eta = z3t*rho_0 +CALL F_NUMERICAL +fres3 = fres +t = t_tmp + 2.0*dist +CALL PERTURBATION_PARAMETER +eta = z3t*rho_0 +CALL F_NUMERICAL +fres4 = fres +t = t_tmp +CALL PERTURBATION_PARAMETER +eta = z3t*rho_0 +CALL F_NUMERICAL +fres5 = fres +! *(KBOL*T)/1.E-30 + +zges = (p * 1.E-30)/(kbol*t*rho_0) + + +f_dt = (-fres4+8.0*fres3-8.0*fres2+fres1)/(12.0*dist) +f_dtdt = (-fres4+16.0*fres3-3.d1*fres5+16.0*fres2-fres1) /(12.0*(dist**2 )) + +s_res = (- f_dt -fres/t)*RGAS*t + RGAS * LOG(zges) +h_res = ( - t*f_dt + zges-1.0 ) * RGAS*t +cv_res = -( t*f_dtdt + 2.0*f_dt ) * RGAS*t + + + +t = t_tmp - 2.0*dist +CALL PERTURBATION_PARAMETER +eta = z3t*rho_0 +CALL P_NUMERICAL +f_1 = pges/(eta*rho_0*(KBOL*T)/1.E-30) + +t = t_tmp - dist +CALL PERTURBATION_PARAMETER +eta = z3t*rho_0 +CALL P_NUMERICAL +f_2 = pges/(eta*rho_0*(KBOL*T)/1.E-30) + +t = t_tmp + dist +CALL PERTURBATION_PARAMETER +eta = z3t*rho_0 +CALL P_NUMERICAL +f_3 = pges/(eta*rho_0*(KBOL*T)/1.E-30) + +t = t_tmp + 2.0*dist +CALL PERTURBATION_PARAMETER +eta = z3t*rho_0 +CALL P_NUMERICAL +f_4 = pges/(eta*rho_0*(KBOL*T)/1.E-30) + +t = t_tmp +CALL PERTURBATION_PARAMETER +eta = z3t*rho_0 +CALL P_NUMERICAL + +f_dr = pges / (eta*rho_0*(KBOL*T)/1.E-30) +f_drdr = pgesdz/ (eta*rho_0*(KBOL*T)/1.E-30) - f_dr*2.0/eta - 1.0/eta**2 + +f_drdt = ( - f_4 + 8.0*f_3 - 8.0*f_2 + f_1 ) / ( 12.0*dist ) + +cp_res = cv_res - RGAS + RGAS*( zges + eta*t*f_drdt)**2 / (1.0 + 2.0*eta*f_dr + eta**2 *f_drdr) +! write (*,*) cv_res,cp_res,eta + + +END SUBROUTINE H_numerical + + + + + + + + + + + +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! + SUBROUTINE F_POLAR ( fdd, fqq, fdq ) +! + USE EOS_VARIABLES, ONLY: ncomp, parame, dd_term, qq_term, dq_term + IMPLICIT NONE +! +! ---------------------------------------------------------------------- + REAL, INTENT(OUT) :: fdd, fqq, fdq +! +! --- local variables--------------------------------------------------- + INTEGER :: dipole + INTEGER :: quadrupole + INTEGER :: dipole_quad +! ---------------------------------------------------------------------- + + fdd = 0.0 + fqq = 0.0 + fdq = 0.0 + + dipole = 0 + quadrupole = 0 + dipole_quad = 0 + IF ( SUM( parame(1:ncomp,6) ) /= 0.0 ) dipole = 1 + IF ( SUM( parame(1:ncomp,7) ) /= 0.0 ) quadrupole = 1 + IF ( dipole == 1 .AND. quadrupole == 1 ) dipole_quad = 1 + + ! -------------------------------------------------------------------- + ! dipole-dipole term + ! -------------------------------------------------------------------- + IF (dipole == 1) THEN + + IF (dd_term == 'GV') CALL F_DD_GROSS_VRABEC( fdd ) + ! IF (dd_term == 'SF') CALL F_DD_SAAGER_FISCHER( k ) + IF (dd_term /= 'GV' .AND. dd_term /= 'SF') write (*,*) 'specify dipole term !' + + ENDIF + + ! -------------------------------------------------------------------- + ! quadrupole-quadrupole term + ! -------------------------------------------------------------------- + IF (quadrupole == 1) THEN + + !IF (qq_term == 'SF') CALL F_QQ_SAAGER_FISCHER( k ) + IF (qq_term == 'JG') CALL F_QQ_GROSS( fqq ) + IF (qq_term /= 'JG' .AND. qq_term /= 'SF') write (*,*) 'specify quadrupole term !' + + ENDIF + + ! -------------------------------------------------------------------- + ! dipole-quadrupole cross term + ! -------------------------------------------------------------------- + IF (dipole_quad == 1) THEN + + IF (dq_term == 'VG') CALL F_DQ_VRABEC_GROSS( fdq ) + IF (dq_term /= 'VG' ) write (*,*) 'specify DQ-cross term !' + + ENDIF + +END SUBROUTINE F_POLAR + + + +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! SUBROUTINE PRESSURE_SPINODAL +! +! iterates the density until the derivative of pressure 'pges' to +! density is equal to zero. A Newton-scheme is used for determining +! the root to the objective function. +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! + SUBROUTINE PRESSURE_SPINODAL +! + USE BASIC_VARIABLES, ONLY: num + USE EOS_VARIABLES + IMPLICIT NONE +! +! ---------------------------------------------------------------------- + INTEGER :: i, max_i + REAL :: eta_iteration + REAL :: error, acc_i, delta_eta +! ---------------------------------------------------------------------- + +acc_i = 1.d-6 +max_i = 30 + +i = 0 +eta_iteration = eta_start + +! ---------------------------------------------------------------------- +! iterate density until p_calc = p +! ---------------------------------------------------------------------- + +error = acc_i + 1.0 +DO WHILE ( ABS(error) > acc_i .AND. i < max_i ) + + i = i + 1 + eta = eta_iteration + + IF ( num == 0 ) THEN + CALL P_EOS + ELSE IF ( num == 1 ) THEN + CALL P_NUMERICAL + ELSE IF ( num == 2 ) THEN + WRITE(*,*) 'CRITICAL RENORM NOT INCLUDED YET' + !!CALL F_EOS_RN + ELSE + write (*,*) 'define calculation option (num)' + END IF + + error = pgesdz + + delta_eta = error/ pgesd2 + IF ( delta_eta > 0.02 ) delta_eta = 0.02 + IF ( delta_eta < -0.02 ) delta_eta = -0.02 + + eta_iteration = eta_iteration - delta_eta + ! write (*,'(a,i3,3G18.10)') 'iter',i, error, eta_iteration, pgesdz + + IF (eta_iteration > 0.9) eta_iteration = 0.5 + IF (eta_iteration <= 0.0) eta_iteration = 1.E-16 + +END DO + +eta = eta_iteration + +END SUBROUTINE PRESSURE_SPINODAL + + +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! + SUBROUTINE F_IDEAL_GAS ( fid ) +! + USE EOS_VARIABLES, ONLY: nc, ncomp, t, x, rho, PI, KBOL, NAv + IMPLICIT NONE +! +!--------------------------------------------------------------------- + REAL, INTENT(IN OUT) :: fid +!--------------------------------------------------------------------- + INTEGER :: i + REAL, DIMENSION(nc) :: rhoi +!---------------------------------------------------------------------- + + !h_Planck = 6.62606896E-34 ! Js + DO i = 1, ncomp + rhoi(i) = x(i) * rho + ! debroglie(i) = h_Planck *1d10 & ! in units Angstrom + ! *SQRT( 1.0 / (2.0*PI *1.0 / NAv / 1000.0 * KBOL*T) ) + ! ! *SQRT( 1.0 / (2.0*PI *mm(i) /NAv/1000.0 * KBOL*T) ) + ! fid = fid + x(i) * ( LOG(rhoi(i)*debroglie(i)**3) - 1.0 ) + fid = fid + x(i) * ( LOG(rhoi(i)) - 1.0 ) + END DO + + END SUBROUTINE F_IDEAL_GAS + +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! + SUBROUTINE F_HARD_SPHERE ( m_mean2, fhs ) +! + USE EOS_VARIABLES, ONLY: z0t, z1t, z2t, z3t, eta, rho + IMPLICIT NONE +! +!--------------------------------------------------------------------- + REAL, INTENT(IN) :: m_mean2 + REAL, INTENT(IN OUT) :: fhs +!--------------------------------------------------------------------- + REAL :: z0, z1, z2, z3, zms +!---------------------------------------------------------------------- + + rho = eta / z3t + z0 = z0t * rho + z1 = z1t * rho + z2 = z2t * rho + z3 = z3t * rho + zms = 1.0 - z3 + + fhs= m_mean2*( 3.0*z1*z2/zms + z2**3 /z3/zms/zms + (z2**3 /z3/z3-z0)*LOG(zms) )/z0 + + + END SUBROUTINE F_HARD_SPHERE + +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! + SUBROUTINE F_CHAIN_TPT1 ( fhc ) +! + USE EOS_VARIABLES, ONLY: nc, ncomp, mseg, x, z0t, z1t, z2t, z3t, & + rho, eta, dij_ab, gij + IMPLICIT NONE +! +!--------------------------------------------------------------------- + REAL, INTENT(IN OUT) :: fhc +!--------------------------------------------------------------------- + INTEGER :: i, j + REAL :: z0, z1, z2, z3, zms +!--------------------------------------------------------------------- + + rho = eta / z3t + z0 = z0t * rho + z1 = z1t * rho + z2 = z2t * rho + z3 = z3t * rho + zms = 1.0 - z3 + + DO i = 1, ncomp + DO j = 1, ncomp + gij(i,j) = 1.0/zms + 3.0*dij_ab(i,j)*z2/zms/zms + 2.0*(dij_ab(i,j)*z2)**2 / zms**3 + END DO + END DO + + fhc = 0.0 + DO i = 1, ncomp + fhc = fhc + x(i) *(1.0- mseg(i)) *LOG(gij(i,i)) + END DO + + END SUBROUTINE F_CHAIN_TPT1 + + +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! + SUBROUTINE F_CHAIN_TPT_D ( fhc ) +! + USE EOS_VARIABLES, ONLY: nc, ncomp, mseg, x, z0t, z1t, z2t, z3t, rho, eta, & + dhs, mseg, dij_ab, gij + IMPLICIT NONE +! +!--------------------------------------------------------------------- + REAL, INTENT(OUT) :: fhc +!--------------------------------------------------------------------- + INTEGER :: i, j + REAL, DIMENSION(nc) :: gij_hd + REAL :: z0, z1, z2, z3, zms +!--------------------------------------------------------------------- + + rho = eta / z3t + z0 = z0t * rho + z1 = z1t * rho + z2 = z2t * rho + z3 = z3t * rho + zms = 1.0 - z3 + + DO i = 1, ncomp + DO j = 1, ncomp + gij(i,j) = 1.0/zms + 3.0*dij_ab(i,j)*z2/zms/zms + 2.0*(dij_ab(i,j)*z2)**2 / zms**3 + END DO + END DO + + DO i = 1, ncomp + gij_hd(i) = 1.0/(2.0*zms) + 3.0*dij_ab(i,i)*z2 / zms**2 + END DO + + fhc = 0.0 + DO i = 1, ncomp + IF ( mseg(i) >= 2.0 ) THEN + fhc = fhc - x(i) * ( mseg(i)/2.0 * LOG( gij(i,i) ) + ( mseg(i)/2.0 - 1.0 ) * LOG( gij_hd(i)) ) + ELSE + fhc = fhc + x(i) * ( 1.0 - mseg(i) ) * LOG( gij(i,i) ) + END IF + END DO + + END SUBROUTINE F_CHAIN_TPT_D + + +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! + SUBROUTINE F_CHAIN_HU_LIU ( fhc ) +! + USE EOS_VARIABLES, ONLY: nc, ncomp, mseg, x, rho, eta + IMPLICIT NONE +! +! This subroutine calculates the hard chain contribution of the TPT-Liu-Hu Eos. +!--------------------------------------------------------------------- + REAL, INTENT(OUT) :: fhc +!--------------------------------------------------------------------- + REAL :: a2, b2, c2, a3, b3, c3 + REAL :: a20, b20, c20, a30, b30, c30 + REAL :: sum1, sum2, am, bm, cm + REAL :: zms +!--------------------------------------------------------------------- + + zms = 1.0 - eta + + sum1 = SUM( x(1:ncomp)*(mseg(1:ncomp)-1.0) ) + sum2 = SUM( x(1:ncomp)/mseg(1:ncomp)*(mseg(1:ncomp)-1.0)*(mseg(1:ncomp)-2.0) ) + + a2 = 0.45696 + a3 = -0.74745 + b2 = 2.10386 + b3 = 3.49695 + c2 = 1.75503 + c3 = 4.83207 + a20 = - a2 + b2 - 3.0*c2 + b20 = - a2 - b2 + c2 + c20 = c2 + a30 = - a3 + b3 - 3.0*c3 + b30 = - a3 - b3 + c3 + c30 = c3 + am = (3.0 + a20) * sum1 + a30 * sum2 + bm = (1.0 + b20) * sum1 + b30 * sum2 + cm = (1.0 + c20) * sum1 + c30 * sum2 + + fhc = - ( (am*eta - bm) / (2.0*zms) + bm/2.0/zms**2 - cm *LOG(ZMS) ) + + + END SUBROUTINE F_CHAIN_HU_LIU + +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! + SUBROUTINE F_CHAIN_HU_LIU_RC ( fhs, fhc ) +! + USE EOS_VARIABLES, ONLY: mseg, chiR, eta + IMPLICIT NONE +! +! This subroutine calculates the hard chain contribution of the TPT-Liu-Hu Eos. +!--------------------------------------------------------------------- + REAL, INTENT(IN) :: fhs + REAL, INTENT(OUT) :: fhc +!--------------------------------------------------------------------- + REAL :: a2, b2, c2, a3, b3, c3 + REAL :: para1,para2,para3,para4 + REAL :: aLH,bLH,cLH +!--------------------------------------------------------------------- + +! This routine is only for pure components + + a2 = 0.45696 + b2 = 2.10386 + c2 = 1.75503 + + para1 = -0.74745 + para2 = 0.299154629727814 + para3 = 1.087271036653154 + para4 = -0.708979110326831 + a3 = para1 + para2*chiR(1) + para3*chiR(1)**2 + para4*chiR(1)**3 + b3 = 3.49695 - (3.49695 + 0.317719074806190)*chiR(1) + c3 = 4.83207 - (4.83207 - 3.480163780334421)*chiR(1) + + aLH = mseg(1)*(1.0 + ((mseg(1)-1.0)/mseg(1))*a2 + ((mseg(1)-1.0)/mseg(1))*((mseg(1)-2.0)/mseg(1))*a3 ) + bLH = mseg(1)*(1.0 + ((mseg(1)-1.0)/mseg(1))*b2 + ((mseg(1)-1.0)/mseg(1))*((mseg(1)-2.0)/mseg(1))*b3 ) + cLH = mseg(1)*(1.0 + ((mseg(1)-1.0)/mseg(1))*c2 + ((mseg(1)-1.0)/mseg(1))*((mseg(1)-2.0)/mseg(1))*c3 ) + + fhc = ((3.0 + aLH - bLH + 3.0*cLH)*eta - (1.0 + aLH + bLH - cLH)) / (2.0*(1.0-eta)) + & + (1.0 + aLH + bLH - cLH) / ( 2.0*(1.0-eta)**2 ) + (cLH - 1.0)*LOG(1.0-eta) + + fhc = fhc - fhs + + END SUBROUTINE F_CHAIN_HU_LIU_RC + + + + +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! + SUBROUTINE F_DISP_PCSAFT ( fdsp ) +! + USE EOS_VARIABLES, ONLY: PI, rho, eta, z0t, apar, bpar, order1, order2 + IMPLICIT NONE +! +!--------------------------------------------------------------------- + REAL, INTENT(IN OUT) :: fdsp +!--------------------------------------------------------------------- + INTEGER :: m + REAL :: I1, I2, c1_con, z3, zms, m_mean +!--------------------------------------------------------------------- + + z3 = eta + zms = 1.0 - eta + m_mean = z0t / ( PI / 6.0 ) + + I1 = 0.0 + I2 = 0.0 + DO m = 0, 6 + I1 = I1 + apar(m) * z3**m + I2 = I2 + bpar(m) * z3**m + END DO + + c1_con= 1.0/ ( 1.0 + m_mean*(8.0*z3-2.0*z3**2 )/zms**4 & + + (1.0-m_mean)*( 20.0*z3-27.0*z3**2 +12.0*z3**3 -2.0*z3**4 )/(zms*(2.0-z3))**2 ) + + fdsp = -2.0*PI*rho*I1*order1 - PI*rho*c1_con*m_mean*I2*order2 + + END SUBROUTINE F_DISP_PCSAFT + +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! + SUBROUTINE F_DISP_CKSAFT ( fdsp ) +! + USE EOS_VARIABLES, ONLY: nc, ncomp, PI, TAU, t, rho, eta, x, z0t, mseg, vij, uij, parame, um + USE EOS_CONSTANTS, ONLY: DNM + IMPLICIT NONE +! +!--------------------------------------------------------------------- + REAL, INTENT(IN OUT) :: fdsp +!--------------------------------------------------------------------- + INTEGER :: i, j, n, m + REAL :: zmr, nmr, m_mean +!--------------------------------------------------------------------- + + m_mean = z0t / ( PI / 6.0 ) + + DO i = 1, ncomp + DO j = 1, ncomp + vij(i,j)=(0.5*((parame(i,2)*(1.0-0.12 *EXP(-3.0*parame(i,3)/t))**3 )**(1.0/3.0) & + +(parame(j,2)*(1.0-0.12 *EXP(-3.0*parame(j,3)/t))**3 )**(1.0/3.0)))**3 + END DO + END DO + zmr = 0.0 + nmr = 0.0 + DO i = 1, ncomp + DO j = 1, ncomp + zmr = zmr + x(i)*x(j)*mseg(i)*mseg(j)*vij(i,j)*uij(i,j) + nmr = nmr + x(i)*x(j)*mseg(i)*mseg(j)*vij(i,j) + END DO + END DO + um = zmr / nmr + fdsp = 0.0 + DO n = 1, 4 + DO m = 1, 9 + fdsp = fdsp + DNM(n,m) * (um/t)**n *(eta/TAU)**m + END DO + END DO + fdsp = m_mean * fdsp + + + END SUBROUTINE F_DISP_CKSAFT + +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! + SUBROUTINE F_ASSOCIATION ( eps_kij, k_kij, fhb ) +! + USE EOS_VARIABLES, ONLY: nc, nsite, ncomp, t, z0t, z1t, z2t, z3t, rho, eta, x, & + parame, sig_ij, dij_ab, gij, nhb_typ, mx, nhb_no + IMPLICIT NONE +! +!--------------------------------------------------------------------- + REAL, INTENT(IN) :: eps_kij, k_kij + REAL, INTENT(IN OUT) :: fhb +!--------------------------------------------------------------------- + LOGICAL :: assoc + INTEGER :: i, j, k, l, no, ass_cnt, max_eval + REAL, DIMENSION(nc,nc) :: kap_hb + REAL, DIMENSION(nc,nc,nsite,nsite) :: eps_hb + REAL, DIMENSION(nc,nsite,nc,nsite) :: delta + REAL, DIMENSION(nc,nsite) :: mx_itr + REAL :: err_sum, sum0, amix, tol, ass_s1, ass_s2 + REAL :: z0, z1, z2, z3, zms +!--------------------------------------------------------------------- + + assoc = .false. + DO i = 1,ncomp + IF (NINT(parame(i,12)) /= 0) assoc = .true. + END DO + IF (assoc) THEN + + rho = eta / z3t + z0 = z0t * rho + z1 = z1t * rho + z2 = z2t * rho + z3 = z3t * rho + zms = 1.0 - z3 + + DO i = 1, ncomp + DO j = 1, ncomp + gij(i,j) = 1.0/zms + 3.0*dij_ab(i,j)*z2/zms/zms + 2.0*(dij_ab(i,j)*z2)**2 / zms**3 + END DO + END DO + + + DO i = 1, ncomp + IF ( NINT(parame(i,12)) /= 0 ) THEN + nhb_typ(i) = NINT( parame(i,12) ) + kap_hb(i,i) = parame(i,13) + no = 0 + DO k = 1,nhb_typ(i) + DO l = 1,nhb_typ(i) + eps_hb(i,i,k,l) = parame(i,(14+no)) + no = no + 1 + END DO + END DO + DO k = 1,nhb_typ(i) + nhb_no(i,k) = parame(i,(14+no)) + no = no + 1 + END DO + ELSE + nhb_typ(i) = 0 + kap_hb(i,i)= 0.0 + DO k = 1,nsite + DO l = 1,nsite + eps_hb(i,i,k,l) = 0.0 + END DO + END DO + END IF + END DO + + DO i = 1,ncomp + DO j = 1,ncomp + IF ( i /= j .AND. (nhb_typ(i) /= 0.AND.nhb_typ(j) /= 0) ) THEN + ! kap_hb(i,j)= (kap_hb(i,i)+kap_hb(j,j))/2.0 + ! kap_hb(i,j)= ( ( kap_hb(i,i)**(1.0/3.0) + kap_hb(j,j)**(1.0/3.0) )/2.0 )**3 + kap_hb(i,j) = (kap_hb(i,i)*kap_hb(j,j))**0.5 & + *((parame(i,2)*parame(j,2))**3 )**0.5 & + / (0.5*(parame(i,2)+parame(j,2)))**3 + kap_hb(i,j)= kap_hb(i,j)*(1.0-k_kij) + DO k = 1,nhb_typ(i) + DO l = 1,nhb_typ(j) + IF ( k /= l .AND. nhb_typ(i) >= 2 .AND. nhb_typ(j) >= 2 ) THEN + eps_hb(i,j,k,l) = (eps_hb(i,i,k,l)+eps_hb(j,j,l,k))/2.0 + ! eps_hb(i,j,k,l) = (eps_hb(i,i,k,l)*eps_hb(j,j,l,k))**0.5 + eps_hb(i,j,k,l) = eps_hb(i,j,k,l)*(1.0-eps_kij) + ELSE IF ( nhb_typ(i) == 1 .AND. l > k ) THEN + eps_hb(i,j,k,l) = (eps_hb(i,i,k,k)+eps_hb(j,j,l,k))/2.0 + eps_hb(j,i,l,k) = (eps_hb(i,i,k,k)+eps_hb(j,j,l,k))/2.0 + eps_hb(i,j,k,l) = eps_hb(i,j,k,l)*(1.0-eps_kij) + eps_hb(j,i,l,k) = eps_hb(j,i,l,k)*(1.0-eps_kij) + END IF + END DO + END DO + END IF + END DO + END DO + +!-----setting the self-association to zero for ionic compounds------ + DO i = 1,ncomp + IF ( parame(i,10) /= 0) kap_hb(i,i)=0.0 + DO j = 1,ncomp + IF ( parame(i,10) /= 0 .AND. parame(j,10) /= 0 ) kap_hb(i,j) = 0.0 + END DO + END DO + ! kap_hb(1,2)=0.050 + ! kap_hb(2,1)=0.050 + ! eps_hb(2,1,1,1)=465.0 + ! eps_hb(1,2,1,1)=465.0 + ! nhb_typ(1) = 1 + ! nhb_typ(2) = 1 + ! nhb_no(1,1)= 1.0 + ! nhb_no(2,1)= 1.0 + + + DO i = 1, ncomp + DO k = 1, nhb_typ(i) + DO j = 1, ncomp + DO l = 1, nhb_typ(j) + delta(i,k,j,l)=gij(i,j)*kap_hb(i,j)*(EXP(eps_hb(i,j,k,l)/t)-1.0) *sig_ij(i,j)**3 +!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! +! IF ((i+j).EQ.3) delta(i,k,j,l)=94.0 +!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! + END DO + END DO + IF ( mx(i,k) == 0.0 ) mx(i,k) = 1.0 + END DO + END DO + +!------constants for Iteration --------------------------------------- + amix = 0.7 + tol = 1.E-10 + IF (eta < 0.2) tol = 1.E-11 + IF (eta < 0.01) tol = 1.E-14 + max_eval = 200 + +! --- Iterate over all components and all sites ------------------------ + ass_cnt = 0 + iterate_TPT1: DO + + ass_cnt = ass_cnt + 1 + + DO i = 1, ncomp + DO k = 1, nhb_typ(i) + sum0 = 0.0 + DO j = 1, ncomp + DO l = 1, nhb_typ(j) + sum0 = sum0 + x(j)* mx(j,l)*nhb_no(j,l) *delta(i,k,j,l) + END DO + END DO + mx_itr(i,k) = 1.0 / (1.0 + sum0*rho) + END DO + END DO + + err_sum = 0.0 + DO i = 1, ncomp + DO k = 1, nhb_typ(i) + err_sum = err_sum + ABS( mx_itr(i,k) - mx(i,k) ) ! / ABS(mx_itr(i,k)) + mx(i,k) = mx_itr(i,k) * amix + mx(i,k) * (1.0 - amix) + IF ( mx(i,k) <= 0.0 ) mx(i,k)=1.E-50 + IF ( mx(i,k) > 1.0 ) mx(i,k)=1.0 + END DO + END DO + + IF ( err_sum <= tol .OR. ass_cnt >= max_eval ) THEN + IF ( ass_cnt >= max_eval ) WRITE(*,*) 'F_NUMERICAL: Max_eval violated = ',err_sum,tol + EXIT iterate_TPT1 + END IF + + END DO iterate_TPT1 + + DO i = 1, ncomp + ass_s1 = 0.0 + ass_s2 = 0.0 + DO k = 1, nhb_typ(i) + ass_s1 = ass_s1 + nhb_no(i,k) * ( 1.0 - mx(i,k) ) + ass_s2 = ass_s2 + nhb_no(i,k) * LOG(mx(i,k)) + END DO + fhb = fhb + x(i) * ( ass_s2 + ass_s1/2.0 ) + END DO + + END IF + + END SUBROUTINE F_ASSOCIATION + + +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! + SUBROUTINE F_ION_DIPOLE_TBH ( fhend ) +! + USE EOS_VARIABLES, ONLY: nc, PI, KBOL, NAv, ncomp, t, rho, eta, x, z0t, parame, uij, sig_ij + IMPLICIT NONE +! +!--------------------------------------------------------------------- + REAL, INTENT(IN OUT) :: fhend +!--------------------------------------------------------------------- + INTEGER :: i, dipole, ions + REAL :: m_mean + REAL :: fh32, fh2, fh52, fh3 + REAL :: e_elem, eps_cc0, rho_sol, dielec + REAL :: polabil, ydd, kappa, x_dipol, x_ions + REAL, DIMENSION(nc) :: my2dd, z_ii, e_cd, x_dd, x_ii + REAL :: sig_c, sig_d, sig_cd, r_s + REAL :: I0cc, I1cc, I2cc, Icd, Idd + REAL :: Iccc, Iccd, Icdd, Iddd +!--------------------------------------------------------------------- + +m_mean = z0t / ( PI / 6.0 ) + +!----------------Dieletric Constant of Water-------------------------- +e_elem = 1.602189246E-19 ! in Unit [Coulomb] +eps_cc0 = 8.854187818E-22 ! in Unit [Coulomb**2 /(J*Angstrom)] +! Correlation of M. Uematsu and E. U. Frank +! (Static Dieletric Constant of Water and Steam) +! valid range of conditions 273,15 K <=T<= 823,15 K +! and density <= 1150 kg/m3 (i.e. 0 <= p <= 500 MPa) +rho_sol = rho * 18.015 * 1.E27/ NAv +rho_sol = rho_sol/1000.0 +dielec = 1.0+(7.62571/(t/293.15))*rho_sol +(2.44E2/(t/293.15)-1.41E2 & + + 2.78E1*(t/293.15))*rho_sol**2 & + + (-9.63E1/(t/293.15)+4.18E1*(t/293.15) & + - 1.02E1*(t/293.15)**2 )*rho_sol**3 +(-4.52E1/(t/293.15)**2 & + + 8.46E1/(t/293.15)-3.59E1)*rho_sol**4 + + +! !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! + +dielec = 1.0 + +! !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! + + +!----------------Dipole-Ion Term----------------------------------- +dipole = 0 +ions = 0 +fhend = 0.0 +DO i = 1, ncomp + IF ( parame(i,6) /= 0.0 .AND. uij(i,i) /= 0.0 .AND. x(i) > 0.0 ) THEN + my2dd(i) = (parame(i,6))**2 *1.E-49 / (uij(i,i)*KBOL*sig_ij(i,i)**3 *1.E-30) + dipole = 1 + ELSE + my2dd(i) = 0.0 + END IF + + z_ii(i) = parame(i,10) + IF ( z_ii(i) /= 0.0 .AND. uij(i,i) /= 0.0 .AND. x(i) > 0.0 ) THEN + e_cd(i) = ( parame(i,10)*e_elem* 1.E5 / SQRT(1.11265005) )**2 & + / ( uij(i,i)*kbol*sig_ij(i,i)*1.E-10 ) + ions = 1 + ELSE + e_cd(i) = 0.0 + END IF +END DO + + +IF ( dipole == 1 .AND. ions == 1 ) THEN + + ydd = 0.0 + kappa = 0.0 + x_dipol = 0.0 + x_ions = 0.0 + polabil = 0.0 + DO i = 1, ncomp + ydd = ydd + x(i)*(parame(i,6))**2 *1.E-49/ (kbol*t*1.E-30) + kappa = kappa + x(i) & + *(parame(i,10)*e_elem* 1.E5/SQRT(1.11265005))**2 /(KBOL*t*1.E-10) + IF (parame(i,10) /= 0.0) THEN + x_ions = x_ions + x(i) + ELSE + polabil = polabil + 4.0*PI*x(i)*rho*1.4573 *1.E-30 & + / (sig_ij(3,3)**3 *1.E-30) + END IF + IF (parame(i,6) /= 0.0) x_dipol= x_dipol+ x(i) + END DO + ydd = ydd * 4.0/9.0 * PI * rho + kappa = SQRT( 4.0 * PI * rho * kappa ) + + fh2 = 0.0 + sig_c = 0.0 + sig_d = 0.0 + DO i=1,ncomp + x_ii(i) = 0.0 + x_dd(i) = 0.0 + IF(parame(i,10) /= 0.0 .AND. x_ions /= 0.0) x_ii(i) = x(i)/x_ions + IF(parame(i,6) /= 0.0 .AND. x_dipol /= 0.0) x_dd(i) = x(i)/x_dipol + sig_c = sig_c + x_ii(i)*parame(i,2) + sig_d = sig_d + x_dd(i)*parame(i,2) + END DO + sig_cd = 0.5 * (sig_c + sig_d) + + r_s = 0.0 + ! DO i=1,ncomp + ! r_s=r_s + rho * x(i) * dhs(i)**3 + ! END DO + r_s = eta*6.0 / PI / m_mean + + I0cc = - (1.0 + 0.97743 * r_s + 0.05257*r_s*r_s) & + /(1.0 + 1.43613 * r_s + 0.41580*r_s*r_s) + ! I1cc = - (10.0 - 2.0*z3 + z3*z3) /20.0/(1.0 + 2.0*z3) + I1cc = - (10.0 - 2.0*r_s*pi/6.0 + r_s*r_s*pi/6.0*pi/6.0) & + /20.0/(1.0 + 2.0*r_s*pi/6.0) +!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! + ! I2cc = + (z3-4.0)*(z3*z3+2.0) /24.0/(1.0+2.0*z3) + ! relation of Stell and Lebowitz + I2cc = -0.33331+0.7418*r_s - 1.2047*r_s*r_s & + + 1.6139*r_s**3 - 1.5487*r_s**4 + 0.6626*r_s**5 +!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! + Icd = (1.0 + 0.79576 *r_s + 0.104556 *r_s*r_s) & + /(1.0 + 0.486704*r_s - 0.0222903*r_s*r_s) + Idd = (1.0 + 0.18158*r_s - 0.11467*r_s*r_s) & + /3.0/(1.0 - 0.49303*r_s + 0.06293*r_s*r_s) + Iccc= 3.0*(1.0 - 1.05560*r_s + 0.26591*r_s*r_s) & + /2.0/(1.0 + 0.53892*r_s - 0.94236*r_s*r_s) + Iccd= 11.0*(1.0 + 2.25642 *r_s + 0.05679 *r_s*r_s) & + /6.0/(1.0 + 2.64178 *r_s + 0.79783 *r_s*r_s) + Icdd= 0.94685*(1.0 + 2.97323 *r_s + 3.11931 *r_s*r_s) & + /(1.0 + 2.70186 *r_s + 1.22989 *r_s*r_s) + Iddd= 5.0*(1.0 + 1.12754*r_s + 0.56192*r_s*r_s) & + /24.0/(1.0 - 0.05495*r_s + 0.13332*r_s*r_s) + + IF ( sig_c <= 0.0 ) WRITE (*,*) 'error in Henderson ion term' + + fh32= - kappa**3 /(12.0*pi*rho) + fh2 = - 3.0* kappa**2 * ydd*Icd /(8.0*pi*rho) / sig_cd & + - kappa**4 *sig_c/(16.0*pi*rho)*I0cc + IF (sig_d /= 0.0) fh2 = fh2 - 27.0* ydd * ydd*Idd & + /(8.0*pi*rho) / sig_d**3 + fh52= (3.0*kappa**3 * ydd + kappa**5 *sig_c**2 *I1cc) & + /(8.0*pi*rho) + fh3 = - kappa**6 * sig_c**3 /(8.0*pi*rho) *(I2cc-Iccc/6.0) & + + kappa**4 * ydd *sig_c/(16.0*pi*rho) & + *( (6.0+5.0/3.0*sig_d/sig_c)*I0cc + 3.0*sig_d/sig_c*Iccd ) & + + 3.0*kappa**2 * ydd*ydd /(8.0*pi*rho) / sig_cd & + *( (2.0-3.21555*sig_d/sig_cd)*Icd +3.0*sig_d/sig_cd*Icdd ) + IF (sig_d /= 0.0) fh3 = fh3 + 27.0*ydd**3 & + /(16.0*pi*rho)/sig_d**3 *Iddd + + fhend = ( fh32 + (fh32*fh32*fh3-2.0*fh32*fh2*fh52+fh2**3 ) & + /(fh2*fh2-fh32*fh52) ) & + / ( 1.0 + (fh32*fh3-fh2*fh52) /(fh2*fh2-fh32*fh52) & + - (fh2*fh3-fh52*fh52) /(fh2*fh2-fh32*fh52) ) +!---------- +! fH32= - kappa**3 /(12.0*PI*rho) +! fH2 = - 3.0* kappa**2 * ydd*Icd /(8.0*PI*rho) / sig_cd +! fH52= (3.0*kappa**3 * ydd)/(8.0*PI*rho) +! fH3 = + kappa**4 * ydd *sig_c/(16.0*PI*rho) & +! *( (6.0+5.0/3.0*sig_d/sig_c)*0.0*I0cc + 3.0*sig_d/sig_c*Iccd) & +! + 3.0*kappa**2 * ydd*ydd /(8.0*PI*rho) / sig_cd & +! *( (2.0-3.215550*sig_d/sig_cd)*Icd +3.0*sig_d/sig_cd*Icdd ) + +! fHcd = ( + (fH32*fH32*fH3-2.0*fH32*fH2*fH52+fH2**3 ) & +! /(fH2*fH2-fH32*fH52) ) & +! / ( 1.0 + (fH32*fH3-fH2*fH52) /(fH2*fH2-fH32*fH52) & +! - (fH2*fH3-fH52*fH52) /(fH2*fH2-fH32*fH52) ) + +END IF + + END SUBROUTINE F_ION_DIPOLE_TBH + + +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! + SUBROUTINE F_ION_ION_PrimMSA ( fcc ) +! + USE EOS_VARIABLES, ONLY: nc, PI, KBOL, NAv, ncomp, t, rho, x, parame, mx + IMPLICIT NONE +! +!--------------------------------------------------------------------- + REAL, INTENT(IN OUT) :: fcc +!--------------------------------------------------------------------- + INTEGER :: i, j, cc_it, ions + REAL :: e_elem, eps_cc0, rho_sol, dielec + REAL :: x_ions + REAL :: cc_sig1, cc_sig2, cc_sig3 + REAL, DIMENSION(nc) :: z_ii, x_ii, sigm_i, my2dd + REAL :: alpha_2, kappa, ii_par + REAL :: cc_omeg, p_n, q2_i, cc_q2, cc_gam + REAL :: cc_error(2), cc_delt + REAL :: rhs, lambda, lam_s +!--------------------------------------------------------------------- + +!----------------Dieletric Constant of Water-------------------------- +e_elem = 1.602189246E-19 ! in Unit [Coulomb] +eps_cc0 = 8.854187818E-22 ! in Unit [Coulomb**2 /(J*Angstrom)] +! Correlation of M. Uematsu and E. U. Frank +! (Static Dieletric Constant of Water and Steam) +! valid range of conditions 273,15 K <=T<= 823,15 K +! and density <= 1150 kg/m3 (i.e. 0 <= p <= 500 MPa) +rho_sol = rho * 18.015 * 1.E27/ NAv +rho_sol = rho_sol/1000.0 +dielec = 1.0+(7.62571/(t/293.15))*rho_sol +(2.44E2/(t/293.15)-1.41E2 & + +2.78E1*(t/293.15))*rho_sol**2 & + +(-9.63E1/(t/293.15)+4.18E1*(t/293.15) & + -1.02E1*(t/293.15)**2 )*rho_sol**3 +(-4.52E1/(t/293.15)**2 & + +8.46E1/(t/293.15)-3.59E1)*rho_sol**4 + + +! !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! + +dielec = 1.0 + +! !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! + + +!----------------Ion-Ion: primitive MSA ------------------------------- +! the (dipole moment)**2 [my**2] corresponds to an attraction from +! point charges of [ SUM(xi * zi**2 * e_elem**2) * 3 * di**2 ] + +! parame(ion,6))**2 * 1.E-49 / (kbol*T) +! = (e_elem* 1.E5/SQRT(1.112650050))**2 +! *x(i)*zi**2 *3.0*sig_ij(1,1)**2 *1.E-20 + +! parame(ion,6))**2 = (e_elem* 1.E5/SQRT(1.112650050))**2 /1.E-49 +! *x(i)*zi**2 *3.0*sig_ij(i,i)**2 *1.E-20 + +! with the units +! my**2 [=] D**2 = 1.E-49 J*m3 +! e_elem **2 [=] C**2 = 1.E5 / SQRT(1.112650050) J*m + + +ions = 0 +x_ions = 0.0 +fcc = 0.0 +DO i = 1, ncomp + z_ii(i) = parame(i,10) + IF (z_ii(i) /= 0.0) THEN + sigm_i(i) = parame(i,2) + ELSE + sigm_i(i) = 0.0 + END IF + IF (z_ii(i) /= 0.0) ions = 1 + IF (z_ii(i) /= 0.0) x_ions = x_ions + x(i) +END DO + +IF (ions == 1 .AND. x_ions > 0.0) THEN + + cc_sig1 = 0.0 + cc_sig2 = 0.0 + cc_sig3 = 0.0 + DO i=1,ncomp + IF (z_ii(i) /= 0.0) THEN + x_ii(i) = x(i)/x_ions + ELSE + x_ii(i) =0.0 + END IF + cc_sig1 = cc_sig1 +x_ii(i)*sigm_i(i) + cc_sig2 = cc_sig2 +x_ii(i)*sigm_i(i)**2 + cc_sig3 = cc_sig3 +x_ii(i)*sigm_i(i)**3 + END DO + + + ! alpha_2 = 4.0*PI*e_elem**2 /eps_cc0/dielec/kbol/T + alpha_2 = e_elem**2 /eps_cc0 / dielec / KBOL/t + kappa = 0.0 + DO i = 1, ncomp + kappa = kappa + x(i)*z_ii(i)*z_ii(i)*mx(i,1) + END DO + kappa = SQRT( rho * alpha_2 * kappa ) + ii_par= kappa * cc_sig1 + + ! Temporaer: nach der Arbeit von Krienke verifiziert + ! noch nicht fuer Mischungen mit unterschiedl. Ladung erweitert + ! ii_par = DSQRT( e_elem**2 /eps_cc0/dielec/kbol/T & + ! *rho*(x(1)*Z_ii(1)**2 + x(2)*Z_ii(2)**2 ) )*cc_sig1 + + + cc_gam = kappa/2.0 + + ! noch offen !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! + cc_delt = 0.0 + DO i = 1, ncomp + cc_delt = cc_delt + x(i)*mx(i,1)*rho*sigm_i(i)**3 + END DO + cc_delt= 1.0 - PI/6.0*cc_delt + + cc_it = 0 + 13 CONTINUE + j = 0 + cc_it = cc_it + 1 + 131 CONTINUE + j = j + 1 + cc_omeg = 0.0 + DO i = 1, ncomp + cc_omeg = cc_omeg +x(i)*mx(i,1)*sigm_i(i)**3 /(1.0+cc_gam*sigm_i(i)) + END DO + cc_omeg = 1.0 + PI/2.0 / cc_delt * rho * cc_omeg + p_n = 0.0 + DO i = 1, ncomp + p_n = p_n + x(i)*mx(i,1)*rho / cc_omeg*sigm_i(i)*z_ii(i) / (1.0+cc_gam*sigm_i(i)) + END DO + q2_i = 0.0 + cc_q2= 0.0 + DO i = 1, ncomp + q2_i = q2_i + rho*x(i)*mx(i,1)*( (z_ii(i)-pi/2.0/cc_delt*sigm_i(i)**2 *p_n) & + /(1.0+cc_gam*sigm_i(i)) )**2 + cc_q2 = cc_q2 + x(i)*mx(i,1)*rho*z_ii(i)**2 / (1.0+cc_gam*sigm_i(i)) + END DO + q2_i = q2_i*alpha_2 / 4.0 + + cc_error(j) = cc_gam - SQRT(q2_i) + IF (j == 1) cc_gam = cc_gam*1.000001 + IF (j == 2) cc_gam = cc_gam - cc_error(2)* (cc_gam-cc_gam/1.000001)/(cc_error(2)-cc_error(1)) + + IF ( j == 1 .AND. ABS(cc_error(1)) > 1.E-15 ) GO TO 131 + IF ( cc_it >= 10 ) THEN + WRITE (*,*) ' cc error' + STOP + END IF + IF ( j /= 1 ) GO TO 13 + + fcc= - alpha_2 / PI/4.0 /rho* (cc_gam*cc_q2 & + + pi/2.0/cc_delt *cc_omeg*p_n**2 ) + cc_gam**3 /pi/3.0/rho + ! Restricted Primitive Model + ! fcc=-(3.0*ii_par*ii_par+6.0*ii_par+2.0 & + ! -2.0*(1.0+2.0*ii_par)**1.50) & + ! /(12.0*PI*rho *cc_sig1**3 ) + + ! fcc = x_ions * fcc + + my2dd(3) = (parame(3,6))**2 *1.E-19 /(KBOL*t) + my2dd(3) = (1.84)**2 *1.E-19 /(kbol*t) + + rhs = 12.0 * PI * rho * x(3) * my2dd(3) + lam_s = 1.0 + 12 CONTINUE + lambda = (rhs/((lam_s+2.0)**2 ) + 16.0/((1.0+lam_s)**4 ) )**0.5 + IF ( ABS(lam_s-lambda) > 1.E-10 )THEN + lam_s = ( lambda + lam_s ) / 2.0 + GO TO 12 + END IF + + ! f_cd = -(ii_par*ii_par)/(4.0*PI*rho*m_mean *cc_sig1**3 ) & + ! *(dielec-1.0)/(1.0 + parame(3,2)/cc_sig1/lambda) + ! write (*,*) ' ',f_cd,fcc,x_ions + ! f_cd = f_cd/(1.0 - fcc/f_cd) + ! fcc = 0.0 + +END IF + + +END SUBROUTINE F_ION_ION_PrimMSA + + +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! + SUBROUTINE F_ION_ION_nonPrimMSA ( fdd, fqq, fdq, fcc ) +! + USE EOS_VARIABLES, ONLY: nc, ncomp, t, eta, x, parame, mseg + IMPLICIT NONE +! +!--------------------------------------------------------------------- + REAL, INTENT(IN OUT) :: fdd, fqq, fdq, fcc +!--------------------------------------------------------------------- + INTEGER :: dipole + !REAL :: A_MSA !, A_CC, A_CD, A_DD, U_MSA, chempot + REAL, DIMENSION(nc) :: x_export, msegm +!--------------------------------------------------------------------- + + dipole = 0 + IF ( SUM( parame(1:ncomp,6) ) > 1.E-5 ) dipole = 1 + + IF ( dipole /= 0 ) THEN ! alternatively ions and dipoles = 1 + fdd = 0.0 + fqq = 0.0 + fdq = 0.0 + fcc = 0.0 + msegm(:) = mseg(:) ! the entries of the vector mseg and x are changed + x_export(:) = x(:) ! in SEMIRESTRICTED because the ions should be positioned first + ! that is why dummy vectors msegm and x_export are defined + !CALL SEMIRESTRICTED (A_MSA,A_CC,A_CD,A_DD,U_MSA, & + ! chempot,ncomp,parame,t,eta,x_export,msegm,0) + !fdd = A_MSA + write (*,*) 'why are individual contrib. A_CC,A_CD,A_DD not used' + stop + END IF + + END SUBROUTINE F_ION_ION_nonPrimMSA + + +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! + SUBROUTINE F_LC_MayerSaupe ( flc ) +! + USE EOS_VARIABLES, ONLY: nc, PI, KBOL, NAv, ncomp, phas, t, rho, eta, & + x, mseg, parame, E_lc, S_lc, dhs + IMPLICIT NONE +! +!--------------------------------------------------------------------- + REAL, INTENT(IN OUT) :: flc +!--------------------------------------------------------------------- + INTEGER :: i, j, k + INTEGER :: liq_crystal, count_lc, steps_lc + REAL :: alpha_lc, tolerance, deltay + REAL :: integrand1, integrand2, accel_lc + REAL :: error_lc, u_term, sphase + REAL, DIMENSION(nc) :: z_lc, S_lc1, S_lc2, sumu + REAL, DIMENSION(nc,nc) :: u_lc, klc +!--------------------------------------------------------------------- +INTEGER :: stabil +COMMON /stabil / stabil +!--------------------------------------------------------------------- + + + klc(1,2) = 0.0 + klc(2,1) = klc(1,2) + + alpha_lc = 1.0 + accel_lc = 4.0 + IF ( eta < 0.35 ) accel_lc = 1.3 + IF ( eta < 0.15 ) accel_lc = 1.0 + + liq_crystal = 0 + DO i = 1, ncomp + DO j = 1, ncomp + E_lc(i,j) = (E_lc(i,i)*E_lc(j,j))**0.5 *(1.0-klc(i,j)) !combining rule + ! E_LC(i,j)= ( E_LC(i,i)+E_LC(j,j) ) * 0.5 !combining rule + ! S_LC(i,j)= ( S_LC(i,i)+S_LC(j,j) ) * 0.5 !combining rule + IF (E_lc(i,j) /= 0.0) liq_crystal = 1 + END DO + END DO + ! S_LC(1,2) = 0.0 + ! S_LC(2,1) = S_LC(1,2) + ! E_LC(1,2) = 60.0 + ! E_LC(2,1) = E_LC(1,2) + + IF ( liq_crystal == 1 .AND. phas == 1 .AND. stabil == 0 ) THEN + + count_lc = 0 + tolerance = 1.E-6 + + steps_lc = 200 + deltay = 1.0 / REAL(steps_lc) + + ! --- dimensionless function U_LC repres. anisotr. intermolecular interactions in l.c. + + DO i = 1, ncomp + DO j = 1, ncomp + u_lc(i,j) = 2.0/3.0*pi*mseg(i)*mseg(j) *(0.5*(dhs(i)+dhs(j)))**3 & ! sig_ij(i,j)**3 + *(E_lc(i,j)/t+S_lc(i,j))*rho + END DO + END DO + + + DO i=1,ncomp + ! S_lc2(i) = 0.0 !for isotropic + S_lc2(i) = 0.5 !for nematic + S_lc1(i) = S_lc2(i) + END DO + + 1 CONTINUE + + DO i = 1, ncomp + IF (S_lc2(i) <= 0.3) S_lc1(i) = S_lc2(i) + IF (S_lc2(i) > 0.3) S_lc1(i) = S_lc1(i) + (S_lc2(i)-S_lc1(i))*accel_lc + END DO + + count_lc = count_lc + 1 + + ! --- single-particle orientation partition function Z_LC in liquid crystals + + DO i = 1, ncomp + sumu(i) = 0.0 + DO j = 1, ncomp + sumu(i) = sumu(i) + x(j)*u_lc(i,j)*S_lc1(j) + END DO + END DO + + DO i = 1, ncomp + z_lc(i) = 0.0 + integrand1 = EXP(-0.5*sumu(i)) !eq. for Z_LC with y=0 + DO k = 1, steps_lc + integrand2 = EXP(0.5*sumu(i)*(3.0*(deltay*REAL(k)) **2 -1.0)) + z_lc(i) = z_lc(i) + (integrand1 + integrand2)/2.0*deltay + integrand1 = integrand2 + END DO !k-index integration + END DO !i-index Z_LC(i) calculation + + ! --- order parameter S_lc in liquid crystals ----------------------- + + error_lc = 0.0 + DO i = 1, ncomp + S_lc2(i) = 0.0 + integrand1 = -1.0/z_lc(i)*0.5*EXP(-0.5*sumu(i)) !for S_lc with y=0 + DO k = 1, steps_lc + integrand2 = 1.0/z_lc(i)*0.5*(3.0*(deltay*REAL(k)) & + **2 -1.0)*EXP(0.5*sumu(i)*(3.0 *(deltay*REAL(k))**2 -1.0)) + S_lc2(i) = S_lc2(i) + (integrand1 + integrand2)/2.0*deltay + integrand1 = integrand2 + END DO !k-index integration + error_lc = error_lc + ABS(S_lc2(i)-S_lc1(i)) + END DO !i-index Z_LC(i) calculation + + sphase = 0.0 + DO i = 1, ncomp + sphase = sphase + S_lc2(i) + END DO + IF (sphase < 1.E-4) THEN + error_lc = 0.0 + DO i = 1, ncomp + S_lc2(i)= 0.0 + z_lc(i) = 1.0 + END DO + END IF + + + ! write (*,*) count_LC,S_lc2(1)-S_lc1(1),S_lc2(2)-S_lc1(2) + IF (error_lc > tolerance .AND. count_lc < 400) GO TO 1 + ! write (*,*) 'done',eta,S_lc2(1),S_lc2(2) + + IF (count_lc == 400) WRITE (*,*) 'LC iteration not converg.' + + ! --- the anisotropic contribution to the Helmholtz energy ---------- + + u_term = 0.0 + DO i = 1, ncomp + DO j = 1, ncomp + u_term = u_term + 0.5*x(i)*x(j)*S_lc2(i) *S_lc2(j)*u_lc(i,j) + END DO + END DO + + flc = 0.0 + DO i = 1, ncomp + IF (z_lc(i) /= 0.0) flc = flc - x(i) * LOG(z_lc(i)) + END DO + flc = flc + u_term + ! pause + + END IF + ! write (*,'(i2,i2,4(f15.8))') phas,stabil,flc,eta,S_lc2(1),x(1) + + + END SUBROUTINE F_LC_MayerSaupe + + + +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! + SUBROUTINE P_POLAR ( zdd, zddz, zddz2, zddz3, zqq, zqqz, zqqz2, zqqz3, zdq, zdqz, zdqz2, zdqz3 ) +! + USE EOS_VARIABLES, ONLY: ncomp, parame, dd_term, qq_term, dq_term + IMPLICIT NONE +! +! ---------------------------------------------------------------------- + REAL, INTENT(OUT) :: zdd, zddz, zddz2, zddz3 + REAL, INTENT(OUT) :: zqq, zqqz, zqqz2, zqqz3 + REAL, INTENT(OUT) :: zdq, zdqz, zdqz2, zdqz3 +! +! --- local variables--------------------------------------------------- + INTEGER :: dipole + INTEGER :: quadrupole + INTEGER :: dipole_quad +! ---------------------------------------------------------------------- + + zdd = 0.0 + zddz = 0.0 + zddz2 = 0.0 + zddz3 = 0.0 + zqq = 0.0 + zqqz = 0.0 + zqqz2 = 0.0 + zqqz3 = 0.0 + zdq = 0.0 + zdqz = 0.0 + zdqz2 = 0.0 + zdqz3 = 0.0 + + dipole = 0 + quadrupole = 0 + dipole_quad = 0 + IF ( SUM( parame(1:ncomp,6) ) /= 0.0 ) dipole = 1 + IF ( SUM( parame(1:ncomp,7) ) /= 0.0 ) quadrupole = 1 + IF ( dipole == 1 .AND. quadrupole == 1 ) dipole_quad = 1 + + ! -------------------------------------------------------------------- + ! dipole-dipole term + ! -------------------------------------------------------------------- + IF (dipole == 1) THEN + + IF (dd_term == 'GV') CALL P_DD_GROSS_VRABEC( zdd, zddz, zddz2, zddz3 ) + ! IF (dd_term == 'SF') CALL F_DD_SAAGER_FISCHER( k ) + IF (dd_term /= 'GV' .AND. dd_term /= 'SF') write (*,*) 'specify dipole term !' + + ENDIF + + ! -------------------------------------------------------------------- + ! quadrupole-quadrupole term + ! -------------------------------------------------------------------- + IF (quadrupole == 1) THEN + + !IF (qq_term == 'SF') CALL F_QQ_SAAGER_FISCHER( k ) + IF (qq_term == 'JG') CALL P_QQ_GROSS( zqq, zqqz, zqqz2, zqqz3 ) + IF (qq_term /= 'JG' .AND. qq_term /= 'SF') write (*,*) 'specify quadrupole term !' + + ENDIF + + ! -------------------------------------------------------------------- + ! dipole-quadrupole cross term + ! -------------------------------------------------------------------- + IF (dipole_quad == 1) THEN + + IF (dq_term == 'VG') CALL P_DQ_VRABEC_GROSS( zdq, zdqz, zdqz2, zdqz3 ) + IF (dq_term /= 'VG' ) write (*,*) 'specify DQ-cross term !' + + ENDIF + +END SUBROUTINE P_POLAR + + +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! + SUBROUTINE P_DD_GROSS_VRABEC( zdd, zddz, zddz2, zddz3 ) +! + USE PARAMETERS, ONLY: PI, KBOL + USE EOS_VARIABLES, ONLY: nc, ncomp, uij, parame, mseg, sig_ij, rho, eta, x, t + USE EOS_CONSTANTS, ONLY: ddp2, ddp3, ddp4 + IMPLICIT NONE +! +! ---------------------------------------------------------------------- + REAL, INTENT(IN OUT) :: zdd, zddz, zddz2, zddz3 +! ---------------------------------------------------------------------- + INTEGER :: i, j, k, m + REAL :: factor2, factor3, z3 + REAL :: xijfa, xijkfa, eij + REAL :: fdddr, fddd2, fddd3, fddd4 + REAL :: fdd2, fdd2z, fdd2z2, fdd2z3, fdd2z4 + REAL :: fdd3, fdd3z, fdd3z2, fdd3z3, fdd3z4 + REAL, DIMENSION(nc) :: my2dd + REAL, DIMENSION(nc,nc) :: Idd2, Idd2z, Idd2z2, Idd2z3, Idd2z4 + REAL, DIMENSION(nc,nc) :: Idd4, Idd4z, Idd4z2, Idd4z3, Idd4z4 + REAL, DIMENSION(nc,nc,nc) :: Idd3, Idd3z, Idd3z2, Idd3z3, Idd3z4 +! ---------------------------------------------------------------------- + + + zdd = 0.0 + zddz = 0.0 + zddz2 = 0.0 + zddz3 = 0.0 + z3 = eta + DO i = 1, ncomp + my2dd(i) = (parame(i,6))**2 *1.E-49 / (uij(i,i)*KBOL*mseg(i)*sig_ij(i,i)**3 *1.E-30) + END DO + + DO i = 1, ncomp + DO j = 1, ncomp + Idd2(i,j) = 0.0 + Idd4(i,j) = 0.0 + Idd2z(i,j) = 0.0 + Idd4z(i,j) = 0.0 + Idd2z2(i,j) = 0.0 + Idd4z2(i,j) = 0.0 + Idd2z3(i,j) = 0.0 + Idd4z3(i,j) = 0.0 + Idd2z4(i,j) = 0.0 + Idd4z4(i,j) = 0.0 + ! IF (paramei,6).NE.0.0 .AND. parame(j,6).NE.0.0) THEN + DO m = 0, 4 + Idd2(i,j) =Idd2(i,j) + ddp2(i,j,m) *z3**(m+1) + Idd4(i,j) =Idd4(i,j) + ddp4(i,j,m) *z3**(m+1) + Idd2z(i,j) =Idd2z(i,j) +ddp2(i,j,m)*REAL(m+1) *z3**m + Idd4z(i,j) =Idd4z(i,j) +ddp4(i,j,m)*REAL(m+1) *z3**m + Idd2z2(i,j)=Idd2z2(i,j)+ddp2(i,j,m)*REAL((m+1)*m) *z3**(m-1) + Idd4z2(i,j)=Idd4z2(i,j)+ddp4(i,j,m)*REAL((m+1)*m) *z3**(m-1) + Idd2z3(i,j)=Idd2z3(i,j)+ddp2(i,j,m)*REAL((m+1)*m*(m-1)) *z3**(m-2) + Idd4z3(i,j)=Idd4z3(i,j)+ddp4(i,j,m)*REAL((m+1)*m*(m-1)) *z3**(m-2) + Idd2z4(i,j)=Idd2z4(i,j)+ddp2(i,j,m)*REAL((m+1)*m*(m-1)*(m-2)) *z3**(m-3) + Idd4z4(i,j)=Idd4z4(i,j)+ddp4(i,j,m)*REAL((m+1)*m*(m-1)*(m-2)) *z3**(m-3) + END DO + DO k = 1, ncomp + Idd3(i,j,k) = 0.0 + Idd3z(i,j,k) = 0.0 + Idd3z2(i,j,k) = 0.0 + Idd3z3(i,j,k) = 0.0 + Idd3z4(i,j,k) = 0.0 + ! IF (parame(k,6).NE.0.0) THEN + DO m = 0, 4 + Idd3(i,j,k) =Idd3(i,j,k) +ddp3(i,j,k,m)*z3**(m+2) + Idd3z(i,j,k) =Idd3z(i,j,k) +ddp3(i,j,k,m)*REAL(m+2)*z3**(m+1) + Idd3z2(i,j,k)=Idd3z2(i,j,k)+ddp3(i,j,k,m)*REAL((m+2)*(m+1))*z3**m + Idd3z3(i,j,k)=Idd3z3(i,j,k)+ddp3(i,j,k,m)*REAL((m+2)*(m+1)*m)*z3**(m-1) + Idd3z4(i,j,k)=Idd3z4(i,j,k)+ddp3(i,j,k,m)*REAL((m+2)*(m+1)*m*(m-1)) *z3**(m-2) + END DO + ! ENDIF + END DO + ! ENDIF + END DO + END DO + + factor2= -PI *rho/z3 + factor3= -4.0/3.0*PI**2 * (rho/z3)**2 + + fdd2 = 0.0 + fdd2z = 0.0 + fdd2z2 = 0.0 + fdd2z3 = 0.0 + fdd2z4 = 0.0 + fdd3 = 0.0 + fdd3z = 0.0 + fdd3z2 = 0.0 + fdd3z3 = 0.0 + fdd3z4 = 0.0 + DO i = 1, ncomp + DO j = 1, ncomp + ! IF (parame(i,6).NE.0.0 .AND. parame(j,6).NE.0.0) THEN + xijfa = x(i)*parame(i,3)/t*parame(i,2)**3 *x(j)*parame(j,3)/t*parame(j,2)**3 & + / ((parame(i,2)+parame(j,2))/2.0)**3 *my2dd(i)*my2dd(j) + eij = (parame(i,3)*parame(j,3))**0.5 + fdd2 = fdd2 +factor2*xijfa*(Idd2(i,j) +eij/t*Idd4(i,j)) + fdd2z = fdd2z +factor2*xijfa*(Idd2z(i,j) +eij/t*Idd4z(i,j)) + fdd2z2 = fdd2z2+factor2*xijfa*(Idd2z2(i,j)+eij/t*Idd4z2(i,j)) + fdd2z3 = fdd2z3+factor2*xijfa*(Idd2z3(i,j)+eij/t*Idd4z3(i,j)) + fdd2z4 = fdd2z4+factor2*xijfa*(Idd2z4(i,j)+eij/t*Idd4z4(i,j)) + DO k = 1, ncomp + ! IF (parame(k,6).NE.0.0) THEN + xijkfa= x(i)*parame(i,3)/t*parame(i,2)**3 *x(j)*parame(j,3)/t*parame(j,2)**3 & + *x(k)*parame(k,3)/t*parame(k,2)**3 /((parame(i,2)+parame(j,2))/2.0) & + /((parame(i,2)+parame(k,2))/2.0) /((parame(j,2)+parame(k,2))/2.0) & + *my2dd(i)*my2dd(j)*my2dd(k) + fdd3 = fdd3 + factor3 * xijkfa*Idd3(i,j,k) + fdd3z = fdd3z + factor3 * xijkfa*Idd3z(i,j,k) + fdd3z2 = fdd3z2 + factor3 * xijkfa*Idd3z2(i,j,k) + fdd3z3 = fdd3z3 + factor3 * xijkfa*Idd3z3(i,j,k) + fdd3z4 = fdd3z4 + factor3 * xijkfa*Idd3z4(i,j,k) + ! ENDIF + END DO + ! ENDIF + END DO + END DO + IF (fdd2 < -1.E-50 .AND. fdd3 /= 0.0 .AND. fdd2z /= 0.0 .AND. fdd3z /= 0.0) THEN + + fdddr= fdd2* (fdd2*fdd2z - 2.0*fdd3*fdd2z+fdd2*fdd3z) / (fdd2-fdd3)**2 + fddd2=(2.0*fdd2*fdd2z*fdd2z +fdd2*fdd2*fdd2z2 & + -2.0*fdd2z**2 *fdd3-2.0*fdd2*fdd2z2*fdd3+fdd2*fdd2*fdd3z2) & + /(fdd2-fdd3)**2 + fdddr * 2.0*(fdd3z-fdd2z)/(fdd2-fdd3) + fddd3=(2.0*fdd2z**3 +6.0*fdd2*fdd2z*fdd2z2+fdd2*fdd2*fdd2z3 & + -6.0*fdd2z*fdd2z2*fdd3-2.0*fdd2z**2 *fdd3z & + -2.0*fdd2*fdd2z3*fdd3 -2.0*fdd2*fdd2z2*fdd3z & + +2.0*fdd2*fdd2z*fdd3z2+fdd2*fdd2*fdd3z3) /(fdd2-fdd3)**2 & + + 2.0/(fdd2-fdd3)* ( 2.0*fddd2*(fdd3z-fdd2z) & + + fdddr*(fdd3z2-fdd2z2) & + - fdddr/(fdd2-fdd3)*(fdd3z-fdd2z)**2 ) + fddd4=( 12.0*fdd2z**2 *fdd2z2+6.0*fdd2*fdd2z2**2 & + +8.0*fdd2*fdd2z*fdd2z3+fdd2*fdd2*fdd2z4-6.0*fdd2z2**2 *fdd3 & + -12.0*fdd2z*fdd2z2*fdd3z -8.0*fdd2z*fdd2z3*fdd3 & + -2.0*fdd2*fdd2z4*fdd3-4.0*fdd2*fdd2z3*fdd3z & + +4.0*fdd2*fdd2z*fdd3z3+fdd2**2 *fdd3z4 ) /(fdd2-fdd3)**2 & + + 6.0/(fdd2-fdd3)* ( fddd3*(fdd3z-fdd2z) & + -fddd2/(fdd2-fdd3)*(fdd3z-fdd2z)**2 & + - fdddr/(fdd2-fdd3)*(fdd3z-fdd2z)*(fdd3z2-fdd2z2) & + + fddd2*(fdd3z2-fdd2z2) +1.0/3.0*fdddr*(fdd3z3-fdd2z3) ) + zdd = fdddr*eta + zddz = fddd2*eta + fdddr + zddz2 = fddd3*eta + 2.0* fddd2 + zddz3 = fddd4*eta + 3.0* fddd3 + + END IF + + +END SUBROUTINE P_DD_GROSS_VRABEC + + + +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! + SUBROUTINE P_QQ_GROSS( zqq, zqqz, zqqz2, zqqz3 ) +! + USE PARAMETERS, ONLY: PI, KBOL + USE EOS_VARIABLES, ONLY: nc, ncomp, uij, parame, mseg, sig_ij, rho, eta, x, t + USE EOS_CONSTANTS, ONLY: qqp2, qqp3, qqp4 + IMPLICIT NONE +! +! ---------------------------------------------------------------------- + REAL, INTENT(IN OUT) :: zqq, zqqz, zqqz2, zqqz3 +! ---------------------------------------------------------------------- + INTEGER :: i, j, k, m + REAL :: factor2, factor3, z3 + REAL :: xijfa, xijkfa, eij + REAL :: fqqdr, fqqd2, fqqd3, fqqd4 + REAL :: fqq2, fqq2z, fqq2z2, fqq2z3, fqq2z4 + REAL :: fqq3, fqq3z, fqq3z2, fqq3z3, fqq3z4 + REAL, DIMENSION(nc) :: qq2 + REAL, DIMENSION(nc,nc) :: Iqq2, Iqq2z, Iqq2z2, Iqq2z3, Iqq2z4 + REAL, DIMENSION(nc,nc) :: Iqq4, Iqq4z, Iqq4z2, Iqq4z3, Iqq4z4 + REAL, DIMENSION(nc,nc,nc) :: Iqq3, Iqq3z, Iqq3z2, Iqq3z3, Iqq3z4 +! ---------------------------------------------------------------------- + + zqq = 0.0 + zqqz = 0.0 + zqqz2 = 0.0 + zqqz3 = 0.0 + z3 = eta + DO i=1,ncomp + qq2(i) = (parame(i,7))**2 *1.E-69 / (uij(i,i)*kbol*mseg(i)*sig_ij(i,i)**5 *1.E-50) + END DO + + DO i = 1, ncomp + DO j = 1, ncomp + Iqq2(i,j) = 0.0 + Iqq4(i,j) = 0.0 + Iqq2z(i,j) = 0.0 + Iqq4z(i,j) = 0.0 + Iqq2z2(i,j) = 0.0 + Iqq4z2(i,j) = 0.0 + Iqq2z3(i,j) = 0.0 + Iqq4z3(i,j) = 0.0 + Iqq2z4(i,j) = 0.0 + Iqq4z4(i,j) = 0.0 + IF (parame(i,7) /= 0.0 .AND. parame(j,7) /= 0.0) THEN + DO m = 0, 4 + Iqq2(i,j) =Iqq2(i,j) + qqp2(i,j,m)*z3**(m+1) + Iqq4(i,j) =Iqq4(i,j) + qqp4(i,j,m)*z3**(m+1) + Iqq2z(i,j) =Iqq2z(i,j) +qqp2(i,j,m)*REAL(m+1)*z3**m + Iqq4z(i,j) =Iqq4z(i,j) +qqp4(i,j,m)*REAL(m+1)*z3**m + Iqq2z2(i,j)=Iqq2z2(i,j)+qqp2(i,j,m)*REAL((m+1)*m)*z3**(m-1) + Iqq4z2(i,j)=Iqq4z2(i,j)+qqp4(i,j,m)*REAL((m+1)*m)*z3**(m-1) + Iqq2z3(i,j)=Iqq2z3(i,j)+qqp2(i,j,m)*REAL((m+1)*m*(m-1)) *z3**(m-2) + Iqq4z3(i,j)=Iqq4z3(i,j)+qqp4(i,j,m)*REAL((m+1)*m*(m-1)) *z3**(m-2) + Iqq2z4(i,j)=Iqq2z4(i,j)+qqp2(i,j,m)*REAL((m+1)*m*(m-1)*(m-2)) *z3**(m-3) + Iqq4z4(i,j)=Iqq4z4(i,j)+qqp4(i,j,m)*REAL((m+1)*m*(m-1)*(m-2)) *z3**(m-3) + END DO + DO k=1,ncomp + Iqq3(i,j,k) = 0.0 + Iqq3z(i,j,k) = 0.0 + Iqq3z2(i,j,k) = 0.0 + Iqq3z3(i,j,k) = 0.0 + Iqq3z4(i,j,k) = 0.0 + IF (parame(k,7) /= 0.0) THEN + DO m=0,4 + Iqq3(i,j,k) =Iqq3(i,j,k) + qqp3(i,j,k,m)*z3**(m+2) + Iqq3z(i,j,k)=Iqq3z(i,j,k)+qqp3(i,j,k,m)*REAL(m+2)*z3**(m+1) + Iqq3z2(i,j,k)=Iqq3z2(i,j,k)+qqp3(i,j,k,m)*REAL((m+2)*(m+1)) *z3**m + Iqq3z3(i,j,k)=Iqq3z3(i,j,k)+qqp3(i,j,k,m)*REAL((m+2)*(m+1)*m) *z3**(m-1) + Iqq3z4(i,j,k)=Iqq3z4(i,j,k)+qqp3(i,j,k,m) *REAL((m+2)*(m+1)*m*(m-1)) *z3**(m-2) + END DO + END IF + END DO + + END IF + END DO + END DO + + factor2= -9.0/16.0*PI *rho/z3 + factor3= 9.0/16.0*PI**2 * (rho/z3)**2 + + fqq2 = 0.0 + fqq2z = 0.0 + fqq2z2 = 0.0 + fqq2z3 = 0.0 + fqq2z4 = 0.0 + fqq3 = 0.0 + fqq3z = 0.0 + fqq3z2 = 0.0 + fqq3z3 = 0.0 + fqq3z4 = 0.0 + DO i = 1, ncomp + DO j = 1, ncomp + IF (parame(i,7) /= 0.0 .AND. parame(j,7) /= 0.0) THEN + xijfa =x(i)*uij(i,i)*qq2(i)*sig_ij(i,i)**5 /t & + *x(j)*uij(j,j)*qq2(j)*sig_ij(j,j)**5 /t/sig_ij(i,j)**7.0 + eij = (parame(i,3)*parame(j,3))**0.5 + fqq2= fqq2 +factor2*xijfa*(Iqq2(i,j) +eij/t*Iqq4(i,j) ) + fqq2z =fqq2z +factor2*xijfa*(Iqq2z(i,j) +eij/t*Iqq4z(i,j) ) + fqq2z2=fqq2z2+factor2*xijfa*(Iqq2z2(i,j)+eij/t*Iqq4z2(i,j)) + fqq2z3=fqq2z3+factor2*xijfa*(Iqq2z3(i,j)+eij/t*Iqq4z3(i,j)) + fqq2z4=fqq2z4+factor2*xijfa*(Iqq2z4(i,j)+eij/t*Iqq4z4(i,j)) + DO k = 1, ncomp + IF (parame(k,7) /= 0.0) THEN + xijkfa=x(i)*uij(i,i)*qq2(i)*sig_ij(i,i)**5 /t/sig_ij(i,j)**3 & + *x(j)*uij(j,j)*qq2(j)*sig_ij(j,j)**5 /t/sig_ij(i,k)**3 & + *x(k)*uij(k,k)*qq2(k)*sig_ij(k,k)**5 /t/sig_ij(j,k)**3 + fqq3 = fqq3 + factor3 * xijkfa*Iqq3(i,j,k) + fqq3z = fqq3z + factor3 * xijkfa*Iqq3z(i,j,k) + fqq3z2 = fqq3z2 + factor3 * xijkfa*Iqq3z2(i,j,k) + fqq3z3 = fqq3z3 + factor3 * xijkfa*Iqq3z3(i,j,k) + fqq3z4 = fqq3z4 + factor3 * xijkfa*Iqq3z4(i,j,k) + END IF + END DO + END IF + END DO + END DO + IF (fqq2 < -1.E-50 .AND. fqq3 /= 0.0 .AND. fqq2z /= 0.0 .AND. fqq3z /= 0.0) THEN + fqqdr = fqq2* (fqq2*fqq2z - 2.0*fqq3*fqq2z+fqq2*fqq3z) /(fqq2-fqq3)**2 + fqqd2= (2.0*fqq2*fqq2z*fqq2z +fqq2*fqq2*fqq2z2 & + -2.0*fqq2z**2 *fqq3-2.0*fqq2*fqq2z2*fqq3+fqq2*fqq2*fqq3z2) & + /(fqq2-fqq3)**2 + fqqdr * 2.0*(fqq3z-fqq2z)/(fqq2-fqq3) + fqqd3=(2.0*fqq2z**3 +6.0*fqq2*fqq2z*fqq2z2+fqq2*fqq2*fqq2z3 & + -6.0*fqq2z*fqq2z2*fqq3-2.0*fqq2z**2 *fqq3z & + -2.0*fqq2*fqq2z3*fqq3 -2.0*fqq2*fqq2z2*fqq3z & + +2.0*fqq2*fqq2z*fqq3z2+fqq2*fqq2*fqq3z3) /(fqq2-fqq3)**2 & + + 2.0/(fqq2-fqq3)* ( 2.0*fqqd2*(fqq3z-fqq2z) & + + fqqdr*(fqq3z2-fqq2z2) - fqqdr/(fqq2-fqq3)*(fqq3z-fqq2z)**2 ) + fqqd4=( 12.0*fqq2z**2 *fqq2z2+6.0*fqq2*fqq2z2**2 & + +8.0*fqq2*fqq2z*fqq2z3+fqq2*fqq2*fqq2z4-6.0*fqq2z2**2 *fqq3 & + -12.0*fqq2z*fqq2z2*fqq3z -8.0*fqq2z*fqq2z3*fqq3 & + -2.0*fqq2*fqq2z4*fqq3-4.0*fqq2*fqq2z3*fqq3z & + +4.0*fqq2*fqq2z*fqq3z3+fqq2**2 *fqq3z4 ) /(fqq2-fqq3)**2 & + + 6.0/(fqq2-fqq3)* ( fqqd3*(fqq3z-fqq2z) & + -fqqd2/(fqq2-fqq3)*(fqq3z-fqq2z)**2 & + - fqqdr/(fqq2-fqq3)*(fqq3z-fqq2z)*(fqq3z2-fqq2z2) & + + fqqd2*(fqq3z2-fqq2z2) +1.0/3.0*fqqdr*(fqq3z3-fqq2z3) ) + zqq = fqqdr*eta + zqqz = fqqd2*eta + fqqdr + zqqz2 = fqqd3*eta + 2.0* fqqd2 + zqqz3 = fqqd4*eta + 3.0* fqqd3 + END IF + + +END SUBROUTINE P_QQ_GROSS + +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! + SUBROUTINE P_DQ_VRABEC_GROSS( zdq, zdqz, zdqz2, zdqz3 ) +! + USE PARAMETERS, ONLY: PI, KBOL + USE EOS_VARIABLES, ONLY: nc, ncomp, uij, parame, mseg, sig_ij, rho, eta, x, t + USE EOS_CONSTANTS, ONLY: dqp2, dqp3, dqp4 + IMPLICIT NONE +! +! ---------------------------------------------------------------------- + REAL, INTENT(IN OUT) :: zdq, zdqz, zdqz2, zdqz3 +! ---------------------------------------------------------------------- + INTEGER :: i, j, k, m + REAL :: factor2, factor3, z3 + REAL :: xijfa, xijkfa, eij + REAL :: fdqdr, fdqd2, fdqd3, fdqd4 + REAL :: fdq2, fdq2z, fdq2z2, fdq2z3, fdq2z4 + REAL :: fdq3, fdq3z, fdq3z2, fdq3z3, fdq3z4 + REAL, DIMENSION(nc) :: my2dd, myfac, qq2, q_fac + REAL, DIMENSION(nc,nc) :: Idq2, Idq2z, Idq2z2, Idq2z3, Idq2z4 + REAL, DIMENSION(nc,nc) :: Idq4, Idq4z, Idq4z2, Idq4z3, Idq4z4 + REAL, DIMENSION(nc,nc,nc) :: Idq3, Idq3z, Idq3z2, Idq3z3, Idq3z4 +! ---------------------------------------------------------------------- + + zdq = 0.0 + zdqz = 0.0 + zdqz2 = 0.0 + zdqz3 = 0.0 + z3 = eta + DO i = 1, ncomp + my2dd(i) = (parame(i,6))**2 *1.E-49 / (uij(i,i)*KBOL*mseg(i)*sig_ij(i,i)**3 *1.E-30) + myfac(i) = parame(i,3)/t*parame(i,2)**4 *my2dd(i) + qq2(i) = (parame(i,7))**2 *1.E-69 / (uij(i,i)*kbol*mseg(i)*sig_ij(i,i)**5 *1.E-50) + q_fac(i) = parame(i,3)/t*parame(i,2)**4 *qq2(i) + END DO + + + DO i = 1, ncomp + DO j = 1, ncomp + Idq2(i,j) = 0.0 + Idq4(i,j) = 0.0 + Idq2z(i,j) = 0.0 + Idq4z(i,j) = 0.0 + Idq2z2(i,j) = 0.0 + Idq4z2(i,j) = 0.0 + Idq2z3(i,j) = 0.0 + Idq4z3(i,j) = 0.0 + Idq2z4(i,j) = 0.0 + Idq4z4(i,j) = 0.0 + IF (myfac(i) /= 0.0 .AND. q_fac(j) /= 0.0) THEN + DO m = 0, 4 + Idq2(i,j) =Idq2(i,j) + dqp2(i,j,m)*z3**(m+1) + Idq4(i,j) =Idq4(i,j) + dqp4(i,j,m)*z3**(m+1) + Idq2z(i,j) =Idq2z(i,j) +dqp2(i,j,m)*REAL(m+1)*z3**m + Idq4z(i,j) =Idq4z(i,j) +dqp4(i,j,m)*REAL(m+1)*z3**m + Idq2z2(i,j)=Idq2z2(i,j)+dqp2(i,j,m)*REAL((m+1)*m)*z3**(m-1) + Idq4z2(i,j)=Idq4z2(i,j)+dqp4(i,j,m)*REAL((m+1)*m)*z3**(m-1) + Idq2z3(i,j)=Idq2z3(i,j)+dqp2(i,j,m)*REAL((m+1)*m*(m-1)) *z3**(m-2) + Idq4z3(i,j)=Idq4z3(i,j)+dqp4(i,j,m)*REAL((m+1)*m*(m-1)) *z3**(m-2) + Idq2z4(i,j)=Idq2z4(i,j)+dqp2(i,j,m)*REAL((m+1)*m*(m-1)*(m-2)) *z3**(m-3) + Idq4z4(i,j)=Idq4z4(i,j)+dqp4(i,j,m)*REAL((m+1)*m*(m-1)*(m-2)) *z3**(m-3) + END DO + DO k = 1, ncomp + Idq3(i,j,k) = 0.0 + Idq3z(i,j,k) = 0.0 + Idq3z2(i,j,k) = 0.0 + Idq3z3(i,j,k) = 0.0 + Idq3z4(i,j,k) = 0.0 + IF (myfac(k) /= 0.0.OR.q_fac(k) /= 0.0) THEN + DO m = 0, 4 + Idq3(i,j,k) =Idq3(i,j,k) + dqp3(i,j,k,m)*z3**(m+2) + Idq3z(i,j,k)=Idq3z(i,j,k)+dqp3(i,j,k,m)*REAL(m+2)*z3**(m+1) + Idq3z2(i,j,k)=Idq3z2(i,j,k)+dqp3(i,j,k,m)*REAL((m+2)*(m+1)) *z3**m + Idq3z3(i,j,k)=Idq3z3(i,j,k)+dqp3(i,j,k,m)*REAL((m+2)*(m+1)*m) *z3**(m-1) + Idq3z4(i,j,k)=Idq3z4(i,j,k)+dqp3(i,j,k,m) & + *REAL((m+2)*(m+1)*m*(m-1)) *z3**(m-2) + END DO + END IF + END DO + + END IF + END DO + END DO + + factor2= -9.0/4.0*PI *rho/z3 + factor3= PI**2 * (rho/z3)**2 + + fdq2 = 0.0 + fdq2z = 0.0 + fdq2z2 = 0.0 + fdq2z3 = 0.0 + fdq2z4 = 0.0 + fdq3 = 0.0 + fdq3z = 0.0 + fdq3z2 = 0.0 + fdq3z3 = 0.0 + fdq3z4 = 0.0 + DO i = 1, ncomp + DO j = 1, ncomp + IF (myfac(i) /= 0.0 .AND. q_fac(j) /= 0.0) THEN + xijfa =x(i)*myfac(i) * x(j)*q_fac(j) /sig_ij(i,j)**5 + eij = (parame(i,3)*parame(j,3))**0.5 + fdq2= fdq2 +factor2*xijfa*(Idq2(i,j) +eij/t*Idq4(i,j) ) + fdq2z =fdq2z +factor2*xijfa*(Idq2z(i,j) +eij/t*Idq4z(i,j) ) + fdq2z2=fdq2z2+factor2*xijfa*(Idq2z2(i,j)+eij/t*Idq4z2(i,j)) + fdq2z3=fdq2z3+factor2*xijfa*(Idq2z3(i,j)+eij/t*Idq4z3(i,j)) + fdq2z4=fdq2z4+factor2*xijfa*(Idq2z4(i,j)+eij/t*Idq4z4(i,j)) + DO k = 1, ncomp + IF (myfac(k) /= 0.0.OR.q_fac(k) /= 0.0) THEN + xijkfa=x(i)*x(j)*x(k)/(sig_ij(i,j)*sig_ij(i,k)*sig_ij(j,k))**2 & + *( myfac(i)*q_fac(j)*myfac(k) + myfac(i)*q_fac(j)*q_fac(k)*1.193735 ) + fdq3 =fdq3 + factor3 * xijkfa*Idq3(i,j,k) + fdq3z =fdq3z + factor3 * xijkfa*Idq3z(i,j,k) + fdq3z2=fdq3z2 + factor3 * xijkfa*Idq3z2(i,j,k) + fdq3z3=fdq3z3 + factor3 * xijkfa*Idq3z3(i,j,k) + fdq3z4=fdq3z4 + factor3 * xijkfa*Idq3z4(i,j,k) + END IF + END DO + END IF + END DO + END DO + IF (fdq2 < -1.E-50 .AND. fdq3 /= 0.0 .AND. fdq2z /= 0.0 .AND. fdq3z /= 0.0) THEN + fdqdr = fdq2* (fdq2*fdq2z - 2.0*fdq3*fdq2z+fdq2*fdq3z) /(fdq2-fdq3)**2 + fdqd2= (2.0*fdq2*fdq2z*fdq2z +fdq2*fdq2*fdq2z2 & + -2.0*fdq2z**2 *fdq3-2.0*fdq2*fdq2z2*fdq3+fdq2*fdq2*fdq3z2) & + /(fdq2-fdq3)**2 + fdqdr * 2.0*(fdq3z-fdq2z)/(fdq2-fdq3) + fdqd3=(2.0*fdq2z**3 +6.0*fdq2*fdq2z*fdq2z2+fdq2*fdq2*fdq2z3 & + -6.0*fdq2z*fdq2z2*fdq3-2.0*fdq2z**2 *fdq3z & + -2.0*fdq2*fdq2z3*fdq3 -2.0*fdq2*fdq2z2*fdq3z & + +2.0*fdq2*fdq2z*fdq3z2+fdq2*fdq2*fdq3z3) /(fdq2-fdq3)**2 & + + 2.0/(fdq2-fdq3)* ( 2.0*fdqd2*(fdq3z-fdq2z) & + + fdqdr*(fdq3z2-fdq2z2) - fdqdr/(fdq2-fdq3)*(fdq3z-fdq2z)**2 ) + fdqd4=( 12.0*fdq2z**2 *fdq2z2+6.0*fdq2*fdq2z2**2 & + +8.0*fdq2*fdq2z*fdq2z3+fdq2*fdq2*fdq2z4-6.0*fdq2z2**2 *fdq3 & + -12.0*fdq2z*fdq2z2*fdq3z -8.0*fdq2z*fdq2z3*fdq3 & + -2.0*fdq2*fdq2z4*fdq3-4.0*fdq2*fdq2z3*fdq3z & + +4.0*fdq2*fdq2z*fdq3z3+fdq2**2 *fdq3z4 ) /(fdq2-fdq3)**2 & + + 6.0/(fdq2-fdq3)* ( fdqd3*(fdq3z-fdq2z) & + -fdqd2/(fdq2-fdq3)*(fdq3z-fdq2z)**2 & + - fdqdr/(fdq2-fdq3)*(fdq3z-fdq2z)*(fdq3z2-fdq2z2) & + + fdqd2*(fdq3z2-fdq2z2) +1.0/3.0*fdqdr*(fdq3z3-fdq2z3) ) + zdq = fdqdr*eta + zdqz = fdqd2*eta + fdqdr + zdqz2 = fdqd3*eta + 2.0* fdqd2 + zdqz3 = fdqd4*eta + 3.0* fdqd3 + END IF + + +END SUBROUTINE P_DQ_VRABEC_GROSS + + + +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! + SUBROUTINE F_pert_theory ( fdsp ) +! + USE EOS_VARIABLES, ONLY: nc, PI, ncomp, t, p, rho, eta, & + x, z0t, mseg, parame, order1, order2 + USE EOS_NUMERICAL_DERIVATIVES, ONLY: disp_term + USE DFT_MODULE + IMPLICIT NONE +! +!--------------------------------------------------------------------- + REAL, INTENT(IN OUT) :: fdsp +!--------------------------------------------------------------------- + REAL :: I1, I2 + REAL :: z3, zms, c1_con, m_mean +!--------------------------------------------------------------------- + + ! caution: positive sign of correlation integral is used here ! + ! (the Helmholtz energy terms are written with a negative sign, while I1 and I2 are positive) + + IF (disp_term == 'PT1') THEN + + CALL f_dft ( I1, I2) + c1_con = 0.0 + I2 = 0.0 + fdsp = + ( - 2.0*PI*rho*I1*order1 ) + + ELSEIF (disp_term == 'PT2') THEN + + CALL f_dft ( I1, I2) + z3 = eta + zms = 1.0 - z3 + m_mean = z0t / ( PI / 6.0 ) + c1_con = 1.0/ ( 1.0 + m_mean*(8.0*z3-2.0*z3**2 )/zms**4 & + + (1.0 - m_mean)*( 20.0*z3 -27.0*z3**2 +12.0*z3**3 -2.0*z3**4 ) & + /(zms*(2.0-z3))**2 ) + fdsp = + ( - 2.0*PI*rho*I1*order1 - PI*rho*c1_con*m_mean*I2*order2 ) + + ELSEIF (disp_term == 'PT_MIX') THEN + + CALL f_pert_theory_mix ( fdsp ) + + ELSEIF (disp_term == 'PT_MF') THEN + + ! mean field theory + I1 = - ( - 8.0/9.0 - 4.0/9.0*(rc**(-9) -3.0*rc**(-3) ) - tau_cut/3.0*(rc**3 -1.0) ) + fdsp = + ( - 2.0*PI*rho*I1*order1 ) + write (*,*) 'caution: not thoroughly checked and tested' + + ELSE + write (*,*) 'define the type of perturbation theory' + stop + END IF + + ! I1 = I1 + 4.0/9.0*(2.5**-9 -3.0*2.5**-3 ) + ! fdsp = + ( - 2.0*PI*rho*I1*order1 - PI*rho*c1_con*m_mean*I2*order2 ) + + END SUBROUTINE F_pert_theory + + + + +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! + SUBROUTINE f_pert_theory_mix ( fdsp ) +! + USE EOS_VARIABLES, ONLY: nc, PI, ncomp, t, rho, eta, x, parame, mseg, dhs, sig_ij, uij + USE DFT_MODULE + IMPLICIT NONE +! +! ---------------------------------------------------------------------- + REAL, INTENT(IN OUT) :: fdsp +! +! ---------------------------------------------------------------------- + INTEGER :: k, ih + INTEGER :: l, m + REAL :: z3 + REAL :: ua, ua_c, rm + REAL, DIMENSION(nc,nc) :: I1 + REAL :: int10, int11 + REAL :: d_ij, dzr_local + REAL :: rad, xg, rdf + REAL :: dg_dz3, dg_dr + ! REAL :: intgrid(0:5000),intgri2(0:5000), utri(5000),I1_spline +! ---------------------------------------------------------------------- + +! -----constants-------------------------------------------------------- + ua_c = 4.0 * ( rc**(-12) - rc**(-6) ) + rm = 2.0**(1.0/6.0) + + I1(:,:) = 0.0 + + DO l = 1, ncomp + DO m = 1, ncomp + + rad = rc + + int10 = rc * rc * ua_c + ! intgrid(0)= int10 + + k = 0 + ih = 85 + + DO WHILE ( rad /= 1.0 ) + + dzr_local = dzr + IF ( rad - dzr_local <= 1.0 ) dzr_local = rad - 1.0 + + rad = rad - dzr_local + + k = k + 1 + + d_ij = 0.5*(dhs(l)+dhs(m)) / sig_ij(l,m) ! dimensionless effective hs-diameter d(T)/sig + xg = rad / d_ij + z3 = eta + rdf = 1.0 + dg_dz3 = 0.0 + IF ( rad <= rg ) THEN + IF ( l == 1 .AND. m == 1 ) CALL BI_CUB_SPLINE (z3,xg,ya_11,x1a_11,x2a_11,y1a_11,y2a_11,y12a_11, & + c_bicub_11,rdf,dg_dz3,dg_dr,den_step,ih,k) + IF ( l /= m ) CALL BI_CUB_SPLINE (z3,xg,ya_12,x1a_12,x2a_12,y1a_12,y2a_12,y12a_12, & + c_bicub_12,rdf,dg_dz3,dg_dr,den_step,ih,k) + IF ( l == 2 .AND. m == 2 ) CALL BI_CUB_SPLINE (z3,xg,ya_22,x1a_22,x2a_22,y1a_22,y2a_22,y12a_22, & + c_bicub_22,rdf,dg_dz3,dg_dr,den_step,ih,k) + END IF + + ua = 4.0 * ( rad**(-12) - rad**(-6) ) + + int11 = rdf * rad * rad * ua + I1(l,m) = I1(l,m) + dzr_local * ( int11 + int10 ) / 2.0 + + int10 = int11 + ! intgrid(k)= int11 + + END DO + + ! stepno = k + ! CALL SPLINE_PARA (dzr,intgrid,utri,stepno) + ! CALL SPLINE_INT (I1_spline,dzr,intgrid,utri,stepno) + + + ! caution: 1st order integral is in F_EOS.f defined with negative sign + ! --------------------------------------------------------------- + ! cut-off corrections + ! --------------------------------------------------------------- + ! I1(l,m) = I1(l,m) + ( 4.0/9.0 * rc**-9 - 4.0/3.0 * rc**-3 ) + ! I2(l,m) = I2(l,m) + 16.0/21.0 * rc**-21 - 32.0/15.0 * rc**-15 + 16.0/9.0 * rc**-9 + + END DO + END DO + + + fdsp = 0.0 + DO l = 1, ncomp + DO m = 1, ncomp + fdsp = fdsp + 2.0*PI*rho*x(l)*x(m)* mseg(l)*mseg(m)*sig_ij(l,m)**3 * uij(l,m)/t *I1(l,m) + ! ( 2.0*PI*rho*I1*order1 - PI*rho*c1_con*m_mean*I2*order2 ) + END DO + END DO + + +!!$ IF (disp_term == 'PT1') THEN +!!$ c1_con = 0.0 +!!$ I2 = 0.0 +!!$ ELSEIF (disp_term == 'PT2') THEN +!!$ zms = 1.0 - z3 +!!$ c1_con = 1.0/ ( 1.0 + m_mean*(8.0*z3-2.0*z3**2 )/zms**4 & +!!$ + (1.0 - m_mean)*( 20.0*z3 -27.0*z3**2 +12.0*z3**3 -2.0*z3**4 ) & +!!$ /(zms*(2.0-z3))**2 ) +!!$ ELSE +!!$ write (*,*) 'define the type of perturbation theory' +!!$ stop +!!$ END IF + + +END SUBROUTINE f_pert_theory_mix + + +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! + SUBROUTINE mu_pert_theory_mix ( mu_dsp ) +! + USE EOS_VARIABLES, ONLY: nc, PI, ncomp, t, rho, eta, x, parame, mseg, dhs, sig_ij, uij + USE DFT_MODULE + IMPLICIT NONE +! +! ---------------------------------------------------------------------- + REAL, INTENT(IN OUT) :: mu_dsp(nc) +! +! ---------------------------------------------------------------------- + INTEGER :: k, ih + INTEGER :: l, m + REAL :: z3 + REAL :: ua, ua_c, rm + REAL, DIMENSION(nc,nc) :: I1, I2 + REAL :: int1_0, int1_1, int2_0, int2_1 + REAL :: d_ij, dzr_local + REAL :: rad, xg, rdf + REAL :: dg_dz3, dg_dr + REAL :: term1(nc), term2 + ! REAL :: intgrid(0:5000),intgri2(0:5000), utri(5000),I1_spline +! ---------------------------------------------------------------------- + +! -----constants-------------------------------------------------------- + ua_c = 4.0 * ( rc**(-12) - rc**(-6) ) + rm = 2.0**(1.0/6.0) + + I1(:,:) = 0.0 + I2(:,:) = 0.0 + + DO l = 1, ncomp + + term1(l) = 0.0 + + DO m = 1, ncomp + + rad = rc + + int1_0 = rc * rc * ua_c + int2_0 = 0.0 + + k = 0 + ih = 85 + + DO WHILE ( rad /= 1.0 ) + + dzr_local = dzr + IF ( rad - dzr_local <= 1.0 ) dzr_local = rad - 1.0 + + rad = rad - dzr_local + k = k + 1 + + d_ij = 0.5*(dhs(l)+dhs(m)) / sig_ij(l,m) ! dimensionless effective hs-diameter d(T)/sig + xg = rad / d_ij + z3 = eta + rdf = 1.0 + dg_dz3 = 0.0 + IF ( rad <= rg ) THEN + IF ( l == 1 .AND. m == 1 ) CALL BI_CUB_SPLINE (z3,xg,ya_11,x1a_11,x2a_11,y1a_11,y2a_11,y12a_11, & + c_bicub_11,rdf,dg_dz3,dg_dr,den_step,ih,k) + IF ( l /= m ) CALL BI_CUB_SPLINE (z3,xg,ya_12,x1a_12,x2a_12,y1a_12,y2a_12,y12a_12, & + c_bicub_12,rdf,dg_dz3,dg_dr,den_step,ih,k) + IF ( l == 2 .AND. m == 2 ) CALL BI_CUB_SPLINE (z3,xg,ya_22,x1a_22,x2a_22,y1a_22,y2a_22,y12a_22, & + c_bicub_22,rdf,dg_dz3,dg_dr,den_step,ih,k) + END IF + + ua = 4.0 * ( rad**(-12) - rad**(-6) ) + + int1_1 = rdf * rad * rad * ua + int2_1 = dg_dz3 * rad * rad * ua + I1(l,m) = I1(l,m) + dzr_local * ( int1_1 + int1_0 ) / 2.0 + I2(l,m) = I2(l,m) + dzr_local * ( int2_1 + int2_0 ) / 2.0 + + int1_0 = int1_1 + int2_0 = int2_1 + + term1(l) = term1(l) +4.0*PI*rho*x(m)* mseg(l)*mseg(m) *sig_ij(l,m)**3 *uij(l,m)/t* dzr_local*(int1_1+int1_0)/2.0 + + END DO + + END DO + END DO + + + ! DO l = 1, ncomp + ! term1(l) = 0.0 + ! DO m = 1, ncomp + ! term1(l) = term1(l) + 4.0*PI*rho*x(m)* mseg(l)*mseg(m) * sig_ij(l,m)**3 * uij(l,m)/t *I1(l,m) + ! END DO + ! END DO + + term2 = 0.0 + DO l = 1, ncomp + DO m = 1, ncomp + term2 = term2 + 2.0*PI*rho*x(l) * rho*x(m)* mseg(l)*mseg(m) * sig_ij(l,m)**3 * uij(l,m)/t *I2(l,m) + END DO + END DO + + DO l = 1, ncomp + mu_dsp(l) = term1(l) + term2 * PI/ 6.0 * mseg(l)*dhs(l)**3 + END DO + +END SUBROUTINE mu_pert_theory_mix + + +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! + SUBROUTINE F_DD_GROSS_VRABEC( fdd ) +! + USE PARAMETERS, ONLY: PI, KBOL + USE EOS_VARIABLES, ONLY: nc, ncomp, uij, parame, mseg, sig_ij, rho, eta, x, t + USE EOS_CONSTANTS, ONLY: ddp2, ddp3, ddp4 + IMPLICIT NONE +! +! ---------------------------------------------------------------------- + REAL, INTENT(IN OUT) :: fdd +! ---------------------------------------------------------------------- + INTEGER :: i, j, k, m + INTEGER :: ddit, ddmax + REAL :: factor2, factor3 + REAL :: xijfa, xijkfa, xijf_j, xijkf_j, eij + REAL :: fdd2, fdd3 + REAL, DIMENSION(nc) :: my2dd, my0, alph_tst, z1dd, z2dd, dderror + REAL, DIMENSION(nc) :: fdd2m, fdd3m, fdd2m2, fdd3m2, fddm, fddm2 + REAL, DIMENSION(nc,nc) :: Idd2, Idd4 + REAL, DIMENSION(nc,nc,nc) :: Idd3 +! ---------------------------------------------------------------------- + + fdd = 0.0 + ddit = 0 + ddmax = 0 ! value assigned, if polarizable compound is present + fddm(:) = 0.0 + DO i = 1, ncomp + IF ( uij(i,i) == 0.0 ) write (*,*) 'F_DD_GROSS_VRABEC: do not use dimensionless units' + IF ( uij(i,i) == 0.0 ) stop + my2dd(i) = (parame(i,6))**2 *1.E-49 /(uij(i,i)*kbol* mseg(i)*sig_ij(i,i)**3 *1.E-30) + alph_tst(i) = parame(i,11) / (mseg(i)*sig_ij(i,i)**3 ) * t/parame(i,3) + IF ( alph_Tst(i) /= 0.0 ) ddmax = 25 ! set maximum number of polarizable RGT-iterations + z1dd(i) = my2dd(i) + 3.0*alph_tst(i) + z2dd(i) = 3.0*alph_tst(i) + my0(i) = my2dd(i) + END DO + + DO i = 1, ncomp + DO j = 1, ncomp + Idd2(i,j) = 0.0 + Idd4(i,j) = 0.0 + ! IF (parame(i,6).NE.0.0 .AND. parame(j,6).NE.0.0) THEN + DO m = 0, 4 + Idd2(i,j) = Idd2(i,j) + ddp2(i,j,m)*eta**m + Idd4(i,j) = Idd4(i,j) + ddp4(i,j,m)*eta**m + END DO + DO k = 1, ncomp + Idd3(i,j,k) = 0.0 + ! IF (parame(k,6).NE.0.0) THEN + DO m = 0, 4 + Idd3(i,j,k) = Idd3(i,j,k) + ddp3(i,j,k,m)*eta**m + END DO + ! ENDIF + END DO + ! ENDIF + END DO + END DO + + factor2 = -PI *rho + factor3 = -4.0/3.0*PI**2 * rho**2 + +9 CONTINUE + + fdd2m(:) = 0.0 + fdd2m2(:) = 0.0 + fdd3m(:) = 0.0 + fdd3m2(:) = 0.0 + fdd2 = 0.0 + fdd3 = 0.0 + DO i = 1, ncomp + DO j = 1, ncomp + ! IF (parame(i,6).NE.0.0 .AND. parame(j,6).NE.0.0) THEN + xijfa =x(i)*parame(i,3)/t*parame(i,2)**3 * x(j)*parame(j,3)/t*parame(j,2)**3 & + /((parame(i,2)+parame(j,2))/2.0)**3 * (z1dd(i)*z1dd(j)-z2dd(i)*z2dd(j)) ! * (1.0-lij(i,j)) + eij = (parame(i,3)*parame(j,3))**0.5 + fdd2= fdd2 + factor2 * xijfa * ( Idd2(i,j) + eij/t*Idd4(i,j) ) + xijf_j = parame(i,3)/t*parame(i,2)**3 *x(j)*parame(j,3)/t*parame(j,2)**3 & + /((parame(i,2)+parame(j,2))/2.0)**3 ! * (1.0-lij(i,j)) + fdd2m(i)=fdd2m(i)+4.0*SQRT(my2dd(i))*z1dd(j)*factor2* xijf_j *(Idd2(i,j)+eij/t*Idd4(i,j)) + fdd2m2(i)=fdd2m2(i) + 4.0*z1dd(j)*factor2* xijf_j *(Idd2(i,j)+eij/t*Idd4(i,j)) + IF (j == i) fdd2m2(i) =fdd2m2(i) +8.0*factor2* xijf_j*my2dd(i) *(Idd2(i,j)+eij/t*Idd4(i,j)) + DO k = 1, ncomp + ! IF (parame(k,6).NE.0.0) THEN + xijkfa = x(i)*parame(i,3)/t*parame(i,2)**3 *x(j)*parame(j,3)/t*parame(j,2)**3 & + *x(k)*parame(k,3)/t*parame(k,2)**3 / ((parame(i,2)+parame(j,2))/2.0) & + /((parame(i,2)+parame(k,2))/2.0) / ((parame(j,2)+parame(k,2))/2.0) & + *(z1dd(i)*z1dd(j)*z1dd(k)-z2dd(i)*z2dd(j)*z2dd(k)) + ! *(1.0-lij(i,j))*(1.0-lij(i,k))*(1.0-lij(j,k)) + fdd3 = fdd3 + factor3 * xijkfa * Idd3(i,j,k) + xijkf_j = parame(i,3)/t*parame(i,2)**3 *x(j)*parame(j,3)/t*parame(j,2)**3 & + *x(k)*parame(k,3)/t*parame(k,2)**3 /((parame(i,2)+parame(j,2))/2.0) & + /((parame(i,2)+parame(k,2))/2.0) /((parame(j,2)+parame(k,2))/2.0) + ! *(1.0-lij(i,j))*(1.0-lij(i,k))*(1.0-lij(j,k)) + fdd3m(i)=fdd3m(i)+6.0*factor3*SQRT(my2dd(i))*z1dd(j)*z1dd(k) *xijkf_j*Idd3(i,j,k) + fdd3m2(i)=fdd3m2(i)+6.0*factor3*z1dd(j)*z1dd(k) *xijkf_j*Idd3(i,j,k) + IF(j == i) fdd3m2(i) =fdd3m2(i)+24.0*factor3*my2dd(i)*z1dd(k) *xijkf_j*Idd3(i,j,k) + ! ENDIF + END DO + ! ENDIF + END DO + END DO + + IF (fdd2 < -1.E-50 .AND. fdd3 /= 0.0) THEN + fdd = fdd2 / ( 1.0 - fdd3/fdd2 ) + IF ( ddmax /= 0 ) THEN + DO i = 1, ncomp + ddit = ddit + 1 + fddm(i) =fdd2*(fdd2*fdd2m(i) -2.0*fdd3*fdd2m(i)+fdd2*fdd3m(i)) /(fdd2-fdd3)**2 + fddm2(i) = fdd2m(i) * (fdd2*fdd2m(i)-2.0*fdd3*fdd2m(i) +fdd2*fdd3m(i)) / (fdd2-fdd3)**2 & + + fdd2*(fdd2*fdd2m2(i) -2.0*fdd3*fdd2m2(i)+fdd2m(i)**2 & + -fdd2m(i)*fdd3m(i) +fdd2*fdd3m2(i)) / (fdd2-fdd3)**2 & + - 2.0*fdd2*(fdd2*fdd2m(i) -2.0*fdd3*fdd2m(i) +fdd2*fdd3m(i)) /(fdd2-fdd3)**3 & + *(fdd2m(i)-fdd3m(i)) + dderror(i)= SQRT( my2dd(i) ) - SQRT( my0(i) ) + alph_Tst(i)*fddm(i) + my2dd(i) = ( SQRT( my2dd(i) ) - dderror(i) / (1.0+alph_Tst(i)*fddm2(i)) )**2 + z1dd(i) = my2dd(i) + 3.0 * alph_Tst(i) + ENDDO + DO i = 1, ncomp + IF (ABS(dderror(i)) > 1.E-11 .AND. ddit < ddmax) GOTO 9 + ENDDO + fdd = fdd + SUM( 0.5*x(1:ncomp)*alph_Tst(1:ncomp)*fddm(1:ncomp)**2 ) + ENDIF + END IF + + +END SUBROUTINE F_DD_GROSS_VRABEC + + + +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! + SUBROUTINE F_QQ_GROSS( fqq ) +! + USE PARAMETERS, ONLY: PI, KBOL + USE EOS_VARIABLES, ONLY: nc, ncomp, uij, parame, mseg, sig_ij, rho, eta, x, t + USE EOS_CONSTANTS, ONLY: qqp2, qqp3, qqp4 + IMPLICIT NONE +! +! ---------------------------------------------------------------------- + REAL, INTENT(IN OUT) :: fqq +! ---------------------------------------------------------------------- + INTEGER :: i, j, k, m + REAL :: factor2, factor3 + REAL :: xijfa, xijkfa, eij + REAL :: fqq2, fqq3 + REAL, DIMENSION(nc) :: qq2 + REAL, DIMENSION(nc,nc) :: Iqq2, Iqq4 + REAL, DIMENSION(nc,nc,nc) :: Iqq3 +! ---------------------------------------------------------------------- + + + fqq = 0.0 + DO i = 1, ncomp + qq2(i) = (parame(i,7))**2 *1.E-69 / (uij(i,i)*kbol*mseg(i)*sig_ij(i,i)**5 *1.E-50) + END DO + + DO i = 1, ncomp + DO j = 1, ncomp + Iqq2(i,j) = 0.0 + Iqq4(i,j) = 0.0 + IF (parame(i,7) /= 0.0 .AND. parame(j,7) /= 0.0) THEN + DO m = 0, 4 + Iqq2(i,j) = Iqq2(i,j) + qqp2(i,j,m)*eta**m + Iqq4(i,j) = Iqq4(i,j) + qqp4(i,j,m)*eta**m + END DO + DO k = 1, ncomp + Iqq3(i,j,k) = 0.0 + IF (parame(k,7) /= 0.0) THEN + DO m = 0, 4 + Iqq3(i,j,k) = Iqq3(i,j,k) + qqp3(i,j,k,m)*eta**m + END DO + END IF + END DO + END IF + END DO + END DO + + factor2 = -9.0/16.0*PI *rho + factor3 = 9.0/16.0*PI**2 * rho**2 + + fqq2 = 0.0 + fqq3 = 0.0 + DO i = 1, ncomp + DO j = 1, ncomp + IF (parame(i,7) /= 0.0 .AND. parame(j,7) /= 0.0) THEN + xijfa=x(i)*uij(i,i)*qq2(i)*sig_ij(i,i)**5 /t & + *x(j)*uij(j,j)*qq2(j)*sig_ij(j,j)**5 /t/sig_ij(i,j)**7.0 + eij = (parame(i,3)*parame(j,3))**0.5 + fqq2= fqq2 +factor2* xijfa * (Iqq2(i,j)+eij/t*Iqq4(i,j)) + DO k = 1, ncomp + IF (parame(k,7) /= 0.0) THEN + xijkfa=x(i)*uij(i,i)*qq2(i)*sig_ij(i,i)**5 /t/sig_ij(i,j)**3 & + *x(j)*uij(j,j)*qq2(j)*sig_ij(j,j)**5 /t/sig_ij(i,k)**3 & + *x(k)*uij(k,k)*qq2(k)*sig_ij(k,k)**5 /t/sig_ij(j,k)**3 + fqq3 = fqq3 + factor3 * xijkfa * Iqq3(i,j,k) + END IF + END DO + END IF + END DO + END DO + + IF ( fqq2 < -1.E-50 .AND. fqq3 /= 0.0 ) THEN + fqq = fqq2 / ( 1.0 - fqq3/fqq2 ) + END IF + + + +END SUBROUTINE F_QQ_GROSS + +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! + SUBROUTINE F_DQ_VRABEC_GROSS( fdq ) +! + USE PARAMETERS, ONLY: PI, KBOL + USE EOS_VARIABLES, ONLY: nc, ncomp, uij, parame, mseg, sig_ij, rho, eta, x, t + USE EOS_CONSTANTS, ONLY: dqp2, dqp3, dqp4 + IMPLICIT NONE +! +! ---------------------------------------------------------------------- + REAL, INTENT(IN OUT) :: fdq +! ---------------------------------------------------------------------- + INTEGER :: i, j, k, m + REAL :: factor2, factor3 + REAL :: xijfa, xijkfa, eij + REAL :: fdq2, fdq3 + REAL, DIMENSION(nc) :: my2dd, myfac, qq2, q_fac + REAL, DIMENSION(nc,nc) :: Idq2, Idq4 + REAL, DIMENSION(nc,nc,nc) :: Idq3 +! ---------------------------------------------------------------------- + + + fdq = 0.0 + DO i = 1, ncomp + my2dd(i) = (parame(i,6))**2 *1.E-49 /(uij(i,i)*kbol* mseg(i)*sig_ij(i,i)**3 *1.E-30) + myfac(i) = parame(i,3)/t*parame(i,2)**4 *my2dd(i) + ! myfac(i)=parame(i,3)/T*parame(i,2)**4 *my2dd_renormalized(i) + qq2(i) = (parame(i,7))**2 *1.E-69 / (uij(i,i)*kbol*mseg(i)*sig_ij(i,i)**5 *1.E-50) + q_fac(i) = parame(i,3)/t*parame(i,2)**4 *qq2(i) + END DO + + DO i = 1, ncomp + DO j = 1, ncomp + Idq2(i,j) = 0.0 + Idq4(i,j) = 0.0 + IF (myfac(i) /= 0.0 .AND. q_fac(j) /= 0.0) THEN + DO m = 0, 4 + Idq2(i,j) = Idq2(i,j) + dqp2(i,j,m)*eta**m + Idq4(i,j) = Idq4(i,j) + dqp4(i,j,m)*eta**m + END DO + DO k = 1, ncomp + Idq3(i,j,k) = 0.0 + IF (myfac(k) /= 0.0 .OR. q_fac(k) /= 0.0) THEN + DO m = 0, 4 + Idq3(i,j,k) = Idq3(i,j,k) + dqp3(i,j,k,m)*eta**m + END DO + END IF + END DO + END IF + END DO + END DO + + factor2 = -9.0/4.0 * PI *rho + factor3 = PI**2 * rho**2 + + fdq2 = 0.0 + fdq3 = 0.0 + DO i = 1, ncomp + DO j = 1, ncomp + IF (myfac(i) /= 0.0 .AND. q_fac(j) /= 0.0) THEN + xijfa = x(i)*myfac(i) * x(j)*q_fac(j) /sig_ij(i,j)**5 + eij = (parame(i,3)*parame(j,3))**0.5 + fdq2 = fdq2 +factor2* xijfa*(Idq2(i,j)+eij/t*Idq4(i,j)) + DO k = 1, ncomp + IF (myfac(k) /= 0.0 .OR. q_fac(k) /= 0.0) THEN + xijkfa=x(i)*x(j)*x(k)/(sig_ij(i,j)*sig_ij(i,k)*sig_ij(j,k))**2 & + *( myfac(i)*q_fac(j)*myfac(k) + myfac(i)*q_fac(j)*q_fac(k)*1.1937350 ) + fdq3 = fdq3 + factor3*xijkfa*Idq3(i,j,k) + END IF + END DO + END IF + END DO + END DO + + IF (fdq2 < -1.E-50 .AND. fdq3 /= 0.0) THEN + fdq = fdq2 / ( 1.0 - fdq3/fdq2 ) + END IF + +END SUBROUTINE F_DQ_VRABEC_GROSS + + +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! + SUBROUTINE f_dft ( I1_dft, I2_dft ) +! + USE EOS_VARIABLES, ONLY: nc, PI, ncomp, t, rho, eta, x, mseg, parame + USE DFT_MODULE + IMPLICIT NONE +! +! ---------------------------------------------------------------------- + REAL, INTENT(OUT) :: I1_dft + REAL, INTENT(OUT) :: I2_dft +! +! ---------------------------------------------------------------------- + INTEGER :: k,ih + ! REAL :: z3 + REAL :: ua, ua_c, ua_2, ua_c_2, rm + REAL :: int10, int11, int20, int21 + REAL :: dg_drho + REAL :: rad, xg, rdf, rho_st, msegm + REAL :: sig_ij + REAL :: dg_dr, dzr_org !,rdf_d + ! REAL :: intgrid(0:NDFT),intgri2(0:NDFT) +! ---------------------------------------------------------------------- + +! -----constants-------------------------------------------------------- +msegm = parame(1,1) +rho_st = rho * parame(1,2)**3 + +ua_c = 4.0 * ( rc**(-12) - rc**(-6) ) +ua_c_2 = ua_c * ua_c +rm = 2.0**(1.0/6.0) + +int10 = rc*rc* ua_c +int20 = rc*rc* ua_c_2 +! intgrid(0)= int10 +! intgri2(0)= int20 + + +sig_ij = parame(1,2) + + +I1_dft = 0.0 +I2_dft = 0.0 +rad = rc +!dzr = dzp / 2.0 ! this line is obsolete. dzr is defined in DFT-nMF2 (dimensionless) +dzr_org= dzr +k = 0 +ih = 85 + +DO WHILE ( rad-dzr+1.E-9 >= 1.0 ) + + rad = rad - dzr + ! IF (rad <= 8.0) dzr = dzp + ! IF (rad <= rg) dzr = dzp/2.0 + k = k + 1 + xg = rad / dhs_st + ua = 4.0 * ( rad**(-12) - rad**(-6) ) + ua_2 = ua * ua + rdf = 1.0 + dg_drho = 0.0 + IF ( rad <= rg ) THEN + CALL BI_CUB_SPLINE (rho_st,xg,ya,x1a,x2a,y1a,y2a,y12a, & + c_bicub,rdf,dg_drho,dg_dr,den_step,ih,k) + END IF + + int11 = rdf*rad*rad* ua + int21 = rdf*rad*rad* ua_2 + I1_dft= I1_dft + dzr*(int11+int10)/2.0 + I2_dft= I2_dft + dzr*(int21+int20)/2.0 + int10 = int11 + int20 = int21 + +END DO + +dzr = dzr_org + +! stepno = k +! CALL SPLINE_PARA (dzr,intgrid,utri,stepno) +! CALL SPLINE_INT (I1,dzr,intgrid,utri,stepno) + +! caution: 1st order integral is in F_EOS.f defined with negative sign +I1_dft= - I1_dft - ( 4.0/9.0 * rc**(-9) - 4.0/3.0 * rc**(-3) ) + +! CALL SPLINE_PARA (dzr,intgri2,utri,stepno) +! CALL SPLINE_INT (I2,dzr,intgri2,utri,stepno) + +I2_dft = I2_dft + 16.0/21.0 * rc**(-21) - 32.0/15.0 * rc**(-15) + 16.0/9.0 * rc**(-9) + + +END SUBROUTINE f_dft + + + + +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! + REAL FUNCTION TANGENT_VALUE2 ( optpara, n ) +! SUBROUTINE TANGENT_VALUE ( fmin, optpara, n ) +! + USE BASIC_VARIABLES + USE STARTING_VALUES + IMPLICIT NONE +! +! ---------------------------------------------------------------------- + INTEGER, INTENT(IN) :: n + REAL, INTENT(IN) :: optpara(n) + !REAL, INTENT(IN) :: optpara(:) + !REAL, INTENT(IN OUT) :: fmin +! +! ---------------------------------------------------------------------- + INTEGER :: i + REAL :: lnphi(np,nc),ph_frac, gibbs_full(np),xlnx1,xlnx2 + REAL, DIMENSION(nc) :: ni_1, ni_2 +! ---------------------------------------------------------------------- + + + ! --- setting of mole fractions --------------------------------------- + DO i = 1, ncomp + IF ( optpara(i) < -300.0 ) THEN + ni_2(i) = 0.0 + ELSE + ni_2(i) = EXP( optpara(i) ) + END IF + END DO + + DO i = 1, ncomp + ni_1(i) = xif(i) - ni_2(i) + IF ( ni_2(i) > xif(i) ) THEN + ni_2(i) = xif(i) + ni_1(i) = xif(i) * 1.E-20 + ENDIF + END DO + + xi(2,1:ncomp) = ni_2(1:ncomp) / SUM( ni_2(1:ncomp) ) + lnx(2,1:ncomp) = optpara(1:ncomp) - LOG( SUM( ni_2(1:ncomp) ) ) + + ph_frac = SUM( ni_1(1:ncomp) ) + xi(1,1:ncomp) = ni_1(1:ncomp) / ph_frac + lnx(1,1:ncomp) = LOG( ni_1(1:ncomp) ) - LOG( ph_frac ) + ! write (*,'(a,4G18.8)') 'FF',(xif(i),i=1,ncomp) + ! write (*,'(a,4G18.8)') 'AA',(xi(1,i),i=1,ncomp) + ! write (*,'(a,3G18.8)') 'BB',(xi(2,i),i=1,ncomp) + + CALL fugacity (lnphi) + !CALL enthalpy_etc + + gibbs(1) = SUM( xi(1,1:ncomp) * lnphi(1,1:ncomp) ) ! dimensionless g/RT + gibbs(2) = SUM( xi(2,1:ncomp) * lnphi(2,1:ncomp) ) + + xlnx1 = SUM( xi(1,1:ncomp)*lnx(1,1:ncomp) ) ! dimensionless s/RT + xlnx2 = SUM( xi(2,1:ncomp)*lnx(2,1:ncomp) ) + + gibbs_full(1) = gibbs(1) + xlnx1 + gibbs_full(2) = gibbs(2) + xlnx2 + + TANGENT_VALUE2 = gibbs_full(1)*ph_frac + gibbs_full(2)*(1.0-ph_frac) + !fmin = gibbs_full(1)*ph_frac + gibbs_full(2)*(1.0-ph_frac) + !write (*,'(a,4G18.8)') 'TP',TANGENT_VALUE2,(lnx(1,i),i=1,ncomp) + !write (*,'(a,4G18.8)') 'al',ph_frac,(lnx(2,i), i=1,ncomp) + !write (*,*) ' ' + !pause + +END FUNCTION TANGENT_VALUE2 + + + + + + + + diff --git a/applications/PUfoam/MoDeNaModels/PolymerDensity/src/DetailedModelCode/getting_started_subroutines.f90 b/applications/PUfoam/MoDeNaModels/PolymerDensity/src/DetailedModelCode/getting_started_subroutines.f90 new file mode 100644 index 000000000..c56278f18 --- /dev/null +++ b/applications/PUfoam/MoDeNaModels/PolymerDensity/src/DetailedModelCode/getting_started_subroutines.f90 @@ -0,0 +1,4102 @@ + +!> This file contains auxiliary subroutines. + + + +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! SUBROUTINE eos_const +! +! This subroutine provides the constants of the PC-SAFT EOS. +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! + SUBROUTINE eos_const (ap,bp,dnm) +! + IMPLICIT NONE +! +! ---------------------------------------------------------------------- + REAL, INTENT(OUT) :: ap(0:6,3) + REAL, INTENT(OUT) :: bp(0:6,3) + REAL, INTENT(OUT) :: dnm(4,9) +! ---------------------------------------------------------------------- + + +! --- dispersion term constants ---------------------------------------- +ap(0,1) = 0.91056314451539 +ap(0,2) = -0.30840169182720 +ap(0,3) = -0.09061483509767 +ap(1,1) = 0.63612814494991 +ap(1,2) = 0.18605311591713 +ap(1,3) = 0.45278428063920 +ap(2,1) = 2.68613478913903 +ap(2,2) = -2.50300472586548 +ap(2,3) = 0.59627007280101 +ap(3,1) = -26.5473624914884 +ap(3,2) = 21.4197936296668 +ap(3,3) = -1.72418291311787 +ap(4,1) = 97.7592087835073 +ap(4,2) = -65.2558853303492 +ap(4,3) = -4.13021125311661 +ap(5,1) = -159.591540865600 +ap(5,2) = 83.3186804808856 +ap(5,3) = 13.7766318697211 +ap(6,1) = 91.2977740839123 +ap(6,2) = -33.7469229297323 +ap(6,3) = -8.67284703679646 + +bp(0,1) = 0.72409469413165 +bp(0,2) = -0.57554980753450 +bp(0,3) = 0.09768831158356 +bp(1,1) = 1.11913959304690 *2.0 +bp(1,2) = 0.34975477607218 *2.0 +bp(1,3) = -0.12787874908050 *2.0 +bp(2,1) = -1.33419498282114 *3.0 +bp(2,2) = 1.29752244631769 *3.0 +bp(2,3) = -3.05195205099107 *3.0 +bp(3,1) = -5.25089420371162 *4.0 +bp(3,2) = -4.30386791194303 *4.0 +bp(3,3) = 5.16051899359931 *4.0 +bp(4,1) = 5.37112827253230 *5.0 +bp(4,2) = 38.5344528930499 *5.0 +bp(4,3) = -7.76088601041257 *5.0 +bp(5,1) = 34.4252230677698 *6.0 +bp(5,2) = -26.9710769414608 *6.0 +bp(5,3) = 15.6044623461691 *6.0 +bp(6,1) = -50.8003365888685 *7.0 +bp(6,2) = -23.6010990650801 *7.0 +bp(6,3) = -4.23812936930675 *7.0 + + +! square-well fluid +! ap(1,1)= 0.79152347258784 +! ap(1,2)= -0.62269805320654 +! ap(1,3)= -0.06798823934067 +! ap(2,1)= 1.07120982251709 +! ap(2,2)= 0.48628215731716 +! ap(2,3)= 0.02837828512515 +! ap(3,1)= 0.92084839459226 +! ap(3,2)= 1.11652038059747 +! ap(3,3)= 0.09713202077943 +! ap(4,1)= -7.84708350369249 +! ap(4,2)= -2.04200599876547 +! ap(4,3)= 0.06475764015088 +! ap(5,1)= 25.90284137818050 +! ap(5,2)= 9.27791640100603 +! ap(5,3)= 0.07729792971827 +! ap(6,1)= -57.1528726997640 +! ap(6,2)= -16.8377999920957 +! ap(6,3)= 0.24883598436184 +! ap(7,1)= 42.02314637860930 +! ap(7,2)= 7.62432635016420 +! ap(7,3)= -0.72472024688888 + +! bp(1,1)= 0.79152347258784 +! bp(1,2)= -0.62269805320654 +! bp(1,3)= -0.06798823934067 +! bp(2,1)= 1.07120982251709 *2.0 +! bp(2,2)= 0.48628215731716 *2.0 +! bp(2,3)= 0.02837828512515 *2.0 +! bp(3,1)= 0.92084839459226 *3.0 +! bp(3,2)= 1.11652038059747 *3.0 +! bp(3,3)= 0.09713202077943 *3.0 +! bp(4,1)= -7.84708350369249 *4.0 +! bp(4,2)= -2.04200599876547 *4.0 +! bp(4,3)= 0.06475764015088 *4.0 +! bp(5,1)= 25.90284137818050 *5.0 +! bp(5,2)= 9.27791640100603 *5.0 +! bp(5,3)= 0.07729792971827 *5.0 +! bp(6,1)= -57.1528726997640 *6.0 +! bp(6,2)= -16.8377999920957 *6.0 +! bp(6,3)= 0.24883598436184 *6.0 +! bp(7,1)= 42.02314637860930 *7.0 +! bp(7,2)= 7.62432635016420 *7.0 +! bp(7,3)= -0.72472024688888 *7.0 + + +dnm(1,1) = -8.8043 +dnm(1,2) = +4.1646270 +dnm(1,3) = -48.203555 +dnm(1,4) = +140.43620 +dnm(1,5) = -195.23339 +dnm(1,6) = +113.51500 +dnm(2,1) = +2.9396 +dnm(2,2) = -6.0865383 +dnm(2,3) = +40.137956 +dnm(2,4) = -76.230797 +dnm(2,5) = -133.70055 +dnm(2,6) = +860.25349 +dnm(2,7) = -1535.3224 +dnm(2,8) = +1221.4261 +dnm(2,9) = -409.10539 +dnm(3,1) = -2.8225 +dnm(3,2) = +4.7600148 +dnm(3,3) = +11.257177 +dnm(3,4) = -66.382743 +dnm(3,5) = +69.248785 +dnm(4,1) = +0.3400 +dnm(4,2) = -3.1875014 +dnm(4,3) = +12.231796 +dnm(4,4) = -12.110681 + +END SUBROUTINE eos_const + + + +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! SUBROUTINE dq_const +! +! This subr. provides the constants of the dipole-quadrupole term. +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! + SUBROUTINE dq_const ( dqp2,dqp3,dqp4 ) +! + USE PARAMETERS, ONLY: nc + USE EOS_VARIABLES, ONLY: ncomp, parame + IMPLICIT NONE +! +! ---------------------------------------------------------------------- + REAL, INTENT(OUT) :: dqp2(nc,nc,0:8) + REAL, INTENT(OUT) :: dqp3(nc,nc,nc,0:8) + REAL, INTENT(OUT) :: dqp4(nc,nc,0:8) +! +! ---------------------------------------------------------------------- + INTEGER :: i, j, k + REAL :: mdq(nc) + REAL :: mf1, mf2, msegij +! ---------------------------------------------------------------------- + +DO i=1,ncomp + mdq(i) = parame(i,1) + IF (mdq(i) > 2.0) mdq(i) = 2.0 +END DO + + +DO i=1,ncomp + DO j=1,ncomp + + msegij=(mdq(i)*mdq(j))**0.5 + mf1 = (msegij-1.0)/msegij + mf2 = mf1*(msegij-2.0)/msegij + + dqp2(i,j,0) = 0.697094963 + mf1*(-0.673459279) + mf2*0.670340770 + dqp2(i,j,1) = -0.633554144 + mf1*(-1.425899106) + mf2*(-4.338471826) + dqp2(i,j,2) = 2.945509028 + mf1 * 4.19441392 + mf2*7.234168360 + dqp2(i,j,3) = -1.467027314 + mf1 * 1.0266216 + dqp2(i,j,4) = 0.0 + + dqp4(i,j,0) = -0.484038322 + mf1 * 0.67651011 + mf2*(-1.167560146) + dqp4(i,j,1) = 1.970405465 + mf1*(-3.013867512) + mf2*2.13488432 + dqp4(i,j,2) = -2.118572671 + mf1 * 0.46742656 + dqp4(i,j,3) = 0.0 + dqp4(i,j,4) = 0.0 + + + DO k=1,ncomp + msegij=(mdq(i)*mdq(j)*mdq(k))**(1.0/3.0) + mf1 = (msegij-1.0)/msegij + mf2 = (msegij-2.0)/msegij + dqp3(i,j,k,0) = 0.795009692 + mf1*(-2.099579397) + dqp3(i,j,k,1) = 3.386863396 + mf1*(-5.941376392) + dqp3(i,j,k,2) = 0.475106328 + mf1*(-0.178820384) + dqp3(i,j,k,3) = 0.0 + dqp3(i,j,k,4) = 0.0 + END DO + + END DO +END DO + +END SUBROUTINE dq_const + + +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! SUBROUTINE dd_const +! +! This subroutine provides the constants of the dipole-term. +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! + SUBROUTINE dd_const ( ddp2,ddp3,ddp4 ) +! + USE PARAMETERS, ONLY: nc, PI + USE EOS_VARIABLES, ONLY: ncomp, parame + IMPLICIT NONE +! +! ---------------------------------------------------------------------- + REAL, INTENT(OUT) :: ddp2(nc,nc,0:8) + REAL, INTENT(OUT) :: ddp3(nc,nc,nc,0:8) + REAL, INTENT(OUT) :: ddp4(nc,nc,0:8) +! +! ---------------------------------------------------------------------- + INTEGER :: i, j, k + REAL :: pardd(nc) + REAL :: mf1,mf2,msegij,sin2t +! ---------------------------------------------------------------------- + +sin2t = SIN( 0.0 * PI / 180.0 ) +sin2t = sin2t*sin2t + +DO i = 1, ncomp + pardd(i) = parame(i,1) + IF (pardd(i) > 2.0) pardd(i) = 2.0 +END DO + +DO i=1,ncomp + DO j=1,ncomp +! IF (parame(i,6).NE.0.0.AND.parame(j,6).NE.0.0) THEN + + msegij=(pardd(i)*pardd(j))**0.5 + mf1 = (msegij-1.0)/msegij + mf2 = mf1*(msegij-2.0)/msegij + + ddp2(i,j,0) = 0.30435038064 + mf1*(0.95346405973+0.201436*sin2t) & + + mf2*(-1.16100802773-1.74114*sin2t) + ddp2(i,j,1) = -0.13585877707 + mf1*(-1.83963831920+1.31649*sin2t) & + + mf2*4.52586067320 + ddp2(i,j,2) = 1.44933285154 + mf1 * 2.01311801180 + mf2*0.97512223853 + ddp2(i,j,3) = 0.35569769252 + mf1*(-7.37249576667) + mf2*(-12.2810377713) + ddp2(i,j,4) = -2.06533084541 + mf1 * 8.23741345333 + mf2*5.93975747420 + + ddp4(i,j,0) = 0.21879385627 + mf1*(-0.58731641193) + mf2*3.48695755800 + ddp4(i,j,1) = -1.18964307357 + mf1 * 1.24891317047 + mf2*(-14.9159739347) + ddp4(i,j,2) = 1.16268885692 + mf1*(-0.50852797392) + mf2*15.3720218600 + ddp4(i,j,3) = 0.0 + ddp4(i,j,4) = 0.0 + + DO k=1,ncomp +! IF (parame(k,6).NE.0.0) THEN + msegij=(pardd(i)*pardd(j)*pardd(k))**(1.0/3.0) + mf1 = (msegij-1.0)/msegij + mf2 = mf1*(msegij-2.0)/msegij + ddp3(i,j,k,0) = -0.06467735252 + mf1*(-0.95208758351+0.28503*sin2t) & + + mf2*(-0.62609792333+2.2195*sin2t) + ddp3(i,j,k,1) = 0.19758818347 + mf1 * 2.99242575222 + mf2*1.29246858189 + ddp3(i,j,k,2) = -0.80875619458 + mf1*(-2.38026356489) + mf2*1.65427830900 + ddp3(i,j,k,3) = 0.69028490492 + mf1*(-0.27012609786) + mf2*(-3.43967436378) + ddp3(i,j,k,4) = 0.0 + +! ENDIF + END DO + +! ENDIF + END DO +END DO + +END SUBROUTINE dd_const + + +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! SUBROUTINE qq_const +! +! This subroutine provides the constants of the quadrupole-term. +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! + SUBROUTINE qq_const ( qqp2,qqp3,qqp4 ) +! + USE PARAMETERS, ONLY: nc + USE EOS_VARIABLES, ONLY: ncomp, parame + IMPLICIT NONE +! +! ---------------------------------------------------------------------- + REAL, INTENT(OUT) :: qqp2(nc,nc,0:8) + REAL, INTENT(OUT) :: qqp3(nc,nc,nc,0:8) + REAL, INTENT(OUT) :: qqp4(nc,nc,0:8) +! +! ---------------------------------------------------------------------- + INTEGER :: i, j, k + REAL :: mqq(nc) + REAL :: mf1, mf2, msegij +! ---------------------------------------------------------------------- + +DO i = 1,ncomp + mqq(i) = parame(i,1) + IF (mqq(i) > 2.0) mqq(i) = 2.0 +END DO + +DO i = 1,ncomp + DO j = 1,ncomp + IF (parame(i,7) /= 0.0 .AND. parame(j,7) /= 0.0) THEN + + msegij=(mqq(i)*mqq(j))**0.5 +! msegij=(parame(i,1)*parame(j,1))**0.50 + mf1 = (msegij-1.0)/msegij + mf2 = mf1*(msegij-2.0)/msegij + + qqp2(i,j,0) = 1.237830788 + mf1 * 1.285410878 + mf2*1.794295401 + qqp2(i,j,1) = 2.435503144 + mf1*(-11.46561451) + mf2*0.769510293 + qqp2(i,j,2) = 1.633090469 + mf1 *22.08689285 + mf2*7.264792255 + qqp2(i,j,3) = -1.611815241 + mf1 * 7.46913832 + mf2*94.48669892 + qqp2(i,j,4) = 6.977118504 + mf1*(-17.19777208) + mf2*(-77.1484579) + + qqp4(i,j,0) = 0.454271755 + mf1*(-0.813734006) + mf2*6.868267516 + qqp4(i,j,1) = -4.501626435 + mf1 * 10.06402986 + mf2*(-5.173223765) + qqp4(i,j,2) = 3.585886783 + mf1*(-10.87663092) + mf2*(-17.2402066) + qqp4(i,j,3) = 0.0 + qqp4(i,j,4) = 0.0 + + DO k = 1,ncomp + IF (parame(k,7) /= 0.0) THEN + msegij=(mqq(i)*mqq(j)*mqq(k))**(1.0/3.0) +! msegij=(parame(i,1)*parame(j,1)*parame(k,1))**(1.0/3.0) + mf1 = (msegij-1.0)/msegij + mf2 = mf1*(msegij-2.0)/msegij + qqp3(i,j,k,0) = -0.500043713 + mf1 * 2.000209381 + mf2*3.135827145 + qqp3(i,j,k,1) = 6.531869153 + mf1*(-6.78386584) + mf2*7.247588801 + qqp3(i,j,k,2) = -16.01477983 + mf1 * 20.38324603 + mf2*3.075947834 + qqp3(i,j,k,3) = 14.42597018 + mf1*(-10.89598394) + qqp3(i,j,k,4) = 0.0 + END IF + END DO + + END IF + END DO +END DO + +END SUBROUTINE qq_const + + + + + + + +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! + SUBROUTINE SET_DEFAULT_EOS_NUMERICAL +! + USE EOS_NUMERICAL_DERIVATIVES + IMPLICIT NONE +! +! ---------------------------------------------------------------------- + + ideal_gas = 'no' ! ( yes, no ) + hard_sphere = 'CSBM' ! ( CSBM, no ) + chain_term = 'TPT1' ! ( TPT1, HuLiu, no ) + disp_term = 'PC-SAFT' ! ( PC-SAFT, CK, PT1, PT2, PT_MF, PT_MIX, no ) + hb_term = 'TPT1_Chap' ! ( TPT1_Chap, no ) + LC_term = 'no' ! ( MSaupe, OVL, no ) + branch_term = 'no' ! ( TPT2, no ) + II_term = 'no' + ID_term = 'no' + + subtract1 = 'no' ! (1PT, 2PT, no) + subtract2 = 'no' ! (ITTpolar, no) + +END SUBROUTINE SET_DEFAULT_EOS_NUMERICAL + + + + + + + + + +! SUBROUTINE READ_INPUT +! ! +! USE BASIC_VARIABLES +! IMPLICIT NONE +! ! +! ! ---------------------------------------------------------------------- +! INTEGER :: i +! REAL :: reading2,reading3,sumfeed +! CHARACTER (LEN=4) :: uoutp, uinp +! CHARACTER (LEN=1) :: uoutt, uint +! CHARACTER (LEN=50) :: filename +! CHARACTER (LEN=30) :: reading1 +! ! ---------------------------------------------------------------------- +! +! filename='./input_file/INPUT.INP' +! CALL file_open(filename,30) +! READ (30,*) eos, pol !J: specify by numbers! eos(1=pcsaft, 2=SRK,...) pol (=polar) yes(1) no(0) +! READ (30,*) t, uint, p, uinp !J: t: value of temp, uint: unit of temp, p: value of pressure, uinp: unit of pressure +! +! ncomp = 0 +! i = 0 +! sumfeed = 0.0 +! read_loop: DO +! READ (30,*) reading1,reading2,reading3 +! IF (reading1 == 'end') EXIT read_loop +! ncomp = ncomp + 1 +! i = i + 1 +! compna(i)= reading1 ! comp.name +! mm(i) = reading2 ! molec.mass (mandatory only for polymers) +! xif(i) = reading3 !J: molefractions +! sumfeed = sumfeed + xif(i) +! ENDDO read_loop +! +! CLOSE (30) +! +! IF (sumfeed /= 0.0 .AND. sumfeed /= 1.0) THEN !J: in case mole fractions dont sum up to 1?? +! xif(1:ncomp) = xif(1:ncomp)/sumfeed +! END IF +! +! uoutt = uint +! uoutp = uinp +! IF (uint == 'C') THEN !J: unit stuff +! u_in_t = 273.15 +! ELSE +! u_in_t = 0.0 +! END IF +! IF (uinp == 'bar') THEN +! u_in_p = 1.E5 +! ELSE IF (uinp == 'mbar') THEN +! u_in_p = 1.E2 +! ELSE IF (uinp == 'MPa') THEN +! u_in_p = 1.E6 +! ELSE IF (uinp == 'kPa') THEN +! u_in_p = 1.E3 +! ELSE +! u_in_p = 1.E0 +! END IF +! +! IF (uoutt == 'C') THEN +! u_out_t = 273.15 +! ELSE +! u_out_t = 0.0 +! END IF +! IF (uoutp == 'bar') THEN +! u_out_p = 1.E5 +! ELSE IF (uoutp == 'mbar') THEN +! u_out_p = 1.E2 +! ELSE IF (uoutp == 'MPa') THEN +! u_out_p = 1.E6 +! ELSE IF (uoutp == 'kPa') THEN +! u_out_p = 1.E3 +! ELSE +! u_out_p = 1.0 +! END IF +! +! t = t + u_in_t !J: calculate temp in Kelvin +! p = p * u_in_p !J: calculate pressure in Pascal +! +! CALL para_input ! retriev pure comp. parameters +! +! +! END SUBROUTINE READ_INPUT + + + + + +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! SUBROUTINE file_open +! +! This subroutine opens files for reading. Beforehand, it checks +! whether this file is available. +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! + SUBROUTINE file_open(filename,file_number) +! +! ---------------------------------------------------------------------- + CHARACTER (LEN=50) :: filename + INTEGER :: file_number + LOGICAL :: filefound +! ---------------------------------------------------------------------- + +INQUIRE (FILE=filename, EXIST = filefound) +IF (filefound) THEN + OPEN (file_number, FILE = filename) +ELSE + write (*,*) ' FOLLOWING FILE CAN NOT BE OPENED', filename + stop +END IF + +END SUBROUTINE file_open + + + +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! SUBROUTINE para_input +! +! This subroutine provides pure component parameters and kij parameters. +! The following syntax applies: +! +! compna(i) component name +! parame(i,k) pure comp. parameter: +! parame(i,1): segment number [/] +! parame(i,2): segment diameter "sigma" [Angstrom] +! parame(i,3): segment energy param. epsilon/k [K] +! parame(i,4): model parameter; not used for PC-SAFT (=0) +! it is 10K most of the time for SAFT [K] +! parame(i,5): Param. for T-dependent segment diameter [/] +! parame(i,6): dipolar moment [debye] +! parame(i,7): quadrupolar moment [debye] +! parame(i,8): number of segments that are part of a branching 4-mer [/] +! parame(i,9): +! parame(i,10): ionic charge number (positiv or negativ) [/] +! parame(i,11): polarizability [A**3] +! parame(i,12): number of association sites [/] +! parame(i,13): (=kap_hb, see below) [/] +! parame(i,14 to 25): (=eps_hb, see below) [K] +! nhb_typ(i) number of different types of association sites (comp. i) +! nhb_no(i,k) number of association sites of type k +! eps_hb depth of association potential [K] +! kap_hb effective width of assoc. potential (angle-averg.) +! mm molec. mass +! scaling param. for roughly scaling the set of objective functions +! +! As opposed to low-molec mass compounds, the molecular mass of a +! polymer is not obtained from this routine. Rather, it is a +! user-specification given in the file INPUT.INP +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! + SUBROUTINE para_input +! + USE BASIC_VARIABLES + IMPLICIT NONE +! +!---------------------------------------------------------------------- + INTEGER :: i +!---------------------------------------------------------------------- + +IF (eos == 1) THEN + CALL pcsaft_par +ELSE IF (eos == 4 .OR. eos == 5 .OR. eos == 6 .OR. eos == 8) THEN + ! CALL lj_par + write (*,*) 'deactivated this line when making a transition to f90' + stop +ELSE IF (eos == 7) THEN + ! CALL sw_par + write (*,*) 'deactivated this line when making a transition to f90' + stop +ELSE IF (eos == 10) THEN + i = 1 + IF (compna(i) == 'LC_generic' .AND. ncomp == 1 ) THEN + mm(i) = 1.0 + parame(i,1) = 7.0 + parame(i,2) = 1.0 + parame(i,3) = 0.0 + ELSE + write (*,*) 'PARA_INPUT: define the component !' + stop + ENDIF +ELSE + !CALL saft_par +END IF + +DO i = 1, ncomp + IF ( mm(i) >= 1.0 .AND. mm(i) < 45.0 ) THEN + scaling(i) = 10000.0 + ELSE IF( mm(i) >= 45.0 .AND. mm(i) < 90.0 ) THEN + scaling(i) = 1000.0 + ELSE IF( mm(i) >= 90.0 .AND. mm(i) < 150.0 ) THEN + scaling(i) = 100.0 + ELSE IF( mm(i) >= 150.0 .AND. mm(i) < 250.0 ) THEN + scaling(i) = 10.0 + ELSE + scaling(i) = 1.0 + END IF + IF (parame(i,10) /= 0.0) scaling(i) = scaling(i) / 1.E4 ! Electrolytes +END DO + +END SUBROUTINE para_input + + + + +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! SUBROUTINE pcsaft_par +! +! pure component parameters and kij parameters +! (as described in SUBROUTINE para_input) +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! + SUBROUTINE pcsaft_par +! + USE BASIC_VARIABLES + IMPLICIT NONE +! +!---------------------------------------------------------------------- + INTEGER :: i, j, k, no + INTEGER, DIMENSION(nc) :: nhb_typ + INTEGER, DIMENSION(nc,nsite) :: nhb_no + REAL, DIMENSION(nc,nc,nsite,nsite) :: eps_hb + REAL, DIMENSION(nc,nc) :: kap_hb +!---------------------------------------------------------------------- + + +DO i = 1, ncomp + parame(i,4) = 0.0 ! T correct. required for SAFT, not PC-SAFT + parame(i,5) = 0.12 ! Param. for T-dependent segment diameter + parame(i,6) = 0.0 ! dipolar moment + parame(i,7) = 0.0 ! quadrupolar moment + parame(i,8) = 0.0 ! number of segments that are part of a branching 4-mer + parame(i,9) = 0.0 + parame(i,10)= 0.0 ! ionic charge number + parame(i,11)= 0.0 ! polarizability + lli(i) = 0.0 + phi_criti(i)= 0.0 + chap(i) = 0.0 + + nhb_typ(i) = 0 + kap_hb(i,i) = 0.0 + ! irgendwann sollten nhb_typ und kap_hb durch parame(i,12) und (i,13) + ! ersetzt werden. + + IF (compna(i) == '14-butandiol') THEN + mm(i) = 90.12 + parame(i,1) = 4.35923557 + parame(i,2) = 3.02947364 + parame(i,3) = 197.11998863 + + ELSE IF (compna(i) == 'air') THEN + mm(i) = 28.899 !n2 and o2 according to mole fractions + parame(i,1) = 1.18938 !n2 and o2 according to mole fractions (weighted artihm. avg) + parame(i,2) = 3.28694 !n2 and o2 according to mole fractions (weighted artihm. avg) + parame(i,3) = 95.672 !n2 and o2 according to mole fractions (weighted artihm. avg) + + + Else IF(compna(i) == 'mdi') THEN + mm(i) = 2.50252E+02 + parame(i,1) = mm(i)*0.030769 + parame(i,2) = 2.886003 + parame(i,3) = 283.052778 + + Else IF(compna(i) == 'po') THEN + mm(i) = 90.12 + parame(i,1) = 4.35923557 + parame(i,2) = 3.02947364 + parame(i,3) = 197.11998863 + Else IF(compna(i) == 'pu') THEN +! mm(i) = 2042.22 !pu n = 5 +! parame(i,1) = mm(i)*0.008845 +! parame(i,2) = 5.680270 +! parame(i,3) = 497.997594 + mm(i) = 340.37 !pu n = 0 + parame(i,1) = mm(i)*0.043312 + parame(i,2) = 3.008359 + parame(i,3) = 273.445205 +! mm(i) = 680.74 !pu n = 1 +! parame(i,1) = mm(i)*0.024106 +! parame(i,2) = 3.744327 +! parame(i,3) = 321.486386 +! mm(i) = 1021.11 !pu n = 2 +! parame(i,1) = mm(i)*0.015076 +! parame(i,2) = 4.537837 +! parame(i,3) = 400.036950 + + + + + Else IF(compna(i) == 'tpg') THEN + mm(i) = 192.25 + parame(i,1) = mm(i)*0.01239 + parame(i,2) = 4.549 + parame(i,3) = 148.678 + parame(i,6) = 0.41 + + nhb_typ(i) = 2 ! no. of different association sites + nhb_no(i,1) = 2 ! no. of sites of type 1 + nhb_no(i,2) = 2 ! no. of sites of type 2 + + eps_hb(i,i,1,2)= 5597.844 + eps_hb(i,i,2,1)= 5597.844 + eps_hb(i,i,1,1)= 0.0 + eps_hb(i,i,2,2)= 0.0 + kap_hb(i,i) = 0.03 + + + + + + ELSE IF (compna(i) == 'ps') THEN + parame(i,1) = mm(i)*1.9E-2 + parame(i,2) = 4.10705961 + parame(i,3) = 267.0 + ELSE IF (compna(i) == 'pg2') THEN !Polyglycerol 2 + mm(i) = 2000.0 + parame(i,1) = mm(i)*2.37E-2 ! from figure 5 PCSAFT paper + parame(i,2) = 3.8 ! from figure 5 PCSAFT paper + parame(i,3) = 270.0 ! starting value for iteration + ! this is the extra parameter + parame(i,8) = mm(i)*2.37E-2 + + nhb_typ(i) = 2 ! no. of different association sites + nhb_no(i,1) = 27 ! no. of sites of type 1 + nhb_no(i,2) = 27 ! no. of sites of type 2 + eps_hb(i,i,1,2)= 2544.6 ! taken from butanol (same M/OH) + eps_hb(i,i,2,1)= 2544.6 + eps_hb(i,i,1,1)= 0.0 + eps_hb(i,i,2,2)= 0.0 + kap_hb(i,i)= .00489087833 ! taken from butanol (same M/OH) + ELSE IF (compna(i) == 'peva') THEN + parame(i,1) = mm(i)*2.63E-2 + ! -- 0 Gew.% VA------------- + ! parame(i,2) = 4.021767 + ! parame(i,3) = 249.5 + ! -- 7.5 Gew.% VA------------- + ! parame(i,2) = 4.011 + ! parame(i,3) = 248.1864 + ! parame(i,3) = 247.6286 + ! ---12.7 Gew.% VA------------ + ! parame(i,2) = 4.0028 + ! parame(i,3) = 247.2075 + ! parame(i,3) = 246.24454 + ! ---27.3 Gew.% VA------------ + ! parame(i,2) = 3.9762 + ! parame(i,3) = 244.114 + ! parame(i,3) = 241.9345 + ! ---31.8 Gew.% VA------------ + parame(i,2) = 3.9666 + parame(i,3) = 243.0436 + ! parame(i,3) = 240.46 + ! ---42.7 Gew.% VA------------ + ! parame(i,2) = 3.9400 + ! parame(i,3) = 240.184 + ! parame(i,3) = 236.62 + ! --------------- + ELSE IF (compna(i) == 'pp') THEN + parame(i,1) = mm(i)*2.2E-2 + parame(i,2) = 4.2 + parame(i,3) = 220.0 + + parame(i,1) = mm(i)*0.0230487701 + parame(i,2) = 4.1 + parame(i,3) = 217.0 + ELSE IF (compna(i) == 'pe') THEN + parame(i,1) = mm(i)*2.622E-2 + parame(i,2) = 4.021767 + parame(i,3) = 252.0 + ! HDPE: extrapolated from pure comp. param. of n-alkane series! + ! parame(i,1) = mm(i)*2.4346E-2 + ! parame(i,2) = 4.07182 + ! parame(i,3) = 269.67 + !! parame(i,3) = 252.5 + ELSE IF (compna(i) == 'ldpe') THEN + parame(i,1) = mm(i)*2.63E-2 + parame(i,2) = 4.021767 + parame(i,3) = 249.5 + ELSE IF (compna(i) == 'pba') THEN + parame(i,1) = mm(i)*2.5872E-2 + parame(i,2) = 3.95 + parame(i,3) = 229.0 + ELSE IF (compna(i) == 'dextran') THEN + parame(i,1) = mm(i)*2.E-2 + parame(i,2) = 4.0 + parame(i,3) = 300.0 + ELSE IF (compna(i) == 'glycol-ethers') THEN + ! mm(i) = 218.0 + ! parame(i,1) = 7.4044 + ! parame(i,2) = 3.61576 + ! parame(i,3) = 244.0034598 + mm(i) = 222.0 + parame(i,1) = 7.994 + parame(i,2) = 3.445377778 + parame(i,3) = 234.916506 + ELSE IF (compna(i) == 'LJ') THEN + mm(i) = 1.0 + parame(i,1) = 1.0 + parame(i,2) = 1.0 + parame(i,3) = 1.0 + ELSE IF (compna(i) == 'LJ1205') THEN + mm(i) = 1.0 + parame(i,1) = 1.0 + parame(i,2) = 1.0 + parame(i,3) = 140.0 + ELSE IF (compna(i) == 'adamantane') THEN + mm(i) = 136.235000000000 + parame(i,1) = 4.81897145432221 + parame(i,2) = 3.47128575274660 + parame(i,3) = 266.936967922521 + ELSE IF (compna(i) == 'methane') THEN + mm(i) = 16.043 + parame(i,1) = 1.0 + parame(i,2) = 3.70388767 + parame(i,3) = 150.033987 + ! LLi(i) = 1.185*parame(i,2) + ! phi_criti(i)= 11.141 + ! chap(i) = 0.787 + lli(i) = 1.398*parame(i,2) + phi_criti(i)= 16.01197 + chap(i) = 0.6 + IF (pol == 2) parame(i,11)= 2.593 + ! --- adjusted to Tc, Pc und omega --- + ! mm(i) = 16.0430000000000 + ! parame(i,1) = 1.03353666429362 + ! parame(i,2) = 3.64824920605089 + ! parame(i,3) = 147.903953522994 + lli(i) = 2.254442763775*parame(i,2) + phi_criti(i)= 42.060975627454 + chap(i) = 0.704895924 + lli(i) = 1.935801125833*parame(i,2) + phi_criti(i)= 26.363325937261 + chap(i) = 0.700112854298 + lli(i) = 2.610103087662*parame(i,2) + phi_criti(i)= 38.192854403173 + chap(i) = 0.812100472735 + ! 2.122960316503 34.937141524804 0.734513223627 + ! 2.082897379591 33.036391564859 0.877578492999 + ELSE IF (compna(i) == 'ethane') THEN + mm(i) = 30.070 + parame(i,1) =mm(i)* .0534364758 + parame(i,2) = 3.5205923 + parame(i,3) = 191.423815 + lli(i) = 1.40*parame(i,2) + phi_criti(i)= 15.38 + chap(i) = 0.520 + IF (pol == 2) parame(i,11)= 4.3 + ! --- adjusted to Tc, Pc und omega --- + ! mm(i) = 30.069 + ! parame(i,1) = 1.74034548122 + ! parame(i,2) = 3.4697441893134 + ! parame(i,3) = 181.90770083591 + IF (pol >= 1) mm(i) = 30.0700000000000 + IF (pol >= 1) parame(i,1) = mm(i)* 5.341907666260094E-002 + IF (pol >= 1) parame(i,2) = 3.52104466654628 + IF (pol >= 1) parame(i,3) = 191.449300423694 + IF (pol >= 1) parame(i,7) = 0.650000000000000 + IF (pol >= 1) lli(i) = 0.0 + IF (pol >= 1) phi_criti(i)= 0.0 + IF (pol >= 1) chap(i) = 0.0 + ELSE IF (compna(i) == 'propane') THEN + mm(i) = 44.096 + parame(i,1) = mm(i)* .0453970622 + parame(i,2) = 3.61835302 + parame(i,3) = 208.110116 + lli(i) = 1.8*parame(i,2) + phi_criti(i)= 21.0 + chap(i) = 1.0 + lli(i) = 1.63*parame(i,2) + phi_criti(i)= 20.37 + chap(i) = 0.397 + IF (pol == 2) parame(i,11)= 6.29 + ELSE IF (compna(i) == 'butane_debug') THEN + mm(i) = 58.123 + parame(i,1) = 2.3374 + parame(i,2) = 3.6655 + parame(i,3) = 214.805 + ELSE IF (compna(i) == 'butane') THEN + mm(i) = 58.123 + parame(i,1) = mm(i)* .0401146927 + parame(i,2) = 3.70860139 + parame(i,3) = 222.877405 + lli(i) = 1.75*parame(i,2) + phi_criti(i)= 23.43 + chap(i) = 0.304 + ! LLi(i) = 1.942079633622*parame(i,2) + ! phi_criti(i)= 24.527323443155 + ! chap(i) = 0.734064026277 + ! LLi(i) = 1.515115760477*parame(i,2) + ! phi_criti(i)= 17.682929717796 + ! chap(i) = 0.335848717079 + IF (pol == 2) parame(i,11)= 8.2 + ! --- adjusted to Tc, Pc und omega --- + ! mm(i) = 58.1230000000 + ! parame(i,1) = 2.45352304112 + ! parame(i,2) = 3.74239117802 + ! parame(i,3) = 214.185157925 + ELSE IF (compna(i) == 'pentane') THEN + mm(i) = 72.146 + parame(i,1) = mm(i)* .03727896 + parame(i,2) = 3.77293174 + parame(i,3) = 231.197015 + IF (pol == 2) parame(i,11)= 9.99 + ELSE IF (compna(i) == 'hexane') THEN + mm(i) = 86.177 + parame(i,1) = mm(i)* .0354812325 + parame(i,2) = 3.79829291 + parame(i,3) = 236.769054 + lli(i) = 2.24*parame(i,2) + phi_criti(i)= 33.25 + chap(i) = 0.205 + IF (pol == 2) parame(i,11)= 11.9 + ELSE IF (compna(i) == 'heptane') THEN + mm(i) = 100.203 + parame(i,1) = mm(i)* .034762384 + parame(i,2) = 3.80487025 + parame(i,3) = 238.400913 + lli(i) = 2.35*parame(i,2) + phi_criti(i)= 38.10 + chap(i) = 0.173 + IF (pol == 2) parame(i,11)= 13.61 + ELSE IF (compna(i) == 'octane') THEN + mm(i) = 114.231 + parame(i,1) = mm(i)* .0334228038 + parame(i,2) = 3.83732677 + parame(i,3) = 242.775853 + ! LLi(i) = 2.0*parame(i,2) + ! phi_criti(i)= 18.75 + ! chap(i) = 1.0 + lli(i) = 2.63*parame(i,2) + phi_criti(i)= 42.06 + chap(i) = 0.155 + IF (pol == 2) parame(i,11)= 15.9 + ELSE IF (compna(i) == 'nonane') THEN + mm(i) = 128.25 + parame(i,1) = mm(i)* .0328062594 + parame(i,2) = 3.84483643 + parame(i,3) = 244.508457 + ELSE IF (compna(i) == 'decane') THEN + mm(i) = 142.285 + parame(i,1) = mm(i)* .03277373 + parame(i,2) = 3.8384498 + parame(i,3) = 243.866074 + lli(i) = 1.845*parame(i,2) + phi_criti(i)= 21.27 + chap(i) = 1.0 + lli(i) = 2.68*parame(i,2) + phi_criti(i)= 45.0 + chap(i) = 0.15 + IF (pol == 2) parame(i,11)= 19.1 + ! --- adjusted to Tc, Pc und omega --- + ! parame(i,1) = 4.794137228322 + ! parame(i,2) = 4.030446690586 + ! parame(i,3) = 236.5884493386 + ELSE IF (compna(i) == 'dodecane') THEN + mm(i) = 170.338 + parame(i,1) = mm(i)* .0311484156 + parame(i,2) = 3.89589236 + parame(i,3) = 249.214532 + ELSE IF (compna(i) == 'hexadecane') THEN + mm(i) = 226.446 + parame(i,1) = mm(i)* .0293593045 + parame(i,2) = 3.95516743 + parame(i,3) = 254.700131 + ELSE IF (compna(i) == 'octadecane') THEN + mm(i) = 254.5 + parame(i,1) = 7.3271 + parame(i,2) = 3.9668 + parame(i,3) = 256.20 + IF (pol == 2) parame(i,11)= 30.2 + ! --- adjusted to Tc, Pc und omega --- + ! mm(i) = 226.446000000000 + ! parame(i,1) = 6.66976520488694 + ! parame(i,2) = 4.25025597912511 + ! parame(i,3) = 249.582941976119 + ELSE IF (compna(i) == 'eicosane') THEN + mm(i) = 282.553 + parame(i,1) = mm(i)* .0282572812 + parame(i,2) = 3.98692612 + parame(i,3) = 257.747939 + ELSE IF (compna(i) == 'triacontane') THEN + ! mm(i) = 422.822 ! polyethylene parameters + ! parame(i,1) = mm(i)*2.622E-2 + ! parame(i,2) = 4.021767 + ! parame(i,3) = 252.0 + mm(i) = 422.822 ! param. by extrapolation of n-alkanes + parame(i,1) = mm(i)* 0.026922527 + parame(i,2) = 4.007608009 + parame(i,3) = 262.28622 + ELSE IF (compna(i) == 'octaeicosane') THEN + mm(i) = 395.0 ! param. by extrapolation of n-alkanes (sloppy!!) + parame(i,1) = mm(i)* 0.026922527 + parame(i,2) = 4.007608009 + parame(i,3) = 262.28622 + ELSE IF (compna(i) == 'tetracontane') THEN + ! mm(i) = 563.1 ! polyethylene parameters + ! parame(i,1) = mm(i)*2.622E-2 + ! parame(i,2) = 4.021767 + ! parame(i,3) = 252.0 + mm(i) = 563.1 ! param. by extrapolation of n-alkanes + parame(i,1) = mm(i)*0.026287593 + parame(i,2) = 4.023277 + parame(i,3) = 264.10466 + ELSE IF (compna(i) == 'isobutane') THEN + mm(i) = 58.123 + parame(i,1) = mm(i)* .0389105395 + parame(i,2) = 3.75735249 + parame(i,3) = 216.528584 + ELSE IF (compna(i) == 'isopentane') THEN + mm(i) = 72.15 + parame(i,1) = 2.5620 + parame(i,2) = 3.8296 + parame(i,3) = 230.75 + ELSE IF (compna(i) == '2-methylpentane') THEN + mm(i) = 86.177 + parame(i,1) = mm(i)* .0340166994 + parame(i,2) = 3.85354665 + parame(i,3) = 235.5801 + ELSE IF (compna(i) == '23-dimethylbutane') THEN + mm(i) = 86.177 + parame(i,1) = mm(i)* .0311599207 + parame(i,2) = 3.9544545 + parame(i,3) = 246.068188 + ELSE IF (compna(i) == 'ethylene') THEN + mm(i) = 28.05 + parame(i,1) = mm(i)* .0567939013 + parame(i,2) = 3.44499904 + parame(i,3) = 176.468725 + IF (pol == 2) parame(i,11)= 4.252 +! eigener 3-ter Anlauf. + IF (pol >= 1) parame(i,1) = mm(i)* 5.574644443117726E-002 + IF (pol >= 1) parame(i,2) = 3.43281482228714 + IF (pol >= 1) parame(i,3) = 178.627308564610 + IF (pol >= 1) parame(i,7) = 1.56885870200446 + IF (pol == 2) parame(i,11)= 4.252 + ELSE IF (compna(i) == 'propylene') THEN + mm(i) = 42.081 + parame(i,1) = mm(i)* .0465710324 + parame(i,2) = 3.53559831 + parame(i,3) = 207.189309 + ! --- adjusted to Tc, Pc und omega --- + ! mm(i) = 42.081 + ! parame(i,1) = 2.086735327675 + ! parame(i,2) = 3.536779407969 + ! parame(i,3) = 198.3529810625 + ELSE IF (compna(i) == '1-butene') THEN + mm(i) = 56.107 + parame(i,1) = mm(i)* .0407524782 + parame(i,2) = 3.64305136 + parame(i,3) = 222.002756 + IF (pol == 2) parame(i,11)= 7.97 + ELSE IF (compna(i) == '1-pentene') THEN + mm(i) = 70.134 + parame(i,1) = 2.6006 + parame(i,2) = 3.7399 + parame(i,3) = 231.99 + ELSE IF (compna(i) == '1-hexene') THEN + mm(i) = 84.616 + parame(i,1) = mm(i)* .0352836857 + parame(i,2) = 3.77529612 + parame(i,3) = 236.810973 + ELSE IF (compna(i) == '1-octene') THEN + mm(i) = 112.215 + parame(i,1) = mm(i)* .033345175 + parame(i,2) = 3.81329011 + parame(i,3) = 243.017587 + ELSE IF (compna(i) == 'cyclopentane') THEN + mm(i) = 70.13 + parame(i,1) = mm(i)* .0337262571 + parame(i,2) = 3.71139254 + parame(i,3) = 265.828755 + ELSE IF (compna(i) == 'cyclohexane') THEN + mm(i) = 84.147 + parame(i,1) = mm(i)* .0300695505 + parame(i,2) = 3.84990887 + parame(i,3) = 278.108786 + IF (pol == 2) parame(i,11)= 10.87 + ELSE IF (compna(i) == 'toluene') THEN + mm(i) = 92.141 + parame(i,1) = mm(i)* .0305499338 + parame(i,2) = 3.71689689 + parame(i,3) = 285.68996 + IF (pol == 2) parame(i,11)= 11.8 + ! --- adjusted to Tc, Pc und omega --- + ! mm(i) = 92.141 + ! parame(i,1) = 3.002119827762 + ! parame(i,2) = 3.803702734224 + ! parame(i,3) = 271.9428642880 + ELSE IF (compna(i) == 'm-xylene') THEN + mm(i) = 106.167 + parame(i,1) = mm(i)* .030011086 + parame(i,2) = 3.75625585 + parame(i,3) = 283.977525 + ELSE IF (compna(i) == 'o-xylene') THEN + mm(i) = 106.167 + parame(i,1) = mm(i)* .0295409161 + parame(i,2) = 3.76000631 + parame(i,3) = 291.049123 + ELSE IF (compna(i) == 'thf') THEN + mm(i) = 72.1057000000000 + ! parame(i,1) = mm(i)* 0.34311391E-01 + parame(i,1) = 2.47404685540709 + parame(i,2) = 3.51369375633677 + parame(i,3) = 274.181927093696 + parame(i,6) = 1.63100000000000 + ELSE IF (compna(i) == 'co2') THEN + mm(i) = 44.01 + parame(i,1) = mm(i)* .0470968503 + parame(i,2) = 2.7851954 + parame(i,3) = 169.207418 + IF (pol >= 1) parame(i,1) = mm(i)* 3.438191426159075E-002 + IF (pol >= 1) parame(i,2) = 3.18693935424469 + IF (pol >= 1) parame(i,3) = 163.333232725156 + IF (pol >= 1) parame(i,7) = 4.400000000000 + IF (pol >= 1) lli(i) = 1.472215*parame(i,2) + IF (pol >= 1) phi_criti(i)= 17.706567 + IF (pol >= 1) chap(i) = 0.5 + IF (pol == 2) parame(i,11)= 2.911 + ELSE IF (compna(i) == 'co') THEN + IF (pol /= 1) write (*,*) 'parameters for co missing' + IF (pol /= 1) stop + IF (pol >= 1) mm(i) = 28.01 + IF (pol >= 1) parame(i,1) = mm(i)* 5.126059746332587E-002 ! 1.43580933494776 + IF (pol >= 1) parame(i,2) = 3.13556624711756 + IF (pol >= 1) parame(i,3) = 87.7191028693595 + IF (pol >= 1) parame(i,6) = 0.1098 + ELSE IF (compna(i) == 'n2') THEN + mm(i) = 28.01 + parame(i,1) = mm(i)* .0430301713 + parame(i,2) = 3.3129702 + parame(i,3) = 90.9606924 + IF (pol >= 1) parame(i,1) = mm(i)* 3.971157114787596E-002 + IF (pol >= 1) parame(i,2) = 3.42116853868336 + IF (pol >= 1) parame(i,3) = 92.3972606842862 + IF (pol >= 1) parame(i,7) = 1.52000000000000 + IF (pol >= 1) lli(i) = 1.5188*parame(i,2) + IF (pol >= 1) phi_criti(i)= 19.9247 + IF (pol >= 1) chap(i) = 0.375 + ! better RGT-results came later, with: 1.5822 21.201 0.3972 + ELSE IF (compna(i) == 'o2') THEN + mm(i) = 32.05 + parame(i,1) = mm(i)* .0353671563 + parame(i,2) = 3.19465166 + parame(i,3) = 114.430197 + ELSE IF (compna(i) == 'hydrogen') THEN + mm(i) = 2.016 + parame(i,1) = mm(i)* .258951975 + parame(i,2) = 4.43304935 + parame(i,3) = 29.6509579 + + mm(i) = 2.016 + parame(i,1) = 1.0 + parame(i,2) = 2.915 + parame(i,3) = 38.0 + + ! mm(i) = 2.016 ! Ghosh et al. 2003 + ! parame(i,1) = 1.0 + ! parame(i,2) = 2.986 + ! parame(i,3) = 19.2775 + ELSE IF (compna(i) == 'argon') THEN + ! mm(i) = 39.948 ! adjusted m !! + ! parame(i,1) = 0.9285 + ! parame(i,2) = 3.4784 + ! parame(i,3) = 122.23 + mm(i) = 39.948 ! enforced m=1 !! + parame(i,1) = 1.0 + parame(i,2) = 3.3658 + parame(i,3) = 118.34 + IF (pol == 2) parame(i,11)= 1.6411 + ELSE IF (compna(i) == 'xenon') THEN + mm(i) = 131.29 + parame(i,1) = 1.0 + parame(i,2) = 3.93143 + parame(i,3) = 227.749 + ELSE IF (compna(i) == 'chlorine') THEN ! Cl2 + mm(i) = 70.906 + parame(i,1) = 1.5514 + parame(i,2) = 3.3672 + parame(i,3) = 265.67 + ELSE IF (compna(i) == 'SF6') THEN + mm(i) = 146.056 ! adjusted m !! + parame(i,1) = 2.48191 + parame(i,2) = 3.32727 + parame(i,3) = 161.639 + ! mm(i) = 146.056 ! enforced m=1 !! + ! parame(i,1) = 1.0 + ! parame(i,2) = 4.55222 + ! parame(i,3) = 263.1356 + ELSE IF (compna(i) == 'benzene') THEN + mm(i) = 78.114 + parame(i,1) = mm(i)* .0315590546 + parame(i,2) = 3.64778975 + parame(i,3) = 287.354574 + IF (pol >= 1) mm(i) = 78.114 ! PCP-SAFT with m=2 in QQ term + IF (pol >= 1) parame(i,1) = mm(i)* 2.932783311E-2 ! = 2.29091435590515 + IF (pol >= 1) parame(i,2) = 3.7563854 + IF (pol >= 1) parame(i,3) = 294.06253 + IF (pol >= 1) parame(i,7) = 5.5907 + ELSE IF (compna(i) == 'ethylbenzene') THEN + mm(i) = 106.167 + parame(i,1) = mm(i)* .0290120497 + parame(i,2) = 3.79741116 + parame(i,3) = 287.348098 + IF (pol == 2) parame(i,11)= 13.3 + ELSE IF (compna(i) == 'propylbenzene') THEN + mm(i) = 120.194 + parame(i,1) = mm(i)* .0278171627 + parame(i,2) = 3.8437772 + parame(i,3) = 288.128269 + ELSE IF (compna(i) == 'n-butylbenzene') THEN + mm(i) = 134.221 + parame(i,1) = mm(i)* .0280642225 + parame(i,2) = 3.87267961 + parame(i,3) = 283.072331 + ELSE IF (compna(i) == 'tetralin') THEN + mm(i) = 132.205 + parame(i,1) = mm(i)* .0250640795 + parame(i,2) = 3.87498866 + parame(i,3) = 325.065688 + ELSE IF (compna(i) == 'methylcyclohexane') THEN + mm(i) = 98.182 + parame(i,1) = mm(i)* .0271259953 + parame(i,2) = 3.99931892 + parame(i,3) = 282.334148 + IF (pol == 2) parame(i,11)= 13.1 + ELSE IF (compna(i) == 'methylcyclopentane') THEN + mm(i) = 84.156 + parame(i,1) = mm(i)* .0310459009 + parame(i,2) = 3.82534693 + parame(i,3) = 265.122799 + ELSE IF (compna(i) == 'acetone') THEN + mm(i) = 58.0800000000000 ! PC-SAFT + parame(i,1) = mm(i)* 4.870380408159182E-002 ! =2.82871694105885 + parame(i,2) = 3.24969003020675 + parame(i,3) = 250.262241927379 + lli(i) = 2.0021*parame(i,2) + phi_criti(i)= 21.336 + chap(i) = 0.24931 + IF (pol >= 1) mm(i) = 58.0800000000000 ! PCP-SAFT + IF (pol >= 1) parame(i,1) = mm(i)* 4.725811736856114E-002 ! =2.74475145676603 + IF (pol >= 1) parame(i,2) = 3.27423145271184 + IF (pol >= 1) parame(i,3) = 232.990879135326 + IF (pol >= 1) parame(i,6) = 2.88000000000000 + IF (pol >= 1) lli(i) = 2.0641*parame(i,2) + IF (pol >= 1) phi_criti(i)= 28.1783 + IF (pol >= 1) chap(i) = 0.22695 + IF (pol >= 2) mm(i) = 58.0800000000000 ! PCIP-SAFT + IF (pol >= 2) parame(i,1) = mm(i)* 4.902301475689938E-002 ! =2.84725669708072 + IF (pol >= 2) parame(i,2) = 3.23880349104868 + IF (pol >= 2) parame(i,3) = 220.884202656054 + IF (pol >= 2) parame(i,6) = 2.88000000000000 + IF (pol == 2) parame(i,11)= 6.40000000000000 + ELSE IF (compna(i) == 'butanone') THEN + mm(i) = 72.1066 ! PC-SAFT + parame(i,1) = mm(i)* 4.264192830122321E-002 ! =3.07476446724498 + parame(i,2) = 3.39324011060028 + parame(i,3) = 252.267273608975 + IF (pol >= 1) mm(i) = 72.1066 ! PCP-SAFT + IF (pol >= 1) parame(i,1) = mm(i)* 4.137668924230600E-002 ! =2.98353238051926 + IF (pol >= 1) parame(i,2) = 3.42393701353423 + IF (pol >= 1) parame(i,3) = 244.994381354681 + IF (pol >= 1) parame(i,6) = 2.78000000000000 + IF (pol >= 2) mm(i) = 72.1066 ! PCIP-SAFT + IF (pol >= 2) parame(i,1) = mm(i)* 4.254697075199448E-002 ! =3.06791740122577 + IF (pol >= 2) parame(i,2) = 3.39138375903252 + IF (pol >= 2) parame(i,3) = 236.527763837528 + IF (pol >= 2) parame(i,6) = 2.78000000000000 + IF (pol == 2) parame(i,11)= 8.13000000000000 + ELSE IF (compna(i) == '2-pentanone') THEN + ! mm(i) = 86.134 ! PC-SAFT + ! parame(i,1) = mm(i)* 3.982654501296355E-002 ! =3.43041962814660 + ! parame(i,2) = 3.46877976946838 + ! parame(i,3) = 249.834724442656 + ! mm(i) = 86.134 ! PCP-SAFT + ! parame(i,1) = mm(i)* 3.893594769994072E-002 ! =3.35370891918669 + ! parame(i,2) = 3.49417356096593 + ! parame(i,3) = 246.656329096835 + ! parame(i,6) = 2.70000000000000 + mm(i) = 86.134 ! PCIP-SAFT + parame(i,1) = mm(i)* 3.973160761515879E-002 ! =3.42224229032409 + parame(i,2) = 3.46827593107280 + parame(i,3) = 240.904278156822 + parame(i,6) = 2.70000000000000 + IF (pol == 2) parame(i,11)= 9.93000000000000 + ELSE IF (compna(i) == '3-pentanone') THEN + mm(i) = 86.134 ! PC-SAFT + parame(i,1) = 3.36439508013322 + parame(i,2) = 3.48770251979329 + parame(i,3) = 252.695415552376 + IF (pol >= 1) mm(i) = 86.134 ! PCP-SAFT + IF (pol >= 1) parame(i,1) = 3.27863398611842 + IF (pol >= 1) parame(i,2) = 3.51592571835030 + IF (pol >= 1) parame(i,3) = 248.690775540981 + IF (pol >= 1) parame(i,6) = 2.82000000000000 + IF (pol == 2) mm(i) = 86.134 ! PCIP-SAFT + IF (pol == 2) parame(i,1) = 3.34821857026283 + IF (pol == 2) parame(i,2) = 3.48903345340516 + IF (pol == 2) parame(i,3) = 242.314578558329 + IF (pol == 2) parame(i,6) = 2.82000000000000 + IF (pol == 2) parame(i,11)= 9.93000000000000 + ELSE IF (compna(i) == 'cyclohexanone') THEN ! from DIPPR + ! IF (pol.GE.1) mm(i) = 98.1430 ! PCP-SAFT + ! IF (pol.GE.1) parame(i,1) = 3.084202 + ! IF (pol.GE.1) parame(i,2) = 3.613681 + ! IF (pol.GE.1) parame(i,3) = 286.15865 + ! IF (pol.GE.1) parame(i,6) = 3.087862 + IF (pol >= 1) mm(i) = 98.1500000000000 + IF (pol >= 1) parame(i,1) = 2.72291913132818 + IF (pol >= 1) parame(i,2) = 3.79018433908522 + IF (pol >= 1) parame(i,3) = 314.772193827344 + IF (pol >= 1) parame(i,6) = 3.24600000000000 + IF (pol /= 1) WRITE (*,*) 'no non-polar param. for cyclohexanone' + IF (pol /= 1) STOP + ELSE IF (compna(i) == 'propanal') THEN + mm(i) = 58.08 ! PC-SAFT + parame(i,1) = 2.67564746980910 + parame(i,2) = 3.26295953984941 + parame(i,3) = 251.888982765626 + IF (pol >= 1) mm(i) = 58.08 ! PCP-SAFT + IF (pol >= 1) parame(i,1) = 2.60007872084995 + IF (pol >= 1) parame(i,2) = 3.28720732189761 + IF (pol >= 1) parame(i,3) = 235.205188090107 + IF (pol >= 1) parame(i,6) = 2.72000000000000 + IF (pol >= 2) mm(i) = 58.08 ! PCIP-SAFT + IF (pol >= 2) parame(i,1) = 2.72471167411028 + IF (pol >= 2) parame(i,2) = 3.24781643022922 + IF (pol >= 2) parame(i,3) = 221.642071811094 + IF (pol >= 2) parame(i,6) = 2.72000000000000 + IF (pol >= 2) parame(i,11)= 6.50000000000000 + ELSE IF (compna(i) == 'butanal') THEN + mm(i) = 72.1066000000000 ! PC-SAFT + parame(i,1) = 2.96824823599784 + parame(i,2) = 3.44068916025889 + parame(i,3) = 253.929404992884 + IF (pol >= 1) mm(i) = 72.1066000000000 ! PCP-SAFT + IF (pol >= 1) parame(i,1) = 2.86783706423953 + IF (pol >= 1) parame(i,2) = 3.47737904036296 + IF (pol >= 1) parame(i,3) = 247.543312127310 + IF (pol >= 1) parame(i,6) = 2.72000000000000 + ELSE IF (compna(i) == 'dmso') THEN + mm(i) = 78.1300000000000 ! PC-SAFT + parame(i,1) = 2.92225114054231 + parame(i,2) = 3.27780791606297 + parame(i,3) = 355.688793038512 + IF (pol >= 1) mm(i) = 78.1300000000000 ! PCP-SAFT + IF (pol >= 1) parame(i,1) = 3.02433694138348 + IF (pol >= 1) parame(i,2) = 3.24270742566613 + IF (pol >= 1) parame(i,3) = 309.357476696679 + IF (pol >= 1) parame(i,6) = 3.96000000000000 + IF (pol >= 2) mm(i) = 78.1300000000000 ! PCIP-SAFT + IF (pol >= 2) parame(i,1) = 3.19078234633277 + IF (pol >= 2) parame(i,2) = 3.19778269816832 + IF (pol >= 2) parame(i,3) = 286.337981216861 + IF (pol >= 2) parame(i,6) = 3.96000000000000 + IF (pol >= 2) parame(i,11)= 7.97000000000000 + ELSE IF (compna(i) == 'acetone_JC') THEN ! Jog-Chapman + ! mm(i) = 58.0800000000000 ! Dominik et al.2005 + ! parame(i,1) = 2.221 + ! parame(i,2) = 3.607908 + ! parame(i,3) = 259.99 + ! parame(i,6) = 2.7 + ! parame(i,8) = 0.2258 + ! mm(i) = 58.0800000000000 + ! parame(i,1) = mm(i)* 3.556617369195472E-002 + ! parame(i,2) = 3.58780367502515 + ! parame(i,3) = 273.025100470307 + ! parame(i,6) = 2.70000000000000 + ! parame(i,8) = 0.229800000000000 + + mm(i) = 58.08 ! Tumakaka Sadowski 2004 + parame(i,1) = mm(i)* 3.766E-2 + parame(i,2) = 3.6028 + parame(i,3) = 245.49 + parame(i,6) = 2.72 + parame(i,8) = 0.2969 + ! mm(i) = 58.0800000000000 ! no adjust. DD-param. + ! parame(i,1) = 1.87041620247774 + ! parame(i,2) = 3.79783535570774 + ! parame(i,3) = 208.885730881588 + ! parame(i,6) = 2.88000000000000 + ! parame(i,8) = 1.0/parame(i,1) + WRITE (*,*) 'caution: parame(i,8) is now used for branching' + STOP + kij(1,2) = -0.005 + kij(2,1)=kij(1,2) + ELSE IF (compna(i) == 'acetone_SF') THEN ! Saager-Fischer + mm(i) = 58.08 + parame(i,1) = mm(i)* 4.603296414764944E-002 + parame(i,2) = 3.29454924451643 + parame(i,3) = 221.052649057645 + parame(i,6) = 2.70000000000000 + parame(i,8) = 0.625410000000000 + mm(i) = 58.08 ! form as expected from me - no DD-param adjusted.dat + parame(i,1) = mm(i)* 4.364264724158790E-002 ! =2.53476495179143 + parame(i,2) = 3.37098670735567 + parame(i,3) = 254.366379701851 + parame(i,6) = 2.88000000000000 + ! mm(i) = 58.08 ! form as expected but w/ sumseg/1.5 - no DD-param adjusted.dat + ! parame(i,1) = mm(i)* 4.694644361257521E-002 ! =2.72664944501837 + ! parame(i,2) = 3.27842292595463 + ! parame(i,3) = 238.398883501772 + ! parame(i,6) = 2.88000000000000 + ! mm(i) = 58.08 ! form as expected but w/ sumseg/1.5 and fdd*sumseg- no DD-param adjusted.dat + ! parame(i,1) = mm(i)* 4.458214655521766E-002 ! =2.58933107192704 + ! parame(i,2) = 3.32050824493493 + ! parame(i,3) = 218.285994651271 + ! parame(i,6) = 2.88000000000000 + WRITE (*,*) 'caution: parame(i,8) is now used for branching' + STOP + kij(1,2) = 0.035 + kij(2,1)=kij(1,2) + ELSE IF (compna(i) == 'ethylacetate_JC') THEN ! Jog-Chapman + ! mm(i) = 88.11 + ! parame(i,1) = 2.7481 + ! parame(i,2) = 3.6511 + ! parame(i,3) = 236.99 + ! parame(i,6) = 1.84 + ! parame(i,8) = 0.5458 + mm(i) = 88.1060000000000 + parame(i,1) = mm(i)* 0.03117 ! 2.74626402 + parame(i,2) = 3.6493 + parame(i,3) = 236.75 + parame(i,6) = 1.8 + parame(i,8) = 0.5462 + ELSE IF (compna(i) == 'ethylacetate_SF') THEN ! Saager-Fischer + mm(i) = 88.106 + parame(i,1) = mm(i)* 3.564165384763394E-002 + parame(i,2) = 3.447379322 + parame(i,3) = 226.0930487 + parame(i,6) = 1.8 + parame(i,8) = 0.849967000000000 + WRITE (*,*) 'caution: parame(i,8) is now used for branching' + STOP + ELSE IF (compna(i) == '12po_JC') THEN ! Jog-Chapman + mm(i) = 58.08 + parame(i,1) = 2.0105 + parame(i,2) = 3.6095 + parame(i,3) = 258.82 + parame(i,6) = 2.0 + parame(i,8) = 0.3979 + WRITE (*,*) 'caution: parame(i,8) is now used for branching' + STOP + ELSE IF (compna(i) == '12po_SF') THEN ! Saager-Fischer + mm(i) = 58.08 + parame(i,1) = 2.1341 + parame(i,2) = 3.4739 + parame(i,3) = 252.95 + parame(i,6) = 2.0 + parame(i,8) = 0.916 + WRITE (*,*) 'caution: parame(i,8) is now used for branching' + STOP + ELSE IF (compna(i) == 'acrylonitrile') THEN + IF (pol >= 2) mm(i) = 53.06 ! PCIP-SAFT + IF (pol >= 2) parame(i,1) = 2.168 + IF (pol >= 2) parame(i,2) = 3.575 + IF (pol >= 2) parame(i,3) = 214.83 + IF (pol >= 2) parame(i,6) = 3.91 + IF (pol == 2) parame(i,11)= 8.04 + IF (pol >= 2) mm(i) = 53.0000000000000 ! second parameter set ?? + IF (pol >= 2) parame(i,1) = 2.45403467006041 + IF (pol >= 2) parame(i,2) = 3.41276825781723 + IF (pol >= 2) parame(i,3) = 195.194353082408 + IF (pol >= 2) parame(i,6) = 3.91000000000000 + IF (pol == 2) parame(i,11)= 8.04000000000000 + ELSE IF (compna(i) == 'butyronitrile') THEN + ! mm(i) = 69.11 + ! parame(i,1) = 2.860 + ! parame(i,2) = 3.478 + ! parame(i,3) = 253.21 + ! parame(i,6) = 4.07 + mm(i) = 69.11 + parame(i,1) = 2.989 + parame(i,2) = 3.441 + parame(i,3) = 234.04 + parame(i,6) = 4.07 + IF (pol == 2) parame(i,11)= 8.4 + ELSE IF (compna(i) == 'propionitrile') THEN + mm(i) = 55.079 ! PC-SAFT + parame(i,1) = 2.66211021227108 + parame(i,2) = 3.34032231132738 + parame(i,3) = 294.078737359580 + IF (pol >= 1) mm(i) = 55.079 ! PCP-SAFT + IF (pol >= 1) parame(i,1) = 2.50958981615666 + IF (pol >= 1) parame(i,2) = 3.39806320429568 + IF (pol >= 1) parame(i,3) = 239.152759066148 + IF (pol >= 1) parame(i,6) = 4.05000000000000 + IF (pol >= 2) mm(i) = 55.079 ! PCIP-SAFT + IF (pol >= 2) parame(i,1) = 2.54684827683436 + IF (pol >= 2) parame(i,2) = 3.41240089912190 + IF (pol >= 2) parame(i,3) = 218.299491580335 + IF (pol >= 2) parame(i,6) = 4.05000000000000 + IF (pol == 2) parame(i,11)= 6.24000000000000 + ! IF (pol.GE.2) mm(i) = 55.079 ! PCIP-SAFT my_DD adjusted + ! IF (pol.GE.2) parame(i,1) = 2.61175151088002 + ! IF (pol.GE.2) parame(i,2) = 3.37194293181453 + ! IF (pol.GE.2) parame(i,3) = 233.346110749402 + ! IF (pol.GE.2) parame(i,6) = 3.74682245835235 + ! IF (pol.EQ.2) parame(i,11)= 6.24000000000000 + ELSE IF (compna(i) == 'nitromethane') THEN + mm(i) = 61.04 ! PC-SAFT + parame(i,1) = mm(i)* 4.233767489308791E-002 ! =2.58429167547409 + parame(i,2) = 3.10839592337018 + parame(i,3) = 310.694151426943 + IF (pol >= 1) mm(i) = 61.04 ! PCP-SAFT + IF (pol >= 1) parame(i,1) = mm(i)* 4.191475020685036E-002 ! =2.55847635262615 + IF (pol >= 1) parame(i,2) = 3.10129282495975 + IF (pol >= 1) parame(i,3) = 256.456941430554 + IF (pol >= 1) parame(i,6) = 3.46000000000000 + IF (pol >= 2) mm(i) = 61.04 ! PCIP-SAFT + IF (pol >= 2) parame(i,1) = mm(i)* 4.394323357988009E-002 ! =2.68229497771588 + IF (pol >= 2) parame(i,2) = 3.10654492320028 + IF (pol >= 2) parame(i,3) = 225.973607468282 + IF (pol >= 2) parame(i,6) = 3.46000000000000 + IF (pol >= 2) parame(i,11)= 7.37000000000000 + ELSE IF (compna(i) == 'nitroethane') THEN + mm(i) = 75.067 ! PC-SAFT + parame(i,1) = mm(i)* 4.019977215251163E-002 ! =3.01767629617259 + parame(i,2) = 3.21364231060938 + parame(i,3) = 286.571650044235 + IF (pol >= 1) mm(i) = 75.067 ! PCP-SAFT + IF (pol >= 1) parame(i,1) = mm(i)* 3.928506808347654E-002 ! =2.94901220582233 + IF (pol >= 1) parame(i,2) = 3.23117331990738 + IF (pol >= 1) parame(i,3) = 265.961000131109 + IF (pol >= 1) parame(i,6) = 3.23000000000000 + IF (pol >= 2) mm(i) = 75.067 ! PCIP-SAFT + IF (pol >= 2) parame(i,1) = mm(i)* 4.117677400894779E-002 ! =3.09101689452968 + IF (pol >= 2) parame(i,2) = 3.19364569858756 + IF (pol >= 2) parame(i,3) = 246.676040248662 + IF (pol >= 2) parame(i,6) = 3.23000000000000 + IF (pol >= 2) parame(i,11)= 9.63000000000000 + ELSE IF (compna(i) == 'acetonitrile') THEN + mm(i) = 41.052 ! PC-SAFT + parame(i,1) = mm(i)* 5.673187410405271E-002 ! =2.32895689571957 + parame(i,2) = 3.18980108373791 + parame(i,3) = 311.307486044181 + IF (pol >= 1) mm(i) = 41.052 ! PCP-SAFT + IF (pol >= 1) parame(i,1) = mm(i)* 5.254832931037250E-002 ! =2.15721401484941 + IF (pol >= 1) parame(i,2) = 3.27301469369132 + IF (pol >= 1) parame(i,3) = 216.888948676921 + IF (pol >= 1) parame(i,6) = 3.92520000000000 + IF (pol >= 2) mm(i) = 41.052 ! PCIP-SAFT + IF (pol >= 2) parame(i,1) = mm(i)* 5.125846581157176E-002 ! =2.10426253849664 + IF (pol >= 2) parame(i,2) = 3.39403305120647 + IF (pol >= 2) parame(i,3) = 199.070191065791 + IF (pol >= 2) parame(i,6) = 3.92520000000000 + IF (pol >= 2) parame(i,11)= 4.40000000000000 + ! IF (pol >= 2) mm(i) = 41.052 ! PCIP-SAFT my_DD adjusted + ! IF (pol >= 2) parame(i,1) = mm(i)* 5.755347845863738E-002 ! =2.36268539768398 + ! IF (pol >= 2) parame(i,2) = 3.18554306395900 + ! IF (pol >= 2) parame(i,3) = 225.143934506015 + ! IF (pol >= 2) parame(i,6) = 3.43151866932598 + ! IF (pol >= 2) parame(i,11)= 4.40000000000000 + ! mm(i) = 41.053 ! PCP-SAFT dipole and quadrupole + ! parame(i,1) = 1.79993 + ! parame(i,2) = 3.47366 + ! parame(i,3) = 211.001 + ! parame(i,6) = 3.93800 + ! parame(i,7) = 2.44000 + ! parame(i,11)= 0.0 + ELSE IF (compna(i) == 'dmf') THEN + mm(i) = 73.09 ! PC-SAFT + parame(i,1) = 2.388 + parame(i,2) = 3.658 + parame(i,3) = 363.77 + IF (pol >= 1) mm(i) = 73.09 ! PCP-SAFT + IF (pol >= 1) parame(i,1) = 2.269 + IF (pol >= 1) parame(i,2) = 3.714 + IF (pol >= 1) parame(i,3) = 331.56 + IF (pol >= 1) parame(i,6) = 3.82 + IF (pol >= 2) mm(i) = 73.09 ! PCIP-SAFT + IF (pol >= 2) parame(i,1) = 2.375 + IF (pol >= 2) parame(i,2) = 3.667 + IF (pol >= 2) parame(i,3) = 308.42 + IF (pol >= 2) parame(i,6) = 3.82 + IF (pol >= 2) parame(i,11)= 7.81 + ELSE IF (compna(i) == 'chloroform') THEN + mm(i) = 119.377 ! PCIP-SAFT + parame(i,1) = 2.5957 + parame(i,2) = 3.4299 + parame(i,3) = 264.664 + parame(i,6) = 1.04 + IF (pol == 2) parame(i,11)= 8.23 + ELSE IF (compna(i) == 'dimethyl-ether') THEN + mm(i) = 46.069 ! PC-SAFT + parame(i,1) = mm(i)* 0.049107715 ! =2.26234331 + parame(i,2) = 3.276640534 + parame(i,3) = 212.9343244 + IF (pol >= 1) mm(i) = 46.0690000000000 ! PCP-SAFT + IF (pol >= 1) parame(i,1) = mm(i)* 0.048170452 ! =2.219164566 + IF (pol >= 1) parame(i,2) = 3.296939638 + IF (pol >= 1) parame(i,3) = 212.1048888 + IF (pol >= 1) parame(i,6) = 1.30000000000000 + IF (pol >= 2) mm(i) = 46.0690000000000 ! PCIP-SAFT + IF (pol >= 2) parame(i,1) = mm(i)* 4.939183716945787E-002 ! =2.27543254655976 + IF (pol >= 2) parame(i,2) = 3.26584718800835 + IF (pol >= 2) parame(i,3) = 206.904551967059 + IF (pol >= 2) parame(i,6) = 1.30000000000000 + IF (pol == 2) parame(i,11)= 5.29000000000000 + ELSE IF (compna(i) == 'methyl-ethyl-ether') THEN + mm(i) = 60.096 + parame(i,1) = mm(i)* .0442404671 + parame(i,2) = 3.37282595 + parame(i,3) = 216.010217 + IF (pol >= 1) mm(i) = 60.096 ! PCP-SAFT + IF (pol >= 1) parame(i,1) = mm(i)* 4.3971676124088D-002 ! =2.64252184835325 + IF (pol >= 1) parame(i,2) = 3.37938465390 + IF (pol >= 1) parame(i,3) = 215.787173860 + IF (pol >= 1) parame(i,6) = 1.17000000000 + IF (pol >= 2) mm(i) = 60.096 ! PICP-SAFT + IF (pol >= 2) parame(i,1) = mm(i)* 4.4580196137984D-002 ! =2.67909146710834 + IF (pol >= 2) parame(i,2) = 3.36105342286 + IF (pol >= 2) parame(i,3) = 212.871911999 + IF (pol >= 2) parame(i,6) = 1.17000000000 + IF (pol >= 2) parame(i,11) = 7.93000000000 + ELSE IF (compna(i) == 'diethyl-ether') THEN + mm(i) = 74.123 ! PC-SAFT + parame(i,1) = mm(i)* .0409704089 + parame(i,2) = 3.48569553 + parame(i,3) = 217.64113 + IF (pol >= 1) mm(i) = 74.123 ! PCP-SAFT + IF (pol >= 1) parame(i,1) = mm(i)* 4.0103121403686E-2 ! =2.97256367 + IF (pol >= 1) parame(i,2) = 3.51268687697978 + IF (pol >= 1) parame(i,3) = 219.527376572135 + IF (pol >= 1) parame(i,6) = 1.15000000000000 + IF (pol >= 2) mm(i) = 74.123 ! PCIP-SAFT + IF (pol >= 2) parame(i,1) = mm(i)* 4.04144179873E-2 ! =2.9956379 + IF (pol >= 2) parame(i,2) = 3.501724569 + IF (pol >= 2) parame(i,3) = 217.8941822 + IF (pol >= 2) parame(i,6) = 1.15 + IF (pol == 2) parame(i,11)= 8.73 + ELSE IF (compna(i) == 'vinylacetate') THEN + mm(i) = 86.092 + parame(i,1) = mm(i)* .0374329292 + parame(i,2) = 3.35278602 + parame(i,3) = 240.492049 + ELSE IF (compna(i) == 'chloromethane') THEN ! R40 + mm(i) = 50.488 ! PC-SAFT + parame(i,1) = mm(i)* 0.039418879 ! 1.9902 + parame(i,2) = 3.1974 + parame(i,3) = 237.27 + IF (pol >= 1) mm(i) = 50.488 ! PCP-SAFT + IF (pol >= 1) parame(i,1) = mm(i)* 0.035790801 ! 1.8070 + IF (pol >= 1) parame(i,2) = 3.3034 + IF (pol >= 1) parame(i,3) = 229.97 + IF (pol >= 1) parame(i,6) = 1.8963 + IF (pol >= 1) lli(i) = 1.67703*parame(i,2) + IF (pol >= 1) phi_criti(i)= 20.75417 + IF (pol >= 1) chap(i) = 0.5 + IF (pol >= 2) mm(i) = 50.488 ! PCIP-SAFT + IF (pol >= 2) parame(i,1) = mm(i)* 3.68559992E-2 ! 1.86078 + IF (pol >= 2) parame(i,2) = 3.275186 + IF (pol >= 2) parame(i,3) = 216.4621 + IF (pol >= 2) parame(i,6) = 1.8963 + IF (pol == 2) parame(i,11)= 4.72 + ELSE IF (compna(i) == 'fluoromethane') THEN ! R41 + IF (pol /= 1) write (*,*) 'non-polar parameters missing for fluoromethane' + IF (pol /= 1) stop + IF (pol >= 1) mm(i) = 34.0329000000000 + IF (pol >= 1) parame(i,1) = 1.94494757526896 + IF (pol >= 1) parame(i,2) = 2.96858005012635 + IF (pol >= 1) parame(i,3) = 168.938697391009 + IF (pol >= 1) parame(i,6) = 1.57823038894029 + ELSE IF (compna(i) == 'dichloromethane') THEN ! R30 + mm(i) = 84.932 ! PC-SAFT + parame(i,1) = 2.3117 + parame(i,2) = 3.3161 + parame(i,3) = 270.98 + IF (pol >= 1) mm(i) = 84.932 ! PCP-SAFT + IF (pol >= 1) parame(i,1) = 2.2687 + IF (pol >= 1) parame(i,2) = 3.3373 + IF (pol >= 1) parame(i,3) = 269.08 + IF (pol >= 1) parame(i,6) = 1.6 + IF (pol >= 2) mm(i) = 84.932 ! PCIP-SAFT + IF (pol >= 2) parame(i,1) = 2.3435 + IF (pol >= 2) parame(i,2) = 3.2987 + IF (pol >= 2) parame(i,3) = 260.66 + IF (pol >= 2) parame(i,6) = 1.6 + IF (pol == 2) parame(i,11)= 6.48 + ELSE IF (compna(i) == 'difluoromethane') THEN ! R32 + IF (pol /= 1) write (*,*) 'non-polar parameters missing for difluoromethane' + IF (pol /= 1) stop + IF (pol >= 1) mm(i) = 52.0236 ! PCP-SAFT + IF (pol >= 1) parame(i,1) = mm(i)* 4.814700934384165E-002 ! 2.50478075530028 + IF (pol >= 1) parame(i,2) = 2.79365980535456 + IF (pol >= 1) parame(i,3) = 160.893555378523 + IF (pol >= 1) parame(i,6) = 1.97850000000000 + ELSE IF (compna(i) == 'trifluoromethane') THEN ! R23 + IF (pol /= 1) write (*,*) 'non-polar parameters missing for trifluoromethane' + IF (pol /= 1) stop + IF (pol >= 1) mm(i) = 70.0138000000000 + IF (pol >= 1) parame(i,1) = 2.66039274225485 + IF (pol >= 1) parame(i,2) = 2.82905884530501 + IF (pol >= 1) parame(i,3) = 149.527709542333 + IF (pol >= 1) parame(i,6) = 1.339963415253999E-002 + ELSE IF (compna(i) == 'tetrachloromethane') THEN ! R10 + mm(i) = 153.822 + parame(i,1) = mm(i)* .0150432213 + parame(i,2) = 3.81801454 + parame(i,3) = 292.838632 + ELSE IF (compna(i) == 'trichlorofluoromethane') THEN ! R11 + IF (pol /= 1) write (*,*) 'non-polar parameters missing for trichlorofluoromethane' + IF (pol /= 1) stop + IF (pol >= 1) mm(i) = 137.368000000000 + IF (pol >= 1) parame(i,1) = 2.28793359008803 + IF (pol >= 1) parame(i,2) = 3.69013104930876 + IF (pol >= 1) parame(i,3) = 248.603173885090 + IF (pol >= 1) parame(i,6) = 0.23225538492979 + ELSE IF (compna(i) == 'chlorodifluoromethane') THEN ! R22 ( CHClF2 or CHF2Cl) + IF (pol /= 1) write (*,*) 'non-polar parameters missing for chlorodifluoromethane' + IF (pol /= 1) stop + IF (pol >= 1) mm(i) = 86.4684000000000 + IF (pol >= 1) parame(i,1) = 2.47218586047893 + IF (pol >= 1) parame(i,2) = 3.13845692489930 + IF (pol >= 1) parame(i,3) = 187.666355083434 + IF (pol >= 1) parame(i,6) = 1.04954264812860 + ELSE IF (compna(i) == 'chloroethane') THEN + mm(i) = 64.514 + parame(i,1) = mm(i)* .0350926868 + parame(i,2) = 3.41602397 + parame(i,3) = 245.42626 + ELSE IF (compna(i) == '11difluoroethane') THEN + ! mm(i) = 66.0500000000000 ! PC-SAFT + ! parame(i,1) = mm(i)* 4.109944338817734E-002 + ! parame(i,2) = 3.10257444633546 + ! parame(i,3) = 192.177159144029 + ! mm(i) = 66.05 ! PC-SAFT assoc + ! parame(i,1)= 2.984947188 + ! parame(i,2)= 2.978630027 + ! parame(i,3)= 137.8192282 + ! nhb_typ(i) = 2 + ! nhb_no(i,1)= 1 + ! nhb_no(i,2)= 1 + ! eps_hb(i,i,1,2)= 823.3478288 + ! eps_hb(i,i,2,1)= 823.3478288 + ! eps_hb(i,i,1,1)= 0.0 + ! eps_hb(i,i,2,2)= 0.0 + ! kap_hb(i,i) = 0.96345994 + IF (pol >= 1) mm(i) = 66.0500000000000 ! PCP-SAFT + IF (pol >= 1) parame(i,1) = mm(i)* 3.949665745363346E-002 ! =2.60875422481249 + IF (pol >= 1) parame(i,2) = 3.13758353925036 + IF (pol >= 1) parame(i,3) = 179.517952627836 + IF (pol >= 1) parame(i,6) = 2.27000000000000 + IF (pol >= 1) lli(i) = 2.03907*parame(i,2) + IF (pol >= 1) phi_criti(i)= 26.5 + IF (pol >= 1) chap(i) = 0.4 + IF (pol >= 2) mm(i) = 66.0500000000000 ! PCIP-SAFT + IF (pol >= 2) parame(i,1) = mm(i)* 4.093647666154238E-002 ! =2.70385428349487 + IF (pol >= 2) parame(i,2) = 3.10437129415885 + IF (pol >= 2) parame(i,3) = 170.464400902455 + IF (pol >= 2) parame(i,6) = 2.27000000000000 + IF (pol == 2) parame(i,11)= 5.01000000000000 + ELSE IF (compna(i) == '1-chlorobutane') THEN + mm(i) = 92.568 + parame(i,1) = mm(i)* .0308793201 + parame(i,2) = 3.64240187 + parame(i,3) = 258.655298 + ELSE IF (compna(i) == 'chlorobenzene') THEN + ! mm(i) = 112.558 + ! parame(i,1) = mm(i)* .0235308686 + ! parame(i,2) = 3.75328494 + ! parame(i,3) = 315.039018 + mm(i) = 112.558 ! PCIP-SAFT + parame(i,1) = mm(i)* 0.023824167 ! =2.6816 + parame(i,2) = 3.7352 + parame(i,3) = 308.82 + parame(i,6) = 1.69 + IF (pol == 2) parame(i,11)= 14.1 + ELSE IF (compna(i) == 'styrene') THEN + mm(i) = 104.150 + parame(i,1) = mm(i)* 2.9124104853E-2 + parame(i,2) = 3.760233548 + parame(i,3) = 298.51287564 + ELSE IF (compna(i) == 'methylmethanoate') THEN + mm(i) = 60.053 + parame(i,1) = mm(i)* .0446000264 + parame(i,2) = 3.08753499 + parame(i,3) = 242.626755 + IF (pol >= 1) mm(i) = 60.053 ! PCP-SAFT + IF (pol >= 1) parame(i,1) = mm(i)* 4.366991153963102E-002 ! =2.62250919768946 + IF (pol >= 1) parame(i,2) = 3.10946396964 + IF (pol >= 1) parame(i,3) = 239.051951942 + IF (pol >= 1) parame(i,6) = 1.77 + IF (pol >= 2) mm(i) = 60.053 ! PCIP-SAFT + IF (pol >= 2) parame(i,1) = mm(i)* 4.492572388931002E-2 ! 2.69792449 + IF (pol >= 2) parame(i,2) = 3.078467837 + IF (pol >= 2) parame(i,3) = 232.1842551 + IF (pol >= 2) parame(i,6) = 1.77 + IF (pol == 2) parame(i,11)= 5.05 + ELSE IF (compna(i) == 'ethylmethanoate') THEN + mm(i) = 74.079 ! PC-SAFT + parame(i,1) = mm(i)* .03898009 + parame(i,2) = 3.31087192 + parame(i,3) = 246.465646 + IF (pol >= 1) mm(i) = 74.079 ! PCP-SAFT + IF (pol >= 1) parame(i,1) = mm(i)* 3.825407152074255E-002 ! =2.83382336418509 + IF (pol >= 1) parame(i,2) = 3.33160046679 + IF (pol >= 1) parame(i,3) = 244.495680932 + IF (pol >= 1) parame(i,6) = 1.93000000000 + ELSE IF (compna(i) == 'propylmethanoate') THEN + mm(i) = 88.106 + parame(i,1) = mm(i)* .0364206062 + parame(i,2) = 3.41679642 + parame(i,3) = 246.457732 + IF (pol >= 1) mm(i) = 88.106 + IF (pol >= 1) parame(i,1) = mm(i)* 3.60050739149E-2 ! =3.17226304235232 + IF (pol >= 1) parame(i,2) = 3.42957609309 + IF (pol >= 1) parame(i,3) = 245.637644107 + IF (pol >= 1) parame(i,6) = 1.89 + ELSE IF (compna(i) == 'methylacetate') THEN + mm(i) = 74.079 ! PC-SAFT + parame(i,1) = mm(i)* 4.286817177E-2 ! =3.175631296 + parame(i,2) = 3.18722021277843 + parame(i,3) = 234.106931032456 + IF (pol >= 1) mm(i) = 74.079 ! PCP-SAFT + IF (pol >= 1) parame(i,1) = mm(i)* 4.228922065E-2 ! =3.132743176 + IF (pol >= 1) parame(i,2) = 3.2011401688 + IF (pol >= 1) parame(i,3) = 233.17562886 + IF (pol >= 1) parame(i,6) = 1.72 + IF (pol >= 2) mm(i) = 74.079 ! PCIP-SAFT + IF (pol >= 2) parame(i,1) = mm(i)* 4.298900538E-2 ! =3.18458252 + IF (pol >= 2) parame(i,2) = 3.180642322 + IF (pol >= 2) parame(i,3) = 229.3132680 + IF (pol >= 2) parame(i,6) = 1.72 + IF (pol == 2) parame(i,11)= 6.94 + ELSE IF (compna(i) == 'ethylacetate') THEN + mm(i) = 88.106 ! PC-SAFT + parame(i,1) = mm(i)* .0401464427 ! =3.537142481 + parame(i,2) = 3.30789258 + parame(i,3) = 230.800689 + IF (pol >= 1) mm(i) = 88.106 ! PCP-SAFT + IF (pol >= 1) parame(i,1) = mm(i)* 0.039792575 ! =3.505964572 + IF (pol >= 1) parame(i,2) = 3.317655188 + IF (pol >= 1) parame(i,3) = 230.2434769 + IF (pol >= 1) parame(i,6) = 1.78 + IF (pol >= 2) mm(i) = 88.106 ! PCIP-SAFT + IF (pol >= 2) parame(i,1) = mm(i)* 0.040270267 ! =3.548052143 + IF (pol >= 2) parame(i,2) = 3.302097562 + IF (pol >= 2) parame(i,3) = 227.5026191 + IF (pol >= 2) parame(i,6) = 1.78 + IF (pol == 2) parame(i,11)= 8.62 + ELSE IF (compna(i) == 'ethyl-propanoate') THEN + mm(i) = 102.133 + parame(i,1) = mm(i)* .0375692464 + parame(i,2) = 3.40306071 + parame(i,3) = 232.778374 + ELSE IF (compna(i) == 'propyl-ethanoate') THEN + mm(i) = 102.133 + parame(i,1) = mm(i)* .0370721275 + parame(i,2) = 3.42272266 + parame(i,3) = 235.758378 + IF (pol >= 1) mm(i) = 102.133 ! PCP-SAFT + IF (pol >= 1) parame(i,1) = mm(i)* 3.687149995200072E-2 ! =3.76579690459769 + IF (pol >= 1) parame(i,2) = 3.4289353421006 + IF (pol >= 1) parame(i,3) = 235.41679442910 + IF (pol >= 1) parame(i,6) = 1.78 + ! IF (pol.EQ.2) parame(i,11)= 10.41 + ELSE IF (compna(i) == 'nbutyl-ethanoate') THEN + mm(i) = 116.16 ! PC-SAFT + parame(i,1) = mm(i)* .03427004 + parame(i,2) = 3.54269638 + parame(i,3) = 242.515768 + IF (pol >= 1) mm(i) = 116.16 ! PCP-SAFT + IF (pol >= 1) parame(i,1) = mm(i)* 3.411585209773470E-002 ! =3.96289737967286 + IF (pol >= 1) parame(i,2) = 3.54821589228130 + IF (pol >= 1) parame(i,3) = 242.274388267447 + IF (pol >= 1) parame(i,6) = 1.87000000000000 + IF (pol >= 2) mm(i) = 116.16 ! PCIP-SAFT + IF (pol >= 2) parame(i,1) = mm(i)* 3.442139015733717E-002 ! =3.99838868067629 + IF (pol >= 2) parame(i,2) = 3.53576054452119 + IF (pol >= 2) parame(i,3) = 240.154409609249 + IF (pol >= 2) parame(i,6) = 1.87000000000000 + IF (pol == 2) parame(i,11)= 14.2000000000000 + ELSE IF (compna(i) == 'methyl-octanoate') THEN + mm(i) = 158.24 ! PC-SAFT + parame(i,1) = 5.2074 + parame(i,2) = 3.6069 + parame(i,3) = 244.12 + ELSE IF (compna(i) == 'methyl-decanoate') THEN + mm(i) = 186.2912 ! PC-SAFT + parame(i,1) = 5.8402 + parame(i,2) = 3.6871 + parame(i,3) = 248.27 + + mm(i) = 186.2912 ! PC-SAFT from GC-method Tim + parame(i,1) = 7.716 + parame(i,2) = 3.337303029 + parame(i,3) = 204.250907 + + mm(i) = 186.2912 ! PC-SAFT from GC-method (tightly fit) Tim + parame(i,1) = 7.728 + parame(i,2) = 3.334023322 + parame(i,3) = 206.9099379 + + ! mm(i) = 186.2912 ! PC-SAFT from fit to DIPPR + ! parame(i,1) = 6.285005 + ! parame(i,2) = 3.594888 + ! parame(i,3) = 236.781461 + ! ! parame(i,6) = 2.08056 + + ! mm(i) = 186.291000000000 + ! parame(i,1) = 6.28500485898895 + ! parame(i,2) = 3.59488828061149 + ! parame(i,3) = 236.781461491921 + ! parame(i,6) = 2.08055996894836 + ! parame(i,8) = 1.00000000000000 + mm(i) = 186.291000000000 + parame(i,1) = 6.14436331493372 + parame(i,2) = 3.61977264863944 + parame(i,3) = 242.071887817656 + + ELSE IF (compna(i) == 'methyl-dodecanoate') THEN + mm(i) = 214.344 ! PC-SAFT + parame(i,1) = 6.5153 + parame(i,2) = 3.7406 + parame(i,3) = 250.7 + ELSE IF (compna(i) == 'methyl-tetradecanoate') THEN + mm(i) = 242.398 ! PC-SAFT + parame(i,1) = 7.1197 + parame(i,2) = 3.7968 + parame(i,3) = 253.77 + ELSE IF (compna(i) == 'methyl-hexadecanoate') THEN + mm(i) = 270.451 ! PC-SAFT + parame(i,1) = 7.891 + parame(i,2) = 3.814 + parame(i,3) = 253.71 + ELSE IF (compna(i) == 'methyl-octadecanoate') THEN + mm(i) = 298.504 ! PC-SAFT + parame(i,1) = 8.8759 + parame(i,2) = 3.7932 + parame(i,3) = 250.81 + ELSE IF (compna(i) == 'CH2F2') THEN + mm(i) = 52.02 + parame(i,1) = 3.110084171 + parame(i,2) = 2.8145230485 + parame(i,3) = 158.98060151 + ELSE IF (compna(i) == 'naphthalene') THEN + ! mm(i) = 128.174000000 + ! parame(i,1) = mm(i)* 2.4877834216412E-2 + ! parame(i,2) = 3.82355815011 + ! parame(i,3) = 341.560675334 + + mm(i) = 128.17400000000 + parame(i,1) = mm(i)* 2.6400924157729E-2 + parame(i,2) = 3.8102186020014 + parame(i,3) = 328.96792935903 + ELSE IF (compna(i) == 'h2s') THEN + mm(i) = 34.0820000000000 ! PC-SAFT + parame(i,1) = mm(i)* 4.838886696385162E-002 ! = 1.64918936386199 + parame(i,2) = 3.05478289838459 + parame(i,3) = 229.838873939562 + nhb_typ(i) = 2 + nhb_no(i,1) = 1 + nhb_no(i,2) = 1 + eps_hb(i,i,1,2)= 536.634834731413 + eps_hb(i,i,2,1)= 536.634834731413 + eps_hb(i,i,1,1)= 0.0 + eps_hb(i,i,2,2)= 0.0 + kap_hb(i,i) = 1.000000000000000E-003 +! PC-SAFT from Xiaohua + mm(i) = 34.082 ! PC-SAFT + parame(i,1) = 1.63677 + parame(i,2) = 3.06565 + parame(i,3) = 230.2121 + nhb_typ(i) = 2 + nhb_no(i,1) = 1 + nhb_no(i,2) = 1 + eps_hb(i,i,1,2)= 275.1088 + eps_hb(i,i,2,1)= 275.1088 + eps_hb(i,i,1,1)= 0.0 + eps_hb(i,i,2,2)= 0.0 + kap_hb(i,i) = 1.E-2 + ! IF (pol.GE.1) mm(i) = 34.082 ! PCP-SAFT with quadrupole + ! IF (pol.GE.1) parame(i,1) = mm(i)* 3.03171032558E-2 ! =1.03326751316478 + ! IF (pol.GE.1) parame(i,2) = 3.6868189914018 + ! IF (pol.GE.1) parame(i,3) = 246.862831266172 + ! IF (pol.GE.1) nhb_typ(i) = 2 + ! IF (pol.GE.1) nhb_no(i,1) = 1 + ! IF (pol.GE.1) nhb_no(i,2) = 1 + ! IF (pol.GE.1) eps_hb(i,i,1,2)= 987.4927232 + ! IF (pol.GE.1) eps_hb(i,i,2,1)= 987.4927232 + ! IF (pol.GE.1) eps_hb(i,i,1,1)= 0.0 + ! IF (pol.GE.1) eps_hb(i,i,2,2)= 0.0 + ! IF (pol.GE.1) kap_hb(i,i) = 5.5480659623d-4 + ! IF (pol.GE.1) parame(i,6) = 0.97833 + ! IF (pol.GE.1) parame(i,7) = 3.8623 + ! IF (pol.GE.1) LLi(i) = 1.2737*parame(i,2) + ! IF (pol.GE.1) phi_criti(i)= 14.316 + ! IF (pol.GE.1) chap(i) = 0.4473 + IF (pol >= 1) mm(i) = 34.0820000000000 ! PCP-SAFT no quadrupoLE + IF (pol >= 1) parame(i,1) = mm(i)* 4.646468487062725E-002 ! 1.58360938976072 + IF (pol >= 1) parame(i,2) = 3.10111012646306 + IF (pol >= 1) parame(i,3) = 230.243457544889 + IF (pol >= 1) nhb_typ(i) = 2 + IF (pol >= 1) nhb_no(i,1) = 1 + IF (pol >= 1) nhb_no(i,2) = 1 + IF (pol >= 1) eps_hb(i,i,1,2)= 584.367708701411 + IF (pol >= 1) eps_hb(i,i,2,1)= 584.367708701411 + IF (pol >= 1) eps_hb(i,i,1,1)= 0.0 + IF (pol >= 1) eps_hb(i,i,2,2)= 0.0 + IF (pol >= 1) kap_hb(i,i) = 1.000000000000000E-003 + IF (pol >= 1) parame(i,6) = 0.978330000000000 + + IF (pol >= 1) lli(i) = 1.2737*parame(i,2) + IF (pol >= 1) phi_criti(i)= 14.316 + IF (pol >= 1) chap(i) = 0.4473 + + + IF (pol == 2) parame(i,7) = 0.0 + IF (pol == 2) mm(i) = 34.0820000000000 ! PCIP-SAFT + IF (pol == 2) parame(i,1) = mm(i)* 4.806418212963168E-002 ! 1.63812345534211 + IF (pol == 2) parame(i,2) = 3.06556006883749 + IF (pol == 2) parame(i,3) = 221.746622243054 + IF (pol == 2) nhb_typ(i) = 2 + IF (pol == 2) nhb_no(i,1) = 1 + IF (pol == 2) nhb_no(i,2) = 1 + IF (pol == 2) eps_hb(i,i,1,2)= 672.164783984789 + IF (pol == 2) eps_hb(i,i,2,1)= 672.164783984789 + IF (pol == 2) eps_hb(i,i,1,1)= 0.0 + IF (pol == 2) eps_hb(i,i,2,2)= 0.0 + IF (pol == 2) kap_hb(i,i) = 1.000000000000000E-003 + IF (pol == 2) parame(i,6) = 0.978330000000000 + IF (pol == 2) parame(i,11) = 3.60200000000000 + IF (pol == 2) parame(i,7) = 0.0 + + IF (pol >= 1)mm(i) = 34.0820000000000 !PCP-SAFT D&Q + IF (pol >= 1)parame(i,1) = mm(i)* 3.974667896078737E-002 ! = 1.35464631234155 + IF (pol >= 1)parame(i,2) = 3.30857082333438 + IF (pol >= 1)parame(i,3) = 234.248947273191 + IF (pol >= 1)nhb_typ(i) = 2 + IF (pol >= 1)nhb_no(i,1) = 1 + IF (pol >= 1)nhb_no(i,2) = 1 + IF (pol >= 1)eps_hb(i,i,1,2)= 780.770936834770 + IF (pol >= 1)eps_hb(i,i,2,1)= 780.770936834770 + IF (pol >= 1)eps_hb(i,i,1,1)= 0.0 + IF (pol >= 1)eps_hb(i,i,2,2)= 0.0 + IF (pol >= 1)kap_hb(i,i) = 1.000000000000000E-003 + IF (pol >= 1)parame(i,6) = 0.978330000000000 + IF (pol >= 1)parame(i,7) = 2.93750500000000 + + ELSE IF (compna(i) == 'methanol') THEN + mm(i) = 32.042 ! PC-SAFT + parame(i,1) = mm(i)* .0476100379 + parame(i,2) = 3.23000005 + parame(i,3) = 188.904644 + nhb_typ(i) = 2 + nhb_no(i,1) = 1 ! no. of sites of type 1 + nhb_no(i,2) = 1 ! no. of sites of type 2 + eps_hb(i,i,1,2)= 2899.49055 + eps_hb(i,i,2,1)= 2899.49055 + eps_hb(i,i,1,1)= 0.0 + eps_hb(i,i,2,2)= 0.0 + kap_hb(i,i) = .0351760892 + IF (pol >= 1) mm(i) = 32.042 ! PCP-SAFT + IF (pol >= 1) parame(i,1) = mm(i)* 7.213091821E-2 ! =2.31121888139672 + IF (pol >= 1) parame(i,2) = 2.8270129502 + IF (pol >= 1) parame(i,3) = 176.3760515 + IF (pol >= 1) nhb_typ(i) = 2 + IF (pol >= 1) nhb_no(i,1) = 1 + IF (pol >= 1) nhb_no(i,2) = 1 + IF (pol >= 1) eps_hb(i,i,1,2)= 2332.5845803 + IF (pol >= 1) eps_hb(i,i,2,1)= 2332.5845803 + IF (pol >= 1) eps_hb(i,i,1,1)= 0.0 + IF (pol >= 1) eps_hb(i,i,2,2)= 0.0 + IF (pol >= 1) kap_hb(i,i) = 8.9248658086E-2 + IF (pol >= 1) parame(i,6) = 1.7 + IF (pol >= 1) lli(i) = 1.75*parame(i,2) + IF (pol >= 1) phi_criti(i)= 23.43 + IF (pol >= 1) chap(i) = 0.304 + IF (pol == 2) mm(i) = 32.042 ! PCIP-SAFT + IF (pol == 2) parame(i,1) = 2.0693 + IF (pol == 2) parame(i,2) = 2.9547 + IF (pol == 2) parame(i,3) = 174.51 + IF (pol == 2) nhb_typ(i) = 2 + IF (pol == 2) nhb_no(i,1) = 1 + IF (pol == 2) nhb_no(i,2) = 1 + IF (pol == 2) eps_hb(i,i,1,2)= 2418.5 + IF (pol == 2) eps_hb(i,i,2,1)= 2418.5 + IF (pol == 2) eps_hb(i,i,1,1)= 0.0 + IF (pol == 2) eps_hb(i,i,2,2)= 0.0 + IF (pol == 2) kap_hb(i,i) = 0.06319 + IF (pol == 2) parame(i,6) = 1.7 + IF (pol == 2) parame(i,11)= 3.29 + ! mm(i) = 32.0420000000000 ! PCP-SAFT with adjusted QQ + ! parame(i,1) = mm(i)* 6.241807629559099E-002 + ! ! parame(i,1) = 2.00000000066333 + ! parame(i,2) = 2.97610169698593 + ! parame(i,3) = 163.268505098639 + ! nhb_typ(i) = 2 + ! nhb_no(i,1) = 1 + ! nhb_no(i,2) = 1 + ! eps_hb(i,i,1,2)= 2449.55621933612 + ! eps_hb(i,i,2,1)= 2449.55621933612 + ! eps_hb(i,i,1,1)= 0.0 + ! eps_hb(i,i,2,2)= 0.0 + ! kap_hb(i,i) = 8.431015160393653E-002 + ! parame(i,6) = 1.72000000000000 + ! parame(i,7) = 1.59810028824523 + ELSE IF (compna(i) == 'ethanol') THEN + mm(i) = 46.069 + parame(i,1) = mm(i)* .0517195521 + parame(i,2) = 3.17705595 + parame(i,3) = 198.236542 + nhb_typ(i) = 2 + nhb_no(i,1) = 1 ! no. of sites of type 1 + nhb_no(i,2) = 1 ! no. of sites of type 2 + eps_hb(i,i,1,2)= 2653.38367 + eps_hb(i,i,2,1)= 2653.38367 + eps_hb(i,i,1,1)= 0.0 + eps_hb(i,i,2,2)= 0.0 + kap_hb(i,i) = .0323840159 + IF (pol >= 1) mm(i) = 46.0690000000000 + IF (pol >= 1) parame(i,1) = mm(i)* 4.753626908781145E-002 ! =2.18994838060639 + IF (pol >= 1) parame(i,2) = 3.30120000000000 + IF (pol >= 1) parame(i,3) = 209.824555801706 + IF (pol >= 1) nhb_typ(i) = 2 + IF (pol >= 1) nhb_no(i,1) = 1 + IF (pol >= 1) nhb_no(i,2) = 1 + IF (pol >= 1) eps_hb(i,i,1,2)= 2584.53116785767 + IF (pol >= 1) eps_hb(i,i,2,1)= 2584.53116785767 + IF (pol >= 1) eps_hb(i,i,1,1)= 0.0 + IF (pol >= 1) eps_hb(i,i,2,2)= 0.0 + IF (pol >= 1) kap_hb(i,i) = 2.349382956935725E-002 + IF (pol >= 1) parame(i,6) = 1.69000000000000 + ! mm(i) = 46.0690000000000 + ! parame(i,1) = mm(i)* 5.117957752785066E-002 ! =2.357791957 + ! parame(i,2) = 3.24027031244304 + ! parame(i,3) = 175.657110615456 + ! nhb_typ(i) = 2 + ! nhb_no(i,1) = 1 + ! nhb_no(i,2) = 1 + ! eps_hb(i,i,1,2)= 2273.62670516146 + ! eps_hb(i,i,2,1)= 2273.62670516146 + ! eps_hb(i,i,1,1)= 0.0 + ! eps_hb(i,i,2,2)= 0.0 + ! kap_hb(i,i) = 7.030279197039477E-002 + ! parame(i,6) = 1.69000000000000 + ! parame(i,7) = 3.63701294195013 + IF (pol == 2) mm(i) = 46.0690000000000 + IF (pol == 2) parame(i,1) = mm(i)* 4.733436280008321E-002 ! =2.18064676 + IF (pol == 2) parame(i,2) = 3.31260000000000 + IF (pol == 2) parame(i,3) = 207.594119926613 + IF (pol == 2) nhb_typ(i) = 2 + IF (pol == 2) nhb_no(i,1) = 1 + IF (pol == 2) nhb_no(i,2) = 1 + IF (pol == 2) eps_hb(i,i,1,2)= 2589.68311382661 + IF (pol == 2) eps_hb(i,i,2,1)= 2589.68311382661 + IF (pol == 2) eps_hb(i,i,1,1)= 0.0 + IF (pol == 2) eps_hb(i,i,2,2)= 0.0 + IF (pol == 2) kap_hb(i,i) = 2.132561218631547E-002 + IF (pol == 2) parame(i,6) = 1.69000000000000 + IF (pol == 2) parame(i,7) = 0.0 + IF (pol == 2) parame(i,11)= 5.11000000000000 + ELSE IF (compna(i) == '1-propanol') THEN + mm(i) = 60.096 + parame(i,1) = mm(i)* .0499154461 + parame(i,2) = 3.25221234 + parame(i,3) = 233.396705 + nhb_typ(i) = 2 + nhb_no(i,1) = 1 ! no. of sites of type 1 + nhb_no(i,2) = 1 ! no. of sites of type 2 + eps_hb(i,i,1,2)= 2276.77867 + eps_hb(i,i,2,1)= 2276.77867 + eps_hb(i,i,1,1)= 0.0 + eps_hb(i,i,2,2)= 0.0 + kap_hb(i,i) = .0152683094 + ELSE IF (compna(i) == '1-butanol') THEN + mm(i) = 74.123 + parame(i,1) = mm(i)* .0341065046 + parame(i,2) = 3.72361538 + parame(i,3) = 269.798048 + nhb_typ(i) = 2 + nhb_no(i,1) = 1 ! no. of sites of type 1 + nhb_no(i,2) = 1 ! no. of sites of type 2 + eps_hb(i,i,1,2)= 2661.37119 + eps_hb(i,i,2,1)= 2661.37119 + eps_hb(i,i,1,1)= 0.0 + eps_hb(i,i,2,2)= 0.0 + kap_hb(i,i) = .00489087833 + mm(i) = 74.1230000000000 + parame(i,1) = mm(i)* 3.329202420547412E-002 ! =2.46770471018236 + parame(i,2) = 3.76179376417092 + parame(i,3) = 270.237284242002 + nhb_typ(i) = 2 + nhb_no(i,1) = 1 + nhb_no(i,2) = 1 + eps_hb(i,i,1,2)= 2669.28754983370 + eps_hb(i,i,2,1)= 2669.28754983370 + eps_hb(i,i,1,1)= 0.0 + eps_hb(i,i,2,2)= 0.0 + kap_hb(i,i) = 4.855584122733399E-003 + parame(i,6) = 1.66000000000000 + ELSE IF (compna(i) == '1-pentanol') THEN + mm(i) = 88.15 ! PC-SAFT + parame(i,1) = mm(i)* .041134139 + parame(i,2) = 3.45079143 + parame(i,3) = 247.278748 + nhb_typ(i) = 2 + nhb_no(i,1) = 1 ! no. of sites of type 1 + nhb_no(i,2) = 1 ! no. of sites of type 2 + eps_hb(i,i,1,2)= 2252.09237 + eps_hb(i,i,2,1)= 2252.09237 + eps_hb(i,i,1,1)= 0.0 + eps_hb(i,i,2,2)= 0.0 + kap_hb(i,i) = .0103189939 + IF (pol >= 1) mm(i) = 88.1500000000000 ! PCP-SAFT + IF (pol >= 1) parame(i,1) = mm(i)* 4.138903382168521E-002 ! =3.64844333138155 + IF (pol >= 1) parame(i,2) = 3.44250118689142 + IF (pol >= 1) parame(i,3) = 246.078034174947 + IF (pol >= 1) nhb_typ(i) = 2 + IF (pol >= 1) nhb_no(i,1) = 1 + IF (pol >= 1) nhb_no(i,2) = 1 + IF (pol >= 1) eps_hb(i,i,1,2)= 2236.72830142446 + IF (pol >= 1) eps_hb(i,i,2,1)= 2236.72830142446 + IF (pol >= 1) eps_hb(i,i,1,1)= 0.0 + IF (pol >= 1) eps_hb(i,i,2,2)= 0.0 + IF (pol >= 1) kap_hb(i,i) = 1.040067895187016E-002 + IF (pol >= 1) parame(i,6) = 1.70000000000000 + IF (pol == 2) mm(i) = 88.1500000000000 ! PCIP-SAFT + IF (pol == 2) parame(i,1) = mm(i)* 4.161521814399406E-002 ! =3.66838147939308 + IF (pol == 2) parame(i,2) = 3.43496654431777 + IF (pol == 2) parame(i,3) = 244.177313808431 + IF (pol == 2) nhb_typ(i) = 2 + IF (pol == 2) nhb_no(i,1) = 1 + IF (pol == 2) nhb_no(i,2) = 1 + IF (pol == 2) eps_hb(i,i,1,2)= 2241.27880639096 + IF (pol == 2) eps_hb(i,i,2,1)= 2241.27880639096 + IF (pol == 2) eps_hb(i,i,1,1)= 0.0 + IF (pol == 2) eps_hb(i,i,2,2)= 0.0 + IF (pol == 2) kap_hb(i,i) = 1.049516309928397E-002 + IF (pol == 2) parame(i,6) = 1.70000000000000 + IF (pol == 2) parame(i,11)= 10.8000000000000 + ELSE IF (compna(i) == '1-octanol') THEN + mm(i) = 130.23 + parame(i,1) = mm(i)* .0334446084 + parame(i,2) = 3.714535 + parame(i,3) = 262.740637 + nhb_typ(i) = 2 + nhb_no(i,1) = 1 ! no. of sites of type 1 + nhb_no(i,2) = 1 ! no. of sites of type 2 + eps_hb(i,i,1,2)= 2754.77272 + eps_hb(i,i,2,1)= 2754.77272 + eps_hb(i,i,1,1)= 0.0 + eps_hb(i,i,2,2)= 0.0 + kap_hb(i,i) = .00219656803 + ELSE IF (compna(i) == '1-nonanol') THEN + mm(i) = 144.257 + parame(i,1) = mm(i)* .0324692669 + parame(i,2) = 3.72924286 + parame(i,3) = 263.636673 + nhb_typ(i) = 2 + nhb_no(i,1) = 1 ! no. of sites of type 1 + nhb_no(i,2) = 1 ! no. of sites of type 2 + eps_hb(i,i,1,2)= 2941.9231 + eps_hb(i,i,2,1)= 2941.9231 + eps_hb(i,i,1,1)= 0.0 + eps_hb(i,i,2,2)= 0.0 + kap_hb(i,i) = .00142696883 + ELSE IF (compna(i) == '2-propanol') THEN + mm(i) = 60.096 + parame(i,1) = mm(i)* .0514663133 + parame(i,2) = 3.20845858 + parame(i,3) = 208.420809 + nhb_typ(i) = 2 + nhb_no(i,1) = 1 ! no. of sites of type 1 + nhb_no(i,2) = 1 ! no. of sites of type 2 + eps_hb(i,i,1,2)= 2253.91064 + eps_hb(i,i,2,1)= 2253.91064 + eps_hb(i,i,1,1)= 0.0 + eps_hb(i,i,2,2)= 0.0 + kap_hb(i,i) = .0246746934 + ELSE IF (compna(i) == '2-methyl-2-butanol') THEN + mm(i) = 88.15 + parame(i,1) = mm(i)* .0289135026 + parame(i,2) = 3.90526707 + parame(i,3) = 266.011828 + nhb_typ(i) = 2 + nhb_no(i,1) = 1 ! no. of sites of type 1 + nhb_no(i,2) = 1 ! no. of sites of type 2 + eps_hb(i,i,1,2)= 2618.80124 + eps_hb(i,i,2,1)= 2618.80124 + eps_hb(i,i,1,1)= 0.0 + eps_hb(i,i,2,2)= 0.0 + kap_hb(i,i) = .00186263367 + ELSE IF (compna(i) == 'acetic-acid') THEN + mm(i) = 60.053 + parame(i,1) = mm(i)* .0227076949 + parame(i,2) = 3.79651163 + parame(i,3) = 199.225066 + nhb_typ(i) = 2 + nhb_no(i,1) = 1 ! no. of sites of type 1 + nhb_no(i,2) = 1 ! no. of sites of type 2 + eps_hb(i,i,1,2)= 3092.40109 + eps_hb(i,i,2,1)= 3092.40109 + eps_hb(i,i,1,1)= 0.0 + eps_hb(i,i,2,2)= 0.0 + kap_hb(i,i) = .0870093874 + + + mm(i) = 60.053 + parame(i,1) = mm(i)* .0181797646 + parame(i,2) = 4.13711044 + parame(i,3) = 207.552969 + nhb_typ(i) = 2 + nhb_no(i,1) = 1 ! no. of sites of type 1 + nhb_no(i,2) = 1 ! no. of sites of type 2 + eps_hb(i,i,1,2)= 3198.84362 + eps_hb(i,i,2,1)= 3198.84362 + eps_hb(i,i,1,1)= 0.0 + eps_hb(i,i,2,2)= 0.0 + kap_hb(i,i) = .0586552968 + +! mit gesetztem Dipol-Moment + mm(i) = 60.0530000000000 + parame(i,1) = mm(i)* 1.736420143637533E-002 + parame(i,2) = 4.25220708070687 + parame(i,3) = 190.957247854820 + parame(i,6) = 3.50000000000000 + nhb_typ(i) = 2 + nhb_no(i,1) = 1 ! no. of sites of type 1 + nhb_no(i,2) = 1 ! no. of sites of type 2 + eps_hb(i,i,1,2)= 3096.36190957945 + eps_hb(i,i,2,1)= 3096.36190957945 + eps_hb(i,i,1,1)= 0.0 + eps_hb(i,i,2,2)= 0.0 + kap_hb(i,i) = 6.154307094782551E-002 + + ELSE IF (compna(i) == 'propionic-acid') THEN + mm(i) = 74.0800000000000 + parame(i,1) = mm(i)* 2.359519915877884E-002 + parame(i,2) = 3.99339224153844 + parame(i,3) = 295.947729838532 + nhb_typ(i) = 2 + nhb_no(i,1) = 1 ! no. of sites of type 1 + nhb_no(i,2) = 1 ! no. of sites of type 2 + eps_hb(i,i,1,2)= 2668.97826430874 + eps_hb(i,i,2,1)= 2668.97826430874 + eps_hb(i,i,1,1)= 0.0 + eps_hb(i,i,2,2)= 0.0 + kap_hb(i,i) = 3.660242292423115E-002 + ELSE IF (compna(i) == 'acrylic-acid') THEN + mm(i) = 72.0636 + parame(i,1) = mm(i)* .0430585424 + parame(i,2) = 3.0545415 + parame(i,3) = 164.115604 + nhb_typ(i) = 2 + nhb_no(i,1) = 1 ! no. of sites of type 1 + nhb_no(i,2) = 1 ! no. of sites of type 2 + eps_hb(i,i,1,2)= 3065.40667 + eps_hb(i,i,2,1)= 3065.40667 + eps_hb(i,i,1,1)= 0.0 + eps_hb(i,i,2,2)= 0.0 + kap_hb(i,i) = .336261669 + ELSE IF (compna(i) == 'caproic-acid') THEN + mm(i) = 116.16 + parame(i,1) = 5.87151 + parame(i,2) = 3.0694697 + parame(i,3) = 241.4569 + nhb_typ(i) = 1 + eps_hb(i,i,1,1)= 2871.37 + kap_hb(i,i) = 3.411613D-3 + ELSE IF (compna(i) == 'aniline') THEN + mm(i) = 93.13 + parame(i,1) = mm(i)* .0285695992 + parame(i,2) = 3.70214085 + parame(i,3) = 335.471062 + nhb_typ(i) = 2 + nhb_no(i,1) = 1 ! no. of sites of type 1 + nhb_no(i,2) = 1 ! no. of sites of type 2 + eps_hb(i,i,1,2)= 1351.64234 + eps_hb(i,i,2,1)= 1351.64234 + eps_hb(i,i,1,1)= 0.0 + eps_hb(i,i,2,2)= 0.0 + kap_hb(i,i) = .0748830615 + + mm(i) = 93.1300000000000 + parame(i,1) = mm(i)* 2.834372610192228E-002 ! =2.63965121187202 + parame(i,2) = 3.71326867619433 + parame(i,3) = 332.253796842009 + nhb_typ(i) = 2 + nhb_no(i,1) = 1 + nhb_no(i,2) = 1 + eps_hb(i,i,1,2)= 1392.14266886674 + eps_hb(i,i,2,1)= 1392.14266886674 + eps_hb(i,i,1,1)= 0.0 + eps_hb(i,i,2,2)= 0.0 + kap_hb(i,i) = 7.424612087328866E-002 + parame(i,6) = 1.55000000000000 + IF (pol == 2) parame(i,11)= 12.1000000000000 + ELSE IF (compna(i) == 'HF') THEN + ! mm(i) = 20.006 ! PC-SAFT + ! parame(i,1) = 0.87731 + ! parame(i,2) = 3.0006 + ! parame(i,3) = 112.24 + ! nhb_typ(i) = 2 + ! nhb_no(i,1) = 1 + ! nhb_no(i,2) = 1 + ! eps_hb(i,i,1,2)= 2208.22 + ! eps_hb(i,i,2,1)= 2208.22 + ! eps_hb(i,i,1,1)= 0.0 + ! eps_hb(i,i,2,2)= 0.0 + ! kap_hb(i,i) = 0.71265 + mm(i) = 20.0060000000000 ! PCP-SAFT + parame(i,1) = 1.00030000000000 + parame(i,2) = 3.17603622195029 + parame(i,3) = 331.133373208282 + nhb_typ(i) = 2 + nhb_no(i,1) = 1 + nhb_no(i,2) = 1 + eps_hb(i,i,1,2)= 348.251433080979 + eps_hb(i,i,2,1)= 348.251433080979 + eps_hb(i,i,1,1)= 0.0 + eps_hb(i,i,2,2)= 0.0 + kap_hb(i,i) = 2.868887975449893E-002 + parame(i,6) = 1.82600000000000 + ELSE IF (compna(i) == 'HCl') THEN + ! mm(i) = 36.4610000000000 + ! parame(i,1) = mm(i)* 3.922046741026943E-002 + ! parame(i,2) = 3.08731180727493 + ! parame(i,3) = 203.898845304388 + ! nhb_typ(i) = 2 + ! nhb_no(i,1) = 1 + ! nhb_no(i,2) = 1 + ! eps_hb(i,i,1,2)= 245.462773177367 + ! eps_hb(i,i,2,1)= 245.462773177367 + ! eps_hb(i,i,1,1)= 0.0 + ! eps_hb(i,i,2,2)= 0.0 + ! kap_hb(i,i) = 0.256454187330899 + mm(i) = 36.461 ! PCIP-SAFT + parame(i,1) = 1.6335 + parame(i,2) = 2.9066 + parame(i,3) = 190.17 + parame(i,6) = 1.1086 + IF (pol == 2) parame(i,11)= 2.63 + ELSE IF (compna(i) == 'gen') THEN + mm(i) = 302.0 + parame(i,1) = 8.7563 + parame(i,2) = 3.604243 + parame(i,3) = 255.6434 + nhb_typ(i) = 2 + nhb_no(i,1) = 1 ! no. of sites of type 1 + nhb_no(i,2) = 1 ! no. of sites of type 2 + eps_hb(i,i,1,2)= 0.0 + eps_hb(i,i,2,1)= 0.0 + eps_hb(i,i,1,1)= 0.0 + eps_hb(i,i,2,2)= 0.0 + kap_hb(i,i) = 0.02 + ELSE IF (compna(i) == 'h2o') THEN + mm(i) = 18.015 + parame(i,1) = mm(i)* .05915 + parame(i,2) = 3.00068335 + parame(i,3) = 366.512135 + nhb_typ(i) = 2 + nhb_no(i,1) = 1 ! no. of sites of type 1 + nhb_no(i,2) = 1 ! no. of sites of type 2 + eps_hb(i,i,1,2)= 2500.6706 + eps_hb(i,i,2,1)= 2500.6706 + eps_hb(i,i,1,1)= 0.0 + eps_hb(i,i,2,2)= 0.0 + kap_hb(i,i) = .0348679836 + + ! mm(i) = 18.015 + ! parame(i,1) = 1.706 + ! parame(i,2) = 2.429 + ! parame(i,3) = 242.19 + ! nhb_typ(i) = 2 + ! nhb_no(i,1) = 1 ! no. of sites of type 1 + ! nhb_no(i,2) = 1 ! no. of sites of type 2 + ! eps_hb(i,i,1,2)= 2644.2 + ! eps_hb(i,i,2,1)= 2644.2 + ! eps_hb(i,i,1,1)= 0.0 + ! eps_hb(i,i,2,2)= 0.0 + ! kap_hb(i,i) = 0.153 + + ! mm(i) = 18.015 + ! parame(i,1) = mm(i)* .0588185709 + ! parame(i,2) = 3.02483704 + ! parame(i,3) = 382.086672 + !c! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! + ! nhb_typ(i) = 2 + ! nhb_no(i,1) = 1 ! no. of sites of type 1 + ! nhb_no(i,2) = 2 ! no. of sites of type 2 + !c! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! + ! eps_hb(i,i,1,2)= 2442.49782 + ! eps_hb(i,i,2,1)= 2442.49782 + ! eps_hb(i,i,1,1)=0.0 + ! eps_hb(i,i,2,2)=0.0 + ! kap_hb(i,i) = .0303754635 + + ! mit gefittetem Dipol-Moment - Haarlem-night + ! mm(i) = 18.015 + ! parame(i,1) = mm(i)* 7.0037160952278E-2 + ! parame(i,2) = 2.79276650240763 + ! parame(i,3) = 270.970053834558 + ! nhb_typ(i) = 2 + ! nhb_no(i,1) = 1 ! no. of sites of type 1 + ! nhb_no(i,2) = 1 ! no. of sites of type 2 + ! eps_hb(i,i,1,2)= 1427.8287 + ! eps_hb(i,i,2,1)= 1427.8287 + ! eps_hb(i,i,1,1)=0.0 + ! eps_hb(i,i,2,2)=0.0 + ! kap_hb(i,i) = 4.335167238E-2 + ! parame(i,6) = 3.968686856378 + + IF (pol >= 1) mm(i) = 18.015 ! PCP-SAFT + IF (pol >= 1) parame(i,1) = 0.922688825223317 + IF (pol >= 1) parame(i,2) = 3.17562052023944 + IF (pol >= 1) parame(i,3) = 388.462197714696 + IF (pol >= 1) nhb_typ(i) = 2 + IF (pol >= 1) nhb_no(i,1) = 1 + IF (pol >= 1) nhb_no(i,2) = 1 + IF (pol >= 1) eps_hb(i,i,1,2)= 2000.67247409031 + IF (pol >= 1) eps_hb(i,i,2,1)= 2000.67247409031 + IF (pol >= 1) eps_hb(i,i,1,1)= 0.0 + IF (pol >= 1) eps_hb(i,i,2,2)= 0.0 + IF (pol >= 1) kap_hb(i,i) = 2.040614952751225E-003 + IF (pol >= 1) parame(i,6) = 1.85500000000000 + IF (pol >= 1) parame(i,7) = 2.00000000000000 + ! IF (pol.EQ.2) mm(i) = 18.015 ! PCIP-SAFT - DQ with my=my_RPT + ! IF (pol.EQ.2) parame(i,1) = 1.0 + ! IF (pol.EQ.2) parame(i,2) = 3.14540664928026 + ! IF (pol.EQ.2) parame(i,3) = 320.283823615925 + ! IF (pol.EQ.2) nhb_typ(i) = 2 + ! IF (pol.EQ.2) nhb_no(i,1) = 2 + ! IF (pol.EQ.2) nhb_no(i,2) = 2 + ! IF (pol.EQ.2) eps_hb(i,i,1,2)= 1335.72887678032 + ! IF (pol.EQ.2) eps_hb(i,i,2,1)= 1335.72887678032 + ! IF (pol.EQ.2) eps_hb(i,i,1,1)= 0.0 + ! IF (pol.EQ.2) eps_hb(i,i,2,2)= 0.0 + ! IF (pol.EQ.2) kap_hb(i,i) = 4.162619960844732E-003 + ! IF (pol.EQ.2) parame(i,6) = 1.85500000000000 + ! IF (pol.EQ.2) parame(i,7) = 2.00000000000000 + ! IF (pol.EQ.2) parame(i,11)= 1.45000000000000 + ! mm(i) = 18.0150000000000 + ! parame(i,1) = 1.0 + ! parame(i,2) = 3.11505069470915 + ! parame(i,3) = 320.991387913502 + ! nhb_typ(i) = 2 + ! nhb_no(i,1) = 1 + ! nhb_no(i,2) = 1 + ! eps_hb(i,i,1,2)= 2037.76329812542 + ! eps_hb(i,i,2,1)= 2037.76329812542 + ! eps_hb(i,i,1,1)= 0.0 + ! eps_hb(i,i,2,2)= 0.0 + ! kap_hb(i,i) = 3.763148982832804E-003 + ! parame(i,6) = 1.85500000000000 + ! parame(i,7) = 2.00000000000000 + ! IF (pol.EQ.2) parame(i,11)= 1.45000000000000 + IF (pol == 2) mm(i) = 18.015 ! PCIP-SAFT - DQ with my=my_0 + IF (pol == 2) parame(i,1) = 1.0 + IF (pol == 2) parame(i,2) = 3.11574491885322 + IF (pol == 2) parame(i,3) = 322.699984283499 + IF (pol == 2) nhb_typ(i) = 2 + IF (pol == 2) nhb_no(i,1) = 1 + IF (pol == 2) nhb_no(i,2) = 1 + IF (pol == 2) eps_hb(i,i,1,2)= 2033.87777692450 + IF (pol == 2) eps_hb(i,i,2,1)= 2033.87777692450 + IF (pol == 2) eps_hb(i,i,1,1)= 0.0 + IF (pol == 2) eps_hb(i,i,2,2)= 0.0 + IF (pol == 2) kap_hb(i,i) = 3.815764667176484E-003 + IF (pol == 2) parame(i,6) = 1.85500000000000 + IF (pol == 2) parame(i,7) = 2.00000000000000 + IF (pol == 2) parame(i,11)= 1.45000000000000 + ! mm(i) = 18.015 ! Dortmund + ! parame(i,1) = 0.11065254*mm(i) + ! parame(i,2) = 2.36393615 + ! parame(i,3) = 300.288589 + ! nhb_typ(i) = 2 + ! nhb_no(i,1) = 1 + ! nhb_no(i,2) = 1 + ! eps_hb(i,i,1,2)= 1193.45585 + ! eps_hb(i,i,2,1)= 1193.45585 + ! eps_hb(i,i,1,1)= 0.0 + ! eps_hb(i,i,2,2)= 0.0 + ! kap_hb(i,i) = 0.091203519 + ! parame(i,6) = 1.8546 + ! parame(i,7) = 0.0 + ! parame(i,11)= 0.0 + ELSE IF (compna(i) == 'MBBA') THEN + mm(i) = 267.37 + parame(i,1) = 12.194 + parame(i,2) = 3.064 + parame(i,3) = 270.7 + e_lc(i,i) = 13.7 !Hino & Prausnitz + s_lc(i,i) = 0.176 !Hino & Prausnitz + ELSE IF (compna(i) == 'PCH5') THEN + mm(i) = 255.41 + parame(i,1) = 11.6 + parame(i,2) = 3.2 + parame(i,3) = 270.7 + ! E_LC(i,i) = 16.7 !Hino & Prausnitz + ! S_LC(i,i) = 0.176 !Hino & Prausnitz + e_lc(i,i) = 8.95 + s_lc(i,i) = 0.2 + + ! mm(i) = 255.41 + ! parame(i,1) = 11.6 + ! parame(i,2) = 3.2 + ! parame(i,3) = 290.7 + ! E_LC(i,i) = 7.18 + ! S_LC(i,i) = 0.2 + + ELSE IF (compna(i) == 'Li') THEN + mm(i) = 6.9 + parame(i,1) = 1.0 + parame(i,2) = 1.4 + parame(i,3) = 96.83 + parame(i,10)= 1.0 +! the self-association is set to zero in routine F_EXPL for ions + ! nhb_typ(i) = 1 + ! nhb_no(i,1) = 3 ! no. of sites of type 1 + ! eps_hb(i,i,1,1)= 2000.0 + ! kap_hb(i,i) = 0.008 + ELSE IF (compna(i) == 'Na') THEN + mm(i) = 23.0 + parame(i,1) = 1.0 + parame(i,2) = 1.9 + parame(i,3) = 147.38 + parame(i,10)= 1.0 +! the self-association is set to zero in routine F_EXPL for ions + nhb_typ(i) = 1 + nhb_no(i,1) = 3 ! no. of sites of type 1 + eps_hb(i,i,1,1)= 8946.28257 ! 25C, 3 sites, dG-ref-1 + kap_hb(i,i) = 0.001648933 + ELSE IF (compna(i) == 'Ka') THEN + mm(i) = 39.1 + parame(i,1) = 1.0 + parame(i,2) = 2.66 + parame(i,3) = 221.44 + parame(i,10)= 1.0 + ! the self-association is set to zero in routine F_EXPL for ions + nhb_typ(i) = 1 + nhb_no(i,1) = 3 ! no. of sites of type 1 + eps_hb(i,i,1,1)= 3118.336216 ! 25C, 3 sites, dG-ref-1 + kap_hb(i,i) = 0.00200559 + ELSE IF (compna(i) == 'Cs') THEN + mm(i) = 132.9 + parame(i,1) = 1.0 + parame(i,2) = 3.38 + parame(i,3) = 523.28 + parame(i,10)= 1.0 + ! the self-association is set to zero in routine F_EXPL for ions + ! nhb_typ(i) = 1 + ! nhb_no(i,1) = 3 ! no. of sites of type 1 + ! eps_hb(i,i,1,1)= 2000.0 + ! kap_hb(i,i) = 0.00200559 + ELSE IF (compna(i) == 'Cl') THEN + mm(i) = 35.5 + parame(i,1) = 1.0 + parame(i,2) = 3.62 + parame(i,3) = 225.44 + parame(i,10)= -1.0 +! the self-association is set to zero in routine F_EXPL for ions + nhb_typ(i) = 1 + nhb_no(i,1) = 4 ! no. of sites of type 1 + eps_hb(i,i,1,1)= 6744.12509 ! 25C, 3 sites, dG-ref-1 + kap_hb(i,i) = 0.00155252 + ELSE IF (compna(i) == 'Br') THEN + mm(i) = 79.9 + parame(i,1) = 1.0 + parame(i,2) = 3.9 + parame(i,3) = 330.82 + parame(i,10)= -1.0 +! the self-association is set to zero in routine F_EXPL for ions + nhb_typ(i) = 1 + nhb_no(i,1) = 4 ! no. of sites of type 1 + eps_hb(i,i,1,1)= 4516.033227 ! 25C, 3 sites, dG-ref-1 + kap_hb(i,i) = 0.00200559 + ELSE IF (compna(i) == 'Io') THEN + mm(i) = 126.9 + parame(i,1) = 1.0 + parame(i,2) = 4.4 + parame(i,3) = 380.60 + parame(i,10)= -1.0 +! the self-association is set to zero in routine F_EXPL for ions + nhb_typ(i) = 1 + nhb_no(i,1) = 4 ! no. of sites of type 1 + eps_hb(i,i,1,1)= 1631.203342 ! 25C, 3 sites, dG-ref-1 + kap_hb(i,i) = 0.00200559 + ELSE IF (compna(i) == 'OH') THEN + mm(i) = 17.0 + parame(i,1) = 1.0 + parame(i,2) = 3.06 + parame(i,3) = 217.26 + parame(i,10)= -1.0 + ! the self-association is set to zero in routine F_EXPL for ions + nhb_typ(i) = 1 + nhb_no(i,1) = 4 ! no. of sites of type 1 + eps_hb(i,i,1,1)= 14118.68089 ! 25C, 3 sites, dG-ref-1 + kap_hb(i,i) = 0.00200559 + ELSE IF (compna(i) == 'NO3') THEN + mm(i) = 62.0 + parame(i,1) = 1.0 + parame(i,2) = 4.12 + parame(i,3) = 239.48 + parame(i,10)= -1.0 + ! the self-association is set to zero in routine F_EXPL for ions + ! nhb_typ(i) = 1 + ! nhb_no(i,1) = 4 ! no. of sites of type 1 + ! eps_hb(i,i,1,1)= 2000.0 + ! kap_hb(i,i) = 0.00200559 + ELSE IF (compna(i) == 'bf4') THEN + mm(i) = 86.8 + parame(i,1) = 1.0 + parame(i,2) = 4.51 ! *0.85 + parame(i,3) = 164.7 + parame(i,10)= -1.0 + ELSE IF (compna(i) == 'pf6') THEN + mm(i) = 145.0 + parame(i,1) = 1.0 + parame(i,2) = 5.06 + parame(i,3) = 224.9 + parame(i,10)= -1.0 + ELSE IF (compna(i) == 'emim') THEN + mm(i) = 111.16 + parame(i,1) = 3.11 + parame(i,2) = 4.0 + parame(i,3) = 250.0 + parame(i,10)= 1.0 + ELSE IF (compna(i) == 'bmim') THEN + mm(i) = 139.21 + ! parame(i,1) = 2.81 + ! parame(i,2) = 3.5 + parame(i,1) = 3.81 + parame(i,2) = 4.0 + parame(i,3) = 250.0 + parame(i,6) = 0.0 + parame(i,10)= 1.0 + ELSE IF (compna(i) == 'hmim') THEN + mm(i) = 167.27 + parame(i,1) = 4.53 + parame(i,2) = 4.0 + parame(i,3) = 250.0 + parame(i,10)= 1.0 + ELSE IF (compna(i) == 'omim') THEN + mm(i) = 195.32 + parame(i,1) = 5.30 + parame(i,2) = 4.0 + parame(i,3) = 250.0 + parame(i,10)= 1.0 + ELSE IF (compna(i) == 'sw') THEN + parame(i,1) = 1.0 + parame(i,2) = 1.0 + parame(i,3) = 100.0 + parame(i,4) = 0.0 + parame(i,5) = 0.0 + mm(i) = 1.0 + parame(i,6) = 0.1175015839*2.0 + ! use Temp. in Kelvin in the input-file. For dimensionless quantities + ! (P*=P*sig**3/epsilon, T*=T*kBol/epsilon, rho*=rho*sig**3) calculate + ! P* = P *1E5 * (1.e-10)^3 / (100*8.31441/6.022045E+23) + ! T* = (T+273.15)/100 + ! for rho* go to utilities.f (subroutine SI_DENS) and write + ! density(ph) = dense(ph)*6.0/PI + ELSE IF (compna(i) == 'c8-sim') THEN + mm(i) = 114.231 + parame(i,1) = mm(i)* 4.095944E-2 ! =4.67883774717337 + parame(i,2) = 3.501769 + parame(i,3) = 163.8606 + ! mm(i) = 114.231000000000 + ! parame(i,1) = mm(i)* 3.547001476437745E-002 ! =4.05177525654960 + ! parame(i,2) = 3.70988567055814 + ! parame(i,3) = 192.787548176343 + ELSE IF (compna(i) == 'argon_ge') THEN + mm(i) = 39.948 + parame(i,1) = mm(i)*0.030327 + parame(i,2) = 3.149910 + parame(i,3) = 100.188975 + ELSE IF (compna(i) == 'argon_ge2') THEN + mm(i) = 39.948 + parame(i,1) = mm(i)*0.030327 + parame(i,2) = 3.149910 + parame(i,3) = 0.8*100.188975 + ELSE + WRITE (*,*) ' pure component parameters missing for ',compna(i) + STOP + END IF + + IF (pol == 2.AND.parame(i,11) == 0.0) THEN + WRITE (*,*) ' polarizability missing for comp. ',compna(i) + STOP + END IF + + IF (nhb_typ(i) /= 0) THEN + parame(i,12) = DBLE(nhb_typ(i)) + parame(i,13) = kap_hb(i,i) + no = 0 + DO j=1,nhb_typ(i) + DO k=1,nhb_typ(i) + parame(i,(14+no))=eps_hb(i,i,j,k) + no=no+1 + END DO + END DO + DO j=1,nhb_typ(i) + parame(i,(14+no))=DBLE(nhb_no(i,j)) + no=no+1 + END DO + ELSE + DO k=12,25 + parame(i,k)=0.0 + END DO + END IF + +END DO + + +DO i = 1,ncomp + DO j = 1,ncomp + IF (compna(i) == 'ps'.AND.compna(j) == 'cyclohexane')THEN + kij(i,j) = 0.0075 + ELSE IF(compna(i) == 'peva'.AND.compna(j) == 'ethylene')THEN +! -- 0 Gew.% VA------------- + ! kij(i,j) = 0.039 +! -- 7.5 Gew.% VA------------- + ! kij(i,j) = 0.0377325 + ! kij(i,j) = 0.0374867 +! ---12.7 Gew.% VA------------ + ! kij(i,j) = 0.036854 + ! kij(i,j) = 0.0366508 +! ---27.3 Gew.% VA------------ + ! kij(i,j) = 0.034386 + ! kij(i,j) = 0.0352375 +! ---31.8 Gew.% VA------------ + kij(i,j) = 0.033626 + ! kij(i,j) = 0.0350795 +! ---42.7 Gew.% VA------------ + ! kij(i,j) = 0.031784 + ! kij(i,j) = 0.035239 + ELSE IF(compna(i) == 'gen'.AND.compna(j) == 'h2o')THEN + kij(i,j) = - 0.2 + ELSE IF(compna(i) == 'peva'.AND.compna(j) == 'vinylacetate')THEN + kij(i,j) = 0.019 + ELSE IF(compna(i) == 'ps'.AND.compna(j) == 'co2') THEN + IF ( pol == 0 ) kij(i,j) = 0.195 + IF ( pol == 1 ) kij(i,j) = 0.06 + ELSE IF(compna(i) == 'ps'.AND.compna(j) == 'acetone') THEN + kij(i,j) = 0.021 + ELSE IF(compna(i) == 'ps'.AND.compna(j) == 'hexane') THEN + kij(i,j) = 0.012 + ELSE IF(compna(i) == 'ps'.AND.compna(j) == 'pentane')THEN + kij(i,j) = 0.005 + ELSE IF(compna(i) == 'ps'.AND.compna(j) == 'methylcyclohexane') THEN + kij(i,j) = 0.0073 + ELSE IF(compna(i) == 'ps'.AND.compna(j) == 'ethylbenzene')THEN + kij(i,j) = 0.008 + ELSE IF(compna(i) == 'pe'.AND.compna(j) == 'co2') THEN + ! kij(i,j) = 0.181 + kij(i,j) = 0.088 + ELSE IF(compna(i) == 'pe'.AND.compna(j) == 'propane') THEN + kij(i,j) = 0.0206 + ELSE IF(compna(i) == 'pe'.AND.compna(j) == 'butane') THEN + kij(i,j) = 0.01 + ELSE IF(compna(i) == 'methane'.AND.compna(j) == 'argon') THEN + kij(i,j) = 0.01 + ELSE IF(compna(i) == 'methane'.AND.compna(j) == 'butane') THEN + kij(i,j) = 0.026 + ELSE IF(compna(i) == 'pe'.AND.compna(j) == 'pentane') THEN + ! kij(i,j) = -0.0195 + ELSE IF(compna(i) == 'pe'.AND.compna(j) == 'hexane') THEN + ! kij(i,j) = 0.008 + kij(i,j) = 0.004 + ELSE IF(compna(i) == 'pe'.AND.compna(j) == 'ethylene') THEN + kij(i,j) = 0.0404 + ! kij(i,j) = 0.0423 + ! kij(i,j) = 0.044 + ELSE IF(compna(i) == 'pe'.AND.compna(j) == 'cyclohexane') THEN + kij(i,j) = -0.1 + ELSE IF(compna(i) == 'ldpe'.AND.compna(j) == 'cyclopentane')THEN + kij(i,j) = -0.016 + ELSE IF(compna(i) == 'pp'.AND.compna(j) == 'propane') THEN + kij(i,j) = 0.0242 + ELSE IF(compna(i) == 'pp'.AND.compna(j) == 'pentane') THEN + kij(i,j) = 0.0137583176 + ELSE IF(compna(i) == 'pp'.AND.compna(j) == 'co2') THEN + kij(i,j) = 0.1767 ! without quadrupol-term + kij(i,j) = 0.063 ! with quadrupol-term + ELSE IF(compna(i) == 'pba'.AND.compna(j) == 'ethylene') THEN + kij(i,j) = 0.026 + ELSE IF(compna(i) == 'decane'.AND.compna(j) == 'ethane') THEN + kij(i,j) = 0.017 + ELSE IF(compna(i) == 'n2'.AND.compna(j) == 'co2') THEN + ! kij(i,j) = -0.04 + ELSE IF(compna(i) == 'methane'.AND.compna(j) == 'co2') THEN + kij(i,j) = 0.051875 ! PC-SAFT + IF (pol == 1) kij(i,j) = -0.0353125 ! PCP-SAFT + ELSE IF(compna(i) == 'methane'.AND.compna(j) == 'co') THEN + ! IF (pol == 1) kij(i,j) = -0.003 ! PCP-SAFT + IF (pol == 1) kij(i,j) = 0.018 ! PCP-SAFT + ELSE IF(compna(i) == 'ethane'.AND.compna(j) == 'co2') THEN + kij(i,j) = 0.095 + kij(i,j) = 0.021 + ! kij(i,j) = 0.024 + ELSE IF(compna(i) == 'propane'.AND.compna(j) == 'co2') THEN + kij(i,j) = 0.042 + ELSE IF(compna(i) == 'argon_ge'.AND.compna(j) == 'argon_ge2') THEN + read (*,*) kij(i,j) + ELSE IF(compna(i) == 'butane'.AND.compna(j) == 'co2') THEN + ! kij(i,j) = 0.115 + ! kij(i,j) = 0.048 + kij(i,j) = 0.036 + ELSE IF(compna(i) == 'pentane'.AND.compna(j) == 'co2') THEN + kij(i,j) = 0.143 ! without quadrupol-term + kij(i,j) = 0.0 ! with quadrupol-term + ELSE IF(compna(i) == 'hexane'.AND.compna(j) == 'co2') THEN + ! kij(i,j) = 0.125 ! without quadrupol-term + kij(i,j) = 0.0495 + ELSE IF(compna(i) == 'heptane'.AND.compna(j) == 'co2') THEN + kij(i,j) = 0.11 ! without quadrupol-term + ! kij(i,j) = 0.05 + ! kij(i,j) = 0.039 ! with quadrupol-term + ELSE IF(compna(i) == 'decane'.AND.compna(j) == 'co2') THEN + ! kij(i,j) = 0.128 ! without quadrupol-term + kij(i,j) = 0.053 ! with quadrupol-term + ELSE IF(compna(i) == 'dodecane'.AND.compna(j) == 'co2') THEN + kij(i,j) = 0.12 ! without quadrupol-term + kij(i,j) = 0.0508 ! with quadrupol-term + ELSE IF(compna(i) == 'benzene'.AND.compna(j) == 'co2') THEN + ! kij(i,j) = 0.087968750000 ! without quadrupol-term + ! kij(i,j) = 0.008203125 ! only co2 quadrupol + kij(i,j) = 0.042 ! both quadrupol + ! kij(i,j) = 0.003 ! both quadrupol + ELSE IF(compna(i) == 'toluene'.AND.compna(j) == 'co2') THEN + ! kij(i,j) = 0.110784912 ! without quadrupol-term + kij(i,j) = 0.0305 ! with quadrupol-term + ELSE IF(compna(i) == 'cyclohexane'.AND.compna(j) == 'co2') THEN + kij(i,j) = 0.13 + lij(i,j) = - 0.00 + ! kij(i,j) = 0.045 + ELSE IF(compna(i) == 'chloromethane'.AND.compna(j) == 'co2')THEN + ! kij(i,j) = 0.04 ! PC-SAFT + kij(i,j) = 0.025 ! PCP-SAFT + ! kij(i,j) = 0.083 ! PCIP-SAFT + ELSE IF(compna(i) == 'acetone'.AND.compna(j) == 'n2')THEN + kij(i,j) = 0.035211 ! PCP-SAFT + lij(i,j) = + 0.013225 ! PCP-SAFT + kij(i,j) = 0.023 ! PCP-SAFT + lij(i,j) = + 0.013225 ! PCP-SAFT + !kij(i,j) = 1.722238535635467E-002 ! PCP-SAFT + !lij(i,j) = 2.815974678394451E-003 ! PCP-SAFT + !kij(i,j) = 1.931522058164026E-002 ! PCP-SAFT + !lij(i,j) = 0.0 ! PCP-SAFT + !kij(i,j) = 1.641053794134795E-002 ! PCP-SAFT + !lij(i,j) = -5.850421759950764E-003 ! PCP-SAFT + if ( num == 0 ) write (*,*) 'calculation with lij only possible with num=1' + if ( num == 0 ) stop + ELSE IF(compna(i) == 'acetone'.AND.compna(j) == 'co2')THEN + kij(i,j) = 0.015 ! PC-SAFT + IF (pol == 1) kij(i,j) = -0.02 ! PCP-SAFT + IF (pol == 2) kij(i,j) = -0.005 ! PCIP-SAFT where DQ with my=my_vacuum + ! IF (pol.EQ.2) kij(i,j) = 0.0 ! PCIP-SAFT where DQ with my=my_RPT + ELSE IF(compna(i) == 'methanol'.AND.compna(j) == 'co2')THEN + ! kij(i,j) = 0.0288 ! PC-SAFT + ! kij(i,j) = - 0.035 ! PCP-SAFT for co2 and PC-SAFT methanol + ! kij(i,j) = - 0.035 ! PCP-SAFT + ! lij(i,j) = 0.3 ! PCP-SAFT + ELSE IF(compna(i) == 'dimethyl-ether'.AND.compna(j) == 'co2')THEN + kij(i,j) = 0.00896894 ! PC-SAFT + ! kij(i,j) = - 0.015 ! PCP-SAFT + ELSE IF(compna(i) == 'dimethyl-ether'.AND.compna(j) == 'h2o')THEN + ! kij(i,j) = -0.134 ! PC-SAFT + ELSE IF(compna(i) == 'dichloromethane'.AND.compna(j) == 'co2')THEN + ! kij(i,j) = 0.06881725 ! PC-SAFT + ! kij(i,j) = 0.05839145 ! PCP-SAFT + kij(i,j) = -0.00944346 ! PCP-SAFT co2 dichloromethane PC-SAFT + ! kij(i,j) = 0.06 ! PCIP-SAFT + ELSE IF(compna(i) == 'h2s'.AND.compna(j) == 'methane')THEN + ! kij(i,j) = 0.0414 ! PC-SAFT + kij(i,j) = 0.0152 ! PCP-SAFT Dipole momnet (d with Q) + ELSE IF(compna(i) == 'butane'.AND.compna(j) == 'h2s')THEN + kij(i,j) = -0.002 ! PCP-SAFT + ELSE IF(compna(i) == 'methanol'.AND.compna(j) == 'h2s')THEN + kij(i,j) = 0.0 ! PCP-SAFT + lij(i,j) = 0.0 ! PCP-SAFT + ELSE IF(compna(i) == 'co2'.AND.compna(j) == 'hydrogen') THEN + ! lij(i,j) = -0.08 !!!!! Lij not kij !!!! + ELSE IF(compna(i) == 'hexane'.AND.compna(j) == 'n2') THEN + kij(i,j) = 0.11 + ELSE IF(compna(i) == 'propane'.AND.compna(j) == 'n2') THEN + kij(i,j) = 0.0251171875 + ELSE IF(compna(i) == 'co2'.AND.compna(j) == 'hexadecane') THEN + ! kij(i,j) = 0.1194 ! PC-SAFT ohne QQ + kij(i,j) = 0.0588 + ELSE IF(compna(i) == 'ethane'.AND.compna(j) == 'acetone') THEN + ! kij(i,j) = 0.065 ! no DD + kij(i,j) = 0.038 ! DD non-polarizable + ! kij(i,j) = 0.025 ! DD polarizable + ELSE IF(compna(i) == 'butane'.AND.compna(j) == 'acetone') THEN + ! kij(i,j) = 0.065 ! no DD + kij(i,j) = 0.037 ! DD non-polarizable + ! kij(i,j) = 0.025 ! DD polarizable + ELSE IF(compna(i) == 'pentane'.AND.compna(j) == 'acetone') THEN + ! kij(i,j) = 0.072 ! no DD + ! kij(i,j) = 0.041 ! DD non-polarizable + kij(i,j) = 0.039 ! DD polarizable + ! kij(i,j) = 0.035 ! DD polarizable + ELSE IF(compna(i) == 'hexane'.AND.compna(j) == 'acetone') THEN + ! kij(i,j) = 0.063 + kij(i,j) = 0.038 ! PCP-SAFT + ! kij(i,j) = 0.036 ! PCIP-SAFT + ELSE IF(compna(i) == 'heptane'.AND.compna(j) == 'acetone') THEN + kij(i,j) = 0.035 ! PCP-SAFT + ELSE IF(compna(i) == 'decane'.AND.compna(j) == 'acetone') THEN + ! kij(i,j) = 0.059 ! no DD + ! kij(i,j) = 0.03281250 ! DD non-polarizable + kij(i,j) = 0.028 ! DD polarizable + ELSE IF(compna(i) == 'hexadecane'.AND.compna(j) == 'acetone') THEN + ! kij(i,j) = 0.07 ! no DD + ! kij(i,j) = 0.0415 ! DD non-polarizable + kij(i,j) = 0.035 ! DD polarizable + ELSE IF(compna(i) == 'hexane'.AND.compna(j) == 'butanone')THEN + kij(i,j) = 0.027 ! PCP-SAFT + ! kij(i,j) = 0.033 ! PCP-SAFT with lij + ! lij(i,j) = 0.13 ! PCP-SAFT + ! kij(i,j) = 0.042 ! PC-SAFT + ELSE IF(compna(i) == 'heptane'.AND.compna(j) == 'butanone')THEN + kij(i,j) = 0.042 ! no DD + ! kij(i,j) = 0.027 ! DD non-polarizable + ELSE IF(compna(i) == 'heptane'.AND.compna(j) == '2-pentanone')THEN + kij(i,j) = 0.041 ! no DD + ! kij(i,j) = 0.031 ! DD non-polarizable + ELSE IF(compna(i) == 'hexane'.AND.compna(j) == '3-pentanone')THEN + kij(i,j) = 0.0 + ELSE IF(compna(i) == 'pentane'.AND.compna(j) == 'propanal')THEN + ! kij(i,j) = 0.055 ! no DD + kij(i,j) = 0.027 ! DD non-polarizable + ! kij(i,j) = 0.026 ! DD polarizable 22 + ELSE IF(compna(i) == 'cyclohexane'.AND.compna(j) == 'propanal')THEN + ! kij(i,j) = 0.06 ! no DD + kij(i,j) = 0.036 ! DD non-polarizable + kij(i,j) = 0.035 ! DD polarizable 22 + ELSE IF(compna(i) == 'heptane'.AND.compna(j) == 'butanal')THEN + kij(i,j) = 0.041 ! no DD + ! kij(i,j) = 0.025 ! DD non-polarizable + ELSE IF(compna(i) == 'hexane'.AND.compna(j) == 'thf')THEN + kij(i,j) = 0.012 ! PCP-SAFT + ELSE IF(compna(i) == 'octane'.AND.compna(j) == 'thf')THEN + kij(i,j) = 0.012 ! PCP-SAFT + ELSE IF(compna(i) == 'decane'.AND.compna(j) == 'thf')THEN + kij(i,j) = 0.012 ! PCP-SAFT + ELSE IF(compna(i) == 'toluene'.AND.compna(j) == 'dmso')THEN + ! kij(i,j) = 0.025 ! no DD + kij(i,j) = - 0.0105 ! DD non-polarizable + ! kij(i,j) = - 0.019 ! DD polarizable + ELSE IF(compna(i) == 'hexane'.AND.compna(j) == 'acrylonitrile')THEN + kij(i,j) = - 0.05 ! DD polarizable + ELSE IF(compna(i) == 'heptane' .AND. compna(j) == 'butyronitrile')THEN + kij(i,j) = - 0.002 ! DD polarizable 11 + kij(i,j) = 0.002 ! DD polarizable 22 + ELSE IF(compna(i) == '1-butene'.AND.compna(j) == 'dmf')THEN + ! kij(i,j) = 0.04 ! no DD + ! kij(i,j) = 0.004 ! DD non-polarizable + kij(i,j) = 0.005 ! DD polarizable 22 + ELSE IF(compna(i) == 'cyclohexane'.AND.compna(j) == 'dmf')THEN + kij(i,j) = 0.0135 ! DD polarizable 11 + kij(i,j) = 0.022 ! DD polarizable 22 + ELSE IF(compna(i) == 'ethylene'.AND.compna(j) == 'dmf')THEN + ! kij(i,j) = - 0.0215 ! DD polarizable 11 + kij(i,j) = - 0.01 ! DD polarizable 22 + ELSE IF(compna(i) == 'nbutyl-ethanoate'.AND.compna(j) == 'dmf')THEN + ! kij(i,j) = 0.016 ! no DD + ! kij(i,j) = -0.01 ! DD non-polarizable + kij(i,j) = - 0.015 ! DD polarizable 22 + ELSE IF(compna(i) == 'methylacetate' .AND. compna(j) == 'cyclohexane')THEN + kij(i,j) = 0.066 ! PC-SAFT + ! kij(i,j) = 0.061 ! PCP-SAFT + ! kij(i,j) = 0.0625 ! PCIP-SAFT + ELSE IF(compna(i) == 'methylacetate'.AND.compna(j) == 'decane')THEN + kij(i,j) = 0.0625 ! PCIP-SAFT + ELSE IF(compna(i) == 'methylacetate' .AND. compna(j) == 'methanol')THEN + ! kij(i,j) = -0.07 ! PCIP-SAFT + ELSE IF(compna(i) == 'pentane' .AND. compna(j) == 'propionitrile')THEN + kij(i,j) = 0.0498 + IF (pol >= 1) kij(i,j) = -0.01 + IF (pol >= 2) kij(i,j) = -0.027 + ELSE IF(compna(i) == 'hexane' .AND. compna(j) == 'propionitrile')THEN + kij(i,j) = 0.05 + IF (pol >= 1) kij(i,j) = 0.0 + IF (pol >= 2) kij(i,j) = -0.03 + ELSE IF(compna(i) == 'octane' .AND. compna(j) == 'propionitrile')THEN + kij(i,j) = 0.0 ! DD polarizable 22 + ELSE IF(compna(i) == 'cyclohexane' .AND. compna(j) == 'nitromethane')THEN + kij(i,j) = 0.14 ! no DD + ! kij(i,j) = 0.07 ! DD non-polarizable + ! kij(i,j) = 0.055 ! DD polarizable 22 + ELSE IF(compna(i) == 'cyclohexane' .AND. compna(j) == 'nitroethane')THEN + ! kij(i,j) = 0.06 ! no DD + kij(i,j) = 0.03 ! DD polarizable 22 + ELSE IF(compna(i) == 'acetone' .AND. compna(j) == 'nitromethane')THEN + ! kij(i,j) = - 0.017 ! no DD + kij(i,j) = - 0.021 ! DD non-polarizable + ! kij(i,j) = - 0.023 ! DD polarizable 22 + ELSE IF(compna(i) == 'acetone' .AND. compna(j) == 'h2o')THEN + kij(i,j) = - 0.2 ! PCP-SAFT (no cross-association) + ELSE IF(compna(i) == 'methylcyclohexane' .AND. compna(j) == 'acetonitrile')THEN + ! kij(i,j) = 0.09 ! no DD + ! kij(i,j) = 0.033 ! DD non-polarizable + ! kij(i,j) = 0.025 ! DD polarizable 22 + kij(i,j) = 0.04 ! DD polarizable 22 und my angepasst + ELSE IF(compna(i) == 'ethylacetate' .AND. compna(j) == 'acetonitrile')THEN + kij(i,j) = 0.007 ! no DD + ! kij(i,j) = -0.045 ! DD polarizable 22 + ELSE IF(compna(i) == 'dimethyl-ether' .AND. compna(j) == 'propane')THEN + ! kij(i,j) = 0.03 ! no DD + kij(i,j) = 0.0225 ! DD non-polarizable + ELSE IF(compna(i) == 'benzene' .AND. compna(j) == 'pentane')THEN + ! kij(i,j) = 0.012968750 ! ohne QQ + ! kij(i,j) = 0.004921875 ! mit QQ=5.6D (gefittet) + ! kij(i,j) = -0.006406250 ! mit QQ=7.45D (Literatur) + ELSE IF(compna(i) == 'benzene' .AND. compna(j) == 'heptane')THEN + kij(i,j) = 0.01328125 + ! kij(i,j) = 0.0038 + ELSE IF(compna(i) == 'benzene' .AND. compna(j) == '1-hexene')THEN + kij(i,j) = 0.0067 + ELSE IF(compna(i) == 'ethylene' .AND. compna(j) == 'co2') THEN + kij(i,j) = 0.04 + kij(i,j) = -0.029 + ELSE IF(compna(i) == 'ethylene' .AND. compna(j) == 'vinylacetate') THEN + kij(i,j) = - 0.013847 + ELSE IF(compna(i) == 'triacontane' .AND. compna(j) == 'ethylene') THEN + kij(i,j) = 0.028 + ELSE IF(compna(i) == 'triacontane' .AND. compna(j) == 'methane')THEN + ! kij(i,j) = 0.061953125 ! polyethylene parameters + kij(i,j) = 0.039609375 ! param. by extrapolation of n-alkanes + ELSE IF(compna(i) == 'tetracontane' .AND. compna(j) == 'methane')THEN + ! kij(i,j) = 0.06515625 ! polyethylene parameters + kij(i,j) = 0.04453125 ! param. by extrapolation of n-alkanes + ! --- kij and lij adjusted ------- + ! kij(i,j) = 0.045786119 ! param. by extrapolation of n-alkanes + ! lij(i,j) = +8.53466437d-4 ! param. by extrapolation of n-alkanes + ELSE IF(compna(i) == 'eicosane' .AND. compna(j) == 'methane')THEN + kij(i,j) = 0.0360134457445 + ELSE IF(compna(i) == 'tetracontane' .AND. compna(j) == 'methane')THEN + kij(i,j) = 0.0360134457445 ! assumed equal to eicosane-C1 + ELSE IF(compna(i) == 'chlorobenzene' .AND. compna(j) == 'cyclohexane') THEN + kij(i,j) = 0.013 + ELSE IF(compna(i) == 'chloroethane' .AND. compna(j) == 'butane')THEN + kij(i,j) = 0.025 + ELSE IF(compna(i) == 'tetrachloromethane' .AND. compna(j) == '2-methylpentane') THEN + kij(i,j) = 0.0070105 + ELSE IF(compna(i) == 'tetrachloromethane' .AND. compna(j) == 'hexane') THEN + kij(i,j) = 0.004 + ELSE IF(compna(i) == 'hydrogen' .AND. compna(j) == 'hexane') THEN + kij(i,j) = 0.1501 + ELSE IF(compna(i) == 'ethanol' .AND. compna(j) == 'co2') THEN + ! kij(i,j) = -0.08 + ELSE IF(compna(i) == 'ethanol' .AND. compna(j) == 'propane') THEN + kij(i,j) = - 0.07 + ELSE IF(compna(i) == 'ethanol' .AND. compna(j) == 'ethane') THEN + kij(i,j) = 0.0 + ELSE IF(compna(i) == 'ethanol' .AND. compna(j) == 'butane') THEN + kij(i,j) = 0.028 + kij(i,j) = 0.016 + ELSE IF(compna(i) == 'ethanol' .AND. compna(j) == 'cyclohexane')THEN + kij(i,j) = 0.037 + ELSE IF(compna(i) == 'ethanol' .AND. compna(j) == '2-methylpentane') THEN + kij(i,j) = 0.028 + ELSE IF(compna(i) == 'ethanol' .AND. compna(j) == '1-octanol')THEN + kij(i,j) = 0.06 + ELSE IF(compna(i) == 'methanol' .AND. compna(j) == 'cyclohexane') THEN + kij(i,j) = 0.0508 + ! kij(i,j) = 0.03 + ELSE IF(compna(i) == 'methanol' .AND. compna(j) == 'heptane')THEN + kij(i,j) = 0.034 + ELSE IF(compna(i) == 'methanol' .AND. compna(j) == 'decane')THEN + ! kij(i,j) = 0.042 ! PC-SAFT + ! kij(i,j) = 0.011 ! PCP-SAFT + kij(i,j) = 0.000 ! PCIP-SAFT + ELSE IF(compna(i) == 'methanol' .AND. compna(j) == 'isobutane') THEN + kij(i,j) = 0.051 + ELSE IF(compna(i) == 'methanol' .AND. compna(j) == '1-octanol') THEN + kij(i,j) = 0.02 + ELSE IF(compna(i) == '1-butanol' .AND. compna(j) == 'butane') THEN + kij(i,j) = 0.015 + ELSE IF(compna(i) == '1-nonanol' .AND. compna(j) == 'co2') THEN + kij(i,j) = 0.076 + kij(i,j) = 0.01443 + ELSE IF(compna(i) == '1-propanol' .AND. compna(j) == 'ethylbenzene') THEN + kij(i,j) = 0.0251757813 + ELSE IF(compna(i) == 'decane'.AND.compna(j) == 'ethanol') THEN + kij(i,j) = 0.085 + ELSE IF(compna(i) == 'hexane'.AND.compna(j) == '1-chlorobutane') THEN + kij(i,j) = 0.017 + ELSE IF(compna(i) == 'aniline'.AND.compna(j) == 'methylcyclopentane') THEN + kij(i,j) = 0.0153 + ELSE IF(compna(i) == 'heptane'.AND.compna(j) == 'nbutyl-ethanoate')THEN + kij(i,j) = 0.027 + ELSE IF(compna(i) == '1-hexene'.AND.compna(j) == 'ethyl-ethanoate')THEN + kij(i,j) = 0.026 + ELSE IF(compna(i) == 'co2'.AND.compna(j) == '1-butanol')THEN + ! kij(i,j) = 0.075 + kij(i,j) = 0.0 + ELSE IF(compna(i) == 'acrylic-acid'.AND.compna(j) == 'co2')THEN + kij(i,j) = -0.1 + ELSE IF(compna(i) == 'bmim'.AND.compna(j) == 'hydrogen')THEN + lij(i,j) = 0.55 !!!!! Lij not kij !!!! + ELSE IF(compna(i) == 'bf4'.AND.compna(j) == 'hydrogen')THEN + lij(i,j) = 0.55 !!!!! Lij not kij !!!! + ELSE IF(compna(i) == 'h2o'.AND.compna(j) == 'butane')THEN !K.R.Hall FPE 2007 254 112-125 kij=0.1850 + kij(i,j) = -0.07 + ELSE IF(compna(i) == 'h2o'.AND.compna(j) == '1-butanol')THEN + kij(i,j) = -0.12 + ELSE IF(compna(i) == 'h2o'.AND.compna(j) == 'aniline')THEN + kij(i,j) = 0.0 + ELSE IF(compna(i) == 'h2o'.AND.compna(j) == 'methanol') THEN + kij(i,j) = -0.02 + ELSE IF(compna(i) == 'h2o'.AND.compna(j) == 'ethanol') THEN + kij(i,j) = -0.027 + ELSE IF(compna(i) == 'h2o'.AND.compna(j) == 'styrene') THEN + kij(i,j) = 0.1 + ELSE IF(compna(i) == 'h2o'.AND.compna(j) == 'propyl-ethanoate') THEN + kij(i,j) = -0.205 + ELSE IF(compna(i) == 'h2o'.AND.compna(j) == 'ethyl-propanoate') THEN + kij(i,j) = 0.0 + ELSE IF(compna(i) == 'h2o'.AND.compna(j) == '1-pentanol') THEN + kij(i,j) = 0.0165 + ! kij(i,j) = 0.0294 + ! kij(i,j) = -0.082 + ELSE IF(compna(i) == 'h2o'.AND.compna(j) == 'methane') THEN + ! kij(i,j) = +0.06 + kij(i,j) = -0.08 + ELSE IF(compna(i) == 'h2o'.AND.compna(j) == 'propane') THEN + kij(i,j) = 0.02 + ELSE IF(compna(i) == 'h2o'.AND.compna(j) == 'hexane') THEN + kij(i,j) = -0.02 + ELSE IF(compna(i) == 'h2o'.AND.compna(j) == 'acetic-acid') THEN + kij(i,j) = -0.0 + ELSE IF(compna(i) == 'h2o'.AND.compna(j) == 'co2') THEN + if (pol == 0) kij(i,j) = 0.0030625 ! for T=50C, according to X.Tang + stop ! very T-dependent + ELSE IF(compna(i) == 'toluene'.AND.compna(j) == 'acetic-acid') THEN + kij(i,j) = -0.1 + ELSE IF(compna(i) == 'caproic-acid'.AND.compna(j) == 'cyclohexane') THEN + kij(i,j) = 0.041531 + ELSE IF(compna(i) == '1-octanol'.AND.compna(j) == 'h2o')THEN + kij(i,j) = 0.07 + ELSE IF(compna(i) == 'acetone'.AND.compna(j) == 'benzene')THEN + kij(i,j) = 0.02132466 ! PC-SAFT + ! kij(i,j) = 0.01495148 ! PCP-SAFT + ! kij(i,j) = -0.00735575 ! PCP-SAFT but non-polar benzene + ELSE IF(compna(i) == '1-propanol'.AND.compna(j) == 'benzene')THEN + kij(i,j) = 0.02017 + ELSE IF(compna(i) == '2-propanol'.AND.compna(j) == 'benzene')THEN + kij(i,j) = 0.021386 + ELSE IF(compna(i) == '1-pentanol'.AND.compna(j) == 'benzene')THEN + kij(i,j) = 0.0129638671875 + ELSE IF(compna(i) == 'CH2F2' .AND. compna(j) == 'co2') THEN + kij(i,j) = 2.2548828125E-2 + ELSE IF(compna(i) == 'dmso' .AND. compna(j) == 'co2') THEN + kij(i,j) = -0.00 + ELSE IF(compna(i) == 'dmf'.AND.compna(j) == 'h2o')THEN + kij(i,j) = -0.0 + ELSE IF(compna(i) == 'decane'.AND.compna(j) == 'h2o')THEN + kij(i,j) = 0.11 + ELSE IF(compna(i) == '11difluoroethane'.AND.compna(j) == 'HF')THEN + kij(i,j) = 0.032 ! association: eps_kij = 0.16 + ELSE IF(compna(i) == '11difluoroethane'.AND.compna(j) == 'co2')THEN + kij(i,j) = -0.004 ! PCP-SAFT (taken from simulation) + ELSE IF(compna(i) == 'difluoromethane'.AND.compna(j) == 'HF')THEN + kij(i,j) = -0.02 + ELSE IF(compna(i) == 'naphthalene'.AND.compna(j) == 'co2')THEN + kij(i,j) = 0.137 ! angepasst an SVLE-Linie (tradition.CO2-Parameter) + kij(i,j) = 0.09 ! angepasst an SVLE-Linie (tradition.CO2-Parameter) + ELSE IF(compna(i) == 'pg2'.AND.compna(j) == 'methanol')THEN + kij(i,j) = 0.03 + ELSE IF(compna(i) == 'pg2'.AND.compna(j) == 'co2')THEN + ! kij(i,j) = 0.05 + ELSE IF(compna(i) == 'PCH5'.AND.compna(j) == 'co2')THEN + ! kij(i,j) = -0.047 + kij(i,j) = +0.055 + ! kij(i,j) = +0.036 + ELSE + END IF + kij(j,i) = kij(i,j) + lij(j,i) = -lij(i,j) + + END DO +END DO + +END SUBROUTINE pcsaft_par + + +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! SUBROUTINE init_vars +! +! This subroutine writes variables from an array "val_init" to the +! system-variables. Those variables +! include some specifications but also some starting values for a +! phase equilibrium calculation. (val_init stands for 'initial value') + +! The array comprises the following elements +! element 0 density of third phase +! element 1 density of first phase +! element 2 density of second phase +! element 3 temperature [K] +! element 4 pressure [Pa] +! element 5,..(5+NCOMP) mole-fraction of comp. i in log. from (phase 1) +! element ... mole-fraction of comp. i in log. from (phase 2) +! element ... mole-fraction of comp. i in log. from (phase 3) +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! + SUBROUTINE init_vars +! + USE BASIC_VARIABLES + IMPLICIT NONE +! + INTEGER :: i, ph +! ---------------------------------------------------------------------- + +densta(3)=val_init(0) +densta(1)=val_init(1) +densta(2)=val_init(2) +t = val_init(3) +p = val_init(4) +DO ph = 1,nphas + DO i = 1,ncomp + lnx(ph,i) = val_init(4+i+(ph-1)*ncomp) + END DO +END DO + +END SUBROUTINE init_vars + + +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! SUBROUTINE converged +! +! Once a converged solution for an equilibrium calculation is found, +! this subroutine writes variables to an array "val_conv". +! (= short for converged values) +! The array comprises the following elements +! element 0 density of third phase +! element 1 density of first phase +! element 2 density of second phase +! element 3 temperature [K] +! element 4 pressure [Pa] +! element 5,..(4+NCOMP) mole-fraction of comp. i in log. from (phase 1) +! element ... mole-fraction of comp. i in log. from (phase 2) +! element ... mole-fraction of comp. i in log. from (phase 3) +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! + SUBROUTINE converged +! + USE BASIC_VARIABLES + IMPLICIT NONE +! + INTEGER :: i, ph +! ---------------------------------------------------------------------- + +val_conv(0) = dense(3) +val_conv(1) = dense(1) +val_conv(2) = dense(2) +val_conv(3) = t +val_conv(4) = p +DO ph = 1,nphas + DO i = 1,ncomp + val_conv(4+i+(ph-1)*ncomp) = lnx(ph,i) + END DO +END DO + +END SUBROUTINE converged + +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! SUBROUTINE PERTURBATION_PARAMETER +! +! calculates density-independent parameters of the equation of state. +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! + SUBROUTINE PERTURBATION_PARAMETER +! + USE PARAMETERS, ONLY: PI, KBOL, RGAS, NAV, TAU + USE EOS_VARIABLES + USE EOS_CONSTANTS + IMPLICIT NONE +! +! --- local variables -------------------------------------------------- + INTEGER :: i, j, k, l, m, no + LOGICAL :: assoc, qudpole, dipole + REAL :: m_mean + REAL, DIMENSION(nc) :: v00, v0, d00, u + REAL, DIMENSION(nc,nc,nsite,nsite) :: eps_hb + REAL, DIMENSION(nc,nc) :: kap_hb + REAL :: zmr, nmr + REAL :: eps_kij, k_kij +! ---------------------------------------------------------------------- + +! ---------------------------------------------------------------------- +! pure component parameters +! ---------------------------------------------------------------------- +DO i = 1, ncomp + u(i) = parame(i,3) * (1.0 + parame(i,4)/t) + mseg(i) = parame(i,1) + IF (eos == 0) THEN + v00(i) = parame(i,2) + v0(i) = v00(i)*(1.0-0.12*EXP(-3.0*parame(i,3)/t))**3 + d00(i) = (1.d30/1.d6 *tau *v00(i)*6.0/PI /NAV)**(1.0/3.0) + dhs(i) = d00(i)*(1.0-0.12*EXP(-3.0*parame(i,3)/t)) + ELSE + dhs(i) = parame(i,2)*(1.0-0.12*EXP(-3.0*parame(i,3)/t)) + d00(i) = parame(i,2) + END IF +END DO + + +! ---------------------------------------------------------------------- +! combination rules +! ---------------------------------------------------------------------- +DO i = 1, ncomp + DO j = 1, ncomp + sig_ij(i,j) = 0.5 * ( d00(i) + d00(j) ) + uij(i,j) = ( 1.0 - kij(i,j) ) * ( u(i)*u(j) )**0.5 + vij(i,j) = ( 0.5*( v0(i)**(1.0/3.0) + v0(j)**(1.0/3.0) ) )**3 + END DO +END DO + + +! ---------------------------------------------------------------------- +! abbreviations +! ---------------------------------------------------------------------- +z0t = PI / 6.0 * SUM( x(1:ncomp) * mseg(1:ncomp) ) +z1t = PI / 6.0 * SUM( x(1:ncomp) * mseg(1:ncomp) * dhs(1:ncomp) ) +z2t = PI / 6.0 * SUM( x(1:ncomp) * mseg(1:ncomp) * dhs(1:ncomp)**2 ) +z3t = PI / 6.0 * SUM( x(1:ncomp) * mseg(1:ncomp) * dhs(1:ncomp)**3 ) + +m_mean = z0t/(PI/6.0) + +DO i = 1, ncomp + DO j = 1, ncomp + dij_ab(i,j) = dhs(i)*dhs(j) / ( dhs(i) + dhs(j) ) + END DO +END DO + +! ---------------------------------------------------------------------- +! dispersion term parameters for chain molecules +! ---------------------------------------------------------------------- +DO m = 0, 6 + apar(m) = ap(m,1) + (1.0-1.0/m_mean)*ap(m,2) & + + (1.0-1.0/m_mean)*(1.0-2.0/m_mean)*ap(m,3) + bpar(m) = bp(m,1) + (1.0-1.0/m_mean)*bp(m,2) & + + (1.0-1.0/m_mean)*(1.0-2.0/m_mean)*bp(m,3) +END DO + + +! ---------------------------------------------------------------------- +! van der Waals mixing rules for perturbation terms +! ---------------------------------------------------------------------- +order1 = 0.0 +order2 = 0.0 +DO i = 1, ncomp + DO j = 1, ncomp + order1 = order1 + x(i)*x(j)* mseg(i)*mseg(j)*sig_ij(i,j)**3 * uij(i,j)/t + order2 = order2 + x(i)*x(j)* mseg(i)*mseg(j)*sig_ij(i,j)**3 * (uij(i,j)/t)**2 + END DO +END DO + + +! ---------------------------------------------------------------------- +! SAFT parameters +! ---------------------------------------------------------------------- +IF (eos == 0) THEN + zmr = 0.0 + nmr = 0.0 + DO i = 1, ncomp + DO j = 1, ncomp + zmr = zmr + x(i)*x(j)*mseg(i)*mseg(j)*vij(i,j)*uij(i,j) + nmr = nmr + x(i)*x(j)*mseg(i)*mseg(j)*vij(i,j) + END DO + END DO + um = zmr / nmr +END IF + + + +! ---------------------------------------------------------------------- +! association and polar parameters +! ---------------------------------------------------------------------- +assoc = .false. +qudpole = .false. +dipole = .false. +DO i = 1, ncomp + IF (NINT(parame(i,12)) /= 0) assoc = .true. + IF (parame(i,7) /= 0.0) qudpole = .true. + IF (parame(i,6) /= 0.0) dipole = .true. +END DO + +! --- dipole and quadrupole constants ---------------------------------- +IF (qudpole) CALL qq_const ( qqp2, qqp3, qqp4 ) +IF (dipole) CALL dd_const ( ddp2, ddp3, ddp4 ) +IF (dipole .AND. qudpole) CALL dq_const ( dqp2, dqp3, dqp4 ) + + +! --- TPT-1-association parameters ------------------------------------- +IF (assoc) THEN + + eps_kij = 0.0 + k_kij = 0.0 + + DO i = 1, ncomp + IF (NINT(parame(i,12)) /= 0) THEN + nhb_typ(i) = NINT(parame(i,12)) + kap_hb(i,i) = parame(i,13) + no = 0 + DO j = 1, nhb_typ(i) + DO k = 1, nhb_typ(i) + eps_hb(i,i,j,k) = parame(i,(14+no)) + no=no+1 + END DO + END DO + DO j = 1, nhb_typ(i) + nhb_no(i,j) = parame(i,(14+no)) + no=no+1 + END DO + ELSE + nhb_typ(i) = 0 + kap_hb(i,i)= 0.0 + DO k = 1, nsite + DO l = 1, nsite + eps_hb(i,i,k,l) = 0.0 + END DO + END DO + END IF + END DO + + DO i = 1, ncomp + DO j = 1, ncomp + IF (i /= j .AND. (nhb_typ(i) /= 0 .AND. nhb_typ(j) /= 0)) THEN + kap_hb(i,j)= (kap_hb(i,i)*kap_hb(j,j))**0.5 & + *((parame(i,2)*parame(j,2))**3 )**0.5 & + /(0.5*(parame(i,2)+parame(j,2)))**3 + kap_hb(i,j)= kap_hb(i,j)*(1.0-k_kij) + DO k = 1, nhb_typ(i) + DO l = 1, nhb_typ(j) + IF (k /= l) THEN + eps_hb(i,j,k,l) = (eps_hb(i,i,k,l)+eps_hb(j,j,l,k))/2.0 + eps_hb(i,j,k,l) = eps_hb(i,j,k,l)*(1.0-eps_kij) + END IF + END DO + END DO + END IF + END DO + END DO + IF (nhb_typ(1) == 3) THEN +! write(*,*)'eps_hb manuell eingegeben' + eps_hb(1,2,3,1) = 0.5*(eps_hb(1,1,3,1)+eps_hb(2,2,1,2)) + eps_hb(2,1,1,3) = eps_hb(1,2,3,1) + END IF + IF (nhb_typ(2) == 3) THEN + eps_hb(2,1,3,1) = 0.5*(eps_hb(2,2,3,1)+eps_hb(1,1,1,2)) + eps_hb(1,2,1,3) = eps_hb(2,1,3,1) + END IF + + DO i = 1, ncomp + DO k = 1, nhb_typ(i) + DO j = 1, ncomp + DO l = 1, nhb_typ(j) + ass_d(i,j,k,l) = kap_hb(i,j) *sig_ij(i,j)**3 *(EXP(eps_hb(i,j,k,l)/t)-1.0) + END DO + END DO + END DO + END DO + +END IF + +END SUBROUTINE PERTURBATION_PARAMETER + + + + +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! SUBROUTINE OUTPUT +! +! The purpose of this subroutine is obvious. +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! + SUBROUTINE OUTPUT +! + USE BASIC_VARIABLES + IMPLICIT NONE +! +! ---------------------------------------------------------------------- + INTEGER :: i + CHARACTER (LEN=4) :: t_ind + CHARACTER (LEN=4) :: p_ind + CHARACTER (LEN=4) :: char_ncomp + REAL :: density(np),w(np,nc) +! ---------------------------------------------------------------------- + + CALL si_dens (density,w) + + IF (u_in_p == 1.E5) THEN + p_ind = ' bar' + ELSE IF (u_in_p == 1.E2) THEN + p_ind = 'mbar' + ELSE IF (u_in_p == 1.E6) THEN + p_ind = ' MPa' + ELSE IF (u_in_p == 1.E3) THEN + p_ind = ' kPa' + ELSE + p_ind = ' Pa' + END IF + IF (u_in_t == 273.15) THEN + t_ind = ' C' + ELSE + t_ind = ' K' + END IF + + WRITE(*,*) '--------------------------------------------------' + WRITE (char_ncomp,'(I3)') ncomp + WRITE(*,'(t2,a,f7.2,2a,f9.4,a)') ' T =',t-u_out_t,t_ind & + ,' P =',p/u_out_p,p_ind + WRITE(*,'(t15,4(a12,1x),10x,a)') (compna(i),i=1,ncomp) + WRITE(*,'(2x,a,'//char_ncomp//'(g13.6,1x))') 'PHASE I w', (w(1,i),i=1,ncomp) + WRITE(*,'(2x,a,'//char_ncomp//'(g13.6,1x))') 'PHASE II w', (w(2,i),i=1,ncomp) + WRITE(*,'(2x,a,'//char_ncomp//'(g13.6,1x))') 'PHASE I x', (EXP(lnx(1,i)),i=1,ncomp) + WRITE(*,'(2x,a,'//char_ncomp//'(g13.6,1x))') 'PHASE II x', (EXP(lnx(2,i)),i=1,ncomp) + WRITE(*,'(2x,a,2(g13.6,1x))') 'DENSITY ', density(1),density(2) + + !-----output to files-------------------------------------------------- + IF (ncomp == 1) THEN + WRITE (40,'(7(2x,f18.8))') t-u_out_t, p/u_out_p, & + density(1), density(2),h_lv,cpres(1),cpres(2) + ! & ,(enthal(2)-enthal(1))/mm(1) + ! WRITE (40,'(4(2x,f15.8))') t, p, 0.3107*dense(1) + ! & /0.1617*(0.689+0.311*(T/1.328)**0.3674),0.3107 + ! & *dense(2)/0.1617*(0.689+0.311*(T/1.328)**0.3674) + ELSE IF (ncomp == 2) THEN + WRITE (40,'(12(2x,G15.8))') 1.0-xi(1,1),1.0-xi(2,1), & + w(1,1),w(2,1),t-u_out_t, p/u_out_p, density(1),density(2) & + ,enthal(1),enthal(2),cpres(1),cpres(2) + ELSE IF (ncomp == 3) THEN + WRITE (40,'(10(2x,f15.8))') xi(1,1),xi(1,2),xi(1,3),xi(2,1),xi(2,2), & + xi(2,3),t-u_out_t, p/u_out_p, density(1),density(2) + END IF + + END SUBROUTINE OUTPUT + + + +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! SUBROUTINE neutr_charge +! +! This subroutine is called for electrolye solutions, where a +! neutral overall-charge has to be enforced in all phases. The basic +! philosophy is similar to the above described routine X_SUMMATION. +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! + SUBROUTINE neutr_charge(i) +! + USE BASIC_VARIABLES + IMPLICIT NONE +! +! ---------------------------------------------------------------------- + INTEGER, INTENT(IN) :: i +! +! ---------------------------------------------------------------------- + INTEGER :: comp_e, ph_e + REAL :: sum_c + CHARACTER (LEN=2) :: phasno + CHARACTER (LEN=2) :: compno +! ---------------------------------------------------------------------- + +phasno = sum_rel(i)(2:2) +READ(phasno,*) ph_e +compno = sum_rel(i)(3:3) +READ(compno,*) comp_e + +sum_c = 0.0 +write (*,*) 'there must be an error in neutr_charge' +stop +! there is an error in the following passage. The index i is an +! argument to this subroutine - I guess it is INTENT(IN), so the +! index in the following loop can not be i. +! +! I have commented the loop until I check the code. +!DO i=1,ncomp +! IF ( comp_e /= i .AND. parame(i,10) /= 0.0) & +! sum_c = sum_c + xi(ph_e,i)*parame(i,10) +!END DO + +xi(ph_e,comp_e) = - sum_c +IF (xi(ph_e,comp_e) < 0.0) xi(ph_e,comp_e)=0.0 +IF (xi(ph_e,comp_e) /= 0.0) THEN + lnx(ph_e,comp_e) = LOG(xi(ph_e,comp_e)) +ELSE + lnx(ph_e,comp_e) = -100000.0 +END IF + +! xi(2,1) = xi(2,2) +! IF (xi(2,1).NE.0.0) lnx(2,1) = LOG(xi(2,1)) + +END SUBROUTINE neutr_charge + + +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! + SUBROUTINE flash_sum +! + USE BASIC_VARIABLES + IMPLICIT NONE +! + INTEGER :: i, j, ph_i, phase1, phase2 +! ---------------------------------------------------------------------- + +phase1=0 +phase2=0 +DO j=1,ncomp + IF (it(j)(2:2) == '1') phase1=phase1+1 + IF (it(j)(2:2) == '2') phase2=phase2+1 +END DO + +IF (phase1 == ncomp-1) THEN + ph_i = 1 +ELSE IF (phase2 == ncomp-1) THEN + ph_i = 2 +ELSE + WRITE (*,*) ' FLASH_SUM: undefined flash-case' + STOP +END IF + + + +IF (ph_i == 1) THEN + DO i=1,ncomp + IF (alpha > DMIN1(1.0,xif(i)/xi(1,i), & + (xif(i)-1.0)/(xi(1,i)-1.0),alpha)) THEN + WRITE (*,*) ' FLASH_SUM: exeeded 1st alpha-bound' + alpha=DMIN1(1.0,xif(i)/xi(1,i),(xif(i)-1.0)/(xi(1,i)-1.0)) + END IF + END DO + DO i=1,ncomp + xi(2,i) = ( xif(i) - alpha*xi(1,i) ) / (1.0-alpha) + IF (xi(2,i) > 0.0) THEN + lnx(2,i) = LOG(xi(2,i)) + ELSE + xi(2,i) = 0.0 + lnx(2,i) = -100000.0 + END IF + END DO +ELSE IF (ph_i == 2) THEN + DO i=1,ncomp + IF (alpha > DMAX1(0.0,(xif(i)-xi(2,i))/(1.0-xi(2,i)), & + 1.0-xif(i)/xi(2,i),alpha)) THEN + WRITE (*,*) ' FLASH_SUM: exeeded 2nd alpha-bound' + WRITE (*,*) 0.0,(xif(i)-xi(2,i))/(1.0-xi(2,i)), 1.0-xif(i)/xi(2,i) + alpha=DMAX1(0.0,(xif(i)-xi(2,i))/(1.0-xi(2,i)), 1.0-xif(i)/xi(2,i)) + END IF + END DO + DO i=1,ncomp + xi(1,i) = ( xif(i) - (1.0-alpha)*xi(2,i) ) / alpha +! write (*,*) 'x1,i',xi(1,i),xi(2,i),alpha + IF (xi(1,i) > 0.0) THEN + lnx(1,i) = LOG(xi(1,i)) + ELSE + xi(1,i) = 0.0 + lnx(1,i) = -100000.0 + END IF + END DO +END IF + +! pause + +RETURN +END SUBROUTINE flash_sum + +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! SUBROUTINE flash_alpha +! +! This subroutine calculates all molefractions of one phase +! from a component balance. What is needed for this calculation +! are all molefractions of the other phase (nphas=2, so far) +! and the phase fraction alpha. +! Alpha is calculated from the mole fraction +! of component {sum_rel(j)(3:3)}. If for example sum_rel(2)='fl3', +! then the alpha is determined from the molefraction of comp. 3 and +! all molefractions of one phase are calculated using that alpha-value. +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! + SUBROUTINE flash_alpha +! + USE BASIC_VARIABLES + IMPLICIT NONE +! +! ---------------------------------------------------------------------- + INTEGER :: i, j, comp_i, phase1, phase2 + CHARACTER (LEN=2) :: compno +! ---------------------------------------------------------------------- + + +! ---------------------------------------------------------------------- +! first calculate the phase fraction alpha from a known composition +! of component sum_rel(j)(3:3). +! ---------------------------------------------------------------------- + +DO j = 1, nphas + IF ( sum_rel(j)(1:2) == 'fl' ) THEN + compno = sum_rel(j)(3:3) + READ(compno,*) comp_i + IF ( (xi(1,comp_i)-xi(2,comp_i)) /= 0.0 ) THEN + alpha = (xif(comp_i)-xi(2,comp_i)) / (xi(1,comp_i)-xi(2,comp_i)) + write (*,*) 'flsh',(xif(comp_i)-xi(2,comp_i)),(xi(1,comp_i)-xi(2,comp_i)) + ELSE + alpha = 0.5 + WRITE (*,*) 'FLASH_ALPHA:error in calc. of phase fraction',comp_i + END IF + ! IF (alpha <= 0.0 .OR. alpha >= 1.0) WRITE(*,*) 'FLASH_ALPHA: error',alpha + IF (alpha > 1.0) alpha = 1.0 + IF (alpha < 0.0) alpha = 0.0 + END IF +END DO + +! ---------------------------------------------------------------------- +! determine which phase is fully determined by iterated molefractions (+ summation relation) +! ---------------------------------------------------------------------- +phase1 = 0 +phase2 = 0 +DO i = 1, ncomp + IF ( it(i)(2:2) == '1' ) phase1 = phase1 + 1 + IF ( it(i)(2:2) == '2' ) phase2 = phase2 + 1 +END DO +DO i = 1, ncomp + IF ( sum_rel(i)(2:2) == '1' ) phase1 = phase1 + 1 + IF ( sum_rel(i)(2:2) == '2' ) phase2 = phase2 + 1 +END DO + + +IF ( phase1 == ncomp ) THEN + ! -------------------------------------------------------------------- + ! phase 1 is defined by iterated molefractions + summation relation + ! phase 2 is determined from componennt balance (using alpha) + ! -------------------------------------------------------------------- + IF ( alpha == 1.0 ) alpha = 1.0 - 1.0E-10 + DO i=1,ncomp + xi(2,i) = ( xif(i) - alpha*xi(1,i) ) / (1.0-alpha) + IF ( xi(2,i) < 0.0 ) xi(2,i) = 0.0 + IF ( xi(2,i) > 1.0 ) xi(2,i) = 1.0 + IF ( xi(2,i) /= 0.0 ) THEN + lnx(2,i) = LOG( xi(2,i) ) + ELSE + lnx(2,i) = -100000.0 + END IF + write (*,*) 'fl_cal ph=2',i,lnx(2,i),xi(2,i) + END DO +ELSE IF ( phase2 == ncomp ) THEN + ! -------------------------------------------------------------------- + ! phase 2 is defined by iterated molefractions + summation relation + ! phase 1 is determined from componennt balance (using alpha) + ! -------------------------------------------------------------------- + DO i = 1, ncomp + xi(1,i) = ( xif(i) - (1.0-alpha)*xi(2,i) ) /alpha + IF ( xi(1,i) < 0.0 ) xi(1,i) = 0.0 + IF ( xi(1,i) > 1.0 ) xi(1,i) = 1.0 + IF ( xi(1,i) /= 0.0 ) THEN + lnx(1,i) = LOG( xi(1,i) ) + ELSE + lnx(1,i) = -100000.0 + END IF + write (*,*) 'fl_cal ph=1',i,lnx(1,i),xi(1,i),alpha + END DO +ELSE + WRITE (*,*) ' FLASH_ALPHA: undefined flash-case' + STOP +END IF + +END SUBROUTINE flash_alpha + + +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! SUBROUTINE SI_DENS (density,w) +! +! This subroutine calculates the (macroskopic) fluid-density in +! units [kg/m3] from the dimensionless density (eta=zeta3). +! Further, mass fractions are calculated from mole fractions. +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! + SUBROUTINE SI_DENS (density,w) +! + USE PARAMETERS, ONLY: pi, nav, tau + USE BASIC_VARIABLES + IMPLICIT NONE +! +! ---------------------------------------------------------------------- + REAL, INTENT(OUT) :: density(np) + REAL, INTENT(OUT) :: w(np,nc) +! +! ---------------------------------------------------------------------- + INTEGER :: i, ph + REAL :: mm_mean, rho, z3t + REAL :: dhs(nc), d00(nc), t_p, pcon, l_st +! ---------------------------------------------------------------------- + + +DO i = 1,ncomp + IF (eos == 1) THEN + dhs(i) = parame(i,2) * ( 1.0 - 0.12 *EXP( -3.0*parame(i,3)/t ) ) + ELSE IF (eos == 0) THEN + d00(i) = ( 1.E30/1.E6*tau*parame(i,2)*6.0/pi/nav )**(1.0/3.0) + dhs(i) = d00(i) * ( 1.0 - 0.12 *EXP( -3.0*parame(i,3)/t ) ) + ELSE IF (eos == 4) THEN + dhs(i) = ( 0.1617/0.3107 / ( 0.689+0.311*(t/parame(i,3)/1.328)**0.3674 ) & + / ( pi/6.0 ) )**(1.0/3.0) * parame(i,2) + ELSE IF (eos == 5.OR.eos == 6) THEN + l_st = parame(1,25) + IF (ncomp /= 1) write (*,*) ' ERROR for EOS = 5' + t_p =((34.037352+17.733741*l_st) /(1.0+0.53237307*l_st+12.860239*l_st**2 ))**0.5 + IF (l_st == 0.0) t_p = t_p/4.0 + IF (eos == 5 .AND. l_st /= 0.0) t_p = t_p/4.0*parame(1,1)**2 + t_p = t/parame(i,3)/t_p + pcon =0.5256+3.2088804*l_st**2 -3.1499114*l_st**2.5 +0.43049357*l_st**4 + dhs(i) = ( pcon/(0.67793+0.32207*(t_p)**0.3674) /(pi/6.0) )**(1.0/3.0) *parame(i,2) + ELSE IF (eos == 8) THEN + dhs(i) = parame(i,2)*(1.0+0.2977*t/parame(i,3)) & + /(1.0+0.33163*t/parame(i,3) +1.0477E-3*(t/parame(i,3))**2 ) + ELSE + write (*,*) 'define EOS in subroutine: SI_DENS' + stop + END IF +END DO + +DO ph = 1,nphas + mm_mean = 0.0 + z3t = 0.0 + DO i = 1, ncomp + mm_mean = mm_mean + xi(ph,i)*mm(i) + z3t = z3t + xi(ph,i) * parame(i,1) * dhs(i)**3 + END DO + z3t = pi/6.0 * z3t + rho = dense(ph)/z3t + density(ph) = rho * mm_mean * 1.E27 /nav + DO i = 1, ncomp + w(ph,i) = xi(ph,i) * mm(i)/mm_mean + END DO +! write (*,*) density(ph),rho,mm_mean,1.d27 /NAV +END DO + +END SUBROUTINE SI_DENS + + + +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! + REAL FUNCTION F_STABILITY ( optpara, n ) +! + USE BASIC_VARIABLES + USE STARTING_VALUES + USE EOS_VARIABLES, ONLY: dhs, PI + IMPLICIT NONE +! +! ---------------------------------------------------------------------- + INTEGER, INTENT(IN) :: n + REAL, INTENT(IN OUT) :: optpara(n) +! +! ---------------------------------------------------------------------- + INTEGER :: i, stabil + REAL :: rhoi(nc),gradterm + REAL :: fden,punish + REAL :: dens +! ---------------------------------------------------------------------- + +COMMON /stabil / stabil + +punish = 0.0 +stabil = 1 + +DO i = 1, n + IF ( optpara(i) < 0.5 ) rhoi(i) = EXP(optpara(i) ) + IF ( optpara(i) >= 0.5) rhoi(i) = EXP(0.5) +END DO + +dens = PI/6.0 * SUM( rhoi(1:ncomp) * parame(1:ncomp,1) * dhs(1:ncomp)**3 ) + +IF (dens > 0.65) THEN + punish = punish + (dens-0.65)*10000.0 + rhoi(1:n) = rhoi(1:n)*0.65/dens +END IF + +CALL fden_calc (fden, rhoi) + +gradterm = sum( grad_fd(1:n) * ( rhoi(1:n) - rhoif(1:n) ) ) + +f_stability = fden - fdenf - gradterm + punish + +! write (*,'(5G16.8)') F_STABILITY,(rhoi(i),i=1,n) +! pause + +stabil = 0 + +END FUNCTION F_STABILITY + + + + +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! SUBROUTINE p_calc (pges_transfer, zges) +! +! This subroutine serves as an iterface to the EOS-routines. The +! system pressure corresponding to given (desity,T,xi) is calculated. +! (Note: the more common interface is SUBROUTINE FUGACITY. This +! routine is only used for one-phase systems, e.g. calculation of +! virial coefficients) +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! + SUBROUTINE p_calc (pges_transfer, zges) +! + USE BASIC_VARIABLES + USE EOS_VARIABLES + IMPLICIT NONE +! +! ---------------------------------------------------------------------- + REAL, INTENT(IN OUT) :: pges_transfer + REAL, INTENT(OUT) :: zges +! ---------------------------------------------------------------------- + +IF (nphas /= 1 ) THEN + write (*,*) 'P_CALC: can only be called for single phases' + stop +ENDIF + +IF (eos < 2) THEN + + phas = 1 + eta = dense(1) + x(1:ncomp) = xi(1,1:ncomp) + + CALL PERTURBATION_PARAMETER + IF (num == 0) CALL P_EOS + IF(num == 1) CALL P_NUMERICAL + !! IF(num == 2) CALL F_EOS_RN + + pges_transfer = pges + rho = eta/z3t + zges = (pges * 1.E-30) / (kbol*t*rho) + +ELSE + write (*,*) ' SUBROUTINE P_CALC not available for cubic EOS' + stop +END IF + +END SUBROUTINE p_calc + + + +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! +SUBROUTINE ONLY_ONE_TERM_EOS_NUMERICAL ( only_term, type_of_term ) +! + USE EOS_NUMERICAL_DERIVATIVES + IMPLICIT NONE +! + character (LEN=9) :: only_term, type_of_term +! ---------------------------------------------------------------------- + + save_eos_terms(1) = ideal_gas + save_eos_terms(2) = hard_sphere + save_eos_terms(3) = chain_term + save_eos_terms(4) = disp_term + save_eos_terms(5) = hb_term + save_eos_terms(6) = LC_term + save_eos_terms(7) = branch_term + save_eos_terms(8) = II_term + save_eos_terms(9) = ID_term + + ideal_gas = 'no' + hard_sphere = 'no' + chain_term = 'no' + disp_term = 'no' + hb_term = 'no' + LC_term = 'no' + branch_term = 'no' + II_term = 'no' + ID_term = 'no' + + IF ( only_term == 'ideal_gas' ) ideal_gas = trim( adjustl( type_of_term ) ) + IF ( only_term == 'hard_sphere' ) hard_sphere = trim( adjustl( type_of_term ) ) + IF ( only_term == 'chain_term' ) chain_term = trim( adjustl( type_of_term ) ) + IF ( only_term == 'disp_term' ) disp_term = trim( adjustl( type_of_term ) ) + IF ( only_term == 'hb_term' ) hb_term = trim( adjustl( type_of_term ) ) + IF ( only_term == 'LC_term' ) LC_term = trim( adjustl( type_of_term ) ) + IF ( only_term == 'branch_term' ) branch_term = trim( adjustl( type_of_term ) ) + IF ( only_term == 'II_term' ) II_term = trim( adjustl( type_of_term ) ) + IF ( only_term == 'ID_term' ) ID_term = trim( adjustl( type_of_term ) ) + +END SUBROUTINE ONLY_ONE_TERM_EOS_NUMERICAL + + +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! +SUBROUTINE RESTORE_PREVIOUS_EOS_NUMERICAL +! + USE EOS_NUMERICAL_DERIVATIVES + IMPLICIT NONE +! +! ---------------------------------------------------------------------- + ideal_gas = trim( adjustl( save_eos_terms(1) ) ) + hard_sphere = trim( adjustl( save_eos_terms(2) ) ) + chain_term = trim( adjustl( save_eos_terms(3) ) ) + disp_term = trim( adjustl( save_eos_terms(4) ) ) + hb_term = trim( adjustl( save_eos_terms(5) ) ) + LC_term = trim( adjustl( save_eos_terms(6) ) ) + branch_term = trim( adjustl( save_eos_terms(7) ) ) + II_term = trim( adjustl( save_eos_terms(8) ) ) + ID_term = trim( adjustl( save_eos_terms(9) ) ) + +END SUBROUTINE RESTORE_PREVIOUS_EOS_NUMERICAL + + + + diff --git a/applications/PUfoam/MoDeNaModels/PolymerDensity/src/DetailedModelCode/main.f90 b/applications/PUfoam/MoDeNaModels/PolymerDensity/src/DetailedModelCode/main.f90 new file mode 100644 index 000000000..467d68829 --- /dev/null +++ b/applications/PUfoam/MoDeNaModels/PolymerDensity/src/DetailedModelCode/main.f90 @@ -0,0 +1,121 @@ + +!> +!!THIS CODE WAS WRITTEN AT +!!UNIVERSITY OF STUTTGART, +!!INSTITUTE OF TECHNICAL THERMODYNAMICS AND THERMAL PROCESS ENGINEERING +!!BY +!!JOACHIM GROSS AND JONAS MAIRHOFER +!! + + +!>WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +!! This program calculates densities of a liquid phase which is in equilibrium with a gas phase +!! using the PC-SAFT equation of state. +!! The input parameters are read from the file "in.txt" which has to +!! be in the same directory as the executable. +!! +!! The input file must have the following format: +!! Line1: Value of temperature in Kelvin +!! Line2: Number of components present in the system (ncomp) +!! Line3 Name of component 1 +!! ... +!! Line3+ncomp Name of component ncomp +!! Line3+ncomp+1 Molar (overall) fraction of component 1 +!! ... +!! Line3+2ncomp Molar (overall) fraction of component ncomp +!! +!! For a binary system, these molar fractions are only treated as an initial guess and may be set to e.g. 0. +!! +!! So far, pressure is set to 1bar in all calculaions +!! +!! +!!If you would like to use this code in your work, please cite the +!!following publications: +!! +!!Gross, Joachim, and Gabriele Sadowski. "Perturbed-chain SAFT: An equation of state based on a perturbation theory for chain molecules." Industrial & engineering chemistry research 40.4 (2001): 1244-1260. +!!Gross, Joachim, and Gabriele Sadowski. "Application of the perturbed-chain SAFT equation of state to associating systems." Industrial & engineering chemistry research 41.22 (2002): 5510-5515. +!!Gross, Joachim, and Jadran Vrabec. "An equation‐of‐state contribution for polar components: Dipolar molecules." AIChE journal 52.3 (2006): 1194-1204. +!! +!!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW + + +PROGRAM PC_SAFT +! +! ---------------------------------------------------------------------- + USE BASIC_VARIABLES + USE EOS_CONSTANTS + USE DFT_MODULE + USE EOS_VARIABLES!, ONLY: dd_term, qq_term, dq_term + IMPLICIT NONE + +!> ---------------------------------------------------------------------- +!!Variables +!! ---------------------------------------------------------------------- + + REAL :: tc,pc,chemPot_total(nc) + REAL :: rhob(2,0:nc),density(np) + CHARACTER (LEN=50) :: filename + INTEGER :: compID,i + REAL :: cif(nc) + +!> ---------------------------------------------------------------------- +!!Read information from inputfile "in.txt" +!! ---------------------------------------------------------------------- + + filename='./in.txt' + CALL file_open(filename,77) + READ (77,*) t + READ (77,*) ncomp ! read number of components in the system + Do i = 1,ncomp ! read component names + READ (77,*) compna(i) + End Do + Do i = 1,ncomp ! read component overall molar concentrations + READ (77,*) xif(i) + End Do + + + + !calculate molar fractions from molar concentrations + !xif(1:ncomp) = cif(1:ncomp) / sum(cif(1:ncomp)) + + + +!> ---------------------------------------------------------------------- +!!General simulation set up +!! ---------------------------------------------------------------------- + + num = 1 ! (num=0: using analytical derivatives of EOS) + ! (num=1: using numerical derivatives of EOS) + ! (num=2: White's renormalization group theory) + IF ( num /= 0 ) CALL SET_DEFAULT_EOS_NUMERICAL + + + eos = 1 + pol = 1 + + p = 1.000e05 + + CALL para_input ! retriev pure comp. parameters + + ensemble_flag = 'tp' ! this specifies, whether the eos-subroutines + ! are executed for constant 'tp' or for constant 'tv' + + +!> ---------------------------------------------------------------------- +!!Start phase equilibrium calculation +!! ---------------------------------------------------------------------- + + CALL EOS_CONST (ap, bp, dnm) + + dd_term = 'GV' ! dipole-dipole term of Gross & Vrabec (2006) + qq_term = 'JG' ! quadrupole-quadrupole term of Gross (2005) + dq_term = 'VG' ! dipole-quadrupole term of Vrabec & Gross (2008) + + + + CALL VLE_MIX(rhob,density,chemPot_total,compID) + + +END PROGRAM PC_SAFT + + diff --git a/applications/PUfoam/MoDeNaModels/PolymerDensity/src/DetailedModelCode/makefile b/applications/PUfoam/MoDeNaModels/PolymerDensity/src/DetailedModelCode/makefile new file mode 100644 index 000000000..cc3271c6d --- /dev/null +++ b/applications/PUfoam/MoDeNaModels/PolymerDensity/src/DetailedModelCode/makefile @@ -0,0 +1,31 @@ + + +#Source files +SOURCE = modules.f90 \ + module_solve_nonlinear.f90 \ + getting_started_subroutines.f90 \ + Numeric_subroutines.f90 \ + VLE_subroutines.f90 \ + VLE_main.f90\ + main.f90 \ + + + + +#Object files +OBJECT = $(SOURCE:%.f90=%.o) + + + +#define target for non-PETSc files +%.o: %.f90 + gfortran -c -fdefault-real-8 $< -o $@ + +EOS: $(OBJECT) + gfortran -o PCSAFT_Density $(OBJECT) + +clean: + rm *.o *.mod + + + diff --git a/applications/PUfoam/MoDeNaModels/PolymerDensity/src/DetailedModelCode/module_solve_nonlinear.f90 b/applications/PUfoam/MoDeNaModels/PolymerDensity/src/DetailedModelCode/module_solve_nonlinear.f90 new file mode 100644 index 000000000..a4582bc27 --- /dev/null +++ b/applications/PUfoam/MoDeNaModels/PolymerDensity/src/DetailedModelCode/module_solve_nonlinear.f90 @@ -0,0 +1,1623 @@ + +MODULE Solve_NonLin + +! Corrections to FUNCTION Enorm - 28 November 2003 + +IMPLICIT NONE +INTEGER, PARAMETER :: dp = SELECTED_REAL_KIND(14, 60) +PRIVATE +PUBLIC :: hbrd, hybrd + + +CONTAINS + + +SUBROUTINE hbrd(fcn, n, x, fvec, epsfcn, tol, info, diag) + +! Code converted using TO_F90 by Alan Miller +! Date: 2003-07-15 Time: 13:27:42 + +INTEGER, INTENT(IN) :: n +REAL (dp), INTENT(IN OUT) :: x(n) +REAL (dp), INTENT(IN OUT) :: fvec(n) +REAL (dp), INTENT(IN) :: epsfcn +REAL (dp), INTENT(IN) :: tol +INTEGER, INTENT(OUT) :: info +REAL (dp), INTENT(OUT) :: diag(n) + +! EXTERNAL fcn +INTERFACE + SUBROUTINE FCN(N, X, FVEC, IFLAG) + IMPLICIT NONE + INTEGER, PARAMETER :: dp = SELECTED_REAL_KIND(14, 60) + INTEGER, INTENT(IN) :: n + REAL (dp), INTENT(IN) :: x(n) + REAL (dp), INTENT(OUT) :: fvec(n) + INTEGER, INTENT(IN OUT) :: iflag + END SUBROUTINE FCN +END INTERFACE + +!> ********** +!! SUBROUTINE HBRD +!! THE PURPOSE OF HBRD IS TO FIND A ZERO OF A SYSTEM OF N NONLINEAR +!! FUNCTIONS IN N VARIABLES BY A MODIFICATION OF THE POWELL HYBRID METHOD. +!! THIS IS DONE BY USING THE MORE GENERAL NONLINEAR EQUATION SOLVER HYBRD. +!! THE USER MUST PROVIDE A SUBROUTINE WHICH CALCULATES THE FUNCTIONS. +!! THE JACOBIAN IS THEN CALCULATED BY A FORWARD-DIFFERENCE APPROXIMATION. +!! THE SUBROUTINE STATEMENT IS +!! SUBROUTINE HBRD(N, X, FVEC, EPSFCN, TOL, INFO, WA, LWA) +!! WHERE +!! FCN IS THE NAME OF THE USER-SUPPLIED SUBROUTINE WHICH CALCULATES +!! THE FUNCTIONS. FCN MUST BE DECLARED IN AN EXTERNAL STATEMENT +!! IN THE USER CALLING PROGRAM, AND SHOULD BE WRITTEN AS FOLLOWS. +!! SUBROUTINE FCN(N, X, FVEC, IFLAG) +!! INTEGER N,IFLAG +!! REAL X(N),FVEC(N) +!! ---------- +!! CALCULATE THE FUNCTIONS AT X AND RETURN THIS VECTOR IN FVEC. +!! --------- +!! RETURN +!! END +!! THE VALUE OF IFLAG NOT BE CHANGED BY FCN UNLESS +!! THE USER WANTS TO TERMINATE THE EXECUTION OF HBRD. +!! IN THIS CASE SET IFLAG TO A NEGATIVE INTEGER. +!! N IS A POSITIVE INTEGER INPUT VARIABLE SET TO THE NUMBER +!! OF FUNCTIONS AND VARIABLES. +!! X IS AN ARRAY OF LENGTH N. ON INPUT X MUST CONTAIN AN INITIAL +!! ESTIMATE OF THE SOLUTION VECTOR. ON OUTPUT X CONTAINS THE +!! FINAL ESTIMATE OF THE SOLUTION VECTOR. +!! FVEC IS AN OUTPUT ARRAY OF LENGTH N WHICH CONTAINS +!! THE FUNCTIONS EVALUATED AT THE OUTPUT X. +!! EPSFCN IS AN INPUT VARIABLE USED IN DETERMINING A SUITABLE STEP LENGTH +!! FOR THE FORWARD-DIFFERENCE APPROXIMATION. THIS APPROXIMATION ASSUMES +!! THAT THE RELATIVE ERRORS IN THE FUNCTIONS ARE OF THE ORDER OF EPSFCN. +!! IF EPSFCN IS LESS THAN THE MACHINE PRECISION, IT IS ASSUMED THAT THE +!! RELATIVE ERRORS IN THE FUNCTIONS ARE OF THE ORDER OF THE MACHINE +!! PRECISION. +!! TOL IS A NONNEGATIVE INPUT VARIABLE. TERMINATION OCCURS WHEN THE +!! ALGORITHM ESTIMATES THAT THE RELATIVE ERROR BETWEEN X AND THE SOLUTION +!! IS AT MOST TOL. +!! INFO IS AN INTEGER OUTPUT VARIABLE. IF THE USER HAS TERMINATED +!! EXECUTION, INFO IS SET TO THE (NEGATIVE) VALUE OF IFLAG. +!! SEE DESCRIPTION OF FCN. OTHERWISE, INFO IS SET AS FOLLOWS. +!! INFO = 0 IMPROPER INPUT PARAMETERS. +!! INFO = 1 ALGORITHM ESTIMATES THAT THE RELATIVE ERROR +!! BETWEEN X AND THE SOLUTION IS AT MOST TOL. +!! INFO = 2 NUMBER OF CALLS TO FCN HAS REACHED OR EXCEEDED 200*(N+1). +!! INFO = 3 TOL IS TOO SMALL. NO FURTHER IMPROVEMENT IN +!! THE APPROXIMATE SOLUTION X IS POSSIBLE. +!! INFO = 4 ITERATION IS NOT MAKING GOOD PROGRESS. +!! SUBPROGRAMS CALLED +!! USER-SUPPLIED ...... FCN +!! MINPACK-SUPPLIED ... HYBRD +!! ARGONNE NATIONAL LABORATORY. MINPACK PROJECT. MARCH 1980. +!! BURTON S. GARBOW, KENNETH E. HILLSTROM, JORGE J. MORE +!! Reference: +!! Powell, M.J.D. 'A hybrid method for nonlinear equations' in Numerical Methods +!! for Nonlinear Algebraic Equations', P.Rabinowitz (editor), Gordon and +!! Breach, London 1970. +!! ********** + + +INTEGER :: maxfev, ml, mode, mu, nfev, nprint +REAL (dp) :: xtol +REAL (dp), PARAMETER :: factor = 1.0_dp, zero = 0.0_dp + +info = 0 + +! CHECK THE INPUT PARAMETERS FOR ERRORS. + + +IF (n <= 0 .OR. epsfcn < zero .OR. tol < zero) GO TO 20 + +! CALL HYBRD. + +maxfev = 200*(n + 1) +xtol = tol +ml = n - 1 +mu = n - 1 +mode = 2 +nprint = 0 +CALL hybrd(fcn, n, x, fvec, xtol, maxfev, ml, mu, epsfcn, diag, mode, & + factor, nprint, info, nfev) +IF (info == 5) info = 4 +20 RETURN + +! LAST CARD OF SUBROUTINE HBRD. + +END SUBROUTINE hbrd + + + +SUBROUTINE hybrd(fcn, n, x, fvec, xtol, maxfev, ml, mu, epsfcn, diag, mode, & + factor, nprint, info, nfev) + +INTEGER, INTENT(IN) :: n +REAL (dp), INTENT(IN OUT) :: x(n) +REAL (dp), INTENT(IN OUT) :: fvec(n) +REAL (dp), INTENT(IN) :: xtol +INTEGER, INTENT(IN OUT) :: maxfev +INTEGER, INTENT(IN OUT) :: ml +INTEGER, INTENT(IN) :: mu +REAL (dp), INTENT(IN) :: epsfcn +REAL (dp), INTENT(OUT) :: diag(n) +INTEGER, INTENT(IN) :: mode +REAL (dp), INTENT(IN) :: factor +INTEGER, INTENT(IN OUT) :: nprint +INTEGER, INTENT(OUT) :: info +INTEGER, INTENT(OUT) :: nfev + +! EXTERNAL fcn +INTERFACE + SUBROUTINE FCN(N, X, FVEC, IFLAG) + IMPLICIT NONE + INTEGER, PARAMETER :: dp = SELECTED_REAL_KIND(14, 60) + INTEGER, INTENT(IN) :: n + REAL (dp), INTENT(IN) :: x(n) + REAL (dp), INTENT(OUT) :: fvec(n) + INTEGER, INTENT(IN OUT) :: iflag + END SUBROUTINE FCN +END INTERFACE + +! ********** + +! SUBROUTINE HYBRD + +! THE PURPOSE OF HYBRD IS TO FIND A ZERO OF A SYSTEM OF N NONLINEAR +! FUNCTIONS IN N VARIABLES BY A MODIFICATION OF THE POWELL HYBRID METHOD. +! THE USER MUST PROVIDE A SUBROUTINE WHICH CALCULATES THE FUNCTIONS. +! THE JACOBIAN IS THEN CALCULATED BY A FORWARD-DIFFERENCE APPROXIMATION. + +! THE SUBROUTINE STATEMENT IS + +! SUBROUTINE HYBRD(FCN, N, X, FVEC, XTOL, MAXFEV, ML, MU, EPSFCN, +! DIAG, MODE, FACTOR, NPRINT, INFO, NFEV, FJAC, +! LDFJAC, R, LR, QTF, WA1, WA2, WA3, WA4) + +! WHERE + +! FCN IS THE NAME OF THE USER-SUPPLIED SUBROUTINE WHICH CALCULATES +! THE FUNCTIONS. FCN MUST BE DECLARED IN AN EXTERNAL STATEMENT IN +! THE USER CALLING PROGRAM, AND SHOULD BE WRITTEN AS FOLLOWS. + +! SUBROUTINE FCN(N, X, FVEC, IFLAG) +! INTEGER N, IFLAG +! REAL X(N), FVEC(N) +! ---------- +! CALCULATE THE FUNCTIONS AT X AND +! RETURN THIS VECTOR IN FVEC. +! --------- +! RETURN +! END + +! THE VALUE OF IFLAG SHOULD NOT BE CHANGED BY FCN UNLESS +! THE USER WANTS TO TERMINATE EXECUTION OF HYBRD. +! IN THIS CASE SET IFLAG TO A NEGATIVE INTEGER. + +! N IS A POSITIVE INTEGER INPUT VARIABLE SET TO THE NUMBER +! OF FUNCTIONS AND VARIABLES. + +! X IS AN ARRAY OF LENGTH N. ON INPUT X MUST CONTAIN AN INITIAL +! ESTIMATE OF THE SOLUTION VECTOR. ON OUTPUT X CONTAINS THE FINAL +! ESTIMATE OF THE SOLUTION VECTOR. + +! FVEC IS AN OUTPUT ARRAY OF LENGTH N WHICH CONTAINS +! THE FUNCTIONS EVALUATED AT THE OUTPUT X. + +! XTOL IS A NONNEGATIVE INPUT VARIABLE. TERMINATION OCCURS WHEN THE +! RELATIVE ERROR BETWEEN TWO CONSECUTIVE ITERATES IS AT MOST XTOL. + +! MAXFEV IS A POSITIVE INTEGER INPUT VARIABLE. TERMINATION OCCURS WHEN +! THE NUMBER OF CALLS TO FCN IS AT LEAST MAXFEV BY THE END OF AN +! ITERATION. + +! ML IS A NONNEGATIVE INTEGER INPUT VARIABLE WHICH SPECIFIES THE +! NUMBER OF SUBDIAGONALS WITHIN THE BAND OF THE JACOBIAN MATRIX. +! IF THE JACOBIAN IS NOT BANDED, SET ML TO AT LEAST N - 1. + +! MU IS A NONNEGATIVE INTEGER INPUT VARIABLE WHICH SPECIFIES THE NUMBER +! OF SUPERDIAGONALS WITHIN THE BAND OF THE JACOBIAN MATRIX. +! IF THE JACOBIAN IS NOT BANDED, SET MU TO AT LEAST N - 1. + +! EPSFCN IS AN INPUT VARIABLE USED IN DETERMINING A SUITABLE STEP LENGTH +! FOR THE FORWARD-DIFFERENCE APPROXIMATION. THIS APPROXIMATION +! ASSUMES THAT THE RELATIVE ERRORS IN THE FUNCTIONS ARE OF THE ORDER +! OF EPSFCN. IF EPSFCN IS LESS THAN THE MACHINE PRECISION, +! IT IS ASSUMED THAT THE RELATIVE ERRORS IN THE FUNCTIONS ARE OF THE +! ORDER OF THE MACHINE PRECISION. + +! DIAG IS AN ARRAY OF LENGTH N. IF MODE = 1 (SEE BELOW), +! DIAG IS INTERNALLY SET. IF MODE = 2, DIAG MUST CONTAIN POSITIVE +! ENTRIES THAT SERVE AS MULTIPLICATIVE SCALE FACTORS FOR THE +! VARIABLES. + +! MODE IS AN INTEGER INPUT VARIABLE. IF MODE = 1, THE VARIABLES WILL BE +! SCALED INTERNALLY. IF MODE = 2, THE SCALING IS SPECIFIED BY THE +! INPUT DIAG. OTHER VALUES OF MODE ARE EQUIVALENT TO MODE = 1. + +! FACTOR IS A POSITIVE INPUT VARIABLE USED IN DETERMINING THE +! INITIAL STEP BOUND. THIS BOUND IS SET TO THE PRODUCT OF +! FACTOR AND THE EUCLIDEAN NORM OF DIAG*X IF NONZERO, OR ELSE +! TO FACTOR ITSELF. IN MOST CASES FACTOR SHOULD LIE IN THE +! INTERVAL (.1,100.). 100. IS A GENERALLY RECOMMENDED VALUE. + +! NPRINT IS AN INTEGER INPUT VARIABLE THAT ENABLES CONTROLLED +! PRINTING OF ITERATES IF IT IS POSITIVE. IN THIS CASE, +! FCN IS CALLED WITH IFLAG = 0 AT THE BEGINNING OF THE FIRST +! ITERATION AND EVERY NPRINT ITERATIONS THEREAFTER AND +! IMMEDIATELY PRIOR TO RETURN, WITH X AND FVEC AVAILABLE +! FOR PRINTING. IF NPRINT IS NOT POSITIVE, NO SPECIAL CALLS +! OF FCN WITH IFLAG = 0 ARE MADE. + +! INFO IS AN INTEGER OUTPUT VARIABLE. IF THE USER HAS +! TERMINATED EXECUTION, INFO IS SET TO THE (NEGATIVE) +! VALUE OF IFLAG. SEE DESCRIPTION OF FCN. OTHERWISE, +! INFO IS SET AS FOLLOWS. + +! INFO = 0 IMPROPER INPUT PARAMETERS. + +! INFO = 1 RELATIVE ERROR BETWEEN TWO CONSECUTIVE ITERATES +! IS AT MOST XTOL. + +! INFO = 2 NUMBER OF CALLS TO FCN HAS REACHED OR EXCEEDED MAXFEV. + +! INFO = 3 XTOL IS TOO SMALL. NO FURTHER IMPROVEMENT IN +! THE APPROXIMATE SOLUTION X IS POSSIBLE. + +! INFO = 4 ITERATION IS NOT MAKING GOOD PROGRESS, AS +! MEASURED BY THE IMPROVEMENT FROM THE LAST +! FIVE JACOBIAN EVALUATIONS. + +! INFO = 5 ITERATION IS NOT MAKING GOOD PROGRESS, AS MEASURED BY +! THE IMPROVEMENT FROM THE LAST TEN ITERATIONS. + +! NFEV IS AN INTEGER OUTPUT VARIABLE SET TO THE NUMBER OF CALLS TO FCN. + +! FJAC IS AN OUTPUT N BY N ARRAY WHICH CONTAINS THE ORTHOGONAL MATRIX Q +! PRODUCED BY THE QR FACTORIZATION OF THE FINAL APPROXIMATE JACOBIAN. + +! LDFJAC IS A POSITIVE INTEGER INPUT VARIABLE NOT LESS THAN N +! WHICH SPECIFIES THE LEADING DIMENSION OF THE ARRAY FJAC. + +! R IS AN OUTPUT ARRAY OF LENGTH LR WHICH CONTAINS THE +! UPPER TRIANGULAR MATRIX PRODUCED BY THE QR FACTORIZATION +! OF THE FINAL APPROXIMATE JACOBIAN, STORED ROWWISE. + +! LR IS A POSITIVE INTEGER INPUT VARIABLE NOT LESS THAN (N*(N+1))/2. + +! QTF IS AN OUTPUT ARRAY OF LENGTH N WHICH CONTAINS +! THE VECTOR (Q TRANSPOSE)*FVEC. + +! WA1, WA2, WA3, AND WA4 ARE WORK ARRAYS OF LENGTH N. + +! SUBPROGRAMS CALLED + +! USER-SUPPLIED ...... FCN + +! MINPACK-SUPPLIED ... DOGLEG,SPMPAR,ENORM,FDJAC1, +! QFORM,QRFAC,R1MPYQ,R1UPDT + +! FORTRAN-SUPPLIED ... ABS,MAX,MIN,MIN,MOD + +! ARGONNE NATIONAL LABORATORY. MINPACK PROJECT. MARCH 1980. +! BURTON S. GARBOW, KENNETH E. HILLSTROM, JORGE J. MORE + +! ********** + +INTEGER :: i, iflag, iter, j, jm1, l, lr, msum, ncfail, ncsuc, nslow1, & + nslow2 +INTEGER :: iwa(1) +LOGICAL :: jeval, sing +REAL (dp) :: actred, delta, epsmch, fnorm, fnorm1, pnorm, prered, & + ratio, sum, temp, xnorm +REAL (dp), PARAMETER :: one = 1.0_dp, p1 = 0.1_dp, p5 = 0.5_dp, & + p001 = 0.001_dp, p0001 = 0.0001_dp, zero = 0.0_dp + +! The following were workspace arguments +REAL (dp) :: fjac(n,n), r(n*(n+1)/2), qtf(n), wa1(n), wa2(n), & + wa3(n), wa4(n) + +! EPSMCH IS THE MACHINE PRECISION. + +epsmch = EPSILON(1.0_dp) + +info = 0 +iflag = 0 +nfev = 0 +lr = n*(n+1)/2 + +! CHECK THE INPUT PARAMETERS FOR ERRORS. + +IF (n > 0 .AND. xtol >= zero .AND. maxfev > 0 .AND. ml >= 0 .AND. mu >= & + 0 .AND. factor > zero ) THEN +IF (mode == 2) THEN + diag(1:n) = one +END IF + +! EVALUATE THE FUNCTION AT THE STARTING POINT AND CALCULATE ITS NORM. + +iflag = 1 +CALL fcn(n, x, fvec, iflag) +nfev = 1 +IF (iflag >= 0) THEN + fnorm = enorm(n, fvec) + +! DETERMINE THE NUMBER OF CALLS TO FCN NEEDED TO COMPUTE THE JACOBIAN MATRIX. + + msum = MIN(ml+mu+1,n) + +! INITIALIZE ITERATION COUNTER AND MONITORS. + + iter = 1 + ncsuc = 0 + ncfail = 0 + nslow1 = 0 + nslow2 = 0 + +! BEGINNING OF THE OUTER LOOP. + + 20 jeval = .true. + +! CALCULATE THE JACOBIAN MATRIX. + + iflag = 2 + CALL fdjac1(fcn, n, x, fvec, fjac, n, iflag, ml, mu, epsfcn, wa1, wa2) + nfev = nfev + msum + IF (iflag >= 0) THEN + +! COMPUTE THE QR FACTORIZATION OF THE JACOBIAN. + + CALL qrfac(n, n, fjac, n, .false., iwa, 1, wa1, wa2, wa3) + +! ON THE FIRST ITERATION AND IF MODE IS 1, SCALE ACCORDING +! TO THE NORMS OF THE COLUMNS OF THE INITIAL JACOBIAN. + + IF (iter == 1) THEN + IF (mode /= 2) THEN + DO j = 1, n + diag(j) = wa2(j) + IF (wa2(j) == zero) diag(j) = one + END DO + END IF + +! ON THE FIRST ITERATION, CALCULATE THE NORM OF THE SCALED X +! AND INITIALIZE THE STEP BOUND DELTA. + + wa3(1:n) = diag(1:n) * x(1:n) + xnorm = enorm(n, wa3) + delta = factor * xnorm + IF (delta == zero) delta = factor + END IF + +! FORM (Q TRANSPOSE)*FVEC AND STORE IN QTF. + + qtf(1:n) = fvec(1:n) + DO j = 1, n + IF (fjac(j,j) /= zero) THEN + sum = zero + DO i = j, n + sum = sum + fjac(i,j) * qtf(i) + END DO + temp = -sum / fjac(j,j) + DO i = j, n + qtf(i) = qtf(i) + fjac(i,j) * temp + END DO + END IF + END DO + +! COPY THE TRIANGULAR FACTOR OF THE QR FACTORIZATION INTO R. + + sing = .false. + DO j = 1, n + l = j + jm1 = j - 1 + IF (jm1 >= 1) THEN + DO i = 1, jm1 + r(l) = fjac(i,j) + l = l + n - i + END DO + END IF + r(l) = wa1(j) + IF (wa1(j) == zero) sing = .true. + END DO + +! ACCUMULATE THE ORTHOGONAL FACTOR IN FJAC. + + CALL qform(n, n, fjac, n, wa1) + +! RESCALE IF NECESSARY. + + IF (mode /= 2) THEN + DO j = 1, n + diag(j) = MAX(diag(j), wa2(j)) + END DO + END IF + +! BEGINNING OF THE INNER LOOP. + +! IF REQUESTED, CALL FCN TO ENABLE PRINTING OF ITERATES. + + 120 IF (nprint > 0) THEN + iflag = 0 + IF (MOD(iter-1, nprint) == 0) CALL fcn(n, x, fvec, iflag) + IF (iflag < 0) GO TO 190 + END IF + +! DETERMINE THE DIRECTION P. + + CALL dogleg(n, r, lr, diag, qtf, delta, wa1, wa2, wa3) + +! STORE THE DIRECTION P AND X + P. CALCULATE THE NORM OF P. + + DO j = 1, n + wa1(j) = -wa1(j) + wa2(j) = x(j) + wa1(j) + wa3(j) = diag(j) * wa1(j) + END DO + pnorm = enorm(n, wa3) + +! ON THE FIRST ITERATION, ADJUST THE INITIAL STEP BOUND. + + IF (iter == 1) delta = MIN(delta, pnorm) + +! EVALUATE THE FUNCTION AT X + P AND CALCULATE ITS NORM. + + iflag = 1 + CALL fcn(n, wa2, wa4, iflag) + nfev = nfev + 1 + IF (iflag >= 0) THEN + fnorm1 = enorm(n, wa4) + +! COMPUTE THE SCALED ACTUAL REDUCTION. + + actred = -one + IF (fnorm1 < fnorm) actred = one - (fnorm1/fnorm) ** 2 + +! COMPUTE THE SCALED PREDICTED REDUCTION. + + l = 1 + DO i = 1, n + sum = zero + DO j = i, n + sum = sum + r(l) * wa1(j) + l = l + 1 + END DO + wa3(i) = qtf(i) + sum + END DO + temp = enorm(n, wa3) + prered = zero + IF (temp < fnorm) prered = one - (temp/fnorm) ** 2 + +! COMPUTE THE RATIO OF THE ACTUAL TO THE PREDICTED REDUCTION. + + ratio = zero + IF (prered > zero) ratio = actred / prered + +! UPDATE THE STEP BOUND. + + IF (ratio < p1) THEN + ncsuc = 0 + ncfail = ncfail + 1 + delta = p5 * delta + ELSE + ncfail = 0 + ncsuc = ncsuc + 1 + IF (ratio >= p5 .OR. ncsuc > 1) delta = MAX(delta,pnorm/p5) + IF (ABS(ratio-one) <= p1) delta = pnorm / p5 + END IF + +! TEST FOR SUCCESSFUL ITERATION. + + IF (ratio >= p0001) THEN + +! SUCCESSFUL ITERATION. UPDATE X, FVEC, AND THEIR NORMS. + + DO j = 1, n + x(j) = wa2(j) + wa2(j) = diag(j) * x(j) + fvec(j) = wa4(j) + END DO + xnorm = enorm(n, wa2) + fnorm = fnorm1 + iter = iter + 1 + END IF + +! DETERMINE THE PROGRESS OF THE ITERATION. + + nslow1 = nslow1 + 1 + IF (actred >= p001) nslow1 = 0 + IF (jeval) nslow2 = nslow2 + 1 + IF (actred >= p1) nslow2 = 0 + +! TEST FOR CONVERGENCE. + + IF (delta <= xtol*xnorm .OR. fnorm == zero) info = 1 + IF (info == 0) THEN + +! TESTS FOR TERMINATION AND STRINGENT TOLERANCES. + + IF (nfev >= maxfev) info = 2 + IF (p1*MAX(p1*delta, pnorm) <= epsmch*xnorm) info = 3 + IF (nslow2 == 5) info = 4 + IF (nslow1 == 10) info = 5 + IF (info == 0) THEN + +! CRITERION FOR RECALCULATING JACOBIAN APPROXIMATION +! BY FORWARD DIFFERENCES. + + IF (ncfail /= 2) THEN + +! CALCULATE THE RANK ONE MODIFICATION TO THE JACOBIAN +! AND UPDATE QTF IF NECESSARY. + + DO j = 1, n + sum = zero + DO i = 1, n + sum = sum + fjac(i,j) * wa4(i) + END DO + wa2(j) = (sum-wa3(j)) / pnorm + wa1(j) = diag(j) * ((diag(j)*wa1(j))/pnorm) + IF (ratio >= p0001) qtf(j) = sum + END DO + +! COMPUTE THE QR FACTORIZATION OF THE UPDATED JACOBIAN. + + CALL r1updt(n, n, r, lr, wa1, wa2, wa3, sing) + CALL r1mpyq(n, n, fjac, n, wa2, wa3) + CALL r1mpyq(1, n, qtf, 1, wa2, wa3) + +! END OF THE INNER LOOP. + + jeval = .false. + GO TO 120 + END IF + +! END OF THE OUTER LOOP. + + GO TO 20 + END IF + END IF + END IF + END IF +END IF +END IF + +! TERMINATION, EITHER NORMAL OR USER IMPOSED. + +190 IF (iflag < 0) info = iflag +iflag = 0 +IF (nprint > 0) CALL fcn(n, x, fvec, iflag) +RETURN + +! LAST CARD OF SUBROUTINE HYBRD. + +END SUBROUTINE hybrd + + + +SUBROUTINE dogleg(n, r, lr, diag, qtb, delta, x, wa1, wa2) + +INTEGER, INTENT(IN) :: n +INTEGER, INTENT(IN) :: lr +REAL (dp), INTENT(IN) :: r(lr) +REAL (dp), INTENT(IN) :: diag(n) +REAL (dp), INTENT(IN) :: qtb(n) +REAL (dp), INTENT(IN) :: delta +REAL (dp), INTENT(IN OUT) :: x(n) +REAL (dp), INTENT(OUT) :: wa1(n) +REAL (dp), INTENT(OUT) :: wa2(n) + + +! ********** + +! SUBROUTINE DOGLEG + +! GIVEN AN M BY N MATRIX A, AN N BY N NONSINGULAR DIAGONAL +! MATRIX D, AN M-VECTOR B, AND A POSITIVE NUMBER DELTA, THE +! PROBLEM IS TO DETERMINE THE CONVEX COMBINATION X OF THE +! GAUSS-NEWTON AND SCALED GRADIENT DIRECTIONS THAT MINIMIZES +! (A*X - B) IN THE LEAST SQUARES SENSE, SUBJECT TO THE +! RESTRICTION THAT THE EUCLIDEAN NORM OF D*X BE AT MOST DELTA. + +! THIS SUBROUTINE COMPLETES THE SOLUTION OF THE PROBLEM +! IF IT IS PROVIDED WITH THE NECESSARY INFORMATION FROM THE +! QR FACTORIZATION OF A. THAT IS, IF A = Q*R, WHERE Q HAS +! ORTHOGONAL COLUMNS AND R IS AN UPPER TRIANGULAR MATRIX, +! THEN DOGLEG EXPECTS THE FULL UPPER TRIANGLE OF R AND +! THE FIRST N COMPONENTS OF (Q TRANSPOSE)*B. + +! THE SUBROUTINE STATEMENT IS + +! SUBROUTINE DOGLEG(N,R,LR,DIAG,QTB,DELTA,X,WA1,WA2) + +! WHERE + +! N IS A POSITIVE INTEGER INPUT VARIABLE SET TO THE ORDER OF R. + +! R IS AN INPUT ARRAY OF LENGTH LR WHICH MUST CONTAIN THE UPPER +! TRIANGULAR MATRIX R STORED BY ROWS. + +! LR IS A POSITIVE INTEGER INPUT VARIABLE NOT LESS THAN +! (N*(N+1))/2. + +! DIAG IS AN INPUT ARRAY OF LENGTH N WHICH MUST CONTAIN THE +! DIAGONAL ELEMENTS OF THE MATRIX D. + +! QTB IS AN INPUT ARRAY OF LENGTH N WHICH MUST CONTAIN THE FIRST +! N ELEMENTS OF THE VECTOR (Q TRANSPOSE)*B. + +! DELTA IS A POSITIVE INPUT VARIABLE WHICH SPECIFIES AN UPPER +! BOUND ON THE EUCLIDEAN NORM OF D*X. + +! X IS AN OUTPUT ARRAY OF LENGTH N WHICH CONTAINS THE DESIRED +! CONVEX COMBINATION OF THE GAUSS-NEWTON DIRECTION AND THE +! SCALED GRADIENT DIRECTION. + +! WA1 AND WA2 ARE WORK ARRAYS OF LENGTH N. + +! SUBPROGRAMS CALLED + +! MINPACK-SUPPLIED ... SPMPAR,ENORM + +! FORTRAN-SUPPLIED ... ABS,MAX,MIN,SQRT + +! ARGONNE NATIONAL LABORATORY. MINPACK PROJECT. MARCH 1980. +! BURTON S. GARBOW, KENNETH E. HILLSTROM, JORGE J. MORE + +! ********** +INTEGER :: i, j, jj, jp1, k, l +REAL (dp) :: alpha, bnorm, epsmch, gnorm, qnorm, sgnorm, sum, temp + +! EPSMCH IS THE MACHINE PRECISION. + +epsmch = EPSILON(1.0_dp) + +! FIRST, CALCULATE THE GAUSS-NEWTON DIRECTION. + +jj = (n*(n+1)) / 2 + 1 +DO k = 1, n + j = n - k + 1 + jp1 = j + 1 + jj = jj - k + l = jj + 1 + sum = 0.0 + IF (n >= jp1) THEN + DO i = jp1, n + sum = sum + r(l) * x(i) + l = l + 1 + END DO + END IF + temp = r(jj) + IF (temp == 0.0) THEN + l = j + DO i = 1, j + temp = MAX(temp,ABS(r(l))) + l = l + n - i + END DO + temp = epsmch * temp + IF (temp == 0.0) temp = epsmch + END IF + x(j) = (qtb(j)-sum) / temp +END DO + +! TEST WHETHER THE GAUSS-NEWTON DIRECTION IS ACCEPTABLE. + +DO j = 1, n + wa1(j) = 0.0 + wa2(j) = diag(j) * x(j) +END DO +qnorm = enorm(n, wa2) +IF (qnorm > delta) THEN + +! THE GAUSS-NEWTON DIRECTION IS NOT ACCEPTABLE. +! NEXT, CALCULATE THE SCALED GRADIENT DIRECTION. + + l = 1 + DO j = 1, n + temp = qtb(j) + DO i = j, n + wa1(i) = wa1(i) + r(l) * temp + l = l + 1 + END DO + wa1(j) = wa1(j) / diag(j) + END DO + +! CALCULATE THE NORM OF THE SCALED GRADIENT AND TEST FOR +! THE SPECIAL CASE IN WHICH THE SCALED GRADIENT IS ZERO. + + gnorm = enorm(n, wa1) + sgnorm = 0.0 + alpha = delta / qnorm + IF (gnorm /= 0.0) THEN + +! CALCULATE THE POINT ALONG THE SCALED GRADIENT +! AT WHICH THE QUADRATIC IS MINIMIZED. + + DO j = 1, n + wa1(j) = (wa1(j)/gnorm) / diag(j) + END DO + l = 1 + DO j = 1, n + sum = 0.0 + DO i = j, n + sum = sum + r(l) * wa1(i) + l = l + 1 + END DO + wa2(j) = sum + END DO + temp = enorm(n, wa2) + sgnorm = (gnorm/temp) / temp + +! TEST WHETHER THE SCALED GRADIENT DIRECTION IS ACCEPTABLE. + + alpha = 0.0 + IF (sgnorm < delta) THEN + +! THE SCALED GRADIENT DIRECTION IS NOT ACCEPTABLE. +! FINALLY, CALCULATE THE POINT ALONG THE DOGLEG +! AT WHICH THE QUADRATIC IS MINIMIZED. + + bnorm = enorm(n, qtb) + temp = (bnorm/gnorm) * (bnorm/qnorm) * (sgnorm/delta) + temp = temp - (delta/qnorm) * (sgnorm/delta) ** 2 + SQRT(( & + temp-(delta/qnorm))**2+(1.0-(delta/qnorm)**2)*(1.0-( sgnorm/delta)**2)) + alpha = ((delta/qnorm)*(1.0-(sgnorm/delta)**2)) / temp + END IF + END IF + +! FORM APPROPRIATE CONVEX COMBINATION OF THE GAUSS-NEWTON +! DIRECTION AND THE SCALED GRADIENT DIRECTION. + + temp = (1.0-alpha) * MIN(sgnorm,delta) + DO j = 1, n + x(j) = temp * wa1(j) + alpha * x(j) + END DO +END IF +RETURN +END SUBROUTINE dogleg + + +SUBROUTINE fdjac1(fcn, n, x, fvec, fjac, ldfjac, iflag, ml, mu, epsfcn, & + wa1, wa2) + +INTEGER, INTENT(IN) :: n +REAL (dp), INTENT(IN OUT) :: x(n) +REAL (dp), INTENT(IN) :: fvec(n) +INTEGER, INTENT(IN) :: ldfjac +REAL (dp), INTENT(OUT) :: fjac(ldfjac,n) +INTEGER, INTENT(IN OUT) :: iflag +INTEGER, INTENT(IN) :: ml +INTEGER, INTENT(IN) :: mu +REAL (dp), INTENT(IN) :: epsfcn +REAL (dp), INTENT(IN OUT) :: wa1(n) +REAL (dp), INTENT(OUT) :: wa2(n) + +! EXTERNAL fcn +INTERFACE + SUBROUTINE FCN(N, X, FVEC, IFLAG) + IMPLICIT NONE + INTEGER, PARAMETER :: dp = SELECTED_REAL_KIND(14, 60) + INTEGER, INTENT(IN) :: n + REAL (dp), INTENT(IN) :: x(n) + REAL (dp), INTENT(OUT) :: fvec(n) + INTEGER, INTENT(IN OUT) :: iflag + END SUBROUTINE FCN +END INTERFACE + +! ********** + +! SUBROUTINE FDJAC1 + +! THIS SUBROUTINE COMPUTES A FORWARD-DIFFERENCE APPROXIMATION TO THE N BY N +! JACOBIAN MATRIX ASSOCIATED WITH A SPECIFIED PROBLEM OF N FUNCTIONS IN N +! VARIABLES. IF THE JACOBIAN HAS A BANDED FORM, THEN FUNCTION EVALUATIONS +! ARE SAVED BY ONLY APPROXIMATING THE NONZERO TERMS. + +! THE SUBROUTINE STATEMENT IS + +! SUBROUTINE FDJAC1(FCN,N,X,FVEC,FJAC,LDFJAC,IFLAG,ML,MU,EPSFCN, +! WA1,WA2) + +! WHERE + +! FCN IS THE NAME OF THE USER-SUPPLIED SUBROUTINE WHICH CALCULATES +! THE FUNCTIONS. FCN MUST BE DECLARED IN AN EXTERNAL STATEMENT IN +! THE USER CALLING PROGRAM, AND SHOULD BE WRITTEN AS FOLLOWS. + +! SUBROUTINE FCN(N,X,FVEC,IFLAG) +! INTEGER N,IFLAG +! REAL X(N),FVEC(N) +! ---------- +! CALCULATE THE FUNCTIONS AT X AND +! RETURN THIS VECTOR IN FVEC. +! ---------- +! RETURN +! END + +! THE VALUE OF IFLAG SHOULD NOT BE CHANGED BY FCN UNLESS +! THE USER WANTS TO TERMINATE EXECUTION OF FDJAC1. +! IN THIS CASE SET IFLAG TO A NEGATIVE INTEGER. + +! N IS A POSITIVE INTEGER INPUT VARIABLE SET TO THE NUMBER +! OF FUNCTIONS AND VARIABLES. + +! X IS AN INPUT ARRAY OF LENGTH N. + +! FVEC IS AN INPUT ARRAY OF LENGTH N WHICH MUST CONTAIN THE +! FUNCTIONS EVALUATED AT X. + +! FJAC IS AN OUTPUT N BY N ARRAY WHICH CONTAINS THE +! APPROXIMATION TO THE JACOBIAN MATRIX EVALUATED AT X. + +! LDFJAC IS A POSITIVE INTEGER INPUT VARIABLE NOT LESS THAN N +! WHICH SPECIFIES THE LEADING DIMENSION OF THE ARRAY FJAC. + +! IFLAG IS AN INTEGER VARIABLE WHICH CAN BE USED TO TERMINATE +! THE EXECUTION OF FDJAC1. SEE DESCRIPTION OF FCN. + +! ML IS A NONNEGATIVE INTEGER INPUT VARIABLE WHICH SPECIFIES +! THE NUMBER OF SUBDIAGONALS WITHIN THE BAND OF THE +! JACOBIAN MATRIX. IF THE JACOBIAN IS NOT BANDED, SET +! ML TO AT LEAST N - 1. + +! EPSFCN IS AN INPUT VARIABLE USED IN DETERMINING A SUITABLE +! STEP LENGTH FOR THE FORWARD-DIFFERENCE APPROXIMATION. THIS +! APPROXIMATION ASSUMES THAT THE RELATIVE ERRORS IN THE +! FUNCTIONS ARE OF THE ORDER OF EPSFCN. IF EPSFCN IS LESS +! THAN THE MACHINE PRECISION, IT IS ASSUMED THAT THE RELATIVE +! ERRORS IN THE FUNCTIONS ARE OF THE ORDER OF THE MACHINE PRECISION. + +! MU IS A NONNEGATIVE INTEGER INPUT VARIABLE WHICH SPECIFIES +! THE NUMBER OF SUPERDIAGONALS WITHIN THE BAND OF THE +! JACOBIAN MATRIX. IF THE JACOBIAN IS NOT BANDED, SET +! MU TO AT LEAST N - 1. + +! WA1 AND WA2 ARE WORK ARRAYS OF LENGTH N. IF ML + MU + 1 IS AT +! LEAST N, THEN THE JACOBIAN IS CONSIDERED DENSE, AND WA2 IS +! NOT REFERENCED. + +! SUBPROGRAMS CALLED + +! MINPACK-SUPPLIED ... SPMPAR + +! FORTRAN-SUPPLIED ... ABS,MAX,SQRT + +! ARGONNE NATIONAL LABORATORY. MINPACK PROJECT. MARCH 1980. +! BURTON S. GARBOW, KENNETH E. HILLSTROM, JORGE J. MORE + +! ********** +INTEGER :: i, j, k, msum +REAL (dp) :: eps, epsmch, h, temp +REAL (dp), PARAMETER :: zero = 0.0_dp + +! EPSMCH IS THE MACHINE PRECISION. + +epsmch = EPSILON(1.0_dp) + +eps = SQRT(MAX(epsfcn, epsmch)) +msum = ml + mu + 1 +IF (msum >= n) THEN + +! COMPUTATION OF DENSE APPROXIMATE JACOBIAN. + + DO j = 1, n + temp = x(j) + h = eps * ABS(temp) + IF (h == zero) h = eps + x(j) = temp + h + CALL fcn(n, x, wa1, iflag) + IF (iflag < 0) EXIT + x(j) = temp + DO i = 1, n + fjac(i,j) = (wa1(i)-fvec(i)) / h + END DO + END DO +ELSE + +! COMPUTATION OF BANDED APPROXIMATE JACOBIAN. + + DO k = 1, msum + DO j = k, n, msum + wa2(j) = x(j) + h = eps * ABS(wa2(j)) + IF (h == zero) h = eps + x(j) = wa2(j) + h + END DO + CALL fcn(n, x, wa1, iflag) + IF (iflag < 0) EXIT + DO j = k, n, msum + x(j) = wa2(j) + h = eps * ABS(wa2(j)) + IF (h == zero) h = eps + DO i = 1, n + fjac(i,j) = zero + IF (i >= j-mu .AND. i <= j+ml) fjac(i,j) = (wa1(i)-fvec(i)) / h + END DO + END DO + END DO +END IF +RETURN + +! LAST CARD OF SUBROUTINE FDJAC1. + +END SUBROUTINE fdjac1 + + + +SUBROUTINE qform(m, n, q, ldq, wa) + +INTEGER, INTENT(IN) :: m +INTEGER, INTENT(IN) :: n +INTEGER, INTENT(IN) :: ldq +REAL (dp), INTENT(OUT) :: q(ldq,m) +REAL (dp), INTENT(OUT) :: wa(m) + + +! ********** + +! SUBROUTINE QFORM + +! THIS SUBROUTINE PROCEEDS FROM THE COMPUTED QR FACTORIZATION OF AN M BY N +! MATRIX A TO ACCUMULATE THE M BY M ORTHOGONAL MATRIX Q FROM ITS FACTORED FORM. + +! THE SUBROUTINE STATEMENT IS + +! SUBROUTINE QFORM(M,N,Q,LDQ,WA) + +! WHERE + +! M IS A POSITIVE INTEGER INPUT VARIABLE SET TO THE NUMBER +! OF ROWS OF A AND THE ORDER OF Q. + +! N IS A POSITIVE INTEGER INPUT VARIABLE SET TO THE NUMBER OF COLUMNS OF A. + +! Q IS AN M BY M ARRAY. ON INPUT THE FULL LOWER TRAPEZOID IN +! THE FIRST MIN(M,N) COLUMNS OF Q CONTAINS THE FACTORED FORM. +! ON OUTPUT Q HAS BEEN ACCUMULATED INTO A SQUARE MATRIX. + +! LDQ IS A POSITIVE INTEGER INPUT VARIABLE NOT LESS THAN M +! WHICH SPECIFIES THE LEADING DIMENSION OF THE ARRAY Q. + +! WA IS A WORK ARRAY OF LENGTH M. + +! SUBPROGRAMS CALLED + +! FORTRAN-SUPPLIED ... MIN + +! ARGONNE NATIONAL LABORATORY. MINPACK PROJECT. MARCH 1980. +! BURTON S. GARBOW, KENNETH E. HILLSTROM, JORGE J. MORE + +! ********** +INTEGER :: i, j, jm1, k, l, minmn, np1 +REAL (dp) :: sum, temp +REAL (dp), PARAMETER :: one = 1.0_dp, zero = 0.0_dp + +! ZERO OUT UPPER TRIANGLE OF Q IN THE FIRST MIN(M,N) COLUMNS. + +minmn = MIN(m,n) +IF (minmn >= 2) THEN + DO j = 2, minmn + jm1 = j - 1 + DO i = 1, jm1 + q(i,j) = zero + END DO + END DO +END IF + +! INITIALIZE REMAINING COLUMNS TO THOSE OF THE IDENTITY MATRIX. + +np1 = n + 1 +IF (m >= np1) THEN + DO j = np1, m + DO i = 1, m + q(i,j) = zero + END DO + q(j,j) = one + END DO +END IF + +! ACCUMULATE Q FROM ITS FACTORED FORM. + +DO l = 1, minmn + k = minmn - l + 1 + DO i = k, m + wa(i) = q(i,k) + q(i,k) = zero + END DO + q(k,k) = one + IF (wa(k) /= zero) THEN + DO j = k, m + sum = zero + DO i = k, m + sum = sum + q(i,j) * wa(i) + END DO + temp = sum / wa(k) + DO i = k, m + q(i,j) = q(i,j) - temp * wa(i) + END DO + END DO + END IF +END DO +RETURN + +! LAST CARD OF SUBROUTINE QFORM. + +END SUBROUTINE qform + + +SUBROUTINE qrfac(m, n, a, lda, pivot, ipvt, lipvt, rdiag, acnorm, wa) + +INTEGER, INTENT(IN) :: m +INTEGER, INTENT(IN) :: n +INTEGER, INTENT(IN) :: lda +REAL (dp), INTENT(IN OUT) :: a(lda,n) +LOGICAL, INTENT(IN) :: pivot +INTEGER, INTENT(IN) :: lipvt +INTEGER, INTENT(OUT) :: ipvt(lipvt) +REAL (dp), INTENT(OUT) :: rdiag(n) +REAL (dp), INTENT(OUT) :: acnorm(n) +REAL (dp), INTENT(OUT) :: wa(n) + + +! ********** + +! SUBROUTINE QRFAC + +! THIS SUBROUTINE USES HOUSEHOLDER TRANSFORMATIONS WITH COLUMN PIVOTING +! (OPTIONAL) TO COMPUTE A QR FACTORIZATION OF THE M BY N MATRIX A. +! THAT IS, QRFAC DETERMINES AN ORTHOGONAL MATRIX Q, A PERMUTATION MATRIX P, +! AND AN UPPER TRAPEZOIDAL MATRIX R WITH DIAGONAL ELEMENTS OF NONINCREASING +! MAGNITUDE, SUCH THAT A*P = Q*R. THE HOUSEHOLDER TRANSFORMATION FOR +! COLUMN K, K = 1,2,...,MIN(M,N), IS OF THE FORM + +! T +! I - (1/U(K))*U*U + +! WHERE U HAS ZEROS IN THE FIRST K-1 POSITIONS. THE FORM OF THIS +! TRANSFORMATION AND THE METHOD OF PIVOTING FIRST APPEARED IN THE +! CORRESPONDING LINPACK SUBROUTINE. + +! THE SUBROUTINE STATEMENT IS + +! SUBROUTINE QRFAC(M,N,A,LDA,PIVOT,IPVT,LIPVT,RDIAG,ACNORM,WA) + +! WHERE + +! M IS A POSITIVE INTEGER INPUT VARIABLE SET TO THE NUMBER OF ROWS OF A. + +! N IS A POSITIVE INTEGER INPUT VARIABLE SET TO THE NUMBER +! OF COLUMNS OF A. + +! A IS AN M BY N ARRAY. ON INPUT A CONTAINS THE MATRIX FOR WHICH THE +! QR FACTORIZATION IS TO BE COMPUTED. ON OUTPUT THE STRICT UPPER +! TRAPEZOIDAL PART OF A CONTAINS THE STRICT UPPER TRAPEZOIDAL PART OF R, +! AND THE LOWER TRAPEZOIDAL PART OF A CONTAINS A FACTORED FORM OF Q +! (THE NON-TRIVIAL ELEMENTS OF THE U VECTORS DESCRIBED ABOVE). + +! LDA IS A POSITIVE INTEGER INPUT VARIABLE NOT LESS THAN M +! WHICH SPECIFIES THE LEADING DIMENSION OF THE ARRAY A. + +! PIVOT IS A LOGICAL INPUT VARIABLE. IF PIVOT IS SET TRUE, +! THEN COLUMN PIVOTING IS ENFORCED. IF PIVOT IS SET FALSE, +! THEN NO COLUMN PIVOTING IS DONE. + +! IPVT IS AN INTEGER OUTPUT ARRAY OF LENGTH LIPVT. IPVT DEFINES THE +! PERMUTATION MATRIX P SUCH THAT A*P = Q*R. +! COLUMN J OF P IS COLUMN IPVT(J) OF THE IDENTITY MATRIX. +! IF PIVOT IS FALSE, IPVT IS NOT REFERENCED. + +! LIPVT IS A POSITIVE INTEGER INPUT VARIABLE. IF PIVOT IS FALSE, +! THEN LIPVT MAY BE AS SMALL AS 1. IF PIVOT IS TRUE, THEN +! LIPVT MUST BE AT LEAST N. + +! RDIAG IS AN OUTPUT ARRAY OF LENGTH N WHICH CONTAINS THE +! DIAGONAL ELEMENTS OF R. + +! ACNORM IS AN OUTPUT ARRAY OF LENGTH N WHICH CONTAINS THE NORMS OF +! THE CORRESPONDING COLUMNS OF THE INPUT MATRIX A. +! IF THIS INFORMATION IS NOT NEEDED, THEN ACNORM CAN COINCIDE WITH RDIAG. + +! WA IS A WORK ARRAY OF LENGTH N. IF PIVOT IS FALSE, THEN WA +! CAN COINCIDE WITH RDIAG. + +! SUBPROGRAMS CALLED + +! MINPACK-SUPPLIED ... SPMPAR,ENORM + +! FORTRAN-SUPPLIED ... MAX,SQRT,MIN + +! ARGONNE NATIONAL LABORATORY. MINPACK PROJECT. MARCH 1980. +! BURTON S. GARBOW, KENNETH E. HILLSTROM, JORGE J. MORE + +! ********** +INTEGER :: i, j, jp1, k, kmax, minmn +REAL (dp) :: ajnorm, epsmch, sum, temp +REAL (dp), PARAMETER :: one = 1.0_dp, p05 = 0.05_dp, zero = 0.0_dp + +! EPSMCH IS THE MACHINE PRECISION. + +epsmch = EPSILON(1.0_dp) + +! COMPUTE THE INITIAL COLUMN NORMS AND INITIALIZE SEVERAL ARRAYS. + +DO j = 1, n + acnorm(j) = enorm(m, a(1:,j)) + rdiag(j) = acnorm(j) + wa(j) = rdiag(j) + IF (pivot) ipvt(j) = j +END DO + +! REDUCE A TO R WITH HOUSEHOLDER TRANSFORMATIONS. + +minmn = MIN(m,n) +DO j = 1, minmn + IF (pivot) THEN + +! BRING THE COLUMN OF LARGEST NORM INTO THE PIVOT POSITION. + + kmax = j + DO k = j, n + IF (rdiag(k) > rdiag(kmax)) kmax = k + END DO + IF (kmax /= j) THEN + DO i = 1, m + temp = a(i,j) + a(i,j) = a(i,kmax) + a(i,kmax) = temp + END DO + rdiag(kmax) = rdiag(j) + wa(kmax) = wa(j) + k = ipvt(j) + ipvt(j) = ipvt(kmax) + ipvt(kmax) = k + END IF + END IF + +! COMPUTE THE HOUSEHOLDER TRANSFORMATION TO REDUCE THE +! J-TH COLUMN OF A TO A MULTIPLE OF THE J-TH UNIT VECTOR. + + ajnorm = enorm(m-j+1, a(j:,j)) + IF (ajnorm /= zero) THEN + IF (a(j,j) < zero) ajnorm = -ajnorm + DO i = j, m + a(i,j) = a(i,j) / ajnorm + END DO + a(j,j) = a(j,j) + one + +! APPLY THE TRANSFORMATION TO THE REMAINING COLUMNS AND UPDATE THE NORMS. + + jp1 = j + 1 + IF (n >= jp1) THEN + DO k = jp1, n + sum = zero + DO i = j, m + sum = sum + a(i,j) * a(i,k) + END DO + temp = sum / a(j,j) + DO i = j, m + a(i,k) = a(i,k) - temp * a(i,j) + END DO + IF (.NOT.(.NOT.pivot.OR.rdiag(k) == zero)) THEN + temp = a(j,k) / rdiag(k) + rdiag(k) = rdiag(k) * SQRT(MAX(zero,one-temp**2)) + IF (p05*(rdiag(k)/wa(k))**2 <= epsmch) THEN + rdiag(k) = enorm(m-j, a(jp1:,k)) + wa(k) = rdiag(k) + END IF + END IF + END DO + END IF + END IF + rdiag(j) = -ajnorm +END DO +RETURN + +! LAST CARD OF SUBROUTINE QRFAC. + +END SUBROUTINE qrfac + + + +SUBROUTINE r1mpyq(m, n, a, lda, v, w) + +INTEGER, INTENT(IN) :: m +INTEGER, INTENT(IN) :: n +INTEGER, INTENT(IN) :: lda +REAL (dp), INTENT(IN OUT) :: a(lda,n) +REAL (dp), INTENT(IN) :: v(n) +REAL (dp), INTENT(IN) :: w(n) + + +! ********** + +! SUBROUTINE R1MPYQ + +! GIVEN AN M BY N MATRIX A, THIS SUBROUTINE COMPUTES A*Q WHERE +! Q IS THE PRODUCT OF 2*(N - 1) TRANSFORMATIONS + +! GV(N-1)*...*GV(1)*GW(1)*...*GW(N-1) + +! AND GV(I), GW(I) ARE GIVENS ROTATIONS IN THE (I,N) PLANE WHICH +! ELIMINATE ELEMENTS IN THE I-TH AND N-TH PLANES, RESPECTIVELY. +! Q ITSELF IS NOT GIVEN, RATHER THE INFORMATION TO RECOVER THE +! GV, GW ROTATIONS IS SUPPLIED. + +! THE SUBROUTINE STATEMENT IS + +! SUBROUTINE R1MPYQ(M, N, A, LDA, V, W) + +! WHERE + +! M IS A POSITIVE INTEGER INPUT VARIABLE SET TO THE NUMBER OF ROWS OF A. + +! N IS A POSITIVE INTEGER INPUT VARIABLE SET TO THE NUMBER OF COLUMNS OF A. + +! A IS AN M BY N ARRAY. ON INPUT A MUST CONTAIN THE MATRIX TO BE +! POSTMULTIPLIED BY THE ORTHOGONAL MATRIX Q DESCRIBED ABOVE. +! ON OUTPUT A*Q HAS REPLACED A. + +! LDA IS A POSITIVE INTEGER INPUT VARIABLE NOT LESS THAN M +! WHICH SPECIFIES THE LEADING DIMENSION OF THE ARRAY A. + +! V IS AN INPUT ARRAY OF LENGTH N. V(I) MUST CONTAIN THE INFORMATION +! NECESSARY TO RECOVER THE GIVENS ROTATION GV(I) DESCRIBED ABOVE. + +! W IS AN INPUT ARRAY OF LENGTH N. W(I) MUST CONTAIN THE INFORMATION +! NECESSARY TO RECOVER THE GIVENS ROTATION GW(I) DESCRIBED ABOVE. + +! SUBROUTINES CALLED + +! FORTRAN-SUPPLIED ... ABS, SQRT + +! ARGONNE NATIONAL LABORATORY. MINPACK PROJECT. MARCH 1980. +! BURTON S. GARBOW, KENNETH E. HILLSTROM, JORGE J. MORE + +! ********** +INTEGER :: i, j, nmj, nm1 +REAL (dp) :: COS, SIN, temp +REAL (dp), PARAMETER :: one = 1.0_dp + +! APPLY THE FIRST SET OF GIVENS ROTATIONS TO A. + +nm1 = n - 1 +IF (nm1 >= 1) THEN + DO nmj = 1, nm1 + j = n - nmj + IF (ABS(v(j)) > one) COS = one / v(j) + IF (ABS(v(j)) > one) SIN = SQRT(one-COS**2) + IF (ABS(v(j)) <= one) SIN = v(j) + IF (ABS(v(j)) <= one) COS = SQRT(one-SIN**2) + DO i = 1, m + temp = COS * a(i,j) - SIN * a(i,n) + a(i,n) = SIN * a(i,j) + COS * a(i,n) + a(i,j) = temp + END DO + END DO + +! APPLY THE SECOND SET OF GIVENS ROTATIONS TO A. + + DO j = 1, nm1 + IF (ABS(w(j)) > one) COS = one / w(j) + IF (ABS(w(j)) > one) SIN = SQRT(one-COS**2) + IF (ABS(w(j)) <= one) SIN = w(j) + IF (ABS(w(j)) <= one) COS = SQRT(one-SIN**2) + DO i = 1, m + temp = COS * a(i,j) + SIN * a(i,n) + a(i,n) = -SIN * a(i,j) + COS * a(i,n) + a(i,j) = temp + END DO + END DO +END IF +RETURN + +! LAST CARD OF SUBROUTINE R1MPYQ. + +END SUBROUTINE r1mpyq + + + +SUBROUTINE r1updt(m, n, s, ls, u, v, w, sing) + +INTEGER, INTENT(IN) :: m +INTEGER, INTENT(IN) :: n +INTEGER, INTENT(IN) :: ls +REAL (dp), INTENT(IN OUT) :: s(ls) +REAL (dp), INTENT(IN) :: u(m) +REAL (dp), INTENT(IN OUT) :: v(n) +REAL (dp), INTENT(OUT) :: w(m) +LOGICAL, INTENT(OUT) :: sing + + +! ********** + +! SUBROUTINE R1UPDT + +! GIVEN AN M BY N LOWER TRAPEZOIDAL MATRIX S, AN M-VECTOR U, +! AND AN N-VECTOR V, THE PROBLEM IS TO DETERMINE AN +! ORTHOGONAL MATRIX Q SUCH THAT + +! T +! (S + U*V )*Q + +! IS AGAIN LOWER TRAPEZOIDAL. + +! THIS SUBROUTINE DETERMINES Q AS THE PRODUCT OF 2*(N - 1) TRANSFORMATIONS + +! GV(N-1)*...*GV(1)*GW(1)*...*GW(N-1) + +! WHERE GV(I), GW(I) ARE GIVENS ROTATIONS IN THE (I,N) PLANE +! WHICH ELIMINATE ELEMENTS IN THE I-TH AND N-TH PLANES, RESPECTIVELY. +! Q ITSELF IS NOT ACCUMULATED, RATHER THE INFORMATION TO RECOVER THE GV, +! GW ROTATIONS IS RETURNED. + +! THE SUBROUTINE STATEMENT IS + +! SUBROUTINE R1UPDT(M,N,S,LS,U,V,W,SING) + +! WHERE + +! M IS A POSITIVE INTEGER INPUT VARIABLE SET TO THE NUMBER OF ROWS OF S. + +! N IS A POSITIVE INTEGER INPUT VARIABLE SET TO THE NUMBER +! OF COLUMNS OF S. N MUST NOT EXCEED M. + +! S IS AN ARRAY OF LENGTH LS. ON INPUT S MUST CONTAIN THE LOWER +! TRAPEZOIDAL MATRIX S STORED BY COLUMNS. ON OUTPUT S CONTAINS +! THE LOWER TRAPEZOIDAL MATRIX PRODUCED AS DESCRIBED ABOVE. + +! LS IS A POSITIVE INTEGER INPUT VARIABLE NOT LESS THAN +! (N*(2*M-N+1))/2. + +! U IS AN INPUT ARRAY OF LENGTH M WHICH MUST CONTAIN THE VECTOR U. + +! V IS AN ARRAY OF LENGTH N. ON INPUT V MUST CONTAIN THE VECTOR V. +! ON OUTPUT V(I) CONTAINS THE INFORMATION NECESSARY TO +! RECOVER THE GIVENS ROTATION GV(I) DESCRIBED ABOVE. + +! W IS AN OUTPUT ARRAY OF LENGTH M. W(I) CONTAINS INFORMATION +! NECESSARY TO RECOVER THE GIVENS ROTATION GW(I) DESCRIBED ABOVE. + +! SING IS A LOGICAL OUTPUT VARIABLE. SING IS SET TRUE IF ANY OF THE +! DIAGONAL ELEMENTS OF THE OUTPUT S ARE ZERO. OTHERWISE SING IS +! SET FALSE. + +! SUBPROGRAMS CALLED + +! MINPACK-SUPPLIED ... SPMPAR + +! FORTRAN-SUPPLIED ... ABS,SQRT + +! ARGONNE NATIONAL LABORATORY. MINPACK PROJECT. MARCH 1980. +! BURTON S. GARBOW, KENNETH E. HILLSTROM, JORGE J. MORE, JOHN L. NAZARETH + +! ********** +INTEGER :: i, j, jj, l, nmj, nm1 +REAL (dp) :: COS, cotan, giant, SIN, TAN, tau, temp +REAL (dp), PARAMETER :: one = 1.0_dp, p5 = 0.5_dp, p25 = 0.25_dp, zero = 0.0_dp + +! GIANT IS THE LARGEST MAGNITUDE. + +giant = HUGE(1.0_dp) + +! INITIALIZE THE DIAGONAL ELEMENT POINTER. + +jj = (n*(2*m-n+1)) / 2 - (m-n) + +! MOVE THE NONTRIVIAL PART OF THE LAST COLUMN OF S INTO W. + +l = jj +DO i = n, m + w(i) = s(l) + l = l + 1 +END DO + +! ROTATE THE VECTOR V INTO A MULTIPLE OF THE N-TH UNIT VECTOR +! IN SUCH A WAY THAT A SPIKE IS INTRODUCED INTO W. + +nm1 = n - 1 +IF (nm1 >= 1) THEN + DO nmj = 1, nm1 + j = n - nmj + jj = jj - (m-j+1) + w(j) = zero + IF (v(j) /= zero) THEN + +! DETERMINE A GIVENS ROTATION WHICH ELIMINATES THE J-TH ELEMENT OF V. + + IF (ABS(v(n)) < ABS(v(j))) THEN + cotan = v(n) / v(j) + SIN = p5 / SQRT(p25+p25*cotan**2) + COS = SIN * cotan + tau = one + IF (ABS(COS)*giant > one) tau = one / COS + ELSE + TAN = v(j) / v(n) + COS = p5 / SQRT(p25+p25*TAN**2) + SIN = COS * TAN + tau = SIN + END IF + +! APPLY THE TRANSFORMATION TO V AND STORE THE INFORMATION +! NECESSARY TO RECOVER THE GIVENS ROTATION. + + v(n) = SIN * v(j) + COS * v(n) + v(j) = tau + +! APPLY THE TRANSFORMATION TO S AND EXTEND THE SPIKE IN W. + + l = jj + DO i = j, m + temp = COS * s(l) - SIN * w(i) + w(i) = SIN * s(l) + COS * w(i) + s(l) = temp + l = l + 1 + END DO + END IF + END DO +END IF + +! ADD THE SPIKE FROM THE RANK 1 UPDATE TO W. + +DO i = 1, m + w(i) = w(i) + v(n) * u(i) +END DO + +! ELIMINATE THE SPIKE. + +sing = .false. +IF (nm1 >= 1) THEN + DO j = 1, nm1 + IF (w(j) /= zero) THEN + +! DETERMINE A GIVENS ROTATION WHICH ELIMINATES THE +! J-TH ELEMENT OF THE SPIKE. + + IF (ABS(s(jj)) < ABS(w(j))) THEN + cotan = s(jj) / w(j) + SIN = p5 / SQRT(p25 + p25*cotan**2) + COS = SIN * cotan + tau = one + IF (ABS(COS)*giant > one) tau = one / COS + ELSE + TAN = w(j) / s(jj) + COS = p5 / SQRT(p25+p25*TAN**2) + SIN = COS * TAN + tau = SIN + END IF + +! APPLY THE TRANSFORMATION TO S AND REDUCE THE SPIKE IN W. + + l = jj + DO i = j, m + temp = COS * s(l) + SIN * w(i) + w(i) = -SIN * s(l) + COS * w(i) + s(l) = temp + l = l + 1 + END DO + +! STORE THE INFORMATION NECESSARY TO RECOVER THE GIVENS ROTATION. + + w(j) = tau + END IF + +! TEST FOR ZERO DIAGONAL ELEMENTS IN THE OUTPUT S. + + IF (s(jj) == zero) sing = .true. + jj = jj + (m-j+1) + END DO +END IF + +! MOVE W BACK INTO THE LAST COLUMN OF THE OUTPUT S. + +l = jj +DO i = n, m + s(l) = w(i) + l = l + 1 +END DO +IF (s(jj) == zero) sing = .true. +RETURN + +! LAST CARD OF SUBROUTINE R1UPDT. + +END SUBROUTINE r1updt + + +FUNCTION enorm(n, x) RESULT(fn_val) + +INTEGER, INTENT(IN) :: n +REAL (dp), INTENT(IN) :: x(n) +REAL (dp) :: fn_val + +! ********** + +! FUNCTION ENORM + +! GIVEN AN N-VECTOR X, THIS FUNCTION CALCULATES THE EUCLIDEAN NORM OF X. + +! THE EUCLIDEAN NORM IS COMPUTED BY ACCUMULATING THE SUM OF SQUARES IN THREE +! DIFFERENT SUMS. THE SUMS OF SQUARES FOR THE SMALL AND LARGE COMPONENTS +! ARE SCALED SO THAT NO OVERFLOWS OCCUR. NON-DESTRUCTIVE UNDERFLOWS ARE +! PERMITTED. UNDERFLOWS AND OVERFLOWS DO NOT OCCUR IN THE COMPUTATION OF THE UNSCALED +! SUM OF SQUARES FOR THE INTERMEDIATE COMPONENTS. +! THE DEFINITIONS OF SMALL, INTERMEDIATE AND LARGE COMPONENTS DEPEND ON +! TWO CONSTANTS, RDWARF AND RGIANT. THE MAIN RESTRICTIONS ON THESE CONSTANTS +! ARE THAT RDWARF**2 NOT UNDERFLOW AND RGIANT**2 NOT OVERFLOW. +! THE CONSTANTS GIVEN HERE ARE SUITABLE FOR EVERY KNOWN COMPUTER. + +! THE FUNCTION STATEMENT IS + +! REAL FUNCTION ENORM(N, X) + +! WHERE + +! N IS A POSITIVE INTEGER INPUT VARIABLE. + +! X IS AN INPUT ARRAY OF LENGTH N. + +! SUBPROGRAMS CALLED + +! FORTRAN-SUPPLIED ... ABS,SQRT + +! ARGONNE NATIONAL LABORATORY. MINPACK PROJECT. MARCH 1980. +! BURTON S. GARBOW, KENNETH E. HILLSTROM, JORGE J. MORE + +! ********** +INTEGER :: i +REAL (dp) :: agiant, floatn, s1, s2, s3, xabs, x1max, x3max +REAL (dp), PARAMETER :: rdwarf = 1.0D-100, rgiant = 1.0D+100 + +s1 = 0.0_dp +s2 = 0.0_dp +s3 = 0.0_dp +x1max = 0.0_dp +x3max = 0.0_dp +floatn = n +agiant = rgiant / floatn +DO i = 1, n + xabs = ABS(x(i)) + IF (xabs <= rdwarf .OR. xabs >= agiant) THEN + IF (xabs > rdwarf) THEN + +! SUM FOR LARGE COMPONENTS. + + IF (xabs > x1max) THEN + s1 = 1.0_dp + s1 * (x1max/xabs) ** 2 + x1max = xabs + ELSE + s1 = s1 + (xabs/x1max) ** 2 + END IF + ELSE + +! SUM FOR SMALL COMPONENTS. + + IF (xabs > x3max) THEN + s3 = 1.0_dp + s3 * (x3max/xabs) ** 2 + x3max = xabs + ELSE + IF (xabs /= 0.0_dp) s3 = s3 + (xabs/x3max) ** 2 + END IF + END IF + ELSE + +! SUM FOR INTERMEDIATE COMPONENTS. + + s2 = s2 + xabs ** 2 + END IF +END DO + +! CALCULATION OF NORM. + +IF (s1 /= 0.0_dp) THEN + fn_val = x1max * SQRT(s1 + (s2/x1max)/x1max) +ELSE + IF (s2 /= 0.0_dp) THEN + IF (s2 >= x3max) fn_val = SQRT(s2*(1.0_dp + (x3max/s2)*(x3max*s3))) + IF (s2 < x3max) fn_val = SQRT(x3max*((s2/x3max) + (x3max*s3))) + ELSE + fn_val = x3max * SQRT(s3) + END IF +END IF +RETURN +END FUNCTION enorm + +END MODULE Solve_NonLin diff --git a/applications/PUfoam/MoDeNaModels/PolymerDensity/src/DetailedModelCode/modules.f90 b/applications/PUfoam/MoDeNaModels/PolymerDensity/src/DetailedModelCode/modules.f90 new file mode 100644 index 000000000..c0a9831f7 --- /dev/null +++ b/applications/PUfoam/MoDeNaModels/PolymerDensity/src/DetailedModelCode/modules.f90 @@ -0,0 +1,366 @@ +!>WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +!! This module contains constants and upper boundaries for the number of +!! components and phases in the system +!!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW + +Module PARAMETERS + + implicit none + save + + integer, parameter :: nc = 6 + integer, parameter :: np = 3 + integer, parameter :: nsite = 5 + + real, parameter :: PI = 3.141592653589793 + real, parameter :: RGAS = 8.31441 + real, parameter :: NAv = 6.022045E23 + real, parameter :: KBOL = RGAS / NAv + real, parameter :: TAU = PI / 3.0 / SQRT(2.0) + +End Module PARAMETERS + + +!>WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +!! This module contains parameters and variables that define the +!! thermodynamic state of the system as well as simulation parameters +!!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW + +Module BASIC_VARIABLES + + use PARAMETERS, only: nc, np, nsite + implicit none + save + +! ---------------------------------------------------------------------- +! basic quantities defining the mixture +! ---------------------------------------------------------------------- + integer :: ncomp + integer :: nphas + + real :: t + !real :: tc + real :: p + real, dimension(np) :: dense + !real, dimension(np) :: rhob + + real, dimension(np, nc) :: xi + real, dimension(np, nc) :: lnx + real, dimension(nc) :: xiF + + real, dimension(nc) :: mm + real, dimension(np, nc, nsite) :: mxx + + real :: alpha + + +! ---------------------------------------------------------------------- +! pure component parameters +! ---------------------------------------------------------------------- + real, dimension(nc, 25) :: parame = 0.0 + real, dimension(nc) :: chiR + character*30, dimension(nc) :: compna + real, dimension(nc, nc) :: kij, lij + real, dimension(nc, nc) :: E_LC, S_LC + real, dimension(nc) :: LLi, phi_criti, chap + + +! ---------------------------------------------------------------------- +! thermodynamic quantities +! ---------------------------------------------------------------------- + real, dimension(np) :: densta + real, dimension(0:nc*np+6) :: val_init, val_conv + + real :: h_lv + real, dimension(np) :: cpres, enthal, entrop, gibbs, f_res + + real, dimension(np) :: dp_dz, dp_dz2 + + +! ---------------------------------------------------------------------- +! choice of EOS-model and solution method +! ---------------------------------------------------------------------- + integer :: eos, pol + integer :: num + character (LEN=2) :: ensemble_flag + character (LEN=10) :: RGT_variant + + +! ---------------------------------------------------------------------- +! for input/output +! ---------------------------------------------------------------------- + integer :: outp, bindiag + real :: u_in_T, u_out_T, u_in_P, u_out_P + + +! ---------------------------------------------------------------------- +! quantities defining the numerical procedure +! ---------------------------------------------------------------------- + integer :: n_unkw + + real :: step_a, acc_a !, acc_i + real, dimension(nc) :: scaling + real, dimension(3500) :: plv_kon + real, dimension(2, 3500) :: d_kond + + character*3, dimension(10) :: it, sum_rel + character*3 :: running + + +End Module BASIC_VARIABLES + + + + +!>WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +!! This module contains parameters and variables to identify thermodynamic +!! properties +!!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW + +Module EOS_VARIABLES + + use PARAMETERS, only: nc, nsite, PI, KBOL, TAU, NAv + use BASIC_VARIABLES, only: ncomp, eos, t, p, parame, E_LC, S_LC, chiR, & + LLi, phi_criti, chap, kij, lij, ensemble_flag + implicit none + save + +! ---------------------------------------------------------------------- +! basic quantities defining the mixture (single phase) +! ---------------------------------------------------------------------- + real :: x(nc) + real :: eta_start + real :: eta + real :: rho + +! ---------------------------------------------------------------------- +! thermodynamic quantities +! ---------------------------------------------------------------------- + real :: fres + real :: lnphi(nc) + real :: pges + real :: pgesdz + real :: pgesd2 + real :: pgesd3 + + real :: h_res + real :: cp_res + real :: s_res + +! ---------------------------------------------------------------------- +! quantities of fluid theory +! ---------------------------------------------------------------------- + real :: gij(nc,nc) + real :: mx(nc,nsite) + + real :: mseg(nc) + real :: dhs(nc) + real :: uij(nc,nc) + real :: sig_ij(nc,nc) + real :: vij(nc,nc) + + real :: um + real :: order1 + real :: order2 + real :: apar(0:6) + real :: bpar(0:6) + + real :: z0t + real :: z1t + real :: z2t + real :: z3t + + integer :: nhb_typ(nc) + real :: ass_d(nc,nc,nsite,nsite) + real :: nhb_no(nc,nsite) + real :: dij_ab(nc,nc) + +! ---------------------------------------------------------------------- +! auxilliary quantities +! ---------------------------------------------------------------------- + real :: tfr + integer :: phas + + character (LEN = 2) :: dd_term, qq_term, dq_term + + real :: densav(3), denold(3) + real :: density_error(3) + + real :: alpha_nematic + real :: alpha_test(2) + +End Module EOS_VARIABLES + + + +!>WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +!! This module contains parameters and variables of the PC-SAFT EoS +!!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW + +Module EOS_CONSTANTS + + use PARAMETERS, only: nc + implicit none + save + + real, dimension(0:6,3) :: ap, bp + real, dimension(4,9) :: dnm + + real, dimension(28) :: c_dd, n_dd, m_dd, k_dd, o_dd + real, dimension(nc,nc,0:8) :: qqp2, qqp4, ddp2, ddp4, dqp2, dqp4 + real, dimension(nc,nc,nc,0:8) :: qqp3, ddp3, dqp3 + +End Module EOS_CONSTANTS + +!>WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +!! This module contains parameters and variables that control the +!! numerical approximation of derivaties of thermodynamic quantities +!!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW + +Module EOS_NUMERICAL_DERIVATIVES + + use EOS_VARIABLES, only: dd_term, qq_term, dq_term + + implicit none + save + + character (LEN=9) :: ideal_gas ! (yes, no) + character (LEN=9) :: hard_sphere ! (CSBM, no) + character (LEN=9) :: chain_term ! (TPT1, no) + character (LEN=9) :: disp_term ! (PC-SAFT, CK, no) + character (LEN=9) :: hb_term ! (TPT1_Chap, no) + character (LEN=9) :: LC_term ! (MSaupe, no) + character (LEN=9) :: branch_term ! (TPT2, no) + character (LEN=9) :: II_term ! (......., no) + character (LEN=9) :: ID_term ! (......., no) + + character (LEN=9) :: subtract1 ! (1PT, 2PT, no) + character (LEN=9) :: subtract2 ! (ITTpolar, no) + + character (LEN=9) :: save_eos_terms(10) + +End Module EOS_NUMERICAL_DERIVATIVES + + +!>WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +!! Module STARTING_VALUES +!! This module contains parameters and variables for a phase stability +!! analyis as part of a flash calculation. +!!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW + + Module STARTING_VALUES + + use PARAMETERS, only: nc + implicit none + save + + REAL, DIMENSION(nc) :: rhoif, rhoi1, rhoi2, grad_fd + REAL :: fdenf + + End Module STARTING_VALUES + + + + + +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! Module DFT_MODULE +! +! This module contains parameters and variables for DFT calculations. +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! + Module DFT_MODULE + + use PARAMETERS, only: nc + implicit none + save + + INTEGER, PARAMETER :: NDFT = 4000 + !!integer :: discret + REAL :: box_l_no_unit + INTEGER, PARAMETER :: r_grid = 200 + INTEGER :: kmax, den_step + LOGICAL :: shift, WCA, MFT + REAL :: rc, rg, dzr, tau_cut,dzp + REAL :: d_hs, dhs_st, z3t_st + REAL :: z_ges + REAL, DIMENSION(r_grid) :: x1a + REAL, DIMENSION(NDFT) :: x2a + REAL, DIMENSION(r_grid,NDFT) :: ya, y1a, y2a, y12a + REAL, DIMENSION(r_grid,NDFT,4,4) :: c_bicub + REAL :: fres_temp + + REAL, DIMENSION(r_grid) :: x1a_11 + REAL, DIMENSION(NDFT) :: x2a_11 + REAL, DIMENSION(r_grid,NDFT) :: ya_11, y1a_11, y2a_11, y12a_11 + REAL, DIMENSION(r_grid,NDFT,4,4) :: c_bicub_11 + REAL, DIMENSION(r_grid) :: x1a_12 + REAL, DIMENSION(NDFT) :: x2a_12 + REAL, DIMENSION(r_grid,NDFT) :: ya_12, y1a_12, y2a_12, y12a_12 + REAL, DIMENSION(r_grid,NDFT,4,4) :: c_bicub_12 + REAL, DIMENSION(r_grid) :: x1a_22 + REAL, DIMENSION(NDFT) :: x2a_22 + REAL, DIMENSION(r_grid,NDFT) :: ya_22, y1a_22, y2a_22, y12a_22 + REAL, DIMENSION(r_grid,NDFT,4,4) :: c_bicub_22 + + End Module DFT_MODULE + + +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! This module ........... +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +Module rdf_variables + + implicit none + save + + real, dimension(0:20) :: fac(0:20) + +End Module rdf_variables + + +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! This module contains the variables that are needed in the core DFT_FCN +! They are not passed directly to DFT_FCN because the nonlinear solver +! needs a certain calling structure: fcn(x,fvec,n) +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +Module DFT_FCN_MODULE + +use PARAMETERS, only: nc +use DFT_MODULE, only: ndft + implicit none + +INTEGER :: irc(nc),irc_j,ih,fa(nc) + REAL, DIMENSION(-NDFT:NDFT) :: zp + REAL, DIMENSION(-NDFT:NDFT) :: f_tot + REAL, DIMENSION(-NDFT:NDFT,2) :: dF_drho_tot + REAL :: rhob_dft(2,0:nc) + REAL :: my0(nc) + +End Module DFT_FCN_MODULE + + + + + + + + +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! Module Module_Heidemann_Khalil +! +! This module .... +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! + Module Module_Heidemann_Khalil + + implicit none + save + + real :: error_condition2 + + End Module + + + + diff --git a/applications/PUfoam/MoDeNaModels/PolymerDensity/src/README.md b/applications/PUfoam/MoDeNaModels/PolymerDensity/src/README.md new file mode 100644 index 000000000..a08cba2b4 --- /dev/null +++ b/applications/PUfoam/MoDeNaModels/PolymerDensity/src/README.md @@ -0,0 +1,28 @@ +# Readme file for PCSAFTi\_Density + +The program is automatically compiled and linked by executing the following two commands: + +``` +cmake . +make +``` + +Afterwards it can be used in some way that Jonas will now explain + +# Minimal test to check that the program works + +Create a file with inputs to the program: + +``` +printf "270.0\n2\nair\npu\n0.\n0." > in.txt +``` + +Create a file in which the program can save the output + +``` +touch out.txt +``` + +``` +./PCSAFT_Density +``` diff --git a/applications/PUfoam/MoDeNaModels/Rheology/README b/applications/PUfoam/MoDeNaModels/Rheology/README new file mode 100644 index 000000000..a0f92b5aa --- /dev/null +++ b/applications/PUfoam/MoDeNaModels/Rheology/README @@ -0,0 +1,29 @@ +How to run? +----------- + +# Make sure PYTHONPATH and LD_LIBRARY_PATH are set +export PKG_CONFIG_PATH=${PKG_CONFIG_PATH:-}:${HOME}/lib/pkgconfig:/usr/local/lib/pkgconfig +export PYTHONPATH=${PYTHONPATH:-}:${HOME}/lib/python2.7/site-packages:/home/christos/Work/tfem_projects/modena/fork/MoDeNa/applications/PUfoam/Models/ +export LD_LIBRARY_PATH=${LD_LIBRARY_PATH:-}:${HOME}/lib/python2.7/site-packages:${HOME}/lib:/usr/local/lib + + +# Compile project specific sources (only locally) +cd src +cmake . +make + +cd autoSrc +cmake . +make + +# Initialise the model in the database +./initModels_rh + +#Loads surrogate model and its parameters to database. There is only one initial implementation yet, detailed models will be uploaded later. + +# Start the workflow +./workflow + +# Run again to see that no fitting is done on the second start +./workflow + diff --git a/applications/PUfoam/MoDeNaModels/Rheology/Rheology.py b/applications/PUfoam/MoDeNaModels/Rheology/Rheology.py new file mode 100644 index 000000000..72470b5c7 --- /dev/null +++ b/applications/PUfoam/MoDeNaModels/Rheology/Rheology.py @@ -0,0 +1,181 @@ +''' + + ooo ooooo oooooooooo. ooooo ooo + `88. .888' `888' `Y8b `888b. `8' + 888b d'888 .ooooo. 888 888 .ooooo. 8 `88b. 8 .oooo. + 8 Y88. .P 888 d88' `88b 888 888 d88' `88b 8 `88b. 8 `P )88b + 8 `888' 888 888 888 888 888 888ooo888 8 `88b.8 .oP"888 + 8 Y 888 888 888 888 d88' 888 .o 8 `888 d8( 888 + o8o o888o `Y8bod8P' o888bood8P' `Y8bod8P' o8o `8 `Y888""8o + +Copyright + 2014 MoDeNa Consortium, All rights reserved. + +License + This file is part of Modena. + + Modena is free software; you can redistribute it and/or modify it under + the terms of the GNU General Public License as published by the Free + Software Foundation, either version 3 of the License, or (at your option) + any later version. + + Modena is distributed in the hope that it will be useful, but WITHOUT ANY + WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS + FOR A PARTICULAR PURPOSE. See the GNU General Public License + for more details. + + You should have received a copy of the GNU General Public License along + with Modena. If not, see . + +Description + Python library of FireTasks + +Authors + Henrik Rusche + +Contributors + Christos Mitrias +''' + +import os +import modena +import SurfaceTension +import polymerViscosity +from modena import ForwardMappingModel, BackwardMappingModel, SurrogateModel, CFunction, ModenaFireTask +import modena.Strategy as Strategy +from fireworks.user_objects.firetasks.script_task import FireTaskBase, ScriptTask +from fireworks import Firework, Workflow, FWAction +from fireworks.utilities.fw_utilities import explicit_serialize +from jinja2 import Template + + +__author__ = 'Henrik Rusche' +__copyright__ = 'Copyright 2014, MoDeNa Project' +__version__ = '0.2' +__maintainer__ = 'Henrik Rusche' +__email__ = 'h.rusche@wikki.co.uk.' +__date__ = 'Sep 4, 2014' + +# ********************************* Class ************************************ # +@explicit_serialize +class RheologyExactTask(ModenaFireTask): + """ + A FireTask that starts a microscopic code and updates the database. + """ + def task(self, fw_spec): + + # Write input + Template('''{{ s['point']['T'] }} + {{ s['point']['shear'] }} + {{ s['point']['X'] }} + {{ s['point']['mu'] }} + {{ s['point']['ST'] }}'''.strip()).stream(s=self).dump('RheologyExact.in') + + + # Execute the detailed model + ret = os.system('../src/rheologyexactdummy') + # This enables backward mapping capabilities (not needed in this example) + self.handleReturnCode(ret) + + # Analyse output + f=open('RheologyExact.out','r') + self['point']['mu_ap'] = float(f.readline()) + f.close() + + os.remove('RheologyExact.in') + os.remove('RheologyExact.out') + + +f = CFunction( + Ccode= ''' +#include "modena.h" +#include "math.h" +#include + +void rheology_SM +( + const double* parameters, + const double* inherited_inputs, + const double* inputs, + double *outputs +) +{ + const double T = inputs[0]; // temperature + const double shear = inputs[1]; // shear rate + const double X = inputs[2]; // conversion + const double lambda = parameters[0]; + const double alpha = parameters[1]; + const double n_rh = parameters[2]; + + const double A_mu = 0.0387; // could be loaded from some library for consistence + const double E_mu = 10000; + const double R_rh = 8.314; + const double mu_a = 1.5; + const double mu_b = 1; + const double mu_c = 0; + const double mu_d = 0.001; + const double X_gel = 0.615; + const double mu_0_const = 0.195; + const double mu_inf_const = 0.266; +// const double lambda = 11.35 ; +// const double alpha = 2; +// const double n_rh = 0.2; + + double mu_0, mu_inf, f_t; + double mu_ap; + + mu_0 = (log(X+mu_d) - log(mu_d) + pow(X_gel / ( X_gel - X ), mu_a + X*mu_b + mu_c*pow(X,2))) * mu_0_const; + mu_inf = (log(X+mu_d) - log(mu_d) + pow(X_gel / ( X_gel - X ), mu_a + X*mu_b + mu_c*pow(X,2)))* mu_inf_const; + f_t = A_mu * exp(E_mu / R_rh / T ); + + mu_ap = (mu_inf + (mu_0 - mu_inf)*pow(1 + pow(lambda*shear,alpha), (n_rh - 1) / alpha)) * f_t; + //printf("apparent viscosity %f", mu_ap); + outputs[0] = mu_ap; +} +''', + # These are global bounds for the function + inputs={ + 'T': {'min': 0, 'max': 9e99, 'argPos': 0 }, + 'shear': {'min': 0, 'max': 9e99, 'argPos': 1 }, + 'X': {'min': 0, 'max': 1, 'argPos': 2 }, + 'mu': {'min': 0, 'max': 1000, 'argPos': 3 }, + 'ST': {'min': 0, 'max': 100, 'argPos': 4 }, + + }, + outputs={ + 'mu_ap': { 'min': 0, 'max': 9e99, 'argPos': 0 }, + }, + parameters={ + 'lamdba': { 'min': 1.35, 'max': 21.35, 'argPos': 0 }, + 'alpha': { 'min': 0, 'max': 2, 'argPos': 1 }, + 'n_rh': { 'min': 0, 'max': 2, 'argPos': 2 }, + }, +) + +m = BackwardMappingModel( + _id= 'Rheology', + surrogateFunction= f, + exactTask= RheologyExactTask(), + substituteModels= [ polymerViscosity.m_polymerViscosity, SurfaceTension.m], +# substituteModels= [ ], + initialisationStrategy= Strategy.InitialPoints( + initialPoints= + { + 'T': [300.0, 310.0], # 310 is the maximum that is supported by Surface Tension Model + 'shear': [0.01, 0.1], + 'X': [0.1, 0.3], + }, + ), + outOfBoundsStrategy= Strategy.ExtendSpaceStochasticSampling( + nNewPoints= 4 + ), + parameterFittingStrategy= Strategy.NonLinFitWithErrorContol( + testDataPercentage= 0.2, + maxError= 0.5, + improveErrorStrategy= Strategy.StochasticSampling( + nNewPoints= 2 + ), + maxIterations= 5 # Currently not used + ), +) + diff --git a/applications/PUfoam/MoDeNaModels/Rheology/WorkflowTest.py b/applications/PUfoam/MoDeNaModels/Rheology/WorkflowTest.py new file mode 100644 index 000000000..f28c03a01 --- /dev/null +++ b/applications/PUfoam/MoDeNaModels/Rheology/WorkflowTest.py @@ -0,0 +1,23 @@ +import os +import modena +from modena import ForwardMappingModel, BackwardMappingModel, SurrogateModel, \ +CFunction +import modena.Strategy as Strategy +from fireworks.user_objects.firetasks.script_task import FireTaskBase, ScriptTask +from fireworks import Firework, Workflow, FWAction +from fireworks.utilities.fw_utilities import explicit_serialize +from blessings import Terminal +from jinja2 import Template +import Rheology + +## Create terminal for colour output +term = Terminal() + + + + +# For the case, when only foam conductivity and no aging is needed. +m = Strategy.BackwardMappingScriptTask( + script=os.path.dirname(os.path.abspath(__file__))+'/src_dummy/workflowdummy' + ) + diff --git a/applications/PUfoam/MoDeNaModels/Rheology/__init__.py b/applications/PUfoam/MoDeNaModels/Rheology/__init__.py new file mode 100644 index 000000000..2c66c26e0 --- /dev/null +++ b/applications/PUfoam/MoDeNaModels/Rheology/__init__.py @@ -0,0 +1,38 @@ +''' + + ooo ooooo oooooooooo. ooooo ooo + `88. .888' `888' `Y8b `888b. `8' + 888b d'888 .ooooo. 888 888 .ooooo. 8 `88b. 8 .oooo. + 8 Y88. .P 888 d88' `88b 888 888 d88' `88b 8 `88b. 8 `P )88b + 8 `888' 888 888 888 888 888 888ooo888 8 `88b.8 .oP"888 + 8 Y 888 888 888 888 d88' 888 .o 8 `888 d8( 888 + o8o o888o `Y8bod8P' o888bood8P' `Y8bod8P' o8o `8 `Y888""8o + +Copyright + 2014-2015 MoDeNa Consortium, All rights reserved. + +License + This file is part of Modena. + + Modena is free software; you can redistribute it and/or modify it under + the terms of the GNU General Public License as published by the Free + Software Foundation, either version 3 of the License, or (at your option) + any later version. + + Modena is distributed in the hope that it will be useful, but WITHOUT ANY + WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS + FOR A PARTICULAR PURPOSE. See the GNU General Public License + for more details. + + You should have received a copy of the GNU General Public License along + with Modena. If not, see . + +Description + Python library of FireTasks + +Authors + Henrik Rusche + +Contributors +''' + diff --git a/applications/PUfoam/MoDeNaModels/Rheology/initModels_rh b/applications/PUfoam/MoDeNaModels/Rheology/initModels_rh new file mode 100755 index 000000000..6da6560d2 --- /dev/null +++ b/applications/PUfoam/MoDeNaModels/Rheology/initModels_rh @@ -0,0 +1,57 @@ +#!/usr/bin/python +''' + + ooo ooooo oooooooooo. ooooo ooo + `88. .888' `888' `Y8b `888b. `8' + 888b d'888 .ooooo. 888 888 .ooooo. 8 `88b. 8 .oooo. + 8 Y88. .P 888 d88' `88b 888 888 d88' `88b 8 `88b. 8 `P )88b + 8 `888' 888 888 888 888 888 888ooo888 8 `88b.8 .oP"888 + 8 Y 888 888 888 888 d88' 888 .o 8 `888 d8( 888 + o8o o888o `Y8bod8P' o888bood8P' `Y8bod8P' o8o `8 `Y888""8o + +Copyright + 2014-2015 MoDeNa Consortium, All rights reserved. + +License + This file is part of Modena. + + Modena is free software; you can redistribute it and/or modify it under + the terms of the GNU General Public License as published by the Free + Software Foundation, either version 3 of the License, or (at your option) + any later version. + + Modena is distributed in the hope that it will be useful, but WITHOUT ANY + WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS + FOR A PARTICULAR PURPOSE. See the GNU General Public License for more + details. + + You should have received a copy of the GNU General Public License along + with Modena. If not, see . + +Description + Initialisation script for the flowRate model. The script calculates a few + data points and fits the surrogate model. Then the model is inserted into + the database. + +Authors + Henrik Rusche + +Contributors + Christos Mitrias +''' + +import Rheology +from fireworks import LaunchPad +from fireworks.core.rocket_launcher import rapidfire + +# set up the LaunchPad and reset it +launchpad = LaunchPad() +launchpad.reset('', require_password=False) + +m = Rheology.m +initWfs = m.initialisationStrategy().workflow(m) + +# store workflow and launch it locally +launchpad.add_wf(initWfs) +rapidfire(launchpad) + diff --git a/applications/PUfoam/MoDeNaModels/Rheology/src/coefficients.out b/applications/PUfoam/MoDeNaModels/Rheology/src/coefficients.out new file mode 100644 index 0000000000000000000000000000000000000000..50ec1470b4d9cb66f01e9acf01aded7ba73ee601 GIT binary patch literal 2632 zcmd;JU|{$K#3z851BhQRGcd3LX(k{>28=)svKUAWP$}I3HSGlXX%vixz(@@NP+oTc zWn?h;U=L#vOaEE<@se*+0Ll6YnQsgRkEw1hA$v#VM?+vV1V%$(Gz3Ts0Z<(R06uUG Ab^rhX literal 0 HcmV?d00001 diff --git a/applications/PUfoam/MoDeNaModels/Rheology/src/mesh.geo b/applications/PUfoam/MoDeNaModels/Rheology/src/mesh.geo new file mode 100644 index 000000000..cef483ea1 --- /dev/null +++ b/applications/PUfoam/MoDeNaModels/Rheology/src/mesh.geo @@ -0,0 +1,37 @@ + ox = -1.00000000000000; + oy = -0.50000000000000; + lx = 2.00000000000000; + ly = 1.00000000000000; + dx_box = 0.10000000000000; + dx_part = 0.01570796326795; + nobj = 9; + biperiodic = 0; + xp[1] = -0.80000001192093; + yp[1] = 0.33999999910593; + rp[1] = 0.10000000000000; + xp[2] = -0.20000001291434; + yp[2] = 0.26000000089407; + rp[2] = 0.10000000000000; + xp[3] = 0.43999998529752; + yp[3] = 0.37999999831120; + rp[3] = 0.10000000000000; + xp[4] = -0.80000001192093; + yp[4] = -0.03999999910593; + rp[4] = 0.10000000000000; + xp[5] = -0.22000001450380; + yp[5] = 0.01999999751647; + rp[5] = 0.10000000000000; + xp[6] = 0.39999998609225; + yp[6] = -0.03999999910593; + rp[6] = 0.10000000000000; + xp[7] = -0.88000001430511; + yp[7] = -0.34000000327826; + rp[7] = 0.10000000000000; + xp[8] = -0.20000001291434; + yp[8] = -0.33999999910593; + rp[8] = 0.10000000000000; + xp[9] = 0.39999998609225; + yp[9] = -0.26000000089407; + rp[9] = 0.10000000000000; + + Include "particles_in_a_box_2D_rp.igo"; diff --git a/applications/PUfoam/MoDeNaModels/Rheology/src/mesh_options_2D.igo b/applications/PUfoam/MoDeNaModels/Rheology/src/mesh_options_2D.igo new file mode 100644 index 000000000..4d8327e65 --- /dev/null +++ b/applications/PUfoam/MoDeNaModels/Rheology/src/mesh_options_2D.igo @@ -0,0 +1,5 @@ + +//Mesh.Algorithm = 6; // Frontal for surfaces +Mesh.ElementOrder = 2; // Second-order elements + +// vim: set filetype=gmsh : // diff --git a/applications/PUfoam/MoDeNaModels/Rheology/src/outputmesh.out b/applications/PUfoam/MoDeNaModels/Rheology/src/outputmesh.out new file mode 100644 index 000000000..e69de29bb diff --git a/applications/PUfoam/MoDeNaModels/Rheology/src/particles_in_a_box_2D_rmsh.igo b/applications/PUfoam/MoDeNaModels/Rheology/src/particles_in_a_box_2D_rmsh.igo new file mode 100644 index 000000000..3d7834773 --- /dev/null +++ b/applications/PUfoam/MoDeNaModels/Rheology/src/particles_in_a_box_2D_rmsh.igo @@ -0,0 +1,110 @@ +// Make a mesh consisting of a rectangle with particles, all defined by +// a mesh consisting of +// four points +// four lines for the box +// nobj lines/curves for particles +// NOTE: the mesh has to be merged before including this file. +// +// The full rectangle, including the particles, is meshed. +// The space between the particles and the rectangle is physical volume 1 +// The space inside the particles is physical volume 2 +// +// The input parameters are: +// +// nobj = the number of particles +// +// NOTE: the parameters have to be defined before including this file.A +// +// The mesh consists of four (Physical) Points and 4+nobj Physical lines + +// Create domain vertices + +Mesh.CharacteristicLengthExtendFromBoundary=0; +For i In {1:4} + Point(i) = {x_geo[i], y_geo[i], 0.0, dx_box}; +EndFor + +Physical Point(1) = p1; +Physical Point(2) = p2; +Physical Point(3) = p3; +Physical Point(4) = p4; + + +Physical Line(1) = {1}; +Physical Line(2) = {2}; +Physical Line(3) = {3}; +Physical Line(4) = {4}; + +//Periodic Line{4} = {-2}; + +// Create outer boundary + +lin_loop[0] = newll; +Line Loop(lin_loop[0]) = { 1, 2, 3, 4 }; + +// Make nobj particles + +For t In {1:nobj} + + lin_loop[t] = newll; + + Line Loop(lin_loop[t]) = {t+4}; + + Physical Line(t+4) = {t+4}; + +EndFor + +// Create surface mesh (with holes) + +Plane Surface(1) = {lin_loop[]}; + +Physical Surface(1) = {1}; + +//For t In {1:nobj} + +// Plane Surface(t+1) = {lin_loop[t]}; + +//EndFor + +//Physical Surface(2) = {2:nobj+1}; +// add refinement points + +If (nrefine > 0 ) + +//generate a list with the refinement points + For t In {1:nrefine} + + p_refine = newp; Point(p_refine) = {xp_refine[t], yp_refine[t], 0.0}; + + //apparently, Gmsh start counting with 0, so t-1 is the first index! + refinement_points[t-1] = p_refine; + + EndFor + +//generate an attractor field that returns the distance to the closest +//refinement point + + For t In {1:nrefine} + + Field[2*t-1] = Attractor; + Field[2*t-1].NodesList = {refinement_points[t-1]}; + +//use the values generated by the attractor field to determine the element size + Field[2*t] = Threshold; + Field[2*t].IField = 2*t-1; + Field[2*t].LcMin = h_fine[t]; + Field[2*t].LcMax = h_coarse[t]; + Field[2*t].DistMin = d_min[t]; + Field[2*t].DistMax = d_max[t]; + + FldList[t-1] = 2*t; + + EndFor + +//use the minimum of all element-size-fields to determine the local element size + Field[2*nrefine+1] = Min; + Field[2*nrefine+1].FieldsList = {FldList[]}; + Background Field = 2*nrefine+1; + +EndIf +// vim: set filetype=gmsh : // diff --git a/applications/PUfoam/MoDeNaModels/Rheology/src/particles_in_a_box_2D_rp.igo b/applications/PUfoam/MoDeNaModels/Rheology/src/particles_in_a_box_2D_rp.igo new file mode 100644 index 000000000..8cc253794 --- /dev/null +++ b/applications/PUfoam/MoDeNaModels/Rheology/src/particles_in_a_box_2D_rp.igo @@ -0,0 +1,138 @@ +// this file is similar to particles_in_a_box_2D.igo, with the excepting +// that refinement points are used to generate meshes that are refined +// around the particle. This has the advantage that is gives more control +// over the element size in the domain + + +// Do not let Gmsh determine the element size (instead the element size +// will be specified using refinement fields) by setting +// Mesh.CharacteristicLengthExtendFromBoundary to 0 (its default value is 1) + +//Mesh.CharacteristicLengthExtendFromBoundary = 0; + + +// Accuracy of evaluation of the LC field (characteristic length of elements) +// for 1D mesh generation (Default value: 1e-09) +// see: http://www.geuz.org/pipermail/gmsh/2013/008319.html + +//Mesh.LcIntegrationPrecision = LcIntegrationPrecision; + + +// Create domain vertices + +Point(1) = {ox, oy, 0.0, dx_box}; +Point(2) = {ox+lx, oy, 0.0, dx_box}; +Point(3) = {ox+lx, oy+ly, 0.0, dx_box}; +Point(4) = {ox, oy+ly, 0.0, dx_box}; + +For i In {1:4} + Physical Point(i) = i; +EndFor + +// Create domain sides + +Line(1) = {1, 2}; +Line(2) = {2, 3}; +Line(3) = {3, 4}; +Line(4) = {4, 1}; + +For i In {1:4} + Physical Line(i) = i; +EndFor + +// Create outer boundary + +lin_loop[0] = newll; +Line Loop(lin_loop[0]) = { 1, 2, 3, 4 }; + +Periodic Line {4} = {-2}; +If ( biperiodic == 1 ) + Periodic Line {3} = {-1}; +EndIf + +// Circle + +Function MakeCircle + + p1 = newp; Point(p1) = {x, y, 0.0, dx_part}; + p2 = newp; Point(p2) = {x-r, y, 0.0, dx_part}; + p3 = newp; Point(p3) = {x+r, y, 0.0, dx_part}; + + c1 = newl; Circle(c1) = {p2, p1, p3}; + c2 = newl; Circle(c2) = {p3, p1, p2}; + + lin_loop[t] = newll; + + Line Loop(lin_loop[t]) = {c1, c2}; + + Physical Line(t+4) = {c1, c2}; + +Return + +// Make nobj circles + +For t In {1:nobj} + + x = xp[t]; + y = yp[t]; + r = rp[t]; + + Call MakeCircle; + +EndFor + +// Create surface mesh (with holes) + +Plane Surface(1) = {lin_loop[]}; + +Physical Surface(1) = {1}; + +// add refinement points + +pcount=0; + +If (0 > 0 ) + + For i In {1:nrefinement_field} + + // generate a list with the refinement points + For t In {1:nrefine[i]} + + p_refine = newp; Point(p_refine) = {xp_refine[t+pcount], + yp_refine[t+pcount], 0.0}; + + // apparently, Gmsh start counting with 0, so t-1 is the first index! + refinement_points[t-1] = p_refine; + + EndFor + + // generate an attractor field that returns the distance to the closest + // refinement point + Field[2*i-1] = Attractor; + Field[2*i-1].NodesList = {refinement_points[]}; + + // use the values generated by the attractor field to determine the + // element size + Field[2*i] = Threshold; + Field[2*i].IField = 2*i-1; + Field[2*i].LcMin = dx_fine[i]; + Field[2*i].LcMax = dx_coarse[i]; + Field[2*i].DistMin = distmin[i]; + Field[2*i].DistMax = distmax[i]; + + pcount=pcount+nrefine[i]; + + EndFor + + // use the minimum of all element-size-fields + Field[2*nrefinement_field+1] = Min; + For i In {1:nrefinement_field} + field_list[i-1] = i*2; + EndFor + Field[2*nrefinement_field+1].FieldsList = {field_list[]}; + Background Field = 2*nrefinement_field+1; + +EndIf + + +// vim: set filetype=gmsh : // diff --git a/applications/PUfoam/MoDeNaModels/Rheology/src/particles_in_a_box_2D_rp_geo.igo b/applications/PUfoam/MoDeNaModels/Rheology/src/particles_in_a_box_2D_rp_geo.igo new file mode 100644 index 000000000..995539db2 --- /dev/null +++ b/applications/PUfoam/MoDeNaModels/Rheology/src/particles_in_a_box_2D_rp_geo.igo @@ -0,0 +1,127 @@ +// Generate a mesh with holes, where the outer boundary is given by a +// collection of geometrical points. +// +// lower left corner : (x_geo[p1], y_geo[p1]) +// lower right corner : (x_geo[p2], y_geo[p2]) +// upper right corner : (x_geo[p3], y_geo[p3]) +// upper left corner : (x_geo[p4], y_geo[p4]) +// +// npoints is the total number of geometrical points on the outer boundary + + +// Do not let Gmsh determine the element size (instead the element size +// will be specified using refinement fields) by setting +// Mesh.CharacteristicLengthExtendFromBoundary to 0 (its default value is 1) + +//Mesh.CharacteristicLengthExtendFromBoundary = 0; + + +// Accuracy of evaluation of the LC field (characteristic length of elements) +// for 1D mesh generation (Default value: 1e-09) +// see: http://www.geuz.org/pipermail/gmsh/2013/008319.html + +//Mesh.LcIntegrationPrecision = LcIntegrationPrecision; + + +// Create domain vertices + +For i In {1:npoints} + Point(i) = {x_geo[i], y_geo[i], 0.0, dx_box}; +EndFor + +Physical Point(1) = p1; +Physical Point(2) = p2; +Physical Point(3) = p3; +Physical Point(4) = p4; + +// Create domain sides + +For i In {1:npoints-1} + Line(i) = {i,i+1}; +EndFor +Line(npoints) = {npoints,1}; + +Physical Line(1) = {1:p2-1}; +Physical Line(2) = {p2:p3-1}; +Physical Line(3) = {p3:p4-1}; +Physical Line(4) = {p4:npoints}; + +// Create outer boundary + +lin_loop[0] = newll; +Line Loop(lin_loop[0]) = { 1:npoints }; + +// make sure the line pieces on curve 2 are periodic +// with the line pieces on curve 4 + +For i In {0:p3-p2-1} + elem_c2 = i+p2; + elem_c4 = npoints-i; + Periodic Line {elem_c4} = {-elem_c2}; +EndFor + +If ( biperiodic == 1 ) + For i In {0:p4-p3-1} + elem_c3 = i+p3; + elem_c1 = p2-1-i; + Periodic Line {elem_c3} = {-elem_c1}; + EndFor +EndIf + + + +// Create surface mesh (with holes) + +Plane Surface(1) = {lin_loop[]}; + +Physical Surface(1) = {1}; + +// add refinement points + +pcount=0; + +If (0 > 0 ) + + For i In {1:nrefinement_field} + + // generate a list with the refinement points + For t In {1:nrefine[i]} + + p_refine = newp; Point(p_refine) = {xp_refine[t+pcount], + yp_refine[t+pcount], 0.0}; + + // apparently, Gmsh start counting with 0, so t-1 is the first index! + refinement_points[t-1] = p_refine; + + EndFor + + // generate an attractor field that returns the distance to the closest + // refinement point + Field[2*i-1] = Attractor; + Field[2*i-1].NodesList = {refinement_points[]}; + + // use the values generated by the attractor field to determine the + // element size + Field[2*i] = Threshold; + Field[2*i].IField = 2*i-1; + Field[2*i].LcMin = dx_fine[i]; + Field[2*i].LcMax = dx_coarse[i]; + Field[2*i].DistMin = distmin[i]; + Field[2*i].DistMax = distmax[i]; + + pcount=pcount+nrefine[i]; + + EndFor + + // use the minimum of all element-size-fields + Field[2*nrefinement_field+1] = Min; + For i In {1:nrefinement_field} + field_list[i-1] = i*2; + EndFor + Field[2*nrefinement_field+1].FieldsList = {field_list[]}; + Background Field = 2*nrefinement_field+1; + +EndIf + + +// vim: set filetype=gmsh : // diff --git a/applications/PUfoam/MoDeNaModels/Rheology/src/rheologyexact b/applications/PUfoam/MoDeNaModels/Rheology/src/rheologyexact new file mode 100755 index 0000000000000000000000000000000000000000..6c3296b10353c38eb5bf777dd0774a9b2787c8ac GIT binary patch literal 8423952 zcmeFaeSB2awLg54$!HXCf`Uec8Z~G%qS1gx1Db(E&%haoiZvogAOsT$kedWViy8>A zIUa_lEwpK?ZQ857wAGq=r8hwd6W$UKF<{jQq7mQDh+qJPh)SOCcb#*R!^^b&{GR)K zp68EeU}o*L_TFo+z4qJMYwvUNM2>cQY)p*ed}5Vb6=L(R&k~aLt0=ikDh20HmXe{w z?Vh=rj9>*GjB$nyF=S$5EZ zUyLXb+<}UcBslX?)-F4~Ys5C8_rjabvhc4g=;Wh#%$Ib(#W(4GE1v@sZ22AN)Q@%J 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zSMe%|;c#!^N~-T__uN#EW~zcQBB=F@)0|%tKxq{J`!LOViNg7K28xP7H41s6KQiaur-Eh!~N2O z`=#_|@lSy_yMGC{{Sstzf=RH!{UQOd9+1B_fYFwqj!r`622cPytcjzv!9Q<+ zEU>lIER3DZ9RaMrnos^23&($q(f@=+Oi*50KnR9K<{y#zOYcemtc&AsSU@lz|7R?} zGzR~S1ql3q1|uRPtf>C0KcvvY-M<|3kFmVG0GQMt zO!yGxKPT`1Mx>oH?EJ#Wj#3uJjsUGc z2#WyVA6o%f{zwS`%O5V#fe{SjHqkA7jv;-60RPGj=wD z5g2LgjZKwJ)ER(`Y|M;6W>`@Yf-x9jEoK2UF!R4|E$nQCVLV3wjW8z*Gms7Tq#$Mp z2*Scf&kUqyW~PRXld&`Y--akd4eaerjA5in18YYU7*J&qbw*KVYimOTTiah)l+7(1 z0kFS+V0sHsg%woT)&N#U*q$H`7WRL^WME-r`2!$8+QP*Iz{1ST0i%){S{T^U0<7!} zU}en20O0b^*&s${M%aV>+j(wK6H^ps00@Y}{9hM<9Rz~CJxl@rumRbDtT5mIx&XHS zwt@bG4g9-}nFV(JHkX+N2!z%2zpMwl0m7pF7aIpmP7@aTKihz?VPIIe|7>IC;DB)a zeH@4b7W6-lgUx0BRc?Q?v4LO-^_z|LSIYfn1H(M>7aMFf4(8wXV1`vpc3AoO^ITXw z*dTwiv4S~%+n1S{1(r;In+yC^&i=9la9TT?s0A7%5`jW9rqn^k~SL. + +Description + Python library of FireTasks + +Authors + Henrik Rusche + +Contributors +''' + +from modena.Strategy import BackwardMappingScriptTask + + +__author__ = 'Henrik Rusche' +__copyright__ = 'Copyright 2014, MoDeNa Project' +__version__ = '0.2' +__maintainer__ = 'Henrik Rusche' +__email__ = 'h.rusche@wikki.co.uk.' +__date__ = 'Sep 4, 2014' + + +# Source code in src/twoTanksMacroscopicProblem.C +m = BackwardMappingScriptTask( + script='../src/MacroscopicProblem' +) + diff --git a/applications/PUfoam/MoDeNaModels/Solubility/ExampleOfUsage/initModels b/applications/PUfoam/MoDeNaModels/Solubility/ExampleOfUsage/initModels new file mode 100755 index 000000000..0d4f5687f --- /dev/null +++ b/applications/PUfoam/MoDeNaModels/Solubility/ExampleOfUsage/initModels @@ -0,0 +1,62 @@ +#!/usr/bin/python +''' + + ooo ooooo oooooooooo. ooooo ooo + `88. .888' `888' `Y8b `888b. `8' + 888b d'888 .ooooo. 888 888 .ooooo. 8 `88b. 8 .oooo. + 8 Y88. .P 888 d88' `88b 888 888 d88' `88b 8 `88b. 8 `P )88b + 8 `888' 888 888 888 888 888 888ooo888 8 `88b.8 .oP"888 + 8 Y 888 888 888 888 d88' 888 .o 8 `888 d8( 888 + o8o o888o `Y8bod8P' o888bood8P' `Y8bod8P' o8o `8 `Y888""8o + +Copyright + 2014-2015 MoDeNa Consortium, All rights reserved. + +License + This file is part of Modena. + + Modena is free software; you can redistribute it and/or modify it under + the terms of the GNU General Public License as published by the Free + Software Foundation, either version 3 of the License, or (at your option) + any later version. + + Modena is distributed in the hope that it will be useful, but WITHOUT ANY + WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS + FOR A PARTICULAR PURPOSE. See the GNU General Public License for more + details. + + You should have received a copy of the GNU General Public License along + with Modena. If not, see . + +Description + Initialisation script for the flowRate model. The script calculates a few + data points and fits the surrogate model. Then the model is inserted into + the database. + +Authors + Henrik Rusche + +Contributors +''' + +from modena import SurrogateModel +from modena.Strategy import Workflow2 +#import flowRate +import modSolubility +from fireworks import LaunchPad +from fireworks.core.rocket_launcher import rapidfire +from fireworks.utilities.fw_serializers import load_object + + +# set up the LaunchPad and reset it +launchpad = LaunchPad() +launchpad.reset('', require_password=False) + +initWfs = Workflow2([]) +for m in SurrogateModel.get_instances(): + initWfs.addNoLink(m.initialisationStrategy().workflow(m)) + +# store workflow and launch it locally +launchpad.add_wf(initWfs) +rapidfire(launchpad) + diff --git a/applications/PUfoam/MoDeNaModels/Solubility/ExampleOfUsage/modSolubility.py b/applications/PUfoam/MoDeNaModels/Solubility/ExampleOfUsage/modSolubility.py new file mode 100644 index 000000000..ad1695cb3 --- /dev/null +++ b/applications/PUfoam/MoDeNaModels/Solubility/ExampleOfUsage/modSolubility.py @@ -0,0 +1,176 @@ + + +''' + + ooo ooooo oooooooooo. ooooo ooo + `88. .888' `888' `Y8b `888b. `8' + 888b d'888 .ooooo. 888 888 .ooooo. 8 `88b. 8 .oooo. + 8 Y88. .P 888 d88' `88b 888 888 d88' `88b 8 `88b. 8 `P )88b + 8 `888' 888 888 888 888 888 888ooo888 8 `88b.8 .oP"888 + 8 Y 888 888 888 888 d88' 888 .o 8 `888 d8( 888 + o8o o888o `Y8bod8P' o888bood8P' `Y8bod8P' o8o `8 `Y888""8o + +Copyright + 2014-2015 MoDeNa Consortium, All rights reserved. + +License + This file is part of Modena. + + Modena is free software; you can redistribute it and/or modify it under + the terms of the GNU General Public License as published by the Free + Software Foundation, either version 3 of the License, or (at your option) + any later version. + + Modena is distributed in the hope that it will be useful, but WITHOUT ANY + WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS + FOR A PARTICULAR PURPOSE. See the GNU General Public License + for more details. + + You should have received a copy of the GNU General Public License along + with Modena. If not, see . + +Description + Python library of FireTasks + +Authors + Henrik Rusche + +Contributors +''' + +import os +import modena +from modena import ForwardMappingModel,BackwardMappingModel,SurrogateModel,CFunction,IndexSet +import modena.Strategy as Strategy +from fireworks.user_objects.firetasks.script_task import FireTaskBase, ScriptTask +from fireworks import Firework, Workflow, FWAction +from fireworks.utilities.fw_utilities import explicit_serialize +from blessings import Terminal +from jinja2 import Template + +# Create terminal for colour output +term = Terminal() + + +__author__ = 'Henrik Rusche' +__copyright__ = 'Copyright 2014, MoDeNa Project' +__version__ = '0.2' +__maintainer__ = 'Henrik Rusche' +__email__ = 'h.rusche@wikki.co.uk.' +__date__ = 'Sep 4, 2014' + + +# ********************************* Class ********************************** # +@explicit_serialize +class SolubilityExactSim(FireTaskBase): + """ + A FireTask that starts a microscopic code and updates the database. + """ + + def run_task(self, fw_spec): + print( + term.yellow + + "Performing exact simulation (microscopic code recipe)" + + term.normal + ) + + # Write input for detailed model + ff = open('in.txt', 'w') + Tstr = str(self['point']['T']) + ff.write('%s \n' %(Tstr)) + + + ##TODO INPUT SHOULD COME FROM IndexSet + + ff.write('2 \n') #number of components in system + ff.write('co2 \n') #component 1 + ff.write('hexane \n') #component 2 + ff.write('0.5 \n') #molar feed (initial) concentration (mol/m^3) component 1 + ff.write('0.5 \n') #molar feed (initial) concentration (mol/m^3) component 2 + ff.close() + + #create output file for detailed code + fff = open('out.txt', 'w+') + fff.close() + + # Execute detailed model + os.system('../src/PCSAFT_Henry') + + # Analyse output + f = open('out.txt', 'r') + self['point']['H'] = float(f.readline()) + f.close() + + return FWAction(mod_spec=[{'_push': self['point']}]) + + + + + + +f = CFunction( + Ccode= ''' +#include "modena.h" +#include "math.h" + +void surroSolubility +( + const double* parameters, + const double* inherited_inputs, + const double* inputs, + double *outputs +) +{ + + const double T = inputs[0]; + + const double P0 = parameters[0]; + const double P1 = parameters[1]; + const double P2 = parameters[2]; + + const double term1 = P1*(1/T - 1/P2); + const double term2 = exp(term1); + + outputs[0] = P0*term2; + + //outputs[0] = P0 + T*P1 + P2*T*T; +} +''', + # These are global bounds for the function + inputs={ + 'T': { 'min': 200.0, 'max': 250.0, 'argPos': 0 }, #check if boundaries reasonable, from this range, the random values for the DOE are chosen! + }, + outputs={ + 'H': { 'min': 9e99, 'max': -9e99, 'argPos': 0 }, + }, + parameters={ + 'param0': { 'min': -1E10, 'max': 1E10, 'argPos': 0 }, #check if boundaries are reasonable!!! + 'param1': { 'min': -1E10, 'max': 1E10, 'argPos': 1 }, + 'param2': { 'min': 1.0, 'max': 1E10, 'argPos': 2 }, + }, +) + +m = BackwardMappingModel( + _id= 'Solubility', + surrogateFunction= f, + exactTask= SolubilityExactSim(), + substituteModels= [ ], + initialisationStrategy= Strategy.InitialPoints( + initialPoints= + { + 'T': [200.0, 220.0], + }, + ), + outOfBoundsStrategy= Strategy.ExtendSpaceStochasticSampling( + nNewPoints= 4 + ), + parameterFittingStrategy= Strategy.NonLinFitWithErrorContol( + testDataPercentage= 0.2, + maxError= 50.0, + improveErrorStrategy= Strategy.StochasticSampling( + nNewPoints= 2 + ), + maxIterations= 5 # Currently not used + ), +) + diff --git a/applications/PUfoam/MoDeNaModels/Solubility/ExampleOfUsage/src/.gitignore b/applications/PUfoam/MoDeNaModels/Solubility/ExampleOfUsage/src/.gitignore new file mode 100644 index 000000000..0c66e77c1 --- /dev/null +++ b/applications/PUfoam/MoDeNaModels/Solubility/ExampleOfUsage/src/.gitignore @@ -0,0 +1,20 @@ +# Backups +*~ +*bak + +# Various intermediate files from automake +CMakeFiles/ +Makefile +libmodena.pc +CMakeCache.txt +cmake_install.cmake +install_manifest.txt + +# Intermediate files generated by SWIG +*_wrap.c + +# locate results (executables and libraries) +*.l[ao] + +flowRateExact +twoTanksMacroscopicProblem diff --git a/applications/PUfoam/MoDeNaModels/Solubility/ExampleOfUsage/src/CMakeLists.txt b/applications/PUfoam/MoDeNaModels/Solubility/ExampleOfUsage/src/CMakeLists.txt new file mode 100644 index 000000000..b55e0d37e --- /dev/null +++ b/applications/PUfoam/MoDeNaModels/Solubility/ExampleOfUsage/src/CMakeLists.txt @@ -0,0 +1,31 @@ +cmake_minimum_required (VERSION 2.8) +project (tutorialModels C CXX) + +if( CMAKE_VERSION VERSION_GREATER "3.0" ) + cmake_policy(SET CMP0042 OLD) + cmake_policy(SET CMP0026 OLD) +endif() + +set(CMAKE_BUILD_TYPE Release) + +add_custom_target(debug + COMMAND ${CMAKE_COMMAND} -DCMAKE_BUILD_TYPE=Debug ${CMAKE_SOURCE_DIR} + COMMAND ${CMAKE_COMMAND} --build ${CMAKE_BINARY_DIR} --target all + COMMENT "Switch CMAKE_BUILD_TYPE to Debug" + ) + +add_custom_target(release + COMMAND ${CMAKE_COMMAND} -DCMAKE_BUILD_TYPE=Release ${CMAKE_SOURCE_DIR} + COMMAND ${CMAKE_COMMAND} --build ${CMAKE_BINARY_DIR} --target all + COMMENT "Switch CMAKE_BUILD_TYPE to Release" + ) + +find_package(MODENA REQUIRED) + +include(CheckCInline) +check_c_inline(C_INLINE) + + +add_executable(MacroscopicProblem MacroscopicProblem.C) +target_link_libraries(MacroscopicProblem MODENA::modena) + diff --git a/applications/PUfoam/MoDeNaModels/Solubility/ExampleOfUsage/src/MacroscopicProblem.C b/applications/PUfoam/MoDeNaModels/Solubility/ExampleOfUsage/src/MacroscopicProblem.C new file mode 100644 index 000000000..1c40b7cce --- /dev/null +++ b/applications/PUfoam/MoDeNaModels/Solubility/ExampleOfUsage/src/MacroscopicProblem.C @@ -0,0 +1,108 @@ +/* + + ooo ooooo oooooooooo. ooooo ooo + `88. .888' `888' `Y8b `888b. `8' + 888b d'888 .ooooo. 888 888 .ooooo. 8 `88b. 8 .oooo. + 8 Y88. .P 888 d88' `88b 888 888 d88' `88b 8 `88b. 8 `P )88b + 8 `888' 888 888 888 888 888 888ooo888 8 `88b.8 .oP"888 + 8 Y 888 888 888 888 d88' 888 .o 8 `888 d8( 888 + o8o o888o `Y8bod8P' o888bood8P' `Y8bod8P' o8o `8 `Y888""8o + +Copyright + 2014-2015 MoDeNa Consortium, All rights reserved. + +License + This file is part of Modena. + + Modena is free software; you can redistribute it and/or modify it under + the terms of the GNU General Public License as published by the Free + Software Foundation, either version 3 of the License, or (at your option) + any later version. + + Modena is distributed in the hope that it will be useful, but WITHOUT ANY + WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS + FOR A PARTICULAR PURPOSE. See the GNU General Public License + for more details. + + You should have received a copy of the GNU General Public License along + with Modena. If not, see . + +Description + Solving the two tank problem the MoDeNa way. + + A prototypical macros-scopic code embeds a micro-scale model (flowRate) + through the MoDeNa interface library. + +Authors + Henrik Rusche + +Contributors +*/ + +#include +#include +#include "modena.h" + +using namespace std; + +int +main(int argc, char *argv[]) +{ + double T = 200; + double Tend = 220.0; + + // Instantiate index set + //modena_index_set_t *indexSet = modena_index_set_new("species"); + + + // Instantiate a model + modena_model_t *model = modena_model_new("Solubility"); //muss das FunctionModule genau so heißen?? + if(modena_error_occurred()) + { + return modena_error(); + } + + // Allocate memory and fetch arg positions + modena_inputs_t *inputs = modena_inputs_new(model); //How many inputs and outputs is defined in the function module!! + modena_outputs_t *outputs = modena_outputs_new(model); + + + size_t Tpos = modena_model_inputs_argPos(model, "T"); + + modena_model_argPos_check(model); + + + while(T < Tend) + { + // Set input vector + modena_inputs_set(inputs, Tpos, T); + + // Call the model + int ret = modena_model_call(model, inputs, outputs); + + // Terminate, if requested + if(modena_error_occurred()) + { + modena_inputs_destroy(inputs); + modena_outputs_destroy(outputs); + modena_model_destroy(model); + + return modena_error(); + } + + // Fetch result + double H = modena_outputs_get(outputs, 0); + + cout << "T = " << T; + + + T = T + 10.0; + } + + + modena_inputs_destroy(inputs); + modena_outputs_destroy(outputs); + modena_model_destroy(model); + + return 0; +} diff --git a/applications/PUfoam/MoDeNaModels/Solubility/ExampleOfUsage/src/srcDetailedCode/Numeric_subroutines.f90 b/applications/PUfoam/MoDeNaModels/Solubility/ExampleOfUsage/src/srcDetailedCode/Numeric_subroutines.f90 new file mode 100644 index 000000000..7a243184b --- /dev/null +++ b/applications/PUfoam/MoDeNaModels/Solubility/ExampleOfUsage/src/srcDetailedCode/Numeric_subroutines.f90 @@ -0,0 +1,1667 @@ +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! + SUBROUTINE bicub_derivative ( ya, x1a, x2a, y1a, y2a, y12a, i_max, k_max ) +! + USE DFT_MODULE, ONLY: NDFT, r_grid + IMPLICIT NONE +! +! ---------------------------------------------------------------------- + REAL, INTENT(IN) :: ya(r_grid,NDFT) + REAL, INTENT(IN) :: x1a(r_grid) + REAL, INTENT(IN) :: x2a(NDFT) + REAL, INTENT(OUT) :: y1a(r_grid,NDFT) + REAL, INTENT(OUT) :: y2a(r_grid,NDFT) + REAL, INTENT(OUT) :: y12a(r_grid,NDFT) + INTEGER, INTENT(IN) :: i_max + INTEGER, INTENT(IN) :: k_max +! +! ---------------------------------------------------------------------- + INTEGER :: i, k +! ---------------------------------------------------------------------- + + +DO i = 2, i_max-1 + DO k = 2, k_max-1 + y1a(i,k) = (ya(i+1,k)-ya(i-1,k)) / (x1a(i+1)-x1a(i-1)) + y2a(i,k) = (ya(i,k+1)-ya(i,k-1)) / (x2a(k+1)-x2a(k-1)) + y12a(i,k)= (ya(i+1,k+1)-ya(i+1,k-1)-ya(i-1,k+1)+ya(i-1,k-1)) & + /((x1a(i+1)-x1a(i-1))*(x2a(k+1)-x2a(k-1))) + END DO +END DO + +i = 1 +DO k = 1, k_max + y1a(i,k) = 0.0 + y2a(i,k) = 0.0 + y12a(i,k)= 0.0 +END DO + +k = 1 +DO i = 1, i_max + y1a(i,k) = 0.0 + y2a(i,k) = 0.0 + y12a(i,k)= 0.0 +END DO + + +i = i_max +DO k = 2, k_max-1 + y1a(i,k) = (ya(i,k)-ya(i-1,k)) / (x1a(i)-x1a(i-1)) + y2a(i,k) = (ya(i,k+1)-ya(i,k-1)) / (x2a(k+1)-x2a(k-1)) + y12a(i,k)= (ya(i,k+1)-ya(i,k-1)-ya(i-1,k+1)+ya(i-1,k-1)) & + /((x1a(i)-x1a(i-1))*(x2a(k+1)-x2a(k-1))) +END DO + + +k = k_max +DO i = 2, i_max-1 + y1a(i,k) = (ya(i+1,k)-ya(i-1,k)) / (x1a(i+1)-x1a(i-1)) + y2a(i,k) = (ya(i,k)-ya(i,k-1)) / (x2a(k)-x2a(k-1)) + y12a(i,k)= (ya(i+1,k)-ya(i+1,k-1)-ya(i-1,k)+ya(i-1,k-1)) & + /((x1a(i+1)-x1a(i-1))*(x2a(k)-x2a(k-1))) +END DO + +k = k_max +i = i_max +y1a(i,k) = (ya(i,k)-ya(i-1,k)) / (x1a(i)-x1a(i-1)) +y2a(i,k) = (ya(i,k)-ya(i,k-1)) / (x2a(k)-x2a(k-1)) +y12a(i,k)= (ya(i,k)-ya(i,k-1)-ya(i-1,k)+ya(i-1,k-1)) & + /((x1a(i)-x1a(i-1))*(x2a(k)-x2a(k-1))) + +END SUBROUTINE bicub_derivative + + +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! + SUBROUTINE bicub_c ( ya, x1a, x2a, y1a, y2a, y12a, c_bicub, i_max, k_max ) +! + USE DFT_MODULE, ONLY: NDFT, r_grid + IMPLICIT NONE +! +! ---------------------------------------------------------------------- + REAL, INTENT(IN) :: ya(r_grid,NDFT) + REAL, INTENT(IN) :: x1a(r_grid) + REAL, INTENT(IN) :: x2a(NDFT) + REAL, INTENT(IN) :: y1a(r_grid,NDFT) + REAL, INTENT(IN) :: y2a(r_grid,NDFT) + REAL, INTENT(IN) :: y12a(r_grid,NDFT) + REAL, INTENT(OUT) :: c_bicub(r_grid,NDFT,4,4) + INTEGER, INTENT(IN) :: i_max + INTEGER, INTENT(IN) :: k_max +! +! ---------------------------------------------------------------------- + INTEGER :: i, k, m, n + REAL :: y(4),y1(4),y2(4),y12(4),x1l,x1u,x2l,x2u + REAL :: c(4,4) +! ---------------------------------------------------------------------- + +DO i = 1, i_max-1 + DO k = 1, k_max-1 + y(1)=ya(i,k) + y(2)=ya(i+1,k) + y(3)=ya(i+1,k+1) + y(4)=ya(i,k+1) + + y1(1)=y1a(i,k) + y1(2)=y1a(i+1,k) + y1(3)=y1a(i+1,k+1) + y1(4)=y1a(i,k+1) + + y2(1)=y2a(i,k) + y2(2)=y2a(i+1,k) + y2(3)=y2a(i+1,k+1) + y2(4)=y2a(i,k+1) + + y12(1)=y12a(i,k) + y12(2)=y12a(i+1,k) + y12(3)=y12a(i+1,k+1) + y12(4)=y12a(i,k+1) + + x1l=x1a(i) + x1u=x1a(i+1) + x2l=x2a(k) + x2u=x2a(k+1) + + CALL bcucof(y,y1,y2,y12,x1u-x1l,x2u-x2l,c) + DO m=1,4 + DO n=1,4 + c_bicub(i,k,m,n)=c(m,n) + END DO + END DO + + END DO +END DO + +END SUBROUTINE bicub_c + +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! + SUBROUTINE bcucof(y,y1,y2,y12,d1,d2,c) +! + IMPLICIT NONE +! +! ---------------------------------------------------------------------- + REAL, INTENT(IN) :: y(4) + REAL, INTENT(IN) :: y1(4) + REAL, INTENT(IN) :: y2(4) + REAL, INTENT(IN) :: y12(4) + REAL, INTENT(IN) :: d1 + REAL, INTENT(IN) :: d2 + REAL, INTENT(OUT) :: c(4,4) +! +! ---------------------------------------------------------------------- + INTEGER :: i,j,k,l + REAL :: d1d2,xx,cl(16),wt(16,16),x(16) + SAVE wt + DATA wt/1,0,-3,2,4*0,-3,0,9,-6,2,0,-6,4,8*0,3,0,-9,6,-2,0,6,-4,10* & + 0,9,-6,2*0,-6,4,2*0,3,-2,6*0,-9,6,2*0,6,-4,4*0,1,0,-3,2,-2,0,6,-4, & + 1,0,-3,2,8*0,-1,0,3,-2,1,0,-3,2,10*0,-3,2,2*0,3,-2,6*0,3,-2,2*0, & + -6,4,2*0,3,-2,0,1,-2,1,5*0,-3,6,-3,0,2,-4,2,9*0,3,-6,3,0,-2,4,-2, & + 10*0,-3,3,2*0,2,-2,2*0,-1,1,6*0,3,-3,2*0,-2,2,5*0,1,-2,1,0,-2,4, & + -2,0,1,-2,1,9*0,-1,2,-1,0,1,-2,1,10*0,1,-1,2*0,-1,1,6*0,-1,1,2*0, & + 2,-2,2*0,-1,1/ +! ---------------------------------------------------------------------- + +d1d2 = d1 * d2 +DO i = 1, 4 + x(i) = y(i) + x(i+4) = y1(i)*d1 + x(i+8) = y2(i)*d2 + x(i+12) = y12(i)*d1d2 +END DO +DO i = 1, 16 + xx = 0.0 + DO k = 1, 16 + xx = xx + wt(i,k) * x(k) + END DO + cl(i) = xx +END DO +l = 0 +DO i = 1, 4 + DO j = 1, 4 + l = l + 1 + c(i,j) = cl(l) + END DO +END DO + +END SUBROUTINE bcucof + + +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! + SUBROUTINE BI_CUB_SPLINE ( rho_rdf, xg, ya, x1a, x2a, y1a, y2a, y12a, & + c_bicub, rdf, dg_drho, dg_dr, i_max, ih, k ) +! + USE DFT_MODULE, ONLY: NDFT, r_grid + IMPLICIT NONE +! +! ---------------------------------------------------------------------- + REAL, INTENT(IN OUT) :: rho_rdf + REAL, INTENT(IN OUT) :: xg + REAL, INTENT(IN) :: ya(r_grid,NDFT) + REAL, INTENT(IN) :: x1a(r_grid) + REAL, INTENT(IN) :: x2a(NDFT) + REAL, INTENT(IN) :: y1a(r_grid,NDFT) + REAL, INTENT(IN) :: y2a(r_grid,NDFT) + REAL, INTENT(IN) :: y12a(r_grid,NDFT) + REAL, INTENT(IN) :: c_bicub(r_grid,NDFT,4,4) + REAL, INTENT(OUT) :: rdf + REAL, INTENT(OUT) :: dg_drho + REAL, INTENT(OUT) :: dg_dr + INTEGER, INTENT(IN OUT) :: i_max + !INTEGER, INTENT(IN OUT) :: k_max + INTEGER, INTENT(OUT) :: ih + INTEGER, INTENT(IN) :: k +! +! ---------------------------------------------------------------------- + INTEGER :: m, n + + REAL :: y(4),y1(4),y2(4),y12(4),x1l,x1u,x2l,x2u + REAL :: c(4,4) +! ---------------------------------------------------------------------- + +IF ( rho_rdf < x1a(1) ) THEN + dg_drho = 0.0 + dg_dr = 0.0 + rdf = 1.0 + RETURN +END IF +IF ( x1a(ih) <= rho_rdf .AND. rho_rdf < x1a(ih+1) ) GO TO 10 +IF ( ih > 2 ) THEN + IF ( x1a(ih-1) <= rho_rdf .AND. rho_rdf < x1a(ih) ) THEN + ih = ih - 1 + GO TO 10 + END IF +END IF +! write (*,*) 'in ',ih +CALL hunt ( x1a, i_max, rho_rdf, ih ) +! write (*,*) 'out',ih +10 CONTINUE +IF ( x2a(k) /= xg ) THEN +! write (*,*) 'error bi-cubic-spline',k,x2a(k),xg +! DO k=1,NDFT +! write (*,*) k,x2a(k) +! ENDDO +! stop +END IF + + + +y(1) = ya(ih,k) +y(2) = ya(ih+1,k) +y(3) = ya(ih+1,k+1) +y(4) = ya(ih,k+1) + +y1(1) = y1a(ih,k) +y1(2) = y1a(ih+1,k) +y1(3) = y1a(ih+1,k+1) +y1(4) = y1a(ih,k+1) + +y2(1) = y2a(ih,k) +y2(2) = y2a(ih+1,k) +y2(3) = y2a(ih+1,k+1) +y2(4) = y2a(ih,k+1) + +y12(1) = y12a(ih,k) +y12(2) = y12a(ih+1,k) +y12(3) = y12a(ih+1,k+1) +y12(4) = y12a(ih,k+1) + +x1l = x1a(ih) +x1u = x1a(ih+1) +x2l = x2a(k) +x2u = x2a(k+1) + +DO m = 1, 4 + DO n = 1, 4 + c(m,n) = c_bicub( ih, k, m, n ) + END DO +END DO +CALL bcuint ( x1l, x1u, x2l, x2u, rho_rdf, xg, c, rdf, dg_drho, dg_dr ) + +END SUBROUTINE BI_CUB_SPLINE + +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! SUBROUTINE hunt +! +! Given an array xx(1:n), and given a value x, returns a value jlo +! such that x is between xx(jlo) and xx(jlo+1). xx(1:n) must be +! monotonic, either increasing or decreasing. jlo=0 or jlo=n is +! returned to indicate that x is out of range. jlo on input is taken +! as the initial guess for jlo on output. +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! + SUBROUTINE hunt ( xx, n, x, jlo ) +! + IMPLICIT NONE +! +! ---------------------------------------------------------------------- + INTEGER, INTENT(IN) :: n + INTEGER, INTENT(OUT) :: jlo + REAL, INTENT(IN) :: xx(n) + REAL :: x +! +! ---------------------------------------------------------------------- + INTEGER :: inc,jhi,jm + LOGICAL :: ascnd +! ---------------------------------------------------------------------- + +ascnd = xx(n) >= xx(1) +IF( jlo <= 0 .OR. jlo > n ) THEN + jlo = 0 + jhi = n + 1 + GO TO 3 +END IF +inc = 1 +IF( x >= xx(jlo) .EQV. ascnd ) THEN +1 jhi = jlo + inc + IF ( jhi > n ) THEN + jhi = n + 1 + ELSE IF ( x >= xx(jhi) .EQV. ascnd ) THEN + jlo = jhi + inc = inc + inc + GO TO 1 + END IF +ELSE + jhi = jlo +2 jlo = jhi - inc + IF ( jlo < 1 ) THEN + jlo = 0 + ELSE IF ( x < xx(jlo) .EQV. ascnd ) THEN + jhi = jlo + inc = inc + inc + GO TO 2 + END IF +END IF +3 IF (jhi-jlo == 1 ) THEN + IF ( x == xx(n)) jlo = n - 1 + IF ( x == xx(1) ) jlo = 1 + RETURN +END IF +jm = ( jhi + jlo ) / 2 +IF ( x >= xx(jm) .EQV. ascnd ) THEN + jlo = jm +ELSE + jhi = jm +END IF +GO TO 3 +END SUBROUTINE hunt + + + +!********************************************************************** +! +!********************************************************************** +! + !SUBROUTINE bcuint ( y, y1, y2, y12, x1l, x1u, x2l, x2u, x1, x2, c, ansy, ansy1, ansy2 ) + SUBROUTINE bcuint ( x1l, x1u, x2l, x2u, x1, x2, c, ansy, ansy1, ansy2 ) +! + IMPLICIT NONE +! +! ---------------------------------------------------------------------- + !REAL, INTENT(IN OUT) :: y(4) + !REAL, INTENT(IN OUT) :: y1(4) + !REAL, INTENT(IN OUT) :: y2(4) + !REAL, INTENT(IN OUT) :: y12(4) + REAL, INTENT(IN OUT) :: x1l + REAL, INTENT(IN OUT) :: x1u + REAL, INTENT(IN OUT) :: x2l + REAL, INTENT(IN OUT) :: x2u + REAL, INTENT(IN OUT) :: x1 + REAL, INTENT(IN OUT) :: x2 + REAL, INTENT(IN) :: c(4,4) + REAL, INTENT(OUT) :: ansy + REAL, INTENT(OUT) :: ansy1 + REAL, INTENT(OUT) :: ansy2 +! +! ---------------------------------------------------------------------- + !U USES bcucof + INTEGER :: i + REAL :: t, u +! ---------------------------------------------------------------------- + +! call bcucof ( y, y1, y2, y12, x1u-x1l, x2u-x2l, c ) + +IF ( x1u == x1l .OR. x2u == x2l ) PAUSE 'bad input in bcuint' +t = (x1-x1l) / (x1u-x1l) +u = (x2-x2l) / (x2u-x2l) +ansy = 0.0 +ansy2 = 0.0 +ansy1 = 0.0 +DO i = 4, 1, -1 + ansy = t *ansy + ( (c(i,4)*u + c(i,3))*u+c(i,2) )*u + c(i,1) + ansy2 = t *ansy2 + ( 3.*c(i,4)*u+2.*c(i,3) )*u + c(i,2) + ansy1 = u *ansy1 + ( 3.*c(4,i)*t+2.*c(3,i) )*t + c(2,i) +END DO +ansy1 = ansy1 / (x1u-x1l) +ansy2 = ansy2 / (x2u-x2l) + +END SUBROUTINE bcuint + + +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! SUBROUTINE spline +! +! Given arrays x(1:n) and y(1:n) containing a tabulated function, +! i.e., yi = f(xi), with x1 < x2 < .. . < xN, and given values yp1 and +! ypn for the first derivative of the interpolating function at points 1 +! and n, respectively, this routine returns an array y2(1:n) of length n +! which contains the second derivatives of the interpolating function at +! the tabulated points xi. If yp1 and/or ypn are equal to 1 1030 or +! larger, the routine is signaled to set the corresponding boundary +! condition for a natural spline, with zero second derivative on that +! boundary. +! Parameter: NMAX is the largest anticipated value of n. +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! + SUBROUTINE spline ( x, y, n, yp1, ypn, y2 ) +! + IMPLICIT NONE +! +! ---------------------------------------------------------------------- + INTEGER, INTENT(IN) :: n + REAL, INTENT(IN) :: x(n) + REAL, INTENT(IN) :: y(n) + REAL, INTENT(IN) :: yp1 + REAL, INTENT(IN) :: ypn + REAL, INTENT(OUT) :: y2(n) +! +! ---------------------------------------------------------------------- + INTEGER, PARAMETER :: NMAX = 500 + INTEGER :: i, k + REAL :: p, qn, sig, un, u(NMAX) +! ---------------------------------------------------------------------- + + IF ( yp1 > 0.99E30 ) THEN + y2(1) = 0.0 + u(1) = 0.0 + ELSE + y2(1) = -0.5 + u(1) = ( 3.0/(x(2)-x(1)) ) * ( (y(2)-y(1))/(x(2)-x(1))-yp1 ) + END IF + DO i = 2, n-1 + IF ( (x(i+1)-x(i)) == 0.0 .OR. (x(i)-x(i-1)) == 0.0 .OR. (x(i+1)-x(i-1)) == 0.0 ) THEN + write (*,*) 'error in spline-interpolation' + stop + END IF + sig = (x(i)-x(i-1)) / (x(i+1)-x(i-1)) + p = sig*y2(i-1) + 2.0 + y2(i) = (sig-1.0) / p + u(i) = ( 6.0 * ((y(i+1)-y(i))/(x(i+1)-x(i))-(y(i)-y(i-1))/(x(i)-x(i-1))) / (x(i+1)-x(i-1)) & + - sig * u(i-1) ) / p + END DO + IF ( ypn > 0.99E30 ) THEN + qn = 0.0 + un = 0.0 + ELSE + qn = 0.5 + un = (3.0/(x(n)-x(n-1))) * (ypn-(y(n)-y(n-1))/(x(n)-x(n-1))) + END IF + y2(n) = (un-qn*u(n-1)) / (qn*y2(n-1)+1.0) + DO k = n-1, 1, -1 + y2(k) = y2(k) * y2(k+1) + u(k) + END DO + +END SUBROUTINE spline + +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! SUBROUTINE splint_integral +! +! Given the arrays xa(1:n) and ya(1:n) of length n, which tabulate a +! function (with the in order), and given the array y2a(1:n), which is +! the output from spline above, and given a value of x, this routine +! returns a cubic-spline interpolated value y. +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! + SUBROUTINE splint_integral ( xa, ya, y2a, n, xlo, xhi, integral ) +! + IMPLICIT NONE +! +! ---------------------------------------------------------------------- + INTEGER, INTENT(IN) :: n + REAL, INTENT(IN) :: xa(n) + REAL, INTENT(IN) :: ya(n) + REAL, INTENT(IN) :: y2a(n) + REAL, INTENT(IN) :: xlo + REAL, INTENT(IN) :: xhi + REAL, INTENT(OUT) :: integral +! +! ---------------------------------------------------------------------- + INTEGER :: k, khi_l, klo_l, khi_h, klo_h + REAL :: xl, xh, h, INT, x0, x1, y0, y1, y20, y21 +! ---------------------------------------------------------------------- + + integral = 0.0 + klo_l = 1 + khi_l = n +1 IF ( khi_l-klo_l > 1 ) THEN + k = ( khi_l + klo_l ) / 2 + IF ( xa(k) > xlo ) THEN + khi_l = k + ELSE + klo_l = k + END IF + GO TO 1 + END IF + + klo_h = 1 + khi_h = n +2 IF ( khi_h-klo_h > 1 ) THEN + k = ( khi_h + klo_h ) / 2 + IF ( xa(k) > xhi ) THEN + khi_h = k + ELSE + klo_h = k + END IF + GO TO 2 + END IF + + ! integration in spline pieces, the lower interval, bracketed + ! by xa(klo_L) and xa(khi_L) is in steps shifted upward. + + ! first: determine upper integration bound + xl = xlo +3 CONTINUE + IF ( khi_h > khi_l ) THEN + xh = xa(khi_l) + ELSE IF ( khi_h == khi_l ) THEN + xh = xhi + ELSE + WRITE (*,*) 'error in spline-integration' + PAUSE + END IF + + h = xa(khi_l) - xa(klo_l) + IF ( h == 0.0 ) PAUSE 'bad xa input in splint' + x0 = xa(klo_l) + x1 = xa(khi_l) + y0 = ya(klo_l) + y1 = ya(khi_l) + y20= y2a(klo_l) + y21= y2a(khi_l) + ! int = -xL/h * ( (x1-.5*xL)*y0 + (0.5*xL-x0)*y1 & + ! +y20/6.*(x1**3-1.5*xL*x1*x1+xL*xL*x1-.25*xL**3) & + ! -y20/6.*h*h*(x1-.5*xL) & + ! +y21/6.*(.25*xL**3-xL*xL*x0+1.5*xL*x0*x0-x0**3) & + ! -y21/6.*h*h*(.5*xL-x0) ) + ! int = int + xH/h * ( (x1-.5*xH)*y0 + (0.5*xH-x0)*y1 & + ! +y20/6.*(x1**3-1.5*xH*x1*x1+xH*xH*x1-.25*xH**3) & + ! -y20/6.*h*h*(x1-.5*xH) & + ! +y21/6.*(.25*xH**3-xH*xH*x0+1.5*xH*x0*x0-x0**3) & + ! -y21/6.*h*h*(.5*xH-x0) ) + INT = -1.0/h * ( xl*((x1-.5*xl)*y0 + (0.5*xl-x0)*y1) & + -y20/24.*(x1-xl)**4 + y20/6.*(0.5*xl*xl-x1*xl)*h*h & + +y21/24.*(xl-x0)**4 - y21/6.*(0.5*xl*xl-x0*xl)*h*h ) + INT = INT + 1.0/h * ( xh*((x1-.5*xh)*y0 + (0.5*xh-x0)*y1) & + -y20/24.*(x1-xh)**4 + y20/6.*(0.5*xh*xh-x1*xh)*h*h & + +y21/24.*(xh-x0)**4 - y21/6.*(0.5*xh*xh-x0*xh)*h*h ) + + integral = integral + INT + ! write (*,*) integral,x1,xH + klo_l = klo_l + 1 + khi_l = khi_l + 1 + xl = x1 + IF (khi_h /= (khi_l-1)) GO TO 3 ! the -1 in (khi_L-1) because khi_L was already counted up + +END SUBROUTINE splint_integral + + + + +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! + REAL FUNCTION praxis( t0, machep, h0, n, prin, x, f, fmin ) + + IMPLICIT NONE + +! ---------------------------------------------------------------------- + REAL, INTENT(IN OUT) :: t0 + REAL, INTENT(IN) :: machep + REAL, INTENT(IN) :: h0 + INTEGER :: n + INTEGER, INTENT(IN OUT) :: prin + REAL, INTENT(IN OUT) :: x(n) + REAL :: f + REAL, INTENT(IN OUT) :: fmin +! ---------------------------------------------------------------------- + +EXTERNAL f + +! PRAXIS RETURNS THE MINIMUM OF THE FUNCTION F(X,N) OF N VARIABLES +! USING THE PRINCIPAL AXIS METHOD. THE GRADIENT OF THE FUNCTION IS +! NOT REQUIRED. + +! FOR A DESCRIPTION OF THE ALGORITHM, SEE CHAPTER SEVEN OF +! "ALGORITHMS FOR FINDING ZEROS AND EXTREMA OF FUNCTIONS WITHOUT +! CALCULATING DERIVATIVES" BY RICHARD P BRENT. + +! THE PARAMETERS ARE: +! T0 IS A TOLERANCE. PRAXIS ATTEMPTS TO RETURN PRAXIS=F(X) +! SUCH THAT IF X0 IS THE TRUE LOCAL MINIMUM NEAR X, THEN +! NORM(X-X0) < T0 + SQUAREROOT(MACHEP)*NORM(X). +! MACHEP IS THE MACHINE PRECISION, THE SMALLEST NUMBER SUCH THAT +! 1 + MACHEP > 1. MACHEP SHOULD BE 16.**-13 (ABOUT +! 2.22D-16) FOR REAL*8 ARITHMETIC ON THE IBM 360. +! H0 IS THE MAXIMUM STEP SIZE. H0 SHOULD BE SET TO ABOUT THE +! MAXIMUM DISTANCE FROM THE INITIAL GUESS TO THE MINIMUM. +! (IF H0 IS SET TOO LARGE OR TOO SMALL, THE INITIAL RATE OF +! CONVERGENCE MAY BE SLOW.) +! N (AT LEAST TWO) IS THE NUMBER OF VARIABLES UPON WHICH +! THE FUNCTION DEPENDS. +! PRIN CONTROLS THE PRINTING OF INTERMEDIATE RESULTS. +! IF PRIN=0, NOTHING IS PRINTED. +! IF PRIN=1, F IS PRINTED AFTER EVERY N+1 OR N+2 LINEAR +! MINIMIZATIONS. FINAL X IS PRINTED, BUT INTERMEDIATE X IS +! PRINTED ONLY IF N IS AT MOST 4. +! IF PRIN=2, THE SCALE FACTORS AND THE PRINCIPAL VALUES OF +! THE APPROXIMATING QUADRATIC FORM ARE ALSO PRINTED. +! IF PRIN=3, X IS ALSO PRINTED AFTER EVERY FEW LINEAR +! MINIMIZATIONS. +! IF PRIN=4, THE PRINCIPAL VECTORS OF THE APPROXIMATING +! QUADRATIC FORM ARE ALSO PRINTED. +! X IS AN ARRAY CONTAINING ON ENTRY A GUESS OF THE POINT OF +! MINIMUM, ON RETURN THE ESTIMATED POINT OF MINIMUM. +! F(X,N) IS THE FUNCTION TO BE MINIMIZED. F SHOULD BE A REAL*8 +! FUNCTION DECLARED EXTERNAL IN THE CALLING PROGRAM. +! FMIN IS AN ESTIMATE OF THE MINIMUM, USED ONLY IN PRINTING +! INTERMEDIATE RESULTS. +! THE APPROXIMATING QUADRATIC FORM IS +! Q(X') = F(X,N) + (1/2) * (X'-X)-TRANSPOSE * A * (X'-X) +! WHERE X IS THE BEST ESTIMATE OF THE MINIMUM AND A IS +! INVERSE(V-TRANSPOSE) * D * INVERSE(V) +! (V(*,*) IS THE MATRIX OF SEARCH DIRECTIONS; D(*) IS THE ARRAY +! OF SECOND DIFFERENCES). IF F HAS CONTINUOUS SECOND DERIVATIVES +! NEAR X0, A WILL TEND TO THE HESSIAN OF F AT X0 AS X APPROACHES X0. + +! IT IS ASSUMED THAT ON FLOATING-POINT UNDERFLOW THE RESULT IS SET +! TO ZERO. +! THE USER SHOULD OBSERVE THE COMMENT ON HEURISTIC NUMBERS AFTER +! THE INITIALIZATION OF MACHINE DEPENDENT NUMBERS. + + LOGICAL :: illc + INTEGER :: nl,nf,kl,kt,ktm,idim,i,j,k,k2,km1,klmk,ii,im1 + REAL :: s,sl,dn,dmin,fx,f1,lds,ldt,t,h,sf,df,qf1,qd0, qd1,qa,qb,qc + REAL :: m2,m4,small,vsmall,large,vlarge,scbd,ldfac,t2, dni,value + REAL :: random + +!.....IF N>20 OR IF N<20 AND YOU NEED MORE SPACE, CHANGE '20' TO THE +! LARGEST VALUE OF N IN THE NEXT CARD, IN THE CARD 'IDIM=20', AND +! IN THE DIMENSION STATEMENTS IN SUBROUTINES MINFIT,MIN,FLIN,QUAD. + + REAL :: d(20),y(20),z(20),q0(20),q1(20),v(20,20) + COMMON /global/ fx,ldt,dmin,nf,nl /q/ v,q0,q1,qa,qb,qc,qd0,qd1,qf1 + +! --------------------------------- +! introduced by Joachim........ + idim = n +! --------------------------------- + + + +!.....INITIALIZATION..... +! MACHINE DEPENDENT NUMBERS: + +small = machep*machep +vsmall = small*small +large = 1.d0/small +vlarge = 1.d0/vsmall +m2 = SQRT(machep) +m4 = SQRT(m2) + +! HEURISTIC NUMBERS: +! IF THE AXES MAY BE BADLY SCALED (WHICH IS TO BE AVOIDED IF +! POSSIBLE), THEN SET SCBD=10. OTHERWISE SET SCBD=1. +! IF THE PROBLEM IS KNOWN TO BE ILL-CONDITIONED, SET ILLC=TRUE. +! OTHERWISE SET ILLC=FALSE. +! KTM IS THE NUMBER OF ITERATIONS WITHOUT IMPROVEMENT BEFORE THE +! ALGORITHM TERMINATES. KTM=4 IS VERY CAUTIOUS; USUALLY KTM=1 +! IS SATISFACTORY. + +scbd = 1.0 +illc = .false. +ktm = 1 + +ldfac = 0.01 +IF (illc) ldfac = 0.1 +kt = 0 +nl = 0 +nf = 1 +fx = f(x,n) +qf1 = fx +t = small+ABS(t0) +t2 = t +dmin = small +h = h0 +IF (h < 100*t) h = 100*t +ldt = h +!.....THE FIRST SET OF SEARCH DIRECTIONS V IS THE IDENTITY MATRIX..... +DO i = 1,n + DO j = 1,n + v(i,j) = 0.0 + END DO + v(i,i) = 1.0 +END DO +d(1) = 0.0 +qd0 = 0.0 +DO i = 1,n + q0(i) = x(i) + q1(i) = x(i) +END DO +IF (prin > 0) CALL PRINT(n,x,prin,fmin) + +!.....THE MAIN LOOP STARTS HERE..... +40 sf=d(1) +d(1)=0.d0 +s=0.d0 + +!.....MINIMIZE ALONG THE FIRST DIRECTION V(*,1). +! FX MUST BE PASSED TO MIN BY VALUE. +value=fx +CALL MIN(n,1,2,d(1),s,value,.false.,f,x,t,machep,h) +IF (s > 0.d0) GO TO 50 +DO i=1,n + v(i,1)=-v(i,1) +END DO +50 IF (sf > 0.9D0*d(1).AND.0.9D0*sf < d(1)) GO TO 70 +DO i=2,n + d(i)=0.d0 +END DO + +!.....THE INNER LOOP STARTS HERE..... +70 DO k=2,n + DO i=1,n + y(i)=x(i) + END DO + sf=fx + IF (kt > 0) illc=.true. + 80 kl=k + df=0.d0 + +!.....A RANDOM STEP FOLLOWS (TO AVOID RESOLUTION VALLEYS). +! PRAXIS ASSUMES THAT RANDOM RETURNS A RANDOM NUMBER UNIFORMLY +! DISTRIBUTED IN (0,1). + + IF(.NOT.illc) GO TO 95 + DO i=1,n + s=(0.1D0*ldt+t2*(10**kt))*(random(n)-0.5D0) + z(i)=s + DO j=1,n + x(j)=x(j)+s*v(j,i) + END DO + END DO + fx=f(x,n) + nf=nf+1 + +!.....MINIMIZE ALONG THE "NON-CONJUGATE" DIRECTIONS V(*,K),...,V(*,N) + + 95 DO k2=k,n + sl=fx + s=0.d0 + value=fx + CALL MIN(n,k2,2,d(k2),s,value,.false.,f,x,t,machep,h) + IF (illc) GO TO 97 + s=sl-fx + GO TO 99 + 97 s=d(k2)*((s+z(k2))**2) + 99 IF (df > s) CYCLE + df=s + kl=k2 + END DO + IF (illc.OR.(df >= ABS((100*machep)*fx))) GO TO 110 + +!.....IF THERE WAS NOT MUCH IMPROVEMENT ON THE FIRST TRY, SET +! ILLC=TRUE AND START THE INNER LOOP AGAIN..... + + illc=.true. + GO TO 80 + 110 IF (k == 2.AND.prin > 1) CALL vcprnt(1,d,n) + +!.....MINIMIZE ALONG THE "CONJUGATE" DIRECTIONS V(*,1),...,V(*,K-1) + + km1=k-1 + DO k2=1,km1 + s=0 + value=fx + CALL MIN(n,k2,2,d(k2),s,value,.false.,f,x,t,machep,h) + END DO + f1=fx + fx=sf + lds=0 + DO i=1,n + sl=x(i) + x(i)=y(i) + sl=sl-y(i) + y(i)=sl + lds=lds+sl*sl + END DO + lds=SQRT(lds) + IF (lds <= small) GO TO 160 + +!.....DISCARD DIRECTION V(*,KL). +! IF NO RANDOM STEP WAS TAKEN, V(*,KL) IS THE "NON-CONJUGATE" +! DIRECTION ALONG WHICH THE GREATEST IMPROVEMENT WAS MADE..... + + klmk=kl-k + IF (klmk < 1) GO TO 141 + DO ii=1,klmk + i=kl-ii + DO j=1,n + v(j,i+1)=v(j,i) + END DO + d(i+1)=d(i) + END DO + 141 d(k)=0 + DO i=1,n + v(i,k)=y(i)/lds + END DO + +!.....MINIMIZE ALONG THE NEW "CONJUGATE" DIRECTION V(*,K), WHICH IS +! THE NORMALIZED VECTOR: (NEW X) - (0LD X)..... + + value=f1 + CALL MIN(n,k,4,d(k),lds,value,.true.,f,x,t,machep,h) + IF (lds > 0.d0) GO TO 160 + lds=-lds + DO i=1,n + v(i,k)=-v(i,k) + END DO + 160 ldt=ldfac*ldt + IF (ldt < lds) ldt=lds + IF (prin > 0) CALL PRINT(n,x,prin,fmin) + t2=0.d0 + DO i=1,n + t2=t2+x(i)**2 + END DO + t2=m2*SQRT(t2)+t + +!.....SEE WHETHER THE LENGTH OF THE STEP TAKEN SINCE STARTING THE +! INNER LOOP EXCEEDS HALF THE TOLERANCE..... + + IF (ldt > (0.5*t2)) kt=-1 + kt=kt+1 + IF (kt > ktm) GO TO 400 +END DO +!.....THE INNER LOOP ENDS HERE. + +! TRY QUADRATIC EXTRAPOLATION IN CASE WE ARE IN A CURVED VALLEY. + +CALL quad(n,f,x,t,machep,h) +dn=0.d0 +DO i=1,n + d(i)=1.d0/SQRT(d(i)) + IF (dn < d(i)) dn=d(i) +END DO +IF (prin > 3) CALL maprnt(1,v,idim,n) +DO j=1,n + s=d(j)/dn + DO i=1,n + v(i,j)=s*v(i,j) + END DO +END DO + +!.....SCALE THE AXES TO TRY TO REDUCE THE CONDITION NUMBER..... + +IF (scbd <= 1.d0) GO TO 200 +s=vlarge +DO i=1,n + sl=0.d0 + DO j=1,n + sl=sl+v(i,j)*v(i,j) + END DO + z(i)=SQRT(sl) + IF (z(i) < m4) z(i)=m4 + IF (s > z(i)) s=z(i) +END DO +DO i=1,n + sl=s/z(i) + z(i)=1.d0/sl + IF (z(i) <= scbd) GO TO 189 + sl=1.d0/scbd + z(i)=scbd + 189 DO j=1,n + v(i,j)=sl*v(i,j) + END DO +END DO + +!.....CALCULATE A NEW SET OF ORTHOGONAL DIRECTIONS BEFORE REPEATING +! THE MAIN LOOP. +! FIRST TRANSPOSE V FOR MINFIT: + +200 DO i=2,n + im1=i-1 + DO j=1,im1 + s=v(i,j) + v(i,j)=v(j,i) + v(j,i)=s + END DO +END DO + +!.....CALL MINFIT TO FIND THE SINGULAR VALUE DECOMPOSITION OF V. +! THIS GIVES THE PRINCIPAL VALUES AND PRINCIPAL DIRECTIONS OF THE +! APPROXIMATING QUADRATIC FORM WITHOUT SQUARING THE CONDITION +! NUMBER..... + +CALL minfit(idim,n,machep,vsmall,v,d) + +!.....UNSCALE THE AXES..... + +IF (scbd <= 1.d0) GO TO 250 +DO i=1,n + s=z(i) + DO j=1,n + v(i,j)=s*v(i,j) + END DO +END DO +DO i=1,n + s=0.d0 + DO j=1,n + s=s+v(j,i)**2 + END DO + s=SQRT(s) + d(i)=s*d(i) + s=1/s + DO j=1,n + v(j,i)=s*v(j,i) + END DO +END DO + +250 DO i=1,n + dni=dn*d(i) + IF (dni > large) GO TO 265 + IF (dni < small) GO TO 260 + d(i)=1/(dni*dni) + CYCLE + 260 d(i)=vlarge + CYCLE + 265 d(i)=vsmall +END DO + +!.....SORT THE EIGENVALUES AND EIGENVECTORS..... + +CALL sort(idim,n,d,v) +dmin=d(n) +IF (dmin < small) dmin=small +illc=.false. +IF (m2*d(1) > dmin) illc=.true. +IF (prin > 1.AND.scbd > 1.d0) CALL vcprnt(2,z,n) +IF (prin > 1) CALL vcprnt(3,d,n) +IF (prin > 3) CALL maprnt(2,v,idim,n) +!.....THE MAIN LOOP ENDS HERE..... + +GO TO 40 + +!.....RETURN..... + +400 IF (prin > 0) CALL vcprnt(4,x,n) +praxis=fx + +END FUNCTION praxis + + +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! + SUBROUTINE minfit(m,n,machep,tol,ab,q) + + IMPLICIT NONE + + INTEGER, INTENT(IN OUT) :: m + INTEGER, INTENT(IN) :: n + REAL, INTENT(IN) :: machep + REAL, INTENT(IN OUT) :: tol + REAL, INTENT(IN OUT) :: ab(m,n) + REAL, INTENT(OUT) :: q(n) + INTEGER :: i,j,k,l, kk,kt,l2,ll2,ii,lp1 +! IMPLICIT REAL (A-H,O-Z) + + +REAL :: x,eps,e(20),g,s, f,h,y,c,z,temp +!...AN IMPROVED VERSION OF MINFIT (SEE GOLUB AND REINSCH, 1969) +! RESTRICTED TO M=N,P=0. +! THE SINGULAR VALUES OF THE ARRAY AB ARE RETURNED IN Q AND AB IS +! OVERWRITTEN WITH THE ORTHOGONAL MATRIX V SUCH THAT U.DIAG(Q) = AB.V, +! WHERE U IS ANOTHER ORTHOGONAL MATRIX. + +!...HOUSEHOLDER'S REDUCTION TO BIDIAGONAL FORM... +IF (n == 1) GO TO 200 +eps = machep +g = 0.d0 +x = 0.d0 +DO i=1,n + e(i) = g + s = 0.d0 + l = i + 1 + DO j=i,n + s = s + ab(j,i)**2 + END DO + g = 0.d0 + IF (s < tol) GO TO 4 + f = ab(i,i) + g = SQRT(s) + IF (f >= 0.d0) g = -g + h = f*g - s + ab(i,i)=f-g + IF (l > n) GO TO 4 + DO j=l,n + f = 0.d0 + DO k=i,n + f = f + ab(k,i)*ab(k,j) + END DO + f = f/h + DO k=i,n + ab(k,j) = ab(k,j) + f*ab(k,i) + END DO + END DO + 4 q(i) = g + s = 0.d0 + IF (i == n) GO TO 6 + DO j=l,n + s = s + ab(i,j)*ab(i,j) + END DO + 6 g = 0.d0 + IF (s < tol) GO TO 10 + IF (i == n) GO TO 16 + f = ab(i,i+1) + 16 g = SQRT(s) + IF (f >= 0.d0) g = -g + h = f*g - s + IF (i == n) GO TO 10 + ab(i,i+1) = f - g + DO j=l,n + e(j) = ab(i,j)/h + END DO + DO j=l,n + s = 0.d0 + DO k=l,n + s = s + ab(j,k)*ab(i,k) + END DO + DO k=l,n + ab(j,k) = ab(j,k) + s*e(k) + END DO + END DO + 10 y = ABS(q(i)) + ABS(e(i)) + IF (y > x) x = y +END DO +!...ACCUMULATION OF RIGHT-HAND TRANSFORMATIONS... +ab(n,n) = 1.d0 +g = e(n) +l = n +DO ii=2,n + i = n - ii + 1 + IF (g == 0.d0) GO TO 23 + h = ab(i,i+1)*g + DO j=l,n + ab(j,i) = ab(i,j)/h + END DO + DO j=l,n + s = 0.d0 + DO k=l,n + s = s + ab(i,k)*ab(k,j) + END DO + DO k=l,n + ab(k,j) = ab(k,j) + s*ab(k,i) + END DO + END DO + 23 DO j=l,n + ab(i,j) = 0.d0 + ab(j,i) = 0.d0 + END DO + ab(i,i) = 1.d0 + g = e(i) + l = i +END DO +!...DIAGONALIZATION OF THE BIDIAGONAL FORM... +eps = eps*x +DO kk=1,n + k = n - kk + 1 + kt = 0 + 101 kt = kt + 1 + IF (kt <= 30) GO TO 102 + e(k) = 0.d0 + WRITE (6,1000) + 1000 FORMAT (' QR FAILED') + 102 DO ll2=1,k + l2 = k - ll2 + 1 + l = l2 + IF (ABS(e(l)) <= eps) GO TO 120 + IF (l == 1) CYCLE + IF (ABS(q(l-1)) <= eps) EXIT + END DO +!...CANCELLATION OF E(L) IF L>1... + c = 0.d0 + s = 1.d0 + DO i=l,k + f = s*e(i) + e(i) = c*e(i) + IF (ABS(f) <= eps) GO TO 120 + g = q(i) +!...Q(I) = H = SQRT(G*G + F*F)... + IF (ABS(f) < ABS(g)) GO TO 113 + IF (f == 0.0) THEN + GO TO 111 + ELSE + GO TO 112 + END IF + 111 h = 0.d0 + GO TO 114 + 112 h = ABS(f)*SQRT(1 + (g/f)**2) + GO TO 114 + 113 h = ABS(g)*SQRT(1 + (f/g)**2) + 114 q(i) = h + IF (h /= 0.d0) GO TO 115 + g = 1.d0 + h = 1.d0 + 115 c = g/h + s = -f/h + END DO +!...TEST FOR CONVERGENCE... + 120 z = q(k) + IF (l == k) GO TO 140 +!...SHIFT FROM BOTTOM 2*2 MINOR... + x = q(l) + y = q(k-1) + g = e(k-1) + h = e(k) + f = ((y - z)*(y + z) + (g - h)*(g + h))/(2*h*y) + g = SQRT(f*f + 1.0D0) + temp = f - g + IF (f >= 0.d0) temp = f + g + f = ((x - z)*(x + z) + h*(y/temp - h))/x +!...NEXT QR TRANSFORMATION... + c = 1.d0 + s = 1.d0 + lp1 = l + 1 + IF (lp1 > k) GO TO 133 + DO i=lp1,k + g = e(i) + y = q(i) + h = s*g + g = g*c + IF (ABS(f) < ABS(h)) GO TO 123 + IF (f == 0.0) THEN + GO TO 121 + ELSE + GO TO 122 + END IF + 121 z = 0.d0 + GO TO 124 + 122 z = ABS(f)*SQRT(1 + (h/f)**2) + GO TO 124 + 123 z = ABS(h)*SQRT(1 + (f/h)**2) + 124 e(i-1) = z + IF (z /= 0.d0) GO TO 125 + f = 1.d0 + z = 1.d0 + 125 c = f/z + s = h/z + f = x*c + g*s + g = -x*s + g*c + h = y*s + y = y*c + DO j=1,n + x = ab(j,i-1) + z = ab(j,i) + ab(j,i-1) = x*c + z*s + ab(j,i) = -x*s + z*c + END DO + IF (ABS(f) < ABS(h)) GO TO 129 + IF (f == 0.0) THEN + GO TO 127 + ELSE + GO TO 128 + END IF + 127 z = 0.d0 + GO TO 130 + 128 z = ABS(f)*SQRT(1 + (h/f)**2) + GO TO 130 + 129 z = ABS(h)*SQRT(1 + (f/h)**2) + 130 q(i-1) = z + IF (z /= 0.d0) GO TO 131 + f = 1.d0 + z = 1.d0 + 131 c = f/z + s = h/z + f = c*g + s*y + x = -s*g + c*y + END DO + 133 e(l) = 0.d0 + e(k) = f + q(k) = x + GO TO 101 +!...CONVERGENCE: Q(K) IS MADE NON-NEGATIVE... + 140 IF (z >= 0.d0) CYCLE + q(k) = -z + DO j=1,n + ab(j,k) = -ab(j,k) + END DO +END DO +RETURN +200 q(1) = ab(1,1) +ab(1,1) = 1.d0 + +END SUBROUTINE minfit + + + + +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! + SUBROUTINE MIN(n,j,nits,d2,x1,f1,fk,f,x,t,machep,h) + + IMPLICIT NONE + + INTEGER, INTENT(IN) :: n + INTEGER :: j + INTEGER :: nits + REAL, INTENT(IN OUT) :: d2 + REAL, INTENT(IN OUT) :: x1 + REAL, INTENT(IN OUT) :: f1 + LOGICAL :: fk + REAL :: f + REAL, INTENT(IN OUT) :: x(n) + REAL, INTENT(IN) :: t + REAL, INTENT(IN) :: machep + REAL, INTENT(IN) :: h + + INTEGER :: i,k + EXTERNAL f + + + REAL :: flin ! function + REAL :: small,sf1,sx1,s,temp, xm,x2,f2,d1 + REAL :: fm,f0,t2 +!---------------------------------------------- + INTEGER :: nf,nl + REAL :: fx,ldt,dmin + REAL :: v(20,20),q0(20),q1(20),qa,qb,qc,qd0,qd1,qf1 + COMMON /global/ fx,ldt,dmin,nf,nl /q/ v,q0,q1,qa,qb,qc,qd0,qd1,qf1 +!---------------------------------------------- +!...THE SUBROUTINE MIN MINIMIZES F FROM X IN THE DIRECTION V(*,J) UNLESS +! J IS LESS THAN 1, WHEN A QUADRATIC SEARCH IS MADE IN THE PLANE +! DEFINED BY Q0,Q1,X. +! D2 IS EITHER ZERO OR AN APPROXIMATION TO HALF F". +! ON ENTRY, X1 IS AN ESTIMATE OF THE DISTANCE FROM X TO THE MINIMUM +! ALONG V(*,J) (OR, IF J=0, A CURVE). ON RETURN, X1 IS THE DISTANCE +! FOUND. +! IF FK=.TRUE., THEN F1 IS FLIN(X1). OTHERWISE X1 AND F1 ARE IGNORED +! ON ENTRY UNLESS FINAL FX IS GREATER THAN F1. +! NITS CONTROLS THE NUMBER OF TIMES AN ATTEMPT WILL BE MADE TO HALVE +! THE INTERVAL. + LOGICAL :: dz + REAL :: m2,m4 + +small = machep**2 +m2 = SQRT(machep) +m4 = SQRT(m2) +sf1 = f1 +sx1 = x1 +k = 0 +xm = 0.d0 +fm = fx +f0 = fx +dz = d2 < machep +!...FIND THE STEP SIZE... +s = 0.d0 +DO i=1,n + s = s + x(i)**2 +END DO +s = SQRT(s) +temp = d2 +IF (dz) temp = dmin +t2 = m4*SQRT(ABS(fx)/temp + s*ldt) + m2*ldt +s = m4*s + t +IF (dz.AND.t2 > s) t2 = s +t2 = DMAX1(t2,small) +t2 = DMIN1(t2,.01D0*h) +IF (.NOT.fk.OR.f1 > fm) GO TO 2 +xm = x1 +fm = f1 +2 IF (fk.AND.ABS(x1) >= t2) GO TO 3 +temp=1.d0 +IF (x1 < 0.d0) temp=-1.d0 +x1=temp*t2 +f1 = flin(n,j,x1,f,x,nf) +3 IF (f1 > fm) GO TO 4 +xm = x1 +fm = f1 +4 IF (.NOT.dz) GO TO 6 +!...EVALUATE FLIN AT ANOTHER POINT AND ESTIMATE THE SECOND DERIVATIVE... +x2 = -x1 +IF (f0 >= f1) x2 = 2.d0*x1 +f2 = flin(n,j,x2,f,x,nf) +IF (f2 > fm) GO TO 5 +xm = x2 +fm = f2 +5 d2 = (x2*(f1 - f0)-x1*(f2 - f0))/((x1*x2)*(x1 - x2)) +!...ESTIMATE THE FIRST DERIVATIVE AT 0... +6 d1 = (f1 - f0)/x1 - x1*d2 +dz = .true. +!...PREDICT THE MINIMUM... +IF (d2 > small) GO TO 7 +x2 = h +IF (d1 >= 0.d0) x2 = -x2 +GO TO 8 +7 x2 = (-.5D0*d1)/d2 +8 IF (ABS(x2) <= h) GO TO 11 +IF (x2 > 0.0) THEN + GO TO 10 +END IF +x2 = -h +GO TO 11 +10 x2 = h +!...EVALUATE F AT THE PREDICTED MINIMUM... +11 f2 = flin(n,j,x2,f,x,nf) +IF (k >= nits.OR.f2 <= f0) GO TO 12 +!...NO SUCCESS, SO TRY AGAIN... +k = k + 1 +IF (f0 < f1.AND.(x1*x2) > 0.d0) GO TO 4 +x2 = 0.5D0*x2 +GO TO 11 +!...INCREMENT THE ONE-DIMENSIONAL SEARCH COUNTER... +12 nl = nl + 1 +IF (f2 <= fm) GO TO 13 +x2 = xm +GO TO 14 +13 fm = f2 +!...GET A NEW ESTIMATE OF THE SECOND DERIVATIVE... +14 IF (ABS(x2*(x2 - x1)) <= small) GO TO 15 +d2 = (x2*(f1-f0) - x1*(fm-f0))/((x1*x2)*(x1 - x2)) +GO TO 16 +15 IF (k > 0) d2 = 0.d0 +16 IF (d2 <= small) d2 = small +x1 = x2 +fx = fm +IF (sf1 >= fx) GO TO 17 +fx = sf1 +x1 = sx1 +!...UPDATE X FOR LINEAR BUT NOT PARABOLIC SEARCH... +17 IF (j == 0) RETURN +DO i=1,n + x(i) = x(i) + x1*v(i,j) +END DO + +END SUBROUTINE MIN + + +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! + SUBROUTINE vcprnt(option,v,n) + + IMPLICIT NONE + INTEGER :: option + REAL, INTENT(IN OUT) :: v(n) + INTEGER :: n + + INTEGER :: i + +SELECT CASE ( option ) + CASE ( 1) + GO TO 1 + CASE ( 2) + GO TO 2 + CASE ( 3) + GO TO 3 + CASE ( 4) + GO TO 4 +END SELECT + +1 WRITE (6,101) (v(i),i=1,n) +RETURN +2 WRITE (6,102) (v(i),i=1,n) +RETURN +3 WRITE (6,103) (v(i),i=1,n) +RETURN +4 WRITE (6,104) (v(i),i=1,n) +RETURN +101 FORMAT (/' THE SECOND DIFFERENCE ARRAY D(*) IS:'/ (e32.14,4E25.14)) +102 FORMAT (/' THE SCALE FACTORS ARE:'/(e32.14,4E25.14)) +103 FORMAT (/' THE APPROXIMATING QUADR. FORM HAS PRINCIPAL VALUES:'/ & + (e32.14,4E25.14)) +104 FORMAT (/' X IS:',e26.14/(e32.14)) +END SUBROUTINE vcprnt + + +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! + SUBROUTINE PRINT(n,x,prin,fmin) + + IMPLICIT NONE + INTEGER :: n + REAL, INTENT(IN OUT) :: x(n) + INTEGER, INTENT(IN OUT) :: prin + REAL, INTENT(IN OUT) :: fmin + + INTEGER :: i + REAL :: ln +!---------------------------------------------- +INTEGER :: nf,nl +REAL :: fx,ldt,dmin +COMMON /global/ fx,ldt,dmin,nf,nl +!---------------------------------------------- +WRITE (6,101) nl,nf,fx + +IF (fx <= fmin) GO TO 1 +ln = LOG10(fx-fmin) +WRITE (6,102) fmin,ln +GO TO 2 +1 WRITE (6,103) fmin +2 IF (n > 4.AND.prin <= 2) RETURN +WRITE (6,104) (x(i),i=1,n) +RETURN +101 FORMAT (/' AFTER',i6, & + ' LINEAR SEARCHES, THE FUNCTION HAS BEEN EVALUATED',i6, & + ' TIMES. THE SMALLEST VALUE FOUND IS F(X) = ',e21.14) +102 FORMAT (' LOG (F(X)-',e21.14,') = ',e21.14) +103 FORMAT (' LOG (F(X)-',e21.14,') IS UNDEFINED.') +104 FORMAT (' X IS:',e26.14/(e32.14)) +END SUBROUTINE PRINT + + +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! + SUBROUTINE maprnt(option,v,m,n) + + IMPLICIT NONE + INTEGER :: option + REAL, INTENT(IN OUT) :: v(m,n) + INTEGER, INTENT(IN OUT) :: m + INTEGER, INTENT(IN) :: n + INTEGER :: i,j + + INTEGER :: low,upp +!...THE SUBROUTINE MAPRNT PRINTS THE COLUMNS OF THE NXN MATRIX V +! WITH A HEADING AS SPECIFIED BY OPTION. +! M IS THE ROW DIMENSION OF V AS DECLARED IN THE CALLING PROGRAM... +low = 1 +upp = 5 +SELECT CASE ( option ) + CASE ( 1) + GO TO 1 + CASE ( 2) + GO TO 2 +END SELECT +1 WRITE (6,101) +101 FORMAT (/' THE NEW DIRECTIONS ARE:') +GO TO 3 +2 WRITE (6,102) +102 FORMAT (' AND THE PRINCIPAL AXES:') +3 IF (n < upp) upp = n +DO i=1,n + WRITE (6,104) (v(i,j),j=low,upp) +END DO +low = low + 5 +IF (n < low) RETURN +upp = upp + 5 +WRITE (6,103) +GO TO 3 +103 FORMAT (' ') +104 FORMAT (e32.14,4E25.14) +END SUBROUTINE maprnt + + +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! + REAL FUNCTION random(naught) + + IMPLICIT NONE + INTEGER, INTENT(IN OUT) :: naught + + REAL :: ran1,ran3(127),half + INTEGER :: i,j,ran2,q,r + LOGICAL :: init + DATA init/.false./ + SAVE init,ran2,ran1,ran3 + +IF (init) GO TO 3 +r = MOD(naught,8190) + 1 +ran2 = 128 +DO i=1,127 + ran2 = ran2 - 1 + ran1 = -2.d0**55 + DO j=1,7 + r = MOD(1756*r,8191) + q = r/32 + ran1 = (ran1 + q)*(1.0D0/256) + END DO + ran3(ran2) = ran1 +END DO +init = .true. +3 IF (ran2 == 1) ran2 = 128 +ran2 = ran2 - 1 +ran1 = ran1 + ran3(ran2) +half = .5D0 +IF (ran1 >= 0.d0) half = -half +ran1 = ran1 + half +ran3(ran2) = ran1 +random = ran1 + .5D0 + +END FUNCTION random + + + +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! + REAL FUNCTION flin (n,j,l,f,x,nf) + IMPLICIT NONE + + INTEGER, INTENT(IN) :: n + INTEGER, INTENT(IN OUT) :: j + REAL, INTENT(IN) :: l + REAL :: f + REAL, INTENT(IN) :: x(n) + INTEGER, INTENT(OUT) :: nf + + INTEGER :: i + REAL :: t(20) + + EXTERNAL f + +!...FLIN IS THE FUNCTION OF ONE REAL VARIABLE L THAT IS MINIMIZED +! BY THE SUBROUTINE MIN... +!---------------------------------------------- + REAL :: v(20,20),q0(20),q1(20),qa,qb,qc,qd0,qd1,qf1 + COMMON /q/ v,q0,q1,qa,qb,qc,qd0,qd1,qf1 +!---------------------------------------------- +IF (j == 0) GO TO 2 +!...THE SEARCH IS LINEAR... +DO i=1,n + t(i) = x(i) + l*v(i,j) +END DO +GO TO 4 +!...THE SEARCH IS ALONG A PARABOLIC SPACE CURVE... +2 qa = (l*(l - qd1))/(qd0*(qd0 + qd1)) +qb = ((l + qd0)*(qd1 - l))/(qd0*qd1) +qc = (l*(l + qd0))/(qd1*(qd0 + qd1)) +DO i=1,n + t(i) = (qa*q0(i) + qb*x(i)) + qc*q1(i) +END DO +!...THE FUNCTION EVALUATION COUNTER NF IS INCREMENTED... +4 nf = nf + 1 +flin = f(t,n) + +END FUNCTION flin + + +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! + SUBROUTINE sort(m,n,d,v) + IMPLICIT NONE +! + INTEGER, INTENT(IN OUT) :: m + INTEGER, INTENT(IN) :: n + REAL, INTENT(IN OUT) :: d(n) + REAL, INTENT(IN OUT) :: v(m,n) + + INTEGER :: i,j,k,nm1,ip1 + REAL :: s +!...SORTS THE ELEMENTS OF D(N) INTO DESCENDING ORDER AND MOVES THE +! CORRESPONDING COLUMNS OF V(N,N). +! M IS THE ROW DIMENSION OF V AS DECLARED IN THE CALLING PROGRAM. +IF (n == 1) RETURN +nm1 = n - 1 +DO i = 1,nm1 + k=i + s = d(i) + ip1 = i + 1 + DO j = ip1,n + IF (d(j) <= s) CYCLE + k = j + s = d(j) + END DO + IF (k <= i) CYCLE + d(k) = d(i) + d(i) = s + DO j = 1,n + s = v(j,i) + v(j,i) = v(j,k) + v(j,k) = s + END DO +END DO +END SUBROUTINE sort + + +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! + SUBROUTINE quad(n,f,x,t,machep,h) + IMPLICIT NONE + + INTEGER, INTENT(IN) :: n + REAL :: f + REAL, INTENT(IN OUT) :: x(n) + REAL, INTENT(IN OUT) :: t + REAL :: machep + REAL, INTENT(IN OUT) :: h +! IMPLICIT REAL (A-H,O-Z) + EXTERNAL f + +!...QUAD LOOKS FOR THE MINIMUM OF F ALONG A CURVE DEFINED BY Q0,Q1,X... + INTEGER :: i + REAL :: l + REAL :: s,value +!---------------------------------------------- + INTEGER :: nf,nl + REAL :: fx,ldt,dmin + +REAL :: v(20,20),q0(20),q1(20),qa,qb,qc,qd0,qd1,qf1 +COMMON /global/ fx,ldt,dmin,nf,nl /q/ v,q0,q1,qa,qb,qc,qd0,qd1,qf1 +!---------------------------------------------- +s = fx +fx = qf1 +qf1 = s +qd1 = 0.d0 +DO i=1,n + s = x(i) + l = q1(i) + x(i) = l + q1(i) = s + qd1 = qd1 + (s-l)**2 +END DO +qd1 = SQRT(qd1) +l = qd1 +s = 0.d0 +IF (qd0 <= 0.d0 .OR. qd1 <= 0.d0 .OR. nl < 3*n*n) GO TO 2 +value=qf1 +CALL MIN(n,0,2,s,l,value,.true.,f,x,t,machep,h) +qa = (l*(l-qd1))/(qd0*(qd0+qd1)) +qb = ((l+qd0)*(qd1-l))/(qd0*qd1) +qc = (l*(l+qd0))/(qd1*(qd0+qd1)) +GO TO 3 +2 fx = qf1 +qa = 0.d0 +qb = qa +qc = 1.d0 +3 qd0 = qd1 +DO i=1,n + s = q0(i) + q0(i) = x(i) + x(i) = (qa*s + qb*x(i)) + qc*q1(i) +END DO +END SUBROUTINE quad + diff --git a/applications/PUfoam/MoDeNaModels/Solubility/ExampleOfUsage/src/srcDetailedCode/VLE_main.f90 b/applications/PUfoam/MoDeNaModels/Solubility/ExampleOfUsage/src/srcDetailedCode/VLE_main.f90 new file mode 100644 index 000000000..d4f0498c7 --- /dev/null +++ b/applications/PUfoam/MoDeNaModels/Solubility/ExampleOfUsage/src/srcDetailedCode/VLE_main.f90 @@ -0,0 +1,102 @@ +SUBROUTINE VLE_MIX(rhob,density,chemPot_total,compID) + + USE parameters, ONLY: PI, RGAS, KBOL + USE basic_variables + USE EOS_VARIABLES, ONLY: fres, eta, eta_start, dhs, mseg, uij, sig_ij, rho, x, z3t + USE DFT_MODULE + USE EOS_NUMERICAL_DERIVATIVES + IMPLICIT NONE + + + +! --------------------------------------------------------------------- +! Variables +! --------------------------------------------------------------------- + + !passed + REAL :: chemPot_total(nc) + REAL :: rhob(2,0:nc),density(np) + INTEGER :: compID + + !local + REAL, DIMENSION(nc) :: dhs_star + REAL :: w(np,nc), lnphi(np,nc) + INTEGER :: converg + CHARACTER(LEN=4) :: char_ncomp + REAL :: Henry + INTEGER :: i + CHARACTER (LEN=50) :: filename + + +! --------------------------------------------------------------------- +! prepare for phase equilibrium calculation for given T +! --------------------------------------------------------------------- + + dhs(1:ncomp) = parame(1:ncomp,2) * ( 1.0 - 0.12*EXP( -3.0*parame(1:ncomp,3)/t ) ) ! needed for rdf_matrix + dhs_star(1:ncomp) = dhs(1:ncomp)/parame(1:ncomp,2) + + nphas = 2 ! number of phases + outp = 0 ! output to terminal + + CALL START_VAR (converg) + + IF ( converg /= 1 ) THEN + WRITE (*,*) 'no VLE found' + RETURN + END IF + + ! rhob(phase,0): molecular density + rhob(1,0) = dense(1) / ( PI/6.0* SUM( xi(1,1:ncomp) * parame(1:ncomp,1) * dhs(1:ncomp)**3 ) ) + rhob(2,0) = dense(2) / ( PI/6.0* SUM( xi(2,1:ncomp) * parame(1:ncomp,1) * dhs(1:ncomp)**3 ) ) + ! rhob(phase,i): molecular component density (with i=(1,...ncomp) ) in units (1/A^3) + rhob(1,1:ncomp) = rhob(1,0)*xi(1,1:ncomp) + rhob(2,1:ncomp) = rhob(2,0)*xi(2,1:ncomp) + + ! get density in SI-units (kg/m**3) + CALL SI_DENS ( density, w ) + + ! calculate residual chemical potentials + ensemble_flag = 'tv' ! this flag is for: mu_res=mu_res(T,rho) + densta(1) = dense(1) ! Index 1 is for liquid density (here: packing fraction eta) + densta(2) = dense(2) ! Index 2 is for vapour density (here: packing fraction eta) + CALL fugacity (lnphi) ! calculate fugacities + + +! --------------------------------------------------------------------- +! Output results of phase equilibrim calculation +! --------------------------------------------------------------------- + + WRITE(*,*) '--------------------------------------------------' + WRITE(*,*)'RESULT OF PHASE EQUILIBRIUM CALCULATION' + WRITE (char_ncomp,'(I3)') ncomp + WRITE (*,*) 'T = ',t, 'K, and p =', p/1.E5,' bar' + WRITE(*,*)' ' + WRITE(*,'(t15,4(a12,1x),10x,a)') (compna(i),i=1,ncomp) + !!WRITE(*,'(2x,a,'//char_ncomp//'(g13.6,1x))') 'PHASE I w', (w(1,i),i=1,ncomp) + !!WRITE(*,'(2x,a,'//char_ncomp//'(g13.6,1x))') 'PHASE II w', (w(2,i),i=1,ncomp) + WRITE(*,'(2x,a,'//char_ncomp//'(g13.6,1x))') 'PHASE I x', (EXP(lnx(1,i)),i=1,ncomp) + WRITE(*,'(2x,a,'//char_ncomp//'(g13.6,1x))') 'PHASE II x', (EXP(lnx(2,i)),i=1,ncomp) + WRITE(*,*)' ' + !!WRITE(*,'(2x,a,'//char_ncomp//'(g13.6,1x))') 'PHASE I density', (rhob(1,i),i=1,ncomp) + !! WRITE(*,'(2x,a,'//char_ncomp//'(g13.6,1x))') 'PHASE II density', (rhob(2,i),i=1,ncomp) + !!WRITE(*,*)' ' + WRITE(*,'(2x,a,'//char_ncomp//'(g13.6,1x))') 'PHASE I chemPot', (lnphi(1,i) + LOG(rhob(1,i)),i=1,ncomp) + WRITE(*,'(2x,a,'//char_ncomp//'(g13.6,1x))') 'PHASE II chemPot', (lnphi(2,i) + LOG(rhob(2,i)),i=1,ncomp) + WRITE(*,*)' ' + !!WRITE(*,*)'Phase densities ' + WRITE(*,'(2x,a,2(g13.6,1x))') 'SI-DENSITY [kg/m3] ', density(1),density(2) + !!WRITE(*,'(2x,a,2(g13.6,1x))') 'NUMBER-DENSITY ', rhob(1,0),rhob(2,0) + WRITE(*,*) + + !Calculate Solubility + !output: Henrys law: xi*H(T) = yi * p -> H = yip/xi + Henry = EXP(lnx(2,1))*p /EXP(lnx(1,1)) + + !write solubility to outputfile "out.txt" + filename='./out.txt' + CALL file_open(filename,78) + write(78,*) Henry / 100000.0 + write(*,*)'Henry coefficient (bar):',Henry / 100000.0 + ! write(*,*)'g_CO2 / g_PU', exp(lnx(1,2)) * mm(2) / (exp(lnx(1,1)) * mm(1)) + +END SUBROUTINE VLE_MIX diff --git a/applications/PUfoam/MoDeNaModels/Solubility/ExampleOfUsage/src/srcDetailedCode/VLE_subroutines.f90 b/applications/PUfoam/MoDeNaModels/Solubility/ExampleOfUsage/src/srcDetailedCode/VLE_subroutines.f90 new file mode 100644 index 000000000..3f54b25ea --- /dev/null +++ b/applications/PUfoam/MoDeNaModels/Solubility/ExampleOfUsage/src/srcDetailedCode/VLE_subroutines.f90 @@ -0,0 +1,7156 @@ +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! SUBROUTINE start_var +! +! This subroutine generates a converged solution for binary systems +! or performes a flash calculation for mixtues. This routine is a +! fairly weak point of the program. +! +! IF a polymer is considered, starting values for mole fractions +! are determined from the SUBROUTINGE POLY_STA_VAR (see below). The +! polymer needs to be placed as component 1 (first line) in INPUT +! file. +! +! A phase equilib. iteration is started at the end of this routine. +! If no solution is found (converg=0), the program will stop within +! this routine. +! +! Currently, this routine assumes two-phase equilibrium and derives +! starting values (xi,density) only for two phases. +! +! Prerequisites are: +! SUBROUTINE INPUT needs to be called prior to this routine, because +! all pure comp. parameters as well as (T,P,kij) need to be in place. +! Also, the variable to be iterated "it(i)" and the variables to be +! calculated through the summation relation "sum_rel(i)" have to be +! defined. +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! + SUBROUTINE start_var(converg) +! + USE BASIC_VARIABLES + USE STARTING_VALUES + IMPLICIT NONE +! +! ---------------------------------------------------------------------- + INTEGER, INTENT(IN OUT) :: converg +! +! ---------------------------------------------------------------------- + INTEGER :: ph, i, k + INTEGER :: ncompsav, n_unkwsav, ph_split + LOGICAL :: lle_check, flashcase, renormalize + REAL :: den1, den2, x_1, x_2 + CHARACTER (LEN=50) :: filename +! ---------------------------------------------------------------------- + +converg = 0 + +! CALL RACHFORD_RICE (converg) +! CALL Heidemann_Khalil + +! ---------------------------------------------------------------------- +! This first condition (eos >= 4) is for LJ models, not for PC-SAFT +! ---------------------------------------------------------------------- + +IF (eos >= 4) THEN + + ncomp = 2 ! set number of components to 2 + n_unkw = ncomp ! number of quantities to be iterated + it(1) = 'x11' ! iteration of mol fraction of comp.1 phase 1 + it(2) = 'x21' ! iteration of mol fraction of comp.1 phase 2 + sum_rel(1) = 'x12' ! summation relation: x12 = 1 - sum(x1j) + sum_rel(2) = 'x22' ! summation relation: x22 = 1 - sum(x2j) + + filename = 'LJ_START_VAL.INC' + CALL file_open(filename,84) + READ (84,*) den1,den2 + READ (84,*) x_1,x_2 + CLOSE (84) + + xi(1,1) = x_1 + xi(2,1) = x_2 + xi(1,2) = 1.0 - xi(1,1) + xi(2,2) = 1.0 - xi(2,1) + lnx(1,1) = LOG(xi(1,1)) + lnx(2,1) = LOG(xi(2,1)) + lnx(1,2) = LOG(xi(1,2)) + lnx(2,2) = LOG(xi(2,2)) + + val_init(1) = den1 + val_init(2) = den2 + val_init(3) = t + val_init(4) = p + DO ph = 1,nphas + DO k = 1,ncomp + val_init(4+k+(ph-1)*ncomp) = LOG(xi(ph,k)) + END DO + END DO + + CALL objective_ctrl (converg) + IF (converg == 1) WRITE (*,*) t, p/1.0E5, xi(1,1), xi(2,1) + IF (converg == 0) WRITE (*,*) ' weak starting values' + + +! ---------------------------------------------------------------------- +! ELSE: PC-SAFT equation of state +! ---------------------------------------------------------------------- + +ELSE + + renormalize = .false. ! for renormalization group theory (RGT) + IF (num == 2) renormalize = .true. + IF (num == 2) num = 0 ! if RGT: initial phase equilibr. is for non-renormalized model + + flashcase = .false. ! .true. when a specific feed conc. xif is given + IF (xif(1) /= 0.0) flashcase = .true. + + lle_check = .true. + +! ---------------------------------------------------------------------- +! IF: non-polymeric system +! ---------------------------------------------------------------------- + IF (mm(1) < 1.0E8) THEN + + DO i=1,ncomp ! setting mole-fractions for the case that + ! anything goes wrong in the coming routines + xi(1,i) = 1.0 / REAL(ncomp) + xi(2,i) = 1.0 / REAL(ncomp) + END DO + + + ! ------------------------------------------------------------------ + ! determine an initial conc. (phase 1) that will phase split + ! ------------------------------------------------------------------ + IF( ncomp == 2 .AND. .NOT.flashcase ) THEN + CALL vle_min( lle_check ) + WRITE(*,*)' INITIAL FEED-COMPOSITION',(xi(1,i), i=1,ncomp),converg + END IF + + ! ------------------------------------------------------------------ + ! perform a phase stability test + ! ------------------------------------------------------------------ + ph_split = 0 + CALL phase_stability ( .false., flashcase, ph_split ) + write (*,*) 'stability analysis I indicates phase-split is:',ph_split + + + ! ------------------------------------------------------------------ + ! determine species i, for which x(i) is calc from summation relation + ! ------------------------------------------------------------------ + CALL select_sum_rel (1,0,1) ! synthax (m,n,o): phase m + ! exclude comp. n + ! assign it(o) and higher + CALL select_sum_rel (2,0,2) ! for ncomp>=3, the quantities + ! to be iterated will be overwritten + + ! ------------------------------------------------------------------ + ! if 2 phases (VLE) + ! ------------------------------------------------------------------ + IF (ph_split == 1) THEN + + ! --- perform tangent plane minimization ------------------------ + CALL tangent_plane + ph_split = 0 + + ! --- determine, for which substance summation relation is used -- + IF (flashcase) THEN + CALL determine_flash_it2 + ELSE + CALL select_sum_rel (1,0,1) + CALL select_sum_rel (2,0,2) + END IF + + ! --- do full phase equilibr. calculation ------------------------ + n_unkw = ncomp ! number of quantities to be iterated + CALL objective_ctrl (converg) + IF (converg == 1 ) write (*,*) ' converged (maybe a VLE)',dense(1),dense(2) + + END IF + + ! ------------------------------------------------------------------ + ! test for LLE + ! ------------------------------------------------------------------ + ph_split = 0 + + IF (lle_check) CALL phase_stability (lle_check,flashcase,ph_split) + IF (lle_check) write (*,*) 'stability analysis II, phase-split is:',ph_split + + + ! ------------------------------------------------------------------ + ! if two phases (LLE) + ! ------------------------------------------------------------------ + IF (ph_split == 1) THEN + + write (*,*) ' LLE-stability test indicates 2 phases (VLE or LLE)' + + ! --- perform tangent plane minimization ------------------------ + IF (flashcase) CALL select_sum_rel (1,0,1) + IF (flashcase) CALL select_sum_rel (2,0,2) + + CALL tangent_plane + + ! --- determine, for which substance summation relation ---------- + IF (flashcase) THEN + CALL determine_flash_it2 + ELSE + CALL select_sum_rel (1,0,1) + CALL select_sum_rel (2,0,2) + END IF + + ! --- do full phase equilibr. calculation ------------------------ + n_unkw = ncomp ! number of quantities to be iterated + val_conv(2) = 0.0 + CALL objective_ctrl (converg) + IF (converg == 1 ) write (*,*) ' converged (maybe an LLE)',dense(1),dense(2) + + END IF + + ! ------------------------------------------------------------------ + ! equilibr. calc. converged: set initial var. for further calc. + ! ------------------------------------------------------------------ + IF (converg == 1) THEN + val_init = val_conv + DO ph = 1,nphas + DO i = 1,ncomp + xi(ph,i) = EXP( val_conv(4+i+(ph-1)*ncomp) ) + END DO + END DO + dense(1:2) = val_conv(1:2) + ELSE + WRITE (*,*) ' NO SOLUTION FOUND FOR THE STARTING VALUES' + STOP + END IF + + + ! --------------------------------------------------------------------- + ! ELSE: for systems with polymers + ! --------------------------------------------------------------------- + + ELSE + + ncompsav = ncomp + ncomp = 2 ! set number of components to 2 + n_unkwsav = n_unkw + + CALL poly_sta_var(converg) + + IF (converg == 1) THEN + val_init = val_conv + ELSE + WRITE (*,*) ' NO SOLUTION FOUND FOR THE STARTING VALUES' + STOP + END IF + + ncomp = ncompsav + n_unkw = n_unkwsav ! number of quantities to be iterated + + END IF + +! --- for RGT: set flag back to num=2 indicating an RGT calculation ---- + IF (renormalize) num = 2 + +END IF + +END SUBROUTINE start_var + + + + +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! SUBROUTINE objective_ctrl +! +! This subroutine controls the iso-fugacity iteration. It uses +! the variables defined in the array "val_init". If successfull, +! the converged values are written to "val_conv", and the flag +! converg is set to 1. +! See also above desciption for subroutine PHASE_EQUILIB +! This routine calls SUBROUTINE HYBRID, which is a solver (modified +! POWELL HYBRID METHOD). HYBRID is freely available for non-commercial +! applications. HYBRID requires three definitions: +! 1.the number of equations to be solved (=No. of variables to be +! iterated). The appropriate parameter is: "n_unkw" +! 2.the equations to be iterated, they are here gathered in the SUB- +! ROUTINE OBJEC_FCT (see below). Since HYBRID is a root finder, +! these objective functions are iterated to be zero (essentially, +! OBJEC_FCT contains the iso-fugacity relation. +! 3.an array of variables is required, containing the quatities to be +! iterated. This array is termed "y(i)" +! +! INPUT VARIABLES: +! val_init(i) array containing (densities,T,P,lnx's) serving as +! starting values for the phase equilibrium calculation +! it(i) contains the information, which variable is deter- +! mined iteratively. For syntax refer e.g.to SUB BINMIX. +! sum_rel(i) indicates, which mole fraction is determined from the +! summation relation sum(xi)=1 +! +! OUTPUT VARIABLES: +! val_conv(i) array containing the converged system variables +! analogous to "val_init" +! converg 0 if no convergence achieved, 1 if converged solution +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! + SUBROUTINE objective_ctrl (converg) +! + USE BASIC_VARIABLES + USE Solve_NonLin + IMPLICIT NONE +! +! ---------------------------------------------------------------------- + INTEGER, INTENT(OUT) :: converg +! +! ---------------------------------------------------------------------- + INTERFACE + SUBROUTINE objec_fct ( iter_no, y, residu, dummy ) + INTEGER, INTENT(IN) :: iter_no + REAL, INTENT(IN) :: y(iter_no) + REAL, INTENT(OUT) :: residu(iter_no) + INTEGER, INTENT(IN OUT) :: dummy + END SUBROUTINE objec_fct + END INTERFACE +! + INTEGER :: info,k,posn,i + INTEGER, PARAMETER :: mxr = nc*(nc+1)/2 + REAL, ALLOCATABLE :: y(:),diag(:),residu(:) + REAL :: x_init, x_solut, r_diff1, r_diff2, totres + REAL :: r_thrash, x_thrash + CHARACTER (LEN=2) :: compon + LOGICAL :: convergence +! ---------------------------------------------------------------------- + +info=1 + +ALLOCATE( y(n_unkw), diag(n_unkw), residu(n_unkw) ) + +IF (num == 0) acc_a = 1.E-7 +IF (num == 0) step_a = 2.E-8 +IF (num == 1) acc_a = 1.E-7 +IF (num == 1) step_a = 2.E-8 +IF (num == 2) acc_a = 5.E-7 +IF (num == 2) step_a = 1.E-7 + +posn = 0 +DO i = 1,n_unkw + posn = posn + 1 + IF (it(i) == 't') y(posn) = val_init(3) + IF (it(i) == 'p') y(posn) = val_init(4) + IF (it(i) == 'lnp') y(posn) = LOG( val_init(4) ) + IF (it(i) == 'fls') y(posn) = alpha + IF (it(i)(1:1) == 'x' .AND. it(i)(2:2) == '1') compon = it(i)(3:3) + IF (it(i)(1:1) == 'x' .AND. it(i)(2:2) == '1') READ(compon,*) k + IF (it(i)(1:1) == 'x' .AND. it(i)(2:2) == '1') y(posn) = val_init(4+k) + IF (it(i)(1:1) == 'x' .AND. it(i)(2:2) == '2') compon = it(i)(3:3) + IF (it(i)(1:1) == 'x' .AND. it(i)(2:2) == '2') READ(compon,*) k + IF (it(i)(1:1) == 'x' .AND. it(i)(2:2) == '2') y(posn) = val_init(4+ncomp+k) + IF (it(i)(1:1) == 'x' .AND. it(i)(2:2) == '3') compon = it(i)(3:3) + IF (it(i)(1:1) == 'x' .AND. it(i)(2:2) == '3') READ(compon,*) k + IF (it(i)(1:1) == 'x' .AND. it(i)(2:2) == '3') y(posn) = val_init(4+ncomp+ncomp+k) +END DO + +CALL init_vars + +x_init = 0.0 +DO i = 1,ncomp + IF (lnx(1,i) /= 0.0 .AND. lnx(2,i) /= 0.0) THEN + x_init = x_init + ABS( 1.0 - lnx(2,i)/lnx(1,i) ) + ELSE + x_init = x_init + ABS( 1.0 - EXP(lnx(2,i))/EXP(lnx(1,i)) ) + END IF +END DO + +CALL hbrd (objec_fct, n_unkw, y, residu, step_a, acc_a, info, diag) + +x_solut = 0.0 +DO i = 1,ncomp + IF ( lnx(1,i) /= 0.0 .AND. lnx(2,i) /= 0.0 ) THEN + x_solut = x_solut + ABS( 1.0 - lnx(2,i)/lnx(1,i) ) + ELSE + IF (lnx(1,i) < 1E300 .AND. lnx(1,i) > -1.E300 ) & + x_solut = x_solut + ABS( 1.0 - EXP(lnx(2,i))/EXP(lnx(1,i)) ) + END IF +END DO +r_diff1 = ABS( 1.0 - dense(1)/dense(2) ) +IF ( val_conv(2) > 0.0 ) THEN + r_diff2 = ABS( 1.0 - val_conv(1)/val_conv(2) ) +ELSE + r_diff2 = 0.0 +END IF + +totres = SUM( ABS( residu(1:n_unkw) ) ) + +r_thrash = 0.0005 +x_thrash = 0.0005 +if (num > 0 ) r_thrash = r_thrash * 10.0 +if (num > 0 ) x_thrash = x_thrash * 100.0 + +convergence = .true. + +IF ( info >= 2 ) convergence = .false. +IF ( ABS( 1.0- dense(1)/dense(2) ) < r_thrash .AND. x_solut < x_thrash ) THEN + IF ( x_init > 0.050 ) convergence = .false. + IF ( ( ABS( 1.0- dense(1)/dense(2) ) + x_solut ) < 1.E-7 ) convergence = .false. +ENDIF +IF ( r_diff2 /= 0.0 .AND. r_diff2 > (4.0*r_diff1) .AND. bindiag == 1 ) convergence = .false. +IF ( ncomp == 1 .AND. totres > 100.0*acc_a ) convergence = .false. +IF ( totres > 1000.0*acc_a ) convergence = .false. +IF ( ncomp == 1 .AND. r_diff1 < 1.d-5 ) convergence = .false. + +IF ( convergence ) THEN + converg = 1 + ! write (*,*) residu(1),residu(2) + CALL converged + IF (num <= 1) CALL enthalpy_etc +ELSE + converg = 0 +END IF + +DEALLOCATE( y, diag, residu ) + +END SUBROUTINE objective_ctrl + + + +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! SUBROUTINE objec_fct +! +! This subroutine contains the equations to be solved numerically +! (iso-fugacity: fi'-fi''=0) as well as other dependent equations, +! which can be solved analytically, namely the summation relation +! xi=1-sum(xj) or the condition of equal charge for electrolyte +! solutions. +! This subroutine is required and controlled by the solver HBRD ! +! HBRD varies the variables "y(i)" and eveluates the result of +! these changes from this routine. +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! + SUBROUTINE objec_fct ( iter_no, y, residu, dummy ) +! + USE BASIC_VARIABLES + USE EOS_VARIABLES, ONLY: density_error + IMPLICIT NONE +! +! ---------------------------------------------------------------------- + INTEGER, INTENT(IN) :: iter_no + REAL, INTENT(IN) :: y(iter_no) + REAL, INTENT(OUT) :: residu(iter_no) + INTEGER, INTENT(IN OUT) :: dummy +! +! ---------------------------------------------------------------------- + INTEGER :: i, ph,k,posn, skip,phase + REAL :: lnphi(np,nc),isofugacity + CHARACTER (LEN=2) :: compon +! ---------------------------------------------------------------------- + + +posn = 0 +DO i = 1,n_unkw + posn = posn + 1 + IF (it(i) == 't') t = y(posn) + IF (it(i) == 'p') p = y(posn) + IF (it(i) == 'lnp') p = EXP( y(posn) ) + IF (it(i) == 'fls') alpha = y(posn) + IF (it(i)(1:1) == 'x' .AND. it(i)(2:2) == '1') compon = it(i)(3:3) + IF (it(i)(1:1) == 'x' .AND. it(i)(2:2) == '1') READ(compon,*) k + IF (it(i)(1:1) == 'x' .AND. it(i)(2:2) == '1') lnx(1,k) = y(posn) + IF (it(i)(1:1) == 'x' .AND. it(i)(2:2) == '2') compon = it(i)(3:3) + IF (it(i)(1:1) == 'x' .AND. it(i)(2:2) == '2') READ(compon,*) k + IF (it(i)(1:1) == 'x' .AND. it(i)(2:2) == '2') lnx(2,k) = y(posn) + IF (it(i)(1:1) == 'x' .AND. it(i)(2:2) == '3') compon = it(i)(3:3) + IF (it(i)(1:1) == 'x' .AND. it(i)(2:2) == '3') READ(compon,*) k + IF (it(i)(1:1) == 'x' .AND. it(i)(2:2) == '3') lnx(3,k) = y(posn) +END DO + +DO k = 1,ncomp + IF (lnx(1,k) > 0.0) lnx(1,k) = 0.0 + IF (lnx(2,k) > 0.0) lnx(2,k) = 0.0 +END DO + +IF (p < 1.E-100) p = 1.E-12 +!IF ( IsNaN( p ) ) p = 1000.0 ! rebounce for the case of NaN-solver output +!IF ( IsNaN( t ) ) t = 300.0 ! rebounce for the case of NaN-solver output +!IF ( IsNaN( alpha ) ) alpha = 0.5 ! rebounce for the case of NaN-solver output +IF ( p /= p ) p = 1000.0 ! rebounce for the case of NaN-solver output +IF ( t /= t ) t = 300.0 ! rebounce for the case of NaN-solver output +IF ( alpha /= alpha ) alpha = 0.5 ! rebounce for the case of NaN-solver output + +! --- setting of mole fractions ---------------------------------------- +DO ph = 1, nphas + DO i = 1, ncomp + IF ( lnx(ph,i) < -300.0 ) THEN + xi(ph,i) = 0.0 + ELSE + xi(ph,i) = EXP( lnx(ph,i) ) + END IF + END DO +END DO + +IF (ncomp > 1) CALL x_summation + +CALL fugacity (lnphi) + +phase = 2 +DO i = 1,n_unkw + skip = 0 !for ions/polymers, the isofug-eq. is not always solved + IF (n_unkw < (ncomp*(nphas-1))) skip = ncomp*(nphas-1) - n_unkw + IF ((i+skip-ncomp*(phase-2)) > ncomp) phase = phase + 1 + residu(i) = isofugacity((i+skip-ncomp*(phase-2)),phase,lnphi) + if ( density_error(phase) /= 0.0 ) residu(i) = residu(i) + SIGN( density_error(phase), residu(i) ) * 0.001 +END DO + +END SUBROUTINE objec_fct + + + +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! REAL FUNCTION isofugacity +! +! calculates the deviation from the condition of equal fugacities in +! logarithmic form. +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! + REAL FUNCTION isofugacity (i,phase,lnphi) +! + USE BASIC_VARIABLES + IMPLICIT NONE +! +! ---------------------------------------------------------------------- + INTEGER, INTENT(IN) :: i + INTEGER, INTENT(IN) :: phase + REAL, INTENT(IN) :: lnphi(np,nc) +! +! ---------------------------------------------------------------------- + INTEGER :: p1, p2 +! ---------------------------------------------------------------------- + + +! p1=1 +p1 = phase-1 +p2 = phase + +isofugacity = scaling(i) *( lnphi(p2,i)+lnx(p2,i)-lnx(p1,i)-lnphi(p1,i) ) +! write (*,'(a, 4G18.8)') ' t, p ',t,p,dense(1),dense(2) +! write (*,'(a,i3,i3,3G18.8)') ' phi_V',i,p2,lnx(p2,i),lnphi(p2,i),dense(p2) +! write (*,'(a,i3,i3,3G18.8)') ' phi_L',i,p1,lnx(p1,i),lnphi(p1,i),dense(p1) +! write (*,*) ' ISOFUGACITY',i,ISOFUGACITY, scaling(i) +! write (*,'(a,i3,4G18.8)') ' ISOFUGACITY',i,ISOFUGACITY, lnphi(p2,i)+lnx(p2,i), -lnx(p1,i)-lnphi(p1,i) +! pause + +END FUNCTION isofugacity + + + + + + + + + + + + + + + + + +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! + SUBROUTINE vle_min(lle_check) +! + USE PARAMETERS, ONLY: RGAS + USE BASIC_VARIABLES + USE STARTING_VALUES + IMPLICIT NONE +! +! ---------------------------------------------------------------------- + LOGICAL, INTENT(OUT) :: lle_check + + INTEGER :: i,j,k,phasen(0:40),steps + REAL :: lnphi(np,nc) + REAL :: vlemin(0:40),llemin(0:40),xval(0:40) + REAL :: start_xv(0:40),start_xl(0:40),x_sav,dg_dx2 +! ---------------------------------------------------------------------- + + + +j = 0 +k = 0 +nphas = 2 + +steps = 40 + +x_sav = xi(1,1) +sum_rel(1) = 'x12' ! summation relation +sum_rel(2) = 'x22' ! summation relation + +DO i = 0, steps + densta(1) = 0.45 + densta(2) = 1.d-6 + xi(1,1) = 1.0 - REAL(i) / REAL(steps) + IF ( xi(1,1) <= 1.E-50 ) xi(1,1) = 1.E-50 + xi(2,1) = xi(1,1) + lnx(1,1) = LOG(xi(1,1)) + lnx(2,1) = LOG(xi(2,1)) + + CALL x_summation + CALL fugacity (lnphi) + CALL enthalpy_etc !!KANN DAS RAUS???? + + + + + xval(i) = xi(1,1) + llemin(i)= gibbs(1) +(xi(1,1)*lnx(1,1)+xi(1,2)*lnx(1,2))*RGAS*t + + IF ( ABS(1.0-dense(1)/dense(2)) > 0.0001 ) THEN + vlemin(i)= gibbs(1) +(xi(1,1)*lnx(1,1)+xi(1,2)*lnx(1,2))*RGAS*t & + - ( gibbs(2) +(xi(2,1)*lnx(2,1)+xi(2,2)*lnx(2,2))*RGAS*t ) + phasen(i) = 2 + ELSE + phasen(i) = 1 + END IF + + IF (i > 0 .AND. phasen(i) == 2) THEN + IF (phasen(i-1) == 2 .AND. ABS(vlemin(i)+vlemin(i-1)) < & + ABS(vlemin(i))+ABS(vlemin(i-1))) THEN + j = j + 1 + start_xv(j)=xval(i-1) + (xval(i)-xval(i-1)) & + * ABS(vlemin(i-1))/ABS(vlemin(i)-vlemin(i-1)) + END IF + END IF + +END DO + + +DO i=2,steps-2 + dg_dx2 = (-llemin(i-2)+16.0*llemin(i-1)-30.0*llemin(i) & + +16.0*llemin(i+1)-llemin(i+2)) / (12.0*((xval(i)-xval(i-1))**2)) + IF (dg_dx2 < 0.0) THEN + k = k + 1 + start_xl(k)=xval(i) + END IF +END DO + + +IF (start_xl(1) == 0.0 .AND. start_xv(1) /= 0.0) THEN + xi(1,1) = start_xv(1) + xi(1,2) = 1.0-xi(1,1) + lle_check=.false. + ! write (*,*) 'VLE is likely', xi(1,1),xi(1,2) +ELSE IF (start_xl(1) /= 0.0 .AND. start_xv(1) == 0.0) THEN + xi(1,1) = start_xl(1) + xi(1,2) = 1.0-xi(1,1) + ! write (*,*) 'LLE is likely', xi(1,1),xi(1,2) + lle_check=.true. +ELSE IF (start_xl(1) /= 0.0 .AND. start_xv(1) /= 0.0) THEN + xi(1,1) = start_xv(1) + xi(1,2) = 1.0-xi(1,1) + ! write(*,*) 'starting with VLE and check for LLE' + lle_check=.true. +ELSE + xi(1,1) = x_sav + xi(1,2) = 1.0 - xi(1,1) +END IF + + +CALL x_summation + +END SUBROUTINE vle_min + + +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! SUBROUTINE phase_stability +! +! the index 'LLE_check' is for the starting density (which determines +! whether a liquid or vapor phase is found) of the trial phase. The +! feed-point exits either as a vapor or as a liquid. If it can exist as +! both (feedphases=2), then both states are tested. +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! + SUBROUTINE phase_stability ( lle_check, flashcase, ph_split ) +! + USE BASIC_VARIABLES + USE STARTING_VALUES + USE EOS_VARIABLES, ONLY: dhs, PI, x, eta, eta_start, z3t, fres + USE EOS_NUMERICAL_DERIVATIVES + IMPLICIT NONE +! +! ---------------------------------------------------------------------- + LOGICAL :: lle_check + LOGICAL, INTENT(IN OUT) :: flashcase + INTEGER, INTENT(OUT) :: ph_split +! ---------------------------------------------------------------------- + + INTERFACE + REAL FUNCTION F_STABILITY ( optpara, n ) + INTEGER, INTENT(IN) :: n + REAL, INTENT(IN OUT) :: optpara(n) + END FUNCTION + END INTERFACE + +!INTERFACE +! SUBROUTINE F_STABILITY (fmin, optpara, n) +! REAL, INTENT(IN OUT) :: fmin +! REAL, INTENT(IN) :: optpara(:) +! INTEGER, INTENT(IN) :: n +! END SUBROUTINE F_STABILITY +! +! SUBROUTINE stability_grad (g, optpara, n) +! REAL, INTENT(IN OUT) :: g(:) +! REAL, INTENT(IN) :: optpara(:) +! INTEGER, INTENT(IN) :: n +! END SUBROUTINE stability_grad +! +! SUBROUTINE stability_hessian (hessian, g, fmin, optpara, n) +! REAL, INTENT(IN OUT) :: hessian(:,:) +! REAL, INTENT(IN OUT) :: g(:) +! REAL, INTENT(IN OUT) :: fmin +! REAL, INTENT(IN) :: optpara(:) +! INTEGER, INTENT(IN) :: n +! END SUBROUTINE stability_hessian +!END INTERFACE + + INTEGER :: n, PRIN + REAL :: fmin, t0, h0, MACHEP, PRAXIS + REAL, ALLOCATABLE :: optpara(:) + + INTEGER :: i, feedphases, trial + REAL :: rhoi(nc),rho_start + REAL :: feeddens, rho_phas(np) + REAL :: fden + REAL :: dens + REAL :: rhot + REAL :: lnphi(np,nc) + REAL :: w(np,nc), mean_mass +! ---------------------------------------------------------------------- + +n = ncomp +ALLOCATE( optpara(n) ) + +IF (lle_check) WRITE (*,*) ' stability test starting with dense phase' + +DO i = 1, ncomp ! setting feed-phase x's + IF (.NOT.flashcase) xif(i) = xi(1,i) + IF (flashcase) xi(1,i) = xif(i) + xi(2,i) = xif(i) ! feed is tested for both: V and L density +END DO + +densta(1) = 0.45 +densta(2) = 1.d-6 + +CALL dens_calc(rho_phas) +IF ( ABS(1.0-dense(1)/dense(2)) > 0.0005 ) THEN + feedphases=2 ! feed-composition can exist both, in V and L +ELSE + feedphases=1 ! feed-composition can exist either in V or L +END IF +densta(1) = dense(1) +feeddens = dense(2) +!write (*,*) 'feedphases',dense(1), dense(2),feedphases + +10 CONTINUE ! IF FeedPhases=2 THEN there is a second cycle + + trial = 1 + + ! -------------------------------------------------------------------- + ! setting trial-phase mole-fractions + ! if there is no phase-split then further trial-phases are + ! considered (loop: 20 CONTINUE) + ! -------------------------------------------------------------------- + DO i = 1, ncomp + w(2,i) = 1.0 / REAL(ncomp) + END DO + mean_mass = 1.0 / SUM( w(2,1:ncomp)/mm(1:ncomp) ) + xi(2,1:ncomp) = w(2,1:ncomp)/mm(1:ncomp) * mean_mass + + 20 CONTINUE + + DO i = 1, ncomp + rhoif(i) = rho_phas(1) * xif(i) + rhoi(i) = rhoif(i) + END DO + + !write (*,'(a,6G16.8)') 'startval',rho_phas(2),xi(2,1:ncomp) + + ! -------------------------------------------------------------------- + ! calc Helmholtz energy density and derivative (numerical) to rhoif(i). + ! The derivative is taken around the "feed-point" not the trial phase + ! -------------------------------------------------------------------- + + rhot = SUM( rhoi(1:ncomp) ) + x(1:ncomp) = rhoi(1:ncomp) / rhot + CALL PERTURBATION_PARAMETER + xi(1,1:ncomp) = x(1:ncomp) + eta = rhot * z3t + eta_start = eta + densta(1) = eta_start + ensemble_flag = 'tv' + CALL FUGACITY (lnphi) + ensemble_flag = 'tp' + + call fden_calc ( fden, rhoi ) + fdenf = fden + + grad_fd(1:ncomp) = lnphi(1,1:ncomp) + LOG( rhoi(1:ncomp) ) + + + ! -------------------------------------------------------------------- + ! starting values for iteration (optpara) + ! -------------------------------------------------------------------- + rho_start = 1.E-5 + IF (lle_check) THEN + densta(2) = 0.45 + CALL dens_calc(rho_phas) + rho_start = rho_phas(2)*0.45/dense(2) + END IF + DO i = 1,ncomp + rhoi(i) = xi(2,i)*rho_start + optpara(i) = LOG( rhoi(i) ) + END DO + + ! -------------------------------------------------------------------- + ! minimizing the objective fct. Phase split for values of fmin < 0.0 + ! -------------------------------------------------------------------- + t0 = 5.E-5 + h0 = 0.5 + PRIN = 0 + MACHEP = 1.E-15 + + fmin = PRAXIS( t0, MACHEP, h0, n, PRIN, optpara, F_STABILITY, fmin ) + + + ! -------------------------------------------------------------------- + ! updating the ln(x) valus from optpara. The optimal optpara-vector is + ! not necessarily the one that was last evaluated. At the very end, + ! cg_decent writes the best values to optpara + ! -------------------------------------------------------------------- + fmin = F_STABILITY( optpara, n ) + + + + ! IF ( n == 2 ) THEN + ! CALL Newton_Opt_2D ( stability_hessian, F_stability, optpara, n, 1.E-8, 1.E-8, g, fmin) + ! ELSE + ! CALL cg_descent (1.d-5, optpara, n, F_STABILITY, stability_grad, STATUS, & + ! gnorm, fmin, iter, nfunc, ngrad, d, g, xtemp, gtemp) + ! ENDIF + ! CALL F_STABILITY (fmin, optpara, n) + + + ! -------------------------------------------------------------------- + ! determine instability & non-trivial solution + ! -------------------------------------------------------------------- + ph_split = 0 + IF (fmin < -1.E-7 .AND. & + ABS( 1.0 - maxval(EXP(optpara),mask=optpara /= 0.0) /maxval(rhoif) ) > 0.0005) THEN + ph_split = 1 + END IF + + IF (ph_split == 1) THEN + + ! ------------------------------------------------------------------ + ! here, there should be IF FeedPhases=2 THEN GOTO 10 + ! and test for another phase (while saving optpara) + ! ------------------------------------------------------------------ + + rhoi2(1:ncomp) = EXP( optpara(1:ncomp) ) + dens = PI/6.0 * SUM( rhoi2(1:ncomp) * parame(1:ncomp,1) * dhs(1:ncomp)**3 ) + rhot = SUM( rhoi2(1:ncomp) ) + xi(2,1:ncomp) = rhoi2(1:ncomp) / rhot + + ELSE + + IF (trial <= ncomp + ncomp) THEN + ! ---------------------------------------------------------------- + ! setting trial-phase x's + ! ---------------------------------------------------------------- + IF (trial <= ncomp) THEN + DO i=1,ncomp + w(2,i) = 1.0 / REAL(ncomp-1) * 0.05 + END DO + w(2,trial) = 0.95 + ELSE + DO i=1,ncomp + w(2,i) = 1.0 / REAL(ncomp-1) * 0.00001 + END DO + w(2,trial-ncomp) = 0.99999 + END IF + mean_mass = 1.0 / SUM( w(2,1:ncomp)/mm(1:ncomp) ) + xi(2,1:ncomp) = w(2,1:ncomp)/mm(1:ncomp) * mean_mass + trial = trial + 1 + GO TO 20 + END IF + ! IF (.NOT.LLE_check) write (*,*) 'no phase split detected' + ! IF (.NOT.LLE_check) pause + IF (feedphases > 1 .AND. .NOT.lle_check .AND. densta(1) > 0.2) THEN + densta(1) = feeddens ! this will be the lower-valued density (vapor) + CALL dens_calc(rho_phas) + ! WRITE (*,*) 'try feed as vapor-phase' + GO TO 10 + END IF + + END IF + +DEALLOCATE( optpara ) + +END SUBROUTINE phase_stability + + +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! SUBROUTINE select_sum_rel +! +! This subroutine determines which component of a phase "ph" is calculated +! from the summation relation x_i = 1 - sum(x_j). The other components are, +! by default, said to be iterated during the phase equilibrium calculation. +! +! Note that for flash calculations not all of these mole fractions are in +! fact iterated - this is raken care of in "determine_flash_it". +! +! ph phase +! excl exclude comp. n +! startindex assign it(startindex) for quantities to be iterated +! (further it(startindex+1) is assigned, for a ternary +! mixture, etc.) +! +! sum_index indicates the component, with the largest mole +! fraction. If ph=1 and sum_index=2, we define +! sum_rel(ph=1)='x12', so that this component is +! calculated from the summation relation. +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! + SUBROUTINE select_sum_rel (ph,excl,startindex) +! + USE BASIC_VARIABLES + IMPLICIT NONE +! +! ---------------------------------------------------------------------- + INTEGER, INTENT(IN) :: ph + INTEGER, INTENT(IN) :: excl + INTEGER, INTENT(IN) :: startindex +! ---------------------------------------------------------------------- + INTEGER :: i,j, sum_index + REAL :: xmax(np) + ! CHARACTER :: compNo*2,phasNo*2 +! ---------------------------------------------------------------------- + +xmax(ph) = 0.0 +DO i = 1, ncomp + + IF ( xi(ph,i) > xmax(ph) ) THEN + xmax(ph) = xi(ph,i) + sum_index = i + + IF (ph == 1 .AND. i == 1) sum_rel(1) = 'x11' + IF (ph == 1 .AND. i == 2) sum_rel(1) = 'x12' + IF (ph == 1 .AND. i == 3) sum_rel(1) = 'x13' + IF (ph == 1 .AND. i == 4) sum_rel(1) = 'x14' + IF (ph == 1 .AND. i == 5) sum_rel(1) = 'x15' + + IF (ph == 2 .AND. i == 1) sum_rel(2) = 'x21' + IF (ph == 2 .AND. i == 2) sum_rel(2) = 'x22' + IF (ph == 2 .AND. i == 3) sum_rel(2) = 'x23' + IF (ph == 2 .AND. i == 4) sum_rel(2) = 'x24' + IF (ph == 2 .AND. i == 5) sum_rel(2) = 'x25' + + IF (ph == 3 .AND. i == 1) sum_rel(3) = 'x31' + IF (ph == 3 .AND. i == 2) sum_rel(3) = 'x32' + IF (ph == 3 .AND. i == 3) sum_rel(3) = 'x33' + IF (ph == 3 .AND. i == 4) sum_rel(3) = 'x34' + IF (ph == 3 .AND. i == 5) sum_rel(3) = 'x35' +! write (*,*) ph,i,xi(ph,i),sum_rel(ph) + END IF + +END DO + +j = 0 +DO i = 1, ncomp + + IF ( i /= sum_index .AND. i /= excl ) THEN + IF (ph == 1 .AND. i == 1) it(startindex+j) = 'x11' + IF (ph == 1 .AND. i == 2) it(startindex+j) = 'x12' + IF (ph == 1 .AND. i == 3) it(startindex+j) = 'x13' + IF (ph == 1 .AND. i == 4) it(startindex+j) = 'x14' + IF (ph == 1 .AND. i == 5) it(startindex+j) = 'x15' + + IF (ph == 2 .AND. i == 1) it(startindex+j) = 'x21' + IF (ph == 2 .AND. i == 2) it(startindex+j) = 'x22' + IF (ph == 2 .AND. i == 3) it(startindex+j) = 'x23' + IF (ph == 2 .AND. i == 4) it(startindex+j) = 'x24' + IF (ph == 2 .AND. i == 5) it(startindex+j) = 'x25' + + IF (ph == 3 .AND. i == 1) it(startindex+j) = 'x31' + IF (ph == 3 .AND. i == 2) it(startindex+j) = 'x32' + IF (ph == 3 .AND. i == 3) it(startindex+j) = 'x33' + IF (ph == 3 .AND. i == 4) it(startindex+j) = 'x34' + IF (ph == 3 .AND. i == 5) it(startindex+j) = 'x35' +! write (*,*) 'iter ',it(startindex+j) + j = j + 1 + END IF + +END DO + +END SUBROUTINE select_sum_rel + + + + +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! + SUBROUTINE tangent_plane +! + USE BASIC_VARIABLES + USE STARTING_VALUES + IMPLICIT NONE +! +! ---------------------------------------------------------------------- +!!$ INTERFACE +!!$ SUBROUTINE tangent_value (fmin, optpara, n) +!!$ INTEGER, INTENT(IN) :: n +!!$ REAL, INTENT(IN OUT) :: fmin +!!$ REAL, INTENT(IN) :: optpara(:) +!!$ END SUBROUTINE tangent_value +!!$ +!!$ SUBROUTINE tangent_grad (g, optpara, n) +!!$ INTEGER, INTENT(IN) :: n +!!$ REAL, INTENT(IN OUT) :: g(:) +!!$ REAL, INTENT(IN) :: optpara(:) +!!$ END SUBROUTINE tangent_grad +!!$ END INTERFACE + +! +! ---------------------------------------------------------------------- + INTERFACE + REAL FUNCTION PRAXIS( t0, MACHEP, h0, n, PRIN, optpara, TANGENT_VALUE, fmin ) + REAL, INTENT(IN OUT) :: t0 + REAL, INTENT(IN) :: machep + REAL, INTENT(IN) :: h0 + INTEGER :: n + INTEGER, INTENT(IN OUT) :: prin + REAL, INTENT(IN OUT) :: optpara(n) + REAL, EXTERNAL :: TANGENT_VALUE + REAL, INTENT(IN OUT) :: fmin + END FUNCTION + + REAL FUNCTION TANGENT_VALUE2 ( optpara, n ) + INTEGER, INTENT(IN) :: n + REAL, INTENT(IN) :: optpara(n) + END FUNCTION + END INTERFACE +! +! ---------------------------------------------------------------------- + INTEGER :: n + INTEGER :: i, k, ph + INTEGER :: small_i, min_ph, other_ph + INTEGER :: PRIN + REAL :: fmin , t0, h0, MACHEP + REAL :: lnphi(np,nc) + REAL, ALLOCATABLE :: optpara(:) + +! INTEGER :: STATUS, iter, nfunc, ngrad +! REAL :: gnorm +! REAL, ALLOCATABLE :: d(:), g(:), xtemp(:), gtemp(:) +! ---------------------------------------------------------------------- + +n = ncomp +t0 = 1.E-4 +h0 = 0.1 +PRIN = 0 +MACHEP = 1.E-15 + +ALLOCATE( optpara(n) ) +!ALLOCATE( d(n) ) +!ALLOCATE( g(n) ) +!ALLOCATE( xtemp(n) ) +!ALLOCATE( gtemp(n) ) + +DO i = 1,ncomp + rhoi1(i) = rhoif(i) + lnx(1,i) = LOG(xi(1,i)) + lnx(2,i) = LOG(xi(2,i)) +END DO + +DO i = 1,ncomp + optpara(i) = LOG( xi(2,i) * 0.001 ) +END DO + +! CALL cg_descent (1.d-4, optpara, n, tangent_value, tangent_grad, STATUS, & +! gnorm, fmin, iter, nfunc, ngrad, d, g, xtemp, gtemp) +! +! updating the ln(x) valus from optpara. The optimal optpara-vector is not necessarily +! the one that was last evaluated. At the very end, cg_decent writes the best values to optpara +! CALL tangent_value (fmin, optpara, n) + + + +fmin = PRAXIS( t0, MACHEP, h0, n, PRIN, optpara, TANGENT_VALUE2, fmin ) + +! The optimal optpara-vector is not necessarily the one that was last evaluated. +! TANGENT_VALUE is reexecuted with the optimal vector optpara, in order to update the ln(x) values +fmin = TANGENT_VALUE2( optpara, n ) + + +! ---------------------------------------------------------------------- +! If one component is a polymer (indicated by a low component-density) +! then get an estimate of the polymer-lean composition, by solving for +! xi_p1 = ( xi_p2 * phii_p2) / phii_p1 (phase equilibrium condition, +! with p1 for phase 1) +! ---------------------------------------------------------------------- +IF ( MINVAL( lnx(1,1:ncomp) ) < MINVAL( lnx(2,1:ncomp) ) ) THEN + min_ph = 1 + other_ph = 2 +ELSE + min_ph = 2 + other_ph = 1 +ENDIF +small_i = MINLOC( lnx(min_ph,1:ncomp), 1 ) +! --- if one component is a polymer ------------------------------------ +IF ( MINVAL( lnx(min_ph,1:ncomp) ) < -20.0 ) THEN + CALL FUGACITY ( lnphi ) + lnx(min_ph,small_i) = lnx(other_ph,small_i)+lnphi(other_ph,small_i) - lnphi(min_ph,small_i) + optpara(small_i) = lnx(2,small_i) + LOG( SUM( EXP( optpara(1:ncomp) ) ) ) +END IF + +! ---------------------------------------------------------------------- +! caution: these initial values are for a flashcase overwritten in +! SUBROUTINE determine_flash_it2, because in that case, the lnx-values +! treated as ln(mole_number). +! ---------------------------------------------------------------------- +val_init(1) = dense(1) +val_init(2) = dense(2) +val_init(3) = t +val_init(4) = p +DO ph = 1,nphas + DO k = 1,ncomp + val_init(4+k+(ph-1)*ncomp) = lnx(ph,k) + END DO +END DO +!alpha = optpara(1) + + +!DEALLOCATE( optpara, d, g, xtemp, gtemp ) +DEALLOCATE( optpara ) + +END SUBROUTINE tangent_plane + + +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! + SUBROUTINE determine_flash_it2 +! + USE BASIC_VARIABLES + IMPLICIT NONE +! +! ---------------------------------------------------------------------- + INTEGER :: i, k, ph + REAL :: n_phase1, n_phase2, max_x_diff +! ---------------------------------------------------------------------- + + IF ( MINVAL( lnx(1,1:ncomp) ) < MINVAL( lnx(2,1:ncomp) ) ) THEN + it(1) = 'x11' + it(2) = 'x12' + IF (ncomp >= 3) it(3) = 'x13' + IF (ncomp >= 4) it(4) = 'x14' + IF (ncomp >= 5) it(5) = 'x15' + sum_rel(1) = 'nfl' + ELSE + it(1) = 'x21' + it(2) = 'x22' + IF (ncomp >= 3) it(3) = 'x23' + IF (ncomp >= 4) it(4) = 'x24' + IF (ncomp >= 5) it(5) = 'x25' + sum_rel(2) = 'nfl' + ENDIF + max_x_diff = 0.0 + DO i = 1,ncomp + IF ( ABS( EXP( lnx(1,i) ) - EXP( lnx(2,i) ) ) > max_x_diff ) THEN + max_x_diff = ABS( EXP( lnx(1,i) ) - EXP( lnx(2,i) ) ) + n_phase1 = ( xif(i) - EXP( lnx(2,i) ) ) / ( EXP( lnx(1,i) ) - EXP( lnx(2,i) ) ) + n_phase2 = 1.0 - n_phase1 + END IF + END DO + lnx(1,1:ncomp) = lnx(1,1:ncomp) + LOG( n_phase1 ) ! these x's are treated as mole numbers + lnx(2,1:ncomp) = lnx(2,1:ncomp) + LOG( n_phase2 ) ! these x's are treated as mole numbers + + + val_init(1) = dense(1) + val_init(2) = dense(2) + val_init(3) = t + val_init(4) = p + DO ph = 1,nphas + DO k = 1,ncomp + val_init(4+k+(ph-1)*ncomp) = lnx(ph,k) ! - LOG( SUM( EXP( lnx(ph,1:ncomp) ) ) ) + ! write (*,*) ph,k, lnx(ph,k) + END DO + END DO + +END SUBROUTINE determine_flash_it2 + +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! SUBROUTINE poly_sta_var +! +! This subroutine generates starting values for mole fractons of +! polymer-solvent systems. +! The determination of these starting values follows a two-step +! procedure. Fist, the equilibrium concentration of the polymer-rich +! phase is estimated with the assumption of zero concentration +! of polymer in the polymer-lean-phase. This is achieved in the +! SUBROUTINE POLYMER_FREE. (Only one equation has to be iterated +! for this case). Once this is achieved, the rigorous calculation +! is triggered. If it converges, fine! If no solution is obtained, +! the pressure is somewhat reduced, the procedure is repeated and +! a calculation is started to approach the originally specified +! pressure. +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! + SUBROUTINE poly_sta_var (converg) +! + USE BASIC_VARIABLES + IMPLICIT NONE +! +! ---------------------------------------------------------------------- + INTEGER, INTENT(IN OUT) :: converg +! +! ---------------------------------------------------------------------- + INTEGER :: k,ph,sol + REAL :: p_spec,solution(10,4+nc*np) +! ---------------------------------------------------------------------- + + p_spec = p + + find_equilibrium: DO + + CALL polymer_free(p_spec,sol,solution) + + WRITE (*,*) ' ' + WRITE (*,*) ' GENERATING STARTING VALUES' + + val_init(1) = solution(1,1) ! approx.solutions for next iteration + val_init(2) = solution(1,2) ! approx.solutions for next iteration + val_init(3) = solution(1,3) ! approx.solutions for next iteration + val_init(4) = solution(1,4) ! approx.solutions for next iteration + DO ph = 1,nphas + DO k = 1,ncomp + val_init(4+k+(ph-1)*ncomp) = solution(1,4+k+(ph-1)*ncomp) + END DO + END DO + val_init(7) = -10000.0 ! start.val. for lnx(2,1) for iterat. + + IF (p /= p_spec) & + WRITE (*,*) ' INITIAL EQUILIBRIUM CALC. FAILD. NEXT STEP STARTS' + + IF (p == p_spec) THEN + n_unkw = ncomp ! number of quantities to be iterated + it(1)='x11' ! iteration of mol fraction of comp.1 phase 1 + it(2)='x21' ! iteration of mol fraction of comp.1 phase 2 + CALL objective_ctrl (converg) + ELSE + outp = 0 ! output to terminal + running ='p' ! Pressure is running var. in PHASE_EQUILIB + CALL phase_equilib(p_spec,5.0,converg) + END IF + + IF (converg == 1) EXIT find_equilibrium + p = p * 0.9 + IF ( p < (0.7*p_spec) ) WRITE (*,*) ' NO SOLUTION FOUND' + IF ( p < (0.7*p_spec) ) STOP + + END DO find_equilibrium + + WRITE (*,*) ' FINISHED: POLY_STA_VAR' + +END SUBROUTINE poly_sta_var + + +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! SUBROUTINE x_summation +! +! This subroutine solves the summation relation: xi=1-sum(xj) +! The variable "sum_rel(i)" contains the information, which mole +! fraction is the one to be calculated here. Consider the example +! sum_rel(1)='x12'. The fist letter 'x' of this variable indicates, +! that this subroutine needs to be executed and that the mole +! fraction of a component has to be calculated. The second letter +! of the string points to phase 1, the third letter to component 2. +! If the fist letter is 'e', not 'x', then the subroutine +! NEUTR_CHARGE is called. This is the case of electrolyte solutions, +! neutral charges have to be enforced in all phases (see below). +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! + SUBROUTINE x_summation +! + USE BASIC_VARIABLES + IMPLICIT NONE +! +! ---------------------------------------------------------------------- + INTEGER :: i, j, comp_i, ph_i + REAL :: sum_x + CHARACTER (LEN=2) :: phasno + CHARACTER (LEN=2) :: compno + LOGICAL :: flashcase2 +! ---------------------------------------------------------------------- + +DO j = 1, nphas + IF (sum_rel(j)(1:3) == 'nfl') THEN + CALL new_flash (j) + RETURN + END IF +END DO + + + +flashcase2 = .false. + +DO j = 1, nphas + + IF (sum_rel(j)(1:1) == 'x') THEN + + phasno = sum_rel(j)(2:2) + READ(phasno,*) ph_i + compno = sum_rel(j)(3:3) + READ(compno,*) comp_i + IF ( sum_rel(nphas+j)(1:1) == 'e' ) CALL neutr_charge(nphas+j) + + sum_x = 0.0 + DO i = 1, ncomp + IF ( i /= comp_i ) sum_x = sum_x + xi(ph_i,i) + END DO + xi(ph_i,comp_i) = 1.0 - sum_x + IF ( xi(ph_i,comp_i ) < 0.0 ) xi(ph_i,comp_i) = 0.0 + IF ( xi(ph_i,comp_i ) /= 0.0 ) THEN + lnx(ph_i,comp_i) = LOG( xi(ph_i,comp_i) ) + ELSE + lnx(ph_i,comp_i) = -100000.0 + END IF + ! write (*,*) 'sum_x',ph_i,comp_i,lnx(ph_i,comp_i),xi(ph_i,comp_i) + + ELSE IF ( sum_rel(j)(1:2) == 'fl' ) THEN + + flashcase2 = .true. + ! ------------------------------------------------------------------ + ! This case is true when all molefractions of one phase are + ! determined from a component balance. What is needed to + ! calculate all molefractions of that phase are all mole- + ! fractions of the other phase (nphas=2, so far) and the + ! phase fraction alpha. + ! Alpha is calculated (in FLASH_ALPHA) from the mole fraction + ! of component {sum_rel(j)(3:3)}. IF sum_rel(2)='fl3', then + ! the alpha is determined from the molefraction of comp. 3 and + ! the molefraction of phase 2 is then completely determined ELSE + ! ------------------------------------------------------------------ + + ELSE + WRITE (*,*) 'summation relation not defined' + STOP + END IF + +END DO + +IF ( it(1) == 'fls' ) CALL flash_sum +IF ( flashcase2 ) CALL flash_alpha + +END SUBROUTINE x_summation + + + +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! SUBROUTINE FUGACITY +! +! This subroutine serves as an interface to the eos-subroutines. +! (1) case 1, when ensemble_flag = 'tp' +! The subroutine gives the residual chemical potential: +! mu_i^res(T,p,x)/kT = ln( phi_i ) +! and in addition, the densities that satisfy the specified p +! (2) case 2, when ensemble_flag = 'tv' +! The subroutine gives the residual chemical potential: +! --> mu_i^res(T,rho,x)/kT +! and in addition the resulting pressure for the given density. +! The term "residual" means difference of the property and the same +! property for an ideal gas mixture. +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! + SUBROUTINE FUGACITY (ln_phi) +! + USE BASIC_VARIABLES + USE EOS_VARIABLES, ONLY: phas, x, eta, eta_start, lnphi, fres, rho, pges, KBOL + IMPLICIT NONE +! +! ---------------------------------------------------------------------- + REAL, INTENT(OUT) :: ln_phi(np,nc) +! +! --- local variables -------------------------------------------------- + INTEGER :: ph +! ---------------------------------------------------------------------- +! +IF (eos < 2) THEN + + DO ph = 1,nphas + + phas = ph + eta_start = densta(ph) + x(1:ncomp) = xi(ph,1:ncomp) + + IF (p < 1.E-100) THEN + WRITE(*,*) ' FUGACITY: PRESSURE TOO LOW', p + p = 1.E-6 + END IF + + IF (num == 0) CALL PHI_EOS + IF (num == 1) CALL PHI_NUMERICAL + !!IF (num == 2) CALL PHI_CRITICAL_RENORM + IF (num == 2) write(*,*) 'CRITICAL RENORM NOT INCLUDED YET' + + dense(ph) = eta + ln_phi(ph,1:ncomp) = lnphi(1:ncomp) + ! gibbs(ph) = fres + sum( xi(ph,1:ncomp)*( log( xi(ph,1:ncomp)*rho) - 1.0 ) ) & + ! + (pges * 1.d-30) / (KBOL*t*rho) ! includes ideal gas contribution + + ! f_res(ph) = fres + ! write (*,'(i3,4G20.11)') ph,eta,lnphi(1),lnphi(2) + ! DO i = 1,ncomp + ! DO j=1,NINT(parame(i,12)) + ! mxx(ph,i,j) = mx(i,j) + ! END DO + ! END DO + + END DO + +ELSE + +! IF (eos == 2) CALL srk_eos (ln_phi) +! IF (eos == 3) CALL pr_eos (ln_phi) +! dense(1) = 0.01 +! dense(2) = 0.3 +! IF (eos == 4.OR.eos == 5.OR.eos == 6.OR.eos == 8) CALL lj_fugacity(ln_phi) +! IF (eos == 7) CALL sw_fugacity(ln_phi) +! IF (eos == 9) CALL lj_bh_fug(ln_phi) + +END IF + +END SUBROUTINE FUGACITY + + +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! SUBROUTINE enthalpy_etc +! +! This subroutine serves as an interface to the EOS-routines. The +! residual enthalpy h_res, residual entropy s_res, residual Gibbs +! enthalpy g_res, and residual heat capacity at constant pressure +! (cp_res) corresponding to converged conditions are calculated. +! The conditions in (T,P,xi,rho) need to be converged equilibrium +! conditions !! +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! + SUBROUTINE enthalpy_etc +! + USE BASIC_VARIABLES + USE EOS_VARIABLES + IMPLICIT NONE +! + INTEGER :: ph +! ------------------------------------------------------------------ + +IF (eos <= 1) THEN + + DO ph=1,nphas + + phas = ph + eta = dense(ph) +! eta_start = dense(ph) + x(1:ncomp) = xi(ph,1:ncomp) + + IF(num == 0) THEN + CALL H_EOS + ELSE + IF(num == 1) CALL H_numerical + IF(num == 2) write (*,*) 'enthalpy_etc: incorporate H_EOS_RN' + IF(num == 2) stop +! IF(num == 2) CALL H_EOS_rn + END IF + enthal(ph) = h_res + entrop(ph) = s_res + ! gibbs(ph) = h_res - t * s_res ! already defined in eos.f90 (including ideal gas) + cpres(ph) = cp_res + + END DO + IF (nphas == 2) h_lv = enthal(2)-enthal(1) + +ENDIF + +END SUBROUTINE enthalpy_etc + + +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! SUBROUTINE dens_calc +! +! This subroutine serves as an interface to the EOS-routines. The +! densities corresponding to given (P,T,xi) are calculated. +! (Note: the more common interface is SUBROUTINE FUGACITY. +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! + SUBROUTINE dens_calc(rho_phas) +! + USE BASIC_VARIABLES + USE EOS_VARIABLES + IMPLICIT NONE +! +! +!------------------------------------------------------------------ + REAL, INTENT(OUT) :: rho_phas(np) +! + INTEGER :: ph +!------------------------------------------------------------------ + + +DO ph = 1, nphas + + IF (eos < 2) THEN + + phas = ph + eta = densta(ph) + eta_start = densta(ph) + x(1:ncomp) = xi(ph,1:ncomp) + + CALL PERTURBATION_PARAMETER + CALL DENSITY_ITERATION + + dense(ph)= eta + rho_phas(ph) = eta/z3t + + ELSE + write (*,*) ' SUBROUTINE DENS_CALC not available for cubic EOS' + stop + END IF + +END DO + +END SUBROUTINE dens_calc + + +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! + SUBROUTINE fden_calc (fden, rhoi) +! + USE BASIC_VARIABLES + USE EOS_VARIABLES + IMPLICIT NONE +! +! ---------------------------------------------------------------------- + REAL, INTENT(OUT) :: fden + REAL, INTENT(IN OUT) :: rhoi(nc) +! ---------------------------------------------------------------------- + REAL :: rhot, fden_id +! ---------------------------------------------------------------------- + + +IF (eos < 2) THEN + + rhot = SUM( rhoi(1:ncomp) ) + x(1:ncomp) = rhoi(1:ncomp) / rhot + + CALL PERTURBATION_PARAMETER + eta = rhot * z3t + eta_start = eta + + IF (num == 0) THEN + CALL F_EOS + ELSE IF(num == 1) THEN + CALL F_NUMERICAL + ELSE + write (*,*) 'deactivated this line when making a transition to f90' + stop + ! CALL F_EOS_rn + END IF + + fden_id = SUM( rhoi(1:ncomp) * ( LOG( rhoi(1:ncomp) ) - 1.0 ) ) + + fden = fres * rhot + fden_id + +ELSE + write (*,*) ' SUBROUTINE FDEN_CALC not available for cubic EOS' + stop +END IF + +END SUBROUTINE fden_calc + + + + +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! SUBROUTINE polymer_free +! +! This subroutine performes a phase equilibrium calculation assuming +! the polymer-lean hase to be polymer-free (x_poly=0). Only the +! equality of the solvent-fugacities has to be ensured (only one +! equation to be iterated). This procedure delivers very good +! appoximations for the polymer-rich phase up-to fairly close to the +! mixture critical point. Both, liquid-liquid and vapor-liquid +! equilibria can be calculated. +! See also comments to SUBROUTINE POLY_STA_VAR. +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! + SUBROUTINE polymer_free (p_spec,sol,solution) +! + USE BASIC_VARIABLES + IMPLICIT NONE +! +! ---------------------------------------------------------------------- + REAL, INTENT(IN OUT) :: p_spec + INTEGER, INTENT(OUT) :: sol + REAL, INTENT(OUT) :: solution(10,4+nc*np) +! +! ---------------------------------------------------------------------- + INTEGER :: k,j,ph, converg + REAL :: grid(10) +! ---------------------------------------------------------------------- + + sol = 0 + + grid(1)=0.98 + grid(2)=0.9 + grid(3)=0.7 + grid(4)=0.5 + grid(5)=0.3 + grid(6)=0.2 + grid(7)=0.1 + grid(8)=0.05 + + DO WHILE ( sol == 0 ) + + DO j = 1,8 + ! Phase 2 is solvent-phase + ! starting value for xi(1,1) of polymer-phase 1: w_polymer=0.95 to 0.05 + ! from simple approximate equation + xi(1,1) = grid(j) / ( (1.0-grid(j)) * mm(1) / mm(2) ) !xi(1,1) Phase 1 Komponente 1 + IF ( mm(1) < 5000.0 ) xi(1,1) = xi(1,1) * 0.8 + xi(1,2) = 1.0 - xi(1,1) !xi(1,2) Phase 1 Komponente 2 + lnx(1,1) = LOG(xi(1,1)) + lnx(1,2) = LOG(xi(1,2)) + lnx(2,1) = -1.E10 !ln(xi) Phase 2 Komponente 1 + lnx(2,2) = 0.0 !ln(xi) Phase 2 Komponente 2 + + + + val_init(1) = 0.45 ! starting density targeting at a liquid phase + val_init(2) = 0.0001 ! starting density targeting at a vapor phase + ! val_init(2) = 0.45 + val_init(3) = t + val_init(4) = p + DO ph = 1,nphas + DO k = 1,ncomp + val_init(4+k+(ph-1)*ncomp) = lnx(ph,k) + END DO + END DO + + + + + n_unkw = ncomp-1 ! number of quantities to be iterated + it(1) = 'x11' ! iteration of mol fraction of comp.1 phase 1 + it(2) = ' ' + sum_rel(1) = 'x12' ! summation relation: x12 = 1 - sum(x1j) + sum_rel(2) = 'x22' + + CALL objective_ctrl (converg) + + IF (converg == 1 .AND. ABS(dense(1)/dense(2)-1.0) > 1.d-3 .AND. dense(1) > 0.1) THEN + IF (sol == 0) THEN + sol = sol + 1 + DO k = 1,4+ncomp*nphas + solution(sol,k) = val_conv(k) + END DO + ELSE IF (ABS(solution(sol,5)/lnx(1,1)-1.0) > 1.d-2) THEN + sol = sol + 1 + DO k = 1,4+ncomp*nphas + solution(sol,k) = val_conv(k) + END DO + END IF + END IF + + END DO + + + + + + IF (sol == 0) THEN + WRITE (*,*) ' no initial solution found' + p = p*0.9 + IF (p < (0.7*p_spec)) WRITE (*,*) ' NO SOLUTION FOUND' + IF (p < (0.7*p_spec)) STOP + ELSE IF (sol > 1) THEN + ! write (*,*) ' ' + ! write (*,*) ' ',sol,' solutions found:' + ! write (*,*) ' lnx(1,1), dichte_1, dichte_2' + ! DO k = 1,sol + ! write (*,*) solution(k,5),solution(k,1),solution(k,2) + ! END DO + END IF + END DO + + n_unkw = ncomp ! number of quantities to be iterated + it(1) = 'x11' ! iteration of mol fraction of comp.1 phase 1 + it(2) = 'x21' ! iteration of mol fraction of comp.1 phase 2 + sum_rel(1) = 'x12' ! summation relation: x12 = 1 - sum(x1j) + sum_rel(2) = 'x22' ! summation relation: x22 = 1 - sum(x2j) + + + END SUBROUTINE polymer_free + + + + + +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! SUBROUTINE phase_equilib +! +! This subroutine varies a predefined "running variable" and +! organizes phase equilibrium calculations. For an isotherm +! calculation e.g., the running variable is often the pressure. The +! code is designed to deliver only converged solutions. In order to +! enforce convergence, a step-width adjustment (reduction) is +! implemented. + +! VARIABLE LIST: +! running defines the running variable. For example: if you want +! to calculate the vapor pressure curve of a component +! starting from 100�C to 200�C, then running is 't'. The +! temperature is step-wise increased until the end- +! -temperature of 200�C is reached. +! (in this example end_x=200+273.15) +! end_x end point for running variable +! steps No. of calculation steps towards the end point of calc. +! converg 0 if no convergence achieved, 1 if converged solution +! +! PREREQUISITES: +! prior to execution of this routine, the follwing variables have to +! be defined: "val_init" an array containing the starting values for +! this iteration, "it(i)" provides the information, which variable is +! determined iteratively, "sum_rel(i)" indicates, which mole fraction +! is determined from the summation relation sum(xi)=1. Furthermore, +! the number of phases and the variables provided by the subroutine +! INPUT are required. +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! + SUBROUTINE phase_equilib (end_x,steps,converg) +! + USE BASIC_VARIABLES + IMPLICIT NONE +! +! ---------------------------------------------------------------------- + REAL, INTENT(IN) :: end_x + REAL, INTENT(IN) :: steps + INTEGER, INTENT(OUT) :: converg +! +! ---------------------------------------------------------------------- + INTEGER :: k, count1,count2,runindex,maxiter + REAL :: delta_x,delta_org,val_org,runvar + CHARACTER (LEN=2) :: compon + LOGICAL :: continue_cycle +! ---------------------------------------------------------------------- + +IF (running(1:2) == 'd1') runindex = 1 +IF (running(1:2) == 'd2') runindex = 2 +IF (running(1:1) == 't') runindex = 3 +IF (running(1:1) == 'p') runindex = 4 +IF (running(1:2) == 'x1') compon = running(3:3) +IF (running(1:2) == 'x1') READ(compon,*) k +IF (running(1:2) == 'x1') runindex = 4+k +IF (running(1:2) == 'x2') compon = running(3:3) +IF (running(1:2) == 'x2') READ(compon,*) k +IF (running(1:2) == 'x2') runindex = 4+ncomp+k +IF (running(1:2) == 'l1') compon = running(3:3) +IF (running(1:2) == 'l1') READ(compon,*) k +IF (running(1:2) == 'l1') runindex = 4+k +IF (running(1:2) == 'l2') compon = running(3:3) +IF (running(1:2) == 'l2') READ(compon,*) k +IF (running(1:2) == 'l2') runindex = 4+ncomp+k + +maxiter = 200 +IF ( ncomp >= 3 ) maxiter = 1000 +count1 = 0 +count2 = 0 +delta_x = ( end_x - val_init(runindex) ) / steps !J: calc increment in running var = (phi_end - phi_init)/steps +delta_org = ( end_x - val_init(runindex) ) / steps +val_org = val_init(runindex) +IF ( running(1:1) == 'x' ) THEN + delta_x = ( end_x - EXP(val_init(runindex)) ) / steps + delta_org = ( end_x - EXP(val_init(runindex)) ) / steps + val_org = EXP(val_init(runindex)) +END IF + +continue_cycle = .true. + +DO WHILE ( continue_cycle ) + + count1 = count1 + 1 + count2 = count2 + 1 + ! val_org = val_init(runindex) + + + CALL objective_ctrl (converg) + + IF (converg == 1) THEN + val_init( 1:(4+ncomp*nphas) ) = val_conv( 1:(4+ncomp*nphas) ) + IF (outp == 1 .AND. (ABS(delta_x) > 0.1*ABS(delta_org) .OR. count2 == 2)) CALL output + ELSE + delta_x = delta_x / 2.0 + IF (num == 2) delta_x = delta_x / 2.0 + val_init(runindex) = val_org + IF (running(1:1) == 'x') val_init(runindex) = LOG(val_org) + continue_cycle = .true. + count2 = 0 + END IF + runvar = val_init(runindex) + IF (running(1:1) == 'x') runvar = EXP(val_init(runindex)) + + IF ( end_x == 0.0 .AND. running(1:1) /= 'x' ) THEN + IF ( ABS(runvar-end_x) < 1.E-8 ) continue_cycle = .false. + ELSE IF ( ABS((runvar-end_x)/end_x) < 1.E-8 ) THEN + ! IF(delta_org.NE.0.0) WRITE (*,*)' FINISHED ITERATION',count1 + continue_cycle = .false. + ELSE IF ( count1 == maxiter ) THEN + WRITE (*,*) ' MAX. NO OF ITERATIONS',count1 + converg = 0 + continue_cycle = .false. + ELSE IF ( ABS(delta_x) < 1.E-5*ABS(delta_org) ) THEN + ! WRITE (*,*) ' CLOSEST APPROACH REACHED',count1 + converg = 0 + continue_cycle = .false. + ELSE + continue_cycle = .true. + val_org = runvar + IF (ABS(runvar+delta_x-end_x) > ABS(runvar-end_x)) delta_x = end_x - runvar ! if end-point passed + val_init(runindex) = runvar + delta_x + IF (running(1:1) == 'x') val_init(runindex) = LOG(runvar+delta_x) + END IF + + IF (ABS(delta_x) < ABS(delta_org) .AND. count2 >= 5) THEN + delta_x = delta_x * 2.0 + count2 = 0 + END IF + +END DO ! continue_cycle + +END SUBROUTINE phase_equilib + +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! + SUBROUTINE new_flash (ph_it) +! + USE BASIC_VARIABLES + IMPLICIT NONE +! +! ---------------------------------------------------------------------- + INTEGER, INTENT(IN) :: ph_it +! +! ---------------------------------------------------------------------- + INTEGER :: i, ph_cal + REAL, DIMENSION(nc) :: ni_1, ni_2 +! ---------------------------------------------------------------------- + + ph_cal = 3 - ph_it ! for two phases only + + DO i = 1, ncomp + IF ( lnx(ph_it,i) < -300.0 ) THEN + ni_2(i) = 0.0 + ELSE + ni_2(i) = EXP( lnx(ph_it,i) ) + END IF + END DO + + DO i = 1, ncomp + ni_1(i) = xif(i)-ni_2(i) + IF ( ni_2(i) > xif(i) ) THEN + ni_2(i) = xif(i) + ni_1(i) = xif(i) * 1.E-20 + ENDIF + END DO + + xi(ph_it,1:ncomp) = ni_2(1:ncomp) / SUM( ni_2(1:ncomp) ) + DO i = 1, ncomp + IF ( xi(ph_it,i) >= 1.E-300 ) lnx(ph_it,i) = LOG( xi(ph_it,i) ) + END DO + xi(ph_cal,1:ncomp) = ni_1(1:ncomp) / SUM( ni_1(1:ncomp) ) + lnx(ph_cal,1:ncomp) = LOG( xi(ph_cal,1:ncomp) ) + +END SUBROUTINE new_flash + + +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! SUBROUTINE PHI_EOS +! +! This subroutine gives the residual chemical potential: +! --> mu_i^res(T,p,x)/kT = ln( phi_i ) when ensemble_flag = 'tp' +! The required input for this case (T, p, x(nc)) and as a starting value +! eta_start +! +! or it gives +! +! --> mu_i^res(T,rho,x)/kT when ensemble_flag = 'tv' +! The required input for this case (T, eta_start, x(nc)). Note that +! eta_start is the specified density (packing fraction) in this case. +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! + SUBROUTINE PHI_EOS +! + USE PARAMETERS + USE EOS_VARIABLES + USE EOS_CONSTANTS + IMPLICIT NONE +! +! --- local variables--------------------------------------------------- + INTEGER :: i, j, k, ki, l, m + REAL :: z0, z1, z2, z3, z0_rk, z1_rk, z2_rk, z3_rk + REAL :: zms, m_mean + REAL, DIMENSION(nc) :: mhs, mdsp, mhc, myres + REAL, DIMENSION(nc) :: m_rk + REAL :: gij_rk(nc,nc) + REAL :: zres, zges + REAL :: dpdz, dpdz2 + + REAL :: I1, I2, I1_rk, I2_rk + REAL :: ord1_rk, ord2_rk + REAL :: c1_con, c2_con, c1_rk + REAL :: zmr, nmr, zmr_rk, nmr_rk, um_rk + REAL, DIMENSION(nc,0:6) :: ap_rk, bp_rk + + LOGICAL :: assoc + REAL :: ass_s2, m_hbon(nc) + + REAL :: fdd_rk, fqq_rk, fdq_rk + REAL, DIMENSION(nc) :: my_dd, my_qq, my_dq +! ---------------------------------------------------------------------- + +! ---------------------------------------------------------------------- +! obtain parameters and density independent expressions +! ---------------------------------------------------------------------- +CALL PERTURBATION_PARAMETER + + +! ---------------------------------------------------------------------- +! density iteration: (pTx)-ensemble OR p calc.: (pvx)-ensemble +! ---------------------------------------------------------------------- +IF (ensemble_flag == 'tp') THEN + CALL DENSITY_ITERATION +ELSEIF (ensemble_flag == 'tv') THEN + eta = eta_start + CALL P_EOS +ELSE + write (*,*) 'PHI_EOS: define ensemble, ensemble_flag == (pv) or (pt)' + stop +END IF + + +! --- Eq.(A.8) --------------------------------------------------------- +rho = eta / z3t +z0 = z0t * rho +z1 = z1t * rho +z2 = z2t * rho +z3 = z3t * rho + +m_mean = z0t / (PI/6.0) +zms = 1.0 - eta + +! ---------------------------------------------------------------------- +! compressibility factor z = p/(kT*rho) +! ---------------------------------------------------------------------- +zges = (p * 1.d-30) / (KBOL*t*rho) +IF ( ensemble_flag == 'tv' ) zges = (pges * 1.d-30) / (KBOL*t*rho) +zres = zges - 1.0 + + + +! ====================================================================== +! calculate the derivatives of f to mole fraction x ( d(f)/d(x) ) +! ====================================================================== + +DO k = 1, ncomp + + z0_rk = PI/6.0 * mseg(k) + z1_rk = PI/6.0 * mseg(k) * dhs(k) + z2_rk = PI/6.0 * mseg(k) * dhs(k)*dhs(k) + z3_rk = PI/6.0 * mseg(k) * dhs(k)**3 + +! --- derivative d(m_mean)/d(x) ---------------------------------------- + m_rk(k) = ( mseg(k) - m_mean ) / rho + ! lij(1,2)= -0.050 + ! lij(2,1)=lij(1,2) + ! r_m2dx(k)=0.0 + ! m_mean2=0.0 + ! DO i =1,ncomp + ! r_m2dx(k)=r_m2dx(k)+2.0*x(i)*(mseg(i)+mseg(k))/2.0*(1.0-lij(i,k)) + ! DO j =1,ncomp + ! m_mean2=m_mean2+x(i)*x(j)*(mseg(i)+mseg(j))/2.0*(1.0-lij(i,j)) + ! ENDDO + ! ENDDO + + ! -------------------------------------------------------------------- + ! d(f)/d(x) : hard sphere contribution + ! -------------------------------------------------------------------- + mhs(k) = 6.0/PI* ( 3.0*(z1_rk*z2+z1*z2_rk)/zms + 3.0*z1*z2*z3_rk/zms/zms & + + 3.0*z2*z2*z2_rk/z3/zms/zms + z2**3 *z3_rk*(3.0*z3-1.0)/z3/z3/zms**3 & + + ((3.0*z2*z2*z2_rk*z3-2.0*z2**3 *z3_rk)/z3**3 -z0_rk) *LOG(zms) & + + (z0-z2**3 /z3/z3)*z3_rk/zms ) + + ! -------------------------------------------------------------------- + ! d(f)/d(x) : chain term + ! -------------------------------------------------------------------- + DO i = 1, ncomp + DO j = 1, ncomp + gij(i,j) = 1.0/zms + 3.0*dij_ab(i,j)*z2/zms/zms + 2.0*(dij_ab(i,j)*z2)**2 /zms**3 + gij_rk(i,j) = z3_rk/zms/zms & + + 3.0*dij_ab(i,j)*(z2_rk+2.0*z2*z3_rk/zms)/zms/zms & + + dij_ab(i,j)**2 *z2/zms**3 *(4.0*z2_rk+6.0*z2*z3_rk/zms) + END DO + END DO + + mhc(k) = 0.0 + DO i = 1, ncomp + mhc(k) = mhc(k) + x(i)*rho * (1.0-mseg(i)) / gij(i,i) * gij_rk(i,i) + END DO + mhc(k) = mhc(k) + ( 1.0-mseg(k)) * LOG( gij(k,k) ) + + + ! -------------------------------------------------------------------- + ! PC-SAFT: d(f)/d(x) : dispersion contribution + ! -------------------------------------------------------------------- + IF (eos == 1) THEN + + ! --- derivatives of apar, bpar to rho_k --------------------------- + DO m = 0, 6 + ap_rk(k,m) = m_rk(k)/m_mean**2 * ( ap(m,2) + (3.0 -4.0/m_mean) *ap(m,3) ) + bp_rk(k,m) = m_rk(k)/m_mean**2 * ( bp(m,2) + (3.0 -4.0/m_mean) *bp(m,3) ) + END DO + + I1 = 0.0 + I2 = 0.0 + I1_rk = 0.0 + I2_rk = 0.0 + DO m = 0, 6 + I1 = I1 + apar(m)*eta**REAL(m) + I2 = I2 + bpar(m)*eta**REAL(m) + I1_rk = I1_rk + apar(m)*REAL(m)*eta**REAL(m-1)*z3_rk + ap_rk(k,m)*eta**REAL(m) + I2_rk = I2_rk + bpar(m)*REAL(m)*eta**REAL(m-1)*z3_rk + bp_rk(k,m)*eta**REAL(m) + END DO + + ord1_rk = 0.0 + ord2_rk = 0.0 + DO i = 1,ncomp + ord1_rk = ord1_rk + 2.0*mseg(k)*rho*x(i)*mseg(i)*sig_ij(i,k)**3 *uij(i,k)/t + ord2_rk = ord2_rk + 2.0*mseg(k)*rho*x(i)*mseg(i)*sig_ij(i,k)**3 *(uij(i,k)/t)**2 + END DO + + c1_con= 1.0/ ( 1.0 + m_mean*(8.0*z3-2.0*z3*z3)/zms**4 & + + (1.0 - m_mean)*(20.0*z3-27.0*z3*z3 +12.0*z3**3 -2.0*z3**4 ) & + /(zms*(2.0-z3))**2 ) + c2_con= - c1_con*c1_con *( m_mean*(-4.0*z3*z3+20.0*z3+8.0)/zms**5 & + + (1.0 - m_mean) *(2.0*z3**3 +12.0*z3*z3-48.0*z3+40.0) & + /(zms*(2.0-z3))**3 ) + c1_rk= c2_con*z3_rk - c1_con*c1_con*m_rk(k) * ( (8.0*z3-2.0*z3*z3)/zms**4 & + - (-2.0*z3**4 +12.0*z3**3 -27.0*z3*z3+20.0*z3) / (zms*(2.0-z3))**2 ) + + mdsp(k) = -2.0*PI* ( order1*rho*rho*I1_rk + ord1_rk*I1 ) & + - PI* c1_con*m_mean * ( order2*rho*rho*I2_rk + ord2_rk*I2 ) & + - PI* ( c1_con*m_rk(k) + c1_rk*m_mean ) * order2*rho*rho*I2 + + ! -------------------------------------------------------------------- + ! SAFT: d(f)/d(x) : dispersion contribution + ! -------------------------------------------------------------------- + ELSE + + zmr = 0.0 + nmr = 0.0 + zmr_rk = 0.0 + nmr_rk = 0.0 + DO i = 1, ncomp + DO j = 1, ncomp + zmr = zmr + x(i)*x(j)*mseg(i)*mseg(j)*vij(i,j)*uij(i,j) + nmr = nmr + x(i)*x(j)*mseg(i)*mseg(j)*vij(i,j) + END DO + zmr_rk = zmr_rk + 2.0*mseg(k) * x(i)*mseg(i)*vij(k,i)*uij(k,i) + nmr_rk = nmr_rk + 2.0*mseg(k) * x(i)*mseg(i)*vij(k,i) + END DO + + um_rk = 1.0/nmr**2 * ( nmr*zmr_rk - zmr*nmr_rk ) + + mdsp(k) = 0.0 + DO i = 1,4 + DO j = 1,9 + mdsp(k) = mdsp(k) + dnm(i,j)*(um/t)**REAL(i)*(eta/tau)**REAL(j) & + * ( 1.0 + z3_rk*rho/eta*REAL(j) + um_rk*rho/um*REAL(i) ) + END DO + END DO + + END IF + ! --- end of dispersion contribution------------------------------------ + + + ! -------------------------------------------------------------------- + ! TPT-1-association according to Chapman et al. + ! -------------------------------------------------------------------- + m_hbon(k) = 0.0 + assoc = .false. + DO i = 1,ncomp + IF (nhb_typ(i) /= 0) assoc = .true. + END DO + IF (assoc) THEN + + ass_s2 = 0.0 + DO l = 1, nhb_typ(k) + ass_s2 = ass_s2 + nhb_no(k,l) * LOG(mx(k,l)) + END DO + + m_hbon(k)=ass_s2 + DO i = 1, ncomp + DO ki = 1, nhb_typ(i) + DO j = 1, ncomp + DO l = 1, nhb_typ(j) + m_hbon(k)= m_hbon(k) - rho*rho/2.0*x(i)*x(j) *mx(i,ki)*mx(j,l) *nhb_no(i,ki)*nhb_no(j,l) & + * gij_rk(i,j) * ass_d(i,j,ki,l) + END DO + END DO + END DO + END DO + + END IF + ! --- end of TPT-1-association accord. to Chapman -------------------- + + + ! -------------------------------------------------------------------- + ! polar terms + ! -------------------------------------------------------------------- + CALL PHI_POLAR ( k, z3_rk, fdd_rk, fqq_rk, fdq_rk ) + my_dd(k) = fdd_rk + my_qq(k) = fqq_rk + my_dq(k) = fdq_rk + + + ! -------------------------------------------------------------------- + ! d(f)/d(x) : summation of all contributions + ! -------------------------------------------------------------------- + myres(k) = mhs(k) +mhc(k) +mdsp(k) +m_hbon(k) +my_dd(k) +my_qq(k) +my_dq(k) + +END DO + + +! ---------------------------------------------------------------------- +! finally calculate +! mu_i^res(T,p,x)/kT = ln( phi_i ) when ensemble_flag = 'tp' +! mu_i^res(T,rho,x)/kT when ensemble_flag = 'tv' +! ---------------------------------------------------------------------- + +DO k = 1, ncomp + ! write (*,*) k,myres(k) +LOG(rho*x(k)),rho + IF (ensemble_flag == 'tp' ) lnphi(k) = myres(k) - LOG(zges) + IF (ensemble_flag == 'tv' ) lnphi(k) = myres(k) + ! write (*,*) 'in',k,EXP(lnphi(k)),LOG(zges),eta +END DO +!write (*,'(5G18.10)') lnphi(1),rho + +dpdz = pgesdz +dpdz2 = pgesd2 + +END SUBROUTINE PHI_EOS + + +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! + SUBROUTINE PHI_NUMERICAL +! + USE EOS_VARIABLES + USE EOS_CONSTANTS + USE DFT_MODULE, ONLY: z_ges, fres_temp + IMPLICIT NONE +! +!-----local variables------------------------------------------------- + INTEGER :: k + REAL :: zres, zges + REAL :: fres1, fres2, fres3, fres4, fres5 + REAL :: delta_rho + REAL, DIMENSION(nc) :: myres + REAL, DIMENSION(nc) :: rhoi, rhoi_0 + REAL :: tfr_1, tfr_2, tfr_3, tfr_4, tfr_5 +!----------------------------------------------------------------------- + + +!----------------------------------------------------------------------- +! density iteration or pressure calculation +!----------------------------------------------------------------------- + +IF (ensemble_flag == 'tp') THEN + CALL DENSITY_ITERATION +ELSEIF (ensemble_flag == 'tv') THEN + eta = eta_start + CALL P_NUMERICAL +ELSE + write (*,*) 'PHI_EOS: define ensemble, ensemble_flag == (tv) or (tp)' + stop +END IF + +!----------------------------------------------------------------------- +! compressibility factor z = p/(kT*rho) +!----------------------------------------------------------------------- + +zges = (p * 1.E-30) / (kbol*t*eta/z3t) +IF ( ensemble_flag == 'tv' ) zges = (pges * 1.E-30) / (kbol*t*eta/z3t) +zres = zges - 1.0 +z_ges = zges + +rhoi_0(1:ncomp) = x(1:ncomp) * eta/z3t +rhoi(1:ncomp) = rhoi_0(1:ncomp) + + +!----------------------------------------------------------------------- +! derivative to rho_k (keeping other rho_i's constant +!----------------------------------------------------------------------- + +DO k = 1, ncomp + + IF ( rhoi_0(k) > 1.d-9 ) THEN + delta_rho = 1.E-13 * 10.0**(0.5*(15.0+LOG10(rhoi_0(k)))) + ELSE + delta_rho = 1.E-10 + END IF + + rhoi(k) = rhoi_0(k) + delta_rho + eta = PI/6.0 * SUM( rhoi(1:ncomp)*mseg(1:ncomp)*dhs(1:ncomp)**3 ) + x(1:ncomp) = rhoi(1:ncomp) / SUM( rhoi(1:ncomp) ) + rho = SUM( rhoi(1:ncomp) ) + CALL F_NUMERICAL + fres1 = fres*rho + tfr_1 = tfr*rho + + rhoi(k) = rhoi_0(k) + 0.5 * delta_rho + eta = PI/6.0 * SUM( rhoi(1:ncomp)*mseg(1:ncomp)*dhs(1:ncomp)**3 ) + x(1:ncomp) = rhoi(1:ncomp) / SUM( rhoi(1:ncomp) ) + rho = SUM( rhoi(1:ncomp) ) + CALL F_NUMERICAL + fres2 = fres*rho + tfr_2 = tfr*rho + + IF ( rhoi_0(k) > 1.E-9 ) THEN + rhoi(k) = rhoi_0(k) - 0.5 * delta_rho + eta = PI/6.0 * SUM( rhoi(1:ncomp)*mseg(1:ncomp)*dhs(1:ncomp)**3 ) + x(1:ncomp) = rhoi(1:ncomp) / SUM( rhoi(1:ncomp) ) + rho = SUM( rhoi(1:ncomp) ) + CALL F_NUMERICAL + fres4 = fres*rho + tfr_4 = tfr*rho + + rhoi(k) = rhoi_0(k) - delta_rho + eta = PI/6.0 * SUM( rhoi(1:ncomp)*mseg(1:ncomp)*dhs(1:ncomp)**3 ) + x(1:ncomp) = rhoi(1:ncomp) / SUM( rhoi(1:ncomp) ) + rho = SUM( rhoi(1:ncomp) ) + CALL F_NUMERICAL + fres5 = fres*rho + tfr_5 = tfr*rho + END IF + + rhoi(k) = rhoi_0(k) + eta = PI/6.0 * SUM( rhoi(1:ncomp)*mseg(1:ncomp)*dhs(1:ncomp)**3 ) + x(1:ncomp) = rhoi(1:ncomp) / SUM( rhoi(1:ncomp) ) + rho = SUM( rhoi(1:ncomp) ) + CALL F_NUMERICAL + fres3 = fres*rho + tfr_3 = tfr*rho + + IF ( rhoi_0(k) > 1.E-9 ) THEN + myres(k) = ( fres5 - 8.0*fres4 + 8.0*fres2 - fres1 ) / ( 6.0*delta_rho ) + ELSE + myres(k) = ( -3.0*fres3 + 4.0*fres2 - fres1 ) / delta_rho + END IF + +END DO + + +!----------------------------------------------------------------------- +! residual Helmholtz energy +!----------------------------------------------------------------------- + +fres_temp = fres + +!----------------------------------------------------------------------- +! residual chemical potential +!----------------------------------------------------------------------- + +DO k = 1, ncomp + IF (ensemble_flag == 'tp') lnphi(k) = myres(k) - LOG(zges) + IF (ensemble_flag == 'tv' .AND. eta >= 0.0) lnphi(k) = myres(k) !+LOG(rho) + ! write (*,*) 'in',k,EXP(lnphi(k)),LOG(zges),eta + ! IF (DFT.GE.98) write (*,*) dft + ! write (*,*) 'lnphi',k,LNPHI(k),x(k),MYRES(k), -LOG(ZGES) + ! pause + ! write (*,*) k, myres(k), fres, ZRES +END DO + +END SUBROUTINE PHI_NUMERICAL + + +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW + +! SUBROUTINE H_EOS (phas,h_res,s_res,cp_res,X,T,P,PARAME, +! 1 KIJ,lij,NCOMP,ETA_START,ETA,eos,tfr) +! IMPLICIT NONE +! INTEGER nc +! PARAMETER (nc=20) +! INTEGER phas,ncomp,eos,i +! REAL kij(nc,nc),lij(nc,nc),x(nc),t,p,parame(nc,25) +! REAL eta_start,eta,tfr,h_res,cp_res,s_res + + +! i=1 + +! IF (i.EQ.1) THEN +! CALL H_EOS_1(phas,h_res,s_res,cp_res,X,T,P,PARAME, +! 1 KIJ,lij,NCOMP,ETA_START,ETA,eos,tfr) +! ELSE +! CALL H_EOS_NUM (phas,h_res,s_res,cp_res,X,T,P,PARAME, +! 1 KIJ,lij,NCOMP,ETA_START,ETA,eos,tfr) +! ENDIF + +! RETURN +! END + + +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! + SUBROUTINE H_EOS +! + USE PARAMETERS, ONLY: RGAS + USE EOS_CONSTANTS + USE EOS_VARIABLES + IMPLICIT NONE +! +! ---------------------------------------------------------------------- + REAL :: zges, df_dt, dfdr, ddfdrdr + REAL :: cv_res, df_dt2, df_drdt + REAL :: fact, dist, t_tmp, rho_0 + REAL :: fdr1, fdr2, fdr3, fdr4 + + INTEGER :: i, m + REAL :: dhsdt(nc), dhsdt2(nc) + REAL :: z0, z1, z2, z3, z1tdt, z2tdt, z3tdt + REAL :: z1dt, z2dt, z3dt, zms, gii + REAL :: fhsdt, fhsdt2 + REAL :: fchdt, fchdt2 + REAL :: fdspdt, fdspdt2 + REAL :: fhbdt, fhbdt2 + REAL :: sumseg, I1, I2, I1dt, I2dt, I1dt2, I2dt2 + REAL :: c1_con, c2_con, c3_con, c1_dt, c1_dt2 + REAL :: z1tdt2, z2tdt2, z3tdt2 + REAL :: z1dt2, z2dt2, z3dt2 + + INTEGER :: j, k, l, no, ass_cnt, max_eval + LOGICAL :: assoc + REAL :: dij, dijdt, dijdt2 + REAL :: gij1dt, gij2dt, gij3dt + REAL :: gij1dt2, gij2dt2, gij3dt2 + REAL, DIMENSION(nc,nc) :: gijdt, gijdt2, kap_hb + REAL, DIMENSION(nc,nc,nsite,nsite) :: ass_d_dt, ass_d_dt2, eps_hb, delta, deltadt, deltadt2 + REAL, DIMENSION(nc,nsite) :: mxdt, mxdt2, mx_itr, mx_itrdt, mx_itrdt2 + REAL :: attenu, tol, suma, sumdt, sumdt2, err_sum + + INTEGER :: dipole + REAL :: fdddt, fdddt2 + REAL, DIMENSION(nc) :: my2dd, my0 + REAL, DIMENSION(nc,nc) :: idd2, idd2dt, idd2dt2, idd4, idd4dt, idd4dt2 + REAL, DIMENSION(nc,nc,nc) :: idd3, idd3dt, idd3dt2 + REAL :: factor2, factor3 + REAL :: fdd2, fdd3, fdd2dt, fdd3dt, fdd2dt2, fdd3dt2 + REAL :: eij, xijmt, xijkmt + + INTEGER :: qudpole + REAL :: fqqdt, fqqdt2 + REAL, DIMENSION(nc) :: qq2 + REAL, DIMENSION(nc,nc) :: iqq2, iqq2dt, iqq2dt2, iqq4, iqq4dt, iqq4dt2 + REAL, DIMENSION(nc,nc,nc) :: iqq3, iqq3dt, iqq3dt2 + REAL :: fqq2, fqq2dt, fqq2dt2, fqq3, fqq3dt, fqq3dt2 + + INTEGER :: dip_quad + REAL :: fdqdt, fdqdt2 + REAL, DIMENSION(nc) :: myfac, q_fac + REAL, DIMENSION(nc,nc) :: idq2, idq2dt, idq2dt2, idq4, idq4dt, idq4dt2 + REAL, DIMENSION(nc,nc,nc) :: idq3, idq3dt, idq3dt2 + REAL :: fdq2, fdq2dt, fdq2dt2, fdq3, fdq3dt, fdq3dt2 +! ---------------------------------------------------------------------- + + +! ---------------------------------------------------------------------- +! Initializing +! ---------------------------------------------------------------------- +CALL PERTURBATION_PARAMETER + +rho = eta/z3t +z0 = z0t*rho +z1 = z1t*rho +z2 = z2t*rho +z3 = z3t*rho + +sumseg = z0t / (PI/6.0) +zms = 1.0 - z3 + + +! ---------------------------------------------------------------------- +! first and second derivative of f to density (dfdr,ddfdrdr) +! ---------------------------------------------------------------------- +CALL P_EOS + +zges = (pges * 1.E-30)/(kbol*t*rho) + +dfdr = pges/(eta*rho*(kbol*t)/1.E-30) +ddfdrdr = pgesdz/(eta*rho*(kbol*t)/1.E-30) - dfdr*2.0/eta - 1.0/eta**2 + + +! ---------------------------------------------------------------------- +! Helmholtz Energy f/kT = fres +! ---------------------------------------------------------------------- +CALL F_EOS + + +! ---------------------------------------------------------------------- +! derivative of some auxilliary properties to temperature +! ---------------------------------------------------------------------- +DO i = 1,ncomp + dhsdt(i)=parame(i,2) *(-3.0*parame(i,3)/t/t)*0.12*EXP(-3.0*parame(i,3)/t) + dhsdt2(i) = dhsdt(i)*3.0*parame(i,3)/t/t & + + 6.0*parame(i,2)*parame(i,3)/t**3 *0.12*EXP(-3.0*parame(i,3)/t) +END DO + +z1tdt = 0.0 +z2tdt = 0.0 +z3tdt = 0.0 +DO i = 1,ncomp + z1tdt = z1tdt + x(i) * mseg(i) * dhsdt(i) + z2tdt = z2tdt + x(i) * mseg(i) * 2.0*dhs(i)*dhsdt(i) + z3tdt = z3tdt + x(i) * mseg(i) * 3.0*dhs(i)*dhs(i)*dhsdt(i) +END DO +z1dt = PI / 6.0*z1tdt *rho +z2dt = PI / 6.0*z2tdt *rho +z3dt = PI / 6.0*z3tdt *rho + + +z1tdt2 = 0.0 +z2tdt2 = 0.0 +z3tdt2 = 0.0 +DO i = 1,ncomp + z1tdt2 = z1tdt2 + x(i)*mseg(i)*dhsdt2(i) + z2tdt2 = z2tdt2 + x(i)*mseg(i)*2.0 *( dhsdt(i)*dhsdt(i) +dhs(i)*dhsdt2(i) ) + z3tdt2 = z3tdt2 + x(i)*mseg(i)*3.0 *( 2.0*dhs(i)*dhsdt(i)* & + dhsdt(i) +dhs(i)*dhs(i)*dhsdt2(i) ) +END DO +z1dt2 = PI / 6.0*z1tdt2 *rho +z2dt2 = PI / 6.0*z2tdt2 *rho +z3dt2 = PI / 6.0*z3tdt2 *rho + + +! ---------------------------------------------------------------------- +! 1st & 2nd derivative of f/kT hard spheres to temp. (fhsdt) +! ---------------------------------------------------------------------- +fhsdt = 6.0/PI/rho*( 3.0*(z1dt*z2+z1*z2dt)/zms + 3.0*z1*z2*z3dt/zms/zms & + + 3.0*z2*z2*z2dt/z3/zms/zms & + + z2**3 *(2.0*z3*z3dt-z3dt*zms)/(z3*z3*zms**3 ) & + + (3.0*z2*z2*z2dt*z3-2.0*z2**3 *z3dt)/z3**3 *LOG(zms) & + + (z0-z2**3 /z3/z3)*z3dt/zms ) + +fhsdt2= 6.0/PI/rho*( 3.0*(z1dt2*z2+2.0*z1dt*z2dt+z1*z2dt2)/zms & + + 6.0*(z1dt*z2+z1*z2dt)*z3dt/zms/zms & + + 3.0*z1*z2*z3dt2/zms/zms + 6.0*z1*z2*z3dt*z3dt/zms**3 & + + 3.0*z2*(2.0*z2dt*z2dt+z2*z2dt2)/z3/zms/zms & + - z2*z2*(6.0*z2dt*z3dt+z2*z3dt2)/(z3*z3*zms*zms) & + + 2.0*z2**3 *z3dt*z3dt/(z3**3 *zms*zms) & + - 4.0*z2**3 *z3dt*z3dt/(z3*z3 *zms**3 ) & + + (12.0*z2*z2*z2dt*z3dt+2.0*z2**3 *z3dt2)/(z3*zms**3 ) & + + 6.0*z2**3 *z3dt*z3dt/(z3*zms**4 ) & + - 2.0*(3.0*z2*z2*z2dt/z3/z3-2.0*z2**3 *z3dt/z3**3 ) *z3dt/zms & + -(z2**3 /z3/z3-z0)*(z3dt2/zms+z3dt*z3dt/zms/zms) & + + ( (6.0*z2*z2dt*z2dt+3.0*z2*z2*z2dt2)/z3/z3 & + - (12.0*z2*z2*z2dt*z3dt+2.0*z2**3 *z3dt2)/z3**3 & + + 6.0*z2**3 *z3dt*z3dt/z3**4 )* LOG(zms) ) + + +! ---------------------------------------------------------------------- +! 1st & 2nd derivative of f/kT of chain term to T (fchdt) +! ---------------------------------------------------------------------- +fchdt = 0.0 +fchdt2 = 0.0 +DO i = 1, ncomp + DO j = 1, ncomp + dij=dhs(i)*dhs(j)/(dhs(i)+dhs(j)) + dijdt =(dhsdt(i)*dhs(j) + dhs(i)*dhsdt(j)) / (dhs(i)+dhs(j)) & + - dhs(i)*dhs(j)/(dhs(i)+dhs(j))**2 *(dhsdt(i)+dhsdt(j)) + dijdt2=(dhsdt2(i)*dhs(j) + 2.0*dhsdt(i)*dhsdt(j) & + + dhs(i)*dhsdt2(j)) / (dhs(i)+dhs(j)) & + - 2.0*(dhsdt(i)*dhs(j) + dhs(i)*dhsdt(j)) & + / (dhs(i)+dhs(j))**2 *(dhsdt(i)+dhsdt(j)) & + + 2.0* dhs(i)*dhs(j) / (dhs(i)+dhs(j))**3 & + * (dhsdt(i)+dhsdt(j))**2 & + - dhs(i)*dhs(j)/(dhs(i)+dhs(j))**2 *(dhsdt2(i)+dhsdt2(j)) + gij1dt = z3dt/zms/zms + gij2dt = 3.0*( z2dt*dij+z2*dijdt )/zms/zms +6.0*z2*dij*z3dt/zms**3 + gij3dt = 4.0*(dij*z2)* (dijdt*z2 + dij*z2dt) /zms**3 & + + 6.0*(dij*z2)**2 * z3dt /zms**4 + gij1dt2 = z3dt2/zms/zms +2.0*z3dt*z3dt/zms**3 + gij2dt2 = 3.0*( z2dt2*dij+2.0*z2dt*dijdt+z2*dijdt2 )/zms/zms & + + 6.0*( z2dt*dij+z2*dijdt )/zms**3 * z3dt & + + 6.0*(z2dt*dij*z3dt+z2*dijdt*z3dt+z2*dij*z3dt2) /zms**3 & + + 18.0*z2*dij*z3dt*z3dt/zms**4 + gij3dt2 = 4.0*(dijdt*z2+dij*z2dt)**2 /zms**3 & + + 4.0*(dij*z2)* (dijdt2*z2+2.0*dijdt*z2dt+dij*z2dt2) /zms**3 & + + 24.0*(dij*z2) *(dijdt*z2+dij*z2dt)/zms**4 *z3dt & + + 6.0*(dij*z2)**2 * z3dt2 /zms**4 & + + 24.0*(dij*z2)**2 * z3dt*z3dt /zms**5 + gijdt(i,j) = gij1dt + gij2dt + gij3dt + gijdt2(i,j) = gij1dt2 + gij2dt2 + gij3dt2 + END DO +END DO + +DO i = 1, ncomp + gii = 1.0/zms + 3.0*dhs(i)/2.0*z2/zms/zms + 2.0*dhs(i)*dhs(i)/4.0*z2*z2/zms**3 + fchdt = fchdt + x(i) * (1.0-mseg(i)) * gijdt(i,i) / gii + fchdt2= fchdt2+ x(i) * (1.0-mseg(i)) & + * (gijdt2(i,i) / gii - (gijdt(i,i)/gii)**2 ) +END DO + + +! ---------------------------------------------------------------------- +! 1st & 2nd derivative of f/kT dispersion term to T (fdspdt) +! ---------------------------------------------------------------------- +I1 = 0.0 +I2 = 0.0 +I1dt = 0.0 +I2dt = 0.0 +I1dt2= 0.0 +I2dt2= 0.0 +DO m = 0, 6 + I1 = I1 + apar(m)*z3**REAL(m) + I2 = I2 + bpar(m)*z3**REAL(m) + I1dt = I1dt + apar(m)*z3dt*REAL(m)*z3**REAL(m-1) + I2dt = I2dt + bpar(m)*z3dt*REAL(m)*z3**REAL(m-1) + I1dt2= I1dt2+ apar(m)*z3dt2*REAL(m)*z3**REAL(m-1) & + + apar(m)*z3dt*z3dt *REAL(m)*REAL(m-1)*z3**REAL(m-2) + I2dt2= I2dt2+ bpar(m)*z3dt2*REAL(m)*z3**REAL(m-1) & + + bpar(m)*z3dt*z3dt *REAL(m)*REAL(m-1)*z3**REAL(m-2) +END DO + +c1_con= 1.0/ ( 1.0 + sumseg*(8.0*z3-2.0*z3**2 )/zms**4 & + + (1.0 - sumseg)*(20.0*z3-27.0*z3**2 +12.0*z3**3 -2.0*z3**4 ) & + /(zms*(2.0-z3))**2 ) +c2_con= - c1_con*c1_con *(sumseg*(-4.0*z3**2 +20.0*z3+8.0)/zms**5 & + + (1.0 - sumseg) *(2.0*z3**3 +12.0*z3**2 -48.0*z3+40.0) & + /(zms*(2.0-z3))**3 ) +c3_con= 2.0 * c2_con*c2_con/c1_con - c1_con*c1_con & + *( sumseg*(-12.0*z3**2 +72.0*z3+60.0)/zms**6 + (1.0 - sumseg) & + *(-6.0*z3**4 -48.0*z3**3 +288.0*z3**2 -480.0*z3+264.0) & + /(zms*(2.0-z3))**4 ) +c1_dt = c2_con*z3dt +c1_dt2 = c3_con*z3dt*z3dt + c2_con*z3dt2 + +fdspdt = - 2.0*PI*rho*(I1dt-I1/t)*order1 & + - PI*rho*sumseg*(c1_dt*I2+c1_con*I2dt-2.0*c1_con*I2/t)*order2 + +fdspdt2 = - 2.0*PI*rho*(I1dt2-2.0*I1dt/t+2.0*I1/t/t)*order1 & + - PI*rho*sumseg*order2*( c1_dt2*I2 +2.0*c1_dt*I2dt -4.0*c1_dt*I2/t & + + 6.0*c1_con*I2/t/t -4.0*c1_con*I2dt/t +c1_con*I2dt2) + + +! ---------------------------------------------------------------------- +! 1st & 2nd derivative of f/kT association term to T (fhbdt) +! ---------------------------------------------------------------------- +fhbdt = 0.0 +fhbdt2 = 0.0 +assoc = .false. +DO i = 1,ncomp + IF ( nhb_typ(i) /= 0 ) assoc = .true. +END DO +IF (assoc) THEN + + DO i = 1,ncomp + IF ( nhb_typ(i) /= 0 ) THEN + kap_hb(i,i) = parame(i,13) + no = 0 + DO j = 1,nhb_typ(i) + DO k = 1,nhb_typ(i) + eps_hb(i,i,j,k) = parame(i,(14+no)) + no = no + 1 + END DO + END DO + DO j = 1,nhb_typ(i) + no = no + 1 + END DO + ELSE + kap_hb(i,i) = 0.0 + DO k = 1,nsite + DO l = 1,nsite + eps_hb(i,i,k,l) = 0.0 + END DO + END DO + END IF + END DO + + DO i = 1,ncomp + DO j = 1,ncomp + IF ( i /= j .AND. (nhb_typ(i) /= 0 .AND. nhb_typ(j) /= 0) ) THEN + kap_hb(i,j)= (kap_hb(i,i)*kap_hb(j,j))**0.5 & + *((parame(i,2)*parame(j,2))**3 )**0.5 & + /(0.5*(parame(i,2)+parame(j,2)))**3 + ! kap_hb(i,j)= kap_hb(i,j)*(1.0-k_kij) + DO k = 1,nhb_typ(i) + DO l = 1,nhb_typ(j) + IF (k /= l) THEN + eps_hb(i,j,k,l)=(eps_hb(i,i,k,l)+eps_hb(j,j,l,k))/2.0 + ! eps_hb(i,j,k,l)=eps_hb(i,j,k,l)*(1.0-eps_kij) + END IF + END DO + END DO + END IF + END DO + END DO + IF (nhb_typ(1) == 3) THEN + eps_hb(1,2,3,1)=0.5*(eps_hb(1,1,3,1)+eps_hb(2,2,1,2)) + eps_hb(2,1,1,3) = eps_hb(1,2,3,1) + END IF + IF (nhb_typ(2) == 3) THEN + eps_hb(2,1,3,1)=0.5*(eps_hb(2,2,3,1)+eps_hb(1,1,1,2)) + eps_hb(1,2,1,3) = eps_hb(2,1,3,1) + END IF + + DO i = 1, ncomp + DO k = 1, nhb_typ(i) + DO j = 1, ncomp + DO l = 1, nhb_typ(j) + ! ass_d(i,j,k,l)=kap_hb(i,j) *sig_ij(i,j)**3 *(EXP(eps_hb(i,j,k,l)/t)-1.0) + ass_d_dt(i,j,k,l)= - kap_hb(i,j) *sig_ij(i,j)**3 * eps_hb(i,j,k,l)/t/t*EXP(eps_hb(i,j,k,l)/t) + ass_d_dt2(i,j,k,l)= - kap_hb(i,j) *sig_ij(i,j)**3 & + * eps_hb(i,j,k,l)/t/t*EXP(eps_hb(i,j,k,l)/t) & + * (-2.0/t - eps_hb(i,j,k,l)/t/t) + END DO + END DO + END DO + END DO + + DO i = 1, ncomp + DO k = 1, nhb_typ(i) + DO j = 1, ncomp + DO l = 1, nhb_typ(j) + delta(i,j,k,l)=gij(i,j)*ass_d(i,j,k,l) + deltadt(i,j,k,l) = gijdt(i,j)*ass_d(i,j,k,l) + gij(i,j)*ass_d_dt(i,j,k,l) + deltadt2(i,j,k,l)= gijdt2(i,j)*ass_d(i,j,k,l) & + + 2.0*gijdt(i,j)*ass_d_dt(i,j,k,l) +gij(i,j)*ass_d_dt2(i,j,k,l) + END DO + END DO + END DO + END DO + + +! ------ constants for iteration --------------------------------------- + attenu = 0.7 + tol = 1.E-10 + IF (eta < 0.2) tol = 1.E-11 + IF (eta < 0.01) tol = 1.E-12 + max_eval = 200 + +! ------ initialize mxdt(i,j) ------------------------------------------ + DO i = 1, ncomp + DO k = 1, nhb_typ(i) + mxdt(i,k) = 0.0 + mxdt2(i,k) = 0.0 + END DO + END DO + + +! ------ iterate over all components and all sites --------------------- + DO ass_cnt = 1, max_eval + + DO i = 1, ncomp + DO k = 1, nhb_typ(i) + suma = 0.0 + sumdt = 0.0 + sumdt2= 0.0 + DO j = 1, ncomp + DO l = 1, nhb_typ(j) + suma = suma + x(j)*nhb_no(j,l)* mx(j,l) *delta(i,j,k,l) + sumdt = sumdt + x(j)*nhb_no(j,l)*( mx(j,l) *deltadt(i,j,k,l) & + + mxdt(j,l)*delta(i,j,k,l) ) + sumdt2 = sumdt2 + x(j)*nhb_no(j,l)*( mx(j,l)*deltadt2(i,j,k,l) & + + 2.0*mxdt(j,l)*deltadt(i,j,k,l) + mxdt2(j,l)*delta(i,j,k,l) ) + END DO + END DO + mx_itr(i,k) = 1.0 / (1.0 + suma * rho) + mx_itrdt(i,k)= - mx_itr(i,k)**2 * sumdt*rho + mx_itrdt2(i,k)= +2.0*mx_itr(i,k)**3 * (sumdt*rho)**2 - mx_itr(i,k)**2 *sumdt2*rho + END DO + END DO + + err_sum = 0.0 + DO i = 1, ncomp + DO k = 1, nhb_typ(i) + err_sum = err_sum + ABS(mx_itr(i,k) - mx(i,k)) & + + ABS(mx_itrdt(i,k) - mxdt(i,k)) + ABS(mx_itrdt2(i,k) - mxdt2(i,k)) + mx(i,k) = mx_itr(i,k) * attenu + mx(i,k) * (1.0 - attenu) + mxdt(i,k)=mx_itrdt(i,k)*attenu +mxdt(i,k)* (1.0 - attenu) + mxdt2(i,k)=mx_itrdt2(i,k)*attenu +mxdt2(i,k)* (1.0 - attenu) + END DO + END DO + IF(err_sum <= tol) GO TO 10 + + END DO + WRITE(6,*) 'CAL_PCSAFT: max_eval violated err_sum = ',err_sum,tol + STOP + 10 CONTINUE + + DO i = 1, ncomp + DO k = 1, nhb_typ(i) + ! fhb = fhb + x(i)* nhb_no(i,k)* ( 0.5 * ( 1.0 - mx(i,k) ) + LOG(mx(i,k)) ) + fhbdt = fhbdt + x(i)*nhb_no(i,k) *mxdt(i,k)*(1.0/mx(i,k)-0.5) + fhbdt2= fhbdt2 + x(i)*nhb_no(i,k) *(mxdt2(i,k)*(1.0/mx(i,k)-0.5) & + -(mxdt(i,k)/mx(i,k))**2 ) + END DO + END DO + +END IF + + +! ---------------------------------------------------------------------- +! derivatives of f/kT of dipole-dipole term to temp. (fdddt) +! ---------------------------------------------------------------------- +fdddt = 0.0 +fdddt2 = 0.0 +dipole = 0 +DO i = 1,ncomp + my2dd(i) = 0.0 + IF ( parame(i,6) /= 0.0 .AND. uij(i,i) /= 0.0 ) THEN + dipole = 1 + my2dd(i) = (parame(i,6))**2 *1.E-49 / (uij(i,i)*kbol*mseg(i)*sig_ij(i,i)**3 *1.E-30) + END IF + my0(i) = my2dd(i) ! needed for dipole-quadrupole-term +END DO + +IF (dipole == 1) THEN + DO i = 1,ncomp + DO j = 1,ncomp + idd2(i,j) =0.0 + idd4(i,j) =0.0 + idd2dt(i,j) =0.0 + idd4dt(i,j) =0.0 + idd2dt2(i,j)=0.0 + idd4dt2(i,j)=0.0 + DO m=0,4 + idd2(i,j) = idd2(i,j) +ddp2(i,j,m)*z3**REAL(m) + idd4(i,j) = idd4(i,j) +ddp4(i,j,m)*z3**REAL(m) + idd2dt(i,j)= idd2dt(i,j) +ddp2(i,j,m)*z3dt*REAL(m)*z3**REAL(m-1) + idd4dt(i,j)= idd4dt(i,j) +ddp4(i,j,m)*z3dt*REAL(m)*z3**REAL(m-1) + idd2dt2(i,j)=idd2dt2(i,j)+ddp2(i,j,m)*z3dt2*REAL(m)*z3**REAL(m-1) & + + ddp2(i,j,m)*z3dt**2 *REAL(m)*REAL(m-1)*z3**REAL(m-2) + idd4dt2(i,j)=idd4dt2(i,j)+ddp4(i,j,m)*z3dt2*REAL(m)*z3**REAL(m-1) & + + ddp4(i,j,m)*z3dt**2 *REAL(m)*REAL(m-1)*z3**REAL(m-2) + END DO + DO k = 1,ncomp + idd3(i,j,k) =0.0 + idd3dt(i,j,k) =0.0 + idd3dt2(i,j,k)=0.0 + DO m = 0, 4 + idd3(i,j,k) = idd3(i,j,k) +ddp3(i,j,k,m)*z3**REAL(m) + idd3dt(i,j,k) = idd3dt(i,j,k)+ddp3(i,j,k,m)*z3dt*REAL(m) *z3**REAL(m-1) + idd3dt2(i,j,k)= idd3dt2(i,j,k)+ddp3(i,j,k,m)*z3dt2*REAL(m) & + *z3**REAL(m-1) +ddp3(i,j,k,m)*z3dt**2 *REAL(m)*REAL(m-1) *z3**REAL(m-2) + END DO + END DO + END DO + END DO + + + factor2= -PI *rho + factor3= -4.0/3.0*PI**2 * rho**2 + + fdd2 = 0.0 + fdd3 = 0.0 + fdd2dt= 0.0 + fdd3dt= 0.0 + fdd2dt2= 0.0 + fdd3dt2= 0.0 + DO i = 1, ncomp + DO j = 1, ncomp + xijmt = x(i)*parame(i,3)*parame(i,2)**3 *x(j)*parame(j,3)*parame(j,2)**3 & + / ((parame(i,2)+parame(j,2))/2.0)**3 *my2dd(i)*my2dd(j) + eij = (parame(i,3)*parame(j,3))**0.5 + fdd2 = fdd2 +factor2* xijmt/t/t*(idd2(i,j)+eij/t*idd4(i,j)) + fdd2dt= fdd2dt+ factor2* xijmt/t/t*(idd2dt(i,j)-2.0*idd2(i,j)/t & + +eij/t*idd4dt(i,j)-3.0*eij/t/t*idd4(i,j)) + fdd2dt2=fdd2dt2+factor2*xijmt/t/t*(idd2dt2(i,j)-4.0*idd2dt(i,j)/t & + +6.0*idd2(i,j)/t/t+eij/t*idd4dt2(i,j) & + -6.0*eij/t/t*idd4dt(i,j)+12.0*eij/t**3 *idd4(i,j)) + DO k = 1, ncomp + xijkmt=x(i)*parame(i,3)*parame(i,2)**3 & + *x(j)*parame(j,3)*parame(j,2)**3 & + *x(k)*parame(k,3)*parame(k,2)**3 & + /((parame(i,2)+parame(j,2))/2.0) /((parame(i,2)+parame(k,2))/2.0) & + /((parame(j,2)+parame(k,2))/2.0) *my2dd(i)*my2dd(j)*my2dd(k) + fdd3 =fdd3 +factor3*xijkmt/t**3 *idd3(i,j,k) + fdd3dt =fdd3dt +factor3*xijkmt/t**3 * (idd3dt(i,j,k)-3.0*idd3(i,j,k)/t) + fdd3dt2=fdd3dt2+factor3*xijkmt/t**3 & + *( idd3dt2(i,j,k)-6.0*idd3dt(i,j,k)/t+12.0*idd3(i,j,k)/t/t ) + END DO + END DO + END DO + + IF ( fdd2 < -1.E-100 .AND. fdd3 /= 0.0 ) THEN + fdddt = fdd2* (fdd2*fdd2dt - 2.0*fdd3*fdd2dt+fdd2*fdd3dt) / (fdd2-fdd3)**2 + fdddt2 = ( 2.0*fdd2*fdd2dt*fdd2dt +fdd2*fdd2*fdd2dt2 & + -2.0*fdd2dt**2 *fdd3 -2.0*fdd2*fdd2dt2*fdd3 +fdd2*fdd2*fdd3dt2 ) & + /(fdd2-fdd3)**2 + fdddt * 2.0*(fdd3dt-fdd2dt)/(fdd2-fdd3) + END IF +END IF + + +! ---------------------------------------------------------------------- +! derivatives f/kT of quadrupole-quadrup. term to T (fqqdt) +! ---------------------------------------------------------------------- +fqqdt = 0.0 +fqqdt2 = 0.0 +qudpole = 0 +DO i = 1, ncomp + qq2(i) = (parame(i,7))**2 *1.E-69 / (uij(i,i)*kbol*mseg(i)*sig_ij(i,i)**5 *1.E-50) + IF (qq2(i) /= 0.0) qudpole = 1 +END DO + +IF (qudpole == 1) THEN + + DO i = 1,ncomp + DO j = 1,ncomp + iqq2(i,j) = 0.0 + iqq4(i,j) = 0.0 + iqq2dt(i,j) = 0.0 + iqq4dt(i,j) = 0.0 + iqq2dt2(i,j)= 0.0 + iqq4dt2(i,j)= 0.0 + DO m = 0, 4 + iqq2(i,j) = iqq2(i,j) + qqp2(i,j,m)*z3**REAL(m) + iqq4(i,j) = iqq4(i,j) + qqp4(i,j,m)*z3**REAL(m) + iqq2dt(i,j) = iqq2dt(i,j)+ qqp2(i,j,m)*z3dt*REAL(m)*z3**REAL(m-1) + iqq4dt(i,j) = iqq4dt(i,j)+ qqp4(i,j,m)*z3dt*REAL(m)*z3**REAL(m-1) + iqq2dt2(i,j)= iqq2dt2(i,j)+qqp2(i,j,m)*z3dt2*REAL(m)*z3**REAL(m-1) & + + qqp2(i,j,m)*z3dt**2 *REAL(m)*REAL(m-1)*z3**REAL(m-2) + iqq4dt2(i,j)= iqq4dt2(i,j)+qqp4(i,j,m)*z3dt2*REAL(m)*z3**REAL(m-1) & + + qqp4(i,j,m)*z3dt**2 *REAL(m)*REAL(m-1)*z3**REAL(m-2) + END DO + DO k = 1,ncomp + iqq3(i,j,k) =0.0 + iqq3dt(i,j,k) =0.0 + iqq3dt2(i,j,k)=0.0 + DO m = 0, 4 + iqq3(i,j,k) = iqq3(i,j,k) + qqp3(i,j,k,m)*z3**REAL(m) + iqq3dt(i,j,k) = iqq3dt(i,j,k)+ qqp3(i,j,k,m)*z3dt*REAL(m) * z3**REAL(m-1) + iqq3dt2(i,j,k)= iqq3dt2(i,j,k)+qqp3(i,j,k,m)*z3dt2*REAL(m) * z3**REAL(m-1) & + + qqp3(i,j,k,m)*z3dt**2 *REAL(m)*REAL(m-1)*z3**REAL(m-2) + END DO + END DO + END DO + END DO + + factor2 = -9.0/16.0 * PI *rho + factor3 = 9.0/16.0 * PI**2 * rho**2 + + fqq2 = 0.0 + fqq3 = 0.0 + fqq2dt = 0.0 + fqq3dt = 0.0 + fqq2dt2= 0.0 + fqq3dt2= 0.0 + DO i = 1,ncomp + DO j = 1,ncomp + xijmt = x(i)*uij(i,i)*qq2(i)*sig_ij(i,i)**5 & + * x(j)*uij(j,j)*qq2(j)*sig_ij(j,j)**5 /sig_ij(i,j)**7.0 + eij = (parame(i,3)*parame(j,3))**0.5 + fqq2 = fqq2 +factor2* xijmt/t/t*(iqq2(i,j)+eij/t*iqq4(i,j)) + fqq2dt= fqq2dt +factor2* xijmt/t/t*(iqq2dt(i,j)-2.0*iqq2(i,j)/t & + + eij/t*iqq4dt(i,j)-3.0*eij/t/t*iqq4(i,j)) + fqq2dt2=fqq2dt2+factor2*xijmt/t/t*(iqq2dt2(i,j)-4.0*iqq2dt(i,j)/t & + + 6.0*iqq2(i,j)/t/t+eij/t*iqq4dt2(i,j) & + - 6.0*eij/t/t*iqq4dt(i,j)+12.0*eij/t**3 *iqq4(i,j)) + DO k = 1,ncomp + xijkmt = x(i)*uij(i,i)*qq2(i)*sig_ij(i,i)**5 /sig_ij(i,j)**3 & + * x(j)*uij(j,j)*qq2(j)*sig_ij(j,j)**5 /sig_ij(i,k)**3 & + * x(k)*uij(k,k)*qq2(k)*sig_ij(k,k)**5 /sig_ij(j,k)**3 + fqq3 = fqq3 +factor3*xijkmt/t**3 *iqq3(i,j,k) + fqq3dt = fqq3dt +factor3*xijkmt/t**3 *(iqq3dt(i,j,k)-3.0*iqq3(i,j,k)/t) + fqq3dt2= fqq3dt2+factor3*xijkmt/t**3 & + * ( iqq3dt2(i,j,k)-6.0*iqq3dt(i,j,k)/t+12.0*iqq3(i,j,k)/t/t ) + END DO + END DO + END DO + + IF ( fqq2 /= 0.0 .AND. fqq3 /= 0.0 ) THEN + fqqdt = fqq2* (fqq2*fqq2dt - 2.0*fqq3*fqq2dt+fqq2*fqq3dt) / (fqq2-fqq3)**2 + fqqdt2 = ( 2.0*fqq2*fqq2dt*fqq2dt +fqq2*fqq2*fqq2dt2 & + - 2.0*fqq2dt**2 *fqq3 -2.0*fqq2*fqq2dt2*fqq3 +fqq2*fqq2*fqq3dt2 ) & + / (fqq2-fqq3)**2 + fqqdt * 2.0*(fqq3dt-fqq2dt)/(fqq2-fqq3) + END IF + +END IF + + +! ---------------------------------------------------------------------- +! derivatives f/kT of dipole-quadruppole term to T (fdqdt) +! ---------------------------------------------------------------------- +fdqdt = 0.0 +fdqdt2= 0.0 +dip_quad = 0 +DO i = 1,ncomp + DO j = 1,ncomp + IF (parame(i,6) /= 0.0 .AND. parame(j,7) /= 0.0) dip_quad = 1 + END DO + myfac(i) = parame(i,3)*parame(i,2)**4 *my0(i) + q_fac(i) = parame(i,3)*parame(i,2)**4 *qq2(i) +END DO + +IF (dip_quad == 1) THEN + + DO i = 1,ncomp + DO j = 1,ncomp + idq2(i,j) = 0.0 + idq4(i,j) = 0.0 + idq2dt(i,j) = 0.0 + idq4dt(i,j) = 0.0 + idq2dt2(i,j)= 0.0 + idq4dt2(i,j)= 0.0 + IF ( myfac(i) /= 0.0 .AND. q_fac(j) /= 0.0 ) THEN + DO m = 0, 4 + idq2(i,j) = idq2(i,j) + dqp2(i,j,m)*z3**REAL(m) + idq4(i,j) = idq4(i,j) + dqp4(i,j,m)*z3**REAL(m) + idq2dt(i,j) = idq2dt(i,j)+ dqp2(i,j,m)*z3dt*REAL(m)*z3**REAL(m-1) + idq4dt(i,j) = idq4dt(i,j)+ dqp4(i,j,m)*z3dt*REAL(m)*z3**REAL(m-1) + idq2dt2(i,j)= idq2dt2(i,j)+dqp2(i,j,m)*z3dt2*REAL(m)*z3**REAL(m-1) & + + dqp2(i,j,m)*z3dt**2 *REAL(m)*REAL(m-1)*z3**REAL(m-2) + idq4dt2(i,j)= idq4dt2(i,j)+dqp4(i,j,m)*z3dt2*REAL(m)*z3**REAL(m-1) & + + dqp4(i,j,m)*z3dt**2 *REAL(m)*REAL(m-1)*z3**REAL(m-2) + END DO + + DO k = 1,ncomp + idq3(i,j,k) = 0.0 + idq3dt(i,j,k) = 0.0 + idq3dt2(i,j,k)= 0.0 + IF ( myfac(k) /= 0.0 .OR. q_fac(k) /= 0.0 ) THEN + DO m = 0, 4 + idq3(i,j,k) = idq3(i,j,k) + dqp3(i,j,k,m)*z3**REAL(m) + idq3dt(i,j,k)= idq3dt(i,j,k)+ dqp3(i,j,k,m)*z3dt*REAL(m) *z3**REAL(m-1) + idq3dt2(i,j,k)= idq3dt2(i,j,k)+dqp3(i,j,k,m)*z3dt2*REAL(m) *z3**REAL(m-1) & + + dqp3(i,j,k,m)*z3dt**2 *REAL(m)*REAL(m-1)*z3**REAL(m-2) + END DO + END IF + END DO + END IF + END DO + END DO + + factor2= -9.0/4.0 * PI * rho + factor3= PI**2 * rho**2 + + fdq2 = 0.0 + fdq3 = 0.0 + fdq2dt= 0.0 + fdq3dt= 0.0 + fdq2dt2=0.0 + fdq3dt2=0.0 + DO i = 1,ncomp + DO j = 1,ncomp + IF ( myfac(i) /= 0.0 .AND. q_fac(j) /= 0.0 ) THEN + xijmt = x(i)*myfac(i) * x(j)*q_fac(j) /sig_ij(i,j)**5 + eij = (parame(i,3)*parame(j,3))**0.5 + fdq2 = fdq2 + factor2* xijmt/t/t*(idq2(i,j)+eij/t*idq4(i,j)) + fdq2dt= fdq2dt+ factor2* xijmt/t/t*(idq2dt(i,j)-2.0*idq2(i,j)/t & + + eij/t*idq4dt(i,j)-3.0*eij/t/t*idq4(i,j)) + fdq2dt2 = fdq2dt2+factor2*xijmt/t/t*(idq2dt2(i,j)-4.0*idq2dt(i,j)/t & + + 6.0*idq2(i,j)/t/t+eij/t*idq4dt2(i,j) & + - 6.0*eij/t/t*idq4dt(i,j)+12.0*eij/t**3 *idq4(i,j)) + DO k = 1,ncomp + IF ( myfac(k) /= 0.0 .OR. q_fac(k) /= 0.0 ) THEN + xijkmt= x(i)*x(j)*x(k)/(sig_ij(i,j)*sig_ij(i,k)*sig_ij(j,k))**2 & + * ( myfac(i)*q_fac(j)*myfac(k) & + + myfac(i)*q_fac(j)*q_fac(k)*1.193735 ) + + fdq3 =fdq3 + factor3*xijkmt/t**3 *idq3(i,j,k) + fdq3dt=fdq3dt+ factor3*xijkmt/t**3 * (idq3dt(i,j,k)-3.0*idq3(i,j,k)/t) + fdq3dt2=fdq3dt2+factor3*xijkmt/t**3 & + *( idq3dt2(i,j,k)-6.0*idq3dt(i,j,k)/t+12.0*idq3(i,j,k)/t/t ) + END IF + END DO + END IF + END DO + END DO + + IF (fdq2 /= 0.0 .AND. fdq3 /= 0.0) THEN + fdqdt = fdq2* (fdq2*fdq2dt - 2.0*fdq3*fdq2dt+fdq2*fdq3dt) / (fdq2-fdq3)**2 + fdqdt2 = ( 2.0*fdq2*fdq2dt*fdq2dt +fdq2*fdq2*fdq2dt2 & + - 2.0*fdq2dt**2 *fdq3 -2.0*fdq2*fdq2dt2*fdq3 +fdq2*fdq2*fdq3dt2 ) & + / (fdq2-fdq3)**2 + fdqdt * 2.0*(fdq3dt-fdq2dt)/(fdq2-fdq3) + END IF + +END IF +! ---------------------------------------------------------------------- + + + + +! ---------------------------------------------------------------------- +! total derivative of fres/kT to temperature +! ---------------------------------------------------------------------- + +df_dt = fhsdt + fchdt + fdspdt + fhbdt + fdddt + fqqdt + fdqdt + + + +! ---------------------------------------------------------------------- +! second derivative of fres/kT to T +! ---------------------------------------------------------------------- + +df_dt2 = fhsdt2 +fchdt2 +fdspdt2 +fhbdt2 +fdddt2 +fqqdt2 +fdqdt2 + + + +! ---------------------------------------------------------------------- +! ------ derivatives of fres/kt to density and to T -------------------- +! ---------------------------------------------------------------------- + +! ---------------------------------------------------------------------- +! the analytic derivative of fres/kT to (density and T) (df_drdt) +! is still missing. A numerical differentiation is implemented. +! ---------------------------------------------------------------------- +fact = 1.0 +dist = t * 100.E-5 * fact +t_tmp = t +rho_0 = rho + + +t = t_tmp - 2.0*dist +CALL PERTURBATION_PARAMETER +eta = z3t*rho_0 +CALL P_EOS +fdr1 = pges / (eta*rho_0*(kbol*t)/1.E-30) +t = t_tmp - dist +CALL PERTURBATION_PARAMETER +eta = z3t*rho_0 +CALL P_EOS +fdr2 = pges / (eta*rho_0*(kbol*t)/1.E-30) + +t = t_tmp + dist +CALL PERTURBATION_PARAMETER +eta = z3t*rho_0 +CALL P_EOS +fdr3 = pges / (eta*rho_0*(kbol*t)/1.E-30) + +t = t_tmp + 2.0*dist +CALL PERTURBATION_PARAMETER +eta = z3t*rho_0 +CALL P_EOS +fdr4 = pges / (eta*rho_0*(kbol*t)/1.E-30) + +t = t_tmp +CALL PERTURBATION_PARAMETER +eta = z3t*rho_0 +CALL P_EOS + + +df_drdt = (-fdr4+8.0*fdr3-8.0*fdr2+fdr1)/(12.0*dist) + + + + + +! ---------------------------------------------------------------------- +! thermodynamic properties +! ---------------------------------------------------------------------- + +s_res = ( - df_dt *t - fres )*RGAS + RGAS * LOG(zges) +h_res = ( - t*df_dt + zges-1.0 ) * RGAS *t +cv_res = - ( t*df_dt2 + 2.0*df_dt ) * RGAS*t +cp_res = cv_res - RGAS + RGAS*(zges +eta*t*df_drdt)**2 & + / (1.0 + 2.0*eta*dfdr +eta**2 *ddfdrdr) + +! write (*,*) 'df_... ', df_dt,df_dt2 +! write (*,*) 'kreuz ', zges,eta*t*df_drdt,eta*dfdr, eta**2 *ddfdrdr +! write (*,*) 'h,cv,cp', h_res,cv_res,cp_res + + +END SUBROUTINE H_EOS + + + +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! SUBROUTINE H_EOS_num +! +! This subroutine calculates enthalpies and heat capacities (cp) by +! taking numerical derivatieves. +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! + SUBROUTINE H_EOS_num +! + USE PARAMETERS, ONLY: RGAS + USE EOS_VARIABLES + IMPLICIT NONE +! +!--------------------------------------------------------------------- + REAL :: dist, fact, rho_0 + REAL :: fres1, fres2, fres3, fres4, fres5 + REAL :: f_1, f_2, f_3, f_4 + REAL :: cv_res, t_tmp, zges + REAL :: df_dt, df_dtdt, df_drdt, dfdr, ddfdrdr + +!----------------------------------------------------------------------- + + +CALL PERTURBATION_PARAMETER +rho_0 = eta/z3t + + +fact = 1.0 +dist = t * 100.E-5 * fact + +t_tmp = t + +t = t_tmp - 2.0*dist +CALL PERTURBATION_PARAMETER +eta = z3t*rho_0 +CALL F_EOS +fres1 = fres +t = t_tmp - dist +CALL PERTURBATION_PARAMETER +eta = z3t*rho_0 +CALL F_EOS +fres2 = fres +t = t_tmp + dist +CALL PERTURBATION_PARAMETER +eta = z3t*rho_0 +CALL F_EOS +fres3 = fres +t = t_tmp + 2.0*dist +CALL PERTURBATION_PARAMETER +eta = z3t*rho_0 +CALL F_EOS +fres4 = fres +t = t_tmp +CALL PERTURBATION_PARAMETER +eta = z3t*rho_0 +CALL F_EOS +fres5 = fres +! *(KBOL*T)/1.E-30 + +zges = (p * 1.E-30)/(kbol*t*rho_0) + + +df_dt = (-fres4+8.0*fres3-8.0*fres2+fres1)/(12.0*dist) +df_dtdt = (-fres4+16.0*fres3-3.d1*fres5+16.0*fres2-fres1) & + /(12.0*(dist**2 )) + + +s_res = (- df_dt -fres/t)*RGAS*t + RGAS * LOG(zges) +h_res = ( - t*df_dt + zges-1.0 ) * RGAS*t +cv_res = -( t*df_dtdt + 2.0*df_dt ) * RGAS*t + + + +t = t_tmp - 2.0*dist +CALL PERTURBATION_PARAMETER +eta = z3t*rho_0 +CALL P_EOS +f_1 = pges/(eta*rho_0*(kbol*t)/1.E-30) + +t = t_tmp - dist +CALL PERTURBATION_PARAMETER +eta = z3t*rho_0 +CALL P_EOS +f_2 = pges/(eta*rho_0*(kbol*t)/1.E-30) + +t = t_tmp + dist +CALL PERTURBATION_PARAMETER +eta = z3t*rho_0 +CALL P_EOS +f_3 = pges/(eta*rho_0*(kbol*t)/1.E-30) + +t = t_tmp + 2.0*dist +CALL PERTURBATION_PARAMETER +eta = z3t*rho_0 +CALL P_EOS +f_4 = pges/(eta*rho_0*(kbol*t)/1.E-30) + +t = t_tmp +CALL PERTURBATION_PARAMETER +eta = z3t*rho_0 +CALL P_EOS + +dfdr = pges / (eta*rho_0*(kbol*t)/1.E-30) +ddfdrdr = pgesdz/(eta*rho_0*(kbol*t)/1.E-30) - dfdr*2.0/eta - 1.0/eta**2 + +df_drdt = ( -f_4 +8.0*f_3 -8.0*f_2 +f_1) / (12.0*dist) + +cp_res = cv_res - RGAS +RGAS*(zges+eta*t*df_drdt)**2 & + * 1.0/(1.0 + 2.0*eta*dfdr + eta**2 *ddfdrdr) + +! write (*,*) 'n',df_dt,df_dtdt +! write (*,*) 'kreuz ', zges,eta*t*df_drdt,eta*dfdr, eta**2 *ddfdrdr +! write (*,*) 'h, cv', h_res, cv_res +! write (*,*) h_res - t*s_res +! write (*,*) cv_res,cp_res,eta +! pause + +END SUBROUTINE H_EOS_num + + +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! SUBROUTINE DENSITY_ITERATION +! +! iterates the density until the calculated pressure 'pges' is equal to +! the specified pressure 'p'. A Newton-scheme is used for determining +! the root to the objective function f(eta) = (pges / p ) - 1.0. +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! + SUBROUTINE DENSITY_ITERATION +! + USE BASIC_VARIABLES, ONLY: num + USE EOS_VARIABLES + IMPLICIT NONE +! +! ---------------------------------------------------------------------- + INTEGER :: i, start, max_i + REAL :: eta_iteration + REAL :: error, dydx, acc_i, delta_eta +! ---------------------------------------------------------------------- + + +IF ( densav(phas) /= 0.0 .AND. eta_start == denold(phas) ) THEN + denold(phas) = eta_start + eta_start = densav(phas) +ELSE + denold(phas) = eta_start + densav(phas) = eta_start +END IF + + +acc_i = 1.d-9 +max_i = 30 +density_error(:) = 0.0 + +i = 0 +eta_iteration = eta_start + +! ---------------------------------------------------------------------- +! iterate density until p_calc = p +! ---------------------------------------------------------------------- +iterate_density: DO + + i = i + 1 + eta = eta_iteration + + IF ( num == 0 ) THEN + CALL P_EOS + ELSE IF ( num == 1 ) THEN + CALL P_NUMERICAL + ELSE IF ( num == 2 ) THEN + WRITE(*,*) 'CRITICAL RENORM NOT INCLUDED YET' + !!CALL F_EOS_RN + ELSE + write (*,*) 'define calculation option (num)' + END IF + + error = (pges / p ) - 1.0 + + ! --- instable region correction ------------------------------------- + IF ( pgesdz < 0.0 .AND. i < max_i ) THEN + IF ( error > 0.0 .AND. pgesd2 > 0.0 ) THEN ! no liquid density + CALL PRESSURE_SPINODAL + eta_iteration = eta + error = (pges / p ) - 1.0 + IF ( ((pges/p ) -1.0) > 0.0 ) eta_iteration = 0.001 ! no solution possible + IF ( ((pges/p ) -1.0) <=0.0 ) eta_iteration = eta_iteration * 1.1 ! no solution found so far + ELSE IF ( error < 0.0 .AND. pgesd2 < 0.0 ) THEN ! no vapor density + CALL PRESSURE_SPINODAL + eta_iteration = eta + error = (pges / p ) - 1.0 + IF ( ((pges/p ) -1.0) < 0.0 ) eta_iteration = 0.5 ! no solution possible + IF ( ((pges/p ) -1.0) >=0.0 ) eta_iteration = eta_iteration * 0.9 ! no solution found so far + ELSE + eta_iteration = (eta_iteration + eta_start) / 2.0 + IF (eta_iteration == eta_start) eta_iteration = eta_iteration + 0.2 + END IF + CYCLE iterate_density + END IF + + + dydx = pgesdz/p + delta_eta = error/ dydx + IF ( delta_eta > 0.05 ) delta_eta = 0.05 + IF ( delta_eta < -0.05 ) delta_eta = -0.05 + + eta_iteration = eta_iteration - delta_eta + + IF (eta_iteration > 0.9) eta_iteration = 0.6 + IF (eta_iteration <= 0.0) eta_iteration = 1.E-16 + start = 1 + + IF ( ABS(error*p/pgesdz) < 1.d-12 ) start = 0 + IF ( ABS(error) < acc_i ) start = 0 + IF ( i > max_i ) THEN + start = 0 + density_error(phas) = ABS( error ) + ! write (*,*) 'density iteration failed' + END IF + + IF (start /= 1) EXIT iterate_density + +END DO iterate_density + +eta = eta_iteration + +IF ((eta > 0.3 .AND. densav(phas) > 0.3) .OR. & + (eta < 0.1 .AND. densav(phas) < 0.1)) densav(phas) = eta + +END SUBROUTINE DENSITY_ITERATION + + + + +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! SUBROUTINE F_EOS +! +! calculates the Helmholtz energy f/kT. The input to the subroutine is +! (T,eta,x), where eta is the packing fraction. +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! + SUBROUTINE F_EOS +! + USE PARAMETERS, ONLY: nc, nsite + USE EOS_VARIABLES + USE EOS_CONSTANTS + IMPLICIT NONE +! +! --- local variables -------------------------------------------------- + INTEGER :: i, j, k, l, m, n + REAL :: z0, z1, z2, z3 + REAL :: zms, m_mean ! ,lij(nc,nc) + REAL :: I1,I2, c1_con + REAL :: fhs, fdsp, fhc + + LOGICAL :: assoc + INTEGER :: ass_cnt,max_eval + REAL :: delta(nc,nc,nsite,nsite) + REAL :: mx_itr(nc,nsite), err_sum, sum, attenu, tol, fhb + REAL :: ass_s1, ass_s2 + + REAL :: fdd, fqq, fdq +! ---------------------------------------------------------------------- + + +! ---------------------------------------------------------------------- +! abbreviations +! ---------------------------------------------------------------------- +rho = eta/z3t +z0 = z0t*rho +z1 = z1t*rho +z2 = z2t*rho +z3 = z3t*rho + +m_mean = z0t / ( PI / 6.0 ) +zms = 1.0 - eta + +! m_mean2 = 0.0 +! lij(1,2) = -0.05 +! lij(2,1) = lij(1,2) +! DO i = 1, ncomp +! DO j = 1, ncomp +! m_mean2 = m_mean2 + x(i)*x(j)*(mseg(i)+mseg(j))/2.0*(1.0-lij(i,j)) +! ENDDO +! ENDDO + + +! ---------------------------------------------------------------------- +! radial distr. function at contact, gij +! ---------------------------------------------------------------------- +DO i = 1, ncomp + DO j=1,ncomp + gij(i,j) = 1.0/zms + 3.0*dij_ab(i,j)*z2/zms/zms + 2.0*(dij_ab(i,j)*z2)**2 /zms**3 + END DO +END DO + + +! ---------------------------------------------------------------------- +! Helmholtz energy : hard sphere contribution +! ---------------------------------------------------------------------- +fhs= m_mean*( 3.0*z1*z2/zms + z2**3 /z3/zms/zms + (z2**3 /z3/z3-z0)*LOG(zms) )/z0 + + +! ---------------------------------------------------------------------- +! Helmholtz energy : chain term +! ---------------------------------------------------------------------- +fhc = 0.0 +DO i = 1, ncomp + fhc = fhc + x(i) *(1.0- mseg(i)) *LOG(gij(i,i)) +END DO + + +! ---------------------------------------------------------------------- +! Helmholtz energy : PC-SAFT dispersion contribution +! ---------------------------------------------------------------------- +IF (eos == 1) THEN + + I1 = 0.0 + I2 = 0.0 + DO m = 0, 6 + I1 = I1 + apar(m)*eta**REAL(m) + I2 = I2 + bpar(m)*eta**REAL(m) + END DO + + c1_con= 1.0/ ( 1.0 + m_mean*(8.0*eta-2.0*eta**2 )/zms**4 & + + (1.0 - m_mean)*(20.0*eta-27.0*eta**2 & + + 12.0*eta**3 -2.0*eta**4 ) /(zms*(2.0-eta))**2 ) + + fdsp = -2.0*PI*rho*I1*order1 - PI*rho*c1_con*m_mean*I2*order2 + +! ---------------------------------------------------------------------- +! Helmholtz energy : SAFT (Chen, Kreglewski) dispersion contribution +! ---------------------------------------------------------------------- +ELSE + + fdsp = 0.0 + DO n = 1,4 + DO m = 1,9 + fdsp = fdsp + dnm(n,m) * (um/t)**REAL(n) *(eta/tau)**REAL(m) + END DO + END DO + fdsp = m_mean * fdsp + +END IF + + +! ---------------------------------------------------------------------- +! TPT-1-association according to Chapman et al. +! ---------------------------------------------------------------------- +fhb = 0.0 +assoc = .false. +DO i = 1, ncomp + IF (nhb_typ(i) /= 0) assoc = .true. +END DO +IF (assoc) THEN + + DO i = 1, ncomp + DO k = 1, nhb_typ(i) + IF (mx(i,k) == 0.0) mx(i,k) = 1.0 ! Initialize mx(i,j) + DO j = 1, ncomp + DO l = 1, nhb_typ(j) + delta(i,j,k,l) = gij(i,j) * ass_d(i,j,k,l) + END DO + END DO + END DO + END DO + + +! --- constants for iteration ------------------------------------------ + attenu = 0.70 + tol = 1.d-10 + IF (eta < 0.2) tol = 1.d-12 + IF (eta < 0.01) tol = 1.d-13 + max_eval = 200 + +! --- iterate over all components and all sites ------------------------ + ass_cnt = 0 + iterate_TPT1: DO + + ass_cnt = ass_cnt + 1 + + DO i = 1, ncomp + DO k = 1, nhb_typ(i) + sum = 0.0 + DO j = 1, ncomp + DO l = 1, nhb_typ(j) + sum = sum + x(j)* mx(j,l)*nhb_no(j,l) *delta(i,j,k,l) +! if (ass_cnt == 1) write (*,*) j,l,x(j), mx(j,l) + END DO + END DO + mx_itr(i,k) = 1.0 / (1.0 + sum * rho) +! if (ass_cnt == 1) write (*,*) 'B',ass_cnt,sum, rho + END DO + END DO + + err_sum = 0.0 + DO i = 1, ncomp + DO k = 1, nhb_typ(i) + err_sum = err_sum + ABS(mx_itr(i,k) - mx(i,k)) ! / ABS(mx_itr(i,k)) + mx(i,k) = mx_itr(i,k) * attenu + mx(i,k) * (1.0 - attenu) + END DO + END DO + + IF ( err_sum <= tol .OR. ass_cnt >= max_eval ) THEN + IF (ass_cnt >= max_eval) WRITE(*,'(a,2G15.7)') 'F_EOS: Max_eval violated (mx) Err_Sum = ',err_sum,tol + EXIT iterate_TPT1 + END IF + + END DO iterate_TPT1 + + DO i = 1, ncomp + ass_s1 = 0.0 + ass_s2 = 0.0 + DO k = 1, nhb_typ(i) + ass_s1 = ass_s1 + nhb_no(i,k) * ( 1.0 - mx(i,k) ) + ass_s2 = ass_s2 + nhb_no(i,k) * LOG( mx(i,k) ) + END DO + fhb = fhb + x(i) * ( ass_s2 + ass_s1 / 2.0 ) + END DO + +END IF +! --- TPT-1-association accord. to Chapman ----------------------------- + + +! ---------------------------------------------------------------------- +! polar terms +! ---------------------------------------------------------------------- + CALL F_POLAR ( fdd, fqq, fdq ) + + +! ---------------------------------------------------------------------- +! resid. Helmholtz energy f/kT +! ---------------------------------------------------------------------- +fres = fhs + fhc + fdsp + fhb + fdd + fqq + fdq + +tfr= fres + +END SUBROUTINE F_EOS + + +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! + SUBROUTINE F_NUMERICAL +! + USE EOS_VARIABLES + USE EOS_CONSTANTS + USE EOS_NUMERICAL_DERIVATIVES, ONLY: ideal_gas, hard_sphere, chain_term, & + disp_term, hb_term, LC_term, branch_term, & + II_term, ID_term, subtract1, subtract2 + IMPLICIT NONE +! +!--------------------------------------------------------------------- + +!-----local variables------------------------------------------------- + INTEGER :: i, j + REAL :: m_mean2 + REAL :: fid, fhs, fdsp, fhc + REAL :: fhb, fdd, fqq, fdq + REAL :: fhend, fcc + REAL :: fbr, flc + REAL :: fref + + REAL :: eps_kij, k_kij +!--------------------------------------------------------------------- + +eps_kij = 0.0 +k_kij = 0.0 + +fid = 0.0 +fhs = 0.0 +fhc = 0.0 +fdsp= 0.0 +fhb = 0.0 +fdd = 0.0 +fqq = 0.0 +fdq = 0.0 +fcc = 0.0 +fbr = 0.0 +flc = 0.0 + + +CALL PERTURBATION_PARAMETER + +! ---------------------------------------------------------------------- +! overwrite the standard mixing rules by those published by Tang & Gross +! using an additional lij parameter +! WARNING : the lij parameter is set to lij = - lji in 'para_input' +! ---------------------------------------------------------------------- +order1 = 0.0 +order2 = 0.0 +DO i = 1, ncomp + DO j = 1, ncomp + order1 = order1 + x(i)*x(j)* mseg(i)*mseg(j) * sig_ij(i,j)**3 * uij(i,j)/t + order2 = order2 + x(i)*x(j)* mseg(i)*mseg(j) * sig_ij(i,j)**3 * (uij(i,j)/t)**2 + END DO +END DO +DO i = 1, ncomp + DO j = 1, ncomp + order1 = order1 + x(i)*mseg(i)/t*( x(j)*mseg(j) & + *sig_ij(i,j)*(uij(i,i)*uij(j,j))**(1.0/6.0) )**3 *lij(i,j) + END DO +END DO + + +! ---------------------------------------------------------------------- +! a non-standard mixing rule scaling the hard-sphere term +! WARNING : the lij parameter is set to lij = - lji in 'para_input' +! (uses an additional lij parameter) +! ---------------------------------------------------------------------- +m_mean2 = 0.0 +DO i = 1, ncomp + DO j = 1, ncomp + m_mean2 = m_mean2 + x(i)*x(j)*(mseg(i)+mseg(j))/2.0 + END DO +END DO +DO i = 1, ncomp + DO j = 1, ncomp + ! m_mean2=m_mean2+x(i)*(x(j)*((mseg(i)+mseg(j))*0.5)**(1.0/3.0) *lij(i,j) )**3 + END DO +END DO + +! --- ideal gas contribution ------------------------------------------- +IF ( ideal_gas == 'yes' ) CALL F_IDEAL_GAS ( fid ) +! ---------------------------------------------------------------------- + +! --- hard-sphere contribution ----------------------------------------- +IF ( hard_sphere == 'CSBM' ) CALL F_HARD_SPHERE ( m_mean2, fhs ) +! ---------------------------------------------------------------------- + +! -- chain term -------------------------------------------------------- +IF ( chain_term == 'TPT1' ) CALL F_CHAIN_TPT1 ( fhc ) +IF ( chain_term == 'TPT2' ) CALL F_CHAIN_TPT_D ( fhc ) +IF ( chain_term == 'HuLiu' ) CALL F_CHAIN_HU_LIU ( fhc ) +IF ( chain_term == 'HuLiu_rc' ) CALL F_CHAIN_HU_LIU_RC ( fhs, fhc ) +!!IF ( chain_term == 'SPT' ) CALL F_SPT ( fhs, fhc ) +IF ( chain_term == 'SPT' ) WRITE(*,*) 'SPT NOT INCLUDED YET' +! ---------------------------------------------------------------------- + +! --- dispersive attraction -------------------------------------------- +IF ( disp_term == 'PC-SAFT') CALL F_DISP_PCSAFT ( fdsp ) +IF ( disp_term == 'CK') CALL F_DISP_CKSAFT ( fdsp ) +IF ( disp_term(1:2) == 'PT') CALL F_pert_theory ( fdsp ) +! ---------------------------------------------------------------------- + +! --- H-bonding contribution / Association ----------------------------- +IF ( hb_term == 'TPT1_Chap') CALL F_ASSOCIATION( eps_kij, k_kij, fhb ) +! ---------------------------------------------------------------------- + +! --- polar terms ------------------------------------------------------ + CALL F_POLAR ( fdd, fqq, fdq ) +! ---------------------------------------------------------------------- + +! --- ion-dipole term -------------------------------------------------- +IF ( ID_term == 'TBH') CALL F_ION_DIPOLE_TBH ( fhend ) +! ---------------------------------------------------------------------- + +! --- ion-ion term ----------------------------------------------------- +IF ( II_term == 'primMSA') CALL F_ION_ION_PrimMSA ( fcc ) +IF ( II_term == 'nprMSA') CALL F_ION_ION_nonPrimMSA ( fdd, fqq, fdq, fcc ) +! ---------------------------------------------------------------------- + +! --- liquid-crystal term ---------------------------------------------- +IF ( LC_term == 'MSaupe') CALL F_LC_MayerSaupe ( flc ) + +!!IF ( LC_term == 'OVL') fref = fhs + fhc +IF ( LC_term == 'OVL') WRITE(*,*) 'OVL NOT INCLUDED YET' +!IF ( LC_term == 'OVL') CALL F_LC_OVL ( fref, flc ) +!! IF ( LC_term == 'SPT') fref = fhs + fhc +IF ( LC_term == 'SPT') WRITE(*,*) 'SPT NOT INCLUDED YET' +!!IF ( LC_term == 'SPT') CALL F_LC_SPT( fref, flc ) +! ---------------------------------------------------------------------- + +! ====================================================================== +! SUBTRACT TERMS (local density approximation) FOR DFT +! ====================================================================== + +!IF ( subtract1 == '1PT') CALL F_subtract_local_pert_theory ( subtract1, fdsp ) +!IF ( subtract1 == '2PT') CALL F_subtract_local_pert_theory ( subtract1, fdsp ) +!IF ( subtract2 =='ITTpolar') CALL F_local_ITT_polar ( fdd ) +! ---------------------------------------------------------------------- + +! ---------------------------------------------------------------------- +! residual Helmholtz energy F/(NkT) +! ---------------------------------------------------------------------- +fres = fid + fhs + fhc + fdsp + fhb + fdd + fqq + fdq + fcc + flc + +tfr = 0.0 + +END SUBROUTINE F_NUMERICAL + + + +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! SUBROUTINE P_EOS +! +! calculates the pressure in units (Pa). +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! + SUBROUTINE P_EOS +! +! ---------------------------------------------------------------------- + USE PARAMETERS, ONLY: nc, nsite + USE EOS_VARIABLES + USE EOS_CONSTANTS + IMPLICIT NONE +! +! --- local variables -------------------------------------------------- + INTEGER :: i, j, k, l, m, n + INTEGER :: ass_cnt,max_eval + LOGICAL :: assoc + REAL :: z0, z1, z2, z3 + REAL :: zms, m_mean + REAL :: zges, zgesdz, zgesd2, zgesd3 + REAL :: zhs, zhsdz, zhsd2, zhsd3 + REAL :: zhc, zhcdz, zhcd2, zhcd3 + REAL, DIMENSION(nc,nc) :: dgijdz, dgijd2, dgijd3, dgijd4 + REAL :: zdsp, zdspdz, zdspd2, zdspd3 + REAL :: c1_con, c2_con, c3_con, c4_con, c5_con + REAL :: I2, edI1dz, edI2dz, edI1d2, edI2d2 + REAL :: edI1d3, edI2d3, edI1d4, edI2d4 + REAL :: fdspdz,fdspd2 + REAL :: zhb, zhbdz, zhbd2, zhbd3 + REAL, DIMENSION(nc,nc,nsite,nsite) :: delta, dq_dz, dq_d2, dq_d3, dq_d4 + REAL, DIMENSION(nc,nsite) :: mx_itr, dmx_dz, ndmxdz, dmx_d2, ndmxd2 + REAL, DIMENSION(nc,nsite) :: dmx_d3, ndmxd3, dmx_d4, ndmxd4 + REAL :: err_sum, sum0, sum1, sum2, sum3, sum4, attenu, tol + REAL :: sum_d1, sum_d2, sum_d3, sum_d4 + REAL :: zdd, zddz, zddz2, zddz3 + REAL :: zqq, zqqz, zqqz2, zqqz3 + REAL :: zdq, zdqz, zdqz2, zdqz3 +! ---------------------------------------------------------------------- + + +! ---------------------------------------------------------------------- +! abbreviations +! ---------------------------------------------------------------------- +rho = eta/z3t +z0 = z0t*rho +z1 = z1t*rho +z2 = z2t*rho +z3 = z3t*rho + +m_mean = z0t/(PI/6.0) +zms = 1.0 -eta + +! m_mean2=0.0 +! lij(1,2)= -0.050 +! lij(2,1)=lij(1,2) +! DO i =1,ncomp +! DO j =1,ncomp +! m_mean2=m_mean2+x(i)*x(j) * (mseg(i)+mseg(j))/2.0*(1.0-lij(i,j)) +! ENDDO +! ENDDO + + +! ---------------------------------------------------------------------- +! radial distr. function at contact, gij , and derivatives +! dgijdz=d(gij)/d(eta) and dgijd2 = dd(gij)/d(eta)**2 +! ---------------------------------------------------------------------- +DO i = 1, ncomp + DO j=1,ncomp + ! j=i + gij(i,j) = 1.0/zms + 3.0*dij_ab(i,j)*z2/zms/zms + 2.0*(dij_ab(i,j)*z2)**2 /zms**3 + dgijdz(i,j)= 1.0/zms/zms + 3.0*dij_ab(i,j)*z2*(1.0+z3)/z3/zms**3 & + + (dij_ab(i,j)*z2/zms/zms)**2 *(4.0+2.0*z3)/z3 + dgijd2(i,j) = 2.0/zms**3 & + + 6.0*dij_ab(i,j)*z2/z3/zms**4 *(2.0+z3) & + + (2.0*dij_ab(i,j)*z2/z3)**2 /zms**5 *(1.0+4.0*z3+z3*z3) + dgijd3(i,j) = 6.0/zms**4 & + + 18.0*dij_ab(i,j)*z2/z3/zms**5 *(3.0+z3) & + + 12.0*(dij_ab(i,j)*z2/z3/zms**3 )**2 *(3.0+6.0*z3+z3*z3) + dgijd4(i,j) = 24.0/zms**5 & + + 72.0*dij_ab(i,j)*z2/z3/zms**6 *(4.0+z3) & + + 48.0*(dij_ab(i,j)*z2/z3)**2 /zms**7 *(6.0+8.0*z3+z3*z3) + END DO +END DO + + +! ---------------------------------------------------------------------- +! p : hard sphere contribution +! ---------------------------------------------------------------------- +zhs = m_mean* ( z3/zms + 3.0*z1*z2/z0/zms/zms + z2**3 /z0*(3.0-z3)/zms**3 ) +zhsdz = m_mean*( 1.0/zms/zms + 3.0*z1*z2/z0/z3*(1.0+z3)/zms**3 & + + 6.0*z2**3 /z0/z3/zms**4 ) +zhsd2 = m_mean*( 2.0/zms**3 + 6.0*z1*z2/z0/z3*(2.0+z3)/zms**4 & + + 6.0*z2**3 /z0/z3/z3*(1.0+3.0*z3)/zms**5 ) +zhsd3 = m_mean*( 6.0/zms**4 + 18.0*z1*z2/z0/z3*(3.0+z3)/zms**5 & + + 24.0*z2**3 /z0/z3/z3*(2.0+3.0*z3)/zms**6 ) + + +! ---------------------------------------------------------------------- +! p : chain term +! ---------------------------------------------------------------------- +zhc = 0.0 +zhcdz = 0.0 +zhcd2 = 0.0 +zhcd3 = 0.0 +DO i= 1, ncomp + zhc = zhc + x(i)*(1.0-mseg(i))*eta/gij(i,i)* dgijdz(i,i) + zhcdz = zhcdz + x(i)*(1.0-mseg(i)) *(-eta*(dgijdz(i,i)/gij(i,i))**2 & + + dgijdz(i,i)/gij(i,i) + eta/gij(i,i)*dgijd2(i,i)) + zhcd2 = zhcd2 + x(i)*(1.0-mseg(i)) & + *( 2.0*eta*(dgijdz(i,i)/gij(i,i))**3 & + -2.0*(dgijdz(i,i)/gij(i,i))**2 & + -3.0*eta/gij(i,i)**2 *dgijdz(i,i)*dgijd2(i,i) & + +2.0/gij(i,i)*dgijd2(i,i) +eta/gij(i,i)*dgijd3(i,i) ) + zhcd3 = zhcd3 + x(i)*(1.0-mseg(i)) *( 6.0*(dgijdz(i,i)/gij(i,i))**3 & + -6.0*eta*(dgijdz(i,i)/gij(i,i))**4 & + +12.0*eta/gij(i,i)**3 *dgijdz(i,i)**2 *dgijd2(i,i) & + -9.0/gij(i,i)**2 *dgijdz(i,i)*dgijd2(i,i) +3.0/gij(i,i)*dgijd3(i,i) & + -3.0*eta*(dgijd2(i,i)/gij(i,i))**2 & + -4.0*eta/gij(i,i)**2 *dgijdz(i,i)*dgijd3(i,i) & + +eta/gij(i,i)*dgijd4(i,i) ) +END DO + +! ---------------------------------------------------------------------- +! p : PC-SAFT dispersion contribution +! note: edI1dz is equal to d(eta*I1)/d(eta), analogous for edI2dz +! ---------------------------------------------------------------------- +IF (eos == 1) THEN + + I2 = 0.0 + edI1dz = 0.0 + edI2dz = 0.0 + edI1d2 = 0.0 + edI2d2 = 0.0 + edI1d3 = 0.0 + edI2d3 = 0.0 + edI1d4 = 0.0 + edI2d4 = 0.0 + DO m=0,6 + I2 = I2 + bpar(m)*z3**REAL(m) + edI1dz= edI1dz+apar(m)*REAL(m+1)*z3**REAL(m) + edI2dz= edI2dz+bpar(m)*REAL(m+1)*z3**REAL(m) + edI1d2= edI1d2+apar(m)*REAL((m+1)*m)*z3**REAL(m-1) + edI2d2= edI2d2+bpar(m)*REAL((m+1)*m)*z3**REAL(m-1) + edI1d3= edI1d3+apar(m)*REAL((m+1)*m*(m-1))*z3**REAL(m-2) + edI2d3= edI2d3+bpar(m)*REAL((m+1)*m*(m-1))*z3**REAL(m-2) + edI1d4= edI1d4+apar(m)*REAL((m+1)*m*(m-1)*(m-2))*z3**REAL(m-3) + edI2d4= edI2d4+bpar(m)*REAL((m+1)*m*(m-1)*(m-2))*z3**REAL(m-3) + END DO + + c1_con= 1.0/ ( 1.0 + m_mean*(8.0*eta-2.0*eta**2 )/zms**4 & + + (1.0 - m_mean)*(20.0*eta-27.0*eta**2 & + + 12.0*eta**3 -2.0*eta**4 ) /(zms*(2.0-eta))**2 ) + c2_con= - c1_con*c1_con & + *(m_mean*(-4.0*eta**2 +20.0*eta+8.0)/zms**5 + (1.0 - m_mean) & + *(2.0*eta**3 +12.0*eta**2 -48.0*eta+40.0) & + /(zms*(2.0-eta))**3 ) + c3_con= 2.0 * c2_con*c2_con/c1_con - c1_con*c1_con & + *( m_mean*(-12.0*eta**2 +72.0*eta+60.0)/zms**6 & + + (1.0 - m_mean) & + *(-6.0*eta**4 -48.0*eta**3 +288.0*eta**2 & + -480.0*eta+264.0) /(zms*(2.0-eta))**4 ) + c4_con= 6.0*c2_con*c3_con/c1_con -6.0*c2_con**3 /c1_con**2 & + - c1_con*c1_con & + *( m_mean*(-48.0*eta**2 +336.0*eta+432.0)/zms**7 & + + (1.0 - m_mean) & + *(24.0*eta**5 +240.0*eta**4 -1920.0*eta**3 & + +4800.0*eta**2 -5280.0*eta+2208.0) /(zms*(2.0-eta))**5 ) + c5_con= 6.0*c3_con**2 /c1_con - 36.0*c2_con**2 /c1_con**2 *c3_con & + + 8.0*c2_con/c1_con*c4_con+24.0*c2_con**4 /c1_con**3 & + - c1_con*c1_con & + *( m_mean*(-240.0*eta**2 +1920.0*eta+3360.0)/zms**8 & + + (1.0 - m_mean) & + *(-120.0*eta**6 -1440.0*eta**5 +14400.0*eta**4 & + -48000.0*eta**3 +79200.0*eta**2 -66240.0*eta+22560.0) & + /(zms*(2.0-eta))**6 ) + + zdsp = - 2.0*PI*rho*edI1dz*order1 & + - PI*rho*order2*m_mean*(c2_con*I2*eta + c1_con*edI2dz) + zdspdz= zdsp/eta - 2.0*PI*rho*edI1d2*order1 & + - PI*rho*order2*m_mean*(c3_con*I2*eta & + + 2.0*c2_con*edI2dz + c1_con*edI2d2) + zdspd2= -2.0*zdsp/eta/eta +2.0*zdspdz/eta & + - 2.0*PI*rho*edI1d3*order1 - PI*rho*order2*m_mean*(c4_con*I2*eta & + + 3.0*c3_con*edI2dz +3.0*c2_con*edI2d2 +c1_con*edI2d3) + zdspd3= 6.0*zdsp/eta**3 -6.0*zdspdz/eta/eta & + + 3.0*zdspd2/eta - 2.0*PI*rho*edI1d4*order1 & + - PI*rho*order2*m_mean*(c5_con*I2*eta & + + 4.0*c4_con*edI2dz +6.0*c3_con*edI2d2 & + + 4.0*c2_con*edI2d3 + c1_con*edI2d4) + + +! ---------------------------------------------------------------------- +! p : SAFT (Chen & Kreglewski) dispersion contribution +! ---------------------------------------------------------------------- +ELSE + + fdspdz = 0.0 + fdspd2 = 0.0 + DO n = 1,4 + DO m = 1,9 + fdspdz = fdspdz + m_mean/tau * dnm(n,m) * (um/t)**REAL(n) *REAL(m)*(eta/tau)**REAL(m-1) + END DO + DO m= 2,9 + fdspd2= fdspd2 + m_mean/tau * dnm(n,m)*(um/t)**REAL(n) *REAL(m)*REAL(m-1) & + * (eta/tau)**REAL(m-2) * 1.0/tau + END DO + END DO + zdsp = eta * fdspdz + zdspdz = (2.0*fdspdz + eta*fdspd2) - zdsp/z3 + +END IF +! --- end of dispersion contribution ----------------------------------- + + +! ---------------------------------------------------------------------- +! p: TPT-1-association accord. to Chapman et al. +! ---------------------------------------------------------------------- +zhb = 0.0 +zhbdz = 0.0 +zhbd2 = 0.0 +zhbd3 = 0.0 +assoc = .false. +DO i = 1,ncomp + IF (nhb_typ(i) /= 0) assoc = .true. +END DO +IF (assoc) THEN + + DO j = 1, ncomp + DO i = 1, nhb_typ(j) + DO k = 1, ncomp + DO l = 1, nhb_typ(k) + delta(j,k,i,l) = gij(j,k) * ass_d(j,k,i,l) + dq_dz(j,k,i,l) = dgijdz(j,k) * ass_d(j,k,i,l) + dq_d2(j,k,i,l) = dgijd2(j,k) * ass_d(j,k,i,l) + dq_d3(j,k,i,l) = dgijd3(j,k) * ass_d(j,k,i,l) + dq_d4(j,k,i,l) = dgijd4(j,k) * ass_d(j,k,i,l) + END DO + END DO + END DO + END DO + +! --- constants for iteration ------------------------------------------ + attenu = 0.7 + tol = 1.d-10 + IF ( eta < 0.2 ) tol = 1.d-12 + IF ( eta < 0.01 ) tol = 1.d-13 + IF ( eta < 1.E-6) tol = 1.d-15 + max_eval = 1000 + +! --- initialize mx(i,j) ----------------------------------------------- + DO i = 1, ncomp + DO j = 1, nhb_typ(i) + mx(i,j) = 1.0 + dmx_dz(i,j) = 0.0 + dmx_d2(i,j) = 0.0 + dmx_d3(i,j) = 0.0 + dmx_d4(i,j) = 0.0 + END DO + END DO + +! --- iterate over all components and all sites ------------------------ + ass_cnt = 0 + err_sum = tol + 1.0 + DO WHILE ( err_sum > tol .AND. ass_cnt <= max_eval) + ass_cnt = ass_cnt + 1 + DO i = 1, ncomp + DO j = 1, nhb_typ(i) + sum0 = 0.0 + sum1 = 0.0 + sum2 = 0.0 + sum3 = 0.0 + sum4 = 0.0 + DO k = 1, ncomp + DO l = 1, nhb_typ(k) + sum0 =sum0 +x(k)*nhb_no(k,l)* mx(k,l)* delta(i,k,j,l) + sum1 =sum1 +x(k)*nhb_no(k,l)*( mx(k,l)* dq_dz(i,k,j,l) & + + dmx_dz(k,l)* delta(i,k,j,l)) + sum2 =sum2 +x(k)*nhb_no(k,l)*( mx(k,l)* dq_d2(i,k,j,l) & + + 2.0*dmx_dz(k,l)* dq_dz(i,k,j,l) & + + dmx_d2(k,l)* delta(i,k,j,l)) + sum3 =sum3 +x(k)*nhb_no(k,l)*( mx(k,l)* dq_d3(i,k,j,l) & + + 3.0*dmx_dz(k,l)* dq_d2(i,k,j,l) & + + 3.0*dmx_d2(k,l)* dq_dz(i,k,j,l) & + + dmx_d3(k,l)* delta(i,k,j,l)) + sum4 =sum4 + x(k)*nhb_no(k,l)*( mx(k,l)* dq_d4(i,k,j,l) & + + 4.0*dmx_dz(k,l)* dq_d3(i,k,j,l) & + + 6.0*dmx_d2(k,l)* dq_d2(i,k,j,l) & + + 4.0*dmx_d3(k,l)* dq_dz(i,k,j,l) & + + dmx_d4(k,l)* delta(i,k,j,l)) + END DO + END DO + mx_itr(i,j)= 1.0 / (1.0 + sum0 * rho) + ndmxdz(i,j)= -(mx_itr(i,j)*mx_itr(i,j))* (sum0/z3t +sum1*rho) + ndmxd2(i,j)= + 2.0/mx_itr(i,j)*ndmxdz(i,j)*ndmxdz(i,j) & + - (mx_itr(i,j)*mx_itr(i,j)) * (2.0/z3t*sum1 + rho*sum2) + ndmxd3(i,j)= - 6.0/mx_itr(i,j)**2 *ndmxdz(i,j)**3 & + + 6.0/mx_itr(i,j)*ndmxdz(i,j)*ndmxd2(i,j) - mx_itr(i,j)*mx_itr(i,j) & + * (3.0/z3t*sum2 + rho*sum3) + ndmxd4(i,j)= 24.0/mx_itr(i,j)**3 *ndmxdz(i,j)**4 & + -36.0/mx_itr(i,j)**2 *ndmxdz(i,j)**2 *ndmxd2(i,j) & + +6.0/mx_itr(i,j)*ndmxd2(i,j)**2 & + +8.0/mx_itr(i,j)*ndmxdz(i,j)*ndmxd3(i,j) - mx_itr(i,j)**2 & + *(4.0/z3t*sum3 + rho*sum4) + END DO + END DO + + err_sum = 0.0 + DO i = 1, ncomp + DO j = 1, nhb_typ(i) + err_sum = err_sum + ABS(mx_itr(i,j) - mx(i,j)) & + + ABS(ndmxdz(i,j) - dmx_dz(i,j)) + ABS(ndmxd2(i,j) - dmx_d2(i,j)) + mx(i,j) = mx_itr(i,j)*attenu + mx(i,j) * (1.0-attenu) + dmx_dz(i,j) = ndmxdz(i,j)*attenu + dmx_dz(i,j) * (1.0-attenu) + dmx_d2(i,j) = ndmxd2(i,j)*attenu + dmx_d2(i,j) * (1.0-attenu) + dmx_d3(i,j) = ndmxd3(i,j)*attenu + dmx_d3(i,j) * (1.0-attenu) + dmx_d4(i,j) = ndmxd4(i,j)*attenu + dmx_d4(i,j) * (1.0-attenu) + END DO + END DO + END DO + + IF ( ass_cnt >= max_eval .AND. err_sum > SQRT(tol) ) THEN + WRITE (*,'(a,2G15.7)') 'P_EOS: Max_eval violated (mx) Err_Sum= ',err_sum,tol + ! stop + END IF + + + ! --- calculate the hydrogen-bonding contribution -------------------- + DO i = 1, ncomp + sum_d1 = 0.0 + sum_d2 = 0.0 + sum_d3 = 0.0 + sum_d4 = 0.0 + DO j = 1, nhb_typ(i) + sum_d1= sum_d1 +nhb_no(i,j)* dmx_dz(i,j)*(1.0/mx(i,j)-0.5) + sum_d2= sum_d2 +nhb_no(i,j)*(dmx_d2(i,j)*(1.0/mx(i,j)-0.5) & + -(dmx_dz(i,j)/mx(i,j))**2 ) + sum_d3= sum_d3 +nhb_no(i,j)*(dmx_d3(i,j)*(1.0/mx(i,j)-0.5) & + -3.0/mx(i,j)**2 *dmx_dz(i,j)*dmx_d2(i,j) + 2.0*(dmx_dz(i,j)/mx(i,j))**3 ) + sum_d4= sum_d4 +nhb_no(i,j)*(dmx_d4(i,j)*(1.0/mx(i,j)-0.5) & + -4.0/mx(i,j)**2 *dmx_dz(i,j)*dmx_d3(i,j) & + + 12.0/mx(i,j)**3 *dmx_dz(i,j)**2 *dmx_d2(i,j) & + - 3.0/mx(i,j)**2 *dmx_d2(i,j)**2 - 6.0*(dmx_dz(i,j)/mx(i,j))**4 ) + END DO + zhb = zhb + x(i) * eta * sum_d1 + zhbdz = zhbdz + x(i) * eta * sum_d2 + zhbd2 = zhbd2 + x(i) * eta * sum_d3 + zhbd3 = zhbd3 + x(i) * eta * sum_d4 + END DO + zhbdz = zhbdz + zhb/eta + zhbd2 = zhbd2 + 2.0/eta*zhbdz-2.0/eta**2 *zhb + zhbd3 = zhbd3 - 6.0/eta**2 *zhbdz+3.0/eta*zhbd2 + 6.0/eta**3 *zhb +END IF +! --- TPT-1-association accord. to Chapman ----------------------------- + + +! ---------------------------------------------------------------------- +! p: polar terms +! ---------------------------------------------------------------------- +CALL P_POLAR ( zdd, zddz, zddz2, zddz3, zqq, zqqz, zqqz2, zqqz3, zdq, zdqz, zdqz2, zdqz3 ) + + +! ---------------------------------------------------------------------- +! compressibility factor z and total p +! as well as derivatives d(z)/d(eta) and d(p)/d(eta) with unit [Pa] +! ---------------------------------------------------------------------- +zges = 1.0 + zhs + zhc + zdsp + zhb + zdd + zqq + zdq +zgesdz = zhsdz + zhcdz + zdspdz + zhbdz + zddz + zqqz + zdqz +zgesd2 = zhsd2 + zhcd2 + zdspd2 + zhbd2 + zddz2 +zqqz2+zdqz2 +zgesd3 = zhsd3 + zhcd3 + zdspd3 + zhbd3 + zddz3 +zqqz3+zdqz3 + +pges = zges *rho *(kbol*t)/1.d-30 +pgesdz = ( zgesdz*rho + zges*rho/z3 )*(kbol*t)/1.d-30 +pgesd2 = ( zgesd2*rho + 2.0*zgesdz*rho/z3 )*(kbol*t)/1.d-30 +pgesd3 = ( zgesd3*rho + 3.0*zgesd2*rho/z3 )*(kbol*t)/1.d-30 + +END SUBROUTINE P_EOS + + + + +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! + SUBROUTINE PHI_POLAR ( k, z3_rk, fdd_rk, fqq_rk, fdq_rk ) +! + USE EOS_VARIABLES, ONLY: ncomp, parame, dd_term, qq_term, dq_term + IMPLICIT NONE +! +! ---------------------------------------------------------------------- + INTEGER, INTENT(IN) :: k + REAL, INTENT(IN) :: z3_rk + REAL, INTENT(OUT) :: fdd_rk, fqq_rk, fdq_rk +! +! --- local variables--------------------------------------------------- + INTEGER :: dipole + INTEGER :: quadrupole + INTEGER :: dipole_quad +! ---------------------------------------------------------------------- + + fdd_rk = 0.0 + fqq_rk = 0.0 + fdq_rk = 0.0 + + dipole = 0 + quadrupole = 0 + dipole_quad = 0 + IF ( SUM( parame(1:ncomp,6) ) /= 0.0 ) dipole = 1 + IF ( SUM( parame(1:ncomp,7) ) /= 0.0 ) quadrupole = 1 + IF ( dipole == 1 .AND. quadrupole == 1 ) dipole_quad = 1 + + ! -------------------------------------------------------------------- + ! dipole-dipole term + ! -------------------------------------------------------------------- + IF (dipole == 1) THEN + + IF (dd_term == 'GV') CALL PHI_DD_GROSS_VRABEC( k, z3_rk, fdd_rk ) + ! IF (dd_term == 'SF') CALL PHI_DD_SAAGER_FISCHER( k ) + + IF (dd_term /= 'GV' .AND. dd_term /= 'SF') write (*,*) 'specify dipole term !' + + ENDIF + + ! -------------------------------------------------------------------- + ! quadrupole-quadrupole term + ! -------------------------------------------------------------------- + IF (quadrupole == 1) THEN + + !IF (qq_term == 'SF') CALL PHI_QQ_SAAGER_FISCHER( k ) + IF (qq_term == 'JG') CALL PHI_QQ_GROSS( k, z3_rk, fqq_rk ) + + IF (qq_term /= 'JG' .AND. qq_term /= 'SF') write (*,*) 'specify quadrupole term !' + + ENDIF + + ! -------------------------------------------------------------------- + ! dipole-quadrupole cross term + ! -------------------------------------------------------------------- + IF (dipole_quad == 1) THEN + + IF (dq_term == 'VG') CALL PHI_DQ_VRABEC_GROSS( k, z3_rk, fdq_rk ) + + IF (dq_term /= 'VG' ) write (*,*) 'specify DQ-cross term !' + + ENDIF + +END SUBROUTINE PHI_POLAR + + +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! + SUBROUTINE PHI_DD_GROSS_VRABEC( k, z3_rk, fdd_rk ) +! + USE PARAMETERS, ONLY: PI, KBOL + USE EOS_VARIABLES, ONLY: nc, ncomp, uij, parame, mseg, sig_ij, rho, eta, x, t + USE EOS_CONSTANTS, ONLY: ddp2, ddp3, ddp4 + IMPLICIT NONE +! +! ---------------------------------------------------------------------- + INTEGER, INTENT(IN) :: k + REAL, INTENT(IN) :: z3_rk + REAL, INTENT(IN OUT) :: fdd_rk +! +! --- local variables--------------------------------------------------- + INTEGER :: i, j, l, m + + REAL :: factor2, factor3, z3 + REAL :: xijfa, xijkfa, xijfa_x, xijkf_x, eij + REAL :: fdd2, fdd3, fdd2x, fdd3x + REAL, DIMENSION(nc) :: my2dd + REAL, DIMENSION(nc,nc) :: Idd2, Idd4, Idd2x, Idd4x + REAL, DIMENSION(nc,nc,nc) :: Idd3, Idd3x +! ---------------------------------------------------------------------- + + + fdd_rk = 0.0 + z3 = eta + DO i = 1, ncomp + IF ( uij(i,i) == 0.0 ) write (*,*) 'PHI_DD_GROSS_VRABEC: do not use dimensionless units' + IF ( uij(i,i) == 0.0 ) stop + my2dd(i) = (parame(i,6))**2 *1.E-49 / (uij(i,i)*KBOL*mseg(i)*sig_ij(i,i)**3 *1.E-30) + END DO + + DO i = 1, ncomp + DO j = 1, ncomp + Idd2(i,j) = 0.0 + Idd4(i,j) = 0.0 + Idd2x(i,j) = 0.0 + Idd4x(i,j) = 0.0 + IF (parame(i,6) /= 0.0 .AND. parame(j,6) /= 0.0) THEN + DO m=0,4 + Idd2(i,j) =Idd2(i,j) + ddp2(i,j,m)*z3**m + Idd4(i,j) =Idd4(i,j) + ddp4(i,j,m)*z3**m + Idd2x(i,j) =Idd2x(i,j)+ ddp2(i,j,m)*REAL(m)*z3**(m-1)*z3_rk + Idd4x(i,j) =Idd4x(i,j)+ ddp4(i,j,m)*REAL(m)*z3**(m-1)*z3_rk + END DO + DO l = 1, ncomp + Idd3(i,j,l) = 0.0 + Idd3x(i,j,l) = 0.0 + IF (parame(l,6) /= 0.0) THEN + DO m=0,4 + Idd3(i,j,l) =Idd3(i,j,l) +ddp3(i,j,l,m)*z3**m + Idd3x(i,j,l)=Idd3x(i,j,l)+ddp3(i,j,l,m)*REAL(m)*z3**(m-1)*z3_rk + END DO + END IF + END DO + END IF + END DO + END DO + + factor2= -PI + factor3= -4.0/3.0*PI**2 + + fdd2 = 0.0 + fdd3 = 0.0 + fdd2x = 0.0 + fdd3x = 0.0 + DO i = 1, ncomp + xijfa_x = 2.0*x(i)*rho*uij(i,i)*my2dd(i)*sig_ij(i,i)**3 /t & + *uij(k,k)*my2dd(k)*sig_ij(k,k)**3 /t/sig_ij(i,k)**3 + eij = (parame(i,3)*parame(k,3))**0.5 + fdd2x = fdd2x + factor2*xijfa_x*( Idd2(i,k) + eij/t*Idd4(i,k) ) + DO j = 1, ncomp + IF (parame(i,6) /= 0.0 .AND. parame(j,6) /= 0.0) THEN + xijfa =x(i)*rho*uij(i,i)*my2dd(i)*sig_ij(i,i)**3 /t & + *x(j)*rho*uij(j,j)*my2dd(j)*sig_ij(j,j)**3 /t/sig_ij(i,j)**3 + eij = (parame(i,3)*parame(j,3))**0.5 + fdd2= fdd2 +factor2*xijfa*(Idd2(i,j) +eij/t*Idd4(i,j) ) + fdd2x =fdd2x +factor2*xijfa*(Idd2x(i,j)+eij/t*Idd4x(i,j)) + !--------------------- + xijkf_x=x(i)*rho*uij(i,i)*my2dd(i)*sig_ij(i,i)**3 /t/sig_ij(i,j) & + *x(j)*rho*uij(j,j)*my2dd(j)*sig_ij(j,j)**3 /t/sig_ij(i,k) & + *3.0* uij(k,k)*my2dd(k)*sig_ij(k,k)**3 /t/sig_ij(j,k) + fdd3x=fdd3x+factor3*xijkf_x*Idd3(i,j,k) + DO l=1,ncomp + IF (parame(l,6) /= 0.0) THEN + xijkfa= x(i)*rho*uij(i,i)/t*my2dd(i)*sig_ij(i,i)**3 & + *x(j)*rho*uij(j,j)/t*my2dd(j)*sig_ij(j,j)**3 & + *x(l)*rho*uij(l,l)/t*my2dd(l)*sig_ij(l,l)**3 & + /sig_ij(i,j)/sig_ij(i,l)/sig_ij(j,l) + fdd3 =fdd3 + factor3 * xijkfa *Idd3(i,j,l) + fdd3x =fdd3x + factor3 * xijkfa *Idd3x(i,j,l) + END IF + END DO + END IF + END DO + END DO + + IF (fdd2 < -1.E-50 .AND. fdd3 /= 0.0 .AND. fdd2x /= 0.0 .AND. fdd3x /= 0.0)THEN + + fdd_rk = fdd2* (fdd2*fdd2x - 2.0*fdd3*fdd2x+fdd2*fdd3x) / (fdd2-fdd3)**2 + + END IF + +END SUBROUTINE PHI_DD_GROSS_VRABEC + + + +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! + SUBROUTINE PHI_QQ_GROSS( k, z3_rk, fqq_rk ) +! + USE PARAMETERS, ONLY: PI, KBOL + USE EOS_VARIABLES, ONLY: nc, ncomp, uij, parame, mseg, sig_ij, rho, eta, x, t + USE EOS_CONSTANTS, ONLY: qqp2, qqp3, qqp4 + IMPLICIT NONE +! +! ---------------------------------------------------------------------- + INTEGER, INTENT(IN) :: k + REAL, INTENT(IN) :: z3_rk + REAL, INTENT(IN OUT) :: fqq_rk +! +! --- local variables--------------------------------------------------- + INTEGER :: i, j, l, m + + REAL :: factor2, factor3, z3 + REAL :: xijfa, xijkfa, xijfa_x, xijkf_x, eij + REAL :: fqq2, fqq3, fqq2x, fqq3x + REAL, DIMENSION(nc) :: qq2 + REAL, DIMENSION(nc,nc) :: Iqq2, Iqq4, Iqq2x, Iqq4x + REAL, DIMENSION(nc,nc,nc) :: Iqq3, Iqq3x +! ---------------------------------------------------------------------- + + + fqq_rk = 0.0 + z3 = eta + DO i = 1, ncomp + IF ( uij(i,i) == 0.0 ) write (*,*) 'PHI_QQ_GROSS: do not use dimensionless units' + qq2(i) = (parame(i,7))**2 *1.E-69 / (uij(i,i)*kbol*mseg(i)*sig_ij(i,i)**5 *1.E-50) + END DO + + DO i = 1, ncomp + DO j = 1, ncomp + Iqq2(i,j) = 0.0 + Iqq4(i,j) = 0.0 + Iqq2x(i,j) = 0.0 + Iqq4x(i,j) = 0.0 + IF (parame(i,7) /= 0.0 .AND. parame(j,7) /= 0.0) THEN + DO m = 0, 4 + Iqq2(i,j) = Iqq2(i,j) + qqp2(i,j,m) * z3**m + Iqq4(i,j) = Iqq4(i,j) + qqp4(i,j,m) * z3**m + Iqq2x(i,j) = Iqq2x(i,j) + qqp2(i,j,m) * REAL(m)*z3**(m-1)*z3_rk + Iqq4x(i,j) = Iqq4x(i,j) + qqp4(i,j,m) * REAL(m)*z3**(m-1)*z3_rk + END DO + DO l = 1, ncomp + Iqq3(i,j,l) = 0.0 + Iqq3x(i,j,l) = 0.0 + IF (parame(l,7) /= 0.0) THEN + DO m = 0, 4 + Iqq3(i,j,l) = Iqq3(i,j,l) + qqp3(i,j,l,m)*z3**m + Iqq3x(i,j,l) = Iqq3x(i,j,l) + qqp3(i,j,l,m)*REAL(m) *z3**(m-1)*z3_rk + END DO + END IF + END DO + END IF + END DO + END DO + + factor2= -9.0/16.0*PI + factor3= 9.0/16.0*PI**2 + + fqq2 = 0.0 + fqq3 = 0.0 + fqq2x = 0.0 + fqq3x = 0.0 + DO i = 1, ncomp + xijfa_x = 2.0*x(i)*rho*uij(i,i)*qq2(i)*sig_ij(i,i)**5 /t & + *uij(k,k)*qq2(k)*sig_ij(k,k)**5 /t/sig_ij(i,k)**7.0 + eij = (parame(i,3)*parame(k,3))**0.5 + fqq2x =fqq2x +factor2*xijfa_x*(Iqq2(i,k)+eij/t*Iqq4(i,k)) + DO j=1,ncomp + IF (parame(i,7) /= 0.0 .AND. parame(j,7) /= 0.0) THEN + xijfa =x(i)*rho*uij(i,i)*qq2(i)*sig_ij(i,i)**5 /t & + *x(j)*rho*uij(j,j)*qq2(j)*sig_ij(j,j)**5 /t/sig_ij(i,j)**7.0 + eij = (parame(i,3)*parame(j,3))**0.5 + fqq2= fqq2 +factor2*xijfa*(Iqq2(i,j) +eij/t*Iqq4(i,j) ) + fqq2x =fqq2x +factor2*xijfa*(Iqq2x(i,j)+eij/t*Iqq4x(i,j)) + ! ------------------ + xijkf_x=x(i)*rho*uij(i,i)*qq2(i)*sig_ij(i,i)**5 /t/sig_ij(i,j)**3 & + *x(j)*rho*uij(j,j)*qq2(j)*sig_ij(j,j)**5 /t/sig_ij(i,k)**3 & + *3.0* uij(k,k)*qq2(k)*sig_ij(k,k)**5 /t/sig_ij(j,k)**3 + fqq3x = fqq3x + factor3*xijkf_x*Iqq3(i,j,k) + DO l = 1, ncomp + IF (parame(l,7) /= 0.0) THEN + xijkfa=x(i)*rho*uij(i,i)*qq2(i)*sig_ij(i,i)**5 /t/sig_ij(i,j)**3 & + *x(j)*rho*uij(j,j)*qq2(j)*sig_ij(j,j)**5 /t/sig_ij(i,l)**3 & + *x(l)*rho*uij(l,l)*qq2(l)*sig_ij(l,l)**5 /t/sig_ij(j,l)**3 + fqq3 =fqq3 + factor3 * xijkfa *Iqq3(i,j,l) + fqq3x =fqq3x + factor3 * xijkfa *Iqq3x(i,j,l) + END IF + END DO + END IF + END DO + END DO + + IF (fqq2 < -1.E-50 .AND. fqq3 /= 0.0 .AND. fqq2x /= 0.0 .AND. fqq3x /= 0.0) THEN + fqq_rk = fqq2* (fqq2*fqq2x - 2.0*fqq3*fqq2x+fqq2*fqq3x) / (fqq2-fqq3)**2 + END IF + +END SUBROUTINE PHI_QQ_GROSS + +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! + SUBROUTINE PHI_DQ_VRABEC_GROSS( k, z3_rk, fdq_rk ) +! + USE PARAMETERS, ONLY: PI, KBOL + USE EOS_VARIABLES, ONLY: nc, ncomp, uij, parame, mseg, sig_ij, rho, eta, x, t + USE EOS_CONSTANTS, ONLY: dqp2, dqp3, dqp4 + IMPLICIT NONE +! +! ---------------------------------------------------------------------- + INTEGER, INTENT(IN) :: k + REAL, INTENT(IN) :: z3_rk + REAL, INTENT(IN OUT) :: fdq_rk +! +! --- local variables--------------------------------------------------- + INTEGER :: i, j, l, m + + REAL :: factor2, factor3, z3 + REAL :: xijfa, xijkfa, xijfa_x, xijkf_x, eij + REAL :: fdq2, fdq3, fdq2x, fdq3x + REAL, DIMENSION(nc) :: my2dd, myfac, qq2, q_fac + REAL, DIMENSION(nc,nc) :: Idq2, Idq4, Idq2x, Idq4x + REAL, DIMENSION(nc,nc,nc) :: Idq3, Idq3x +! ---------------------------------------------------------------------- + + fdq_rk = 0.0 + z3 = eta + DO i=1,ncomp + my2dd(i) = (parame(i,6))**2 *1.E-49 / (uij(i,i)*KBOL*mseg(i)*sig_ij(i,i)**3 *1.E-30) + myfac(i) = parame(i,3)/t*parame(i,2)**4 *my2dd(i) + qq2(i) = (parame(i,7))**2 *1.E-69 / (uij(i,i)*kbol*mseg(i)*sig_ij(i,i)**5 *1.E-50) + q_fac(i) = parame(i,3)/t*parame(i,2)**4 *qq2(i) + END DO + + DO i = 1, ncomp + DO j = 1, ncomp + Idq2(i,j) = 0.0 + Idq4(i,j) = 0.0 + Idq2x(i,j) = 0.0 + Idq4x(i,j) = 0.0 + DO m = 0, 4 + Idq2(i,j) = Idq2(i,j) + dqp2(i,j,m)*z3**m + Idq4(i,j) = Idq4(i,j) + dqp4(i,j,m)*z3**m + Idq2x(i,j) = Idq2x(i,j) + dqp2(i,j,m)*REAL(m)*z3**(m-1) *z3_rk + Idq4x(i,j) = Idq4x(i,j) + dqp4(i,j,m)*REAL(m)*z3**(m-1) *z3_rk + END DO + DO l = 1, ncomp + Idq3(i,j,l) = 0.0 + Idq3x(i,j,l) = 0.0 + DO m = 0, 4 + Idq3(i,j,l) =Idq3(i,j,l) +dqp3(i,j,l,m)*z3**m + Idq3x(i,j,l)=Idq3x(i,j,l)+dqp3(i,j,l,m)*REAL(m)*z3**(m-1)*z3_rk + END DO + END DO + END DO + END DO + + factor2= -9.0/4.0*PI + factor3= PI**2 + + fdq2 = 0.0 + fdq3 = 0.0 + fdq2x = 0.0 + fdq3x = 0.0 + DO i = 1, ncomp + xijfa_x = x(i)*rho*( myfac(i)*q_fac(k) + myfac(k)*q_fac(i) ) / sig_ij(i,k)**5 + eij = (parame(i,3)*parame(k,3))**0.5 + fdq2x =fdq2x +factor2*xijfa_x*(Idq2(i,k)+eij/t*Idq4(i,k)) + DO j=1,ncomp + xijfa =x(i)*rho*myfac(i) * x(j)*rho*q_fac(j) /sig_ij(i,j)**5 + eij = (parame(i,3)*parame(j,3))**0.5 + fdq2= fdq2 +factor2*xijfa*(Idq2(i,j) +eij/t*Idq4(i,j) ) + fdq2x =fdq2x +factor2*xijfa*(Idq2x(i,j) +eij/t*Idq4x(i,j)) + !--------------------- + xijkf_x=x(i)*rho*x(j)*rho/(sig_ij(i,j)*sig_ij(i,k)*sig_ij(j,k))**2 & + *( myfac(i)*q_fac(j)*myfac(k) + myfac(i)*q_fac(k)*myfac(j) & + + myfac(k)*q_fac(i)*myfac(j) +myfac(i)*q_fac(j)*q_fac(k)*1.1937350 & + +myfac(i)*q_fac(k)*q_fac(j)*1.193735 & + +myfac(k)*q_fac(i)*q_fac(j)*1.193735 ) + fdq3x = fdq3x + factor3*xijkf_x*Idq3(i,j,k) + DO l = 1, ncomp + xijkfa=x(i)*rho*x(j)*rho*x(l)*rho/(sig_ij(i,j)*sig_ij(i,l)*sig_ij(j,l))**2 & + *( myfac(i)*q_fac(j)*myfac(l) & + +myfac(i)*q_fac(j)*q_fac(l)*1.193735 ) + fdq3 =fdq3 + factor3 * xijkfa *Idq3(i,j,l) + fdq3x =fdq3x + factor3 * xijkfa *Idq3x(i,j,l) + END DO + END DO + END DO + + IF (fdq2 < -1.E-50 .AND. fdq3 /= 0.0 .AND. fdq2x /= 0.0 .AND. fdq3x /= 0.0)THEN + + fdq_rk = fdq2* (fdq2*fdq2x - 2.0*fdq3*fdq2x+fdq2*fdq3x) / (fdq2-fdq3)**2 + + END IF + +END SUBROUTINE PHI_DQ_VRABEC_GROSS + + + +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! + SUBROUTINE P_NUMERICAL +! + USE EOS_VARIABLES + IMPLICIT NONE +! +!-----local variables------------------------------------------------- + REAL :: dzetdv, eta_0, dist, fact + REAL :: fres1, fres2, fres3, fres4, fres5 + REAL :: df_dr, df_drdr, pideal, dpiddz + REAL :: tfr_1, tfr_2, tfr_3, tfr_4, tfr_5 +!----------------------------------------------------------------------- + + +IF (eta > 0.1) THEN + fact = 1.0 +ELSE IF (eta <= 0.1 .AND. eta > 0.01) THEN + fact = 10.0 +ELSE + fact = 10.0 +END IF +dist = eta*3.d-3 *fact +! dist = eta*4.d-3 *fact +!***************************** +! fuer MC simulation: neues dist: +! dist = eta*5.d-3*fact + +eta_0 = eta +eta = eta_0 - 2.0*dist +CALL F_NUMERICAL +fres1 = fres +tfr_1 = tfr +eta = eta_0 - dist +CALL F_NUMERICAL +fres2 = fres +tfr_2 = tfr +eta = eta_0 + dist +CALL F_NUMERICAL +fres3 = fres +tfr_3 = tfr +eta = eta_0 + 2.0*dist +CALL F_NUMERICAL +fres4 = fres +tfr_4 = tfr +eta = eta_0 +CALL F_NUMERICAL +fres5 = fres +tfr_5 = tfr + +!--------------------------------------------------------- +! ptfr = (-tfr_4+8.0*tfr_3-8.0*tfr_2+tfr_1)/(12.0*dist) +! & *dzetdv*(KBOL*T)/1.E-30 +! ztfr =ptfr /( rho * (KBOL*t) / 1.E-30) +! ptfrdz = (-tfr_4+16.0*tfr_3-3.d1*tfr_5+16.0*tfr_2-tfr_1) +! & /(12.0*(dist**2 ))* dzetdv*(KBOL*T)/1.E-30 +! & + (-tfr_4+8.0*tfr_3-8.0*tfr_2+tfr_1) +! & /(12.0*dist) * 2.0 *eta*6.0/PI/D +! & *(KBOL*T)/1.E-30 +! ztfrdz=ptfrdz/( rho*(kbol*T)/1.E-30 ) - ztfr/eta +! write (*,*) eta,ztfr,ztfrdz + +! dtfr_dr = (-tfr_4+8.0*tfr_3-8.0*tfr_2+tfr_1)/(12.0*dist) +! write (*,*) eta,dtfr_dr +! stop +!--------------------------------------------------------- + +df_dr = (-fres4+8.0*fres3-8.0*fres2+fres1) / (12.0*dist) +df_drdr = (-fres4+16.0*fres3-3.d1*fres5+16.0*fres2-fres1) & + /(12.0*(dist**2 )) + + +dzetdv = eta*rho + +pges = (-fres4+8.0*fres3-8.0*fres2+fres1) & + /(12.0*dist) *dzetdv*(kbol*t)/1.E-30 + +dpiddz = 1.0/z3t*(kbol*t)/1.E-30 +pgesdz = (-fres4+16.0*fres3-3.d1*fres5+16.0*fres2-fres1) & + /(12.0*(dist**2 ))* dzetdv*(kbol*t)/1.E-30 & + + (-fres4+8.0*fres3-8.0*fres2+fres1) /(12.0*dist) * 2.0 *rho & + *(kbol*t)/1.E-30 + dpiddz + +pgesd2 = (fres4-2.0*fres3+2.0*fres2-fres1) /(2.0*dist**3 ) & + * dzetdv*(kbol*t)/1.E-30 & + + (-fres4+16.0*fres3-3.d1*fres5+16.0*fres2-fres1) /(12.0*(dist**2 )) & + * 4.0 *rho *(kbol*t)/1.E-30 + (-fres4+8.0*fres3-8.0*fres2+fres1) & + /(12.0*dist) * 2.0 /z3t *(kbol*t)/1.E-30 +pgesd3 = (fres4-4.0*fres3+6.0*fres5-4.0*fres2+fres1) /(dist**4 ) & + * dzetdv*(kbol*t)/1.E-30 + (fres4-2.0*fres3+2.0*fres2-fres1) & + /(2.0*dist**3 ) * 6.0 *rho *(kbol*t)/1.E-30 & + + (-fres4+16.0*fres3-3.d1*fres5+16.0*fres2-fres1) & + /(12.0*dist**2 )* 6.0 /z3t *(kbol*t)/1.E-30 + +!------------------p ideal------------------------------------ +pideal = rho * (kbol*t) / 1.E-30 + +!------------------p summation, p comes out in Pa ------------ +pges = pideal + pges + +END SUBROUTINE P_NUMERICAL + + +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! + SUBROUTINE H_numerical +! + USE PARAMETERS, ONLY: RGAS + USE EOS_VARIABLES + IMPLICIT NONE +! +!--------------------------------------------------------------------- + REAL :: dist, fact, rho_0 + REAL :: fres1,fres2,fres3,fres4,fres5 + REAL :: f_1, f_2, f_3, f_4 + REAL :: cv_res, t_tmp, zges + REAL :: f_dt, f_dtdt, f_dr, f_drdr, f_drdt +!----------------------------------------------------------------------- + + +CALL PERTURBATION_PARAMETER +rho_0 = eta/z3t + + +fact = 1.0 +dist = t * 100.E-5 * fact + +t_tmp = t + +t = t_tmp - 2.0*dist +CALL PERTURBATION_PARAMETER +eta = z3t*rho_0 +CALL F_NUMERICAL +fres1 = fres +t = t_tmp - dist +CALL PERTURBATION_PARAMETER +eta = z3t*rho_0 +CALL F_NUMERICAL +fres2 = fres +t = t_tmp + dist +CALL PERTURBATION_PARAMETER +eta = z3t*rho_0 +CALL F_NUMERICAL +fres3 = fres +t = t_tmp + 2.0*dist +CALL PERTURBATION_PARAMETER +eta = z3t*rho_0 +CALL F_NUMERICAL +fres4 = fres +t = t_tmp +CALL PERTURBATION_PARAMETER +eta = z3t*rho_0 +CALL F_NUMERICAL +fres5 = fres +! *(KBOL*T)/1.E-30 + +zges = (p * 1.E-30)/(kbol*t*rho_0) + + +f_dt = (-fres4+8.0*fres3-8.0*fres2+fres1)/(12.0*dist) +f_dtdt = (-fres4+16.0*fres3-3.d1*fres5+16.0*fres2-fres1) /(12.0*(dist**2 )) + +s_res = (- f_dt -fres/t)*RGAS*t + RGAS * LOG(zges) +h_res = ( - t*f_dt + zges-1.0 ) * RGAS*t +cv_res = -( t*f_dtdt + 2.0*f_dt ) * RGAS*t + + + +t = t_tmp - 2.0*dist +CALL PERTURBATION_PARAMETER +eta = z3t*rho_0 +CALL P_NUMERICAL +f_1 = pges/(eta*rho_0*(KBOL*T)/1.E-30) + +t = t_tmp - dist +CALL PERTURBATION_PARAMETER +eta = z3t*rho_0 +CALL P_NUMERICAL +f_2 = pges/(eta*rho_0*(KBOL*T)/1.E-30) + +t = t_tmp + dist +CALL PERTURBATION_PARAMETER +eta = z3t*rho_0 +CALL P_NUMERICAL +f_3 = pges/(eta*rho_0*(KBOL*T)/1.E-30) + +t = t_tmp + 2.0*dist +CALL PERTURBATION_PARAMETER +eta = z3t*rho_0 +CALL P_NUMERICAL +f_4 = pges/(eta*rho_0*(KBOL*T)/1.E-30) + +t = t_tmp +CALL PERTURBATION_PARAMETER +eta = z3t*rho_0 +CALL P_NUMERICAL + +f_dr = pges / (eta*rho_0*(KBOL*T)/1.E-30) +f_drdr = pgesdz/ (eta*rho_0*(KBOL*T)/1.E-30) - f_dr*2.0/eta - 1.0/eta**2 + +f_drdt = ( - f_4 + 8.0*f_3 - 8.0*f_2 + f_1 ) / ( 12.0*dist ) + +cp_res = cv_res - RGAS + RGAS*( zges + eta*t*f_drdt)**2 / (1.0 + 2.0*eta*f_dr + eta**2 *f_drdr) +! write (*,*) cv_res,cp_res,eta + + +END SUBROUTINE H_numerical + + + + + + + + + + + +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! + SUBROUTINE F_POLAR ( fdd, fqq, fdq ) +! + USE EOS_VARIABLES, ONLY: ncomp, parame, dd_term, qq_term, dq_term + IMPLICIT NONE +! +! ---------------------------------------------------------------------- + REAL, INTENT(OUT) :: fdd, fqq, fdq +! +! --- local variables--------------------------------------------------- + INTEGER :: dipole + INTEGER :: quadrupole + INTEGER :: dipole_quad +! ---------------------------------------------------------------------- + + fdd = 0.0 + fqq = 0.0 + fdq = 0.0 + + dipole = 0 + quadrupole = 0 + dipole_quad = 0 + IF ( SUM( parame(1:ncomp,6) ) /= 0.0 ) dipole = 1 + IF ( SUM( parame(1:ncomp,7) ) /= 0.0 ) quadrupole = 1 + IF ( dipole == 1 .AND. quadrupole == 1 ) dipole_quad = 1 + + ! -------------------------------------------------------------------- + ! dipole-dipole term + ! -------------------------------------------------------------------- + IF (dipole == 1) THEN + + IF (dd_term == 'GV') CALL F_DD_GROSS_VRABEC( fdd ) + ! IF (dd_term == 'SF') CALL F_DD_SAAGER_FISCHER( k ) + IF (dd_term /= 'GV' .AND. dd_term /= 'SF') write (*,*) 'specify dipole term !' + + ENDIF + + ! -------------------------------------------------------------------- + ! quadrupole-quadrupole term + ! -------------------------------------------------------------------- + IF (quadrupole == 1) THEN + + !IF (qq_term == 'SF') CALL F_QQ_SAAGER_FISCHER( k ) + IF (qq_term == 'JG') CALL F_QQ_GROSS( fqq ) + IF (qq_term /= 'JG' .AND. qq_term /= 'SF') write (*,*) 'specify quadrupole term !' + + ENDIF + + ! -------------------------------------------------------------------- + ! dipole-quadrupole cross term + ! -------------------------------------------------------------------- + IF (dipole_quad == 1) THEN + + IF (dq_term == 'VG') CALL F_DQ_VRABEC_GROSS( fdq ) + IF (dq_term /= 'VG' ) write (*,*) 'specify DQ-cross term !' + + ENDIF + +END SUBROUTINE F_POLAR + + + +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! SUBROUTINE PRESSURE_SPINODAL +! +! iterates the density until the derivative of pressure 'pges' to +! density is equal to zero. A Newton-scheme is used for determining +! the root to the objective function. +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! + SUBROUTINE PRESSURE_SPINODAL +! + USE BASIC_VARIABLES, ONLY: num + USE EOS_VARIABLES + IMPLICIT NONE +! +! ---------------------------------------------------------------------- + INTEGER :: i, max_i + REAL :: eta_iteration + REAL :: error, acc_i, delta_eta +! ---------------------------------------------------------------------- + +acc_i = 1.d-6 +max_i = 30 + +i = 0 +eta_iteration = eta_start + +! ---------------------------------------------------------------------- +! iterate density until p_calc = p +! ---------------------------------------------------------------------- + +error = acc_i + 1.0 +DO WHILE ( ABS(error) > acc_i .AND. i < max_i ) + + i = i + 1 + eta = eta_iteration + + IF ( num == 0 ) THEN + CALL P_EOS + ELSE IF ( num == 1 ) THEN + CALL P_NUMERICAL + ELSE IF ( num == 2 ) THEN + WRITE(*,*) 'CRITICAL RENORM NOT INCLUDED YET' + !!CALL F_EOS_RN + ELSE + write (*,*) 'define calculation option (num)' + END IF + + error = pgesdz + + delta_eta = error/ pgesd2 + IF ( delta_eta > 0.02 ) delta_eta = 0.02 + IF ( delta_eta < -0.02 ) delta_eta = -0.02 + + eta_iteration = eta_iteration - delta_eta + ! write (*,'(a,i3,3G18.10)') 'iter',i, error, eta_iteration, pgesdz + + IF (eta_iteration > 0.9) eta_iteration = 0.5 + IF (eta_iteration <= 0.0) eta_iteration = 1.E-16 + +END DO + +eta = eta_iteration + +END SUBROUTINE PRESSURE_SPINODAL + + +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! + SUBROUTINE F_IDEAL_GAS ( fid ) +! + USE EOS_VARIABLES, ONLY: nc, ncomp, t, x, rho, PI, KBOL, NAv + IMPLICIT NONE +! +!--------------------------------------------------------------------- + REAL, INTENT(IN OUT) :: fid +!--------------------------------------------------------------------- + INTEGER :: i + REAL, DIMENSION(nc) :: rhoi +!---------------------------------------------------------------------- + + !h_Planck = 6.62606896E-34 ! Js + DO i = 1, ncomp + rhoi(i) = x(i) * rho + ! debroglie(i) = h_Planck *1d10 & ! in units Angstrom + ! *SQRT( 1.0 / (2.0*PI *1.0 / NAv / 1000.0 * KBOL*T) ) + ! ! *SQRT( 1.0 / (2.0*PI *mm(i) /NAv/1000.0 * KBOL*T) ) + ! fid = fid + x(i) * ( LOG(rhoi(i)*debroglie(i)**3) - 1.0 ) + fid = fid + x(i) * ( LOG(rhoi(i)) - 1.0 ) + END DO + + END SUBROUTINE F_IDEAL_GAS + +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! + SUBROUTINE F_HARD_SPHERE ( m_mean2, fhs ) +! + USE EOS_VARIABLES, ONLY: z0t, z1t, z2t, z3t, eta, rho + IMPLICIT NONE +! +!--------------------------------------------------------------------- + REAL, INTENT(IN) :: m_mean2 + REAL, INTENT(IN OUT) :: fhs +!--------------------------------------------------------------------- + REAL :: z0, z1, z2, z3, zms +!---------------------------------------------------------------------- + + rho = eta / z3t + z0 = z0t * rho + z1 = z1t * rho + z2 = z2t * rho + z3 = z3t * rho + zms = 1.0 - z3 + + fhs= m_mean2*( 3.0*z1*z2/zms + z2**3 /z3/zms/zms + (z2**3 /z3/z3-z0)*LOG(zms) )/z0 + + + END SUBROUTINE F_HARD_SPHERE + +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! + SUBROUTINE F_CHAIN_TPT1 ( fhc ) +! + USE EOS_VARIABLES, ONLY: nc, ncomp, mseg, x, z0t, z1t, z2t, z3t, & + rho, eta, dij_ab, gij + IMPLICIT NONE +! +!--------------------------------------------------------------------- + REAL, INTENT(IN OUT) :: fhc +!--------------------------------------------------------------------- + INTEGER :: i, j + REAL :: z0, z1, z2, z3, zms +!--------------------------------------------------------------------- + + rho = eta / z3t + z0 = z0t * rho + z1 = z1t * rho + z2 = z2t * rho + z3 = z3t * rho + zms = 1.0 - z3 + + DO i = 1, ncomp + DO j = 1, ncomp + gij(i,j) = 1.0/zms + 3.0*dij_ab(i,j)*z2/zms/zms + 2.0*(dij_ab(i,j)*z2)**2 / zms**3 + END DO + END DO + + fhc = 0.0 + DO i = 1, ncomp + fhc = fhc + x(i) *(1.0- mseg(i)) *LOG(gij(i,i)) + END DO + + END SUBROUTINE F_CHAIN_TPT1 + + +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! + SUBROUTINE F_CHAIN_TPT_D ( fhc ) +! + USE EOS_VARIABLES, ONLY: nc, ncomp, mseg, x, z0t, z1t, z2t, z3t, rho, eta, & + dhs, mseg, dij_ab, gij + IMPLICIT NONE +! +!--------------------------------------------------------------------- + REAL, INTENT(OUT) :: fhc +!--------------------------------------------------------------------- + INTEGER :: i, j + REAL, DIMENSION(nc) :: gij_hd + REAL :: z0, z1, z2, z3, zms +!--------------------------------------------------------------------- + + rho = eta / z3t + z0 = z0t * rho + z1 = z1t * rho + z2 = z2t * rho + z3 = z3t * rho + zms = 1.0 - z3 + + DO i = 1, ncomp + DO j = 1, ncomp + gij(i,j) = 1.0/zms + 3.0*dij_ab(i,j)*z2/zms/zms + 2.0*(dij_ab(i,j)*z2)**2 / zms**3 + END DO + END DO + + DO i = 1, ncomp + gij_hd(i) = 1.0/(2.0*zms) + 3.0*dij_ab(i,i)*z2 / zms**2 + END DO + + fhc = 0.0 + DO i = 1, ncomp + IF ( mseg(i) >= 2.0 ) THEN + fhc = fhc - x(i) * ( mseg(i)/2.0 * LOG( gij(i,i) ) + ( mseg(i)/2.0 - 1.0 ) * LOG( gij_hd(i)) ) + ELSE + fhc = fhc + x(i) * ( 1.0 - mseg(i) ) * LOG( gij(i,i) ) + END IF + END DO + + END SUBROUTINE F_CHAIN_TPT_D + + +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! + SUBROUTINE F_CHAIN_HU_LIU ( fhc ) +! + USE EOS_VARIABLES, ONLY: nc, ncomp, mseg, x, rho, eta + IMPLICIT NONE +! +! This subroutine calculates the hard chain contribution of the TPT-Liu-Hu Eos. +!--------------------------------------------------------------------- + REAL, INTENT(OUT) :: fhc +!--------------------------------------------------------------------- + REAL :: a2, b2, c2, a3, b3, c3 + REAL :: a20, b20, c20, a30, b30, c30 + REAL :: sum1, sum2, am, bm, cm + REAL :: zms +!--------------------------------------------------------------------- + + zms = 1.0 - eta + + sum1 = SUM( x(1:ncomp)*(mseg(1:ncomp)-1.0) ) + sum2 = SUM( x(1:ncomp)/mseg(1:ncomp)*(mseg(1:ncomp)-1.0)*(mseg(1:ncomp)-2.0) ) + + a2 = 0.45696 + a3 = -0.74745 + b2 = 2.10386 + b3 = 3.49695 + c2 = 1.75503 + c3 = 4.83207 + a20 = - a2 + b2 - 3.0*c2 + b20 = - a2 - b2 + c2 + c20 = c2 + a30 = - a3 + b3 - 3.0*c3 + b30 = - a3 - b3 + c3 + c30 = c3 + am = (3.0 + a20) * sum1 + a30 * sum2 + bm = (1.0 + b20) * sum1 + b30 * sum2 + cm = (1.0 + c20) * sum1 + c30 * sum2 + + fhc = - ( (am*eta - bm) / (2.0*zms) + bm/2.0/zms**2 - cm *LOG(ZMS) ) + + + END SUBROUTINE F_CHAIN_HU_LIU + +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! + SUBROUTINE F_CHAIN_HU_LIU_RC ( fhs, fhc ) +! + USE EOS_VARIABLES, ONLY: mseg, chiR, eta + IMPLICIT NONE +! +! This subroutine calculates the hard chain contribution of the TPT-Liu-Hu Eos. +!--------------------------------------------------------------------- + REAL, INTENT(IN) :: fhs + REAL, INTENT(OUT) :: fhc +!--------------------------------------------------------------------- + REAL :: a2, b2, c2, a3, b3, c3 + REAL :: para1,para2,para3,para4 + REAL :: aLH,bLH,cLH +!--------------------------------------------------------------------- + +! This routine is only for pure components + + a2 = 0.45696 + b2 = 2.10386 + c2 = 1.75503 + + para1 = -0.74745 + para2 = 0.299154629727814 + para3 = 1.087271036653154 + para4 = -0.708979110326831 + a3 = para1 + para2*chiR(1) + para3*chiR(1)**2 + para4*chiR(1)**3 + b3 = 3.49695 - (3.49695 + 0.317719074806190)*chiR(1) + c3 = 4.83207 - (4.83207 - 3.480163780334421)*chiR(1) + + aLH = mseg(1)*(1.0 + ((mseg(1)-1.0)/mseg(1))*a2 + ((mseg(1)-1.0)/mseg(1))*((mseg(1)-2.0)/mseg(1))*a3 ) + bLH = mseg(1)*(1.0 + ((mseg(1)-1.0)/mseg(1))*b2 + ((mseg(1)-1.0)/mseg(1))*((mseg(1)-2.0)/mseg(1))*b3 ) + cLH = mseg(1)*(1.0 + ((mseg(1)-1.0)/mseg(1))*c2 + ((mseg(1)-1.0)/mseg(1))*((mseg(1)-2.0)/mseg(1))*c3 ) + + fhc = ((3.0 + aLH - bLH + 3.0*cLH)*eta - (1.0 + aLH + bLH - cLH)) / (2.0*(1.0-eta)) + & + (1.0 + aLH + bLH - cLH) / ( 2.0*(1.0-eta)**2 ) + (cLH - 1.0)*LOG(1.0-eta) + + fhc = fhc - fhs + + END SUBROUTINE F_CHAIN_HU_LIU_RC + + + + +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! + SUBROUTINE F_DISP_PCSAFT ( fdsp ) +! + USE EOS_VARIABLES, ONLY: PI, rho, eta, z0t, apar, bpar, order1, order2 + IMPLICIT NONE +! +!--------------------------------------------------------------------- + REAL, INTENT(IN OUT) :: fdsp +!--------------------------------------------------------------------- + INTEGER :: m + REAL :: I1, I2, c1_con, z3, zms, m_mean +!--------------------------------------------------------------------- + + z3 = eta + zms = 1.0 - eta + m_mean = z0t / ( PI / 6.0 ) + + I1 = 0.0 + I2 = 0.0 + DO m = 0, 6 + I1 = I1 + apar(m) * z3**m + I2 = I2 + bpar(m) * z3**m + END DO + + c1_con= 1.0/ ( 1.0 + m_mean*(8.0*z3-2.0*z3**2 )/zms**4 & + + (1.0-m_mean)*( 20.0*z3-27.0*z3**2 +12.0*z3**3 -2.0*z3**4 )/(zms*(2.0-z3))**2 ) + + fdsp = -2.0*PI*rho*I1*order1 - PI*rho*c1_con*m_mean*I2*order2 + + END SUBROUTINE F_DISP_PCSAFT + +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! + SUBROUTINE F_DISP_CKSAFT ( fdsp ) +! + USE EOS_VARIABLES, ONLY: nc, ncomp, PI, TAU, t, rho, eta, x, z0t, mseg, vij, uij, parame, um + USE EOS_CONSTANTS, ONLY: DNM + IMPLICIT NONE +! +!--------------------------------------------------------------------- + REAL, INTENT(IN OUT) :: fdsp +!--------------------------------------------------------------------- + INTEGER :: i, j, n, m + REAL :: zmr, nmr, m_mean +!--------------------------------------------------------------------- + + m_mean = z0t / ( PI / 6.0 ) + + DO i = 1, ncomp + DO j = 1, ncomp + vij(i,j)=(0.5*((parame(i,2)*(1.0-0.12 *EXP(-3.0*parame(i,3)/t))**3 )**(1.0/3.0) & + +(parame(j,2)*(1.0-0.12 *EXP(-3.0*parame(j,3)/t))**3 )**(1.0/3.0)))**3 + END DO + END DO + zmr = 0.0 + nmr = 0.0 + DO i = 1, ncomp + DO j = 1, ncomp + zmr = zmr + x(i)*x(j)*mseg(i)*mseg(j)*vij(i,j)*uij(i,j) + nmr = nmr + x(i)*x(j)*mseg(i)*mseg(j)*vij(i,j) + END DO + END DO + um = zmr / nmr + fdsp = 0.0 + DO n = 1, 4 + DO m = 1, 9 + fdsp = fdsp + DNM(n,m) * (um/t)**n *(eta/TAU)**m + END DO + END DO + fdsp = m_mean * fdsp + + + END SUBROUTINE F_DISP_CKSAFT + +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! + SUBROUTINE F_ASSOCIATION ( eps_kij, k_kij, fhb ) +! + USE EOS_VARIABLES, ONLY: nc, nsite, ncomp, t, z0t, z1t, z2t, z3t, rho, eta, x, & + parame, sig_ij, dij_ab, gij, nhb_typ, mx, nhb_no + IMPLICIT NONE +! +!--------------------------------------------------------------------- + REAL, INTENT(IN) :: eps_kij, k_kij + REAL, INTENT(IN OUT) :: fhb +!--------------------------------------------------------------------- + LOGICAL :: assoc + INTEGER :: i, j, k, l, no, ass_cnt, max_eval + REAL, DIMENSION(nc,nc) :: kap_hb + REAL, DIMENSION(nc,nc,nsite,nsite) :: eps_hb + REAL, DIMENSION(nc,nsite,nc,nsite) :: delta + REAL, DIMENSION(nc,nsite) :: mx_itr + REAL :: err_sum, sum0, amix, tol, ass_s1, ass_s2 + REAL :: z0, z1, z2, z3, zms +!--------------------------------------------------------------------- + + assoc = .false. + DO i = 1,ncomp + IF (NINT(parame(i,12)) /= 0) assoc = .true. + END DO + IF (assoc) THEN + + rho = eta / z3t + z0 = z0t * rho + z1 = z1t * rho + z2 = z2t * rho + z3 = z3t * rho + zms = 1.0 - z3 + + DO i = 1, ncomp + DO j = 1, ncomp + gij(i,j) = 1.0/zms + 3.0*dij_ab(i,j)*z2/zms/zms + 2.0*(dij_ab(i,j)*z2)**2 / zms**3 + END DO + END DO + + + DO i = 1, ncomp + IF ( NINT(parame(i,12)) /= 0 ) THEN + nhb_typ(i) = NINT( parame(i,12) ) + kap_hb(i,i) = parame(i,13) + no = 0 + DO k = 1,nhb_typ(i) + DO l = 1,nhb_typ(i) + eps_hb(i,i,k,l) = parame(i,(14+no)) + no = no + 1 + END DO + END DO + DO k = 1,nhb_typ(i) + nhb_no(i,k) = parame(i,(14+no)) + no = no + 1 + END DO + ELSE + nhb_typ(i) = 0 + kap_hb(i,i)= 0.0 + DO k = 1,nsite + DO l = 1,nsite + eps_hb(i,i,k,l) = 0.0 + END DO + END DO + END IF + END DO + + DO i = 1,ncomp + DO j = 1,ncomp + IF ( i /= j .AND. (nhb_typ(i) /= 0.AND.nhb_typ(j) /= 0) ) THEN + ! kap_hb(i,j)= (kap_hb(i,i)+kap_hb(j,j))/2.0 + ! kap_hb(i,j)= ( ( kap_hb(i,i)**(1.0/3.0) + kap_hb(j,j)**(1.0/3.0) )/2.0 )**3 + kap_hb(i,j) = (kap_hb(i,i)*kap_hb(j,j))**0.5 & + *((parame(i,2)*parame(j,2))**3 )**0.5 & + / (0.5*(parame(i,2)+parame(j,2)))**3 + kap_hb(i,j)= kap_hb(i,j)*(1.0-k_kij) + DO k = 1,nhb_typ(i) + DO l = 1,nhb_typ(j) + IF ( k /= l .AND. nhb_typ(i) >= 2 .AND. nhb_typ(j) >= 2 ) THEN + eps_hb(i,j,k,l) = (eps_hb(i,i,k,l)+eps_hb(j,j,l,k))/2.0 + ! eps_hb(i,j,k,l) = (eps_hb(i,i,k,l)*eps_hb(j,j,l,k))**0.5 + eps_hb(i,j,k,l) = eps_hb(i,j,k,l)*(1.0-eps_kij) + ELSE IF ( nhb_typ(i) == 1 .AND. l > k ) THEN + eps_hb(i,j,k,l) = (eps_hb(i,i,k,k)+eps_hb(j,j,l,k))/2.0 + eps_hb(j,i,l,k) = (eps_hb(i,i,k,k)+eps_hb(j,j,l,k))/2.0 + eps_hb(i,j,k,l) = eps_hb(i,j,k,l)*(1.0-eps_kij) + eps_hb(j,i,l,k) = eps_hb(j,i,l,k)*(1.0-eps_kij) + END IF + END DO + END DO + END IF + END DO + END DO + +!-----setting the self-association to zero for ionic compounds------ + DO i = 1,ncomp + IF ( parame(i,10) /= 0) kap_hb(i,i)=0.0 + DO j = 1,ncomp + IF ( parame(i,10) /= 0 .AND. parame(j,10) /= 0 ) kap_hb(i,j) = 0.0 + END DO + END DO + ! kap_hb(1,2)=0.050 + ! kap_hb(2,1)=0.050 + ! eps_hb(2,1,1,1)=465.0 + ! eps_hb(1,2,1,1)=465.0 + ! nhb_typ(1) = 1 + ! nhb_typ(2) = 1 + ! nhb_no(1,1)= 1.0 + ! nhb_no(2,1)= 1.0 + + + DO i = 1, ncomp + DO k = 1, nhb_typ(i) + DO j = 1, ncomp + DO l = 1, nhb_typ(j) + delta(i,k,j,l)=gij(i,j)*kap_hb(i,j)*(EXP(eps_hb(i,j,k,l)/t)-1.0) *sig_ij(i,j)**3 +!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! +! IF ((i+j).EQ.3) delta(i,k,j,l)=94.0 +!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! + END DO + END DO + IF ( mx(i,k) == 0.0 ) mx(i,k) = 1.0 + END DO + END DO + +!------constants for Iteration --------------------------------------- + amix = 0.7 + tol = 1.E-10 + IF (eta < 0.2) tol = 1.E-11 + IF (eta < 0.01) tol = 1.E-14 + max_eval = 200 + +! --- Iterate over all components and all sites ------------------------ + ass_cnt = 0 + iterate_TPT1: DO + + ass_cnt = ass_cnt + 1 + + DO i = 1, ncomp + DO k = 1, nhb_typ(i) + sum0 = 0.0 + DO j = 1, ncomp + DO l = 1, nhb_typ(j) + sum0 = sum0 + x(j)* mx(j,l)*nhb_no(j,l) *delta(i,k,j,l) + END DO + END DO + mx_itr(i,k) = 1.0 / (1.0 + sum0*rho) + END DO + END DO + + err_sum = 0.0 + DO i = 1, ncomp + DO k = 1, nhb_typ(i) + err_sum = err_sum + ABS( mx_itr(i,k) - mx(i,k) ) ! / ABS(mx_itr(i,k)) + mx(i,k) = mx_itr(i,k) * amix + mx(i,k) * (1.0 - amix) + IF ( mx(i,k) <= 0.0 ) mx(i,k)=1.E-50 + IF ( mx(i,k) > 1.0 ) mx(i,k)=1.0 + END DO + END DO + + IF ( err_sum <= tol .OR. ass_cnt >= max_eval ) THEN + IF ( ass_cnt >= max_eval ) WRITE(*,*) 'F_NUMERICAL: Max_eval violated = ',err_sum,tol + EXIT iterate_TPT1 + END IF + + END DO iterate_TPT1 + + DO i = 1, ncomp + ass_s1 = 0.0 + ass_s2 = 0.0 + DO k = 1, nhb_typ(i) + ass_s1 = ass_s1 + nhb_no(i,k) * ( 1.0 - mx(i,k) ) + ass_s2 = ass_s2 + nhb_no(i,k) * LOG(mx(i,k)) + END DO + fhb = fhb + x(i) * ( ass_s2 + ass_s1/2.0 ) + END DO + + END IF + + END SUBROUTINE F_ASSOCIATION + + +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! + SUBROUTINE F_ION_DIPOLE_TBH ( fhend ) +! + USE EOS_VARIABLES, ONLY: nc, PI, KBOL, NAv, ncomp, t, rho, eta, x, z0t, parame, uij, sig_ij + IMPLICIT NONE +! +!--------------------------------------------------------------------- + REAL, INTENT(IN OUT) :: fhend +!--------------------------------------------------------------------- + INTEGER :: i, dipole, ions + REAL :: m_mean + REAL :: fh32, fh2, fh52, fh3 + REAL :: e_elem, eps_cc0, rho_sol, dielec + REAL :: polabil, ydd, kappa, x_dipol, x_ions + REAL, DIMENSION(nc) :: my2dd, z_ii, e_cd, x_dd, x_ii + REAL :: sig_c, sig_d, sig_cd, r_s + REAL :: I0cc, I1cc, I2cc, Icd, Idd + REAL :: Iccc, Iccd, Icdd, Iddd +!--------------------------------------------------------------------- + +m_mean = z0t / ( PI / 6.0 ) + +!----------------Dieletric Constant of Water-------------------------- +e_elem = 1.602189246E-19 ! in Unit [Coulomb] +eps_cc0 = 8.854187818E-22 ! in Unit [Coulomb**2 /(J*Angstrom)] +! Correlation of M. Uematsu and E. U. Frank +! (Static Dieletric Constant of Water and Steam) +! valid range of conditions 273,15 K <=T<= 823,15 K +! and density <= 1150 kg/m3 (i.e. 0 <= p <= 500 MPa) +rho_sol = rho * 18.015 * 1.E27/ NAv +rho_sol = rho_sol/1000.0 +dielec = 1.0+(7.62571/(t/293.15))*rho_sol +(2.44E2/(t/293.15)-1.41E2 & + + 2.78E1*(t/293.15))*rho_sol**2 & + + (-9.63E1/(t/293.15)+4.18E1*(t/293.15) & + - 1.02E1*(t/293.15)**2 )*rho_sol**3 +(-4.52E1/(t/293.15)**2 & + + 8.46E1/(t/293.15)-3.59E1)*rho_sol**4 + + +! !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! + +dielec = 1.0 + +! !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! + + +!----------------Dipole-Ion Term----------------------------------- +dipole = 0 +ions = 0 +fhend = 0.0 +DO i = 1, ncomp + IF ( parame(i,6) /= 0.0 .AND. uij(i,i) /= 0.0 .AND. x(i) > 0.0 ) THEN + my2dd(i) = (parame(i,6))**2 *1.E-49 / (uij(i,i)*KBOL*sig_ij(i,i)**3 *1.E-30) + dipole = 1 + ELSE + my2dd(i) = 0.0 + END IF + + z_ii(i) = parame(i,10) + IF ( z_ii(i) /= 0.0 .AND. uij(i,i) /= 0.0 .AND. x(i) > 0.0 ) THEN + e_cd(i) = ( parame(i,10)*e_elem* 1.E5 / SQRT(1.11265005) )**2 & + / ( uij(i,i)*kbol*sig_ij(i,i)*1.E-10 ) + ions = 1 + ELSE + e_cd(i) = 0.0 + END IF +END DO + + +IF ( dipole == 1 .AND. ions == 1 ) THEN + + ydd = 0.0 + kappa = 0.0 + x_dipol = 0.0 + x_ions = 0.0 + polabil = 0.0 + DO i = 1, ncomp + ydd = ydd + x(i)*(parame(i,6))**2 *1.E-49/ (kbol*t*1.E-30) + kappa = kappa + x(i) & + *(parame(i,10)*e_elem* 1.E5/SQRT(1.11265005))**2 /(KBOL*t*1.E-10) + IF (parame(i,10) /= 0.0) THEN + x_ions = x_ions + x(i) + ELSE + polabil = polabil + 4.0*PI*x(i)*rho*1.4573 *1.E-30 & + / (sig_ij(3,3)**3 *1.E-30) + END IF + IF (parame(i,6) /= 0.0) x_dipol= x_dipol+ x(i) + END DO + ydd = ydd * 4.0/9.0 * PI * rho + kappa = SQRT( 4.0 * PI * rho * kappa ) + + fh2 = 0.0 + sig_c = 0.0 + sig_d = 0.0 + DO i=1,ncomp + x_ii(i) = 0.0 + x_dd(i) = 0.0 + IF(parame(i,10) /= 0.0 .AND. x_ions /= 0.0) x_ii(i) = x(i)/x_ions + IF(parame(i,6) /= 0.0 .AND. x_dipol /= 0.0) x_dd(i) = x(i)/x_dipol + sig_c = sig_c + x_ii(i)*parame(i,2) + sig_d = sig_d + x_dd(i)*parame(i,2) + END DO + sig_cd = 0.5 * (sig_c + sig_d) + + r_s = 0.0 + ! DO i=1,ncomp + ! r_s=r_s + rho * x(i) * dhs(i)**3 + ! END DO + r_s = eta*6.0 / PI / m_mean + + I0cc = - (1.0 + 0.97743 * r_s + 0.05257*r_s*r_s) & + /(1.0 + 1.43613 * r_s + 0.41580*r_s*r_s) + ! I1cc = - (10.0 - 2.0*z3 + z3*z3) /20.0/(1.0 + 2.0*z3) + I1cc = - (10.0 - 2.0*r_s*pi/6.0 + r_s*r_s*pi/6.0*pi/6.0) & + /20.0/(1.0 + 2.0*r_s*pi/6.0) +!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! + ! I2cc = + (z3-4.0)*(z3*z3+2.0) /24.0/(1.0+2.0*z3) + ! relation of Stell and Lebowitz + I2cc = -0.33331+0.7418*r_s - 1.2047*r_s*r_s & + + 1.6139*r_s**3 - 1.5487*r_s**4 + 0.6626*r_s**5 +!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! + Icd = (1.0 + 0.79576 *r_s + 0.104556 *r_s*r_s) & + /(1.0 + 0.486704*r_s - 0.0222903*r_s*r_s) + Idd = (1.0 + 0.18158*r_s - 0.11467*r_s*r_s) & + /3.0/(1.0 - 0.49303*r_s + 0.06293*r_s*r_s) + Iccc= 3.0*(1.0 - 1.05560*r_s + 0.26591*r_s*r_s) & + /2.0/(1.0 + 0.53892*r_s - 0.94236*r_s*r_s) + Iccd= 11.0*(1.0 + 2.25642 *r_s + 0.05679 *r_s*r_s) & + /6.0/(1.0 + 2.64178 *r_s + 0.79783 *r_s*r_s) + Icdd= 0.94685*(1.0 + 2.97323 *r_s + 3.11931 *r_s*r_s) & + /(1.0 + 2.70186 *r_s + 1.22989 *r_s*r_s) + Iddd= 5.0*(1.0 + 1.12754*r_s + 0.56192*r_s*r_s) & + /24.0/(1.0 - 0.05495*r_s + 0.13332*r_s*r_s) + + IF ( sig_c <= 0.0 ) WRITE (*,*) 'error in Henderson ion term' + + fh32= - kappa**3 /(12.0*pi*rho) + fh2 = - 3.0* kappa**2 * ydd*Icd /(8.0*pi*rho) / sig_cd & + - kappa**4 *sig_c/(16.0*pi*rho)*I0cc + IF (sig_d /= 0.0) fh2 = fh2 - 27.0* ydd * ydd*Idd & + /(8.0*pi*rho) / sig_d**3 + fh52= (3.0*kappa**3 * ydd + kappa**5 *sig_c**2 *I1cc) & + /(8.0*pi*rho) + fh3 = - kappa**6 * sig_c**3 /(8.0*pi*rho) *(I2cc-Iccc/6.0) & + + kappa**4 * ydd *sig_c/(16.0*pi*rho) & + *( (6.0+5.0/3.0*sig_d/sig_c)*I0cc + 3.0*sig_d/sig_c*Iccd ) & + + 3.0*kappa**2 * ydd*ydd /(8.0*pi*rho) / sig_cd & + *( (2.0-3.21555*sig_d/sig_cd)*Icd +3.0*sig_d/sig_cd*Icdd ) + IF (sig_d /= 0.0) fh3 = fh3 + 27.0*ydd**3 & + /(16.0*pi*rho)/sig_d**3 *Iddd + + fhend = ( fh32 + (fh32*fh32*fh3-2.0*fh32*fh2*fh52+fh2**3 ) & + /(fh2*fh2-fh32*fh52) ) & + / ( 1.0 + (fh32*fh3-fh2*fh52) /(fh2*fh2-fh32*fh52) & + - (fh2*fh3-fh52*fh52) /(fh2*fh2-fh32*fh52) ) +!---------- +! fH32= - kappa**3 /(12.0*PI*rho) +! fH2 = - 3.0* kappa**2 * ydd*Icd /(8.0*PI*rho) / sig_cd +! fH52= (3.0*kappa**3 * ydd)/(8.0*PI*rho) +! fH3 = + kappa**4 * ydd *sig_c/(16.0*PI*rho) & +! *( (6.0+5.0/3.0*sig_d/sig_c)*0.0*I0cc + 3.0*sig_d/sig_c*Iccd) & +! + 3.0*kappa**2 * ydd*ydd /(8.0*PI*rho) / sig_cd & +! *( (2.0-3.215550*sig_d/sig_cd)*Icd +3.0*sig_d/sig_cd*Icdd ) + +! fHcd = ( + (fH32*fH32*fH3-2.0*fH32*fH2*fH52+fH2**3 ) & +! /(fH2*fH2-fH32*fH52) ) & +! / ( 1.0 + (fH32*fH3-fH2*fH52) /(fH2*fH2-fH32*fH52) & +! - (fH2*fH3-fH52*fH52) /(fH2*fH2-fH32*fH52) ) + +END IF + + END SUBROUTINE F_ION_DIPOLE_TBH + + +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! + SUBROUTINE F_ION_ION_PrimMSA ( fcc ) +! + USE EOS_VARIABLES, ONLY: nc, PI, KBOL, NAv, ncomp, t, rho, x, parame, mx + IMPLICIT NONE +! +!--------------------------------------------------------------------- + REAL, INTENT(IN OUT) :: fcc +!--------------------------------------------------------------------- + INTEGER :: i, j, cc_it, ions + REAL :: e_elem, eps_cc0, rho_sol, dielec + REAL :: x_ions + REAL :: cc_sig1, cc_sig2, cc_sig3 + REAL, DIMENSION(nc) :: z_ii, x_ii, sigm_i, my2dd + REAL :: alpha_2, kappa, ii_par + REAL :: cc_omeg, p_n, q2_i, cc_q2, cc_gam + REAL :: cc_error(2), cc_delt + REAL :: rhs, lambda, lam_s +!--------------------------------------------------------------------- + +!----------------Dieletric Constant of Water-------------------------- +e_elem = 1.602189246E-19 ! in Unit [Coulomb] +eps_cc0 = 8.854187818E-22 ! in Unit [Coulomb**2 /(J*Angstrom)] +! Correlation of M. Uematsu and E. U. Frank +! (Static Dieletric Constant of Water and Steam) +! valid range of conditions 273,15 K <=T<= 823,15 K +! and density <= 1150 kg/m3 (i.e. 0 <= p <= 500 MPa) +rho_sol = rho * 18.015 * 1.E27/ NAv +rho_sol = rho_sol/1000.0 +dielec = 1.0+(7.62571/(t/293.15))*rho_sol +(2.44E2/(t/293.15)-1.41E2 & + +2.78E1*(t/293.15))*rho_sol**2 & + +(-9.63E1/(t/293.15)+4.18E1*(t/293.15) & + -1.02E1*(t/293.15)**2 )*rho_sol**3 +(-4.52E1/(t/293.15)**2 & + +8.46E1/(t/293.15)-3.59E1)*rho_sol**4 + + +! !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! + +dielec = 1.0 + +! !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! + + +!----------------Ion-Ion: primitive MSA ------------------------------- +! the (dipole moment)**2 [my**2] corresponds to an attraction from +! point charges of [ SUM(xi * zi**2 * e_elem**2) * 3 * di**2 ] + +! parame(ion,6))**2 * 1.E-49 / (kbol*T) +! = (e_elem* 1.E5/SQRT(1.112650050))**2 +! *x(i)*zi**2 *3.0*sig_ij(1,1)**2 *1.E-20 + +! parame(ion,6))**2 = (e_elem* 1.E5/SQRT(1.112650050))**2 /1.E-49 +! *x(i)*zi**2 *3.0*sig_ij(i,i)**2 *1.E-20 + +! with the units +! my**2 [=] D**2 = 1.E-49 J*m3 +! e_elem **2 [=] C**2 = 1.E5 / SQRT(1.112650050) J*m + + +ions = 0 +x_ions = 0.0 +fcc = 0.0 +DO i = 1, ncomp + z_ii(i) = parame(i,10) + IF (z_ii(i) /= 0.0) THEN + sigm_i(i) = parame(i,2) + ELSE + sigm_i(i) = 0.0 + END IF + IF (z_ii(i) /= 0.0) ions = 1 + IF (z_ii(i) /= 0.0) x_ions = x_ions + x(i) +END DO + +IF (ions == 1 .AND. x_ions > 0.0) THEN + + cc_sig1 = 0.0 + cc_sig2 = 0.0 + cc_sig3 = 0.0 + DO i=1,ncomp + IF (z_ii(i) /= 0.0) THEN + x_ii(i) = x(i)/x_ions + ELSE + x_ii(i) =0.0 + END IF + cc_sig1 = cc_sig1 +x_ii(i)*sigm_i(i) + cc_sig2 = cc_sig2 +x_ii(i)*sigm_i(i)**2 + cc_sig3 = cc_sig3 +x_ii(i)*sigm_i(i)**3 + END DO + + + ! alpha_2 = 4.0*PI*e_elem**2 /eps_cc0/dielec/kbol/T + alpha_2 = e_elem**2 /eps_cc0 / dielec / KBOL/t + kappa = 0.0 + DO i = 1, ncomp + kappa = kappa + x(i)*z_ii(i)*z_ii(i)*mx(i,1) + END DO + kappa = SQRT( rho * alpha_2 * kappa ) + ii_par= kappa * cc_sig1 + + ! Temporaer: nach der Arbeit von Krienke verifiziert + ! noch nicht fuer Mischungen mit unterschiedl. Ladung erweitert + ! ii_par = DSQRT( e_elem**2 /eps_cc0/dielec/kbol/T & + ! *rho*(x(1)*Z_ii(1)**2 + x(2)*Z_ii(2)**2 ) )*cc_sig1 + + + cc_gam = kappa/2.0 + + ! noch offen !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! + cc_delt = 0.0 + DO i = 1, ncomp + cc_delt = cc_delt + x(i)*mx(i,1)*rho*sigm_i(i)**3 + END DO + cc_delt= 1.0 - PI/6.0*cc_delt + + cc_it = 0 + 13 CONTINUE + j = 0 + cc_it = cc_it + 1 + 131 CONTINUE + j = j + 1 + cc_omeg = 0.0 + DO i = 1, ncomp + cc_omeg = cc_omeg +x(i)*mx(i,1)*sigm_i(i)**3 /(1.0+cc_gam*sigm_i(i)) + END DO + cc_omeg = 1.0 + PI/2.0 / cc_delt * rho * cc_omeg + p_n = 0.0 + DO i = 1, ncomp + p_n = p_n + x(i)*mx(i,1)*rho / cc_omeg*sigm_i(i)*z_ii(i) / (1.0+cc_gam*sigm_i(i)) + END DO + q2_i = 0.0 + cc_q2= 0.0 + DO i = 1, ncomp + q2_i = q2_i + rho*x(i)*mx(i,1)*( (z_ii(i)-pi/2.0/cc_delt*sigm_i(i)**2 *p_n) & + /(1.0+cc_gam*sigm_i(i)) )**2 + cc_q2 = cc_q2 + x(i)*mx(i,1)*rho*z_ii(i)**2 / (1.0+cc_gam*sigm_i(i)) + END DO + q2_i = q2_i*alpha_2 / 4.0 + + cc_error(j) = cc_gam - SQRT(q2_i) + IF (j == 1) cc_gam = cc_gam*1.000001 + IF (j == 2) cc_gam = cc_gam - cc_error(2)* (cc_gam-cc_gam/1.000001)/(cc_error(2)-cc_error(1)) + + IF ( j == 1 .AND. ABS(cc_error(1)) > 1.E-15 ) GO TO 131 + IF ( cc_it >= 10 ) THEN + WRITE (*,*) ' cc error' + STOP + END IF + IF ( j /= 1 ) GO TO 13 + + fcc= - alpha_2 / PI/4.0 /rho* (cc_gam*cc_q2 & + + pi/2.0/cc_delt *cc_omeg*p_n**2 ) + cc_gam**3 /pi/3.0/rho + ! Restricted Primitive Model + ! fcc=-(3.0*ii_par*ii_par+6.0*ii_par+2.0 & + ! -2.0*(1.0+2.0*ii_par)**1.50) & + ! /(12.0*PI*rho *cc_sig1**3 ) + + ! fcc = x_ions * fcc + + my2dd(3) = (parame(3,6))**2 *1.E-19 /(KBOL*t) + my2dd(3) = (1.84)**2 *1.E-19 /(kbol*t) + + rhs = 12.0 * PI * rho * x(3) * my2dd(3) + lam_s = 1.0 + 12 CONTINUE + lambda = (rhs/((lam_s+2.0)**2 ) + 16.0/((1.0+lam_s)**4 ) )**0.5 + IF ( ABS(lam_s-lambda) > 1.E-10 )THEN + lam_s = ( lambda + lam_s ) / 2.0 + GO TO 12 + END IF + + ! f_cd = -(ii_par*ii_par)/(4.0*PI*rho*m_mean *cc_sig1**3 ) & + ! *(dielec-1.0)/(1.0 + parame(3,2)/cc_sig1/lambda) + ! write (*,*) ' ',f_cd,fcc,x_ions + ! f_cd = f_cd/(1.0 - fcc/f_cd) + ! fcc = 0.0 + +END IF + + +END SUBROUTINE F_ION_ION_PrimMSA + + +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! + SUBROUTINE F_ION_ION_nonPrimMSA ( fdd, fqq, fdq, fcc ) +! + USE EOS_VARIABLES, ONLY: nc, ncomp, t, eta, x, parame, mseg + IMPLICIT NONE +! +!--------------------------------------------------------------------- + REAL, INTENT(IN OUT) :: fdd, fqq, fdq, fcc +!--------------------------------------------------------------------- + INTEGER :: dipole + !REAL :: A_MSA !, A_CC, A_CD, A_DD, U_MSA, chempot + REAL, DIMENSION(nc) :: x_export, msegm +!--------------------------------------------------------------------- + + dipole = 0 + IF ( SUM( parame(1:ncomp,6) ) > 1.E-5 ) dipole = 1 + + IF ( dipole /= 0 ) THEN ! alternatively ions and dipoles = 1 + fdd = 0.0 + fqq = 0.0 + fdq = 0.0 + fcc = 0.0 + msegm(:) = mseg(:) ! the entries of the vector mseg and x are changed + x_export(:) = x(:) ! in SEMIRESTRICTED because the ions should be positioned first + ! that is why dummy vectors msegm and x_export are defined + !CALL SEMIRESTRICTED (A_MSA,A_CC,A_CD,A_DD,U_MSA, & + ! chempot,ncomp,parame,t,eta,x_export,msegm,0) + !fdd = A_MSA + write (*,*) 'why are individual contrib. A_CC,A_CD,A_DD not used' + stop + END IF + + END SUBROUTINE F_ION_ION_nonPrimMSA + + +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! + SUBROUTINE F_LC_MayerSaupe ( flc ) +! + USE EOS_VARIABLES, ONLY: nc, PI, KBOL, NAv, ncomp, phas, t, rho, eta, & + x, mseg, parame, E_lc, S_lc, dhs + IMPLICIT NONE +! +!--------------------------------------------------------------------- + REAL, INTENT(IN OUT) :: flc +!--------------------------------------------------------------------- + INTEGER :: i, j, k + INTEGER :: liq_crystal, count_lc, steps_lc + REAL :: alpha_lc, tolerance, deltay + REAL :: integrand1, integrand2, accel_lc + REAL :: error_lc, u_term, sphase + REAL, DIMENSION(nc) :: z_lc, S_lc1, S_lc2, sumu + REAL, DIMENSION(nc,nc) :: u_lc, klc +!--------------------------------------------------------------------- +INTEGER :: stabil +COMMON /stabil / stabil +!--------------------------------------------------------------------- + + + klc(1,2) = 0.0 + klc(2,1) = klc(1,2) + + alpha_lc = 1.0 + accel_lc = 4.0 + IF ( eta < 0.35 ) accel_lc = 1.3 + IF ( eta < 0.15 ) accel_lc = 1.0 + + liq_crystal = 0 + DO i = 1, ncomp + DO j = 1, ncomp + E_lc(i,j) = (E_lc(i,i)*E_lc(j,j))**0.5 *(1.0-klc(i,j)) !combining rule + ! E_LC(i,j)= ( E_LC(i,i)+E_LC(j,j) ) * 0.5 !combining rule + ! S_LC(i,j)= ( S_LC(i,i)+S_LC(j,j) ) * 0.5 !combining rule + IF (E_lc(i,j) /= 0.0) liq_crystal = 1 + END DO + END DO + ! S_LC(1,2) = 0.0 + ! S_LC(2,1) = S_LC(1,2) + ! E_LC(1,2) = 60.0 + ! E_LC(2,1) = E_LC(1,2) + + IF ( liq_crystal == 1 .AND. phas == 1 .AND. stabil == 0 ) THEN + + count_lc = 0 + tolerance = 1.E-6 + + steps_lc = 200 + deltay = 1.0 / REAL(steps_lc) + + ! --- dimensionless function U_LC repres. anisotr. intermolecular interactions in l.c. + + DO i = 1, ncomp + DO j = 1, ncomp + u_lc(i,j) = 2.0/3.0*pi*mseg(i)*mseg(j) *(0.5*(dhs(i)+dhs(j)))**3 & ! sig_ij(i,j)**3 + *(E_lc(i,j)/t+S_lc(i,j))*rho + END DO + END DO + + + DO i=1,ncomp + ! S_lc2(i) = 0.0 !for isotropic + S_lc2(i) = 0.5 !for nematic + S_lc1(i) = S_lc2(i) + END DO + + 1 CONTINUE + + DO i = 1, ncomp + IF (S_lc2(i) <= 0.3) S_lc1(i) = S_lc2(i) + IF (S_lc2(i) > 0.3) S_lc1(i) = S_lc1(i) + (S_lc2(i)-S_lc1(i))*accel_lc + END DO + + count_lc = count_lc + 1 + + ! --- single-particle orientation partition function Z_LC in liquid crystals + + DO i = 1, ncomp + sumu(i) = 0.0 + DO j = 1, ncomp + sumu(i) = sumu(i) + x(j)*u_lc(i,j)*S_lc1(j) + END DO + END DO + + DO i = 1, ncomp + z_lc(i) = 0.0 + integrand1 = EXP(-0.5*sumu(i)) !eq. for Z_LC with y=0 + DO k = 1, steps_lc + integrand2 = EXP(0.5*sumu(i)*(3.0*(deltay*REAL(k)) **2 -1.0)) + z_lc(i) = z_lc(i) + (integrand1 + integrand2)/2.0*deltay + integrand1 = integrand2 + END DO !k-index integration + END DO !i-index Z_LC(i) calculation + + ! --- order parameter S_lc in liquid crystals ----------------------- + + error_lc = 0.0 + DO i = 1, ncomp + S_lc2(i) = 0.0 + integrand1 = -1.0/z_lc(i)*0.5*EXP(-0.5*sumu(i)) !for S_lc with y=0 + DO k = 1, steps_lc + integrand2 = 1.0/z_lc(i)*0.5*(3.0*(deltay*REAL(k)) & + **2 -1.0)*EXP(0.5*sumu(i)*(3.0 *(deltay*REAL(k))**2 -1.0)) + S_lc2(i) = S_lc2(i) + (integrand1 + integrand2)/2.0*deltay + integrand1 = integrand2 + END DO !k-index integration + error_lc = error_lc + ABS(S_lc2(i)-S_lc1(i)) + END DO !i-index Z_LC(i) calculation + + sphase = 0.0 + DO i = 1, ncomp + sphase = sphase + S_lc2(i) + END DO + IF (sphase < 1.E-4) THEN + error_lc = 0.0 + DO i = 1, ncomp + S_lc2(i)= 0.0 + z_lc(i) = 1.0 + END DO + END IF + + + ! write (*,*) count_LC,S_lc2(1)-S_lc1(1),S_lc2(2)-S_lc1(2) + IF (error_lc > tolerance .AND. count_lc < 400) GO TO 1 + ! write (*,*) 'done',eta,S_lc2(1),S_lc2(2) + + IF (count_lc == 400) WRITE (*,*) 'LC iteration not converg.' + + ! --- the anisotropic contribution to the Helmholtz energy ---------- + + u_term = 0.0 + DO i = 1, ncomp + DO j = 1, ncomp + u_term = u_term + 0.5*x(i)*x(j)*S_lc2(i) *S_lc2(j)*u_lc(i,j) + END DO + END DO + + flc = 0.0 + DO i = 1, ncomp + IF (z_lc(i) /= 0.0) flc = flc - x(i) * LOG(z_lc(i)) + END DO + flc = flc + u_term + ! pause + + END IF + ! write (*,'(i2,i2,4(f15.8))') phas,stabil,flc,eta,S_lc2(1),x(1) + + + END SUBROUTINE F_LC_MayerSaupe + + + +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! + SUBROUTINE P_POLAR ( zdd, zddz, zddz2, zddz3, zqq, zqqz, zqqz2, zqqz3, zdq, zdqz, zdqz2, zdqz3 ) +! + USE EOS_VARIABLES, ONLY: ncomp, parame, dd_term, qq_term, dq_term + IMPLICIT NONE +! +! ---------------------------------------------------------------------- + REAL, INTENT(OUT) :: zdd, zddz, zddz2, zddz3 + REAL, INTENT(OUT) :: zqq, zqqz, zqqz2, zqqz3 + REAL, INTENT(OUT) :: zdq, zdqz, zdqz2, zdqz3 +! +! --- local variables--------------------------------------------------- + INTEGER :: dipole + INTEGER :: quadrupole + INTEGER :: dipole_quad +! ---------------------------------------------------------------------- + + zdd = 0.0 + zddz = 0.0 + zddz2 = 0.0 + zddz3 = 0.0 + zqq = 0.0 + zqqz = 0.0 + zqqz2 = 0.0 + zqqz3 = 0.0 + zdq = 0.0 + zdqz = 0.0 + zdqz2 = 0.0 + zdqz3 = 0.0 + + dipole = 0 + quadrupole = 0 + dipole_quad = 0 + IF ( SUM( parame(1:ncomp,6) ) /= 0.0 ) dipole = 1 + IF ( SUM( parame(1:ncomp,7) ) /= 0.0 ) quadrupole = 1 + IF ( dipole == 1 .AND. quadrupole == 1 ) dipole_quad = 1 + + ! -------------------------------------------------------------------- + ! dipole-dipole term + ! -------------------------------------------------------------------- + IF (dipole == 1) THEN + + IF (dd_term == 'GV') CALL P_DD_GROSS_VRABEC( zdd, zddz, zddz2, zddz3 ) + ! IF (dd_term == 'SF') CALL F_DD_SAAGER_FISCHER( k ) + IF (dd_term /= 'GV' .AND. dd_term /= 'SF') write (*,*) 'specify dipole term !' + + ENDIF + + ! -------------------------------------------------------------------- + ! quadrupole-quadrupole term + ! -------------------------------------------------------------------- + IF (quadrupole == 1) THEN + + !IF (qq_term == 'SF') CALL F_QQ_SAAGER_FISCHER( k ) + IF (qq_term == 'JG') CALL P_QQ_GROSS( zqq, zqqz, zqqz2, zqqz3 ) + IF (qq_term /= 'JG' .AND. qq_term /= 'SF') write (*,*) 'specify quadrupole term !' + + ENDIF + + ! -------------------------------------------------------------------- + ! dipole-quadrupole cross term + ! -------------------------------------------------------------------- + IF (dipole_quad == 1) THEN + + IF (dq_term == 'VG') CALL P_DQ_VRABEC_GROSS( zdq, zdqz, zdqz2, zdqz3 ) + IF (dq_term /= 'VG' ) write (*,*) 'specify DQ-cross term !' + + ENDIF + +END SUBROUTINE P_POLAR + + +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! + SUBROUTINE P_DD_GROSS_VRABEC( zdd, zddz, zddz2, zddz3 ) +! + USE PARAMETERS, ONLY: PI, KBOL + USE EOS_VARIABLES, ONLY: nc, ncomp, uij, parame, mseg, sig_ij, rho, eta, x, t + USE EOS_CONSTANTS, ONLY: ddp2, ddp3, ddp4 + IMPLICIT NONE +! +! ---------------------------------------------------------------------- + REAL, INTENT(IN OUT) :: zdd, zddz, zddz2, zddz3 +! ---------------------------------------------------------------------- + INTEGER :: i, j, k, m + REAL :: factor2, factor3, z3 + REAL :: xijfa, xijkfa, eij + REAL :: fdddr, fddd2, fddd3, fddd4 + REAL :: fdd2, fdd2z, fdd2z2, fdd2z3, fdd2z4 + REAL :: fdd3, fdd3z, fdd3z2, fdd3z3, fdd3z4 + REAL, DIMENSION(nc) :: my2dd + REAL, DIMENSION(nc,nc) :: Idd2, Idd2z, Idd2z2, Idd2z3, Idd2z4 + REAL, DIMENSION(nc,nc) :: Idd4, Idd4z, Idd4z2, Idd4z3, Idd4z4 + REAL, DIMENSION(nc,nc,nc) :: Idd3, Idd3z, Idd3z2, Idd3z3, Idd3z4 +! ---------------------------------------------------------------------- + + + zdd = 0.0 + zddz = 0.0 + zddz2 = 0.0 + zddz3 = 0.0 + z3 = eta + DO i = 1, ncomp + my2dd(i) = (parame(i,6))**2 *1.E-49 / (uij(i,i)*KBOL*mseg(i)*sig_ij(i,i)**3 *1.E-30) + END DO + + DO i = 1, ncomp + DO j = 1, ncomp + Idd2(i,j) = 0.0 + Idd4(i,j) = 0.0 + Idd2z(i,j) = 0.0 + Idd4z(i,j) = 0.0 + Idd2z2(i,j) = 0.0 + Idd4z2(i,j) = 0.0 + Idd2z3(i,j) = 0.0 + Idd4z3(i,j) = 0.0 + Idd2z4(i,j) = 0.0 + Idd4z4(i,j) = 0.0 + ! IF (paramei,6).NE.0.0 .AND. parame(j,6).NE.0.0) THEN + DO m = 0, 4 + Idd2(i,j) =Idd2(i,j) + ddp2(i,j,m) *z3**(m+1) + Idd4(i,j) =Idd4(i,j) + ddp4(i,j,m) *z3**(m+1) + Idd2z(i,j) =Idd2z(i,j) +ddp2(i,j,m)*REAL(m+1) *z3**m + Idd4z(i,j) =Idd4z(i,j) +ddp4(i,j,m)*REAL(m+1) *z3**m + Idd2z2(i,j)=Idd2z2(i,j)+ddp2(i,j,m)*REAL((m+1)*m) *z3**(m-1) + Idd4z2(i,j)=Idd4z2(i,j)+ddp4(i,j,m)*REAL((m+1)*m) *z3**(m-1) + Idd2z3(i,j)=Idd2z3(i,j)+ddp2(i,j,m)*REAL((m+1)*m*(m-1)) *z3**(m-2) + Idd4z3(i,j)=Idd4z3(i,j)+ddp4(i,j,m)*REAL((m+1)*m*(m-1)) *z3**(m-2) + Idd2z4(i,j)=Idd2z4(i,j)+ddp2(i,j,m)*REAL((m+1)*m*(m-1)*(m-2)) *z3**(m-3) + Idd4z4(i,j)=Idd4z4(i,j)+ddp4(i,j,m)*REAL((m+1)*m*(m-1)*(m-2)) *z3**(m-3) + END DO + DO k = 1, ncomp + Idd3(i,j,k) = 0.0 + Idd3z(i,j,k) = 0.0 + Idd3z2(i,j,k) = 0.0 + Idd3z3(i,j,k) = 0.0 + Idd3z4(i,j,k) = 0.0 + ! IF (parame(k,6).NE.0.0) THEN + DO m = 0, 4 + Idd3(i,j,k) =Idd3(i,j,k) +ddp3(i,j,k,m)*z3**(m+2) + Idd3z(i,j,k) =Idd3z(i,j,k) +ddp3(i,j,k,m)*REAL(m+2)*z3**(m+1) + Idd3z2(i,j,k)=Idd3z2(i,j,k)+ddp3(i,j,k,m)*REAL((m+2)*(m+1))*z3**m + Idd3z3(i,j,k)=Idd3z3(i,j,k)+ddp3(i,j,k,m)*REAL((m+2)*(m+1)*m)*z3**(m-1) + Idd3z4(i,j,k)=Idd3z4(i,j,k)+ddp3(i,j,k,m)*REAL((m+2)*(m+1)*m*(m-1)) *z3**(m-2) + END DO + ! ENDIF + END DO + ! ENDIF + END DO + END DO + + factor2= -PI *rho/z3 + factor3= -4.0/3.0*PI**2 * (rho/z3)**2 + + fdd2 = 0.0 + fdd2z = 0.0 + fdd2z2 = 0.0 + fdd2z3 = 0.0 + fdd2z4 = 0.0 + fdd3 = 0.0 + fdd3z = 0.0 + fdd3z2 = 0.0 + fdd3z3 = 0.0 + fdd3z4 = 0.0 + DO i = 1, ncomp + DO j = 1, ncomp + ! IF (parame(i,6).NE.0.0 .AND. parame(j,6).NE.0.0) THEN + xijfa = x(i)*parame(i,3)/t*parame(i,2)**3 *x(j)*parame(j,3)/t*parame(j,2)**3 & + / ((parame(i,2)+parame(j,2))/2.0)**3 *my2dd(i)*my2dd(j) + eij = (parame(i,3)*parame(j,3))**0.5 + fdd2 = fdd2 +factor2*xijfa*(Idd2(i,j) +eij/t*Idd4(i,j)) + fdd2z = fdd2z +factor2*xijfa*(Idd2z(i,j) +eij/t*Idd4z(i,j)) + fdd2z2 = fdd2z2+factor2*xijfa*(Idd2z2(i,j)+eij/t*Idd4z2(i,j)) + fdd2z3 = fdd2z3+factor2*xijfa*(Idd2z3(i,j)+eij/t*Idd4z3(i,j)) + fdd2z4 = fdd2z4+factor2*xijfa*(Idd2z4(i,j)+eij/t*Idd4z4(i,j)) + DO k = 1, ncomp + ! IF (parame(k,6).NE.0.0) THEN + xijkfa= x(i)*parame(i,3)/t*parame(i,2)**3 *x(j)*parame(j,3)/t*parame(j,2)**3 & + *x(k)*parame(k,3)/t*parame(k,2)**3 /((parame(i,2)+parame(j,2))/2.0) & + /((parame(i,2)+parame(k,2))/2.0) /((parame(j,2)+parame(k,2))/2.0) & + *my2dd(i)*my2dd(j)*my2dd(k) + fdd3 = fdd3 + factor3 * xijkfa*Idd3(i,j,k) + fdd3z = fdd3z + factor3 * xijkfa*Idd3z(i,j,k) + fdd3z2 = fdd3z2 + factor3 * xijkfa*Idd3z2(i,j,k) + fdd3z3 = fdd3z3 + factor3 * xijkfa*Idd3z3(i,j,k) + fdd3z4 = fdd3z4 + factor3 * xijkfa*Idd3z4(i,j,k) + ! ENDIF + END DO + ! ENDIF + END DO + END DO + IF (fdd2 < -1.E-50 .AND. fdd3 /= 0.0 .AND. fdd2z /= 0.0 .AND. fdd3z /= 0.0) THEN + + fdddr= fdd2* (fdd2*fdd2z - 2.0*fdd3*fdd2z+fdd2*fdd3z) / (fdd2-fdd3)**2 + fddd2=(2.0*fdd2*fdd2z*fdd2z +fdd2*fdd2*fdd2z2 & + -2.0*fdd2z**2 *fdd3-2.0*fdd2*fdd2z2*fdd3+fdd2*fdd2*fdd3z2) & + /(fdd2-fdd3)**2 + fdddr * 2.0*(fdd3z-fdd2z)/(fdd2-fdd3) + fddd3=(2.0*fdd2z**3 +6.0*fdd2*fdd2z*fdd2z2+fdd2*fdd2*fdd2z3 & + -6.0*fdd2z*fdd2z2*fdd3-2.0*fdd2z**2 *fdd3z & + -2.0*fdd2*fdd2z3*fdd3 -2.0*fdd2*fdd2z2*fdd3z & + +2.0*fdd2*fdd2z*fdd3z2+fdd2*fdd2*fdd3z3) /(fdd2-fdd3)**2 & + + 2.0/(fdd2-fdd3)* ( 2.0*fddd2*(fdd3z-fdd2z) & + + fdddr*(fdd3z2-fdd2z2) & + - fdddr/(fdd2-fdd3)*(fdd3z-fdd2z)**2 ) + fddd4=( 12.0*fdd2z**2 *fdd2z2+6.0*fdd2*fdd2z2**2 & + +8.0*fdd2*fdd2z*fdd2z3+fdd2*fdd2*fdd2z4-6.0*fdd2z2**2 *fdd3 & + -12.0*fdd2z*fdd2z2*fdd3z -8.0*fdd2z*fdd2z3*fdd3 & + -2.0*fdd2*fdd2z4*fdd3-4.0*fdd2*fdd2z3*fdd3z & + +4.0*fdd2*fdd2z*fdd3z3+fdd2**2 *fdd3z4 ) /(fdd2-fdd3)**2 & + + 6.0/(fdd2-fdd3)* ( fddd3*(fdd3z-fdd2z) & + -fddd2/(fdd2-fdd3)*(fdd3z-fdd2z)**2 & + - fdddr/(fdd2-fdd3)*(fdd3z-fdd2z)*(fdd3z2-fdd2z2) & + + fddd2*(fdd3z2-fdd2z2) +1.0/3.0*fdddr*(fdd3z3-fdd2z3) ) + zdd = fdddr*eta + zddz = fddd2*eta + fdddr + zddz2 = fddd3*eta + 2.0* fddd2 + zddz3 = fddd4*eta + 3.0* fddd3 + + END IF + + +END SUBROUTINE P_DD_GROSS_VRABEC + + + +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! + SUBROUTINE P_QQ_GROSS( zqq, zqqz, zqqz2, zqqz3 ) +! + USE PARAMETERS, ONLY: PI, KBOL + USE EOS_VARIABLES, ONLY: nc, ncomp, uij, parame, mseg, sig_ij, rho, eta, x, t + USE EOS_CONSTANTS, ONLY: qqp2, qqp3, qqp4 + IMPLICIT NONE +! +! ---------------------------------------------------------------------- + REAL, INTENT(IN OUT) :: zqq, zqqz, zqqz2, zqqz3 +! ---------------------------------------------------------------------- + INTEGER :: i, j, k, m + REAL :: factor2, factor3, z3 + REAL :: xijfa, xijkfa, eij + REAL :: fqqdr, fqqd2, fqqd3, fqqd4 + REAL :: fqq2, fqq2z, fqq2z2, fqq2z3, fqq2z4 + REAL :: fqq3, fqq3z, fqq3z2, fqq3z3, fqq3z4 + REAL, DIMENSION(nc) :: qq2 + REAL, DIMENSION(nc,nc) :: Iqq2, Iqq2z, Iqq2z2, Iqq2z3, Iqq2z4 + REAL, DIMENSION(nc,nc) :: Iqq4, Iqq4z, Iqq4z2, Iqq4z3, Iqq4z4 + REAL, DIMENSION(nc,nc,nc) :: Iqq3, Iqq3z, Iqq3z2, Iqq3z3, Iqq3z4 +! ---------------------------------------------------------------------- + + zqq = 0.0 + zqqz = 0.0 + zqqz2 = 0.0 + zqqz3 = 0.0 + z3 = eta + DO i=1,ncomp + qq2(i) = (parame(i,7))**2 *1.E-69 / (uij(i,i)*kbol*mseg(i)*sig_ij(i,i)**5 *1.E-50) + END DO + + DO i = 1, ncomp + DO j = 1, ncomp + Iqq2(i,j) = 0.0 + Iqq4(i,j) = 0.0 + Iqq2z(i,j) = 0.0 + Iqq4z(i,j) = 0.0 + Iqq2z2(i,j) = 0.0 + Iqq4z2(i,j) = 0.0 + Iqq2z3(i,j) = 0.0 + Iqq4z3(i,j) = 0.0 + Iqq2z4(i,j) = 0.0 + Iqq4z4(i,j) = 0.0 + IF (parame(i,7) /= 0.0 .AND. parame(j,7) /= 0.0) THEN + DO m = 0, 4 + Iqq2(i,j) =Iqq2(i,j) + qqp2(i,j,m)*z3**(m+1) + Iqq4(i,j) =Iqq4(i,j) + qqp4(i,j,m)*z3**(m+1) + Iqq2z(i,j) =Iqq2z(i,j) +qqp2(i,j,m)*REAL(m+1)*z3**m + Iqq4z(i,j) =Iqq4z(i,j) +qqp4(i,j,m)*REAL(m+1)*z3**m + Iqq2z2(i,j)=Iqq2z2(i,j)+qqp2(i,j,m)*REAL((m+1)*m)*z3**(m-1) + Iqq4z2(i,j)=Iqq4z2(i,j)+qqp4(i,j,m)*REAL((m+1)*m)*z3**(m-1) + Iqq2z3(i,j)=Iqq2z3(i,j)+qqp2(i,j,m)*REAL((m+1)*m*(m-1)) *z3**(m-2) + Iqq4z3(i,j)=Iqq4z3(i,j)+qqp4(i,j,m)*REAL((m+1)*m*(m-1)) *z3**(m-2) + Iqq2z4(i,j)=Iqq2z4(i,j)+qqp2(i,j,m)*REAL((m+1)*m*(m-1)*(m-2)) *z3**(m-3) + Iqq4z4(i,j)=Iqq4z4(i,j)+qqp4(i,j,m)*REAL((m+1)*m*(m-1)*(m-2)) *z3**(m-3) + END DO + DO k=1,ncomp + Iqq3(i,j,k) = 0.0 + Iqq3z(i,j,k) = 0.0 + Iqq3z2(i,j,k) = 0.0 + Iqq3z3(i,j,k) = 0.0 + Iqq3z4(i,j,k) = 0.0 + IF (parame(k,7) /= 0.0) THEN + DO m=0,4 + Iqq3(i,j,k) =Iqq3(i,j,k) + qqp3(i,j,k,m)*z3**(m+2) + Iqq3z(i,j,k)=Iqq3z(i,j,k)+qqp3(i,j,k,m)*REAL(m+2)*z3**(m+1) + Iqq3z2(i,j,k)=Iqq3z2(i,j,k)+qqp3(i,j,k,m)*REAL((m+2)*(m+1)) *z3**m + Iqq3z3(i,j,k)=Iqq3z3(i,j,k)+qqp3(i,j,k,m)*REAL((m+2)*(m+1)*m) *z3**(m-1) + Iqq3z4(i,j,k)=Iqq3z4(i,j,k)+qqp3(i,j,k,m) *REAL((m+2)*(m+1)*m*(m-1)) *z3**(m-2) + END DO + END IF + END DO + + END IF + END DO + END DO + + factor2= -9.0/16.0*PI *rho/z3 + factor3= 9.0/16.0*PI**2 * (rho/z3)**2 + + fqq2 = 0.0 + fqq2z = 0.0 + fqq2z2 = 0.0 + fqq2z3 = 0.0 + fqq2z4 = 0.0 + fqq3 = 0.0 + fqq3z = 0.0 + fqq3z2 = 0.0 + fqq3z3 = 0.0 + fqq3z4 = 0.0 + DO i = 1, ncomp + DO j = 1, ncomp + IF (parame(i,7) /= 0.0 .AND. parame(j,7) /= 0.0) THEN + xijfa =x(i)*uij(i,i)*qq2(i)*sig_ij(i,i)**5 /t & + *x(j)*uij(j,j)*qq2(j)*sig_ij(j,j)**5 /t/sig_ij(i,j)**7.0 + eij = (parame(i,3)*parame(j,3))**0.5 + fqq2= fqq2 +factor2*xijfa*(Iqq2(i,j) +eij/t*Iqq4(i,j) ) + fqq2z =fqq2z +factor2*xijfa*(Iqq2z(i,j) +eij/t*Iqq4z(i,j) ) + fqq2z2=fqq2z2+factor2*xijfa*(Iqq2z2(i,j)+eij/t*Iqq4z2(i,j)) + fqq2z3=fqq2z3+factor2*xijfa*(Iqq2z3(i,j)+eij/t*Iqq4z3(i,j)) + fqq2z4=fqq2z4+factor2*xijfa*(Iqq2z4(i,j)+eij/t*Iqq4z4(i,j)) + DO k = 1, ncomp + IF (parame(k,7) /= 0.0) THEN + xijkfa=x(i)*uij(i,i)*qq2(i)*sig_ij(i,i)**5 /t/sig_ij(i,j)**3 & + *x(j)*uij(j,j)*qq2(j)*sig_ij(j,j)**5 /t/sig_ij(i,k)**3 & + *x(k)*uij(k,k)*qq2(k)*sig_ij(k,k)**5 /t/sig_ij(j,k)**3 + fqq3 = fqq3 + factor3 * xijkfa*Iqq3(i,j,k) + fqq3z = fqq3z + factor3 * xijkfa*Iqq3z(i,j,k) + fqq3z2 = fqq3z2 + factor3 * xijkfa*Iqq3z2(i,j,k) + fqq3z3 = fqq3z3 + factor3 * xijkfa*Iqq3z3(i,j,k) + fqq3z4 = fqq3z4 + factor3 * xijkfa*Iqq3z4(i,j,k) + END IF + END DO + END IF + END DO + END DO + IF (fqq2 < -1.E-50 .AND. fqq3 /= 0.0 .AND. fqq2z /= 0.0 .AND. fqq3z /= 0.0) THEN + fqqdr = fqq2* (fqq2*fqq2z - 2.0*fqq3*fqq2z+fqq2*fqq3z) /(fqq2-fqq3)**2 + fqqd2= (2.0*fqq2*fqq2z*fqq2z +fqq2*fqq2*fqq2z2 & + -2.0*fqq2z**2 *fqq3-2.0*fqq2*fqq2z2*fqq3+fqq2*fqq2*fqq3z2) & + /(fqq2-fqq3)**2 + fqqdr * 2.0*(fqq3z-fqq2z)/(fqq2-fqq3) + fqqd3=(2.0*fqq2z**3 +6.0*fqq2*fqq2z*fqq2z2+fqq2*fqq2*fqq2z3 & + -6.0*fqq2z*fqq2z2*fqq3-2.0*fqq2z**2 *fqq3z & + -2.0*fqq2*fqq2z3*fqq3 -2.0*fqq2*fqq2z2*fqq3z & + +2.0*fqq2*fqq2z*fqq3z2+fqq2*fqq2*fqq3z3) /(fqq2-fqq3)**2 & + + 2.0/(fqq2-fqq3)* ( 2.0*fqqd2*(fqq3z-fqq2z) & + + fqqdr*(fqq3z2-fqq2z2) - fqqdr/(fqq2-fqq3)*(fqq3z-fqq2z)**2 ) + fqqd4=( 12.0*fqq2z**2 *fqq2z2+6.0*fqq2*fqq2z2**2 & + +8.0*fqq2*fqq2z*fqq2z3+fqq2*fqq2*fqq2z4-6.0*fqq2z2**2 *fqq3 & + -12.0*fqq2z*fqq2z2*fqq3z -8.0*fqq2z*fqq2z3*fqq3 & + -2.0*fqq2*fqq2z4*fqq3-4.0*fqq2*fqq2z3*fqq3z & + +4.0*fqq2*fqq2z*fqq3z3+fqq2**2 *fqq3z4 ) /(fqq2-fqq3)**2 & + + 6.0/(fqq2-fqq3)* ( fqqd3*(fqq3z-fqq2z) & + -fqqd2/(fqq2-fqq3)*(fqq3z-fqq2z)**2 & + - fqqdr/(fqq2-fqq3)*(fqq3z-fqq2z)*(fqq3z2-fqq2z2) & + + fqqd2*(fqq3z2-fqq2z2) +1.0/3.0*fqqdr*(fqq3z3-fqq2z3) ) + zqq = fqqdr*eta + zqqz = fqqd2*eta + fqqdr + zqqz2 = fqqd3*eta + 2.0* fqqd2 + zqqz3 = fqqd4*eta + 3.0* fqqd3 + END IF + + +END SUBROUTINE P_QQ_GROSS + +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! + SUBROUTINE P_DQ_VRABEC_GROSS( zdq, zdqz, zdqz2, zdqz3 ) +! + USE PARAMETERS, ONLY: PI, KBOL + USE EOS_VARIABLES, ONLY: nc, ncomp, uij, parame, mseg, sig_ij, rho, eta, x, t + USE EOS_CONSTANTS, ONLY: dqp2, dqp3, dqp4 + IMPLICIT NONE +! +! ---------------------------------------------------------------------- + REAL, INTENT(IN OUT) :: zdq, zdqz, zdqz2, zdqz3 +! ---------------------------------------------------------------------- + INTEGER :: i, j, k, m + REAL :: factor2, factor3, z3 + REAL :: xijfa, xijkfa, eij + REAL :: fdqdr, fdqd2, fdqd3, fdqd4 + REAL :: fdq2, fdq2z, fdq2z2, fdq2z3, fdq2z4 + REAL :: fdq3, fdq3z, fdq3z2, fdq3z3, fdq3z4 + REAL, DIMENSION(nc) :: my2dd, myfac, qq2, q_fac + REAL, DIMENSION(nc,nc) :: Idq2, Idq2z, Idq2z2, Idq2z3, Idq2z4 + REAL, DIMENSION(nc,nc) :: Idq4, Idq4z, Idq4z2, Idq4z3, Idq4z4 + REAL, DIMENSION(nc,nc,nc) :: Idq3, Idq3z, Idq3z2, Idq3z3, Idq3z4 +! ---------------------------------------------------------------------- + + zdq = 0.0 + zdqz = 0.0 + zdqz2 = 0.0 + zdqz3 = 0.0 + z3 = eta + DO i = 1, ncomp + my2dd(i) = (parame(i,6))**2 *1.E-49 / (uij(i,i)*KBOL*mseg(i)*sig_ij(i,i)**3 *1.E-30) + myfac(i) = parame(i,3)/t*parame(i,2)**4 *my2dd(i) + qq2(i) = (parame(i,7))**2 *1.E-69 / (uij(i,i)*kbol*mseg(i)*sig_ij(i,i)**5 *1.E-50) + q_fac(i) = parame(i,3)/t*parame(i,2)**4 *qq2(i) + END DO + + + DO i = 1, ncomp + DO j = 1, ncomp + Idq2(i,j) = 0.0 + Idq4(i,j) = 0.0 + Idq2z(i,j) = 0.0 + Idq4z(i,j) = 0.0 + Idq2z2(i,j) = 0.0 + Idq4z2(i,j) = 0.0 + Idq2z3(i,j) = 0.0 + Idq4z3(i,j) = 0.0 + Idq2z4(i,j) = 0.0 + Idq4z4(i,j) = 0.0 + IF (myfac(i) /= 0.0 .AND. q_fac(j) /= 0.0) THEN + DO m = 0, 4 + Idq2(i,j) =Idq2(i,j) + dqp2(i,j,m)*z3**(m+1) + Idq4(i,j) =Idq4(i,j) + dqp4(i,j,m)*z3**(m+1) + Idq2z(i,j) =Idq2z(i,j) +dqp2(i,j,m)*REAL(m+1)*z3**m + Idq4z(i,j) =Idq4z(i,j) +dqp4(i,j,m)*REAL(m+1)*z3**m + Idq2z2(i,j)=Idq2z2(i,j)+dqp2(i,j,m)*REAL((m+1)*m)*z3**(m-1) + Idq4z2(i,j)=Idq4z2(i,j)+dqp4(i,j,m)*REAL((m+1)*m)*z3**(m-1) + Idq2z3(i,j)=Idq2z3(i,j)+dqp2(i,j,m)*REAL((m+1)*m*(m-1)) *z3**(m-2) + Idq4z3(i,j)=Idq4z3(i,j)+dqp4(i,j,m)*REAL((m+1)*m*(m-1)) *z3**(m-2) + Idq2z4(i,j)=Idq2z4(i,j)+dqp2(i,j,m)*REAL((m+1)*m*(m-1)*(m-2)) *z3**(m-3) + Idq4z4(i,j)=Idq4z4(i,j)+dqp4(i,j,m)*REAL((m+1)*m*(m-1)*(m-2)) *z3**(m-3) + END DO + DO k = 1, ncomp + Idq3(i,j,k) = 0.0 + Idq3z(i,j,k) = 0.0 + Idq3z2(i,j,k) = 0.0 + Idq3z3(i,j,k) = 0.0 + Idq3z4(i,j,k) = 0.0 + IF (myfac(k) /= 0.0.OR.q_fac(k) /= 0.0) THEN + DO m = 0, 4 + Idq3(i,j,k) =Idq3(i,j,k) + dqp3(i,j,k,m)*z3**(m+2) + Idq3z(i,j,k)=Idq3z(i,j,k)+dqp3(i,j,k,m)*REAL(m+2)*z3**(m+1) + Idq3z2(i,j,k)=Idq3z2(i,j,k)+dqp3(i,j,k,m)*REAL((m+2)*(m+1)) *z3**m + Idq3z3(i,j,k)=Idq3z3(i,j,k)+dqp3(i,j,k,m)*REAL((m+2)*(m+1)*m) *z3**(m-1) + Idq3z4(i,j,k)=Idq3z4(i,j,k)+dqp3(i,j,k,m) & + *REAL((m+2)*(m+1)*m*(m-1)) *z3**(m-2) + END DO + END IF + END DO + + END IF + END DO + END DO + + factor2= -9.0/4.0*PI *rho/z3 + factor3= PI**2 * (rho/z3)**2 + + fdq2 = 0.0 + fdq2z = 0.0 + fdq2z2 = 0.0 + fdq2z3 = 0.0 + fdq2z4 = 0.0 + fdq3 = 0.0 + fdq3z = 0.0 + fdq3z2 = 0.0 + fdq3z3 = 0.0 + fdq3z4 = 0.0 + DO i = 1, ncomp + DO j = 1, ncomp + IF (myfac(i) /= 0.0 .AND. q_fac(j) /= 0.0) THEN + xijfa =x(i)*myfac(i) * x(j)*q_fac(j) /sig_ij(i,j)**5 + eij = (parame(i,3)*parame(j,3))**0.5 + fdq2= fdq2 +factor2*xijfa*(Idq2(i,j) +eij/t*Idq4(i,j) ) + fdq2z =fdq2z +factor2*xijfa*(Idq2z(i,j) +eij/t*Idq4z(i,j) ) + fdq2z2=fdq2z2+factor2*xijfa*(Idq2z2(i,j)+eij/t*Idq4z2(i,j)) + fdq2z3=fdq2z3+factor2*xijfa*(Idq2z3(i,j)+eij/t*Idq4z3(i,j)) + fdq2z4=fdq2z4+factor2*xijfa*(Idq2z4(i,j)+eij/t*Idq4z4(i,j)) + DO k = 1, ncomp + IF (myfac(k) /= 0.0.OR.q_fac(k) /= 0.0) THEN + xijkfa=x(i)*x(j)*x(k)/(sig_ij(i,j)*sig_ij(i,k)*sig_ij(j,k))**2 & + *( myfac(i)*q_fac(j)*myfac(k) + myfac(i)*q_fac(j)*q_fac(k)*1.193735 ) + fdq3 =fdq3 + factor3 * xijkfa*Idq3(i,j,k) + fdq3z =fdq3z + factor3 * xijkfa*Idq3z(i,j,k) + fdq3z2=fdq3z2 + factor3 * xijkfa*Idq3z2(i,j,k) + fdq3z3=fdq3z3 + factor3 * xijkfa*Idq3z3(i,j,k) + fdq3z4=fdq3z4 + factor3 * xijkfa*Idq3z4(i,j,k) + END IF + END DO + END IF + END DO + END DO + IF (fdq2 < -1.E-50 .AND. fdq3 /= 0.0 .AND. fdq2z /= 0.0 .AND. fdq3z /= 0.0) THEN + fdqdr = fdq2* (fdq2*fdq2z - 2.0*fdq3*fdq2z+fdq2*fdq3z) /(fdq2-fdq3)**2 + fdqd2= (2.0*fdq2*fdq2z*fdq2z +fdq2*fdq2*fdq2z2 & + -2.0*fdq2z**2 *fdq3-2.0*fdq2*fdq2z2*fdq3+fdq2*fdq2*fdq3z2) & + /(fdq2-fdq3)**2 + fdqdr * 2.0*(fdq3z-fdq2z)/(fdq2-fdq3) + fdqd3=(2.0*fdq2z**3 +6.0*fdq2*fdq2z*fdq2z2+fdq2*fdq2*fdq2z3 & + -6.0*fdq2z*fdq2z2*fdq3-2.0*fdq2z**2 *fdq3z & + -2.0*fdq2*fdq2z3*fdq3 -2.0*fdq2*fdq2z2*fdq3z & + +2.0*fdq2*fdq2z*fdq3z2+fdq2*fdq2*fdq3z3) /(fdq2-fdq3)**2 & + + 2.0/(fdq2-fdq3)* ( 2.0*fdqd2*(fdq3z-fdq2z) & + + fdqdr*(fdq3z2-fdq2z2) - fdqdr/(fdq2-fdq3)*(fdq3z-fdq2z)**2 ) + fdqd4=( 12.0*fdq2z**2 *fdq2z2+6.0*fdq2*fdq2z2**2 & + +8.0*fdq2*fdq2z*fdq2z3+fdq2*fdq2*fdq2z4-6.0*fdq2z2**2 *fdq3 & + -12.0*fdq2z*fdq2z2*fdq3z -8.0*fdq2z*fdq2z3*fdq3 & + -2.0*fdq2*fdq2z4*fdq3-4.0*fdq2*fdq2z3*fdq3z & + +4.0*fdq2*fdq2z*fdq3z3+fdq2**2 *fdq3z4 ) /(fdq2-fdq3)**2 & + + 6.0/(fdq2-fdq3)* ( fdqd3*(fdq3z-fdq2z) & + -fdqd2/(fdq2-fdq3)*(fdq3z-fdq2z)**2 & + - fdqdr/(fdq2-fdq3)*(fdq3z-fdq2z)*(fdq3z2-fdq2z2) & + + fdqd2*(fdq3z2-fdq2z2) +1.0/3.0*fdqdr*(fdq3z3-fdq2z3) ) + zdq = fdqdr*eta + zdqz = fdqd2*eta + fdqdr + zdqz2 = fdqd3*eta + 2.0* fdqd2 + zdqz3 = fdqd4*eta + 3.0* fdqd3 + END IF + + +END SUBROUTINE P_DQ_VRABEC_GROSS + + + +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! + SUBROUTINE F_pert_theory ( fdsp ) +! + USE EOS_VARIABLES, ONLY: nc, PI, ncomp, t, p, rho, eta, & + x, z0t, mseg, parame, order1, order2 + USE EOS_NUMERICAL_DERIVATIVES, ONLY: disp_term + USE DFT_MODULE + IMPLICIT NONE +! +!--------------------------------------------------------------------- + REAL, INTENT(IN OUT) :: fdsp +!--------------------------------------------------------------------- + REAL :: I1, I2 + REAL :: z3, zms, c1_con, m_mean +!--------------------------------------------------------------------- + + ! caution: positive sign of correlation integral is used here ! + ! (the Helmholtz energy terms are written with a negative sign, while I1 and I2 are positive) + + IF (disp_term == 'PT1') THEN + + CALL f_dft ( I1, I2) + c1_con = 0.0 + I2 = 0.0 + fdsp = + ( - 2.0*PI*rho*I1*order1 ) + + ELSEIF (disp_term == 'PT2') THEN + + CALL f_dft ( I1, I2) + z3 = eta + zms = 1.0 - z3 + m_mean = z0t / ( PI / 6.0 ) + c1_con = 1.0/ ( 1.0 + m_mean*(8.0*z3-2.0*z3**2 )/zms**4 & + + (1.0 - m_mean)*( 20.0*z3 -27.0*z3**2 +12.0*z3**3 -2.0*z3**4 ) & + /(zms*(2.0-z3))**2 ) + fdsp = + ( - 2.0*PI*rho*I1*order1 - PI*rho*c1_con*m_mean*I2*order2 ) + + ELSEIF (disp_term == 'PT_MIX') THEN + + CALL f_pert_theory_mix ( fdsp ) + + ELSEIF (disp_term == 'PT_MF') THEN + + ! mean field theory + I1 = - ( - 8.0/9.0 - 4.0/9.0*(rc**(-9) -3.0*rc**(-3) ) - tau_cut/3.0*(rc**3 -1.0) ) + fdsp = + ( - 2.0*PI*rho*I1*order1 ) + write (*,*) 'caution: not thoroughly checked and tested' + + ELSE + write (*,*) 'define the type of perturbation theory' + stop + END IF + + ! I1 = I1 + 4.0/9.0*(2.5**-9 -3.0*2.5**-3 ) + ! fdsp = + ( - 2.0*PI*rho*I1*order1 - PI*rho*c1_con*m_mean*I2*order2 ) + + END SUBROUTINE F_pert_theory + + + + +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! + SUBROUTINE f_pert_theory_mix ( fdsp ) +! + USE EOS_VARIABLES, ONLY: nc, PI, ncomp, t, rho, eta, x, parame, mseg, dhs, sig_ij, uij + USE DFT_MODULE + IMPLICIT NONE +! +! ---------------------------------------------------------------------- + REAL, INTENT(IN OUT) :: fdsp +! +! ---------------------------------------------------------------------- + INTEGER :: k, ih + INTEGER :: l, m + REAL :: z3 + REAL :: ua, ua_c, rm + REAL, DIMENSION(nc,nc) :: I1 + REAL :: int10, int11 + REAL :: d_ij, dzr_local + REAL :: rad, xg, rdf + REAL :: dg_dz3, dg_dr + ! REAL :: intgrid(0:5000),intgri2(0:5000), utri(5000),I1_spline +! ---------------------------------------------------------------------- + +! -----constants-------------------------------------------------------- + ua_c = 4.0 * ( rc**(-12) - rc**(-6) ) + rm = 2.0**(1.0/6.0) + + I1(:,:) = 0.0 + + DO l = 1, ncomp + DO m = 1, ncomp + + rad = rc + + int10 = rc * rc * ua_c + ! intgrid(0)= int10 + + k = 0 + ih = 85 + + DO WHILE ( rad /= 1.0 ) + + dzr_local = dzr + IF ( rad - dzr_local <= 1.0 ) dzr_local = rad - 1.0 + + rad = rad - dzr_local + + k = k + 1 + + d_ij = 0.5*(dhs(l)+dhs(m)) / sig_ij(l,m) ! dimensionless effective hs-diameter d(T)/sig + xg = rad / d_ij + z3 = eta + rdf = 1.0 + dg_dz3 = 0.0 + IF ( rad <= rg ) THEN + IF ( l == 1 .AND. m == 1 ) CALL BI_CUB_SPLINE (z3,xg,ya_11,x1a_11,x2a_11,y1a_11,y2a_11,y12a_11, & + c_bicub_11,rdf,dg_dz3,dg_dr,den_step,ih,k) + IF ( l /= m ) CALL BI_CUB_SPLINE (z3,xg,ya_12,x1a_12,x2a_12,y1a_12,y2a_12,y12a_12, & + c_bicub_12,rdf,dg_dz3,dg_dr,den_step,ih,k) + IF ( l == 2 .AND. m == 2 ) CALL BI_CUB_SPLINE (z3,xg,ya_22,x1a_22,x2a_22,y1a_22,y2a_22,y12a_22, & + c_bicub_22,rdf,dg_dz3,dg_dr,den_step,ih,k) + END IF + + ua = 4.0 * ( rad**(-12) - rad**(-6) ) + + int11 = rdf * rad * rad * ua + I1(l,m) = I1(l,m) + dzr_local * ( int11 + int10 ) / 2.0 + + int10 = int11 + ! intgrid(k)= int11 + + END DO + + ! stepno = k + ! CALL SPLINE_PARA (dzr,intgrid,utri,stepno) + ! CALL SPLINE_INT (I1_spline,dzr,intgrid,utri,stepno) + + + ! caution: 1st order integral is in F_EOS.f defined with negative sign + ! --------------------------------------------------------------- + ! cut-off corrections + ! --------------------------------------------------------------- + ! I1(l,m) = I1(l,m) + ( 4.0/9.0 * rc**-9 - 4.0/3.0 * rc**-3 ) + ! I2(l,m) = I2(l,m) + 16.0/21.0 * rc**-21 - 32.0/15.0 * rc**-15 + 16.0/9.0 * rc**-9 + + END DO + END DO + + + fdsp = 0.0 + DO l = 1, ncomp + DO m = 1, ncomp + fdsp = fdsp + 2.0*PI*rho*x(l)*x(m)* mseg(l)*mseg(m)*sig_ij(l,m)**3 * uij(l,m)/t *I1(l,m) + ! ( 2.0*PI*rho*I1*order1 - PI*rho*c1_con*m_mean*I2*order2 ) + END DO + END DO + + +!!$ IF (disp_term == 'PT1') THEN +!!$ c1_con = 0.0 +!!$ I2 = 0.0 +!!$ ELSEIF (disp_term == 'PT2') THEN +!!$ zms = 1.0 - z3 +!!$ c1_con = 1.0/ ( 1.0 + m_mean*(8.0*z3-2.0*z3**2 )/zms**4 & +!!$ + (1.0 - m_mean)*( 20.0*z3 -27.0*z3**2 +12.0*z3**3 -2.0*z3**4 ) & +!!$ /(zms*(2.0-z3))**2 ) +!!$ ELSE +!!$ write (*,*) 'define the type of perturbation theory' +!!$ stop +!!$ END IF + + +END SUBROUTINE f_pert_theory_mix + + +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! + SUBROUTINE mu_pert_theory_mix ( mu_dsp ) +! + USE EOS_VARIABLES, ONLY: nc, PI, ncomp, t, rho, eta, x, parame, mseg, dhs, sig_ij, uij + USE DFT_MODULE + IMPLICIT NONE +! +! ---------------------------------------------------------------------- + REAL, INTENT(IN OUT) :: mu_dsp(nc) +! +! ---------------------------------------------------------------------- + INTEGER :: k, ih + INTEGER :: l, m + REAL :: z3 + REAL :: ua, ua_c, rm + REAL, DIMENSION(nc,nc) :: I1, I2 + REAL :: int1_0, int1_1, int2_0, int2_1 + REAL :: d_ij, dzr_local + REAL :: rad, xg, rdf + REAL :: dg_dz3, dg_dr + REAL :: term1(nc), term2 + ! REAL :: intgrid(0:5000),intgri2(0:5000), utri(5000),I1_spline +! ---------------------------------------------------------------------- + +! -----constants-------------------------------------------------------- + ua_c = 4.0 * ( rc**(-12) - rc**(-6) ) + rm = 2.0**(1.0/6.0) + + I1(:,:) = 0.0 + I2(:,:) = 0.0 + + DO l = 1, ncomp + + term1(l) = 0.0 + + DO m = 1, ncomp + + rad = rc + + int1_0 = rc * rc * ua_c + int2_0 = 0.0 + + k = 0 + ih = 85 + + DO WHILE ( rad /= 1.0 ) + + dzr_local = dzr + IF ( rad - dzr_local <= 1.0 ) dzr_local = rad - 1.0 + + rad = rad - dzr_local + k = k + 1 + + d_ij = 0.5*(dhs(l)+dhs(m)) / sig_ij(l,m) ! dimensionless effective hs-diameter d(T)/sig + xg = rad / d_ij + z3 = eta + rdf = 1.0 + dg_dz3 = 0.0 + IF ( rad <= rg ) THEN + IF ( l == 1 .AND. m == 1 ) CALL BI_CUB_SPLINE (z3,xg,ya_11,x1a_11,x2a_11,y1a_11,y2a_11,y12a_11, & + c_bicub_11,rdf,dg_dz3,dg_dr,den_step,ih,k) + IF ( l /= m ) CALL BI_CUB_SPLINE (z3,xg,ya_12,x1a_12,x2a_12,y1a_12,y2a_12,y12a_12, & + c_bicub_12,rdf,dg_dz3,dg_dr,den_step,ih,k) + IF ( l == 2 .AND. m == 2 ) CALL BI_CUB_SPLINE (z3,xg,ya_22,x1a_22,x2a_22,y1a_22,y2a_22,y12a_22, & + c_bicub_22,rdf,dg_dz3,dg_dr,den_step,ih,k) + END IF + + ua = 4.0 * ( rad**(-12) - rad**(-6) ) + + int1_1 = rdf * rad * rad * ua + int2_1 = dg_dz3 * rad * rad * ua + I1(l,m) = I1(l,m) + dzr_local * ( int1_1 + int1_0 ) / 2.0 + I2(l,m) = I2(l,m) + dzr_local * ( int2_1 + int2_0 ) / 2.0 + + int1_0 = int1_1 + int2_0 = int2_1 + + term1(l) = term1(l) +4.0*PI*rho*x(m)* mseg(l)*mseg(m) *sig_ij(l,m)**3 *uij(l,m)/t* dzr_local*(int1_1+int1_0)/2.0 + + END DO + + END DO + END DO + + + ! DO l = 1, ncomp + ! term1(l) = 0.0 + ! DO m = 1, ncomp + ! term1(l) = term1(l) + 4.0*PI*rho*x(m)* mseg(l)*mseg(m) * sig_ij(l,m)**3 * uij(l,m)/t *I1(l,m) + ! END DO + ! END DO + + term2 = 0.0 + DO l = 1, ncomp + DO m = 1, ncomp + term2 = term2 + 2.0*PI*rho*x(l) * rho*x(m)* mseg(l)*mseg(m) * sig_ij(l,m)**3 * uij(l,m)/t *I2(l,m) + END DO + END DO + + DO l = 1, ncomp + mu_dsp(l) = term1(l) + term2 * PI/ 6.0 * mseg(l)*dhs(l)**3 + END DO + +END SUBROUTINE mu_pert_theory_mix + + +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! + SUBROUTINE F_DD_GROSS_VRABEC( fdd ) +! + USE PARAMETERS, ONLY: PI, KBOL + USE EOS_VARIABLES, ONLY: nc, ncomp, uij, parame, mseg, sig_ij, rho, eta, x, t + USE EOS_CONSTANTS, ONLY: ddp2, ddp3, ddp4 + IMPLICIT NONE +! +! ---------------------------------------------------------------------- + REAL, INTENT(IN OUT) :: fdd +! ---------------------------------------------------------------------- + INTEGER :: i, j, k, m + INTEGER :: ddit, ddmax + REAL :: factor2, factor3 + REAL :: xijfa, xijkfa, xijf_j, xijkf_j, eij + REAL :: fdd2, fdd3 + REAL, DIMENSION(nc) :: my2dd, my0, alph_tst, z1dd, z2dd, dderror + REAL, DIMENSION(nc) :: fdd2m, fdd3m, fdd2m2, fdd3m2, fddm, fddm2 + REAL, DIMENSION(nc,nc) :: Idd2, Idd4 + REAL, DIMENSION(nc,nc,nc) :: Idd3 +! ---------------------------------------------------------------------- + + fdd = 0.0 + ddit = 0 + ddmax = 0 ! value assigned, if polarizable compound is present + fddm(:) = 0.0 + DO i = 1, ncomp + IF ( uij(i,i) == 0.0 ) write (*,*) 'F_DD_GROSS_VRABEC: do not use dimensionless units' + IF ( uij(i,i) == 0.0 ) stop + my2dd(i) = (parame(i,6))**2 *1.E-49 /(uij(i,i)*kbol* mseg(i)*sig_ij(i,i)**3 *1.E-30) + alph_tst(i) = parame(i,11) / (mseg(i)*sig_ij(i,i)**3 ) * t/parame(i,3) + IF ( alph_Tst(i) /= 0.0 ) ddmax = 25 ! set maximum number of polarizable RGT-iterations + z1dd(i) = my2dd(i) + 3.0*alph_tst(i) + z2dd(i) = 3.0*alph_tst(i) + my0(i) = my2dd(i) + END DO + + DO i = 1, ncomp + DO j = 1, ncomp + Idd2(i,j) = 0.0 + Idd4(i,j) = 0.0 + ! IF (parame(i,6).NE.0.0 .AND. parame(j,6).NE.0.0) THEN + DO m = 0, 4 + Idd2(i,j) = Idd2(i,j) + ddp2(i,j,m)*eta**m + Idd4(i,j) = Idd4(i,j) + ddp4(i,j,m)*eta**m + END DO + DO k = 1, ncomp + Idd3(i,j,k) = 0.0 + ! IF (parame(k,6).NE.0.0) THEN + DO m = 0, 4 + Idd3(i,j,k) = Idd3(i,j,k) + ddp3(i,j,k,m)*eta**m + END DO + ! ENDIF + END DO + ! ENDIF + END DO + END DO + + factor2 = -PI *rho + factor3 = -4.0/3.0*PI**2 * rho**2 + +9 CONTINUE + + fdd2m(:) = 0.0 + fdd2m2(:) = 0.0 + fdd3m(:) = 0.0 + fdd3m2(:) = 0.0 + fdd2 = 0.0 + fdd3 = 0.0 + DO i = 1, ncomp + DO j = 1, ncomp + ! IF (parame(i,6).NE.0.0 .AND. parame(j,6).NE.0.0) THEN + xijfa =x(i)*parame(i,3)/t*parame(i,2)**3 * x(j)*parame(j,3)/t*parame(j,2)**3 & + /((parame(i,2)+parame(j,2))/2.0)**3 * (z1dd(i)*z1dd(j)-z2dd(i)*z2dd(j)) ! * (1.0-lij(i,j)) + eij = (parame(i,3)*parame(j,3))**0.5 + fdd2= fdd2 + factor2 * xijfa * ( Idd2(i,j) + eij/t*Idd4(i,j) ) + xijf_j = parame(i,3)/t*parame(i,2)**3 *x(j)*parame(j,3)/t*parame(j,2)**3 & + /((parame(i,2)+parame(j,2))/2.0)**3 ! * (1.0-lij(i,j)) + fdd2m(i)=fdd2m(i)+4.0*SQRT(my2dd(i))*z1dd(j)*factor2* xijf_j *(Idd2(i,j)+eij/t*Idd4(i,j)) + fdd2m2(i)=fdd2m2(i) + 4.0*z1dd(j)*factor2* xijf_j *(Idd2(i,j)+eij/t*Idd4(i,j)) + IF (j == i) fdd2m2(i) =fdd2m2(i) +8.0*factor2* xijf_j*my2dd(i) *(Idd2(i,j)+eij/t*Idd4(i,j)) + DO k = 1, ncomp + ! IF (parame(k,6).NE.0.0) THEN + xijkfa = x(i)*parame(i,3)/t*parame(i,2)**3 *x(j)*parame(j,3)/t*parame(j,2)**3 & + *x(k)*parame(k,3)/t*parame(k,2)**3 / ((parame(i,2)+parame(j,2))/2.0) & + /((parame(i,2)+parame(k,2))/2.0) / ((parame(j,2)+parame(k,2))/2.0) & + *(z1dd(i)*z1dd(j)*z1dd(k)-z2dd(i)*z2dd(j)*z2dd(k)) + ! *(1.0-lij(i,j))*(1.0-lij(i,k))*(1.0-lij(j,k)) + fdd3 = fdd3 + factor3 * xijkfa * Idd3(i,j,k) + xijkf_j = parame(i,3)/t*parame(i,2)**3 *x(j)*parame(j,3)/t*parame(j,2)**3 & + *x(k)*parame(k,3)/t*parame(k,2)**3 /((parame(i,2)+parame(j,2))/2.0) & + /((parame(i,2)+parame(k,2))/2.0) /((parame(j,2)+parame(k,2))/2.0) + ! *(1.0-lij(i,j))*(1.0-lij(i,k))*(1.0-lij(j,k)) + fdd3m(i)=fdd3m(i)+6.0*factor3*SQRT(my2dd(i))*z1dd(j)*z1dd(k) *xijkf_j*Idd3(i,j,k) + fdd3m2(i)=fdd3m2(i)+6.0*factor3*z1dd(j)*z1dd(k) *xijkf_j*Idd3(i,j,k) + IF(j == i) fdd3m2(i) =fdd3m2(i)+24.0*factor3*my2dd(i)*z1dd(k) *xijkf_j*Idd3(i,j,k) + ! ENDIF + END DO + ! ENDIF + END DO + END DO + + IF (fdd2 < -1.E-50 .AND. fdd3 /= 0.0) THEN + fdd = fdd2 / ( 1.0 - fdd3/fdd2 ) + IF ( ddmax /= 0 ) THEN + DO i = 1, ncomp + ddit = ddit + 1 + fddm(i) =fdd2*(fdd2*fdd2m(i) -2.0*fdd3*fdd2m(i)+fdd2*fdd3m(i)) /(fdd2-fdd3)**2 + fddm2(i) = fdd2m(i) * (fdd2*fdd2m(i)-2.0*fdd3*fdd2m(i) +fdd2*fdd3m(i)) / (fdd2-fdd3)**2 & + + fdd2*(fdd2*fdd2m2(i) -2.0*fdd3*fdd2m2(i)+fdd2m(i)**2 & + -fdd2m(i)*fdd3m(i) +fdd2*fdd3m2(i)) / (fdd2-fdd3)**2 & + - 2.0*fdd2*(fdd2*fdd2m(i) -2.0*fdd3*fdd2m(i) +fdd2*fdd3m(i)) /(fdd2-fdd3)**3 & + *(fdd2m(i)-fdd3m(i)) + dderror(i)= SQRT( my2dd(i) ) - SQRT( my0(i) ) + alph_Tst(i)*fddm(i) + my2dd(i) = ( SQRT( my2dd(i) ) - dderror(i) / (1.0+alph_Tst(i)*fddm2(i)) )**2 + z1dd(i) = my2dd(i) + 3.0 * alph_Tst(i) + ENDDO + DO i = 1, ncomp + IF (ABS(dderror(i)) > 1.E-11 .AND. ddit < ddmax) GOTO 9 + ENDDO + fdd = fdd + SUM( 0.5*x(1:ncomp)*alph_Tst(1:ncomp)*fddm(1:ncomp)**2 ) + ENDIF + END IF + + +END SUBROUTINE F_DD_GROSS_VRABEC + + + +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! + SUBROUTINE F_QQ_GROSS( fqq ) +! + USE PARAMETERS, ONLY: PI, KBOL + USE EOS_VARIABLES, ONLY: nc, ncomp, uij, parame, mseg, sig_ij, rho, eta, x, t + USE EOS_CONSTANTS, ONLY: qqp2, qqp3, qqp4 + IMPLICIT NONE +! +! ---------------------------------------------------------------------- + REAL, INTENT(IN OUT) :: fqq +! ---------------------------------------------------------------------- + INTEGER :: i, j, k, m + REAL :: factor2, factor3 + REAL :: xijfa, xijkfa, eij + REAL :: fqq2, fqq3 + REAL, DIMENSION(nc) :: qq2 + REAL, DIMENSION(nc,nc) :: Iqq2, Iqq4 + REAL, DIMENSION(nc,nc,nc) :: Iqq3 +! ---------------------------------------------------------------------- + + + fqq = 0.0 + DO i = 1, ncomp + qq2(i) = (parame(i,7))**2 *1.E-69 / (uij(i,i)*kbol*mseg(i)*sig_ij(i,i)**5 *1.E-50) + END DO + + DO i = 1, ncomp + DO j = 1, ncomp + Iqq2(i,j) = 0.0 + Iqq4(i,j) = 0.0 + IF (parame(i,7) /= 0.0 .AND. parame(j,7) /= 0.0) THEN + DO m = 0, 4 + Iqq2(i,j) = Iqq2(i,j) + qqp2(i,j,m)*eta**m + Iqq4(i,j) = Iqq4(i,j) + qqp4(i,j,m)*eta**m + END DO + DO k = 1, ncomp + Iqq3(i,j,k) = 0.0 + IF (parame(k,7) /= 0.0) THEN + DO m = 0, 4 + Iqq3(i,j,k) = Iqq3(i,j,k) + qqp3(i,j,k,m)*eta**m + END DO + END IF + END DO + END IF + END DO + END DO + + factor2 = -9.0/16.0*PI *rho + factor3 = 9.0/16.0*PI**2 * rho**2 + + fqq2 = 0.0 + fqq3 = 0.0 + DO i = 1, ncomp + DO j = 1, ncomp + IF (parame(i,7) /= 0.0 .AND. parame(j,7) /= 0.0) THEN + xijfa=x(i)*uij(i,i)*qq2(i)*sig_ij(i,i)**5 /t & + *x(j)*uij(j,j)*qq2(j)*sig_ij(j,j)**5 /t/sig_ij(i,j)**7.0 + eij = (parame(i,3)*parame(j,3))**0.5 + fqq2= fqq2 +factor2* xijfa * (Iqq2(i,j)+eij/t*Iqq4(i,j)) + DO k = 1, ncomp + IF (parame(k,7) /= 0.0) THEN + xijkfa=x(i)*uij(i,i)*qq2(i)*sig_ij(i,i)**5 /t/sig_ij(i,j)**3 & + *x(j)*uij(j,j)*qq2(j)*sig_ij(j,j)**5 /t/sig_ij(i,k)**3 & + *x(k)*uij(k,k)*qq2(k)*sig_ij(k,k)**5 /t/sig_ij(j,k)**3 + fqq3 = fqq3 + factor3 * xijkfa * Iqq3(i,j,k) + END IF + END DO + END IF + END DO + END DO + + IF ( fqq2 < -1.E-50 .AND. fqq3 /= 0.0 ) THEN + fqq = fqq2 / ( 1.0 - fqq3/fqq2 ) + END IF + + + +END SUBROUTINE F_QQ_GROSS + +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! + SUBROUTINE F_DQ_VRABEC_GROSS( fdq ) +! + USE PARAMETERS, ONLY: PI, KBOL + USE EOS_VARIABLES, ONLY: nc, ncomp, uij, parame, mseg, sig_ij, rho, eta, x, t + USE EOS_CONSTANTS, ONLY: dqp2, dqp3, dqp4 + IMPLICIT NONE +! +! ---------------------------------------------------------------------- + REAL, INTENT(IN OUT) :: fdq +! ---------------------------------------------------------------------- + INTEGER :: i, j, k, m + REAL :: factor2, factor3 + REAL :: xijfa, xijkfa, eij + REAL :: fdq2, fdq3 + REAL, DIMENSION(nc) :: my2dd, myfac, qq2, q_fac + REAL, DIMENSION(nc,nc) :: Idq2, Idq4 + REAL, DIMENSION(nc,nc,nc) :: Idq3 +! ---------------------------------------------------------------------- + + + fdq = 0.0 + DO i = 1, ncomp + my2dd(i) = (parame(i,6))**2 *1.E-49 /(uij(i,i)*kbol* mseg(i)*sig_ij(i,i)**3 *1.E-30) + myfac(i) = parame(i,3)/t*parame(i,2)**4 *my2dd(i) + ! myfac(i)=parame(i,3)/T*parame(i,2)**4 *my2dd_renormalized(i) + qq2(i) = (parame(i,7))**2 *1.E-69 / (uij(i,i)*kbol*mseg(i)*sig_ij(i,i)**5 *1.E-50) + q_fac(i) = parame(i,3)/t*parame(i,2)**4 *qq2(i) + END DO + + DO i = 1, ncomp + DO j = 1, ncomp + Idq2(i,j) = 0.0 + Idq4(i,j) = 0.0 + IF (myfac(i) /= 0.0 .AND. q_fac(j) /= 0.0) THEN + DO m = 0, 4 + Idq2(i,j) = Idq2(i,j) + dqp2(i,j,m)*eta**m + Idq4(i,j) = Idq4(i,j) + dqp4(i,j,m)*eta**m + END DO + DO k = 1, ncomp + Idq3(i,j,k) = 0.0 + IF (myfac(k) /= 0.0 .OR. q_fac(k) /= 0.0) THEN + DO m = 0, 4 + Idq3(i,j,k) = Idq3(i,j,k) + dqp3(i,j,k,m)*eta**m + END DO + END IF + END DO + END IF + END DO + END DO + + factor2 = -9.0/4.0 * PI *rho + factor3 = PI**2 * rho**2 + + fdq2 = 0.0 + fdq3 = 0.0 + DO i = 1, ncomp + DO j = 1, ncomp + IF (myfac(i) /= 0.0 .AND. q_fac(j) /= 0.0) THEN + xijfa = x(i)*myfac(i) * x(j)*q_fac(j) /sig_ij(i,j)**5 + eij = (parame(i,3)*parame(j,3))**0.5 + fdq2 = fdq2 +factor2* xijfa*(Idq2(i,j)+eij/t*Idq4(i,j)) + DO k = 1, ncomp + IF (myfac(k) /= 0.0 .OR. q_fac(k) /= 0.0) THEN + xijkfa=x(i)*x(j)*x(k)/(sig_ij(i,j)*sig_ij(i,k)*sig_ij(j,k))**2 & + *( myfac(i)*q_fac(j)*myfac(k) + myfac(i)*q_fac(j)*q_fac(k)*1.1937350 ) + fdq3 = fdq3 + factor3*xijkfa*Idq3(i,j,k) + END IF + END DO + END IF + END DO + END DO + + IF (fdq2 < -1.E-50 .AND. fdq3 /= 0.0) THEN + fdq = fdq2 / ( 1.0 - fdq3/fdq2 ) + END IF + +END SUBROUTINE F_DQ_VRABEC_GROSS + + +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! + SUBROUTINE f_dft ( I1_dft, I2_dft ) +! + USE EOS_VARIABLES, ONLY: nc, PI, ncomp, t, rho, eta, x, mseg, parame + USE DFT_MODULE + IMPLICIT NONE +! +! ---------------------------------------------------------------------- + REAL, INTENT(OUT) :: I1_dft + REAL, INTENT(OUT) :: I2_dft +! +! ---------------------------------------------------------------------- + INTEGER :: k,ih + ! REAL :: z3 + REAL :: ua, ua_c, ua_2, ua_c_2, rm + REAL :: int10, int11, int20, int21 + REAL :: dg_drho + REAL :: rad, xg, rdf, rho_st, msegm + REAL :: sig_ij + REAL :: dg_dr, dzr_org !,rdf_d + ! REAL :: intgrid(0:NDFT),intgri2(0:NDFT) +! ---------------------------------------------------------------------- + +! -----constants-------------------------------------------------------- +msegm = parame(1,1) +rho_st = rho * parame(1,2)**3 + +ua_c = 4.0 * ( rc**(-12) - rc**(-6) ) +ua_c_2 = ua_c * ua_c +rm = 2.0**(1.0/6.0) + +int10 = rc*rc* ua_c +int20 = rc*rc* ua_c_2 +! intgrid(0)= int10 +! intgri2(0)= int20 + + +sig_ij = parame(1,2) + + +I1_dft = 0.0 +I2_dft = 0.0 +rad = rc +!dzr = dzp / 2.0 ! this line is obsolete. dzr is defined in DFT-nMF2 (dimensionless) +dzr_org= dzr +k = 0 +ih = 85 + +DO WHILE ( rad-dzr+1.E-9 >= 1.0 ) + + rad = rad - dzr + ! IF (rad <= 8.0) dzr = dzp + ! IF (rad <= rg) dzr = dzp/2.0 + k = k + 1 + xg = rad / dhs_st + ua = 4.0 * ( rad**(-12) - rad**(-6) ) + ua_2 = ua * ua + rdf = 1.0 + dg_drho = 0.0 + IF ( rad <= rg ) THEN + CALL BI_CUB_SPLINE (rho_st,xg,ya,x1a,x2a,y1a,y2a,y12a, & + c_bicub,rdf,dg_drho,dg_dr,den_step,ih,k) + END IF + + int11 = rdf*rad*rad* ua + int21 = rdf*rad*rad* ua_2 + I1_dft= I1_dft + dzr*(int11+int10)/2.0 + I2_dft= I2_dft + dzr*(int21+int20)/2.0 + int10 = int11 + int20 = int21 + +END DO + +dzr = dzr_org + +! stepno = k +! CALL SPLINE_PARA (dzr,intgrid,utri,stepno) +! CALL SPLINE_INT (I1,dzr,intgrid,utri,stepno) + +! caution: 1st order integral is in F_EOS.f defined with negative sign +I1_dft= - I1_dft - ( 4.0/9.0 * rc**(-9) - 4.0/3.0 * rc**(-3) ) + +! CALL SPLINE_PARA (dzr,intgri2,utri,stepno) +! CALL SPLINE_INT (I2,dzr,intgri2,utri,stepno) + +I2_dft = I2_dft + 16.0/21.0 * rc**(-21) - 32.0/15.0 * rc**(-15) + 16.0/9.0 * rc**(-9) + + +END SUBROUTINE f_dft + + + + +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! + REAL FUNCTION TANGENT_VALUE2 ( optpara, n ) +! SUBROUTINE TANGENT_VALUE ( fmin, optpara, n ) +! + USE BASIC_VARIABLES + USE STARTING_VALUES + IMPLICIT NONE +! +! ---------------------------------------------------------------------- + INTEGER, INTENT(IN) :: n + REAL, INTENT(IN) :: optpara(n) + !REAL, INTENT(IN) :: optpara(:) + !REAL, INTENT(IN OUT) :: fmin +! +! ---------------------------------------------------------------------- + INTEGER :: i + REAL :: lnphi(np,nc),ph_frac, gibbs_full(np),xlnx1,xlnx2 + REAL, DIMENSION(nc) :: ni_1, ni_2 +! ---------------------------------------------------------------------- + + + ! --- setting of mole fractions --------------------------------------- + DO i = 1, ncomp + IF ( optpara(i) < -300.0 ) THEN + ni_2(i) = 0.0 + ELSE + ni_2(i) = EXP( optpara(i) ) + END IF + END DO + + DO i = 1, ncomp + ni_1(i) = xif(i) - ni_2(i) + IF ( ni_2(i) > xif(i) ) THEN + ni_2(i) = xif(i) + ni_1(i) = xif(i) * 1.E-20 + ENDIF + END DO + + xi(2,1:ncomp) = ni_2(1:ncomp) / SUM( ni_2(1:ncomp) ) + lnx(2,1:ncomp) = optpara(1:ncomp) - LOG( SUM( ni_2(1:ncomp) ) ) + + ph_frac = SUM( ni_1(1:ncomp) ) + xi(1,1:ncomp) = ni_1(1:ncomp) / ph_frac + lnx(1,1:ncomp) = LOG( ni_1(1:ncomp) ) - LOG( ph_frac ) + ! write (*,'(a,4G18.8)') 'FF',(xif(i),i=1,ncomp) + ! write (*,'(a,4G18.8)') 'AA',(xi(1,i),i=1,ncomp) + ! write (*,'(a,3G18.8)') 'BB',(xi(2,i),i=1,ncomp) + + CALL fugacity (lnphi) + !CALL enthalpy_etc + + gibbs(1) = SUM( xi(1,1:ncomp) * lnphi(1,1:ncomp) ) ! dimensionless g/RT + gibbs(2) = SUM( xi(2,1:ncomp) * lnphi(2,1:ncomp) ) + + xlnx1 = SUM( xi(1,1:ncomp)*lnx(1,1:ncomp) ) ! dimensionless s/RT + xlnx2 = SUM( xi(2,1:ncomp)*lnx(2,1:ncomp) ) + + gibbs_full(1) = gibbs(1) + xlnx1 + gibbs_full(2) = gibbs(2) + xlnx2 + + TANGENT_VALUE2 = gibbs_full(1)*ph_frac + gibbs_full(2)*(1.0-ph_frac) + !fmin = gibbs_full(1)*ph_frac + gibbs_full(2)*(1.0-ph_frac) + !write (*,'(a,4G18.8)') 'TP',TANGENT_VALUE2,(lnx(1,i),i=1,ncomp) + !write (*,'(a,4G18.8)') 'al',ph_frac,(lnx(2,i), i=1,ncomp) + !write (*,*) ' ' + !pause + +END FUNCTION TANGENT_VALUE2 + + + + + + + + diff --git a/applications/PUfoam/MoDeNaModels/Solubility/ExampleOfUsage/src/srcDetailedCode/getting_started_subroutines.f90 b/applications/PUfoam/MoDeNaModels/Solubility/ExampleOfUsage/src/srcDetailedCode/getting_started_subroutines.f90 new file mode 100644 index 000000000..a09221fd4 --- /dev/null +++ b/applications/PUfoam/MoDeNaModels/Solubility/ExampleOfUsage/src/srcDetailedCode/getting_started_subroutines.f90 @@ -0,0 +1,4078 @@ +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! SUBROUTINE eos_const +! +! This subroutine provides the constants of the PC-SAFT EOS. +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! + SUBROUTINE eos_const (ap,bp,dnm) +! + IMPLICIT NONE +! +! ---------------------------------------------------------------------- + REAL, INTENT(OUT) :: ap(0:6,3) + REAL, INTENT(OUT) :: bp(0:6,3) + REAL, INTENT(OUT) :: dnm(4,9) +! ---------------------------------------------------------------------- + + +! --- dispersion term constants ---------------------------------------- +ap(0,1) = 0.91056314451539 +ap(0,2) = -0.30840169182720 +ap(0,3) = -0.09061483509767 +ap(1,1) = 0.63612814494991 +ap(1,2) = 0.18605311591713 +ap(1,3) = 0.45278428063920 +ap(2,1) = 2.68613478913903 +ap(2,2) = -2.50300472586548 +ap(2,3) = 0.59627007280101 +ap(3,1) = -26.5473624914884 +ap(3,2) = 21.4197936296668 +ap(3,3) = -1.72418291311787 +ap(4,1) = 97.7592087835073 +ap(4,2) = -65.2558853303492 +ap(4,3) = -4.13021125311661 +ap(5,1) = -159.591540865600 +ap(5,2) = 83.3186804808856 +ap(5,3) = 13.7766318697211 +ap(6,1) = 91.2977740839123 +ap(6,2) = -33.7469229297323 +ap(6,3) = -8.67284703679646 + +bp(0,1) = 0.72409469413165 +bp(0,2) = -0.57554980753450 +bp(0,3) = 0.09768831158356 +bp(1,1) = 1.11913959304690 *2.0 +bp(1,2) = 0.34975477607218 *2.0 +bp(1,3) = -0.12787874908050 *2.0 +bp(2,1) = -1.33419498282114 *3.0 +bp(2,2) = 1.29752244631769 *3.0 +bp(2,3) = -3.05195205099107 *3.0 +bp(3,1) = -5.25089420371162 *4.0 +bp(3,2) = -4.30386791194303 *4.0 +bp(3,3) = 5.16051899359931 *4.0 +bp(4,1) = 5.37112827253230 *5.0 +bp(4,2) = 38.5344528930499 *5.0 +bp(4,3) = -7.76088601041257 *5.0 +bp(5,1) = 34.4252230677698 *6.0 +bp(5,2) = -26.9710769414608 *6.0 +bp(5,3) = 15.6044623461691 *6.0 +bp(6,1) = -50.8003365888685 *7.0 +bp(6,2) = -23.6010990650801 *7.0 +bp(6,3) = -4.23812936930675 *7.0 + + +! square-well fluid +! ap(1,1)= 0.79152347258784 +! ap(1,2)= -0.62269805320654 +! ap(1,3)= -0.06798823934067 +! ap(2,1)= 1.07120982251709 +! ap(2,2)= 0.48628215731716 +! ap(2,3)= 0.02837828512515 +! ap(3,1)= 0.92084839459226 +! ap(3,2)= 1.11652038059747 +! ap(3,3)= 0.09713202077943 +! ap(4,1)= -7.84708350369249 +! ap(4,2)= -2.04200599876547 +! ap(4,3)= 0.06475764015088 +! ap(5,1)= 25.90284137818050 +! ap(5,2)= 9.27791640100603 +! ap(5,3)= 0.07729792971827 +! ap(6,1)= -57.1528726997640 +! ap(6,2)= -16.8377999920957 +! ap(6,3)= 0.24883598436184 +! ap(7,1)= 42.02314637860930 +! ap(7,2)= 7.62432635016420 +! ap(7,3)= -0.72472024688888 + +! bp(1,1)= 0.79152347258784 +! bp(1,2)= -0.62269805320654 +! bp(1,3)= -0.06798823934067 +! bp(2,1)= 1.07120982251709 *2.0 +! bp(2,2)= 0.48628215731716 *2.0 +! bp(2,3)= 0.02837828512515 *2.0 +! bp(3,1)= 0.92084839459226 *3.0 +! bp(3,2)= 1.11652038059747 *3.0 +! bp(3,3)= 0.09713202077943 *3.0 +! bp(4,1)= -7.84708350369249 *4.0 +! bp(4,2)= -2.04200599876547 *4.0 +! bp(4,3)= 0.06475764015088 *4.0 +! bp(5,1)= 25.90284137818050 *5.0 +! bp(5,2)= 9.27791640100603 *5.0 +! bp(5,3)= 0.07729792971827 *5.0 +! bp(6,1)= -57.1528726997640 *6.0 +! bp(6,2)= -16.8377999920957 *6.0 +! bp(6,3)= 0.24883598436184 *6.0 +! bp(7,1)= 42.02314637860930 *7.0 +! bp(7,2)= 7.62432635016420 *7.0 +! bp(7,3)= -0.72472024688888 *7.0 + + +dnm(1,1) = -8.8043 +dnm(1,2) = +4.1646270 +dnm(1,3) = -48.203555 +dnm(1,4) = +140.43620 +dnm(1,5) = -195.23339 +dnm(1,6) = +113.51500 +dnm(2,1) = +2.9396 +dnm(2,2) = -6.0865383 +dnm(2,3) = +40.137956 +dnm(2,4) = -76.230797 +dnm(2,5) = -133.70055 +dnm(2,6) = +860.25349 +dnm(2,7) = -1535.3224 +dnm(2,8) = +1221.4261 +dnm(2,9) = -409.10539 +dnm(3,1) = -2.8225 +dnm(3,2) = +4.7600148 +dnm(3,3) = +11.257177 +dnm(3,4) = -66.382743 +dnm(3,5) = +69.248785 +dnm(4,1) = +0.3400 +dnm(4,2) = -3.1875014 +dnm(4,3) = +12.231796 +dnm(4,4) = -12.110681 + +END SUBROUTINE eos_const + + + +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! SUBROUTINE dq_const +! +! This subr. provides the constants of the dipole-quadrupole term. +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! + SUBROUTINE dq_const ( dqp2,dqp3,dqp4 ) +! + USE PARAMETERS, ONLY: nc + USE EOS_VARIABLES, ONLY: ncomp, parame + IMPLICIT NONE +! +! ---------------------------------------------------------------------- + REAL, INTENT(OUT) :: dqp2(nc,nc,0:8) + REAL, INTENT(OUT) :: dqp3(nc,nc,nc,0:8) + REAL, INTENT(OUT) :: dqp4(nc,nc,0:8) +! +! ---------------------------------------------------------------------- + INTEGER :: i, j, k + REAL :: mdq(nc) + REAL :: mf1, mf2, msegij +! ---------------------------------------------------------------------- + +DO i=1,ncomp + mdq(i) = parame(i,1) + IF (mdq(i) > 2.0) mdq(i) = 2.0 +END DO + + +DO i=1,ncomp + DO j=1,ncomp + + msegij=(mdq(i)*mdq(j))**0.5 + mf1 = (msegij-1.0)/msegij + mf2 = mf1*(msegij-2.0)/msegij + + dqp2(i,j,0) = 0.697094963 + mf1*(-0.673459279) + mf2*0.670340770 + dqp2(i,j,1) = -0.633554144 + mf1*(-1.425899106) + mf2*(-4.338471826) + dqp2(i,j,2) = 2.945509028 + mf1 * 4.19441392 + mf2*7.234168360 + dqp2(i,j,3) = -1.467027314 + mf1 * 1.0266216 + dqp2(i,j,4) = 0.0 + + dqp4(i,j,0) = -0.484038322 + mf1 * 0.67651011 + mf2*(-1.167560146) + dqp4(i,j,1) = 1.970405465 + mf1*(-3.013867512) + mf2*2.13488432 + dqp4(i,j,2) = -2.118572671 + mf1 * 0.46742656 + dqp4(i,j,3) = 0.0 + dqp4(i,j,4) = 0.0 + + + DO k=1,ncomp + msegij=(mdq(i)*mdq(j)*mdq(k))**(1.0/3.0) + mf1 = (msegij-1.0)/msegij + mf2 = (msegij-2.0)/msegij + dqp3(i,j,k,0) = 0.795009692 + mf1*(-2.099579397) + dqp3(i,j,k,1) = 3.386863396 + mf1*(-5.941376392) + dqp3(i,j,k,2) = 0.475106328 + mf1*(-0.178820384) + dqp3(i,j,k,3) = 0.0 + dqp3(i,j,k,4) = 0.0 + END DO + + END DO +END DO + +END SUBROUTINE dq_const + + +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! SUBROUTINE dd_const +! +! This subroutine provides the constants of the dipole-term. +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! + SUBROUTINE dd_const ( ddp2,ddp3,ddp4 ) +! + USE PARAMETERS, ONLY: nc, PI + USE EOS_VARIABLES, ONLY: ncomp, parame + IMPLICIT NONE +! +! ---------------------------------------------------------------------- + REAL, INTENT(OUT) :: ddp2(nc,nc,0:8) + REAL, INTENT(OUT) :: ddp3(nc,nc,nc,0:8) + REAL, INTENT(OUT) :: ddp4(nc,nc,0:8) +! +! ---------------------------------------------------------------------- + INTEGER :: i, j, k + REAL :: pardd(nc) + REAL :: mf1,mf2,msegij,sin2t +! ---------------------------------------------------------------------- + +sin2t = SIN( 0.0 * PI / 180.0 ) +sin2t = sin2t*sin2t + +DO i = 1, ncomp + pardd(i) = parame(i,1) + IF (pardd(i) > 2.0) pardd(i) = 2.0 +END DO + +DO i=1,ncomp + DO j=1,ncomp +! IF (parame(i,6).NE.0.0.AND.parame(j,6).NE.0.0) THEN + + msegij=(pardd(i)*pardd(j))**0.5 + mf1 = (msegij-1.0)/msegij + mf2 = mf1*(msegij-2.0)/msegij + + ddp2(i,j,0) = 0.30435038064 + mf1*(0.95346405973+0.201436*sin2t) & + + mf2*(-1.16100802773-1.74114*sin2t) + ddp2(i,j,1) = -0.13585877707 + mf1*(-1.83963831920+1.31649*sin2t) & + + mf2*4.52586067320 + ddp2(i,j,2) = 1.44933285154 + mf1 * 2.01311801180 + mf2*0.97512223853 + ddp2(i,j,3) = 0.35569769252 + mf1*(-7.37249576667) + mf2*(-12.2810377713) + ddp2(i,j,4) = -2.06533084541 + mf1 * 8.23741345333 + mf2*5.93975747420 + + ddp4(i,j,0) = 0.21879385627 + mf1*(-0.58731641193) + mf2*3.48695755800 + ddp4(i,j,1) = -1.18964307357 + mf1 * 1.24891317047 + mf2*(-14.9159739347) + ddp4(i,j,2) = 1.16268885692 + mf1*(-0.50852797392) + mf2*15.3720218600 + ddp4(i,j,3) = 0.0 + ddp4(i,j,4) = 0.0 + + DO k=1,ncomp +! IF (parame(k,6).NE.0.0) THEN + msegij=(pardd(i)*pardd(j)*pardd(k))**(1.0/3.0) + mf1 = (msegij-1.0)/msegij + mf2 = mf1*(msegij-2.0)/msegij + ddp3(i,j,k,0) = -0.06467735252 + mf1*(-0.95208758351+0.28503*sin2t) & + + mf2*(-0.62609792333+2.2195*sin2t) + ddp3(i,j,k,1) = 0.19758818347 + mf1 * 2.99242575222 + mf2*1.29246858189 + ddp3(i,j,k,2) = -0.80875619458 + mf1*(-2.38026356489) + mf2*1.65427830900 + ddp3(i,j,k,3) = 0.69028490492 + mf1*(-0.27012609786) + mf2*(-3.43967436378) + ddp3(i,j,k,4) = 0.0 + +! ENDIF + END DO + +! ENDIF + END DO +END DO + +END SUBROUTINE dd_const + + +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! SUBROUTINE qq_const +! +! This subroutine provides the constants of the quadrupole-term. +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! + SUBROUTINE qq_const ( qqp2,qqp3,qqp4 ) +! + USE PARAMETERS, ONLY: nc + USE EOS_VARIABLES, ONLY: ncomp, parame + IMPLICIT NONE +! +! ---------------------------------------------------------------------- + REAL, INTENT(OUT) :: qqp2(nc,nc,0:8) + REAL, INTENT(OUT) :: qqp3(nc,nc,nc,0:8) + REAL, INTENT(OUT) :: qqp4(nc,nc,0:8) +! +! ---------------------------------------------------------------------- + INTEGER :: i, j, k + REAL :: mqq(nc) + REAL :: mf1, mf2, msegij +! ---------------------------------------------------------------------- + +DO i = 1,ncomp + mqq(i) = parame(i,1) + IF (mqq(i) > 2.0) mqq(i) = 2.0 +END DO + +DO i = 1,ncomp + DO j = 1,ncomp + IF (parame(i,7) /= 0.0 .AND. parame(j,7) /= 0.0) THEN + + msegij=(mqq(i)*mqq(j))**0.5 +! msegij=(parame(i,1)*parame(j,1))**0.50 + mf1 = (msegij-1.0)/msegij + mf2 = mf1*(msegij-2.0)/msegij + + qqp2(i,j,0) = 1.237830788 + mf1 * 1.285410878 + mf2*1.794295401 + qqp2(i,j,1) = 2.435503144 + mf1*(-11.46561451) + mf2*0.769510293 + qqp2(i,j,2) = 1.633090469 + mf1 *22.08689285 + mf2*7.264792255 + qqp2(i,j,3) = -1.611815241 + mf1 * 7.46913832 + mf2*94.48669892 + qqp2(i,j,4) = 6.977118504 + mf1*(-17.19777208) + mf2*(-77.1484579) + + qqp4(i,j,0) = 0.454271755 + mf1*(-0.813734006) + mf2*6.868267516 + qqp4(i,j,1) = -4.501626435 + mf1 * 10.06402986 + mf2*(-5.173223765) + qqp4(i,j,2) = 3.585886783 + mf1*(-10.87663092) + mf2*(-17.2402066) + qqp4(i,j,3) = 0.0 + qqp4(i,j,4) = 0.0 + + DO k = 1,ncomp + IF (parame(k,7) /= 0.0) THEN + msegij=(mqq(i)*mqq(j)*mqq(k))**(1.0/3.0) +! msegij=(parame(i,1)*parame(j,1)*parame(k,1))**(1.0/3.0) + mf1 = (msegij-1.0)/msegij + mf2 = mf1*(msegij-2.0)/msegij + qqp3(i,j,k,0) = -0.500043713 + mf1 * 2.000209381 + mf2*3.135827145 + qqp3(i,j,k,1) = 6.531869153 + mf1*(-6.78386584) + mf2*7.247588801 + qqp3(i,j,k,2) = -16.01477983 + mf1 * 20.38324603 + mf2*3.075947834 + qqp3(i,j,k,3) = 14.42597018 + mf1*(-10.89598394) + qqp3(i,j,k,4) = 0.0 + END IF + END DO + + END IF + END DO +END DO + +END SUBROUTINE qq_const + + + + + + + +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! + SUBROUTINE SET_DEFAULT_EOS_NUMERICAL +! + USE EOS_NUMERICAL_DERIVATIVES + IMPLICIT NONE +! +! ---------------------------------------------------------------------- + + ideal_gas = 'no' ! ( yes, no ) + hard_sphere = 'CSBM' ! ( CSBM, no ) + chain_term = 'TPT1' ! ( TPT1, HuLiu, no ) + disp_term = 'PC-SAFT' ! ( PC-SAFT, CK, PT1, PT2, PT_MF, PT_MIX, no ) + hb_term = 'TPT1_Chap' ! ( TPT1_Chap, no ) + LC_term = 'no' ! ( MSaupe, OVL, no ) + branch_term = 'no' ! ( TPT2, no ) + II_term = 'no' + ID_term = 'no' + + subtract1 = 'no' ! (1PT, 2PT, no) + subtract2 = 'no' ! (ITTpolar, no) + +END SUBROUTINE SET_DEFAULT_EOS_NUMERICAL + + + + + + + + + +! SUBROUTINE READ_INPUT +! ! +! USE BASIC_VARIABLES +! IMPLICIT NONE +! ! +! ! ---------------------------------------------------------------------- +! INTEGER :: i +! REAL :: reading2,reading3,sumfeed +! CHARACTER (LEN=4) :: uoutp, uinp +! CHARACTER (LEN=1) :: uoutt, uint +! CHARACTER (LEN=50) :: filename +! CHARACTER (LEN=30) :: reading1 +! ! ---------------------------------------------------------------------- +! +! filename='./input_file/INPUT.INP' +! CALL file_open(filename,30) +! READ (30,*) eos, pol !J: specify by numbers! eos(1=pcsaft, 2=SRK,...) pol (=polar) yes(1) no(0) +! READ (30,*) t, uint, p, uinp !J: t: value of temp, uint: unit of temp, p: value of pressure, uinp: unit of pressure +! +! ncomp = 0 +! i = 0 +! sumfeed = 0.0 +! read_loop: DO +! READ (30,*) reading1,reading2,reading3 +! IF (reading1 == 'end') EXIT read_loop +! ncomp = ncomp + 1 +! i = i + 1 +! compna(i)= reading1 ! comp.name +! mm(i) = reading2 ! molec.mass (mandatory only for polymers) +! xif(i) = reading3 !J: molefractions +! sumfeed = sumfeed + xif(i) +! ENDDO read_loop +! +! CLOSE (30) +! +! IF (sumfeed /= 0.0 .AND. sumfeed /= 1.0) THEN !J: in case mole fractions dont sum up to 1?? +! xif(1:ncomp) = xif(1:ncomp)/sumfeed +! END IF +! +! uoutt = uint +! uoutp = uinp +! IF (uint == 'C') THEN !J: unit stuff +! u_in_t = 273.15 +! ELSE +! u_in_t = 0.0 +! END IF +! IF (uinp == 'bar') THEN +! u_in_p = 1.E5 +! ELSE IF (uinp == 'mbar') THEN +! u_in_p = 1.E2 +! ELSE IF (uinp == 'MPa') THEN +! u_in_p = 1.E6 +! ELSE IF (uinp == 'kPa') THEN +! u_in_p = 1.E3 +! ELSE +! u_in_p = 1.E0 +! END IF +! +! IF (uoutt == 'C') THEN +! u_out_t = 273.15 +! ELSE +! u_out_t = 0.0 +! END IF +! IF (uoutp == 'bar') THEN +! u_out_p = 1.E5 +! ELSE IF (uoutp == 'mbar') THEN +! u_out_p = 1.E2 +! ELSE IF (uoutp == 'MPa') THEN +! u_out_p = 1.E6 +! ELSE IF (uoutp == 'kPa') THEN +! u_out_p = 1.E3 +! ELSE +! u_out_p = 1.0 +! END IF +! +! t = t + u_in_t !J: calculate temp in Kelvin +! p = p * u_in_p !J: calculate pressure in Pascal +! +! CALL para_input ! retriev pure comp. parameters +! +! +! END SUBROUTINE READ_INPUT + + + + + +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! SUBROUTINE file_open +! +! This subroutine opens files for reading. Beforehand, it checks +! whether this file is available. +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! + SUBROUTINE file_open(filename,file_number) +! +! ---------------------------------------------------------------------- + CHARACTER (LEN=50) :: filename + INTEGER :: file_number + LOGICAL :: filefound +! ---------------------------------------------------------------------- + +INQUIRE (FILE=filename, EXIST = filefound) +IF (filefound) THEN + OPEN (file_number, FILE = filename) +ELSE + write (*,*) ' FOLLOWING FILE CAN NOT BE OPENED', filename + stop +END IF + +END SUBROUTINE file_open + + + +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! SUBROUTINE para_input +! +! This subroutine provides pure component parameters and kij parameters. +! The following syntax applies: +! +! compna(i) component name +! parame(i,k) pure comp. parameter: +! parame(i,1): segment number [/] +! parame(i,2): segment diameter "sigma" [Angstrom] +! parame(i,3): segment energy param. epsilon/k [K] +! parame(i,4): model parameter; not used for PC-SAFT (=0) +! it is 10K most of the time for SAFT [K] +! parame(i,5): Param. for T-dependent segment diameter [/] +! parame(i,6): dipolar moment [debye] +! parame(i,7): quadrupolar moment [debye] +! parame(i,8): number of segments that are part of a branching 4-mer [/] +! parame(i,9): +! parame(i,10): ionic charge number (positiv or negativ) [/] +! parame(i,11): polarizability [A**3] +! parame(i,12): number of association sites [/] +! parame(i,13): (=kap_hb, see below) [/] +! parame(i,14 to 25): (=eps_hb, see below) [K] +! nhb_typ(i) number of different types of association sites (comp. i) +! nhb_no(i,k) number of association sites of type k +! eps_hb depth of association potential [K] +! kap_hb effective width of assoc. potential (angle-averg.) +! mm molec. mass +! scaling param. for roughly scaling the set of objective functions +! +! As opposed to low-molec mass compounds, the molecular mass of a +! polymer is not obtained from this routine. Rather, it is a +! user-specification given in the file INPUT.INP +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! + SUBROUTINE para_input +! + USE BASIC_VARIABLES + IMPLICIT NONE +! +!---------------------------------------------------------------------- + INTEGER :: i +!---------------------------------------------------------------------- + +IF (eos == 1) THEN + CALL pcsaft_par +ELSE IF (eos == 4 .OR. eos == 5 .OR. eos == 6 .OR. eos == 8) THEN + ! CALL lj_par + write (*,*) 'deactivated this line when making a transition to f90' + stop +ELSE IF (eos == 7) THEN + ! CALL sw_par + write (*,*) 'deactivated this line when making a transition to f90' + stop +ELSE IF (eos == 10) THEN + i = 1 + IF (compna(i) == 'LC_generic' .AND. ncomp == 1 ) THEN + mm(i) = 1.0 + parame(i,1) = 7.0 + parame(i,2) = 1.0 + parame(i,3) = 0.0 + ELSE + write (*,*) 'PARA_INPUT: define the component !' + stop + ENDIF +ELSE + !CALL saft_par +END IF + +DO i = 1, ncomp + IF ( mm(i) >= 1.0 .AND. mm(i) < 45.0 ) THEN + scaling(i) = 10000.0 + ELSE IF( mm(i) >= 45.0 .AND. mm(i) < 90.0 ) THEN + scaling(i) = 1000.0 + ELSE IF( mm(i) >= 90.0 .AND. mm(i) < 150.0 ) THEN + scaling(i) = 100.0 + ELSE IF( mm(i) >= 150.0 .AND. mm(i) < 250.0 ) THEN + scaling(i) = 10.0 + ELSE + scaling(i) = 1.0 + END IF + IF (parame(i,10) /= 0.0) scaling(i) = scaling(i) / 1.E4 ! Electrolytes +END DO + +END SUBROUTINE para_input + + + + +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! SUBROUTINE pcsaft_par +! +! pure component parameters and kij parameters +! (as described in SUBROUTINE para_input) +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! + SUBROUTINE pcsaft_par +! + USE BASIC_VARIABLES + IMPLICIT NONE +! +!---------------------------------------------------------------------- + INTEGER :: i, j, k, no + INTEGER, DIMENSION(nc) :: nhb_typ + INTEGER, DIMENSION(nc,nsite) :: nhb_no + REAL, DIMENSION(nc,nc,nsite,nsite) :: eps_hb + REAL, DIMENSION(nc,nc) :: kap_hb +!---------------------------------------------------------------------- + + +DO i = 1, ncomp + parame(i,4) = 0.0 ! T correct. required for SAFT, not PC-SAFT + parame(i,5) = 0.12 ! Param. for T-dependent segment diameter + parame(i,6) = 0.0 ! dipolar moment + parame(i,7) = 0.0 ! quadrupolar moment + parame(i,8) = 0.0 ! number of segments that are part of a branching 4-mer + parame(i,9) = 0.0 + parame(i,10)= 0.0 ! ionic charge number + parame(i,11)= 0.0 ! polarizability + lli(i) = 0.0 + phi_criti(i)= 0.0 + chap(i) = 0.0 + + nhb_typ(i) = 0 + kap_hb(i,i) = 0.0 + + IF (compna(i) == '14-butandiol') THEN + mm(i) = 90.12 + parame(i,1) = 4.35923557 + parame(i,2) = 3.02947364 + parame(i,3) = 197.11998863 + + + ELSE IF (compna(i) == 'ps') THEN + parame(i,1) = mm(i)*1.9E-2 + parame(i,2) = 4.10705961 + parame(i,3) = 267.0 + ELSE IF (compna(i) == 'pg2') THEN !Polyglycerol 2 + mm(i) = 2000.0 + parame(i,1) = mm(i)*2.37E-2 ! from figure 5 PCSAFT paper + parame(i,2) = 3.8 ! from figure 5 PCSAFT paper + parame(i,3) = 270.0 ! starting value for iteration + ! this is the extra parameter + parame(i,8) = mm(i)*2.37E-2 + + nhb_typ(i) = 2 ! no. of different association sites + nhb_no(i,1) = 27 ! no. of sites of type 1 + nhb_no(i,2) = 27 ! no. of sites of type 2 + eps_hb(i,i,1,2)= 2544.6 ! taken from butanol (same M/OH) + eps_hb(i,i,2,1)= 2544.6 + eps_hb(i,i,1,1)= 0.0 + eps_hb(i,i,2,2)= 0.0 + kap_hb(i,i)= .00489087833 ! taken from butanol (same M/OH) + ELSE IF (compna(i) == 'peva') THEN + parame(i,1) = mm(i)*2.63E-2 + ! -- 0 Gew.% VA------------- + ! parame(i,2) = 4.021767 + ! parame(i,3) = 249.5 + ! -- 7.5 Gew.% VA------------- + ! parame(i,2) = 4.011 + ! parame(i,3) = 248.1864 + ! parame(i,3) = 247.6286 + ! ---12.7 Gew.% VA------------ + ! parame(i,2) = 4.0028 + ! parame(i,3) = 247.2075 + ! parame(i,3) = 246.24454 + ! ---27.3 Gew.% VA------------ + ! parame(i,2) = 3.9762 + ! parame(i,3) = 244.114 + ! parame(i,3) = 241.9345 + ! ---31.8 Gew.% VA------------ + parame(i,2) = 3.9666 + parame(i,3) = 243.0436 + ! parame(i,3) = 240.46 + ! ---42.7 Gew.% VA------------ + ! parame(i,2) = 3.9400 + ! parame(i,3) = 240.184 + ! parame(i,3) = 236.62 + ! --------------- + ELSE IF (compna(i) == 'pp') THEN + parame(i,1) = mm(i)*2.2E-2 + parame(i,2) = 4.2 + parame(i,3) = 220.0 + + parame(i,1) = mm(i)*0.0230487701 + parame(i,2) = 4.1 + parame(i,3) = 217.0 + ELSE IF (compna(i) == 'pe') THEN + parame(i,1) = mm(i)*2.622E-2 + parame(i,2) = 4.021767 + parame(i,3) = 252.0 + ! HDPE: extrapolated from pure comp. param. of n-alkane series! + ! parame(i,1) = mm(i)*2.4346E-2 + ! parame(i,2) = 4.07182 + ! parame(i,3) = 269.67 + !! parame(i,3) = 252.5 + ELSE IF (compna(i) == 'ldpe') THEN + parame(i,1) = mm(i)*2.63E-2 + parame(i,2) = 4.021767 + parame(i,3) = 249.5 + ELSE IF (compna(i) == 'pba') THEN + parame(i,1) = mm(i)*2.5872E-2 + parame(i,2) = 3.95 + parame(i,3) = 229.0 + ELSE IF (compna(i) == 'dextran') THEN + parame(i,1) = mm(i)*2.E-2 + parame(i,2) = 4.0 + parame(i,3) = 300.0 + ELSE IF (compna(i) == 'glycol-ethers') THEN + ! mm(i) = 218.0 + ! parame(i,1) = 7.4044 + ! parame(i,2) = 3.61576 + ! parame(i,3) = 244.0034598 + mm(i) = 222.0 + parame(i,1) = 7.994 + parame(i,2) = 3.445377778 + parame(i,3) = 234.916506 + ELSE IF (compna(i) == 'LJ') THEN + mm(i) = 1.0 + parame(i,1) = 1.0 + parame(i,2) = 1.0 + parame(i,3) = 1.0 + ELSE IF (compna(i) == 'LJ1205') THEN + mm(i) = 1.0 + parame(i,1) = 1.0 + parame(i,2) = 1.0 + parame(i,3) = 140.0 + ELSE IF (compna(i) == 'adamantane') THEN + mm(i) = 136.235000000000 + parame(i,1) = 4.81897145432221 + parame(i,2) = 3.47128575274660 + parame(i,3) = 266.936967922521 + ELSE IF (compna(i) == 'methane') THEN + mm(i) = 16.043 + parame(i,1) = 1.0 + parame(i,2) = 3.70388767 + parame(i,3) = 150.033987 + ! LLi(i) = 1.185*parame(i,2) + ! phi_criti(i)= 11.141 + ! chap(i) = 0.787 + lli(i) = 1.398*parame(i,2) + phi_criti(i)= 16.01197 + chap(i) = 0.6 + IF (pol == 2) parame(i,11)= 2.593 + ! --- adjusted to Tc, Pc und omega --- + ! mm(i) = 16.0430000000000 + ! parame(i,1) = 1.03353666429362 + ! parame(i,2) = 3.64824920605089 + ! parame(i,3) = 147.903953522994 + lli(i) = 2.254442763775*parame(i,2) + phi_criti(i)= 42.060975627454 + chap(i) = 0.704895924 + lli(i) = 1.935801125833*parame(i,2) + phi_criti(i)= 26.363325937261 + chap(i) = 0.700112854298 + lli(i) = 2.610103087662*parame(i,2) + phi_criti(i)= 38.192854403173 + chap(i) = 0.812100472735 + ! 2.122960316503 34.937141524804 0.734513223627 + ! 2.082897379591 33.036391564859 0.877578492999 + ELSE IF (compna(i) == 'ethane') THEN + mm(i) = 30.070 + parame(i,1) =mm(i)* .0534364758 + parame(i,2) = 3.5205923 + parame(i,3) = 191.423815 + lli(i) = 1.40*parame(i,2) + phi_criti(i)= 15.38 + chap(i) = 0.520 + IF (pol == 2) parame(i,11)= 4.3 + ! --- adjusted to Tc, Pc und omega --- + ! mm(i) = 30.069 + ! parame(i,1) = 1.74034548122 + ! parame(i,2) = 3.4697441893134 + ! parame(i,3) = 181.90770083591 + IF (pol >= 1) mm(i) = 30.0700000000000 + IF (pol >= 1) parame(i,1) = mm(i)* 5.341907666260094E-002 + IF (pol >= 1) parame(i,2) = 3.52104466654628 + IF (pol >= 1) parame(i,3) = 191.449300423694 + IF (pol >= 1) parame(i,7) = 0.650000000000000 + IF (pol >= 1) lli(i) = 0.0 + IF (pol >= 1) phi_criti(i)= 0.0 + IF (pol >= 1) chap(i) = 0.0 + ELSE IF (compna(i) == 'propane') THEN + mm(i) = 44.096 + parame(i,1) = mm(i)* .0453970622 + parame(i,2) = 3.61835302 + parame(i,3) = 208.110116 + lli(i) = 1.8*parame(i,2) + phi_criti(i)= 21.0 + chap(i) = 1.0 + lli(i) = 1.63*parame(i,2) + phi_criti(i)= 20.37 + chap(i) = 0.397 + IF (pol == 2) parame(i,11)= 6.29 + ELSE IF (compna(i) == 'butane_debug') THEN + mm(i) = 58.123 + parame(i,1) = 2.3374 + parame(i,2) = 3.6655 + parame(i,3) = 214.805 + ELSE IF (compna(i) == 'butane') THEN + mm(i) = 58.123 + parame(i,1) = mm(i)* .0401146927 + parame(i,2) = 3.70860139 + parame(i,3) = 222.877405 + lli(i) = 1.75*parame(i,2) + phi_criti(i)= 23.43 + chap(i) = 0.304 + ! LLi(i) = 1.942079633622*parame(i,2) + ! phi_criti(i)= 24.527323443155 + ! chap(i) = 0.734064026277 + ! LLi(i) = 1.515115760477*parame(i,2) + ! phi_criti(i)= 17.682929717796 + ! chap(i) = 0.335848717079 + IF (pol == 2) parame(i,11)= 8.2 + ! --- adjusted to Tc, Pc und omega --- + ! mm(i) = 58.1230000000 + ! parame(i,1) = 2.45352304112 + ! parame(i,2) = 3.74239117802 + ! parame(i,3) = 214.185157925 + ELSE IF (compna(i) == 'pentane') THEN + mm(i) = 72.146 + parame(i,1) = mm(i)* .03727896 + parame(i,2) = 3.77293174 + parame(i,3) = 231.197015 + IF (pol == 2) parame(i,11)= 9.99 + ELSE IF (compna(i) == 'hexane') THEN + mm(i) = 86.177 + parame(i,1) = mm(i)* .0354812325 + parame(i,2) = 3.79829291 + parame(i,3) = 236.769054 + lli(i) = 2.24*parame(i,2) + phi_criti(i)= 33.25 + chap(i) = 0.205 + IF (pol == 2) parame(i,11)= 11.9 + ELSE IF (compna(i) == 'heptane') THEN + mm(i) = 100.203 + parame(i,1) = mm(i)* .034762384 + parame(i,2) = 3.80487025 + parame(i,3) = 238.400913 + lli(i) = 2.35*parame(i,2) + phi_criti(i)= 38.10 + chap(i) = 0.173 + IF (pol == 2) parame(i,11)= 13.61 + ELSE IF (compna(i) == 'octane') THEN + mm(i) = 114.231 + parame(i,1) = mm(i)* .0334228038 + parame(i,2) = 3.83732677 + parame(i,3) = 242.775853 + ! LLi(i) = 2.0*parame(i,2) + ! phi_criti(i)= 18.75 + ! chap(i) = 1.0 + lli(i) = 2.63*parame(i,2) + phi_criti(i)= 42.06 + chap(i) = 0.155 + IF (pol == 2) parame(i,11)= 15.9 + ELSE IF (compna(i) == 'nonane') THEN + mm(i) = 128.25 + parame(i,1) = mm(i)* .0328062594 + parame(i,2) = 3.84483643 + parame(i,3) = 244.508457 + ELSE IF (compna(i) == 'decane') THEN + mm(i) = 142.285 + parame(i,1) = mm(i)* .03277373 + parame(i,2) = 3.8384498 + parame(i,3) = 243.866074 + lli(i) = 1.845*parame(i,2) + phi_criti(i)= 21.27 + chap(i) = 1.0 + lli(i) = 2.68*parame(i,2) + phi_criti(i)= 45.0 + chap(i) = 0.15 + IF (pol == 2) parame(i,11)= 19.1 + ! --- adjusted to Tc, Pc und omega --- + ! parame(i,1) = 4.794137228322 + ! parame(i,2) = 4.030446690586 + ! parame(i,3) = 236.5884493386 + ELSE IF (compna(i) == 'dodecane') THEN + mm(i) = 170.338 + parame(i,1) = mm(i)* .0311484156 + parame(i,2) = 3.89589236 + parame(i,3) = 249.214532 + ELSE IF (compna(i) == 'hexadecane') THEN + mm(i) = 226.446 + parame(i,1) = mm(i)* .0293593045 + parame(i,2) = 3.95516743 + parame(i,3) = 254.700131 + ELSE IF (compna(i) == 'octadecane') THEN + mm(i) = 254.5 + parame(i,1) = 7.3271 + parame(i,2) = 3.9668 + parame(i,3) = 256.20 + IF (pol == 2) parame(i,11)= 30.2 + ! --- adjusted to Tc, Pc und omega --- + ! mm(i) = 226.446000000000 + ! parame(i,1) = 6.66976520488694 + ! parame(i,2) = 4.25025597912511 + ! parame(i,3) = 249.582941976119 + ELSE IF (compna(i) == 'eicosane') THEN + mm(i) = 282.553 + parame(i,1) = mm(i)* .0282572812 + parame(i,2) = 3.98692612 + parame(i,3) = 257.747939 + ELSE IF (compna(i) == 'triacontane') THEN + ! mm(i) = 422.822 ! polyethylene parameters + ! parame(i,1) = mm(i)*2.622E-2 + ! parame(i,2) = 4.021767 + ! parame(i,3) = 252.0 + mm(i) = 422.822 ! param. by extrapolation of n-alkanes + parame(i,1) = mm(i)* 0.026922527 + parame(i,2) = 4.007608009 + parame(i,3) = 262.28622 + ELSE IF (compna(i) == 'octaeicosane') THEN + mm(i) = 395.0 ! param. by extrapolation of n-alkanes (sloppy!!) + parame(i,1) = mm(i)* 0.026922527 + parame(i,2) = 4.007608009 + parame(i,3) = 262.28622 + ELSE IF (compna(i) == 'tetracontane') THEN + ! mm(i) = 563.1 ! polyethylene parameters + ! parame(i,1) = mm(i)*2.622E-2 + ! parame(i,2) = 4.021767 + ! parame(i,3) = 252.0 + mm(i) = 563.1 ! param. by extrapolation of n-alkanes + parame(i,1) = mm(i)*0.026287593 + parame(i,2) = 4.023277 + parame(i,3) = 264.10466 + ELSE IF (compna(i) == 'isobutane') THEN + mm(i) = 58.123 + parame(i,1) = mm(i)* .0389105395 + parame(i,2) = 3.75735249 + parame(i,3) = 216.528584 + ELSE IF (compna(i) == 'isopentane') THEN + mm(i) = 72.15 + parame(i,1) = 2.5620 + parame(i,2) = 3.8296 + parame(i,3) = 230.75 + ELSE IF (compna(i) == '2-methylpentane') THEN + mm(i) = 86.177 + parame(i,1) = mm(i)* .0340166994 + parame(i,2) = 3.85354665 + parame(i,3) = 235.5801 + ELSE IF (compna(i) == '23-dimethylbutane') THEN + mm(i) = 86.177 + parame(i,1) = mm(i)* .0311599207 + parame(i,2) = 3.9544545 + parame(i,3) = 246.068188 + ELSE IF (compna(i) == 'ethylene') THEN + mm(i) = 28.05 + parame(i,1) = mm(i)* .0567939013 + parame(i,2) = 3.44499904 + parame(i,3) = 176.468725 + IF (pol == 2) parame(i,11)= 4.252 +! eigener 3-ter Anlauf. + IF (pol >= 1) parame(i,1) = mm(i)* 5.574644443117726E-002 + IF (pol >= 1) parame(i,2) = 3.43281482228714 + IF (pol >= 1) parame(i,3) = 178.627308564610 + IF (pol >= 1) parame(i,7) = 1.56885870200446 + IF (pol == 2) parame(i,11)= 4.252 + ELSE IF (compna(i) == 'propylene') THEN + mm(i) = 42.081 + parame(i,1) = mm(i)* .0465710324 + parame(i,2) = 3.53559831 + parame(i,3) = 207.189309 + ! --- adjusted to Tc, Pc und omega --- + ! mm(i) = 42.081 + ! parame(i,1) = 2.086735327675 + ! parame(i,2) = 3.536779407969 + ! parame(i,3) = 198.3529810625 + ELSE IF (compna(i) == '1-butene') THEN + mm(i) = 56.107 + parame(i,1) = mm(i)* .0407524782 + parame(i,2) = 3.64305136 + parame(i,3) = 222.002756 + IF (pol == 2) parame(i,11)= 7.97 + ELSE IF (compna(i) == '1-pentene') THEN + mm(i) = 70.134 + parame(i,1) = 2.6006 + parame(i,2) = 3.7399 + parame(i,3) = 231.99 + ELSE IF (compna(i) == '1-hexene') THEN + mm(i) = 84.616 + parame(i,1) = mm(i)* .0352836857 + parame(i,2) = 3.77529612 + parame(i,3) = 236.810973 + ELSE IF (compna(i) == '1-octene') THEN + mm(i) = 112.215 + parame(i,1) = mm(i)* .033345175 + parame(i,2) = 3.81329011 + parame(i,3) = 243.017587 + ELSE IF (compna(i) == 'cyclopentane') THEN + mm(i) = 70.13 + parame(i,1) = mm(i)* .0337262571 + parame(i,2) = 3.71139254 + parame(i,3) = 265.828755 + ELSE IF (compna(i) == 'cyclohexane') THEN + mm(i) = 84.147 + parame(i,1) = mm(i)* .0300695505 + parame(i,2) = 3.84990887 + parame(i,3) = 278.108786 + IF (pol == 2) parame(i,11)= 10.87 + ELSE IF (compna(i) == 'toluene') THEN + mm(i) = 92.141 + parame(i,1) = mm(i)* .0305499338 + parame(i,2) = 3.71689689 + parame(i,3) = 285.68996 + IF (pol == 2) parame(i,11)= 11.8 + ! --- adjusted to Tc, Pc und omega --- + ! mm(i) = 92.141 + ! parame(i,1) = 3.002119827762 + ! parame(i,2) = 3.803702734224 + ! parame(i,3) = 271.9428642880 + ELSE IF (compna(i) == 'm-xylene') THEN + mm(i) = 106.167 + parame(i,1) = mm(i)* .030011086 + parame(i,2) = 3.75625585 + parame(i,3) = 283.977525 + ELSE IF (compna(i) == 'o-xylene') THEN + mm(i) = 106.167 + parame(i,1) = mm(i)* .0295409161 + parame(i,2) = 3.76000631 + parame(i,3) = 291.049123 + ELSE IF (compna(i) == 'thf') THEN + mm(i) = 72.1057000000000 + ! parame(i,1) = mm(i)* 0.34311391E-01 + parame(i,1) = 2.47404685540709 + parame(i,2) = 3.51369375633677 + parame(i,3) = 274.181927093696 + parame(i,6) = 1.63100000000000 + + + Else IF(compna(i) == 'po') THEN + mm(i) = 90.12 + parame(i,1) = 4.35923557 + parame(i,2) = 3.02947364 + parame(i,3) = 197.11998863 + + Else IF(compna(i) == 'mdi') THEN + mm(i) = 2.50252E+02 + parame(i,1) = mm(i)*0.030769 + parame(i,2) = 2.886003 + parame(i,3) = 283.052778 + + Else IF(compna(i) == 'pu') THEN +! mm(i) = 2042.22 !pu n = 5 +! parame(i,1) = mm(i)*0.008845 +! parame(i,2) = 5.680270 +! parame(i,3) = 497.997594 +! mm(i) = 340.37 !pu n = 0 +! parame(i,1) = mm(i)*0.043312 +! parame(i,2) = 3.008359 +! parame(i,3) = 273.445205 +! mm(i) = 680.74 !pu n = 1 +! parame(i,1) = mm(i)*0.024106 +! parame(i,2) = 3.744327 +! parame(i,3) = 321.486386 + mm(i) = 1021.11 !pu n = 2 + parame(i,1) = mm(i)*0.015076 + parame(i,2) = 4.537837 + parame(i,3) = 400.036950 + + ELSE IF (compna(i) == 'air') THEN + mm(i) = 28.899 !n2 and o2 according to mole fractions + parame(i,1) = 1.18938 !n2 and o2 according to mole fractions (weighted artihm. avg) + parame(i,2) = 3.28694 !n2 and o2 according to mole fractions (weighted artihm. avg) + parame(i,3) = 95.672 !n2 and o2 according to mole fractions (weighted artihm. avg) + + + + + + ELSE IF (compna(i) == 'co2') THEN + mm(i) = 44.01 + parame(i,1) = mm(i)* .0470968503 + parame(i,2) = 2.7851954 + parame(i,3) = 169.207418 + IF (pol >= 1) parame(i,1) = mm(i)* 3.438191426159075E-002 + IF (pol >= 1) parame(i,2) = 3.18693935424469 + IF (pol >= 1) parame(i,3) = 163.333232725156 + IF (pol >= 1) parame(i,7) = 4.400000000000 + IF (pol >= 1) lli(i) = 1.472215*parame(i,2) + IF (pol >= 1) phi_criti(i)= 17.706567 + IF (pol >= 1) chap(i) = 0.5 + IF (pol == 2) parame(i,11)= 2.911 + ELSE IF (compna(i) == 'co') THEN + IF (pol /= 1) write (*,*) 'parameters for co missing' + IF (pol /= 1) stop + IF (pol >= 1) mm(i) = 28.01 + IF (pol >= 1) parame(i,1) = mm(i)* 5.126059746332587E-002 ! 1.43580933494776 + IF (pol >= 1) parame(i,2) = 3.13556624711756 + IF (pol >= 1) parame(i,3) = 87.7191028693595 + IF (pol >= 1) parame(i,6) = 0.1098 + ELSE IF (compna(i) == 'n2') THEN + mm(i) = 28.01 + parame(i,1) = mm(i)* .0430301713 + parame(i,2) = 3.3129702 + parame(i,3) = 90.9606924 + IF (pol >= 1) parame(i,1) = mm(i)* 3.971157114787596E-002 + IF (pol >= 1) parame(i,2) = 3.42116853868336 + IF (pol >= 1) parame(i,3) = 92.3972606842862 + IF (pol >= 1) parame(i,7) = 1.52000000000000 + IF (pol >= 1) lli(i) = 1.5188*parame(i,2) + IF (pol >= 1) phi_criti(i)= 19.9247 + IF (pol >= 1) chap(i) = 0.375 + ! better RGT-results came later, with: 1.5822 21.201 0.3972 + ELSE IF (compna(i) == 'o2') THEN + mm(i) = 32.05 + parame(i,1) = mm(i)* .0353671563 + parame(i,2) = 3.19465166 + parame(i,3) = 114.430197 + ELSE IF (compna(i) == 'hydrogen') THEN + mm(i) = 2.016 + parame(i,1) = mm(i)* .258951975 + parame(i,2) = 4.43304935 + parame(i,3) = 29.6509579 + + mm(i) = 2.016 + parame(i,1) = 1.0 + parame(i,2) = 2.915 + parame(i,3) = 38.0 + + ! mm(i) = 2.016 ! Ghosh et al. 2003 + ! parame(i,1) = 1.0 + ! parame(i,2) = 2.986 + ! parame(i,3) = 19.2775 + ELSE IF (compna(i) == 'argon') THEN + ! mm(i) = 39.948 ! adjusted m !! + ! parame(i,1) = 0.9285 + ! parame(i,2) = 3.4784 + ! parame(i,3) = 122.23 + mm(i) = 39.948 ! enforced m=1 !! + parame(i,1) = 1.0 + parame(i,2) = 3.3658 + parame(i,3) = 118.34 + IF (pol == 2) parame(i,11)= 1.6411 + ELSE IF (compna(i) == 'xenon') THEN + mm(i) = 131.29 + parame(i,1) = 1.0 + parame(i,2) = 3.93143 + parame(i,3) = 227.749 + ELSE IF (compna(i) == 'chlorine') THEN ! Cl2 + mm(i) = 70.906 + parame(i,1) = 1.5514 + parame(i,2) = 3.3672 + parame(i,3) = 265.67 + ELSE IF (compna(i) == 'SF6') THEN + mm(i) = 146.056 ! adjusted m !! + parame(i,1) = 2.48191 + parame(i,2) = 3.32727 + parame(i,3) = 161.639 + ! mm(i) = 146.056 ! enforced m=1 !! + ! parame(i,1) = 1.0 + ! parame(i,2) = 4.55222 + ! parame(i,3) = 263.1356 + ELSE IF (compna(i) == 'benzene') THEN + mm(i) = 78.114 + parame(i,1) = mm(i)* .0315590546 + parame(i,2) = 3.64778975 + parame(i,3) = 287.354574 + IF (pol >= 1) mm(i) = 78.114 ! PCP-SAFT with m=2 in QQ term + IF (pol >= 1) parame(i,1) = mm(i)* 2.932783311E-2 ! = 2.29091435590515 + IF (pol >= 1) parame(i,2) = 3.7563854 + IF (pol >= 1) parame(i,3) = 294.06253 + IF (pol >= 1) parame(i,7) = 5.5907 + ELSE IF (compna(i) == 'ethylbenzene') THEN + mm(i) = 106.167 + parame(i,1) = mm(i)* .0290120497 + parame(i,2) = 3.79741116 + parame(i,3) = 287.348098 + IF (pol == 2) parame(i,11)= 13.3 + ELSE IF (compna(i) == 'propylbenzene') THEN + mm(i) = 120.194 + parame(i,1) = mm(i)* .0278171627 + parame(i,2) = 3.8437772 + parame(i,3) = 288.128269 + ELSE IF (compna(i) == 'n-butylbenzene') THEN + mm(i) = 134.221 + parame(i,1) = mm(i)* .0280642225 + parame(i,2) = 3.87267961 + parame(i,3) = 283.072331 + ELSE IF (compna(i) == 'tetralin') THEN + mm(i) = 132.205 + parame(i,1) = mm(i)* .0250640795 + parame(i,2) = 3.87498866 + parame(i,3) = 325.065688 + ELSE IF (compna(i) == 'methylcyclohexane') THEN + mm(i) = 98.182 + parame(i,1) = mm(i)* .0271259953 + parame(i,2) = 3.99931892 + parame(i,3) = 282.334148 + IF (pol == 2) parame(i,11)= 13.1 + ELSE IF (compna(i) == 'methylcyclopentane') THEN + mm(i) = 84.156 + parame(i,1) = mm(i)* .0310459009 + parame(i,2) = 3.82534693 + parame(i,3) = 265.122799 + ELSE IF (compna(i) == 'acetone') THEN + mm(i) = 58.0800000000000 ! PC-SAFT + parame(i,1) = mm(i)* 4.870380408159182E-002 ! =2.82871694105885 + parame(i,2) = 3.24969003020675 + parame(i,3) = 250.262241927379 + lli(i) = 2.0021*parame(i,2) + phi_criti(i)= 21.336 + chap(i) = 0.24931 + IF (pol >= 1) mm(i) = 58.0800000000000 ! PCP-SAFT + IF (pol >= 1) parame(i,1) = mm(i)* 4.725811736856114E-002 ! =2.74475145676603 + IF (pol >= 1) parame(i,2) = 3.27423145271184 + IF (pol >= 1) parame(i,3) = 232.990879135326 + IF (pol >= 1) parame(i,6) = 2.88000000000000 + IF (pol >= 1) lli(i) = 2.0641*parame(i,2) + IF (pol >= 1) phi_criti(i)= 28.1783 + IF (pol >= 1) chap(i) = 0.22695 + IF (pol >= 2) mm(i) = 58.0800000000000 ! PCIP-SAFT + IF (pol >= 2) parame(i,1) = mm(i)* 4.902301475689938E-002 ! =2.84725669708072 + IF (pol >= 2) parame(i,2) = 3.23880349104868 + IF (pol >= 2) parame(i,3) = 220.884202656054 + IF (pol >= 2) parame(i,6) = 2.88000000000000 + IF (pol == 2) parame(i,11)= 6.40000000000000 + ELSE IF (compna(i) == 'butanone') THEN + mm(i) = 72.1066 ! PC-SAFT + parame(i,1) = mm(i)* 4.264192830122321E-002 ! =3.07476446724498 + parame(i,2) = 3.39324011060028 + parame(i,3) = 252.267273608975 + IF (pol >= 1) mm(i) = 72.1066 ! PCP-SAFT + IF (pol >= 1) parame(i,1) = mm(i)* 4.137668924230600E-002 ! =2.98353238051926 + IF (pol >= 1) parame(i,2) = 3.42393701353423 + IF (pol >= 1) parame(i,3) = 244.994381354681 + IF (pol >= 1) parame(i,6) = 2.78000000000000 + IF (pol >= 2) mm(i) = 72.1066 ! PCIP-SAFT + IF (pol >= 2) parame(i,1) = mm(i)* 4.254697075199448E-002 ! =3.06791740122577 + IF (pol >= 2) parame(i,2) = 3.39138375903252 + IF (pol >= 2) parame(i,3) = 236.527763837528 + IF (pol >= 2) parame(i,6) = 2.78000000000000 + IF (pol == 2) parame(i,11)= 8.13000000000000 + ELSE IF (compna(i) == '2-pentanone') THEN + ! mm(i) = 86.134 ! PC-SAFT + ! parame(i,1) = mm(i)* 3.982654501296355E-002 ! =3.43041962814660 + ! parame(i,2) = 3.46877976946838 + ! parame(i,3) = 249.834724442656 + ! mm(i) = 86.134 ! PCP-SAFT + ! parame(i,1) = mm(i)* 3.893594769994072E-002 ! =3.35370891918669 + ! parame(i,2) = 3.49417356096593 + ! parame(i,3) = 246.656329096835 + ! parame(i,6) = 2.70000000000000 + mm(i) = 86.134 ! PCIP-SAFT + parame(i,1) = mm(i)* 3.973160761515879E-002 ! =3.42224229032409 + parame(i,2) = 3.46827593107280 + parame(i,3) = 240.904278156822 + parame(i,6) = 2.70000000000000 + IF (pol == 2) parame(i,11)= 9.93000000000000 + ELSE IF (compna(i) == '3-pentanone') THEN + mm(i) = 86.134 ! PC-SAFT + parame(i,1) = 3.36439508013322 + parame(i,2) = 3.48770251979329 + parame(i,3) = 252.695415552376 + IF (pol >= 1) mm(i) = 86.134 ! PCP-SAFT + IF (pol >= 1) parame(i,1) = 3.27863398611842 + IF (pol >= 1) parame(i,2) = 3.51592571835030 + IF (pol >= 1) parame(i,3) = 248.690775540981 + IF (pol >= 1) parame(i,6) = 2.82000000000000 + IF (pol == 2) mm(i) = 86.134 ! PCIP-SAFT + IF (pol == 2) parame(i,1) = 3.34821857026283 + IF (pol == 2) parame(i,2) = 3.48903345340516 + IF (pol == 2) parame(i,3) = 242.314578558329 + IF (pol == 2) parame(i,6) = 2.82000000000000 + IF (pol == 2) parame(i,11)= 9.93000000000000 + ELSE IF (compna(i) == 'cyclohexanone') THEN ! from DIPPR + ! IF (pol.GE.1) mm(i) = 98.1430 ! PCP-SAFT + ! IF (pol.GE.1) parame(i,1) = 3.084202 + ! IF (pol.GE.1) parame(i,2) = 3.613681 + ! IF (pol.GE.1) parame(i,3) = 286.15865 + ! IF (pol.GE.1) parame(i,6) = 3.087862 + IF (pol >= 1) mm(i) = 98.1500000000000 + IF (pol >= 1) parame(i,1) = 2.72291913132818 + IF (pol >= 1) parame(i,2) = 3.79018433908522 + IF (pol >= 1) parame(i,3) = 314.772193827344 + IF (pol >= 1) parame(i,6) = 3.24600000000000 + IF (pol /= 1) WRITE (*,*) 'no non-polar param. for cyclohexanone' + IF (pol /= 1) STOP + ELSE IF (compna(i) == 'propanal') THEN + mm(i) = 58.08 ! PC-SAFT + parame(i,1) = 2.67564746980910 + parame(i,2) = 3.26295953984941 + parame(i,3) = 251.888982765626 + IF (pol >= 1) mm(i) = 58.08 ! PCP-SAFT + IF (pol >= 1) parame(i,1) = 2.60007872084995 + IF (pol >= 1) parame(i,2) = 3.28720732189761 + IF (pol >= 1) parame(i,3) = 235.205188090107 + IF (pol >= 1) parame(i,6) = 2.72000000000000 + IF (pol >= 2) mm(i) = 58.08 ! PCIP-SAFT + IF (pol >= 2) parame(i,1) = 2.72471167411028 + IF (pol >= 2) parame(i,2) = 3.24781643022922 + IF (pol >= 2) parame(i,3) = 221.642071811094 + IF (pol >= 2) parame(i,6) = 2.72000000000000 + IF (pol >= 2) parame(i,11)= 6.50000000000000 + ELSE IF (compna(i) == 'butanal') THEN + mm(i) = 72.1066000000000 ! PC-SAFT + parame(i,1) = 2.96824823599784 + parame(i,2) = 3.44068916025889 + parame(i,3) = 253.929404992884 + IF (pol >= 1) mm(i) = 72.1066000000000 ! PCP-SAFT + IF (pol >= 1) parame(i,1) = 2.86783706423953 + IF (pol >= 1) parame(i,2) = 3.47737904036296 + IF (pol >= 1) parame(i,3) = 247.543312127310 + IF (pol >= 1) parame(i,6) = 2.72000000000000 + ELSE IF (compna(i) == 'dmso') THEN + mm(i) = 78.1300000000000 ! PC-SAFT + parame(i,1) = 2.92225114054231 + parame(i,2) = 3.27780791606297 + parame(i,3) = 355.688793038512 + IF (pol >= 1) mm(i) = 78.1300000000000 ! PCP-SAFT + IF (pol >= 1) parame(i,1) = 3.02433694138348 + IF (pol >= 1) parame(i,2) = 3.24270742566613 + IF (pol >= 1) parame(i,3) = 309.357476696679 + IF (pol >= 1) parame(i,6) = 3.96000000000000 + IF (pol >= 2) mm(i) = 78.1300000000000 ! PCIP-SAFT + IF (pol >= 2) parame(i,1) = 3.19078234633277 + IF (pol >= 2) parame(i,2) = 3.19778269816832 + IF (pol >= 2) parame(i,3) = 286.337981216861 + IF (pol >= 2) parame(i,6) = 3.96000000000000 + IF (pol >= 2) parame(i,11)= 7.97000000000000 + ELSE IF (compna(i) == 'acetone_JC') THEN ! Jog-Chapman + ! mm(i) = 58.0800000000000 ! Dominik et al.2005 + ! parame(i,1) = 2.221 + ! parame(i,2) = 3.607908 + ! parame(i,3) = 259.99 + ! parame(i,6) = 2.7 + ! parame(i,8) = 0.2258 + ! mm(i) = 58.0800000000000 + ! parame(i,1) = mm(i)* 3.556617369195472E-002 + ! parame(i,2) = 3.58780367502515 + ! parame(i,3) = 273.025100470307 + ! parame(i,6) = 2.70000000000000 + ! parame(i,8) = 0.229800000000000 + + mm(i) = 58.08 ! Tumakaka Sadowski 2004 + parame(i,1) = mm(i)* 3.766E-2 + parame(i,2) = 3.6028 + parame(i,3) = 245.49 + parame(i,6) = 2.72 + parame(i,8) = 0.2969 + ! mm(i) = 58.0800000000000 ! no adjust. DD-param. + ! parame(i,1) = 1.87041620247774 + ! parame(i,2) = 3.79783535570774 + ! parame(i,3) = 208.885730881588 + ! parame(i,6) = 2.88000000000000 + ! parame(i,8) = 1.0/parame(i,1) + WRITE (*,*) 'caution: parame(i,8) is now used for branching' + STOP + kij(1,2) = -0.005 + kij(2,1)=kij(1,2) + ELSE IF (compna(i) == 'acetone_SF') THEN ! Saager-Fischer + mm(i) = 58.08 + parame(i,1) = mm(i)* 4.603296414764944E-002 + parame(i,2) = 3.29454924451643 + parame(i,3) = 221.052649057645 + parame(i,6) = 2.70000000000000 + parame(i,8) = 0.625410000000000 + mm(i) = 58.08 ! form as expected from me - no DD-param adjusted.dat + parame(i,1) = mm(i)* 4.364264724158790E-002 ! =2.53476495179143 + parame(i,2) = 3.37098670735567 + parame(i,3) = 254.366379701851 + parame(i,6) = 2.88000000000000 + ! mm(i) = 58.08 ! form as expected but w/ sumseg/1.5 - no DD-param adjusted.dat + ! parame(i,1) = mm(i)* 4.694644361257521E-002 ! =2.72664944501837 + ! parame(i,2) = 3.27842292595463 + ! parame(i,3) = 238.398883501772 + ! parame(i,6) = 2.88000000000000 + ! mm(i) = 58.08 ! form as expected but w/ sumseg/1.5 and fdd*sumseg- no DD-param adjusted.dat + ! parame(i,1) = mm(i)* 4.458214655521766E-002 ! =2.58933107192704 + ! parame(i,2) = 3.32050824493493 + ! parame(i,3) = 218.285994651271 + ! parame(i,6) = 2.88000000000000 + WRITE (*,*) 'caution: parame(i,8) is now used for branching' + STOP + kij(1,2) = 0.035 + kij(2,1)=kij(1,2) + ELSE IF (compna(i) == 'ethylacetate_JC') THEN ! Jog-Chapman + ! mm(i) = 88.11 + ! parame(i,1) = 2.7481 + ! parame(i,2) = 3.6511 + ! parame(i,3) = 236.99 + ! parame(i,6) = 1.84 + ! parame(i,8) = 0.5458 + mm(i) = 88.1060000000000 + parame(i,1) = mm(i)* 0.03117 ! 2.74626402 + parame(i,2) = 3.6493 + parame(i,3) = 236.75 + parame(i,6) = 1.8 + parame(i,8) = 0.5462 + ELSE IF (compna(i) == 'ethylacetate_SF') THEN ! Saager-Fischer + mm(i) = 88.106 + parame(i,1) = mm(i)* 3.564165384763394E-002 + parame(i,2) = 3.447379322 + parame(i,3) = 226.0930487 + parame(i,6) = 1.8 + parame(i,8) = 0.849967000000000 + WRITE (*,*) 'caution: parame(i,8) is now used for branching' + STOP + ELSE IF (compna(i) == '12po_JC') THEN ! Jog-Chapman + mm(i) = 58.08 + parame(i,1) = 2.0105 + parame(i,2) = 3.6095 + parame(i,3) = 258.82 + parame(i,6) = 2.0 + parame(i,8) = 0.3979 + WRITE (*,*) 'caution: parame(i,8) is now used for branching' + STOP + ELSE IF (compna(i) == '12po_SF') THEN ! Saager-Fischer + mm(i) = 58.08 + parame(i,1) = 2.1341 + parame(i,2) = 3.4739 + parame(i,3) = 252.95 + parame(i,6) = 2.0 + parame(i,8) = 0.916 + WRITE (*,*) 'caution: parame(i,8) is now used for branching' + STOP + ELSE IF (compna(i) == 'acrylonitrile') THEN + IF (pol >= 2) mm(i) = 53.06 ! PCIP-SAFT + IF (pol >= 2) parame(i,1) = 2.168 + IF (pol >= 2) parame(i,2) = 3.575 + IF (pol >= 2) parame(i,3) = 214.83 + IF (pol >= 2) parame(i,6) = 3.91 + IF (pol == 2) parame(i,11)= 8.04 + IF (pol >= 2) mm(i) = 53.0000000000000 ! second parameter set ?? + IF (pol >= 2) parame(i,1) = 2.45403467006041 + IF (pol >= 2) parame(i,2) = 3.41276825781723 + IF (pol >= 2) parame(i,3) = 195.194353082408 + IF (pol >= 2) parame(i,6) = 3.91000000000000 + IF (pol == 2) parame(i,11)= 8.04000000000000 + ELSE IF (compna(i) == 'butyronitrile') THEN + ! mm(i) = 69.11 + ! parame(i,1) = 2.860 + ! parame(i,2) = 3.478 + ! parame(i,3) = 253.21 + ! parame(i,6) = 4.07 + mm(i) = 69.11 + parame(i,1) = 2.989 + parame(i,2) = 3.441 + parame(i,3) = 234.04 + parame(i,6) = 4.07 + IF (pol == 2) parame(i,11)= 8.4 + ELSE IF (compna(i) == 'propionitrile') THEN + mm(i) = 55.079 ! PC-SAFT + parame(i,1) = 2.66211021227108 + parame(i,2) = 3.34032231132738 + parame(i,3) = 294.078737359580 + IF (pol >= 1) mm(i) = 55.079 ! PCP-SAFT + IF (pol >= 1) parame(i,1) = 2.50958981615666 + IF (pol >= 1) parame(i,2) = 3.39806320429568 + IF (pol >= 1) parame(i,3) = 239.152759066148 + IF (pol >= 1) parame(i,6) = 4.05000000000000 + IF (pol >= 2) mm(i) = 55.079 ! PCIP-SAFT + IF (pol >= 2) parame(i,1) = 2.54684827683436 + IF (pol >= 2) parame(i,2) = 3.41240089912190 + IF (pol >= 2) parame(i,3) = 218.299491580335 + IF (pol >= 2) parame(i,6) = 4.05000000000000 + IF (pol == 2) parame(i,11)= 6.24000000000000 + ! IF (pol.GE.2) mm(i) = 55.079 ! PCIP-SAFT my_DD adjusted + ! IF (pol.GE.2) parame(i,1) = 2.61175151088002 + ! IF (pol.GE.2) parame(i,2) = 3.37194293181453 + ! IF (pol.GE.2) parame(i,3) = 233.346110749402 + ! IF (pol.GE.2) parame(i,6) = 3.74682245835235 + ! IF (pol.EQ.2) parame(i,11)= 6.24000000000000 + ELSE IF (compna(i) == 'nitromethane') THEN + mm(i) = 61.04 ! PC-SAFT + parame(i,1) = mm(i)* 4.233767489308791E-002 ! =2.58429167547409 + parame(i,2) = 3.10839592337018 + parame(i,3) = 310.694151426943 + IF (pol >= 1) mm(i) = 61.04 ! PCP-SAFT + IF (pol >= 1) parame(i,1) = mm(i)* 4.191475020685036E-002 ! =2.55847635262615 + IF (pol >= 1) parame(i,2) = 3.10129282495975 + IF (pol >= 1) parame(i,3) = 256.456941430554 + IF (pol >= 1) parame(i,6) = 3.46000000000000 + IF (pol >= 2) mm(i) = 61.04 ! PCIP-SAFT + IF (pol >= 2) parame(i,1) = mm(i)* 4.394323357988009E-002 ! =2.68229497771588 + IF (pol >= 2) parame(i,2) = 3.10654492320028 + IF (pol >= 2) parame(i,3) = 225.973607468282 + IF (pol >= 2) parame(i,6) = 3.46000000000000 + IF (pol >= 2) parame(i,11)= 7.37000000000000 + ELSE IF (compna(i) == 'nitroethane') THEN + mm(i) = 75.067 ! PC-SAFT + parame(i,1) = mm(i)* 4.019977215251163E-002 ! =3.01767629617259 + parame(i,2) = 3.21364231060938 + parame(i,3) = 286.571650044235 + IF (pol >= 1) mm(i) = 75.067 ! PCP-SAFT + IF (pol >= 1) parame(i,1) = mm(i)* 3.928506808347654E-002 ! =2.94901220582233 + IF (pol >= 1) parame(i,2) = 3.23117331990738 + IF (pol >= 1) parame(i,3) = 265.961000131109 + IF (pol >= 1) parame(i,6) = 3.23000000000000 + IF (pol >= 2) mm(i) = 75.067 ! PCIP-SAFT + IF (pol >= 2) parame(i,1) = mm(i)* 4.117677400894779E-002 ! =3.09101689452968 + IF (pol >= 2) parame(i,2) = 3.19364569858756 + IF (pol >= 2) parame(i,3) = 246.676040248662 + IF (pol >= 2) parame(i,6) = 3.23000000000000 + IF (pol >= 2) parame(i,11)= 9.63000000000000 + ELSE IF (compna(i) == 'acetonitrile') THEN + mm(i) = 41.052 ! PC-SAFT + parame(i,1) = mm(i)* 5.673187410405271E-002 ! =2.32895689571957 + parame(i,2) = 3.18980108373791 + parame(i,3) = 311.307486044181 + IF (pol >= 1) mm(i) = 41.052 ! PCP-SAFT + IF (pol >= 1) parame(i,1) = mm(i)* 5.254832931037250E-002 ! =2.15721401484941 + IF (pol >= 1) parame(i,2) = 3.27301469369132 + IF (pol >= 1) parame(i,3) = 216.888948676921 + IF (pol >= 1) parame(i,6) = 3.92520000000000 + IF (pol >= 2) mm(i) = 41.052 ! PCIP-SAFT + IF (pol >= 2) parame(i,1) = mm(i)* 5.125846581157176E-002 ! =2.10426253849664 + IF (pol >= 2) parame(i,2) = 3.39403305120647 + IF (pol >= 2) parame(i,3) = 199.070191065791 + IF (pol >= 2) parame(i,6) = 3.92520000000000 + IF (pol >= 2) parame(i,11)= 4.40000000000000 + ! IF (pol >= 2) mm(i) = 41.052 ! PCIP-SAFT my_DD adjusted + ! IF (pol >= 2) parame(i,1) = mm(i)* 5.755347845863738E-002 ! =2.36268539768398 + ! IF (pol >= 2) parame(i,2) = 3.18554306395900 + ! IF (pol >= 2) parame(i,3) = 225.143934506015 + ! IF (pol >= 2) parame(i,6) = 3.43151866932598 + ! IF (pol >= 2) parame(i,11)= 4.40000000000000 + ! mm(i) = 41.053 ! PCP-SAFT dipole and quadrupole + ! parame(i,1) = 1.79993 + ! parame(i,2) = 3.47366 + ! parame(i,3) = 211.001 + ! parame(i,6) = 3.93800 + ! parame(i,7) = 2.44000 + ! parame(i,11)= 0.0 + ELSE IF (compna(i) == 'dmf') THEN + mm(i) = 73.09 ! PC-SAFT + parame(i,1) = 2.388 + parame(i,2) = 3.658 + parame(i,3) = 363.77 + IF (pol >= 1) mm(i) = 73.09 ! PCP-SAFT + IF (pol >= 1) parame(i,1) = 2.269 + IF (pol >= 1) parame(i,2) = 3.714 + IF (pol >= 1) parame(i,3) = 331.56 + IF (pol >= 1) parame(i,6) = 3.82 + IF (pol >= 2) mm(i) = 73.09 ! PCIP-SAFT + IF (pol >= 2) parame(i,1) = 2.375 + IF (pol >= 2) parame(i,2) = 3.667 + IF (pol >= 2) parame(i,3) = 308.42 + IF (pol >= 2) parame(i,6) = 3.82 + IF (pol >= 2) parame(i,11)= 7.81 + ELSE IF (compna(i) == 'chloroform') THEN + mm(i) = 119.377 ! PCIP-SAFT + parame(i,1) = 2.5957 + parame(i,2) = 3.4299 + parame(i,3) = 264.664 + parame(i,6) = 1.04 + IF (pol == 2) parame(i,11)= 8.23 + ELSE IF (compna(i) == 'dimethyl-ether') THEN + mm(i) = 46.069 ! PC-SAFT + parame(i,1) = mm(i)* 0.049107715 ! =2.26234331 + parame(i,2) = 3.276640534 + parame(i,3) = 212.9343244 + IF (pol >= 1) mm(i) = 46.0690000000000 ! PCP-SAFT + IF (pol >= 1) parame(i,1) = mm(i)* 0.048170452 ! =2.219164566 + IF (pol >= 1) parame(i,2) = 3.296939638 + IF (pol >= 1) parame(i,3) = 212.1048888 + IF (pol >= 1) parame(i,6) = 1.30000000000000 + IF (pol >= 2) mm(i) = 46.0690000000000 ! PCIP-SAFT + IF (pol >= 2) parame(i,1) = mm(i)* 4.939183716945787E-002 ! =2.27543254655976 + IF (pol >= 2) parame(i,2) = 3.26584718800835 + IF (pol >= 2) parame(i,3) = 206.904551967059 + IF (pol >= 2) parame(i,6) = 1.30000000000000 + IF (pol == 2) parame(i,11)= 5.29000000000000 + ELSE IF (compna(i) == 'methyl-ethyl-ether') THEN + mm(i) = 60.096 + parame(i,1) = mm(i)* .0442404671 + parame(i,2) = 3.37282595 + parame(i,3) = 216.010217 + IF (pol >= 1) mm(i) = 60.096 ! PCP-SAFT + IF (pol >= 1) parame(i,1) = mm(i)* 4.3971676124088D-002 ! =2.64252184835325 + IF (pol >= 1) parame(i,2) = 3.37938465390 + IF (pol >= 1) parame(i,3) = 215.787173860 + IF (pol >= 1) parame(i,6) = 1.17000000000 + IF (pol >= 2) mm(i) = 60.096 ! PICP-SAFT + IF (pol >= 2) parame(i,1) = mm(i)* 4.4580196137984D-002 ! =2.67909146710834 + IF (pol >= 2) parame(i,2) = 3.36105342286 + IF (pol >= 2) parame(i,3) = 212.871911999 + IF (pol >= 2) parame(i,6) = 1.17000000000 + IF (pol >= 2) parame(i,11) = 7.93000000000 + ELSE IF (compna(i) == 'diethyl-ether') THEN + mm(i) = 74.123 ! PC-SAFT + parame(i,1) = mm(i)* .0409704089 + parame(i,2) = 3.48569553 + parame(i,3) = 217.64113 + IF (pol >= 1) mm(i) = 74.123 ! PCP-SAFT + IF (pol >= 1) parame(i,1) = mm(i)* 4.0103121403686E-2 ! =2.97256367 + IF (pol >= 1) parame(i,2) = 3.51268687697978 + IF (pol >= 1) parame(i,3) = 219.527376572135 + IF (pol >= 1) parame(i,6) = 1.15000000000000 + IF (pol >= 2) mm(i) = 74.123 ! PCIP-SAFT + IF (pol >= 2) parame(i,1) = mm(i)* 4.04144179873E-2 ! =2.9956379 + IF (pol >= 2) parame(i,2) = 3.501724569 + IF (pol >= 2) parame(i,3) = 217.8941822 + IF (pol >= 2) parame(i,6) = 1.15 + IF (pol == 2) parame(i,11)= 8.73 + ELSE IF (compna(i) == 'vinylacetate') THEN + mm(i) = 86.092 + parame(i,1) = mm(i)* .0374329292 + parame(i,2) = 3.35278602 + parame(i,3) = 240.492049 + ELSE IF (compna(i) == 'chloromethane') THEN ! R40 + mm(i) = 50.488 ! PC-SAFT + parame(i,1) = mm(i)* 0.039418879 ! 1.9902 + parame(i,2) = 3.1974 + parame(i,3) = 237.27 + IF (pol >= 1) mm(i) = 50.488 ! PCP-SAFT + IF (pol >= 1) parame(i,1) = mm(i)* 0.035790801 ! 1.8070 + IF (pol >= 1) parame(i,2) = 3.3034 + IF (pol >= 1) parame(i,3) = 229.97 + IF (pol >= 1) parame(i,6) = 1.8963 + IF (pol >= 1) lli(i) = 1.67703*parame(i,2) + IF (pol >= 1) phi_criti(i)= 20.75417 + IF (pol >= 1) chap(i) = 0.5 + IF (pol >= 2) mm(i) = 50.488 ! PCIP-SAFT + IF (pol >= 2) parame(i,1) = mm(i)* 3.68559992E-2 ! 1.86078 + IF (pol >= 2) parame(i,2) = 3.275186 + IF (pol >= 2) parame(i,3) = 216.4621 + IF (pol >= 2) parame(i,6) = 1.8963 + IF (pol == 2) parame(i,11)= 4.72 + ELSE IF (compna(i) == 'fluoromethane') THEN ! R41 + IF (pol /= 1) write (*,*) 'non-polar parameters missing for fluoromethane' + IF (pol /= 1) stop + IF (pol >= 1) mm(i) = 34.0329000000000 + IF (pol >= 1) parame(i,1) = 1.94494757526896 + IF (pol >= 1) parame(i,2) = 2.96858005012635 + IF (pol >= 1) parame(i,3) = 168.938697391009 + IF (pol >= 1) parame(i,6) = 1.57823038894029 + ELSE IF (compna(i) == 'dichloromethane') THEN ! R30 + mm(i) = 84.932 ! PC-SAFT + parame(i,1) = 2.3117 + parame(i,2) = 3.3161 + parame(i,3) = 270.98 + IF (pol >= 1) mm(i) = 84.932 ! PCP-SAFT + IF (pol >= 1) parame(i,1) = 2.2687 + IF (pol >= 1) parame(i,2) = 3.3373 + IF (pol >= 1) parame(i,3) = 269.08 + IF (pol >= 1) parame(i,6) = 1.6 + IF (pol >= 2) mm(i) = 84.932 ! PCIP-SAFT + IF (pol >= 2) parame(i,1) = 2.3435 + IF (pol >= 2) parame(i,2) = 3.2987 + IF (pol >= 2) parame(i,3) = 260.66 + IF (pol >= 2) parame(i,6) = 1.6 + IF (pol == 2) parame(i,11)= 6.48 + ELSE IF (compna(i) == 'difluoromethane') THEN ! R32 + IF (pol /= 1) write (*,*) 'non-polar parameters missing for difluoromethane' + IF (pol /= 1) stop + IF (pol >= 1) mm(i) = 52.0236 ! PCP-SAFT + IF (pol >= 1) parame(i,1) = mm(i)* 4.814700934384165E-002 ! 2.50478075530028 + IF (pol >= 1) parame(i,2) = 2.79365980535456 + IF (pol >= 1) parame(i,3) = 160.893555378523 + IF (pol >= 1) parame(i,6) = 1.97850000000000 + ELSE IF (compna(i) == 'trifluoromethane') THEN ! R23 + IF (pol /= 1) write (*,*) 'non-polar parameters missing for trifluoromethane' + IF (pol /= 1) stop + IF (pol >= 1) mm(i) = 70.0138000000000 + IF (pol >= 1) parame(i,1) = 2.66039274225485 + IF (pol >= 1) parame(i,2) = 2.82905884530501 + IF (pol >= 1) parame(i,3) = 149.527709542333 + IF (pol >= 1) parame(i,6) = 1.339963415253999E-002 + ELSE IF (compna(i) == 'tetrachloromethane') THEN ! R10 + mm(i) = 153.822 + parame(i,1) = mm(i)* .0150432213 + parame(i,2) = 3.81801454 + parame(i,3) = 292.838632 + ELSE IF (compna(i) == 'trichlorofluoromethane') THEN ! R11 + IF (pol /= 1) write (*,*) 'non-polar parameters missing for trichlorofluoromethane' + IF (pol /= 1) stop + IF (pol >= 1) mm(i) = 137.368000000000 + IF (pol >= 1) parame(i,1) = 2.28793359008803 + IF (pol >= 1) parame(i,2) = 3.69013104930876 + IF (pol >= 1) parame(i,3) = 248.603173885090 + IF (pol >= 1) parame(i,6) = 0.23225538492979 + ELSE IF (compna(i) == 'chlorodifluoromethane') THEN ! R22 ( CHClF2 or CHF2Cl) + IF (pol /= 1) write (*,*) 'non-polar parameters missing for chlorodifluoromethane' + IF (pol /= 1) stop + IF (pol >= 1) mm(i) = 86.4684000000000 + IF (pol >= 1) parame(i,1) = 2.47218586047893 + IF (pol >= 1) parame(i,2) = 3.13845692489930 + IF (pol >= 1) parame(i,3) = 187.666355083434 + IF (pol >= 1) parame(i,6) = 1.04954264812860 + ELSE IF (compna(i) == 'chloroethane') THEN + mm(i) = 64.514 + parame(i,1) = mm(i)* .0350926868 + parame(i,2) = 3.41602397 + parame(i,3) = 245.42626 + ELSE IF (compna(i) == '11difluoroethane') THEN + ! mm(i) = 66.0500000000000 ! PC-SAFT + ! parame(i,1) = mm(i)* 4.109944338817734E-002 + ! parame(i,2) = 3.10257444633546 + ! parame(i,3) = 192.177159144029 + ! mm(i) = 66.05 ! PC-SAFT assoc + ! parame(i,1)= 2.984947188 + ! parame(i,2)= 2.978630027 + ! parame(i,3)= 137.8192282 + ! nhb_typ(i) = 2 + ! nhb_no(i,1)= 1 + ! nhb_no(i,2)= 1 + ! eps_hb(i,i,1,2)= 823.3478288 + ! eps_hb(i,i,2,1)= 823.3478288 + ! eps_hb(i,i,1,1)= 0.0 + ! eps_hb(i,i,2,2)= 0.0 + ! kap_hb(i,i) = 0.96345994 + IF (pol >= 1) mm(i) = 66.0500000000000 ! PCP-SAFT + IF (pol >= 1) parame(i,1) = mm(i)* 3.949665745363346E-002 ! =2.60875422481249 + IF (pol >= 1) parame(i,2) = 3.13758353925036 + IF (pol >= 1) parame(i,3) = 179.517952627836 + IF (pol >= 1) parame(i,6) = 2.27000000000000 + IF (pol >= 1) lli(i) = 2.03907*parame(i,2) + IF (pol >= 1) phi_criti(i)= 26.5 + IF (pol >= 1) chap(i) = 0.4 + IF (pol >= 2) mm(i) = 66.0500000000000 ! PCIP-SAFT + IF (pol >= 2) parame(i,1) = mm(i)* 4.093647666154238E-002 ! =2.70385428349487 + IF (pol >= 2) parame(i,2) = 3.10437129415885 + IF (pol >= 2) parame(i,3) = 170.464400902455 + IF (pol >= 2) parame(i,6) = 2.27000000000000 + IF (pol == 2) parame(i,11)= 5.01000000000000 + ELSE IF (compna(i) == '1-chlorobutane') THEN + mm(i) = 92.568 + parame(i,1) = mm(i)* .0308793201 + parame(i,2) = 3.64240187 + parame(i,3) = 258.655298 + ELSE IF (compna(i) == 'chlorobenzene') THEN + ! mm(i) = 112.558 + ! parame(i,1) = mm(i)* .0235308686 + ! parame(i,2) = 3.75328494 + ! parame(i,3) = 315.039018 + mm(i) = 112.558 ! PCIP-SAFT + parame(i,1) = mm(i)* 0.023824167 ! =2.6816 + parame(i,2) = 3.7352 + parame(i,3) = 308.82 + parame(i,6) = 1.69 + IF (pol == 2) parame(i,11)= 14.1 + ELSE IF (compna(i) == 'styrene') THEN + mm(i) = 104.150 + parame(i,1) = mm(i)* 2.9124104853E-2 + parame(i,2) = 3.760233548 + parame(i,3) = 298.51287564 + ELSE IF (compna(i) == 'methylmethanoate') THEN + mm(i) = 60.053 + parame(i,1) = mm(i)* .0446000264 + parame(i,2) = 3.08753499 + parame(i,3) = 242.626755 + IF (pol >= 1) mm(i) = 60.053 ! PCP-SAFT + IF (pol >= 1) parame(i,1) = mm(i)* 4.366991153963102E-002 ! =2.62250919768946 + IF (pol >= 1) parame(i,2) = 3.10946396964 + IF (pol >= 1) parame(i,3) = 239.051951942 + IF (pol >= 1) parame(i,6) = 1.77 + IF (pol >= 2) mm(i) = 60.053 ! PCIP-SAFT + IF (pol >= 2) parame(i,1) = mm(i)* 4.492572388931002E-2 ! 2.69792449 + IF (pol >= 2) parame(i,2) = 3.078467837 + IF (pol >= 2) parame(i,3) = 232.1842551 + IF (pol >= 2) parame(i,6) = 1.77 + IF (pol == 2) parame(i,11)= 5.05 + ELSE IF (compna(i) == 'ethylmethanoate') THEN + mm(i) = 74.079 ! PC-SAFT + parame(i,1) = mm(i)* .03898009 + parame(i,2) = 3.31087192 + parame(i,3) = 246.465646 + IF (pol >= 1) mm(i) = 74.079 ! PCP-SAFT + IF (pol >= 1) parame(i,1) = mm(i)* 3.825407152074255E-002 ! =2.83382336418509 + IF (pol >= 1) parame(i,2) = 3.33160046679 + IF (pol >= 1) parame(i,3) = 244.495680932 + IF (pol >= 1) parame(i,6) = 1.93000000000 + ELSE IF (compna(i) == 'propylmethanoate') THEN + mm(i) = 88.106 + parame(i,1) = mm(i)* .0364206062 + parame(i,2) = 3.41679642 + parame(i,3) = 246.457732 + IF (pol >= 1) mm(i) = 88.106 + IF (pol >= 1) parame(i,1) = mm(i)* 3.60050739149E-2 ! =3.17226304235232 + IF (pol >= 1) parame(i,2) = 3.42957609309 + IF (pol >= 1) parame(i,3) = 245.637644107 + IF (pol >= 1) parame(i,6) = 1.89 + ELSE IF (compna(i) == 'methylacetate') THEN + mm(i) = 74.079 ! PC-SAFT + parame(i,1) = mm(i)* 4.286817177E-2 ! =3.175631296 + parame(i,2) = 3.18722021277843 + parame(i,3) = 234.106931032456 + IF (pol >= 1) mm(i) = 74.079 ! PCP-SAFT + IF (pol >= 1) parame(i,1) = mm(i)* 4.228922065E-2 ! =3.132743176 + IF (pol >= 1) parame(i,2) = 3.2011401688 + IF (pol >= 1) parame(i,3) = 233.17562886 + IF (pol >= 1) parame(i,6) = 1.72 + IF (pol >= 2) mm(i) = 74.079 ! PCIP-SAFT + IF (pol >= 2) parame(i,1) = mm(i)* 4.298900538E-2 ! =3.18458252 + IF (pol >= 2) parame(i,2) = 3.180642322 + IF (pol >= 2) parame(i,3) = 229.3132680 + IF (pol >= 2) parame(i,6) = 1.72 + IF (pol == 2) parame(i,11)= 6.94 + ELSE IF (compna(i) == 'ethylacetate') THEN + mm(i) = 88.106 ! PC-SAFT + parame(i,1) = mm(i)* .0401464427 ! =3.537142481 + parame(i,2) = 3.30789258 + parame(i,3) = 230.800689 + IF (pol >= 1) mm(i) = 88.106 ! PCP-SAFT + IF (pol >= 1) parame(i,1) = mm(i)* 0.039792575 ! =3.505964572 + IF (pol >= 1) parame(i,2) = 3.317655188 + IF (pol >= 1) parame(i,3) = 230.2434769 + IF (pol >= 1) parame(i,6) = 1.78 + IF (pol >= 2) mm(i) = 88.106 ! PCIP-SAFT + IF (pol >= 2) parame(i,1) = mm(i)* 0.040270267 ! =3.548052143 + IF (pol >= 2) parame(i,2) = 3.302097562 + IF (pol >= 2) parame(i,3) = 227.5026191 + IF (pol >= 2) parame(i,6) = 1.78 + IF (pol == 2) parame(i,11)= 8.62 + ELSE IF (compna(i) == 'ethyl-propanoate') THEN + mm(i) = 102.133 + parame(i,1) = mm(i)* .0375692464 + parame(i,2) = 3.40306071 + parame(i,3) = 232.778374 + ELSE IF (compna(i) == 'propyl-ethanoate') THEN + mm(i) = 102.133 + parame(i,1) = mm(i)* .0370721275 + parame(i,2) = 3.42272266 + parame(i,3) = 235.758378 + IF (pol >= 1) mm(i) = 102.133 ! PCP-SAFT + IF (pol >= 1) parame(i,1) = mm(i)* 3.687149995200072E-2 ! =3.76579690459769 + IF (pol >= 1) parame(i,2) = 3.4289353421006 + IF (pol >= 1) parame(i,3) = 235.41679442910 + IF (pol >= 1) parame(i,6) = 1.78 + ! IF (pol.EQ.2) parame(i,11)= 10.41 + ELSE IF (compna(i) == 'nbutyl-ethanoate') THEN + mm(i) = 116.16 ! PC-SAFT + parame(i,1) = mm(i)* .03427004 + parame(i,2) = 3.54269638 + parame(i,3) = 242.515768 + IF (pol >= 1) mm(i) = 116.16 ! PCP-SAFT + IF (pol >= 1) parame(i,1) = mm(i)* 3.411585209773470E-002 ! =3.96289737967286 + IF (pol >= 1) parame(i,2) = 3.54821589228130 + IF (pol >= 1) parame(i,3) = 242.274388267447 + IF (pol >= 1) parame(i,6) = 1.87000000000000 + IF (pol >= 2) mm(i) = 116.16 ! PCIP-SAFT + IF (pol >= 2) parame(i,1) = mm(i)* 3.442139015733717E-002 ! =3.99838868067629 + IF (pol >= 2) parame(i,2) = 3.53576054452119 + IF (pol >= 2) parame(i,3) = 240.154409609249 + IF (pol >= 2) parame(i,6) = 1.87000000000000 + IF (pol == 2) parame(i,11)= 14.2000000000000 + ELSE IF (compna(i) == 'methyl-octanoate') THEN + mm(i) = 158.24 ! PC-SAFT + parame(i,1) = 5.2074 + parame(i,2) = 3.6069 + parame(i,3) = 244.12 + ELSE IF (compna(i) == 'methyl-decanoate') THEN + mm(i) = 186.2912 ! PC-SAFT + parame(i,1) = 5.8402 + parame(i,2) = 3.6871 + parame(i,3) = 248.27 + + mm(i) = 186.2912 ! PC-SAFT from GC-method Tim + parame(i,1) = 7.716 + parame(i,2) = 3.337303029 + parame(i,3) = 204.250907 + + mm(i) = 186.2912 ! PC-SAFT from GC-method (tightly fit) Tim + parame(i,1) = 7.728 + parame(i,2) = 3.334023322 + parame(i,3) = 206.9099379 + + ! mm(i) = 186.2912 ! PC-SAFT from fit to DIPPR + ! parame(i,1) = 6.285005 + ! parame(i,2) = 3.594888 + ! parame(i,3) = 236.781461 + ! ! parame(i,6) = 2.08056 + + ! mm(i) = 186.291000000000 + ! parame(i,1) = 6.28500485898895 + ! parame(i,2) = 3.59488828061149 + ! parame(i,3) = 236.781461491921 + ! parame(i,6) = 2.08055996894836 + ! parame(i,8) = 1.00000000000000 + mm(i) = 186.291000000000 + parame(i,1) = 6.14436331493372 + parame(i,2) = 3.61977264863944 + parame(i,3) = 242.071887817656 + + ELSE IF (compna(i) == 'methyl-dodecanoate') THEN + mm(i) = 214.344 ! PC-SAFT + parame(i,1) = 6.5153 + parame(i,2) = 3.7406 + parame(i,3) = 250.7 + ELSE IF (compna(i) == 'methyl-tetradecanoate') THEN + mm(i) = 242.398 ! PC-SAFT + parame(i,1) = 7.1197 + parame(i,2) = 3.7968 + parame(i,3) = 253.77 + ELSE IF (compna(i) == 'methyl-hexadecanoate') THEN + mm(i) = 270.451 ! PC-SAFT + parame(i,1) = 7.891 + parame(i,2) = 3.814 + parame(i,3) = 253.71 + ELSE IF (compna(i) == 'methyl-octadecanoate') THEN + mm(i) = 298.504 ! PC-SAFT + parame(i,1) = 8.8759 + parame(i,2) = 3.7932 + parame(i,3) = 250.81 + ELSE IF (compna(i) == 'CH2F2') THEN + mm(i) = 52.02 + parame(i,1) = 3.110084171 + parame(i,2) = 2.8145230485 + parame(i,3) = 158.98060151 + ELSE IF (compna(i) == 'naphthalene') THEN + ! mm(i) = 128.174000000 + ! parame(i,1) = mm(i)* 2.4877834216412E-2 + ! parame(i,2) = 3.82355815011 + ! parame(i,3) = 341.560675334 + + mm(i) = 128.17400000000 + parame(i,1) = mm(i)* 2.6400924157729E-2 + parame(i,2) = 3.8102186020014 + parame(i,3) = 328.96792935903 + ELSE IF (compna(i) == 'h2s') THEN + mm(i) = 34.0820000000000 ! PC-SAFT + parame(i,1) = mm(i)* 4.838886696385162E-002 ! = 1.64918936386199 + parame(i,2) = 3.05478289838459 + parame(i,3) = 229.838873939562 + nhb_typ(i) = 2 + nhb_no(i,1) = 1 + nhb_no(i,2) = 1 + eps_hb(i,i,1,2)= 536.634834731413 + eps_hb(i,i,2,1)= 536.634834731413 + eps_hb(i,i,1,1)= 0.0 + eps_hb(i,i,2,2)= 0.0 + kap_hb(i,i) = 1.000000000000000E-003 +! PC-SAFT from Xiaohua + mm(i) = 34.082 ! PC-SAFT + parame(i,1) = 1.63677 + parame(i,2) = 3.06565 + parame(i,3) = 230.2121 + nhb_typ(i) = 2 + nhb_no(i,1) = 1 + nhb_no(i,2) = 1 + eps_hb(i,i,1,2)= 275.1088 + eps_hb(i,i,2,1)= 275.1088 + eps_hb(i,i,1,1)= 0.0 + eps_hb(i,i,2,2)= 0.0 + kap_hb(i,i) = 1.E-2 + ! IF (pol.GE.1) mm(i) = 34.082 ! PCP-SAFT with quadrupole + ! IF (pol.GE.1) parame(i,1) = mm(i)* 3.03171032558E-2 ! =1.03326751316478 + ! IF (pol.GE.1) parame(i,2) = 3.6868189914018 + ! IF (pol.GE.1) parame(i,3) = 246.862831266172 + ! IF (pol.GE.1) nhb_typ(i) = 2 + ! IF (pol.GE.1) nhb_no(i,1) = 1 + ! IF (pol.GE.1) nhb_no(i,2) = 1 + ! IF (pol.GE.1) eps_hb(i,i,1,2)= 987.4927232 + ! IF (pol.GE.1) eps_hb(i,i,2,1)= 987.4927232 + ! IF (pol.GE.1) eps_hb(i,i,1,1)= 0.0 + ! IF (pol.GE.1) eps_hb(i,i,2,2)= 0.0 + ! IF (pol.GE.1) kap_hb(i,i) = 5.5480659623d-4 + ! IF (pol.GE.1) parame(i,6) = 0.97833 + ! IF (pol.GE.1) parame(i,7) = 3.8623 + ! IF (pol.GE.1) LLi(i) = 1.2737*parame(i,2) + ! IF (pol.GE.1) phi_criti(i)= 14.316 + ! IF (pol.GE.1) chap(i) = 0.4473 + IF (pol >= 1) mm(i) = 34.0820000000000 ! PCP-SAFT no quadrupoLE + IF (pol >= 1) parame(i,1) = mm(i)* 4.646468487062725E-002 ! 1.58360938976072 + IF (pol >= 1) parame(i,2) = 3.10111012646306 + IF (pol >= 1) parame(i,3) = 230.243457544889 + IF (pol >= 1) nhb_typ(i) = 2 + IF (pol >= 1) nhb_no(i,1) = 1 + IF (pol >= 1) nhb_no(i,2) = 1 + IF (pol >= 1) eps_hb(i,i,1,2)= 584.367708701411 + IF (pol >= 1) eps_hb(i,i,2,1)= 584.367708701411 + IF (pol >= 1) eps_hb(i,i,1,1)= 0.0 + IF (pol >= 1) eps_hb(i,i,2,2)= 0.0 + IF (pol >= 1) kap_hb(i,i) = 1.000000000000000E-003 + IF (pol >= 1) parame(i,6) = 0.978330000000000 + + IF (pol >= 1) lli(i) = 1.2737*parame(i,2) + IF (pol >= 1) phi_criti(i)= 14.316 + IF (pol >= 1) chap(i) = 0.4473 + + + IF (pol == 2) parame(i,7) = 0.0 + IF (pol == 2) mm(i) = 34.0820000000000 ! PCIP-SAFT + IF (pol == 2) parame(i,1) = mm(i)* 4.806418212963168E-002 ! 1.63812345534211 + IF (pol == 2) parame(i,2) = 3.06556006883749 + IF (pol == 2) parame(i,3) = 221.746622243054 + IF (pol == 2) nhb_typ(i) = 2 + IF (pol == 2) nhb_no(i,1) = 1 + IF (pol == 2) nhb_no(i,2) = 1 + IF (pol == 2) eps_hb(i,i,1,2)= 672.164783984789 + IF (pol == 2) eps_hb(i,i,2,1)= 672.164783984789 + IF (pol == 2) eps_hb(i,i,1,1)= 0.0 + IF (pol == 2) eps_hb(i,i,2,2)= 0.0 + IF (pol == 2) kap_hb(i,i) = 1.000000000000000E-003 + IF (pol == 2) parame(i,6) = 0.978330000000000 + IF (pol == 2) parame(i,11) = 3.60200000000000 + IF (pol == 2) parame(i,7) = 0.0 + + IF (pol >= 1)mm(i) = 34.0820000000000 !PCP-SAFT D&Q + IF (pol >= 1)parame(i,1) = mm(i)* 3.974667896078737E-002 ! = 1.35464631234155 + IF (pol >= 1)parame(i,2) = 3.30857082333438 + IF (pol >= 1)parame(i,3) = 234.248947273191 + IF (pol >= 1)nhb_typ(i) = 2 + IF (pol >= 1)nhb_no(i,1) = 1 + IF (pol >= 1)nhb_no(i,2) = 1 + IF (pol >= 1)eps_hb(i,i,1,2)= 780.770936834770 + IF (pol >= 1)eps_hb(i,i,2,1)= 780.770936834770 + IF (pol >= 1)eps_hb(i,i,1,1)= 0.0 + IF (pol >= 1)eps_hb(i,i,2,2)= 0.0 + IF (pol >= 1)kap_hb(i,i) = 1.000000000000000E-003 + IF (pol >= 1)parame(i,6) = 0.978330000000000 + IF (pol >= 1)parame(i,7) = 2.93750500000000 + + ELSE IF (compna(i) == 'methanol') THEN + mm(i) = 32.042 ! PC-SAFT + parame(i,1) = mm(i)* .0476100379 + parame(i,2) = 3.23000005 + parame(i,3) = 188.904644 + nhb_typ(i) = 2 + nhb_no(i,1) = 1 ! no. of sites of type 1 + nhb_no(i,2) = 1 ! no. of sites of type 2 + eps_hb(i,i,1,2)= 2899.49055 + eps_hb(i,i,2,1)= 2899.49055 + eps_hb(i,i,1,1)= 0.0 + eps_hb(i,i,2,2)= 0.0 + kap_hb(i,i) = .0351760892 + IF (pol >= 1) mm(i) = 32.042 ! PCP-SAFT + IF (pol >= 1) parame(i,1) = mm(i)* 7.213091821E-2 ! =2.31121888139672 + IF (pol >= 1) parame(i,2) = 2.8270129502 + IF (pol >= 1) parame(i,3) = 176.3760515 + IF (pol >= 1) nhb_typ(i) = 2 + IF (pol >= 1) nhb_no(i,1) = 1 + IF (pol >= 1) nhb_no(i,2) = 1 + IF (pol >= 1) eps_hb(i,i,1,2)= 2332.5845803 + IF (pol >= 1) eps_hb(i,i,2,1)= 2332.5845803 + IF (pol >= 1) eps_hb(i,i,1,1)= 0.0 + IF (pol >= 1) eps_hb(i,i,2,2)= 0.0 + IF (pol >= 1) kap_hb(i,i) = 8.9248658086E-2 + IF (pol >= 1) parame(i,6) = 1.7 + IF (pol >= 1) lli(i) = 1.75*parame(i,2) + IF (pol >= 1) phi_criti(i)= 23.43 + IF (pol >= 1) chap(i) = 0.304 + IF (pol == 2) mm(i) = 32.042 ! PCIP-SAFT + IF (pol == 2) parame(i,1) = 2.0693 + IF (pol == 2) parame(i,2) = 2.9547 + IF (pol == 2) parame(i,3) = 174.51 + IF (pol == 2) nhb_typ(i) = 2 + IF (pol == 2) nhb_no(i,1) = 1 + IF (pol == 2) nhb_no(i,2) = 1 + IF (pol == 2) eps_hb(i,i,1,2)= 2418.5 + IF (pol == 2) eps_hb(i,i,2,1)= 2418.5 + IF (pol == 2) eps_hb(i,i,1,1)= 0.0 + IF (pol == 2) eps_hb(i,i,2,2)= 0.0 + IF (pol == 2) kap_hb(i,i) = 0.06319 + IF (pol == 2) parame(i,6) = 1.7 + IF (pol == 2) parame(i,11)= 3.29 + ! mm(i) = 32.0420000000000 ! PCP-SAFT with adjusted QQ + ! parame(i,1) = mm(i)* 6.241807629559099E-002 + ! ! parame(i,1) = 2.00000000066333 + ! parame(i,2) = 2.97610169698593 + ! parame(i,3) = 163.268505098639 + ! nhb_typ(i) = 2 + ! nhb_no(i,1) = 1 + ! nhb_no(i,2) = 1 + ! eps_hb(i,i,1,2)= 2449.55621933612 + ! eps_hb(i,i,2,1)= 2449.55621933612 + ! eps_hb(i,i,1,1)= 0.0 + ! eps_hb(i,i,2,2)= 0.0 + ! kap_hb(i,i) = 8.431015160393653E-002 + ! parame(i,6) = 1.72000000000000 + ! parame(i,7) = 1.59810028824523 + ELSE IF (compna(i) == 'ethanol') THEN + mm(i) = 46.069 + parame(i,1) = mm(i)* .0517195521 + parame(i,2) = 3.17705595 + parame(i,3) = 198.236542 + nhb_typ(i) = 2 + nhb_no(i,1) = 1 ! no. of sites of type 1 + nhb_no(i,2) = 1 ! no. of sites of type 2 + eps_hb(i,i,1,2)= 2653.38367 + eps_hb(i,i,2,1)= 2653.38367 + eps_hb(i,i,1,1)= 0.0 + eps_hb(i,i,2,2)= 0.0 + kap_hb(i,i) = .0323840159 + IF (pol >= 1) mm(i) = 46.0690000000000 + IF (pol >= 1) parame(i,1) = mm(i)* 4.753626908781145E-002 ! =2.18994838060639 + IF (pol >= 1) parame(i,2) = 3.30120000000000 + IF (pol >= 1) parame(i,3) = 209.824555801706 + IF (pol >= 1) nhb_typ(i) = 2 + IF (pol >= 1) nhb_no(i,1) = 1 + IF (pol >= 1) nhb_no(i,2) = 1 + IF (pol >= 1) eps_hb(i,i,1,2)= 2584.53116785767 + IF (pol >= 1) eps_hb(i,i,2,1)= 2584.53116785767 + IF (pol >= 1) eps_hb(i,i,1,1)= 0.0 + IF (pol >= 1) eps_hb(i,i,2,2)= 0.0 + IF (pol >= 1) kap_hb(i,i) = 2.349382956935725E-002 + IF (pol >= 1) parame(i,6) = 1.69000000000000 + ! mm(i) = 46.0690000000000 + ! parame(i,1) = mm(i)* 5.117957752785066E-002 ! =2.357791957 + ! parame(i,2) = 3.24027031244304 + ! parame(i,3) = 175.657110615456 + ! nhb_typ(i) = 2 + ! nhb_no(i,1) = 1 + ! nhb_no(i,2) = 1 + ! eps_hb(i,i,1,2)= 2273.62670516146 + ! eps_hb(i,i,2,1)= 2273.62670516146 + ! eps_hb(i,i,1,1)= 0.0 + ! eps_hb(i,i,2,2)= 0.0 + ! kap_hb(i,i) = 7.030279197039477E-002 + ! parame(i,6) = 1.69000000000000 + ! parame(i,7) = 3.63701294195013 + IF (pol == 2) mm(i) = 46.0690000000000 + IF (pol == 2) parame(i,1) = mm(i)* 4.733436280008321E-002 ! =2.18064676 + IF (pol == 2) parame(i,2) = 3.31260000000000 + IF (pol == 2) parame(i,3) = 207.594119926613 + IF (pol == 2) nhb_typ(i) = 2 + IF (pol == 2) nhb_no(i,1) = 1 + IF (pol == 2) nhb_no(i,2) = 1 + IF (pol == 2) eps_hb(i,i,1,2)= 2589.68311382661 + IF (pol == 2) eps_hb(i,i,2,1)= 2589.68311382661 + IF (pol == 2) eps_hb(i,i,1,1)= 0.0 + IF (pol == 2) eps_hb(i,i,2,2)= 0.0 + IF (pol == 2) kap_hb(i,i) = 2.132561218631547E-002 + IF (pol == 2) parame(i,6) = 1.69000000000000 + IF (pol == 2) parame(i,7) = 0.0 + IF (pol == 2) parame(i,11)= 5.11000000000000 + ELSE IF (compna(i) == '1-propanol') THEN + mm(i) = 60.096 + parame(i,1) = mm(i)* .0499154461 + parame(i,2) = 3.25221234 + parame(i,3) = 233.396705 + nhb_typ(i) = 2 + nhb_no(i,1) = 1 ! no. of sites of type 1 + nhb_no(i,2) = 1 ! no. of sites of type 2 + eps_hb(i,i,1,2)= 2276.77867 + eps_hb(i,i,2,1)= 2276.77867 + eps_hb(i,i,1,1)= 0.0 + eps_hb(i,i,2,2)= 0.0 + kap_hb(i,i) = .0152683094 + ELSE IF (compna(i) == '1-butanol') THEN + mm(i) = 74.123 + parame(i,1) = mm(i)* .0341065046 + parame(i,2) = 3.72361538 + parame(i,3) = 269.798048 + nhb_typ(i) = 2 + nhb_no(i,1) = 1 ! no. of sites of type 1 + nhb_no(i,2) = 1 ! no. of sites of type 2 + eps_hb(i,i,1,2)= 2661.37119 + eps_hb(i,i,2,1)= 2661.37119 + eps_hb(i,i,1,1)= 0.0 + eps_hb(i,i,2,2)= 0.0 + kap_hb(i,i) = .00489087833 + mm(i) = 74.1230000000000 + parame(i,1) = mm(i)* 3.329202420547412E-002 ! =2.46770471018236 + parame(i,2) = 3.76179376417092 + parame(i,3) = 270.237284242002 + nhb_typ(i) = 2 + nhb_no(i,1) = 1 + nhb_no(i,2) = 1 + eps_hb(i,i,1,2)= 2669.28754983370 + eps_hb(i,i,2,1)= 2669.28754983370 + eps_hb(i,i,1,1)= 0.0 + eps_hb(i,i,2,2)= 0.0 + kap_hb(i,i) = 4.855584122733399E-003 + parame(i,6) = 1.66000000000000 + ELSE IF (compna(i) == '1-pentanol') THEN + mm(i) = 88.15 ! PC-SAFT + parame(i,1) = mm(i)* .041134139 + parame(i,2) = 3.45079143 + parame(i,3) = 247.278748 + nhb_typ(i) = 2 + nhb_no(i,1) = 1 ! no. of sites of type 1 + nhb_no(i,2) = 1 ! no. of sites of type 2 + eps_hb(i,i,1,2)= 2252.09237 + eps_hb(i,i,2,1)= 2252.09237 + eps_hb(i,i,1,1)= 0.0 + eps_hb(i,i,2,2)= 0.0 + kap_hb(i,i) = .0103189939 + IF (pol >= 1) mm(i) = 88.1500000000000 ! PCP-SAFT + IF (pol >= 1) parame(i,1) = mm(i)* 4.138903382168521E-002 ! =3.64844333138155 + IF (pol >= 1) parame(i,2) = 3.44250118689142 + IF (pol >= 1) parame(i,3) = 246.078034174947 + IF (pol >= 1) nhb_typ(i) = 2 + IF (pol >= 1) nhb_no(i,1) = 1 + IF (pol >= 1) nhb_no(i,2) = 1 + IF (pol >= 1) eps_hb(i,i,1,2)= 2236.72830142446 + IF (pol >= 1) eps_hb(i,i,2,1)= 2236.72830142446 + IF (pol >= 1) eps_hb(i,i,1,1)= 0.0 + IF (pol >= 1) eps_hb(i,i,2,2)= 0.0 + IF (pol >= 1) kap_hb(i,i) = 1.040067895187016E-002 + IF (pol >= 1) parame(i,6) = 1.70000000000000 + IF (pol == 2) mm(i) = 88.1500000000000 ! PCIP-SAFT + IF (pol == 2) parame(i,1) = mm(i)* 4.161521814399406E-002 ! =3.66838147939308 + IF (pol == 2) parame(i,2) = 3.43496654431777 + IF (pol == 2) parame(i,3) = 244.177313808431 + IF (pol == 2) nhb_typ(i) = 2 + IF (pol == 2) nhb_no(i,1) = 1 + IF (pol == 2) nhb_no(i,2) = 1 + IF (pol == 2) eps_hb(i,i,1,2)= 2241.27880639096 + IF (pol == 2) eps_hb(i,i,2,1)= 2241.27880639096 + IF (pol == 2) eps_hb(i,i,1,1)= 0.0 + IF (pol == 2) eps_hb(i,i,2,2)= 0.0 + IF (pol == 2) kap_hb(i,i) = 1.049516309928397E-002 + IF (pol == 2) parame(i,6) = 1.70000000000000 + IF (pol == 2) parame(i,11)= 10.8000000000000 + ELSE IF (compna(i) == '1-octanol') THEN + mm(i) = 130.23 + parame(i,1) = mm(i)* .0334446084 + parame(i,2) = 3.714535 + parame(i,3) = 262.740637 + nhb_typ(i) = 2 + nhb_no(i,1) = 1 ! no. of sites of type 1 + nhb_no(i,2) = 1 ! no. of sites of type 2 + eps_hb(i,i,1,2)= 2754.77272 + eps_hb(i,i,2,1)= 2754.77272 + eps_hb(i,i,1,1)= 0.0 + eps_hb(i,i,2,2)= 0.0 + kap_hb(i,i) = .00219656803 + ELSE IF (compna(i) == '1-nonanol') THEN + mm(i) = 144.257 + parame(i,1) = mm(i)* .0324692669 + parame(i,2) = 3.72924286 + parame(i,3) = 263.636673 + nhb_typ(i) = 2 + nhb_no(i,1) = 1 ! no. of sites of type 1 + nhb_no(i,2) = 1 ! no. of sites of type 2 + eps_hb(i,i,1,2)= 2941.9231 + eps_hb(i,i,2,1)= 2941.9231 + eps_hb(i,i,1,1)= 0.0 + eps_hb(i,i,2,2)= 0.0 + kap_hb(i,i) = .00142696883 + ELSE IF (compna(i) == '2-propanol') THEN + mm(i) = 60.096 + parame(i,1) = mm(i)* .0514663133 + parame(i,2) = 3.20845858 + parame(i,3) = 208.420809 + nhb_typ(i) = 2 + nhb_no(i,1) = 1 ! no. of sites of type 1 + nhb_no(i,2) = 1 ! no. of sites of type 2 + eps_hb(i,i,1,2)= 2253.91064 + eps_hb(i,i,2,1)= 2253.91064 + eps_hb(i,i,1,1)= 0.0 + eps_hb(i,i,2,2)= 0.0 + kap_hb(i,i) = .0246746934 + ELSE IF (compna(i) == '2-methyl-2-butanol') THEN + mm(i) = 88.15 + parame(i,1) = mm(i)* .0289135026 + parame(i,2) = 3.90526707 + parame(i,3) = 266.011828 + nhb_typ(i) = 2 + nhb_no(i,1) = 1 ! no. of sites of type 1 + nhb_no(i,2) = 1 ! no. of sites of type 2 + eps_hb(i,i,1,2)= 2618.80124 + eps_hb(i,i,2,1)= 2618.80124 + eps_hb(i,i,1,1)= 0.0 + eps_hb(i,i,2,2)= 0.0 + kap_hb(i,i) = .00186263367 + ELSE IF (compna(i) == 'acetic-acid') THEN + mm(i) = 60.053 + parame(i,1) = mm(i)* .0227076949 + parame(i,2) = 3.79651163 + parame(i,3) = 199.225066 + nhb_typ(i) = 2 + nhb_no(i,1) = 1 ! no. of sites of type 1 + nhb_no(i,2) = 1 ! no. of sites of type 2 + eps_hb(i,i,1,2)= 3092.40109 + eps_hb(i,i,2,1)= 3092.40109 + eps_hb(i,i,1,1)= 0.0 + eps_hb(i,i,2,2)= 0.0 + kap_hb(i,i) = .0870093874 + + + mm(i) = 60.053 + parame(i,1) = mm(i)* .0181797646 + parame(i,2) = 4.13711044 + parame(i,3) = 207.552969 + nhb_typ(i) = 2 + nhb_no(i,1) = 1 ! no. of sites of type 1 + nhb_no(i,2) = 1 ! no. of sites of type 2 + eps_hb(i,i,1,2)= 3198.84362 + eps_hb(i,i,2,1)= 3198.84362 + eps_hb(i,i,1,1)= 0.0 + eps_hb(i,i,2,2)= 0.0 + kap_hb(i,i) = .0586552968 + +! mit gesetztem Dipol-Moment + mm(i) = 60.0530000000000 + parame(i,1) = mm(i)* 1.736420143637533E-002 + parame(i,2) = 4.25220708070687 + parame(i,3) = 190.957247854820 + parame(i,6) = 3.50000000000000 + nhb_typ(i) = 2 + nhb_no(i,1) = 1 ! no. of sites of type 1 + nhb_no(i,2) = 1 ! no. of sites of type 2 + eps_hb(i,i,1,2)= 3096.36190957945 + eps_hb(i,i,2,1)= 3096.36190957945 + eps_hb(i,i,1,1)= 0.0 + eps_hb(i,i,2,2)= 0.0 + kap_hb(i,i) = 6.154307094782551E-002 + + ELSE IF (compna(i) == 'propionic-acid') THEN + mm(i) = 74.0800000000000 + parame(i,1) = mm(i)* 2.359519915877884E-002 + parame(i,2) = 3.99339224153844 + parame(i,3) = 295.947729838532 + nhb_typ(i) = 2 + nhb_no(i,1) = 1 ! no. of sites of type 1 + nhb_no(i,2) = 1 ! no. of sites of type 2 + eps_hb(i,i,1,2)= 2668.97826430874 + eps_hb(i,i,2,1)= 2668.97826430874 + eps_hb(i,i,1,1)= 0.0 + eps_hb(i,i,2,2)= 0.0 + kap_hb(i,i) = 3.660242292423115E-002 + ELSE IF (compna(i) == 'acrylic-acid') THEN + mm(i) = 72.0636 + parame(i,1) = mm(i)* .0430585424 + parame(i,2) = 3.0545415 + parame(i,3) = 164.115604 + nhb_typ(i) = 2 + nhb_no(i,1) = 1 ! no. of sites of type 1 + nhb_no(i,2) = 1 ! no. of sites of type 2 + eps_hb(i,i,1,2)= 3065.40667 + eps_hb(i,i,2,1)= 3065.40667 + eps_hb(i,i,1,1)= 0.0 + eps_hb(i,i,2,2)= 0.0 + kap_hb(i,i) = .336261669 + ELSE IF (compna(i) == 'caproic-acid') THEN + mm(i) = 116.16 + parame(i,1) = 5.87151 + parame(i,2) = 3.0694697 + parame(i,3) = 241.4569 + nhb_typ(i) = 1 + eps_hb(i,i,1,1)= 2871.37 + kap_hb(i,i) = 3.411613D-3 + ELSE IF (compna(i) == 'aniline') THEN + mm(i) = 93.13 + parame(i,1) = mm(i)* .0285695992 + parame(i,2) = 3.70214085 + parame(i,3) = 335.471062 + nhb_typ(i) = 2 + nhb_no(i,1) = 1 ! no. of sites of type 1 + nhb_no(i,2) = 1 ! no. of sites of type 2 + eps_hb(i,i,1,2)= 1351.64234 + eps_hb(i,i,2,1)= 1351.64234 + eps_hb(i,i,1,1)= 0.0 + eps_hb(i,i,2,2)= 0.0 + kap_hb(i,i) = .0748830615 + + mm(i) = 93.1300000000000 + parame(i,1) = mm(i)* 2.834372610192228E-002 ! =2.63965121187202 + parame(i,2) = 3.71326867619433 + parame(i,3) = 332.253796842009 + nhb_typ(i) = 2 + nhb_no(i,1) = 1 + nhb_no(i,2) = 1 + eps_hb(i,i,1,2)= 1392.14266886674 + eps_hb(i,i,2,1)= 1392.14266886674 + eps_hb(i,i,1,1)= 0.0 + eps_hb(i,i,2,2)= 0.0 + kap_hb(i,i) = 7.424612087328866E-002 + parame(i,6) = 1.55000000000000 + IF (pol == 2) parame(i,11)= 12.1000000000000 + ELSE IF (compna(i) == 'HF') THEN + ! mm(i) = 20.006 ! PC-SAFT + ! parame(i,1) = 0.87731 + ! parame(i,2) = 3.0006 + ! parame(i,3) = 112.24 + ! nhb_typ(i) = 2 + ! nhb_no(i,1) = 1 + ! nhb_no(i,2) = 1 + ! eps_hb(i,i,1,2)= 2208.22 + ! eps_hb(i,i,2,1)= 2208.22 + ! eps_hb(i,i,1,1)= 0.0 + ! eps_hb(i,i,2,2)= 0.0 + ! kap_hb(i,i) = 0.71265 + mm(i) = 20.0060000000000 ! PCP-SAFT + parame(i,1) = 1.00030000000000 + parame(i,2) = 3.17603622195029 + parame(i,3) = 331.133373208282 + nhb_typ(i) = 2 + nhb_no(i,1) = 1 + nhb_no(i,2) = 1 + eps_hb(i,i,1,2)= 348.251433080979 + eps_hb(i,i,2,1)= 348.251433080979 + eps_hb(i,i,1,1)= 0.0 + eps_hb(i,i,2,2)= 0.0 + kap_hb(i,i) = 2.868887975449893E-002 + parame(i,6) = 1.82600000000000 + ELSE IF (compna(i) == 'HCl') THEN + ! mm(i) = 36.4610000000000 + ! parame(i,1) = mm(i)* 3.922046741026943E-002 + ! parame(i,2) = 3.08731180727493 + ! parame(i,3) = 203.898845304388 + ! nhb_typ(i) = 2 + ! nhb_no(i,1) = 1 + ! nhb_no(i,2) = 1 + ! eps_hb(i,i,1,2)= 245.462773177367 + ! eps_hb(i,i,2,1)= 245.462773177367 + ! eps_hb(i,i,1,1)= 0.0 + ! eps_hb(i,i,2,2)= 0.0 + ! kap_hb(i,i) = 0.256454187330899 + mm(i) = 36.461 ! PCIP-SAFT + parame(i,1) = 1.6335 + parame(i,2) = 2.9066 + parame(i,3) = 190.17 + parame(i,6) = 1.1086 + IF (pol == 2) parame(i,11)= 2.63 + ELSE IF (compna(i) == 'gen') THEN + mm(i) = 302.0 + parame(i,1) = 8.7563 + parame(i,2) = 3.604243 + parame(i,3) = 255.6434 + nhb_typ(i) = 2 + nhb_no(i,1) = 1 ! no. of sites of type 1 + nhb_no(i,2) = 1 ! no. of sites of type 2 + eps_hb(i,i,1,2)= 0.0 + eps_hb(i,i,2,1)= 0.0 + eps_hb(i,i,1,1)= 0.0 + eps_hb(i,i,2,2)= 0.0 + kap_hb(i,i) = 0.02 + ELSE IF (compna(i) == 'h2o') THEN + mm(i) = 18.015 + parame(i,1) = mm(i)* .05915 + parame(i,2) = 3.00068335 + parame(i,3) = 366.512135 + nhb_typ(i) = 2 + nhb_no(i,1) = 1 ! no. of sites of type 1 + nhb_no(i,2) = 1 ! no. of sites of type 2 + eps_hb(i,i,1,2)= 2500.6706 + eps_hb(i,i,2,1)= 2500.6706 + eps_hb(i,i,1,1)= 0.0 + eps_hb(i,i,2,2)= 0.0 + kap_hb(i,i) = .0348679836 + + ! mm(i) = 18.015 + ! parame(i,1) = 1.706 + ! parame(i,2) = 2.429 + ! parame(i,3) = 242.19 + ! nhb_typ(i) = 2 + ! nhb_no(i,1) = 1 ! no. of sites of type 1 + ! nhb_no(i,2) = 1 ! no. of sites of type 2 + ! eps_hb(i,i,1,2)= 2644.2 + ! eps_hb(i,i,2,1)= 2644.2 + ! eps_hb(i,i,1,1)= 0.0 + ! eps_hb(i,i,2,2)= 0.0 + ! kap_hb(i,i) = 0.153 + + ! mm(i) = 18.015 + ! parame(i,1) = mm(i)* .0588185709 + ! parame(i,2) = 3.02483704 + ! parame(i,3) = 382.086672 + !c! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! + ! nhb_typ(i) = 2 + ! nhb_no(i,1) = 1 ! no. of sites of type 1 + ! nhb_no(i,2) = 2 ! no. of sites of type 2 + !c! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! + ! eps_hb(i,i,1,2)= 2442.49782 + ! eps_hb(i,i,2,1)= 2442.49782 + ! eps_hb(i,i,1,1)=0.0 + ! eps_hb(i,i,2,2)=0.0 + ! kap_hb(i,i) = .0303754635 + + ! mit gefittetem Dipol-Moment - Haarlem-night + ! mm(i) = 18.015 + ! parame(i,1) = mm(i)* 7.0037160952278E-2 + ! parame(i,2) = 2.79276650240763 + ! parame(i,3) = 270.970053834558 + ! nhb_typ(i) = 2 + ! nhb_no(i,1) = 1 ! no. of sites of type 1 + ! nhb_no(i,2) = 1 ! no. of sites of type 2 + ! eps_hb(i,i,1,2)= 1427.8287 + ! eps_hb(i,i,2,1)= 1427.8287 + ! eps_hb(i,i,1,1)=0.0 + ! eps_hb(i,i,2,2)=0.0 + ! kap_hb(i,i) = 4.335167238E-2 + ! parame(i,6) = 3.968686856378 + + IF (pol >= 1) mm(i) = 18.015 ! PCP-SAFT + IF (pol >= 1) parame(i,1) = 0.922688825223317 + IF (pol >= 1) parame(i,2) = 3.17562052023944 + IF (pol >= 1) parame(i,3) = 388.462197714696 + IF (pol >= 1) nhb_typ(i) = 2 + IF (pol >= 1) nhb_no(i,1) = 1 + IF (pol >= 1) nhb_no(i,2) = 1 + IF (pol >= 1) eps_hb(i,i,1,2)= 2000.67247409031 + IF (pol >= 1) eps_hb(i,i,2,1)= 2000.67247409031 + IF (pol >= 1) eps_hb(i,i,1,1)= 0.0 + IF (pol >= 1) eps_hb(i,i,2,2)= 0.0 + IF (pol >= 1) kap_hb(i,i) = 2.040614952751225E-003 + IF (pol >= 1) parame(i,6) = 1.85500000000000 + IF (pol >= 1) parame(i,7) = 2.00000000000000 + ! IF (pol.EQ.2) mm(i) = 18.015 ! PCIP-SAFT - DQ with my=my_RPT + ! IF (pol.EQ.2) parame(i,1) = 1.0 + ! IF (pol.EQ.2) parame(i,2) = 3.14540664928026 + ! IF (pol.EQ.2) parame(i,3) = 320.283823615925 + ! IF (pol.EQ.2) nhb_typ(i) = 2 + ! IF (pol.EQ.2) nhb_no(i,1) = 2 + ! IF (pol.EQ.2) nhb_no(i,2) = 2 + ! IF (pol.EQ.2) eps_hb(i,i,1,2)= 1335.72887678032 + ! IF (pol.EQ.2) eps_hb(i,i,2,1)= 1335.72887678032 + ! IF (pol.EQ.2) eps_hb(i,i,1,1)= 0.0 + ! IF (pol.EQ.2) eps_hb(i,i,2,2)= 0.0 + ! IF (pol.EQ.2) kap_hb(i,i) = 4.162619960844732E-003 + ! IF (pol.EQ.2) parame(i,6) = 1.85500000000000 + ! IF (pol.EQ.2) parame(i,7) = 2.00000000000000 + ! IF (pol.EQ.2) parame(i,11)= 1.45000000000000 + ! mm(i) = 18.0150000000000 + ! parame(i,1) = 1.0 + ! parame(i,2) = 3.11505069470915 + ! parame(i,3) = 320.991387913502 + ! nhb_typ(i) = 2 + ! nhb_no(i,1) = 1 + ! nhb_no(i,2) = 1 + ! eps_hb(i,i,1,2)= 2037.76329812542 + ! eps_hb(i,i,2,1)= 2037.76329812542 + ! eps_hb(i,i,1,1)= 0.0 + ! eps_hb(i,i,2,2)= 0.0 + ! kap_hb(i,i) = 3.763148982832804E-003 + ! parame(i,6) = 1.85500000000000 + ! parame(i,7) = 2.00000000000000 + ! IF (pol.EQ.2) parame(i,11)= 1.45000000000000 + IF (pol == 2) mm(i) = 18.015 ! PCIP-SAFT - DQ with my=my_0 + IF (pol == 2) parame(i,1) = 1.0 + IF (pol == 2) parame(i,2) = 3.11574491885322 + IF (pol == 2) parame(i,3) = 322.699984283499 + IF (pol == 2) nhb_typ(i) = 2 + IF (pol == 2) nhb_no(i,1) = 1 + IF (pol == 2) nhb_no(i,2) = 1 + IF (pol == 2) eps_hb(i,i,1,2)= 2033.87777692450 + IF (pol == 2) eps_hb(i,i,2,1)= 2033.87777692450 + IF (pol == 2) eps_hb(i,i,1,1)= 0.0 + IF (pol == 2) eps_hb(i,i,2,2)= 0.0 + IF (pol == 2) kap_hb(i,i) = 3.815764667176484E-003 + IF (pol == 2) parame(i,6) = 1.85500000000000 + IF (pol == 2) parame(i,7) = 2.00000000000000 + IF (pol == 2) parame(i,11)= 1.45000000000000 + ! mm(i) = 18.015 ! Dortmund + ! parame(i,1) = 0.11065254*mm(i) + ! parame(i,2) = 2.36393615 + ! parame(i,3) = 300.288589 + ! nhb_typ(i) = 2 + ! nhb_no(i,1) = 1 + ! nhb_no(i,2) = 1 + ! eps_hb(i,i,1,2)= 1193.45585 + ! eps_hb(i,i,2,1)= 1193.45585 + ! eps_hb(i,i,1,1)= 0.0 + ! eps_hb(i,i,2,2)= 0.0 + ! kap_hb(i,i) = 0.091203519 + ! parame(i,6) = 1.8546 + ! parame(i,7) = 0.0 + ! parame(i,11)= 0.0 + ELSE IF (compna(i) == 'MBBA') THEN + mm(i) = 267.37 + parame(i,1) = 12.194 + parame(i,2) = 3.064 + parame(i,3) = 270.7 + e_lc(i,i) = 13.7 !Hino & Prausnitz + s_lc(i,i) = 0.176 !Hino & Prausnitz + ELSE IF (compna(i) == 'PCH5') THEN + mm(i) = 255.41 + parame(i,1) = 11.6 + parame(i,2) = 3.2 + parame(i,3) = 270.7 + ! E_LC(i,i) = 16.7 !Hino & Prausnitz + ! S_LC(i,i) = 0.176 !Hino & Prausnitz + e_lc(i,i) = 8.95 + s_lc(i,i) = 0.2 + + ! mm(i) = 255.41 + ! parame(i,1) = 11.6 + ! parame(i,2) = 3.2 + ! parame(i,3) = 290.7 + ! E_LC(i,i) = 7.18 + ! S_LC(i,i) = 0.2 + + ELSE IF (compna(i) == 'Li') THEN + mm(i) = 6.9 + parame(i,1) = 1.0 + parame(i,2) = 1.4 + parame(i,3) = 96.83 + parame(i,10)= 1.0 +! the self-association is set to zero in routine F_EXPL for ions + ! nhb_typ(i) = 1 + ! nhb_no(i,1) = 3 ! no. of sites of type 1 + ! eps_hb(i,i,1,1)= 2000.0 + ! kap_hb(i,i) = 0.008 + ELSE IF (compna(i) == 'Na') THEN + mm(i) = 23.0 + parame(i,1) = 1.0 + parame(i,2) = 1.9 + parame(i,3) = 147.38 + parame(i,10)= 1.0 +! the self-association is set to zero in routine F_EXPL for ions + nhb_typ(i) = 1 + nhb_no(i,1) = 3 ! no. of sites of type 1 + eps_hb(i,i,1,1)= 8946.28257 ! 25C, 3 sites, dG-ref-1 + kap_hb(i,i) = 0.001648933 + ELSE IF (compna(i) == 'Ka') THEN + mm(i) = 39.1 + parame(i,1) = 1.0 + parame(i,2) = 2.66 + parame(i,3) = 221.44 + parame(i,10)= 1.0 + ! the self-association is set to zero in routine F_EXPL for ions + nhb_typ(i) = 1 + nhb_no(i,1) = 3 ! no. of sites of type 1 + eps_hb(i,i,1,1)= 3118.336216 ! 25C, 3 sites, dG-ref-1 + kap_hb(i,i) = 0.00200559 + ELSE IF (compna(i) == 'Cs') THEN + mm(i) = 132.9 + parame(i,1) = 1.0 + parame(i,2) = 3.38 + parame(i,3) = 523.28 + parame(i,10)= 1.0 + ! the self-association is set to zero in routine F_EXPL for ions + ! nhb_typ(i) = 1 + ! nhb_no(i,1) = 3 ! no. of sites of type 1 + ! eps_hb(i,i,1,1)= 2000.0 + ! kap_hb(i,i) = 0.00200559 + ELSE IF (compna(i) == 'Cl') THEN + mm(i) = 35.5 + parame(i,1) = 1.0 + parame(i,2) = 3.62 + parame(i,3) = 225.44 + parame(i,10)= -1.0 +! the self-association is set to zero in routine F_EXPL for ions + nhb_typ(i) = 1 + nhb_no(i,1) = 4 ! no. of sites of type 1 + eps_hb(i,i,1,1)= 6744.12509 ! 25C, 3 sites, dG-ref-1 + kap_hb(i,i) = 0.00155252 + ELSE IF (compna(i) == 'Br') THEN + mm(i) = 79.9 + parame(i,1) = 1.0 + parame(i,2) = 3.9 + parame(i,3) = 330.82 + parame(i,10)= -1.0 +! the self-association is set to zero in routine F_EXPL for ions + nhb_typ(i) = 1 + nhb_no(i,1) = 4 ! no. of sites of type 1 + eps_hb(i,i,1,1)= 4516.033227 ! 25C, 3 sites, dG-ref-1 + kap_hb(i,i) = 0.00200559 + ELSE IF (compna(i) == 'Io') THEN + mm(i) = 126.9 + parame(i,1) = 1.0 + parame(i,2) = 4.4 + parame(i,3) = 380.60 + parame(i,10)= -1.0 +! the self-association is set to zero in routine F_EXPL for ions + nhb_typ(i) = 1 + nhb_no(i,1) = 4 ! no. of sites of type 1 + eps_hb(i,i,1,1)= 1631.203342 ! 25C, 3 sites, dG-ref-1 + kap_hb(i,i) = 0.00200559 + ELSE IF (compna(i) == 'OH') THEN + mm(i) = 17.0 + parame(i,1) = 1.0 + parame(i,2) = 3.06 + parame(i,3) = 217.26 + parame(i,10)= -1.0 + ! the self-association is set to zero in routine F_EXPL for ions + nhb_typ(i) = 1 + nhb_no(i,1) = 4 ! no. of sites of type 1 + eps_hb(i,i,1,1)= 14118.68089 ! 25C, 3 sites, dG-ref-1 + kap_hb(i,i) = 0.00200559 + ELSE IF (compna(i) == 'NO3') THEN + mm(i) = 62.0 + parame(i,1) = 1.0 + parame(i,2) = 4.12 + parame(i,3) = 239.48 + parame(i,10)= -1.0 + ! the self-association is set to zero in routine F_EXPL for ions + ! nhb_typ(i) = 1 + ! nhb_no(i,1) = 4 ! no. of sites of type 1 + ! eps_hb(i,i,1,1)= 2000.0 + ! kap_hb(i,i) = 0.00200559 + ELSE IF (compna(i) == 'bf4') THEN + mm(i) = 86.8 + parame(i,1) = 1.0 + parame(i,2) = 4.51 ! *0.85 + parame(i,3) = 164.7 + parame(i,10)= -1.0 + ELSE IF (compna(i) == 'pf6') THEN + mm(i) = 145.0 + parame(i,1) = 1.0 + parame(i,2) = 5.06 + parame(i,3) = 224.9 + parame(i,10)= -1.0 + ELSE IF (compna(i) == 'emim') THEN + mm(i) = 111.16 + parame(i,1) = 3.11 + parame(i,2) = 4.0 + parame(i,3) = 250.0 + parame(i,10)= 1.0 + ELSE IF (compna(i) == 'bmim') THEN + mm(i) = 139.21 + ! parame(i,1) = 2.81 + ! parame(i,2) = 3.5 + parame(i,1) = 3.81 + parame(i,2) = 4.0 + parame(i,3) = 250.0 + parame(i,6) = 0.0 + parame(i,10)= 1.0 + ELSE IF (compna(i) == 'hmim') THEN + mm(i) = 167.27 + parame(i,1) = 4.53 + parame(i,2) = 4.0 + parame(i,3) = 250.0 + parame(i,10)= 1.0 + ELSE IF (compna(i) == 'omim') THEN + mm(i) = 195.32 + parame(i,1) = 5.30 + parame(i,2) = 4.0 + parame(i,3) = 250.0 + parame(i,10)= 1.0 + ELSE IF (compna(i) == 'sw') THEN + parame(i,1) = 1.0 + parame(i,2) = 1.0 + parame(i,3) = 100.0 + parame(i,4) = 0.0 + parame(i,5) = 0.0 + mm(i) = 1.0 + parame(i,6) = 0.1175015839*2.0 + ! use Temp. in Kelvin in the input-file. For dimensionless quantities + ! (P*=P*sig**3/epsilon, T*=T*kBol/epsilon, rho*=rho*sig**3) calculate + ! P* = P *1E5 * (1.e-10)^3 / (100*8.31441/6.022045E+23) + ! T* = (T+273.15)/100 + ! for rho* go to utilities.f (subroutine SI_DENS) and write + ! density(ph) = dense(ph)*6.0/PI + ELSE IF (compna(i) == 'c8-sim') THEN + mm(i) = 114.231 + parame(i,1) = mm(i)* 4.095944E-2 ! =4.67883774717337 + parame(i,2) = 3.501769 + parame(i,3) = 163.8606 + ! mm(i) = 114.231000000000 + ! parame(i,1) = mm(i)* 3.547001476437745E-002 ! =4.05177525654960 + ! parame(i,2) = 3.70988567055814 + ! parame(i,3) = 192.787548176343 + ELSE IF (compna(i) == 'argon_ge') THEN + mm(i) = 39.948 + parame(i,1) = mm(i)*0.030327 + parame(i,2) = 3.149910 + parame(i,3) = 100.188975 + ELSE IF (compna(i) == 'argon_ge2') THEN + mm(i) = 39.948 + parame(i,1) = mm(i)*0.030327 + parame(i,2) = 3.149910 + parame(i,3) = 0.8*100.188975 + ELSE + WRITE (*,*) ' pure component parameters missing for ',compna(i) + STOP + END IF + + IF (pol == 2.AND.parame(i,11) == 0.0) THEN + WRITE (*,*) ' polarizability missing for comp. ',compna(i) + STOP + END IF + + IF (nhb_typ(i) /= 0) THEN + parame(i,12) = DBLE(nhb_typ(i)) + parame(i,13) = kap_hb(i,i) + no = 0 + DO j=1,nhb_typ(i) + DO k=1,nhb_typ(i) + parame(i,(14+no))=eps_hb(i,i,j,k) + no=no+1 + END DO + END DO + DO j=1,nhb_typ(i) + parame(i,(14+no))=DBLE(nhb_no(i,j)) + no=no+1 + END DO + ELSE + DO k=12,25 + parame(i,k)=0.0 + END DO + END IF + +END DO + + +DO i = 1,ncomp + DO j = 1,ncomp + IF (compna(i) == 'ps'.AND.compna(j) == 'cyclohexane')THEN + kij(i,j) = 0.0075 + ELSE IF(compna(i) == 'peva'.AND.compna(j) == 'ethylene')THEN +! -- 0 Gew.% VA------------- + ! kij(i,j) = 0.039 +! -- 7.5 Gew.% VA------------- + ! kij(i,j) = 0.0377325 + ! kij(i,j) = 0.0374867 +! ---12.7 Gew.% VA------------ + ! kij(i,j) = 0.036854 + ! kij(i,j) = 0.0366508 +! ---27.3 Gew.% VA------------ + ! kij(i,j) = 0.034386 + ! kij(i,j) = 0.0352375 +! ---31.8 Gew.% VA------------ + kij(i,j) = 0.033626 + ! kij(i,j) = 0.0350795 +! ---42.7 Gew.% VA------------ + ! kij(i,j) = 0.031784 + ! kij(i,j) = 0.035239 + ELSE IF(compna(i) == 'gen'.AND.compna(j) == 'h2o')THEN + kij(i,j) = - 0.2 + ELSE IF(compna(i) == 'peva'.AND.compna(j) == 'vinylacetate')THEN + kij(i,j) = 0.019 + ELSE IF(compna(i) == 'ps'.AND.compna(j) == 'co2') THEN + IF ( pol == 0 ) kij(i,j) = 0.195 + IF ( pol == 1 ) kij(i,j) = 0.06 + ELSE IF(compna(i) == 'ps'.AND.compna(j) == 'acetone') THEN + kij(i,j) = 0.021 + ELSE IF(compna(i) == 'ps'.AND.compna(j) == 'hexane') THEN + kij(i,j) = 0.012 + ELSE IF(compna(i) == 'ps'.AND.compna(j) == 'pentane')THEN + kij(i,j) = 0.005 + ELSE IF(compna(i) == 'ps'.AND.compna(j) == 'methylcyclohexane') THEN + kij(i,j) = 0.0073 + ELSE IF(compna(i) == 'ps'.AND.compna(j) == 'ethylbenzene')THEN + kij(i,j) = 0.008 + ELSE IF(compna(i) == 'pe'.AND.compna(j) == 'co2') THEN + ! kij(i,j) = 0.181 + kij(i,j) = 0.088 + ELSE IF(compna(i) == 'pe'.AND.compna(j) == 'propane') THEN + kij(i,j) = 0.0206 + ELSE IF(compna(i) == 'pe'.AND.compna(j) == 'butane') THEN + kij(i,j) = 0.01 + ELSE IF(compna(i) == 'methane'.AND.compna(j) == 'argon') THEN + kij(i,j) = 0.01 + ELSE IF(compna(i) == 'methane'.AND.compna(j) == 'butane') THEN + kij(i,j) = 0.026 + ELSE IF(compna(i) == 'pe'.AND.compna(j) == 'pentane') THEN + ! kij(i,j) = -0.0195 + ELSE IF(compna(i) == 'pe'.AND.compna(j) == 'hexane') THEN + ! kij(i,j) = 0.008 + kij(i,j) = 0.004 + ELSE IF(compna(i) == 'pe'.AND.compna(j) == 'ethylene') THEN + kij(i,j) = 0.0404 + ! kij(i,j) = 0.0423 + ! kij(i,j) = 0.044 + ELSE IF(compna(i) == 'pe'.AND.compna(j) == 'cyclohexane') THEN + kij(i,j) = -0.1 + ELSE IF(compna(i) == 'ldpe'.AND.compna(j) == 'cyclopentane')THEN + kij(i,j) = -0.016 + ELSE IF(compna(i) == 'pp'.AND.compna(j) == 'propane') THEN + kij(i,j) = 0.0242 + ELSE IF(compna(i) == 'pp'.AND.compna(j) == 'pentane') THEN + kij(i,j) = 0.0137583176 + ELSE IF(compna(i) == 'pp'.AND.compna(j) == 'co2') THEN + kij(i,j) = 0.1767 ! without quadrupol-term + kij(i,j) = 0.063 ! with quadrupol-term + ELSE IF(compna(i) == 'pba'.AND.compna(j) == 'ethylene') THEN + kij(i,j) = 0.026 + ELSE IF(compna(i) == 'decane'.AND.compna(j) == 'ethane') THEN + kij(i,j) = 0.017 + ELSE IF(compna(i) == 'n2'.AND.compna(j) == 'co2') THEN + ! kij(i,j) = -0.04 + ELSE IF(compna(i) == 'methane'.AND.compna(j) == 'co2') THEN + kij(i,j) = 0.051875 ! PC-SAFT + IF (pol == 1) kij(i,j) = -0.0353125 ! PCP-SAFT + ELSE IF(compna(i) == 'methane'.AND.compna(j) == 'co') THEN + ! IF (pol == 1) kij(i,j) = -0.003 ! PCP-SAFT + IF (pol == 1) kij(i,j) = 0.018 ! PCP-SAFT + ELSE IF(compna(i) == 'ethane'.AND.compna(j) == 'co2') THEN + kij(i,j) = 0.095 + kij(i,j) = 0.021 + ! kij(i,j) = 0.024 + ELSE IF(compna(i) == 'propane'.AND.compna(j) == 'co2') THEN + kij(i,j) = 0.042 + ELSE IF(compna(i) == 'argon_ge'.AND.compna(j) == 'argon_ge2') THEN + read (*,*) kij(i,j) + ELSE IF(compna(i) == 'butane'.AND.compna(j) == 'co2') THEN + ! kij(i,j) = 0.115 + ! kij(i,j) = 0.048 + kij(i,j) = 0.036 + ELSE IF(compna(i) == 'pentane'.AND.compna(j) == 'co2') THEN + kij(i,j) = 0.143 ! without quadrupol-term + kij(i,j) = 0.0 ! with quadrupol-term + ELSE IF(compna(i) == 'hexane'.AND.compna(j) == 'co2') THEN + ! kij(i,j) = 0.125 ! without quadrupol-term + kij(i,j) = 0.0495 + ELSE IF(compna(i) == 'heptane'.AND.compna(j) == 'co2') THEN + kij(i,j) = 0.11 ! without quadrupol-term + ! kij(i,j) = 0.05 + ! kij(i,j) = 0.039 ! with quadrupol-term + ELSE IF(compna(i) == 'decane'.AND.compna(j) == 'co2') THEN + ! kij(i,j) = 0.128 ! without quadrupol-term + kij(i,j) = 0.053 ! with quadrupol-term + ELSE IF(compna(i) == 'dodecane'.AND.compna(j) == 'co2') THEN + kij(i,j) = 0.12 ! without quadrupol-term + kij(i,j) = 0.0508 ! with quadrupol-term + ELSE IF(compna(i) == 'benzene'.AND.compna(j) == 'co2') THEN + ! kij(i,j) = 0.087968750000 ! without quadrupol-term + ! kij(i,j) = 0.008203125 ! only co2 quadrupol + kij(i,j) = 0.042 ! both quadrupol + ! kij(i,j) = 0.003 ! both quadrupol + ELSE IF(compna(i) == 'toluene'.AND.compna(j) == 'co2') THEN + ! kij(i,j) = 0.110784912 ! without quadrupol-term + kij(i,j) = 0.0305 ! with quadrupol-term + ELSE IF(compna(i) == 'cyclohexane'.AND.compna(j) == 'co2') THEN + kij(i,j) = 0.13 + lij(i,j) = - 0.00 + ! kij(i,j) = 0.045 + ELSE IF(compna(i) == 'chloromethane'.AND.compna(j) == 'co2')THEN + ! kij(i,j) = 0.04 ! PC-SAFT + kij(i,j) = 0.025 ! PCP-SAFT + ! kij(i,j) = 0.083 ! PCIP-SAFT + ELSE IF(compna(i) == 'acetone'.AND.compna(j) == 'n2')THEN + kij(i,j) = 0.035211 ! PCP-SAFT + lij(i,j) = + 0.013225 ! PCP-SAFT + kij(i,j) = 0.023 ! PCP-SAFT + lij(i,j) = + 0.013225 ! PCP-SAFT + !kij(i,j) = 1.722238535635467E-002 ! PCP-SAFT + !lij(i,j) = 2.815974678394451E-003 ! PCP-SAFT + !kij(i,j) = 1.931522058164026E-002 ! PCP-SAFT + !lij(i,j) = 0.0 ! PCP-SAFT + !kij(i,j) = 1.641053794134795E-002 ! PCP-SAFT + !lij(i,j) = -5.850421759950764E-003 ! PCP-SAFT + if ( num == 0 ) write (*,*) 'calculation with lij only possible with num=1' + if ( num == 0 ) stop + ELSE IF(compna(i) == 'acetone'.AND.compna(j) == 'co2')THEN + kij(i,j) = 0.015 ! PC-SAFT + IF (pol == 1) kij(i,j) = -0.02 ! PCP-SAFT + IF (pol == 2) kij(i,j) = -0.005 ! PCIP-SAFT where DQ with my=my_vacuum + ! IF (pol.EQ.2) kij(i,j) = 0.0 ! PCIP-SAFT where DQ with my=my_RPT + ELSE IF(compna(i) == 'methanol'.AND.compna(j) == 'co2')THEN + ! kij(i,j) = 0.0288 ! PC-SAFT + ! kij(i,j) = - 0.035 ! PCP-SAFT for co2 and PC-SAFT methanol + ! kij(i,j) = - 0.035 ! PCP-SAFT + ! lij(i,j) = 0.3 ! PCP-SAFT + ELSE IF(compna(i) == 'dimethyl-ether'.AND.compna(j) == 'co2')THEN + kij(i,j) = 0.00896894 ! PC-SAFT + ! kij(i,j) = - 0.015 ! PCP-SAFT + ELSE IF(compna(i) == 'dimethyl-ether'.AND.compna(j) == 'h2o')THEN + ! kij(i,j) = -0.134 ! PC-SAFT + ELSE IF(compna(i) == 'dichloromethane'.AND.compna(j) == 'co2')THEN + ! kij(i,j) = 0.06881725 ! PC-SAFT + ! kij(i,j) = 0.05839145 ! PCP-SAFT + kij(i,j) = -0.00944346 ! PCP-SAFT co2 dichloromethane PC-SAFT + ! kij(i,j) = 0.06 ! PCIP-SAFT + ELSE IF(compna(i) == 'h2s'.AND.compna(j) == 'methane')THEN + ! kij(i,j) = 0.0414 ! PC-SAFT + kij(i,j) = 0.0152 ! PCP-SAFT Dipole momnet (d with Q) + ELSE IF(compna(i) == 'butane'.AND.compna(j) == 'h2s')THEN + kij(i,j) = -0.002 ! PCP-SAFT + ELSE IF(compna(i) == 'methanol'.AND.compna(j) == 'h2s')THEN + kij(i,j) = 0.0 ! PCP-SAFT + lij(i,j) = 0.0 ! PCP-SAFT + ELSE IF(compna(i) == 'co2'.AND.compna(j) == 'hydrogen') THEN + ! lij(i,j) = -0.08 !!!!! Lij not kij !!!! + ELSE IF(compna(i) == 'hexane'.AND.compna(j) == 'n2') THEN + kij(i,j) = 0.11 + ELSE IF(compna(i) == 'propane'.AND.compna(j) == 'n2') THEN + kij(i,j) = 0.0251171875 + ELSE IF(compna(i) == 'co2'.AND.compna(j) == 'hexadecane') THEN + ! kij(i,j) = 0.1194 ! PC-SAFT ohne QQ + kij(i,j) = 0.0588 + ELSE IF(compna(i) == 'ethane'.AND.compna(j) == 'acetone') THEN + ! kij(i,j) = 0.065 ! no DD + kij(i,j) = 0.038 ! DD non-polarizable + ! kij(i,j) = 0.025 ! DD polarizable + ELSE IF(compna(i) == 'butane'.AND.compna(j) == 'acetone') THEN + ! kij(i,j) = 0.065 ! no DD + kij(i,j) = 0.037 ! DD non-polarizable + ! kij(i,j) = 0.025 ! DD polarizable + ELSE IF(compna(i) == 'pentane'.AND.compna(j) == 'acetone') THEN + ! kij(i,j) = 0.072 ! no DD + ! kij(i,j) = 0.041 ! DD non-polarizable + kij(i,j) = 0.039 ! DD polarizable + ! kij(i,j) = 0.035 ! DD polarizable + ELSE IF(compna(i) == 'hexane'.AND.compna(j) == 'acetone') THEN + ! kij(i,j) = 0.063 + kij(i,j) = 0.038 ! PCP-SAFT + ! kij(i,j) = 0.036 ! PCIP-SAFT + ELSE IF(compna(i) == 'heptane'.AND.compna(j) == 'acetone') THEN + kij(i,j) = 0.035 ! PCP-SAFT + ELSE IF(compna(i) == 'decane'.AND.compna(j) == 'acetone') THEN + ! kij(i,j) = 0.059 ! no DD + ! kij(i,j) = 0.03281250 ! DD non-polarizable + kij(i,j) = 0.028 ! DD polarizable + ELSE IF(compna(i) == 'hexadecane'.AND.compna(j) == 'acetone') THEN + ! kij(i,j) = 0.07 ! no DD + ! kij(i,j) = 0.0415 ! DD non-polarizable + kij(i,j) = 0.035 ! DD polarizable + ELSE IF(compna(i) == 'hexane'.AND.compna(j) == 'butanone')THEN + kij(i,j) = 0.027 ! PCP-SAFT + ! kij(i,j) = 0.033 ! PCP-SAFT with lij + ! lij(i,j) = 0.13 ! PCP-SAFT + ! kij(i,j) = 0.042 ! PC-SAFT + ELSE IF(compna(i) == 'heptane'.AND.compna(j) == 'butanone')THEN + kij(i,j) = 0.042 ! no DD + ! kij(i,j) = 0.027 ! DD non-polarizable + ELSE IF(compna(i) == 'heptane'.AND.compna(j) == '2-pentanone')THEN + kij(i,j) = 0.041 ! no DD + ! kij(i,j) = 0.031 ! DD non-polarizable + ELSE IF(compna(i) == 'hexane'.AND.compna(j) == '3-pentanone')THEN + kij(i,j) = 0.0 + ELSE IF(compna(i) == 'pentane'.AND.compna(j) == 'propanal')THEN + ! kij(i,j) = 0.055 ! no DD + kij(i,j) = 0.027 ! DD non-polarizable + ! kij(i,j) = 0.026 ! DD polarizable 22 + ELSE IF(compna(i) == 'cyclohexane'.AND.compna(j) == 'propanal')THEN + ! kij(i,j) = 0.06 ! no DD + kij(i,j) = 0.036 ! DD non-polarizable + kij(i,j) = 0.035 ! DD polarizable 22 + ELSE IF(compna(i) == 'heptane'.AND.compna(j) == 'butanal')THEN + kij(i,j) = 0.041 ! no DD + ! kij(i,j) = 0.025 ! DD non-polarizable + ELSE IF(compna(i) == 'hexane'.AND.compna(j) == 'thf')THEN + kij(i,j) = 0.012 ! PCP-SAFT + ELSE IF(compna(i) == 'octane'.AND.compna(j) == 'thf')THEN + kij(i,j) = 0.012 ! PCP-SAFT + ELSE IF(compna(i) == 'decane'.AND.compna(j) == 'thf')THEN + kij(i,j) = 0.012 ! PCP-SAFT + ELSE IF(compna(i) == 'toluene'.AND.compna(j) == 'dmso')THEN + ! kij(i,j) = 0.025 ! no DD + kij(i,j) = - 0.0105 ! DD non-polarizable + ! kij(i,j) = - 0.019 ! DD polarizable + ELSE IF(compna(i) == 'hexane'.AND.compna(j) == 'acrylonitrile')THEN + kij(i,j) = - 0.05 ! DD polarizable + ELSE IF(compna(i) == 'heptane' .AND. compna(j) == 'butyronitrile')THEN + kij(i,j) = - 0.002 ! DD polarizable 11 + kij(i,j) = 0.002 ! DD polarizable 22 + ELSE IF(compna(i) == '1-butene'.AND.compna(j) == 'dmf')THEN + ! kij(i,j) = 0.04 ! no DD + ! kij(i,j) = 0.004 ! DD non-polarizable + kij(i,j) = 0.005 ! DD polarizable 22 + ELSE IF(compna(i) == 'cyclohexane'.AND.compna(j) == 'dmf')THEN + kij(i,j) = 0.0135 ! DD polarizable 11 + kij(i,j) = 0.022 ! DD polarizable 22 + ELSE IF(compna(i) == 'ethylene'.AND.compna(j) == 'dmf')THEN + ! kij(i,j) = - 0.0215 ! DD polarizable 11 + kij(i,j) = - 0.01 ! DD polarizable 22 + ELSE IF(compna(i) == 'nbutyl-ethanoate'.AND.compna(j) == 'dmf')THEN + ! kij(i,j) = 0.016 ! no DD + ! kij(i,j) = -0.01 ! DD non-polarizable + kij(i,j) = - 0.015 ! DD polarizable 22 + ELSE IF(compna(i) == 'methylacetate' .AND. compna(j) == 'cyclohexane')THEN + kij(i,j) = 0.066 ! PC-SAFT + ! kij(i,j) = 0.061 ! PCP-SAFT + ! kij(i,j) = 0.0625 ! PCIP-SAFT + ELSE IF(compna(i) == 'methylacetate'.AND.compna(j) == 'decane')THEN + kij(i,j) = 0.0625 ! PCIP-SAFT + ELSE IF(compna(i) == 'methylacetate' .AND. compna(j) == 'methanol')THEN + ! kij(i,j) = -0.07 ! PCIP-SAFT + ELSE IF(compna(i) == 'pentane' .AND. compna(j) == 'propionitrile')THEN + kij(i,j) = 0.0498 + IF (pol >= 1) kij(i,j) = -0.01 + IF (pol >= 2) kij(i,j) = -0.027 + ELSE IF(compna(i) == 'hexane' .AND. compna(j) == 'propionitrile')THEN + kij(i,j) = 0.05 + IF (pol >= 1) kij(i,j) = 0.0 + IF (pol >= 2) kij(i,j) = -0.03 + ELSE IF(compna(i) == 'octane' .AND. compna(j) == 'propionitrile')THEN + kij(i,j) = 0.0 ! DD polarizable 22 + ELSE IF(compna(i) == 'cyclohexane' .AND. compna(j) == 'nitromethane')THEN + kij(i,j) = 0.14 ! no DD + ! kij(i,j) = 0.07 ! DD non-polarizable + ! kij(i,j) = 0.055 ! DD polarizable 22 + ELSE IF(compna(i) == 'cyclohexane' .AND. compna(j) == 'nitroethane')THEN + ! kij(i,j) = 0.06 ! no DD + kij(i,j) = 0.03 ! DD polarizable 22 + ELSE IF(compna(i) == 'acetone' .AND. compna(j) == 'nitromethane')THEN + ! kij(i,j) = - 0.017 ! no DD + kij(i,j) = - 0.021 ! DD non-polarizable + ! kij(i,j) = - 0.023 ! DD polarizable 22 + ELSE IF(compna(i) == 'acetone' .AND. compna(j) == 'h2o')THEN + kij(i,j) = - 0.2 ! PCP-SAFT (no cross-association) + ELSE IF(compna(i) == 'methylcyclohexane' .AND. compna(j) == 'acetonitrile')THEN + ! kij(i,j) = 0.09 ! no DD + ! kij(i,j) = 0.033 ! DD non-polarizable + ! kij(i,j) = 0.025 ! DD polarizable 22 + kij(i,j) = 0.04 ! DD polarizable 22 und my angepasst + ELSE IF(compna(i) == 'ethylacetate' .AND. compna(j) == 'acetonitrile')THEN + kij(i,j) = 0.007 ! no DD + ! kij(i,j) = -0.045 ! DD polarizable 22 + ELSE IF(compna(i) == 'dimethyl-ether' .AND. compna(j) == 'propane')THEN + ! kij(i,j) = 0.03 ! no DD + kij(i,j) = 0.0225 ! DD non-polarizable + ELSE IF(compna(i) == 'benzene' .AND. compna(j) == 'pentane')THEN + ! kij(i,j) = 0.012968750 ! ohne QQ + ! kij(i,j) = 0.004921875 ! mit QQ=5.6D (gefittet) + ! kij(i,j) = -0.006406250 ! mit QQ=7.45D (Literatur) + ELSE IF(compna(i) == 'benzene' .AND. compna(j) == 'heptane')THEN + kij(i,j) = 0.01328125 + ! kij(i,j) = 0.0038 + ELSE IF(compna(i) == 'benzene' .AND. compna(j) == '1-hexene')THEN + kij(i,j) = 0.0067 + ELSE IF(compna(i) == 'ethylene' .AND. compna(j) == 'co2') THEN + kij(i,j) = 0.04 + kij(i,j) = -0.029 + ELSE IF(compna(i) == 'ethylene' .AND. compna(j) == 'vinylacetate') THEN + kij(i,j) = - 0.013847 + ELSE IF(compna(i) == 'triacontane' .AND. compna(j) == 'ethylene') THEN + kij(i,j) = 0.028 + ELSE IF(compna(i) == 'triacontane' .AND. compna(j) == 'methane')THEN + ! kij(i,j) = 0.061953125 ! polyethylene parameters + kij(i,j) = 0.039609375 ! param. by extrapolation of n-alkanes + ELSE IF(compna(i) == 'tetracontane' .AND. compna(j) == 'methane')THEN + ! kij(i,j) = 0.06515625 ! polyethylene parameters + kij(i,j) = 0.04453125 ! param. by extrapolation of n-alkanes + ! --- kij and lij adjusted ------- + ! kij(i,j) = 0.045786119 ! param. by extrapolation of n-alkanes + ! lij(i,j) = +8.53466437d-4 ! param. by extrapolation of n-alkanes + ELSE IF(compna(i) == 'eicosane' .AND. compna(j) == 'methane')THEN + kij(i,j) = 0.0360134457445 + ELSE IF(compna(i) == 'tetracontane' .AND. compna(j) == 'methane')THEN + kij(i,j) = 0.0360134457445 ! assumed equal to eicosane-C1 + ELSE IF(compna(i) == 'chlorobenzene' .AND. compna(j) == 'cyclohexane') THEN + kij(i,j) = 0.013 + ELSE IF(compna(i) == 'chloroethane' .AND. compna(j) == 'butane')THEN + kij(i,j) = 0.025 + ELSE IF(compna(i) == 'tetrachloromethane' .AND. compna(j) == '2-methylpentane') THEN + kij(i,j) = 0.0070105 + ELSE IF(compna(i) == 'tetrachloromethane' .AND. compna(j) == 'hexane') THEN + kij(i,j) = 0.004 + ELSE IF(compna(i) == 'hydrogen' .AND. compna(j) == 'hexane') THEN + kij(i,j) = 0.1501 + ELSE IF(compna(i) == 'ethanol' .AND. compna(j) == 'co2') THEN + ! kij(i,j) = -0.08 + ELSE IF(compna(i) == 'ethanol' .AND. compna(j) == 'propane') THEN + kij(i,j) = - 0.07 + ELSE IF(compna(i) == 'ethanol' .AND. compna(j) == 'ethane') THEN + kij(i,j) = 0.0 + ELSE IF(compna(i) == 'ethanol' .AND. compna(j) == 'butane') THEN + kij(i,j) = 0.028 + kij(i,j) = 0.016 + ELSE IF(compna(i) == 'ethanol' .AND. compna(j) == 'cyclohexane')THEN + kij(i,j) = 0.037 + ELSE IF(compna(i) == 'ethanol' .AND. compna(j) == '2-methylpentane') THEN + kij(i,j) = 0.028 + ELSE IF(compna(i) == 'ethanol' .AND. compna(j) == '1-octanol')THEN + kij(i,j) = 0.06 + ELSE IF(compna(i) == 'methanol' .AND. compna(j) == 'cyclohexane') THEN + kij(i,j) = 0.0508 + ! kij(i,j) = 0.03 + ELSE IF(compna(i) == 'methanol' .AND. compna(j) == 'heptane')THEN + kij(i,j) = 0.034 + ELSE IF(compna(i) == 'methanol' .AND. compna(j) == 'decane')THEN + ! kij(i,j) = 0.042 ! PC-SAFT + ! kij(i,j) = 0.011 ! PCP-SAFT + kij(i,j) = 0.000 ! PCIP-SAFT + ELSE IF(compna(i) == 'methanol' .AND. compna(j) == 'isobutane') THEN + kij(i,j) = 0.051 + ELSE IF(compna(i) == 'methanol' .AND. compna(j) == '1-octanol') THEN + kij(i,j) = 0.02 + ELSE IF(compna(i) == '1-butanol' .AND. compna(j) == 'butane') THEN + kij(i,j) = 0.015 + ELSE IF(compna(i) == '1-nonanol' .AND. compna(j) == 'co2') THEN + kij(i,j) = 0.076 + kij(i,j) = 0.01443 + ELSE IF(compna(i) == '1-propanol' .AND. compna(j) == 'ethylbenzene') THEN + kij(i,j) = 0.0251757813 + ELSE IF(compna(i) == 'decane'.AND.compna(j) == 'ethanol') THEN + kij(i,j) = 0.085 + ELSE IF(compna(i) == 'hexane'.AND.compna(j) == '1-chlorobutane') THEN + kij(i,j) = 0.017 + ELSE IF(compna(i) == 'aniline'.AND.compna(j) == 'methylcyclopentane') THEN + kij(i,j) = 0.0153 + ELSE IF(compna(i) == 'heptane'.AND.compna(j) == 'nbutyl-ethanoate')THEN + kij(i,j) = 0.027 + ELSE IF(compna(i) == '1-hexene'.AND.compna(j) == 'ethyl-ethanoate')THEN + kij(i,j) = 0.026 + ELSE IF(compna(i) == 'co2'.AND.compna(j) == '1-butanol')THEN + ! kij(i,j) = 0.075 + kij(i,j) = 0.0 + ELSE IF(compna(i) == 'acrylic-acid'.AND.compna(j) == 'co2')THEN + kij(i,j) = -0.1 + ELSE IF(compna(i) == 'bmim'.AND.compna(j) == 'hydrogen')THEN + lij(i,j) = 0.55 !!!!! Lij not kij !!!! + ELSE IF(compna(i) == 'bf4'.AND.compna(j) == 'hydrogen')THEN + lij(i,j) = 0.55 !!!!! Lij not kij !!!! + ELSE IF(compna(i) == 'h2o'.AND.compna(j) == 'butane')THEN !K.R.Hall FPE 2007 254 112-125 kij=0.1850 + kij(i,j) = -0.07 + ELSE IF(compna(i) == 'h2o'.AND.compna(j) == '1-butanol')THEN + kij(i,j) = -0.12 + ELSE IF(compna(i) == 'h2o'.AND.compna(j) == 'aniline')THEN + kij(i,j) = 0.0 + ELSE IF(compna(i) == 'h2o'.AND.compna(j) == 'methanol') THEN + kij(i,j) = -0.02 + ELSE IF(compna(i) == 'h2o'.AND.compna(j) == 'ethanol') THEN + kij(i,j) = -0.027 + ELSE IF(compna(i) == 'h2o'.AND.compna(j) == 'styrene') THEN + kij(i,j) = 0.1 + ELSE IF(compna(i) == 'h2o'.AND.compna(j) == 'propyl-ethanoate') THEN + kij(i,j) = -0.205 + ELSE IF(compna(i) == 'h2o'.AND.compna(j) == 'ethyl-propanoate') THEN + kij(i,j) = 0.0 + ELSE IF(compna(i) == 'h2o'.AND.compna(j) == '1-pentanol') THEN + kij(i,j) = 0.0165 + ! kij(i,j) = 0.0294 + ! kij(i,j) = -0.082 + ELSE IF(compna(i) == 'h2o'.AND.compna(j) == 'methane') THEN + ! kij(i,j) = +0.06 + kij(i,j) = -0.08 + ELSE IF(compna(i) == 'h2o'.AND.compna(j) == 'propane') THEN + kij(i,j) = 0.02 + ELSE IF(compna(i) == 'h2o'.AND.compna(j) == 'hexane') THEN + kij(i,j) = -0.02 + ELSE IF(compna(i) == 'h2o'.AND.compna(j) == 'acetic-acid') THEN + kij(i,j) = -0.0 + ELSE IF(compna(i) == 'h2o'.AND.compna(j) == 'co2') THEN + if (pol == 0) kij(i,j) = 0.0030625 ! for T=50C, according to X.Tang + stop ! very T-dependent + ELSE IF(compna(i) == 'toluene'.AND.compna(j) == 'acetic-acid') THEN + kij(i,j) = -0.1 + ELSE IF(compna(i) == 'caproic-acid'.AND.compna(j) == 'cyclohexane') THEN + kij(i,j) = 0.041531 + ELSE IF(compna(i) == '1-octanol'.AND.compna(j) == 'h2o')THEN + kij(i,j) = 0.07 + ELSE IF(compna(i) == 'acetone'.AND.compna(j) == 'benzene')THEN + kij(i,j) = 0.02132466 ! PC-SAFT + ! kij(i,j) = 0.01495148 ! PCP-SAFT + ! kij(i,j) = -0.00735575 ! PCP-SAFT but non-polar benzene + ELSE IF(compna(i) == '1-propanol'.AND.compna(j) == 'benzene')THEN + kij(i,j) = 0.02017 + ELSE IF(compna(i) == '2-propanol'.AND.compna(j) == 'benzene')THEN + kij(i,j) = 0.021386 + ELSE IF(compna(i) == '1-pentanol'.AND.compna(j) == 'benzene')THEN + kij(i,j) = 0.0129638671875 + ELSE IF(compna(i) == 'CH2F2' .AND. compna(j) == 'co2') THEN + kij(i,j) = 2.2548828125E-2 + ELSE IF(compna(i) == 'dmso' .AND. compna(j) == 'co2') THEN + kij(i,j) = -0.00 + ELSE IF(compna(i) == 'dmf'.AND.compna(j) == 'h2o')THEN + kij(i,j) = -0.0 + ELSE IF(compna(i) == 'decane'.AND.compna(j) == 'h2o')THEN + kij(i,j) = 0.11 + ELSE IF(compna(i) == '11difluoroethane'.AND.compna(j) == 'HF')THEN + kij(i,j) = 0.032 ! association: eps_kij = 0.16 + ELSE IF(compna(i) == '11difluoroethane'.AND.compna(j) == 'co2')THEN + kij(i,j) = -0.004 ! PCP-SAFT (taken from simulation) + ELSE IF(compna(i) == 'difluoromethane'.AND.compna(j) == 'HF')THEN + kij(i,j) = -0.02 + ELSE IF(compna(i) == 'naphthalene'.AND.compna(j) == 'co2')THEN + kij(i,j) = 0.137 ! angepasst an SVLE-Linie (tradition.CO2-Parameter) + kij(i,j) = 0.09 ! angepasst an SVLE-Linie (tradition.CO2-Parameter) + ELSE IF(compna(i) == 'pg2'.AND.compna(j) == 'methanol')THEN + kij(i,j) = 0.03 + ELSE IF(compna(i) == 'pg2'.AND.compna(j) == 'co2')THEN + ! kij(i,j) = 0.05 + ELSE IF(compna(i) == 'PCH5'.AND.compna(j) == 'co2')THEN + ! kij(i,j) = -0.047 + kij(i,j) = +0.055 + ! kij(i,j) = +0.036 + ELSE + END IF + kij(j,i) = kij(i,j) + lij(j,i) = -lij(i,j) + + END DO +END DO + +END SUBROUTINE pcsaft_par + + +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! SUBROUTINE init_vars +! +! This subroutine writes variables from an array "val_init" to the +! system-variables. Those variables +! include some specifications but also some starting values for a +! phase equilibrium calculation. (val_init stands for 'initial value') + +! The array comprises the following elements +! element 0 density of third phase +! element 1 density of first phase +! element 2 density of second phase +! element 3 temperature [K] +! element 4 pressure [Pa] +! element 5,..(5+NCOMP) mole-fraction of comp. i in log. from (phase 1) +! element ... mole-fraction of comp. i in log. from (phase 2) +! element ... mole-fraction of comp. i in log. from (phase 3) +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! + SUBROUTINE init_vars +! + USE BASIC_VARIABLES + IMPLICIT NONE +! + INTEGER :: i, ph +! ---------------------------------------------------------------------- + +densta(3)=val_init(0) +densta(1)=val_init(1) +densta(2)=val_init(2) +t = val_init(3) +p = val_init(4) +DO ph = 1,nphas + DO i = 1,ncomp + lnx(ph,i) = val_init(4+i+(ph-1)*ncomp) + END DO +END DO + +END SUBROUTINE init_vars + + +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! SUBROUTINE converged +! +! Once a converged solution for an equilibrium calculation is found, +! this subroutine writes variables to an array "val_conv". +! (= short for converged values) +! The array comprises the following elements +! element 0 density of third phase +! element 1 density of first phase +! element 2 density of second phase +! element 3 temperature [K] +! element 4 pressure [Pa] +! element 5,..(4+NCOMP) mole-fraction of comp. i in log. from (phase 1) +! element ... mole-fraction of comp. i in log. from (phase 2) +! element ... mole-fraction of comp. i in log. from (phase 3) +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! + SUBROUTINE converged +! + USE BASIC_VARIABLES + IMPLICIT NONE +! + INTEGER :: i, ph +! ---------------------------------------------------------------------- + +val_conv(0) = dense(3) +val_conv(1) = dense(1) +val_conv(2) = dense(2) +val_conv(3) = t +val_conv(4) = p +DO ph = 1,nphas + DO i = 1,ncomp + val_conv(4+i+(ph-1)*ncomp) = lnx(ph,i) + END DO +END DO + +END SUBROUTINE converged + +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! SUBROUTINE PERTURBATION_PARAMETER +! +! calculates density-independent parameters of the equation of state. +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! + SUBROUTINE PERTURBATION_PARAMETER +! + USE PARAMETERS, ONLY: PI, KBOL, RGAS, NAV, TAU + USE EOS_VARIABLES + USE EOS_CONSTANTS + IMPLICIT NONE +! +! --- local variables -------------------------------------------------- + INTEGER :: i, j, k, l, m, no + LOGICAL :: assoc, qudpole, dipole + REAL :: m_mean + REAL, DIMENSION(nc) :: v00, v0, d00, u + REAL, DIMENSION(nc,nc,nsite,nsite) :: eps_hb + REAL, DIMENSION(nc,nc) :: kap_hb + REAL :: zmr, nmr + REAL :: eps_kij, k_kij +! ---------------------------------------------------------------------- + +! ---------------------------------------------------------------------- +! pure component parameters +! ---------------------------------------------------------------------- +DO i = 1, ncomp + u(i) = parame(i,3) * (1.0 + parame(i,4)/t) + mseg(i) = parame(i,1) + IF (eos == 0) THEN + v00(i) = parame(i,2) + v0(i) = v00(i)*(1.0-0.12*EXP(-3.0*parame(i,3)/t))**3 + d00(i) = (1.d30/1.d6 *tau *v00(i)*6.0/PI /NAV)**(1.0/3.0) + dhs(i) = d00(i)*(1.0-0.12*EXP(-3.0*parame(i,3)/t)) + ELSE + dhs(i) = parame(i,2)*(1.0-0.12*EXP(-3.0*parame(i,3)/t)) + d00(i) = parame(i,2) + END IF +END DO + + +! ---------------------------------------------------------------------- +! combination rules +! ---------------------------------------------------------------------- +DO i = 1, ncomp + DO j = 1, ncomp + sig_ij(i,j) = 0.5 * ( d00(i) + d00(j) ) + uij(i,j) = ( 1.0 - kij(i,j) ) * ( u(i)*u(j) )**0.5 + vij(i,j) = ( 0.5*( v0(i)**(1.0/3.0) + v0(j)**(1.0/3.0) ) )**3 + END DO +END DO + + +! ---------------------------------------------------------------------- +! abbreviations +! ---------------------------------------------------------------------- +z0t = PI / 6.0 * SUM( x(1:ncomp) * mseg(1:ncomp) ) +z1t = PI / 6.0 * SUM( x(1:ncomp) * mseg(1:ncomp) * dhs(1:ncomp) ) +z2t = PI / 6.0 * SUM( x(1:ncomp) * mseg(1:ncomp) * dhs(1:ncomp)**2 ) +z3t = PI / 6.0 * SUM( x(1:ncomp) * mseg(1:ncomp) * dhs(1:ncomp)**3 ) + +m_mean = z0t/(PI/6.0) + +DO i = 1, ncomp + DO j = 1, ncomp + dij_ab(i,j) = dhs(i)*dhs(j) / ( dhs(i) + dhs(j) ) + END DO +END DO + +! ---------------------------------------------------------------------- +! dispersion term parameters for chain molecules +! ---------------------------------------------------------------------- +DO m = 0, 6 + apar(m) = ap(m,1) + (1.0-1.0/m_mean)*ap(m,2) & + + (1.0-1.0/m_mean)*(1.0-2.0/m_mean)*ap(m,3) + bpar(m) = bp(m,1) + (1.0-1.0/m_mean)*bp(m,2) & + + (1.0-1.0/m_mean)*(1.0-2.0/m_mean)*bp(m,3) +END DO + + +! ---------------------------------------------------------------------- +! van der Waals mixing rules for perturbation terms +! ---------------------------------------------------------------------- +order1 = 0.0 +order2 = 0.0 +DO i = 1, ncomp + DO j = 1, ncomp + order1 = order1 + x(i)*x(j)* mseg(i)*mseg(j)*sig_ij(i,j)**3 * uij(i,j)/t + order2 = order2 + x(i)*x(j)* mseg(i)*mseg(j)*sig_ij(i,j)**3 * (uij(i,j)/t)**2 + END DO +END DO + + +! ---------------------------------------------------------------------- +! SAFT parameters +! ---------------------------------------------------------------------- +IF (eos == 0) THEN + zmr = 0.0 + nmr = 0.0 + DO i = 1, ncomp + DO j = 1, ncomp + zmr = zmr + x(i)*x(j)*mseg(i)*mseg(j)*vij(i,j)*uij(i,j) + nmr = nmr + x(i)*x(j)*mseg(i)*mseg(j)*vij(i,j) + END DO + END DO + um = zmr / nmr +END IF + + + +! ---------------------------------------------------------------------- +! association and polar parameters +! ---------------------------------------------------------------------- +assoc = .false. +qudpole = .false. +dipole = .false. +DO i = 1, ncomp + IF (NINT(parame(i,12)) /= 0) assoc = .true. + IF (parame(i,7) /= 0.0) qudpole = .true. + IF (parame(i,6) /= 0.0) dipole = .true. +END DO + +! --- dipole and quadrupole constants ---------------------------------- +IF (qudpole) CALL qq_const ( qqp2, qqp3, qqp4 ) +IF (dipole) CALL dd_const ( ddp2, ddp3, ddp4 ) +IF (dipole .AND. qudpole) CALL dq_const ( dqp2, dqp3, dqp4 ) + + +! --- TPT-1-association parameters ------------------------------------- +IF (assoc) THEN + + eps_kij = 0.0 + k_kij = 0.0 + + DO i = 1, ncomp + IF (NINT(parame(i,12)) /= 0) THEN + nhb_typ(i) = NINT(parame(i,12)) + kap_hb(i,i) = parame(i,13) + no = 0 + DO j = 1, nhb_typ(i) + DO k = 1, nhb_typ(i) + eps_hb(i,i,j,k) = parame(i,(14+no)) + no=no+1 + END DO + END DO + DO j = 1, nhb_typ(i) + nhb_no(i,j) = parame(i,(14+no)) + no=no+1 + END DO + ELSE + nhb_typ(i) = 0 + kap_hb(i,i)= 0.0 + DO k = 1, nsite + DO l = 1, nsite + eps_hb(i,i,k,l) = 0.0 + END DO + END DO + END IF + END DO + + DO i = 1, ncomp + DO j = 1, ncomp + IF (i /= j .AND. (nhb_typ(i) /= 0 .AND. nhb_typ(j) /= 0)) THEN + kap_hb(i,j)= (kap_hb(i,i)*kap_hb(j,j))**0.5 & + *((parame(i,2)*parame(j,2))**3 )**0.5 & + /(0.5*(parame(i,2)+parame(j,2)))**3 + kap_hb(i,j)= kap_hb(i,j)*(1.0-k_kij) + DO k = 1, nhb_typ(i) + DO l = 1, nhb_typ(j) + IF (k /= l) THEN + eps_hb(i,j,k,l) = (eps_hb(i,i,k,l)+eps_hb(j,j,l,k))/2.0 + eps_hb(i,j,k,l) = eps_hb(i,j,k,l)*(1.0-eps_kij) + END IF + END DO + END DO + END IF + END DO + END DO + IF (nhb_typ(1) == 3) THEN +! write(*,*)'eps_hb manuell eingegeben' + eps_hb(1,2,3,1) = 0.5*(eps_hb(1,1,3,1)+eps_hb(2,2,1,2)) + eps_hb(2,1,1,3) = eps_hb(1,2,3,1) + END IF + IF (nhb_typ(2) == 3) THEN + eps_hb(2,1,3,1) = 0.5*(eps_hb(2,2,3,1)+eps_hb(1,1,1,2)) + eps_hb(1,2,1,3) = eps_hb(2,1,3,1) + END IF + + DO i = 1, ncomp + DO k = 1, nhb_typ(i) + DO j = 1, ncomp + DO l = 1, nhb_typ(j) + ass_d(i,j,k,l) = kap_hb(i,j) *sig_ij(i,j)**3 *(EXP(eps_hb(i,j,k,l)/t)-1.0) + END DO + END DO + END DO + END DO + +END IF + +END SUBROUTINE PERTURBATION_PARAMETER + + + + +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! SUBROUTINE OUTPUT +! +! The purpose of this subroutine is obvious. +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! + SUBROUTINE OUTPUT +! + USE BASIC_VARIABLES + IMPLICIT NONE +! +! ---------------------------------------------------------------------- + INTEGER :: i + CHARACTER (LEN=4) :: t_ind + CHARACTER (LEN=4) :: p_ind + CHARACTER (LEN=4) :: char_ncomp + REAL :: density(np),w(np,nc) +! ---------------------------------------------------------------------- + + CALL si_dens (density,w) + + IF (u_in_p == 1.E5) THEN + p_ind = ' bar' + ELSE IF (u_in_p == 1.E2) THEN + p_ind = 'mbar' + ELSE IF (u_in_p == 1.E6) THEN + p_ind = ' MPa' + ELSE IF (u_in_p == 1.E3) THEN + p_ind = ' kPa' + ELSE + p_ind = ' Pa' + END IF + IF (u_in_t == 273.15) THEN + t_ind = ' C' + ELSE + t_ind = ' K' + END IF + + WRITE(*,*) '--------------------------------------------------' + WRITE (char_ncomp,'(I3)') ncomp + WRITE(*,'(t2,a,f7.2,2a,f9.4,a)') ' T =',t-u_out_t,t_ind & + ,' P =',p/u_out_p,p_ind + WRITE(*,'(t15,4(a12,1x),10x,a)') (compna(i),i=1,ncomp) + WRITE(*,'(2x,a,'//char_ncomp//'(g13.6,1x))') 'PHASE I w', (w(1,i),i=1,ncomp) + WRITE(*,'(2x,a,'//char_ncomp//'(g13.6,1x))') 'PHASE II w', (w(2,i),i=1,ncomp) + WRITE(*,'(2x,a,'//char_ncomp//'(g13.6,1x))') 'PHASE I x', (EXP(lnx(1,i)),i=1,ncomp) + WRITE(*,'(2x,a,'//char_ncomp//'(g13.6,1x))') 'PHASE II x', (EXP(lnx(2,i)),i=1,ncomp) + WRITE(*,'(2x,a,2(g13.6,1x))') 'DENSITY ', density(1),density(2) + + !-----output to files-------------------------------------------------- + IF (ncomp == 1) THEN + WRITE (40,'(7(2x,f18.8))') t-u_out_t, p/u_out_p, & + density(1), density(2),h_lv,cpres(1),cpres(2) + ! & ,(enthal(2)-enthal(1))/mm(1) + ! WRITE (40,'(4(2x,f15.8))') t, p, 0.3107*dense(1) + ! & /0.1617*(0.689+0.311*(T/1.328)**0.3674),0.3107 + ! & *dense(2)/0.1617*(0.689+0.311*(T/1.328)**0.3674) + ELSE IF (ncomp == 2) THEN + WRITE (40,'(12(2x,G15.8))') 1.0-xi(1,1),1.0-xi(2,1), & + w(1,1),w(2,1),t-u_out_t, p/u_out_p, density(1),density(2) & + ,enthal(1),enthal(2),cpres(1),cpres(2) + ELSE IF (ncomp == 3) THEN + WRITE (40,'(10(2x,f15.8))') xi(1,1),xi(1,2),xi(1,3),xi(2,1),xi(2,2), & + xi(2,3),t-u_out_t, p/u_out_p, density(1),density(2) + END IF + + END SUBROUTINE OUTPUT + + + +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! SUBROUTINE neutr_charge +! +! This subroutine is called for electrolye solutions, where a +! neutral overall-charge has to be enforced in all phases. The basic +! philosophy is similar to the above described routine X_SUMMATION. +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! + SUBROUTINE neutr_charge(i) +! + USE BASIC_VARIABLES + IMPLICIT NONE +! +! ---------------------------------------------------------------------- + INTEGER, INTENT(IN) :: i +! +! ---------------------------------------------------------------------- + INTEGER :: comp_e, ph_e + REAL :: sum_c + CHARACTER (LEN=2) :: phasno + CHARACTER (LEN=2) :: compno +! ---------------------------------------------------------------------- + +phasno = sum_rel(i)(2:2) +READ(phasno,*) ph_e +compno = sum_rel(i)(3:3) +READ(compno,*) comp_e + +sum_c = 0.0 +write (*,*) 'there must be an error in neutr_charge' +stop +! there is an error in the following passage. The index i is an +! argument to this subroutine - I guess it is INTENT(IN), so the +! index in the following loop can not be i. +! +! I have commented the loop until I check the code. +!DO i=1,ncomp +! IF ( comp_e /= i .AND. parame(i,10) /= 0.0) & +! sum_c = sum_c + xi(ph_e,i)*parame(i,10) +!END DO + +xi(ph_e,comp_e) = - sum_c +IF (xi(ph_e,comp_e) < 0.0) xi(ph_e,comp_e)=0.0 +IF (xi(ph_e,comp_e) /= 0.0) THEN + lnx(ph_e,comp_e) = LOG(xi(ph_e,comp_e)) +ELSE + lnx(ph_e,comp_e) = -100000.0 +END IF + +! xi(2,1) = xi(2,2) +! IF (xi(2,1).NE.0.0) lnx(2,1) = LOG(xi(2,1)) + +END SUBROUTINE neutr_charge + + +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! + SUBROUTINE flash_sum +! + USE BASIC_VARIABLES + IMPLICIT NONE +! + INTEGER :: i, j, ph_i, phase1, phase2 +! ---------------------------------------------------------------------- + +phase1=0 +phase2=0 +DO j=1,ncomp + IF (it(j)(2:2) == '1') phase1=phase1+1 + IF (it(j)(2:2) == '2') phase2=phase2+1 +END DO + +IF (phase1 == ncomp-1) THEN + ph_i = 1 +ELSE IF (phase2 == ncomp-1) THEN + ph_i = 2 +ELSE + WRITE (*,*) ' FLASH_SUM: undefined flash-case' + STOP +END IF + + + +IF (ph_i == 1) THEN + DO i=1,ncomp + IF (alpha > DMIN1(1.0,xif(i)/xi(1,i), & + (xif(i)-1.0)/(xi(1,i)-1.0),alpha)) THEN + WRITE (*,*) ' FLASH_SUM: exeeded 1st alpha-bound' + alpha=DMIN1(1.0,xif(i)/xi(1,i),(xif(i)-1.0)/(xi(1,i)-1.0)) + END IF + END DO + DO i=1,ncomp + xi(2,i) = ( xif(i) - alpha*xi(1,i) ) / (1.0-alpha) + IF (xi(2,i) > 0.0) THEN + lnx(2,i) = LOG(xi(2,i)) + ELSE + xi(2,i) = 0.0 + lnx(2,i) = -100000.0 + END IF + END DO +ELSE IF (ph_i == 2) THEN + DO i=1,ncomp + IF (alpha > DMAX1(0.0,(xif(i)-xi(2,i))/(1.0-xi(2,i)), & + 1.0-xif(i)/xi(2,i),alpha)) THEN + WRITE (*,*) ' FLASH_SUM: exeeded 2nd alpha-bound' + WRITE (*,*) 0.0,(xif(i)-xi(2,i))/(1.0-xi(2,i)), 1.0-xif(i)/xi(2,i) + alpha=DMAX1(0.0,(xif(i)-xi(2,i))/(1.0-xi(2,i)), 1.0-xif(i)/xi(2,i)) + END IF + END DO + DO i=1,ncomp + xi(1,i) = ( xif(i) - (1.0-alpha)*xi(2,i) ) / alpha +! write (*,*) 'x1,i',xi(1,i),xi(2,i),alpha + IF (xi(1,i) > 0.0) THEN + lnx(1,i) = LOG(xi(1,i)) + ELSE + xi(1,i) = 0.0 + lnx(1,i) = -100000.0 + END IF + END DO +END IF + +! pause + +RETURN +END SUBROUTINE flash_sum + +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! SUBROUTINE flash_alpha +! +! This subroutine calculates all molefractions of one phase +! from a component balance. What is needed for this calculation +! are all molefractions of the other phase (nphas=2, so far) +! and the phase fraction alpha. +! Alpha is calculated from the mole fraction +! of component {sum_rel(j)(3:3)}. If for example sum_rel(2)='fl3', +! then the alpha is determined from the molefraction of comp. 3 and +! all molefractions of one phase are calculated using that alpha-value. +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! + SUBROUTINE flash_alpha +! + USE BASIC_VARIABLES + IMPLICIT NONE +! +! ---------------------------------------------------------------------- + INTEGER :: i, j, comp_i, phase1, phase2 + CHARACTER (LEN=2) :: compno +! ---------------------------------------------------------------------- + + +! ---------------------------------------------------------------------- +! first calculate the phase fraction alpha from a known composition +! of component sum_rel(j)(3:3). +! ---------------------------------------------------------------------- + +DO j = 1, nphas + IF ( sum_rel(j)(1:2) == 'fl' ) THEN + compno = sum_rel(j)(3:3) + READ(compno,*) comp_i + IF ( (xi(1,comp_i)-xi(2,comp_i)) /= 0.0 ) THEN + alpha = (xif(comp_i)-xi(2,comp_i)) / (xi(1,comp_i)-xi(2,comp_i)) + write (*,*) 'flsh',(xif(comp_i)-xi(2,comp_i)),(xi(1,comp_i)-xi(2,comp_i)) + ELSE + alpha = 0.5 + WRITE (*,*) 'FLASH_ALPHA:error in calc. of phase fraction',comp_i + END IF + ! IF (alpha <= 0.0 .OR. alpha >= 1.0) WRITE(*,*) 'FLASH_ALPHA: error',alpha + IF (alpha > 1.0) alpha = 1.0 + IF (alpha < 0.0) alpha = 0.0 + END IF +END DO + +! ---------------------------------------------------------------------- +! determine which phase is fully determined by iterated molefractions (+ summation relation) +! ---------------------------------------------------------------------- +phase1 = 0 +phase2 = 0 +DO i = 1, ncomp + IF ( it(i)(2:2) == '1' ) phase1 = phase1 + 1 + IF ( it(i)(2:2) == '2' ) phase2 = phase2 + 1 +END DO +DO i = 1, ncomp + IF ( sum_rel(i)(2:2) == '1' ) phase1 = phase1 + 1 + IF ( sum_rel(i)(2:2) == '2' ) phase2 = phase2 + 1 +END DO + + +IF ( phase1 == ncomp ) THEN + ! -------------------------------------------------------------------- + ! phase 1 is defined by iterated molefractions + summation relation + ! phase 2 is determined from componennt balance (using alpha) + ! -------------------------------------------------------------------- + IF ( alpha == 1.0 ) alpha = 1.0 - 1.0E-10 + DO i=1,ncomp + xi(2,i) = ( xif(i) - alpha*xi(1,i) ) / (1.0-alpha) + IF ( xi(2,i) < 0.0 ) xi(2,i) = 0.0 + IF ( xi(2,i) > 1.0 ) xi(2,i) = 1.0 + IF ( xi(2,i) /= 0.0 ) THEN + lnx(2,i) = LOG( xi(2,i) ) + ELSE + lnx(2,i) = -100000.0 + END IF + write (*,*) 'fl_cal ph=2',i,lnx(2,i),xi(2,i) + END DO +ELSE IF ( phase2 == ncomp ) THEN + ! -------------------------------------------------------------------- + ! phase 2 is defined by iterated molefractions + summation relation + ! phase 1 is determined from componennt balance (using alpha) + ! -------------------------------------------------------------------- + DO i = 1, ncomp + xi(1,i) = ( xif(i) - (1.0-alpha)*xi(2,i) ) /alpha + IF ( xi(1,i) < 0.0 ) xi(1,i) = 0.0 + IF ( xi(1,i) > 1.0 ) xi(1,i) = 1.0 + IF ( xi(1,i) /= 0.0 ) THEN + lnx(1,i) = LOG( xi(1,i) ) + ELSE + lnx(1,i) = -100000.0 + END IF + write (*,*) 'fl_cal ph=1',i,lnx(1,i),xi(1,i),alpha + END DO +ELSE + WRITE (*,*) ' FLASH_ALPHA: undefined flash-case' + STOP +END IF + +END SUBROUTINE flash_alpha + + +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! SUBROUTINE SI_DENS (density,w) +! +! This subroutine calculates the (macroskopic) fluid-density in +! units [kg/m3] from the dimensionless density (eta=zeta3). +! Further, mass fractions are calculated from mole fractions. +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! + SUBROUTINE SI_DENS (density,w) +! + USE PARAMETERS, ONLY: pi, nav, tau + USE BASIC_VARIABLES + IMPLICIT NONE +! +! ---------------------------------------------------------------------- + REAL, INTENT(OUT) :: density(np) + REAL, INTENT(OUT) :: w(np,nc) +! +! ---------------------------------------------------------------------- + INTEGER :: i, ph + REAL :: mm_mean, rho, z3t + REAL :: dhs(nc), d00(nc), t_p, pcon, l_st +! ---------------------------------------------------------------------- + + +DO i = 1,ncomp + IF (eos == 1) THEN + dhs(i) = parame(i,2) * ( 1.0 - 0.12 *EXP( -3.0*parame(i,3)/t ) ) + ELSE IF (eos == 0) THEN + d00(i) = ( 1.E30/1.E6*tau*parame(i,2)*6.0/pi/nav )**(1.0/3.0) + dhs(i) = d00(i) * ( 1.0 - 0.12 *EXP( -3.0*parame(i,3)/t ) ) + ELSE IF (eos == 4) THEN + dhs(i) = ( 0.1617/0.3107 / ( 0.689+0.311*(t/parame(i,3)/1.328)**0.3674 ) & + / ( pi/6.0 ) )**(1.0/3.0) * parame(i,2) + ELSE IF (eos == 5.OR.eos == 6) THEN + l_st = parame(1,25) + IF (ncomp /= 1) write (*,*) ' ERROR for EOS = 5' + t_p =((34.037352+17.733741*l_st) /(1.0+0.53237307*l_st+12.860239*l_st**2 ))**0.5 + IF (l_st == 0.0) t_p = t_p/4.0 + IF (eos == 5 .AND. l_st /= 0.0) t_p = t_p/4.0*parame(1,1)**2 + t_p = t/parame(i,3)/t_p + pcon =0.5256+3.2088804*l_st**2 -3.1499114*l_st**2.5 +0.43049357*l_st**4 + dhs(i) = ( pcon/(0.67793+0.32207*(t_p)**0.3674) /(pi/6.0) )**(1.0/3.0) *parame(i,2) + ELSE IF (eos == 8) THEN + dhs(i) = parame(i,2)*(1.0+0.2977*t/parame(i,3)) & + /(1.0+0.33163*t/parame(i,3) +1.0477E-3*(t/parame(i,3))**2 ) + ELSE + write (*,*) 'define EOS in subroutine: SI_DENS' + stop + END IF +END DO + +DO ph = 1,nphas + mm_mean = 0.0 + z3t = 0.0 + DO i = 1, ncomp + mm_mean = mm_mean + xi(ph,i)*mm(i) + z3t = z3t + xi(ph,i) * parame(i,1) * dhs(i)**3 + END DO + z3t = pi/6.0 * z3t + rho = dense(ph)/z3t + density(ph) = rho * mm_mean * 1.E27 /nav + DO i = 1, ncomp + w(ph,i) = xi(ph,i) * mm(i)/mm_mean + END DO +! write (*,*) density(ph),rho,mm_mean,1.d27 /NAV +END DO + +END SUBROUTINE SI_DENS + + + +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! + REAL FUNCTION F_STABILITY ( optpara, n ) +! + USE BASIC_VARIABLES + USE STARTING_VALUES + USE EOS_VARIABLES, ONLY: dhs, PI + IMPLICIT NONE +! +! ---------------------------------------------------------------------- + INTEGER, INTENT(IN) :: n + REAL, INTENT(IN OUT) :: optpara(n) +! +! ---------------------------------------------------------------------- + INTEGER :: i, stabil + REAL :: rhoi(nc),gradterm + REAL :: fden,punish + REAL :: dens +! ---------------------------------------------------------------------- + +COMMON /stabil / stabil + +punish = 0.0 +stabil = 1 + +DO i = 1, n + IF ( optpara(i) < 0.5 ) rhoi(i) = EXP(optpara(i) ) + IF ( optpara(i) >= 0.5) rhoi(i) = EXP(0.5) +END DO + +dens = PI/6.0 * SUM( rhoi(1:ncomp) * parame(1:ncomp,1) * dhs(1:ncomp)**3 ) + +IF (dens > 0.65) THEN + punish = punish + (dens-0.65)*10000.0 + rhoi(1:n) = rhoi(1:n)*0.65/dens +END IF + +CALL fden_calc (fden, rhoi) + +gradterm = sum( grad_fd(1:n) * ( rhoi(1:n) - rhoif(1:n) ) ) + +f_stability = fden - fdenf - gradterm + punish + +! write (*,'(5G16.8)') F_STABILITY,(rhoi(i),i=1,n) +! pause + +stabil = 0 + +END FUNCTION F_STABILITY + + + + +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! SUBROUTINE p_calc (pges_transfer, zges) +! +! This subroutine serves as an iterface to the EOS-routines. The +! system pressure corresponding to given (desity,T,xi) is calculated. +! (Note: the more common interface is SUBROUTINE FUGACITY. This +! routine is only used for one-phase systems, e.g. calculation of +! virial coefficients) +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! + SUBROUTINE p_calc (pges_transfer, zges) +! + USE BASIC_VARIABLES + USE EOS_VARIABLES + IMPLICIT NONE +! +! ---------------------------------------------------------------------- + REAL, INTENT(IN OUT) :: pges_transfer + REAL, INTENT(OUT) :: zges +! ---------------------------------------------------------------------- + +IF (nphas /= 1 ) THEN + write (*,*) 'P_CALC: can only be called for single phases' + stop +ENDIF + +IF (eos < 2) THEN + + phas = 1 + eta = dense(1) + x(1:ncomp) = xi(1,1:ncomp) + + CALL PERTURBATION_PARAMETER + IF (num == 0) CALL P_EOS + IF(num == 1) CALL P_NUMERICAL + !! IF(num == 2) CALL F_EOS_RN + + pges_transfer = pges + rho = eta/z3t + zges = (pges * 1.E-30) / (kbol*t*rho) + +ELSE + write (*,*) ' SUBROUTINE P_CALC not available for cubic EOS' + stop +END IF + +END SUBROUTINE p_calc + + + +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! +SUBROUTINE ONLY_ONE_TERM_EOS_NUMERICAL ( only_term, type_of_term ) +! + USE EOS_NUMERICAL_DERIVATIVES + IMPLICIT NONE +! + character (LEN=9) :: only_term, type_of_term +! ---------------------------------------------------------------------- + + save_eos_terms(1) = ideal_gas + save_eos_terms(2) = hard_sphere + save_eos_terms(3) = chain_term + save_eos_terms(4) = disp_term + save_eos_terms(5) = hb_term + save_eos_terms(6) = LC_term + save_eos_terms(7) = branch_term + save_eos_terms(8) = II_term + save_eos_terms(9) = ID_term + + ideal_gas = 'no' + hard_sphere = 'no' + chain_term = 'no' + disp_term = 'no' + hb_term = 'no' + LC_term = 'no' + branch_term = 'no' + II_term = 'no' + ID_term = 'no' + + IF ( only_term == 'ideal_gas' ) ideal_gas = trim( adjustl( type_of_term ) ) + IF ( only_term == 'hard_sphere' ) hard_sphere = trim( adjustl( type_of_term ) ) + IF ( only_term == 'chain_term' ) chain_term = trim( adjustl( type_of_term ) ) + IF ( only_term == 'disp_term' ) disp_term = trim( adjustl( type_of_term ) ) + IF ( only_term == 'hb_term' ) hb_term = trim( adjustl( type_of_term ) ) + IF ( only_term == 'LC_term' ) LC_term = trim( adjustl( type_of_term ) ) + IF ( only_term == 'branch_term' ) branch_term = trim( adjustl( type_of_term ) ) + IF ( only_term == 'II_term' ) II_term = trim( adjustl( type_of_term ) ) + IF ( only_term == 'ID_term' ) ID_term = trim( adjustl( type_of_term ) ) + +END SUBROUTINE ONLY_ONE_TERM_EOS_NUMERICAL + + +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! +SUBROUTINE RESTORE_PREVIOUS_EOS_NUMERICAL +! + USE EOS_NUMERICAL_DERIVATIVES + IMPLICIT NONE +! +! ---------------------------------------------------------------------- + ideal_gas = trim( adjustl( save_eos_terms(1) ) ) + hard_sphere = trim( adjustl( save_eos_terms(2) ) ) + chain_term = trim( adjustl( save_eos_terms(3) ) ) + disp_term = trim( adjustl( save_eos_terms(4) ) ) + hb_term = trim( adjustl( save_eos_terms(5) ) ) + LC_term = trim( adjustl( save_eos_terms(6) ) ) + branch_term = trim( adjustl( save_eos_terms(7) ) ) + II_term = trim( adjustl( save_eos_terms(8) ) ) + ID_term = trim( adjustl( save_eos_terms(9) ) ) + +END SUBROUTINE RESTORE_PREVIOUS_EOS_NUMERICAL + + + + diff --git a/applications/PUfoam/MoDeNaModels/Solubility/ExampleOfUsage/src/srcDetailedCode/in.txt b/applications/PUfoam/MoDeNaModels/Solubility/ExampleOfUsage/src/srcDetailedCode/in.txt new file mode 100644 index 000000000..c6f3172fc --- /dev/null +++ b/applications/PUfoam/MoDeNaModels/Solubility/ExampleOfUsage/src/srcDetailedCode/in.txt @@ -0,0 +1,8 @@ +380.0 +3 +co2 +mdi +po +0.1 +0.5 +0.4 \ No newline at end of file diff --git a/applications/PUfoam/MoDeNaModels/Solubility/ExampleOfUsage/src/srcDetailedCode/main.f90 b/applications/PUfoam/MoDeNaModels/Solubility/ExampleOfUsage/src/srcDetailedCode/main.f90 new file mode 100644 index 000000000..4c7ff58c8 --- /dev/null +++ b/applications/PUfoam/MoDeNaModels/Solubility/ExampleOfUsage/src/srcDetailedCode/main.f90 @@ -0,0 +1,129 @@ + + +! +!THIS CODE WAS WRITTEN AT +!UNIVERSITY OF STUTTGART, +!INSTITUTE OF TECHNICAL THERMODYNAMICS AND THERMAL PROCESS ENGINEERING +!BY +!JOACHIM GROSS +! +! +! +! + + + + + +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! This program calculates solubilities (Henry coefficients) using the +! PC-SAFT equation of state. +! The input parameters are read from the file "in.txt" which has to +! be in the same directory as the executable. +! +! The input file must have the following format: +! Line1: Value of temperature in Kelvin +! Line2: Number of components present in the system (ncomp) +! Line3 Name of component 1 +! ... +! Line3+ncomp Name of component ncomp +! Line3+ncomp+1 Molar (overall) concentration of component 1 +! ... +! Line3+2ncomp Molar (overall) concentration of component ncomp +! +! For a binary system, these molar concentrations are only treated as an initial guess and may be set to e.g. 0.5 +! +! +! So far, pressure is set to 1bar in all calculaions +! +! +!If you would like to use this code in your work, please cite the +!following publications: +! +!Gross, Joachim, and Gabriele Sadowski. "Perturbed-chain SAFT: An equation of state based on a perturbation theory for chain molecules." Industrial & engineering chemistry research 40.4 (2001): 1244-1260. +!Gross, Joachim, and Gabriele Sadowski. "Application of the perturbed-chain SAFT equation of state to associating systems." Industrial & engineering chemistry research 41.22 (2002): 5510-5515. +!Gross, Joachim, and Jadran Vrabec. "An equation‐of‐state contribution for polar components: Dipolar molecules." AIChE journal 52.3 (2006): 1194-1204. + +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! + + +PROGRAM PC_SAFT +! +! ---------------------------------------------------------------------- + USE BASIC_VARIABLES + USE EOS_CONSTANTS + USE DFT_MODULE + USE EOS_VARIABLES + IMPLICIT NONE + + +! ---------------------------------------------------------------------- +!Variables +! ---------------------------------------------------------------------- + + REAL :: tc,pc,chemPot_total(nc) + REAL :: rhob(2,0:nc),density(np) + CHARACTER (LEN=50) :: filename + INTEGER :: compID,i + + +! ---------------------------------------------------------------------- +!Read information from inputfile "in.txt" +! ---------------------------------------------------------------------- + + filename='./in.txt' + CALL file_open(filename,77) ! open input file + READ (77,*) t ! read temperature + READ (77,*) ncomp ! read number of components in the system + Do i = 1,ncomp ! read component names + READ (77,*) compna(i) + End Do + Do i = 1,ncomp ! read component overall molar concentrations + READ (77,*) cif(i) + End Do + + + !calculate molar fractions from molar concentrations + xif(1:ncomp) = cif(1:ncomp) / sum(cif(1:ncomp)) + + + +! ---------------------------------------------------------------------- +!General simulation set up +! ---------------------------------------------------------------------- + + num = 1 ! (num=0: using analytical derivatives of EOS) + ! (num=1: using numerical derivatives of EOS) + ! (num=2: White's renormalization group theory) + IF ( num /= 0 ) CALL SET_DEFAULT_EOS_NUMERICAL + + eos = 1 ! eos=1: use PC-SAFT equation of state + pol = 1 ! pol=1: include polar interactions (use PCP-SAFT parameters) + + p = 1.000e05 ! pressure is fixed to 1bar in all simulations + + CALL para_input ! retriev pure comp. parameters + + ensemble_flag = 'tp' ! this specifies, whether the eos-subroutines + ! are executed for constant 'tp' or for constant 'tv' + +! ---------------------------------------------------------------------- +!Start phase equilibrium calculation +! ---------------------------------------------------------------------- + + CALL EOS_CONST (ap, bp, dnm) ! read EOS constants + + dd_term = 'GV' ! dipole-dipole term of Gross & Vrabec (2006) + qq_term = 'JG' ! quadrupole-quadrupole term of Gross (2005) + dq_term = 'VG' ! dipole-quadrupole term of Vrabec & Gross (2008) + + CALL VLE_MIX(rhob,density,chemPot_total,compID) ! call routine that calculates phase equilibria + + + + + +END PROGRAM PC_SAFT + + diff --git a/applications/PUfoam/MoDeNaModels/Solubility/ExampleOfUsage/src/srcDetailedCode/makefile b/applications/PUfoam/MoDeNaModels/Solubility/ExampleOfUsage/src/srcDetailedCode/makefile new file mode 100644 index 000000000..8926c29b5 --- /dev/null +++ b/applications/PUfoam/MoDeNaModels/Solubility/ExampleOfUsage/src/srcDetailedCode/makefile @@ -0,0 +1,31 @@ + + +#Source files +SOURCE = modules.f90 \ + module_solve_nonlinear.f90 \ + getting_started_subroutines.f90 \ + Numeric_subroutines.f90 \ + VLE_subroutines.f90 \ + VLE_main.f90\ + main.f90 \ + + + + +#Object files +OBJECT = $(SOURCE:%.f90=%.o) + + + +#define target for non-PETSc files +%.o: %.f90 + gfortran -c -fdefault-real-8 $< -o $@ + +EOS: $(OBJECT) + gfortran -o PCSAFT_Henry $(OBJECT) + +clean: + rm *.o *.mod + + + diff --git a/applications/PUfoam/MoDeNaModels/Solubility/ExampleOfUsage/src/srcDetailedCode/module_solve_nonlinear.f90 b/applications/PUfoam/MoDeNaModels/Solubility/ExampleOfUsage/src/srcDetailedCode/module_solve_nonlinear.f90 new file mode 100644 index 000000000..595a8ba80 --- /dev/null +++ b/applications/PUfoam/MoDeNaModels/Solubility/ExampleOfUsage/src/srcDetailedCode/module_solve_nonlinear.f90 @@ -0,0 +1,1645 @@ + +MODULE Solve_NonLin + +! Corrections to FUNCTION Enorm - 28 November 2003 + +IMPLICIT NONE +INTEGER, PARAMETER :: dp = SELECTED_REAL_KIND(14, 60) +PRIVATE +PUBLIC :: hbrd, hybrd + + +CONTAINS + + +SUBROUTINE hbrd(fcn, n, x, fvec, epsfcn, tol, info, diag) + +! Code converted using TO_F90 by Alan Miller +! Date: 2003-07-15 Time: 13:27:42 + +INTEGER, INTENT(IN) :: n +REAL (dp), INTENT(IN OUT) :: x(n) +REAL (dp), INTENT(IN OUT) :: fvec(n) +REAL (dp), INTENT(IN) :: epsfcn +REAL (dp), INTENT(IN) :: tol +INTEGER, INTENT(OUT) :: info +REAL (dp), INTENT(OUT) :: diag(n) + +! EXTERNAL fcn +INTERFACE + SUBROUTINE FCN(N, X, FVEC, IFLAG) + IMPLICIT NONE + INTEGER, PARAMETER :: dp = SELECTED_REAL_KIND(14, 60) + INTEGER, INTENT(IN) :: n + REAL (dp), INTENT(IN) :: x(n) + REAL (dp), INTENT(OUT) :: fvec(n) + INTEGER, INTENT(IN OUT) :: iflag + END SUBROUTINE FCN +END INTERFACE + +! ********** + +! SUBROUTINE HBRD + +! THE PURPOSE OF HBRD IS TO FIND A ZERO OF A SYSTEM OF N NONLINEAR +! FUNCTIONS IN N VARIABLES BY A MODIFICATION OF THE POWELL HYBRID METHOD. +! THIS IS DONE BY USING THE MORE GENERAL NONLINEAR EQUATION SOLVER HYBRD. +! THE USER MUST PROVIDE A SUBROUTINE WHICH CALCULATES THE FUNCTIONS. +! THE JACOBIAN IS THEN CALCULATED BY A FORWARD-DIFFERENCE APPROXIMATION. + +! THE SUBROUTINE STATEMENT IS + +! SUBROUTINE HBRD(N, X, FVEC, EPSFCN, TOL, INFO, WA, LWA) + +! WHERE + +! FCN IS THE NAME OF THE USER-SUPPLIED SUBROUTINE WHICH CALCULATES +! THE FUNCTIONS. FCN MUST BE DECLARED IN AN EXTERNAL STATEMENT +! IN THE USER CALLING PROGRAM, AND SHOULD BE WRITTEN AS FOLLOWS. + +! SUBROUTINE FCN(N, X, FVEC, IFLAG) +! INTEGER N,IFLAG +! REAL X(N),FVEC(N) +! ---------- +! CALCULATE THE FUNCTIONS AT X AND RETURN THIS VECTOR IN FVEC. +! --------- +! RETURN +! END + +! THE VALUE OF IFLAG NOT BE CHANGED BY FCN UNLESS +! THE USER WANTS TO TERMINATE THE EXECUTION OF HBRD. +! IN THIS CASE SET IFLAG TO A NEGATIVE INTEGER. + +! N IS A POSITIVE INTEGER INPUT VARIABLE SET TO THE NUMBER +! OF FUNCTIONS AND VARIABLES. + +! X IS AN ARRAY OF LENGTH N. ON INPUT X MUST CONTAIN AN INITIAL +! ESTIMATE OF THE SOLUTION VECTOR. ON OUTPUT X CONTAINS THE +! FINAL ESTIMATE OF THE SOLUTION VECTOR. + +! FVEC IS AN OUTPUT ARRAY OF LENGTH N WHICH CONTAINS +! THE FUNCTIONS EVALUATED AT THE OUTPUT X. + +! EPSFCN IS AN INPUT VARIABLE USED IN DETERMINING A SUITABLE STEP LENGTH +! FOR THE FORWARD-DIFFERENCE APPROXIMATION. THIS APPROXIMATION ASSUMES +! THAT THE RELATIVE ERRORS IN THE FUNCTIONS ARE OF THE ORDER OF EPSFCN. +! IF EPSFCN IS LESS THAN THE MACHINE PRECISION, IT IS ASSUMED THAT THE +! RELATIVE ERRORS IN THE FUNCTIONS ARE OF THE ORDER OF THE MACHINE +! PRECISION. + +! TOL IS A NONNEGATIVE INPUT VARIABLE. TERMINATION OCCURS WHEN THE +! ALGORITHM ESTIMATES THAT THE RELATIVE ERROR BETWEEN X AND THE SOLUTION +! IS AT MOST TOL. + +! INFO IS AN INTEGER OUTPUT VARIABLE. IF THE USER HAS TERMINATED +! EXECUTION, INFO IS SET TO THE (NEGATIVE) VALUE OF IFLAG. +! SEE DESCRIPTION OF FCN. OTHERWISE, INFO IS SET AS FOLLOWS. + +! INFO = 0 IMPROPER INPUT PARAMETERS. + +! INFO = 1 ALGORITHM ESTIMATES THAT THE RELATIVE ERROR +! BETWEEN X AND THE SOLUTION IS AT MOST TOL. + +! INFO = 2 NUMBER OF CALLS TO FCN HAS REACHED OR EXCEEDED 200*(N+1). + +! INFO = 3 TOL IS TOO SMALL. NO FURTHER IMPROVEMENT IN +! THE APPROXIMATE SOLUTION X IS POSSIBLE. + +! INFO = 4 ITERATION IS NOT MAKING GOOD PROGRESS. + +! SUBPROGRAMS CALLED + +! USER-SUPPLIED ...... FCN + +! MINPACK-SUPPLIED ... HYBRD + +! ARGONNE NATIONAL LABORATORY. MINPACK PROJECT. MARCH 1980. +! BURTON S. GARBOW, KENNETH E. HILLSTROM, JORGE J. MORE + +! Reference: +! Powell, M.J.D. 'A hybrid method for nonlinear equations' in Numerical Methods +! for Nonlinear Algebraic Equations', P.Rabinowitz (editor), Gordon and +! Breach, London 1970. +! ********** +INTEGER :: maxfev, ml, mode, mu, nfev, nprint +REAL (dp) :: xtol +REAL (dp), PARAMETER :: factor = 1.0_dp, zero = 0.0_dp + +info = 0 + +! CHECK THE INPUT PARAMETERS FOR ERRORS. + + +IF (n <= 0 .OR. epsfcn < zero .OR. tol < zero) GO TO 20 + +! CALL HYBRD. + +maxfev = 200*(n + 1) +xtol = tol +ml = n - 1 +mu = n - 1 +mode = 2 +nprint = 0 +CALL hybrd(fcn, n, x, fvec, xtol, maxfev, ml, mu, epsfcn, diag, mode, & + factor, nprint, info, nfev) +IF (info == 5) info = 4 +20 RETURN + +! LAST CARD OF SUBROUTINE HBRD. + +END SUBROUTINE hbrd + + + +SUBROUTINE hybrd(fcn, n, x, fvec, xtol, maxfev, ml, mu, epsfcn, diag, mode, & + factor, nprint, info, nfev) + +INTEGER, INTENT(IN) :: n +REAL (dp), INTENT(IN OUT) :: x(n) +REAL (dp), INTENT(IN OUT) :: fvec(n) +REAL (dp), INTENT(IN) :: xtol +INTEGER, INTENT(IN OUT) :: maxfev +INTEGER, INTENT(IN OUT) :: ml +INTEGER, INTENT(IN) :: mu +REAL (dp), INTENT(IN) :: epsfcn +REAL (dp), INTENT(OUT) :: diag(n) +INTEGER, INTENT(IN) :: mode +REAL (dp), INTENT(IN) :: factor +INTEGER, INTENT(IN OUT) :: nprint +INTEGER, INTENT(OUT) :: info +INTEGER, INTENT(OUT) :: nfev + +! EXTERNAL fcn +INTERFACE + SUBROUTINE FCN(N, X, FVEC, IFLAG) + IMPLICIT NONE + INTEGER, PARAMETER :: dp = SELECTED_REAL_KIND(14, 60) + INTEGER, INTENT(IN) :: n + REAL (dp), INTENT(IN) :: x(n) + REAL (dp), INTENT(OUT) :: fvec(n) + INTEGER, INTENT(IN OUT) :: iflag + END SUBROUTINE FCN +END INTERFACE + +! ********** + +! SUBROUTINE HYBRD + +! THE PURPOSE OF HYBRD IS TO FIND A ZERO OF A SYSTEM OF N NONLINEAR +! FUNCTIONS IN N VARIABLES BY A MODIFICATION OF THE POWELL HYBRID METHOD. +! THE USER MUST PROVIDE A SUBROUTINE WHICH CALCULATES THE FUNCTIONS. +! THE JACOBIAN IS THEN CALCULATED BY A FORWARD-DIFFERENCE APPROXIMATION. + +! THE SUBROUTINE STATEMENT IS + +! SUBROUTINE HYBRD(FCN, N, X, FVEC, XTOL, MAXFEV, ML, MU, EPSFCN, +! DIAG, MODE, FACTOR, NPRINT, INFO, NFEV, FJAC, +! LDFJAC, R, LR, QTF, WA1, WA2, WA3, WA4) + +! WHERE + +! FCN IS THE NAME OF THE USER-SUPPLIED SUBROUTINE WHICH CALCULATES +! THE FUNCTIONS. FCN MUST BE DECLARED IN AN EXTERNAL STATEMENT IN +! THE USER CALLING PROGRAM, AND SHOULD BE WRITTEN AS FOLLOWS. + +! SUBROUTINE FCN(N, X, FVEC, IFLAG) +! INTEGER N, IFLAG +! REAL X(N), FVEC(N) +! ---------- +! CALCULATE THE FUNCTIONS AT X AND +! RETURN THIS VECTOR IN FVEC. +! --------- +! RETURN +! END + +! THE VALUE OF IFLAG SHOULD NOT BE CHANGED BY FCN UNLESS +! THE USER WANTS TO TERMINATE EXECUTION OF HYBRD. +! IN THIS CASE SET IFLAG TO A NEGATIVE INTEGER. + +! N IS A POSITIVE INTEGER INPUT VARIABLE SET TO THE NUMBER +! OF FUNCTIONS AND VARIABLES. + +! X IS AN ARRAY OF LENGTH N. ON INPUT X MUST CONTAIN AN INITIAL +! ESTIMATE OF THE SOLUTION VECTOR. ON OUTPUT X CONTAINS THE FINAL +! ESTIMATE OF THE SOLUTION VECTOR. + +! FVEC IS AN OUTPUT ARRAY OF LENGTH N WHICH CONTAINS +! THE FUNCTIONS EVALUATED AT THE OUTPUT X. + +! XTOL IS A NONNEGATIVE INPUT VARIABLE. TERMINATION OCCURS WHEN THE +! RELATIVE ERROR BETWEEN TWO CONSECUTIVE ITERATES IS AT MOST XTOL. + +! MAXFEV IS A POSITIVE INTEGER INPUT VARIABLE. TERMINATION OCCURS WHEN +! THE NUMBER OF CALLS TO FCN IS AT LEAST MAXFEV BY THE END OF AN +! ITERATION. + +! ML IS A NONNEGATIVE INTEGER INPUT VARIABLE WHICH SPECIFIES THE +! NUMBER OF SUBDIAGONALS WITHIN THE BAND OF THE JACOBIAN MATRIX. +! IF THE JACOBIAN IS NOT BANDED, SET ML TO AT LEAST N - 1. + +! MU IS A NONNEGATIVE INTEGER INPUT VARIABLE WHICH SPECIFIES THE NUMBER +! OF SUPERDIAGONALS WITHIN THE BAND OF THE JACOBIAN MATRIX. +! IF THE JACOBIAN IS NOT BANDED, SET MU TO AT LEAST N - 1. + +! EPSFCN IS AN INPUT VARIABLE USED IN DETERMINING A SUITABLE STEP LENGTH +! FOR THE FORWARD-DIFFERENCE APPROXIMATION. THIS APPROXIMATION +! ASSUMES THAT THE RELATIVE ERRORS IN THE FUNCTIONS ARE OF THE ORDER +! OF EPSFCN. IF EPSFCN IS LESS THAN THE MACHINE PRECISION, +! IT IS ASSUMED THAT THE RELATIVE ERRORS IN THE FUNCTIONS ARE OF THE +! ORDER OF THE MACHINE PRECISION. + +! DIAG IS AN ARRAY OF LENGTH N. IF MODE = 1 (SEE BELOW), +! DIAG IS INTERNALLY SET. IF MODE = 2, DIAG MUST CONTAIN POSITIVE +! ENTRIES THAT SERVE AS MULTIPLICATIVE SCALE FACTORS FOR THE +! VARIABLES. + +! MODE IS AN INTEGER INPUT VARIABLE. IF MODE = 1, THE VARIABLES WILL BE +! SCALED INTERNALLY. IF MODE = 2, THE SCALING IS SPECIFIED BY THE +! INPUT DIAG. OTHER VALUES OF MODE ARE EQUIVALENT TO MODE = 1. + +! FACTOR IS A POSITIVE INPUT VARIABLE USED IN DETERMINING THE +! INITIAL STEP BOUND. THIS BOUND IS SET TO THE PRODUCT OF +! FACTOR AND THE EUCLIDEAN NORM OF DIAG*X IF NONZERO, OR ELSE +! TO FACTOR ITSELF. IN MOST CASES FACTOR SHOULD LIE IN THE +! INTERVAL (.1,100.). 100. IS A GENERALLY RECOMMENDED VALUE. + +! NPRINT IS AN INTEGER INPUT VARIABLE THAT ENABLES CONTROLLED +! PRINTING OF ITERATES IF IT IS POSITIVE. IN THIS CASE, +! FCN IS CALLED WITH IFLAG = 0 AT THE BEGINNING OF THE FIRST +! ITERATION AND EVERY NPRINT ITERATIONS THEREAFTER AND +! IMMEDIATELY PRIOR TO RETURN, WITH X AND FVEC AVAILABLE +! FOR PRINTING. IF NPRINT IS NOT POSITIVE, NO SPECIAL CALLS +! OF FCN WITH IFLAG = 0 ARE MADE. + +! INFO IS AN INTEGER OUTPUT VARIABLE. IF THE USER HAS +! TERMINATED EXECUTION, INFO IS SET TO THE (NEGATIVE) +! VALUE OF IFLAG. SEE DESCRIPTION OF FCN. OTHERWISE, +! INFO IS SET AS FOLLOWS. + +! INFO = 0 IMPROPER INPUT PARAMETERS. + +! INFO = 1 RELATIVE ERROR BETWEEN TWO CONSECUTIVE ITERATES +! IS AT MOST XTOL. + +! INFO = 2 NUMBER OF CALLS TO FCN HAS REACHED OR EXCEEDED MAXFEV. + +! INFO = 3 XTOL IS TOO SMALL. NO FURTHER IMPROVEMENT IN +! THE APPROXIMATE SOLUTION X IS POSSIBLE. + +! INFO = 4 ITERATION IS NOT MAKING GOOD PROGRESS, AS +! MEASURED BY THE IMPROVEMENT FROM THE LAST +! FIVE JACOBIAN EVALUATIONS. + +! INFO = 5 ITERATION IS NOT MAKING GOOD PROGRESS, AS MEASURED BY +! THE IMPROVEMENT FROM THE LAST TEN ITERATIONS. + +! NFEV IS AN INTEGER OUTPUT VARIABLE SET TO THE NUMBER OF CALLS TO FCN. + +! FJAC IS AN OUTPUT N BY N ARRAY WHICH CONTAINS THE ORTHOGONAL MATRIX Q +! PRODUCED BY THE QR FACTORIZATION OF THE FINAL APPROXIMATE JACOBIAN. + +! LDFJAC IS A POSITIVE INTEGER INPUT VARIABLE NOT LESS THAN N +! WHICH SPECIFIES THE LEADING DIMENSION OF THE ARRAY FJAC. + +! R IS AN OUTPUT ARRAY OF LENGTH LR WHICH CONTAINS THE +! UPPER TRIANGULAR MATRIX PRODUCED BY THE QR FACTORIZATION +! OF THE FINAL APPROXIMATE JACOBIAN, STORED ROWWISE. + +! LR IS A POSITIVE INTEGER INPUT VARIABLE NOT LESS THAN (N*(N+1))/2. + +! QTF IS AN OUTPUT ARRAY OF LENGTH N WHICH CONTAINS +! THE VECTOR (Q TRANSPOSE)*FVEC. + +! WA1, WA2, WA3, AND WA4 ARE WORK ARRAYS OF LENGTH N. + +! SUBPROGRAMS CALLED + +! USER-SUPPLIED ...... FCN + +! MINPACK-SUPPLIED ... DOGLEG,SPMPAR,ENORM,FDJAC1, +! QFORM,QRFAC,R1MPYQ,R1UPDT + +! FORTRAN-SUPPLIED ... ABS,MAX,MIN,MIN,MOD + +! ARGONNE NATIONAL LABORATORY. MINPACK PROJECT. MARCH 1980. +! BURTON S. GARBOW, KENNETH E. HILLSTROM, JORGE J. MORE + +! ********** + +INTEGER :: i, iflag, iter, j, jm1, l, lr, msum, ncfail, ncsuc, nslow1, & + nslow2 +INTEGER :: iwa(1) +LOGICAL :: jeval, sing +REAL (dp) :: actred, delta, epsmch, fnorm, fnorm1, pnorm, prered, & + ratio, sum, temp, xnorm +REAL (dp), PARAMETER :: one = 1.0_dp, p1 = 0.1_dp, p5 = 0.5_dp, & + p001 = 0.001_dp, p0001 = 0.0001_dp, zero = 0.0_dp + +! The following were workspace arguments +REAL (dp) :: fjac(n,n), r(n*(n+1)/2), qtf(n), wa1(n), wa2(n), & + wa3(n), wa4(n) + +! EPSMCH IS THE MACHINE PRECISION. + +epsmch = EPSILON(1.0_dp) + +info = 0 +iflag = 0 +nfev = 0 +lr = n*(n+1)/2 + +! CHECK THE INPUT PARAMETERS FOR ERRORS. + +IF (n > 0 .AND. xtol >= zero .AND. maxfev > 0 .AND. ml >= 0 .AND. mu >= & + 0 .AND. factor > zero ) THEN +IF (mode == 2) THEN + diag(1:n) = one +END IF + +! EVALUATE THE FUNCTION AT THE STARTING POINT AND CALCULATE ITS NORM. + +iflag = 1 +CALL fcn(n, x, fvec, iflag) +nfev = 1 +IF (iflag >= 0) THEN + fnorm = enorm(n, fvec) + +! DETERMINE THE NUMBER OF CALLS TO FCN NEEDED TO COMPUTE THE JACOBIAN MATRIX. + + msum = MIN(ml+mu+1,n) + +! INITIALIZE ITERATION COUNTER AND MONITORS. + + iter = 1 + ncsuc = 0 + ncfail = 0 + nslow1 = 0 + nslow2 = 0 + +! BEGINNING OF THE OUTER LOOP. + + 20 jeval = .true. + +! CALCULATE THE JACOBIAN MATRIX. + + iflag = 2 + CALL fdjac1(fcn, n, x, fvec, fjac, n, iflag, ml, mu, epsfcn, wa1, wa2) + nfev = nfev + msum + IF (iflag >= 0) THEN + +! COMPUTE THE QR FACTORIZATION OF THE JACOBIAN. + + CALL qrfac(n, n, fjac, n, .false., iwa, 1, wa1, wa2, wa3) + +! ON THE FIRST ITERATION AND IF MODE IS 1, SCALE ACCORDING +! TO THE NORMS OF THE COLUMNS OF THE INITIAL JACOBIAN. + + IF (iter == 1) THEN + IF (mode /= 2) THEN + DO j = 1, n + diag(j) = wa2(j) + IF (wa2(j) == zero) diag(j) = one + END DO + END IF + +! ON THE FIRST ITERATION, CALCULATE THE NORM OF THE SCALED X +! AND INITIALIZE THE STEP BOUND DELTA. + + wa3(1:n) = diag(1:n) * x(1:n) + xnorm = enorm(n, wa3) + delta = factor * xnorm + IF (delta == zero) delta = factor + END IF + +! FORM (Q TRANSPOSE)*FVEC AND STORE IN QTF. + + qtf(1:n) = fvec(1:n) + DO j = 1, n + IF (fjac(j,j) /= zero) THEN + sum = zero + DO i = j, n + sum = sum + fjac(i,j) * qtf(i) + END DO + temp = -sum / fjac(j,j) + DO i = j, n + qtf(i) = qtf(i) + fjac(i,j) * temp + END DO + END IF + END DO + +! COPY THE TRIANGULAR FACTOR OF THE QR FACTORIZATION INTO R. + + sing = .false. + DO j = 1, n + l = j + jm1 = j - 1 + IF (jm1 >= 1) THEN + DO i = 1, jm1 + r(l) = fjac(i,j) + l = l + n - i + END DO + END IF + r(l) = wa1(j) + IF (wa1(j) == zero) sing = .true. + END DO + +! ACCUMULATE THE ORTHOGONAL FACTOR IN FJAC. + + CALL qform(n, n, fjac, n, wa1) + +! RESCALE IF NECESSARY. + + IF (mode /= 2) THEN + DO j = 1, n + diag(j) = MAX(diag(j), wa2(j)) + END DO + END IF + +! BEGINNING OF THE INNER LOOP. + +! IF REQUESTED, CALL FCN TO ENABLE PRINTING OF ITERATES. + + 120 IF (nprint > 0) THEN + iflag = 0 + IF (MOD(iter-1, nprint) == 0) CALL fcn(n, x, fvec, iflag) + IF (iflag < 0) GO TO 190 + END IF + +! DETERMINE THE DIRECTION P. + + CALL dogleg(n, r, lr, diag, qtf, delta, wa1, wa2, wa3) + +! STORE THE DIRECTION P AND X + P. CALCULATE THE NORM OF P. + + DO j = 1, n + wa1(j) = -wa1(j) + wa2(j) = x(j) + wa1(j) + wa3(j) = diag(j) * wa1(j) + END DO + pnorm = enorm(n, wa3) + +! ON THE FIRST ITERATION, ADJUST THE INITIAL STEP BOUND. + + IF (iter == 1) delta = MIN(delta, pnorm) + +! EVALUATE THE FUNCTION AT X + P AND CALCULATE ITS NORM. + + iflag = 1 + CALL fcn(n, wa2, wa4, iflag) + nfev = nfev + 1 + IF (iflag >= 0) THEN + fnorm1 = enorm(n, wa4) + +! COMPUTE THE SCALED ACTUAL REDUCTION. + + actred = -one + IF (fnorm1 < fnorm) actred = one - (fnorm1/fnorm) ** 2 + +! COMPUTE THE SCALED PREDICTED REDUCTION. + + l = 1 + DO i = 1, n + sum = zero + DO j = i, n + sum = sum + r(l) * wa1(j) + l = l + 1 + END DO + wa3(i) = qtf(i) + sum + END DO + temp = enorm(n, wa3) + prered = zero + IF (temp < fnorm) prered = one - (temp/fnorm) ** 2 + +! COMPUTE THE RATIO OF THE ACTUAL TO THE PREDICTED REDUCTION. + + ratio = zero + IF (prered > zero) ratio = actred / prered + +! UPDATE THE STEP BOUND. + + IF (ratio < p1) THEN + ncsuc = 0 + ncfail = ncfail + 1 + delta = p5 * delta + ELSE + ncfail = 0 + ncsuc = ncsuc + 1 + IF (ratio >= p5 .OR. ncsuc > 1) delta = MAX(delta,pnorm/p5) + IF (ABS(ratio-one) <= p1) delta = pnorm / p5 + END IF + +! TEST FOR SUCCESSFUL ITERATION. + + IF (ratio >= p0001) THEN + +! SUCCESSFUL ITERATION. UPDATE X, FVEC, AND THEIR NORMS. + + DO j = 1, n + x(j) = wa2(j) + wa2(j) = diag(j) * x(j) + fvec(j) = wa4(j) + END DO + xnorm = enorm(n, wa2) + fnorm = fnorm1 + iter = iter + 1 + END IF + +! DETERMINE THE PROGRESS OF THE ITERATION. + + nslow1 = nslow1 + 1 + IF (actred >= p001) nslow1 = 0 + IF (jeval) nslow2 = nslow2 + 1 + IF (actred >= p1) nslow2 = 0 + +! TEST FOR CONVERGENCE. + + IF (delta <= xtol*xnorm .OR. fnorm == zero) info = 1 + IF (info == 0) THEN + +! TESTS FOR TERMINATION AND STRINGENT TOLERANCES. + + IF (nfev >= maxfev) info = 2 + IF (p1*MAX(p1*delta, pnorm) <= epsmch*xnorm) info = 3 + IF (nslow2 == 5) info = 4 + IF (nslow1 == 10) info = 5 + IF (info == 0) THEN + +! CRITERION FOR RECALCULATING JACOBIAN APPROXIMATION +! BY FORWARD DIFFERENCES. + + IF (ncfail /= 2) THEN + +! CALCULATE THE RANK ONE MODIFICATION TO THE JACOBIAN +! AND UPDATE QTF IF NECESSARY. + + DO j = 1, n + sum = zero + DO i = 1, n + sum = sum + fjac(i,j) * wa4(i) + END DO + wa2(j) = (sum-wa3(j)) / pnorm + wa1(j) = diag(j) * ((diag(j)*wa1(j))/pnorm) + IF (ratio >= p0001) qtf(j) = sum + END DO + +! COMPUTE THE QR FACTORIZATION OF THE UPDATED JACOBIAN. + + CALL r1updt(n, n, r, lr, wa1, wa2, wa3, sing) + CALL r1mpyq(n, n, fjac, n, wa2, wa3) + CALL r1mpyq(1, n, qtf, 1, wa2, wa3) + +! END OF THE INNER LOOP. + + jeval = .false. + GO TO 120 + END IF + +! END OF THE OUTER LOOP. + + GO TO 20 + END IF + END IF + END IF + END IF +END IF +END IF + +! TERMINATION, EITHER NORMAL OR USER IMPOSED. + +190 IF (iflag < 0) info = iflag +iflag = 0 +IF (nprint > 0) CALL fcn(n, x, fvec, iflag) +RETURN + +! LAST CARD OF SUBROUTINE HYBRD. + +END SUBROUTINE hybrd + + + +SUBROUTINE dogleg(n, r, lr, diag, qtb, delta, x, wa1, wa2) + +INTEGER, INTENT(IN) :: n +INTEGER, INTENT(IN) :: lr +REAL (dp), INTENT(IN) :: r(lr) +REAL (dp), INTENT(IN) :: diag(n) +REAL (dp), INTENT(IN) :: qtb(n) +REAL (dp), INTENT(IN) :: delta +REAL (dp), INTENT(IN OUT) :: x(n) +REAL (dp), INTENT(OUT) :: wa1(n) +REAL (dp), INTENT(OUT) :: wa2(n) + + +! ********** + +! SUBROUTINE DOGLEG + +! GIVEN AN M BY N MATRIX A, AN N BY N NONSINGULAR DIAGONAL +! MATRIX D, AN M-VECTOR B, AND A POSITIVE NUMBER DELTA, THE +! PROBLEM IS TO DETERMINE THE CONVEX COMBINATION X OF THE +! GAUSS-NEWTON AND SCALED GRADIENT DIRECTIONS THAT MINIMIZES +! (A*X - B) IN THE LEAST SQUARES SENSE, SUBJECT TO THE +! RESTRICTION THAT THE EUCLIDEAN NORM OF D*X BE AT MOST DELTA. + +! THIS SUBROUTINE COMPLETES THE SOLUTION OF THE PROBLEM +! IF IT IS PROVIDED WITH THE NECESSARY INFORMATION FROM THE +! QR FACTORIZATION OF A. THAT IS, IF A = Q*R, WHERE Q HAS +! ORTHOGONAL COLUMNS AND R IS AN UPPER TRIANGULAR MATRIX, +! THEN DOGLEG EXPECTS THE FULL UPPER TRIANGLE OF R AND +! THE FIRST N COMPONENTS OF (Q TRANSPOSE)*B. + +! THE SUBROUTINE STATEMENT IS + +! SUBROUTINE DOGLEG(N,R,LR,DIAG,QTB,DELTA,X,WA1,WA2) + +! WHERE + +! N IS A POSITIVE INTEGER INPUT VARIABLE SET TO THE ORDER OF R. + +! R IS AN INPUT ARRAY OF LENGTH LR WHICH MUST CONTAIN THE UPPER +! TRIANGULAR MATRIX R STORED BY ROWS. + +! LR IS A POSITIVE INTEGER INPUT VARIABLE NOT LESS THAN +! (N*(N+1))/2. + +! DIAG IS AN INPUT ARRAY OF LENGTH N WHICH MUST CONTAIN THE +! DIAGONAL ELEMENTS OF THE MATRIX D. + +! QTB IS AN INPUT ARRAY OF LENGTH N WHICH MUST CONTAIN THE FIRST +! N ELEMENTS OF THE VECTOR (Q TRANSPOSE)*B. + +! DELTA IS A POSITIVE INPUT VARIABLE WHICH SPECIFIES AN UPPER +! BOUND ON THE EUCLIDEAN NORM OF D*X. + +! X IS AN OUTPUT ARRAY OF LENGTH N WHICH CONTAINS THE DESIRED +! CONVEX COMBINATION OF THE GAUSS-NEWTON DIRECTION AND THE +! SCALED GRADIENT DIRECTION. + +! WA1 AND WA2 ARE WORK ARRAYS OF LENGTH N. + +! SUBPROGRAMS CALLED + +! MINPACK-SUPPLIED ... SPMPAR,ENORM + +! FORTRAN-SUPPLIED ... ABS,MAX,MIN,SQRT + +! ARGONNE NATIONAL LABORATORY. MINPACK PROJECT. MARCH 1980. +! BURTON S. GARBOW, KENNETH E. HILLSTROM, JORGE J. MORE + +! ********** +INTEGER :: i, j, jj, jp1, k, l +REAL (dp) :: alpha, bnorm, epsmch, gnorm, qnorm, sgnorm, sum, temp + +! EPSMCH IS THE MACHINE PRECISION. + +epsmch = EPSILON(1.0_dp) + +! FIRST, CALCULATE THE GAUSS-NEWTON DIRECTION. + +jj = (n*(n+1)) / 2 + 1 +DO k = 1, n + j = n - k + 1 + jp1 = j + 1 + jj = jj - k + l = jj + 1 + sum = 0.0 + IF (n >= jp1) THEN + DO i = jp1, n + sum = sum + r(l) * x(i) + l = l + 1 + END DO + END IF + temp = r(jj) + IF (temp == 0.0) THEN + l = j + DO i = 1, j + temp = MAX(temp,ABS(r(l))) + l = l + n - i + END DO + temp = epsmch * temp + IF (temp == 0.0) temp = epsmch + END IF + x(j) = (qtb(j)-sum) / temp +END DO + +! TEST WHETHER THE GAUSS-NEWTON DIRECTION IS ACCEPTABLE. + +DO j = 1, n + wa1(j) = 0.0 + wa2(j) = diag(j) * x(j) +END DO +qnorm = enorm(n, wa2) +IF (qnorm > delta) THEN + +! THE GAUSS-NEWTON DIRECTION IS NOT ACCEPTABLE. +! NEXT, CALCULATE THE SCALED GRADIENT DIRECTION. + + l = 1 + DO j = 1, n + temp = qtb(j) + DO i = j, n + wa1(i) = wa1(i) + r(l) * temp + l = l + 1 + END DO + wa1(j) = wa1(j) / diag(j) + END DO + +! CALCULATE THE NORM OF THE SCALED GRADIENT AND TEST FOR +! THE SPECIAL CASE IN WHICH THE SCALED GRADIENT IS ZERO. + + gnorm = enorm(n, wa1) + sgnorm = 0.0 + alpha = delta / qnorm + IF (gnorm /= 0.0) THEN + +! CALCULATE THE POINT ALONG THE SCALED GRADIENT +! AT WHICH THE QUADRATIC IS MINIMIZED. + + DO j = 1, n + wa1(j) = (wa1(j)/gnorm) / diag(j) + END DO + l = 1 + DO j = 1, n + sum = 0.0 + DO i = j, n + sum = sum + r(l) * wa1(i) + l = l + 1 + END DO + wa2(j) = sum + END DO + temp = enorm(n, wa2) + sgnorm = (gnorm/temp) / temp + +! TEST WHETHER THE SCALED GRADIENT DIRECTION IS ACCEPTABLE. + + alpha = 0.0 + IF (sgnorm < delta) THEN + +! THE SCALED GRADIENT DIRECTION IS NOT ACCEPTABLE. +! FINALLY, CALCULATE THE POINT ALONG THE DOGLEG +! AT WHICH THE QUADRATIC IS MINIMIZED. + + bnorm = enorm(n, qtb) + temp = (bnorm/gnorm) * (bnorm/qnorm) * (sgnorm/delta) + temp = temp - (delta/qnorm) * (sgnorm/delta) ** 2 + SQRT(( & + temp-(delta/qnorm))**2+(1.0-(delta/qnorm)**2)*(1.0-( sgnorm/delta)**2)) + alpha = ((delta/qnorm)*(1.0-(sgnorm/delta)**2)) / temp + END IF + END IF + +! FORM APPROPRIATE CONVEX COMBINATION OF THE GAUSS-NEWTON +! DIRECTION AND THE SCALED GRADIENT DIRECTION. + + temp = (1.0-alpha) * MIN(sgnorm,delta) + DO j = 1, n + x(j) = temp * wa1(j) + alpha * x(j) + END DO +END IF +RETURN +END SUBROUTINE dogleg + + +SUBROUTINE fdjac1(fcn, n, x, fvec, fjac, ldfjac, iflag, ml, mu, epsfcn, & + wa1, wa2) + +INTEGER, INTENT(IN) :: n +REAL (dp), INTENT(IN OUT) :: x(n) +REAL (dp), INTENT(IN) :: fvec(n) +INTEGER, INTENT(IN) :: ldfjac +REAL (dp), INTENT(OUT) :: fjac(ldfjac,n) +INTEGER, INTENT(IN OUT) :: iflag +INTEGER, INTENT(IN) :: ml +INTEGER, INTENT(IN) :: mu +REAL (dp), INTENT(IN) :: epsfcn +REAL (dp), INTENT(IN OUT) :: wa1(n) +REAL (dp), INTENT(OUT) :: wa2(n) + +! EXTERNAL fcn +INTERFACE + SUBROUTINE FCN(N, X, FVEC, IFLAG) + IMPLICIT NONE + INTEGER, PARAMETER :: dp = SELECTED_REAL_KIND(14, 60) + INTEGER, INTENT(IN) :: n + REAL (dp), INTENT(IN) :: x(n) + REAL (dp), INTENT(OUT) :: fvec(n) + INTEGER, INTENT(IN OUT) :: iflag + END SUBROUTINE FCN +END INTERFACE + +! ********** + +! SUBROUTINE FDJAC1 + +! THIS SUBROUTINE COMPUTES A FORWARD-DIFFERENCE APPROXIMATION TO THE N BY N +! JACOBIAN MATRIX ASSOCIATED WITH A SPECIFIED PROBLEM OF N FUNCTIONS IN N +! VARIABLES. IF THE JACOBIAN HAS A BANDED FORM, THEN FUNCTION EVALUATIONS +! ARE SAVED BY ONLY APPROXIMATING THE NONZERO TERMS. + +! THE SUBROUTINE STATEMENT IS + +! SUBROUTINE FDJAC1(FCN,N,X,FVEC,FJAC,LDFJAC,IFLAG,ML,MU,EPSFCN, +! WA1,WA2) + +! WHERE + +! FCN IS THE NAME OF THE USER-SUPPLIED SUBROUTINE WHICH CALCULATES +! THE FUNCTIONS. FCN MUST BE DECLARED IN AN EXTERNAL STATEMENT IN +! THE USER CALLING PROGRAM, AND SHOULD BE WRITTEN AS FOLLOWS. + +! SUBROUTINE FCN(N,X,FVEC,IFLAG) +! INTEGER N,IFLAG +! REAL X(N),FVEC(N) +! ---------- +! CALCULATE THE FUNCTIONS AT X AND +! RETURN THIS VECTOR IN FVEC. +! ---------- +! RETURN +! END + +! THE VALUE OF IFLAG SHOULD NOT BE CHANGED BY FCN UNLESS +! THE USER WANTS TO TERMINATE EXECUTION OF FDJAC1. +! IN THIS CASE SET IFLAG TO A NEGATIVE INTEGER. + +! N IS A POSITIVE INTEGER INPUT VARIABLE SET TO THE NUMBER +! OF FUNCTIONS AND VARIABLES. + +! X IS AN INPUT ARRAY OF LENGTH N. + +! FVEC IS AN INPUT ARRAY OF LENGTH N WHICH MUST CONTAIN THE +! FUNCTIONS EVALUATED AT X. + +! FJAC IS AN OUTPUT N BY N ARRAY WHICH CONTAINS THE +! APPROXIMATION TO THE JACOBIAN MATRIX EVALUATED AT X. + +! LDFJAC IS A POSITIVE INTEGER INPUT VARIABLE NOT LESS THAN N +! WHICH SPECIFIES THE LEADING DIMENSION OF THE ARRAY FJAC. + +! IFLAG IS AN INTEGER VARIABLE WHICH CAN BE USED TO TERMINATE +! THE EXECUTION OF FDJAC1. SEE DESCRIPTION OF FCN. + +! ML IS A NONNEGATIVE INTEGER INPUT VARIABLE WHICH SPECIFIES +! THE NUMBER OF SUBDIAGONALS WITHIN THE BAND OF THE +! JACOBIAN MATRIX. IF THE JACOBIAN IS NOT BANDED, SET +! ML TO AT LEAST N - 1. + +! EPSFCN IS AN INPUT VARIABLE USED IN DETERMINING A SUITABLE +! STEP LENGTH FOR THE FORWARD-DIFFERENCE APPROXIMATION. THIS +! APPROXIMATION ASSUMES THAT THE RELATIVE ERRORS IN THE +! FUNCTIONS ARE OF THE ORDER OF EPSFCN. IF EPSFCN IS LESS +! THAN THE MACHINE PRECISION, IT IS ASSUMED THAT THE RELATIVE +! ERRORS IN THE FUNCTIONS ARE OF THE ORDER OF THE MACHINE PRECISION. + +! MU IS A NONNEGATIVE INTEGER INPUT VARIABLE WHICH SPECIFIES +! THE NUMBER OF SUPERDIAGONALS WITHIN THE BAND OF THE +! JACOBIAN MATRIX. IF THE JACOBIAN IS NOT BANDED, SET +! MU TO AT LEAST N - 1. + +! WA1 AND WA2 ARE WORK ARRAYS OF LENGTH N. IF ML + MU + 1 IS AT +! LEAST N, THEN THE JACOBIAN IS CONSIDERED DENSE, AND WA2 IS +! NOT REFERENCED. + +! SUBPROGRAMS CALLED + +! MINPACK-SUPPLIED ... SPMPAR + +! FORTRAN-SUPPLIED ... ABS,MAX,SQRT + +! ARGONNE NATIONAL LABORATORY. MINPACK PROJECT. MARCH 1980. +! BURTON S. GARBOW, KENNETH E. HILLSTROM, JORGE J. MORE + +! ********** +INTEGER :: i, j, k, msum +REAL (dp) :: eps, epsmch, h, temp +REAL (dp), PARAMETER :: zero = 0.0_dp + +! EPSMCH IS THE MACHINE PRECISION. + +epsmch = EPSILON(1.0_dp) + +eps = SQRT(MAX(epsfcn, epsmch)) +msum = ml + mu + 1 +IF (msum >= n) THEN + +! COMPUTATION OF DENSE APPROXIMATE JACOBIAN. + + DO j = 1, n + temp = x(j) + h = eps * ABS(temp) + IF (h == zero) h = eps + x(j) = temp + h + CALL fcn(n, x, wa1, iflag) + IF (iflag < 0) EXIT + x(j) = temp + DO i = 1, n + fjac(i,j) = (wa1(i)-fvec(i)) / h + END DO + END DO +ELSE + +! COMPUTATION OF BANDED APPROXIMATE JACOBIAN. + + DO k = 1, msum + DO j = k, n, msum + wa2(j) = x(j) + h = eps * ABS(wa2(j)) + IF (h == zero) h = eps + x(j) = wa2(j) + h + END DO + CALL fcn(n, x, wa1, iflag) + IF (iflag < 0) EXIT + DO j = k, n, msum + x(j) = wa2(j) + h = eps * ABS(wa2(j)) + IF (h == zero) h = eps + DO i = 1, n + fjac(i,j) = zero + IF (i >= j-mu .AND. i <= j+ml) fjac(i,j) = (wa1(i)-fvec(i)) / h + END DO + END DO + END DO +END IF +RETURN + +! LAST CARD OF SUBROUTINE FDJAC1. + +END SUBROUTINE fdjac1 + + + +SUBROUTINE qform(m, n, q, ldq, wa) + +INTEGER, INTENT(IN) :: m +INTEGER, INTENT(IN) :: n +INTEGER, INTENT(IN) :: ldq +REAL (dp), INTENT(OUT) :: q(ldq,m) +REAL (dp), INTENT(OUT) :: wa(m) + + +! ********** + +! SUBROUTINE QFORM + +! THIS SUBROUTINE PROCEEDS FROM THE COMPUTED QR FACTORIZATION OF AN M BY N +! MATRIX A TO ACCUMULATE THE M BY M ORTHOGONAL MATRIX Q FROM ITS FACTORED FORM. + +! THE SUBROUTINE STATEMENT IS + +! SUBROUTINE QFORM(M,N,Q,LDQ,WA) + +! WHERE + +! M IS A POSITIVE INTEGER INPUT VARIABLE SET TO THE NUMBER +! OF ROWS OF A AND THE ORDER OF Q. + +! N IS A POSITIVE INTEGER INPUT VARIABLE SET TO THE NUMBER OF COLUMNS OF A. + +! Q IS AN M BY M ARRAY. ON INPUT THE FULL LOWER TRAPEZOID IN +! THE FIRST MIN(M,N) COLUMNS OF Q CONTAINS THE FACTORED FORM. +! ON OUTPUT Q HAS BEEN ACCUMULATED INTO A SQUARE MATRIX. + +! LDQ IS A POSITIVE INTEGER INPUT VARIABLE NOT LESS THAN M +! WHICH SPECIFIES THE LEADING DIMENSION OF THE ARRAY Q. + +! WA IS A WORK ARRAY OF LENGTH M. + +! SUBPROGRAMS CALLED + +! FORTRAN-SUPPLIED ... MIN + +! ARGONNE NATIONAL LABORATORY. MINPACK PROJECT. MARCH 1980. +! BURTON S. GARBOW, KENNETH E. HILLSTROM, JORGE J. MORE + +! ********** +INTEGER :: i, j, jm1, k, l, minmn, np1 +REAL (dp) :: sum, temp +REAL (dp), PARAMETER :: one = 1.0_dp, zero = 0.0_dp + +! ZERO OUT UPPER TRIANGLE OF Q IN THE FIRST MIN(M,N) COLUMNS. + +minmn = MIN(m,n) +IF (minmn >= 2) THEN + DO j = 2, minmn + jm1 = j - 1 + DO i = 1, jm1 + q(i,j) = zero + END DO + END DO +END IF + +! INITIALIZE REMAINING COLUMNS TO THOSE OF THE IDENTITY MATRIX. + +np1 = n + 1 +IF (m >= np1) THEN + DO j = np1, m + DO i = 1, m + q(i,j) = zero + END DO + q(j,j) = one + END DO +END IF + +! ACCUMULATE Q FROM ITS FACTORED FORM. + +DO l = 1, minmn + k = minmn - l + 1 + DO i = k, m + wa(i) = q(i,k) + q(i,k) = zero + END DO + q(k,k) = one + IF (wa(k) /= zero) THEN + DO j = k, m + sum = zero + DO i = k, m + sum = sum + q(i,j) * wa(i) + END DO + temp = sum / wa(k) + DO i = k, m + q(i,j) = q(i,j) - temp * wa(i) + END DO + END DO + END IF +END DO +RETURN + +! LAST CARD OF SUBROUTINE QFORM. + +END SUBROUTINE qform + + +SUBROUTINE qrfac(m, n, a, lda, pivot, ipvt, lipvt, rdiag, acnorm, wa) + +INTEGER, INTENT(IN) :: m +INTEGER, INTENT(IN) :: n +INTEGER, INTENT(IN) :: lda +REAL (dp), INTENT(IN OUT) :: a(lda,n) +LOGICAL, INTENT(IN) :: pivot +INTEGER, INTENT(IN) :: lipvt +INTEGER, INTENT(OUT) :: ipvt(lipvt) +REAL (dp), INTENT(OUT) :: rdiag(n) +REAL (dp), INTENT(OUT) :: acnorm(n) +REAL (dp), INTENT(OUT) :: wa(n) + + +! ********** + +! SUBROUTINE QRFAC + +! THIS SUBROUTINE USES HOUSEHOLDER TRANSFORMATIONS WITH COLUMN PIVOTING +! (OPTIONAL) TO COMPUTE A QR FACTORIZATION OF THE M BY N MATRIX A. +! THAT IS, QRFAC DETERMINES AN ORTHOGONAL MATRIX Q, A PERMUTATION MATRIX P, +! AND AN UPPER TRAPEZOIDAL MATRIX R WITH DIAGONAL ELEMENTS OF NONINCREASING +! MAGNITUDE, SUCH THAT A*P = Q*R. THE HOUSEHOLDER TRANSFORMATION FOR +! COLUMN K, K = 1,2,...,MIN(M,N), IS OF THE FORM + +! T +! I - (1/U(K))*U*U + +! WHERE U HAS ZEROS IN THE FIRST K-1 POSITIONS. THE FORM OF THIS +! TRANSFORMATION AND THE METHOD OF PIVOTING FIRST APPEARED IN THE +! CORRESPONDING LINPACK SUBROUTINE. + +! THE SUBROUTINE STATEMENT IS + +! SUBROUTINE QRFAC(M,N,A,LDA,PIVOT,IPVT,LIPVT,RDIAG,ACNORM,WA) + +! WHERE + +! M IS A POSITIVE INTEGER INPUT VARIABLE SET TO THE NUMBER OF ROWS OF A. + +! N IS A POSITIVE INTEGER INPUT VARIABLE SET TO THE NUMBER +! OF COLUMNS OF A. + +! A IS AN M BY N ARRAY. ON INPUT A CONTAINS THE MATRIX FOR WHICH THE +! QR FACTORIZATION IS TO BE COMPUTED. ON OUTPUT THE STRICT UPPER +! TRAPEZOIDAL PART OF A CONTAINS THE STRICT UPPER TRAPEZOIDAL PART OF R, +! AND THE LOWER TRAPEZOIDAL PART OF A CONTAINS A FACTORED FORM OF Q +! (THE NON-TRIVIAL ELEMENTS OF THE U VECTORS DESCRIBED ABOVE). + +! LDA IS A POSITIVE INTEGER INPUT VARIABLE NOT LESS THAN M +! WHICH SPECIFIES THE LEADING DIMENSION OF THE ARRAY A. + +! PIVOT IS A LOGICAL INPUT VARIABLE. IF PIVOT IS SET TRUE, +! THEN COLUMN PIVOTING IS ENFORCED. IF PIVOT IS SET FALSE, +! THEN NO COLUMN PIVOTING IS DONE. + +! IPVT IS AN INTEGER OUTPUT ARRAY OF LENGTH LIPVT. IPVT DEFINES THE +! PERMUTATION MATRIX P SUCH THAT A*P = Q*R. +! COLUMN J OF P IS COLUMN IPVT(J) OF THE IDENTITY MATRIX. +! IF PIVOT IS FALSE, IPVT IS NOT REFERENCED. + +! LIPVT IS A POSITIVE INTEGER INPUT VARIABLE. IF PIVOT IS FALSE, +! THEN LIPVT MAY BE AS SMALL AS 1. IF PIVOT IS TRUE, THEN +! LIPVT MUST BE AT LEAST N. + +! RDIAG IS AN OUTPUT ARRAY OF LENGTH N WHICH CONTAINS THE +! DIAGONAL ELEMENTS OF R. + +! ACNORM IS AN OUTPUT ARRAY OF LENGTH N WHICH CONTAINS THE NORMS OF +! THE CORRESPONDING COLUMNS OF THE INPUT MATRIX A. +! IF THIS INFORMATION IS NOT NEEDED, THEN ACNORM CAN COINCIDE WITH RDIAG. + +! WA IS A WORK ARRAY OF LENGTH N. IF PIVOT IS FALSE, THEN WA +! CAN COINCIDE WITH RDIAG. + +! SUBPROGRAMS CALLED + +! MINPACK-SUPPLIED ... SPMPAR,ENORM + +! FORTRAN-SUPPLIED ... MAX,SQRT,MIN + +! ARGONNE NATIONAL LABORATORY. MINPACK PROJECT. MARCH 1980. +! BURTON S. GARBOW, KENNETH E. HILLSTROM, JORGE J. MORE + +! ********** +INTEGER :: i, j, jp1, k, kmax, minmn +REAL (dp) :: ajnorm, epsmch, sum, temp +REAL (dp), PARAMETER :: one = 1.0_dp, p05 = 0.05_dp, zero = 0.0_dp + +! EPSMCH IS THE MACHINE PRECISION. + +epsmch = EPSILON(1.0_dp) + +! COMPUTE THE INITIAL COLUMN NORMS AND INITIALIZE SEVERAL ARRAYS. + +DO j = 1, n + acnorm(j) = enorm(m, a(1:,j)) + rdiag(j) = acnorm(j) + wa(j) = rdiag(j) + IF (pivot) ipvt(j) = j +END DO + +! REDUCE A TO R WITH HOUSEHOLDER TRANSFORMATIONS. + +minmn = MIN(m,n) +DO j = 1, minmn + IF (pivot) THEN + +! BRING THE COLUMN OF LARGEST NORM INTO THE PIVOT POSITION. + + kmax = j + DO k = j, n + IF (rdiag(k) > rdiag(kmax)) kmax = k + END DO + IF (kmax /= j) THEN + DO i = 1, m + temp = a(i,j) + a(i,j) = a(i,kmax) + a(i,kmax) = temp + END DO + rdiag(kmax) = rdiag(j) + wa(kmax) = wa(j) + k = ipvt(j) + ipvt(j) = ipvt(kmax) + ipvt(kmax) = k + END IF + END IF + +! COMPUTE THE HOUSEHOLDER TRANSFORMATION TO REDUCE THE +! J-TH COLUMN OF A TO A MULTIPLE OF THE J-TH UNIT VECTOR. + + ajnorm = enorm(m-j+1, a(j:,j)) + IF (ajnorm /= zero) THEN + IF (a(j,j) < zero) ajnorm = -ajnorm + DO i = j, m + a(i,j) = a(i,j) / ajnorm + END DO + a(j,j) = a(j,j) + one + +! APPLY THE TRANSFORMATION TO THE REMAINING COLUMNS AND UPDATE THE NORMS. + + jp1 = j + 1 + IF (n >= jp1) THEN + DO k = jp1, n + sum = zero + DO i = j, m + sum = sum + a(i,j) * a(i,k) + END DO + temp = sum / a(j,j) + DO i = j, m + a(i,k) = a(i,k) - temp * a(i,j) + END DO + IF (.NOT.(.NOT.pivot.OR.rdiag(k) == zero)) THEN + temp = a(j,k) / rdiag(k) + rdiag(k) = rdiag(k) * SQRT(MAX(zero,one-temp**2)) + IF (p05*(rdiag(k)/wa(k))**2 <= epsmch) THEN + rdiag(k) = enorm(m-j, a(jp1:,k)) + wa(k) = rdiag(k) + END IF + END IF + END DO + END IF + END IF + rdiag(j) = -ajnorm +END DO +RETURN + +! LAST CARD OF SUBROUTINE QRFAC. + +END SUBROUTINE qrfac + + + +SUBROUTINE r1mpyq(m, n, a, lda, v, w) + +INTEGER, INTENT(IN) :: m +INTEGER, INTENT(IN) :: n +INTEGER, INTENT(IN) :: lda +REAL (dp), INTENT(IN OUT) :: a(lda,n) +REAL (dp), INTENT(IN) :: v(n) +REAL (dp), INTENT(IN) :: w(n) + + +! ********** + +! SUBROUTINE R1MPYQ + +! GIVEN AN M BY N MATRIX A, THIS SUBROUTINE COMPUTES A*Q WHERE +! Q IS THE PRODUCT OF 2*(N - 1) TRANSFORMATIONS + +! GV(N-1)*...*GV(1)*GW(1)*...*GW(N-1) + +! AND GV(I), GW(I) ARE GIVENS ROTATIONS IN THE (I,N) PLANE WHICH +! ELIMINATE ELEMENTS IN THE I-TH AND N-TH PLANES, RESPECTIVELY. +! Q ITSELF IS NOT GIVEN, RATHER THE INFORMATION TO RECOVER THE +! GV, GW ROTATIONS IS SUPPLIED. + +! THE SUBROUTINE STATEMENT IS + +! SUBROUTINE R1MPYQ(M, N, A, LDA, V, W) + +! WHERE + +! M IS A POSITIVE INTEGER INPUT VARIABLE SET TO THE NUMBER OF ROWS OF A. + +! N IS A POSITIVE INTEGER INPUT VARIABLE SET TO THE NUMBER OF COLUMNS OF A. + +! A IS AN M BY N ARRAY. ON INPUT A MUST CONTAIN THE MATRIX TO BE +! POSTMULTIPLIED BY THE ORTHOGONAL MATRIX Q DESCRIBED ABOVE. +! ON OUTPUT A*Q HAS REPLACED A. + +! LDA IS A POSITIVE INTEGER INPUT VARIABLE NOT LESS THAN M +! WHICH SPECIFIES THE LEADING DIMENSION OF THE ARRAY A. + +! V IS AN INPUT ARRAY OF LENGTH N. V(I) MUST CONTAIN THE INFORMATION +! NECESSARY TO RECOVER THE GIVENS ROTATION GV(I) DESCRIBED ABOVE. + +! W IS AN INPUT ARRAY OF LENGTH N. W(I) MUST CONTAIN THE INFORMATION +! NECESSARY TO RECOVER THE GIVENS ROTATION GW(I) DESCRIBED ABOVE. + +! SUBROUTINES CALLED + +! FORTRAN-SUPPLIED ... ABS, SQRT + +! ARGONNE NATIONAL LABORATORY. MINPACK PROJECT. MARCH 1980. +! BURTON S. GARBOW, KENNETH E. HILLSTROM, JORGE J. MORE + +! ********** +INTEGER :: i, j, nmj, nm1 +REAL (dp) :: COS, SIN, temp +REAL (dp), PARAMETER :: one = 1.0_dp + +! APPLY THE FIRST SET OF GIVENS ROTATIONS TO A. + +nm1 = n - 1 +IF (nm1 >= 1) THEN + DO nmj = 1, nm1 + j = n - nmj + IF (ABS(v(j)) > one) COS = one / v(j) + IF (ABS(v(j)) > one) SIN = SQRT(one-COS**2) + IF (ABS(v(j)) <= one) SIN = v(j) + IF (ABS(v(j)) <= one) COS = SQRT(one-SIN**2) + DO i = 1, m + temp = COS * a(i,j) - SIN * a(i,n) + a(i,n) = SIN * a(i,j) + COS * a(i,n) + a(i,j) = temp + END DO + END DO + +! APPLY THE SECOND SET OF GIVENS ROTATIONS TO A. + + DO j = 1, nm1 + IF (ABS(w(j)) > one) COS = one / w(j) + IF (ABS(w(j)) > one) SIN = SQRT(one-COS**2) + IF (ABS(w(j)) <= one) SIN = w(j) + IF (ABS(w(j)) <= one) COS = SQRT(one-SIN**2) + DO i = 1, m + temp = COS * a(i,j) + SIN * a(i,n) + a(i,n) = -SIN * a(i,j) + COS * a(i,n) + a(i,j) = temp + END DO + END DO +END IF +RETURN + +! LAST CARD OF SUBROUTINE R1MPYQ. + +END SUBROUTINE r1mpyq + + + +SUBROUTINE r1updt(m, n, s, ls, u, v, w, sing) + +INTEGER, INTENT(IN) :: m +INTEGER, INTENT(IN) :: n +INTEGER, INTENT(IN) :: ls +REAL (dp), INTENT(IN OUT) :: s(ls) +REAL (dp), INTENT(IN) :: u(m) +REAL (dp), INTENT(IN OUT) :: v(n) +REAL (dp), INTENT(OUT) :: w(m) +LOGICAL, INTENT(OUT) :: sing + + +! ********** + +! SUBROUTINE R1UPDT + +! GIVEN AN M BY N LOWER TRAPEZOIDAL MATRIX S, AN M-VECTOR U, +! AND AN N-VECTOR V, THE PROBLEM IS TO DETERMINE AN +! ORTHOGONAL MATRIX Q SUCH THAT + +! T +! (S + U*V )*Q + +! IS AGAIN LOWER TRAPEZOIDAL. + +! THIS SUBROUTINE DETERMINES Q AS THE PRODUCT OF 2*(N - 1) TRANSFORMATIONS + +! GV(N-1)*...*GV(1)*GW(1)*...*GW(N-1) + +! WHERE GV(I), GW(I) ARE GIVENS ROTATIONS IN THE (I,N) PLANE +! WHICH ELIMINATE ELEMENTS IN THE I-TH AND N-TH PLANES, RESPECTIVELY. +! Q ITSELF IS NOT ACCUMULATED, RATHER THE INFORMATION TO RECOVER THE GV, +! GW ROTATIONS IS RETURNED. + +! THE SUBROUTINE STATEMENT IS + +! SUBROUTINE R1UPDT(M,N,S,LS,U,V,W,SING) + +! WHERE + +! M IS A POSITIVE INTEGER INPUT VARIABLE SET TO THE NUMBER OF ROWS OF S. + +! N IS A POSITIVE INTEGER INPUT VARIABLE SET TO THE NUMBER +! OF COLUMNS OF S. N MUST NOT EXCEED M. + +! S IS AN ARRAY OF LENGTH LS. ON INPUT S MUST CONTAIN THE LOWER +! TRAPEZOIDAL MATRIX S STORED BY COLUMNS. ON OUTPUT S CONTAINS +! THE LOWER TRAPEZOIDAL MATRIX PRODUCED AS DESCRIBED ABOVE. + +! LS IS A POSITIVE INTEGER INPUT VARIABLE NOT LESS THAN +! (N*(2*M-N+1))/2. + +! U IS AN INPUT ARRAY OF LENGTH M WHICH MUST CONTAIN THE VECTOR U. + +! V IS AN ARRAY OF LENGTH N. ON INPUT V MUST CONTAIN THE VECTOR V. +! ON OUTPUT V(I) CONTAINS THE INFORMATION NECESSARY TO +! RECOVER THE GIVENS ROTATION GV(I) DESCRIBED ABOVE. + +! W IS AN OUTPUT ARRAY OF LENGTH M. W(I) CONTAINS INFORMATION +! NECESSARY TO RECOVER THE GIVENS ROTATION GW(I) DESCRIBED ABOVE. + +! SING IS A LOGICAL OUTPUT VARIABLE. SING IS SET TRUE IF ANY OF THE +! DIAGONAL ELEMENTS OF THE OUTPUT S ARE ZERO. OTHERWISE SING IS +! SET FALSE. + +! SUBPROGRAMS CALLED + +! MINPACK-SUPPLIED ... SPMPAR + +! FORTRAN-SUPPLIED ... ABS,SQRT + +! ARGONNE NATIONAL LABORATORY. MINPACK PROJECT. MARCH 1980. +! BURTON S. GARBOW, KENNETH E. HILLSTROM, JORGE J. MORE, JOHN L. NAZARETH + +! ********** +INTEGER :: i, j, jj, l, nmj, nm1 +REAL (dp) :: COS, cotan, giant, SIN, TAN, tau, temp +REAL (dp), PARAMETER :: one = 1.0_dp, p5 = 0.5_dp, p25 = 0.25_dp, zero = 0.0_dp + +! GIANT IS THE LARGEST MAGNITUDE. + +giant = HUGE(1.0_dp) + +! INITIALIZE THE DIAGONAL ELEMENT POINTER. + +jj = (n*(2*m-n+1)) / 2 - (m-n) + +! MOVE THE NONTRIVIAL PART OF THE LAST COLUMN OF S INTO W. + +l = jj +DO i = n, m + w(i) = s(l) + l = l + 1 +END DO + +! ROTATE THE VECTOR V INTO A MULTIPLE OF THE N-TH UNIT VECTOR +! IN SUCH A WAY THAT A SPIKE IS INTRODUCED INTO W. + +nm1 = n - 1 +IF (nm1 >= 1) THEN + DO nmj = 1, nm1 + j = n - nmj + jj = jj - (m-j+1) + w(j) = zero + IF (v(j) /= zero) THEN + +! DETERMINE A GIVENS ROTATION WHICH ELIMINATES THE J-TH ELEMENT OF V. + + IF (ABS(v(n)) < ABS(v(j))) THEN + cotan = v(n) / v(j) + SIN = p5 / SQRT(p25+p25*cotan**2) + COS = SIN * cotan + tau = one + IF (ABS(COS)*giant > one) tau = one / COS + ELSE + TAN = v(j) / v(n) + COS = p5 / SQRT(p25+p25*TAN**2) + SIN = COS * TAN + tau = SIN + END IF + +! APPLY THE TRANSFORMATION TO V AND STORE THE INFORMATION +! NECESSARY TO RECOVER THE GIVENS ROTATION. + + v(n) = SIN * v(j) + COS * v(n) + v(j) = tau + +! APPLY THE TRANSFORMATION TO S AND EXTEND THE SPIKE IN W. + + l = jj + DO i = j, m + temp = COS * s(l) - SIN * w(i) + w(i) = SIN * s(l) + COS * w(i) + s(l) = temp + l = l + 1 + END DO + END IF + END DO +END IF + +! ADD THE SPIKE FROM THE RANK 1 UPDATE TO W. + +DO i = 1, m + w(i) = w(i) + v(n) * u(i) +END DO + +! ELIMINATE THE SPIKE. + +sing = .false. +IF (nm1 >= 1) THEN + DO j = 1, nm1 + IF (w(j) /= zero) THEN + +! DETERMINE A GIVENS ROTATION WHICH ELIMINATES THE +! J-TH ELEMENT OF THE SPIKE. + + IF (ABS(s(jj)) < ABS(w(j))) THEN + cotan = s(jj) / w(j) + SIN = p5 / SQRT(p25 + p25*cotan**2) + COS = SIN * cotan + tau = one + IF (ABS(COS)*giant > one) tau = one / COS + ELSE + TAN = w(j) / s(jj) + COS = p5 / SQRT(p25+p25*TAN**2) + SIN = COS * TAN + tau = SIN + END IF + +! APPLY THE TRANSFORMATION TO S AND REDUCE THE SPIKE IN W. + + l = jj + DO i = j, m + temp = COS * s(l) + SIN * w(i) + w(i) = -SIN * s(l) + COS * w(i) + s(l) = temp + l = l + 1 + END DO + +! STORE THE INFORMATION NECESSARY TO RECOVER THE GIVENS ROTATION. + + w(j) = tau + END IF + +! TEST FOR ZERO DIAGONAL ELEMENTS IN THE OUTPUT S. + + IF (s(jj) == zero) sing = .true. + jj = jj + (m-j+1) + END DO +END IF + +! MOVE W BACK INTO THE LAST COLUMN OF THE OUTPUT S. + +l = jj +DO i = n, m + s(l) = w(i) + l = l + 1 +END DO +IF (s(jj) == zero) sing = .true. +RETURN + +! LAST CARD OF SUBROUTINE R1UPDT. + +END SUBROUTINE r1updt + + +FUNCTION enorm(n, x) RESULT(fn_val) + +INTEGER, INTENT(IN) :: n +REAL (dp), INTENT(IN) :: x(n) +REAL (dp) :: fn_val + +! ********** + +! FUNCTION ENORM + +! GIVEN AN N-VECTOR X, THIS FUNCTION CALCULATES THE EUCLIDEAN NORM OF X. + +! THE EUCLIDEAN NORM IS COMPUTED BY ACCUMULATING THE SUM OF SQUARES IN THREE +! DIFFERENT SUMS. THE SUMS OF SQUARES FOR THE SMALL AND LARGE COMPONENTS +! ARE SCALED SO THAT NO OVERFLOWS OCCUR. NON-DESTRUCTIVE UNDERFLOWS ARE +! PERMITTED. UNDERFLOWS AND OVERFLOWS DO NOT OCCUR IN THE COMPUTATION OF THE UNSCALED +! SUM OF SQUARES FOR THE INTERMEDIATE COMPONENTS. +! THE DEFINITIONS OF SMALL, INTERMEDIATE AND LARGE COMPONENTS DEPEND ON +! TWO CONSTANTS, RDWARF AND RGIANT. THE MAIN RESTRICTIONS ON THESE CONSTANTS +! ARE THAT RDWARF**2 NOT UNDERFLOW AND RGIANT**2 NOT OVERFLOW. +! THE CONSTANTS GIVEN HERE ARE SUITABLE FOR EVERY KNOWN COMPUTER. + +! THE FUNCTION STATEMENT IS + +! REAL FUNCTION ENORM(N, X) + +! WHERE + +! N IS A POSITIVE INTEGER INPUT VARIABLE. + +! X IS AN INPUT ARRAY OF LENGTH N. + +! SUBPROGRAMS CALLED + +! FORTRAN-SUPPLIED ... ABS,SQRT + +! ARGONNE NATIONAL LABORATORY. MINPACK PROJECT. MARCH 1980. +! BURTON S. GARBOW, KENNETH E. HILLSTROM, JORGE J. MORE + +! ********** +INTEGER :: i +REAL (dp) :: agiant, floatn, s1, s2, s3, xabs, x1max, x3max +REAL (dp), PARAMETER :: rdwarf = 1.0D-100, rgiant = 1.0D+100 + +s1 = 0.0_dp +s2 = 0.0_dp +s3 = 0.0_dp +x1max = 0.0_dp +x3max = 0.0_dp +floatn = n +agiant = rgiant / floatn +DO i = 1, n + xabs = ABS(x(i)) + IF (xabs <= rdwarf .OR. xabs >= agiant) THEN + IF (xabs > rdwarf) THEN + +! SUM FOR LARGE COMPONENTS. + + IF (xabs > x1max) THEN + s1 = 1.0_dp + s1 * (x1max/xabs) ** 2 + x1max = xabs + ELSE + s1 = s1 + (xabs/x1max) ** 2 + END IF + ELSE + +! SUM FOR SMALL COMPONENTS. + + IF (xabs > x3max) THEN + s3 = 1.0_dp + s3 * (x3max/xabs) ** 2 + x3max = xabs + ELSE + IF (xabs /= 0.0_dp) s3 = s3 + (xabs/x3max) ** 2 + END IF + END IF + ELSE + +! SUM FOR INTERMEDIATE COMPONENTS. + + s2 = s2 + xabs ** 2 + END IF +END DO + +! CALCULATION OF NORM. + +IF (s1 /= 0.0_dp) THEN + fn_val = x1max * SQRT(s1 + (s2/x1max)/x1max) +ELSE + IF (s2 /= 0.0_dp) THEN + IF (s2 >= x3max) fn_val = SQRT(s2*(1.0_dp + (x3max/s2)*(x3max*s3))) + IF (s2 < x3max) fn_val = SQRT(x3max*((s2/x3max) + (x3max*s3))) + ELSE + fn_val = x3max * SQRT(s3) + END IF +END IF +RETURN +END FUNCTION enorm + +END MODULE Solve_NonLin diff --git a/applications/PUfoam/MoDeNaModels/Solubility/ExampleOfUsage/src/srcDetailedCode/modules.f90 b/applications/PUfoam/MoDeNaModels/Solubility/ExampleOfUsage/src/srcDetailedCode/modules.f90 new file mode 100644 index 000000000..53ea371b6 --- /dev/null +++ b/applications/PUfoam/MoDeNaModels/Solubility/ExampleOfUsage/src/srcDetailedCode/modules.f90 @@ -0,0 +1,364 @@ +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! This module contains parameters and constants +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW + +Module PARAMETERS + + implicit none + save + + integer, parameter :: nc = 6 + integer, parameter :: np = 3 + integer, parameter :: nsite = 5 + + real, parameter :: PI = 3.141592653589793 + real, parameter :: RGAS = 8.31441 + real, parameter :: NAv = 6.022045E23 + real, parameter :: KBOL = RGAS / NAv + real, parameter :: TAU = PI / 3.0 / SQRT(2.0) + +End Module PARAMETERS + + +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! This module contains some frequently used variables +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW + +Module BASIC_VARIABLES + + use PARAMETERS, only: nc, np, nsite + implicit none + save + +! ---------------------------------------------------------------------- +! basic quantities defining the mixture +! ---------------------------------------------------------------------- + integer :: ncomp + integer :: nphas + + real :: t + !real :: tc + real :: p + real, dimension(np) :: dense + !real, dimension(np) :: rhob + + real, dimension(np, nc) :: xi + real, dimension(np, nc) :: lnx + real, dimension(nc) :: xiF + real, dimension(nc) :: ciF + + + real, dimension(nc) :: mm + real, dimension(np, nc, nsite) :: mxx + + real :: alpha + + +! ---------------------------------------------------------------------- +! pure component parameters +! ---------------------------------------------------------------------- + real, dimension(nc, 25) :: parame = 0.0 + real, dimension(nc) :: chiR + character*30, dimension(nc) :: compna + real, dimension(nc, nc) :: kij, lij + real, dimension(nc, nc) :: E_LC, S_LC + real, dimension(nc) :: LLi, phi_criti, chap + + +! ---------------------------------------------------------------------- +! thermodynamic quantities +! ---------------------------------------------------------------------- + real, dimension(np) :: densta + real, dimension(0:nc*np+6) :: val_init, val_conv + + real :: h_lv + real, dimension(np) :: cpres, enthal, entrop, gibbs, f_res + + real, dimension(np) :: dp_dz, dp_dz2 + + +! ---------------------------------------------------------------------- +! choice of EOS-model and solution method +! ---------------------------------------------------------------------- + integer :: eos, pol + integer :: num + character (LEN=2) :: ensemble_flag + character (LEN=10) :: RGT_variant + + +! ---------------------------------------------------------------------- +! for input/output +! ---------------------------------------------------------------------- + integer :: outp, bindiag + real :: u_in_T, u_out_T, u_in_P, u_out_P + + +! ---------------------------------------------------------------------- +! quantities defining the numerical procedure +! ---------------------------------------------------------------------- + integer :: n_unkw + + real :: step_a, acc_a !, acc_i + real, dimension(nc) :: scaling + real, dimension(3500) :: plv_kon + real, dimension(2, 3500) :: d_kond + + character*3, dimension(10) :: it, sum_rel + character*3 :: running + + +End Module BASIC_VARIABLES + + + + +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! This module contains parameters and variables for the use of the EOS +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW + +Module EOS_VARIABLES + + use PARAMETERS, only: nc, nsite, PI, KBOL, TAU, NAv + use BASIC_VARIABLES, only: ncomp, eos, t, p, parame, E_LC, S_LC, chiR, & + LLi, phi_criti, chap, kij, lij, ensemble_flag + implicit none + save + +! ---------------------------------------------------------------------- +! basic quantities defining the mixture (single phase) +! ---------------------------------------------------------------------- + real :: x(nc) + real :: eta_start + real :: eta + real :: rho + +! ---------------------------------------------------------------------- +! thermodynamic quantities +! ---------------------------------------------------------------------- + real :: fres + real :: lnphi(nc) + real :: pges + real :: pgesdz + real :: pgesd2 + real :: pgesd3 + + real :: h_res + real :: cp_res + real :: s_res + +! ---------------------------------------------------------------------- +! quantities of fluid theory +! ---------------------------------------------------------------------- + real :: gij(nc,nc) + real :: mx(nc,nsite) + + real :: mseg(nc) + real :: dhs(nc) + real :: uij(nc,nc) + real :: sig_ij(nc,nc) + real :: vij(nc,nc) + + real :: um + real :: order1 + real :: order2 + real :: apar(0:6) + real :: bpar(0:6) + + real :: z0t + real :: z1t + real :: z2t + real :: z3t + + integer :: nhb_typ(nc) + real :: ass_d(nc,nc,nsite,nsite) + real :: nhb_no(nc,nsite) + real :: dij_ab(nc,nc) + +! ---------------------------------------------------------------------- +! auxilliary quantities +! ---------------------------------------------------------------------- + real :: tfr + integer :: phas + + character (LEN = 2) :: dd_term, qq_term, dq_term + + real :: densav(3), denold(3) + real :: density_error(3) + + real :: alpha_nematic + real :: alpha_test(2) + +End Module EOS_VARIABLES + + + +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! This module contains variables to store the EOS model constants +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW + +Module EOS_CONSTANTS + + use PARAMETERS, only: nc + implicit none + save + + real, dimension(0:6,3) :: ap, bp + real, dimension(4,9) :: dnm + + real, dimension(28) :: c_dd, n_dd, m_dd, k_dd, o_dd + real, dimension(nc,nc,0:8) :: qqp2, qqp4, ddp2, ddp4, dqp2, dqp4 + real, dimension(nc,nc,nc,0:8) :: qqp3, ddp3, dqp3 + +End Module EOS_CONSTANTS + +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! This module contains parameters and variables for the numerical +! evaluation of derivatives of the EOS +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW + +Module EOS_NUMERICAL_DERIVATIVES + + use EOS_VARIABLES, only: dd_term, qq_term, dq_term + + implicit none + save + + character (LEN=9) :: ideal_gas ! (yes, no) + character (LEN=9) :: hard_sphere ! (CSBM, no) + character (LEN=9) :: chain_term ! (TPT1, no) + character (LEN=9) :: disp_term ! (PC-SAFT, CK, no) + character (LEN=9) :: hb_term ! (TPT1_Chap, no) + character (LEN=9) :: LC_term ! (MSaupe, no) + character (LEN=9) :: branch_term ! (TPT2, no) + character (LEN=9) :: II_term ! (......., no) + character (LEN=9) :: ID_term ! (......., no) + + character (LEN=9) :: subtract1 ! (1PT, 2PT, no) + character (LEN=9) :: subtract2 ! (ITTpolar, no) + + character (LEN=9) :: save_eos_terms(10) + +End Module EOS_NUMERICAL_DERIVATIVES + + +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! Module STARTING_VALUES +! +! This module contains parameters and variables for a phase stability +! analyis as part of a flash calculation. +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW + + Module STARTING_VALUES + + use PARAMETERS, only: nc + implicit none + save + + REAL, DIMENSION(nc) :: rhoif, rhoi1, rhoi2, grad_fd + REAL :: fdenf + + End Module STARTING_VALUES + + + + + +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! Module DFT_MODULE +! +! This module contains parameters and variables for DFT calculations. +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! + Module DFT_MODULE + + use PARAMETERS, only: nc + implicit none + save + + INTEGER, PARAMETER :: NDFT = 4000 + !!integer :: discret + REAL :: box_l_no_unit + INTEGER, PARAMETER :: r_grid = 200 + INTEGER :: kmax, den_step + LOGICAL :: shift, WCA, MFT + REAL :: rc, rg, dzr, tau_cut,dzp + REAL :: d_hs, dhs_st, z3t_st + REAL :: z_ges + REAL, DIMENSION(r_grid) :: x1a + REAL, DIMENSION(NDFT) :: x2a + REAL, DIMENSION(r_grid,NDFT) :: ya, y1a, y2a, y12a + REAL, DIMENSION(r_grid,NDFT,4,4) :: c_bicub + REAL :: fres_temp + + REAL, DIMENSION(r_grid) :: x1a_11 + REAL, DIMENSION(NDFT) :: x2a_11 + REAL, DIMENSION(r_grid,NDFT) :: ya_11, y1a_11, y2a_11, y12a_11 + REAL, DIMENSION(r_grid,NDFT,4,4) :: c_bicub_11 + REAL, DIMENSION(r_grid) :: x1a_12 + REAL, DIMENSION(NDFT) :: x2a_12 + REAL, DIMENSION(r_grid,NDFT) :: ya_12, y1a_12, y2a_12, y12a_12 + REAL, DIMENSION(r_grid,NDFT,4,4) :: c_bicub_12 + REAL, DIMENSION(r_grid) :: x1a_22 + REAL, DIMENSION(NDFT) :: x2a_22 + REAL, DIMENSION(r_grid,NDFT) :: ya_22, y1a_22, y2a_22, y12a_22 + REAL, DIMENSION(r_grid,NDFT,4,4) :: c_bicub_22 + + End Module DFT_MODULE + + +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +Module rdf_variables + + implicit none + save + + real, dimension(0:20) :: fac(0:20) + +End Module rdf_variables + + +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! This module contains the variavles that are needed in the core DFT_FCN +! They are not passed directly to DFT_FCN because the nonlinear solver +! needs a certain calling structure: fcn(x,fvec,n) +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +Module DFT_FCN_MODULE + +use PARAMETERS, only: nc +use DFT_MODULE, only: ndft + implicit none + +INTEGER :: irc(nc),irc_j,ih,fa(nc) + REAL, DIMENSION(-NDFT:NDFT) :: zp + REAL, DIMENSION(-NDFT:NDFT) :: f_tot + REAL, DIMENSION(-NDFT:NDFT,2) :: dF_drho_tot + REAL :: rhob_dft(2,0:nc) + REAL :: my0(nc) + +End Module DFT_FCN_MODULE + + + + + + + + +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! Module Module_Heidemann_Khalil +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! + Module Module_Heidemann_Khalil + + implicit none + save + + real :: error_condition2 + + End Module + + + + diff --git a/applications/PUfoam/MoDeNaModels/Solubility/ExampleOfUsage/src/srcDetailedCode/out.txt b/applications/PUfoam/MoDeNaModels/Solubility/ExampleOfUsage/src/srcDetailedCode/out.txt new file mode 100644 index 000000000..3a68e692a --- /dev/null +++ b/applications/PUfoam/MoDeNaModels/Solubility/ExampleOfUsage/src/srcDetailedCode/out.txt @@ -0,0 +1 @@ + 2.2654943032705011 diff --git a/applications/PUfoam/MoDeNaModels/Solubility/ExampleOfUsage/workflow b/applications/PUfoam/MoDeNaModels/Solubility/ExampleOfUsage/workflow new file mode 100755 index 000000000..63676605b --- /dev/null +++ b/applications/PUfoam/MoDeNaModels/Solubility/ExampleOfUsage/workflow @@ -0,0 +1,57 @@ +#!/usr/bin/python +''' + + ooo ooooo oooooooooo. ooooo ooo + `88. .888' `888' `Y8b `888b. `8' + 888b d'888 .ooooo. 888 888 .ooooo. 8 `88b. 8 .oooo. + 8 Y88. .P 888 d88' `88b 888 888 d88' `88b 8 `88b. 8 `P )88b + 8 `888' 888 888 888 888 888 888ooo888 8 `88b.8 .oP"888 + 8 Y 888 888 888 888 d88' 888 .o 8 `888 d8( 888 + o8o o888o `Y8bod8P' o888bood8P' `Y8bod8P' o8o `8 `Y888""8o + +Copyright + 2014-2015 MoDeNa Consortium, All rights reserved. + +License + This file is part of Modena. + + Modena is free software; you can redistribute it and/or modify it under + the terms of the GNU General Public License as published by the Free + Software Foundation, either version 3 of the License, or (at your option) + any later version. + + Modena is distributed in the hope that it will be useful, but WITHOUT ANY + WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS + FOR A PARTICULAR PURPOSE. See the GNU General Public License for more + details. + + You should have received a copy of the GNU General Public License along + with Modena. If not, see . + +Description + A simple workflow + +Authors + Henrik Rusche + +Contributors +''' + +from fireworks import Firework, Workflow, LaunchPad +from fireworks.core.rocket_launcher import rapidfire +import Solubility +from modulefinder import ModuleFinder + + +# set up the LaunchPad and reset it +launchpad = LaunchPad() +launchpad.reset('', require_password=False) + +# create the individual FireWorks and Workflow +# Source code in src/twoTanksMacroscopicProblem.C +wf = Workflow([Firework(Solubility.m)], {}, name="simulation") + +# store workflow and launch it locally +launchpad.add_wf(wf) +rapidfire(launchpad) + diff --git a/applications/PUfoam/MoDeNaModels/Solubility/Solubility.py b/applications/PUfoam/MoDeNaModels/Solubility/Solubility.py new file mode 100644 index 000000000..4b6dc1842 --- /dev/null +++ b/applications/PUfoam/MoDeNaModels/Solubility/Solubility.py @@ -0,0 +1,194 @@ +'''@cond + + ooo ooooo oooooooooo. ooooo ooo + `88. .888' `888' `Y8b `888b. `8' + 888b d'888 .ooooo. 888 888 .ooooo. 8 `88b. 8 .oooo. + 8 Y88. .P 888 d88' `88b 888 888 d88' `88b 8 `88b. 8 `P )88b + 8 `888' 888 888 888 888 888 888ooo888 8 `88b.8 .oP"888 + 8 Y 888 888 888 888 d88' 888 .o 8 `888 d8( 888 + o8o o888o `Y8bod8P' o888bood8P' `Y8bod8P' o8o `8 `Y888""8o + +Copyright + 2014-2015 MoDeNa Consortium, All rights reserved. + +License + This file is part of Modena. + + Modena is free software; you can redistribute it and/or modify it under + the terms of the GNU General Public License as published by the Free + Software Foundation, either version 3 of the License, or (at your option) + any later version. + + Modena is distributed in the hope that it will be useful, but WITHOUT ANY + WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS + FOR A PARTICULAR PURPOSE. See the GNU General Public License + for more details. + + You should have received a copy of the GNU General Public License along + with Modena. If not, see . +@endcond''' + +""" +@file +Python library of FireTasks +This is the Solubility python module. Basically, it contains the following: + +The FireTask which controls the call of the detailed model. This detailed model is called +at the very beginning of the simulation in order to generate initial data points +which can be used to fit the parameters of the surrogate model and during a running simulation +as soon as the Solubility model is called with input parameters which lie outside the range +the parameters of the surrogate model was so far fitted for. This FireTask is stored in the class +"SolubilityExactSim" and a more detailed description of the detailed model can be found +in the description of this class. + +Furthermore, this module contains the code of the surrogate model function as well as the +definitions of its input and output values and its fittable parameters. Care should be +taken to set reasonable bounds for these variables. + +Also, this module contains the backward mapping model. This model consits of the +surrogate model function, an initialisation strategy, the out of bounds strategy and the +parameter fitting strategy. The initialisation strategy defines the initial data points where the +detailed model will be evaluated at simulation start for an initial fit of the surrogate model parameters. +The out of bounds strategy determines, how many new points and where to place these new +points, once the Solubility model is called for input values outside of the +fitted range. The parameter fitting strategy defines tolerances and maximal iterations +which are passed to the numerical solver which performs the actual fitting of the +surrogate model parameters. + +@author Jonas Mairhofer +@copyright 2014-2015, MoDeNa Project. GNU Public License. +@ingroup app_foaming +""" + +import os +import modena +from modena import ForwardMappingModel,BackwardMappingModel,SurrogateModel,CFunction,IndexSet +import modena.Strategy as Strategy +from fireworks.user_objects.firetasks.script_task import FireTaskBase, ScriptTask +from fireworks import Firework, Workflow, FWAction +from fireworks.utilities.fw_utilities import explicit_serialize +from blessings import Terminal +from jinja2 import Template + +# Create terminal for colour output +term = Terminal() + +@explicit_serialize +class SolubilityExactSim(FireTaskBase): + """ + This FireTask controls the execution of the detailed model of the Solubility model. + The detailed model uses the PC-SAFT equation of state. A + detailed description of PC-SAFT model can be found in Deliverable 1.3 on the MoDeNa website. + + In order to start the detailed model, the input values for the model are first written to the + file "in.txt". The detailed model code picks them up from this file and performs the according + calculation. Once it is done, the output value is written to the file "out.txt". This FireTask + then reads in the calculated solubility from "out.txt" and inserts this value into the + database. + """ + + + def run_task(self, fw_spec): + print( + term.yellow + + "Performing exact simulation (microscopic code recipe)" + + term.normal + ) + + # Write input for detailed model + ff = open('in.txt', 'w') + Tstr = str(self['point']['T']) + ff.write('%s \n' %(Tstr)) + + + ##TODO INPUT SHOULD COME FROM IndexSet + + ff.write('2 \n') #number of components in system + ff.write('co2 \n') #component 1 + ff.write('hexane \n') #component 2 + ff.write('0.5 \n') #molar feed (initial) concentration (mol/m^3) component 1 + ff.write('0.5 \n') #molar feed (initial) concentration (mol/m^3) component 2 + ff.close() + + #create output file for detailed code + fff = open('out.txt', 'w+') + fff.close() + + # Execute detailed model + os.system('../src/PCSAFT_Henry') + + # Analyse output + f = open('out.txt', 'r') + self['point']['H'] = float(f.readline()) + f.close() + + return FWAction(mod_spec=[{'_push': self['point']}]) + + +f = CFunction( + Ccode= ''' +#include "modena.h" +#include "math.h" + +void surroSolubility +( + const double* parameters, + const double* inherited_inputs, + const double* inputs, + double *outputs +) +{ + + const double T = inputs[0]; + + const double P0 = parameters[0]; + const double P1 = parameters[1]; + const double P2 = parameters[2]; + + const double term1 = P1*(1/T - 1/P2); + const double term2 = exp(term1); + + outputs[0] = P0*term2; + + //outputs[0] = P0 + T*P1 + P2*T*T; +} +''', + # These are global bounds for the function + inputs={ + 'T': { 'min': 200.0, 'max': 250.0, 'argPos': 0 }, #check if boundaries reasonable, from this range, the random values for the DOE are chosen! + }, + outputs={ + 'H': { 'min': 9e99, 'max': -9e99, 'argPos': 0 }, + }, + parameters={ + 'param0': { 'min': -1E10, 'max': 1E10, 'argPos': 0 }, #check if boundaries are reasonable!!! + 'param1': { 'min': -1E10, 'max': 1E10, 'argPos': 1 }, + 'param2': { 'min': 1.0, 'max': 1E10, 'argPos': 2 }, + }, +) + + +m = BackwardMappingModel( + _id= 'Solubility', + surrogateFunction= f, + exactTask= SolubilityExactSim(), + substituteModels= [ ], + initialisationStrategy= Strategy.InitialPoints( + initialPoints= + { + 'T': [200.0, 220.0], + }, + ), + outOfBoundsStrategy= Strategy.ExtendSpaceStochasticSampling( + nNewPoints= 4 + ), + parameterFittingStrategy= Strategy.NonLinFitWithErrorContol( + testDataPercentage= 0.2, + maxError= 50.0, + improveErrorStrategy= Strategy.StochasticSampling( + nNewPoints= 2 + ), + maxIterations= 5 # Currently not used + ), +) + diff --git a/applications/PUfoam/MoDeNaModels/Solubility/__init__.py b/applications/PUfoam/MoDeNaModels/Solubility/__init__.py new file mode 100644 index 000000000..74decabba --- /dev/null +++ b/applications/PUfoam/MoDeNaModels/Solubility/__init__.py @@ -0,0 +1,41 @@ +''' + + ooo ooooo oooooooooo. ooooo ooo + `88. .888' `888' `Y8b `888b. `8' + 888b d'888 .ooooo. 888 888 .ooooo. 8 `88b. 8 .oooo. + 8 Y88. .P 888 d88' `88b 888 888 d88' `88b 8 `88b. 8 `P )88b + 8 `888' 888 888 888 888 888 888ooo888 8 `88b.8 .oP"888 + 8 Y 888 888 888 888 d88' 888 .o 8 `888 d8( 888 + o8o o888o `Y8bod8P' o888bood8P' `Y8bod8P' o8o `8 `Y888""8o + +Copyright + 2014-2015 MoDeNa Consortium, All rights reserved. + +License + This file is part of Modena. + + Modena is free software; you can redistribute it and/or modify it under + the terms of the GNU General Public License as published by the Free + Software Foundation, either version 3 of the License, or (at your option) + any later version. + + Modena is distributed in the hope that it will be useful, but WITHOUT ANY + WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS + FOR A PARTICULAR PURPOSE. See the GNU General Public License + for more details. + + You should have received a copy of the GNU General Public License along + with Modena. If not, see . + +Description + Python library of FireTasks + +Authors + Henrik Rusche + +Contributors +''' +from modSolubility import f +from modSolubility import m_solubilityCO2 +from modSolubility import m_solubilityAir +from modSolubility import m_solubilityCyclopentane diff --git a/applications/PUfoam/MoDeNaModels/Solubility/initModels b/applications/PUfoam/MoDeNaModels/Solubility/initModels new file mode 100755 index 000000000..0d4f5687f --- /dev/null +++ b/applications/PUfoam/MoDeNaModels/Solubility/initModels @@ -0,0 +1,62 @@ +#!/usr/bin/python +''' + + ooo ooooo oooooooooo. ooooo ooo + `88. .888' `888' `Y8b `888b. `8' + 888b d'888 .ooooo. 888 888 .ooooo. 8 `88b. 8 .oooo. + 8 Y88. .P 888 d88' `88b 888 888 d88' `88b 8 `88b. 8 `P )88b + 8 `888' 888 888 888 888 888 888ooo888 8 `88b.8 .oP"888 + 8 Y 888 888 888 888 d88' 888 .o 8 `888 d8( 888 + o8o o888o `Y8bod8P' o888bood8P' `Y8bod8P' o8o `8 `Y888""8o + +Copyright + 2014-2015 MoDeNa Consortium, All rights reserved. + +License + This file is part of Modena. + + Modena is free software; you can redistribute it and/or modify it under + the terms of the GNU General Public License as published by the Free + Software Foundation, either version 3 of the License, or (at your option) + any later version. + + Modena is distributed in the hope that it will be useful, but WITHOUT ANY + WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS + FOR A PARTICULAR PURPOSE. See the GNU General Public License for more + details. + + You should have received a copy of the GNU General Public License along + with Modena. If not, see . + +Description + Initialisation script for the flowRate model. The script calculates a few + data points and fits the surrogate model. Then the model is inserted into + the database. + +Authors + Henrik Rusche + +Contributors +''' + +from modena import SurrogateModel +from modena.Strategy import Workflow2 +#import flowRate +import modSolubility +from fireworks import LaunchPad +from fireworks.core.rocket_launcher import rapidfire +from fireworks.utilities.fw_serializers import load_object + + +# set up the LaunchPad and reset it +launchpad = LaunchPad() +launchpad.reset('', require_password=False) + +initWfs = Workflow2([]) +for m in SurrogateModel.get_instances(): + initWfs.addNoLink(m.initialisationStrategy().workflow(m)) + +# store workflow and launch it locally +launchpad.add_wf(initWfs) +rapidfire(launchpad) + diff --git a/applications/PUfoam/MoDeNaModels/Solubility/src/Numeric_subroutines.f90 b/applications/PUfoam/MoDeNaModels/Solubility/src/Numeric_subroutines.f90 new file mode 100644 index 000000000..5a0eb6a30 --- /dev/null +++ b/applications/PUfoam/MoDeNaModels/Solubility/src/Numeric_subroutines.f90 @@ -0,0 +1,1672 @@ +!>WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +!! This file contains subroutines for subtasks like spline interpolations, +!! spline integration and function minimization +!!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW + + + + + +SUBROUTINE bicub_derivative ( ya, x1a, x2a, y1a, y2a, y12a, i_max, k_max ) +! + USE DFT_MODULE, ONLY: NDFT, r_grid + IMPLICIT NONE +! +! ---------------------------------------------------------------------- + REAL, INTENT(IN) :: ya(r_grid,NDFT) + REAL, INTENT(IN) :: x1a(r_grid) + REAL, INTENT(IN) :: x2a(NDFT) + REAL, INTENT(OUT) :: y1a(r_grid,NDFT) + REAL, INTENT(OUT) :: y2a(r_grid,NDFT) + REAL, INTENT(OUT) :: y12a(r_grid,NDFT) + INTEGER, INTENT(IN) :: i_max + INTEGER, INTENT(IN) :: k_max +! +! ---------------------------------------------------------------------- + INTEGER :: i, k +! ---------------------------------------------------------------------- + + +DO i = 2, i_max-1 + DO k = 2, k_max-1 + y1a(i,k) = (ya(i+1,k)-ya(i-1,k)) / (x1a(i+1)-x1a(i-1)) + y2a(i,k) = (ya(i,k+1)-ya(i,k-1)) / (x2a(k+1)-x2a(k-1)) + y12a(i,k)= (ya(i+1,k+1)-ya(i+1,k-1)-ya(i-1,k+1)+ya(i-1,k-1)) & + /((x1a(i+1)-x1a(i-1))*(x2a(k+1)-x2a(k-1))) + END DO +END DO + +i = 1 +DO k = 1, k_max + y1a(i,k) = 0.0 + y2a(i,k) = 0.0 + y12a(i,k)= 0.0 +END DO + +k = 1 +DO i = 1, i_max + y1a(i,k) = 0.0 + y2a(i,k) = 0.0 + y12a(i,k)= 0.0 +END DO + + +i = i_max +DO k = 2, k_max-1 + y1a(i,k) = (ya(i,k)-ya(i-1,k)) / (x1a(i)-x1a(i-1)) + y2a(i,k) = (ya(i,k+1)-ya(i,k-1)) / (x2a(k+1)-x2a(k-1)) + y12a(i,k)= (ya(i,k+1)-ya(i,k-1)-ya(i-1,k+1)+ya(i-1,k-1)) & + /((x1a(i)-x1a(i-1))*(x2a(k+1)-x2a(k-1))) +END DO + + +k = k_max +DO i = 2, i_max-1 + y1a(i,k) = (ya(i+1,k)-ya(i-1,k)) / (x1a(i+1)-x1a(i-1)) + y2a(i,k) = (ya(i,k)-ya(i,k-1)) / (x2a(k)-x2a(k-1)) + y12a(i,k)= (ya(i+1,k)-ya(i+1,k-1)-ya(i-1,k)+ya(i-1,k-1)) & + /((x1a(i+1)-x1a(i-1))*(x2a(k)-x2a(k-1))) +END DO + +k = k_max +i = i_max +y1a(i,k) = (ya(i,k)-ya(i-1,k)) / (x1a(i)-x1a(i-1)) +y2a(i,k) = (ya(i,k)-ya(i,k-1)) / (x2a(k)-x2a(k-1)) +y12a(i,k)= (ya(i,k)-ya(i,k-1)-ya(i-1,k)+ya(i-1,k-1)) & + /((x1a(i)-x1a(i-1))*(x2a(k)-x2a(k-1))) + +END SUBROUTINE bicub_derivative + + +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! + SUBROUTINE bicub_c ( ya, x1a, x2a, y1a, y2a, y12a, c_bicub, i_max, k_max ) +! + USE DFT_MODULE, ONLY: NDFT, r_grid + IMPLICIT NONE +! +! ---------------------------------------------------------------------- + REAL, INTENT(IN) :: ya(r_grid,NDFT) + REAL, INTENT(IN) :: x1a(r_grid) + REAL, INTENT(IN) :: x2a(NDFT) + REAL, INTENT(IN) :: y1a(r_grid,NDFT) + REAL, INTENT(IN) :: y2a(r_grid,NDFT) + REAL, INTENT(IN) :: y12a(r_grid,NDFT) + REAL, INTENT(OUT) :: c_bicub(r_grid,NDFT,4,4) + INTEGER, INTENT(IN) :: i_max + INTEGER, INTENT(IN) :: k_max +! +! ---------------------------------------------------------------------- + INTEGER :: i, k, m, n + REAL :: y(4),y1(4),y2(4),y12(4),x1l,x1u,x2l,x2u + REAL :: c(4,4) +! ---------------------------------------------------------------------- + +DO i = 1, i_max-1 + DO k = 1, k_max-1 + y(1)=ya(i,k) + y(2)=ya(i+1,k) + y(3)=ya(i+1,k+1) + y(4)=ya(i,k+1) + + y1(1)=y1a(i,k) + y1(2)=y1a(i+1,k) + y1(3)=y1a(i+1,k+1) + y1(4)=y1a(i,k+1) + + y2(1)=y2a(i,k) + y2(2)=y2a(i+1,k) + y2(3)=y2a(i+1,k+1) + y2(4)=y2a(i,k+1) + + y12(1)=y12a(i,k) + y12(2)=y12a(i+1,k) + y12(3)=y12a(i+1,k+1) + y12(4)=y12a(i,k+1) + + x1l=x1a(i) + x1u=x1a(i+1) + x2l=x2a(k) + x2u=x2a(k+1) + + CALL bcucof(y,y1,y2,y12,x1u-x1l,x2u-x2l,c) + DO m=1,4 + DO n=1,4 + c_bicub(i,k,m,n)=c(m,n) + END DO + END DO + + END DO +END DO + +END SUBROUTINE bicub_c + +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! + SUBROUTINE bcucof(y,y1,y2,y12,d1,d2,c) +! + IMPLICIT NONE +! +! ---------------------------------------------------------------------- + REAL, INTENT(IN) :: y(4) + REAL, INTENT(IN) :: y1(4) + REAL, INTENT(IN) :: y2(4) + REAL, INTENT(IN) :: y12(4) + REAL, INTENT(IN) :: d1 + REAL, INTENT(IN) :: d2 + REAL, INTENT(OUT) :: c(4,4) +! +! ---------------------------------------------------------------------- + INTEGER :: i,j,k,l + REAL :: d1d2,xx,cl(16),wt(16,16),x(16) + SAVE wt + DATA wt/1,0,-3,2,4*0,-3,0,9,-6,2,0,-6,4,8*0,3,0,-9,6,-2,0,6,-4,10* & + 0,9,-6,2*0,-6,4,2*0,3,-2,6*0,-9,6,2*0,6,-4,4*0,1,0,-3,2,-2,0,6,-4, & + 1,0,-3,2,8*0,-1,0,3,-2,1,0,-3,2,10*0,-3,2,2*0,3,-2,6*0,3,-2,2*0, & + -6,4,2*0,3,-2,0,1,-2,1,5*0,-3,6,-3,0,2,-4,2,9*0,3,-6,3,0,-2,4,-2, & + 10*0,-3,3,2*0,2,-2,2*0,-1,1,6*0,3,-3,2*0,-2,2,5*0,1,-2,1,0,-2,4, & + -2,0,1,-2,1,9*0,-1,2,-1,0,1,-2,1,10*0,1,-1,2*0,-1,1,6*0,-1,1,2*0, & + 2,-2,2*0,-1,1/ +! ---------------------------------------------------------------------- + +d1d2 = d1 * d2 +DO i = 1, 4 + x(i) = y(i) + x(i+4) = y1(i)*d1 + x(i+8) = y2(i)*d2 + x(i+12) = y12(i)*d1d2 +END DO +DO i = 1, 16 + xx = 0.0 + DO k = 1, 16 + xx = xx + wt(i,k) * x(k) + END DO + cl(i) = xx +END DO +l = 0 +DO i = 1, 4 + DO j = 1, 4 + l = l + 1 + c(i,j) = cl(l) + END DO +END DO + +END SUBROUTINE bcucof + + +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! + SUBROUTINE BI_CUB_SPLINE ( rho_rdf, xg, ya, x1a, x2a, y1a, y2a, y12a, & + c_bicub, rdf, dg_drho, dg_dr, i_max, ih, k ) +! + USE DFT_MODULE, ONLY: NDFT, r_grid + IMPLICIT NONE +! +! ---------------------------------------------------------------------- + REAL, INTENT(IN OUT) :: rho_rdf + REAL, INTENT(IN OUT) :: xg + REAL, INTENT(IN) :: ya(r_grid,NDFT) + REAL, INTENT(IN) :: x1a(r_grid) + REAL, INTENT(IN) :: x2a(NDFT) + REAL, INTENT(IN) :: y1a(r_grid,NDFT) + REAL, INTENT(IN) :: y2a(r_grid,NDFT) + REAL, INTENT(IN) :: y12a(r_grid,NDFT) + REAL, INTENT(IN) :: c_bicub(r_grid,NDFT,4,4) + REAL, INTENT(OUT) :: rdf + REAL, INTENT(OUT) :: dg_drho + REAL, INTENT(OUT) :: dg_dr + INTEGER, INTENT(IN OUT) :: i_max + !INTEGER, INTENT(IN OUT) :: k_max + INTEGER, INTENT(OUT) :: ih + INTEGER, INTENT(IN) :: k +! +! ---------------------------------------------------------------------- + INTEGER :: m, n + + REAL :: y(4),y1(4),y2(4),y12(4),x1l,x1u,x2l,x2u + REAL :: c(4,4) +! ---------------------------------------------------------------------- + +IF ( rho_rdf < x1a(1) ) THEN + dg_drho = 0.0 + dg_dr = 0.0 + rdf = 1.0 + RETURN +END IF +IF ( x1a(ih) <= rho_rdf .AND. rho_rdf < x1a(ih+1) ) GO TO 10 +IF ( ih > 2 ) THEN + IF ( x1a(ih-1) <= rho_rdf .AND. rho_rdf < x1a(ih) ) THEN + ih = ih - 1 + GO TO 10 + END IF +END IF +! write (*,*) 'in ',ih +CALL hunt ( x1a, i_max, rho_rdf, ih ) +! write (*,*) 'out',ih +10 CONTINUE +IF ( x2a(k) /= xg ) THEN +! write (*,*) 'error bi-cubic-spline',k,x2a(k),xg +! DO k=1,NDFT +! write (*,*) k,x2a(k) +! ENDDO +! stop +END IF + + + +y(1) = ya(ih,k) +y(2) = ya(ih+1,k) +y(3) = ya(ih+1,k+1) +y(4) = ya(ih,k+1) + +y1(1) = y1a(ih,k) +y1(2) = y1a(ih+1,k) +y1(3) = y1a(ih+1,k+1) +y1(4) = y1a(ih,k+1) + +y2(1) = y2a(ih,k) +y2(2) = y2a(ih+1,k) +y2(3) = y2a(ih+1,k+1) +y2(4) = y2a(ih,k+1) + +y12(1) = y12a(ih,k) +y12(2) = y12a(ih+1,k) +y12(3) = y12a(ih+1,k+1) +y12(4) = y12a(ih,k+1) + +x1l = x1a(ih) +x1u = x1a(ih+1) +x2l = x2a(k) +x2u = x2a(k+1) + +DO m = 1, 4 + DO n = 1, 4 + c(m,n) = c_bicub( ih, k, m, n ) + END DO +END DO +CALL bcuint ( x1l, x1u, x2l, x2u, rho_rdf, xg, c, rdf, dg_drho, dg_dr ) + +END SUBROUTINE BI_CUB_SPLINE + +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! SUBROUTINE hunt +! +! Given an array xx(1:n), and given a value x, returns a value jlo +! such that x is between xx(jlo) and xx(jlo+1). xx(1:n) must be +! monotonic, either increasing or decreasing. jlo=0 or jlo=n is +! returned to indicate that x is out of range. jlo on input is taken +! as the initial guess for jlo on output. +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! + SUBROUTINE hunt ( xx, n, x, jlo ) +! + IMPLICIT NONE +! +! ---------------------------------------------------------------------- + INTEGER, INTENT(IN) :: n + INTEGER, INTENT(OUT) :: jlo + REAL, INTENT(IN) :: xx(n) + REAL :: x +! +! ---------------------------------------------------------------------- + INTEGER :: inc,jhi,jm + LOGICAL :: ascnd +! ---------------------------------------------------------------------- + +ascnd = xx(n) >= xx(1) +IF( jlo <= 0 .OR. jlo > n ) THEN + jlo = 0 + jhi = n + 1 + GO TO 3 +END IF +inc = 1 +IF( x >= xx(jlo) .EQV. ascnd ) THEN +1 jhi = jlo + inc + IF ( jhi > n ) THEN + jhi = n + 1 + ELSE IF ( x >= xx(jhi) .EQV. ascnd ) THEN + jlo = jhi + inc = inc + inc + GO TO 1 + END IF +ELSE + jhi = jlo +2 jlo = jhi - inc + IF ( jlo < 1 ) THEN + jlo = 0 + ELSE IF ( x < xx(jlo) .EQV. ascnd ) THEN + jhi = jlo + inc = inc + inc + GO TO 2 + END IF +END IF +3 IF (jhi-jlo == 1 ) THEN + IF ( x == xx(n)) jlo = n - 1 + IF ( x == xx(1) ) jlo = 1 + RETURN +END IF +jm = ( jhi + jlo ) / 2 +IF ( x >= xx(jm) .EQV. ascnd ) THEN + jlo = jm +ELSE + jhi = jm +END IF +GO TO 3 +END SUBROUTINE hunt + + + +!********************************************************************** +! +!********************************************************************** +! + !SUBROUTINE bcuint ( y, y1, y2, y12, x1l, x1u, x2l, x2u, x1, x2, c, ansy, ansy1, ansy2 ) + SUBROUTINE bcuint ( x1l, x1u, x2l, x2u, x1, x2, c, ansy, ansy1, ansy2 ) +! + IMPLICIT NONE +! +! ---------------------------------------------------------------------- + !REAL, INTENT(IN OUT) :: y(4) + !REAL, INTENT(IN OUT) :: y1(4) + !REAL, INTENT(IN OUT) :: y2(4) + !REAL, INTENT(IN OUT) :: y12(4) + REAL, INTENT(IN OUT) :: x1l + REAL, INTENT(IN OUT) :: x1u + REAL, INTENT(IN OUT) :: x2l + REAL, INTENT(IN OUT) :: x2u + REAL, INTENT(IN OUT) :: x1 + REAL, INTENT(IN OUT) :: x2 + REAL, INTENT(IN) :: c(4,4) + REAL, INTENT(OUT) :: ansy + REAL, INTENT(OUT) :: ansy1 + REAL, INTENT(OUT) :: ansy2 +! +! ---------------------------------------------------------------------- + !U USES bcucof + INTEGER :: i + REAL :: t, u +! ---------------------------------------------------------------------- + +! call bcucof ( y, y1, y2, y12, x1u-x1l, x2u-x2l, c ) + +IF ( x1u == x1l .OR. x2u == x2l ) PAUSE 'bad input in bcuint' +t = (x1-x1l) / (x1u-x1l) +u = (x2-x2l) / (x2u-x2l) +ansy = 0.0 +ansy2 = 0.0 +ansy1 = 0.0 +DO i = 4, 1, -1 + ansy = t *ansy + ( (c(i,4)*u + c(i,3))*u+c(i,2) )*u + c(i,1) + ansy2 = t *ansy2 + ( 3.*c(i,4)*u+2.*c(i,3) )*u + c(i,2) + ansy1 = u *ansy1 + ( 3.*c(4,i)*t+2.*c(3,i) )*t + c(2,i) +END DO +ansy1 = ansy1 / (x1u-x1l) +ansy2 = ansy2 / (x2u-x2l) + +END SUBROUTINE bcuint + + +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! SUBROUTINE spline +! +! Given arrays x(1:n) and y(1:n) containing a tabulated function, +! i.e., yi = f(xi), with x1 < x2 < .. . < xN, and given values yp1 and +! ypn for the first derivative of the interpolating function at points 1 +! and n, respectively, this routine returns an array y2(1:n) of length n +! which contains the second derivatives of the interpolating function at +! the tabulated points xi. If yp1 and/or ypn are equal to 1 1030 or +! larger, the routine is signaled to set the corresponding boundary +! condition for a natural spline, with zero second derivative on that +! boundary. +! Parameter: NMAX is the largest anticipated value of n. +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! + SUBROUTINE spline ( x, y, n, yp1, ypn, y2 ) +! + IMPLICIT NONE +! +! ---------------------------------------------------------------------- + INTEGER, INTENT(IN) :: n + REAL, INTENT(IN) :: x(n) + REAL, INTENT(IN) :: y(n) + REAL, INTENT(IN) :: yp1 + REAL, INTENT(IN) :: ypn + REAL, INTENT(OUT) :: y2(n) +! +! ---------------------------------------------------------------------- + INTEGER, PARAMETER :: NMAX = 500 + INTEGER :: i, k + REAL :: p, qn, sig, un, u(NMAX) +! ---------------------------------------------------------------------- + + IF ( yp1 > 0.99E30 ) THEN + y2(1) = 0.0 + u(1) = 0.0 + ELSE + y2(1) = -0.5 + u(1) = ( 3.0/(x(2)-x(1)) ) * ( (y(2)-y(1))/(x(2)-x(1))-yp1 ) + END IF + DO i = 2, n-1 + IF ( (x(i+1)-x(i)) == 0.0 .OR. (x(i)-x(i-1)) == 0.0 .OR. (x(i+1)-x(i-1)) == 0.0 ) THEN + write (*,*) 'error in spline-interpolation' + stop + END IF + sig = (x(i)-x(i-1)) / (x(i+1)-x(i-1)) + p = sig*y2(i-1) + 2.0 + y2(i) = (sig-1.0) / p + u(i) = ( 6.0 * ((y(i+1)-y(i))/(x(i+1)-x(i))-(y(i)-y(i-1))/(x(i)-x(i-1))) / (x(i+1)-x(i-1)) & + - sig * u(i-1) ) / p + END DO + IF ( ypn > 0.99E30 ) THEN + qn = 0.0 + un = 0.0 + ELSE + qn = 0.5 + un = (3.0/(x(n)-x(n-1))) * (ypn-(y(n)-y(n-1))/(x(n)-x(n-1))) + END IF + y2(n) = (un-qn*u(n-1)) / (qn*y2(n-1)+1.0) + DO k = n-1, 1, -1 + y2(k) = y2(k) * y2(k+1) + u(k) + END DO + +END SUBROUTINE spline + +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! SUBROUTINE splint_integral +! +! Given the arrays xa(1:n) and ya(1:n) of length n, which tabulate a +! function (with the in order), and given the array y2a(1:n), which is +! the output from spline above, and given a value of x, this routine +! returns a cubic-spline interpolated value y. +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! + SUBROUTINE splint_integral ( xa, ya, y2a, n, xlo, xhi, integral ) +! + IMPLICIT NONE +! +! ---------------------------------------------------------------------- + INTEGER, INTENT(IN) :: n + REAL, INTENT(IN) :: xa(n) + REAL, INTENT(IN) :: ya(n) + REAL, INTENT(IN) :: y2a(n) + REAL, INTENT(IN) :: xlo + REAL, INTENT(IN) :: xhi + REAL, INTENT(OUT) :: integral +! +! ---------------------------------------------------------------------- + INTEGER :: k, khi_l, klo_l, khi_h, klo_h + REAL :: xl, xh, h, INT, x0, x1, y0, y1, y20, y21 +! ---------------------------------------------------------------------- + + integral = 0.0 + klo_l = 1 + khi_l = n +1 IF ( khi_l-klo_l > 1 ) THEN + k = ( khi_l + klo_l ) / 2 + IF ( xa(k) > xlo ) THEN + khi_l = k + ELSE + klo_l = k + END IF + GO TO 1 + END IF + + klo_h = 1 + khi_h = n +2 IF ( khi_h-klo_h > 1 ) THEN + k = ( khi_h + klo_h ) / 2 + IF ( xa(k) > xhi ) THEN + khi_h = k + ELSE + klo_h = k + END IF + GO TO 2 + END IF + + ! integration in spline pieces, the lower interval, bracketed + ! by xa(klo_L) and xa(khi_L) is in steps shifted upward. + + ! first: determine upper integration bound + xl = xlo +3 CONTINUE + IF ( khi_h > khi_l ) THEN + xh = xa(khi_l) + ELSE IF ( khi_h == khi_l ) THEN + xh = xhi + ELSE + WRITE (*,*) 'error in spline-integration' + PAUSE + END IF + + h = xa(khi_l) - xa(klo_l) + IF ( h == 0.0 ) PAUSE 'bad xa input in splint' + x0 = xa(klo_l) + x1 = xa(khi_l) + y0 = ya(klo_l) + y1 = ya(khi_l) + y20= y2a(klo_l) + y21= y2a(khi_l) + ! int = -xL/h * ( (x1-.5*xL)*y0 + (0.5*xL-x0)*y1 & + ! +y20/6.*(x1**3-1.5*xL*x1*x1+xL*xL*x1-.25*xL**3) & + ! -y20/6.*h*h*(x1-.5*xL) & + ! +y21/6.*(.25*xL**3-xL*xL*x0+1.5*xL*x0*x0-x0**3) & + ! -y21/6.*h*h*(.5*xL-x0) ) + ! int = int + xH/h * ( (x1-.5*xH)*y0 + (0.5*xH-x0)*y1 & + ! +y20/6.*(x1**3-1.5*xH*x1*x1+xH*xH*x1-.25*xH**3) & + ! -y20/6.*h*h*(x1-.5*xH) & + ! +y21/6.*(.25*xH**3-xH*xH*x0+1.5*xH*x0*x0-x0**3) & + ! -y21/6.*h*h*(.5*xH-x0) ) + INT = -1.0/h * ( xl*((x1-.5*xl)*y0 + (0.5*xl-x0)*y1) & + -y20/24.*(x1-xl)**4 + y20/6.*(0.5*xl*xl-x1*xl)*h*h & + +y21/24.*(xl-x0)**4 - y21/6.*(0.5*xl*xl-x0*xl)*h*h ) + INT = INT + 1.0/h * ( xh*((x1-.5*xh)*y0 + (0.5*xh-x0)*y1) & + -y20/24.*(x1-xh)**4 + y20/6.*(0.5*xh*xh-x1*xh)*h*h & + +y21/24.*(xh-x0)**4 - y21/6.*(0.5*xh*xh-x0*xh)*h*h ) + + integral = integral + INT + ! write (*,*) integral,x1,xH + klo_l = klo_l + 1 + khi_l = khi_l + 1 + xl = x1 + IF (khi_h /= (khi_l-1)) GO TO 3 ! the -1 in (khi_L-1) because khi_L was already counted up + +END SUBROUTINE splint_integral + + + + +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! + REAL FUNCTION praxis( t0, machep, h0, n, prin, x, f, fmin ) + + IMPLICIT NONE + +! ---------------------------------------------------------------------- + REAL, INTENT(IN OUT) :: t0 + REAL, INTENT(IN) :: machep + REAL, INTENT(IN) :: h0 + INTEGER :: n + INTEGER, INTENT(IN OUT) :: prin + REAL, INTENT(IN OUT) :: x(n) + REAL :: f + REAL, INTENT(IN OUT) :: fmin +! ---------------------------------------------------------------------- + +EXTERNAL f + +! PRAXIS RETURNS THE MINIMUM OF THE FUNCTION F(X,N) OF N VARIABLES +! USING THE PRINCIPAL AXIS METHOD. THE GRADIENT OF THE FUNCTION IS +! NOT REQUIRED. + +! FOR A DESCRIPTION OF THE ALGORITHM, SEE CHAPTER SEVEN OF +! "ALGORITHMS FOR FINDING ZEROS AND EXTREMA OF FUNCTIONS WITHOUT +! CALCULATING DERIVATIVES" BY RICHARD P BRENT. + +! THE PARAMETERS ARE: +! T0 IS A TOLERANCE. PRAXIS ATTEMPTS TO RETURN PRAXIS=F(X) +! SUCH THAT IF X0 IS THE TRUE LOCAL MINIMUM NEAR X, THEN +! NORM(X-X0) < T0 + SQUAREROOT(MACHEP)*NORM(X). +! MACHEP IS THE MACHINE PRECISION, THE SMALLEST NUMBER SUCH THAT +! 1 + MACHEP > 1. MACHEP SHOULD BE 16.**-13 (ABOUT +! 2.22D-16) FOR REAL*8 ARITHMETIC ON THE IBM 360. +! H0 IS THE MAXIMUM STEP SIZE. H0 SHOULD BE SET TO ABOUT THE +! MAXIMUM DISTANCE FROM THE INITIAL GUESS TO THE MINIMUM. +! (IF H0 IS SET TOO LARGE OR TOO SMALL, THE INITIAL RATE OF +! CONVERGENCE MAY BE SLOW.) +! N (AT LEAST TWO) IS THE NUMBER OF VARIABLES UPON WHICH +! THE FUNCTION DEPENDS. +! PRIN CONTROLS THE PRINTING OF INTERMEDIATE RESULTS. +! IF PRIN=0, NOTHING IS PRINTED. +! IF PRIN=1, F IS PRINTED AFTER EVERY N+1 OR N+2 LINEAR +! MINIMIZATIONS. FINAL X IS PRINTED, BUT INTERMEDIATE X IS +! PRINTED ONLY IF N IS AT MOST 4. +! IF PRIN=2, THE SCALE FACTORS AND THE PRINCIPAL VALUES OF +! THE APPROXIMATING QUADRATIC FORM ARE ALSO PRINTED. +! IF PRIN=3, X IS ALSO PRINTED AFTER EVERY FEW LINEAR +! MINIMIZATIONS. +! IF PRIN=4, THE PRINCIPAL VECTORS OF THE APPROXIMATING +! QUADRATIC FORM ARE ALSO PRINTED. +! X IS AN ARRAY CONTAINING ON ENTRY A GUESS OF THE POINT OF +! MINIMUM, ON RETURN THE ESTIMATED POINT OF MINIMUM. +! F(X,N) IS THE FUNCTION TO BE MINIMIZED. F SHOULD BE A REAL*8 +! FUNCTION DECLARED EXTERNAL IN THE CALLING PROGRAM. +! FMIN IS AN ESTIMATE OF THE MINIMUM, USED ONLY IN PRINTING +! INTERMEDIATE RESULTS. +! THE APPROXIMATING QUADRATIC FORM IS +! Q(X') = F(X,N) + (1/2) * (X'-X)-TRANSPOSE * A * (X'-X) +! WHERE X IS THE BEST ESTIMATE OF THE MINIMUM AND A IS +! INVERSE(V-TRANSPOSE) * D * INVERSE(V) +! (V(*,*) IS THE MATRIX OF SEARCH DIRECTIONS; D(*) IS THE ARRAY +! OF SECOND DIFFERENCES). IF F HAS CONTINUOUS SECOND DERIVATIVES +! NEAR X0, A WILL TEND TO THE HESSIAN OF F AT X0 AS X APPROACHES X0. + +! IT IS ASSUMED THAT ON FLOATING-POINT UNDERFLOW THE RESULT IS SET +! TO ZERO. +! THE USER SHOULD OBSERVE THE COMMENT ON HEURISTIC NUMBERS AFTER +! THE INITIALIZATION OF MACHINE DEPENDENT NUMBERS. + + LOGICAL :: illc + INTEGER :: nl,nf,kl,kt,ktm,idim,i,j,k,k2,km1,klmk,ii,im1 + REAL :: s,sl,dn,dmin,fx,f1,lds,ldt,t,h,sf,df,qf1,qd0, qd1,qa,qb,qc + REAL :: m2,m4,small,vsmall,large,vlarge,scbd,ldfac,t2, dni,value + REAL :: random + +!.....IF N>20 OR IF N<20 AND YOU NEED MORE SPACE, CHANGE '20' TO THE +! LARGEST VALUE OF N IN THE NEXT CARD, IN THE CARD 'IDIM=20', AND +! IN THE DIMENSION STATEMENTS IN SUBROUTINES MINFIT,MIN,FLIN,QUAD. + + REAL :: d(20),y(20),z(20),q0(20),q1(20),v(20,20) + COMMON /global/ fx,ldt,dmin,nf,nl /q/ v,q0,q1,qa,qb,qc,qd0,qd1,qf1 + +! --------------------------------- +! introduced by Joachim........ + idim = n +! --------------------------------- + + + +!.....INITIALIZATION..... +! MACHINE DEPENDENT NUMBERS: + +small = machep*machep +vsmall = small*small +large = 1.d0/small +vlarge = 1.d0/vsmall +m2 = SQRT(machep) +m4 = SQRT(m2) + +! HEURISTIC NUMBERS: +! IF THE AXES MAY BE BADLY SCALED (WHICH IS TO BE AVOIDED IF +! POSSIBLE), THEN SET SCBD=10. OTHERWISE SET SCBD=1. +! IF THE PROBLEM IS KNOWN TO BE ILL-CONDITIONED, SET ILLC=TRUE. +! OTHERWISE SET ILLC=FALSE. +! KTM IS THE NUMBER OF ITERATIONS WITHOUT IMPROVEMENT BEFORE THE +! ALGORITHM TERMINATES. KTM=4 IS VERY CAUTIOUS; USUALLY KTM=1 +! IS SATISFACTORY. + +scbd = 1.0 +illc = .false. +ktm = 1 + +ldfac = 0.01 +IF (illc) ldfac = 0.1 +kt = 0 +nl = 0 +nf = 1 +fx = f(x,n) +qf1 = fx +t = small+ABS(t0) +t2 = t +dmin = small +h = h0 +IF (h < 100*t) h = 100*t +ldt = h +!.....THE FIRST SET OF SEARCH DIRECTIONS V IS THE IDENTITY MATRIX..... +DO i = 1,n + DO j = 1,n + v(i,j) = 0.0 + END DO + v(i,i) = 1.0 +END DO +d(1) = 0.0 +qd0 = 0.0 +DO i = 1,n + q0(i) = x(i) + q1(i) = x(i) +END DO +IF (prin > 0) CALL PRINT(n,x,prin,fmin) + +!.....THE MAIN LOOP STARTS HERE..... +40 sf=d(1) +d(1)=0.d0 +s=0.d0 + +!.....MINIMIZE ALONG THE FIRST DIRECTION V(*,1). +! FX MUST BE PASSED TO MIN BY VALUE. +value=fx +CALL MIN(n,1,2,d(1),s,value,.false.,f,x,t,machep,h) +IF (s > 0.d0) GO TO 50 +DO i=1,n + v(i,1)=-v(i,1) +END DO +50 IF (sf > 0.9D0*d(1).AND.0.9D0*sf < d(1)) GO TO 70 +DO i=2,n + d(i)=0.d0 +END DO + +!.....THE INNER LOOP STARTS HERE..... +70 DO k=2,n + DO i=1,n + y(i)=x(i) + END DO + sf=fx + IF (kt > 0) illc=.true. + 80 kl=k + df=0.d0 + +!.....A RANDOM STEP FOLLOWS (TO AVOID RESOLUTION VALLEYS). +! PRAXIS ASSUMES THAT RANDOM RETURNS A RANDOM NUMBER UNIFORMLY +! DISTRIBUTED IN (0,1). + + IF(.NOT.illc) GO TO 95 + DO i=1,n + s=(0.1D0*ldt+t2*(10**kt))*(random(n)-0.5D0) + z(i)=s + DO j=1,n + x(j)=x(j)+s*v(j,i) + END DO + END DO + fx=f(x,n) + nf=nf+1 + +!.....MINIMIZE ALONG THE "NON-CONJUGATE" DIRECTIONS V(*,K),...,V(*,N) + + 95 DO k2=k,n + sl=fx + s=0.d0 + value=fx + CALL MIN(n,k2,2,d(k2),s,value,.false.,f,x,t,machep,h) + IF (illc) GO TO 97 + s=sl-fx + GO TO 99 + 97 s=d(k2)*((s+z(k2))**2) + 99 IF (df > s) CYCLE + df=s + kl=k2 + END DO + IF (illc.OR.(df >= ABS((100*machep)*fx))) GO TO 110 + +!.....IF THERE WAS NOT MUCH IMPROVEMENT ON THE FIRST TRY, SET +! ILLC=TRUE AND START THE INNER LOOP AGAIN..... + + illc=.true. + GO TO 80 + 110 IF (k == 2.AND.prin > 1) CALL vcprnt(1,d,n) + +!.....MINIMIZE ALONG THE "CONJUGATE" DIRECTIONS V(*,1),...,V(*,K-1) + + km1=k-1 + DO k2=1,km1 + s=0 + value=fx + CALL MIN(n,k2,2,d(k2),s,value,.false.,f,x,t,machep,h) + END DO + f1=fx + fx=sf + lds=0 + DO i=1,n + sl=x(i) + x(i)=y(i) + sl=sl-y(i) + y(i)=sl + lds=lds+sl*sl + END DO + lds=SQRT(lds) + IF (lds <= small) GO TO 160 + +!.....DISCARD DIRECTION V(*,KL). +! IF NO RANDOM STEP WAS TAKEN, V(*,KL) IS THE "NON-CONJUGATE" +! DIRECTION ALONG WHICH THE GREATEST IMPROVEMENT WAS MADE..... + + klmk=kl-k + IF (klmk < 1) GO TO 141 + DO ii=1,klmk + i=kl-ii + DO j=1,n + v(j,i+1)=v(j,i) + END DO + d(i+1)=d(i) + END DO + 141 d(k)=0 + DO i=1,n + v(i,k)=y(i)/lds + END DO + +!.....MINIMIZE ALONG THE NEW "CONJUGATE" DIRECTION V(*,K), WHICH IS +! THE NORMALIZED VECTOR: (NEW X) - (0LD X)..... + + value=f1 + CALL MIN(n,k,4,d(k),lds,value,.true.,f,x,t,machep,h) + IF (lds > 0.d0) GO TO 160 + lds=-lds + DO i=1,n + v(i,k)=-v(i,k) + END DO + 160 ldt=ldfac*ldt + IF (ldt < lds) ldt=lds + IF (prin > 0) CALL PRINT(n,x,prin,fmin) + t2=0.d0 + DO i=1,n + t2=t2+x(i)**2 + END DO + t2=m2*SQRT(t2)+t + +!.....SEE WHETHER THE LENGTH OF THE STEP TAKEN SINCE STARTING THE +! INNER LOOP EXCEEDS HALF THE TOLERANCE..... + + IF (ldt > (0.5*t2)) kt=-1 + kt=kt+1 + IF (kt > ktm) GO TO 400 +END DO +!.....THE INNER LOOP ENDS HERE. + +! TRY QUADRATIC EXTRAPOLATION IN CASE WE ARE IN A CURVED VALLEY. + +CALL quad(n,f,x,t,machep,h) +dn=0.d0 +DO i=1,n + d(i)=1.d0/SQRT(d(i)) + IF (dn < d(i)) dn=d(i) +END DO +IF (prin > 3) CALL maprnt(1,v,idim,n) +DO j=1,n + s=d(j)/dn + DO i=1,n + v(i,j)=s*v(i,j) + END DO +END DO + +!.....SCALE THE AXES TO TRY TO REDUCE THE CONDITION NUMBER..... + +IF (scbd <= 1.d0) GO TO 200 +s=vlarge +DO i=1,n + sl=0.d0 + DO j=1,n + sl=sl+v(i,j)*v(i,j) + END DO + z(i)=SQRT(sl) + IF (z(i) < m4) z(i)=m4 + IF (s > z(i)) s=z(i) +END DO +DO i=1,n + sl=s/z(i) + z(i)=1.d0/sl + IF (z(i) <= scbd) GO TO 189 + sl=1.d0/scbd + z(i)=scbd + 189 DO j=1,n + v(i,j)=sl*v(i,j) + END DO +END DO + +!.....CALCULATE A NEW SET OF ORTHOGONAL DIRECTIONS BEFORE REPEATING +! THE MAIN LOOP. +! FIRST TRANSPOSE V FOR MINFIT: + +200 DO i=2,n + im1=i-1 + DO j=1,im1 + s=v(i,j) + v(i,j)=v(j,i) + v(j,i)=s + END DO +END DO + +!.....CALL MINFIT TO FIND THE SINGULAR VALUE DECOMPOSITION OF V. +! THIS GIVES THE PRINCIPAL VALUES AND PRINCIPAL DIRECTIONS OF THE +! APPROXIMATING QUADRATIC FORM WITHOUT SQUARING THE CONDITION +! NUMBER..... + +CALL minfit(idim,n,machep,vsmall,v,d) + +!.....UNSCALE THE AXES..... + +IF (scbd <= 1.d0) GO TO 250 +DO i=1,n + s=z(i) + DO j=1,n + v(i,j)=s*v(i,j) + END DO +END DO +DO i=1,n + s=0.d0 + DO j=1,n + s=s+v(j,i)**2 + END DO + s=SQRT(s) + d(i)=s*d(i) + s=1/s + DO j=1,n + v(j,i)=s*v(j,i) + END DO +END DO + +250 DO i=1,n + dni=dn*d(i) + IF (dni > large) GO TO 265 + IF (dni < small) GO TO 260 + d(i)=1/(dni*dni) + CYCLE + 260 d(i)=vlarge + CYCLE + 265 d(i)=vsmall +END DO + +!.....SORT THE EIGENVALUES AND EIGENVECTORS..... + +CALL sort(idim,n,d,v) +dmin=d(n) +IF (dmin < small) dmin=small +illc=.false. +IF (m2*d(1) > dmin) illc=.true. +IF (prin > 1.AND.scbd > 1.d0) CALL vcprnt(2,z,n) +IF (prin > 1) CALL vcprnt(3,d,n) +IF (prin > 3) CALL maprnt(2,v,idim,n) +!.....THE MAIN LOOP ENDS HERE..... + +GO TO 40 + +!.....RETURN..... + +400 IF (prin > 0) CALL vcprnt(4,x,n) +praxis=fx + +END FUNCTION praxis + + +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! + SUBROUTINE minfit(m,n,machep,tol,ab,q) + + IMPLICIT NONE + + INTEGER, INTENT(IN OUT) :: m + INTEGER, INTENT(IN) :: n + REAL, INTENT(IN) :: machep + REAL, INTENT(IN OUT) :: tol + REAL, INTENT(IN OUT) :: ab(m,n) + REAL, INTENT(OUT) :: q(n) + INTEGER :: i,j,k,l, kk,kt,l2,ll2,ii,lp1 +! IMPLICIT REAL (A-H,O-Z) + + +REAL :: x,eps,e(20),g,s, f,h,y,c,z,temp +!...AN IMPROVED VERSION OF MINFIT (SEE GOLUB AND REINSCH, 1969) +! RESTRICTED TO M=N,P=0. +! THE SINGULAR VALUES OF THE ARRAY AB ARE RETURNED IN Q AND AB IS +! OVERWRITTEN WITH THE ORTHOGONAL MATRIX V SUCH THAT U.DIAG(Q) = AB.V, +! WHERE U IS ANOTHER ORTHOGONAL MATRIX. + +!...HOUSEHOLDER'S REDUCTION TO BIDIAGONAL FORM... +IF (n == 1) GO TO 200 +eps = machep +g = 0.d0 +x = 0.d0 +DO i=1,n + e(i) = g + s = 0.d0 + l = i + 1 + DO j=i,n + s = s + ab(j,i)**2 + END DO + g = 0.d0 + IF (s < tol) GO TO 4 + f = ab(i,i) + g = SQRT(s) + IF (f >= 0.d0) g = -g + h = f*g - s + ab(i,i)=f-g + IF (l > n) GO TO 4 + DO j=l,n + f = 0.d0 + DO k=i,n + f = f + ab(k,i)*ab(k,j) + END DO + f = f/h + DO k=i,n + ab(k,j) = ab(k,j) + f*ab(k,i) + END DO + END DO + 4 q(i) = g + s = 0.d0 + IF (i == n) GO TO 6 + DO j=l,n + s = s + ab(i,j)*ab(i,j) + END DO + 6 g = 0.d0 + IF (s < tol) GO TO 10 + IF (i == n) GO TO 16 + f = ab(i,i+1) + 16 g = SQRT(s) + IF (f >= 0.d0) g = -g + h = f*g - s + IF (i == n) GO TO 10 + ab(i,i+1) = f - g + DO j=l,n + e(j) = ab(i,j)/h + END DO + DO j=l,n + s = 0.d0 + DO k=l,n + s = s + ab(j,k)*ab(i,k) + END DO + DO k=l,n + ab(j,k) = ab(j,k) + s*e(k) + END DO + END DO + 10 y = ABS(q(i)) + ABS(e(i)) + IF (y > x) x = y +END DO +!...ACCUMULATION OF RIGHT-HAND TRANSFORMATIONS... +ab(n,n) = 1.d0 +g = e(n) +l = n +DO ii=2,n + i = n - ii + 1 + IF (g == 0.d0) GO TO 23 + h = ab(i,i+1)*g + DO j=l,n + ab(j,i) = ab(i,j)/h + END DO + DO j=l,n + s = 0.d0 + DO k=l,n + s = s + ab(i,k)*ab(k,j) + END DO + DO k=l,n + ab(k,j) = ab(k,j) + s*ab(k,i) + END DO + END DO + 23 DO j=l,n + ab(i,j) = 0.d0 + ab(j,i) = 0.d0 + END DO + ab(i,i) = 1.d0 + g = e(i) + l = i +END DO +!...DIAGONALIZATION OF THE BIDIAGONAL FORM... +eps = eps*x +DO kk=1,n + k = n - kk + 1 + kt = 0 + 101 kt = kt + 1 + IF (kt <= 30) GO TO 102 + e(k) = 0.d0 + WRITE (6,1000) + 1000 FORMAT (' QR FAILED') + 102 DO ll2=1,k + l2 = k - ll2 + 1 + l = l2 + IF (ABS(e(l)) <= eps) GO TO 120 + IF (l == 1) CYCLE + IF (ABS(q(l-1)) <= eps) EXIT + END DO +!...CANCELLATION OF E(L) IF L>1... + c = 0.d0 + s = 1.d0 + DO i=l,k + f = s*e(i) + e(i) = c*e(i) + IF (ABS(f) <= eps) GO TO 120 + g = q(i) +!...Q(I) = H = SQRT(G*G + F*F)... + IF (ABS(f) < ABS(g)) GO TO 113 + IF (f == 0.0) THEN + GO TO 111 + ELSE + GO TO 112 + END IF + 111 h = 0.d0 + GO TO 114 + 112 h = ABS(f)*SQRT(1 + (g/f)**2) + GO TO 114 + 113 h = ABS(g)*SQRT(1 + (f/g)**2) + 114 q(i) = h + IF (h /= 0.d0) GO TO 115 + g = 1.d0 + h = 1.d0 + 115 c = g/h + s = -f/h + END DO +!...TEST FOR CONVERGENCE... + 120 z = q(k) + IF (l == k) GO TO 140 +!...SHIFT FROM BOTTOM 2*2 MINOR... + x = q(l) + y = q(k-1) + g = e(k-1) + h = e(k) + f = ((y - z)*(y + z) + (g - h)*(g + h))/(2*h*y) + g = SQRT(f*f + 1.0D0) + temp = f - g + IF (f >= 0.d0) temp = f + g + f = ((x - z)*(x + z) + h*(y/temp - h))/x +!...NEXT QR TRANSFORMATION... + c = 1.d0 + s = 1.d0 + lp1 = l + 1 + IF (lp1 > k) GO TO 133 + DO i=lp1,k + g = e(i) + y = q(i) + h = s*g + g = g*c + IF (ABS(f) < ABS(h)) GO TO 123 + IF (f == 0.0) THEN + GO TO 121 + ELSE + GO TO 122 + END IF + 121 z = 0.d0 + GO TO 124 + 122 z = ABS(f)*SQRT(1 + (h/f)**2) + GO TO 124 + 123 z = ABS(h)*SQRT(1 + (f/h)**2) + 124 e(i-1) = z + IF (z /= 0.d0) GO TO 125 + f = 1.d0 + z = 1.d0 + 125 c = f/z + s = h/z + f = x*c + g*s + g = -x*s + g*c + h = y*s + y = y*c + DO j=1,n + x = ab(j,i-1) + z = ab(j,i) + ab(j,i-1) = x*c + z*s + ab(j,i) = -x*s + z*c + END DO + IF (ABS(f) < ABS(h)) GO TO 129 + IF (f == 0.0) THEN + GO TO 127 + ELSE + GO TO 128 + END IF + 127 z = 0.d0 + GO TO 130 + 128 z = ABS(f)*SQRT(1 + (h/f)**2) + GO TO 130 + 129 z = ABS(h)*SQRT(1 + (f/h)**2) + 130 q(i-1) = z + IF (z /= 0.d0) GO TO 131 + f = 1.d0 + z = 1.d0 + 131 c = f/z + s = h/z + f = c*g + s*y + x = -s*g + c*y + END DO + 133 e(l) = 0.d0 + e(k) = f + q(k) = x + GO TO 101 +!...CONVERGENCE: Q(K) IS MADE NON-NEGATIVE... + 140 IF (z >= 0.d0) CYCLE + q(k) = -z + DO j=1,n + ab(j,k) = -ab(j,k) + END DO +END DO +RETURN +200 q(1) = ab(1,1) +ab(1,1) = 1.d0 + +END SUBROUTINE minfit + + + + +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! + SUBROUTINE MIN(n,j,nits,d2,x1,f1,fk,f,x,t,machep,h) + + IMPLICIT NONE + + INTEGER, INTENT(IN) :: n + INTEGER :: j + INTEGER :: nits + REAL, INTENT(IN OUT) :: d2 + REAL, INTENT(IN OUT) :: x1 + REAL, INTENT(IN OUT) :: f1 + LOGICAL :: fk + REAL :: f + REAL, INTENT(IN OUT) :: x(n) + REAL, INTENT(IN) :: t + REAL, INTENT(IN) :: machep + REAL, INTENT(IN) :: h + + INTEGER :: i,k + EXTERNAL f + + + REAL :: flin ! function + REAL :: small,sf1,sx1,s,temp, xm,x2,f2,d1 + REAL :: fm,f0,t2 +!---------------------------------------------- + INTEGER :: nf,nl + REAL :: fx,ldt,dmin + REAL :: v(20,20),q0(20),q1(20),qa,qb,qc,qd0,qd1,qf1 + COMMON /global/ fx,ldt,dmin,nf,nl /q/ v,q0,q1,qa,qb,qc,qd0,qd1,qf1 +!---------------------------------------------- +!...THE SUBROUTINE MIN MINIMIZES F FROM X IN THE DIRECTION V(*,J) UNLESS +! J IS LESS THAN 1, WHEN A QUADRATIC SEARCH IS MADE IN THE PLANE +! DEFINED BY Q0,Q1,X. +! D2 IS EITHER ZERO OR AN APPROXIMATION TO HALF F". +! ON ENTRY, X1 IS AN ESTIMATE OF THE DISTANCE FROM X TO THE MINIMUM +! ALONG V(*,J) (OR, IF J=0, A CURVE). ON RETURN, X1 IS THE DISTANCE +! FOUND. +! IF FK=.TRUE., THEN F1 IS FLIN(X1). OTHERWISE X1 AND F1 ARE IGNORED +! ON ENTRY UNLESS FINAL FX IS GREATER THAN F1. +! NITS CONTROLS THE NUMBER OF TIMES AN ATTEMPT WILL BE MADE TO HALVE +! THE INTERVAL. + LOGICAL :: dz + REAL :: m2,m4 + +small = machep**2 +m2 = SQRT(machep) +m4 = SQRT(m2) +sf1 = f1 +sx1 = x1 +k = 0 +xm = 0.d0 +fm = fx +f0 = fx +dz = d2 < machep +!...FIND THE STEP SIZE... +s = 0.d0 +DO i=1,n + s = s + x(i)**2 +END DO +s = SQRT(s) +temp = d2 +IF (dz) temp = dmin +t2 = m4*SQRT(ABS(fx)/temp + s*ldt) + m2*ldt +s = m4*s + t +IF (dz.AND.t2 > s) t2 = s +t2 = DMAX1(t2,small) +t2 = DMIN1(t2,.01D0*h) +IF (.NOT.fk.OR.f1 > fm) GO TO 2 +xm = x1 +fm = f1 +2 IF (fk.AND.ABS(x1) >= t2) GO TO 3 +temp=1.d0 +IF (x1 < 0.d0) temp=-1.d0 +x1=temp*t2 +f1 = flin(n,j,x1,f,x,nf) +3 IF (f1 > fm) GO TO 4 +xm = x1 +fm = f1 +4 IF (.NOT.dz) GO TO 6 +!...EVALUATE FLIN AT ANOTHER POINT AND ESTIMATE THE SECOND DERIVATIVE... +x2 = -x1 +IF (f0 >= f1) x2 = 2.d0*x1 +f2 = flin(n,j,x2,f,x,nf) +IF (f2 > fm) GO TO 5 +xm = x2 +fm = f2 +5 d2 = (x2*(f1 - f0)-x1*(f2 - f0))/((x1*x2)*(x1 - x2)) +!...ESTIMATE THE FIRST DERIVATIVE AT 0... +6 d1 = (f1 - f0)/x1 - x1*d2 +dz = .true. +!...PREDICT THE MINIMUM... +IF (d2 > small) GO TO 7 +x2 = h +IF (d1 >= 0.d0) x2 = -x2 +GO TO 8 +7 x2 = (-.5D0*d1)/d2 +8 IF (ABS(x2) <= h) GO TO 11 +IF (x2 > 0.0) THEN + GO TO 10 +END IF +x2 = -h +GO TO 11 +10 x2 = h +!...EVALUATE F AT THE PREDICTED MINIMUM... +11 f2 = flin(n,j,x2,f,x,nf) +IF (k >= nits.OR.f2 <= f0) GO TO 12 +!...NO SUCCESS, SO TRY AGAIN... +k = k + 1 +IF (f0 < f1.AND.(x1*x2) > 0.d0) GO TO 4 +x2 = 0.5D0*x2 +GO TO 11 +!...INCREMENT THE ONE-DIMENSIONAL SEARCH COUNTER... +12 nl = nl + 1 +IF (f2 <= fm) GO TO 13 +x2 = xm +GO TO 14 +13 fm = f2 +!...GET A NEW ESTIMATE OF THE SECOND DERIVATIVE... +14 IF (ABS(x2*(x2 - x1)) <= small) GO TO 15 +d2 = (x2*(f1-f0) - x1*(fm-f0))/((x1*x2)*(x1 - x2)) +GO TO 16 +15 IF (k > 0) d2 = 0.d0 +16 IF (d2 <= small) d2 = small +x1 = x2 +fx = fm +IF (sf1 >= fx) GO TO 17 +fx = sf1 +x1 = sx1 +!...UPDATE X FOR LINEAR BUT NOT PARABOLIC SEARCH... +17 IF (j == 0) RETURN +DO i=1,n + x(i) = x(i) + x1*v(i,j) +END DO + +END SUBROUTINE MIN + + +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! + SUBROUTINE vcprnt(option,v,n) + + IMPLICIT NONE + INTEGER :: option + REAL, INTENT(IN OUT) :: v(n) + INTEGER :: n + + INTEGER :: i + +SELECT CASE ( option ) + CASE ( 1) + GO TO 1 + CASE ( 2) + GO TO 2 + CASE ( 3) + GO TO 3 + CASE ( 4) + GO TO 4 +END SELECT + +1 WRITE (6,101) (v(i),i=1,n) +RETURN +2 WRITE (6,102) (v(i),i=1,n) +RETURN +3 WRITE (6,103) (v(i),i=1,n) +RETURN +4 WRITE (6,104) (v(i),i=1,n) +RETURN +101 FORMAT (/' THE SECOND DIFFERENCE ARRAY D(*) IS:'/ (e32.14,4E25.14)) +102 FORMAT (/' THE SCALE FACTORS ARE:'/(e32.14,4E25.14)) +103 FORMAT (/' THE APPROXIMATING QUADR. FORM HAS PRINCIPAL VALUES:'/ & + (e32.14,4E25.14)) +104 FORMAT (/' X IS:',e26.14/(e32.14)) +END SUBROUTINE vcprnt + + +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! + SUBROUTINE PRINT(n,x,prin,fmin) + + IMPLICIT NONE + INTEGER :: n + REAL, INTENT(IN OUT) :: x(n) + INTEGER, INTENT(IN OUT) :: prin + REAL, INTENT(IN OUT) :: fmin + + INTEGER :: i + REAL :: ln +!---------------------------------------------- +INTEGER :: nf,nl +REAL :: fx,ldt,dmin +COMMON /global/ fx,ldt,dmin,nf,nl +!---------------------------------------------- +WRITE (6,101) nl,nf,fx + +IF (fx <= fmin) GO TO 1 +ln = LOG10(fx-fmin) +WRITE (6,102) fmin,ln +GO TO 2 +1 WRITE (6,103) fmin +2 IF (n > 4.AND.prin <= 2) RETURN +WRITE (6,104) (x(i),i=1,n) +RETURN +101 FORMAT (/' AFTER',i6, & + ' LINEAR SEARCHES, THE FUNCTION HAS BEEN EVALUATED',i6, & + ' TIMES. THE SMALLEST VALUE FOUND IS F(X) = ',e21.14) +102 FORMAT (' LOG (F(X)-',e21.14,') = ',e21.14) +103 FORMAT (' LOG (F(X)-',e21.14,') IS UNDEFINED.') +104 FORMAT (' X IS:',e26.14/(e32.14)) +END SUBROUTINE PRINT + + +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! + SUBROUTINE maprnt(option,v,m,n) + + IMPLICIT NONE + INTEGER :: option + REAL, INTENT(IN OUT) :: v(m,n) + INTEGER, INTENT(IN OUT) :: m + INTEGER, INTENT(IN) :: n + INTEGER :: i,j + + INTEGER :: low,upp +!...THE SUBROUTINE MAPRNT PRINTS THE COLUMNS OF THE NXN MATRIX V +! WITH A HEADING AS SPECIFIED BY OPTION. +! M IS THE ROW DIMENSION OF V AS DECLARED IN THE CALLING PROGRAM... +low = 1 +upp = 5 +SELECT CASE ( option ) + CASE ( 1) + GO TO 1 + CASE ( 2) + GO TO 2 +END SELECT +1 WRITE (6,101) +101 FORMAT (/' THE NEW DIRECTIONS ARE:') +GO TO 3 +2 WRITE (6,102) +102 FORMAT (' AND THE PRINCIPAL AXES:') +3 IF (n < upp) upp = n +DO i=1,n + WRITE (6,104) (v(i,j),j=low,upp) +END DO +low = low + 5 +IF (n < low) RETURN +upp = upp + 5 +WRITE (6,103) +GO TO 3 +103 FORMAT (' ') +104 FORMAT (e32.14,4E25.14) +END SUBROUTINE maprnt + + +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! + REAL FUNCTION random(naught) + + IMPLICIT NONE + INTEGER, INTENT(IN OUT) :: naught + + REAL :: ran1,ran3(127),half + INTEGER :: i,j,ran2,q,r + LOGICAL :: init + DATA init/.false./ + SAVE init,ran2,ran1,ran3 + +IF (init) GO TO 3 +r = MOD(naught,8190) + 1 +ran2 = 128 +DO i=1,127 + ran2 = ran2 - 1 + ran1 = -2.d0**55 + DO j=1,7 + r = MOD(1756*r,8191) + q = r/32 + ran1 = (ran1 + q)*(1.0D0/256) + END DO + ran3(ran2) = ran1 +END DO +init = .true. +3 IF (ran2 == 1) ran2 = 128 +ran2 = ran2 - 1 +ran1 = ran1 + ran3(ran2) +half = .5D0 +IF (ran1 >= 0.d0) half = -half +ran1 = ran1 + half +ran3(ran2) = ran1 +random = ran1 + .5D0 + +END FUNCTION random + + + +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! + REAL FUNCTION flin (n,j,l,f,x,nf) + IMPLICIT NONE + + INTEGER, INTENT(IN) :: n + INTEGER, INTENT(IN OUT) :: j + REAL, INTENT(IN) :: l + REAL :: f + REAL, INTENT(IN) :: x(n) + INTEGER, INTENT(OUT) :: nf + + INTEGER :: i + REAL :: t(20) + + EXTERNAL f + +!...FLIN IS THE FUNCTION OF ONE REAL VARIABLE L THAT IS MINIMIZED +! BY THE SUBROUTINE MIN... +!---------------------------------------------- + REAL :: v(20,20),q0(20),q1(20),qa,qb,qc,qd0,qd1,qf1 + COMMON /q/ v,q0,q1,qa,qb,qc,qd0,qd1,qf1 +!---------------------------------------------- +IF (j == 0) GO TO 2 +!...THE SEARCH IS LINEAR... +DO i=1,n + t(i) = x(i) + l*v(i,j) +END DO +GO TO 4 +!...THE SEARCH IS ALONG A PARABOLIC SPACE CURVE... +2 qa = (l*(l - qd1))/(qd0*(qd0 + qd1)) +qb = ((l + qd0)*(qd1 - l))/(qd0*qd1) +qc = (l*(l + qd0))/(qd1*(qd0 + qd1)) +DO i=1,n + t(i) = (qa*q0(i) + qb*x(i)) + qc*q1(i) +END DO +!...THE FUNCTION EVALUATION COUNTER NF IS INCREMENTED... +4 nf = nf + 1 +flin = f(t,n) + +END FUNCTION flin + + +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! + SUBROUTINE sort(m,n,d,v) + IMPLICIT NONE +! + INTEGER, INTENT(IN OUT) :: m + INTEGER, INTENT(IN) :: n + REAL, INTENT(IN OUT) :: d(n) + REAL, INTENT(IN OUT) :: v(m,n) + + INTEGER :: i,j,k,nm1,ip1 + REAL :: s +!...SORTS THE ELEMENTS OF D(N) INTO DESCENDING ORDER AND MOVES THE +! CORRESPONDING COLUMNS OF V(N,N). +! M IS THE ROW DIMENSION OF V AS DECLARED IN THE CALLING PROGRAM. +IF (n == 1) RETURN +nm1 = n - 1 +DO i = 1,nm1 + k=i + s = d(i) + ip1 = i + 1 + DO j = ip1,n + IF (d(j) <= s) CYCLE + k = j + s = d(j) + END DO + IF (k <= i) CYCLE + d(k) = d(i) + d(i) = s + DO j = 1,n + s = v(j,i) + v(j,i) = v(j,k) + v(j,k) = s + END DO +END DO +END SUBROUTINE sort + + +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! + SUBROUTINE quad(n,f,x,t,machep,h) + IMPLICIT NONE + + INTEGER, INTENT(IN) :: n + REAL :: f + REAL, INTENT(IN OUT) :: x(n) + REAL, INTENT(IN OUT) :: t + REAL :: machep + REAL, INTENT(IN OUT) :: h +! IMPLICIT REAL (A-H,O-Z) + EXTERNAL f + +!...QUAD LOOKS FOR THE MINIMUM OF F ALONG A CURVE DEFINED BY Q0,Q1,X... + INTEGER :: i + REAL :: l + REAL :: s,value +!---------------------------------------------- + INTEGER :: nf,nl + REAL :: fx,ldt,dmin + +REAL :: v(20,20),q0(20),q1(20),qa,qb,qc,qd0,qd1,qf1 +COMMON /global/ fx,ldt,dmin,nf,nl /q/ v,q0,q1,qa,qb,qc,qd0,qd1,qf1 +!---------------------------------------------- +s = fx +fx = qf1 +qf1 = s +qd1 = 0.d0 +DO i=1,n + s = x(i) + l = q1(i) + x(i) = l + q1(i) = s + qd1 = qd1 + (s-l)**2 +END DO +qd1 = SQRT(qd1) +l = qd1 +s = 0.d0 +IF (qd0 <= 0.d0 .OR. qd1 <= 0.d0 .OR. nl < 3*n*n) GO TO 2 +value=qf1 +CALL MIN(n,0,2,s,l,value,.true.,f,x,t,machep,h) +qa = (l*(l-qd1))/(qd0*(qd0+qd1)) +qb = ((l+qd0)*(qd1-l))/(qd0*qd1) +qc = (l*(l+qd0))/(qd1*(qd0+qd1)) +GO TO 3 +2 fx = qf1 +qa = 0.d0 +qb = qa +qc = 1.d0 +3 qd0 = qd1 +DO i=1,n + s = q0(i) + q0(i) = x(i) + x(i) = (qa*s + qb*x(i)) + qc*q1(i) +END DO +END SUBROUTINE quad + diff --git a/applications/PUfoam/MoDeNaModels/Solubility/src/VLE_main.f90 b/applications/PUfoam/MoDeNaModels/Solubility/src/VLE_main.f90 new file mode 100644 index 000000000..207513d51 --- /dev/null +++ b/applications/PUfoam/MoDeNaModels/Solubility/src/VLE_main.f90 @@ -0,0 +1,105 @@ +!> This file contains the subroutine which starts the phase equilibrium calculation. +!! It also prints the calculated density to the outputfile "out.txt". + +SUBROUTINE VLE_MIX(rhob,density,chemPot_total,compID) + + USE parameters, ONLY: PI, RGAS, KBOL + USE basic_variables + USE EOS_VARIABLES, ONLY: fres, eta, eta_start, dhs, mseg, uij, sig_ij, rho, x, z3t + USE DFT_MODULE + USE EOS_NUMERICAL_DERIVATIVES + IMPLICIT NONE + + + +!> --------------------------------------------------------------------- +!! Variables +!! --------------------------------------------------------------------- + + !passed + REAL :: chemPot_total(nc) + REAL :: rhob(2,0:nc),density(np) + INTEGER :: compID + + !local + REAL, DIMENSION(nc) :: dhs_star + REAL :: w(np,nc), lnphi(np,nc) + INTEGER :: converg + CHARACTER(LEN=4) :: char_ncomp + REAL :: Henry + INTEGER :: i + CHARACTER (LEN=50) :: filename + + +!> --------------------------------------------------------------------- +!! prepare for phase equilibrium calculation for given T +!! --------------------------------------------------------------------- + + dhs(1:ncomp) = parame(1:ncomp,2) * ( 1.0 - 0.12*EXP( -3.0*parame(1:ncomp,3)/t ) ) ! needed for rdf_matrix + dhs_star(1:ncomp) = dhs(1:ncomp)/parame(1:ncomp,2) + + nphas = 2 ! number of phases + outp = 0 ! output to terminal + + CALL START_VAR (converg) + + IF ( converg /= 1 ) THEN + WRITE (*,*) 'no VLE found' + RETURN + END IF + + ! rhob(phase,0): molecular density + rhob(1,0) = dense(1) / ( PI/6.0* SUM( xi(1,1:ncomp) * parame(1:ncomp,1) * dhs(1:ncomp)**3 ) ) + rhob(2,0) = dense(2) / ( PI/6.0* SUM( xi(2,1:ncomp) * parame(1:ncomp,1) * dhs(1:ncomp)**3 ) ) + ! rhob(phase,i): molecular component density (with i=(1,...ncomp) ) in units (1/A^3) + rhob(1,1:ncomp) = rhob(1,0)*xi(1,1:ncomp) + rhob(2,1:ncomp) = rhob(2,0)*xi(2,1:ncomp) + + ! get density in SI-units (kg/m**3) + CALL SI_DENS ( density, w ) + + ! calculate residual chemical potentials + ensemble_flag = 'tv' ! this flag is for: mu_res=mu_res(T,rho) + densta(1) = dense(1) ! Index 1 is for liquid density (here: packing fraction eta) + densta(2) = dense(2) ! Index 2 is for vapour density (here: packing fraction eta) + CALL fugacity (lnphi) ! calculate fugacities + + +!> --------------------------------------------------------------------- +!! Output results of phase equilibrim calculation +!! --------------------------------------------------------------------- + + WRITE(*,*) '--------------------------------------------------' + WRITE(*,*)'RESULT OF PHASE EQUILIBRIUM CALCULATION' + WRITE (char_ncomp,'(I3)') ncomp + WRITE (*,*) 'T = ',t, 'K, and p =', p/1.E5,' bar' + WRITE(*,*)' ' + WRITE(*,'(t15,4(a12,1x),10x,a)') (compna(i),i=1,ncomp) + !!WRITE(*,'(2x,a,'//char_ncomp//'(g13.6,1x))') 'PHASE I w', (w(1,i),i=1,ncomp) + !!WRITE(*,'(2x,a,'//char_ncomp//'(g13.6,1x))') 'PHASE II w', (w(2,i),i=1,ncomp) + WRITE(*,'(2x,a,'//char_ncomp//'(g13.6,1x))') 'PHASE I x', (EXP(lnx(1,i)),i=1,ncomp) + WRITE(*,'(2x,a,'//char_ncomp//'(g13.6,1x))') 'PHASE II x', (EXP(lnx(2,i)),i=1,ncomp) + WRITE(*,*)' ' + !!WRITE(*,'(2x,a,'//char_ncomp//'(g13.6,1x))') 'PHASE I density', (rhob(1,i),i=1,ncomp) + !! WRITE(*,'(2x,a,'//char_ncomp//'(g13.6,1x))') 'PHASE II density', (rhob(2,i),i=1,ncomp) + !!WRITE(*,*)' ' + WRITE(*,'(2x,a,'//char_ncomp//'(g13.6,1x))') 'PHASE I chemPot', (lnphi(1,i) + LOG(rhob(1,i)),i=1,ncomp) + WRITE(*,'(2x,a,'//char_ncomp//'(g13.6,1x))') 'PHASE II chemPot', (lnphi(2,i) + LOG(rhob(2,i)),i=1,ncomp) + WRITE(*,*)' ' + !!WRITE(*,*)'Phase densities ' + WRITE(*,'(2x,a,2(g13.6,1x))') 'SI-DENSITY [kg/m3] ', density(1),density(2) + !!WRITE(*,'(2x,a,2(g13.6,1x))') 'NUMBER-DENSITY ', rhob(1,0),rhob(2,0) + WRITE(*,*) + + !Calculate Solubility + !output: Henrys law: xi*H(T) = yi * p -> H = yip/xi + Henry = EXP(lnx(2,1))*p /EXP(lnx(1,1)) + + !>write solubility to outputfile "out.txt" + filename='./out.txt' + CALL file_open(filename,78) + write(78,*) Henry / 100000.0 + write(*,*)'Henry coefficient (bar):',Henry / 100000.0 + ! write(*,*)'g_CO2 / g_PU', exp(lnx(1,2)) * mm(2) / (exp(lnx(1,1)) * mm(1)) + +END SUBROUTINE VLE_MIX diff --git a/applications/PUfoam/MoDeNaModels/Solubility/src/VLE_subroutines.f90 b/applications/PUfoam/MoDeNaModels/Solubility/src/VLE_subroutines.f90 new file mode 100644 index 000000000..a35f0130b --- /dev/null +++ b/applications/PUfoam/MoDeNaModels/Solubility/src/VLE_subroutines.f90 @@ -0,0 +1,7161 @@ +!> This file contains the subroutines which perform and control the +!! phase equilibrium calculation. + + + + + +!>WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +!! SUBROUTINE start_var +!! +!! This subroutine generates a converged solution for binary systems +!! or performes a flash calculation for mixtues. This routine is a +!! fairly weak point of the program. +!! +!! IF a polymer is considered, starting values for mole fractions +!! are determined from the SUBROUTINGE POLY_STA_VAR (see below). The +!! polymer needs to be placed as component 1 (first line) in INPUT +!! file. +!! +!! A phase equilib. iteration is started at the end of this routine. +!! If no solution is found (converg=0), the program will stop within +!! this routine. +!! +!! Currently, this routine assumes two-phase equilibrium and derives +!! starting values (xi,density) only for two phases. +!! +!! Prerequisites are: +!! SUBROUTINE INPUT needs to be called prior to this routine, because +!! all pure comp. parameters as well as (T,P,kij) need to be in place. +!! Also, the variable to be iterated "it(i)" and the variables to be +!! calculated through the summation relation "sum_rel(i)" have to be +!! defined. +!!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW + SUBROUTINE start_var(converg) +! + USE BASIC_VARIABLES + USE STARTING_VALUES + IMPLICIT NONE +! +! ---------------------------------------------------------------------- + INTEGER, INTENT(IN OUT) :: converg +! +! ---------------------------------------------------------------------- + INTEGER :: ph, i, k + INTEGER :: ncompsav, n_unkwsav, ph_split + LOGICAL :: lle_check, flashcase, renormalize + REAL :: den1, den2, x_1, x_2 + CHARACTER (LEN=50) :: filename +! ---------------------------------------------------------------------- + +converg = 0 + +! CALL RACHFORD_RICE (converg) +! CALL Heidemann_Khalil + +! ---------------------------------------------------------------------- +! This first condition (eos >= 4) is for LJ models, not for PC-SAFT +! ---------------------------------------------------------------------- + +IF (eos >= 4) THEN + + ncomp = 2 ! set number of components to 2 + n_unkw = ncomp ! number of quantities to be iterated + it(1) = 'x11' ! iteration of mol fraction of comp.1 phase 1 + it(2) = 'x21' ! iteration of mol fraction of comp.1 phase 2 + sum_rel(1) = 'x12' ! summation relation: x12 = 1 - sum(x1j) + sum_rel(2) = 'x22' ! summation relation: x22 = 1 - sum(x2j) + + filename = 'LJ_START_VAL.INC' + CALL file_open(filename,84) + READ (84,*) den1,den2 + READ (84,*) x_1,x_2 + CLOSE (84) + + xi(1,1) = x_1 + xi(2,1) = x_2 + xi(1,2) = 1.0 - xi(1,1) + xi(2,2) = 1.0 - xi(2,1) + lnx(1,1) = LOG(xi(1,1)) + lnx(2,1) = LOG(xi(2,1)) + lnx(1,2) = LOG(xi(1,2)) + lnx(2,2) = LOG(xi(2,2)) + + val_init(1) = den1 + val_init(2) = den2 + val_init(3) = t + val_init(4) = p + DO ph = 1,nphas + DO k = 1,ncomp + val_init(4+k+(ph-1)*ncomp) = LOG(xi(ph,k)) + END DO + END DO + + CALL objective_ctrl (converg) + IF (converg == 1) WRITE (*,*) t, p/1.0E5, xi(1,1), xi(2,1) + IF (converg == 0) WRITE (*,*) ' weak starting values' + + +! ---------------------------------------------------------------------- +! ELSE: PC-SAFT equation of state +! ---------------------------------------------------------------------- + +ELSE + + renormalize = .false. ! for renormalization group theory (RGT) + IF (num == 2) renormalize = .true. + IF (num == 2) num = 0 ! if RGT: initial phase equilibr. is for non-renormalized model + + flashcase = .false. ! .true. when a specific feed conc. xif is given + IF (xif(1) /= 0.0) flashcase = .true. + + lle_check = .true. + +! ---------------------------------------------------------------------- +! IF: non-polymeric system +! ---------------------------------------------------------------------- + IF (mm(1) < 1.0E8) THEN + + DO i=1,ncomp ! setting mole-fractions for the case that + ! anything goes wrong in the coming routines + xi(1,i) = 1.0 / REAL(ncomp) + xi(2,i) = 1.0 / REAL(ncomp) + END DO + + + ! ------------------------------------------------------------------ + ! determine an initial conc. (phase 1) that will phase split + ! ------------------------------------------------------------------ + IF( ncomp == 2 .AND. .NOT.flashcase ) THEN + CALL vle_min( lle_check ) + WRITE(*,*)' INITIAL FEED-COMPOSITION',(xi(1,i), i=1,ncomp),converg + END IF + + ! ------------------------------------------------------------------ + ! perform a phase stability test + ! ------------------------------------------------------------------ + ph_split = 0 + CALL phase_stability ( .false., flashcase, ph_split ) + write (*,*) 'stability analysis I indicates phase-split is:',ph_split + + + ! ------------------------------------------------------------------ + ! determine species i, for which x(i) is calc from summation relation + ! ------------------------------------------------------------------ + CALL select_sum_rel (1,0,1) ! synthax (m,n,o): phase m + ! exclude comp. n + ! assign it(o) and higher + CALL select_sum_rel (2,0,2) ! for ncomp>=3, the quantities + ! to be iterated will be overwritten + + ! ------------------------------------------------------------------ + ! if 2 phases (VLE) + ! ------------------------------------------------------------------ + IF (ph_split == 1) THEN + + ! --- perform tangent plane minimization ------------------------ + CALL tangent_plane + ph_split = 0 + + ! --- determine, for which substance summation relation is used -- + IF (flashcase) THEN + CALL determine_flash_it2 + ELSE + CALL select_sum_rel (1,0,1) + CALL select_sum_rel (2,0,2) + END IF + + ! --- do full phase equilibr. calculation ------------------------ + n_unkw = ncomp ! number of quantities to be iterated + CALL objective_ctrl (converg) + IF (converg == 1 ) write (*,*) ' converged (maybe a VLE)',dense(1),dense(2) + + END IF + + ! ------------------------------------------------------------------ + ! test for LLE + ! ------------------------------------------------------------------ + ph_split = 0 + + IF (lle_check) CALL phase_stability (lle_check,flashcase,ph_split) + IF (lle_check) write (*,*) 'stability analysis II, phase-split is:',ph_split + + + ! ------------------------------------------------------------------ + ! if two phases (LLE) + ! ------------------------------------------------------------------ + IF (ph_split == 1) THEN + + write (*,*) ' LLE-stability test indicates 2 phases (VLE or LLE)' + + ! --- perform tangent plane minimization ------------------------ + IF (flashcase) CALL select_sum_rel (1,0,1) + IF (flashcase) CALL select_sum_rel (2,0,2) + + CALL tangent_plane + + ! --- determine, for which substance summation relation ---------- + IF (flashcase) THEN + CALL determine_flash_it2 + ELSE + CALL select_sum_rel (1,0,1) + CALL select_sum_rel (2,0,2) + END IF + + ! --- do full phase equilibr. calculation ------------------------ + n_unkw = ncomp ! number of quantities to be iterated + val_conv(2) = 0.0 + CALL objective_ctrl (converg) + IF (converg == 1 ) write (*,*) ' converged (maybe an LLE)',dense(1),dense(2) + + END IF + + ! ------------------------------------------------------------------ + ! equilibr. calc. converged: set initial var. for further calc. + ! ------------------------------------------------------------------ + IF (converg == 1) THEN + val_init = val_conv + DO ph = 1,nphas + DO i = 1,ncomp + xi(ph,i) = EXP( val_conv(4+i+(ph-1)*ncomp) ) + END DO + END DO + dense(1:2) = val_conv(1:2) + ELSE + WRITE (*,*) ' NO SOLUTION FOUND FOR THE STARTING VALUES' + STOP + END IF + + + ! --------------------------------------------------------------------- + ! ELSE: for systems with polymers + ! --------------------------------------------------------------------- + + ELSE + + ncompsav = ncomp + ncomp = 2 ! set number of components to 2 + n_unkwsav = n_unkw + + CALL poly_sta_var(converg) + + IF (converg == 1) THEN + val_init = val_conv + ELSE + WRITE (*,*) ' NO SOLUTION FOUND FOR THE STARTING VALUES' + STOP + END IF + + ncomp = ncompsav + n_unkw = n_unkwsav ! number of quantities to be iterated + + END IF + +! --- for RGT: set flag back to num=2 indicating an RGT calculation ---- + IF (renormalize) num = 2 + +END IF + +END SUBROUTINE start_var + + + + +!>WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +!! SUBROUTINE objective_ctrl +!! +!! This subroutine controls the iso-fugacity iteration. It uses +!! the variables defined in the array "val_init". If successfull, +!! the converged values are written to "val_conv", and the flag +!! converg is set to 1. +!! See also above desciption for subroutine PHASE_EQUILIB +!! This routine calls SUBROUTINE HYBRID, which is a solver (modified +!! POWELL HYBRID METHOD). HYBRID is freely available for non-commercial +!! applications. HYBRID requires three definitions: +!! 1.the number of equations to be solved (=No. of variables to be +!! iterated). The appropriate parameter is: "n_unkw" +!! 2.the equations to be iterated, they are here gathered in the SUB- +!! ROUTINE OBJEC_FCT (see below). Since HYBRID is a root finder, +!! these objective functions are iterated to be zero (essentially, +!! OBJEC_FCT contains the iso-fugacity relation. +!! 3.an array of variables is required, containing the quatities to be +!! iterated. This array is termed "y(i)" +!! +!! INPUT VARIABLES: +!! val_init(i) array containing (densities,T,P,lnx's) serving as +!! starting values for the phase equilibrium calculation +!! it(i) contains the information, which variable is deter- +!! mined iteratively. For syntax refer e.g.to SUB BINMIX. +!! sum_rel(i) indicates, which mole fraction is determined from the +!! summation relation sum(xi)=1 +!! +!! OUTPUT VARIABLES: +!! val_conv(i) array containing the converged system variables +!! analogous to "val_init" +!! converg 0 if no convergence achieved, 1 if converged solution +!!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +!! + SUBROUTINE objective_ctrl (converg) +! + USE BASIC_VARIABLES + USE Solve_NonLin + IMPLICIT NONE +! +! ---------------------------------------------------------------------- + INTEGER, INTENT(OUT) :: converg +! +! ---------------------------------------------------------------------- + INTERFACE + SUBROUTINE objec_fct ( iter_no, y, residu, dummy ) + INTEGER, INTENT(IN) :: iter_no + REAL, INTENT(IN) :: y(iter_no) + REAL, INTENT(OUT) :: residu(iter_no) + INTEGER, INTENT(IN OUT) :: dummy + END SUBROUTINE objec_fct + END INTERFACE +! + INTEGER :: info,k,posn,i + INTEGER, PARAMETER :: mxr = nc*(nc+1)/2 + REAL, ALLOCATABLE :: y(:),diag(:),residu(:) + REAL :: x_init, x_solut, r_diff1, r_diff2, totres + REAL :: r_thrash, x_thrash + CHARACTER (LEN=2) :: compon + LOGICAL :: convergence +! ---------------------------------------------------------------------- + +info=1 + +ALLOCATE( y(n_unkw), diag(n_unkw), residu(n_unkw) ) + +IF (num == 0) acc_a = 1.E-7 +IF (num == 0) step_a = 2.E-8 +IF (num == 1) acc_a = 1.E-7 +IF (num == 1) step_a = 2.E-8 +IF (num == 2) acc_a = 5.E-7 +IF (num == 2) step_a = 1.E-7 + +posn = 0 +DO i = 1,n_unkw + posn = posn + 1 + IF (it(i) == 't') y(posn) = val_init(3) + IF (it(i) == 'p') y(posn) = val_init(4) + IF (it(i) == 'lnp') y(posn) = LOG( val_init(4) ) + IF (it(i) == 'fls') y(posn) = alpha + IF (it(i)(1:1) == 'x' .AND. it(i)(2:2) == '1') compon = it(i)(3:3) + IF (it(i)(1:1) == 'x' .AND. it(i)(2:2) == '1') READ(compon,*) k + IF (it(i)(1:1) == 'x' .AND. it(i)(2:2) == '1') y(posn) = val_init(4+k) + IF (it(i)(1:1) == 'x' .AND. it(i)(2:2) == '2') compon = it(i)(3:3) + IF (it(i)(1:1) == 'x' .AND. it(i)(2:2) == '2') READ(compon,*) k + IF (it(i)(1:1) == 'x' .AND. it(i)(2:2) == '2') y(posn) = val_init(4+ncomp+k) + IF (it(i)(1:1) == 'x' .AND. it(i)(2:2) == '3') compon = it(i)(3:3) + IF (it(i)(1:1) == 'x' .AND. it(i)(2:2) == '3') READ(compon,*) k + IF (it(i)(1:1) == 'x' .AND. it(i)(2:2) == '3') y(posn) = val_init(4+ncomp+ncomp+k) +END DO + +CALL init_vars + +x_init = 0.0 +DO i = 1,ncomp + IF (lnx(1,i) /= 0.0 .AND. lnx(2,i) /= 0.0) THEN + x_init = x_init + ABS( 1.0 - lnx(2,i)/lnx(1,i) ) + ELSE + x_init = x_init + ABS( 1.0 - EXP(lnx(2,i))/EXP(lnx(1,i)) ) + END IF +END DO + +CALL hbrd (objec_fct, n_unkw, y, residu, step_a, acc_a, info, diag) + +x_solut = 0.0 +DO i = 1,ncomp + IF ( lnx(1,i) /= 0.0 .AND. lnx(2,i) /= 0.0 ) THEN + x_solut = x_solut + ABS( 1.0 - lnx(2,i)/lnx(1,i) ) + ELSE + IF (lnx(1,i) < 1E300 .AND. lnx(1,i) > -1.E300 ) & + x_solut = x_solut + ABS( 1.0 - EXP(lnx(2,i))/EXP(lnx(1,i)) ) + END IF +END DO +r_diff1 = ABS( 1.0 - dense(1)/dense(2) ) +IF ( val_conv(2) > 0.0 ) THEN + r_diff2 = ABS( 1.0 - val_conv(1)/val_conv(2) ) +ELSE + r_diff2 = 0.0 +END IF + +totres = SUM( ABS( residu(1:n_unkw) ) ) + +r_thrash = 0.0005 +x_thrash = 0.0005 +if (num > 0 ) r_thrash = r_thrash * 10.0 +if (num > 0 ) x_thrash = x_thrash * 100.0 + +convergence = .true. + +IF ( info >= 2 ) convergence = .false. +IF ( ABS( 1.0- dense(1)/dense(2) ) < r_thrash .AND. x_solut < x_thrash ) THEN + IF ( x_init > 0.050 ) convergence = .false. + IF ( ( ABS( 1.0- dense(1)/dense(2) ) + x_solut ) < 1.E-7 ) convergence = .false. +ENDIF +IF ( r_diff2 /= 0.0 .AND. r_diff2 > (4.0*r_diff1) .AND. bindiag == 1 ) convergence = .false. +IF ( ncomp == 1 .AND. totres > 100.0*acc_a ) convergence = .false. +IF ( totres > 1000.0*acc_a ) convergence = .false. +IF ( ncomp == 1 .AND. r_diff1 < 1.d-5 ) convergence = .false. + +IF ( convergence ) THEN + converg = 1 + ! write (*,*) residu(1),residu(2) + CALL converged + IF (num <= 1) CALL enthalpy_etc +ELSE + converg = 0 +END IF + +DEALLOCATE( y, diag, residu ) + +END SUBROUTINE objective_ctrl + + +!>WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +!! SUBROUTINE objec_fct +!! +!! This subroutine contains the equations to be solved numerically +!! (iso-fugacity: fi'-fi''=0) as well as other dependent equations, +!! which can be solved analytically, namely the summation relation +!! xi=1-sum(xj) or the condition of equal charge for electrolyte +!! solutions. +!! This subroutine is required and controlled by the solver HBRD ! +!! HBRD varies the variables "y(i)" and eveluates the result of +!! these changes from this routine. +!!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +!! + SUBROUTINE objec_fct ( iter_no, y, residu, dummy ) +! + USE BASIC_VARIABLES + USE EOS_VARIABLES, ONLY: density_error + IMPLICIT NONE +! +! ---------------------------------------------------------------------- + INTEGER, INTENT(IN) :: iter_no + REAL, INTENT(IN) :: y(iter_no) + REAL, INTENT(OUT) :: residu(iter_no) + INTEGER, INTENT(IN OUT) :: dummy +! +! ---------------------------------------------------------------------- + INTEGER :: i, ph,k,posn, skip,phase + REAL :: lnphi(np,nc),isofugacity + CHARACTER (LEN=2) :: compon +! ---------------------------------------------------------------------- + + +posn = 0 +DO i = 1,n_unkw + posn = posn + 1 + IF (it(i) == 't') t = y(posn) + IF (it(i) == 'p') p = y(posn) + IF (it(i) == 'lnp') p = EXP( y(posn) ) + IF (it(i) == 'fls') alpha = y(posn) + IF (it(i)(1:1) == 'x' .AND. it(i)(2:2) == '1') compon = it(i)(3:3) + IF (it(i)(1:1) == 'x' .AND. it(i)(2:2) == '1') READ(compon,*) k + IF (it(i)(1:1) == 'x' .AND. it(i)(2:2) == '1') lnx(1,k) = y(posn) + IF (it(i)(1:1) == 'x' .AND. it(i)(2:2) == '2') compon = it(i)(3:3) + IF (it(i)(1:1) == 'x' .AND. it(i)(2:2) == '2') READ(compon,*) k + IF (it(i)(1:1) == 'x' .AND. it(i)(2:2) == '2') lnx(2,k) = y(posn) + IF (it(i)(1:1) == 'x' .AND. it(i)(2:2) == '3') compon = it(i)(3:3) + IF (it(i)(1:1) == 'x' .AND. it(i)(2:2) == '3') READ(compon,*) k + IF (it(i)(1:1) == 'x' .AND. it(i)(2:2) == '3') lnx(3,k) = y(posn) +END DO + +DO k = 1,ncomp + IF (lnx(1,k) > 0.0) lnx(1,k) = 0.0 + IF (lnx(2,k) > 0.0) lnx(2,k) = 0.0 +END DO + +IF (p < 1.E-100) p = 1.E-12 +!IF ( IsNaN( p ) ) p = 1000.0 ! rebounce for the case of NaN-solver output +!IF ( IsNaN( t ) ) t = 300.0 ! rebounce for the case of NaN-solver output +!IF ( IsNaN( alpha ) ) alpha = 0.5 ! rebounce for the case of NaN-solver output +IF ( p /= p ) p = 1000.0 ! rebounce for the case of NaN-solver output +IF ( t /= t ) t = 300.0 ! rebounce for the case of NaN-solver output +IF ( alpha /= alpha ) alpha = 0.5 ! rebounce for the case of NaN-solver output + +! --- setting of mole fractions ---------------------------------------- +DO ph = 1, nphas + DO i = 1, ncomp + IF ( lnx(ph,i) < -300.0 ) THEN + xi(ph,i) = 0.0 + ELSE + xi(ph,i) = EXP( lnx(ph,i) ) + END IF + END DO +END DO + +IF (ncomp > 1) CALL x_summation + +CALL fugacity (lnphi) + +phase = 2 +DO i = 1,n_unkw + skip = 0 !for ions/polymers, the isofug-eq. is not always solved + IF (n_unkw < (ncomp*(nphas-1))) skip = ncomp*(nphas-1) - n_unkw + IF ((i+skip-ncomp*(phase-2)) > ncomp) phase = phase + 1 + residu(i) = isofugacity((i+skip-ncomp*(phase-2)),phase,lnphi) + if ( density_error(phase) /= 0.0 ) residu(i) = residu(i) + SIGN( density_error(phase), residu(i) ) * 0.001 +END DO + +END SUBROUTINE objec_fct + + + +!>WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +!! REAL FUNCTION isofugacity +!! +!! calculates the deviation from the condition of equal fugacities in +!! logarithmic form. +!!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +!! + REAL FUNCTION isofugacity (i,phase,lnphi) +! + USE BASIC_VARIABLES + IMPLICIT NONE +! +! ---------------------------------------------------------------------- + INTEGER, INTENT(IN) :: i + INTEGER, INTENT(IN) :: phase + REAL, INTENT(IN) :: lnphi(np,nc) +! +! ---------------------------------------------------------------------- + INTEGER :: p1, p2 +! ---------------------------------------------------------------------- + + +! p1=1 +p1 = phase-1 +p2 = phase + +isofugacity = scaling(i) *( lnphi(p2,i)+lnx(p2,i)-lnx(p1,i)-lnphi(p1,i) ) +! write (*,'(a, 4G18.8)') ' t, p ',t,p,dense(1),dense(2) +! write (*,'(a,i3,i3,3G18.8)') ' phi_V',i,p2,lnx(p2,i),lnphi(p2,i),dense(p2) +! write (*,'(a,i3,i3,3G18.8)') ' phi_L',i,p1,lnx(p1,i),lnphi(p1,i),dense(p1) +! write (*,*) ' ISOFUGACITY',i,ISOFUGACITY, scaling(i) +! write (*,'(a,i3,4G18.8)') ' ISOFUGACITY',i,ISOFUGACITY, lnphi(p2,i)+lnx(p2,i), -lnx(p1,i)-lnphi(p1,i) +! pause + +END FUNCTION isofugacity + + + + + + + + + + + + + + + + + +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! + SUBROUTINE vle_min(lle_check) +! + USE PARAMETERS, ONLY: RGAS + USE BASIC_VARIABLES + USE STARTING_VALUES + IMPLICIT NONE +! +! ---------------------------------------------------------------------- + LOGICAL, INTENT(OUT) :: lle_check + + INTEGER :: i,j,k,phasen(0:40),steps + REAL :: lnphi(np,nc) + REAL :: vlemin(0:40),llemin(0:40),xval(0:40) + REAL :: start_xv(0:40),start_xl(0:40),x_sav,dg_dx2 +! ---------------------------------------------------------------------- + + + +j = 0 +k = 0 +nphas = 2 + +steps = 40 + +x_sav = xi(1,1) +sum_rel(1) = 'x12' ! summation relation +sum_rel(2) = 'x22' ! summation relation + +DO i = 0, steps + densta(1) = 0.45 + densta(2) = 1.d-6 + xi(1,1) = 1.0 - REAL(i) / REAL(steps) + IF ( xi(1,1) <= 1.E-50 ) xi(1,1) = 1.E-50 + xi(2,1) = xi(1,1) + lnx(1,1) = LOG(xi(1,1)) + lnx(2,1) = LOG(xi(2,1)) + + CALL x_summation + CALL fugacity (lnphi) + CALL enthalpy_etc !!KANN DAS RAUS???? + + + + + xval(i) = xi(1,1) + llemin(i)= gibbs(1) +(xi(1,1)*lnx(1,1)+xi(1,2)*lnx(1,2))*RGAS*t + + IF ( ABS(1.0-dense(1)/dense(2)) > 0.0001 ) THEN + vlemin(i)= gibbs(1) +(xi(1,1)*lnx(1,1)+xi(1,2)*lnx(1,2))*RGAS*t & + - ( gibbs(2) +(xi(2,1)*lnx(2,1)+xi(2,2)*lnx(2,2))*RGAS*t ) + phasen(i) = 2 + ELSE + phasen(i) = 1 + END IF + + IF (i > 0 .AND. phasen(i) == 2) THEN + IF (phasen(i-1) == 2 .AND. ABS(vlemin(i)+vlemin(i-1)) < & + ABS(vlemin(i))+ABS(vlemin(i-1))) THEN + j = j + 1 + start_xv(j)=xval(i-1) + (xval(i)-xval(i-1)) & + * ABS(vlemin(i-1))/ABS(vlemin(i)-vlemin(i-1)) + END IF + END IF + +END DO + + +DO i=2,steps-2 + dg_dx2 = (-llemin(i-2)+16.0*llemin(i-1)-30.0*llemin(i) & + +16.0*llemin(i+1)-llemin(i+2)) / (12.0*((xval(i)-xval(i-1))**2)) + IF (dg_dx2 < 0.0) THEN + k = k + 1 + start_xl(k)=xval(i) + END IF +END DO + + +IF (start_xl(1) == 0.0 .AND. start_xv(1) /= 0.0) THEN + xi(1,1) = start_xv(1) + xi(1,2) = 1.0-xi(1,1) + lle_check=.false. + ! write (*,*) 'VLE is likely', xi(1,1),xi(1,2) +ELSE IF (start_xl(1) /= 0.0 .AND. start_xv(1) == 0.0) THEN + xi(1,1) = start_xl(1) + xi(1,2) = 1.0-xi(1,1) + ! write (*,*) 'LLE is likely', xi(1,1),xi(1,2) + lle_check=.true. +ELSE IF (start_xl(1) /= 0.0 .AND. start_xv(1) /= 0.0) THEN + xi(1,1) = start_xv(1) + xi(1,2) = 1.0-xi(1,1) + ! write(*,*) 'starting with VLE and check for LLE' + lle_check=.true. +ELSE + xi(1,1) = x_sav + xi(1,2) = 1.0 - xi(1,1) +END IF + + +CALL x_summation + +END SUBROUTINE vle_min + + +!>WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +!! SUBROUTINE phase_stability +!! +!! the index 'LLE_check' is for the starting density (which determines +!! whether a liquid or vapor phase is found) of the trial phase. The +!! feed-point exits either as a vapor or as a liquid. If it can exist as +!! both (feedphases=2), then both states are tested. +!!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +!! + SUBROUTINE phase_stability ( lle_check, flashcase, ph_split ) +! + USE BASIC_VARIABLES + USE STARTING_VALUES + USE EOS_VARIABLES, ONLY: dhs, PI, x, eta, eta_start, z3t, fres + USE EOS_NUMERICAL_DERIVATIVES + IMPLICIT NONE +! +! ---------------------------------------------------------------------- + LOGICAL :: lle_check + LOGICAL, INTENT(IN OUT) :: flashcase + INTEGER, INTENT(OUT) :: ph_split +! ---------------------------------------------------------------------- + + INTERFACE + REAL FUNCTION F_STABILITY ( optpara, n ) + INTEGER, INTENT(IN) :: n + REAL, INTENT(IN OUT) :: optpara(n) + END FUNCTION + END INTERFACE + +!INTERFACE +! SUBROUTINE F_STABILITY (fmin, optpara, n) +! REAL, INTENT(IN OUT) :: fmin +! REAL, INTENT(IN) :: optpara(:) +! INTEGER, INTENT(IN) :: n +! END SUBROUTINE F_STABILITY +! +! SUBROUTINE stability_grad (g, optpara, n) +! REAL, INTENT(IN OUT) :: g(:) +! REAL, INTENT(IN) :: optpara(:) +! INTEGER, INTENT(IN) :: n +! END SUBROUTINE stability_grad +! +! SUBROUTINE stability_hessian (hessian, g, fmin, optpara, n) +! REAL, INTENT(IN OUT) :: hessian(:,:) +! REAL, INTENT(IN OUT) :: g(:) +! REAL, INTENT(IN OUT) :: fmin +! REAL, INTENT(IN) :: optpara(:) +! INTEGER, INTENT(IN) :: n +! END SUBROUTINE stability_hessian +!END INTERFACE + + INTEGER :: n, PRIN + REAL :: fmin, t0, h0, MACHEP, PRAXIS + REAL, ALLOCATABLE :: optpara(:) + + INTEGER :: i, feedphases, trial + REAL :: rhoi(nc),rho_start + REAL :: feeddens, rho_phas(np) + REAL :: fden + REAL :: dens + REAL :: rhot + REAL :: lnphi(np,nc) + REAL :: w(np,nc), mean_mass +! ---------------------------------------------------------------------- + +n = ncomp +ALLOCATE( optpara(n) ) + +IF (lle_check) WRITE (*,*) ' stability test starting with dense phase' + +DO i = 1, ncomp ! setting feed-phase x's + IF (.NOT.flashcase) xif(i) = xi(1,i) + IF (flashcase) xi(1,i) = xif(i) + xi(2,i) = xif(i) ! feed is tested for both: V and L density +END DO + +densta(1) = 0.45 +densta(2) = 1.d-6 + +CALL dens_calc(rho_phas) +IF ( ABS(1.0-dense(1)/dense(2)) > 0.0005 ) THEN + feedphases=2 ! feed-composition can exist both, in V and L +ELSE + feedphases=1 ! feed-composition can exist either in V or L +END IF +densta(1) = dense(1) +feeddens = dense(2) +!write (*,*) 'feedphases',dense(1), dense(2),feedphases + +10 CONTINUE ! IF FeedPhases=2 THEN there is a second cycle + + trial = 1 + + ! -------------------------------------------------------------------- + ! setting trial-phase mole-fractions + ! if there is no phase-split then further trial-phases are + ! considered (loop: 20 CONTINUE) + ! -------------------------------------------------------------------- + DO i = 1, ncomp + w(2,i) = 1.0 / REAL(ncomp) + END DO + mean_mass = 1.0 / SUM( w(2,1:ncomp)/mm(1:ncomp) ) + xi(2,1:ncomp) = w(2,1:ncomp)/mm(1:ncomp) * mean_mass + + 20 CONTINUE + + DO i = 1, ncomp + rhoif(i) = rho_phas(1) * xif(i) + rhoi(i) = rhoif(i) + END DO + + !write (*,'(a,6G16.8)') 'startval',rho_phas(2),xi(2,1:ncomp) + + ! -------------------------------------------------------------------- + ! calc Helmholtz energy density and derivative (numerical) to rhoif(i). + ! The derivative is taken around the "feed-point" not the trial phase + ! -------------------------------------------------------------------- + + rhot = SUM( rhoi(1:ncomp) ) + x(1:ncomp) = rhoi(1:ncomp) / rhot + CALL PERTURBATION_PARAMETER + xi(1,1:ncomp) = x(1:ncomp) + eta = rhot * z3t + eta_start = eta + densta(1) = eta_start + ensemble_flag = 'tv' + CALL FUGACITY (lnphi) + ensemble_flag = 'tp' + + call fden_calc ( fden, rhoi ) + fdenf = fden + + grad_fd(1:ncomp) = lnphi(1,1:ncomp) + LOG( rhoi(1:ncomp) ) + + + ! -------------------------------------------------------------------- + ! starting values for iteration (optpara) + ! -------------------------------------------------------------------- + rho_start = 1.E-5 + IF (lle_check) THEN + densta(2) = 0.45 + CALL dens_calc(rho_phas) + rho_start = rho_phas(2)*0.45/dense(2) + END IF + DO i = 1,ncomp + rhoi(i) = xi(2,i)*rho_start + optpara(i) = LOG( rhoi(i) ) + END DO + + ! -------------------------------------------------------------------- + ! minimizing the objective fct. Phase split for values of fmin < 0.0 + ! -------------------------------------------------------------------- + t0 = 5.E-5 + h0 = 0.5 + PRIN = 0 + MACHEP = 1.E-15 + + fmin = PRAXIS( t0, MACHEP, h0, n, PRIN, optpara, F_STABILITY, fmin ) + + + ! -------------------------------------------------------------------- + ! updating the ln(x) valus from optpara. The optimal optpara-vector is + ! not necessarily the one that was last evaluated. At the very end, + ! cg_decent writes the best values to optpara + ! -------------------------------------------------------------------- + fmin = F_STABILITY( optpara, n ) + + + + ! IF ( n == 2 ) THEN + ! CALL Newton_Opt_2D ( stability_hessian, F_stability, optpara, n, 1.E-8, 1.E-8, g, fmin) + ! ELSE + ! CALL cg_descent (1.d-5, optpara, n, F_STABILITY, stability_grad, STATUS, & + ! gnorm, fmin, iter, nfunc, ngrad, d, g, xtemp, gtemp) + ! ENDIF + ! CALL F_STABILITY (fmin, optpara, n) + + + ! -------------------------------------------------------------------- + ! determine instability & non-trivial solution + ! -------------------------------------------------------------------- + ph_split = 0 + IF (fmin < -1.E-7 .AND. & + ABS( 1.0 - maxval(EXP(optpara),mask=optpara /= 0.0) /maxval(rhoif) ) > 0.0005) THEN + ph_split = 1 + END IF + + IF (ph_split == 1) THEN + + ! ------------------------------------------------------------------ + ! here, there should be IF FeedPhases=2 THEN GOTO 10 + ! and test for another phase (while saving optpara) + ! ------------------------------------------------------------------ + + rhoi2(1:ncomp) = EXP( optpara(1:ncomp) ) + dens = PI/6.0 * SUM( rhoi2(1:ncomp) * parame(1:ncomp,1) * dhs(1:ncomp)**3 ) + rhot = SUM( rhoi2(1:ncomp) ) + xi(2,1:ncomp) = rhoi2(1:ncomp) / rhot + + ELSE + + IF (trial <= ncomp + ncomp) THEN + ! ---------------------------------------------------------------- + ! setting trial-phase x's + ! ---------------------------------------------------------------- + IF (trial <= ncomp) THEN + DO i=1,ncomp + w(2,i) = 1.0 / REAL(ncomp-1) * 0.05 + END DO + w(2,trial) = 0.95 + ELSE + DO i=1,ncomp + w(2,i) = 1.0 / REAL(ncomp-1) * 0.00001 + END DO + w(2,trial-ncomp) = 0.99999 + END IF + mean_mass = 1.0 / SUM( w(2,1:ncomp)/mm(1:ncomp) ) + xi(2,1:ncomp) = w(2,1:ncomp)/mm(1:ncomp) * mean_mass + trial = trial + 1 + GO TO 20 + END IF + ! IF (.NOT.LLE_check) write (*,*) 'no phase split detected' + ! IF (.NOT.LLE_check) pause + IF (feedphases > 1 .AND. .NOT.lle_check .AND. densta(1) > 0.2) THEN + densta(1) = feeddens ! this will be the lower-valued density (vapor) + CALL dens_calc(rho_phas) + ! WRITE (*,*) 'try feed as vapor-phase' + GO TO 10 + END IF + + END IF + +DEALLOCATE( optpara ) + +END SUBROUTINE phase_stability + + +!>WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +!! SUBROUTINE select_sum_rel +!! +!! This subroutine determines which component of a phase "ph" is calculated +!! from the summation relation x_i = 1 - sum(x_j). The other components are, +!! by default, said to be iterated during the phase equilibrium calculation. +!! +!! Note that for flash calculations not all of these mole fractions are in +!! fact iterated - this is raken care of in "determine_flash_it". +!! +!! ph phase +!! excl exclude comp. n +!! startindex assign it(startindex) for quantities to be iterated +!! (further it(startindex+1) is assigned, for a ternary +!! mixture, etc.) +!! +!! sum_index indicates the component, with the largest mole +!! fraction. If ph=1 and sum_index=2, we define +!! sum_rel(ph=1)='x12', so that this component is +!! calculated from the summation relation. +!!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +!! + SUBROUTINE select_sum_rel (ph,excl,startindex) +! + USE BASIC_VARIABLES + IMPLICIT NONE +! +! ---------------------------------------------------------------------- + INTEGER, INTENT(IN) :: ph + INTEGER, INTENT(IN) :: excl + INTEGER, INTENT(IN) :: startindex +! ---------------------------------------------------------------------- + INTEGER :: i,j, sum_index + REAL :: xmax(np) + ! CHARACTER :: compNo*2,phasNo*2 +! ---------------------------------------------------------------------- + +xmax(ph) = 0.0 +DO i = 1, ncomp + + IF ( xi(ph,i) > xmax(ph) ) THEN + xmax(ph) = xi(ph,i) + sum_index = i + + IF (ph == 1 .AND. i == 1) sum_rel(1) = 'x11' + IF (ph == 1 .AND. i == 2) sum_rel(1) = 'x12' + IF (ph == 1 .AND. i == 3) sum_rel(1) = 'x13' + IF (ph == 1 .AND. i == 4) sum_rel(1) = 'x14' + IF (ph == 1 .AND. i == 5) sum_rel(1) = 'x15' + + IF (ph == 2 .AND. i == 1) sum_rel(2) = 'x21' + IF (ph == 2 .AND. i == 2) sum_rel(2) = 'x22' + IF (ph == 2 .AND. i == 3) sum_rel(2) = 'x23' + IF (ph == 2 .AND. i == 4) sum_rel(2) = 'x24' + IF (ph == 2 .AND. i == 5) sum_rel(2) = 'x25' + + IF (ph == 3 .AND. i == 1) sum_rel(3) = 'x31' + IF (ph == 3 .AND. i == 2) sum_rel(3) = 'x32' + IF (ph == 3 .AND. i == 3) sum_rel(3) = 'x33' + IF (ph == 3 .AND. i == 4) sum_rel(3) = 'x34' + IF (ph == 3 .AND. i == 5) sum_rel(3) = 'x35' +! write (*,*) ph,i,xi(ph,i),sum_rel(ph) + END IF + +END DO + +j = 0 +DO i = 1, ncomp + + IF ( i /= sum_index .AND. i /= excl ) THEN + IF (ph == 1 .AND. i == 1) it(startindex+j) = 'x11' + IF (ph == 1 .AND. i == 2) it(startindex+j) = 'x12' + IF (ph == 1 .AND. i == 3) it(startindex+j) = 'x13' + IF (ph == 1 .AND. i == 4) it(startindex+j) = 'x14' + IF (ph == 1 .AND. i == 5) it(startindex+j) = 'x15' + + IF (ph == 2 .AND. i == 1) it(startindex+j) = 'x21' + IF (ph == 2 .AND. i == 2) it(startindex+j) = 'x22' + IF (ph == 2 .AND. i == 3) it(startindex+j) = 'x23' + IF (ph == 2 .AND. i == 4) it(startindex+j) = 'x24' + IF (ph == 2 .AND. i == 5) it(startindex+j) = 'x25' + + IF (ph == 3 .AND. i == 1) it(startindex+j) = 'x31' + IF (ph == 3 .AND. i == 2) it(startindex+j) = 'x32' + IF (ph == 3 .AND. i == 3) it(startindex+j) = 'x33' + IF (ph == 3 .AND. i == 4) it(startindex+j) = 'x34' + IF (ph == 3 .AND. i == 5) it(startindex+j) = 'x35' +! write (*,*) 'iter ',it(startindex+j) + j = j + 1 + END IF + +END DO + +END SUBROUTINE select_sum_rel + + + + +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! + SUBROUTINE tangent_plane +! + USE BASIC_VARIABLES + USE STARTING_VALUES + IMPLICIT NONE +! +! ---------------------------------------------------------------------- +!!$ INTERFACE +!!$ SUBROUTINE tangent_value (fmin, optpara, n) +!!$ INTEGER, INTENT(IN) :: n +!!$ REAL, INTENT(IN OUT) :: fmin +!!$ REAL, INTENT(IN) :: optpara(:) +!!$ END SUBROUTINE tangent_value +!!$ +!!$ SUBROUTINE tangent_grad (g, optpara, n) +!!$ INTEGER, INTENT(IN) :: n +!!$ REAL, INTENT(IN OUT) :: g(:) +!!$ REAL, INTENT(IN) :: optpara(:) +!!$ END SUBROUTINE tangent_grad +!!$ END INTERFACE + +! +! ---------------------------------------------------------------------- + INTERFACE + REAL FUNCTION PRAXIS( t0, MACHEP, h0, n, PRIN, optpara, TANGENT_VALUE, fmin ) + REAL, INTENT(IN OUT) :: t0 + REAL, INTENT(IN) :: machep + REAL, INTENT(IN) :: h0 + INTEGER :: n + INTEGER, INTENT(IN OUT) :: prin + REAL, INTENT(IN OUT) :: optpara(n) + REAL, EXTERNAL :: TANGENT_VALUE + REAL, INTENT(IN OUT) :: fmin + END FUNCTION + + REAL FUNCTION TANGENT_VALUE2 ( optpara, n ) + INTEGER, INTENT(IN) :: n + REAL, INTENT(IN) :: optpara(n) + END FUNCTION + END INTERFACE +! +! ---------------------------------------------------------------------- + INTEGER :: n + INTEGER :: i, k, ph + INTEGER :: small_i, min_ph, other_ph + INTEGER :: PRIN + REAL :: fmin , t0, h0, MACHEP + REAL :: lnphi(np,nc) + REAL, ALLOCATABLE :: optpara(:) + +! INTEGER :: STATUS, iter, nfunc, ngrad +! REAL :: gnorm +! REAL, ALLOCATABLE :: d(:), g(:), xtemp(:), gtemp(:) +! ---------------------------------------------------------------------- + +n = ncomp +t0 = 1.E-4 +h0 = 0.1 +PRIN = 0 +MACHEP = 1.E-15 + +ALLOCATE( optpara(n) ) +!ALLOCATE( d(n) ) +!ALLOCATE( g(n) ) +!ALLOCATE( xtemp(n) ) +!ALLOCATE( gtemp(n) ) + +DO i = 1,ncomp + rhoi1(i) = rhoif(i) + lnx(1,i) = LOG(xi(1,i)) + lnx(2,i) = LOG(xi(2,i)) +END DO + +DO i = 1,ncomp + optpara(i) = LOG( xi(2,i) * 0.001 ) +END DO + +! CALL cg_descent (1.d-4, optpara, n, tangent_value, tangent_grad, STATUS, & +! gnorm, fmin, iter, nfunc, ngrad, d, g, xtemp, gtemp) +! +! updating the ln(x) valus from optpara. The optimal optpara-vector is not necessarily +! the one that was last evaluated. At the very end, cg_decent writes the best values to optpara +! CALL tangent_value (fmin, optpara, n) + + + +fmin = PRAXIS( t0, MACHEP, h0, n, PRIN, optpara, TANGENT_VALUE2, fmin ) + +! The optimal optpara-vector is not necessarily the one that was last evaluated. +! TANGENT_VALUE is reexecuted with the optimal vector optpara, in order to update the ln(x) values +fmin = TANGENT_VALUE2( optpara, n ) + + +! ---------------------------------------------------------------------- +! If one component is a polymer (indicated by a low component-density) +! then get an estimate of the polymer-lean composition, by solving for +! xi_p1 = ( xi_p2 * phii_p2) / phii_p1 (phase equilibrium condition, +! with p1 for phase 1) +! ---------------------------------------------------------------------- +IF ( MINVAL( lnx(1,1:ncomp) ) < MINVAL( lnx(2,1:ncomp) ) ) THEN + min_ph = 1 + other_ph = 2 +ELSE + min_ph = 2 + other_ph = 1 +ENDIF +small_i = MINLOC( lnx(min_ph,1:ncomp), 1 ) +! --- if one component is a polymer ------------------------------------ +IF ( MINVAL( lnx(min_ph,1:ncomp) ) < -20.0 ) THEN + CALL FUGACITY ( lnphi ) + lnx(min_ph,small_i) = lnx(other_ph,small_i)+lnphi(other_ph,small_i) - lnphi(min_ph,small_i) + optpara(small_i) = lnx(2,small_i) + LOG( SUM( EXP( optpara(1:ncomp) ) ) ) +END IF + +! ---------------------------------------------------------------------- +! caution: these initial values are for a flashcase overwritten in +! SUBROUTINE determine_flash_it2, because in that case, the lnx-values +! treated as ln(mole_number). +! ---------------------------------------------------------------------- +val_init(1) = dense(1) +val_init(2) = dense(2) +val_init(3) = t +val_init(4) = p +DO ph = 1,nphas + DO k = 1,ncomp + val_init(4+k+(ph-1)*ncomp) = lnx(ph,k) + END DO +END DO +!alpha = optpara(1) + + +!DEALLOCATE( optpara, d, g, xtemp, gtemp ) +DEALLOCATE( optpara ) + +END SUBROUTINE tangent_plane + + +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! + SUBROUTINE determine_flash_it2 +! + USE BASIC_VARIABLES + IMPLICIT NONE +! +! ---------------------------------------------------------------------- + INTEGER :: i, k, ph + REAL :: n_phase1, n_phase2, max_x_diff +! ---------------------------------------------------------------------- + + IF ( MINVAL( lnx(1,1:ncomp) ) < MINVAL( lnx(2,1:ncomp) ) ) THEN + it(1) = 'x11' + it(2) = 'x12' + IF (ncomp >= 3) it(3) = 'x13' + IF (ncomp >= 4) it(4) = 'x14' + IF (ncomp >= 5) it(5) = 'x15' + sum_rel(1) = 'nfl' + ELSE + it(1) = 'x21' + it(2) = 'x22' + IF (ncomp >= 3) it(3) = 'x23' + IF (ncomp >= 4) it(4) = 'x24' + IF (ncomp >= 5) it(5) = 'x25' + sum_rel(2) = 'nfl' + ENDIF + max_x_diff = 0.0 + DO i = 1,ncomp + IF ( ABS( EXP( lnx(1,i) ) - EXP( lnx(2,i) ) ) > max_x_diff ) THEN + max_x_diff = ABS( EXP( lnx(1,i) ) - EXP( lnx(2,i) ) ) + n_phase1 = ( xif(i) - EXP( lnx(2,i) ) ) / ( EXP( lnx(1,i) ) - EXP( lnx(2,i) ) ) + n_phase2 = 1.0 - n_phase1 + END IF + END DO + lnx(1,1:ncomp) = lnx(1,1:ncomp) + LOG( n_phase1 ) ! these x's are treated as mole numbers + lnx(2,1:ncomp) = lnx(2,1:ncomp) + LOG( n_phase2 ) ! these x's are treated as mole numbers + + + val_init(1) = dense(1) + val_init(2) = dense(2) + val_init(3) = t + val_init(4) = p + DO ph = 1,nphas + DO k = 1,ncomp + val_init(4+k+(ph-1)*ncomp) = lnx(ph,k) ! - LOG( SUM( EXP( lnx(ph,1:ncomp) ) ) ) + ! write (*,*) ph,k, lnx(ph,k) + END DO + END DO + +END SUBROUTINE determine_flash_it2 + +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! SUBROUTINE poly_sta_var +! +! This subroutine generates starting values for mole fractons of +! polymer-solvent systems. +! The determination of these starting values follows a two-step +! procedure. Fist, the equilibrium concentration of the polymer-rich +! phase is estimated with the assumption of zero concentration +! of polymer in the polymer-lean-phase. This is achieved in the +! SUBROUTINE POLYMER_FREE. (Only one equation has to be iterated +! for this case). Once this is achieved, the rigorous calculation +! is triggered. If it converges, fine! If no solution is obtained, +! the pressure is somewhat reduced, the procedure is repeated and +! a calculation is started to approach the originally specified +! pressure. +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! + SUBROUTINE poly_sta_var (converg) +! + USE BASIC_VARIABLES + IMPLICIT NONE +! +! ---------------------------------------------------------------------- + INTEGER, INTENT(IN OUT) :: converg +! +! ---------------------------------------------------------------------- + INTEGER :: k,ph,sol + REAL :: p_spec,solution(10,4+nc*np) +! ---------------------------------------------------------------------- + + p_spec = p + + find_equilibrium: DO + + CALL polymer_free(p_spec,sol,solution) + + WRITE (*,*) ' ' + WRITE (*,*) ' GENERATING STARTING VALUES' + + val_init(1) = solution(1,1) ! approx.solutions for next iteration + val_init(2) = solution(1,2) ! approx.solutions for next iteration + val_init(3) = solution(1,3) ! approx.solutions for next iteration + val_init(4) = solution(1,4) ! approx.solutions for next iteration + DO ph = 1,nphas + DO k = 1,ncomp + val_init(4+k+(ph-1)*ncomp) = solution(1,4+k+(ph-1)*ncomp) + END DO + END DO + val_init(7) = -10000.0 ! start.val. for lnx(2,1) for iterat. + + IF (p /= p_spec) & + WRITE (*,*) ' INITIAL EQUILIBRIUM CALC. FAILD. NEXT STEP STARTS' + + IF (p == p_spec) THEN + n_unkw = ncomp ! number of quantities to be iterated + it(1)='x11' ! iteration of mol fraction of comp.1 phase 1 + it(2)='x21' ! iteration of mol fraction of comp.1 phase 2 + CALL objective_ctrl (converg) + ELSE + outp = 0 ! output to terminal + running ='p' ! Pressure is running var. in PHASE_EQUILIB + CALL phase_equilib(p_spec,5.0,converg) + END IF + + IF (converg == 1) EXIT find_equilibrium + p = p * 0.9 + IF ( p < (0.7*p_spec) ) WRITE (*,*) ' NO SOLUTION FOUND' + IF ( p < (0.7*p_spec) ) STOP + + END DO find_equilibrium + + WRITE (*,*) ' FINISHED: POLY_STA_VAR' + +END SUBROUTINE poly_sta_var + + +!>WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +!! SUBROUTINE x_summation +!! +!! This subroutine solves the summation relation: xi=1-sum(xj) +!! The variable "sum_rel(i)" contains the information, which mole +!! fraction is the one to be calculated here. Consider the example +!! sum_rel(1)='x12'. The fist letter 'x' of this variable indicates, +!! that this subroutine needs to be executed and that the mole +!! fraction of a component has to be calculated. The second letter +!! of the string points to phase 1, the third letter to component 2. +!! If the fist letter is 'e', not 'x', then the subroutine +!! NEUTR_CHARGE is called. This is the case of electrolyte solutions, +!! neutral charges have to be enforced in all phases (see below). +!!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +!! + SUBROUTINE x_summation +! + USE BASIC_VARIABLES + IMPLICIT NONE +! +! ---------------------------------------------------------------------- + INTEGER :: i, j, comp_i, ph_i + REAL :: sum_x + CHARACTER (LEN=2) :: phasno + CHARACTER (LEN=2) :: compno + LOGICAL :: flashcase2 +! ---------------------------------------------------------------------- + +DO j = 1, nphas + IF (sum_rel(j)(1:3) == 'nfl') THEN + CALL new_flash (j) + RETURN + END IF +END DO + + + +flashcase2 = .false. + +DO j = 1, nphas + + IF (sum_rel(j)(1:1) == 'x') THEN + + phasno = sum_rel(j)(2:2) + READ(phasno,*) ph_i + compno = sum_rel(j)(3:3) + READ(compno,*) comp_i + IF ( sum_rel(nphas+j)(1:1) == 'e' ) CALL neutr_charge(nphas+j) + + sum_x = 0.0 + DO i = 1, ncomp + IF ( i /= comp_i ) sum_x = sum_x + xi(ph_i,i) + END DO + xi(ph_i,comp_i) = 1.0 - sum_x + IF ( xi(ph_i,comp_i ) < 0.0 ) xi(ph_i,comp_i) = 0.0 + IF ( xi(ph_i,comp_i ) /= 0.0 ) THEN + lnx(ph_i,comp_i) = LOG( xi(ph_i,comp_i) ) + ELSE + lnx(ph_i,comp_i) = -100000.0 + END IF + ! write (*,*) 'sum_x',ph_i,comp_i,lnx(ph_i,comp_i),xi(ph_i,comp_i) + + ELSE IF ( sum_rel(j)(1:2) == 'fl' ) THEN + + flashcase2 = .true. + ! ------------------------------------------------------------------ + ! This case is true when all molefractions of one phase are + ! determined from a component balance. What is needed to + ! calculate all molefractions of that phase are all mole- + ! fractions of the other phase (nphas=2, so far) and the + ! phase fraction alpha. + ! Alpha is calculated (in FLASH_ALPHA) from the mole fraction + ! of component {sum_rel(j)(3:3)}. IF sum_rel(2)='fl3', then + ! the alpha is determined from the molefraction of comp. 3 and + ! the molefraction of phase 2 is then completely determined ELSE + ! ------------------------------------------------------------------ + + ELSE + WRITE (*,*) 'summation relation not defined' + STOP + END IF + +END DO + +IF ( it(1) == 'fls' ) CALL flash_sum +IF ( flashcase2 ) CALL flash_alpha + +END SUBROUTINE x_summation + + + +!>WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +!! SUBROUTINE FUGACITY +!! +!! This subroutine serves as an interface to the eos-subroutines. +!! (1) case 1, when ensemble_flag = 'tp' +!! The subroutine gives the residual chemical potential: +!! mu_i^res(T,p,x)/kT = ln( phi_i ) +!! and in addition, the densities that satisfy the specified p +!! (2) case 2, when ensemble_flag = 'tv' +!! The subroutine gives the residual chemical potential: +!! --> mu_i^res(T,rho,x)/kT +!! and in addition the resulting pressure for the given density. +!! The term "residual" means difference of the property and the same +!! property for an ideal gas mixture. +!!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +!! + SUBROUTINE FUGACITY (ln_phi) +! + USE BASIC_VARIABLES + USE EOS_VARIABLES, ONLY: phas, x, eta, eta_start, lnphi, fres, rho, pges, KBOL + IMPLICIT NONE +! +! ---------------------------------------------------------------------- + REAL, INTENT(OUT) :: ln_phi(np,nc) +! +! --- local variables -------------------------------------------------- + INTEGER :: ph +! ---------------------------------------------------------------------- +! +IF (eos < 2) THEN + + DO ph = 1,nphas + + phas = ph + eta_start = densta(ph) + x(1:ncomp) = xi(ph,1:ncomp) + + IF (p < 1.E-100) THEN + WRITE(*,*) ' FUGACITY: PRESSURE TOO LOW', p + p = 1.E-6 + END IF + + IF (num == 0) CALL PHI_EOS + IF (num == 1) CALL PHI_NUMERICAL + !!IF (num == 2) CALL PHI_CRITICAL_RENORM + IF (num == 2) write(*,*) 'CRITICAL RENORM NOT INCLUDED YET' + + dense(ph) = eta + ln_phi(ph,1:ncomp) = lnphi(1:ncomp) + ! gibbs(ph) = fres + sum( xi(ph,1:ncomp)*( log( xi(ph,1:ncomp)*rho) - 1.0 ) ) & + ! + (pges * 1.d-30) / (KBOL*t*rho) ! includes ideal gas contribution + + ! f_res(ph) = fres + ! write (*,'(i3,4G20.11)') ph,eta,lnphi(1),lnphi(2) + ! DO i = 1,ncomp + ! DO j=1,NINT(parame(i,12)) + ! mxx(ph,i,j) = mx(i,j) + ! END DO + ! END DO + + END DO + +ELSE + +! IF (eos == 2) CALL srk_eos (ln_phi) +! IF (eos == 3) CALL pr_eos (ln_phi) +! dense(1) = 0.01 +! dense(2) = 0.3 +! IF (eos == 4.OR.eos == 5.OR.eos == 6.OR.eos == 8) CALL lj_fugacity(ln_phi) +! IF (eos == 7) CALL sw_fugacity(ln_phi) +! IF (eos == 9) CALL lj_bh_fug(ln_phi) + +END IF + +END SUBROUTINE FUGACITY + + +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! SUBROUTINE enthalpy_etc +! +! This subroutine serves as an interface to the EOS-routines. The +! residual enthalpy h_res, residual entropy s_res, residual Gibbs +! enthalpy g_res, and residual heat capacity at constant pressure +! (cp_res) corresponding to converged conditions are calculated. +! The conditions in (T,P,xi,rho) need to be converged equilibrium +! conditions !! +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! + SUBROUTINE enthalpy_etc +! + USE BASIC_VARIABLES + USE EOS_VARIABLES + IMPLICIT NONE +! + INTEGER :: ph +! ------------------------------------------------------------------ + +IF (eos <= 1) THEN + + DO ph=1,nphas + + phas = ph + eta = dense(ph) +! eta_start = dense(ph) + x(1:ncomp) = xi(ph,1:ncomp) + + IF(num == 0) THEN + CALL H_EOS + ELSE + IF(num == 1) CALL H_numerical + IF(num == 2) write (*,*) 'enthalpy_etc: incorporate H_EOS_RN' + IF(num == 2) stop +! IF(num == 2) CALL H_EOS_rn + END IF + enthal(ph) = h_res + entrop(ph) = s_res + ! gibbs(ph) = h_res - t * s_res ! already defined in eos.f90 (including ideal gas) + cpres(ph) = cp_res + + END DO + IF (nphas == 2) h_lv = enthal(2)-enthal(1) + +ENDIF + +END SUBROUTINE enthalpy_etc + + +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! SUBROUTINE dens_calc +! +! This subroutine serves as an interface to the EOS-routines. The +! densities corresponding to given (P,T,xi) are calculated. +! (Note: the more common interface is SUBROUTINE FUGACITY. +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! + SUBROUTINE dens_calc(rho_phas) +! + USE BASIC_VARIABLES + USE EOS_VARIABLES + IMPLICIT NONE +! +! +!------------------------------------------------------------------ + REAL, INTENT(OUT) :: rho_phas(np) +! + INTEGER :: ph +!------------------------------------------------------------------ + + +DO ph = 1, nphas + + IF (eos < 2) THEN + + phas = ph + eta = densta(ph) + eta_start = densta(ph) + x(1:ncomp) = xi(ph,1:ncomp) + + CALL PERTURBATION_PARAMETER + CALL DENSITY_ITERATION + + dense(ph)= eta + rho_phas(ph) = eta/z3t + + ELSE + write (*,*) ' SUBROUTINE DENS_CALC not available for cubic EOS' + stop + END IF + +END DO + +END SUBROUTINE dens_calc + + +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! + SUBROUTINE fden_calc (fden, rhoi) +! + USE BASIC_VARIABLES + USE EOS_VARIABLES + IMPLICIT NONE +! +! ---------------------------------------------------------------------- + REAL, INTENT(OUT) :: fden + REAL, INTENT(IN OUT) :: rhoi(nc) +! ---------------------------------------------------------------------- + REAL :: rhot, fden_id +! ---------------------------------------------------------------------- + + +IF (eos < 2) THEN + + rhot = SUM( rhoi(1:ncomp) ) + x(1:ncomp) = rhoi(1:ncomp) / rhot + + CALL PERTURBATION_PARAMETER + eta = rhot * z3t + eta_start = eta + + IF (num == 0) THEN + CALL F_EOS + ELSE IF(num == 1) THEN + CALL F_NUMERICAL + ELSE + write (*,*) 'deactivated this line when making a transition to f90' + stop + ! CALL F_EOS_rn + END IF + + fden_id = SUM( rhoi(1:ncomp) * ( LOG( rhoi(1:ncomp) ) - 1.0 ) ) + + fden = fres * rhot + fden_id + +ELSE + write (*,*) ' SUBROUTINE FDEN_CALC not available for cubic EOS' + stop +END IF + +END SUBROUTINE fden_calc + + + + +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! SUBROUTINE polymer_free +! +! This subroutine performes a phase equilibrium calculation assuming +! the polymer-lean hase to be polymer-free (x_poly=0). Only the +! equality of the solvent-fugacities has to be ensured (only one +! equation to be iterated). This procedure delivers very good +! appoximations for the polymer-rich phase up-to fairly close to the +! mixture critical point. Both, liquid-liquid and vapor-liquid +! equilibria can be calculated. +! See also comments to SUBROUTINE POLY_STA_VAR. +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! + SUBROUTINE polymer_free (p_spec,sol,solution) +! + USE BASIC_VARIABLES + IMPLICIT NONE +! +! ---------------------------------------------------------------------- + REAL, INTENT(IN OUT) :: p_spec + INTEGER, INTENT(OUT) :: sol + REAL, INTENT(OUT) :: solution(10,4+nc*np) +! +! ---------------------------------------------------------------------- + INTEGER :: k,j,ph, converg + REAL :: grid(10) +! ---------------------------------------------------------------------- + + sol = 0 + + grid(1)=0.98 + grid(2)=0.9 + grid(3)=0.7 + grid(4)=0.5 + grid(5)=0.3 + grid(6)=0.2 + grid(7)=0.1 + grid(8)=0.05 + + DO WHILE ( sol == 0 ) + + DO j = 1,8 + ! Phase 2 is solvent-phase + ! starting value for xi(1,1) of polymer-phase 1: w_polymer=0.95 to 0.05 + ! from simple approximate equation + xi(1,1) = grid(j) / ( (1.0-grid(j)) * mm(1) / mm(2) ) !xi(1,1) Phase 1 Komponente 1 + IF ( mm(1) < 5000.0 ) xi(1,1) = xi(1,1) * 0.8 + xi(1,2) = 1.0 - xi(1,1) !xi(1,2) Phase 1 Komponente 2 + lnx(1,1) = LOG(xi(1,1)) + lnx(1,2) = LOG(xi(1,2)) + lnx(2,1) = -1.E10 !ln(xi) Phase 2 Komponente 1 + lnx(2,2) = 0.0 !ln(xi) Phase 2 Komponente 2 + + + + val_init(1) = 0.45 ! starting density targeting at a liquid phase + val_init(2) = 0.0001 ! starting density targeting at a vapor phase + ! val_init(2) = 0.45 + val_init(3) = t + val_init(4) = p + DO ph = 1,nphas + DO k = 1,ncomp + val_init(4+k+(ph-1)*ncomp) = lnx(ph,k) + END DO + END DO + + + + + n_unkw = ncomp-1 ! number of quantities to be iterated + it(1) = 'x11' ! iteration of mol fraction of comp.1 phase 1 + it(2) = ' ' + sum_rel(1) = 'x12' ! summation relation: x12 = 1 - sum(x1j) + sum_rel(2) = 'x22' + + CALL objective_ctrl (converg) + + IF (converg == 1 .AND. ABS(dense(1)/dense(2)-1.0) > 1.d-3 .AND. dense(1) > 0.1) THEN + IF (sol == 0) THEN + sol = sol + 1 + DO k = 1,4+ncomp*nphas + solution(sol,k) = val_conv(k) + END DO + ELSE IF (ABS(solution(sol,5)/lnx(1,1)-1.0) > 1.d-2) THEN + sol = sol + 1 + DO k = 1,4+ncomp*nphas + solution(sol,k) = val_conv(k) + END DO + END IF + END IF + + END DO + + + + + + IF (sol == 0) THEN + WRITE (*,*) ' no initial solution found' + p = p*0.9 + IF (p < (0.7*p_spec)) WRITE (*,*) ' NO SOLUTION FOUND' + IF (p < (0.7*p_spec)) STOP + ELSE IF (sol > 1) THEN + ! write (*,*) ' ' + ! write (*,*) ' ',sol,' solutions found:' + ! write (*,*) ' lnx(1,1), dichte_1, dichte_2' + ! DO k = 1,sol + ! write (*,*) solution(k,5),solution(k,1),solution(k,2) + ! END DO + END IF + END DO + + n_unkw = ncomp ! number of quantities to be iterated + it(1) = 'x11' ! iteration of mol fraction of comp.1 phase 1 + it(2) = 'x21' ! iteration of mol fraction of comp.1 phase 2 + sum_rel(1) = 'x12' ! summation relation: x12 = 1 - sum(x1j) + sum_rel(2) = 'x22' ! summation relation: x22 = 1 - sum(x2j) + + + END SUBROUTINE polymer_free + + + + + +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! SUBROUTINE phase_equilib +! +! This subroutine varies a predefined "running variable" and +! organizes phase equilibrium calculations. For an isotherm +! calculation e.g., the running variable is often the pressure. The +! code is designed to deliver only converged solutions. In order to +! enforce convergence, a step-width adjustment (reduction) is +! implemented. + +! VARIABLE LIST: +! running defines the running variable. For example: if you want +! to calculate the vapor pressure curve of a component +! starting from 100�C to 200�C, then running is 't'. The +! temperature is step-wise increased until the end- +! -temperature of 200�C is reached. +! (in this example end_x=200+273.15) +! end_x end point for running variable +! steps No. of calculation steps towards the end point of calc. +! converg 0 if no convergence achieved, 1 if converged solution +! +! PREREQUISITES: +! prior to execution of this routine, the follwing variables have to +! be defined: "val_init" an array containing the starting values for +! this iteration, "it(i)" provides the information, which variable is +! determined iteratively, "sum_rel(i)" indicates, which mole fraction +! is determined from the summation relation sum(xi)=1. Furthermore, +! the number of phases and the variables provided by the subroutine +! INPUT are required. +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! + SUBROUTINE phase_equilib (end_x,steps,converg) +! + USE BASIC_VARIABLES + IMPLICIT NONE +! +! ---------------------------------------------------------------------- + REAL, INTENT(IN) :: end_x + REAL, INTENT(IN) :: steps + INTEGER, INTENT(OUT) :: converg +! +! ---------------------------------------------------------------------- + INTEGER :: k, count1,count2,runindex,maxiter + REAL :: delta_x,delta_org,val_org,runvar + CHARACTER (LEN=2) :: compon + LOGICAL :: continue_cycle +! ---------------------------------------------------------------------- + +IF (running(1:2) == 'd1') runindex = 1 +IF (running(1:2) == 'd2') runindex = 2 +IF (running(1:1) == 't') runindex = 3 +IF (running(1:1) == 'p') runindex = 4 +IF (running(1:2) == 'x1') compon = running(3:3) +IF (running(1:2) == 'x1') READ(compon,*) k +IF (running(1:2) == 'x1') runindex = 4+k +IF (running(1:2) == 'x2') compon = running(3:3) +IF (running(1:2) == 'x2') READ(compon,*) k +IF (running(1:2) == 'x2') runindex = 4+ncomp+k +IF (running(1:2) == 'l1') compon = running(3:3) +IF (running(1:2) == 'l1') READ(compon,*) k +IF (running(1:2) == 'l1') runindex = 4+k +IF (running(1:2) == 'l2') compon = running(3:3) +IF (running(1:2) == 'l2') READ(compon,*) k +IF (running(1:2) == 'l2') runindex = 4+ncomp+k + +maxiter = 200 +IF ( ncomp >= 3 ) maxiter = 1000 +count1 = 0 +count2 = 0 +delta_x = ( end_x - val_init(runindex) ) / steps !J: calc increment in running var = (phi_end - phi_init)/steps +delta_org = ( end_x - val_init(runindex) ) / steps +val_org = val_init(runindex) +IF ( running(1:1) == 'x' ) THEN + delta_x = ( end_x - EXP(val_init(runindex)) ) / steps + delta_org = ( end_x - EXP(val_init(runindex)) ) / steps + val_org = EXP(val_init(runindex)) +END IF + +continue_cycle = .true. + +DO WHILE ( continue_cycle ) + + count1 = count1 + 1 + count2 = count2 + 1 + ! val_org = val_init(runindex) + + + CALL objective_ctrl (converg) + + IF (converg == 1) THEN + val_init( 1:(4+ncomp*nphas) ) = val_conv( 1:(4+ncomp*nphas) ) + IF (outp == 1 .AND. (ABS(delta_x) > 0.1*ABS(delta_org) .OR. count2 == 2)) CALL output + ELSE + delta_x = delta_x / 2.0 + IF (num == 2) delta_x = delta_x / 2.0 + val_init(runindex) = val_org + IF (running(1:1) == 'x') val_init(runindex) = LOG(val_org) + continue_cycle = .true. + count2 = 0 + END IF + runvar = val_init(runindex) + IF (running(1:1) == 'x') runvar = EXP(val_init(runindex)) + + IF ( end_x == 0.0 .AND. running(1:1) /= 'x' ) THEN + IF ( ABS(runvar-end_x) < 1.E-8 ) continue_cycle = .false. + ELSE IF ( ABS((runvar-end_x)/end_x) < 1.E-8 ) THEN + ! IF(delta_org.NE.0.0) WRITE (*,*)' FINISHED ITERATION',count1 + continue_cycle = .false. + ELSE IF ( count1 == maxiter ) THEN + WRITE (*,*) ' MAX. NO OF ITERATIONS',count1 + converg = 0 + continue_cycle = .false. + ELSE IF ( ABS(delta_x) < 1.E-5*ABS(delta_org) ) THEN + ! WRITE (*,*) ' CLOSEST APPROACH REACHED',count1 + converg = 0 + continue_cycle = .false. + ELSE + continue_cycle = .true. + val_org = runvar + IF (ABS(runvar+delta_x-end_x) > ABS(runvar-end_x)) delta_x = end_x - runvar ! if end-point passed + val_init(runindex) = runvar + delta_x + IF (running(1:1) == 'x') val_init(runindex) = LOG(runvar+delta_x) + END IF + + IF (ABS(delta_x) < ABS(delta_org) .AND. count2 >= 5) THEN + delta_x = delta_x * 2.0 + count2 = 0 + END IF + +END DO ! continue_cycle + +END SUBROUTINE phase_equilib + +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! + SUBROUTINE new_flash (ph_it) +! + USE BASIC_VARIABLES + IMPLICIT NONE +! +! ---------------------------------------------------------------------- + INTEGER, INTENT(IN) :: ph_it +! +! ---------------------------------------------------------------------- + INTEGER :: i, ph_cal + REAL, DIMENSION(nc) :: ni_1, ni_2 +! ---------------------------------------------------------------------- + + ph_cal = 3 - ph_it ! for two phases only + + DO i = 1, ncomp + IF ( lnx(ph_it,i) < -300.0 ) THEN + ni_2(i) = 0.0 + ELSE + ni_2(i) = EXP( lnx(ph_it,i) ) + END IF + END DO + + DO i = 1, ncomp + ni_1(i) = xif(i)-ni_2(i) + IF ( ni_2(i) > xif(i) ) THEN + ni_2(i) = xif(i) + ni_1(i) = xif(i) * 1.E-20 + ENDIF + END DO + + xi(ph_it,1:ncomp) = ni_2(1:ncomp) / SUM( ni_2(1:ncomp) ) + DO i = 1, ncomp + IF ( xi(ph_it,i) >= 1.E-300 ) lnx(ph_it,i) = LOG( xi(ph_it,i) ) + END DO + xi(ph_cal,1:ncomp) = ni_1(1:ncomp) / SUM( ni_1(1:ncomp) ) + lnx(ph_cal,1:ncomp) = LOG( xi(ph_cal,1:ncomp) ) + +END SUBROUTINE new_flash + + +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! SUBROUTINE PHI_EOS +! +! This subroutine gives the residual chemical potential: +! --> mu_i^res(T,p,x)/kT = ln( phi_i ) when ensemble_flag = 'tp' +! The required input for this case (T, p, x(nc)) and as a starting value +! eta_start +! +! or it gives +! +! --> mu_i^res(T,rho,x)/kT when ensemble_flag = 'tv' +! The required input for this case (T, eta_start, x(nc)). Note that +! eta_start is the specified density (packing fraction) in this case. +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! + SUBROUTINE PHI_EOS +! + USE PARAMETERS + USE EOS_VARIABLES + USE EOS_CONSTANTS + IMPLICIT NONE +! +! --- local variables--------------------------------------------------- + INTEGER :: i, j, k, ki, l, m + REAL :: z0, z1, z2, z3, z0_rk, z1_rk, z2_rk, z3_rk + REAL :: zms, m_mean + REAL, DIMENSION(nc) :: mhs, mdsp, mhc, myres + REAL, DIMENSION(nc) :: m_rk + REAL :: gij_rk(nc,nc) + REAL :: zres, zges + REAL :: dpdz, dpdz2 + + REAL :: I1, I2, I1_rk, I2_rk + REAL :: ord1_rk, ord2_rk + REAL :: c1_con, c2_con, c1_rk + REAL :: zmr, nmr, zmr_rk, nmr_rk, um_rk + REAL, DIMENSION(nc,0:6) :: ap_rk, bp_rk + + LOGICAL :: assoc + REAL :: ass_s2, m_hbon(nc) + + REAL :: fdd_rk, fqq_rk, fdq_rk + REAL, DIMENSION(nc) :: my_dd, my_qq, my_dq +! ---------------------------------------------------------------------- + +! ---------------------------------------------------------------------- +! obtain parameters and density independent expressions +! ---------------------------------------------------------------------- +CALL PERTURBATION_PARAMETER + + +! ---------------------------------------------------------------------- +! density iteration: (pTx)-ensemble OR p calc.: (pvx)-ensemble +! ---------------------------------------------------------------------- +IF (ensemble_flag == 'tp') THEN + CALL DENSITY_ITERATION +ELSEIF (ensemble_flag == 'tv') THEN + eta = eta_start + CALL P_EOS +ELSE + write (*,*) 'PHI_EOS: define ensemble, ensemble_flag == (pv) or (pt)' + stop +END IF + + +! --- Eq.(A.8) --------------------------------------------------------- +rho = eta / z3t +z0 = z0t * rho +z1 = z1t * rho +z2 = z2t * rho +z3 = z3t * rho + +m_mean = z0t / (PI/6.0) +zms = 1.0 - eta + +! ---------------------------------------------------------------------- +! compressibility factor z = p/(kT*rho) +! ---------------------------------------------------------------------- +zges = (p * 1.d-30) / (KBOL*t*rho) +IF ( ensemble_flag == 'tv' ) zges = (pges * 1.d-30) / (KBOL*t*rho) +zres = zges - 1.0 + + + +! ====================================================================== +! calculate the derivatives of f to mole fraction x ( d(f)/d(x) ) +! ====================================================================== + +DO k = 1, ncomp + + z0_rk = PI/6.0 * mseg(k) + z1_rk = PI/6.0 * mseg(k) * dhs(k) + z2_rk = PI/6.0 * mseg(k) * dhs(k)*dhs(k) + z3_rk = PI/6.0 * mseg(k) * dhs(k)**3 + +! --- derivative d(m_mean)/d(x) ---------------------------------------- + m_rk(k) = ( mseg(k) - m_mean ) / rho + ! lij(1,2)= -0.050 + ! lij(2,1)=lij(1,2) + ! r_m2dx(k)=0.0 + ! m_mean2=0.0 + ! DO i =1,ncomp + ! r_m2dx(k)=r_m2dx(k)+2.0*x(i)*(mseg(i)+mseg(k))/2.0*(1.0-lij(i,k)) + ! DO j =1,ncomp + ! m_mean2=m_mean2+x(i)*x(j)*(mseg(i)+mseg(j))/2.0*(1.0-lij(i,j)) + ! ENDDO + ! ENDDO + + ! -------------------------------------------------------------------- + ! d(f)/d(x) : hard sphere contribution + ! -------------------------------------------------------------------- + mhs(k) = 6.0/PI* ( 3.0*(z1_rk*z2+z1*z2_rk)/zms + 3.0*z1*z2*z3_rk/zms/zms & + + 3.0*z2*z2*z2_rk/z3/zms/zms + z2**3 *z3_rk*(3.0*z3-1.0)/z3/z3/zms**3 & + + ((3.0*z2*z2*z2_rk*z3-2.0*z2**3 *z3_rk)/z3**3 -z0_rk) *LOG(zms) & + + (z0-z2**3 /z3/z3)*z3_rk/zms ) + + ! -------------------------------------------------------------------- + ! d(f)/d(x) : chain term + ! -------------------------------------------------------------------- + DO i = 1, ncomp + DO j = 1, ncomp + gij(i,j) = 1.0/zms + 3.0*dij_ab(i,j)*z2/zms/zms + 2.0*(dij_ab(i,j)*z2)**2 /zms**3 + gij_rk(i,j) = z3_rk/zms/zms & + + 3.0*dij_ab(i,j)*(z2_rk+2.0*z2*z3_rk/zms)/zms/zms & + + dij_ab(i,j)**2 *z2/zms**3 *(4.0*z2_rk+6.0*z2*z3_rk/zms) + END DO + END DO + + mhc(k) = 0.0 + DO i = 1, ncomp + mhc(k) = mhc(k) + x(i)*rho * (1.0-mseg(i)) / gij(i,i) * gij_rk(i,i) + END DO + mhc(k) = mhc(k) + ( 1.0-mseg(k)) * LOG( gij(k,k) ) + + + ! -------------------------------------------------------------------- + ! PC-SAFT: d(f)/d(x) : dispersion contribution + ! -------------------------------------------------------------------- + IF (eos == 1) THEN + + ! --- derivatives of apar, bpar to rho_k --------------------------- + DO m = 0, 6 + ap_rk(k,m) = m_rk(k)/m_mean**2 * ( ap(m,2) + (3.0 -4.0/m_mean) *ap(m,3) ) + bp_rk(k,m) = m_rk(k)/m_mean**2 * ( bp(m,2) + (3.0 -4.0/m_mean) *bp(m,3) ) + END DO + + I1 = 0.0 + I2 = 0.0 + I1_rk = 0.0 + I2_rk = 0.0 + DO m = 0, 6 + I1 = I1 + apar(m)*eta**REAL(m) + I2 = I2 + bpar(m)*eta**REAL(m) + I1_rk = I1_rk + apar(m)*REAL(m)*eta**REAL(m-1)*z3_rk + ap_rk(k,m)*eta**REAL(m) + I2_rk = I2_rk + bpar(m)*REAL(m)*eta**REAL(m-1)*z3_rk + bp_rk(k,m)*eta**REAL(m) + END DO + + ord1_rk = 0.0 + ord2_rk = 0.0 + DO i = 1,ncomp + ord1_rk = ord1_rk + 2.0*mseg(k)*rho*x(i)*mseg(i)*sig_ij(i,k)**3 *uij(i,k)/t + ord2_rk = ord2_rk + 2.0*mseg(k)*rho*x(i)*mseg(i)*sig_ij(i,k)**3 *(uij(i,k)/t)**2 + END DO + + c1_con= 1.0/ ( 1.0 + m_mean*(8.0*z3-2.0*z3*z3)/zms**4 & + + (1.0 - m_mean)*(20.0*z3-27.0*z3*z3 +12.0*z3**3 -2.0*z3**4 ) & + /(zms*(2.0-z3))**2 ) + c2_con= - c1_con*c1_con *( m_mean*(-4.0*z3*z3+20.0*z3+8.0)/zms**5 & + + (1.0 - m_mean) *(2.0*z3**3 +12.0*z3*z3-48.0*z3+40.0) & + /(zms*(2.0-z3))**3 ) + c1_rk= c2_con*z3_rk - c1_con*c1_con*m_rk(k) * ( (8.0*z3-2.0*z3*z3)/zms**4 & + - (-2.0*z3**4 +12.0*z3**3 -27.0*z3*z3+20.0*z3) / (zms*(2.0-z3))**2 ) + + mdsp(k) = -2.0*PI* ( order1*rho*rho*I1_rk + ord1_rk*I1 ) & + - PI* c1_con*m_mean * ( order2*rho*rho*I2_rk + ord2_rk*I2 ) & + - PI* ( c1_con*m_rk(k) + c1_rk*m_mean ) * order2*rho*rho*I2 + + ! -------------------------------------------------------------------- + ! SAFT: d(f)/d(x) : dispersion contribution + ! -------------------------------------------------------------------- + ELSE + + zmr = 0.0 + nmr = 0.0 + zmr_rk = 0.0 + nmr_rk = 0.0 + DO i = 1, ncomp + DO j = 1, ncomp + zmr = zmr + x(i)*x(j)*mseg(i)*mseg(j)*vij(i,j)*uij(i,j) + nmr = nmr + x(i)*x(j)*mseg(i)*mseg(j)*vij(i,j) + END DO + zmr_rk = zmr_rk + 2.0*mseg(k) * x(i)*mseg(i)*vij(k,i)*uij(k,i) + nmr_rk = nmr_rk + 2.0*mseg(k) * x(i)*mseg(i)*vij(k,i) + END DO + + um_rk = 1.0/nmr**2 * ( nmr*zmr_rk - zmr*nmr_rk ) + + mdsp(k) = 0.0 + DO i = 1,4 + DO j = 1,9 + mdsp(k) = mdsp(k) + dnm(i,j)*(um/t)**REAL(i)*(eta/tau)**REAL(j) & + * ( 1.0 + z3_rk*rho/eta*REAL(j) + um_rk*rho/um*REAL(i) ) + END DO + END DO + + END IF + ! --- end of dispersion contribution------------------------------------ + + + ! -------------------------------------------------------------------- + ! TPT-1-association according to Chapman et al. + ! -------------------------------------------------------------------- + m_hbon(k) = 0.0 + assoc = .false. + DO i = 1,ncomp + IF (nhb_typ(i) /= 0) assoc = .true. + END DO + IF (assoc) THEN + + ass_s2 = 0.0 + DO l = 1, nhb_typ(k) + ass_s2 = ass_s2 + nhb_no(k,l) * LOG(mx(k,l)) + END DO + + m_hbon(k)=ass_s2 + DO i = 1, ncomp + DO ki = 1, nhb_typ(i) + DO j = 1, ncomp + DO l = 1, nhb_typ(j) + m_hbon(k)= m_hbon(k) - rho*rho/2.0*x(i)*x(j) *mx(i,ki)*mx(j,l) *nhb_no(i,ki)*nhb_no(j,l) & + * gij_rk(i,j) * ass_d(i,j,ki,l) + END DO + END DO + END DO + END DO + + END IF + ! --- end of TPT-1-association accord. to Chapman -------------------- + + + ! -------------------------------------------------------------------- + ! polar terms + ! -------------------------------------------------------------------- + CALL PHI_POLAR ( k, z3_rk, fdd_rk, fqq_rk, fdq_rk ) + my_dd(k) = fdd_rk + my_qq(k) = fqq_rk + my_dq(k) = fdq_rk + + + ! -------------------------------------------------------------------- + ! d(f)/d(x) : summation of all contributions + ! -------------------------------------------------------------------- + myres(k) = mhs(k) +mhc(k) +mdsp(k) +m_hbon(k) +my_dd(k) +my_qq(k) +my_dq(k) + +END DO + + +! ---------------------------------------------------------------------- +! finally calculate +! mu_i^res(T,p,x)/kT = ln( phi_i ) when ensemble_flag = 'tp' +! mu_i^res(T,rho,x)/kT when ensemble_flag = 'tv' +! ---------------------------------------------------------------------- + +DO k = 1, ncomp + ! write (*,*) k,myres(k) +LOG(rho*x(k)),rho + IF (ensemble_flag == 'tp' ) lnphi(k) = myres(k) - LOG(zges) + IF (ensemble_flag == 'tv' ) lnphi(k) = myres(k) + ! write (*,*) 'in',k,EXP(lnphi(k)),LOG(zges),eta +END DO +!write (*,'(5G18.10)') lnphi(1),rho + +dpdz = pgesdz +dpdz2 = pgesd2 + +END SUBROUTINE PHI_EOS + + +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! + SUBROUTINE PHI_NUMERICAL +! + USE EOS_VARIABLES + USE EOS_CONSTANTS + USE DFT_MODULE, ONLY: z_ges, fres_temp + IMPLICIT NONE +! +!-----local variables------------------------------------------------- + INTEGER :: k + REAL :: zres, zges + REAL :: fres1, fres2, fres3, fres4, fres5 + REAL :: delta_rho + REAL, DIMENSION(nc) :: myres + REAL, DIMENSION(nc) :: rhoi, rhoi_0 + REAL :: tfr_1, tfr_2, tfr_3, tfr_4, tfr_5 +!----------------------------------------------------------------------- + + +!----------------------------------------------------------------------- +! density iteration or pressure calculation +!----------------------------------------------------------------------- + +IF (ensemble_flag == 'tp') THEN + CALL DENSITY_ITERATION +ELSEIF (ensemble_flag == 'tv') THEN + eta = eta_start + CALL P_NUMERICAL +ELSE + write (*,*) 'PHI_EOS: define ensemble, ensemble_flag == (tv) or (tp)' + stop +END IF + +!----------------------------------------------------------------------- +! compressibility factor z = p/(kT*rho) +!----------------------------------------------------------------------- + +zges = (p * 1.E-30) / (kbol*t*eta/z3t) +IF ( ensemble_flag == 'tv' ) zges = (pges * 1.E-30) / (kbol*t*eta/z3t) +zres = zges - 1.0 +z_ges = zges + +rhoi_0(1:ncomp) = x(1:ncomp) * eta/z3t +rhoi(1:ncomp) = rhoi_0(1:ncomp) + + +!----------------------------------------------------------------------- +! derivative to rho_k (keeping other rho_i's constant +!----------------------------------------------------------------------- + +DO k = 1, ncomp + + IF ( rhoi_0(k) > 1.d-9 ) THEN + delta_rho = 1.E-13 * 10.0**(0.5*(15.0+LOG10(rhoi_0(k)))) + ELSE + delta_rho = 1.E-10 + END IF + + rhoi(k) = rhoi_0(k) + delta_rho + eta = PI/6.0 * SUM( rhoi(1:ncomp)*mseg(1:ncomp)*dhs(1:ncomp)**3 ) + x(1:ncomp) = rhoi(1:ncomp) / SUM( rhoi(1:ncomp) ) + rho = SUM( rhoi(1:ncomp) ) + CALL F_NUMERICAL + fres1 = fres*rho + tfr_1 = tfr*rho + + rhoi(k) = rhoi_0(k) + 0.5 * delta_rho + eta = PI/6.0 * SUM( rhoi(1:ncomp)*mseg(1:ncomp)*dhs(1:ncomp)**3 ) + x(1:ncomp) = rhoi(1:ncomp) / SUM( rhoi(1:ncomp) ) + rho = SUM( rhoi(1:ncomp) ) + CALL F_NUMERICAL + fres2 = fres*rho + tfr_2 = tfr*rho + + IF ( rhoi_0(k) > 1.E-9 ) THEN + rhoi(k) = rhoi_0(k) - 0.5 * delta_rho + eta = PI/6.0 * SUM( rhoi(1:ncomp)*mseg(1:ncomp)*dhs(1:ncomp)**3 ) + x(1:ncomp) = rhoi(1:ncomp) / SUM( rhoi(1:ncomp) ) + rho = SUM( rhoi(1:ncomp) ) + CALL F_NUMERICAL + fres4 = fres*rho + tfr_4 = tfr*rho + + rhoi(k) = rhoi_0(k) - delta_rho + eta = PI/6.0 * SUM( rhoi(1:ncomp)*mseg(1:ncomp)*dhs(1:ncomp)**3 ) + x(1:ncomp) = rhoi(1:ncomp) / SUM( rhoi(1:ncomp) ) + rho = SUM( rhoi(1:ncomp) ) + CALL F_NUMERICAL + fres5 = fres*rho + tfr_5 = tfr*rho + END IF + + rhoi(k) = rhoi_0(k) + eta = PI/6.0 * SUM( rhoi(1:ncomp)*mseg(1:ncomp)*dhs(1:ncomp)**3 ) + x(1:ncomp) = rhoi(1:ncomp) / SUM( rhoi(1:ncomp) ) + rho = SUM( rhoi(1:ncomp) ) + CALL F_NUMERICAL + fres3 = fres*rho + tfr_3 = tfr*rho + + IF ( rhoi_0(k) > 1.E-9 ) THEN + myres(k) = ( fres5 - 8.0*fres4 + 8.0*fres2 - fres1 ) / ( 6.0*delta_rho ) + ELSE + myres(k) = ( -3.0*fres3 + 4.0*fres2 - fres1 ) / delta_rho + END IF + +END DO + + +!----------------------------------------------------------------------- +! residual Helmholtz energy +!----------------------------------------------------------------------- + +fres_temp = fres + +!----------------------------------------------------------------------- +! residual chemical potential +!----------------------------------------------------------------------- + +DO k = 1, ncomp + IF (ensemble_flag == 'tp') lnphi(k) = myres(k) - LOG(zges) + IF (ensemble_flag == 'tv' .AND. eta >= 0.0) lnphi(k) = myres(k) !+LOG(rho) + ! write (*,*) 'in',k,EXP(lnphi(k)),LOG(zges),eta + ! IF (DFT.GE.98) write (*,*) dft + ! write (*,*) 'lnphi',k,LNPHI(k),x(k),MYRES(k), -LOG(ZGES) + ! pause + ! write (*,*) k, myres(k), fres, ZRES +END DO + +END SUBROUTINE PHI_NUMERICAL + + +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW + +! SUBROUTINE H_EOS (phas,h_res,s_res,cp_res,X,T,P,PARAME, +! 1 KIJ,lij,NCOMP,ETA_START,ETA,eos,tfr) +! IMPLICIT NONE +! INTEGER nc +! PARAMETER (nc=20) +! INTEGER phas,ncomp,eos,i +! REAL kij(nc,nc),lij(nc,nc),x(nc),t,p,parame(nc,25) +! REAL eta_start,eta,tfr,h_res,cp_res,s_res + + +! i=1 + +! IF (i.EQ.1) THEN +! CALL H_EOS_1(phas,h_res,s_res,cp_res,X,T,P,PARAME, +! 1 KIJ,lij,NCOMP,ETA_START,ETA,eos,tfr) +! ELSE +! CALL H_EOS_NUM (phas,h_res,s_res,cp_res,X,T,P,PARAME, +! 1 KIJ,lij,NCOMP,ETA_START,ETA,eos,tfr) +! ENDIF + +! RETURN +! END + + +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! + SUBROUTINE H_EOS +! + USE PARAMETERS, ONLY: RGAS + USE EOS_CONSTANTS + USE EOS_VARIABLES + IMPLICIT NONE +! +! ---------------------------------------------------------------------- + REAL :: zges, df_dt, dfdr, ddfdrdr + REAL :: cv_res, df_dt2, df_drdt + REAL :: fact, dist, t_tmp, rho_0 + REAL :: fdr1, fdr2, fdr3, fdr4 + + INTEGER :: i, m + REAL :: dhsdt(nc), dhsdt2(nc) + REAL :: z0, z1, z2, z3, z1tdt, z2tdt, z3tdt + REAL :: z1dt, z2dt, z3dt, zms, gii + REAL :: fhsdt, fhsdt2 + REAL :: fchdt, fchdt2 + REAL :: fdspdt, fdspdt2 + REAL :: fhbdt, fhbdt2 + REAL :: sumseg, I1, I2, I1dt, I2dt, I1dt2, I2dt2 + REAL :: c1_con, c2_con, c3_con, c1_dt, c1_dt2 + REAL :: z1tdt2, z2tdt2, z3tdt2 + REAL :: z1dt2, z2dt2, z3dt2 + + INTEGER :: j, k, l, no, ass_cnt, max_eval + LOGICAL :: assoc + REAL :: dij, dijdt, dijdt2 + REAL :: gij1dt, gij2dt, gij3dt + REAL :: gij1dt2, gij2dt2, gij3dt2 + REAL, DIMENSION(nc,nc) :: gijdt, gijdt2, kap_hb + REAL, DIMENSION(nc,nc,nsite,nsite) :: ass_d_dt, ass_d_dt2, eps_hb, delta, deltadt, deltadt2 + REAL, DIMENSION(nc,nsite) :: mxdt, mxdt2, mx_itr, mx_itrdt, mx_itrdt2 + REAL :: attenu, tol, suma, sumdt, sumdt2, err_sum + + INTEGER :: dipole + REAL :: fdddt, fdddt2 + REAL, DIMENSION(nc) :: my2dd, my0 + REAL, DIMENSION(nc,nc) :: idd2, idd2dt, idd2dt2, idd4, idd4dt, idd4dt2 + REAL, DIMENSION(nc,nc,nc) :: idd3, idd3dt, idd3dt2 + REAL :: factor2, factor3 + REAL :: fdd2, fdd3, fdd2dt, fdd3dt, fdd2dt2, fdd3dt2 + REAL :: eij, xijmt, xijkmt + + INTEGER :: qudpole + REAL :: fqqdt, fqqdt2 + REAL, DIMENSION(nc) :: qq2 + REAL, DIMENSION(nc,nc) :: iqq2, iqq2dt, iqq2dt2, iqq4, iqq4dt, iqq4dt2 + REAL, DIMENSION(nc,nc,nc) :: iqq3, iqq3dt, iqq3dt2 + REAL :: fqq2, fqq2dt, fqq2dt2, fqq3, fqq3dt, fqq3dt2 + + INTEGER :: dip_quad + REAL :: fdqdt, fdqdt2 + REAL, DIMENSION(nc) :: myfac, q_fac + REAL, DIMENSION(nc,nc) :: idq2, idq2dt, idq2dt2, idq4, idq4dt, idq4dt2 + REAL, DIMENSION(nc,nc,nc) :: idq3, idq3dt, idq3dt2 + REAL :: fdq2, fdq2dt, fdq2dt2, fdq3, fdq3dt, fdq3dt2 +! ---------------------------------------------------------------------- + + +! ---------------------------------------------------------------------- +! Initializing +! ---------------------------------------------------------------------- +CALL PERTURBATION_PARAMETER + +rho = eta/z3t +z0 = z0t*rho +z1 = z1t*rho +z2 = z2t*rho +z3 = z3t*rho + +sumseg = z0t / (PI/6.0) +zms = 1.0 - z3 + + +! ---------------------------------------------------------------------- +! first and second derivative of f to density (dfdr,ddfdrdr) +! ---------------------------------------------------------------------- +CALL P_EOS + +zges = (pges * 1.E-30)/(kbol*t*rho) + +dfdr = pges/(eta*rho*(kbol*t)/1.E-30) +ddfdrdr = pgesdz/(eta*rho*(kbol*t)/1.E-30) - dfdr*2.0/eta - 1.0/eta**2 + + +! ---------------------------------------------------------------------- +! Helmholtz Energy f/kT = fres +! ---------------------------------------------------------------------- +CALL F_EOS + + +! ---------------------------------------------------------------------- +! derivative of some auxilliary properties to temperature +! ---------------------------------------------------------------------- +DO i = 1,ncomp + dhsdt(i)=parame(i,2) *(-3.0*parame(i,3)/t/t)*0.12*EXP(-3.0*parame(i,3)/t) + dhsdt2(i) = dhsdt(i)*3.0*parame(i,3)/t/t & + + 6.0*parame(i,2)*parame(i,3)/t**3 *0.12*EXP(-3.0*parame(i,3)/t) +END DO + +z1tdt = 0.0 +z2tdt = 0.0 +z3tdt = 0.0 +DO i = 1,ncomp + z1tdt = z1tdt + x(i) * mseg(i) * dhsdt(i) + z2tdt = z2tdt + x(i) * mseg(i) * 2.0*dhs(i)*dhsdt(i) + z3tdt = z3tdt + x(i) * mseg(i) * 3.0*dhs(i)*dhs(i)*dhsdt(i) +END DO +z1dt = PI / 6.0*z1tdt *rho +z2dt = PI / 6.0*z2tdt *rho +z3dt = PI / 6.0*z3tdt *rho + + +z1tdt2 = 0.0 +z2tdt2 = 0.0 +z3tdt2 = 0.0 +DO i = 1,ncomp + z1tdt2 = z1tdt2 + x(i)*mseg(i)*dhsdt2(i) + z2tdt2 = z2tdt2 + x(i)*mseg(i)*2.0 *( dhsdt(i)*dhsdt(i) +dhs(i)*dhsdt2(i) ) + z3tdt2 = z3tdt2 + x(i)*mseg(i)*3.0 *( 2.0*dhs(i)*dhsdt(i)* & + dhsdt(i) +dhs(i)*dhs(i)*dhsdt2(i) ) +END DO +z1dt2 = PI / 6.0*z1tdt2 *rho +z2dt2 = PI / 6.0*z2tdt2 *rho +z3dt2 = PI / 6.0*z3tdt2 *rho + + +! ---------------------------------------------------------------------- +! 1st & 2nd derivative of f/kT hard spheres to temp. (fhsdt) +! ---------------------------------------------------------------------- +fhsdt = 6.0/PI/rho*( 3.0*(z1dt*z2+z1*z2dt)/zms + 3.0*z1*z2*z3dt/zms/zms & + + 3.0*z2*z2*z2dt/z3/zms/zms & + + z2**3 *(2.0*z3*z3dt-z3dt*zms)/(z3*z3*zms**3 ) & + + (3.0*z2*z2*z2dt*z3-2.0*z2**3 *z3dt)/z3**3 *LOG(zms) & + + (z0-z2**3 /z3/z3)*z3dt/zms ) + +fhsdt2= 6.0/PI/rho*( 3.0*(z1dt2*z2+2.0*z1dt*z2dt+z1*z2dt2)/zms & + + 6.0*(z1dt*z2+z1*z2dt)*z3dt/zms/zms & + + 3.0*z1*z2*z3dt2/zms/zms + 6.0*z1*z2*z3dt*z3dt/zms**3 & + + 3.0*z2*(2.0*z2dt*z2dt+z2*z2dt2)/z3/zms/zms & + - z2*z2*(6.0*z2dt*z3dt+z2*z3dt2)/(z3*z3*zms*zms) & + + 2.0*z2**3 *z3dt*z3dt/(z3**3 *zms*zms) & + - 4.0*z2**3 *z3dt*z3dt/(z3*z3 *zms**3 ) & + + (12.0*z2*z2*z2dt*z3dt+2.0*z2**3 *z3dt2)/(z3*zms**3 ) & + + 6.0*z2**3 *z3dt*z3dt/(z3*zms**4 ) & + - 2.0*(3.0*z2*z2*z2dt/z3/z3-2.0*z2**3 *z3dt/z3**3 ) *z3dt/zms & + -(z2**3 /z3/z3-z0)*(z3dt2/zms+z3dt*z3dt/zms/zms) & + + ( (6.0*z2*z2dt*z2dt+3.0*z2*z2*z2dt2)/z3/z3 & + - (12.0*z2*z2*z2dt*z3dt+2.0*z2**3 *z3dt2)/z3**3 & + + 6.0*z2**3 *z3dt*z3dt/z3**4 )* LOG(zms) ) + + +! ---------------------------------------------------------------------- +! 1st & 2nd derivative of f/kT of chain term to T (fchdt) +! ---------------------------------------------------------------------- +fchdt = 0.0 +fchdt2 = 0.0 +DO i = 1, ncomp + DO j = 1, ncomp + dij=dhs(i)*dhs(j)/(dhs(i)+dhs(j)) + dijdt =(dhsdt(i)*dhs(j) + dhs(i)*dhsdt(j)) / (dhs(i)+dhs(j)) & + - dhs(i)*dhs(j)/(dhs(i)+dhs(j))**2 *(dhsdt(i)+dhsdt(j)) + dijdt2=(dhsdt2(i)*dhs(j) + 2.0*dhsdt(i)*dhsdt(j) & + + dhs(i)*dhsdt2(j)) / (dhs(i)+dhs(j)) & + - 2.0*(dhsdt(i)*dhs(j) + dhs(i)*dhsdt(j)) & + / (dhs(i)+dhs(j))**2 *(dhsdt(i)+dhsdt(j)) & + + 2.0* dhs(i)*dhs(j) / (dhs(i)+dhs(j))**3 & + * (dhsdt(i)+dhsdt(j))**2 & + - dhs(i)*dhs(j)/(dhs(i)+dhs(j))**2 *(dhsdt2(i)+dhsdt2(j)) + gij1dt = z3dt/zms/zms + gij2dt = 3.0*( z2dt*dij+z2*dijdt )/zms/zms +6.0*z2*dij*z3dt/zms**3 + gij3dt = 4.0*(dij*z2)* (dijdt*z2 + dij*z2dt) /zms**3 & + + 6.0*(dij*z2)**2 * z3dt /zms**4 + gij1dt2 = z3dt2/zms/zms +2.0*z3dt*z3dt/zms**3 + gij2dt2 = 3.0*( z2dt2*dij+2.0*z2dt*dijdt+z2*dijdt2 )/zms/zms & + + 6.0*( z2dt*dij+z2*dijdt )/zms**3 * z3dt & + + 6.0*(z2dt*dij*z3dt+z2*dijdt*z3dt+z2*dij*z3dt2) /zms**3 & + + 18.0*z2*dij*z3dt*z3dt/zms**4 + gij3dt2 = 4.0*(dijdt*z2+dij*z2dt)**2 /zms**3 & + + 4.0*(dij*z2)* (dijdt2*z2+2.0*dijdt*z2dt+dij*z2dt2) /zms**3 & + + 24.0*(dij*z2) *(dijdt*z2+dij*z2dt)/zms**4 *z3dt & + + 6.0*(dij*z2)**2 * z3dt2 /zms**4 & + + 24.0*(dij*z2)**2 * z3dt*z3dt /zms**5 + gijdt(i,j) = gij1dt + gij2dt + gij3dt + gijdt2(i,j) = gij1dt2 + gij2dt2 + gij3dt2 + END DO +END DO + +DO i = 1, ncomp + gii = 1.0/zms + 3.0*dhs(i)/2.0*z2/zms/zms + 2.0*dhs(i)*dhs(i)/4.0*z2*z2/zms**3 + fchdt = fchdt + x(i) * (1.0-mseg(i)) * gijdt(i,i) / gii + fchdt2= fchdt2+ x(i) * (1.0-mseg(i)) & + * (gijdt2(i,i) / gii - (gijdt(i,i)/gii)**2 ) +END DO + + +! ---------------------------------------------------------------------- +! 1st & 2nd derivative of f/kT dispersion term to T (fdspdt) +! ---------------------------------------------------------------------- +I1 = 0.0 +I2 = 0.0 +I1dt = 0.0 +I2dt = 0.0 +I1dt2= 0.0 +I2dt2= 0.0 +DO m = 0, 6 + I1 = I1 + apar(m)*z3**REAL(m) + I2 = I2 + bpar(m)*z3**REAL(m) + I1dt = I1dt + apar(m)*z3dt*REAL(m)*z3**REAL(m-1) + I2dt = I2dt + bpar(m)*z3dt*REAL(m)*z3**REAL(m-1) + I1dt2= I1dt2+ apar(m)*z3dt2*REAL(m)*z3**REAL(m-1) & + + apar(m)*z3dt*z3dt *REAL(m)*REAL(m-1)*z3**REAL(m-2) + I2dt2= I2dt2+ bpar(m)*z3dt2*REAL(m)*z3**REAL(m-1) & + + bpar(m)*z3dt*z3dt *REAL(m)*REAL(m-1)*z3**REAL(m-2) +END DO + +c1_con= 1.0/ ( 1.0 + sumseg*(8.0*z3-2.0*z3**2 )/zms**4 & + + (1.0 - sumseg)*(20.0*z3-27.0*z3**2 +12.0*z3**3 -2.0*z3**4 ) & + /(zms*(2.0-z3))**2 ) +c2_con= - c1_con*c1_con *(sumseg*(-4.0*z3**2 +20.0*z3+8.0)/zms**5 & + + (1.0 - sumseg) *(2.0*z3**3 +12.0*z3**2 -48.0*z3+40.0) & + /(zms*(2.0-z3))**3 ) +c3_con= 2.0 * c2_con*c2_con/c1_con - c1_con*c1_con & + *( sumseg*(-12.0*z3**2 +72.0*z3+60.0)/zms**6 + (1.0 - sumseg) & + *(-6.0*z3**4 -48.0*z3**3 +288.0*z3**2 -480.0*z3+264.0) & + /(zms*(2.0-z3))**4 ) +c1_dt = c2_con*z3dt +c1_dt2 = c3_con*z3dt*z3dt + c2_con*z3dt2 + +fdspdt = - 2.0*PI*rho*(I1dt-I1/t)*order1 & + - PI*rho*sumseg*(c1_dt*I2+c1_con*I2dt-2.0*c1_con*I2/t)*order2 + +fdspdt2 = - 2.0*PI*rho*(I1dt2-2.0*I1dt/t+2.0*I1/t/t)*order1 & + - PI*rho*sumseg*order2*( c1_dt2*I2 +2.0*c1_dt*I2dt -4.0*c1_dt*I2/t & + + 6.0*c1_con*I2/t/t -4.0*c1_con*I2dt/t +c1_con*I2dt2) + + +! ---------------------------------------------------------------------- +! 1st & 2nd derivative of f/kT association term to T (fhbdt) +! ---------------------------------------------------------------------- +fhbdt = 0.0 +fhbdt2 = 0.0 +assoc = .false. +DO i = 1,ncomp + IF ( nhb_typ(i) /= 0 ) assoc = .true. +END DO +IF (assoc) THEN + + DO i = 1,ncomp + IF ( nhb_typ(i) /= 0 ) THEN + kap_hb(i,i) = parame(i,13) + no = 0 + DO j = 1,nhb_typ(i) + DO k = 1,nhb_typ(i) + eps_hb(i,i,j,k) = parame(i,(14+no)) + no = no + 1 + END DO + END DO + DO j = 1,nhb_typ(i) + no = no + 1 + END DO + ELSE + kap_hb(i,i) = 0.0 + DO k = 1,nsite + DO l = 1,nsite + eps_hb(i,i,k,l) = 0.0 + END DO + END DO + END IF + END DO + + DO i = 1,ncomp + DO j = 1,ncomp + IF ( i /= j .AND. (nhb_typ(i) /= 0 .AND. nhb_typ(j) /= 0) ) THEN + kap_hb(i,j)= (kap_hb(i,i)*kap_hb(j,j))**0.5 & + *((parame(i,2)*parame(j,2))**3 )**0.5 & + /(0.5*(parame(i,2)+parame(j,2)))**3 + ! kap_hb(i,j)= kap_hb(i,j)*(1.0-k_kij) + DO k = 1,nhb_typ(i) + DO l = 1,nhb_typ(j) + IF (k /= l) THEN + eps_hb(i,j,k,l)=(eps_hb(i,i,k,l)+eps_hb(j,j,l,k))/2.0 + ! eps_hb(i,j,k,l)=eps_hb(i,j,k,l)*(1.0-eps_kij) + END IF + END DO + END DO + END IF + END DO + END DO + IF (nhb_typ(1) == 3) THEN + eps_hb(1,2,3,1)=0.5*(eps_hb(1,1,3,1)+eps_hb(2,2,1,2)) + eps_hb(2,1,1,3) = eps_hb(1,2,3,1) + END IF + IF (nhb_typ(2) == 3) THEN + eps_hb(2,1,3,1)=0.5*(eps_hb(2,2,3,1)+eps_hb(1,1,1,2)) + eps_hb(1,2,1,3) = eps_hb(2,1,3,1) + END IF + + DO i = 1, ncomp + DO k = 1, nhb_typ(i) + DO j = 1, ncomp + DO l = 1, nhb_typ(j) + ! ass_d(i,j,k,l)=kap_hb(i,j) *sig_ij(i,j)**3 *(EXP(eps_hb(i,j,k,l)/t)-1.0) + ass_d_dt(i,j,k,l)= - kap_hb(i,j) *sig_ij(i,j)**3 * eps_hb(i,j,k,l)/t/t*EXP(eps_hb(i,j,k,l)/t) + ass_d_dt2(i,j,k,l)= - kap_hb(i,j) *sig_ij(i,j)**3 & + * eps_hb(i,j,k,l)/t/t*EXP(eps_hb(i,j,k,l)/t) & + * (-2.0/t - eps_hb(i,j,k,l)/t/t) + END DO + END DO + END DO + END DO + + DO i = 1, ncomp + DO k = 1, nhb_typ(i) + DO j = 1, ncomp + DO l = 1, nhb_typ(j) + delta(i,j,k,l)=gij(i,j)*ass_d(i,j,k,l) + deltadt(i,j,k,l) = gijdt(i,j)*ass_d(i,j,k,l) + gij(i,j)*ass_d_dt(i,j,k,l) + deltadt2(i,j,k,l)= gijdt2(i,j)*ass_d(i,j,k,l) & + + 2.0*gijdt(i,j)*ass_d_dt(i,j,k,l) +gij(i,j)*ass_d_dt2(i,j,k,l) + END DO + END DO + END DO + END DO + + +! ------ constants for iteration --------------------------------------- + attenu = 0.7 + tol = 1.E-10 + IF (eta < 0.2) tol = 1.E-11 + IF (eta < 0.01) tol = 1.E-12 + max_eval = 200 + +! ------ initialize mxdt(i,j) ------------------------------------------ + DO i = 1, ncomp + DO k = 1, nhb_typ(i) + mxdt(i,k) = 0.0 + mxdt2(i,k) = 0.0 + END DO + END DO + + +! ------ iterate over all components and all sites --------------------- + DO ass_cnt = 1, max_eval + + DO i = 1, ncomp + DO k = 1, nhb_typ(i) + suma = 0.0 + sumdt = 0.0 + sumdt2= 0.0 + DO j = 1, ncomp + DO l = 1, nhb_typ(j) + suma = suma + x(j)*nhb_no(j,l)* mx(j,l) *delta(i,j,k,l) + sumdt = sumdt + x(j)*nhb_no(j,l)*( mx(j,l) *deltadt(i,j,k,l) & + + mxdt(j,l)*delta(i,j,k,l) ) + sumdt2 = sumdt2 + x(j)*nhb_no(j,l)*( mx(j,l)*deltadt2(i,j,k,l) & + + 2.0*mxdt(j,l)*deltadt(i,j,k,l) + mxdt2(j,l)*delta(i,j,k,l) ) + END DO + END DO + mx_itr(i,k) = 1.0 / (1.0 + suma * rho) + mx_itrdt(i,k)= - mx_itr(i,k)**2 * sumdt*rho + mx_itrdt2(i,k)= +2.0*mx_itr(i,k)**3 * (sumdt*rho)**2 - mx_itr(i,k)**2 *sumdt2*rho + END DO + END DO + + err_sum = 0.0 + DO i = 1, ncomp + DO k = 1, nhb_typ(i) + err_sum = err_sum + ABS(mx_itr(i,k) - mx(i,k)) & + + ABS(mx_itrdt(i,k) - mxdt(i,k)) + ABS(mx_itrdt2(i,k) - mxdt2(i,k)) + mx(i,k) = mx_itr(i,k) * attenu + mx(i,k) * (1.0 - attenu) + mxdt(i,k)=mx_itrdt(i,k)*attenu +mxdt(i,k)* (1.0 - attenu) + mxdt2(i,k)=mx_itrdt2(i,k)*attenu +mxdt2(i,k)* (1.0 - attenu) + END DO + END DO + IF(err_sum <= tol) GO TO 10 + + END DO + WRITE(6,*) 'CAL_PCSAFT: max_eval violated err_sum = ',err_sum,tol + STOP + 10 CONTINUE + + DO i = 1, ncomp + DO k = 1, nhb_typ(i) + ! fhb = fhb + x(i)* nhb_no(i,k)* ( 0.5 * ( 1.0 - mx(i,k) ) + LOG(mx(i,k)) ) + fhbdt = fhbdt + x(i)*nhb_no(i,k) *mxdt(i,k)*(1.0/mx(i,k)-0.5) + fhbdt2= fhbdt2 + x(i)*nhb_no(i,k) *(mxdt2(i,k)*(1.0/mx(i,k)-0.5) & + -(mxdt(i,k)/mx(i,k))**2 ) + END DO + END DO + +END IF + + +! ---------------------------------------------------------------------- +! derivatives of f/kT of dipole-dipole term to temp. (fdddt) +! ---------------------------------------------------------------------- +fdddt = 0.0 +fdddt2 = 0.0 +dipole = 0 +DO i = 1,ncomp + my2dd(i) = 0.0 + IF ( parame(i,6) /= 0.0 .AND. uij(i,i) /= 0.0 ) THEN + dipole = 1 + my2dd(i) = (parame(i,6))**2 *1.E-49 / (uij(i,i)*kbol*mseg(i)*sig_ij(i,i)**3 *1.E-30) + END IF + my0(i) = my2dd(i) ! needed for dipole-quadrupole-term +END DO + +IF (dipole == 1) THEN + DO i = 1,ncomp + DO j = 1,ncomp + idd2(i,j) =0.0 + idd4(i,j) =0.0 + idd2dt(i,j) =0.0 + idd4dt(i,j) =0.0 + idd2dt2(i,j)=0.0 + idd4dt2(i,j)=0.0 + DO m=0,4 + idd2(i,j) = idd2(i,j) +ddp2(i,j,m)*z3**REAL(m) + idd4(i,j) = idd4(i,j) +ddp4(i,j,m)*z3**REAL(m) + idd2dt(i,j)= idd2dt(i,j) +ddp2(i,j,m)*z3dt*REAL(m)*z3**REAL(m-1) + idd4dt(i,j)= idd4dt(i,j) +ddp4(i,j,m)*z3dt*REAL(m)*z3**REAL(m-1) + idd2dt2(i,j)=idd2dt2(i,j)+ddp2(i,j,m)*z3dt2*REAL(m)*z3**REAL(m-1) & + + ddp2(i,j,m)*z3dt**2 *REAL(m)*REAL(m-1)*z3**REAL(m-2) + idd4dt2(i,j)=idd4dt2(i,j)+ddp4(i,j,m)*z3dt2*REAL(m)*z3**REAL(m-1) & + + ddp4(i,j,m)*z3dt**2 *REAL(m)*REAL(m-1)*z3**REAL(m-2) + END DO + DO k = 1,ncomp + idd3(i,j,k) =0.0 + idd3dt(i,j,k) =0.0 + idd3dt2(i,j,k)=0.0 + DO m = 0, 4 + idd3(i,j,k) = idd3(i,j,k) +ddp3(i,j,k,m)*z3**REAL(m) + idd3dt(i,j,k) = idd3dt(i,j,k)+ddp3(i,j,k,m)*z3dt*REAL(m) *z3**REAL(m-1) + idd3dt2(i,j,k)= idd3dt2(i,j,k)+ddp3(i,j,k,m)*z3dt2*REAL(m) & + *z3**REAL(m-1) +ddp3(i,j,k,m)*z3dt**2 *REAL(m)*REAL(m-1) *z3**REAL(m-2) + END DO + END DO + END DO + END DO + + + factor2= -PI *rho + factor3= -4.0/3.0*PI**2 * rho**2 + + fdd2 = 0.0 + fdd3 = 0.0 + fdd2dt= 0.0 + fdd3dt= 0.0 + fdd2dt2= 0.0 + fdd3dt2= 0.0 + DO i = 1, ncomp + DO j = 1, ncomp + xijmt = x(i)*parame(i,3)*parame(i,2)**3 *x(j)*parame(j,3)*parame(j,2)**3 & + / ((parame(i,2)+parame(j,2))/2.0)**3 *my2dd(i)*my2dd(j) + eij = (parame(i,3)*parame(j,3))**0.5 + fdd2 = fdd2 +factor2* xijmt/t/t*(idd2(i,j)+eij/t*idd4(i,j)) + fdd2dt= fdd2dt+ factor2* xijmt/t/t*(idd2dt(i,j)-2.0*idd2(i,j)/t & + +eij/t*idd4dt(i,j)-3.0*eij/t/t*idd4(i,j)) + fdd2dt2=fdd2dt2+factor2*xijmt/t/t*(idd2dt2(i,j)-4.0*idd2dt(i,j)/t & + +6.0*idd2(i,j)/t/t+eij/t*idd4dt2(i,j) & + -6.0*eij/t/t*idd4dt(i,j)+12.0*eij/t**3 *idd4(i,j)) + DO k = 1, ncomp + xijkmt=x(i)*parame(i,3)*parame(i,2)**3 & + *x(j)*parame(j,3)*parame(j,2)**3 & + *x(k)*parame(k,3)*parame(k,2)**3 & + /((parame(i,2)+parame(j,2))/2.0) /((parame(i,2)+parame(k,2))/2.0) & + /((parame(j,2)+parame(k,2))/2.0) *my2dd(i)*my2dd(j)*my2dd(k) + fdd3 =fdd3 +factor3*xijkmt/t**3 *idd3(i,j,k) + fdd3dt =fdd3dt +factor3*xijkmt/t**3 * (idd3dt(i,j,k)-3.0*idd3(i,j,k)/t) + fdd3dt2=fdd3dt2+factor3*xijkmt/t**3 & + *( idd3dt2(i,j,k)-6.0*idd3dt(i,j,k)/t+12.0*idd3(i,j,k)/t/t ) + END DO + END DO + END DO + + IF ( fdd2 < -1.E-100 .AND. fdd3 /= 0.0 ) THEN + fdddt = fdd2* (fdd2*fdd2dt - 2.0*fdd3*fdd2dt+fdd2*fdd3dt) / (fdd2-fdd3)**2 + fdddt2 = ( 2.0*fdd2*fdd2dt*fdd2dt +fdd2*fdd2*fdd2dt2 & + -2.0*fdd2dt**2 *fdd3 -2.0*fdd2*fdd2dt2*fdd3 +fdd2*fdd2*fdd3dt2 ) & + /(fdd2-fdd3)**2 + fdddt * 2.0*(fdd3dt-fdd2dt)/(fdd2-fdd3) + END IF +END IF + + +! ---------------------------------------------------------------------- +! derivatives f/kT of quadrupole-quadrup. term to T (fqqdt) +! ---------------------------------------------------------------------- +fqqdt = 0.0 +fqqdt2 = 0.0 +qudpole = 0 +DO i = 1, ncomp + qq2(i) = (parame(i,7))**2 *1.E-69 / (uij(i,i)*kbol*mseg(i)*sig_ij(i,i)**5 *1.E-50) + IF (qq2(i) /= 0.0) qudpole = 1 +END DO + +IF (qudpole == 1) THEN + + DO i = 1,ncomp + DO j = 1,ncomp + iqq2(i,j) = 0.0 + iqq4(i,j) = 0.0 + iqq2dt(i,j) = 0.0 + iqq4dt(i,j) = 0.0 + iqq2dt2(i,j)= 0.0 + iqq4dt2(i,j)= 0.0 + DO m = 0, 4 + iqq2(i,j) = iqq2(i,j) + qqp2(i,j,m)*z3**REAL(m) + iqq4(i,j) = iqq4(i,j) + qqp4(i,j,m)*z3**REAL(m) + iqq2dt(i,j) = iqq2dt(i,j)+ qqp2(i,j,m)*z3dt*REAL(m)*z3**REAL(m-1) + iqq4dt(i,j) = iqq4dt(i,j)+ qqp4(i,j,m)*z3dt*REAL(m)*z3**REAL(m-1) + iqq2dt2(i,j)= iqq2dt2(i,j)+qqp2(i,j,m)*z3dt2*REAL(m)*z3**REAL(m-1) & + + qqp2(i,j,m)*z3dt**2 *REAL(m)*REAL(m-1)*z3**REAL(m-2) + iqq4dt2(i,j)= iqq4dt2(i,j)+qqp4(i,j,m)*z3dt2*REAL(m)*z3**REAL(m-1) & + + qqp4(i,j,m)*z3dt**2 *REAL(m)*REAL(m-1)*z3**REAL(m-2) + END DO + DO k = 1,ncomp + iqq3(i,j,k) =0.0 + iqq3dt(i,j,k) =0.0 + iqq3dt2(i,j,k)=0.0 + DO m = 0, 4 + iqq3(i,j,k) = iqq3(i,j,k) + qqp3(i,j,k,m)*z3**REAL(m) + iqq3dt(i,j,k) = iqq3dt(i,j,k)+ qqp3(i,j,k,m)*z3dt*REAL(m) * z3**REAL(m-1) + iqq3dt2(i,j,k)= iqq3dt2(i,j,k)+qqp3(i,j,k,m)*z3dt2*REAL(m) * z3**REAL(m-1) & + + qqp3(i,j,k,m)*z3dt**2 *REAL(m)*REAL(m-1)*z3**REAL(m-2) + END DO + END DO + END DO + END DO + + factor2 = -9.0/16.0 * PI *rho + factor3 = 9.0/16.0 * PI**2 * rho**2 + + fqq2 = 0.0 + fqq3 = 0.0 + fqq2dt = 0.0 + fqq3dt = 0.0 + fqq2dt2= 0.0 + fqq3dt2= 0.0 + DO i = 1,ncomp + DO j = 1,ncomp + xijmt = x(i)*uij(i,i)*qq2(i)*sig_ij(i,i)**5 & + * x(j)*uij(j,j)*qq2(j)*sig_ij(j,j)**5 /sig_ij(i,j)**7.0 + eij = (parame(i,3)*parame(j,3))**0.5 + fqq2 = fqq2 +factor2* xijmt/t/t*(iqq2(i,j)+eij/t*iqq4(i,j)) + fqq2dt= fqq2dt +factor2* xijmt/t/t*(iqq2dt(i,j)-2.0*iqq2(i,j)/t & + + eij/t*iqq4dt(i,j)-3.0*eij/t/t*iqq4(i,j)) + fqq2dt2=fqq2dt2+factor2*xijmt/t/t*(iqq2dt2(i,j)-4.0*iqq2dt(i,j)/t & + + 6.0*iqq2(i,j)/t/t+eij/t*iqq4dt2(i,j) & + - 6.0*eij/t/t*iqq4dt(i,j)+12.0*eij/t**3 *iqq4(i,j)) + DO k = 1,ncomp + xijkmt = x(i)*uij(i,i)*qq2(i)*sig_ij(i,i)**5 /sig_ij(i,j)**3 & + * x(j)*uij(j,j)*qq2(j)*sig_ij(j,j)**5 /sig_ij(i,k)**3 & + * x(k)*uij(k,k)*qq2(k)*sig_ij(k,k)**5 /sig_ij(j,k)**3 + fqq3 = fqq3 +factor3*xijkmt/t**3 *iqq3(i,j,k) + fqq3dt = fqq3dt +factor3*xijkmt/t**3 *(iqq3dt(i,j,k)-3.0*iqq3(i,j,k)/t) + fqq3dt2= fqq3dt2+factor3*xijkmt/t**3 & + * ( iqq3dt2(i,j,k)-6.0*iqq3dt(i,j,k)/t+12.0*iqq3(i,j,k)/t/t ) + END DO + END DO + END DO + + IF ( fqq2 /= 0.0 .AND. fqq3 /= 0.0 ) THEN + fqqdt = fqq2* (fqq2*fqq2dt - 2.0*fqq3*fqq2dt+fqq2*fqq3dt) / (fqq2-fqq3)**2 + fqqdt2 = ( 2.0*fqq2*fqq2dt*fqq2dt +fqq2*fqq2*fqq2dt2 & + - 2.0*fqq2dt**2 *fqq3 -2.0*fqq2*fqq2dt2*fqq3 +fqq2*fqq2*fqq3dt2 ) & + / (fqq2-fqq3)**2 + fqqdt * 2.0*(fqq3dt-fqq2dt)/(fqq2-fqq3) + END IF + +END IF + + +! ---------------------------------------------------------------------- +! derivatives f/kT of dipole-quadruppole term to T (fdqdt) +! ---------------------------------------------------------------------- +fdqdt = 0.0 +fdqdt2= 0.0 +dip_quad = 0 +DO i = 1,ncomp + DO j = 1,ncomp + IF (parame(i,6) /= 0.0 .AND. parame(j,7) /= 0.0) dip_quad = 1 + END DO + myfac(i) = parame(i,3)*parame(i,2)**4 *my0(i) + q_fac(i) = parame(i,3)*parame(i,2)**4 *qq2(i) +END DO + +IF (dip_quad == 1) THEN + + DO i = 1,ncomp + DO j = 1,ncomp + idq2(i,j) = 0.0 + idq4(i,j) = 0.0 + idq2dt(i,j) = 0.0 + idq4dt(i,j) = 0.0 + idq2dt2(i,j)= 0.0 + idq4dt2(i,j)= 0.0 + IF ( myfac(i) /= 0.0 .AND. q_fac(j) /= 0.0 ) THEN + DO m = 0, 4 + idq2(i,j) = idq2(i,j) + dqp2(i,j,m)*z3**REAL(m) + idq4(i,j) = idq4(i,j) + dqp4(i,j,m)*z3**REAL(m) + idq2dt(i,j) = idq2dt(i,j)+ dqp2(i,j,m)*z3dt*REAL(m)*z3**REAL(m-1) + idq4dt(i,j) = idq4dt(i,j)+ dqp4(i,j,m)*z3dt*REAL(m)*z3**REAL(m-1) + idq2dt2(i,j)= idq2dt2(i,j)+dqp2(i,j,m)*z3dt2*REAL(m)*z3**REAL(m-1) & + + dqp2(i,j,m)*z3dt**2 *REAL(m)*REAL(m-1)*z3**REAL(m-2) + idq4dt2(i,j)= idq4dt2(i,j)+dqp4(i,j,m)*z3dt2*REAL(m)*z3**REAL(m-1) & + + dqp4(i,j,m)*z3dt**2 *REAL(m)*REAL(m-1)*z3**REAL(m-2) + END DO + + DO k = 1,ncomp + idq3(i,j,k) = 0.0 + idq3dt(i,j,k) = 0.0 + idq3dt2(i,j,k)= 0.0 + IF ( myfac(k) /= 0.0 .OR. q_fac(k) /= 0.0 ) THEN + DO m = 0, 4 + idq3(i,j,k) = idq3(i,j,k) + dqp3(i,j,k,m)*z3**REAL(m) + idq3dt(i,j,k)= idq3dt(i,j,k)+ dqp3(i,j,k,m)*z3dt*REAL(m) *z3**REAL(m-1) + idq3dt2(i,j,k)= idq3dt2(i,j,k)+dqp3(i,j,k,m)*z3dt2*REAL(m) *z3**REAL(m-1) & + + dqp3(i,j,k,m)*z3dt**2 *REAL(m)*REAL(m-1)*z3**REAL(m-2) + END DO + END IF + END DO + END IF + END DO + END DO + + factor2= -9.0/4.0 * PI * rho + factor3= PI**2 * rho**2 + + fdq2 = 0.0 + fdq3 = 0.0 + fdq2dt= 0.0 + fdq3dt= 0.0 + fdq2dt2=0.0 + fdq3dt2=0.0 + DO i = 1,ncomp + DO j = 1,ncomp + IF ( myfac(i) /= 0.0 .AND. q_fac(j) /= 0.0 ) THEN + xijmt = x(i)*myfac(i) * x(j)*q_fac(j) /sig_ij(i,j)**5 + eij = (parame(i,3)*parame(j,3))**0.5 + fdq2 = fdq2 + factor2* xijmt/t/t*(idq2(i,j)+eij/t*idq4(i,j)) + fdq2dt= fdq2dt+ factor2* xijmt/t/t*(idq2dt(i,j)-2.0*idq2(i,j)/t & + + eij/t*idq4dt(i,j)-3.0*eij/t/t*idq4(i,j)) + fdq2dt2 = fdq2dt2+factor2*xijmt/t/t*(idq2dt2(i,j)-4.0*idq2dt(i,j)/t & + + 6.0*idq2(i,j)/t/t+eij/t*idq4dt2(i,j) & + - 6.0*eij/t/t*idq4dt(i,j)+12.0*eij/t**3 *idq4(i,j)) + DO k = 1,ncomp + IF ( myfac(k) /= 0.0 .OR. q_fac(k) /= 0.0 ) THEN + xijkmt= x(i)*x(j)*x(k)/(sig_ij(i,j)*sig_ij(i,k)*sig_ij(j,k))**2 & + * ( myfac(i)*q_fac(j)*myfac(k) & + + myfac(i)*q_fac(j)*q_fac(k)*1.193735 ) + + fdq3 =fdq3 + factor3*xijkmt/t**3 *idq3(i,j,k) + fdq3dt=fdq3dt+ factor3*xijkmt/t**3 * (idq3dt(i,j,k)-3.0*idq3(i,j,k)/t) + fdq3dt2=fdq3dt2+factor3*xijkmt/t**3 & + *( idq3dt2(i,j,k)-6.0*idq3dt(i,j,k)/t+12.0*idq3(i,j,k)/t/t ) + END IF + END DO + END IF + END DO + END DO + + IF (fdq2 /= 0.0 .AND. fdq3 /= 0.0) THEN + fdqdt = fdq2* (fdq2*fdq2dt - 2.0*fdq3*fdq2dt+fdq2*fdq3dt) / (fdq2-fdq3)**2 + fdqdt2 = ( 2.0*fdq2*fdq2dt*fdq2dt +fdq2*fdq2*fdq2dt2 & + - 2.0*fdq2dt**2 *fdq3 -2.0*fdq2*fdq2dt2*fdq3 +fdq2*fdq2*fdq3dt2 ) & + / (fdq2-fdq3)**2 + fdqdt * 2.0*(fdq3dt-fdq2dt)/(fdq2-fdq3) + END IF + +END IF +! ---------------------------------------------------------------------- + + + + +! ---------------------------------------------------------------------- +! total derivative of fres/kT to temperature +! ---------------------------------------------------------------------- + +df_dt = fhsdt + fchdt + fdspdt + fhbdt + fdddt + fqqdt + fdqdt + + + +! ---------------------------------------------------------------------- +! second derivative of fres/kT to T +! ---------------------------------------------------------------------- + +df_dt2 = fhsdt2 +fchdt2 +fdspdt2 +fhbdt2 +fdddt2 +fqqdt2 +fdqdt2 + + + +! ---------------------------------------------------------------------- +! ------ derivatives of fres/kt to density and to T -------------------- +! ---------------------------------------------------------------------- + +! ---------------------------------------------------------------------- +! the analytic derivative of fres/kT to (density and T) (df_drdt) +! is still missing. A numerical differentiation is implemented. +! ---------------------------------------------------------------------- +fact = 1.0 +dist = t * 100.E-5 * fact +t_tmp = t +rho_0 = rho + + +t = t_tmp - 2.0*dist +CALL PERTURBATION_PARAMETER +eta = z3t*rho_0 +CALL P_EOS +fdr1 = pges / (eta*rho_0*(kbol*t)/1.E-30) +t = t_tmp - dist +CALL PERTURBATION_PARAMETER +eta = z3t*rho_0 +CALL P_EOS +fdr2 = pges / (eta*rho_0*(kbol*t)/1.E-30) + +t = t_tmp + dist +CALL PERTURBATION_PARAMETER +eta = z3t*rho_0 +CALL P_EOS +fdr3 = pges / (eta*rho_0*(kbol*t)/1.E-30) + +t = t_tmp + 2.0*dist +CALL PERTURBATION_PARAMETER +eta = z3t*rho_0 +CALL P_EOS +fdr4 = pges / (eta*rho_0*(kbol*t)/1.E-30) + +t = t_tmp +CALL PERTURBATION_PARAMETER +eta = z3t*rho_0 +CALL P_EOS + + +df_drdt = (-fdr4+8.0*fdr3-8.0*fdr2+fdr1)/(12.0*dist) + + + + + +! ---------------------------------------------------------------------- +! thermodynamic properties +! ---------------------------------------------------------------------- + +s_res = ( - df_dt *t - fres )*RGAS + RGAS * LOG(zges) +h_res = ( - t*df_dt + zges-1.0 ) * RGAS *t +cv_res = - ( t*df_dt2 + 2.0*df_dt ) * RGAS*t +cp_res = cv_res - RGAS + RGAS*(zges +eta*t*df_drdt)**2 & + / (1.0 + 2.0*eta*dfdr +eta**2 *ddfdrdr) + +! write (*,*) 'df_... ', df_dt,df_dt2 +! write (*,*) 'kreuz ', zges,eta*t*df_drdt,eta*dfdr, eta**2 *ddfdrdr +! write (*,*) 'h,cv,cp', h_res,cv_res,cp_res + + +END SUBROUTINE H_EOS + + + +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! SUBROUTINE H_EOS_num +! +! This subroutine calculates enthalpies and heat capacities (cp) by +! taking numerical derivatieves. +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! + SUBROUTINE H_EOS_num +! + USE PARAMETERS, ONLY: RGAS + USE EOS_VARIABLES + IMPLICIT NONE +! +!--------------------------------------------------------------------- + REAL :: dist, fact, rho_0 + REAL :: fres1, fres2, fres3, fres4, fres5 + REAL :: f_1, f_2, f_3, f_4 + REAL :: cv_res, t_tmp, zges + REAL :: df_dt, df_dtdt, df_drdt, dfdr, ddfdrdr + +!----------------------------------------------------------------------- + + +CALL PERTURBATION_PARAMETER +rho_0 = eta/z3t + + +fact = 1.0 +dist = t * 100.E-5 * fact + +t_tmp = t + +t = t_tmp - 2.0*dist +CALL PERTURBATION_PARAMETER +eta = z3t*rho_0 +CALL F_EOS +fres1 = fres +t = t_tmp - dist +CALL PERTURBATION_PARAMETER +eta = z3t*rho_0 +CALL F_EOS +fres2 = fres +t = t_tmp + dist +CALL PERTURBATION_PARAMETER +eta = z3t*rho_0 +CALL F_EOS +fres3 = fres +t = t_tmp + 2.0*dist +CALL PERTURBATION_PARAMETER +eta = z3t*rho_0 +CALL F_EOS +fres4 = fres +t = t_tmp +CALL PERTURBATION_PARAMETER +eta = z3t*rho_0 +CALL F_EOS +fres5 = fres +! *(KBOL*T)/1.E-30 + +zges = (p * 1.E-30)/(kbol*t*rho_0) + + +df_dt = (-fres4+8.0*fres3-8.0*fres2+fres1)/(12.0*dist) +df_dtdt = (-fres4+16.0*fres3-3.d1*fres5+16.0*fres2-fres1) & + /(12.0*(dist**2 )) + + +s_res = (- df_dt -fres/t)*RGAS*t + RGAS * LOG(zges) +h_res = ( - t*df_dt + zges-1.0 ) * RGAS*t +cv_res = -( t*df_dtdt + 2.0*df_dt ) * RGAS*t + + + +t = t_tmp - 2.0*dist +CALL PERTURBATION_PARAMETER +eta = z3t*rho_0 +CALL P_EOS +f_1 = pges/(eta*rho_0*(kbol*t)/1.E-30) + +t = t_tmp - dist +CALL PERTURBATION_PARAMETER +eta = z3t*rho_0 +CALL P_EOS +f_2 = pges/(eta*rho_0*(kbol*t)/1.E-30) + +t = t_tmp + dist +CALL PERTURBATION_PARAMETER +eta = z3t*rho_0 +CALL P_EOS +f_3 = pges/(eta*rho_0*(kbol*t)/1.E-30) + +t = t_tmp + 2.0*dist +CALL PERTURBATION_PARAMETER +eta = z3t*rho_0 +CALL P_EOS +f_4 = pges/(eta*rho_0*(kbol*t)/1.E-30) + +t = t_tmp +CALL PERTURBATION_PARAMETER +eta = z3t*rho_0 +CALL P_EOS + +dfdr = pges / (eta*rho_0*(kbol*t)/1.E-30) +ddfdrdr = pgesdz/(eta*rho_0*(kbol*t)/1.E-30) - dfdr*2.0/eta - 1.0/eta**2 + +df_drdt = ( -f_4 +8.0*f_3 -8.0*f_2 +f_1) / (12.0*dist) + +cp_res = cv_res - RGAS +RGAS*(zges+eta*t*df_drdt)**2 & + * 1.0/(1.0 + 2.0*eta*dfdr + eta**2 *ddfdrdr) + +! write (*,*) 'n',df_dt,df_dtdt +! write (*,*) 'kreuz ', zges,eta*t*df_drdt,eta*dfdr, eta**2 *ddfdrdr +! write (*,*) 'h, cv', h_res, cv_res +! write (*,*) h_res - t*s_res +! write (*,*) cv_res,cp_res,eta +! pause + +END SUBROUTINE H_EOS_num + + +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! SUBROUTINE DENSITY_ITERATION +! +! iterates the density until the calculated pressure 'pges' is equal to +! the specified pressure 'p'. A Newton-scheme is used for determining +! the root to the objective function f(eta) = (pges / p ) - 1.0. +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! + SUBROUTINE DENSITY_ITERATION +! + USE BASIC_VARIABLES, ONLY: num + USE EOS_VARIABLES + IMPLICIT NONE +! +! ---------------------------------------------------------------------- + INTEGER :: i, start, max_i + REAL :: eta_iteration + REAL :: error, dydx, acc_i, delta_eta +! ---------------------------------------------------------------------- + + +IF ( densav(phas) /= 0.0 .AND. eta_start == denold(phas) ) THEN + denold(phas) = eta_start + eta_start = densav(phas) +ELSE + denold(phas) = eta_start + densav(phas) = eta_start +END IF + + +acc_i = 1.d-9 +max_i = 30 +density_error(:) = 0.0 + +i = 0 +eta_iteration = eta_start + +! ---------------------------------------------------------------------- +! iterate density until p_calc = p +! ---------------------------------------------------------------------- +iterate_density: DO + + i = i + 1 + eta = eta_iteration + + IF ( num == 0 ) THEN + CALL P_EOS + ELSE IF ( num == 1 ) THEN + CALL P_NUMERICAL + ELSE IF ( num == 2 ) THEN + WRITE(*,*) 'CRITICAL RENORM NOT INCLUDED YET' + !!CALL F_EOS_RN + ELSE + write (*,*) 'define calculation option (num)' + END IF + + error = (pges / p ) - 1.0 + + ! --- instable region correction ------------------------------------- + IF ( pgesdz < 0.0 .AND. i < max_i ) THEN + IF ( error > 0.0 .AND. pgesd2 > 0.0 ) THEN ! no liquid density + CALL PRESSURE_SPINODAL + eta_iteration = eta + error = (pges / p ) - 1.0 + IF ( ((pges/p ) -1.0) > 0.0 ) eta_iteration = 0.001 ! no solution possible + IF ( ((pges/p ) -1.0) <=0.0 ) eta_iteration = eta_iteration * 1.1 ! no solution found so far + ELSE IF ( error < 0.0 .AND. pgesd2 < 0.0 ) THEN ! no vapor density + CALL PRESSURE_SPINODAL + eta_iteration = eta + error = (pges / p ) - 1.0 + IF ( ((pges/p ) -1.0) < 0.0 ) eta_iteration = 0.5 ! no solution possible + IF ( ((pges/p ) -1.0) >=0.0 ) eta_iteration = eta_iteration * 0.9 ! no solution found so far + ELSE + eta_iteration = (eta_iteration + eta_start) / 2.0 + IF (eta_iteration == eta_start) eta_iteration = eta_iteration + 0.2 + END IF + CYCLE iterate_density + END IF + + + dydx = pgesdz/p + delta_eta = error/ dydx + IF ( delta_eta > 0.05 ) delta_eta = 0.05 + IF ( delta_eta < -0.05 ) delta_eta = -0.05 + + eta_iteration = eta_iteration - delta_eta + + IF (eta_iteration > 0.9) eta_iteration = 0.6 + IF (eta_iteration <= 0.0) eta_iteration = 1.E-16 + start = 1 + + IF ( ABS(error*p/pgesdz) < 1.d-12 ) start = 0 + IF ( ABS(error) < acc_i ) start = 0 + IF ( i > max_i ) THEN + start = 0 + density_error(phas) = ABS( error ) + ! write (*,*) 'density iteration failed' + END IF + + IF (start /= 1) EXIT iterate_density + +END DO iterate_density + +eta = eta_iteration + +IF ((eta > 0.3 .AND. densav(phas) > 0.3) .OR. & + (eta < 0.1 .AND. densav(phas) < 0.1)) densav(phas) = eta + +END SUBROUTINE DENSITY_ITERATION + + + + +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! SUBROUTINE F_EOS +! +! calculates the Helmholtz energy f/kT. The input to the subroutine is +! (T,eta,x), where eta is the packing fraction. +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! + SUBROUTINE F_EOS +! + USE PARAMETERS, ONLY: nc, nsite + USE EOS_VARIABLES + USE EOS_CONSTANTS + IMPLICIT NONE +! +! --- local variables -------------------------------------------------- + INTEGER :: i, j, k, l, m, n + REAL :: z0, z1, z2, z3 + REAL :: zms, m_mean ! ,lij(nc,nc) + REAL :: I1,I2, c1_con + REAL :: fhs, fdsp, fhc + + LOGICAL :: assoc + INTEGER :: ass_cnt,max_eval + REAL :: delta(nc,nc,nsite,nsite) + REAL :: mx_itr(nc,nsite), err_sum, sum, attenu, tol, fhb + REAL :: ass_s1, ass_s2 + + REAL :: fdd, fqq, fdq +! ---------------------------------------------------------------------- + + +! ---------------------------------------------------------------------- +! abbreviations +! ---------------------------------------------------------------------- +rho = eta/z3t +z0 = z0t*rho +z1 = z1t*rho +z2 = z2t*rho +z3 = z3t*rho + +m_mean = z0t / ( PI / 6.0 ) +zms = 1.0 - eta + +! m_mean2 = 0.0 +! lij(1,2) = -0.05 +! lij(2,1) = lij(1,2) +! DO i = 1, ncomp +! DO j = 1, ncomp +! m_mean2 = m_mean2 + x(i)*x(j)*(mseg(i)+mseg(j))/2.0*(1.0-lij(i,j)) +! ENDDO +! ENDDO + + +! ---------------------------------------------------------------------- +! radial distr. function at contact, gij +! ---------------------------------------------------------------------- +DO i = 1, ncomp + DO j=1,ncomp + gij(i,j) = 1.0/zms + 3.0*dij_ab(i,j)*z2/zms/zms + 2.0*(dij_ab(i,j)*z2)**2 /zms**3 + END DO +END DO + + +! ---------------------------------------------------------------------- +! Helmholtz energy : hard sphere contribution +! ---------------------------------------------------------------------- +fhs= m_mean*( 3.0*z1*z2/zms + z2**3 /z3/zms/zms + (z2**3 /z3/z3-z0)*LOG(zms) )/z0 + + +! ---------------------------------------------------------------------- +! Helmholtz energy : chain term +! ---------------------------------------------------------------------- +fhc = 0.0 +DO i = 1, ncomp + fhc = fhc + x(i) *(1.0- mseg(i)) *LOG(gij(i,i)) +END DO + + +! ---------------------------------------------------------------------- +! Helmholtz energy : PC-SAFT dispersion contribution +! ---------------------------------------------------------------------- +IF (eos == 1) THEN + + I1 = 0.0 + I2 = 0.0 + DO m = 0, 6 + I1 = I1 + apar(m)*eta**REAL(m) + I2 = I2 + bpar(m)*eta**REAL(m) + END DO + + c1_con= 1.0/ ( 1.0 + m_mean*(8.0*eta-2.0*eta**2 )/zms**4 & + + (1.0 - m_mean)*(20.0*eta-27.0*eta**2 & + + 12.0*eta**3 -2.0*eta**4 ) /(zms*(2.0-eta))**2 ) + + fdsp = -2.0*PI*rho*I1*order1 - PI*rho*c1_con*m_mean*I2*order2 + +! ---------------------------------------------------------------------- +! Helmholtz energy : SAFT (Chen, Kreglewski) dispersion contribution +! ---------------------------------------------------------------------- +ELSE + + fdsp = 0.0 + DO n = 1,4 + DO m = 1,9 + fdsp = fdsp + dnm(n,m) * (um/t)**REAL(n) *(eta/tau)**REAL(m) + END DO + END DO + fdsp = m_mean * fdsp + +END IF + + +! ---------------------------------------------------------------------- +! TPT-1-association according to Chapman et al. +! ---------------------------------------------------------------------- +fhb = 0.0 +assoc = .false. +DO i = 1, ncomp + IF (nhb_typ(i) /= 0) assoc = .true. +END DO +IF (assoc) THEN + + DO i = 1, ncomp + DO k = 1, nhb_typ(i) + IF (mx(i,k) == 0.0) mx(i,k) = 1.0 ! Initialize mx(i,j) + DO j = 1, ncomp + DO l = 1, nhb_typ(j) + delta(i,j,k,l) = gij(i,j) * ass_d(i,j,k,l) + END DO + END DO + END DO + END DO + + +! --- constants for iteration ------------------------------------------ + attenu = 0.70 + tol = 1.d-10 + IF (eta < 0.2) tol = 1.d-12 + IF (eta < 0.01) tol = 1.d-13 + max_eval = 200 + +! --- iterate over all components and all sites ------------------------ + ass_cnt = 0 + iterate_TPT1: DO + + ass_cnt = ass_cnt + 1 + + DO i = 1, ncomp + DO k = 1, nhb_typ(i) + sum = 0.0 + DO j = 1, ncomp + DO l = 1, nhb_typ(j) + sum = sum + x(j)* mx(j,l)*nhb_no(j,l) *delta(i,j,k,l) +! if (ass_cnt == 1) write (*,*) j,l,x(j), mx(j,l) + END DO + END DO + mx_itr(i,k) = 1.0 / (1.0 + sum * rho) +! if (ass_cnt == 1) write (*,*) 'B',ass_cnt,sum, rho + END DO + END DO + + err_sum = 0.0 + DO i = 1, ncomp + DO k = 1, nhb_typ(i) + err_sum = err_sum + ABS(mx_itr(i,k) - mx(i,k)) ! / ABS(mx_itr(i,k)) + mx(i,k) = mx_itr(i,k) * attenu + mx(i,k) * (1.0 - attenu) + END DO + END DO + + IF ( err_sum <= tol .OR. ass_cnt >= max_eval ) THEN + IF (ass_cnt >= max_eval) WRITE(*,'(a,2G15.7)') 'F_EOS: Max_eval violated (mx) Err_Sum = ',err_sum,tol + EXIT iterate_TPT1 + END IF + + END DO iterate_TPT1 + + DO i = 1, ncomp + ass_s1 = 0.0 + ass_s2 = 0.0 + DO k = 1, nhb_typ(i) + ass_s1 = ass_s1 + nhb_no(i,k) * ( 1.0 - mx(i,k) ) + ass_s2 = ass_s2 + nhb_no(i,k) * LOG( mx(i,k) ) + END DO + fhb = fhb + x(i) * ( ass_s2 + ass_s1 / 2.0 ) + END DO + +END IF +! --- TPT-1-association accord. to Chapman ----------------------------- + + +! ---------------------------------------------------------------------- +! polar terms +! ---------------------------------------------------------------------- + CALL F_POLAR ( fdd, fqq, fdq ) + + +! ---------------------------------------------------------------------- +! resid. Helmholtz energy f/kT +! ---------------------------------------------------------------------- +fres = fhs + fhc + fdsp + fhb + fdd + fqq + fdq + +tfr= fres + +END SUBROUTINE F_EOS + + +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! + SUBROUTINE F_NUMERICAL +! + USE EOS_VARIABLES + USE EOS_CONSTANTS + USE EOS_NUMERICAL_DERIVATIVES, ONLY: ideal_gas, hard_sphere, chain_term, & + disp_term, hb_term, LC_term, branch_term, & + II_term, ID_term, subtract1, subtract2 + IMPLICIT NONE +! +!--------------------------------------------------------------------- + +!-----local variables------------------------------------------------- + INTEGER :: i, j + REAL :: m_mean2 + REAL :: fid, fhs, fdsp, fhc + REAL :: fhb, fdd, fqq, fdq + REAL :: fhend, fcc + REAL :: fbr, flc + REAL :: fref + + REAL :: eps_kij, k_kij +!--------------------------------------------------------------------- + +eps_kij = 0.0 +k_kij = 0.0 + +fid = 0.0 +fhs = 0.0 +fhc = 0.0 +fdsp= 0.0 +fhb = 0.0 +fdd = 0.0 +fqq = 0.0 +fdq = 0.0 +fcc = 0.0 +fbr = 0.0 +flc = 0.0 + + +CALL PERTURBATION_PARAMETER + +! ---------------------------------------------------------------------- +! overwrite the standard mixing rules by those published by Tang & Gross +! using an additional lij parameter +! WARNING : the lij parameter is set to lij = - lji in 'para_input' +! ---------------------------------------------------------------------- +order1 = 0.0 +order2 = 0.0 +DO i = 1, ncomp + DO j = 1, ncomp + order1 = order1 + x(i)*x(j)* mseg(i)*mseg(j) * sig_ij(i,j)**3 * uij(i,j)/t + order2 = order2 + x(i)*x(j)* mseg(i)*mseg(j) * sig_ij(i,j)**3 * (uij(i,j)/t)**2 + END DO +END DO +DO i = 1, ncomp + DO j = 1, ncomp + order1 = order1 + x(i)*mseg(i)/t*( x(j)*mseg(j) & + *sig_ij(i,j)*(uij(i,i)*uij(j,j))**(1.0/6.0) )**3 *lij(i,j) + END DO +END DO + + +! ---------------------------------------------------------------------- +! a non-standard mixing rule scaling the hard-sphere term +! WARNING : the lij parameter is set to lij = - lji in 'para_input' +! (uses an additional lij parameter) +! ---------------------------------------------------------------------- +m_mean2 = 0.0 +DO i = 1, ncomp + DO j = 1, ncomp + m_mean2 = m_mean2 + x(i)*x(j)*(mseg(i)+mseg(j))/2.0 + END DO +END DO +DO i = 1, ncomp + DO j = 1, ncomp + ! m_mean2=m_mean2+x(i)*(x(j)*((mseg(i)+mseg(j))*0.5)**(1.0/3.0) *lij(i,j) )**3 + END DO +END DO + +! --- ideal gas contribution ------------------------------------------- +IF ( ideal_gas == 'yes' ) CALL F_IDEAL_GAS ( fid ) +! ---------------------------------------------------------------------- + +! --- hard-sphere contribution ----------------------------------------- +IF ( hard_sphere == 'CSBM' ) CALL F_HARD_SPHERE ( m_mean2, fhs ) +! ---------------------------------------------------------------------- + +! -- chain term -------------------------------------------------------- +IF ( chain_term == 'TPT1' ) CALL F_CHAIN_TPT1 ( fhc ) +IF ( chain_term == 'TPT2' ) CALL F_CHAIN_TPT_D ( fhc ) +IF ( chain_term == 'HuLiu' ) CALL F_CHAIN_HU_LIU ( fhc ) +IF ( chain_term == 'HuLiu_rc' ) CALL F_CHAIN_HU_LIU_RC ( fhs, fhc ) +!!IF ( chain_term == 'SPT' ) CALL F_SPT ( fhs, fhc ) +IF ( chain_term == 'SPT' ) WRITE(*,*) 'SPT NOT INCLUDED YET' +! ---------------------------------------------------------------------- + +! --- dispersive attraction -------------------------------------------- +IF ( disp_term == 'PC-SAFT') CALL F_DISP_PCSAFT ( fdsp ) +IF ( disp_term == 'CK') CALL F_DISP_CKSAFT ( fdsp ) +IF ( disp_term(1:2) == 'PT') CALL F_pert_theory ( fdsp ) +! ---------------------------------------------------------------------- + +! --- H-bonding contribution / Association ----------------------------- +IF ( hb_term == 'TPT1_Chap') CALL F_ASSOCIATION( eps_kij, k_kij, fhb ) +! ---------------------------------------------------------------------- + +! --- polar terms ------------------------------------------------------ + CALL F_POLAR ( fdd, fqq, fdq ) +! ---------------------------------------------------------------------- + +! --- ion-dipole term -------------------------------------------------- +IF ( ID_term == 'TBH') CALL F_ION_DIPOLE_TBH ( fhend ) +! ---------------------------------------------------------------------- + +! --- ion-ion term ----------------------------------------------------- +IF ( II_term == 'primMSA') CALL F_ION_ION_PrimMSA ( fcc ) +IF ( II_term == 'nprMSA') CALL F_ION_ION_nonPrimMSA ( fdd, fqq, fdq, fcc ) +! ---------------------------------------------------------------------- + +! --- liquid-crystal term ---------------------------------------------- +IF ( LC_term == 'MSaupe') CALL F_LC_MayerSaupe ( flc ) + +!!IF ( LC_term == 'OVL') fref = fhs + fhc +IF ( LC_term == 'OVL') WRITE(*,*) 'OVL NOT INCLUDED YET' +!IF ( LC_term == 'OVL') CALL F_LC_OVL ( fref, flc ) +!! IF ( LC_term == 'SPT') fref = fhs + fhc +IF ( LC_term == 'SPT') WRITE(*,*) 'SPT NOT INCLUDED YET' +!!IF ( LC_term == 'SPT') CALL F_LC_SPT( fref, flc ) +! ---------------------------------------------------------------------- + +! ====================================================================== +! SUBTRACT TERMS (local density approximation) FOR DFT +! ====================================================================== + +!IF ( subtract1 == '1PT') CALL F_subtract_local_pert_theory ( subtract1, fdsp ) +!IF ( subtract1 == '2PT') CALL F_subtract_local_pert_theory ( subtract1, fdsp ) +!IF ( subtract2 =='ITTpolar') CALL F_local_ITT_polar ( fdd ) +! ---------------------------------------------------------------------- + +! ---------------------------------------------------------------------- +! residual Helmholtz energy F/(NkT) +! ---------------------------------------------------------------------- +fres = fid + fhs + fhc + fdsp + fhb + fdd + fqq + fdq + fcc + flc + +tfr = 0.0 + +END SUBROUTINE F_NUMERICAL + + + +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! SUBROUTINE P_EOS +! +! calculates the pressure in units (Pa). +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! + SUBROUTINE P_EOS +! +! ---------------------------------------------------------------------- + USE PARAMETERS, ONLY: nc, nsite + USE EOS_VARIABLES + USE EOS_CONSTANTS + IMPLICIT NONE +! +! --- local variables -------------------------------------------------- + INTEGER :: i, j, k, l, m, n + INTEGER :: ass_cnt,max_eval + LOGICAL :: assoc + REAL :: z0, z1, z2, z3 + REAL :: zms, m_mean + REAL :: zges, zgesdz, zgesd2, zgesd3 + REAL :: zhs, zhsdz, zhsd2, zhsd3 + REAL :: zhc, zhcdz, zhcd2, zhcd3 + REAL, DIMENSION(nc,nc) :: dgijdz, dgijd2, dgijd3, dgijd4 + REAL :: zdsp, zdspdz, zdspd2, zdspd3 + REAL :: c1_con, c2_con, c3_con, c4_con, c5_con + REAL :: I2, edI1dz, edI2dz, edI1d2, edI2d2 + REAL :: edI1d3, edI2d3, edI1d4, edI2d4 + REAL :: fdspdz,fdspd2 + REAL :: zhb, zhbdz, zhbd2, zhbd3 + REAL, DIMENSION(nc,nc,nsite,nsite) :: delta, dq_dz, dq_d2, dq_d3, dq_d4 + REAL, DIMENSION(nc,nsite) :: mx_itr, dmx_dz, ndmxdz, dmx_d2, ndmxd2 + REAL, DIMENSION(nc,nsite) :: dmx_d3, ndmxd3, dmx_d4, ndmxd4 + REAL :: err_sum, sum0, sum1, sum2, sum3, sum4, attenu, tol + REAL :: sum_d1, sum_d2, sum_d3, sum_d4 + REAL :: zdd, zddz, zddz2, zddz3 + REAL :: zqq, zqqz, zqqz2, zqqz3 + REAL :: zdq, zdqz, zdqz2, zdqz3 +! ---------------------------------------------------------------------- + + +! ---------------------------------------------------------------------- +! abbreviations +! ---------------------------------------------------------------------- +rho = eta/z3t +z0 = z0t*rho +z1 = z1t*rho +z2 = z2t*rho +z3 = z3t*rho + +m_mean = z0t/(PI/6.0) +zms = 1.0 -eta + +! m_mean2=0.0 +! lij(1,2)= -0.050 +! lij(2,1)=lij(1,2) +! DO i =1,ncomp +! DO j =1,ncomp +! m_mean2=m_mean2+x(i)*x(j) * (mseg(i)+mseg(j))/2.0*(1.0-lij(i,j)) +! ENDDO +! ENDDO + + +! ---------------------------------------------------------------------- +! radial distr. function at contact, gij , and derivatives +! dgijdz=d(gij)/d(eta) and dgijd2 = dd(gij)/d(eta)**2 +! ---------------------------------------------------------------------- +DO i = 1, ncomp + DO j=1,ncomp + ! j=i + gij(i,j) = 1.0/zms + 3.0*dij_ab(i,j)*z2/zms/zms + 2.0*(dij_ab(i,j)*z2)**2 /zms**3 + dgijdz(i,j)= 1.0/zms/zms + 3.0*dij_ab(i,j)*z2*(1.0+z3)/z3/zms**3 & + + (dij_ab(i,j)*z2/zms/zms)**2 *(4.0+2.0*z3)/z3 + dgijd2(i,j) = 2.0/zms**3 & + + 6.0*dij_ab(i,j)*z2/z3/zms**4 *(2.0+z3) & + + (2.0*dij_ab(i,j)*z2/z3)**2 /zms**5 *(1.0+4.0*z3+z3*z3) + dgijd3(i,j) = 6.0/zms**4 & + + 18.0*dij_ab(i,j)*z2/z3/zms**5 *(3.0+z3) & + + 12.0*(dij_ab(i,j)*z2/z3/zms**3 )**2 *(3.0+6.0*z3+z3*z3) + dgijd4(i,j) = 24.0/zms**5 & + + 72.0*dij_ab(i,j)*z2/z3/zms**6 *(4.0+z3) & + + 48.0*(dij_ab(i,j)*z2/z3)**2 /zms**7 *(6.0+8.0*z3+z3*z3) + END DO +END DO + + +! ---------------------------------------------------------------------- +! p : hard sphere contribution +! ---------------------------------------------------------------------- +zhs = m_mean* ( z3/zms + 3.0*z1*z2/z0/zms/zms + z2**3 /z0*(3.0-z3)/zms**3 ) +zhsdz = m_mean*( 1.0/zms/zms + 3.0*z1*z2/z0/z3*(1.0+z3)/zms**3 & + + 6.0*z2**3 /z0/z3/zms**4 ) +zhsd2 = m_mean*( 2.0/zms**3 + 6.0*z1*z2/z0/z3*(2.0+z3)/zms**4 & + + 6.0*z2**3 /z0/z3/z3*(1.0+3.0*z3)/zms**5 ) +zhsd3 = m_mean*( 6.0/zms**4 + 18.0*z1*z2/z0/z3*(3.0+z3)/zms**5 & + + 24.0*z2**3 /z0/z3/z3*(2.0+3.0*z3)/zms**6 ) + + +! ---------------------------------------------------------------------- +! p : chain term +! ---------------------------------------------------------------------- +zhc = 0.0 +zhcdz = 0.0 +zhcd2 = 0.0 +zhcd3 = 0.0 +DO i= 1, ncomp + zhc = zhc + x(i)*(1.0-mseg(i))*eta/gij(i,i)* dgijdz(i,i) + zhcdz = zhcdz + x(i)*(1.0-mseg(i)) *(-eta*(dgijdz(i,i)/gij(i,i))**2 & + + dgijdz(i,i)/gij(i,i) + eta/gij(i,i)*dgijd2(i,i)) + zhcd2 = zhcd2 + x(i)*(1.0-mseg(i)) & + *( 2.0*eta*(dgijdz(i,i)/gij(i,i))**3 & + -2.0*(dgijdz(i,i)/gij(i,i))**2 & + -3.0*eta/gij(i,i)**2 *dgijdz(i,i)*dgijd2(i,i) & + +2.0/gij(i,i)*dgijd2(i,i) +eta/gij(i,i)*dgijd3(i,i) ) + zhcd3 = zhcd3 + x(i)*(1.0-mseg(i)) *( 6.0*(dgijdz(i,i)/gij(i,i))**3 & + -6.0*eta*(dgijdz(i,i)/gij(i,i))**4 & + +12.0*eta/gij(i,i)**3 *dgijdz(i,i)**2 *dgijd2(i,i) & + -9.0/gij(i,i)**2 *dgijdz(i,i)*dgijd2(i,i) +3.0/gij(i,i)*dgijd3(i,i) & + -3.0*eta*(dgijd2(i,i)/gij(i,i))**2 & + -4.0*eta/gij(i,i)**2 *dgijdz(i,i)*dgijd3(i,i) & + +eta/gij(i,i)*dgijd4(i,i) ) +END DO + +! ---------------------------------------------------------------------- +! p : PC-SAFT dispersion contribution +! note: edI1dz is equal to d(eta*I1)/d(eta), analogous for edI2dz +! ---------------------------------------------------------------------- +IF (eos == 1) THEN + + I2 = 0.0 + edI1dz = 0.0 + edI2dz = 0.0 + edI1d2 = 0.0 + edI2d2 = 0.0 + edI1d3 = 0.0 + edI2d3 = 0.0 + edI1d4 = 0.0 + edI2d4 = 0.0 + DO m=0,6 + I2 = I2 + bpar(m)*z3**REAL(m) + edI1dz= edI1dz+apar(m)*REAL(m+1)*z3**REAL(m) + edI2dz= edI2dz+bpar(m)*REAL(m+1)*z3**REAL(m) + edI1d2= edI1d2+apar(m)*REAL((m+1)*m)*z3**REAL(m-1) + edI2d2= edI2d2+bpar(m)*REAL((m+1)*m)*z3**REAL(m-1) + edI1d3= edI1d3+apar(m)*REAL((m+1)*m*(m-1))*z3**REAL(m-2) + edI2d3= edI2d3+bpar(m)*REAL((m+1)*m*(m-1))*z3**REAL(m-2) + edI1d4= edI1d4+apar(m)*REAL((m+1)*m*(m-1)*(m-2))*z3**REAL(m-3) + edI2d4= edI2d4+bpar(m)*REAL((m+1)*m*(m-1)*(m-2))*z3**REAL(m-3) + END DO + + c1_con= 1.0/ ( 1.0 + m_mean*(8.0*eta-2.0*eta**2 )/zms**4 & + + (1.0 - m_mean)*(20.0*eta-27.0*eta**2 & + + 12.0*eta**3 -2.0*eta**4 ) /(zms*(2.0-eta))**2 ) + c2_con= - c1_con*c1_con & + *(m_mean*(-4.0*eta**2 +20.0*eta+8.0)/zms**5 + (1.0 - m_mean) & + *(2.0*eta**3 +12.0*eta**2 -48.0*eta+40.0) & + /(zms*(2.0-eta))**3 ) + c3_con= 2.0 * c2_con*c2_con/c1_con - c1_con*c1_con & + *( m_mean*(-12.0*eta**2 +72.0*eta+60.0)/zms**6 & + + (1.0 - m_mean) & + *(-6.0*eta**4 -48.0*eta**3 +288.0*eta**2 & + -480.0*eta+264.0) /(zms*(2.0-eta))**4 ) + c4_con= 6.0*c2_con*c3_con/c1_con -6.0*c2_con**3 /c1_con**2 & + - c1_con*c1_con & + *( m_mean*(-48.0*eta**2 +336.0*eta+432.0)/zms**7 & + + (1.0 - m_mean) & + *(24.0*eta**5 +240.0*eta**4 -1920.0*eta**3 & + +4800.0*eta**2 -5280.0*eta+2208.0) /(zms*(2.0-eta))**5 ) + c5_con= 6.0*c3_con**2 /c1_con - 36.0*c2_con**2 /c1_con**2 *c3_con & + + 8.0*c2_con/c1_con*c4_con+24.0*c2_con**4 /c1_con**3 & + - c1_con*c1_con & + *( m_mean*(-240.0*eta**2 +1920.0*eta+3360.0)/zms**8 & + + (1.0 - m_mean) & + *(-120.0*eta**6 -1440.0*eta**5 +14400.0*eta**4 & + -48000.0*eta**3 +79200.0*eta**2 -66240.0*eta+22560.0) & + /(zms*(2.0-eta))**6 ) + + zdsp = - 2.0*PI*rho*edI1dz*order1 & + - PI*rho*order2*m_mean*(c2_con*I2*eta + c1_con*edI2dz) + zdspdz= zdsp/eta - 2.0*PI*rho*edI1d2*order1 & + - PI*rho*order2*m_mean*(c3_con*I2*eta & + + 2.0*c2_con*edI2dz + c1_con*edI2d2) + zdspd2= -2.0*zdsp/eta/eta +2.0*zdspdz/eta & + - 2.0*PI*rho*edI1d3*order1 - PI*rho*order2*m_mean*(c4_con*I2*eta & + + 3.0*c3_con*edI2dz +3.0*c2_con*edI2d2 +c1_con*edI2d3) + zdspd3= 6.0*zdsp/eta**3 -6.0*zdspdz/eta/eta & + + 3.0*zdspd2/eta - 2.0*PI*rho*edI1d4*order1 & + - PI*rho*order2*m_mean*(c5_con*I2*eta & + + 4.0*c4_con*edI2dz +6.0*c3_con*edI2d2 & + + 4.0*c2_con*edI2d3 + c1_con*edI2d4) + + +! ---------------------------------------------------------------------- +! p : SAFT (Chen & Kreglewski) dispersion contribution +! ---------------------------------------------------------------------- +ELSE + + fdspdz = 0.0 + fdspd2 = 0.0 + DO n = 1,4 + DO m = 1,9 + fdspdz = fdspdz + m_mean/tau * dnm(n,m) * (um/t)**REAL(n) *REAL(m)*(eta/tau)**REAL(m-1) + END DO + DO m= 2,9 + fdspd2= fdspd2 + m_mean/tau * dnm(n,m)*(um/t)**REAL(n) *REAL(m)*REAL(m-1) & + * (eta/tau)**REAL(m-2) * 1.0/tau + END DO + END DO + zdsp = eta * fdspdz + zdspdz = (2.0*fdspdz + eta*fdspd2) - zdsp/z3 + +END IF +! --- end of dispersion contribution ----------------------------------- + + +! ---------------------------------------------------------------------- +! p: TPT-1-association accord. to Chapman et al. +! ---------------------------------------------------------------------- +zhb = 0.0 +zhbdz = 0.0 +zhbd2 = 0.0 +zhbd3 = 0.0 +assoc = .false. +DO i = 1,ncomp + IF (nhb_typ(i) /= 0) assoc = .true. +END DO +IF (assoc) THEN + + DO j = 1, ncomp + DO i = 1, nhb_typ(j) + DO k = 1, ncomp + DO l = 1, nhb_typ(k) + delta(j,k,i,l) = gij(j,k) * ass_d(j,k,i,l) + dq_dz(j,k,i,l) = dgijdz(j,k) * ass_d(j,k,i,l) + dq_d2(j,k,i,l) = dgijd2(j,k) * ass_d(j,k,i,l) + dq_d3(j,k,i,l) = dgijd3(j,k) * ass_d(j,k,i,l) + dq_d4(j,k,i,l) = dgijd4(j,k) * ass_d(j,k,i,l) + END DO + END DO + END DO + END DO + +! --- constants for iteration ------------------------------------------ + attenu = 0.7 + tol = 1.d-10 + IF ( eta < 0.2 ) tol = 1.d-12 + IF ( eta < 0.01 ) tol = 1.d-13 + IF ( eta < 1.E-6) tol = 1.d-15 + max_eval = 1000 + +! --- initialize mx(i,j) ----------------------------------------------- + DO i = 1, ncomp + DO j = 1, nhb_typ(i) + mx(i,j) = 1.0 + dmx_dz(i,j) = 0.0 + dmx_d2(i,j) = 0.0 + dmx_d3(i,j) = 0.0 + dmx_d4(i,j) = 0.0 + END DO + END DO + +! --- iterate over all components and all sites ------------------------ + ass_cnt = 0 + err_sum = tol + 1.0 + DO WHILE ( err_sum > tol .AND. ass_cnt <= max_eval) + ass_cnt = ass_cnt + 1 + DO i = 1, ncomp + DO j = 1, nhb_typ(i) + sum0 = 0.0 + sum1 = 0.0 + sum2 = 0.0 + sum3 = 0.0 + sum4 = 0.0 + DO k = 1, ncomp + DO l = 1, nhb_typ(k) + sum0 =sum0 +x(k)*nhb_no(k,l)* mx(k,l)* delta(i,k,j,l) + sum1 =sum1 +x(k)*nhb_no(k,l)*( mx(k,l)* dq_dz(i,k,j,l) & + + dmx_dz(k,l)* delta(i,k,j,l)) + sum2 =sum2 +x(k)*nhb_no(k,l)*( mx(k,l)* dq_d2(i,k,j,l) & + + 2.0*dmx_dz(k,l)* dq_dz(i,k,j,l) & + + dmx_d2(k,l)* delta(i,k,j,l)) + sum3 =sum3 +x(k)*nhb_no(k,l)*( mx(k,l)* dq_d3(i,k,j,l) & + + 3.0*dmx_dz(k,l)* dq_d2(i,k,j,l) & + + 3.0*dmx_d2(k,l)* dq_dz(i,k,j,l) & + + dmx_d3(k,l)* delta(i,k,j,l)) + sum4 =sum4 + x(k)*nhb_no(k,l)*( mx(k,l)* dq_d4(i,k,j,l) & + + 4.0*dmx_dz(k,l)* dq_d3(i,k,j,l) & + + 6.0*dmx_d2(k,l)* dq_d2(i,k,j,l) & + + 4.0*dmx_d3(k,l)* dq_dz(i,k,j,l) & + + dmx_d4(k,l)* delta(i,k,j,l)) + END DO + END DO + mx_itr(i,j)= 1.0 / (1.0 + sum0 * rho) + ndmxdz(i,j)= -(mx_itr(i,j)*mx_itr(i,j))* (sum0/z3t +sum1*rho) + ndmxd2(i,j)= + 2.0/mx_itr(i,j)*ndmxdz(i,j)*ndmxdz(i,j) & + - (mx_itr(i,j)*mx_itr(i,j)) * (2.0/z3t*sum1 + rho*sum2) + ndmxd3(i,j)= - 6.0/mx_itr(i,j)**2 *ndmxdz(i,j)**3 & + + 6.0/mx_itr(i,j)*ndmxdz(i,j)*ndmxd2(i,j) - mx_itr(i,j)*mx_itr(i,j) & + * (3.0/z3t*sum2 + rho*sum3) + ndmxd4(i,j)= 24.0/mx_itr(i,j)**3 *ndmxdz(i,j)**4 & + -36.0/mx_itr(i,j)**2 *ndmxdz(i,j)**2 *ndmxd2(i,j) & + +6.0/mx_itr(i,j)*ndmxd2(i,j)**2 & + +8.0/mx_itr(i,j)*ndmxdz(i,j)*ndmxd3(i,j) - mx_itr(i,j)**2 & + *(4.0/z3t*sum3 + rho*sum4) + END DO + END DO + + err_sum = 0.0 + DO i = 1, ncomp + DO j = 1, nhb_typ(i) + err_sum = err_sum + ABS(mx_itr(i,j) - mx(i,j)) & + + ABS(ndmxdz(i,j) - dmx_dz(i,j)) + ABS(ndmxd2(i,j) - dmx_d2(i,j)) + mx(i,j) = mx_itr(i,j)*attenu + mx(i,j) * (1.0-attenu) + dmx_dz(i,j) = ndmxdz(i,j)*attenu + dmx_dz(i,j) * (1.0-attenu) + dmx_d2(i,j) = ndmxd2(i,j)*attenu + dmx_d2(i,j) * (1.0-attenu) + dmx_d3(i,j) = ndmxd3(i,j)*attenu + dmx_d3(i,j) * (1.0-attenu) + dmx_d4(i,j) = ndmxd4(i,j)*attenu + dmx_d4(i,j) * (1.0-attenu) + END DO + END DO + END DO + + IF ( ass_cnt >= max_eval .AND. err_sum > SQRT(tol) ) THEN + WRITE (*,'(a,2G15.7)') 'P_EOS: Max_eval violated (mx) Err_Sum= ',err_sum,tol + ! stop + END IF + + + ! --- calculate the hydrogen-bonding contribution -------------------- + DO i = 1, ncomp + sum_d1 = 0.0 + sum_d2 = 0.0 + sum_d3 = 0.0 + sum_d4 = 0.0 + DO j = 1, nhb_typ(i) + sum_d1= sum_d1 +nhb_no(i,j)* dmx_dz(i,j)*(1.0/mx(i,j)-0.5) + sum_d2= sum_d2 +nhb_no(i,j)*(dmx_d2(i,j)*(1.0/mx(i,j)-0.5) & + -(dmx_dz(i,j)/mx(i,j))**2 ) + sum_d3= sum_d3 +nhb_no(i,j)*(dmx_d3(i,j)*(1.0/mx(i,j)-0.5) & + -3.0/mx(i,j)**2 *dmx_dz(i,j)*dmx_d2(i,j) + 2.0*(dmx_dz(i,j)/mx(i,j))**3 ) + sum_d4= sum_d4 +nhb_no(i,j)*(dmx_d4(i,j)*(1.0/mx(i,j)-0.5) & + -4.0/mx(i,j)**2 *dmx_dz(i,j)*dmx_d3(i,j) & + + 12.0/mx(i,j)**3 *dmx_dz(i,j)**2 *dmx_d2(i,j) & + - 3.0/mx(i,j)**2 *dmx_d2(i,j)**2 - 6.0*(dmx_dz(i,j)/mx(i,j))**4 ) + END DO + zhb = zhb + x(i) * eta * sum_d1 + zhbdz = zhbdz + x(i) * eta * sum_d2 + zhbd2 = zhbd2 + x(i) * eta * sum_d3 + zhbd3 = zhbd3 + x(i) * eta * sum_d4 + END DO + zhbdz = zhbdz + zhb/eta + zhbd2 = zhbd2 + 2.0/eta*zhbdz-2.0/eta**2 *zhb + zhbd3 = zhbd3 - 6.0/eta**2 *zhbdz+3.0/eta*zhbd2 + 6.0/eta**3 *zhb +END IF +! --- TPT-1-association accord. to Chapman ----------------------------- + + +! ---------------------------------------------------------------------- +! p: polar terms +! ---------------------------------------------------------------------- +CALL P_POLAR ( zdd, zddz, zddz2, zddz3, zqq, zqqz, zqqz2, zqqz3, zdq, zdqz, zdqz2, zdqz3 ) + + +! ---------------------------------------------------------------------- +! compressibility factor z and total p +! as well as derivatives d(z)/d(eta) and d(p)/d(eta) with unit [Pa] +! ---------------------------------------------------------------------- +zges = 1.0 + zhs + zhc + zdsp + zhb + zdd + zqq + zdq +zgesdz = zhsdz + zhcdz + zdspdz + zhbdz + zddz + zqqz + zdqz +zgesd2 = zhsd2 + zhcd2 + zdspd2 + zhbd2 + zddz2 +zqqz2+zdqz2 +zgesd3 = zhsd3 + zhcd3 + zdspd3 + zhbd3 + zddz3 +zqqz3+zdqz3 + +pges = zges *rho *(kbol*t)/1.d-30 +pgesdz = ( zgesdz*rho + zges*rho/z3 )*(kbol*t)/1.d-30 +pgesd2 = ( zgesd2*rho + 2.0*zgesdz*rho/z3 )*(kbol*t)/1.d-30 +pgesd3 = ( zgesd3*rho + 3.0*zgesd2*rho/z3 )*(kbol*t)/1.d-30 + +END SUBROUTINE P_EOS + + + + +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! + SUBROUTINE PHI_POLAR ( k, z3_rk, fdd_rk, fqq_rk, fdq_rk ) +! + USE EOS_VARIABLES, ONLY: ncomp, parame, dd_term, qq_term, dq_term + IMPLICIT NONE +! +! ---------------------------------------------------------------------- + INTEGER, INTENT(IN) :: k + REAL, INTENT(IN) :: z3_rk + REAL, INTENT(OUT) :: fdd_rk, fqq_rk, fdq_rk +! +! --- local variables--------------------------------------------------- + INTEGER :: dipole + INTEGER :: quadrupole + INTEGER :: dipole_quad +! ---------------------------------------------------------------------- + + fdd_rk = 0.0 + fqq_rk = 0.0 + fdq_rk = 0.0 + + dipole = 0 + quadrupole = 0 + dipole_quad = 0 + IF ( SUM( parame(1:ncomp,6) ) /= 0.0 ) dipole = 1 + IF ( SUM( parame(1:ncomp,7) ) /= 0.0 ) quadrupole = 1 + IF ( dipole == 1 .AND. quadrupole == 1 ) dipole_quad = 1 + + ! -------------------------------------------------------------------- + ! dipole-dipole term + ! -------------------------------------------------------------------- + IF (dipole == 1) THEN + + IF (dd_term == 'GV') CALL PHI_DD_GROSS_VRABEC( k, z3_rk, fdd_rk ) + ! IF (dd_term == 'SF') CALL PHI_DD_SAAGER_FISCHER( k ) + + IF (dd_term /= 'GV' .AND. dd_term /= 'SF') write (*,*) 'specify dipole term !' + + ENDIF + + ! -------------------------------------------------------------------- + ! quadrupole-quadrupole term + ! -------------------------------------------------------------------- + IF (quadrupole == 1) THEN + + !IF (qq_term == 'SF') CALL PHI_QQ_SAAGER_FISCHER( k ) + IF (qq_term == 'JG') CALL PHI_QQ_GROSS( k, z3_rk, fqq_rk ) + + IF (qq_term /= 'JG' .AND. qq_term /= 'SF') write (*,*) 'specify quadrupole term !' + + ENDIF + + ! -------------------------------------------------------------------- + ! dipole-quadrupole cross term + ! -------------------------------------------------------------------- + IF (dipole_quad == 1) THEN + + IF (dq_term == 'VG') CALL PHI_DQ_VRABEC_GROSS( k, z3_rk, fdq_rk ) + + IF (dq_term /= 'VG' ) write (*,*) 'specify DQ-cross term !' + + ENDIF + +END SUBROUTINE PHI_POLAR + + +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! + SUBROUTINE PHI_DD_GROSS_VRABEC( k, z3_rk, fdd_rk ) +! + USE PARAMETERS, ONLY: PI, KBOL + USE EOS_VARIABLES, ONLY: nc, ncomp, uij, parame, mseg, sig_ij, rho, eta, x, t + USE EOS_CONSTANTS, ONLY: ddp2, ddp3, ddp4 + IMPLICIT NONE +! +! ---------------------------------------------------------------------- + INTEGER, INTENT(IN) :: k + REAL, INTENT(IN) :: z3_rk + REAL, INTENT(IN OUT) :: fdd_rk +! +! --- local variables--------------------------------------------------- + INTEGER :: i, j, l, m + + REAL :: factor2, factor3, z3 + REAL :: xijfa, xijkfa, xijfa_x, xijkf_x, eij + REAL :: fdd2, fdd3, fdd2x, fdd3x + REAL, DIMENSION(nc) :: my2dd + REAL, DIMENSION(nc,nc) :: Idd2, Idd4, Idd2x, Idd4x + REAL, DIMENSION(nc,nc,nc) :: Idd3, Idd3x +! ---------------------------------------------------------------------- + + + fdd_rk = 0.0 + z3 = eta + DO i = 1, ncomp + IF ( uij(i,i) == 0.0 ) write (*,*) 'PHI_DD_GROSS_VRABEC: do not use dimensionless units' + IF ( uij(i,i) == 0.0 ) stop + my2dd(i) = (parame(i,6))**2 *1.E-49 / (uij(i,i)*KBOL*mseg(i)*sig_ij(i,i)**3 *1.E-30) + END DO + + DO i = 1, ncomp + DO j = 1, ncomp + Idd2(i,j) = 0.0 + Idd4(i,j) = 0.0 + Idd2x(i,j) = 0.0 + Idd4x(i,j) = 0.0 + IF (parame(i,6) /= 0.0 .AND. parame(j,6) /= 0.0) THEN + DO m=0,4 + Idd2(i,j) =Idd2(i,j) + ddp2(i,j,m)*z3**m + Idd4(i,j) =Idd4(i,j) + ddp4(i,j,m)*z3**m + Idd2x(i,j) =Idd2x(i,j)+ ddp2(i,j,m)*REAL(m)*z3**(m-1)*z3_rk + Idd4x(i,j) =Idd4x(i,j)+ ddp4(i,j,m)*REAL(m)*z3**(m-1)*z3_rk + END DO + DO l = 1, ncomp + Idd3(i,j,l) = 0.0 + Idd3x(i,j,l) = 0.0 + IF (parame(l,6) /= 0.0) THEN + DO m=0,4 + Idd3(i,j,l) =Idd3(i,j,l) +ddp3(i,j,l,m)*z3**m + Idd3x(i,j,l)=Idd3x(i,j,l)+ddp3(i,j,l,m)*REAL(m)*z3**(m-1)*z3_rk + END DO + END IF + END DO + END IF + END DO + END DO + + factor2= -PI + factor3= -4.0/3.0*PI**2 + + fdd2 = 0.0 + fdd3 = 0.0 + fdd2x = 0.0 + fdd3x = 0.0 + DO i = 1, ncomp + xijfa_x = 2.0*x(i)*rho*uij(i,i)*my2dd(i)*sig_ij(i,i)**3 /t & + *uij(k,k)*my2dd(k)*sig_ij(k,k)**3 /t/sig_ij(i,k)**3 + eij = (parame(i,3)*parame(k,3))**0.5 + fdd2x = fdd2x + factor2*xijfa_x*( Idd2(i,k) + eij/t*Idd4(i,k) ) + DO j = 1, ncomp + IF (parame(i,6) /= 0.0 .AND. parame(j,6) /= 0.0) THEN + xijfa =x(i)*rho*uij(i,i)*my2dd(i)*sig_ij(i,i)**3 /t & + *x(j)*rho*uij(j,j)*my2dd(j)*sig_ij(j,j)**3 /t/sig_ij(i,j)**3 + eij = (parame(i,3)*parame(j,3))**0.5 + fdd2= fdd2 +factor2*xijfa*(Idd2(i,j) +eij/t*Idd4(i,j) ) + fdd2x =fdd2x +factor2*xijfa*(Idd2x(i,j)+eij/t*Idd4x(i,j)) + !--------------------- + xijkf_x=x(i)*rho*uij(i,i)*my2dd(i)*sig_ij(i,i)**3 /t/sig_ij(i,j) & + *x(j)*rho*uij(j,j)*my2dd(j)*sig_ij(j,j)**3 /t/sig_ij(i,k) & + *3.0* uij(k,k)*my2dd(k)*sig_ij(k,k)**3 /t/sig_ij(j,k) + fdd3x=fdd3x+factor3*xijkf_x*Idd3(i,j,k) + DO l=1,ncomp + IF (parame(l,6) /= 0.0) THEN + xijkfa= x(i)*rho*uij(i,i)/t*my2dd(i)*sig_ij(i,i)**3 & + *x(j)*rho*uij(j,j)/t*my2dd(j)*sig_ij(j,j)**3 & + *x(l)*rho*uij(l,l)/t*my2dd(l)*sig_ij(l,l)**3 & + /sig_ij(i,j)/sig_ij(i,l)/sig_ij(j,l) + fdd3 =fdd3 + factor3 * xijkfa *Idd3(i,j,l) + fdd3x =fdd3x + factor3 * xijkfa *Idd3x(i,j,l) + END IF + END DO + END IF + END DO + END DO + + IF (fdd2 < -1.E-50 .AND. fdd3 /= 0.0 .AND. fdd2x /= 0.0 .AND. fdd3x /= 0.0)THEN + + fdd_rk = fdd2* (fdd2*fdd2x - 2.0*fdd3*fdd2x+fdd2*fdd3x) / (fdd2-fdd3)**2 + + END IF + +END SUBROUTINE PHI_DD_GROSS_VRABEC + + + +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! + SUBROUTINE PHI_QQ_GROSS( k, z3_rk, fqq_rk ) +! + USE PARAMETERS, ONLY: PI, KBOL + USE EOS_VARIABLES, ONLY: nc, ncomp, uij, parame, mseg, sig_ij, rho, eta, x, t + USE EOS_CONSTANTS, ONLY: qqp2, qqp3, qqp4 + IMPLICIT NONE +! +! ---------------------------------------------------------------------- + INTEGER, INTENT(IN) :: k + REAL, INTENT(IN) :: z3_rk + REAL, INTENT(IN OUT) :: fqq_rk +! +! --- local variables--------------------------------------------------- + INTEGER :: i, j, l, m + + REAL :: factor2, factor3, z3 + REAL :: xijfa, xijkfa, xijfa_x, xijkf_x, eij + REAL :: fqq2, fqq3, fqq2x, fqq3x + REAL, DIMENSION(nc) :: qq2 + REAL, DIMENSION(nc,nc) :: Iqq2, Iqq4, Iqq2x, Iqq4x + REAL, DIMENSION(nc,nc,nc) :: Iqq3, Iqq3x +! ---------------------------------------------------------------------- + + + fqq_rk = 0.0 + z3 = eta + DO i = 1, ncomp + IF ( uij(i,i) == 0.0 ) write (*,*) 'PHI_QQ_GROSS: do not use dimensionless units' + qq2(i) = (parame(i,7))**2 *1.E-69 / (uij(i,i)*kbol*mseg(i)*sig_ij(i,i)**5 *1.E-50) + END DO + + DO i = 1, ncomp + DO j = 1, ncomp + Iqq2(i,j) = 0.0 + Iqq4(i,j) = 0.0 + Iqq2x(i,j) = 0.0 + Iqq4x(i,j) = 0.0 + IF (parame(i,7) /= 0.0 .AND. parame(j,7) /= 0.0) THEN + DO m = 0, 4 + Iqq2(i,j) = Iqq2(i,j) + qqp2(i,j,m) * z3**m + Iqq4(i,j) = Iqq4(i,j) + qqp4(i,j,m) * z3**m + Iqq2x(i,j) = Iqq2x(i,j) + qqp2(i,j,m) * REAL(m)*z3**(m-1)*z3_rk + Iqq4x(i,j) = Iqq4x(i,j) + qqp4(i,j,m) * REAL(m)*z3**(m-1)*z3_rk + END DO + DO l = 1, ncomp + Iqq3(i,j,l) = 0.0 + Iqq3x(i,j,l) = 0.0 + IF (parame(l,7) /= 0.0) THEN + DO m = 0, 4 + Iqq3(i,j,l) = Iqq3(i,j,l) + qqp3(i,j,l,m)*z3**m + Iqq3x(i,j,l) = Iqq3x(i,j,l) + qqp3(i,j,l,m)*REAL(m) *z3**(m-1)*z3_rk + END DO + END IF + END DO + END IF + END DO + END DO + + factor2= -9.0/16.0*PI + factor3= 9.0/16.0*PI**2 + + fqq2 = 0.0 + fqq3 = 0.0 + fqq2x = 0.0 + fqq3x = 0.0 + DO i = 1, ncomp + xijfa_x = 2.0*x(i)*rho*uij(i,i)*qq2(i)*sig_ij(i,i)**5 /t & + *uij(k,k)*qq2(k)*sig_ij(k,k)**5 /t/sig_ij(i,k)**7.0 + eij = (parame(i,3)*parame(k,3))**0.5 + fqq2x =fqq2x +factor2*xijfa_x*(Iqq2(i,k)+eij/t*Iqq4(i,k)) + DO j=1,ncomp + IF (parame(i,7) /= 0.0 .AND. parame(j,7) /= 0.0) THEN + xijfa =x(i)*rho*uij(i,i)*qq2(i)*sig_ij(i,i)**5 /t & + *x(j)*rho*uij(j,j)*qq2(j)*sig_ij(j,j)**5 /t/sig_ij(i,j)**7.0 + eij = (parame(i,3)*parame(j,3))**0.5 + fqq2= fqq2 +factor2*xijfa*(Iqq2(i,j) +eij/t*Iqq4(i,j) ) + fqq2x =fqq2x +factor2*xijfa*(Iqq2x(i,j)+eij/t*Iqq4x(i,j)) + ! ------------------ + xijkf_x=x(i)*rho*uij(i,i)*qq2(i)*sig_ij(i,i)**5 /t/sig_ij(i,j)**3 & + *x(j)*rho*uij(j,j)*qq2(j)*sig_ij(j,j)**5 /t/sig_ij(i,k)**3 & + *3.0* uij(k,k)*qq2(k)*sig_ij(k,k)**5 /t/sig_ij(j,k)**3 + fqq3x = fqq3x + factor3*xijkf_x*Iqq3(i,j,k) + DO l = 1, ncomp + IF (parame(l,7) /= 0.0) THEN + xijkfa=x(i)*rho*uij(i,i)*qq2(i)*sig_ij(i,i)**5 /t/sig_ij(i,j)**3 & + *x(j)*rho*uij(j,j)*qq2(j)*sig_ij(j,j)**5 /t/sig_ij(i,l)**3 & + *x(l)*rho*uij(l,l)*qq2(l)*sig_ij(l,l)**5 /t/sig_ij(j,l)**3 + fqq3 =fqq3 + factor3 * xijkfa *Iqq3(i,j,l) + fqq3x =fqq3x + factor3 * xijkfa *Iqq3x(i,j,l) + END IF + END DO + END IF + END DO + END DO + + IF (fqq2 < -1.E-50 .AND. fqq3 /= 0.0 .AND. fqq2x /= 0.0 .AND. fqq3x /= 0.0) THEN + fqq_rk = fqq2* (fqq2*fqq2x - 2.0*fqq3*fqq2x+fqq2*fqq3x) / (fqq2-fqq3)**2 + END IF + +END SUBROUTINE PHI_QQ_GROSS + +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! + SUBROUTINE PHI_DQ_VRABEC_GROSS( k, z3_rk, fdq_rk ) +! + USE PARAMETERS, ONLY: PI, KBOL + USE EOS_VARIABLES, ONLY: nc, ncomp, uij, parame, mseg, sig_ij, rho, eta, x, t + USE EOS_CONSTANTS, ONLY: dqp2, dqp3, dqp4 + IMPLICIT NONE +! +! ---------------------------------------------------------------------- + INTEGER, INTENT(IN) :: k + REAL, INTENT(IN) :: z3_rk + REAL, INTENT(IN OUT) :: fdq_rk +! +! --- local variables--------------------------------------------------- + INTEGER :: i, j, l, m + + REAL :: factor2, factor3, z3 + REAL :: xijfa, xijkfa, xijfa_x, xijkf_x, eij + REAL :: fdq2, fdq3, fdq2x, fdq3x + REAL, DIMENSION(nc) :: my2dd, myfac, qq2, q_fac + REAL, DIMENSION(nc,nc) :: Idq2, Idq4, Idq2x, Idq4x + REAL, DIMENSION(nc,nc,nc) :: Idq3, Idq3x +! ---------------------------------------------------------------------- + + fdq_rk = 0.0 + z3 = eta + DO i=1,ncomp + my2dd(i) = (parame(i,6))**2 *1.E-49 / (uij(i,i)*KBOL*mseg(i)*sig_ij(i,i)**3 *1.E-30) + myfac(i) = parame(i,3)/t*parame(i,2)**4 *my2dd(i) + qq2(i) = (parame(i,7))**2 *1.E-69 / (uij(i,i)*kbol*mseg(i)*sig_ij(i,i)**5 *1.E-50) + q_fac(i) = parame(i,3)/t*parame(i,2)**4 *qq2(i) + END DO + + DO i = 1, ncomp + DO j = 1, ncomp + Idq2(i,j) = 0.0 + Idq4(i,j) = 0.0 + Idq2x(i,j) = 0.0 + Idq4x(i,j) = 0.0 + DO m = 0, 4 + Idq2(i,j) = Idq2(i,j) + dqp2(i,j,m)*z3**m + Idq4(i,j) = Idq4(i,j) + dqp4(i,j,m)*z3**m + Idq2x(i,j) = Idq2x(i,j) + dqp2(i,j,m)*REAL(m)*z3**(m-1) *z3_rk + Idq4x(i,j) = Idq4x(i,j) + dqp4(i,j,m)*REAL(m)*z3**(m-1) *z3_rk + END DO + DO l = 1, ncomp + Idq3(i,j,l) = 0.0 + Idq3x(i,j,l) = 0.0 + DO m = 0, 4 + Idq3(i,j,l) =Idq3(i,j,l) +dqp3(i,j,l,m)*z3**m + Idq3x(i,j,l)=Idq3x(i,j,l)+dqp3(i,j,l,m)*REAL(m)*z3**(m-1)*z3_rk + END DO + END DO + END DO + END DO + + factor2= -9.0/4.0*PI + factor3= PI**2 + + fdq2 = 0.0 + fdq3 = 0.0 + fdq2x = 0.0 + fdq3x = 0.0 + DO i = 1, ncomp + xijfa_x = x(i)*rho*( myfac(i)*q_fac(k) + myfac(k)*q_fac(i) ) / sig_ij(i,k)**5 + eij = (parame(i,3)*parame(k,3))**0.5 + fdq2x =fdq2x +factor2*xijfa_x*(Idq2(i,k)+eij/t*Idq4(i,k)) + DO j=1,ncomp + xijfa =x(i)*rho*myfac(i) * x(j)*rho*q_fac(j) /sig_ij(i,j)**5 + eij = (parame(i,3)*parame(j,3))**0.5 + fdq2= fdq2 +factor2*xijfa*(Idq2(i,j) +eij/t*Idq4(i,j) ) + fdq2x =fdq2x +factor2*xijfa*(Idq2x(i,j) +eij/t*Idq4x(i,j)) + !--------------------- + xijkf_x=x(i)*rho*x(j)*rho/(sig_ij(i,j)*sig_ij(i,k)*sig_ij(j,k))**2 & + *( myfac(i)*q_fac(j)*myfac(k) + myfac(i)*q_fac(k)*myfac(j) & + + myfac(k)*q_fac(i)*myfac(j) +myfac(i)*q_fac(j)*q_fac(k)*1.1937350 & + +myfac(i)*q_fac(k)*q_fac(j)*1.193735 & + +myfac(k)*q_fac(i)*q_fac(j)*1.193735 ) + fdq3x = fdq3x + factor3*xijkf_x*Idq3(i,j,k) + DO l = 1, ncomp + xijkfa=x(i)*rho*x(j)*rho*x(l)*rho/(sig_ij(i,j)*sig_ij(i,l)*sig_ij(j,l))**2 & + *( myfac(i)*q_fac(j)*myfac(l) & + +myfac(i)*q_fac(j)*q_fac(l)*1.193735 ) + fdq3 =fdq3 + factor3 * xijkfa *Idq3(i,j,l) + fdq3x =fdq3x + factor3 * xijkfa *Idq3x(i,j,l) + END DO + END DO + END DO + + IF (fdq2 < -1.E-50 .AND. fdq3 /= 0.0 .AND. fdq2x /= 0.0 .AND. fdq3x /= 0.0)THEN + + fdq_rk = fdq2* (fdq2*fdq2x - 2.0*fdq3*fdq2x+fdq2*fdq3x) / (fdq2-fdq3)**2 + + END IF + +END SUBROUTINE PHI_DQ_VRABEC_GROSS + + + +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! + SUBROUTINE P_NUMERICAL +! + USE EOS_VARIABLES + IMPLICIT NONE +! +!-----local variables------------------------------------------------- + REAL :: dzetdv, eta_0, dist, fact + REAL :: fres1, fres2, fres3, fres4, fres5 + REAL :: df_dr, df_drdr, pideal, dpiddz + REAL :: tfr_1, tfr_2, tfr_3, tfr_4, tfr_5 +!----------------------------------------------------------------------- + + +IF (eta > 0.1) THEN + fact = 1.0 +ELSE IF (eta <= 0.1 .AND. eta > 0.01) THEN + fact = 10.0 +ELSE + fact = 10.0 +END IF +dist = eta*3.d-3 *fact +! dist = eta*4.d-3 *fact +!***************************** +! fuer MC simulation: neues dist: +! dist = eta*5.d-3*fact + +eta_0 = eta +eta = eta_0 - 2.0*dist +CALL F_NUMERICAL +fres1 = fres +tfr_1 = tfr +eta = eta_0 - dist +CALL F_NUMERICAL +fres2 = fres +tfr_2 = tfr +eta = eta_0 + dist +CALL F_NUMERICAL +fres3 = fres +tfr_3 = tfr +eta = eta_0 + 2.0*dist +CALL F_NUMERICAL +fres4 = fres +tfr_4 = tfr +eta = eta_0 +CALL F_NUMERICAL +fres5 = fres +tfr_5 = tfr + +!--------------------------------------------------------- +! ptfr = (-tfr_4+8.0*tfr_3-8.0*tfr_2+tfr_1)/(12.0*dist) +! & *dzetdv*(KBOL*T)/1.E-30 +! ztfr =ptfr /( rho * (KBOL*t) / 1.E-30) +! ptfrdz = (-tfr_4+16.0*tfr_3-3.d1*tfr_5+16.0*tfr_2-tfr_1) +! & /(12.0*(dist**2 ))* dzetdv*(KBOL*T)/1.E-30 +! & + (-tfr_4+8.0*tfr_3-8.0*tfr_2+tfr_1) +! & /(12.0*dist) * 2.0 *eta*6.0/PI/D +! & *(KBOL*T)/1.E-30 +! ztfrdz=ptfrdz/( rho*(kbol*T)/1.E-30 ) - ztfr/eta +! write (*,*) eta,ztfr,ztfrdz + +! dtfr_dr = (-tfr_4+8.0*tfr_3-8.0*tfr_2+tfr_1)/(12.0*dist) +! write (*,*) eta,dtfr_dr +! stop +!--------------------------------------------------------- + +df_dr = (-fres4+8.0*fres3-8.0*fres2+fres1) / (12.0*dist) +df_drdr = (-fres4+16.0*fres3-3.d1*fres5+16.0*fres2-fres1) & + /(12.0*(dist**2 )) + + +dzetdv = eta*rho + +pges = (-fres4+8.0*fres3-8.0*fres2+fres1) & + /(12.0*dist) *dzetdv*(kbol*t)/1.E-30 + +dpiddz = 1.0/z3t*(kbol*t)/1.E-30 +pgesdz = (-fres4+16.0*fres3-3.d1*fres5+16.0*fres2-fres1) & + /(12.0*(dist**2 ))* dzetdv*(kbol*t)/1.E-30 & + + (-fres4+8.0*fres3-8.0*fres2+fres1) /(12.0*dist) * 2.0 *rho & + *(kbol*t)/1.E-30 + dpiddz + +pgesd2 = (fres4-2.0*fres3+2.0*fres2-fres1) /(2.0*dist**3 ) & + * dzetdv*(kbol*t)/1.E-30 & + + (-fres4+16.0*fres3-3.d1*fres5+16.0*fres2-fres1) /(12.0*(dist**2 )) & + * 4.0 *rho *(kbol*t)/1.E-30 + (-fres4+8.0*fres3-8.0*fres2+fres1) & + /(12.0*dist) * 2.0 /z3t *(kbol*t)/1.E-30 +pgesd3 = (fres4-4.0*fres3+6.0*fres5-4.0*fres2+fres1) /(dist**4 ) & + * dzetdv*(kbol*t)/1.E-30 + (fres4-2.0*fres3+2.0*fres2-fres1) & + /(2.0*dist**3 ) * 6.0 *rho *(kbol*t)/1.E-30 & + + (-fres4+16.0*fres3-3.d1*fres5+16.0*fres2-fres1) & + /(12.0*dist**2 )* 6.0 /z3t *(kbol*t)/1.E-30 + +!------------------p ideal------------------------------------ +pideal = rho * (kbol*t) / 1.E-30 + +!------------------p summation, p comes out in Pa ------------ +pges = pideal + pges + +END SUBROUTINE P_NUMERICAL + + +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! + SUBROUTINE H_numerical +! + USE PARAMETERS, ONLY: RGAS + USE EOS_VARIABLES + IMPLICIT NONE +! +!--------------------------------------------------------------------- + REAL :: dist, fact, rho_0 + REAL :: fres1,fres2,fres3,fres4,fres5 + REAL :: f_1, f_2, f_3, f_4 + REAL :: cv_res, t_tmp, zges + REAL :: f_dt, f_dtdt, f_dr, f_drdr, f_drdt +!----------------------------------------------------------------------- + + +CALL PERTURBATION_PARAMETER +rho_0 = eta/z3t + + +fact = 1.0 +dist = t * 100.E-5 * fact + +t_tmp = t + +t = t_tmp - 2.0*dist +CALL PERTURBATION_PARAMETER +eta = z3t*rho_0 +CALL F_NUMERICAL +fres1 = fres +t = t_tmp - dist +CALL PERTURBATION_PARAMETER +eta = z3t*rho_0 +CALL F_NUMERICAL +fres2 = fres +t = t_tmp + dist +CALL PERTURBATION_PARAMETER +eta = z3t*rho_0 +CALL F_NUMERICAL +fres3 = fres +t = t_tmp + 2.0*dist +CALL PERTURBATION_PARAMETER +eta = z3t*rho_0 +CALL F_NUMERICAL +fres4 = fres +t = t_tmp +CALL PERTURBATION_PARAMETER +eta = z3t*rho_0 +CALL F_NUMERICAL +fres5 = fres +! *(KBOL*T)/1.E-30 + +zges = (p * 1.E-30)/(kbol*t*rho_0) + + +f_dt = (-fres4+8.0*fres3-8.0*fres2+fres1)/(12.0*dist) +f_dtdt = (-fres4+16.0*fres3-3.d1*fres5+16.0*fres2-fres1) /(12.0*(dist**2 )) + +s_res = (- f_dt -fres/t)*RGAS*t + RGAS * LOG(zges) +h_res = ( - t*f_dt + zges-1.0 ) * RGAS*t +cv_res = -( t*f_dtdt + 2.0*f_dt ) * RGAS*t + + + +t = t_tmp - 2.0*dist +CALL PERTURBATION_PARAMETER +eta = z3t*rho_0 +CALL P_NUMERICAL +f_1 = pges/(eta*rho_0*(KBOL*T)/1.E-30) + +t = t_tmp - dist +CALL PERTURBATION_PARAMETER +eta = z3t*rho_0 +CALL P_NUMERICAL +f_2 = pges/(eta*rho_0*(KBOL*T)/1.E-30) + +t = t_tmp + dist +CALL PERTURBATION_PARAMETER +eta = z3t*rho_0 +CALL P_NUMERICAL +f_3 = pges/(eta*rho_0*(KBOL*T)/1.E-30) + +t = t_tmp + 2.0*dist +CALL PERTURBATION_PARAMETER +eta = z3t*rho_0 +CALL P_NUMERICAL +f_4 = pges/(eta*rho_0*(KBOL*T)/1.E-30) + +t = t_tmp +CALL PERTURBATION_PARAMETER +eta = z3t*rho_0 +CALL P_NUMERICAL + +f_dr = pges / (eta*rho_0*(KBOL*T)/1.E-30) +f_drdr = pgesdz/ (eta*rho_0*(KBOL*T)/1.E-30) - f_dr*2.0/eta - 1.0/eta**2 + +f_drdt = ( - f_4 + 8.0*f_3 - 8.0*f_2 + f_1 ) / ( 12.0*dist ) + +cp_res = cv_res - RGAS + RGAS*( zges + eta*t*f_drdt)**2 / (1.0 + 2.0*eta*f_dr + eta**2 *f_drdr) +! write (*,*) cv_res,cp_res,eta + + +END SUBROUTINE H_numerical + + + + + + + + + + + +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! + SUBROUTINE F_POLAR ( fdd, fqq, fdq ) +! + USE EOS_VARIABLES, ONLY: ncomp, parame, dd_term, qq_term, dq_term + IMPLICIT NONE +! +! ---------------------------------------------------------------------- + REAL, INTENT(OUT) :: fdd, fqq, fdq +! +! --- local variables--------------------------------------------------- + INTEGER :: dipole + INTEGER :: quadrupole + INTEGER :: dipole_quad +! ---------------------------------------------------------------------- + + fdd = 0.0 + fqq = 0.0 + fdq = 0.0 + + dipole = 0 + quadrupole = 0 + dipole_quad = 0 + IF ( SUM( parame(1:ncomp,6) ) /= 0.0 ) dipole = 1 + IF ( SUM( parame(1:ncomp,7) ) /= 0.0 ) quadrupole = 1 + IF ( dipole == 1 .AND. quadrupole == 1 ) dipole_quad = 1 + + ! -------------------------------------------------------------------- + ! dipole-dipole term + ! -------------------------------------------------------------------- + IF (dipole == 1) THEN + + IF (dd_term == 'GV') CALL F_DD_GROSS_VRABEC( fdd ) + ! IF (dd_term == 'SF') CALL F_DD_SAAGER_FISCHER( k ) + IF (dd_term /= 'GV' .AND. dd_term /= 'SF') write (*,*) 'specify dipole term !' + + ENDIF + + ! -------------------------------------------------------------------- + ! quadrupole-quadrupole term + ! -------------------------------------------------------------------- + IF (quadrupole == 1) THEN + + !IF (qq_term == 'SF') CALL F_QQ_SAAGER_FISCHER( k ) + IF (qq_term == 'JG') CALL F_QQ_GROSS( fqq ) + IF (qq_term /= 'JG' .AND. qq_term /= 'SF') write (*,*) 'specify quadrupole term !' + + ENDIF + + ! -------------------------------------------------------------------- + ! dipole-quadrupole cross term + ! -------------------------------------------------------------------- + IF (dipole_quad == 1) THEN + + IF (dq_term == 'VG') CALL F_DQ_VRABEC_GROSS( fdq ) + IF (dq_term /= 'VG' ) write (*,*) 'specify DQ-cross term !' + + ENDIF + +END SUBROUTINE F_POLAR + + + +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! SUBROUTINE PRESSURE_SPINODAL +! +! iterates the density until the derivative of pressure 'pges' to +! density is equal to zero. A Newton-scheme is used for determining +! the root to the objective function. +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! + SUBROUTINE PRESSURE_SPINODAL +! + USE BASIC_VARIABLES, ONLY: num + USE EOS_VARIABLES + IMPLICIT NONE +! +! ---------------------------------------------------------------------- + INTEGER :: i, max_i + REAL :: eta_iteration + REAL :: error, acc_i, delta_eta +! ---------------------------------------------------------------------- + +acc_i = 1.d-6 +max_i = 30 + +i = 0 +eta_iteration = eta_start + +! ---------------------------------------------------------------------- +! iterate density until p_calc = p +! ---------------------------------------------------------------------- + +error = acc_i + 1.0 +DO WHILE ( ABS(error) > acc_i .AND. i < max_i ) + + i = i + 1 + eta = eta_iteration + + IF ( num == 0 ) THEN + CALL P_EOS + ELSE IF ( num == 1 ) THEN + CALL P_NUMERICAL + ELSE IF ( num == 2 ) THEN + WRITE(*,*) 'CRITICAL RENORM NOT INCLUDED YET' + !!CALL F_EOS_RN + ELSE + write (*,*) 'define calculation option (num)' + END IF + + error = pgesdz + + delta_eta = error/ pgesd2 + IF ( delta_eta > 0.02 ) delta_eta = 0.02 + IF ( delta_eta < -0.02 ) delta_eta = -0.02 + + eta_iteration = eta_iteration - delta_eta + ! write (*,'(a,i3,3G18.10)') 'iter',i, error, eta_iteration, pgesdz + + IF (eta_iteration > 0.9) eta_iteration = 0.5 + IF (eta_iteration <= 0.0) eta_iteration = 1.E-16 + +END DO + +eta = eta_iteration + +END SUBROUTINE PRESSURE_SPINODAL + + +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! + SUBROUTINE F_IDEAL_GAS ( fid ) +! + USE EOS_VARIABLES, ONLY: nc, ncomp, t, x, rho, PI, KBOL, NAv + IMPLICIT NONE +! +!--------------------------------------------------------------------- + REAL, INTENT(IN OUT) :: fid +!--------------------------------------------------------------------- + INTEGER :: i + REAL, DIMENSION(nc) :: rhoi +!---------------------------------------------------------------------- + + !h_Planck = 6.62606896E-34 ! Js + DO i = 1, ncomp + rhoi(i) = x(i) * rho + ! debroglie(i) = h_Planck *1d10 & ! in units Angstrom + ! *SQRT( 1.0 / (2.0*PI *1.0 / NAv / 1000.0 * KBOL*T) ) + ! ! *SQRT( 1.0 / (2.0*PI *mm(i) /NAv/1000.0 * KBOL*T) ) + ! fid = fid + x(i) * ( LOG(rhoi(i)*debroglie(i)**3) - 1.0 ) + fid = fid + x(i) * ( LOG(rhoi(i)) - 1.0 ) + END DO + + END SUBROUTINE F_IDEAL_GAS + +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! + SUBROUTINE F_HARD_SPHERE ( m_mean2, fhs ) +! + USE EOS_VARIABLES, ONLY: z0t, z1t, z2t, z3t, eta, rho + IMPLICIT NONE +! +!--------------------------------------------------------------------- + REAL, INTENT(IN) :: m_mean2 + REAL, INTENT(IN OUT) :: fhs +!--------------------------------------------------------------------- + REAL :: z0, z1, z2, z3, zms +!---------------------------------------------------------------------- + + rho = eta / z3t + z0 = z0t * rho + z1 = z1t * rho + z2 = z2t * rho + z3 = z3t * rho + zms = 1.0 - z3 + + fhs= m_mean2*( 3.0*z1*z2/zms + z2**3 /z3/zms/zms + (z2**3 /z3/z3-z0)*LOG(zms) )/z0 + + + END SUBROUTINE F_HARD_SPHERE + +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! + SUBROUTINE F_CHAIN_TPT1 ( fhc ) +! + USE EOS_VARIABLES, ONLY: nc, ncomp, mseg, x, z0t, z1t, z2t, z3t, & + rho, eta, dij_ab, gij + IMPLICIT NONE +! +!--------------------------------------------------------------------- + REAL, INTENT(IN OUT) :: fhc +!--------------------------------------------------------------------- + INTEGER :: i, j + REAL :: z0, z1, z2, z3, zms +!--------------------------------------------------------------------- + + rho = eta / z3t + z0 = z0t * rho + z1 = z1t * rho + z2 = z2t * rho + z3 = z3t * rho + zms = 1.0 - z3 + + DO i = 1, ncomp + DO j = 1, ncomp + gij(i,j) = 1.0/zms + 3.0*dij_ab(i,j)*z2/zms/zms + 2.0*(dij_ab(i,j)*z2)**2 / zms**3 + END DO + END DO + + fhc = 0.0 + DO i = 1, ncomp + fhc = fhc + x(i) *(1.0- mseg(i)) *LOG(gij(i,i)) + END DO + + END SUBROUTINE F_CHAIN_TPT1 + + +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! + SUBROUTINE F_CHAIN_TPT_D ( fhc ) +! + USE EOS_VARIABLES, ONLY: nc, ncomp, mseg, x, z0t, z1t, z2t, z3t, rho, eta, & + dhs, mseg, dij_ab, gij + IMPLICIT NONE +! +!--------------------------------------------------------------------- + REAL, INTENT(OUT) :: fhc +!--------------------------------------------------------------------- + INTEGER :: i, j + REAL, DIMENSION(nc) :: gij_hd + REAL :: z0, z1, z2, z3, zms +!--------------------------------------------------------------------- + + rho = eta / z3t + z0 = z0t * rho + z1 = z1t * rho + z2 = z2t * rho + z3 = z3t * rho + zms = 1.0 - z3 + + DO i = 1, ncomp + DO j = 1, ncomp + gij(i,j) = 1.0/zms + 3.0*dij_ab(i,j)*z2/zms/zms + 2.0*(dij_ab(i,j)*z2)**2 / zms**3 + END DO + END DO + + DO i = 1, ncomp + gij_hd(i) = 1.0/(2.0*zms) + 3.0*dij_ab(i,i)*z2 / zms**2 + END DO + + fhc = 0.0 + DO i = 1, ncomp + IF ( mseg(i) >= 2.0 ) THEN + fhc = fhc - x(i) * ( mseg(i)/2.0 * LOG( gij(i,i) ) + ( mseg(i)/2.0 - 1.0 ) * LOG( gij_hd(i)) ) + ELSE + fhc = fhc + x(i) * ( 1.0 - mseg(i) ) * LOG( gij(i,i) ) + END IF + END DO + + END SUBROUTINE F_CHAIN_TPT_D + + +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! + SUBROUTINE F_CHAIN_HU_LIU ( fhc ) +! + USE EOS_VARIABLES, ONLY: nc, ncomp, mseg, x, rho, eta + IMPLICIT NONE +! +! This subroutine calculates the hard chain contribution of the TPT-Liu-Hu Eos. +!--------------------------------------------------------------------- + REAL, INTENT(OUT) :: fhc +!--------------------------------------------------------------------- + REAL :: a2, b2, c2, a3, b3, c3 + REAL :: a20, b20, c20, a30, b30, c30 + REAL :: sum1, sum2, am, bm, cm + REAL :: zms +!--------------------------------------------------------------------- + + zms = 1.0 - eta + + sum1 = SUM( x(1:ncomp)*(mseg(1:ncomp)-1.0) ) + sum2 = SUM( x(1:ncomp)/mseg(1:ncomp)*(mseg(1:ncomp)-1.0)*(mseg(1:ncomp)-2.0) ) + + a2 = 0.45696 + a3 = -0.74745 + b2 = 2.10386 + b3 = 3.49695 + c2 = 1.75503 + c3 = 4.83207 + a20 = - a2 + b2 - 3.0*c2 + b20 = - a2 - b2 + c2 + c20 = c2 + a30 = - a3 + b3 - 3.0*c3 + b30 = - a3 - b3 + c3 + c30 = c3 + am = (3.0 + a20) * sum1 + a30 * sum2 + bm = (1.0 + b20) * sum1 + b30 * sum2 + cm = (1.0 + c20) * sum1 + c30 * sum2 + + fhc = - ( (am*eta - bm) / (2.0*zms) + bm/2.0/zms**2 - cm *LOG(ZMS) ) + + + END SUBROUTINE F_CHAIN_HU_LIU + +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! + SUBROUTINE F_CHAIN_HU_LIU_RC ( fhs, fhc ) +! + USE EOS_VARIABLES, ONLY: mseg, chiR, eta + IMPLICIT NONE +! +! This subroutine calculates the hard chain contribution of the TPT-Liu-Hu Eos. +!--------------------------------------------------------------------- + REAL, INTENT(IN) :: fhs + REAL, INTENT(OUT) :: fhc +!--------------------------------------------------------------------- + REAL :: a2, b2, c2, a3, b3, c3 + REAL :: para1,para2,para3,para4 + REAL :: aLH,bLH,cLH +!--------------------------------------------------------------------- + +! This routine is only for pure components + + a2 = 0.45696 + b2 = 2.10386 + c2 = 1.75503 + + para1 = -0.74745 + para2 = 0.299154629727814 + para3 = 1.087271036653154 + para4 = -0.708979110326831 + a3 = para1 + para2*chiR(1) + para3*chiR(1)**2 + para4*chiR(1)**3 + b3 = 3.49695 - (3.49695 + 0.317719074806190)*chiR(1) + c3 = 4.83207 - (4.83207 - 3.480163780334421)*chiR(1) + + aLH = mseg(1)*(1.0 + ((mseg(1)-1.0)/mseg(1))*a2 + ((mseg(1)-1.0)/mseg(1))*((mseg(1)-2.0)/mseg(1))*a3 ) + bLH = mseg(1)*(1.0 + ((mseg(1)-1.0)/mseg(1))*b2 + ((mseg(1)-1.0)/mseg(1))*((mseg(1)-2.0)/mseg(1))*b3 ) + cLH = mseg(1)*(1.0 + ((mseg(1)-1.0)/mseg(1))*c2 + ((mseg(1)-1.0)/mseg(1))*((mseg(1)-2.0)/mseg(1))*c3 ) + + fhc = ((3.0 + aLH - bLH + 3.0*cLH)*eta - (1.0 + aLH + bLH - cLH)) / (2.0*(1.0-eta)) + & + (1.0 + aLH + bLH - cLH) / ( 2.0*(1.0-eta)**2 ) + (cLH - 1.0)*LOG(1.0-eta) + + fhc = fhc - fhs + + END SUBROUTINE F_CHAIN_HU_LIU_RC + + + + +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! + SUBROUTINE F_DISP_PCSAFT ( fdsp ) +! + USE EOS_VARIABLES, ONLY: PI, rho, eta, z0t, apar, bpar, order1, order2 + IMPLICIT NONE +! +!--------------------------------------------------------------------- + REAL, INTENT(IN OUT) :: fdsp +!--------------------------------------------------------------------- + INTEGER :: m + REAL :: I1, I2, c1_con, z3, zms, m_mean +!--------------------------------------------------------------------- + + z3 = eta + zms = 1.0 - eta + m_mean = z0t / ( PI / 6.0 ) + + I1 = 0.0 + I2 = 0.0 + DO m = 0, 6 + I1 = I1 + apar(m) * z3**m + I2 = I2 + bpar(m) * z3**m + END DO + + c1_con= 1.0/ ( 1.0 + m_mean*(8.0*z3-2.0*z3**2 )/zms**4 & + + (1.0-m_mean)*( 20.0*z3-27.0*z3**2 +12.0*z3**3 -2.0*z3**4 )/(zms*(2.0-z3))**2 ) + + fdsp = -2.0*PI*rho*I1*order1 - PI*rho*c1_con*m_mean*I2*order2 + + END SUBROUTINE F_DISP_PCSAFT + +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! + SUBROUTINE F_DISP_CKSAFT ( fdsp ) +! + USE EOS_VARIABLES, ONLY: nc, ncomp, PI, TAU, t, rho, eta, x, z0t, mseg, vij, uij, parame, um + USE EOS_CONSTANTS, ONLY: DNM + IMPLICIT NONE +! +!--------------------------------------------------------------------- + REAL, INTENT(IN OUT) :: fdsp +!--------------------------------------------------------------------- + INTEGER :: i, j, n, m + REAL :: zmr, nmr, m_mean +!--------------------------------------------------------------------- + + m_mean = z0t / ( PI / 6.0 ) + + DO i = 1, ncomp + DO j = 1, ncomp + vij(i,j)=(0.5*((parame(i,2)*(1.0-0.12 *EXP(-3.0*parame(i,3)/t))**3 )**(1.0/3.0) & + +(parame(j,2)*(1.0-0.12 *EXP(-3.0*parame(j,3)/t))**3 )**(1.0/3.0)))**3 + END DO + END DO + zmr = 0.0 + nmr = 0.0 + DO i = 1, ncomp + DO j = 1, ncomp + zmr = zmr + x(i)*x(j)*mseg(i)*mseg(j)*vij(i,j)*uij(i,j) + nmr = nmr + x(i)*x(j)*mseg(i)*mseg(j)*vij(i,j) + END DO + END DO + um = zmr / nmr + fdsp = 0.0 + DO n = 1, 4 + DO m = 1, 9 + fdsp = fdsp + DNM(n,m) * (um/t)**n *(eta/TAU)**m + END DO + END DO + fdsp = m_mean * fdsp + + + END SUBROUTINE F_DISP_CKSAFT + +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! + SUBROUTINE F_ASSOCIATION ( eps_kij, k_kij, fhb ) +! + USE EOS_VARIABLES, ONLY: nc, nsite, ncomp, t, z0t, z1t, z2t, z3t, rho, eta, x, & + parame, sig_ij, dij_ab, gij, nhb_typ, mx, nhb_no + IMPLICIT NONE +! +!--------------------------------------------------------------------- + REAL, INTENT(IN) :: eps_kij, k_kij + REAL, INTENT(IN OUT) :: fhb +!--------------------------------------------------------------------- + LOGICAL :: assoc + INTEGER :: i, j, k, l, no, ass_cnt, max_eval + REAL, DIMENSION(nc,nc) :: kap_hb + REAL, DIMENSION(nc,nc,nsite,nsite) :: eps_hb + REAL, DIMENSION(nc,nsite,nc,nsite) :: delta + REAL, DIMENSION(nc,nsite) :: mx_itr + REAL :: err_sum, sum0, amix, tol, ass_s1, ass_s2 + REAL :: z0, z1, z2, z3, zms +!--------------------------------------------------------------------- + + assoc = .false. + DO i = 1,ncomp + IF (NINT(parame(i,12)) /= 0) assoc = .true. + END DO + IF (assoc) THEN + + rho = eta / z3t + z0 = z0t * rho + z1 = z1t * rho + z2 = z2t * rho + z3 = z3t * rho + zms = 1.0 - z3 + + DO i = 1, ncomp + DO j = 1, ncomp + gij(i,j) = 1.0/zms + 3.0*dij_ab(i,j)*z2/zms/zms + 2.0*(dij_ab(i,j)*z2)**2 / zms**3 + END DO + END DO + + + DO i = 1, ncomp + IF ( NINT(parame(i,12)) /= 0 ) THEN + nhb_typ(i) = NINT( parame(i,12) ) + kap_hb(i,i) = parame(i,13) + no = 0 + DO k = 1,nhb_typ(i) + DO l = 1,nhb_typ(i) + eps_hb(i,i,k,l) = parame(i,(14+no)) + no = no + 1 + END DO + END DO + DO k = 1,nhb_typ(i) + nhb_no(i,k) = parame(i,(14+no)) + no = no + 1 + END DO + ELSE + nhb_typ(i) = 0 + kap_hb(i,i)= 0.0 + DO k = 1,nsite + DO l = 1,nsite + eps_hb(i,i,k,l) = 0.0 + END DO + END DO + END IF + END DO + + DO i = 1,ncomp + DO j = 1,ncomp + IF ( i /= j .AND. (nhb_typ(i) /= 0.AND.nhb_typ(j) /= 0) ) THEN + ! kap_hb(i,j)= (kap_hb(i,i)+kap_hb(j,j))/2.0 + ! kap_hb(i,j)= ( ( kap_hb(i,i)**(1.0/3.0) + kap_hb(j,j)**(1.0/3.0) )/2.0 )**3 + kap_hb(i,j) = (kap_hb(i,i)*kap_hb(j,j))**0.5 & + *((parame(i,2)*parame(j,2))**3 )**0.5 & + / (0.5*(parame(i,2)+parame(j,2)))**3 + kap_hb(i,j)= kap_hb(i,j)*(1.0-k_kij) + DO k = 1,nhb_typ(i) + DO l = 1,nhb_typ(j) + IF ( k /= l .AND. nhb_typ(i) >= 2 .AND. nhb_typ(j) >= 2 ) THEN + eps_hb(i,j,k,l) = (eps_hb(i,i,k,l)+eps_hb(j,j,l,k))/2.0 + ! eps_hb(i,j,k,l) = (eps_hb(i,i,k,l)*eps_hb(j,j,l,k))**0.5 + eps_hb(i,j,k,l) = eps_hb(i,j,k,l)*(1.0-eps_kij) + ELSE IF ( nhb_typ(i) == 1 .AND. l > k ) THEN + eps_hb(i,j,k,l) = (eps_hb(i,i,k,k)+eps_hb(j,j,l,k))/2.0 + eps_hb(j,i,l,k) = (eps_hb(i,i,k,k)+eps_hb(j,j,l,k))/2.0 + eps_hb(i,j,k,l) = eps_hb(i,j,k,l)*(1.0-eps_kij) + eps_hb(j,i,l,k) = eps_hb(j,i,l,k)*(1.0-eps_kij) + END IF + END DO + END DO + END IF + END DO + END DO + +!-----setting the self-association to zero for ionic compounds------ + DO i = 1,ncomp + IF ( parame(i,10) /= 0) kap_hb(i,i)=0.0 + DO j = 1,ncomp + IF ( parame(i,10) /= 0 .AND. parame(j,10) /= 0 ) kap_hb(i,j) = 0.0 + END DO + END DO + ! kap_hb(1,2)=0.050 + ! kap_hb(2,1)=0.050 + ! eps_hb(2,1,1,1)=465.0 + ! eps_hb(1,2,1,1)=465.0 + ! nhb_typ(1) = 1 + ! nhb_typ(2) = 1 + ! nhb_no(1,1)= 1.0 + ! nhb_no(2,1)= 1.0 + + + DO i = 1, ncomp + DO k = 1, nhb_typ(i) + DO j = 1, ncomp + DO l = 1, nhb_typ(j) + delta(i,k,j,l)=gij(i,j)*kap_hb(i,j)*(EXP(eps_hb(i,j,k,l)/t)-1.0) *sig_ij(i,j)**3 +!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! +! IF ((i+j).EQ.3) delta(i,k,j,l)=94.0 +!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! + END DO + END DO + IF ( mx(i,k) == 0.0 ) mx(i,k) = 1.0 + END DO + END DO + +!------constants for Iteration --------------------------------------- + amix = 0.7 + tol = 1.E-10 + IF (eta < 0.2) tol = 1.E-11 + IF (eta < 0.01) tol = 1.E-14 + max_eval = 200 + +! --- Iterate over all components and all sites ------------------------ + ass_cnt = 0 + iterate_TPT1: DO + + ass_cnt = ass_cnt + 1 + + DO i = 1, ncomp + DO k = 1, nhb_typ(i) + sum0 = 0.0 + DO j = 1, ncomp + DO l = 1, nhb_typ(j) + sum0 = sum0 + x(j)* mx(j,l)*nhb_no(j,l) *delta(i,k,j,l) + END DO + END DO + mx_itr(i,k) = 1.0 / (1.0 + sum0*rho) + END DO + END DO + + err_sum = 0.0 + DO i = 1, ncomp + DO k = 1, nhb_typ(i) + err_sum = err_sum + ABS( mx_itr(i,k) - mx(i,k) ) ! / ABS(mx_itr(i,k)) + mx(i,k) = mx_itr(i,k) * amix + mx(i,k) * (1.0 - amix) + IF ( mx(i,k) <= 0.0 ) mx(i,k)=1.E-50 + IF ( mx(i,k) > 1.0 ) mx(i,k)=1.0 + END DO + END DO + + IF ( err_sum <= tol .OR. ass_cnt >= max_eval ) THEN + IF ( ass_cnt >= max_eval ) WRITE(*,*) 'F_NUMERICAL: Max_eval violated = ',err_sum,tol + EXIT iterate_TPT1 + END IF + + END DO iterate_TPT1 + + DO i = 1, ncomp + ass_s1 = 0.0 + ass_s2 = 0.0 + DO k = 1, nhb_typ(i) + ass_s1 = ass_s1 + nhb_no(i,k) * ( 1.0 - mx(i,k) ) + ass_s2 = ass_s2 + nhb_no(i,k) * LOG(mx(i,k)) + END DO + fhb = fhb + x(i) * ( ass_s2 + ass_s1/2.0 ) + END DO + + END IF + + END SUBROUTINE F_ASSOCIATION + + +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! + SUBROUTINE F_ION_DIPOLE_TBH ( fhend ) +! + USE EOS_VARIABLES, ONLY: nc, PI, KBOL, NAv, ncomp, t, rho, eta, x, z0t, parame, uij, sig_ij + IMPLICIT NONE +! +!--------------------------------------------------------------------- + REAL, INTENT(IN OUT) :: fhend +!--------------------------------------------------------------------- + INTEGER :: i, dipole, ions + REAL :: m_mean + REAL :: fh32, fh2, fh52, fh3 + REAL :: e_elem, eps_cc0, rho_sol, dielec + REAL :: polabil, ydd, kappa, x_dipol, x_ions + REAL, DIMENSION(nc) :: my2dd, z_ii, e_cd, x_dd, x_ii + REAL :: sig_c, sig_d, sig_cd, r_s + REAL :: I0cc, I1cc, I2cc, Icd, Idd + REAL :: Iccc, Iccd, Icdd, Iddd +!--------------------------------------------------------------------- + +m_mean = z0t / ( PI / 6.0 ) + +!----------------Dieletric Constant of Water-------------------------- +e_elem = 1.602189246E-19 ! in Unit [Coulomb] +eps_cc0 = 8.854187818E-22 ! in Unit [Coulomb**2 /(J*Angstrom)] +! Correlation of M. Uematsu and E. U. Frank +! (Static Dieletric Constant of Water and Steam) +! valid range of conditions 273,15 K <=T<= 823,15 K +! and density <= 1150 kg/m3 (i.e. 0 <= p <= 500 MPa) +rho_sol = rho * 18.015 * 1.E27/ NAv +rho_sol = rho_sol/1000.0 +dielec = 1.0+(7.62571/(t/293.15))*rho_sol +(2.44E2/(t/293.15)-1.41E2 & + + 2.78E1*(t/293.15))*rho_sol**2 & + + (-9.63E1/(t/293.15)+4.18E1*(t/293.15) & + - 1.02E1*(t/293.15)**2 )*rho_sol**3 +(-4.52E1/(t/293.15)**2 & + + 8.46E1/(t/293.15)-3.59E1)*rho_sol**4 + + +! !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! + +dielec = 1.0 + +! !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! + + +!----------------Dipole-Ion Term----------------------------------- +dipole = 0 +ions = 0 +fhend = 0.0 +DO i = 1, ncomp + IF ( parame(i,6) /= 0.0 .AND. uij(i,i) /= 0.0 .AND. x(i) > 0.0 ) THEN + my2dd(i) = (parame(i,6))**2 *1.E-49 / (uij(i,i)*KBOL*sig_ij(i,i)**3 *1.E-30) + dipole = 1 + ELSE + my2dd(i) = 0.0 + END IF + + z_ii(i) = parame(i,10) + IF ( z_ii(i) /= 0.0 .AND. uij(i,i) /= 0.0 .AND. x(i) > 0.0 ) THEN + e_cd(i) = ( parame(i,10)*e_elem* 1.E5 / SQRT(1.11265005) )**2 & + / ( uij(i,i)*kbol*sig_ij(i,i)*1.E-10 ) + ions = 1 + ELSE + e_cd(i) = 0.0 + END IF +END DO + + +IF ( dipole == 1 .AND. ions == 1 ) THEN + + ydd = 0.0 + kappa = 0.0 + x_dipol = 0.0 + x_ions = 0.0 + polabil = 0.0 + DO i = 1, ncomp + ydd = ydd + x(i)*(parame(i,6))**2 *1.E-49/ (kbol*t*1.E-30) + kappa = kappa + x(i) & + *(parame(i,10)*e_elem* 1.E5/SQRT(1.11265005))**2 /(KBOL*t*1.E-10) + IF (parame(i,10) /= 0.0) THEN + x_ions = x_ions + x(i) + ELSE + polabil = polabil + 4.0*PI*x(i)*rho*1.4573 *1.E-30 & + / (sig_ij(3,3)**3 *1.E-30) + END IF + IF (parame(i,6) /= 0.0) x_dipol= x_dipol+ x(i) + END DO + ydd = ydd * 4.0/9.0 * PI * rho + kappa = SQRT( 4.0 * PI * rho * kappa ) + + fh2 = 0.0 + sig_c = 0.0 + sig_d = 0.0 + DO i=1,ncomp + x_ii(i) = 0.0 + x_dd(i) = 0.0 + IF(parame(i,10) /= 0.0 .AND. x_ions /= 0.0) x_ii(i) = x(i)/x_ions + IF(parame(i,6) /= 0.0 .AND. x_dipol /= 0.0) x_dd(i) = x(i)/x_dipol + sig_c = sig_c + x_ii(i)*parame(i,2) + sig_d = sig_d + x_dd(i)*parame(i,2) + END DO + sig_cd = 0.5 * (sig_c + sig_d) + + r_s = 0.0 + ! DO i=1,ncomp + ! r_s=r_s + rho * x(i) * dhs(i)**3 + ! END DO + r_s = eta*6.0 / PI / m_mean + + I0cc = - (1.0 + 0.97743 * r_s + 0.05257*r_s*r_s) & + /(1.0 + 1.43613 * r_s + 0.41580*r_s*r_s) + ! I1cc = - (10.0 - 2.0*z3 + z3*z3) /20.0/(1.0 + 2.0*z3) + I1cc = - (10.0 - 2.0*r_s*pi/6.0 + r_s*r_s*pi/6.0*pi/6.0) & + /20.0/(1.0 + 2.0*r_s*pi/6.0) +!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! + ! I2cc = + (z3-4.0)*(z3*z3+2.0) /24.0/(1.0+2.0*z3) + ! relation of Stell and Lebowitz + I2cc = -0.33331+0.7418*r_s - 1.2047*r_s*r_s & + + 1.6139*r_s**3 - 1.5487*r_s**4 + 0.6626*r_s**5 +!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! + Icd = (1.0 + 0.79576 *r_s + 0.104556 *r_s*r_s) & + /(1.0 + 0.486704*r_s - 0.0222903*r_s*r_s) + Idd = (1.0 + 0.18158*r_s - 0.11467*r_s*r_s) & + /3.0/(1.0 - 0.49303*r_s + 0.06293*r_s*r_s) + Iccc= 3.0*(1.0 - 1.05560*r_s + 0.26591*r_s*r_s) & + /2.0/(1.0 + 0.53892*r_s - 0.94236*r_s*r_s) + Iccd= 11.0*(1.0 + 2.25642 *r_s + 0.05679 *r_s*r_s) & + /6.0/(1.0 + 2.64178 *r_s + 0.79783 *r_s*r_s) + Icdd= 0.94685*(1.0 + 2.97323 *r_s + 3.11931 *r_s*r_s) & + /(1.0 + 2.70186 *r_s + 1.22989 *r_s*r_s) + Iddd= 5.0*(1.0 + 1.12754*r_s + 0.56192*r_s*r_s) & + /24.0/(1.0 - 0.05495*r_s + 0.13332*r_s*r_s) + + IF ( sig_c <= 0.0 ) WRITE (*,*) 'error in Henderson ion term' + + fh32= - kappa**3 /(12.0*pi*rho) + fh2 = - 3.0* kappa**2 * ydd*Icd /(8.0*pi*rho) / sig_cd & + - kappa**4 *sig_c/(16.0*pi*rho)*I0cc + IF (sig_d /= 0.0) fh2 = fh2 - 27.0* ydd * ydd*Idd & + /(8.0*pi*rho) / sig_d**3 + fh52= (3.0*kappa**3 * ydd + kappa**5 *sig_c**2 *I1cc) & + /(8.0*pi*rho) + fh3 = - kappa**6 * sig_c**3 /(8.0*pi*rho) *(I2cc-Iccc/6.0) & + + kappa**4 * ydd *sig_c/(16.0*pi*rho) & + *( (6.0+5.0/3.0*sig_d/sig_c)*I0cc + 3.0*sig_d/sig_c*Iccd ) & + + 3.0*kappa**2 * ydd*ydd /(8.0*pi*rho) / sig_cd & + *( (2.0-3.21555*sig_d/sig_cd)*Icd +3.0*sig_d/sig_cd*Icdd ) + IF (sig_d /= 0.0) fh3 = fh3 + 27.0*ydd**3 & + /(16.0*pi*rho)/sig_d**3 *Iddd + + fhend = ( fh32 + (fh32*fh32*fh3-2.0*fh32*fh2*fh52+fh2**3 ) & + /(fh2*fh2-fh32*fh52) ) & + / ( 1.0 + (fh32*fh3-fh2*fh52) /(fh2*fh2-fh32*fh52) & + - (fh2*fh3-fh52*fh52) /(fh2*fh2-fh32*fh52) ) +!---------- +! fH32= - kappa**3 /(12.0*PI*rho) +! fH2 = - 3.0* kappa**2 * ydd*Icd /(8.0*PI*rho) / sig_cd +! fH52= (3.0*kappa**3 * ydd)/(8.0*PI*rho) +! fH3 = + kappa**4 * ydd *sig_c/(16.0*PI*rho) & +! *( (6.0+5.0/3.0*sig_d/sig_c)*0.0*I0cc + 3.0*sig_d/sig_c*Iccd) & +! + 3.0*kappa**2 * ydd*ydd /(8.0*PI*rho) / sig_cd & +! *( (2.0-3.215550*sig_d/sig_cd)*Icd +3.0*sig_d/sig_cd*Icdd ) + +! fHcd = ( + (fH32*fH32*fH3-2.0*fH32*fH2*fH52+fH2**3 ) & +! /(fH2*fH2-fH32*fH52) ) & +! / ( 1.0 + (fH32*fH3-fH2*fH52) /(fH2*fH2-fH32*fH52) & +! - (fH2*fH3-fH52*fH52) /(fH2*fH2-fH32*fH52) ) + +END IF + + END SUBROUTINE F_ION_DIPOLE_TBH + + +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! + SUBROUTINE F_ION_ION_PrimMSA ( fcc ) +! + USE EOS_VARIABLES, ONLY: nc, PI, KBOL, NAv, ncomp, t, rho, x, parame, mx + IMPLICIT NONE +! +!--------------------------------------------------------------------- + REAL, INTENT(IN OUT) :: fcc +!--------------------------------------------------------------------- + INTEGER :: i, j, cc_it, ions + REAL :: e_elem, eps_cc0, rho_sol, dielec + REAL :: x_ions + REAL :: cc_sig1, cc_sig2, cc_sig3 + REAL, DIMENSION(nc) :: z_ii, x_ii, sigm_i, my2dd + REAL :: alpha_2, kappa, ii_par + REAL :: cc_omeg, p_n, q2_i, cc_q2, cc_gam + REAL :: cc_error(2), cc_delt + REAL :: rhs, lambda, lam_s +!--------------------------------------------------------------------- + +!----------------Dieletric Constant of Water-------------------------- +e_elem = 1.602189246E-19 ! in Unit [Coulomb] +eps_cc0 = 8.854187818E-22 ! in Unit [Coulomb**2 /(J*Angstrom)] +! Correlation of M. Uematsu and E. U. Frank +! (Static Dieletric Constant of Water and Steam) +! valid range of conditions 273,15 K <=T<= 823,15 K +! and density <= 1150 kg/m3 (i.e. 0 <= p <= 500 MPa) +rho_sol = rho * 18.015 * 1.E27/ NAv +rho_sol = rho_sol/1000.0 +dielec = 1.0+(7.62571/(t/293.15))*rho_sol +(2.44E2/(t/293.15)-1.41E2 & + +2.78E1*(t/293.15))*rho_sol**2 & + +(-9.63E1/(t/293.15)+4.18E1*(t/293.15) & + -1.02E1*(t/293.15)**2 )*rho_sol**3 +(-4.52E1/(t/293.15)**2 & + +8.46E1/(t/293.15)-3.59E1)*rho_sol**4 + + +! !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! + +dielec = 1.0 + +! !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! + + +!----------------Ion-Ion: primitive MSA ------------------------------- +! the (dipole moment)**2 [my**2] corresponds to an attraction from +! point charges of [ SUM(xi * zi**2 * e_elem**2) * 3 * di**2 ] + +! parame(ion,6))**2 * 1.E-49 / (kbol*T) +! = (e_elem* 1.E5/SQRT(1.112650050))**2 +! *x(i)*zi**2 *3.0*sig_ij(1,1)**2 *1.E-20 + +! parame(ion,6))**2 = (e_elem* 1.E5/SQRT(1.112650050))**2 /1.E-49 +! *x(i)*zi**2 *3.0*sig_ij(i,i)**2 *1.E-20 + +! with the units +! my**2 [=] D**2 = 1.E-49 J*m3 +! e_elem **2 [=] C**2 = 1.E5 / SQRT(1.112650050) J*m + + +ions = 0 +x_ions = 0.0 +fcc = 0.0 +DO i = 1, ncomp + z_ii(i) = parame(i,10) + IF (z_ii(i) /= 0.0) THEN + sigm_i(i) = parame(i,2) + ELSE + sigm_i(i) = 0.0 + END IF + IF (z_ii(i) /= 0.0) ions = 1 + IF (z_ii(i) /= 0.0) x_ions = x_ions + x(i) +END DO + +IF (ions == 1 .AND. x_ions > 0.0) THEN + + cc_sig1 = 0.0 + cc_sig2 = 0.0 + cc_sig3 = 0.0 + DO i=1,ncomp + IF (z_ii(i) /= 0.0) THEN + x_ii(i) = x(i)/x_ions + ELSE + x_ii(i) =0.0 + END IF + cc_sig1 = cc_sig1 +x_ii(i)*sigm_i(i) + cc_sig2 = cc_sig2 +x_ii(i)*sigm_i(i)**2 + cc_sig3 = cc_sig3 +x_ii(i)*sigm_i(i)**3 + END DO + + + ! alpha_2 = 4.0*PI*e_elem**2 /eps_cc0/dielec/kbol/T + alpha_2 = e_elem**2 /eps_cc0 / dielec / KBOL/t + kappa = 0.0 + DO i = 1, ncomp + kappa = kappa + x(i)*z_ii(i)*z_ii(i)*mx(i,1) + END DO + kappa = SQRT( rho * alpha_2 * kappa ) + ii_par= kappa * cc_sig1 + + ! Temporaer: nach der Arbeit von Krienke verifiziert + ! noch nicht fuer Mischungen mit unterschiedl. Ladung erweitert + ! ii_par = DSQRT( e_elem**2 /eps_cc0/dielec/kbol/T & + ! *rho*(x(1)*Z_ii(1)**2 + x(2)*Z_ii(2)**2 ) )*cc_sig1 + + + cc_gam = kappa/2.0 + + ! noch offen !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! + cc_delt = 0.0 + DO i = 1, ncomp + cc_delt = cc_delt + x(i)*mx(i,1)*rho*sigm_i(i)**3 + END DO + cc_delt= 1.0 - PI/6.0*cc_delt + + cc_it = 0 + 13 CONTINUE + j = 0 + cc_it = cc_it + 1 + 131 CONTINUE + j = j + 1 + cc_omeg = 0.0 + DO i = 1, ncomp + cc_omeg = cc_omeg +x(i)*mx(i,1)*sigm_i(i)**3 /(1.0+cc_gam*sigm_i(i)) + END DO + cc_omeg = 1.0 + PI/2.0 / cc_delt * rho * cc_omeg + p_n = 0.0 + DO i = 1, ncomp + p_n = p_n + x(i)*mx(i,1)*rho / cc_omeg*sigm_i(i)*z_ii(i) / (1.0+cc_gam*sigm_i(i)) + END DO + q2_i = 0.0 + cc_q2= 0.0 + DO i = 1, ncomp + q2_i = q2_i + rho*x(i)*mx(i,1)*( (z_ii(i)-pi/2.0/cc_delt*sigm_i(i)**2 *p_n) & + /(1.0+cc_gam*sigm_i(i)) )**2 + cc_q2 = cc_q2 + x(i)*mx(i,1)*rho*z_ii(i)**2 / (1.0+cc_gam*sigm_i(i)) + END DO + q2_i = q2_i*alpha_2 / 4.0 + + cc_error(j) = cc_gam - SQRT(q2_i) + IF (j == 1) cc_gam = cc_gam*1.000001 + IF (j == 2) cc_gam = cc_gam - cc_error(2)* (cc_gam-cc_gam/1.000001)/(cc_error(2)-cc_error(1)) + + IF ( j == 1 .AND. ABS(cc_error(1)) > 1.E-15 ) GO TO 131 + IF ( cc_it >= 10 ) THEN + WRITE (*,*) ' cc error' + STOP + END IF + IF ( j /= 1 ) GO TO 13 + + fcc= - alpha_2 / PI/4.0 /rho* (cc_gam*cc_q2 & + + pi/2.0/cc_delt *cc_omeg*p_n**2 ) + cc_gam**3 /pi/3.0/rho + ! Restricted Primitive Model + ! fcc=-(3.0*ii_par*ii_par+6.0*ii_par+2.0 & + ! -2.0*(1.0+2.0*ii_par)**1.50) & + ! /(12.0*PI*rho *cc_sig1**3 ) + + ! fcc = x_ions * fcc + + my2dd(3) = (parame(3,6))**2 *1.E-19 /(KBOL*t) + my2dd(3) = (1.84)**2 *1.E-19 /(kbol*t) + + rhs = 12.0 * PI * rho * x(3) * my2dd(3) + lam_s = 1.0 + 12 CONTINUE + lambda = (rhs/((lam_s+2.0)**2 ) + 16.0/((1.0+lam_s)**4 ) )**0.5 + IF ( ABS(lam_s-lambda) > 1.E-10 )THEN + lam_s = ( lambda + lam_s ) / 2.0 + GO TO 12 + END IF + + ! f_cd = -(ii_par*ii_par)/(4.0*PI*rho*m_mean *cc_sig1**3 ) & + ! *(dielec-1.0)/(1.0 + parame(3,2)/cc_sig1/lambda) + ! write (*,*) ' ',f_cd,fcc,x_ions + ! f_cd = f_cd/(1.0 - fcc/f_cd) + ! fcc = 0.0 + +END IF + + +END SUBROUTINE F_ION_ION_PrimMSA + + +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! + SUBROUTINE F_ION_ION_nonPrimMSA ( fdd, fqq, fdq, fcc ) +! + USE EOS_VARIABLES, ONLY: nc, ncomp, t, eta, x, parame, mseg + IMPLICIT NONE +! +!--------------------------------------------------------------------- + REAL, INTENT(IN OUT) :: fdd, fqq, fdq, fcc +!--------------------------------------------------------------------- + INTEGER :: dipole + !REAL :: A_MSA !, A_CC, A_CD, A_DD, U_MSA, chempot + REAL, DIMENSION(nc) :: x_export, msegm +!--------------------------------------------------------------------- + + dipole = 0 + IF ( SUM( parame(1:ncomp,6) ) > 1.E-5 ) dipole = 1 + + IF ( dipole /= 0 ) THEN ! alternatively ions and dipoles = 1 + fdd = 0.0 + fqq = 0.0 + fdq = 0.0 + fcc = 0.0 + msegm(:) = mseg(:) ! the entries of the vector mseg and x are changed + x_export(:) = x(:) ! in SEMIRESTRICTED because the ions should be positioned first + ! that is why dummy vectors msegm and x_export are defined + !CALL SEMIRESTRICTED (A_MSA,A_CC,A_CD,A_DD,U_MSA, & + ! chempot,ncomp,parame,t,eta,x_export,msegm,0) + !fdd = A_MSA + write (*,*) 'why are individual contrib. A_CC,A_CD,A_DD not used' + stop + END IF + + END SUBROUTINE F_ION_ION_nonPrimMSA + + +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! + SUBROUTINE F_LC_MayerSaupe ( flc ) +! + USE EOS_VARIABLES, ONLY: nc, PI, KBOL, NAv, ncomp, phas, t, rho, eta, & + x, mseg, parame, E_lc, S_lc, dhs + IMPLICIT NONE +! +!--------------------------------------------------------------------- + REAL, INTENT(IN OUT) :: flc +!--------------------------------------------------------------------- + INTEGER :: i, j, k + INTEGER :: liq_crystal, count_lc, steps_lc + REAL :: alpha_lc, tolerance, deltay + REAL :: integrand1, integrand2, accel_lc + REAL :: error_lc, u_term, sphase + REAL, DIMENSION(nc) :: z_lc, S_lc1, S_lc2, sumu + REAL, DIMENSION(nc,nc) :: u_lc, klc +!--------------------------------------------------------------------- +INTEGER :: stabil +COMMON /stabil / stabil +!--------------------------------------------------------------------- + + + klc(1,2) = 0.0 + klc(2,1) = klc(1,2) + + alpha_lc = 1.0 + accel_lc = 4.0 + IF ( eta < 0.35 ) accel_lc = 1.3 + IF ( eta < 0.15 ) accel_lc = 1.0 + + liq_crystal = 0 + DO i = 1, ncomp + DO j = 1, ncomp + E_lc(i,j) = (E_lc(i,i)*E_lc(j,j))**0.5 *(1.0-klc(i,j)) !combining rule + ! E_LC(i,j)= ( E_LC(i,i)+E_LC(j,j) ) * 0.5 !combining rule + ! S_LC(i,j)= ( S_LC(i,i)+S_LC(j,j) ) * 0.5 !combining rule + IF (E_lc(i,j) /= 0.0) liq_crystal = 1 + END DO + END DO + ! S_LC(1,2) = 0.0 + ! S_LC(2,1) = S_LC(1,2) + ! E_LC(1,2) = 60.0 + ! E_LC(2,1) = E_LC(1,2) + + IF ( liq_crystal == 1 .AND. phas == 1 .AND. stabil == 0 ) THEN + + count_lc = 0 + tolerance = 1.E-6 + + steps_lc = 200 + deltay = 1.0 / REAL(steps_lc) + + ! --- dimensionless function U_LC repres. anisotr. intermolecular interactions in l.c. + + DO i = 1, ncomp + DO j = 1, ncomp + u_lc(i,j) = 2.0/3.0*pi*mseg(i)*mseg(j) *(0.5*(dhs(i)+dhs(j)))**3 & ! sig_ij(i,j)**3 + *(E_lc(i,j)/t+S_lc(i,j))*rho + END DO + END DO + + + DO i=1,ncomp + ! S_lc2(i) = 0.0 !for isotropic + S_lc2(i) = 0.5 !for nematic + S_lc1(i) = S_lc2(i) + END DO + + 1 CONTINUE + + DO i = 1, ncomp + IF (S_lc2(i) <= 0.3) S_lc1(i) = S_lc2(i) + IF (S_lc2(i) > 0.3) S_lc1(i) = S_lc1(i) + (S_lc2(i)-S_lc1(i))*accel_lc + END DO + + count_lc = count_lc + 1 + + ! --- single-particle orientation partition function Z_LC in liquid crystals + + DO i = 1, ncomp + sumu(i) = 0.0 + DO j = 1, ncomp + sumu(i) = sumu(i) + x(j)*u_lc(i,j)*S_lc1(j) + END DO + END DO + + DO i = 1, ncomp + z_lc(i) = 0.0 + integrand1 = EXP(-0.5*sumu(i)) !eq. for Z_LC with y=0 + DO k = 1, steps_lc + integrand2 = EXP(0.5*sumu(i)*(3.0*(deltay*REAL(k)) **2 -1.0)) + z_lc(i) = z_lc(i) + (integrand1 + integrand2)/2.0*deltay + integrand1 = integrand2 + END DO !k-index integration + END DO !i-index Z_LC(i) calculation + + ! --- order parameter S_lc in liquid crystals ----------------------- + + error_lc = 0.0 + DO i = 1, ncomp + S_lc2(i) = 0.0 + integrand1 = -1.0/z_lc(i)*0.5*EXP(-0.5*sumu(i)) !for S_lc with y=0 + DO k = 1, steps_lc + integrand2 = 1.0/z_lc(i)*0.5*(3.0*(deltay*REAL(k)) & + **2 -1.0)*EXP(0.5*sumu(i)*(3.0 *(deltay*REAL(k))**2 -1.0)) + S_lc2(i) = S_lc2(i) + (integrand1 + integrand2)/2.0*deltay + integrand1 = integrand2 + END DO !k-index integration + error_lc = error_lc + ABS(S_lc2(i)-S_lc1(i)) + END DO !i-index Z_LC(i) calculation + + sphase = 0.0 + DO i = 1, ncomp + sphase = sphase + S_lc2(i) + END DO + IF (sphase < 1.E-4) THEN + error_lc = 0.0 + DO i = 1, ncomp + S_lc2(i)= 0.0 + z_lc(i) = 1.0 + END DO + END IF + + + ! write (*,*) count_LC,S_lc2(1)-S_lc1(1),S_lc2(2)-S_lc1(2) + IF (error_lc > tolerance .AND. count_lc < 400) GO TO 1 + ! write (*,*) 'done',eta,S_lc2(1),S_lc2(2) + + IF (count_lc == 400) WRITE (*,*) 'LC iteration not converg.' + + ! --- the anisotropic contribution to the Helmholtz energy ---------- + + u_term = 0.0 + DO i = 1, ncomp + DO j = 1, ncomp + u_term = u_term + 0.5*x(i)*x(j)*S_lc2(i) *S_lc2(j)*u_lc(i,j) + END DO + END DO + + flc = 0.0 + DO i = 1, ncomp + IF (z_lc(i) /= 0.0) flc = flc - x(i) * LOG(z_lc(i)) + END DO + flc = flc + u_term + ! pause + + END IF + ! write (*,'(i2,i2,4(f15.8))') phas,stabil,flc,eta,S_lc2(1),x(1) + + + END SUBROUTINE F_LC_MayerSaupe + + + +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! + SUBROUTINE P_POLAR ( zdd, zddz, zddz2, zddz3, zqq, zqqz, zqqz2, zqqz3, zdq, zdqz, zdqz2, zdqz3 ) +! + USE EOS_VARIABLES, ONLY: ncomp, parame, dd_term, qq_term, dq_term + IMPLICIT NONE +! +! ---------------------------------------------------------------------- + REAL, INTENT(OUT) :: zdd, zddz, zddz2, zddz3 + REAL, INTENT(OUT) :: zqq, zqqz, zqqz2, zqqz3 + REAL, INTENT(OUT) :: zdq, zdqz, zdqz2, zdqz3 +! +! --- local variables--------------------------------------------------- + INTEGER :: dipole + INTEGER :: quadrupole + INTEGER :: dipole_quad +! ---------------------------------------------------------------------- + + zdd = 0.0 + zddz = 0.0 + zddz2 = 0.0 + zddz3 = 0.0 + zqq = 0.0 + zqqz = 0.0 + zqqz2 = 0.0 + zqqz3 = 0.0 + zdq = 0.0 + zdqz = 0.0 + zdqz2 = 0.0 + zdqz3 = 0.0 + + dipole = 0 + quadrupole = 0 + dipole_quad = 0 + IF ( SUM( parame(1:ncomp,6) ) /= 0.0 ) dipole = 1 + IF ( SUM( parame(1:ncomp,7) ) /= 0.0 ) quadrupole = 1 + IF ( dipole == 1 .AND. quadrupole == 1 ) dipole_quad = 1 + + ! -------------------------------------------------------------------- + ! dipole-dipole term + ! -------------------------------------------------------------------- + IF (dipole == 1) THEN + + IF (dd_term == 'GV') CALL P_DD_GROSS_VRABEC( zdd, zddz, zddz2, zddz3 ) + ! IF (dd_term == 'SF') CALL F_DD_SAAGER_FISCHER( k ) + IF (dd_term /= 'GV' .AND. dd_term /= 'SF') write (*,*) 'specify dipole term !' + + ENDIF + + ! -------------------------------------------------------------------- + ! quadrupole-quadrupole term + ! -------------------------------------------------------------------- + IF (quadrupole == 1) THEN + + !IF (qq_term == 'SF') CALL F_QQ_SAAGER_FISCHER( k ) + IF (qq_term == 'JG') CALL P_QQ_GROSS( zqq, zqqz, zqqz2, zqqz3 ) + IF (qq_term /= 'JG' .AND. qq_term /= 'SF') write (*,*) 'specify quadrupole term !' + + ENDIF + + ! -------------------------------------------------------------------- + ! dipole-quadrupole cross term + ! -------------------------------------------------------------------- + IF (dipole_quad == 1) THEN + + IF (dq_term == 'VG') CALL P_DQ_VRABEC_GROSS( zdq, zdqz, zdqz2, zdqz3 ) + IF (dq_term /= 'VG' ) write (*,*) 'specify DQ-cross term !' + + ENDIF + +END SUBROUTINE P_POLAR + + +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! + SUBROUTINE P_DD_GROSS_VRABEC( zdd, zddz, zddz2, zddz3 ) +! + USE PARAMETERS, ONLY: PI, KBOL + USE EOS_VARIABLES, ONLY: nc, ncomp, uij, parame, mseg, sig_ij, rho, eta, x, t + USE EOS_CONSTANTS, ONLY: ddp2, ddp3, ddp4 + IMPLICIT NONE +! +! ---------------------------------------------------------------------- + REAL, INTENT(IN OUT) :: zdd, zddz, zddz2, zddz3 +! ---------------------------------------------------------------------- + INTEGER :: i, j, k, m + REAL :: factor2, factor3, z3 + REAL :: xijfa, xijkfa, eij + REAL :: fdddr, fddd2, fddd3, fddd4 + REAL :: fdd2, fdd2z, fdd2z2, fdd2z3, fdd2z4 + REAL :: fdd3, fdd3z, fdd3z2, fdd3z3, fdd3z4 + REAL, DIMENSION(nc) :: my2dd + REAL, DIMENSION(nc,nc) :: Idd2, Idd2z, Idd2z2, Idd2z3, Idd2z4 + REAL, DIMENSION(nc,nc) :: Idd4, Idd4z, Idd4z2, Idd4z3, Idd4z4 + REAL, DIMENSION(nc,nc,nc) :: Idd3, Idd3z, Idd3z2, Idd3z3, Idd3z4 +! ---------------------------------------------------------------------- + + + zdd = 0.0 + zddz = 0.0 + zddz2 = 0.0 + zddz3 = 0.0 + z3 = eta + DO i = 1, ncomp + my2dd(i) = (parame(i,6))**2 *1.E-49 / (uij(i,i)*KBOL*mseg(i)*sig_ij(i,i)**3 *1.E-30) + END DO + + DO i = 1, ncomp + DO j = 1, ncomp + Idd2(i,j) = 0.0 + Idd4(i,j) = 0.0 + Idd2z(i,j) = 0.0 + Idd4z(i,j) = 0.0 + Idd2z2(i,j) = 0.0 + Idd4z2(i,j) = 0.0 + Idd2z3(i,j) = 0.0 + Idd4z3(i,j) = 0.0 + Idd2z4(i,j) = 0.0 + Idd4z4(i,j) = 0.0 + ! IF (paramei,6).NE.0.0 .AND. parame(j,6).NE.0.0) THEN + DO m = 0, 4 + Idd2(i,j) =Idd2(i,j) + ddp2(i,j,m) *z3**(m+1) + Idd4(i,j) =Idd4(i,j) + ddp4(i,j,m) *z3**(m+1) + Idd2z(i,j) =Idd2z(i,j) +ddp2(i,j,m)*REAL(m+1) *z3**m + Idd4z(i,j) =Idd4z(i,j) +ddp4(i,j,m)*REAL(m+1) *z3**m + Idd2z2(i,j)=Idd2z2(i,j)+ddp2(i,j,m)*REAL((m+1)*m) *z3**(m-1) + Idd4z2(i,j)=Idd4z2(i,j)+ddp4(i,j,m)*REAL((m+1)*m) *z3**(m-1) + Idd2z3(i,j)=Idd2z3(i,j)+ddp2(i,j,m)*REAL((m+1)*m*(m-1)) *z3**(m-2) + Idd4z3(i,j)=Idd4z3(i,j)+ddp4(i,j,m)*REAL((m+1)*m*(m-1)) *z3**(m-2) + Idd2z4(i,j)=Idd2z4(i,j)+ddp2(i,j,m)*REAL((m+1)*m*(m-1)*(m-2)) *z3**(m-3) + Idd4z4(i,j)=Idd4z4(i,j)+ddp4(i,j,m)*REAL((m+1)*m*(m-1)*(m-2)) *z3**(m-3) + END DO + DO k = 1, ncomp + Idd3(i,j,k) = 0.0 + Idd3z(i,j,k) = 0.0 + Idd3z2(i,j,k) = 0.0 + Idd3z3(i,j,k) = 0.0 + Idd3z4(i,j,k) = 0.0 + ! IF (parame(k,6).NE.0.0) THEN + DO m = 0, 4 + Idd3(i,j,k) =Idd3(i,j,k) +ddp3(i,j,k,m)*z3**(m+2) + Idd3z(i,j,k) =Idd3z(i,j,k) +ddp3(i,j,k,m)*REAL(m+2)*z3**(m+1) + Idd3z2(i,j,k)=Idd3z2(i,j,k)+ddp3(i,j,k,m)*REAL((m+2)*(m+1))*z3**m + Idd3z3(i,j,k)=Idd3z3(i,j,k)+ddp3(i,j,k,m)*REAL((m+2)*(m+1)*m)*z3**(m-1) + Idd3z4(i,j,k)=Idd3z4(i,j,k)+ddp3(i,j,k,m)*REAL((m+2)*(m+1)*m*(m-1)) *z3**(m-2) + END DO + ! ENDIF + END DO + ! ENDIF + END DO + END DO + + factor2= -PI *rho/z3 + factor3= -4.0/3.0*PI**2 * (rho/z3)**2 + + fdd2 = 0.0 + fdd2z = 0.0 + fdd2z2 = 0.0 + fdd2z3 = 0.0 + fdd2z4 = 0.0 + fdd3 = 0.0 + fdd3z = 0.0 + fdd3z2 = 0.0 + fdd3z3 = 0.0 + fdd3z4 = 0.0 + DO i = 1, ncomp + DO j = 1, ncomp + ! IF (parame(i,6).NE.0.0 .AND. parame(j,6).NE.0.0) THEN + xijfa = x(i)*parame(i,3)/t*parame(i,2)**3 *x(j)*parame(j,3)/t*parame(j,2)**3 & + / ((parame(i,2)+parame(j,2))/2.0)**3 *my2dd(i)*my2dd(j) + eij = (parame(i,3)*parame(j,3))**0.5 + fdd2 = fdd2 +factor2*xijfa*(Idd2(i,j) +eij/t*Idd4(i,j)) + fdd2z = fdd2z +factor2*xijfa*(Idd2z(i,j) +eij/t*Idd4z(i,j)) + fdd2z2 = fdd2z2+factor2*xijfa*(Idd2z2(i,j)+eij/t*Idd4z2(i,j)) + fdd2z3 = fdd2z3+factor2*xijfa*(Idd2z3(i,j)+eij/t*Idd4z3(i,j)) + fdd2z4 = fdd2z4+factor2*xijfa*(Idd2z4(i,j)+eij/t*Idd4z4(i,j)) + DO k = 1, ncomp + ! IF (parame(k,6).NE.0.0) THEN + xijkfa= x(i)*parame(i,3)/t*parame(i,2)**3 *x(j)*parame(j,3)/t*parame(j,2)**3 & + *x(k)*parame(k,3)/t*parame(k,2)**3 /((parame(i,2)+parame(j,2))/2.0) & + /((parame(i,2)+parame(k,2))/2.0) /((parame(j,2)+parame(k,2))/2.0) & + *my2dd(i)*my2dd(j)*my2dd(k) + fdd3 = fdd3 + factor3 * xijkfa*Idd3(i,j,k) + fdd3z = fdd3z + factor3 * xijkfa*Idd3z(i,j,k) + fdd3z2 = fdd3z2 + factor3 * xijkfa*Idd3z2(i,j,k) + fdd3z3 = fdd3z3 + factor3 * xijkfa*Idd3z3(i,j,k) + fdd3z4 = fdd3z4 + factor3 * xijkfa*Idd3z4(i,j,k) + ! ENDIF + END DO + ! ENDIF + END DO + END DO + IF (fdd2 < -1.E-50 .AND. fdd3 /= 0.0 .AND. fdd2z /= 0.0 .AND. fdd3z /= 0.0) THEN + + fdddr= fdd2* (fdd2*fdd2z - 2.0*fdd3*fdd2z+fdd2*fdd3z) / (fdd2-fdd3)**2 + fddd2=(2.0*fdd2*fdd2z*fdd2z +fdd2*fdd2*fdd2z2 & + -2.0*fdd2z**2 *fdd3-2.0*fdd2*fdd2z2*fdd3+fdd2*fdd2*fdd3z2) & + /(fdd2-fdd3)**2 + fdddr * 2.0*(fdd3z-fdd2z)/(fdd2-fdd3) + fddd3=(2.0*fdd2z**3 +6.0*fdd2*fdd2z*fdd2z2+fdd2*fdd2*fdd2z3 & + -6.0*fdd2z*fdd2z2*fdd3-2.0*fdd2z**2 *fdd3z & + -2.0*fdd2*fdd2z3*fdd3 -2.0*fdd2*fdd2z2*fdd3z & + +2.0*fdd2*fdd2z*fdd3z2+fdd2*fdd2*fdd3z3) /(fdd2-fdd3)**2 & + + 2.0/(fdd2-fdd3)* ( 2.0*fddd2*(fdd3z-fdd2z) & + + fdddr*(fdd3z2-fdd2z2) & + - fdddr/(fdd2-fdd3)*(fdd3z-fdd2z)**2 ) + fddd4=( 12.0*fdd2z**2 *fdd2z2+6.0*fdd2*fdd2z2**2 & + +8.0*fdd2*fdd2z*fdd2z3+fdd2*fdd2*fdd2z4-6.0*fdd2z2**2 *fdd3 & + -12.0*fdd2z*fdd2z2*fdd3z -8.0*fdd2z*fdd2z3*fdd3 & + -2.0*fdd2*fdd2z4*fdd3-4.0*fdd2*fdd2z3*fdd3z & + +4.0*fdd2*fdd2z*fdd3z3+fdd2**2 *fdd3z4 ) /(fdd2-fdd3)**2 & + + 6.0/(fdd2-fdd3)* ( fddd3*(fdd3z-fdd2z) & + -fddd2/(fdd2-fdd3)*(fdd3z-fdd2z)**2 & + - fdddr/(fdd2-fdd3)*(fdd3z-fdd2z)*(fdd3z2-fdd2z2) & + + fddd2*(fdd3z2-fdd2z2) +1.0/3.0*fdddr*(fdd3z3-fdd2z3) ) + zdd = fdddr*eta + zddz = fddd2*eta + fdddr + zddz2 = fddd3*eta + 2.0* fddd2 + zddz3 = fddd4*eta + 3.0* fddd3 + + END IF + + +END SUBROUTINE P_DD_GROSS_VRABEC + + + +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! + SUBROUTINE P_QQ_GROSS( zqq, zqqz, zqqz2, zqqz3 ) +! + USE PARAMETERS, ONLY: PI, KBOL + USE EOS_VARIABLES, ONLY: nc, ncomp, uij, parame, mseg, sig_ij, rho, eta, x, t + USE EOS_CONSTANTS, ONLY: qqp2, qqp3, qqp4 + IMPLICIT NONE +! +! ---------------------------------------------------------------------- + REAL, INTENT(IN OUT) :: zqq, zqqz, zqqz2, zqqz3 +! ---------------------------------------------------------------------- + INTEGER :: i, j, k, m + REAL :: factor2, factor3, z3 + REAL :: xijfa, xijkfa, eij + REAL :: fqqdr, fqqd2, fqqd3, fqqd4 + REAL :: fqq2, fqq2z, fqq2z2, fqq2z3, fqq2z4 + REAL :: fqq3, fqq3z, fqq3z2, fqq3z3, fqq3z4 + REAL, DIMENSION(nc) :: qq2 + REAL, DIMENSION(nc,nc) :: Iqq2, Iqq2z, Iqq2z2, Iqq2z3, Iqq2z4 + REAL, DIMENSION(nc,nc) :: Iqq4, Iqq4z, Iqq4z2, Iqq4z3, Iqq4z4 + REAL, DIMENSION(nc,nc,nc) :: Iqq3, Iqq3z, Iqq3z2, Iqq3z3, Iqq3z4 +! ---------------------------------------------------------------------- + + zqq = 0.0 + zqqz = 0.0 + zqqz2 = 0.0 + zqqz3 = 0.0 + z3 = eta + DO i=1,ncomp + qq2(i) = (parame(i,7))**2 *1.E-69 / (uij(i,i)*kbol*mseg(i)*sig_ij(i,i)**5 *1.E-50) + END DO + + DO i = 1, ncomp + DO j = 1, ncomp + Iqq2(i,j) = 0.0 + Iqq4(i,j) = 0.0 + Iqq2z(i,j) = 0.0 + Iqq4z(i,j) = 0.0 + Iqq2z2(i,j) = 0.0 + Iqq4z2(i,j) = 0.0 + Iqq2z3(i,j) = 0.0 + Iqq4z3(i,j) = 0.0 + Iqq2z4(i,j) = 0.0 + Iqq4z4(i,j) = 0.0 + IF (parame(i,7) /= 0.0 .AND. parame(j,7) /= 0.0) THEN + DO m = 0, 4 + Iqq2(i,j) =Iqq2(i,j) + qqp2(i,j,m)*z3**(m+1) + Iqq4(i,j) =Iqq4(i,j) + qqp4(i,j,m)*z3**(m+1) + Iqq2z(i,j) =Iqq2z(i,j) +qqp2(i,j,m)*REAL(m+1)*z3**m + Iqq4z(i,j) =Iqq4z(i,j) +qqp4(i,j,m)*REAL(m+1)*z3**m + Iqq2z2(i,j)=Iqq2z2(i,j)+qqp2(i,j,m)*REAL((m+1)*m)*z3**(m-1) + Iqq4z2(i,j)=Iqq4z2(i,j)+qqp4(i,j,m)*REAL((m+1)*m)*z3**(m-1) + Iqq2z3(i,j)=Iqq2z3(i,j)+qqp2(i,j,m)*REAL((m+1)*m*(m-1)) *z3**(m-2) + Iqq4z3(i,j)=Iqq4z3(i,j)+qqp4(i,j,m)*REAL((m+1)*m*(m-1)) *z3**(m-2) + Iqq2z4(i,j)=Iqq2z4(i,j)+qqp2(i,j,m)*REAL((m+1)*m*(m-1)*(m-2)) *z3**(m-3) + Iqq4z4(i,j)=Iqq4z4(i,j)+qqp4(i,j,m)*REAL((m+1)*m*(m-1)*(m-2)) *z3**(m-3) + END DO + DO k=1,ncomp + Iqq3(i,j,k) = 0.0 + Iqq3z(i,j,k) = 0.0 + Iqq3z2(i,j,k) = 0.0 + Iqq3z3(i,j,k) = 0.0 + Iqq3z4(i,j,k) = 0.0 + IF (parame(k,7) /= 0.0) THEN + DO m=0,4 + Iqq3(i,j,k) =Iqq3(i,j,k) + qqp3(i,j,k,m)*z3**(m+2) + Iqq3z(i,j,k)=Iqq3z(i,j,k)+qqp3(i,j,k,m)*REAL(m+2)*z3**(m+1) + Iqq3z2(i,j,k)=Iqq3z2(i,j,k)+qqp3(i,j,k,m)*REAL((m+2)*(m+1)) *z3**m + Iqq3z3(i,j,k)=Iqq3z3(i,j,k)+qqp3(i,j,k,m)*REAL((m+2)*(m+1)*m) *z3**(m-1) + Iqq3z4(i,j,k)=Iqq3z4(i,j,k)+qqp3(i,j,k,m) *REAL((m+2)*(m+1)*m*(m-1)) *z3**(m-2) + END DO + END IF + END DO + + END IF + END DO + END DO + + factor2= -9.0/16.0*PI *rho/z3 + factor3= 9.0/16.0*PI**2 * (rho/z3)**2 + + fqq2 = 0.0 + fqq2z = 0.0 + fqq2z2 = 0.0 + fqq2z3 = 0.0 + fqq2z4 = 0.0 + fqq3 = 0.0 + fqq3z = 0.0 + fqq3z2 = 0.0 + fqq3z3 = 0.0 + fqq3z4 = 0.0 + DO i = 1, ncomp + DO j = 1, ncomp + IF (parame(i,7) /= 0.0 .AND. parame(j,7) /= 0.0) THEN + xijfa =x(i)*uij(i,i)*qq2(i)*sig_ij(i,i)**5 /t & + *x(j)*uij(j,j)*qq2(j)*sig_ij(j,j)**5 /t/sig_ij(i,j)**7.0 + eij = (parame(i,3)*parame(j,3))**0.5 + fqq2= fqq2 +factor2*xijfa*(Iqq2(i,j) +eij/t*Iqq4(i,j) ) + fqq2z =fqq2z +factor2*xijfa*(Iqq2z(i,j) +eij/t*Iqq4z(i,j) ) + fqq2z2=fqq2z2+factor2*xijfa*(Iqq2z2(i,j)+eij/t*Iqq4z2(i,j)) + fqq2z3=fqq2z3+factor2*xijfa*(Iqq2z3(i,j)+eij/t*Iqq4z3(i,j)) + fqq2z4=fqq2z4+factor2*xijfa*(Iqq2z4(i,j)+eij/t*Iqq4z4(i,j)) + DO k = 1, ncomp + IF (parame(k,7) /= 0.0) THEN + xijkfa=x(i)*uij(i,i)*qq2(i)*sig_ij(i,i)**5 /t/sig_ij(i,j)**3 & + *x(j)*uij(j,j)*qq2(j)*sig_ij(j,j)**5 /t/sig_ij(i,k)**3 & + *x(k)*uij(k,k)*qq2(k)*sig_ij(k,k)**5 /t/sig_ij(j,k)**3 + fqq3 = fqq3 + factor3 * xijkfa*Iqq3(i,j,k) + fqq3z = fqq3z + factor3 * xijkfa*Iqq3z(i,j,k) + fqq3z2 = fqq3z2 + factor3 * xijkfa*Iqq3z2(i,j,k) + fqq3z3 = fqq3z3 + factor3 * xijkfa*Iqq3z3(i,j,k) + fqq3z4 = fqq3z4 + factor3 * xijkfa*Iqq3z4(i,j,k) + END IF + END DO + END IF + END DO + END DO + IF (fqq2 < -1.E-50 .AND. fqq3 /= 0.0 .AND. fqq2z /= 0.0 .AND. fqq3z /= 0.0) THEN + fqqdr = fqq2* (fqq2*fqq2z - 2.0*fqq3*fqq2z+fqq2*fqq3z) /(fqq2-fqq3)**2 + fqqd2= (2.0*fqq2*fqq2z*fqq2z +fqq2*fqq2*fqq2z2 & + -2.0*fqq2z**2 *fqq3-2.0*fqq2*fqq2z2*fqq3+fqq2*fqq2*fqq3z2) & + /(fqq2-fqq3)**2 + fqqdr * 2.0*(fqq3z-fqq2z)/(fqq2-fqq3) + fqqd3=(2.0*fqq2z**3 +6.0*fqq2*fqq2z*fqq2z2+fqq2*fqq2*fqq2z3 & + -6.0*fqq2z*fqq2z2*fqq3-2.0*fqq2z**2 *fqq3z & + -2.0*fqq2*fqq2z3*fqq3 -2.0*fqq2*fqq2z2*fqq3z & + +2.0*fqq2*fqq2z*fqq3z2+fqq2*fqq2*fqq3z3) /(fqq2-fqq3)**2 & + + 2.0/(fqq2-fqq3)* ( 2.0*fqqd2*(fqq3z-fqq2z) & + + fqqdr*(fqq3z2-fqq2z2) - fqqdr/(fqq2-fqq3)*(fqq3z-fqq2z)**2 ) + fqqd4=( 12.0*fqq2z**2 *fqq2z2+6.0*fqq2*fqq2z2**2 & + +8.0*fqq2*fqq2z*fqq2z3+fqq2*fqq2*fqq2z4-6.0*fqq2z2**2 *fqq3 & + -12.0*fqq2z*fqq2z2*fqq3z -8.0*fqq2z*fqq2z3*fqq3 & + -2.0*fqq2*fqq2z4*fqq3-4.0*fqq2*fqq2z3*fqq3z & + +4.0*fqq2*fqq2z*fqq3z3+fqq2**2 *fqq3z4 ) /(fqq2-fqq3)**2 & + + 6.0/(fqq2-fqq3)* ( fqqd3*(fqq3z-fqq2z) & + -fqqd2/(fqq2-fqq3)*(fqq3z-fqq2z)**2 & + - fqqdr/(fqq2-fqq3)*(fqq3z-fqq2z)*(fqq3z2-fqq2z2) & + + fqqd2*(fqq3z2-fqq2z2) +1.0/3.0*fqqdr*(fqq3z3-fqq2z3) ) + zqq = fqqdr*eta + zqqz = fqqd2*eta + fqqdr + zqqz2 = fqqd3*eta + 2.0* fqqd2 + zqqz3 = fqqd4*eta + 3.0* fqqd3 + END IF + + +END SUBROUTINE P_QQ_GROSS + +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! + SUBROUTINE P_DQ_VRABEC_GROSS( zdq, zdqz, zdqz2, zdqz3 ) +! + USE PARAMETERS, ONLY: PI, KBOL + USE EOS_VARIABLES, ONLY: nc, ncomp, uij, parame, mseg, sig_ij, rho, eta, x, t + USE EOS_CONSTANTS, ONLY: dqp2, dqp3, dqp4 + IMPLICIT NONE +! +! ---------------------------------------------------------------------- + REAL, INTENT(IN OUT) :: zdq, zdqz, zdqz2, zdqz3 +! ---------------------------------------------------------------------- + INTEGER :: i, j, k, m + REAL :: factor2, factor3, z3 + REAL :: xijfa, xijkfa, eij + REAL :: fdqdr, fdqd2, fdqd3, fdqd4 + REAL :: fdq2, fdq2z, fdq2z2, fdq2z3, fdq2z4 + REAL :: fdq3, fdq3z, fdq3z2, fdq3z3, fdq3z4 + REAL, DIMENSION(nc) :: my2dd, myfac, qq2, q_fac + REAL, DIMENSION(nc,nc) :: Idq2, Idq2z, Idq2z2, Idq2z3, Idq2z4 + REAL, DIMENSION(nc,nc) :: Idq4, Idq4z, Idq4z2, Idq4z3, Idq4z4 + REAL, DIMENSION(nc,nc,nc) :: Idq3, Idq3z, Idq3z2, Idq3z3, Idq3z4 +! ---------------------------------------------------------------------- + + zdq = 0.0 + zdqz = 0.0 + zdqz2 = 0.0 + zdqz3 = 0.0 + z3 = eta + DO i = 1, ncomp + my2dd(i) = (parame(i,6))**2 *1.E-49 / (uij(i,i)*KBOL*mseg(i)*sig_ij(i,i)**3 *1.E-30) + myfac(i) = parame(i,3)/t*parame(i,2)**4 *my2dd(i) + qq2(i) = (parame(i,7))**2 *1.E-69 / (uij(i,i)*kbol*mseg(i)*sig_ij(i,i)**5 *1.E-50) + q_fac(i) = parame(i,3)/t*parame(i,2)**4 *qq2(i) + END DO + + + DO i = 1, ncomp + DO j = 1, ncomp + Idq2(i,j) = 0.0 + Idq4(i,j) = 0.0 + Idq2z(i,j) = 0.0 + Idq4z(i,j) = 0.0 + Idq2z2(i,j) = 0.0 + Idq4z2(i,j) = 0.0 + Idq2z3(i,j) = 0.0 + Idq4z3(i,j) = 0.0 + Idq2z4(i,j) = 0.0 + Idq4z4(i,j) = 0.0 + IF (myfac(i) /= 0.0 .AND. q_fac(j) /= 0.0) THEN + DO m = 0, 4 + Idq2(i,j) =Idq2(i,j) + dqp2(i,j,m)*z3**(m+1) + Idq4(i,j) =Idq4(i,j) + dqp4(i,j,m)*z3**(m+1) + Idq2z(i,j) =Idq2z(i,j) +dqp2(i,j,m)*REAL(m+1)*z3**m + Idq4z(i,j) =Idq4z(i,j) +dqp4(i,j,m)*REAL(m+1)*z3**m + Idq2z2(i,j)=Idq2z2(i,j)+dqp2(i,j,m)*REAL((m+1)*m)*z3**(m-1) + Idq4z2(i,j)=Idq4z2(i,j)+dqp4(i,j,m)*REAL((m+1)*m)*z3**(m-1) + Idq2z3(i,j)=Idq2z3(i,j)+dqp2(i,j,m)*REAL((m+1)*m*(m-1)) *z3**(m-2) + Idq4z3(i,j)=Idq4z3(i,j)+dqp4(i,j,m)*REAL((m+1)*m*(m-1)) *z3**(m-2) + Idq2z4(i,j)=Idq2z4(i,j)+dqp2(i,j,m)*REAL((m+1)*m*(m-1)*(m-2)) *z3**(m-3) + Idq4z4(i,j)=Idq4z4(i,j)+dqp4(i,j,m)*REAL((m+1)*m*(m-1)*(m-2)) *z3**(m-3) + END DO + DO k = 1, ncomp + Idq3(i,j,k) = 0.0 + Idq3z(i,j,k) = 0.0 + Idq3z2(i,j,k) = 0.0 + Idq3z3(i,j,k) = 0.0 + Idq3z4(i,j,k) = 0.0 + IF (myfac(k) /= 0.0.OR.q_fac(k) /= 0.0) THEN + DO m = 0, 4 + Idq3(i,j,k) =Idq3(i,j,k) + dqp3(i,j,k,m)*z3**(m+2) + Idq3z(i,j,k)=Idq3z(i,j,k)+dqp3(i,j,k,m)*REAL(m+2)*z3**(m+1) + Idq3z2(i,j,k)=Idq3z2(i,j,k)+dqp3(i,j,k,m)*REAL((m+2)*(m+1)) *z3**m + Idq3z3(i,j,k)=Idq3z3(i,j,k)+dqp3(i,j,k,m)*REAL((m+2)*(m+1)*m) *z3**(m-1) + Idq3z4(i,j,k)=Idq3z4(i,j,k)+dqp3(i,j,k,m) & + *REAL((m+2)*(m+1)*m*(m-1)) *z3**(m-2) + END DO + END IF + END DO + + END IF + END DO + END DO + + factor2= -9.0/4.0*PI *rho/z3 + factor3= PI**2 * (rho/z3)**2 + + fdq2 = 0.0 + fdq2z = 0.0 + fdq2z2 = 0.0 + fdq2z3 = 0.0 + fdq2z4 = 0.0 + fdq3 = 0.0 + fdq3z = 0.0 + fdq3z2 = 0.0 + fdq3z3 = 0.0 + fdq3z4 = 0.0 + DO i = 1, ncomp + DO j = 1, ncomp + IF (myfac(i) /= 0.0 .AND. q_fac(j) /= 0.0) THEN + xijfa =x(i)*myfac(i) * x(j)*q_fac(j) /sig_ij(i,j)**5 + eij = (parame(i,3)*parame(j,3))**0.5 + fdq2= fdq2 +factor2*xijfa*(Idq2(i,j) +eij/t*Idq4(i,j) ) + fdq2z =fdq2z +factor2*xijfa*(Idq2z(i,j) +eij/t*Idq4z(i,j) ) + fdq2z2=fdq2z2+factor2*xijfa*(Idq2z2(i,j)+eij/t*Idq4z2(i,j)) + fdq2z3=fdq2z3+factor2*xijfa*(Idq2z3(i,j)+eij/t*Idq4z3(i,j)) + fdq2z4=fdq2z4+factor2*xijfa*(Idq2z4(i,j)+eij/t*Idq4z4(i,j)) + DO k = 1, ncomp + IF (myfac(k) /= 0.0.OR.q_fac(k) /= 0.0) THEN + xijkfa=x(i)*x(j)*x(k)/(sig_ij(i,j)*sig_ij(i,k)*sig_ij(j,k))**2 & + *( myfac(i)*q_fac(j)*myfac(k) + myfac(i)*q_fac(j)*q_fac(k)*1.193735 ) + fdq3 =fdq3 + factor3 * xijkfa*Idq3(i,j,k) + fdq3z =fdq3z + factor3 * xijkfa*Idq3z(i,j,k) + fdq3z2=fdq3z2 + factor3 * xijkfa*Idq3z2(i,j,k) + fdq3z3=fdq3z3 + factor3 * xijkfa*Idq3z3(i,j,k) + fdq3z4=fdq3z4 + factor3 * xijkfa*Idq3z4(i,j,k) + END IF + END DO + END IF + END DO + END DO + IF (fdq2 < -1.E-50 .AND. fdq3 /= 0.0 .AND. fdq2z /= 0.0 .AND. fdq3z /= 0.0) THEN + fdqdr = fdq2* (fdq2*fdq2z - 2.0*fdq3*fdq2z+fdq2*fdq3z) /(fdq2-fdq3)**2 + fdqd2= (2.0*fdq2*fdq2z*fdq2z +fdq2*fdq2*fdq2z2 & + -2.0*fdq2z**2 *fdq3-2.0*fdq2*fdq2z2*fdq3+fdq2*fdq2*fdq3z2) & + /(fdq2-fdq3)**2 + fdqdr * 2.0*(fdq3z-fdq2z)/(fdq2-fdq3) + fdqd3=(2.0*fdq2z**3 +6.0*fdq2*fdq2z*fdq2z2+fdq2*fdq2*fdq2z3 & + -6.0*fdq2z*fdq2z2*fdq3-2.0*fdq2z**2 *fdq3z & + -2.0*fdq2*fdq2z3*fdq3 -2.0*fdq2*fdq2z2*fdq3z & + +2.0*fdq2*fdq2z*fdq3z2+fdq2*fdq2*fdq3z3) /(fdq2-fdq3)**2 & + + 2.0/(fdq2-fdq3)* ( 2.0*fdqd2*(fdq3z-fdq2z) & + + fdqdr*(fdq3z2-fdq2z2) - fdqdr/(fdq2-fdq3)*(fdq3z-fdq2z)**2 ) + fdqd4=( 12.0*fdq2z**2 *fdq2z2+6.0*fdq2*fdq2z2**2 & + +8.0*fdq2*fdq2z*fdq2z3+fdq2*fdq2*fdq2z4-6.0*fdq2z2**2 *fdq3 & + -12.0*fdq2z*fdq2z2*fdq3z -8.0*fdq2z*fdq2z3*fdq3 & + -2.0*fdq2*fdq2z4*fdq3-4.0*fdq2*fdq2z3*fdq3z & + +4.0*fdq2*fdq2z*fdq3z3+fdq2**2 *fdq3z4 ) /(fdq2-fdq3)**2 & + + 6.0/(fdq2-fdq3)* ( fdqd3*(fdq3z-fdq2z) & + -fdqd2/(fdq2-fdq3)*(fdq3z-fdq2z)**2 & + - fdqdr/(fdq2-fdq3)*(fdq3z-fdq2z)*(fdq3z2-fdq2z2) & + + fdqd2*(fdq3z2-fdq2z2) +1.0/3.0*fdqdr*(fdq3z3-fdq2z3) ) + zdq = fdqdr*eta + zdqz = fdqd2*eta + fdqdr + zdqz2 = fdqd3*eta + 2.0* fdqd2 + zdqz3 = fdqd4*eta + 3.0* fdqd3 + END IF + + +END SUBROUTINE P_DQ_VRABEC_GROSS + + + +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! + SUBROUTINE F_pert_theory ( fdsp ) +! + USE EOS_VARIABLES, ONLY: nc, PI, ncomp, t, p, rho, eta, & + x, z0t, mseg, parame, order1, order2 + USE EOS_NUMERICAL_DERIVATIVES, ONLY: disp_term + USE DFT_MODULE + IMPLICIT NONE +! +!--------------------------------------------------------------------- + REAL, INTENT(IN OUT) :: fdsp +!--------------------------------------------------------------------- + REAL :: I1, I2 + REAL :: z3, zms, c1_con, m_mean +!--------------------------------------------------------------------- + + ! caution: positive sign of correlation integral is used here ! + ! (the Helmholtz energy terms are written with a negative sign, while I1 and I2 are positive) + + IF (disp_term == 'PT1') THEN + + CALL f_dft ( I1, I2) + c1_con = 0.0 + I2 = 0.0 + fdsp = + ( - 2.0*PI*rho*I1*order1 ) + + ELSEIF (disp_term == 'PT2') THEN + + CALL f_dft ( I1, I2) + z3 = eta + zms = 1.0 - z3 + m_mean = z0t / ( PI / 6.0 ) + c1_con = 1.0/ ( 1.0 + m_mean*(8.0*z3-2.0*z3**2 )/zms**4 & + + (1.0 - m_mean)*( 20.0*z3 -27.0*z3**2 +12.0*z3**3 -2.0*z3**4 ) & + /(zms*(2.0-z3))**2 ) + fdsp = + ( - 2.0*PI*rho*I1*order1 - PI*rho*c1_con*m_mean*I2*order2 ) + + ELSEIF (disp_term == 'PT_MIX') THEN + + CALL f_pert_theory_mix ( fdsp ) + + ELSEIF (disp_term == 'PT_MF') THEN + + ! mean field theory + I1 = - ( - 8.0/9.0 - 4.0/9.0*(rc**(-9) -3.0*rc**(-3) ) - tau_cut/3.0*(rc**3 -1.0) ) + fdsp = + ( - 2.0*PI*rho*I1*order1 ) + write (*,*) 'caution: not thoroughly checked and tested' + + ELSE + write (*,*) 'define the type of perturbation theory' + stop + END IF + + ! I1 = I1 + 4.0/9.0*(2.5**-9 -3.0*2.5**-3 ) + ! fdsp = + ( - 2.0*PI*rho*I1*order1 - PI*rho*c1_con*m_mean*I2*order2 ) + + END SUBROUTINE F_pert_theory + + + + +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! + SUBROUTINE f_pert_theory_mix ( fdsp ) +! + USE EOS_VARIABLES, ONLY: nc, PI, ncomp, t, rho, eta, x, parame, mseg, dhs, sig_ij, uij + USE DFT_MODULE + IMPLICIT NONE +! +! ---------------------------------------------------------------------- + REAL, INTENT(IN OUT) :: fdsp +! +! ---------------------------------------------------------------------- + INTEGER :: k, ih + INTEGER :: l, m + REAL :: z3 + REAL :: ua, ua_c, rm + REAL, DIMENSION(nc,nc) :: I1 + REAL :: int10, int11 + REAL :: d_ij, dzr_local + REAL :: rad, xg, rdf + REAL :: dg_dz3, dg_dr + ! REAL :: intgrid(0:5000),intgri2(0:5000), utri(5000),I1_spline +! ---------------------------------------------------------------------- + +! -----constants-------------------------------------------------------- + ua_c = 4.0 * ( rc**(-12) - rc**(-6) ) + rm = 2.0**(1.0/6.0) + + I1(:,:) = 0.0 + + DO l = 1, ncomp + DO m = 1, ncomp + + rad = rc + + int10 = rc * rc * ua_c + ! intgrid(0)= int10 + + k = 0 + ih = 85 + + DO WHILE ( rad /= 1.0 ) + + dzr_local = dzr + IF ( rad - dzr_local <= 1.0 ) dzr_local = rad - 1.0 + + rad = rad - dzr_local + + k = k + 1 + + d_ij = 0.5*(dhs(l)+dhs(m)) / sig_ij(l,m) ! dimensionless effective hs-diameter d(T)/sig + xg = rad / d_ij + z3 = eta + rdf = 1.0 + dg_dz3 = 0.0 + IF ( rad <= rg ) THEN + IF ( l == 1 .AND. m == 1 ) CALL BI_CUB_SPLINE (z3,xg,ya_11,x1a_11,x2a_11,y1a_11,y2a_11,y12a_11, & + c_bicub_11,rdf,dg_dz3,dg_dr,den_step,ih,k) + IF ( l /= m ) CALL BI_CUB_SPLINE (z3,xg,ya_12,x1a_12,x2a_12,y1a_12,y2a_12,y12a_12, & + c_bicub_12,rdf,dg_dz3,dg_dr,den_step,ih,k) + IF ( l == 2 .AND. m == 2 ) CALL BI_CUB_SPLINE (z3,xg,ya_22,x1a_22,x2a_22,y1a_22,y2a_22,y12a_22, & + c_bicub_22,rdf,dg_dz3,dg_dr,den_step,ih,k) + END IF + + ua = 4.0 * ( rad**(-12) - rad**(-6) ) + + int11 = rdf * rad * rad * ua + I1(l,m) = I1(l,m) + dzr_local * ( int11 + int10 ) / 2.0 + + int10 = int11 + ! intgrid(k)= int11 + + END DO + + ! stepno = k + ! CALL SPLINE_PARA (dzr,intgrid,utri,stepno) + ! CALL SPLINE_INT (I1_spline,dzr,intgrid,utri,stepno) + + + ! caution: 1st order integral is in F_EOS.f defined with negative sign + ! --------------------------------------------------------------- + ! cut-off corrections + ! --------------------------------------------------------------- + ! I1(l,m) = I1(l,m) + ( 4.0/9.0 * rc**-9 - 4.0/3.0 * rc**-3 ) + ! I2(l,m) = I2(l,m) + 16.0/21.0 * rc**-21 - 32.0/15.0 * rc**-15 + 16.0/9.0 * rc**-9 + + END DO + END DO + + + fdsp = 0.0 + DO l = 1, ncomp + DO m = 1, ncomp + fdsp = fdsp + 2.0*PI*rho*x(l)*x(m)* mseg(l)*mseg(m)*sig_ij(l,m)**3 * uij(l,m)/t *I1(l,m) + ! ( 2.0*PI*rho*I1*order1 - PI*rho*c1_con*m_mean*I2*order2 ) + END DO + END DO + + +!!$ IF (disp_term == 'PT1') THEN +!!$ c1_con = 0.0 +!!$ I2 = 0.0 +!!$ ELSEIF (disp_term == 'PT2') THEN +!!$ zms = 1.0 - z3 +!!$ c1_con = 1.0/ ( 1.0 + m_mean*(8.0*z3-2.0*z3**2 )/zms**4 & +!!$ + (1.0 - m_mean)*( 20.0*z3 -27.0*z3**2 +12.0*z3**3 -2.0*z3**4 ) & +!!$ /(zms*(2.0-z3))**2 ) +!!$ ELSE +!!$ write (*,*) 'define the type of perturbation theory' +!!$ stop +!!$ END IF + + +END SUBROUTINE f_pert_theory_mix + + +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! + SUBROUTINE mu_pert_theory_mix ( mu_dsp ) +! + USE EOS_VARIABLES, ONLY: nc, PI, ncomp, t, rho, eta, x, parame, mseg, dhs, sig_ij, uij + USE DFT_MODULE + IMPLICIT NONE +! +! ---------------------------------------------------------------------- + REAL, INTENT(IN OUT) :: mu_dsp(nc) +! +! ---------------------------------------------------------------------- + INTEGER :: k, ih + INTEGER :: l, m + REAL :: z3 + REAL :: ua, ua_c, rm + REAL, DIMENSION(nc,nc) :: I1, I2 + REAL :: int1_0, int1_1, int2_0, int2_1 + REAL :: d_ij, dzr_local + REAL :: rad, xg, rdf + REAL :: dg_dz3, dg_dr + REAL :: term1(nc), term2 + ! REAL :: intgrid(0:5000),intgri2(0:5000), utri(5000),I1_spline +! ---------------------------------------------------------------------- + +! -----constants-------------------------------------------------------- + ua_c = 4.0 * ( rc**(-12) - rc**(-6) ) + rm = 2.0**(1.0/6.0) + + I1(:,:) = 0.0 + I2(:,:) = 0.0 + + DO l = 1, ncomp + + term1(l) = 0.0 + + DO m = 1, ncomp + + rad = rc + + int1_0 = rc * rc * ua_c + int2_0 = 0.0 + + k = 0 + ih = 85 + + DO WHILE ( rad /= 1.0 ) + + dzr_local = dzr + IF ( rad - dzr_local <= 1.0 ) dzr_local = rad - 1.0 + + rad = rad - dzr_local + k = k + 1 + + d_ij = 0.5*(dhs(l)+dhs(m)) / sig_ij(l,m) ! dimensionless effective hs-diameter d(T)/sig + xg = rad / d_ij + z3 = eta + rdf = 1.0 + dg_dz3 = 0.0 + IF ( rad <= rg ) THEN + IF ( l == 1 .AND. m == 1 ) CALL BI_CUB_SPLINE (z3,xg,ya_11,x1a_11,x2a_11,y1a_11,y2a_11,y12a_11, & + c_bicub_11,rdf,dg_dz3,dg_dr,den_step,ih,k) + IF ( l /= m ) CALL BI_CUB_SPLINE (z3,xg,ya_12,x1a_12,x2a_12,y1a_12,y2a_12,y12a_12, & + c_bicub_12,rdf,dg_dz3,dg_dr,den_step,ih,k) + IF ( l == 2 .AND. m == 2 ) CALL BI_CUB_SPLINE (z3,xg,ya_22,x1a_22,x2a_22,y1a_22,y2a_22,y12a_22, & + c_bicub_22,rdf,dg_dz3,dg_dr,den_step,ih,k) + END IF + + ua = 4.0 * ( rad**(-12) - rad**(-6) ) + + int1_1 = rdf * rad * rad * ua + int2_1 = dg_dz3 * rad * rad * ua + I1(l,m) = I1(l,m) + dzr_local * ( int1_1 + int1_0 ) / 2.0 + I2(l,m) = I2(l,m) + dzr_local * ( int2_1 + int2_0 ) / 2.0 + + int1_0 = int1_1 + int2_0 = int2_1 + + term1(l) = term1(l) +4.0*PI*rho*x(m)* mseg(l)*mseg(m) *sig_ij(l,m)**3 *uij(l,m)/t* dzr_local*(int1_1+int1_0)/2.0 + + END DO + + END DO + END DO + + + ! DO l = 1, ncomp + ! term1(l) = 0.0 + ! DO m = 1, ncomp + ! term1(l) = term1(l) + 4.0*PI*rho*x(m)* mseg(l)*mseg(m) * sig_ij(l,m)**3 * uij(l,m)/t *I1(l,m) + ! END DO + ! END DO + + term2 = 0.0 + DO l = 1, ncomp + DO m = 1, ncomp + term2 = term2 + 2.0*PI*rho*x(l) * rho*x(m)* mseg(l)*mseg(m) * sig_ij(l,m)**3 * uij(l,m)/t *I2(l,m) + END DO + END DO + + DO l = 1, ncomp + mu_dsp(l) = term1(l) + term2 * PI/ 6.0 * mseg(l)*dhs(l)**3 + END DO + +END SUBROUTINE mu_pert_theory_mix + + +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! + SUBROUTINE F_DD_GROSS_VRABEC( fdd ) +! + USE PARAMETERS, ONLY: PI, KBOL + USE EOS_VARIABLES, ONLY: nc, ncomp, uij, parame, mseg, sig_ij, rho, eta, x, t + USE EOS_CONSTANTS, ONLY: ddp2, ddp3, ddp4 + IMPLICIT NONE +! +! ---------------------------------------------------------------------- + REAL, INTENT(IN OUT) :: fdd +! ---------------------------------------------------------------------- + INTEGER :: i, j, k, m + INTEGER :: ddit, ddmax + REAL :: factor2, factor3 + REAL :: xijfa, xijkfa, xijf_j, xijkf_j, eij + REAL :: fdd2, fdd3 + REAL, DIMENSION(nc) :: my2dd, my0, alph_tst, z1dd, z2dd, dderror + REAL, DIMENSION(nc) :: fdd2m, fdd3m, fdd2m2, fdd3m2, fddm, fddm2 + REAL, DIMENSION(nc,nc) :: Idd2, Idd4 + REAL, DIMENSION(nc,nc,nc) :: Idd3 +! ---------------------------------------------------------------------- + + fdd = 0.0 + ddit = 0 + ddmax = 0 ! value assigned, if polarizable compound is present + fddm(:) = 0.0 + DO i = 1, ncomp + IF ( uij(i,i) == 0.0 ) write (*,*) 'F_DD_GROSS_VRABEC: do not use dimensionless units' + IF ( uij(i,i) == 0.0 ) stop + my2dd(i) = (parame(i,6))**2 *1.E-49 /(uij(i,i)*kbol* mseg(i)*sig_ij(i,i)**3 *1.E-30) + alph_tst(i) = parame(i,11) / (mseg(i)*sig_ij(i,i)**3 ) * t/parame(i,3) + IF ( alph_Tst(i) /= 0.0 ) ddmax = 25 ! set maximum number of polarizable RGT-iterations + z1dd(i) = my2dd(i) + 3.0*alph_tst(i) + z2dd(i) = 3.0*alph_tst(i) + my0(i) = my2dd(i) + END DO + + DO i = 1, ncomp + DO j = 1, ncomp + Idd2(i,j) = 0.0 + Idd4(i,j) = 0.0 + ! IF (parame(i,6).NE.0.0 .AND. parame(j,6).NE.0.0) THEN + DO m = 0, 4 + Idd2(i,j) = Idd2(i,j) + ddp2(i,j,m)*eta**m + Idd4(i,j) = Idd4(i,j) + ddp4(i,j,m)*eta**m + END DO + DO k = 1, ncomp + Idd3(i,j,k) = 0.0 + ! IF (parame(k,6).NE.0.0) THEN + DO m = 0, 4 + Idd3(i,j,k) = Idd3(i,j,k) + ddp3(i,j,k,m)*eta**m + END DO + ! ENDIF + END DO + ! ENDIF + END DO + END DO + + factor2 = -PI *rho + factor3 = -4.0/3.0*PI**2 * rho**2 + +9 CONTINUE + + fdd2m(:) = 0.0 + fdd2m2(:) = 0.0 + fdd3m(:) = 0.0 + fdd3m2(:) = 0.0 + fdd2 = 0.0 + fdd3 = 0.0 + DO i = 1, ncomp + DO j = 1, ncomp + ! IF (parame(i,6).NE.0.0 .AND. parame(j,6).NE.0.0) THEN + xijfa =x(i)*parame(i,3)/t*parame(i,2)**3 * x(j)*parame(j,3)/t*parame(j,2)**3 & + /((parame(i,2)+parame(j,2))/2.0)**3 * (z1dd(i)*z1dd(j)-z2dd(i)*z2dd(j)) ! * (1.0-lij(i,j)) + eij = (parame(i,3)*parame(j,3))**0.5 + fdd2= fdd2 + factor2 * xijfa * ( Idd2(i,j) + eij/t*Idd4(i,j) ) + xijf_j = parame(i,3)/t*parame(i,2)**3 *x(j)*parame(j,3)/t*parame(j,2)**3 & + /((parame(i,2)+parame(j,2))/2.0)**3 ! * (1.0-lij(i,j)) + fdd2m(i)=fdd2m(i)+4.0*SQRT(my2dd(i))*z1dd(j)*factor2* xijf_j *(Idd2(i,j)+eij/t*Idd4(i,j)) + fdd2m2(i)=fdd2m2(i) + 4.0*z1dd(j)*factor2* xijf_j *(Idd2(i,j)+eij/t*Idd4(i,j)) + IF (j == i) fdd2m2(i) =fdd2m2(i) +8.0*factor2* xijf_j*my2dd(i) *(Idd2(i,j)+eij/t*Idd4(i,j)) + DO k = 1, ncomp + ! IF (parame(k,6).NE.0.0) THEN + xijkfa = x(i)*parame(i,3)/t*parame(i,2)**3 *x(j)*parame(j,3)/t*parame(j,2)**3 & + *x(k)*parame(k,3)/t*parame(k,2)**3 / ((parame(i,2)+parame(j,2))/2.0) & + /((parame(i,2)+parame(k,2))/2.0) / ((parame(j,2)+parame(k,2))/2.0) & + *(z1dd(i)*z1dd(j)*z1dd(k)-z2dd(i)*z2dd(j)*z2dd(k)) + ! *(1.0-lij(i,j))*(1.0-lij(i,k))*(1.0-lij(j,k)) + fdd3 = fdd3 + factor3 * xijkfa * Idd3(i,j,k) + xijkf_j = parame(i,3)/t*parame(i,2)**3 *x(j)*parame(j,3)/t*parame(j,2)**3 & + *x(k)*parame(k,3)/t*parame(k,2)**3 /((parame(i,2)+parame(j,2))/2.0) & + /((parame(i,2)+parame(k,2))/2.0) /((parame(j,2)+parame(k,2))/2.0) + ! *(1.0-lij(i,j))*(1.0-lij(i,k))*(1.0-lij(j,k)) + fdd3m(i)=fdd3m(i)+6.0*factor3*SQRT(my2dd(i))*z1dd(j)*z1dd(k) *xijkf_j*Idd3(i,j,k) + fdd3m2(i)=fdd3m2(i)+6.0*factor3*z1dd(j)*z1dd(k) *xijkf_j*Idd3(i,j,k) + IF(j == i) fdd3m2(i) =fdd3m2(i)+24.0*factor3*my2dd(i)*z1dd(k) *xijkf_j*Idd3(i,j,k) + ! ENDIF + END DO + ! ENDIF + END DO + END DO + + IF (fdd2 < -1.E-50 .AND. fdd3 /= 0.0) THEN + fdd = fdd2 / ( 1.0 - fdd3/fdd2 ) + IF ( ddmax /= 0 ) THEN + DO i = 1, ncomp + ddit = ddit + 1 + fddm(i) =fdd2*(fdd2*fdd2m(i) -2.0*fdd3*fdd2m(i)+fdd2*fdd3m(i)) /(fdd2-fdd3)**2 + fddm2(i) = fdd2m(i) * (fdd2*fdd2m(i)-2.0*fdd3*fdd2m(i) +fdd2*fdd3m(i)) / (fdd2-fdd3)**2 & + + fdd2*(fdd2*fdd2m2(i) -2.0*fdd3*fdd2m2(i)+fdd2m(i)**2 & + -fdd2m(i)*fdd3m(i) +fdd2*fdd3m2(i)) / (fdd2-fdd3)**2 & + - 2.0*fdd2*(fdd2*fdd2m(i) -2.0*fdd3*fdd2m(i) +fdd2*fdd3m(i)) /(fdd2-fdd3)**3 & + *(fdd2m(i)-fdd3m(i)) + dderror(i)= SQRT( my2dd(i) ) - SQRT( my0(i) ) + alph_Tst(i)*fddm(i) + my2dd(i) = ( SQRT( my2dd(i) ) - dderror(i) / (1.0+alph_Tst(i)*fddm2(i)) )**2 + z1dd(i) = my2dd(i) + 3.0 * alph_Tst(i) + ENDDO + DO i = 1, ncomp + IF (ABS(dderror(i)) > 1.E-11 .AND. ddit < ddmax) GOTO 9 + ENDDO + fdd = fdd + SUM( 0.5*x(1:ncomp)*alph_Tst(1:ncomp)*fddm(1:ncomp)**2 ) + ENDIF + END IF + + +END SUBROUTINE F_DD_GROSS_VRABEC + + + +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! + SUBROUTINE F_QQ_GROSS( fqq ) +! + USE PARAMETERS, ONLY: PI, KBOL + USE EOS_VARIABLES, ONLY: nc, ncomp, uij, parame, mseg, sig_ij, rho, eta, x, t + USE EOS_CONSTANTS, ONLY: qqp2, qqp3, qqp4 + IMPLICIT NONE +! +! ---------------------------------------------------------------------- + REAL, INTENT(IN OUT) :: fqq +! ---------------------------------------------------------------------- + INTEGER :: i, j, k, m + REAL :: factor2, factor3 + REAL :: xijfa, xijkfa, eij + REAL :: fqq2, fqq3 + REAL, DIMENSION(nc) :: qq2 + REAL, DIMENSION(nc,nc) :: Iqq2, Iqq4 + REAL, DIMENSION(nc,nc,nc) :: Iqq3 +! ---------------------------------------------------------------------- + + + fqq = 0.0 + DO i = 1, ncomp + qq2(i) = (parame(i,7))**2 *1.E-69 / (uij(i,i)*kbol*mseg(i)*sig_ij(i,i)**5 *1.E-50) + END DO + + DO i = 1, ncomp + DO j = 1, ncomp + Iqq2(i,j) = 0.0 + Iqq4(i,j) = 0.0 + IF (parame(i,7) /= 0.0 .AND. parame(j,7) /= 0.0) THEN + DO m = 0, 4 + Iqq2(i,j) = Iqq2(i,j) + qqp2(i,j,m)*eta**m + Iqq4(i,j) = Iqq4(i,j) + qqp4(i,j,m)*eta**m + END DO + DO k = 1, ncomp + Iqq3(i,j,k) = 0.0 + IF (parame(k,7) /= 0.0) THEN + DO m = 0, 4 + Iqq3(i,j,k) = Iqq3(i,j,k) + qqp3(i,j,k,m)*eta**m + END DO + END IF + END DO + END IF + END DO + END DO + + factor2 = -9.0/16.0*PI *rho + factor3 = 9.0/16.0*PI**2 * rho**2 + + fqq2 = 0.0 + fqq3 = 0.0 + DO i = 1, ncomp + DO j = 1, ncomp + IF (parame(i,7) /= 0.0 .AND. parame(j,7) /= 0.0) THEN + xijfa=x(i)*uij(i,i)*qq2(i)*sig_ij(i,i)**5 /t & + *x(j)*uij(j,j)*qq2(j)*sig_ij(j,j)**5 /t/sig_ij(i,j)**7.0 + eij = (parame(i,3)*parame(j,3))**0.5 + fqq2= fqq2 +factor2* xijfa * (Iqq2(i,j)+eij/t*Iqq4(i,j)) + DO k = 1, ncomp + IF (parame(k,7) /= 0.0) THEN + xijkfa=x(i)*uij(i,i)*qq2(i)*sig_ij(i,i)**5 /t/sig_ij(i,j)**3 & + *x(j)*uij(j,j)*qq2(j)*sig_ij(j,j)**5 /t/sig_ij(i,k)**3 & + *x(k)*uij(k,k)*qq2(k)*sig_ij(k,k)**5 /t/sig_ij(j,k)**3 + fqq3 = fqq3 + factor3 * xijkfa * Iqq3(i,j,k) + END IF + END DO + END IF + END DO + END DO + + IF ( fqq2 < -1.E-50 .AND. fqq3 /= 0.0 ) THEN + fqq = fqq2 / ( 1.0 - fqq3/fqq2 ) + END IF + + + +END SUBROUTINE F_QQ_GROSS + +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! + SUBROUTINE F_DQ_VRABEC_GROSS( fdq ) +! + USE PARAMETERS, ONLY: PI, KBOL + USE EOS_VARIABLES, ONLY: nc, ncomp, uij, parame, mseg, sig_ij, rho, eta, x, t + USE EOS_CONSTANTS, ONLY: dqp2, dqp3, dqp4 + IMPLICIT NONE +! +! ---------------------------------------------------------------------- + REAL, INTENT(IN OUT) :: fdq +! ---------------------------------------------------------------------- + INTEGER :: i, j, k, m + REAL :: factor2, factor3 + REAL :: xijfa, xijkfa, eij + REAL :: fdq2, fdq3 + REAL, DIMENSION(nc) :: my2dd, myfac, qq2, q_fac + REAL, DIMENSION(nc,nc) :: Idq2, Idq4 + REAL, DIMENSION(nc,nc,nc) :: Idq3 +! ---------------------------------------------------------------------- + + + fdq = 0.0 + DO i = 1, ncomp + my2dd(i) = (parame(i,6))**2 *1.E-49 /(uij(i,i)*kbol* mseg(i)*sig_ij(i,i)**3 *1.E-30) + myfac(i) = parame(i,3)/t*parame(i,2)**4 *my2dd(i) + ! myfac(i)=parame(i,3)/T*parame(i,2)**4 *my2dd_renormalized(i) + qq2(i) = (parame(i,7))**2 *1.E-69 / (uij(i,i)*kbol*mseg(i)*sig_ij(i,i)**5 *1.E-50) + q_fac(i) = parame(i,3)/t*parame(i,2)**4 *qq2(i) + END DO + + DO i = 1, ncomp + DO j = 1, ncomp + Idq2(i,j) = 0.0 + Idq4(i,j) = 0.0 + IF (myfac(i) /= 0.0 .AND. q_fac(j) /= 0.0) THEN + DO m = 0, 4 + Idq2(i,j) = Idq2(i,j) + dqp2(i,j,m)*eta**m + Idq4(i,j) = Idq4(i,j) + dqp4(i,j,m)*eta**m + END DO + DO k = 1, ncomp + Idq3(i,j,k) = 0.0 + IF (myfac(k) /= 0.0 .OR. q_fac(k) /= 0.0) THEN + DO m = 0, 4 + Idq3(i,j,k) = Idq3(i,j,k) + dqp3(i,j,k,m)*eta**m + END DO + END IF + END DO + END IF + END DO + END DO + + factor2 = -9.0/4.0 * PI *rho + factor3 = PI**2 * rho**2 + + fdq2 = 0.0 + fdq3 = 0.0 + DO i = 1, ncomp + DO j = 1, ncomp + IF (myfac(i) /= 0.0 .AND. q_fac(j) /= 0.0) THEN + xijfa = x(i)*myfac(i) * x(j)*q_fac(j) /sig_ij(i,j)**5 + eij = (parame(i,3)*parame(j,3))**0.5 + fdq2 = fdq2 +factor2* xijfa*(Idq2(i,j)+eij/t*Idq4(i,j)) + DO k = 1, ncomp + IF (myfac(k) /= 0.0 .OR. q_fac(k) /= 0.0) THEN + xijkfa=x(i)*x(j)*x(k)/(sig_ij(i,j)*sig_ij(i,k)*sig_ij(j,k))**2 & + *( myfac(i)*q_fac(j)*myfac(k) + myfac(i)*q_fac(j)*q_fac(k)*1.1937350 ) + fdq3 = fdq3 + factor3*xijkfa*Idq3(i,j,k) + END IF + END DO + END IF + END DO + END DO + + IF (fdq2 < -1.E-50 .AND. fdq3 /= 0.0) THEN + fdq = fdq2 / ( 1.0 - fdq3/fdq2 ) + END IF + +END SUBROUTINE F_DQ_VRABEC_GROSS + + +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! + SUBROUTINE f_dft ( I1_dft, I2_dft ) +! + USE EOS_VARIABLES, ONLY: nc, PI, ncomp, t, rho, eta, x, mseg, parame + USE DFT_MODULE + IMPLICIT NONE +! +! ---------------------------------------------------------------------- + REAL, INTENT(OUT) :: I1_dft + REAL, INTENT(OUT) :: I2_dft +! +! ---------------------------------------------------------------------- + INTEGER :: k,ih + ! REAL :: z3 + REAL :: ua, ua_c, ua_2, ua_c_2, rm + REAL :: int10, int11, int20, int21 + REAL :: dg_drho + REAL :: rad, xg, rdf, rho_st, msegm + REAL :: sig_ij + REAL :: dg_dr, dzr_org !,rdf_d + ! REAL :: intgrid(0:NDFT),intgri2(0:NDFT) +! ---------------------------------------------------------------------- + +! -----constants-------------------------------------------------------- +msegm = parame(1,1) +rho_st = rho * parame(1,2)**3 + +ua_c = 4.0 * ( rc**(-12) - rc**(-6) ) +ua_c_2 = ua_c * ua_c +rm = 2.0**(1.0/6.0) + +int10 = rc*rc* ua_c +int20 = rc*rc* ua_c_2 +! intgrid(0)= int10 +! intgri2(0)= int20 + + +sig_ij = parame(1,2) + + +I1_dft = 0.0 +I2_dft = 0.0 +rad = rc +!dzr = dzp / 2.0 ! this line is obsolete. dzr is defined in DFT-nMF2 (dimensionless) +dzr_org= dzr +k = 0 +ih = 85 + +DO WHILE ( rad-dzr+1.E-9 >= 1.0 ) + + rad = rad - dzr + ! IF (rad <= 8.0) dzr = dzp + ! IF (rad <= rg) dzr = dzp/2.0 + k = k + 1 + xg = rad / dhs_st + ua = 4.0 * ( rad**(-12) - rad**(-6) ) + ua_2 = ua * ua + rdf = 1.0 + dg_drho = 0.0 + IF ( rad <= rg ) THEN + CALL BI_CUB_SPLINE (rho_st,xg,ya,x1a,x2a,y1a,y2a,y12a, & + c_bicub,rdf,dg_drho,dg_dr,den_step,ih,k) + END IF + + int11 = rdf*rad*rad* ua + int21 = rdf*rad*rad* ua_2 + I1_dft= I1_dft + dzr*(int11+int10)/2.0 + I2_dft= I2_dft + dzr*(int21+int20)/2.0 + int10 = int11 + int20 = int21 + +END DO + +dzr = dzr_org + +! stepno = k +! CALL SPLINE_PARA (dzr,intgrid,utri,stepno) +! CALL SPLINE_INT (I1,dzr,intgrid,utri,stepno) + +! caution: 1st order integral is in F_EOS.f defined with negative sign +I1_dft= - I1_dft - ( 4.0/9.0 * rc**(-9) - 4.0/3.0 * rc**(-3) ) + +! CALL SPLINE_PARA (dzr,intgri2,utri,stepno) +! CALL SPLINE_INT (I2,dzr,intgri2,utri,stepno) + +I2_dft = I2_dft + 16.0/21.0 * rc**(-21) - 32.0/15.0 * rc**(-15) + 16.0/9.0 * rc**(-9) + + +END SUBROUTINE f_dft + + + + +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! + REAL FUNCTION TANGENT_VALUE2 ( optpara, n ) +! SUBROUTINE TANGENT_VALUE ( fmin, optpara, n ) +! + USE BASIC_VARIABLES + USE STARTING_VALUES + IMPLICIT NONE +! +! ---------------------------------------------------------------------- + INTEGER, INTENT(IN) :: n + REAL, INTENT(IN) :: optpara(n) + !REAL, INTENT(IN) :: optpara(:) + !REAL, INTENT(IN OUT) :: fmin +! +! ---------------------------------------------------------------------- + INTEGER :: i + REAL :: lnphi(np,nc),ph_frac, gibbs_full(np),xlnx1,xlnx2 + REAL, DIMENSION(nc) :: ni_1, ni_2 +! ---------------------------------------------------------------------- + + + ! --- setting of mole fractions --------------------------------------- + DO i = 1, ncomp + IF ( optpara(i) < -300.0 ) THEN + ni_2(i) = 0.0 + ELSE + ni_2(i) = EXP( optpara(i) ) + END IF + END DO + + DO i = 1, ncomp + ni_1(i) = xif(i) - ni_2(i) + IF ( ni_2(i) > xif(i) ) THEN + ni_2(i) = xif(i) + ni_1(i) = xif(i) * 1.E-20 + ENDIF + END DO + + xi(2,1:ncomp) = ni_2(1:ncomp) / SUM( ni_2(1:ncomp) ) + lnx(2,1:ncomp) = optpara(1:ncomp) - LOG( SUM( ni_2(1:ncomp) ) ) + + ph_frac = SUM( ni_1(1:ncomp) ) + xi(1,1:ncomp) = ni_1(1:ncomp) / ph_frac + lnx(1,1:ncomp) = LOG( ni_1(1:ncomp) ) - LOG( ph_frac ) + ! write (*,'(a,4G18.8)') 'FF',(xif(i),i=1,ncomp) + ! write (*,'(a,4G18.8)') 'AA',(xi(1,i),i=1,ncomp) + ! write (*,'(a,3G18.8)') 'BB',(xi(2,i),i=1,ncomp) + + CALL fugacity (lnphi) + !CALL enthalpy_etc + + gibbs(1) = SUM( xi(1,1:ncomp) * lnphi(1,1:ncomp) ) ! dimensionless g/RT + gibbs(2) = SUM( xi(2,1:ncomp) * lnphi(2,1:ncomp) ) + + xlnx1 = SUM( xi(1,1:ncomp)*lnx(1,1:ncomp) ) ! dimensionless s/RT + xlnx2 = SUM( xi(2,1:ncomp)*lnx(2,1:ncomp) ) + + gibbs_full(1) = gibbs(1) + xlnx1 + gibbs_full(2) = gibbs(2) + xlnx2 + + TANGENT_VALUE2 = gibbs_full(1)*ph_frac + gibbs_full(2)*(1.0-ph_frac) + !fmin = gibbs_full(1)*ph_frac + gibbs_full(2)*(1.0-ph_frac) + !write (*,'(a,4G18.8)') 'TP',TANGENT_VALUE2,(lnx(1,i),i=1,ncomp) + !write (*,'(a,4G18.8)') 'al',ph_frac,(lnx(2,i), i=1,ncomp) + !write (*,*) ' ' + !pause + +END FUNCTION TANGENT_VALUE2 + + + + + + + + diff --git a/applications/PUfoam/MoDeNaModels/Solubility/src/getting_started_subroutines.f90 b/applications/PUfoam/MoDeNaModels/Solubility/src/getting_started_subroutines.f90 new file mode 100644 index 000000000..582a8c822 --- /dev/null +++ b/applications/PUfoam/MoDeNaModels/Solubility/src/getting_started_subroutines.f90 @@ -0,0 +1,4082 @@ + +!> This file contains auxiliary subroutines. + + +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! SUBROUTINE eos_const +! +! This subroutine provides the constants of the PC-SAFT EOS. +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! + SUBROUTINE eos_const (ap,bp,dnm) +! + IMPLICIT NONE +! +! ---------------------------------------------------------------------- + REAL, INTENT(OUT) :: ap(0:6,3) + REAL, INTENT(OUT) :: bp(0:6,3) + REAL, INTENT(OUT) :: dnm(4,9) +! ---------------------------------------------------------------------- + + +! --- dispersion term constants ---------------------------------------- +ap(0,1) = 0.91056314451539 +ap(0,2) = -0.30840169182720 +ap(0,3) = -0.09061483509767 +ap(1,1) = 0.63612814494991 +ap(1,2) = 0.18605311591713 +ap(1,3) = 0.45278428063920 +ap(2,1) = 2.68613478913903 +ap(2,2) = -2.50300472586548 +ap(2,3) = 0.59627007280101 +ap(3,1) = -26.5473624914884 +ap(3,2) = 21.4197936296668 +ap(3,3) = -1.72418291311787 +ap(4,1) = 97.7592087835073 +ap(4,2) = -65.2558853303492 +ap(4,3) = -4.13021125311661 +ap(5,1) = -159.591540865600 +ap(5,2) = 83.3186804808856 +ap(5,3) = 13.7766318697211 +ap(6,1) = 91.2977740839123 +ap(6,2) = -33.7469229297323 +ap(6,3) = -8.67284703679646 + +bp(0,1) = 0.72409469413165 +bp(0,2) = -0.57554980753450 +bp(0,3) = 0.09768831158356 +bp(1,1) = 1.11913959304690 *2.0 +bp(1,2) = 0.34975477607218 *2.0 +bp(1,3) = -0.12787874908050 *2.0 +bp(2,1) = -1.33419498282114 *3.0 +bp(2,2) = 1.29752244631769 *3.0 +bp(2,3) = -3.05195205099107 *3.0 +bp(3,1) = -5.25089420371162 *4.0 +bp(3,2) = -4.30386791194303 *4.0 +bp(3,3) = 5.16051899359931 *4.0 +bp(4,1) = 5.37112827253230 *5.0 +bp(4,2) = 38.5344528930499 *5.0 +bp(4,3) = -7.76088601041257 *5.0 +bp(5,1) = 34.4252230677698 *6.0 +bp(5,2) = -26.9710769414608 *6.0 +bp(5,3) = 15.6044623461691 *6.0 +bp(6,1) = -50.8003365888685 *7.0 +bp(6,2) = -23.6010990650801 *7.0 +bp(6,3) = -4.23812936930675 *7.0 + + +! square-well fluid +! ap(1,1)= 0.79152347258784 +! ap(1,2)= -0.62269805320654 +! ap(1,3)= -0.06798823934067 +! ap(2,1)= 1.07120982251709 +! ap(2,2)= 0.48628215731716 +! ap(2,3)= 0.02837828512515 +! ap(3,1)= 0.92084839459226 +! ap(3,2)= 1.11652038059747 +! ap(3,3)= 0.09713202077943 +! ap(4,1)= -7.84708350369249 +! ap(4,2)= -2.04200599876547 +! ap(4,3)= 0.06475764015088 +! ap(5,1)= 25.90284137818050 +! ap(5,2)= 9.27791640100603 +! ap(5,3)= 0.07729792971827 +! ap(6,1)= -57.1528726997640 +! ap(6,2)= -16.8377999920957 +! ap(6,3)= 0.24883598436184 +! ap(7,1)= 42.02314637860930 +! ap(7,2)= 7.62432635016420 +! ap(7,3)= -0.72472024688888 + +! bp(1,1)= 0.79152347258784 +! bp(1,2)= -0.62269805320654 +! bp(1,3)= -0.06798823934067 +! bp(2,1)= 1.07120982251709 *2.0 +! bp(2,2)= 0.48628215731716 *2.0 +! bp(2,3)= 0.02837828512515 *2.0 +! bp(3,1)= 0.92084839459226 *3.0 +! bp(3,2)= 1.11652038059747 *3.0 +! bp(3,3)= 0.09713202077943 *3.0 +! bp(4,1)= -7.84708350369249 *4.0 +! bp(4,2)= -2.04200599876547 *4.0 +! bp(4,3)= 0.06475764015088 *4.0 +! bp(5,1)= 25.90284137818050 *5.0 +! bp(5,2)= 9.27791640100603 *5.0 +! bp(5,3)= 0.07729792971827 *5.0 +! bp(6,1)= -57.1528726997640 *6.0 +! bp(6,2)= -16.8377999920957 *6.0 +! bp(6,3)= 0.24883598436184 *6.0 +! bp(7,1)= 42.02314637860930 *7.0 +! bp(7,2)= 7.62432635016420 *7.0 +! bp(7,3)= -0.72472024688888 *7.0 + + +dnm(1,1) = -8.8043 +dnm(1,2) = +4.1646270 +dnm(1,3) = -48.203555 +dnm(1,4) = +140.43620 +dnm(1,5) = -195.23339 +dnm(1,6) = +113.51500 +dnm(2,1) = +2.9396 +dnm(2,2) = -6.0865383 +dnm(2,3) = +40.137956 +dnm(2,4) = -76.230797 +dnm(2,5) = -133.70055 +dnm(2,6) = +860.25349 +dnm(2,7) = -1535.3224 +dnm(2,8) = +1221.4261 +dnm(2,9) = -409.10539 +dnm(3,1) = -2.8225 +dnm(3,2) = +4.7600148 +dnm(3,3) = +11.257177 +dnm(3,4) = -66.382743 +dnm(3,5) = +69.248785 +dnm(4,1) = +0.3400 +dnm(4,2) = -3.1875014 +dnm(4,3) = +12.231796 +dnm(4,4) = -12.110681 + +END SUBROUTINE eos_const + + + +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! SUBROUTINE dq_const +! +! This subr. provides the constants of the dipole-quadrupole term. +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! + SUBROUTINE dq_const ( dqp2,dqp3,dqp4 ) +! + USE PARAMETERS, ONLY: nc + USE EOS_VARIABLES, ONLY: ncomp, parame + IMPLICIT NONE +! +! ---------------------------------------------------------------------- + REAL, INTENT(OUT) :: dqp2(nc,nc,0:8) + REAL, INTENT(OUT) :: dqp3(nc,nc,nc,0:8) + REAL, INTENT(OUT) :: dqp4(nc,nc,0:8) +! +! ---------------------------------------------------------------------- + INTEGER :: i, j, k + REAL :: mdq(nc) + REAL :: mf1, mf2, msegij +! ---------------------------------------------------------------------- + +DO i=1,ncomp + mdq(i) = parame(i,1) + IF (mdq(i) > 2.0) mdq(i) = 2.0 +END DO + + +DO i=1,ncomp + DO j=1,ncomp + + msegij=(mdq(i)*mdq(j))**0.5 + mf1 = (msegij-1.0)/msegij + mf2 = mf1*(msegij-2.0)/msegij + + dqp2(i,j,0) = 0.697094963 + mf1*(-0.673459279) + mf2*0.670340770 + dqp2(i,j,1) = -0.633554144 + mf1*(-1.425899106) + mf2*(-4.338471826) + dqp2(i,j,2) = 2.945509028 + mf1 * 4.19441392 + mf2*7.234168360 + dqp2(i,j,3) = -1.467027314 + mf1 * 1.0266216 + dqp2(i,j,4) = 0.0 + + dqp4(i,j,0) = -0.484038322 + mf1 * 0.67651011 + mf2*(-1.167560146) + dqp4(i,j,1) = 1.970405465 + mf1*(-3.013867512) + mf2*2.13488432 + dqp4(i,j,2) = -2.118572671 + mf1 * 0.46742656 + dqp4(i,j,3) = 0.0 + dqp4(i,j,4) = 0.0 + + + DO k=1,ncomp + msegij=(mdq(i)*mdq(j)*mdq(k))**(1.0/3.0) + mf1 = (msegij-1.0)/msegij + mf2 = (msegij-2.0)/msegij + dqp3(i,j,k,0) = 0.795009692 + mf1*(-2.099579397) + dqp3(i,j,k,1) = 3.386863396 + mf1*(-5.941376392) + dqp3(i,j,k,2) = 0.475106328 + mf1*(-0.178820384) + dqp3(i,j,k,3) = 0.0 + dqp3(i,j,k,4) = 0.0 + END DO + + END DO +END DO + +END SUBROUTINE dq_const + + +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! SUBROUTINE dd_const +! +! This subroutine provides the constants of the dipole-term. +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! + SUBROUTINE dd_const ( ddp2,ddp3,ddp4 ) +! + USE PARAMETERS, ONLY: nc, PI + USE EOS_VARIABLES, ONLY: ncomp, parame + IMPLICIT NONE +! +! ---------------------------------------------------------------------- + REAL, INTENT(OUT) :: ddp2(nc,nc,0:8) + REAL, INTENT(OUT) :: ddp3(nc,nc,nc,0:8) + REAL, INTENT(OUT) :: ddp4(nc,nc,0:8) +! +! ---------------------------------------------------------------------- + INTEGER :: i, j, k + REAL :: pardd(nc) + REAL :: mf1,mf2,msegij,sin2t +! ---------------------------------------------------------------------- + +sin2t = SIN( 0.0 * PI / 180.0 ) +sin2t = sin2t*sin2t + +DO i = 1, ncomp + pardd(i) = parame(i,1) + IF (pardd(i) > 2.0) pardd(i) = 2.0 +END DO + +DO i=1,ncomp + DO j=1,ncomp +! IF (parame(i,6).NE.0.0.AND.parame(j,6).NE.0.0) THEN + + msegij=(pardd(i)*pardd(j))**0.5 + mf1 = (msegij-1.0)/msegij + mf2 = mf1*(msegij-2.0)/msegij + + ddp2(i,j,0) = 0.30435038064 + mf1*(0.95346405973+0.201436*sin2t) & + + mf2*(-1.16100802773-1.74114*sin2t) + ddp2(i,j,1) = -0.13585877707 + mf1*(-1.83963831920+1.31649*sin2t) & + + mf2*4.52586067320 + ddp2(i,j,2) = 1.44933285154 + mf1 * 2.01311801180 + mf2*0.97512223853 + ddp2(i,j,3) = 0.35569769252 + mf1*(-7.37249576667) + mf2*(-12.2810377713) + ddp2(i,j,4) = -2.06533084541 + mf1 * 8.23741345333 + mf2*5.93975747420 + + ddp4(i,j,0) = 0.21879385627 + mf1*(-0.58731641193) + mf2*3.48695755800 + ddp4(i,j,1) = -1.18964307357 + mf1 * 1.24891317047 + mf2*(-14.9159739347) + ddp4(i,j,2) = 1.16268885692 + mf1*(-0.50852797392) + mf2*15.3720218600 + ddp4(i,j,3) = 0.0 + ddp4(i,j,4) = 0.0 + + DO k=1,ncomp +! IF (parame(k,6).NE.0.0) THEN + msegij=(pardd(i)*pardd(j)*pardd(k))**(1.0/3.0) + mf1 = (msegij-1.0)/msegij + mf2 = mf1*(msegij-2.0)/msegij + ddp3(i,j,k,0) = -0.06467735252 + mf1*(-0.95208758351+0.28503*sin2t) & + + mf2*(-0.62609792333+2.2195*sin2t) + ddp3(i,j,k,1) = 0.19758818347 + mf1 * 2.99242575222 + mf2*1.29246858189 + ddp3(i,j,k,2) = -0.80875619458 + mf1*(-2.38026356489) + mf2*1.65427830900 + ddp3(i,j,k,3) = 0.69028490492 + mf1*(-0.27012609786) + mf2*(-3.43967436378) + ddp3(i,j,k,4) = 0.0 + +! ENDIF + END DO + +! ENDIF + END DO +END DO + +END SUBROUTINE dd_const + + +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! SUBROUTINE qq_const +! +! This subroutine provides the constants of the quadrupole-term. +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! + SUBROUTINE qq_const ( qqp2,qqp3,qqp4 ) +! + USE PARAMETERS, ONLY: nc + USE EOS_VARIABLES, ONLY: ncomp, parame + IMPLICIT NONE +! +! ---------------------------------------------------------------------- + REAL, INTENT(OUT) :: qqp2(nc,nc,0:8) + REAL, INTENT(OUT) :: qqp3(nc,nc,nc,0:8) + REAL, INTENT(OUT) :: qqp4(nc,nc,0:8) +! +! ---------------------------------------------------------------------- + INTEGER :: i, j, k + REAL :: mqq(nc) + REAL :: mf1, mf2, msegij +! ---------------------------------------------------------------------- + +DO i = 1,ncomp + mqq(i) = parame(i,1) + IF (mqq(i) > 2.0) mqq(i) = 2.0 +END DO + +DO i = 1,ncomp + DO j = 1,ncomp + IF (parame(i,7) /= 0.0 .AND. parame(j,7) /= 0.0) THEN + + msegij=(mqq(i)*mqq(j))**0.5 +! msegij=(parame(i,1)*parame(j,1))**0.50 + mf1 = (msegij-1.0)/msegij + mf2 = mf1*(msegij-2.0)/msegij + + qqp2(i,j,0) = 1.237830788 + mf1 * 1.285410878 + mf2*1.794295401 + qqp2(i,j,1) = 2.435503144 + mf1*(-11.46561451) + mf2*0.769510293 + qqp2(i,j,2) = 1.633090469 + mf1 *22.08689285 + mf2*7.264792255 + qqp2(i,j,3) = -1.611815241 + mf1 * 7.46913832 + mf2*94.48669892 + qqp2(i,j,4) = 6.977118504 + mf1*(-17.19777208) + mf2*(-77.1484579) + + qqp4(i,j,0) = 0.454271755 + mf1*(-0.813734006) + mf2*6.868267516 + qqp4(i,j,1) = -4.501626435 + mf1 * 10.06402986 + mf2*(-5.173223765) + qqp4(i,j,2) = 3.585886783 + mf1*(-10.87663092) + mf2*(-17.2402066) + qqp4(i,j,3) = 0.0 + qqp4(i,j,4) = 0.0 + + DO k = 1,ncomp + IF (parame(k,7) /= 0.0) THEN + msegij=(mqq(i)*mqq(j)*mqq(k))**(1.0/3.0) +! msegij=(parame(i,1)*parame(j,1)*parame(k,1))**(1.0/3.0) + mf1 = (msegij-1.0)/msegij + mf2 = mf1*(msegij-2.0)/msegij + qqp3(i,j,k,0) = -0.500043713 + mf1 * 2.000209381 + mf2*3.135827145 + qqp3(i,j,k,1) = 6.531869153 + mf1*(-6.78386584) + mf2*7.247588801 + qqp3(i,j,k,2) = -16.01477983 + mf1 * 20.38324603 + mf2*3.075947834 + qqp3(i,j,k,3) = 14.42597018 + mf1*(-10.89598394) + qqp3(i,j,k,4) = 0.0 + END IF + END DO + + END IF + END DO +END DO + +END SUBROUTINE qq_const + + + + + + + +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! + SUBROUTINE SET_DEFAULT_EOS_NUMERICAL +! + USE EOS_NUMERICAL_DERIVATIVES + IMPLICIT NONE +! +! ---------------------------------------------------------------------- + + ideal_gas = 'no' ! ( yes, no ) + hard_sphere = 'CSBM' ! ( CSBM, no ) + chain_term = 'TPT1' ! ( TPT1, HuLiu, no ) + disp_term = 'PC-SAFT' ! ( PC-SAFT, CK, PT1, PT2, PT_MF, PT_MIX, no ) + hb_term = 'TPT1_Chap' ! ( TPT1_Chap, no ) + LC_term = 'no' ! ( MSaupe, OVL, no ) + branch_term = 'no' ! ( TPT2, no ) + II_term = 'no' + ID_term = 'no' + + subtract1 = 'no' ! (1PT, 2PT, no) + subtract2 = 'no' ! (ITTpolar, no) + +END SUBROUTINE SET_DEFAULT_EOS_NUMERICAL + + + + + + + + + +! SUBROUTINE READ_INPUT +! ! +! USE BASIC_VARIABLES +! IMPLICIT NONE +! ! +! ! ---------------------------------------------------------------------- +! INTEGER :: i +! REAL :: reading2,reading3,sumfeed +! CHARACTER (LEN=4) :: uoutp, uinp +! CHARACTER (LEN=1) :: uoutt, uint +! CHARACTER (LEN=50) :: filename +! CHARACTER (LEN=30) :: reading1 +! ! ---------------------------------------------------------------------- +! +! filename='./input_file/INPUT.INP' +! CALL file_open(filename,30) +! READ (30,*) eos, pol !J: specify by numbers! eos(1=pcsaft, 2=SRK,...) pol (=polar) yes(1) no(0) +! READ (30,*) t, uint, p, uinp !J: t: value of temp, uint: unit of temp, p: value of pressure, uinp: unit of pressure +! +! ncomp = 0 +! i = 0 +! sumfeed = 0.0 +! read_loop: DO +! READ (30,*) reading1,reading2,reading3 +! IF (reading1 == 'end') EXIT read_loop +! ncomp = ncomp + 1 +! i = i + 1 +! compna(i)= reading1 ! comp.name +! mm(i) = reading2 ! molec.mass (mandatory only for polymers) +! xif(i) = reading3 !J: molefractions +! sumfeed = sumfeed + xif(i) +! ENDDO read_loop +! +! CLOSE (30) +! +! IF (sumfeed /= 0.0 .AND. sumfeed /= 1.0) THEN !J: in case mole fractions dont sum up to 1?? +! xif(1:ncomp) = xif(1:ncomp)/sumfeed +! END IF +! +! uoutt = uint +! uoutp = uinp +! IF (uint == 'C') THEN !J: unit stuff +! u_in_t = 273.15 +! ELSE +! u_in_t = 0.0 +! END IF +! IF (uinp == 'bar') THEN +! u_in_p = 1.E5 +! ELSE IF (uinp == 'mbar') THEN +! u_in_p = 1.E2 +! ELSE IF (uinp == 'MPa') THEN +! u_in_p = 1.E6 +! ELSE IF (uinp == 'kPa') THEN +! u_in_p = 1.E3 +! ELSE +! u_in_p = 1.E0 +! END IF +! +! IF (uoutt == 'C') THEN +! u_out_t = 273.15 +! ELSE +! u_out_t = 0.0 +! END IF +! IF (uoutp == 'bar') THEN +! u_out_p = 1.E5 +! ELSE IF (uoutp == 'mbar') THEN +! u_out_p = 1.E2 +! ELSE IF (uoutp == 'MPa') THEN +! u_out_p = 1.E6 +! ELSE IF (uoutp == 'kPa') THEN +! u_out_p = 1.E3 +! ELSE +! u_out_p = 1.0 +! END IF +! +! t = t + u_in_t !J: calculate temp in Kelvin +! p = p * u_in_p !J: calculate pressure in Pascal +! +! CALL para_input ! retriev pure comp. parameters +! +! +! END SUBROUTINE READ_INPUT + + + + + +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! SUBROUTINE file_open +! +! This subroutine opens files for reading. Beforehand, it checks +! whether this file is available. +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! + SUBROUTINE file_open(filename,file_number) +! +! ---------------------------------------------------------------------- + CHARACTER (LEN=50) :: filename + INTEGER :: file_number + LOGICAL :: filefound +! ---------------------------------------------------------------------- + +INQUIRE (FILE=filename, EXIST = filefound) +IF (filefound) THEN + OPEN (file_number, FILE = filename) +ELSE + write (*,*) ' FOLLOWING FILE CAN NOT BE OPENED', filename + stop +END IF + +END SUBROUTINE file_open + + + +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! SUBROUTINE para_input +! +! This subroutine provides pure component parameters and kij parameters. +! The following syntax applies: +! +! compna(i) component name +! parame(i,k) pure comp. parameter: +! parame(i,1): segment number [/] +! parame(i,2): segment diameter "sigma" [Angstrom] +! parame(i,3): segment energy param. epsilon/k [K] +! parame(i,4): model parameter; not used for PC-SAFT (=0) +! it is 10K most of the time for SAFT [K] +! parame(i,5): Param. for T-dependent segment diameter [/] +! parame(i,6): dipolar moment [debye] +! parame(i,7): quadrupolar moment [debye] +! parame(i,8): number of segments that are part of a branching 4-mer [/] +! parame(i,9): +! parame(i,10): ionic charge number (positiv or negativ) [/] +! parame(i,11): polarizability [A**3] +! parame(i,12): number of association sites [/] +! parame(i,13): (=kap_hb, see below) [/] +! parame(i,14 to 25): (=eps_hb, see below) [K] +! nhb_typ(i) number of different types of association sites (comp. i) +! nhb_no(i,k) number of association sites of type k +! eps_hb depth of association potential [K] +! kap_hb effective width of assoc. potential (angle-averg.) +! mm molec. mass +! scaling param. for roughly scaling the set of objective functions +! +! As opposed to low-molec mass compounds, the molecular mass of a +! polymer is not obtained from this routine. Rather, it is a +! user-specification given in the file INPUT.INP +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! + SUBROUTINE para_input +! + USE BASIC_VARIABLES + IMPLICIT NONE +! +!---------------------------------------------------------------------- + INTEGER :: i +!---------------------------------------------------------------------- + +IF (eos == 1) THEN + CALL pcsaft_par +ELSE IF (eos == 4 .OR. eos == 5 .OR. eos == 6 .OR. eos == 8) THEN + ! CALL lj_par + write (*,*) 'deactivated this line when making a transition to f90' + stop +ELSE IF (eos == 7) THEN + ! CALL sw_par + write (*,*) 'deactivated this line when making a transition to f90' + stop +ELSE IF (eos == 10) THEN + i = 1 + IF (compna(i) == 'LC_generic' .AND. ncomp == 1 ) THEN + mm(i) = 1.0 + parame(i,1) = 7.0 + parame(i,2) = 1.0 + parame(i,3) = 0.0 + ELSE + write (*,*) 'PARA_INPUT: define the component !' + stop + ENDIF +ELSE + !CALL saft_par +END IF + +DO i = 1, ncomp + IF ( mm(i) >= 1.0 .AND. mm(i) < 45.0 ) THEN + scaling(i) = 10000.0 + ELSE IF( mm(i) >= 45.0 .AND. mm(i) < 90.0 ) THEN + scaling(i) = 1000.0 + ELSE IF( mm(i) >= 90.0 .AND. mm(i) < 150.0 ) THEN + scaling(i) = 100.0 + ELSE IF( mm(i) >= 150.0 .AND. mm(i) < 250.0 ) THEN + scaling(i) = 10.0 + ELSE + scaling(i) = 1.0 + END IF + IF (parame(i,10) /= 0.0) scaling(i) = scaling(i) / 1.E4 ! Electrolytes +END DO + +END SUBROUTINE para_input + + + + +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! SUBROUTINE pcsaft_par +! +! pure component parameters and kij parameters +! (as described in SUBROUTINE para_input) +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! + SUBROUTINE pcsaft_par +! + USE BASIC_VARIABLES + IMPLICIT NONE +! +!---------------------------------------------------------------------- + INTEGER :: i, j, k, no + INTEGER, DIMENSION(nc) :: nhb_typ + INTEGER, DIMENSION(nc,nsite) :: nhb_no + REAL, DIMENSION(nc,nc,nsite,nsite) :: eps_hb + REAL, DIMENSION(nc,nc) :: kap_hb +!---------------------------------------------------------------------- + + +DO i = 1, ncomp + parame(i,4) = 0.0 ! T correct. required for SAFT, not PC-SAFT + parame(i,5) = 0.12 ! Param. for T-dependent segment diameter + parame(i,6) = 0.0 ! dipolar moment + parame(i,7) = 0.0 ! quadrupolar moment + parame(i,8) = 0.0 ! number of segments that are part of a branching 4-mer + parame(i,9) = 0.0 + parame(i,10)= 0.0 ! ionic charge number + parame(i,11)= 0.0 ! polarizability + lli(i) = 0.0 + phi_criti(i)= 0.0 + chap(i) = 0.0 + + nhb_typ(i) = 0 + kap_hb(i,i) = 0.0 + + IF (compna(i) == '14-butandiol') THEN + mm(i) = 90.12 + parame(i,1) = 4.35923557 + parame(i,2) = 3.02947364 + parame(i,3) = 197.11998863 + + + ELSE IF (compna(i) == 'ps') THEN + parame(i,1) = mm(i)*1.9E-2 + parame(i,2) = 4.10705961 + parame(i,3) = 267.0 + ELSE IF (compna(i) == 'pg2') THEN !Polyglycerol 2 + mm(i) = 2000.0 + parame(i,1) = mm(i)*2.37E-2 ! from figure 5 PCSAFT paper + parame(i,2) = 3.8 ! from figure 5 PCSAFT paper + parame(i,3) = 270.0 ! starting value for iteration + ! this is the extra parameter + parame(i,8) = mm(i)*2.37E-2 + + nhb_typ(i) = 2 ! no. of different association sites + nhb_no(i,1) = 27 ! no. of sites of type 1 + nhb_no(i,2) = 27 ! no. of sites of type 2 + eps_hb(i,i,1,2)= 2544.6 ! taken from butanol (same M/OH) + eps_hb(i,i,2,1)= 2544.6 + eps_hb(i,i,1,1)= 0.0 + eps_hb(i,i,2,2)= 0.0 + kap_hb(i,i)= .00489087833 ! taken from butanol (same M/OH) + ELSE IF (compna(i) == 'peva') THEN + parame(i,1) = mm(i)*2.63E-2 + ! -- 0 Gew.% VA------------- + ! parame(i,2) = 4.021767 + ! parame(i,3) = 249.5 + ! -- 7.5 Gew.% VA------------- + ! parame(i,2) = 4.011 + ! parame(i,3) = 248.1864 + ! parame(i,3) = 247.6286 + ! ---12.7 Gew.% VA------------ + ! parame(i,2) = 4.0028 + ! parame(i,3) = 247.2075 + ! parame(i,3) = 246.24454 + ! ---27.3 Gew.% VA------------ + ! parame(i,2) = 3.9762 + ! parame(i,3) = 244.114 + ! parame(i,3) = 241.9345 + ! ---31.8 Gew.% VA------------ + parame(i,2) = 3.9666 + parame(i,3) = 243.0436 + ! parame(i,3) = 240.46 + ! ---42.7 Gew.% VA------------ + ! parame(i,2) = 3.9400 + ! parame(i,3) = 240.184 + ! parame(i,3) = 236.62 + ! --------------- + ELSE IF (compna(i) == 'pp') THEN + parame(i,1) = mm(i)*2.2E-2 + parame(i,2) = 4.2 + parame(i,3) = 220.0 + + parame(i,1) = mm(i)*0.0230487701 + parame(i,2) = 4.1 + parame(i,3) = 217.0 + ELSE IF (compna(i) == 'pe') THEN + parame(i,1) = mm(i)*2.622E-2 + parame(i,2) = 4.021767 + parame(i,3) = 252.0 + ! HDPE: extrapolated from pure comp. param. of n-alkane series! + ! parame(i,1) = mm(i)*2.4346E-2 + ! parame(i,2) = 4.07182 + ! parame(i,3) = 269.67 + !! parame(i,3) = 252.5 + ELSE IF (compna(i) == 'ldpe') THEN + parame(i,1) = mm(i)*2.63E-2 + parame(i,2) = 4.021767 + parame(i,3) = 249.5 + ELSE IF (compna(i) == 'pba') THEN + parame(i,1) = mm(i)*2.5872E-2 + parame(i,2) = 3.95 + parame(i,3) = 229.0 + ELSE IF (compna(i) == 'dextran') THEN + parame(i,1) = mm(i)*2.E-2 + parame(i,2) = 4.0 + parame(i,3) = 300.0 + ELSE IF (compna(i) == 'glycol-ethers') THEN + ! mm(i) = 218.0 + ! parame(i,1) = 7.4044 + ! parame(i,2) = 3.61576 + ! parame(i,3) = 244.0034598 + mm(i) = 222.0 + parame(i,1) = 7.994 + parame(i,2) = 3.445377778 + parame(i,3) = 234.916506 + ELSE IF (compna(i) == 'LJ') THEN + mm(i) = 1.0 + parame(i,1) = 1.0 + parame(i,2) = 1.0 + parame(i,3) = 1.0 + ELSE IF (compna(i) == 'LJ1205') THEN + mm(i) = 1.0 + parame(i,1) = 1.0 + parame(i,2) = 1.0 + parame(i,3) = 140.0 + ELSE IF (compna(i) == 'adamantane') THEN + mm(i) = 136.235000000000 + parame(i,1) = 4.81897145432221 + parame(i,2) = 3.47128575274660 + parame(i,3) = 266.936967922521 + ELSE IF (compna(i) == 'methane') THEN + mm(i) = 16.043 + parame(i,1) = 1.0 + parame(i,2) = 3.70388767 + parame(i,3) = 150.033987 + ! LLi(i) = 1.185*parame(i,2) + ! phi_criti(i)= 11.141 + ! chap(i) = 0.787 + lli(i) = 1.398*parame(i,2) + phi_criti(i)= 16.01197 + chap(i) = 0.6 + IF (pol == 2) parame(i,11)= 2.593 + ! --- adjusted to Tc, Pc und omega --- + ! mm(i) = 16.0430000000000 + ! parame(i,1) = 1.03353666429362 + ! parame(i,2) = 3.64824920605089 + ! parame(i,3) = 147.903953522994 + lli(i) = 2.254442763775*parame(i,2) + phi_criti(i)= 42.060975627454 + chap(i) = 0.704895924 + lli(i) = 1.935801125833*parame(i,2) + phi_criti(i)= 26.363325937261 + chap(i) = 0.700112854298 + lli(i) = 2.610103087662*parame(i,2) + phi_criti(i)= 38.192854403173 + chap(i) = 0.812100472735 + ! 2.122960316503 34.937141524804 0.734513223627 + ! 2.082897379591 33.036391564859 0.877578492999 + ELSE IF (compna(i) == 'ethane') THEN + mm(i) = 30.070 + parame(i,1) =mm(i)* .0534364758 + parame(i,2) = 3.5205923 + parame(i,3) = 191.423815 + lli(i) = 1.40*parame(i,2) + phi_criti(i)= 15.38 + chap(i) = 0.520 + IF (pol == 2) parame(i,11)= 4.3 + ! --- adjusted to Tc, Pc und omega --- + ! mm(i) = 30.069 + ! parame(i,1) = 1.74034548122 + ! parame(i,2) = 3.4697441893134 + ! parame(i,3) = 181.90770083591 + IF (pol >= 1) mm(i) = 30.0700000000000 + IF (pol >= 1) parame(i,1) = mm(i)* 5.341907666260094E-002 + IF (pol >= 1) parame(i,2) = 3.52104466654628 + IF (pol >= 1) parame(i,3) = 191.449300423694 + IF (pol >= 1) parame(i,7) = 0.650000000000000 + IF (pol >= 1) lli(i) = 0.0 + IF (pol >= 1) phi_criti(i)= 0.0 + IF (pol >= 1) chap(i) = 0.0 + ELSE IF (compna(i) == 'propane') THEN + mm(i) = 44.096 + parame(i,1) = mm(i)* .0453970622 + parame(i,2) = 3.61835302 + parame(i,3) = 208.110116 + lli(i) = 1.8*parame(i,2) + phi_criti(i)= 21.0 + chap(i) = 1.0 + lli(i) = 1.63*parame(i,2) + phi_criti(i)= 20.37 + chap(i) = 0.397 + IF (pol == 2) parame(i,11)= 6.29 + ELSE IF (compna(i) == 'butane_debug') THEN + mm(i) = 58.123 + parame(i,1) = 2.3374 + parame(i,2) = 3.6655 + parame(i,3) = 214.805 + ELSE IF (compna(i) == 'butane') THEN + mm(i) = 58.123 + parame(i,1) = mm(i)* .0401146927 + parame(i,2) = 3.70860139 + parame(i,3) = 222.877405 + lli(i) = 1.75*parame(i,2) + phi_criti(i)= 23.43 + chap(i) = 0.304 + ! LLi(i) = 1.942079633622*parame(i,2) + ! phi_criti(i)= 24.527323443155 + ! chap(i) = 0.734064026277 + ! LLi(i) = 1.515115760477*parame(i,2) + ! phi_criti(i)= 17.682929717796 + ! chap(i) = 0.335848717079 + IF (pol == 2) parame(i,11)= 8.2 + ! --- adjusted to Tc, Pc und omega --- + ! mm(i) = 58.1230000000 + ! parame(i,1) = 2.45352304112 + ! parame(i,2) = 3.74239117802 + ! parame(i,3) = 214.185157925 + ELSE IF (compna(i) == 'pentane') THEN + mm(i) = 72.146 + parame(i,1) = mm(i)* .03727896 + parame(i,2) = 3.77293174 + parame(i,3) = 231.197015 + IF (pol == 2) parame(i,11)= 9.99 + ELSE IF (compna(i) == 'hexane') THEN + mm(i) = 86.177 + parame(i,1) = mm(i)* .0354812325 + parame(i,2) = 3.79829291 + parame(i,3) = 236.769054 + lli(i) = 2.24*parame(i,2) + phi_criti(i)= 33.25 + chap(i) = 0.205 + IF (pol == 2) parame(i,11)= 11.9 + ELSE IF (compna(i) == 'heptane') THEN + mm(i) = 100.203 + parame(i,1) = mm(i)* .034762384 + parame(i,2) = 3.80487025 + parame(i,3) = 238.400913 + lli(i) = 2.35*parame(i,2) + phi_criti(i)= 38.10 + chap(i) = 0.173 + IF (pol == 2) parame(i,11)= 13.61 + ELSE IF (compna(i) == 'octane') THEN + mm(i) = 114.231 + parame(i,1) = mm(i)* .0334228038 + parame(i,2) = 3.83732677 + parame(i,3) = 242.775853 + ! LLi(i) = 2.0*parame(i,2) + ! phi_criti(i)= 18.75 + ! chap(i) = 1.0 + lli(i) = 2.63*parame(i,2) + phi_criti(i)= 42.06 + chap(i) = 0.155 + IF (pol == 2) parame(i,11)= 15.9 + ELSE IF (compna(i) == 'nonane') THEN + mm(i) = 128.25 + parame(i,1) = mm(i)* .0328062594 + parame(i,2) = 3.84483643 + parame(i,3) = 244.508457 + ELSE IF (compna(i) == 'decane') THEN + mm(i) = 142.285 + parame(i,1) = mm(i)* .03277373 + parame(i,2) = 3.8384498 + parame(i,3) = 243.866074 + lli(i) = 1.845*parame(i,2) + phi_criti(i)= 21.27 + chap(i) = 1.0 + lli(i) = 2.68*parame(i,2) + phi_criti(i)= 45.0 + chap(i) = 0.15 + IF (pol == 2) parame(i,11)= 19.1 + ! --- adjusted to Tc, Pc und omega --- + ! parame(i,1) = 4.794137228322 + ! parame(i,2) = 4.030446690586 + ! parame(i,3) = 236.5884493386 + ELSE IF (compna(i) == 'dodecane') THEN + mm(i) = 170.338 + parame(i,1) = mm(i)* .0311484156 + parame(i,2) = 3.89589236 + parame(i,3) = 249.214532 + ELSE IF (compna(i) == 'hexadecane') THEN + mm(i) = 226.446 + parame(i,1) = mm(i)* .0293593045 + parame(i,2) = 3.95516743 + parame(i,3) = 254.700131 + ELSE IF (compna(i) == 'octadecane') THEN + mm(i) = 254.5 + parame(i,1) = 7.3271 + parame(i,2) = 3.9668 + parame(i,3) = 256.20 + IF (pol == 2) parame(i,11)= 30.2 + ! --- adjusted to Tc, Pc und omega --- + ! mm(i) = 226.446000000000 + ! parame(i,1) = 6.66976520488694 + ! parame(i,2) = 4.25025597912511 + ! parame(i,3) = 249.582941976119 + ELSE IF (compna(i) == 'eicosane') THEN + mm(i) = 282.553 + parame(i,1) = mm(i)* .0282572812 + parame(i,2) = 3.98692612 + parame(i,3) = 257.747939 + ELSE IF (compna(i) == 'triacontane') THEN + ! mm(i) = 422.822 ! polyethylene parameters + ! parame(i,1) = mm(i)*2.622E-2 + ! parame(i,2) = 4.021767 + ! parame(i,3) = 252.0 + mm(i) = 422.822 ! param. by extrapolation of n-alkanes + parame(i,1) = mm(i)* 0.026922527 + parame(i,2) = 4.007608009 + parame(i,3) = 262.28622 + ELSE IF (compna(i) == 'octaeicosane') THEN + mm(i) = 395.0 ! param. by extrapolation of n-alkanes (sloppy!!) + parame(i,1) = mm(i)* 0.026922527 + parame(i,2) = 4.007608009 + parame(i,3) = 262.28622 + ELSE IF (compna(i) == 'tetracontane') THEN + ! mm(i) = 563.1 ! polyethylene parameters + ! parame(i,1) = mm(i)*2.622E-2 + ! parame(i,2) = 4.021767 + ! parame(i,3) = 252.0 + mm(i) = 563.1 ! param. by extrapolation of n-alkanes + parame(i,1) = mm(i)*0.026287593 + parame(i,2) = 4.023277 + parame(i,3) = 264.10466 + ELSE IF (compna(i) == 'isobutane') THEN + mm(i) = 58.123 + parame(i,1) = mm(i)* .0389105395 + parame(i,2) = 3.75735249 + parame(i,3) = 216.528584 + ELSE IF (compna(i) == 'isopentane') THEN + mm(i) = 72.15 + parame(i,1) = 2.5620 + parame(i,2) = 3.8296 + parame(i,3) = 230.75 + ELSE IF (compna(i) == '2-methylpentane') THEN + mm(i) = 86.177 + parame(i,1) = mm(i)* .0340166994 + parame(i,2) = 3.85354665 + parame(i,3) = 235.5801 + ELSE IF (compna(i) == '23-dimethylbutane') THEN + mm(i) = 86.177 + parame(i,1) = mm(i)* .0311599207 + parame(i,2) = 3.9544545 + parame(i,3) = 246.068188 + ELSE IF (compna(i) == 'ethylene') THEN + mm(i) = 28.05 + parame(i,1) = mm(i)* .0567939013 + parame(i,2) = 3.44499904 + parame(i,3) = 176.468725 + IF (pol == 2) parame(i,11)= 4.252 +! eigener 3-ter Anlauf. + IF (pol >= 1) parame(i,1) = mm(i)* 5.574644443117726E-002 + IF (pol >= 1) parame(i,2) = 3.43281482228714 + IF (pol >= 1) parame(i,3) = 178.627308564610 + IF (pol >= 1) parame(i,7) = 1.56885870200446 + IF (pol == 2) parame(i,11)= 4.252 + ELSE IF (compna(i) == 'propylene') THEN + mm(i) = 42.081 + parame(i,1) = mm(i)* .0465710324 + parame(i,2) = 3.53559831 + parame(i,3) = 207.189309 + ! --- adjusted to Tc, Pc und omega --- + ! mm(i) = 42.081 + ! parame(i,1) = 2.086735327675 + ! parame(i,2) = 3.536779407969 + ! parame(i,3) = 198.3529810625 + ELSE IF (compna(i) == '1-butene') THEN + mm(i) = 56.107 + parame(i,1) = mm(i)* .0407524782 + parame(i,2) = 3.64305136 + parame(i,3) = 222.002756 + IF (pol == 2) parame(i,11)= 7.97 + ELSE IF (compna(i) == '1-pentene') THEN + mm(i) = 70.134 + parame(i,1) = 2.6006 + parame(i,2) = 3.7399 + parame(i,3) = 231.99 + ELSE IF (compna(i) == '1-hexene') THEN + mm(i) = 84.616 + parame(i,1) = mm(i)* .0352836857 + parame(i,2) = 3.77529612 + parame(i,3) = 236.810973 + ELSE IF (compna(i) == '1-octene') THEN + mm(i) = 112.215 + parame(i,1) = mm(i)* .033345175 + parame(i,2) = 3.81329011 + parame(i,3) = 243.017587 + ELSE IF (compna(i) == 'cyclopentane') THEN + mm(i) = 70.13 + parame(i,1) = mm(i)* .0337262571 + parame(i,2) = 3.71139254 + parame(i,3) = 265.828755 + ELSE IF (compna(i) == 'cyclohexane') THEN + mm(i) = 84.147 + parame(i,1) = mm(i)* .0300695505 + parame(i,2) = 3.84990887 + parame(i,3) = 278.108786 + IF (pol == 2) parame(i,11)= 10.87 + ELSE IF (compna(i) == 'toluene') THEN + mm(i) = 92.141 + parame(i,1) = mm(i)* .0305499338 + parame(i,2) = 3.71689689 + parame(i,3) = 285.68996 + IF (pol == 2) parame(i,11)= 11.8 + ! --- adjusted to Tc, Pc und omega --- + ! mm(i) = 92.141 + ! parame(i,1) = 3.002119827762 + ! parame(i,2) = 3.803702734224 + ! parame(i,3) = 271.9428642880 + ELSE IF (compna(i) == 'm-xylene') THEN + mm(i) = 106.167 + parame(i,1) = mm(i)* .030011086 + parame(i,2) = 3.75625585 + parame(i,3) = 283.977525 + ELSE IF (compna(i) == 'o-xylene') THEN + mm(i) = 106.167 + parame(i,1) = mm(i)* .0295409161 + parame(i,2) = 3.76000631 + parame(i,3) = 291.049123 + ELSE IF (compna(i) == 'thf') THEN + mm(i) = 72.1057000000000 + ! parame(i,1) = mm(i)* 0.34311391E-01 + parame(i,1) = 2.47404685540709 + parame(i,2) = 3.51369375633677 + parame(i,3) = 274.181927093696 + parame(i,6) = 1.63100000000000 + + + Else IF(compna(i) == 'po') THEN + mm(i) = 90.12 + parame(i,1) = 4.35923557 + parame(i,2) = 3.02947364 + parame(i,3) = 197.11998863 + + Else IF(compna(i) == 'mdi') THEN + mm(i) = 2.50252E+02 + parame(i,1) = mm(i)*0.030769 + parame(i,2) = 2.886003 + parame(i,3) = 283.052778 + + Else IF(compna(i) == 'pu') THEN +! mm(i) = 2042.22 !pu n = 5 +! parame(i,1) = mm(i)*0.008845 +! parame(i,2) = 5.680270 +! parame(i,3) = 497.997594 +! mm(i) = 340.37 !pu n = 0 +! parame(i,1) = mm(i)*0.043312 +! parame(i,2) = 3.008359 +! parame(i,3) = 273.445205 +! mm(i) = 680.74 !pu n = 1 +! parame(i,1) = mm(i)*0.024106 +! parame(i,2) = 3.744327 +! parame(i,3) = 321.486386 + mm(i) = 1021.11 !pu n = 2 + parame(i,1) = mm(i)*0.015076 + parame(i,2) = 4.537837 + parame(i,3) = 400.036950 + + ELSE IF (compna(i) == 'air') THEN + mm(i) = 28.899 !n2 and o2 according to mole fractions + parame(i,1) = 1.18938 !n2 and o2 according to mole fractions (weighted artihm. avg) + parame(i,2) = 3.28694 !n2 and o2 according to mole fractions (weighted artihm. avg) + parame(i,3) = 95.672 !n2 and o2 according to mole fractions (weighted artihm. avg) + + + + + + ELSE IF (compna(i) == 'co2') THEN + mm(i) = 44.01 + parame(i,1) = mm(i)* .0470968503 + parame(i,2) = 2.7851954 + parame(i,3) = 169.207418 + IF (pol >= 1) parame(i,1) = mm(i)* 3.438191426159075E-002 + IF (pol >= 1) parame(i,2) = 3.18693935424469 + IF (pol >= 1) parame(i,3) = 163.333232725156 + IF (pol >= 1) parame(i,7) = 4.400000000000 + IF (pol >= 1) lli(i) = 1.472215*parame(i,2) + IF (pol >= 1) phi_criti(i)= 17.706567 + IF (pol >= 1) chap(i) = 0.5 + IF (pol == 2) parame(i,11)= 2.911 + ELSE IF (compna(i) == 'co') THEN + IF (pol /= 1) write (*,*) 'parameters for co missing' + IF (pol /= 1) stop + IF (pol >= 1) mm(i) = 28.01 + IF (pol >= 1) parame(i,1) = mm(i)* 5.126059746332587E-002 ! 1.43580933494776 + IF (pol >= 1) parame(i,2) = 3.13556624711756 + IF (pol >= 1) parame(i,3) = 87.7191028693595 + IF (pol >= 1) parame(i,6) = 0.1098 + ELSE IF (compna(i) == 'n2') THEN + mm(i) = 28.01 + parame(i,1) = mm(i)* .0430301713 + parame(i,2) = 3.3129702 + parame(i,3) = 90.9606924 + IF (pol >= 1) parame(i,1) = mm(i)* 3.971157114787596E-002 + IF (pol >= 1) parame(i,2) = 3.42116853868336 + IF (pol >= 1) parame(i,3) = 92.3972606842862 + IF (pol >= 1) parame(i,7) = 1.52000000000000 + IF (pol >= 1) lli(i) = 1.5188*parame(i,2) + IF (pol >= 1) phi_criti(i)= 19.9247 + IF (pol >= 1) chap(i) = 0.375 + ! better RGT-results came later, with: 1.5822 21.201 0.3972 + ELSE IF (compna(i) == 'o2') THEN + mm(i) = 32.05 + parame(i,1) = mm(i)* .0353671563 + parame(i,2) = 3.19465166 + parame(i,3) = 114.430197 + ELSE IF (compna(i) == 'hydrogen') THEN + mm(i) = 2.016 + parame(i,1) = mm(i)* .258951975 + parame(i,2) = 4.43304935 + parame(i,3) = 29.6509579 + + mm(i) = 2.016 + parame(i,1) = 1.0 + parame(i,2) = 2.915 + parame(i,3) = 38.0 + + ! mm(i) = 2.016 ! Ghosh et al. 2003 + ! parame(i,1) = 1.0 + ! parame(i,2) = 2.986 + ! parame(i,3) = 19.2775 + ELSE IF (compna(i) == 'argon') THEN + ! mm(i) = 39.948 ! adjusted m !! + ! parame(i,1) = 0.9285 + ! parame(i,2) = 3.4784 + ! parame(i,3) = 122.23 + mm(i) = 39.948 ! enforced m=1 !! + parame(i,1) = 1.0 + parame(i,2) = 3.3658 + parame(i,3) = 118.34 + IF (pol == 2) parame(i,11)= 1.6411 + ELSE IF (compna(i) == 'xenon') THEN + mm(i) = 131.29 + parame(i,1) = 1.0 + parame(i,2) = 3.93143 + parame(i,3) = 227.749 + ELSE IF (compna(i) == 'chlorine') THEN ! Cl2 + mm(i) = 70.906 + parame(i,1) = 1.5514 + parame(i,2) = 3.3672 + parame(i,3) = 265.67 + ELSE IF (compna(i) == 'SF6') THEN + mm(i) = 146.056 ! adjusted m !! + parame(i,1) = 2.48191 + parame(i,2) = 3.32727 + parame(i,3) = 161.639 + ! mm(i) = 146.056 ! enforced m=1 !! + ! parame(i,1) = 1.0 + ! parame(i,2) = 4.55222 + ! parame(i,3) = 263.1356 + ELSE IF (compna(i) == 'benzene') THEN + mm(i) = 78.114 + parame(i,1) = mm(i)* .0315590546 + parame(i,2) = 3.64778975 + parame(i,3) = 287.354574 + IF (pol >= 1) mm(i) = 78.114 ! PCP-SAFT with m=2 in QQ term + IF (pol >= 1) parame(i,1) = mm(i)* 2.932783311E-2 ! = 2.29091435590515 + IF (pol >= 1) parame(i,2) = 3.7563854 + IF (pol >= 1) parame(i,3) = 294.06253 + IF (pol >= 1) parame(i,7) = 5.5907 + ELSE IF (compna(i) == 'ethylbenzene') THEN + mm(i) = 106.167 + parame(i,1) = mm(i)* .0290120497 + parame(i,2) = 3.79741116 + parame(i,3) = 287.348098 + IF (pol == 2) parame(i,11)= 13.3 + ELSE IF (compna(i) == 'propylbenzene') THEN + mm(i) = 120.194 + parame(i,1) = mm(i)* .0278171627 + parame(i,2) = 3.8437772 + parame(i,3) = 288.128269 + ELSE IF (compna(i) == 'n-butylbenzene') THEN + mm(i) = 134.221 + parame(i,1) = mm(i)* .0280642225 + parame(i,2) = 3.87267961 + parame(i,3) = 283.072331 + ELSE IF (compna(i) == 'tetralin') THEN + mm(i) = 132.205 + parame(i,1) = mm(i)* .0250640795 + parame(i,2) = 3.87498866 + parame(i,3) = 325.065688 + ELSE IF (compna(i) == 'methylcyclohexane') THEN + mm(i) = 98.182 + parame(i,1) = mm(i)* .0271259953 + parame(i,2) = 3.99931892 + parame(i,3) = 282.334148 + IF (pol == 2) parame(i,11)= 13.1 + ELSE IF (compna(i) == 'methylcyclopentane') THEN + mm(i) = 84.156 + parame(i,1) = mm(i)* .0310459009 + parame(i,2) = 3.82534693 + parame(i,3) = 265.122799 + ELSE IF (compna(i) == 'acetone') THEN + mm(i) = 58.0800000000000 ! PC-SAFT + parame(i,1) = mm(i)* 4.870380408159182E-002 ! =2.82871694105885 + parame(i,2) = 3.24969003020675 + parame(i,3) = 250.262241927379 + lli(i) = 2.0021*parame(i,2) + phi_criti(i)= 21.336 + chap(i) = 0.24931 + IF (pol >= 1) mm(i) = 58.0800000000000 ! PCP-SAFT + IF (pol >= 1) parame(i,1) = mm(i)* 4.725811736856114E-002 ! =2.74475145676603 + IF (pol >= 1) parame(i,2) = 3.27423145271184 + IF (pol >= 1) parame(i,3) = 232.990879135326 + IF (pol >= 1) parame(i,6) = 2.88000000000000 + IF (pol >= 1) lli(i) = 2.0641*parame(i,2) + IF (pol >= 1) phi_criti(i)= 28.1783 + IF (pol >= 1) chap(i) = 0.22695 + IF (pol >= 2) mm(i) = 58.0800000000000 ! PCIP-SAFT + IF (pol >= 2) parame(i,1) = mm(i)* 4.902301475689938E-002 ! =2.84725669708072 + IF (pol >= 2) parame(i,2) = 3.23880349104868 + IF (pol >= 2) parame(i,3) = 220.884202656054 + IF (pol >= 2) parame(i,6) = 2.88000000000000 + IF (pol == 2) parame(i,11)= 6.40000000000000 + ELSE IF (compna(i) == 'butanone') THEN + mm(i) = 72.1066 ! PC-SAFT + parame(i,1) = mm(i)* 4.264192830122321E-002 ! =3.07476446724498 + parame(i,2) = 3.39324011060028 + parame(i,3) = 252.267273608975 + IF (pol >= 1) mm(i) = 72.1066 ! PCP-SAFT + IF (pol >= 1) parame(i,1) = mm(i)* 4.137668924230600E-002 ! =2.98353238051926 + IF (pol >= 1) parame(i,2) = 3.42393701353423 + IF (pol >= 1) parame(i,3) = 244.994381354681 + IF (pol >= 1) parame(i,6) = 2.78000000000000 + IF (pol >= 2) mm(i) = 72.1066 ! PCIP-SAFT + IF (pol >= 2) parame(i,1) = mm(i)* 4.254697075199448E-002 ! =3.06791740122577 + IF (pol >= 2) parame(i,2) = 3.39138375903252 + IF (pol >= 2) parame(i,3) = 236.527763837528 + IF (pol >= 2) parame(i,6) = 2.78000000000000 + IF (pol == 2) parame(i,11)= 8.13000000000000 + ELSE IF (compna(i) == '2-pentanone') THEN + ! mm(i) = 86.134 ! PC-SAFT + ! parame(i,1) = mm(i)* 3.982654501296355E-002 ! =3.43041962814660 + ! parame(i,2) = 3.46877976946838 + ! parame(i,3) = 249.834724442656 + ! mm(i) = 86.134 ! PCP-SAFT + ! parame(i,1) = mm(i)* 3.893594769994072E-002 ! =3.35370891918669 + ! parame(i,2) = 3.49417356096593 + ! parame(i,3) = 246.656329096835 + ! parame(i,6) = 2.70000000000000 + mm(i) = 86.134 ! PCIP-SAFT + parame(i,1) = mm(i)* 3.973160761515879E-002 ! =3.42224229032409 + parame(i,2) = 3.46827593107280 + parame(i,3) = 240.904278156822 + parame(i,6) = 2.70000000000000 + IF (pol == 2) parame(i,11)= 9.93000000000000 + ELSE IF (compna(i) == '3-pentanone') THEN + mm(i) = 86.134 ! PC-SAFT + parame(i,1) = 3.36439508013322 + parame(i,2) = 3.48770251979329 + parame(i,3) = 252.695415552376 + IF (pol >= 1) mm(i) = 86.134 ! PCP-SAFT + IF (pol >= 1) parame(i,1) = 3.27863398611842 + IF (pol >= 1) parame(i,2) = 3.51592571835030 + IF (pol >= 1) parame(i,3) = 248.690775540981 + IF (pol >= 1) parame(i,6) = 2.82000000000000 + IF (pol == 2) mm(i) = 86.134 ! PCIP-SAFT + IF (pol == 2) parame(i,1) = 3.34821857026283 + IF (pol == 2) parame(i,2) = 3.48903345340516 + IF (pol == 2) parame(i,3) = 242.314578558329 + IF (pol == 2) parame(i,6) = 2.82000000000000 + IF (pol == 2) parame(i,11)= 9.93000000000000 + ELSE IF (compna(i) == 'cyclohexanone') THEN ! from DIPPR + ! IF (pol.GE.1) mm(i) = 98.1430 ! PCP-SAFT + ! IF (pol.GE.1) parame(i,1) = 3.084202 + ! IF (pol.GE.1) parame(i,2) = 3.613681 + ! IF (pol.GE.1) parame(i,3) = 286.15865 + ! IF (pol.GE.1) parame(i,6) = 3.087862 + IF (pol >= 1) mm(i) = 98.1500000000000 + IF (pol >= 1) parame(i,1) = 2.72291913132818 + IF (pol >= 1) parame(i,2) = 3.79018433908522 + IF (pol >= 1) parame(i,3) = 314.772193827344 + IF (pol >= 1) parame(i,6) = 3.24600000000000 + IF (pol /= 1) WRITE (*,*) 'no non-polar param. for cyclohexanone' + IF (pol /= 1) STOP + ELSE IF (compna(i) == 'propanal') THEN + mm(i) = 58.08 ! PC-SAFT + parame(i,1) = 2.67564746980910 + parame(i,2) = 3.26295953984941 + parame(i,3) = 251.888982765626 + IF (pol >= 1) mm(i) = 58.08 ! PCP-SAFT + IF (pol >= 1) parame(i,1) = 2.60007872084995 + IF (pol >= 1) parame(i,2) = 3.28720732189761 + IF (pol >= 1) parame(i,3) = 235.205188090107 + IF (pol >= 1) parame(i,6) = 2.72000000000000 + IF (pol >= 2) mm(i) = 58.08 ! PCIP-SAFT + IF (pol >= 2) parame(i,1) = 2.72471167411028 + IF (pol >= 2) parame(i,2) = 3.24781643022922 + IF (pol >= 2) parame(i,3) = 221.642071811094 + IF (pol >= 2) parame(i,6) = 2.72000000000000 + IF (pol >= 2) parame(i,11)= 6.50000000000000 + ELSE IF (compna(i) == 'butanal') THEN + mm(i) = 72.1066000000000 ! PC-SAFT + parame(i,1) = 2.96824823599784 + parame(i,2) = 3.44068916025889 + parame(i,3) = 253.929404992884 + IF (pol >= 1) mm(i) = 72.1066000000000 ! PCP-SAFT + IF (pol >= 1) parame(i,1) = 2.86783706423953 + IF (pol >= 1) parame(i,2) = 3.47737904036296 + IF (pol >= 1) parame(i,3) = 247.543312127310 + IF (pol >= 1) parame(i,6) = 2.72000000000000 + ELSE IF (compna(i) == 'dmso') THEN + mm(i) = 78.1300000000000 ! PC-SAFT + parame(i,1) = 2.92225114054231 + parame(i,2) = 3.27780791606297 + parame(i,3) = 355.688793038512 + IF (pol >= 1) mm(i) = 78.1300000000000 ! PCP-SAFT + IF (pol >= 1) parame(i,1) = 3.02433694138348 + IF (pol >= 1) parame(i,2) = 3.24270742566613 + IF (pol >= 1) parame(i,3) = 309.357476696679 + IF (pol >= 1) parame(i,6) = 3.96000000000000 + IF (pol >= 2) mm(i) = 78.1300000000000 ! PCIP-SAFT + IF (pol >= 2) parame(i,1) = 3.19078234633277 + IF (pol >= 2) parame(i,2) = 3.19778269816832 + IF (pol >= 2) parame(i,3) = 286.337981216861 + IF (pol >= 2) parame(i,6) = 3.96000000000000 + IF (pol >= 2) parame(i,11)= 7.97000000000000 + ELSE IF (compna(i) == 'acetone_JC') THEN ! Jog-Chapman + ! mm(i) = 58.0800000000000 ! Dominik et al.2005 + ! parame(i,1) = 2.221 + ! parame(i,2) = 3.607908 + ! parame(i,3) = 259.99 + ! parame(i,6) = 2.7 + ! parame(i,8) = 0.2258 + ! mm(i) = 58.0800000000000 + ! parame(i,1) = mm(i)* 3.556617369195472E-002 + ! parame(i,2) = 3.58780367502515 + ! parame(i,3) = 273.025100470307 + ! parame(i,6) = 2.70000000000000 + ! parame(i,8) = 0.229800000000000 + + mm(i) = 58.08 ! Tumakaka Sadowski 2004 + parame(i,1) = mm(i)* 3.766E-2 + parame(i,2) = 3.6028 + parame(i,3) = 245.49 + parame(i,6) = 2.72 + parame(i,8) = 0.2969 + ! mm(i) = 58.0800000000000 ! no adjust. DD-param. + ! parame(i,1) = 1.87041620247774 + ! parame(i,2) = 3.79783535570774 + ! parame(i,3) = 208.885730881588 + ! parame(i,6) = 2.88000000000000 + ! parame(i,8) = 1.0/parame(i,1) + WRITE (*,*) 'caution: parame(i,8) is now used for branching' + STOP + kij(1,2) = -0.005 + kij(2,1)=kij(1,2) + ELSE IF (compna(i) == 'acetone_SF') THEN ! Saager-Fischer + mm(i) = 58.08 + parame(i,1) = mm(i)* 4.603296414764944E-002 + parame(i,2) = 3.29454924451643 + parame(i,3) = 221.052649057645 + parame(i,6) = 2.70000000000000 + parame(i,8) = 0.625410000000000 + mm(i) = 58.08 ! form as expected from me - no DD-param adjusted.dat + parame(i,1) = mm(i)* 4.364264724158790E-002 ! =2.53476495179143 + parame(i,2) = 3.37098670735567 + parame(i,3) = 254.366379701851 + parame(i,6) = 2.88000000000000 + ! mm(i) = 58.08 ! form as expected but w/ sumseg/1.5 - no DD-param adjusted.dat + ! parame(i,1) = mm(i)* 4.694644361257521E-002 ! =2.72664944501837 + ! parame(i,2) = 3.27842292595463 + ! parame(i,3) = 238.398883501772 + ! parame(i,6) = 2.88000000000000 + ! mm(i) = 58.08 ! form as expected but w/ sumseg/1.5 and fdd*sumseg- no DD-param adjusted.dat + ! parame(i,1) = mm(i)* 4.458214655521766E-002 ! =2.58933107192704 + ! parame(i,2) = 3.32050824493493 + ! parame(i,3) = 218.285994651271 + ! parame(i,6) = 2.88000000000000 + WRITE (*,*) 'caution: parame(i,8) is now used for branching' + STOP + kij(1,2) = 0.035 + kij(2,1)=kij(1,2) + ELSE IF (compna(i) == 'ethylacetate_JC') THEN ! Jog-Chapman + ! mm(i) = 88.11 + ! parame(i,1) = 2.7481 + ! parame(i,2) = 3.6511 + ! parame(i,3) = 236.99 + ! parame(i,6) = 1.84 + ! parame(i,8) = 0.5458 + mm(i) = 88.1060000000000 + parame(i,1) = mm(i)* 0.03117 ! 2.74626402 + parame(i,2) = 3.6493 + parame(i,3) = 236.75 + parame(i,6) = 1.8 + parame(i,8) = 0.5462 + ELSE IF (compna(i) == 'ethylacetate_SF') THEN ! Saager-Fischer + mm(i) = 88.106 + parame(i,1) = mm(i)* 3.564165384763394E-002 + parame(i,2) = 3.447379322 + parame(i,3) = 226.0930487 + parame(i,6) = 1.8 + parame(i,8) = 0.849967000000000 + WRITE (*,*) 'caution: parame(i,8) is now used for branching' + STOP + ELSE IF (compna(i) == '12po_JC') THEN ! Jog-Chapman + mm(i) = 58.08 + parame(i,1) = 2.0105 + parame(i,2) = 3.6095 + parame(i,3) = 258.82 + parame(i,6) = 2.0 + parame(i,8) = 0.3979 + WRITE (*,*) 'caution: parame(i,8) is now used for branching' + STOP + ELSE IF (compna(i) == '12po_SF') THEN ! Saager-Fischer + mm(i) = 58.08 + parame(i,1) = 2.1341 + parame(i,2) = 3.4739 + parame(i,3) = 252.95 + parame(i,6) = 2.0 + parame(i,8) = 0.916 + WRITE (*,*) 'caution: parame(i,8) is now used for branching' + STOP + ELSE IF (compna(i) == 'acrylonitrile') THEN + IF (pol >= 2) mm(i) = 53.06 ! PCIP-SAFT + IF (pol >= 2) parame(i,1) = 2.168 + IF (pol >= 2) parame(i,2) = 3.575 + IF (pol >= 2) parame(i,3) = 214.83 + IF (pol >= 2) parame(i,6) = 3.91 + IF (pol == 2) parame(i,11)= 8.04 + IF (pol >= 2) mm(i) = 53.0000000000000 ! second parameter set ?? + IF (pol >= 2) parame(i,1) = 2.45403467006041 + IF (pol >= 2) parame(i,2) = 3.41276825781723 + IF (pol >= 2) parame(i,3) = 195.194353082408 + IF (pol >= 2) parame(i,6) = 3.91000000000000 + IF (pol == 2) parame(i,11)= 8.04000000000000 + ELSE IF (compna(i) == 'butyronitrile') THEN + ! mm(i) = 69.11 + ! parame(i,1) = 2.860 + ! parame(i,2) = 3.478 + ! parame(i,3) = 253.21 + ! parame(i,6) = 4.07 + mm(i) = 69.11 + parame(i,1) = 2.989 + parame(i,2) = 3.441 + parame(i,3) = 234.04 + parame(i,6) = 4.07 + IF (pol == 2) parame(i,11)= 8.4 + ELSE IF (compna(i) == 'propionitrile') THEN + mm(i) = 55.079 ! PC-SAFT + parame(i,1) = 2.66211021227108 + parame(i,2) = 3.34032231132738 + parame(i,3) = 294.078737359580 + IF (pol >= 1) mm(i) = 55.079 ! PCP-SAFT + IF (pol >= 1) parame(i,1) = 2.50958981615666 + IF (pol >= 1) parame(i,2) = 3.39806320429568 + IF (pol >= 1) parame(i,3) = 239.152759066148 + IF (pol >= 1) parame(i,6) = 4.05000000000000 + IF (pol >= 2) mm(i) = 55.079 ! PCIP-SAFT + IF (pol >= 2) parame(i,1) = 2.54684827683436 + IF (pol >= 2) parame(i,2) = 3.41240089912190 + IF (pol >= 2) parame(i,3) = 218.299491580335 + IF (pol >= 2) parame(i,6) = 4.05000000000000 + IF (pol == 2) parame(i,11)= 6.24000000000000 + ! IF (pol.GE.2) mm(i) = 55.079 ! PCIP-SAFT my_DD adjusted + ! IF (pol.GE.2) parame(i,1) = 2.61175151088002 + ! IF (pol.GE.2) parame(i,2) = 3.37194293181453 + ! IF (pol.GE.2) parame(i,3) = 233.346110749402 + ! IF (pol.GE.2) parame(i,6) = 3.74682245835235 + ! IF (pol.EQ.2) parame(i,11)= 6.24000000000000 + ELSE IF (compna(i) == 'nitromethane') THEN + mm(i) = 61.04 ! PC-SAFT + parame(i,1) = mm(i)* 4.233767489308791E-002 ! =2.58429167547409 + parame(i,2) = 3.10839592337018 + parame(i,3) = 310.694151426943 + IF (pol >= 1) mm(i) = 61.04 ! PCP-SAFT + IF (pol >= 1) parame(i,1) = mm(i)* 4.191475020685036E-002 ! =2.55847635262615 + IF (pol >= 1) parame(i,2) = 3.10129282495975 + IF (pol >= 1) parame(i,3) = 256.456941430554 + IF (pol >= 1) parame(i,6) = 3.46000000000000 + IF (pol >= 2) mm(i) = 61.04 ! PCIP-SAFT + IF (pol >= 2) parame(i,1) = mm(i)* 4.394323357988009E-002 ! =2.68229497771588 + IF (pol >= 2) parame(i,2) = 3.10654492320028 + IF (pol >= 2) parame(i,3) = 225.973607468282 + IF (pol >= 2) parame(i,6) = 3.46000000000000 + IF (pol >= 2) parame(i,11)= 7.37000000000000 + ELSE IF (compna(i) == 'nitroethane') THEN + mm(i) = 75.067 ! PC-SAFT + parame(i,1) = mm(i)* 4.019977215251163E-002 ! =3.01767629617259 + parame(i,2) = 3.21364231060938 + parame(i,3) = 286.571650044235 + IF (pol >= 1) mm(i) = 75.067 ! PCP-SAFT + IF (pol >= 1) parame(i,1) = mm(i)* 3.928506808347654E-002 ! =2.94901220582233 + IF (pol >= 1) parame(i,2) = 3.23117331990738 + IF (pol >= 1) parame(i,3) = 265.961000131109 + IF (pol >= 1) parame(i,6) = 3.23000000000000 + IF (pol >= 2) mm(i) = 75.067 ! PCIP-SAFT + IF (pol >= 2) parame(i,1) = mm(i)* 4.117677400894779E-002 ! =3.09101689452968 + IF (pol >= 2) parame(i,2) = 3.19364569858756 + IF (pol >= 2) parame(i,3) = 246.676040248662 + IF (pol >= 2) parame(i,6) = 3.23000000000000 + IF (pol >= 2) parame(i,11)= 9.63000000000000 + ELSE IF (compna(i) == 'acetonitrile') THEN + mm(i) = 41.052 ! PC-SAFT + parame(i,1) = mm(i)* 5.673187410405271E-002 ! =2.32895689571957 + parame(i,2) = 3.18980108373791 + parame(i,3) = 311.307486044181 + IF (pol >= 1) mm(i) = 41.052 ! PCP-SAFT + IF (pol >= 1) parame(i,1) = mm(i)* 5.254832931037250E-002 ! =2.15721401484941 + IF (pol >= 1) parame(i,2) = 3.27301469369132 + IF (pol >= 1) parame(i,3) = 216.888948676921 + IF (pol >= 1) parame(i,6) = 3.92520000000000 + IF (pol >= 2) mm(i) = 41.052 ! PCIP-SAFT + IF (pol >= 2) parame(i,1) = mm(i)* 5.125846581157176E-002 ! =2.10426253849664 + IF (pol >= 2) parame(i,2) = 3.39403305120647 + IF (pol >= 2) parame(i,3) = 199.070191065791 + IF (pol >= 2) parame(i,6) = 3.92520000000000 + IF (pol >= 2) parame(i,11)= 4.40000000000000 + ! IF (pol >= 2) mm(i) = 41.052 ! PCIP-SAFT my_DD adjusted + ! IF (pol >= 2) parame(i,1) = mm(i)* 5.755347845863738E-002 ! =2.36268539768398 + ! IF (pol >= 2) parame(i,2) = 3.18554306395900 + ! IF (pol >= 2) parame(i,3) = 225.143934506015 + ! IF (pol >= 2) parame(i,6) = 3.43151866932598 + ! IF (pol >= 2) parame(i,11)= 4.40000000000000 + ! mm(i) = 41.053 ! PCP-SAFT dipole and quadrupole + ! parame(i,1) = 1.79993 + ! parame(i,2) = 3.47366 + ! parame(i,3) = 211.001 + ! parame(i,6) = 3.93800 + ! parame(i,7) = 2.44000 + ! parame(i,11)= 0.0 + ELSE IF (compna(i) == 'dmf') THEN + mm(i) = 73.09 ! PC-SAFT + parame(i,1) = 2.388 + parame(i,2) = 3.658 + parame(i,3) = 363.77 + IF (pol >= 1) mm(i) = 73.09 ! PCP-SAFT + IF (pol >= 1) parame(i,1) = 2.269 + IF (pol >= 1) parame(i,2) = 3.714 + IF (pol >= 1) parame(i,3) = 331.56 + IF (pol >= 1) parame(i,6) = 3.82 + IF (pol >= 2) mm(i) = 73.09 ! PCIP-SAFT + IF (pol >= 2) parame(i,1) = 2.375 + IF (pol >= 2) parame(i,2) = 3.667 + IF (pol >= 2) parame(i,3) = 308.42 + IF (pol >= 2) parame(i,6) = 3.82 + IF (pol >= 2) parame(i,11)= 7.81 + ELSE IF (compna(i) == 'chloroform') THEN + mm(i) = 119.377 ! PCIP-SAFT + parame(i,1) = 2.5957 + parame(i,2) = 3.4299 + parame(i,3) = 264.664 + parame(i,6) = 1.04 + IF (pol == 2) parame(i,11)= 8.23 + ELSE IF (compna(i) == 'dimethyl-ether') THEN + mm(i) = 46.069 ! PC-SAFT + parame(i,1) = mm(i)* 0.049107715 ! =2.26234331 + parame(i,2) = 3.276640534 + parame(i,3) = 212.9343244 + IF (pol >= 1) mm(i) = 46.0690000000000 ! PCP-SAFT + IF (pol >= 1) parame(i,1) = mm(i)* 0.048170452 ! =2.219164566 + IF (pol >= 1) parame(i,2) = 3.296939638 + IF (pol >= 1) parame(i,3) = 212.1048888 + IF (pol >= 1) parame(i,6) = 1.30000000000000 + IF (pol >= 2) mm(i) = 46.0690000000000 ! PCIP-SAFT + IF (pol >= 2) parame(i,1) = mm(i)* 4.939183716945787E-002 ! =2.27543254655976 + IF (pol >= 2) parame(i,2) = 3.26584718800835 + IF (pol >= 2) parame(i,3) = 206.904551967059 + IF (pol >= 2) parame(i,6) = 1.30000000000000 + IF (pol == 2) parame(i,11)= 5.29000000000000 + ELSE IF (compna(i) == 'methyl-ethyl-ether') THEN + mm(i) = 60.096 + parame(i,1) = mm(i)* .0442404671 + parame(i,2) = 3.37282595 + parame(i,3) = 216.010217 + IF (pol >= 1) mm(i) = 60.096 ! PCP-SAFT + IF (pol >= 1) parame(i,1) = mm(i)* 4.3971676124088D-002 ! =2.64252184835325 + IF (pol >= 1) parame(i,2) = 3.37938465390 + IF (pol >= 1) parame(i,3) = 215.787173860 + IF (pol >= 1) parame(i,6) = 1.17000000000 + IF (pol >= 2) mm(i) = 60.096 ! PICP-SAFT + IF (pol >= 2) parame(i,1) = mm(i)* 4.4580196137984D-002 ! =2.67909146710834 + IF (pol >= 2) parame(i,2) = 3.36105342286 + IF (pol >= 2) parame(i,3) = 212.871911999 + IF (pol >= 2) parame(i,6) = 1.17000000000 + IF (pol >= 2) parame(i,11) = 7.93000000000 + ELSE IF (compna(i) == 'diethyl-ether') THEN + mm(i) = 74.123 ! PC-SAFT + parame(i,1) = mm(i)* .0409704089 + parame(i,2) = 3.48569553 + parame(i,3) = 217.64113 + IF (pol >= 1) mm(i) = 74.123 ! PCP-SAFT + IF (pol >= 1) parame(i,1) = mm(i)* 4.0103121403686E-2 ! =2.97256367 + IF (pol >= 1) parame(i,2) = 3.51268687697978 + IF (pol >= 1) parame(i,3) = 219.527376572135 + IF (pol >= 1) parame(i,6) = 1.15000000000000 + IF (pol >= 2) mm(i) = 74.123 ! PCIP-SAFT + IF (pol >= 2) parame(i,1) = mm(i)* 4.04144179873E-2 ! =2.9956379 + IF (pol >= 2) parame(i,2) = 3.501724569 + IF (pol >= 2) parame(i,3) = 217.8941822 + IF (pol >= 2) parame(i,6) = 1.15 + IF (pol == 2) parame(i,11)= 8.73 + ELSE IF (compna(i) == 'vinylacetate') THEN + mm(i) = 86.092 + parame(i,1) = mm(i)* .0374329292 + parame(i,2) = 3.35278602 + parame(i,3) = 240.492049 + ELSE IF (compna(i) == 'chloromethane') THEN ! R40 + mm(i) = 50.488 ! PC-SAFT + parame(i,1) = mm(i)* 0.039418879 ! 1.9902 + parame(i,2) = 3.1974 + parame(i,3) = 237.27 + IF (pol >= 1) mm(i) = 50.488 ! PCP-SAFT + IF (pol >= 1) parame(i,1) = mm(i)* 0.035790801 ! 1.8070 + IF (pol >= 1) parame(i,2) = 3.3034 + IF (pol >= 1) parame(i,3) = 229.97 + IF (pol >= 1) parame(i,6) = 1.8963 + IF (pol >= 1) lli(i) = 1.67703*parame(i,2) + IF (pol >= 1) phi_criti(i)= 20.75417 + IF (pol >= 1) chap(i) = 0.5 + IF (pol >= 2) mm(i) = 50.488 ! PCIP-SAFT + IF (pol >= 2) parame(i,1) = mm(i)* 3.68559992E-2 ! 1.86078 + IF (pol >= 2) parame(i,2) = 3.275186 + IF (pol >= 2) parame(i,3) = 216.4621 + IF (pol >= 2) parame(i,6) = 1.8963 + IF (pol == 2) parame(i,11)= 4.72 + ELSE IF (compna(i) == 'fluoromethane') THEN ! R41 + IF (pol /= 1) write (*,*) 'non-polar parameters missing for fluoromethane' + IF (pol /= 1) stop + IF (pol >= 1) mm(i) = 34.0329000000000 + IF (pol >= 1) parame(i,1) = 1.94494757526896 + IF (pol >= 1) parame(i,2) = 2.96858005012635 + IF (pol >= 1) parame(i,3) = 168.938697391009 + IF (pol >= 1) parame(i,6) = 1.57823038894029 + ELSE IF (compna(i) == 'dichloromethane') THEN ! R30 + mm(i) = 84.932 ! PC-SAFT + parame(i,1) = 2.3117 + parame(i,2) = 3.3161 + parame(i,3) = 270.98 + IF (pol >= 1) mm(i) = 84.932 ! PCP-SAFT + IF (pol >= 1) parame(i,1) = 2.2687 + IF (pol >= 1) parame(i,2) = 3.3373 + IF (pol >= 1) parame(i,3) = 269.08 + IF (pol >= 1) parame(i,6) = 1.6 + IF (pol >= 2) mm(i) = 84.932 ! PCIP-SAFT + IF (pol >= 2) parame(i,1) = 2.3435 + IF (pol >= 2) parame(i,2) = 3.2987 + IF (pol >= 2) parame(i,3) = 260.66 + IF (pol >= 2) parame(i,6) = 1.6 + IF (pol == 2) parame(i,11)= 6.48 + ELSE IF (compna(i) == 'difluoromethane') THEN ! R32 + IF (pol /= 1) write (*,*) 'non-polar parameters missing for difluoromethane' + IF (pol /= 1) stop + IF (pol >= 1) mm(i) = 52.0236 ! PCP-SAFT + IF (pol >= 1) parame(i,1) = mm(i)* 4.814700934384165E-002 ! 2.50478075530028 + IF (pol >= 1) parame(i,2) = 2.79365980535456 + IF (pol >= 1) parame(i,3) = 160.893555378523 + IF (pol >= 1) parame(i,6) = 1.97850000000000 + ELSE IF (compna(i) == 'trifluoromethane') THEN ! R23 + IF (pol /= 1) write (*,*) 'non-polar parameters missing for trifluoromethane' + IF (pol /= 1) stop + IF (pol >= 1) mm(i) = 70.0138000000000 + IF (pol >= 1) parame(i,1) = 2.66039274225485 + IF (pol >= 1) parame(i,2) = 2.82905884530501 + IF (pol >= 1) parame(i,3) = 149.527709542333 + IF (pol >= 1) parame(i,6) = 1.339963415253999E-002 + ELSE IF (compna(i) == 'tetrachloromethane') THEN ! R10 + mm(i) = 153.822 + parame(i,1) = mm(i)* .0150432213 + parame(i,2) = 3.81801454 + parame(i,3) = 292.838632 + ELSE IF (compna(i) == 'trichlorofluoromethane') THEN ! R11 + IF (pol /= 1) write (*,*) 'non-polar parameters missing for trichlorofluoromethane' + IF (pol /= 1) stop + IF (pol >= 1) mm(i) = 137.368000000000 + IF (pol >= 1) parame(i,1) = 2.28793359008803 + IF (pol >= 1) parame(i,2) = 3.69013104930876 + IF (pol >= 1) parame(i,3) = 248.603173885090 + IF (pol >= 1) parame(i,6) = 0.23225538492979 + ELSE IF (compna(i) == 'chlorodifluoromethane') THEN ! R22 ( CHClF2 or CHF2Cl) + IF (pol /= 1) write (*,*) 'non-polar parameters missing for chlorodifluoromethane' + IF (pol /= 1) stop + IF (pol >= 1) mm(i) = 86.4684000000000 + IF (pol >= 1) parame(i,1) = 2.47218586047893 + IF (pol >= 1) parame(i,2) = 3.13845692489930 + IF (pol >= 1) parame(i,3) = 187.666355083434 + IF (pol >= 1) parame(i,6) = 1.04954264812860 + ELSE IF (compna(i) == 'chloroethane') THEN + mm(i) = 64.514 + parame(i,1) = mm(i)* .0350926868 + parame(i,2) = 3.41602397 + parame(i,3) = 245.42626 + ELSE IF (compna(i) == '11difluoroethane') THEN + ! mm(i) = 66.0500000000000 ! PC-SAFT + ! parame(i,1) = mm(i)* 4.109944338817734E-002 + ! parame(i,2) = 3.10257444633546 + ! parame(i,3) = 192.177159144029 + ! mm(i) = 66.05 ! PC-SAFT assoc + ! parame(i,1)= 2.984947188 + ! parame(i,2)= 2.978630027 + ! parame(i,3)= 137.8192282 + ! nhb_typ(i) = 2 + ! nhb_no(i,1)= 1 + ! nhb_no(i,2)= 1 + ! eps_hb(i,i,1,2)= 823.3478288 + ! eps_hb(i,i,2,1)= 823.3478288 + ! eps_hb(i,i,1,1)= 0.0 + ! eps_hb(i,i,2,2)= 0.0 + ! kap_hb(i,i) = 0.96345994 + IF (pol >= 1) mm(i) = 66.0500000000000 ! PCP-SAFT + IF (pol >= 1) parame(i,1) = mm(i)* 3.949665745363346E-002 ! =2.60875422481249 + IF (pol >= 1) parame(i,2) = 3.13758353925036 + IF (pol >= 1) parame(i,3) = 179.517952627836 + IF (pol >= 1) parame(i,6) = 2.27000000000000 + IF (pol >= 1) lli(i) = 2.03907*parame(i,2) + IF (pol >= 1) phi_criti(i)= 26.5 + IF (pol >= 1) chap(i) = 0.4 + IF (pol >= 2) mm(i) = 66.0500000000000 ! PCIP-SAFT + IF (pol >= 2) parame(i,1) = mm(i)* 4.093647666154238E-002 ! =2.70385428349487 + IF (pol >= 2) parame(i,2) = 3.10437129415885 + IF (pol >= 2) parame(i,3) = 170.464400902455 + IF (pol >= 2) parame(i,6) = 2.27000000000000 + IF (pol == 2) parame(i,11)= 5.01000000000000 + ELSE IF (compna(i) == '1-chlorobutane') THEN + mm(i) = 92.568 + parame(i,1) = mm(i)* .0308793201 + parame(i,2) = 3.64240187 + parame(i,3) = 258.655298 + ELSE IF (compna(i) == 'chlorobenzene') THEN + ! mm(i) = 112.558 + ! parame(i,1) = mm(i)* .0235308686 + ! parame(i,2) = 3.75328494 + ! parame(i,3) = 315.039018 + mm(i) = 112.558 ! PCIP-SAFT + parame(i,1) = mm(i)* 0.023824167 ! =2.6816 + parame(i,2) = 3.7352 + parame(i,3) = 308.82 + parame(i,6) = 1.69 + IF (pol == 2) parame(i,11)= 14.1 + ELSE IF (compna(i) == 'styrene') THEN + mm(i) = 104.150 + parame(i,1) = mm(i)* 2.9124104853E-2 + parame(i,2) = 3.760233548 + parame(i,3) = 298.51287564 + ELSE IF (compna(i) == 'methylmethanoate') THEN + mm(i) = 60.053 + parame(i,1) = mm(i)* .0446000264 + parame(i,2) = 3.08753499 + parame(i,3) = 242.626755 + IF (pol >= 1) mm(i) = 60.053 ! PCP-SAFT + IF (pol >= 1) parame(i,1) = mm(i)* 4.366991153963102E-002 ! =2.62250919768946 + IF (pol >= 1) parame(i,2) = 3.10946396964 + IF (pol >= 1) parame(i,3) = 239.051951942 + IF (pol >= 1) parame(i,6) = 1.77 + IF (pol >= 2) mm(i) = 60.053 ! PCIP-SAFT + IF (pol >= 2) parame(i,1) = mm(i)* 4.492572388931002E-2 ! 2.69792449 + IF (pol >= 2) parame(i,2) = 3.078467837 + IF (pol >= 2) parame(i,3) = 232.1842551 + IF (pol >= 2) parame(i,6) = 1.77 + IF (pol == 2) parame(i,11)= 5.05 + ELSE IF (compna(i) == 'ethylmethanoate') THEN + mm(i) = 74.079 ! PC-SAFT + parame(i,1) = mm(i)* .03898009 + parame(i,2) = 3.31087192 + parame(i,3) = 246.465646 + IF (pol >= 1) mm(i) = 74.079 ! PCP-SAFT + IF (pol >= 1) parame(i,1) = mm(i)* 3.825407152074255E-002 ! =2.83382336418509 + IF (pol >= 1) parame(i,2) = 3.33160046679 + IF (pol >= 1) parame(i,3) = 244.495680932 + IF (pol >= 1) parame(i,6) = 1.93000000000 + ELSE IF (compna(i) == 'propylmethanoate') THEN + mm(i) = 88.106 + parame(i,1) = mm(i)* .0364206062 + parame(i,2) = 3.41679642 + parame(i,3) = 246.457732 + IF (pol >= 1) mm(i) = 88.106 + IF (pol >= 1) parame(i,1) = mm(i)* 3.60050739149E-2 ! =3.17226304235232 + IF (pol >= 1) parame(i,2) = 3.42957609309 + IF (pol >= 1) parame(i,3) = 245.637644107 + IF (pol >= 1) parame(i,6) = 1.89 + ELSE IF (compna(i) == 'methylacetate') THEN + mm(i) = 74.079 ! PC-SAFT + parame(i,1) = mm(i)* 4.286817177E-2 ! =3.175631296 + parame(i,2) = 3.18722021277843 + parame(i,3) = 234.106931032456 + IF (pol >= 1) mm(i) = 74.079 ! PCP-SAFT + IF (pol >= 1) parame(i,1) = mm(i)* 4.228922065E-2 ! =3.132743176 + IF (pol >= 1) parame(i,2) = 3.2011401688 + IF (pol >= 1) parame(i,3) = 233.17562886 + IF (pol >= 1) parame(i,6) = 1.72 + IF (pol >= 2) mm(i) = 74.079 ! PCIP-SAFT + IF (pol >= 2) parame(i,1) = mm(i)* 4.298900538E-2 ! =3.18458252 + IF (pol >= 2) parame(i,2) = 3.180642322 + IF (pol >= 2) parame(i,3) = 229.3132680 + IF (pol >= 2) parame(i,6) = 1.72 + IF (pol == 2) parame(i,11)= 6.94 + ELSE IF (compna(i) == 'ethylacetate') THEN + mm(i) = 88.106 ! PC-SAFT + parame(i,1) = mm(i)* .0401464427 ! =3.537142481 + parame(i,2) = 3.30789258 + parame(i,3) = 230.800689 + IF (pol >= 1) mm(i) = 88.106 ! PCP-SAFT + IF (pol >= 1) parame(i,1) = mm(i)* 0.039792575 ! =3.505964572 + IF (pol >= 1) parame(i,2) = 3.317655188 + IF (pol >= 1) parame(i,3) = 230.2434769 + IF (pol >= 1) parame(i,6) = 1.78 + IF (pol >= 2) mm(i) = 88.106 ! PCIP-SAFT + IF (pol >= 2) parame(i,1) = mm(i)* 0.040270267 ! =3.548052143 + IF (pol >= 2) parame(i,2) = 3.302097562 + IF (pol >= 2) parame(i,3) = 227.5026191 + IF (pol >= 2) parame(i,6) = 1.78 + IF (pol == 2) parame(i,11)= 8.62 + ELSE IF (compna(i) == 'ethyl-propanoate') THEN + mm(i) = 102.133 + parame(i,1) = mm(i)* .0375692464 + parame(i,2) = 3.40306071 + parame(i,3) = 232.778374 + ELSE IF (compna(i) == 'propyl-ethanoate') THEN + mm(i) = 102.133 + parame(i,1) = mm(i)* .0370721275 + parame(i,2) = 3.42272266 + parame(i,3) = 235.758378 + IF (pol >= 1) mm(i) = 102.133 ! PCP-SAFT + IF (pol >= 1) parame(i,1) = mm(i)* 3.687149995200072E-2 ! =3.76579690459769 + IF (pol >= 1) parame(i,2) = 3.4289353421006 + IF (pol >= 1) parame(i,3) = 235.41679442910 + IF (pol >= 1) parame(i,6) = 1.78 + ! IF (pol.EQ.2) parame(i,11)= 10.41 + ELSE IF (compna(i) == 'nbutyl-ethanoate') THEN + mm(i) = 116.16 ! PC-SAFT + parame(i,1) = mm(i)* .03427004 + parame(i,2) = 3.54269638 + parame(i,3) = 242.515768 + IF (pol >= 1) mm(i) = 116.16 ! PCP-SAFT + IF (pol >= 1) parame(i,1) = mm(i)* 3.411585209773470E-002 ! =3.96289737967286 + IF (pol >= 1) parame(i,2) = 3.54821589228130 + IF (pol >= 1) parame(i,3) = 242.274388267447 + IF (pol >= 1) parame(i,6) = 1.87000000000000 + IF (pol >= 2) mm(i) = 116.16 ! PCIP-SAFT + IF (pol >= 2) parame(i,1) = mm(i)* 3.442139015733717E-002 ! =3.99838868067629 + IF (pol >= 2) parame(i,2) = 3.53576054452119 + IF (pol >= 2) parame(i,3) = 240.154409609249 + IF (pol >= 2) parame(i,6) = 1.87000000000000 + IF (pol == 2) parame(i,11)= 14.2000000000000 + ELSE IF (compna(i) == 'methyl-octanoate') THEN + mm(i) = 158.24 ! PC-SAFT + parame(i,1) = 5.2074 + parame(i,2) = 3.6069 + parame(i,3) = 244.12 + ELSE IF (compna(i) == 'methyl-decanoate') THEN + mm(i) = 186.2912 ! PC-SAFT + parame(i,1) = 5.8402 + parame(i,2) = 3.6871 + parame(i,3) = 248.27 + + mm(i) = 186.2912 ! PC-SAFT from GC-method Tim + parame(i,1) = 7.716 + parame(i,2) = 3.337303029 + parame(i,3) = 204.250907 + + mm(i) = 186.2912 ! PC-SAFT from GC-method (tightly fit) Tim + parame(i,1) = 7.728 + parame(i,2) = 3.334023322 + parame(i,3) = 206.9099379 + + ! mm(i) = 186.2912 ! PC-SAFT from fit to DIPPR + ! parame(i,1) = 6.285005 + ! parame(i,2) = 3.594888 + ! parame(i,3) = 236.781461 + ! ! parame(i,6) = 2.08056 + + ! mm(i) = 186.291000000000 + ! parame(i,1) = 6.28500485898895 + ! parame(i,2) = 3.59488828061149 + ! parame(i,3) = 236.781461491921 + ! parame(i,6) = 2.08055996894836 + ! parame(i,8) = 1.00000000000000 + mm(i) = 186.291000000000 + parame(i,1) = 6.14436331493372 + parame(i,2) = 3.61977264863944 + parame(i,3) = 242.071887817656 + + ELSE IF (compna(i) == 'methyl-dodecanoate') THEN + mm(i) = 214.344 ! PC-SAFT + parame(i,1) = 6.5153 + parame(i,2) = 3.7406 + parame(i,3) = 250.7 + ELSE IF (compna(i) == 'methyl-tetradecanoate') THEN + mm(i) = 242.398 ! PC-SAFT + parame(i,1) = 7.1197 + parame(i,2) = 3.7968 + parame(i,3) = 253.77 + ELSE IF (compna(i) == 'methyl-hexadecanoate') THEN + mm(i) = 270.451 ! PC-SAFT + parame(i,1) = 7.891 + parame(i,2) = 3.814 + parame(i,3) = 253.71 + ELSE IF (compna(i) == 'methyl-octadecanoate') THEN + mm(i) = 298.504 ! PC-SAFT + parame(i,1) = 8.8759 + parame(i,2) = 3.7932 + parame(i,3) = 250.81 + ELSE IF (compna(i) == 'CH2F2') THEN + mm(i) = 52.02 + parame(i,1) = 3.110084171 + parame(i,2) = 2.8145230485 + parame(i,3) = 158.98060151 + ELSE IF (compna(i) == 'naphthalene') THEN + ! mm(i) = 128.174000000 + ! parame(i,1) = mm(i)* 2.4877834216412E-2 + ! parame(i,2) = 3.82355815011 + ! parame(i,3) = 341.560675334 + + mm(i) = 128.17400000000 + parame(i,1) = mm(i)* 2.6400924157729E-2 + parame(i,2) = 3.8102186020014 + parame(i,3) = 328.96792935903 + ELSE IF (compna(i) == 'h2s') THEN + mm(i) = 34.0820000000000 ! PC-SAFT + parame(i,1) = mm(i)* 4.838886696385162E-002 ! = 1.64918936386199 + parame(i,2) = 3.05478289838459 + parame(i,3) = 229.838873939562 + nhb_typ(i) = 2 + nhb_no(i,1) = 1 + nhb_no(i,2) = 1 + eps_hb(i,i,1,2)= 536.634834731413 + eps_hb(i,i,2,1)= 536.634834731413 + eps_hb(i,i,1,1)= 0.0 + eps_hb(i,i,2,2)= 0.0 + kap_hb(i,i) = 1.000000000000000E-003 +! PC-SAFT from Xiaohua + mm(i) = 34.082 ! PC-SAFT + parame(i,1) = 1.63677 + parame(i,2) = 3.06565 + parame(i,3) = 230.2121 + nhb_typ(i) = 2 + nhb_no(i,1) = 1 + nhb_no(i,2) = 1 + eps_hb(i,i,1,2)= 275.1088 + eps_hb(i,i,2,1)= 275.1088 + eps_hb(i,i,1,1)= 0.0 + eps_hb(i,i,2,2)= 0.0 + kap_hb(i,i) = 1.E-2 + ! IF (pol.GE.1) mm(i) = 34.082 ! PCP-SAFT with quadrupole + ! IF (pol.GE.1) parame(i,1) = mm(i)* 3.03171032558E-2 ! =1.03326751316478 + ! IF (pol.GE.1) parame(i,2) = 3.6868189914018 + ! IF (pol.GE.1) parame(i,3) = 246.862831266172 + ! IF (pol.GE.1) nhb_typ(i) = 2 + ! IF (pol.GE.1) nhb_no(i,1) = 1 + ! IF (pol.GE.1) nhb_no(i,2) = 1 + ! IF (pol.GE.1) eps_hb(i,i,1,2)= 987.4927232 + ! IF (pol.GE.1) eps_hb(i,i,2,1)= 987.4927232 + ! IF (pol.GE.1) eps_hb(i,i,1,1)= 0.0 + ! IF (pol.GE.1) eps_hb(i,i,2,2)= 0.0 + ! IF (pol.GE.1) kap_hb(i,i) = 5.5480659623d-4 + ! IF (pol.GE.1) parame(i,6) = 0.97833 + ! IF (pol.GE.1) parame(i,7) = 3.8623 + ! IF (pol.GE.1) LLi(i) = 1.2737*parame(i,2) + ! IF (pol.GE.1) phi_criti(i)= 14.316 + ! IF (pol.GE.1) chap(i) = 0.4473 + IF (pol >= 1) mm(i) = 34.0820000000000 ! PCP-SAFT no quadrupoLE + IF (pol >= 1) parame(i,1) = mm(i)* 4.646468487062725E-002 ! 1.58360938976072 + IF (pol >= 1) parame(i,2) = 3.10111012646306 + IF (pol >= 1) parame(i,3) = 230.243457544889 + IF (pol >= 1) nhb_typ(i) = 2 + IF (pol >= 1) nhb_no(i,1) = 1 + IF (pol >= 1) nhb_no(i,2) = 1 + IF (pol >= 1) eps_hb(i,i,1,2)= 584.367708701411 + IF (pol >= 1) eps_hb(i,i,2,1)= 584.367708701411 + IF (pol >= 1) eps_hb(i,i,1,1)= 0.0 + IF (pol >= 1) eps_hb(i,i,2,2)= 0.0 + IF (pol >= 1) kap_hb(i,i) = 1.000000000000000E-003 + IF (pol >= 1) parame(i,6) = 0.978330000000000 + + IF (pol >= 1) lli(i) = 1.2737*parame(i,2) + IF (pol >= 1) phi_criti(i)= 14.316 + IF (pol >= 1) chap(i) = 0.4473 + + + IF (pol == 2) parame(i,7) = 0.0 + IF (pol == 2) mm(i) = 34.0820000000000 ! PCIP-SAFT + IF (pol == 2) parame(i,1) = mm(i)* 4.806418212963168E-002 ! 1.63812345534211 + IF (pol == 2) parame(i,2) = 3.06556006883749 + IF (pol == 2) parame(i,3) = 221.746622243054 + IF (pol == 2) nhb_typ(i) = 2 + IF (pol == 2) nhb_no(i,1) = 1 + IF (pol == 2) nhb_no(i,2) = 1 + IF (pol == 2) eps_hb(i,i,1,2)= 672.164783984789 + IF (pol == 2) eps_hb(i,i,2,1)= 672.164783984789 + IF (pol == 2) eps_hb(i,i,1,1)= 0.0 + IF (pol == 2) eps_hb(i,i,2,2)= 0.0 + IF (pol == 2) kap_hb(i,i) = 1.000000000000000E-003 + IF (pol == 2) parame(i,6) = 0.978330000000000 + IF (pol == 2) parame(i,11) = 3.60200000000000 + IF (pol == 2) parame(i,7) = 0.0 + + IF (pol >= 1)mm(i) = 34.0820000000000 !PCP-SAFT D&Q + IF (pol >= 1)parame(i,1) = mm(i)* 3.974667896078737E-002 ! = 1.35464631234155 + IF (pol >= 1)parame(i,2) = 3.30857082333438 + IF (pol >= 1)parame(i,3) = 234.248947273191 + IF (pol >= 1)nhb_typ(i) = 2 + IF (pol >= 1)nhb_no(i,1) = 1 + IF (pol >= 1)nhb_no(i,2) = 1 + IF (pol >= 1)eps_hb(i,i,1,2)= 780.770936834770 + IF (pol >= 1)eps_hb(i,i,2,1)= 780.770936834770 + IF (pol >= 1)eps_hb(i,i,1,1)= 0.0 + IF (pol >= 1)eps_hb(i,i,2,2)= 0.0 + IF (pol >= 1)kap_hb(i,i) = 1.000000000000000E-003 + IF (pol >= 1)parame(i,6) = 0.978330000000000 + IF (pol >= 1)parame(i,7) = 2.93750500000000 + + ELSE IF (compna(i) == 'methanol') THEN + mm(i) = 32.042 ! PC-SAFT + parame(i,1) = mm(i)* .0476100379 + parame(i,2) = 3.23000005 + parame(i,3) = 188.904644 + nhb_typ(i) = 2 + nhb_no(i,1) = 1 ! no. of sites of type 1 + nhb_no(i,2) = 1 ! no. of sites of type 2 + eps_hb(i,i,1,2)= 2899.49055 + eps_hb(i,i,2,1)= 2899.49055 + eps_hb(i,i,1,1)= 0.0 + eps_hb(i,i,2,2)= 0.0 + kap_hb(i,i) = .0351760892 + IF (pol >= 1) mm(i) = 32.042 ! PCP-SAFT + IF (pol >= 1) parame(i,1) = mm(i)* 7.213091821E-2 ! =2.31121888139672 + IF (pol >= 1) parame(i,2) = 2.8270129502 + IF (pol >= 1) parame(i,3) = 176.3760515 + IF (pol >= 1) nhb_typ(i) = 2 + IF (pol >= 1) nhb_no(i,1) = 1 + IF (pol >= 1) nhb_no(i,2) = 1 + IF (pol >= 1) eps_hb(i,i,1,2)= 2332.5845803 + IF (pol >= 1) eps_hb(i,i,2,1)= 2332.5845803 + IF (pol >= 1) eps_hb(i,i,1,1)= 0.0 + IF (pol >= 1) eps_hb(i,i,2,2)= 0.0 + IF (pol >= 1) kap_hb(i,i) = 8.9248658086E-2 + IF (pol >= 1) parame(i,6) = 1.7 + IF (pol >= 1) lli(i) = 1.75*parame(i,2) + IF (pol >= 1) phi_criti(i)= 23.43 + IF (pol >= 1) chap(i) = 0.304 + IF (pol == 2) mm(i) = 32.042 ! PCIP-SAFT + IF (pol == 2) parame(i,1) = 2.0693 + IF (pol == 2) parame(i,2) = 2.9547 + IF (pol == 2) parame(i,3) = 174.51 + IF (pol == 2) nhb_typ(i) = 2 + IF (pol == 2) nhb_no(i,1) = 1 + IF (pol == 2) nhb_no(i,2) = 1 + IF (pol == 2) eps_hb(i,i,1,2)= 2418.5 + IF (pol == 2) eps_hb(i,i,2,1)= 2418.5 + IF (pol == 2) eps_hb(i,i,1,1)= 0.0 + IF (pol == 2) eps_hb(i,i,2,2)= 0.0 + IF (pol == 2) kap_hb(i,i) = 0.06319 + IF (pol == 2) parame(i,6) = 1.7 + IF (pol == 2) parame(i,11)= 3.29 + ! mm(i) = 32.0420000000000 ! PCP-SAFT with adjusted QQ + ! parame(i,1) = mm(i)* 6.241807629559099E-002 + ! ! parame(i,1) = 2.00000000066333 + ! parame(i,2) = 2.97610169698593 + ! parame(i,3) = 163.268505098639 + ! nhb_typ(i) = 2 + ! nhb_no(i,1) = 1 + ! nhb_no(i,2) = 1 + ! eps_hb(i,i,1,2)= 2449.55621933612 + ! eps_hb(i,i,2,1)= 2449.55621933612 + ! eps_hb(i,i,1,1)= 0.0 + ! eps_hb(i,i,2,2)= 0.0 + ! kap_hb(i,i) = 8.431015160393653E-002 + ! parame(i,6) = 1.72000000000000 + ! parame(i,7) = 1.59810028824523 + ELSE IF (compna(i) == 'ethanol') THEN + mm(i) = 46.069 + parame(i,1) = mm(i)* .0517195521 + parame(i,2) = 3.17705595 + parame(i,3) = 198.236542 + nhb_typ(i) = 2 + nhb_no(i,1) = 1 ! no. of sites of type 1 + nhb_no(i,2) = 1 ! no. of sites of type 2 + eps_hb(i,i,1,2)= 2653.38367 + eps_hb(i,i,2,1)= 2653.38367 + eps_hb(i,i,1,1)= 0.0 + eps_hb(i,i,2,2)= 0.0 + kap_hb(i,i) = .0323840159 + IF (pol >= 1) mm(i) = 46.0690000000000 + IF (pol >= 1) parame(i,1) = mm(i)* 4.753626908781145E-002 ! =2.18994838060639 + IF (pol >= 1) parame(i,2) = 3.30120000000000 + IF (pol >= 1) parame(i,3) = 209.824555801706 + IF (pol >= 1) nhb_typ(i) = 2 + IF (pol >= 1) nhb_no(i,1) = 1 + IF (pol >= 1) nhb_no(i,2) = 1 + IF (pol >= 1) eps_hb(i,i,1,2)= 2584.53116785767 + IF (pol >= 1) eps_hb(i,i,2,1)= 2584.53116785767 + IF (pol >= 1) eps_hb(i,i,1,1)= 0.0 + IF (pol >= 1) eps_hb(i,i,2,2)= 0.0 + IF (pol >= 1) kap_hb(i,i) = 2.349382956935725E-002 + IF (pol >= 1) parame(i,6) = 1.69000000000000 + ! mm(i) = 46.0690000000000 + ! parame(i,1) = mm(i)* 5.117957752785066E-002 ! =2.357791957 + ! parame(i,2) = 3.24027031244304 + ! parame(i,3) = 175.657110615456 + ! nhb_typ(i) = 2 + ! nhb_no(i,1) = 1 + ! nhb_no(i,2) = 1 + ! eps_hb(i,i,1,2)= 2273.62670516146 + ! eps_hb(i,i,2,1)= 2273.62670516146 + ! eps_hb(i,i,1,1)= 0.0 + ! eps_hb(i,i,2,2)= 0.0 + ! kap_hb(i,i) = 7.030279197039477E-002 + ! parame(i,6) = 1.69000000000000 + ! parame(i,7) = 3.63701294195013 + IF (pol == 2) mm(i) = 46.0690000000000 + IF (pol == 2) parame(i,1) = mm(i)* 4.733436280008321E-002 ! =2.18064676 + IF (pol == 2) parame(i,2) = 3.31260000000000 + IF (pol == 2) parame(i,3) = 207.594119926613 + IF (pol == 2) nhb_typ(i) = 2 + IF (pol == 2) nhb_no(i,1) = 1 + IF (pol == 2) nhb_no(i,2) = 1 + IF (pol == 2) eps_hb(i,i,1,2)= 2589.68311382661 + IF (pol == 2) eps_hb(i,i,2,1)= 2589.68311382661 + IF (pol == 2) eps_hb(i,i,1,1)= 0.0 + IF (pol == 2) eps_hb(i,i,2,2)= 0.0 + IF (pol == 2) kap_hb(i,i) = 2.132561218631547E-002 + IF (pol == 2) parame(i,6) = 1.69000000000000 + IF (pol == 2) parame(i,7) = 0.0 + IF (pol == 2) parame(i,11)= 5.11000000000000 + ELSE IF (compna(i) == '1-propanol') THEN + mm(i) = 60.096 + parame(i,1) = mm(i)* .0499154461 + parame(i,2) = 3.25221234 + parame(i,3) = 233.396705 + nhb_typ(i) = 2 + nhb_no(i,1) = 1 ! no. of sites of type 1 + nhb_no(i,2) = 1 ! no. of sites of type 2 + eps_hb(i,i,1,2)= 2276.77867 + eps_hb(i,i,2,1)= 2276.77867 + eps_hb(i,i,1,1)= 0.0 + eps_hb(i,i,2,2)= 0.0 + kap_hb(i,i) = .0152683094 + ELSE IF (compna(i) == '1-butanol') THEN + mm(i) = 74.123 + parame(i,1) = mm(i)* .0341065046 + parame(i,2) = 3.72361538 + parame(i,3) = 269.798048 + nhb_typ(i) = 2 + nhb_no(i,1) = 1 ! no. of sites of type 1 + nhb_no(i,2) = 1 ! no. of sites of type 2 + eps_hb(i,i,1,2)= 2661.37119 + eps_hb(i,i,2,1)= 2661.37119 + eps_hb(i,i,1,1)= 0.0 + eps_hb(i,i,2,2)= 0.0 + kap_hb(i,i) = .00489087833 + mm(i) = 74.1230000000000 + parame(i,1) = mm(i)* 3.329202420547412E-002 ! =2.46770471018236 + parame(i,2) = 3.76179376417092 + parame(i,3) = 270.237284242002 + nhb_typ(i) = 2 + nhb_no(i,1) = 1 + nhb_no(i,2) = 1 + eps_hb(i,i,1,2)= 2669.28754983370 + eps_hb(i,i,2,1)= 2669.28754983370 + eps_hb(i,i,1,1)= 0.0 + eps_hb(i,i,2,2)= 0.0 + kap_hb(i,i) = 4.855584122733399E-003 + parame(i,6) = 1.66000000000000 + ELSE IF (compna(i) == '1-pentanol') THEN + mm(i) = 88.15 ! PC-SAFT + parame(i,1) = mm(i)* .041134139 + parame(i,2) = 3.45079143 + parame(i,3) = 247.278748 + nhb_typ(i) = 2 + nhb_no(i,1) = 1 ! no. of sites of type 1 + nhb_no(i,2) = 1 ! no. of sites of type 2 + eps_hb(i,i,1,2)= 2252.09237 + eps_hb(i,i,2,1)= 2252.09237 + eps_hb(i,i,1,1)= 0.0 + eps_hb(i,i,2,2)= 0.0 + kap_hb(i,i) = .0103189939 + IF (pol >= 1) mm(i) = 88.1500000000000 ! PCP-SAFT + IF (pol >= 1) parame(i,1) = mm(i)* 4.138903382168521E-002 ! =3.64844333138155 + IF (pol >= 1) parame(i,2) = 3.44250118689142 + IF (pol >= 1) parame(i,3) = 246.078034174947 + IF (pol >= 1) nhb_typ(i) = 2 + IF (pol >= 1) nhb_no(i,1) = 1 + IF (pol >= 1) nhb_no(i,2) = 1 + IF (pol >= 1) eps_hb(i,i,1,2)= 2236.72830142446 + IF (pol >= 1) eps_hb(i,i,2,1)= 2236.72830142446 + IF (pol >= 1) eps_hb(i,i,1,1)= 0.0 + IF (pol >= 1) eps_hb(i,i,2,2)= 0.0 + IF (pol >= 1) kap_hb(i,i) = 1.040067895187016E-002 + IF (pol >= 1) parame(i,6) = 1.70000000000000 + IF (pol == 2) mm(i) = 88.1500000000000 ! PCIP-SAFT + IF (pol == 2) parame(i,1) = mm(i)* 4.161521814399406E-002 ! =3.66838147939308 + IF (pol == 2) parame(i,2) = 3.43496654431777 + IF (pol == 2) parame(i,3) = 244.177313808431 + IF (pol == 2) nhb_typ(i) = 2 + IF (pol == 2) nhb_no(i,1) = 1 + IF (pol == 2) nhb_no(i,2) = 1 + IF (pol == 2) eps_hb(i,i,1,2)= 2241.27880639096 + IF (pol == 2) eps_hb(i,i,2,1)= 2241.27880639096 + IF (pol == 2) eps_hb(i,i,1,1)= 0.0 + IF (pol == 2) eps_hb(i,i,2,2)= 0.0 + IF (pol == 2) kap_hb(i,i) = 1.049516309928397E-002 + IF (pol == 2) parame(i,6) = 1.70000000000000 + IF (pol == 2) parame(i,11)= 10.8000000000000 + ELSE IF (compna(i) == '1-octanol') THEN + mm(i) = 130.23 + parame(i,1) = mm(i)* .0334446084 + parame(i,2) = 3.714535 + parame(i,3) = 262.740637 + nhb_typ(i) = 2 + nhb_no(i,1) = 1 ! no. of sites of type 1 + nhb_no(i,2) = 1 ! no. of sites of type 2 + eps_hb(i,i,1,2)= 2754.77272 + eps_hb(i,i,2,1)= 2754.77272 + eps_hb(i,i,1,1)= 0.0 + eps_hb(i,i,2,2)= 0.0 + kap_hb(i,i) = .00219656803 + ELSE IF (compna(i) == '1-nonanol') THEN + mm(i) = 144.257 + parame(i,1) = mm(i)* .0324692669 + parame(i,2) = 3.72924286 + parame(i,3) = 263.636673 + nhb_typ(i) = 2 + nhb_no(i,1) = 1 ! no. of sites of type 1 + nhb_no(i,2) = 1 ! no. of sites of type 2 + eps_hb(i,i,1,2)= 2941.9231 + eps_hb(i,i,2,1)= 2941.9231 + eps_hb(i,i,1,1)= 0.0 + eps_hb(i,i,2,2)= 0.0 + kap_hb(i,i) = .00142696883 + ELSE IF (compna(i) == '2-propanol') THEN + mm(i) = 60.096 + parame(i,1) = mm(i)* .0514663133 + parame(i,2) = 3.20845858 + parame(i,3) = 208.420809 + nhb_typ(i) = 2 + nhb_no(i,1) = 1 ! no. of sites of type 1 + nhb_no(i,2) = 1 ! no. of sites of type 2 + eps_hb(i,i,1,2)= 2253.91064 + eps_hb(i,i,2,1)= 2253.91064 + eps_hb(i,i,1,1)= 0.0 + eps_hb(i,i,2,2)= 0.0 + kap_hb(i,i) = .0246746934 + ELSE IF (compna(i) == '2-methyl-2-butanol') THEN + mm(i) = 88.15 + parame(i,1) = mm(i)* .0289135026 + parame(i,2) = 3.90526707 + parame(i,3) = 266.011828 + nhb_typ(i) = 2 + nhb_no(i,1) = 1 ! no. of sites of type 1 + nhb_no(i,2) = 1 ! no. of sites of type 2 + eps_hb(i,i,1,2)= 2618.80124 + eps_hb(i,i,2,1)= 2618.80124 + eps_hb(i,i,1,1)= 0.0 + eps_hb(i,i,2,2)= 0.0 + kap_hb(i,i) = .00186263367 + ELSE IF (compna(i) == 'acetic-acid') THEN + mm(i) = 60.053 + parame(i,1) = mm(i)* .0227076949 + parame(i,2) = 3.79651163 + parame(i,3) = 199.225066 + nhb_typ(i) = 2 + nhb_no(i,1) = 1 ! no. of sites of type 1 + nhb_no(i,2) = 1 ! no. of sites of type 2 + eps_hb(i,i,1,2)= 3092.40109 + eps_hb(i,i,2,1)= 3092.40109 + eps_hb(i,i,1,1)= 0.0 + eps_hb(i,i,2,2)= 0.0 + kap_hb(i,i) = .0870093874 + + + mm(i) = 60.053 + parame(i,1) = mm(i)* .0181797646 + parame(i,2) = 4.13711044 + parame(i,3) = 207.552969 + nhb_typ(i) = 2 + nhb_no(i,1) = 1 ! no. of sites of type 1 + nhb_no(i,2) = 1 ! no. of sites of type 2 + eps_hb(i,i,1,2)= 3198.84362 + eps_hb(i,i,2,1)= 3198.84362 + eps_hb(i,i,1,1)= 0.0 + eps_hb(i,i,2,2)= 0.0 + kap_hb(i,i) = .0586552968 + +! mit gesetztem Dipol-Moment + mm(i) = 60.0530000000000 + parame(i,1) = mm(i)* 1.736420143637533E-002 + parame(i,2) = 4.25220708070687 + parame(i,3) = 190.957247854820 + parame(i,6) = 3.50000000000000 + nhb_typ(i) = 2 + nhb_no(i,1) = 1 ! no. of sites of type 1 + nhb_no(i,2) = 1 ! no. of sites of type 2 + eps_hb(i,i,1,2)= 3096.36190957945 + eps_hb(i,i,2,1)= 3096.36190957945 + eps_hb(i,i,1,1)= 0.0 + eps_hb(i,i,2,2)= 0.0 + kap_hb(i,i) = 6.154307094782551E-002 + + ELSE IF (compna(i) == 'propionic-acid') THEN + mm(i) = 74.0800000000000 + parame(i,1) = mm(i)* 2.359519915877884E-002 + parame(i,2) = 3.99339224153844 + parame(i,3) = 295.947729838532 + nhb_typ(i) = 2 + nhb_no(i,1) = 1 ! no. of sites of type 1 + nhb_no(i,2) = 1 ! no. of sites of type 2 + eps_hb(i,i,1,2)= 2668.97826430874 + eps_hb(i,i,2,1)= 2668.97826430874 + eps_hb(i,i,1,1)= 0.0 + eps_hb(i,i,2,2)= 0.0 + kap_hb(i,i) = 3.660242292423115E-002 + ELSE IF (compna(i) == 'acrylic-acid') THEN + mm(i) = 72.0636 + parame(i,1) = mm(i)* .0430585424 + parame(i,2) = 3.0545415 + parame(i,3) = 164.115604 + nhb_typ(i) = 2 + nhb_no(i,1) = 1 ! no. of sites of type 1 + nhb_no(i,2) = 1 ! no. of sites of type 2 + eps_hb(i,i,1,2)= 3065.40667 + eps_hb(i,i,2,1)= 3065.40667 + eps_hb(i,i,1,1)= 0.0 + eps_hb(i,i,2,2)= 0.0 + kap_hb(i,i) = .336261669 + ELSE IF (compna(i) == 'caproic-acid') THEN + mm(i) = 116.16 + parame(i,1) = 5.87151 + parame(i,2) = 3.0694697 + parame(i,3) = 241.4569 + nhb_typ(i) = 1 + eps_hb(i,i,1,1)= 2871.37 + kap_hb(i,i) = 3.411613D-3 + ELSE IF (compna(i) == 'aniline') THEN + mm(i) = 93.13 + parame(i,1) = mm(i)* .0285695992 + parame(i,2) = 3.70214085 + parame(i,3) = 335.471062 + nhb_typ(i) = 2 + nhb_no(i,1) = 1 ! no. of sites of type 1 + nhb_no(i,2) = 1 ! no. of sites of type 2 + eps_hb(i,i,1,2)= 1351.64234 + eps_hb(i,i,2,1)= 1351.64234 + eps_hb(i,i,1,1)= 0.0 + eps_hb(i,i,2,2)= 0.0 + kap_hb(i,i) = .0748830615 + + mm(i) = 93.1300000000000 + parame(i,1) = mm(i)* 2.834372610192228E-002 ! =2.63965121187202 + parame(i,2) = 3.71326867619433 + parame(i,3) = 332.253796842009 + nhb_typ(i) = 2 + nhb_no(i,1) = 1 + nhb_no(i,2) = 1 + eps_hb(i,i,1,2)= 1392.14266886674 + eps_hb(i,i,2,1)= 1392.14266886674 + eps_hb(i,i,1,1)= 0.0 + eps_hb(i,i,2,2)= 0.0 + kap_hb(i,i) = 7.424612087328866E-002 + parame(i,6) = 1.55000000000000 + IF (pol == 2) parame(i,11)= 12.1000000000000 + ELSE IF (compna(i) == 'HF') THEN + ! mm(i) = 20.006 ! PC-SAFT + ! parame(i,1) = 0.87731 + ! parame(i,2) = 3.0006 + ! parame(i,3) = 112.24 + ! nhb_typ(i) = 2 + ! nhb_no(i,1) = 1 + ! nhb_no(i,2) = 1 + ! eps_hb(i,i,1,2)= 2208.22 + ! eps_hb(i,i,2,1)= 2208.22 + ! eps_hb(i,i,1,1)= 0.0 + ! eps_hb(i,i,2,2)= 0.0 + ! kap_hb(i,i) = 0.71265 + mm(i) = 20.0060000000000 ! PCP-SAFT + parame(i,1) = 1.00030000000000 + parame(i,2) = 3.17603622195029 + parame(i,3) = 331.133373208282 + nhb_typ(i) = 2 + nhb_no(i,1) = 1 + nhb_no(i,2) = 1 + eps_hb(i,i,1,2)= 348.251433080979 + eps_hb(i,i,2,1)= 348.251433080979 + eps_hb(i,i,1,1)= 0.0 + eps_hb(i,i,2,2)= 0.0 + kap_hb(i,i) = 2.868887975449893E-002 + parame(i,6) = 1.82600000000000 + ELSE IF (compna(i) == 'HCl') THEN + ! mm(i) = 36.4610000000000 + ! parame(i,1) = mm(i)* 3.922046741026943E-002 + ! parame(i,2) = 3.08731180727493 + ! parame(i,3) = 203.898845304388 + ! nhb_typ(i) = 2 + ! nhb_no(i,1) = 1 + ! nhb_no(i,2) = 1 + ! eps_hb(i,i,1,2)= 245.462773177367 + ! eps_hb(i,i,2,1)= 245.462773177367 + ! eps_hb(i,i,1,1)= 0.0 + ! eps_hb(i,i,2,2)= 0.0 + ! kap_hb(i,i) = 0.256454187330899 + mm(i) = 36.461 ! PCIP-SAFT + parame(i,1) = 1.6335 + parame(i,2) = 2.9066 + parame(i,3) = 190.17 + parame(i,6) = 1.1086 + IF (pol == 2) parame(i,11)= 2.63 + ELSE IF (compna(i) == 'gen') THEN + mm(i) = 302.0 + parame(i,1) = 8.7563 + parame(i,2) = 3.604243 + parame(i,3) = 255.6434 + nhb_typ(i) = 2 + nhb_no(i,1) = 1 ! no. of sites of type 1 + nhb_no(i,2) = 1 ! no. of sites of type 2 + eps_hb(i,i,1,2)= 0.0 + eps_hb(i,i,2,1)= 0.0 + eps_hb(i,i,1,1)= 0.0 + eps_hb(i,i,2,2)= 0.0 + kap_hb(i,i) = 0.02 + ELSE IF (compna(i) == 'h2o') THEN + mm(i) = 18.015 + parame(i,1) = mm(i)* .05915 + parame(i,2) = 3.00068335 + parame(i,3) = 366.512135 + nhb_typ(i) = 2 + nhb_no(i,1) = 1 ! no. of sites of type 1 + nhb_no(i,2) = 1 ! no. of sites of type 2 + eps_hb(i,i,1,2)= 2500.6706 + eps_hb(i,i,2,1)= 2500.6706 + eps_hb(i,i,1,1)= 0.0 + eps_hb(i,i,2,2)= 0.0 + kap_hb(i,i) = .0348679836 + + ! mm(i) = 18.015 + ! parame(i,1) = 1.706 + ! parame(i,2) = 2.429 + ! parame(i,3) = 242.19 + ! nhb_typ(i) = 2 + ! nhb_no(i,1) = 1 ! no. of sites of type 1 + ! nhb_no(i,2) = 1 ! no. of sites of type 2 + ! eps_hb(i,i,1,2)= 2644.2 + ! eps_hb(i,i,2,1)= 2644.2 + ! eps_hb(i,i,1,1)= 0.0 + ! eps_hb(i,i,2,2)= 0.0 + ! kap_hb(i,i) = 0.153 + + ! mm(i) = 18.015 + ! parame(i,1) = mm(i)* .0588185709 + ! parame(i,2) = 3.02483704 + ! parame(i,3) = 382.086672 + !c! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! + ! nhb_typ(i) = 2 + ! nhb_no(i,1) = 1 ! no. of sites of type 1 + ! nhb_no(i,2) = 2 ! no. of sites of type 2 + !c! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! + ! eps_hb(i,i,1,2)= 2442.49782 + ! eps_hb(i,i,2,1)= 2442.49782 + ! eps_hb(i,i,1,1)=0.0 + ! eps_hb(i,i,2,2)=0.0 + ! kap_hb(i,i) = .0303754635 + + ! mit gefittetem Dipol-Moment - Haarlem-night + ! mm(i) = 18.015 + ! parame(i,1) = mm(i)* 7.0037160952278E-2 + ! parame(i,2) = 2.79276650240763 + ! parame(i,3) = 270.970053834558 + ! nhb_typ(i) = 2 + ! nhb_no(i,1) = 1 ! no. of sites of type 1 + ! nhb_no(i,2) = 1 ! no. of sites of type 2 + ! eps_hb(i,i,1,2)= 1427.8287 + ! eps_hb(i,i,2,1)= 1427.8287 + ! eps_hb(i,i,1,1)=0.0 + ! eps_hb(i,i,2,2)=0.0 + ! kap_hb(i,i) = 4.335167238E-2 + ! parame(i,6) = 3.968686856378 + + IF (pol >= 1) mm(i) = 18.015 ! PCP-SAFT + IF (pol >= 1) parame(i,1) = 0.922688825223317 + IF (pol >= 1) parame(i,2) = 3.17562052023944 + IF (pol >= 1) parame(i,3) = 388.462197714696 + IF (pol >= 1) nhb_typ(i) = 2 + IF (pol >= 1) nhb_no(i,1) = 1 + IF (pol >= 1) nhb_no(i,2) = 1 + IF (pol >= 1) eps_hb(i,i,1,2)= 2000.67247409031 + IF (pol >= 1) eps_hb(i,i,2,1)= 2000.67247409031 + IF (pol >= 1) eps_hb(i,i,1,1)= 0.0 + IF (pol >= 1) eps_hb(i,i,2,2)= 0.0 + IF (pol >= 1) kap_hb(i,i) = 2.040614952751225E-003 + IF (pol >= 1) parame(i,6) = 1.85500000000000 + IF (pol >= 1) parame(i,7) = 2.00000000000000 + ! IF (pol.EQ.2) mm(i) = 18.015 ! PCIP-SAFT - DQ with my=my_RPT + ! IF (pol.EQ.2) parame(i,1) = 1.0 + ! IF (pol.EQ.2) parame(i,2) = 3.14540664928026 + ! IF (pol.EQ.2) parame(i,3) = 320.283823615925 + ! IF (pol.EQ.2) nhb_typ(i) = 2 + ! IF (pol.EQ.2) nhb_no(i,1) = 2 + ! IF (pol.EQ.2) nhb_no(i,2) = 2 + ! IF (pol.EQ.2) eps_hb(i,i,1,2)= 1335.72887678032 + ! IF (pol.EQ.2) eps_hb(i,i,2,1)= 1335.72887678032 + ! IF (pol.EQ.2) eps_hb(i,i,1,1)= 0.0 + ! IF (pol.EQ.2) eps_hb(i,i,2,2)= 0.0 + ! IF (pol.EQ.2) kap_hb(i,i) = 4.162619960844732E-003 + ! IF (pol.EQ.2) parame(i,6) = 1.85500000000000 + ! IF (pol.EQ.2) parame(i,7) = 2.00000000000000 + ! IF (pol.EQ.2) parame(i,11)= 1.45000000000000 + ! mm(i) = 18.0150000000000 + ! parame(i,1) = 1.0 + ! parame(i,2) = 3.11505069470915 + ! parame(i,3) = 320.991387913502 + ! nhb_typ(i) = 2 + ! nhb_no(i,1) = 1 + ! nhb_no(i,2) = 1 + ! eps_hb(i,i,1,2)= 2037.76329812542 + ! eps_hb(i,i,2,1)= 2037.76329812542 + ! eps_hb(i,i,1,1)= 0.0 + ! eps_hb(i,i,2,2)= 0.0 + ! kap_hb(i,i) = 3.763148982832804E-003 + ! parame(i,6) = 1.85500000000000 + ! parame(i,7) = 2.00000000000000 + ! IF (pol.EQ.2) parame(i,11)= 1.45000000000000 + IF (pol == 2) mm(i) = 18.015 ! PCIP-SAFT - DQ with my=my_0 + IF (pol == 2) parame(i,1) = 1.0 + IF (pol == 2) parame(i,2) = 3.11574491885322 + IF (pol == 2) parame(i,3) = 322.699984283499 + IF (pol == 2) nhb_typ(i) = 2 + IF (pol == 2) nhb_no(i,1) = 1 + IF (pol == 2) nhb_no(i,2) = 1 + IF (pol == 2) eps_hb(i,i,1,2)= 2033.87777692450 + IF (pol == 2) eps_hb(i,i,2,1)= 2033.87777692450 + IF (pol == 2) eps_hb(i,i,1,1)= 0.0 + IF (pol == 2) eps_hb(i,i,2,2)= 0.0 + IF (pol == 2) kap_hb(i,i) = 3.815764667176484E-003 + IF (pol == 2) parame(i,6) = 1.85500000000000 + IF (pol == 2) parame(i,7) = 2.00000000000000 + IF (pol == 2) parame(i,11)= 1.45000000000000 + ! mm(i) = 18.015 ! Dortmund + ! parame(i,1) = 0.11065254*mm(i) + ! parame(i,2) = 2.36393615 + ! parame(i,3) = 300.288589 + ! nhb_typ(i) = 2 + ! nhb_no(i,1) = 1 + ! nhb_no(i,2) = 1 + ! eps_hb(i,i,1,2)= 1193.45585 + ! eps_hb(i,i,2,1)= 1193.45585 + ! eps_hb(i,i,1,1)= 0.0 + ! eps_hb(i,i,2,2)= 0.0 + ! kap_hb(i,i) = 0.091203519 + ! parame(i,6) = 1.8546 + ! parame(i,7) = 0.0 + ! parame(i,11)= 0.0 + ELSE IF (compna(i) == 'MBBA') THEN + mm(i) = 267.37 + parame(i,1) = 12.194 + parame(i,2) = 3.064 + parame(i,3) = 270.7 + e_lc(i,i) = 13.7 !Hino & Prausnitz + s_lc(i,i) = 0.176 !Hino & Prausnitz + ELSE IF (compna(i) == 'PCH5') THEN + mm(i) = 255.41 + parame(i,1) = 11.6 + parame(i,2) = 3.2 + parame(i,3) = 270.7 + ! E_LC(i,i) = 16.7 !Hino & Prausnitz + ! S_LC(i,i) = 0.176 !Hino & Prausnitz + e_lc(i,i) = 8.95 + s_lc(i,i) = 0.2 + + ! mm(i) = 255.41 + ! parame(i,1) = 11.6 + ! parame(i,2) = 3.2 + ! parame(i,3) = 290.7 + ! E_LC(i,i) = 7.18 + ! S_LC(i,i) = 0.2 + + ELSE IF (compna(i) == 'Li') THEN + mm(i) = 6.9 + parame(i,1) = 1.0 + parame(i,2) = 1.4 + parame(i,3) = 96.83 + parame(i,10)= 1.0 +! the self-association is set to zero in routine F_EXPL for ions + ! nhb_typ(i) = 1 + ! nhb_no(i,1) = 3 ! no. of sites of type 1 + ! eps_hb(i,i,1,1)= 2000.0 + ! kap_hb(i,i) = 0.008 + ELSE IF (compna(i) == 'Na') THEN + mm(i) = 23.0 + parame(i,1) = 1.0 + parame(i,2) = 1.9 + parame(i,3) = 147.38 + parame(i,10)= 1.0 +! the self-association is set to zero in routine F_EXPL for ions + nhb_typ(i) = 1 + nhb_no(i,1) = 3 ! no. of sites of type 1 + eps_hb(i,i,1,1)= 8946.28257 ! 25C, 3 sites, dG-ref-1 + kap_hb(i,i) = 0.001648933 + ELSE IF (compna(i) == 'Ka') THEN + mm(i) = 39.1 + parame(i,1) = 1.0 + parame(i,2) = 2.66 + parame(i,3) = 221.44 + parame(i,10)= 1.0 + ! the self-association is set to zero in routine F_EXPL for ions + nhb_typ(i) = 1 + nhb_no(i,1) = 3 ! no. of sites of type 1 + eps_hb(i,i,1,1)= 3118.336216 ! 25C, 3 sites, dG-ref-1 + kap_hb(i,i) = 0.00200559 + ELSE IF (compna(i) == 'Cs') THEN + mm(i) = 132.9 + parame(i,1) = 1.0 + parame(i,2) = 3.38 + parame(i,3) = 523.28 + parame(i,10)= 1.0 + ! the self-association is set to zero in routine F_EXPL for ions + ! nhb_typ(i) = 1 + ! nhb_no(i,1) = 3 ! no. of sites of type 1 + ! eps_hb(i,i,1,1)= 2000.0 + ! kap_hb(i,i) = 0.00200559 + ELSE IF (compna(i) == 'Cl') THEN + mm(i) = 35.5 + parame(i,1) = 1.0 + parame(i,2) = 3.62 + parame(i,3) = 225.44 + parame(i,10)= -1.0 +! the self-association is set to zero in routine F_EXPL for ions + nhb_typ(i) = 1 + nhb_no(i,1) = 4 ! no. of sites of type 1 + eps_hb(i,i,1,1)= 6744.12509 ! 25C, 3 sites, dG-ref-1 + kap_hb(i,i) = 0.00155252 + ELSE IF (compna(i) == 'Br') THEN + mm(i) = 79.9 + parame(i,1) = 1.0 + parame(i,2) = 3.9 + parame(i,3) = 330.82 + parame(i,10)= -1.0 +! the self-association is set to zero in routine F_EXPL for ions + nhb_typ(i) = 1 + nhb_no(i,1) = 4 ! no. of sites of type 1 + eps_hb(i,i,1,1)= 4516.033227 ! 25C, 3 sites, dG-ref-1 + kap_hb(i,i) = 0.00200559 + ELSE IF (compna(i) == 'Io') THEN + mm(i) = 126.9 + parame(i,1) = 1.0 + parame(i,2) = 4.4 + parame(i,3) = 380.60 + parame(i,10)= -1.0 +! the self-association is set to zero in routine F_EXPL for ions + nhb_typ(i) = 1 + nhb_no(i,1) = 4 ! no. of sites of type 1 + eps_hb(i,i,1,1)= 1631.203342 ! 25C, 3 sites, dG-ref-1 + kap_hb(i,i) = 0.00200559 + ELSE IF (compna(i) == 'OH') THEN + mm(i) = 17.0 + parame(i,1) = 1.0 + parame(i,2) = 3.06 + parame(i,3) = 217.26 + parame(i,10)= -1.0 + ! the self-association is set to zero in routine F_EXPL for ions + nhb_typ(i) = 1 + nhb_no(i,1) = 4 ! no. of sites of type 1 + eps_hb(i,i,1,1)= 14118.68089 ! 25C, 3 sites, dG-ref-1 + kap_hb(i,i) = 0.00200559 + ELSE IF (compna(i) == 'NO3') THEN + mm(i) = 62.0 + parame(i,1) = 1.0 + parame(i,2) = 4.12 + parame(i,3) = 239.48 + parame(i,10)= -1.0 + ! the self-association is set to zero in routine F_EXPL for ions + ! nhb_typ(i) = 1 + ! nhb_no(i,1) = 4 ! no. of sites of type 1 + ! eps_hb(i,i,1,1)= 2000.0 + ! kap_hb(i,i) = 0.00200559 + ELSE IF (compna(i) == 'bf4') THEN + mm(i) = 86.8 + parame(i,1) = 1.0 + parame(i,2) = 4.51 ! *0.85 + parame(i,3) = 164.7 + parame(i,10)= -1.0 + ELSE IF (compna(i) == 'pf6') THEN + mm(i) = 145.0 + parame(i,1) = 1.0 + parame(i,2) = 5.06 + parame(i,3) = 224.9 + parame(i,10)= -1.0 + ELSE IF (compna(i) == 'emim') THEN + mm(i) = 111.16 + parame(i,1) = 3.11 + parame(i,2) = 4.0 + parame(i,3) = 250.0 + parame(i,10)= 1.0 + ELSE IF (compna(i) == 'bmim') THEN + mm(i) = 139.21 + ! parame(i,1) = 2.81 + ! parame(i,2) = 3.5 + parame(i,1) = 3.81 + parame(i,2) = 4.0 + parame(i,3) = 250.0 + parame(i,6) = 0.0 + parame(i,10)= 1.0 + ELSE IF (compna(i) == 'hmim') THEN + mm(i) = 167.27 + parame(i,1) = 4.53 + parame(i,2) = 4.0 + parame(i,3) = 250.0 + parame(i,10)= 1.0 + ELSE IF (compna(i) == 'omim') THEN + mm(i) = 195.32 + parame(i,1) = 5.30 + parame(i,2) = 4.0 + parame(i,3) = 250.0 + parame(i,10)= 1.0 + ELSE IF (compna(i) == 'sw') THEN + parame(i,1) = 1.0 + parame(i,2) = 1.0 + parame(i,3) = 100.0 + parame(i,4) = 0.0 + parame(i,5) = 0.0 + mm(i) = 1.0 + parame(i,6) = 0.1175015839*2.0 + ! use Temp. in Kelvin in the input-file. For dimensionless quantities + ! (P*=P*sig**3/epsilon, T*=T*kBol/epsilon, rho*=rho*sig**3) calculate + ! P* = P *1E5 * (1.e-10)^3 / (100*8.31441/6.022045E+23) + ! T* = (T+273.15)/100 + ! for rho* go to utilities.f (subroutine SI_DENS) and write + ! density(ph) = dense(ph)*6.0/PI + ELSE IF (compna(i) == 'c8-sim') THEN + mm(i) = 114.231 + parame(i,1) = mm(i)* 4.095944E-2 ! =4.67883774717337 + parame(i,2) = 3.501769 + parame(i,3) = 163.8606 + ! mm(i) = 114.231000000000 + ! parame(i,1) = mm(i)* 3.547001476437745E-002 ! =4.05177525654960 + ! parame(i,2) = 3.70988567055814 + ! parame(i,3) = 192.787548176343 + ELSE IF (compna(i) == 'argon_ge') THEN + mm(i) = 39.948 + parame(i,1) = mm(i)*0.030327 + parame(i,2) = 3.149910 + parame(i,3) = 100.188975 + ELSE IF (compna(i) == 'argon_ge2') THEN + mm(i) = 39.948 + parame(i,1) = mm(i)*0.030327 + parame(i,2) = 3.149910 + parame(i,3) = 0.8*100.188975 + ELSE + WRITE (*,*) ' pure component parameters missing for ',compna(i) + STOP + END IF + + IF (pol == 2.AND.parame(i,11) == 0.0) THEN + WRITE (*,*) ' polarizability missing for comp. ',compna(i) + STOP + END IF + + IF (nhb_typ(i) /= 0) THEN + parame(i,12) = DBLE(nhb_typ(i)) + parame(i,13) = kap_hb(i,i) + no = 0 + DO j=1,nhb_typ(i) + DO k=1,nhb_typ(i) + parame(i,(14+no))=eps_hb(i,i,j,k) + no=no+1 + END DO + END DO + DO j=1,nhb_typ(i) + parame(i,(14+no))=DBLE(nhb_no(i,j)) + no=no+1 + END DO + ELSE + DO k=12,25 + parame(i,k)=0.0 + END DO + END IF + +END DO + + +DO i = 1,ncomp + DO j = 1,ncomp + IF (compna(i) == 'ps'.AND.compna(j) == 'cyclohexane')THEN + kij(i,j) = 0.0075 + ELSE IF(compna(i) == 'peva'.AND.compna(j) == 'ethylene')THEN +! -- 0 Gew.% VA------------- + ! kij(i,j) = 0.039 +! -- 7.5 Gew.% VA------------- + ! kij(i,j) = 0.0377325 + ! kij(i,j) = 0.0374867 +! ---12.7 Gew.% VA------------ + ! kij(i,j) = 0.036854 + ! kij(i,j) = 0.0366508 +! ---27.3 Gew.% VA------------ + ! kij(i,j) = 0.034386 + ! kij(i,j) = 0.0352375 +! ---31.8 Gew.% VA------------ + kij(i,j) = 0.033626 + ! kij(i,j) = 0.0350795 +! ---42.7 Gew.% VA------------ + ! kij(i,j) = 0.031784 + ! kij(i,j) = 0.035239 + ELSE IF(compna(i) == 'gen'.AND.compna(j) == 'h2o')THEN + kij(i,j) = - 0.2 + ELSE IF(compna(i) == 'peva'.AND.compna(j) == 'vinylacetate')THEN + kij(i,j) = 0.019 + ELSE IF(compna(i) == 'ps'.AND.compna(j) == 'co2') THEN + IF ( pol == 0 ) kij(i,j) = 0.195 + IF ( pol == 1 ) kij(i,j) = 0.06 + ELSE IF(compna(i) == 'ps'.AND.compna(j) == 'acetone') THEN + kij(i,j) = 0.021 + ELSE IF(compna(i) == 'ps'.AND.compna(j) == 'hexane') THEN + kij(i,j) = 0.012 + ELSE IF(compna(i) == 'ps'.AND.compna(j) == 'pentane')THEN + kij(i,j) = 0.005 + ELSE IF(compna(i) == 'ps'.AND.compna(j) == 'methylcyclohexane') THEN + kij(i,j) = 0.0073 + ELSE IF(compna(i) == 'ps'.AND.compna(j) == 'ethylbenzene')THEN + kij(i,j) = 0.008 + ELSE IF(compna(i) == 'pe'.AND.compna(j) == 'co2') THEN + ! kij(i,j) = 0.181 + kij(i,j) = 0.088 + ELSE IF(compna(i) == 'pe'.AND.compna(j) == 'propane') THEN + kij(i,j) = 0.0206 + ELSE IF(compna(i) == 'pe'.AND.compna(j) == 'butane') THEN + kij(i,j) = 0.01 + ELSE IF(compna(i) == 'methane'.AND.compna(j) == 'argon') THEN + kij(i,j) = 0.01 + ELSE IF(compna(i) == 'methane'.AND.compna(j) == 'butane') THEN + kij(i,j) = 0.026 + ELSE IF(compna(i) == 'pe'.AND.compna(j) == 'pentane') THEN + ! kij(i,j) = -0.0195 + ELSE IF(compna(i) == 'pe'.AND.compna(j) == 'hexane') THEN + ! kij(i,j) = 0.008 + kij(i,j) = 0.004 + ELSE IF(compna(i) == 'pe'.AND.compna(j) == 'ethylene') THEN + kij(i,j) = 0.0404 + ! kij(i,j) = 0.0423 + ! kij(i,j) = 0.044 + ELSE IF(compna(i) == 'pe'.AND.compna(j) == 'cyclohexane') THEN + kij(i,j) = -0.1 + ELSE IF(compna(i) == 'ldpe'.AND.compna(j) == 'cyclopentane')THEN + kij(i,j) = -0.016 + ELSE IF(compna(i) == 'pp'.AND.compna(j) == 'propane') THEN + kij(i,j) = 0.0242 + ELSE IF(compna(i) == 'pp'.AND.compna(j) == 'pentane') THEN + kij(i,j) = 0.0137583176 + ELSE IF(compna(i) == 'pp'.AND.compna(j) == 'co2') THEN + kij(i,j) = 0.1767 ! without quadrupol-term + kij(i,j) = 0.063 ! with quadrupol-term + ELSE IF(compna(i) == 'pba'.AND.compna(j) == 'ethylene') THEN + kij(i,j) = 0.026 + ELSE IF(compna(i) == 'decane'.AND.compna(j) == 'ethane') THEN + kij(i,j) = 0.017 + ELSE IF(compna(i) == 'n2'.AND.compna(j) == 'co2') THEN + ! kij(i,j) = -0.04 + ELSE IF(compna(i) == 'methane'.AND.compna(j) == 'co2') THEN + kij(i,j) = 0.051875 ! PC-SAFT + IF (pol == 1) kij(i,j) = -0.0353125 ! PCP-SAFT + ELSE IF(compna(i) == 'methane'.AND.compna(j) == 'co') THEN + ! IF (pol == 1) kij(i,j) = -0.003 ! PCP-SAFT + IF (pol == 1) kij(i,j) = 0.018 ! PCP-SAFT + ELSE IF(compna(i) == 'ethane'.AND.compna(j) == 'co2') THEN + kij(i,j) = 0.095 + kij(i,j) = 0.021 + ! kij(i,j) = 0.024 + ELSE IF(compna(i) == 'propane'.AND.compna(j) == 'co2') THEN + kij(i,j) = 0.042 + ELSE IF(compna(i) == 'argon_ge'.AND.compna(j) == 'argon_ge2') THEN + read (*,*) kij(i,j) + ELSE IF(compna(i) == 'butane'.AND.compna(j) == 'co2') THEN + ! kij(i,j) = 0.115 + ! kij(i,j) = 0.048 + kij(i,j) = 0.036 + ELSE IF(compna(i) == 'pentane'.AND.compna(j) == 'co2') THEN + kij(i,j) = 0.143 ! without quadrupol-term + kij(i,j) = 0.0 ! with quadrupol-term + ELSE IF(compna(i) == 'hexane'.AND.compna(j) == 'co2') THEN + ! kij(i,j) = 0.125 ! without quadrupol-term + kij(i,j) = 0.0495 + ELSE IF(compna(i) == 'heptane'.AND.compna(j) == 'co2') THEN + kij(i,j) = 0.11 ! without quadrupol-term + ! kij(i,j) = 0.05 + ! kij(i,j) = 0.039 ! with quadrupol-term + ELSE IF(compna(i) == 'decane'.AND.compna(j) == 'co2') THEN + ! kij(i,j) = 0.128 ! without quadrupol-term + kij(i,j) = 0.053 ! with quadrupol-term + ELSE IF(compna(i) == 'dodecane'.AND.compna(j) == 'co2') THEN + kij(i,j) = 0.12 ! without quadrupol-term + kij(i,j) = 0.0508 ! with quadrupol-term + ELSE IF(compna(i) == 'benzene'.AND.compna(j) == 'co2') THEN + ! kij(i,j) = 0.087968750000 ! without quadrupol-term + ! kij(i,j) = 0.008203125 ! only co2 quadrupol + kij(i,j) = 0.042 ! both quadrupol + ! kij(i,j) = 0.003 ! both quadrupol + ELSE IF(compna(i) == 'toluene'.AND.compna(j) == 'co2') THEN + ! kij(i,j) = 0.110784912 ! without quadrupol-term + kij(i,j) = 0.0305 ! with quadrupol-term + ELSE IF(compna(i) == 'cyclohexane'.AND.compna(j) == 'co2') THEN + kij(i,j) = 0.13 + lij(i,j) = - 0.00 + ! kij(i,j) = 0.045 + ELSE IF(compna(i) == 'chloromethane'.AND.compna(j) == 'co2')THEN + ! kij(i,j) = 0.04 ! PC-SAFT + kij(i,j) = 0.025 ! PCP-SAFT + ! kij(i,j) = 0.083 ! PCIP-SAFT + ELSE IF(compna(i) == 'acetone'.AND.compna(j) == 'n2')THEN + kij(i,j) = 0.035211 ! PCP-SAFT + lij(i,j) = + 0.013225 ! PCP-SAFT + kij(i,j) = 0.023 ! PCP-SAFT + lij(i,j) = + 0.013225 ! PCP-SAFT + !kij(i,j) = 1.722238535635467E-002 ! PCP-SAFT + !lij(i,j) = 2.815974678394451E-003 ! PCP-SAFT + !kij(i,j) = 1.931522058164026E-002 ! PCP-SAFT + !lij(i,j) = 0.0 ! PCP-SAFT + !kij(i,j) = 1.641053794134795E-002 ! PCP-SAFT + !lij(i,j) = -5.850421759950764E-003 ! PCP-SAFT + if ( num == 0 ) write (*,*) 'calculation with lij only possible with num=1' + if ( num == 0 ) stop + ELSE IF(compna(i) == 'acetone'.AND.compna(j) == 'co2')THEN + kij(i,j) = 0.015 ! PC-SAFT + IF (pol == 1) kij(i,j) = -0.02 ! PCP-SAFT + IF (pol == 2) kij(i,j) = -0.005 ! PCIP-SAFT where DQ with my=my_vacuum + ! IF (pol.EQ.2) kij(i,j) = 0.0 ! PCIP-SAFT where DQ with my=my_RPT + ELSE IF(compna(i) == 'methanol'.AND.compna(j) == 'co2')THEN + ! kij(i,j) = 0.0288 ! PC-SAFT + ! kij(i,j) = - 0.035 ! PCP-SAFT for co2 and PC-SAFT methanol + ! kij(i,j) = - 0.035 ! PCP-SAFT + ! lij(i,j) = 0.3 ! PCP-SAFT + ELSE IF(compna(i) == 'dimethyl-ether'.AND.compna(j) == 'co2')THEN + kij(i,j) = 0.00896894 ! PC-SAFT + ! kij(i,j) = - 0.015 ! PCP-SAFT + ELSE IF(compna(i) == 'dimethyl-ether'.AND.compna(j) == 'h2o')THEN + ! kij(i,j) = -0.134 ! PC-SAFT + ELSE IF(compna(i) == 'dichloromethane'.AND.compna(j) == 'co2')THEN + ! kij(i,j) = 0.06881725 ! PC-SAFT + ! kij(i,j) = 0.05839145 ! PCP-SAFT + kij(i,j) = -0.00944346 ! PCP-SAFT co2 dichloromethane PC-SAFT + ! kij(i,j) = 0.06 ! PCIP-SAFT + ELSE IF(compna(i) == 'h2s'.AND.compna(j) == 'methane')THEN + ! kij(i,j) = 0.0414 ! PC-SAFT + kij(i,j) = 0.0152 ! PCP-SAFT Dipole momnet (d with Q) + ELSE IF(compna(i) == 'butane'.AND.compna(j) == 'h2s')THEN + kij(i,j) = -0.002 ! PCP-SAFT + ELSE IF(compna(i) == 'methanol'.AND.compna(j) == 'h2s')THEN + kij(i,j) = 0.0 ! PCP-SAFT + lij(i,j) = 0.0 ! PCP-SAFT + ELSE IF(compna(i) == 'co2'.AND.compna(j) == 'hydrogen') THEN + ! lij(i,j) = -0.08 !!!!! Lij not kij !!!! + ELSE IF(compna(i) == 'hexane'.AND.compna(j) == 'n2') THEN + kij(i,j) = 0.11 + ELSE IF(compna(i) == 'propane'.AND.compna(j) == 'n2') THEN + kij(i,j) = 0.0251171875 + ELSE IF(compna(i) == 'co2'.AND.compna(j) == 'hexadecane') THEN + ! kij(i,j) = 0.1194 ! PC-SAFT ohne QQ + kij(i,j) = 0.0588 + ELSE IF(compna(i) == 'ethane'.AND.compna(j) == 'acetone') THEN + ! kij(i,j) = 0.065 ! no DD + kij(i,j) = 0.038 ! DD non-polarizable + ! kij(i,j) = 0.025 ! DD polarizable + ELSE IF(compna(i) == 'butane'.AND.compna(j) == 'acetone') THEN + ! kij(i,j) = 0.065 ! no DD + kij(i,j) = 0.037 ! DD non-polarizable + ! kij(i,j) = 0.025 ! DD polarizable + ELSE IF(compna(i) == 'pentane'.AND.compna(j) == 'acetone') THEN + ! kij(i,j) = 0.072 ! no DD + ! kij(i,j) = 0.041 ! DD non-polarizable + kij(i,j) = 0.039 ! DD polarizable + ! kij(i,j) = 0.035 ! DD polarizable + ELSE IF(compna(i) == 'hexane'.AND.compna(j) == 'acetone') THEN + ! kij(i,j) = 0.063 + kij(i,j) = 0.038 ! PCP-SAFT + ! kij(i,j) = 0.036 ! PCIP-SAFT + ELSE IF(compna(i) == 'heptane'.AND.compna(j) == 'acetone') THEN + kij(i,j) = 0.035 ! PCP-SAFT + ELSE IF(compna(i) == 'decane'.AND.compna(j) == 'acetone') THEN + ! kij(i,j) = 0.059 ! no DD + ! kij(i,j) = 0.03281250 ! DD non-polarizable + kij(i,j) = 0.028 ! DD polarizable + ELSE IF(compna(i) == 'hexadecane'.AND.compna(j) == 'acetone') THEN + ! kij(i,j) = 0.07 ! no DD + ! kij(i,j) = 0.0415 ! DD non-polarizable + kij(i,j) = 0.035 ! DD polarizable + ELSE IF(compna(i) == 'hexane'.AND.compna(j) == 'butanone')THEN + kij(i,j) = 0.027 ! PCP-SAFT + ! kij(i,j) = 0.033 ! PCP-SAFT with lij + ! lij(i,j) = 0.13 ! PCP-SAFT + ! kij(i,j) = 0.042 ! PC-SAFT + ELSE IF(compna(i) == 'heptane'.AND.compna(j) == 'butanone')THEN + kij(i,j) = 0.042 ! no DD + ! kij(i,j) = 0.027 ! DD non-polarizable + ELSE IF(compna(i) == 'heptane'.AND.compna(j) == '2-pentanone')THEN + kij(i,j) = 0.041 ! no DD + ! kij(i,j) = 0.031 ! DD non-polarizable + ELSE IF(compna(i) == 'hexane'.AND.compna(j) == '3-pentanone')THEN + kij(i,j) = 0.0 + ELSE IF(compna(i) == 'pentane'.AND.compna(j) == 'propanal')THEN + ! kij(i,j) = 0.055 ! no DD + kij(i,j) = 0.027 ! DD non-polarizable + ! kij(i,j) = 0.026 ! DD polarizable 22 + ELSE IF(compna(i) == 'cyclohexane'.AND.compna(j) == 'propanal')THEN + ! kij(i,j) = 0.06 ! no DD + kij(i,j) = 0.036 ! DD non-polarizable + kij(i,j) = 0.035 ! DD polarizable 22 + ELSE IF(compna(i) == 'heptane'.AND.compna(j) == 'butanal')THEN + kij(i,j) = 0.041 ! no DD + ! kij(i,j) = 0.025 ! DD non-polarizable + ELSE IF(compna(i) == 'hexane'.AND.compna(j) == 'thf')THEN + kij(i,j) = 0.012 ! PCP-SAFT + ELSE IF(compna(i) == 'octane'.AND.compna(j) == 'thf')THEN + kij(i,j) = 0.012 ! PCP-SAFT + ELSE IF(compna(i) == 'decane'.AND.compna(j) == 'thf')THEN + kij(i,j) = 0.012 ! PCP-SAFT + ELSE IF(compna(i) == 'toluene'.AND.compna(j) == 'dmso')THEN + ! kij(i,j) = 0.025 ! no DD + kij(i,j) = - 0.0105 ! DD non-polarizable + ! kij(i,j) = - 0.019 ! DD polarizable + ELSE IF(compna(i) == 'hexane'.AND.compna(j) == 'acrylonitrile')THEN + kij(i,j) = - 0.05 ! DD polarizable + ELSE IF(compna(i) == 'heptane' .AND. compna(j) == 'butyronitrile')THEN + kij(i,j) = - 0.002 ! DD polarizable 11 + kij(i,j) = 0.002 ! DD polarizable 22 + ELSE IF(compna(i) == '1-butene'.AND.compna(j) == 'dmf')THEN + ! kij(i,j) = 0.04 ! no DD + ! kij(i,j) = 0.004 ! DD non-polarizable + kij(i,j) = 0.005 ! DD polarizable 22 + ELSE IF(compna(i) == 'cyclohexane'.AND.compna(j) == 'dmf')THEN + kij(i,j) = 0.0135 ! DD polarizable 11 + kij(i,j) = 0.022 ! DD polarizable 22 + ELSE IF(compna(i) == 'ethylene'.AND.compna(j) == 'dmf')THEN + ! kij(i,j) = - 0.0215 ! DD polarizable 11 + kij(i,j) = - 0.01 ! DD polarizable 22 + ELSE IF(compna(i) == 'nbutyl-ethanoate'.AND.compna(j) == 'dmf')THEN + ! kij(i,j) = 0.016 ! no DD + ! kij(i,j) = -0.01 ! DD non-polarizable + kij(i,j) = - 0.015 ! DD polarizable 22 + ELSE IF(compna(i) == 'methylacetate' .AND. compna(j) == 'cyclohexane')THEN + kij(i,j) = 0.066 ! PC-SAFT + ! kij(i,j) = 0.061 ! PCP-SAFT + ! kij(i,j) = 0.0625 ! PCIP-SAFT + ELSE IF(compna(i) == 'methylacetate'.AND.compna(j) == 'decane')THEN + kij(i,j) = 0.0625 ! PCIP-SAFT + ELSE IF(compna(i) == 'methylacetate' .AND. compna(j) == 'methanol')THEN + ! kij(i,j) = -0.07 ! PCIP-SAFT + ELSE IF(compna(i) == 'pentane' .AND. compna(j) == 'propionitrile')THEN + kij(i,j) = 0.0498 + IF (pol >= 1) kij(i,j) = -0.01 + IF (pol >= 2) kij(i,j) = -0.027 + ELSE IF(compna(i) == 'hexane' .AND. compna(j) == 'propionitrile')THEN + kij(i,j) = 0.05 + IF (pol >= 1) kij(i,j) = 0.0 + IF (pol >= 2) kij(i,j) = -0.03 + ELSE IF(compna(i) == 'octane' .AND. compna(j) == 'propionitrile')THEN + kij(i,j) = 0.0 ! DD polarizable 22 + ELSE IF(compna(i) == 'cyclohexane' .AND. compna(j) == 'nitromethane')THEN + kij(i,j) = 0.14 ! no DD + ! kij(i,j) = 0.07 ! DD non-polarizable + ! kij(i,j) = 0.055 ! DD polarizable 22 + ELSE IF(compna(i) == 'cyclohexane' .AND. compna(j) == 'nitroethane')THEN + ! kij(i,j) = 0.06 ! no DD + kij(i,j) = 0.03 ! DD polarizable 22 + ELSE IF(compna(i) == 'acetone' .AND. compna(j) == 'nitromethane')THEN + ! kij(i,j) = - 0.017 ! no DD + kij(i,j) = - 0.021 ! DD non-polarizable + ! kij(i,j) = - 0.023 ! DD polarizable 22 + ELSE IF(compna(i) == 'acetone' .AND. compna(j) == 'h2o')THEN + kij(i,j) = - 0.2 ! PCP-SAFT (no cross-association) + ELSE IF(compna(i) == 'methylcyclohexane' .AND. compna(j) == 'acetonitrile')THEN + ! kij(i,j) = 0.09 ! no DD + ! kij(i,j) = 0.033 ! DD non-polarizable + ! kij(i,j) = 0.025 ! DD polarizable 22 + kij(i,j) = 0.04 ! DD polarizable 22 und my angepasst + ELSE IF(compna(i) == 'ethylacetate' .AND. compna(j) == 'acetonitrile')THEN + kij(i,j) = 0.007 ! no DD + ! kij(i,j) = -0.045 ! DD polarizable 22 + ELSE IF(compna(i) == 'dimethyl-ether' .AND. compna(j) == 'propane')THEN + ! kij(i,j) = 0.03 ! no DD + kij(i,j) = 0.0225 ! DD non-polarizable + ELSE IF(compna(i) == 'benzene' .AND. compna(j) == 'pentane')THEN + ! kij(i,j) = 0.012968750 ! ohne QQ + ! kij(i,j) = 0.004921875 ! mit QQ=5.6D (gefittet) + ! kij(i,j) = -0.006406250 ! mit QQ=7.45D (Literatur) + ELSE IF(compna(i) == 'benzene' .AND. compna(j) == 'heptane')THEN + kij(i,j) = 0.01328125 + ! kij(i,j) = 0.0038 + ELSE IF(compna(i) == 'benzene' .AND. compna(j) == '1-hexene')THEN + kij(i,j) = 0.0067 + ELSE IF(compna(i) == 'ethylene' .AND. compna(j) == 'co2') THEN + kij(i,j) = 0.04 + kij(i,j) = -0.029 + ELSE IF(compna(i) == 'ethylene' .AND. compna(j) == 'vinylacetate') THEN + kij(i,j) = - 0.013847 + ELSE IF(compna(i) == 'triacontane' .AND. compna(j) == 'ethylene') THEN + kij(i,j) = 0.028 + ELSE IF(compna(i) == 'triacontane' .AND. compna(j) == 'methane')THEN + ! kij(i,j) = 0.061953125 ! polyethylene parameters + kij(i,j) = 0.039609375 ! param. by extrapolation of n-alkanes + ELSE IF(compna(i) == 'tetracontane' .AND. compna(j) == 'methane')THEN + ! kij(i,j) = 0.06515625 ! polyethylene parameters + kij(i,j) = 0.04453125 ! param. by extrapolation of n-alkanes + ! --- kij and lij adjusted ------- + ! kij(i,j) = 0.045786119 ! param. by extrapolation of n-alkanes + ! lij(i,j) = +8.53466437d-4 ! param. by extrapolation of n-alkanes + ELSE IF(compna(i) == 'eicosane' .AND. compna(j) == 'methane')THEN + kij(i,j) = 0.0360134457445 + ELSE IF(compna(i) == 'tetracontane' .AND. compna(j) == 'methane')THEN + kij(i,j) = 0.0360134457445 ! assumed equal to eicosane-C1 + ELSE IF(compna(i) == 'chlorobenzene' .AND. compna(j) == 'cyclohexane') THEN + kij(i,j) = 0.013 + ELSE IF(compna(i) == 'chloroethane' .AND. compna(j) == 'butane')THEN + kij(i,j) = 0.025 + ELSE IF(compna(i) == 'tetrachloromethane' .AND. compna(j) == '2-methylpentane') THEN + kij(i,j) = 0.0070105 + ELSE IF(compna(i) == 'tetrachloromethane' .AND. compna(j) == 'hexane') THEN + kij(i,j) = 0.004 + ELSE IF(compna(i) == 'hydrogen' .AND. compna(j) == 'hexane') THEN + kij(i,j) = 0.1501 + ELSE IF(compna(i) == 'ethanol' .AND. compna(j) == 'co2') THEN + ! kij(i,j) = -0.08 + ELSE IF(compna(i) == 'ethanol' .AND. compna(j) == 'propane') THEN + kij(i,j) = - 0.07 + ELSE IF(compna(i) == 'ethanol' .AND. compna(j) == 'ethane') THEN + kij(i,j) = 0.0 + ELSE IF(compna(i) == 'ethanol' .AND. compna(j) == 'butane') THEN + kij(i,j) = 0.028 + kij(i,j) = 0.016 + ELSE IF(compna(i) == 'ethanol' .AND. compna(j) == 'cyclohexane')THEN + kij(i,j) = 0.037 + ELSE IF(compna(i) == 'ethanol' .AND. compna(j) == '2-methylpentane') THEN + kij(i,j) = 0.028 + ELSE IF(compna(i) == 'ethanol' .AND. compna(j) == '1-octanol')THEN + kij(i,j) = 0.06 + ELSE IF(compna(i) == 'methanol' .AND. compna(j) == 'cyclohexane') THEN + kij(i,j) = 0.0508 + ! kij(i,j) = 0.03 + ELSE IF(compna(i) == 'methanol' .AND. compna(j) == 'heptane')THEN + kij(i,j) = 0.034 + ELSE IF(compna(i) == 'methanol' .AND. compna(j) == 'decane')THEN + ! kij(i,j) = 0.042 ! PC-SAFT + ! kij(i,j) = 0.011 ! PCP-SAFT + kij(i,j) = 0.000 ! PCIP-SAFT + ELSE IF(compna(i) == 'methanol' .AND. compna(j) == 'isobutane') THEN + kij(i,j) = 0.051 + ELSE IF(compna(i) == 'methanol' .AND. compna(j) == '1-octanol') THEN + kij(i,j) = 0.02 + ELSE IF(compna(i) == '1-butanol' .AND. compna(j) == 'butane') THEN + kij(i,j) = 0.015 + ELSE IF(compna(i) == '1-nonanol' .AND. compna(j) == 'co2') THEN + kij(i,j) = 0.076 + kij(i,j) = 0.01443 + ELSE IF(compna(i) == '1-propanol' .AND. compna(j) == 'ethylbenzene') THEN + kij(i,j) = 0.0251757813 + ELSE IF(compna(i) == 'decane'.AND.compna(j) == 'ethanol') THEN + kij(i,j) = 0.085 + ELSE IF(compna(i) == 'hexane'.AND.compna(j) == '1-chlorobutane') THEN + kij(i,j) = 0.017 + ELSE IF(compna(i) == 'aniline'.AND.compna(j) == 'methylcyclopentane') THEN + kij(i,j) = 0.0153 + ELSE IF(compna(i) == 'heptane'.AND.compna(j) == 'nbutyl-ethanoate')THEN + kij(i,j) = 0.027 + ELSE IF(compna(i) == '1-hexene'.AND.compna(j) == 'ethyl-ethanoate')THEN + kij(i,j) = 0.026 + ELSE IF(compna(i) == 'co2'.AND.compna(j) == '1-butanol')THEN + ! kij(i,j) = 0.075 + kij(i,j) = 0.0 + ELSE IF(compna(i) == 'acrylic-acid'.AND.compna(j) == 'co2')THEN + kij(i,j) = -0.1 + ELSE IF(compna(i) == 'bmim'.AND.compna(j) == 'hydrogen')THEN + lij(i,j) = 0.55 !!!!! Lij not kij !!!! + ELSE IF(compna(i) == 'bf4'.AND.compna(j) == 'hydrogen')THEN + lij(i,j) = 0.55 !!!!! Lij not kij !!!! + ELSE IF(compna(i) == 'h2o'.AND.compna(j) == 'butane')THEN !K.R.Hall FPE 2007 254 112-125 kij=0.1850 + kij(i,j) = -0.07 + ELSE IF(compna(i) == 'h2o'.AND.compna(j) == '1-butanol')THEN + kij(i,j) = -0.12 + ELSE IF(compna(i) == 'h2o'.AND.compna(j) == 'aniline')THEN + kij(i,j) = 0.0 + ELSE IF(compna(i) == 'h2o'.AND.compna(j) == 'methanol') THEN + kij(i,j) = -0.02 + ELSE IF(compna(i) == 'h2o'.AND.compna(j) == 'ethanol') THEN + kij(i,j) = -0.027 + ELSE IF(compna(i) == 'h2o'.AND.compna(j) == 'styrene') THEN + kij(i,j) = 0.1 + ELSE IF(compna(i) == 'h2o'.AND.compna(j) == 'propyl-ethanoate') THEN + kij(i,j) = -0.205 + ELSE IF(compna(i) == 'h2o'.AND.compna(j) == 'ethyl-propanoate') THEN + kij(i,j) = 0.0 + ELSE IF(compna(i) == 'h2o'.AND.compna(j) == '1-pentanol') THEN + kij(i,j) = 0.0165 + ! kij(i,j) = 0.0294 + ! kij(i,j) = -0.082 + ELSE IF(compna(i) == 'h2o'.AND.compna(j) == 'methane') THEN + ! kij(i,j) = +0.06 + kij(i,j) = -0.08 + ELSE IF(compna(i) == 'h2o'.AND.compna(j) == 'propane') THEN + kij(i,j) = 0.02 + ELSE IF(compna(i) == 'h2o'.AND.compna(j) == 'hexane') THEN + kij(i,j) = -0.02 + ELSE IF(compna(i) == 'h2o'.AND.compna(j) == 'acetic-acid') THEN + kij(i,j) = -0.0 + ELSE IF(compna(i) == 'h2o'.AND.compna(j) == 'co2') THEN + if (pol == 0) kij(i,j) = 0.0030625 ! for T=50C, according to X.Tang + stop ! very T-dependent + ELSE IF(compna(i) == 'toluene'.AND.compna(j) == 'acetic-acid') THEN + kij(i,j) = -0.1 + ELSE IF(compna(i) == 'caproic-acid'.AND.compna(j) == 'cyclohexane') THEN + kij(i,j) = 0.041531 + ELSE IF(compna(i) == '1-octanol'.AND.compna(j) == 'h2o')THEN + kij(i,j) = 0.07 + ELSE IF(compna(i) == 'acetone'.AND.compna(j) == 'benzene')THEN + kij(i,j) = 0.02132466 ! PC-SAFT + ! kij(i,j) = 0.01495148 ! PCP-SAFT + ! kij(i,j) = -0.00735575 ! PCP-SAFT but non-polar benzene + ELSE IF(compna(i) == '1-propanol'.AND.compna(j) == 'benzene')THEN + kij(i,j) = 0.02017 + ELSE IF(compna(i) == '2-propanol'.AND.compna(j) == 'benzene')THEN + kij(i,j) = 0.021386 + ELSE IF(compna(i) == '1-pentanol'.AND.compna(j) == 'benzene')THEN + kij(i,j) = 0.0129638671875 + ELSE IF(compna(i) == 'CH2F2' .AND. compna(j) == 'co2') THEN + kij(i,j) = 2.2548828125E-2 + ELSE IF(compna(i) == 'dmso' .AND. compna(j) == 'co2') THEN + kij(i,j) = -0.00 + ELSE IF(compna(i) == 'dmf'.AND.compna(j) == 'h2o')THEN + kij(i,j) = -0.0 + ELSE IF(compna(i) == 'decane'.AND.compna(j) == 'h2o')THEN + kij(i,j) = 0.11 + ELSE IF(compna(i) == '11difluoroethane'.AND.compna(j) == 'HF')THEN + kij(i,j) = 0.032 ! association: eps_kij = 0.16 + ELSE IF(compna(i) == '11difluoroethane'.AND.compna(j) == 'co2')THEN + kij(i,j) = -0.004 ! PCP-SAFT (taken from simulation) + ELSE IF(compna(i) == 'difluoromethane'.AND.compna(j) == 'HF')THEN + kij(i,j) = -0.02 + ELSE IF(compna(i) == 'naphthalene'.AND.compna(j) == 'co2')THEN + kij(i,j) = 0.137 ! angepasst an SVLE-Linie (tradition.CO2-Parameter) + kij(i,j) = 0.09 ! angepasst an SVLE-Linie (tradition.CO2-Parameter) + ELSE IF(compna(i) == 'pg2'.AND.compna(j) == 'methanol')THEN + kij(i,j) = 0.03 + ELSE IF(compna(i) == 'pg2'.AND.compna(j) == 'co2')THEN + ! kij(i,j) = 0.05 + ELSE IF(compna(i) == 'PCH5'.AND.compna(j) == 'co2')THEN + ! kij(i,j) = -0.047 + kij(i,j) = +0.055 + ! kij(i,j) = +0.036 + ELSE + END IF + kij(j,i) = kij(i,j) + lij(j,i) = -lij(i,j) + + END DO +END DO + +END SUBROUTINE pcsaft_par + + +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! SUBROUTINE init_vars +! +! This subroutine writes variables from an array "val_init" to the +! system-variables. Those variables +! include some specifications but also some starting values for a +! phase equilibrium calculation. (val_init stands for 'initial value') + +! The array comprises the following elements +! element 0 density of third phase +! element 1 density of first phase +! element 2 density of second phase +! element 3 temperature [K] +! element 4 pressure [Pa] +! element 5,..(5+NCOMP) mole-fraction of comp. i in log. from (phase 1) +! element ... mole-fraction of comp. i in log. from (phase 2) +! element ... mole-fraction of comp. i in log. from (phase 3) +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! + SUBROUTINE init_vars +! + USE BASIC_VARIABLES + IMPLICIT NONE +! + INTEGER :: i, ph +! ---------------------------------------------------------------------- + +densta(3)=val_init(0) +densta(1)=val_init(1) +densta(2)=val_init(2) +t = val_init(3) +p = val_init(4) +DO ph = 1,nphas + DO i = 1,ncomp + lnx(ph,i) = val_init(4+i+(ph-1)*ncomp) + END DO +END DO + +END SUBROUTINE init_vars + + +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! SUBROUTINE converged +! +! Once a converged solution for an equilibrium calculation is found, +! this subroutine writes variables to an array "val_conv". +! (= short for converged values) +! The array comprises the following elements +! element 0 density of third phase +! element 1 density of first phase +! element 2 density of second phase +! element 3 temperature [K] +! element 4 pressure [Pa] +! element 5,..(4+NCOMP) mole-fraction of comp. i in log. from (phase 1) +! element ... mole-fraction of comp. i in log. from (phase 2) +! element ... mole-fraction of comp. i in log. from (phase 3) +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! + SUBROUTINE converged +! + USE BASIC_VARIABLES + IMPLICIT NONE +! + INTEGER :: i, ph +! ---------------------------------------------------------------------- + +val_conv(0) = dense(3) +val_conv(1) = dense(1) +val_conv(2) = dense(2) +val_conv(3) = t +val_conv(4) = p +DO ph = 1,nphas + DO i = 1,ncomp + val_conv(4+i+(ph-1)*ncomp) = lnx(ph,i) + END DO +END DO + +END SUBROUTINE converged + +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! SUBROUTINE PERTURBATION_PARAMETER +! +! calculates density-independent parameters of the equation of state. +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! + SUBROUTINE PERTURBATION_PARAMETER +! + USE PARAMETERS, ONLY: PI, KBOL, RGAS, NAV, TAU + USE EOS_VARIABLES + USE EOS_CONSTANTS + IMPLICIT NONE +! +! --- local variables -------------------------------------------------- + INTEGER :: i, j, k, l, m, no + LOGICAL :: assoc, qudpole, dipole + REAL :: m_mean + REAL, DIMENSION(nc) :: v00, v0, d00, u + REAL, DIMENSION(nc,nc,nsite,nsite) :: eps_hb + REAL, DIMENSION(nc,nc) :: kap_hb + REAL :: zmr, nmr + REAL :: eps_kij, k_kij +! ---------------------------------------------------------------------- + +! ---------------------------------------------------------------------- +! pure component parameters +! ---------------------------------------------------------------------- +DO i = 1, ncomp + u(i) = parame(i,3) * (1.0 + parame(i,4)/t) + mseg(i) = parame(i,1) + IF (eos == 0) THEN + v00(i) = parame(i,2) + v0(i) = v00(i)*(1.0-0.12*EXP(-3.0*parame(i,3)/t))**3 + d00(i) = (1.d30/1.d6 *tau *v00(i)*6.0/PI /NAV)**(1.0/3.0) + dhs(i) = d00(i)*(1.0-0.12*EXP(-3.0*parame(i,3)/t)) + ELSE + dhs(i) = parame(i,2)*(1.0-0.12*EXP(-3.0*parame(i,3)/t)) + d00(i) = parame(i,2) + END IF +END DO + + +! ---------------------------------------------------------------------- +! combination rules +! ---------------------------------------------------------------------- +DO i = 1, ncomp + DO j = 1, ncomp + sig_ij(i,j) = 0.5 * ( d00(i) + d00(j) ) + uij(i,j) = ( 1.0 - kij(i,j) ) * ( u(i)*u(j) )**0.5 + vij(i,j) = ( 0.5*( v0(i)**(1.0/3.0) + v0(j)**(1.0/3.0) ) )**3 + END DO +END DO + + +! ---------------------------------------------------------------------- +! abbreviations +! ---------------------------------------------------------------------- +z0t = PI / 6.0 * SUM( x(1:ncomp) * mseg(1:ncomp) ) +z1t = PI / 6.0 * SUM( x(1:ncomp) * mseg(1:ncomp) * dhs(1:ncomp) ) +z2t = PI / 6.0 * SUM( x(1:ncomp) * mseg(1:ncomp) * dhs(1:ncomp)**2 ) +z3t = PI / 6.0 * SUM( x(1:ncomp) * mseg(1:ncomp) * dhs(1:ncomp)**3 ) + +m_mean = z0t/(PI/6.0) + +DO i = 1, ncomp + DO j = 1, ncomp + dij_ab(i,j) = dhs(i)*dhs(j) / ( dhs(i) + dhs(j) ) + END DO +END DO + +! ---------------------------------------------------------------------- +! dispersion term parameters for chain molecules +! ---------------------------------------------------------------------- +DO m = 0, 6 + apar(m) = ap(m,1) + (1.0-1.0/m_mean)*ap(m,2) & + + (1.0-1.0/m_mean)*(1.0-2.0/m_mean)*ap(m,3) + bpar(m) = bp(m,1) + (1.0-1.0/m_mean)*bp(m,2) & + + (1.0-1.0/m_mean)*(1.0-2.0/m_mean)*bp(m,3) +END DO + + +! ---------------------------------------------------------------------- +! van der Waals mixing rules for perturbation terms +! ---------------------------------------------------------------------- +order1 = 0.0 +order2 = 0.0 +DO i = 1, ncomp + DO j = 1, ncomp + order1 = order1 + x(i)*x(j)* mseg(i)*mseg(j)*sig_ij(i,j)**3 * uij(i,j)/t + order2 = order2 + x(i)*x(j)* mseg(i)*mseg(j)*sig_ij(i,j)**3 * (uij(i,j)/t)**2 + END DO +END DO + + +! ---------------------------------------------------------------------- +! SAFT parameters +! ---------------------------------------------------------------------- +IF (eos == 0) THEN + zmr = 0.0 + nmr = 0.0 + DO i = 1, ncomp + DO j = 1, ncomp + zmr = zmr + x(i)*x(j)*mseg(i)*mseg(j)*vij(i,j)*uij(i,j) + nmr = nmr + x(i)*x(j)*mseg(i)*mseg(j)*vij(i,j) + END DO + END DO + um = zmr / nmr +END IF + + + +! ---------------------------------------------------------------------- +! association and polar parameters +! ---------------------------------------------------------------------- +assoc = .false. +qudpole = .false. +dipole = .false. +DO i = 1, ncomp + IF (NINT(parame(i,12)) /= 0) assoc = .true. + IF (parame(i,7) /= 0.0) qudpole = .true. + IF (parame(i,6) /= 0.0) dipole = .true. +END DO + +! --- dipole and quadrupole constants ---------------------------------- +IF (qudpole) CALL qq_const ( qqp2, qqp3, qqp4 ) +IF (dipole) CALL dd_const ( ddp2, ddp3, ddp4 ) +IF (dipole .AND. qudpole) CALL dq_const ( dqp2, dqp3, dqp4 ) + + +! --- TPT-1-association parameters ------------------------------------- +IF (assoc) THEN + + eps_kij = 0.0 + k_kij = 0.0 + + DO i = 1, ncomp + IF (NINT(parame(i,12)) /= 0) THEN + nhb_typ(i) = NINT(parame(i,12)) + kap_hb(i,i) = parame(i,13) + no = 0 + DO j = 1, nhb_typ(i) + DO k = 1, nhb_typ(i) + eps_hb(i,i,j,k) = parame(i,(14+no)) + no=no+1 + END DO + END DO + DO j = 1, nhb_typ(i) + nhb_no(i,j) = parame(i,(14+no)) + no=no+1 + END DO + ELSE + nhb_typ(i) = 0 + kap_hb(i,i)= 0.0 + DO k = 1, nsite + DO l = 1, nsite + eps_hb(i,i,k,l) = 0.0 + END DO + END DO + END IF + END DO + + DO i = 1, ncomp + DO j = 1, ncomp + IF (i /= j .AND. (nhb_typ(i) /= 0 .AND. nhb_typ(j) /= 0)) THEN + kap_hb(i,j)= (kap_hb(i,i)*kap_hb(j,j))**0.5 & + *((parame(i,2)*parame(j,2))**3 )**0.5 & + /(0.5*(parame(i,2)+parame(j,2)))**3 + kap_hb(i,j)= kap_hb(i,j)*(1.0-k_kij) + DO k = 1, nhb_typ(i) + DO l = 1, nhb_typ(j) + IF (k /= l) THEN + eps_hb(i,j,k,l) = (eps_hb(i,i,k,l)+eps_hb(j,j,l,k))/2.0 + eps_hb(i,j,k,l) = eps_hb(i,j,k,l)*(1.0-eps_kij) + END IF + END DO + END DO + END IF + END DO + END DO + IF (nhb_typ(1) == 3) THEN +! write(*,*)'eps_hb manuell eingegeben' + eps_hb(1,2,3,1) = 0.5*(eps_hb(1,1,3,1)+eps_hb(2,2,1,2)) + eps_hb(2,1,1,3) = eps_hb(1,2,3,1) + END IF + IF (nhb_typ(2) == 3) THEN + eps_hb(2,1,3,1) = 0.5*(eps_hb(2,2,3,1)+eps_hb(1,1,1,2)) + eps_hb(1,2,1,3) = eps_hb(2,1,3,1) + END IF + + DO i = 1, ncomp + DO k = 1, nhb_typ(i) + DO j = 1, ncomp + DO l = 1, nhb_typ(j) + ass_d(i,j,k,l) = kap_hb(i,j) *sig_ij(i,j)**3 *(EXP(eps_hb(i,j,k,l)/t)-1.0) + END DO + END DO + END DO + END DO + +END IF + +END SUBROUTINE PERTURBATION_PARAMETER + + + + +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! SUBROUTINE OUTPUT +! +! The purpose of this subroutine is obvious. +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! + SUBROUTINE OUTPUT +! + USE BASIC_VARIABLES + IMPLICIT NONE +! +! ---------------------------------------------------------------------- + INTEGER :: i + CHARACTER (LEN=4) :: t_ind + CHARACTER (LEN=4) :: p_ind + CHARACTER (LEN=4) :: char_ncomp + REAL :: density(np),w(np,nc) +! ---------------------------------------------------------------------- + + CALL si_dens (density,w) + + IF (u_in_p == 1.E5) THEN + p_ind = ' bar' + ELSE IF (u_in_p == 1.E2) THEN + p_ind = 'mbar' + ELSE IF (u_in_p == 1.E6) THEN + p_ind = ' MPa' + ELSE IF (u_in_p == 1.E3) THEN + p_ind = ' kPa' + ELSE + p_ind = ' Pa' + END IF + IF (u_in_t == 273.15) THEN + t_ind = ' C' + ELSE + t_ind = ' K' + END IF + + WRITE(*,*) '--------------------------------------------------' + WRITE (char_ncomp,'(I3)') ncomp + WRITE(*,'(t2,a,f7.2,2a,f9.4,a)') ' T =',t-u_out_t,t_ind & + ,' P =',p/u_out_p,p_ind + WRITE(*,'(t15,4(a12,1x),10x,a)') (compna(i),i=1,ncomp) + WRITE(*,'(2x,a,'//char_ncomp//'(g13.6,1x))') 'PHASE I w', (w(1,i),i=1,ncomp) + WRITE(*,'(2x,a,'//char_ncomp//'(g13.6,1x))') 'PHASE II w', (w(2,i),i=1,ncomp) + WRITE(*,'(2x,a,'//char_ncomp//'(g13.6,1x))') 'PHASE I x', (EXP(lnx(1,i)),i=1,ncomp) + WRITE(*,'(2x,a,'//char_ncomp//'(g13.6,1x))') 'PHASE II x', (EXP(lnx(2,i)),i=1,ncomp) + WRITE(*,'(2x,a,2(g13.6,1x))') 'DENSITY ', density(1),density(2) + + !-----output to files-------------------------------------------------- + IF (ncomp == 1) THEN + WRITE (40,'(7(2x,f18.8))') t-u_out_t, p/u_out_p, & + density(1), density(2),h_lv,cpres(1),cpres(2) + ! & ,(enthal(2)-enthal(1))/mm(1) + ! WRITE (40,'(4(2x,f15.8))') t, p, 0.3107*dense(1) + ! & /0.1617*(0.689+0.311*(T/1.328)**0.3674),0.3107 + ! & *dense(2)/0.1617*(0.689+0.311*(T/1.328)**0.3674) + ELSE IF (ncomp == 2) THEN + WRITE (40,'(12(2x,G15.8))') 1.0-xi(1,1),1.0-xi(2,1), & + w(1,1),w(2,1),t-u_out_t, p/u_out_p, density(1),density(2) & + ,enthal(1),enthal(2),cpres(1),cpres(2) + ELSE IF (ncomp == 3) THEN + WRITE (40,'(10(2x,f15.8))') xi(1,1),xi(1,2),xi(1,3),xi(2,1),xi(2,2), & + xi(2,3),t-u_out_t, p/u_out_p, density(1),density(2) + END IF + + END SUBROUTINE OUTPUT + + + +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! SUBROUTINE neutr_charge +! +! This subroutine is called for electrolye solutions, where a +! neutral overall-charge has to be enforced in all phases. The basic +! philosophy is similar to the above described routine X_SUMMATION. +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! + SUBROUTINE neutr_charge(i) +! + USE BASIC_VARIABLES + IMPLICIT NONE +! +! ---------------------------------------------------------------------- + INTEGER, INTENT(IN) :: i +! +! ---------------------------------------------------------------------- + INTEGER :: comp_e, ph_e + REAL :: sum_c + CHARACTER (LEN=2) :: phasno + CHARACTER (LEN=2) :: compno +! ---------------------------------------------------------------------- + +phasno = sum_rel(i)(2:2) +READ(phasno,*) ph_e +compno = sum_rel(i)(3:3) +READ(compno,*) comp_e + +sum_c = 0.0 +write (*,*) 'there must be an error in neutr_charge' +stop +! there is an error in the following passage. The index i is an +! argument to this subroutine - I guess it is INTENT(IN), so the +! index in the following loop can not be i. +! +! I have commented the loop until I check the code. +!DO i=1,ncomp +! IF ( comp_e /= i .AND. parame(i,10) /= 0.0) & +! sum_c = sum_c + xi(ph_e,i)*parame(i,10) +!END DO + +xi(ph_e,comp_e) = - sum_c +IF (xi(ph_e,comp_e) < 0.0) xi(ph_e,comp_e)=0.0 +IF (xi(ph_e,comp_e) /= 0.0) THEN + lnx(ph_e,comp_e) = LOG(xi(ph_e,comp_e)) +ELSE + lnx(ph_e,comp_e) = -100000.0 +END IF + +! xi(2,1) = xi(2,2) +! IF (xi(2,1).NE.0.0) lnx(2,1) = LOG(xi(2,1)) + +END SUBROUTINE neutr_charge + + +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! + SUBROUTINE flash_sum +! + USE BASIC_VARIABLES + IMPLICIT NONE +! + INTEGER :: i, j, ph_i, phase1, phase2 +! ---------------------------------------------------------------------- + +phase1=0 +phase2=0 +DO j=1,ncomp + IF (it(j)(2:2) == '1') phase1=phase1+1 + IF (it(j)(2:2) == '2') phase2=phase2+1 +END DO + +IF (phase1 == ncomp-1) THEN + ph_i = 1 +ELSE IF (phase2 == ncomp-1) THEN + ph_i = 2 +ELSE + WRITE (*,*) ' FLASH_SUM: undefined flash-case' + STOP +END IF + + + +IF (ph_i == 1) THEN + DO i=1,ncomp + IF (alpha > DMIN1(1.0,xif(i)/xi(1,i), & + (xif(i)-1.0)/(xi(1,i)-1.0),alpha)) THEN + WRITE (*,*) ' FLASH_SUM: exeeded 1st alpha-bound' + alpha=DMIN1(1.0,xif(i)/xi(1,i),(xif(i)-1.0)/(xi(1,i)-1.0)) + END IF + END DO + DO i=1,ncomp + xi(2,i) = ( xif(i) - alpha*xi(1,i) ) / (1.0-alpha) + IF (xi(2,i) > 0.0) THEN + lnx(2,i) = LOG(xi(2,i)) + ELSE + xi(2,i) = 0.0 + lnx(2,i) = -100000.0 + END IF + END DO +ELSE IF (ph_i == 2) THEN + DO i=1,ncomp + IF (alpha > DMAX1(0.0,(xif(i)-xi(2,i))/(1.0-xi(2,i)), & + 1.0-xif(i)/xi(2,i),alpha)) THEN + WRITE (*,*) ' FLASH_SUM: exeeded 2nd alpha-bound' + WRITE (*,*) 0.0,(xif(i)-xi(2,i))/(1.0-xi(2,i)), 1.0-xif(i)/xi(2,i) + alpha=DMAX1(0.0,(xif(i)-xi(2,i))/(1.0-xi(2,i)), 1.0-xif(i)/xi(2,i)) + END IF + END DO + DO i=1,ncomp + xi(1,i) = ( xif(i) - (1.0-alpha)*xi(2,i) ) / alpha +! write (*,*) 'x1,i',xi(1,i),xi(2,i),alpha + IF (xi(1,i) > 0.0) THEN + lnx(1,i) = LOG(xi(1,i)) + ELSE + xi(1,i) = 0.0 + lnx(1,i) = -100000.0 + END IF + END DO +END IF + +! pause + +RETURN +END SUBROUTINE flash_sum + +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! SUBROUTINE flash_alpha +! +! This subroutine calculates all molefractions of one phase +! from a component balance. What is needed for this calculation +! are all molefractions of the other phase (nphas=2, so far) +! and the phase fraction alpha. +! Alpha is calculated from the mole fraction +! of component {sum_rel(j)(3:3)}. If for example sum_rel(2)='fl3', +! then the alpha is determined from the molefraction of comp. 3 and +! all molefractions of one phase are calculated using that alpha-value. +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! + SUBROUTINE flash_alpha +! + USE BASIC_VARIABLES + IMPLICIT NONE +! +! ---------------------------------------------------------------------- + INTEGER :: i, j, comp_i, phase1, phase2 + CHARACTER (LEN=2) :: compno +! ---------------------------------------------------------------------- + + +! ---------------------------------------------------------------------- +! first calculate the phase fraction alpha from a known composition +! of component sum_rel(j)(3:3). +! ---------------------------------------------------------------------- + +DO j = 1, nphas + IF ( sum_rel(j)(1:2) == 'fl' ) THEN + compno = sum_rel(j)(3:3) + READ(compno,*) comp_i + IF ( (xi(1,comp_i)-xi(2,comp_i)) /= 0.0 ) THEN + alpha = (xif(comp_i)-xi(2,comp_i)) / (xi(1,comp_i)-xi(2,comp_i)) + write (*,*) 'flsh',(xif(comp_i)-xi(2,comp_i)),(xi(1,comp_i)-xi(2,comp_i)) + ELSE + alpha = 0.5 + WRITE (*,*) 'FLASH_ALPHA:error in calc. of phase fraction',comp_i + END IF + ! IF (alpha <= 0.0 .OR. alpha >= 1.0) WRITE(*,*) 'FLASH_ALPHA: error',alpha + IF (alpha > 1.0) alpha = 1.0 + IF (alpha < 0.0) alpha = 0.0 + END IF +END DO + +! ---------------------------------------------------------------------- +! determine which phase is fully determined by iterated molefractions (+ summation relation) +! ---------------------------------------------------------------------- +phase1 = 0 +phase2 = 0 +DO i = 1, ncomp + IF ( it(i)(2:2) == '1' ) phase1 = phase1 + 1 + IF ( it(i)(2:2) == '2' ) phase2 = phase2 + 1 +END DO +DO i = 1, ncomp + IF ( sum_rel(i)(2:2) == '1' ) phase1 = phase1 + 1 + IF ( sum_rel(i)(2:2) == '2' ) phase2 = phase2 + 1 +END DO + + +IF ( phase1 == ncomp ) THEN + ! -------------------------------------------------------------------- + ! phase 1 is defined by iterated molefractions + summation relation + ! phase 2 is determined from componennt balance (using alpha) + ! -------------------------------------------------------------------- + IF ( alpha == 1.0 ) alpha = 1.0 - 1.0E-10 + DO i=1,ncomp + xi(2,i) = ( xif(i) - alpha*xi(1,i) ) / (1.0-alpha) + IF ( xi(2,i) < 0.0 ) xi(2,i) = 0.0 + IF ( xi(2,i) > 1.0 ) xi(2,i) = 1.0 + IF ( xi(2,i) /= 0.0 ) THEN + lnx(2,i) = LOG( xi(2,i) ) + ELSE + lnx(2,i) = -100000.0 + END IF + write (*,*) 'fl_cal ph=2',i,lnx(2,i),xi(2,i) + END DO +ELSE IF ( phase2 == ncomp ) THEN + ! -------------------------------------------------------------------- + ! phase 2 is defined by iterated molefractions + summation relation + ! phase 1 is determined from componennt balance (using alpha) + ! -------------------------------------------------------------------- + DO i = 1, ncomp + xi(1,i) = ( xif(i) - (1.0-alpha)*xi(2,i) ) /alpha + IF ( xi(1,i) < 0.0 ) xi(1,i) = 0.0 + IF ( xi(1,i) > 1.0 ) xi(1,i) = 1.0 + IF ( xi(1,i) /= 0.0 ) THEN + lnx(1,i) = LOG( xi(1,i) ) + ELSE + lnx(1,i) = -100000.0 + END IF + write (*,*) 'fl_cal ph=1',i,lnx(1,i),xi(1,i),alpha + END DO +ELSE + WRITE (*,*) ' FLASH_ALPHA: undefined flash-case' + STOP +END IF + +END SUBROUTINE flash_alpha + + +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! SUBROUTINE SI_DENS (density,w) +! +! This subroutine calculates the (macroskopic) fluid-density in +! units [kg/m3] from the dimensionless density (eta=zeta3). +! Further, mass fractions are calculated from mole fractions. +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! + SUBROUTINE SI_DENS (density,w) +! + USE PARAMETERS, ONLY: pi, nav, tau + USE BASIC_VARIABLES + IMPLICIT NONE +! +! ---------------------------------------------------------------------- + REAL, INTENT(OUT) :: density(np) + REAL, INTENT(OUT) :: w(np,nc) +! +! ---------------------------------------------------------------------- + INTEGER :: i, ph + REAL :: mm_mean, rho, z3t + REAL :: dhs(nc), d00(nc), t_p, pcon, l_st +! ---------------------------------------------------------------------- + + +DO i = 1,ncomp + IF (eos == 1) THEN + dhs(i) = parame(i,2) * ( 1.0 - 0.12 *EXP( -3.0*parame(i,3)/t ) ) + ELSE IF (eos == 0) THEN + d00(i) = ( 1.E30/1.E6*tau*parame(i,2)*6.0/pi/nav )**(1.0/3.0) + dhs(i) = d00(i) * ( 1.0 - 0.12 *EXP( -3.0*parame(i,3)/t ) ) + ELSE IF (eos == 4) THEN + dhs(i) = ( 0.1617/0.3107 / ( 0.689+0.311*(t/parame(i,3)/1.328)**0.3674 ) & + / ( pi/6.0 ) )**(1.0/3.0) * parame(i,2) + ELSE IF (eos == 5.OR.eos == 6) THEN + l_st = parame(1,25) + IF (ncomp /= 1) write (*,*) ' ERROR for EOS = 5' + t_p =((34.037352+17.733741*l_st) /(1.0+0.53237307*l_st+12.860239*l_st**2 ))**0.5 + IF (l_st == 0.0) t_p = t_p/4.0 + IF (eos == 5 .AND. l_st /= 0.0) t_p = t_p/4.0*parame(1,1)**2 + t_p = t/parame(i,3)/t_p + pcon =0.5256+3.2088804*l_st**2 -3.1499114*l_st**2.5 +0.43049357*l_st**4 + dhs(i) = ( pcon/(0.67793+0.32207*(t_p)**0.3674) /(pi/6.0) )**(1.0/3.0) *parame(i,2) + ELSE IF (eos == 8) THEN + dhs(i) = parame(i,2)*(1.0+0.2977*t/parame(i,3)) & + /(1.0+0.33163*t/parame(i,3) +1.0477E-3*(t/parame(i,3))**2 ) + ELSE + write (*,*) 'define EOS in subroutine: SI_DENS' + stop + END IF +END DO + +DO ph = 1,nphas + mm_mean = 0.0 + z3t = 0.0 + DO i = 1, ncomp + mm_mean = mm_mean + xi(ph,i)*mm(i) + z3t = z3t + xi(ph,i) * parame(i,1) * dhs(i)**3 + END DO + z3t = pi/6.0 * z3t + rho = dense(ph)/z3t + density(ph) = rho * mm_mean * 1.E27 /nav + DO i = 1, ncomp + w(ph,i) = xi(ph,i) * mm(i)/mm_mean + END DO +! write (*,*) density(ph),rho,mm_mean,1.d27 /NAV +END DO + +END SUBROUTINE SI_DENS + + + +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! + REAL FUNCTION F_STABILITY ( optpara, n ) +! + USE BASIC_VARIABLES + USE STARTING_VALUES + USE EOS_VARIABLES, ONLY: dhs, PI + IMPLICIT NONE +! +! ---------------------------------------------------------------------- + INTEGER, INTENT(IN) :: n + REAL, INTENT(IN OUT) :: optpara(n) +! +! ---------------------------------------------------------------------- + INTEGER :: i, stabil + REAL :: rhoi(nc),gradterm + REAL :: fden,punish + REAL :: dens +! ---------------------------------------------------------------------- + +COMMON /stabil / stabil + +punish = 0.0 +stabil = 1 + +DO i = 1, n + IF ( optpara(i) < 0.5 ) rhoi(i) = EXP(optpara(i) ) + IF ( optpara(i) >= 0.5) rhoi(i) = EXP(0.5) +END DO + +dens = PI/6.0 * SUM( rhoi(1:ncomp) * parame(1:ncomp,1) * dhs(1:ncomp)**3 ) + +IF (dens > 0.65) THEN + punish = punish + (dens-0.65)*10000.0 + rhoi(1:n) = rhoi(1:n)*0.65/dens +END IF + +CALL fden_calc (fden, rhoi) + +gradterm = sum( grad_fd(1:n) * ( rhoi(1:n) - rhoif(1:n) ) ) + +f_stability = fden - fdenf - gradterm + punish + +! write (*,'(5G16.8)') F_STABILITY,(rhoi(i),i=1,n) +! pause + +stabil = 0 + +END FUNCTION F_STABILITY + + + + +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! SUBROUTINE p_calc (pges_transfer, zges) +! +! This subroutine serves as an iterface to the EOS-routines. The +! system pressure corresponding to given (desity,T,xi) is calculated. +! (Note: the more common interface is SUBROUTINE FUGACITY. This +! routine is only used for one-phase systems, e.g. calculation of +! virial coefficients) +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! + SUBROUTINE p_calc (pges_transfer, zges) +! + USE BASIC_VARIABLES + USE EOS_VARIABLES + IMPLICIT NONE +! +! ---------------------------------------------------------------------- + REAL, INTENT(IN OUT) :: pges_transfer + REAL, INTENT(OUT) :: zges +! ---------------------------------------------------------------------- + +IF (nphas /= 1 ) THEN + write (*,*) 'P_CALC: can only be called for single phases' + stop +ENDIF + +IF (eos < 2) THEN + + phas = 1 + eta = dense(1) + x(1:ncomp) = xi(1,1:ncomp) + + CALL PERTURBATION_PARAMETER + IF (num == 0) CALL P_EOS + IF(num == 1) CALL P_NUMERICAL + !! IF(num == 2) CALL F_EOS_RN + + pges_transfer = pges + rho = eta/z3t + zges = (pges * 1.E-30) / (kbol*t*rho) + +ELSE + write (*,*) ' SUBROUTINE P_CALC not available for cubic EOS' + stop +END IF + +END SUBROUTINE p_calc + + + +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! +SUBROUTINE ONLY_ONE_TERM_EOS_NUMERICAL ( only_term, type_of_term ) +! + USE EOS_NUMERICAL_DERIVATIVES + IMPLICIT NONE +! + character (LEN=9) :: only_term, type_of_term +! ---------------------------------------------------------------------- + + save_eos_terms(1) = ideal_gas + save_eos_terms(2) = hard_sphere + save_eos_terms(3) = chain_term + save_eos_terms(4) = disp_term + save_eos_terms(5) = hb_term + save_eos_terms(6) = LC_term + save_eos_terms(7) = branch_term + save_eos_terms(8) = II_term + save_eos_terms(9) = ID_term + + ideal_gas = 'no' + hard_sphere = 'no' + chain_term = 'no' + disp_term = 'no' + hb_term = 'no' + LC_term = 'no' + branch_term = 'no' + II_term = 'no' + ID_term = 'no' + + IF ( only_term == 'ideal_gas' ) ideal_gas = trim( adjustl( type_of_term ) ) + IF ( only_term == 'hard_sphere' ) hard_sphere = trim( adjustl( type_of_term ) ) + IF ( only_term == 'chain_term' ) chain_term = trim( adjustl( type_of_term ) ) + IF ( only_term == 'disp_term' ) disp_term = trim( adjustl( type_of_term ) ) + IF ( only_term == 'hb_term' ) hb_term = trim( adjustl( type_of_term ) ) + IF ( only_term == 'LC_term' ) LC_term = trim( adjustl( type_of_term ) ) + IF ( only_term == 'branch_term' ) branch_term = trim( adjustl( type_of_term ) ) + IF ( only_term == 'II_term' ) II_term = trim( adjustl( type_of_term ) ) + IF ( only_term == 'ID_term' ) ID_term = trim( adjustl( type_of_term ) ) + +END SUBROUTINE ONLY_ONE_TERM_EOS_NUMERICAL + + +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! +SUBROUTINE RESTORE_PREVIOUS_EOS_NUMERICAL +! + USE EOS_NUMERICAL_DERIVATIVES + IMPLICIT NONE +! +! ---------------------------------------------------------------------- + ideal_gas = trim( adjustl( save_eos_terms(1) ) ) + hard_sphere = trim( adjustl( save_eos_terms(2) ) ) + chain_term = trim( adjustl( save_eos_terms(3) ) ) + disp_term = trim( adjustl( save_eos_terms(4) ) ) + hb_term = trim( adjustl( save_eos_terms(5) ) ) + LC_term = trim( adjustl( save_eos_terms(6) ) ) + branch_term = trim( adjustl( save_eos_terms(7) ) ) + II_term = trim( adjustl( save_eos_terms(8) ) ) + ID_term = trim( adjustl( save_eos_terms(9) ) ) + +END SUBROUTINE RESTORE_PREVIOUS_EOS_NUMERICAL + + + + diff --git a/applications/PUfoam/MoDeNaModels/Solubility/src/in.txt b/applications/PUfoam/MoDeNaModels/Solubility/src/in.txt new file mode 100644 index 000000000..c6f3172fc --- /dev/null +++ b/applications/PUfoam/MoDeNaModels/Solubility/src/in.txt @@ -0,0 +1,8 @@ +380.0 +3 +co2 +mdi +po +0.1 +0.5 +0.4 \ No newline at end of file diff --git a/applications/PUfoam/MoDeNaModels/Solubility/src/main.f90 b/applications/PUfoam/MoDeNaModels/Solubility/src/main.f90 new file mode 100644 index 000000000..523c5d814 --- /dev/null +++ b/applications/PUfoam/MoDeNaModels/Solubility/src/main.f90 @@ -0,0 +1,125 @@ + + +!> +!!THIS CODE WAS WRITTEN AT +!!UNIVERSITY OF STUTTGART, +!!INSTITUTE OF TECHNICAL THERMODYNAMICS AND THERMAL PROCESS ENGINEERING +!!BY +!!JOACHIM GROSS AND JONAS MAIRHOFER +!! + + + + + +!>WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +!! This program calculates solubilities (Henry coefficients) using the +!! PC-SAFT equation of state. +!! The input parameters are read from the file "in.txt" which has to +!! be in the same directory as the executable. +!! +!! The input file must have the following format: +!! Line1: Value of temperature in Kelvin +!! Line2: Number of components present in the system (ncomp) +!! Line3 Name of component 1 +!! ... +!! Line3+ncomp Name of component ncomp +!! Line3+ncomp+1 Molar (overall) concentration of component 1 +!! ... +!! Line3+2ncomp Molar (overall) concentration of component ncomp +!! +!! For a binary system, these molar concentrations are only treated as an initial guess and may be set to e.g. 0.5 +!! +!! +!! So far, pressure is set to 1bar in all calculaions +!! +!! +!!If you would like to use this code in your work, please cite the +!!following publications: +!! +!!Gross, Joachim, and Gabriele Sadowski. "Perturbed-chain SAFT: An equation of state based on a perturbation theory for chain molecules." Industrial & engineering chemistry research 40.4 (2001): 1244-1260. +!!Gross, Joachim, and Gabriele Sadowski. "Application of the perturbed-chain SAFT equation of state to associating systems." Industrial & engineering chemistry research 41.22 (2002): 5510-5515. +!!Gross, Joachim, and Jadran Vrabec. "An equation‐of‐state contribution for polar components: Dipolar molecules." AIChE journal 52.3 (2006): 1194-1204. +!!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +!! + + +PROGRAM PC_SAFT +! +! ---------------------------------------------------------------------- + USE BASIC_VARIABLES + USE EOS_CONSTANTS + USE DFT_MODULE + USE EOS_VARIABLES + IMPLICIT NONE + + +!> ---------------------------------------------------------------------- +!!Variables +!! ---------------------------------------------------------------------- + + REAL :: tc,pc,chemPot_total(nc) + REAL :: rhob(2,0:nc),density(np) + CHARACTER (LEN=50) :: filename + INTEGER :: compID,i + + +!> ---------------------------------------------------------------------- +!!Read information from inputfile "in.txt" +!! ---------------------------------------------------------------------- + + filename='./in.txt' + CALL file_open(filename,77) ! open input file + READ (77,*) t ! read temperature + READ (77,*) ncomp ! read number of components in the system + Do i = 1,ncomp ! read component names + READ (77,*) compna(i) + End Do + Do i = 1,ncomp ! read component overall molar concentrations + READ (77,*) cif(i) + End Do + + + !calculate molar fractions from molar concentrations + xif(1:ncomp) = cif(1:ncomp) / sum(cif(1:ncomp)) + + + +!> ---------------------------------------------------------------------- +!!General simulation set up +!! ---------------------------------------------------------------------- + + num = 1 ! (num=0: using analytical derivatives of EOS) + ! (num=1: using numerical derivatives of EOS) + ! (num=2: White's renormalization group theory) + IF ( num /= 0 ) CALL SET_DEFAULT_EOS_NUMERICAL + + eos = 1 ! eos=1: use PC-SAFT equation of state + pol = 1 ! pol=1: include polar interactions (use PCP-SAFT parameters) + + p = 1.000e05 ! pressure is fixed to 1bar in all simulations + + CALL para_input ! retriev pure comp. parameters + + ensemble_flag = 'tp' ! this specifies, whether the eos-subroutines + ! are executed for constant 'tp' or for constant 'tv' + +!> ---------------------------------------------------------------------- +!!Start phase equilibrium calculation +!! ---------------------------------------------------------------------- + + CALL EOS_CONST (ap, bp, dnm) ! read EOS constants + + dd_term = 'GV' ! dipole-dipole term of Gross & Vrabec (2006) + qq_term = 'JG' ! quadrupole-quadrupole term of Gross (2005) + dq_term = 'VG' ! dipole-quadrupole term of Vrabec & Gross (2008) + + CALL VLE_MIX(rhob,density,chemPot_total,compID) ! call routine that calculates phase equilibria + + + + + +END PROGRAM PC_SAFT + + diff --git a/applications/PUfoam/MoDeNaModels/Solubility/src/makefile b/applications/PUfoam/MoDeNaModels/Solubility/src/makefile new file mode 100644 index 000000000..8926c29b5 --- /dev/null +++ b/applications/PUfoam/MoDeNaModels/Solubility/src/makefile @@ -0,0 +1,31 @@ + + +#Source files +SOURCE = modules.f90 \ + module_solve_nonlinear.f90 \ + getting_started_subroutines.f90 \ + Numeric_subroutines.f90 \ + VLE_subroutines.f90 \ + VLE_main.f90\ + main.f90 \ + + + + +#Object files +OBJECT = $(SOURCE:%.f90=%.o) + + + +#define target for non-PETSc files +%.o: %.f90 + gfortran -c -fdefault-real-8 $< -o $@ + +EOS: $(OBJECT) + gfortran -o PCSAFT_Henry $(OBJECT) + +clean: + rm *.o *.mod + + + diff --git a/applications/PUfoam/MoDeNaModels/Solubility/src/module_solve_nonlinear.f90 b/applications/PUfoam/MoDeNaModels/Solubility/src/module_solve_nonlinear.f90 new file mode 100644 index 000000000..b850209f2 --- /dev/null +++ b/applications/PUfoam/MoDeNaModels/Solubility/src/module_solve_nonlinear.f90 @@ -0,0 +1,1622 @@ + +MODULE Solve_NonLin + +! Corrections to FUNCTION Enorm - 28 November 2003 + +IMPLICIT NONE +INTEGER, PARAMETER :: dp = SELECTED_REAL_KIND(14, 60) +PRIVATE +PUBLIC :: hbrd, hybrd + + +CONTAINS + + +SUBROUTINE hbrd(fcn, n, x, fvec, epsfcn, tol, info, diag) + +! Code converted using TO_F90 by Alan Miller +! Date: 2003-07-15 Time: 13:27:42 + +INTEGER, INTENT(IN) :: n +REAL (dp), INTENT(IN OUT) :: x(n) +REAL (dp), INTENT(IN OUT) :: fvec(n) +REAL (dp), INTENT(IN) :: epsfcn +REAL (dp), INTENT(IN) :: tol +INTEGER, INTENT(OUT) :: info +REAL (dp), INTENT(OUT) :: diag(n) + +! EXTERNAL fcn +INTERFACE + SUBROUTINE FCN(N, X, FVEC, IFLAG) + IMPLICIT NONE + INTEGER, PARAMETER :: dp = SELECTED_REAL_KIND(14, 60) + INTEGER, INTENT(IN) :: n + REAL (dp), INTENT(IN) :: x(n) + REAL (dp), INTENT(OUT) :: fvec(n) + INTEGER, INTENT(IN OUT) :: iflag + END SUBROUTINE FCN +END INTERFACE + +!> ********** +!! SUBROUTINE HBRD +!! THE PURPOSE OF HBRD IS TO FIND A ZERO OF A SYSTEM OF N NONLINEAR +!! FUNCTIONS IN N VARIABLES BY A MODIFICATION OF THE POWELL HYBRID METHOD. +!! THIS IS DONE BY USING THE MORE GENERAL NONLINEAR EQUATION SOLVER HYBRD. +!! THE USER MUST PROVIDE A SUBROUTINE WHICH CALCULATES THE FUNCTIONS. +!! THE JACOBIAN IS THEN CALCULATED BY A FORWARD-DIFFERENCE APPROXIMATION. +!! THE SUBROUTINE STATEMENT IS +!! SUBROUTINE HBRD(N, X, FVEC, EPSFCN, TOL, INFO, WA, LWA) +!! WHERE +!! FCN IS THE NAME OF THE USER-SUPPLIED SUBROUTINE WHICH CALCULATES +!! THE FUNCTIONS. FCN MUST BE DECLARED IN AN EXTERNAL STATEMENT +!! IN THE USER CALLING PROGRAM, AND SHOULD BE WRITTEN AS FOLLOWS. +!! SUBROUTINE FCN(N, X, FVEC, IFLAG) +!! INTEGER N,IFLAG +!! REAL X(N),FVEC(N) +!! ---------- +!! CALCULATE THE FUNCTIONS AT X AND RETURN THIS VECTOR IN FVEC. +!! --------- +!! RETURN +!! END +!! THE VALUE OF IFLAG NOT BE CHANGED BY FCN UNLESS +!! THE USER WANTS TO TERMINATE THE EXECUTION OF HBRD. +!! IN THIS CASE SET IFLAG TO A NEGATIVE INTEGER. +!! N IS A POSITIVE INTEGER INPUT VARIABLE SET TO THE NUMBER +!! OF FUNCTIONS AND VARIABLES. +!! X IS AN ARRAY OF LENGTH N. ON INPUT X MUST CONTAIN AN INITIAL +!! ESTIMATE OF THE SOLUTION VECTOR. ON OUTPUT X CONTAINS THE +!! FINAL ESTIMATE OF THE SOLUTION VECTOR. +!! FVEC IS AN OUTPUT ARRAY OF LENGTH N WHICH CONTAINS +!! THE FUNCTIONS EVALUATED AT THE OUTPUT X. +!! EPSFCN IS AN INPUT VARIABLE USED IN DETERMINING A SUITABLE STEP LENGTH +!! FOR THE FORWARD-DIFFERENCE APPROXIMATION. THIS APPROXIMATION ASSUMES +!! THAT THE RELATIVE ERRORS IN THE FUNCTIONS ARE OF THE ORDER OF EPSFCN. +!! IF EPSFCN IS LESS THAN THE MACHINE PRECISION, IT IS ASSUMED THAT THE +!! RELATIVE ERRORS IN THE FUNCTIONS ARE OF THE ORDER OF THE MACHINE +!! PRECISION. +!! TOL IS A NONNEGATIVE INPUT VARIABLE. TERMINATION OCCURS WHEN THE +!! ALGORITHM ESTIMATES THAT THE RELATIVE ERROR BETWEEN X AND THE SOLUTION +!! IS AT MOST TOL. +!! INFO IS AN INTEGER OUTPUT VARIABLE. IF THE USER HAS TERMINATED +!! EXECUTION, INFO IS SET TO THE (NEGATIVE) VALUE OF IFLAG. +!! SEE DESCRIPTION OF FCN. OTHERWISE, INFO IS SET AS FOLLOWS. +!! INFO = 0 IMPROPER INPUT PARAMETERS. +!! INFO = 1 ALGORITHM ESTIMATES THAT THE RELATIVE ERROR +!! BETWEEN X AND THE SOLUTION IS AT MOST TOL. +!! INFO = 2 NUMBER OF CALLS TO FCN HAS REACHED OR EXCEEDED 200*(N+1). +!! INFO = 3 TOL IS TOO SMALL. NO FURTHER IMPROVEMENT IN +!! THE APPROXIMATE SOLUTION X IS POSSIBLE. +!! INFO = 4 ITERATION IS NOT MAKING GOOD PROGRESS. +!! SUBPROGRAMS CALLED +!! USER-SUPPLIED ...... FCN +!! MINPACK-SUPPLIED ... HYBRD +!! ARGONNE NATIONAL LABORATORY. MINPACK PROJECT. MARCH 1980. +!! BURTON S. GARBOW, KENNETH E. HILLSTROM, JORGE J. MORE +!! Reference: +!! Powell, M.J.D. 'A hybrid method for nonlinear equations' in Numerical Methods +!! for Nonlinear Algebraic Equations', P.Rabinowitz (editor), Gordon and +!! Breach, London 1970. +!! ********** + +INTEGER :: maxfev, ml, mode, mu, nfev, nprint +REAL (dp) :: xtol +REAL (dp), PARAMETER :: factor = 1.0_dp, zero = 0.0_dp + +info = 0 + +! CHECK THE INPUT PARAMETERS FOR ERRORS. + + +IF (n <= 0 .OR. epsfcn < zero .OR. tol < zero) GO TO 20 + +! CALL HYBRD. + +maxfev = 200*(n + 1) +xtol = tol +ml = n - 1 +mu = n - 1 +mode = 2 +nprint = 0 +CALL hybrd(fcn, n, x, fvec, xtol, maxfev, ml, mu, epsfcn, diag, mode, & + factor, nprint, info, nfev) +IF (info == 5) info = 4 +20 RETURN + +! LAST CARD OF SUBROUTINE HBRD. + +END SUBROUTINE hbrd + + + +SUBROUTINE hybrd(fcn, n, x, fvec, xtol, maxfev, ml, mu, epsfcn, diag, mode, & + factor, nprint, info, nfev) + +INTEGER, INTENT(IN) :: n +REAL (dp), INTENT(IN OUT) :: x(n) +REAL (dp), INTENT(IN OUT) :: fvec(n) +REAL (dp), INTENT(IN) :: xtol +INTEGER, INTENT(IN OUT) :: maxfev +INTEGER, INTENT(IN OUT) :: ml +INTEGER, INTENT(IN) :: mu +REAL (dp), INTENT(IN) :: epsfcn +REAL (dp), INTENT(OUT) :: diag(n) +INTEGER, INTENT(IN) :: mode +REAL (dp), INTENT(IN) :: factor +INTEGER, INTENT(IN OUT) :: nprint +INTEGER, INTENT(OUT) :: info +INTEGER, INTENT(OUT) :: nfev + +! EXTERNAL fcn +INTERFACE + SUBROUTINE FCN(N, X, FVEC, IFLAG) + IMPLICIT NONE + INTEGER, PARAMETER :: dp = SELECTED_REAL_KIND(14, 60) + INTEGER, INTENT(IN) :: n + REAL (dp), INTENT(IN) :: x(n) + REAL (dp), INTENT(OUT) :: fvec(n) + INTEGER, INTENT(IN OUT) :: iflag + END SUBROUTINE FCN +END INTERFACE + +! ********** + +! SUBROUTINE HYBRD + +! THE PURPOSE OF HYBRD IS TO FIND A ZERO OF A SYSTEM OF N NONLINEAR +! FUNCTIONS IN N VARIABLES BY A MODIFICATION OF THE POWELL HYBRID METHOD. +! THE USER MUST PROVIDE A SUBROUTINE WHICH CALCULATES THE FUNCTIONS. +! THE JACOBIAN IS THEN CALCULATED BY A FORWARD-DIFFERENCE APPROXIMATION. + +! THE SUBROUTINE STATEMENT IS + +! SUBROUTINE HYBRD(FCN, N, X, FVEC, XTOL, MAXFEV, ML, MU, EPSFCN, +! DIAG, MODE, FACTOR, NPRINT, INFO, NFEV, FJAC, +! LDFJAC, R, LR, QTF, WA1, WA2, WA3, WA4) + +! WHERE + +! FCN IS THE NAME OF THE USER-SUPPLIED SUBROUTINE WHICH CALCULATES +! THE FUNCTIONS. FCN MUST BE DECLARED IN AN EXTERNAL STATEMENT IN +! THE USER CALLING PROGRAM, AND SHOULD BE WRITTEN AS FOLLOWS. + +! SUBROUTINE FCN(N, X, FVEC, IFLAG) +! INTEGER N, IFLAG +! REAL X(N), FVEC(N) +! ---------- +! CALCULATE THE FUNCTIONS AT X AND +! RETURN THIS VECTOR IN FVEC. +! --------- +! RETURN +! END + +! THE VALUE OF IFLAG SHOULD NOT BE CHANGED BY FCN UNLESS +! THE USER WANTS TO TERMINATE EXECUTION OF HYBRD. +! IN THIS CASE SET IFLAG TO A NEGATIVE INTEGER. + +! N IS A POSITIVE INTEGER INPUT VARIABLE SET TO THE NUMBER +! OF FUNCTIONS AND VARIABLES. + +! X IS AN ARRAY OF LENGTH N. ON INPUT X MUST CONTAIN AN INITIAL +! ESTIMATE OF THE SOLUTION VECTOR. ON OUTPUT X CONTAINS THE FINAL +! ESTIMATE OF THE SOLUTION VECTOR. + +! FVEC IS AN OUTPUT ARRAY OF LENGTH N WHICH CONTAINS +! THE FUNCTIONS EVALUATED AT THE OUTPUT X. + +! XTOL IS A NONNEGATIVE INPUT VARIABLE. TERMINATION OCCURS WHEN THE +! RELATIVE ERROR BETWEEN TWO CONSECUTIVE ITERATES IS AT MOST XTOL. + +! MAXFEV IS A POSITIVE INTEGER INPUT VARIABLE. TERMINATION OCCURS WHEN +! THE NUMBER OF CALLS TO FCN IS AT LEAST MAXFEV BY THE END OF AN +! ITERATION. + +! ML IS A NONNEGATIVE INTEGER INPUT VARIABLE WHICH SPECIFIES THE +! NUMBER OF SUBDIAGONALS WITHIN THE BAND OF THE JACOBIAN MATRIX. +! IF THE JACOBIAN IS NOT BANDED, SET ML TO AT LEAST N - 1. + +! MU IS A NONNEGATIVE INTEGER INPUT VARIABLE WHICH SPECIFIES THE NUMBER +! OF SUPERDIAGONALS WITHIN THE BAND OF THE JACOBIAN MATRIX. +! IF THE JACOBIAN IS NOT BANDED, SET MU TO AT LEAST N - 1. + +! EPSFCN IS AN INPUT VARIABLE USED IN DETERMINING A SUITABLE STEP LENGTH +! FOR THE FORWARD-DIFFERENCE APPROXIMATION. THIS APPROXIMATION +! ASSUMES THAT THE RELATIVE ERRORS IN THE FUNCTIONS ARE OF THE ORDER +! OF EPSFCN. IF EPSFCN IS LESS THAN THE MACHINE PRECISION, +! IT IS ASSUMED THAT THE RELATIVE ERRORS IN THE FUNCTIONS ARE OF THE +! ORDER OF THE MACHINE PRECISION. + +! DIAG IS AN ARRAY OF LENGTH N. IF MODE = 1 (SEE BELOW), +! DIAG IS INTERNALLY SET. IF MODE = 2, DIAG MUST CONTAIN POSITIVE +! ENTRIES THAT SERVE AS MULTIPLICATIVE SCALE FACTORS FOR THE +! VARIABLES. + +! MODE IS AN INTEGER INPUT VARIABLE. IF MODE = 1, THE VARIABLES WILL BE +! SCALED INTERNALLY. IF MODE = 2, THE SCALING IS SPECIFIED BY THE +! INPUT DIAG. OTHER VALUES OF MODE ARE EQUIVALENT TO MODE = 1. + +! FACTOR IS A POSITIVE INPUT VARIABLE USED IN DETERMINING THE +! INITIAL STEP BOUND. THIS BOUND IS SET TO THE PRODUCT OF +! FACTOR AND THE EUCLIDEAN NORM OF DIAG*X IF NONZERO, OR ELSE +! TO FACTOR ITSELF. IN MOST CASES FACTOR SHOULD LIE IN THE +! INTERVAL (.1,100.). 100. IS A GENERALLY RECOMMENDED VALUE. + +! NPRINT IS AN INTEGER INPUT VARIABLE THAT ENABLES CONTROLLED +! PRINTING OF ITERATES IF IT IS POSITIVE. IN THIS CASE, +! FCN IS CALLED WITH IFLAG = 0 AT THE BEGINNING OF THE FIRST +! ITERATION AND EVERY NPRINT ITERATIONS THEREAFTER AND +! IMMEDIATELY PRIOR TO RETURN, WITH X AND FVEC AVAILABLE +! FOR PRINTING. IF NPRINT IS NOT POSITIVE, NO SPECIAL CALLS +! OF FCN WITH IFLAG = 0 ARE MADE. + +! INFO IS AN INTEGER OUTPUT VARIABLE. IF THE USER HAS +! TERMINATED EXECUTION, INFO IS SET TO THE (NEGATIVE) +! VALUE OF IFLAG. SEE DESCRIPTION OF FCN. OTHERWISE, +! INFO IS SET AS FOLLOWS. + +! INFO = 0 IMPROPER INPUT PARAMETERS. + +! INFO = 1 RELATIVE ERROR BETWEEN TWO CONSECUTIVE ITERATES +! IS AT MOST XTOL. + +! INFO = 2 NUMBER OF CALLS TO FCN HAS REACHED OR EXCEEDED MAXFEV. + +! INFO = 3 XTOL IS TOO SMALL. NO FURTHER IMPROVEMENT IN +! THE APPROXIMATE SOLUTION X IS POSSIBLE. + +! INFO = 4 ITERATION IS NOT MAKING GOOD PROGRESS, AS +! MEASURED BY THE IMPROVEMENT FROM THE LAST +! FIVE JACOBIAN EVALUATIONS. + +! INFO = 5 ITERATION IS NOT MAKING GOOD PROGRESS, AS MEASURED BY +! THE IMPROVEMENT FROM THE LAST TEN ITERATIONS. + +! NFEV IS AN INTEGER OUTPUT VARIABLE SET TO THE NUMBER OF CALLS TO FCN. + +! FJAC IS AN OUTPUT N BY N ARRAY WHICH CONTAINS THE ORTHOGONAL MATRIX Q +! PRODUCED BY THE QR FACTORIZATION OF THE FINAL APPROXIMATE JACOBIAN. + +! LDFJAC IS A POSITIVE INTEGER INPUT VARIABLE NOT LESS THAN N +! WHICH SPECIFIES THE LEADING DIMENSION OF THE ARRAY FJAC. + +! R IS AN OUTPUT ARRAY OF LENGTH LR WHICH CONTAINS THE +! UPPER TRIANGULAR MATRIX PRODUCED BY THE QR FACTORIZATION +! OF THE FINAL APPROXIMATE JACOBIAN, STORED ROWWISE. + +! LR IS A POSITIVE INTEGER INPUT VARIABLE NOT LESS THAN (N*(N+1))/2. + +! QTF IS AN OUTPUT ARRAY OF LENGTH N WHICH CONTAINS +! THE VECTOR (Q TRANSPOSE)*FVEC. + +! WA1, WA2, WA3, AND WA4 ARE WORK ARRAYS OF LENGTH N. + +! SUBPROGRAMS CALLED + +! USER-SUPPLIED ...... FCN + +! MINPACK-SUPPLIED ... DOGLEG,SPMPAR,ENORM,FDJAC1, +! QFORM,QRFAC,R1MPYQ,R1UPDT + +! FORTRAN-SUPPLIED ... ABS,MAX,MIN,MIN,MOD + +! ARGONNE NATIONAL LABORATORY. MINPACK PROJECT. MARCH 1980. +! BURTON S. GARBOW, KENNETH E. HILLSTROM, JORGE J. MORE + +! ********** + +INTEGER :: i, iflag, iter, j, jm1, l, lr, msum, ncfail, ncsuc, nslow1, & + nslow2 +INTEGER :: iwa(1) +LOGICAL :: jeval, sing +REAL (dp) :: actred, delta, epsmch, fnorm, fnorm1, pnorm, prered, & + ratio, sum, temp, xnorm +REAL (dp), PARAMETER :: one = 1.0_dp, p1 = 0.1_dp, p5 = 0.5_dp, & + p001 = 0.001_dp, p0001 = 0.0001_dp, zero = 0.0_dp + +! The following were workspace arguments +REAL (dp) :: fjac(n,n), r(n*(n+1)/2), qtf(n), wa1(n), wa2(n), & + wa3(n), wa4(n) + +! EPSMCH IS THE MACHINE PRECISION. + +epsmch = EPSILON(1.0_dp) + +info = 0 +iflag = 0 +nfev = 0 +lr = n*(n+1)/2 + +! CHECK THE INPUT PARAMETERS FOR ERRORS. + +IF (n > 0 .AND. xtol >= zero .AND. maxfev > 0 .AND. ml >= 0 .AND. mu >= & + 0 .AND. factor > zero ) THEN +IF (mode == 2) THEN + diag(1:n) = one +END IF + +! EVALUATE THE FUNCTION AT THE STARTING POINT AND CALCULATE ITS NORM. + +iflag = 1 +CALL fcn(n, x, fvec, iflag) +nfev = 1 +IF (iflag >= 0) THEN + fnorm = enorm(n, fvec) + +! DETERMINE THE NUMBER OF CALLS TO FCN NEEDED TO COMPUTE THE JACOBIAN MATRIX. + + msum = MIN(ml+mu+1,n) + +! INITIALIZE ITERATION COUNTER AND MONITORS. + + iter = 1 + ncsuc = 0 + ncfail = 0 + nslow1 = 0 + nslow2 = 0 + +! BEGINNING OF THE OUTER LOOP. + + 20 jeval = .true. + +! CALCULATE THE JACOBIAN MATRIX. + + iflag = 2 + CALL fdjac1(fcn, n, x, fvec, fjac, n, iflag, ml, mu, epsfcn, wa1, wa2) + nfev = nfev + msum + IF (iflag >= 0) THEN + +! COMPUTE THE QR FACTORIZATION OF THE JACOBIAN. + + CALL qrfac(n, n, fjac, n, .false., iwa, 1, wa1, wa2, wa3) + +! ON THE FIRST ITERATION AND IF MODE IS 1, SCALE ACCORDING +! TO THE NORMS OF THE COLUMNS OF THE INITIAL JACOBIAN. + + IF (iter == 1) THEN + IF (mode /= 2) THEN + DO j = 1, n + diag(j) = wa2(j) + IF (wa2(j) == zero) diag(j) = one + END DO + END IF + +! ON THE FIRST ITERATION, CALCULATE THE NORM OF THE SCALED X +! AND INITIALIZE THE STEP BOUND DELTA. + + wa3(1:n) = diag(1:n) * x(1:n) + xnorm = enorm(n, wa3) + delta = factor * xnorm + IF (delta == zero) delta = factor + END IF + +! FORM (Q TRANSPOSE)*FVEC AND STORE IN QTF. + + qtf(1:n) = fvec(1:n) + DO j = 1, n + IF (fjac(j,j) /= zero) THEN + sum = zero + DO i = j, n + sum = sum + fjac(i,j) * qtf(i) + END DO + temp = -sum / fjac(j,j) + DO i = j, n + qtf(i) = qtf(i) + fjac(i,j) * temp + END DO + END IF + END DO + +! COPY THE TRIANGULAR FACTOR OF THE QR FACTORIZATION INTO R. + + sing = .false. + DO j = 1, n + l = j + jm1 = j - 1 + IF (jm1 >= 1) THEN + DO i = 1, jm1 + r(l) = fjac(i,j) + l = l + n - i + END DO + END IF + r(l) = wa1(j) + IF (wa1(j) == zero) sing = .true. + END DO + +! ACCUMULATE THE ORTHOGONAL FACTOR IN FJAC. + + CALL qform(n, n, fjac, n, wa1) + +! RESCALE IF NECESSARY. + + IF (mode /= 2) THEN + DO j = 1, n + diag(j) = MAX(diag(j), wa2(j)) + END DO + END IF + +! BEGINNING OF THE INNER LOOP. + +! IF REQUESTED, CALL FCN TO ENABLE PRINTING OF ITERATES. + + 120 IF (nprint > 0) THEN + iflag = 0 + IF (MOD(iter-1, nprint) == 0) CALL fcn(n, x, fvec, iflag) + IF (iflag < 0) GO TO 190 + END IF + +! DETERMINE THE DIRECTION P. + + CALL dogleg(n, r, lr, diag, qtf, delta, wa1, wa2, wa3) + +! STORE THE DIRECTION P AND X + P. CALCULATE THE NORM OF P. + + DO j = 1, n + wa1(j) = -wa1(j) + wa2(j) = x(j) + wa1(j) + wa3(j) = diag(j) * wa1(j) + END DO + pnorm = enorm(n, wa3) + +! ON THE FIRST ITERATION, ADJUST THE INITIAL STEP BOUND. + + IF (iter == 1) delta = MIN(delta, pnorm) + +! EVALUATE THE FUNCTION AT X + P AND CALCULATE ITS NORM. + + iflag = 1 + CALL fcn(n, wa2, wa4, iflag) + nfev = nfev + 1 + IF (iflag >= 0) THEN + fnorm1 = enorm(n, wa4) + +! COMPUTE THE SCALED ACTUAL REDUCTION. + + actred = -one + IF (fnorm1 < fnorm) actred = one - (fnorm1/fnorm) ** 2 + +! COMPUTE THE SCALED PREDICTED REDUCTION. + + l = 1 + DO i = 1, n + sum = zero + DO j = i, n + sum = sum + r(l) * wa1(j) + l = l + 1 + END DO + wa3(i) = qtf(i) + sum + END DO + temp = enorm(n, wa3) + prered = zero + IF (temp < fnorm) prered = one - (temp/fnorm) ** 2 + +! COMPUTE THE RATIO OF THE ACTUAL TO THE PREDICTED REDUCTION. + + ratio = zero + IF (prered > zero) ratio = actred / prered + +! UPDATE THE STEP BOUND. + + IF (ratio < p1) THEN + ncsuc = 0 + ncfail = ncfail + 1 + delta = p5 * delta + ELSE + ncfail = 0 + ncsuc = ncsuc + 1 + IF (ratio >= p5 .OR. ncsuc > 1) delta = MAX(delta,pnorm/p5) + IF (ABS(ratio-one) <= p1) delta = pnorm / p5 + END IF + +! TEST FOR SUCCESSFUL ITERATION. + + IF (ratio >= p0001) THEN + +! SUCCESSFUL ITERATION. UPDATE X, FVEC, AND THEIR NORMS. + + DO j = 1, n + x(j) = wa2(j) + wa2(j) = diag(j) * x(j) + fvec(j) = wa4(j) + END DO + xnorm = enorm(n, wa2) + fnorm = fnorm1 + iter = iter + 1 + END IF + +! DETERMINE THE PROGRESS OF THE ITERATION. + + nslow1 = nslow1 + 1 + IF (actred >= p001) nslow1 = 0 + IF (jeval) nslow2 = nslow2 + 1 + IF (actred >= p1) nslow2 = 0 + +! TEST FOR CONVERGENCE. + + IF (delta <= xtol*xnorm .OR. fnorm == zero) info = 1 + IF (info == 0) THEN + +! TESTS FOR TERMINATION AND STRINGENT TOLERANCES. + + IF (nfev >= maxfev) info = 2 + IF (p1*MAX(p1*delta, pnorm) <= epsmch*xnorm) info = 3 + IF (nslow2 == 5) info = 4 + IF (nslow1 == 10) info = 5 + IF (info == 0) THEN + +! CRITERION FOR RECALCULATING JACOBIAN APPROXIMATION +! BY FORWARD DIFFERENCES. + + IF (ncfail /= 2) THEN + +! CALCULATE THE RANK ONE MODIFICATION TO THE JACOBIAN +! AND UPDATE QTF IF NECESSARY. + + DO j = 1, n + sum = zero + DO i = 1, n + sum = sum + fjac(i,j) * wa4(i) + END DO + wa2(j) = (sum-wa3(j)) / pnorm + wa1(j) = diag(j) * ((diag(j)*wa1(j))/pnorm) + IF (ratio >= p0001) qtf(j) = sum + END DO + +! COMPUTE THE QR FACTORIZATION OF THE UPDATED JACOBIAN. + + CALL r1updt(n, n, r, lr, wa1, wa2, wa3, sing) + CALL r1mpyq(n, n, fjac, n, wa2, wa3) + CALL r1mpyq(1, n, qtf, 1, wa2, wa3) + +! END OF THE INNER LOOP. + + jeval = .false. + GO TO 120 + END IF + +! END OF THE OUTER LOOP. + + GO TO 20 + END IF + END IF + END IF + END IF +END IF +END IF + +! TERMINATION, EITHER NORMAL OR USER IMPOSED. + +190 IF (iflag < 0) info = iflag +iflag = 0 +IF (nprint > 0) CALL fcn(n, x, fvec, iflag) +RETURN + +! LAST CARD OF SUBROUTINE HYBRD. + +END SUBROUTINE hybrd + + + +SUBROUTINE dogleg(n, r, lr, diag, qtb, delta, x, wa1, wa2) + +INTEGER, INTENT(IN) :: n +INTEGER, INTENT(IN) :: lr +REAL (dp), INTENT(IN) :: r(lr) +REAL (dp), INTENT(IN) :: diag(n) +REAL (dp), INTENT(IN) :: qtb(n) +REAL (dp), INTENT(IN) :: delta +REAL (dp), INTENT(IN OUT) :: x(n) +REAL (dp), INTENT(OUT) :: wa1(n) +REAL (dp), INTENT(OUT) :: wa2(n) + + +! ********** + +! SUBROUTINE DOGLEG + +! GIVEN AN M BY N MATRIX A, AN N BY N NONSINGULAR DIAGONAL +! MATRIX D, AN M-VECTOR B, AND A POSITIVE NUMBER DELTA, THE +! PROBLEM IS TO DETERMINE THE CONVEX COMBINATION X OF THE +! GAUSS-NEWTON AND SCALED GRADIENT DIRECTIONS THAT MINIMIZES +! (A*X - B) IN THE LEAST SQUARES SENSE, SUBJECT TO THE +! RESTRICTION THAT THE EUCLIDEAN NORM OF D*X BE AT MOST DELTA. + +! THIS SUBROUTINE COMPLETES THE SOLUTION OF THE PROBLEM +! IF IT IS PROVIDED WITH THE NECESSARY INFORMATION FROM THE +! QR FACTORIZATION OF A. THAT IS, IF A = Q*R, WHERE Q HAS +! ORTHOGONAL COLUMNS AND R IS AN UPPER TRIANGULAR MATRIX, +! THEN DOGLEG EXPECTS THE FULL UPPER TRIANGLE OF R AND +! THE FIRST N COMPONENTS OF (Q TRANSPOSE)*B. + +! THE SUBROUTINE STATEMENT IS + +! SUBROUTINE DOGLEG(N,R,LR,DIAG,QTB,DELTA,X,WA1,WA2) + +! WHERE + +! N IS A POSITIVE INTEGER INPUT VARIABLE SET TO THE ORDER OF R. + +! R IS AN INPUT ARRAY OF LENGTH LR WHICH MUST CONTAIN THE UPPER +! TRIANGULAR MATRIX R STORED BY ROWS. + +! LR IS A POSITIVE INTEGER INPUT VARIABLE NOT LESS THAN +! (N*(N+1))/2. + +! DIAG IS AN INPUT ARRAY OF LENGTH N WHICH MUST CONTAIN THE +! DIAGONAL ELEMENTS OF THE MATRIX D. + +! QTB IS AN INPUT ARRAY OF LENGTH N WHICH MUST CONTAIN THE FIRST +! N ELEMENTS OF THE VECTOR (Q TRANSPOSE)*B. + +! DELTA IS A POSITIVE INPUT VARIABLE WHICH SPECIFIES AN UPPER +! BOUND ON THE EUCLIDEAN NORM OF D*X. + +! X IS AN OUTPUT ARRAY OF LENGTH N WHICH CONTAINS THE DESIRED +! CONVEX COMBINATION OF THE GAUSS-NEWTON DIRECTION AND THE +! SCALED GRADIENT DIRECTION. + +! WA1 AND WA2 ARE WORK ARRAYS OF LENGTH N. + +! SUBPROGRAMS CALLED + +! MINPACK-SUPPLIED ... SPMPAR,ENORM + +! FORTRAN-SUPPLIED ... ABS,MAX,MIN,SQRT + +! ARGONNE NATIONAL LABORATORY. MINPACK PROJECT. MARCH 1980. +! BURTON S. GARBOW, KENNETH E. HILLSTROM, JORGE J. MORE + +! ********** +INTEGER :: i, j, jj, jp1, k, l +REAL (dp) :: alpha, bnorm, epsmch, gnorm, qnorm, sgnorm, sum, temp + +! EPSMCH IS THE MACHINE PRECISION. + +epsmch = EPSILON(1.0_dp) + +! FIRST, CALCULATE THE GAUSS-NEWTON DIRECTION. + +jj = (n*(n+1)) / 2 + 1 +DO k = 1, n + j = n - k + 1 + jp1 = j + 1 + jj = jj - k + l = jj + 1 + sum = 0.0 + IF (n >= jp1) THEN + DO i = jp1, n + sum = sum + r(l) * x(i) + l = l + 1 + END DO + END IF + temp = r(jj) + IF (temp == 0.0) THEN + l = j + DO i = 1, j + temp = MAX(temp,ABS(r(l))) + l = l + n - i + END DO + temp = epsmch * temp + IF (temp == 0.0) temp = epsmch + END IF + x(j) = (qtb(j)-sum) / temp +END DO + +! TEST WHETHER THE GAUSS-NEWTON DIRECTION IS ACCEPTABLE. + +DO j = 1, n + wa1(j) = 0.0 + wa2(j) = diag(j) * x(j) +END DO +qnorm = enorm(n, wa2) +IF (qnorm > delta) THEN + +! THE GAUSS-NEWTON DIRECTION IS NOT ACCEPTABLE. +! NEXT, CALCULATE THE SCALED GRADIENT DIRECTION. + + l = 1 + DO j = 1, n + temp = qtb(j) + DO i = j, n + wa1(i) = wa1(i) + r(l) * temp + l = l + 1 + END DO + wa1(j) = wa1(j) / diag(j) + END DO + +! CALCULATE THE NORM OF THE SCALED GRADIENT AND TEST FOR +! THE SPECIAL CASE IN WHICH THE SCALED GRADIENT IS ZERO. + + gnorm = enorm(n, wa1) + sgnorm = 0.0 + alpha = delta / qnorm + IF (gnorm /= 0.0) THEN + +! CALCULATE THE POINT ALONG THE SCALED GRADIENT +! AT WHICH THE QUADRATIC IS MINIMIZED. + + DO j = 1, n + wa1(j) = (wa1(j)/gnorm) / diag(j) + END DO + l = 1 + DO j = 1, n + sum = 0.0 + DO i = j, n + sum = sum + r(l) * wa1(i) + l = l + 1 + END DO + wa2(j) = sum + END DO + temp = enorm(n, wa2) + sgnorm = (gnorm/temp) / temp + +! TEST WHETHER THE SCALED GRADIENT DIRECTION IS ACCEPTABLE. + + alpha = 0.0 + IF (sgnorm < delta) THEN + +! THE SCALED GRADIENT DIRECTION IS NOT ACCEPTABLE. +! FINALLY, CALCULATE THE POINT ALONG THE DOGLEG +! AT WHICH THE QUADRATIC IS MINIMIZED. + + bnorm = enorm(n, qtb) + temp = (bnorm/gnorm) * (bnorm/qnorm) * (sgnorm/delta) + temp = temp - (delta/qnorm) * (sgnorm/delta) ** 2 + SQRT(( & + temp-(delta/qnorm))**2+(1.0-(delta/qnorm)**2)*(1.0-( sgnorm/delta)**2)) + alpha = ((delta/qnorm)*(1.0-(sgnorm/delta)**2)) / temp + END IF + END IF + +! FORM APPROPRIATE CONVEX COMBINATION OF THE GAUSS-NEWTON +! DIRECTION AND THE SCALED GRADIENT DIRECTION. + + temp = (1.0-alpha) * MIN(sgnorm,delta) + DO j = 1, n + x(j) = temp * wa1(j) + alpha * x(j) + END DO +END IF +RETURN +END SUBROUTINE dogleg + + +SUBROUTINE fdjac1(fcn, n, x, fvec, fjac, ldfjac, iflag, ml, mu, epsfcn, & + wa1, wa2) + +INTEGER, INTENT(IN) :: n +REAL (dp), INTENT(IN OUT) :: x(n) +REAL (dp), INTENT(IN) :: fvec(n) +INTEGER, INTENT(IN) :: ldfjac +REAL (dp), INTENT(OUT) :: fjac(ldfjac,n) +INTEGER, INTENT(IN OUT) :: iflag +INTEGER, INTENT(IN) :: ml +INTEGER, INTENT(IN) :: mu +REAL (dp), INTENT(IN) :: epsfcn +REAL (dp), INTENT(IN OUT) :: wa1(n) +REAL (dp), INTENT(OUT) :: wa2(n) + +! EXTERNAL fcn +INTERFACE + SUBROUTINE FCN(N, X, FVEC, IFLAG) + IMPLICIT NONE + INTEGER, PARAMETER :: dp = SELECTED_REAL_KIND(14, 60) + INTEGER, INTENT(IN) :: n + REAL (dp), INTENT(IN) :: x(n) + REAL (dp), INTENT(OUT) :: fvec(n) + INTEGER, INTENT(IN OUT) :: iflag + END SUBROUTINE FCN +END INTERFACE + +! ********** + +! SUBROUTINE FDJAC1 + +! THIS SUBROUTINE COMPUTES A FORWARD-DIFFERENCE APPROXIMATION TO THE N BY N +! JACOBIAN MATRIX ASSOCIATED WITH A SPECIFIED PROBLEM OF N FUNCTIONS IN N +! VARIABLES. IF THE JACOBIAN HAS A BANDED FORM, THEN FUNCTION EVALUATIONS +! ARE SAVED BY ONLY APPROXIMATING THE NONZERO TERMS. + +! THE SUBROUTINE STATEMENT IS + +! SUBROUTINE FDJAC1(FCN,N,X,FVEC,FJAC,LDFJAC,IFLAG,ML,MU,EPSFCN, +! WA1,WA2) + +! WHERE + +! FCN IS THE NAME OF THE USER-SUPPLIED SUBROUTINE WHICH CALCULATES +! THE FUNCTIONS. FCN MUST BE DECLARED IN AN EXTERNAL STATEMENT IN +! THE USER CALLING PROGRAM, AND SHOULD BE WRITTEN AS FOLLOWS. + +! SUBROUTINE FCN(N,X,FVEC,IFLAG) +! INTEGER N,IFLAG +! REAL X(N),FVEC(N) +! ---------- +! CALCULATE THE FUNCTIONS AT X AND +! RETURN THIS VECTOR IN FVEC. +! ---------- +! RETURN +! END + +! THE VALUE OF IFLAG SHOULD NOT BE CHANGED BY FCN UNLESS +! THE USER WANTS TO TERMINATE EXECUTION OF FDJAC1. +! IN THIS CASE SET IFLAG TO A NEGATIVE INTEGER. + +! N IS A POSITIVE INTEGER INPUT VARIABLE SET TO THE NUMBER +! OF FUNCTIONS AND VARIABLES. + +! X IS AN INPUT ARRAY OF LENGTH N. + +! FVEC IS AN INPUT ARRAY OF LENGTH N WHICH MUST CONTAIN THE +! FUNCTIONS EVALUATED AT X. + +! FJAC IS AN OUTPUT N BY N ARRAY WHICH CONTAINS THE +! APPROXIMATION TO THE JACOBIAN MATRIX EVALUATED AT X. + +! LDFJAC IS A POSITIVE INTEGER INPUT VARIABLE NOT LESS THAN N +! WHICH SPECIFIES THE LEADING DIMENSION OF THE ARRAY FJAC. + +! IFLAG IS AN INTEGER VARIABLE WHICH CAN BE USED TO TERMINATE +! THE EXECUTION OF FDJAC1. SEE DESCRIPTION OF FCN. + +! ML IS A NONNEGATIVE INTEGER INPUT VARIABLE WHICH SPECIFIES +! THE NUMBER OF SUBDIAGONALS WITHIN THE BAND OF THE +! JACOBIAN MATRIX. IF THE JACOBIAN IS NOT BANDED, SET +! ML TO AT LEAST N - 1. + +! EPSFCN IS AN INPUT VARIABLE USED IN DETERMINING A SUITABLE +! STEP LENGTH FOR THE FORWARD-DIFFERENCE APPROXIMATION. THIS +! APPROXIMATION ASSUMES THAT THE RELATIVE ERRORS IN THE +! FUNCTIONS ARE OF THE ORDER OF EPSFCN. IF EPSFCN IS LESS +! THAN THE MACHINE PRECISION, IT IS ASSUMED THAT THE RELATIVE +! ERRORS IN THE FUNCTIONS ARE OF THE ORDER OF THE MACHINE PRECISION. + +! MU IS A NONNEGATIVE INTEGER INPUT VARIABLE WHICH SPECIFIES +! THE NUMBER OF SUPERDIAGONALS WITHIN THE BAND OF THE +! JACOBIAN MATRIX. IF THE JACOBIAN IS NOT BANDED, SET +! MU TO AT LEAST N - 1. + +! WA1 AND WA2 ARE WORK ARRAYS OF LENGTH N. IF ML + MU + 1 IS AT +! LEAST N, THEN THE JACOBIAN IS CONSIDERED DENSE, AND WA2 IS +! NOT REFERENCED. + +! SUBPROGRAMS CALLED + +! MINPACK-SUPPLIED ... SPMPAR + +! FORTRAN-SUPPLIED ... ABS,MAX,SQRT + +! ARGONNE NATIONAL LABORATORY. MINPACK PROJECT. MARCH 1980. +! BURTON S. GARBOW, KENNETH E. HILLSTROM, JORGE J. MORE + +! ********** +INTEGER :: i, j, k, msum +REAL (dp) :: eps, epsmch, h, temp +REAL (dp), PARAMETER :: zero = 0.0_dp + +! EPSMCH IS THE MACHINE PRECISION. + +epsmch = EPSILON(1.0_dp) + +eps = SQRT(MAX(epsfcn, epsmch)) +msum = ml + mu + 1 +IF (msum >= n) THEN + +! COMPUTATION OF DENSE APPROXIMATE JACOBIAN. + + DO j = 1, n + temp = x(j) + h = eps * ABS(temp) + IF (h == zero) h = eps + x(j) = temp + h + CALL fcn(n, x, wa1, iflag) + IF (iflag < 0) EXIT + x(j) = temp + DO i = 1, n + fjac(i,j) = (wa1(i)-fvec(i)) / h + END DO + END DO +ELSE + +! COMPUTATION OF BANDED APPROXIMATE JACOBIAN. + + DO k = 1, msum + DO j = k, n, msum + wa2(j) = x(j) + h = eps * ABS(wa2(j)) + IF (h == zero) h = eps + x(j) = wa2(j) + h + END DO + CALL fcn(n, x, wa1, iflag) + IF (iflag < 0) EXIT + DO j = k, n, msum + x(j) = wa2(j) + h = eps * ABS(wa2(j)) + IF (h == zero) h = eps + DO i = 1, n + fjac(i,j) = zero + IF (i >= j-mu .AND. i <= j+ml) fjac(i,j) = (wa1(i)-fvec(i)) / h + END DO + END DO + END DO +END IF +RETURN + +! LAST CARD OF SUBROUTINE FDJAC1. + +END SUBROUTINE fdjac1 + + + +SUBROUTINE qform(m, n, q, ldq, wa) + +INTEGER, INTENT(IN) :: m +INTEGER, INTENT(IN) :: n +INTEGER, INTENT(IN) :: ldq +REAL (dp), INTENT(OUT) :: q(ldq,m) +REAL (dp), INTENT(OUT) :: wa(m) + + +! ********** + +! SUBROUTINE QFORM + +! THIS SUBROUTINE PROCEEDS FROM THE COMPUTED QR FACTORIZATION OF AN M BY N +! MATRIX A TO ACCUMULATE THE M BY M ORTHOGONAL MATRIX Q FROM ITS FACTORED FORM. + +! THE SUBROUTINE STATEMENT IS + +! SUBROUTINE QFORM(M,N,Q,LDQ,WA) + +! WHERE + +! M IS A POSITIVE INTEGER INPUT VARIABLE SET TO THE NUMBER +! OF ROWS OF A AND THE ORDER OF Q. + +! N IS A POSITIVE INTEGER INPUT VARIABLE SET TO THE NUMBER OF COLUMNS OF A. + +! Q IS AN M BY M ARRAY. ON INPUT THE FULL LOWER TRAPEZOID IN +! THE FIRST MIN(M,N) COLUMNS OF Q CONTAINS THE FACTORED FORM. +! ON OUTPUT Q HAS BEEN ACCUMULATED INTO A SQUARE MATRIX. + +! LDQ IS A POSITIVE INTEGER INPUT VARIABLE NOT LESS THAN M +! WHICH SPECIFIES THE LEADING DIMENSION OF THE ARRAY Q. + +! WA IS A WORK ARRAY OF LENGTH M. + +! SUBPROGRAMS CALLED + +! FORTRAN-SUPPLIED ... MIN + +! ARGONNE NATIONAL LABORATORY. MINPACK PROJECT. MARCH 1980. +! BURTON S. GARBOW, KENNETH E. HILLSTROM, JORGE J. MORE + +! ********** +INTEGER :: i, j, jm1, k, l, minmn, np1 +REAL (dp) :: sum, temp +REAL (dp), PARAMETER :: one = 1.0_dp, zero = 0.0_dp + +! ZERO OUT UPPER TRIANGLE OF Q IN THE FIRST MIN(M,N) COLUMNS. + +minmn = MIN(m,n) +IF (minmn >= 2) THEN + DO j = 2, minmn + jm1 = j - 1 + DO i = 1, jm1 + q(i,j) = zero + END DO + END DO +END IF + +! INITIALIZE REMAINING COLUMNS TO THOSE OF THE IDENTITY MATRIX. + +np1 = n + 1 +IF (m >= np1) THEN + DO j = np1, m + DO i = 1, m + q(i,j) = zero + END DO + q(j,j) = one + END DO +END IF + +! ACCUMULATE Q FROM ITS FACTORED FORM. + +DO l = 1, minmn + k = minmn - l + 1 + DO i = k, m + wa(i) = q(i,k) + q(i,k) = zero + END DO + q(k,k) = one + IF (wa(k) /= zero) THEN + DO j = k, m + sum = zero + DO i = k, m + sum = sum + q(i,j) * wa(i) + END DO + temp = sum / wa(k) + DO i = k, m + q(i,j) = q(i,j) - temp * wa(i) + END DO + END DO + END IF +END DO +RETURN + +! LAST CARD OF SUBROUTINE QFORM. + +END SUBROUTINE qform + + +SUBROUTINE qrfac(m, n, a, lda, pivot, ipvt, lipvt, rdiag, acnorm, wa) + +INTEGER, INTENT(IN) :: m +INTEGER, INTENT(IN) :: n +INTEGER, INTENT(IN) :: lda +REAL (dp), INTENT(IN OUT) :: a(lda,n) +LOGICAL, INTENT(IN) :: pivot +INTEGER, INTENT(IN) :: lipvt +INTEGER, INTENT(OUT) :: ipvt(lipvt) +REAL (dp), INTENT(OUT) :: rdiag(n) +REAL (dp), INTENT(OUT) :: acnorm(n) +REAL (dp), INTENT(OUT) :: wa(n) + + +! ********** + +! SUBROUTINE QRFAC + +! THIS SUBROUTINE USES HOUSEHOLDER TRANSFORMATIONS WITH COLUMN PIVOTING +! (OPTIONAL) TO COMPUTE A QR FACTORIZATION OF THE M BY N MATRIX A. +! THAT IS, QRFAC DETERMINES AN ORTHOGONAL MATRIX Q, A PERMUTATION MATRIX P, +! AND AN UPPER TRAPEZOIDAL MATRIX R WITH DIAGONAL ELEMENTS OF NONINCREASING +! MAGNITUDE, SUCH THAT A*P = Q*R. THE HOUSEHOLDER TRANSFORMATION FOR +! COLUMN K, K = 1,2,...,MIN(M,N), IS OF THE FORM + +! T +! I - (1/U(K))*U*U + +! WHERE U HAS ZEROS IN THE FIRST K-1 POSITIONS. THE FORM OF THIS +! TRANSFORMATION AND THE METHOD OF PIVOTING FIRST APPEARED IN THE +! CORRESPONDING LINPACK SUBROUTINE. + +! THE SUBROUTINE STATEMENT IS + +! SUBROUTINE QRFAC(M,N,A,LDA,PIVOT,IPVT,LIPVT,RDIAG,ACNORM,WA) + +! WHERE + +! M IS A POSITIVE INTEGER INPUT VARIABLE SET TO THE NUMBER OF ROWS OF A. + +! N IS A POSITIVE INTEGER INPUT VARIABLE SET TO THE NUMBER +! OF COLUMNS OF A. + +! A IS AN M BY N ARRAY. ON INPUT A CONTAINS THE MATRIX FOR WHICH THE +! QR FACTORIZATION IS TO BE COMPUTED. ON OUTPUT THE STRICT UPPER +! TRAPEZOIDAL PART OF A CONTAINS THE STRICT UPPER TRAPEZOIDAL PART OF R, +! AND THE LOWER TRAPEZOIDAL PART OF A CONTAINS A FACTORED FORM OF Q +! (THE NON-TRIVIAL ELEMENTS OF THE U VECTORS DESCRIBED ABOVE). + +! LDA IS A POSITIVE INTEGER INPUT VARIABLE NOT LESS THAN M +! WHICH SPECIFIES THE LEADING DIMENSION OF THE ARRAY A. + +! PIVOT IS A LOGICAL INPUT VARIABLE. IF PIVOT IS SET TRUE, +! THEN COLUMN PIVOTING IS ENFORCED. IF PIVOT IS SET FALSE, +! THEN NO COLUMN PIVOTING IS DONE. + +! IPVT IS AN INTEGER OUTPUT ARRAY OF LENGTH LIPVT. IPVT DEFINES THE +! PERMUTATION MATRIX P SUCH THAT A*P = Q*R. +! COLUMN J OF P IS COLUMN IPVT(J) OF THE IDENTITY MATRIX. +! IF PIVOT IS FALSE, IPVT IS NOT REFERENCED. + +! LIPVT IS A POSITIVE INTEGER INPUT VARIABLE. IF PIVOT IS FALSE, +! THEN LIPVT MAY BE AS SMALL AS 1. IF PIVOT IS TRUE, THEN +! LIPVT MUST BE AT LEAST N. + +! RDIAG IS AN OUTPUT ARRAY OF LENGTH N WHICH CONTAINS THE +! DIAGONAL ELEMENTS OF R. + +! ACNORM IS AN OUTPUT ARRAY OF LENGTH N WHICH CONTAINS THE NORMS OF +! THE CORRESPONDING COLUMNS OF THE INPUT MATRIX A. +! IF THIS INFORMATION IS NOT NEEDED, THEN ACNORM CAN COINCIDE WITH RDIAG. + +! WA IS A WORK ARRAY OF LENGTH N. IF PIVOT IS FALSE, THEN WA +! CAN COINCIDE WITH RDIAG. + +! SUBPROGRAMS CALLED + +! MINPACK-SUPPLIED ... SPMPAR,ENORM + +! FORTRAN-SUPPLIED ... MAX,SQRT,MIN + +! ARGONNE NATIONAL LABORATORY. MINPACK PROJECT. MARCH 1980. +! BURTON S. GARBOW, KENNETH E. HILLSTROM, JORGE J. MORE + +! ********** +INTEGER :: i, j, jp1, k, kmax, minmn +REAL (dp) :: ajnorm, epsmch, sum, temp +REAL (dp), PARAMETER :: one = 1.0_dp, p05 = 0.05_dp, zero = 0.0_dp + +! EPSMCH IS THE MACHINE PRECISION. + +epsmch = EPSILON(1.0_dp) + +! COMPUTE THE INITIAL COLUMN NORMS AND INITIALIZE SEVERAL ARRAYS. + +DO j = 1, n + acnorm(j) = enorm(m, a(1:,j)) + rdiag(j) = acnorm(j) + wa(j) = rdiag(j) + IF (pivot) ipvt(j) = j +END DO + +! REDUCE A TO R WITH HOUSEHOLDER TRANSFORMATIONS. + +minmn = MIN(m,n) +DO j = 1, minmn + IF (pivot) THEN + +! BRING THE COLUMN OF LARGEST NORM INTO THE PIVOT POSITION. + + kmax = j + DO k = j, n + IF (rdiag(k) > rdiag(kmax)) kmax = k + END DO + IF (kmax /= j) THEN + DO i = 1, m + temp = a(i,j) + a(i,j) = a(i,kmax) + a(i,kmax) = temp + END DO + rdiag(kmax) = rdiag(j) + wa(kmax) = wa(j) + k = ipvt(j) + ipvt(j) = ipvt(kmax) + ipvt(kmax) = k + END IF + END IF + +! COMPUTE THE HOUSEHOLDER TRANSFORMATION TO REDUCE THE +! J-TH COLUMN OF A TO A MULTIPLE OF THE J-TH UNIT VECTOR. + + ajnorm = enorm(m-j+1, a(j:,j)) + IF (ajnorm /= zero) THEN + IF (a(j,j) < zero) ajnorm = -ajnorm + DO i = j, m + a(i,j) = a(i,j) / ajnorm + END DO + a(j,j) = a(j,j) + one + +! APPLY THE TRANSFORMATION TO THE REMAINING COLUMNS AND UPDATE THE NORMS. + + jp1 = j + 1 + IF (n >= jp1) THEN + DO k = jp1, n + sum = zero + DO i = j, m + sum = sum + a(i,j) * a(i,k) + END DO + temp = sum / a(j,j) + DO i = j, m + a(i,k) = a(i,k) - temp * a(i,j) + END DO + IF (.NOT.(.NOT.pivot.OR.rdiag(k) == zero)) THEN + temp = a(j,k) / rdiag(k) + rdiag(k) = rdiag(k) * SQRT(MAX(zero,one-temp**2)) + IF (p05*(rdiag(k)/wa(k))**2 <= epsmch) THEN + rdiag(k) = enorm(m-j, a(jp1:,k)) + wa(k) = rdiag(k) + END IF + END IF + END DO + END IF + END IF + rdiag(j) = -ajnorm +END DO +RETURN + +! LAST CARD OF SUBROUTINE QRFAC. + +END SUBROUTINE qrfac + + + +SUBROUTINE r1mpyq(m, n, a, lda, v, w) + +INTEGER, INTENT(IN) :: m +INTEGER, INTENT(IN) :: n +INTEGER, INTENT(IN) :: lda +REAL (dp), INTENT(IN OUT) :: a(lda,n) +REAL (dp), INTENT(IN) :: v(n) +REAL (dp), INTENT(IN) :: w(n) + + +! ********** + +! SUBROUTINE R1MPYQ + +! GIVEN AN M BY N MATRIX A, THIS SUBROUTINE COMPUTES A*Q WHERE +! Q IS THE PRODUCT OF 2*(N - 1) TRANSFORMATIONS + +! GV(N-1)*...*GV(1)*GW(1)*...*GW(N-1) + +! AND GV(I), GW(I) ARE GIVENS ROTATIONS IN THE (I,N) PLANE WHICH +! ELIMINATE ELEMENTS IN THE I-TH AND N-TH PLANES, RESPECTIVELY. +! Q ITSELF IS NOT GIVEN, RATHER THE INFORMATION TO RECOVER THE +! GV, GW ROTATIONS IS SUPPLIED. + +! THE SUBROUTINE STATEMENT IS + +! SUBROUTINE R1MPYQ(M, N, A, LDA, V, W) + +! WHERE + +! M IS A POSITIVE INTEGER INPUT VARIABLE SET TO THE NUMBER OF ROWS OF A. + +! N IS A POSITIVE INTEGER INPUT VARIABLE SET TO THE NUMBER OF COLUMNS OF A. + +! A IS AN M BY N ARRAY. ON INPUT A MUST CONTAIN THE MATRIX TO BE +! POSTMULTIPLIED BY THE ORTHOGONAL MATRIX Q DESCRIBED ABOVE. +! ON OUTPUT A*Q HAS REPLACED A. + +! LDA IS A POSITIVE INTEGER INPUT VARIABLE NOT LESS THAN M +! WHICH SPECIFIES THE LEADING DIMENSION OF THE ARRAY A. + +! V IS AN INPUT ARRAY OF LENGTH N. V(I) MUST CONTAIN THE INFORMATION +! NECESSARY TO RECOVER THE GIVENS ROTATION GV(I) DESCRIBED ABOVE. + +! W IS AN INPUT ARRAY OF LENGTH N. W(I) MUST CONTAIN THE INFORMATION +! NECESSARY TO RECOVER THE GIVENS ROTATION GW(I) DESCRIBED ABOVE. + +! SUBROUTINES CALLED + +! FORTRAN-SUPPLIED ... ABS, SQRT + +! ARGONNE NATIONAL LABORATORY. MINPACK PROJECT. MARCH 1980. +! BURTON S. GARBOW, KENNETH E. HILLSTROM, JORGE J. MORE + +! ********** +INTEGER :: i, j, nmj, nm1 +REAL (dp) :: COS, SIN, temp +REAL (dp), PARAMETER :: one = 1.0_dp + +! APPLY THE FIRST SET OF GIVENS ROTATIONS TO A. + +nm1 = n - 1 +IF (nm1 >= 1) THEN + DO nmj = 1, nm1 + j = n - nmj + IF (ABS(v(j)) > one) COS = one / v(j) + IF (ABS(v(j)) > one) SIN = SQRT(one-COS**2) + IF (ABS(v(j)) <= one) SIN = v(j) + IF (ABS(v(j)) <= one) COS = SQRT(one-SIN**2) + DO i = 1, m + temp = COS * a(i,j) - SIN * a(i,n) + a(i,n) = SIN * a(i,j) + COS * a(i,n) + a(i,j) = temp + END DO + END DO + +! APPLY THE SECOND SET OF GIVENS ROTATIONS TO A. + + DO j = 1, nm1 + IF (ABS(w(j)) > one) COS = one / w(j) + IF (ABS(w(j)) > one) SIN = SQRT(one-COS**2) + IF (ABS(w(j)) <= one) SIN = w(j) + IF (ABS(w(j)) <= one) COS = SQRT(one-SIN**2) + DO i = 1, m + temp = COS * a(i,j) + SIN * a(i,n) + a(i,n) = -SIN * a(i,j) + COS * a(i,n) + a(i,j) = temp + END DO + END DO +END IF +RETURN + +! LAST CARD OF SUBROUTINE R1MPYQ. + +END SUBROUTINE r1mpyq + + + +SUBROUTINE r1updt(m, n, s, ls, u, v, w, sing) + +INTEGER, INTENT(IN) :: m +INTEGER, INTENT(IN) :: n +INTEGER, INTENT(IN) :: ls +REAL (dp), INTENT(IN OUT) :: s(ls) +REAL (dp), INTENT(IN) :: u(m) +REAL (dp), INTENT(IN OUT) :: v(n) +REAL (dp), INTENT(OUT) :: w(m) +LOGICAL, INTENT(OUT) :: sing + + +! ********** + +! SUBROUTINE R1UPDT + +! GIVEN AN M BY N LOWER TRAPEZOIDAL MATRIX S, AN M-VECTOR U, +! AND AN N-VECTOR V, THE PROBLEM IS TO DETERMINE AN +! ORTHOGONAL MATRIX Q SUCH THAT + +! T +! (S + U*V )*Q + +! IS AGAIN LOWER TRAPEZOIDAL. + +! THIS SUBROUTINE DETERMINES Q AS THE PRODUCT OF 2*(N - 1) TRANSFORMATIONS + +! GV(N-1)*...*GV(1)*GW(1)*...*GW(N-1) + +! WHERE GV(I), GW(I) ARE GIVENS ROTATIONS IN THE (I,N) PLANE +! WHICH ELIMINATE ELEMENTS IN THE I-TH AND N-TH PLANES, RESPECTIVELY. +! Q ITSELF IS NOT ACCUMULATED, RATHER THE INFORMATION TO RECOVER THE GV, +! GW ROTATIONS IS RETURNED. + +! THE SUBROUTINE STATEMENT IS + +! SUBROUTINE R1UPDT(M,N,S,LS,U,V,W,SING) + +! WHERE + +! M IS A POSITIVE INTEGER INPUT VARIABLE SET TO THE NUMBER OF ROWS OF S. + +! N IS A POSITIVE INTEGER INPUT VARIABLE SET TO THE NUMBER +! OF COLUMNS OF S. N MUST NOT EXCEED M. + +! S IS AN ARRAY OF LENGTH LS. ON INPUT S MUST CONTAIN THE LOWER +! TRAPEZOIDAL MATRIX S STORED BY COLUMNS. ON OUTPUT S CONTAINS +! THE LOWER TRAPEZOIDAL MATRIX PRODUCED AS DESCRIBED ABOVE. + +! LS IS A POSITIVE INTEGER INPUT VARIABLE NOT LESS THAN +! (N*(2*M-N+1))/2. + +! U IS AN INPUT ARRAY OF LENGTH M WHICH MUST CONTAIN THE VECTOR U. + +! V IS AN ARRAY OF LENGTH N. ON INPUT V MUST CONTAIN THE VECTOR V. +! ON OUTPUT V(I) CONTAINS THE INFORMATION NECESSARY TO +! RECOVER THE GIVENS ROTATION GV(I) DESCRIBED ABOVE. + +! W IS AN OUTPUT ARRAY OF LENGTH M. W(I) CONTAINS INFORMATION +! NECESSARY TO RECOVER THE GIVENS ROTATION GW(I) DESCRIBED ABOVE. + +! SING IS A LOGICAL OUTPUT VARIABLE. SING IS SET TRUE IF ANY OF THE +! DIAGONAL ELEMENTS OF THE OUTPUT S ARE ZERO. OTHERWISE SING IS +! SET FALSE. + +! SUBPROGRAMS CALLED + +! MINPACK-SUPPLIED ... SPMPAR + +! FORTRAN-SUPPLIED ... ABS,SQRT + +! ARGONNE NATIONAL LABORATORY. MINPACK PROJECT. MARCH 1980. +! BURTON S. GARBOW, KENNETH E. HILLSTROM, JORGE J. MORE, JOHN L. NAZARETH + +! ********** +INTEGER :: i, j, jj, l, nmj, nm1 +REAL (dp) :: COS, cotan, giant, SIN, TAN, tau, temp +REAL (dp), PARAMETER :: one = 1.0_dp, p5 = 0.5_dp, p25 = 0.25_dp, zero = 0.0_dp + +! GIANT IS THE LARGEST MAGNITUDE. + +giant = HUGE(1.0_dp) + +! INITIALIZE THE DIAGONAL ELEMENT POINTER. + +jj = (n*(2*m-n+1)) / 2 - (m-n) + +! MOVE THE NONTRIVIAL PART OF THE LAST COLUMN OF S INTO W. + +l = jj +DO i = n, m + w(i) = s(l) + l = l + 1 +END DO + +! ROTATE THE VECTOR V INTO A MULTIPLE OF THE N-TH UNIT VECTOR +! IN SUCH A WAY THAT A SPIKE IS INTRODUCED INTO W. + +nm1 = n - 1 +IF (nm1 >= 1) THEN + DO nmj = 1, nm1 + j = n - nmj + jj = jj - (m-j+1) + w(j) = zero + IF (v(j) /= zero) THEN + +! DETERMINE A GIVENS ROTATION WHICH ELIMINATES THE J-TH ELEMENT OF V. + + IF (ABS(v(n)) < ABS(v(j))) THEN + cotan = v(n) / v(j) + SIN = p5 / SQRT(p25+p25*cotan**2) + COS = SIN * cotan + tau = one + IF (ABS(COS)*giant > one) tau = one / COS + ELSE + TAN = v(j) / v(n) + COS = p5 / SQRT(p25+p25*TAN**2) + SIN = COS * TAN + tau = SIN + END IF + +! APPLY THE TRANSFORMATION TO V AND STORE THE INFORMATION +! NECESSARY TO RECOVER THE GIVENS ROTATION. + + v(n) = SIN * v(j) + COS * v(n) + v(j) = tau + +! APPLY THE TRANSFORMATION TO S AND EXTEND THE SPIKE IN W. + + l = jj + DO i = j, m + temp = COS * s(l) - SIN * w(i) + w(i) = SIN * s(l) + COS * w(i) + s(l) = temp + l = l + 1 + END DO + END IF + END DO +END IF + +! ADD THE SPIKE FROM THE RANK 1 UPDATE TO W. + +DO i = 1, m + w(i) = w(i) + v(n) * u(i) +END DO + +! ELIMINATE THE SPIKE. + +sing = .false. +IF (nm1 >= 1) THEN + DO j = 1, nm1 + IF (w(j) /= zero) THEN + +! DETERMINE A GIVENS ROTATION WHICH ELIMINATES THE +! J-TH ELEMENT OF THE SPIKE. + + IF (ABS(s(jj)) < ABS(w(j))) THEN + cotan = s(jj) / w(j) + SIN = p5 / SQRT(p25 + p25*cotan**2) + COS = SIN * cotan + tau = one + IF (ABS(COS)*giant > one) tau = one / COS + ELSE + TAN = w(j) / s(jj) + COS = p5 / SQRT(p25+p25*TAN**2) + SIN = COS * TAN + tau = SIN + END IF + +! APPLY THE TRANSFORMATION TO S AND REDUCE THE SPIKE IN W. + + l = jj + DO i = j, m + temp = COS * s(l) + SIN * w(i) + w(i) = -SIN * s(l) + COS * w(i) + s(l) = temp + l = l + 1 + END DO + +! STORE THE INFORMATION NECESSARY TO RECOVER THE GIVENS ROTATION. + + w(j) = tau + END IF + +! TEST FOR ZERO DIAGONAL ELEMENTS IN THE OUTPUT S. + + IF (s(jj) == zero) sing = .true. + jj = jj + (m-j+1) + END DO +END IF + +! MOVE W BACK INTO THE LAST COLUMN OF THE OUTPUT S. + +l = jj +DO i = n, m + s(l) = w(i) + l = l + 1 +END DO +IF (s(jj) == zero) sing = .true. +RETURN + +! LAST CARD OF SUBROUTINE R1UPDT. + +END SUBROUTINE r1updt + + +FUNCTION enorm(n, x) RESULT(fn_val) + +INTEGER, INTENT(IN) :: n +REAL (dp), INTENT(IN) :: x(n) +REAL (dp) :: fn_val + +! ********** + +! FUNCTION ENORM + +! GIVEN AN N-VECTOR X, THIS FUNCTION CALCULATES THE EUCLIDEAN NORM OF X. + +! THE EUCLIDEAN NORM IS COMPUTED BY ACCUMULATING THE SUM OF SQUARES IN THREE +! DIFFERENT SUMS. THE SUMS OF SQUARES FOR THE SMALL AND LARGE COMPONENTS +! ARE SCALED SO THAT NO OVERFLOWS OCCUR. NON-DESTRUCTIVE UNDERFLOWS ARE +! PERMITTED. UNDERFLOWS AND OVERFLOWS DO NOT OCCUR IN THE COMPUTATION OF THE UNSCALED +! SUM OF SQUARES FOR THE INTERMEDIATE COMPONENTS. +! THE DEFINITIONS OF SMALL, INTERMEDIATE AND LARGE COMPONENTS DEPEND ON +! TWO CONSTANTS, RDWARF AND RGIANT. THE MAIN RESTRICTIONS ON THESE CONSTANTS +! ARE THAT RDWARF**2 NOT UNDERFLOW AND RGIANT**2 NOT OVERFLOW. +! THE CONSTANTS GIVEN HERE ARE SUITABLE FOR EVERY KNOWN COMPUTER. + +! THE FUNCTION STATEMENT IS + +! REAL FUNCTION ENORM(N, X) + +! WHERE + +! N IS A POSITIVE INTEGER INPUT VARIABLE. + +! X IS AN INPUT ARRAY OF LENGTH N. + +! SUBPROGRAMS CALLED + +! FORTRAN-SUPPLIED ... ABS,SQRT + +! ARGONNE NATIONAL LABORATORY. MINPACK PROJECT. MARCH 1980. +! BURTON S. GARBOW, KENNETH E. HILLSTROM, JORGE J. MORE + +! ********** +INTEGER :: i +REAL (dp) :: agiant, floatn, s1, s2, s3, xabs, x1max, x3max +REAL (dp), PARAMETER :: rdwarf = 1.0D-100, rgiant = 1.0D+100 + +s1 = 0.0_dp +s2 = 0.0_dp +s3 = 0.0_dp +x1max = 0.0_dp +x3max = 0.0_dp +floatn = n +agiant = rgiant / floatn +DO i = 1, n + xabs = ABS(x(i)) + IF (xabs <= rdwarf .OR. xabs >= agiant) THEN + IF (xabs > rdwarf) THEN + +! SUM FOR LARGE COMPONENTS. + + IF (xabs > x1max) THEN + s1 = 1.0_dp + s1 * (x1max/xabs) ** 2 + x1max = xabs + ELSE + s1 = s1 + (xabs/x1max) ** 2 + END IF + ELSE + +! SUM FOR SMALL COMPONENTS. + + IF (xabs > x3max) THEN + s3 = 1.0_dp + s3 * (x3max/xabs) ** 2 + x3max = xabs + ELSE + IF (xabs /= 0.0_dp) s3 = s3 + (xabs/x3max) ** 2 + END IF + END IF + ELSE + +! SUM FOR INTERMEDIATE COMPONENTS. + + s2 = s2 + xabs ** 2 + END IF +END DO + +! CALCULATION OF NORM. + +IF (s1 /= 0.0_dp) THEN + fn_val = x1max * SQRT(s1 + (s2/x1max)/x1max) +ELSE + IF (s2 /= 0.0_dp) THEN + IF (s2 >= x3max) fn_val = SQRT(s2*(1.0_dp + (x3max/s2)*(x3max*s3))) + IF (s2 < x3max) fn_val = SQRT(x3max*((s2/x3max) + (x3max*s3))) + ELSE + fn_val = x3max * SQRT(s3) + END IF +END IF +RETURN +END FUNCTION enorm + +END MODULE Solve_NonLin diff --git a/applications/PUfoam/MoDeNaModels/Solubility/src/modules.f90 b/applications/PUfoam/MoDeNaModels/Solubility/src/modules.f90 new file mode 100644 index 000000000..0aa1d08f0 --- /dev/null +++ b/applications/PUfoam/MoDeNaModels/Solubility/src/modules.f90 @@ -0,0 +1,366 @@ +!>WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +!! This module contains constants and upper boundaries for the number of +!! components and phases in the system +!!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW + +Module PARAMETERS + + implicit none + save + + integer, parameter :: nc = 6 + integer, parameter :: np = 3 + integer, parameter :: nsite = 5 + + real, parameter :: PI = 3.141592653589793 + real, parameter :: RGAS = 8.31441 + real, parameter :: NAv = 6.022045E23 + real, parameter :: KBOL = RGAS / NAv + real, parameter :: TAU = PI / 3.0 / SQRT(2.0) + +End Module PARAMETERS + + +!>WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +!! This module contains parameters and variables that define the +!! thermodynamic state of the system as well as simulation parameters +!!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW + +Module BASIC_VARIABLES + + use PARAMETERS, only: nc, np, nsite + implicit none + save + +! ---------------------------------------------------------------------- +! basic quantities defining the mixture +! ---------------------------------------------------------------------- + integer :: ncomp + integer :: nphas + + real :: t + !real :: tc + real :: p + real, dimension(np) :: dense + !real, dimension(np) :: rhob + + real, dimension(np, nc) :: xi + real, dimension(np, nc) :: lnx + real, dimension(nc) :: xiF + real, dimension(nc) :: ciF + + + real, dimension(nc) :: mm + real, dimension(np, nc, nsite) :: mxx + + real :: alpha + + +! ---------------------------------------------------------------------- +! pure component parameters +! ---------------------------------------------------------------------- + real, dimension(nc, 25) :: parame = 0.0 + real, dimension(nc) :: chiR + character*30, dimension(nc) :: compna + real, dimension(nc, nc) :: kij, lij + real, dimension(nc, nc) :: E_LC, S_LC + real, dimension(nc) :: LLi, phi_criti, chap + + +! ---------------------------------------------------------------------- +! thermodynamic quantities +! ---------------------------------------------------------------------- + real, dimension(np) :: densta + real, dimension(0:nc*np+6) :: val_init, val_conv + + real :: h_lv + real, dimension(np) :: cpres, enthal, entrop, gibbs, f_res + + real, dimension(np) :: dp_dz, dp_dz2 + + +! ---------------------------------------------------------------------- +! choice of EOS-model and solution method +! ---------------------------------------------------------------------- + integer :: eos, pol + integer :: num + character (LEN=2) :: ensemble_flag + character (LEN=10) :: RGT_variant + + +! ---------------------------------------------------------------------- +! for input/output +! ---------------------------------------------------------------------- + integer :: outp, bindiag + real :: u_in_T, u_out_T, u_in_P, u_out_P + + +! ---------------------------------------------------------------------- +! quantities defining the numerical procedure +! ---------------------------------------------------------------------- + integer :: n_unkw + + real :: step_a, acc_a !, acc_i + real, dimension(nc) :: scaling + real, dimension(3500) :: plv_kon + real, dimension(2, 3500) :: d_kond + + character*3, dimension(10) :: it, sum_rel + character*3 :: running + + +End Module BASIC_VARIABLES + + + + +!>WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +!! This module contains parameters and variables to identify thermodynamic +!! properties +!!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW + +Module EOS_VARIABLES + + use PARAMETERS, only: nc, nsite, PI, KBOL, TAU, NAv + use BASIC_VARIABLES, only: ncomp, eos, t, p, parame, E_LC, S_LC, chiR, & + LLi, phi_criti, chap, kij, lij, ensemble_flag + implicit none + save + +! ---------------------------------------------------------------------- +! basic quantities defining the mixture (single phase) +! ---------------------------------------------------------------------- + real :: x(nc) + real :: eta_start + real :: eta + real :: rho + +! ---------------------------------------------------------------------- +! thermodynamic quantities +! ---------------------------------------------------------------------- + real :: fres + real :: lnphi(nc) + real :: pges + real :: pgesdz + real :: pgesd2 + real :: pgesd3 + + real :: h_res + real :: cp_res + real :: s_res + +! ---------------------------------------------------------------------- +! quantities of fluid theory +! ---------------------------------------------------------------------- + real :: gij(nc,nc) + real :: mx(nc,nsite) + + real :: mseg(nc) + real :: dhs(nc) + real :: uij(nc,nc) + real :: sig_ij(nc,nc) + real :: vij(nc,nc) + + real :: um + real :: order1 + real :: order2 + real :: apar(0:6) + real :: bpar(0:6) + + real :: z0t + real :: z1t + real :: z2t + real :: z3t + + integer :: nhb_typ(nc) + real :: ass_d(nc,nc,nsite,nsite) + real :: nhb_no(nc,nsite) + real :: dij_ab(nc,nc) + +! ---------------------------------------------------------------------- +! auxilliary quantities +! ---------------------------------------------------------------------- + real :: tfr + integer :: phas + + character (LEN = 2) :: dd_term, qq_term, dq_term + + real :: densav(3), denold(3) + real :: density_error(3) + + real :: alpha_nematic + real :: alpha_test(2) + +End Module EOS_VARIABLES + + + +!>WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +!! This module contains variables to store the EOS model constants +!!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW + +Module EOS_CONSTANTS + + use PARAMETERS, only: nc + implicit none + save + + real, dimension(0:6,3) :: ap, bp + real, dimension(4,9) :: dnm + + real, dimension(28) :: c_dd, n_dd, m_dd, k_dd, o_dd + real, dimension(nc,nc,0:8) :: qqp2, qqp4, ddp2, ddp4, dqp2, dqp4 + real, dimension(nc,nc,nc,0:8) :: qqp3, ddp3, dqp3 + +End Module EOS_CONSTANTS + +!>WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +!! This module contains parameters and variables for the numerical +!! evaluation of derivatives of the EOS +!!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW + +Module EOS_NUMERICAL_DERIVATIVES + + use EOS_VARIABLES, only: dd_term, qq_term, dq_term + + implicit none + save + + character (LEN=9) :: ideal_gas ! (yes, no) + character (LEN=9) :: hard_sphere ! (CSBM, no) + character (LEN=9) :: chain_term ! (TPT1, no) + character (LEN=9) :: disp_term ! (PC-SAFT, CK, no) + character (LEN=9) :: hb_term ! (TPT1_Chap, no) + character (LEN=9) :: LC_term ! (MSaupe, no) + character (LEN=9) :: branch_term ! (TPT2, no) + character (LEN=9) :: II_term ! (......., no) + character (LEN=9) :: ID_term ! (......., no) + + character (LEN=9) :: subtract1 ! (1PT, 2PT, no) + character (LEN=9) :: subtract2 ! (ITTpolar, no) + + character (LEN=9) :: save_eos_terms(10) + +End Module EOS_NUMERICAL_DERIVATIVES + + +!>WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +!! Module STARTING_VALUES +!! This module contains parameters and variables for a phase stability +!! analyis as part of a flash calculation. +!!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW + + Module STARTING_VALUES + + use PARAMETERS, only: nc + implicit none + save + + REAL, DIMENSION(nc) :: rhoif, rhoi1, rhoi2, grad_fd + REAL :: fdenf + + End Module STARTING_VALUES + + + + + +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! Module DFT_MODULE +! +! This module contains parameters and variables for DFT calculations. +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! + Module DFT_MODULE + + use PARAMETERS, only: nc + implicit none + save + + INTEGER, PARAMETER :: NDFT = 4000 + !!integer :: discret + REAL :: box_l_no_unit + INTEGER, PARAMETER :: r_grid = 200 + INTEGER :: kmax, den_step + LOGICAL :: shift, WCA, MFT + REAL :: rc, rg, dzr, tau_cut,dzp + REAL :: d_hs, dhs_st, z3t_st + REAL :: z_ges + REAL, DIMENSION(r_grid) :: x1a + REAL, DIMENSION(NDFT) :: x2a + REAL, DIMENSION(r_grid,NDFT) :: ya, y1a, y2a, y12a + REAL, DIMENSION(r_grid,NDFT,4,4) :: c_bicub + REAL :: fres_temp + + REAL, DIMENSION(r_grid) :: x1a_11 + REAL, DIMENSION(NDFT) :: x2a_11 + REAL, DIMENSION(r_grid,NDFT) :: ya_11, y1a_11, y2a_11, y12a_11 + REAL, DIMENSION(r_grid,NDFT,4,4) :: c_bicub_11 + REAL, DIMENSION(r_grid) :: x1a_12 + REAL, DIMENSION(NDFT) :: x2a_12 + REAL, DIMENSION(r_grid,NDFT) :: ya_12, y1a_12, y2a_12, y12a_12 + REAL, DIMENSION(r_grid,NDFT,4,4) :: c_bicub_12 + REAL, DIMENSION(r_grid) :: x1a_22 + REAL, DIMENSION(NDFT) :: x2a_22 + REAL, DIMENSION(r_grid,NDFT) :: ya_22, y1a_22, y2a_22, y12a_22 + REAL, DIMENSION(r_grid,NDFT,4,4) :: c_bicub_22 + + End Module DFT_MODULE + + +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +Module rdf_variables + + implicit none + save + + real, dimension(0:20) :: fac(0:20) + +End Module rdf_variables + + +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! This module contains the variavles that are needed in the core DFT_FCN +! They are not passed directly to DFT_FCN because the nonlinear solver +! needs a certain calling structure: fcn(x,fvec,n) +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +Module DFT_FCN_MODULE + +use PARAMETERS, only: nc +use DFT_MODULE, only: ndft + implicit none + +INTEGER :: irc(nc),irc_j,ih,fa(nc) + REAL, DIMENSION(-NDFT:NDFT) :: zp + REAL, DIMENSION(-NDFT:NDFT) :: f_tot + REAL, DIMENSION(-NDFT:NDFT,2) :: dF_drho_tot + REAL :: rhob_dft(2,0:nc) + REAL :: my0(nc) + +End Module DFT_FCN_MODULE + + + + + + + + +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! Module Module_Heidemann_Khalil +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! + Module Module_Heidemann_Khalil + + implicit none + save + + real :: error_condition2 + + End Module + + + + diff --git a/applications/PUfoam/MoDeNaModels/Solubility/src/out.txt b/applications/PUfoam/MoDeNaModels/Solubility/src/out.txt new file mode 100644 index 000000000..3a68e692a --- /dev/null +++ b/applications/PUfoam/MoDeNaModels/Solubility/src/out.txt @@ -0,0 +1 @@ + 2.2654943032705011 diff --git a/applications/PUfoam/MoDeNaModels/SurfaceTension/Description_SurfaceTension.pdf b/applications/PUfoam/MoDeNaModels/SurfaceTension/Description_SurfaceTension.pdf new file mode 100644 index 0000000000000000000000000000000000000000..81a10a39bf8c6bf1c84ceff4b2eaa57e4096d37c GIT binary patch literal 80494 zcmb5WbyywGlP`?By9R;>x8T7cxNC3%1a}K|2<{HS3GPmCIJg9Nm*8#(=Wx#D``g|3 z?)&aOd+$4cOwV*zS69{4bbqF*pP^TimSy8&|AAf)~RNb}kR1{h<^geAex^5KEf@jO~kx^yE5z9iVa@Xbv?|mlnbK2b( zwA#7zU}gnv+{U@z5~HeXm%#2(owhtiv!M3i1qOluBDC4|Pe*qQNu;)@jrBwpLTsFJ zU0cBdt!RV7I7+2K<@lXs?lZ2X;L?Lwh<@S`KD*PZ7yw&(eLGi`4*mpDJ_Tt)Rx$Jn zB*36ZmCEJQvKeA_^r>kgv8?8Y)4@kV%-X$hgC9i$$-jrK7%Z*92Udy*xyP@Rj{YB$ zq-7-iT2qUTpAROix%VfEjQn24;xC(ldWal9tGe-$?m{+ekvFs^AWhbS%xm3%u}nTQ z0$<(H@U;XhlZS_gR0f}|q_uYVjG5|CukzEDj?>F#d8Mq#oPQd02mZD8Mb|9{-I2m~xCJhO z{X2nju|4M)FN_QBLJAtJ^zPR!*o-|KscIqH2qP)Y6iHY_X1veb=B3{qBphK+%9{w7 z+FEEjf6WblCTl@^1>vpKsaM8Ic;%O8(Ho44Y52(WlaXnCP;=p%Gg~Qbi_1| zw+rEVIJ>%eDgVAw)+fr%^KJwslGP~UlRrB)>IpngnmFMl_Q5K+i@)=}CA?rqUm#be zaK((8*UR_8(n+s>7k=s7;cvQ{c ztMois=ev>9DLtY0-p8V5iM9-XD|Y|VWlIrj>xsWKH{R7-jyCLaT-pgm zc~QUklt#PqH>T(KIukp7{hfcs?Kdp*UduJXeafSaOvGr|0m9<7*F{5z*tvWd=JG1i9OwOjoj{1?3itcf(P# zTc6>w(F~}@$hPPx@~V(9ely7*vnnfUO6hC|UZ6#c?)S7VB;fweknfF^+yj|L_)?fE zvp$8Y>PF_3a`zJ(N6p6DB-CmpWZ|*;v_700T;dS824Aq zgqSj)_0tmD`TKEkdLSXcrI*k2`s!#v^zgg7tv^Q$wPO5X%VD@W-utDvR{RKY4N6d< zJUECX!S**Y{jRa_tHDOK=$kvdfJZIHIm}OWRSdas?%z17&$XKpj}h=f3i+!Vqey9Y z6m{DYt7dGYG?&e@f3BKlG7rR}R0qEQVoq*PN?Z=w&?#-$>_DyfwT;m zM_iu?p=W>g+c8y{i}>sTe^r1`3gQ=c5-~;GKB6^=q+yD=8L28d~-7mub&CN*W9ct{o09Ua1X6X+e=MpErLAmrbgxz*Essn%Qql zR)1yJLLO*}CRMHWR{t0#?6pn+B!r<{z z51y3$<1#tL8Mi&n)hy^Jh|0j8cQgy<#(BG6^pwaGB6d

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new file mode 100644 index 000000000..7d428701a --- /dev/null +++ b/applications/PUfoam/MoDeNaModels/SurfaceTension/ExampleOfUsage/README @@ -0,0 +1,35 @@ + +Example simulation with Surface Tension model: + +A simple macroscopic code calls the Surface Tension model for different temperatures. + + +How to run? +----------- + +# Make sure PYTHONPATH and LD_LIBRARY_PATH are set +# TODO: +# Make this easier to use +export PKG_CONFIG_PATH=${PKG_CONFIG_PATH:-}:${HOME}/lib/pkgconfig:/usr/local/lib/pkgconfig +export PYTHONPATH=${PYTHONPATH:-}:${HOME}/lib/python2.7/site-packages +export LD_LIBRARY_PATH=${LD_LIBRARY_PATH:-}:${HOME}/lib/python2.7/site-packages:${HOME}/lib:/usr/local/lib + +# Compile project specific sources (only locally) +cd src +cmake . +make + + +#Compile detailed model code (PETSc 3.4.4 needs to be installed) +cd src/srcDetailedCode/ +make DFT + +#copy executable of detailed model (PCSAFT_SurfaceTension) in src folder + + +# Initialise the model in the database +./initModel + +# Start the workflow +./workflow + diff --git a/applications/PUfoam/MoDeNaModels/SurfaceTension/ExampleOfUsage/SurfaceTension.py b/applications/PUfoam/MoDeNaModels/SurfaceTension/ExampleOfUsage/SurfaceTension.py new file mode 100644 index 000000000..566484755 --- /dev/null +++ b/applications/PUfoam/MoDeNaModels/SurfaceTension/ExampleOfUsage/SurfaceTension.py @@ -0,0 +1,54 @@ +''' + + ooo ooooo oooooooooo. ooooo ooo + `88. .888' `888' `Y8b `888b. `8' + 888b d'888 .ooooo. 888 888 .ooooo. 8 `88b. 8 .oooo. + 8 Y88. .P 888 d88' `88b 888 888 d88' `88b 8 `88b. 8 `P )88b + 8 `888' 888 888 888 888 888 888ooo888 8 `88b.8 .oP"888 + 8 Y 888 888 888 888 d88' 888 .o 8 `888 d8( 888 + o8o o888o `Y8bod8P' o888bood8P' `Y8bod8P' o8o `8 `Y888""8o + +Copyright + 2014-2015 MoDeNa Consortium, All rights reserved. + +License + This file is part of Modena. + + Modena is free software; you can redistribute it and/or modify it under + the terms of the GNU General Public License as published by the Free + Software Foundation, either version 3 of the License, or (at your option) + any later version. + + Modena is distributed in the hope that it will be useful, but WITHOUT ANY + WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS + FOR A PARTICULAR PURPOSE. See the GNU General Public License + for more details. + + You should have received a copy of the GNU General Public License along + with Modena. If not, see . + +Description + Python library of FireTasks + +Authors + Henrik Rusche + +Contributors +''' + +from modena.Strategy import BackwardMappingScriptTask + + +__author__ = 'Henrik Rusche' +__copyright__ = 'Copyright 2014, MoDeNa Project' +__version__ = '0.2' +__maintainer__ = 'Henrik Rusche' +__email__ = 'h.rusche@wikki.co.uk.' +__date__ = 'Sep 4, 2014' + + +# Source code in src/twoTanksMacroscopicProblem.C +m = BackwardMappingScriptTask( + script='../src/MacroscopicProblem' +) + diff --git a/applications/PUfoam/MoDeNaModels/SurfaceTension/ExampleOfUsage/initModels b/applications/PUfoam/MoDeNaModels/SurfaceTension/ExampleOfUsage/initModels new file mode 100755 index 000000000..dd47b9cb2 --- /dev/null +++ b/applications/PUfoam/MoDeNaModels/SurfaceTension/ExampleOfUsage/initModels @@ -0,0 +1,62 @@ +#!/usr/bin/python +''' + + ooo ooooo oooooooooo. ooooo ooo + `88. .888' `888' `Y8b `888b. `8' + 888b d'888 .ooooo. 888 888 .ooooo. 8 `88b. 8 .oooo. + 8 Y88. .P 888 d88' `88b 888 888 d88' `88b 8 `88b. 8 `P )88b + 8 `888' 888 888 888 888 888 888ooo888 8 `88b.8 .oP"888 + 8 Y 888 888 888 888 d88' 888 .o 8 `888 d8( 888 + o8o o888o `Y8bod8P' o888bood8P' `Y8bod8P' o8o `8 `Y888""8o + +Copyright + 2014-2015 MoDeNa Consortium, All rights reserved. + +License + This file is part of Modena. + + Modena is free software; you can redistribute it and/or modify it under + the terms of the GNU General Public License as published by the Free + Software Foundation, either version 3 of the License, or (at your option) + any later version. + + Modena is distributed in the hope that it will be useful, but WITHOUT ANY + WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS + FOR A PARTICULAR PURPOSE. See the GNU General Public License for more + details. + + You should have received a copy of the GNU General Public License along + with Modena. If not, see . + +Description + Initialisation script for the flowRate model. The script calculates a few + data points and fits the surrogate model. Then the model is inserted into + the database. + +Authors + Henrik Rusche + +Contributors +''' + +from modena import SurrogateModel +from modena.Strategy import Workflow2 +#import flowRate +import modSurfaceTension +from fireworks import LaunchPad +from fireworks.core.rocket_launcher import rapidfire +from fireworks.utilities.fw_serializers import load_object + + +# set up the LaunchPad and reset it +launchpad = LaunchPad() +launchpad.reset('', require_password=False) + +initWfs = Workflow2([]) +for m in SurrogateModel.get_instances(): + initWfs.addNoLink(m.initialisationStrategy().workflow(m)) + +# store workflow and launch it locally +launchpad.add_wf(initWfs) +rapidfire(launchpad) + diff --git a/applications/PUfoam/MoDeNaModels/SurfaceTension/ExampleOfUsage/modSurfaceTension.py b/applications/PUfoam/MoDeNaModels/SurfaceTension/ExampleOfUsage/modSurfaceTension.py new file mode 100644 index 000000000..3a9e890c4 --- /dev/null +++ b/applications/PUfoam/MoDeNaModels/SurfaceTension/ExampleOfUsage/modSurfaceTension.py @@ -0,0 +1,184 @@ + +''' + + ooo ooooo oooooooooo. ooooo ooo + `88. .888' `888' `Y8b `888b. `8' + 888b d'888 .ooooo. 888 888 .ooooo. 8 `88b. 8 .oooo. + 8 Y88. .P 888 d88' `88b 888 888 d88' `88b 8 `88b. 8 `P )88b + 8 `888' 888 888 888 888 888 888ooo888 8 `88b.8 .oP"888 + 8 Y 888 888 888 888 d88' 888 .o 8 `888 d8( 888 + o8o o888o `Y8bod8P' o888bood8P' `Y8bod8P' o8o `8 `Y888""8o + +Copyright + 2014-2015 MoDeNa Consortium, All rights reserved. + +License + This file is part of Modena. + + Modena is free software; you can redistribute it and/or modify it under + the terms of the GNU General Public License as published by the Free + Software Foundation, either version 3 of the License, or (at your option) + any later version. + + Modena is distributed in the hope that it will be useful, but WITHOUT ANY + WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS + FOR A PARTICULAR PURPOSE. See the GNU General Public License + for more details. + + You should have received a copy of the GNU General Public License along + with Modena. If not, see . + +Description + Python library of FireTasks + +Authors + Henrik Rusche + +Contributors +''' + +import os +import modena +from modena import ForwardMappingModel,BackwardMappingModel,SurrogateModel,CFunction,IndexSet +import modena.Strategy as Strategy +from fireworks.user_objects.firetasks.script_task import FireTaskBase, ScriptTask +from fireworks import Firework, Workflow, FWAction +from fireworks.utilities.fw_utilities import explicit_serialize +from blessings import Terminal +from jinja2 import Template + +# Create terminal for colour output +term = Terminal() + + +__author__ = 'Henrik Rusche' +__copyright__ = 'Copyright 2014, MoDeNa Project' +__version__ = '0.2' +__maintainer__ = 'Henrik Rusche' +__email__ = 'h.rusche@wikki.co.uk.' +__date__ = 'Sep 4, 2014' + + +# ********************************* Class ********************************** # +@explicit_serialize +class SurfaceTensionExactSim(FireTaskBase): + """ + A FireTask that starts a microscopic code and updates the database. + """ + + def run_task(self, fw_spec): + print( + term.yellow + + "Performing exact simulation (microscopic code recipe)" + + term.normal + ) + + # Write input for detailed model + ff = open('in.txt', 'w') + Tstr = str(self['point']['T']) + ff.write('%s \n' %(Tstr)) + + + ##TODO INPUT SHOULD COME FROM IndexSet + + ff.write('2 \n') #number of components in system + ff.write('air \n') #component 1 + ff.write('thf \n') #component 2 + ff.write('0. \n') #molar feed (initial) composition component 1 + ff.write('0. \n') #molar feed (initial) composition component 2 + ff.close() + + #create output file for detailed code + fff = open('out.txt', 'w+') + fff.close() + + # Execute detailed model + run_command = '''../src/./PCSAFT_SurfaceTension -snes_monitor_short -ksp_monitor_short \ + -nx 800 -rc 9.0 -box 300 -erel 1e-08 -init_pert 0 \ + -snes_type newtonls -snes_converged_reason \ + -snes_atol 1e-07 -snes_rtol 1e-07 -snes_stol 1e-07 -snes_max_it 20 \ + -ksp_max_it 15 -ksp_gmres_restart 50 \ + -snes_linesearch_type l2 -snes_linesearch_damping 0.3 -snes_linesearch_monitor \ + -snes_max_fail 1 -snes_max_linear_solve_fail 100 \ + -ksp_gmres_cgs_refinement_type refine_always \ + -snes_ksp_ew -snes_ksp_ew_version 1 -snes_ksp_ew_rtol0 0.5 -snes_ksp_ew_rtolmax 0.9 -snes_ksp_ew_threshold 0.1 \ + -jac 0 -pc_type none ''' + + + os.system(run_command) + + #os.system('../src/./PCSAFT_SurfaceTension') + + # Analyse output + f = open('out.txt', 'r') + self['point']['ST'] = float(f.readline()) + f.close() + + return FWAction(mod_spec=[{'_push': self['point']}]) + + + + + + +f = CFunction( + Ccode= ''' +#include "modena.h" +#include "math.h" + +void surroSurfaceTension +( + const double* parameters, + const double* inherited_inputs, + const double* inputs, + double *outputs +) +{ + + const double T = inputs[0]; + + const double P0 = parameters[0]; + const double P1 = parameters[1]; + const double P2 = parameters[2]; + + outputs[0] = P0 + T*P1 + P2*T*T; +} +''', + # These are global bounds for the function + inputs={ + 'T': { 'min': 270.0, 'max': 310.0, 'argPos': 0 }, #check if boundaries reasonable, from this range, the random values for the DOE are chosen! + }, + outputs={ + 'ST': { 'min': 9e99, 'max': -9e99, 'argPos': 0 }, + }, + parameters={ + 'param0': { 'min': -1E10, 'max': 1E10, 'argPos': 0 }, #check if boundaries are reasonable!!! + 'param1': { 'min': -1E10, 'max': 1E10, 'argPos': 1 }, + 'param2': { 'min': -1E10, 'max': 1E10, 'argPos': 2 }, + }, +) + +m = BackwardMappingModel( + _id= 'SurfaceTension', + surrogateFunction= f, + exactTask= SurfaceTensionExactSim(), + substituteModels= [ ], + initialisationStrategy= Strategy.InitialPoints( + initialPoints= + { + 'T': [270.0, 290.0, 300.0], + }, + ), + outOfBoundsStrategy= Strategy.ExtendSpaceStochasticSampling( + nNewPoints= 4 + ), + parameterFittingStrategy= Strategy.NonLinFitWithErrorContol( + testDataPercentage= 0.2, + maxError= 30.0, + improveErrorStrategy= Strategy.StochasticSampling( + nNewPoints= 2 + ), + maxIterations= 5 # Currently not used + ), +) + diff --git a/applications/PUfoam/MoDeNaModels/SurfaceTension/ExampleOfUsage/src/.gitignore b/applications/PUfoam/MoDeNaModels/SurfaceTension/ExampleOfUsage/src/.gitignore new file mode 100644 index 000000000..0c66e77c1 --- /dev/null +++ b/applications/PUfoam/MoDeNaModels/SurfaceTension/ExampleOfUsage/src/.gitignore @@ -0,0 +1,20 @@ +# Backups +*~ +*bak + +# Various intermediate files from automake +CMakeFiles/ +Makefile +libmodena.pc +CMakeCache.txt +cmake_install.cmake +install_manifest.txt + +# Intermediate files generated by SWIG +*_wrap.c + +# locate results (executables and libraries) +*.l[ao] + +flowRateExact +twoTanksMacroscopicProblem diff --git a/applications/PUfoam/MoDeNaModels/SurfaceTension/ExampleOfUsage/src/CMakeLists.txt b/applications/PUfoam/MoDeNaModels/SurfaceTension/ExampleOfUsage/src/CMakeLists.txt new file mode 100644 index 000000000..b55e0d37e --- /dev/null +++ b/applications/PUfoam/MoDeNaModels/SurfaceTension/ExampleOfUsage/src/CMakeLists.txt @@ -0,0 +1,31 @@ +cmake_minimum_required (VERSION 2.8) +project (tutorialModels C CXX) + +if( CMAKE_VERSION VERSION_GREATER "3.0" ) + cmake_policy(SET CMP0042 OLD) + cmake_policy(SET CMP0026 OLD) +endif() + +set(CMAKE_BUILD_TYPE Release) + +add_custom_target(debug + COMMAND ${CMAKE_COMMAND} -DCMAKE_BUILD_TYPE=Debug ${CMAKE_SOURCE_DIR} + COMMAND ${CMAKE_COMMAND} --build ${CMAKE_BINARY_DIR} --target all + COMMENT "Switch CMAKE_BUILD_TYPE to Debug" + ) + +add_custom_target(release + COMMAND ${CMAKE_COMMAND} -DCMAKE_BUILD_TYPE=Release ${CMAKE_SOURCE_DIR} + COMMAND ${CMAKE_COMMAND} --build ${CMAKE_BINARY_DIR} --target all + COMMENT "Switch CMAKE_BUILD_TYPE to Release" + ) + +find_package(MODENA REQUIRED) + +include(CheckCInline) +check_c_inline(C_INLINE) + + +add_executable(MacroscopicProblem MacroscopicProblem.C) +target_link_libraries(MacroscopicProblem MODENA::modena) + diff --git 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memory and fetch arg positions + modena_inputs_t *inputs = modena_inputs_new(model); //How many inputs and outputs is defined in the function module!! + modena_outputs_t *outputs = modena_outputs_new(model); + + + size_t Tpos = modena_model_inputs_argPos(model, "T"); + + modena_model_argPos_check(model); + + + while(T < Tend) + { + // Set input vector + modena_inputs_set(inputs, Tpos, T); + + // Call the model + int ret = modena_model_call(model, inputs, outputs); + + // Terminate, if requested + if(modena_error_occurred()) + { + modena_inputs_destroy(inputs); + modena_outputs_destroy(outputs); + modena_model_destroy(model); + + return modena_error(); + } + + // Fetch result + double rho = modena_outputs_get(outputs, 0); + + cout << "T = " << T; + + + T = T + 10.0; + } + + + modena_inputs_destroy(inputs); + modena_outputs_destroy(outputs); + modena_model_destroy(model); + + return 0; +} diff --git a/applications/PUfoam/MoDeNaModels/SurfaceTension/ExampleOfUsage/src/srcDetailedCode/ 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000000000..d4e6d913f --- /dev/null +++ b/applications/PUfoam/MoDeNaModels/SurfaceTension/ExampleOfUsage/src/srcDetailedCode/AD_Routines.F90 @@ -0,0 +1,234 @@ + +! Generated by TAPENADE (INRIA, Tropics team) +! Tapenade 3.10 (r5498) - 20 Jan 2015 09:48 +! +! Differentiation of formfunctionlocal in forward (tangent) mode: +! variations of useful results: f rhop +! with respect to varying inputs: rhop +! RW status of diff variables: f:out rhop:in-out +SUBROUTINE FORMFUNCTIONLOCAL_D(rhop, rhopd_nogp, fd, user, ierr) + + +!PETSc modules + Use PetscManagement + + +!DFT modules + USE MOD_DFT_FMT + USE MOD_DFT_CHAIN + USE MOD_DFT_FMT_d + USE MOD_DFT_CHAIN_d + USE MOD_DFT_DISP_WDA_D + + + USE BASIC_VARIABLES, ONLY : ncomp + USE EOS_VARIABLES, Only:dhs, rho + USE VLE_VAR, Only: rhob + USE MOD_DFT, ONLY : fa, zp + USE DFT_FCN_MODULE, ONLY : chempot_res + USE GLOBAL_X, ONLY : ngrid, ngp + IMPLICIT NONE + +#include + +! Input/output variables: + type (userctx) user + PetscScalar rhop(ncomp,user%gxs:user%gxe) + PetscScalar rhopd_nogp(ncomp,user%xs:user%xe) + !PetscScalar f(ncomp,user%xs:user%xe) + PetscScalar fd(ncomp,user%xs:user%xe) + PetscErrorCode ierr + +! Local variables: + PetscInt i + PetscInt k + REAL,dimension(user%gxs:user%gxe) :: n0,n1,n2,n3,nv1,nv2 !ngp muss groesser als fa+fa/2 sein!! + REAL,dimension(user%gxs:user%gxe) :: phi_dn0,phi_dn1,phi_dn2,phi_dn3,phi_dnv1,phi_dnv2 + REAL,dimension(user%gxs:user%gxe) :: phi_dn0d,phi_dn1d,phi_dn2d,phi_dn3d,phi_dnv1d,phi_dnv2d + REAL,dimension(user%xs:user%xe,ncomp) :: dF_drho_FMT,dF_drho_FMTd + REAL,dimension(user%gxs:user%gxe,ncomp) :: rhobar,lambda,rhobard,lambdad + REAL,dimension(user%xs:user%xe,ncomp) :: dF_drho_CHAIN,dF_drho_CHAINd + REAL :: Vext(ncomp) + + !DISP VAR + REAL,dimension(user%gxs:user%gxe,ncomp) :: rhop_wd,my_disp,df_disp_drk + REAL,dimension(user%gxs:user%gxe,ncomp) :: rhop_wdd,my_dispd + REAL,dimension(user%gxs:user%gxe) :: f_disp + REAL, dimension(ncomp) :: dF_drho_disp + REAL, dimension(ncomp) :: dF_drho_dispd + + + + INTRINSIC EXP + REAL :: arg1 + REAL :: arg1d + PetscScalar :: rhopd(ncomp,user%gxs:user%gxe) + + rhopd = 0.0 + rhopd(1:ncomp,user%xs:user%xe) = rhopd_nogp(1:ncomp,user%xs:user%xe) + + + +!calculate weighted densities + CALL FMT_WEIGHTED_DENSITIES_D(rhop, rhopd, n0, n1, n2, n3, nv1, nv2, & +& phi_dn0, phi_dn0d, phi_dn1, phi_dn1d, phi_dn2& +& , phi_dn2d, phi_dn3, phi_dn3d, phi_dnv1, & +& phi_dnv1d, phi_dnv2, phi_dnv2d, user) +!calculate averaged density rhobar and lambda (both needed for chain term) + CALL CHAIN_AUX_D(rhop, rhopd, rhobar, rhobard, lambda, lambdad, user) +!HIER DISP!!! + CALL DISP_WEIGHTED_DENSITIES_D(rhop, rhopd, rhop_wd, rhop_wdd, user) + CALL DISP_MU_D(rhop_wd, rhop_wdd, f_disp, my_disp, my_dispd, & +& df_disp_drk, user) + + fd = 0.0 + df_drho_chaind = 0.0 + df_drho_fmtd = 0.0 + df_drho_dispd = 0.0 + + DO i = user%xs,user%xe + CALL FMT_DFDRHO_D(i, fa, user, phi_dn0, phi_dn0d, phi_dn1, phi_dn1d& +& , phi_dn2, phi_dn2d, phi_dn3, phi_dn3d, phi_dnv1, & +& phi_dnv1d, phi_dnv2, phi_dnv2d, df_drho_fmt, & +& df_drho_fmtd) + CALL CHAIN_DFDRHO_D(i, rhop, rhopd, lambda, lambdad, rhobar, rhobard& +& , df_drho_chain, df_drho_chaind, user) + +!HIER DISP!!! + CALL DISP_DFDRHO_WDA_D(i, rhop, rhop_wd, my_disp, my_dispd, f_disp, & +& df_disp_drk, df_drho_disp, df_drho_dispd, user) + + + vext(1:ncomp) = 0.0 + DO k=1,ncomp + IF (zp(i) .LT. dhs(k)/2.0) vext(k) = 100000.0 +! If( zp(ngrid) - zp(i) < dhs(k)/2.0 ) Vext(k) = 100000.0 + arg1d = -df_drho_fmtd(i,k)-df_drho_chaind(i,k)-df_drho_dispd(k) + arg1 = chempot_res(k) - vext(k) - df_drho_fmt(i, k) - & +& df_drho_chain(i, k) - df_drho_disp(k) + + fd(k, i) = rhob(1,k)*arg1d*EXP(arg1) - rhopd(k, i) + !f(k, i) = xx(k)*rho*EXP(arg1) - rhop(k, i) + END DO + END DO +END SUBROUTINE FORMFUNCTIONLOCAL_D + + + + + + + + + +!------------------------------------------------------------------------------------------------ +!This Subroutine calculates the Jacobi-Vector product using derivatives obtained via AD +!------------------------------------------------------------------------------------------------ +Subroutine Jac_Shell_AD(Jshell,v_in,v_out) + +use Global_x, only: x,snes +Use PetscManagement + +#include "finclude/petsc.h90" + + +!passed + Mat :: Jshell + Vec :: v_in !has global size discret (NOT discret +- ghost points!!) + Vec :: v_out +!local + PetscScalar, pointer :: xd(:), rhop_loc(:,:),fd(:) !for dof2, xd and fd are twice the size as for dof1 + PetscErrorCode :: ierr + Type (userctx) :: user + DM :: da + Vec :: rhop_local + + + +!get the user context and DM which are associated with nonlinear solver + call SNESGetApplicationContext(snes,user,ierr) + call SNESGetDM(snes,da,ierr) + +!get local vector for x (needed because we need the ghost point values of x) + call DMGetLocalVector(da,rhop_local,ierr) + +!copy global to local for x (then x_local also contains ghost points) + call DMGlobalToLocalBegin(da,x,INSERT_VALUES,rhop_local,ierr) + call DMGlobalToLocalEnd(da,x,INSERT_VALUES,rhop_local,ierr) + +!get pointers to the vectors x_local,v_in and v_out + call DMDAVecGetArrayF90(da,rhop_local,rhop_loc,ierr) + call VecGetArrayF90(v_in, xd, ierr ) + call VecGetArrayF90(v_out, fd, ierr ) + +! Get local grid boundaries (dont know why this is neccessary again!) + call DMDAGetCorners(da, & !the distributed array + & user%xs, & !corner index in x direction + & PETSC_NULL_INTEGER, & !corner index in y direction + & PETSC_NULL_INTEGER, & !corner index in z direction + & user%xm, & !width of locally owned part in x direction + & PETSC_NULL_INTEGER, & !width of locally owned part in y direction + & PETSC_NULL_INTEGER, & !width of locally owned part in z direction + & ierr) !error check + + call DMDAGetGhostCorners(da, & !the distributed array + & user%gxs, & !corner index in x direction (but now counting includes ghost points) + & PETSC_NULL_INTEGER, & !corner index in y direction (but now counting includes ghost points) + & PETSC_NULL_INTEGER, & !corner index in z direction (but now counting includes ghost points) + & user%gxm, & !width of locally owned part in x direction (but now including ghost points) + & PETSC_NULL_INTEGER, & !width of locally owned part in y direction (but now including ghost points) + & PETSC_NULL_INTEGER, & !width of locally owned part in z direction (but now including ghost points) + & ierr) !error check + + +! Here we shift the starting indices up by one so that we can easily +! use the Fortran convention of 1-based indices (rather 0-based indices). + user%xs = user%xs+1 + user%gxs = user%gxs+1 + + user%xe = user%xs+user%xm-1 + user%gxe = user%gxs+user%gxm-1 + + +!--------------------------------------------------------- +!call AD generated Routine + !x_loc: x + !xd : direction which the derivative is calculated for + !fd : the directional derivative in direction xd + + call FORMFUNCTIONLOCAL_D(rhop_loc,xd,fd,user,ierr) +!--------------------------------------------------------- + + + + +!restore arrays + call DMDAVecRestoreArrayF90(da,rhop_local,rhop_loc,ierr ) + call VecRestoreArrayF90( v_in, xd, ierr ) + call VecRestoreArrayF90( v_out, fd, ierr ) + call DMRestoreLocalVector(da,rhop_local,ierr) + + +End Subroutine Jac_Shell_AD + + + + +! empty subroutine for shell jacobian; probably should copy v_x to x, as they might not be same +Subroutine Jac_Matrix_Empty(snes,v_x,jac,B,flag,dummy,ierr) + implicit none +#include "finclude/petsc.h90" + SNES :: snes + Vec :: v_x + Mat :: jac,B + MatStructure :: flag + PetscErrorCode :: ierr + integer dummy(*) +End Subroutine Jac_Matrix_Empty + + + + + + + diff --git a/applications/PUfoam/MoDeNaModels/SurfaceTension/ExampleOfUsage/src/srcDetailedCode/Function.F90 b/applications/PUfoam/MoDeNaModels/SurfaceTension/ExampleOfUsage/src/srcDetailedCode/Function.F90 new file mode 100644 index 000000000..96e87d653 --- /dev/null +++ b/applications/PUfoam/MoDeNaModels/SurfaceTension/ExampleOfUsage/src/srcDetailedCode/Function.F90 @@ -0,0 +1,240 @@ + +Subroutine FormFunction(snes,X,F,user,ierr) +Use PetscManagement +Implicit None +#include +#include +#include +#include +#include +#include +#include +#include + +! Input/output variables: + SNES snes + Vec X,F + PetscErrorCode ierr + type (userctx) user + DM da + +! Declarations for use with local arrays: + PetscScalar,pointer :: lx_v(:,:),lf_v(:,:) + Vec localX + +! Scatter ghost points to local vector, using the 2-step process +! DMGlobalToLocalBegin(), DMGlobalToLocalEnd(). +! By placing code between these two statements, computations can +! be done while messages are in transition. + call SNESGetDM(snes,da,ierr) + call DMGetLocalVector(da,localX,ierr) + call DMGlobalToLocalBegin(da,X,INSERT_VALUES, & + & localX,ierr) + call DMGlobalToLocalEnd(da,X,INSERT_VALUES,localX,ierr) + + + !call VecGetArrayF90(localX,lx_v,ierr) !only for DOF=1 + !call VecGetArrayF90(F,lf_v,ierr) !only for DOF=1 + call DMDAVecGetArrayF90(da,localX,lx_v,ierr) + call DMDAVecGetArrayF90(da,F,lf_v,ierr) + +! Compute function over the locally owned part of the grid + call FormFunctionLocal(lx_v,lf_v,user,ierr) + +! Restore vectors + !call VecRestoreArrayF90(localX,lx_v,ierr) !only for DOF=1 + !call VecRestoreArrayF90(F,lf_v,ierr) !only for DOF=1 + call DMDAVecRestoreArrayF90(da,localX,lx_v,ierr) + call DMDAVecRestoreArrayF90(da,F,lf_v,ierr) + + +! Insert values into global vector + + call DMRestoreLocalVector(da,localX,ierr) + + return +End Subroutine FormFunction + + + + + + + + + + + + + + + +Subroutine FormFunctionLocal(rhop,f,user,ierr) +!PETSc modules + Use PetscManagement +!DFT modules + Use mod_DFT_FMT + Use mod_DFT_CHAIN + Use mod_DFT_DISP_WDA + Use PARAMETERS, Only: PI ,muhs,muhc,mudisp + Use BASIC_VARIABLES, Only: ncomp,nc,np ,nphas,xi,dense,parame,ensemble_flag !nphas nur fur fugacity call + Use EOS_VARIABLES, Only:dhs,rho ,phas,eta_start,x,mseg,eta !letze 4 nur zum Test for aufruf eos_phi!! + Use mod_DFT, Only: fa,zp,dzp,free,pbulk, fa_disp, ab_disp !letzen beiden nur fur elmars version + Use VLE_VAR, Only: rhob + Use DFT_FCN_MODULE, Only: ChemPot_res,ChemPot_total + Use Global_x, Only: ngrid, ngp + + +Implicit None + +! Input/output variables: + type (userctx) user + PetscScalar rhop(ncomp,user%gxs:user%gxe) + PetscScalar f(ncomp,user%xs:user%xe) + PetscErrorCode ierr + +! Local variables: + PetscInt i + PetscInt k + + !FMT + REAL,dimension(user%gxs:user%gxe) :: n0,n1,n2,n3,nv1,nv2 !ngp muss groesser als fa+fa/2 sein!! + REAL,dimension(user%gxs:user%gxe) :: phi_dn0,phi_dn1,phi_dn2,phi_dn3,phi_dnv1,phi_dnv2 + REAL :: f_fmt,temp,zs + REAL,dimension(user%xs:user%xe,ncomp) :: dF_drho_FMT + + !Chain + REAL,dimension(user%gxs:user%gxe,ncomp) :: rhobar,lambda + REAL :: f_ch + REAL,dimension(user%xs:user%xe,ncomp) :: dF_drho_CHAIN + + !DISP VAR + REAL,dimension(user%gxs:user%gxe,ncomp) :: rhop_wd,my_disp,df_disp_drk + REAL,dimension(user%gxs:user%gxe) :: f_disp + REAL, dimension(ncomp) :: dF_drho_disp + !for Elmars Version + REAL, DIMENSION(user%gxs:user%gxe,ncomp):: rhoi_disp,mydisp,dadisp_dr + REAL, DIMENSION(user%gxs:user%gxe) :: adisp,rho_disp,rhop_sum + REAL :: dF_drho_att(ncomp) + INTEGER :: fa_psi_max,WDA_var + + + !polar + REAL :: fres_polar,fdd,fqq,fdq,mu_polar(nc) + REAL :: fdd_rk, fqq_rk, fdq_rk, z3_rk + INTEGER :: ik + !association + REAL :: f_assoc + REAL :: mu_assoc(nc) + REAL :: lnphi(np,nc), fres + + REAL :: f_tot, delta_f + REAL :: Vext(ncomp) + + + Do k = 1,ncomp + Do i= user%xs,user%xe + If( rhop(k,i) < epsilon(dhs) ) rhop(k,i) = epsilon(dhs) + End Do + End Do + + DO i = user%gxs,user%gxe + rhop_sum(i) = sum( rhop(1:ncomp,i) ) + END DO + + + + !calculate weighted densities + call FMT_Weighted_Densities(rhop,n0,n1,n2,n3,nv1,nv2,phi_dn0,phi_dn1,phi_dn2,phi_dn3,phi_dnv1,phi_dnv2,user) + + !calculate averaged density rhobar and lambda (both needed for chain term) + call Chain_aux(rhop,rhobar,lambda,user) + + + !weighted densities for Dispersion +! call DISP_Weighted_Densities(rhop, rhop_wd, user) +! call DISP_mu(rhop_wd,f_disp,my_disp,df_disp_drk,user) + + !Elmars Version + fa_psi_max = maxval(fa_disp(1:ncomp)) + call rhoi_disp_wd ( ngrid, fa_disp, fa_psi_max, ab_disp, rhop, rhoi_disp,user ) + CALL a_disp_pcsaft ( ngrid, fa_disp, fa_psi_max, rhoi_disp, rho_disp, adisp, mydisp, dadisp_dr,user ) + + + free = 0.0 + + DO i = user%xs,user%xe + + !FMT + call FMT_dFdrho(i,fa,user,phi_dn0,phi_dn1,phi_dn2,phi_dn3,phi_dnv1,phi_dnv2,dF_drho_FMT) + zs = 1.0 - n3(i) + temp = log(zs) + f_fmt = - n0(i)*temp + n1(i)*n2(i)/zs - nv1(i)*nv2(i)/zs & !see for example eq. 30 in "Fundamental measure theory for hard-sphere mixtures revisited: the White bear version (Roth) + + (n2(i)**3 -3.0*n2(i)*nv2(i)*nv2(i)) *(n3(i)+zs*zs*temp) & + /36.0/PI/zs/zs/n3(i)**2 + + !Chain + call Chain_dFdrho(i,rhop,lambda,rhobar,dF_drho_CHAIN,f_ch,user) + + !Dispersion + WDA_var = 1 + call dF_disp_drho_wda( i, WDA_var, fa_disp, ab_disp, rhop, rhop_sum, & + rhoi_disp, rho_disp, adisp, mydisp, dadisp_dr, dF_drho_att,user ) + + if(WDA_var == 1) adisp(i) = rho_disp(i) * adisp(i) + if(WDA_var == 2) adisp(i) = rhop_sum(i) * adisp(i) + + + !polar as LDA + fres_polar = 0.0 + mu_polar(:) = 0.0 + dense(1) = PI / 6.0 * SUM( rhop(1:ncomp,i) * mseg(1:ncomp) * dhs(1:ncomp)**3 ) + xi(1,1:ncomp) = rhop(1:ncomp,i) / SUM( rhop(1:ncomp,i) ) + ensemble_flag = 'tv' + IF ( SUM( parame(1:ncomp,6) ) > 1.E-10 .OR. SUM( parame(1:ncomp,7) ) > 1.E-10 ) THEN + eta = dense(1) + rho = SUM(rhop(1:ncomp,i)) + x(1:ncomp) = xi(1,1:ncomp) + call F_POLAR ( fdd, fqq, fdq ) + fres_polar = ( fdd + fqq + fdq ) * SUM( rhop(1:ncomp,i) ) + DO ik = 1, ncomp + z3_rk = PI/6.0 * mseg(ik) * dhs(ik)**3 + call PHI_POLAR ( ik, z3_rk, fdd_rk, fqq_rk, fdq_rk ) + mu_polar(ik) = fdd_rk + fqq_rk + fdq_rk + END DO + END IF + + !association as LDA + f_assoc = 0.0 + mu_assoc(:) = 0.0 + IF ( SUM( NINT(parame(1:ncomp,12)) ) > 0) THEN + call ONLY_ONE_TERM_EOS_NUMERICAL ( 'hb_term ', 'TPT1_Chap' ) + call FUGACITY ( lnphi ) + call RESTORE_PREVIOUS_EOS_NUMERICAL + f_assoc = fres * SUM( rhop(1:ncomp,i) ) + mu_assoc(1:ncomp) = lnphi(1,1:ncomp) + END IF + + f_tot = f_fmt + f_ch + adisp(i) + fres_polar + f_assoc & + + SUM( rhop(1:ncomp,i)*( LOG(rhop(1:ncomp,i)/rhob(1,1:ncomp))-1.0 ) ) + delta_f = f_tot - ( SUM(rhop(1:ncomp,i)*chemPot_res(1:ncomp)) - pbulk) ! all quantities .../(kT) + free = free + delta_f*dzp + + + + Do k=1,ncomp + f(k,i) = -(rhob(1,k) * exp(ChemPot_res(k)-dF_drho_FMT(i,k)-dF_drho_CHAIN(i,k)-dF_drho_att(k) & + -mu_polar(k) - mu_assoc(k)) - rhop(k,i)) + End Do + + END DO + + + +End Subroutine FormFunctionLocal + + + + + + diff --git a/applications/PUfoam/MoDeNaModels/SurfaceTension/ExampleOfUsage/src/srcDetailedCode/Helfer_Routinen.F90 b/applications/PUfoam/MoDeNaModels/SurfaceTension/ExampleOfUsage/src/srcDetailedCode/Helfer_Routinen.F90 new file mode 100644 index 000000000..a13e61d5c --- /dev/null +++ b/applications/PUfoam/MoDeNaModels/SurfaceTension/ExampleOfUsage/src/srcDetailedCode/Helfer_Routinen.F90 @@ -0,0 +1,51 @@ + +Subroutine PrintGlobalVec(GlobalVec,filename) +Implicit None +#include +#include +#include +#include + + + Vec :: GlobalVec + character(80) :: filename + + PetscViewer viewer + PetscErrorCode ierr + +!Print global vector to a file + call PetscViewerASCIIOpen(PETSC_COMM_WORLD,filename,viewer,ierr) + call VecView(GlobalVec,viewer,ierr) + + call PetscViewerDestroy(viewer,ierr) + +End Subroutine PrintGlobalVec + + + +Subroutine PrintLocalVec(GlobalVec,da,filename) +Implicit None +#include +#include +#include +#include +#include +#include + + Vec GlobalVec + Vec LocalVec + DM da + character(80) :: filename + + PetscViewer viewer + PetscErrorCode ierr + + call DMGetLocalVector(da,LocalVec,ierr) !create a locally owned part of a global distribued array + call DMGlobalToLocalBegin(da,GlobalVec,INSERT_VALUES,LocalVec,ierr) !copy values from global array to local arrays + call DMGlobalToLocalEnd(da,GlobalVec,INSERT_VALUES,LocalVec,ierr) + call PetscViewerASCIIOpen(PETSC_COMM_SELF,filename,viewer,ierr) !associate viewer with file + call VecView(LocalVec,viewer,ierr) !every processor prints his local array to a file + call DMRestoreLocalVector(da,LocalVec,ierr) !Free memory of local vector + + +End Subroutine PrintLocalVec diff --git a/applications/PUfoam/MoDeNaModels/SurfaceTension/ExampleOfUsage/src/srcDetailedCode/InitialGuess.F90 b/applications/PUfoam/MoDeNaModels/SurfaceTension/ExampleOfUsage/src/srcDetailedCode/InitialGuess.F90 new file mode 100644 index 000000000..700f86f4f --- /dev/null +++ b/applications/PUfoam/MoDeNaModels/SurfaceTension/ExampleOfUsage/src/srcDetailedCode/InitialGuess.F90 @@ -0,0 +1,249 @@ + +Subroutine FormInitialGuess(snes,X,ierr) +Use PetscManagement +Use f90moduleinterfaces + +Implicit None + + +#include +#include +#include +#include +#include +#include +#include +#include + +! Input/output variables: + SNES snes + type(userctx), pointer:: puser + Vec X + PetscErrorCode ierr + DM da + +! Declarations for use with local arrays: + PetscScalar,pointer :: lx_v(:,:) + Vec :: localX + + ierr = 0 + call SNESGetDM(snes,da,ierr) + call SNESGetApplicationContext(snes,puser,ierr) + +! Get a pointer to vector data. + call DMGetLocalVector(da,localX,ierr) + !call VecGetArrayF90(localX,lx_v,ierr) !only for DOF=1 + call DMDAVecGetArrayF90(da,localX,lx_v,ierr) + + + +! Compute initial guess over the locally owned part of the grid + call InitialGuessLocal(puser,lx_v,ierr) + +! Restore vector + !call VecRestoreArrayF90(localX,lx_v,ierr) !only for DOF=1 + call DMDAVecRestoreArrayF90(da,localX,lx_v,ierr) + + +! Insert values into global vector + call DMLocalToGlobalBegin(da,localX,INSERT_VALUES,X,ierr) + call DMLocalToGlobalEnd(da,localX,INSERT_VALUES,X,ierr) + call DMRestoreLocalVector(da,localX,ierr) + +End Subroutine FormInitialGuess + + + + + + +Subroutine InitialGuessLocal(user,rhop,ierr) + +!PETSc modules + use PetscManagement +!VLE and DFT modules + Use BASIC_VARIABLES, ONLY: ncomp,t,parame + Use EOS_VARIABLES, Only:rho + Use VLE_VAR, Only: rhob,tc + Use PARAMETERS, Only: PI + Use mod_DFT, Only: box,zp,dzp + Use Global_x, Only: ngrid + + + implicit none + +#include +#include +#include +#include +#include +#include +#include +#include + +! Input/output variables: + type (userctx) :: user + PetscScalar :: rhop(ncomp,user%gxs:user%gxe) + PetscErrorCode :: ierr + + +! Local variables: + PetscInt i,k + PetscBool flg + REAL :: arg + INTEGER :: pert + REAL :: tanhfac + REAL :: zp_i + REAL :: zp_middle + + + +!normal or perturbed inital profile? + call PetscOptionsGetInt(PETSC_NULL_CHARACTER,'-init_pert',pert,flg,ierr) + + + zp_middle = (ngrid/2)*dzp + tanhfac = -2.3625*t/tc + 2.4728 + + + !default: no perturbation, start with bulk density + + +IF(user%num_procs == 1) THEN !if only one processor involved + + Do k = 1,ncomp + Do i=user%gxs,user%gxe !proc 0 has to calculate values for ghost points out of physical domain (from -irc to -1 and discret to discret+irc) and its regular part + zp_i = zp(i) + rhop(k,i) = ( TANH(-(zp_i -zp_middle) / parame(k,2) *tanhfac) + 1.0 ) * rhob(1,k)/2.0 & + - ( TANH(-(zp_i - zp_middle) / parame(k,2) *tanhfac) - 1.0 ) * rhob(2,k)/2.0 +!rhop(k,i) = rhob(1,k) + !make sure density is nonzero + If(rhop(k,i) == 0.0) rhop(k,i) = rhop(k,i-1) + End Do + End Do + + + +Else !parallel simulation + + + + IF(user%rank == 0) THEN !watch the user%xs vs user%gxs (first no ghost points, second with ghost points) + + Do k=1,ncomp !loop over dof = loop over components + Do i=user%gxs,user%xe !proc 0 has to calculate values for ghost points out of physical domain (from -irc to -1) and its regular part + zp_i = zp(i) + !perturb = (rhob(1,j)-rhob(2,j))/2.0 * i * (discret - i) / (damp*discret)**2 + !rhop(k,i) = ( TANH(-(zp_i -zp_middle) / parame(k,2) *tanhfac) + 1.0 ) * rhob(1,k)/2.0 & + ! - ( TANH(-(zp_i - zp_middle) / parame(k,2) *tanhfac) - 1.0 ) * rhob(2,k)/2.0 !+ perturb +rhop(k,i) = rhob(1,k) + !make sure density is nonzero + If(rhop(k,i) == 0.0) rhop(k,i) = rhop(k,i-1) + End Do + End Do + + + ELSE IF(user%rank == user%num_procs-1) THEN + + Do k=1,ncomp !loop over dof = loop over components + Do i=user%gxs,user%gxe !last proc has to calculate values for ghost points out of physical domain (from discret to discret+irc) and its regular part + zp_i = zp(i) + !perturb = (rhob(1,j)-rhob(2,j))/2.0 * i * (discret - i) / (damp*discret)**2 + !rhop(k,i) = ( TANH(-(zp_i -zp_middle) / parame(k,2) *tanhfac) + 1.0 ) * rhob(1,k)/2.0 & + ! - ( TANH(-(zp_i - zp_middle) / parame(k,2) *tanhfac) - 1.0 ) * rhob(2,k)/2.0 !+ perturb +rhop(k,i) = rhob(1,k) + !make sure density is nonzero + If(rhop(k,i) == 0.0) rhop(k,i) = rhop(k,i-1) + End Do + End Do + + + ELSE + + Do k=1,ncomp !loop over dof = loop over components + Do i=user%xs,user%xe !middle procs have to calculate only their regular part + zp_i = zp(i) + !perturb = (rhob(1,j)-rhob(2,j))/2.0 * i * (discret - i) / (damp*discret)**2 + !rhop(k,i) = ( TANH(-(zp_i -zp_middle) / parame(k,2) *tanhfac) + 1.0 ) * rhob(1,k)/2.0 & + ! - ( TANH(-(zp_i - zp_middle) / parame(k,2) *tanhfac) - 1.0 ) * rhob(2,k)/2.0 !+ perturb +rhop(k,i) = rhob(1,k) + !make sure density is nonzero + If(rhop(k,i) == 0.0) rhop(k,i) = rhop(k,i-1) + End Do + End Do + + END IF + + +End If + + + + + + + + + + + + + + + + + + + +! If(pert == 1) Then +! Do i=user%xs,user%xe +! arg = zp(i) * PI / box +! rhop(k,i) = rhob(1,k) + 0.5*rhob(1,k) * sin(arg) +! End Do +! End If +! +! If(pert == 2) Then +! Do i=user%xs,user%xe +! arg = zp(i) * 2.0 * PI / box +! rhop(k,i) = rhob(1,k) + 0.5*rhob(1,k) * sin(arg) +! End Do +! End If +! +! If(pert == 3) Then +! Do i=user%xs,user%xe +! arg = zp(i) * 3.0 * PI / box +! rhop(k,i) = rhob(1,k) + 0.5*rhob(1,k) * sin(arg) +! End Do +! 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476 Pls +6573 486 Pls +6634 503 Pls +6692 468 Pls +6753 481 Pls +6579 4486 Pls +% End plot #1 +1.000 UL +LTb +686 4619 N +686 448 L +6261 0 V +0 4171 V +-6261 0 V +Z stroke +1.000 UP +1.000 UL +LTb +stroke +grestore +end +showpage +%%Trailer +%%DocumentFonts: Helvetica diff --git a/applications/PUfoam/MoDeNaModels/SurfaceTension/ExampleOfUsage/src/srcDetailedCode/Main.F90 b/applications/PUfoam/MoDeNaModels/SurfaceTension/ExampleOfUsage/src/srcDetailedCode/Main.F90 new file mode 100644 index 000000000..92e77131b --- /dev/null +++ b/applications/PUfoam/MoDeNaModels/SurfaceTension/ExampleOfUsage/src/srcDetailedCode/Main.F90 @@ -0,0 +1,234 @@ + +! +!THIS CODE WAS WRITTEN AT +!UNIVERSITY OF STUTTGART, +!INSTITUTE OF TECHNICAL THERMODYNAMICS AND THERMAL PROCESS ENGINEERING +!BY +!JOACHIM GROSS +!JONAS MAIRHOFER +! +! + + + + + + + + + + + + +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! This program calculates surface tensions using the a Density Functional +! Theory based on the PC-SAFTequation of state. +! The contributions to the Helmholtz energy functional are calculated +! as folows: +! Hard Sphere Contribution: White-Bear Version of the Fundamental Measure Theory +! Chain Formation: TPT1 +! Dispersion is treated in a weighted density approximation +! Associative and polar contributions are treated in a local density approximation +! +! +! The input parameters are read from the file "in.txt" which has to +! be in the same directory as the executable. +! +! The input file must have the following format: +! Line1: Value of temperature in Kelvin +! Line2: Number of components present in the system (ncomp) +! Line3 Name of component 1 +! ... +! Line3+ncomp Name of component ncomp +! Line3+ncomp+1 Molar (overall) concentration of component 1 +! ... +! Line3+2ncomp Molar (overall) concentration of component ncomp +! +! For a binary system, these molar fractions are only treated as an initial guess and may be set to e.g. 0. +! +! +! So far, pressure is set to 1bar in all calculaions +! +! +!If you would like to use this code in your work, please cite the +!following publications: +! +!Gross, Joachim, and Gabriele Sadowski. "Perturbed-chain SAFT: An equation of state based on a perturbation theory for chain molecules." Industrial & engineering chemistry research 40.4 (2001): 1244-1260. +!Gross, Joachim, and Gabriele Sadowski. "Application of the perturbed-chain SAFT equation of state to associating systems." Industrial & engineering chemistry research 41.22 (2002): 5510-5515. +!Gross, Joachim, and Jadran Vrabec. "An equation?of?state contribution for polar components: Dipolar molecules." AIChE journal 52.3 (2006): 1194-1204. +!Gross, Joachim. "A density functional theory for vapor-liquid interfaces using the PCP-SAFT equation of state." The Journal of chemical physics 131.20 (2009): 204705. +!Klink, Christoph, and Joachim Gross. "A density functional theory for vapor?liquid interfaces of mixtures using the perturbed-chain polar statistical associating fluid theory equation of state." Industrial & Engineering Chemistry Research 53.14 (2014): 6169-6178. +! +! +! In order to run this code, PETSc 3.4.4 has to be installed +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! + + +Program DFT + +Use PARAMETERS, Only: np,nc,KBOL +Use BASIC_VARIABLES, Only: ncomp,t,p,ensemble_flag,num,parame,eos,pol,xif,compna +Use EOS_VARIABLES, Only: dhs,mseg,eta,dd_term,dq_term,qq_term +Use EOS_CONSTANTS, Only: ap,bp,dnm +Use mod_DFT, Only: box,dzp,fa,zp,fa_disp,ab_disp,pbulk +Use VLE_VAR, ONLY: tc,pc,rhob,density +USE DFT_FCN_MODULE, ONLY: chemPot_total + +!PETSc modules +Use PetscManagement +Use f90moduleinterfaces +Use Global_x !(snes,ngrid,ngp,x,r,timer) + + +Implicit None + +#include + +! ---------------------------------------------------------------------- +!Variables +! ---------------------------------------------------------------------- + +PetscErrorCode :: ierr +type (userctx) :: user +PetscBool :: flg +INTEGER :: i +character(80) :: filename='' +REAL :: zges(np) +REAL :: dhs_save(nc) +REAL :: cif(nc) +REAL :: psi_factor + +!external subroutines associated with Solver +external FormInitialGuess +external FormFunction + + +! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - +! Initialize program +! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - + call PetscInitialize(PETSC_NULL_CHARACTER,ierr) + call MPI_Comm_rank(PETSC_COMM_WORLD,user%rank,ierr) + call MPI_Comm_size(PETSC_COMM_WORLD,user%num_procs,ierr) + +! ---------------------------------------------------------------------- +!Read information from inputfile "in.txt" +! ---------------------------------------------------------------------- + + filename='./in.txt' + CALL file_open(filename,77) ! open input file + READ (77,*) t ! read temperature + READ (77,*) ncomp ! read number of components in the system + Do i = 1,ncomp ! read component names + READ (77,*) compna(i) + End Do + Do i = 1,ncomp ! read component overall molar concentrations + READ (77,*) xif(i) + End Do + +! !calculate molar fractions from molar concentrations +! xif(1:ncomp) =cif(1:ncomp) / sum(cif(1:ncomp)) + + +! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - +! GENERAL SIMULATION SET UP +! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - + + num = 0 ! (num=0: using analytical derivatives of EOS) + ! (num=1: using numerical derivatives of EOS) + ! (num=2: White's renormalization group theory) + IF ( num /= 0 ) CALL SET_DEFAULT_EOS_NUMERICAL + + eos = 1 + pol = 1 + + p = 1.000e05 + + CALL para_input ! retriev pure comp. parameters + + ensemble_flag = 'tp' ! this specifies, whether the eos-subroutines + ! are executed for constant 'tp' or for constant 'tv' + + + +! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - +! Start phase equilibrium calculation and determine critical point +! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - + + CALL EOS_CONST (ap, bp, dnm) + + dd_term = 'GV' ! dipole-dipole term of Gross & Vrabec (2006) + qq_term = 'JG' ! quadrupole-quadrupole term of Gross (2005) + dq_term = 'VG' ! dipole-quadrupole term of Vrabec & Gross (2008) + + CALL VLE_MIX(rhob,density,chemPot_total,user) !user is passed so user%rank is known and only node 0 prints out the reslts of the VLE calculation + + !determine critical point + num = 0 + dhs_save = dhs !needed because subroutine CRIT_POINT_MIX changes the value + CALL CRIT_POINT_MIX(tc,user) !of the global variable dhs! In cases where Tc doesnt converge + dhs = dhs_save !dhs can be NAN after CRIT_POINT_MIX!! + !chance to overwite NAN results +! IF(user%rank == 0) THEN +! WRITE (*,*) 'Give final value of Tc:' +! READ (*,*) tc +! END IF +! CALL MPI_Bcast(tc,1,MPI_DOUBLE_PRECISION,0,PETSC_COMM_WORLD,ierr) + + + + +!------------------------------------------- +!DFT Set Up +!------------------------------------------- + + num = 1 + CALL SET_DEFAULT_EOS_NUMERICAL + + !set default values (overwritten from makefile) + box = 45.0 !box length [A] + ngrid = 614 !grid points + + !overwrite box size and ngrid if options are set in makefile + call PetscOptionsGetReal(PETSC_NULL_CHARACTER,'-box',box,flg,ierr) + call PetscOptionsGetInt(PETSC_NULL_CHARACTER,'-nx',ngrid,flg,ierr) + + + dzp = box / REAL(ngrid) !grid spacing [A] + Allocate(fa(ncomp)) + fa(1:ncomp) = NINT( parame(1:ncomp,2) / dzp ) !grid points per sigma [-] + + !FOR DISP + ALLOCATE(fa_disp(ncomp),ab_disp(ncomp)) + psi_factor = 1.5 + fa_disp(1:ncomp) = NINT( psi_factor * REAL(fa(1:ncomp)) ) + Do i=1,ncomp + if( MOD(fa_disp(i),2) /= 0 ) fa_disp(i) = fa_disp(i) + 1 + End Do + + + ab_disp(1:ncomp) = psi_factor * dhs(1:ncomp) + + + ngp = 2 * maxval(fa_disp(1:ncomp)) + 5 !number of ghost points (+5 kann eig weg) + + Allocate(zp(-ngp:ngrid+ngp)) + + Do i=-ngp,ngrid+ngp + zp(i) = REAL(i) * dzp !z-distance from origin of grid points [A] + End Do + + pbulk = ( p * 1.E-30 ) / ( KBOL*t* rhob(1,0) ) * rhob(1,0) !p/kT + + + !update z3t, the T-dependent quantity that relates eta and rho, as eta = z3t*rho + CALL PERTURBATION_PARAMETER + +!------------------------------------------- +!Evaluate Initial Guess,Set up solver,solve system +!------------------------------------------- + call SolverSetup + + + +End Program DFT diff --git a/applications/PUfoam/MoDeNaModels/SurfaceTension/ExampleOfUsage/src/srcDetailedCode/Modules.F90 b/applications/PUfoam/MoDeNaModels/SurfaceTension/ExampleOfUsage/src/srcDetailedCode/Modules.F90 new file mode 100644 index 000000000..c04ed3cad --- /dev/null +++ b/applications/PUfoam/MoDeNaModels/SurfaceTension/ExampleOfUsage/src/srcDetailedCode/Modules.F90 @@ -0,0 +1,545 @@ + + + + + + + + +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! This module contains parameters and variables .... +! ................ +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW + +Module PARAMETERS + + implicit none + save + + integer, parameter :: nc = 3 + integer, parameter :: np = 3 + integer, parameter :: nsite = 5 + + real, parameter :: PI = 3.141592653589793 + real, parameter :: RGAS = 8.31441 + real, parameter :: NAv = 6.022045E23 + real, parameter :: KBOL = RGAS / NAv + real, parameter :: TAU = PI / 3.0 / SQRT(2.0) + +real :: muhs(3) +real :: muhc(3) +real :: mudisp(3) + + + +End Module PARAMETERS + + + +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! This module contains parameters and variables .... +! ................ +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW + + +Module VLE_VAR +USE PARAMETERS, ONLY: nc,np +implicit none + +REAL :: tc +REAL :: pc +REAL :: rhob(2,0:nc) +REAL :: density(np) + +End Module VLE_VAR + + + + + + + + +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! This module contains parameters and variables .... +! ................ +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW + +Module BASIC_VARIABLES + + use PARAMETERS, only: nc, np, nsite + implicit none + save + +! ---------------------------------------------------------------------- +! basic quantities defining the mixture +! ---------------------------------------------------------------------- + integer :: ncomp + integer :: nphas + + real :: t + !real :: tc + real :: p + real, dimension(np) :: dense + !real, dimension(np) :: rhob + + real, dimension(np, nc) :: xi + real, dimension(np, nc) :: lnx + real, dimension(nc) :: xiF + + real, dimension(nc) :: mm + real, dimension(np, nc, nsite) :: mxx + + real :: alpha + + +! ---------------------------------------------------------------------- +! pure component parameters +! ---------------------------------------------------------------------- + real, dimension(nc, 25) :: parame = 0.0 + real, dimension(nc) :: chiR + character*30, dimension(nc) :: compna + real, dimension(nc, nc) :: kij, lij + real, dimension(nc, nc) :: E_LC, S_LC + real, dimension(nc) :: LLi, phi_criti, chap + + +! ---------------------------------------------------------------------- +! thermodynamic quantities +! ---------------------------------------------------------------------- + real, dimension(np) :: densta + real, dimension(0:nc*np+6) :: val_init, val_conv + + real :: h_lv + real, dimension(np) :: cpres, enthal, entrop, gibbs, f_res + + real, dimension(np) :: dp_dz, dp_dz2 + + +! ---------------------------------------------------------------------- +! choice of EOS-model and solution method +! ---------------------------------------------------------------------- + integer :: eos, pol + integer :: num + character (LEN=2) :: ensemble_flag + character (LEN=10) :: RGT_variant + + +! ---------------------------------------------------------------------- +! for input/output +! ---------------------------------------------------------------------- + integer :: outp, bindiag + real :: u_in_T, u_out_T, u_in_P, u_out_P + + +! ---------------------------------------------------------------------- +! quantities defining the numerical procedure +! ---------------------------------------------------------------------- + integer :: n_unkw + + real :: step_a, acc_a !, acc_i + real, dimension(nc) :: scaling + real, dimension(3500) :: plv_kon + real, dimension(2, 3500) :: d_kond + + character*3, dimension(10) :: it, sum_rel + character*3 :: running + + +End Module BASIC_VARIABLES + + + + +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! This module contains parameters and variables .... +! ................ +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW + +Module EOS_VARIABLES + + use PARAMETERS, only: nc, nsite, PI, KBOL, TAU, NAv + use BASIC_VARIABLES, only: ncomp, eos, t, p, parame, E_LC, S_LC, chiR, & + LLi, phi_criti, chap, kij, lij, ensemble_flag + implicit none + save + +! ---------------------------------------------------------------------- +! basic quantities defining the mixture (single phase) +! ---------------------------------------------------------------------- + real :: x(nc) + real :: eta_start + real :: eta + real :: rho + +! ---------------------------------------------------------------------- +! thermodynamic quantities +! ---------------------------------------------------------------------- + real :: fres + real :: lnphi(nc) + real :: pges + real :: pgesdz + real :: pgesd2 + real :: pgesd3 + + real :: h_res + real :: cp_res + real :: s_res + +! ---------------------------------------------------------------------- +! quantities of fluid theory +! ---------------------------------------------------------------------- + real :: gij(nc,nc) + real :: mx(nc,nsite) + + real :: mseg(nc) + real :: dhs(nc) + real :: uij(nc,nc) + real :: sig_ij(nc,nc) + real :: vij(nc,nc) + + real :: um + real :: order1 + real :: order2 + real :: apar(0:6) + real :: bpar(0:6) + + real :: z0t + real :: z1t + real :: z2t + real :: z3t + + integer :: nhb_typ(nc) + real :: ass_d(nc,nc,nsite,nsite) + real :: nhb_no(nc,nsite) + real :: dij_ab(nc,nc) + +! ---------------------------------------------------------------------- +! auxilliary quantities +! ---------------------------------------------------------------------- + real :: tfr + integer :: phas + + character (LEN = 2) :: dd_term, qq_term, dq_term + + real :: densav(3), denold(3) + real :: density_error(3) + + real :: alpha_nematic + real :: alpha_test(2) + +End Module EOS_VARIABLES + + + +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! This module contains parameters and variables .... +! ................ +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW + +Module EOS_CONSTANTS + + use PARAMETERS, only: nc + implicit none + save + + real, dimension(0:6,3) :: ap, bp + real, dimension(4,9) :: dnm + + real, dimension(28) :: c_dd, n_dd, m_dd, k_dd, o_dd + real, dimension(nc,nc,0:8) :: qqp2, qqp4, ddp2, ddp4, dqp2, dqp4 + real, dimension(nc,nc,nc,0:8) :: qqp3, ddp3, dqp3 + +End Module EOS_CONSTANTS + +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! This module contains parameters and variables .... +! ................ +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW + +Module EOS_NUMERICAL_DERIVATIVES + + use EOS_VARIABLES, only: dd_term, qq_term, dq_term + + implicit none + save + + character (LEN=9) :: ideal_gas ! (yes, no) + character (LEN=9) :: hard_sphere ! (CSBM, no) + character (LEN=9) :: chain_term ! (TPT1, no) + character (LEN=9) :: disp_term ! (PC-SAFT, CK, no) + character (LEN=9) :: hb_term ! (TPT1_Chap, no) + character (LEN=9) :: LC_term ! (MSaupe, no) + character (LEN=9) :: branch_term ! (TPT2, no) + character (LEN=9) :: II_term ! (......., no) + character (LEN=9) :: ID_term ! (......., no) + + character (LEN=9) :: subtract1 ! (1PT, 2PT, no) + character (LEN=9) :: subtract2 ! (ITTpolar, no) + + character (LEN=9) :: save_eos_terms(10) + +End Module EOS_NUMERICAL_DERIVATIVES + + +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! Module STARTING_VALUES +! +! This module contains parameters and variables for a phase stability +! analyis as part of a flash calculation. +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW + + Module STARTING_VALUES + + use PARAMETERS, only: nc + implicit none + save + + REAL, DIMENSION(nc) :: rhoif, rhoi1, rhoi2, grad_fd + REAL :: fdenf + + End Module STARTING_VALUES + + + + + +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! Module DFT_MODULE +! +! This module contains parameters and variables for DFT calculations. +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! + Module DFT_MODULE + + use PARAMETERS, only: nc + implicit none + save + +INTEGER, PARAMETER :: NDFT = 4000 +INTEGER, PARAMETER :: NDFT2 = 4000 + +INTEGER, PARAMETER :: r_grid = 200 + integer :: discret + REAL :: box_l_no_unit +! REAL :: pbulk + INTEGER :: kmax, den_step + LOGICAL :: shift, WCA, MFT + REAL :: rc, rg, dzr, tau_cut + REAL :: d_hs, dhs_st, z3t_st + REAL :: z_ges + REAL, DIMENSION(r_grid) :: x1a + REAL, DIMENSION(NDFT) :: x2a + REAL, DIMENSION(r_grid,NDFT) :: ya, y1a, y2a, y12a + REAL, DIMENSION(r_grid,NDFT,4,4) :: c_bicub + REAL :: fres_temp +! REAL :: free + + REAL, DIMENSION(r_grid) :: x1a_11 + REAL, DIMENSION(NDFT) :: x2a_11 + REAL, DIMENSION(r_grid,NDFT) :: ya_11, y1a_11, y2a_11, y12a_11 + REAL, DIMENSION(r_grid,NDFT,4,4) :: c_bicub_11 + REAL, DIMENSION(r_grid) :: x1a_12 + REAL, DIMENSION(NDFT) :: x2a_12 + REAL, DIMENSION(r_grid,NDFT) :: ya_12, y1a_12, y2a_12, y12a_12 + REAL, DIMENSION(r_grid,NDFT,4,4) :: c_bicub_12 + REAL, DIMENSION(r_grid) :: x1a_22 + REAL, DIMENSION(NDFT) :: x2a_22 + REAL, DIMENSION(r_grid,NDFT) :: ya_22, y1a_22, y2a_22, y12a_22 + REAL, DIMENSION(r_grid,NDFT,4,4) :: c_bicub_22 + + End Module DFT_MODULE + + +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! This module ........... +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +Module rdf_variables + + implicit none + save + + real, dimension(0:20) :: fac(0:20) + +End Module rdf_variables + + +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! This module contains the variavles that are needed in the core DFT_FCN +! They are not passed directly to DFT_FCN because the nonlinear solver +! needs a certain calling structure: fcn(x,fvec,n) +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +Module DFT_FCN_MODULE + +use PARAMETERS, only: nc + implicit none + +!INTEGER :: irc(nc),irc_j,ih,fa(nc) +! REAL, DIMENSION(-NDFT:NDFT) :: zp +! REAL, DIMENSION(-NDFT:NDFT) :: f_tot +! REAL, DIMENSION(-NDFT:NDFT,2) :: dF_drho_tot +! REAL :: rhob_dft(2,0:nc) + !REAL :: my0(nc) + REAL :: chemPot_total(nc) + REAL :: chemPot_res(nc) + +End Module DFT_FCN_MODULE + + +Module mod_DFT + +Implicit None + +REAL :: box !box length [A] +!INTEGER :: ngrid !grid points +!INTEGER :: ngp !ghost points +REAL :: dzp !grid spacing [A] +INTEGER,allocatable :: fa(:) !grid points per sigma [-] +REAL, allocatable :: zp(:) !z-distance from origin [A] +INTEGER,allocatable :: fa_disp(:) !integraition interval for dispersion wda +REAL,allocatable :: ab_disp(:) !integraition interval for dispersion wda +REAL :: pbulk, free + + + +End Module mod_DFT + + + + + + + + + + +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! Module Module_Heidemann_Khalil +! +! This module .... +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! + Module Module_Heidemann_Khalil + + implicit none + save + + real :: error_condition2 + + End Module + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +! ! ! Module PARAMETERS +! ! ! +! ! ! Implicit None +! ! ! +! ! ! REAL, parameter :: PI = 3.141592653589793 +! ! ! Integer, parameter :: nc = 3 +! ! ! Integer, parameter :: np = 3 +! ! ! +! ! ! End Module PARAMETERS +! ! ! +! ! ! +! ! ! +! ! ! +! ! ! +! ! ! +! ! ! +! ! ! +! ! ! Module BASIC_VARIABLES +! ! ! +! ! ! Use Parameters, Only: nc +! ! ! +! ! ! Implicit None +! ! ! +! ! ! INTEGER :: ncomp +! ! ! REAL :: t +! ! ! REAL :: kij(nc,nc) +! ! ! Integer :: eos, pol +! ! ! Integer :: num +! ! ! character (LEN=2) :: ensemble_flag +! ! ! +! ! ! +! ! ! End Module BASIC_VARIABLES +! ! ! +! ! ! +! ! ! +! ! ! +! ! ! Module EOS_VARIABLES +! ! ! +! ! ! Implicit None +! ! ! +! ! ! +! ! ! REAL, allocatable :: mseg(:) +! ! ! REAL, allocatable :: eps(:) +! ! ! REAL, allocatable :: sig(:) +! ! ! REAL, allocatable :: dhs(:) +! ! ! +! ! ! REAL :: eta +! ! ! REAL :: rho +! ! ! REAL, allocatable :: xx(:) +! ! ! REAL,allocatable :: sig_ij(:,:), uij(:,:) +! ! ! +! ! ! character (LEN = 2) :: dd_term, qq_term, dq_term +! ! ! +! ! ! End Module EOS_VARIABLES +! ! ! +! ! ! +! ! ! +! ! ! +! ! ! +! ! ! Module EOS_CONSTANTS +! ! ! +! ! ! Implicit None +! ! ! +! ! ! REAL :: ap(0:6,3),bp(0:6,3) +! ! ! +! ! ! End Module EOS_CONSTANTS +! ! ! +! ! ! +! ! ! +! ! ! +! ! ! +! ! ! +! ! ! +! ! ! diff --git a/applications/PUfoam/MoDeNaModels/SurfaceTension/ExampleOfUsage/src/srcDetailedCode/Numeric_subroutines.F90 b/applications/PUfoam/MoDeNaModels/SurfaceTension/ExampleOfUsage/src/srcDetailedCode/Numeric_subroutines.F90 new file mode 100644 index 000000000..8a8866c10 --- /dev/null +++ b/applications/PUfoam/MoDeNaModels/SurfaceTension/ExampleOfUsage/src/srcDetailedCode/Numeric_subroutines.F90 @@ -0,0 +1,1671 @@ +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! + SUBROUTINE bicub_derivative ( ya, x1a, x2a, y1a, y2a, y12a, i_max, k_max ) +! + USE DFT_MODULE, ONLY: NDFT, r_grid + IMPLICIT NONE +! +! ---------------------------------------------------------------------- + REAL, INTENT(IN) :: ya(r_grid,NDFT) + REAL, INTENT(IN) :: x1a(r_grid) + REAL, INTENT(IN) :: x2a(NDFT) + REAL, INTENT(OUT) :: y1a(r_grid,NDFT) + REAL, INTENT(OUT) :: y2a(r_grid,NDFT) + REAL, INTENT(OUT) :: y12a(r_grid,NDFT) + INTEGER, INTENT(IN) :: i_max + INTEGER, INTENT(IN) :: k_max +! +! ---------------------------------------------------------------------- + INTEGER :: i, k +! ---------------------------------------------------------------------- + + +DO i = 2, i_max-1 + DO k = 2, k_max-1 + y1a(i,k) = (ya(i+1,k)-ya(i-1,k)) / (x1a(i+1)-x1a(i-1)) + y2a(i,k) = (ya(i,k+1)-ya(i,k-1)) / (x2a(k+1)-x2a(k-1)) + y12a(i,k)= (ya(i+1,k+1)-ya(i+1,k-1)-ya(i-1,k+1)+ya(i-1,k-1)) & + /((x1a(i+1)-x1a(i-1))*(x2a(k+1)-x2a(k-1))) + END DO +END DO + +i = 1 +DO k = 1, k_max + y1a(i,k) = 0.0 + y2a(i,k) = 0.0 + y12a(i,k)= 0.0 +END DO + +k = 1 +DO i = 1, i_max + y1a(i,k) = 0.0 + y2a(i,k) = 0.0 + y12a(i,k)= 0.0 +END DO + + +i = i_max +DO k = 2, k_max-1 + y1a(i,k) = (ya(i,k)-ya(i-1,k)) / (x1a(i)-x1a(i-1)) + y2a(i,k) = (ya(i,k+1)-ya(i,k-1)) / (x2a(k+1)-x2a(k-1)) + y12a(i,k)= (ya(i,k+1)-ya(i,k-1)-ya(i-1,k+1)+ya(i-1,k-1)) & + /((x1a(i)-x1a(i-1))*(x2a(k+1)-x2a(k-1))) +END DO + + +k = k_max +DO i = 2, i_max-1 + y1a(i,k) = (ya(i+1,k)-ya(i-1,k)) / (x1a(i+1)-x1a(i-1)) + y2a(i,k) = (ya(i,k)-ya(i,k-1)) / (x2a(k)-x2a(k-1)) + y12a(i,k)= (ya(i+1,k)-ya(i+1,k-1)-ya(i-1,k)+ya(i-1,k-1)) & + /((x1a(i+1)-x1a(i-1))*(x2a(k)-x2a(k-1))) +END DO + +k = k_max +i = i_max +y1a(i,k) = (ya(i,k)-ya(i-1,k)) / (x1a(i)-x1a(i-1)) +y2a(i,k) = (ya(i,k)-ya(i,k-1)) / (x2a(k)-x2a(k-1)) +y12a(i,k)= (ya(i,k)-ya(i,k-1)-ya(i-1,k)+ya(i-1,k-1)) & + /((x1a(i)-x1a(i-1))*(x2a(k)-x2a(k-1))) + +END SUBROUTINE bicub_derivative + + +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! + SUBROUTINE bicub_c ( ya, x1a, x2a, y1a, y2a, y12a, c_bicub, i_max, k_max ) +! + USE DFT_MODULE, ONLY: NDFT, r_grid + IMPLICIT NONE +! +! ---------------------------------------------------------------------- + REAL, INTENT(IN) :: ya(r_grid,NDFT) + REAL, INTENT(IN) :: x1a(r_grid) + REAL, INTENT(IN) :: x2a(NDFT) + REAL, INTENT(IN) :: y1a(r_grid,NDFT) + REAL, INTENT(IN) :: y2a(r_grid,NDFT) + REAL, INTENT(IN) :: y12a(r_grid,NDFT) + REAL, INTENT(OUT) :: c_bicub(r_grid,NDFT,4,4) + INTEGER, INTENT(IN) :: i_max + INTEGER, INTENT(IN) :: k_max +! +! ---------------------------------------------------------------------- + INTEGER :: i, k, m, n + REAL :: y(4),y1(4),y2(4),y12(4),x1l,x1u,x2l,x2u + REAL :: c(4,4) +! ---------------------------------------------------------------------- + +DO i = 1, i_max-1 + DO k = 1, k_max-1 + y(1)=ya(i,k) + y(2)=ya(i+1,k) + y(3)=ya(i+1,k+1) + y(4)=ya(i,k+1) + + y1(1)=y1a(i,k) + y1(2)=y1a(i+1,k) + y1(3)=y1a(i+1,k+1) + y1(4)=y1a(i,k+1) + + y2(1)=y2a(i,k) + y2(2)=y2a(i+1,k) + y2(3)=y2a(i+1,k+1) + y2(4)=y2a(i,k+1) + + y12(1)=y12a(i,k) + y12(2)=y12a(i+1,k) + y12(3)=y12a(i+1,k+1) + y12(4)=y12a(i,k+1) + + x1l=x1a(i) + x1u=x1a(i+1) + x2l=x2a(k) + x2u=x2a(k+1) + + CALL bcucof(y,y1,y2,y12,x1u-x1l,x2u-x2l,c) + DO m=1,4 + DO n=1,4 + c_bicub(i,k,m,n)=c(m,n) + END DO + END DO + + END DO +END DO + +END SUBROUTINE bicub_c + +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! + SUBROUTINE bcucof(y,y1,y2,y12,d1,d2,c) +! + IMPLICIT NONE +! +! ---------------------------------------------------------------------- + REAL, INTENT(IN) :: y(4) + REAL, INTENT(IN) :: y1(4) + REAL, INTENT(IN) :: y2(4) + REAL, INTENT(IN) :: y12(4) + REAL, INTENT(IN) :: d1 + REAL, INTENT(IN) :: d2 + REAL, INTENT(OUT) :: c(4,4) +! +! ---------------------------------------------------------------------- + INTEGER :: i,j,k,l + REAL :: d1d2,xx,cl(16),wt(16,16),x(16) + SAVE wt + DATA wt/1,0,-3,2,4*0,-3,0,9,-6,2,0,-6,4,8*0,3,0,-9,6,-2,0,6,-4,10* & + 0,9,-6,2*0,-6,4,2*0,3,-2,6*0,-9,6,2*0,6,-4,4*0,1,0,-3,2,-2,0,6,-4, & + 1,0,-3,2,8*0,-1,0,3,-2,1,0,-3,2,10*0,-3,2,2*0,3,-2,6*0,3,-2,2*0, & + -6,4,2*0,3,-2,0,1,-2,1,5*0,-3,6,-3,0,2,-4,2,9*0,3,-6,3,0,-2,4,-2, & + 10*0,-3,3,2*0,2,-2,2*0,-1,1,6*0,3,-3,2*0,-2,2,5*0,1,-2,1,0,-2,4, & + -2,0,1,-2,1,9*0,-1,2,-1,0,1,-2,1,10*0,1,-1,2*0,-1,1,6*0,-1,1,2*0, & + 2,-2,2*0,-1,1/ +! ---------------------------------------------------------------------- + +d1d2 = d1 * d2 +DO i = 1, 4 + x(i) = y(i) + x(i+4) = y1(i)*d1 + x(i+8) = y2(i)*d2 + x(i+12) = y12(i)*d1d2 +END DO +DO i = 1, 16 + xx = 0.0 + DO k = 1, 16 + xx = xx + wt(i,k) * x(k) + END DO + cl(i) = xx +END DO +l = 0 +DO i = 1, 4 + DO j = 1, 4 + l = l + 1 + c(i,j) = cl(l) + END DO +END DO + +END SUBROUTINE bcucof + + +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! + SUBROUTINE BI_CUB_SPLINE ( rho_rdf, xg, ya, x1a, x2a, y1a, y2a, y12a, & + c_bicub, rdf, dg_drho, dg_dr, i_max, ih, k ) +! + USE DFT_MODULE, ONLY: NDFT, r_grid + IMPLICIT NONE +! +! ---------------------------------------------------------------------- + REAL, INTENT(IN OUT) :: rho_rdf + REAL, INTENT(IN OUT) :: xg + REAL, INTENT(IN) :: ya(r_grid,NDFT) + REAL, INTENT(IN) :: x1a(r_grid) + REAL, INTENT(IN) :: x2a(NDFT) + REAL, INTENT(IN) :: y1a(r_grid,NDFT) + REAL, INTENT(IN) :: y2a(r_grid,NDFT) + REAL, INTENT(IN) :: y12a(r_grid,NDFT) + REAL, INTENT(IN) :: c_bicub(r_grid,NDFT,4,4) + REAL, INTENT(OUT) :: rdf + REAL, INTENT(OUT) :: dg_drho + REAL, INTENT(OUT) :: dg_dr + INTEGER, INTENT(IN OUT) :: i_max + !INTEGER, INTENT(IN OUT) :: k_max + INTEGER, INTENT(OUT) :: ih + INTEGER, INTENT(IN) :: k +! +! ---------------------------------------------------------------------- + INTEGER :: m, n + + REAL :: y(4),y1(4),y2(4),y12(4),x1l,x1u,x2l,x2u + REAL :: c(4,4) +! ---------------------------------------------------------------------- + +IF ( rho_rdf < x1a(1) ) THEN + dg_drho = 0.0 + dg_dr = 0.0 + rdf = 1.0 + RETURN +END IF +IF ( x1a(ih) <= rho_rdf .AND. rho_rdf < x1a(ih+1) ) GO TO 10 +IF ( ih > 2 ) THEN + IF ( x1a(ih-1) <= rho_rdf .AND. rho_rdf < x1a(ih) ) THEN + ih = ih - 1 + GO TO 10 + END IF +END IF +! write (*,*) 'in ',ih +CALL hunt ( x1a, i_max, rho_rdf, ih ) +! write (*,*) 'out',ih +10 CONTINUE +IF ( x2a(k) /= xg ) THEN +! write (*,*) 'error bi-cubic-spline',k,x2a(k),xg +! DO k=1,NDFT +! write (*,*) k,x2a(k) +! ENDDO +! stop +END IF + + + +y(1) = ya(ih,k) +y(2) = ya(ih+1,k) +y(3) = ya(ih+1,k+1) +y(4) = ya(ih,k+1) + +y1(1) = y1a(ih,k) +y1(2) = y1a(ih+1,k) +y1(3) = y1a(ih+1,k+1) +y1(4) = y1a(ih,k+1) + +y2(1) = y2a(ih,k) +y2(2) = y2a(ih+1,k) +y2(3) = y2a(ih+1,k+1) +y2(4) = y2a(ih,k+1) + +y12(1) = y12a(ih,k) +y12(2) = y12a(ih+1,k) +y12(3) = y12a(ih+1,k+1) +y12(4) = y12a(ih,k+1) + +x1l = x1a(ih) +x1u = x1a(ih+1) +x2l = x2a(k) +x2u = x2a(k+1) + +DO m = 1, 4 + DO n = 1, 4 + c(m,n) = c_bicub( ih, k, m, n ) + END DO +END DO +CALL bcuint ( x1l, x1u, x2l, x2u, rho_rdf, xg, c, rdf, dg_drho, dg_dr ) + +END SUBROUTINE BI_CUB_SPLINE + +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! SUBROUTINE hunt +! +! Given an array xx(1:n), and given a value x, returns a value jlo +! such that x is between xx(jlo) and xx(jlo+1). xx(1:n) must be +! monotonic, either increasing or decreasing. jlo=0 or jlo=n is +! returned to indicate that x is out of range. jlo on input is taken +! as the initial guess for jlo on output. +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! + SUBROUTINE hunt ( xx, n, x, jlo ) +! + IMPLICIT NONE +! +! ---------------------------------------------------------------------- + INTEGER, INTENT(IN) :: n + INTEGER, INTENT(OUT) :: jlo + REAL, INTENT(IN) :: xx(n) + REAL :: x +! +! ---------------------------------------------------------------------- + INTEGER :: inc,jhi,jm + LOGICAL :: ascnd +! ---------------------------------------------------------------------- + +ascnd = xx(n) >= xx(1) +IF( jlo <= 0 .OR. jlo > n ) THEN + jlo = 0 + jhi = n + 1 + GO TO 3 +END IF +inc = 1 +IF( x >= xx(jlo) .EQV. ascnd ) THEN +1 jhi = jlo + inc + IF ( jhi > n ) THEN + jhi = n + 1 + ELSE IF ( x >= xx(jhi) .EQV. ascnd ) THEN + jlo = jhi + inc = inc + inc + GO TO 1 + END IF +ELSE + jhi = jlo +2 jlo = jhi - inc + IF ( jlo < 1 ) THEN + jlo = 0 + ELSE IF ( x < xx(jlo) .EQV. ascnd ) THEN + jhi = jlo + inc = inc + inc + GO TO 2 + END IF +END IF +3 IF (jhi-jlo == 1 ) THEN + IF ( x == xx(n)) jlo = n - 1 + IF ( x == xx(1) ) jlo = 1 + RETURN +END IF +jm = ( jhi + jlo ) / 2 +IF ( x >= xx(jm) .EQV. ascnd ) THEN + jlo = jm +ELSE + jhi = jm +END IF +GO TO 3 +END SUBROUTINE hunt + + + +!********************************************************************** +! +!********************************************************************** +! + !SUBROUTINE bcuint ( y, y1, y2, y12, x1l, x1u, x2l, x2u, x1, x2, c, ansy, ansy1, ansy2 ) + SUBROUTINE bcuint ( x1l, x1u, x2l, x2u, x1, x2, c, ansy, ansy1, ansy2 ) +! + IMPLICIT NONE +! +! ---------------------------------------------------------------------- + !REAL, INTENT(IN OUT) :: y(4) + !REAL, INTENT(IN OUT) :: y1(4) + !REAL, INTENT(IN OUT) :: y2(4) + !REAL, INTENT(IN OUT) :: y12(4) + REAL, INTENT(IN OUT) :: x1l + REAL, INTENT(IN OUT) :: x1u + REAL, INTENT(IN OUT) :: x2l + REAL, INTENT(IN OUT) :: x2u + REAL, INTENT(IN OUT) :: x1 + REAL, INTENT(IN OUT) :: x2 + REAL, INTENT(IN) :: c(4,4) + REAL, INTENT(OUT) :: ansy + REAL, INTENT(OUT) :: ansy1 + REAL, INTENT(OUT) :: ansy2 +! +! ---------------------------------------------------------------------- + !U USES bcucof + INTEGER :: i + REAL :: t, u +! ---------------------------------------------------------------------- + +! call bcucof ( y, y1, y2, y12, x1u-x1l, x2u-x2l, c ) + +IF ( x1u == x1l .OR. x2u == x2l ) PAUSE 'bad input in bcuint' +t = (x1-x1l) / (x1u-x1l) +u = (x2-x2l) / (x2u-x2l) +ansy = 0.0 +ansy2 = 0.0 +ansy1 = 0.0 +DO i = 4, 1, -1 + ansy = t *ansy + ( (c(i,4)*u + c(i,3))*u+c(i,2) )*u + c(i,1) + ansy2 = t *ansy2 + ( 3.*c(i,4)*u+2.*c(i,3) )*u + c(i,2) + ansy1 = u *ansy1 + ( 3.*c(4,i)*t+2.*c(3,i) )*t + c(2,i) +END DO +ansy1 = ansy1 / (x1u-x1l) +ansy2 = ansy2 / (x2u-x2l) + +END SUBROUTINE bcuint + + +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! SUBROUTINE spline +! +! Given arrays x(1:n) and y(1:n) containing a tabulated function, +! i.e., yi = f(xi), with x1 < x2 < .. . < xN, and given values yp1 and +! ypn for the first derivative of the interpolating function at points 1 +! and n, respectively, this routine returns an array y2(1:n) of length n +! which contains the second derivatives of the interpolating function at +! the tabulated points xi. If yp1 and/or ypn are equal to 1 1030 or +! larger, the routine is signaled to set the corresponding boundary +! condition for a natural spline, with zero second derivative on that +! boundary. +! Parameter: NMAX is the largest anticipated value of n. +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! + SUBROUTINE spline ( x, y, n, yp1, ypn, y2 ) +! + IMPLICIT NONE +! +! ---------------------------------------------------------------------- + INTEGER, INTENT(IN) :: n + REAL, INTENT(IN) :: x(n) + REAL, INTENT(IN) :: y(n) + REAL, INTENT(IN) :: yp1 + REAL, INTENT(IN) :: ypn + REAL, INTENT(OUT) :: y2(n) +! +! ---------------------------------------------------------------------- + INTEGER, PARAMETER :: NMAX = 1000 + INTEGER :: i, k + REAL :: p, qn, sig, un, u(NMAX) +! ---------------------------------------------------------------------- + +If(n > NMAX) stop 'Increase NMAX in Spline!!' + + + + IF ( yp1 > 0.99E30 ) THEN + y2(1) = 0.0 + u(1) = 0.0 + ELSE + y2(1) = -0.5 + u(1) = ( 3.0/(x(2)-x(1)) ) * ( (y(2)-y(1))/(x(2)-x(1))-yp1 ) + END IF + DO i = 2, n-1 + IF ( (x(i+1)-x(i)) == 0.0 .OR. (x(i)-x(i-1)) == 0.0 .OR. (x(i+1)-x(i-1)) == 0.0 ) THEN + write (*,*) 'error in spline-interpolation' + stop + END IF + sig = (x(i)-x(i-1)) / (x(i+1)-x(i-1)) + p = sig*y2(i-1) + 2.0 + y2(i) = (sig-1.0) / p + u(i) = ( 6.0 * ((y(i+1)-y(i))/(x(i+1)-x(i))-(y(i)-y(i-1))/(x(i)-x(i-1))) / (x(i+1)-x(i-1)) & + - sig * u(i-1) ) / p + END DO + IF ( ypn > 0.99E30 ) THEN + qn = 0.0 + un = 0.0 + ELSE + qn = 0.5 + un = (3.0/(x(n)-x(n-1))) * (ypn-(y(n)-y(n-1))/(x(n)-x(n-1))) + END IF + y2(n) = (un-qn*u(n-1)) / (qn*y2(n-1)+1.0) + DO k = n-1, 1, -1 + y2(k) = y2(k) * y2(k+1) + u(k) + END DO + +END SUBROUTINE spline + +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! SUBROUTINE splint_integral +! +! Given the arrays xa(1:n) and ya(1:n) of length n, which tabulate a +! function (with the in order), and given the array y2a(1:n), which is +! the output from spline above, and given a value of x, this routine +! returns a cubic-spline interpolated value y. +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! + SUBROUTINE splint_integral ( xa, ya, y2a, n, xlo, xhi, integral ) +! + IMPLICIT NONE +! +! ---------------------------------------------------------------------- + INTEGER, INTENT(IN) :: n + REAL, INTENT(IN) :: xa(n) + REAL, INTENT(IN) :: ya(n) + REAL, INTENT(IN) :: y2a(n) + REAL, INTENT(IN) :: xlo + REAL, INTENT(IN) :: xhi + REAL, INTENT(OUT) :: integral +! +! ---------------------------------------------------------------------- + INTEGER :: k, khi_l, klo_l, khi_h, klo_h + REAL :: xl, xh, h, INT, x0, x1, y0, y1, y20, y21 +! ---------------------------------------------------------------------- + + integral = 0.0 + klo_l = 1 + khi_l = n +1 IF ( khi_l-klo_l > 1 ) THEN + k = ( khi_l + klo_l ) / 2 + IF ( xa(k) > xlo ) THEN + khi_l = k + ELSE + klo_l = k + END IF + GO TO 1 + END IF + + klo_h = 1 + khi_h = n +2 IF ( khi_h-klo_h > 1 ) THEN + k = ( khi_h + klo_h ) / 2 + IF ( xa(k) > xhi ) THEN + khi_h = k + ELSE + klo_h = k + END IF + GO TO 2 + END IF + + ! integration in spline pieces, the lower interval, bracketed + ! by xa(klo_L) and xa(khi_L) is in steps shifted upward. + + ! first: determine upper integration bound + xl = xlo +3 CONTINUE + IF ( khi_h > khi_l ) THEN + xh = xa(khi_l) + ELSE IF ( khi_h == khi_l ) THEN + xh = xhi + ELSE + WRITE (*,*) 'error in spline-integration' + PAUSE + END IF + + h = xa(khi_l) - xa(klo_l) + IF ( h == 0.0 ) PAUSE 'bad xa input in splint' + x0 = xa(klo_l) + x1 = xa(khi_l) + y0 = ya(klo_l) + y1 = ya(khi_l) + y20= y2a(klo_l) + y21= y2a(khi_l) + ! int = -xL/h * ( (x1-.5*xL)*y0 + (0.5*xL-x0)*y1 & + ! +y20/6.*(x1**3-1.5*xL*x1*x1+xL*xL*x1-.25*xL**3) & + ! -y20/6.*h*h*(x1-.5*xL) & + ! +y21/6.*(.25*xL**3-xL*xL*x0+1.5*xL*x0*x0-x0**3) & + ! -y21/6.*h*h*(.5*xL-x0) ) + ! int = int + xH/h * ( (x1-.5*xH)*y0 + (0.5*xH-x0)*y1 & + ! +y20/6.*(x1**3-1.5*xH*x1*x1+xH*xH*x1-.25*xH**3) & + ! -y20/6.*h*h*(x1-.5*xH) & + ! +y21/6.*(.25*xH**3-xH*xH*x0+1.5*xH*x0*x0-x0**3) & + ! -y21/6.*h*h*(.5*xH-x0) ) + INT = -1.0/h * ( xl*((x1-.5*xl)*y0 + (0.5*xl-x0)*y1) & + -y20/24.*(x1-xl)**4 + y20/6.*(0.5*xl*xl-x1*xl)*h*h & + +y21/24.*(xl-x0)**4 - y21/6.*(0.5*xl*xl-x0*xl)*h*h ) + INT = INT + 1.0/h * ( xh*((x1-.5*xh)*y0 + (0.5*xh-x0)*y1) & + -y20/24.*(x1-xh)**4 + y20/6.*(0.5*xh*xh-x1*xh)*h*h & + +y21/24.*(xh-x0)**4 - y21/6.*(0.5*xh*xh-x0*xh)*h*h ) + + integral = integral + INT + ! write (*,*) integral,x1,xH + klo_l = klo_l + 1 + khi_l = khi_l + 1 + xl = x1 + IF (khi_h /= (khi_l-1)) GO TO 3 ! the -1 in (khi_L-1) because khi_L was already counted up + +END SUBROUTINE splint_integral + + + + +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! + REAL FUNCTION praxis( t0, machep, h0, n, prin, x, f, fmin ) + + IMPLICIT NONE + +! ---------------------------------------------------------------------- + REAL, INTENT(IN OUT) :: t0 + REAL, INTENT(IN) :: machep + REAL, INTENT(IN) :: h0 + INTEGER :: n + INTEGER, INTENT(IN OUT) :: prin + REAL, INTENT(IN OUT) :: x(n) + REAL :: f + REAL, INTENT(IN OUT) :: fmin +! ---------------------------------------------------------------------- + +EXTERNAL f + +! PRAXIS RETURNS THE MINIMUM OF THE FUNCTION F(X,N) OF N VARIABLES +! USING THE PRINCIPAL AXIS METHOD. THE GRADIENT OF THE FUNCTION IS +! NOT REQUIRED. + +! FOR A DESCRIPTION OF THE ALGORITHM, SEE CHAPTER SEVEN OF +! "ALGORITHMS FOR FINDING ZEROS AND EXTREMA OF FUNCTIONS WITHOUT +! CALCULATING DERIVATIVES" BY RICHARD P BRENT. + +! THE PARAMETERS ARE: +! T0 IS A TOLERANCE. PRAXIS ATTEMPTS TO RETURN PRAXIS=F(X) +! SUCH THAT IF X0 IS THE TRUE LOCAL MINIMUM NEAR X, THEN +! NORM(X-X0) < T0 + SQUAREROOT(MACHEP)*NORM(X). +! MACHEP IS THE MACHINE PRECISION, THE SMALLEST NUMBER SUCH THAT +! 1 + MACHEP > 1. MACHEP SHOULD BE 16.**-13 (ABOUT +! 2.22D-16) FOR REAL*8 ARITHMETIC ON THE IBM 360. +! H0 IS THE MAXIMUM STEP SIZE. H0 SHOULD BE SET TO ABOUT THE +! MAXIMUM DISTANCE FROM THE INITIAL GUESS TO THE MINIMUM. +! (IF H0 IS SET TOO LARGE OR TOO SMALL, THE INITIAL RATE OF +! CONVERGENCE MAY BE SLOW.) +! N (AT LEAST TWO) IS THE NUMBER OF VARIABLES UPON WHICH +! THE FUNCTION DEPENDS. +! PRIN CONTROLS THE PRINTING OF INTERMEDIATE RESULTS. +! IF PRIN=0, NOTHING IS PRINTED. +! IF PRIN=1, F IS PRINTED AFTER EVERY N+1 OR N+2 LINEAR +! MINIMIZATIONS. FINAL X IS PRINTED, BUT INTERMEDIATE X IS +! PRINTED ONLY IF N IS AT MOST 4. +! IF PRIN=2, THE SCALE FACTORS AND THE PRINCIPAL VALUES OF +! THE APPROXIMATING QUADRATIC FORM ARE ALSO PRINTED. +! IF PRIN=3, X IS ALSO PRINTED AFTER EVERY FEW LINEAR +! MINIMIZATIONS. +! IF PRIN=4, THE PRINCIPAL VECTORS OF THE APPROXIMATING +! QUADRATIC FORM ARE ALSO PRINTED. +! X IS AN ARRAY CONTAINING ON ENTRY A GUESS OF THE POINT OF +! MINIMUM, ON RETURN THE ESTIMATED POINT OF MINIMUM. +! F(X,N) IS THE FUNCTION TO BE MINIMIZED. F SHOULD BE A REAL*8 +! FUNCTION DECLARED EXTERNAL IN THE CALLING PROGRAM. +! FMIN IS AN ESTIMATE OF THE MINIMUM, USED ONLY IN PRINTING +! INTERMEDIATE RESULTS. +! THE APPROXIMATING QUADRATIC FORM IS +! Q(X') = F(X,N) + (1/2) * (X'-X)-TRANSPOSE * A * (X'-X) +! WHERE X IS THE BEST ESTIMATE OF THE MINIMUM AND A IS +! INVERSE(V-TRANSPOSE) * D * INVERSE(V) +! (V(*,*) IS THE MATRIX OF SEARCH DIRECTIONS; D(*) IS THE ARRAY +! OF SECOND DIFFERENCES). IF F HAS CONTINUOUS SECOND DERIVATIVES +! NEAR X0, A WILL TEND TO THE HESSIAN OF F AT X0 AS X APPROACHES X0. + +! IT IS ASSUMED THAT ON FLOATING-POINT UNDERFLOW THE RESULT IS SET +! TO ZERO. +! THE USER SHOULD OBSERVE THE COMMENT ON HEURISTIC NUMBERS AFTER +! THE INITIALIZATION OF MACHINE DEPENDENT NUMBERS. + + LOGICAL :: illc + INTEGER :: nl,nf,kl,kt,ktm,idim,i,j,k,k2,km1,klmk,ii,im1 + REAL :: s,sl,dn,dmin,fx,f1,lds,ldt,t,h,sf,df,qf1,qd0, qd1,qa,qb,qc + REAL :: m2,m4,small,vsmall,large,vlarge,scbd,ldfac,t2, dni,value + REAL :: random + +!.....IF N>20 OR IF N<20 AND YOU NEED MORE SPACE, CHANGE '20' TO THE +! LARGEST VALUE OF N IN THE NEXT CARD, IN THE CARD 'IDIM=20', AND +! IN THE DIMENSION STATEMENTS IN SUBROUTINES MINFIT,MIN,FLIN,QUAD. + + REAL :: d(20),y(20),z(20),q0(20),q1(20),v(20,20) + COMMON /global/ fx,ldt,dmin,nf,nl /q/ v,q0,q1,qa,qb,qc,qd0,qd1,qf1 + +! --------------------------------- +! introduced by Joachim........ + idim = n +! --------------------------------- + + + +!.....INITIALIZATION..... +! MACHINE DEPENDENT NUMBERS: + +small = machep*machep +vsmall = small*small +large = 1.d0/small +vlarge = 1.d0/vsmall +m2 = SQRT(machep) +m4 = SQRT(m2) + +! HEURISTIC NUMBERS: +! IF THE AXES MAY BE BADLY SCALED (WHICH IS TO BE AVOIDED IF +! POSSIBLE), THEN SET SCBD=10. OTHERWISE SET SCBD=1. +! IF THE PROBLEM IS KNOWN TO BE ILL-CONDITIONED, SET ILLC=TRUE. +! OTHERWISE SET ILLC=FALSE. +! KTM IS THE NUMBER OF ITERATIONS WITHOUT IMPROVEMENT BEFORE THE +! ALGORITHM TERMINATES. KTM=4 IS VERY CAUTIOUS; USUALLY KTM=1 +! IS SATISFACTORY. + +scbd = 1.0 +illc = .false. +ktm = 1 + +ldfac = 0.01 +IF (illc) ldfac = 0.1 +kt = 0 +nl = 0 +nf = 1 +fx = f(x,n) +qf1 = fx +t = small+ABS(t0) +t2 = t +dmin = small +h = h0 +IF (h < 100*t) h = 100*t +ldt = h +!.....THE FIRST SET OF SEARCH DIRECTIONS V IS THE IDENTITY MATRIX..... +DO i = 1,n + DO j = 1,n + v(i,j) = 0.0 + END DO + v(i,i) = 1.0 +END DO +d(1) = 0.0 +qd0 = 0.0 +DO i = 1,n + q0(i) = x(i) + q1(i) = x(i) +END DO +IF (prin > 0) CALL PRINT(n,x,prin,fmin) + +!.....THE MAIN LOOP STARTS HERE..... +40 sf=d(1) +d(1)=0.d0 +s=0.d0 + +!.....MINIMIZE ALONG THE FIRST DIRECTION V(*,1). +! FX MUST BE PASSED TO MIN BY VALUE. +value=fx +CALL MIN(n,1,2,d(1),s,value,.false.,f,x,t,machep,h) +IF (s > 0.d0) GO TO 50 +DO i=1,n + v(i,1)=-v(i,1) +END DO +50 IF (sf > 0.9D0*d(1).AND.0.9D0*sf < d(1)) GO TO 70 +DO i=2,n + d(i)=0.d0 +END DO + +!.....THE INNER LOOP STARTS HERE..... +70 DO k=2,n + DO i=1,n + y(i)=x(i) + END DO + sf=fx + IF (kt > 0) illc=.true. + 80 kl=k + df=0.d0 + +!.....A RANDOM STEP FOLLOWS (TO AVOID RESOLUTION VALLEYS). +! PRAXIS ASSUMES THAT RANDOM RETURNS A RANDOM NUMBER UNIFORMLY +! DISTRIBUTED IN (0,1). + + IF(.NOT.illc) GO TO 95 + DO i=1,n + s=(0.1D0*ldt+t2*(10**kt))*(random(n)-0.5D0) + z(i)=s + DO j=1,n + x(j)=x(j)+s*v(j,i) + END DO + END DO + fx=f(x,n) + nf=nf+1 + +!.....MINIMIZE ALONG THE "NON-CONJUGATE" DIRECTIONS V(*,K),...,V(*,N) + + 95 DO k2=k,n + sl=fx + s=0.d0 + value=fx + CALL MIN(n,k2,2,d(k2),s,value,.false.,f,x,t,machep,h) + IF (illc) GO TO 97 + s=sl-fx + GO TO 99 + 97 s=d(k2)*((s+z(k2))**2) + 99 IF (df > s) CYCLE + df=s + kl=k2 + END DO + IF (illc.OR.(df >= ABS((100*machep)*fx))) GO TO 110 + +!.....IF THERE WAS NOT MUCH IMPROVEMENT ON THE FIRST TRY, SET +! ILLC=TRUE AND START THE INNER LOOP AGAIN..... + + illc=.true. + GO TO 80 + 110 IF (k == 2.AND.prin > 1) CALL vcprnt(1,d,n) + +!.....MINIMIZE ALONG THE "CONJUGATE" DIRECTIONS V(*,1),...,V(*,K-1) + + km1=k-1 + DO k2=1,km1 + s=0 + value=fx + CALL MIN(n,k2,2,d(k2),s,value,.false.,f,x,t,machep,h) + END DO + f1=fx + fx=sf + lds=0 + DO i=1,n + sl=x(i) + x(i)=y(i) + sl=sl-y(i) + y(i)=sl + lds=lds+sl*sl + END DO + lds=SQRT(lds) + IF (lds <= small) GO TO 160 + +!.....DISCARD DIRECTION V(*,KL). +! IF NO RANDOM STEP WAS TAKEN, V(*,KL) IS THE "NON-CONJUGATE" +! DIRECTION ALONG WHICH THE GREATEST IMPROVEMENT WAS MADE..... + + klmk=kl-k + IF (klmk < 1) GO TO 141 + DO ii=1,klmk + i=kl-ii + DO j=1,n + v(j,i+1)=v(j,i) + END DO + d(i+1)=d(i) + END DO + 141 d(k)=0 + DO i=1,n + v(i,k)=y(i)/lds + END DO + +!.....MINIMIZE ALONG THE NEW "CONJUGATE" DIRECTION V(*,K), WHICH IS +! THE NORMALIZED VECTOR: (NEW X) - (0LD X)..... + + value=f1 + CALL MIN(n,k,4,d(k),lds,value,.true.,f,x,t,machep,h) + IF (lds > 0.d0) GO TO 160 + lds=-lds + DO i=1,n + v(i,k)=-v(i,k) + END DO + 160 ldt=ldfac*ldt + IF (ldt < lds) ldt=lds + IF (prin > 0) CALL PRINT(n,x,prin,fmin) + t2=0.d0 + DO i=1,n + t2=t2+x(i)**2 + END DO + t2=m2*SQRT(t2)+t + +!.....SEE WHETHER THE LENGTH OF THE STEP TAKEN SINCE STARTING THE +! INNER LOOP EXCEEDS HALF THE TOLERANCE..... + + IF (ldt > (0.5*t2)) kt=-1 + kt=kt+1 + IF (kt > ktm) GO TO 400 +END DO +!.....THE INNER LOOP ENDS HERE. + +! TRY QUADRATIC EXTRAPOLATION IN CASE WE ARE IN A CURVED VALLEY. + +CALL quad(n,f,x,t,machep,h) +dn=0.d0 +DO i=1,n + d(i)=1.d0/SQRT(d(i)) + IF (dn < d(i)) dn=d(i) +END DO +IF (prin > 3) CALL maprnt(1,v,idim,n) +DO j=1,n + s=d(j)/dn + DO i=1,n + v(i,j)=s*v(i,j) + END DO +END DO + +!.....SCALE THE AXES TO TRY TO REDUCE THE CONDITION NUMBER..... + +IF (scbd <= 1.d0) GO TO 200 +s=vlarge +DO i=1,n + sl=0.d0 + DO j=1,n + sl=sl+v(i,j)*v(i,j) + END DO + z(i)=SQRT(sl) + IF (z(i) < m4) z(i)=m4 + IF (s > z(i)) s=z(i) +END DO +DO i=1,n + sl=s/z(i) + z(i)=1.d0/sl + IF (z(i) <= scbd) GO TO 189 + sl=1.d0/scbd + z(i)=scbd + 189 DO j=1,n + v(i,j)=sl*v(i,j) + END DO +END DO + +!.....CALCULATE A NEW SET OF ORTHOGONAL DIRECTIONS BEFORE REPEATING +! THE MAIN LOOP. +! FIRST TRANSPOSE V FOR MINFIT: + +200 DO i=2,n + im1=i-1 + DO j=1,im1 + s=v(i,j) + v(i,j)=v(j,i) + v(j,i)=s + END DO +END DO + +!.....CALL MINFIT TO FIND THE SINGULAR VALUE DECOMPOSITION OF V. +! THIS GIVES THE PRINCIPAL VALUES AND PRINCIPAL DIRECTIONS OF THE +! APPROXIMATING QUADRATIC FORM WITHOUT SQUARING THE CONDITION +! NUMBER..... + +CALL minfit(idim,n,machep,vsmall,v,d) + +!.....UNSCALE THE AXES..... + +IF (scbd <= 1.d0) GO TO 250 +DO i=1,n + s=z(i) + DO j=1,n + v(i,j)=s*v(i,j) + END DO +END DO +DO i=1,n + s=0.d0 + DO j=1,n + s=s+v(j,i)**2 + END DO + s=SQRT(s) + d(i)=s*d(i) + s=1/s + DO j=1,n + v(j,i)=s*v(j,i) + END DO +END DO + +250 DO i=1,n + dni=dn*d(i) + IF (dni > large) GO TO 265 + IF (dni < small) GO TO 260 + d(i)=1/(dni*dni) + CYCLE + 260 d(i)=vlarge + CYCLE + 265 d(i)=vsmall +END DO + +!.....SORT THE EIGENVALUES AND EIGENVECTORS..... + +CALL sort(idim,n,d,v) +dmin=d(n) +IF (dmin < small) dmin=small +illc=.false. +IF (m2*d(1) > dmin) illc=.true. +IF (prin > 1.AND.scbd > 1.d0) CALL vcprnt(2,z,n) +IF (prin > 1) CALL vcprnt(3,d,n) +IF (prin > 3) CALL maprnt(2,v,idim,n) +!.....THE MAIN LOOP ENDS HERE..... + +GO TO 40 + +!.....RETURN..... + +400 IF (prin > 0) CALL vcprnt(4,x,n) +praxis=fx + +END FUNCTION praxis + + +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! + SUBROUTINE minfit(m,n,machep,tol,ab,q) + + IMPLICIT NONE + + INTEGER, INTENT(IN OUT) :: m + INTEGER, INTENT(IN) :: n + REAL, INTENT(IN) :: machep + REAL, INTENT(IN OUT) :: tol + REAL, INTENT(IN OUT) :: ab(m,n) + REAL, INTENT(OUT) :: q(n) + INTEGER :: i,j,k,l, kk,kt,l2,ll2,ii,lp1 +! IMPLICIT REAL (A-H,O-Z) + + +REAL :: x,eps,e(20),g,s, f,h,y,c,z,temp +!...AN IMPROVED VERSION OF MINFIT (SEE GOLUB AND REINSCH, 1969) +! RESTRICTED TO M=N,P=0. +! THE SINGULAR VALUES OF THE ARRAY AB ARE RETURNED IN Q AND AB IS +! OVERWRITTEN WITH THE ORTHOGONAL MATRIX V SUCH THAT U.DIAG(Q) = AB.V, +! WHERE U IS ANOTHER ORTHOGONAL MATRIX. + +!...HOUSEHOLDER'S REDUCTION TO BIDIAGONAL FORM... +IF (n == 1) GO TO 200 +eps = machep +g = 0.d0 +x = 0.d0 +DO i=1,n + e(i) = g + s = 0.d0 + l = i + 1 + DO j=i,n + s = s + ab(j,i)**2 + END DO + g = 0.d0 + IF (s < tol) GO TO 4 + f = ab(i,i) + g = SQRT(s) + IF (f >= 0.d0) g = -g + h = f*g - s + ab(i,i)=f-g + IF (l > n) GO TO 4 + DO j=l,n + f = 0.d0 + DO k=i,n + f = f + ab(k,i)*ab(k,j) + END DO + f = f/h + DO k=i,n + ab(k,j) = ab(k,j) + f*ab(k,i) + END DO + END DO + 4 q(i) = g + s = 0.d0 + IF (i == n) GO TO 6 + DO j=l,n + s = s + ab(i,j)*ab(i,j) + END DO + 6 g = 0.d0 + IF (s < tol) GO TO 10 + IF (i == n) GO TO 16 + f = ab(i,i+1) + 16 g = SQRT(s) + IF (f >= 0.d0) g = -g + h = f*g - s + IF (i == n) GO TO 10 + ab(i,i+1) = f - g + DO j=l,n + e(j) = ab(i,j)/h + END DO + DO j=l,n + s = 0.d0 + DO k=l,n + s = s + ab(j,k)*ab(i,k) + END DO + DO k=l,n + ab(j,k) = ab(j,k) + s*e(k) + END DO + END DO + 10 y = ABS(q(i)) + ABS(e(i)) + IF (y > x) x = y +END DO +!...ACCUMULATION OF RIGHT-HAND TRANSFORMATIONS... +ab(n,n) = 1.d0 +g = e(n) +l = n +DO ii=2,n + i = n - ii + 1 + IF (g == 0.d0) GO TO 23 + h = ab(i,i+1)*g + DO j=l,n + ab(j,i) = ab(i,j)/h + END DO + DO j=l,n + s = 0.d0 + DO k=l,n + s = s + ab(i,k)*ab(k,j) + END DO + DO k=l,n + ab(k,j) = ab(k,j) + s*ab(k,i) + END DO + END DO + 23 DO j=l,n + ab(i,j) = 0.d0 + ab(j,i) = 0.d0 + END DO + ab(i,i) = 1.d0 + g = e(i) + l = i +END DO +!...DIAGONALIZATION OF THE BIDIAGONAL FORM... +eps = eps*x +DO kk=1,n + k = n - kk + 1 + kt = 0 + 101 kt = kt + 1 + IF (kt <= 30) GO TO 102 + e(k) = 0.d0 + WRITE (6,1000) + 1000 FORMAT (' QR FAILED') + 102 DO ll2=1,k + l2 = k - ll2 + 1 + l = l2 + IF (ABS(e(l)) <= eps) GO TO 120 + IF (l == 1) CYCLE + IF (ABS(q(l-1)) <= eps) EXIT + END DO +!...CANCELLATION OF E(L) IF L>1... + c = 0.d0 + s = 1.d0 + DO i=l,k + f = s*e(i) + e(i) = c*e(i) + IF (ABS(f) <= eps) GO TO 120 + g = q(i) +!...Q(I) = H = SQRT(G*G + F*F)... + IF (ABS(f) < ABS(g)) GO TO 113 + IF (f == 0.0) THEN + GO TO 111 + ELSE + GO TO 112 + END IF + 111 h = 0.d0 + GO TO 114 + 112 h = ABS(f)*SQRT(1 + (g/f)**2) + GO TO 114 + 113 h = ABS(g)*SQRT(1 + (f/g)**2) + 114 q(i) = h + IF (h /= 0.d0) GO TO 115 + g = 1.d0 + h = 1.d0 + 115 c = g/h + s = -f/h + END DO +!...TEST FOR CONVERGENCE... + 120 z = q(k) + IF (l == k) GO TO 140 +!...SHIFT FROM BOTTOM 2*2 MINOR... + x = q(l) + y = q(k-1) + g = e(k-1) + h = e(k) + f = ((y - z)*(y + z) + (g - h)*(g + h))/(2*h*y) + g = SQRT(f*f + 1.0D0) + temp = f - g + IF (f >= 0.d0) temp = f + g + f = ((x - z)*(x + z) + h*(y/temp - h))/x +!...NEXT QR TRANSFORMATION... + c = 1.d0 + s = 1.d0 + lp1 = l + 1 + IF (lp1 > k) GO TO 133 + DO i=lp1,k + g = e(i) + y = q(i) + h = s*g + g = g*c + IF (ABS(f) < ABS(h)) GO TO 123 + IF (f == 0.0) THEN + GO TO 121 + ELSE + GO TO 122 + END IF + 121 z = 0.d0 + GO TO 124 + 122 z = ABS(f)*SQRT(1 + (h/f)**2) + GO TO 124 + 123 z = ABS(h)*SQRT(1 + (f/h)**2) + 124 e(i-1) = z + IF (z /= 0.d0) GO TO 125 + f = 1.d0 + z = 1.d0 + 125 c = f/z + s = h/z + f = x*c + g*s + g = -x*s + g*c + h = y*s + y = y*c + DO j=1,n + x = ab(j,i-1) + z = ab(j,i) + ab(j,i-1) = x*c + z*s + ab(j,i) = -x*s + z*c + END DO + IF (ABS(f) < ABS(h)) GO TO 129 + IF (f == 0.0) THEN + GO TO 127 + ELSE + GO TO 128 + END IF + 127 z = 0.d0 + GO TO 130 + 128 z = ABS(f)*SQRT(1 + (h/f)**2) + GO TO 130 + 129 z = ABS(h)*SQRT(1 + (f/h)**2) + 130 q(i-1) = z + IF (z /= 0.d0) GO TO 131 + f = 1.d0 + z = 1.d0 + 131 c = f/z + s = h/z + f = c*g + s*y + x = -s*g + c*y + END DO + 133 e(l) = 0.d0 + e(k) = f + q(k) = x + GO TO 101 +!...CONVERGENCE: Q(K) IS MADE NON-NEGATIVE... + 140 IF (z >= 0.d0) CYCLE + q(k) = -z + DO j=1,n + ab(j,k) = -ab(j,k) + END DO +END DO +RETURN +200 q(1) = ab(1,1) +ab(1,1) = 1.d0 + +END SUBROUTINE minfit + + + + +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! + SUBROUTINE MIN(n,j,nits,d2,x1,f1,fk,f,x,t,machep,h) + + IMPLICIT NONE + + INTEGER, INTENT(IN) :: n + INTEGER :: j + INTEGER :: nits + REAL, INTENT(IN OUT) :: d2 + REAL, INTENT(IN OUT) :: x1 + REAL, INTENT(IN OUT) :: f1 + LOGICAL :: fk + REAL :: f + REAL, INTENT(IN OUT) :: x(n) + REAL, INTENT(IN) :: t + REAL, INTENT(IN) :: machep + REAL, INTENT(IN) :: h + + INTEGER :: i,k + EXTERNAL f + + + REAL :: flin ! function + REAL :: small,sf1,sx1,s,temp, xm,x2,f2,d1 + REAL :: fm,f0,t2 +!---------------------------------------------- + INTEGER :: nf,nl + REAL :: fx,ldt,dmin + REAL :: v(20,20),q0(20),q1(20),qa,qb,qc,qd0,qd1,qf1 + COMMON /global/ fx,ldt,dmin,nf,nl /q/ v,q0,q1,qa,qb,qc,qd0,qd1,qf1 +!---------------------------------------------- +!...THE SUBROUTINE MIN MINIMIZES F FROM X IN THE DIRECTION V(*,J) UNLESS +! J IS LESS THAN 1, WHEN A QUADRATIC SEARCH IS MADE IN THE PLANE +! DEFINED BY Q0,Q1,X. +! D2 IS EITHER ZERO OR AN APPROXIMATION TO HALF F". +! ON ENTRY, X1 IS AN ESTIMATE OF THE DISTANCE FROM X TO THE MINIMUM +! ALONG V(*,J) (OR, IF J=0, A CURVE). ON RETURN, X1 IS THE DISTANCE +! FOUND. +! IF FK=.TRUE., THEN F1 IS FLIN(X1). OTHERWISE X1 AND F1 ARE IGNORED +! ON ENTRY UNLESS FINAL FX IS GREATER THAN F1. +! NITS CONTROLS THE NUMBER OF TIMES AN ATTEMPT WILL BE MADE TO HALVE +! THE INTERVAL. + LOGICAL :: dz + REAL :: m2,m4 + +small = machep**2 +m2 = SQRT(machep) +m4 = SQRT(m2) +sf1 = f1 +sx1 = x1 +k = 0 +xm = 0.d0 +fm = fx +f0 = fx +dz = d2 < machep +!...FIND THE STEP SIZE... +s = 0.d0 +DO i=1,n + s = s + x(i)**2 +END DO +s = SQRT(s) +temp = d2 +IF (dz) temp = dmin +t2 = m4*SQRT(ABS(fx)/temp + s*ldt) + m2*ldt +s = m4*s + t +IF (dz.AND.t2 > s) t2 = s +t2 = DMAX1(t2,small) +t2 = DMIN1(t2,.01D0*h) +IF (.NOT.fk.OR.f1 > fm) GO TO 2 +xm = x1 +fm = f1 +2 IF (fk.AND.ABS(x1) >= t2) GO TO 3 +temp=1.d0 +IF (x1 < 0.d0) temp=-1.d0 +x1=temp*t2 +f1 = flin(n,j,x1,f,x,nf) +3 IF (f1 > fm) GO TO 4 +xm = x1 +fm = f1 +4 IF (.NOT.dz) GO TO 6 +!...EVALUATE FLIN AT ANOTHER POINT AND ESTIMATE THE SECOND DERIVATIVE... +x2 = -x1 +IF (f0 >= f1) x2 = 2.d0*x1 +f2 = flin(n,j,x2,f,x,nf) +IF (f2 > fm) GO TO 5 +xm = x2 +fm = f2 +5 d2 = (x2*(f1 - f0)-x1*(f2 - f0))/((x1*x2)*(x1 - x2)) +!...ESTIMATE THE FIRST DERIVATIVE AT 0... +6 d1 = (f1 - f0)/x1 - x1*d2 +dz = .true. +!...PREDICT THE MINIMUM... +IF (d2 > small) GO TO 7 +x2 = h +IF (d1 >= 0.d0) x2 = -x2 +GO TO 8 +7 x2 = (-.5D0*d1)/d2 +8 IF (ABS(x2) <= h) GO TO 11 +IF (x2 > 0.0) THEN + GO TO 10 +END IF +x2 = -h +GO TO 11 +10 x2 = h +!...EVALUATE F AT THE PREDICTED MINIMUM... +11 f2 = flin(n,j,x2,f,x,nf) +IF (k >= nits.OR.f2 <= f0) GO TO 12 +!...NO SUCCESS, SO TRY AGAIN... +k = k + 1 +IF (f0 < f1.AND.(x1*x2) > 0.d0) GO TO 4 +x2 = 0.5D0*x2 +GO TO 11 +!...INCREMENT THE ONE-DIMENSIONAL SEARCH COUNTER... +12 nl = nl + 1 +IF (f2 <= fm) GO TO 13 +x2 = xm +GO TO 14 +13 fm = f2 +!...GET A NEW ESTIMATE OF THE SECOND DERIVATIVE... +14 IF (ABS(x2*(x2 - x1)) <= small) GO TO 15 +d2 = (x2*(f1-f0) - x1*(fm-f0))/((x1*x2)*(x1 - x2)) +GO TO 16 +15 IF (k > 0) d2 = 0.d0 +16 IF (d2 <= small) d2 = small +x1 = x2 +fx = fm +IF (sf1 >= fx) GO TO 17 +fx = sf1 +x1 = sx1 +!...UPDATE X FOR LINEAR BUT NOT PARABOLIC SEARCH... +17 IF (j == 0) RETURN +DO i=1,n + x(i) = x(i) + x1*v(i,j) +END DO + +END SUBROUTINE MIN + + +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! + SUBROUTINE vcprnt(option,v,n) + + IMPLICIT NONE + INTEGER :: option + REAL, INTENT(IN OUT) :: v(n) + INTEGER :: n + + INTEGER :: i + +SELECT CASE ( option ) + CASE ( 1) + GO TO 1 + CASE ( 2) + GO TO 2 + CASE ( 3) + GO TO 3 + CASE ( 4) + GO TO 4 +END SELECT + +1 WRITE (6,101) (v(i),i=1,n) +RETURN +2 WRITE (6,102) (v(i),i=1,n) +RETURN +3 WRITE (6,103) (v(i),i=1,n) +RETURN +4 WRITE (6,104) (v(i),i=1,n) +RETURN +101 FORMAT (/' THE SECOND DIFFERENCE ARRAY D(*) IS:'/ (e32.14,4E25.14)) +102 FORMAT (/' THE SCALE FACTORS ARE:'/(e32.14,4E25.14)) +103 FORMAT (/' THE APPROXIMATING QUADR. FORM HAS PRINCIPAL VALUES:'/ & + (e32.14,4E25.14)) +104 FORMAT (/' X IS:',e26.14/(e32.14)) +END SUBROUTINE vcprnt + + +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! + SUBROUTINE PRINT(n,x,prin,fmin) + + IMPLICIT NONE + INTEGER :: n + REAL, INTENT(IN OUT) :: x(n) + INTEGER, INTENT(IN OUT) :: prin + REAL, INTENT(IN OUT) :: fmin + + INTEGER :: i + REAL :: ln +!---------------------------------------------- +INTEGER :: nf,nl +REAL :: fx,ldt,dmin +COMMON /global/ fx,ldt,dmin,nf,nl +!---------------------------------------------- +WRITE (6,101) nl,nf,fx + +IF (fx <= fmin) GO TO 1 +ln = LOG10(fx-fmin) +WRITE (6,102) fmin,ln +GO TO 2 +1 WRITE (6,103) fmin +2 IF (n > 4.AND.prin <= 2) RETURN +WRITE (6,104) (x(i),i=1,n) +RETURN +101 FORMAT (/' AFTER',i6, & + ' LINEAR SEARCHES, THE FUNCTION HAS BEEN EVALUATED',i6, & + ' TIMES. THE SMALLEST VALUE FOUND IS F(X) = ',e21.14) +102 FORMAT (' LOG (F(X)-',e21.14,') = ',e21.14) +103 FORMAT (' LOG (F(X)-',e21.14,') IS UNDEFINED.') +104 FORMAT (' X IS:',e26.14/(e32.14)) +END SUBROUTINE PRINT + + +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! + SUBROUTINE maprnt(option,v,m,n) + + IMPLICIT NONE + INTEGER :: option + REAL, INTENT(IN OUT) :: v(m,n) + INTEGER, INTENT(IN OUT) :: m + INTEGER, INTENT(IN) :: n + INTEGER :: i,j + + INTEGER :: low,upp +!...THE SUBROUTINE MAPRNT PRINTS THE COLUMNS OF THE NXN MATRIX V +! WITH A HEADING AS SPECIFIED BY OPTION. +! M IS THE ROW DIMENSION OF V AS DECLARED IN THE CALLING PROGRAM... +low = 1 +upp = 5 +SELECT CASE ( option ) + CASE ( 1) + GO TO 1 + CASE ( 2) + GO TO 2 +END SELECT +1 WRITE (6,101) +101 FORMAT (/' THE NEW DIRECTIONS ARE:') +GO TO 3 +2 WRITE (6,102) +102 FORMAT (' AND THE PRINCIPAL AXES:') +3 IF (n < upp) upp = n +DO i=1,n + WRITE (6,104) (v(i,j),j=low,upp) +END DO +low = low + 5 +IF (n < low) RETURN +upp = upp + 5 +WRITE (6,103) +GO TO 3 +103 FORMAT (' ') +104 FORMAT (e32.14,4E25.14) +END SUBROUTINE maprnt + + +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! + REAL FUNCTION random(naught) + + IMPLICIT NONE + INTEGER, INTENT(IN OUT) :: naught + + REAL :: ran1,ran3(127),half + INTEGER :: i,j,ran2,q,r + LOGICAL :: init + DATA init/.false./ + SAVE init,ran2,ran1,ran3 + +IF (init) GO TO 3 +r = MOD(naught,8190) + 1 +ran2 = 128 +DO i=1,127 + ran2 = ran2 - 1 + ran1 = -2.d0**55 + DO j=1,7 + r = MOD(1756*r,8191) + q = r/32 + ran1 = (ran1 + q)*(1.0D0/256) + END DO + ran3(ran2) = ran1 +END DO +init = .true. +3 IF (ran2 == 1) ran2 = 128 +ran2 = ran2 - 1 +ran1 = ran1 + ran3(ran2) +half = .5D0 +IF (ran1 >= 0.d0) half = -half +ran1 = ran1 + half +ran3(ran2) = ran1 +random = ran1 + .5D0 + +END FUNCTION random + + + +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! + REAL FUNCTION flin (n,j,l,f,x,nf) + IMPLICIT NONE + + INTEGER, INTENT(IN) :: n + INTEGER, INTENT(IN OUT) :: j + REAL, INTENT(IN) :: l + REAL :: f + REAL, INTENT(IN) :: x(n) + INTEGER, INTENT(OUT) :: nf + + INTEGER :: i + REAL :: t(20) + + EXTERNAL f + +!...FLIN IS THE FUNCTION OF ONE REAL VARIABLE L THAT IS MINIMIZED +! BY THE SUBROUTINE MIN... +!---------------------------------------------- + REAL :: v(20,20),q0(20),q1(20),qa,qb,qc,qd0,qd1,qf1 + COMMON /q/ v,q0,q1,qa,qb,qc,qd0,qd1,qf1 +!---------------------------------------------- +IF (j == 0) GO TO 2 +!...THE SEARCH IS LINEAR... +DO i=1,n + t(i) = x(i) + l*v(i,j) +END DO +GO TO 4 +!...THE SEARCH IS ALONG A PARABOLIC SPACE CURVE... +2 qa = (l*(l - qd1))/(qd0*(qd0 + qd1)) +qb = ((l + qd0)*(qd1 - l))/(qd0*qd1) +qc = (l*(l + qd0))/(qd1*(qd0 + qd1)) +DO i=1,n + t(i) = (qa*q0(i) + qb*x(i)) + qc*q1(i) +END DO +!...THE FUNCTION EVALUATION COUNTER NF IS INCREMENTED... +4 nf = nf + 1 +flin = f(t,n) + +END FUNCTION flin + + +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! + SUBROUTINE sort(m,n,d,v) + IMPLICIT NONE +! + INTEGER, INTENT(IN OUT) :: m + INTEGER, INTENT(IN) :: n + REAL, INTENT(IN OUT) :: d(n) + REAL, INTENT(IN OUT) :: v(m,n) + + INTEGER :: i,j,k,nm1,ip1 + REAL :: s +!...SORTS THE ELEMENTS OF D(N) INTO DESCENDING ORDER AND MOVES THE +! CORRESPONDING COLUMNS OF V(N,N). +! M IS THE ROW DIMENSION OF V AS DECLARED IN THE CALLING PROGRAM. +IF (n == 1) RETURN +nm1 = n - 1 +DO i = 1,nm1 + k=i + s = d(i) + ip1 = i + 1 + DO j = ip1,n + IF (d(j) <= s) CYCLE + k = j + s = d(j) + END DO + IF (k <= i) CYCLE + d(k) = d(i) + d(i) = s + DO j = 1,n + s = v(j,i) + v(j,i) = v(j,k) + v(j,k) = s + END DO +END DO +END SUBROUTINE sort + + +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! + SUBROUTINE quad(n,f,x,t,machep,h) + IMPLICIT NONE + + INTEGER, INTENT(IN) :: n + REAL :: f + REAL, INTENT(IN OUT) :: x(n) + REAL, INTENT(IN OUT) :: t + REAL :: machep + REAL, INTENT(IN OUT) :: h +! IMPLICIT REAL (A-H,O-Z) + EXTERNAL f + +!...QUAD LOOKS FOR THE MINIMUM OF F ALONG A CURVE DEFINED BY Q0,Q1,X... + INTEGER :: i + REAL :: l + REAL :: s,value +!---------------------------------------------- + INTEGER :: nf,nl + REAL :: fx,ldt,dmin + +REAL :: v(20,20),q0(20),q1(20),qa,qb,qc,qd0,qd1,qf1 +COMMON /global/ fx,ldt,dmin,nf,nl /q/ v,q0,q1,qa,qb,qc,qd0,qd1,qf1 +!---------------------------------------------- +s = fx +fx = qf1 +qf1 = s +qd1 = 0.d0 +DO i=1,n + s = x(i) + l = q1(i) + x(i) = l + q1(i) = s + qd1 = qd1 + (s-l)**2 +END DO +qd1 = SQRT(qd1) +l = qd1 +s = 0.d0 +IF (qd0 <= 0.d0 .OR. qd1 <= 0.d0 .OR. nl < 3*n*n) GO TO 2 +value=qf1 +CALL MIN(n,0,2,s,l,value,.true.,f,x,t,machep,h) +qa = (l*(l-qd1))/(qd0*(qd0+qd1)) +qb = ((l+qd0)*(qd1-l))/(qd0*qd1) +qc = (l*(l+qd0))/(qd1*(qd0+qd1)) +GO TO 3 +2 fx = qf1 +qa = 0.d0 +qb = qa +qc = 1.d0 +3 qd0 = qd1 +DO i=1,n + s = q0(i) + q0(i) = x(i) + x(i) = (qa*s + qb*x(i)) + qc*q1(i) +END DO +END SUBROUTINE quad + diff --git 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-T = [] -RHO0 = [] -P0 = [] -P1 = [] - -indata=open('out.txt','r') -for aline in indata: - t,rho0,p0,p1,=aline.strip().split() - T.append(t) - RHO0.append(rho0) - P0.append(p0) - P1.append(p1) -indata.close() - -plt.plot(T,P0, label = 'p0') -plt.plot(T,P1, label = 'p1') -plt.xlabel('Time', fontsize=14, fontweight='bold') -plt.ylabel('Pressure', fontsize=14, fontweight='bold') -plt.legend(loc='upper left') -plt.legend() -plt.show() \ No newline at end of file diff --git a/Content/Figures/Plotsparam.py b/Content/Figures/Plotsparam.py deleted file mode 100644 index 2657e5a7f..000000000 --- a/Content/Figures/Plotsparam.py +++ /dev/null @@ -1,24 +0,0 @@ -import matplotlib.pyplot as plt - -P1 = [] -P2 = [] -LNR = [] -count = 1 -indata=open('output.txt','r') -for aline in indata: - LNR.append(count) - param1, param2 =aline.strip().split() - P1.append(param1) - P2.append(param2) - count = count + 1 -indata.close() - - -fig, ax1 = plt.subplots() -ax1.plot(LNR,P1, label = 'P1', color = 'b') 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-} bind def - -/GrayDirectClassPacket -{ - % - % Get a DirectClass packet; convert to grayscale. - % - % Parameters: - % red - % green - % blue - % length: number of pixels minus one of this color (optional). - % - currentfile color_packet readhexstring pop pop - color_packet 0 get 0.299 mul - color_packet 1 get 0.587 mul add - color_packet 2 get 0.114 mul add - cvi - /gray_packet exch def - compression 0 eq - { - /number_pixels 1 def - } - { - currentfile byte readhexstring pop 0 get - /number_pixels exch 1 add def - } ifelse - 0 1 number_pixels 1 sub - { - pixels exch gray_packet put - } for - pixels 0 number_pixels getinterval -} bind def - -/GrayPseudoClassPacket -{ - % - % Get a PseudoClass packet; convert to grayscale. - % - % Parameters: - % index: index into the colormap. - % length: number of pixels minus one of this color (optional). - % - currentfile byte readhexstring pop 0 get - /offset exch 3 mul def - /color_packet colormap offset 3 getinterval def - color_packet 0 get 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b/applications/PUfoam/MoDeNaModels/SurfaceTension/ExampleOfUsage/src/srcDetailedCode/SolverSetup.F90 new file mode 100644 index 000000000..2caad6f44 --- /dev/null +++ b/applications/PUfoam/MoDeNaModels/SurfaceTension/ExampleOfUsage/src/srcDetailedCode/SolverSetup.F90 @@ -0,0 +1,299 @@ + +Subroutine SolverSetup + +Use BASIC_VARIABLES, Only: ncomp + +!PETSc modules +Use PetscManagement +Use f90moduleinterfaces +Use Global_x !(snes,ngrid,ngp,x,r,timer) + +Implicit None + +#include +#include +#include +#include +#include +#include +#include +#include +#include +#include + + +DM :: da +PetscErrorCode :: ierr +type (userctx) :: user +Mat :: J +PetscReal :: erel +PetscBool :: flg +INTEGER :: jac_id +PetscInt :: JacLocal + +character(80) :: filename='' + +!external subroutines associated with Solver +external FormInitialGuess +external FormFunction +external Jac_Shell_AD +external Jac_Matrix_Empty +external MonitorTimer + + + call MPI_Comm_rank(PETSC_COMM_WORLD,user%rank,ierr) + call MPI_Comm_size(PETSC_COMM_WORLD,user%num_procs,ierr) + + +! Create solver context + call SNESCreate(PETSC_COMM_WORLD,snes,ierr) + +! Create distributed array (DMDA) to manage parallel grid and vectors + call DMDACreate1d(PETSC_COMM_WORLD, & !MPI communicator + & DMDA_BOUNDARY_GHOSTED, & !Boundary type at boundary of physical domain + & ngrid, & !global dimension of array (if negative number, then value can be changed by user via command line!) + & ncomp, & !number of degrees of freedom per grid point (number of unknowns at each grid point) + & ngp, & !number of ghost points accessible for local vectors + & PETSC_NULL_INTEGER, & !could be an array to specify the number of grid points per processor + & da, & !the resulting distributed array object + & ierr) + +! Extract global arrays from DMDA: x: unknowns, r: residual + call DMCreateGlobalVector(da,x,ierr) + call VecDuplicate(x,r,ierr) + +! Get local grid boundaries (for 1-dimensional DMDA) + call DMDAGetCorners(da, & !the distributed array + & user%xs, & !corner index in x direction + & PETSC_NULL_INTEGER, & !corner index in y direction + & PETSC_NULL_INTEGER, & !corner index in z direction + & user%xm, & !width of locally owned part in x direction + & PETSC_NULL_INTEGER, & !width of locally owned part in y direction + & PETSC_NULL_INTEGER, & !width of locally owned part in z direction + & ierr) !error check + + call DMDAGetGhostCorners(da, & !the distributed array + & user%gxs, & !corner index in x direction (but now counting includes ghost points) + & PETSC_NULL_INTEGER, & !corner index in y direction (but now counting includes ghost points) + & PETSC_NULL_INTEGER, & !corner index in z direction (but now counting includes ghost points) + & user%gxm, & !width of locally owned part in x direction (but now including ghost points) + & PETSC_NULL_INTEGER, & !width of locally owned part in y direction (but now including ghost points) + & PETSC_NULL_INTEGER, & !width of locally owned part in z direction (but now including ghost points) + & ierr) !error check + +! Here we shift the starting indices up by one so that we can easily +! use the Fortran convention of 1-based indices (rather 0-based indices). + user%xs = user%xs+1 + user%gxs = user%gxs+1 + user%xe = user%xs+user%xm-1 + user%gxe = user%gxs+user%gxm-1 + + call SNESSetFunction(snes,r,FormFunction,user,ierr) + call SNESSetApplicationContext(snes,user,ierr) + call SNESSetDM(snes,da,ierr) + +! !Set up matrix free jacobian +! erel = 1e-08 +! call MatCreateSNESMF(snes,J,ierr) !matrix free jacobi matrix +! call MatMFFDSetFunctionError(J,erel,ierr) +! call SNESSetJacobian(snes,J,J,MatMFFDComputeJacobian,PETSC_NULL_OBJECT,ierr) + + +! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - +! Set up nonlinear solver depending on option set in makefile (with -jac) +! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - + call PetscOptionsGetInt(PETSC_NULL_CHARACTER,'-jac',jac_id,flg,ierr) + If(flg) Then + + Else + jac_id = 0 + write(*,*)'Option -jac not set in makefile, using matrix-free with numerical approximations.' + End If + + Select Case(jac_id) + + Case(-1) !for options that dont need a jacobian: Anderson mixing, Picard + + Case (0) !matrix-free with numerical approximation of J(x)v + !default value of erel + erel = 1e-08 + !check if value for erel is specified in makefile + call PetscOptionsGetReal(PETSC_NULL_CHARACTER,'-erel',erel,flg,ierr) + If(user%rank == 0) write(*,*)'Using matrix-free Jacobian with numerical approximations. erel:',erel + call MatCreateSNESMF(snes,J,ierr) !matrix free jacobi matrix + call MatMFFDSetFunctionError(J,erel,ierr) + call SNESSetJacobian(snes,J,J,MatMFFDComputeJacobian,PETSC_NULL_OBJECT,ierr) + + Case (1) !matrix-free with AD-calculated J(x)v + If(user%rank == 0) write(*,*)'Using matrix-free AD Jacobian.' + !determine local size of shell matrix + JacLocal = INT(ngrid / user%num_procs) + If(mod(ngrid,user%num_procs) /= 0 ) Stop 'Dimensions and number of cores dont match! mod(ngrid,nc) must equal 0' + !Make sure that local parts of JacShell have the same size as the local DMDA-Arrays (local size JacShell != user%xm!!) + If(JacLocal /= user%xm) Stop 'Shell-Jacobi-Matrix and DMDA have to be parallelized accordingly!!(JacLocal = user%xm)' + call MatCreateShell(PETSC_COMM_WORLD,ncomp*JacLocal,ncomp*JacLocal,ncomp*ngrid,ncomp*ngrid,PETSC_NULL_OBJECT,J,ierr) + call MatShellSetOperation( J, MATOP_MULT, Jac_Shell_AD, ierr ) + call SNESSetJacobian( snes, J, J, Jac_Matrix_Empty, PETSC_NULL_OBJECT, ierr) + + Case (2) !build complete Jacobi matrix via finite-differences + If(user%rank == 0) write(*,*)'Using finite-difference Jacobian.' +!Now in makefile: -snes_fd +! call MatCreate(PETSC_COMM_WORLD,J,ierr) +! call MatSetSizes(J,PETSC_DECIDE,PETSC_DECIDE,ngrid,ngrid,ierr) +! call MatSetFromOptions(J,ierr) +! call MatSetUp(J,ierr) !!sets up the internal matrix data structure +! call SNESSetJacobian(snes,J,J,SNESComputeJacobianDefault,PETSC_NULL_OBJECT,ierr) + + + Case (3) !build the complete Jacobi matrix via AD + If(user%rank == 0) write(*,*)'Using AD-generated Jacobian.' + write(*,*)'Funktioniert noch nicht!' + stop + !create Matrix that has the appropriate sparsity pattern for the da + !But that also means that when values are inserted in positions that + !dont fit this structure, an error occurs! + !i.e. when calculating the jacobi matrix it is not possible anymore + !to ignore the sparsity pattern and just create a dense jacobian!! + + !call DMCreateMatrix(da,MATMPIAIJ,J,ierr) !CAUTION: in newer PETSc Versions DMCreateMatrix does not contain the MatType argument anymore! + !call SNESSetJacobian(snes,J,J,Jac_AD,PETSC_NULL_OBJECT,ierr) + + Case default + write(*,*) 'No valid option set for -jac in makefile, using full Jacobi via finite-differences.' + call SNESSetJacobian(snes,J,J,SNESComputeJacobianDefault,PETSC_NULL_OBJECT,ierr) + + End Select + +!Set monitoring function that ouputs the surface tension at every iteration + call SNESMonitorSet(snes,MonitorTimer,PETSC_NULL_OBJECT,PETSC_NULL_FUNCTION,ierr) + +!Enable modification from makefile + call SNESSetFromOptions(snes,ierr) + +!Evaluate Initial Guess + call FormInitialGuess(snes,x,ierr) + write(filename,*)'0_initial_profile_global.xlo' + call PrintGlobalVec(x,filename) + + !start timer + total_time = 0.0 + timer_old = MPI_WTIME() + +!Solve system + call SNESSolve(snes,PETSC_NULL_OBJECT,x,ierr) + write(filename,*)'1_final_profile_global.xlo' + call PrintGlobalVec(x,filename) + write(filename,'(a,I3.3,a)') '2_final_profile_local_proc_',user%rank,'.xlo' + call PrintLocalVec(x,da,filename) + + !plot residual vs time graph + !call system('gnuplot gnuplot_script.srp') + + +End Subroutine SolverSetup + + + + + + + +subroutine MonitorTimer(snes,its,norm,dummy,ierr) + + Use Global_x, Only: timer,timer_old,total_time,r + Use mod_DFT, Only: free + Use PARAMETERS, Only: KBOL,PI + Use BASIC_VARIABLES, Only: t,parame, ncomp + Use VLE_VAR, Only: rhob,tc + +! ! !PETSc modules +! ! use f90module +! ! !DFT modules +! ! use DFT_MODULE, ONLY: free +! ! use VLE_VAR, ONLY: tc,rhob +! ! use BASIC_VARIABLES, ONLY:t,parame,ncomp +! ! use PARAMETERS, ONLY: PI,KBOL + + implicit none + +#include +#include + +! Input/output variables: + SNES snes + PetscInt dummy + Integer :: its + REAL :: norm + PetscErrorCode ierr +! local + PetscReal :: f2norm + Vec :: current_solution + DOUBLE PRECISION :: delta_time + INTEGER :: rank + REAL :: m_average,surftens,st_macro + character(80) :: filename='' + + + + !calculate interfacial tension + !sum up the variable free from all procs on proc 0 + call MPI_Reduce(free,free,1,MPI_DOUBLE_PRECISION,MPI_SUM,0,PETSC_COMM_WORLD,ierr) + + !Only proc 0 calculates surface tension + call MPI_Comm_rank(PETSC_COMM_WORLD,rank,ierr) + IF(rank == 0) THEN + + !calculate surface tension + surftens = KBOL * t *1.E20*1000.0 *free + m_average = SUM( rhob(1,1:ncomp)*parame(1:ncomp,1) ) / rhob(1,0) + + st_macro = surftens / ( 1.0 + 3.0/8.0/PI *t/tc & + * (1.0/2.55)**2 / (0.0674*m_average+0.0045) ) + write(*,*)'ST',st_macro + + !write result to outputfile + filename='./out.txt' + CALL file_open(filename,99) + WRITE (99,*) st_macro + close(99) + + End If + + + + + + !calculate elapsed time + timer = MPI_WTIME() + delta_time = timer - timer_old + timer_old = timer + total_time = total_time + delta_time + + !get norm of residual array + call VecNorm(r,2,f2norm,ierr) + + IF(rank == 0) THEN + !print results to file + filename = 'ItsTimeNorm.dat' + open(unit = 44, file = filename) + write(44,*) its,total_time,f2norm + End If + +end subroutine MonitorTimer + + + + + + + + + + + + + + + + + diff --git a/applications/PUfoam/MoDeNaModels/SurfaceTension/ExampleOfUsage/src/srcDetailedCode/Spline_Integration_d.F90 b/applications/PUfoam/MoDeNaModels/SurfaceTension/ExampleOfUsage/src/srcDetailedCode/Spline_Integration_d.F90 new file mode 100644 index 000000000..dc143ece7 --- /dev/null +++ b/applications/PUfoam/MoDeNaModels/SurfaceTension/ExampleOfUsage/src/srcDetailedCode/Spline_Integration_d.F90 @@ -0,0 +1,217 @@ + +! Generated by TAPENADE (INRIA, Tropics team) +! Tapenade 3.10 (r5498) - 20 Jan 2015 09:48 +! +! Differentiation of spline in forward (tangent) mode: +! variations of useful results: y2 +! with respect to varying inputs: y2 y +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! SUBROUTINE spline +! +! Given arrays x(1:n) and y(1:n) containing a tabulated function, +! i.e., yi = f(xi), with x1 < x2 < .. . < xN, and given values yp1 and +! ypn for the first derivative of the interpolating function at points 1 +! and n, respectively, this routine returns an array y2(1:n) of length n +! which contains the second derivatives of the interpolating function at +! the tabulated points xi. If yp1 and/or ypn are equal to 1 1030 or +! larger, the routine is signaled to set the corresponding boundary +! condition for a natural spline, with zero second derivative on that +! boundary. +! Parameter: NMAX is the largest anticipated value of n. +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! +SUBROUTINE SPLINE_D(x, y, yd, n, yp1, ypn, y2, y2d) + IMPLICIT NONE +! +! ---------------------------------------------------------------------- + INTEGER, INTENT(IN) :: n + REAL, INTENT(IN) :: x(n) + REAL, INTENT(IN) :: y(n) + REAL, INTENT(IN) :: yd(n) + REAL, INTENT(IN) :: yp1 + REAL, INTENT(IN) :: ypn + REAL, INTENT(OUT) :: y2(n) + REAL, INTENT(OUT) :: y2d(n) +! +! ---------------------------------------------------------------------- + INTEGER, PARAMETER :: nmax=1000 + INTEGER :: i, k + REAL :: p, qn, sig, un, u(nmax) + REAL :: pd, und, ud(nmax) +! ---------------------------------------------------------------------- + IF (yp1 .GT. 0.99e30) THEN + y2d(1) = 0.0 + y2(1) = 0.0 + u(1) = 0.0 + ud = 0.0 + ELSE + y2d(1) = 0.0 + y2(1) = -0.5 + ud = 0.0 + ud(1) = 3.0*(yd(2)-yd(1))/(x(2)-x(1))**2 + u(1) = 3.0/(x(2)-x(1))*((y(2)-y(1))/(x(2)-x(1))-yp1) + END IF + DO i=2,n-1 + IF ((x(i+1) - x(i) .EQ. 0.0 .OR. x(i) - x(i-1) .EQ. 0.0) .OR. x(i+1)& +& - x(i-1) .EQ. 0.0) THEN + GOTO 100 + ELSE + sig = (x(i)-x(i-1))/(x(i+1)-x(i-1)) + pd = sig*y2d(i-1) + p = sig*y2(i-1) + 2.0 + y2d(i) = -((sig-1.0)*pd/p**2) + y2(i) = (sig-1.0)/p + ud(i) = ((6.0*((yd(i+1)-yd(i))/(x(i+1)-x(i))-(yd(i)-yd(i-1))/(x(i)& +& -x(i-1)))/(x(i+1)-x(i-1))-sig*ud(i-1))*p-(6.0*((y(i+1)-y(i))/(x(& +& i+1)-x(i))-(y(i)-y(i-1))/(x(i)-x(i-1)))/(x(i+1)-x(i-1))-sig*u(i-& +& 1))*pd)/p**2 + u(i) = (6.0*((y(i+1)-y(i))/(x(i+1)-x(i))-(y(i)-y(i-1))/(x(i)-x(i-1& +& )))/(x(i+1)-x(i-1))-sig*u(i-1))/p + END IF + END DO + IF (ypn .GT. 0.99e30) THEN + qn = 0.0 + un = 0.0 + und = 0.0 + ELSE + qn = 0.5 + und = -(3.0*(yd(n)-yd(n-1))/(x(n)-x(n-1))**2) + un = 3.0/(x(n)-x(n-1))*(ypn-(y(n)-y(n-1))/(x(n)-x(n-1))) + END IF + y2d(n) = ((und-qn*ud(n-1))*(qn*y2(n-1)+1.0)-(un-qn*u(n-1))*qn*y2d(n-1)& +& )/(qn*y2(n-1)+1.0)**2 + y2(n) = (un-qn*u(n-1))/(qn*y2(n-1)+1.0) + DO k=n-1,1,-1 + y2d(k) = y2d(k)*y2(k+1) + y2(k)*y2d(k+1) + ud(k) + y2(k) = y2(k)*y2(k+1) + u(k) + END DO + GOTO 110 + 100 WRITE(*, *) 'i x', i, x(i+1), x(i), x(i-1) + WRITE(*, *) 'error in spline-interpolation' + STOP + 110 CONTINUE +END SUBROUTINE SPLINE_D + + + + + + +! Generated by TAPENADE (INRIA, Tropics team) +! Tapenade 3.10 (r5498) - 20 Jan 2015 09:48 +! +! Differentiation of splint_integral in forward (tangent) mode: +! variations of useful results: integral +! with respect to varying inputs: y2a ya +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! SUBROUTINE splint_integral +! +! Given the arrays xa(1:n) and ya(1:n) of length n, which tabulate a +! function (with the in order), and given the array y2a(1:n), which is +! the output from spline above, and given a value of x, this routine +! returns a cubic-spline interpolated value y. +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! +SUBROUTINE SPLINT_INTEGRAL_D(xa, ya, yad, y2a, y2ad, n, xlo, xhi, & +& integral, integrald) + IMPLICIT NONE +! the -1 in (khi_L-1) because khi_L was already counted up +! +! ---------------------------------------------------------------------- + INTEGER, INTENT(IN) :: n + REAL, INTENT(IN) :: xa(n) + REAL, INTENT(IN) :: ya(n) + REAL, INTENT(IN) :: yad(n) + REAL, INTENT(IN) :: y2a(n) + REAL, INTENT(IN) :: y2ad(n) + REAL, INTENT(IN) :: xlo + REAL, INTENT(IN) :: xhi + REAL, INTENT(OUT) :: integral + REAL, INTENT(OUT) :: integrald +! +! ---------------------------------------------------------------------- + INTEGER :: k, khi_l, klo_l, khi_h, klo_h + REAL :: xl, xh, h, int, x0, x1, y0, y1, y20, y21 + REAL :: intd, y0d, y1d, y20d, y21d +! ---------------------------------------------------------------------- + integral = 0.0 + klo_l = 1 + khi_l = n + 1 IF (khi_l - klo_l .GT. 1) THEN + k = (khi_l+klo_l)/2 + IF (xa(k) .GT. xlo) THEN + khi_l = k + ELSE + klo_l = k + END IF + GOTO 1 + END IF + klo_h = 1 + khi_h = n + 2 IF (khi_h - klo_h .GT. 1) THEN + k = (khi_h+klo_h)/2 + IF (xa(k) .GT. xhi) THEN + khi_h = k + ELSE + klo_h = k + END IF + GOTO 2 + END IF +! integration in spline pieces, the lower interval, bracketed +! by xa(klo_L) and xa(khi_L) is in steps shifted upward. +! first: determine upper integration bound + xl = xlo + integrald = 0.0 + 3 IF (khi_h .GT. khi_l) THEN + xh = xa(khi_l) + ELSE IF (khi_h .EQ. khi_l) THEN + xh = xhi + ELSE + WRITE(*, *) 'error in spline-integration' + PAUSE + END IF + h = xa(khi_l) - xa(klo_l) + IF (h .EQ. 0.0) PAUSE'bad xa input in splint' + x0 = xa(klo_l) + x1 = xa(khi_l) + y0d = yad(klo_l) + y0 = ya(klo_l) + y1d = yad(khi_l) + y1 = ya(khi_l) + y20d = y2ad(klo_l) + y20 = y2a(klo_l) + y21d = y2ad(khi_l) + y21 = y2a(khi_l) +! int = -xL/h * ( (x1-.5*xL)*y0 + (0.5*xL-x0)*y1 & +! +y20/6.*(x1**3-1.5*xL*x1*x1+xL*xL*x1-.25*xL**3) & +! -y20/6.*h*h*(x1-.5*xL) & +! +y21/6.*(.25*xL**3-xL*xL*x0+1.5*xL*x0*x0-x0**3) & +! -y21/6.*h*h*(.5*xL-x0) ) +! int = int + xH/h * ( (x1-.5*xH)*y0 + (0.5*xH-x0)*y1 & +! +y20/6.*(x1**3-1.5*xH*x1*x1+xH*xH*x1-.25*xH**3) & +! -y20/6.*h*h*(x1-.5*xH) & +! +y21/6.*(.25*xH**3-xH*xH*x0+1.5*xH*x0*x0-x0**3) & +! -y21/6.*h*h*(.5*xH-x0) ) + intd = -((xl*((x1-.5*xl)*y0d+(0.5*xl-x0)*y1d)-(x1-xl)**4*y20d/24.+(0.5& +& *xl*xl-x1*xl)*h**2*y20d/6.+(xl-x0)**4*y21d/24.-(0.5*xl*xl-x0*xl)*h**& +& 2*y21d/6.)/h) + int = -(1.0/h*(xl*((x1-.5*xl)*y0+(0.5*xl-x0)*y1)-y20/24.*(x1-xl)**4+& +& y20/6.*(0.5*xl*xl-x1*xl)*h*h+y21/24.*(xl-x0)**4-y21/6.*(0.5*xl*xl-x0& +& *xl)*h*h)) + intd = intd + (xh*((x1-.5*xh)*y0d+(0.5*xh-x0)*y1d)-(x1-xh)**4*y20d/24.& +& +(0.5*xh*xh-x1*xh)*h**2*y20d/6.+(xh-x0)**4*y21d/24.-(0.5*xh*xh-x0*xh& +& )*h**2*y21d/6.)/h + int = int + 1.0/h*(xh*((x1-.5*xh)*y0+(0.5*xh-x0)*y1)-y20/24.*(x1-xh)**& +& 4+y20/6.*(0.5*xh*xh-x1*xh)*h*h+y21/24.*(xh-x0)**4-y21/6.*(0.5*xh*xh-& +& x0*xh)*h*h) + integrald = integrald + intd + integral = integral + int +! write (*,*) integral,x1,xH + klo_l = klo_l + 1 + khi_l = khi_l + 1 + xl = x1 + IF (khi_h .NE. khi_l - 1) GOTO 3 +END SUBROUTINE SPLINT_INTEGRAL_D + + + diff --git a/applications/PUfoam/MoDeNaModels/SurfaceTension/ExampleOfUsage/src/srcDetailedCode/VLE_main.F90 b/applications/PUfoam/MoDeNaModels/SurfaceTension/ExampleOfUsage/src/srcDetailedCode/VLE_main.F90 new file mode 100644 index 000000000..3b0217a66 --- /dev/null +++ b/applications/PUfoam/MoDeNaModels/SurfaceTension/ExampleOfUsage/src/srcDetailedCode/VLE_main.F90 @@ -0,0 +1,90 @@ +SUBROUTINE VLE_MIX(rhob,density,chemPot_total,user) + + +!Petsc modules + USE PetscManagement + + +!VLE modules + USE parameters, ONLY: PI, RGAS, KBOL, muhs,muhc,mudisp + USE basic_variables + USE EOS_VARIABLES, ONLY: fres, eta, eta_start, dhs, mseg, uij, sig_ij, rho, x, z3t + USE DFT_MODULE + USE EOS_NUMERICAL_DERIVATIVES + USE DFT_FCN_MODULE, ONLY: chemPot_res + IMPLICIT NONE + +! --------------------------------------------------------------------- +! Variables +! --------------------------------------------------------------------- + +!passed + type (userctx) user + REAL :: chemPot_total(nc) + REAL :: rhob(2,0:nc),density(np) + +!local + REAL, DIMENSION(nc) :: dhs_star + REAL :: w(np,nc), lnphi(np,nc) + INTEGER :: converg + + ! --------------------------------------------------------------------- + ! prepare for phase equilibrium calculation for given T + ! --------------------------------------------------------------------- + + dhs(1:ncomp) = parame(1:ncomp,2) * ( 1.0 - 0.12*EXP( -3.0*parame(1:ncomp,3)/t ) ) ! needed for rdf_matrix + dhs_star(1:ncomp) = dhs(1:ncomp)/parame(1:ncomp,2) + + nphas = 2 + outp = 0 ! output to terminal + + CALL START_VAR (converg,user) ! gets starting values, sets "val_init" + + IF ( converg /= 1 ) THEN + IF(user%rank == 0) THEN + WRITE (*,*) 'no VLE found' + END IF + RETURN + END IF + +! rhob(phase,0): molecular density + rhob(1,0) = dense(1) / ( PI/6.0* SUM( xi(1,1:ncomp) * parame(1:ncomp,1) * dhs(1:ncomp)**3 ) ) + rhob(2,0) = dense(2) / ( PI/6.0* SUM( xi(2,1:ncomp) * parame(1:ncomp,1) * dhs(1:ncomp)**3 ) ) + ! rhob(phase,i): molecular component density (with i=(1,...ncomp) ) in units (1/A^3) + rhob(1,1:ncomp) = rhob(1,0)*xi(1,1:ncomp) + rhob(2,1:ncomp) = rhob(2,0)*xi(2,1:ncomp) + +! --- get density in SI-units (kg/m**3) ------------------------------- + CALL SI_DENS ( density, w ) + +!--- calculate residual chemical potentials + ensemble_flag = 'tv' ! this flag is for: mu_res=mu_res(T,rho) + densta(1) = dense(1) ! Index 1 is for liquid density (here: packing fraction eta) + densta(2) = dense(2) ! Index 2 is for vapour density (here: packing fraction eta) + CALL fugacity (lnphi) + chemPot_res(1:ncomp) = lnphi(1,1:ncomp) + chemPot_total(1:ncomp) = lnphi(1,1:ncomp) + LOG( rhob(1,1:ncomp) ) ! my0 = mu_res(T,rho_bulk_L) + ln(rho_bulk_l) + + +! --------------------------------------------------------------------- +! Output results of phase equilibrim calculation +! --------------------------------------------------------------------- + + +IF(user%rank == 0) THEN + WRITE(*,*) '--------------------------------------------------' + WRITE(*,*)'RESULT OF PHASE EQUILIBRIUM CALCULATION' + WRITE (*,*) ' ' + WRITE (*,*) 'temperature ',t, 'K, and p=', p/1.E5,' bar' + WRITE (*,*) 'x1_liquid ',xi(1,1),' x1_vapor', xi(2,1) + WRITE (*,*) 'densities ',rhob(1,0), rhob(2,0) + WRITE (*,*) 'dense ',dense(1), dense(2) + WRITE (*,*) 'density [kg/m3] ',density(1), density(2) + write (*,*) 'chemical potentials comp1' , lnphi(1,1) + LOG( rhob(1,1) ), lnphi(2,1) + lnx(2,1) + LOG(rhob(2,0)) !LOG( rhob(2,1) ) + write (*,*) 'chemical potentials comp2' ,lnphi(1,2) + LOG( rhob(1,2) ), lnphi(2,2) + LOG( rhob(2,2) ) +END IF + + + + +END SUBROUTINE VLE_MIX diff --git a/applications/PUfoam/MoDeNaModels/SurfaceTension/ExampleOfUsage/src/srcDetailedCode/VLE_subroutines.F90 b/applications/PUfoam/MoDeNaModels/SurfaceTension/ExampleOfUsage/src/srcDetailedCode/VLE_subroutines.F90 new file mode 100644 index 000000000..66391e045 --- /dev/null +++ b/applications/PUfoam/MoDeNaModels/SurfaceTension/ExampleOfUsage/src/srcDetailedCode/VLE_subroutines.F90 @@ -0,0 +1,7607 @@ +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! SUBROUTINE start_var +! +! This subroutine generates a converged solution for binary systems +! or performes a flash calculation for mixtues. This routine is a +! fairly weak point of the program. +! +! IF a polymer is considered, starting values for mole fractions +! are determined from the SUBROUTINGE POLY_STA_VAR (see below). The +! polymer needs to be placed as component 1 (first line) in INPUT +! file. +! +! A phase equilib. iteration is started at the end of this routine. +! If no solution is found (converg=0), the program will stop within +! this routine. +! +! Currently, this routine assumes two-phase equilibrium and derives +! starting values (xi,density) only for two phases. +! +! Prerequisites are: +! SUBROUTINE INPUT needs to be called prior to this routine, because +! all pure comp. parameters as well as (T,P,kij) need to be in place. +! Also, the variable to be iterated "it(i)" and the variables to be +! calculated through the summation relation "sum_rel(i)" have to be +! defined. +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! + SUBROUTINE start_var(converg,user) + +!Petsc modules + USE PetscManagement + +!VLE modules + USE BASIC_VARIABLES + USE STARTING_VALUES + IMPLICIT NONE +! +! ---------------------------------------------------------------------- +type (userctx) user + INTEGER, INTENT(IN OUT) :: converg +! +! ---------------------------------------------------------------------- + INTEGER :: ph, i, k + INTEGER :: ncompsav, n_unkwsav, ph_split + LOGICAL :: lle_check, flashcase, renormalize + REAL :: den1, den2, x_1, x_2 + CHARACTER (LEN=50) :: filename +! ---------------------------------------------------------------------- + +converg = 0 + +! CALL RACHFORD_RICE (converg) +! CALL Heidemann_Khalil + +! ---------------------------------------------------------------------- +! This first condition (eos >= 4) is for LJ models, not for PC-SAFT +! ---------------------------------------------------------------------- + +IF (eos >= 4) THEN + + ncomp = 2 ! set number of components to 2 + n_unkw = ncomp ! number of quantities to be iterated + it(1) = 'x11' ! iteration of mol fraction of comp.1 phase 1 + it(2) = 'x21' ! iteration of mol fraction of comp.1 phase 2 + sum_rel(1) = 'x12' ! summation relation: x12 = 1 - sum(x1j) + sum_rel(2) = 'x22' ! summation relation: x22 = 1 - sum(x2j) + + filename = 'LJ_START_VAL.INC' + CALL file_open(filename,84) + READ (84,*) den1,den2 + READ (84,*) x_1,x_2 + CLOSE (84) + + xi(1,1) = x_1 + xi(2,1) = x_2 + xi(1,2) = 1.0 - xi(1,1) + xi(2,2) = 1.0 - xi(2,1) + lnx(1,1) = LOG(xi(1,1)) + lnx(2,1) = LOG(xi(2,1)) + lnx(1,2) = LOG(xi(1,2)) + lnx(2,2) = LOG(xi(2,2)) + + val_init(1) = den1 + val_init(2) = den2 + val_init(3) = t + val_init(4) = p + DO ph = 1,nphas + DO k = 1,ncomp + val_init(4+k+(ph-1)*ncomp) = LOG(xi(ph,k)) + END DO + END DO + + CALL objective_ctrl (converg) + + IF(user%rank == 0) THEN + IF (converg == 1) WRITE (*,*) t, p/1.0E5, xi(1,1), xi(2,1) + IF (converg == 0) WRITE (*,*) ' weak starting values' + END IF + +! ---------------------------------------------------------------------- +! ELSE: PC-SAFT equation of state +! ---------------------------------------------------------------------- + +ELSE + + renormalize = .false. ! for renormalization group theory (RGT) + IF (num == 2) renormalize = .true. + IF (num == 2) num = 0 ! if RGT: initial phase equilibr. is for non-renormalized model + + flashcase = .false. ! .true. when a specific feed conc. xif is given + IF (xif(1) /= 0.0) flashcase = .true. + + lle_check = .true. + +! ---------------------------------------------------------------------- +! IF: non-polymeric system +! ---------------------------------------------------------------------- + IF (mm(1) < 2000.0) THEN + + DO i=1,ncomp ! setting mole-fractions for the case that + ! anything goes wrong in the coming routines + xi(1,i) = 1.0 / REAL(ncomp) + xi(2,i) = 1.0 / REAL(ncomp) + END DO + + + ! ------------------------------------------------------------------ + ! determine an initial conc. (phase 1) that will phase split + ! ------------------------------------------------------------------ + IF( ncomp == 2 .AND. .NOT.flashcase ) THEN + CALL vle_min( lle_check ) + IF(user%rank == 0) THEN + WRITE(*,*)' INITIAL FEED-COMPOSITION',(xi(1,i), i=1,ncomp),converg + END IF + END IF + + ! ------------------------------------------------------------------ + ! perform a phase stability test + ! ------------------------------------------------------------------ + ph_split = 0 + CALL phase_stability ( .false., flashcase, ph_split,user ) + IF(user%rank == 0) THEN + write (*,*) 'stability analysis I indicates phase-split is:',ph_split + END IF + + ! ------------------------------------------------------------------ + ! determine species i, for which x(i) is calc from summation relation + ! ------------------------------------------------------------------ + CALL select_sum_rel (1,0,1) ! synthax (m,n,o): phase m + ! exclude comp. n + ! assign it(o) and higher + CALL select_sum_rel (2,0,2) ! for ncomp>=3, the quantities + ! to be iterated will be overwritten + + ! ------------------------------------------------------------------ + ! if 2 phases (VLE) + ! ------------------------------------------------------------------ + IF (ph_split == 1) THEN + + ! --- perform tangent plane minimization ------------------------ + CALL tangent_plane + ph_split = 0 + + ! --- determine, for which substance summation relation is used -- + IF (flashcase) THEN + CALL determine_flash_it2 + ELSE + CALL select_sum_rel (1,0,1) + CALL select_sum_rel (2,0,2) + END IF + + ! --- do full phase equilibr. calculation ------------------------ + n_unkw = ncomp ! number of quantities to be iterated + CALL objective_ctrl (converg) + IF(user%rank == 0) THEN + IF (converg == 1 ) write (*,*) ' converged (maybe a VLE)',dense(1),dense(2) + END IF + END IF + + ! ------------------------------------------------------------------ + ! test for LLE + ! ------------------------------------------------------------------ + ph_split = 0 + + IF (lle_check) CALL phase_stability (lle_check,flashcase,ph_split) + IF(user%rank == 0) THEN + IF (lle_check) write (*,*) 'stability analysis II, phase-split is:',ph_split + END IF + + ! ------------------------------------------------------------------ + ! if two phases (LLE) + ! ------------------------------------------------------------------ + IF (ph_split == 1) THEN + IF(user%rank == 0) THEN + write (*,*) ' LLE-stability test indicates 2 phases (VLE or LLE)' + END IF + + ! --- perform tangent plane minimization ------------------------ + IF (flashcase) CALL select_sum_rel (1,0,1) + IF (flashcase) CALL select_sum_rel (2,0,2) + + CALL tangent_plane + + ! --- determine, for which substance summation relation ---------- + IF (flashcase) THEN + CALL determine_flash_it2 + ELSE + CALL select_sum_rel (1,0,1) + CALL select_sum_rel (2,0,2) + END IF + + ! --- do full phase equilibr. calculation ------------------------ + n_unkw = ncomp ! number of quantities to be iterated + val_conv(2) = 0.0 + CALL objective_ctrl (converg) + IF(user%rank == 0) THEN + IF (converg == 1 ) write (*,*) ' converged (maybe an LLE)',dense(1),dense(2) + END IF + END IF + + ! ------------------------------------------------------------------ + ! equilibr. calc. converged: set initial var. for further calc. + ! ------------------------------------------------------------------ + IF (converg == 1) THEN + val_init = val_conv + DO ph = 1,nphas + DO i = 1,ncomp + xi(ph,i) = EXP( val_conv(4+i+(ph-1)*ncomp) ) + END DO + END DO + dense(1:2) = val_conv(1:2) + ELSE + IF(user%rank == 0) THEN + WRITE (*,*) ' NO SOLUTION FOUND FOR THE STARTING VALUES' + END IF + STOP + END IF + + + ! --------------------------------------------------------------------- + ! ELSE: for systems with polymers + ! --------------------------------------------------------------------- + + ELSE + + ncompsav = ncomp + ncomp = 2 ! set number of components to 2 + n_unkwsav = n_unkw + + CALL poly_sta_var(converg) + + IF (converg == 1) THEN + val_init = val_conv + ELSE + + IF(user%rank == 0) THEN + WRITE (*,*) ' NO SOLUTION FOUND FOR THE STARTING VALUES' + END IF + STOP + END IF + + ncomp = ncompsav + n_unkw = n_unkwsav ! number of quantities to be iterated + + END IF + +! --- for RGT: set flag back to num=2 indicating an RGT calculation ---- + IF (renormalize) num = 2 + +END IF + +END SUBROUTINE start_var + + + + +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! SUBROUTINE objective_ctrl +! +! This subroutine controls the iso-fugacity iteration. It uses +! the variables defined in the array "val_init". If successfull, +! the converged values are written to "val_conv", and the flag +! converg is set to 1. +! See also above desciption for subroutine PHASE_EQUILIB +! This routine calls SUBROUTINE HYBRID, which is a solver (modified +! POWELL HYBRID METHOD). HYBRID is freely available for non-commercial +! applications. HYBRID requires three definitions: +! 1.the number of equations to be solved (=No. of variables to be +! iterated). The appropriate parameter is: "n_unkw" +! 2.the equations to be iterated, they are here gathered in the SUB- +! ROUTINE OBJEC_FCT (see below). Since HYBRID is a root finder, +! these objective functions are iterated to be zero (essentially, +! OBJEC_FCT contains the iso-fugacity relation. +! 3.an array of variables is required, containing the quatities to be +! iterated. This array is termed "y(i)" +! +! INPUT VARIABLES: +! val_init(i) array containing (densities,T,P,lnx's) serving as +! starting values for the phase equilibrium calculation +! it(i) contains the information, which variable is deter- +! mined iteratively. For syntax refer e.g.to SUB BINMIX. +! sum_rel(i) indicates, which mole fraction is determined from the +! summation relation sum(xi)=1 +! +! OUTPUT VARIABLES: +! val_conv(i) array containing the converged system variables +! analogous to "val_init" +! converg 0 if no convergence achieved, 1 if converged solution +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! + SUBROUTINE objective_ctrl (converg) +! + USE BASIC_VARIABLES + USE Solve_NonLin + IMPLICIT NONE +! +! ---------------------------------------------------------------------- + INTEGER, INTENT(OUT) :: converg +! +! ---------------------------------------------------------------------- + INTERFACE + SUBROUTINE objec_fct ( iter_no, y, residu, dummy ) + INTEGER, INTENT(IN) :: iter_no + REAL, INTENT(IN) :: y(iter_no) + REAL, INTENT(OUT) :: residu(iter_no) + INTEGER, INTENT(IN OUT) :: dummy + END SUBROUTINE objec_fct + END INTERFACE +! + INTEGER :: info,k,posn,i + INTEGER, PARAMETER :: mxr = nc*(nc+1)/2 + REAL, ALLOCATABLE :: y(:),diag(:),residu(:) + REAL :: x_init, x_solut, r_diff1, r_diff2, totres + REAL :: r_thrash, x_thrash + CHARACTER (LEN=2) :: compon + LOGICAL :: convergence +! ---------------------------------------------------------------------- + +info=1 + +ALLOCATE( y(n_unkw), diag(n_unkw), residu(n_unkw) ) + +IF (num == 0) acc_a = 1.E-7 +IF (num == 0) step_a = 2.E-8 +IF (num == 1) acc_a = 1.E-7 +IF (num == 1) step_a = 2.E-8 +IF (num == 2) acc_a = 5.E-7 +IF (num == 2) step_a = 1.E-7 + +posn = 0 +DO i = 1,n_unkw + posn = posn + 1 + IF (it(i) == 't') y(posn) = val_init(3) + IF (it(i) == 'p') y(posn) = val_init(4) + IF (it(i) == 'lnp') y(posn) = LOG( val_init(4) ) + IF (it(i) == 'fls') y(posn) = alpha + IF (it(i)(1:1) == 'x' .AND. it(i)(2:2) == '1') compon = it(i)(3:3) + IF (it(i)(1:1) == 'x' .AND. it(i)(2:2) == '1') READ(compon,*) k + IF (it(i)(1:1) == 'x' .AND. it(i)(2:2) == '1') y(posn) = val_init(4+k) + IF (it(i)(1:1) == 'x' .AND. it(i)(2:2) == '2') compon = it(i)(3:3) + IF (it(i)(1:1) == 'x' .AND. it(i)(2:2) == '2') READ(compon,*) k + IF (it(i)(1:1) == 'x' .AND. it(i)(2:2) == '2') y(posn) = val_init(4+ncomp+k) + IF (it(i)(1:1) == 'x' .AND. it(i)(2:2) == '3') compon = it(i)(3:3) + IF (it(i)(1:1) == 'x' .AND. it(i)(2:2) == '3') READ(compon,*) k + IF (it(i)(1:1) == 'x' .AND. it(i)(2:2) == '3') y(posn) = val_init(4+ncomp+ncomp+k) +END DO + +CALL init_vars + +x_init = 0.0 +DO i = 1,ncomp + IF (lnx(1,i) /= 0.0 .AND. lnx(2,i) /= 0.0) THEN + x_init = x_init + ABS( 1.0 - lnx(2,i)/lnx(1,i) ) + ELSE + x_init = x_init + ABS( 1.0 - EXP(lnx(2,i))/EXP(lnx(1,i)) ) + END IF +END DO + +CALL hbrd (objec_fct, n_unkw, y, residu, step_a, acc_a, info, diag) + +x_solut = 0.0 +DO i = 1,ncomp + IF ( lnx(1,i) /= 0.0 .AND. lnx(2,i) /= 0.0 ) THEN + x_solut = x_solut + ABS( 1.0 - lnx(2,i)/lnx(1,i) ) + ELSE + IF (lnx(1,i) < 1E300 .AND. lnx(1,i) > -1.E300 ) & + x_solut = x_solut + ABS( 1.0 - EXP(lnx(2,i))/EXP(lnx(1,i)) ) + END IF +END DO +r_diff1 = ABS( 1.0 - dense(1)/dense(2) ) +IF ( val_conv(2) > 0.0 ) THEN + r_diff2 = ABS( 1.0 - val_conv(1)/val_conv(2) ) +ELSE + r_diff2 = 0.0 +END IF + +totres = SUM( ABS( residu(1:n_unkw) ) ) + +r_thrash = 0.0005 +x_thrash = 0.0005 +if (num > 0 ) r_thrash = r_thrash * 10.0 +if (num > 0 ) x_thrash = x_thrash * 100.0 + +convergence = .true. + +IF ( info >= 2 ) convergence = .false. +IF ( ABS( 1.0- dense(1)/dense(2) ) < r_thrash .AND. x_solut < x_thrash ) THEN + IF ( x_init > 0.050 ) convergence = .false. + IF ( ( ABS( 1.0- dense(1)/dense(2) ) + x_solut ) < 1.E-7 ) convergence = .false. +ENDIF +IF ( r_diff2 /= 0.0 .AND. r_diff2 > (4.0*r_diff1) .AND. bindiag == 1 ) convergence = .false. +IF ( ncomp == 1 .AND. totres > 100.0*acc_a ) convergence = .false. +IF ( totres > 1000.0*acc_a ) convergence = .false. +IF ( ncomp == 1 .AND. r_diff1 < 1.d-5 ) convergence = .false. + +IF ( convergence ) THEN + converg = 1 + ! write (*,*) residu(1),residu(2) + CALL converged + IF (num <= 1) CALL enthalpy_etc +ELSE + converg = 0 +END IF + +DEALLOCATE( y, diag, residu ) + +END SUBROUTINE objective_ctrl + + + +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! SUBROUTINE objec_fct +! +! This subroutine contains the equations to be solved numerically +! (iso-fugacity: fi'-fi''=0) as well as other dependent equations, +! which can be solved analytically, namely the summation relation +! xi=1-sum(xj) or the condition of equal charge for electrolyte +! solutions. +! This subroutine is required and controlled by the solver HBRD ! +! HBRD varies the variables "y(i)" and eveluates the result of +! these changes from this routine. +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! + SUBROUTINE objec_fct ( iter_no, y, residu, dummy ) +! + USE BASIC_VARIABLES + USE EOS_VARIABLES, ONLY: density_error + IMPLICIT NONE +! +! ---------------------------------------------------------------------- + INTEGER, INTENT(IN) :: iter_no + REAL, INTENT(IN) :: y(iter_no) + REAL, INTENT(OUT) :: residu(iter_no) + INTEGER, INTENT(IN OUT) :: dummy +! +! ---------------------------------------------------------------------- + INTEGER :: i, ph,k,posn, skip,phase + REAL :: lnphi(np,nc),isofugacity + CHARACTER (LEN=2) :: compon +! ---------------------------------------------------------------------- + + +posn = 0 +DO i = 1,n_unkw + posn = posn + 1 + IF (it(i) == 't') t = y(posn) + IF (it(i) == 'p') p = y(posn) + IF (it(i) == 'lnp') p = EXP( y(posn) ) + IF (it(i) == 'fls') alpha = y(posn) + IF (it(i)(1:1) == 'x' .AND. it(i)(2:2) == '1') compon = it(i)(3:3) + IF (it(i)(1:1) == 'x' .AND. it(i)(2:2) == '1') READ(compon,*) k + IF (it(i)(1:1) == 'x' .AND. it(i)(2:2) == '1') lnx(1,k) = y(posn) + IF (it(i)(1:1) == 'x' .AND. it(i)(2:2) == '2') compon = it(i)(3:3) + IF (it(i)(1:1) == 'x' .AND. it(i)(2:2) == '2') READ(compon,*) k + IF (it(i)(1:1) == 'x' .AND. it(i)(2:2) == '2') lnx(2,k) = y(posn) + IF (it(i)(1:1) == 'x' .AND. it(i)(2:2) == '3') compon = it(i)(3:3) + IF (it(i)(1:1) == 'x' .AND. it(i)(2:2) == '3') READ(compon,*) k + IF (it(i)(1:1) == 'x' .AND. it(i)(2:2) == '3') lnx(3,k) = y(posn) +END DO + +DO k = 1,ncomp + IF (lnx(1,k) > 0.0) lnx(1,k) = 0.0 + IF (lnx(2,k) > 0.0) lnx(2,k) = 0.0 +END DO + +IF (p < 1.E-100) p = 1.E-12 +!IF ( IsNaN( p ) ) p = 1000.0 ! rebounce for the case of NaN-solver output +!IF ( IsNaN( t ) ) t = 300.0 ! rebounce for the case of NaN-solver output +!IF ( IsNaN( alpha ) ) alpha = 0.5 ! rebounce for the case of NaN-solver output +IF ( p /= p ) p = 1000.0 ! rebounce for the case of NaN-solver output +IF ( t /= t ) t = 300.0 ! rebounce for the case of NaN-solver output +IF ( alpha /= alpha ) alpha = 0.5 ! rebounce for the case of NaN-solver output + +! --- setting of mole fractions ---------------------------------------- +DO ph = 1, nphas + DO i = 1, ncomp + IF ( lnx(ph,i) < -300.0 ) THEN + xi(ph,i) = 0.0 + ELSE + xi(ph,i) = EXP( lnx(ph,i) ) + END IF + END DO +END DO + +IF (ncomp > 1) CALL x_summation + +CALL fugacity (lnphi) + +phase = 2 +DO i = 1,n_unkw + skip = 0 !for ions/polymers, the isofug-eq. is not always solved + IF (n_unkw < (ncomp*(nphas-1))) skip = ncomp*(nphas-1) - n_unkw + IF ((i+skip-ncomp*(phase-2)) > ncomp) phase = phase + 1 + residu(i) = isofugacity((i+skip-ncomp*(phase-2)),phase,lnphi) + if ( density_error(phase) /= 0.0 ) residu(i) = residu(i) + SIGN( density_error(phase), residu(i) ) * 0.001 +END DO + +END SUBROUTINE objec_fct + + + +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! REAL FUNCTION isofugacity +! +! calculates the deviation from the condition of equal fugacities in +! logarithmic form. +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! + REAL FUNCTION isofugacity (i,phase,lnphi) +! + USE BASIC_VARIABLES + IMPLICIT NONE +! +! ---------------------------------------------------------------------- + INTEGER, INTENT(IN) :: i + INTEGER, INTENT(IN) :: phase + REAL, INTENT(IN) :: lnphi(np,nc) +! +! ---------------------------------------------------------------------- + INTEGER :: p1, p2 +! ---------------------------------------------------------------------- + + +! p1=1 +p1 = phase-1 +p2 = phase + +isofugacity = scaling(i) *( lnphi(p2,i)+lnx(p2,i)-lnx(p1,i)-lnphi(p1,i) ) +! write (*,'(a, 4G18.8)') ' t, p ',t,p,dense(1),dense(2) +! write (*,'(a,i3,i3,3G18.8)') ' phi_V',i,p2,lnx(p2,i),lnphi(p2,i),dense(p2) +! write (*,'(a,i3,i3,3G18.8)') ' phi_L',i,p1,lnx(p1,i),lnphi(p1,i),dense(p1) +! write (*,*) ' ISOFUGACITY',i,ISOFUGACITY, scaling(i) +! write (*,'(a,i3,4G18.8)') ' ISOFUGACITY',i,ISOFUGACITY, lnphi(p2,i)+lnx(p2,i), -lnx(p1,i)-lnphi(p1,i) +! pause + +END FUNCTION isofugacity + + + + + + + + + + + + + + + + + +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! + SUBROUTINE vle_min(lle_check) +! + USE PARAMETERS, ONLY: RGAS + USE BASIC_VARIABLES + USE STARTING_VALUES + IMPLICIT NONE +! +! ---------------------------------------------------------------------- + LOGICAL, INTENT(OUT) :: lle_check + + INTEGER :: i,j,k,phasen(0:40),steps + REAL :: lnphi(np,nc) + REAL :: vlemin(0:40),llemin(0:40),xval(0:40) + REAL :: start_xv(0:40),start_xl(0:40),x_sav,dg_dx2 +! ---------------------------------------------------------------------- + + + +j = 0 +k = 0 +nphas = 2 + +steps = 40 + +x_sav = xi(1,1) +sum_rel(1) = 'x12' ! summation relation +sum_rel(2) = 'x22' ! summation relation + +DO i = 0, steps + densta(1) = 0.45 + densta(2) = 1.d-6 + xi(1,1) = 1.0 - REAL(i) / REAL(steps) + IF ( xi(1,1) <= 1.E-50 ) xi(1,1) = 1.E-50 + xi(2,1) = xi(1,1) + lnx(1,1) = LOG(xi(1,1)) + lnx(2,1) = LOG(xi(2,1)) + + CALL x_summation + CALL fugacity (lnphi) + CALL enthalpy_etc !!KANN DAS RAUS???? + + + + + xval(i) = xi(1,1) + llemin(i)= gibbs(1) +(xi(1,1)*lnx(1,1)+xi(1,2)*lnx(1,2))*RGAS*t + + IF ( ABS(1.0-dense(1)/dense(2)) > 0.0001 ) THEN + vlemin(i)= gibbs(1) +(xi(1,1)*lnx(1,1)+xi(1,2)*lnx(1,2))*RGAS*t & + - ( gibbs(2) +(xi(2,1)*lnx(2,1)+xi(2,2)*lnx(2,2))*RGAS*t ) + phasen(i) = 2 + ELSE + phasen(i) = 1 + END IF + + IF (i > 0 .AND. phasen(i) == 2) THEN + IF (phasen(i-1) == 2 .AND. ABS(vlemin(i)+vlemin(i-1)) < & + ABS(vlemin(i))+ABS(vlemin(i-1))) THEN + j = j + 1 + start_xv(j)=xval(i-1) + (xval(i)-xval(i-1)) & + * ABS(vlemin(i-1))/ABS(vlemin(i)-vlemin(i-1)) + END IF + END IF + +END DO + + +DO i=2,steps-2 + dg_dx2 = (-llemin(i-2)+16.0*llemin(i-1)-30.0*llemin(i) & + +16.0*llemin(i+1)-llemin(i+2)) / (12.0*((xval(i)-xval(i-1))**2)) + IF (dg_dx2 < 0.0) THEN + k = k + 1 + start_xl(k)=xval(i) + END IF +END DO + + +IF (start_xl(1) == 0.0 .AND. start_xv(1) /= 0.0) THEN + xi(1,1) = start_xv(1) + xi(1,2) = 1.0-xi(1,1) + lle_check=.false. + ! write (*,*) 'VLE is likely', xi(1,1),xi(1,2) +ELSE IF (start_xl(1) /= 0.0 .AND. start_xv(1) == 0.0) THEN + xi(1,1) = start_xl(1) + xi(1,2) = 1.0-xi(1,1) + ! write (*,*) 'LLE is likely', xi(1,1),xi(1,2) + lle_check=.true. +ELSE IF (start_xl(1) /= 0.0 .AND. start_xv(1) /= 0.0) THEN + xi(1,1) = start_xv(1) + xi(1,2) = 1.0-xi(1,1) + ! write(*,*) 'starting with VLE and check for LLE' + lle_check=.true. +ELSE + xi(1,1) = x_sav + xi(1,2) = 1.0 - xi(1,1) +END IF + + +CALL x_summation + +END SUBROUTINE vle_min + + +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! SUBROUTINE phase_stability +! +! the index 'LLE_check' is for the starting density (which determines +! whether a liquid or vapor phase is found) of the trial phase. The +! feed-point exits either as a vapor or as a liquid. If it can exist as +! both (feedphases=2), then both states are tested. +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! + SUBROUTINE phase_stability ( lle_check, flashcase, ph_split,user ) + +!Petsc modules + USE PetscManagement + +!VLE modules + USE BASIC_VARIABLES + USE STARTING_VALUES + USE EOS_VARIABLES, ONLY: dhs, PI, x, eta, eta_start, z3t, fres + USE EOS_NUMERICAL_DERIVATIVES + IMPLICIT NONE +! +! ---------------------------------------------------------------------- + type (userctx) user + LOGICAL :: lle_check + LOGICAL, INTENT(IN OUT) :: flashcase + INTEGER, INTENT(OUT) :: ph_split +! ---------------------------------------------------------------------- + + INTERFACE + REAL FUNCTION F_STABILITY ( optpara, n ) + INTEGER, INTENT(IN) :: n + REAL, INTENT(IN OUT) :: optpara(n) + END FUNCTION + END INTERFACE + +!INTERFACE +! SUBROUTINE F_STABILITY (fmin, optpara, n) +! REAL, INTENT(IN OUT) :: fmin +! REAL, INTENT(IN) :: optpara(:) +! INTEGER, INTENT(IN) :: n +! END SUBROUTINE F_STABILITY +! +! SUBROUTINE stability_grad (g, optpara, n) +! REAL, INTENT(IN OUT) :: g(:) +! REAL, INTENT(IN) :: optpara(:) +! INTEGER, INTENT(IN) :: n +! END SUBROUTINE stability_grad +! +! SUBROUTINE stability_hessian (hessian, g, fmin, optpara, n) +! REAL, INTENT(IN OUT) :: hessian(:,:) +! REAL, INTENT(IN OUT) :: g(:) +! REAL, INTENT(IN OUT) :: fmin +! REAL, INTENT(IN) :: optpara(:) +! INTEGER, INTENT(IN) :: n +! END SUBROUTINE stability_hessian +!END INTERFACE + + INTEGER :: n, PRIN + REAL :: fmin, t0, h0, MACHEP, PRAXIS + REAL, ALLOCATABLE :: optpara(:) + + INTEGER :: i, feedphases, trial + REAL :: rhoi(nc),rho_start + REAL :: feeddens, rho_phas(np) + REAL :: fden + REAL :: dens + REAL :: rhot + REAL :: lnphi(np,nc) + REAL :: w(np,nc), mean_mass +! ---------------------------------------------------------------------- + +n = ncomp +ALLOCATE( optpara(n) ) + + +IF(user%rank == 0) THEN + IF (lle_check) WRITE (*,*) ' stability test starting with dense phase' +END IF + +DO i = 1, ncomp ! setting feed-phase x's + IF (.NOT.flashcase) xif(i) = xi(1,i) + IF (flashcase) xi(1,i) = xif(i) + xi(2,i) = xif(i) ! feed is tested for both: V and L density +END DO + +densta(1) = 0.45 +densta(2) = 1.d-6 + +CALL dens_calc(rho_phas) +IF ( ABS(1.0-dense(1)/dense(2)) > 0.0005 ) THEN + feedphases=2 ! feed-composition can exist both, in V and L +ELSE + feedphases=1 ! feed-composition can exist either in V or L +END IF +densta(1) = dense(1) +feeddens = dense(2) +!write (*,*) 'feedphases',dense(1), dense(2),feedphases + +10 CONTINUE ! IF FeedPhases=2 THEN there is a second cycle + + trial = 1 + + ! -------------------------------------------------------------------- + ! setting trial-phase mole-fractions + ! if there is no phase-split then further trial-phases are + ! considered (loop: 20 CONTINUE) + ! -------------------------------------------------------------------- + DO i = 1, ncomp + w(2,i) = 1.0 / REAL(ncomp) + END DO + mean_mass = 1.0 / SUM( w(2,1:ncomp)/mm(1:ncomp) ) + xi(2,1:ncomp) = w(2,1:ncomp)/mm(1:ncomp) * mean_mass + + 20 CONTINUE + + DO i = 1, ncomp + rhoif(i) = rho_phas(1) * xif(i) + rhoi(i) = rhoif(i) + END DO + + !write (*,'(a,6G16.8)') 'startval',rho_phas(2),xi(2,1:ncomp) + + ! -------------------------------------------------------------------- + ! calc Helmholtz energy density and derivative (numerical) to rhoif(i). + ! The derivative is taken around the "feed-point" not the trial phase + ! -------------------------------------------------------------------- + + rhot = SUM( rhoi(1:ncomp) ) + x(1:ncomp) = rhoi(1:ncomp) / rhot + CALL PERTURBATION_PARAMETER + xi(1,1:ncomp) = x(1:ncomp) + eta = rhot * z3t + eta_start = eta + densta(1) = eta_start + ensemble_flag = 'tv' + CALL FUGACITY (lnphi) + ensemble_flag = 'tp' + + call fden_calc ( fden, rhoi ) + fdenf = fden + + grad_fd(1:ncomp) = lnphi(1,1:ncomp) + LOG( rhoi(1:ncomp) ) + + + ! -------------------------------------------------------------------- + ! starting values for iteration (optpara) + ! -------------------------------------------------------------------- + rho_start = 1.E-5 + IF (lle_check) THEN + densta(2) = 0.45 + CALL dens_calc(rho_phas) + rho_start = rho_phas(2)*0.45/dense(2) + END IF + DO i = 1,ncomp + rhoi(i) = xi(2,i)*rho_start + optpara(i) = LOG( rhoi(i) ) + END DO + + ! -------------------------------------------------------------------- + ! minimizing the objective fct. Phase split for values of fmin < 0.0 + ! -------------------------------------------------------------------- + t0 = 5.E-5 + h0 = 0.5 + PRIN = 0 + MACHEP = 1.E-15 + + fmin = PRAXIS( t0, MACHEP, h0, n, PRIN, optpara, F_STABILITY, fmin ) + + + ! -------------------------------------------------------------------- + ! updating the ln(x) valus from optpara. The optimal optpara-vector is + ! not necessarily the one that was last evaluated. At the very end, + ! cg_decent writes the best values to optpara + ! -------------------------------------------------------------------- + fmin = F_STABILITY( optpara, n ) + + + + ! IF ( n == 2 ) THEN + ! CALL Newton_Opt_2D ( stability_hessian, F_stability, optpara, n, 1.E-8, 1.E-8, g, fmin) + ! ELSE + ! CALL cg_descent (1.d-5, optpara, n, F_STABILITY, stability_grad, STATUS, & + ! gnorm, fmin, iter, nfunc, ngrad, d, g, xtemp, gtemp) + ! ENDIF + ! CALL F_STABILITY (fmin, optpara, n) + + + ! -------------------------------------------------------------------- + ! determine instability & non-trivial solution + ! -------------------------------------------------------------------- + ph_split = 0 + IF (fmin < -1.E-7 .AND. & + ABS( 1.0 - maxval(EXP(optpara),mask=optpara /= 0.0) /maxval(rhoif) ) > 0.0005) THEN + ph_split = 1 + END IF + + IF (ph_split == 1) THEN + + ! ------------------------------------------------------------------ + ! here, there should be IF FeedPhases=2 THEN GOTO 10 + ! and test for another phase (while saving optpara) + ! ------------------------------------------------------------------ + + rhoi2(1:ncomp) = EXP( optpara(1:ncomp) ) + dens = PI/6.0 * SUM( rhoi2(1:ncomp) * parame(1:ncomp,1) * dhs(1:ncomp)**3 ) + rhot = SUM( rhoi2(1:ncomp) ) + xi(2,1:ncomp) = rhoi2(1:ncomp) / rhot + + ELSE + + IF (trial <= ncomp + ncomp) THEN + ! ---------------------------------------------------------------- + ! setting trial-phase x's + ! ---------------------------------------------------------------- + IF (trial <= ncomp) THEN + DO i=1,ncomp + w(2,i) = 1.0 / REAL(ncomp-1) * 0.05 + END DO + w(2,trial) = 0.95 + ELSE + DO i=1,ncomp + w(2,i) = 1.0 / REAL(ncomp-1) * 0.00001 + END DO + w(2,trial-ncomp) = 0.99999 + END IF + mean_mass = 1.0 / SUM( w(2,1:ncomp)/mm(1:ncomp) ) + xi(2,1:ncomp) = w(2,1:ncomp)/mm(1:ncomp) * mean_mass + trial = trial + 1 + GO TO 20 + END IF + ! IF (.NOT.LLE_check) write (*,*) 'no phase split detected' + ! IF (.NOT.LLE_check) pause + IF (feedphases > 1 .AND. .NOT.lle_check .AND. densta(1) > 0.2) THEN + densta(1) = feeddens ! this will be the lower-valued density (vapor) + CALL dens_calc(rho_phas) + ! WRITE (*,*) 'try feed as vapor-phase' + GO TO 10 + END IF + + END IF + +DEALLOCATE( optpara ) + +END SUBROUTINE phase_stability + + +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! SUBROUTINE select_sum_rel +! +! This subroutine determines which component of a phase "ph" is calculated +! from the summation relation x_i = 1 - sum(x_j). The other components are, +! by default, said to be iterated during the phase equilibrium calculation. +! +! Note that for flash calculations not all of these mole fractions are in +! fact iterated - this is raken care of in "determine_flash_it". +! +! ph phase +! excl exclude comp. n +! startindex assign it(startindex) for quantities to be iterated +! (further it(startindex+1) is assigned, for a ternary +! mixture, etc.) +! +! sum_index indicates the component, with the largest mole +! fraction. If ph=1 and sum_index=2, we define +! sum_rel(ph=1)='x12', so that this component is +! calculated from the summation relation. +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! + SUBROUTINE select_sum_rel (ph,excl,startindex) +! + USE BASIC_VARIABLES + IMPLICIT NONE +! +! ---------------------------------------------------------------------- + INTEGER, INTENT(IN) :: ph + INTEGER, INTENT(IN) :: excl + INTEGER, INTENT(IN) :: startindex +! ---------------------------------------------------------------------- + INTEGER :: i,j, sum_index + REAL :: xmax(np) + ! CHARACTER :: compNo*2,phasNo*2 +! ---------------------------------------------------------------------- + +xmax(ph) = 0.0 +DO i = 1, ncomp + + IF ( xi(ph,i) > xmax(ph) ) THEN + xmax(ph) = xi(ph,i) + sum_index = i + + IF (ph == 1 .AND. i == 1) sum_rel(1) = 'x11' + IF (ph == 1 .AND. i == 2) sum_rel(1) = 'x12' + IF (ph == 1 .AND. i == 3) sum_rel(1) = 'x13' + IF (ph == 1 .AND. i == 4) sum_rel(1) = 'x14' + IF (ph == 1 .AND. i == 5) sum_rel(1) = 'x15' + + IF (ph == 2 .AND. i == 1) sum_rel(2) = 'x21' + IF (ph == 2 .AND. i == 2) sum_rel(2) = 'x22' + IF (ph == 2 .AND. i == 3) sum_rel(2) = 'x23' + IF (ph == 2 .AND. i == 4) sum_rel(2) = 'x24' + IF (ph == 2 .AND. i == 5) sum_rel(2) = 'x25' + + IF (ph == 3 .AND. i == 1) sum_rel(3) = 'x31' + IF (ph == 3 .AND. i == 2) sum_rel(3) = 'x32' + IF (ph == 3 .AND. i == 3) sum_rel(3) = 'x33' + IF (ph == 3 .AND. i == 4) sum_rel(3) = 'x34' + IF (ph == 3 .AND. i == 5) sum_rel(3) = 'x35' +! write (*,*) ph,i,xi(ph,i),sum_rel(ph) + END IF + +END DO + +j = 0 +DO i = 1, ncomp + + IF ( i /= sum_index .AND. i /= excl ) THEN + IF (ph == 1 .AND. i == 1) it(startindex+j) = 'x11' + IF (ph == 1 .AND. i == 2) it(startindex+j) = 'x12' + IF (ph == 1 .AND. i == 3) it(startindex+j) = 'x13' + IF (ph == 1 .AND. i == 4) it(startindex+j) = 'x14' + IF (ph == 1 .AND. i == 5) it(startindex+j) = 'x15' + + IF (ph == 2 .AND. i == 1) it(startindex+j) = 'x21' + IF (ph == 2 .AND. i == 2) it(startindex+j) = 'x22' + IF (ph == 2 .AND. i == 3) it(startindex+j) = 'x23' + IF (ph == 2 .AND. i == 4) it(startindex+j) = 'x24' + IF (ph == 2 .AND. i == 5) it(startindex+j) = 'x25' + + IF (ph == 3 .AND. i == 1) it(startindex+j) = 'x31' + IF (ph == 3 .AND. i == 2) it(startindex+j) = 'x32' + IF (ph == 3 .AND. i == 3) it(startindex+j) = 'x33' + IF (ph == 3 .AND. i == 4) it(startindex+j) = 'x34' + IF (ph == 3 .AND. i == 5) it(startindex+j) = 'x35' +! write (*,*) 'iter ',it(startindex+j) + j = j + 1 + END IF + +END DO + +END SUBROUTINE select_sum_rel + + + + +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! + SUBROUTINE tangent_plane +! + USE BASIC_VARIABLES + USE STARTING_VALUES + IMPLICIT NONE +! +! ---------------------------------------------------------------------- +!!$ INTERFACE +!!$ SUBROUTINE tangent_value (fmin, optpara, n) +!!$ INTEGER, INTENT(IN) :: n +!!$ REAL, INTENT(IN OUT) :: fmin +!!$ REAL, INTENT(IN) :: optpara(:) +!!$ END SUBROUTINE tangent_value +!!$ +!!$ SUBROUTINE tangent_grad (g, optpara, n) +!!$ INTEGER, INTENT(IN) :: n +!!$ REAL, INTENT(IN OUT) :: g(:) +!!$ REAL, INTENT(IN) :: optpara(:) +!!$ END SUBROUTINE tangent_grad +!!$ END INTERFACE + +! +! ---------------------------------------------------------------------- + INTERFACE + REAL FUNCTION PRAXIS( t0, MACHEP, h0, n, PRIN, optpara, TANGENT_VALUE, fmin ) + REAL, INTENT(IN OUT) :: t0 + REAL, INTENT(IN) :: machep + REAL, INTENT(IN) :: h0 + INTEGER :: n + INTEGER, INTENT(IN OUT) :: prin + REAL, INTENT(IN OUT) :: optpara(n) + REAL, EXTERNAL :: TANGENT_VALUE + REAL, INTENT(IN OUT) :: fmin + END FUNCTION + + REAL FUNCTION TANGENT_VALUE2 ( optpara, n ) + INTEGER, INTENT(IN) :: n + REAL, INTENT(IN) :: optpara(n) + END FUNCTION + END INTERFACE +! +! ---------------------------------------------------------------------- + INTEGER :: n + INTEGER :: i, k, ph + INTEGER :: small_i, min_ph, other_ph + INTEGER :: PRIN + REAL :: fmin , t0, h0, MACHEP + REAL :: lnphi(np,nc) + REAL, ALLOCATABLE :: optpara(:) + +! INTEGER :: STATUS, iter, nfunc, ngrad +! REAL :: gnorm +! REAL, ALLOCATABLE :: d(:), g(:), xtemp(:), gtemp(:) +! ---------------------------------------------------------------------- + +n = ncomp +t0 = 1.E-4 +h0 = 0.1 +PRIN = 0 +MACHEP = 1.E-15 + +ALLOCATE( optpara(n) ) +!ALLOCATE( d(n) ) +!ALLOCATE( g(n) ) +!ALLOCATE( xtemp(n) ) +!ALLOCATE( gtemp(n) ) + +DO i = 1,ncomp + rhoi1(i) = rhoif(i) + lnx(1,i) = LOG(xi(1,i)) + lnx(2,i) = LOG(xi(2,i)) +END DO + +DO i = 1,ncomp + optpara(i) = LOG( xi(2,i) * 0.001 ) +END DO + +! CALL cg_descent (1.d-4, optpara, n, tangent_value, tangent_grad, STATUS, & +! gnorm, fmin, iter, nfunc, ngrad, d, g, xtemp, gtemp) +! +! updating the ln(x) valus from optpara. The optimal optpara-vector is not necessarily +! the one that was last evaluated. At the very end, cg_decent writes the best values to optpara +! CALL tangent_value (fmin, optpara, n) + + + +fmin = PRAXIS( t0, MACHEP, h0, n, PRIN, optpara, TANGENT_VALUE2, fmin ) + +! The optimal optpara-vector is not necessarily the one that was last evaluated. +! TANGENT_VALUE is reexecuted with the optimal vector optpara, in order to update the ln(x) values +fmin = TANGENT_VALUE2( optpara, n ) + + +! ---------------------------------------------------------------------- +! If one component is a polymer (indicated by a low component-density) +! then get an estimate of the polymer-lean composition, by solving for +! xi_p1 = ( xi_p2 * phii_p2) / phii_p1 (phase equilibrium condition, +! with p1 for phase 1) +! ---------------------------------------------------------------------- +IF ( MINVAL( lnx(1,1:ncomp) ) < MINVAL( lnx(2,1:ncomp) ) ) THEN + min_ph = 1 + other_ph = 2 +ELSE + min_ph = 2 + other_ph = 1 +ENDIF +small_i = MINLOC( lnx(min_ph,1:ncomp), 1 ) +! --- if one component is a polymer ------------------------------------ +IF ( MINVAL( lnx(min_ph,1:ncomp) ) < -20.0 ) THEN + CALL FUGACITY ( lnphi ) + lnx(min_ph,small_i) = lnx(other_ph,small_i)+lnphi(other_ph,small_i) - lnphi(min_ph,small_i) + optpara(small_i) = lnx(2,small_i) + LOG( SUM( EXP( optpara(1:ncomp) ) ) ) +END IF + +! ---------------------------------------------------------------------- +! caution: these initial values are for a flashcase overwritten in +! SUBROUTINE determine_flash_it2, because in that case, the lnx-values +! treated as ln(mole_number). +! ---------------------------------------------------------------------- +val_init(1) = dense(1) +val_init(2) = dense(2) +val_init(3) = t +val_init(4) = p +DO ph = 1,nphas + DO k = 1,ncomp + val_init(4+k+(ph-1)*ncomp) = lnx(ph,k) + END DO +END DO +!alpha = optpara(1) + + +!DEALLOCATE( optpara, d, g, xtemp, gtemp ) +DEALLOCATE( optpara ) + +END SUBROUTINE tangent_plane + + +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! + SUBROUTINE determine_flash_it2 +! + USE BASIC_VARIABLES + IMPLICIT NONE +! +! ---------------------------------------------------------------------- + INTEGER :: i, k, ph + REAL :: n_phase1, n_phase2, max_x_diff +! ---------------------------------------------------------------------- + + IF ( MINVAL( lnx(1,1:ncomp) ) < MINVAL( lnx(2,1:ncomp) ) ) THEN + it(1) = 'x11' + it(2) = 'x12' + IF (ncomp >= 3) it(3) = 'x13' + IF (ncomp >= 4) it(4) = 'x14' + IF (ncomp >= 5) it(5) = 'x15' + sum_rel(1) = 'nfl' + ELSE + it(1) = 'x21' + it(2) = 'x22' + IF (ncomp >= 3) it(3) = 'x23' + IF (ncomp >= 4) it(4) = 'x24' + IF (ncomp >= 5) it(5) = 'x25' + sum_rel(2) = 'nfl' + ENDIF + max_x_diff = 0.0 + DO i = 1,ncomp + IF ( ABS( EXP( lnx(1,i) ) - EXP( lnx(2,i) ) ) > max_x_diff ) THEN + max_x_diff = ABS( EXP( lnx(1,i) ) - EXP( lnx(2,i) ) ) + n_phase1 = ( xif(i) - EXP( lnx(2,i) ) ) / ( EXP( lnx(1,i) ) - EXP( lnx(2,i) ) ) + n_phase2 = 1.0 - n_phase1 + END IF + END DO + lnx(1,1:ncomp) = lnx(1,1:ncomp) + LOG( n_phase1 ) ! these x's are treated as mole numbers + lnx(2,1:ncomp) = lnx(2,1:ncomp) + LOG( n_phase2 ) ! these x's are treated as mole numbers + + + val_init(1) = dense(1) + val_init(2) = dense(2) + val_init(3) = t + val_init(4) = p + DO ph = 1,nphas + DO k = 1,ncomp + val_init(4+k+(ph-1)*ncomp) = lnx(ph,k) ! - LOG( SUM( EXP( lnx(ph,1:ncomp) ) ) ) + ! write (*,*) ph,k, lnx(ph,k) + END DO + END DO + +END SUBROUTINE determine_flash_it2 + +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! SUBROUTINE poly_sta_var +! +! This subroutine generates starting values for mole fractons of +! polymer-solvent systems. +! The determination of these starting values follows a two-step +! procedure. Fist, the equilibrium concentration of the polymer-rich +! phase is estimated with the assumption of zero concentration +! of polymer in the polymer-lean-phase. This is achieved in the +! SUBROUTINE POLYMER_FREE. (Only one equation has to be iterated +! for this case). Once this is achieved, the rigorous calculation +! is triggered. If it converges, fine! If no solution is obtained, +! the pressure is somewhat reduced, the procedure is repeated and +! a calculation is started to approach the originally specified +! pressure. +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! + SUBROUTINE poly_sta_var (converg) +! + USE BASIC_VARIABLES + IMPLICIT NONE +! +! ---------------------------------------------------------------------- + INTEGER, INTENT(IN OUT) :: converg +! +! ---------------------------------------------------------------------- + INTEGER :: k,ph,sol + REAL :: p_spec,solution(10,4+nc*np) +! ---------------------------------------------------------------------- + + p_spec = p + + find_equilibrium: DO + + CALL polymer_free(p_spec,sol,solution) + + WRITE (*,*) ' ' + WRITE (*,*) ' GENERATING STARTING VALUES' + + val_init(1) = solution(1,1) ! approx.solutions for next iteration + val_init(2) = solution(1,2) ! approx.solutions for next iteration + val_init(3) = solution(1,3) ! approx.solutions for next iteration + val_init(4) = solution(1,4) ! approx.solutions for next iteration + DO ph = 1,nphas + DO k = 1,ncomp + val_init(4+k+(ph-1)*ncomp) = solution(1,4+k+(ph-1)*ncomp) + END DO + END DO + val_init(7) = -10000.0 ! start.val. for lnx(2,1) for iterat. + + IF (p /= p_spec) & + WRITE (*,*) ' INITIAL EQUILIBRIUM CALC. FAILD. NEXT STEP STARTS' + + IF (p == p_spec) THEN + n_unkw = ncomp ! number of quantities to be iterated + it(1)='x11' ! iteration of mol fraction of comp.1 phase 1 + it(2)='x21' ! iteration of mol fraction of comp.1 phase 2 + CALL objective_ctrl (converg) + ELSE + outp = 0 ! output to terminal + running ='p' ! Pressure is running var. in PHASE_EQUILIB + CALL phase_equilib(p_spec,5.0,converg) + END IF + + IF (converg == 1) EXIT find_equilibrium + p = p * 0.9 + IF ( p < (0.7*p_spec) ) WRITE (*,*) ' NO SOLUTION FOUND' + IF ( p < (0.7*p_spec) ) STOP + + END DO find_equilibrium + + WRITE (*,*) ' FINISHED: POLY_STA_VAR' + +END SUBROUTINE poly_sta_var + + +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! SUBROUTINE x_summation +! +! This subroutine solves the summation relation: xi=1-sum(xj) +! The variable "sum_rel(i)" contains the information, which mole +! fraction is the one to be calculated here. Consider the example +! sum_rel(1)='x12'. The fist letter 'x' of this variable indicates, +! that this subroutine needs to be executed and that the mole +! fraction of a component has to be calculated. The second letter +! of the string points to phase 1, the third letter to component 2. +! If the fist letter is 'e', not 'x', then the subroutine +! NEUTR_CHARGE is called. This is the case of electrolyte solutions, +! neutral charges have to be enforced in all phases (see below). +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! + SUBROUTINE x_summation +! + USE BASIC_VARIABLES + IMPLICIT NONE +! +! ---------------------------------------------------------------------- + INTEGER :: i, j, comp_i, ph_i + REAL :: sum_x + CHARACTER (LEN=2) :: phasno + CHARACTER (LEN=2) :: compno + LOGICAL :: flashcase2 +! ---------------------------------------------------------------------- + +DO j = 1, nphas + IF (sum_rel(j)(1:3) == 'nfl') THEN + CALL new_flash (j) + RETURN + END IF +END DO + + + +flashcase2 = .false. + +DO j = 1, nphas + + IF (sum_rel(j)(1:1) == 'x') THEN + + phasno = sum_rel(j)(2:2) + READ(phasno,*) ph_i + compno = sum_rel(j)(3:3) + READ(compno,*) comp_i + IF ( sum_rel(nphas+j)(1:1) == 'e' ) CALL neutr_charge(nphas+j) + + sum_x = 0.0 + DO i = 1, ncomp + IF ( i /= comp_i ) sum_x = sum_x + xi(ph_i,i) + END DO + xi(ph_i,comp_i) = 1.0 - sum_x + IF ( xi(ph_i,comp_i ) < 0.0 ) xi(ph_i,comp_i) = 0.0 + IF ( xi(ph_i,comp_i ) /= 0.0 ) THEN + lnx(ph_i,comp_i) = LOG( xi(ph_i,comp_i) ) + ELSE + lnx(ph_i,comp_i) = -100000.0 + END IF + ! write (*,*) 'sum_x',ph_i,comp_i,lnx(ph_i,comp_i),xi(ph_i,comp_i) + + ELSE IF ( sum_rel(j)(1:2) == 'fl' ) THEN + + flashcase2 = .true. + ! ------------------------------------------------------------------ + ! This case is true when all molefractions of one phase are + ! determined from a component balance. What is needed to + ! calculate all molefractions of that phase are all mole- + ! fractions of the other phase (nphas=2, so far) and the + ! phase fraction alpha. + ! Alpha is calculated (in FLASH_ALPHA) from the mole fraction + ! of component {sum_rel(j)(3:3)}. IF sum_rel(2)='fl3', then + ! the alpha is determined from the molefraction of comp. 3 and + ! the molefraction of phase 2 is then completely determined ELSE + ! ------------------------------------------------------------------ + + ELSE + WRITE (*,*) 'summation relation not defined' + STOP + END IF + +END DO + +IF ( it(1) == 'fls' ) CALL flash_sum +IF ( flashcase2 ) CALL flash_alpha + +END SUBROUTINE x_summation + + + +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! SUBROUTINE FUGACITY +! +! This subroutine serves as an interface to the eos-subroutines. +! (1) case 1, when ensemble_flag = 'tp' +! The subroutine gives the residual chemical potential: +! mu_i^res(T,p,x)/kT = ln( phi_i ) +! and in addition, the densities that satisfy the specified p +! (2) case 2, when ensemble_flag = 'tv' +! The subroutine gives the residual chemical potential: +! --> mu_i^res(T,rho,x)/kT +! and in addition the resulting pressure for the given density. +! The term "residual" means difference of the property and the same +! property for an ideal gas mixture. +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! + SUBROUTINE FUGACITY (ln_phi) +! + USE BASIC_VARIABLES + USE EOS_VARIABLES, ONLY: phas, x, eta, eta_start, lnphi, fres, rho, pges, KBOL + IMPLICIT NONE +! +! ---------------------------------------------------------------------- + REAL, INTENT(OUT) :: ln_phi(np,nc) +! +! --- local variables -------------------------------------------------- + INTEGER :: ph +! ---------------------------------------------------------------------- +! +IF (eos < 2) THEN + + DO ph = 1,nphas + + phas = ph + eta_start = densta(ph) + x(1:ncomp) = xi(ph,1:ncomp) + + IF (p < 1.E-100) THEN + WRITE(*,*) ' FUGACITY: PRESSURE TOO LOW', p + p = 1.E-6 + END IF + + IF (num == 0) CALL PHI_EOS + IF (num == 1) CALL PHI_NUMERICAL + !!IF (num == 2) CALL PHI_CRITICAL_RENORM + IF (num == 2) write(*,*) 'CRITICAL RENORM NOT INCLUDED YET' + + dense(ph) = eta + ln_phi(ph,1:ncomp) = lnphi(1:ncomp) + ! gibbs(ph) = fres + sum( xi(ph,1:ncomp)*( log( xi(ph,1:ncomp)*rho) - 1.0 ) ) & + ! + (pges * 1.d-30) / (KBOL*t*rho) ! includes ideal gas contribution + + ! f_res(ph) = fres + ! write (*,'(i3,4G20.11)') ph,eta,lnphi(1),lnphi(2) + ! DO i = 1,ncomp + ! DO j=1,NINT(parame(i,12)) + ! mxx(ph,i,j) = mx(i,j) + ! END DO + ! END DO + + END DO + +ELSE + +! IF (eos == 2) CALL srk_eos (ln_phi) +! IF (eos == 3) CALL pr_eos (ln_phi) +! dense(1) = 0.01 +! dense(2) = 0.3 +! IF (eos == 4.OR.eos == 5.OR.eos == 6.OR.eos == 8) CALL lj_fugacity(ln_phi) +! IF (eos == 7) CALL sw_fugacity(ln_phi) +! IF (eos == 9) CALL lj_bh_fug(ln_phi) + +END IF + +END SUBROUTINE FUGACITY + + + + + + + +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! SUBROUTINE FUGACITY +! +! This subroutine serves as an interface to the eos-subroutines. +! (1) case 1, when ensemble_flag = 'tp' +! The subroutine gives the residual chemical potential: +! mu_i^res(T,p,x)/kT = ln( phi_i ) +! and in addition, the densities that satisfy the specified p +! (2) case 2, when ensemble_flag = 'tv' +! The subroutine gives the residual chemical potential: +! --> mu_i^res(T,rho,x)/kT +! and in addition the resulting pressure for the given density. +! The term "residual" means difference of the property and the same +! property for an ideal gas mixture. +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! + SUBROUTINE FUGACITY2 (ln_phi) +! + USE BASIC_VARIABLES + USE EOS_VARIABLES, ONLY: phas, x, eta, eta_start, lnphi, fres, rho, pges, KBOL + IMPLICIT NONE +! +! ---------------------------------------------------------------------- + REAL, INTENT(OUT) :: ln_phi(np,nc) +! +! --- local variables -------------------------------------------------- + INTEGER :: ph +! ---------------------------------------------------------------------- +! +IF (eos < 2) THEN + + ! DO ph = 1,nphas + + phas = 2! ph + eta_start = densta(2) + x(1:ncomp) = xi(2,1:ncomp) + + IF (p < 1.E-100) THEN + WRITE(*,*) ' FUGACITY: PRESSURE TOO LOW', p + p = 1.E-6 + END IF + + IF (num == 0) CALL PHI_EOS2 + IF (num == 1) CALL PHI_NUMERICAL + !!IF (num == 2) CALL PHI_CRITICAL_RENORM + IF (num == 2) write(*,*) 'CRITICAL RENORM NOT INCLUDED YET' + + dense(2) = eta + ln_phi(2,1:ncomp) = lnphi(1:ncomp) + ! gibbs(ph) = fres + sum( xi(ph,1:ncomp)*( log( xi(ph,1:ncomp)*rho) - 1.0 ) ) & + ! + (pges * 1.d-30) / (KBOL*t*rho) ! includes ideal gas contribution + + ! f_res(ph) = fres + ! write (*,'(i3,4G20.11)') ph,eta,lnphi(1),lnphi(2) + ! DO i = 1,ncomp + ! DO j=1,NINT(parame(i,12)) + ! mxx(ph,i,j) = mx(i,j) + ! END DO + ! END DO + + ! END DO + +ELSE + +! IF (eos == 2) CALL srk_eos (ln_phi) +! IF (eos == 3) CALL pr_eos (ln_phi) +! dense(1) = 0.01 +! dense(2) = 0.3 +! IF (eos == 4.OR.eos == 5.OR.eos == 6.OR.eos == 8) CALL lj_fugacity(ln_phi) +! IF (eos == 7) CALL sw_fugacity(ln_phi) +! IF (eos == 9) CALL lj_bh_fug(ln_phi) + +END IF + +END SUBROUTINE FUGACITY2 + + + + + + + + + + +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! SUBROUTINE enthalpy_etc +! +! This subroutine serves as an interface to the EOS-routines. The +! residual enthalpy h_res, residual entropy s_res, residual Gibbs +! enthalpy g_res, and residual heat capacity at constant pressure +! (cp_res) corresponding to converged conditions are calculated. +! The conditions in (T,P,xi,rho) need to be converged equilibrium +! conditions !! +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! + SUBROUTINE enthalpy_etc +! + USE BASIC_VARIABLES + USE EOS_VARIABLES + IMPLICIT NONE +! + INTEGER :: ph +! ------------------------------------------------------------------ + +IF (eos <= 1) THEN + + DO ph=1,nphas + + phas = ph + eta = dense(ph) +! eta_start = dense(ph) + x(1:ncomp) = xi(ph,1:ncomp) + + IF(num == 0) THEN + CALL H_EOS + ELSE + IF(num == 1) CALL H_numerical + IF(num == 2) write (*,*) 'enthalpy_etc: incorporate H_EOS_RN' + IF(num == 2) stop +! IF(num == 2) CALL H_EOS_rn + END IF + enthal(ph) = h_res + entrop(ph) = s_res + ! gibbs(ph) = h_res - t * s_res ! already defined in eos.f90 (including ideal gas) + cpres(ph) = cp_res + + END DO + IF (nphas == 2) h_lv = enthal(2)-enthal(1) + +ENDIF + +END SUBROUTINE enthalpy_etc + + +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! SUBROUTINE dens_calc +! +! This subroutine serves as an interface to the EOS-routines. The +! densities corresponding to given (P,T,xi) are calculated. +! (Note: the more common interface is SUBROUTINE FUGACITY. +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! + SUBROUTINE dens_calc(rho_phas) +! + USE BASIC_VARIABLES + USE EOS_VARIABLES + IMPLICIT NONE +! +! +!------------------------------------------------------------------ + REAL, INTENT(OUT) :: rho_phas(np) +! + INTEGER :: ph +!------------------------------------------------------------------ + + +DO ph = 1, nphas + + IF (eos < 2) THEN + + phas = ph + eta = densta(ph) + eta_start = densta(ph) + x(1:ncomp) = xi(ph,1:ncomp) + + CALL PERTURBATION_PARAMETER + CALL DENSITY_ITERATION + + dense(ph)= eta + rho_phas(ph) = eta/z3t + + ELSE + write (*,*) ' SUBROUTINE DENS_CALC not available for cubic EOS' + stop + END IF + +END DO + +END SUBROUTINE dens_calc + + +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! + SUBROUTINE fden_calc (fden, rhoi) +! + USE BASIC_VARIABLES + USE EOS_VARIABLES + IMPLICIT NONE +! +! ---------------------------------------------------------------------- + REAL, INTENT(OUT) :: fden + REAL, INTENT(IN OUT) :: rhoi(nc) +! ---------------------------------------------------------------------- + REAL :: rhot, fden_id +! ---------------------------------------------------------------------- + + +IF (eos < 2) THEN + + rhot = SUM( rhoi(1:ncomp) ) + x(1:ncomp) = rhoi(1:ncomp) / rhot + + CALL PERTURBATION_PARAMETER + eta = rhot * z3t + eta_start = eta + + IF (num == 0) THEN + CALL F_EOS + ELSE IF(num == 1) THEN + CALL F_NUMERICAL + ELSE + write (*,*) 'deactivated this line when making a transition to f90' + stop + ! CALL F_EOS_rn + END IF + + fden_id = SUM( rhoi(1:ncomp) * ( LOG( rhoi(1:ncomp) ) - 1.0 ) ) + + fden = fres * rhot + fden_id + +ELSE + write (*,*) ' SUBROUTINE FDEN_CALC not available for cubic EOS' + stop +END IF + +END SUBROUTINE fden_calc + + + + +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! SUBROUTINE polymer_free +! +! This subroutine performes a phase equilibrium calculation assuming +! the polymer-lean hase to be polymer-free (x_poly=0). Only the +! equality of the solvent-fugacities has to be ensured (only one +! equation to be iterated). This procedure delivers very good +! appoximations for the polymer-rich phase up-to fairly close to the +! mixture critical point. Both, liquid-liquid and vapor-liquid +! equilibria can be calculated. +! See also comments to SUBROUTINE POLY_STA_VAR. +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! + SUBROUTINE polymer_free (p_spec,sol,solution) +! + USE BASIC_VARIABLES + IMPLICIT NONE +! +! ---------------------------------------------------------------------- + REAL, INTENT(IN OUT) :: p_spec + INTEGER, INTENT(OUT) :: sol + REAL, INTENT(OUT) :: solution(10,4+nc*np) +! +! ---------------------------------------------------------------------- + INTEGER :: k,j,ph, converg + REAL :: grid(10) +! ---------------------------------------------------------------------- + + sol = 0 + + grid(1)=0.98 + grid(2)=0.9 + grid(3)=0.7 + grid(4)=0.5 + grid(5)=0.3 + grid(6)=0.2 + grid(7)=0.1 + grid(8)=0.05 + + DO WHILE ( sol == 0 ) + + DO j = 1,8 + ! Phase 2 is solvent-phase + ! starting value for xi(1,1) of polymer-phase 1: w_polymer=0.95 to 0.05 + ! from simple approximate equation + xi(1,1) = grid(j) / ( (1.0-grid(j)) * mm(1) / mm(2) ) !xi(1,1) Phase 1 Komponente 1 + IF ( mm(1) < 5000.0 ) xi(1,1) = xi(1,1) * 0.8 + xi(1,2) = 1.0 - xi(1,1) !xi(1,2) Phase 1 Komponente 2 + lnx(1,1) = LOG(xi(1,1)) + lnx(1,2) = LOG(xi(1,2)) + lnx(2,1) = -1.E10 !ln(xi) Phase 2 Komponente 1 + lnx(2,2) = 0.0 !ln(xi) Phase 2 Komponente 2 + + + + val_init(1) = 0.45 ! starting density targeting at a liquid phase + val_init(2) = 0.0001 ! starting density targeting at a vapor phase + ! val_init(2) = 0.45 + val_init(3) = t + val_init(4) = p + DO ph = 1,nphas + DO k = 1,ncomp + val_init(4+k+(ph-1)*ncomp) = lnx(ph,k) + END DO + END DO + + + + + n_unkw = ncomp-1 ! number of quantities to be iterated + it(1) = 'x11' ! iteration of mol fraction of comp.1 phase 1 + it(2) = ' ' + sum_rel(1) = 'x12' ! summation relation: x12 = 1 - sum(x1j) + sum_rel(2) = 'x22' + + CALL objective_ctrl (converg) + + IF (converg == 1 .AND. ABS(dense(1)/dense(2)-1.0) > 1.d-3 .AND. dense(1) > 0.1) THEN + IF (sol == 0) THEN + sol = sol + 1 + DO k = 1,4+ncomp*nphas + solution(sol,k) = val_conv(k) + END DO + ELSE IF (ABS(solution(sol,5)/lnx(1,1)-1.0) > 1.d-2) THEN + sol = sol + 1 + DO k = 1,4+ncomp*nphas + solution(sol,k) = val_conv(k) + END DO + END IF + END IF + + END DO + + + + + + IF (sol == 0) THEN + WRITE (*,*) ' no initial solution found' + p = p*0.9 + IF (p < (0.7*p_spec)) WRITE (*,*) ' NO SOLUTION FOUND' + IF (p < (0.7*p_spec)) STOP + ELSE IF (sol > 1) THEN + ! write (*,*) ' ' + ! write (*,*) ' ',sol,' solutions found:' + ! write (*,*) ' lnx(1,1), dichte_1, dichte_2' + ! DO k = 1,sol + ! write (*,*) solution(k,5),solution(k,1),solution(k,2) + ! END DO + END IF + END DO + + n_unkw = ncomp ! number of quantities to be iterated + it(1) = 'x11' ! iteration of mol fraction of comp.1 phase 1 + it(2) = 'x21' ! iteration of mol fraction of comp.1 phase 2 + sum_rel(1) = 'x12' ! summation relation: x12 = 1 - sum(x1j) + sum_rel(2) = 'x22' ! summation relation: x22 = 1 - sum(x2j) + + + END SUBROUTINE polymer_free + + + + + +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! SUBROUTINE phase_equilib +! +! This subroutine varies a predefined "running variable" and +! organizes phase equilibrium calculations. For an isotherm +! calculation e.g., the running variable is often the pressure. The +! code is designed to deliver only converged solutions. In order to +! enforce convergence, a step-width adjustment (reduction) is +! implemented. + +! VARIABLE LIST: +! running defines the running variable. For example: if you want +! to calculate the vapor pressure curve of a component +! starting from 100�C to 200�C, then running is 't'. The +! temperature is step-wise increased until the end- +! -temperature of 200�C is reached. +! (in this example end_x=200+273.15) +! end_x end point for running variable +! steps No. of calculation steps towards the end point of calc. +! converg 0 if no convergence achieved, 1 if converged solution +! +! PREREQUISITES: +! prior to execution of this routine, the follwing variables have to +! be defined: "val_init" an array containing the starting values for +! this iteration, "it(i)" provides the information, which variable is +! determined iteratively, "sum_rel(i)" indicates, which mole fraction +! is determined from the summation relation sum(xi)=1. Furthermore, +! the number of phases and the variables provided by the subroutine +! INPUT are required. +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! + SUBROUTINE phase_equilib (end_x,steps,converg) +! + USE BASIC_VARIABLES + IMPLICIT NONE +! +! ---------------------------------------------------------------------- + REAL, INTENT(IN) :: end_x + REAL, INTENT(IN) :: steps + INTEGER, INTENT(OUT) :: converg +! +! ---------------------------------------------------------------------- + INTEGER :: k, count1,count2,runindex,maxiter + REAL :: delta_x,delta_org,val_org,runvar + CHARACTER (LEN=2) :: compon + LOGICAL :: continue_cycle +! ---------------------------------------------------------------------- + +IF (running(1:2) == 'd1') runindex = 1 +IF (running(1:2) == 'd2') runindex = 2 +IF (running(1:1) == 't') runindex = 3 +IF (running(1:1) == 'p') runindex = 4 +IF (running(1:2) == 'x1') compon = running(3:3) +IF (running(1:2) == 'x1') READ(compon,*) k +IF (running(1:2) == 'x1') runindex = 4+k +IF (running(1:2) == 'x2') compon = running(3:3) +IF (running(1:2) == 'x2') READ(compon,*) k +IF (running(1:2) == 'x2') runindex = 4+ncomp+k +IF (running(1:2) == 'l1') compon = running(3:3) +IF (running(1:2) == 'l1') READ(compon,*) k +IF (running(1:2) == 'l1') runindex = 4+k +IF (running(1:2) == 'l2') compon = running(3:3) +IF (running(1:2) == 'l2') READ(compon,*) k +IF (running(1:2) == 'l2') runindex = 4+ncomp+k + +maxiter = 200 +IF ( ncomp >= 3 ) maxiter = 1000 +count1 = 0 +count2 = 0 +delta_x = ( end_x - val_init(runindex) ) / steps !J: calc increment in running var = (phi_end - phi_init)/steps +delta_org = ( end_x - val_init(runindex) ) / steps +val_org = val_init(runindex) +IF ( running(1:1) == 'x' ) THEN + delta_x = ( end_x - EXP(val_init(runindex)) ) / steps + delta_org = ( end_x - EXP(val_init(runindex)) ) / steps + val_org = EXP(val_init(runindex)) +END IF + +continue_cycle = .true. + +DO WHILE ( continue_cycle ) + + count1 = count1 + 1 + count2 = count2 + 1 + ! val_org = val_init(runindex) + + + CALL objective_ctrl (converg) + + IF (converg == 1) THEN + val_init( 1:(4+ncomp*nphas) ) = val_conv( 1:(4+ncomp*nphas) ) + IF (outp == 1 .AND. (ABS(delta_x) > 0.1*ABS(delta_org) .OR. count2 == 2)) CALL output + ELSE + delta_x = delta_x / 2.0 + IF (num == 2) delta_x = delta_x / 2.0 + val_init(runindex) = val_org + IF (running(1:1) == 'x') val_init(runindex) = LOG(val_org) + continue_cycle = .true. + count2 = 0 + END IF + runvar = val_init(runindex) + IF (running(1:1) == 'x') runvar = EXP(val_init(runindex)) + + IF ( end_x == 0.0 .AND. running(1:1) /= 'x' ) THEN + IF ( ABS(runvar-end_x) < 1.E-8 ) continue_cycle = .false. + ELSE IF ( ABS((runvar-end_x)/end_x) < 1.E-8 ) THEN + ! IF(delta_org.NE.0.0) WRITE (*,*)' FINISHED ITERATION',count1 + continue_cycle = .false. + ELSE IF ( count1 == maxiter ) THEN + WRITE (*,*) ' MAX. NO OF ITERATIONS',count1 + converg = 0 + continue_cycle = .false. + ELSE IF ( ABS(delta_x) < 1.E-5*ABS(delta_org) ) THEN + ! WRITE (*,*) ' CLOSEST APPROACH REACHED',count1 + converg = 0 + continue_cycle = .false. + ELSE + continue_cycle = .true. + val_org = runvar + IF (ABS(runvar+delta_x-end_x) > ABS(runvar-end_x)) delta_x = end_x - runvar ! if end-point passed + val_init(runindex) = runvar + delta_x + IF (running(1:1) == 'x') val_init(runindex) = LOG(runvar+delta_x) + END IF + + IF (ABS(delta_x) < ABS(delta_org) .AND. count2 >= 5) THEN + delta_x = delta_x * 2.0 + count2 = 0 + END IF + +END DO ! continue_cycle + +END SUBROUTINE phase_equilib + +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! + SUBROUTINE new_flash (ph_it) +! + USE BASIC_VARIABLES + IMPLICIT NONE +! +! ---------------------------------------------------------------------- + INTEGER, INTENT(IN) :: ph_it +! +! ---------------------------------------------------------------------- + INTEGER :: i, ph_cal + REAL, DIMENSION(nc) :: ni_1, ni_2 +! ---------------------------------------------------------------------- + + ph_cal = 3 - ph_it ! for two phases only + + DO i = 1, ncomp + IF ( lnx(ph_it,i) < -300.0 ) THEN + ni_2(i) = 0.0 + ELSE + ni_2(i) = EXP( lnx(ph_it,i) ) + END IF + END DO + + DO i = 1, ncomp + ni_1(i) = xif(i)-ni_2(i) + IF ( ni_2(i) > xif(i) ) THEN + ni_2(i) = xif(i) + ni_1(i) = xif(i) * 1.E-20 + ENDIF + END DO + + xi(ph_it,1:ncomp) = ni_2(1:ncomp) / SUM( ni_2(1:ncomp) ) + DO i = 1, ncomp + IF ( xi(ph_it,i) >= 1.E-300 ) lnx(ph_it,i) = LOG( xi(ph_it,i) ) + END DO + xi(ph_cal,1:ncomp) = ni_1(1:ncomp) / SUM( ni_1(1:ncomp) ) + lnx(ph_cal,1:ncomp) = LOG( xi(ph_cal,1:ncomp) ) + +END SUBROUTINE new_flash + + +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! SUBROUTINE PHI_EOS +! +! This subroutine gives the residual chemical potential: +! --> mu_i^res(T,p,x)/kT = ln( phi_i ) when ensemble_flag = 'tp' +! The required input for this case (T, p, x(nc)) and as a starting value +! eta_start +! +! or it gives +! +! --> mu_i^res(T,rho,x)/kT when ensemble_flag = 'tv' +! The required input for this case (T, eta_start, x(nc)). Note that +! eta_start is the specified density (packing fraction) in this case. +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! + SUBROUTINE PHI_EOS +! + USE PARAMETERS + USE EOS_VARIABLES + USE EOS_CONSTANTS + + + IMPLICIT NONE +! +! --- local variables--------------------------------------------------- + INTEGER :: i, j, k, ki, l, m + REAL :: z0, z1, z2, z3, z0_rk, z1_rk, z2_rk, z3_rk + REAL :: zms, m_mean + REAL, DIMENSION(nc) :: mhs, mdsp, mhc, myres + REAL, DIMENSION(nc) :: m_rk + REAL :: gij_rk(nc,nc) + REAL :: zres, zges + REAL :: dpdz, dpdz2 + + REAL :: I1, I2, I1_rk, I2_rk + REAL :: ord1_rk, ord2_rk + REAL :: c1_con, c2_con, c1_rk + REAL :: zmr, nmr, zmr_rk, nmr_rk, um_rk + REAL, DIMENSION(nc,0:6) :: ap_rk, bp_rk + + LOGICAL :: assoc + REAL :: ass_s2, m_hbon(nc) + + REAL :: fdd_rk, fqq_rk, fdq_rk + REAL, DIMENSION(nc) :: my_dd, my_qq, my_dq +! ---------------------------------------------------------------------- + +! ---------------------------------------------------------------------- +! obtain parameters and density independent expressions +! ---------------------------------------------------------------------- +CALL PERTURBATION_PARAMETER + + +! ---------------------------------------------------------------------- +! density iteration: (pTx)-ensemble OR p calc.: (pvx)-ensemble +! ---------------------------------------------------------------------- +IF (ensemble_flag == 'tp') THEN + CALL DENSITY_ITERATION +ELSEIF (ensemble_flag == 'tv') THEN + eta = eta_start + CALL P_EOS +ELSE + write (*,*) 'PHI_EOS: define ensemble, ensemble_flag == (pv) or (pt)' + stop +END IF + + +! --- Eq.(A.8) --------------------------------------------------------- +rho = eta / z3t +z0 = z0t * rho +z1 = z1t * rho +z2 = z2t * rho +z3 = z3t * rho + +m_mean = z0t / (PI/6.0) +zms = 1.0 - eta + +! ---------------------------------------------------------------------- +! compressibility factor z = p/(kT*rho) +! ---------------------------------------------------------------------- +zges = (p * 1.d-30) / (KBOL*t*rho) +IF ( ensemble_flag == 'tv' ) zges = (pges * 1.d-30) / (KBOL*t*rho) +zres = zges - 1.0 + + + +! ====================================================================== +! calculate the derivatives of f to mole fraction x ( d(f)/d(x) ) +! ====================================================================== + +DO k = 1, ncomp + + z0_rk = PI/6.0 * mseg(k) + z1_rk = PI/6.0 * mseg(k) * dhs(k) + z2_rk = PI/6.0 * mseg(k) * dhs(k)*dhs(k) + z3_rk = PI/6.0 * mseg(k) * dhs(k)**3 + +! --- derivative d(m_mean)/d(x) ---------------------------------------- + m_rk(k) = ( mseg(k) - m_mean ) / rho + ! lij(1,2)= -0.050 + ! lij(2,1)=lij(1,2) + ! r_m2dx(k)=0.0 + ! m_mean2=0.0 + ! DO i =1,ncomp + ! r_m2dx(k)=r_m2dx(k)+2.0*x(i)*(mseg(i)+mseg(k))/2.0*(1.0-lij(i,k)) + ! DO j =1,ncomp + ! m_mean2=m_mean2+x(i)*x(j)*(mseg(i)+mseg(j))/2.0*(1.0-lij(i,j)) + ! ENDDO + ! ENDDO + + ! -------------------------------------------------------------------- + ! d(f)/d(x) : hard sphere contribution + ! -------------------------------------------------------------------- + mhs(k) = 6.0/PI* ( 3.0*(z1_rk*z2+z1*z2_rk)/zms + 3.0*z1*z2*z3_rk/zms/zms & + + 3.0*z2*z2*z2_rk/z3/zms/zms + z2**3 *z3_rk*(3.0*z3-1.0)/z3/z3/zms**3 & + + ((3.0*z2*z2*z2_rk*z3-2.0*z2**3 *z3_rk)/z3**3 -z0_rk) *LOG(zms) & + + (z0-z2**3 /z3/z3)*z3_rk/zms ) + + ! -------------------------------------------------------------------- + ! d(f)/d(x) : chain term + ! -------------------------------------------------------------------- + DO i = 1, ncomp + DO j = 1, ncomp + gij(i,j) = 1.0/zms + 3.0*dij_ab(i,j)*z2/zms/zms + 2.0*(dij_ab(i,j)*z2)**2 /zms**3 + gij_rk(i,j) = z3_rk/zms/zms & + + 3.0*dij_ab(i,j)*(z2_rk+2.0*z2*z3_rk/zms)/zms/zms & + + dij_ab(i,j)**2 *z2/zms**3 *(4.0*z2_rk+6.0*z2*z3_rk/zms) + END DO + END DO + + mhc(k) = 0.0 + DO i = 1, ncomp + mhc(k) = mhc(k) + x(i)*rho * (1.0-mseg(i)) / gij(i,i) * gij_rk(i,i) + END DO + mhc(k) = mhc(k) + ( 1.0-mseg(k)) * LOG( gij(k,k) ) + + + ! -------------------------------------------------------------------- + ! PC-SAFT: d(f)/d(x) : dispersion contribution + ! -------------------------------------------------------------------- + IF (eos == 1) THEN + + ! --- derivatives of apar, bpar to rho_k --------------------------- + DO m = 0, 6 + ap_rk(k,m) = m_rk(k)/m_mean**2 * ( ap(m,2) + (3.0 -4.0/m_mean) *ap(m,3) ) + bp_rk(k,m) = m_rk(k)/m_mean**2 * ( bp(m,2) + (3.0 -4.0/m_mean) *bp(m,3) ) + END DO + + I1 = 0.0 + I2 = 0.0 + I1_rk = 0.0 + I2_rk = 0.0 + DO m = 0, 6 + I1 = I1 + apar(m)*eta**REAL(m) + I2 = I2 + bpar(m)*eta**REAL(m) + I1_rk = I1_rk + apar(m)*REAL(m)*eta**REAL(m-1)*z3_rk + ap_rk(k,m)*eta**REAL(m) + I2_rk = I2_rk + bpar(m)*REAL(m)*eta**REAL(m-1)*z3_rk + bp_rk(k,m)*eta**REAL(m) + END DO + + ord1_rk = 0.0 + ord2_rk = 0.0 + DO i = 1,ncomp + ord1_rk = ord1_rk + 2.0*mseg(k)*rho*x(i)*mseg(i)*sig_ij(i,k)**3 *uij(i,k)/t + ord2_rk = ord2_rk + 2.0*mseg(k)*rho*x(i)*mseg(i)*sig_ij(i,k)**3 *(uij(i,k)/t)**2 + END DO + + c1_con= 1.0/ ( 1.0 + m_mean*(8.0*z3-2.0*z3*z3)/zms**4 & + + (1.0 - m_mean)*(20.0*z3-27.0*z3*z3 +12.0*z3**3 -2.0*z3**4 ) & + /(zms*(2.0-z3))**2 ) + c2_con= - c1_con*c1_con *( m_mean*(-4.0*z3*z3+20.0*z3+8.0)/zms**5 & + + (1.0 - m_mean) *(2.0*z3**3 +12.0*z3*z3-48.0*z3+40.0) & + /(zms*(2.0-z3))**3 ) + c1_rk= c2_con*z3_rk - c1_con*c1_con*m_rk(k) * ( (8.0*z3-2.0*z3*z3)/zms**4 & + - (-2.0*z3**4 +12.0*z3**3 -27.0*z3*z3+20.0*z3) / (zms*(2.0-z3))**2 ) + + mdsp(k) = -2.0*PI* ( order1*rho*rho*I1_rk + ord1_rk*I1 ) & + - PI* c1_con*m_mean * ( order2*rho*rho*I2_rk + ord2_rk*I2 ) & + - PI* ( c1_con*m_rk(k) + c1_rk*m_mean ) * order2*rho*rho*I2 + + ! -------------------------------------------------------------------- + ! SAFT: d(f)/d(x) : dispersion contribution + ! -------------------------------------------------------------------- + ELSE + + zmr = 0.0 + nmr = 0.0 + zmr_rk = 0.0 + nmr_rk = 0.0 + DO i = 1, ncomp + DO j = 1, ncomp + zmr = zmr + x(i)*x(j)*mseg(i)*mseg(j)*vij(i,j)*uij(i,j) + nmr = nmr + x(i)*x(j)*mseg(i)*mseg(j)*vij(i,j) + END DO + zmr_rk = zmr_rk + 2.0*mseg(k) * x(i)*mseg(i)*vij(k,i)*uij(k,i) + nmr_rk = nmr_rk + 2.0*mseg(k) * x(i)*mseg(i)*vij(k,i) + END DO + + um_rk = 1.0/nmr**2 * ( nmr*zmr_rk - zmr*nmr_rk ) + + mdsp(k) = 0.0 + DO i = 1,4 + DO j = 1,9 + mdsp(k) = mdsp(k) + dnm(i,j)*(um/t)**REAL(i)*(eta/tau)**REAL(j) & + * ( 1.0 + z3_rk*rho/eta*REAL(j) + um_rk*rho/um*REAL(i) ) + END DO + END DO + + END IF + ! --- end of dispersion contribution------------------------------------ + + + ! -------------------------------------------------------------------- + ! TPT-1-association according to Chapman et al. + ! -------------------------------------------------------------------- + m_hbon(k) = 0.0 + assoc = .false. + DO i = 1,ncomp + IF (nhb_typ(i) /= 0) assoc = .true. + END DO + IF (assoc) THEN + + ass_s2 = 0.0 + DO l = 1, nhb_typ(k) + ass_s2 = ass_s2 + nhb_no(k,l) * LOG(mx(k,l)) + END DO + + m_hbon(k)=ass_s2 + DO i = 1, ncomp + DO ki = 1, nhb_typ(i) + DO j = 1, ncomp + DO l = 1, nhb_typ(j) + m_hbon(k)= m_hbon(k) - rho*rho/2.0*x(i)*x(j) *mx(i,ki)*mx(j,l) *nhb_no(i,ki)*nhb_no(j,l) & + * gij_rk(i,j) * ass_d(i,j,ki,l) + END DO + END DO + END DO + END DO + + END IF + ! --- end of TPT-1-association accord. to Chapman -------------------- + + + ! -------------------------------------------------------------------- + ! polar terms + ! -------------------------------------------------------------------- + CALL PHI_POLAR ( k, z3_rk, fdd_rk, fqq_rk, fdq_rk ) + my_dd(k) = fdd_rk + my_qq(k) = fqq_rk + my_dq(k) = fdq_rk + + + ! -------------------------------------------------------------------- + ! d(f)/d(x) : summation of all contributions + ! -------------------------------------------------------------------- + myres(k) = mhs(k) +mhc(k) +mdsp(k) +m_hbon(k) +my_dd(k) +my_qq(k) +my_dq(k) + + + + +END DO + + +! ---------------------------------------------------------------------- +! finally calculate +! mu_i^res(T,p,x)/kT = ln( phi_i ) when ensemble_flag = 'tp' +! mu_i^res(T,rho,x)/kT when ensemble_flag = 'tv' +! ---------------------------------------------------------------------- + +DO k = 1, ncomp + ! write (*,*) k,myres(k) +LOG(rho*x(k)),rho + IF (ensemble_flag == 'tp' ) lnphi(k) = myres(k) - LOG(zges) + IF (ensemble_flag == 'tv' ) lnphi(k) = myres(k) + ! write (*,*) 'in',k,EXP(lnphi(k)),LOG(zges),eta +END DO +!write (*,'(5G18.10)') lnphi(1),rho + +dpdz = pgesdz +dpdz2 = pgesd2 + +END SUBROUTINE PHI_EOS + + + + + + + + +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! SUBROUTINE PHI_EOS +! +! This subroutine gives the residual chemical potential: +! --> mu_i^res(T,p,x)/kT = ln( phi_i ) when ensemble_flag = 'tp' +! The required input for this case (T, p, x(nc)) and as a starting value +! eta_start +! +! or it gives +! +! --> mu_i^res(T,rho,x)/kT when ensemble_flag = 'tv' +! The required input for this case (T, eta_start, x(nc)). Note that +! eta_start is the specified density (packing fraction) in this case. +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! + SUBROUTINE PHI_EOS2 +! + USE PARAMETERS + USE EOS_VARIABLES + USE EOS_CONSTANTS + + + IMPLICIT NONE +! +! --- local variables--------------------------------------------------- + INTEGER :: i, j, k, ki, l, m + REAL :: z0, z1, z2, z3, z0_rk, z1_rk, z2_rk, z3_rk + REAL :: zms, m_mean + REAL, DIMENSION(nc) :: mhs, mdsp, mhc, myres + REAL, DIMENSION(nc) :: m_rk + REAL :: gij_rk(nc,nc) + REAL :: zres, zges + REAL :: dpdz, dpdz2 + + REAL :: I1, I2, I1_rk, I2_rk + REAL :: ord1_rk, ord2_rk + REAL :: c1_con, c2_con, c1_rk + REAL :: zmr, nmr, zmr_rk, nmr_rk, um_rk + REAL, DIMENSION(nc,0:6) :: ap_rk, bp_rk + + LOGICAL :: assoc + REAL :: ass_s2, m_hbon(nc) + + REAL :: fdd_rk, fqq_rk, fdq_rk + REAL, DIMENSION(nc) :: my_dd, my_qq, my_dq +! ---------------------------------------------------------------------- + +! ---------------------------------------------------------------------- +! obtain parameters and density independent expressions +! ---------------------------------------------------------------------- +CALL PERTURBATION_PARAMETER + + +! ---------------------------------------------------------------------- +! density iteration: (pTx)-ensemble OR p calc.: (pvx)-ensemble +! ---------------------------------------------------------------------- +IF (ensemble_flag == 'tp') THEN + CALL DENSITY_ITERATION +ELSEIF (ensemble_flag == 'tv') THEN + eta = eta_start + CALL P_EOS +ELSE + write (*,*) 'PHI_EOS: define ensemble, ensemble_flag == (pv) or (pt)' + stop +END IF + + +! --- Eq.(A.8) --------------------------------------------------------- +rho = eta / z3t +z0 = z0t * rho +z1 = z1t * rho +z2 = z2t * rho +z3 = z3t * rho + +m_mean = z0t / (PI/6.0) +zms = 1.0 - eta + +! ---------------------------------------------------------------------- +! compressibility factor z = p/(kT*rho) +! ---------------------------------------------------------------------- +zges = (p * 1.d-30) / (KBOL*t*rho) +IF ( ensemble_flag == 'tv' ) zges = (pges * 1.d-30) / (KBOL*t*rho) +zres = zges - 1.0 + + + +! ====================================================================== +! calculate the derivatives of f to mole fraction x ( d(f)/d(x) ) +! ====================================================================== + +DO k = 1, ncomp + + z0_rk = PI/6.0 * mseg(k) + z1_rk = PI/6.0 * mseg(k) * dhs(k) + z2_rk = PI/6.0 * mseg(k) * dhs(k)*dhs(k) + z3_rk = PI/6.0 * mseg(k) * dhs(k)**3 + +! --- derivative d(m_mean)/d(x) ---------------------------------------- + m_rk(k) = ( mseg(k) - m_mean ) / rho + ! lij(1,2)= -0.050 + ! lij(2,1)=lij(1,2) + ! r_m2dx(k)=0.0 + ! m_mean2=0.0 + ! DO i =1,ncomp + ! r_m2dx(k)=r_m2dx(k)+2.0*x(i)*(mseg(i)+mseg(k))/2.0*(1.0-lij(i,k)) + ! DO j =1,ncomp + ! m_mean2=m_mean2+x(i)*x(j)*(mseg(i)+mseg(j))/2.0*(1.0-lij(i,j)) + ! ENDDO + ! ENDDO + + ! -------------------------------------------------------------------- + ! d(f)/d(x) : hard sphere contribution + ! -------------------------------------------------------------------- + mhs(k) = 6.0/PI* ( 3.0*(z1_rk*z2+z1*z2_rk)/zms + 3.0*z1*z2*z3_rk/zms/zms & + + 3.0*z2*z2*z2_rk/z3/zms/zms + z2**3 *z3_rk*(3.0*z3-1.0)/z3/z3/zms**3 & + + ((3.0*z2*z2*z2_rk*z3-2.0*z2**3 *z3_rk)/z3**3 -z0_rk) *LOG(zms) & + + (z0-z2**3 /z3/z3)*z3_rk/zms ) + + ! -------------------------------------------------------------------- + ! d(f)/d(x) : chain term + ! -------------------------------------------------------------------- + DO i = 1, ncomp + DO j = 1, ncomp + gij(i,j) = 1.0/zms + 3.0*dij_ab(i,j)*z2/zms/zms + 2.0*(dij_ab(i,j)*z2)**2 /zms**3 + gij_rk(i,j) = z3_rk/zms/zms & + + 3.0*dij_ab(i,j)*(z2_rk+2.0*z2*z3_rk/zms)/zms/zms & + + dij_ab(i,j)**2 *z2/zms**3 *(4.0*z2_rk+6.0*z2*z3_rk/zms) + END DO + END DO + + mhc(k) = 0.0 + DO i = 1, ncomp + mhc(k) = mhc(k) + x(i)*rho * (1.0-mseg(i)) / gij(i,i) * gij_rk(i,i) + END DO + mhc(k) = mhc(k) + ( 1.0-mseg(k)) * LOG( gij(k,k) ) + + + ! -------------------------------------------------------------------- + ! PC-SAFT: d(f)/d(x) : dispersion contribution + ! -------------------------------------------------------------------- + IF (eos == 1) THEN + + ! --- derivatives of apar, bpar to rho_k --------------------------- + DO m = 0, 6 + ap_rk(k,m) = m_rk(k)/m_mean**2 * ( ap(m,2) + (3.0 -4.0/m_mean) *ap(m,3) ) + bp_rk(k,m) = m_rk(k)/m_mean**2 * ( bp(m,2) + (3.0 -4.0/m_mean) *bp(m,3) ) + END DO + + I1 = 0.0 + I2 = 0.0 + I1_rk = 0.0 + I2_rk = 0.0 + DO m = 0, 6 + I1 = I1 + apar(m)*eta**REAL(m) + I2 = I2 + bpar(m)*eta**REAL(m) + I1_rk = I1_rk + apar(m)*REAL(m)*eta**REAL(m-1)*z3_rk + ap_rk(k,m)*eta**REAL(m) + I2_rk = I2_rk + bpar(m)*REAL(m)*eta**REAL(m-1)*z3_rk + bp_rk(k,m)*eta**REAL(m) + END DO + + ord1_rk = 0.0 + ord2_rk = 0.0 + DO i = 1,ncomp + ord1_rk = ord1_rk + 2.0*mseg(k)*rho*x(i)*mseg(i)*sig_ij(i,k)**3 *uij(i,k)/t + ord2_rk = ord2_rk + 2.0*mseg(k)*rho*x(i)*mseg(i)*sig_ij(i,k)**3 *(uij(i,k)/t)**2 + END DO + + c1_con= 1.0/ ( 1.0 + m_mean*(8.0*z3-2.0*z3*z3)/zms**4 & + + (1.0 - m_mean)*(20.0*z3-27.0*z3*z3 +12.0*z3**3 -2.0*z3**4 ) & + /(zms*(2.0-z3))**2 ) + c2_con= - c1_con*c1_con *( m_mean*(-4.0*z3*z3+20.0*z3+8.0)/zms**5 & + + (1.0 - m_mean) *(2.0*z3**3 +12.0*z3*z3-48.0*z3+40.0) & + /(zms*(2.0-z3))**3 ) + c1_rk= c2_con*z3_rk - c1_con*c1_con*m_rk(k) * ( (8.0*z3-2.0*z3*z3)/zms**4 & + - (-2.0*z3**4 +12.0*z3**3 -27.0*z3*z3+20.0*z3) / (zms*(2.0-z3))**2 ) + + mdsp(k) = -2.0*PI* ( order1*rho*rho*I1_rk + ord1_rk*I1 ) & + - PI* c1_con*m_mean * ( order2*rho*rho*I2_rk + ord2_rk*I2 ) & + - PI* ( c1_con*m_rk(k) + c1_rk*m_mean ) * order2*rho*rho*I2 + + ! -------------------------------------------------------------------- + ! SAFT: d(f)/d(x) : dispersion contribution + ! -------------------------------------------------------------------- + ELSE + + zmr = 0.0 + nmr = 0.0 + zmr_rk = 0.0 + nmr_rk = 0.0 + DO i = 1, ncomp + DO j = 1, ncomp + zmr = zmr + x(i)*x(j)*mseg(i)*mseg(j)*vij(i,j)*uij(i,j) + nmr = nmr + x(i)*x(j)*mseg(i)*mseg(j)*vij(i,j) + END DO + zmr_rk = zmr_rk + 2.0*mseg(k) * x(i)*mseg(i)*vij(k,i)*uij(k,i) + nmr_rk = nmr_rk + 2.0*mseg(k) * x(i)*mseg(i)*vij(k,i) + END DO + + um_rk = 1.0/nmr**2 * ( nmr*zmr_rk - zmr*nmr_rk ) + + mdsp(k) = 0.0 + DO i = 1,4 + DO j = 1,9 + mdsp(k) = mdsp(k) + dnm(i,j)*(um/t)**REAL(i)*(eta/tau)**REAL(j) & + * ( 1.0 + z3_rk*rho/eta*REAL(j) + um_rk*rho/um*REAL(i) ) + END DO + END DO + + END IF + ! --- end of dispersion contribution------------------------------------ + + + ! -------------------------------------------------------------------- + ! TPT-1-association according to Chapman et al. + ! -------------------------------------------------------------------- + m_hbon(k) = 0.0 + assoc = .false. + DO i = 1,ncomp + IF (nhb_typ(i) /= 0) assoc = .true. + END DO + IF (assoc) THEN + + ass_s2 = 0.0 + DO l = 1, nhb_typ(k) + ass_s2 = ass_s2 + nhb_no(k,l) * LOG(mx(k,l)) + END DO + + m_hbon(k)=ass_s2 + DO i = 1, ncomp + DO ki = 1, nhb_typ(i) + DO j = 1, ncomp + DO l = 1, nhb_typ(j) + m_hbon(k)= m_hbon(k) - rho*rho/2.0*x(i)*x(j) *mx(i,ki)*mx(j,l) *nhb_no(i,ki)*nhb_no(j,l) & + * gij_rk(i,j) * ass_d(i,j,ki,l) + END DO + END DO + END DO + END DO + + END IF + ! --- end of TPT-1-association accord. to Chapman -------------------- + + + ! -------------------------------------------------------------------- + ! polar terms + ! -------------------------------------------------------------------- + CALL PHI_POLAR ( k, z3_rk, fdd_rk, fqq_rk, fdq_rk ) + my_dd(k) = fdd_rk + my_qq(k) = fqq_rk + my_dq(k) = fdq_rk + + + ! -------------------------------------------------------------------- + ! d(f)/d(x) : summation of all contributions + ! -------------------------------------------------------------------- + myres(k) = mhs(k) +mhc(k) +mdsp(k) +m_hbon(k) +my_dd(k) +my_qq(k) +my_dq(k) + + +END DO + + + + +muhs(1:ncomp) = mhs(1:ncomp) +muhc(1:ncomp) = mhc(1:ncomp) +mudisp(1:ncomp) = mdsp(1:ncomp) + + + + +! ---------------------------------------------------------------------- +! finally calculate +! mu_i^res(T,p,x)/kT = ln( phi_i ) when ensemble_flag = 'tp' +! mu_i^res(T,rho,x)/kT when ensemble_flag = 'tv' +! ---------------------------------------------------------------------- + +DO k = 1, ncomp + ! write (*,*) k,myres(k) +LOG(rho*x(k)),rho + IF (ensemble_flag == 'tp' ) lnphi(k) = myres(k) - LOG(zges) + IF (ensemble_flag == 'tv' ) lnphi(k) = myres(k) + ! write (*,*) 'in',k,EXP(lnphi(k)),LOG(zges),eta +END DO +!write (*,'(5G18.10)') lnphi(1),rho + +dpdz = pgesdz +dpdz2 = pgesd2 + + +write(*,*)'tp?',myres(1), lnphi(1) + +END SUBROUTINE PHI_EOS2 + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! + SUBROUTINE PHI_NUMERICAL +! + USE EOS_VARIABLES + USE EOS_CONSTANTS + USE DFT_MODULE, ONLY: z_ges, fres_temp + IMPLICIT NONE +! +!-----local variables------------------------------------------------- + INTEGER :: k + REAL :: zres, zges + REAL :: fres1, fres2, fres3, fres4, fres5 + REAL :: delta_rho + REAL, DIMENSION(nc) :: myres + REAL, DIMENSION(nc) :: rhoi, rhoi_0 + REAL :: tfr_1, tfr_2, tfr_3, tfr_4, tfr_5 +!----------------------------------------------------------------------- + + +!----------------------------------------------------------------------- +! density iteration or pressure calculation +!----------------------------------------------------------------------- + +IF (ensemble_flag == 'tp') THEN + CALL DENSITY_ITERATION +ELSEIF (ensemble_flag == 'tv') THEN + eta = eta_start + CALL P_NUMERICAL +ELSE + write (*,*) 'PHI_EOS: define ensemble, ensemble_flag == (tv) or (tp)' + stop +END IF + +!----------------------------------------------------------------------- +! compressibility factor z = p/(kT*rho) +!----------------------------------------------------------------------- + +zges = (p * 1.E-30) / (kbol*t*eta/z3t) +IF ( ensemble_flag == 'tv' ) zges = (pges * 1.E-30) / (kbol*t*eta/z3t) +zres = zges - 1.0 +z_ges = zges + +rhoi_0(1:ncomp) = x(1:ncomp) * eta/z3t +rhoi(1:ncomp) = rhoi_0(1:ncomp) + + +!----------------------------------------------------------------------- +! derivative to rho_k (keeping other rho_i's constant +!----------------------------------------------------------------------- + +DO k = 1, ncomp + + IF ( rhoi_0(k) > 1.d-9 ) THEN + delta_rho = 1.E-13 * 10.0**(0.5*(15.0+LOG10(rhoi_0(k)))) + ELSE + delta_rho = 1.E-10 + END IF + + rhoi(k) = rhoi_0(k) + delta_rho + eta = PI/6.0 * SUM( rhoi(1:ncomp)*mseg(1:ncomp)*dhs(1:ncomp)**3 ) + x(1:ncomp) = rhoi(1:ncomp) / SUM( rhoi(1:ncomp) ) + rho = SUM( rhoi(1:ncomp) ) + CALL F_NUMERICAL + fres1 = fres*rho + tfr_1 = tfr*rho + + rhoi(k) = rhoi_0(k) + 0.5 * delta_rho + eta = PI/6.0 * SUM( rhoi(1:ncomp)*mseg(1:ncomp)*dhs(1:ncomp)**3 ) + x(1:ncomp) = rhoi(1:ncomp) / SUM( rhoi(1:ncomp) ) + rho = SUM( rhoi(1:ncomp) ) + CALL F_NUMERICAL + fres2 = fres*rho + tfr_2 = tfr*rho + + IF ( rhoi_0(k) > 1.E-9 ) THEN + rhoi(k) = rhoi_0(k) - 0.5 * delta_rho + eta = PI/6.0 * SUM( rhoi(1:ncomp)*mseg(1:ncomp)*dhs(1:ncomp)**3 ) + x(1:ncomp) = rhoi(1:ncomp) / SUM( rhoi(1:ncomp) ) + rho = SUM( rhoi(1:ncomp) ) + CALL F_NUMERICAL + fres4 = fres*rho + tfr_4 = tfr*rho + + rhoi(k) = rhoi_0(k) - delta_rho + eta = PI/6.0 * SUM( rhoi(1:ncomp)*mseg(1:ncomp)*dhs(1:ncomp)**3 ) + x(1:ncomp) = rhoi(1:ncomp) / SUM( rhoi(1:ncomp) ) + rho = SUM( rhoi(1:ncomp) ) + CALL F_NUMERICAL + fres5 = fres*rho + tfr_5 = tfr*rho + END IF + + rhoi(k) = rhoi_0(k) + eta = PI/6.0 * SUM( rhoi(1:ncomp)*mseg(1:ncomp)*dhs(1:ncomp)**3 ) + x(1:ncomp) = rhoi(1:ncomp) / SUM( rhoi(1:ncomp) ) + rho = SUM( rhoi(1:ncomp) ) + CALL F_NUMERICAL + fres3 = fres*rho + tfr_3 = tfr*rho + + IF ( rhoi_0(k) > 1.E-9 ) THEN + myres(k) = ( fres5 - 8.0*fres4 + 8.0*fres2 - fres1 ) / ( 6.0*delta_rho ) + ELSE + myres(k) = ( -3.0*fres3 + 4.0*fres2 - fres1 ) / delta_rho + END IF + +END DO + + +!----------------------------------------------------------------------- +! residual Helmholtz energy +!----------------------------------------------------------------------- + +fres_temp = fres + +!----------------------------------------------------------------------- +! residual chemical potential +!----------------------------------------------------------------------- + +DO k = 1, ncomp + IF (ensemble_flag == 'tp') lnphi(k) = myres(k) - LOG(zges) + IF (ensemble_flag == 'tv' .AND. eta >= 0.0) lnphi(k) = myres(k) !+LOG(rho) + ! write (*,*) 'in',k,EXP(lnphi(k)),LOG(zges),eta + ! IF (DFT.GE.98) write (*,*) dft + ! write (*,*) 'lnphi',k,LNPHI(k),x(k),MYRES(k), -LOG(ZGES) + ! pause + ! write (*,*) k, myres(k), fres, ZRES +END DO + +END SUBROUTINE PHI_NUMERICAL + + +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW + +! SUBROUTINE H_EOS (phas,h_res,s_res,cp_res,X,T,P,PARAME, +! 1 KIJ,lij,NCOMP,ETA_START,ETA,eos,tfr) +! IMPLICIT NONE +! INTEGER nc +! PARAMETER (nc=20) +! INTEGER phas,ncomp,eos,i +! REAL kij(nc,nc),lij(nc,nc),x(nc),t,p,parame(nc,25) +! REAL eta_start,eta,tfr,h_res,cp_res,s_res + + +! i=1 + +! IF (i.EQ.1) THEN +! CALL H_EOS_1(phas,h_res,s_res,cp_res,X,T,P,PARAME, +! 1 KIJ,lij,NCOMP,ETA_START,ETA,eos,tfr) +! ELSE +! CALL H_EOS_NUM (phas,h_res,s_res,cp_res,X,T,P,PARAME, +! 1 KIJ,lij,NCOMP,ETA_START,ETA,eos,tfr) +! ENDIF + +! RETURN +! END + + +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! + SUBROUTINE H_EOS +! + USE PARAMETERS, ONLY: RGAS + USE EOS_CONSTANTS + USE EOS_VARIABLES + IMPLICIT NONE +! +! ---------------------------------------------------------------------- + REAL :: zges, df_dt, dfdr, ddfdrdr + REAL :: cv_res, df_dt2, df_drdt + REAL :: fact, dist, t_tmp, rho_0 + REAL :: fdr1, fdr2, fdr3, fdr4 + + INTEGER :: i, m + REAL :: dhsdt(nc), dhsdt2(nc) + REAL :: z0, z1, z2, z3, z1tdt, z2tdt, z3tdt + REAL :: z1dt, z2dt, z3dt, zms, gii + REAL :: fhsdt, fhsdt2 + REAL :: fchdt, fchdt2 + REAL :: fdspdt, fdspdt2 + REAL :: fhbdt, fhbdt2 + REAL :: sumseg, I1, I2, I1dt, I2dt, I1dt2, I2dt2 + REAL :: c1_con, c2_con, c3_con, c1_dt, c1_dt2 + REAL :: z1tdt2, z2tdt2, z3tdt2 + REAL :: z1dt2, z2dt2, z3dt2 + + INTEGER :: j, k, l, no, ass_cnt, max_eval + LOGICAL :: assoc + REAL :: dij, dijdt, dijdt2 + REAL :: gij1dt, gij2dt, gij3dt + REAL :: gij1dt2, gij2dt2, gij3dt2 + REAL, DIMENSION(nc,nc) :: gijdt, gijdt2, kap_hb + REAL, DIMENSION(nc,nc,nsite,nsite) :: ass_d_dt, ass_d_dt2, eps_hb, delta, deltadt, deltadt2 + REAL, DIMENSION(nc,nsite) :: mxdt, mxdt2, mx_itr, mx_itrdt, mx_itrdt2 + REAL :: attenu, tol, suma, sumdt, sumdt2, err_sum + + INTEGER :: dipole + REAL :: fdddt, fdddt2 + REAL, DIMENSION(nc) :: my2dd, my0 + REAL, DIMENSION(nc,nc) :: idd2, idd2dt, idd2dt2, idd4, idd4dt, idd4dt2 + REAL, DIMENSION(nc,nc,nc) :: idd3, idd3dt, idd3dt2 + REAL :: factor2, factor3 + REAL :: fdd2, fdd3, fdd2dt, fdd3dt, fdd2dt2, fdd3dt2 + REAL :: eij, xijmt, xijkmt + + INTEGER :: qudpole + REAL :: fqqdt, fqqdt2 + REAL, DIMENSION(nc) :: qq2 + REAL, DIMENSION(nc,nc) :: iqq2, iqq2dt, iqq2dt2, iqq4, iqq4dt, iqq4dt2 + REAL, DIMENSION(nc,nc,nc) :: iqq3, iqq3dt, iqq3dt2 + REAL :: fqq2, fqq2dt, fqq2dt2, fqq3, fqq3dt, fqq3dt2 + + INTEGER :: dip_quad + REAL :: fdqdt, fdqdt2 + REAL, DIMENSION(nc) :: myfac, q_fac + REAL, DIMENSION(nc,nc) :: idq2, idq2dt, idq2dt2, idq4, idq4dt, idq4dt2 + REAL, DIMENSION(nc,nc,nc) :: idq3, idq3dt, idq3dt2 + REAL :: fdq2, fdq2dt, fdq2dt2, fdq3, fdq3dt, fdq3dt2 +! ---------------------------------------------------------------------- + + +! ---------------------------------------------------------------------- +! Initializing +! ---------------------------------------------------------------------- +CALL PERTURBATION_PARAMETER + +rho = eta/z3t +z0 = z0t*rho +z1 = z1t*rho +z2 = z2t*rho +z3 = z3t*rho + +sumseg = z0t / (PI/6.0) +zms = 1.0 - z3 + + +! ---------------------------------------------------------------------- +! first and second derivative of f to density (dfdr,ddfdrdr) +! ---------------------------------------------------------------------- +CALL P_EOS + +zges = (pges * 1.E-30)/(kbol*t*rho) + +dfdr = pges/(eta*rho*(kbol*t)/1.E-30) +ddfdrdr = pgesdz/(eta*rho*(kbol*t)/1.E-30) - dfdr*2.0/eta - 1.0/eta**2 + + +! ---------------------------------------------------------------------- +! Helmholtz Energy f/kT = fres +! ---------------------------------------------------------------------- +CALL F_EOS + + +! ---------------------------------------------------------------------- +! derivative of some auxilliary properties to temperature +! ---------------------------------------------------------------------- +DO i = 1,ncomp + dhsdt(i)=parame(i,2) *(-3.0*parame(i,3)/t/t)*0.12*EXP(-3.0*parame(i,3)/t) + dhsdt2(i) = dhsdt(i)*3.0*parame(i,3)/t/t & + + 6.0*parame(i,2)*parame(i,3)/t**3 *0.12*EXP(-3.0*parame(i,3)/t) +END DO + +z1tdt = 0.0 +z2tdt = 0.0 +z3tdt = 0.0 +DO i = 1,ncomp + z1tdt = z1tdt + x(i) * mseg(i) * dhsdt(i) + z2tdt = z2tdt + x(i) * mseg(i) * 2.0*dhs(i)*dhsdt(i) + z3tdt = z3tdt + x(i) * mseg(i) * 3.0*dhs(i)*dhs(i)*dhsdt(i) +END DO +z1dt = PI / 6.0*z1tdt *rho +z2dt = PI / 6.0*z2tdt *rho +z3dt = PI / 6.0*z3tdt *rho + + +z1tdt2 = 0.0 +z2tdt2 = 0.0 +z3tdt2 = 0.0 +DO i = 1,ncomp + z1tdt2 = z1tdt2 + x(i)*mseg(i)*dhsdt2(i) + z2tdt2 = z2tdt2 + x(i)*mseg(i)*2.0 *( dhsdt(i)*dhsdt(i) +dhs(i)*dhsdt2(i) ) + z3tdt2 = z3tdt2 + x(i)*mseg(i)*3.0 *( 2.0*dhs(i)*dhsdt(i)* & + dhsdt(i) +dhs(i)*dhs(i)*dhsdt2(i) ) +END DO +z1dt2 = PI / 6.0*z1tdt2 *rho +z2dt2 = PI / 6.0*z2tdt2 *rho +z3dt2 = PI / 6.0*z3tdt2 *rho + + +! ---------------------------------------------------------------------- +! 1st & 2nd derivative of f/kT hard spheres to temp. (fhsdt) +! ---------------------------------------------------------------------- +fhsdt = 6.0/PI/rho*( 3.0*(z1dt*z2+z1*z2dt)/zms + 3.0*z1*z2*z3dt/zms/zms & + + 3.0*z2*z2*z2dt/z3/zms/zms & + + z2**3 *(2.0*z3*z3dt-z3dt*zms)/(z3*z3*zms**3 ) & + + (3.0*z2*z2*z2dt*z3-2.0*z2**3 *z3dt)/z3**3 *LOG(zms) & + + (z0-z2**3 /z3/z3)*z3dt/zms ) + +fhsdt2= 6.0/PI/rho*( 3.0*(z1dt2*z2+2.0*z1dt*z2dt+z1*z2dt2)/zms & + + 6.0*(z1dt*z2+z1*z2dt)*z3dt/zms/zms & + + 3.0*z1*z2*z3dt2/zms/zms + 6.0*z1*z2*z3dt*z3dt/zms**3 & + + 3.0*z2*(2.0*z2dt*z2dt+z2*z2dt2)/z3/zms/zms & + - z2*z2*(6.0*z2dt*z3dt+z2*z3dt2)/(z3*z3*zms*zms) & + + 2.0*z2**3 *z3dt*z3dt/(z3**3 *zms*zms) & + - 4.0*z2**3 *z3dt*z3dt/(z3*z3 *zms**3 ) & + + (12.0*z2*z2*z2dt*z3dt+2.0*z2**3 *z3dt2)/(z3*zms**3 ) & + + 6.0*z2**3 *z3dt*z3dt/(z3*zms**4 ) & + - 2.0*(3.0*z2*z2*z2dt/z3/z3-2.0*z2**3 *z3dt/z3**3 ) *z3dt/zms & + -(z2**3 /z3/z3-z0)*(z3dt2/zms+z3dt*z3dt/zms/zms) & + + ( (6.0*z2*z2dt*z2dt+3.0*z2*z2*z2dt2)/z3/z3 & + - (12.0*z2*z2*z2dt*z3dt+2.0*z2**3 *z3dt2)/z3**3 & + + 6.0*z2**3 *z3dt*z3dt/z3**4 )* LOG(zms) ) + + +! ---------------------------------------------------------------------- +! 1st & 2nd derivative of f/kT of chain term to T (fchdt) +! ---------------------------------------------------------------------- +fchdt = 0.0 +fchdt2 = 0.0 +DO i = 1, ncomp + DO j = 1, ncomp + dij=dhs(i)*dhs(j)/(dhs(i)+dhs(j)) + dijdt =(dhsdt(i)*dhs(j) + dhs(i)*dhsdt(j)) / (dhs(i)+dhs(j)) & + - dhs(i)*dhs(j)/(dhs(i)+dhs(j))**2 *(dhsdt(i)+dhsdt(j)) + dijdt2=(dhsdt2(i)*dhs(j) + 2.0*dhsdt(i)*dhsdt(j) & + + dhs(i)*dhsdt2(j)) / (dhs(i)+dhs(j)) & + - 2.0*(dhsdt(i)*dhs(j) + dhs(i)*dhsdt(j)) & + / (dhs(i)+dhs(j))**2 *(dhsdt(i)+dhsdt(j)) & + + 2.0* dhs(i)*dhs(j) / (dhs(i)+dhs(j))**3 & + * (dhsdt(i)+dhsdt(j))**2 & + - dhs(i)*dhs(j)/(dhs(i)+dhs(j))**2 *(dhsdt2(i)+dhsdt2(j)) + gij1dt = z3dt/zms/zms + gij2dt = 3.0*( z2dt*dij+z2*dijdt )/zms/zms +6.0*z2*dij*z3dt/zms**3 + gij3dt = 4.0*(dij*z2)* (dijdt*z2 + dij*z2dt) /zms**3 & + + 6.0*(dij*z2)**2 * z3dt /zms**4 + gij1dt2 = z3dt2/zms/zms +2.0*z3dt*z3dt/zms**3 + gij2dt2 = 3.0*( z2dt2*dij+2.0*z2dt*dijdt+z2*dijdt2 )/zms/zms & + + 6.0*( z2dt*dij+z2*dijdt )/zms**3 * z3dt & + + 6.0*(z2dt*dij*z3dt+z2*dijdt*z3dt+z2*dij*z3dt2) /zms**3 & + + 18.0*z2*dij*z3dt*z3dt/zms**4 + gij3dt2 = 4.0*(dijdt*z2+dij*z2dt)**2 /zms**3 & + + 4.0*(dij*z2)* (dijdt2*z2+2.0*dijdt*z2dt+dij*z2dt2) /zms**3 & + + 24.0*(dij*z2) *(dijdt*z2+dij*z2dt)/zms**4 *z3dt & + + 6.0*(dij*z2)**2 * z3dt2 /zms**4 & + + 24.0*(dij*z2)**2 * z3dt*z3dt /zms**5 + gijdt(i,j) = gij1dt + gij2dt + gij3dt + gijdt2(i,j) = gij1dt2 + gij2dt2 + gij3dt2 + END DO +END DO + +DO i = 1, ncomp + gii = 1.0/zms + 3.0*dhs(i)/2.0*z2/zms/zms + 2.0*dhs(i)*dhs(i)/4.0*z2*z2/zms**3 + fchdt = fchdt + x(i) * (1.0-mseg(i)) * gijdt(i,i) / gii + fchdt2= fchdt2+ x(i) * (1.0-mseg(i)) & + * (gijdt2(i,i) / gii - (gijdt(i,i)/gii)**2 ) +END DO + + +! ---------------------------------------------------------------------- +! 1st & 2nd derivative of f/kT dispersion term to T (fdspdt) +! ---------------------------------------------------------------------- +I1 = 0.0 +I2 = 0.0 +I1dt = 0.0 +I2dt = 0.0 +I1dt2= 0.0 +I2dt2= 0.0 +DO m = 0, 6 + I1 = I1 + apar(m)*z3**REAL(m) + I2 = I2 + bpar(m)*z3**REAL(m) + I1dt = I1dt + apar(m)*z3dt*REAL(m)*z3**REAL(m-1) + I2dt = I2dt + bpar(m)*z3dt*REAL(m)*z3**REAL(m-1) + I1dt2= I1dt2+ apar(m)*z3dt2*REAL(m)*z3**REAL(m-1) & + + apar(m)*z3dt*z3dt *REAL(m)*REAL(m-1)*z3**REAL(m-2) + I2dt2= I2dt2+ bpar(m)*z3dt2*REAL(m)*z3**REAL(m-1) & + + bpar(m)*z3dt*z3dt *REAL(m)*REAL(m-1)*z3**REAL(m-2) +END DO + +c1_con= 1.0/ ( 1.0 + sumseg*(8.0*z3-2.0*z3**2 )/zms**4 & + + (1.0 - sumseg)*(20.0*z3-27.0*z3**2 +12.0*z3**3 -2.0*z3**4 ) & + /(zms*(2.0-z3))**2 ) +c2_con= - c1_con*c1_con *(sumseg*(-4.0*z3**2 +20.0*z3+8.0)/zms**5 & + + (1.0 - sumseg) *(2.0*z3**3 +12.0*z3**2 -48.0*z3+40.0) & + /(zms*(2.0-z3))**3 ) +c3_con= 2.0 * c2_con*c2_con/c1_con - c1_con*c1_con & + *( sumseg*(-12.0*z3**2 +72.0*z3+60.0)/zms**6 + (1.0 - sumseg) & + *(-6.0*z3**4 -48.0*z3**3 +288.0*z3**2 -480.0*z3+264.0) & + /(zms*(2.0-z3))**4 ) +c1_dt = c2_con*z3dt +c1_dt2 = c3_con*z3dt*z3dt + c2_con*z3dt2 + +fdspdt = - 2.0*PI*rho*(I1dt-I1/t)*order1 & + - PI*rho*sumseg*(c1_dt*I2+c1_con*I2dt-2.0*c1_con*I2/t)*order2 + +fdspdt2 = - 2.0*PI*rho*(I1dt2-2.0*I1dt/t+2.0*I1/t/t)*order1 & + - PI*rho*sumseg*order2*( c1_dt2*I2 +2.0*c1_dt*I2dt -4.0*c1_dt*I2/t & + + 6.0*c1_con*I2/t/t -4.0*c1_con*I2dt/t +c1_con*I2dt2) + + +! ---------------------------------------------------------------------- +! 1st & 2nd derivative of f/kT association term to T (fhbdt) +! ---------------------------------------------------------------------- +fhbdt = 0.0 +fhbdt2 = 0.0 +assoc = .false. +DO i = 1,ncomp + IF ( nhb_typ(i) /= 0 ) assoc = .true. +END DO +IF (assoc) THEN + + DO i = 1,ncomp + IF ( nhb_typ(i) /= 0 ) THEN + kap_hb(i,i) = parame(i,13) + no = 0 + DO j = 1,nhb_typ(i) + DO k = 1,nhb_typ(i) + eps_hb(i,i,j,k) = parame(i,(14+no)) + no = no + 1 + END DO + END DO + DO j = 1,nhb_typ(i) + no = no + 1 + END DO + ELSE + kap_hb(i,i) = 0.0 + DO k = 1,nsite + DO l = 1,nsite + eps_hb(i,i,k,l) = 0.0 + END DO + END DO + END IF + END DO + + DO i = 1,ncomp + DO j = 1,ncomp + IF ( i /= j .AND. (nhb_typ(i) /= 0 .AND. nhb_typ(j) /= 0) ) THEN + kap_hb(i,j)= (kap_hb(i,i)*kap_hb(j,j))**0.5 & + *((parame(i,2)*parame(j,2))**3 )**0.5 & + /(0.5*(parame(i,2)+parame(j,2)))**3 + ! kap_hb(i,j)= kap_hb(i,j)*(1.0-k_kij) + DO k = 1,nhb_typ(i) + DO l = 1,nhb_typ(j) + IF (k /= l) THEN + eps_hb(i,j,k,l)=(eps_hb(i,i,k,l)+eps_hb(j,j,l,k))/2.0 + ! eps_hb(i,j,k,l)=eps_hb(i,j,k,l)*(1.0-eps_kij) + END IF + END DO + END DO + END IF + END DO + END DO + IF (nhb_typ(1) == 3) THEN + eps_hb(1,2,3,1)=0.5*(eps_hb(1,1,3,1)+eps_hb(2,2,1,2)) + eps_hb(2,1,1,3) = eps_hb(1,2,3,1) + END IF + IF (nhb_typ(2) == 3) THEN + eps_hb(2,1,3,1)=0.5*(eps_hb(2,2,3,1)+eps_hb(1,1,1,2)) + eps_hb(1,2,1,3) = eps_hb(2,1,3,1) + END IF + + DO i = 1, ncomp + DO k = 1, nhb_typ(i) + DO j = 1, ncomp + DO l = 1, nhb_typ(j) + ! ass_d(i,j,k,l)=kap_hb(i,j) *sig_ij(i,j)**3 *(EXP(eps_hb(i,j,k,l)/t)-1.0) + ass_d_dt(i,j,k,l)= - kap_hb(i,j) *sig_ij(i,j)**3 * eps_hb(i,j,k,l)/t/t*EXP(eps_hb(i,j,k,l)/t) + ass_d_dt2(i,j,k,l)= - kap_hb(i,j) *sig_ij(i,j)**3 & + * eps_hb(i,j,k,l)/t/t*EXP(eps_hb(i,j,k,l)/t) & + * (-2.0/t - eps_hb(i,j,k,l)/t/t) + END DO + END DO + END DO + END DO + + DO i = 1, ncomp + DO k = 1, nhb_typ(i) + DO j = 1, ncomp + DO l = 1, nhb_typ(j) + delta(i,j,k,l)=gij(i,j)*ass_d(i,j,k,l) + deltadt(i,j,k,l) = gijdt(i,j)*ass_d(i,j,k,l) + gij(i,j)*ass_d_dt(i,j,k,l) + deltadt2(i,j,k,l)= gijdt2(i,j)*ass_d(i,j,k,l) & + + 2.0*gijdt(i,j)*ass_d_dt(i,j,k,l) +gij(i,j)*ass_d_dt2(i,j,k,l) + END DO + END DO + END DO + END DO + + +! ------ constants for iteration --------------------------------------- + attenu = 0.7 + tol = 1.E-10 + IF (eta < 0.2) tol = 1.E-11 + IF (eta < 0.01) tol = 1.E-12 + max_eval = 200 + +! ------ initialize mxdt(i,j) ------------------------------------------ + DO i = 1, ncomp + DO k = 1, nhb_typ(i) + mxdt(i,k) = 0.0 + mxdt2(i,k) = 0.0 + END DO + END DO + + +! ------ iterate over all components and all sites --------------------- + DO ass_cnt = 1, max_eval + + DO i = 1, ncomp + DO k = 1, nhb_typ(i) + suma = 0.0 + sumdt = 0.0 + sumdt2= 0.0 + DO j = 1, ncomp + DO l = 1, nhb_typ(j) + suma = suma + x(j)*nhb_no(j,l)* mx(j,l) *delta(i,j,k,l) + sumdt = sumdt + x(j)*nhb_no(j,l)*( mx(j,l) *deltadt(i,j,k,l) & + + mxdt(j,l)*delta(i,j,k,l) ) + sumdt2 = sumdt2 + x(j)*nhb_no(j,l)*( mx(j,l)*deltadt2(i,j,k,l) & + + 2.0*mxdt(j,l)*deltadt(i,j,k,l) + mxdt2(j,l)*delta(i,j,k,l) ) + END DO + END DO + mx_itr(i,k) = 1.0 / (1.0 + suma * rho) + mx_itrdt(i,k)= - mx_itr(i,k)**2 * sumdt*rho + mx_itrdt2(i,k)= +2.0*mx_itr(i,k)**3 * (sumdt*rho)**2 - mx_itr(i,k)**2 *sumdt2*rho + END DO + END DO + + err_sum = 0.0 + DO i = 1, ncomp + DO k = 1, nhb_typ(i) + err_sum = err_sum + ABS(mx_itr(i,k) - mx(i,k)) & + + ABS(mx_itrdt(i,k) - mxdt(i,k)) + ABS(mx_itrdt2(i,k) - mxdt2(i,k)) + mx(i,k) = mx_itr(i,k) * attenu + mx(i,k) * (1.0 - attenu) + mxdt(i,k)=mx_itrdt(i,k)*attenu +mxdt(i,k)* (1.0 - attenu) + mxdt2(i,k)=mx_itrdt2(i,k)*attenu +mxdt2(i,k)* (1.0 - attenu) + END DO + END DO + IF(err_sum <= tol) GO TO 10 + + END DO + WRITE(6,*) 'CAL_PCSAFT: max_eval violated err_sum = ',err_sum,tol + STOP + 10 CONTINUE + + DO i = 1, ncomp + DO k = 1, nhb_typ(i) + ! fhb = fhb + x(i)* nhb_no(i,k)* ( 0.5 * ( 1.0 - mx(i,k) ) + LOG(mx(i,k)) ) + fhbdt = fhbdt + x(i)*nhb_no(i,k) *mxdt(i,k)*(1.0/mx(i,k)-0.5) + fhbdt2= fhbdt2 + x(i)*nhb_no(i,k) *(mxdt2(i,k)*(1.0/mx(i,k)-0.5) & + -(mxdt(i,k)/mx(i,k))**2 ) + END DO + END DO + +END IF + + +! ---------------------------------------------------------------------- +! derivatives of f/kT of dipole-dipole term to temp. (fdddt) +! ---------------------------------------------------------------------- +fdddt = 0.0 +fdddt2 = 0.0 +dipole = 0 +DO i = 1,ncomp + my2dd(i) = 0.0 + IF ( parame(i,6) /= 0.0 .AND. uij(i,i) /= 0.0 ) THEN + dipole = 1 + my2dd(i) = (parame(i,6))**2 *1.E-49 / (uij(i,i)*kbol*mseg(i)*sig_ij(i,i)**3 *1.E-30) + END IF + my0(i) = my2dd(i) ! needed for dipole-quadrupole-term +END DO + +IF (dipole == 1) THEN + DO i = 1,ncomp + DO j = 1,ncomp + idd2(i,j) =0.0 + idd4(i,j) =0.0 + idd2dt(i,j) =0.0 + idd4dt(i,j) =0.0 + idd2dt2(i,j)=0.0 + idd4dt2(i,j)=0.0 + DO m=0,4 + idd2(i,j) = idd2(i,j) +ddp2(i,j,m)*z3**REAL(m) + idd4(i,j) = idd4(i,j) +ddp4(i,j,m)*z3**REAL(m) + idd2dt(i,j)= idd2dt(i,j) +ddp2(i,j,m)*z3dt*REAL(m)*z3**REAL(m-1) + idd4dt(i,j)= idd4dt(i,j) +ddp4(i,j,m)*z3dt*REAL(m)*z3**REAL(m-1) + idd2dt2(i,j)=idd2dt2(i,j)+ddp2(i,j,m)*z3dt2*REAL(m)*z3**REAL(m-1) & + + ddp2(i,j,m)*z3dt**2 *REAL(m)*REAL(m-1)*z3**REAL(m-2) + idd4dt2(i,j)=idd4dt2(i,j)+ddp4(i,j,m)*z3dt2*REAL(m)*z3**REAL(m-1) & + + ddp4(i,j,m)*z3dt**2 *REAL(m)*REAL(m-1)*z3**REAL(m-2) + END DO + DO k = 1,ncomp + idd3(i,j,k) =0.0 + idd3dt(i,j,k) =0.0 + idd3dt2(i,j,k)=0.0 + DO m = 0, 4 + idd3(i,j,k) = idd3(i,j,k) +ddp3(i,j,k,m)*z3**REAL(m) + idd3dt(i,j,k) = idd3dt(i,j,k)+ddp3(i,j,k,m)*z3dt*REAL(m) *z3**REAL(m-1) + idd3dt2(i,j,k)= idd3dt2(i,j,k)+ddp3(i,j,k,m)*z3dt2*REAL(m) & + *z3**REAL(m-1) +ddp3(i,j,k,m)*z3dt**2 *REAL(m)*REAL(m-1) *z3**REAL(m-2) + END DO + END DO + END DO + END DO + + + factor2= -PI *rho + factor3= -4.0/3.0*PI**2 * rho**2 + + fdd2 = 0.0 + fdd3 = 0.0 + fdd2dt= 0.0 + fdd3dt= 0.0 + fdd2dt2= 0.0 + fdd3dt2= 0.0 + DO i = 1, ncomp + DO j = 1, ncomp + xijmt = x(i)*parame(i,3)*parame(i,2)**3 *x(j)*parame(j,3)*parame(j,2)**3 & + / ((parame(i,2)+parame(j,2))/2.0)**3 *my2dd(i)*my2dd(j) + eij = (parame(i,3)*parame(j,3))**0.5 + fdd2 = fdd2 +factor2* xijmt/t/t*(idd2(i,j)+eij/t*idd4(i,j)) + fdd2dt= fdd2dt+ factor2* xijmt/t/t*(idd2dt(i,j)-2.0*idd2(i,j)/t & + +eij/t*idd4dt(i,j)-3.0*eij/t/t*idd4(i,j)) + fdd2dt2=fdd2dt2+factor2*xijmt/t/t*(idd2dt2(i,j)-4.0*idd2dt(i,j)/t & + +6.0*idd2(i,j)/t/t+eij/t*idd4dt2(i,j) & + -6.0*eij/t/t*idd4dt(i,j)+12.0*eij/t**3 *idd4(i,j)) + DO k = 1, ncomp + xijkmt=x(i)*parame(i,3)*parame(i,2)**3 & + *x(j)*parame(j,3)*parame(j,2)**3 & + *x(k)*parame(k,3)*parame(k,2)**3 & + /((parame(i,2)+parame(j,2))/2.0) /((parame(i,2)+parame(k,2))/2.0) & + /((parame(j,2)+parame(k,2))/2.0) *my2dd(i)*my2dd(j)*my2dd(k) + fdd3 =fdd3 +factor3*xijkmt/t**3 *idd3(i,j,k) + fdd3dt =fdd3dt +factor3*xijkmt/t**3 * (idd3dt(i,j,k)-3.0*idd3(i,j,k)/t) + fdd3dt2=fdd3dt2+factor3*xijkmt/t**3 & + *( idd3dt2(i,j,k)-6.0*idd3dt(i,j,k)/t+12.0*idd3(i,j,k)/t/t ) + END DO + END DO + END DO + + IF ( fdd2 < -1.E-100 .AND. fdd3 /= 0.0 ) THEN + fdddt = fdd2* (fdd2*fdd2dt - 2.0*fdd3*fdd2dt+fdd2*fdd3dt) / (fdd2-fdd3)**2 + fdddt2 = ( 2.0*fdd2*fdd2dt*fdd2dt +fdd2*fdd2*fdd2dt2 & + -2.0*fdd2dt**2 *fdd3 -2.0*fdd2*fdd2dt2*fdd3 +fdd2*fdd2*fdd3dt2 ) & + /(fdd2-fdd3)**2 + fdddt * 2.0*(fdd3dt-fdd2dt)/(fdd2-fdd3) + END IF +END IF + + +! ---------------------------------------------------------------------- +! derivatives f/kT of quadrupole-quadrup. term to T (fqqdt) +! ---------------------------------------------------------------------- +fqqdt = 0.0 +fqqdt2 = 0.0 +qudpole = 0 +DO i = 1, ncomp + qq2(i) = (parame(i,7))**2 *1.E-69 / (uij(i,i)*kbol*mseg(i)*sig_ij(i,i)**5 *1.E-50) + IF (qq2(i) /= 0.0) qudpole = 1 +END DO + +IF (qudpole == 1) THEN + + DO i = 1,ncomp + DO j = 1,ncomp + iqq2(i,j) = 0.0 + iqq4(i,j) = 0.0 + iqq2dt(i,j) = 0.0 + iqq4dt(i,j) = 0.0 + iqq2dt2(i,j)= 0.0 + iqq4dt2(i,j)= 0.0 + DO m = 0, 4 + iqq2(i,j) = iqq2(i,j) + qqp2(i,j,m)*z3**REAL(m) + iqq4(i,j) = iqq4(i,j) + qqp4(i,j,m)*z3**REAL(m) + iqq2dt(i,j) = iqq2dt(i,j)+ qqp2(i,j,m)*z3dt*REAL(m)*z3**REAL(m-1) + iqq4dt(i,j) = iqq4dt(i,j)+ qqp4(i,j,m)*z3dt*REAL(m)*z3**REAL(m-1) + iqq2dt2(i,j)= iqq2dt2(i,j)+qqp2(i,j,m)*z3dt2*REAL(m)*z3**REAL(m-1) & + + qqp2(i,j,m)*z3dt**2 *REAL(m)*REAL(m-1)*z3**REAL(m-2) + iqq4dt2(i,j)= iqq4dt2(i,j)+qqp4(i,j,m)*z3dt2*REAL(m)*z3**REAL(m-1) & + + qqp4(i,j,m)*z3dt**2 *REAL(m)*REAL(m-1)*z3**REAL(m-2) + END DO + DO k = 1,ncomp + iqq3(i,j,k) =0.0 + iqq3dt(i,j,k) =0.0 + iqq3dt2(i,j,k)=0.0 + DO m = 0, 4 + iqq3(i,j,k) = iqq3(i,j,k) + qqp3(i,j,k,m)*z3**REAL(m) + iqq3dt(i,j,k) = iqq3dt(i,j,k)+ qqp3(i,j,k,m)*z3dt*REAL(m) * z3**REAL(m-1) + iqq3dt2(i,j,k)= iqq3dt2(i,j,k)+qqp3(i,j,k,m)*z3dt2*REAL(m) * z3**REAL(m-1) & + + qqp3(i,j,k,m)*z3dt**2 *REAL(m)*REAL(m-1)*z3**REAL(m-2) + END DO + END DO + END DO + END DO + + factor2 = -9.0/16.0 * PI *rho + factor3 = 9.0/16.0 * PI**2 * rho**2 + + fqq2 = 0.0 + fqq3 = 0.0 + fqq2dt = 0.0 + fqq3dt = 0.0 + fqq2dt2= 0.0 + fqq3dt2= 0.0 + DO i = 1,ncomp + DO j = 1,ncomp + xijmt = x(i)*uij(i,i)*qq2(i)*sig_ij(i,i)**5 & + * x(j)*uij(j,j)*qq2(j)*sig_ij(j,j)**5 /sig_ij(i,j)**7.0 + eij = (parame(i,3)*parame(j,3))**0.5 + fqq2 = fqq2 +factor2* xijmt/t/t*(iqq2(i,j)+eij/t*iqq4(i,j)) + fqq2dt= fqq2dt +factor2* xijmt/t/t*(iqq2dt(i,j)-2.0*iqq2(i,j)/t & + + eij/t*iqq4dt(i,j)-3.0*eij/t/t*iqq4(i,j)) + fqq2dt2=fqq2dt2+factor2*xijmt/t/t*(iqq2dt2(i,j)-4.0*iqq2dt(i,j)/t & + + 6.0*iqq2(i,j)/t/t+eij/t*iqq4dt2(i,j) & + - 6.0*eij/t/t*iqq4dt(i,j)+12.0*eij/t**3 *iqq4(i,j)) + DO k = 1,ncomp + xijkmt = x(i)*uij(i,i)*qq2(i)*sig_ij(i,i)**5 /sig_ij(i,j)**3 & + * x(j)*uij(j,j)*qq2(j)*sig_ij(j,j)**5 /sig_ij(i,k)**3 & + * x(k)*uij(k,k)*qq2(k)*sig_ij(k,k)**5 /sig_ij(j,k)**3 + fqq3 = fqq3 +factor3*xijkmt/t**3 *iqq3(i,j,k) + fqq3dt = fqq3dt +factor3*xijkmt/t**3 *(iqq3dt(i,j,k)-3.0*iqq3(i,j,k)/t) + fqq3dt2= fqq3dt2+factor3*xijkmt/t**3 & + * ( iqq3dt2(i,j,k)-6.0*iqq3dt(i,j,k)/t+12.0*iqq3(i,j,k)/t/t ) + END DO + END DO + END DO + + IF ( fqq2 /= 0.0 .AND. fqq3 /= 0.0 ) THEN + fqqdt = fqq2* (fqq2*fqq2dt - 2.0*fqq3*fqq2dt+fqq2*fqq3dt) / (fqq2-fqq3)**2 + fqqdt2 = ( 2.0*fqq2*fqq2dt*fqq2dt +fqq2*fqq2*fqq2dt2 & + - 2.0*fqq2dt**2 *fqq3 -2.0*fqq2*fqq2dt2*fqq3 +fqq2*fqq2*fqq3dt2 ) & + / (fqq2-fqq3)**2 + fqqdt * 2.0*(fqq3dt-fqq2dt)/(fqq2-fqq3) + END IF + +END IF + + +! ---------------------------------------------------------------------- +! derivatives f/kT of dipole-quadruppole term to T (fdqdt) +! ---------------------------------------------------------------------- +fdqdt = 0.0 +fdqdt2= 0.0 +dip_quad = 0 +DO i = 1,ncomp + DO j = 1,ncomp + IF (parame(i,6) /= 0.0 .AND. parame(j,7) /= 0.0) dip_quad = 1 + END DO + myfac(i) = parame(i,3)*parame(i,2)**4 *my0(i) + q_fac(i) = parame(i,3)*parame(i,2)**4 *qq2(i) +END DO + +IF (dip_quad == 1) THEN + + DO i = 1,ncomp + DO j = 1,ncomp + idq2(i,j) = 0.0 + idq4(i,j) = 0.0 + idq2dt(i,j) = 0.0 + idq4dt(i,j) = 0.0 + idq2dt2(i,j)= 0.0 + idq4dt2(i,j)= 0.0 + IF ( myfac(i) /= 0.0 .AND. q_fac(j) /= 0.0 ) THEN + DO m = 0, 4 + idq2(i,j) = idq2(i,j) + dqp2(i,j,m)*z3**REAL(m) + idq4(i,j) = idq4(i,j) + dqp4(i,j,m)*z3**REAL(m) + idq2dt(i,j) = idq2dt(i,j)+ dqp2(i,j,m)*z3dt*REAL(m)*z3**REAL(m-1) + idq4dt(i,j) = idq4dt(i,j)+ dqp4(i,j,m)*z3dt*REAL(m)*z3**REAL(m-1) + idq2dt2(i,j)= idq2dt2(i,j)+dqp2(i,j,m)*z3dt2*REAL(m)*z3**REAL(m-1) & + + dqp2(i,j,m)*z3dt**2 *REAL(m)*REAL(m-1)*z3**REAL(m-2) + idq4dt2(i,j)= idq4dt2(i,j)+dqp4(i,j,m)*z3dt2*REAL(m)*z3**REAL(m-1) & + + dqp4(i,j,m)*z3dt**2 *REAL(m)*REAL(m-1)*z3**REAL(m-2) + END DO + + DO k = 1,ncomp + idq3(i,j,k) = 0.0 + idq3dt(i,j,k) = 0.0 + idq3dt2(i,j,k)= 0.0 + IF ( myfac(k) /= 0.0 .OR. q_fac(k) /= 0.0 ) THEN + DO m = 0, 4 + idq3(i,j,k) = idq3(i,j,k) + dqp3(i,j,k,m)*z3**REAL(m) + idq3dt(i,j,k)= idq3dt(i,j,k)+ dqp3(i,j,k,m)*z3dt*REAL(m) *z3**REAL(m-1) + idq3dt2(i,j,k)= idq3dt2(i,j,k)+dqp3(i,j,k,m)*z3dt2*REAL(m) *z3**REAL(m-1) & + + dqp3(i,j,k,m)*z3dt**2 *REAL(m)*REAL(m-1)*z3**REAL(m-2) + END DO + END IF + END DO + END IF + END DO + END DO + + factor2= -9.0/4.0 * PI * rho + factor3= PI**2 * rho**2 + + fdq2 = 0.0 + fdq3 = 0.0 + fdq2dt= 0.0 + fdq3dt= 0.0 + fdq2dt2=0.0 + fdq3dt2=0.0 + DO i = 1,ncomp + DO j = 1,ncomp + IF ( myfac(i) /= 0.0 .AND. q_fac(j) /= 0.0 ) THEN + xijmt = x(i)*myfac(i) * x(j)*q_fac(j) /sig_ij(i,j)**5 + eij = (parame(i,3)*parame(j,3))**0.5 + fdq2 = fdq2 + factor2* xijmt/t/t*(idq2(i,j)+eij/t*idq4(i,j)) + fdq2dt= fdq2dt+ factor2* xijmt/t/t*(idq2dt(i,j)-2.0*idq2(i,j)/t & + + eij/t*idq4dt(i,j)-3.0*eij/t/t*idq4(i,j)) + fdq2dt2 = fdq2dt2+factor2*xijmt/t/t*(idq2dt2(i,j)-4.0*idq2dt(i,j)/t & + + 6.0*idq2(i,j)/t/t+eij/t*idq4dt2(i,j) & + - 6.0*eij/t/t*idq4dt(i,j)+12.0*eij/t**3 *idq4(i,j)) + DO k = 1,ncomp + IF ( myfac(k) /= 0.0 .OR. q_fac(k) /= 0.0 ) THEN + xijkmt= x(i)*x(j)*x(k)/(sig_ij(i,j)*sig_ij(i,k)*sig_ij(j,k))**2 & + * ( myfac(i)*q_fac(j)*myfac(k) & + + myfac(i)*q_fac(j)*q_fac(k)*1.193735 ) + + fdq3 =fdq3 + factor3*xijkmt/t**3 *idq3(i,j,k) + fdq3dt=fdq3dt+ factor3*xijkmt/t**3 * (idq3dt(i,j,k)-3.0*idq3(i,j,k)/t) + fdq3dt2=fdq3dt2+factor3*xijkmt/t**3 & + *( idq3dt2(i,j,k)-6.0*idq3dt(i,j,k)/t+12.0*idq3(i,j,k)/t/t ) + END IF + END DO + END IF + END DO + END DO + + IF (fdq2 /= 0.0 .AND. fdq3 /= 0.0) THEN + fdqdt = fdq2* (fdq2*fdq2dt - 2.0*fdq3*fdq2dt+fdq2*fdq3dt) / (fdq2-fdq3)**2 + fdqdt2 = ( 2.0*fdq2*fdq2dt*fdq2dt +fdq2*fdq2*fdq2dt2 & + - 2.0*fdq2dt**2 *fdq3 -2.0*fdq2*fdq2dt2*fdq3 +fdq2*fdq2*fdq3dt2 ) & + / (fdq2-fdq3)**2 + fdqdt * 2.0*(fdq3dt-fdq2dt)/(fdq2-fdq3) + END IF + +END IF +! ---------------------------------------------------------------------- + + + + +! ---------------------------------------------------------------------- +! total derivative of fres/kT to temperature +! ---------------------------------------------------------------------- + +df_dt = fhsdt + fchdt + fdspdt + fhbdt + fdddt + fqqdt + fdqdt + + + +! ---------------------------------------------------------------------- +! second derivative of fres/kT to T +! ---------------------------------------------------------------------- + +df_dt2 = fhsdt2 +fchdt2 +fdspdt2 +fhbdt2 +fdddt2 +fqqdt2 +fdqdt2 + + + +! ---------------------------------------------------------------------- +! ------ derivatives of fres/kt to density and to T -------------------- +! ---------------------------------------------------------------------- + +! ---------------------------------------------------------------------- +! the analytic derivative of fres/kT to (density and T) (df_drdt) +! is still missing. A numerical differentiation is implemented. +! ---------------------------------------------------------------------- +fact = 1.0 +dist = t * 100.E-5 * fact +t_tmp = t +rho_0 = rho + + +t = t_tmp - 2.0*dist +CALL PERTURBATION_PARAMETER +eta = z3t*rho_0 +CALL P_EOS +fdr1 = pges / (eta*rho_0*(kbol*t)/1.E-30) +t = t_tmp - dist +CALL PERTURBATION_PARAMETER +eta = z3t*rho_0 +CALL P_EOS +fdr2 = pges / (eta*rho_0*(kbol*t)/1.E-30) + +t = t_tmp + dist +CALL PERTURBATION_PARAMETER +eta = z3t*rho_0 +CALL P_EOS +fdr3 = pges / (eta*rho_0*(kbol*t)/1.E-30) + +t = t_tmp + 2.0*dist +CALL PERTURBATION_PARAMETER +eta = z3t*rho_0 +CALL P_EOS +fdr4 = pges / (eta*rho_0*(kbol*t)/1.E-30) + +t = t_tmp +CALL PERTURBATION_PARAMETER +eta = z3t*rho_0 +CALL P_EOS + + +df_drdt = (-fdr4+8.0*fdr3-8.0*fdr2+fdr1)/(12.0*dist) + + + + + +! ---------------------------------------------------------------------- +! thermodynamic properties +! ---------------------------------------------------------------------- + +s_res = ( - df_dt *t - fres )*RGAS + RGAS * LOG(zges) +h_res = ( - t*df_dt + zges-1.0 ) * RGAS *t +cv_res = - ( t*df_dt2 + 2.0*df_dt ) * RGAS*t +cp_res = cv_res - RGAS + RGAS*(zges +eta*t*df_drdt)**2 & + / (1.0 + 2.0*eta*dfdr +eta**2 *ddfdrdr) + +! write (*,*) 'df_... ', df_dt,df_dt2 +! write (*,*) 'kreuz ', zges,eta*t*df_drdt,eta*dfdr, eta**2 *ddfdrdr +! write (*,*) 'h,cv,cp', h_res,cv_res,cp_res + + +END SUBROUTINE H_EOS + + + +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! SUBROUTINE H_EOS_num +! +! This subroutine calculates enthalpies and heat capacities (cp) by +! taking numerical derivatieves. +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! + SUBROUTINE H_EOS_num +! + USE PARAMETERS, ONLY: RGAS + USE EOS_VARIABLES + IMPLICIT NONE +! +!--------------------------------------------------------------------- + REAL :: dist, fact, rho_0 + REAL :: fres1, fres2, fres3, fres4, fres5 + REAL :: f_1, f_2, f_3, f_4 + REAL :: cv_res, t_tmp, zges + REAL :: df_dt, df_dtdt, df_drdt, dfdr, ddfdrdr + +!----------------------------------------------------------------------- + + +CALL PERTURBATION_PARAMETER +rho_0 = eta/z3t + + +fact = 1.0 +dist = t * 100.E-5 * fact + +t_tmp = t + +t = t_tmp - 2.0*dist +CALL PERTURBATION_PARAMETER +eta = z3t*rho_0 +CALL F_EOS +fres1 = fres +t = t_tmp - dist +CALL PERTURBATION_PARAMETER +eta = z3t*rho_0 +CALL F_EOS +fres2 = fres +t = t_tmp + dist +CALL PERTURBATION_PARAMETER +eta = z3t*rho_0 +CALL F_EOS +fres3 = fres +t = t_tmp + 2.0*dist +CALL PERTURBATION_PARAMETER +eta = z3t*rho_0 +CALL F_EOS +fres4 = fres +t = t_tmp +CALL PERTURBATION_PARAMETER +eta = z3t*rho_0 +CALL F_EOS +fres5 = fres +! *(KBOL*T)/1.E-30 + +zges = (p * 1.E-30)/(kbol*t*rho_0) + + +df_dt = (-fres4+8.0*fres3-8.0*fres2+fres1)/(12.0*dist) +df_dtdt = (-fres4+16.0*fres3-3.d1*fres5+16.0*fres2-fres1) & + /(12.0*(dist**2 )) + + +s_res = (- df_dt -fres/t)*RGAS*t + RGAS * LOG(zges) +h_res = ( - t*df_dt + zges-1.0 ) * RGAS*t +cv_res = -( t*df_dtdt + 2.0*df_dt ) * RGAS*t + + + +t = t_tmp - 2.0*dist +CALL PERTURBATION_PARAMETER +eta = z3t*rho_0 +CALL P_EOS +f_1 = pges/(eta*rho_0*(kbol*t)/1.E-30) + +t = t_tmp - dist +CALL PERTURBATION_PARAMETER +eta = z3t*rho_0 +CALL P_EOS +f_2 = pges/(eta*rho_0*(kbol*t)/1.E-30) + +t = t_tmp + dist +CALL PERTURBATION_PARAMETER +eta = z3t*rho_0 +CALL P_EOS +f_3 = pges/(eta*rho_0*(kbol*t)/1.E-30) + +t = t_tmp + 2.0*dist +CALL PERTURBATION_PARAMETER +eta = z3t*rho_0 +CALL P_EOS +f_4 = pges/(eta*rho_0*(kbol*t)/1.E-30) + +t = t_tmp +CALL PERTURBATION_PARAMETER +eta = z3t*rho_0 +CALL P_EOS + +dfdr = pges / (eta*rho_0*(kbol*t)/1.E-30) +ddfdrdr = pgesdz/(eta*rho_0*(kbol*t)/1.E-30) - dfdr*2.0/eta - 1.0/eta**2 + +df_drdt = ( -f_4 +8.0*f_3 -8.0*f_2 +f_1) / (12.0*dist) + +cp_res = cv_res - RGAS +RGAS*(zges+eta*t*df_drdt)**2 & + * 1.0/(1.0 + 2.0*eta*dfdr + eta**2 *ddfdrdr) + +! write (*,*) 'n',df_dt,df_dtdt +! write (*,*) 'kreuz ', zges,eta*t*df_drdt,eta*dfdr, eta**2 *ddfdrdr +! write (*,*) 'h, cv', h_res, cv_res +! write (*,*) h_res - t*s_res +! write (*,*) cv_res,cp_res,eta +! pause + +END SUBROUTINE H_EOS_num + + +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! SUBROUTINE DENSITY_ITERATION +! +! iterates the density until the calculated pressure 'pges' is equal to +! the specified pressure 'p'. A Newton-scheme is used for determining +! the root to the objective function f(eta) = (pges / p ) - 1.0. +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! + SUBROUTINE DENSITY_ITERATION +! + USE BASIC_VARIABLES, ONLY: num + USE EOS_VARIABLES + IMPLICIT NONE +! +! ---------------------------------------------------------------------- + INTEGER :: i, start, max_i + REAL :: eta_iteration + REAL :: error, dydx, acc_i, delta_eta +! ---------------------------------------------------------------------- + + +IF ( densav(phas) /= 0.0 .AND. eta_start == denold(phas) ) THEN + denold(phas) = eta_start + eta_start = densav(phas) +ELSE + denold(phas) = eta_start + densav(phas) = eta_start +END IF + + +acc_i = 1.d-9 +max_i = 30 +density_error(:) = 0.0 + +i = 0 +eta_iteration = eta_start + +! ---------------------------------------------------------------------- +! iterate density until p_calc = p +! ---------------------------------------------------------------------- +iterate_density: DO + + i = i + 1 + eta = eta_iteration + + IF ( num == 0 ) THEN + CALL P_EOS + ELSE IF ( num == 1 ) THEN + CALL P_NUMERICAL + ELSE IF ( num == 2 ) THEN + WRITE(*,*) 'CRITICAL RENORM NOT INCLUDED YET' + !!CALL F_EOS_RN + ELSE + write (*,*) 'define calculation option (num)' + END IF + + error = (pges / p ) - 1.0 + + ! --- instable region correction ------------------------------------- + IF ( pgesdz < 0.0 .AND. i < max_i ) THEN + IF ( error > 0.0 .AND. pgesd2 > 0.0 ) THEN ! no liquid density + CALL PRESSURE_SPINODAL + eta_iteration = eta + error = (pges / p ) - 1.0 + IF ( ((pges/p ) -1.0) > 0.0 ) eta_iteration = 0.001 ! no solution possible + IF ( ((pges/p ) -1.0) <=0.0 ) eta_iteration = eta_iteration * 1.1 ! no solution found so far + ELSE IF ( error < 0.0 .AND. pgesd2 < 0.0 ) THEN ! no vapor density + CALL PRESSURE_SPINODAL + eta_iteration = eta + error = (pges / p ) - 1.0 + IF ( ((pges/p ) -1.0) < 0.0 ) eta_iteration = 0.5 ! no solution possible + IF ( ((pges/p ) -1.0) >=0.0 ) eta_iteration = eta_iteration * 0.9 ! no solution found so far + ELSE + eta_iteration = (eta_iteration + eta_start) / 2.0 + IF (eta_iteration == eta_start) eta_iteration = eta_iteration + 0.2 + END IF + CYCLE iterate_density + END IF + + + dydx = pgesdz/p + delta_eta = error/ dydx + IF ( delta_eta > 0.05 ) delta_eta = 0.05 + IF ( delta_eta < -0.05 ) delta_eta = -0.05 + + eta_iteration = eta_iteration - delta_eta + + IF (eta_iteration > 0.9) eta_iteration = 0.6 + IF (eta_iteration <= 0.0) eta_iteration = 1.E-16 + start = 1 + + IF ( ABS(error*p/pgesdz) < 1.d-12 ) start = 0 + IF ( ABS(error) < acc_i ) start = 0 + IF ( i > max_i ) THEN + start = 0 + density_error(phas) = ABS( error ) + ! write (*,*) 'density iteration failed' + END IF + + IF (start /= 1) EXIT iterate_density + +END DO iterate_density + +eta = eta_iteration + +IF ((eta > 0.3 .AND. densav(phas) > 0.3) .OR. & + (eta < 0.1 .AND. densav(phas) < 0.1)) densav(phas) = eta + +END SUBROUTINE DENSITY_ITERATION + + + + +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! SUBROUTINE F_EOS +! +! calculates the Helmholtz energy f/kT. The input to the subroutine is +! (T,eta,x), where eta is the packing fraction. +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! + SUBROUTINE F_EOS +! + USE PARAMETERS, ONLY: nc, nsite + USE EOS_VARIABLES + USE EOS_CONSTANTS + IMPLICIT NONE +! +! --- local variables -------------------------------------------------- + INTEGER :: i, j, k, l, m, n + REAL :: z0, z1, z2, z3 + REAL :: zms, m_mean ! ,lij(nc,nc) + REAL :: I1,I2, c1_con + REAL :: fhs, fdsp, fhc + + LOGICAL :: assoc + INTEGER :: ass_cnt,max_eval + REAL :: delta(nc,nc,nsite,nsite) + REAL :: mx_itr(nc,nsite), err_sum, sum, attenu, tol, fhb + REAL :: ass_s1, ass_s2 + + REAL :: fdd, fqq, fdq +! ---------------------------------------------------------------------- + + +! ---------------------------------------------------------------------- +! abbreviations +! ---------------------------------------------------------------------- +rho = eta/z3t +z0 = z0t*rho +z1 = z1t*rho +z2 = z2t*rho +z3 = z3t*rho + +m_mean = z0t / ( PI / 6.0 ) +zms = 1.0 - eta + +! m_mean2 = 0.0 +! lij(1,2) = -0.05 +! lij(2,1) = lij(1,2) +! DO i = 1, ncomp +! DO j = 1, ncomp +! m_mean2 = m_mean2 + x(i)*x(j)*(mseg(i)+mseg(j))/2.0*(1.0-lij(i,j)) +! ENDDO +! ENDDO + + +! ---------------------------------------------------------------------- +! radial distr. function at contact, gij +! ---------------------------------------------------------------------- +DO i = 1, ncomp + DO j=1,ncomp + gij(i,j) = 1.0/zms + 3.0*dij_ab(i,j)*z2/zms/zms + 2.0*(dij_ab(i,j)*z2)**2 /zms**3 + END DO +END DO + + +! ---------------------------------------------------------------------- +! Helmholtz energy : hard sphere contribution +! ---------------------------------------------------------------------- +fhs= m_mean*( 3.0*z1*z2/zms + z2**3 /z3/zms/zms + (z2**3 /z3/z3-z0)*LOG(zms) )/z0 + + +! ---------------------------------------------------------------------- +! Helmholtz energy : chain term +! ---------------------------------------------------------------------- +fhc = 0.0 +DO i = 1, ncomp + fhc = fhc + x(i) *(1.0- mseg(i)) *LOG(gij(i,i)) +END DO + + +! ---------------------------------------------------------------------- +! Helmholtz energy : PC-SAFT dispersion contribution +! ---------------------------------------------------------------------- +IF (eos == 1) THEN + + I1 = 0.0 + I2 = 0.0 + DO m = 0, 6 + I1 = I1 + apar(m)*eta**REAL(m) + I2 = I2 + bpar(m)*eta**REAL(m) + END DO + + c1_con= 1.0/ ( 1.0 + m_mean*(8.0*eta-2.0*eta**2 )/zms**4 & + + (1.0 - m_mean)*(20.0*eta-27.0*eta**2 & + + 12.0*eta**3 -2.0*eta**4 ) /(zms*(2.0-eta))**2 ) + + fdsp = -2.0*PI*rho*I1*order1 - PI*rho*c1_con*m_mean*I2*order2 + +! ---------------------------------------------------------------------- +! Helmholtz energy : SAFT (Chen, Kreglewski) dispersion contribution +! ---------------------------------------------------------------------- +ELSE + + fdsp = 0.0 + DO n = 1,4 + DO m = 1,9 + fdsp = fdsp + dnm(n,m) * (um/t)**REAL(n) *(eta/tau)**REAL(m) + END DO + END DO + fdsp = m_mean * fdsp + +END IF + + +! ---------------------------------------------------------------------- +! TPT-1-association according to Chapman et al. +! ---------------------------------------------------------------------- +fhb = 0.0 +assoc = .false. +DO i = 1, ncomp + IF (nhb_typ(i) /= 0) assoc = .true. +END DO +IF (assoc) THEN + + DO i = 1, ncomp + DO k = 1, nhb_typ(i) + IF (mx(i,k) == 0.0) mx(i,k) = 1.0 ! Initialize mx(i,j) + DO j = 1, ncomp + DO l = 1, nhb_typ(j) + delta(i,j,k,l) = gij(i,j) * ass_d(i,j,k,l) + END DO + END DO + END DO + END DO + + +! --- constants for iteration ------------------------------------------ + attenu = 0.70 + tol = 1.d-10 + IF (eta < 0.2) tol = 1.d-12 + IF (eta < 0.01) tol = 1.d-13 + max_eval = 200 + +! --- iterate over all components and all sites ------------------------ + ass_cnt = 0 + iterate_TPT1: DO + + ass_cnt = ass_cnt + 1 + + DO i = 1, ncomp + DO k = 1, nhb_typ(i) + sum = 0.0 + DO j = 1, ncomp + DO l = 1, nhb_typ(j) + sum = sum + x(j)* mx(j,l)*nhb_no(j,l) *delta(i,j,k,l) +! if (ass_cnt == 1) write (*,*) j,l,x(j), mx(j,l) + END DO + END DO + mx_itr(i,k) = 1.0 / (1.0 + sum * rho) +! if (ass_cnt == 1) write (*,*) 'B',ass_cnt,sum, rho + END DO + END DO + + err_sum = 0.0 + DO i = 1, ncomp + DO k = 1, nhb_typ(i) + err_sum = err_sum + ABS(mx_itr(i,k) - mx(i,k)) ! / ABS(mx_itr(i,k)) + mx(i,k) = mx_itr(i,k) * attenu + mx(i,k) * (1.0 - attenu) + END DO + END DO + + IF ( err_sum <= tol .OR. ass_cnt >= max_eval ) THEN + IF (ass_cnt >= max_eval) WRITE(*,'(a,2G15.7)') 'F_EOS: Max_eval violated (mx) Err_Sum = ',err_sum,tol + EXIT iterate_TPT1 + END IF + + END DO iterate_TPT1 + + DO i = 1, ncomp + ass_s1 = 0.0 + ass_s2 = 0.0 + DO k = 1, nhb_typ(i) + ass_s1 = ass_s1 + nhb_no(i,k) * ( 1.0 - mx(i,k) ) + ass_s2 = ass_s2 + nhb_no(i,k) * LOG( mx(i,k) ) + END DO + fhb = fhb + x(i) * ( ass_s2 + ass_s1 / 2.0 ) + END DO + +END IF +! --- TPT-1-association accord. to Chapman ----------------------------- + + +! ---------------------------------------------------------------------- +! polar terms +! ---------------------------------------------------------------------- + CALL F_POLAR ( fdd, fqq, fdq ) + + +! ---------------------------------------------------------------------- +! resid. Helmholtz energy f/kT +! ---------------------------------------------------------------------- +fres = fhs + fhc + fdsp + fhb + fdd + fqq + fdq + +tfr= fres + +END SUBROUTINE F_EOS + + +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! + SUBROUTINE F_NUMERICAL +! + USE EOS_VARIABLES + USE EOS_CONSTANTS + USE EOS_NUMERICAL_DERIVATIVES, ONLY: ideal_gas, hard_sphere, chain_term, & + disp_term, hb_term, LC_term, branch_term, & + II_term, ID_term, subtract1, subtract2 + IMPLICIT NONE +! +!--------------------------------------------------------------------- + +!-----local variables------------------------------------------------- + INTEGER :: i, j + REAL :: m_mean2 + REAL :: fid, fhs, fdsp, fhc + REAL :: fhb, fdd, fqq, fdq + REAL :: fhend, fcc + REAL :: fbr, flc + REAL :: fref + + REAL :: eps_kij, k_kij +!--------------------------------------------------------------------- + +eps_kij = 0.0 +k_kij = 0.0 + +fid = 0.0 +fhs = 0.0 +fhc = 0.0 +fdsp= 0.0 +fhb = 0.0 +fdd = 0.0 +fqq = 0.0 +fdq = 0.0 +fcc = 0.0 +fbr = 0.0 +flc = 0.0 + + +CALL PERTURBATION_PARAMETER + +! ---------------------------------------------------------------------- +! overwrite the standard mixing rules by those published by Tang & Gross +! using an additional lij parameter +! WARNING : the lij parameter is set to lij = - lji in 'para_input' +! ---------------------------------------------------------------------- +order1 = 0.0 +order2 = 0.0 +DO i = 1, ncomp + DO j = 1, ncomp + order1 = order1 + x(i)*x(j)* mseg(i)*mseg(j) * sig_ij(i,j)**3 * uij(i,j)/t + order2 = order2 + x(i)*x(j)* mseg(i)*mseg(j) * sig_ij(i,j)**3 * (uij(i,j)/t)**2 + END DO +END DO +DO i = 1, ncomp + DO j = 1, ncomp + order1 = order1 + x(i)*mseg(i)/t*( x(j)*mseg(j) & + *sig_ij(i,j)*(uij(i,i)*uij(j,j))**(1.0/6.0) )**3 *lij(i,j) + END DO +END DO + + +! ---------------------------------------------------------------------- +! a non-standard mixing rule scaling the hard-sphere term +! WARNING : the lij parameter is set to lij = - lji in 'para_input' +! (uses an additional lij parameter) +! ---------------------------------------------------------------------- +m_mean2 = 0.0 +DO i = 1, ncomp + DO j = 1, ncomp + m_mean2 = m_mean2 + x(i)*x(j)*(mseg(i)+mseg(j))/2.0 + END DO +END DO +DO i = 1, ncomp + DO j = 1, ncomp + ! m_mean2=m_mean2+x(i)*(x(j)*((mseg(i)+mseg(j))*0.5)**(1.0/3.0) *lij(i,j) )**3 + END DO +END DO + +! --- ideal gas contribution ------------------------------------------- +IF ( ideal_gas == 'yes' ) CALL F_IDEAL_GAS ( fid ) +! ---------------------------------------------------------------------- + +! --- hard-sphere contribution ----------------------------------------- +IF ( hard_sphere == 'CSBM' ) CALL F_HARD_SPHERE ( m_mean2, fhs ) +! ---------------------------------------------------------------------- + +! -- chain term -------------------------------------------------------- +IF ( chain_term == 'TPT1' ) CALL F_CHAIN_TPT1 ( fhc ) +IF ( chain_term == 'TPT2' ) CALL F_CHAIN_TPT_D ( fhc ) +IF ( chain_term == 'HuLiu' ) CALL F_CHAIN_HU_LIU ( fhc ) +IF ( chain_term == 'HuLiu_rc' ) CALL F_CHAIN_HU_LIU_RC ( fhs, fhc ) +!!IF ( chain_term == 'SPT' ) CALL F_SPT ( fhs, fhc ) +IF ( chain_term == 'SPT' ) WRITE(*,*) 'SPT NOT INCLUDED YET' +! ---------------------------------------------------------------------- + +! --- dispersive attraction -------------------------------------------- +IF ( disp_term == 'PC-SAFT') CALL F_DISP_PCSAFT ( fdsp ) +IF ( disp_term == 'CK') CALL F_DISP_CKSAFT ( fdsp ) +IF ( disp_term(1:2) == 'PT') CALL F_pert_theory ( fdsp ) +! ---------------------------------------------------------------------- + +! --- H-bonding contribution / Association ----------------------------- +IF ( hb_term == 'TPT1_Chap') CALL F_ASSOCIATION( eps_kij, k_kij, fhb ) +! ---------------------------------------------------------------------- + +! --- polar terms ------------------------------------------------------ + CALL F_POLAR ( fdd, fqq, fdq ) +! ---------------------------------------------------------------------- + +! --- ion-dipole term -------------------------------------------------- +IF ( ID_term == 'TBH') CALL F_ION_DIPOLE_TBH ( fhend ) +! ---------------------------------------------------------------------- + +! --- ion-ion term ----------------------------------------------------- +IF ( II_term == 'primMSA') CALL F_ION_ION_PrimMSA ( fcc ) +IF ( II_term == 'nprMSA') CALL F_ION_ION_nonPrimMSA ( fdd, fqq, fdq, fcc ) +! ---------------------------------------------------------------------- + +! --- liquid-crystal term ---------------------------------------------- +IF ( LC_term == 'MSaupe') CALL F_LC_MayerSaupe ( flc ) + +!!IF ( LC_term == 'OVL') fref = fhs + fhc +IF ( LC_term == 'OVL') WRITE(*,*) 'OVL NOT INCLUDED YET' +!IF ( LC_term == 'OVL') CALL F_LC_OVL ( fref, flc ) +!! IF ( LC_term == 'SPT') fref = fhs + fhc +IF ( LC_term == 'SPT') WRITE(*,*) 'SPT NOT INCLUDED YET' +!!IF ( LC_term == 'SPT') CALL F_LC_SPT( fref, flc ) +! ---------------------------------------------------------------------- + +! ====================================================================== +! SUBTRACT TERMS (local density approximation) FOR DFT +! ====================================================================== + +!IF ( subtract1 == '1PT') CALL F_subtract_local_pert_theory ( subtract1, fdsp ) +!IF ( subtract1 == '2PT') CALL F_subtract_local_pert_theory ( subtract1, fdsp ) +!IF ( subtract2 =='ITTpolar') CALL F_local_ITT_polar ( fdd ) +! ---------------------------------------------------------------------- + +! ---------------------------------------------------------------------- +! residual Helmholtz energy F/(NkT) +! ---------------------------------------------------------------------- +fres = fid + fhs + fhc + fdsp + fhb + fdd + fqq + fdq + fcc + flc + +tfr = 0.0 + +END SUBROUTINE F_NUMERICAL + + + +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! SUBROUTINE P_EOS +! +! calculates the pressure in units (Pa). +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! + SUBROUTINE P_EOS +! +! ---------------------------------------------------------------------- + USE PARAMETERS, ONLY: nc, nsite + USE EOS_VARIABLES + USE EOS_CONSTANTS + IMPLICIT NONE +! +! --- local variables -------------------------------------------------- + INTEGER :: i, j, k, l, m, n + INTEGER :: ass_cnt,max_eval + LOGICAL :: assoc + REAL :: z0, z1, z2, z3 + REAL :: zms, m_mean + REAL :: zges, zgesdz, zgesd2, zgesd3 + REAL :: zhs, zhsdz, zhsd2, zhsd3 + REAL :: zhc, zhcdz, zhcd2, zhcd3 + REAL, DIMENSION(nc,nc) :: dgijdz, dgijd2, dgijd3, dgijd4 + REAL :: zdsp, zdspdz, zdspd2, zdspd3 + REAL :: c1_con, c2_con, c3_con, c4_con, c5_con + REAL :: I2, edI1dz, edI2dz, edI1d2, edI2d2 + REAL :: edI1d3, edI2d3, edI1d4, edI2d4 + REAL :: fdspdz,fdspd2 + REAL :: zhb, zhbdz, zhbd2, zhbd3 + REAL, DIMENSION(nc,nc,nsite,nsite) :: delta, dq_dz, dq_d2, dq_d3, dq_d4 + REAL, DIMENSION(nc,nsite) :: mx_itr, dmx_dz, ndmxdz, dmx_d2, ndmxd2 + REAL, DIMENSION(nc,nsite) :: dmx_d3, ndmxd3, dmx_d4, ndmxd4 + REAL :: err_sum, sum0, sum1, sum2, sum3, sum4, attenu, tol + REAL :: sum_d1, sum_d2, sum_d3, sum_d4 + REAL :: zdd, zddz, zddz2, zddz3 + REAL :: zqq, zqqz, zqqz2, zqqz3 + REAL :: zdq, zdqz, zdqz2, zdqz3 +! ---------------------------------------------------------------------- + + +! ---------------------------------------------------------------------- +! abbreviations +! ---------------------------------------------------------------------- +rho = eta/z3t +z0 = z0t*rho +z1 = z1t*rho +z2 = z2t*rho +z3 = z3t*rho + +m_mean = z0t/(PI/6.0) +zms = 1.0 -eta + +! m_mean2=0.0 +! lij(1,2)= -0.050 +! lij(2,1)=lij(1,2) +! DO i =1,ncomp +! DO j =1,ncomp +! m_mean2=m_mean2+x(i)*x(j) * (mseg(i)+mseg(j))/2.0*(1.0-lij(i,j)) +! ENDDO +! ENDDO + + +! ---------------------------------------------------------------------- +! radial distr. function at contact, gij , and derivatives +! dgijdz=d(gij)/d(eta) and dgijd2 = dd(gij)/d(eta)**2 +! ---------------------------------------------------------------------- +DO i = 1, ncomp + DO j=1,ncomp + ! j=i + gij(i,j) = 1.0/zms + 3.0*dij_ab(i,j)*z2/zms/zms + 2.0*(dij_ab(i,j)*z2)**2 /zms**3 + dgijdz(i,j)= 1.0/zms/zms + 3.0*dij_ab(i,j)*z2*(1.0+z3)/z3/zms**3 & + + (dij_ab(i,j)*z2/zms/zms)**2 *(4.0+2.0*z3)/z3 + dgijd2(i,j) = 2.0/zms**3 & + + 6.0*dij_ab(i,j)*z2/z3/zms**4 *(2.0+z3) & + + (2.0*dij_ab(i,j)*z2/z3)**2 /zms**5 *(1.0+4.0*z3+z3*z3) + dgijd3(i,j) = 6.0/zms**4 & + + 18.0*dij_ab(i,j)*z2/z3/zms**5 *(3.0+z3) & + + 12.0*(dij_ab(i,j)*z2/z3/zms**3 )**2 *(3.0+6.0*z3+z3*z3) + dgijd4(i,j) = 24.0/zms**5 & + + 72.0*dij_ab(i,j)*z2/z3/zms**6 *(4.0+z3) & + + 48.0*(dij_ab(i,j)*z2/z3)**2 /zms**7 *(6.0+8.0*z3+z3*z3) + END DO +END DO + + +! ---------------------------------------------------------------------- +! p : hard sphere contribution +! ---------------------------------------------------------------------- +zhs = m_mean* ( z3/zms + 3.0*z1*z2/z0/zms/zms + z2**3 /z0*(3.0-z3)/zms**3 ) +zhsdz = m_mean*( 1.0/zms/zms + 3.0*z1*z2/z0/z3*(1.0+z3)/zms**3 & + + 6.0*z2**3 /z0/z3/zms**4 ) +zhsd2 = m_mean*( 2.0/zms**3 + 6.0*z1*z2/z0/z3*(2.0+z3)/zms**4 & + + 6.0*z2**3 /z0/z3/z3*(1.0+3.0*z3)/zms**5 ) +zhsd3 = m_mean*( 6.0/zms**4 + 18.0*z1*z2/z0/z3*(3.0+z3)/zms**5 & + + 24.0*z2**3 /z0/z3/z3*(2.0+3.0*z3)/zms**6 ) + + +! ---------------------------------------------------------------------- +! p : chain term +! ---------------------------------------------------------------------- +zhc = 0.0 +zhcdz = 0.0 +zhcd2 = 0.0 +zhcd3 = 0.0 +DO i= 1, ncomp + zhc = zhc + x(i)*(1.0-mseg(i))*eta/gij(i,i)* dgijdz(i,i) + zhcdz = zhcdz + x(i)*(1.0-mseg(i)) *(-eta*(dgijdz(i,i)/gij(i,i))**2 & + + dgijdz(i,i)/gij(i,i) + eta/gij(i,i)*dgijd2(i,i)) + zhcd2 = zhcd2 + x(i)*(1.0-mseg(i)) & + *( 2.0*eta*(dgijdz(i,i)/gij(i,i))**3 & + -2.0*(dgijdz(i,i)/gij(i,i))**2 & + -3.0*eta/gij(i,i)**2 *dgijdz(i,i)*dgijd2(i,i) & + +2.0/gij(i,i)*dgijd2(i,i) +eta/gij(i,i)*dgijd3(i,i) ) + zhcd3 = zhcd3 + x(i)*(1.0-mseg(i)) *( 6.0*(dgijdz(i,i)/gij(i,i))**3 & + -6.0*eta*(dgijdz(i,i)/gij(i,i))**4 & + +12.0*eta/gij(i,i)**3 *dgijdz(i,i)**2 *dgijd2(i,i) & + -9.0/gij(i,i)**2 *dgijdz(i,i)*dgijd2(i,i) +3.0/gij(i,i)*dgijd3(i,i) & + -3.0*eta*(dgijd2(i,i)/gij(i,i))**2 & + -4.0*eta/gij(i,i)**2 *dgijdz(i,i)*dgijd3(i,i) & + +eta/gij(i,i)*dgijd4(i,i) ) +END DO + +! ---------------------------------------------------------------------- +! p : PC-SAFT dispersion contribution +! note: edI1dz is equal to d(eta*I1)/d(eta), analogous for edI2dz +! ---------------------------------------------------------------------- +IF (eos == 1) THEN + + I2 = 0.0 + edI1dz = 0.0 + edI2dz = 0.0 + edI1d2 = 0.0 + edI2d2 = 0.0 + edI1d3 = 0.0 + edI2d3 = 0.0 + edI1d4 = 0.0 + edI2d4 = 0.0 + DO m=0,6 + I2 = I2 + bpar(m)*z3**REAL(m) + edI1dz= edI1dz+apar(m)*REAL(m+1)*z3**REAL(m) + edI2dz= edI2dz+bpar(m)*REAL(m+1)*z3**REAL(m) + edI1d2= edI1d2+apar(m)*REAL((m+1)*m)*z3**REAL(m-1) + edI2d2= edI2d2+bpar(m)*REAL((m+1)*m)*z3**REAL(m-1) + edI1d3= edI1d3+apar(m)*REAL((m+1)*m*(m-1))*z3**REAL(m-2) + edI2d3= edI2d3+bpar(m)*REAL((m+1)*m*(m-1))*z3**REAL(m-2) + edI1d4= edI1d4+apar(m)*REAL((m+1)*m*(m-1)*(m-2))*z3**REAL(m-3) + edI2d4= edI2d4+bpar(m)*REAL((m+1)*m*(m-1)*(m-2))*z3**REAL(m-3) + END DO + + c1_con= 1.0/ ( 1.0 + m_mean*(8.0*eta-2.0*eta**2 )/zms**4 & + + (1.0 - m_mean)*(20.0*eta-27.0*eta**2 & + + 12.0*eta**3 -2.0*eta**4 ) /(zms*(2.0-eta))**2 ) + c2_con= - c1_con*c1_con & + *(m_mean*(-4.0*eta**2 +20.0*eta+8.0)/zms**5 + (1.0 - m_mean) & + *(2.0*eta**3 +12.0*eta**2 -48.0*eta+40.0) & + /(zms*(2.0-eta))**3 ) + c3_con= 2.0 * c2_con*c2_con/c1_con - c1_con*c1_con & + *( m_mean*(-12.0*eta**2 +72.0*eta+60.0)/zms**6 & + + (1.0 - m_mean) & + *(-6.0*eta**4 -48.0*eta**3 +288.0*eta**2 & + -480.0*eta+264.0) /(zms*(2.0-eta))**4 ) + c4_con= 6.0*c2_con*c3_con/c1_con -6.0*c2_con**3 /c1_con**2 & + - c1_con*c1_con & + *( m_mean*(-48.0*eta**2 +336.0*eta+432.0)/zms**7 & + + (1.0 - m_mean) & + *(24.0*eta**5 +240.0*eta**4 -1920.0*eta**3 & + +4800.0*eta**2 -5280.0*eta+2208.0) /(zms*(2.0-eta))**5 ) + c5_con= 6.0*c3_con**2 /c1_con - 36.0*c2_con**2 /c1_con**2 *c3_con & + + 8.0*c2_con/c1_con*c4_con+24.0*c2_con**4 /c1_con**3 & + - c1_con*c1_con & + *( m_mean*(-240.0*eta**2 +1920.0*eta+3360.0)/zms**8 & + + (1.0 - m_mean) & + *(-120.0*eta**6 -1440.0*eta**5 +14400.0*eta**4 & + -48000.0*eta**3 +79200.0*eta**2 -66240.0*eta+22560.0) & + /(zms*(2.0-eta))**6 ) + + zdsp = - 2.0*PI*rho*edI1dz*order1 & + - PI*rho*order2*m_mean*(c2_con*I2*eta + c1_con*edI2dz) + zdspdz= zdsp/eta - 2.0*PI*rho*edI1d2*order1 & + - PI*rho*order2*m_mean*(c3_con*I2*eta & + + 2.0*c2_con*edI2dz + c1_con*edI2d2) + zdspd2= -2.0*zdsp/eta/eta +2.0*zdspdz/eta & + - 2.0*PI*rho*edI1d3*order1 - PI*rho*order2*m_mean*(c4_con*I2*eta & + + 3.0*c3_con*edI2dz +3.0*c2_con*edI2d2 +c1_con*edI2d3) + zdspd3= 6.0*zdsp/eta**3 -6.0*zdspdz/eta/eta & + + 3.0*zdspd2/eta - 2.0*PI*rho*edI1d4*order1 & + - PI*rho*order2*m_mean*(c5_con*I2*eta & + + 4.0*c4_con*edI2dz +6.0*c3_con*edI2d2 & + + 4.0*c2_con*edI2d3 + c1_con*edI2d4) + + +! ---------------------------------------------------------------------- +! p : SAFT (Chen & Kreglewski) dispersion contribution +! ---------------------------------------------------------------------- +ELSE + + fdspdz = 0.0 + fdspd2 = 0.0 + DO n = 1,4 + DO m = 1,9 + fdspdz = fdspdz + m_mean/tau * dnm(n,m) * (um/t)**REAL(n) *REAL(m)*(eta/tau)**REAL(m-1) + END DO + DO m= 2,9 + fdspd2= fdspd2 + m_mean/tau * dnm(n,m)*(um/t)**REAL(n) *REAL(m)*REAL(m-1) & + * (eta/tau)**REAL(m-2) * 1.0/tau + END DO + END DO + zdsp = eta * fdspdz + zdspdz = (2.0*fdspdz + eta*fdspd2) - zdsp/z3 + +END IF +! --- end of dispersion contribution ----------------------------------- + + +! ---------------------------------------------------------------------- +! p: TPT-1-association accord. to Chapman et al. +! ---------------------------------------------------------------------- +zhb = 0.0 +zhbdz = 0.0 +zhbd2 = 0.0 +zhbd3 = 0.0 +assoc = .false. +DO i = 1,ncomp + IF (nhb_typ(i) /= 0) assoc = .true. +END DO +IF (assoc) THEN + + DO j = 1, ncomp + DO i = 1, nhb_typ(j) + DO k = 1, ncomp + DO l = 1, nhb_typ(k) + delta(j,k,i,l) = gij(j,k) * ass_d(j,k,i,l) + dq_dz(j,k,i,l) = dgijdz(j,k) * ass_d(j,k,i,l) + dq_d2(j,k,i,l) = dgijd2(j,k) * ass_d(j,k,i,l) + dq_d3(j,k,i,l) = dgijd3(j,k) * ass_d(j,k,i,l) + dq_d4(j,k,i,l) = dgijd4(j,k) * ass_d(j,k,i,l) + END DO + END DO + END DO + END DO + +! --- constants for iteration ------------------------------------------ + attenu = 0.7 + tol = 1.d-10 + IF ( eta < 0.2 ) tol = 1.d-12 + IF ( eta < 0.01 ) tol = 1.d-13 + IF ( eta < 1.E-6) tol = 1.d-15 + max_eval = 1000 + +! --- initialize mx(i,j) ----------------------------------------------- + DO i = 1, ncomp + DO j = 1, nhb_typ(i) + mx(i,j) = 1.0 + dmx_dz(i,j) = 0.0 + dmx_d2(i,j) = 0.0 + dmx_d3(i,j) = 0.0 + dmx_d4(i,j) = 0.0 + END DO + END DO + +! --- iterate over all components and all sites ------------------------ + ass_cnt = 0 + err_sum = tol + 1.0 + DO WHILE ( err_sum > tol .AND. ass_cnt <= max_eval) + ass_cnt = ass_cnt + 1 + DO i = 1, ncomp + DO j = 1, nhb_typ(i) + sum0 = 0.0 + sum1 = 0.0 + sum2 = 0.0 + sum3 = 0.0 + sum4 = 0.0 + DO k = 1, ncomp + DO l = 1, nhb_typ(k) + sum0 =sum0 +x(k)*nhb_no(k,l)* mx(k,l)* delta(i,k,j,l) + sum1 =sum1 +x(k)*nhb_no(k,l)*( mx(k,l)* dq_dz(i,k,j,l) & + + dmx_dz(k,l)* delta(i,k,j,l)) + sum2 =sum2 +x(k)*nhb_no(k,l)*( mx(k,l)* dq_d2(i,k,j,l) & + + 2.0*dmx_dz(k,l)* dq_dz(i,k,j,l) & + + dmx_d2(k,l)* delta(i,k,j,l)) + sum3 =sum3 +x(k)*nhb_no(k,l)*( mx(k,l)* dq_d3(i,k,j,l) & + + 3.0*dmx_dz(k,l)* dq_d2(i,k,j,l) & + + 3.0*dmx_d2(k,l)* dq_dz(i,k,j,l) & + + dmx_d3(k,l)* delta(i,k,j,l)) + sum4 =sum4 + x(k)*nhb_no(k,l)*( mx(k,l)* dq_d4(i,k,j,l) & + + 4.0*dmx_dz(k,l)* dq_d3(i,k,j,l) & + + 6.0*dmx_d2(k,l)* dq_d2(i,k,j,l) & + + 4.0*dmx_d3(k,l)* dq_dz(i,k,j,l) & + + dmx_d4(k,l)* delta(i,k,j,l)) + END DO + END DO + mx_itr(i,j)= 1.0 / (1.0 + sum0 * rho) + ndmxdz(i,j)= -(mx_itr(i,j)*mx_itr(i,j))* (sum0/z3t +sum1*rho) + ndmxd2(i,j)= + 2.0/mx_itr(i,j)*ndmxdz(i,j)*ndmxdz(i,j) & + - (mx_itr(i,j)*mx_itr(i,j)) * (2.0/z3t*sum1 + rho*sum2) + ndmxd3(i,j)= - 6.0/mx_itr(i,j)**2 *ndmxdz(i,j)**3 & + + 6.0/mx_itr(i,j)*ndmxdz(i,j)*ndmxd2(i,j) - mx_itr(i,j)*mx_itr(i,j) & + * (3.0/z3t*sum2 + rho*sum3) + ndmxd4(i,j)= 24.0/mx_itr(i,j)**3 *ndmxdz(i,j)**4 & + -36.0/mx_itr(i,j)**2 *ndmxdz(i,j)**2 *ndmxd2(i,j) & + +6.0/mx_itr(i,j)*ndmxd2(i,j)**2 & + +8.0/mx_itr(i,j)*ndmxdz(i,j)*ndmxd3(i,j) - mx_itr(i,j)**2 & + *(4.0/z3t*sum3 + rho*sum4) + END DO + END DO + + err_sum = 0.0 + DO i = 1, ncomp + DO j = 1, nhb_typ(i) + err_sum = err_sum + ABS(mx_itr(i,j) - mx(i,j)) & + + ABS(ndmxdz(i,j) - dmx_dz(i,j)) + ABS(ndmxd2(i,j) - dmx_d2(i,j)) + mx(i,j) = mx_itr(i,j)*attenu + mx(i,j) * (1.0-attenu) + dmx_dz(i,j) = ndmxdz(i,j)*attenu + dmx_dz(i,j) * (1.0-attenu) + dmx_d2(i,j) = ndmxd2(i,j)*attenu + dmx_d2(i,j) * (1.0-attenu) + dmx_d3(i,j) = ndmxd3(i,j)*attenu + dmx_d3(i,j) * (1.0-attenu) + dmx_d4(i,j) = ndmxd4(i,j)*attenu + dmx_d4(i,j) * (1.0-attenu) + END DO + END DO + END DO + + IF ( ass_cnt >= max_eval .AND. err_sum > SQRT(tol) ) THEN + WRITE (*,'(a,2G15.7)') 'P_EOS: Max_eval violated (mx) Err_Sum= ',err_sum,tol + ! stop + END IF + + + ! --- calculate the hydrogen-bonding contribution -------------------- + DO i = 1, ncomp + sum_d1 = 0.0 + sum_d2 = 0.0 + sum_d3 = 0.0 + sum_d4 = 0.0 + DO j = 1, nhb_typ(i) + sum_d1= sum_d1 +nhb_no(i,j)* dmx_dz(i,j)*(1.0/mx(i,j)-0.5) + sum_d2= sum_d2 +nhb_no(i,j)*(dmx_d2(i,j)*(1.0/mx(i,j)-0.5) & + -(dmx_dz(i,j)/mx(i,j))**2 ) + sum_d3= sum_d3 +nhb_no(i,j)*(dmx_d3(i,j)*(1.0/mx(i,j)-0.5) & + -3.0/mx(i,j)**2 *dmx_dz(i,j)*dmx_d2(i,j) + 2.0*(dmx_dz(i,j)/mx(i,j))**3 ) + sum_d4= sum_d4 +nhb_no(i,j)*(dmx_d4(i,j)*(1.0/mx(i,j)-0.5) & + -4.0/mx(i,j)**2 *dmx_dz(i,j)*dmx_d3(i,j) & + + 12.0/mx(i,j)**3 *dmx_dz(i,j)**2 *dmx_d2(i,j) & + - 3.0/mx(i,j)**2 *dmx_d2(i,j)**2 - 6.0*(dmx_dz(i,j)/mx(i,j))**4 ) + END DO + zhb = zhb + x(i) * eta * sum_d1 + zhbdz = zhbdz + x(i) * eta * sum_d2 + zhbd2 = zhbd2 + x(i) * eta * sum_d3 + zhbd3 = zhbd3 + x(i) * eta * sum_d4 + END DO + zhbdz = zhbdz + zhb/eta + zhbd2 = zhbd2 + 2.0/eta*zhbdz-2.0/eta**2 *zhb + zhbd3 = zhbd3 - 6.0/eta**2 *zhbdz+3.0/eta*zhbd2 + 6.0/eta**3 *zhb +END IF +! --- TPT-1-association accord. to Chapman ----------------------------- + + +! ---------------------------------------------------------------------- +! p: polar terms +! ---------------------------------------------------------------------- +CALL P_POLAR ( zdd, zddz, zddz2, zddz3, zqq, zqqz, zqqz2, zqqz3, zdq, zdqz, zdqz2, zdqz3 ) + + +! ---------------------------------------------------------------------- +! compressibility factor z and total p +! as well as derivatives d(z)/d(eta) and d(p)/d(eta) with unit [Pa] +! ---------------------------------------------------------------------- +zges = 1.0 + zhs + zhc + zdsp + zhb + zdd + zqq + zdq +zgesdz = zhsdz + zhcdz + zdspdz + zhbdz + zddz + zqqz + zdqz +zgesd2 = zhsd2 + zhcd2 + zdspd2 + zhbd2 + zddz2 +zqqz2+zdqz2 +zgesd3 = zhsd3 + zhcd3 + zdspd3 + zhbd3 + zddz3 +zqqz3+zdqz3 + +pges = zges *rho *(kbol*t)/1.d-30 +pgesdz = ( zgesdz*rho + zges*rho/z3 )*(kbol*t)/1.d-30 +pgesd2 = ( zgesd2*rho + 2.0*zgesdz*rho/z3 )*(kbol*t)/1.d-30 +pgesd3 = ( zgesd3*rho + 3.0*zgesd2*rho/z3 )*(kbol*t)/1.d-30 + +END SUBROUTINE P_EOS + + + + +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! + SUBROUTINE PHI_POLAR ( k, z3_rk, fdd_rk, fqq_rk, fdq_rk ) +! + USE EOS_VARIABLES, ONLY: ncomp, parame, dd_term, qq_term, dq_term + IMPLICIT NONE +! +! ---------------------------------------------------------------------- + INTEGER, INTENT(IN) :: k + REAL, INTENT(IN) :: z3_rk + REAL, INTENT(OUT) :: fdd_rk, fqq_rk, fdq_rk +! +! --- local variables--------------------------------------------------- + INTEGER :: dipole + INTEGER :: quadrupole + INTEGER :: dipole_quad +! ---------------------------------------------------------------------- + + fdd_rk = 0.0 + fqq_rk = 0.0 + fdq_rk = 0.0 + + dipole = 0 + quadrupole = 0 + dipole_quad = 0 + IF ( SUM( parame(1:ncomp,6) ) /= 0.0 ) dipole = 1 + IF ( SUM( parame(1:ncomp,7) ) /= 0.0 ) quadrupole = 1 + IF ( dipole == 1 .AND. quadrupole == 1 ) dipole_quad = 1 + + ! -------------------------------------------------------------------- + ! dipole-dipole term + ! -------------------------------------------------------------------- + IF (dipole == 1) THEN + + IF (dd_term == 'GV') CALL PHI_DD_GROSS_VRABEC( k, z3_rk, fdd_rk ) + ! IF (dd_term == 'SF') CALL PHI_DD_SAAGER_FISCHER( k ) + + IF (dd_term /= 'GV' .AND. dd_term /= 'SF') write (*,*) 'specify dipole term !' + + ENDIF + + ! -------------------------------------------------------------------- + ! quadrupole-quadrupole term + ! -------------------------------------------------------------------- + IF (quadrupole == 1) THEN + + !IF (qq_term == 'SF') CALL PHI_QQ_SAAGER_FISCHER( k ) + IF (qq_term == 'JG') CALL PHI_QQ_GROSS( k, z3_rk, fqq_rk ) + + IF (qq_term /= 'JG' .AND. qq_term /= 'SF') write (*,*) 'specify quadrupole term !' + + ENDIF + + ! -------------------------------------------------------------------- + ! dipole-quadrupole cross term + ! -------------------------------------------------------------------- + IF (dipole_quad == 1) THEN + + IF (dq_term == 'VG') CALL PHI_DQ_VRABEC_GROSS( k, z3_rk, fdq_rk ) + + IF (dq_term /= 'VG' ) write (*,*) 'specify DQ-cross term !' + + ENDIF + +END SUBROUTINE PHI_POLAR + + +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! + SUBROUTINE PHI_DD_GROSS_VRABEC( k, z3_rk, fdd_rk ) +! + USE PARAMETERS, ONLY: PI, KBOL + USE EOS_VARIABLES, ONLY: nc, ncomp, uij, parame, mseg, sig_ij, rho, eta, x, t + USE EOS_CONSTANTS, ONLY: ddp2, ddp3, ddp4 + IMPLICIT NONE +! +! ---------------------------------------------------------------------- + INTEGER, INTENT(IN) :: k + REAL, INTENT(IN) :: z3_rk + REAL, INTENT(IN OUT) :: fdd_rk +! +! --- local variables--------------------------------------------------- + INTEGER :: i, j, l, m + + REAL :: factor2, factor3, z3 + REAL :: xijfa, xijkfa, xijfa_x, xijkf_x, eij + REAL :: fdd2, fdd3, fdd2x, fdd3x + REAL, DIMENSION(nc) :: my2dd + REAL, DIMENSION(nc,nc) :: Idd2, Idd4, Idd2x, Idd4x + REAL, DIMENSION(nc,nc,nc) :: Idd3, Idd3x +! ---------------------------------------------------------------------- + + + fdd_rk = 0.0 + z3 = eta + DO i = 1, ncomp + IF ( uij(i,i) == 0.0 ) write (*,*) 'PHI_DD_GROSS_VRABEC: do not use dimensionless units' + IF ( uij(i,i) == 0.0 ) stop + my2dd(i) = (parame(i,6))**2 *1.E-49 / (uij(i,i)*KBOL*mseg(i)*sig_ij(i,i)**3 *1.E-30) + END DO + + DO i = 1, ncomp + DO j = 1, ncomp + Idd2(i,j) = 0.0 + Idd4(i,j) = 0.0 + Idd2x(i,j) = 0.0 + Idd4x(i,j) = 0.0 + IF (parame(i,6) /= 0.0 .AND. parame(j,6) /= 0.0) THEN + DO m=0,4 + Idd2(i,j) =Idd2(i,j) + ddp2(i,j,m)*z3**m + Idd4(i,j) =Idd4(i,j) + ddp4(i,j,m)*z3**m + Idd2x(i,j) =Idd2x(i,j)+ ddp2(i,j,m)*REAL(m)*z3**(m-1)*z3_rk + Idd4x(i,j) =Idd4x(i,j)+ ddp4(i,j,m)*REAL(m)*z3**(m-1)*z3_rk + END DO + DO l = 1, ncomp + Idd3(i,j,l) = 0.0 + Idd3x(i,j,l) = 0.0 + IF (parame(l,6) /= 0.0) THEN + DO m=0,4 + Idd3(i,j,l) =Idd3(i,j,l) +ddp3(i,j,l,m)*z3**m + Idd3x(i,j,l)=Idd3x(i,j,l)+ddp3(i,j,l,m)*REAL(m)*z3**(m-1)*z3_rk + END DO + END IF + END DO + END IF + END DO + END DO + + factor2= -PI + factor3= -4.0/3.0*PI**2 + + fdd2 = 0.0 + fdd3 = 0.0 + fdd2x = 0.0 + fdd3x = 0.0 + DO i = 1, ncomp + xijfa_x = 2.0*x(i)*rho*uij(i,i)*my2dd(i)*sig_ij(i,i)**3 /t & + *uij(k,k)*my2dd(k)*sig_ij(k,k)**3 /t/sig_ij(i,k)**3 + eij = (parame(i,3)*parame(k,3))**0.5 + fdd2x = fdd2x + factor2*xijfa_x*( Idd2(i,k) + eij/t*Idd4(i,k) ) + DO j = 1, ncomp + IF (parame(i,6) /= 0.0 .AND. parame(j,6) /= 0.0) THEN + xijfa =x(i)*rho*uij(i,i)*my2dd(i)*sig_ij(i,i)**3 /t & + *x(j)*rho*uij(j,j)*my2dd(j)*sig_ij(j,j)**3 /t/sig_ij(i,j)**3 + eij = (parame(i,3)*parame(j,3))**0.5 + fdd2= fdd2 +factor2*xijfa*(Idd2(i,j) +eij/t*Idd4(i,j) ) + fdd2x =fdd2x +factor2*xijfa*(Idd2x(i,j)+eij/t*Idd4x(i,j)) + !--------------------- + xijkf_x=x(i)*rho*uij(i,i)*my2dd(i)*sig_ij(i,i)**3 /t/sig_ij(i,j) & + *x(j)*rho*uij(j,j)*my2dd(j)*sig_ij(j,j)**3 /t/sig_ij(i,k) & + *3.0* uij(k,k)*my2dd(k)*sig_ij(k,k)**3 /t/sig_ij(j,k) + fdd3x=fdd3x+factor3*xijkf_x*Idd3(i,j,k) + DO l=1,ncomp + IF (parame(l,6) /= 0.0) THEN + xijkfa= x(i)*rho*uij(i,i)/t*my2dd(i)*sig_ij(i,i)**3 & + *x(j)*rho*uij(j,j)/t*my2dd(j)*sig_ij(j,j)**3 & + *x(l)*rho*uij(l,l)/t*my2dd(l)*sig_ij(l,l)**3 & + /sig_ij(i,j)/sig_ij(i,l)/sig_ij(j,l) + fdd3 =fdd3 + factor3 * xijkfa *Idd3(i,j,l) + fdd3x =fdd3x + factor3 * xijkfa *Idd3x(i,j,l) + END IF + END DO + END IF + END DO + END DO + + IF (fdd2 < -1.E-50 .AND. fdd3 /= 0.0 .AND. fdd2x /= 0.0 .AND. fdd3x /= 0.0)THEN + + fdd_rk = fdd2* (fdd2*fdd2x - 2.0*fdd3*fdd2x+fdd2*fdd3x) / (fdd2-fdd3)**2 + + END IF + +END SUBROUTINE PHI_DD_GROSS_VRABEC + + + +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! + SUBROUTINE PHI_QQ_GROSS( k, z3_rk, fqq_rk ) +! + USE PARAMETERS, ONLY: PI, KBOL + USE EOS_VARIABLES, ONLY: nc, ncomp, uij, parame, mseg, sig_ij, rho, eta, x, t + USE EOS_CONSTANTS, ONLY: qqp2, qqp3, qqp4 + IMPLICIT NONE +! +! ---------------------------------------------------------------------- + INTEGER, INTENT(IN) :: k + REAL, INTENT(IN) :: z3_rk + REAL, INTENT(IN OUT) :: fqq_rk +! +! --- local variables--------------------------------------------------- + INTEGER :: i, j, l, m + + REAL :: factor2, factor3, z3 + REAL :: xijfa, xijkfa, xijfa_x, xijkf_x, eij + REAL :: fqq2, fqq3, fqq2x, fqq3x + REAL, DIMENSION(nc) :: qq2 + REAL, DIMENSION(nc,nc) :: Iqq2, Iqq4, Iqq2x, Iqq4x + REAL, DIMENSION(nc,nc,nc) :: Iqq3, Iqq3x +! ---------------------------------------------------------------------- + + + fqq_rk = 0.0 + z3 = eta + DO i = 1, ncomp + IF ( uij(i,i) == 0.0 ) write (*,*) 'PHI_QQ_GROSS: do not use dimensionless units' + qq2(i) = (parame(i,7))**2 *1.E-69 / (uij(i,i)*kbol*mseg(i)*sig_ij(i,i)**5 *1.E-50) + END DO + + DO i = 1, ncomp + DO j = 1, ncomp + Iqq2(i,j) = 0.0 + Iqq4(i,j) = 0.0 + Iqq2x(i,j) = 0.0 + Iqq4x(i,j) = 0.0 + IF (parame(i,7) /= 0.0 .AND. parame(j,7) /= 0.0) THEN + DO m = 0, 4 + Iqq2(i,j) = Iqq2(i,j) + qqp2(i,j,m) * z3**m + Iqq4(i,j) = Iqq4(i,j) + qqp4(i,j,m) * z3**m + Iqq2x(i,j) = Iqq2x(i,j) + qqp2(i,j,m) * REAL(m)*z3**(m-1)*z3_rk + Iqq4x(i,j) = Iqq4x(i,j) + qqp4(i,j,m) * REAL(m)*z3**(m-1)*z3_rk + END DO + DO l = 1, ncomp + Iqq3(i,j,l) = 0.0 + Iqq3x(i,j,l) = 0.0 + IF (parame(l,7) /= 0.0) THEN + DO m = 0, 4 + Iqq3(i,j,l) = Iqq3(i,j,l) + qqp3(i,j,l,m)*z3**m + Iqq3x(i,j,l) = Iqq3x(i,j,l) + qqp3(i,j,l,m)*REAL(m) *z3**(m-1)*z3_rk + END DO + END IF + END DO + END IF + END DO + END DO + + factor2= -9.0/16.0*PI + factor3= 9.0/16.0*PI**2 + + fqq2 = 0.0 + fqq3 = 0.0 + fqq2x = 0.0 + fqq3x = 0.0 + DO i = 1, ncomp + xijfa_x = 2.0*x(i)*rho*uij(i,i)*qq2(i)*sig_ij(i,i)**5 /t & + *uij(k,k)*qq2(k)*sig_ij(k,k)**5 /t/sig_ij(i,k)**7.0 + eij = (parame(i,3)*parame(k,3))**0.5 + fqq2x =fqq2x +factor2*xijfa_x*(Iqq2(i,k)+eij/t*Iqq4(i,k)) + DO j=1,ncomp + IF (parame(i,7) /= 0.0 .AND. parame(j,7) /= 0.0) THEN + xijfa =x(i)*rho*uij(i,i)*qq2(i)*sig_ij(i,i)**5 /t & + *x(j)*rho*uij(j,j)*qq2(j)*sig_ij(j,j)**5 /t/sig_ij(i,j)**7.0 + eij = (parame(i,3)*parame(j,3))**0.5 + fqq2= fqq2 +factor2*xijfa*(Iqq2(i,j) +eij/t*Iqq4(i,j) ) + fqq2x =fqq2x +factor2*xijfa*(Iqq2x(i,j)+eij/t*Iqq4x(i,j)) + ! ------------------ + xijkf_x=x(i)*rho*uij(i,i)*qq2(i)*sig_ij(i,i)**5 /t/sig_ij(i,j)**3 & + *x(j)*rho*uij(j,j)*qq2(j)*sig_ij(j,j)**5 /t/sig_ij(i,k)**3 & + *3.0* uij(k,k)*qq2(k)*sig_ij(k,k)**5 /t/sig_ij(j,k)**3 + fqq3x = fqq3x + factor3*xijkf_x*Iqq3(i,j,k) + DO l = 1, ncomp + IF (parame(l,7) /= 0.0) THEN + xijkfa=x(i)*rho*uij(i,i)*qq2(i)*sig_ij(i,i)**5 /t/sig_ij(i,j)**3 & + *x(j)*rho*uij(j,j)*qq2(j)*sig_ij(j,j)**5 /t/sig_ij(i,l)**3 & + *x(l)*rho*uij(l,l)*qq2(l)*sig_ij(l,l)**5 /t/sig_ij(j,l)**3 + fqq3 =fqq3 + factor3 * xijkfa *Iqq3(i,j,l) + fqq3x =fqq3x + factor3 * xijkfa *Iqq3x(i,j,l) + END IF + END DO + END IF + END DO + END DO + + IF (fqq2 < -1.E-50 .AND. fqq3 /= 0.0 .AND. fqq2x /= 0.0 .AND. fqq3x /= 0.0) THEN + fqq_rk = fqq2* (fqq2*fqq2x - 2.0*fqq3*fqq2x+fqq2*fqq3x) / (fqq2-fqq3)**2 + END IF + +END SUBROUTINE PHI_QQ_GROSS + +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! + SUBROUTINE PHI_DQ_VRABEC_GROSS( k, z3_rk, fdq_rk ) +! + USE PARAMETERS, ONLY: PI, KBOL + USE EOS_VARIABLES, ONLY: nc, ncomp, uij, parame, mseg, sig_ij, rho, eta, x, t + USE EOS_CONSTANTS, ONLY: dqp2, dqp3, dqp4 + IMPLICIT NONE +! +! ---------------------------------------------------------------------- + INTEGER, INTENT(IN) :: k + REAL, INTENT(IN) :: z3_rk + REAL, INTENT(IN OUT) :: fdq_rk +! +! --- local variables--------------------------------------------------- + INTEGER :: i, j, l, m + + REAL :: factor2, factor3, z3 + REAL :: xijfa, xijkfa, xijfa_x, xijkf_x, eij + REAL :: fdq2, fdq3, fdq2x, fdq3x + REAL, DIMENSION(nc) :: my2dd, myfac, qq2, q_fac + REAL, DIMENSION(nc,nc) :: Idq2, Idq4, Idq2x, Idq4x + REAL, DIMENSION(nc,nc,nc) :: Idq3, Idq3x +! ---------------------------------------------------------------------- + + fdq_rk = 0.0 + z3 = eta + DO i=1,ncomp + my2dd(i) = (parame(i,6))**2 *1.E-49 / (uij(i,i)*KBOL*mseg(i)*sig_ij(i,i)**3 *1.E-30) + myfac(i) = parame(i,3)/t*parame(i,2)**4 *my2dd(i) + qq2(i) = (parame(i,7))**2 *1.E-69 / (uij(i,i)*kbol*mseg(i)*sig_ij(i,i)**5 *1.E-50) + q_fac(i) = parame(i,3)/t*parame(i,2)**4 *qq2(i) + END DO + + DO i = 1, ncomp + DO j = 1, ncomp + Idq2(i,j) = 0.0 + Idq4(i,j) = 0.0 + Idq2x(i,j) = 0.0 + Idq4x(i,j) = 0.0 + DO m = 0, 4 + Idq2(i,j) = Idq2(i,j) + dqp2(i,j,m)*z3**m + Idq4(i,j) = Idq4(i,j) + dqp4(i,j,m)*z3**m + Idq2x(i,j) = Idq2x(i,j) + dqp2(i,j,m)*REAL(m)*z3**(m-1) *z3_rk + Idq4x(i,j) = Idq4x(i,j) + dqp4(i,j,m)*REAL(m)*z3**(m-1) *z3_rk + END DO + DO l = 1, ncomp + Idq3(i,j,l) = 0.0 + Idq3x(i,j,l) = 0.0 + DO m = 0, 4 + Idq3(i,j,l) =Idq3(i,j,l) +dqp3(i,j,l,m)*z3**m + Idq3x(i,j,l)=Idq3x(i,j,l)+dqp3(i,j,l,m)*REAL(m)*z3**(m-1)*z3_rk + END DO + END DO + END DO + END DO + + factor2= -9.0/4.0*PI + factor3= PI**2 + + fdq2 = 0.0 + fdq3 = 0.0 + fdq2x = 0.0 + fdq3x = 0.0 + DO i = 1, ncomp + xijfa_x = x(i)*rho*( myfac(i)*q_fac(k) + myfac(k)*q_fac(i) ) / sig_ij(i,k)**5 + eij = (parame(i,3)*parame(k,3))**0.5 + fdq2x =fdq2x +factor2*xijfa_x*(Idq2(i,k)+eij/t*Idq4(i,k)) + DO j=1,ncomp + xijfa =x(i)*rho*myfac(i) * x(j)*rho*q_fac(j) /sig_ij(i,j)**5 + eij = (parame(i,3)*parame(j,3))**0.5 + fdq2= fdq2 +factor2*xijfa*(Idq2(i,j) +eij/t*Idq4(i,j) ) + fdq2x =fdq2x +factor2*xijfa*(Idq2x(i,j) +eij/t*Idq4x(i,j)) + !--------------------- + xijkf_x=x(i)*rho*x(j)*rho/(sig_ij(i,j)*sig_ij(i,k)*sig_ij(j,k))**2 & + *( myfac(i)*q_fac(j)*myfac(k) + myfac(i)*q_fac(k)*myfac(j) & + + myfac(k)*q_fac(i)*myfac(j) +myfac(i)*q_fac(j)*q_fac(k)*1.1937350 & + +myfac(i)*q_fac(k)*q_fac(j)*1.193735 & + +myfac(k)*q_fac(i)*q_fac(j)*1.193735 ) + fdq3x = fdq3x + factor3*xijkf_x*Idq3(i,j,k) + DO l = 1, ncomp + xijkfa=x(i)*rho*x(j)*rho*x(l)*rho/(sig_ij(i,j)*sig_ij(i,l)*sig_ij(j,l))**2 & + *( myfac(i)*q_fac(j)*myfac(l) & + +myfac(i)*q_fac(j)*q_fac(l)*1.193735 ) + fdq3 =fdq3 + factor3 * xijkfa *Idq3(i,j,l) + fdq3x =fdq3x + factor3 * xijkfa *Idq3x(i,j,l) + END DO + END DO + END DO + + IF (fdq2 < -1.E-50 .AND. fdq3 /= 0.0 .AND. fdq2x /= 0.0 .AND. fdq3x /= 0.0)THEN + + fdq_rk = fdq2* (fdq2*fdq2x - 2.0*fdq3*fdq2x+fdq2*fdq3x) / (fdq2-fdq3)**2 + + END IF + +END SUBROUTINE PHI_DQ_VRABEC_GROSS + + + +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! + SUBROUTINE P_NUMERICAL +! + USE EOS_VARIABLES + IMPLICIT NONE +! +!-----local variables------------------------------------------------- + REAL :: dzetdv, eta_0, dist, fact + REAL :: fres1, fres2, fres3, fres4, fres5 + REAL :: df_dr, df_drdr, pideal, dpiddz + REAL :: tfr_1, tfr_2, tfr_3, tfr_4, tfr_5 +!----------------------------------------------------------------------- + + +IF (eta > 0.1) THEN + fact = 1.0 +ELSE IF (eta <= 0.1 .AND. eta > 0.01) THEN + fact = 10.0 +ELSE + fact = 10.0 +END IF +dist = eta*3.d-3 *fact +! dist = eta*4.d-3 *fact +!***************************** +! fuer MC simulation: neues dist: +! dist = eta*5.d-3*fact + +eta_0 = eta +eta = eta_0 - 2.0*dist +CALL F_NUMERICAL +fres1 = fres +tfr_1 = tfr +eta = eta_0 - dist +CALL F_NUMERICAL +fres2 = fres +tfr_2 = tfr +eta = eta_0 + dist +CALL F_NUMERICAL +fres3 = fres +tfr_3 = tfr +eta = eta_0 + 2.0*dist +CALL F_NUMERICAL +fres4 = fres +tfr_4 = tfr +eta = eta_0 +CALL F_NUMERICAL +fres5 = fres +tfr_5 = tfr + +!--------------------------------------------------------- +! ptfr = (-tfr_4+8.0*tfr_3-8.0*tfr_2+tfr_1)/(12.0*dist) +! & *dzetdv*(KBOL*T)/1.E-30 +! ztfr =ptfr /( rho * (KBOL*t) / 1.E-30) +! ptfrdz = (-tfr_4+16.0*tfr_3-3.d1*tfr_5+16.0*tfr_2-tfr_1) +! & /(12.0*(dist**2 ))* dzetdv*(KBOL*T)/1.E-30 +! & + (-tfr_4+8.0*tfr_3-8.0*tfr_2+tfr_1) +! & /(12.0*dist) * 2.0 *eta*6.0/PI/D +! & *(KBOL*T)/1.E-30 +! ztfrdz=ptfrdz/( rho*(kbol*T)/1.E-30 ) - ztfr/eta +! write (*,*) eta,ztfr,ztfrdz + +! dtfr_dr = (-tfr_4+8.0*tfr_3-8.0*tfr_2+tfr_1)/(12.0*dist) +! write (*,*) eta,dtfr_dr +! stop +!--------------------------------------------------------- + +df_dr = (-fres4+8.0*fres3-8.0*fres2+fres1) / (12.0*dist) +df_drdr = (-fres4+16.0*fres3-3.d1*fres5+16.0*fres2-fres1) & + /(12.0*(dist**2 )) + + +dzetdv = eta*rho + +pges = (-fres4+8.0*fres3-8.0*fres2+fres1) & + /(12.0*dist) *dzetdv*(kbol*t)/1.E-30 + +dpiddz = 1.0/z3t*(kbol*t)/1.E-30 +pgesdz = (-fres4+16.0*fres3-3.d1*fres5+16.0*fres2-fres1) & + /(12.0*(dist**2 ))* dzetdv*(kbol*t)/1.E-30 & + + (-fres4+8.0*fres3-8.0*fres2+fres1) /(12.0*dist) * 2.0 *rho & + *(kbol*t)/1.E-30 + dpiddz + +pgesd2 = (fres4-2.0*fres3+2.0*fres2-fres1) /(2.0*dist**3 ) & + * dzetdv*(kbol*t)/1.E-30 & + + (-fres4+16.0*fres3-3.d1*fres5+16.0*fres2-fres1) /(12.0*(dist**2 )) & + * 4.0 *rho *(kbol*t)/1.E-30 + (-fres4+8.0*fres3-8.0*fres2+fres1) & + /(12.0*dist) * 2.0 /z3t *(kbol*t)/1.E-30 +pgesd3 = (fres4-4.0*fres3+6.0*fres5-4.0*fres2+fres1) /(dist**4 ) & + * dzetdv*(kbol*t)/1.E-30 + (fres4-2.0*fres3+2.0*fres2-fres1) & + /(2.0*dist**3 ) * 6.0 *rho *(kbol*t)/1.E-30 & + + (-fres4+16.0*fres3-3.d1*fres5+16.0*fres2-fres1) & + /(12.0*dist**2 )* 6.0 /z3t *(kbol*t)/1.E-30 + +!------------------p ideal------------------------------------ +pideal = rho * (kbol*t) / 1.E-30 + +!------------------p summation, p comes out in Pa ------------ +pges = pideal + pges + +END SUBROUTINE P_NUMERICAL + + +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! + SUBROUTINE H_numerical +! + USE PARAMETERS, ONLY: RGAS + USE EOS_VARIABLES + IMPLICIT NONE +! +!--------------------------------------------------------------------- + REAL :: dist, fact, rho_0 + REAL :: fres1,fres2,fres3,fres4,fres5 + REAL :: f_1, f_2, f_3, f_4 + REAL :: cv_res, t_tmp, zges + REAL :: f_dt, f_dtdt, f_dr, f_drdr, f_drdt +!----------------------------------------------------------------------- + + +CALL PERTURBATION_PARAMETER +rho_0 = eta/z3t + + +fact = 1.0 +dist = t * 100.E-5 * fact + +t_tmp = t + +t = t_tmp - 2.0*dist +CALL PERTURBATION_PARAMETER +eta = z3t*rho_0 +CALL F_NUMERICAL +fres1 = fres +t = t_tmp - dist +CALL PERTURBATION_PARAMETER +eta = z3t*rho_0 +CALL F_NUMERICAL +fres2 = fres +t = t_tmp + dist +CALL PERTURBATION_PARAMETER +eta = z3t*rho_0 +CALL F_NUMERICAL +fres3 = fres +t = t_tmp + 2.0*dist +CALL PERTURBATION_PARAMETER +eta = z3t*rho_0 +CALL F_NUMERICAL +fres4 = fres +t = t_tmp +CALL PERTURBATION_PARAMETER +eta = z3t*rho_0 +CALL F_NUMERICAL +fres5 = fres +! *(KBOL*T)/1.E-30 + +zges = (p * 1.E-30)/(kbol*t*rho_0) + + +f_dt = (-fres4+8.0*fres3-8.0*fres2+fres1)/(12.0*dist) +f_dtdt = (-fres4+16.0*fres3-3.d1*fres5+16.0*fres2-fres1) /(12.0*(dist**2 )) + +s_res = (- f_dt -fres/t)*RGAS*t + RGAS * LOG(zges) +h_res = ( - t*f_dt + zges-1.0 ) * RGAS*t +cv_res = -( t*f_dtdt + 2.0*f_dt ) * RGAS*t + + + +t = t_tmp - 2.0*dist +CALL PERTURBATION_PARAMETER +eta = z3t*rho_0 +CALL P_NUMERICAL +f_1 = pges/(eta*rho_0*(KBOL*T)/1.E-30) + +t = t_tmp - dist +CALL PERTURBATION_PARAMETER +eta = z3t*rho_0 +CALL P_NUMERICAL +f_2 = pges/(eta*rho_0*(KBOL*T)/1.E-30) + +t = t_tmp + dist +CALL PERTURBATION_PARAMETER +eta = z3t*rho_0 +CALL P_NUMERICAL +f_3 = pges/(eta*rho_0*(KBOL*T)/1.E-30) + +t = t_tmp + 2.0*dist +CALL PERTURBATION_PARAMETER +eta = z3t*rho_0 +CALL P_NUMERICAL +f_4 = pges/(eta*rho_0*(KBOL*T)/1.E-30) + +t = t_tmp +CALL PERTURBATION_PARAMETER +eta = z3t*rho_0 +CALL P_NUMERICAL + +f_dr = pges / (eta*rho_0*(KBOL*T)/1.E-30) +f_drdr = pgesdz/ (eta*rho_0*(KBOL*T)/1.E-30) - f_dr*2.0/eta - 1.0/eta**2 + +f_drdt = ( - f_4 + 8.0*f_3 - 8.0*f_2 + f_1 ) / ( 12.0*dist ) + +cp_res = cv_res - RGAS + RGAS*( zges + eta*t*f_drdt)**2 / (1.0 + 2.0*eta*f_dr + eta**2 *f_drdr) +! write (*,*) cv_res,cp_res,eta + + +END SUBROUTINE H_numerical + + + + + + + + + + + +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! + SUBROUTINE F_POLAR ( fdd, fqq, fdq ) +! + USE EOS_VARIABLES, ONLY: ncomp, parame, dd_term, qq_term, dq_term + IMPLICIT NONE +! +! ---------------------------------------------------------------------- + REAL, INTENT(OUT) :: fdd, fqq, fdq +! +! --- local variables--------------------------------------------------- + INTEGER :: dipole + INTEGER :: quadrupole + INTEGER :: dipole_quad +! ---------------------------------------------------------------------- + + fdd = 0.0 + fqq = 0.0 + fdq = 0.0 + + dipole = 0 + quadrupole = 0 + dipole_quad = 0 + IF ( SUM( parame(1:ncomp,6) ) /= 0.0 ) dipole = 1 + IF ( SUM( parame(1:ncomp,7) ) /= 0.0 ) quadrupole = 1 + IF ( dipole == 1 .AND. quadrupole == 1 ) dipole_quad = 1 + + ! -------------------------------------------------------------------- + ! dipole-dipole term + ! -------------------------------------------------------------------- + IF (dipole == 1) THEN + + IF (dd_term == 'GV') CALL F_DD_GROSS_VRABEC( fdd ) + ! IF (dd_term == 'SF') CALL F_DD_SAAGER_FISCHER( k ) + IF (dd_term /= 'GV' .AND. dd_term /= 'SF') write (*,*) 'specify dipole term !' + + ENDIF + + ! -------------------------------------------------------------------- + ! quadrupole-quadrupole term + ! -------------------------------------------------------------------- + IF (quadrupole == 1) THEN + + !IF (qq_term == 'SF') CALL F_QQ_SAAGER_FISCHER( k ) + IF (qq_term == 'JG') CALL F_QQ_GROSS( fqq ) + IF (qq_term /= 'JG' .AND. qq_term /= 'SF') write (*,*) 'specify quadrupole term !' + + ENDIF + + ! -------------------------------------------------------------------- + ! dipole-quadrupole cross term + ! -------------------------------------------------------------------- + IF (dipole_quad == 1) THEN + + IF (dq_term == 'VG') CALL F_DQ_VRABEC_GROSS( fdq ) + IF (dq_term /= 'VG' ) write (*,*) 'specify DQ-cross term !' + + ENDIF + +END SUBROUTINE F_POLAR + + + +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! SUBROUTINE PRESSURE_SPINODAL +! +! iterates the density until the derivative of pressure 'pges' to +! density is equal to zero. A Newton-scheme is used for determining +! the root to the objective function. +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! + SUBROUTINE PRESSURE_SPINODAL +! + USE BASIC_VARIABLES, ONLY: num + USE EOS_VARIABLES + IMPLICIT NONE +! +! ---------------------------------------------------------------------- + INTEGER :: i, max_i + REAL :: eta_iteration + REAL :: error, acc_i, delta_eta +! ---------------------------------------------------------------------- + +acc_i = 1.d-6 +max_i = 30 + +i = 0 +eta_iteration = eta_start + +! ---------------------------------------------------------------------- +! iterate density until p_calc = p +! ---------------------------------------------------------------------- + +error = acc_i + 1.0 +DO WHILE ( ABS(error) > acc_i .AND. i < max_i ) + + i = i + 1 + eta = eta_iteration + + IF ( num == 0 ) THEN + CALL P_EOS + ELSE IF ( num == 1 ) THEN + CALL P_NUMERICAL + ELSE IF ( num == 2 ) THEN + WRITE(*,*) 'CRITICAL RENORM NOT INCLUDED YET' + !!CALL F_EOS_RN + ELSE + write (*,*) 'define calculation option (num)' + END IF + + error = pgesdz + + delta_eta = error/ pgesd2 + IF ( delta_eta > 0.02 ) delta_eta = 0.02 + IF ( delta_eta < -0.02 ) delta_eta = -0.02 + + eta_iteration = eta_iteration - delta_eta + ! write (*,'(a,i3,3G18.10)') 'iter',i, error, eta_iteration, pgesdz + + IF (eta_iteration > 0.9) eta_iteration = 0.5 + IF (eta_iteration <= 0.0) eta_iteration = 1.E-16 + +END DO + +eta = eta_iteration + +END SUBROUTINE PRESSURE_SPINODAL + + +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! + SUBROUTINE F_IDEAL_GAS ( fid ) +! + USE EOS_VARIABLES, ONLY: nc, ncomp, t, x, rho, PI, KBOL, NAv + IMPLICIT NONE +! +!--------------------------------------------------------------------- + REAL, INTENT(IN OUT) :: fid +!--------------------------------------------------------------------- + INTEGER :: i + REAL, DIMENSION(nc) :: rhoi +!---------------------------------------------------------------------- + + !h_Planck = 6.62606896E-34 ! Js + DO i = 1, ncomp + rhoi(i) = x(i) * rho + ! debroglie(i) = h_Planck *1d10 & ! in units Angstrom + ! *SQRT( 1.0 / (2.0*PI *1.0 / NAv / 1000.0 * KBOL*T) ) + ! ! *SQRT( 1.0 / (2.0*PI *mm(i) /NAv/1000.0 * KBOL*T) ) + ! fid = fid + x(i) * ( LOG(rhoi(i)*debroglie(i)**3) - 1.0 ) + fid = fid + x(i) * ( LOG(rhoi(i)) - 1.0 ) + END DO + + END SUBROUTINE F_IDEAL_GAS + +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! + SUBROUTINE F_HARD_SPHERE ( m_mean2, fhs ) +! + USE EOS_VARIABLES, ONLY: z0t, z1t, z2t, z3t, eta, rho + IMPLICIT NONE +! +!--------------------------------------------------------------------- + REAL, INTENT(IN) :: m_mean2 + REAL, INTENT(IN OUT) :: fhs +!--------------------------------------------------------------------- + REAL :: z0, z1, z2, z3, zms +!---------------------------------------------------------------------- + + rho = eta / z3t + z0 = z0t * rho + z1 = z1t * rho + z2 = z2t * rho + z3 = z3t * rho + zms = 1.0 - z3 + + fhs= m_mean2*( 3.0*z1*z2/zms + z2**3 /z3/zms/zms + (z2**3 /z3/z3-z0)*LOG(zms) )/z0 + + + END SUBROUTINE F_HARD_SPHERE + +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! + SUBROUTINE F_CHAIN_TPT1 ( fhc ) +! + USE EOS_VARIABLES, ONLY: nc, ncomp, mseg, x, z0t, z1t, z2t, z3t, & + rho, eta, dij_ab, gij + IMPLICIT NONE +! +!--------------------------------------------------------------------- + REAL, INTENT(IN OUT) :: fhc +!--------------------------------------------------------------------- + INTEGER :: i, j + REAL :: z0, z1, z2, z3, zms +!--------------------------------------------------------------------- + + rho = eta / z3t + z0 = z0t * rho + z1 = z1t * rho + z2 = z2t * rho + z3 = z3t * rho + zms = 1.0 - z3 + + DO i = 1, ncomp + DO j = 1, ncomp + gij(i,j) = 1.0/zms + 3.0*dij_ab(i,j)*z2/zms/zms + 2.0*(dij_ab(i,j)*z2)**2 / zms**3 + END DO + END DO + + fhc = 0.0 + DO i = 1, ncomp + fhc = fhc + x(i) *(1.0- mseg(i)) *LOG(gij(i,i)) + END DO + + END SUBROUTINE F_CHAIN_TPT1 + + +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! + SUBROUTINE F_CHAIN_TPT_D ( fhc ) +! + USE EOS_VARIABLES, ONLY: nc, ncomp, mseg, x, z0t, z1t, z2t, z3t, rho, eta, & + dhs, mseg, dij_ab, gij + IMPLICIT NONE +! +!--------------------------------------------------------------------- + REAL, INTENT(OUT) :: fhc +!--------------------------------------------------------------------- + INTEGER :: i, j + REAL, DIMENSION(nc) :: gij_hd + REAL :: z0, z1, z2, z3, zms +!--------------------------------------------------------------------- + + rho = eta / z3t + z0 = z0t * rho + z1 = z1t * rho + z2 = z2t * rho + z3 = z3t * rho + zms = 1.0 - z3 + + DO i = 1, ncomp + DO j = 1, ncomp + gij(i,j) = 1.0/zms + 3.0*dij_ab(i,j)*z2/zms/zms + 2.0*(dij_ab(i,j)*z2)**2 / zms**3 + END DO + END DO + + DO i = 1, ncomp + gij_hd(i) = 1.0/(2.0*zms) + 3.0*dij_ab(i,i)*z2 / zms**2 + END DO + + fhc = 0.0 + DO i = 1, ncomp + IF ( mseg(i) >= 2.0 ) THEN + fhc = fhc - x(i) * ( mseg(i)/2.0 * LOG( gij(i,i) ) + ( mseg(i)/2.0 - 1.0 ) * LOG( gij_hd(i)) ) + ELSE + fhc = fhc + x(i) * ( 1.0 - mseg(i) ) * LOG( gij(i,i) ) + END IF + END DO + + END SUBROUTINE F_CHAIN_TPT_D + + +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! + SUBROUTINE F_CHAIN_HU_LIU ( fhc ) +! + USE EOS_VARIABLES, ONLY: nc, ncomp, mseg, x, rho, eta + IMPLICIT NONE +! +! This subroutine calculates the hard chain contribution of the TPT-Liu-Hu Eos. +!--------------------------------------------------------------------- + REAL, INTENT(OUT) :: fhc +!--------------------------------------------------------------------- + REAL :: a2, b2, c2, a3, b3, c3 + REAL :: a20, b20, c20, a30, b30, c30 + REAL :: sum1, sum2, am, bm, cm + REAL :: zms +!--------------------------------------------------------------------- + + zms = 1.0 - eta + + sum1 = SUM( x(1:ncomp)*(mseg(1:ncomp)-1.0) ) + sum2 = SUM( x(1:ncomp)/mseg(1:ncomp)*(mseg(1:ncomp)-1.0)*(mseg(1:ncomp)-2.0) ) + + a2 = 0.45696 + a3 = -0.74745 + b2 = 2.10386 + b3 = 3.49695 + c2 = 1.75503 + c3 = 4.83207 + a20 = - a2 + b2 - 3.0*c2 + b20 = - a2 - b2 + c2 + c20 = c2 + a30 = - a3 + b3 - 3.0*c3 + b30 = - a3 - b3 + c3 + c30 = c3 + am = (3.0 + a20) * sum1 + a30 * sum2 + bm = (1.0 + b20) * sum1 + b30 * sum2 + cm = (1.0 + c20) * sum1 + c30 * sum2 + + fhc = - ( (am*eta - bm) / (2.0*zms) + bm/2.0/zms**2 - cm *LOG(ZMS) ) + + + END SUBROUTINE F_CHAIN_HU_LIU + +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! + SUBROUTINE F_CHAIN_HU_LIU_RC ( fhs, fhc ) +! + USE EOS_VARIABLES, ONLY: mseg, chiR, eta + IMPLICIT NONE +! +! This subroutine calculates the hard chain contribution of the TPT-Liu-Hu Eos. +!--------------------------------------------------------------------- + REAL, INTENT(IN) :: fhs + REAL, INTENT(OUT) :: fhc +!--------------------------------------------------------------------- + REAL :: a2, b2, c2, a3, b3, c3 + REAL :: para1,para2,para3,para4 + REAL :: aLH,bLH,cLH +!--------------------------------------------------------------------- + +! This routine is only for pure components + + a2 = 0.45696 + b2 = 2.10386 + c2 = 1.75503 + + para1 = -0.74745 + para2 = 0.299154629727814 + para3 = 1.087271036653154 + para4 = -0.708979110326831 + a3 = para1 + para2*chiR(1) + para3*chiR(1)**2 + para4*chiR(1)**3 + b3 = 3.49695 - (3.49695 + 0.317719074806190)*chiR(1) + c3 = 4.83207 - (4.83207 - 3.480163780334421)*chiR(1) + + aLH = mseg(1)*(1.0 + ((mseg(1)-1.0)/mseg(1))*a2 + ((mseg(1)-1.0)/mseg(1))*((mseg(1)-2.0)/mseg(1))*a3 ) + bLH = mseg(1)*(1.0 + ((mseg(1)-1.0)/mseg(1))*b2 + ((mseg(1)-1.0)/mseg(1))*((mseg(1)-2.0)/mseg(1))*b3 ) + cLH = mseg(1)*(1.0 + ((mseg(1)-1.0)/mseg(1))*c2 + ((mseg(1)-1.0)/mseg(1))*((mseg(1)-2.0)/mseg(1))*c3 ) + + fhc = ((3.0 + aLH - bLH + 3.0*cLH)*eta - (1.0 + aLH + bLH - cLH)) / (2.0*(1.0-eta)) + & + (1.0 + aLH + bLH - cLH) / ( 2.0*(1.0-eta)**2 ) + (cLH - 1.0)*LOG(1.0-eta) + + fhc = fhc - fhs + + END SUBROUTINE F_CHAIN_HU_LIU_RC + + + + +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! + SUBROUTINE F_DISP_PCSAFT ( fdsp ) +! + USE EOS_VARIABLES, ONLY: PI, rho, eta, z0t, apar, bpar, order1, order2 + IMPLICIT NONE +! +!--------------------------------------------------------------------- + REAL, INTENT(IN OUT) :: fdsp +!--------------------------------------------------------------------- + INTEGER :: m + REAL :: I1, I2, c1_con, z3, zms, m_mean +!--------------------------------------------------------------------- + + z3 = eta + zms = 1.0 - eta + m_mean = z0t / ( PI / 6.0 ) + + I1 = 0.0 + I2 = 0.0 + DO m = 0, 6 + I1 = I1 + apar(m) * z3**m + I2 = I2 + bpar(m) * z3**m + END DO + + c1_con= 1.0/ ( 1.0 + m_mean*(8.0*z3-2.0*z3**2 )/zms**4 & + + (1.0-m_mean)*( 20.0*z3-27.0*z3**2 +12.0*z3**3 -2.0*z3**4 )/(zms*(2.0-z3))**2 ) + + fdsp = -2.0*PI*rho*I1*order1 - PI*rho*c1_con*m_mean*I2*order2 + + END SUBROUTINE F_DISP_PCSAFT + +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! + SUBROUTINE F_DISP_CKSAFT ( fdsp ) +! + USE EOS_VARIABLES, ONLY: nc, ncomp, PI, TAU, t, rho, eta, x, z0t, mseg, vij, uij, parame, um + USE EOS_CONSTANTS, ONLY: DNM + IMPLICIT NONE +! +!--------------------------------------------------------------------- + REAL, INTENT(IN OUT) :: fdsp +!--------------------------------------------------------------------- + INTEGER :: i, j, n, m + REAL :: zmr, nmr, m_mean +!--------------------------------------------------------------------- + + m_mean = z0t / ( PI / 6.0 ) + + DO i = 1, ncomp + DO j = 1, ncomp + vij(i,j)=(0.5*((parame(i,2)*(1.0-0.12 *EXP(-3.0*parame(i,3)/t))**3 )**(1.0/3.0) & + +(parame(j,2)*(1.0-0.12 *EXP(-3.0*parame(j,3)/t))**3 )**(1.0/3.0)))**3 + END DO + END DO + zmr = 0.0 + nmr = 0.0 + DO i = 1, ncomp + DO j = 1, ncomp + zmr = zmr + x(i)*x(j)*mseg(i)*mseg(j)*vij(i,j)*uij(i,j) + nmr = nmr + x(i)*x(j)*mseg(i)*mseg(j)*vij(i,j) + END DO + END DO + um = zmr / nmr + fdsp = 0.0 + DO n = 1, 4 + DO m = 1, 9 + fdsp = fdsp + DNM(n,m) * (um/t)**n *(eta/TAU)**m + END DO + END DO + fdsp = m_mean * fdsp + + + END SUBROUTINE F_DISP_CKSAFT + +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! + SUBROUTINE F_ASSOCIATION ( eps_kij, k_kij, fhb ) +! + USE EOS_VARIABLES, ONLY: nc, nsite, ncomp, t, z0t, z1t, z2t, z3t, rho, eta, x, & + parame, sig_ij, dij_ab, gij, nhb_typ, mx, nhb_no + IMPLICIT NONE +! +!--------------------------------------------------------------------- + REAL, INTENT(IN) :: eps_kij, k_kij + REAL, INTENT(IN OUT) :: fhb +!--------------------------------------------------------------------- + LOGICAL :: assoc + INTEGER :: i, j, k, l, no, ass_cnt, max_eval + REAL, DIMENSION(nc,nc) :: kap_hb + REAL, DIMENSION(nc,nc,nsite,nsite) :: eps_hb + REAL, DIMENSION(nc,nsite,nc,nsite) :: delta + REAL, DIMENSION(nc,nsite) :: mx_itr + REAL :: err_sum, sum0, amix, tol, ass_s1, ass_s2 + REAL :: z0, z1, z2, z3, zms +!--------------------------------------------------------------------- + + assoc = .false. + DO i = 1,ncomp + IF (NINT(parame(i,12)) /= 0) assoc = .true. + END DO + IF (assoc) THEN + + rho = eta / z3t + z0 = z0t * rho + z1 = z1t * rho + z2 = z2t * rho + z3 = z3t * rho + zms = 1.0 - z3 + + DO i = 1, ncomp + DO j = 1, ncomp + gij(i,j) = 1.0/zms + 3.0*dij_ab(i,j)*z2/zms/zms + 2.0*(dij_ab(i,j)*z2)**2 / zms**3 + END DO + END DO + + + DO i = 1, ncomp + IF ( NINT(parame(i,12)) /= 0 ) THEN + nhb_typ(i) = NINT( parame(i,12) ) + kap_hb(i,i) = parame(i,13) + no = 0 + DO k = 1,nhb_typ(i) + DO l = 1,nhb_typ(i) + eps_hb(i,i,k,l) = parame(i,(14+no)) + no = no + 1 + END DO + END DO + DO k = 1,nhb_typ(i) + nhb_no(i,k) = parame(i,(14+no)) + no = no + 1 + END DO + ELSE + nhb_typ(i) = 0 + kap_hb(i,i)= 0.0 + DO k = 1,nsite + DO l = 1,nsite + eps_hb(i,i,k,l) = 0.0 + END DO + END DO + END IF + END DO + + DO i = 1,ncomp + DO j = 1,ncomp + IF ( i /= j .AND. (nhb_typ(i) /= 0.AND.nhb_typ(j) /= 0) ) THEN + ! kap_hb(i,j)= (kap_hb(i,i)+kap_hb(j,j))/2.0 + ! kap_hb(i,j)= ( ( kap_hb(i,i)**(1.0/3.0) + kap_hb(j,j)**(1.0/3.0) )/2.0 )**3 + kap_hb(i,j) = (kap_hb(i,i)*kap_hb(j,j))**0.5 & + *((parame(i,2)*parame(j,2))**3 )**0.5 & + / (0.5*(parame(i,2)+parame(j,2)))**3 + kap_hb(i,j)= kap_hb(i,j)*(1.0-k_kij) + DO k = 1,nhb_typ(i) + DO l = 1,nhb_typ(j) + IF ( k /= l .AND. nhb_typ(i) >= 2 .AND. nhb_typ(j) >= 2 ) THEN + eps_hb(i,j,k,l) = (eps_hb(i,i,k,l)+eps_hb(j,j,l,k))/2.0 + ! eps_hb(i,j,k,l) = (eps_hb(i,i,k,l)*eps_hb(j,j,l,k))**0.5 + eps_hb(i,j,k,l) = eps_hb(i,j,k,l)*(1.0-eps_kij) + ELSE IF ( nhb_typ(i) == 1 .AND. l > k ) THEN + eps_hb(i,j,k,l) = (eps_hb(i,i,k,k)+eps_hb(j,j,l,k))/2.0 + eps_hb(j,i,l,k) = (eps_hb(i,i,k,k)+eps_hb(j,j,l,k))/2.0 + eps_hb(i,j,k,l) = eps_hb(i,j,k,l)*(1.0-eps_kij) + eps_hb(j,i,l,k) = eps_hb(j,i,l,k)*(1.0-eps_kij) + END IF + END DO + END DO + END IF + END DO + END DO + +!-----setting the self-association to zero for ionic compounds------ + DO i = 1,ncomp + IF ( parame(i,10) /= 0) kap_hb(i,i)=0.0 + DO j = 1,ncomp + IF ( parame(i,10) /= 0 .AND. parame(j,10) /= 0 ) kap_hb(i,j) = 0.0 + END DO + END DO + ! kap_hb(1,2)=0.050 + ! kap_hb(2,1)=0.050 + ! eps_hb(2,1,1,1)=465.0 + ! eps_hb(1,2,1,1)=465.0 + ! nhb_typ(1) = 1 + ! nhb_typ(2) = 1 + ! nhb_no(1,1)= 1.0 + ! nhb_no(2,1)= 1.0 + + + DO i = 1, ncomp + DO k = 1, nhb_typ(i) + DO j = 1, ncomp + DO l = 1, nhb_typ(j) + delta(i,k,j,l)=gij(i,j)*kap_hb(i,j)*(EXP(eps_hb(i,j,k,l)/t)-1.0) *sig_ij(i,j)**3 +!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! +! IF ((i+j).EQ.3) delta(i,k,j,l)=94.0 +!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! + END DO + END DO + IF ( mx(i,k) == 0.0 ) mx(i,k) = 1.0 + END DO + END DO + +!------constants for Iteration --------------------------------------- + amix = 0.7 + tol = 1.E-10 + IF (eta < 0.2) tol = 1.E-11 + IF (eta < 0.01) tol = 1.E-14 + max_eval = 200 + +! --- Iterate over all components and all sites ------------------------ + ass_cnt = 0 + iterate_TPT1: DO + + ass_cnt = ass_cnt + 1 + + DO i = 1, ncomp + DO k = 1, nhb_typ(i) + sum0 = 0.0 + DO j = 1, ncomp + DO l = 1, nhb_typ(j) + sum0 = sum0 + x(j)* mx(j,l)*nhb_no(j,l) *delta(i,k,j,l) + END DO + END DO + mx_itr(i,k) = 1.0 / (1.0 + sum0*rho) + END DO + END DO + + err_sum = 0.0 + DO i = 1, ncomp + DO k = 1, nhb_typ(i) + err_sum = err_sum + ABS( mx_itr(i,k) - mx(i,k) ) ! / ABS(mx_itr(i,k)) + mx(i,k) = mx_itr(i,k) * amix + mx(i,k) * (1.0 - amix) + IF ( mx(i,k) <= 0.0 ) mx(i,k)=1.E-50 + IF ( mx(i,k) > 1.0 ) mx(i,k)=1.0 + END DO + END DO + + IF ( err_sum <= tol .OR. ass_cnt >= max_eval ) THEN + IF ( ass_cnt >= max_eval ) WRITE(*,*) 'F_NUMERICAL: Max_eval violated = ',err_sum,tol + EXIT iterate_TPT1 + END IF + + END DO iterate_TPT1 + + DO i = 1, ncomp + ass_s1 = 0.0 + ass_s2 = 0.0 + DO k = 1, nhb_typ(i) + ass_s1 = ass_s1 + nhb_no(i,k) * ( 1.0 - mx(i,k) ) + ass_s2 = ass_s2 + nhb_no(i,k) * LOG(mx(i,k)) + END DO + fhb = fhb + x(i) * ( ass_s2 + ass_s1/2.0 ) + END DO + + END IF + + END SUBROUTINE F_ASSOCIATION + + +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! + SUBROUTINE F_ION_DIPOLE_TBH ( fhend ) +! + USE EOS_VARIABLES, ONLY: nc, PI, KBOL, NAv, ncomp, t, rho, eta, x, z0t, parame, uij, sig_ij + IMPLICIT NONE +! +!--------------------------------------------------------------------- + REAL, INTENT(IN OUT) :: fhend +!--------------------------------------------------------------------- + INTEGER :: i, dipole, ions + REAL :: m_mean + REAL :: fh32, fh2, fh52, fh3 + REAL :: e_elem, eps_cc0, rho_sol, dielec + REAL :: polabil, ydd, kappa, x_dipol, x_ions + REAL, DIMENSION(nc) :: my2dd, z_ii, e_cd, x_dd, x_ii + REAL :: sig_c, sig_d, sig_cd, r_s + REAL :: I0cc, I1cc, I2cc, Icd, Idd + REAL :: Iccc, Iccd, Icdd, Iddd +!--------------------------------------------------------------------- + +m_mean = z0t / ( PI / 6.0 ) + +!----------------Dieletric Constant of Water-------------------------- +e_elem = 1.602189246E-19 ! in Unit [Coulomb] +eps_cc0 = 8.854187818E-22 ! in Unit [Coulomb**2 /(J*Angstrom)] +! Correlation of M. Uematsu and E. U. Frank +! (Static Dieletric Constant of Water and Steam) +! valid range of conditions 273,15 K <=T<= 823,15 K +! and density <= 1150 kg/m3 (i.e. 0 <= p <= 500 MPa) +rho_sol = rho * 18.015 * 1.E27/ NAv +rho_sol = rho_sol/1000.0 +dielec = 1.0+(7.62571/(t/293.15))*rho_sol +(2.44E2/(t/293.15)-1.41E2 & + + 2.78E1*(t/293.15))*rho_sol**2 & + + (-9.63E1/(t/293.15)+4.18E1*(t/293.15) & + - 1.02E1*(t/293.15)**2 )*rho_sol**3 +(-4.52E1/(t/293.15)**2 & + + 8.46E1/(t/293.15)-3.59E1)*rho_sol**4 + + +! !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! + +dielec = 1.0 + +! !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! + + +!----------------Dipole-Ion Term----------------------------------- +dipole = 0 +ions = 0 +fhend = 0.0 +DO i = 1, ncomp + IF ( parame(i,6) /= 0.0 .AND. uij(i,i) /= 0.0 .AND. x(i) > 0.0 ) THEN + my2dd(i) = (parame(i,6))**2 *1.E-49 / (uij(i,i)*KBOL*sig_ij(i,i)**3 *1.E-30) + dipole = 1 + ELSE + my2dd(i) = 0.0 + END IF + + z_ii(i) = parame(i,10) + IF ( z_ii(i) /= 0.0 .AND. uij(i,i) /= 0.0 .AND. x(i) > 0.0 ) THEN + e_cd(i) = ( parame(i,10)*e_elem* 1.E5 / SQRT(1.11265005) )**2 & + / ( uij(i,i)*kbol*sig_ij(i,i)*1.E-10 ) + ions = 1 + ELSE + e_cd(i) = 0.0 + END IF +END DO + + +IF ( dipole == 1 .AND. ions == 1 ) THEN + + ydd = 0.0 + kappa = 0.0 + x_dipol = 0.0 + x_ions = 0.0 + polabil = 0.0 + DO i = 1, ncomp + ydd = ydd + x(i)*(parame(i,6))**2 *1.E-49/ (kbol*t*1.E-30) + kappa = kappa + x(i) & + *(parame(i,10)*e_elem* 1.E5/SQRT(1.11265005))**2 /(KBOL*t*1.E-10) + IF (parame(i,10) /= 0.0) THEN + x_ions = x_ions + x(i) + ELSE + polabil = polabil + 4.0*PI*x(i)*rho*1.4573 *1.E-30 & + / (sig_ij(3,3)**3 *1.E-30) + END IF + IF (parame(i,6) /= 0.0) x_dipol= x_dipol+ x(i) + END DO + ydd = ydd * 4.0/9.0 * PI * rho + kappa = SQRT( 4.0 * PI * rho * kappa ) + + fh2 = 0.0 + sig_c = 0.0 + sig_d = 0.0 + DO i=1,ncomp + x_ii(i) = 0.0 + x_dd(i) = 0.0 + IF(parame(i,10) /= 0.0 .AND. x_ions /= 0.0) x_ii(i) = x(i)/x_ions + IF(parame(i,6) /= 0.0 .AND. x_dipol /= 0.0) x_dd(i) = x(i)/x_dipol + sig_c = sig_c + x_ii(i)*parame(i,2) + sig_d = sig_d + x_dd(i)*parame(i,2) + END DO + sig_cd = 0.5 * (sig_c + sig_d) + + r_s = 0.0 + ! DO i=1,ncomp + ! r_s=r_s + rho * x(i) * dhs(i)**3 + ! END DO + r_s = eta*6.0 / PI / m_mean + + I0cc = - (1.0 + 0.97743 * r_s + 0.05257*r_s*r_s) & + /(1.0 + 1.43613 * r_s + 0.41580*r_s*r_s) + ! I1cc = - (10.0 - 2.0*z3 + z3*z3) /20.0/(1.0 + 2.0*z3) + I1cc = - (10.0 - 2.0*r_s*pi/6.0 + r_s*r_s*pi/6.0*pi/6.0) & + /20.0/(1.0 + 2.0*r_s*pi/6.0) +!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! + ! I2cc = + (z3-4.0)*(z3*z3+2.0) /24.0/(1.0+2.0*z3) + ! relation of Stell and Lebowitz + I2cc = -0.33331+0.7418*r_s - 1.2047*r_s*r_s & + + 1.6139*r_s**3 - 1.5487*r_s**4 + 0.6626*r_s**5 +!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! + Icd = (1.0 + 0.79576 *r_s + 0.104556 *r_s*r_s) & + /(1.0 + 0.486704*r_s - 0.0222903*r_s*r_s) + Idd = (1.0 + 0.18158*r_s - 0.11467*r_s*r_s) & + /3.0/(1.0 - 0.49303*r_s + 0.06293*r_s*r_s) + Iccc= 3.0*(1.0 - 1.05560*r_s + 0.26591*r_s*r_s) & + /2.0/(1.0 + 0.53892*r_s - 0.94236*r_s*r_s) + Iccd= 11.0*(1.0 + 2.25642 *r_s + 0.05679 *r_s*r_s) & + /6.0/(1.0 + 2.64178 *r_s + 0.79783 *r_s*r_s) + Icdd= 0.94685*(1.0 + 2.97323 *r_s + 3.11931 *r_s*r_s) & + /(1.0 + 2.70186 *r_s + 1.22989 *r_s*r_s) + Iddd= 5.0*(1.0 + 1.12754*r_s + 0.56192*r_s*r_s) & + /24.0/(1.0 - 0.05495*r_s + 0.13332*r_s*r_s) + + IF ( sig_c <= 0.0 ) WRITE (*,*) 'error in Henderson ion term' + + fh32= - kappa**3 /(12.0*pi*rho) + fh2 = - 3.0* kappa**2 * ydd*Icd /(8.0*pi*rho) / sig_cd & + - kappa**4 *sig_c/(16.0*pi*rho)*I0cc + IF (sig_d /= 0.0) fh2 = fh2 - 27.0* ydd * ydd*Idd & + /(8.0*pi*rho) / sig_d**3 + fh52= (3.0*kappa**3 * ydd + kappa**5 *sig_c**2 *I1cc) & + /(8.0*pi*rho) + fh3 = - kappa**6 * sig_c**3 /(8.0*pi*rho) *(I2cc-Iccc/6.0) & + + kappa**4 * ydd *sig_c/(16.0*pi*rho) & + *( (6.0+5.0/3.0*sig_d/sig_c)*I0cc + 3.0*sig_d/sig_c*Iccd ) & + + 3.0*kappa**2 * ydd*ydd /(8.0*pi*rho) / sig_cd & + *( (2.0-3.21555*sig_d/sig_cd)*Icd +3.0*sig_d/sig_cd*Icdd ) + IF (sig_d /= 0.0) fh3 = fh3 + 27.0*ydd**3 & + /(16.0*pi*rho)/sig_d**3 *Iddd + + fhend = ( fh32 + (fh32*fh32*fh3-2.0*fh32*fh2*fh52+fh2**3 ) & + /(fh2*fh2-fh32*fh52) ) & + / ( 1.0 + (fh32*fh3-fh2*fh52) /(fh2*fh2-fh32*fh52) & + - (fh2*fh3-fh52*fh52) /(fh2*fh2-fh32*fh52) ) +!---------- +! fH32= - kappa**3 /(12.0*PI*rho) +! fH2 = - 3.0* kappa**2 * ydd*Icd /(8.0*PI*rho) / sig_cd +! fH52= (3.0*kappa**3 * ydd)/(8.0*PI*rho) +! fH3 = + kappa**4 * ydd *sig_c/(16.0*PI*rho) & +! *( (6.0+5.0/3.0*sig_d/sig_c)*0.0*I0cc + 3.0*sig_d/sig_c*Iccd) & +! + 3.0*kappa**2 * ydd*ydd /(8.0*PI*rho) / sig_cd & +! *( (2.0-3.215550*sig_d/sig_cd)*Icd +3.0*sig_d/sig_cd*Icdd ) + +! fHcd = ( + (fH32*fH32*fH3-2.0*fH32*fH2*fH52+fH2**3 ) & +! /(fH2*fH2-fH32*fH52) ) & +! / ( 1.0 + (fH32*fH3-fH2*fH52) /(fH2*fH2-fH32*fH52) & +! - (fH2*fH3-fH52*fH52) /(fH2*fH2-fH32*fH52) ) + +END IF + + END SUBROUTINE F_ION_DIPOLE_TBH + + +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! + SUBROUTINE F_ION_ION_PrimMSA ( fcc ) +! + USE EOS_VARIABLES, ONLY: nc, PI, KBOL, NAv, ncomp, t, rho, x, parame, mx + IMPLICIT NONE +! +!--------------------------------------------------------------------- + REAL, INTENT(IN OUT) :: fcc +!--------------------------------------------------------------------- + INTEGER :: i, j, cc_it, ions + REAL :: e_elem, eps_cc0, rho_sol, dielec + REAL :: x_ions + REAL :: cc_sig1, cc_sig2, cc_sig3 + REAL, DIMENSION(nc) :: z_ii, x_ii, sigm_i, my2dd + REAL :: alpha_2, kappa, ii_par + REAL :: cc_omeg, p_n, q2_i, cc_q2, cc_gam + REAL :: cc_error(2), cc_delt + REAL :: rhs, lambda, lam_s +!--------------------------------------------------------------------- + +!----------------Dieletric Constant of Water-------------------------- +e_elem = 1.602189246E-19 ! in Unit [Coulomb] +eps_cc0 = 8.854187818E-22 ! in Unit [Coulomb**2 /(J*Angstrom)] +! Correlation of M. Uematsu and E. U. Frank +! (Static Dieletric Constant of Water and Steam) +! valid range of conditions 273,15 K <=T<= 823,15 K +! and density <= 1150 kg/m3 (i.e. 0 <= p <= 500 MPa) +rho_sol = rho * 18.015 * 1.E27/ NAv +rho_sol = rho_sol/1000.0 +dielec = 1.0+(7.62571/(t/293.15))*rho_sol +(2.44E2/(t/293.15)-1.41E2 & + +2.78E1*(t/293.15))*rho_sol**2 & + +(-9.63E1/(t/293.15)+4.18E1*(t/293.15) & + -1.02E1*(t/293.15)**2 )*rho_sol**3 +(-4.52E1/(t/293.15)**2 & + +8.46E1/(t/293.15)-3.59E1)*rho_sol**4 + + +! !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! + +dielec = 1.0 + +! !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! + + +!----------------Ion-Ion: primitive MSA ------------------------------- +! the (dipole moment)**2 [my**2] corresponds to an attraction from +! point charges of [ SUM(xi * zi**2 * e_elem**2) * 3 * di**2 ] + +! parame(ion,6))**2 * 1.E-49 / (kbol*T) +! = (e_elem* 1.E5/SQRT(1.112650050))**2 +! *x(i)*zi**2 *3.0*sig_ij(1,1)**2 *1.E-20 + +! parame(ion,6))**2 = (e_elem* 1.E5/SQRT(1.112650050))**2 /1.E-49 +! *x(i)*zi**2 *3.0*sig_ij(i,i)**2 *1.E-20 + +! with the units +! my**2 [=] D**2 = 1.E-49 J*m3 +! e_elem **2 [=] C**2 = 1.E5 / SQRT(1.112650050) J*m + + +ions = 0 +x_ions = 0.0 +fcc = 0.0 +DO i = 1, ncomp + z_ii(i) = parame(i,10) + IF (z_ii(i) /= 0.0) THEN + sigm_i(i) = parame(i,2) + ELSE + sigm_i(i) = 0.0 + END IF + IF (z_ii(i) /= 0.0) ions = 1 + IF (z_ii(i) /= 0.0) x_ions = x_ions + x(i) +END DO + +IF (ions == 1 .AND. x_ions > 0.0) THEN + + cc_sig1 = 0.0 + cc_sig2 = 0.0 + cc_sig3 = 0.0 + DO i=1,ncomp + IF (z_ii(i) /= 0.0) THEN + x_ii(i) = x(i)/x_ions + ELSE + x_ii(i) =0.0 + END IF + cc_sig1 = cc_sig1 +x_ii(i)*sigm_i(i) + cc_sig2 = cc_sig2 +x_ii(i)*sigm_i(i)**2 + cc_sig3 = cc_sig3 +x_ii(i)*sigm_i(i)**3 + END DO + + + ! alpha_2 = 4.0*PI*e_elem**2 /eps_cc0/dielec/kbol/T + alpha_2 = e_elem**2 /eps_cc0 / dielec / KBOL/t + kappa = 0.0 + DO i = 1, ncomp + kappa = kappa + x(i)*z_ii(i)*z_ii(i)*mx(i,1) + END DO + kappa = SQRT( rho * alpha_2 * kappa ) + ii_par= kappa * cc_sig1 + + ! Temporaer: nach der Arbeit von Krienke verifiziert + ! noch nicht fuer Mischungen mit unterschiedl. Ladung erweitert + ! ii_par = DSQRT( e_elem**2 /eps_cc0/dielec/kbol/T & + ! *rho*(x(1)*Z_ii(1)**2 + x(2)*Z_ii(2)**2 ) )*cc_sig1 + + + cc_gam = kappa/2.0 + + ! noch offen !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! + cc_delt = 0.0 + DO i = 1, ncomp + cc_delt = cc_delt + x(i)*mx(i,1)*rho*sigm_i(i)**3 + END DO + cc_delt= 1.0 - PI/6.0*cc_delt + + cc_it = 0 + 13 CONTINUE + j = 0 + cc_it = cc_it + 1 + 131 CONTINUE + j = j + 1 + cc_omeg = 0.0 + DO i = 1, ncomp + cc_omeg = cc_omeg +x(i)*mx(i,1)*sigm_i(i)**3 /(1.0+cc_gam*sigm_i(i)) + END DO + cc_omeg = 1.0 + PI/2.0 / cc_delt * rho * cc_omeg + p_n = 0.0 + DO i = 1, ncomp + p_n = p_n + x(i)*mx(i,1)*rho / cc_omeg*sigm_i(i)*z_ii(i) / (1.0+cc_gam*sigm_i(i)) + END DO + q2_i = 0.0 + cc_q2= 0.0 + DO i = 1, ncomp + q2_i = q2_i + rho*x(i)*mx(i,1)*( (z_ii(i)-pi/2.0/cc_delt*sigm_i(i)**2 *p_n) & + /(1.0+cc_gam*sigm_i(i)) )**2 + cc_q2 = cc_q2 + x(i)*mx(i,1)*rho*z_ii(i)**2 / (1.0+cc_gam*sigm_i(i)) + END DO + q2_i = q2_i*alpha_2 / 4.0 + + cc_error(j) = cc_gam - SQRT(q2_i) + IF (j == 1) cc_gam = cc_gam*1.000001 + IF (j == 2) cc_gam = cc_gam - cc_error(2)* (cc_gam-cc_gam/1.000001)/(cc_error(2)-cc_error(1)) + + IF ( j == 1 .AND. ABS(cc_error(1)) > 1.E-15 ) GO TO 131 + IF ( cc_it >= 10 ) THEN + WRITE (*,*) ' cc error' + STOP + END IF + IF ( j /= 1 ) GO TO 13 + + fcc= - alpha_2 / PI/4.0 /rho* (cc_gam*cc_q2 & + + pi/2.0/cc_delt *cc_omeg*p_n**2 ) + cc_gam**3 /pi/3.0/rho + ! Restricted Primitive Model + ! fcc=-(3.0*ii_par*ii_par+6.0*ii_par+2.0 & + ! -2.0*(1.0+2.0*ii_par)**1.50) & + ! /(12.0*PI*rho *cc_sig1**3 ) + + ! fcc = x_ions * fcc + + my2dd(3) = (parame(3,6))**2 *1.E-19 /(KBOL*t) + my2dd(3) = (1.84)**2 *1.E-19 /(kbol*t) + + rhs = 12.0 * PI * rho * x(3) * my2dd(3) + lam_s = 1.0 + 12 CONTINUE + lambda = (rhs/((lam_s+2.0)**2 ) + 16.0/((1.0+lam_s)**4 ) )**0.5 + IF ( ABS(lam_s-lambda) > 1.E-10 )THEN + lam_s = ( lambda + lam_s ) / 2.0 + GO TO 12 + END IF + + ! f_cd = -(ii_par*ii_par)/(4.0*PI*rho*m_mean *cc_sig1**3 ) & + ! *(dielec-1.0)/(1.0 + parame(3,2)/cc_sig1/lambda) + ! write (*,*) ' ',f_cd,fcc,x_ions + ! f_cd = f_cd/(1.0 - fcc/f_cd) + ! fcc = 0.0 + +END IF + + +END SUBROUTINE F_ION_ION_PrimMSA + + +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! + SUBROUTINE F_ION_ION_nonPrimMSA ( fdd, fqq, fdq, fcc ) +! + USE EOS_VARIABLES, ONLY: nc, ncomp, t, eta, x, parame, mseg + IMPLICIT NONE +! +!--------------------------------------------------------------------- + REAL, INTENT(IN OUT) :: fdd, fqq, fdq, fcc +!--------------------------------------------------------------------- + INTEGER :: dipole + !REAL :: A_MSA !, A_CC, A_CD, A_DD, U_MSA, chempot + REAL, DIMENSION(nc) :: x_export, msegm +!--------------------------------------------------------------------- + + dipole = 0 + IF ( SUM( parame(1:ncomp,6) ) > 1.E-5 ) dipole = 1 + + IF ( dipole /= 0 ) THEN ! alternatively ions and dipoles = 1 + fdd = 0.0 + fqq = 0.0 + fdq = 0.0 + fcc = 0.0 + msegm(:) = mseg(:) ! the entries of the vector mseg and x are changed + x_export(:) = x(:) ! in SEMIRESTRICTED because the ions should be positioned first + ! that is why dummy vectors msegm and x_export are defined + !CALL SEMIRESTRICTED (A_MSA,A_CC,A_CD,A_DD,U_MSA, & + ! chempot,ncomp,parame,t,eta,x_export,msegm,0) + !fdd = A_MSA + write (*,*) 'why are individual contrib. A_CC,A_CD,A_DD not used' + stop + END IF + + END SUBROUTINE F_ION_ION_nonPrimMSA + + +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! + SUBROUTINE F_LC_MayerSaupe ( flc ) +! + USE EOS_VARIABLES, ONLY: nc, PI, KBOL, NAv, ncomp, phas, t, rho, eta, & + x, mseg, parame, E_lc, S_lc, dhs + IMPLICIT NONE +! +!--------------------------------------------------------------------- + REAL, INTENT(IN OUT) :: flc +!--------------------------------------------------------------------- + INTEGER :: i, j, k + INTEGER :: liq_crystal, count_lc, steps_lc + REAL :: alpha_lc, tolerance, deltay + REAL :: integrand1, integrand2, accel_lc + REAL :: error_lc, u_term, sphase + REAL, DIMENSION(nc) :: z_lc, S_lc1, S_lc2, sumu + REAL, DIMENSION(nc,nc) :: u_lc, klc +!--------------------------------------------------------------------- +INTEGER :: stabil +COMMON /stabil / stabil +!--------------------------------------------------------------------- + + + klc(1,2) = 0.0 + klc(2,1) = klc(1,2) + + alpha_lc = 1.0 + accel_lc = 4.0 + IF ( eta < 0.35 ) accel_lc = 1.3 + IF ( eta < 0.15 ) accel_lc = 1.0 + + liq_crystal = 0 + DO i = 1, ncomp + DO j = 1, ncomp + E_lc(i,j) = (E_lc(i,i)*E_lc(j,j))**0.5 *(1.0-klc(i,j)) !combining rule + ! E_LC(i,j)= ( E_LC(i,i)+E_LC(j,j) ) * 0.5 !combining rule + ! S_LC(i,j)= ( S_LC(i,i)+S_LC(j,j) ) * 0.5 !combining rule + IF (E_lc(i,j) /= 0.0) liq_crystal = 1 + END DO + END DO + ! S_LC(1,2) = 0.0 + ! S_LC(2,1) = S_LC(1,2) + ! E_LC(1,2) = 60.0 + ! E_LC(2,1) = E_LC(1,2) + + IF ( liq_crystal == 1 .AND. phas == 1 .AND. stabil == 0 ) THEN + + count_lc = 0 + tolerance = 1.E-6 + + steps_lc = 200 + deltay = 1.0 / REAL(steps_lc) + + ! --- dimensionless function U_LC repres. anisotr. intermolecular interactions in l.c. + + DO i = 1, ncomp + DO j = 1, ncomp + u_lc(i,j) = 2.0/3.0*pi*mseg(i)*mseg(j) *(0.5*(dhs(i)+dhs(j)))**3 & ! sig_ij(i,j)**3 + *(E_lc(i,j)/t+S_lc(i,j))*rho + END DO + END DO + + + DO i=1,ncomp + ! S_lc2(i) = 0.0 !for isotropic + S_lc2(i) = 0.5 !for nematic + S_lc1(i) = S_lc2(i) + END DO + + 1 CONTINUE + + DO i = 1, ncomp + IF (S_lc2(i) <= 0.3) S_lc1(i) = S_lc2(i) + IF (S_lc2(i) > 0.3) S_lc1(i) = S_lc1(i) + (S_lc2(i)-S_lc1(i))*accel_lc + END DO + + count_lc = count_lc + 1 + + ! --- single-particle orientation partition function Z_LC in liquid crystals + + DO i = 1, ncomp + sumu(i) = 0.0 + DO j = 1, ncomp + sumu(i) = sumu(i) + x(j)*u_lc(i,j)*S_lc1(j) + END DO + END DO + + DO i = 1, ncomp + z_lc(i) = 0.0 + integrand1 = EXP(-0.5*sumu(i)) !eq. for Z_LC with y=0 + DO k = 1, steps_lc + integrand2 = EXP(0.5*sumu(i)*(3.0*(deltay*REAL(k)) **2 -1.0)) + z_lc(i) = z_lc(i) + (integrand1 + integrand2)/2.0*deltay + integrand1 = integrand2 + END DO !k-index integration + END DO !i-index Z_LC(i) calculation + + ! --- order parameter S_lc in liquid crystals ----------------------- + + error_lc = 0.0 + DO i = 1, ncomp + S_lc2(i) = 0.0 + integrand1 = -1.0/z_lc(i)*0.5*EXP(-0.5*sumu(i)) !for S_lc with y=0 + DO k = 1, steps_lc + integrand2 = 1.0/z_lc(i)*0.5*(3.0*(deltay*REAL(k)) & + **2 -1.0)*EXP(0.5*sumu(i)*(3.0 *(deltay*REAL(k))**2 -1.0)) + S_lc2(i) = S_lc2(i) + (integrand1 + integrand2)/2.0*deltay + integrand1 = integrand2 + END DO !k-index integration + error_lc = error_lc + ABS(S_lc2(i)-S_lc1(i)) + END DO !i-index Z_LC(i) calculation + + sphase = 0.0 + DO i = 1, ncomp + sphase = sphase + S_lc2(i) + END DO + IF (sphase < 1.E-4) THEN + error_lc = 0.0 + DO i = 1, ncomp + S_lc2(i)= 0.0 + z_lc(i) = 1.0 + END DO + END IF + + + ! write (*,*) count_LC,S_lc2(1)-S_lc1(1),S_lc2(2)-S_lc1(2) + IF (error_lc > tolerance .AND. count_lc < 400) GO TO 1 + ! write (*,*) 'done',eta,S_lc2(1),S_lc2(2) + + IF (count_lc == 400) WRITE (*,*) 'LC iteration not converg.' + + ! --- the anisotropic contribution to the Helmholtz energy ---------- + + u_term = 0.0 + DO i = 1, ncomp + DO j = 1, ncomp + u_term = u_term + 0.5*x(i)*x(j)*S_lc2(i) *S_lc2(j)*u_lc(i,j) + END DO + END DO + + flc = 0.0 + DO i = 1, ncomp + IF (z_lc(i) /= 0.0) flc = flc - x(i) * LOG(z_lc(i)) + END DO + flc = flc + u_term + ! pause + + END IF + ! write (*,'(i2,i2,4(f15.8))') phas,stabil,flc,eta,S_lc2(1),x(1) + + + END SUBROUTINE F_LC_MayerSaupe + + + +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! + SUBROUTINE P_POLAR ( zdd, zddz, zddz2, zddz3, zqq, zqqz, zqqz2, zqqz3, zdq, zdqz, zdqz2, zdqz3 ) +! + USE EOS_VARIABLES, ONLY: ncomp, parame, dd_term, qq_term, dq_term + IMPLICIT NONE +! +! ---------------------------------------------------------------------- + REAL, INTENT(OUT) :: zdd, zddz, zddz2, zddz3 + REAL, INTENT(OUT) :: zqq, zqqz, zqqz2, zqqz3 + REAL, INTENT(OUT) :: zdq, zdqz, zdqz2, zdqz3 +! +! --- local variables--------------------------------------------------- + INTEGER :: dipole + INTEGER :: quadrupole + INTEGER :: dipole_quad +! ---------------------------------------------------------------------- + + zdd = 0.0 + zddz = 0.0 + zddz2 = 0.0 + zddz3 = 0.0 + zqq = 0.0 + zqqz = 0.0 + zqqz2 = 0.0 + zqqz3 = 0.0 + zdq = 0.0 + zdqz = 0.0 + zdqz2 = 0.0 + zdqz3 = 0.0 + + dipole = 0 + quadrupole = 0 + dipole_quad = 0 + IF ( SUM( parame(1:ncomp,6) ) /= 0.0 ) dipole = 1 + IF ( SUM( parame(1:ncomp,7) ) /= 0.0 ) quadrupole = 1 + IF ( dipole == 1 .AND. quadrupole == 1 ) dipole_quad = 1 + + ! -------------------------------------------------------------------- + ! dipole-dipole term + ! -------------------------------------------------------------------- + IF (dipole == 1) THEN + + IF (dd_term == 'GV') CALL P_DD_GROSS_VRABEC( zdd, zddz, zddz2, zddz3 ) + ! IF (dd_term == 'SF') CALL F_DD_SAAGER_FISCHER( k ) + IF (dd_term /= 'GV' .AND. dd_term /= 'SF') write (*,*) 'specify dipole term !' + + ENDIF + + ! -------------------------------------------------------------------- + ! quadrupole-quadrupole term + ! -------------------------------------------------------------------- + IF (quadrupole == 1) THEN + + !IF (qq_term == 'SF') CALL F_QQ_SAAGER_FISCHER( k ) + IF (qq_term == 'JG') CALL P_QQ_GROSS( zqq, zqqz, zqqz2, zqqz3 ) + IF (qq_term /= 'JG' .AND. qq_term /= 'SF') write (*,*) 'specify quadrupole term !' + + ENDIF + + ! -------------------------------------------------------------------- + ! dipole-quadrupole cross term + ! -------------------------------------------------------------------- + IF (dipole_quad == 1) THEN + + IF (dq_term == 'VG') CALL P_DQ_VRABEC_GROSS( zdq, zdqz, zdqz2, zdqz3 ) + IF (dq_term /= 'VG' ) write (*,*) 'specify DQ-cross term !' + + ENDIF + +END SUBROUTINE P_POLAR + + +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! + SUBROUTINE P_DD_GROSS_VRABEC( zdd, zddz, zddz2, zddz3 ) +! + USE PARAMETERS, ONLY: PI, KBOL + USE EOS_VARIABLES, ONLY: nc, ncomp, uij, parame, mseg, sig_ij, rho, eta, x, t + USE EOS_CONSTANTS, ONLY: ddp2, ddp3, ddp4 + IMPLICIT NONE +! +! ---------------------------------------------------------------------- + REAL, INTENT(IN OUT) :: zdd, zddz, zddz2, zddz3 +! ---------------------------------------------------------------------- + INTEGER :: i, j, k, m + REAL :: factor2, factor3, z3 + REAL :: xijfa, xijkfa, eij + REAL :: fdddr, fddd2, fddd3, fddd4 + REAL :: fdd2, fdd2z, fdd2z2, fdd2z3, fdd2z4 + REAL :: fdd3, fdd3z, fdd3z2, fdd3z3, fdd3z4 + REAL, DIMENSION(nc) :: my2dd + REAL, DIMENSION(nc,nc) :: Idd2, Idd2z, Idd2z2, Idd2z3, Idd2z4 + REAL, DIMENSION(nc,nc) :: Idd4, Idd4z, Idd4z2, Idd4z3, Idd4z4 + REAL, DIMENSION(nc,nc,nc) :: Idd3, Idd3z, Idd3z2, Idd3z3, Idd3z4 +! ---------------------------------------------------------------------- + + + zdd = 0.0 + zddz = 0.0 + zddz2 = 0.0 + zddz3 = 0.0 + z3 = eta + DO i = 1, ncomp + my2dd(i) = (parame(i,6))**2 *1.E-49 / (uij(i,i)*KBOL*mseg(i)*sig_ij(i,i)**3 *1.E-30) + END DO + + DO i = 1, ncomp + DO j = 1, ncomp + Idd2(i,j) = 0.0 + Idd4(i,j) = 0.0 + Idd2z(i,j) = 0.0 + Idd4z(i,j) = 0.0 + Idd2z2(i,j) = 0.0 + Idd4z2(i,j) = 0.0 + Idd2z3(i,j) = 0.0 + Idd4z3(i,j) = 0.0 + Idd2z4(i,j) = 0.0 + Idd4z4(i,j) = 0.0 + ! IF (paramei,6).NE.0.0 .AND. parame(j,6).NE.0.0) THEN + DO m = 0, 4 + Idd2(i,j) =Idd2(i,j) + ddp2(i,j,m) *z3**(m+1) + Idd4(i,j) =Idd4(i,j) + ddp4(i,j,m) *z3**(m+1) + Idd2z(i,j) =Idd2z(i,j) +ddp2(i,j,m)*REAL(m+1) *z3**m + Idd4z(i,j) =Idd4z(i,j) +ddp4(i,j,m)*REAL(m+1) *z3**m + Idd2z2(i,j)=Idd2z2(i,j)+ddp2(i,j,m)*REAL((m+1)*m) *z3**(m-1) + Idd4z2(i,j)=Idd4z2(i,j)+ddp4(i,j,m)*REAL((m+1)*m) *z3**(m-1) + Idd2z3(i,j)=Idd2z3(i,j)+ddp2(i,j,m)*REAL((m+1)*m*(m-1)) *z3**(m-2) + Idd4z3(i,j)=Idd4z3(i,j)+ddp4(i,j,m)*REAL((m+1)*m*(m-1)) *z3**(m-2) + Idd2z4(i,j)=Idd2z4(i,j)+ddp2(i,j,m)*REAL((m+1)*m*(m-1)*(m-2)) *z3**(m-3) + Idd4z4(i,j)=Idd4z4(i,j)+ddp4(i,j,m)*REAL((m+1)*m*(m-1)*(m-2)) *z3**(m-3) + END DO + DO k = 1, ncomp + Idd3(i,j,k) = 0.0 + Idd3z(i,j,k) = 0.0 + Idd3z2(i,j,k) = 0.0 + Idd3z3(i,j,k) = 0.0 + Idd3z4(i,j,k) = 0.0 + ! IF (parame(k,6).NE.0.0) THEN + DO m = 0, 4 + Idd3(i,j,k) =Idd3(i,j,k) +ddp3(i,j,k,m)*z3**(m+2) + Idd3z(i,j,k) =Idd3z(i,j,k) +ddp3(i,j,k,m)*REAL(m+2)*z3**(m+1) + Idd3z2(i,j,k)=Idd3z2(i,j,k)+ddp3(i,j,k,m)*REAL((m+2)*(m+1))*z3**m + Idd3z3(i,j,k)=Idd3z3(i,j,k)+ddp3(i,j,k,m)*REAL((m+2)*(m+1)*m)*z3**(m-1) + Idd3z4(i,j,k)=Idd3z4(i,j,k)+ddp3(i,j,k,m)*REAL((m+2)*(m+1)*m*(m-1)) *z3**(m-2) + END DO + ! ENDIF + END DO + ! ENDIF + END DO + END DO + + factor2= -PI *rho/z3 + factor3= -4.0/3.0*PI**2 * (rho/z3)**2 + + fdd2 = 0.0 + fdd2z = 0.0 + fdd2z2 = 0.0 + fdd2z3 = 0.0 + fdd2z4 = 0.0 + fdd3 = 0.0 + fdd3z = 0.0 + fdd3z2 = 0.0 + fdd3z3 = 0.0 + fdd3z4 = 0.0 + DO i = 1, ncomp + DO j = 1, ncomp + ! IF (parame(i,6).NE.0.0 .AND. parame(j,6).NE.0.0) THEN + xijfa = x(i)*parame(i,3)/t*parame(i,2)**3 *x(j)*parame(j,3)/t*parame(j,2)**3 & + / ((parame(i,2)+parame(j,2))/2.0)**3 *my2dd(i)*my2dd(j) + eij = (parame(i,3)*parame(j,3))**0.5 + fdd2 = fdd2 +factor2*xijfa*(Idd2(i,j) +eij/t*Idd4(i,j)) + fdd2z = fdd2z +factor2*xijfa*(Idd2z(i,j) +eij/t*Idd4z(i,j)) + fdd2z2 = fdd2z2+factor2*xijfa*(Idd2z2(i,j)+eij/t*Idd4z2(i,j)) + fdd2z3 = fdd2z3+factor2*xijfa*(Idd2z3(i,j)+eij/t*Idd4z3(i,j)) + fdd2z4 = fdd2z4+factor2*xijfa*(Idd2z4(i,j)+eij/t*Idd4z4(i,j)) + DO k = 1, ncomp + ! IF (parame(k,6).NE.0.0) THEN + xijkfa= x(i)*parame(i,3)/t*parame(i,2)**3 *x(j)*parame(j,3)/t*parame(j,2)**3 & + *x(k)*parame(k,3)/t*parame(k,2)**3 /((parame(i,2)+parame(j,2))/2.0) & + /((parame(i,2)+parame(k,2))/2.0) /((parame(j,2)+parame(k,2))/2.0) & + *my2dd(i)*my2dd(j)*my2dd(k) + fdd3 = fdd3 + factor3 * xijkfa*Idd3(i,j,k) + fdd3z = fdd3z + factor3 * xijkfa*Idd3z(i,j,k) + fdd3z2 = fdd3z2 + factor3 * xijkfa*Idd3z2(i,j,k) + fdd3z3 = fdd3z3 + factor3 * xijkfa*Idd3z3(i,j,k) + fdd3z4 = fdd3z4 + factor3 * xijkfa*Idd3z4(i,j,k) + ! ENDIF + END DO + ! ENDIF + END DO + END DO + IF (fdd2 < -1.E-50 .AND. fdd3 /= 0.0 .AND. fdd2z /= 0.0 .AND. fdd3z /= 0.0) THEN + + fdddr= fdd2* (fdd2*fdd2z - 2.0*fdd3*fdd2z+fdd2*fdd3z) / (fdd2-fdd3)**2 + fddd2=(2.0*fdd2*fdd2z*fdd2z +fdd2*fdd2*fdd2z2 & + -2.0*fdd2z**2 *fdd3-2.0*fdd2*fdd2z2*fdd3+fdd2*fdd2*fdd3z2) & + /(fdd2-fdd3)**2 + fdddr * 2.0*(fdd3z-fdd2z)/(fdd2-fdd3) + fddd3=(2.0*fdd2z**3 +6.0*fdd2*fdd2z*fdd2z2+fdd2*fdd2*fdd2z3 & + -6.0*fdd2z*fdd2z2*fdd3-2.0*fdd2z**2 *fdd3z & + -2.0*fdd2*fdd2z3*fdd3 -2.0*fdd2*fdd2z2*fdd3z & + +2.0*fdd2*fdd2z*fdd3z2+fdd2*fdd2*fdd3z3) /(fdd2-fdd3)**2 & + + 2.0/(fdd2-fdd3)* ( 2.0*fddd2*(fdd3z-fdd2z) & + + fdddr*(fdd3z2-fdd2z2) & + - fdddr/(fdd2-fdd3)*(fdd3z-fdd2z)**2 ) + fddd4=( 12.0*fdd2z**2 *fdd2z2+6.0*fdd2*fdd2z2**2 & + +8.0*fdd2*fdd2z*fdd2z3+fdd2*fdd2*fdd2z4-6.0*fdd2z2**2 *fdd3 & + -12.0*fdd2z*fdd2z2*fdd3z -8.0*fdd2z*fdd2z3*fdd3 & + -2.0*fdd2*fdd2z4*fdd3-4.0*fdd2*fdd2z3*fdd3z & + +4.0*fdd2*fdd2z*fdd3z3+fdd2**2 *fdd3z4 ) /(fdd2-fdd3)**2 & + + 6.0/(fdd2-fdd3)* ( fddd3*(fdd3z-fdd2z) & + -fddd2/(fdd2-fdd3)*(fdd3z-fdd2z)**2 & + - fdddr/(fdd2-fdd3)*(fdd3z-fdd2z)*(fdd3z2-fdd2z2) & + + fddd2*(fdd3z2-fdd2z2) +1.0/3.0*fdddr*(fdd3z3-fdd2z3) ) + zdd = fdddr*eta + zddz = fddd2*eta + fdddr + zddz2 = fddd3*eta + 2.0* fddd2 + zddz3 = fddd4*eta + 3.0* fddd3 + + END IF + + +END SUBROUTINE P_DD_GROSS_VRABEC + + + +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! + SUBROUTINE P_QQ_GROSS( zqq, zqqz, zqqz2, zqqz3 ) +! + USE PARAMETERS, ONLY: PI, KBOL + USE EOS_VARIABLES, ONLY: nc, ncomp, uij, parame, mseg, sig_ij, rho, eta, x, t + USE EOS_CONSTANTS, ONLY: qqp2, qqp3, qqp4 + IMPLICIT NONE +! +! ---------------------------------------------------------------------- + REAL, INTENT(IN OUT) :: zqq, zqqz, zqqz2, zqqz3 +! ---------------------------------------------------------------------- + INTEGER :: i, j, k, m + REAL :: factor2, factor3, z3 + REAL :: xijfa, xijkfa, eij + REAL :: fqqdr, fqqd2, fqqd3, fqqd4 + REAL :: fqq2, fqq2z, fqq2z2, fqq2z3, fqq2z4 + REAL :: fqq3, fqq3z, fqq3z2, fqq3z3, fqq3z4 + REAL, DIMENSION(nc) :: qq2 + REAL, DIMENSION(nc,nc) :: Iqq2, Iqq2z, Iqq2z2, Iqq2z3, Iqq2z4 + REAL, DIMENSION(nc,nc) :: Iqq4, Iqq4z, Iqq4z2, Iqq4z3, Iqq4z4 + REAL, DIMENSION(nc,nc,nc) :: Iqq3, Iqq3z, Iqq3z2, Iqq3z3, Iqq3z4 +! ---------------------------------------------------------------------- + + zqq = 0.0 + zqqz = 0.0 + zqqz2 = 0.0 + zqqz3 = 0.0 + z3 = eta + DO i=1,ncomp + qq2(i) = (parame(i,7))**2 *1.E-69 / (uij(i,i)*kbol*mseg(i)*sig_ij(i,i)**5 *1.E-50) + END DO + + DO i = 1, ncomp + DO j = 1, ncomp + Iqq2(i,j) = 0.0 + Iqq4(i,j) = 0.0 + Iqq2z(i,j) = 0.0 + Iqq4z(i,j) = 0.0 + Iqq2z2(i,j) = 0.0 + Iqq4z2(i,j) = 0.0 + Iqq2z3(i,j) = 0.0 + Iqq4z3(i,j) = 0.0 + Iqq2z4(i,j) = 0.0 + Iqq4z4(i,j) = 0.0 + IF (parame(i,7) /= 0.0 .AND. parame(j,7) /= 0.0) THEN + DO m = 0, 4 + Iqq2(i,j) =Iqq2(i,j) + qqp2(i,j,m)*z3**(m+1) + Iqq4(i,j) =Iqq4(i,j) + qqp4(i,j,m)*z3**(m+1) + Iqq2z(i,j) =Iqq2z(i,j) +qqp2(i,j,m)*REAL(m+1)*z3**m + Iqq4z(i,j) =Iqq4z(i,j) +qqp4(i,j,m)*REAL(m+1)*z3**m + Iqq2z2(i,j)=Iqq2z2(i,j)+qqp2(i,j,m)*REAL((m+1)*m)*z3**(m-1) + Iqq4z2(i,j)=Iqq4z2(i,j)+qqp4(i,j,m)*REAL((m+1)*m)*z3**(m-1) + Iqq2z3(i,j)=Iqq2z3(i,j)+qqp2(i,j,m)*REAL((m+1)*m*(m-1)) *z3**(m-2) + Iqq4z3(i,j)=Iqq4z3(i,j)+qqp4(i,j,m)*REAL((m+1)*m*(m-1)) *z3**(m-2) + Iqq2z4(i,j)=Iqq2z4(i,j)+qqp2(i,j,m)*REAL((m+1)*m*(m-1)*(m-2)) *z3**(m-3) + Iqq4z4(i,j)=Iqq4z4(i,j)+qqp4(i,j,m)*REAL((m+1)*m*(m-1)*(m-2)) *z3**(m-3) + END DO + DO k=1,ncomp + Iqq3(i,j,k) = 0.0 + Iqq3z(i,j,k) = 0.0 + Iqq3z2(i,j,k) = 0.0 + Iqq3z3(i,j,k) = 0.0 + Iqq3z4(i,j,k) = 0.0 + IF (parame(k,7) /= 0.0) THEN + DO m=0,4 + Iqq3(i,j,k) =Iqq3(i,j,k) + qqp3(i,j,k,m)*z3**(m+2) + Iqq3z(i,j,k)=Iqq3z(i,j,k)+qqp3(i,j,k,m)*REAL(m+2)*z3**(m+1) + Iqq3z2(i,j,k)=Iqq3z2(i,j,k)+qqp3(i,j,k,m)*REAL((m+2)*(m+1)) *z3**m + Iqq3z3(i,j,k)=Iqq3z3(i,j,k)+qqp3(i,j,k,m)*REAL((m+2)*(m+1)*m) *z3**(m-1) + Iqq3z4(i,j,k)=Iqq3z4(i,j,k)+qqp3(i,j,k,m) *REAL((m+2)*(m+1)*m*(m-1)) *z3**(m-2) + END DO + END IF + END DO + + END IF + END DO + END DO + + factor2= -9.0/16.0*PI *rho/z3 + factor3= 9.0/16.0*PI**2 * (rho/z3)**2 + + fqq2 = 0.0 + fqq2z = 0.0 + fqq2z2 = 0.0 + fqq2z3 = 0.0 + fqq2z4 = 0.0 + fqq3 = 0.0 + fqq3z = 0.0 + fqq3z2 = 0.0 + fqq3z3 = 0.0 + fqq3z4 = 0.0 + DO i = 1, ncomp + DO j = 1, ncomp + IF (parame(i,7) /= 0.0 .AND. parame(j,7) /= 0.0) THEN + xijfa =x(i)*uij(i,i)*qq2(i)*sig_ij(i,i)**5 /t & + *x(j)*uij(j,j)*qq2(j)*sig_ij(j,j)**5 /t/sig_ij(i,j)**7.0 + eij = (parame(i,3)*parame(j,3))**0.5 + fqq2= fqq2 +factor2*xijfa*(Iqq2(i,j) +eij/t*Iqq4(i,j) ) + fqq2z =fqq2z +factor2*xijfa*(Iqq2z(i,j) +eij/t*Iqq4z(i,j) ) + fqq2z2=fqq2z2+factor2*xijfa*(Iqq2z2(i,j)+eij/t*Iqq4z2(i,j)) + fqq2z3=fqq2z3+factor2*xijfa*(Iqq2z3(i,j)+eij/t*Iqq4z3(i,j)) + fqq2z4=fqq2z4+factor2*xijfa*(Iqq2z4(i,j)+eij/t*Iqq4z4(i,j)) + DO k = 1, ncomp + IF (parame(k,7) /= 0.0) THEN + xijkfa=x(i)*uij(i,i)*qq2(i)*sig_ij(i,i)**5 /t/sig_ij(i,j)**3 & + *x(j)*uij(j,j)*qq2(j)*sig_ij(j,j)**5 /t/sig_ij(i,k)**3 & + *x(k)*uij(k,k)*qq2(k)*sig_ij(k,k)**5 /t/sig_ij(j,k)**3 + fqq3 = fqq3 + factor3 * xijkfa*Iqq3(i,j,k) + fqq3z = fqq3z + factor3 * xijkfa*Iqq3z(i,j,k) + fqq3z2 = fqq3z2 + factor3 * xijkfa*Iqq3z2(i,j,k) + fqq3z3 = fqq3z3 + factor3 * xijkfa*Iqq3z3(i,j,k) + fqq3z4 = fqq3z4 + factor3 * xijkfa*Iqq3z4(i,j,k) + END IF + END DO + END IF + END DO + END DO + IF (fqq2 < -1.E-50 .AND. fqq3 /= 0.0 .AND. fqq2z /= 0.0 .AND. fqq3z /= 0.0) THEN + fqqdr = fqq2* (fqq2*fqq2z - 2.0*fqq3*fqq2z+fqq2*fqq3z) /(fqq2-fqq3)**2 + fqqd2= (2.0*fqq2*fqq2z*fqq2z +fqq2*fqq2*fqq2z2 & + -2.0*fqq2z**2 *fqq3-2.0*fqq2*fqq2z2*fqq3+fqq2*fqq2*fqq3z2) & + /(fqq2-fqq3)**2 + fqqdr * 2.0*(fqq3z-fqq2z)/(fqq2-fqq3) + fqqd3=(2.0*fqq2z**3 +6.0*fqq2*fqq2z*fqq2z2+fqq2*fqq2*fqq2z3 & + -6.0*fqq2z*fqq2z2*fqq3-2.0*fqq2z**2 *fqq3z & + -2.0*fqq2*fqq2z3*fqq3 -2.0*fqq2*fqq2z2*fqq3z & + +2.0*fqq2*fqq2z*fqq3z2+fqq2*fqq2*fqq3z3) /(fqq2-fqq3)**2 & + + 2.0/(fqq2-fqq3)* ( 2.0*fqqd2*(fqq3z-fqq2z) & + + fqqdr*(fqq3z2-fqq2z2) - fqqdr/(fqq2-fqq3)*(fqq3z-fqq2z)**2 ) + fqqd4=( 12.0*fqq2z**2 *fqq2z2+6.0*fqq2*fqq2z2**2 & + +8.0*fqq2*fqq2z*fqq2z3+fqq2*fqq2*fqq2z4-6.0*fqq2z2**2 *fqq3 & + -12.0*fqq2z*fqq2z2*fqq3z -8.0*fqq2z*fqq2z3*fqq3 & + -2.0*fqq2*fqq2z4*fqq3-4.0*fqq2*fqq2z3*fqq3z & + +4.0*fqq2*fqq2z*fqq3z3+fqq2**2 *fqq3z4 ) /(fqq2-fqq3)**2 & + + 6.0/(fqq2-fqq3)* ( fqqd3*(fqq3z-fqq2z) & + -fqqd2/(fqq2-fqq3)*(fqq3z-fqq2z)**2 & + - fqqdr/(fqq2-fqq3)*(fqq3z-fqq2z)*(fqq3z2-fqq2z2) & + + fqqd2*(fqq3z2-fqq2z2) +1.0/3.0*fqqdr*(fqq3z3-fqq2z3) ) + zqq = fqqdr*eta + zqqz = fqqd2*eta + fqqdr + zqqz2 = fqqd3*eta + 2.0* fqqd2 + zqqz3 = fqqd4*eta + 3.0* fqqd3 + END IF + + +END SUBROUTINE P_QQ_GROSS + +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! + SUBROUTINE P_DQ_VRABEC_GROSS( zdq, zdqz, zdqz2, zdqz3 ) +! + USE PARAMETERS, ONLY: PI, KBOL + USE EOS_VARIABLES, ONLY: nc, ncomp, uij, parame, mseg, sig_ij, rho, eta, x, t + USE EOS_CONSTANTS, ONLY: dqp2, dqp3, dqp4 + IMPLICIT NONE +! +! ---------------------------------------------------------------------- + REAL, INTENT(IN OUT) :: zdq, zdqz, zdqz2, zdqz3 +! ---------------------------------------------------------------------- + INTEGER :: i, j, k, m + REAL :: factor2, factor3, z3 + REAL :: xijfa, xijkfa, eij + REAL :: fdqdr, fdqd2, fdqd3, fdqd4 + REAL :: fdq2, fdq2z, fdq2z2, fdq2z3, fdq2z4 + REAL :: fdq3, fdq3z, fdq3z2, fdq3z3, fdq3z4 + REAL, DIMENSION(nc) :: my2dd, myfac, qq2, q_fac + REAL, DIMENSION(nc,nc) :: Idq2, Idq2z, Idq2z2, Idq2z3, Idq2z4 + REAL, DIMENSION(nc,nc) :: Idq4, Idq4z, Idq4z2, Idq4z3, Idq4z4 + REAL, DIMENSION(nc,nc,nc) :: Idq3, Idq3z, Idq3z2, Idq3z3, Idq3z4 +! ---------------------------------------------------------------------- + + zdq = 0.0 + zdqz = 0.0 + zdqz2 = 0.0 + zdqz3 = 0.0 + z3 = eta + DO i = 1, ncomp + my2dd(i) = (parame(i,6))**2 *1.E-49 / (uij(i,i)*KBOL*mseg(i)*sig_ij(i,i)**3 *1.E-30) + myfac(i) = parame(i,3)/t*parame(i,2)**4 *my2dd(i) + qq2(i) = (parame(i,7))**2 *1.E-69 / (uij(i,i)*kbol*mseg(i)*sig_ij(i,i)**5 *1.E-50) + q_fac(i) = parame(i,3)/t*parame(i,2)**4 *qq2(i) + END DO + + + DO i = 1, ncomp + DO j = 1, ncomp + Idq2(i,j) = 0.0 + Idq4(i,j) = 0.0 + Idq2z(i,j) = 0.0 + Idq4z(i,j) = 0.0 + Idq2z2(i,j) = 0.0 + Idq4z2(i,j) = 0.0 + Idq2z3(i,j) = 0.0 + Idq4z3(i,j) = 0.0 + Idq2z4(i,j) = 0.0 + Idq4z4(i,j) = 0.0 + IF (myfac(i) /= 0.0 .AND. q_fac(j) /= 0.0) THEN + DO m = 0, 4 + Idq2(i,j) =Idq2(i,j) + dqp2(i,j,m)*z3**(m+1) + Idq4(i,j) =Idq4(i,j) + dqp4(i,j,m)*z3**(m+1) + Idq2z(i,j) =Idq2z(i,j) +dqp2(i,j,m)*REAL(m+1)*z3**m + Idq4z(i,j) =Idq4z(i,j) +dqp4(i,j,m)*REAL(m+1)*z3**m + Idq2z2(i,j)=Idq2z2(i,j)+dqp2(i,j,m)*REAL((m+1)*m)*z3**(m-1) + Idq4z2(i,j)=Idq4z2(i,j)+dqp4(i,j,m)*REAL((m+1)*m)*z3**(m-1) + Idq2z3(i,j)=Idq2z3(i,j)+dqp2(i,j,m)*REAL((m+1)*m*(m-1)) *z3**(m-2) + Idq4z3(i,j)=Idq4z3(i,j)+dqp4(i,j,m)*REAL((m+1)*m*(m-1)) *z3**(m-2) + Idq2z4(i,j)=Idq2z4(i,j)+dqp2(i,j,m)*REAL((m+1)*m*(m-1)*(m-2)) *z3**(m-3) + Idq4z4(i,j)=Idq4z4(i,j)+dqp4(i,j,m)*REAL((m+1)*m*(m-1)*(m-2)) *z3**(m-3) + END DO + DO k = 1, ncomp + Idq3(i,j,k) = 0.0 + Idq3z(i,j,k) = 0.0 + Idq3z2(i,j,k) = 0.0 + Idq3z3(i,j,k) = 0.0 + Idq3z4(i,j,k) = 0.0 + IF (myfac(k) /= 0.0.OR.q_fac(k) /= 0.0) THEN + DO m = 0, 4 + Idq3(i,j,k) =Idq3(i,j,k) + dqp3(i,j,k,m)*z3**(m+2) + Idq3z(i,j,k)=Idq3z(i,j,k)+dqp3(i,j,k,m)*REAL(m+2)*z3**(m+1) + Idq3z2(i,j,k)=Idq3z2(i,j,k)+dqp3(i,j,k,m)*REAL((m+2)*(m+1)) *z3**m + Idq3z3(i,j,k)=Idq3z3(i,j,k)+dqp3(i,j,k,m)*REAL((m+2)*(m+1)*m) *z3**(m-1) + Idq3z4(i,j,k)=Idq3z4(i,j,k)+dqp3(i,j,k,m) & + *REAL((m+2)*(m+1)*m*(m-1)) *z3**(m-2) + END DO + END IF + END DO + + END IF + END DO + END DO + + factor2= -9.0/4.0*PI *rho/z3 + factor3= PI**2 * (rho/z3)**2 + + fdq2 = 0.0 + fdq2z = 0.0 + fdq2z2 = 0.0 + fdq2z3 = 0.0 + fdq2z4 = 0.0 + fdq3 = 0.0 + fdq3z = 0.0 + fdq3z2 = 0.0 + fdq3z3 = 0.0 + fdq3z4 = 0.0 + DO i = 1, ncomp + DO j = 1, ncomp + IF (myfac(i) /= 0.0 .AND. q_fac(j) /= 0.0) THEN + xijfa =x(i)*myfac(i) * x(j)*q_fac(j) /sig_ij(i,j)**5 + eij = (parame(i,3)*parame(j,3))**0.5 + fdq2= fdq2 +factor2*xijfa*(Idq2(i,j) +eij/t*Idq4(i,j) ) + fdq2z =fdq2z +factor2*xijfa*(Idq2z(i,j) +eij/t*Idq4z(i,j) ) + fdq2z2=fdq2z2+factor2*xijfa*(Idq2z2(i,j)+eij/t*Idq4z2(i,j)) + fdq2z3=fdq2z3+factor2*xijfa*(Idq2z3(i,j)+eij/t*Idq4z3(i,j)) + fdq2z4=fdq2z4+factor2*xijfa*(Idq2z4(i,j)+eij/t*Idq4z4(i,j)) + DO k = 1, ncomp + IF (myfac(k) /= 0.0.OR.q_fac(k) /= 0.0) THEN + xijkfa=x(i)*x(j)*x(k)/(sig_ij(i,j)*sig_ij(i,k)*sig_ij(j,k))**2 & + *( myfac(i)*q_fac(j)*myfac(k) + myfac(i)*q_fac(j)*q_fac(k)*1.193735 ) + fdq3 =fdq3 + factor3 * xijkfa*Idq3(i,j,k) + fdq3z =fdq3z + factor3 * xijkfa*Idq3z(i,j,k) + fdq3z2=fdq3z2 + factor3 * xijkfa*Idq3z2(i,j,k) + fdq3z3=fdq3z3 + factor3 * xijkfa*Idq3z3(i,j,k) + fdq3z4=fdq3z4 + factor3 * xijkfa*Idq3z4(i,j,k) + END IF + END DO + END IF + END DO + END DO + IF (fdq2 < -1.E-50 .AND. fdq3 /= 0.0 .AND. fdq2z /= 0.0 .AND. fdq3z /= 0.0) THEN + fdqdr = fdq2* (fdq2*fdq2z - 2.0*fdq3*fdq2z+fdq2*fdq3z) /(fdq2-fdq3)**2 + fdqd2= (2.0*fdq2*fdq2z*fdq2z +fdq2*fdq2*fdq2z2 & + -2.0*fdq2z**2 *fdq3-2.0*fdq2*fdq2z2*fdq3+fdq2*fdq2*fdq3z2) & + /(fdq2-fdq3)**2 + fdqdr * 2.0*(fdq3z-fdq2z)/(fdq2-fdq3) + fdqd3=(2.0*fdq2z**3 +6.0*fdq2*fdq2z*fdq2z2+fdq2*fdq2*fdq2z3 & + -6.0*fdq2z*fdq2z2*fdq3-2.0*fdq2z**2 *fdq3z & + -2.0*fdq2*fdq2z3*fdq3 -2.0*fdq2*fdq2z2*fdq3z & + +2.0*fdq2*fdq2z*fdq3z2+fdq2*fdq2*fdq3z3) /(fdq2-fdq3)**2 & + + 2.0/(fdq2-fdq3)* ( 2.0*fdqd2*(fdq3z-fdq2z) & + + fdqdr*(fdq3z2-fdq2z2) - fdqdr/(fdq2-fdq3)*(fdq3z-fdq2z)**2 ) + fdqd4=( 12.0*fdq2z**2 *fdq2z2+6.0*fdq2*fdq2z2**2 & + +8.0*fdq2*fdq2z*fdq2z3+fdq2*fdq2*fdq2z4-6.0*fdq2z2**2 *fdq3 & + -12.0*fdq2z*fdq2z2*fdq3z -8.0*fdq2z*fdq2z3*fdq3 & + -2.0*fdq2*fdq2z4*fdq3-4.0*fdq2*fdq2z3*fdq3z & + +4.0*fdq2*fdq2z*fdq3z3+fdq2**2 *fdq3z4 ) /(fdq2-fdq3)**2 & + + 6.0/(fdq2-fdq3)* ( fdqd3*(fdq3z-fdq2z) & + -fdqd2/(fdq2-fdq3)*(fdq3z-fdq2z)**2 & + - fdqdr/(fdq2-fdq3)*(fdq3z-fdq2z)*(fdq3z2-fdq2z2) & + + fdqd2*(fdq3z2-fdq2z2) +1.0/3.0*fdqdr*(fdq3z3-fdq2z3) ) + zdq = fdqdr*eta + zdqz = fdqd2*eta + fdqdr + zdqz2 = fdqd3*eta + 2.0* fdqd2 + zdqz3 = fdqd4*eta + 3.0* fdqd3 + END IF + + +END SUBROUTINE P_DQ_VRABEC_GROSS + + + +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! + SUBROUTINE F_pert_theory ( fdsp ) +! + USE EOS_VARIABLES, ONLY: nc, PI, ncomp, t, p, rho, eta, & + x, z0t, mseg, parame, order1, order2 + USE EOS_NUMERICAL_DERIVATIVES, ONLY: disp_term + USE DFT_MODULE + IMPLICIT NONE +! +!--------------------------------------------------------------------- + REAL, INTENT(IN OUT) :: fdsp +!--------------------------------------------------------------------- + REAL :: I1, I2 + REAL :: z3, zms, c1_con, m_mean +!--------------------------------------------------------------------- + + ! caution: positive sign of correlation integral is used here ! + ! (the Helmholtz energy terms are written with a negative sign, while I1 and I2 are positive) + + IF (disp_term == 'PT1') THEN + + CALL f_dft ( I1, I2) + c1_con = 0.0 + I2 = 0.0 + fdsp = + ( - 2.0*PI*rho*I1*order1 ) + + ELSEIF (disp_term == 'PT2') THEN + + CALL f_dft ( I1, I2) + z3 = eta + zms = 1.0 - z3 + m_mean = z0t / ( PI / 6.0 ) + c1_con = 1.0/ ( 1.0 + m_mean*(8.0*z3-2.0*z3**2 )/zms**4 & + + (1.0 - m_mean)*( 20.0*z3 -27.0*z3**2 +12.0*z3**3 -2.0*z3**4 ) & + /(zms*(2.0-z3))**2 ) + fdsp = + ( - 2.0*PI*rho*I1*order1 - PI*rho*c1_con*m_mean*I2*order2 ) + + ELSEIF (disp_term == 'PT_MIX') THEN + + CALL f_pert_theory_mix ( fdsp ) + + ELSEIF (disp_term == 'PT_MF') THEN + + ! mean field theory + I1 = - ( - 8.0/9.0 - 4.0/9.0*(rc**(-9) -3.0*rc**(-3) ) - tau_cut/3.0*(rc**3 -1.0) ) + fdsp = + ( - 2.0*PI*rho*I1*order1 ) + write (*,*) 'caution: not thoroughly checked and tested' + + ELSE + write (*,*) 'define the type of perturbation theory' + stop + END IF + + ! I1 = I1 + 4.0/9.0*(2.5**-9 -3.0*2.5**-3 ) + ! fdsp = + ( - 2.0*PI*rho*I1*order1 - PI*rho*c1_con*m_mean*I2*order2 ) + + END SUBROUTINE F_pert_theory + + + + +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! + SUBROUTINE f_pert_theory_mix ( fdsp ) +! + USE EOS_VARIABLES, ONLY: nc, PI, ncomp, t, rho, eta, x, parame, mseg, dhs, sig_ij, uij + USE DFT_MODULE + IMPLICIT NONE +! +! ---------------------------------------------------------------------- + REAL, INTENT(IN OUT) :: fdsp +! +! ---------------------------------------------------------------------- + INTEGER :: k, ih + INTEGER :: l, m + REAL :: z3 + REAL :: ua, ua_c, rm + REAL, DIMENSION(nc,nc) :: I1 + REAL :: int10, int11 + REAL :: d_ij, dzr_local + REAL :: rad, xg, rdf + REAL :: dg_dz3, dg_dr + ! REAL :: intgrid(0:5000),intgri2(0:5000), utri(5000),I1_spline +! ---------------------------------------------------------------------- + +! -----constants-------------------------------------------------------- + ua_c = 4.0 * ( rc**(-12) - rc**(-6) ) + rm = 2.0**(1.0/6.0) + + I1(:,:) = 0.0 + + DO l = 1, ncomp + DO m = 1, ncomp + + rad = rc + + int10 = rc * rc * ua_c + ! intgrid(0)= int10 + + k = 0 + ih = 85 + + DO WHILE ( rad /= 1.0 ) + + dzr_local = dzr + IF ( rad - dzr_local <= 1.0 ) dzr_local = rad - 1.0 + + rad = rad - dzr_local + + k = k + 1 + + d_ij = 0.5*(dhs(l)+dhs(m)) / sig_ij(l,m) ! dimensionless effective hs-diameter d(T)/sig + xg = rad / d_ij + z3 = eta + rdf = 1.0 + dg_dz3 = 0.0 + IF ( rad <= rg ) THEN + IF ( l == 1 .AND. m == 1 ) CALL BI_CUB_SPLINE (z3,xg,ya_11,x1a_11,x2a_11,y1a_11,y2a_11,y12a_11, & + c_bicub_11,rdf,dg_dz3,dg_dr,den_step,ih,k) + IF ( l /= m ) CALL BI_CUB_SPLINE (z3,xg,ya_12,x1a_12,x2a_12,y1a_12,y2a_12,y12a_12, & + c_bicub_12,rdf,dg_dz3,dg_dr,den_step,ih,k) + IF ( l == 2 .AND. m == 2 ) CALL BI_CUB_SPLINE (z3,xg,ya_22,x1a_22,x2a_22,y1a_22,y2a_22,y12a_22, & + c_bicub_22,rdf,dg_dz3,dg_dr,den_step,ih,k) + END IF + + ua = 4.0 * ( rad**(-12) - rad**(-6) ) + + int11 = rdf * rad * rad * ua + I1(l,m) = I1(l,m) + dzr_local * ( int11 + int10 ) / 2.0 + + int10 = int11 + ! intgrid(k)= int11 + + END DO + + ! stepno = k + ! CALL SPLINE_PARA (dzr,intgrid,utri,stepno) + ! CALL SPLINE_INT (I1_spline,dzr,intgrid,utri,stepno) + + + ! caution: 1st order integral is in F_EOS.f defined with negative sign + ! --------------------------------------------------------------- + ! cut-off corrections + ! --------------------------------------------------------------- + ! I1(l,m) = I1(l,m) + ( 4.0/9.0 * rc**-9 - 4.0/3.0 * rc**-3 ) + ! I2(l,m) = I2(l,m) + 16.0/21.0 * rc**-21 - 32.0/15.0 * rc**-15 + 16.0/9.0 * rc**-9 + + END DO + END DO + + + fdsp = 0.0 + DO l = 1, ncomp + DO m = 1, ncomp + fdsp = fdsp + 2.0*PI*rho*x(l)*x(m)* mseg(l)*mseg(m)*sig_ij(l,m)**3 * uij(l,m)/t *I1(l,m) + ! ( 2.0*PI*rho*I1*order1 - PI*rho*c1_con*m_mean*I2*order2 ) + END DO + END DO + + +!!$ IF (disp_term == 'PT1') THEN +!!$ c1_con = 0.0 +!!$ I2 = 0.0 +!!$ ELSEIF (disp_term == 'PT2') THEN +!!$ zms = 1.0 - z3 +!!$ c1_con = 1.0/ ( 1.0 + m_mean*(8.0*z3-2.0*z3**2 )/zms**4 & +!!$ + (1.0 - m_mean)*( 20.0*z3 -27.0*z3**2 +12.0*z3**3 -2.0*z3**4 ) & +!!$ /(zms*(2.0-z3))**2 ) +!!$ ELSE +!!$ write (*,*) 'define the type of perturbation theory' +!!$ stop +!!$ END IF + + +END SUBROUTINE f_pert_theory_mix + + +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! + SUBROUTINE mu_pert_theory_mix ( mu_dsp ) +! + USE EOS_VARIABLES, ONLY: nc, PI, ncomp, t, rho, eta, x, parame, mseg, dhs, sig_ij, uij + USE DFT_MODULE + IMPLICIT NONE +! +! ---------------------------------------------------------------------- + REAL, INTENT(IN OUT) :: mu_dsp(nc) +! +! ---------------------------------------------------------------------- + INTEGER :: k, ih + INTEGER :: l, m + REAL :: z3 + REAL :: ua, ua_c, rm + REAL, DIMENSION(nc,nc) :: I1, I2 + REAL :: int1_0, int1_1, int2_0, int2_1 + REAL :: d_ij, dzr_local + REAL :: rad, xg, rdf + REAL :: dg_dz3, dg_dr + REAL :: term1(nc), term2 + ! REAL :: intgrid(0:5000),intgri2(0:5000), utri(5000),I1_spline +! ---------------------------------------------------------------------- + +! -----constants-------------------------------------------------------- + ua_c = 4.0 * ( rc**(-12) - rc**(-6) ) + rm = 2.0**(1.0/6.0) + + I1(:,:) = 0.0 + I2(:,:) = 0.0 + + DO l = 1, ncomp + + term1(l) = 0.0 + + DO m = 1, ncomp + + rad = rc + + int1_0 = rc * rc * ua_c + int2_0 = 0.0 + + k = 0 + ih = 85 + + DO WHILE ( rad /= 1.0 ) + + dzr_local = dzr + IF ( rad - dzr_local <= 1.0 ) dzr_local = rad - 1.0 + + rad = rad - dzr_local + k = k + 1 + + d_ij = 0.5*(dhs(l)+dhs(m)) / sig_ij(l,m) ! dimensionless effective hs-diameter d(T)/sig + xg = rad / d_ij + z3 = eta + rdf = 1.0 + dg_dz3 = 0.0 + IF ( rad <= rg ) THEN + IF ( l == 1 .AND. m == 1 ) CALL BI_CUB_SPLINE (z3,xg,ya_11,x1a_11,x2a_11,y1a_11,y2a_11,y12a_11, & + c_bicub_11,rdf,dg_dz3,dg_dr,den_step,ih,k) + IF ( l /= m ) CALL BI_CUB_SPLINE (z3,xg,ya_12,x1a_12,x2a_12,y1a_12,y2a_12,y12a_12, & + c_bicub_12,rdf,dg_dz3,dg_dr,den_step,ih,k) + IF ( l == 2 .AND. m == 2 ) CALL BI_CUB_SPLINE (z3,xg,ya_22,x1a_22,x2a_22,y1a_22,y2a_22,y12a_22, & + c_bicub_22,rdf,dg_dz3,dg_dr,den_step,ih,k) + END IF + + ua = 4.0 * ( rad**(-12) - rad**(-6) ) + + int1_1 = rdf * rad * rad * ua + int2_1 = dg_dz3 * rad * rad * ua + I1(l,m) = I1(l,m) + dzr_local * ( int1_1 + int1_0 ) / 2.0 + I2(l,m) = I2(l,m) + dzr_local * ( int2_1 + int2_0 ) / 2.0 + + int1_0 = int1_1 + int2_0 = int2_1 + + term1(l) = term1(l) +4.0*PI*rho*x(m)* mseg(l)*mseg(m) *sig_ij(l,m)**3 *uij(l,m)/t* dzr_local*(int1_1+int1_0)/2.0 + + END DO + + END DO + END DO + + + ! DO l = 1, ncomp + ! term1(l) = 0.0 + ! DO m = 1, ncomp + ! term1(l) = term1(l) + 4.0*PI*rho*x(m)* mseg(l)*mseg(m) * sig_ij(l,m)**3 * uij(l,m)/t *I1(l,m) + ! END DO + ! END DO + + term2 = 0.0 + DO l = 1, ncomp + DO m = 1, ncomp + term2 = term2 + 2.0*PI*rho*x(l) * rho*x(m)* mseg(l)*mseg(m) * sig_ij(l,m)**3 * uij(l,m)/t *I2(l,m) + END DO + END DO + + DO l = 1, ncomp + mu_dsp(l) = term1(l) + term2 * PI/ 6.0 * mseg(l)*dhs(l)**3 + END DO + +END SUBROUTINE mu_pert_theory_mix + + +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! + SUBROUTINE F_DD_GROSS_VRABEC( fdd ) +! + USE PARAMETERS, ONLY: PI, KBOL + USE EOS_VARIABLES, ONLY: nc, ncomp, uij, parame, mseg, sig_ij, rho, eta, x, t + USE EOS_CONSTANTS, ONLY: ddp2, ddp3, ddp4 + IMPLICIT NONE +! +! ---------------------------------------------------------------------- + REAL, INTENT(IN OUT) :: fdd +! ---------------------------------------------------------------------- + INTEGER :: i, j, k, m + INTEGER :: ddit, ddmax + REAL :: factor2, factor3 + REAL :: xijfa, xijkfa, xijf_j, xijkf_j, eij + REAL :: fdd2, fdd3 + REAL, DIMENSION(nc) :: my2dd, my0, alph_tst, z1dd, z2dd, dderror + REAL, DIMENSION(nc) :: fdd2m, fdd3m, fdd2m2, fdd3m2, fddm, fddm2 + REAL, DIMENSION(nc,nc) :: Idd2, Idd4 + REAL, DIMENSION(nc,nc,nc) :: Idd3 +! ---------------------------------------------------------------------- + + fdd = 0.0 + ddit = 0 + ddmax = 0 ! value assigned, if polarizable compound is present + fddm(:) = 0.0 + DO i = 1, ncomp + IF ( uij(i,i) == 0.0 ) write (*,*) 'F_DD_GROSS_VRABEC: do not use dimensionless units' + IF ( uij(i,i) == 0.0 ) stop + my2dd(i) = (parame(i,6))**2 *1.E-49 /(uij(i,i)*kbol* mseg(i)*sig_ij(i,i)**3 *1.E-30) + alph_tst(i) = parame(i,11) / (mseg(i)*sig_ij(i,i)**3 ) * t/parame(i,3) + IF ( alph_Tst(i) /= 0.0 ) ddmax = 25 ! set maximum number of polarizable RGT-iterations + z1dd(i) = my2dd(i) + 3.0*alph_tst(i) + z2dd(i) = 3.0*alph_tst(i) + my0(i) = my2dd(i) + END DO + + DO i = 1, ncomp + DO j = 1, ncomp + Idd2(i,j) = 0.0 + Idd4(i,j) = 0.0 + ! IF (parame(i,6).NE.0.0 .AND. parame(j,6).NE.0.0) THEN + DO m = 0, 4 + Idd2(i,j) = Idd2(i,j) + ddp2(i,j,m)*eta**m + Idd4(i,j) = Idd4(i,j) + ddp4(i,j,m)*eta**m + END DO + DO k = 1, ncomp + Idd3(i,j,k) = 0.0 + ! IF (parame(k,6).NE.0.0) THEN + DO m = 0, 4 + Idd3(i,j,k) = Idd3(i,j,k) + ddp3(i,j,k,m)*eta**m + END DO + ! ENDIF + END DO + ! ENDIF + END DO + END DO + + factor2 = -PI *rho + factor3 = -4.0/3.0*PI**2 * rho**2 + +9 CONTINUE + + fdd2m(:) = 0.0 + fdd2m2(:) = 0.0 + fdd3m(:) = 0.0 + fdd3m2(:) = 0.0 + fdd2 = 0.0 + fdd3 = 0.0 + DO i = 1, ncomp + DO j = 1, ncomp + ! IF (parame(i,6).NE.0.0 .AND. parame(j,6).NE.0.0) THEN + xijfa =x(i)*parame(i,3)/t*parame(i,2)**3 * x(j)*parame(j,3)/t*parame(j,2)**3 & + /((parame(i,2)+parame(j,2))/2.0)**3 * (z1dd(i)*z1dd(j)-z2dd(i)*z2dd(j)) ! * (1.0-lij(i,j)) + eij = (parame(i,3)*parame(j,3))**0.5 + fdd2= fdd2 + factor2 * xijfa * ( Idd2(i,j) + eij/t*Idd4(i,j) ) + xijf_j = parame(i,3)/t*parame(i,2)**3 *x(j)*parame(j,3)/t*parame(j,2)**3 & + /((parame(i,2)+parame(j,2))/2.0)**3 ! * (1.0-lij(i,j)) + fdd2m(i)=fdd2m(i)+4.0*SQRT(my2dd(i))*z1dd(j)*factor2* xijf_j *(Idd2(i,j)+eij/t*Idd4(i,j)) + fdd2m2(i)=fdd2m2(i) + 4.0*z1dd(j)*factor2* xijf_j *(Idd2(i,j)+eij/t*Idd4(i,j)) + IF (j == i) fdd2m2(i) =fdd2m2(i) +8.0*factor2* xijf_j*my2dd(i) *(Idd2(i,j)+eij/t*Idd4(i,j)) + DO k = 1, ncomp + ! IF (parame(k,6).NE.0.0) THEN + xijkfa = x(i)*parame(i,3)/t*parame(i,2)**3 *x(j)*parame(j,3)/t*parame(j,2)**3 & + *x(k)*parame(k,3)/t*parame(k,2)**3 / ((parame(i,2)+parame(j,2))/2.0) & + /((parame(i,2)+parame(k,2))/2.0) / ((parame(j,2)+parame(k,2))/2.0) & + *(z1dd(i)*z1dd(j)*z1dd(k)-z2dd(i)*z2dd(j)*z2dd(k)) + ! *(1.0-lij(i,j))*(1.0-lij(i,k))*(1.0-lij(j,k)) + fdd3 = fdd3 + factor3 * xijkfa * Idd3(i,j,k) + xijkf_j = parame(i,3)/t*parame(i,2)**3 *x(j)*parame(j,3)/t*parame(j,2)**3 & + *x(k)*parame(k,3)/t*parame(k,2)**3 /((parame(i,2)+parame(j,2))/2.0) & + /((parame(i,2)+parame(k,2))/2.0) /((parame(j,2)+parame(k,2))/2.0) + ! *(1.0-lij(i,j))*(1.0-lij(i,k))*(1.0-lij(j,k)) + fdd3m(i)=fdd3m(i)+6.0*factor3*SQRT(my2dd(i))*z1dd(j)*z1dd(k) *xijkf_j*Idd3(i,j,k) + fdd3m2(i)=fdd3m2(i)+6.0*factor3*z1dd(j)*z1dd(k) *xijkf_j*Idd3(i,j,k) + IF(j == i) fdd3m2(i) =fdd3m2(i)+24.0*factor3*my2dd(i)*z1dd(k) *xijkf_j*Idd3(i,j,k) + ! ENDIF + END DO + ! ENDIF + END DO + END DO + + IF (fdd2 < -1.E-50 .AND. fdd3 /= 0.0) THEN + fdd = fdd2 / ( 1.0 - fdd3/fdd2 ) + IF ( ddmax /= 0 ) THEN + DO i = 1, ncomp + ddit = ddit + 1 + fddm(i) =fdd2*(fdd2*fdd2m(i) -2.0*fdd3*fdd2m(i)+fdd2*fdd3m(i)) /(fdd2-fdd3)**2 + fddm2(i) = fdd2m(i) * (fdd2*fdd2m(i)-2.0*fdd3*fdd2m(i) +fdd2*fdd3m(i)) / (fdd2-fdd3)**2 & + + fdd2*(fdd2*fdd2m2(i) -2.0*fdd3*fdd2m2(i)+fdd2m(i)**2 & + -fdd2m(i)*fdd3m(i) +fdd2*fdd3m2(i)) / (fdd2-fdd3)**2 & + - 2.0*fdd2*(fdd2*fdd2m(i) -2.0*fdd3*fdd2m(i) +fdd2*fdd3m(i)) /(fdd2-fdd3)**3 & + *(fdd2m(i)-fdd3m(i)) + dderror(i)= SQRT( my2dd(i) ) - SQRT( my0(i) ) + alph_Tst(i)*fddm(i) + my2dd(i) = ( SQRT( my2dd(i) ) - dderror(i) / (1.0+alph_Tst(i)*fddm2(i)) )**2 + z1dd(i) = my2dd(i) + 3.0 * alph_Tst(i) + ENDDO + DO i = 1, ncomp + IF (ABS(dderror(i)) > 1.E-11 .AND. ddit < ddmax) GOTO 9 + ENDDO + fdd = fdd + SUM( 0.5*x(1:ncomp)*alph_Tst(1:ncomp)*fddm(1:ncomp)**2 ) + ENDIF + END IF + + +END SUBROUTINE F_DD_GROSS_VRABEC + + + +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! + SUBROUTINE F_QQ_GROSS( fqq ) +! + USE PARAMETERS, ONLY: PI, KBOL + USE EOS_VARIABLES, ONLY: nc, ncomp, uij, parame, mseg, sig_ij, rho, eta, x, t + USE EOS_CONSTANTS, ONLY: qqp2, qqp3, qqp4 + IMPLICIT NONE +! +! ---------------------------------------------------------------------- + REAL, INTENT(IN OUT) :: fqq +! ---------------------------------------------------------------------- + INTEGER :: i, j, k, m + REAL :: factor2, factor3 + REAL :: xijfa, xijkfa, eij + REAL :: fqq2, fqq3 + REAL, DIMENSION(nc) :: qq2 + REAL, DIMENSION(nc,nc) :: Iqq2, Iqq4 + REAL, DIMENSION(nc,nc,nc) :: Iqq3 +! ---------------------------------------------------------------------- + + + fqq = 0.0 + DO i = 1, ncomp + qq2(i) = (parame(i,7))**2 *1.E-69 / (uij(i,i)*kbol*mseg(i)*sig_ij(i,i)**5 *1.E-50) + END DO + + DO i = 1, ncomp + DO j = 1, ncomp + Iqq2(i,j) = 0.0 + Iqq4(i,j) = 0.0 + IF (parame(i,7) /= 0.0 .AND. parame(j,7) /= 0.0) THEN + DO m = 0, 4 + Iqq2(i,j) = Iqq2(i,j) + qqp2(i,j,m)*eta**m + Iqq4(i,j) = Iqq4(i,j) + qqp4(i,j,m)*eta**m + END DO + DO k = 1, ncomp + Iqq3(i,j,k) = 0.0 + IF (parame(k,7) /= 0.0) THEN + DO m = 0, 4 + Iqq3(i,j,k) = Iqq3(i,j,k) + qqp3(i,j,k,m)*eta**m + END DO + END IF + END DO + END IF + END DO + END DO + + factor2 = -9.0/16.0*PI *rho + factor3 = 9.0/16.0*PI**2 * rho**2 + + fqq2 = 0.0 + fqq3 = 0.0 + DO i = 1, ncomp + DO j = 1, ncomp + IF (parame(i,7) /= 0.0 .AND. parame(j,7) /= 0.0) THEN + xijfa=x(i)*uij(i,i)*qq2(i)*sig_ij(i,i)**5 /t & + *x(j)*uij(j,j)*qq2(j)*sig_ij(j,j)**5 /t/sig_ij(i,j)**7.0 + eij = (parame(i,3)*parame(j,3))**0.5 + fqq2= fqq2 +factor2* xijfa * (Iqq2(i,j)+eij/t*Iqq4(i,j)) + DO k = 1, ncomp + IF (parame(k,7) /= 0.0) THEN + xijkfa=x(i)*uij(i,i)*qq2(i)*sig_ij(i,i)**5 /t/sig_ij(i,j)**3 & + *x(j)*uij(j,j)*qq2(j)*sig_ij(j,j)**5 /t/sig_ij(i,k)**3 & + *x(k)*uij(k,k)*qq2(k)*sig_ij(k,k)**5 /t/sig_ij(j,k)**3 + fqq3 = fqq3 + factor3 * xijkfa * Iqq3(i,j,k) + END IF + END DO + END IF + END DO + END DO + + IF ( fqq2 < -1.E-50 .AND. fqq3 /= 0.0 ) THEN + fqq = fqq2 / ( 1.0 - fqq3/fqq2 ) + END IF + + + +END SUBROUTINE F_QQ_GROSS + +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! + SUBROUTINE F_DQ_VRABEC_GROSS( fdq ) +! + USE PARAMETERS, ONLY: PI, KBOL + USE EOS_VARIABLES, ONLY: nc, ncomp, uij, parame, mseg, sig_ij, rho, eta, x, t + USE EOS_CONSTANTS, ONLY: dqp2, dqp3, dqp4 + IMPLICIT NONE +! +! ---------------------------------------------------------------------- + REAL, INTENT(IN OUT) :: fdq +! ---------------------------------------------------------------------- + INTEGER :: i, j, k, m + REAL :: factor2, factor3 + REAL :: xijfa, xijkfa, eij + REAL :: fdq2, fdq3 + REAL, DIMENSION(nc) :: my2dd, myfac, qq2, q_fac + REAL, DIMENSION(nc,nc) :: Idq2, Idq4 + REAL, DIMENSION(nc,nc,nc) :: Idq3 +! ---------------------------------------------------------------------- + + + fdq = 0.0 + DO i = 1, ncomp + my2dd(i) = (parame(i,6))**2 *1.E-49 /(uij(i,i)*kbol* mseg(i)*sig_ij(i,i)**3 *1.E-30) + myfac(i) = parame(i,3)/t*parame(i,2)**4 *my2dd(i) + ! myfac(i)=parame(i,3)/T*parame(i,2)**4 *my2dd_renormalized(i) + qq2(i) = (parame(i,7))**2 *1.E-69 / (uij(i,i)*kbol*mseg(i)*sig_ij(i,i)**5 *1.E-50) + q_fac(i) = parame(i,3)/t*parame(i,2)**4 *qq2(i) + END DO + + DO i = 1, ncomp + DO j = 1, ncomp + Idq2(i,j) = 0.0 + Idq4(i,j) = 0.0 + IF (myfac(i) /= 0.0 .AND. q_fac(j) /= 0.0) THEN + DO m = 0, 4 + Idq2(i,j) = Idq2(i,j) + dqp2(i,j,m)*eta**m + Idq4(i,j) = Idq4(i,j) + dqp4(i,j,m)*eta**m + END DO + DO k = 1, ncomp + Idq3(i,j,k) = 0.0 + IF (myfac(k) /= 0.0 .OR. q_fac(k) /= 0.0) THEN + DO m = 0, 4 + Idq3(i,j,k) = Idq3(i,j,k) + dqp3(i,j,k,m)*eta**m + END DO + END IF + END DO + END IF + END DO + END DO + + factor2 = -9.0/4.0 * PI *rho + factor3 = PI**2 * rho**2 + + fdq2 = 0.0 + fdq3 = 0.0 + DO i = 1, ncomp + DO j = 1, ncomp + IF (myfac(i) /= 0.0 .AND. q_fac(j) /= 0.0) THEN + xijfa = x(i)*myfac(i) * x(j)*q_fac(j) /sig_ij(i,j)**5 + eij = (parame(i,3)*parame(j,3))**0.5 + fdq2 = fdq2 +factor2* xijfa*(Idq2(i,j)+eij/t*Idq4(i,j)) + DO k = 1, ncomp + IF (myfac(k) /= 0.0 .OR. q_fac(k) /= 0.0) THEN + xijkfa=x(i)*x(j)*x(k)/(sig_ij(i,j)*sig_ij(i,k)*sig_ij(j,k))**2 & + *( myfac(i)*q_fac(j)*myfac(k) + myfac(i)*q_fac(j)*q_fac(k)*1.1937350 ) + fdq3 = fdq3 + factor3*xijkfa*Idq3(i,j,k) + END IF + END DO + END IF + END DO + END DO + + IF (fdq2 < -1.E-50 .AND. fdq3 /= 0.0) THEN + fdq = fdq2 / ( 1.0 - fdq3/fdq2 ) + END IF + +END SUBROUTINE F_DQ_VRABEC_GROSS + + +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! + SUBROUTINE f_dft ( I1_dft, I2_dft ) +! + USE EOS_VARIABLES, ONLY: nc, PI, ncomp, t, rho, eta, x, mseg, parame + USE DFT_MODULE + IMPLICIT NONE +! +! ---------------------------------------------------------------------- + REAL, INTENT(OUT) :: I1_dft + REAL, INTENT(OUT) :: I2_dft +! +! ---------------------------------------------------------------------- + INTEGER :: k,ih + ! REAL :: z3 + REAL :: ua, ua_c, ua_2, ua_c_2, rm + REAL :: int10, int11, int20, int21 + REAL :: dg_drho + REAL :: rad, xg, rdf, rho_st, msegm + REAL :: sig_ij + REAL :: dg_dr, dzr_org !,rdf_d + ! REAL :: intgrid(0:NDFT),intgri2(0:NDFT) +! ---------------------------------------------------------------------- + +! -----constants-------------------------------------------------------- +msegm = parame(1,1) +rho_st = rho * parame(1,2)**3 + +ua_c = 4.0 * ( rc**(-12) - rc**(-6) ) +ua_c_2 = ua_c * ua_c +rm = 2.0**(1.0/6.0) + +int10 = rc*rc* ua_c +int20 = rc*rc* ua_c_2 +! intgrid(0)= int10 +! intgri2(0)= int20 + + +sig_ij = parame(1,2) + + +I1_dft = 0.0 +I2_dft = 0.0 +rad = rc +!dzr = dzp / 2.0 ! this line is obsolete. dzr is defined in DFT-nMF2 (dimensionless) +dzr_org= dzr +k = 0 +ih = 85 + +DO WHILE ( rad-dzr+1.E-9 >= 1.0 ) + + rad = rad - dzr + ! IF (rad <= 8.0) dzr = dzp + ! IF (rad <= rg) dzr = dzp/2.0 + k = k + 1 + xg = rad / dhs_st + ua = 4.0 * ( rad**(-12) - rad**(-6) ) + ua_2 = ua * ua + rdf = 1.0 + dg_drho = 0.0 + IF ( rad <= rg ) THEN + CALL BI_CUB_SPLINE (rho_st,xg,ya,x1a,x2a,y1a,y2a,y12a, & + c_bicub,rdf,dg_drho,dg_dr,den_step,ih,k) + END IF + + int11 = rdf*rad*rad* ua + int21 = rdf*rad*rad* ua_2 + I1_dft= I1_dft + dzr*(int11+int10)/2.0 + I2_dft= I2_dft + dzr*(int21+int20)/2.0 + int10 = int11 + int20 = int21 + +END DO + +dzr = dzr_org + +! stepno = k +! CALL SPLINE_PARA (dzr,intgrid,utri,stepno) +! CALL SPLINE_INT (I1,dzr,intgrid,utri,stepno) + +! caution: 1st order integral is in F_EOS.f defined with negative sign +I1_dft= - I1_dft - ( 4.0/9.0 * rc**(-9) - 4.0/3.0 * rc**(-3) ) + +! CALL SPLINE_PARA (dzr,intgri2,utri,stepno) +! CALL SPLINE_INT (I2,dzr,intgri2,utri,stepno) + +I2_dft = I2_dft + 16.0/21.0 * rc**(-21) - 32.0/15.0 * rc**(-15) + 16.0/9.0 * rc**(-9) + + +END SUBROUTINE f_dft + + + + +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! + REAL FUNCTION TANGENT_VALUE2 ( optpara, n ) +! SUBROUTINE TANGENT_VALUE ( fmin, optpara, n ) +! + USE BASIC_VARIABLES + USE STARTING_VALUES + IMPLICIT NONE +! +! ---------------------------------------------------------------------- + INTEGER, INTENT(IN) :: n + REAL, INTENT(IN) :: optpara(n) + !REAL, INTENT(IN) :: optpara(:) + !REAL, INTENT(IN OUT) :: fmin +! +! ---------------------------------------------------------------------- + INTEGER :: i + REAL :: lnphi(np,nc),ph_frac, gibbs_full(np),xlnx1,xlnx2 + REAL, DIMENSION(nc) :: ni_1, ni_2 +! ---------------------------------------------------------------------- + + + ! --- setting of mole fractions --------------------------------------- + DO i = 1, ncomp + IF ( optpara(i) < -300.0 ) THEN + ni_2(i) = 0.0 + ELSE + ni_2(i) = EXP( optpara(i) ) + END IF + END DO + + DO i = 1, ncomp + ni_1(i) = xif(i) - ni_2(i) + IF ( ni_2(i) > xif(i) ) THEN + ni_2(i) = xif(i) + ni_1(i) = xif(i) * 1.E-20 + ENDIF + END DO + + xi(2,1:ncomp) = ni_2(1:ncomp) / SUM( ni_2(1:ncomp) ) + lnx(2,1:ncomp) = optpara(1:ncomp) - LOG( SUM( ni_2(1:ncomp) ) ) + + ph_frac = SUM( ni_1(1:ncomp) ) + xi(1,1:ncomp) = ni_1(1:ncomp) / ph_frac + lnx(1,1:ncomp) = LOG( ni_1(1:ncomp) ) - LOG( ph_frac ) + ! write (*,'(a,4G18.8)') 'FF',(xif(i),i=1,ncomp) + ! write (*,'(a,4G18.8)') 'AA',(xi(1,i),i=1,ncomp) + ! write (*,'(a,3G18.8)') 'BB',(xi(2,i),i=1,ncomp) + + CALL fugacity (lnphi) + !CALL enthalpy_etc + + gibbs(1) = SUM( xi(1,1:ncomp) * lnphi(1,1:ncomp) ) ! dimensionless g/RT + gibbs(2) = SUM( xi(2,1:ncomp) * lnphi(2,1:ncomp) ) + + xlnx1 = SUM( xi(1,1:ncomp)*lnx(1,1:ncomp) ) ! dimensionless s/RT + xlnx2 = SUM( xi(2,1:ncomp)*lnx(2,1:ncomp) ) + + gibbs_full(1) = gibbs(1) + xlnx1 + gibbs_full(2) = gibbs(2) + xlnx2 + + TANGENT_VALUE2 = gibbs_full(1)*ph_frac + gibbs_full(2)*(1.0-ph_frac) + !fmin = gibbs_full(1)*ph_frac + gibbs_full(2)*(1.0-ph_frac) + !write (*,'(a,4G18.8)') 'TP',TANGENT_VALUE2,(lnx(1,i),i=1,ncomp) + !write (*,'(a,4G18.8)') 'al',ph_frac,(lnx(2,i), i=1,ncomp) + !write (*,*) ' ' + !pause + +END FUNCTION TANGENT_VALUE2 + + + + + + + + diff --git a/applications/PUfoam/MoDeNaModels/SurfaceTension/ExampleOfUsage/src/srcDetailedCode/crit_point_mixtures.F90 b/applications/PUfoam/MoDeNaModels/SurfaceTension/ExampleOfUsage/src/srcDetailedCode/crit_point_mixtures.F90 new file mode 100644 index 000000000..2df622679 --- /dev/null +++ b/applications/PUfoam/MoDeNaModels/SurfaceTension/ExampleOfUsage/src/srcDetailedCode/crit_point_mixtures.F90 @@ -0,0 +1,471 @@ + +SUBROUTINE CRIT_POINT_MIX(tc,user) + +!PETSc module +USE PetscManagement + +!VLE and DFT modules +USE BASIC_VARIABLES + +IMPLICIT NONE + +#include + +type (userctx) user +REAL :: tc +!local +REAL :: tc_L, tc_V, xi_save(np,nc),p_save +PetscErrorCode ierr + + +!!J:save value of pressure because it is changed during the calculation +p_save = p + +! --------------------------------------------------------------------- + ! determine the critical temp. to xi of liquid and to xi of vapor + ! --------------------------------------------------------------------- + + + xi_save(:,:) = xi(:,:) + dense(1) = 0.15 + + !call MPI_Barrier(PETSC_COMM_WORLD,ierr) + + !only proc 0 reads in the estimate and then sends it to all other procs using MPI_Bcast +! IF(user%rank == 0) THEN +! WRITE (*,*) 'provide an estimate of the crit. Temp. of the mixture' +! READ (*,*) t +! END IF + + t = 1.2 * t !initial estimate of critical temperature + + CALL MPI_Bcast(t,1,MPI_DOUBLE_PRECISION,0,PETSC_COMM_WORLD,ierr) + + xiF(1:ncomp) = xi_save(1,1:ncomp) + CALL Heidemann_Khalil + tc_L = t +! IF(user%rank == 0) THEN +! WRITE (*,*) 'critical temperature to xi_liquid',tc_L +! END IF + + xiF(1:ncomp) = xi_save(2,1:ncomp) + ! dense(1) = 0.15 + ! WRITE (*,*) 'provide an estimate of the crit. Temp. of the mixture' + ! READ (*,*) t + CALL Heidemann_Khalil + tc_V = t +! IF(user%rank == 0) THEN +! WRITE (*,*) 'critical temperature to xi_vapor ',tc_V +! END IF + + ! tc_L = 600.0 + ! WRITE (*,*) 'I have tentitativly set tc=700 ' + ! pause + + + !tc = ( tc_L + tc_V ) / 2.0 + tc = tc_L + xi(:,:) = xi_save(:,:) + densta(1:nphas) = val_conv(1:nphas) + dense(1:nphas) = val_conv(1:nphas) + t = val_conv(3) + IF(user%rank == 0) THEN + WRITE (*,*) 'estimate of critical temperature:',tc,'K' + WRITE (*,*) ' ' + END IF + +!!J: set pressure to its regular value +p = p_save + + +END SUBROUTINE CRIT_POINT_MIX + + + + + + + + + +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! SUBROUTINE Heidemann_Khalil +! +! This subroutine .... +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! + SUBROUTINE Heidemann_Khalil +! + USE PARAMETERS, ONLY: PI + USE BASIC_VARIABLES + USE Module_Heidemann_Khalil + USE Solve_NonLin + IMPLICIT NONE +! +! ---------------------------------------------------------------------- + INTERFACE + SUBROUTINE Heidemann_Khalil_obj ( iter_no, y, residu, dummy ) + INTEGER, INTENT(IN) :: iter_no + REAL, INTENT(IN) :: y(iter_no) + REAL, INTENT(OUT) :: residu(iter_no) + INTEGER, INTENT(IN OUT) :: dummy + END SUBROUTINE Heidemann_Khalil_obj + END INTERFACE +! + INTEGER :: info + REAL, ALLOCATABLE :: y(:),diag(:),residu(:) + + INTEGER :: i, count, nphas_save + REAL :: error0, error1, dense0, dfdx, delta_rho + CHARACTER (LEN=2) :: ensemble_save +! ---------------------------------------------------------------------- + + ensemble_save = ensemble_flag + ensemble_flag = 'tv' + + nphas_save = nphas + nphas = 1 + + ! xiF(2) = 0.5 * ( 0.71928411 + 0.72025642 ) + ! xiF(1) = 1.0 - xiF(2) + ! dense(1) = 0.5 * ( 0.159315 + 0.158817 ) + 0.02 + ! t = 500.0 + + dense0 = dense(1) + + info = 1 + n_unkw = ncomp + 1 + acc_a = 5.E-8 + step_a = 1.E-8 + + + ALLOCATE( y(n_unkw), diag(n_unkw), residu(n_unkw) ) + DO i = 1,ncomp + y(i) = 1.0 / SQRT( REAL( ncomp ) ) + END DO + y(ncomp+1) = t + count = 0 + error0 = 1.0 + + DO WHILE ( ABS( error0) > 0.001 .AND. count < 20 ) + count = count + 1 + + dense(1) = dense0 + 0.0001 + CALL hbrd (Heidemann_Khalil_obj, n_unkw, y, residu, step_a, acc_a, info, diag) + error1 = error_condition2 + IF (SUM( ABS( residu(1:n_unkw) ) ) > 1.E-5) write (*,*) 'caution: error 1st inner loop', SUM( ABS( residu(1:n_unkw) ) ) + + dense(1) = dense0 + CALL hbrd (Heidemann_Khalil_obj, n_unkw, y, residu, step_a, acc_a, info, diag) + IF (SUM( ABS( residu(1:n_unkw) ) ) > 1.E-5) write (*,*) 'caution: error 2nd inner loop', SUM( ABS( residu(1:n_unkw) ) ) + error0 = error_condition2 + + ! write (*,'(a,4G18.10)') ' t, p, eta error', t, p, dense(1), error0 + ! pause + dfdx = ( error1 - error0 ) / 0.0001 + delta_rho = MIN( error0 / dfdx, 0.02) + delta_rho = MAX( delta_rho, -0.02) + dense0 = dense0 - delta_rho + dense(1) = dense0 + + END DO + + !tc = t + !pc = p + + DEALLOCATE( y, diag, residu ) + + ensemble_flag = ensemble_save + nphas = nphas_save + IF ( ABS( error_condition2 ) > 1.E-1 ) write (*,*) 'caution: error outer loop', ABS( error_condition2 ) + +END SUBROUTINE Heidemann_Khalil + + +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! SUBROUTINE Heidemann_Khalil +! +! This subroutine .... +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! + SUBROUTINE Heidemann_Khalil_obj ( iter_no, y, residu, dummy ) +! + USE PARAMETERS, ONLY: PI + USE BASIC_VARIABLES + USE Module_Heidemann_Khalil + IMPLICIT NONE +! +! ---------------------------------------------------------------------- + INTEGER, INTENT(IN) :: iter_no + REAL, INTENT(IN) :: y(iter_no) + REAL, INTENT(OUT) :: residu(iter_no) + INTEGER, INTENT(IN OUT) :: dummy +! +! ---------------------------------------------------------------------- + INTEGER :: i, j, k + REAL, DIMENSION(nc) :: dn + REAL, DIMENSION(nc) :: dhs, rhoi00, rhoi0 + REAL :: rho, d_rho + ! REAL :: lnphi(np,nc) + REAL :: qij(nc,nc), qij0(nc,nc), qijk(nc,nc,nc) + ! CHARACTER (LEN=3) :: char_len +! ---------------------------------------------------------------------- + + dn(1:ncomp) = y(1:ncomp) + t = y(ncomp+1) + !dense(1) = y(ncomp+2) + + dhs(1:ncomp) = parame(1:ncomp,2) * ( 1.0 - 0.12 *EXP( -3.0*parame(1:ncomp,3)/t ) ) + rho = dense(1) / SUM( PI/6.0*xiF(1:ncomp)*parame(1:ncomp,1)* dhs(1:ncomp)**3 ) + rhoi00(1:ncomp) = xiF(1:ncomp)*rho + + d_rho = 0.000001 + + DO k = 1, ncomp + + rhoi0(1:ncomp) = rhoi00(1:ncomp) + rhoi0(k) = rhoi00(k) + d_rho + CALL qij_matrix ( rhoi0, dhs, d_rho, qij ) + qij0(:,:) = qij(:,:) + + rhoi0(1:ncomp) = rhoi00(1:ncomp) + CALL qij_matrix ( rhoi0, dhs, d_rho, qij ) + + DO i = 1, ncomp + DO j = 1, ncomp + qijk(i,j,k) = ( qij0(i,j) - qij(i,j) ) / d_rho + ! write(*,*) i,j,k,qijk(i,j,k) + END DO + END DO + + END DO + + ! write (*,'(a,4G18.10)') 'det',qij(2,2)*qij(1,1) - qij(2,1)*qij(1,2) + ! write (*,'(a,3G18.10)') ' t,p,eta ', t, p, dense(1) + DO j = 1, ncomp + residu(j) = SUM( qij(1:ncomp,j)*dn(1:ncomp) ) + END DO + residu(ncomp+1) = 1.0 - SUM( dn(1:ncomp)*dn(1:ncomp) ) + + error_condition2 = 0.0 + DO k = 1, ncomp + DO i = 1, ncomp + DO j = 1, ncomp + error_condition2 = error_condition2 + qijk(i,j,k) * dn(i) * dn(j) * dn(k) + END DO + END DO + END DO + error_condition2 = error_condition2 * 1.E-4 ! the values are scaled down to prevent numerical dominance of this error + !residu(ncomp+2) = error_condition2 + + !write (char_len,'(I3)') ncomp+2 + !write (*,'(a,'//char_len//'G18.10)') ' error',residu(1:ncomp+1) + !write (*,*) ' ' + !pause + +END SUBROUTINE Heidemann_Khalil_obj + + +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! SUBROUTINE Heidemann_Khalil +! +! This subroutine calculates the spinodal for a binary mixture to given +! T, p and for a given starting value of the density vector rhoi +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! + SUBROUTINE binary_tp_spinodal ( rhoi, p_sp ) +! + USE PARAMETERS, ONLY: PI + USE BASIC_VARIABLES + USE Module_Heidemann_Khalil + USE Solve_NonLin + IMPLICIT NONE +! +! ---------------------------------------------------------------------- + INTERFACE + SUBROUTINE binary_spinodal_obj ( iter_no, y, residu, dummy ) + INTEGER, INTENT(IN) :: iter_no + REAL, INTENT(IN) :: y(iter_no) + REAL, INTENT(OUT) :: residu(iter_no) + INTEGER, INTENT(IN OUT) :: dummy + END SUBROUTINE binary_spinodal_obj + END INTERFACE + + REAL, dimension(nc) :: rhoi + REAL :: p_sp +! ---------------------------------------------------------------------- + + INTEGER :: info + REAL, ALLOCATABLE :: y(:), diag(:), residu(:) + + INTEGER :: i, nphas_save + CHARACTER (LEN=2) :: ensemble_save +! ---------------------------------------------------------------------- + + ensemble_save = ensemble_flag + ensemble_flag = 'tv' + + nphas_save = nphas + nphas = 1 + + info = 1 + n_unkw = ncomp + 2 + acc_a = 5.E-8 + step_a = 1.E-8 + + + ALLOCATE( y(n_unkw), diag(n_unkw), residu(n_unkw) ) + DO i = 1, ncomp + y(i) = 1.0 / SQRT( REAL( ncomp ) ) + END DO + DO i = 1, ncomp + y( ncomp + i ) = rhoi( i ) + END DO + + CALL hbrd (binary_spinodal_obj, n_unkw, y, residu, step_a, acc_a, info, diag) + + DO i = 1, ncomp + rhoi( i ) = y( ncomp + i ) + END DO + write (*,*) 'info',info + write (*,*) 'rhoi',rhoi(1:ncomp) + !write (*,*) 'eta',PI / 6.0 * sum( rhoi(1:ncomp)*mseg(1:ncomp)*dhs(1:ncomp)**3 ) + write (*,*) 'x',rhoi(1:ncomp) / sum( rhoi(1:ncomp) ) + + DEALLOCATE( y, diag, residu ) + + ensemble_flag = ensemble_save + nphas = nphas_save + +END SUBROUTINE binary_tp_spinodal + + +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! SUBROUTINE Heidemann_Khalil +! +! This subroutine .... +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! + SUBROUTINE binary_spinodal_obj ( iter_no, y, residu, dummy ) +! + USE PARAMETERS, ONLY: PI + USE BASIC_VARIABLES + USE Module_Heidemann_Khalil + IMPLICIT NONE +! +! ---------------------------------------------------------------------- + INTEGER, INTENT(IN) :: iter_no + REAL, INTENT(IN) :: y(iter_no) + REAL, INTENT(OUT) :: residu(iter_no) + INTEGER, INTENT(IN OUT) :: dummy +! +! ---------------------------------------------------------------------- + INTEGER :: j, k + REAL :: p_calculated, zges, p_sp + REAL :: d_rho + REAL, DIMENSION(nc) :: dn + REAL, DIMENSION(nc) :: dhs, rhoi + REAL, DIMENSION(nc,nc) :: qij +! ---------------------------------------------------------------------- + + dn(1:ncomp) = y(1:ncomp) + rhoi(1:ncomp) = y( (ncomp+1) : (ncomp+ncomp) ) + dhs(1:ncomp) = parame(1:ncomp,2) * ( 1.0 - 0.12 *EXP( -3.0*parame(1:ncomp,3)/t ) ) ! is this calc. needed? + + call p_calc ( p_calculated, zges ) + + d_rho = 0.000001 + + DO k = 1, ncomp + + CALL qij_matrix ( rhoi, dhs, d_rho, qij ) + + END DO + + !write (*,'(a,4G18.10)') 'det',qij(2,2)*qij(1,1) - qij(2,1)*qij(1,2) + write (*,'(a,3G18.10)') ' t,p,eta ', t, p, dense(1) + DO j = 1, ncomp + residu(j) = SUM( qij(1:ncomp,j)*dn(1:ncomp) ) + END DO + residu(ncomp+1) = 1.0 - SUM( dn(1:ncomp)*dn(1:ncomp) ) + write (*,*) 'p_sp has to be handed over to the obj fct properly!' + write (*,*) 'Can I simply set p = p_sp? In other words is p altered during the calculation?' + stop + residu(ncomp+2) = p_sp - p_calculated + + write (*,'(a,4G18.10)') ' error',residu(1:4) + write (*,*) ' ' + pause + +END SUBROUTINE binary_spinodal_obj + + +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! SUBROUTINE Heidemann_Khalil +! +! This subroutine .... +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! + SUBROUTINE qij_matrix ( rhoi0, dhs, d_rho, qij ) +! + USE PARAMETERS, ONLY: PI, KBOL + USE BASIC_VARIABLES + USE EOS_VARIABLES, ONLY: pges + IMPLICIT NONE +! +! ---------------------------------------------------------------------- + REAL, DIMENSION(nc), INTENT(IN) :: rhoi0 + REAL, DIMENSION(nc), INTENT(IN) :: dhs + REAL, INTENT(IN) :: d_rho + REAL, DIMENSION(nc,nc), INTENT(OUT) :: qij +! +! ---------------------------------------------------------------------- + INTEGER :: i + REAL, DIMENSION(nc) :: rhoi, lnf0, lnf1, lnf2 + REAL :: lnphi(np,nc), zges +! ---------------------------------------------------------------------- + + + DO i = 1, ncomp + rhoi(1:ncomp) = rhoi0(1:ncomp) + rhoi(i) = rhoi0(i) + d_rho + dense(1) = SUM( PI/6.0*rhoi(1:ncomp)*parame(1:ncomp,1)* dhs(1:ncomp)**3 ) + densta(1) = dense(1) + xi(1,1:ncomp) = rhoi(1:ncomp) / SUM( rhoi(1:ncomp) ) + CALL FUGACITY ( lnphi ) + p = pges + zges = (pges * 1.d-30) / ( KBOL*t*SUM(rhoi(1:ncomp)) ) + lnf1(1:ncomp) = lnphi(1,1:ncomp) + LOG( rhoi(1:ncomp) ) + + IF (rhoi0(i) - d_rho > 0.0 ) THEN + rhoi(1:ncomp) = rhoi0(1:ncomp) + rhoi(i) = rhoi0(i) - d_rho + dense(1) = SUM( PI/6.0*rhoi(1:ncomp)*parame(1:ncomp,1)* dhs(1:ncomp)**3 ) + densta(1) = dense(1) + xi(1,1:ncomp) = rhoi(1:ncomp) / SUM( rhoi(1:ncomp) ) + CALL FUGACITY ( lnphi ) + p = pges + zges = (pges * 1.d-30) / ( KBOL*t*SUM(rhoi(1:ncomp)) ) + lnf2(1:ncomp) = lnphi(1,1:ncomp) + LOG( rhoi(1:ncomp) ) + END IF + + rhoi(1:ncomp) = rhoi0(1:ncomp) + dense(1) = SUM( PI/6.0*rhoi(1:ncomp)*parame(1:ncomp,1)* dhs(1:ncomp)**3 ) + densta(1) = dense(1) + xi(1,1:ncomp) = rhoi(1:ncomp) / SUM( rhoi(1:ncomp) ) + CALL FUGACITY ( lnphi ) + p = pges + zges = (pges * 1.d-30) / ( KBOL*t*SUM(rhoi(1:ncomp)) ) + lnf0(1:ncomp) = lnphi(1,1:ncomp) + LOG( rhoi(1:ncomp) ) + + IF (rhoi0(i) - d_rho > 0.0 ) THEN + qij(i,1:ncomp) = ( lnf1(1:ncomp) - lnf2(1:ncomp) ) / (2.0*d_rho) ! qij = d(F/V) / (d_rho_i*d_rho_j) + ELSE + qij(i,1:ncomp) = ( lnf1(1:ncomp) - lnf0(1:ncomp) ) / d_rho ! qij = d(F/V) / (d_rho_i*d_rho_j) + END IF + ! write (*,*) i,1,qij(i,1) + ! write (*,*) i,2,qij(i,2) + END DO + +END SUBROUTINE qij_matrix + diff --git a/applications/PUfoam/MoDeNaModels/SurfaceTension/ExampleOfUsage/src/srcDetailedCode/fort.40 b/applications/PUfoam/MoDeNaModels/SurfaceTension/ExampleOfUsage/src/srcDetailedCode/fort.40 new file mode 100644 index 000000000..b01fbd7fd --- /dev/null +++ b/applications/PUfoam/MoDeNaModels/SurfaceTension/ExampleOfUsage/src/srcDetailedCode/fort.40 @@ -0,0 +1 @@ + x1_ph1 x2_ph1 x3_ph1 x1_ph2 x2_ph2 x3_ph2 T P rho1 rho2 diff --git a/applications/PUfoam/MoDeNaModels/SurfaceTension/ExampleOfUsage/src/srcDetailedCode/getting_started_subroutines.F90 b/applications/PUfoam/MoDeNaModels/SurfaceTension/ExampleOfUsage/src/srcDetailedCode/getting_started_subroutines.F90 new file mode 100644 index 000000000..4d469c5c8 --- /dev/null +++ b/applications/PUfoam/MoDeNaModels/SurfaceTension/ExampleOfUsage/src/srcDetailedCode/getting_started_subroutines.F90 @@ -0,0 +1,4121 @@ +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! SUBROUTINE eos_const +! +! This subroutine provides the constants of the PC-SAFT EOS. +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! + SUBROUTINE eos_const (ap,bp,dnm) +! + IMPLICIT NONE +! +! ---------------------------------------------------------------------- + REAL, INTENT(OUT) :: ap(0:6,3) + REAL, INTENT(OUT) :: bp(0:6,3) + REAL, INTENT(OUT) :: dnm(4,9) +! ---------------------------------------------------------------------- + + +! --- dispersion term constants ---------------------------------------- +ap(0,1) = 0.91056314451539 +ap(0,2) = -0.30840169182720 +ap(0,3) = -0.09061483509767 +ap(1,1) = 0.63612814494991 +ap(1,2) = 0.18605311591713 +ap(1,3) = 0.45278428063920 +ap(2,1) = 2.68613478913903 +ap(2,2) = -2.50300472586548 +ap(2,3) = 0.59627007280101 +ap(3,1) = -26.5473624914884 +ap(3,2) = 21.4197936296668 +ap(3,3) = -1.72418291311787 +ap(4,1) = 97.7592087835073 +ap(4,2) = -65.2558853303492 +ap(4,3) = -4.13021125311661 +ap(5,1) = -159.591540865600 +ap(5,2) = 83.3186804808856 +ap(5,3) = 13.7766318697211 +ap(6,1) = 91.2977740839123 +ap(6,2) = -33.7469229297323 +ap(6,3) = -8.67284703679646 + +bp(0,1) = 0.72409469413165 +bp(0,2) = -0.57554980753450 +bp(0,3) = 0.09768831158356 +bp(1,1) = 1.11913959304690 *2.0 +bp(1,2) = 0.34975477607218 *2.0 +bp(1,3) = -0.12787874908050 *2.0 +bp(2,1) = -1.33419498282114 *3.0 +bp(2,2) = 1.29752244631769 *3.0 +bp(2,3) = -3.05195205099107 *3.0 +bp(3,1) = -5.25089420371162 *4.0 +bp(3,2) = -4.30386791194303 *4.0 +bp(3,3) = 5.16051899359931 *4.0 +bp(4,1) = 5.37112827253230 *5.0 +bp(4,2) = 38.5344528930499 *5.0 +bp(4,3) = -7.76088601041257 *5.0 +bp(5,1) = 34.4252230677698 *6.0 +bp(5,2) = -26.9710769414608 *6.0 +bp(5,3) = 15.6044623461691 *6.0 +bp(6,1) = -50.8003365888685 *7.0 +bp(6,2) = -23.6010990650801 *7.0 +bp(6,3) = -4.23812936930675 *7.0 + + +! square-well fluid +! ap(1,1)= 0.79152347258784 +! ap(1,2)= -0.62269805320654 +! ap(1,3)= -0.06798823934067 +! ap(2,1)= 1.07120982251709 +! ap(2,2)= 0.48628215731716 +! ap(2,3)= 0.02837828512515 +! ap(3,1)= 0.92084839459226 +! ap(3,2)= 1.11652038059747 +! ap(3,3)= 0.09713202077943 +! ap(4,1)= -7.84708350369249 +! ap(4,2)= -2.04200599876547 +! ap(4,3)= 0.06475764015088 +! ap(5,1)= 25.90284137818050 +! ap(5,2)= 9.27791640100603 +! ap(5,3)= 0.07729792971827 +! ap(6,1)= -57.1528726997640 +! ap(6,2)= -16.8377999920957 +! ap(6,3)= 0.24883598436184 +! ap(7,1)= 42.02314637860930 +! ap(7,2)= 7.62432635016420 +! ap(7,3)= -0.72472024688888 + +! bp(1,1)= 0.79152347258784 +! bp(1,2)= -0.62269805320654 +! bp(1,3)= -0.06798823934067 +! bp(2,1)= 1.07120982251709 *2.0 +! bp(2,2)= 0.48628215731716 *2.0 +! bp(2,3)= 0.02837828512515 *2.0 +! bp(3,1)= 0.92084839459226 *3.0 +! bp(3,2)= 1.11652038059747 *3.0 +! bp(3,3)= 0.09713202077943 *3.0 +! bp(4,1)= -7.84708350369249 *4.0 +! bp(4,2)= -2.04200599876547 *4.0 +! bp(4,3)= 0.06475764015088 *4.0 +! bp(5,1)= 25.90284137818050 *5.0 +! bp(5,2)= 9.27791640100603 *5.0 +! bp(5,3)= 0.07729792971827 *5.0 +! bp(6,1)= -57.1528726997640 *6.0 +! bp(6,2)= -16.8377999920957 *6.0 +! bp(6,3)= 0.24883598436184 *6.0 +! bp(7,1)= 42.02314637860930 *7.0 +! bp(7,2)= 7.62432635016420 *7.0 +! bp(7,3)= -0.72472024688888 *7.0 + + +dnm(1,1) = -8.8043 +dnm(1,2) = +4.1646270 +dnm(1,3) = -48.203555 +dnm(1,4) = +140.43620 +dnm(1,5) = -195.23339 +dnm(1,6) = +113.51500 +dnm(2,1) = +2.9396 +dnm(2,2) = -6.0865383 +dnm(2,3) = +40.137956 +dnm(2,4) = -76.230797 +dnm(2,5) = -133.70055 +dnm(2,6) = +860.25349 +dnm(2,7) = -1535.3224 +dnm(2,8) = +1221.4261 +dnm(2,9) = -409.10539 +dnm(3,1) = -2.8225 +dnm(3,2) = +4.7600148 +dnm(3,3) = +11.257177 +dnm(3,4) = -66.382743 +dnm(3,5) = +69.248785 +dnm(4,1) = +0.3400 +dnm(4,2) = -3.1875014 +dnm(4,3) = +12.231796 +dnm(4,4) = -12.110681 + +END SUBROUTINE eos_const + + + +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! SUBROUTINE dq_const +! +! This subr. provides the constants of the dipole-quadrupole term. +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! + SUBROUTINE dq_const ( dqp2,dqp3,dqp4 ) +! + USE PARAMETERS, ONLY: nc + USE EOS_VARIABLES, ONLY: ncomp, parame + IMPLICIT NONE +! +! ---------------------------------------------------------------------- + REAL, INTENT(OUT) :: dqp2(nc,nc,0:8) + REAL, INTENT(OUT) :: dqp3(nc,nc,nc,0:8) + REAL, INTENT(OUT) :: dqp4(nc,nc,0:8) +! +! ---------------------------------------------------------------------- + INTEGER :: i, j, k + REAL :: mdq(nc) + REAL :: mf1, mf2, msegij +! ---------------------------------------------------------------------- + +DO i=1,ncomp + mdq(i) = parame(i,1) + IF (mdq(i) > 2.0) mdq(i) = 2.0 +END DO + + +DO i=1,ncomp + DO j=1,ncomp + + msegij=(mdq(i)*mdq(j))**0.5 + mf1 = (msegij-1.0)/msegij + mf2 = mf1*(msegij-2.0)/msegij + + dqp2(i,j,0) = 0.697094963 + mf1*(-0.673459279) + mf2*0.670340770 + dqp2(i,j,1) = -0.633554144 + mf1*(-1.425899106) + mf2*(-4.338471826) + dqp2(i,j,2) = 2.945509028 + mf1 * 4.19441392 + mf2*7.234168360 + dqp2(i,j,3) = -1.467027314 + mf1 * 1.0266216 + dqp2(i,j,4) = 0.0 + + dqp4(i,j,0) = -0.484038322 + mf1 * 0.67651011 + mf2*(-1.167560146) + dqp4(i,j,1) = 1.970405465 + mf1*(-3.013867512) + mf2*2.13488432 + dqp4(i,j,2) = -2.118572671 + mf1 * 0.46742656 + dqp4(i,j,3) = 0.0 + dqp4(i,j,4) = 0.0 + + + DO k=1,ncomp + msegij=(mdq(i)*mdq(j)*mdq(k))**(1.0/3.0) + mf1 = (msegij-1.0)/msegij + mf2 = (msegij-2.0)/msegij + dqp3(i,j,k,0) = 0.795009692 + mf1*(-2.099579397) + dqp3(i,j,k,1) = 3.386863396 + mf1*(-5.941376392) + dqp3(i,j,k,2) = 0.475106328 + mf1*(-0.178820384) + dqp3(i,j,k,3) = 0.0 + dqp3(i,j,k,4) = 0.0 + END DO + + END DO +END DO + +END SUBROUTINE dq_const + + +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! SUBROUTINE dd_const +! +! This subroutine provides the constants of the dipole-term. +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! + SUBROUTINE dd_const ( ddp2,ddp3,ddp4 ) +! + USE PARAMETERS, ONLY: nc, PI + USE EOS_VARIABLES, ONLY: ncomp, parame + IMPLICIT NONE +! +! ---------------------------------------------------------------------- + REAL, INTENT(OUT) :: ddp2(nc,nc,0:8) + REAL, INTENT(OUT) :: ddp3(nc,nc,nc,0:8) + REAL, INTENT(OUT) :: ddp4(nc,nc,0:8) +! +! ---------------------------------------------------------------------- + INTEGER :: i, j, k + REAL :: pardd(nc) + REAL :: mf1,mf2,msegij,sin2t +! ---------------------------------------------------------------------- + +sin2t = SIN( 0.0 * PI / 180.0 ) +sin2t = sin2t*sin2t + +DO i = 1, ncomp + pardd(i) = parame(i,1) + IF (pardd(i) > 2.0) pardd(i) = 2.0 +END DO + +DO i=1,ncomp + DO j=1,ncomp +! IF (parame(i,6).NE.0.0.AND.parame(j,6).NE.0.0) THEN + + msegij=(pardd(i)*pardd(j))**0.5 + mf1 = (msegij-1.0)/msegij + mf2 = mf1*(msegij-2.0)/msegij + + ddp2(i,j,0) = 0.30435038064 + mf1*(0.95346405973+0.201436*sin2t) & + + mf2*(-1.16100802773-1.74114*sin2t) + ddp2(i,j,1) = -0.13585877707 + mf1*(-1.83963831920+1.31649*sin2t) & + + mf2*4.52586067320 + ddp2(i,j,2) = 1.44933285154 + mf1 * 2.01311801180 + mf2*0.97512223853 + ddp2(i,j,3) = 0.35569769252 + mf1*(-7.37249576667) + mf2*(-12.2810377713) + ddp2(i,j,4) = -2.06533084541 + mf1 * 8.23741345333 + mf2*5.93975747420 + + ddp4(i,j,0) = 0.21879385627 + mf1*(-0.58731641193) + mf2*3.48695755800 + ddp4(i,j,1) = -1.18964307357 + mf1 * 1.24891317047 + mf2*(-14.9159739347) + ddp4(i,j,2) = 1.16268885692 + mf1*(-0.50852797392) + mf2*15.3720218600 + ddp4(i,j,3) = 0.0 + ddp4(i,j,4) = 0.0 + + DO k=1,ncomp +! IF (parame(k,6).NE.0.0) THEN + msegij=(pardd(i)*pardd(j)*pardd(k))**(1.0/3.0) + mf1 = (msegij-1.0)/msegij + mf2 = mf1*(msegij-2.0)/msegij + ddp3(i,j,k,0) = -0.06467735252 + mf1*(-0.95208758351+0.28503*sin2t) & + + mf2*(-0.62609792333+2.2195*sin2t) + ddp3(i,j,k,1) = 0.19758818347 + mf1 * 2.99242575222 + mf2*1.29246858189 + ddp3(i,j,k,2) = -0.80875619458 + mf1*(-2.38026356489) + mf2*1.65427830900 + ddp3(i,j,k,3) = 0.69028490492 + mf1*(-0.27012609786) + mf2*(-3.43967436378) + ddp3(i,j,k,4) = 0.0 + +! ENDIF + END DO + +! ENDIF + END DO +END DO + +END SUBROUTINE dd_const + + +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! SUBROUTINE qq_const +! +! This subroutine provides the constants of the quadrupole-term. +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! + SUBROUTINE qq_const ( qqp2,qqp3,qqp4 ) +! + USE PARAMETERS, ONLY: nc + USE EOS_VARIABLES, ONLY: ncomp, parame + IMPLICIT NONE +! +! ---------------------------------------------------------------------- + REAL, INTENT(OUT) :: qqp2(nc,nc,0:8) + REAL, INTENT(OUT) :: qqp3(nc,nc,nc,0:8) + REAL, INTENT(OUT) :: qqp4(nc,nc,0:8) +! +! ---------------------------------------------------------------------- + INTEGER :: i, j, k + REAL :: mqq(nc) + REAL :: mf1, mf2, msegij +! ---------------------------------------------------------------------- + +DO i = 1,ncomp + mqq(i) = parame(i,1) + IF (mqq(i) > 2.0) mqq(i) = 2.0 +END DO + +DO i = 1,ncomp + DO j = 1,ncomp + IF (parame(i,7) /= 0.0 .AND. parame(j,7) /= 0.0) THEN + + msegij=(mqq(i)*mqq(j))**0.5 +! msegij=(parame(i,1)*parame(j,1))**0.50 + mf1 = (msegij-1.0)/msegij + mf2 = mf1*(msegij-2.0)/msegij + + qqp2(i,j,0) = 1.237830788 + mf1 * 1.285410878 + mf2*1.794295401 + qqp2(i,j,1) = 2.435503144 + mf1*(-11.46561451) + mf2*0.769510293 + qqp2(i,j,2) = 1.633090469 + mf1 *22.08689285 + mf2*7.264792255 + qqp2(i,j,3) = -1.611815241 + mf1 * 7.46913832 + mf2*94.48669892 + qqp2(i,j,4) = 6.977118504 + mf1*(-17.19777208) + mf2*(-77.1484579) + + qqp4(i,j,0) = 0.454271755 + mf1*(-0.813734006) + mf2*6.868267516 + qqp4(i,j,1) = -4.501626435 + mf1 * 10.06402986 + mf2*(-5.173223765) + qqp4(i,j,2) = 3.585886783 + mf1*(-10.87663092) + mf2*(-17.2402066) + qqp4(i,j,3) = 0.0 + qqp4(i,j,4) = 0.0 + + DO k = 1,ncomp + IF (parame(k,7) /= 0.0) THEN + msegij=(mqq(i)*mqq(j)*mqq(k))**(1.0/3.0) +! msegij=(parame(i,1)*parame(j,1)*parame(k,1))**(1.0/3.0) + mf1 = (msegij-1.0)/msegij + mf2 = mf1*(msegij-2.0)/msegij + qqp3(i,j,k,0) = -0.500043713 + mf1 * 2.000209381 + mf2*3.135827145 + qqp3(i,j,k,1) = 6.531869153 + mf1*(-6.78386584) + mf2*7.247588801 + qqp3(i,j,k,2) = -16.01477983 + mf1 * 20.38324603 + mf2*3.075947834 + qqp3(i,j,k,3) = 14.42597018 + mf1*(-10.89598394) + qqp3(i,j,k,4) = 0.0 + END IF + END DO + + END IF + END DO +END DO + +END SUBROUTINE qq_const + + + + + + + +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! + SUBROUTINE SET_DEFAULT_EOS_NUMERICAL +! + USE EOS_NUMERICAL_DERIVATIVES + IMPLICIT NONE +! +! ---------------------------------------------------------------------- + + ideal_gas = 'no' ! ( yes, no ) + hard_sphere = 'CSBM' ! ( CSBM, no ) + chain_term = 'TPT1' ! ( TPT1, HuLiu, no ) + disp_term = 'PC-SAFT' ! ( PC-SAFT, CK, PT1, PT2, PT_MF, PT_MIX, no ) + hb_term = 'TPT1_Chap' ! ( TPT1_Chap, no ) + LC_term = 'no' ! ( MSaupe, OVL, no ) + branch_term = 'no' ! ( TPT2, no ) + II_term = 'no' + ID_term = 'no' + + subtract1 = 'no' ! (1PT, 2PT, no) + subtract2 = 'no' ! (ITTpolar, no) + +END SUBROUTINE SET_DEFAULT_EOS_NUMERICAL + + + + + + + + + +SUBROUTINE READ_INPUT +! + USE BASIC_VARIABLES + IMPLICIT NONE +! +! ---------------------------------------------------------------------- + INTEGER :: i + REAL :: reading2,reading3,sumfeed + CHARACTER (LEN=4) :: uoutp, uinp + CHARACTER (LEN=1) :: uoutt, uint + CHARACTER (LEN=50) :: filename + CHARACTER (LEN=30) :: reading1 +! ---------------------------------------------------------------------- + + filename='./input_file/INPUT.INP' + CALL file_open(filename,30) + READ (30,*) eos, pol !J: specify by numbers! eos(1=pcsaft, 2=SRK,...) pol (=polar) yes(1) no(0) + READ (30,*) t, uint, p, uinp !J: t: value of temp, uint: unit of temp, p: value of pressure, uinp: unit of pressure + + ncomp = 0 + i = 0 + sumfeed = 0.0 + read_loop: DO + READ (30,*) reading1,reading2,reading3 + IF (reading1 == 'end') EXIT read_loop + ncomp = ncomp + 1 + i = i + 1 + compna(i)= reading1 ! comp.name + mm(i) = reading2 ! molec.mass (mandatory only for polymers) + xif(i) = reading3 !J: molefractions + sumfeed = sumfeed + xif(i) + ENDDO read_loop + + CLOSE (30) + + IF (sumfeed /= 0.0 .AND. sumfeed /= 1.0) THEN !J: in case mole fractions dont sum up to 1?? + xif(1:ncomp) = xif(1:ncomp)/sumfeed + END IF + + uoutt = uint + uoutp = uinp + IF (uint == 'C') THEN !J: unit stuff + u_in_t = 273.15 + ELSE + u_in_t = 0.0 + END IF + IF (uinp == 'bar') THEN + u_in_p = 1.E5 + ELSE IF (uinp == 'mbar') THEN + u_in_p = 1.E2 + ELSE IF (uinp == 'MPa') THEN + u_in_p = 1.E6 + ELSE IF (uinp == 'kPa') THEN + u_in_p = 1.E3 + ELSE + u_in_p = 1.E0 + END IF + + IF (uoutt == 'C') THEN + u_out_t = 273.15 + ELSE + u_out_t = 0.0 + END IF + IF (uoutp == 'bar') THEN + u_out_p = 1.E5 + ELSE IF (uoutp == 'mbar') THEN + u_out_p = 1.E2 + ELSE IF (uoutp == 'MPa') THEN + u_out_p = 1.E6 + ELSE IF (uoutp == 'kPa') THEN + u_out_p = 1.E3 + ELSE + u_out_p = 1.0 + END IF + + t = t + u_in_t !J: calculate temp in Kelvin + p = p * u_in_p !J: calculate pressure in Pascal + + CALL para_input ! retriev pure comp. parameters + + IF (ncomp == 1) THEN + WRITE (40,*) ' T P rho_1 rho_2 h_LV' + ELSE IF (ncomp == 2) THEN + ! WRITE (40,*) ' x2_phase1 x2_phase2 w1_phase1 w2_phase2 T P rho1 rho2' + WRITE (40,*) ' ' + ELSE IF (ncomp == 3) THEN + WRITE (40,*) ' x1_ph1 x2_ph1 x3_ph1 x1_ph2', & + ' x2_ph2 x3_ph2 T P rho1 rho2' + END IF + + END SUBROUTINE READ_INPUT + + + + + +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! SUBROUTINE file_open +! +! This subroutine opens files for reading. Beforehand, it checks +! whether this file is available. +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! + SUBROUTINE file_open(filename,file_number) +! +! ---------------------------------------------------------------------- + CHARACTER (LEN=50) :: filename + INTEGER :: file_number + LOGICAL :: filefound +! ---------------------------------------------------------------------- + +INQUIRE (FILE=filename, EXIST = filefound) +IF (filefound) THEN + OPEN (file_number, FILE = filename) +ELSE + write (*,*) ' FOLLOWING FILE CAN NOT BE OPENED', filename + stop +END IF + +END SUBROUTINE file_open + + + +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! SUBROUTINE para_input +! +! This subroutine provides pure component parameters and kij parameters. +! The following syntax applies: +! +! compna(i) component name +! parame(i,k) pure comp. parameter: +! parame(i,1): segment number [/] +! parame(i,2): segment diameter "sigma" [Angstrom] +! parame(i,3): segment energy param. epsilon/k [K] +! parame(i,4): model parameter; not used for PC-SAFT (=0) +! it is 10K most of the time for SAFT [K] +! parame(i,5): Param. for T-dependent segment diameter [/] +! parame(i,6): dipolar moment [debye] +! parame(i,7): quadrupolar moment [debye] +! parame(i,8): number of segments that are part of a branching 4-mer [/] +! parame(i,9): +! parame(i,10): ionic charge number (positiv or negativ) [/] +! parame(i,11): polarizability [A**3] +! parame(i,12): number of association sites [/] +! parame(i,13): (=kap_hb, see below) [/] +! parame(i,14 to 25): (=eps_hb, see below) [K] +! nhb_typ(i) number of different types of association sites (comp. i) +! nhb_no(i,k) number of association sites of type k +! eps_hb depth of association potential [K] +! kap_hb effective width of assoc. potential (angle-averg.) +! mm molec. mass +! scaling param. for roughly scaling the set of objective functions +! +! As opposed to low-molec mass compounds, the molecular mass of a +! polymer is not obtained from this routine. Rather, it is a +! user-specification given in the file INPUT.INP +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! + SUBROUTINE para_input +! + USE BASIC_VARIABLES + IMPLICIT NONE +! +!---------------------------------------------------------------------- + INTEGER :: i +!---------------------------------------------------------------------- + +IF (eos == 1) THEN + CALL pcsaft_par +ELSE IF (eos == 4 .OR. eos == 5 .OR. eos == 6 .OR. eos == 8) THEN + ! CALL lj_par + write (*,*) 'deactivated this line when making a transition to f90' + stop +ELSE IF (eos == 7) THEN + ! CALL sw_par + write (*,*) 'deactivated this line when making a transition to f90' + stop +ELSE IF (eos == 10) THEN + i = 1 + IF (compna(i) == 'LC_generic' .AND. ncomp == 1 ) THEN + mm(i) = 1.0 + parame(i,1) = 7.0 + parame(i,2) = 1.0 + parame(i,3) = 0.0 + ELSE + write (*,*) 'PARA_INPUT: define the component !' + stop + ENDIF +ELSE + !CALL saft_par +END IF + +DO i = 1, ncomp + IF ( mm(i) >= 1.0 .AND. mm(i) < 45.0 ) THEN + scaling(i) = 10000.0 + ELSE IF( mm(i) >= 45.0 .AND. mm(i) < 90.0 ) THEN + scaling(i) = 1000.0 + ELSE IF( mm(i) >= 90.0 .AND. mm(i) < 150.0 ) THEN + scaling(i) = 100.0 + ELSE IF( mm(i) >= 150.0 .AND. mm(i) < 250.0 ) THEN + scaling(i) = 10.0 + ELSE + scaling(i) = 1.0 + END IF + IF (parame(i,10) /= 0.0) scaling(i) = scaling(i) / 1.E4 ! Electrolytes +END DO + +END SUBROUTINE para_input + + + + +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! SUBROUTINE pcsaft_par +! +! pure component parameters and kij parameters +! (as described in SUBROUTINE para_input) +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! + SUBROUTINE pcsaft_par +! + USE BASIC_VARIABLES + IMPLICIT NONE +! +!---------------------------------------------------------------------- + INTEGER :: i, j, k, no + INTEGER, DIMENSION(nc) :: nhb_typ + INTEGER, DIMENSION(nc,nsite) :: nhb_no + REAL, DIMENSION(nc,nc,nsite,nsite) :: eps_hb + REAL, DIMENSION(nc,nc) :: kap_hb +!---------------------------------------------------------------------- + + +DO i = 1, ncomp + parame(i,4) = 0.0 ! T correct. required for SAFT, not PC-SAFT + parame(i,5) = 0.12 ! Param. for T-dependent segment diameter + parame(i,6) = 0.0 ! dipolar moment + parame(i,7) = 0.0 ! quadrupolar moment + parame(i,8) = 0.0 ! number of segments that are part of a branching 4-mer + parame(i,9) = 0.0 + parame(i,10)= 0.0 ! ionic charge number + parame(i,11)= 0.0 ! polarizability + lli(i) = 0.0 + phi_criti(i)= 0.0 + chap(i) = 0.0 + + nhb_typ(i) = 0 + kap_hb(i,i) = 0.0 + ! irgendwann sollten nhb_typ und kap_hb durch parame(i,12) und (i,13) + ! ersetzt werden. + IF (compna(i) == 'ps') THEN + parame(i,1) = mm(i)*1.9E-2 + parame(i,2) = 4.10705961 + parame(i,3) = 267.0 + ELSE IF (compna(i) == 'ps_J') THEN !from Xu,Diego: DFT for polymer-co2 mixtures: A PC-SAFT approach + parame(i,1) = mm(i)*0.0253 + parame(i,2) = 3.45 + parame(i,3) = 328.1 + ELSE IF (compna(i) == 'co2_J') THEN !from Xu,Diego: DFT for polymer-co2 mixtures: A PC-SAFT approach + parame(i,1) = 2.0 + parame(i,2) = 2.79 + parame(i,3) = 170.5 + + + + ELSE IF (compna(i) == 'pg2') THEN !Polyglycerol 2 + mm(i) = 2000.0 + parame(i,1) = mm(i)*2.37E-2 ! from figure 5 PCSAFT paper + parame(i,2) = 3.8 ! from figure 5 PCSAFT paper + parame(i,3) = 270.0 ! starting value for iteration + ! this is the extra parameter + parame(i,8) = mm(i)*2.37E-2 + + nhb_typ(i) = 2 ! no. of different association sites + nhb_no(i,1) = 27 ! no. of sites of type 1 + nhb_no(i,2) = 27 ! no. of sites of type 2 + eps_hb(i,i,1,2)= 2544.6 ! taken from butanol (same M/OH) + eps_hb(i,i,2,1)= 2544.6 + eps_hb(i,i,1,1)= 0.0 + eps_hb(i,i,2,2)= 0.0 + kap_hb(i,i)= .00489087833 ! taken from butanol (same M/OH) + ELSE IF (compna(i) == 'peva') THEN + parame(i,1) = mm(i)*2.63E-2 + ! -- 0 Gew.% VA------------- + ! parame(i,2) = 4.021767 + ! parame(i,3) = 249.5 + ! -- 7.5 Gew.% VA------------- + ! parame(i,2) = 4.011 + ! parame(i,3) = 248.1864 + ! parame(i,3) = 247.6286 + ! ---12.7 Gew.% VA------------ + ! parame(i,2) = 4.0028 + ! parame(i,3) = 247.2075 + ! parame(i,3) = 246.24454 + ! ---27.3 Gew.% VA------------ + ! parame(i,2) = 3.9762 + ! parame(i,3) = 244.114 + ! parame(i,3) = 241.9345 + ! ---31.8 Gew.% VA------------ + parame(i,2) = 3.9666 + parame(i,3) = 243.0436 + ! parame(i,3) = 240.46 + ! ---42.7 Gew.% VA------------ + ! parame(i,2) = 3.9400 + ! parame(i,3) = 240.184 + ! parame(i,3) = 236.62 + ! --------------- + ELSE IF (compna(i) == 'pp') THEN + parame(i,1) = mm(i)*2.2E-2 + parame(i,2) = 4.2 + parame(i,3) = 220.0 + + parame(i,1) = mm(i)*0.0230487701 + parame(i,2) = 4.1 + parame(i,3) = 217.0 + ELSE IF (compna(i) == 'pe') THEN + parame(i,1) = mm(i)*2.622E-2 + parame(i,2) = 4.021767 + parame(i,3) = 252.0 + ! HDPE: extrapolated from pure comp. param. of n-alkane series! + ! parame(i,1) = mm(i)*2.4346E-2 + ! parame(i,2) = 4.07182 + ! parame(i,3) = 269.67 + !! parame(i,3) = 252.5 + ELSE IF (compna(i) == 'ldpe') THEN + parame(i,1) = mm(i)*2.63E-2 + parame(i,2) = 4.021767 + parame(i,3) = 249.5 + ELSE IF (compna(i) == 'pba') THEN + parame(i,1) = mm(i)*2.5872E-2 + parame(i,2) = 3.95 + parame(i,3) = 229.0 + ELSE IF (compna(i) == 'dextran') THEN + parame(i,1) = mm(i)*2.E-2 + parame(i,2) = 4.0 + parame(i,3) = 300.0 + ELSE IF (compna(i) == 'glycol-ethers') THEN + ! mm(i) = 218.0 + ! parame(i,1) = 7.4044 + ! parame(i,2) = 3.61576 + ! parame(i,3) = 244.0034598 + mm(i) = 222.0 + parame(i,1) = 7.994 + parame(i,2) = 3.445377778 + parame(i,3) = 234.916506 + ELSE IF (compna(i) == 'LJ') THEN + mm(i) = 1.0 + parame(i,1) = 1.0 + parame(i,2) = 1.0 + parame(i,3) = 1.0 + ELSE IF (compna(i) == 'LJ1205') THEN + mm(i) = 1.0 + parame(i,1) = 1.0 + parame(i,2) = 1.0 + parame(i,3) = 140.0 + ELSE IF (compna(i) == 'adamantane') THEN + mm(i) = 136.235000000000 + parame(i,1) = 4.81897145432221 + parame(i,2) = 3.47128575274660 + parame(i,3) = 266.936967922521 + + Else IF (compna(i) == '14-butandiol') THEN + mm(i) = 90.12 + parame(i,1) = 4.35923557 + parame(i,2) = 3.02947364 + parame(i,3) = 197.11998863 + + Else IF(compna(i) == 'po') THEN + mm(i) = 90.12 + parame(i,1) = 4.35923557 + parame(i,2) = 3.02947364 + parame(i,3) = 197.11998863 + + ELSE IF (compna(i) == 'air') THEN + mm(i) = 28.899 !n2 and o2 according to mole fractions + parame(i,1) = 1.18938 !n2 and o2 according to mole fractions (weighted artihm. avg) + parame(i,2) = 3.28694 !n2 and o2 according to mole fractions (weighted artihm. avg) + parame(i,3) = 95.672 !n2 and o2 according to mole fractions (weighted artihm. avg) + + + + Else IF(compna(i) == 'mdi') THEN + mm(i) = 2.50252E+02 + parame(i,1) = mm(i)*0.030769 + parame(i,2) = 2.886003 + parame(i,3) = 283.052778 + + Else IF(compna(i) == 'pu') THEN +! mm(i) = 2042.22 !pu n = 5 +! parame(i,1) = mm(i)*0.008845 +! parame(i,2) = 5.680270 +! parame(i,3) = 497.997594 + mm(i) = 340.37 !pu n = 0 + parame(i,1) = mm(i)*0.043312 + parame(i,2) = 3.008359 + parame(i,3) = 273.445205 +! mm(i) = 680.74 !pu n = 1 +! parame(i,1) = mm(i)*0.024106 +! parame(i,2) = 3.744327 +! parame(i,3) = 321.486386 +! mm(i) = 1021.11 !pu n = 2 +! parame(i,1) = mm(i)*0.015076 +! parame(i,2) = 4.537837 +! parame(i,3) = 400.036950 + + + Else IF(compna(i) == 'tpg') THEN + mm(i) = 192.25 + parame(i,1) = mm(i)*0.01239 + parame(i,2) = 4.549 + parame(i,3) = 148.678 + parame(i,6) = 0.41 + + nhb_typ(i) = 2 ! no. of different association sites + nhb_no(i,1) = 2 ! no. of sites of type 1 + nhb_no(i,2) = 2 ! no. of sites of type 2 + + eps_hb(i,i,1,2)= 5597.844 + eps_hb(i,i,2,1)= 5597.844 + eps_hb(i,i,1,1)= 0.0 + eps_hb(i,i,2,2)= 0.0 + kap_hb(i,i) = 0.03 + + + ELSE IF (compna(i) == 'methane') THEN + mm(i) = 16.043 + parame(i,1) = 1.0 + parame(i,2) = 3.70388767 + parame(i,3) = 150.033987 + ! LLi(i) = 1.185*parame(i,2) + ! phi_criti(i)= 11.141 + ! chap(i) = 0.787 + lli(i) = 1.398*parame(i,2) + phi_criti(i)= 16.01197 + chap(i) = 0.6 + IF (pol == 2) parame(i,11)= 2.593 + ! --- adjusted to Tc, Pc und omega --- + ! mm(i) = 16.0430000000000 + ! parame(i,1) = 1.03353666429362 + ! parame(i,2) = 3.64824920605089 + ! parame(i,3) = 147.903953522994 + lli(i) = 2.254442763775*parame(i,2) + phi_criti(i)= 42.060975627454 + chap(i) = 0.704895924 + lli(i) = 1.935801125833*parame(i,2) + phi_criti(i)= 26.363325937261 + chap(i) = 0.700112854298 + lli(i) = 2.610103087662*parame(i,2) + phi_criti(i)= 38.192854403173 + chap(i) = 0.812100472735 + ! 2.122960316503 34.937141524804 0.734513223627 + ! 2.082897379591 33.036391564859 0.877578492999 + ELSE IF (compna(i) == 'ethane') THEN + mm(i) = 30.070 + parame(i,1) =mm(i)* .0534364758 + parame(i,2) = 3.5205923 + parame(i,3) = 191.423815 + lli(i) = 1.40*parame(i,2) + phi_criti(i)= 15.38 + chap(i) = 0.520 + IF (pol == 2) parame(i,11)= 4.3 + ! --- adjusted to Tc, Pc und omega --- + ! mm(i) = 30.069 + ! parame(i,1) = 1.74034548122 + ! parame(i,2) = 3.4697441893134 + ! parame(i,3) = 181.90770083591 + IF (pol >= 1) mm(i) = 30.0700000000000 + IF (pol >= 1) parame(i,1) = mm(i)* 5.341907666260094E-002 + IF (pol >= 1) parame(i,2) = 3.52104466654628 + IF (pol >= 1) parame(i,3) = 191.449300423694 + IF (pol >= 1) parame(i,7) = 0.650000000000000 + IF (pol >= 1) lli(i) = 0.0 + IF (pol >= 1) phi_criti(i)= 0.0 + IF (pol >= 1) chap(i) = 0.0 + ELSE IF (compna(i) == 'propane') THEN + mm(i) = 44.096 + parame(i,1) = mm(i)* .0453970622 + parame(i,2) = 3.61835302 + parame(i,3) = 208.110116 + lli(i) = 1.8*parame(i,2) + phi_criti(i)= 21.0 + chap(i) = 1.0 + lli(i) = 1.63*parame(i,2) + phi_criti(i)= 20.37 + chap(i) = 0.397 + IF (pol == 2) parame(i,11)= 6.29 + ELSE IF (compna(i) == 'butane_debug') THEN + mm(i) = 58.123 + parame(i,1) = 2.3374 + parame(i,2) = 3.6655 + parame(i,3) = 214.805 + ELSE IF (compna(i) == 'butane') THEN + mm(i) = 58.123 + parame(i,1) = mm(i)* .0401146927 + parame(i,2) = 3.70860139 + parame(i,3) = 222.877405 + lli(i) = 1.75*parame(i,2) + phi_criti(i)= 23.43 + chap(i) = 0.304 + ! LLi(i) = 1.942079633622*parame(i,2) + ! phi_criti(i)= 24.527323443155 + ! chap(i) = 0.734064026277 + ! LLi(i) = 1.515115760477*parame(i,2) + ! phi_criti(i)= 17.682929717796 + ! chap(i) = 0.335848717079 + IF (pol == 2) parame(i,11)= 8.2 + ! --- adjusted to Tc, Pc und omega --- + ! mm(i) = 58.1230000000 + ! parame(i,1) = 2.45352304112 + ! parame(i,2) = 3.74239117802 + ! parame(i,3) = 214.185157925 + ELSE IF (compna(i) == 'pentane') THEN + mm(i) = 72.146 + parame(i,1) = mm(i)* .03727896 + parame(i,2) = 3.77293174 + parame(i,3) = 231.197015 + IF (pol == 2) parame(i,11)= 9.99 + ELSE IF (compna(i) == 'hexane') THEN + mm(i) = 86.177 + parame(i,1) = mm(i)* .0354812325 + parame(i,2) = 3.79829291 + parame(i,3) = 236.769054 + lli(i) = 2.24*parame(i,2) + phi_criti(i)= 33.25 + chap(i) = 0.205 + IF (pol == 2) parame(i,11)= 11.9 + ELSE IF (compna(i) == 'heptane') THEN + mm(i) = 100.203 + parame(i,1) = mm(i)* .034762384 + parame(i,2) = 3.80487025 + parame(i,3) = 238.400913 + lli(i) = 2.35*parame(i,2) + phi_criti(i)= 38.10 + chap(i) = 0.173 + IF (pol == 2) parame(i,11)= 13.61 + ELSE IF (compna(i) == 'octane') THEN + mm(i) = 114.231 + parame(i,1) = mm(i)* .0334228038 + parame(i,2) = 3.83732677 + parame(i,3) = 242.775853 + ! LLi(i) = 2.0*parame(i,2) + ! phi_criti(i)= 18.75 + ! chap(i) = 1.0 + lli(i) = 2.63*parame(i,2) + phi_criti(i)= 42.06 + chap(i) = 0.155 + IF (pol == 2) parame(i,11)= 15.9 + ELSE IF (compna(i) == 'nonane') THEN + mm(i) = 128.25 + parame(i,1) = mm(i)* .0328062594 + parame(i,2) = 3.84483643 + parame(i,3) = 244.508457 + ELSE IF (compna(i) == 'decane') THEN + mm(i) = 142.285 + parame(i,1) = mm(i)* .03277373 + parame(i,2) = 3.8384498 + parame(i,3) = 243.866074 + lli(i) = 1.845*parame(i,2) + phi_criti(i)= 21.27 + chap(i) = 1.0 + lli(i) = 2.68*parame(i,2) + phi_criti(i)= 45.0 + chap(i) = 0.15 + IF (pol == 2) parame(i,11)= 19.1 + ! --- adjusted to Tc, Pc und omega --- + ! parame(i,1) = 4.794137228322 + ! parame(i,2) = 4.030446690586 + ! parame(i,3) = 236.5884493386 + ELSE IF (compna(i) == 'dodecane') THEN + mm(i) = 170.338 + parame(i,1) = mm(i)* .0311484156 + parame(i,2) = 3.89589236 + parame(i,3) = 249.214532 +ELSE IF (compna(i) == 'tetradecane') THEN + mm(i) = 198.39 + parame(i,1) = 5.9002!mm(i)* .0311484156 + parame(i,2) = 3.9396 + parame(i,3) = 254.21 + ELSE IF (compna(i) == 'hexadecane') THEN + mm(i) = 226.446 + parame(i,1) = mm(i)* .0293593045 + parame(i,2) = 3.95516743 + parame(i,3) = 254.700131 + ELSE IF (compna(i) == 'octadecane') THEN + mm(i) = 254.5 + parame(i,1) = 7.3271 + parame(i,2) = 3.9668 + parame(i,3) = 256.20 + IF (pol == 2) parame(i,11)= 30.2 + ! --- adjusted to Tc, Pc und omega --- + ! mm(i) = 226.446000000000 + ! parame(i,1) = 6.66976520488694 + ! parame(i,2) = 4.25025597912511 + ! parame(i,3) = 249.582941976119 + ELSE IF (compna(i) == 'eicosane') THEN + mm(i) = 282.553 + parame(i,1) = mm(i)* .0282572812 + parame(i,2) = 3.98692612 + parame(i,3) = 257.747939 + ELSE IF (compna(i) == 'triacontane') THEN + ! mm(i) = 422.822 ! polyethylene parameters + ! parame(i,1) = mm(i)*2.622E-2 + ! parame(i,2) = 4.021767 + ! parame(i,3) = 252.0 + mm(i) = 422.822 ! param. by extrapolation of n-alkanes + parame(i,1) = mm(i)* 0.026922527 + parame(i,2) = 4.007608009 + parame(i,3) = 262.28622 + ELSE IF (compna(i) == 'octaeicosane') THEN + mm(i) = 395.0 ! param. by extrapolation of n-alkanes (sloppy!!) + parame(i,1) = mm(i)* 0.026922527 + parame(i,2) = 4.007608009 + parame(i,3) = 262.28622 + ELSE IF (compna(i) == 'tetracontane') THEN + ! mm(i) = 563.1 ! polyethylene parameters + ! parame(i,1) = mm(i)*2.622E-2 + ! parame(i,2) = 4.021767 + ! parame(i,3) = 252.0 + mm(i) = 563.1 ! param. by extrapolation of n-alkanes + parame(i,1) = mm(i)*0.026287593 + parame(i,2) = 4.023277 + parame(i,3) = 264.10466 + ELSE IF (compna(i) == 'isobutane') THEN + mm(i) = 58.123 + parame(i,1) = mm(i)* .0389105395 + parame(i,2) = 3.75735249 + parame(i,3) = 216.528584 + ELSE IF (compna(i) == 'isopentane') THEN + mm(i) = 72.15 + parame(i,1) = 2.5620 + parame(i,2) = 3.8296 + parame(i,3) = 230.75 + ELSE IF (compna(i) == '2-methylpentane') THEN + mm(i) = 86.177 + parame(i,1) = mm(i)* .0340166994 + parame(i,2) = 3.85354665 + parame(i,3) = 235.5801 + ELSE IF (compna(i) == '23-dimethylbutane') THEN + mm(i) = 86.177 + parame(i,1) = mm(i)* .0311599207 + parame(i,2) = 3.9544545 + parame(i,3) = 246.068188 + ELSE IF (compna(i) == 'ethylene') THEN + mm(i) = 28.05 + parame(i,1) = mm(i)* .0567939013 + parame(i,2) = 3.44499904 + parame(i,3) = 176.468725 + IF (pol == 2) parame(i,11)= 4.252 +! eigener 3-ter Anlauf. + IF (pol >= 1) parame(i,1) = mm(i)* 5.574644443117726E-002 + IF (pol >= 1) parame(i,2) = 3.43281482228714 + IF (pol >= 1) parame(i,3) = 178.627308564610 + IF (pol >= 1) parame(i,7) = 1.56885870200446 + IF (pol == 2) parame(i,11)= 4.252 + ELSE IF (compna(i) == 'propylene') THEN + mm(i) = 42.081 + parame(i,1) = mm(i)* .0465710324 + parame(i,2) = 3.53559831 + parame(i,3) = 207.189309 + ! --- adjusted to Tc, Pc und omega --- + ! mm(i) = 42.081 + ! parame(i,1) = 2.086735327675 + ! parame(i,2) = 3.536779407969 + ! parame(i,3) = 198.3529810625 + ELSE IF (compna(i) == '1-butene') THEN + mm(i) = 56.107 + parame(i,1) = mm(i)* .0407524782 + parame(i,2) = 3.64305136 + parame(i,3) = 222.002756 + IF (pol == 2) parame(i,11)= 7.97 + ELSE IF (compna(i) == '1-pentene') THEN + mm(i) = 70.134 + parame(i,1) = 2.6006 + parame(i,2) = 3.7399 + parame(i,3) = 231.99 + ELSE IF (compna(i) == '1-hexene') THEN + mm(i) = 84.616 + parame(i,1) = mm(i)* .0352836857 + parame(i,2) = 3.77529612 + parame(i,3) = 236.810973 + ELSE IF (compna(i) == '1-octene') THEN + mm(i) = 112.215 + parame(i,1) = mm(i)* .033345175 + parame(i,2) = 3.81329011 + parame(i,3) = 243.017587 + ELSE IF (compna(i) == 'cyclopentane') THEN + mm(i) = 70.13 + parame(i,1) = mm(i)* .0337262571 + parame(i,2) = 3.71139254 + parame(i,3) = 265.828755 + ELSE IF (compna(i) == 'cyclohexane') THEN + mm(i) = 84.147 + parame(i,1) = mm(i)* .0300695505 + parame(i,2) = 3.84990887 + parame(i,3) = 278.108786 + IF (pol == 2) parame(i,11)= 10.87 + ELSE IF (compna(i) == 'toluene') THEN + mm(i) = 92.141 + parame(i,1) = mm(i)* .0305499338 + parame(i,2) = 3.71689689 + parame(i,3) = 285.68996 + IF (pol == 2) parame(i,11)= 11.8 + ! --- adjusted to Tc, Pc und omega --- + ! mm(i) = 92.141 + ! parame(i,1) = 3.002119827762 + ! parame(i,2) = 3.803702734224 + ! parame(i,3) = 271.9428642880 + ELSE IF (compna(i) == 'm-xylene') THEN + mm(i) = 106.167 + parame(i,1) = mm(i)* .030011086 + parame(i,2) = 3.75625585 + parame(i,3) = 283.977525 + ELSE IF (compna(i) == 'o-xylene') THEN + mm(i) = 106.167 + parame(i,1) = mm(i)* .0295409161 + parame(i,2) = 3.76000631 + parame(i,3) = 291.049123 + ELSE IF (compna(i) == 'thf') THEN + mm(i) = 72.1057000000000 + ! parame(i,1) = mm(i)* 0.34311391E-01 + parame(i,1) = 2.47404685540709 + parame(i,2) = 3.51369375633677 + parame(i,3) = 274.181927093696 + parame(i,6) = 1.63100000000000 + ELSE IF (compna(i) == 'co2') THEN + mm(i) = 44.01 + parame(i,1) = mm(i)* .0470968503 + parame(i,2) = 2.7851954 + parame(i,3) = 169.207418 + IF (pol >= 1) parame(i,1) = mm(i)* 3.438191426159075E-002 + IF (pol >= 1) parame(i,2) = 3.18693935424469 + IF (pol >= 1) parame(i,3) = 163.333232725156 + IF (pol >= 1) parame(i,7) = 4.400000000000 + IF (pol >= 1) lli(i) = 1.472215*parame(i,2) + IF (pol >= 1) phi_criti(i)= 17.706567 + IF (pol >= 1) chap(i) = 0.5 + IF (pol == 2) parame(i,11)= 2.911 + ELSE IF (compna(i) == 'co') THEN + IF (pol /= 1) write (*,*) 'parameters for co missing' + IF (pol /= 1) stop + IF (pol >= 1) mm(i) = 28.01 + IF (pol >= 1) parame(i,1) = mm(i)* 5.126059746332587E-002 ! 1.43580933494776 + IF (pol >= 1) parame(i,2) = 3.13556624711756 + IF (pol >= 1) parame(i,3) = 87.7191028693595 + IF (pol >= 1) parame(i,6) = 0.1098 + ELSE IF (compna(i) == 'n2') THEN + mm(i) = 28.01 + parame(i,1) = mm(i)* .0430301713 + parame(i,2) = 3.3129702 + parame(i,3) = 90.9606924 + IF (pol >= 1) parame(i,1) = mm(i)* 3.971157114787596E-002 + IF (pol >= 1) parame(i,2) = 3.42116853868336 + IF (pol >= 1) parame(i,3) = 92.3972606842862 + IF (pol >= 1) parame(i,7) = 1.52000000000000 + IF (pol >= 1) lli(i) = 1.5188*parame(i,2) + IF (pol >= 1) phi_criti(i)= 19.9247 + IF (pol >= 1) chap(i) = 0.375 + ! better RGT-results came later, with: 1.5822 21.201 0.3972 + ELSE IF (compna(i) == 'o2') THEN + mm(i) = 32.05 + parame(i,1) = mm(i)* .0353671563 + parame(i,2) = 3.19465166 + parame(i,3) = 114.430197 + ELSE IF (compna(i) == 'hydrogen') THEN + mm(i) = 2.016 + parame(i,1) = mm(i)* .258951975 + parame(i,2) = 4.43304935 + parame(i,3) = 29.6509579 + + mm(i) = 2.016 + parame(i,1) = 1.0 + parame(i,2) = 2.915 + parame(i,3) = 38.0 + + ! mm(i) = 2.016 ! Ghosh et al. 2003 + ! parame(i,1) = 1.0 + ! parame(i,2) = 2.986 + ! parame(i,3) = 19.2775 + ELSE IF (compna(i) == 'argon') THEN + ! mm(i) = 39.948 ! adjusted m !! + ! parame(i,1) = 0.9285 + ! parame(i,2) = 3.4784 + ! parame(i,3) = 122.23 + mm(i) = 39.948 ! enforced m=1 !! + parame(i,1) = 1.0 + parame(i,2) = 3.3658 + parame(i,3) = 118.34 + IF (pol == 2) parame(i,11)= 1.6411 + ELSE IF (compna(i) == 'xenon') THEN + mm(i) = 131.29 + parame(i,1) = 1.0 + parame(i,2) = 3.93143 + parame(i,3) = 227.749 + ELSE IF (compna(i) == 'chlorine') THEN ! Cl2 + mm(i) = 70.906 + parame(i,1) = 1.5514 + parame(i,2) = 3.3672 + parame(i,3) = 265.67 + ELSE IF (compna(i) == 'SF6') THEN + mm(i) = 146.056 ! adjusted m !! + parame(i,1) = 2.48191 + parame(i,2) = 3.32727 + parame(i,3) = 161.639 + ! mm(i) = 146.056 ! enforced m=1 !! + ! parame(i,1) = 1.0 + ! parame(i,2) = 4.55222 + ! parame(i,3) = 263.1356 + ELSE IF (compna(i) == 'benzene') THEN + mm(i) = 78.114 + parame(i,1) = mm(i)* .0315590546 + parame(i,2) = 3.64778975 + parame(i,3) = 287.354574 + IF (pol >= 1) mm(i) = 78.114 ! PCP-SAFT with m=2 in QQ term + IF (pol >= 1) parame(i,1) = mm(i)* 2.932783311E-2 ! = 2.29091435590515 + IF (pol >= 1) parame(i,2) = 3.7563854 + IF (pol >= 1) parame(i,3) = 294.06253 + IF (pol >= 1) parame(i,7) = 5.5907 + ELSE IF (compna(i) == 'ethylbenzene') THEN + mm(i) = 106.167 + parame(i,1) = mm(i)* .0290120497 + parame(i,2) = 3.79741116 + parame(i,3) = 287.348098 + IF (pol == 2) parame(i,11)= 13.3 + ELSE IF (compna(i) == 'propylbenzene') THEN + mm(i) = 120.194 + parame(i,1) = mm(i)* .0278171627 + parame(i,2) = 3.8437772 + parame(i,3) = 288.128269 + ELSE IF (compna(i) == 'n-butylbenzene') THEN + mm(i) = 134.221 + parame(i,1) = mm(i)* .0280642225 + parame(i,2) = 3.87267961 + parame(i,3) = 283.072331 + ELSE IF (compna(i) == 'tetralin') THEN + mm(i) = 132.205 + parame(i,1) = mm(i)* .0250640795 + parame(i,2) = 3.87498866 + parame(i,3) = 325.065688 + ELSE IF (compna(i) == 'methylcyclohexane') THEN + mm(i) = 98.182 + parame(i,1) = mm(i)* .0271259953 + parame(i,2) = 3.99931892 + parame(i,3) = 282.334148 + IF (pol == 2) parame(i,11)= 13.1 + ELSE IF (compna(i) == 'methylcyclopentane') THEN + mm(i) = 84.156 + parame(i,1) = mm(i)* .0310459009 + parame(i,2) = 3.82534693 + parame(i,3) = 265.122799 + ELSE IF (compna(i) == 'acetone') THEN + mm(i) = 58.0800000000000 ! PC-SAFT + parame(i,1) = mm(i)* 4.870380408159182E-002 ! =2.82871694105885 + parame(i,2) = 3.24969003020675 + parame(i,3) = 250.262241927379 + lli(i) = 2.0021*parame(i,2) + phi_criti(i)= 21.336 + chap(i) = 0.24931 + IF (pol >= 1) mm(i) = 58.0800000000000 ! PCP-SAFT + IF (pol >= 1) parame(i,1) = mm(i)* 4.725811736856114E-002 ! =2.74475145676603 + IF (pol >= 1) parame(i,2) = 3.27423145271184 + IF (pol >= 1) parame(i,3) = 232.990879135326 + IF (pol >= 1) parame(i,6) = 2.88000000000000 + IF (pol >= 1) lli(i) = 2.0641*parame(i,2) + IF (pol >= 1) phi_criti(i)= 28.1783 + IF (pol >= 1) chap(i) = 0.22695 + IF (pol >= 2) mm(i) = 58.0800000000000 ! PCIP-SAFT + IF (pol >= 2) parame(i,1) = mm(i)* 4.902301475689938E-002 ! =2.84725669708072 + IF (pol >= 2) parame(i,2) = 3.23880349104868 + IF (pol >= 2) parame(i,3) = 220.884202656054 + IF (pol >= 2) parame(i,6) = 2.88000000000000 + IF (pol == 2) parame(i,11)= 6.40000000000000 + ELSE IF (compna(i) == 'butanone') THEN + mm(i) = 72.1066 ! PC-SAFT + parame(i,1) = mm(i)* 4.264192830122321E-002 ! =3.07476446724498 + parame(i,2) = 3.39324011060028 + parame(i,3) = 252.267273608975 + IF (pol >= 1) mm(i) = 72.1066 ! PCP-SAFT + IF (pol >= 1) parame(i,1) = mm(i)* 4.137668924230600E-002 ! =2.98353238051926 + IF (pol >= 1) parame(i,2) = 3.42393701353423 + IF (pol >= 1) parame(i,3) = 244.994381354681 + IF (pol >= 1) parame(i,6) = 2.78000000000000 + IF (pol >= 2) mm(i) = 72.1066 ! PCIP-SAFT + IF (pol >= 2) parame(i,1) = mm(i)* 4.254697075199448E-002 ! =3.06791740122577 + IF (pol >= 2) parame(i,2) = 3.39138375903252 + IF (pol >= 2) parame(i,3) = 236.527763837528 + IF (pol >= 2) parame(i,6) = 2.78000000000000 + IF (pol == 2) parame(i,11)= 8.13000000000000 + ELSE IF (compna(i) == '2-pentanone') THEN + ! mm(i) = 86.134 ! PC-SAFT + ! parame(i,1) = mm(i)* 3.982654501296355E-002 ! =3.43041962814660 + ! parame(i,2) = 3.46877976946838 + ! parame(i,3) = 249.834724442656 + ! mm(i) = 86.134 ! PCP-SAFT + ! parame(i,1) = mm(i)* 3.893594769994072E-002 ! =3.35370891918669 + ! parame(i,2) = 3.49417356096593 + ! parame(i,3) = 246.656329096835 + ! parame(i,6) = 2.70000000000000 + mm(i) = 86.134 ! PCIP-SAFT + parame(i,1) = mm(i)* 3.973160761515879E-002 ! =3.42224229032409 + parame(i,2) = 3.46827593107280 + parame(i,3) = 240.904278156822 + parame(i,6) = 2.70000000000000 + IF (pol == 2) parame(i,11)= 9.93000000000000 + ELSE IF (compna(i) == '3-pentanone') THEN + mm(i) = 86.134 ! PC-SAFT + parame(i,1) = 3.36439508013322 + parame(i,2) = 3.48770251979329 + parame(i,3) = 252.695415552376 + IF (pol >= 1) mm(i) = 86.134 ! PCP-SAFT + IF (pol >= 1) parame(i,1) = 3.27863398611842 + IF (pol >= 1) parame(i,2) = 3.51592571835030 + IF (pol >= 1) parame(i,3) = 248.690775540981 + IF (pol >= 1) parame(i,6) = 2.82000000000000 + IF (pol == 2) mm(i) = 86.134 ! PCIP-SAFT + IF (pol == 2) parame(i,1) = 3.34821857026283 + IF (pol == 2) parame(i,2) = 3.48903345340516 + IF (pol == 2) parame(i,3) = 242.314578558329 + IF (pol == 2) parame(i,6) = 2.82000000000000 + IF (pol == 2) parame(i,11)= 9.93000000000000 + ELSE IF (compna(i) == 'cyclohexanone') THEN ! from DIPPR + ! IF (pol.GE.1) mm(i) = 98.1430 ! PCP-SAFT + ! IF (pol.GE.1) parame(i,1) = 3.084202 + ! IF (pol.GE.1) parame(i,2) = 3.613681 + ! IF (pol.GE.1) parame(i,3) = 286.15865 + ! IF (pol.GE.1) parame(i,6) = 3.087862 + IF (pol >= 1) mm(i) = 98.1500000000000 + IF (pol >= 1) parame(i,1) = 2.72291913132818 + IF (pol >= 1) parame(i,2) = 3.79018433908522 + IF (pol >= 1) parame(i,3) = 314.772193827344 + IF (pol >= 1) parame(i,6) = 3.24600000000000 + IF (pol /= 1) WRITE (*,*) 'no non-polar param. for cyclohexanone' + IF (pol /= 1) STOP + ELSE IF (compna(i) == 'propanal') THEN + mm(i) = 58.08 ! PC-SAFT + parame(i,1) = 2.67564746980910 + parame(i,2) = 3.26295953984941 + parame(i,3) = 251.888982765626 + IF (pol >= 1) mm(i) = 58.08 ! PCP-SAFT + IF (pol >= 1) parame(i,1) = 2.60007872084995 + IF (pol >= 1) parame(i,2) = 3.28720732189761 + IF (pol >= 1) parame(i,3) = 235.205188090107 + IF (pol >= 1) parame(i,6) = 2.72000000000000 + IF (pol >= 2) mm(i) = 58.08 ! PCIP-SAFT + IF (pol >= 2) parame(i,1) = 2.72471167411028 + IF (pol >= 2) parame(i,2) = 3.24781643022922 + IF (pol >= 2) parame(i,3) = 221.642071811094 + IF (pol >= 2) parame(i,6) = 2.72000000000000 + IF (pol >= 2) parame(i,11)= 6.50000000000000 + ELSE IF (compna(i) == 'butanal') THEN + mm(i) = 72.1066000000000 ! PC-SAFT + parame(i,1) = 2.96824823599784 + parame(i,2) = 3.44068916025889 + parame(i,3) = 253.929404992884 + IF (pol >= 1) mm(i) = 72.1066000000000 ! PCP-SAFT + IF (pol >= 1) parame(i,1) = 2.86783706423953 + IF (pol >= 1) parame(i,2) = 3.47737904036296 + IF (pol >= 1) parame(i,3) = 247.543312127310 + IF (pol >= 1) parame(i,6) = 2.72000000000000 + ELSE IF (compna(i) == 'dmso') THEN + mm(i) = 78.1300000000000 ! PC-SAFT + parame(i,1) = 2.92225114054231 + parame(i,2) = 3.27780791606297 + parame(i,3) = 355.688793038512 + IF (pol >= 1) mm(i) = 78.1300000000000 ! PCP-SAFT + IF (pol >= 1) parame(i,1) = 3.02433694138348 + IF (pol >= 1) parame(i,2) = 3.24270742566613 + IF (pol >= 1) parame(i,3) = 309.357476696679 + IF (pol >= 1) parame(i,6) = 3.96000000000000 + IF (pol >= 2) mm(i) = 78.1300000000000 ! PCIP-SAFT + IF (pol >= 2) parame(i,1) = 3.19078234633277 + IF (pol >= 2) parame(i,2) = 3.19778269816832 + IF (pol >= 2) parame(i,3) = 286.337981216861 + IF (pol >= 2) parame(i,6) = 3.96000000000000 + IF (pol >= 2) parame(i,11)= 7.97000000000000 + ELSE IF (compna(i) == 'acetone_JC') THEN ! Jog-Chapman + ! mm(i) = 58.0800000000000 ! Dominik et al.2005 + ! parame(i,1) = 2.221 + ! parame(i,2) = 3.607908 + ! parame(i,3) = 259.99 + ! parame(i,6) = 2.7 + ! parame(i,8) = 0.2258 + ! mm(i) = 58.0800000000000 + ! parame(i,1) = mm(i)* 3.556617369195472E-002 + ! parame(i,2) = 3.58780367502515 + ! parame(i,3) = 273.025100470307 + ! parame(i,6) = 2.70000000000000 + ! parame(i,8) = 0.229800000000000 + + mm(i) = 58.08 ! Tumakaka Sadowski 2004 + parame(i,1) = mm(i)* 3.766E-2 + parame(i,2) = 3.6028 + parame(i,3) = 245.49 + parame(i,6) = 2.72 + parame(i,8) = 0.2969 + ! mm(i) = 58.0800000000000 ! no adjust. DD-param. + ! parame(i,1) = 1.87041620247774 + ! parame(i,2) = 3.79783535570774 + ! parame(i,3) = 208.885730881588 + ! parame(i,6) = 2.88000000000000 + ! parame(i,8) = 1.0/parame(i,1) + WRITE (*,*) 'caution: parame(i,8) is now used for branching' + STOP + kij(1,2) = -0.005 + kij(2,1)=kij(1,2) + ELSE IF (compna(i) == 'acetone_SF') THEN ! Saager-Fischer + mm(i) = 58.08 + parame(i,1) = mm(i)* 4.603296414764944E-002 + parame(i,2) = 3.29454924451643 + parame(i,3) = 221.052649057645 + parame(i,6) = 2.70000000000000 + parame(i,8) = 0.625410000000000 + mm(i) = 58.08 ! form as expected from me - no DD-param adjusted.dat + parame(i,1) = mm(i)* 4.364264724158790E-002 ! =2.53476495179143 + parame(i,2) = 3.37098670735567 + parame(i,3) = 254.366379701851 + parame(i,6) = 2.88000000000000 + ! mm(i) = 58.08 ! form as expected but w/ sumseg/1.5 - no DD-param adjusted.dat + ! parame(i,1) = mm(i)* 4.694644361257521E-002 ! =2.72664944501837 + ! parame(i,2) = 3.27842292595463 + ! parame(i,3) = 238.398883501772 + ! parame(i,6) = 2.88000000000000 + ! mm(i) = 58.08 ! form as expected but w/ sumseg/1.5 and fdd*sumseg- no DD-param adjusted.dat + ! parame(i,1) = mm(i)* 4.458214655521766E-002 ! =2.58933107192704 + ! parame(i,2) = 3.32050824493493 + ! parame(i,3) = 218.285994651271 + ! parame(i,6) = 2.88000000000000 + WRITE (*,*) 'caution: parame(i,8) is now used for branching' + STOP + kij(1,2) = 0.035 + kij(2,1)=kij(1,2) + ELSE IF (compna(i) == 'ethylacetate_JC') THEN ! Jog-Chapman + ! mm(i) = 88.11 + ! parame(i,1) = 2.7481 + ! parame(i,2) = 3.6511 + ! parame(i,3) = 236.99 + ! parame(i,6) = 1.84 + ! parame(i,8) = 0.5458 + mm(i) = 88.1060000000000 + parame(i,1) = mm(i)* 0.03117 ! 2.74626402 + parame(i,2) = 3.6493 + parame(i,3) = 236.75 + parame(i,6) = 1.8 + parame(i,8) = 0.5462 + ELSE IF (compna(i) == 'ethylacetate_SF') THEN ! Saager-Fischer + mm(i) = 88.106 + parame(i,1) = mm(i)* 3.564165384763394E-002 + parame(i,2) = 3.447379322 + parame(i,3) = 226.0930487 + parame(i,6) = 1.8 + parame(i,8) = 0.849967000000000 + WRITE (*,*) 'caution: parame(i,8) is now used for branching' + STOP + ELSE IF (compna(i) == '12po_JC') THEN ! Jog-Chapman + mm(i) = 58.08 + parame(i,1) = 2.0105 + parame(i,2) = 3.6095 + parame(i,3) = 258.82 + parame(i,6) = 2.0 + parame(i,8) = 0.3979 + WRITE (*,*) 'caution: parame(i,8) is now used for branching' + STOP + ELSE IF (compna(i) == '12po_SF') THEN ! Saager-Fischer + mm(i) = 58.08 + parame(i,1) = 2.1341 + parame(i,2) = 3.4739 + parame(i,3) = 252.95 + parame(i,6) = 2.0 + parame(i,8) = 0.916 + WRITE (*,*) 'caution: parame(i,8) is now used for branching' + STOP + ELSE IF (compna(i) == 'acrylonitrile') THEN + IF (pol >= 2) mm(i) = 53.06 ! PCIP-SAFT + IF (pol >= 2) parame(i,1) = 2.168 + IF (pol >= 2) parame(i,2) = 3.575 + IF (pol >= 2) parame(i,3) = 214.83 + IF (pol >= 2) parame(i,6) = 3.91 + IF (pol == 2) parame(i,11)= 8.04 + IF (pol >= 2) mm(i) = 53.0000000000000 ! second parameter set ?? + IF (pol >= 2) parame(i,1) = 2.45403467006041 + IF (pol >= 2) parame(i,2) = 3.41276825781723 + IF (pol >= 2) parame(i,3) = 195.194353082408 + IF (pol >= 2) parame(i,6) = 3.91000000000000 + IF (pol == 2) parame(i,11)= 8.04000000000000 + ELSE IF (compna(i) == 'butyronitrile') THEN + ! mm(i) = 69.11 + ! parame(i,1) = 2.860 + ! parame(i,2) = 3.478 + ! parame(i,3) = 253.21 + ! parame(i,6) = 4.07 + mm(i) = 69.11 + parame(i,1) = 2.989 + parame(i,2) = 3.441 + parame(i,3) = 234.04 + parame(i,6) = 4.07 + IF (pol == 2) parame(i,11)= 8.4 + ELSE IF (compna(i) == 'propionitrile') THEN + mm(i) = 55.079 ! PC-SAFT + parame(i,1) = 2.66211021227108 + parame(i,2) = 3.34032231132738 + parame(i,3) = 294.078737359580 + IF (pol >= 1) mm(i) = 55.079 ! PCP-SAFT + IF (pol >= 1) parame(i,1) = 2.50958981615666 + IF (pol >= 1) parame(i,2) = 3.39806320429568 + IF (pol >= 1) parame(i,3) = 239.152759066148 + IF (pol >= 1) parame(i,6) = 4.05000000000000 + IF (pol >= 2) mm(i) = 55.079 ! PCIP-SAFT + IF (pol >= 2) parame(i,1) = 2.54684827683436 + IF (pol >= 2) parame(i,2) = 3.41240089912190 + IF (pol >= 2) parame(i,3) = 218.299491580335 + IF (pol >= 2) parame(i,6) = 4.05000000000000 + IF (pol == 2) parame(i,11)= 6.24000000000000 + ! IF (pol.GE.2) mm(i) = 55.079 ! PCIP-SAFT my_DD adjusted + ! IF (pol.GE.2) parame(i,1) = 2.61175151088002 + ! IF (pol.GE.2) parame(i,2) = 3.37194293181453 + ! IF (pol.GE.2) parame(i,3) = 233.346110749402 + ! IF (pol.GE.2) parame(i,6) = 3.74682245835235 + ! IF (pol.EQ.2) parame(i,11)= 6.24000000000000 + ELSE IF (compna(i) == 'nitromethane') THEN + mm(i) = 61.04 ! PC-SAFT + parame(i,1) = mm(i)* 4.233767489308791E-002 ! =2.58429167547409 + parame(i,2) = 3.10839592337018 + parame(i,3) = 310.694151426943 + IF (pol >= 1) mm(i) = 61.04 ! PCP-SAFT + IF (pol >= 1) parame(i,1) = mm(i)* 4.191475020685036E-002 ! =2.55847635262615 + IF (pol >= 1) parame(i,2) = 3.10129282495975 + IF (pol >= 1) parame(i,3) = 256.456941430554 + IF (pol >= 1) parame(i,6) = 3.46000000000000 + IF (pol >= 2) mm(i) = 61.04 ! PCIP-SAFT + IF (pol >= 2) parame(i,1) = mm(i)* 4.394323357988009E-002 ! =2.68229497771588 + IF (pol >= 2) parame(i,2) = 3.10654492320028 + IF (pol >= 2) parame(i,3) = 225.973607468282 + IF (pol >= 2) parame(i,6) = 3.46000000000000 + IF (pol >= 2) parame(i,11)= 7.37000000000000 + ELSE IF (compna(i) == 'nitroethane') THEN + mm(i) = 75.067 ! PC-SAFT + parame(i,1) = mm(i)* 4.019977215251163E-002 ! =3.01767629617259 + parame(i,2) = 3.21364231060938 + parame(i,3) = 286.571650044235 + IF (pol >= 1) mm(i) = 75.067 ! PCP-SAFT + IF (pol >= 1) parame(i,1) = mm(i)* 3.928506808347654E-002 ! =2.94901220582233 + IF (pol >= 1) parame(i,2) = 3.23117331990738 + IF (pol >= 1) parame(i,3) = 265.961000131109 + IF (pol >= 1) parame(i,6) = 3.23000000000000 + IF (pol >= 2) mm(i) = 75.067 ! PCIP-SAFT + IF (pol >= 2) parame(i,1) = mm(i)* 4.117677400894779E-002 ! =3.09101689452968 + IF (pol >= 2) parame(i,2) = 3.19364569858756 + IF (pol >= 2) parame(i,3) = 246.676040248662 + IF (pol >= 2) parame(i,6) = 3.23000000000000 + IF (pol >= 2) parame(i,11)= 9.63000000000000 + ELSE IF (compna(i) == 'acetonitrile') THEN + mm(i) = 41.052 ! PC-SAFT + parame(i,1) = mm(i)* 5.673187410405271E-002 ! =2.32895689571957 + parame(i,2) = 3.18980108373791 + parame(i,3) = 311.307486044181 + IF (pol >= 1) mm(i) = 41.052 ! PCP-SAFT + IF (pol >= 1) parame(i,1) = mm(i)* 5.254832931037250E-002 ! =2.15721401484941 + IF (pol >= 1) parame(i,2) = 3.27301469369132 + IF (pol >= 1) parame(i,3) = 216.888948676921 + IF (pol >= 1) parame(i,6) = 3.92520000000000 + IF (pol >= 2) mm(i) = 41.052 ! PCIP-SAFT + IF (pol >= 2) parame(i,1) = mm(i)* 5.125846581157176E-002 ! =2.10426253849664 + IF (pol >= 2) parame(i,2) = 3.39403305120647 + IF (pol >= 2) parame(i,3) = 199.070191065791 + IF (pol >= 2) parame(i,6) = 3.92520000000000 + IF (pol >= 2) parame(i,11)= 4.40000000000000 + ! IF (pol >= 2) mm(i) = 41.052 ! PCIP-SAFT my_DD adjusted + ! IF (pol >= 2) parame(i,1) = mm(i)* 5.755347845863738E-002 ! =2.36268539768398 + ! IF (pol >= 2) parame(i,2) = 3.18554306395900 + ! IF (pol >= 2) parame(i,3) = 225.143934506015 + ! IF (pol >= 2) parame(i,6) = 3.43151866932598 + ! IF (pol >= 2) parame(i,11)= 4.40000000000000 + ! mm(i) = 41.053 ! PCP-SAFT dipole and quadrupole + ! parame(i,1) = 1.79993 + ! parame(i,2) = 3.47366 + ! parame(i,3) = 211.001 + ! parame(i,6) = 3.93800 + ! parame(i,7) = 2.44000 + ! parame(i,11)= 0.0 + ELSE IF (compna(i) == 'dmf') THEN + mm(i) = 73.09 ! PC-SAFT + parame(i,1) = 2.388 + parame(i,2) = 3.658 + parame(i,3) = 363.77 + IF (pol >= 1) mm(i) = 73.09 ! PCP-SAFT + IF (pol >= 1) parame(i,1) = 2.269 + IF (pol >= 1) parame(i,2) = 3.714 + IF (pol >= 1) parame(i,3) = 331.56 + IF (pol >= 1) parame(i,6) = 3.82 + IF (pol >= 2) mm(i) = 73.09 ! PCIP-SAFT + IF (pol >= 2) parame(i,1) = 2.375 + IF (pol >= 2) parame(i,2) = 3.667 + IF (pol >= 2) parame(i,3) = 308.42 + IF (pol >= 2) parame(i,6) = 3.82 + IF (pol >= 2) parame(i,11)= 7.81 + ELSE IF (compna(i) == 'chloroform') THEN + mm(i) = 119.377 ! PCIP-SAFT + parame(i,1) = 2.5957 + parame(i,2) = 3.4299 + parame(i,3) = 264.664 + parame(i,6) = 1.04 + IF (pol == 2) parame(i,11)= 8.23 + ELSE IF (compna(i) == 'dimethyl-ether') THEN + mm(i) = 46.069 ! PC-SAFT + parame(i,1) = mm(i)* 0.049107715 ! =2.26234331 + parame(i,2) = 3.276640534 + parame(i,3) = 212.9343244 + IF (pol >= 1) mm(i) = 46.0690000000000 ! PCP-SAFT + IF (pol >= 1) parame(i,1) = mm(i)* 0.048170452 ! =2.219164566 + IF (pol >= 1) parame(i,2) = 3.296939638 + IF (pol >= 1) parame(i,3) = 212.1048888 + IF (pol >= 1) parame(i,6) = 1.30000000000000 + IF (pol >= 2) mm(i) = 46.0690000000000 ! PCIP-SAFT + IF (pol >= 2) parame(i,1) = mm(i)* 4.939183716945787E-002 ! =2.27543254655976 + IF (pol >= 2) parame(i,2) = 3.26584718800835 + IF (pol >= 2) parame(i,3) = 206.904551967059 + IF (pol >= 2) parame(i,6) = 1.30000000000000 + IF (pol == 2) parame(i,11)= 5.29000000000000 + ELSE IF (compna(i) == 'methyl-ethyl-ether') THEN + mm(i) = 60.096 + parame(i,1) = mm(i)* .0442404671 + parame(i,2) = 3.37282595 + parame(i,3) = 216.010217 + IF (pol >= 1) mm(i) = 60.096 ! PCP-SAFT + IF (pol >= 1) parame(i,1) = mm(i)* 4.3971676124088D-002 ! =2.64252184835325 + IF (pol >= 1) parame(i,2) = 3.37938465390 + IF (pol >= 1) parame(i,3) = 215.787173860 + IF (pol >= 1) parame(i,6) = 1.17000000000 + IF (pol >= 2) mm(i) = 60.096 ! PICP-SAFT + IF (pol >= 2) parame(i,1) = mm(i)* 4.4580196137984D-002 ! =2.67909146710834 + IF (pol >= 2) parame(i,2) = 3.36105342286 + IF (pol >= 2) parame(i,3) = 212.871911999 + IF (pol >= 2) parame(i,6) = 1.17000000000 + IF (pol >= 2) parame(i,11) = 7.93000000000 + ELSE IF (compna(i) == 'diethyl-ether') THEN + mm(i) = 74.123 ! PC-SAFT + parame(i,1) = mm(i)* .0409704089 + parame(i,2) = 3.48569553 + parame(i,3) = 217.64113 + IF (pol >= 1) mm(i) = 74.123 ! PCP-SAFT + IF (pol >= 1) parame(i,1) = mm(i)* 4.0103121403686E-2 ! =2.97256367 + IF (pol >= 1) parame(i,2) = 3.51268687697978 + IF (pol >= 1) parame(i,3) = 219.527376572135 + IF (pol >= 1) parame(i,6) = 1.15000000000000 + IF (pol >= 2) mm(i) = 74.123 ! PCIP-SAFT + IF (pol >= 2) parame(i,1) = mm(i)* 4.04144179873E-2 ! =2.9956379 + IF (pol >= 2) parame(i,2) = 3.501724569 + IF (pol >= 2) parame(i,3) = 217.8941822 + IF (pol >= 2) parame(i,6) = 1.15 + IF (pol == 2) parame(i,11)= 8.73 + ELSE IF (compna(i) == 'vinylacetate') THEN + mm(i) = 86.092 + parame(i,1) = mm(i)* .0374329292 + parame(i,2) = 3.35278602 + parame(i,3) = 240.492049 + ELSE IF (compna(i) == 'chloromethane') THEN ! R40 + mm(i) = 50.488 ! PC-SAFT + parame(i,1) = mm(i)* 0.039418879 ! 1.9902 + parame(i,2) = 3.1974 + parame(i,3) = 237.27 + IF (pol >= 1) mm(i) = 50.488 ! PCP-SAFT + IF (pol >= 1) parame(i,1) = mm(i)* 0.035790801 ! 1.8070 + IF (pol >= 1) parame(i,2) = 3.3034 + IF (pol >= 1) parame(i,3) = 229.97 + IF (pol >= 1) parame(i,6) = 1.8963 + IF (pol >= 1) lli(i) = 1.67703*parame(i,2) + IF (pol >= 1) phi_criti(i)= 20.75417 + IF (pol >= 1) chap(i) = 0.5 + IF (pol >= 2) mm(i) = 50.488 ! PCIP-SAFT + IF (pol >= 2) parame(i,1) = mm(i)* 3.68559992E-2 ! 1.86078 + IF (pol >= 2) parame(i,2) = 3.275186 + IF (pol >= 2) parame(i,3) = 216.4621 + IF (pol >= 2) parame(i,6) = 1.8963 + IF (pol == 2) parame(i,11)= 4.72 + ELSE IF (compna(i) == 'fluoromethane') THEN ! R41 + IF (pol /= 1) write (*,*) 'non-polar parameters missing for fluoromethane' + IF (pol /= 1) stop + IF (pol >= 1) mm(i) = 34.0329000000000 + IF (pol >= 1) parame(i,1) = 1.94494757526896 + IF (pol >= 1) parame(i,2) = 2.96858005012635 + IF (pol >= 1) parame(i,3) = 168.938697391009 + IF (pol >= 1) parame(i,6) = 1.57823038894029 + ELSE IF (compna(i) == 'dichloromethane') THEN ! R30 + mm(i) = 84.932 ! PC-SAFT + parame(i,1) = 2.3117 + parame(i,2) = 3.3161 + parame(i,3) = 270.98 + IF (pol >= 1) mm(i) = 84.932 ! PCP-SAFT + IF (pol >= 1) parame(i,1) = 2.2687 + IF (pol >= 1) parame(i,2) = 3.3373 + IF (pol >= 1) parame(i,3) = 269.08 + IF (pol >= 1) parame(i,6) = 1.6 + IF (pol >= 2) mm(i) = 84.932 ! PCIP-SAFT + IF (pol >= 2) parame(i,1) = 2.3435 + IF (pol >= 2) parame(i,2) = 3.2987 + IF (pol >= 2) parame(i,3) = 260.66 + IF (pol >= 2) parame(i,6) = 1.6 + IF (pol == 2) parame(i,11)= 6.48 + ELSE IF (compna(i) == 'difluoromethane') THEN ! R32 + IF (pol /= 1) write (*,*) 'non-polar parameters missing for difluoromethane' + IF (pol /= 1) stop + IF (pol >= 1) mm(i) = 52.0236 ! PCP-SAFT + IF (pol >= 1) parame(i,1) = mm(i)* 4.814700934384165E-002 ! 2.50478075530028 + IF (pol >= 1) parame(i,2) = 2.79365980535456 + IF (pol >= 1) parame(i,3) = 160.893555378523 + IF (pol >= 1) parame(i,6) = 1.97850000000000 + ELSE IF (compna(i) == 'trifluoromethane') THEN ! R23 + IF (pol /= 1) write (*,*) 'non-polar parameters missing for trifluoromethane' + IF (pol /= 1) stop + IF (pol >= 1) mm(i) = 70.0138000000000 + IF (pol >= 1) parame(i,1) = 2.66039274225485 + IF (pol >= 1) parame(i,2) = 2.82905884530501 + IF (pol >= 1) parame(i,3) = 149.527709542333 + IF (pol >= 1) parame(i,6) = 1.339963415253999E-002 + ELSE IF (compna(i) == 'tetrachloromethane') THEN ! R10 + mm(i) = 153.822 + parame(i,1) = mm(i)* .0150432213 + parame(i,2) = 3.81801454 + parame(i,3) = 292.838632 + ELSE IF (compna(i) == 'trichlorofluoromethane') THEN ! R11 + IF (pol /= 1) write (*,*) 'non-polar parameters missing for trichlorofluoromethane' + IF (pol /= 1) stop + IF (pol >= 1) mm(i) = 137.368000000000 + IF (pol >= 1) parame(i,1) = 2.28793359008803 + IF (pol >= 1) parame(i,2) = 3.69013104930876 + IF (pol >= 1) parame(i,3) = 248.603173885090 + IF (pol >= 1) parame(i,6) = 0.23225538492979 + ELSE IF (compna(i) == 'chlorodifluoromethane') THEN ! R22 ( CHClF2 or CHF2Cl) + IF (pol /= 1) write (*,*) 'non-polar parameters missing for chlorodifluoromethane' + IF (pol /= 1) stop + IF (pol >= 1) mm(i) = 86.4684000000000 + IF (pol >= 1) parame(i,1) = 2.47218586047893 + IF (pol >= 1) parame(i,2) = 3.13845692489930 + IF (pol >= 1) parame(i,3) = 187.666355083434 + IF (pol >= 1) parame(i,6) = 1.04954264812860 + ELSE IF (compna(i) == 'chloroethane') THEN + mm(i) = 64.514 + parame(i,1) = mm(i)* .0350926868 + parame(i,2) = 3.41602397 + parame(i,3) = 245.42626 + ELSE IF (compna(i) == '11difluoroethane') THEN + ! mm(i) = 66.0500000000000 ! PC-SAFT + ! parame(i,1) = mm(i)* 4.109944338817734E-002 + ! parame(i,2) = 3.10257444633546 + ! parame(i,3) = 192.177159144029 + ! mm(i) = 66.05 ! PC-SAFT assoc + ! parame(i,1)= 2.984947188 + ! parame(i,2)= 2.978630027 + ! parame(i,3)= 137.8192282 + ! nhb_typ(i) = 2 + ! nhb_no(i,1)= 1 + ! nhb_no(i,2)= 1 + ! eps_hb(i,i,1,2)= 823.3478288 + ! eps_hb(i,i,2,1)= 823.3478288 + ! eps_hb(i,i,1,1)= 0.0 + ! eps_hb(i,i,2,2)= 0.0 + ! kap_hb(i,i) = 0.96345994 + IF (pol >= 1) mm(i) = 66.0500000000000 ! PCP-SAFT + IF (pol >= 1) parame(i,1) = mm(i)* 3.949665745363346E-002 ! =2.60875422481249 + IF (pol >= 1) parame(i,2) = 3.13758353925036 + IF (pol >= 1) parame(i,3) = 179.517952627836 + IF (pol >= 1) parame(i,6) = 2.27000000000000 + IF (pol >= 1) lli(i) = 2.03907*parame(i,2) + IF (pol >= 1) phi_criti(i)= 26.5 + IF (pol >= 1) chap(i) = 0.4 + IF (pol >= 2) mm(i) = 66.0500000000000 ! PCIP-SAFT + IF (pol >= 2) parame(i,1) = mm(i)* 4.093647666154238E-002 ! =2.70385428349487 + IF (pol >= 2) parame(i,2) = 3.10437129415885 + IF (pol >= 2) parame(i,3) = 170.464400902455 + IF (pol >= 2) parame(i,6) = 2.27000000000000 + IF (pol == 2) parame(i,11)= 5.01000000000000 + ELSE IF (compna(i) == '1-chlorobutane') THEN + mm(i) = 92.568 + parame(i,1) = mm(i)* .0308793201 + parame(i,2) = 3.64240187 + parame(i,3) = 258.655298 + ELSE IF (compna(i) == 'chlorobenzene') THEN + ! mm(i) = 112.558 + ! parame(i,1) = mm(i)* .0235308686 + ! parame(i,2) = 3.75328494 + ! parame(i,3) = 315.039018 + mm(i) = 112.558 ! PCIP-SAFT + parame(i,1) = mm(i)* 0.023824167 ! =2.6816 + parame(i,2) = 3.7352 + parame(i,3) = 308.82 + parame(i,6) = 1.69 + IF (pol == 2) parame(i,11)= 14.1 + ELSE IF (compna(i) == 'styrene') THEN + mm(i) = 104.150 + parame(i,1) = mm(i)* 2.9124104853E-2 + parame(i,2) = 3.760233548 + parame(i,3) = 298.51287564 + ELSE IF (compna(i) == 'methylmethanoate') THEN + mm(i) = 60.053 + parame(i,1) = mm(i)* .0446000264 + parame(i,2) = 3.08753499 + parame(i,3) = 242.626755 + IF (pol >= 1) mm(i) = 60.053 ! PCP-SAFT + IF (pol >= 1) parame(i,1) = mm(i)* 4.366991153963102E-002 ! =2.62250919768946 + IF (pol >= 1) parame(i,2) = 3.10946396964 + IF (pol >= 1) parame(i,3) = 239.051951942 + IF (pol >= 1) parame(i,6) = 1.77 + IF (pol >= 2) mm(i) = 60.053 ! PCIP-SAFT + IF (pol >= 2) parame(i,1) = mm(i)* 4.492572388931002E-2 ! 2.69792449 + IF (pol >= 2) parame(i,2) = 3.078467837 + IF (pol >= 2) parame(i,3) = 232.1842551 + IF (pol >= 2) parame(i,6) = 1.77 + IF (pol == 2) parame(i,11)= 5.05 + ELSE IF (compna(i) == 'ethylmethanoate') THEN + mm(i) = 74.079 ! PC-SAFT + parame(i,1) = mm(i)* .03898009 + parame(i,2) = 3.31087192 + parame(i,3) = 246.465646 + IF (pol >= 1) mm(i) = 74.079 ! PCP-SAFT + IF (pol >= 1) parame(i,1) = mm(i)* 3.825407152074255E-002 ! =2.83382336418509 + IF (pol >= 1) parame(i,2) = 3.33160046679 + IF (pol >= 1) parame(i,3) = 244.495680932 + IF (pol >= 1) parame(i,6) = 1.93000000000 + ELSE IF (compna(i) == 'propylmethanoate') THEN + mm(i) = 88.106 + parame(i,1) = mm(i)* .0364206062 + parame(i,2) = 3.41679642 + parame(i,3) = 246.457732 + IF (pol >= 1) mm(i) = 88.106 + IF (pol >= 1) parame(i,1) = mm(i)* 3.60050739149E-2 ! =3.17226304235232 + IF (pol >= 1) parame(i,2) = 3.42957609309 + IF (pol >= 1) parame(i,3) = 245.637644107 + IF (pol >= 1) parame(i,6) = 1.89 + ELSE IF (compna(i) == 'methylacetate') THEN + mm(i) = 74.079 ! PC-SAFT + parame(i,1) = mm(i)* 4.286817177E-2 ! =3.175631296 + parame(i,2) = 3.18722021277843 + parame(i,3) = 234.106931032456 + IF (pol >= 1) mm(i) = 74.079 ! PCP-SAFT + IF (pol >= 1) parame(i,1) = mm(i)* 4.228922065E-2 ! =3.132743176 + IF (pol >= 1) parame(i,2) = 3.2011401688 + IF (pol >= 1) parame(i,3) = 233.17562886 + IF (pol >= 1) parame(i,6) = 1.72 + IF (pol >= 2) mm(i) = 74.079 ! PCIP-SAFT + IF (pol >= 2) parame(i,1) = mm(i)* 4.298900538E-2 ! =3.18458252 + IF (pol >= 2) parame(i,2) = 3.180642322 + IF (pol >= 2) parame(i,3) = 229.3132680 + IF (pol >= 2) parame(i,6) = 1.72 + IF (pol == 2) parame(i,11)= 6.94 + ELSE IF (compna(i) == 'ethylacetate') THEN + mm(i) = 88.106 ! PC-SAFT + parame(i,1) = mm(i)* .0401464427 ! =3.537142481 + parame(i,2) = 3.30789258 + parame(i,3) = 230.800689 + IF (pol >= 1) mm(i) = 88.106 ! PCP-SAFT + IF (pol >= 1) parame(i,1) = mm(i)* 0.039792575 ! =3.505964572 + IF (pol >= 1) parame(i,2) = 3.317655188 + IF (pol >= 1) parame(i,3) = 230.2434769 + IF (pol >= 1) parame(i,6) = 1.78 + IF (pol >= 2) mm(i) = 88.106 ! PCIP-SAFT + IF (pol >= 2) parame(i,1) = mm(i)* 0.040270267 ! =3.548052143 + IF (pol >= 2) parame(i,2) = 3.302097562 + IF (pol >= 2) parame(i,3) = 227.5026191 + IF (pol >= 2) parame(i,6) = 1.78 + IF (pol == 2) parame(i,11)= 8.62 + ELSE IF (compna(i) == 'ethyl-propanoate') THEN + mm(i) = 102.133 + parame(i,1) = mm(i)* .0375692464 + parame(i,2) = 3.40306071 + parame(i,3) = 232.778374 + ELSE IF (compna(i) == 'propyl-ethanoate') THEN + mm(i) = 102.133 + parame(i,1) = mm(i)* .0370721275 + parame(i,2) = 3.42272266 + parame(i,3) = 235.758378 + IF (pol >= 1) mm(i) = 102.133 ! PCP-SAFT + IF (pol >= 1) parame(i,1) = mm(i)* 3.687149995200072E-2 ! =3.76579690459769 + IF (pol >= 1) parame(i,2) = 3.4289353421006 + IF (pol >= 1) parame(i,3) = 235.41679442910 + IF (pol >= 1) parame(i,6) = 1.78 + ! IF (pol.EQ.2) parame(i,11)= 10.41 + ELSE IF (compna(i) == 'nbutyl-ethanoate') THEN + mm(i) = 116.16 ! PC-SAFT + parame(i,1) = mm(i)* .03427004 + parame(i,2) = 3.54269638 + parame(i,3) = 242.515768 + IF (pol >= 1) mm(i) = 116.16 ! PCP-SAFT + IF (pol >= 1) parame(i,1) = mm(i)* 3.411585209773470E-002 ! =3.96289737967286 + IF (pol >= 1) parame(i,2) = 3.54821589228130 + IF (pol >= 1) parame(i,3) = 242.274388267447 + IF (pol >= 1) parame(i,6) = 1.87000000000000 + IF (pol >= 2) mm(i) = 116.16 ! PCIP-SAFT + IF (pol >= 2) parame(i,1) = mm(i)* 3.442139015733717E-002 ! =3.99838868067629 + IF (pol >= 2) parame(i,2) = 3.53576054452119 + IF (pol >= 2) parame(i,3) = 240.154409609249 + IF (pol >= 2) parame(i,6) = 1.87000000000000 + IF (pol == 2) parame(i,11)= 14.2000000000000 + ELSE IF (compna(i) == 'methyl-octanoate') THEN + mm(i) = 158.24 ! PC-SAFT + parame(i,1) = 5.2074 + parame(i,2) = 3.6069 + parame(i,3) = 244.12 + ELSE IF (compna(i) == 'methyl-decanoate') THEN + mm(i) = 186.2912 ! PC-SAFT + parame(i,1) = 5.8402 + parame(i,2) = 3.6871 + parame(i,3) = 248.27 + + mm(i) = 186.2912 ! PC-SAFT from GC-method Tim + parame(i,1) = 7.716 + parame(i,2) = 3.337303029 + parame(i,3) = 204.250907 + + mm(i) = 186.2912 ! PC-SAFT from GC-method (tightly fit) Tim + parame(i,1) = 7.728 + parame(i,2) = 3.334023322 + parame(i,3) = 206.9099379 + + ! mm(i) = 186.2912 ! PC-SAFT from fit to DIPPR + ! parame(i,1) = 6.285005 + ! parame(i,2) = 3.594888 + ! parame(i,3) = 236.781461 + ! ! parame(i,6) = 2.08056 + + ! mm(i) = 186.291000000000 + ! parame(i,1) = 6.28500485898895 + ! parame(i,2) = 3.59488828061149 + ! parame(i,3) = 236.781461491921 + ! parame(i,6) = 2.08055996894836 + ! parame(i,8) = 1.00000000000000 + mm(i) = 186.291000000000 + parame(i,1) = 6.14436331493372 + parame(i,2) = 3.61977264863944 + parame(i,3) = 242.071887817656 + + ELSE IF (compna(i) == 'methyl-dodecanoate') THEN + mm(i) = 214.344 ! PC-SAFT + parame(i,1) = 6.5153 + parame(i,2) = 3.7406 + parame(i,3) = 250.7 + ELSE IF (compna(i) == 'methyl-tetradecanoate') THEN + mm(i) = 242.398 ! PC-SAFT + parame(i,1) = 7.1197 + parame(i,2) = 3.7968 + parame(i,3) = 253.77 + ELSE IF (compna(i) == 'methyl-hexadecanoate') THEN + mm(i) = 270.451 ! PC-SAFT + parame(i,1) = 7.891 + parame(i,2) = 3.814 + parame(i,3) = 253.71 + ELSE IF (compna(i) == 'methyl-octadecanoate') THEN + mm(i) = 298.504 ! PC-SAFT + parame(i,1) = 8.8759 + parame(i,2) = 3.7932 + parame(i,3) = 250.81 + ELSE IF (compna(i) == 'CH2F2') THEN + mm(i) = 52.02 + parame(i,1) = 3.110084171 + parame(i,2) = 2.8145230485 + parame(i,3) = 158.98060151 + ELSE IF (compna(i) == 'naphthalene') THEN + ! mm(i) = 128.174000000 + ! parame(i,1) = mm(i)* 2.4877834216412E-2 + ! parame(i,2) = 3.82355815011 + ! parame(i,3) = 341.560675334 + + mm(i) = 128.17400000000 + parame(i,1) = mm(i)* 2.6400924157729E-2 + parame(i,2) = 3.8102186020014 + parame(i,3) = 328.96792935903 + ELSE IF (compna(i) == 'h2s') THEN + mm(i) = 34.0820000000000 ! PC-SAFT + parame(i,1) = mm(i)* 4.838886696385162E-002 ! = 1.64918936386199 + parame(i,2) = 3.05478289838459 + parame(i,3) = 229.838873939562 + nhb_typ(i) = 2 + nhb_no(i,1) = 1 + nhb_no(i,2) = 1 + eps_hb(i,i,1,2)= 536.634834731413 + eps_hb(i,i,2,1)= 536.634834731413 + eps_hb(i,i,1,1)= 0.0 + eps_hb(i,i,2,2)= 0.0 + kap_hb(i,i) = 1.000000000000000E-003 +! PC-SAFT from Xiaohua + mm(i) = 34.082 ! PC-SAFT + parame(i,1) = 1.63677 + parame(i,2) = 3.06565 + parame(i,3) = 230.2121 + nhb_typ(i) = 2 + nhb_no(i,1) = 1 + nhb_no(i,2) = 1 + eps_hb(i,i,1,2)= 275.1088 + eps_hb(i,i,2,1)= 275.1088 + eps_hb(i,i,1,1)= 0.0 + eps_hb(i,i,2,2)= 0.0 + kap_hb(i,i) = 1.E-2 + ! IF (pol.GE.1) mm(i) = 34.082 ! PCP-SAFT with quadrupole + ! IF (pol.GE.1) parame(i,1) = mm(i)* 3.03171032558E-2 ! =1.03326751316478 + ! IF (pol.GE.1) parame(i,2) = 3.6868189914018 + ! IF (pol.GE.1) parame(i,3) = 246.862831266172 + ! IF (pol.GE.1) nhb_typ(i) = 2 + ! IF (pol.GE.1) nhb_no(i,1) = 1 + ! IF (pol.GE.1) nhb_no(i,2) = 1 + ! IF (pol.GE.1) eps_hb(i,i,1,2)= 987.4927232 + ! IF (pol.GE.1) eps_hb(i,i,2,1)= 987.4927232 + ! IF (pol.GE.1) eps_hb(i,i,1,1)= 0.0 + ! IF (pol.GE.1) eps_hb(i,i,2,2)= 0.0 + ! IF (pol.GE.1) kap_hb(i,i) = 5.5480659623d-4 + ! IF (pol.GE.1) parame(i,6) = 0.97833 + ! IF (pol.GE.1) parame(i,7) = 3.8623 + ! IF (pol.GE.1) LLi(i) = 1.2737*parame(i,2) + ! IF (pol.GE.1) phi_criti(i)= 14.316 + ! IF (pol.GE.1) chap(i) = 0.4473 + IF (pol >= 1) mm(i) = 34.0820000000000 ! PCP-SAFT no quadrupoLE + IF (pol >= 1) parame(i,1) = mm(i)* 4.646468487062725E-002 ! 1.58360938976072 + IF (pol >= 1) parame(i,2) = 3.10111012646306 + IF (pol >= 1) parame(i,3) = 230.243457544889 + IF (pol >= 1) nhb_typ(i) = 2 + IF (pol >= 1) nhb_no(i,1) = 1 + IF (pol >= 1) nhb_no(i,2) = 1 + IF (pol >= 1) eps_hb(i,i,1,2)= 584.367708701411 + IF (pol >= 1) eps_hb(i,i,2,1)= 584.367708701411 + IF (pol >= 1) eps_hb(i,i,1,1)= 0.0 + IF (pol >= 1) eps_hb(i,i,2,2)= 0.0 + IF (pol >= 1) kap_hb(i,i) = 1.000000000000000E-003 + IF (pol >= 1) parame(i,6) = 0.978330000000000 + + IF (pol >= 1) lli(i) = 1.2737*parame(i,2) + IF (pol >= 1) phi_criti(i)= 14.316 + IF (pol >= 1) chap(i) = 0.4473 + + + IF (pol == 2) parame(i,7) = 0.0 + IF (pol == 2) mm(i) = 34.0820000000000 ! PCIP-SAFT + IF (pol == 2) parame(i,1) = mm(i)* 4.806418212963168E-002 ! 1.63812345534211 + IF (pol == 2) parame(i,2) = 3.06556006883749 + IF (pol == 2) parame(i,3) = 221.746622243054 + IF (pol == 2) nhb_typ(i) = 2 + IF (pol == 2) nhb_no(i,1) = 1 + IF (pol == 2) nhb_no(i,2) = 1 + IF (pol == 2) eps_hb(i,i,1,2)= 672.164783984789 + IF (pol == 2) eps_hb(i,i,2,1)= 672.164783984789 + IF (pol == 2) eps_hb(i,i,1,1)= 0.0 + IF (pol == 2) eps_hb(i,i,2,2)= 0.0 + IF (pol == 2) kap_hb(i,i) = 1.000000000000000E-003 + IF (pol == 2) parame(i,6) = 0.978330000000000 + IF (pol == 2) parame(i,11) = 3.60200000000000 + IF (pol == 2) parame(i,7) = 0.0 + + IF (pol >= 1)mm(i) = 34.0820000000000 !PCP-SAFT D&Q + IF (pol >= 1)parame(i,1) = mm(i)* 3.974667896078737E-002 ! = 1.35464631234155 + IF (pol >= 1)parame(i,2) = 3.30857082333438 + IF (pol >= 1)parame(i,3) = 234.248947273191 + IF (pol >= 1)nhb_typ(i) = 2 + IF (pol >= 1)nhb_no(i,1) = 1 + IF (pol >= 1)nhb_no(i,2) = 1 + IF (pol >= 1)eps_hb(i,i,1,2)= 780.770936834770 + IF (pol >= 1)eps_hb(i,i,2,1)= 780.770936834770 + IF (pol >= 1)eps_hb(i,i,1,1)= 0.0 + IF (pol >= 1)eps_hb(i,i,2,2)= 0.0 + IF (pol >= 1)kap_hb(i,i) = 1.000000000000000E-003 + IF (pol >= 1)parame(i,6) = 0.978330000000000 + IF (pol >= 1)parame(i,7) = 2.93750500000000 + + ELSE IF (compna(i) == 'methanol') THEN + mm(i) = 32.042 ! PC-SAFT + parame(i,1) = mm(i)* .0476100379 + parame(i,2) = 3.23000005 + parame(i,3) = 188.904644 + nhb_typ(i) = 2 + nhb_no(i,1) = 1 ! no. of sites of type 1 + nhb_no(i,2) = 1 ! no. of sites of type 2 + eps_hb(i,i,1,2)= 2899.49055 + eps_hb(i,i,2,1)= 2899.49055 + eps_hb(i,i,1,1)= 0.0 + eps_hb(i,i,2,2)= 0.0 + kap_hb(i,i) = .0351760892 + IF (pol >= 1) mm(i) = 32.042 ! PCP-SAFT + IF (pol >= 1) parame(i,1) = mm(i)* 7.213091821E-2 ! =2.31121888139672 + IF (pol >= 1) parame(i,2) = 2.8270129502 + IF (pol >= 1) parame(i,3) = 176.3760515 + IF (pol >= 1) nhb_typ(i) = 2 + IF (pol >= 1) nhb_no(i,1) = 1 + IF (pol >= 1) nhb_no(i,2) = 1 + IF (pol >= 1) eps_hb(i,i,1,2)= 2332.5845803 + IF (pol >= 1) eps_hb(i,i,2,1)= 2332.5845803 + IF (pol >= 1) eps_hb(i,i,1,1)= 0.0 + IF (pol >= 1) eps_hb(i,i,2,2)= 0.0 + IF (pol >= 1) kap_hb(i,i) = 8.9248658086E-2 + IF (pol >= 1) parame(i,6) = 1.7 + IF (pol >= 1) lli(i) = 1.75*parame(i,2) + IF (pol >= 1) phi_criti(i)= 23.43 + IF (pol >= 1) chap(i) = 0.304 + IF (pol == 2) mm(i) = 32.042 ! PCIP-SAFT + IF (pol == 2) parame(i,1) = 2.0693 + IF (pol == 2) parame(i,2) = 2.9547 + IF (pol == 2) parame(i,3) = 174.51 + IF (pol == 2) nhb_typ(i) = 2 + IF (pol == 2) nhb_no(i,1) = 1 + IF (pol == 2) nhb_no(i,2) = 1 + IF (pol == 2) eps_hb(i,i,1,2)= 2418.5 + IF (pol == 2) eps_hb(i,i,2,1)= 2418.5 + IF (pol == 2) eps_hb(i,i,1,1)= 0.0 + IF (pol == 2) eps_hb(i,i,2,2)= 0.0 + IF (pol == 2) kap_hb(i,i) = 0.06319 + IF (pol == 2) parame(i,6) = 1.7 + IF (pol == 2) parame(i,11)= 3.29 + ! mm(i) = 32.0420000000000 ! PCP-SAFT with adjusted QQ + ! parame(i,1) = mm(i)* 6.241807629559099E-002 + ! ! parame(i,1) = 2.00000000066333 + ! parame(i,2) = 2.97610169698593 + ! parame(i,3) = 163.268505098639 + ! nhb_typ(i) = 2 + ! nhb_no(i,1) = 1 + ! nhb_no(i,2) = 1 + ! eps_hb(i,i,1,2)= 2449.55621933612 + ! eps_hb(i,i,2,1)= 2449.55621933612 + ! eps_hb(i,i,1,1)= 0.0 + ! eps_hb(i,i,2,2)= 0.0 + ! kap_hb(i,i) = 8.431015160393653E-002 + ! parame(i,6) = 1.72000000000000 + ! parame(i,7) = 1.59810028824523 + ELSE IF (compna(i) == 'ethanol') THEN + mm(i) = 46.069 + parame(i,1) = mm(i)* .0517195521 + parame(i,2) = 3.17705595 + parame(i,3) = 198.236542 + nhb_typ(i) = 2 + nhb_no(i,1) = 1 ! no. of sites of type 1 + nhb_no(i,2) = 1 ! no. of sites of type 2 + eps_hb(i,i,1,2)= 2653.38367 + eps_hb(i,i,2,1)= 2653.38367 + eps_hb(i,i,1,1)= 0.0 + eps_hb(i,i,2,2)= 0.0 + kap_hb(i,i) = .0323840159 + IF (pol >= 1) mm(i) = 46.0690000000000 + IF (pol >= 1) parame(i,1) = mm(i)* 4.753626908781145E-002 ! =2.18994838060639 + IF (pol >= 1) parame(i,2) = 3.30120000000000 + IF (pol >= 1) parame(i,3) = 209.824555801706 + IF (pol >= 1) nhb_typ(i) = 2 + IF (pol >= 1) nhb_no(i,1) = 1 + IF (pol >= 1) nhb_no(i,2) = 1 + IF (pol >= 1) eps_hb(i,i,1,2)= 2584.53116785767 + IF (pol >= 1) eps_hb(i,i,2,1)= 2584.53116785767 + IF (pol >= 1) eps_hb(i,i,1,1)= 0.0 + IF (pol >= 1) eps_hb(i,i,2,2)= 0.0 + IF (pol >= 1) kap_hb(i,i) = 2.349382956935725E-002 + IF (pol >= 1) parame(i,6) = 1.69000000000000 + ! mm(i) = 46.0690000000000 + ! parame(i,1) = mm(i)* 5.117957752785066E-002 ! =2.357791957 + ! parame(i,2) = 3.24027031244304 + ! parame(i,3) = 175.657110615456 + ! nhb_typ(i) = 2 + ! nhb_no(i,1) = 1 + ! nhb_no(i,2) = 1 + ! eps_hb(i,i,1,2)= 2273.62670516146 + ! eps_hb(i,i,2,1)= 2273.62670516146 + ! eps_hb(i,i,1,1)= 0.0 + ! eps_hb(i,i,2,2)= 0.0 + ! kap_hb(i,i) = 7.030279197039477E-002 + ! parame(i,6) = 1.69000000000000 + ! parame(i,7) = 3.63701294195013 + IF (pol == 2) mm(i) = 46.0690000000000 + IF (pol == 2) parame(i,1) = mm(i)* 4.733436280008321E-002 ! =2.18064676 + IF (pol == 2) parame(i,2) = 3.31260000000000 + IF (pol == 2) parame(i,3) = 207.594119926613 + IF (pol == 2) nhb_typ(i) = 2 + IF (pol == 2) nhb_no(i,1) = 1 + IF (pol == 2) nhb_no(i,2) = 1 + IF (pol == 2) eps_hb(i,i,1,2)= 2589.68311382661 + IF (pol == 2) eps_hb(i,i,2,1)= 2589.68311382661 + IF (pol == 2) eps_hb(i,i,1,1)= 0.0 + IF (pol == 2) eps_hb(i,i,2,2)= 0.0 + IF (pol == 2) kap_hb(i,i) = 2.132561218631547E-002 + IF (pol == 2) parame(i,6) = 1.69000000000000 + IF (pol == 2) parame(i,7) = 0.0 + IF (pol == 2) parame(i,11)= 5.11000000000000 + ELSE IF (compna(i) == '1-propanol') THEN + mm(i) = 60.096 + parame(i,1) = mm(i)* .0499154461 + parame(i,2) = 3.25221234 + parame(i,3) = 233.396705 + nhb_typ(i) = 2 + nhb_no(i,1) = 1 ! no. of sites of type 1 + nhb_no(i,2) = 1 ! no. of sites of type 2 + eps_hb(i,i,1,2)= 2276.77867 + eps_hb(i,i,2,1)= 2276.77867 + eps_hb(i,i,1,1)= 0.0 + eps_hb(i,i,2,2)= 0.0 + kap_hb(i,i) = .0152683094 + ELSE IF (compna(i) == '1-butanol') THEN + mm(i) = 74.123 + parame(i,1) = mm(i)* .0341065046 + parame(i,2) = 3.72361538 + parame(i,3) = 269.798048 + nhb_typ(i) = 2 + nhb_no(i,1) = 1 ! no. of sites of type 1 + nhb_no(i,2) = 1 ! no. of sites of type 2 + eps_hb(i,i,1,2)= 2661.37119 + eps_hb(i,i,2,1)= 2661.37119 + eps_hb(i,i,1,1)= 0.0 + eps_hb(i,i,2,2)= 0.0 + kap_hb(i,i) = .00489087833 + mm(i) = 74.1230000000000 + parame(i,1) = mm(i)* 3.329202420547412E-002 ! =2.46770471018236 + parame(i,2) = 3.76179376417092 + parame(i,3) = 270.237284242002 + nhb_typ(i) = 2 + nhb_no(i,1) = 1 + nhb_no(i,2) = 1 + eps_hb(i,i,1,2)= 2669.28754983370 + eps_hb(i,i,2,1)= 2669.28754983370 + eps_hb(i,i,1,1)= 0.0 + eps_hb(i,i,2,2)= 0.0 + kap_hb(i,i) = 4.855584122733399E-003 + parame(i,6) = 1.66000000000000 + ELSE IF (compna(i) == '1-pentanol') THEN + mm(i) = 88.15 ! PC-SAFT + parame(i,1) = mm(i)* .041134139 + parame(i,2) = 3.45079143 + parame(i,3) = 247.278748 + nhb_typ(i) = 2 + nhb_no(i,1) = 1 ! no. of sites of type 1 + nhb_no(i,2) = 1 ! no. of sites of type 2 + eps_hb(i,i,1,2)= 2252.09237 + eps_hb(i,i,2,1)= 2252.09237 + eps_hb(i,i,1,1)= 0.0 + eps_hb(i,i,2,2)= 0.0 + kap_hb(i,i) = .0103189939 + IF (pol >= 1) mm(i) = 88.1500000000000 ! PCP-SAFT + IF (pol >= 1) parame(i,1) = mm(i)* 4.138903382168521E-002 ! =3.64844333138155 + IF (pol >= 1) parame(i,2) = 3.44250118689142 + IF (pol >= 1) parame(i,3) = 246.078034174947 + IF (pol >= 1) nhb_typ(i) = 2 + IF (pol >= 1) nhb_no(i,1) = 1 + IF (pol >= 1) nhb_no(i,2) = 1 + IF (pol >= 1) eps_hb(i,i,1,2)= 2236.72830142446 + IF (pol >= 1) eps_hb(i,i,2,1)= 2236.72830142446 + IF (pol >= 1) eps_hb(i,i,1,1)= 0.0 + IF (pol >= 1) eps_hb(i,i,2,2)= 0.0 + IF (pol >= 1) kap_hb(i,i) = 1.040067895187016E-002 + IF (pol >= 1) parame(i,6) = 1.70000000000000 + IF (pol == 2) mm(i) = 88.1500000000000 ! PCIP-SAFT + IF (pol == 2) parame(i,1) = mm(i)* 4.161521814399406E-002 ! =3.66838147939308 + IF (pol == 2) parame(i,2) = 3.43496654431777 + IF (pol == 2) parame(i,3) = 244.177313808431 + IF (pol == 2) nhb_typ(i) = 2 + IF (pol == 2) nhb_no(i,1) = 1 + IF (pol == 2) nhb_no(i,2) = 1 + IF (pol == 2) eps_hb(i,i,1,2)= 2241.27880639096 + IF (pol == 2) eps_hb(i,i,2,1)= 2241.27880639096 + IF (pol == 2) eps_hb(i,i,1,1)= 0.0 + IF (pol == 2) eps_hb(i,i,2,2)= 0.0 + IF (pol == 2) kap_hb(i,i) = 1.049516309928397E-002 + IF (pol == 2) parame(i,6) = 1.70000000000000 + IF (pol == 2) parame(i,11)= 10.8000000000000 + ELSE IF (compna(i) == '1-octanol') THEN + mm(i) = 130.23 + parame(i,1) = mm(i)* .0334446084 + parame(i,2) = 3.714535 + parame(i,3) = 262.740637 + nhb_typ(i) = 2 + nhb_no(i,1) = 1 ! no. of sites of type 1 + nhb_no(i,2) = 1 ! no. of sites of type 2 + eps_hb(i,i,1,2)= 2754.77272 + eps_hb(i,i,2,1)= 2754.77272 + eps_hb(i,i,1,1)= 0.0 + eps_hb(i,i,2,2)= 0.0 + kap_hb(i,i) = .00219656803 + ELSE IF (compna(i) == '1-nonanol') THEN + mm(i) = 144.257 + parame(i,1) = mm(i)* .0324692669 + parame(i,2) = 3.72924286 + parame(i,3) = 263.636673 + nhb_typ(i) = 2 + nhb_no(i,1) = 1 ! no. of sites of type 1 + nhb_no(i,2) = 1 ! no. of sites of type 2 + eps_hb(i,i,1,2)= 2941.9231 + eps_hb(i,i,2,1)= 2941.9231 + eps_hb(i,i,1,1)= 0.0 + eps_hb(i,i,2,2)= 0.0 + kap_hb(i,i) = .00142696883 + ELSE IF (compna(i) == '2-propanol') THEN + mm(i) = 60.096 + parame(i,1) = mm(i)* .0514663133 + parame(i,2) = 3.20845858 + parame(i,3) = 208.420809 + nhb_typ(i) = 2 + nhb_no(i,1) = 1 ! no. of sites of type 1 + nhb_no(i,2) = 1 ! no. of sites of type 2 + eps_hb(i,i,1,2)= 2253.91064 + eps_hb(i,i,2,1)= 2253.91064 + eps_hb(i,i,1,1)= 0.0 + eps_hb(i,i,2,2)= 0.0 + kap_hb(i,i) = .0246746934 + ELSE IF (compna(i) == '2-methyl-2-butanol') THEN + mm(i) = 88.15 + parame(i,1) = mm(i)* .0289135026 + parame(i,2) = 3.90526707 + parame(i,3) = 266.011828 + nhb_typ(i) = 2 + nhb_no(i,1) = 1 ! no. of sites of type 1 + nhb_no(i,2) = 1 ! no. of sites of type 2 + eps_hb(i,i,1,2)= 2618.80124 + eps_hb(i,i,2,1)= 2618.80124 + eps_hb(i,i,1,1)= 0.0 + eps_hb(i,i,2,2)= 0.0 + kap_hb(i,i) = .00186263367 + ELSE IF (compna(i) == 'acetic-acid') THEN + mm(i) = 60.053 + parame(i,1) = mm(i)* .0227076949 + parame(i,2) = 3.79651163 + parame(i,3) = 199.225066 + nhb_typ(i) = 2 + nhb_no(i,1) = 1 ! no. of sites of type 1 + nhb_no(i,2) = 1 ! no. of sites of type 2 + eps_hb(i,i,1,2)= 3092.40109 + eps_hb(i,i,2,1)= 3092.40109 + eps_hb(i,i,1,1)= 0.0 + eps_hb(i,i,2,2)= 0.0 + kap_hb(i,i) = .0870093874 + + + mm(i) = 60.053 + parame(i,1) = mm(i)* .0181797646 + parame(i,2) = 4.13711044 + parame(i,3) = 207.552969 + nhb_typ(i) = 2 + nhb_no(i,1) = 1 ! no. of sites of type 1 + nhb_no(i,2) = 1 ! no. of sites of type 2 + eps_hb(i,i,1,2)= 3198.84362 + eps_hb(i,i,2,1)= 3198.84362 + eps_hb(i,i,1,1)= 0.0 + eps_hb(i,i,2,2)= 0.0 + kap_hb(i,i) = .0586552968 + +! mit gesetztem Dipol-Moment + mm(i) = 60.0530000000000 + parame(i,1) = mm(i)* 1.736420143637533E-002 + parame(i,2) = 4.25220708070687 + parame(i,3) = 190.957247854820 + parame(i,6) = 3.50000000000000 + nhb_typ(i) = 2 + nhb_no(i,1) = 1 ! no. of sites of type 1 + nhb_no(i,2) = 1 ! no. of sites of type 2 + eps_hb(i,i,1,2)= 3096.36190957945 + eps_hb(i,i,2,1)= 3096.36190957945 + eps_hb(i,i,1,1)= 0.0 + eps_hb(i,i,2,2)= 0.0 + kap_hb(i,i) = 6.154307094782551E-002 + + ELSE IF (compna(i) == 'propionic-acid') THEN + mm(i) = 74.0800000000000 + parame(i,1) = mm(i)* 2.359519915877884E-002 + parame(i,2) = 3.99339224153844 + parame(i,3) = 295.947729838532 + nhb_typ(i) = 2 + nhb_no(i,1) = 1 ! no. of sites of type 1 + nhb_no(i,2) = 1 ! no. of sites of type 2 + eps_hb(i,i,1,2)= 2668.97826430874 + eps_hb(i,i,2,1)= 2668.97826430874 + eps_hb(i,i,1,1)= 0.0 + eps_hb(i,i,2,2)= 0.0 + kap_hb(i,i) = 3.660242292423115E-002 + ELSE IF (compna(i) == 'acrylic-acid') THEN + mm(i) = 72.0636 + parame(i,1) = mm(i)* .0430585424 + parame(i,2) = 3.0545415 + parame(i,3) = 164.115604 + nhb_typ(i) = 2 + nhb_no(i,1) = 1 ! no. of sites of type 1 + nhb_no(i,2) = 1 ! no. of sites of type 2 + eps_hb(i,i,1,2)= 3065.40667 + eps_hb(i,i,2,1)= 3065.40667 + eps_hb(i,i,1,1)= 0.0 + eps_hb(i,i,2,2)= 0.0 + kap_hb(i,i) = .336261669 + ELSE IF (compna(i) == 'caproic-acid') THEN + mm(i) = 116.16 + parame(i,1) = 5.87151 + parame(i,2) = 3.0694697 + parame(i,3) = 241.4569 + nhb_typ(i) = 1 + eps_hb(i,i,1,1)= 2871.37 + kap_hb(i,i) = 3.411613D-3 + ELSE IF (compna(i) == 'aniline') THEN + mm(i) = 93.13 + parame(i,1) = mm(i)* .0285695992 + parame(i,2) = 3.70214085 + parame(i,3) = 335.471062 + nhb_typ(i) = 2 + nhb_no(i,1) = 1 ! no. of sites of type 1 + nhb_no(i,2) = 1 ! no. of sites of type 2 + eps_hb(i,i,1,2)= 1351.64234 + eps_hb(i,i,2,1)= 1351.64234 + eps_hb(i,i,1,1)= 0.0 + eps_hb(i,i,2,2)= 0.0 + kap_hb(i,i) = .0748830615 + + mm(i) = 93.1300000000000 + parame(i,1) = mm(i)* 2.834372610192228E-002 ! =2.63965121187202 + parame(i,2) = 3.71326867619433 + parame(i,3) = 332.253796842009 + nhb_typ(i) = 2 + nhb_no(i,1) = 1 + nhb_no(i,2) = 1 + eps_hb(i,i,1,2)= 1392.14266886674 + eps_hb(i,i,2,1)= 1392.14266886674 + eps_hb(i,i,1,1)= 0.0 + eps_hb(i,i,2,2)= 0.0 + kap_hb(i,i) = 7.424612087328866E-002 + parame(i,6) = 1.55000000000000 + IF (pol == 2) parame(i,11)= 12.1000000000000 + ELSE IF (compna(i) == 'HF') THEN + ! mm(i) = 20.006 ! PC-SAFT + ! parame(i,1) = 0.87731 + ! parame(i,2) = 3.0006 + ! parame(i,3) = 112.24 + ! nhb_typ(i) = 2 + ! nhb_no(i,1) = 1 + ! nhb_no(i,2) = 1 + ! eps_hb(i,i,1,2)= 2208.22 + ! eps_hb(i,i,2,1)= 2208.22 + ! eps_hb(i,i,1,1)= 0.0 + ! eps_hb(i,i,2,2)= 0.0 + ! kap_hb(i,i) = 0.71265 + mm(i) = 20.0060000000000 ! PCP-SAFT + parame(i,1) = 1.00030000000000 + parame(i,2) = 3.17603622195029 + parame(i,3) = 331.133373208282 + nhb_typ(i) = 2 + nhb_no(i,1) = 1 + nhb_no(i,2) = 1 + eps_hb(i,i,1,2)= 348.251433080979 + eps_hb(i,i,2,1)= 348.251433080979 + eps_hb(i,i,1,1)= 0.0 + eps_hb(i,i,2,2)= 0.0 + kap_hb(i,i) = 2.868887975449893E-002 + parame(i,6) = 1.82600000000000 + ELSE IF (compna(i) == 'HCl') THEN + ! mm(i) = 36.4610000000000 + ! parame(i,1) = mm(i)* 3.922046741026943E-002 + ! parame(i,2) = 3.08731180727493 + ! parame(i,3) = 203.898845304388 + ! nhb_typ(i) = 2 + ! nhb_no(i,1) = 1 + ! nhb_no(i,2) = 1 + ! eps_hb(i,i,1,2)= 245.462773177367 + ! eps_hb(i,i,2,1)= 245.462773177367 + ! eps_hb(i,i,1,1)= 0.0 + ! eps_hb(i,i,2,2)= 0.0 + ! kap_hb(i,i) = 0.256454187330899 + mm(i) = 36.461 ! PCIP-SAFT + parame(i,1) = 1.6335 + parame(i,2) = 2.9066 + parame(i,3) = 190.17 + parame(i,6) = 1.1086 + IF (pol == 2) parame(i,11)= 2.63 + ELSE IF (compna(i) == 'gen') THEN + mm(i) = 302.0 + parame(i,1) = 8.7563 + parame(i,2) = 3.604243 + parame(i,3) = 255.6434 + nhb_typ(i) = 2 + nhb_no(i,1) = 1 ! no. of sites of type 1 + nhb_no(i,2) = 1 ! no. of sites of type 2 + eps_hb(i,i,1,2)= 0.0 + eps_hb(i,i,2,1)= 0.0 + eps_hb(i,i,1,1)= 0.0 + eps_hb(i,i,2,2)= 0.0 + kap_hb(i,i) = 0.02 + ELSE IF (compna(i) == 'h2o') THEN + mm(i) = 18.015 + parame(i,1) = mm(i)* .05915 + parame(i,2) = 3.00068335 + parame(i,3) = 366.512135 + nhb_typ(i) = 2 + nhb_no(i,1) = 1 ! no. of sites of type 1 + nhb_no(i,2) = 1 ! no. of sites of type 2 + eps_hb(i,i,1,2)= 2500.6706 + eps_hb(i,i,2,1)= 2500.6706 + eps_hb(i,i,1,1)= 0.0 + eps_hb(i,i,2,2)= 0.0 + kap_hb(i,i) = .0348679836 + + ! mm(i) = 18.015 + ! parame(i,1) = 1.706 + ! parame(i,2) = 2.429 + ! parame(i,3) = 242.19 + ! nhb_typ(i) = 2 + ! nhb_no(i,1) = 1 ! no. of sites of type 1 + ! nhb_no(i,2) = 1 ! no. of sites of type 2 + ! eps_hb(i,i,1,2)= 2644.2 + ! eps_hb(i,i,2,1)= 2644.2 + ! eps_hb(i,i,1,1)= 0.0 + ! eps_hb(i,i,2,2)= 0.0 + ! kap_hb(i,i) = 0.153 + + ! mm(i) = 18.015 + ! parame(i,1) = mm(i)* .0588185709 + ! parame(i,2) = 3.02483704 + ! parame(i,3) = 382.086672 + !c! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! + ! nhb_typ(i) = 2 + ! nhb_no(i,1) = 1 ! no. of sites of type 1 + ! nhb_no(i,2) = 2 ! no. of sites of type 2 + !c! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! + ! eps_hb(i,i,1,2)= 2442.49782 + ! eps_hb(i,i,2,1)= 2442.49782 + ! eps_hb(i,i,1,1)=0.0 + ! eps_hb(i,i,2,2)=0.0 + ! kap_hb(i,i) = .0303754635 + + ! mit gefittetem Dipol-Moment - Haarlem-night + ! mm(i) = 18.015 + ! parame(i,1) = mm(i)* 7.0037160952278E-2 + ! parame(i,2) = 2.79276650240763 + ! parame(i,3) = 270.970053834558 + ! nhb_typ(i) = 2 + ! nhb_no(i,1) = 1 ! no. of sites of type 1 + ! nhb_no(i,2) = 1 ! no. of sites of type 2 + ! eps_hb(i,i,1,2)= 1427.8287 + ! eps_hb(i,i,2,1)= 1427.8287 + ! eps_hb(i,i,1,1)=0.0 + ! eps_hb(i,i,2,2)=0.0 + ! kap_hb(i,i) = 4.335167238E-2 + ! parame(i,6) = 3.968686856378 + + IF (pol >= 1) mm(i) = 18.015 ! PCP-SAFT + IF (pol >= 1) parame(i,1) = 0.922688825223317 + IF (pol >= 1) parame(i,2) = 3.17562052023944 + IF (pol >= 1) parame(i,3) = 388.462197714696 + IF (pol >= 1) nhb_typ(i) = 2 + IF (pol >= 1) nhb_no(i,1) = 1 + IF (pol >= 1) nhb_no(i,2) = 1 + IF (pol >= 1) eps_hb(i,i,1,2)= 2000.67247409031 + IF (pol >= 1) eps_hb(i,i,2,1)= 2000.67247409031 + IF (pol >= 1) eps_hb(i,i,1,1)= 0.0 + IF (pol >= 1) eps_hb(i,i,2,2)= 0.0 + IF (pol >= 1) kap_hb(i,i) = 2.040614952751225E-003 + IF (pol >= 1) parame(i,6) = 1.85500000000000 + IF (pol >= 1) parame(i,7) = 2.00000000000000 + ! IF (pol.EQ.2) mm(i) = 18.015 ! PCIP-SAFT - DQ with my=my_RPT + ! IF (pol.EQ.2) parame(i,1) = 1.0 + ! IF (pol.EQ.2) parame(i,2) = 3.14540664928026 + ! IF (pol.EQ.2) parame(i,3) = 320.283823615925 + ! IF (pol.EQ.2) nhb_typ(i) = 2 + ! IF (pol.EQ.2) nhb_no(i,1) = 2 + ! IF (pol.EQ.2) nhb_no(i,2) = 2 + ! IF (pol.EQ.2) eps_hb(i,i,1,2)= 1335.72887678032 + ! IF (pol.EQ.2) eps_hb(i,i,2,1)= 1335.72887678032 + ! IF (pol.EQ.2) eps_hb(i,i,1,1)= 0.0 + ! IF (pol.EQ.2) eps_hb(i,i,2,2)= 0.0 + ! IF (pol.EQ.2) kap_hb(i,i) = 4.162619960844732E-003 + ! IF (pol.EQ.2) parame(i,6) = 1.85500000000000 + ! IF (pol.EQ.2) parame(i,7) = 2.00000000000000 + ! IF (pol.EQ.2) parame(i,11)= 1.45000000000000 + ! mm(i) = 18.0150000000000 + ! parame(i,1) = 1.0 + ! parame(i,2) = 3.11505069470915 + ! parame(i,3) = 320.991387913502 + ! nhb_typ(i) = 2 + ! nhb_no(i,1) = 1 + ! nhb_no(i,2) = 1 + ! eps_hb(i,i,1,2)= 2037.76329812542 + ! eps_hb(i,i,2,1)= 2037.76329812542 + ! eps_hb(i,i,1,1)= 0.0 + ! eps_hb(i,i,2,2)= 0.0 + ! kap_hb(i,i) = 3.763148982832804E-003 + ! parame(i,6) = 1.85500000000000 + ! parame(i,7) = 2.00000000000000 + ! IF (pol.EQ.2) parame(i,11)= 1.45000000000000 + IF (pol == 2) mm(i) = 18.015 ! PCIP-SAFT - DQ with my=my_0 + IF (pol == 2) parame(i,1) = 1.0 + IF (pol == 2) parame(i,2) = 3.11574491885322 + IF (pol == 2) parame(i,3) = 322.699984283499 + IF (pol == 2) nhb_typ(i) = 2 + IF (pol == 2) nhb_no(i,1) = 1 + IF (pol == 2) nhb_no(i,2) = 1 + IF (pol == 2) eps_hb(i,i,1,2)= 2033.87777692450 + IF (pol == 2) eps_hb(i,i,2,1)= 2033.87777692450 + IF (pol == 2) eps_hb(i,i,1,1)= 0.0 + IF (pol == 2) eps_hb(i,i,2,2)= 0.0 + IF (pol == 2) kap_hb(i,i) = 3.815764667176484E-003 + IF (pol == 2) parame(i,6) = 1.85500000000000 + IF (pol == 2) parame(i,7) = 2.00000000000000 + IF (pol == 2) parame(i,11)= 1.45000000000000 + ! mm(i) = 18.015 ! Dortmund + ! parame(i,1) = 0.11065254*mm(i) + ! parame(i,2) = 2.36393615 + ! parame(i,3) = 300.288589 + ! nhb_typ(i) = 2 + ! nhb_no(i,1) = 1 + ! nhb_no(i,2) = 1 + ! eps_hb(i,i,1,2)= 1193.45585 + ! eps_hb(i,i,2,1)= 1193.45585 + ! eps_hb(i,i,1,1)= 0.0 + ! eps_hb(i,i,2,2)= 0.0 + ! kap_hb(i,i) = 0.091203519 + ! parame(i,6) = 1.8546 + ! parame(i,7) = 0.0 + ! parame(i,11)= 0.0 + ELSE IF (compna(i) == 'MBBA') THEN + mm(i) = 267.37 + parame(i,1) = 12.194 + parame(i,2) = 3.064 + parame(i,3) = 270.7 + e_lc(i,i) = 13.7 !Hino & Prausnitz + s_lc(i,i) = 0.176 !Hino & Prausnitz + ELSE IF (compna(i) == 'PCH5') THEN + mm(i) = 255.41 + parame(i,1) = 11.6 + parame(i,2) = 3.2 + parame(i,3) = 270.7 + ! E_LC(i,i) = 16.7 !Hino & Prausnitz + ! S_LC(i,i) = 0.176 !Hino & Prausnitz + e_lc(i,i) = 8.95 + s_lc(i,i) = 0.2 + + ! mm(i) = 255.41 + ! parame(i,1) = 11.6 + ! parame(i,2) = 3.2 + ! parame(i,3) = 290.7 + ! E_LC(i,i) = 7.18 + ! S_LC(i,i) = 0.2 + + ELSE IF (compna(i) == 'Li') THEN + mm(i) = 6.9 + parame(i,1) = 1.0 + parame(i,2) = 1.4 + parame(i,3) = 96.83 + parame(i,10)= 1.0 +! the self-association is set to zero in routine F_EXPL for ions + ! nhb_typ(i) = 1 + ! nhb_no(i,1) = 3 ! no. of sites of type 1 + ! eps_hb(i,i,1,1)= 2000.0 + ! kap_hb(i,i) = 0.008 + ELSE IF (compna(i) == 'Na') THEN + mm(i) = 23.0 + parame(i,1) = 1.0 + parame(i,2) = 1.9 + parame(i,3) = 147.38 + parame(i,10)= 1.0 +! the self-association is set to zero in routine F_EXPL for ions + nhb_typ(i) = 1 + nhb_no(i,1) = 3 ! no. of sites of type 1 + eps_hb(i,i,1,1)= 8946.28257 ! 25C, 3 sites, dG-ref-1 + kap_hb(i,i) = 0.001648933 + ELSE IF (compna(i) == 'Ka') THEN + mm(i) = 39.1 + parame(i,1) = 1.0 + parame(i,2) = 2.66 + parame(i,3) = 221.44 + parame(i,10)= 1.0 + ! the self-association is set to zero in routine F_EXPL for ions + nhb_typ(i) = 1 + nhb_no(i,1) = 3 ! no. of sites of type 1 + eps_hb(i,i,1,1)= 3118.336216 ! 25C, 3 sites, dG-ref-1 + kap_hb(i,i) = 0.00200559 + ELSE IF (compna(i) == 'Cs') THEN + mm(i) = 132.9 + parame(i,1) = 1.0 + parame(i,2) = 3.38 + parame(i,3) = 523.28 + parame(i,10)= 1.0 + ! the self-association is set to zero in routine F_EXPL for ions + ! nhb_typ(i) = 1 + ! nhb_no(i,1) = 3 ! no. of sites of type 1 + ! eps_hb(i,i,1,1)= 2000.0 + ! kap_hb(i,i) = 0.00200559 + ELSE IF (compna(i) == 'Cl') THEN + mm(i) = 35.5 + parame(i,1) = 1.0 + parame(i,2) = 3.62 + parame(i,3) = 225.44 + parame(i,10)= -1.0 +! the self-association is set to zero in routine F_EXPL for ions + nhb_typ(i) = 1 + nhb_no(i,1) = 4 ! no. of sites of type 1 + eps_hb(i,i,1,1)= 6744.12509 ! 25C, 3 sites, dG-ref-1 + kap_hb(i,i) = 0.00155252 + ELSE IF (compna(i) == 'Br') THEN + mm(i) = 79.9 + parame(i,1) = 1.0 + parame(i,2) = 3.9 + parame(i,3) = 330.82 + parame(i,10)= -1.0 +! the self-association is set to zero in routine F_EXPL for ions + nhb_typ(i) = 1 + nhb_no(i,1) = 4 ! no. of sites of type 1 + eps_hb(i,i,1,1)= 4516.033227 ! 25C, 3 sites, dG-ref-1 + kap_hb(i,i) = 0.00200559 + ELSE IF (compna(i) == 'Io') THEN + mm(i) = 126.9 + parame(i,1) = 1.0 + parame(i,2) = 4.4 + parame(i,3) = 380.60 + parame(i,10)= -1.0 +! the self-association is set to zero in routine F_EXPL for ions + nhb_typ(i) = 1 + nhb_no(i,1) = 4 ! no. of sites of type 1 + eps_hb(i,i,1,1)= 1631.203342 ! 25C, 3 sites, dG-ref-1 + kap_hb(i,i) = 0.00200559 + ELSE IF (compna(i) == 'OH') THEN + mm(i) = 17.0 + parame(i,1) = 1.0 + parame(i,2) = 3.06 + parame(i,3) = 217.26 + parame(i,10)= -1.0 + ! the self-association is set to zero in routine F_EXPL for ions + nhb_typ(i) = 1 + nhb_no(i,1) = 4 ! no. of sites of type 1 + eps_hb(i,i,1,1)= 14118.68089 ! 25C, 3 sites, dG-ref-1 + kap_hb(i,i) = 0.00200559 + ELSE IF (compna(i) == 'NO3') THEN + mm(i) = 62.0 + parame(i,1) = 1.0 + parame(i,2) = 4.12 + parame(i,3) = 239.48 + parame(i,10)= -1.0 + ! the self-association is set to zero in routine F_EXPL for ions + ! nhb_typ(i) = 1 + ! nhb_no(i,1) = 4 ! no. of sites of type 1 + ! eps_hb(i,i,1,1)= 2000.0 + ! kap_hb(i,i) = 0.00200559 + ELSE IF (compna(i) == 'bf4') THEN + mm(i) = 86.8 + parame(i,1) = 1.0 + parame(i,2) = 4.51 ! *0.85 + parame(i,3) = 164.7 + parame(i,10)= -1.0 + ELSE IF (compna(i) == 'pf6') THEN + mm(i) = 145.0 + parame(i,1) = 1.0 + parame(i,2) = 5.06 + parame(i,3) = 224.9 + parame(i,10)= -1.0 + ELSE IF (compna(i) == 'emim') THEN + mm(i) = 111.16 + parame(i,1) = 3.11 + parame(i,2) = 4.0 + parame(i,3) = 250.0 + parame(i,10)= 1.0 + ELSE IF (compna(i) == 'bmim') THEN + mm(i) = 139.21 + ! parame(i,1) = 2.81 + ! parame(i,2) = 3.5 + parame(i,1) = 3.81 + parame(i,2) = 4.0 + parame(i,3) = 250.0 + parame(i,6) = 0.0 + parame(i,10)= 1.0 + ELSE IF (compna(i) == 'hmim') THEN + mm(i) = 167.27 + parame(i,1) = 4.53 + parame(i,2) = 4.0 + parame(i,3) = 250.0 + parame(i,10)= 1.0 + ELSE IF (compna(i) == 'omim') THEN + mm(i) = 195.32 + parame(i,1) = 5.30 + parame(i,2) = 4.0 + parame(i,3) = 250.0 + parame(i,10)= 1.0 + ELSE IF (compna(i) == 'sw') THEN + parame(i,1) = 1.0 + parame(i,2) = 1.0 + parame(i,3) = 100.0 + parame(i,4) = 0.0 + parame(i,5) = 0.0 + mm(i) = 1.0 + parame(i,6) = 0.1175015839*2.0 + ! use Temp. in Kelvin in the input-file. For dimensionless quantities + ! (P*=P*sig**3/epsilon, T*=T*kBol/epsilon, rho*=rho*sig**3) calculate + ! P* = P *1E5 * (1.e-10)^3 / (100*8.31441/6.022045E+23) + ! T* = (T+273.15)/100 + ! for rho* go to utilities.f (subroutine SI_DENS) and write + ! density(ph) = dense(ph)*6.0/PI + ELSE IF (compna(i) == 'c8-sim') THEN + mm(i) = 114.231 + parame(i,1) = mm(i)* 4.095944E-2 ! =4.67883774717337 + parame(i,2) = 3.501769 + parame(i,3) = 163.8606 + ! mm(i) = 114.231000000000 + ! parame(i,1) = mm(i)* 3.547001476437745E-002 ! =4.05177525654960 + ! parame(i,2) = 3.70988567055814 + ! parame(i,3) = 192.787548176343 + ELSE IF (compna(i) == 'argon_ge') THEN + mm(i) = 39.948 + parame(i,1) = mm(i)*0.030327 + parame(i,2) = 3.149910 + parame(i,3) = 100.188975 + ELSE IF (compna(i) == 'argon_ge2') THEN + mm(i) = 39.948 + parame(i,1) = mm(i)*0.030327 + parame(i,2) = 3.149910 + parame(i,3) = 0.8*100.188975 + ELSE + WRITE (*,*) ' pure component parameters missing for ',compna(i) + STOP + END IF + + IF (pol == 2.AND.parame(i,11) == 0.0) THEN + WRITE (*,*) ' polarizability missing for comp. ',compna(i) + STOP + END IF + + IF (nhb_typ(i) /= 0) THEN + parame(i,12) = DBLE(nhb_typ(i)) + parame(i,13) = kap_hb(i,i) + no = 0 + DO j=1,nhb_typ(i) + DO k=1,nhb_typ(i) + parame(i,(14+no))=eps_hb(i,i,j,k) + no=no+1 + END DO + END DO + DO j=1,nhb_typ(i) + parame(i,(14+no))=DBLE(nhb_no(i,j)) + no=no+1 + END DO + ELSE + DO k=12,25 + parame(i,k)=0.0 + END DO + END IF + +END DO + + +DO i = 1,ncomp + DO j = 1,ncomp + IF (compna(i) == 'ps'.AND.compna(j) == 'cyclohexane')THEN + kij(i,j) = 0.0075 + ELSE IF(compna(i) == 'peva'.AND.compna(j) == 'ethylene')THEN +! -- 0 Gew.% VA------------- + ! kij(i,j) = 0.039 +! -- 7.5 Gew.% VA------------- + ! kij(i,j) = 0.0377325 + ! kij(i,j) = 0.0374867 +! ---12.7 Gew.% VA------------ + ! kij(i,j) = 0.036854 + ! kij(i,j) = 0.0366508 +! ---27.3 Gew.% VA------------ + ! kij(i,j) = 0.034386 + ! kij(i,j) = 0.0352375 +! ---31.8 Gew.% VA------------ + kij(i,j) = 0.033626 + ! kij(i,j) = 0.0350795 +! ---42.7 Gew.% VA------------ + ! kij(i,j) = 0.031784 + ! kij(i,j) = 0.035239 + ELSE IF(compna(i) == 'ps_J'.AND.compna(j) == 'co2_J')THEN !from: Xu, Diego: DFT for polymer-co2 mixtures: A PC-SAFT approach + kij(i,j) = - 0.00296 + ELSE IF(compna(i) == 'gen'.AND.compna(j) == 'h2o')THEN + kij(i,j) = - 0.2 + ELSE IF(compna(i) == 'peva'.AND.compna(j) == 'vinylacetate')THEN + kij(i,j) = 0.019 + ELSE IF(compna(i) == 'ps'.AND.compna(j) == 'co2') THEN + IF ( pol == 0 ) kij(i,j) = 0.195 + IF ( pol == 1 ) kij(i,j) = 0.06 + ELSE IF(compna(i) == 'ps'.AND.compna(j) == 'acetone') THEN + kij(i,j) = 0.021 + ELSE IF(compna(i) == 'ps'.AND.compna(j) == 'hexane') THEN + kij(i,j) = 0.012 + ELSE IF(compna(i) == 'ps'.AND.compna(j) == 'pentane')THEN + kij(i,j) = 0.005 + ELSE IF(compna(i) == 'ps'.AND.compna(j) == 'methylcyclohexane') THEN + kij(i,j) = 0.0073 + ELSE IF(compna(i) == 'ps'.AND.compna(j) == 'ethylbenzene')THEN + kij(i,j) = 0.008 + ELSE IF(compna(i) == 'pe'.AND.compna(j) == 'co2') THEN + ! kij(i,j) = 0.181 + kij(i,j) = 0.088 + ELSE IF(compna(i) == 'pe'.AND.compna(j) == 'propane') THEN + kij(i,j) = 0.0206 + ELSE IF(compna(i) == 'pe'.AND.compna(j) == 'butane') THEN + kij(i,j) = 0.01 + ELSE IF(compna(i) == 'methane'.AND.compna(j) == 'argon') THEN + kij(i,j) = 0.01 + ELSE IF(compna(i) == 'methane'.AND.compna(j) == 'butane') THEN + kij(i,j) = 0.026 + ELSE IF(compna(i) == 'pe'.AND.compna(j) == 'pentane') THEN + ! kij(i,j) = -0.0195 + ELSE IF(compna(i) == 'pe'.AND.compna(j) == 'hexane') THEN + ! kij(i,j) = 0.008 + kij(i,j) = 0.004 + ELSE IF(compna(i) == 'pe'.AND.compna(j) == 'ethylene') THEN + kij(i,j) = 0.0404 + ! kij(i,j) = 0.0423 + ! kij(i,j) = 0.044 + ELSE IF(compna(i) == 'pe'.AND.compna(j) == 'cyclohexane') THEN + kij(i,j) = -0.1 + ELSE IF(compna(i) == 'ldpe'.AND.compna(j) == 'cyclopentane')THEN + kij(i,j) = -0.016 + ELSE IF(compna(i) == 'pp'.AND.compna(j) == 'propane') THEN + kij(i,j) = 0.0242 + ELSE IF(compna(i) == 'pp'.AND.compna(j) == 'pentane') THEN + kij(i,j) = 0.0137583176 + ELSE IF(compna(i) == 'pp'.AND.compna(j) == 'co2') THEN + kij(i,j) = 0.1767 ! without quadrupol-term + kij(i,j) = 0.063 ! with quadrupol-term + ELSE IF(compna(i) == 'pba'.AND.compna(j) == 'ethylene') THEN + kij(i,j) = 0.026 + ELSE IF(compna(i) == 'decane'.AND.compna(j) == 'ethane') THEN + kij(i,j) = 0.017 + ELSE IF(compna(i) == 'n2'.AND.compna(j) == 'co2') THEN + ! kij(i,j) = -0.04 + ELSE IF(compna(i) == 'methane'.AND.compna(j) == 'co2') THEN + kij(i,j) = 0.051875 ! PC-SAFT + IF (pol == 1) kij(i,j) = -0.0353125 ! PCP-SAFT + ELSE IF(compna(i) == 'methane'.AND.compna(j) == 'co') THEN + ! IF (pol == 1) kij(i,j) = -0.003 ! PCP-SAFT + IF (pol == 1) kij(i,j) = 0.018 ! PCP-SAFT + ELSE IF(compna(i) == 'ethane'.AND.compna(j) == 'co2') THEN + kij(i,j) = 0.095 + kij(i,j) = 0.021 + ! kij(i,j) = 0.024 + ELSE IF(compna(i) == 'propane'.AND.compna(j) == 'co2') THEN + kij(i,j) = 0.042 + ELSE IF(compna(i) == 'argon_ge'.AND.compna(j) == 'argon_ge2') THEN + read (*,*) kij(i,j) + ELSE IF(compna(i) == 'butane'.AND.compna(j) == 'co2') THEN + ! kij(i,j) = 0.115 + ! kij(i,j) = 0.048 + kij(i,j) = 0.036 + ELSE IF(compna(i) == 'pentane'.AND.compna(j) == 'co2') THEN + kij(i,j) = 0.143 ! without quadrupol-term + kij(i,j) = 0.0 ! with quadrupol-term + ELSE IF(compna(i) == 'hexane'.AND.compna(j) == 'co2') THEN + ! kij(i,j) = 0.125 ! without quadrupol-term + kij(i,j) = 0.0495 + ELSE IF(compna(i) == 'heptane'.AND.compna(j) == 'co2') THEN + kij(i,j) = 0.11 ! without quadrupol-term + ! kij(i,j) = 0.05 + ! kij(i,j) = 0.039 ! with quadrupol-term + ELSE IF(compna(i) == 'decane'.AND.compna(j) == 'co2') THEN + ! kij(i,j) = 0.128 ! without quadrupol-term + kij(i,j) = 0.053 ! with quadrupol-term + ELSE IF(compna(i) == 'dodecane'.AND.compna(j) == 'co2') THEN + kij(i,j) = 0.12 ! without quadrupol-term + kij(i,j) = 0.0508 ! with quadrupol-term + ELSE IF(compna(i) == 'benzene'.AND.compna(j) == 'co2') THEN + ! kij(i,j) = 0.087968750000 ! without quadrupol-term + ! kij(i,j) = 0.008203125 ! only co2 quadrupol + kij(i,j) = 0.042 ! both quadrupol + ! kij(i,j) = 0.003 ! both quadrupol + ELSE IF(compna(i) == 'toluene'.AND.compna(j) == 'co2') THEN + ! kij(i,j) = 0.110784912 ! without quadrupol-term + kij(i,j) = 0.0305 ! with quadrupol-term + ELSE IF(compna(i) == 'cyclohexane'.AND.compna(j) == 'co2') THEN + kij(i,j) = 0.13 + lij(i,j) = - 0.00 + ! kij(i,j) = 0.045 + ELSE IF(compna(i) == 'chloromethane'.AND.compna(j) == 'co2')THEN + ! kij(i,j) = 0.04 ! PC-SAFT + kij(i,j) = 0.025 ! PCP-SAFT + ! kij(i,j) = 0.083 ! PCIP-SAFT + ELSE IF(compna(i) == 'acetone'.AND.compna(j) == 'n2')THEN + kij(i,j) = 0.035211 ! PCP-SAFT + lij(i,j) = + 0.013225 ! PCP-SAFT + kij(i,j) = 0.023 ! PCP-SAFT + lij(i,j) = + 0.013225 ! PCP-SAFT + !kij(i,j) = 1.722238535635467E-002 ! PCP-SAFT + !lij(i,j) = 2.815974678394451E-003 ! PCP-SAFT + !kij(i,j) = 1.931522058164026E-002 ! PCP-SAFT + !lij(i,j) = 0.0 ! PCP-SAFT + !kij(i,j) = 1.641053794134795E-002 ! PCP-SAFT + !lij(i,j) = -5.850421759950764E-003 ! PCP-SAFT + if ( num == 0 ) write (*,*) 'calculation with lij only possible with num=1' + if ( num == 0 ) stop + ELSE IF(compna(i) == 'acetone'.AND.compna(j) == 'co2')THEN + kij(i,j) = 0.015 ! PC-SAFT + IF (pol == 1) kij(i,j) = -0.02 ! PCP-SAFT + IF (pol == 2) kij(i,j) = -0.005 ! PCIP-SAFT where DQ with my=my_vacuum + ! IF (pol.EQ.2) kij(i,j) = 0.0 ! PCIP-SAFT where DQ with my=my_RPT + ELSE IF(compna(i) == 'methanol'.AND.compna(j) == 'co2')THEN + ! kij(i,j) = 0.0288 ! PC-SAFT + ! kij(i,j) = - 0.035 ! PCP-SAFT for co2 and PC-SAFT methanol + ! kij(i,j) = - 0.035 ! PCP-SAFT + ! lij(i,j) = 0.3 ! PCP-SAFT + ELSE IF(compna(i) == 'dimethyl-ether'.AND.compna(j) == 'co2')THEN + kij(i,j) = 0.00896894 ! PC-SAFT + ! kij(i,j) = - 0.015 ! PCP-SAFT + ELSE IF(compna(i) == 'dimethyl-ether'.AND.compna(j) == 'h2o')THEN + ! kij(i,j) = -0.134 ! PC-SAFT + ELSE IF(compna(i) == 'dichloromethane'.AND.compna(j) == 'co2')THEN + ! kij(i,j) = 0.06881725 ! PC-SAFT + ! kij(i,j) = 0.05839145 ! PCP-SAFT + kij(i,j) = -0.00944346 ! PCP-SAFT co2 dichloromethane PC-SAFT + ! kij(i,j) = 0.06 ! PCIP-SAFT + ELSE IF(compna(i) == 'h2s'.AND.compna(j) == 'methane')THEN + ! kij(i,j) = 0.0414 ! PC-SAFT + kij(i,j) = 0.0152 ! PCP-SAFT Dipole momnet (d with Q) + ELSE IF(compna(i) == 'butane'.AND.compna(j) == 'h2s')THEN + kij(i,j) = -0.002 ! PCP-SAFT + ELSE IF(compna(i) == 'methanol'.AND.compna(j) == 'h2s')THEN + kij(i,j) = 0.0 ! PCP-SAFT + lij(i,j) = 0.0 ! PCP-SAFT + ELSE IF(compna(i) == 'co2'.AND.compna(j) == 'hydrogen') THEN + ! lij(i,j) = -0.08 !!!!! Lij not kij !!!! + ELSE IF(compna(i) == 'hexane'.AND.compna(j) == 'n2') THEN + kij(i,j) = 0.11 + ELSE IF(compna(i) == 'propane'.AND.compna(j) == 'n2') THEN + kij(i,j) = 0.0251171875 + ELSE IF(compna(i) == 'co2'.AND.compna(j) == 'hexadecane') THEN + ! kij(i,j) = 0.1194 ! PC-SAFT ohne QQ + kij(i,j) = 0.0588 + ELSE IF(compna(i) == 'ethane'.AND.compna(j) == 'acetone') THEN + ! kij(i,j) = 0.065 ! no DD + kij(i,j) = 0.038 ! DD non-polarizable + ! kij(i,j) = 0.025 ! DD polarizable + ELSE IF(compna(i) == 'butane'.AND.compna(j) == 'acetone') THEN + ! kij(i,j) = 0.065 ! no DD + kij(i,j) = 0.037 ! DD non-polarizable + ! kij(i,j) = 0.025 ! DD polarizable + ELSE IF(compna(i) == 'pentane'.AND.compna(j) == 'acetone') THEN + ! kij(i,j) = 0.072 ! no DD + ! kij(i,j) = 0.041 ! DD non-polarizable + kij(i,j) = 0.039 ! DD polarizable + ! kij(i,j) = 0.035 ! DD polarizable + ELSE IF(compna(i) == 'hexane'.AND.compna(j) == 'acetone') THEN + ! kij(i,j) = 0.063 + kij(i,j) = 0.038 ! PCP-SAFT + ! kij(i,j) = 0.036 ! PCIP-SAFT + ELSE IF(compna(i) == 'heptane'.AND.compna(j) == 'acetone') THEN + kij(i,j) = 0.035 ! PCP-SAFT + ELSE IF(compna(i) == 'decane'.AND.compna(j) == 'acetone') THEN + ! kij(i,j) = 0.059 ! no DD + ! kij(i,j) = 0.03281250 ! DD non-polarizable + kij(i,j) = 0.028 ! DD polarizable + ELSE IF(compna(i) == 'hexadecane'.AND.compna(j) == 'acetone') THEN + ! kij(i,j) = 0.07 ! no DD + ! kij(i,j) = 0.0415 ! DD non-polarizable + kij(i,j) = 0.035 ! DD polarizable + ELSE IF(compna(i) == 'hexane'.AND.compna(j) == 'butanone')THEN + kij(i,j) = 0.027 ! PCP-SAFT + ! kij(i,j) = 0.033 ! PCP-SAFT with lij + ! lij(i,j) = 0.13 ! PCP-SAFT + ! kij(i,j) = 0.042 ! PC-SAFT + ELSE IF(compna(i) == 'heptane'.AND.compna(j) == 'butanone')THEN + kij(i,j) = 0.042 ! no DD + ! kij(i,j) = 0.027 ! DD non-polarizable + ELSE IF(compna(i) == 'heptane'.AND.compna(j) == '2-pentanone')THEN + kij(i,j) = 0.041 ! no DD + ! kij(i,j) = 0.031 ! DD non-polarizable + ELSE IF(compna(i) == 'hexane'.AND.compna(j) == '3-pentanone')THEN + kij(i,j) = 0.0 + ELSE IF(compna(i) == 'pentane'.AND.compna(j) == 'propanal')THEN + ! kij(i,j) = 0.055 ! no DD + kij(i,j) = 0.027 ! DD non-polarizable + ! kij(i,j) = 0.026 ! DD polarizable 22 + ELSE IF(compna(i) == 'cyclohexane'.AND.compna(j) == 'propanal')THEN + ! kij(i,j) = 0.06 ! no DD + kij(i,j) = 0.036 ! DD non-polarizable + kij(i,j) = 0.035 ! DD polarizable 22 + ELSE IF(compna(i) == 'heptane'.AND.compna(j) == 'butanal')THEN + kij(i,j) = 0.041 ! no DD + ! kij(i,j) = 0.025 ! DD non-polarizable + ELSE IF(compna(i) == 'hexane'.AND.compna(j) == 'thf')THEN + kij(i,j) = 0.012 ! PCP-SAFT + ELSE IF(compna(i) == 'octane'.AND.compna(j) == 'thf')THEN + kij(i,j) = 0.012 ! PCP-SAFT + ELSE IF(compna(i) == 'decane'.AND.compna(j) == 'thf')THEN + kij(i,j) = 0.012 ! PCP-SAFT + ELSE IF(compna(i) == 'toluene'.AND.compna(j) == 'dmso')THEN + ! kij(i,j) = 0.025 ! no DD + kij(i,j) = - 0.0105 ! DD non-polarizable + ! kij(i,j) = - 0.019 ! DD polarizable + ELSE IF(compna(i) == 'hexane'.AND.compna(j) == 'acrylonitrile')THEN + kij(i,j) = - 0.05 ! DD polarizable + ELSE IF(compna(i) == 'heptane' .AND. compna(j) == 'butyronitrile')THEN + kij(i,j) = - 0.002 ! DD polarizable 11 + kij(i,j) = 0.002 ! DD polarizable 22 + ELSE IF(compna(i) == '1-butene'.AND.compna(j) == 'dmf')THEN + ! kij(i,j) = 0.04 ! no DD + ! kij(i,j) = 0.004 ! DD non-polarizable + kij(i,j) = 0.005 ! DD polarizable 22 + ELSE IF(compna(i) == 'cyclohexane'.AND.compna(j) == 'dmf')THEN + kij(i,j) = 0.0135 ! DD polarizable 11 + kij(i,j) = 0.022 ! DD polarizable 22 + ELSE IF(compna(i) == 'ethylene'.AND.compna(j) == 'dmf')THEN + ! kij(i,j) = - 0.0215 ! DD polarizable 11 + kij(i,j) = - 0.01 ! DD polarizable 22 + ELSE IF(compna(i) == 'nbutyl-ethanoate'.AND.compna(j) == 'dmf')THEN + ! kij(i,j) = 0.016 ! no DD + ! kij(i,j) = -0.01 ! DD non-polarizable + kij(i,j) = - 0.015 ! DD polarizable 22 + ELSE IF(compna(i) == 'methylacetate' .AND. compna(j) == 'cyclohexane')THEN + kij(i,j) = 0.066 ! PC-SAFT + ! kij(i,j) = 0.061 ! PCP-SAFT + ! kij(i,j) = 0.0625 ! PCIP-SAFT + ELSE IF(compna(i) == 'methylacetate'.AND.compna(j) == 'decane')THEN + kij(i,j) = 0.0625 ! PCIP-SAFT + ELSE IF(compna(i) == 'methylacetate' .AND. compna(j) == 'methanol')THEN + ! kij(i,j) = -0.07 ! PCIP-SAFT + ELSE IF(compna(i) == 'pentane' .AND. compna(j) == 'propionitrile')THEN + kij(i,j) = 0.0498 + IF (pol >= 1) kij(i,j) = -0.01 + IF (pol >= 2) kij(i,j) = -0.027 + ELSE IF(compna(i) == 'hexane' .AND. compna(j) == 'propionitrile')THEN + kij(i,j) = 0.05 + IF (pol >= 1) kij(i,j) = 0.0 + IF (pol >= 2) kij(i,j) = -0.03 + ELSE IF(compna(i) == 'octane' .AND. compna(j) == 'propionitrile')THEN + kij(i,j) = 0.0 ! DD polarizable 22 + ELSE IF(compna(i) == 'cyclohexane' .AND. compna(j) == 'nitromethane')THEN + kij(i,j) = 0.14 ! no DD + ! kij(i,j) = 0.07 ! DD non-polarizable + ! kij(i,j) = 0.055 ! DD polarizable 22 + ELSE IF(compna(i) == 'cyclohexane' .AND. compna(j) == 'nitroethane')THEN + ! kij(i,j) = 0.06 ! no DD + kij(i,j) = 0.03 ! DD polarizable 22 + ELSE IF(compna(i) == 'acetone' .AND. compna(j) == 'nitromethane')THEN + ! kij(i,j) = - 0.017 ! no DD + kij(i,j) = - 0.021 ! DD non-polarizable + ! kij(i,j) = - 0.023 ! DD polarizable 22 + ELSE IF(compna(i) == 'acetone' .AND. compna(j) == 'h2o')THEN + kij(i,j) = - 0.2 ! PCP-SAFT (no cross-association) + ELSE IF(compna(i) == 'methylcyclohexane' .AND. compna(j) == 'acetonitrile')THEN + ! kij(i,j) = 0.09 ! no DD + ! kij(i,j) = 0.033 ! DD non-polarizable + ! kij(i,j) = 0.025 ! DD polarizable 22 + kij(i,j) = 0.04 ! DD polarizable 22 und my angepasst + ELSE IF(compna(i) == 'ethylacetate' .AND. compna(j) == 'acetonitrile')THEN + kij(i,j) = 0.007 ! no DD + ! kij(i,j) = -0.045 ! DD polarizable 22 + ELSE IF(compna(i) == 'dimethyl-ether' .AND. compna(j) == 'propane')THEN + ! kij(i,j) = 0.03 ! no DD + kij(i,j) = 0.0225 ! DD non-polarizable + ELSE IF(compna(i) == 'benzene' .AND. compna(j) == 'pentane')THEN + ! kij(i,j) = 0.012968750 ! ohne QQ + ! kij(i,j) = 0.004921875 ! mit QQ=5.6D (gefittet) + ! kij(i,j) = -0.006406250 ! mit QQ=7.45D (Literatur) + ELSE IF(compna(i) == 'benzene' .AND. compna(j) == 'heptane')THEN + kij(i,j) = 0.01328125 + ! kij(i,j) = 0.0038 + ELSE IF(compna(i) == 'benzene' .AND. compna(j) == '1-hexene')THEN + kij(i,j) = 0.0067 + ELSE IF(compna(i) == 'ethylene' .AND. compna(j) == 'co2') THEN + kij(i,j) = 0.04 + kij(i,j) = -0.029 + ELSE IF(compna(i) == 'ethylene' .AND. compna(j) == 'vinylacetate') THEN + kij(i,j) = - 0.013847 + ELSE IF(compna(i) == 'triacontane' .AND. compna(j) == 'ethylene') THEN + kij(i,j) = 0.028 + ELSE IF(compna(i) == 'triacontane' .AND. compna(j) == 'methane')THEN + ! kij(i,j) = 0.061953125 ! polyethylene parameters + kij(i,j) = 0.039609375 ! param. by extrapolation of n-alkanes + ELSE IF(compna(i) == 'tetracontane' .AND. compna(j) == 'methane')THEN + ! kij(i,j) = 0.06515625 ! polyethylene parameters + kij(i,j) = 0.04453125 ! param. by extrapolation of n-alkanes + ! --- kij and lij adjusted ------- + ! kij(i,j) = 0.045786119 ! param. by extrapolation of n-alkanes + ! lij(i,j) = +8.53466437d-4 ! param. by extrapolation of n-alkanes + ELSE IF(compna(i) == 'eicosane' .AND. compna(j) == 'methane')THEN + kij(i,j) = 0.0360134457445 + ELSE IF(compna(i) == 'tetracontane' .AND. compna(j) == 'methane')THEN + kij(i,j) = 0.0360134457445 ! assumed equal to eicosane-C1 + ELSE IF(compna(i) == 'chlorobenzene' .AND. compna(j) == 'cyclohexane') THEN + kij(i,j) = 0.013 + ELSE IF(compna(i) == 'chloroethane' .AND. compna(j) == 'butane')THEN + kij(i,j) = 0.025 + ELSE IF(compna(i) == 'tetrachloromethane' .AND. compna(j) == '2-methylpentane') THEN + kij(i,j) = 0.0070105 + ELSE IF(compna(i) == 'tetrachloromethane' .AND. compna(j) == 'hexane') THEN + kij(i,j) = 0.004 + ELSE IF(compna(i) == 'hydrogen' .AND. compna(j) == 'hexane') THEN + kij(i,j) = 0.1501 + ELSE IF(compna(i) == 'ethanol' .AND. compna(j) == 'co2') THEN + ! kij(i,j) = -0.08 + ELSE IF(compna(i) == 'ethanol' .AND. compna(j) == 'propane') THEN + kij(i,j) = - 0.07 + ELSE IF(compna(i) == 'ethanol' .AND. compna(j) == 'ethane') THEN + kij(i,j) = 0.0 + ELSE IF(compna(i) == 'ethanol' .AND. compna(j) == 'butane') THEN + kij(i,j) = 0.028 + kij(i,j) = 0.016 + ELSE IF(compna(i) == 'ethanol' .AND. compna(j) == 'cyclohexane')THEN + kij(i,j) = 0.037 + ELSE IF(compna(i) == 'ethanol' .AND. compna(j) == '2-methylpentane') THEN + kij(i,j) = 0.028 + ELSE IF(compna(i) == 'ethanol' .AND. compna(j) == '1-octanol')THEN + kij(i,j) = 0.06 + ELSE IF(compna(i) == 'methanol' .AND. compna(j) == 'cyclohexane') THEN + kij(i,j) = 0.0508 + ! kij(i,j) = 0.03 + ELSE IF(compna(i) == 'methanol' .AND. compna(j) == 'heptane')THEN + kij(i,j) = 0.034 + ELSE IF(compna(i) == 'methanol' .AND. compna(j) == 'decane')THEN + ! kij(i,j) = 0.042 ! PC-SAFT + ! kij(i,j) = 0.011 ! PCP-SAFT + kij(i,j) = 0.000 ! PCIP-SAFT + ELSE IF(compna(i) == 'methanol' .AND. compna(j) == 'isobutane') THEN + kij(i,j) = 0.051 + ELSE IF(compna(i) == 'methanol' .AND. compna(j) == '1-octanol') THEN + kij(i,j) = 0.02 + ELSE IF(compna(i) == '1-butanol' .AND. compna(j) == 'butane') THEN + kij(i,j) = 0.015 + ELSE IF(compna(i) == '1-nonanol' .AND. compna(j) == 'co2') THEN + kij(i,j) = 0.076 + kij(i,j) = 0.01443 + ELSE IF(compna(i) == '1-propanol' .AND. compna(j) == 'ethylbenzene') THEN + kij(i,j) = 0.0251757813 + ELSE IF(compna(i) == 'decane'.AND.compna(j) == 'ethanol') THEN + kij(i,j) = 0.085 + ELSE IF(compna(i) == 'hexane'.AND.compna(j) == '1-chlorobutane') THEN + kij(i,j) = 0.017 + ELSE IF(compna(i) == 'aniline'.AND.compna(j) == 'methylcyclopentane') THEN + kij(i,j) = 0.0153 + ELSE IF(compna(i) == 'heptane'.AND.compna(j) == 'nbutyl-ethanoate')THEN + kij(i,j) = 0.027 + ELSE IF(compna(i) == '1-hexene'.AND.compna(j) == 'ethyl-ethanoate')THEN + kij(i,j) = 0.026 + ELSE IF(compna(i) == 'co2'.AND.compna(j) == '1-butanol')THEN + ! kij(i,j) = 0.075 + kij(i,j) = 0.0 + ELSE IF(compna(i) == 'acrylic-acid'.AND.compna(j) == 'co2')THEN + kij(i,j) = -0.1 + ELSE IF(compna(i) == 'bmim'.AND.compna(j) == 'hydrogen')THEN + lij(i,j) = 0.55 !!!!! Lij not kij !!!! + ELSE IF(compna(i) == 'bf4'.AND.compna(j) == 'hydrogen')THEN + lij(i,j) = 0.55 !!!!! Lij not kij !!!! + ELSE IF(compna(i) == 'h2o'.AND.compna(j) == 'butane')THEN !K.R.Hall FPE 2007 254 112-125 kij=0.1850 + kij(i,j) = -0.07 + ELSE IF(compna(i) == 'h2o'.AND.compna(j) == '1-butanol')THEN + kij(i,j) = -0.12 + ELSE IF(compna(i) == 'h2o'.AND.compna(j) == 'aniline')THEN + kij(i,j) = 0.0 + ELSE IF(compna(i) == 'h2o'.AND.compna(j) == 'methanol') THEN + kij(i,j) = -0.02 + ELSE IF(compna(i) == 'h2o'.AND.compna(j) == 'ethanol') THEN + kij(i,j) = -0.027 + ELSE IF(compna(i) == 'h2o'.AND.compna(j) == 'styrene') THEN + kij(i,j) = 0.1 + ELSE IF(compna(i) == 'h2o'.AND.compna(j) == 'propyl-ethanoate') THEN + kij(i,j) = -0.205 + ELSE IF(compna(i) == 'h2o'.AND.compna(j) == 'ethyl-propanoate') THEN + kij(i,j) = 0.0 + ELSE IF(compna(i) == 'h2o'.AND.compna(j) == '1-pentanol') THEN + kij(i,j) = 0.0165 + ! kij(i,j) = 0.0294 + ! kij(i,j) = -0.082 + ELSE IF(compna(i) == 'h2o'.AND.compna(j) == 'methane') THEN + ! kij(i,j) = +0.06 + kij(i,j) = -0.08 + ELSE IF(compna(i) == 'h2o'.AND.compna(j) == 'propane') THEN + kij(i,j) = 0.02 + ELSE IF(compna(i) == 'h2o'.AND.compna(j) == 'hexane') THEN + kij(i,j) = -0.02 + ELSE IF(compna(i) == 'h2o'.AND.compna(j) == 'acetic-acid') THEN + kij(i,j) = -0.0 + ELSE IF(compna(i) == 'h2o'.AND.compna(j) == 'co2') THEN + if (pol == 0) kij(i,j) = 0.0030625 ! for T=50C, according to X.Tang + stop ! very T-dependent + ELSE IF(compna(i) == 'toluene'.AND.compna(j) == 'acetic-acid') THEN + kij(i,j) = -0.1 + ELSE IF(compna(i) == 'caproic-acid'.AND.compna(j) == 'cyclohexane') THEN + kij(i,j) = 0.041531 + ELSE IF(compna(i) == '1-octanol'.AND.compna(j) == 'h2o')THEN + kij(i,j) = 0.07 + ELSE IF(compna(i) == 'acetone'.AND.compna(j) == 'benzene')THEN + kij(i,j) = 0.02132466 ! PC-SAFT + ! kij(i,j) = 0.01495148 ! PCP-SAFT + ! kij(i,j) = -0.00735575 ! PCP-SAFT but non-polar benzene + ELSE IF(compna(i) == '1-propanol'.AND.compna(j) == 'benzene')THEN + kij(i,j) = 0.02017 + ELSE IF(compna(i) == '2-propanol'.AND.compna(j) == 'benzene')THEN + kij(i,j) = 0.021386 + ELSE IF(compna(i) == '1-pentanol'.AND.compna(j) == 'benzene')THEN + kij(i,j) = 0.0129638671875 + ELSE IF(compna(i) == 'CH2F2' .AND. compna(j) == 'co2') THEN + kij(i,j) = 2.2548828125E-2 + ELSE IF(compna(i) == 'dmso' .AND. compna(j) == 'co2') THEN + kij(i,j) = -0.00 + ELSE IF(compna(i) == 'dmf'.AND.compna(j) == 'h2o')THEN + kij(i,j) = -0.0 + ELSE IF(compna(i) == 'decane'.AND.compna(j) == 'h2o')THEN + kij(i,j) = 0.11 + ELSE IF(compna(i) == '11difluoroethane'.AND.compna(j) == 'HF')THEN + kij(i,j) = 0.032 ! association: eps_kij = 0.16 + ELSE IF(compna(i) == '11difluoroethane'.AND.compna(j) == 'co2')THEN + kij(i,j) = -0.004 ! PCP-SAFT (taken from simulation) + ELSE IF(compna(i) == 'difluoromethane'.AND.compna(j) == 'HF')THEN + kij(i,j) = -0.02 + ELSE IF(compna(i) == 'naphthalene'.AND.compna(j) == 'co2')THEN + kij(i,j) = 0.137 ! angepasst an SVLE-Linie (tradition.CO2-Parameter) + kij(i,j) = 0.09 ! angepasst an SVLE-Linie (tradition.CO2-Parameter) + ELSE IF(compna(i) == 'pg2'.AND.compna(j) == 'methanol')THEN + kij(i,j) = 0.03 + ELSE IF(compna(i) == 'pg2'.AND.compna(j) == 'co2')THEN + ! kij(i,j) = 0.05 + ELSE IF(compna(i) == 'PCH5'.AND.compna(j) == 'co2')THEN + ! kij(i,j) = -0.047 + kij(i,j) = +0.055 + ! kij(i,j) = +0.036 + ELSE + END IF + kij(j,i) = kij(i,j) + lij(j,i) = -lij(i,j) + + END DO +END DO + +END SUBROUTINE pcsaft_par + + +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! SUBROUTINE init_vars +! +! This subroutine writes variables from an array "val_init" to the +! system-variables. Those variables +! include some specifications but also some starting values for a +! phase equilibrium calculation. (val_init stands for 'initial value') + +! The array comprises the following elements +! element 0 density of third phase +! element 1 density of first phase +! element 2 density of second phase +! element 3 temperature [K] +! element 4 pressure [Pa] +! element 5,..(5+NCOMP) mole-fraction of comp. i in log. from (phase 1) +! element ... mole-fraction of comp. i in log. from (phase 2) +! element ... mole-fraction of comp. i in log. from (phase 3) +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! + SUBROUTINE init_vars +! + USE BASIC_VARIABLES + IMPLICIT NONE +! + INTEGER :: i, ph +! ---------------------------------------------------------------------- + +densta(3)=val_init(0) +densta(1)=val_init(1) +densta(2)=val_init(2) +t = val_init(3) +p = val_init(4) +DO ph = 1,nphas + DO i = 1,ncomp + lnx(ph,i) = val_init(4+i+(ph-1)*ncomp) + END DO +END DO + +END SUBROUTINE init_vars + + +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! SUBROUTINE converged +! +! Once a converged solution for an equilibrium calculation is found, +! this subroutine writes variables to an array "val_conv". +! (= short for converged values) +! The array comprises the following elements +! element 0 density of third phase +! element 1 density of first phase +! element 2 density of second phase +! element 3 temperature [K] +! element 4 pressure [Pa] +! element 5,..(4+NCOMP) mole-fraction of comp. i in log. from (phase 1) +! element ... mole-fraction of comp. i in log. from (phase 2) +! element ... mole-fraction of comp. i in log. from (phase 3) +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! + SUBROUTINE converged +! + USE BASIC_VARIABLES + IMPLICIT NONE +! + INTEGER :: i, ph +! ---------------------------------------------------------------------- + +val_conv(0) = dense(3) +val_conv(1) = dense(1) +val_conv(2) = dense(2) +val_conv(3) = t +val_conv(4) = p +DO ph = 1,nphas + DO i = 1,ncomp + val_conv(4+i+(ph-1)*ncomp) = lnx(ph,i) + END DO +END DO + +END SUBROUTINE converged + +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! SUBROUTINE PERTURBATION_PARAMETER +! +! calculates density-independent parameters of the equation of state. +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! + SUBROUTINE PERTURBATION_PARAMETER +! + USE PARAMETERS, ONLY: PI, KBOL, RGAS, NAV, TAU + USE EOS_VARIABLES + USE EOS_CONSTANTS + IMPLICIT NONE +! +! --- local variables -------------------------------------------------- + INTEGER :: i, j, k, l, m, no + LOGICAL :: assoc, qudpole, dipole + REAL :: m_mean + REAL, DIMENSION(nc) :: v00, v0, d00, u + REAL, DIMENSION(nc,nc,nsite,nsite) :: eps_hb + REAL, DIMENSION(nc,nc) :: kap_hb + REAL :: zmr, nmr + REAL :: eps_kij, k_kij +! ---------------------------------------------------------------------- + +! ---------------------------------------------------------------------- +! pure component parameters +! ---------------------------------------------------------------------- +DO i = 1, ncomp + u(i) = parame(i,3) * (1.0 + parame(i,4)/t) + mseg(i) = parame(i,1) + IF (eos == 0) THEN + v00(i) = parame(i,2) + v0(i) = v00(i)*(1.0-0.12*EXP(-3.0*parame(i,3)/t))**3 + d00(i) = (1.d30/1.d6 *tau *v00(i)*6.0/PI /NAV)**(1.0/3.0) + dhs(i) = d00(i)*(1.0-0.12*EXP(-3.0*parame(i,3)/t)) + ELSE + dhs(i) = parame(i,2)*(1.0-0.12*EXP(-3.0*parame(i,3)/t)) + d00(i) = parame(i,2) + END IF +END DO + + +! ---------------------------------------------------------------------- +! combination rules +! ---------------------------------------------------------------------- +DO i = 1, ncomp + DO j = 1, ncomp + sig_ij(i,j) = 0.5 * ( d00(i) + d00(j) ) + uij(i,j) = ( 1.0 - kij(i,j) ) * ( u(i)*u(j) )**0.5 + vij(i,j) = ( 0.5*( v0(i)**(1.0/3.0) + v0(j)**(1.0/3.0) ) )**3 + END DO +END DO + + +! ---------------------------------------------------------------------- +! abbreviations +! ---------------------------------------------------------------------- +z0t = PI / 6.0 * SUM( x(1:ncomp) * mseg(1:ncomp) ) +z1t = PI / 6.0 * SUM( x(1:ncomp) * mseg(1:ncomp) * dhs(1:ncomp) ) +z2t = PI / 6.0 * SUM( x(1:ncomp) * mseg(1:ncomp) * dhs(1:ncomp)**2 ) +z3t = PI / 6.0 * SUM( x(1:ncomp) * mseg(1:ncomp) * dhs(1:ncomp)**3 ) + +m_mean = z0t/(PI/6.0) + +DO i = 1, ncomp + DO j = 1, ncomp + dij_ab(i,j) = dhs(i)*dhs(j) / ( dhs(i) + dhs(j) ) + END DO +END DO + +! ---------------------------------------------------------------------- +! dispersion term parameters for chain molecules +! ---------------------------------------------------------------------- +DO m = 0, 6 + apar(m) = ap(m,1) + (1.0-1.0/m_mean)*ap(m,2) & + + (1.0-1.0/m_mean)*(1.0-2.0/m_mean)*ap(m,3) + bpar(m) = bp(m,1) + (1.0-1.0/m_mean)*bp(m,2) & + + (1.0-1.0/m_mean)*(1.0-2.0/m_mean)*bp(m,3) +END DO + + +! ---------------------------------------------------------------------- +! van der Waals mixing rules for perturbation terms +! ---------------------------------------------------------------------- +order1 = 0.0 +order2 = 0.0 +DO i = 1, ncomp + DO j = 1, ncomp + order1 = order1 + x(i)*x(j)* mseg(i)*mseg(j)*sig_ij(i,j)**3 * uij(i,j)/t + order2 = order2 + x(i)*x(j)* mseg(i)*mseg(j)*sig_ij(i,j)**3 * (uij(i,j)/t)**2 + END DO +END DO + + +! ---------------------------------------------------------------------- +! SAFT parameters +! ---------------------------------------------------------------------- +IF (eos == 0) THEN + zmr = 0.0 + nmr = 0.0 + DO i = 1, ncomp + DO j = 1, ncomp + zmr = zmr + x(i)*x(j)*mseg(i)*mseg(j)*vij(i,j)*uij(i,j) + nmr = nmr + x(i)*x(j)*mseg(i)*mseg(j)*vij(i,j) + END DO + END DO + um = zmr / nmr +END IF + + + +! ---------------------------------------------------------------------- +! association and polar parameters +! ---------------------------------------------------------------------- +assoc = .false. +qudpole = .false. +dipole = .false. +DO i = 1, ncomp + IF (NINT(parame(i,12)) /= 0) assoc = .true. + IF (parame(i,7) /= 0.0) qudpole = .true. + IF (parame(i,6) /= 0.0) dipole = .true. +END DO + +! --- dipole and quadrupole constants ---------------------------------- +IF (qudpole) CALL qq_const ( qqp2, qqp3, qqp4 ) +IF (dipole) CALL dd_const ( ddp2, ddp3, ddp4 ) +IF (dipole .AND. qudpole) CALL dq_const ( dqp2, dqp3, dqp4 ) + + +! --- TPT-1-association parameters ------------------------------------- +IF (assoc) THEN + + eps_kij = 0.0 + k_kij = 0.0 + + DO i = 1, ncomp + IF (NINT(parame(i,12)) /= 0) THEN + nhb_typ(i) = NINT(parame(i,12)) + kap_hb(i,i) = parame(i,13) + no = 0 + DO j = 1, nhb_typ(i) + DO k = 1, nhb_typ(i) + eps_hb(i,i,j,k) = parame(i,(14+no)) + no=no+1 + END DO + END DO + DO j = 1, nhb_typ(i) + nhb_no(i,j) = parame(i,(14+no)) + no=no+1 + END DO + ELSE + nhb_typ(i) = 0 + kap_hb(i,i)= 0.0 + DO k = 1, nsite + DO l = 1, nsite + eps_hb(i,i,k,l) = 0.0 + END DO + END DO + END IF + END DO + + DO i = 1, ncomp + DO j = 1, ncomp + IF (i /= j .AND. (nhb_typ(i) /= 0 .AND. nhb_typ(j) /= 0)) THEN + kap_hb(i,j)= (kap_hb(i,i)*kap_hb(j,j))**0.5 & + *((parame(i,2)*parame(j,2))**3 )**0.5 & + /(0.5*(parame(i,2)+parame(j,2)))**3 + kap_hb(i,j)= kap_hb(i,j)*(1.0-k_kij) + DO k = 1, nhb_typ(i) + DO l = 1, nhb_typ(j) + IF (k /= l) THEN + eps_hb(i,j,k,l) = (eps_hb(i,i,k,l)+eps_hb(j,j,l,k))/2.0 + eps_hb(i,j,k,l) = eps_hb(i,j,k,l)*(1.0-eps_kij) + END IF + END DO + END DO + END IF + END DO + END DO + IF (nhb_typ(1) == 3) THEN +! write(*,*)'eps_hb manuell eingegeben' + eps_hb(1,2,3,1) = 0.5*(eps_hb(1,1,3,1)+eps_hb(2,2,1,2)) + eps_hb(2,1,1,3) = eps_hb(1,2,3,1) + END IF + IF (nhb_typ(2) == 3) THEN + eps_hb(2,1,3,1) = 0.5*(eps_hb(2,2,3,1)+eps_hb(1,1,1,2)) + eps_hb(1,2,1,3) = eps_hb(2,1,3,1) + END IF + + DO i = 1, ncomp + DO k = 1, nhb_typ(i) + DO j = 1, ncomp + DO l = 1, nhb_typ(j) + ass_d(i,j,k,l) = kap_hb(i,j) *sig_ij(i,j)**3 *(EXP(eps_hb(i,j,k,l)/t)-1.0) + END DO + END DO + END DO + END DO + +END IF + +END SUBROUTINE PERTURBATION_PARAMETER + + + + +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! SUBROUTINE OUTPUT +! +! The purpose of this subroutine is obvious. +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! + SUBROUTINE OUTPUT +! + USE BASIC_VARIABLES + IMPLICIT NONE +! +! ---------------------------------------------------------------------- + INTEGER :: i + CHARACTER (LEN=4) :: t_ind + CHARACTER (LEN=4) :: p_ind + CHARACTER (LEN=4) :: char_ncomp + REAL :: density(np),w(np,nc) +! ---------------------------------------------------------------------- + + CALL si_dens (density,w) + + IF (u_in_p == 1.E5) THEN + p_ind = ' bar' + ELSE IF (u_in_p == 1.E2) THEN + p_ind = 'mbar' + ELSE IF (u_in_p == 1.E6) THEN + p_ind = ' MPa' + ELSE IF (u_in_p == 1.E3) THEN + p_ind = ' kPa' + ELSE + p_ind = ' Pa' + END IF + IF (u_in_t == 273.15) THEN + t_ind = ' C' + ELSE + t_ind = ' K' + END IF + + WRITE(*,*) '--------------------------------------------------' + WRITE (char_ncomp,'(I3)') ncomp + WRITE(*,'(t2,a,f7.2,2a,f9.4,a)') ' T =',t-u_out_t,t_ind & + ,' P =',p/u_out_p,p_ind + WRITE(*,'(t15,4(a12,1x),10x,a)') (compna(i),i=1,ncomp) + WRITE(*,'(2x,a,'//char_ncomp//'(g13.6,1x))') 'PHASE I w', (w(1,i),i=1,ncomp) + WRITE(*,'(2x,a,'//char_ncomp//'(g13.6,1x))') 'PHASE II w', (w(2,i),i=1,ncomp) + WRITE(*,'(2x,a,'//char_ncomp//'(g13.6,1x))') 'PHASE I x', (EXP(lnx(1,i)),i=1,ncomp) + WRITE(*,'(2x,a,'//char_ncomp//'(g13.6,1x))') 'PHASE II x', (EXP(lnx(2,i)),i=1,ncomp) + WRITE(*,'(2x,a,2(g13.6,1x))') 'DENSITY ', density(1),density(2) + + !-----output to files-------------------------------------------------- + IF (ncomp == 1) THEN + WRITE (40,'(7(2x,f18.8))') t-u_out_t, p/u_out_p, & + density(1), density(2),h_lv,cpres(1),cpres(2) + ! & ,(enthal(2)-enthal(1))/mm(1) + ! WRITE (40,'(4(2x,f15.8))') t, p, 0.3107*dense(1) + ! & /0.1617*(0.689+0.311*(T/1.328)**0.3674),0.3107 + ! & *dense(2)/0.1617*(0.689+0.311*(T/1.328)**0.3674) + ELSE IF (ncomp == 2) THEN + WRITE (40,'(12(2x,G15.8))') 1.0-xi(1,1),1.0-xi(2,1), & + w(1,1),w(2,1),t-u_out_t, p/u_out_p, density(1),density(2) & + ,enthal(1),enthal(2),cpres(1),cpres(2) + ELSE IF (ncomp == 3) THEN + WRITE (40,'(10(2x,f15.8))') xi(1,1),xi(1,2),xi(1,3),xi(2,1),xi(2,2), & + xi(2,3),t-u_out_t, p/u_out_p, density(1),density(2) + END IF + + END SUBROUTINE OUTPUT + + + +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! SUBROUTINE neutr_charge +! +! This subroutine is called for electrolye solutions, where a +! neutral overall-charge has to be enforced in all phases. The basic +! philosophy is similar to the above described routine X_SUMMATION. +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! + SUBROUTINE neutr_charge(i) +! + USE BASIC_VARIABLES + IMPLICIT NONE +! +! ---------------------------------------------------------------------- + INTEGER, INTENT(IN) :: i +! +! ---------------------------------------------------------------------- + INTEGER :: comp_e, ph_e + REAL :: sum_c + CHARACTER (LEN=2) :: phasno + CHARACTER (LEN=2) :: compno +! ---------------------------------------------------------------------- + +phasno = sum_rel(i)(2:2) +READ(phasno,*) ph_e +compno = sum_rel(i)(3:3) +READ(compno,*) comp_e + +sum_c = 0.0 +write (*,*) 'there must be an error in neutr_charge' +stop +! there is an error in the following passage. The index i is an +! argument to this subroutine - I guess it is INTENT(IN), so the +! index in the following loop can not be i. +! +! I have commented the loop until I check the code. +!DO i=1,ncomp +! IF ( comp_e /= i .AND. parame(i,10) /= 0.0) & +! sum_c = sum_c + xi(ph_e,i)*parame(i,10) +!END DO + +xi(ph_e,comp_e) = - sum_c +IF (xi(ph_e,comp_e) < 0.0) xi(ph_e,comp_e)=0.0 +IF (xi(ph_e,comp_e) /= 0.0) THEN + lnx(ph_e,comp_e) = LOG(xi(ph_e,comp_e)) +ELSE + lnx(ph_e,comp_e) = -100000.0 +END IF + +! xi(2,1) = xi(2,2) +! IF (xi(2,1).NE.0.0) lnx(2,1) = LOG(xi(2,1)) + +END SUBROUTINE neutr_charge + + +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! + SUBROUTINE flash_sum +! + USE BASIC_VARIABLES + IMPLICIT NONE +! + INTEGER :: i, j, ph_i, phase1, phase2 +! ---------------------------------------------------------------------- + +phase1=0 +phase2=0 +DO j=1,ncomp + IF (it(j)(2:2) == '1') phase1=phase1+1 + IF (it(j)(2:2) == '2') phase2=phase2+1 +END DO + +IF (phase1 == ncomp-1) THEN + ph_i = 1 +ELSE IF (phase2 == ncomp-1) THEN + ph_i = 2 +ELSE + WRITE (*,*) ' FLASH_SUM: undefined flash-case' + STOP +END IF + + + +IF (ph_i == 1) THEN + DO i=1,ncomp + IF (alpha > DMIN1(1.0,xif(i)/xi(1,i), & + (xif(i)-1.0)/(xi(1,i)-1.0),alpha)) THEN + WRITE (*,*) ' FLASH_SUM: exeeded 1st alpha-bound' + alpha=DMIN1(1.0,xif(i)/xi(1,i),(xif(i)-1.0)/(xi(1,i)-1.0)) + END IF + END DO + DO i=1,ncomp + xi(2,i) = ( xif(i) - alpha*xi(1,i) ) / (1.0-alpha) + IF (xi(2,i) > 0.0) THEN + lnx(2,i) = LOG(xi(2,i)) + ELSE + xi(2,i) = 0.0 + lnx(2,i) = -100000.0 + END IF + END DO +ELSE IF (ph_i == 2) THEN + DO i=1,ncomp + IF (alpha > DMAX1(0.0,(xif(i)-xi(2,i))/(1.0-xi(2,i)), & + 1.0-xif(i)/xi(2,i),alpha)) THEN + WRITE (*,*) ' FLASH_SUM: exeeded 2nd alpha-bound' + WRITE (*,*) 0.0,(xif(i)-xi(2,i))/(1.0-xi(2,i)), 1.0-xif(i)/xi(2,i) + alpha=DMAX1(0.0,(xif(i)-xi(2,i))/(1.0-xi(2,i)), 1.0-xif(i)/xi(2,i)) + END IF + END DO + DO i=1,ncomp + xi(1,i) = ( xif(i) - (1.0-alpha)*xi(2,i) ) / alpha +! write (*,*) 'x1,i',xi(1,i),xi(2,i),alpha + IF (xi(1,i) > 0.0) THEN + lnx(1,i) = LOG(xi(1,i)) + ELSE + xi(1,i) = 0.0 + lnx(1,i) = -100000.0 + END IF + END DO +END IF + +! pause + +RETURN +END SUBROUTINE flash_sum + +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! SUBROUTINE flash_alpha +! +! This subroutine calculates all molefractions of one phase +! from a component balance. What is needed for this calculation +! are all molefractions of the other phase (nphas=2, so far) +! and the phase fraction alpha. +! Alpha is calculated from the mole fraction +! of component {sum_rel(j)(3:3)}. If for example sum_rel(2)='fl3', +! then the alpha is determined from the molefraction of comp. 3 and +! all molefractions of one phase are calculated using that alpha-value. +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! + SUBROUTINE flash_alpha +! + USE BASIC_VARIABLES + IMPLICIT NONE +! +! ---------------------------------------------------------------------- + INTEGER :: i, j, comp_i, phase1, phase2 + CHARACTER (LEN=2) :: compno +! ---------------------------------------------------------------------- + + +! ---------------------------------------------------------------------- +! first calculate the phase fraction alpha from a known composition +! of component sum_rel(j)(3:3). +! ---------------------------------------------------------------------- + +DO j = 1, nphas + IF ( sum_rel(j)(1:2) == 'fl' ) THEN + compno = sum_rel(j)(3:3) + READ(compno,*) comp_i + IF ( (xi(1,comp_i)-xi(2,comp_i)) /= 0.0 ) THEN + alpha = (xif(comp_i)-xi(2,comp_i)) / (xi(1,comp_i)-xi(2,comp_i)) + write (*,*) 'flsh',(xif(comp_i)-xi(2,comp_i)),(xi(1,comp_i)-xi(2,comp_i)) + ELSE + alpha = 0.5 + WRITE (*,*) 'FLASH_ALPHA:error in calc. of phase fraction',comp_i + END IF + ! IF (alpha <= 0.0 .OR. alpha >= 1.0) WRITE(*,*) 'FLASH_ALPHA: error',alpha + IF (alpha > 1.0) alpha = 1.0 + IF (alpha < 0.0) alpha = 0.0 + END IF +END DO + +! ---------------------------------------------------------------------- +! determine which phase is fully determined by iterated molefractions (+ summation relation) +! ---------------------------------------------------------------------- +phase1 = 0 +phase2 = 0 +DO i = 1, ncomp + IF ( it(i)(2:2) == '1' ) phase1 = phase1 + 1 + IF ( it(i)(2:2) == '2' ) phase2 = phase2 + 1 +END DO +DO i = 1, ncomp + IF ( sum_rel(i)(2:2) == '1' ) phase1 = phase1 + 1 + IF ( sum_rel(i)(2:2) == '2' ) phase2 = phase2 + 1 +END DO + + +IF ( phase1 == ncomp ) THEN + ! -------------------------------------------------------------------- + ! phase 1 is defined by iterated molefractions + summation relation + ! phase 2 is determined from componennt balance (using alpha) + ! -------------------------------------------------------------------- + IF ( alpha == 1.0 ) alpha = 1.0 - 1.0E-10 + DO i=1,ncomp + xi(2,i) = ( xif(i) - alpha*xi(1,i) ) / (1.0-alpha) + IF ( xi(2,i) < 0.0 ) xi(2,i) = 0.0 + IF ( xi(2,i) > 1.0 ) xi(2,i) = 1.0 + IF ( xi(2,i) /= 0.0 ) THEN + lnx(2,i) = LOG( xi(2,i) ) + ELSE + lnx(2,i) = -100000.0 + END IF + write (*,*) 'fl_cal ph=2',i,lnx(2,i),xi(2,i) + END DO +ELSE IF ( phase2 == ncomp ) THEN + ! -------------------------------------------------------------------- + ! phase 2 is defined by iterated molefractions + summation relation + ! phase 1 is determined from componennt balance (using alpha) + ! -------------------------------------------------------------------- + DO i = 1, ncomp + xi(1,i) = ( xif(i) - (1.0-alpha)*xi(2,i) ) /alpha + IF ( xi(1,i) < 0.0 ) xi(1,i) = 0.0 + IF ( xi(1,i) > 1.0 ) xi(1,i) = 1.0 + IF ( xi(1,i) /= 0.0 ) THEN + lnx(1,i) = LOG( xi(1,i) ) + ELSE + lnx(1,i) = -100000.0 + END IF + write (*,*) 'fl_cal ph=1',i,lnx(1,i),xi(1,i),alpha + END DO +ELSE + WRITE (*,*) ' FLASH_ALPHA: undefined flash-case' + STOP +END IF + +END SUBROUTINE flash_alpha + + +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! SUBROUTINE SI_DENS (density,w) +! +! This subroutine calculates the (macroskopic) fluid-density in +! units [kg/m3] from the dimensionless density (eta=zeta3). +! Further, mass fractions are calculated from mole fractions. +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! + SUBROUTINE SI_DENS (density,w) +! + USE PARAMETERS, ONLY: pi, nav, tau + USE BASIC_VARIABLES + IMPLICIT NONE +! +! ---------------------------------------------------------------------- + REAL, INTENT(OUT) :: density(np) + REAL, INTENT(OUT) :: w(np,nc) +! +! ---------------------------------------------------------------------- + INTEGER :: i, ph + REAL :: mm_mean, rho, z3t + REAL :: dhs(nc), d00(nc), t_p, pcon, l_st +! ---------------------------------------------------------------------- + + +DO i = 1,ncomp + IF (eos == 1) THEN + dhs(i) = parame(i,2) * ( 1.0 - 0.12 *EXP( -3.0*parame(i,3)/t ) ) + ELSE IF (eos == 0) THEN + d00(i) = ( 1.E30/1.E6*tau*parame(i,2)*6.0/pi/nav )**(1.0/3.0) + dhs(i) = d00(i) * ( 1.0 - 0.12 *EXP( -3.0*parame(i,3)/t ) ) + ELSE IF (eos == 4) THEN + dhs(i) = ( 0.1617/0.3107 / ( 0.689+0.311*(t/parame(i,3)/1.328)**0.3674 ) & + / ( pi/6.0 ) )**(1.0/3.0) * parame(i,2) + ELSE IF (eos == 5.OR.eos == 6) THEN + l_st = parame(1,25) + IF (ncomp /= 1) write (*,*) ' ERROR for EOS = 5' + t_p =((34.037352+17.733741*l_st) /(1.0+0.53237307*l_st+12.860239*l_st**2 ))**0.5 + IF (l_st == 0.0) t_p = t_p/4.0 + IF (eos == 5 .AND. l_st /= 0.0) t_p = t_p/4.0*parame(1,1)**2 + t_p = t/parame(i,3)/t_p + pcon =0.5256+3.2088804*l_st**2 -3.1499114*l_st**2.5 +0.43049357*l_st**4 + dhs(i) = ( pcon/(0.67793+0.32207*(t_p)**0.3674) /(pi/6.0) )**(1.0/3.0) *parame(i,2) + ELSE IF (eos == 8) THEN + dhs(i) = parame(i,2)*(1.0+0.2977*t/parame(i,3)) & + /(1.0+0.33163*t/parame(i,3) +1.0477E-3*(t/parame(i,3))**2 ) + ELSE + write (*,*) 'define EOS in subroutine: SI_DENS' + stop + END IF +END DO + +DO ph = 1,nphas + mm_mean = 0.0 + z3t = 0.0 + DO i = 1, ncomp + mm_mean = mm_mean + xi(ph,i)*mm(i) + z3t = z3t + xi(ph,i) * parame(i,1) * dhs(i)**3 + END DO + z3t = pi/6.0 * z3t + rho = dense(ph)/z3t + density(ph) = rho * mm_mean * 1.E27 /nav + DO i = 1, ncomp + w(ph,i) = xi(ph,i) * mm(i)/mm_mean + END DO +! write (*,*) density(ph),rho,mm_mean,1.d27 /NAV +END DO + +END SUBROUTINE SI_DENS + + + +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! + REAL FUNCTION F_STABILITY ( optpara, n ) +! + USE BASIC_VARIABLES + USE STARTING_VALUES + USE EOS_VARIABLES, ONLY: dhs, PI + IMPLICIT NONE +! +! ---------------------------------------------------------------------- + INTEGER, INTENT(IN) :: n + REAL, INTENT(IN OUT) :: optpara(n) +! +! ---------------------------------------------------------------------- + INTEGER :: i, stabil + REAL :: rhoi(nc),gradterm + REAL :: fden,punish + REAL :: dens +! ---------------------------------------------------------------------- + +COMMON /stabil / stabil + +punish = 0.0 +stabil = 1 + +DO i = 1, n + IF ( optpara(i) < 0.5 ) rhoi(i) = EXP(optpara(i) ) + IF ( optpara(i) >= 0.5) rhoi(i) = EXP(0.5) +END DO + +dens = PI/6.0 * SUM( rhoi(1:ncomp) * parame(1:ncomp,1) * dhs(1:ncomp)**3 ) + +IF (dens > 0.65) THEN + punish = punish + (dens-0.65)*10000.0 + rhoi(1:n) = rhoi(1:n)*0.65/dens +END IF + +CALL fden_calc (fden, rhoi) + +gradterm = sum( grad_fd(1:n) * ( rhoi(1:n) - rhoif(1:n) ) ) + +f_stability = fden - fdenf - gradterm + punish + +! write (*,'(5G16.8)') F_STABILITY,(rhoi(i),i=1,n) +! pause + +stabil = 0 + +END FUNCTION F_STABILITY + + + + +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! SUBROUTINE p_calc (pges_transfer, zges) +! +! This subroutine serves as an iterface to the EOS-routines. The +! system pressure corresponding to given (desity,T,xi) is calculated. +! (Note: the more common interface is SUBROUTINE FUGACITY. This +! routine is only used for one-phase systems, e.g. calculation of +! virial coefficients) +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! + SUBROUTINE p_calc (pges_transfer, zges) +! + USE BASIC_VARIABLES + USE EOS_VARIABLES + IMPLICIT NONE +! +! ---------------------------------------------------------------------- + REAL, INTENT(IN OUT) :: pges_transfer + REAL, INTENT(OUT) :: zges +! ---------------------------------------------------------------------- + +IF (nphas /= 1 ) THEN + write (*,*) 'P_CALC: can only be called for single phases' + stop +ENDIF + +IF (eos < 2) THEN + + phas = 1 + eta = dense(1) + x(1:ncomp) = xi(1,1:ncomp) + + CALL PERTURBATION_PARAMETER + IF (num == 0) CALL P_EOS + IF(num == 1) CALL P_NUMERICAL + !! IF(num == 2) CALL F_EOS_RN + + pges_transfer = pges + rho = eta/z3t + zges = (pges * 1.E-30) / (kbol*t*rho) + +ELSE + write (*,*) ' SUBROUTINE P_CALC not available for cubic EOS' + stop +END IF + +END SUBROUTINE p_calc + + + +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! +SUBROUTINE ONLY_ONE_TERM_EOS_NUMERICAL ( only_term, type_of_term ) +! + USE EOS_NUMERICAL_DERIVATIVES + IMPLICIT NONE +! + character (LEN=9) :: only_term, type_of_term +! ---------------------------------------------------------------------- + + save_eos_terms(1) = ideal_gas + save_eos_terms(2) = hard_sphere + save_eos_terms(3) = chain_term + save_eos_terms(4) = disp_term + save_eos_terms(5) = hb_term + save_eos_terms(6) = LC_term + save_eos_terms(7) = branch_term + save_eos_terms(8) = II_term + save_eos_terms(9) = ID_term + + ideal_gas = 'no' + hard_sphere = 'no' + chain_term = 'no' + disp_term = 'no' + hb_term = 'no' + LC_term = 'no' + branch_term = 'no' + II_term = 'no' + ID_term = 'no' + + IF ( only_term == 'ideal_gas' ) ideal_gas = trim( adjustl( type_of_term ) ) + IF ( only_term == 'hard_sphere' ) hard_sphere = trim( adjustl( type_of_term ) ) + IF ( only_term == 'chain_term' ) chain_term = trim( adjustl( type_of_term ) ) + IF ( only_term == 'disp_term' ) disp_term = trim( adjustl( type_of_term ) ) + IF ( only_term == 'hb_term' ) hb_term = trim( adjustl( type_of_term ) ) + IF ( only_term == 'LC_term' ) LC_term = trim( adjustl( type_of_term ) ) + IF ( only_term == 'branch_term' ) branch_term = trim( adjustl( type_of_term ) ) + IF ( only_term == 'II_term' ) II_term = trim( adjustl( type_of_term ) ) + IF ( only_term == 'ID_term' ) ID_term = trim( adjustl( type_of_term ) ) + +END SUBROUTINE ONLY_ONE_TERM_EOS_NUMERICAL + + +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! +SUBROUTINE RESTORE_PREVIOUS_EOS_NUMERICAL +! + USE EOS_NUMERICAL_DERIVATIVES + IMPLICIT NONE +! +! ---------------------------------------------------------------------- + ideal_gas = trim( adjustl( save_eos_terms(1) ) ) + hard_sphere = trim( adjustl( save_eos_terms(2) ) ) + chain_term = trim( adjustl( save_eos_terms(3) ) ) + disp_term = trim( adjustl( save_eos_terms(4) ) ) + hb_term = trim( adjustl( save_eos_terms(5) ) ) + LC_term = trim( adjustl( save_eos_terms(6) ) ) + branch_term = trim( adjustl( save_eos_terms(7) ) ) + II_term = trim( adjustl( save_eos_terms(8) ) ) + ID_term = trim( adjustl( save_eos_terms(9) ) ) + +END SUBROUTINE RESTORE_PREVIOUS_EOS_NUMERICAL + + + + diff --git a/applications/PUfoam/MoDeNaModels/SurfaceTension/ExampleOfUsage/src/srcDetailedCode/gnuplot_script.srp b/applications/PUfoam/MoDeNaModels/SurfaceTension/ExampleOfUsage/src/srcDetailedCode/gnuplot_script.srp new file mode 100644 index 000000000..393ce9af6 --- /dev/null +++ b/applications/PUfoam/MoDeNaModels/SurfaceTension/ExampleOfUsage/src/srcDetailedCode/gnuplot_script.srp @@ -0,0 +1,55 @@ + + +plotfile = 'ItsTimeNorm.eps' +readfile = 'ItsTimeNorm.dat' +Titel = 'Zeitverlauf der Residuen' +NameX = 'Zeit t' +NameY1 = '|F|' +#NameY2 = 'rho(r)exp(...)-rho(r)' + +set terminal postscript eps +set output plotfile + + +#Set labels +set title Titel +set xlabel NameX +set ylabel NameY1 +#set y2label NameY2 +#set ytics +#set y2tics +#set ytics nomirror + +##Read min and max values to scale the axes +#stats readfile using 2 nooutput +#y1max = STATS_max +#y1min = STATS_min +#stats readfile using 3 nooutput +#y2max = STATS_max +#y2min = STATS_min +#this is needed to get a symmetric plot about 0 where the 0 is at the same height for +#both y axes +#if (abs(y1max) > abs(y1min)) { +# y1range = y1max +# } else { +# y1range = abs(y1min) +# } + +#if (abs(y2max) > abs(y2min)) { +# y2range = y2max +# } else { +# y2range = abs(y2min) +# } + +#set yrange[-1.1*y1range:1.1*y1range] +#set y2range[-1.1*y2range:1.1*y2range] + +#set size square + +#set autoscale y +#set autoscale y2 + + +#plot readfile using 1:2 with lines axes x1y1 title NameY1 , readfile using 1:3 with lines axes x2y2 title NameY2 +plot readfile using 2:3 title NameY1 + diff --git a/applications/PUfoam/MoDeNaModels/SurfaceTension/ExampleOfUsage/src/srcDetailedCode/in.txt b/applications/PUfoam/MoDeNaModels/SurfaceTension/ExampleOfUsage/src/srcDetailedCode/in.txt new file mode 100644 index 000000000..2d712ecf4 --- /dev/null +++ b/applications/PUfoam/MoDeNaModels/SurfaceTension/ExampleOfUsage/src/srcDetailedCode/in.txt @@ -0,0 +1,6 @@ +260.0 +2 +air +thf +0. +0. \ No newline at end of file diff --git a/applications/PUfoam/MoDeNaModels/SurfaceTension/ExampleOfUsage/src/srcDetailedCode/makefile b/applications/PUfoam/MoDeNaModels/SurfaceTension/ExampleOfUsage/src/srcDetailedCode/makefile new file mode 100644 index 000000000..ab6537b9f --- /dev/null +++ b/applications/PUfoam/MoDeNaModels/SurfaceTension/ExampleOfUsage/src/srcDetailedCode/makefile @@ -0,0 +1,344 @@ + +#include /usr/ITT/mhofer/Documents/Diss/NumericalMethods/Libraries/Petsc/petsc-3.4.4/conf/variables +#include /usr/ITT/mhofer/Documents/Diss/NumericalMethods/Libraries/Petsc/petsc-3.4.4/conf/rules + +#include ~/NumLib/PETSc/petsc-3.4.4/conf/variables +#include ~/NumLib/PETSc/petsc-3.4.4/conf/rules + + +include /${PETSC_DIR}/conf/variables +include /${PETSC_DIR}/conf/rules + + + +SOURCE = Modules.F90 \ + mod_PETSc.F90 \ + mod_DFT_FMT.F90 \ + mod_DFT_FMT_d.F90 \ + mod_DFT_CHAIN.F90 \ + mod_DFT_CHAIN_d.F90 \ + mod_DFT_DISP_WDA.F90 \ + mod_DFT_DISP_WDA_d.F90 \ + module_solve_nonlinear.F90 \ + getting_started_subroutines.F90 \ + Helfer_Routinen.F90 \ + Numeric_subroutines.F90 \ + Spline_Integration_d.F90 \ + VLE_main.F90 \ + VLE_subroutines.F90 \ + crit_point_mixtures.F90 \ + Function.F90 \ + AD_Routines.F90 \ + InitialGuess.F90 \ + SolverSetup.F90 \ + Main.F90 \ + +#Object files +OBJECT = $(SOURCE:%.F90=%.o) + +#define target for non-PETSc files +%.o: %.F90 + ${PETSC_FCOMPILE} -fdefault-real-8 -c $< -o $@ + +DFT: $(OBJECT) + -${FLINKER} -o PCSAFT_SurfaceTension $(OBJECT) ${PETSC_SNES_LIB} + +#-------------------------------------------------------------------------- + +#Anzahl Prozessoren +NP = 1 + +#Initial profile: 0: normal, 1-3: add perturbation to regular initial profile +PERT = 0 + +#DFT Settings +NGRID = 800 +CUTOFF = 9.0 +BOXSIZE = 300.0 + +#Solver Settings +ITS_SNES = 20 +ITS_KSP = 15 +E_REL = 1e-08 + +#Its for Anderson Mixing +ITS_SNES_ANDERSON = 100 +#Its for Picard Iterations +ITS_SNES_PICARD = 100 + +#Toleranzen +ATOL_SNES = 1e-08 +RTOL_SNES = 1e-08 +STOL_SNES = 1e-08 + +ATOL_KSP = 1e-08 +RTOL_KSP = 1e-04 + +#D�mpfungsfaktoren +DAMP = 0.3 +DAMP_LBFGS = 1.0 +DAMP_ANDERSON = 0.01 +DAMP_PICARD = 0.01 + +#------------------------------------------------------------------------------ +#1) Inexact-Newton type solvers (iterative solver for linear system) +#------------------------------------------------------------------------------ + +#matrix-free, numerical approximation of directional derivatives (choose between trust region and line search) +run_mf: + -@${MPIEXEC} -n $(NP) ./PCSAFT_SurfaceTension -snes_monitor_short -ksp_monitor_short \ + -nx $(NGRID) \ + -rc $(CUTOFF) \ + -box $(BOXSIZE) \ + -erel $(E_REL) \ + -init_pert $(PERT) \ + -snes_type newtonls -snes_converged_reason \ + -snes_atol $(ATOL_SNES) -snes_rtol $(RTOL_SNES) -snes_stol $(STOL_SNES) -snes_max_it $(ITS_SNES) \ + -ksp_atol $(ATOL_KSP) -ksp_rtol $(RTOL_KSP) -ksp_max_it $(ITS_KSP) -ksp_gmres_restart 50 \ + -snes_linesearch_type bt -snes_linesearch_damping $(DAMP) -snes_linesearch_monitor \ + -snes_max_fail 1 -snes_max_linear_solve_fail 100 \ + -ksp_gmres_cgs_refinement_type refine_always \ + -snes_ksp_ew -snes_ksp_ew_version 1 -snes_ksp_ew_rtol0 0.5 -snes_ksp_ew_rtolmax 0.9 -snes_ksp_ew_threshold 0.1 \ + -jac 0 \ + -pc_type none \ + + + +#matrix-free, AD-calculation directional derivatives (choose between trust region and line search) +run_ad: + -@${MPIEXEC} -n $(NP) ./PCSAFT_SurfaceTension -snes_monitor_short -ksp_monitor_short \ + -nx $(NGRID) \ + -rc $(CUTOFF) \ + -box $(BOXSIZE) \ + -init_pert $(PERT) \ + -snes_type newtonls -snes_converged_reason \ + -snes_atol $(ATOL_SNES) -snes_rtol $(RTOL_SNES) -snes_stol $(STOL_SNES) -snes_max_it $(ITS_SNES) \ + -ksp_atol $(ATOL_KSP) -ksp_rtol $(RTOL_KSP) -ksp_max_it $(ITS_KSP) -ksp_gmres_restart 50 \ + -snes_linesearch_type bt -snes_linesearch_damping $(DAMP) -snes_linesearch_monitor \ + -snes_max_fail 1 -snes_max_linear_solve_fail 100 \ + -ksp_gmres_cgs_refinement_type refine_always \ + -snes_ksp_ew -snes_ksp_ew_version 1 -snes_ksp_ew_rtol0 0.5 -snes_ksp_ew_rtolmax 0.9 -snes_ksp_ew_threshold 0.1 \ + -jac 1 \ +# -pc_type none + +#finite-difference approximation of Jacobi matrix (-> PC can be used!) (choose between trust region and line search) +run_fd: + -@${MPIEXEC} -n $(NP) ./PCSAFT_SurfaceTension -snes_fd -snes_monitor_short -ksp_monitor_short \ + -nx $(NGRID) \ + -rc $(CUTOFF) \ + -box $(BOXSIZE) \ + -init_pert $(PERT) \ + -snes_type newtonls -snes_converged_reason \ + -snes_atol $(ATOL_SNES) -snes_rtol $(RTOL_SNES) -snes_stol $(STOL_SNES) -snes_max_it $(ITS_SNES) \ + -ksp_atol $(ATOL_KSP) -ksp_rtol $(RTOL_KSP) -ksp_max_it $(ITS_KSP) -ksp_gmres_restart 50 \ + -snes_linesearch_type bt -snes_linesearch_damping $(DAMP) -snes_linesearch_monitor \ + -snes_max_fail 1 -snes_max_linear_solve_fail 100 \ + -ksp_gmres_cgs_refinement_type refine_always \ + -snes_ksp_ew -snes_ksp_ew_version 1 -snes_ksp_ew_rtol0 0.5 -snes_ksp_ew_rtolmax 0.9 -snes_ksp_ew_threshold 0.1 \ + -jac 2 \ + -dm_mat_type aij \ +# -pc_type ilu + +#Build complete Jacobi matrix with AD (-> PC can be used!) (choose between trust region and line search) +run_anad: + -@${MPIEXEC} -n $(NP) ./PCSAFT_SurfaceTension -snes_monitor_short -ksp_monitor_short \ + -nx $(NGRID) \ + -rc $(CUTOFF) \ + -box $(BOXSIZE) \ + -init_pert $(PERT) \ + -snes_type newtonls -snes_converged_reason \ + -snes_atol $(ATOL_SNES) -snes_rtol $(RTOL_SNES) -snes_stol $(STOL_SNES) -snes_max_it $(ITS_SNES) \ + -ksp_atol $(ATOL_KSP) -ksp_rtol $(RTOL_KSP) -ksp_max_it $(ITS_KSP) -ksp_gmres_restart 50 \ + -snes_linesearch_type bt -snes_linesearch_damping $(DAMP) -snes_linesearch_monitor \ + -snes_max_fail 1 -snes_max_linear_solve_fail 100 \ + -ksp_gmres_cgs_refinement_type refine_always \ + -snes_ksp_ew -snes_ksp_ew_version 1 -snes_ksp_ew_rtol0 0.5 -snes_ksp_ew_rtolmax 0.9 -snes_ksp_ew_threshold 0.1 \ + -jac 3 \ + + + +#------------------------------------------------------------------------------ +#2) Newton type solvers (direct solver for linear system) +#------------------------------------------------------------------------------ + +#finite-difference approximation of Jacobi matrix (-> PC can be used!) (choose between trust region and line search) +run_fdmumps: + -@${MPIEXEC} -n $(NP) ./PCSAFT_SurfaceTension -snes_monitor_short -ksp_monitor_short \ + -nx $(NGRID) \ + -rc $(CUTOFF) \ + -box $(BOXSIZE) \ + -init_pert $(PERT) \ + -snes_type newtonls -snes_converged_reason \ + -snes_atol $(ATOL_SNES) -snes_rtol $(RTOL_SNES) -snes_stol $(STOL_SNES) -snes_max_it $(ITS_SNES) \ + -snes_linesearch_type bt -snes_linesearch_damping $(DAMP) -snes_linesearch_monitor \ + -snes_max_fail 1 -snes_max_linear_solve_fail 100 \ + -jac 2 \ + -dm_mat_type aij \ + -pc_type lu -pc_factor_mat_solver_package mumps \ + +#Build complete Jacobi matrix with AD (-> PC can be used!) (choose between trust region and line search) +run_anadmumps: + -@${MPIEXEC} -n $(NP) ./PCSAFT_SurfaceTension -snes_monitor_short -ksp_monitor_short \ + -nx $(NGRID) \ + -rc $(CUTOFF) \ + -box $(BOXSIZE) \ + -init_pert $(PERT) \ + -snes_type newtonls -snes_converged_reason \ + -snes_atol $(ATOL_SNES) -snes_rtol $(RTOL_SNES) -snes_stol $(STOL_SNES) -snes_max_it $(ITS_SNES) \ + -snes_linesearch_type bt -snes_linesearch_damping $(DAMP) -snes_linesearch_monitor \ + -snes_max_fail 1 -snes_max_linear_solve_fail 100 \ + -jac 3 \ + -pc_type lu -pc_factor_mat_solver_package mumps \ + + +#------------------------------------------------------------------------------ +#3) Quasi-Newton type solvers (secant updates for approximation to inverse Jacobian) +#------------------------------------------------------------------------------ + +#limitd memory quasi newton with BFGS updates -> choose restart parameter +run_LBFGS: + -@${MPIEXEC} -n $(NP) ./PCSAFT_SurfaceTension -snes_monitor_short -ksp_monitor_short \ + -nx $(NGRID) \ + -rc $(CUTOFF) \ + -box $(BOXSIZE) \ + -init_pert $(PERT) \ + -snes_type qn -snes_qn_type lbfgs \ + -snes_converged_reason \ + -snes_linesearch_type cp -snes_linesearch_damping $(DAMP_LBFGS) \ + -snes_atol $(ATOL_SNES) -snes_rtol $(RTOL_SNES) -snes_stol $(STOL_SNES) -snes_max_it $(ITS_SNES) \ + -snes_ksp_ew -snes_ksp_ew_version 1 -snes_ksp_ew_rtol0 0.5 -snes_ksp_ew_rtolmax 0.9 -snes_ksp_ew_threshold 0.1 \ + -ksp_atol $(ATOL_KSP) -ksp_rtol $(RTOL_KSP) -ksp_max_it $(ITS_KSP) -ksp_gmres_restart 50 \ + -snes_max_fail 1 -snes_max_linear_solve_fail 100 \ + -jac -1 \ + +#limitd memory quasi newton with BFGS updates -> choose restart parameter +#calculate initial jacobian with AD, then use BFGS updates in later iterations + +#anpassen damping, jac 0/1 + +run_LBFGSinitJac: + -@${MPIEXEC} -n $(NP) ./PCSAFT_SurfaceTension -snes_monitor_short -ksp_monitor_short \ + -nx $(NGRID) \ + -rc $(CUTOFF) \ + -box $(BOXSIZE) \ + -init_pert $(PERT) \ + -snes_type qn -snes_qn_type lbfgs -snes_qn_scale_type jacobian \ + -snes_converged_reason \ + -snes_linesearch_type bt -snes_linesearch_damping $(DAMP_LBFGS) \ + -snes_atol $(ATOL_SNES) -snes_rtol $(RTOL_SNES) -snes_stol $(STOL_SNES) -snes_max_it $(ITS_SNES) \ + -snes_ksp_ew -snes_ksp_ew_version 1 -snes_ksp_ew_rtol0 0.5 -snes_ksp_ew_rtolmax 0.9 -snes_ksp_ew_threshold 0.1 \ + -ksp_atol $(ATOL_KSP) -ksp_rtol $(RTOL_KSP) -ksp_max_it $(ITS_KSP) -ksp_gmres_restart 50 \ + -snes_max_fail 1 -snes_max_linear_solve_fail 100 \ + -jac 0 \ + + +#use a direct solver for linear system + +#limitd memory quasi newton with BFGS updates -> choose restart parameter +#calculate initial jacobian with AD, then use BFGS updates in later iterations +run_LBFGSinitJac2: + -@${MPIEXEC} -n $(NP) ./PCSAFT_SurfaceTension -snes_monitor_short -ksp_monitor_short \ + -nx $(NGRID) \ + -rc $(CUTOFF) \ + -box $(BOXSIZE) \ + -init_pert $(PERT) \ + -snes_type qn -snes_qn_type lbfgs -snes_qn_scale_type jacobian \ + -snes_converged_reason \ + -snes_linesearch_type bt -snes_linesearch_damping $(DAMP_LBFGS) \ + -snes_atol $(ATOL_SNES) -snes_rtol $(RTOL_SNES) -snes_stol $(STOL_SNES) -snes_max_it $(ITS_SNES) \ + -ksp_atol $(ATOL_KSP) -ksp_rtol $(RTOL_KSP) -ksp_max_it $(ITS_KSP) -ksp_gmres_restart 50 \ + -snes_max_fail 1 -snes_max_linear_solve_fail 100 \ + -jac 3 \ + + + +#------------------------------------------------------------------------------ +#4) Simple Fixpoint Iterations +#------------------------------------------------------------------------------ + + +#Anderson mixing +run_Anderson: + -@${MPIEXEC} -n $(NP) ./PCSAFT_SurfaceTension -snes_monitor_short -ksp_monitor_short \ + -nx $(NGRID) \ + -rc $(CUTOFF) \ + -box $(BOXSIZE) \ + -init_pert $(PERT) \ + -snes_type anderson \ + -snes_atol $(ATOL_SNES) -snes_rtol $(RTOL_SNES) -snes_stol $(STOL_SNES) -snes_max_it $(ITS_SNES_ANDERSON) \ + -snes_converged_reason \ + -snes_linesearch_type l2 -snes_linesearch_damping $(DAMP_ANDERSON) -snes_linesearch_monitor \ + -jac -1 \ + + +#Picard Iteration +run_Picard: + -@${MPIEXEC} -n $(NP) ./PCSAFT_SurfaceTension -snes_monitor_short -ksp_monitor_short \ + -nx $(NGRID) \ + -rc $(CUTOFF) \ + -box $(BOXSIZE) \ + -init_pert $(PERT) \ + -snes_type nrichardson \ + -snes_atol $(ATOL_SNES) -snes_rtol $(RTOL_SNES) -snes_stol $(STOL_SNES) -snes_max_it $(ITS_SNES_PICARD) \ + -snes_converged_reason \ + -snes_linesearch_type l2 -snes_linesearch_damping $(DAMP_PICARD) -snes_linesearch_monitor \ + -jac -1 \ + + + + +# # #-------------------------------------------------------------------------- +# # +# # #Anzahl Prozessoren +# # NP = 1 +# # +# # +# # #DFT Settings +# # NGRID = 800 +# # CUTOFF = 9.0 +# # BOXSIZE = 10.0 +# # +# # #Solver Settings +# # ITS_SNES = 40 +# # ITS_KSP = 20 +# # E_REL = 1e-11 +# # +# # #Its for Anderson Mixing +# # ITS_SNES_ANDERSON = 250 +# # #Its for Picard Iterations +# # ITS_SNES_PICARD = 250 +# # +# # #Toleranzen +# # ATOL_SNES = 1e-08 +# # RTOL_SNES = 1e-08 +# # STOL_SNES = 1e-08 +# # +# # ATOL_KSP = 1e-08 +# # RTOL_KSP = 1e-04 +# # +# # #D�mpfungsfaktoren +# # DAMP = 0.5 +# # DAMP_LBFGS = 0.5 +# # DAMP_ANDERSON = 0.5 +# # DAMP_PICARD = 0.01 +# # +# # #------------------------------------------------------------------------------ +# # #1) Inexact-Newton type solvers (iterative solver for linear system) +# # #------------------------------------------------------------------------------ +# # +# # #matrix-free, numerical approximation of directional derivatives (choose between trust region and line search) +# # runNLsolver_mf: +# # -@${MPIEXEC} -n $(NP) ./NLsolver -snes_monitor_short -ksp_monitor_short \ +# # -nx $(NGRID) \ +# # -rc $(CUTOFF) \ +# # -box $(BOXSIZE) \ +# # -erel $(E_REL) \ +# # -snes_type newtonls -snes_converged_reason \ +# # -snes_atol $(ATOL_SNES) -snes_rtol $(RTOL_SNES) -snes_stol $(STOL_SNES) -snes_max_it $(ITS_SNES) \ +# # -ksp_atol $(ATOL_KSP) -ksp_rtol $(RTOL_KSP) -ksp_max_it $(ITS_KSP) -ksp_gmres_restart 50 \ +# # -snes_linesearch_type bt -snes_linesearch_damping $(DAMP) -snes_linesearch_monitor \ +# # -snes_max_fail 1 -snes_max_linear_solve_fail 100 \ +# # -ksp_gmres_cgs_refinement_type refine_always \ +# # -snes_ksp_ew -snes_ksp_ew_version 1 -snes_ksp_ew_rtol0 0.5 -snes_ksp_ew_rtolmax 0.9 -snes_ksp_ew_threshold 0.1 \ +# # -jac 0 \ +# # -pc_type none \ diff --git a/applications/PUfoam/MoDeNaModels/SurfaceTension/ExampleOfUsage/src/srcDetailedCode/mod_ChemPot.F90 b/applications/PUfoam/MoDeNaModels/SurfaceTension/ExampleOfUsage/src/srcDetailedCode/mod_ChemPot.F90 new file mode 100644 index 000000000..6f1b96c1c --- /dev/null +++ b/applications/PUfoam/MoDeNaModels/SurfaceTension/ExampleOfUsage/src/srcDetailedCode/mod_ChemPot.F90 @@ -0,0 +1,250 @@ +Module mod_ChemPot + + + +Implicit None + + + +private + +public :: Chemical_Potential +public :: PCSAFT_const +REAL, public, allocatable :: ChemPot_tot(:) +REAL, public, allocatable :: ChemPot_res(:) + + contains + + + + +Subroutine Chemical_Potential + +Use BASIC_VARIABLES +Use EOS_VARIABLES +Use PARAMETERS +USe EOS_CONSTANTS + +Integer :: k,i,j +REAL :: z0t,z1t,z2t,z3t +REAL :: z0,z1,z2,z3,zms +REAL :: z0_rk,z1_rk,z2_rk,z3_rk +REAL, allocatable :: mhs(:), mhc(:) +REAL, allocatable :: gij(:,:), gij_rk(:,:), dij_ab(:,:) + +!DISP HERE!!! +INTEGER :: m +REAL :: m_mean,I1,I2,I1_rk,I2_rk +REAL :: ord1_rk,ord2_rk +REAL :: c1_con,c2_con,c1_rk +REAL :: order1,order2 +REAL :: apar(0:6),bpar(0:6) +REAL, allocatable :: m_rk(:),mdsp(:) +REAL, allocatable :: ap_rk(:,:),bp_rk(:,:) + +Allocate(mdsp(ncomp),m_rk(ncomp),ap_rk(ncomp,0:6),bp_rk(ncomp,0:6)) +Allocate(sig_ij(ncomp,ncomp),uij(ncomp,ncomp)) + +kij = 0.0 + + + +Allocate(mhs(ncomp), mhc(ncomp), ChemPot_res(ncomp), ChemPot_tot(ncomp) ) +Allocate(gij(ncomp,ncomp), gij_rk(ncomp,ncomp), dij_ab(ncomp,ncomp) ) + + +!belege dichteunabh�ngige Parameter (z0z,z1t,z2t,z3t) +z0t = PI / 6.0 * SUM( xx(1:ncomp) * mseg(1:ncomp) ) +z1t = PI / 6.0 * SUM( xx(1:ncomp) * mseg(1:ncomp) * dhs(1:ncomp) ) +z2t = PI / 6.0 * SUM( xx(1:ncomp) * mseg(1:ncomp) * dhs(1:ncomp)**2 ) +z3t = PI / 6.0 * SUM( xx(1:ncomp) * mseg(1:ncomp) * dhs(1:ncomp)**3 ) + + + +! --- Eq.(A.8) --------------------------------------------------------- +rho = eta / z3t !total number density [particles/A^3] +z0 = z0t * rho +z1 = z1t * rho +z2 = z2t * rho +z3 = z3t * rho + +zms = 1.0 - eta + +call PCSAFT_const(ap,bp) !get PCSAFT constants + +DO k = 1, ncomp + + z0_rk = PI/6.0 * mseg(k) + z1_rk = PI/6.0 * mseg(k) * dhs(k) + z2_rk = PI/6.0 * mseg(k) * dhs(k)*dhs(k) + z3_rk = PI/6.0 * mseg(k) * dhs(k)**3 + + ! -------------------------------------------------------------------- + ! d(f)/d(x) : hard sphere contribution + ! -------------------------------------------------------------------- + mhs(k) = 6.0/PI* ( 3.0*(z1_rk*z2+z1*z2_rk)/zms + 3.0*z1*z2*z3_rk/zms/zms & + + 3.0*z2*z2*z2_rk/z3/zms/zms + z2**3 *z3_rk*(3.0*z3-1.0)/z3/z3/zms**3 & + + ((3.0*z2*z2*z2_rk*z3-2.0*z2**3 *z3_rk)/z3**3 -z0_rk) *LOG(zms) & + + (z0-z2**3 /z3/z3)*z3_rk/zms ) + + + ! -------------------------------------------------------------------- + ! d(f)/d(x) : chain term + ! -------------------------------------------------------------------- + DO i = 1, ncomp + DO j = 1, ncomp + dij_ab(i,j) = dhs(i)*dhs(j) / ( dhs(i) + dhs(j) ) + END DO + END DO + + DO i = 1, ncomp + DO j = 1, ncomp + gij(i,j) = 1.0/zms + 3.0*dij_ab(i,j)*z2/zms/zms + 2.0*(dij_ab(i,j)*z2)**2 /zms**3 + gij_rk(i,j) = z3_rk/zms/zms & + + 3.0*dij_ab(i,j)*(z2_rk+2.0*z2*z3_rk/zms)/zms/zms & + + dij_ab(i,j)**2 *z2/zms**3 *(4.0*z2_rk+6.0*z2*z3_rk/zms) + END DO + END DO + + mhc(k) = 0.0 + DO i = 1, ncomp + mhc(k) = mhc(k) + xx(i)*rho * (1.0-mseg(i)) / gij(i,i) * gij_rk(i,i) + END DO + mhc(k) = mhc(k) + ( 1.0-mseg(k)) * LOG( gij(k,k) ) + + ! -------------------------------------------------------------------- + ! PC-SAFT: d(f)/d(x) : dispersion contribution + ! -------------------------------------------------------------------- + + m_mean = z0t / (PI/6.0) + m_rk(k) = ( mseg(k) - m_mean ) / rho + + + DO m = 0, 6 + apar(m) = ap(m,1) + (1.0-1.0/m_mean)*ap(m,2) & + + (1.0-1.0/m_mean)*(1.0-2.0/m_mean)*ap(m,3) + bpar(m) = bp(m,1) + (1.0-1.0/m_mean)*bp(m,2) & + + (1.0-1.0/m_mean)*(1.0-2.0/m_mean)*bp(m,3) + + ! --- derivatives of apar, bpar to rho_k --------------------------- + ap_rk(k,m) = m_rk(k)/m_mean**2 * ( ap(m,2) + (3.0 -4.0/m_mean) *ap(m,3) ) + bp_rk(k,m) = m_rk(k)/m_mean**2 * ( bp(m,2) + (3.0 -4.0/m_mean) *bp(m,3) ) + END DO + + I1 = 0.0 + I2 = 0.0 + I1_rk = 0.0 + I2_rk = 0.0 + DO m = 0, 6 + I1 = I1 + apar(m)*eta**REAL(m) + I2 = I2 + bpar(m)*eta**REAL(m) + I1_rk = I1_rk + apar(m)*REAL(m)*eta**REAL(m-1)*z3_rk + ap_rk(k,m)*eta**REAL(m) + I2_rk = I2_rk + bpar(m)*REAL(m)*eta**REAL(m-1)*z3_rk + bp_rk(k,m)*eta**REAL(m) + END DO + + ord1_rk = 0.0 + ord2_rk = 0.0 + order1 = 0.0 + order2 = 0.0 + DO i = 1,ncomp + sig_ij(i,k) = 0.5 * ( dhs(i) + dhs(k) ) + uij(i,k) = (1.0 - kij(i,k)) * SQRT( eps(i) * eps(k) ) + order1 = order1 + xx(i)*xx(k)* mseg(i)*mseg(k)*sig_ij(i,k)**3 * uij(i,k)/t + order2 = order2 + xx(i)*xx(k)* mseg(i)*mseg(k)*sig_ij(i,k)**3 * (uij(i,k)/t)**2 + ord1_rk = ord1_rk + 2.0*mseg(k)*rho*xx(i)*mseg(i)*sig_ij(i,k)**3 *uij(i,k)/t + ord2_rk = ord2_rk + 2.0*mseg(k)*rho*xx(i)*mseg(i)*sig_ij(i,k)**3 *(uij(i,k)/t)**2 + END DO + + + c1_con= 1.0/ ( 1.0 + m_mean*(8.0*z3-2.0*z3*z3)/zms**4 & + + (1.0 - m_mean)*(20.0*z3-27.0*z3*z3 +12.0*z3**3 -2.0*z3**4 ) & + /(zms*(2.0-z3))**2 ) + c2_con= - c1_con*c1_con *( m_mean*(-4.0*z3*z3+20.0*z3+8.0)/zms**5 & + + (1.0 - m_mean) *(2.0*z3**3 +12.0*z3*z3-48.0*z3+40.0) & + /(zms*(2.0-z3))**3 ) + c1_rk= c2_con*z3_rk - c1_con*c1_con*m_rk(k) * ( (8.0*z3-2.0*z3*z3)/zms**4 & + - (-2.0*z3**4 +12.0*z3**3 -27.0*z3*z3+20.0*z3) / (zms*(2.0-z3))**2 ) + + mdsp(k) = -2.0*PI* ( order1*rho*rho*I1_rk + ord1_rk*I1 ) & + - PI* c1_con*m_mean * ( order2*rho*rho*I2_rk + ord2_rk*I2 ) & + - PI* ( c1_con*m_rk(k) + c1_rk*m_mean ) * order2*rho*rho*I2 + + +End Do + +!residual + ChemPot_res(1:ncomp) = mhs(1:ncomp) + mhc(1:ncomp) + mdsp(1:ncomp) ! /kT [-] +!total + ChemPot_tot(1:ncomp) = ChemPot_res(1:ncomp) + log( xx(1:ncomp)*rho ) ! /kT [-] + +write(*,*)'rhob',xx(1:ncomp)*rho + +End Subroutine Chemical_Potential + + + + + + + + + +Subroutine PCSAFT_const(ap,bp) + +Implicit None + +!passed +REAL, INTENT(OUT) :: ap(0:6,3) +REAL, INTENT(OUT) :: bp(0:6,3) + +! --- dispersion term constants ---------------------------------------- +ap(0,1) = 0.91056314451539 +ap(0,2) = -0.30840169182720 +ap(0,3) = -0.09061483509767 +ap(1,1) = 0.63612814494991 +ap(1,2) = 0.18605311591713 +ap(1,3) = 0.45278428063920 +ap(2,1) = 2.68613478913903 +ap(2,2) = -2.50300472586548 +ap(2,3) = 0.59627007280101 +ap(3,1) = -26.5473624914884 +ap(3,2) = 21.4197936296668 +ap(3,3) = -1.72418291311787 +ap(4,1) = 97.7592087835073 +ap(4,2) = -65.2558853303492 +ap(4,3) = -4.13021125311661 +ap(5,1) = -159.591540865600 +ap(5,2) = 83.3186804808856 +ap(5,3) = 13.7766318697211 +ap(6,1) = 91.2977740839123 +ap(6,2) = -33.7469229297323 +ap(6,3) = -8.67284703679646 + +bp(0,1) = 0.72409469413165 +bp(0,2) = -0.57554980753450 +bp(0,3) = 0.09768831158356 +bp(1,1) = 1.11913959304690 *2.0 +bp(1,2) = 0.34975477607218 *2.0 +bp(1,3) = -0.12787874908050 *2.0 +bp(2,1) = -1.33419498282114 *3.0 +bp(2,2) = 1.29752244631769 *3.0 +bp(2,3) = -3.05195205099107 *3.0 +bp(3,1) = -5.25089420371162 *4.0 +bp(3,2) = -4.30386791194303 *4.0 +bp(3,3) = 5.16051899359931 *4.0 +bp(4,1) = 5.37112827253230 *5.0 +bp(4,2) = 38.5344528930499 *5.0 +bp(4,3) = -7.76088601041257 *5.0 +bp(5,1) = 34.4252230677698 *6.0 +bp(5,2) = -26.9710769414608 *6.0 +bp(5,3) = 15.6044623461691 *6.0 +bp(6,1) = -50.8003365888685 *7.0 +bp(6,2) = -23.6010990650801 *7.0 +bp(6,3) = -4.23812936930675 *7.0 + + +End Subroutine PCSAFT_const + + + +End Module mod_ChemPot diff --git a/applications/PUfoam/MoDeNaModels/SurfaceTension/ExampleOfUsage/src/srcDetailedCode/mod_DFT_CHAIN.F90 b/applications/PUfoam/MoDeNaModels/SurfaceTension/ExampleOfUsage/src/srcDetailedCode/mod_DFT_CHAIN.F90 new file mode 100644 index 000000000..909d7bf7c --- /dev/null +++ b/applications/PUfoam/MoDeNaModels/SurfaceTension/ExampleOfUsage/src/srcDetailedCode/mod_DFT_CHAIN.F90 @@ -0,0 +1,347 @@ +Module mod_DFT_CHAIN + +Implicit None +private + + +public :: Chain_aux +public :: Chain_dFdrho + + + contains + + + +Subroutine Chain_aux(rhop,rhobar,lambda,user) + +Use BASIC_VARIABLES, Only: ncomp +Use EOS_VARIABLES, Only: dhs,rho +Use mod_DFT, Only: zp,dzp,fa + + +!PETSc module +Use PetscManagement + +#include + +!passed +type (userctx) :: user +PetscScalar :: rhop(ncomp,user%gxs:user%gxe) +REAL,INTENT(OUT) :: rhobar(user%gxs:user%gxe,ncomp) +REAL,INTENT(OUT) :: lambda(user%gxs:user%gxe,ncomp) + +!local +INTEGER :: i,j,k +REAL :: dhsk +INTEGER :: fak,n +REAL :: zz,dz,xlo,xhi,integral_lamb,integral_rb +INTEGER, parameter :: NMAX = 800 +REAL,dimension(NMAX) :: x_int, lamb_int, rb_int +REAL,dimension(NMAX) :: y2_lamb, y2_rb +REAL :: rhopjk,rhopjp1k + + +!fak = maxval(fa(1:ncomp)) + +Do k = 1,ncomp + dhsk = dhs(k) + fak = fa(k) + 1 + + Do i = user%xs-fak,user%xe+fak !lambda und rhobar werden bis i+-sig gebraucht -> Schleife bis +- fa + n = 1 !this is the index of the arrays that will be passed to the spline integration routines + x_int = 0.0 + lamb_int = 0.0 + rb_int = 0.0 + + Do j = i-fak,i+fak !um lambda bei i zu berechnen, muss bis +- sig um i integriert werden -> Schleife bis +- fa + rhopjk = rhop(k,j) + rhopjp1k = rhop(k,j+1) + + + If( ( zp(i)-zp(j+1) ) < dhsk .and. ( zp(i) - zp(j) ) >= dhsk ) Then !the position of j+1 is already within i-d while j is still outside this range in this case, the integration steplength (dz) is just the distance, which j+1 overlaps with i-d and what is integrated is the interpolated value of the integrand + + If(n/= 1) stop 'n /=1 in Chain_aux' !here always n=1! + zz = zp(j) - zp(i) !distance between grid points j and i + dz = zp(j+1) - (zp(i) - dhsk) !the part of the intervall between zp(j) and zp(j+1) which is already within i-d + !if(dz < epsilon(dz)) dz = epsilon(dz) !bei unguenstiger Kombination von sig und ngrid kann dz unter Machinengenauigkeit epsilon liegen, dann ist x(2) = x(1) + dz = x(1) -> das fuehrt zu Abbruch in Spline Interpolation + x_int(n) = 0.0 !array containing x-values for spline integration + + lamb_int(n) = rhopjk + (rhopjp1k - rhopjk)/dzp * (dzp-dz) !lineare interpolation analog zum FMT Teil + rb_int(n) = 0.0 !erklärung analog wie bei n3_int in FMT Teil + + + Else If (zp(j) > (zp(i)-dhsk) .and. zp(j) <= (zp(i)+dhsk)) Then !grid point j within i+-d + + n = n + 1 + x_int(n) = x_int(n-1) + dz !first time in this If condition, dz is stil the old value from above! + zz = zp(j) - zp(i) + dz = dzp + lamb_int(n) = rhopjk + rb_int(n) = rhopjk * ( dhsk**2 - zz**2 ) + + If (zp(j) < (zp(i)+dhsk) .and. zp(j+1) >= (zp(i)+dhsk) ) Then !zp(j) is still within zp(i)+d but zp(j+1) is already outside zp(i)+d + + dz = zp(i) + dhsk - zp(j) + !If(dz <= epsilon(dz)) exit !wie oben, kann auch hier bei ungluecklicher Wahl von sig und ngrid dz < eps werden und somit x(n) = x(n-1) -> Abbruch in Spline interpolation. Dann einfach ngrid aendern! + zz = zp(j) - zp(i) + n = n + 1 + x_int(n) = x_int(n-1) + dz + rb_int(n) = 0.0 + lamb_int(n) = rhopjk + (rhopjp1k - rhopjk)/dzp * dz +! If(x_int(n) == x_int(n-1)) Then +! n = n - 1 +! exit +! End If + + End If + End If + End Do + + + + !spline integration + xlo = x_int(1) + xhi = x_int(n) + + If(n > NMAX) stop 'Increase NMAX in Chain_aux (auch in AD Routine!!)' + + call spline ( x_int, lamb_int, n, 1.E30, 1.E30, y2_lamb ) + call spline ( x_int, rb_int, n, 1.E30, 1.E30, y2_rb ) + + call splint_integral ( x_int, lamb_int, y2_lamb, n, xlo, xhi, integral_lamb ) + call splint_integral ( x_int, rb_int, y2_rb, n, xlo, xhi, integral_rb ) + lambda(i,k) = 0.5 * integral_lamb / dhsk + rhobar(i,k) = 0.75 * integral_rb / dhsk**3 + + If(lambda(i,k) < epsilon(dz) ) lambda(i,k) = epsilon(dz) + !If ( lambda(i,k) < 0.5*xx(k)*rho ) write (*,*) 'warning: lambda too low',i,lambda(i,k) + !If ( k == 1 .AND. lambda(i,k) < 0.5*rhob(2,k) ) lambda(i,k) = 0.5*rhob(2,k) + + + End Do + +End Do + + +End Subroutine Chain_aux + + + + + + + + +Subroutine Chain_dFdrho(i,rhop,lambda,rhobar,dF_drho_CHAIN,f_ch,user) + +Use BASIC_VARIABLES, Only: ncomp,parame +Use EOS_VARIABLES, Only: dhs +Use mod_DFT, Only: zp,dzp,fa + +!PETSc module +Use PetscManagement + +#include + +!passed +INTEGER, INTENT(IN) :: i !the grid point to calculate dFdrho at +type (userctx) :: user +PetscScalar :: rhop(ncomp,user%gxs:user%gxe) +REAL,INTENT(IN) :: rhobar(user%gxs:user%gxe,ncomp) +REAL,INTENT(IN) :: lambda(user%gxs:user%gxe,ncomp) +REAL,INTENT(OUT) :: dF_drho_CHAIN(user%xs:user%xe,ncomp) +REAL, INTENT(OUT) :: f_ch + + +!local +INTEGER :: j,k,n +REAL :: dhsk +INTEGER :: fak +REAL :: rhopjk,rhopjp1k,logrho,xlo,xhi +REAL :: ycorr(ncomp),dlny(ncomp,ncomp) +INTEGER, parameter :: NMAX = 800 +REAL,dimension(NMAX) :: x_int, int_1,int_2 !Fehlerwarnung falls 800 ueberschritten einbauen +REAL,dimension(NMAX) :: y2_1, y2_2 +REAL :: dz,zz,integral_1,integral_2 +REAL :: lamy + + + call Cavity_mix(rhobar(i,1:ncomp),ycorr,dlny) + + f_ch = 0.0 + + Do k = 1,ncomp + fak = fa(k) + dhsk = dhs(k) + n = 1 + x_int = 0.0 + int_1 = 0.0 + int_2 = 0.0 + + + Do j = i-fak,i+fak !es muss bis +- sig um i integriert werden + rhopjk = rhop(k,j) + rhopjp1k = rhop(k,j+1) + + If( ( zp(i)-zp(j+1) ) < dhsk .and. ( zp(i) - zp(j) ) >= dhsk ) Then !the position of j+1 is already within i-d while j is still outside this range in this case, the integration steplength (dz) is just the distance, which j+1 overlaps with i-d and what is integrated is the interpolated value of the integrand + + If(n/= 1) stop 'n /=1 in Chain_dFdrho' !here always n=1! + zz = zp(j) - zp(i) !distance between grid points j and i + dz = zp(j+1) - (zp(i) - dhsk) !the part of the intervall between zp(j) and zp(j+1) which is already within i-d + !if(dz < epsilon(dz)) dz = epsilon(dz) !bei unguenstiger Kombination von sig und ngrid kann dz unter Machinengenauigkeit epsilon liegen, dann ist x(2) = x(1) + dz = x(1) -> das fuehrt zu Abbruch in Spline Interpolation + x_int(n) = 0.0 !array containing x-values for spline integration + int_1(n) = 0.0 !erklärung analog wie bei n3_int in FMT Teil + int_2(n) = rhopjk*lambda(j,k) + (rhopjp1k*lambda(j+1,k) - rhopjk*lambda(j,k) )/dzp * (dzp-dz) !lineare interpolation analog zum FMT Teil + + Else If (zp(j) > (zp(i)-dhsk) .and. zp(j) <= (zp(i)+dhsk)) Then !grid point j within i+-d + + n = n + 1 + x_int(n) = x_int(n-1) + dz !first time in this If condition, dz is stil the old value from above! + zz = zp(j) - zp(i) + dz = dzp + int_1(n) = SUM( ( parame(1:ncomp,1)-1.0 ) * rhop(1:ncomp,j)*dlny(1:ncomp,k) ) & + * 0.75/dhsk**3 * (dhsk**2-zz**2) + int_2(n) = rhopjk / lambda(j,k) + + If (zp(j) < (zp(i)+dhsk) .and. zp(j+1) >= (zp(i)+dhsk) ) Then !zp(j) is still within zp(i)+d but zp(j+1) is already outside zp(i)+d + + dz = zp(i) + dhsk - zp(j) + !If(dz <= epsilon(dz)) exit !wie oben, kann auch hier bei ungluecklicher Wahl von sig und ngrid dz < eps werden und somit x(n) = x(n-1) -> Abbruch in Spline interpolation. Dann einfach ngrid aendern! + zz = zp(j) - zp(i) + n = n + 1 + x_int(n) = x_int(n-1) + dz + int_1(n) = 0.0 + int_2(n) = rhopjk*lambda(j,k) + (rhopjp1k*lambda(j+1,k) - rhopjk*lambda(j,k) )/dzp * dz + +! If(x_int(n) == x_int(n-1)) Then +! n = n - 1 +! exit +! End If + + End If + End If + End Do + + !Spline Integration + xlo = x_int(1) + xhi = x_int(n) + + If(n > NMAX) stop 'Increase NMAX in Chain_dFdrho (auch in AD Routine!!)' + + CALL spline ( x_int, int_1, n, 1.E30, 1.E30, y2_1 ) + CALL splint_integral( x_int, int_1, y2_1, n, xlo, xhi, integral_1 ) + CALL spline ( x_int, int_2, n, 1.E30, 1.E30, y2_2 ) + CALL splint_integral( x_int, int_2, y2_2, n, xlo, xhi, integral_2 ) + + If(rhop(k,i) < epsilon(dz)) rhop = epsilon(dz) + + dF_drho_CHAIN(i,k) = (parame(k,1) - 1.0)*log(rhop(k,i)) & + - (parame(k,1) - 1.0) * ( log(ycorr(k)*lambda(i,k))-1.0 + 0.5*integral_2/dhsk ) - integral_1 + + + f_ch = f_ch + ( parame(k,1) - 1.0 ) * rhop(k,i) * ( log(rhop(k,i)) - 1.0 ) & + - ( parame(k,1) - 1.0 ) * rhop(k,i) * ( log(ycorr(k)*lambda(i,k)) - 1.0 ) + + + + + +End Do + + + + + + + + + + + + +End Subroutine Chain_dFdrho + + + + + + + + + + + + + + + + +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! + SUBROUTINE Cavity_mix ( rhoi, ycorr, dlnydr ) +! + USE PARAMETERS, ONLY: PI + USE BASIC_VARIABLES, ONLY: ncomp,parame + USE EOS_VARIABLES, Only: dhs + IMPLICIT NONE +! +! ---------------------------------------------------------------------- + REAL, INTENT(IN) :: rhoi(ncomp) + REAL, INTENT(OUT) :: ycorr(ncomp) + REAL, INTENT(OUT) :: dlnydr(ncomp,ncomp) ! this is: d( ln( yij ) ) / d( rho(k) ) used with i=j +! +! ---------------------------------------------------------------------- + INTEGER :: i, j, k + REAL :: z0, z1, z2, z3, zms, z1_rk, z2_rk, z3_rk + REAL, DIMENSION(ncomp,ncomp) :: dij_ab, gij, gij_rk +! ---------------------------------------------------------------------- + + z0 = PI / 6.0 * SUM( rhoi(1:ncomp) * parame(1:ncomp,1) ) + z1 = PI / 6.0 * SUM( rhoi(1:ncomp) * parame(1:ncomp,1) * dhs(1:ncomp) ) + z2 = PI / 6.0 * SUM( rhoi(1:ncomp) * parame(1:ncomp,1) * dhs(1:ncomp)**2 ) + z3 = PI / 6.0 * SUM( rhoi(1:ncomp) * parame(1:ncomp,1) * dhs(1:ncomp)**3 ) + + zms = 1.0 - z3 + + DO i = 1,ncomp + DO j=1,ncomp + dij_ab(i,j)=dhs(i)*dhs(j)/(dhs(i)+dhs(j)) + ENDDO + END DO + + DO k = 1, ncomp + DO i = 1, ncomp + z1_rk = PI/6.0 * parame(k,1) * dhs(k) + z2_rk = PI/6.0 * parame(k,1) * dhs(k)*dhs(k) + z3_rk = PI/6.0 * parame(k,1) * dhs(k)**3 + !DO j = 1, ncomp + j = i + gij(i,j) = 1.0/zms + 3.0*dij_ab(i,j)*z2/zms/zms & + + 2.0*(dij_ab(i,j)*z2)**2 /zms**3 + !dgijdz(i,j)= 1.0/zms/zms + 3.0*dij_ab(i,j)*z2*(1.0+z3)/z3/zms**3 & + ! + (dij_ab(i,j)*z2/zms/zms)**2 *(4.0+2.0*z3)/z3 + gij_rk(i,j) = z3_rk/zms/zms & + + 3.0*dij_ab(i,j)*(z2_rk+2.0*z2*z3_rk/zms)/zms/zms & + + dij_ab(i,j)**2 *z2/zms**3 *(4.0*z2_rk+6.0*z2*z3_rk/zms) + !END DO + + ycorr(i) = gij(i,i) + dlnydr(i,k) = gij_rk(i,i) / gij(i,i) + + END DO + END DO + +END SUBROUTINE Cavity_mix + + + + + + + + + + +End Module mod_DFT_CHAIN \ No newline at end of file diff --git a/applications/PUfoam/MoDeNaModels/SurfaceTension/ExampleOfUsage/src/srcDetailedCode/mod_DFT_CHAIN_d.F90 b/applications/PUfoam/MoDeNaModels/SurfaceTension/ExampleOfUsage/src/srcDetailedCode/mod_DFT_CHAIN_d.F90 new file mode 100644 index 000000000..1a774a042 --- /dev/null +++ b/applications/PUfoam/MoDeNaModels/SurfaceTension/ExampleOfUsage/src/srcDetailedCode/mod_DFT_CHAIN_d.F90 @@ -0,0 +1,427 @@ + +! Generated by TAPENADE (INRIA, Tropics team) +! Tapenade 3.10 (r5498) - 20 Jan 2015 09:48 +! +MODULE MOD_DFT_CHAIN_D + IMPLICIT NONE + PRIVATE + PUBLIC chain_aux_d + PUBLIC chain_dfdrho_d + +CONTAINS +! Differentiation of chain_aux in forward (tangent) mode: +! variations of useful results: rhobar lambda +! with respect to varying inputs: rhop + SUBROUTINE CHAIN_AUX_D(rhop, rhopd, rhobar, rhobard, lambda, lambdad, & +& user) + USE BASIC_VARIABLES, ONLY : ncomp + USE EOS_VARIABLES, Only: dhs,rho + USE MOD_DFT, ONLY : zp, dzp, fa + + !PETSc module + Use PetscManagement + + IMPLICIT NONE + +#include + + +!passed +type (userctx) :: user +PetscScalar :: rhop(ncomp,user%gxs:user%gxe) +PetscScalar :: rhopd(ncomp,user%gxs:user%gxe) +REAL,INTENT(OUT) :: rhobar(user%gxs:user%gxe,ncomp) +REAL,INTENT(OUT) :: rhobard(user%gxs:user%gxe,ncomp) +REAL,INTENT(OUT) :: lambda(user%gxs:user%gxe,ncomp) +REAL,INTENT(OUT) :: lambdad(user%gxs:user%gxe,ncomp) + +!local + INTEGER :: i, j, k + REAL :: dhsk + INTEGER :: fak, n + REAL :: zz, dz, xlo, xhi, integral_lamb, integral_rb + REAL :: integral_lambd, integral_rbd + INTEGER, parameter :: NMAX = 800 + REAL, DIMENSION(NMAX) :: x_int, lamb_int, rb_int + REAL, DIMENSION(NMAX) :: lamb_intd, rb_intd + REAL, DIMENSION(NMAX) :: y2_lamb, y2_rb + REAL, DIMENSION(NMAX) :: y2_lambd, y2_rbd + REAL :: rhopjk, rhopjp1k + REAL :: rhopjkd, rhopjp1kd + INTRINSIC EPSILON + REAL :: result1 + + + + rhobard = 0.0 + lambdad = 0.0 + y2_rbd = 0.0 + y2_lambd = 0.0 +!fak = maxval(fa(1:ncomp)) + DO k=1,ncomp + dhsk = dhs(k) + fak = fa(k) + 1 + + Do i = user%xs-fak,user%xe+fak !lambda und rhobar werden bis i+-sig gebraucht -> Schleife bis +- fa + n = 1 + x_int = 0.0 + lamb_int = 0.0 + rb_int = 0.0 + rb_intd = 0.0 + lamb_intd = 0.0 +!um lambda bei i zu berechnen, muss bis +- sig um i integriert werden -> Schleife bis +- fa + DO j=i-fak,i+fak + rhopjkd = rhopd(k, j) + rhopjk = rhop(k, j) + rhopjp1kd = rhopd(k, j+1) + rhopjp1k = rhop(k, j+1) + IF (zp(i) - zp(j+1) .LT. dhsk .AND. zp(i) - zp(j) .GE. dhsk) & +& THEN +!the position of j+1 is already within i-d while j is still outside this range in this case, the integration steplength (dz) is j +!ust the distance, which j+1 overlaps with i-d and what is integrated is the interpolated value of the integrand +!here always n=1! + IF (n .NE. 1) THEN + GOTO 100 + ELSE +!distance between grid points j and i + zz = zp(j) - zp(i) +!the part of the intervall between zp(j) and zp(j+1) which is already within i-d + dz = zp(j+1) - (zp(i)-dhsk) +!if(dz < epsilon(dz)) dz = epsilon(dz) !bei unguenstiger Kombination von sig und ngrid kann dz unter Machinengenauigkeit epsilon +!liegen, dann ist x(2) = x(1) + dz = x(1) -> das fuehrt zu Abbruch in Spline Interpolation +!array containing x-values for spline integration + x_int(n) = 0.0 +!lineare interpolation analog zum FMT Teil + lamb_intd(n) = rhopjkd + (dzp-dz)*(rhopjp1kd-rhopjkd)/dzp + lamb_int(n) = rhopjk + (rhopjp1k-rhopjk)/dzp*(dzp-dz) +!erklärung analog wie bei n3_int in FMT Teil + rb_intd(n) = 0.0 + rb_int(n) = 0.0 + END IF + ELSE IF (zp(j) .GT. zp(i) - dhsk .AND. zp(j) .LE. zp(i) + dhsk& +& ) THEN +!grid point j within i+-d + n = n + 1 +!first time in this If condition, dz is stil the old value from above! + x_int(n) = x_int(n-1) + dz + zz = zp(j) - zp(i) + dz = dzp + lamb_intd(n) = rhopjkd + lamb_int(n) = rhopjk + rb_intd(n) = (dhsk**2-zz**2)*rhopjkd + rb_int(n) = rhopjk*(dhsk**2-zz**2) + IF (zp(j) .LT. zp(i) + dhsk .AND. zp(j+1) .GE. zp(i) + dhsk& +& ) THEN +!zp(j) is still within zp(i)+d but zp(j+1) is already outside zp(i)+d + dz = zp(i) + dhsk - zp(j) +!If(dz <= epsilon(dz)) exit !wie oben, kann auch hier bei ungluecklicher Wahl von sig und ngrid dz < eps werden und somit x(n) +!= x(n-1) -> Abbruch in Spline interpolation. Dann einfach ngrid aendern! + zz = zp(j) - zp(i) + n = n + 1 + x_int(n) = x_int(n-1) + dz + rb_intd(n) = 0.0 + rb_int(n) = 0.0 + lamb_intd(n) = rhopjkd + dz*(rhopjp1kd-rhopjkd)/dzp + lamb_int(n) = rhopjk + (rhopjp1k-rhopjk)/dzp*dz +! If(x_int(n) == x_int(n-1)) Then +! n = n - 1 +! exit +! End If + END IF + END IF + END DO +!spline integration + xlo = x_int(1) + xhi = x_int(n) + CALL SPLINE_D(x_int, lamb_int, lamb_intd, n, 1.e30, 1.e30, & +& y2_lamb, y2_lambd) + CALL SPLINE_D(x_int, rb_int, rb_intd, n, 1.e30, 1.e30, y2_rb, & +& y2_rbd) + CALL SPLINT_INTEGRAL_D(x_int, lamb_int, lamb_intd, y2_lamb, & +& y2_lambd, n, xlo, xhi, integral_lamb, & +& integral_lambd) + CALL SPLINT_INTEGRAL_D(x_int, rb_int, rb_intd, y2_rb, y2_rbd, n& +& , xlo, xhi, integral_rb, integral_rbd) + lambdad(i, k) = 0.5*integral_lambd/dhsk + lambda(i, k) = 0.5*integral_lamb/dhsk + rhobard(i, k) = 0.75*integral_rbd/dhsk**3 + rhobar(i, k) = 0.75*integral_rb/dhsk**3 + result1 = EPSILON(dz) + IF (lambda(i, k) .LT. result1) lambda(i, k) = EPSILON(dz) + END DO + END DO + GOTO 110 + 100 STOP + 110 CONTINUE + END SUBROUTINE CHAIN_AUX_D + + + + +! Differentiation of chain_dfdrho in forward (tangent) mode: +! variations of useful results: df_drho_chain rhop +! with respect to varying inputs: rhobar df_drho_chain lambda +! rhop + SUBROUTINE CHAIN_DFDRHO_D(i, rhop, rhopd, lambda, lambdad, rhobar, & +& rhobard, df_drho_chain, df_drho_chaind, user) + USE BASIC_VARIABLES, ONLY : ncomp,parame + USE EOS_VARIABLES, Only: dhs + USE MOD_DFT, ONLY : zp, dzp, fa + + !PETSc module + Use PetscManagement + IMPLICIT NONE + +#include + + +!passed +INTEGER, INTENT(IN) :: i !the grid point to calculate dFdrho at +type (userctx) :: user +PetscScalar :: rhop(ncomp,user%gxs:user%gxe) +PetscScalar :: rhopd(ncomp,user%gxs:user%gxe) +REAL,INTENT(IN) :: rhobar(user%gxs:user%gxe,ncomp) +REAL,INTENT(IN) :: rhobard(user%gxs:user%gxe,ncomp) +REAL,INTENT(IN) :: lambda(user%gxs:user%gxe,ncomp) +REAL,INTENT(IN) :: lambdad(user%gxs:user%gxe,ncomp) + + + +REAL,INTENT(OUT) :: dF_drho_CHAIN(user%xs:user%xe,ncomp) +REAL,INTENT(OUT) :: dF_drho_CHAINd(user%xs:user%xe,ncomp) + + +!local + INTEGER :: j, k, n + REAL :: dhsk + INTEGER :: fak + REAL :: rhopjk, rhopjp1k, logrho, xlo, xhi + REAL :: rhopjkd, rhopjp1kd + REAL :: ycorr(ncomp), dlny(ncomp, ncomp) + REAL :: ycorrd(ncomp), dlnyd(ncomp, ncomp) + INTEGER, parameter :: NMAX = 800 + REAL, DIMENSION(NMAX) :: x_int, int_1, int_2 + REAL, DIMENSION(NMAX) :: int_1d, int_2d + REAL, DIMENSION(NMAX) :: y2_1, y2_2 + REAL, DIMENSION(NMAX) :: y2_1d, y2_2d + REAL :: dz, zz, integral_1, integral_2 + REAL :: integral_1d, integral_2d + REAL :: lamy + INTRINSIC SUM + INTRINSIC EPSILON + INTRINSIC LOG + REAL, DIMENSION(ncomp) :: arg1 + REAL, DIMENSION(ncomp) :: arg1d + REAL :: result1 + REAL :: arg10 + REAL :: arg10d + + + + + + CALL CAVITY_MIX_D(rhobar(i, 1:ncomp), rhobard(i, 1:ncomp), ycorr, & +& ycorrd, dlny, dlnyd) + y2_1d = 0.0 + y2_2d = 0.0 + DO k=1,ncomp + fak = fa(k) + dhsk = dhs(k) + n = 1 + x_int = 0.0 + int_1 = 0.0 + int_2 = 0.0 + int_1d = 0.0 + int_2d = 0.0 +!es muss bis +- sig um i integriert werden + DO j=i-fak,i+fak + rhopjkd = rhopd(k, j) + rhopjk = rhop(k, j) + rhopjp1kd = rhopd(k, j+1) + rhopjp1k = rhop(k, j+1) + IF (zp(i) - zp(j+1) .LT. dhsk .AND. zp(i) - zp(j) .GE. dhsk) & +& THEN +!the position of j+1 is already within i-d while j is still outside this range in this case, the integration steplength (dz) is j +!ust the distance, which j+1 overlaps with i-d and what is integrated is the interpolated value of the integrand +!here always n=1! + IF (n .NE. 1) THEN + GOTO 100 + ELSE +!distance between grid points j and i + zz = zp(j) - zp(i) +!the part of the intervall between zp(j) and zp(j+1) which is already within i-d + dz = zp(j+1) - (zp(i)-dhsk) +!if(dz < epsilon(dz)) dz = epsilon(dz) !bei unguenstiger Kombination von sig und ngrid kann dz unter Machinengenauigkeit epsilon +!liegen, dann ist x(2) = x(1) + dz = x(1) -> das fuehrt zu Abbruch in Spline Interpolation +!array containing x-values for spline integration + x_int(n) = 0.0 +!erklärung analog wie bei n3_int in FMT Teil + int_1d(n) = 0.0 + int_1(n) = 0.0 +!lineare interpolation analog zum FMT Teil + int_2d(n) = rhopjkd*lambda(j, k) + rhopjk*lambdad(j, k) + (& +& dzp-dz)*(rhopjp1kd*lambda(j+1, k)+rhopjp1k*lambdad(j+1, k)& +& -rhopjkd*lambda(j, k)-rhopjk*lambdad(j, k))/dzp + int_2(n) = rhopjk*lambda(j, k) + (rhopjp1k*lambda(j+1, k)-& +& rhopjk*lambda(j, k))/dzp*(dzp-dz) + END IF + ELSE IF (zp(j) .GT. zp(i) - dhsk .AND. zp(j) .LE. zp(i) + dhsk) & +& THEN +!grid point j within i+-d + n = n + 1 +!first time in this If condition, dz is stil the old value from above! + x_int(n) = x_int(n-1) + dz + zz = zp(j) - zp(i) + dz = dzp + arg1d(:) = (parame(1:ncomp,1)-1.0)*(rhopd(1:ncomp, j)*dlny(1:ncomp& +& , k)+rhop(1:ncomp, j)*dlnyd(1:ncomp, k)) + arg1(:) = (parame(1:ncomp,1)-1.0)*rhop(1:ncomp, j)*dlny(1:ncomp, k& +& ) + int_1d(n) = (dhsk**2-zz**2)*0.75*SUM(arg1d(:))/dhsk**3 + int_1(n) = SUM(arg1(:))*0.75/dhsk**3*(dhsk**2-zz**2) + int_2d(n) = (rhopjkd*lambda(j, k)-rhopjk*lambdad(j, k))/lambda& +& (j, k)**2 + int_2(n) = rhopjk/lambda(j, k) + IF (zp(j) .LT. zp(i) + dhsk .AND. zp(j+1) .GE. zp(i) + dhsk) & +& THEN +!zp(j) is still within zp(i)+d but zp(j+1) is already outside zp(i)+d + dz = zp(i) + dhsk - zp(j) +!If(dz <= epsilon(dz)) exit !wie oben, kann auch hier bei ungluecklicher Wahl von sig und ngrid dz < eps werden und somit x(n) +!= x(n-1) -> Abbruch in Spline interpolation. Dann einfach ngrid aendern! + zz = zp(j) - zp(i) + n = n + 1 + x_int(n) = x_int(n-1) + dz + int_1d(n) = 0.0 + int_1(n) = 0.0 + int_2d(n) = rhopjkd*lambda(j, k) + rhopjk*lambdad(j, k) + dz& +& *(rhopjp1kd*lambda(j+1, k)+rhopjp1k*lambdad(j+1, k)-& +& rhopjkd*lambda(j, k)-rhopjk*lambdad(j, k))/dzp + int_2(n) = rhopjk*lambda(j, k) + (rhopjp1k*lambda(j+1, k)-& +& rhopjk*lambda(j, k))/dzp*dz +! If(x_int(n) == x_int(n-1)) Then +! n = n - 1 +! exit +! End If + END IF + END IF + END DO +!Spline Integration + xlo = x_int(1) + xhi = x_int(n) + CALL SPLINE_D(x_int, int_1, int_1d, n, 1.e30, 1.e30, y2_1, y2_1d) + CALL SPLINT_INTEGRAL_D(x_int, int_1, int_1d, y2_1, y2_1d, n, xlo, & +& xhi, integral_1, integral_1d) + CALL SPLINE_D(x_int, int_2, int_2d, n, 1.e30, 1.e30, y2_2, y2_2d) + CALL SPLINT_INTEGRAL_D(x_int, int_2, int_2d, y2_2, y2_2d, n, xlo, & +& xhi, integral_2, integral_2d) + result1 = EPSILON(dz) + IF (rhop(k, i) .LT. result1) THEN + rhop = EPSILON(dz) + rhopd = 0.0 + END IF + arg10d = ycorrd(k)*lambda(i, k) + ycorr(k)*lambdad(i, k) + arg10 = ycorr(k)*lambda(i, k) + df_drho_chaind(i, k) = (parame(k,1)-1.0)*rhopd(k, i)/rhop(k, i) - (& +& parame(k,1)-1.0)*(arg10d/arg10+0.5*integral_2d/dhsk) - integral_1d + df_drho_chain(i, k) = (parame(k,1)-1.0)*LOG(rhop(k, i)) - (parame(k,1)-1.0& +& )*(LOG(arg10)-1.0+0.5*integral_2/dhsk) - integral_1 + END DO + GOTO 110 + 100 STOP + 110 CONTINUE + END SUBROUTINE CHAIN_DFDRHO_D + + + +! Differentiation of cavity_mix in forward (tangent) mode: +! variations of useful results: ycorr dlnydr +! with respect to varying inputs: rhoi +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! + SUBROUTINE CAVITY_MIX_D(rhoi, rhoid, ycorr, ycorrd, dlnydr, dlnydrd) +! + USE PARAMETERS, ONLY : pi + USE BASIC_VARIABLES, ONLY : ncomp,parame + USE EOS_VARIABLES, Only: dhs + IMPLICIT NONE +! +! ---------------------------------------------------------------------- + REAL, INTENT(IN) :: rhoi(ncomp) + REAL, INTENT(IN) :: rhoid(ncomp) + REAL, INTENT(OUT) :: ycorr(ncomp) + REAL, INTENT(OUT) :: ycorrd(ncomp) +! this is: d( ln( yij ) ) / d( rho(k) ) used with i=j + REAL, INTENT(OUT) :: dlnydr(ncomp, ncomp) + REAL, INTENT(OUT) :: dlnydrd(ncomp, ncomp) +! +! ---------------------------------------------------------------------- + INTEGER :: i, j, k + REAL :: z0, z1, z2, z3, zms, z1_rk, z2_rk, z3_rk + REAL :: z2d, z3d, zmsd + REAL, DIMENSION(ncomp, ncomp) :: dij_ab, gij, gij_rk + REAL, DIMENSION(ncomp, ncomp) :: gijd, gij_rkd + INTRINSIC SUM + REAL, DIMENSION(ncomp) :: arg1 + REAL, DIMENSION(ncomp) :: arg1d +! ---------------------------------------------------------------------- + arg1(:) = rhoi(1:ncomp)*parame(1:ncomp,1) + z0 = pi/6.0*SUM(arg1(:)) + arg1(:) = rhoi(1:ncomp)*parame(1:ncomp,1)*dhs(1:ncomp) + z1 = pi/6.0*SUM(arg1(:)) + arg1d(:) = parame(1:ncomp,1)*dhs(1:ncomp)**2*rhoid(1:ncomp) + arg1(:) = rhoi(1:ncomp)*parame(1:ncomp,1)*dhs(1:ncomp)**2 + z2d = pi*SUM(arg1d(:))/6.0 + z2 = pi/6.0*SUM(arg1(:)) + arg1d(:) = parame(1:ncomp,1)*dhs(1:ncomp)**3*rhoid(1:ncomp) + arg1(:) = rhoi(1:ncomp)*parame(1:ncomp,1)*dhs(1:ncomp)**3 + z3d = pi*SUM(arg1d(:))/6.0 + z3 = pi/6.0*SUM(arg1(:)) + zmsd = -z3d + zms = 1.0 - z3 + DO i=1,ncomp + DO j=1,ncomp + dij_ab(i, j) = dhs(i)*dhs(j)/(dhs(i)+dhs(j)) + END DO + END DO + ycorrd = 0.0 + dlnydrd = 0.0 + gij_rkd = 0.0 + gijd = 0.0 + DO k=1,ncomp + DO i=1,ncomp + z1_rk = pi/6.0*parame(k,1)*dhs(k) + z2_rk = pi/6.0*parame(k,1)*dhs(k)*dhs(k) + z3_rk = pi/6.0*parame(k,1)*dhs(k)**3 +!DO j = 1, ncomp + j = i + gijd(i, j) = ((3.0*dij_ab(i, j)*z2d*zms-3.0*dij_ab(i, j)*z2*zmsd& +& )/zms-3.0*dij_ab(i, j)*z2*zmsd/zms)/zms**2 - zmsd/zms**2 + (& +& 2.0*2*dij_ab(i, j)**2*z2*z2d*zms**3-2.0*dij_ab(i, j)**2*z2**2*& +& 3*zms**2*zmsd)/(zms**3)**2 + gij(i, j) = 1.0/zms + 3.0*dij_ab(i, j)*z2/zms/zms + 2.0*(dij_ab(& +& i, j)*z2)**2/zms**3 +!dgijdz(i,j)= 1.0/zms/zms + 3.0*dij_ab(i,j)*z2*(1.0+z3)/z3/zms**3 & +! + (dij_ab(i,j)*z2/zms/zms)**2 *(4.0+2.0*z3)/z3 + gij_rkd(i, j) = (-2)*(z3_rk*zmsd/zms)/zms**2 + ((3.0*dij_ab(i, j& +& )*(2.0*z3_rk*z2d*zms-2.0*z2*z3_rk*zmsd)/zms-3.0*dij_ab(i, j)*(& +& z2_rk+2.0*z2*z3_rk/zms)*zmsd)/zms-3.0*dij_ab(i, j)*(z2_rk+2.0*& +& z2*z3_rk/zms)*zmsd/zms)/zms**2 + (dij_ab(i, j)**2*z2d*zms**3-& +& dij_ab(i, j)**2*z2*3*zms**2*zmsd)*(4.0*z2_rk+6.0*z2*z3_rk/zms)& +& /zms**6 + dij_ab(i, j)**2*z2*(6.0*z3_rk*z2d*zms-6.0*z2*z3_rk*& +& zmsd)/zms**5 + gij_rk(i, j) = z3_rk/zms/zms + 3.0*dij_ab(i, j)*(z2_rk+2.0*z2*& +& z3_rk/zms)/zms/zms + dij_ab(i, j)**2*z2/zms**3*(4.0*z2_rk+6.0*& +& z2*z3_rk/zms) +!END DO + ycorrd(i) = gijd(i, i) + ycorr(i) = gij(i, i) + dlnydrd(i, k) = (gij_rkd(i, i)*gij(i, i)-gij_rk(i, i)*gijd(i, i)& +& )/gij(i, i)**2 + dlnydr(i, k) = gij_rk(i, i)/gij(i, i) + END DO + END DO + END SUBROUTINE CAVITY_MIX_D + +END MODULE MOD_DFT_CHAIN_D diff --git a/applications/PUfoam/MoDeNaModels/SurfaceTension/ExampleOfUsage/src/srcDetailedCode/mod_DFT_DISP_WDA.F90 b/applications/PUfoam/MoDeNaModels/SurfaceTension/ExampleOfUsage/src/srcDetailedCode/mod_DFT_DISP_WDA.F90 new file mode 100644 index 000000000..6893cfef3 --- /dev/null +++ b/applications/PUfoam/MoDeNaModels/SurfaceTension/ExampleOfUsage/src/srcDetailedCode/mod_DFT_DISP_WDA.F90 @@ -0,0 +1,688 @@ +Module mod_DFT_DISP_WDA + + +Implicit None + +Private + +Public :: rhoi_disp_wd +Public :: a_disp_pcsaft +Public :: dF_disp_drho_wda + + + + + + Contains + + + + SUBROUTINE rhoi_disp_wd ( discret, fa_psi, fa_psi_max, psi_j, rhop, rhoi_disp,user ) + + + Use PetscManagement + Use basic_variables, ONLY: ncomp, t, parame + Use mod_DFT, Only: zp,dzp + IMPLICIT NONE + +#include + +! +! ---------------------------------------------------------------------- + Type (userctx) :: user + PetscScalar :: rhop(ncomp,user%gxs:user%gxe) + INTEGER, INTENT(IN) :: discret + INTEGER, INTENT(IN) :: fa_psi(ncomp) + INTEGER, INTENT(IN) :: fa_psi_max +! REAL, INTENT(IN) :: dzp + REAL, INTENT(IN) :: psi_j(ncomp) +! REAL, INTENT(IN) :: zp(user%gxs:user%gxe) + REAL, INTENT(OUT) :: rhoi_disp(user%gxs:user%gxe,ncomp) +! ---------------------------------------------------------------------- + INTEGER :: ii, jj, icomp, nn + REAL :: zmin, zl, zr + REAL :: int1, zz1, xl, xh + REAL, DIMENSION(700) :: y2, rx, ry1 +! ---------------------------------------------------------------------- + +!write(*,*)'rhoi_wd' + + zmin = 1d-6 + DO icomp = 1, ncomp + DO ii = (user%xs-fa_psi_max),(user%xe+fa_psi_max)!(-fa_psi_max), (discret+fa_psi_max) + nn = 0 + zl = zp(ii) - psi_j(icomp) + zr = zp(ii) + psi_j(icomp) + DO jj = (ii-fa_psi(icomp)), (ii+fa_psi(icomp)) + IF ( zp(jj+1) > (zl+zmin) ) THEN + ! first position: left side of the sphere: zl. Linear Interpolation of h's + IF ( nn == 0 ) THEN + nn = nn + 1 + rx(1) = zl + ry1(1) = 0.0 ! = 0.75*rhop(ii-fa,icomp)*( d.**2 -d.**2 ) +!write(*,*)'FIRST',nn,rx(nn),ry1(nn) + ! middle position: within the sphere: zl < jj < zr + ELSE + nn = nn + 1 + zz1 = zp(jj)-zp(ii) ! distance z12 between 1 and 2 + rx(nn) = zp(jj) + ry1(nn) = rhop(icomp,jj) * (psi_j(icomp)*psi_j(icomp) - zz1*zz1) +!write(*,*)'MIDDLE',nn,rx(nn),ry1(nn) + ! last position: right side of the sphere: zr. Linear Interpolation of h's + IF ( zp(jj+1) > (zr-zmin) ) THEN + nn = nn + 1 + rx(nn) = zr + ry1(nn) = 0.0 +!write(*,*)'LAST',nn,rx(nn),ry1(nn) + EXIT + END IF + END IF + END IF + END DO + xl = rx(1) + xh = rx(nn) + + if( nn >= 700 ) then + write(*,*) 'rhoi_disp_wd: bigger vectors rx, ry1, ry2, ... required!', nn + pause + end if + + CALL spline ( rx(1:nn), ry1(1:nn), nn, 1.E30, 1.E30, y2(1:nn) ) + CALL splint_integral ( rx(1:nn), ry1(1:nn), y2(1:nn), nn, xl, xh, int1 ) + rhoi_disp(ii,icomp) = int1 * 0.75/psi_j(icomp)**3 + + if ( rhoi_disp(ii,icomp) < 0.0 ) then + rhoi_disp(ii,icomp) = 0.0 + do jj = 2, nn + rhoi_disp(ii,icomp) = rhoi_disp(ii,icomp) + (ry1(jj)+ry1(jj-1))/2.0 *(rx(jj)-rx(jj-1)) + end do + end if + if ( rhoi_disp(ii,icomp) < 0.0 ) rhoi_disp(ii,icomp) = rhop(icomp,ii) + END DO + END DO + + +END SUBROUTINE rhoi_disp_wd + + + + + + + + + +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! SUBROUTINE a_disp_pcsaft +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! + SUBROUTINE a_disp_pcsaft( discret, fa_psi, fa_psi_max, rhoi_disp, rho_disp, adisp, mydisp, dadisp_dr,user ) + + Use PetscManagement +! + USE parameters, ONLY: PI, np, nc + USE basic_variables, ONLY: ncomp, t, parame, xi, densta, ensemble_flag + USE eos_variables, ONLY: dhs, sig_ij, uij + USE eos_constants, ONLY: ap, bp + IMPLICIT NONE + +#include + + + + +! +! ---------------------------------------------------------------------- + Type (userctx) :: user + INTEGER, INTENT(IN) :: discret + INTEGER, INTENT(IN) :: fa_psi(ncomp) + INTEGER, INTENT(IN) :: fa_psi_max + REAL, INTENT(IN) :: rhoi_disp(user%gxs:user%gxe,ncomp) + REAL, INTENT(OUT) :: rho_disp(user%gxs:user%gxe) + REAL, INTENT(OUT) :: adisp(user%gxs:user%gxe) + REAL, INTENT(OUT) :: mydisp(user%gxs:user%gxe,ncomp) + REAL, INTENT(OUT) :: dadisp_dr(user%gxs:user%gxe,ncomp) +! ---------------------------------------------------------------------- + INTEGER :: jj, m + INTEGER :: icomp, jcomp, kcomp + REAL, DIMENSION(ncomp) :: x_disp + REAL :: eta_disp, zms_disp + REAL, DIMENSION(0:6) :: apar, bpar, apar_rk, bpar_rk + REAL :: m_mean, C1, I1, I2 + REAL :: r2_ord1, r2_ord2 + REAL :: eta_rk, m_mean_rk, zms2eta + REAL :: C1_m_mean, C1_eta, C1_rk + REAL :: I1_rk, I2_rk + REAL :: r2_ord1_rk, r2_ord2_rk + REAL :: term1, term2, term3 + INTEGER :: iphas + REAL, DIMENSION(np,nc) :: mydisp2 +! ---------------------------------------------------------------------- + + DO icomp = 1, ncomp + DO jj = (user%xs-fa_psi_max),(user%xe+fa_psi_max)!(-fa_psi_max), (discret+fa_psi_max) + m_mean = 0. + eta_disp = 0. +! rho_disp(jj) = sum( rhop(jj,1:ncomp) ) + rho_disp(jj) = sum( rhoi_disp(jj,1:ncomp) ) + do kcomp=1, ncomp +! x_disp(kcomp) = rhop(jj,kcomp) / rho_disp(jj) + x_disp(kcomp) = rhoi_disp(jj,kcomp) / rho_disp(jj) + m_mean = m_mean + x_disp(kcomp) * parame(kcomp,1) +! eta_disp = eta_disp + rhop(jj,kcomp) * parame(kcomp,1) * dhs(kcomp)**3. + eta_disp = eta_disp + rhoi_disp(jj,kcomp) * parame(kcomp,1) * dhs(kcomp)**3. + end do + eta_disp = eta_disp * PI / 6. + zms_disp = 1. - eta_disp + if( zms_disp <= 0. ) write(*,'(a56,i6,f12.5)') 'system too dense for disp contribution ( jj, eta_disp ):', jj, eta_disp + + + ! quantities of the dispersive free energy contribution + I1 = 0. + I2 = 0. + do m = 0, 6 + apar(m) = ap(m,1) + (1.-1./m_mean)*ap(m,2) + (1.-1./m_mean)*(1.-2./m_mean)*ap(m,3) + bpar(m) = bp(m,1) + (1.-1./m_mean)*bp(m,2) + (1.-1./m_mean)*(1.-2./m_mean)*bp(m,3) + I1 = I1 + apar(m) * eta_disp**m + I2 = I2 + bpar(m) * eta_disp**m + end do + + r2_ord1 = 0. + r2_ord2 = 0. + do kcomp = 1, ncomp + do jcomp = 1, ncomp + r2_ord1 = r2_ord1 + rhoi_disp(jj,kcomp)*rhoi_disp(jj,jcomp)*parame(kcomp,1) & + *parame(jcomp,1)*sig_ij(kcomp,jcomp)**3 * uij(kcomp,jcomp)/t + r2_ord2 = r2_ord2 + rhoi_disp(jj,kcomp)*rhoi_disp(jj,jcomp)*parame(kcomp,1) & + *parame(jcomp,1)*sig_ij(kcomp,jcomp)**3 * (uij(kcomp,jcomp)/t)**2 + end do + end do + + C1 = (1.-m_mean)*(20.*eta_disp-27.*eta_disp**2 +12.*eta_disp**3 -2.*eta_disp**4 )/(zms_disp*(2.-eta_disp))**2 + C1 = 1. + m_mean*(8.*eta_disp-2.*eta_disp**2)/zms_disp**4 + C1 + C1 = 1. / C1 + + + ! dispersive free energy contribution + adisp(jj) = -2.*PI*I1*r2_ord1/rho_disp(jj) - PI*C1*m_mean*I2*r2_ord2/rho_disp(jj) + + + ! quantity-derivatives of the dispersive free energy contribution + m_mean_rk = ( parame(icomp,1) - m_mean ) / rho_disp(jj) + + do m = 0, 6 + apar_rk(m) = m_mean_rk/m_mean**2 * ( ap(m,2) + (3. - 4./m_mean) * ap(m,3) ) + bpar_rk(m) = m_mean_rk/m_mean**2 * ( bp(m,2) + (3. - 4./m_mean) * bp(m,3) ) + end do + eta_rk = parame(icomp,1) * dhs(icomp)**3. * PI / 6. + I1_rk = apar_rk(0) + apar(1)*eta_rk + apar_rk(1)*eta_disp + I2_rk = bpar_rk(0) + bpar(1)*eta_rk + bpar_rk(1)*eta_disp + do m = 2, 6 + I1_rk = I1_rk + apar(m)*REAL(m)*eta_disp**REAL(m-1)*eta_rk + apar_rk(m)*eta_disp**REAL(m) + I2_rk = I2_rk + bpar(m)*REAL(m)*eta_disp**REAL(m-1)*eta_rk + bpar_rk(m)*eta_disp**REAL(m) + end do + + r2_ord1_rk = 0. + r2_ord2_rk = 0. + do kcomp = 1,ncomp + r2_ord1_rk = r2_ord1_rk + rhoi_disp(jj,kcomp) * parame(kcomp,1) * sig_ij(icomp,kcomp)**3 * uij(icomp,kcomp)/t + r2_ord2_rk = r2_ord2_rk + rhoi_disp(jj,kcomp) * parame(kcomp,1) * sig_ij(icomp,kcomp)**3 *(uij(icomp,kcomp)/t)**2 + end do + r2_ord1_rk = 2. * parame(icomp,1) * r2_ord1_rk + r2_ord2_rk = 2. * parame(icomp,1) * r2_ord2_rk + + zms2eta = zms_disp * (2.-eta_disp) + C1_m_mean = ( 8.*eta_disp - 2.*eta_disp*eta_disp ) / zms_disp**4 & + - ( 20.*eta_disp - 27.*eta_disp*eta_disp + 12.*eta_disp**3 - 2.*eta_disp**4 ) / zms2eta**2 + C1_eta = m_mean * ( 8. + 20.*eta_disp - 4.*eta_disp*eta_disp ) / zms_disp**5 & + + (1. - m_mean) * ( 40. - 48.*eta_disp + 12.*eta_disp*eta_disp + 2.*eta_disp**3 ) / zms2eta**3 + C1_rk = - C1 * C1 * ( eta_rk * C1_eta + m_mean_rk * C1_m_mean ) + + + ! chemical potential and derivative of adisp (analytically) + term1 = - 2. * PI * ( I1 * r2_ord1_rk + r2_ord1 * I1_rk ) + term2 = - PI * C1 * m_mean * ( I2 * r2_ord2_rk + r2_ord2 * I2_rk ) + term3 = - PI * I2 * r2_ord2 * ( m_mean * C1_rk + C1 * m_mean_rk ) + mydisp(jj,icomp) = term1 + term2 + term3 + dadisp_dr(jj,icomp) = ( mydisp(jj,icomp) - adisp(jj) ) / rho_disp(jj) + + + ! chemical potential and derivative of adisp (numerically) +! do kcomp=1, ncomp +! xi(1,kcomp) = x_disp(kcomp) +! end do +! iphas = 1 +! ensemble_flag = 'tv' +! densta(1) = eta_disp +! call ONLY_ONE_TERM_EOS_NUMERICAL ( 'disp_term', 'PC-SAFT ' ) +! if( rho_disp(jj) /= 0. ) CALL FUGACITY(mydisp2) +! call RESTORE_PREVIOUS_EOS_NUMERICAL +! mydisp(jj,1:ncomp) = mydisp2(iphas,1:ncomp) +! dadisp_dr(jj,icomp) = ( mydisp(jj,icomp) - adisp(jj) ) / rho_disp(jj) + + + if( rho_disp(jj) == 0. ) then + adisp(jj) = 0. + mydisp(jj,icomp) = 0. + dadisp_dr(jj,icomp) = 0. + end if + + END DO + END DO + + +END SUBROUTINE a_disp_pcsaft + + + + + + + +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! SUBROUTINE dF_disp_drho_wda +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! + SUBROUTINE dF_disp_drho_wda( ii, WDA_var, fa_psi, psi_j, rhop, rhop_sum, & + rhoi_disp, rho_disp, adisp, mydisp, dadisp_dr, dF_drho_att,user ) + + Use PetscManagement + Use basic_variables, ONLY: ncomp + Use mod_DFT, Only: zp + IMPLICIT NONE + +#include + +! +! ---------------------------------------------------------------------- + Type (userctx) :: user + PetscScalar :: rhop(ncomp,user%gxs:user%gxe) +! +! ---------------------------------------------------------------------- + INTEGER, INTENT(IN) :: ii, WDA_var + INTEGER, INTENT(IN) :: fa_psi(ncomp) + REAL, INTENT(IN) :: psi_j(ncomp) +! REAL, INTENT(IN) :: zp(user%gxs:user%gxe) + REAL, INTENT(IN) :: adisp(user%gxs:user%gxe) + REAL, INTENT(IN) :: mydisp(user%gxs:user%gxe,ncomp) + REAL, INTENT(IN) :: rhop_sum(user%gxs:user%gxe) + REAL, INTENT(IN) :: rhoi_disp(user%gxs:user%gxe,ncomp) + REAL, INTENT(IN) :: rho_disp(user%gxs:user%gxe) + REAL, INTENT(IN) :: dadisp_dr(user%gxs:user%gxe,ncomp) + REAL, INTENT(OUT) :: dF_drho_att(ncomp) +! ---------------------------------------------------------------------- + INTEGER :: jj, icomp, nn + REAL :: int3 + REAL :: zmin, zl, zr, zz1, xl, xh + REAL, DIMENSION(700) :: y2, hx, hy3 +! ---------------------------------------------------------------------- + + zmin = 1d-6 + DO icomp = 1, ncomp + nn = 0 + zl = zp(ii) - psi_j(icomp) + zr = zp(ii) + psi_j(icomp) + DO jj = (ii-fa_psi(icomp)), (ii+fa_psi(icomp)) + IF ( zp(jj+1) > (zl+zmin) ) THEN + ! first position: left side of the sphere: zl. Linear Interpolation of h's + IF ( nn == 0 ) THEN + nn = nn + 1 + hx(1) = zl + hy3(1) = 0. +!write(*,*)'FIRST',nn,hx(nn),hy3(nn) + ! middle position: within the sphere: zl < jj < zr + ELSE + nn = nn + 1 + zz1 = zp(jj) - zp(ii) ! distance z12 between 1 and 2 + hx(nn) = zp(jj) + if(WDA_var == 1) hy3(nn) = mydisp(jj,icomp) * ( psi_j(icomp)*psi_j(icomp) - zz1**2 ) + if(WDA_var == 2) hy3(nn) = rhop_sum(jj) * dadisp_dr(jj,icomp) * ( psi_j(icomp)*psi_j(icomp) - zz1**2 ) +!write(*,*)'MIDDLE',nn,hx(nn),hy3(nn) + ! last position: right side of the sphere: zr. Linear Interpolation of h's + IF ( zp(jj+1) > (zr-zmin) ) THEN + nn = nn + 1 + hx(nn) = zr + hy3(nn) = 0. +!write(*,*)'LAST',nn,hx(nn),hy3(nn) + + EXIT + END IF + END IF + END IF + END DO + xl = hx(1) + xh = hx(nn) + + if( nn >= 700 ) then + write(*,*) 'dF_disp_wd_pcsaft: bigger vectors hx, hy3, ... required!', nn + pause + end if + + CALL spline ( hx(1:nn), hy3(1:nn), nn, 1.E30, 1.E30, y2(1:nn) ) + CALL splint_integral( hx(1:nn), hy3(1:nn), y2(1:nn), nn, xl, xh, int3 ) + + if(WDA_var == 1) dF_drho_att(icomp) = int3 * 0.75 / psi_j(icomp)**3. + if(WDA_var == 2) dF_drho_att(icomp) = int3 * 0.75 / psi_j(icomp)**3. + adisp(ii) + END DO + + +END SUBROUTINE dF_disp_drho_wda + + + +End Module mod_DFT_DISP_WDA + + +! ! ! +! ! ! Subroutine DISP_Weighted_Densities(rhop, rhop_wd, user) +! ! ! +! ! ! Use PetscManagement +! ! ! Use BASIC_VARIABLES, Only: ncomp +! ! ! Use mod_DFT, Only: fa_disp,ab_disp,zp,dzp +! ! ! Implicit None +! ! ! +! ! ! #include +! ! ! +! ! ! !passed +! ! ! Type (userctx) :: user +! ! ! PetscScalar :: rhop(ncomp,user%gxs:user%gxe) +! ! ! REAL, INTENT(OUT) :: rhop_wd(user%gxs:user%gxe,ncomp) +! ! ! +! ! ! +! ! ! !local +! ! ! INTEGER :: i,j,k +! ! ! INTEGER :: n +! ! ! INTEGER, parameter :: NMAX = 800 +! ! ! REAL :: x_int(NMAX),y_int(NMAX),y2(NMAX) !Fehlermeldung einbauen, falls dim > 400!! +! ! ! REAL :: zmin,dz,zz +! ! ! REAL :: xlo,xhi,int1 +! ! ! INTEGER :: fa_disp_max +! ! ! +! ! ! +! ! ! +! ! ! zmin = 1d-6 +! ! ! fa_disp_max = maxval(fa_disp(1:ncomp)) +! ! ! +! ! ! Do k = 1,ncomp +! ! ! +! ! ! Do i = user%xs - fa_disp_max , user%xe + fa_disp_max +! ! ! n = 1 +! ! ! x_int = 0.0 +! ! ! y_int = 0.0 +! ! ! +! ! ! Do j = i-fa_disp(k),i+fa_disp(k) +! ! ! +! ! ! If( ( zp(i)-zp(j+1) ) < ab_disp(k) .and. ( zp(i) - zp(j) ) >= ab_disp(k) ) Then !the position of j+1 is already within i-d/2 while j is still outside this range in this case, the integration steplength (dz) is just the distance, which j+1 overlaps with i-d/2 and what is integrated is the interpolated value of the integrand +! ! ! +! ! ! If(n/= 1) stop 'n /=1 in DISP_Weighted_Densities' !here always n=1! +! ! ! zz = zp(j) - zp(i) !distance between grid points j and i +! ! ! dz = zp(j+1) - (zp(i) - ab_disp(k)) !the part of the intervall between zp(j) and zp(j+1) which is already within i-d/2 +! ! ! !if(dz < epsilon(dz)) dz = epsilon(dz) !bei unguenstiger Kombination von sig und ngrid kann dz unter Machinengenauigkeit epsilon liegen, dann ist x(2) = x(1) + dz = x(1) -> das fuehrt zu Abbruch in Spline Interpolation +! ! ! x_int(n) = 0.0 !array containing x-values for spline integration +! ! ! y_int(n) = 0.0 +! ! ! +! ! ! +! ! ! Else If (zp(j) > (zp(i)-ab_disp(k)) .and. zp(j) <= (zp(i)+ab_disp(k))) Then !grid point j within i+-d2 +! ! ! +! ! ! n = n + 1 +! ! ! x_int(n) = x_int(n-1) + dz !first time in this If condition, dz is stil the old value from above! +! ! ! zz = zp(j) - zp(i) +! ! ! dz = dzp +! ! ! y_int(n) = rhop(k,j) * (ab_disp(k)*ab_disp(k) - zz*zz ) +! ! ! +! ! ! +! ! ! If (zp(j) < (zp(i)+ab_disp(k)) .and. zp(j+1) >= (zp(i)+ab_disp(k)) ) Then !zp(j) is still within zp(i)+d2 but zp(j+1) is already outside zp(i)+d2 +! ! ! dz = zp(i) + ab_disp(k) - zp(j) +! ! ! !If(dz <= epsilon(dz)) exit !wie oben, kann auch hier bei ungluecklicher Wahl von sig und ngrid dz < eps werden und somit x(n) = x(n-1) -> Abbruch in Spline interpolation. Dann einfach ngrid aendern! +! ! ! zz = zp(j) - zp(i) +! ! ! n = n + 1 +! ! ! x_int(n) = x_int(n-1) + dz +! ! ! y_int(n) = 0.0 +! ! ! +! ! ! +! ! ! End If +! ! ! End If +! ! ! End Do +! ! ! +! ! ! +! ! ! xlo = x_int(1) +! ! ! xhi = x_int(n) +! ! ! +! ! ! If(n > NMAX) stop 'Increase NMAX in DISP_Weighted_Densities (auch in AD Routine!!)' +! ! ! +! ! ! write(*,*)'n',n +! ! ! pause +! ! ! write(*,*)'rx',x_int(1:n) +! ! ! pause +! ! ! write(*,*)'ry',y_int(1:n) +! ! ! pause +! ! ! +! ! ! +! ! ! +! ! ! CALL spline( x_int(1:n), y_int(1:n), n, 1.E30, 1.E30, y2(1:n) ) +! ! ! CALL splint_integral ( x_int(1:n), y_int(1:n), y2(1:n), n, xlo, xhi, int1 ) +! ! ! rhop_wd(i,k) = 0.75 * int1 / ab_disp(k)**3 +! ! ! +! ! ! if ( rhop_wd(i,k) < 0.0 ) then +! ! ! rhop_wd(i,k) = 0.0 +! ! ! do j = 2, n +! ! ! rhop_wd(i,k) = rhop_wd(i,k) + (y_int(j)+y_int(j-1))/2.0 *(x_int(j)-x_int(j-1)) +! ! ! end do +! ! ! end if +! ! ! if ( rhop_wd(i,k) < 0.0 ) rhop_wd(i,k) = rhop(k,i) +! ! ! +! ! ! End Do +! ! ! End Do +! ! ! +! ! ! +! ! ! End Subroutine DISP_Weighted_Densities +! ! ! +! ! ! +! ! ! +! ! ! Subroutine DISP_mu(rhop_wd,f_disp,my_disp,df_disp_drk,user) +! ! ! +! ! ! Use PetscManagement +! ! ! Use PARAMETERS, Only: PI +! ! ! Use EOS_CONSTANTS, Only: ap,bp +! ! ! Use BASIC_VARIABLES, Only: ncomp,t,parame +! ! ! Use EOS_VARIABLES, Only: dhs,sig_ij,uij +! ! ! Use mod_DFT, Only: fa_disp +! ! ! Implicit None +! ! ! +! ! ! #include +! ! ! +! ! ! !passed +! ! ! Type (userctx) :: user +! ! ! REAL, INTENT(IN) :: rhop_wd(user%gxs:user%gxe,ncomp) +! ! ! REAL, INTENT(OUT) :: my_disp(user%gxs:user%gxe,ncomp) !chemPot_disp / kT +! ! ! REAL, INTENT(OUT) :: f_disp(user%gxs:user%gxe) !F_disp / NkT +! ! ! REAL, INTENT(OUT) :: df_disp_drk(user%gxs:user%gxe,ncomp) ! d(F/NkT) / drho_k = (mu/kT - F_disp / NkT)/rho +! ! ! +! ! ! ! ! !local +! ! ! ! ! INTEGER :: k,ii,kk,m +! ! ! ! ! REAL :: m_mean, m_rk(ncomp) +! ! ! ! ! REAL :: apar(0:6),bpar(0:6) +! ! ! ! ! REAL :: ap_rk(ncomp,0:6),bp_rk(ncomp,0:6) +! ! ! ! ! REAL :: xi(ncomp),z3 +! ! ! ! ! REAL :: I1,I2,I1_rk,I2_rk +! ! ! ! ! REAL :: order1,order2,ord1_rk,ord2_rk +! ! ! ! ! REAL :: c1_con,c2_con, c1_rk,rho2 +! ! ! ! ! REAL :: rhop_wd_sum, eta_disp, eta_rk, zms +! ! ! ! ! INTEGER :: fa_disp_max +! ! ! ! ! +! ! ! ! ! +! ! ! ! ! fa_disp_max = maxval(fa_disp(1:ncomp)) +! ! ! ! ! +! ! ! ! ! Do k = 1,ncomp +! ! ! ! ! Do ii = user%xs-fa_disp_max,user%xe+fa_disp_max +! ! ! ! ! +! ! ! ! ! rhop_wd_sum = SUM(rhop_wd(ii,1:ncomp)) +! ! ! ! ! +! ! ! ! ! m_mean = 0.0 +! ! ! ! ! eta_disp = 0.0 +! ! ! ! ! Do kk = 1,ncomp +! ! ! ! ! xi(kk) = rhop_wd(ii,kk) / rhop_wd_sum +! ! ! ! ! m_mean = m_mean + xi(kk)*parame(kk,1) +! ! ! ! ! eta_disp = eta_disp + rhop_wd(ii,kk)*parame(kk,1)*dhs(kk)**3 +! ! ! ! ! End Do +! ! ! ! ! +! ! ! ! ! eta_disp = eta_disp * PI / 6.0 +! ! ! ! ! eta_rk = parame(k,1) * dhs(k)**3 * PI / 6.0 +! ! ! ! ! +! ! ! ! ! m_rk(k) = ( parame(k,1) - m_mean ) / rhop_wd_sum +! ! ! ! ! +! ! ! ! ! +! ! ! ! ! DO m = 0, 6 +! ! ! ! ! apar(m) = ap(m,1) + (1.0-1.0/m_mean)*ap(m,2) & +! ! ! ! ! + (1.0-1.0/m_mean)*(1.0-2.0/m_mean)*ap(m,3) +! ! ! ! ! bpar(m) = bp(m,1) + (1.0-1.0/m_mean)*bp(m,2) & +! ! ! ! ! + (1.0-1.0/m_mean)*(1.0-2.0/m_mean)*bp(m,3) +! ! ! ! ! +! ! ! ! ! ! --- derivatives of apar, bpar to rho_k --------------------------- +! ! ! ! ! ap_rk(k,m) = m_rk(k)/m_mean**2 * ( ap(m,2) + (3.0 -4.0/m_mean) *ap(m,3) ) +! ! ! ! ! bp_rk(k,m) = m_rk(k)/m_mean**2 * ( bp(m,2) + (3.0 -4.0/m_mean) *bp(m,3) ) +! ! ! ! ! END DO +! ! ! ! ! +! ! ! ! ! +! ! ! ! ! I1 = 0.0 +! ! ! ! ! I2 = 0.0 +! ! ! ! ! I1_rk = 0.0 +! ! ! ! ! I2_rk = 0.0 +! ! ! ! ! DO m = 0, 6 +! ! ! ! ! I1 = I1 + apar(m)*eta_disp**REAL(m) +! ! ! ! ! I2 = I2 + bpar(m)*eta_disp**REAL(m) +! ! ! ! ! I1_rk = I1_rk + apar(m)*REAL(m)*eta_disp**REAL(m-1)*eta_rk + ap_rk(k,m)*eta_disp**REAL(m) +! ! ! ! ! I2_rk = I2_rk + bpar(m)*REAL(m)*eta_disp**REAL(m-1)*eta_rk + bp_rk(k,m)*eta_disp**REAL(m) +! ! ! ! ! END DO +! ! ! ! ! +! ! ! ! ! +! ! ! ! ! ord1_rk = 0.0 +! ! ! ! ! ord2_rk = 0.0 +! ! ! ! ! order1 = 0.0 +! ! ! ! ! order2 = 0.0 +! ! ! ! ! DO kk = 1,ncomp +! ! ! ! ! !sig_ij(kk,k) = 0.5 * ( dhs(kk) + dhs(k) ) +! ! ! ! ! !uij(kk,k) = (1.0 - kij(kk,k)) * SQRT( eps(kk) * eps(k) ) +! ! ! ! ! order1 = order1 + xi(kk)*xi(k)* parame(kk,1)*parame(k,1)*sig_ij(kk,k)**3 * uij(kk,k)/t +! ! ! ! ! order2 = order2 + xi(kk)*xi(k)* parame(kk,1)*parame(k,1)*sig_ij(kk,k)**3 * (uij(kk,k)/t)**2 +! ! ! ! ! ord1_rk = ord1_rk + 2.0*parame(k,1)*rhop_wd_sum*xi(kk)*parame(kk,1)*sig_ij(kk,k)**3 *uij(kk,k)/t +! ! ! ! ! ord2_rk = ord2_rk + 2.0*parame(k,1)*rhop_wd_sum*xi(kk)*parame(kk,1)*sig_ij(kk,k)**3 *(uij(kk,k)/t)**2 +! ! ! ! ! END DO +! ! ! ! ! +! ! ! ! ! z3 = eta_disp +! ! ! ! ! zms = 1.0 - z3 +! ! ! ! ! +! ! ! ! ! c1_con= 1.0/ ( 1.0 + m_mean*(8.0*z3-2.0*z3*z3)/zms**4 & +! ! ! ! ! + (1.0 - m_mean)*(20.0*z3-27.0*z3*z3 +12.0*z3**3 -2.0*z3**4 ) & +! ! ! ! ! /(zms*(2.0-z3))**2 ) +! ! ! ! ! c2_con= - c1_con*c1_con *( m_mean*(-4.0*z3*z3+20.0*z3+8.0)/zms**5 & +! ! ! ! ! + (1.0 - m_mean) *(2.0*z3**3 +12.0*z3*z3-48.0*z3+40.0) & +! ! ! ! ! /(zms*(2.0-z3))**3 ) +! ! ! ! ! c1_rk= c2_con*eta_rk - c1_con*c1_con*m_rk(k) * ( (8.0*z3-2.0*z3*z3)/zms**4 & +! ! ! ! ! - (-2.0*z3**4 +12.0*z3**3 -27.0*z3*z3+20.0*z3) / (zms*(2.0-z3))**2 ) +! ! ! ! ! +! ! ! ! ! +! ! ! ! ! rho2 = rhop_wd_sum * rhop_wd_sum +! ! ! ! ! +! ! ! ! ! my_disp(ii,k) = -2.0*PI* ( order1*rho2*I1_rk + ord1_rk*I1 ) & +! ! ! ! ! - PI* c1_con*m_mean * ( order2*rho2*I2_rk + ord2_rk*I2 ) & +! ! ! ! ! - PI* ( c1_con*m_rk(k) + c1_rk*m_mean ) * order2*rho2*I2 +! ! ! ! ! +! ! ! ! ! f_disp(ii) = -2.0 * PI * rhop_wd_sum * I1 * order1 & !hier * rho_wd_sum, bei Elmar/rho_wd_sum, da in order1 bei Elmar mit rhoi, hier mit xi!! +! ! ! ! ! -PI * rhop_wd_sum * c1_con * m_mean * I2 * order2 +! ! ! ! ! +! ! ! ! ! df_disp_drk(ii,k) = ( my_disp(ii,k) - f_disp(ii) ) / rhop_wd_sum +! ! ! ! ! +! ! ! ! ! End Do +! ! ! ! ! +! ! ! ! ! End Do +! ! ! +! ! ! +! ! ! End Subroutine DISP_mu +! ! ! +! ! ! +! ! ! +! ! ! Subroutine DISP_dFdrho_wda(ii,rhop,rhop_wd,my_disp,f_disp,df_disp_drk,dF_drho_disp,user) +! ! ! +! ! ! Use PetscManagement +! ! ! +! ! ! Use BASIC_VARIABLES, Only: ncomp +! ! ! Use mod_DFT, Only: zp,dzp,fa_disp,ab_disp +! ! ! +! ! ! Implicit None +! ! ! #include +! ! ! +! ! ! !passed +! ! ! INTEGER, INTENT(IN) :: ii +! ! ! Type (userctx) :: user +! ! ! PetscScalar :: rhop(ncomp,user%gxs:user%gxe) +! ! ! REAL, INTENT(IN) :: rhop_wd(user%gxs:user%gxe,ncomp) +! ! ! REAL, INTENT(IN) :: my_disp(user%gxs:user%gxe,ncomp) !chemPot_disp / kT +! ! ! REAL, INTENT(IN) :: f_disp(user%gxs:user%gxe) !F_disp / NkT +! ! ! REAL, INTENT(IN) :: df_disp_drk(user%gxs:user%gxe,ncomp) ! d(F/NkT) / drho_k = (mu/kT - F_disp / NkT)/rho +! ! ! REAL, INTENT(OUT) :: dF_drho_disp(ncomp) +! ! ! +! ! ! ! ! !local +! ! ! ! ! INTEGER :: n,icomp,jj +! ! ! ! ! REAL :: zmin,zz,dz +! ! ! ! ! INTEGER, parameter :: NMAX = 800 +! ! ! ! ! REAL :: x_int(NMAX), y_int(NMAX), y2(NMAX) +! ! ! ! ! REAL :: xhi,xlo,int2 +! ! ! ! ! REAL :: rhop_sum +! ! ! ! ! +! ! ! ! ! zmin = 1d-6 +! ! ! ! ! DO icomp = 1, ncomp +! ! ! ! ! n = 1 +! ! ! ! ! x_int = 0.0 +! ! ! ! ! y_int = 0.0 +! ! ! ! ! +! ! ! ! ! DO jj = (ii-fa_disp(icomp)), (ii+fa_disp(icomp)) +! ! ! ! ! +! ! ! ! ! !IF ( zp(jj+1) > (zl+zmin) ) THEN +! ! ! ! ! If( ( zp(ii)-zp(jj+1) ) < ab_disp(icomp) .and. ( zp(ii) - zp(jj) ) >= ab_disp(icomp) ) Then !the position of j+1 is already within i-d/2 while j is still outside this range in this case, the integration steplength (dz) is just the distance, which j+1 overlaps with i-d/2 and what is integrated is the interpolated value of the integrand +! ! ! ! ! +! ! ! ! ! If(n/= 1) stop 'n /=1 in DISP_Weighted_Densities' !here always n=1! +! ! ! ! ! zz = zp(jj) - zp(ii) !distance between grid points j and i +! ! ! ! ! dz = zp(jj+1) - (zp(ii) - ab_disp(icomp)) !the part of the intervall between zp(j) and zp(j+1) which is already within i-d/2 +! ! ! ! ! !if(dz < epsilon(dz)) dz = epsilon(dz) !bei unguenstiger Kombination von sig und ngrid kann dz unter Machinengenauigkeit epsilon liegen, dann ist x(2) = x(1) + dz = x(1) -> das fuehrt zu Abbruch in Spline Interpolation +! ! ! ! ! x_int(n) = 0.0 !array containing x-values for spline integration +! ! ! ! ! y_int(n) = 0.0 +! ! ! ! ! +! ! ! ! ! Else If (zp(jj) > (zp(ii)-ab_disp(icomp)) .and. zp(jj) <= (zp(ii)+ab_disp(icomp))) Then !grid point j within i+-d2 +! ! ! ! ! +! ! ! ! ! n = n + 1 +! ! ! ! ! x_int(n) = x_int(n-1) + dz !first time in this If condition, dz is stil the old value from above! +! ! ! ! ! zz = zp(jj) - zp(ii) +! ! ! ! ! dz = dzp +! ! ! ! ! y_int(n) = my_disp(jj,icomp) * (ab_disp(icomp)*ab_disp(icomp) - zz*zz ) +! ! ! ! ! +! ! ! ! ! !rhop_sum = sum(rhop(1:ncomp,jj)) +! ! ! ! ! !y_int(n) = rhop_sum * df_disp_drk(jj,icomp) * (ab_disp(icomp)*ab_disp(icomp) - zz*zz) +! ! ! ! ! +! ! ! ! ! If (zp(jj) < (zp(ii)+ab_disp(icomp)) .and. zp(jj+1) >= (zp(ii)+ab_disp(icomp)) ) Then !zp(j) is still within zp(i)+d2 but zp(j+1) is already outside zp(i)+d2 +! ! ! ! ! dz = zp(ii) + ab_disp(icomp) - zp(jj) +! ! ! ! ! !If(dz <= epsilon(dz)) exit !wie oben, kann auch hier bei ungluecklicher Wahl von sig und ngrid dz < eps werden und somit x(n) = x(n-1) -> Abbruch in Spline interpolation. Dann einfach ngrid aendern! +! ! ! ! ! zz = zp(jj) - zp(ii) +! ! ! ! ! n = n + 1 +! ! ! ! ! x_int(n) = x_int(n-1) + dz +! ! ! ! ! y_int(n) = 0.0 +! ! ! ! ! +! ! ! ! ! End If +! ! ! ! ! End If +! ! ! ! ! END DO +! ! ! ! ! xlo = x_int(1) +! ! ! ! ! xhi = x_int(n) +! ! ! ! ! +! ! ! ! ! If(n > NMAX) stop 'Increase NMAX in DISP_dFdrho_wda (auch in AD Routine!!)' +! ! ! ! ! +! ! ! ! ! CALL spline ( x_int(1:n), y_int(1:n), n, 1.E30, 1.E30, y2(1:n) ) +! ! ! ! ! CALL splint_integral( x_int(1:n), y_int(1:n), y2(1:n), n, xlo, xhi, int2 ) +! ! ! ! ! +! ! ! ! ! dF_drho_disp(icomp) = int2 * 0.75 / ab_disp(icomp)**3 +! ! ! ! ! !dF_drho_disp(icomp) = int2 * 0.75 / ab_disp(icomp)**3 + f_disp(ii) +! ! ! ! ! END DO +! ! ! ! ! +! ! ! +! ! ! End Subroutine DISP_dFdrho_wda +! ! ! + diff --git a/applications/PUfoam/MoDeNaModels/SurfaceTension/ExampleOfUsage/src/srcDetailedCode/mod_DFT_DISP_WDA_d.F90 b/applications/PUfoam/MoDeNaModels/SurfaceTension/ExampleOfUsage/src/srcDetailedCode/mod_DFT_DISP_WDA_d.F90 new file mode 100644 index 000000000..e943abde0 --- /dev/null +++ b/applications/PUfoam/MoDeNaModels/SurfaceTension/ExampleOfUsage/src/srcDetailedCode/mod_DFT_DISP_WDA_d.F90 @@ -0,0 +1,505 @@ +! Generated by TAPENADE (INRIA, Tropics team) +! Tapenade 3.10 (r5498) - 20 Jan 2015 09:48 +! +MODULE MOD_DFT_DISP_WDA_D + IMPLICIT NONE + PRIVATE + PUBLIC disp_weighted_densities_d + PUBLIC disp_mu_d + PUBLIC disp_dfdrho_wda_d + + CONTAINS + + ! Differentiation of disp_weighted_densities in forward (tangent) mode: +! variations of useful results: rhop_wd +! with respect to varying inputs: rhop + SUBROUTINE DISP_WEIGHTED_DENSITIES_D(rhop, rhopd, rhop_wd, rhop_wdd, & +& user) + Use PetscManagement + USE BASIC_VARIABLES, ONLY : ncomp + USE MOD_DFT, ONLY : fa_disp, ab_disp, zp, dzp + IMPLICIT NONE + +#include + +!passed +Type (userctx) :: user +PetscScalar :: rhop(ncomp,user%gxs:user%gxe) +PetscScalar :: rhopd(ncomp,user%gxs:user%gxe) +REAL, INTENT(OUT) :: rhop_wd(user%gxs:user%gxe,ncomp) +REAL, INTENT(OUT) :: rhop_wdd(user%gxs:user%gxe,ncomp) + + +! ! !local +! ! INTEGER :: i, j, k +! ! INTEGER :: n +! ! !Fehlermeldung einbauen, falls dim > 400!! +! ! REAL :: x_int(400), y_int(400), y2(400) +! ! REAL :: y_intd(400), y2d(400) +! ! REAL :: zmin, dz, zz +! ! REAL :: xlo, xhi, int1 +! ! REAL :: int1d +! ! INTEGER :: fa_disp_max +! ! INTRINSIC MAXVAL +! ! zmin = 1d-6 +! ! fa_disp_max = MAXVAL(fa_disp(1:ncomp)) +! ! rhop_wdd = 0.0 +! ! y2d = 0.0 +! ! DO k=1,ncomp +! ! Do i = user%xs - fa_disp_max , user%xe + fa_disp_max +! ! n = 1 +! ! x_int = 0.0 +! ! y_int = 0.0 +! ! y_intd = 0.0 +! ! DO j=i-fa_disp(k),i+fa_disp(k) +! ! IF (zp(i) - zp(j+1) .LT. ab_disp(k) .AND. zp(i) - zp(j) .GE. & +! ! & ab_disp(k)) THEN +! ! !the position of j+1 is already within i-d/2 while j is still outside this range in this case, the integration steplength (dz) is +! ! ! just the distance, which j+1 overlaps with i-d/2 and what is integrated is the interpolated value of the integrand +! ! !here always n=1! +! ! IF (n .NE. 1) THEN +! ! GOTO 100 +! ! ELSE +! ! !distance between grid points j and i +! ! zz = zp(j) - zp(i) +! ! !the part of the intervall between zp(j) and zp(j+1) which is already within i-d/2 +! ! dz = zp(j+1) - (zp(i)-ab_disp(k)) +! ! !if(dz < epsilon(dz)) dz = epsilon(dz) !bei unguenstiger Kombination von sig und ngrid kann dz unter Machinengenauigkeit epsilon +! ! !liegen, dann ist x(2) = x(1) + dz = x(1) -> das fuehrt zu Abbruch in Spline Interpolation +! ! !array containing x-values for spline integration +! ! x_int(n) = 0.0 +! ! y_intd(n) = 0.0 +! ! y_int(n) = 0.0 +! ! END IF +! ! ELSE IF (zp(j) .GT. zp(i) - ab_disp(k) .AND. zp(j) .LE. zp(i) & +! ! & + ab_disp(k)) THEN +! ! !grid point j within i+-d2 +! ! n = n + 1 +! ! !first time in this If condition, dz is stil the old value from above! +! ! x_int(n) = x_int(n-1) + dz +! ! zz = zp(j) - zp(i) +! ! dz = dzp +! ! y_intd(n) = (ab_disp(k)*ab_disp(k)-zz*zz)*rhopd(k, j) +! ! y_int(n) = rhop(k, j)*(ab_disp(k)*ab_disp(k)-zz*zz) +! ! IF (zp(j) .LT. zp(i) + ab_disp(k) .AND. zp(j+1) .GE. zp(i) +& +! ! & ab_disp(k)) THEN +! ! !zp(j) is still within zp(i)+d2 but zp(j+1) is already outside zp(i)+d2 +! ! dz = zp(i) + ab_disp(k) - zp(j) +! ! !If(dz <= epsilon(dz)) exit !wie oben, kann auch hier bei ungluecklicher Wahl von sig und ngrid dz < eps werden und somit x(n) +! ! != x(n-1) -> Abbruch in Spline interpolation. Dann einfach ngrid aendern! +! ! zz = zp(j) - zp(i) +! ! n = n + 1 +! ! x_int(n) = x_int(n-1) + dz +! ! y_intd(n) = 0.0 +! ! y_int(n) = 0.0 +! ! END IF +! ! END IF +! ! END DO +! ! xlo = x_int(1) +! ! xhi = x_int(n) +! ! CALL SPLINE_D(x_int(1:n), y_int(1:n), y_intd(1:n), n, 1.e30, & +! ! & 1.e30, y2(1:n), y2d(1:n)) +! ! CALL SPLINT_INTEGRAL_D(x_int(1:n), y_int(1:n), y_intd(1:n), y2(1& +! ! & :n), y2d(1:n), n, xlo, xhi, int1, int1d) +! ! rhop_wdd(i, k) = 0.75*int1d/ab_disp(k)**3 +! ! rhop_wd(i, k) = 0.75*int1/ab_disp(k)**3 +! ! IF (rhop_wd(i, k) .LT. 0.0) THEN +! ! rhop_wdd(i, k) = 0.0 +! ! rhop_wd(i, k) = 0.0 +! ! DO j=2,n +! ! rhop_wdd(i, k) = rhop_wdd(i, k) + (x_int(j)-x_int(j-1))*(& +! ! & y_intd(j)+y_intd(j-1))/2.0 +! ! rhop_wd(i, k) = rhop_wd(i, k) + (y_int(j)+y_int(j-1))/2.0*(& +! ! & x_int(j)-x_int(j-1)) +! ! END DO +! ! END IF +! ! IF (rhop_wd(i, k) .LT. 0.0) THEN +! ! rhop_wdd(i, k) = rhopd(k, i) +! ! rhop_wd(i, k) = rhop(k, i) +! ! END IF +! ! END DO +! ! END DO +! ! GOTO 110 +! ! 100 STOP +! ! 110 CONTINUE + END SUBROUTINE DISP_WEIGHTED_DENSITIES_D + + + +! Differentiation of disp_mu in forward (tangent) mode: +! variations of useful results: my_disp +! with respect to varying inputs: rhop_wd + SUBROUTINE DISP_MU_D(rhop_wd, rhop_wdd, f_disp, my_disp, my_dispd, & +& df_disp_drk, user) + + Use PetscManagement + USE PARAMETERS, ONLY : pi + USE EOS_CONSTANTS, ONLY : ap, bp + USE BASIC_VARIABLES, ONLY : ncomp, t, parame + USE EOS_VARIABLES, Only: dhs, sig_ij, uij + USE MOD_DFT, ONLY : fa_disp + IMPLICIT NONE +#include + +!passed +Type (userctx) :: user +REAL, INTENT(IN) :: rhop_wd(user%gxs:user%gxe,ncomp) +REAL, INTENT(IN) :: rhop_wdd(user%gxs:user%gxe,ncomp) +REAL, INTENT(OUT) :: my_disp(user%gxs:user%gxe,ncomp) !chemPot_disp / kT +REAL, INTENT(OUT) :: my_dispd(user%gxs:user%gxe,ncomp) !chemPot_disp / kT +REAL, INTENT(OUT) :: f_disp(user%gxs:user%gxe) !F_disp / NkT +REAL, INTENT(OUT) :: df_disp_drk(user%gxs:user%gxe,ncomp) ! d(F/NkT) / drho_k = (mu/kT - F_disp / NkT)/rho + +! ! !local +! ! INTEGER :: k, ii, kk, m +! ! REAL :: m_mean, m_rk(ncomp) +! ! REAL :: m_meand, m_rkd(ncomp) +! ! REAL :: apar(0:6), bpar(0:6) +! ! REAL :: apard(0:6), bpard(0:6) +! ! REAL :: ap_rk(ncomp, 0:6), bp_rk(ncomp, 0:6) +! ! REAL :: ap_rkd(ncomp, 0:6), bp_rkd(ncomp, 0:6) +! ! REAL :: xi(ncomp), z3 +! ! REAL :: xid(ncomp), z3d +! ! REAL :: i1, i2, i1_rk, i2_rk +! ! REAL :: i1d, i2d, i1_rkd, i2_rkd +! ! REAL :: order1, order2, ord1_rk, ord2_rk +! ! REAL :: order1d, order2d, ord1_rkd, ord2_rkd +! ! REAL :: c1_con, c2_con, c1_rk, rho2 +! ! REAL :: c1_cond, c2_cond, c1_rkd, rho2d +! ! REAL :: rhop_wd_sum, eta_disp, eta_rk, zms +! ! REAL :: rhop_wd_sumd, eta_dispd, zmsd +! ! INTEGER :: fa_disp_max +! ! INTRINSIC MAXVAL +! ! INTRINSIC SUM +! ! INTRINSIC REAL +! ! REAL :: pwy1 +! ! REAL :: pwr1 +! ! REAL :: pwr1d +! ! REAL :: pwy2 +! ! REAL :: pwr2 +! ! REAL :: pwr2d +! ! fa_disp_max = MAXVAL(fa_disp(1:ncomp)) +! ! my_dispd = 0.0 +! ! xid = 0.0 +! ! m_rkd = 0.0 +! ! ap_rkd = 0.0 +! ! bpard = 0.0 +! ! apard = 0.0 +! ! bp_rkd = 0.0 +! ! DO k=1,ncomp +! ! Do ii = user%xs-fa_disp_max,user%xe+fa_disp_max +! ! rhop_wd_sumd = SUM(rhop_wdd(ii, 1:ncomp)) +! ! rhop_wd_sum = SUM(rhop_wd(ii, 1:ncomp)) +! ! m_mean = 0.0 +! ! eta_disp = 0.0 +! ! eta_dispd = 0.0 +! ! m_meand = 0.0 +! ! DO kk=1,ncomp +! ! xid(kk) = (rhop_wdd(ii, kk)*rhop_wd_sum-rhop_wd(ii, kk)*& +! ! & rhop_wd_sumd)/rhop_wd_sum**2 +! ! xi(kk) = rhop_wd(ii, kk)/rhop_wd_sum +! ! m_meand = m_meand + parame(kk,1)*xid(kk) +! ! m_mean = m_mean + xi(kk)*parame(kk,1) +! ! eta_dispd = eta_dispd + parame(kk,1)*dhs(kk)**3*rhop_wdd(ii, kk) +! ! eta_disp = eta_disp + rhop_wd(ii, kk)*parame(kk,1)*dhs(kk)**3 +! ! END DO +! ! eta_dispd = pi*eta_dispd/6.0 +! ! eta_disp = eta_disp*pi/6.0 +! ! eta_rk = parame(k,1)*dhs(k)**3*pi/6.0 +! ! m_rkd(k) = (-(m_meand*rhop_wd_sum)-(parame(k,1)-m_mean)*rhop_wd_sumd& +! ! & )/rhop_wd_sum**2 +! ! m_rk(k) = (parame(k,1)-m_mean)/rhop_wd_sum +! ! DO m=0,6 +! ! apard(m) = ap(m, 2)*m_meand/m_mean**2 + ap(m, 3)*(m_meand*(1.0& +! ! & -2.0/m_mean)/m_mean**2+(1.0-1.0/m_mean)*2.0*m_meand/m_mean**& +! ! & 2) +! ! apar(m) = ap(m, 1) + (1.0-1.0/m_mean)*ap(m, 2) + (1.0-1.0/& +! ! & m_mean)*(1.0-2.0/m_mean)*ap(m, 3) +! ! bpard(m) = bp(m, 2)*m_meand/m_mean**2 + bp(m, 3)*(m_meand*(1.0& +! ! & -2.0/m_mean)/m_mean**2+(1.0-1.0/m_mean)*2.0*m_meand/m_mean**& +! ! & 2) +! ! bpar(m) = bp(m, 1) + (1.0-1.0/m_mean)*bp(m, 2) + (1.0-1.0/& +! ! & m_mean)*(1.0-2.0/m_mean)*bp(m, 3) +! ! ! --- derivatives of apar, bpar to rho_k --------------------------- +! ! ap_rkd(k, m) = (m_rkd(k)*m_mean**2-m_rk(k)*2*m_mean*m_meand)*(& +! ! & ap(m, 2)+(3.0-4.0/m_mean)*ap(m, 3))/m_mean**4 + m_rk(k)*ap(m& +! ! & , 3)*4.0*m_meand/m_mean**4 +! ! ap_rk(k, m) = m_rk(k)/m_mean**2*(ap(m, 2)+(3.0-4.0/m_mean)*ap(& +! ! & m, 3)) +! ! bp_rkd(k, m) = (m_rkd(k)*m_mean**2-m_rk(k)*2*m_mean*m_meand)*(& +! ! & bp(m, 2)+(3.0-4.0/m_mean)*bp(m, 3))/m_mean**4 + m_rk(k)*bp(m& +! ! & , 3)*4.0*m_meand/m_mean**4 +! ! bp_rk(k, m) = m_rk(k)/m_mean**2*(bp(m, 2)+(3.0-4.0/m_mean)*bp(& +! ! & m, 3)) +! ! END DO +! ! i1 = 0.0 +! ! i2 = 0.0 +! ! i1_rk = 0.0 +! ! i2_rk = 0.0 +! ! i1_rkd = 0.0 +! ! i1d = 0.0 +! ! i2d = 0.0 +! ! i2_rkd = 0.0 +! ! DO m=0,6 +! ! pwy1 = REAL(m) +! ! IF (eta_disp .GT. 0.0 .OR. (eta_disp .LT. 0.0 .AND. pwy1 .EQ. & +! ! & INT(pwy1))) THEN +! ! pwr1d = pwy1*eta_disp**(pwy1-1)*eta_dispd +! ! ELSE IF (eta_disp .EQ. 0.0 .AND. pwy1 .EQ. 1.0) THEN +! ! pwr1d = eta_dispd +! ! ELSE +! ! pwr1d = 0.0 +! ! END IF +! ! pwr1 = eta_disp**pwy1 +! ! i1d = i1d + apard(m)*pwr1 + apar(m)*pwr1d +! ! i1 = i1 + apar(m)*pwr1 +! ! pwy1 = REAL(m) +! ! IF (eta_disp .GT. 0.0 .OR. (eta_disp .LT. 0.0 .AND. pwy1 .EQ. & +! ! & INT(pwy1))) THEN +! ! pwr1d = pwy1*eta_disp**(pwy1-1)*eta_dispd +! ! ELSE IF (eta_disp .EQ. 0.0 .AND. pwy1 .EQ. 1.0) THEN +! ! pwr1d = eta_dispd +! ! ELSE +! ! pwr1d = 0.0 +! ! END IF +! ! pwr1 = eta_disp**pwy1 +! ! i2d = i2d + bpard(m)*pwr1 + bpar(m)*pwr1d +! ! i2 = i2 + bpar(m)*pwr1 +! ! pwy1 = REAL(m - 1) +! ! IF (eta_disp .GT. 0.0 .OR. (eta_disp .LT. 0.0 .AND. pwy1 .EQ. & +! ! & INT(pwy1))) THEN +! ! pwr1d = pwy1*eta_disp**(pwy1-1)*eta_dispd +! ! ELSE IF (eta_disp .EQ. 0.0 .AND. pwy1 .EQ. 1.0) THEN +! ! pwr1d = eta_dispd +! ! ELSE +! ! pwr1d = 0.0 +! ! END IF +! ! pwr1 = eta_disp**pwy1 +! ! pwy2 = REAL(m) +! ! IF (eta_disp .GT. 0.0 .OR. (eta_disp .LT. 0.0 .AND. pwy2 .EQ. & +! ! & INT(pwy2))) THEN +! ! pwr2d = pwy2*eta_disp**(pwy2-1)*eta_dispd +! ! ELSE IF (eta_disp .EQ. 0.0 .AND. pwy2 .EQ. 1.0) THEN +! ! pwr2d = eta_dispd +! ! ELSE +! ! pwr2d = 0.0 +! ! END IF +! ! pwr2 = eta_disp**pwy2 +! ! i1_rkd = i1_rkd + REAL(m)*eta_rk*(apard(m)*pwr1+apar(m)*pwr1d)& +! ! & + ap_rkd(k, m)*pwr2 + ap_rk(k, m)*pwr2d +! ! i1_rk = i1_rk + apar(m)*REAL(m)*pwr1*eta_rk + ap_rk(k, m)*pwr2 +! ! pwy1 = REAL(m - 1) +! ! IF (eta_disp .GT. 0.0 .OR. (eta_disp .LT. 0.0 .AND. pwy1 .EQ. & +! ! & INT(pwy1))) THEN +! ! pwr1d = pwy1*eta_disp**(pwy1-1)*eta_dispd +! ! ELSE IF (eta_disp .EQ. 0.0 .AND. pwy1 .EQ. 1.0) THEN +! ! pwr1d = eta_dispd +! ! ELSE +! ! pwr1d = 0.0 +! ! END IF +! ! pwr1 = eta_disp**pwy1 +! ! pwy2 = REAL(m) +! ! IF (eta_disp .GT. 0.0 .OR. (eta_disp .LT. 0.0 .AND. pwy2 .EQ. & +! ! & INT(pwy2))) THEN +! ! pwr2d = pwy2*eta_disp**(pwy2-1)*eta_dispd +! ! ELSE IF (eta_disp .EQ. 0.0 .AND. pwy2 .EQ. 1.0) THEN +! ! pwr2d = eta_dispd +! ! ELSE +! ! pwr2d = 0.0 +! ! END IF +! ! pwr2 = eta_disp**pwy2 +! ! i2_rkd = i2_rkd + REAL(m)*eta_rk*(bpard(m)*pwr1+bpar(m)*pwr1d)& +! ! & + bp_rkd(k, m)*pwr2 + bp_rk(k, m)*pwr2d +! ! i2_rk = i2_rk + bpar(m)*REAL(m)*pwr1*eta_rk + bp_rk(k, m)*pwr2 +! ! END DO +! ! ord1_rk = 0.0 +! ! ord2_rk = 0.0 +! ! order1 = 0.0 +! ! order2 = 0.0 +! ! order1d = 0.0 +! ! order2d = 0.0 +! ! ord2_rkd = 0.0 +! ! ord1_rkd = 0.0 +! ! DO kk=1,ncomp +! ! !sig_ij(kk,k) = 0.5 * ( dhs(kk) + dhs(k) ) +! ! !uij(kk,k) = (1.0 - kij(kk,k)) * SQRT( eps(kk) * eps(k) ) +! ! order1d = order1d + parame(kk,1)*parame(k,1)*sig_ij(kk, k)**3*uij(kk, & +! ! & k)*(xid(kk)*xi(k)+xi(kk)*xid(k))/t +! ! order1 = order1 + xi(kk)*xi(k)*parame(kk,1)*parame(k,1)*sig_ij(kk, k)& +! ! & **3*uij(kk, k)/t +! ! order2d = order2d + parame(kk,1)*parame(k,1)*sig_ij(kk, k)**3*uij(kk, & +! ! & k)**2*(xid(kk)*xi(k)+xi(kk)*xid(k))/t**2 +! ! order2 = order2 + xi(kk)*xi(k)*parame(kk,1)*parame(k,1)*sig_ij(kk, k)& +! ! & **3*(uij(kk, k)/t)**2 +! ! ord1_rkd = ord1_rkd + 2.0*parame(k,1)*parame(kk,1)*sig_ij(kk, k)**3*& +! ! & uij(kk, k)*(rhop_wd_sumd*xi(kk)+rhop_wd_sum*xid(kk))/t +! ! ord1_rk = ord1_rk + 2.0*parame(k,1)*rhop_wd_sum*xi(kk)*parame(kk,1)*& +! ! & sig_ij(kk, k)**3*uij(kk, k)/t +! ! ord2_rkd = ord2_rkd + 2.0*parame(k,1)*parame(kk,1)*sig_ij(kk, k)**3*& +! ! & uij(kk, k)**2*(rhop_wd_sumd*xi(kk)+rhop_wd_sum*xid(kk))/t**2 +! ! ord2_rk = ord2_rk + 2.0*parame(k,1)*rhop_wd_sum*xi(kk)*parame(kk,1)*& +! ! & sig_ij(kk, k)**3*(uij(kk, k)/t)**2 +! ! END DO +! ! z3d = eta_dispd +! ! z3 = eta_disp +! ! zmsd = -z3d +! ! zms = 1.0 - z3 +! ! c1_cond = -((((m_meand*(8.0*z3-2.0*z3*z3)+m_mean*(8.0*z3d-2.0*(& +! ! & z3d*z3+z3*z3d)))*zms**4-m_mean*(8.0*z3-2.0*z3*z3)*4*zms**3*& +! ! & zmsd)/(zms**4)**2+(((1.0-m_mean)*(20.0*z3d-27.0*(z3d*z3+z3*z3d& +! ! & )+12.0*3*z3**2*z3d-2.0*4*z3**3*z3d)-m_meand*(20.0*z3-27.0*z3*& +! ! & z3+12.0*z3**3-2.0*z3**4))*zms**2*(2.0-z3)**2-(1.0-m_mean)*(& +! ! & 20.0*z3-27.0*z3*z3+12.0*z3**3-2.0*z3**4)*2*zms*(2.0-z3)*(zmsd*& +! ! & (2.0-z3)-zms*z3d))/((zms*(2.0-z3))**2)**2)/(1.0+m_mean*(8.0*z3& +! ! & -2.0*z3*z3)/zms**4+(1.0-m_mean)*(20.0*z3-27.0*z3*z3+12.0*z3**3& +! ! & -2.0*z3**4)/(zms*(2.0-z3))**2)**2) +! ! c1_con = 1.0/(1.0+m_mean*(8.0*z3-2.0*z3*z3)/zms**4+(1.0-m_mean)*& +! ! & (20.0*z3-27.0*z3*z3+12.0*z3**3-2.0*z3**4)/(zms*(2.0-z3))**2) +! ! c2_cond = -((c1_cond*c1_con+c1_con*c1_cond)*(m_mean*(-(4.0*z3*z3& +! ! & )+20.0*z3+8.0)/zms**5+(1.0-m_mean)*(2.0*z3**3+12.0*z3*z3-48.0*& +! ! & z3+40.0)/(zms*(2.0-z3))**3)+c1_con**2*(((m_meand*(-(4.0*z3*z3)& +! ! & +20.0*z3+8.0)+m_mean*(20.0*z3d-4.0*(z3d*z3+z3*z3d)))*zms**5-& +! ! & m_mean*(-(4.0*z3*z3)+20.0*z3+8.0)*5*zms**4*zmsd)/(zms**5)**2+(& +! ! & ((1.0-m_mean)*(2.0*3*z3**2*z3d+12.0*(z3d*z3+z3*z3d)-48.0*z3d)-& +! ! & m_meand*(2.0*z3**3+12.0*z3*z3-48.0*z3+40.0))*zms**3*(2.0-z3)**& +! ! & 3-(1.0-m_mean)*(2.0*z3**3+12.0*z3*z3-48.0*z3+40.0)*3*zms**2*(& +! ! & 2.0-z3)**2*(zmsd*(2.0-z3)-zms*z3d))/((zms*(2.0-z3))**3)**2)) +! ! c2_con = -(c1_con*c1_con*(m_mean*(-(4.0*z3*z3)+20.0*z3+8.0)/zms& +! ! & **5+(1.0-m_mean)*(2.0*z3**3+12.0*z3*z3-48.0*z3+40.0)/(zms*(2.0& +! ! & -z3))**3)) +! ! c1_rkd = eta_rk*c2_cond - ((c1_cond*c1_con+c1_con*c1_cond)*m_rk(& +! ! & k)+c1_con**2*m_rkd(k))*((8.0*z3-2.0*z3*z3)/zms**4-(-(2.0*z3**4& +! ! & )+12.0*z3**3-27.0*z3*z3+20.0*z3)/(zms*(2.0-z3))**2) - c1_con**& +! ! & 2*m_rk(k)*(((8.0*z3d-2.0*(z3d*z3+z3*z3d))*zms**4-(8.0*z3-2.0*& +! ! & z3*z3)*4*zms**3*zmsd)/(zms**4)**2-((12.0*3*z3**2*z3d-2.0*4*z3& +! ! & **3*z3d-27.0*(z3d*z3+z3*z3d)+20.0*z3d)*zms**2*(2.0-z3)**2-(-(& +! ! & 2.0*z3**4)+12.0*z3**3-27.0*z3*z3+20.0*z3)*2*zms*(2.0-z3)*(zmsd& +! ! & *(2.0-z3)-zms*z3d))/((zms*(2.0-z3))**2)**2) +! ! c1_rk = c2_con*eta_rk - c1_con*c1_con*m_rk(k)*((8.0*z3-2.0*z3*z3& +! ! & )/zms**4-(-(2.0*z3**4)+12.0*z3**3-27.0*z3*z3+20.0*z3)/(zms*(& +! ! & 2.0-z3))**2) +! ! rho2d = rhop_wd_sumd*rhop_wd_sum + rhop_wd_sum*rhop_wd_sumd +! ! rho2 = rhop_wd_sum*rhop_wd_sum +! ! my_dispd(ii, k) = -(2.0*pi*((order1d*rho2+order1*rho2d)*i1_rk+& +! ! & order1*rho2*i1_rkd+ord1_rkd*i1+ord1_rk*i1d)) - pi*((c1_cond*& +! ! & m_mean+c1_con*m_meand)*(order2*rho2*i2_rk+ord2_rk*i2)+c1_con*& +! ! & m_mean*((order2d*rho2+order2*rho2d)*i2_rk+order2*rho2*i2_rkd+& +! ! & ord2_rkd*i2+ord2_rk*i2d)) - pi*((c1_cond*m_rk(k)+c1_con*m_rkd(& +! ! & k)+c1_rkd*m_mean+c1_rk*m_meand)*order2*rho2*i2+(c1_con*m_rk(k)& +! ! & +c1_rk*m_mean)*((order2d*rho2+order2*rho2d)*i2+order2*rho2*i2d& +! ! & )) +! ! my_disp(ii, k) = -(2.0*pi*(order1*rho2*i1_rk+ord1_rk*i1)) - pi*& +! ! & c1_con*m_mean*(order2*rho2*i2_rk+ord2_rk*i2) - pi*(c1_con*m_rk& +! ! & (k)+c1_rk*m_mean)*order2*rho2*i2 +! ! f_disp(ii) = -(2.0*pi*rhop_wd_sum*i1*order1) - pi*rhop_wd_sum*& +! ! & c1_con*m_mean*i2*order2 +! ! df_disp_drk(ii, k) = (my_disp(ii, k)-f_disp(ii))/rhop_wd_sum +! ! END DO +! ! END DO + END SUBROUTINE DISP_MU_D + + + +! Differentiation of disp_dfdrho_wda in forward (tangent) mode: +! variations of useful results: df_drho_disp +! with respect to varying inputs: my_disp df_drho_disp + SUBROUTINE DISP_DFDRHO_WDA_D(ii, rhop, rhop_wd, my_disp, my_dispd, & +& f_disp, df_disp_drk, df_drho_disp, df_drho_dispd, user) + + Use PetscManagement + USE BASIC_VARIABLES, ONLY : ncomp + USE MOD_DFT, ONLY : zp, dzp, fa_disp, ab_disp + IMPLICIT NONE +#include + +!passed +INTEGER, INTENT(IN) :: ii +Type (userctx) :: user +PetscScalar :: rhop(ncomp,user%gxs:user%gxe) +REAL, INTENT(IN) :: rhop_wd(user%gxs:user%gxe,ncomp) +REAL, INTENT(IN) :: my_disp(user%gxs:user%gxe,ncomp) !chemPot_disp / kT +REAL, INTENT(IN) :: my_dispd(user%gxs:user%gxe,ncomp) !chemPot_disp / kT +REAL, INTENT(IN) :: f_disp(user%gxs:user%gxe) !F_disp / NkT +REAL, INTENT(IN) :: df_disp_drk(user%gxs:user%gxe,ncomp) ! d(F/NkT) / drho_k = (mu/kT - F_disp / NkT)/rho +REAL, INTENT(OUT) :: dF_drho_disp(ncomp) +REAL, INTENT(OUT) :: dF_drho_dispd(ncomp) + +! ! !local +! ! INTEGER :: n, icomp, jj +! ! REAL :: zmin, zz, dz +! ! REAL :: x_int(400), y_int(400), y2(400) +! ! REAL :: y_intd(400), y2d(400) +! ! REAL :: xhi, xlo, int2 +! ! REAL :: int2d +! ! REAL :: rhop_sum +! ! zmin = 1d-6 +! ! y2d = 0.0 +! ! DO icomp=1,ncomp +! ! n = 1 +! ! x_int = 0.0 +! ! y_int = 0.0 +! ! y_intd = 0.0 +! ! DO jj=ii-fa_disp(icomp),ii+fa_disp(icomp) +! ! !IF ( zp(jj+1) > (zl+zmin) ) THEN +! ! IF (zp(ii) - zp(jj+1) .LT. ab_disp(icomp) .AND. zp(ii) - zp(jj) & +! ! & .GE. ab_disp(icomp)) THEN +! ! !the position of j+1 is already within i-d/2 while j is still outside this range in this case, the integration steplength (dz) is +! ! ! just the distance, which j+1 overlaps with i-d/2 and what is integrated is the interpolated value of the integrand +! ! !here always n=1! +! ! IF (n .NE. 1) THEN +! ! GOTO 100 +! ! ELSE +! ! !distance between grid points j and i +! ! zz = zp(jj) - zp(ii) +! ! !the part of the intervall between zp(j) and zp(j+1) which is already within i-d/2 +! ! dz = zp(jj+1) - (zp(ii)-ab_disp(icomp)) +! ! !if(dz < epsilon(dz)) dz = epsilon(dz) !bei unguenstiger Kombination von sig und ngrid kann dz unter Machinengenauigkeit epsilon +! ! !liegen, dann ist x(2) = x(1) + dz = x(1) -> das fuehrt zu Abbruch in Spline Interpolation +! ! !array containing x-values for spline integration +! ! x_int(n) = 0.0 +! ! y_intd(n) = 0.0 +! ! y_int(n) = 0.0 +! ! END IF +! ! ELSE IF (zp(jj) .GT. zp(ii) - ab_disp(icomp) .AND. zp(jj) .LE. & +! ! & zp(ii) + ab_disp(icomp)) THEN +! ! !grid point j within i+-d2 +! ! n = n + 1 +! ! !first time in this If condition, dz is stil the old value from above! +! ! x_int(n) = x_int(n-1) + dz +! ! zz = zp(jj) - zp(ii) +! ! dz = dzp +! ! y_intd(n) = (ab_disp(icomp)*ab_disp(icomp)-zz*zz)*my_dispd(jj& +! ! & , icomp) +! ! y_int(n) = my_disp(jj, icomp)*(ab_disp(icomp)*ab_disp(icomp)-& +! ! & zz*zz) +! ! !rhop_sum = sum(rhop(1:ncomp,jj)) +! ! !y_int(n) = rhop_sum * df_disp_drk(jj,icomp) * (ab_disp(icomp)*ab_disp(icomp) - zz*zz) +! ! IF (zp(jj) .LT. zp(ii) + ab_disp(icomp) .AND. zp(jj+1) .GE. zp& +! ! & (ii) + ab_disp(icomp)) THEN +! ! !zp(j) is still within zp(i)+d2 but zp(j+1) is already outside zp(i)+d2 +! ! dz = zp(ii) + ab_disp(icomp) - zp(jj) +! ! !If(dz <= epsilon(dz)) exit !wie oben, kann auch hier bei ungluecklicher Wahl von sig und ngrid dz < eps werden und somit x(n) +! ! != x(n-1) -> Abbruch in Spline interpolation. Dann einfach ngrid aendern! +! ! zz = zp(jj) - zp(ii) +! ! n = n + 1 +! ! x_int(n) = x_int(n-1) + dz +! ! y_intd(n) = 0.0 +! ! y_int(n) = 0.0 +! ! END IF +! ! END IF +! ! END DO +! ! xlo = x_int(1) +! ! xhi = x_int(n) +! ! CALL SPLINE_D(x_int(1:n), y_int(1:n), y_intd(1:n), n, 1.e30, 1.e30& +! ! & , y2(1:n), y2d(1:n)) +! ! CALL SPLINT_INTEGRAL_D(x_int(1:n), y_int(1:n), y_intd(1:n), y2(1:n& +! ! & ), y2d(1:n), n, xlo, xhi, int2, int2d) +! ! df_drho_dispd(icomp) = 0.75*int2d/ab_disp(icomp)**3 +! ! df_drho_disp(icomp) = int2*0.75/ab_disp(icomp)**3 +! ! END DO +! ! GOTO 110 +! ! 100 STOP +! ! 110 CONTINUE + END SUBROUTINE DISP_DFDRHO_WDA_D + +END MODULE MOD_DFT_DISP_WDA_D diff --git a/applications/PUfoam/MoDeNaModels/SurfaceTension/ExampleOfUsage/src/srcDetailedCode/mod_DFT_FMT.F90 b/applications/PUfoam/MoDeNaModels/SurfaceTension/ExampleOfUsage/src/srcDetailedCode/mod_DFT_FMT.F90 new file mode 100644 index 000000000..6629cb83c --- /dev/null +++ b/applications/PUfoam/MoDeNaModels/SurfaceTension/ExampleOfUsage/src/srcDetailedCode/mod_DFT_FMT.F90 @@ -0,0 +1,346 @@ + + +!All equations are taken from the appendix of: +!Gross: 'A density functional theory for vapor-liquid interfaces using the PCP-SAFT eos' +!But: here we dont treat chain-molecules!! -> no multiplications with segment number + + + +Module mod_DFT_FMT + +Implicit None + +Private + +Public :: FMT_Weighted_Densities +Public :: FMT_dFdrho + + Contains + + + + + +Subroutine FMT_Weighted_Densities(rhop,n0,n1,n2,n3,nv1,nv2,phi_dn0,phi_dn1,phi_dn2,phi_dn3,phi_dnv1,phi_dnv2,user) + +Use PARAMETERS, ONLY: PI +Use BASIC_VARIABLES, Only: ncomp,parame +Use EOS_VARIABLES, Only: dhs +Use mod_DFT, Only: zp,dzp,fa + +!PETSc module +Use PetscManagement + +#include + +!passed +Type (userctx) :: user +PetscScalar :: rhop(ncomp,user%gxs:user%gxe) +REAL,dimension(user%gxs:user%gxe),Intent(OUT) :: n0,n1,n2,n3,nv1,nv2 !ngp muss groesser als fa+fa/2 sein!! +REAL,dimension(user%gxs:user%gxe),Intent(OUT) :: phi_dn0,phi_dn1,phi_dn2,phi_dn3,phi_dnv1,phi_dnv2 + +!local +Integer :: k,i,j +Integer :: fa2 +REAL :: dz,d2,zz +INTEGER :: n +INTEGER, parameter :: NMAX = 800 +REAL,dimension(NMAX) :: x_int,n2_int,n3_int,nv2_int !Fehlerwarnung falls 200 ueberschritten einbauen +REAL,dimension(NMAX) :: y2_n2, y2_n3,y2_nv2 +REAL :: int_n2,int_n3,int_nv2,xhi,xlo +REAL :: zms,zms2,zms3,logzms +REAL :: nn0,nn1,nn2,nn3,nnv1,nnv2 +REAL :: rhopjk, rhopjp1k + + + n0 = 0.0 + n1 = 0.0 + n2 = 0.0 + n3 = 0.0 + nv1 = 0.0 + nv2 = 0.0 + + fa2 = maxval(fa(1:ncomp) + 5) / 2 + +Do k=1,ncomp + !fa2 = (fa(k) + 5) / 2 !grid points in sig/2 + d2 = dhs(k) / 2.0 !half of dhs [A] + + + Do i=user%xs-fa2,user%xe+fa2 !to evaluate dF/drho at any point, the derivatives dphi/dn have to be evaluated at +-d/2 around this point + n = 1 !this is the index of the arrays that will be passed to the spline integration routines + x_int = 0.0 + n2_int = 0.0 + n3_int = 0.0 + nv2_int = 0.0 + + Do j=i-fa2,i+fa2 !to evaluate dphi/dn at a given point, the weighted densities are needed at +-d/2 around this point + + rhopjk = rhop(k,j) * parame(k,1) + rhopjp1k = rhop(k,j+1) * parame(k,1) + + If( ( zp(i)-zp(j+1) ) < d2 .and. ( zp(i) - zp(j) ) >= d2 ) Then !the position of j+1 is already within i-d/2 while j is still outside this range in this case, the integration steplength (dz) is just the distance, which j+1 overlaps with i-d/2 and what is integrated is the interpolated value of the integrand + + If(n/= 1) stop 'n /=1 in FMT_Weighted_Densities' !here always n=1! + zz = zp(j) - zp(i) !distance between grid points j and i + dz = zp(j+1) - (zp(i) - d2) !the part of the intervall between zp(j) and zp(j+1) which is already within i-d/2 + !if(dz < epsilon(dz)) dz = epsilon(dz) !bei unguenstiger Kombination von sig und ngrid kann dz unter Machinengenauigkeit epsilon liegen, dann ist x(2) = x(1) + dz = x(1) -> das fuehrt zu Abbruch in Spline Interpolation + x_int(n) = 0.0 !array containing x-values for spline integration + n2_int(n) = rhopjk + (rhopjp1k-rhopjk) / (dzp) * (dzp-dz) !integrand f�r n2 (=rhop) linear interpoliert f�r den Punk zp(i)-d/2 + n3_int(n) = 0.0 !integrand f�r n3: rhop*(d2**2 - z'**2), da hier gerade z' = d2 -> integrand wird hier = 0!! + nv2_int(n) = rhopjk*zz +(rhopjp1k*(zp(j+1)-zp(i))-rhopjk*zz)/(dzp)*(dzp-dz) !analog + + + Else If (zp(j) > (zp(i)-d2) .and. zp(j) <= (zp(i)+d2)) Then !grid point j within i+-d2 + + n = n + 1 + x_int(n) = x_int(n-1) + dz !first time in this If condition, dz is stil the old value from above! + zz = zp(j) - zp(i) + dz = dzp + n2_int(n) = rhopjk + n3_int(n) = rhopjk * (d2**2 - zz**2) + nv2_int(n) = rhopjk * zz + + If (zp(j) < (zp(i)+d2) .and. zp(j+1) >= (zp(i)+d2) ) Then !zp(j) is still within zp(i)+d2 but zp(j+1) is already outside zp(i)+d2 + + dz = zp(i) + d2 - zp(j) + !If(dz <= epsilon(dz)) exit !wie oben, kann auch hier bei ungluecklicher Wahl von sig und ngrid dz < eps werden und somit x(n) = x(n-1) -> Abbruch in Spline interpolation. Dann einfach ngrid aendern! + zz = zp(j) - zp(i) + n = n + 1 + x_int(n) = x_int(n-1) + dz +! If(x_int(n) == x_int(n-1)) Then +! n = n - 1 +! exit +! End If + n2_int(n) = rhopjk + (rhopjp1k-rhopjk) / (dzp) * dz + n3_int(n) = 0.0 !Begr�ndung wie oben + nv2_int(n) = rhopjk*zz + (rhopjp1k*(zp(j+1)-zp(i)) - rhopjk*zz) / (dzp) * dz + + End If + + End If + + + End Do + + !spline integration + xlo = x_int(1) + xhi = x_int(n) + + If(n > NMAX) stop 'Increase NMAX in FMT_Weighted_Densities (auch in AD Routine!!)' + + call spline ( x_int, n2_int, n, 1.E30, 1.E30, y2_n2 ) + call spline ( x_int, n3_int, n, 1.E30, 1.E30, y2_n3 ) + call spline ( x_int, nv2_int, n, 1.E30, 1.E30, y2_nv2 ) + + call splint_integral ( x_int, n2_int, y2_n2, n, xlo, xhi, int_n2 ) + call splint_integral ( x_int, n3_int, y2_n3, n, xlo, xhi, int_n3 ) + call splint_integral ( x_int, nv2_int, y2_nv2, n, xlo, xhi, int_nv2 ) + + !weighted densities + n2(i) = n2(i) + PI * dhs(k) * int_n2 + n1(i) = n1(i) + 0.5 * int_n2 + n0(i) = n0(i) + int_n2/dhs(k) + n3(i) = n3(i) + PI * int_n3 + nv2(i) = nv2(i) -2.0 * PI * int_nv2 + nv1(i) = nv1(i) -int_nv2 / dhs(k) + +! If(i < 5) Then +! write(*,*)'i dens',i,nv2(i),n1(i),n0(i) +! write(*,*)'i dens',i,n3(i),nv1(i),nv2(i) +! end if +! +! If(i > 95) then +! write(*,*)'i dens',i,nv2(i),n1(i),n0(i) +! write(*,*)'i dens',i,n3(i),nv1(i),nv2(i) +! End If +! + End Do + + ! pause + +End Do + + +!derivatives of FMT helmholtz energy density w.r.t. weighted densities +Do i=user%xs-maxval((fa(1:ncomp)+1)/2),user%xe+maxval((fa(1:ncomp)+1)/2) + !weils k�rzer ist + nn0 = n0(i) + nn1 = n1(i) + nn2 = n2(i) + nn3 = n3(i) + nnv1 = nv1(i) + nnv2 = nv2(i) + + zms = 1.0 - nn3 + zms2 = zms*zms + zms3 = zms2*zms + logzms = log(zms) + if(isnan(logzms)) stop 'zms < 0, log(zms) undefined FMT_Weighted_Densities' + + phi_dn0(i) = -logzms + phi_dn1(i) = nn2/zms + phi_dn2(i) = nn1/zms + 3.0*(nn2*nn2-nnv2*nnv2) * (nn3+zms2*logzms) / (36.0*PI*nn3*nn3*zms2) + + phi_dn3(i) = nn0/zms + (nn1*nn2-nnv1*nnv2)/zms2 - (nn2**3-3.0*nn2*nnv2*nnv2) * (nn3*(nn3**2-5.0*nn3+2.0)+2.0*zms3*logzms) & + / (36.0*PI*nn3**3*zms3) + + phi_dnv1(i) = -nnv2/zms + + phi_dnv2(i) = -nnv1/zms - 6.0*nn2*nnv2*(nn3+zms2*logzms)/(36.0*PI*nn3**2*zms2) + +End Do + +End Subroutine FMT_Weighted_Densities + + + + + + + +Subroutine FMT_dFdrho(i,fa,user,phi_dn0,phi_dn1,phi_dn2,phi_dn3,phi_dnv1,phi_dnv2,dF_drho_FMT) + +Use BASIC_VARIABLES, Only: ncomp,parame +Use EOS_VARIABLES, Only: dhs +Use mod_DFT, Only: zp,dzp +Use PARAMETERS, ONLY: PI + +!PETSc module +Use PetscManagement + +!passed +INTEGER, INTENT(IN) :: i !the grid point at which to calculate dFdrho +INTEGER, INTENT(IN) :: fa(ncomp) +Type (userctx) :: user +REAL,dimension(user%gxs:user%gxe),INTENT(IN) :: phi_dn0,phi_dn1,phi_dn2,phi_dn3,phi_dnv1,phi_dnv2 +REAL,dimension(user%xs:user%xe,ncomp), INTENT(OUT) :: dF_drho_FMT + + +!local +INTEGER :: j,k,n +INTEGER :: fa2 +REAL :: dz,d2,zz, zz_jp1 +INTEGER, parameter :: NMAX = 800 +REAL,dimension(NMAX) :: x_int,y_int,y0_int,y1_int,y2_int,y3_int,yv1_int,yv2_int,y2 +REAL :: xhi,xlo,integral,int0,int1,int2,int3,intv1,intv2 +REAL :: at_j, at_jp1 + + +!Das Integral (Gleichung A1 in Gross DFT 2009) wird hier in einem Schlag berechnet! +!Falls die einzelnen Terme einzeln integriert werden sollen, einfach die auskommentierte Version verwenden + +Do k=1,ncomp !das einzige, das hier von k abhaengt, sind fa und dhs!! die Ableitungen phi_dn... sind nicht Komponentenspez, da die + !gewichteten Dichten ja uch nicht mehr Komponentenspez sind (n_i = sum n_i(k)) + + n = 1 + fa2 = ( fa(k) + 5 ) / 2 !number of grid points within dhs/2 + d2 = dhs(k)/2.0 + + Do j = i-fa2,i+fa2 + + If( ( zp(i)-zp(j+1) ) < d2 .and. ( zp(i) - zp(j) ) >= d2 ) Then !the position of j+1 is already within i-d/2 while j is still outside this range in this case, the integration steplength (dz) is just the distance, which j+1 overlaps with i-d/2 and what is integrated is the interpolated value of the integrand + x_int(n) = 0.0 + If(n/=1) stop 'error in FMT_dFdrho, n should be 1 here!' + dz = zp(j+1) - (zp(i) - d2) + zz = zp(j) - zp(i) + zz_jp1 = zp(j+1) - zp(i) + at_j = phi_dn0(j)/dhs(k) + 0.5*phi_dn1(j) + PI*dhs(k)*phi_dn2(j) & + + PI*phi_dn3(j)*(d2**2 - zz**2) + phi_dnv1(j)*zz/dhs(k) + 2.0*PI*phi_dnv2(j)*zz + + at_jp1 = phi_dn0(j+1)/dhs(k) + 0.5*phi_dn1(j+1) + PI*dhs(k)*phi_dn2(j+1) & + + PI*phi_dn3(j+1)*(d2**2 - zz_jp1**2) + phi_dnv1(j+1)*zz_jp1/dhs(k) + 2.0*PI*phi_dnv2(j+1)*zz_jp1 + + y_int(n) = at_j + (at_jp1-at_j)/dzp * (dzp-dz) !lineare interpolation genau, wie in FMT_Weighted_Densities +! y0_int(n) = phi_dn0(j) + (phi_dn0(j+1) -phi_dn0(j))/dzp * (dzp-dz) +! y1_int(n) = phi_dn1(j) + (phi_dn1(j+1) -phi_dn1(j))/dzp * (dzp-dz) +! y2_int(n) = phi_dn2(j) + (phi_dn2(j+1) -phi_dn2(j))/dzp * (dzp-dz) +! y3_int(n) = phi_dn3(j)*(d2**2-zz**2) + (phi_dn3(j+1)*(d2**2-zz_jp1**2) - phi_dn3(j)*(d2**2-zz**2) )/dzp * (dzp-dz) +! yv1_int(n) = phi_dnv1(j)*zz + (phi_dnv1(j+1)*zz_jp1 - phi_dnv1(j)*zz)/dzp * (dzp-dz) +! yv2_int(n) = phi_dnv2(j)*zz + (phi_dnv2(j+1)*zz_jp1 - phi_dnv2(j)*zz)/dzp * (dzp-dz) +! + + Else If (zp(j) > (zp(i)-d2) .and. zp(j) <= (zp(i)+d2)) Then !grid points j and j+1 are completely within i+-d2 + + n = n + 1 + zz = zp(j) - zp(i) + x_int(n) = x_int(n-1) + dz + + + y_int(n) = phi_dn0(j)/dhs(k) + 0.5*phi_dn1(j) + PI*dhs(k)*phi_dn2(j) & + + PI*phi_dn3(j)*(d2**2 - zz**2) + phi_dnv1(j)*zz/dhs(k) + 2.0*PI*phi_dnv2(j)*zz + + +! y0_int(n) = phi_dn0(j) +! y1_int(n) = phi_dn1(j) +! y2_int(n) = phi_dn2(j) +! y3_int(n) = phi_dn3(j)*(d2**2-zz**2) +! yv1_int(n) = phi_dnv1(j)*zz +! yv2_int(n) = phi_dnv2(j)*zz +! + + dz = dzp + + If (zp(j) < (zp(i)+d2) .and. zp(j+1) > (zp(i)+d2) ) Then !zp(j) is still within zp(i)+d2 but zp(j+1) is already out side zp(i)+d2 + + n = n + 1 + zz = zp(j) - zp(i) + zz_jp1 = zp(j+1) - zp(i) + dz = zp(i) + d2 - zp(j) + x_int(n) = x_int(n-1) + dz + at_j = phi_dn0(j)/dhs(k) + 0.5*phi_dn1(j) + PI*dhs(k)*phi_dn2(j) & + + PI*phi_dn3(j)*(d2**2 - zz**2) + phi_dnv1(j)*zz/dhs(k) + 2.0*PI*phi_dnv2(j)*zz + at_jp1 = phi_dn0(j+1)/dhs(k) + 0.5*phi_dn1(j+1) + PI*dhs(k)*phi_dn2(j+1) & + + PI*phi_dn3(j+1)*(d2**2 - zz_jp1**2) + phi_dnv1(j+1)*zz_jp1/dhs(k) + 2.0*PI*phi_dnv2(j+1)*zz_jp1 + y_int(n) = at_j + (at_jp1-at_j)/dzp * dz + + +! y0_int(n) = phi_dn0(j) + (phi_dn0(j+1) - phi_dn0(j))/dzp * dz +! y1_int(n) = phi_dn1(j) + (phi_dn1(j+1) - phi_dn1(j))/dzp * dz +! y2_int(n) = phi_dn2(j) + (phi_dn2(j+1) - phi_dn2(j))/dzp * dz +! y3_int(n) = phi_dn3(j)*(d2**2 - zz**2) + (phi_dn3(j+1)*(d2**2 - zz_jp1**2) - phi_dn3(j)*(d2**2 - zz**2))/dzp * dz +! yv1_int(n) = phi_dnv1(j)*zz + (phi_dnv1(j+1)*zz_jp1 - phi_dnv1(j)*zz)/dzp * dz +! yv2_int(n) = phi_dnv2(j)*zz + (phi_dnv2(j+1)*zz_jp1 - phi_dnv2(j)*zz)/dzp * dz +! + + + End If + + End If + + + End Do + + !spline integration + xlo = x_int(1) + xhi = x_int(n) + + If(n > NMAX) stop 'Increase NMAX in FMT_dFdrho (auch in AD Routine!!)' + + call spline(x_int,y_int,n,1.E30,1.E30,y2) + call splint_integral(x_int,y_int,y2,n,xlo,xhi,integral) + +! call spline ( x_int, y0_int, n, 1.E30, 1.E30, y2 ) +! call splint_integral ( x_int, y0_int, y2, n, xlo, xhi, int0 ) +! call spline ( x_int, y1_int, n, 1.E30, 1.E30, y2 ) +! call splint_integral ( x_int, y1_int, y2, n, xlo, xhi, int1 ) +! call spline ( x_int, y2_int, n, 1.E30, 1.E30, y2 ) +! call splint_integral ( x_int, y2_int, y2, n, xlo, xhi, int2 ) +! call spline ( x_int, y3_int, n, 1.E30, 1.E30, y2 ) +! call splint_integral ( x_int, y3_int, y2, n, xlo, xhi, int3 ) +! call spline ( x_int, yv1_int, n, 1.E30, 1.E30, y2 ) +! call splint_integral ( x_int, yv1_int, y2, n, xlo, xhi, intv1 ) +! call spline ( x_int, yv2_int, n, 1.E30, 1.E30, y2 ) +! call splint_integral ( x_int, yv2_int, y2, n, xlo, xhi, intv2 ) +! + + !dF_drho_FMT(i,k) = int0/dhs(k) + 0.5*int1 + PI*dhs(k)*int2 + PI*int3 + intv1/dhs(k) + 2.0*PI*intv2 + dF_drho_FMT(i,k) = integral*parame(k,1) + +End Do + + +End Subroutine FMT_dFdrho + + +End Module mod_DFT_FMT diff --git a/applications/PUfoam/MoDeNaModels/SurfaceTension/ExampleOfUsage/src/srcDetailedCode/mod_DFT_FMT_d.F90 b/applications/PUfoam/MoDeNaModels/SurfaceTension/ExampleOfUsage/src/srcDetailedCode/mod_DFT_FMT_d.F90 new file mode 100644 index 000000000..38d8ee77a --- /dev/null +++ b/applications/PUfoam/MoDeNaModels/SurfaceTension/ExampleOfUsage/src/srcDetailedCode/mod_DFT_FMT_d.F90 @@ -0,0 +1,457 @@ +! Generated by TAPENADE (INRIA, Tropics team) +! Tapenade 3.10 (r5498) - 20 Jan 2015 09:48 +! +!All equations are taken from the appendix of: +!Gross: 'A density functional theory for vapor-liquid interfaces using the PCP-SAFT eos' +!But: here we dont treat chain-molecules!! -> no multiplications with segment number +MODULE MOD_DFT_FMT_D + IMPLICIT NONE + PRIVATE + PUBLIC fmt_weighted_densities_d + PUBLIC fmt_dfdrho_d + +CONTAINS +! Differentiation of fmt_weighted_densities in forward (tangent) mode: +! variations of useful results: phi_dn0 phi_dn1 phi_dn2 phi_dnv1 +! phi_dn3 phi_dnv2 +! with respect to varying inputs: rhop + SUBROUTINE FMT_WEIGHTED_DENSITIES_D(rhop, rhopd, n0, n1, n2, n3, nv1, & +& nv2, phi_dn0, phi_dn0d, phi_dn1, phi_dn1d, phi_dn2, phi_dn2d, & +& phi_dn3, phi_dn3d, phi_dnv1, phi_dnv1d, phi_dnv2, phi_dnv2d, user) + USE PARAMETERS, ONLY : pi + USE BASIC_VARIABLES, ONLY : ncomp,parame + USE EOS_VARIABLES, Only: dhs + USE MOD_DFT, ONLY : zp, dzp, fa + + +!PETSc module +Use PetscManagement +IMPLICIT NONE + +#include + +!passed +Type (userctx) :: user +PetscScalar :: rhop(ncomp,user%gxs:user%gxe) +PetscScalar :: rhopd(ncomp,user%gxs:user%gxe) +REAL,dimension(user%gxs:user%gxe),Intent(OUT) :: n0,n1,n2,n3,nv1,nv2 !ngp muss groesser als fa+fa/2 sein!! +REAL,dimension(user%gxs:user%gxe),Intent(OUT) :: phi_dn0,phi_dn1,phi_dn2,phi_dn3,phi_dnv1,phi_dnv2 +REAL,dimension(user%gxs:user%gxe),Intent(OUT) :: phi_dn0d,phi_dn1d,phi_dn2d,phi_dn3d,phi_dnv1d,phi_dnv2d + + + + +!local + REAL, DIMENSION(user%gxs:user%gxe) :: n0d,n1d,n2d,n3d,nv1d,nv2d + INTEGER :: k, i, j + INTEGER :: fa2 + REAL :: dz, d2, zz + INTEGER :: n + INTEGER, parameter :: NMAX = 800 + REAL, DIMENSION(NMAX) :: x_int, n2_int, n3_int, nv2_int + REAL, DIMENSION(NMAX) :: n2_intd, n3_intd, nv2_intd + REAL, DIMENSION(NMAX) :: y2_n2, y2_n3, y2_nv2 + REAL, DIMENSION(NMAX) :: y2_n2d, y2_n3d, y2_nv2d + REAL :: int_n2, int_n3, int_nv2, xhi, xlo + REAL :: int_n2d, int_n3d, int_nv2d + REAL :: zms, zms2, zms3, logzms + REAL :: zmsd, zms2d, zms3d, logzmsd + REAL :: nn0, nn1, nn2, nn3, nnv1, nnv2 + REAL :: nn0d, nn1d, nn2d, nn3d, nnv1d, nnv2d + REAL :: rhopjk, rhopjp1k + REAL :: rhopjkd, rhopjp1kd + INTRINSIC MAXVAL + INTRINSIC LOG + REAL :: result1 + + + + n0 = 0.0 + n1 = 0.0 + n2 = 0.0 + n3 = 0.0 + nv1 = 0.0 + nv2 = 0.0 + result1 = MAXVAL(fa(1:ncomp) + 5) + fa2 = result1/2 + nv1d = 0.0 + nv2d = 0.0 + n0d = 0.0 + n1d = 0.0 + n2d = 0.0 + n3d = 0.0 + y2_n2d = 0.0 + y2_n3d = 0.0 + y2_nv2d = 0.0 + DO k=1,ncomp +!fa2 = (fa(k) + 5) / 2 !grid points in sig/2 +!half of dhs [A] + d2 = dhs(k)/2.0 + + + + + Do i=user%xs-fa2,user%xe+fa2 !to evaluate dF/drho at any point, the derivatives dphi/dn have to be evaluated at +-d/2 around this point + + n = 1 + x_int = 0.0 + n2_int = 0.0 + n3_int = 0.0 + nv2_int = 0.0 + n2_intd = 0.0 + nv2_intd = 0.0 + n3_intd = 0.0 +!to evaluate dphi/dn at a given point, the weighted densities are needed at +-d/2 around this point + DO j=i-fa2,i+fa2 + rhopjkd = parame(k,1)*rhopd(k, j) + rhopjk = rhop(k, j)*parame(k,1) + rhopjp1kd = parame(k,1)*rhopd(k, j+1) + rhopjp1k = rhop(k, j+1)*parame(k,1) + IF (zp(i) - zp(j+1) .LT. d2 .AND. zp(i) - zp(j) .GE. d2) THEN +!the position of j+1 is already within i-d/2 while j is still outside this range in this case, the integration steplength (dz) is +! just the distance, which j+1 overlaps with i-d/2 and what is integrated is the interpolated value of the integrand +!here always n=1! + IF (n .NE. 1) THEN + GOTO 100 + ELSE +!distance between grid points j and i + zz = zp(j) - zp(i) +!the part of the intervall between zp(j) and zp(j+1) which is already within i-d/2 + dz = zp(j+1) - (zp(i)-d2) +!if(dz < epsilon(dz)) dz = epsilon(dz) !bei unguenstiger Kombination von sig und ngrid kann dz unter Machinengenauigkeit epsilon +!liegen, dann ist x(2) = x(1) + dz = x(1) -> das fuehrt zu Abbruch in Spline Interpolation +!array containing x-values for spline integration + x_int(n) = 0.0 +!integrand f�r n2 (=rhop) linear interpoliert f�r den Punk zp(i)-d/2 + n2_intd(n) = rhopjkd + (dzp-dz)*(rhopjp1kd-rhopjkd)/dzp + n2_int(n) = rhopjk + (rhopjp1k-rhopjk)/dzp*(dzp-dz) +!integrand f�r n3: rhop*(d2**2 - z'**2), da hier gerade z' = d2 -> integrand wird hier = 0!! + n3_intd(n) = 0.0 + n3_int(n) = 0.0 +!analog + nv2_intd(n) = zz*rhopjkd + (dzp-dz)*((zp(j+1)-zp(i))*& +& rhopjp1kd-zz*rhopjkd)/dzp + nv2_int(n) = rhopjk*zz + (rhopjp1k*(zp(j+1)-zp(i))-rhopjk*& +& zz)/dzp*(dzp-dz) + END IF + ELSE IF (zp(j) .GT. zp(i) - d2 .AND. zp(j) .LE. zp(i) + d2) & +& THEN +!grid point j within i+-d2 + n = n + 1 +!first time in this If condition, dz is stil the old value from above! + x_int(n) = x_int(n-1) + dz + zz = zp(j) - zp(i) + dz = dzp + n2_intd(n) = rhopjkd + n2_int(n) = rhopjk + n3_intd(n) = (d2**2-zz**2)*rhopjkd + n3_int(n) = rhopjk*(d2**2-zz**2) + nv2_intd(n) = zz*rhopjkd + nv2_int(n) = rhopjk*zz + IF (zp(j) .LT. zp(i) + d2 .AND. zp(j+1) .GE. zp(i) + d2) & +& THEN +!zp(j) is still within zp(i)+d2 but zp(j+1) is already outside zp(i)+d2 + dz = zp(i) + d2 - zp(j) +!If(dz <= epsilon(dz)) exit !wie oben, kann auch hier bei ungluecklicher Wahl von sig und ngrid dz < eps werden und somit x(n) +!= x(n-1) -> Abbruch in Spline interpolation. Dann einfach ngrid aendern! + zz = zp(j) - zp(i) + n = n + 1 + x_int(n) = x_int(n-1) + dz +! If(x_int(n) == x_int(n-1)) Then +! n = n - 1 +! exit +! End If + n2_intd(n) = rhopjkd + dz*(rhopjp1kd-rhopjkd)/dzp + n2_int(n) = rhopjk + (rhopjp1k-rhopjk)/dzp*dz +!Begr�ndung wie oben + n3_intd(n) = 0.0 + n3_int(n) = 0.0 + nv2_intd(n) = zz*rhopjkd + dz*((zp(j+1)-zp(i))*rhopjp1kd-& +& zz*rhopjkd)/dzp + nv2_int(n) = rhopjk*zz + (rhopjp1k*(zp(j+1)-zp(i))-rhopjk*& +& zz)/dzp*dz + END IF + END IF + END DO +!spline integration + xlo = x_int(1) + xhi = x_int(n) + CALL SPLINE_D(x_int, n2_int, n2_intd, n, 1.e30, 1.e30, y2_n2, & +& y2_n2d) + CALL SPLINE_D(x_int, n3_int, n3_intd, n, 1.e30, 1.e30, y2_n3, & +& y2_n3d) + CALL SPLINE_D(x_int, nv2_int, nv2_intd, n, 1.e30, 1.e30, y2_nv2& +& , y2_nv2d) + CALL SPLINT_INTEGRAL_D(x_int, n2_int, n2_intd, y2_n2, y2_n2d, n& +& , xlo, xhi, int_n2, int_n2d) + CALL SPLINT_INTEGRAL_D(x_int, n3_int, n3_intd, y2_n3, y2_n3d, n& +& , xlo, xhi, int_n3, int_n3d) + CALL SPLINT_INTEGRAL_D(x_int, nv2_int, nv2_intd, y2_nv2, y2_nv2d& +& , n, xlo, xhi, int_nv2, int_nv2d) +!weighted densities + n2d(i) = n2d(i) + pi*dhs(k)*int_n2d + n2(i) = n2(i) + pi*dhs(k)*int_n2 + n1d(i) = n1d(i) + 0.5*int_n2d + n1(i) = n1(i) + 0.5*int_n2 + n0d(i) = n0d(i) + int_n2d/dhs(k) + n0(i) = n0(i) + int_n2/dhs(k) + n3d(i) = n3d(i) + pi*int_n3d + n3(i) = n3(i) + pi*int_n3 + nv2d(i) = nv2d(i) - 2.0*pi*int_nv2d + nv2(i) = nv2(i) - 2.0*pi*int_nv2 + nv1d(i) = nv1d(i) - int_nv2d/dhs(k) + nv1(i) = nv1(i) - int_nv2/dhs(k) + END DO + END DO + phi_dn0d = 0.0 + phi_dn1d = 0.0 + phi_dn2d = 0.0 + phi_dnv1d = 0.0 + phi_dn3d = 0.0 + phi_dnv2d = 0.0 +! If(i < 5) Then +! write(*,*)'i dens',i,nv2(i),n1(i),n0(i) +! write(*,*)'i dens',i,n3(i),nv1(i),nv2(i) +! end if +! +! If(i > 95) then +! write(*,*)'i dens',i,nv2(i),n1(i),n0(i) +! write(*,*)'i dens',i,n3(i),nv1(i),nv2(i) +! End If +! +! pause + + +!derivatives of FMT helmholtz energy density w.r.t. weighted densities +Do i=user%xs-maxval((fa(1:ncomp)+1)/2),user%xe+maxval((fa(1:ncomp)+1)/2) +!weils k�rzer ist + nn0d = n0d(i) + nn0 = n0(i) + nn1d = n1d(i) + nn1 = n1(i) + nn2d = n2d(i) + nn2 = n2(i) + nn3d = n3d(i) + nn3 = n3(i) + nnv1d = nv1d(i) + nnv1 = nv1(i) + nnv2d = nv2d(i) + nnv2 = nv2(i) + zmsd = -nn3d + zms = 1.0 - nn3 + zms2d = zmsd*zms + zms*zmsd + zms2 = zms*zms + zms3d = zms2d*zms + zms2*zmsd + zms3 = zms2*zms + logzmsd = zmsd/zms + logzms = LOG(zms) +!if(isnan(logzms)) stop 'zms < 0, log(zms) undefined FMT_Weighted_Densities' + phi_dn0d(i) = -logzmsd + phi_dn0(i) = -logzms + phi_dn1d(i) = (nn2d*zms-nn2*zmsd)/zms**2 + phi_dn1(i) = nn2/zms + phi_dn2d(i) = (nn1d*zms-nn1*zmsd)/zms**2 + (3.0*((nn2d*nn2+nn2*& +& nn2d-nnv2d*nnv2-nnv2*nnv2d)*(nn3+zms2*logzms)+(nn2*nn2-nnv2*nnv2& +& )*(nn3d+zms2d*logzms+zms2*logzmsd))*36.0*pi*nn3**2*zms2-3.0*(nn2& +& *nn2-nnv2*nnv2)*(nn3+zms2*logzms)*36.0*pi*((nn3d*nn3+nn3*nn3d)*& +& zms2+nn3**2*zms2d))/(36.0*pi*nn3*nn3*zms2)**2 + phi_dn2(i) = nn1/zms + 3.0*(nn2*nn2-nnv2*nnv2)*(nn3+zms2*logzms)/(& +& 36.0*pi*nn3*nn3*zms2) + phi_dn3d(i) = (nn0d*zms-nn0*zmsd)/zms**2 + ((nn1d*nn2+nn1*nn2d-& +& nnv1d*nnv2-nnv1*nnv2d)*zms2-(nn1*nn2-nnv1*nnv2)*zms2d)/zms2**2 -& +& (((3*nn2**2*nn2d-3.0*((nn2d*nnv2+nn2*nnv2d)*nnv2+nn2*nnv2*nnv2d)& +& )*(nn3*(nn3**2-5.0*nn3+2.0)+2.0*zms3*logzms)+(nn2**3-3.0*nn2*& +& nnv2*nnv2)*(nn3d*(nn3**2-5.0*nn3+2.0)+nn3*(2*nn3*nn3d-5.0*nn3d)+& +& 2.0*(zms3d*logzms+zms3*logzmsd)))*36.0*pi*nn3**3*zms3-(nn2**3-& +& 3.0*nn2*nnv2*nnv2)*(nn3*(nn3**2-5.0*nn3+2.0)+2.0*zms3*logzms)*& +& 36.0*pi*(3*nn3**2*nn3d*zms3+nn3**3*zms3d))/(36.0*pi*nn3**3*zms3)& +& **2 + phi_dn3(i) = nn0/zms + (nn1*nn2-nnv1*nnv2)/zms2 - (nn2**3-3.0*nn2*& +& nnv2*nnv2)*(nn3*(nn3**2-5.0*nn3+2.0)+2.0*zms3*logzms)/(36.0*pi*& +& nn3**3*zms3) + phi_dnv1d(i) = -((nnv2d*zms-nnv2*zmsd)/zms**2) + phi_dnv1(i) = -(nnv2/zms) + phi_dnv2d(i) = -((nnv1d*zms-nnv1*zmsd)/zms**2) - (6.0*((nn2d*nnv2+& +& nn2*nnv2d)*(nn3+zms2*logzms)+nn2*nnv2*(nn3d+zms2d*logzms+zms2*& +& logzmsd))*36.0*pi*nn3**2*zms2-6.0*nn2*nnv2*(nn3+zms2*logzms)*& +& 36.0*pi*(2*nn3*nn3d*zms2+nn3**2*zms2d))/(36.0*pi*nn3**2*zms2)**2 + phi_dnv2(i) = -(nnv1/zms) - 6.0*nn2*nnv2*(nn3+zms2*logzms)/(36.0*& +& pi*nn3**2*zms2) + END DO + GOTO 110 + 100 STOP + 110 CONTINUE + END SUBROUTINE FMT_WEIGHTED_DENSITIES_D + + + +! Differentiation of fmt_dfdrho in forward (tangent) mode: +! variations of useful results: df_drho_fmt +! with respect to varying inputs: df_drho_fmt phi_dn0 phi_dn1 +! phi_dn2 phi_dnv1 phi_dn3 phi_dnv2 + SUBROUTINE FMT_DFDRHO_D(i, fa, user, phi_dn0, phi_dn0d, phi_dn1, & +& phi_dn1d, phi_dn2, phi_dn2d, phi_dn3, phi_dn3d, phi_dnv1, phi_dnv1d& +& , phi_dnv2, phi_dnv2d, df_drho_fmt, df_drho_fmtd) + USE BASIC_VARIABLES, ONLY : ncomp,parame + USE EOS_VARIABLES, Only: dhs + USE MOD_DFT, ONLY : zp, dzp + USE PARAMETERS, ONLY : pi + + +!PETSc module +Use PetscManagement + + IMPLICIT NONE + +!passed +INTEGER, INTENT(IN) :: i !the grid point at which to calculate dFdrho +INTEGER, INTENT(IN) :: fa(ncomp) +Type (userctx) :: user +REAL,dimension(user%gxs:user%gxe),INTENT(IN) :: phi_dn0,phi_dn1,phi_dn2,phi_dn3,phi_dnv1,phi_dnv2 +REAL,dimension(user%gxs:user%gxe),INTENT(IN) :: phi_dn0d,phi_dn1d,phi_dn2d,phi_dn3d,phi_dnv1d,phi_dnv2d + +REAL,dimension(user%xs:user%xe,ncomp), INTENT(OUT) :: dF_drho_FMT +REAL,dimension(user%xs:user%xe,ncomp), INTENT(OUT) :: dF_drho_FMTd + + +!local + INTEGER :: j, k, n + INTEGER :: fa2 + REAL :: dz, d2, zz, zz_jp1 + INTEGER, parameter :: NMAX = 800 + REAL, DIMENSION(NMAX) :: x_int, y_int, y0_int, y1_int, y2_int, y3_int& +& , yv1_int, yv2_int, y2 + REAL, DIMENSION(NMAX) :: y_intd, y2d + REAL :: xhi, xlo, integral, int0, int1, int2, int3, intv1, intv2 + REAL :: integrald + REAL :: at_j, at_jp1 + REAL :: at_jd, at_jp1d + + + y2d = 0.0 + y_intd = 0.0 +!Das Integral (Gleichung A1 in Gross DFT 2009) wird hier in einem Schlag berechnet! +!Falls die einzelnen Terme einzeln integriert werden sollen, einfach die auskommentierte Version verwenden +!das einzige, das hier von k abhaengt, sind fa und dhs!! die Ableitungen phi_dn... sind nicht Komponentenspez, da die + DO k=1,ncomp +!gewichteten Dichten ja uch nicht mehr Komponentenspez sind (n_i = sum n_i(k)) + n = 1 +!number of grid points within dhs/2 + fa2 = (fa(k)+5)/2 + d2 = dhs(k)/2.0 + DO j=i-fa2,i+fa2 + IF (zp(i) - zp(j+1) .LT. d2 .AND. zp(i) - zp(j) .GE. d2) THEN +!the position of j+1 is already within i-d/2 while j is still outside this range in this case, the integration steplength (dz) is +! just the distance, which j+1 overlaps with i-d/2 and what is integrated is the interpolated value of the integrand + x_int(n) = 0.0 + IF (n .NE. 1) THEN + GOTO 100 + ELSE + dz = zp(j+1) - (zp(i)-d2) + zz = zp(j) - zp(i) + zz_jp1 = zp(j+1) - zp(i) + at_jd = phi_dn0d(j)/dhs(k) + 0.5*phi_dn1d(j) + pi*dhs(k)*& +& phi_dn2d(j) + pi*(d2**2-zz**2)*phi_dn3d(j) + zz*phi_dnv1d(& +& j)/dhs(k) + 2.0*pi*zz*phi_dnv2d(j) + at_j = phi_dn0(j)/dhs(k) + 0.5*phi_dn1(j) + pi*dhs(k)*& +& phi_dn2(j) + pi*phi_dn3(j)*(d2**2-zz**2) + phi_dnv1(j)*zz/& +& dhs(k) + 2.0*pi*phi_dnv2(j)*zz + at_jp1d = phi_dn0d(j+1)/dhs(k) + 0.5*phi_dn1d(j+1) + pi*dhs(& +& k)*phi_dn2d(j+1) + pi*(d2**2-zz_jp1**2)*phi_dn3d(j+1) + & +& zz_jp1*phi_dnv1d(j+1)/dhs(k) + 2.0*pi*zz_jp1*phi_dnv2d(j+1& +& ) + at_jp1 = phi_dn0(j+1)/dhs(k) + 0.5*phi_dn1(j+1) + pi*dhs(k)*& +& phi_dn2(j+1) + pi*phi_dn3(j+1)*(d2**2-zz_jp1**2) + & +& phi_dnv1(j+1)*zz_jp1/dhs(k) + 2.0*pi*phi_dnv2(j+1)*zz_jp1 +!lineare interpolation genau, wie in FMT_Weighted_Densities + y_intd(n) = at_jd + (dzp-dz)*(at_jp1d-at_jd)/dzp + y_int(n) = at_j + (at_jp1-at_j)/dzp*(dzp-dz) +! y0_int(n) = phi_dn0(j) + (phi_dn0(j+1) -phi_dn0(j))/dzp * (dzp-dz) +! y1_int(n) = phi_dn1(j) + (phi_dn1(j+1) -phi_dn1(j))/dzp * (dzp-dz) +! y2_int(n) = phi_dn2(j) + (phi_dn2(j+1) -phi_dn2(j))/dzp * (dzp-dz) +! y3_int(n) = phi_dn3(j)*(d2**2-zz**2) + (phi_dn3(j+1)*(d2**2-zz_jp1**2) - phi_dn3(j)*(d2**2-zz**2) )/dzp * (dzp-dz) +! yv1_int(n) = phi_dnv1(j)*zz + (phi_dnv1(j+1)*zz_jp1 - phi_dnv1(j)*zz)/dzp * (dzp-dz) +! yv2_int(n) = phi_dnv2(j)*zz + (phi_dnv2(j+1)*zz_jp1 - phi_dnv2(j)*zz)/dzp * (dzp-dz) +! + END IF + ELSE IF (zp(j) .GT. zp(i) - d2 .AND. zp(j) .LE. zp(i) + d2) THEN +!grid points j and j+1 are completely within i+-d2 + n = n + 1 + zz = zp(j) - zp(i) + x_int(n) = x_int(n-1) + dz + y_intd(n) = phi_dn0d(j)/dhs(k) + 0.5*phi_dn1d(j) + pi*dhs(k)*& +& phi_dn2d(j) + pi*(d2**2-zz**2)*phi_dn3d(j) + zz*phi_dnv1d(j)& +& /dhs(k) + 2.0*pi*zz*phi_dnv2d(j) + y_int(n) = phi_dn0(j)/dhs(k) + 0.5*phi_dn1(j) + pi*dhs(k)*& +& phi_dn2(j) + pi*phi_dn3(j)*(d2**2-zz**2) + phi_dnv1(j)*zz/& +& dhs(k) + 2.0*pi*phi_dnv2(j)*zz +! y0_int(n) = phi_dn0(j) +! y1_int(n) = phi_dn1(j) +! y2_int(n) = phi_dn2(j) +! y3_int(n) = phi_dn3(j)*(d2**2-zz**2) +! yv1_int(n) = phi_dnv1(j)*zz +! yv2_int(n) = phi_dnv2(j)*zz +! + dz = dzp + IF (zp(j) .LT. zp(i) + d2 .AND. zp(j+1) .GT. zp(i) + d2) THEN +!zp(j) is still within zp(i)+d2 but zp(j+1) is already out side zp(i)+d2 + n = n + 1 + zz = zp(j) - zp(i) + zz_jp1 = zp(j+1) - zp(i) + dz = zp(i) + d2 - zp(j) + x_int(n) = x_int(n-1) + dz + at_jd = phi_dn0d(j)/dhs(k) + 0.5*phi_dn1d(j) + pi*dhs(k)*& +& phi_dn2d(j) + pi*(d2**2-zz**2)*phi_dn3d(j) + zz*phi_dnv1d(& +& j)/dhs(k) + 2.0*pi*zz*phi_dnv2d(j) + at_j = phi_dn0(j)/dhs(k) + 0.5*phi_dn1(j) + pi*dhs(k)*& +& phi_dn2(j) + pi*phi_dn3(j)*(d2**2-zz**2) + phi_dnv1(j)*zz/& +& dhs(k) + 2.0*pi*phi_dnv2(j)*zz + at_jp1d = phi_dn0d(j+1)/dhs(k) + 0.5*phi_dn1d(j+1) + pi*dhs(& +& k)*phi_dn2d(j+1) + pi*(d2**2-zz_jp1**2)*phi_dn3d(j+1) + & +& zz_jp1*phi_dnv1d(j+1)/dhs(k) + 2.0*pi*zz_jp1*phi_dnv2d(j+1& +& ) + at_jp1 = phi_dn0(j+1)/dhs(k) + 0.5*phi_dn1(j+1) + pi*dhs(k)*& +& phi_dn2(j+1) + pi*phi_dn3(j+1)*(d2**2-zz_jp1**2) + & +& phi_dnv1(j+1)*zz_jp1/dhs(k) + 2.0*pi*phi_dnv2(j+1)*zz_jp1 + y_intd(n) = at_jd + dz*(at_jp1d-at_jd)/dzp + y_int(n) = at_j + (at_jp1-at_j)/dzp*dz +! y0_int(n) = phi_dn0(j) + (phi_dn0(j+1) - phi_dn0(j))/dzp * dz +! y1_int(n) = phi_dn1(j) + (phi_dn1(j+1) - phi_dn1(j))/dzp * dz +! y2_int(n) = phi_dn2(j) + (phi_dn2(j+1) - phi_dn2(j))/dzp * dz +! y3_int(n) = phi_dn3(j)*(d2**2 - zz**2) + (phi_dn3(j+1)*(d2**2 - zz_jp1**2) - phi_dn3(j)*(d2**2 - zz**2))/dzp * dz +! yv1_int(n) = phi_dnv1(j)*zz + (phi_dnv1(j+1)*zz_jp1 - phi_dnv1(j)*zz)/dzp * dz +! yv2_int(n) = phi_dnv2(j)*zz + (phi_dnv2(j+1)*zz_jp1 - phi_dnv2(j)*zz)/dzp * dz +! + END IF + END IF + END DO +!spline integration + xlo = x_int(1) + xhi = x_int(n) + CALL SPLINE_D(x_int, y_int, y_intd, n, 1.e30, 1.e30, y2, y2d) + CALL SPLINT_INTEGRAL_D(x_int, y_int, y_intd, y2, y2d, n, xlo, xhi& +& , integral, integrald) +! call spline ( x_int, y0_int, n, 1.E30, 1.E30, y2 ) +! call splint_integral ( x_int, y0_int, y2, n, xlo, xhi, int0 ) +! call spline ( x_int, y1_int, n, 1.E30, 1.E30, y2 ) +! call splint_integral ( x_int, y1_int, y2, n, xlo, xhi, int1 ) +! call spline ( x_int, y2_int, n, 1.E30, 1.E30, y2 ) +! call splint_integral ( x_int, y2_int, y2, n, xlo, xhi, int2 ) +! call spline ( x_int, y3_int, n, 1.E30, 1.E30, y2 ) +! call splint_integral ( x_int, y3_int, y2, n, xlo, xhi, int3 ) +! call spline ( x_int, yv1_int, n, 1.E30, 1.E30, y2 ) +! call splint_integral ( x_int, yv1_int, y2, n, xlo, xhi, intv1 ) +! call spline ( x_int, yv2_int, n, 1.E30, 1.E30, y2 ) +! call splint_integral ( x_int, yv2_int, y2, n, xlo, xhi, intv2 ) +! +!dF_drho_FMT(i,k) = int0/dhs(k) + 0.5*int1 + PI*dhs(k)*int2 + PI*int3 + intv1/dhs(k) + 2.0*PI*intv2 + df_drho_fmtd(i, k) = parame(k,1)*integrald + df_drho_fmt(i, k) = integral*parame(k,1) + END DO + GOTO 110 + 100 STOP + 110 CONTINUE + END SUBROUTINE FMT_DFDRHO_D + +END MODULE MOD_DFT_FMT_D + diff --git a/applications/PUfoam/MoDeNaModels/SurfaceTension/ExampleOfUsage/src/srcDetailedCode/mod_PETSc.F90 b/applications/PUfoam/MoDeNaModels/SurfaceTension/ExampleOfUsage/src/srcDetailedCode/mod_PETSc.F90 new file mode 100644 index 000000000..4527bb698 --- /dev/null +++ b/applications/PUfoam/MoDeNaModels/SurfaceTension/ExampleOfUsage/src/srcDetailedCode/mod_PETSc.F90 @@ -0,0 +1,63 @@ +Module PetscManagement + + type userctx +#include +#include +#include + PetscInt xs,xe,xm,gxs,gxe,gxm,mx + PetscMPIInt rank + PetscMPIInt num_procs + end type userctx + +End Module + + + + + +Module Global_x +Implicit None +#include +#include +#include + +SNES :: snes !nonlinear solver context +Vec :: x !array of unknowns +Vec :: r !array of residuals +PetscInt :: ngrid !number of grid points +PetscInt :: ngp !number of ghost points + +DOUBLE PRECISION :: timer ! timer +DOUBLE PRECISION :: timer_old ! timer +DOUBLE PRECISION :: total_time ! timer + + +End Module Global_x + + + +Module f90moduleinterfaces +Use PetscManagement +#include + + Interface SNESSetApplicationContext + Subroutine SNESSetApplicationContext(snes,ctx,ierr) + use PetscManagement + SNES snes + type(userctx) ctx + PetscErrorCode ierr + End Subroutine + End Interface SNESSetApplicationContext + + Interface SNESGetApplicationContext + Subroutine SNESGetApplicationContext(snes,ctx,ierr) + use PetscManagement + SNES snes + type(userctx), pointer :: ctx + PetscErrorCode ierr + End Subroutine + End Interface SNESGetApplicationContext + +End Module f90moduleinterfaces + + diff --git a/applications/PUfoam/MoDeNaModels/SurfaceTension/ExampleOfUsage/src/srcDetailedCode/module_solve_nonlinear.F90 b/applications/PUfoam/MoDeNaModels/SurfaceTension/ExampleOfUsage/src/srcDetailedCode/module_solve_nonlinear.F90 new file mode 100644 index 000000000..595a8ba80 --- /dev/null +++ b/applications/PUfoam/MoDeNaModels/SurfaceTension/ExampleOfUsage/src/srcDetailedCode/module_solve_nonlinear.F90 @@ -0,0 +1,1645 @@ + +MODULE Solve_NonLin + +! Corrections to FUNCTION Enorm - 28 November 2003 + +IMPLICIT NONE +INTEGER, PARAMETER :: dp = SELECTED_REAL_KIND(14, 60) +PRIVATE +PUBLIC :: hbrd, hybrd + + +CONTAINS + + +SUBROUTINE hbrd(fcn, n, x, fvec, epsfcn, tol, info, diag) + +! Code converted using TO_F90 by Alan Miller +! Date: 2003-07-15 Time: 13:27:42 + +INTEGER, INTENT(IN) :: n +REAL (dp), INTENT(IN OUT) :: x(n) +REAL (dp), INTENT(IN OUT) :: fvec(n) +REAL (dp), INTENT(IN) :: epsfcn +REAL (dp), INTENT(IN) :: tol +INTEGER, INTENT(OUT) :: info +REAL (dp), INTENT(OUT) :: diag(n) + +! EXTERNAL fcn +INTERFACE + SUBROUTINE FCN(N, X, FVEC, IFLAG) + IMPLICIT NONE + INTEGER, PARAMETER :: dp = SELECTED_REAL_KIND(14, 60) + INTEGER, INTENT(IN) :: n + REAL (dp), INTENT(IN) :: x(n) + REAL (dp), INTENT(OUT) :: fvec(n) + INTEGER, INTENT(IN OUT) :: iflag + END SUBROUTINE FCN +END INTERFACE + +! ********** + +! SUBROUTINE HBRD + +! THE PURPOSE OF HBRD IS TO FIND A ZERO OF A SYSTEM OF N NONLINEAR +! FUNCTIONS IN N VARIABLES BY A MODIFICATION OF THE POWELL HYBRID METHOD. +! THIS IS DONE BY USING THE MORE GENERAL NONLINEAR EQUATION SOLVER HYBRD. +! THE USER MUST PROVIDE A SUBROUTINE WHICH CALCULATES THE FUNCTIONS. +! THE JACOBIAN IS THEN CALCULATED BY A FORWARD-DIFFERENCE APPROXIMATION. + +! THE SUBROUTINE STATEMENT IS + +! SUBROUTINE HBRD(N, X, FVEC, EPSFCN, TOL, INFO, WA, LWA) + +! WHERE + +! FCN IS THE NAME OF THE USER-SUPPLIED SUBROUTINE WHICH CALCULATES +! THE FUNCTIONS. FCN MUST BE DECLARED IN AN EXTERNAL STATEMENT +! IN THE USER CALLING PROGRAM, AND SHOULD BE WRITTEN AS FOLLOWS. + +! SUBROUTINE FCN(N, X, FVEC, IFLAG) +! INTEGER N,IFLAG +! REAL X(N),FVEC(N) +! ---------- +! CALCULATE THE FUNCTIONS AT X AND RETURN THIS VECTOR IN FVEC. +! --------- +! RETURN +! END + +! THE VALUE OF IFLAG NOT BE CHANGED BY FCN UNLESS +! THE USER WANTS TO TERMINATE THE EXECUTION OF HBRD. +! IN THIS CASE SET IFLAG TO A NEGATIVE INTEGER. + +! N IS A POSITIVE INTEGER INPUT VARIABLE SET TO THE NUMBER +! OF FUNCTIONS AND VARIABLES. + +! X IS AN ARRAY OF LENGTH N. ON INPUT X MUST CONTAIN AN INITIAL +! ESTIMATE OF THE SOLUTION VECTOR. ON OUTPUT X CONTAINS THE +! FINAL ESTIMATE OF THE SOLUTION VECTOR. + +! FVEC IS AN OUTPUT ARRAY OF LENGTH N WHICH CONTAINS +! THE FUNCTIONS EVALUATED AT THE OUTPUT X. + +! EPSFCN IS AN INPUT VARIABLE USED IN DETERMINING A SUITABLE STEP LENGTH +! FOR THE FORWARD-DIFFERENCE APPROXIMATION. THIS APPROXIMATION ASSUMES +! THAT THE RELATIVE ERRORS IN THE FUNCTIONS ARE OF THE ORDER OF EPSFCN. +! IF EPSFCN IS LESS THAN THE MACHINE PRECISION, IT IS ASSUMED THAT THE +! RELATIVE ERRORS IN THE FUNCTIONS ARE OF THE ORDER OF THE MACHINE +! PRECISION. + +! TOL IS A NONNEGATIVE INPUT VARIABLE. TERMINATION OCCURS WHEN THE +! ALGORITHM ESTIMATES THAT THE RELATIVE ERROR BETWEEN X AND THE SOLUTION +! IS AT MOST TOL. + +! INFO IS AN INTEGER OUTPUT VARIABLE. IF THE USER HAS TERMINATED +! EXECUTION, INFO IS SET TO THE (NEGATIVE) VALUE OF IFLAG. +! SEE DESCRIPTION OF FCN. OTHERWISE, INFO IS SET AS FOLLOWS. + +! INFO = 0 IMPROPER INPUT PARAMETERS. + +! INFO = 1 ALGORITHM ESTIMATES THAT THE RELATIVE ERROR +! BETWEEN X AND THE SOLUTION IS AT MOST TOL. + +! INFO = 2 NUMBER OF CALLS TO FCN HAS REACHED OR EXCEEDED 200*(N+1). + +! INFO = 3 TOL IS TOO SMALL. NO FURTHER IMPROVEMENT IN +! THE APPROXIMATE SOLUTION X IS POSSIBLE. + +! INFO = 4 ITERATION IS NOT MAKING GOOD PROGRESS. + +! SUBPROGRAMS CALLED + +! USER-SUPPLIED ...... FCN + +! MINPACK-SUPPLIED ... HYBRD + +! ARGONNE NATIONAL LABORATORY. MINPACK PROJECT. MARCH 1980. +! BURTON S. GARBOW, KENNETH E. HILLSTROM, JORGE J. MORE + +! Reference: +! Powell, M.J.D. 'A hybrid method for nonlinear equations' in Numerical Methods +! for Nonlinear Algebraic Equations', P.Rabinowitz (editor), Gordon and +! Breach, London 1970. +! ********** +INTEGER :: maxfev, ml, mode, mu, nfev, nprint +REAL (dp) :: xtol +REAL (dp), PARAMETER :: factor = 1.0_dp, zero = 0.0_dp + +info = 0 + +! CHECK THE INPUT PARAMETERS FOR ERRORS. + + +IF (n <= 0 .OR. epsfcn < zero .OR. tol < zero) GO TO 20 + +! CALL HYBRD. + +maxfev = 200*(n + 1) +xtol = tol +ml = n - 1 +mu = n - 1 +mode = 2 +nprint = 0 +CALL hybrd(fcn, n, x, fvec, xtol, maxfev, ml, mu, epsfcn, diag, mode, & + factor, nprint, info, nfev) +IF (info == 5) info = 4 +20 RETURN + +! LAST CARD OF SUBROUTINE HBRD. + +END SUBROUTINE hbrd + + + +SUBROUTINE hybrd(fcn, n, x, fvec, xtol, maxfev, ml, mu, epsfcn, diag, mode, & + factor, nprint, info, nfev) + +INTEGER, INTENT(IN) :: n +REAL (dp), INTENT(IN OUT) :: x(n) +REAL (dp), INTENT(IN OUT) :: fvec(n) +REAL (dp), INTENT(IN) :: xtol +INTEGER, INTENT(IN OUT) :: maxfev +INTEGER, INTENT(IN OUT) :: ml +INTEGER, INTENT(IN) :: mu +REAL (dp), INTENT(IN) :: epsfcn +REAL (dp), INTENT(OUT) :: diag(n) +INTEGER, INTENT(IN) :: mode +REAL (dp), INTENT(IN) :: factor +INTEGER, INTENT(IN OUT) :: nprint +INTEGER, INTENT(OUT) :: info +INTEGER, INTENT(OUT) :: nfev + +! EXTERNAL fcn +INTERFACE + SUBROUTINE FCN(N, X, FVEC, IFLAG) + IMPLICIT NONE + INTEGER, PARAMETER :: dp = SELECTED_REAL_KIND(14, 60) + INTEGER, INTENT(IN) :: n + REAL (dp), INTENT(IN) :: x(n) + REAL (dp), INTENT(OUT) :: fvec(n) + INTEGER, INTENT(IN OUT) :: iflag + END SUBROUTINE FCN +END INTERFACE + +! ********** + +! SUBROUTINE HYBRD + +! THE PURPOSE OF HYBRD IS TO FIND A ZERO OF A SYSTEM OF N NONLINEAR +! FUNCTIONS IN N VARIABLES BY A MODIFICATION OF THE POWELL HYBRID METHOD. +! THE USER MUST PROVIDE A SUBROUTINE WHICH CALCULATES THE FUNCTIONS. +! THE JACOBIAN IS THEN CALCULATED BY A FORWARD-DIFFERENCE APPROXIMATION. + +! THE SUBROUTINE STATEMENT IS + +! SUBROUTINE HYBRD(FCN, N, X, FVEC, XTOL, MAXFEV, ML, MU, EPSFCN, +! DIAG, MODE, FACTOR, NPRINT, INFO, NFEV, FJAC, +! LDFJAC, R, LR, QTF, WA1, WA2, WA3, WA4) + +! WHERE + +! FCN IS THE NAME OF THE USER-SUPPLIED SUBROUTINE WHICH CALCULATES +! THE FUNCTIONS. FCN MUST BE DECLARED IN AN EXTERNAL STATEMENT IN +! THE USER CALLING PROGRAM, AND SHOULD BE WRITTEN AS FOLLOWS. + +! SUBROUTINE FCN(N, X, FVEC, IFLAG) +! INTEGER N, IFLAG +! REAL X(N), FVEC(N) +! ---------- +! CALCULATE THE FUNCTIONS AT X AND +! RETURN THIS VECTOR IN FVEC. +! --------- +! RETURN +! END + +! THE VALUE OF IFLAG SHOULD NOT BE CHANGED BY FCN UNLESS +! THE USER WANTS TO TERMINATE EXECUTION OF HYBRD. +! IN THIS CASE SET IFLAG TO A NEGATIVE INTEGER. + +! N IS A POSITIVE INTEGER INPUT VARIABLE SET TO THE NUMBER +! OF FUNCTIONS AND VARIABLES. + +! X IS AN ARRAY OF LENGTH N. ON INPUT X MUST CONTAIN AN INITIAL +! ESTIMATE OF THE SOLUTION VECTOR. ON OUTPUT X CONTAINS THE FINAL +! ESTIMATE OF THE SOLUTION VECTOR. + +! FVEC IS AN OUTPUT ARRAY OF LENGTH N WHICH CONTAINS +! THE FUNCTIONS EVALUATED AT THE OUTPUT X. + +! XTOL IS A NONNEGATIVE INPUT VARIABLE. TERMINATION OCCURS WHEN THE +! RELATIVE ERROR BETWEEN TWO CONSECUTIVE ITERATES IS AT MOST XTOL. + +! MAXFEV IS A POSITIVE INTEGER INPUT VARIABLE. TERMINATION OCCURS WHEN +! THE NUMBER OF CALLS TO FCN IS AT LEAST MAXFEV BY THE END OF AN +! ITERATION. + +! ML IS A NONNEGATIVE INTEGER INPUT VARIABLE WHICH SPECIFIES THE +! NUMBER OF SUBDIAGONALS WITHIN THE BAND OF THE JACOBIAN MATRIX. +! IF THE JACOBIAN IS NOT BANDED, SET ML TO AT LEAST N - 1. + +! MU IS A NONNEGATIVE INTEGER INPUT VARIABLE WHICH SPECIFIES THE NUMBER +! OF SUPERDIAGONALS WITHIN THE BAND OF THE JACOBIAN MATRIX. +! IF THE JACOBIAN IS NOT BANDED, SET MU TO AT LEAST N - 1. + +! EPSFCN IS AN INPUT VARIABLE USED IN DETERMINING A SUITABLE STEP LENGTH +! FOR THE FORWARD-DIFFERENCE APPROXIMATION. THIS APPROXIMATION +! ASSUMES THAT THE RELATIVE ERRORS IN THE FUNCTIONS ARE OF THE ORDER +! OF EPSFCN. IF EPSFCN IS LESS THAN THE MACHINE PRECISION, +! IT IS ASSUMED THAT THE RELATIVE ERRORS IN THE FUNCTIONS ARE OF THE +! ORDER OF THE MACHINE PRECISION. + +! DIAG IS AN ARRAY OF LENGTH N. IF MODE = 1 (SEE BELOW), +! DIAG IS INTERNALLY SET. IF MODE = 2, DIAG MUST CONTAIN POSITIVE +! ENTRIES THAT SERVE AS MULTIPLICATIVE SCALE FACTORS FOR THE +! VARIABLES. + +! MODE IS AN INTEGER INPUT VARIABLE. IF MODE = 1, THE VARIABLES WILL BE +! SCALED INTERNALLY. IF MODE = 2, THE SCALING IS SPECIFIED BY THE +! INPUT DIAG. OTHER VALUES OF MODE ARE EQUIVALENT TO MODE = 1. + +! FACTOR IS A POSITIVE INPUT VARIABLE USED IN DETERMINING THE +! INITIAL STEP BOUND. THIS BOUND IS SET TO THE PRODUCT OF +! FACTOR AND THE EUCLIDEAN NORM OF DIAG*X IF NONZERO, OR ELSE +! TO FACTOR ITSELF. IN MOST CASES FACTOR SHOULD LIE IN THE +! INTERVAL (.1,100.). 100. IS A GENERALLY RECOMMENDED VALUE. + +! NPRINT IS AN INTEGER INPUT VARIABLE THAT ENABLES CONTROLLED +! PRINTING OF ITERATES IF IT IS POSITIVE. IN THIS CASE, +! FCN IS CALLED WITH IFLAG = 0 AT THE BEGINNING OF THE FIRST +! ITERATION AND EVERY NPRINT ITERATIONS THEREAFTER AND +! IMMEDIATELY PRIOR TO RETURN, WITH X AND FVEC AVAILABLE +! FOR PRINTING. IF NPRINT IS NOT POSITIVE, NO SPECIAL CALLS +! OF FCN WITH IFLAG = 0 ARE MADE. + +! INFO IS AN INTEGER OUTPUT VARIABLE. IF THE USER HAS +! TERMINATED EXECUTION, INFO IS SET TO THE (NEGATIVE) +! VALUE OF IFLAG. SEE DESCRIPTION OF FCN. OTHERWISE, +! INFO IS SET AS FOLLOWS. + +! INFO = 0 IMPROPER INPUT PARAMETERS. + +! INFO = 1 RELATIVE ERROR BETWEEN TWO CONSECUTIVE ITERATES +! IS AT MOST XTOL. + +! INFO = 2 NUMBER OF CALLS TO FCN HAS REACHED OR EXCEEDED MAXFEV. + +! INFO = 3 XTOL IS TOO SMALL. NO FURTHER IMPROVEMENT IN +! THE APPROXIMATE SOLUTION X IS POSSIBLE. + +! INFO = 4 ITERATION IS NOT MAKING GOOD PROGRESS, AS +! MEASURED BY THE IMPROVEMENT FROM THE LAST +! FIVE JACOBIAN EVALUATIONS. + +! INFO = 5 ITERATION IS NOT MAKING GOOD PROGRESS, AS MEASURED BY +! THE IMPROVEMENT FROM THE LAST TEN ITERATIONS. + +! NFEV IS AN INTEGER OUTPUT VARIABLE SET TO THE NUMBER OF CALLS TO FCN. + +! FJAC IS AN OUTPUT N BY N ARRAY WHICH CONTAINS THE ORTHOGONAL MATRIX Q +! PRODUCED BY THE QR FACTORIZATION OF THE FINAL APPROXIMATE JACOBIAN. + +! LDFJAC IS A POSITIVE INTEGER INPUT VARIABLE NOT LESS THAN N +! WHICH SPECIFIES THE LEADING DIMENSION OF THE ARRAY FJAC. + +! R IS AN OUTPUT ARRAY OF LENGTH LR WHICH CONTAINS THE +! UPPER TRIANGULAR MATRIX PRODUCED BY THE QR FACTORIZATION +! OF THE FINAL APPROXIMATE JACOBIAN, STORED ROWWISE. + +! LR IS A POSITIVE INTEGER INPUT VARIABLE NOT LESS THAN (N*(N+1))/2. + +! QTF IS AN OUTPUT ARRAY OF LENGTH N WHICH CONTAINS +! THE VECTOR (Q TRANSPOSE)*FVEC. + +! WA1, WA2, WA3, AND WA4 ARE WORK ARRAYS OF LENGTH N. + +! SUBPROGRAMS CALLED + +! USER-SUPPLIED ...... FCN + +! MINPACK-SUPPLIED ... DOGLEG,SPMPAR,ENORM,FDJAC1, +! QFORM,QRFAC,R1MPYQ,R1UPDT + +! FORTRAN-SUPPLIED ... ABS,MAX,MIN,MIN,MOD + +! ARGONNE NATIONAL LABORATORY. MINPACK PROJECT. MARCH 1980. +! BURTON S. GARBOW, KENNETH E. HILLSTROM, JORGE J. MORE + +! ********** + +INTEGER :: i, iflag, iter, j, jm1, l, lr, msum, ncfail, ncsuc, nslow1, & + nslow2 +INTEGER :: iwa(1) +LOGICAL :: jeval, sing +REAL (dp) :: actred, delta, epsmch, fnorm, fnorm1, pnorm, prered, & + ratio, sum, temp, xnorm +REAL (dp), PARAMETER :: one = 1.0_dp, p1 = 0.1_dp, p5 = 0.5_dp, & + p001 = 0.001_dp, p0001 = 0.0001_dp, zero = 0.0_dp + +! The following were workspace arguments +REAL (dp) :: fjac(n,n), r(n*(n+1)/2), qtf(n), wa1(n), wa2(n), & + wa3(n), wa4(n) + +! EPSMCH IS THE MACHINE PRECISION. + +epsmch = EPSILON(1.0_dp) + +info = 0 +iflag = 0 +nfev = 0 +lr = n*(n+1)/2 + +! CHECK THE INPUT PARAMETERS FOR ERRORS. + +IF (n > 0 .AND. xtol >= zero .AND. maxfev > 0 .AND. ml >= 0 .AND. mu >= & + 0 .AND. factor > zero ) THEN +IF (mode == 2) THEN + diag(1:n) = one +END IF + +! EVALUATE THE FUNCTION AT THE STARTING POINT AND CALCULATE ITS NORM. + +iflag = 1 +CALL fcn(n, x, fvec, iflag) +nfev = 1 +IF (iflag >= 0) THEN + fnorm = enorm(n, fvec) + +! DETERMINE THE NUMBER OF CALLS TO FCN NEEDED TO COMPUTE THE JACOBIAN MATRIX. + + msum = MIN(ml+mu+1,n) + +! INITIALIZE ITERATION COUNTER AND MONITORS. + + iter = 1 + ncsuc = 0 + ncfail = 0 + nslow1 = 0 + nslow2 = 0 + +! BEGINNING OF THE OUTER LOOP. + + 20 jeval = .true. + +! CALCULATE THE JACOBIAN MATRIX. + + iflag = 2 + CALL fdjac1(fcn, n, x, fvec, fjac, n, iflag, ml, mu, epsfcn, wa1, wa2) + nfev = nfev + msum + IF (iflag >= 0) THEN + +! COMPUTE THE QR FACTORIZATION OF THE JACOBIAN. + + CALL qrfac(n, n, fjac, n, .false., iwa, 1, wa1, wa2, wa3) + +! ON THE FIRST ITERATION AND IF MODE IS 1, SCALE ACCORDING +! TO THE NORMS OF THE COLUMNS OF THE INITIAL JACOBIAN. + + IF (iter == 1) THEN + IF (mode /= 2) THEN + DO j = 1, n + diag(j) = wa2(j) + IF (wa2(j) == zero) diag(j) = one + END DO + END IF + +! ON THE FIRST ITERATION, CALCULATE THE NORM OF THE SCALED X +! AND INITIALIZE THE STEP BOUND DELTA. + + wa3(1:n) = diag(1:n) * x(1:n) + xnorm = enorm(n, wa3) + delta = factor * xnorm + IF (delta == zero) delta = factor + END IF + +! FORM (Q TRANSPOSE)*FVEC AND STORE IN QTF. + + qtf(1:n) = fvec(1:n) + DO j = 1, n + IF (fjac(j,j) /= zero) THEN + sum = zero + DO i = j, n + sum = sum + fjac(i,j) * qtf(i) + END DO + temp = -sum / fjac(j,j) + DO i = j, n + qtf(i) = qtf(i) + fjac(i,j) * temp + END DO + END IF + END DO + +! COPY THE TRIANGULAR FACTOR OF THE QR FACTORIZATION INTO R. + + sing = .false. + DO j = 1, n + l = j + jm1 = j - 1 + IF (jm1 >= 1) THEN + DO i = 1, jm1 + r(l) = fjac(i,j) + l = l + n - i + END DO + END IF + r(l) = wa1(j) + IF (wa1(j) == zero) sing = .true. + END DO + +! ACCUMULATE THE ORTHOGONAL FACTOR IN FJAC. + + CALL qform(n, n, fjac, n, wa1) + +! RESCALE IF NECESSARY. + + IF (mode /= 2) THEN + DO j = 1, n + diag(j) = MAX(diag(j), wa2(j)) + END DO + END IF + +! BEGINNING OF THE INNER LOOP. + +! IF REQUESTED, CALL FCN TO ENABLE PRINTING OF ITERATES. + + 120 IF (nprint > 0) THEN + iflag = 0 + IF (MOD(iter-1, nprint) == 0) CALL fcn(n, x, fvec, iflag) + IF (iflag < 0) GO TO 190 + END IF + +! DETERMINE THE DIRECTION P. + + CALL dogleg(n, r, lr, diag, qtf, delta, wa1, wa2, wa3) + +! STORE THE DIRECTION P AND X + P. CALCULATE THE NORM OF P. + + DO j = 1, n + wa1(j) = -wa1(j) + wa2(j) = x(j) + wa1(j) + wa3(j) = diag(j) * wa1(j) + END DO + pnorm = enorm(n, wa3) + +! ON THE FIRST ITERATION, ADJUST THE INITIAL STEP BOUND. + + IF (iter == 1) delta = MIN(delta, pnorm) + +! EVALUATE THE FUNCTION AT X + P AND CALCULATE ITS NORM. + + iflag = 1 + CALL fcn(n, wa2, wa4, iflag) + nfev = nfev + 1 + IF (iflag >= 0) THEN + fnorm1 = enorm(n, wa4) + +! COMPUTE THE SCALED ACTUAL REDUCTION. + + actred = -one + IF (fnorm1 < fnorm) actred = one - (fnorm1/fnorm) ** 2 + +! COMPUTE THE SCALED PREDICTED REDUCTION. + + l = 1 + DO i = 1, n + sum = zero + DO j = i, n + sum = sum + r(l) * wa1(j) + l = l + 1 + END DO + wa3(i) = qtf(i) + sum + END DO + temp = enorm(n, wa3) + prered = zero + IF (temp < fnorm) prered = one - (temp/fnorm) ** 2 + +! COMPUTE THE RATIO OF THE ACTUAL TO THE PREDICTED REDUCTION. + + ratio = zero + IF (prered > zero) ratio = actred / prered + +! UPDATE THE STEP BOUND. + + IF (ratio < p1) THEN + ncsuc = 0 + ncfail = ncfail + 1 + delta = p5 * delta + ELSE + ncfail = 0 + ncsuc = ncsuc + 1 + IF (ratio >= p5 .OR. ncsuc > 1) delta = MAX(delta,pnorm/p5) + IF (ABS(ratio-one) <= p1) delta = pnorm / p5 + END IF + +! TEST FOR SUCCESSFUL ITERATION. + + IF (ratio >= p0001) THEN + +! SUCCESSFUL ITERATION. UPDATE X, FVEC, AND THEIR NORMS. + + DO j = 1, n + x(j) = wa2(j) + wa2(j) = diag(j) * x(j) + fvec(j) = wa4(j) + END DO + xnorm = enorm(n, wa2) + fnorm = fnorm1 + iter = iter + 1 + END IF + +! DETERMINE THE PROGRESS OF THE ITERATION. + + nslow1 = nslow1 + 1 + IF (actred >= p001) nslow1 = 0 + IF (jeval) nslow2 = nslow2 + 1 + IF (actred >= p1) nslow2 = 0 + +! TEST FOR CONVERGENCE. + + IF (delta <= xtol*xnorm .OR. fnorm == zero) info = 1 + IF (info == 0) THEN + +! TESTS FOR TERMINATION AND STRINGENT TOLERANCES. + + IF (nfev >= maxfev) info = 2 + IF (p1*MAX(p1*delta, pnorm) <= epsmch*xnorm) info = 3 + IF (nslow2 == 5) info = 4 + IF (nslow1 == 10) info = 5 + IF (info == 0) THEN + +! CRITERION FOR RECALCULATING JACOBIAN APPROXIMATION +! BY FORWARD DIFFERENCES. + + IF (ncfail /= 2) THEN + +! CALCULATE THE RANK ONE MODIFICATION TO THE JACOBIAN +! AND UPDATE QTF IF NECESSARY. + + DO j = 1, n + sum = zero + DO i = 1, n + sum = sum + fjac(i,j) * wa4(i) + END DO + wa2(j) = (sum-wa3(j)) / pnorm + wa1(j) = diag(j) * ((diag(j)*wa1(j))/pnorm) + IF (ratio >= p0001) qtf(j) = sum + END DO + +! COMPUTE THE QR FACTORIZATION OF THE UPDATED JACOBIAN. + + CALL r1updt(n, n, r, lr, wa1, wa2, wa3, sing) + CALL r1mpyq(n, n, fjac, n, wa2, wa3) + CALL r1mpyq(1, n, qtf, 1, wa2, wa3) + +! END OF THE INNER LOOP. + + jeval = .false. + GO TO 120 + END IF + +! END OF THE OUTER LOOP. + + GO TO 20 + END IF + END IF + END IF + END IF +END IF +END IF + +! TERMINATION, EITHER NORMAL OR USER IMPOSED. + +190 IF (iflag < 0) info = iflag +iflag = 0 +IF (nprint > 0) CALL fcn(n, x, fvec, iflag) +RETURN + +! LAST CARD OF SUBROUTINE HYBRD. + +END SUBROUTINE hybrd + + + +SUBROUTINE dogleg(n, r, lr, diag, qtb, delta, x, wa1, wa2) + +INTEGER, INTENT(IN) :: n +INTEGER, INTENT(IN) :: lr +REAL (dp), INTENT(IN) :: r(lr) +REAL (dp), INTENT(IN) :: diag(n) +REAL (dp), INTENT(IN) :: qtb(n) +REAL (dp), INTENT(IN) :: delta +REAL (dp), INTENT(IN OUT) :: x(n) +REAL (dp), INTENT(OUT) :: wa1(n) +REAL (dp), INTENT(OUT) :: wa2(n) + + +! ********** + +! SUBROUTINE DOGLEG + +! GIVEN AN M BY N MATRIX A, AN N BY N NONSINGULAR DIAGONAL +! MATRIX D, AN M-VECTOR B, AND A POSITIVE NUMBER DELTA, THE +! PROBLEM IS TO DETERMINE THE CONVEX COMBINATION X OF THE +! GAUSS-NEWTON AND SCALED GRADIENT DIRECTIONS THAT MINIMIZES +! (A*X - B) IN THE LEAST SQUARES SENSE, SUBJECT TO THE +! RESTRICTION THAT THE EUCLIDEAN NORM OF D*X BE AT MOST DELTA. + +! THIS SUBROUTINE COMPLETES THE SOLUTION OF THE PROBLEM +! IF IT IS PROVIDED WITH THE NECESSARY INFORMATION FROM THE +! QR FACTORIZATION OF A. THAT IS, IF A = Q*R, WHERE Q HAS +! ORTHOGONAL COLUMNS AND R IS AN UPPER TRIANGULAR MATRIX, +! THEN DOGLEG EXPECTS THE FULL UPPER TRIANGLE OF R AND +! THE FIRST N COMPONENTS OF (Q TRANSPOSE)*B. + +! THE SUBROUTINE STATEMENT IS + +! SUBROUTINE DOGLEG(N,R,LR,DIAG,QTB,DELTA,X,WA1,WA2) + +! WHERE + +! N IS A POSITIVE INTEGER INPUT VARIABLE SET TO THE ORDER OF R. + +! R IS AN INPUT ARRAY OF LENGTH LR WHICH MUST CONTAIN THE UPPER +! TRIANGULAR MATRIX R STORED BY ROWS. + +! LR IS A POSITIVE INTEGER INPUT VARIABLE NOT LESS THAN +! (N*(N+1))/2. + +! DIAG IS AN INPUT ARRAY OF LENGTH N WHICH MUST CONTAIN THE +! DIAGONAL ELEMENTS OF THE MATRIX D. + +! QTB IS AN INPUT ARRAY OF LENGTH N WHICH MUST CONTAIN THE FIRST +! N ELEMENTS OF THE VECTOR (Q TRANSPOSE)*B. + +! DELTA IS A POSITIVE INPUT VARIABLE WHICH SPECIFIES AN UPPER +! BOUND ON THE EUCLIDEAN NORM OF D*X. + +! X IS AN OUTPUT ARRAY OF LENGTH N WHICH CONTAINS THE DESIRED +! CONVEX COMBINATION OF THE GAUSS-NEWTON DIRECTION AND THE +! SCALED GRADIENT DIRECTION. + +! WA1 AND WA2 ARE WORK ARRAYS OF LENGTH N. + +! SUBPROGRAMS CALLED + +! MINPACK-SUPPLIED ... SPMPAR,ENORM + +! FORTRAN-SUPPLIED ... ABS,MAX,MIN,SQRT + +! ARGONNE NATIONAL LABORATORY. MINPACK PROJECT. MARCH 1980. +! BURTON S. GARBOW, KENNETH E. HILLSTROM, JORGE J. MORE + +! ********** +INTEGER :: i, j, jj, jp1, k, l +REAL (dp) :: alpha, bnorm, epsmch, gnorm, qnorm, sgnorm, sum, temp + +! EPSMCH IS THE MACHINE PRECISION. + +epsmch = EPSILON(1.0_dp) + +! FIRST, CALCULATE THE GAUSS-NEWTON DIRECTION. + +jj = (n*(n+1)) / 2 + 1 +DO k = 1, n + j = n - k + 1 + jp1 = j + 1 + jj = jj - k + l = jj + 1 + sum = 0.0 + IF (n >= jp1) THEN + DO i = jp1, n + sum = sum + r(l) * x(i) + l = l + 1 + END DO + END IF + temp = r(jj) + IF (temp == 0.0) THEN + l = j + DO i = 1, j + temp = MAX(temp,ABS(r(l))) + l = l + n - i + END DO + temp = epsmch * temp + IF (temp == 0.0) temp = epsmch + END IF + x(j) = (qtb(j)-sum) / temp +END DO + +! TEST WHETHER THE GAUSS-NEWTON DIRECTION IS ACCEPTABLE. + +DO j = 1, n + wa1(j) = 0.0 + wa2(j) = diag(j) * x(j) +END DO +qnorm = enorm(n, wa2) +IF (qnorm > delta) THEN + +! THE GAUSS-NEWTON DIRECTION IS NOT ACCEPTABLE. +! NEXT, CALCULATE THE SCALED GRADIENT DIRECTION. + + l = 1 + DO j = 1, n + temp = qtb(j) + DO i = j, n + wa1(i) = wa1(i) + r(l) * temp + l = l + 1 + END DO + wa1(j) = wa1(j) / diag(j) + END DO + +! CALCULATE THE NORM OF THE SCALED GRADIENT AND TEST FOR +! THE SPECIAL CASE IN WHICH THE SCALED GRADIENT IS ZERO. + + gnorm = enorm(n, wa1) + sgnorm = 0.0 + alpha = delta / qnorm + IF (gnorm /= 0.0) THEN + +! CALCULATE THE POINT ALONG THE SCALED GRADIENT +! AT WHICH THE QUADRATIC IS MINIMIZED. + + DO j = 1, n + wa1(j) = (wa1(j)/gnorm) / diag(j) + END DO + l = 1 + DO j = 1, n + sum = 0.0 + DO i = j, n + sum = sum + r(l) * wa1(i) + l = l + 1 + END DO + wa2(j) = sum + END DO + temp = enorm(n, wa2) + sgnorm = (gnorm/temp) / temp + +! TEST WHETHER THE SCALED GRADIENT DIRECTION IS ACCEPTABLE. + + alpha = 0.0 + IF (sgnorm < delta) THEN + +! THE SCALED GRADIENT DIRECTION IS NOT ACCEPTABLE. +! FINALLY, CALCULATE THE POINT ALONG THE DOGLEG +! AT WHICH THE QUADRATIC IS MINIMIZED. + + bnorm = enorm(n, qtb) + temp = (bnorm/gnorm) * (bnorm/qnorm) * (sgnorm/delta) + temp = temp - (delta/qnorm) * (sgnorm/delta) ** 2 + SQRT(( & + temp-(delta/qnorm))**2+(1.0-(delta/qnorm)**2)*(1.0-( sgnorm/delta)**2)) + alpha = ((delta/qnorm)*(1.0-(sgnorm/delta)**2)) / temp + END IF + END IF + +! FORM APPROPRIATE CONVEX COMBINATION OF THE GAUSS-NEWTON +! DIRECTION AND THE SCALED GRADIENT DIRECTION. + + temp = (1.0-alpha) * MIN(sgnorm,delta) + DO j = 1, n + x(j) = temp * wa1(j) + alpha * x(j) + END DO +END IF +RETURN +END SUBROUTINE dogleg + + +SUBROUTINE fdjac1(fcn, n, x, fvec, fjac, ldfjac, iflag, ml, mu, epsfcn, & + wa1, wa2) + +INTEGER, INTENT(IN) :: n +REAL (dp), INTENT(IN OUT) :: x(n) +REAL (dp), INTENT(IN) :: fvec(n) +INTEGER, INTENT(IN) :: ldfjac +REAL (dp), INTENT(OUT) :: fjac(ldfjac,n) +INTEGER, INTENT(IN OUT) :: iflag +INTEGER, INTENT(IN) :: ml +INTEGER, INTENT(IN) :: mu +REAL (dp), INTENT(IN) :: epsfcn +REAL (dp), INTENT(IN OUT) :: wa1(n) +REAL (dp), INTENT(OUT) :: wa2(n) + +! EXTERNAL fcn +INTERFACE + SUBROUTINE FCN(N, X, FVEC, IFLAG) + IMPLICIT NONE + INTEGER, PARAMETER :: dp = SELECTED_REAL_KIND(14, 60) + INTEGER, INTENT(IN) :: n + REAL (dp), INTENT(IN) :: x(n) + REAL (dp), INTENT(OUT) :: fvec(n) + INTEGER, INTENT(IN OUT) :: iflag + END SUBROUTINE FCN +END INTERFACE + +! ********** + +! SUBROUTINE FDJAC1 + +! THIS SUBROUTINE COMPUTES A FORWARD-DIFFERENCE APPROXIMATION TO THE N BY N +! JACOBIAN MATRIX ASSOCIATED WITH A SPECIFIED PROBLEM OF N FUNCTIONS IN N +! VARIABLES. IF THE JACOBIAN HAS A BANDED FORM, THEN FUNCTION EVALUATIONS +! ARE SAVED BY ONLY APPROXIMATING THE NONZERO TERMS. + +! THE SUBROUTINE STATEMENT IS + +! SUBROUTINE FDJAC1(FCN,N,X,FVEC,FJAC,LDFJAC,IFLAG,ML,MU,EPSFCN, +! WA1,WA2) + +! WHERE + +! FCN IS THE NAME OF THE USER-SUPPLIED SUBROUTINE WHICH CALCULATES +! THE FUNCTIONS. FCN MUST BE DECLARED IN AN EXTERNAL STATEMENT IN +! THE USER CALLING PROGRAM, AND SHOULD BE WRITTEN AS FOLLOWS. + +! SUBROUTINE FCN(N,X,FVEC,IFLAG) +! INTEGER N,IFLAG +! REAL X(N),FVEC(N) +! ---------- +! CALCULATE THE FUNCTIONS AT X AND +! RETURN THIS VECTOR IN FVEC. +! ---------- +! RETURN +! END + +! THE VALUE OF IFLAG SHOULD NOT BE CHANGED BY FCN UNLESS +! THE USER WANTS TO TERMINATE EXECUTION OF FDJAC1. +! IN THIS CASE SET IFLAG TO A NEGATIVE INTEGER. + +! N IS A POSITIVE INTEGER INPUT VARIABLE SET TO THE NUMBER +! OF FUNCTIONS AND VARIABLES. + +! X IS AN INPUT ARRAY OF LENGTH N. + +! FVEC IS AN INPUT ARRAY OF LENGTH N WHICH MUST CONTAIN THE +! FUNCTIONS EVALUATED AT X. + +! FJAC IS AN OUTPUT N BY N ARRAY WHICH CONTAINS THE +! APPROXIMATION TO THE JACOBIAN MATRIX EVALUATED AT X. + +! LDFJAC IS A POSITIVE INTEGER INPUT VARIABLE NOT LESS THAN N +! WHICH SPECIFIES THE LEADING DIMENSION OF THE ARRAY FJAC. + +! IFLAG IS AN INTEGER VARIABLE WHICH CAN BE USED TO TERMINATE +! THE EXECUTION OF FDJAC1. SEE DESCRIPTION OF FCN. + +! ML IS A NONNEGATIVE INTEGER INPUT VARIABLE WHICH SPECIFIES +! THE NUMBER OF SUBDIAGONALS WITHIN THE BAND OF THE +! JACOBIAN MATRIX. IF THE JACOBIAN IS NOT BANDED, SET +! ML TO AT LEAST N - 1. + +! EPSFCN IS AN INPUT VARIABLE USED IN DETERMINING A SUITABLE +! STEP LENGTH FOR THE FORWARD-DIFFERENCE APPROXIMATION. THIS +! APPROXIMATION ASSUMES THAT THE RELATIVE ERRORS IN THE +! FUNCTIONS ARE OF THE ORDER OF EPSFCN. IF EPSFCN IS LESS +! THAN THE MACHINE PRECISION, IT IS ASSUMED THAT THE RELATIVE +! ERRORS IN THE FUNCTIONS ARE OF THE ORDER OF THE MACHINE PRECISION. + +! MU IS A NONNEGATIVE INTEGER INPUT VARIABLE WHICH SPECIFIES +! THE NUMBER OF SUPERDIAGONALS WITHIN THE BAND OF THE +! JACOBIAN MATRIX. IF THE JACOBIAN IS NOT BANDED, SET +! MU TO AT LEAST N - 1. + +! WA1 AND WA2 ARE WORK ARRAYS OF LENGTH N. IF ML + MU + 1 IS AT +! LEAST N, THEN THE JACOBIAN IS CONSIDERED DENSE, AND WA2 IS +! NOT REFERENCED. + +! SUBPROGRAMS CALLED + +! MINPACK-SUPPLIED ... SPMPAR + +! FORTRAN-SUPPLIED ... ABS,MAX,SQRT + +! ARGONNE NATIONAL LABORATORY. MINPACK PROJECT. MARCH 1980. +! BURTON S. GARBOW, KENNETH E. HILLSTROM, JORGE J. MORE + +! ********** +INTEGER :: i, j, k, msum +REAL (dp) :: eps, epsmch, h, temp +REAL (dp), PARAMETER :: zero = 0.0_dp + +! EPSMCH IS THE MACHINE PRECISION. + +epsmch = EPSILON(1.0_dp) + +eps = SQRT(MAX(epsfcn, epsmch)) +msum = ml + mu + 1 +IF (msum >= n) THEN + +! COMPUTATION OF DENSE APPROXIMATE JACOBIAN. + + DO j = 1, n + temp = x(j) + h = eps * ABS(temp) + IF (h == zero) h = eps + x(j) = temp + h + CALL fcn(n, x, wa1, iflag) + IF (iflag < 0) EXIT + x(j) = temp + DO i = 1, n + fjac(i,j) = (wa1(i)-fvec(i)) / h + END DO + END DO +ELSE + +! COMPUTATION OF BANDED APPROXIMATE JACOBIAN. + + DO k = 1, msum + DO j = k, n, msum + wa2(j) = x(j) + h = eps * ABS(wa2(j)) + IF (h == zero) h = eps + x(j) = wa2(j) + h + END DO + CALL fcn(n, x, wa1, iflag) + IF (iflag < 0) EXIT + DO j = k, n, msum + x(j) = wa2(j) + h = eps * ABS(wa2(j)) + IF (h == zero) h = eps + DO i = 1, n + fjac(i,j) = zero + IF (i >= j-mu .AND. i <= j+ml) fjac(i,j) = (wa1(i)-fvec(i)) / h + END DO + END DO + END DO +END IF +RETURN + +! LAST CARD OF SUBROUTINE FDJAC1. + +END SUBROUTINE fdjac1 + + + +SUBROUTINE qform(m, n, q, ldq, wa) + +INTEGER, INTENT(IN) :: m +INTEGER, INTENT(IN) :: n +INTEGER, INTENT(IN) :: ldq +REAL (dp), INTENT(OUT) :: q(ldq,m) +REAL (dp), INTENT(OUT) :: wa(m) + + +! ********** + +! SUBROUTINE QFORM + +! THIS SUBROUTINE PROCEEDS FROM THE COMPUTED QR FACTORIZATION OF AN M BY N +! MATRIX A TO ACCUMULATE THE M BY M ORTHOGONAL MATRIX Q FROM ITS FACTORED FORM. + +! THE SUBROUTINE STATEMENT IS + +! SUBROUTINE QFORM(M,N,Q,LDQ,WA) + +! WHERE + +! M IS A POSITIVE INTEGER INPUT VARIABLE SET TO THE NUMBER +! OF ROWS OF A AND THE ORDER OF Q. + +! N IS A POSITIVE INTEGER INPUT VARIABLE SET TO THE NUMBER OF COLUMNS OF A. + +! Q IS AN M BY M ARRAY. ON INPUT THE FULL LOWER TRAPEZOID IN +! THE FIRST MIN(M,N) COLUMNS OF Q CONTAINS THE FACTORED FORM. +! ON OUTPUT Q HAS BEEN ACCUMULATED INTO A SQUARE MATRIX. + +! LDQ IS A POSITIVE INTEGER INPUT VARIABLE NOT LESS THAN M +! WHICH SPECIFIES THE LEADING DIMENSION OF THE ARRAY Q. + +! WA IS A WORK ARRAY OF LENGTH M. + +! SUBPROGRAMS CALLED + +! FORTRAN-SUPPLIED ... MIN + +! ARGONNE NATIONAL LABORATORY. MINPACK PROJECT. MARCH 1980. +! BURTON S. GARBOW, KENNETH E. HILLSTROM, JORGE J. MORE + +! ********** +INTEGER :: i, j, jm1, k, l, minmn, np1 +REAL (dp) :: sum, temp +REAL (dp), PARAMETER :: one = 1.0_dp, zero = 0.0_dp + +! ZERO OUT UPPER TRIANGLE OF Q IN THE FIRST MIN(M,N) COLUMNS. + +minmn = MIN(m,n) +IF (minmn >= 2) THEN + DO j = 2, minmn + jm1 = j - 1 + DO i = 1, jm1 + q(i,j) = zero + END DO + END DO +END IF + +! INITIALIZE REMAINING COLUMNS TO THOSE OF THE IDENTITY MATRIX. + +np1 = n + 1 +IF (m >= np1) THEN + DO j = np1, m + DO i = 1, m + q(i,j) = zero + END DO + q(j,j) = one + END DO +END IF + +! ACCUMULATE Q FROM ITS FACTORED FORM. + +DO l = 1, minmn + k = minmn - l + 1 + DO i = k, m + wa(i) = q(i,k) + q(i,k) = zero + END DO + q(k,k) = one + IF (wa(k) /= zero) THEN + DO j = k, m + sum = zero + DO i = k, m + sum = sum + q(i,j) * wa(i) + END DO + temp = sum / wa(k) + DO i = k, m + q(i,j) = q(i,j) - temp * wa(i) + END DO + END DO + END IF +END DO +RETURN + +! LAST CARD OF SUBROUTINE QFORM. + +END SUBROUTINE qform + + +SUBROUTINE qrfac(m, n, a, lda, pivot, ipvt, lipvt, rdiag, acnorm, wa) + +INTEGER, INTENT(IN) :: m +INTEGER, INTENT(IN) :: n +INTEGER, INTENT(IN) :: lda +REAL (dp), INTENT(IN OUT) :: a(lda,n) +LOGICAL, INTENT(IN) :: pivot +INTEGER, INTENT(IN) :: lipvt +INTEGER, INTENT(OUT) :: ipvt(lipvt) +REAL (dp), INTENT(OUT) :: rdiag(n) +REAL (dp), INTENT(OUT) :: acnorm(n) +REAL (dp), INTENT(OUT) :: wa(n) + + +! ********** + +! SUBROUTINE QRFAC + +! THIS SUBROUTINE USES HOUSEHOLDER TRANSFORMATIONS WITH COLUMN PIVOTING +! (OPTIONAL) TO COMPUTE A QR FACTORIZATION OF THE M BY N MATRIX A. +! THAT IS, QRFAC DETERMINES AN ORTHOGONAL MATRIX Q, A PERMUTATION MATRIX P, +! AND AN UPPER TRAPEZOIDAL MATRIX R WITH DIAGONAL ELEMENTS OF NONINCREASING +! MAGNITUDE, SUCH THAT A*P = Q*R. THE HOUSEHOLDER TRANSFORMATION FOR +! COLUMN K, K = 1,2,...,MIN(M,N), IS OF THE FORM + +! T +! I - (1/U(K))*U*U + +! WHERE U HAS ZEROS IN THE FIRST K-1 POSITIONS. THE FORM OF THIS +! TRANSFORMATION AND THE METHOD OF PIVOTING FIRST APPEARED IN THE +! CORRESPONDING LINPACK SUBROUTINE. + +! THE SUBROUTINE STATEMENT IS + +! SUBROUTINE QRFAC(M,N,A,LDA,PIVOT,IPVT,LIPVT,RDIAG,ACNORM,WA) + +! WHERE + +! M IS A POSITIVE INTEGER INPUT VARIABLE SET TO THE NUMBER OF ROWS OF A. + +! N IS A POSITIVE INTEGER INPUT VARIABLE SET TO THE NUMBER +! OF COLUMNS OF A. + +! A IS AN M BY N ARRAY. ON INPUT A CONTAINS THE MATRIX FOR WHICH THE +! QR FACTORIZATION IS TO BE COMPUTED. ON OUTPUT THE STRICT UPPER +! TRAPEZOIDAL PART OF A CONTAINS THE STRICT UPPER TRAPEZOIDAL PART OF R, +! AND THE LOWER TRAPEZOIDAL PART OF A CONTAINS A FACTORED FORM OF Q +! (THE NON-TRIVIAL ELEMENTS OF THE U VECTORS DESCRIBED ABOVE). + +! LDA IS A POSITIVE INTEGER INPUT VARIABLE NOT LESS THAN M +! WHICH SPECIFIES THE LEADING DIMENSION OF THE ARRAY A. + +! PIVOT IS A LOGICAL INPUT VARIABLE. IF PIVOT IS SET TRUE, +! THEN COLUMN PIVOTING IS ENFORCED. IF PIVOT IS SET FALSE, +! THEN NO COLUMN PIVOTING IS DONE. + +! IPVT IS AN INTEGER OUTPUT ARRAY OF LENGTH LIPVT. IPVT DEFINES THE +! PERMUTATION MATRIX P SUCH THAT A*P = Q*R. +! COLUMN J OF P IS COLUMN IPVT(J) OF THE IDENTITY MATRIX. +! IF PIVOT IS FALSE, IPVT IS NOT REFERENCED. + +! LIPVT IS A POSITIVE INTEGER INPUT VARIABLE. IF PIVOT IS FALSE, +! THEN LIPVT MAY BE AS SMALL AS 1. IF PIVOT IS TRUE, THEN +! LIPVT MUST BE AT LEAST N. + +! RDIAG IS AN OUTPUT ARRAY OF LENGTH N WHICH CONTAINS THE +! DIAGONAL ELEMENTS OF R. + +! ACNORM IS AN OUTPUT ARRAY OF LENGTH N WHICH CONTAINS THE NORMS OF +! THE CORRESPONDING COLUMNS OF THE INPUT MATRIX A. +! IF THIS INFORMATION IS NOT NEEDED, THEN ACNORM CAN COINCIDE WITH RDIAG. + +! WA IS A WORK ARRAY OF LENGTH N. IF PIVOT IS FALSE, THEN WA +! CAN COINCIDE WITH RDIAG. + +! SUBPROGRAMS CALLED + +! MINPACK-SUPPLIED ... SPMPAR,ENORM + +! FORTRAN-SUPPLIED ... MAX,SQRT,MIN + +! ARGONNE NATIONAL LABORATORY. MINPACK PROJECT. MARCH 1980. +! BURTON S. GARBOW, KENNETH E. HILLSTROM, JORGE J. MORE + +! ********** +INTEGER :: i, j, jp1, k, kmax, minmn +REAL (dp) :: ajnorm, epsmch, sum, temp +REAL (dp), PARAMETER :: one = 1.0_dp, p05 = 0.05_dp, zero = 0.0_dp + +! EPSMCH IS THE MACHINE PRECISION. + +epsmch = EPSILON(1.0_dp) + +! COMPUTE THE INITIAL COLUMN NORMS AND INITIALIZE SEVERAL ARRAYS. + +DO j = 1, n + acnorm(j) = enorm(m, a(1:,j)) + rdiag(j) = acnorm(j) + wa(j) = rdiag(j) + IF (pivot) ipvt(j) = j +END DO + +! REDUCE A TO R WITH HOUSEHOLDER TRANSFORMATIONS. + +minmn = MIN(m,n) +DO j = 1, minmn + IF (pivot) THEN + +! BRING THE COLUMN OF LARGEST NORM INTO THE PIVOT POSITION. + + kmax = j + DO k = j, n + IF (rdiag(k) > rdiag(kmax)) kmax = k + END DO + IF (kmax /= j) THEN + DO i = 1, m + temp = a(i,j) + a(i,j) = a(i,kmax) + a(i,kmax) = temp + END DO + rdiag(kmax) = rdiag(j) + wa(kmax) = wa(j) + k = ipvt(j) + ipvt(j) = ipvt(kmax) + ipvt(kmax) = k + END IF + END IF + +! COMPUTE THE HOUSEHOLDER TRANSFORMATION TO REDUCE THE +! J-TH COLUMN OF A TO A MULTIPLE OF THE J-TH UNIT VECTOR. + + ajnorm = enorm(m-j+1, a(j:,j)) + IF (ajnorm /= zero) THEN + IF (a(j,j) < zero) ajnorm = -ajnorm + DO i = j, m + a(i,j) = a(i,j) / ajnorm + END DO + a(j,j) = a(j,j) + one + +! APPLY THE TRANSFORMATION TO THE REMAINING COLUMNS AND UPDATE THE NORMS. + + jp1 = j + 1 + IF (n >= jp1) THEN + DO k = jp1, n + sum = zero + DO i = j, m + sum = sum + a(i,j) * a(i,k) + END DO + temp = sum / a(j,j) + DO i = j, m + a(i,k) = a(i,k) - temp * a(i,j) + END DO + IF (.NOT.(.NOT.pivot.OR.rdiag(k) == zero)) THEN + temp = a(j,k) / rdiag(k) + rdiag(k) = rdiag(k) * SQRT(MAX(zero,one-temp**2)) + IF (p05*(rdiag(k)/wa(k))**2 <= epsmch) THEN + rdiag(k) = enorm(m-j, a(jp1:,k)) + wa(k) = rdiag(k) + END IF + END IF + END DO + END IF + END IF + rdiag(j) = -ajnorm +END DO +RETURN + +! LAST CARD OF SUBROUTINE QRFAC. + +END SUBROUTINE qrfac + + + +SUBROUTINE r1mpyq(m, n, a, lda, v, w) + +INTEGER, INTENT(IN) :: m +INTEGER, INTENT(IN) :: n +INTEGER, INTENT(IN) :: lda +REAL (dp), INTENT(IN OUT) :: a(lda,n) +REAL (dp), INTENT(IN) :: v(n) +REAL (dp), INTENT(IN) :: w(n) + + +! ********** + +! SUBROUTINE R1MPYQ + +! GIVEN AN M BY N MATRIX A, THIS SUBROUTINE COMPUTES A*Q WHERE +! Q IS THE PRODUCT OF 2*(N - 1) TRANSFORMATIONS + +! GV(N-1)*...*GV(1)*GW(1)*...*GW(N-1) + +! AND GV(I), GW(I) ARE GIVENS ROTATIONS IN THE (I,N) PLANE WHICH +! ELIMINATE ELEMENTS IN THE I-TH AND N-TH PLANES, RESPECTIVELY. +! Q ITSELF IS NOT GIVEN, RATHER THE INFORMATION TO RECOVER THE +! GV, GW ROTATIONS IS SUPPLIED. + +! THE SUBROUTINE STATEMENT IS + +! SUBROUTINE R1MPYQ(M, N, A, LDA, V, W) + +! WHERE + +! M IS A POSITIVE INTEGER INPUT VARIABLE SET TO THE NUMBER OF ROWS OF A. + +! N IS A POSITIVE INTEGER INPUT VARIABLE SET TO THE NUMBER OF COLUMNS OF A. + +! A IS AN M BY N ARRAY. ON INPUT A MUST CONTAIN THE MATRIX TO BE +! POSTMULTIPLIED BY THE ORTHOGONAL MATRIX Q DESCRIBED ABOVE. +! ON OUTPUT A*Q HAS REPLACED A. + +! LDA IS A POSITIVE INTEGER INPUT VARIABLE NOT LESS THAN M +! WHICH SPECIFIES THE LEADING DIMENSION OF THE ARRAY A. + +! V IS AN INPUT ARRAY OF LENGTH N. V(I) MUST CONTAIN THE INFORMATION +! NECESSARY TO RECOVER THE GIVENS ROTATION GV(I) DESCRIBED ABOVE. + +! W IS AN INPUT ARRAY OF LENGTH N. W(I) MUST CONTAIN THE INFORMATION +! NECESSARY TO RECOVER THE GIVENS ROTATION GW(I) DESCRIBED ABOVE. + +! SUBROUTINES CALLED + +! FORTRAN-SUPPLIED ... ABS, SQRT + +! ARGONNE NATIONAL LABORATORY. MINPACK PROJECT. MARCH 1980. +! BURTON S. GARBOW, KENNETH E. HILLSTROM, JORGE J. MORE + +! ********** +INTEGER :: i, j, nmj, nm1 +REAL (dp) :: COS, SIN, temp +REAL (dp), PARAMETER :: one = 1.0_dp + +! APPLY THE FIRST SET OF GIVENS ROTATIONS TO A. + +nm1 = n - 1 +IF (nm1 >= 1) THEN + DO nmj = 1, nm1 + j = n - nmj + IF (ABS(v(j)) > one) COS = one / v(j) + IF (ABS(v(j)) > one) SIN = SQRT(one-COS**2) + IF (ABS(v(j)) <= one) SIN = v(j) + IF (ABS(v(j)) <= one) COS = SQRT(one-SIN**2) + DO i = 1, m + temp = COS * a(i,j) - SIN * a(i,n) + a(i,n) = SIN * a(i,j) + COS * a(i,n) + a(i,j) = temp + END DO + END DO + +! APPLY THE SECOND SET OF GIVENS ROTATIONS TO A. + + DO j = 1, nm1 + IF (ABS(w(j)) > one) COS = one / w(j) + IF (ABS(w(j)) > one) SIN = SQRT(one-COS**2) + IF (ABS(w(j)) <= one) SIN = w(j) + IF (ABS(w(j)) <= one) COS = SQRT(one-SIN**2) + DO i = 1, m + temp = COS * a(i,j) + SIN * a(i,n) + a(i,n) = -SIN * a(i,j) + COS * a(i,n) + a(i,j) = temp + END DO + END DO +END IF +RETURN + +! LAST CARD OF SUBROUTINE R1MPYQ. + +END SUBROUTINE r1mpyq + + + +SUBROUTINE r1updt(m, n, s, ls, u, v, w, sing) + +INTEGER, INTENT(IN) :: m +INTEGER, INTENT(IN) :: n +INTEGER, INTENT(IN) :: ls +REAL (dp), INTENT(IN OUT) :: s(ls) +REAL (dp), INTENT(IN) :: u(m) +REAL (dp), INTENT(IN OUT) :: v(n) +REAL (dp), INTENT(OUT) :: w(m) +LOGICAL, INTENT(OUT) :: sing + + +! ********** + +! SUBROUTINE R1UPDT + +! GIVEN AN M BY N LOWER TRAPEZOIDAL MATRIX S, AN M-VECTOR U, +! AND AN N-VECTOR V, THE PROBLEM IS TO DETERMINE AN +! ORTHOGONAL MATRIX Q SUCH THAT + +! T +! (S + U*V )*Q + +! IS AGAIN LOWER TRAPEZOIDAL. + +! THIS SUBROUTINE DETERMINES Q AS THE PRODUCT OF 2*(N - 1) TRANSFORMATIONS + +! GV(N-1)*...*GV(1)*GW(1)*...*GW(N-1) + +! WHERE GV(I), GW(I) ARE GIVENS ROTATIONS IN THE (I,N) PLANE +! WHICH ELIMINATE ELEMENTS IN THE I-TH AND N-TH PLANES, RESPECTIVELY. +! Q ITSELF IS NOT ACCUMULATED, RATHER THE INFORMATION TO RECOVER THE GV, +! GW ROTATIONS IS RETURNED. + +! THE SUBROUTINE STATEMENT IS + +! SUBROUTINE R1UPDT(M,N,S,LS,U,V,W,SING) + +! WHERE + +! M IS A POSITIVE INTEGER INPUT VARIABLE SET TO THE NUMBER OF ROWS OF S. + +! N IS A POSITIVE INTEGER INPUT VARIABLE SET TO THE NUMBER +! OF COLUMNS OF S. N MUST NOT EXCEED M. + +! S IS AN ARRAY OF LENGTH LS. ON INPUT S MUST CONTAIN THE LOWER +! TRAPEZOIDAL MATRIX S STORED BY COLUMNS. ON OUTPUT S CONTAINS +! THE LOWER TRAPEZOIDAL MATRIX PRODUCED AS DESCRIBED ABOVE. + +! LS IS A POSITIVE INTEGER INPUT VARIABLE NOT LESS THAN +! (N*(2*M-N+1))/2. + +! U IS AN INPUT ARRAY OF LENGTH M WHICH MUST CONTAIN THE VECTOR U. + +! V IS AN ARRAY OF LENGTH N. ON INPUT V MUST CONTAIN THE VECTOR V. +! ON OUTPUT V(I) CONTAINS THE INFORMATION NECESSARY TO +! RECOVER THE GIVENS ROTATION GV(I) DESCRIBED ABOVE. + +! W IS AN OUTPUT ARRAY OF LENGTH M. W(I) CONTAINS INFORMATION +! NECESSARY TO RECOVER THE GIVENS ROTATION GW(I) DESCRIBED ABOVE. + +! SING IS A LOGICAL OUTPUT VARIABLE. SING IS SET TRUE IF ANY OF THE +! DIAGONAL ELEMENTS OF THE OUTPUT S ARE ZERO. OTHERWISE SING IS +! SET FALSE. + +! SUBPROGRAMS CALLED + +! MINPACK-SUPPLIED ... SPMPAR + +! FORTRAN-SUPPLIED ... ABS,SQRT + +! ARGONNE NATIONAL LABORATORY. MINPACK PROJECT. MARCH 1980. +! BURTON S. GARBOW, KENNETH E. HILLSTROM, JORGE J. MORE, JOHN L. NAZARETH + +! ********** +INTEGER :: i, j, jj, l, nmj, nm1 +REAL (dp) :: COS, cotan, giant, SIN, TAN, tau, temp +REAL (dp), PARAMETER :: one = 1.0_dp, p5 = 0.5_dp, p25 = 0.25_dp, zero = 0.0_dp + +! GIANT IS THE LARGEST MAGNITUDE. + +giant = HUGE(1.0_dp) + +! INITIALIZE THE DIAGONAL ELEMENT POINTER. + +jj = (n*(2*m-n+1)) / 2 - (m-n) + +! MOVE THE NONTRIVIAL PART OF THE LAST COLUMN OF S INTO W. + +l = jj +DO i = n, m + w(i) = s(l) + l = l + 1 +END DO + +! ROTATE THE VECTOR V INTO A MULTIPLE OF THE N-TH UNIT VECTOR +! IN SUCH A WAY THAT A SPIKE IS INTRODUCED INTO W. + +nm1 = n - 1 +IF (nm1 >= 1) THEN + DO nmj = 1, nm1 + j = n - nmj + jj = jj - (m-j+1) + w(j) = zero + IF (v(j) /= zero) THEN + +! DETERMINE A GIVENS ROTATION WHICH ELIMINATES THE J-TH ELEMENT OF V. + + IF (ABS(v(n)) < ABS(v(j))) THEN + cotan = v(n) / v(j) + SIN = p5 / SQRT(p25+p25*cotan**2) + COS = SIN * cotan + tau = one + IF (ABS(COS)*giant > one) tau = one / COS + ELSE + TAN = v(j) / v(n) + COS = p5 / SQRT(p25+p25*TAN**2) + SIN = COS * TAN + tau = SIN + END IF + +! APPLY THE TRANSFORMATION TO V AND STORE THE INFORMATION +! NECESSARY TO RECOVER THE GIVENS ROTATION. + + v(n) = SIN * v(j) + COS * v(n) + v(j) = tau + +! APPLY THE TRANSFORMATION TO S AND EXTEND THE SPIKE IN W. + + l = jj + DO i = j, m + temp = COS * s(l) - SIN * w(i) + w(i) = SIN * s(l) + COS * w(i) + s(l) = temp + l = l + 1 + END DO + END IF + END DO +END IF + +! ADD THE SPIKE FROM THE RANK 1 UPDATE TO W. + +DO i = 1, m + w(i) = w(i) + v(n) * u(i) +END DO + +! ELIMINATE THE SPIKE. + +sing = .false. +IF (nm1 >= 1) THEN + DO j = 1, nm1 + IF (w(j) /= zero) THEN + +! DETERMINE A GIVENS ROTATION WHICH ELIMINATES THE +! J-TH ELEMENT OF THE SPIKE. + + IF (ABS(s(jj)) < ABS(w(j))) THEN + cotan = s(jj) / w(j) + SIN = p5 / SQRT(p25 + p25*cotan**2) + COS = SIN * cotan + tau = one + IF (ABS(COS)*giant > one) tau = one / COS + ELSE + TAN = w(j) / s(jj) + COS = p5 / SQRT(p25+p25*TAN**2) + SIN = COS * TAN + tau = SIN + END IF + +! APPLY THE TRANSFORMATION TO S AND REDUCE THE SPIKE IN W. + + l = jj + DO i = j, m + temp = COS * s(l) + SIN * w(i) + w(i) = -SIN * s(l) + COS * w(i) + s(l) = temp + l = l + 1 + END DO + +! STORE THE INFORMATION NECESSARY TO RECOVER THE GIVENS ROTATION. + + w(j) = tau + END IF + +! TEST FOR ZERO DIAGONAL ELEMENTS IN THE OUTPUT S. + + IF (s(jj) == zero) sing = .true. + jj = jj + (m-j+1) + END DO +END IF + +! MOVE W BACK INTO THE LAST COLUMN OF THE OUTPUT S. + +l = jj +DO i = n, m + s(l) = w(i) + l = l + 1 +END DO +IF (s(jj) == zero) sing = .true. +RETURN + +! LAST CARD OF SUBROUTINE R1UPDT. + +END SUBROUTINE r1updt + + +FUNCTION enorm(n, x) RESULT(fn_val) + +INTEGER, INTENT(IN) :: n +REAL (dp), INTENT(IN) :: x(n) +REAL (dp) :: fn_val + +! ********** + +! FUNCTION ENORM + +! GIVEN AN N-VECTOR X, THIS FUNCTION CALCULATES THE EUCLIDEAN NORM OF X. + +! THE EUCLIDEAN NORM IS COMPUTED BY ACCUMULATING THE SUM OF SQUARES IN THREE +! DIFFERENT SUMS. THE SUMS OF SQUARES FOR THE SMALL AND LARGE COMPONENTS +! ARE SCALED SO THAT NO OVERFLOWS OCCUR. NON-DESTRUCTIVE UNDERFLOWS ARE +! PERMITTED. UNDERFLOWS AND OVERFLOWS DO NOT OCCUR IN THE COMPUTATION OF THE UNSCALED +! SUM OF SQUARES FOR THE INTERMEDIATE COMPONENTS. +! THE DEFINITIONS OF SMALL, INTERMEDIATE AND LARGE COMPONENTS DEPEND ON +! TWO CONSTANTS, RDWARF AND RGIANT. THE MAIN RESTRICTIONS ON THESE CONSTANTS +! ARE THAT RDWARF**2 NOT UNDERFLOW AND RGIANT**2 NOT OVERFLOW. +! THE CONSTANTS GIVEN HERE ARE SUITABLE FOR EVERY KNOWN COMPUTER. + +! THE FUNCTION STATEMENT IS + +! REAL FUNCTION ENORM(N, X) + +! WHERE + +! N IS A POSITIVE INTEGER INPUT VARIABLE. + +! X IS AN INPUT ARRAY OF LENGTH N. + +! SUBPROGRAMS CALLED + +! FORTRAN-SUPPLIED ... ABS,SQRT + +! ARGONNE NATIONAL LABORATORY. MINPACK PROJECT. MARCH 1980. +! BURTON S. GARBOW, KENNETH E. HILLSTROM, JORGE J. MORE + +! ********** +INTEGER :: i +REAL (dp) :: agiant, floatn, s1, s2, s3, xabs, x1max, x3max +REAL (dp), PARAMETER :: rdwarf = 1.0D-100, rgiant = 1.0D+100 + +s1 = 0.0_dp +s2 = 0.0_dp +s3 = 0.0_dp +x1max = 0.0_dp +x3max = 0.0_dp +floatn = n +agiant = rgiant / floatn +DO i = 1, n + xabs = ABS(x(i)) + IF (xabs <= rdwarf .OR. xabs >= agiant) THEN + IF (xabs > rdwarf) THEN + +! SUM FOR LARGE COMPONENTS. + + IF (xabs > x1max) THEN + s1 = 1.0_dp + s1 * (x1max/xabs) ** 2 + x1max = xabs + ELSE + s1 = s1 + (xabs/x1max) ** 2 + END IF + ELSE + +! SUM FOR SMALL COMPONENTS. + + IF (xabs > x3max) THEN + s3 = 1.0_dp + s3 * (x3max/xabs) ** 2 + x3max = xabs + ELSE + IF (xabs /= 0.0_dp) s3 = s3 + (xabs/x3max) ** 2 + END IF + END IF + ELSE + +! SUM FOR INTERMEDIATE COMPONENTS. + + s2 = s2 + xabs ** 2 + END IF +END DO + +! CALCULATION OF NORM. + +IF (s1 /= 0.0_dp) THEN + fn_val = x1max * SQRT(s1 + (s2/x1max)/x1max) +ELSE + IF (s2 /= 0.0_dp) THEN + IF (s2 >= x3max) fn_val = SQRT(s2*(1.0_dp + (x3max/s2)*(x3max*s3))) + IF (s2 < x3max) fn_val = SQRT(x3max*((s2/x3max) + (x3max*s3))) + ELSE + fn_val = x3max * SQRT(s3) + END IF +END IF +RETURN +END FUNCTION enorm + +END MODULE Solve_NonLin diff --git a/applications/PUfoam/MoDeNaModels/SurfaceTension/ExampleOfUsage/src/srcDetailedCode/out.txt b/applications/PUfoam/MoDeNaModels/SurfaceTension/ExampleOfUsage/src/srcDetailedCode/out.txt new file mode 100644 index 000000000..247f493f1 --- /dev/null +++ b/applications/PUfoam/MoDeNaModels/SurfaceTension/ExampleOfUsage/src/srcDetailedCode/out.txt @@ -0,0 +1 @@ + 33.518519488031210 diff --git a/applications/PUfoam/MoDeNaModels/SurfaceTension/ExampleOfUsage/workflow b/applications/PUfoam/MoDeNaModels/SurfaceTension/ExampleOfUsage/workflow new file mode 100755 index 000000000..aab826a04 --- /dev/null +++ b/applications/PUfoam/MoDeNaModels/SurfaceTension/ExampleOfUsage/workflow @@ -0,0 +1,57 @@ +#!/usr/bin/python +''' + + ooo ooooo oooooooooo. ooooo ooo + `88. .888' `888' `Y8b `888b. `8' + 888b d'888 .ooooo. 888 888 .ooooo. 8 `88b. 8 .oooo. + 8 Y88. .P 888 d88' `88b 888 888 d88' `88b 8 `88b. 8 `P )88b + 8 `888' 888 888 888 888 888 888ooo888 8 `88b.8 .oP"888 + 8 Y 888 888 888 888 d88' 888 .o 8 `888 d8( 888 + o8o o888o `Y8bod8P' o888bood8P' `Y8bod8P' o8o `8 `Y888""8o + +Copyright + 2014-2015 MoDeNa Consortium, All rights reserved. + +License + This file is part of Modena. + + Modena is free software; you can redistribute it and/or modify it under + the terms of the GNU General Public License as published by the Free + Software Foundation, either version 3 of the License, or (at your option) + any later version. + + Modena is distributed in the hope that it will be useful, but WITHOUT ANY + WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS + FOR A PARTICULAR PURPOSE. See the GNU General Public License for more + details. + + You should have received a copy of the GNU General Public License along + with Modena. If not, see . + +Description + A simple workflow + +Authors + Henrik Rusche + +Contributors +''' + +from fireworks import Firework, Workflow, LaunchPad +from fireworks.core.rocket_launcher import rapidfire +import SurfaceTension +from modulefinder import ModuleFinder + + +# set up the LaunchPad and reset it +launchpad = LaunchPad() +launchpad.reset('', require_password=False) + +# create the individual FireWorks and Workflow +# Source code in src/twoTanksMacroscopicProblem.C +wf = Workflow([Firework(SurfaceTension.m)], {}, name="simulation") + +# store workflow and launch it locally +launchpad.add_wf(wf) +rapidfire(launchpad) + diff --git a/applications/PUfoam/MoDeNaModels/SurfaceTension/SurfaceTension.py b/applications/PUfoam/MoDeNaModels/SurfaceTension/SurfaceTension.py new file mode 100644 index 000000000..18a5cd77e --- /dev/null +++ b/applications/PUfoam/MoDeNaModels/SurfaceTension/SurfaceTension.py @@ -0,0 +1,198 @@ +'''@cond + + ooo ooooo oooooooooo. ooooo ooo + `88. .888' `888' `Y8b `888b. `8' + 888b d'888 .ooooo. 888 888 .ooooo. 8 `88b. 8 .oooo. + 8 Y88. .P 888 d88' `88b 888 888 d88' `88b 8 `88b. 8 `P )88b + 8 `888' 888 888 888 888 888 888ooo888 8 `88b.8 .oP"888 + 8 Y 888 888 888 888 d88' 888 .o 8 `888 d8( 888 + o8o o888o `Y8bod8P' o888bood8P' `Y8bod8P' o8o `8 `Y888""8o + +Copyright + 2014-2015 MoDeNa Consortium, All rights reserved. + +License + This file is part of Modena. + + Modena is free software; you can redistribute it and/or modify it under + the terms of the GNU General Public License as published by the Free + Software Foundation, either version 3 of the License, or (at your option) + any later version. + + Modena is distributed in the hope that it will be useful, but WITHOUT ANY + WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS + FOR A PARTICULAR PURPOSE. See the GNU General Public License + for more details. + + You should have received a copy of the GNU General Public License along + with Modena. If not, see . +@endcond''' + +""" +@file +Python library of FireTasks +This is the Surface Tension python module. Basically, it contains the following: + +The FireTask which controls the call of the detailed model. This detailed model is called +at the very beginning of the simulation in order to generate initial data points +which can be used to fit the parameters of the surrogate model and during a running simulation +as soon as the Surface Tension model is called with input parameters which lie outside the range +the parameters of the surrogate model was so far fitted for. This FireTask is stored in the class +"SurfaceTensionExactSim" and a more detailed description of the detailed model can be found +in the description of this class. + +Furthermore, this module contains the code of the surrogate model function as well as the +definitions of its input and output values and its fittable parameters. Care should be +taken to set reasonable bounds for these variables. + +Also, this module contains the backward mapping model. This model consits of the +surrogate model function, an initialisation strategy, the out of bounds strategy and the +parameter fitting strategy. The initialisation strategy defines the initial data points where the +detailed model will be evaluated at simulation start for an initial fit of the surrogate model parameters. +The out of bounds strategy determines, how many new points and where to place these new +points, once the Surface Tension model is called for input values outside of the +fitted range. The parameter fitting strategy defines tolerances and maximal iterations +which are passed to the numerical solver which performs the actual fitting of the +surrogate model parameters. + + +@author Jonas Mairhofer +@copyright 2014-2015, MoDeNa Project. GNU Public License. +@ingroup app_foaming +""" + +import os +import modena +from modena import ForwardMappingModel, BackwardMappingModel, SurrogateModel, CFunction, IndexSet, ModenaFireTask +import modena.Strategy as Strategy +from fireworks import Firework, Workflow, FWAction +from fireworks.utilities.fw_utilities import explicit_serialize +from jinja2 import Template + + +__author__ = 'Henrik Rusche' +__copyright__ = 'Copyright 2014, MoDeNa Project' +__version__ = '0.2' +__maintainer__ = 'Henrik Rusche' +__email__ = 'h.rusche@wikki.co.uk.' +__date__ = 'Sep 4, 2014' + + +# ********************************* Class ********************************** # +@explicit_serialize +class SurfaceTensionExactSim(ModenaFireTask): + """ + This FireTask controls the execution of the detailed model of the Surface Tension model. + The detailed model is a density functional theory implementation based on PC-SAFT. A + detailed description of this model can be found in Deliverable 1.3 on the MoDeNa website. + + In order to start the detailed model, the input values for the model are first written to the + file "in.txt". The detailed model code picks them up from this file and performs the according + calculation. Once it is done, the output value is written to the file "out.txt". This FireTask + then reads in the calculated surface tension from "out.txt" and inserts this value into the + database. + """ + + def task(self, fw_spec): + # Write input for detailed model + ff = open('in.txt', 'w') + Tstr = str(self['point']['T']) + ff.write('%s \n' %(Tstr)) + + + ##TODO INPUT SHOULD COME FROM IndexSet + + ff.write('2 \n') #number of components in system + ff.write('air \n') #component 1 + ff.write('thf \n') #component 2 + ff.write('0. \n') #molar feed (initial) composition component 1 + ff.write('0. \n') #molar feed (initial) composition component 2 + ff.close() + + #create output file for detailed code + fff = open('out.txt', 'w+') + fff.close() + + # Execute detailed model + run_command = os.path.dirname(os.path.abspath(__file__))+'/src/PCSAFT_SurfaceTension -snes_monitor_short -ksp_monitor_short \ + -nx 800 -rc 9.0 -box 300 -erel 1e-08 -init_pert 0 \ + -snes_type newtonls -snes_converged_reason \ + -snes_atol 1e-07 -snes_rtol 1e-07 -snes_stol 1e-07 -snes_max_it 20 \ + -ksp_max_it 15 -ksp_gmres_restart 50 \ + -snes_linesearch_type l2 -snes_linesearch_damping 0.3 -snes_linesearch_monitor \ + -snes_max_fail 1 -snes_max_linear_solve_fail 100 \ + -ksp_gmres_cgs_refinement_type refine_always \ + -snes_ksp_ew -snes_ksp_ew_version 1 -snes_ksp_ew_rtol0 0.5 -snes_ksp_ew_rtolmax 0.9 -snes_ksp_ew_threshold 0.1 \ + -jac 0 -pc_type none > log' + + + ret = os.system(run_command) + # This call enables backward mapping capabilities (not needed in this example) + self.handleReturnCode(ret) + + # Analyse output + f = open('out.txt', 'r') + self['point']['ST'] = float(f.readline()) + f.close() + + +f = CFunction( + Ccode= r''' +#include "modena.h" +#include "math.h" + +void surroSurfaceTension +( + const double* parameters, + const double* inherited_inputs, + const double* inputs, + double *outputs +) +{ + const double T = inputs[0]; + + const double P0 = parameters[0]; + const double P1 = parameters[1]; + const double P2 = parameters[2]; + + outputs[0] = P0 + T*P1 + P2*T*T; +} +''', + # These are global bounds for the function + inputs={ + 'T': { 'min': 270.0, 'max': 310.0, 'argPos': 0 }, #check if boundaries reasonable, from this range, the random values for the DOE are chosen! + }, + outputs={ + 'ST': { 'min': 9e99, 'max': -9e99, 'argPos': 0 }, + }, + parameters={ + 'param0': { 'min': -1E10, 'max': 1E10, 'argPos': 0 }, #check if boundaries are reasonable!!! + 'param1': { 'min': -1E10, 'max': 1E10, 'argPos': 1 }, + 'param2': { 'min': -1E10, 'max': 1E10, 'argPos': 2 }, + }, +) + +m = BackwardMappingModel( + _id= 'SurfaceTension', + surrogateFunction= f, + exactTask= SurfaceTensionExactSim(), + substituteModels= [ ], + initialisationStrategy= Strategy.InitialPoints( + initialPoints= + { + 'T': [270.0, 290.0, 300.0], + }, + ), + outOfBoundsStrategy= Strategy.ExtendSpaceStochasticSampling( + nNewPoints= 4 + ), + parameterFittingStrategy= Strategy.NonLinFitWithErrorContol( + testDataPercentage= 0.2, + maxError= 30.0, + improveErrorStrategy= Strategy.StochasticSampling( + nNewPoints= 2 + ), + maxIterations= 5 # Currently not used + ), +) + diff --git a/applications/PUfoam/MoDeNaModels/SurfaceTension/__init__.py b/applications/PUfoam/MoDeNaModels/SurfaceTension/__init__.py new file mode 100644 index 000000000..e1447e6fe --- /dev/null +++ b/applications/PUfoam/MoDeNaModels/SurfaceTension/__init__.py @@ -0,0 +1,39 @@ +''' + + ooo ooooo oooooooooo. ooooo ooo + `88. .888' `888' `Y8b `888b. `8' + 888b d'888 .ooooo. 888 888 .ooooo. 8 `88b. 8 .oooo. + 8 Y88. .P 888 d88' `88b 888 888 d88' `88b 8 `88b. 8 `P )88b + 8 `888' 888 888 888 888 888 888ooo888 8 `88b.8 .oP"888 + 8 Y 888 888 888 888 d88' 888 .o 8 `888 d8( 888 + o8o o888o `Y8bod8P' o888bood8P' `Y8bod8P' o8o `8 `Y888""8o + +Copyright + 2014-2015 MoDeNa Consortium, All rights reserved. + +License + This file is part of Modena. + + Modena is free software; you can redistribute it and/or modify it under + the terms of the GNU General Public License as published by the Free + Software Foundation, either version 3 of the License, or (at your option) + any later version. + + Modena is distributed in the hope that it will be useful, but WITHOUT ANY + WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS + FOR A PARTICULAR PURPOSE. See the GNU General Public License + for more details. + + You should have received a copy of the GNU General Public License along + with Modena. If not, see . + +Description + Python library of FireTasks + +Authors + Henrik Rusche + +Contributors +''' + +from SurfaceTension import m diff --git a/applications/PUfoam/MoDeNaModels/SurfaceTension/initModels b/applications/PUfoam/MoDeNaModels/SurfaceTension/initModels new file mode 100755 index 000000000..5dc3db8c0 --- /dev/null +++ b/applications/PUfoam/MoDeNaModels/SurfaceTension/initModels @@ -0,0 +1,62 @@ +#!/usr/bin/python +''' + + ooo ooooo oooooooooo. ooooo ooo + `88. .888' `888' `Y8b `888b. `8' + 888b d'888 .ooooo. 888 888 .ooooo. 8 `88b. 8 .oooo. + 8 Y88. .P 888 d88' `88b 888 888 d88' `88b 8 `88b. 8 `P )88b + 8 `888' 888 888 888 888 888 888ooo888 8 `88b.8 .oP"888 + 8 Y 888 888 888 888 d88' 888 .o 8 `888 d8( 888 + o8o o888o `Y8bod8P' o888bood8P' `Y8bod8P' o8o `8 `Y888""8o + +Copyright + 2014-2015 MoDeNa Consortium, All rights reserved. + +License + This file is part of Modena. + + Modena is free software; you can redistribute it and/or modify it under + the terms of the GNU General Public License as published by the Free + Software Foundation, either version 3 of the License, or (at your option) + any later version. + + Modena is distributed in the hope that it will be useful, but WITHOUT ANY + WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS + FOR A PARTICULAR PURPOSE. See the GNU General Public License for more + details. + + You should have received a copy of the GNU General Public License along + with Modena. If not, see . + +Description + Initialisation script for the flowRate model. The script calculates a few + data points and fits the surrogate model. Then the model is inserted into + the database. + +Authors + Henrik Rusche + +Contributors +''' + +from modena import SurrogateModel +from modena.Strategy import Workflow2 +#import flowRate +import SurfaceTension +from fireworks import LaunchPad +from fireworks.core.rocket_launcher import rapidfire +from fireworks.utilities.fw_serializers import load_object + + +# set up the LaunchPad and reset it +launchpad = LaunchPad() +launchpad.reset('', require_password=False) + +initWfs = Workflow2([]) +for m in SurrogateModel.get_instances(): + initWfs.addNoLink(m.initialisationStrategy().workflow(m)) + +# store workflow and launch it locally +launchpad.add_wf(initWfs) +rapidfire(launchpad) + diff --git a/applications/PUfoam/MoDeNaModels/SurfaceTension/src/ 0_initial_profile_global.xlo b/applications/PUfoam/MoDeNaModels/SurfaceTension/src/ 0_initial_profile_global.xlo new file mode 100644 index 000000000..a3e56c411 --- /dev/null +++ b/applications/PUfoam/MoDeNaModels/SurfaceTension/src/ 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Generated by TAPENADE (INRIA, Tropics team) +! Tapenade 3.10 (r5498) - 20 Jan 2015 09:48 +! +! Differentiation of formfunctionlocal in forward (tangent) mode: +! variations of useful results: f rhop +! with respect to varying inputs: rhop +! RW status of diff variables: f:out rhop:in-out +SUBROUTINE FORMFUNCTIONLOCAL_D(rhop, rhopd_nogp, fd, user, ierr) + + +!PETSc modules + Use PetscManagement + + +!DFT modules + USE MOD_DFT_FMT + USE MOD_DFT_CHAIN + USE MOD_DFT_FMT_d + USE MOD_DFT_CHAIN_d + USE MOD_DFT_DISP_WDA_D + + + USE BASIC_VARIABLES, ONLY : ncomp + USE EOS_VARIABLES, Only:dhs, rho + USE VLE_VAR, Only: rhob + USE MOD_DFT, ONLY : fa, zp + USE DFT_FCN_MODULE, ONLY : chempot_res + USE GLOBAL_X, ONLY : ngrid, ngp + IMPLICIT NONE + +#include + +! Input/output variables: + type (userctx) user + PetscScalar rhop(ncomp,user%gxs:user%gxe) + PetscScalar rhopd_nogp(ncomp,user%xs:user%xe) + !PetscScalar f(ncomp,user%xs:user%xe) + PetscScalar fd(ncomp,user%xs:user%xe) + PetscErrorCode ierr + +! Local variables: + PetscInt i + PetscInt k + REAL,dimension(user%gxs:user%gxe) :: n0,n1,n2,n3,nv1,nv2 !ngp muss groesser als fa+fa/2 sein!! + REAL,dimension(user%gxs:user%gxe) :: phi_dn0,phi_dn1,phi_dn2,phi_dn3,phi_dnv1,phi_dnv2 + REAL,dimension(user%gxs:user%gxe) :: phi_dn0d,phi_dn1d,phi_dn2d,phi_dn3d,phi_dnv1d,phi_dnv2d + REAL,dimension(user%xs:user%xe,ncomp) :: dF_drho_FMT,dF_drho_FMTd + REAL,dimension(user%gxs:user%gxe,ncomp) :: rhobar,lambda,rhobard,lambdad + REAL,dimension(user%xs:user%xe,ncomp) :: dF_drho_CHAIN,dF_drho_CHAINd + REAL :: Vext(ncomp) + + !DISP VAR + REAL,dimension(user%gxs:user%gxe,ncomp) :: rhop_wd,my_disp,df_disp_drk + REAL,dimension(user%gxs:user%gxe,ncomp) :: rhop_wdd,my_dispd + REAL,dimension(user%gxs:user%gxe) :: f_disp + REAL, dimension(ncomp) :: dF_drho_disp + REAL, dimension(ncomp) :: dF_drho_dispd + + + + INTRINSIC EXP + REAL :: arg1 + REAL :: arg1d + PetscScalar :: rhopd(ncomp,user%gxs:user%gxe) + + rhopd = 0.0 + rhopd(1:ncomp,user%xs:user%xe) = rhopd_nogp(1:ncomp,user%xs:user%xe) + + + +!calculate weighted densities + CALL FMT_WEIGHTED_DENSITIES_D(rhop, rhopd, n0, n1, n2, n3, nv1, nv2, & +& phi_dn0, phi_dn0d, phi_dn1, phi_dn1d, phi_dn2& +& , phi_dn2d, phi_dn3, phi_dn3d, phi_dnv1, & +& phi_dnv1d, phi_dnv2, phi_dnv2d, user) +!calculate averaged density rhobar and lambda (both needed for chain term) + CALL CHAIN_AUX_D(rhop, rhopd, rhobar, rhobard, lambda, lambdad, user) +!HIER DISP!!! + CALL DISP_WEIGHTED_DENSITIES_D(rhop, rhopd, rhop_wd, rhop_wdd, user) + CALL DISP_MU_D(rhop_wd, rhop_wdd, f_disp, my_disp, my_dispd, & +& df_disp_drk, user) + + fd = 0.0 + df_drho_chaind = 0.0 + df_drho_fmtd = 0.0 + df_drho_dispd = 0.0 + + DO i = user%xs,user%xe + CALL FMT_DFDRHO_D(i, fa, user, phi_dn0, phi_dn0d, phi_dn1, phi_dn1d& +& , phi_dn2, phi_dn2d, phi_dn3, phi_dn3d, phi_dnv1, & +& phi_dnv1d, phi_dnv2, phi_dnv2d, df_drho_fmt, & +& df_drho_fmtd) + CALL CHAIN_DFDRHO_D(i, rhop, rhopd, lambda, lambdad, rhobar, rhobard& +& , df_drho_chain, df_drho_chaind, user) + +!HIER DISP!!! + CALL DISP_DFDRHO_WDA_D(i, rhop, rhop_wd, my_disp, my_dispd, f_disp, & +& df_disp_drk, df_drho_disp, df_drho_dispd, user) + + + vext(1:ncomp) = 0.0 + DO k=1,ncomp + IF (zp(i) .LT. dhs(k)/2.0) vext(k) = 100000.0 +! If( zp(ngrid) - zp(i) < dhs(k)/2.0 ) Vext(k) = 100000.0 + arg1d = -df_drho_fmtd(i,k)-df_drho_chaind(i,k)-df_drho_dispd(k) + arg1 = chempot_res(k) - vext(k) - df_drho_fmt(i, k) - & +& df_drho_chain(i, k) - df_drho_disp(k) + + fd(k, i) = rhob(1,k)*arg1d*EXP(arg1) - rhopd(k, i) + !f(k, i) = xx(k)*rho*EXP(arg1) - rhop(k, i) + END DO + END DO +END SUBROUTINE FORMFUNCTIONLOCAL_D + + + + + + + + + +!------------------------------------------------------------------------------------------------ +!This Subroutine calculates the Jacobi-Vector product using derivatives obtained via AD +!------------------------------------------------------------------------------------------------ +Subroutine Jac_Shell_AD(Jshell,v_in,v_out) + +use Global_x, only: x,snes +Use PetscManagement + +#include "finclude/petsc.h90" + + +!passed + Mat :: Jshell + Vec :: v_in !has global size discret (NOT discret +- ghost points!!) + Vec :: v_out +!local + PetscScalar, pointer :: xd(:), rhop_loc(:,:),fd(:) !for dof2, xd and fd are twice the size as for dof1 + PetscErrorCode :: ierr + Type (userctx) :: user + DM :: da + Vec :: rhop_local + + + +!get the user context and DM which are associated with nonlinear solver + call SNESGetApplicationContext(snes,user,ierr) + call SNESGetDM(snes,da,ierr) + +!get local vector for x (needed because we need the ghost point values of x) + call DMGetLocalVector(da,rhop_local,ierr) + +!copy global to local for x (then x_local also contains ghost points) + call DMGlobalToLocalBegin(da,x,INSERT_VALUES,rhop_local,ierr) + call DMGlobalToLocalEnd(da,x,INSERT_VALUES,rhop_local,ierr) + +!get pointers to the vectors x_local,v_in and v_out + call DMDAVecGetArrayF90(da,rhop_local,rhop_loc,ierr) + call VecGetArrayF90(v_in, xd, ierr ) + call VecGetArrayF90(v_out, fd, ierr ) + +! Get local grid boundaries (dont know why this is neccessary again!) + call DMDAGetCorners(da, & !the distributed array + & user%xs, & !corner index in x direction + & PETSC_NULL_INTEGER, & !corner index in y direction + & PETSC_NULL_INTEGER, & !corner index in z direction + & user%xm, & !width of locally owned part in x direction + & PETSC_NULL_INTEGER, & !width of locally owned part in y direction + & PETSC_NULL_INTEGER, & !width of locally owned part in z direction + & ierr) !error check + + call DMDAGetGhostCorners(da, & !the distributed array + & user%gxs, & !corner index in x direction (but now counting includes ghost points) + & PETSC_NULL_INTEGER, & !corner index in y direction (but now counting includes ghost points) + & PETSC_NULL_INTEGER, & !corner index in z direction (but now counting includes ghost points) + & user%gxm, & !width of locally owned part in x direction (but now including ghost points) + & PETSC_NULL_INTEGER, & !width of locally owned part in y direction (but now including ghost points) + & PETSC_NULL_INTEGER, & !width of locally owned part in z direction (but now including ghost points) + & ierr) !error check + + +! Here we shift the starting indices up by one so that we can easily +! use the Fortran convention of 1-based indices (rather 0-based indices). + user%xs = user%xs+1 + user%gxs = user%gxs+1 + + user%xe = user%xs+user%xm-1 + user%gxe = user%gxs+user%gxm-1 + + +!--------------------------------------------------------- +!call AD generated Routine + !x_loc: x + !xd : direction which the derivative is calculated for + !fd : the directional derivative in direction xd + + call FORMFUNCTIONLOCAL_D(rhop_loc,xd,fd,user,ierr) +!--------------------------------------------------------- + + + + +!restore arrays + call DMDAVecRestoreArrayF90(da,rhop_local,rhop_loc,ierr ) + call VecRestoreArrayF90( v_in, xd, ierr ) + call VecRestoreArrayF90( v_out, fd, ierr ) + call DMRestoreLocalVector(da,rhop_local,ierr) + + +End Subroutine Jac_Shell_AD + + + + +! empty subroutine for shell jacobian; probably should copy v_x to x, as they might not be same +Subroutine Jac_Matrix_Empty(snes,v_x,jac,B,flag,dummy,ierr) + implicit none +#include "finclude/petsc.h90" + SNES :: snes + Vec :: v_x + Mat :: jac,B + MatStructure :: flag + PetscErrorCode :: ierr + integer dummy(*) +End Subroutine Jac_Matrix_Empty + + + + + + + diff --git a/applications/PUfoam/MoDeNaModels/SurfaceTension/src/Function.F90 b/applications/PUfoam/MoDeNaModels/SurfaceTension/src/Function.F90 new file mode 100644 index 000000000..0080485a0 --- /dev/null +++ b/applications/PUfoam/MoDeNaModels/SurfaceTension/src/Function.F90 @@ -0,0 +1,251 @@ +!>This file contains the residual function of the density functional theory +!!calculation. + + + +!>The subroutine FormFunction is a wrapper function which takes care of +!!handling the global PETSc data structures and creates local copys for +!!every processor. It then calls the subroutine FormFunctionLocal which +!!performs the actual calculation of the residual at every grid point. + + +Subroutine FormFunction(snes,X,F,user,ierr) +Use PetscManagement +Implicit None +#include +#include +#include +#include +#include +#include +#include +#include + +! Input/output variables: + SNES snes + Vec X,F + PetscErrorCode ierr + type (userctx) user + DM da + +! Declarations for use with local arrays: + PetscScalar,pointer :: lx_v(:,:),lf_v(:,:) + Vec localX + +! Scatter ghost points to local vector, using the 2-step process +! DMGlobalToLocalBegin(), DMGlobalToLocalEnd(). +! By placing code between these two statements, computations can +! be done while messages are in transition. + call SNESGetDM(snes,da,ierr) + call DMGetLocalVector(da,localX,ierr) + call DMGlobalToLocalBegin(da,X,INSERT_VALUES, & + & localX,ierr) + call DMGlobalToLocalEnd(da,X,INSERT_VALUES,localX,ierr) + + + !call VecGetArrayF90(localX,lx_v,ierr) !only for DOF=1 + !call VecGetArrayF90(F,lf_v,ierr) !only for DOF=1 + call DMDAVecGetArrayF90(da,localX,lx_v,ierr) + call DMDAVecGetArrayF90(da,F,lf_v,ierr) + +! Compute function over the locally owned part of the grid + call FormFunctionLocal(lx_v,lf_v,user,ierr) + +! Restore vectors + !call VecRestoreArrayF90(localX,lx_v,ierr) !only for DOF=1 + !call VecRestoreArrayF90(F,lf_v,ierr) !only for DOF=1 + call DMDAVecRestoreArrayF90(da,localX,lx_v,ierr) + call DMDAVecRestoreArrayF90(da,F,lf_v,ierr) + + +! Insert values into global vector + + call DMRestoreLocalVector(da,localX,ierr) + + return +End Subroutine FormFunction + + + + + + + + + + + +!>This subroutine performs the local evaluation of the residual function. +!!It calls the subroutines which calculate the different contributions to +!!the Helmholtz energy functional. + + +Subroutine FormFunctionLocal(rhop,f,user,ierr) +!PETSc modules + Use PetscManagement +!DFT modules + Use mod_DFT_FMT + Use mod_DFT_CHAIN + Use mod_DFT_DISP_WDA + Use PARAMETERS, Only: PI ,muhs,muhc,mudisp + Use BASIC_VARIABLES, Only: ncomp,nc,np ,nphas,xi,dense,parame,ensemble_flag !nphas nur fur fugacity call + Use EOS_VARIABLES, Only:dhs,rho ,phas,eta_start,x,mseg,eta !letze 4 nur zum Test for aufruf eos_phi!! + Use mod_DFT, Only: fa,zp,dzp,free,pbulk, fa_disp, ab_disp !letzen beiden nur fur elmars version + Use VLE_VAR, Only: rhob + Use DFT_FCN_MODULE, Only: ChemPot_res,ChemPot_total + Use Global_x, Only: ngrid, ngp + + +Implicit None + +! Input/output variables: + type (userctx) user + PetscScalar rhop(ncomp,user%gxs:user%gxe) + PetscScalar f(ncomp,user%xs:user%xe) + PetscErrorCode ierr + +! Local variables: + PetscInt i + PetscInt k + + !FMT + REAL,dimension(user%gxs:user%gxe) :: n0,n1,n2,n3,nv1,nv2 !ngp muss groesser als fa+fa/2 sein!! + REAL,dimension(user%gxs:user%gxe) :: phi_dn0,phi_dn1,phi_dn2,phi_dn3,phi_dnv1,phi_dnv2 + REAL :: f_fmt,temp,zs + REAL,dimension(user%xs:user%xe,ncomp) :: dF_drho_FMT + + !Chain + REAL,dimension(user%gxs:user%gxe,ncomp) :: rhobar,lambda + REAL :: f_ch + REAL,dimension(user%xs:user%xe,ncomp) :: dF_drho_CHAIN + + !DISP VAR + REAL,dimension(user%gxs:user%gxe,ncomp) :: rhop_wd,my_disp,df_disp_drk + REAL,dimension(user%gxs:user%gxe) :: f_disp + REAL, dimension(ncomp) :: dF_drho_disp + !for Elmars Version + REAL, DIMENSION(user%gxs:user%gxe,ncomp):: rhoi_disp,mydisp,dadisp_dr + REAL, DIMENSION(user%gxs:user%gxe) :: adisp,rho_disp,rhop_sum + REAL :: dF_drho_att(ncomp) + INTEGER :: fa_psi_max,WDA_var + + + !polar + REAL :: fres_polar,fdd,fqq,fdq,mu_polar(nc) + REAL :: fdd_rk, fqq_rk, fdq_rk, z3_rk + INTEGER :: ik + !association + REAL :: f_assoc + REAL :: mu_assoc(nc) + REAL :: lnphi(np,nc), fres + + REAL :: f_tot, delta_f + REAL :: Vext(ncomp) + + + Do k = 1,ncomp + Do i= user%xs,user%xe + If( rhop(k,i) < epsilon(dhs) ) rhop(k,i) = epsilon(dhs) + End Do + End Do + + DO i = user%gxs,user%gxe + rhop_sum(i) = sum( rhop(1:ncomp,i) ) + END DO + + + + !calculate weighted densities + call FMT_Weighted_Densities(rhop,n0,n1,n2,n3,nv1,nv2,phi_dn0,phi_dn1,phi_dn2,phi_dn3,phi_dnv1,phi_dnv2,user) + + !calculate averaged density rhobar and lambda (both needed for chain term) + call Chain_aux(rhop,rhobar,lambda,user) + + + !weighted densities for Dispersion +! call DISP_Weighted_Densities(rhop, rhop_wd, user) +! call DISP_mu(rhop_wd,f_disp,my_disp,df_disp_drk,user) + + !Elmars Version + fa_psi_max = maxval(fa_disp(1:ncomp)) + call rhoi_disp_wd ( ngrid, fa_disp, fa_psi_max, ab_disp, rhop, rhoi_disp,user ) + CALL a_disp_pcsaft ( ngrid, fa_disp, fa_psi_max, rhoi_disp, rho_disp, adisp, mydisp, dadisp_dr,user ) + + + free = 0.0 + + DO i = user%xs,user%xe + + !FMT + call FMT_dFdrho(i,fa,user,phi_dn0,phi_dn1,phi_dn2,phi_dn3,phi_dnv1,phi_dnv2,dF_drho_FMT) + zs = 1.0 - n3(i) + temp = log(zs) + f_fmt = - n0(i)*temp + n1(i)*n2(i)/zs - nv1(i)*nv2(i)/zs & !see for example eq. 30 in "Fundamental measure theory for hard-sphere mixtures revisited: the White bear version (Roth) + + (n2(i)**3 -3.0*n2(i)*nv2(i)*nv2(i)) *(n3(i)+zs*zs*temp) & + /36.0/PI/zs/zs/n3(i)**2 + + !Chain + call Chain_dFdrho(i,rhop,lambda,rhobar,dF_drho_CHAIN,f_ch,user) + + !Dispersion + WDA_var = 1 + call dF_disp_drho_wda( i, WDA_var, fa_disp, ab_disp, rhop, rhop_sum, & + rhoi_disp, rho_disp, adisp, mydisp, dadisp_dr, dF_drho_att,user ) + + if(WDA_var == 1) adisp(i) = rho_disp(i) * adisp(i) + if(WDA_var == 2) adisp(i) = rhop_sum(i) * adisp(i) + + + !polar as LDA + fres_polar = 0.0 + mu_polar(:) = 0.0 + dense(1) = PI / 6.0 * SUM( rhop(1:ncomp,i) * mseg(1:ncomp) * dhs(1:ncomp)**3 ) + xi(1,1:ncomp) = rhop(1:ncomp,i) / SUM( rhop(1:ncomp,i) ) + ensemble_flag = 'tv' + IF ( SUM( parame(1:ncomp,6) ) > 1.E-10 .OR. SUM( parame(1:ncomp,7) ) > 1.E-10 ) THEN + eta = dense(1) + rho = SUM(rhop(1:ncomp,i)) + x(1:ncomp) = xi(1,1:ncomp) + call F_POLAR ( fdd, fqq, fdq ) + fres_polar = ( fdd + fqq + fdq ) * SUM( rhop(1:ncomp,i) ) + DO ik = 1, ncomp + z3_rk = PI/6.0 * mseg(ik) * dhs(ik)**3 + call PHI_POLAR ( ik, z3_rk, fdd_rk, fqq_rk, fdq_rk ) + mu_polar(ik) = fdd_rk + fqq_rk + fdq_rk + END DO + END IF + + !association as LDA + f_assoc = 0.0 + mu_assoc(:) = 0.0 + IF ( SUM( NINT(parame(1:ncomp,12)) ) > 0) THEN + call ONLY_ONE_TERM_EOS_NUMERICAL ( 'hb_term ', 'TPT1_Chap' ) + call FUGACITY ( lnphi ) + call RESTORE_PREVIOUS_EOS_NUMERICAL + f_assoc = fres * SUM( rhop(1:ncomp,i) ) + mu_assoc(1:ncomp) = lnphi(1,1:ncomp) + END IF + + f_tot = f_fmt + f_ch + adisp(i) + fres_polar + f_assoc & + + SUM( rhop(1:ncomp,i)*( LOG(rhop(1:ncomp,i)/rhob(1,1:ncomp))-1.0 ) ) + delta_f = f_tot - ( SUM(rhop(1:ncomp,i)*chemPot_res(1:ncomp)) - pbulk) ! all quantities .../(kT) + free = free + delta_f*dzp + + + + Do k=1,ncomp + f(k,i) = -(rhob(1,k) * exp(ChemPot_res(k)-dF_drho_FMT(i,k)-dF_drho_CHAIN(i,k)-dF_drho_att(k) & + -mu_polar(k) - mu_assoc(k)) - rhop(k,i)) + End Do + + END DO + + + +End Subroutine FormFunctionLocal + + + + + + diff --git a/applications/PUfoam/MoDeNaModels/SurfaceTension/src/Helfer_Routinen.F90 b/applications/PUfoam/MoDeNaModels/SurfaceTension/src/Helfer_Routinen.F90 new file mode 100644 index 000000000..a4adc4019 --- /dev/null +++ b/applications/PUfoam/MoDeNaModels/SurfaceTension/src/Helfer_Routinen.F90 @@ -0,0 +1,56 @@ + +!>This file contains subroutines that make printing of +!!local and global PETSc arrays easier. + + + +Subroutine PrintGlobalVec(GlobalVec,filename) +Implicit None +#include +#include +#include +#include + + + Vec :: GlobalVec + character(80) :: filename + + PetscViewer viewer + PetscErrorCode ierr + +!Print global vector to a file + call PetscViewerASCIIOpen(PETSC_COMM_WORLD,filename,viewer,ierr) + call VecView(GlobalVec,viewer,ierr) + + call PetscViewerDestroy(viewer,ierr) + +End Subroutine PrintGlobalVec + + + +Subroutine PrintLocalVec(GlobalVec,da,filename) +Implicit None +#include +#include +#include +#include +#include +#include + + Vec GlobalVec + Vec LocalVec + DM da + character(80) :: filename + + PetscViewer viewer + PetscErrorCode ierr + + call DMGetLocalVector(da,LocalVec,ierr) !create a locally owned part of a global distribued array + call DMGlobalToLocalBegin(da,GlobalVec,INSERT_VALUES,LocalVec,ierr) !copy values from global array to local arrays + call DMGlobalToLocalEnd(da,GlobalVec,INSERT_VALUES,LocalVec,ierr) + call PetscViewerASCIIOpen(PETSC_COMM_SELF,filename,viewer,ierr) !associate viewer with file + call VecView(LocalVec,viewer,ierr) !every processor prints his local array to a file + call DMRestoreLocalVector(da,LocalVec,ierr) !Free memory of local vector + + +End Subroutine PrintLocalVec diff --git a/applications/PUfoam/MoDeNaModels/SurfaceTension/src/InitialGuess.F90 b/applications/PUfoam/MoDeNaModels/SurfaceTension/src/InitialGuess.F90 new file mode 100644 index 000000000..d40b9d993 --- /dev/null +++ b/applications/PUfoam/MoDeNaModels/SurfaceTension/src/InitialGuess.F90 @@ -0,0 +1,260 @@ +!>This file contains the subroutines to set the initial density profile. + + + + +!>The subroutine FormFunction is a wrapper function which takes care of +!!handling the global PETSc data structures and creates local copys for +!!every processor. It then calls the subroutine InitialGuessLocal which +!!sets the initial density values. + +Subroutine FormInitialGuess(snes,X,ierr) +Use PetscManagement +Use f90moduleinterfaces + +Implicit None + + +#include +#include +#include +#include +#include +#include +#include +#include + +! Input/output variables: + SNES snes + type(userctx), pointer:: puser + Vec X + PetscErrorCode ierr + DM da + +! Declarations for use with local arrays: + PetscScalar,pointer :: lx_v(:,:) + Vec :: localX + + ierr = 0 + call SNESGetDM(snes,da,ierr) + call SNESGetApplicationContext(snes,puser,ierr) + +! Get a pointer to vector data. + call DMGetLocalVector(da,localX,ierr) + !call VecGetArrayF90(localX,lx_v,ierr) !only for DOF=1 + call DMDAVecGetArrayF90(da,localX,lx_v,ierr) + + + +! Compute initial guess over the locally owned part of the grid + call InitialGuessLocal(puser,lx_v,ierr) + +! Restore vector + !call VecRestoreArrayF90(localX,lx_v,ierr) !only for DOF=1 + call DMDAVecRestoreArrayF90(da,localX,lx_v,ierr) + + +! Insert values into global vector + call DMLocalToGlobalBegin(da,localX,INSERT_VALUES,X,ierr) + call DMLocalToGlobalEnd(da,localX,INSERT_VALUES,X,ierr) + call DMRestoreLocalVector(da,localX,ierr) + +End Subroutine FormInitialGuess + + + + + +!>In this subroutine every processor sets the initial density values +!!at its locally owned part of the grid. + +Subroutine InitialGuessLocal(user,rhop,ierr) + +!PETSc modules + use PetscManagement +!VLE and DFT modules + Use BASIC_VARIABLES, ONLY: ncomp,t,parame + Use EOS_VARIABLES, Only:rho + Use VLE_VAR, Only: rhob,tc + Use PARAMETERS, Only: PI + Use mod_DFT, Only: box,zp,dzp + Use Global_x, Only: ngrid + + + implicit none + +#include +#include +#include +#include +#include +#include +#include +#include + +! Input/output variables: + type (userctx) :: user + PetscScalar :: rhop(ncomp,user%gxs:user%gxe) + PetscErrorCode :: ierr + + +! Local variables: + PetscInt i,k + PetscBool flg + REAL :: arg + INTEGER :: pert + REAL :: tanhfac + REAL :: zp_i + REAL :: zp_middle + + + +!normal or perturbed inital profile? + call PetscOptionsGetInt(PETSC_NULL_CHARACTER,'-init_pert',pert,flg,ierr) + + + zp_middle = (ngrid/2)*dzp + tanhfac = -2.3625*t/tc + 2.4728 + + + !default: no perturbation, start with bulk density + + +IF(user%num_procs == 1) THEN !if only one processor involved + + Do k = 1,ncomp + Do i=user%gxs,user%gxe !proc 0 has to calculate values for ghost points out of physical domain (from -irc to -1 and discret to discret+irc) and its regular part + zp_i = zp(i) + rhop(k,i) = ( TANH(-(zp_i -zp_middle) / parame(k,2) *tanhfac) + 1.0 ) * rhob(1,k)/2.0 & + - ( TANH(-(zp_i - zp_middle) / parame(k,2) *tanhfac) - 1.0 ) * rhob(2,k)/2.0 +!rhop(k,i) = rhob(1,k) + !make sure density is nonzero + If(rhop(k,i) == 0.0) rhop(k,i) = rhop(k,i-1) + End Do + End Do + + + +Else !parallel simulation + + + + IF(user%rank == 0) THEN !watch the user%xs vs user%gxs (first no ghost points, second with ghost points) + + Do k=1,ncomp !loop over dof = loop over components + Do i=user%gxs,user%xe !proc 0 has to calculate values for ghost points out of physical domain (from -irc to -1) and its regular part + zp_i = zp(i) + !perturb = (rhob(1,j)-rhob(2,j))/2.0 * i * (discret - i) / (damp*discret)**2 + !rhop(k,i) = ( TANH(-(zp_i -zp_middle) / parame(k,2) *tanhfac) + 1.0 ) * rhob(1,k)/2.0 & + ! - ( TANH(-(zp_i - zp_middle) / parame(k,2) *tanhfac) - 1.0 ) * rhob(2,k)/2.0 !+ perturb +rhop(k,i) = rhob(1,k) + !make sure density is nonzero + If(rhop(k,i) == 0.0) rhop(k,i) = rhop(k,i-1) + End Do + End Do + + + ELSE IF(user%rank == user%num_procs-1) THEN + + Do k=1,ncomp !loop over dof = loop over components + Do i=user%gxs,user%gxe !last proc has to calculate values for ghost points out of physical domain (from discret to discret+irc) and its regular part + zp_i = zp(i) + !perturb = (rhob(1,j)-rhob(2,j))/2.0 * i * (discret - i) / (damp*discret)**2 + !rhop(k,i) = ( TANH(-(zp_i -zp_middle) / parame(k,2) *tanhfac) + 1.0 ) * rhob(1,k)/2.0 & + ! - ( TANH(-(zp_i - zp_middle) / parame(k,2) *tanhfac) - 1.0 ) * rhob(2,k)/2.0 !+ perturb +rhop(k,i) = rhob(1,k) + !make sure density is nonzero + If(rhop(k,i) == 0.0) rhop(k,i) = rhop(k,i-1) + End Do + End Do + + + ELSE + + Do k=1,ncomp !loop over dof = loop over components + Do i=user%xs,user%xe !middle procs have to calculate only their regular part + zp_i = zp(i) + !perturb = (rhob(1,j)-rhob(2,j))/2.0 * i * (discret - i) / (damp*discret)**2 + !rhop(k,i) = ( TANH(-(zp_i -zp_middle) / parame(k,2) *tanhfac) + 1.0 ) * rhob(1,k)/2.0 & + ! - ( TANH(-(zp_i - zp_middle) / parame(k,2) *tanhfac) - 1.0 ) * rhob(2,k)/2.0 !+ perturb +rhop(k,i) = rhob(1,k) + !make sure density is nonzero + If(rhop(k,i) == 0.0) rhop(k,i) = rhop(k,i-1) + End Do + End Do + + END IF + + +End If + + + + + + + + + + + + + + + + + + + +! If(pert == 1) Then +! Do i=user%xs,user%xe +! arg = zp(i) * PI / box +! rhop(k,i) = rhob(1,k) + 0.5*rhob(1,k) * sin(arg) +! End Do +! End If +! +! If(pert == 2) Then +! Do i=user%xs,user%xe +! arg = zp(i) * 2.0 * PI / box +! rhop(k,i) = rhob(1,k) + 0.5*rhob(1,k) * sin(arg) +! End Do +! End If +! +! If(pert == 3) Then +! Do i=user%xs,user%xe +! arg = zp(i) * 3.0 * PI / box +! rhop(k,i) = rhob(1,k) + 0.5*rhob(1,k) * sin(arg) +! End Do +! 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+1.000 UP +1.000 UL +LTb +stroke +grestore +end +showpage +%%Trailer +%%DocumentFonts: Helvetica diff --git a/applications/PUfoam/MoDeNaModels/SurfaceTension/src/Main.F90 b/applications/PUfoam/MoDeNaModels/SurfaceTension/src/Main.F90 new file mode 100644 index 000000000..3ad6d2814 --- /dev/null +++ b/applications/PUfoam/MoDeNaModels/SurfaceTension/src/Main.F90 @@ -0,0 +1,234 @@ + +!> +!!THIS CODE WAS WRITTEN AT +!!UNIVERSITY OF STUTTGART, +!!INSTITUTE OF TECHNICAL THERMODYNAMICS AND THERMAL PROCESS ENGINEERING +!!BY +!!JOACHIM GROSS +!!JONAS MAIRHOFER +!! +!! + + + + + + + + + + + + +!>WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +!! This program calculates surface tensions using the a Density Functional +!! Theory based on the PC-SAFTequation of state. +!! The contributions to the Helmholtz energy functional are calculated +!! as folows: +!! Hard Sphere Contribution: White-Bear Version of the Fundamental Measure Theory +!! Chain Formation: TPT1 +!! Dispersion is treated in a weighted density approximation +!! Associative and polar contributions are treated in a local density approximation +!! +!! +!! The input parameters are read from the file "in.txt" which has to +!! be in the same directory as the executable. +!! +!! The input file must have the following format: +!! Line1: Value of temperature in Kelvin +!! Line2: Number of components present in the system (ncomp) +!! Line3 Name of component 1 +!! ... +!! Line3+ncomp Name of component ncomp +!! Line3+ncomp+1 Molar (overall) concentration of component 1 +!! ... +!! Line3+2ncomp Molar (overall) concentration of component ncomp +!! +!! For a binary system, these molar fractions are only treated as an initial guess and may be set to e.g. 0. +!! +!! +!! So far, pressure is set to 1bar in all calculaions +!! +!! +!!If you would like to use this code in your work, please cite the +!!following publications: +!! +!!Gross, Joachim, and Gabriele Sadowski. "Perturbed-chain SAFT: An equation of state based on a perturbation theory for chain molecules." Industrial & engineering chemistry research 40.4 (2001): 1244-1260. +!!Gross, Joachim, and Gabriele Sadowski. "Application of the perturbed-chain SAFT equation of state to associating systems." Industrial & engineering chemistry research 41.22 (2002): 5510-5515. +!!Gross, Joachim, and Jadran Vrabec. "An equation?of?state contribution for polar components: Dipolar molecules." AIChE journal 52.3 (2006): 1194-1204. +!!Gross, Joachim. "A density functional theory for vapor-liquid interfaces using the PCP-SAFT equation of state." The Journal of chemical physics 131.20 (2009): 204705. +!!Klink, Christoph, and Joachim Gross. "A density functional theory for vapor?liquid interfaces of mixtures using the perturbed-chain polar statistical associating fluid theory equation of state." Industrial & Engineering Chemistry Research 53.14 (2014): 6169-6178. +!! +!! +!! In order to run this code, PETSc 3.4.4 has to be installed +!!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! + + +Program DFT + +Use PARAMETERS, Only: np,nc,KBOL +Use BASIC_VARIABLES, Only: ncomp,t,p,ensemble_flag,num,parame,eos,pol,xif,compna +Use EOS_VARIABLES, Only: dhs,mseg,eta,dd_term,dq_term,qq_term +Use EOS_CONSTANTS, Only: ap,bp,dnm +Use mod_DFT, Only: box,dzp,fa,zp,fa_disp,ab_disp,pbulk +Use VLE_VAR, ONLY: tc,pc,rhob,density +USE DFT_FCN_MODULE, ONLY: chemPot_total + +!PETSc modules +Use PetscManagement +Use f90moduleinterfaces +Use Global_x !(snes,ngrid,ngp,x,r,timer) + + +Implicit None + +#include + +!> ---------------------------------------------------------------------- +!!Variables +!! ---------------------------------------------------------------------- + +PetscErrorCode :: ierr +type (userctx) :: user +PetscBool :: flg +INTEGER :: i +character(80) :: filename='' +REAL :: zges(np) +REAL :: dhs_save(nc) +REAL :: cif(nc) +REAL :: psi_factor + +!external subroutines associated with Solver +external FormInitialGuess +external FormFunction + + +!> - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - +!! Initialize program +!! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - + call PetscInitialize(PETSC_NULL_CHARACTER,ierr) + call MPI_Comm_rank(PETSC_COMM_WORLD,user%rank,ierr) + call MPI_Comm_size(PETSC_COMM_WORLD,user%num_procs,ierr) + +!> ---------------------------------------------------------------------- +!!Read information from inputfile "in.txt" +!! ---------------------------------------------------------------------- + + filename='./in.txt' + CALL file_open(filename,77) ! open input file + READ (77,*) t ! read temperature + READ (77,*) ncomp ! read number of components in the system + Do i = 1,ncomp ! read component names + READ (77,*) compna(i) + End Do + Do i = 1,ncomp ! read component overall molar concentrations + READ (77,*) xif(i) + End Do + +! !calculate molar fractions from molar concentrations +! xif(1:ncomp) =cif(1:ncomp) / sum(cif(1:ncomp)) + + +! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - +! GENERAL SIMULATION SET UP +! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - + + num = 0 ! (num=0: using analytical derivatives of EOS) + ! (num=1: using numerical derivatives of EOS) + ! (num=2: White's renormalization group theory) + IF ( num /= 0 ) CALL SET_DEFAULT_EOS_NUMERICAL + + eos = 1 + pol = 1 + + p = 1.000e05 + + CALL para_input ! retriev pure comp. parameters + + ensemble_flag = 'tp' ! this specifies, whether the eos-subroutines + ! are executed for constant 'tp' or for constant 'tv' + + + +!> - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - +!! Start phase equilibrium calculation and determine critical point +!! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - + + CALL EOS_CONST (ap, bp, dnm) + + dd_term = 'GV' ! dipole-dipole term of Gross & Vrabec (2006) + qq_term = 'JG' ! quadrupole-quadrupole term of Gross (2005) + dq_term = 'VG' ! dipole-quadrupole term of Vrabec & Gross (2008) + + CALL VLE_MIX(rhob,density,chemPot_total,user) !user is passed so user%rank is known and only node 0 prints out the reslts of the VLE calculation + + !determine critical point + num = 0 + dhs_save = dhs !needed because subroutine CRIT_POINT_MIX changes the value + CALL CRIT_POINT_MIX(tc,user) !of the global variable dhs! In cases where Tc doesnt converge + dhs = dhs_save !dhs can be NAN after CRIT_POINT_MIX!! + !chance to overwite NAN results +! IF(user%rank == 0) THEN +! WRITE (*,*) 'Give final value of Tc:' +! READ (*,*) tc +! END IF +! CALL MPI_Bcast(tc,1,MPI_DOUBLE_PRECISION,0,PETSC_COMM_WORLD,ierr) + + + + +!>------------------------------------------- +!!DFT Set Up +!!------------------------------------------- + + num = 1 + CALL SET_DEFAULT_EOS_NUMERICAL + + !set default values (overwritten from makefile) + box = 45.0 !box length [A] + ngrid = 614 !grid points + + !overwrite box size and ngrid if options are set in makefile + call PetscOptionsGetReal(PETSC_NULL_CHARACTER,'-box',box,flg,ierr) + call PetscOptionsGetInt(PETSC_NULL_CHARACTER,'-nx',ngrid,flg,ierr) + + + dzp = box / REAL(ngrid) !grid spacing [A] + Allocate(fa(ncomp)) + fa(1:ncomp) = NINT( parame(1:ncomp,2) / dzp ) !grid points per sigma [-] + + !FOR DISP + ALLOCATE(fa_disp(ncomp),ab_disp(ncomp)) + psi_factor = 1.5 + fa_disp(1:ncomp) = NINT( psi_factor * REAL(fa(1:ncomp)) ) + Do i=1,ncomp + if( MOD(fa_disp(i),2) /= 0 ) fa_disp(i) = fa_disp(i) + 1 + End Do + + + ab_disp(1:ncomp) = psi_factor * dhs(1:ncomp) + + + ngp = 2 * maxval(fa_disp(1:ncomp)) + 5 !number of ghost points (+5 kann eig weg) + + Allocate(zp(-ngp:ngrid+ngp)) + + Do i=-ngp,ngrid+ngp + zp(i) = REAL(i) * dzp !z-distance from origin of grid points [A] + End Do + + pbulk = ( p * 1.E-30 ) / ( KBOL*t* rhob(1,0) ) * rhob(1,0) !p/kT + + + !update z3t, the T-dependent quantity that relates eta and rho, as eta = z3t*rho + CALL PERTURBATION_PARAMETER + +!>------------------------------------------- +!!Evaluate Initial Guess,Set up solver,solve system +!!------------------------------------------- + call SolverSetup + + + +End Program DFT diff --git a/applications/PUfoam/MoDeNaModels/SurfaceTension/src/Modules.F90 b/applications/PUfoam/MoDeNaModels/SurfaceTension/src/Modules.F90 new file mode 100644 index 000000000..d8045cdfb --- /dev/null +++ b/applications/PUfoam/MoDeNaModels/SurfaceTension/src/Modules.F90 @@ -0,0 +1,527 @@ +!>WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +!! This module contains constants and upper boundaries for the number of +!! components and phases in the system +!!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW + +Module PARAMETERS + + implicit none + save + + integer, parameter :: nc = 3 + integer, parameter :: np = 3 + integer, parameter :: nsite = 5 + + real, parameter :: PI = 3.141592653589793 + real, parameter :: RGAS = 8.31441 + real, parameter :: NAv = 6.022045E23 + real, parameter :: KBOL = RGAS / NAv + real, parameter :: TAU = PI / 3.0 / SQRT(2.0) + +real :: muhs(3) +real :: muhc(3) +real :: mudisp(3) + + + +End Module PARAMETERS + + + + + +Module VLE_VAR +USE PARAMETERS, ONLY: nc,np +implicit none + +REAL :: tc +REAL :: pc +REAL :: rhob(2,0:nc) +REAL :: density(np) + +End Module VLE_VAR + + + + + + + + +!>WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +!! This module contains parameters and variables that define the +!! thermodynamic state of the system as well as simulation parameters +!!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW + +Module BASIC_VARIABLES + + use PARAMETERS, only: nc, np, nsite + implicit none + save + +! ---------------------------------------------------------------------- +! basic quantities defining the mixture +! ---------------------------------------------------------------------- + integer :: ncomp + integer :: nphas + + real :: t + !real :: tc + real :: p + real, dimension(np) :: dense + !real, dimension(np) :: rhob + + real, dimension(np, nc) :: xi + real, dimension(np, nc) :: lnx + real, dimension(nc) :: xiF + + real, dimension(nc) :: mm + real, dimension(np, nc, nsite) :: mxx + + real :: alpha + + +! ---------------------------------------------------------------------- +! pure component parameters +! ---------------------------------------------------------------------- + real, dimension(nc, 25) :: parame = 0.0 + real, dimension(nc) :: chiR + character*30, dimension(nc) :: compna + real, dimension(nc, nc) :: kij, lij + real, dimension(nc, nc) :: E_LC, S_LC + real, dimension(nc) :: LLi, phi_criti, chap + + +! ---------------------------------------------------------------------- +! thermodynamic quantities +! ---------------------------------------------------------------------- + real, dimension(np) :: densta + real, dimension(0:nc*np+6) :: val_init, val_conv + + real :: h_lv + real, dimension(np) :: cpres, enthal, entrop, gibbs, f_res + + real, dimension(np) :: dp_dz, dp_dz2 + + +! ---------------------------------------------------------------------- +! choice of EOS-model and solution method +! ---------------------------------------------------------------------- + integer :: eos, pol + integer :: num + character (LEN=2) :: ensemble_flag + character (LEN=10) :: RGT_variant + + +! ---------------------------------------------------------------------- +! for input/output +! ---------------------------------------------------------------------- + integer :: outp, bindiag + real :: u_in_T, u_out_T, u_in_P, u_out_P + + +! ---------------------------------------------------------------------- +! quantities defining the numerical procedure +! ---------------------------------------------------------------------- + integer :: n_unkw + + real :: step_a, acc_a !, acc_i + real, dimension(nc) :: scaling + real, dimension(3500) :: plv_kon + real, dimension(2, 3500) :: d_kond + + character*3, dimension(10) :: it, sum_rel + character*3 :: running + + +End Module BASIC_VARIABLES + + + + +!>WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +!! This module contains parameters and variables to identify thermodynamic +!! properties +!!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW + +Module EOS_VARIABLES + + use PARAMETERS, only: nc, nsite, PI, KBOL, TAU, NAv + use BASIC_VARIABLES, only: ncomp, eos, t, p, parame, E_LC, S_LC, chiR, & + LLi, phi_criti, chap, kij, lij, ensemble_flag + implicit none + save + +! ---------------------------------------------------------------------- +! basic quantities defining the mixture (single phase) +! ---------------------------------------------------------------------- + real :: x(nc) + real :: eta_start + real :: eta + real :: rho + +! ---------------------------------------------------------------------- +! thermodynamic quantities +! ---------------------------------------------------------------------- + real :: fres + real :: lnphi(nc) + real :: pges + real :: pgesdz + real :: pgesd2 + real :: pgesd3 + + real :: h_res + real :: cp_res + real :: s_res + +! ---------------------------------------------------------------------- +! quantities of fluid theory +! ---------------------------------------------------------------------- + real :: gij(nc,nc) + real :: mx(nc,nsite) + + real :: mseg(nc) + real :: dhs(nc) + real :: uij(nc,nc) + real :: sig_ij(nc,nc) + real :: vij(nc,nc) + + real :: um + real :: order1 + real :: order2 + real :: apar(0:6) + real :: bpar(0:6) + + real :: z0t + real :: z1t + real :: z2t + real :: z3t + + integer :: nhb_typ(nc) + real :: ass_d(nc,nc,nsite,nsite) + real :: nhb_no(nc,nsite) + real :: dij_ab(nc,nc) + +! ---------------------------------------------------------------------- +! auxilliary quantities +! ---------------------------------------------------------------------- + real :: tfr + integer :: phas + + character (LEN = 2) :: dd_term, qq_term, dq_term + + real :: densav(3), denold(3) + real :: density_error(3) + + real :: alpha_nematic + real :: alpha_test(2) + +End Module EOS_VARIABLES + + + +!>WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +!! This module contains variables to store the EOS model constants +!!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW + +Module EOS_CONSTANTS + + use PARAMETERS, only: nc + implicit none + save + + real, dimension(0:6,3) :: ap, bp + real, dimension(4,9) :: dnm + + real, dimension(28) :: c_dd, n_dd, m_dd, k_dd, o_dd + real, dimension(nc,nc,0:8) :: qqp2, qqp4, ddp2, ddp4, dqp2, dqp4 + real, dimension(nc,nc,nc,0:8) :: qqp3, ddp3, dqp3 + +End Module EOS_CONSTANTS + +!>WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +!! This module contains parameters and variables for the numerical +!! evaluation of derivatives of the EOS +!!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW + +Module EOS_NUMERICAL_DERIVATIVES + + use EOS_VARIABLES, only: dd_term, qq_term, dq_term + + implicit none + save + + character (LEN=9) :: ideal_gas ! (yes, no) + character (LEN=9) :: hard_sphere ! (CSBM, no) + character (LEN=9) :: chain_term ! (TPT1, no) + character (LEN=9) :: disp_term ! (PC-SAFT, CK, no) + character (LEN=9) :: hb_term ! (TPT1_Chap, no) + character (LEN=9) :: LC_term ! (MSaupe, no) + character (LEN=9) :: branch_term ! (TPT2, no) + character (LEN=9) :: II_term ! (......., no) + character (LEN=9) :: ID_term ! (......., no) + + character (LEN=9) :: subtract1 ! (1PT, 2PT, no) + character (LEN=9) :: subtract2 ! (ITTpolar, no) + + character (LEN=9) :: save_eos_terms(10) + +End Module EOS_NUMERICAL_DERIVATIVES + + +!>WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +!! Module STARTING_VALUES +!! This module contains parameters and variables for a phase stability +!! analyis as part of a flash calculation. +!!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW + + Module STARTING_VALUES + + use PARAMETERS, only: nc + implicit none + save + + REAL, DIMENSION(nc) :: rhoif, rhoi1, rhoi2, grad_fd + REAL :: fdenf + + End Module STARTING_VALUES + + + + + +!>WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +!! Module DFT_MODULE +!! This module contains parameters and variables for DFT calculations. +!!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +!! + Module DFT_MODULE + + use PARAMETERS, only: nc + implicit none + save + +INTEGER, PARAMETER :: NDFT = 4000 +INTEGER, PARAMETER :: NDFT2 = 4000 + +INTEGER, PARAMETER :: r_grid = 200 + integer :: discret + REAL :: box_l_no_unit +! REAL :: pbulk + INTEGER :: kmax, den_step + LOGICAL :: shift, WCA, MFT + REAL :: rc, rg, dzr, tau_cut + REAL :: d_hs, dhs_st, z3t_st + REAL :: z_ges + REAL, DIMENSION(r_grid) :: x1a + REAL, DIMENSION(NDFT) :: x2a + REAL, DIMENSION(r_grid,NDFT) :: ya, y1a, y2a, y12a + REAL, DIMENSION(r_grid,NDFT,4,4) :: c_bicub + REAL :: fres_temp +! REAL :: free + + REAL, DIMENSION(r_grid) :: x1a_11 + REAL, DIMENSION(NDFT) :: x2a_11 + REAL, DIMENSION(r_grid,NDFT) :: ya_11, y1a_11, y2a_11, y12a_11 + REAL, DIMENSION(r_grid,NDFT,4,4) :: c_bicub_11 + REAL, DIMENSION(r_grid) :: x1a_12 + REAL, DIMENSION(NDFT) :: x2a_12 + REAL, DIMENSION(r_grid,NDFT) :: ya_12, y1a_12, y2a_12, y12a_12 + REAL, DIMENSION(r_grid,NDFT,4,4) :: c_bicub_12 + REAL, DIMENSION(r_grid) :: x1a_22 + REAL, DIMENSION(NDFT) :: x2a_22 + REAL, DIMENSION(r_grid,NDFT) :: ya_22, y1a_22, y2a_22, y12a_22 + REAL, DIMENSION(r_grid,NDFT,4,4) :: c_bicub_22 + + End Module DFT_MODULE + + +Module rdf_variables + + implicit none + save + + real, dimension(0:20) :: fac(0:20) + +End Module rdf_variables + + +!>WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +!! This module contains the variavles that are needed in the core DFT_FCN +!! They are not passed directly to DFT_FCN because the nonlinear solver +!! needs a certain calling structure: fcn(x,fvec,n) +!!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +Module DFT_FCN_MODULE + +use PARAMETERS, only: nc + implicit none + +!INTEGER :: irc(nc),irc_j,ih,fa(nc) +! REAL, DIMENSION(-NDFT:NDFT) :: zp +! REAL, DIMENSION(-NDFT:NDFT) :: f_tot +! REAL, DIMENSION(-NDFT:NDFT,2) :: dF_drho_tot +! REAL :: rhob_dft(2,0:nc) + !REAL :: my0(nc) + REAL :: chemPot_total(nc) + REAL :: chemPot_res(nc) + +End Module DFT_FCN_MODULE + + +Module mod_DFT + +Implicit None + +REAL :: box !box length [A] +!INTEGER :: ngrid !grid points +!INTEGER :: ngp !ghost points +REAL :: dzp !grid spacing [A] +INTEGER,allocatable :: fa(:) !grid points per sigma [-] +REAL, allocatable :: zp(:) !z-distance from origin [A] +INTEGER,allocatable :: fa_disp(:) !integraition interval for dispersion wda +REAL,allocatable :: ab_disp(:) !integraition interval for dispersion wda +REAL :: pbulk, free + + + +End Module mod_DFT + + + + + + + + + + +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! Module Module_Heidemann_Khalil +! +! This module .... +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! + Module Module_Heidemann_Khalil + + implicit none + save + + real :: error_condition2 + + End Module + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +! ! ! Module PARAMETERS +! ! ! +! ! ! Implicit None +! ! ! +! ! ! REAL, parameter :: PI = 3.141592653589793 +! ! ! Integer, parameter :: nc = 3 +! ! ! Integer, parameter :: np = 3 +! ! ! +! ! ! End Module PARAMETERS +! ! ! +! ! ! +! ! ! +! ! ! +! ! ! +! ! ! +! ! ! +! ! ! +! ! ! Module BASIC_VARIABLES +! ! ! +! ! ! Use Parameters, Only: nc +! ! ! +! ! ! Implicit None +! ! ! +! ! ! INTEGER :: ncomp +! ! ! REAL :: t +! ! ! REAL :: kij(nc,nc) +! ! ! Integer :: eos, pol +! ! ! Integer :: num +! ! ! character (LEN=2) :: ensemble_flag +! ! ! +! ! ! +! ! ! End Module BASIC_VARIABLES +! ! ! +! ! ! +! ! ! +! ! ! +! ! ! Module EOS_VARIABLES +! ! ! +! ! ! Implicit None +! ! ! +! ! ! +! ! ! REAL, allocatable :: mseg(:) +! ! ! REAL, allocatable :: eps(:) +! ! ! REAL, allocatable :: sig(:) +! ! ! REAL, allocatable :: dhs(:) +! ! ! +! ! ! REAL :: eta +! ! ! REAL :: rho +! ! ! REAL, allocatable :: xx(:) +! ! ! REAL,allocatable :: sig_ij(:,:), uij(:,:) +! ! ! +! ! ! character (LEN = 2) :: dd_term, qq_term, dq_term +! ! ! +! ! ! End Module EOS_VARIABLES +! ! ! +! ! ! +! ! ! +! ! ! +! ! ! +! ! ! Module EOS_CONSTANTS +! ! ! +! ! ! Implicit None +! ! ! +! ! ! REAL :: ap(0:6,3),bp(0:6,3) +! ! ! +! ! ! End Module EOS_CONSTANTS +! ! ! +! ! ! +! ! ! +! ! ! +! ! ! +! ! ! +! ! ! +! ! ! diff --git a/applications/PUfoam/MoDeNaModels/SurfaceTension/src/Numeric_subroutines.F90 b/applications/PUfoam/MoDeNaModels/SurfaceTension/src/Numeric_subroutines.F90 new file mode 100644 index 000000000..fe8f1c1bf --- /dev/null +++ b/applications/PUfoam/MoDeNaModels/SurfaceTension/src/Numeric_subroutines.F90 @@ -0,0 +1,1676 @@ +!>WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +!! This file contains subroutines for subtasks like spline interpolations, +!! spline integration and function minimization +!!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW + + + + + +SUBROUTINE bicub_derivative ( ya, x1a, x2a, y1a, y2a, y12a, i_max, k_max ) +! + USE DFT_MODULE, ONLY: NDFT, r_grid + IMPLICIT NONE +! +! ---------------------------------------------------------------------- + REAL, INTENT(IN) :: ya(r_grid,NDFT) + REAL, INTENT(IN) :: x1a(r_grid) + REAL, INTENT(IN) :: x2a(NDFT) + REAL, INTENT(OUT) :: y1a(r_grid,NDFT) + REAL, INTENT(OUT) :: y2a(r_grid,NDFT) + REAL, INTENT(OUT) :: y12a(r_grid,NDFT) + INTEGER, INTENT(IN) :: i_max + INTEGER, INTENT(IN) :: k_max +! +! ---------------------------------------------------------------------- + INTEGER :: i, k +! ---------------------------------------------------------------------- + + +DO i = 2, i_max-1 + DO k = 2, k_max-1 + y1a(i,k) = (ya(i+1,k)-ya(i-1,k)) / (x1a(i+1)-x1a(i-1)) + y2a(i,k) = (ya(i,k+1)-ya(i,k-1)) / (x2a(k+1)-x2a(k-1)) + y12a(i,k)= (ya(i+1,k+1)-ya(i+1,k-1)-ya(i-1,k+1)+ya(i-1,k-1)) & + /((x1a(i+1)-x1a(i-1))*(x2a(k+1)-x2a(k-1))) + END DO +END DO + +i = 1 +DO k = 1, k_max + y1a(i,k) = 0.0 + y2a(i,k) = 0.0 + y12a(i,k)= 0.0 +END DO + +k = 1 +DO i = 1, i_max + y1a(i,k) = 0.0 + y2a(i,k) = 0.0 + y12a(i,k)= 0.0 +END DO + + +i = i_max +DO k = 2, k_max-1 + y1a(i,k) = (ya(i,k)-ya(i-1,k)) / (x1a(i)-x1a(i-1)) + y2a(i,k) = (ya(i,k+1)-ya(i,k-1)) / (x2a(k+1)-x2a(k-1)) + y12a(i,k)= (ya(i,k+1)-ya(i,k-1)-ya(i-1,k+1)+ya(i-1,k-1)) & + /((x1a(i)-x1a(i-1))*(x2a(k+1)-x2a(k-1))) +END DO + + +k = k_max +DO i = 2, i_max-1 + y1a(i,k) = (ya(i+1,k)-ya(i-1,k)) / (x1a(i+1)-x1a(i-1)) + y2a(i,k) = (ya(i,k)-ya(i,k-1)) / (x2a(k)-x2a(k-1)) + y12a(i,k)= (ya(i+1,k)-ya(i+1,k-1)-ya(i-1,k)+ya(i-1,k-1)) & + /((x1a(i+1)-x1a(i-1))*(x2a(k)-x2a(k-1))) +END DO + +k = k_max +i = i_max +y1a(i,k) = (ya(i,k)-ya(i-1,k)) / (x1a(i)-x1a(i-1)) +y2a(i,k) = (ya(i,k)-ya(i,k-1)) / (x2a(k)-x2a(k-1)) +y12a(i,k)= (ya(i,k)-ya(i,k-1)-ya(i-1,k)+ya(i-1,k-1)) & + /((x1a(i)-x1a(i-1))*(x2a(k)-x2a(k-1))) + +END SUBROUTINE bicub_derivative + + +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! + SUBROUTINE bicub_c ( ya, x1a, x2a, y1a, y2a, y12a, c_bicub, i_max, k_max ) +! + USE DFT_MODULE, ONLY: NDFT, r_grid + IMPLICIT NONE +! +! ---------------------------------------------------------------------- + REAL, INTENT(IN) :: ya(r_grid,NDFT) + REAL, INTENT(IN) :: x1a(r_grid) + REAL, INTENT(IN) :: x2a(NDFT) + REAL, INTENT(IN) :: y1a(r_grid,NDFT) + REAL, INTENT(IN) :: y2a(r_grid,NDFT) + REAL, INTENT(IN) :: y12a(r_grid,NDFT) + REAL, INTENT(OUT) :: c_bicub(r_grid,NDFT,4,4) + INTEGER, INTENT(IN) :: i_max + INTEGER, INTENT(IN) :: k_max +! +! ---------------------------------------------------------------------- + INTEGER :: i, k, m, n + REAL :: y(4),y1(4),y2(4),y12(4),x1l,x1u,x2l,x2u + REAL :: c(4,4) +! ---------------------------------------------------------------------- + +DO i = 1, i_max-1 + DO k = 1, k_max-1 + y(1)=ya(i,k) + y(2)=ya(i+1,k) + y(3)=ya(i+1,k+1) + y(4)=ya(i,k+1) + + y1(1)=y1a(i,k) + y1(2)=y1a(i+1,k) + y1(3)=y1a(i+1,k+1) + y1(4)=y1a(i,k+1) + + y2(1)=y2a(i,k) + y2(2)=y2a(i+1,k) + y2(3)=y2a(i+1,k+1) + y2(4)=y2a(i,k+1) + + y12(1)=y12a(i,k) + y12(2)=y12a(i+1,k) + y12(3)=y12a(i+1,k+1) + y12(4)=y12a(i,k+1) + + x1l=x1a(i) + x1u=x1a(i+1) + x2l=x2a(k) + x2u=x2a(k+1) + + CALL bcucof(y,y1,y2,y12,x1u-x1l,x2u-x2l,c) + DO m=1,4 + DO n=1,4 + c_bicub(i,k,m,n)=c(m,n) + END DO + END DO + + END DO +END DO + +END SUBROUTINE bicub_c + +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! + SUBROUTINE bcucof(y,y1,y2,y12,d1,d2,c) +! + IMPLICIT NONE +! +! ---------------------------------------------------------------------- + REAL, INTENT(IN) :: y(4) + REAL, INTENT(IN) :: y1(4) + REAL, INTENT(IN) :: y2(4) + REAL, INTENT(IN) :: y12(4) + REAL, INTENT(IN) :: d1 + REAL, INTENT(IN) :: d2 + REAL, INTENT(OUT) :: c(4,4) +! +! ---------------------------------------------------------------------- + INTEGER :: i,j,k,l + REAL :: d1d2,xx,cl(16),wt(16,16),x(16) + SAVE wt + DATA wt/1,0,-3,2,4*0,-3,0,9,-6,2,0,-6,4,8*0,3,0,-9,6,-2,0,6,-4,10* & + 0,9,-6,2*0,-6,4,2*0,3,-2,6*0,-9,6,2*0,6,-4,4*0,1,0,-3,2,-2,0,6,-4, & + 1,0,-3,2,8*0,-1,0,3,-2,1,0,-3,2,10*0,-3,2,2*0,3,-2,6*0,3,-2,2*0, & + -6,4,2*0,3,-2,0,1,-2,1,5*0,-3,6,-3,0,2,-4,2,9*0,3,-6,3,0,-2,4,-2, & + 10*0,-3,3,2*0,2,-2,2*0,-1,1,6*0,3,-3,2*0,-2,2,5*0,1,-2,1,0,-2,4, & + -2,0,1,-2,1,9*0,-1,2,-1,0,1,-2,1,10*0,1,-1,2*0,-1,1,6*0,-1,1,2*0, & + 2,-2,2*0,-1,1/ +! ---------------------------------------------------------------------- + +d1d2 = d1 * d2 +DO i = 1, 4 + x(i) = y(i) + x(i+4) = y1(i)*d1 + x(i+8) = y2(i)*d2 + x(i+12) = y12(i)*d1d2 +END DO +DO i = 1, 16 + xx = 0.0 + DO k = 1, 16 + xx = xx + wt(i,k) * x(k) + END DO + cl(i) = xx +END DO +l = 0 +DO i = 1, 4 + DO j = 1, 4 + l = l + 1 + c(i,j) = cl(l) + END DO +END DO + +END SUBROUTINE bcucof + + +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! + SUBROUTINE BI_CUB_SPLINE ( rho_rdf, xg, ya, x1a, x2a, y1a, y2a, y12a, & + c_bicub, rdf, dg_drho, dg_dr, i_max, ih, k ) +! + USE DFT_MODULE, ONLY: NDFT, r_grid + IMPLICIT NONE +! +! ---------------------------------------------------------------------- + REAL, INTENT(IN OUT) :: rho_rdf + REAL, INTENT(IN OUT) :: xg + REAL, INTENT(IN) :: ya(r_grid,NDFT) + REAL, INTENT(IN) :: x1a(r_grid) + REAL, INTENT(IN) :: x2a(NDFT) + REAL, INTENT(IN) :: y1a(r_grid,NDFT) + REAL, INTENT(IN) :: y2a(r_grid,NDFT) + REAL, INTENT(IN) :: y12a(r_grid,NDFT) + REAL, INTENT(IN) :: c_bicub(r_grid,NDFT,4,4) + REAL, INTENT(OUT) :: rdf + REAL, INTENT(OUT) :: dg_drho + REAL, INTENT(OUT) :: dg_dr + INTEGER, INTENT(IN OUT) :: i_max + !INTEGER, INTENT(IN OUT) :: k_max + INTEGER, INTENT(OUT) :: ih + INTEGER, INTENT(IN) :: k +! +! ---------------------------------------------------------------------- + INTEGER :: m, n + + REAL :: y(4),y1(4),y2(4),y12(4),x1l,x1u,x2l,x2u + REAL :: c(4,4) +! ---------------------------------------------------------------------- + +IF ( rho_rdf < x1a(1) ) THEN + dg_drho = 0.0 + dg_dr = 0.0 + rdf = 1.0 + RETURN +END IF +IF ( x1a(ih) <= rho_rdf .AND. rho_rdf < x1a(ih+1) ) GO TO 10 +IF ( ih > 2 ) THEN + IF ( x1a(ih-1) <= rho_rdf .AND. rho_rdf < x1a(ih) ) THEN + ih = ih - 1 + GO TO 10 + END IF +END IF +! write (*,*) 'in ',ih +CALL hunt ( x1a, i_max, rho_rdf, ih ) +! write (*,*) 'out',ih +10 CONTINUE +IF ( x2a(k) /= xg ) THEN +! write (*,*) 'error bi-cubic-spline',k,x2a(k),xg +! DO k=1,NDFT +! write (*,*) k,x2a(k) +! ENDDO +! stop +END IF + + + +y(1) = ya(ih,k) +y(2) = ya(ih+1,k) +y(3) = ya(ih+1,k+1) +y(4) = ya(ih,k+1) + +y1(1) = y1a(ih,k) +y1(2) = y1a(ih+1,k) +y1(3) = y1a(ih+1,k+1) +y1(4) = y1a(ih,k+1) + +y2(1) = y2a(ih,k) +y2(2) = y2a(ih+1,k) +y2(3) = y2a(ih+1,k+1) +y2(4) = y2a(ih,k+1) + +y12(1) = y12a(ih,k) +y12(2) = y12a(ih+1,k) +y12(3) = y12a(ih+1,k+1) +y12(4) = y12a(ih,k+1) + +x1l = x1a(ih) +x1u = x1a(ih+1) +x2l = x2a(k) +x2u = x2a(k+1) + +DO m = 1, 4 + DO n = 1, 4 + c(m,n) = c_bicub( ih, k, m, n ) + END DO +END DO +CALL bcuint ( x1l, x1u, x2l, x2u, rho_rdf, xg, c, rdf, dg_drho, dg_dr ) + +END SUBROUTINE BI_CUB_SPLINE + +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! SUBROUTINE hunt +! +! Given an array xx(1:n), and given a value x, returns a value jlo +! such that x is between xx(jlo) and xx(jlo+1). xx(1:n) must be +! monotonic, either increasing or decreasing. jlo=0 or jlo=n is +! returned to indicate that x is out of range. jlo on input is taken +! as the initial guess for jlo on output. +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! + SUBROUTINE hunt ( xx, n, x, jlo ) +! + IMPLICIT NONE +! +! ---------------------------------------------------------------------- + INTEGER, INTENT(IN) :: n + INTEGER, INTENT(OUT) :: jlo + REAL, INTENT(IN) :: xx(n) + REAL :: x +! +! ---------------------------------------------------------------------- + INTEGER :: inc,jhi,jm + LOGICAL :: ascnd +! ---------------------------------------------------------------------- + +ascnd = xx(n) >= xx(1) +IF( jlo <= 0 .OR. jlo > n ) THEN + jlo = 0 + jhi = n + 1 + GO TO 3 +END IF +inc = 1 +IF( x >= xx(jlo) .EQV. ascnd ) THEN +1 jhi = jlo + inc + IF ( jhi > n ) THEN + jhi = n + 1 + ELSE IF ( x >= xx(jhi) .EQV. ascnd ) THEN + jlo = jhi + inc = inc + inc + GO TO 1 + END IF +ELSE + jhi = jlo +2 jlo = jhi - inc + IF ( jlo < 1 ) THEN + jlo = 0 + ELSE IF ( x < xx(jlo) .EQV. ascnd ) THEN + jhi = jlo + inc = inc + inc + GO TO 2 + END IF +END IF +3 IF (jhi-jlo == 1 ) THEN + IF ( x == xx(n)) jlo = n - 1 + IF ( x == xx(1) ) jlo = 1 + RETURN +END IF +jm = ( jhi + jlo ) / 2 +IF ( x >= xx(jm) .EQV. ascnd ) THEN + jlo = jm +ELSE + jhi = jm +END IF +GO TO 3 +END SUBROUTINE hunt + + + +!********************************************************************** +! +!********************************************************************** +! + !SUBROUTINE bcuint ( y, y1, y2, y12, x1l, x1u, x2l, x2u, x1, x2, c, ansy, ansy1, ansy2 ) + SUBROUTINE bcuint ( x1l, x1u, x2l, x2u, x1, x2, c, ansy, ansy1, ansy2 ) +! + IMPLICIT NONE +! +! ---------------------------------------------------------------------- + !REAL, INTENT(IN OUT) :: y(4) + !REAL, INTENT(IN OUT) :: y1(4) + !REAL, INTENT(IN OUT) :: y2(4) + !REAL, INTENT(IN OUT) :: y12(4) + REAL, INTENT(IN OUT) :: x1l + REAL, INTENT(IN OUT) :: x1u + REAL, INTENT(IN OUT) :: x2l + REAL, INTENT(IN OUT) :: x2u + REAL, INTENT(IN OUT) :: x1 + REAL, INTENT(IN OUT) :: x2 + REAL, INTENT(IN) :: c(4,4) + REAL, INTENT(OUT) :: ansy + REAL, INTENT(OUT) :: ansy1 + REAL, INTENT(OUT) :: ansy2 +! +! ---------------------------------------------------------------------- + !U USES bcucof + INTEGER :: i + REAL :: t, u +! ---------------------------------------------------------------------- + +! call bcucof ( y, y1, y2, y12, x1u-x1l, x2u-x2l, c ) + +IF ( x1u == x1l .OR. x2u == x2l ) PAUSE 'bad input in bcuint' +t = (x1-x1l) / (x1u-x1l) +u = (x2-x2l) / (x2u-x2l) +ansy = 0.0 +ansy2 = 0.0 +ansy1 = 0.0 +DO i = 4, 1, -1 + ansy = t *ansy + ( (c(i,4)*u + c(i,3))*u+c(i,2) )*u + c(i,1) + ansy2 = t *ansy2 + ( 3.*c(i,4)*u+2.*c(i,3) )*u + c(i,2) + ansy1 = u *ansy1 + ( 3.*c(4,i)*t+2.*c(3,i) )*t + c(2,i) +END DO +ansy1 = ansy1 / (x1u-x1l) +ansy2 = ansy2 / (x2u-x2l) + +END SUBROUTINE bcuint + + +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! SUBROUTINE spline +! +! Given arrays x(1:n) and y(1:n) containing a tabulated function, +! i.e., yi = f(xi), with x1 < x2 < .. . < xN, and given values yp1 and +! ypn for the first derivative of the interpolating function at points 1 +! and n, respectively, this routine returns an array y2(1:n) of length n +! which contains the second derivatives of the interpolating function at +! the tabulated points xi. If yp1 and/or ypn are equal to 1 1030 or +! larger, the routine is signaled to set the corresponding boundary +! condition for a natural spline, with zero second derivative on that +! boundary. +! Parameter: NMAX is the largest anticipated value of n. +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! + SUBROUTINE spline ( x, y, n, yp1, ypn, y2 ) +! + IMPLICIT NONE +! +! ---------------------------------------------------------------------- + INTEGER, INTENT(IN) :: n + REAL, INTENT(IN) :: x(n) + REAL, INTENT(IN) :: y(n) + REAL, INTENT(IN) :: yp1 + REAL, INTENT(IN) :: ypn + REAL, INTENT(OUT) :: y2(n) +! +! ---------------------------------------------------------------------- + INTEGER, PARAMETER :: NMAX = 1000 + INTEGER :: i, k + REAL :: p, qn, sig, un, u(NMAX) +! ---------------------------------------------------------------------- + +If(n > NMAX) stop 'Increase NMAX in Spline!!' + + + + IF ( yp1 > 0.99E30 ) THEN + y2(1) = 0.0 + u(1) = 0.0 + ELSE + y2(1) = -0.5 + u(1) = ( 3.0/(x(2)-x(1)) ) * ( (y(2)-y(1))/(x(2)-x(1))-yp1 ) + END IF + DO i = 2, n-1 + IF ( (x(i+1)-x(i)) == 0.0 .OR. (x(i)-x(i-1)) == 0.0 .OR. (x(i+1)-x(i-1)) == 0.0 ) THEN + write (*,*) 'error in spline-interpolation' + stop + END IF + sig = (x(i)-x(i-1)) / (x(i+1)-x(i-1)) + p = sig*y2(i-1) + 2.0 + y2(i) = (sig-1.0) / p + u(i) = ( 6.0 * ((y(i+1)-y(i))/(x(i+1)-x(i))-(y(i)-y(i-1))/(x(i)-x(i-1))) / (x(i+1)-x(i-1)) & + - sig * u(i-1) ) / p + END DO + IF ( ypn > 0.99E30 ) THEN + qn = 0.0 + un = 0.0 + ELSE + qn = 0.5 + un = (3.0/(x(n)-x(n-1))) * (ypn-(y(n)-y(n-1))/(x(n)-x(n-1))) + END IF + y2(n) = (un-qn*u(n-1)) / (qn*y2(n-1)+1.0) + DO k = n-1, 1, -1 + y2(k) = y2(k) * y2(k+1) + u(k) + END DO + +END SUBROUTINE spline + +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! SUBROUTINE splint_integral +! +! Given the arrays xa(1:n) and ya(1:n) of length n, which tabulate a +! function (with the in order), and given the array y2a(1:n), which is +! the output from spline above, and given a value of x, this routine +! returns a cubic-spline interpolated value y. +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! + SUBROUTINE splint_integral ( xa, ya, y2a, n, xlo, xhi, integral ) +! + IMPLICIT NONE +! +! ---------------------------------------------------------------------- + INTEGER, INTENT(IN) :: n + REAL, INTENT(IN) :: xa(n) + REAL, INTENT(IN) :: ya(n) + REAL, INTENT(IN) :: y2a(n) + REAL, INTENT(IN) :: xlo + REAL, INTENT(IN) :: xhi + REAL, INTENT(OUT) :: integral +! +! ---------------------------------------------------------------------- + INTEGER :: k, khi_l, klo_l, khi_h, klo_h + REAL :: xl, xh, h, INT, x0, x1, y0, y1, y20, y21 +! ---------------------------------------------------------------------- + + integral = 0.0 + klo_l = 1 + khi_l = n +1 IF ( khi_l-klo_l > 1 ) THEN + k = ( khi_l + klo_l ) / 2 + IF ( xa(k) > xlo ) THEN + khi_l = k + ELSE + klo_l = k + END IF + GO TO 1 + END IF + + klo_h = 1 + khi_h = n +2 IF ( khi_h-klo_h > 1 ) THEN + k = ( khi_h + klo_h ) / 2 + IF ( xa(k) > xhi ) THEN + khi_h = k + ELSE + klo_h = k + END IF + GO TO 2 + END IF + + ! integration in spline pieces, the lower interval, bracketed + ! by xa(klo_L) and xa(khi_L) is in steps shifted upward. + + ! first: determine upper integration bound + xl = xlo +3 CONTINUE + IF ( khi_h > khi_l ) THEN + xh = xa(khi_l) + ELSE IF ( khi_h == khi_l ) THEN + xh = xhi + ELSE + WRITE (*,*) 'error in spline-integration' + PAUSE + END IF + + h = xa(khi_l) - xa(klo_l) + IF ( h == 0.0 ) PAUSE 'bad xa input in splint' + x0 = xa(klo_l) + x1 = xa(khi_l) + y0 = ya(klo_l) + y1 = ya(khi_l) + y20= y2a(klo_l) + y21= y2a(khi_l) + ! int = -xL/h * ( (x1-.5*xL)*y0 + (0.5*xL-x0)*y1 & + ! +y20/6.*(x1**3-1.5*xL*x1*x1+xL*xL*x1-.25*xL**3) & + ! -y20/6.*h*h*(x1-.5*xL) & + ! +y21/6.*(.25*xL**3-xL*xL*x0+1.5*xL*x0*x0-x0**3) & + ! -y21/6.*h*h*(.5*xL-x0) ) + ! int = int + xH/h * ( (x1-.5*xH)*y0 + (0.5*xH-x0)*y1 & + ! +y20/6.*(x1**3-1.5*xH*x1*x1+xH*xH*x1-.25*xH**3) & + ! -y20/6.*h*h*(x1-.5*xH) & + ! +y21/6.*(.25*xH**3-xH*xH*x0+1.5*xH*x0*x0-x0**3) & + ! -y21/6.*h*h*(.5*xH-x0) ) + INT = -1.0/h * ( xl*((x1-.5*xl)*y0 + (0.5*xl-x0)*y1) & + -y20/24.*(x1-xl)**4 + y20/6.*(0.5*xl*xl-x1*xl)*h*h & + +y21/24.*(xl-x0)**4 - y21/6.*(0.5*xl*xl-x0*xl)*h*h ) + INT = INT + 1.0/h * ( xh*((x1-.5*xh)*y0 + (0.5*xh-x0)*y1) & + -y20/24.*(x1-xh)**4 + y20/6.*(0.5*xh*xh-x1*xh)*h*h & + +y21/24.*(xh-x0)**4 - y21/6.*(0.5*xh*xh-x0*xh)*h*h ) + + integral = integral + INT + ! write (*,*) integral,x1,xH + klo_l = klo_l + 1 + khi_l = khi_l + 1 + xl = x1 + IF (khi_h /= (khi_l-1)) GO TO 3 ! the -1 in (khi_L-1) because khi_L was already counted up + +END SUBROUTINE splint_integral + + + + +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! + REAL FUNCTION praxis( t0, machep, h0, n, prin, x, f, fmin ) + + IMPLICIT NONE + +! ---------------------------------------------------------------------- + REAL, INTENT(IN OUT) :: t0 + REAL, INTENT(IN) :: machep + REAL, INTENT(IN) :: h0 + INTEGER :: n + INTEGER, INTENT(IN OUT) :: prin + REAL, INTENT(IN OUT) :: x(n) + REAL :: f + REAL, INTENT(IN OUT) :: fmin +! ---------------------------------------------------------------------- + +EXTERNAL f + +! PRAXIS RETURNS THE MINIMUM OF THE FUNCTION F(X,N) OF N VARIABLES +! USING THE PRINCIPAL AXIS METHOD. THE GRADIENT OF THE FUNCTION IS +! NOT REQUIRED. + +! FOR A DESCRIPTION OF THE ALGORITHM, SEE CHAPTER SEVEN OF +! "ALGORITHMS FOR FINDING ZEROS AND EXTREMA OF FUNCTIONS WITHOUT +! CALCULATING DERIVATIVES" BY RICHARD P BRENT. + +! THE PARAMETERS ARE: +! T0 IS A TOLERANCE. PRAXIS ATTEMPTS TO RETURN PRAXIS=F(X) +! SUCH THAT IF X0 IS THE TRUE LOCAL MINIMUM NEAR X, THEN +! NORM(X-X0) < T0 + SQUAREROOT(MACHEP)*NORM(X). +! MACHEP IS THE MACHINE PRECISION, THE SMALLEST NUMBER SUCH THAT +! 1 + MACHEP > 1. MACHEP SHOULD BE 16.**-13 (ABOUT +! 2.22D-16) FOR REAL*8 ARITHMETIC ON THE IBM 360. +! H0 IS THE MAXIMUM STEP SIZE. H0 SHOULD BE SET TO ABOUT THE +! MAXIMUM DISTANCE FROM THE INITIAL GUESS TO THE MINIMUM. +! (IF H0 IS SET TOO LARGE OR TOO SMALL, THE INITIAL RATE OF +! CONVERGENCE MAY BE SLOW.) +! N (AT LEAST TWO) IS THE NUMBER OF VARIABLES UPON WHICH +! THE FUNCTION DEPENDS. +! PRIN CONTROLS THE PRINTING OF INTERMEDIATE RESULTS. +! IF PRIN=0, NOTHING IS PRINTED. +! IF PRIN=1, F IS PRINTED AFTER EVERY N+1 OR N+2 LINEAR +! MINIMIZATIONS. FINAL X IS PRINTED, BUT INTERMEDIATE X IS +! PRINTED ONLY IF N IS AT MOST 4. +! IF PRIN=2, THE SCALE FACTORS AND THE PRINCIPAL VALUES OF +! THE APPROXIMATING QUADRATIC FORM ARE ALSO PRINTED. +! IF PRIN=3, X IS ALSO PRINTED AFTER EVERY FEW LINEAR +! MINIMIZATIONS. +! IF PRIN=4, THE PRINCIPAL VECTORS OF THE APPROXIMATING +! QUADRATIC FORM ARE ALSO PRINTED. +! X IS AN ARRAY CONTAINING ON ENTRY A GUESS OF THE POINT OF +! MINIMUM, ON RETURN THE ESTIMATED POINT OF MINIMUM. +! F(X,N) IS THE FUNCTION TO BE MINIMIZED. F SHOULD BE A REAL*8 +! FUNCTION DECLARED EXTERNAL IN THE CALLING PROGRAM. +! FMIN IS AN ESTIMATE OF THE MINIMUM, USED ONLY IN PRINTING +! INTERMEDIATE RESULTS. +! THE APPROXIMATING QUADRATIC FORM IS +! Q(X') = F(X,N) + (1/2) * (X'-X)-TRANSPOSE * A * (X'-X) +! WHERE X IS THE BEST ESTIMATE OF THE MINIMUM AND A IS +! INVERSE(V-TRANSPOSE) * D * INVERSE(V) +! (V(*,*) IS THE MATRIX OF SEARCH DIRECTIONS; D(*) IS THE ARRAY +! OF SECOND DIFFERENCES). IF F HAS CONTINUOUS SECOND DERIVATIVES +! NEAR X0, A WILL TEND TO THE HESSIAN OF F AT X0 AS X APPROACHES X0. + +! IT IS ASSUMED THAT ON FLOATING-POINT UNDERFLOW THE RESULT IS SET +! TO ZERO. +! THE USER SHOULD OBSERVE THE COMMENT ON HEURISTIC NUMBERS AFTER +! THE INITIALIZATION OF MACHINE DEPENDENT NUMBERS. + + LOGICAL :: illc + INTEGER :: nl,nf,kl,kt,ktm,idim,i,j,k,k2,km1,klmk,ii,im1 + REAL :: s,sl,dn,dmin,fx,f1,lds,ldt,t,h,sf,df,qf1,qd0, qd1,qa,qb,qc + REAL :: m2,m4,small,vsmall,large,vlarge,scbd,ldfac,t2, dni,value + REAL :: random + +!.....IF N>20 OR IF N<20 AND YOU NEED MORE SPACE, CHANGE '20' TO THE +! LARGEST VALUE OF N IN THE NEXT CARD, IN THE CARD 'IDIM=20', AND +! IN THE DIMENSION STATEMENTS IN SUBROUTINES MINFIT,MIN,FLIN,QUAD. + + REAL :: d(20),y(20),z(20),q0(20),q1(20),v(20,20) + COMMON /global/ fx,ldt,dmin,nf,nl /q/ v,q0,q1,qa,qb,qc,qd0,qd1,qf1 + +! --------------------------------- +! introduced by Joachim........ + idim = n +! --------------------------------- + + + +!.....INITIALIZATION..... +! MACHINE DEPENDENT NUMBERS: + +small = machep*machep +vsmall = small*small +large = 1.d0/small +vlarge = 1.d0/vsmall +m2 = SQRT(machep) +m4 = SQRT(m2) + +! HEURISTIC NUMBERS: +! IF THE AXES MAY BE BADLY SCALED (WHICH IS TO BE AVOIDED IF +! POSSIBLE), THEN SET SCBD=10. OTHERWISE SET SCBD=1. +! IF THE PROBLEM IS KNOWN TO BE ILL-CONDITIONED, SET ILLC=TRUE. +! OTHERWISE SET ILLC=FALSE. +! KTM IS THE NUMBER OF ITERATIONS WITHOUT IMPROVEMENT BEFORE THE +! ALGORITHM TERMINATES. KTM=4 IS VERY CAUTIOUS; USUALLY KTM=1 +! IS SATISFACTORY. + +scbd = 1.0 +illc = .false. +ktm = 1 + +ldfac = 0.01 +IF (illc) ldfac = 0.1 +kt = 0 +nl = 0 +nf = 1 +fx = f(x,n) +qf1 = fx +t = small+ABS(t0) +t2 = t +dmin = small +h = h0 +IF (h < 100*t) h = 100*t +ldt = h +!.....THE FIRST SET OF SEARCH DIRECTIONS V IS THE IDENTITY MATRIX..... +DO i = 1,n + DO j = 1,n + v(i,j) = 0.0 + END DO + v(i,i) = 1.0 +END DO +d(1) = 0.0 +qd0 = 0.0 +DO i = 1,n + q0(i) = x(i) + q1(i) = x(i) +END DO +IF (prin > 0) CALL PRINT(n,x,prin,fmin) + +!.....THE MAIN LOOP STARTS HERE..... +40 sf=d(1) +d(1)=0.d0 +s=0.d0 + +!.....MINIMIZE ALONG THE FIRST DIRECTION V(*,1). +! FX MUST BE PASSED TO MIN BY VALUE. +value=fx +CALL MIN(n,1,2,d(1),s,value,.false.,f,x,t,machep,h) +IF (s > 0.d0) GO TO 50 +DO i=1,n + v(i,1)=-v(i,1) +END DO +50 IF (sf > 0.9D0*d(1).AND.0.9D0*sf < d(1)) GO TO 70 +DO i=2,n + d(i)=0.d0 +END DO + +!.....THE INNER LOOP STARTS HERE..... +70 DO k=2,n + DO i=1,n + y(i)=x(i) + END DO + sf=fx + IF (kt > 0) illc=.true. + 80 kl=k + df=0.d0 + +!.....A RANDOM STEP FOLLOWS (TO AVOID RESOLUTION VALLEYS). +! PRAXIS ASSUMES THAT RANDOM RETURNS A RANDOM NUMBER UNIFORMLY +! DISTRIBUTED IN (0,1). + + IF(.NOT.illc) GO TO 95 + DO i=1,n + s=(0.1D0*ldt+t2*(10**kt))*(random(n)-0.5D0) + z(i)=s + DO j=1,n + x(j)=x(j)+s*v(j,i) + END DO + END DO + fx=f(x,n) + nf=nf+1 + +!.....MINIMIZE ALONG THE "NON-CONJUGATE" DIRECTIONS V(*,K),...,V(*,N) + + 95 DO k2=k,n + sl=fx + s=0.d0 + value=fx + CALL MIN(n,k2,2,d(k2),s,value,.false.,f,x,t,machep,h) + IF (illc) GO TO 97 + s=sl-fx + GO TO 99 + 97 s=d(k2)*((s+z(k2))**2) + 99 IF (df > s) CYCLE + df=s + kl=k2 + END DO + IF (illc.OR.(df >= ABS((100*machep)*fx))) GO TO 110 + +!.....IF THERE WAS NOT MUCH IMPROVEMENT ON THE FIRST TRY, SET +! ILLC=TRUE AND START THE INNER LOOP AGAIN..... + + illc=.true. + GO TO 80 + 110 IF (k == 2.AND.prin > 1) CALL vcprnt(1,d,n) + +!.....MINIMIZE ALONG THE "CONJUGATE" DIRECTIONS V(*,1),...,V(*,K-1) + + km1=k-1 + DO k2=1,km1 + s=0 + value=fx + CALL MIN(n,k2,2,d(k2),s,value,.false.,f,x,t,machep,h) + END DO + f1=fx + fx=sf + lds=0 + DO i=1,n + sl=x(i) + x(i)=y(i) + sl=sl-y(i) + y(i)=sl + lds=lds+sl*sl + END DO + lds=SQRT(lds) + IF (lds <= small) GO TO 160 + +!.....DISCARD DIRECTION V(*,KL). +! IF NO RANDOM STEP WAS TAKEN, V(*,KL) IS THE "NON-CONJUGATE" +! DIRECTION ALONG WHICH THE GREATEST IMPROVEMENT WAS MADE..... + + klmk=kl-k + IF (klmk < 1) GO TO 141 + DO ii=1,klmk + i=kl-ii + DO j=1,n + v(j,i+1)=v(j,i) + END DO + d(i+1)=d(i) + END DO + 141 d(k)=0 + DO i=1,n + v(i,k)=y(i)/lds + END DO + +!.....MINIMIZE ALONG THE NEW "CONJUGATE" DIRECTION V(*,K), WHICH IS +! THE NORMALIZED VECTOR: (NEW X) - (0LD X)..... + + value=f1 + CALL MIN(n,k,4,d(k),lds,value,.true.,f,x,t,machep,h) + IF (lds > 0.d0) GO TO 160 + lds=-lds + DO i=1,n + v(i,k)=-v(i,k) + END DO + 160 ldt=ldfac*ldt + IF (ldt < lds) ldt=lds + IF (prin > 0) CALL PRINT(n,x,prin,fmin) + t2=0.d0 + DO i=1,n + t2=t2+x(i)**2 + END DO + t2=m2*SQRT(t2)+t + +!.....SEE WHETHER THE LENGTH OF THE STEP TAKEN SINCE STARTING THE +! INNER LOOP EXCEEDS HALF THE TOLERANCE..... + + IF (ldt > (0.5*t2)) kt=-1 + kt=kt+1 + IF (kt > ktm) GO TO 400 +END DO +!.....THE INNER LOOP ENDS HERE. + +! TRY QUADRATIC EXTRAPOLATION IN CASE WE ARE IN A CURVED VALLEY. + +CALL quad(n,f,x,t,machep,h) +dn=0.d0 +DO i=1,n + d(i)=1.d0/SQRT(d(i)) + IF (dn < d(i)) dn=d(i) +END DO +IF (prin > 3) CALL maprnt(1,v,idim,n) +DO j=1,n + s=d(j)/dn + DO i=1,n + v(i,j)=s*v(i,j) + END DO +END DO + +!.....SCALE THE AXES TO TRY TO REDUCE THE CONDITION NUMBER..... + +IF (scbd <= 1.d0) GO TO 200 +s=vlarge +DO i=1,n + sl=0.d0 + DO j=1,n + sl=sl+v(i,j)*v(i,j) + END DO + z(i)=SQRT(sl) + IF (z(i) < m4) z(i)=m4 + IF (s > z(i)) s=z(i) +END DO +DO i=1,n + sl=s/z(i) + z(i)=1.d0/sl + IF (z(i) <= scbd) GO TO 189 + sl=1.d0/scbd + z(i)=scbd + 189 DO j=1,n + v(i,j)=sl*v(i,j) + END DO +END DO + +!.....CALCULATE A NEW SET OF ORTHOGONAL DIRECTIONS BEFORE REPEATING +! THE MAIN LOOP. +! FIRST TRANSPOSE V FOR MINFIT: + +200 DO i=2,n + im1=i-1 + DO j=1,im1 + s=v(i,j) + v(i,j)=v(j,i) + v(j,i)=s + END DO +END DO + +!.....CALL MINFIT TO FIND THE SINGULAR VALUE DECOMPOSITION OF V. +! THIS GIVES THE PRINCIPAL VALUES AND PRINCIPAL DIRECTIONS OF THE +! APPROXIMATING QUADRATIC FORM WITHOUT SQUARING THE CONDITION +! NUMBER..... + +CALL minfit(idim,n,machep,vsmall,v,d) + +!.....UNSCALE THE AXES..... + +IF (scbd <= 1.d0) GO TO 250 +DO i=1,n + s=z(i) + DO j=1,n + v(i,j)=s*v(i,j) + END DO +END DO +DO i=1,n + s=0.d0 + DO j=1,n + s=s+v(j,i)**2 + END DO + s=SQRT(s) + d(i)=s*d(i) + s=1/s + DO j=1,n + v(j,i)=s*v(j,i) + END DO +END DO + +250 DO i=1,n + dni=dn*d(i) + IF (dni > large) GO TO 265 + IF (dni < small) GO TO 260 + d(i)=1/(dni*dni) + CYCLE + 260 d(i)=vlarge + CYCLE + 265 d(i)=vsmall +END DO + +!.....SORT THE EIGENVALUES AND EIGENVECTORS..... + +CALL sort(idim,n,d,v) +dmin=d(n) +IF (dmin < small) dmin=small +illc=.false. +IF (m2*d(1) > dmin) illc=.true. +IF (prin > 1.AND.scbd > 1.d0) CALL vcprnt(2,z,n) +IF (prin > 1) CALL vcprnt(3,d,n) +IF (prin > 3) CALL maprnt(2,v,idim,n) +!.....THE MAIN LOOP ENDS HERE..... + +GO TO 40 + +!.....RETURN..... + +400 IF (prin > 0) CALL vcprnt(4,x,n) +praxis=fx + +END FUNCTION praxis + + +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! + SUBROUTINE minfit(m,n,machep,tol,ab,q) + + IMPLICIT NONE + + INTEGER, INTENT(IN OUT) :: m + INTEGER, INTENT(IN) :: n + REAL, INTENT(IN) :: machep + REAL, INTENT(IN OUT) :: tol + REAL, INTENT(IN OUT) :: ab(m,n) + REAL, INTENT(OUT) :: q(n) + INTEGER :: i,j,k,l, kk,kt,l2,ll2,ii,lp1 +! IMPLICIT REAL (A-H,O-Z) + + +REAL :: x,eps,e(20),g,s, f,h,y,c,z,temp +!...AN IMPROVED VERSION OF MINFIT (SEE GOLUB AND REINSCH, 1969) +! RESTRICTED TO M=N,P=0. +! THE SINGULAR VALUES OF THE ARRAY AB ARE RETURNED IN Q AND AB IS +! OVERWRITTEN WITH THE ORTHOGONAL MATRIX V SUCH THAT U.DIAG(Q) = AB.V, +! WHERE U IS ANOTHER ORTHOGONAL MATRIX. + +!...HOUSEHOLDER'S REDUCTION TO BIDIAGONAL FORM... +IF (n == 1) GO TO 200 +eps = machep +g = 0.d0 +x = 0.d0 +DO i=1,n + e(i) = g + s = 0.d0 + l = i + 1 + DO j=i,n + s = s + ab(j,i)**2 + END DO + g = 0.d0 + IF (s < tol) GO TO 4 + f = ab(i,i) + g = SQRT(s) + IF (f >= 0.d0) g = -g + h = f*g - s + ab(i,i)=f-g + IF (l > n) GO TO 4 + DO j=l,n + f = 0.d0 + DO k=i,n + f = f + ab(k,i)*ab(k,j) + END DO + f = f/h + DO k=i,n + ab(k,j) = ab(k,j) + f*ab(k,i) + END DO + END DO + 4 q(i) = g + s = 0.d0 + IF (i == n) GO TO 6 + DO j=l,n + s = s + ab(i,j)*ab(i,j) + END DO + 6 g = 0.d0 + IF (s < tol) GO TO 10 + IF (i == n) GO TO 16 + f = ab(i,i+1) + 16 g = SQRT(s) + IF (f >= 0.d0) g = -g + h = f*g - s + IF (i == n) GO TO 10 + ab(i,i+1) = f - g + DO j=l,n + e(j) = ab(i,j)/h + END DO + DO j=l,n + s = 0.d0 + DO k=l,n + s = s + ab(j,k)*ab(i,k) + END DO + DO k=l,n + ab(j,k) = ab(j,k) + s*e(k) + END DO + END DO + 10 y = ABS(q(i)) + ABS(e(i)) + IF (y > x) x = y +END DO +!...ACCUMULATION OF RIGHT-HAND TRANSFORMATIONS... +ab(n,n) = 1.d0 +g = e(n) +l = n +DO ii=2,n + i = n - ii + 1 + IF (g == 0.d0) GO TO 23 + h = ab(i,i+1)*g + DO j=l,n + ab(j,i) = ab(i,j)/h + END DO + DO j=l,n + s = 0.d0 + DO k=l,n + s = s + ab(i,k)*ab(k,j) + END DO + DO k=l,n + ab(k,j) = ab(k,j) + s*ab(k,i) + END DO + END DO + 23 DO j=l,n + ab(i,j) = 0.d0 + ab(j,i) = 0.d0 + END DO + ab(i,i) = 1.d0 + g = e(i) + l = i +END DO +!...DIAGONALIZATION OF THE BIDIAGONAL FORM... +eps = eps*x +DO kk=1,n + k = n - kk + 1 + kt = 0 + 101 kt = kt + 1 + IF (kt <= 30) GO TO 102 + e(k) = 0.d0 + WRITE (6,1000) + 1000 FORMAT (' QR FAILED') + 102 DO ll2=1,k + l2 = k - ll2 + 1 + l = l2 + IF (ABS(e(l)) <= eps) GO TO 120 + IF (l == 1) CYCLE + IF (ABS(q(l-1)) <= eps) EXIT + END DO +!...CANCELLATION OF E(L) IF L>1... + c = 0.d0 + s = 1.d0 + DO i=l,k + f = s*e(i) + e(i) = c*e(i) + IF (ABS(f) <= eps) GO TO 120 + g = q(i) +!...Q(I) = H = SQRT(G*G + F*F)... + IF (ABS(f) < ABS(g)) GO TO 113 + IF (f == 0.0) THEN + GO TO 111 + ELSE + GO TO 112 + END IF + 111 h = 0.d0 + GO TO 114 + 112 h = ABS(f)*SQRT(1 + (g/f)**2) + GO TO 114 + 113 h = ABS(g)*SQRT(1 + (f/g)**2) + 114 q(i) = h + IF (h /= 0.d0) GO TO 115 + g = 1.d0 + h = 1.d0 + 115 c = g/h + s = -f/h + END DO +!...TEST FOR CONVERGENCE... + 120 z = q(k) + IF (l == k) GO TO 140 +!...SHIFT FROM BOTTOM 2*2 MINOR... + x = q(l) + y = q(k-1) + g = e(k-1) + h = e(k) + f = ((y - z)*(y + z) + (g - h)*(g + h))/(2*h*y) + g = SQRT(f*f + 1.0D0) + temp = f - g + IF (f >= 0.d0) temp = f + g + f = ((x - z)*(x + z) + h*(y/temp - h))/x +!...NEXT QR TRANSFORMATION... + c = 1.d0 + s = 1.d0 + lp1 = l + 1 + IF (lp1 > k) GO TO 133 + DO i=lp1,k + g = e(i) + y = q(i) + h = s*g + g = g*c + IF (ABS(f) < ABS(h)) GO TO 123 + IF (f == 0.0) THEN + GO TO 121 + ELSE + GO TO 122 + END IF + 121 z = 0.d0 + GO TO 124 + 122 z = ABS(f)*SQRT(1 + (h/f)**2) + GO TO 124 + 123 z = ABS(h)*SQRT(1 + (f/h)**2) + 124 e(i-1) = z + IF (z /= 0.d0) GO TO 125 + f = 1.d0 + z = 1.d0 + 125 c = f/z + s = h/z + f = x*c + g*s + g = -x*s + g*c + h = y*s + y = y*c + DO j=1,n + x = ab(j,i-1) + z = ab(j,i) + ab(j,i-1) = x*c + z*s + ab(j,i) = -x*s + z*c + END DO + IF (ABS(f) < ABS(h)) GO TO 129 + IF (f == 0.0) THEN + GO TO 127 + ELSE + GO TO 128 + END IF + 127 z = 0.d0 + GO TO 130 + 128 z = ABS(f)*SQRT(1 + (h/f)**2) + GO TO 130 + 129 z = ABS(h)*SQRT(1 + (f/h)**2) + 130 q(i-1) = z + IF (z /= 0.d0) GO TO 131 + f = 1.d0 + z = 1.d0 + 131 c = f/z + s = h/z + f = c*g + s*y + x = -s*g + c*y + END DO + 133 e(l) = 0.d0 + e(k) = f + q(k) = x + GO TO 101 +!...CONVERGENCE: Q(K) IS MADE NON-NEGATIVE... + 140 IF (z >= 0.d0) CYCLE + q(k) = -z + DO j=1,n + ab(j,k) = -ab(j,k) + END DO +END DO +RETURN +200 q(1) = ab(1,1) +ab(1,1) = 1.d0 + +END SUBROUTINE minfit + + + + +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! + SUBROUTINE MIN(n,j,nits,d2,x1,f1,fk,f,x,t,machep,h) + + IMPLICIT NONE + + INTEGER, INTENT(IN) :: n + INTEGER :: j + INTEGER :: nits + REAL, INTENT(IN OUT) :: d2 + REAL, INTENT(IN OUT) :: x1 + REAL, INTENT(IN OUT) :: f1 + LOGICAL :: fk + REAL :: f + REAL, INTENT(IN OUT) :: x(n) + REAL, INTENT(IN) :: t + REAL, INTENT(IN) :: machep + REAL, INTENT(IN) :: h + + INTEGER :: i,k + EXTERNAL f + + + REAL :: flin ! function + REAL :: small,sf1,sx1,s,temp, xm,x2,f2,d1 + REAL :: fm,f0,t2 +!---------------------------------------------- + INTEGER :: nf,nl + REAL :: fx,ldt,dmin + REAL :: v(20,20),q0(20),q1(20),qa,qb,qc,qd0,qd1,qf1 + COMMON /global/ fx,ldt,dmin,nf,nl /q/ v,q0,q1,qa,qb,qc,qd0,qd1,qf1 +!---------------------------------------------- +!...THE SUBROUTINE MIN MINIMIZES F FROM X IN THE DIRECTION V(*,J) UNLESS +! J IS LESS THAN 1, WHEN A QUADRATIC SEARCH IS MADE IN THE PLANE +! DEFINED BY Q0,Q1,X. +! D2 IS EITHER ZERO OR AN APPROXIMATION TO HALF F". +! ON ENTRY, X1 IS AN ESTIMATE OF THE DISTANCE FROM X TO THE MINIMUM +! ALONG V(*,J) (OR, IF J=0, A CURVE). ON RETURN, X1 IS THE DISTANCE +! FOUND. +! IF FK=.TRUE., THEN F1 IS FLIN(X1). OTHERWISE X1 AND F1 ARE IGNORED +! ON ENTRY UNLESS FINAL FX IS GREATER THAN F1. +! NITS CONTROLS THE NUMBER OF TIMES AN ATTEMPT WILL BE MADE TO HALVE +! THE INTERVAL. + LOGICAL :: dz + REAL :: m2,m4 + +small = machep**2 +m2 = SQRT(machep) +m4 = SQRT(m2) +sf1 = f1 +sx1 = x1 +k = 0 +xm = 0.d0 +fm = fx +f0 = fx +dz = d2 < machep +!...FIND THE STEP SIZE... +s = 0.d0 +DO i=1,n + s = s + x(i)**2 +END DO +s = SQRT(s) +temp = d2 +IF (dz) temp = dmin +t2 = m4*SQRT(ABS(fx)/temp + s*ldt) + m2*ldt +s = m4*s + t +IF (dz.AND.t2 > s) t2 = s +t2 = DMAX1(t2,small) +t2 = DMIN1(t2,.01D0*h) +IF (.NOT.fk.OR.f1 > fm) GO TO 2 +xm = x1 +fm = f1 +2 IF (fk.AND.ABS(x1) >= t2) GO TO 3 +temp=1.d0 +IF (x1 < 0.d0) temp=-1.d0 +x1=temp*t2 +f1 = flin(n,j,x1,f,x,nf) +3 IF (f1 > fm) GO TO 4 +xm = x1 +fm = f1 +4 IF (.NOT.dz) GO TO 6 +!...EVALUATE FLIN AT ANOTHER POINT AND ESTIMATE THE SECOND DERIVATIVE... +x2 = -x1 +IF (f0 >= f1) x2 = 2.d0*x1 +f2 = flin(n,j,x2,f,x,nf) +IF (f2 > fm) GO TO 5 +xm = x2 +fm = f2 +5 d2 = (x2*(f1 - f0)-x1*(f2 - f0))/((x1*x2)*(x1 - x2)) +!...ESTIMATE THE FIRST DERIVATIVE AT 0... +6 d1 = (f1 - f0)/x1 - x1*d2 +dz = .true. +!...PREDICT THE MINIMUM... +IF (d2 > small) GO TO 7 +x2 = h +IF (d1 >= 0.d0) x2 = -x2 +GO TO 8 +7 x2 = (-.5D0*d1)/d2 +8 IF (ABS(x2) <= h) GO TO 11 +IF (x2 > 0.0) THEN + GO TO 10 +END IF +x2 = -h +GO TO 11 +10 x2 = h +!...EVALUATE F AT THE PREDICTED MINIMUM... +11 f2 = flin(n,j,x2,f,x,nf) +IF (k >= nits.OR.f2 <= f0) GO TO 12 +!...NO SUCCESS, SO TRY AGAIN... +k = k + 1 +IF (f0 < f1.AND.(x1*x2) > 0.d0) GO TO 4 +x2 = 0.5D0*x2 +GO TO 11 +!...INCREMENT THE ONE-DIMENSIONAL SEARCH COUNTER... +12 nl = nl + 1 +IF (f2 <= fm) GO TO 13 +x2 = xm +GO TO 14 +13 fm = f2 +!...GET A NEW ESTIMATE OF THE SECOND DERIVATIVE... +14 IF (ABS(x2*(x2 - x1)) <= small) GO TO 15 +d2 = (x2*(f1-f0) - x1*(fm-f0))/((x1*x2)*(x1 - x2)) +GO TO 16 +15 IF (k > 0) d2 = 0.d0 +16 IF (d2 <= small) d2 = small +x1 = x2 +fx = fm +IF (sf1 >= fx) GO TO 17 +fx = sf1 +x1 = sx1 +!...UPDATE X FOR LINEAR BUT NOT PARABOLIC SEARCH... +17 IF (j == 0) RETURN +DO i=1,n + x(i) = x(i) + x1*v(i,j) +END DO + +END SUBROUTINE MIN + + +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! + SUBROUTINE vcprnt(option,v,n) + + IMPLICIT NONE + INTEGER :: option + REAL, INTENT(IN OUT) :: v(n) + INTEGER :: n + + INTEGER :: i + +SELECT CASE ( option ) + CASE ( 1) + GO TO 1 + CASE ( 2) + GO TO 2 + CASE ( 3) + GO TO 3 + CASE ( 4) + GO TO 4 +END SELECT + +1 WRITE (6,101) (v(i),i=1,n) +RETURN +2 WRITE (6,102) (v(i),i=1,n) +RETURN +3 WRITE (6,103) (v(i),i=1,n) +RETURN +4 WRITE (6,104) (v(i),i=1,n) +RETURN +101 FORMAT (/' THE SECOND DIFFERENCE ARRAY D(*) IS:'/ (e32.14,4E25.14)) +102 FORMAT (/' THE SCALE FACTORS ARE:'/(e32.14,4E25.14)) +103 FORMAT (/' THE APPROXIMATING QUADR. FORM HAS PRINCIPAL VALUES:'/ & + (e32.14,4E25.14)) +104 FORMAT (/' X IS:',e26.14/(e32.14)) +END SUBROUTINE vcprnt + + +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! + SUBROUTINE PRINT(n,x,prin,fmin) + + IMPLICIT NONE + INTEGER :: n + REAL, INTENT(IN OUT) :: x(n) + INTEGER, INTENT(IN OUT) :: prin + REAL, INTENT(IN OUT) :: fmin + + INTEGER :: i + REAL :: ln +!---------------------------------------------- +INTEGER :: nf,nl +REAL :: fx,ldt,dmin +COMMON /global/ fx,ldt,dmin,nf,nl +!---------------------------------------------- +WRITE (6,101) nl,nf,fx + +IF (fx <= fmin) GO TO 1 +ln = LOG10(fx-fmin) +WRITE (6,102) fmin,ln +GO TO 2 +1 WRITE (6,103) fmin +2 IF (n > 4.AND.prin <= 2) RETURN +WRITE (6,104) (x(i),i=1,n) +RETURN +101 FORMAT (/' AFTER',i6, & + ' LINEAR SEARCHES, THE FUNCTION HAS BEEN EVALUATED',i6, & + ' TIMES. THE SMALLEST VALUE FOUND IS F(X) = ',e21.14) +102 FORMAT (' LOG (F(X)-',e21.14,') = ',e21.14) +103 FORMAT (' LOG (F(X)-',e21.14,') IS UNDEFINED.') +104 FORMAT (' X IS:',e26.14/(e32.14)) +END SUBROUTINE PRINT + + +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! + SUBROUTINE maprnt(option,v,m,n) + + IMPLICIT NONE + INTEGER :: option + REAL, INTENT(IN OUT) :: v(m,n) + INTEGER, INTENT(IN OUT) :: m + INTEGER, INTENT(IN) :: n + INTEGER :: i,j + + INTEGER :: low,upp +!...THE SUBROUTINE MAPRNT PRINTS THE COLUMNS OF THE NXN MATRIX V +! WITH A HEADING AS SPECIFIED BY OPTION. +! M IS THE ROW DIMENSION OF V AS DECLARED IN THE CALLING PROGRAM... +low = 1 +upp = 5 +SELECT CASE ( option ) + CASE ( 1) + GO TO 1 + CASE ( 2) + GO TO 2 +END SELECT +1 WRITE (6,101) +101 FORMAT (/' THE NEW DIRECTIONS ARE:') +GO TO 3 +2 WRITE (6,102) +102 FORMAT (' AND THE PRINCIPAL AXES:') +3 IF (n < upp) upp = n +DO i=1,n + WRITE (6,104) (v(i,j),j=low,upp) +END DO +low = low + 5 +IF (n < low) RETURN +upp = upp + 5 +WRITE (6,103) +GO TO 3 +103 FORMAT (' ') +104 FORMAT (e32.14,4E25.14) +END SUBROUTINE maprnt + + +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! + REAL FUNCTION random(naught) + + IMPLICIT NONE + INTEGER, INTENT(IN OUT) :: naught + + REAL :: ran1,ran3(127),half + INTEGER :: i,j,ran2,q,r + LOGICAL :: init + DATA init/.false./ + SAVE init,ran2,ran1,ran3 + +IF (init) GO TO 3 +r = MOD(naught,8190) + 1 +ran2 = 128 +DO i=1,127 + ran2 = ran2 - 1 + ran1 = -2.d0**55 + DO j=1,7 + r = MOD(1756*r,8191) + q = r/32 + ran1 = (ran1 + q)*(1.0D0/256) + END DO + ran3(ran2) = ran1 +END DO +init = .true. +3 IF (ran2 == 1) ran2 = 128 +ran2 = ran2 - 1 +ran1 = ran1 + ran3(ran2) +half = .5D0 +IF (ran1 >= 0.d0) half = -half +ran1 = ran1 + half +ran3(ran2) = ran1 +random = ran1 + .5D0 + +END FUNCTION random + + + +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! + REAL FUNCTION flin (n,j,l,f,x,nf) + IMPLICIT NONE + + INTEGER, INTENT(IN) :: n + INTEGER, INTENT(IN OUT) :: j + REAL, INTENT(IN) :: l + REAL :: f + REAL, INTENT(IN) :: x(n) + INTEGER, INTENT(OUT) :: nf + + INTEGER :: i + REAL :: t(20) + + EXTERNAL f + +!...FLIN IS THE FUNCTION OF ONE REAL VARIABLE L THAT IS MINIMIZED +! BY THE SUBROUTINE MIN... +!---------------------------------------------- + REAL :: v(20,20),q0(20),q1(20),qa,qb,qc,qd0,qd1,qf1 + COMMON /q/ v,q0,q1,qa,qb,qc,qd0,qd1,qf1 +!---------------------------------------------- +IF (j == 0) GO TO 2 +!...THE SEARCH IS LINEAR... +DO i=1,n + t(i) = x(i) + l*v(i,j) +END DO +GO TO 4 +!...THE SEARCH IS ALONG A PARABOLIC SPACE CURVE... +2 qa = (l*(l - qd1))/(qd0*(qd0 + qd1)) +qb = ((l + qd0)*(qd1 - l))/(qd0*qd1) +qc = (l*(l + qd0))/(qd1*(qd0 + qd1)) +DO i=1,n + t(i) = (qa*q0(i) + qb*x(i)) + qc*q1(i) +END DO +!...THE FUNCTION EVALUATION COUNTER NF IS INCREMENTED... +4 nf = nf + 1 +flin = f(t,n) + +END FUNCTION flin + + +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! + SUBROUTINE sort(m,n,d,v) + IMPLICIT NONE +! + INTEGER, INTENT(IN OUT) :: m + INTEGER, INTENT(IN) :: n + REAL, INTENT(IN OUT) :: d(n) + REAL, INTENT(IN OUT) :: v(m,n) + + INTEGER :: i,j,k,nm1,ip1 + REAL :: s +!...SORTS THE ELEMENTS OF D(N) INTO DESCENDING ORDER AND MOVES THE +! CORRESPONDING COLUMNS OF V(N,N). +! M IS THE ROW DIMENSION OF V AS DECLARED IN THE CALLING PROGRAM. +IF (n == 1) RETURN +nm1 = n - 1 +DO i = 1,nm1 + k=i + s = d(i) + ip1 = i + 1 + DO j = ip1,n + IF (d(j) <= s) CYCLE + k = j + s = d(j) + END DO + IF (k <= i) CYCLE + d(k) = d(i) + d(i) = s + DO j = 1,n + s = v(j,i) + v(j,i) = v(j,k) + v(j,k) = s + END DO +END DO +END SUBROUTINE sort + + +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! + SUBROUTINE quad(n,f,x,t,machep,h) + IMPLICIT NONE + + INTEGER, INTENT(IN) :: n + REAL :: f + REAL, INTENT(IN OUT) :: x(n) + REAL, INTENT(IN OUT) :: t + REAL :: machep + REAL, INTENT(IN OUT) :: h +! IMPLICIT REAL (A-H,O-Z) + EXTERNAL f + +!...QUAD LOOKS FOR THE MINIMUM OF F ALONG A CURVE DEFINED BY Q0,Q1,X... + INTEGER :: i + REAL :: l + REAL :: s,value +!---------------------------------------------- + INTEGER :: nf,nl + REAL :: fx,ldt,dmin + +REAL :: v(20,20),q0(20),q1(20),qa,qb,qc,qd0,qd1,qf1 +COMMON /global/ fx,ldt,dmin,nf,nl /q/ v,q0,q1,qa,qb,qc,qd0,qd1,qf1 +!---------------------------------------------- +s = fx +fx = qf1 +qf1 = s +qd1 = 0.d0 +DO i=1,n + s = x(i) + l = q1(i) + x(i) = l + q1(i) = s + qd1 = qd1 + (s-l)**2 +END DO +qd1 = SQRT(qd1) +l = qd1 +s = 0.d0 +IF (qd0 <= 0.d0 .OR. qd1 <= 0.d0 .OR. nl < 3*n*n) GO TO 2 +value=qf1 +CALL MIN(n,0,2,s,l,value,.true.,f,x,t,machep,h) +qa = (l*(l-qd1))/(qd0*(qd0+qd1)) +qb = ((l+qd0)*(qd1-l))/(qd0*qd1) +qc = (l*(l+qd0))/(qd1*(qd0+qd1)) +GO TO 3 +2 fx = qf1 +qa = 0.d0 +qb = qa +qc = 1.d0 +3 qd0 = qd1 +DO i=1,n + s = q0(i) + q0(i) = x(i) + x(i) = (qa*s + qb*x(i)) + qc*q1(i) +END DO +END SUBROUTINE quad + diff --git a/applications/PUfoam/MoDeNaModels/SurfaceTension/src/SolverSetup.F90 b/applications/PUfoam/MoDeNaModels/SurfaceTension/src/SolverSetup.F90 new file mode 100644 index 000000000..c60e7f69e --- /dev/null +++ b/applications/PUfoam/MoDeNaModels/SurfaceTension/src/SolverSetup.F90 @@ -0,0 +1,305 @@ +!>This file contains the subroutine which sets the method used to +!!solve the nonlinear system of equations depending on the specifications +!!made in the makefile. + + + + +Subroutine SolverSetup + +Use BASIC_VARIABLES, Only: ncomp + +!PETSc modules +Use PetscManagement +Use f90moduleinterfaces +Use Global_x !(snes,ngrid,ngp,x,r,timer) + +Implicit None + +#include +#include +#include +#include +#include +#include +#include +#include +#include +#include + + +DM :: da +PetscErrorCode :: ierr +type (userctx) :: user +Mat :: J +PetscReal :: erel +PetscBool :: flg +INTEGER :: jac_id +PetscInt :: JacLocal + +character(80) :: filename='' + +!external subroutines associated with Solver +external FormInitialGuess +external FormFunction +external Jac_Shell_AD +external Jac_Matrix_Empty +external MonitorTimer + + + call MPI_Comm_rank(PETSC_COMM_WORLD,user%rank,ierr) + call MPI_Comm_size(PETSC_COMM_WORLD,user%num_procs,ierr) + + +! Create solver context + call SNESCreate(PETSC_COMM_WORLD,snes,ierr) + +! Create distributed array (DMDA) to manage parallel grid and vectors + call DMDACreate1d(PETSC_COMM_WORLD, & !MPI communicator + & DMDA_BOUNDARY_GHOSTED, & !Boundary type at boundary of physical domain + & ngrid, & !global dimension of array (if negative number, then value can be changed by user via command line!) + & ncomp, & !number of degrees of freedom per grid point (number of unknowns at each grid point) + & ngp, & !number of ghost points accessible for local vectors + & PETSC_NULL_INTEGER, & !could be an array to specify the number of grid points per processor + & da, & !the resulting distributed array object + & ierr) + +! Extract global arrays from DMDA: x: unknowns, r: residual + call DMCreateGlobalVector(da,x,ierr) + call VecDuplicate(x,r,ierr) + +! Get local grid boundaries (for 1-dimensional DMDA) + call DMDAGetCorners(da, & !the distributed array + & user%xs, & !corner index in x direction + & PETSC_NULL_INTEGER, & !corner index in y direction + & PETSC_NULL_INTEGER, & !corner index in z direction + & user%xm, & !width of locally owned part in x direction + & PETSC_NULL_INTEGER, & !width of locally owned part in y direction + & PETSC_NULL_INTEGER, & !width of locally owned part in z direction + & ierr) !error check + + call DMDAGetGhostCorners(da, & !the distributed array + & user%gxs, & !corner index in x direction (but now counting includes ghost points) + & PETSC_NULL_INTEGER, & !corner index in y direction (but now counting includes ghost points) + & PETSC_NULL_INTEGER, & !corner index in z direction (but now counting includes ghost points) + & user%gxm, & !width of locally owned part in x direction (but now including ghost points) + & PETSC_NULL_INTEGER, & !width of locally owned part in y direction (but now including ghost points) + & PETSC_NULL_INTEGER, & !width of locally owned part in z direction (but now including ghost points) + & ierr) !error check + +! Here we shift the starting indices up by one so that we can easily +! use the Fortran convention of 1-based indices (rather 0-based indices). + user%xs = user%xs+1 + user%gxs = user%gxs+1 + user%xe = user%xs+user%xm-1 + user%gxe = user%gxs+user%gxm-1 + + call SNESSetFunction(snes,r,FormFunction,user,ierr) + call SNESSetApplicationContext(snes,user,ierr) + call SNESSetDM(snes,da,ierr) + +! !Set up matrix free jacobian +! erel = 1e-08 +! call MatCreateSNESMF(snes,J,ierr) !matrix free jacobi matrix +! call MatMFFDSetFunctionError(J,erel,ierr) +! call SNESSetJacobian(snes,J,J,MatMFFDComputeJacobian,PETSC_NULL_OBJECT,ierr) + + +! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - +! Set up nonlinear solver depending on option set in makefile (with -jac) +! - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - + call PetscOptionsGetInt(PETSC_NULL_CHARACTER,'-jac',jac_id,flg,ierr) + If(flg) Then + + Else + jac_id = 0 + write(*,*)'Option -jac not set in makefile, using matrix-free with numerical approximations.' + End If + + Select Case(jac_id) + + Case(-1) !for options that dont need a jacobian: Anderson mixing, Picard + + Case (0) !matrix-free with numerical approximation of J(x)v + !default value of erel + erel = 1e-08 + !check if value for erel is specified in makefile + call PetscOptionsGetReal(PETSC_NULL_CHARACTER,'-erel',erel,flg,ierr) + If(user%rank == 0) write(*,*)'Using matrix-free Jacobian with numerical approximations. erel:',erel + call MatCreateSNESMF(snes,J,ierr) !matrix free jacobi matrix + call MatMFFDSetFunctionError(J,erel,ierr) + call SNESSetJacobian(snes,J,J,MatMFFDComputeJacobian,PETSC_NULL_OBJECT,ierr) + + Case (1) !matrix-free with AD-calculated J(x)v + If(user%rank == 0) write(*,*)'Using matrix-free AD Jacobian.' + !determine local size of shell matrix + JacLocal = INT(ngrid / user%num_procs) + If(mod(ngrid,user%num_procs) /= 0 ) Stop 'Dimensions and number of cores dont match! mod(ngrid,nc) must equal 0' + !Make sure that local parts of JacShell have the same size as the local DMDA-Arrays (local size JacShell != user%xm!!) + If(JacLocal /= user%xm) Stop 'Shell-Jacobi-Matrix and DMDA have to be parallelized accordingly!!(JacLocal = user%xm)' + call MatCreateShell(PETSC_COMM_WORLD,ncomp*JacLocal,ncomp*JacLocal,ncomp*ngrid,ncomp*ngrid,PETSC_NULL_OBJECT,J,ierr) + call MatShellSetOperation( J, MATOP_MULT, Jac_Shell_AD, ierr ) + call SNESSetJacobian( snes, J, J, Jac_Matrix_Empty, PETSC_NULL_OBJECT, ierr) + + Case (2) !build complete Jacobi matrix via finite-differences + If(user%rank == 0) write(*,*)'Using finite-difference Jacobian.' +!Now in makefile: -snes_fd +! call MatCreate(PETSC_COMM_WORLD,J,ierr) +! call MatSetSizes(J,PETSC_DECIDE,PETSC_DECIDE,ngrid,ngrid,ierr) +! call MatSetFromOptions(J,ierr) +! call MatSetUp(J,ierr) !!sets up the internal matrix data structure +! call SNESSetJacobian(snes,J,J,SNESComputeJacobianDefault,PETSC_NULL_OBJECT,ierr) + + + Case (3) !build the complete Jacobi matrix via AD + If(user%rank == 0) write(*,*)'Using AD-generated Jacobian.' + write(*,*)'Funktioniert noch nicht!' + stop + !create Matrix that has the appropriate sparsity pattern for the da + !But that also means that when values are inserted in positions that + !dont fit this structure, an error occurs! + !i.e. when calculating the jacobi matrix it is not possible anymore + !to ignore the sparsity pattern and just create a dense jacobian!! + + !call DMCreateMatrix(da,MATMPIAIJ,J,ierr) !CAUTION: in newer PETSc Versions DMCreateMatrix does not contain the MatType argument anymore! + !call SNESSetJacobian(snes,J,J,Jac_AD,PETSC_NULL_OBJECT,ierr) + + Case default + write(*,*) 'No valid option set for -jac in makefile, using full Jacobi via finite-differences.' + call SNESSetJacobian(snes,J,J,SNESComputeJacobianDefault,PETSC_NULL_OBJECT,ierr) + + End Select + +!Set monitoring function that ouputs the surface tension at every iteration + call SNESMonitorSet(snes,MonitorTimer,PETSC_NULL_OBJECT,PETSC_NULL_FUNCTION,ierr) + +!Enable modification from makefile + call SNESSetFromOptions(snes,ierr) + +!Evaluate Initial Guess + call FormInitialGuess(snes,x,ierr) + write(filename,*)'0_initial_profile_global.xlo' + call PrintGlobalVec(x,filename) + + !start timer + total_time = 0.0 + timer_old = MPI_WTIME() + +!Solve system + call SNESSolve(snes,PETSC_NULL_OBJECT,x,ierr) + write(filename,*)'1_final_profile_global.xlo' + call PrintGlobalVec(x,filename) + write(filename,'(a,I3.3,a)') '2_final_profile_local_proc_',user%rank,'.xlo' + call PrintLocalVec(x,da,filename) + + !plot residual vs time graph + !call system('gnuplot gnuplot_script.srp') + + +End Subroutine SolverSetup + + + + + + + +subroutine MonitorTimer(snes,its,norm,dummy,ierr) + + Use Global_x, Only: timer,timer_old,total_time,r + Use mod_DFT, Only: free + Use PARAMETERS, Only: KBOL,PI + Use BASIC_VARIABLES, Only: t,parame, ncomp + Use VLE_VAR, Only: rhob,tc + +! ! !PETSc modules +! ! use f90module +! ! !DFT modules +! ! use DFT_MODULE, ONLY: free +! ! use VLE_VAR, ONLY: tc,rhob +! ! use BASIC_VARIABLES, ONLY:t,parame,ncomp +! ! use PARAMETERS, ONLY: PI,KBOL + + implicit none + +#include +#include + +! Input/output variables: + SNES snes + PetscInt dummy + Integer :: its + REAL :: norm + PetscErrorCode ierr +! local + PetscReal :: f2norm + Vec :: current_solution + DOUBLE PRECISION :: delta_time + INTEGER :: rank + REAL :: m_average,surftens,st_macro + character(80) :: filename='' + + + + !calculate interfacial tension + !sum up the variable free from all procs on proc 0 + call MPI_Reduce(free,free,1,MPI_DOUBLE_PRECISION,MPI_SUM,0,PETSC_COMM_WORLD,ierr) + + !Only proc 0 calculates surface tension + call MPI_Comm_rank(PETSC_COMM_WORLD,rank,ierr) + IF(rank == 0) THEN + + !calculate surface tension + surftens = KBOL * t *1.E20*1000.0 *free + m_average = SUM( rhob(1,1:ncomp)*parame(1:ncomp,1) ) / rhob(1,0) + + st_macro = surftens / ( 1.0 + 3.0/8.0/PI *t/tc & + * (1.0/2.55)**2 / (0.0674*m_average+0.0045) ) + write(*,*)'ST',st_macro + + !write result to outputfile + filename='./out.txt' + CALL file_open(filename,99) + WRITE (99,*) st_macro + close(99) + + End If + + + + + + !calculate elapsed time + timer = MPI_WTIME() + delta_time = timer - timer_old + timer_old = timer + total_time = total_time + delta_time + + !get norm of residual array + call VecNorm(r,2,f2norm,ierr) + + IF(rank == 0) THEN + !print results to file + filename = 'ItsTimeNorm.dat' + open(unit = 44, file = filename) + write(44,*) its,total_time,f2norm + End If + +end subroutine MonitorTimer + + + + + + + + + + + + + + + + + diff --git a/applications/PUfoam/MoDeNaModels/SurfaceTension/src/Spline_Integration_d.F90 b/applications/PUfoam/MoDeNaModels/SurfaceTension/src/Spline_Integration_d.F90 new file mode 100644 index 000000000..919c9aea1 --- /dev/null +++ b/applications/PUfoam/MoDeNaModels/SurfaceTension/src/Spline_Integration_d.F90 @@ -0,0 +1,230 @@ +!>This file contains the automatic differentiation results +!!of the subroutines which perform spline interpolation and +!!spline integration. + + + + + + + + + + + +! Generated by TAPENADE (INRIA, Tropics team) +! Tapenade 3.10 (r5498) - 20 Jan 2015 09:48 +! +! Differentiation of spline in forward (tangent) mode: +! variations of useful results: y2 +! with respect to varying inputs: y2 y +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! SUBROUTINE spline +! +! Given arrays x(1:n) and y(1:n) containing a tabulated function, +! i.e., yi = f(xi), with x1 < x2 < .. . < xN, and given values yp1 and +! ypn for the first derivative of the interpolating function at points 1 +! and n, respectively, this routine returns an array y2(1:n) of length n +! which contains the second derivatives of the interpolating function at +! the tabulated points xi. If yp1 and/or ypn are equal to 1 1030 or +! larger, the routine is signaled to set the corresponding boundary +! condition for a natural spline, with zero second derivative on that +! boundary. +! Parameter: NMAX is the largest anticipated value of n. +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! +SUBROUTINE SPLINE_D(x, y, yd, n, yp1, ypn, y2, y2d) + IMPLICIT NONE +! +! ---------------------------------------------------------------------- + INTEGER, INTENT(IN) :: n + REAL, INTENT(IN) :: x(n) + REAL, INTENT(IN) :: y(n) + REAL, INTENT(IN) :: yd(n) + REAL, INTENT(IN) :: yp1 + REAL, INTENT(IN) :: ypn + REAL, INTENT(OUT) :: y2(n) + REAL, INTENT(OUT) :: y2d(n) +! +! ---------------------------------------------------------------------- + INTEGER, PARAMETER :: nmax=1000 + INTEGER :: i, k + REAL :: p, qn, sig, un, u(nmax) + REAL :: pd, und, ud(nmax) +! ---------------------------------------------------------------------- + IF (yp1 .GT. 0.99e30) THEN + y2d(1) = 0.0 + y2(1) = 0.0 + u(1) = 0.0 + ud = 0.0 + ELSE + y2d(1) = 0.0 + y2(1) = -0.5 + ud = 0.0 + ud(1) = 3.0*(yd(2)-yd(1))/(x(2)-x(1))**2 + u(1) = 3.0/(x(2)-x(1))*((y(2)-y(1))/(x(2)-x(1))-yp1) + END IF + DO i=2,n-1 + IF ((x(i+1) - x(i) .EQ. 0.0 .OR. x(i) - x(i-1) .EQ. 0.0) .OR. x(i+1)& +& - x(i-1) .EQ. 0.0) THEN + GOTO 100 + ELSE + sig = (x(i)-x(i-1))/(x(i+1)-x(i-1)) + pd = sig*y2d(i-1) + p = sig*y2(i-1) + 2.0 + y2d(i) = -((sig-1.0)*pd/p**2) + y2(i) = (sig-1.0)/p + ud(i) = ((6.0*((yd(i+1)-yd(i))/(x(i+1)-x(i))-(yd(i)-yd(i-1))/(x(i)& +& -x(i-1)))/(x(i+1)-x(i-1))-sig*ud(i-1))*p-(6.0*((y(i+1)-y(i))/(x(& +& i+1)-x(i))-(y(i)-y(i-1))/(x(i)-x(i-1)))/(x(i+1)-x(i-1))-sig*u(i-& +& 1))*pd)/p**2 + u(i) = (6.0*((y(i+1)-y(i))/(x(i+1)-x(i))-(y(i)-y(i-1))/(x(i)-x(i-1& +& )))/(x(i+1)-x(i-1))-sig*u(i-1))/p + END IF + END DO + IF (ypn .GT. 0.99e30) THEN + qn = 0.0 + un = 0.0 + und = 0.0 + ELSE + qn = 0.5 + und = -(3.0*(yd(n)-yd(n-1))/(x(n)-x(n-1))**2) + un = 3.0/(x(n)-x(n-1))*(ypn-(y(n)-y(n-1))/(x(n)-x(n-1))) + END IF + y2d(n) = ((und-qn*ud(n-1))*(qn*y2(n-1)+1.0)-(un-qn*u(n-1))*qn*y2d(n-1)& +& )/(qn*y2(n-1)+1.0)**2 + y2(n) = (un-qn*u(n-1))/(qn*y2(n-1)+1.0) + DO k=n-1,1,-1 + y2d(k) = y2d(k)*y2(k+1) + y2(k)*y2d(k+1) + ud(k) + y2(k) = y2(k)*y2(k+1) + u(k) + END DO + GOTO 110 + 100 WRITE(*, *) 'i x', i, x(i+1), x(i), x(i-1) + WRITE(*, *) 'error in spline-interpolation' + STOP + 110 CONTINUE +END SUBROUTINE SPLINE_D + + + + + + +! Generated by TAPENADE (INRIA, Tropics team) +! Tapenade 3.10 (r5498) - 20 Jan 2015 09:48 +! +! Differentiation of splint_integral in forward (tangent) mode: +! variations of useful results: integral +! with respect to varying inputs: y2a ya +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! SUBROUTINE splint_integral +! +! Given the arrays xa(1:n) and ya(1:n) of length n, which tabulate a +! function (with the in order), and given the array y2a(1:n), which is +! the output from spline above, and given a value of x, this routine +! returns a cubic-spline interpolated value y. +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! +SUBROUTINE SPLINT_INTEGRAL_D(xa, ya, yad, y2a, y2ad, n, xlo, xhi, & +& integral, integrald) + IMPLICIT NONE +! the -1 in (khi_L-1) because khi_L was already counted up +! +! ---------------------------------------------------------------------- + INTEGER, INTENT(IN) :: n + REAL, INTENT(IN) :: xa(n) + REAL, INTENT(IN) :: ya(n) + REAL, INTENT(IN) :: yad(n) + REAL, INTENT(IN) :: y2a(n) + REAL, INTENT(IN) :: y2ad(n) + REAL, INTENT(IN) :: xlo + REAL, INTENT(IN) :: xhi + REAL, INTENT(OUT) :: integral + REAL, INTENT(OUT) :: integrald +! +! ---------------------------------------------------------------------- + INTEGER :: k, khi_l, klo_l, khi_h, klo_h + REAL :: xl, xh, h, int, x0, x1, y0, y1, y20, y21 + REAL :: intd, y0d, y1d, y20d, y21d +! ---------------------------------------------------------------------- + integral = 0.0 + klo_l = 1 + khi_l = n + 1 IF (khi_l - klo_l .GT. 1) THEN + k = (khi_l+klo_l)/2 + IF (xa(k) .GT. xlo) THEN + khi_l = k + ELSE + klo_l = k + END IF + GOTO 1 + END IF + klo_h = 1 + khi_h = n + 2 IF (khi_h - klo_h .GT. 1) THEN + k = (khi_h+klo_h)/2 + IF (xa(k) .GT. xhi) THEN + khi_h = k + ELSE + klo_h = k + END IF + GOTO 2 + END IF +! integration in spline pieces, the lower interval, bracketed +! by xa(klo_L) and xa(khi_L) is in steps shifted upward. +! first: determine upper integration bound + xl = xlo + integrald = 0.0 + 3 IF (khi_h .GT. khi_l) THEN + xh = xa(khi_l) + ELSE IF (khi_h .EQ. khi_l) THEN + xh = xhi + ELSE + WRITE(*, *) 'error in spline-integration' + PAUSE + END IF + h = xa(khi_l) - xa(klo_l) + IF (h .EQ. 0.0) PAUSE'bad xa input in splint' + x0 = xa(klo_l) + x1 = xa(khi_l) + y0d = yad(klo_l) + y0 = ya(klo_l) + y1d = yad(khi_l) + y1 = ya(khi_l) + y20d = y2ad(klo_l) + y20 = y2a(klo_l) + y21d = y2ad(khi_l) + y21 = y2a(khi_l) +! int = -xL/h * ( (x1-.5*xL)*y0 + (0.5*xL-x0)*y1 & +! +y20/6.*(x1**3-1.5*xL*x1*x1+xL*xL*x1-.25*xL**3) & +! -y20/6.*h*h*(x1-.5*xL) & +! +y21/6.*(.25*xL**3-xL*xL*x0+1.5*xL*x0*x0-x0**3) & +! -y21/6.*h*h*(.5*xL-x0) ) +! int = int + xH/h * ( (x1-.5*xH)*y0 + (0.5*xH-x0)*y1 & +! +y20/6.*(x1**3-1.5*xH*x1*x1+xH*xH*x1-.25*xH**3) & +! -y20/6.*h*h*(x1-.5*xH) & +! +y21/6.*(.25*xH**3-xH*xH*x0+1.5*xH*x0*x0-x0**3) & +! -y21/6.*h*h*(.5*xH-x0) ) + intd = -((xl*((x1-.5*xl)*y0d+(0.5*xl-x0)*y1d)-(x1-xl)**4*y20d/24.+(0.5& +& *xl*xl-x1*xl)*h**2*y20d/6.+(xl-x0)**4*y21d/24.-(0.5*xl*xl-x0*xl)*h**& +& 2*y21d/6.)/h) + int = -(1.0/h*(xl*((x1-.5*xl)*y0+(0.5*xl-x0)*y1)-y20/24.*(x1-xl)**4+& +& y20/6.*(0.5*xl*xl-x1*xl)*h*h+y21/24.*(xl-x0)**4-y21/6.*(0.5*xl*xl-x0& +& *xl)*h*h)) + intd = intd + (xh*((x1-.5*xh)*y0d+(0.5*xh-x0)*y1d)-(x1-xh)**4*y20d/24.& +& +(0.5*xh*xh-x1*xh)*h**2*y20d/6.+(xh-x0)**4*y21d/24.-(0.5*xh*xh-x0*xh& +& )*h**2*y21d/6.)/h + int = int + 1.0/h*(xh*((x1-.5*xh)*y0+(0.5*xh-x0)*y1)-y20/24.*(x1-xh)**& +& 4+y20/6.*(0.5*xh*xh-x1*xh)*h*h+y21/24.*(xh-x0)**4-y21/6.*(0.5*xh*xh-& +& x0*xh)*h*h) + integrald = integrald + intd + integral = integral + int +! write (*,*) integral,x1,xH + klo_l = klo_l + 1 + khi_l = khi_l + 1 + xl = x1 + IF (khi_h .NE. khi_l - 1) GOTO 3 +END SUBROUTINE SPLINT_INTEGRAL_D + + + diff --git a/applications/PUfoam/MoDeNaModels/SurfaceTension/src/VLE_main.F90 b/applications/PUfoam/MoDeNaModels/SurfaceTension/src/VLE_main.F90 new file mode 100644 index 000000000..aa84d6036 --- /dev/null +++ b/applications/PUfoam/MoDeNaModels/SurfaceTension/src/VLE_main.F90 @@ -0,0 +1,95 @@ +!> This file contains the subroutine which starts the phase equilibrium calculation. +!! It also prints the calculated density to the outputfile "out.txt". + + + +SUBROUTINE VLE_MIX(rhob,density,chemPot_total,user) + + +!Petsc modules + USE PetscManagement + + +!VLE modules + USE parameters, ONLY: PI, RGAS, KBOL, muhs,muhc,mudisp + USE basic_variables + USE EOS_VARIABLES, ONLY: fres, eta, eta_start, dhs, mseg, uij, sig_ij, rho, x, z3t + USE DFT_MODULE + USE EOS_NUMERICAL_DERIVATIVES + USE DFT_FCN_MODULE, ONLY: chemPot_res + IMPLICIT NONE + +!> --------------------------------------------------------------------- +!! Variables +!! --------------------------------------------------------------------- + +!passed + type (userctx) user + REAL :: chemPot_total(nc) + REAL :: rhob(2,0:nc),density(np) + +!local + REAL, DIMENSION(nc) :: dhs_star + REAL :: w(np,nc), lnphi(np,nc) + INTEGER :: converg + + !> --------------------------------------------------------------------- + !! prepare for phase equilibrium calculation for given T + !! --------------------------------------------------------------------- + + dhs(1:ncomp) = parame(1:ncomp,2) * ( 1.0 - 0.12*EXP( -3.0*parame(1:ncomp,3)/t ) ) ! needed for rdf_matrix + dhs_star(1:ncomp) = dhs(1:ncomp)/parame(1:ncomp,2) + + nphas = 2 + outp = 0 ! output to terminal + + CALL START_VAR (converg,user) ! gets starting values, sets "val_init" + + IF ( converg /= 1 ) THEN + IF(user%rank == 0) THEN + WRITE (*,*) 'no VLE found' + END IF + RETURN + END IF + +! rhob(phase,0): molecular density + rhob(1,0) = dense(1) / ( PI/6.0* SUM( xi(1,1:ncomp) * parame(1:ncomp,1) * dhs(1:ncomp)**3 ) ) + rhob(2,0) = dense(2) / ( PI/6.0* SUM( xi(2,1:ncomp) * parame(1:ncomp,1) * dhs(1:ncomp)**3 ) ) + ! rhob(phase,i): molecular component density (with i=(1,...ncomp) ) in units (1/A^3) + rhob(1,1:ncomp) = rhob(1,0)*xi(1,1:ncomp) + rhob(2,1:ncomp) = rhob(2,0)*xi(2,1:ncomp) + +! --- get density in SI-units (kg/m**3) ------------------------------- + CALL SI_DENS ( density, w ) + +!--- calculate residual chemical potentials + ensemble_flag = 'tv' ! this flag is for: mu_res=mu_res(T,rho) + densta(1) = dense(1) ! Index 1 is for liquid density (here: packing fraction eta) + densta(2) = dense(2) ! Index 2 is for vapour density (here: packing fraction eta) + CALL fugacity (lnphi) + chemPot_res(1:ncomp) = lnphi(1,1:ncomp) + chemPot_total(1:ncomp) = lnphi(1,1:ncomp) + LOG( rhob(1,1:ncomp) ) ! my0 = mu_res(T,rho_bulk_L) + ln(rho_bulk_l) + + +!> --------------------------------------------------------------------- +!! Output results of phase equilibrim calculation +!! --------------------------------------------------------------------- + + +IF(user%rank == 0) THEN + WRITE(*,*) '--------------------------------------------------' + WRITE(*,*)'RESULT OF PHASE EQUILIBRIUM CALCULATION' + WRITE (*,*) ' ' + WRITE (*,*) 'temperature ',t, 'K, and p=', p/1.E5,' bar' + WRITE (*,*) 'x1_liquid ',xi(1,1),' x1_vapor', xi(2,1) + WRITE (*,*) 'densities ',rhob(1,0), rhob(2,0) + WRITE (*,*) 'dense ',dense(1), dense(2) + WRITE (*,*) 'density [kg/m3] ',density(1), density(2) + write (*,*) 'chemical potentials comp1' , lnphi(1,1) + LOG( rhob(1,1) ), lnphi(2,1) + lnx(2,1) + LOG(rhob(2,0)) !LOG( rhob(2,1) ) + write (*,*) 'chemical potentials comp2' ,lnphi(1,2) + LOG( rhob(1,2) ), lnphi(2,2) + LOG( rhob(2,2) ) +END IF + + + + +END SUBROUTINE VLE_MIX diff --git a/applications/PUfoam/MoDeNaModels/SurfaceTension/src/VLE_subroutines.F90 b/applications/PUfoam/MoDeNaModels/SurfaceTension/src/VLE_subroutines.F90 new file mode 100644 index 000000000..1e0928a3a --- /dev/null +++ b/applications/PUfoam/MoDeNaModels/SurfaceTension/src/VLE_subroutines.F90 @@ -0,0 +1,7612 @@ +!> This file contains the subroutines which perform and control the +!! phase equilibrium calculation. + + + + + +!>WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +!! SUBROUTINE start_var +!! +!! This subroutine generates a converged solution for binary systems +!! or performes a flash calculation for mixtues. This routine is a +!! fairly weak point of the program. +!! +!! IF a polymer is considered, starting values for mole fractions +!! are determined from the SUBROUTINGE POLY_STA_VAR (see below). The +!! polymer needs to be placed as component 1 (first line) in INPUT +!! file. +!! +!! A phase equilib. iteration is started at the end of this routine. +!! If no solution is found (converg=0), the program will stop within +!! this routine. +!! +!! Currently, this routine assumes two-phase equilibrium and derives +!! starting values (xi,density) only for two phases. +!! +!! Prerequisites are: +!! SUBROUTINE INPUT needs to be called prior to this routine, because +!! all pure comp. parameters as well as (T,P,kij) need to be in place. +!! Also, the variable to be iterated "it(i)" and the variables to be +!! calculated through the summation relation "sum_rel(i)" have to be +!! defined. +!!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW + SUBROUTINE start_var(converg,user) + +!Petsc modules + USE PetscManagement + +!VLE modules + USE BASIC_VARIABLES + USE STARTING_VALUES + IMPLICIT NONE +! +! ---------------------------------------------------------------------- +type (userctx) user + INTEGER, INTENT(IN OUT) :: converg +! +! ---------------------------------------------------------------------- + INTEGER :: ph, i, k + INTEGER :: ncompsav, n_unkwsav, ph_split + LOGICAL :: lle_check, flashcase, renormalize + REAL :: den1, den2, x_1, x_2 + CHARACTER (LEN=50) :: filename +! ---------------------------------------------------------------------- + +converg = 0 + +! CALL RACHFORD_RICE (converg) +! CALL Heidemann_Khalil + +! ---------------------------------------------------------------------- +! This first condition (eos >= 4) is for LJ models, not for PC-SAFT +! ---------------------------------------------------------------------- + +IF (eos >= 4) THEN + + ncomp = 2 ! set number of components to 2 + n_unkw = ncomp ! number of quantities to be iterated + it(1) = 'x11' ! iteration of mol fraction of comp.1 phase 1 + it(2) = 'x21' ! iteration of mol fraction of comp.1 phase 2 + sum_rel(1) = 'x12' ! summation relation: x12 = 1 - sum(x1j) + sum_rel(2) = 'x22' ! summation relation: x22 = 1 - sum(x2j) + + filename = 'LJ_START_VAL.INC' + CALL file_open(filename,84) + READ (84,*) den1,den2 + READ (84,*) x_1,x_2 + CLOSE (84) + + xi(1,1) = x_1 + xi(2,1) = x_2 + xi(1,2) = 1.0 - xi(1,1) + xi(2,2) = 1.0 - xi(2,1) + lnx(1,1) = LOG(xi(1,1)) + lnx(2,1) = LOG(xi(2,1)) + lnx(1,2) = LOG(xi(1,2)) + lnx(2,2) = LOG(xi(2,2)) + + val_init(1) = den1 + val_init(2) = den2 + val_init(3) = t + val_init(4) = p + DO ph = 1,nphas + DO k = 1,ncomp + val_init(4+k+(ph-1)*ncomp) = LOG(xi(ph,k)) + END DO + END DO + + CALL objective_ctrl (converg) + + IF(user%rank == 0) THEN + IF (converg == 1) WRITE (*,*) t, p/1.0E5, xi(1,1), xi(2,1) + IF (converg == 0) WRITE (*,*) ' weak starting values' + END IF + +! ---------------------------------------------------------------------- +! ELSE: PC-SAFT equation of state +! ---------------------------------------------------------------------- + +ELSE + + renormalize = .false. ! for renormalization group theory (RGT) + IF (num == 2) renormalize = .true. + IF (num == 2) num = 0 ! if RGT: initial phase equilibr. is for non-renormalized model + + flashcase = .false. ! .true. when a specific feed conc. xif is given + IF (xif(1) /= 0.0) flashcase = .true. + + lle_check = .true. + +! ---------------------------------------------------------------------- +! IF: non-polymeric system +! ---------------------------------------------------------------------- + IF (mm(1) < 2000.0) THEN + + DO i=1,ncomp ! setting mole-fractions for the case that + ! anything goes wrong in the coming routines + xi(1,i) = 1.0 / REAL(ncomp) + xi(2,i) = 1.0 / REAL(ncomp) + END DO + + + ! ------------------------------------------------------------------ + ! determine an initial conc. (phase 1) that will phase split + ! ------------------------------------------------------------------ + IF( ncomp == 2 .AND. .NOT.flashcase ) THEN + CALL vle_min( lle_check ) + IF(user%rank == 0) THEN + WRITE(*,*)' INITIAL FEED-COMPOSITION',(xi(1,i), i=1,ncomp),converg + END IF + END IF + + ! ------------------------------------------------------------------ + ! perform a phase stability test + ! ------------------------------------------------------------------ + ph_split = 0 + CALL phase_stability ( .false., flashcase, ph_split,user ) + IF(user%rank == 0) THEN + write (*,*) 'stability analysis I indicates phase-split is:',ph_split + END IF + + ! ------------------------------------------------------------------ + ! determine species i, for which x(i) is calc from summation relation + ! ------------------------------------------------------------------ + CALL select_sum_rel (1,0,1) ! synthax (m,n,o): phase m + ! exclude comp. n + ! assign it(o) and higher + CALL select_sum_rel (2,0,2) ! for ncomp>=3, the quantities + ! to be iterated will be overwritten + + ! ------------------------------------------------------------------ + ! if 2 phases (VLE) + ! ------------------------------------------------------------------ + IF (ph_split == 1) THEN + + ! --- perform tangent plane minimization ------------------------ + CALL tangent_plane + ph_split = 0 + + ! --- determine, for which substance summation relation is used -- + IF (flashcase) THEN + CALL determine_flash_it2 + ELSE + CALL select_sum_rel (1,0,1) + CALL select_sum_rel (2,0,2) + END IF + + ! --- do full phase equilibr. calculation ------------------------ + n_unkw = ncomp ! number of quantities to be iterated + CALL objective_ctrl (converg) + IF(user%rank == 0) THEN + IF (converg == 1 ) write (*,*) ' converged (maybe a VLE)',dense(1),dense(2) + END IF + END IF + + ! ------------------------------------------------------------------ + ! test for LLE + ! ------------------------------------------------------------------ + ph_split = 0 + + IF (lle_check) CALL phase_stability (lle_check,flashcase,ph_split) + IF(user%rank == 0) THEN + IF (lle_check) write (*,*) 'stability analysis II, phase-split is:',ph_split + END IF + + ! ------------------------------------------------------------------ + ! if two phases (LLE) + ! ------------------------------------------------------------------ + IF (ph_split == 1) THEN + IF(user%rank == 0) THEN + write (*,*) ' LLE-stability test indicates 2 phases (VLE or LLE)' + END IF + + ! --- perform tangent plane minimization ------------------------ + IF (flashcase) CALL select_sum_rel (1,0,1) + IF (flashcase) CALL select_sum_rel (2,0,2) + + CALL tangent_plane + + ! --- determine, for which substance summation relation ---------- + IF (flashcase) THEN + CALL determine_flash_it2 + ELSE + CALL select_sum_rel (1,0,1) + CALL select_sum_rel (2,0,2) + END IF + + ! --- do full phase equilibr. calculation ------------------------ + n_unkw = ncomp ! number of quantities to be iterated + val_conv(2) = 0.0 + CALL objective_ctrl (converg) + IF(user%rank == 0) THEN + IF (converg == 1 ) write (*,*) ' converged (maybe an LLE)',dense(1),dense(2) + END IF + END IF + + ! ------------------------------------------------------------------ + ! equilibr. calc. converged: set initial var. for further calc. + ! ------------------------------------------------------------------ + IF (converg == 1) THEN + val_init = val_conv + DO ph = 1,nphas + DO i = 1,ncomp + xi(ph,i) = EXP( val_conv(4+i+(ph-1)*ncomp) ) + END DO + END DO + dense(1:2) = val_conv(1:2) + ELSE + IF(user%rank == 0) THEN + WRITE (*,*) ' NO SOLUTION FOUND FOR THE STARTING VALUES' + END IF + STOP + END IF + + + ! --------------------------------------------------------------------- + ! ELSE: for systems with polymers + ! --------------------------------------------------------------------- + + ELSE + + ncompsav = ncomp + ncomp = 2 ! set number of components to 2 + n_unkwsav = n_unkw + + CALL poly_sta_var(converg) + + IF (converg == 1) THEN + val_init = val_conv + ELSE + + IF(user%rank == 0) THEN + WRITE (*,*) ' NO SOLUTION FOUND FOR THE STARTING VALUES' + END IF + STOP + END IF + + ncomp = ncompsav + n_unkw = n_unkwsav ! number of quantities to be iterated + + END IF + +! --- for RGT: set flag back to num=2 indicating an RGT calculation ---- + IF (renormalize) num = 2 + +END IF + +END SUBROUTINE start_var + + + + +!>WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +!! SUBROUTINE objective_ctrl +!! +!! This subroutine controls the iso-fugacity iteration. It uses +!! the variables defined in the array "val_init". If successfull, +!! the converged values are written to "val_conv", and the flag +!! converg is set to 1. +!! See also above desciption for subroutine PHASE_EQUILIB +!! This routine calls SUBROUTINE HYBRID, which is a solver (modified +!! POWELL HYBRID METHOD). HYBRID is freely available for non-commercial +!! applications. HYBRID requires three definitions: +!! 1.the number of equations to be solved (=No. of variables to be +!! iterated). The appropriate parameter is: "n_unkw" +!! 2.the equations to be iterated, they are here gathered in the SUB- +!! ROUTINE OBJEC_FCT (see below). Since HYBRID is a root finder, +!! these objective functions are iterated to be zero (essentially, +!! OBJEC_FCT contains the iso-fugacity relation. +!! 3.an array of variables is required, containing the quatities to be +!! iterated. This array is termed "y(i)" +!! +!! INPUT VARIABLES: +!! val_init(i) array containing (densities,T,P,lnx's) serving as +!! starting values for the phase equilibrium calculation +!! it(i) contains the information, which variable is deter- +!! mined iteratively. For syntax refer e.g.to SUB BINMIX. +!! sum_rel(i) indicates, which mole fraction is determined from the +!! summation relation sum(xi)=1 +!! +!! OUTPUT VARIABLES: +!! val_conv(i) array containing the converged system variables +!! analogous to "val_init" +!! converg 0 if no convergence achieved, 1 if converged solution +!!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +!! + SUBROUTINE objective_ctrl (converg) +! + USE BASIC_VARIABLES + USE Solve_NonLin + IMPLICIT NONE +! +! ---------------------------------------------------------------------- + INTEGER, INTENT(OUT) :: converg +! +! ---------------------------------------------------------------------- + INTERFACE + SUBROUTINE objec_fct ( iter_no, y, residu, dummy ) + INTEGER, INTENT(IN) :: iter_no + REAL, INTENT(IN) :: y(iter_no) + REAL, INTENT(OUT) :: residu(iter_no) + INTEGER, INTENT(IN OUT) :: dummy + END SUBROUTINE objec_fct + END INTERFACE +! + INTEGER :: info,k,posn,i + INTEGER, PARAMETER :: mxr = nc*(nc+1)/2 + REAL, ALLOCATABLE :: y(:),diag(:),residu(:) + REAL :: x_init, x_solut, r_diff1, r_diff2, totres + REAL :: r_thrash, x_thrash + CHARACTER (LEN=2) :: compon + LOGICAL :: convergence +! ---------------------------------------------------------------------- + +info=1 + +ALLOCATE( y(n_unkw), diag(n_unkw), residu(n_unkw) ) + +IF (num == 0) acc_a = 1.E-7 +IF (num == 0) step_a = 2.E-8 +IF (num == 1) acc_a = 1.E-7 +IF (num == 1) step_a = 2.E-8 +IF (num == 2) acc_a = 5.E-7 +IF (num == 2) step_a = 1.E-7 + +posn = 0 +DO i = 1,n_unkw + posn = posn + 1 + IF (it(i) == 't') y(posn) = val_init(3) + IF (it(i) == 'p') y(posn) = val_init(4) + IF (it(i) == 'lnp') y(posn) = LOG( val_init(4) ) + IF (it(i) == 'fls') y(posn) = alpha + IF (it(i)(1:1) == 'x' .AND. it(i)(2:2) == '1') compon = it(i)(3:3) + IF (it(i)(1:1) == 'x' .AND. it(i)(2:2) == '1') READ(compon,*) k + IF (it(i)(1:1) == 'x' .AND. it(i)(2:2) == '1') y(posn) = val_init(4+k) + IF (it(i)(1:1) == 'x' .AND. it(i)(2:2) == '2') compon = it(i)(3:3) + IF (it(i)(1:1) == 'x' .AND. it(i)(2:2) == '2') READ(compon,*) k + IF (it(i)(1:1) == 'x' .AND. it(i)(2:2) == '2') y(posn) = val_init(4+ncomp+k) + IF (it(i)(1:1) == 'x' .AND. it(i)(2:2) == '3') compon = it(i)(3:3) + IF (it(i)(1:1) == 'x' .AND. it(i)(2:2) == '3') READ(compon,*) k + IF (it(i)(1:1) == 'x' .AND. it(i)(2:2) == '3') y(posn) = val_init(4+ncomp+ncomp+k) +END DO + +CALL init_vars + +x_init = 0.0 +DO i = 1,ncomp + IF (lnx(1,i) /= 0.0 .AND. lnx(2,i) /= 0.0) THEN + x_init = x_init + ABS( 1.0 - lnx(2,i)/lnx(1,i) ) + ELSE + x_init = x_init + ABS( 1.0 - EXP(lnx(2,i))/EXP(lnx(1,i)) ) + END IF +END DO + +CALL hbrd (objec_fct, n_unkw, y, residu, step_a, acc_a, info, diag) + +x_solut = 0.0 +DO i = 1,ncomp + IF ( lnx(1,i) /= 0.0 .AND. lnx(2,i) /= 0.0 ) THEN + x_solut = x_solut + ABS( 1.0 - lnx(2,i)/lnx(1,i) ) + ELSE + IF (lnx(1,i) < 1E300 .AND. lnx(1,i) > -1.E300 ) & + x_solut = x_solut + ABS( 1.0 - EXP(lnx(2,i))/EXP(lnx(1,i)) ) + END IF +END DO +r_diff1 = ABS( 1.0 - dense(1)/dense(2) ) +IF ( val_conv(2) > 0.0 ) THEN + r_diff2 = ABS( 1.0 - val_conv(1)/val_conv(2) ) +ELSE + r_diff2 = 0.0 +END IF + +totres = SUM( ABS( residu(1:n_unkw) ) ) + +r_thrash = 0.0005 +x_thrash = 0.0005 +if (num > 0 ) r_thrash = r_thrash * 10.0 +if (num > 0 ) x_thrash = x_thrash * 100.0 + +convergence = .true. + +IF ( info >= 2 ) convergence = .false. +IF ( ABS( 1.0- dense(1)/dense(2) ) < r_thrash .AND. x_solut < x_thrash ) THEN + IF ( x_init > 0.050 ) convergence = .false. + IF ( ( ABS( 1.0- dense(1)/dense(2) ) + x_solut ) < 1.E-7 ) convergence = .false. +ENDIF +IF ( r_diff2 /= 0.0 .AND. r_diff2 > (4.0*r_diff1) .AND. bindiag == 1 ) convergence = .false. +IF ( ncomp == 1 .AND. totres > 100.0*acc_a ) convergence = .false. +IF ( totres > 1000.0*acc_a ) convergence = .false. +IF ( ncomp == 1 .AND. r_diff1 < 1.d-5 ) convergence = .false. + +IF ( convergence ) THEN + converg = 1 + ! write (*,*) residu(1),residu(2) + CALL converged + IF (num <= 1) CALL enthalpy_etc +ELSE + converg = 0 +END IF + +DEALLOCATE( y, diag, residu ) + +END SUBROUTINE objective_ctrl + + + +!>WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +!! SUBROUTINE objec_fct +!! +!! This subroutine contains the equations to be solved numerically +!! (iso-fugacity: fi'-fi''=0) as well as other dependent equations, +!! which can be solved analytically, namely the summation relation +!! xi=1-sum(xj) or the condition of equal charge for electrolyte +!! solutions. +!! This subroutine is required and controlled by the solver HBRD ! +!! HBRD varies the variables "y(i)" and eveluates the result of +!! these changes from this routine. +!!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +!! + SUBROUTINE objec_fct ( iter_no, y, residu, dummy ) +! + USE BASIC_VARIABLES + USE EOS_VARIABLES, ONLY: density_error + IMPLICIT NONE +! +! ---------------------------------------------------------------------- + INTEGER, INTENT(IN) :: iter_no + REAL, INTENT(IN) :: y(iter_no) + REAL, INTENT(OUT) :: residu(iter_no) + INTEGER, INTENT(IN OUT) :: dummy +! +! ---------------------------------------------------------------------- + INTEGER :: i, ph,k,posn, skip,phase + REAL :: lnphi(np,nc),isofugacity + CHARACTER (LEN=2) :: compon +! ---------------------------------------------------------------------- + + +posn = 0 +DO i = 1,n_unkw + posn = posn + 1 + IF (it(i) == 't') t = y(posn) + IF (it(i) == 'p') p = y(posn) + IF (it(i) == 'lnp') p = EXP( y(posn) ) + IF (it(i) == 'fls') alpha = y(posn) + IF (it(i)(1:1) == 'x' .AND. it(i)(2:2) == '1') compon = it(i)(3:3) + IF (it(i)(1:1) == 'x' .AND. it(i)(2:2) == '1') READ(compon,*) k + IF (it(i)(1:1) == 'x' .AND. it(i)(2:2) == '1') lnx(1,k) = y(posn) + IF (it(i)(1:1) == 'x' .AND. it(i)(2:2) == '2') compon = it(i)(3:3) + IF (it(i)(1:1) == 'x' .AND. it(i)(2:2) == '2') READ(compon,*) k + IF (it(i)(1:1) == 'x' .AND. it(i)(2:2) == '2') lnx(2,k) = y(posn) + IF (it(i)(1:1) == 'x' .AND. it(i)(2:2) == '3') compon = it(i)(3:3) + IF (it(i)(1:1) == 'x' .AND. it(i)(2:2) == '3') READ(compon,*) k + IF (it(i)(1:1) == 'x' .AND. it(i)(2:2) == '3') lnx(3,k) = y(posn) +END DO + +DO k = 1,ncomp + IF (lnx(1,k) > 0.0) lnx(1,k) = 0.0 + IF (lnx(2,k) > 0.0) lnx(2,k) = 0.0 +END DO + +IF (p < 1.E-100) p = 1.E-12 +!IF ( IsNaN( p ) ) p = 1000.0 ! rebounce for the case of NaN-solver output +!IF ( IsNaN( t ) ) t = 300.0 ! rebounce for the case of NaN-solver output +!IF ( IsNaN( alpha ) ) alpha = 0.5 ! rebounce for the case of NaN-solver output +IF ( p /= p ) p = 1000.0 ! rebounce for the case of NaN-solver output +IF ( t /= t ) t = 300.0 ! rebounce for the case of NaN-solver output +IF ( alpha /= alpha ) alpha = 0.5 ! rebounce for the case of NaN-solver output + +! --- setting of mole fractions ---------------------------------------- +DO ph = 1, nphas + DO i = 1, ncomp + IF ( lnx(ph,i) < -300.0 ) THEN + xi(ph,i) = 0.0 + ELSE + xi(ph,i) = EXP( lnx(ph,i) ) + END IF + END DO +END DO + +IF (ncomp > 1) CALL x_summation + +CALL fugacity (lnphi) + +phase = 2 +DO i = 1,n_unkw + skip = 0 !for ions/polymers, the isofug-eq. is not always solved + IF (n_unkw < (ncomp*(nphas-1))) skip = ncomp*(nphas-1) - n_unkw + IF ((i+skip-ncomp*(phase-2)) > ncomp) phase = phase + 1 + residu(i) = isofugacity((i+skip-ncomp*(phase-2)),phase,lnphi) + if ( density_error(phase) /= 0.0 ) residu(i) = residu(i) + SIGN( density_error(phase), residu(i) ) * 0.001 +END DO + +END SUBROUTINE objec_fct + + + +!>WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +!! REAL FUNCTION isofugacity +!! +!! calculates the deviation from the condition of equal fugacities in +!! logarithmic form. +!!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +!! + REAL FUNCTION isofugacity (i,phase,lnphi) +! + USE BASIC_VARIABLES + IMPLICIT NONE +! +! ---------------------------------------------------------------------- + INTEGER, INTENT(IN) :: i + INTEGER, INTENT(IN) :: phase + REAL, INTENT(IN) :: lnphi(np,nc) +! +! ---------------------------------------------------------------------- + INTEGER :: p1, p2 +! ---------------------------------------------------------------------- + + +! p1=1 +p1 = phase-1 +p2 = phase + +isofugacity = scaling(i) *( lnphi(p2,i)+lnx(p2,i)-lnx(p1,i)-lnphi(p1,i) ) +! write (*,'(a, 4G18.8)') ' t, p ',t,p,dense(1),dense(2) +! write (*,'(a,i3,i3,3G18.8)') ' phi_V',i,p2,lnx(p2,i),lnphi(p2,i),dense(p2) +! write (*,'(a,i3,i3,3G18.8)') ' phi_L',i,p1,lnx(p1,i),lnphi(p1,i),dense(p1) +! write (*,*) ' ISOFUGACITY',i,ISOFUGACITY, scaling(i) +! write (*,'(a,i3,4G18.8)') ' ISOFUGACITY',i,ISOFUGACITY, lnphi(p2,i)+lnx(p2,i), -lnx(p1,i)-lnphi(p1,i) +! pause + +END FUNCTION isofugacity + + + + + + + + + + + + + + + + + +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! + SUBROUTINE vle_min(lle_check) +! + USE PARAMETERS, ONLY: RGAS + USE BASIC_VARIABLES + USE STARTING_VALUES + IMPLICIT NONE +! +! ---------------------------------------------------------------------- + LOGICAL, INTENT(OUT) :: lle_check + + INTEGER :: i,j,k,phasen(0:40),steps + REAL :: lnphi(np,nc) + REAL :: vlemin(0:40),llemin(0:40),xval(0:40) + REAL :: start_xv(0:40),start_xl(0:40),x_sav,dg_dx2 +! ---------------------------------------------------------------------- + + + +j = 0 +k = 0 +nphas = 2 + +steps = 40 + +x_sav = xi(1,1) +sum_rel(1) = 'x12' ! summation relation +sum_rel(2) = 'x22' ! summation relation + +DO i = 0, steps + densta(1) = 0.45 + densta(2) = 1.d-6 + xi(1,1) = 1.0 - REAL(i) / REAL(steps) + IF ( xi(1,1) <= 1.E-50 ) xi(1,1) = 1.E-50 + xi(2,1) = xi(1,1) + lnx(1,1) = LOG(xi(1,1)) + lnx(2,1) = LOG(xi(2,1)) + + CALL x_summation + CALL fugacity (lnphi) + CALL enthalpy_etc !!KANN DAS RAUS???? + + + + + xval(i) = xi(1,1) + llemin(i)= gibbs(1) +(xi(1,1)*lnx(1,1)+xi(1,2)*lnx(1,2))*RGAS*t + + IF ( ABS(1.0-dense(1)/dense(2)) > 0.0001 ) THEN + vlemin(i)= gibbs(1) +(xi(1,1)*lnx(1,1)+xi(1,2)*lnx(1,2))*RGAS*t & + - ( gibbs(2) +(xi(2,1)*lnx(2,1)+xi(2,2)*lnx(2,2))*RGAS*t ) + phasen(i) = 2 + ELSE + phasen(i) = 1 + END IF + + IF (i > 0 .AND. phasen(i) == 2) THEN + IF (phasen(i-1) == 2 .AND. ABS(vlemin(i)+vlemin(i-1)) < & + ABS(vlemin(i))+ABS(vlemin(i-1))) THEN + j = j + 1 + start_xv(j)=xval(i-1) + (xval(i)-xval(i-1)) & + * ABS(vlemin(i-1))/ABS(vlemin(i)-vlemin(i-1)) + END IF + END IF + +END DO + + +DO i=2,steps-2 + dg_dx2 = (-llemin(i-2)+16.0*llemin(i-1)-30.0*llemin(i) & + +16.0*llemin(i+1)-llemin(i+2)) / (12.0*((xval(i)-xval(i-1))**2)) + IF (dg_dx2 < 0.0) THEN + k = k + 1 + start_xl(k)=xval(i) + END IF +END DO + + +IF (start_xl(1) == 0.0 .AND. start_xv(1) /= 0.0) THEN + xi(1,1) = start_xv(1) + xi(1,2) = 1.0-xi(1,1) + lle_check=.false. + ! write (*,*) 'VLE is likely', xi(1,1),xi(1,2) +ELSE IF (start_xl(1) /= 0.0 .AND. start_xv(1) == 0.0) THEN + xi(1,1) = start_xl(1) + xi(1,2) = 1.0-xi(1,1) + ! write (*,*) 'LLE is likely', xi(1,1),xi(1,2) + lle_check=.true. +ELSE IF (start_xl(1) /= 0.0 .AND. start_xv(1) /= 0.0) THEN + xi(1,1) = start_xv(1) + xi(1,2) = 1.0-xi(1,1) + ! write(*,*) 'starting with VLE and check for LLE' + lle_check=.true. +ELSE + xi(1,1) = x_sav + xi(1,2) = 1.0 - xi(1,1) +END IF + + +CALL x_summation + +END SUBROUTINE vle_min + + +!>WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +!! SUBROUTINE phase_stability +!! +!! the index 'LLE_check' is for the starting density (which determines +!! whether a liquid or vapor phase is found) of the trial phase. The +!! feed-point exits either as a vapor or as a liquid. If it can exist as +!! both (feedphases=2), then both states are tested. +!!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +!! + SUBROUTINE phase_stability ( lle_check, flashcase, ph_split,user ) + +!Petsc modules + USE PetscManagement + +!VLE modules + USE BASIC_VARIABLES + USE STARTING_VALUES + USE EOS_VARIABLES, ONLY: dhs, PI, x, eta, eta_start, z3t, fres + USE EOS_NUMERICAL_DERIVATIVES + IMPLICIT NONE +! +! ---------------------------------------------------------------------- + type (userctx) user + LOGICAL :: lle_check + LOGICAL, INTENT(IN OUT) :: flashcase + INTEGER, INTENT(OUT) :: ph_split +! ---------------------------------------------------------------------- + + INTERFACE + REAL FUNCTION F_STABILITY ( optpara, n ) + INTEGER, INTENT(IN) :: n + REAL, INTENT(IN OUT) :: optpara(n) + END FUNCTION + END INTERFACE + +!INTERFACE +! SUBROUTINE F_STABILITY (fmin, optpara, n) +! REAL, INTENT(IN OUT) :: fmin +! REAL, INTENT(IN) :: optpara(:) +! INTEGER, INTENT(IN) :: n +! END SUBROUTINE F_STABILITY +! +! SUBROUTINE stability_grad (g, optpara, n) +! REAL, INTENT(IN OUT) :: g(:) +! REAL, INTENT(IN) :: optpara(:) +! INTEGER, INTENT(IN) :: n +! END SUBROUTINE stability_grad +! +! SUBROUTINE stability_hessian (hessian, g, fmin, optpara, n) +! REAL, INTENT(IN OUT) :: hessian(:,:) +! REAL, INTENT(IN OUT) :: g(:) +! REAL, INTENT(IN OUT) :: fmin +! REAL, INTENT(IN) :: optpara(:) +! INTEGER, INTENT(IN) :: n +! END SUBROUTINE stability_hessian +!END INTERFACE + + INTEGER :: n, PRIN + REAL :: fmin, t0, h0, MACHEP, PRAXIS + REAL, ALLOCATABLE :: optpara(:) + + INTEGER :: i, feedphases, trial + REAL :: rhoi(nc),rho_start + REAL :: feeddens, rho_phas(np) + REAL :: fden + REAL :: dens + REAL :: rhot + REAL :: lnphi(np,nc) + REAL :: w(np,nc), mean_mass +! ---------------------------------------------------------------------- + +n = ncomp +ALLOCATE( optpara(n) ) + + +IF(user%rank == 0) THEN + IF (lle_check) WRITE (*,*) ' stability test starting with dense phase' +END IF + +DO i = 1, ncomp ! setting feed-phase x's + IF (.NOT.flashcase) xif(i) = xi(1,i) + IF (flashcase) xi(1,i) = xif(i) + xi(2,i) = xif(i) ! feed is tested for both: V and L density +END DO + +densta(1) = 0.45 +densta(2) = 1.d-6 + +CALL dens_calc(rho_phas) +IF ( ABS(1.0-dense(1)/dense(2)) > 0.0005 ) THEN + feedphases=2 ! feed-composition can exist both, in V and L +ELSE + feedphases=1 ! feed-composition can exist either in V or L +END IF +densta(1) = dense(1) +feeddens = dense(2) +!write (*,*) 'feedphases',dense(1), dense(2),feedphases + +10 CONTINUE ! IF FeedPhases=2 THEN there is a second cycle + + trial = 1 + + ! -------------------------------------------------------------------- + ! setting trial-phase mole-fractions + ! if there is no phase-split then further trial-phases are + ! considered (loop: 20 CONTINUE) + ! -------------------------------------------------------------------- + DO i = 1, ncomp + w(2,i) = 1.0 / REAL(ncomp) + END DO + mean_mass = 1.0 / SUM( w(2,1:ncomp)/mm(1:ncomp) ) + xi(2,1:ncomp) = w(2,1:ncomp)/mm(1:ncomp) * mean_mass + + 20 CONTINUE + + DO i = 1, ncomp + rhoif(i) = rho_phas(1) * xif(i) + rhoi(i) = rhoif(i) + END DO + + !write (*,'(a,6G16.8)') 'startval',rho_phas(2),xi(2,1:ncomp) + + ! -------------------------------------------------------------------- + ! calc Helmholtz energy density and derivative (numerical) to rhoif(i). + ! The derivative is taken around the "feed-point" not the trial phase + ! -------------------------------------------------------------------- + + rhot = SUM( rhoi(1:ncomp) ) + x(1:ncomp) = rhoi(1:ncomp) / rhot + CALL PERTURBATION_PARAMETER + xi(1,1:ncomp) = x(1:ncomp) + eta = rhot * z3t + eta_start = eta + densta(1) = eta_start + ensemble_flag = 'tv' + CALL FUGACITY (lnphi) + ensemble_flag = 'tp' + + call fden_calc ( fden, rhoi ) + fdenf = fden + + grad_fd(1:ncomp) = lnphi(1,1:ncomp) + LOG( rhoi(1:ncomp) ) + + + ! -------------------------------------------------------------------- + ! starting values for iteration (optpara) + ! -------------------------------------------------------------------- + rho_start = 1.E-5 + IF (lle_check) THEN + densta(2) = 0.45 + CALL dens_calc(rho_phas) + rho_start = rho_phas(2)*0.45/dense(2) + END IF + DO i = 1,ncomp + rhoi(i) = xi(2,i)*rho_start + optpara(i) = LOG( rhoi(i) ) + END DO + + ! -------------------------------------------------------------------- + ! minimizing the objective fct. Phase split for values of fmin < 0.0 + ! -------------------------------------------------------------------- + t0 = 5.E-5 + h0 = 0.5 + PRIN = 0 + MACHEP = 1.E-15 + + fmin = PRAXIS( t0, MACHEP, h0, n, PRIN, optpara, F_STABILITY, fmin ) + + + ! -------------------------------------------------------------------- + ! updating the ln(x) valus from optpara. The optimal optpara-vector is + ! not necessarily the one that was last evaluated. At the very end, + ! cg_decent writes the best values to optpara + ! -------------------------------------------------------------------- + fmin = F_STABILITY( optpara, n ) + + + + ! IF ( n == 2 ) THEN + ! CALL Newton_Opt_2D ( stability_hessian, F_stability, optpara, n, 1.E-8, 1.E-8, g, fmin) + ! ELSE + ! CALL cg_descent (1.d-5, optpara, n, F_STABILITY, stability_grad, STATUS, & + ! gnorm, fmin, iter, nfunc, ngrad, d, g, xtemp, gtemp) + ! ENDIF + ! CALL F_STABILITY (fmin, optpara, n) + + + ! -------------------------------------------------------------------- + ! determine instability & non-trivial solution + ! -------------------------------------------------------------------- + ph_split = 0 + IF (fmin < -1.E-7 .AND. & + ABS( 1.0 - maxval(EXP(optpara),mask=optpara /= 0.0) /maxval(rhoif) ) > 0.0005) THEN + ph_split = 1 + END IF + + IF (ph_split == 1) THEN + + ! ------------------------------------------------------------------ + ! here, there should be IF FeedPhases=2 THEN GOTO 10 + ! and test for another phase (while saving optpara) + ! ------------------------------------------------------------------ + + rhoi2(1:ncomp) = EXP( optpara(1:ncomp) ) + dens = PI/6.0 * SUM( rhoi2(1:ncomp) * parame(1:ncomp,1) * dhs(1:ncomp)**3 ) + rhot = SUM( rhoi2(1:ncomp) ) + xi(2,1:ncomp) = rhoi2(1:ncomp) / rhot + + ELSE + + IF (trial <= ncomp + ncomp) THEN + ! ---------------------------------------------------------------- + ! setting trial-phase x's + ! ---------------------------------------------------------------- + IF (trial <= ncomp) THEN + DO i=1,ncomp + w(2,i) = 1.0 / REAL(ncomp-1) * 0.05 + END DO + w(2,trial) = 0.95 + ELSE + DO i=1,ncomp + w(2,i) = 1.0 / REAL(ncomp-1) * 0.00001 + END DO + w(2,trial-ncomp) = 0.99999 + END IF + mean_mass = 1.0 / SUM( w(2,1:ncomp)/mm(1:ncomp) ) + xi(2,1:ncomp) = w(2,1:ncomp)/mm(1:ncomp) * mean_mass + trial = trial + 1 + GO TO 20 + END IF + ! IF (.NOT.LLE_check) write (*,*) 'no phase split detected' + ! IF (.NOT.LLE_check) pause + IF (feedphases > 1 .AND. .NOT.lle_check .AND. densta(1) > 0.2) THEN + densta(1) = feeddens ! this will be the lower-valued density (vapor) + CALL dens_calc(rho_phas) + ! WRITE (*,*) 'try feed as vapor-phase' + GO TO 10 + END IF + + END IF + +DEALLOCATE( optpara ) + +END SUBROUTINE phase_stability + + +!>WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +!! SUBROUTINE select_sum_rel +!! +!! This subroutine determines which component of a phase "ph" is calculated +!! from the summation relation x_i = 1 - sum(x_j). The other components are, +!! by default, said to be iterated during the phase equilibrium calculation. +!! +!! Note that for flash calculations not all of these mole fractions are in +!! fact iterated - this is raken care of in "determine_flash_it". +!! +!! ph phase +!! excl exclude comp. n +!! startindex assign it(startindex) for quantities to be iterated +!! (further it(startindex+1) is assigned, for a ternary +!! mixture, etc.) +!! +!! sum_index indicates the component, with the largest mole +!! fraction. If ph=1 and sum_index=2, we define +!! sum_rel(ph=1)='x12', so that this component is +!! calculated from the summation relation. +!!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +!! + SUBROUTINE select_sum_rel (ph,excl,startindex) +! + USE BASIC_VARIABLES + IMPLICIT NONE +! +! ---------------------------------------------------------------------- + INTEGER, INTENT(IN) :: ph + INTEGER, INTENT(IN) :: excl + INTEGER, INTENT(IN) :: startindex +! ---------------------------------------------------------------------- + INTEGER :: i,j, sum_index + REAL :: xmax(np) + ! CHARACTER :: compNo*2,phasNo*2 +! ---------------------------------------------------------------------- + +xmax(ph) = 0.0 +DO i = 1, ncomp + + IF ( xi(ph,i) > xmax(ph) ) THEN + xmax(ph) = xi(ph,i) + sum_index = i + + IF (ph == 1 .AND. i == 1) sum_rel(1) = 'x11' + IF (ph == 1 .AND. i == 2) sum_rel(1) = 'x12' + IF (ph == 1 .AND. i == 3) sum_rel(1) = 'x13' + IF (ph == 1 .AND. i == 4) sum_rel(1) = 'x14' + IF (ph == 1 .AND. i == 5) sum_rel(1) = 'x15' + + IF (ph == 2 .AND. i == 1) sum_rel(2) = 'x21' + IF (ph == 2 .AND. i == 2) sum_rel(2) = 'x22' + IF (ph == 2 .AND. i == 3) sum_rel(2) = 'x23' + IF (ph == 2 .AND. i == 4) sum_rel(2) = 'x24' + IF (ph == 2 .AND. i == 5) sum_rel(2) = 'x25' + + IF (ph == 3 .AND. i == 1) sum_rel(3) = 'x31' + IF (ph == 3 .AND. i == 2) sum_rel(3) = 'x32' + IF (ph == 3 .AND. i == 3) sum_rel(3) = 'x33' + IF (ph == 3 .AND. i == 4) sum_rel(3) = 'x34' + IF (ph == 3 .AND. i == 5) sum_rel(3) = 'x35' +! write (*,*) ph,i,xi(ph,i),sum_rel(ph) + END IF + +END DO + +j = 0 +DO i = 1, ncomp + + IF ( i /= sum_index .AND. i /= excl ) THEN + IF (ph == 1 .AND. i == 1) it(startindex+j) = 'x11' + IF (ph == 1 .AND. i == 2) it(startindex+j) = 'x12' + IF (ph == 1 .AND. i == 3) it(startindex+j) = 'x13' + IF (ph == 1 .AND. i == 4) it(startindex+j) = 'x14' + IF (ph == 1 .AND. i == 5) it(startindex+j) = 'x15' + + IF (ph == 2 .AND. i == 1) it(startindex+j) = 'x21' + IF (ph == 2 .AND. i == 2) it(startindex+j) = 'x22' + IF (ph == 2 .AND. i == 3) it(startindex+j) = 'x23' + IF (ph == 2 .AND. i == 4) it(startindex+j) = 'x24' + IF (ph == 2 .AND. i == 5) it(startindex+j) = 'x25' + + IF (ph == 3 .AND. i == 1) it(startindex+j) = 'x31' + IF (ph == 3 .AND. i == 2) it(startindex+j) = 'x32' + IF (ph == 3 .AND. i == 3) it(startindex+j) = 'x33' + IF (ph == 3 .AND. i == 4) it(startindex+j) = 'x34' + IF (ph == 3 .AND. i == 5) it(startindex+j) = 'x35' +! write (*,*) 'iter ',it(startindex+j) + j = j + 1 + END IF + +END DO + +END SUBROUTINE select_sum_rel + + + + +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! + SUBROUTINE tangent_plane +! + USE BASIC_VARIABLES + USE STARTING_VALUES + IMPLICIT NONE +! +! ---------------------------------------------------------------------- +!!$ INTERFACE +!!$ SUBROUTINE tangent_value (fmin, optpara, n) +!!$ INTEGER, INTENT(IN) :: n +!!$ REAL, INTENT(IN OUT) :: fmin +!!$ REAL, INTENT(IN) :: optpara(:) +!!$ END SUBROUTINE tangent_value +!!$ +!!$ SUBROUTINE tangent_grad (g, optpara, n) +!!$ INTEGER, INTENT(IN) :: n +!!$ REAL, INTENT(IN OUT) :: g(:) +!!$ REAL, INTENT(IN) :: optpara(:) +!!$ END SUBROUTINE tangent_grad +!!$ END INTERFACE + +! +! ---------------------------------------------------------------------- + INTERFACE + REAL FUNCTION PRAXIS( t0, MACHEP, h0, n, PRIN, optpara, TANGENT_VALUE, fmin ) + REAL, INTENT(IN OUT) :: t0 + REAL, INTENT(IN) :: machep + REAL, INTENT(IN) :: h0 + INTEGER :: n + INTEGER, INTENT(IN OUT) :: prin + REAL, INTENT(IN OUT) :: optpara(n) + REAL, EXTERNAL :: TANGENT_VALUE + REAL, INTENT(IN OUT) :: fmin + END FUNCTION + + REAL FUNCTION TANGENT_VALUE2 ( optpara, n ) + INTEGER, INTENT(IN) :: n + REAL, INTENT(IN) :: optpara(n) + END FUNCTION + END INTERFACE +! +! ---------------------------------------------------------------------- + INTEGER :: n + INTEGER :: i, k, ph + INTEGER :: small_i, min_ph, other_ph + INTEGER :: PRIN + REAL :: fmin , t0, h0, MACHEP + REAL :: lnphi(np,nc) + REAL, ALLOCATABLE :: optpara(:) + +! INTEGER :: STATUS, iter, nfunc, ngrad +! REAL :: gnorm +! REAL, ALLOCATABLE :: d(:), g(:), xtemp(:), gtemp(:) +! ---------------------------------------------------------------------- + +n = ncomp +t0 = 1.E-4 +h0 = 0.1 +PRIN = 0 +MACHEP = 1.E-15 + +ALLOCATE( optpara(n) ) +!ALLOCATE( d(n) ) +!ALLOCATE( g(n) ) +!ALLOCATE( xtemp(n) ) +!ALLOCATE( gtemp(n) ) + +DO i = 1,ncomp + rhoi1(i) = rhoif(i) + lnx(1,i) = LOG(xi(1,i)) + lnx(2,i) = LOG(xi(2,i)) +END DO + +DO i = 1,ncomp + optpara(i) = LOG( xi(2,i) * 0.001 ) +END DO + +! CALL cg_descent (1.d-4, optpara, n, tangent_value, tangent_grad, STATUS, & +! gnorm, fmin, iter, nfunc, ngrad, d, g, xtemp, gtemp) +! +! updating the ln(x) valus from optpara. The optimal optpara-vector is not necessarily +! the one that was last evaluated. At the very end, cg_decent writes the best values to optpara +! CALL tangent_value (fmin, optpara, n) + + + +fmin = PRAXIS( t0, MACHEP, h0, n, PRIN, optpara, TANGENT_VALUE2, fmin ) + +! The optimal optpara-vector is not necessarily the one that was last evaluated. +! TANGENT_VALUE is reexecuted with the optimal vector optpara, in order to update the ln(x) values +fmin = TANGENT_VALUE2( optpara, n ) + + +! ---------------------------------------------------------------------- +! If one component is a polymer (indicated by a low component-density) +! then get an estimate of the polymer-lean composition, by solving for +! xi_p1 = ( xi_p2 * phii_p2) / phii_p1 (phase equilibrium condition, +! with p1 for phase 1) +! ---------------------------------------------------------------------- +IF ( MINVAL( lnx(1,1:ncomp) ) < MINVAL( lnx(2,1:ncomp) ) ) THEN + min_ph = 1 + other_ph = 2 +ELSE + min_ph = 2 + other_ph = 1 +ENDIF +small_i = MINLOC( lnx(min_ph,1:ncomp), 1 ) +! --- if one component is a polymer ------------------------------------ +IF ( MINVAL( lnx(min_ph,1:ncomp) ) < -20.0 ) THEN + CALL FUGACITY ( lnphi ) + lnx(min_ph,small_i) = lnx(other_ph,small_i)+lnphi(other_ph,small_i) - lnphi(min_ph,small_i) + optpara(small_i) = lnx(2,small_i) + LOG( SUM( EXP( optpara(1:ncomp) ) ) ) +END IF + +! ---------------------------------------------------------------------- +! caution: these initial values are for a flashcase overwritten in +! SUBROUTINE determine_flash_it2, because in that case, the lnx-values +! treated as ln(mole_number). +! ---------------------------------------------------------------------- +val_init(1) = dense(1) +val_init(2) = dense(2) +val_init(3) = t +val_init(4) = p +DO ph = 1,nphas + DO k = 1,ncomp + val_init(4+k+(ph-1)*ncomp) = lnx(ph,k) + END DO +END DO +!alpha = optpara(1) + + +!DEALLOCATE( optpara, d, g, xtemp, gtemp ) +DEALLOCATE( optpara ) + +END SUBROUTINE tangent_plane + + +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! + SUBROUTINE determine_flash_it2 +! + USE BASIC_VARIABLES + IMPLICIT NONE +! +! ---------------------------------------------------------------------- + INTEGER :: i, k, ph + REAL :: n_phase1, n_phase2, max_x_diff +! ---------------------------------------------------------------------- + + IF ( MINVAL( lnx(1,1:ncomp) ) < MINVAL( lnx(2,1:ncomp) ) ) THEN + it(1) = 'x11' + it(2) = 'x12' + IF (ncomp >= 3) it(3) = 'x13' + IF (ncomp >= 4) it(4) = 'x14' + IF (ncomp >= 5) it(5) = 'x15' + sum_rel(1) = 'nfl' + ELSE + it(1) = 'x21' + it(2) = 'x22' + IF (ncomp >= 3) it(3) = 'x23' + IF (ncomp >= 4) it(4) = 'x24' + IF (ncomp >= 5) it(5) = 'x25' + sum_rel(2) = 'nfl' + ENDIF + max_x_diff = 0.0 + DO i = 1,ncomp + IF ( ABS( EXP( lnx(1,i) ) - EXP( lnx(2,i) ) ) > max_x_diff ) THEN + max_x_diff = ABS( EXP( lnx(1,i) ) - EXP( lnx(2,i) ) ) + n_phase1 = ( xif(i) - EXP( lnx(2,i) ) ) / ( EXP( lnx(1,i) ) - EXP( lnx(2,i) ) ) + n_phase2 = 1.0 - n_phase1 + END IF + END DO + lnx(1,1:ncomp) = lnx(1,1:ncomp) + LOG( n_phase1 ) ! these x's are treated as mole numbers + lnx(2,1:ncomp) = lnx(2,1:ncomp) + LOG( n_phase2 ) ! these x's are treated as mole numbers + + + val_init(1) = dense(1) + val_init(2) = dense(2) + val_init(3) = t + val_init(4) = p + DO ph = 1,nphas + DO k = 1,ncomp + val_init(4+k+(ph-1)*ncomp) = lnx(ph,k) ! - LOG( SUM( EXP( lnx(ph,1:ncomp) ) ) ) + ! write (*,*) ph,k, lnx(ph,k) + END DO + END DO + +END SUBROUTINE determine_flash_it2 + +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! SUBROUTINE poly_sta_var +! +! This subroutine generates starting values for mole fractons of +! polymer-solvent systems. +! The determination of these starting values follows a two-step +! procedure. Fist, the equilibrium concentration of the polymer-rich +! phase is estimated with the assumption of zero concentration +! of polymer in the polymer-lean-phase. This is achieved in the +! SUBROUTINE POLYMER_FREE. (Only one equation has to be iterated +! for this case). Once this is achieved, the rigorous calculation +! is triggered. If it converges, fine! If no solution is obtained, +! the pressure is somewhat reduced, the procedure is repeated and +! a calculation is started to approach the originally specified +! pressure. +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! + SUBROUTINE poly_sta_var (converg) +! + USE BASIC_VARIABLES + IMPLICIT NONE +! +! ---------------------------------------------------------------------- + INTEGER, INTENT(IN OUT) :: converg +! +! ---------------------------------------------------------------------- + INTEGER :: k,ph,sol + REAL :: p_spec,solution(10,4+nc*np) +! ---------------------------------------------------------------------- + + p_spec = p + + find_equilibrium: DO + + CALL polymer_free(p_spec,sol,solution) + + WRITE (*,*) ' ' + WRITE (*,*) ' GENERATING STARTING VALUES' + + val_init(1) = solution(1,1) ! approx.solutions for next iteration + val_init(2) = solution(1,2) ! approx.solutions for next iteration + val_init(3) = solution(1,3) ! approx.solutions for next iteration + val_init(4) = solution(1,4) ! approx.solutions for next iteration + DO ph = 1,nphas + DO k = 1,ncomp + val_init(4+k+(ph-1)*ncomp) = solution(1,4+k+(ph-1)*ncomp) + END DO + END DO + val_init(7) = -10000.0 ! start.val. for lnx(2,1) for iterat. + + IF (p /= p_spec) & + WRITE (*,*) ' INITIAL EQUILIBRIUM CALC. FAILD. NEXT STEP STARTS' + + IF (p == p_spec) THEN + n_unkw = ncomp ! number of quantities to be iterated + it(1)='x11' ! iteration of mol fraction of comp.1 phase 1 + it(2)='x21' ! iteration of mol fraction of comp.1 phase 2 + CALL objective_ctrl (converg) + ELSE + outp = 0 ! output to terminal + running ='p' ! Pressure is running var. in PHASE_EQUILIB + CALL phase_equilib(p_spec,5.0,converg) + END IF + + IF (converg == 1) EXIT find_equilibrium + p = p * 0.9 + IF ( p < (0.7*p_spec) ) WRITE (*,*) ' NO SOLUTION FOUND' + IF ( p < (0.7*p_spec) ) STOP + + END DO find_equilibrium + + WRITE (*,*) ' FINISHED: POLY_STA_VAR' + +END SUBROUTINE poly_sta_var + + +!>WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +!! SUBROUTINE x_summation +!! +!! This subroutine solves the summation relation: xi=1-sum(xj) +!! The variable "sum_rel(i)" contains the information, which mole +!! fraction is the one to be calculated here. Consider the example +!! sum_rel(1)='x12'. The fist letter 'x' of this variable indicates, +!! that this subroutine needs to be executed and that the mole +!! fraction of a component has to be calculated. The second letter +!! of the string points to phase 1, the third letter to component 2. +!! If the fist letter is 'e', not 'x', then the subroutine +!! NEUTR_CHARGE is called. This is the case of electrolyte solutions, +!! neutral charges have to be enforced in all phases (see below). +!!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +!! + SUBROUTINE x_summation +! + USE BASIC_VARIABLES + IMPLICIT NONE +! +! ---------------------------------------------------------------------- + INTEGER :: i, j, comp_i, ph_i + REAL :: sum_x + CHARACTER (LEN=2) :: phasno + CHARACTER (LEN=2) :: compno + LOGICAL :: flashcase2 +! ---------------------------------------------------------------------- + +DO j = 1, nphas + IF (sum_rel(j)(1:3) == 'nfl') THEN + CALL new_flash (j) + RETURN + END IF +END DO + + + +flashcase2 = .false. + +DO j = 1, nphas + + IF (sum_rel(j)(1:1) == 'x') THEN + + phasno = sum_rel(j)(2:2) + READ(phasno,*) ph_i + compno = sum_rel(j)(3:3) + READ(compno,*) comp_i + IF ( sum_rel(nphas+j)(1:1) == 'e' ) CALL neutr_charge(nphas+j) + + sum_x = 0.0 + DO i = 1, ncomp + IF ( i /= comp_i ) sum_x = sum_x + xi(ph_i,i) + END DO + xi(ph_i,comp_i) = 1.0 - sum_x + IF ( xi(ph_i,comp_i ) < 0.0 ) xi(ph_i,comp_i) = 0.0 + IF ( xi(ph_i,comp_i ) /= 0.0 ) THEN + lnx(ph_i,comp_i) = LOG( xi(ph_i,comp_i) ) + ELSE + lnx(ph_i,comp_i) = -100000.0 + END IF + ! write (*,*) 'sum_x',ph_i,comp_i,lnx(ph_i,comp_i),xi(ph_i,comp_i) + + ELSE IF ( sum_rel(j)(1:2) == 'fl' ) THEN + + flashcase2 = .true. + ! ------------------------------------------------------------------ + ! This case is true when all molefractions of one phase are + ! determined from a component balance. What is needed to + ! calculate all molefractions of that phase are all mole- + ! fractions of the other phase (nphas=2, so far) and the + ! phase fraction alpha. + ! Alpha is calculated (in FLASH_ALPHA) from the mole fraction + ! of component {sum_rel(j)(3:3)}. IF sum_rel(2)='fl3', then + ! the alpha is determined from the molefraction of comp. 3 and + ! the molefraction of phase 2 is then completely determined ELSE + ! ------------------------------------------------------------------ + + ELSE + WRITE (*,*) 'summation relation not defined' + STOP + END IF + +END DO + +IF ( it(1) == 'fls' ) CALL flash_sum +IF ( flashcase2 ) CALL flash_alpha + +END SUBROUTINE x_summation + + + +!>WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +!! SUBROUTINE FUGACITY +!! +!! This subroutine serves as an interface to the eos-subroutines. +!! (1) case 1, when ensemble_flag = 'tp' +!! mu_i^res(T,p,x)/kT = ln( phi_i ) +!! and in addition, the densities that satisfy the specified p +!! (2) case 2, when ensemble_flag = 'tv' +!! The subroutine gives the residual chemical potential: +!! --> mu_i^res(T,rho,x)/kT +!! and in addition the resulting pressure for the given density. +!! The term "residual" means difference of the property and the same +!! property for an ideal gas mixture. +!!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +!! + SUBROUTINE FUGACITY (ln_phi) +! + USE BASIC_VARIABLES + USE EOS_VARIABLES, ONLY: phas, x, eta, eta_start, lnphi, fres, rho, pges, KBOL + IMPLICIT NONE +! +! ---------------------------------------------------------------------- + REAL, INTENT(OUT) :: ln_phi(np,nc) +! +! --- local variables -------------------------------------------------- + INTEGER :: ph +! ---------------------------------------------------------------------- +! +IF (eos < 2) THEN + + DO ph = 1,nphas + + phas = ph + eta_start = densta(ph) + x(1:ncomp) = xi(ph,1:ncomp) + + IF (p < 1.E-100) THEN + WRITE(*,*) ' FUGACITY: PRESSURE TOO LOW', p + p = 1.E-6 + END IF + + IF (num == 0) CALL PHI_EOS + IF (num == 1) CALL PHI_NUMERICAL + !!IF (num == 2) CALL PHI_CRITICAL_RENORM + IF (num == 2) write(*,*) 'CRITICAL RENORM NOT INCLUDED YET' + + dense(ph) = eta + ln_phi(ph,1:ncomp) = lnphi(1:ncomp) + ! gibbs(ph) = fres + sum( xi(ph,1:ncomp)*( log( xi(ph,1:ncomp)*rho) - 1.0 ) ) & + ! + (pges * 1.d-30) / (KBOL*t*rho) ! includes ideal gas contribution + + ! f_res(ph) = fres + ! write (*,'(i3,4G20.11)') ph,eta,lnphi(1),lnphi(2) + ! DO i = 1,ncomp + ! DO j=1,NINT(parame(i,12)) + ! mxx(ph,i,j) = mx(i,j) + ! END DO + ! END DO + + END DO + +ELSE + +! IF (eos == 2) CALL srk_eos (ln_phi) +! IF (eos == 3) CALL pr_eos (ln_phi) +! dense(1) = 0.01 +! dense(2) = 0.3 +! IF (eos == 4.OR.eos == 5.OR.eos == 6.OR.eos == 8) CALL lj_fugacity(ln_phi) +! IF (eos == 7) CALL sw_fugacity(ln_phi) +! IF (eos == 9) CALL lj_bh_fug(ln_phi) + +END IF + +END SUBROUTINE FUGACITY + + + + + + + +!>WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +!! SUBROUTINE FUGACITY +!! +!! This subroutine serves as an interface to the eos-subroutines. +!! (1) case 1, when ensemble_flag = 'tp' +!! The subroutine gives the residual chemical potential: +!! mu_i^res(T,p,x)/kT = ln( phi_i ) +!! and in addition, the densities that satisfy the specified p +!! (2) case 2, when ensemble_flag = 'tv' +!! The subroutine gives the residual chemical potential: +!! --> mu_i^res(T,rho,x)/kT +!! and in addition the resulting pressure for the given density. +!! The term "residual" means difference of the property and the same +!! property for an ideal gas mixture. +!!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +!! + SUBROUTINE FUGACITY2 (ln_phi) +! + USE BASIC_VARIABLES + USE EOS_VARIABLES, ONLY: phas, x, eta, eta_start, lnphi, fres, rho, pges, KBOL + IMPLICIT NONE +! +! ---------------------------------------------------------------------- + REAL, INTENT(OUT) :: ln_phi(np,nc) +! +! --- local variables -------------------------------------------------- + INTEGER :: ph +! ---------------------------------------------------------------------- +! +IF (eos < 2) THEN + + ! DO ph = 1,nphas + + phas = 2! ph + eta_start = densta(2) + x(1:ncomp) = xi(2,1:ncomp) + + IF (p < 1.E-100) THEN + WRITE(*,*) ' FUGACITY: PRESSURE TOO LOW', p + p = 1.E-6 + END IF + + IF (num == 0) CALL PHI_EOS2 + IF (num == 1) CALL PHI_NUMERICAL + !!IF (num == 2) CALL PHI_CRITICAL_RENORM + IF (num == 2) write(*,*) 'CRITICAL RENORM NOT INCLUDED YET' + + dense(2) = eta + ln_phi(2,1:ncomp) = lnphi(1:ncomp) + ! gibbs(ph) = fres + sum( xi(ph,1:ncomp)*( log( xi(ph,1:ncomp)*rho) - 1.0 ) ) & + ! + (pges * 1.d-30) / (KBOL*t*rho) ! includes ideal gas contribution + + ! f_res(ph) = fres + ! write (*,'(i3,4G20.11)') ph,eta,lnphi(1),lnphi(2) + ! DO i = 1,ncomp + ! DO j=1,NINT(parame(i,12)) + ! mxx(ph,i,j) = mx(i,j) + ! END DO + ! END DO + + ! END DO + +ELSE + +! IF (eos == 2) CALL srk_eos (ln_phi) +! IF (eos == 3) CALL pr_eos (ln_phi) +! dense(1) = 0.01 +! dense(2) = 0.3 +! IF (eos == 4.OR.eos == 5.OR.eos == 6.OR.eos == 8) CALL lj_fugacity(ln_phi) +! IF (eos == 7) CALL sw_fugacity(ln_phi) +! IF (eos == 9) CALL lj_bh_fug(ln_phi) + +END IF + +END SUBROUTINE FUGACITY2 + + + + + + + + + + +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! SUBROUTINE enthalpy_etc +! +! This subroutine serves as an interface to the EOS-routines. The +! residual enthalpy h_res, residual entropy s_res, residual Gibbs +! enthalpy g_res, and residual heat capacity at constant pressure +! (cp_res) corresponding to converged conditions are calculated. +! The conditions in (T,P,xi,rho) need to be converged equilibrium +! conditions !! +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! + SUBROUTINE enthalpy_etc +! + USE BASIC_VARIABLES + USE EOS_VARIABLES + IMPLICIT NONE +! + INTEGER :: ph +! ------------------------------------------------------------------ + +IF (eos <= 1) THEN + + DO ph=1,nphas + + phas = ph + eta = dense(ph) +! eta_start = dense(ph) + x(1:ncomp) = xi(ph,1:ncomp) + + IF(num == 0) THEN + CALL H_EOS + ELSE + IF(num == 1) CALL H_numerical + IF(num == 2) write (*,*) 'enthalpy_etc: incorporate H_EOS_RN' + IF(num == 2) stop +! IF(num == 2) CALL H_EOS_rn + END IF + enthal(ph) = h_res + entrop(ph) = s_res + ! gibbs(ph) = h_res - t * s_res ! already defined in eos.f90 (including ideal gas) + cpres(ph) = cp_res + + END DO + IF (nphas == 2) h_lv = enthal(2)-enthal(1) + +ENDIF + +END SUBROUTINE enthalpy_etc + + +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! SUBROUTINE dens_calc +! +! This subroutine serves as an interface to the EOS-routines. The +! densities corresponding to given (P,T,xi) are calculated. +! (Note: the more common interface is SUBROUTINE FUGACITY. +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! + SUBROUTINE dens_calc(rho_phas) +! + USE BASIC_VARIABLES + USE EOS_VARIABLES + IMPLICIT NONE +! +! +!------------------------------------------------------------------ + REAL, INTENT(OUT) :: rho_phas(np) +! + INTEGER :: ph +!------------------------------------------------------------------ + + +DO ph = 1, nphas + + IF (eos < 2) THEN + + phas = ph + eta = densta(ph) + eta_start = densta(ph) + x(1:ncomp) = xi(ph,1:ncomp) + + CALL PERTURBATION_PARAMETER + CALL DENSITY_ITERATION + + dense(ph)= eta + rho_phas(ph) = eta/z3t + + ELSE + write (*,*) ' SUBROUTINE DENS_CALC not available for cubic EOS' + stop + END IF + +END DO + +END SUBROUTINE dens_calc + + +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! + SUBROUTINE fden_calc (fden, rhoi) +! + USE BASIC_VARIABLES + USE EOS_VARIABLES + IMPLICIT NONE +! +! ---------------------------------------------------------------------- + REAL, INTENT(OUT) :: fden + REAL, INTENT(IN OUT) :: rhoi(nc) +! ---------------------------------------------------------------------- + REAL :: rhot, fden_id +! ---------------------------------------------------------------------- + + +IF (eos < 2) THEN + + rhot = SUM( rhoi(1:ncomp) ) + x(1:ncomp) = rhoi(1:ncomp) / rhot + + CALL PERTURBATION_PARAMETER + eta = rhot * z3t + eta_start = eta + + IF (num == 0) THEN + CALL F_EOS + ELSE IF(num == 1) THEN + CALL F_NUMERICAL + ELSE + write (*,*) 'deactivated this line when making a transition to f90' + stop + ! CALL F_EOS_rn + END IF + + fden_id = SUM( rhoi(1:ncomp) * ( LOG( rhoi(1:ncomp) ) - 1.0 ) ) + + fden = fres * rhot + fden_id + +ELSE + write (*,*) ' SUBROUTINE FDEN_CALC not available for cubic EOS' + stop +END IF + +END SUBROUTINE fden_calc + + + + +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! SUBROUTINE polymer_free +! +! This subroutine performes a phase equilibrium calculation assuming +! the polymer-lean hase to be polymer-free (x_poly=0). Only the +! equality of the solvent-fugacities has to be ensured (only one +! equation to be iterated). This procedure delivers very good +! appoximations for the polymer-rich phase up-to fairly close to the +! mixture critical point. Both, liquid-liquid and vapor-liquid +! equilibria can be calculated. +! See also comments to SUBROUTINE POLY_STA_VAR. +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! + SUBROUTINE polymer_free (p_spec,sol,solution) +! + USE BASIC_VARIABLES + IMPLICIT NONE +! +! ---------------------------------------------------------------------- + REAL, INTENT(IN OUT) :: p_spec + INTEGER, INTENT(OUT) :: sol + REAL, INTENT(OUT) :: solution(10,4+nc*np) +! +! ---------------------------------------------------------------------- + INTEGER :: k,j,ph, converg + REAL :: grid(10) +! ---------------------------------------------------------------------- + + sol = 0 + + grid(1)=0.98 + grid(2)=0.9 + grid(3)=0.7 + grid(4)=0.5 + grid(5)=0.3 + grid(6)=0.2 + grid(7)=0.1 + grid(8)=0.05 + + DO WHILE ( sol == 0 ) + + DO j = 1,8 + ! Phase 2 is solvent-phase + ! starting value for xi(1,1) of polymer-phase 1: w_polymer=0.95 to 0.05 + ! from simple approximate equation + xi(1,1) = grid(j) / ( (1.0-grid(j)) * mm(1) / mm(2) ) !xi(1,1) Phase 1 Komponente 1 + IF ( mm(1) < 5000.0 ) xi(1,1) = xi(1,1) * 0.8 + xi(1,2) = 1.0 - xi(1,1) !xi(1,2) Phase 1 Komponente 2 + lnx(1,1) = LOG(xi(1,1)) + lnx(1,2) = LOG(xi(1,2)) + lnx(2,1) = -1.E10 !ln(xi) Phase 2 Komponente 1 + lnx(2,2) = 0.0 !ln(xi) Phase 2 Komponente 2 + + + + val_init(1) = 0.45 ! starting density targeting at a liquid phase + val_init(2) = 0.0001 ! starting density targeting at a vapor phase + ! val_init(2) = 0.45 + val_init(3) = t + val_init(4) = p + DO ph = 1,nphas + DO k = 1,ncomp + val_init(4+k+(ph-1)*ncomp) = lnx(ph,k) + END DO + END DO + + + + + n_unkw = ncomp-1 ! number of quantities to be iterated + it(1) = 'x11' ! iteration of mol fraction of comp.1 phase 1 + it(2) = ' ' + sum_rel(1) = 'x12' ! summation relation: x12 = 1 - sum(x1j) + sum_rel(2) = 'x22' + + CALL objective_ctrl (converg) + + IF (converg == 1 .AND. ABS(dense(1)/dense(2)-1.0) > 1.d-3 .AND. dense(1) > 0.1) THEN + IF (sol == 0) THEN + sol = sol + 1 + DO k = 1,4+ncomp*nphas + solution(sol,k) = val_conv(k) + END DO + ELSE IF (ABS(solution(sol,5)/lnx(1,1)-1.0) > 1.d-2) THEN + sol = sol + 1 + DO k = 1,4+ncomp*nphas + solution(sol,k) = val_conv(k) + END DO + END IF + END IF + + END DO + + + + + + IF (sol == 0) THEN + WRITE (*,*) ' no initial solution found' + p = p*0.9 + IF (p < (0.7*p_spec)) WRITE (*,*) ' NO SOLUTION FOUND' + IF (p < (0.7*p_spec)) STOP + ELSE IF (sol > 1) THEN + ! write (*,*) ' ' + ! write (*,*) ' ',sol,' solutions found:' + ! write (*,*) ' lnx(1,1), dichte_1, dichte_2' + ! DO k = 1,sol + ! write (*,*) solution(k,5),solution(k,1),solution(k,2) + ! END DO + END IF + END DO + + n_unkw = ncomp ! number of quantities to be iterated + it(1) = 'x11' ! iteration of mol fraction of comp.1 phase 1 + it(2) = 'x21' ! iteration of mol fraction of comp.1 phase 2 + sum_rel(1) = 'x12' ! summation relation: x12 = 1 - sum(x1j) + sum_rel(2) = 'x22' ! summation relation: x22 = 1 - sum(x2j) + + + END SUBROUTINE polymer_free + + + + + +!>WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +!! SUBROUTINE phase_equilib +!! +!! This subroutine varies a predefined "running variable" and +!! organizes phase equilibrium calculations. For an isotherm +!! calculation e.g., the running variable is often the pressure. The +!! code is designed to deliver only converged solutions. In order to +!! enforce convergence, a step-width adjustment (reduction) is +!! implemented. +!! +!! VARIABLE LIST: +!! running defines the running variable. For example: if you want +!! to calculate the vapor pressure curve of a component +!! starting from 100�C to 200�C, then running is 't'. The +!! temperature is step-wise increased until the end- +!! -temperature of 200�C is reached. +!! (in this example end_x=200+273.15) +!! end_x end point for running variable +!! steps No. of calculation steps towards the end point of calc. +!! converg 0 if no convergence achieved, 1 if converged solution +!! +!! PREREQUISITES: +!! prior to execution of this routine, the follwing variables have to +!! be defined: "val_init" an array containing the starting values for +!! this iteration, "it(i)" provides the information, which variable is +!! determined iteratively, "sum_rel(i)" indicates, which mole fraction +!! is determined from the summation relation sum(xi)=1. Furthermore, +!! the number of phases and the variables provided by the subroutine +!! INPUT are required. +!!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +!! + SUBROUTINE phase_equilib (end_x,steps,converg) +! + USE BASIC_VARIABLES + IMPLICIT NONE +! +! ---------------------------------------------------------------------- + REAL, INTENT(IN) :: end_x + REAL, INTENT(IN) :: steps + INTEGER, INTENT(OUT) :: converg +! +! ---------------------------------------------------------------------- + INTEGER :: k, count1,count2,runindex,maxiter + REAL :: delta_x,delta_org,val_org,runvar + CHARACTER (LEN=2) :: compon + LOGICAL :: continue_cycle +! ---------------------------------------------------------------------- + +IF (running(1:2) == 'd1') runindex = 1 +IF (running(1:2) == 'd2') runindex = 2 +IF (running(1:1) == 't') runindex = 3 +IF (running(1:1) == 'p') runindex = 4 +IF (running(1:2) == 'x1') compon = running(3:3) +IF (running(1:2) == 'x1') READ(compon,*) k +IF (running(1:2) == 'x1') runindex = 4+k +IF (running(1:2) == 'x2') compon = running(3:3) +IF (running(1:2) == 'x2') READ(compon,*) k +IF (running(1:2) == 'x2') runindex = 4+ncomp+k +IF (running(1:2) == 'l1') compon = running(3:3) +IF (running(1:2) == 'l1') READ(compon,*) k +IF (running(1:2) == 'l1') runindex = 4+k +IF (running(1:2) == 'l2') compon = running(3:3) +IF (running(1:2) == 'l2') READ(compon,*) k +IF (running(1:2) == 'l2') runindex = 4+ncomp+k + +maxiter = 200 +IF ( ncomp >= 3 ) maxiter = 1000 +count1 = 0 +count2 = 0 +delta_x = ( end_x - val_init(runindex) ) / steps !J: calc increment in running var = (phi_end - phi_init)/steps +delta_org = ( end_x - val_init(runindex) ) / steps +val_org = val_init(runindex) +IF ( running(1:1) == 'x' ) THEN + delta_x = ( end_x - EXP(val_init(runindex)) ) / steps + delta_org = ( end_x - EXP(val_init(runindex)) ) / steps + val_org = EXP(val_init(runindex)) +END IF + +continue_cycle = .true. + +DO WHILE ( continue_cycle ) + + count1 = count1 + 1 + count2 = count2 + 1 + ! val_org = val_init(runindex) + + + CALL objective_ctrl (converg) + + IF (converg == 1) THEN + val_init( 1:(4+ncomp*nphas) ) = val_conv( 1:(4+ncomp*nphas) ) + IF (outp == 1 .AND. (ABS(delta_x) > 0.1*ABS(delta_org) .OR. count2 == 2)) CALL output + ELSE + delta_x = delta_x / 2.0 + IF (num == 2) delta_x = delta_x / 2.0 + val_init(runindex) = val_org + IF (running(1:1) == 'x') val_init(runindex) = LOG(val_org) + continue_cycle = .true. + count2 = 0 + END IF + runvar = val_init(runindex) + IF (running(1:1) == 'x') runvar = EXP(val_init(runindex)) + + IF ( end_x == 0.0 .AND. running(1:1) /= 'x' ) THEN + IF ( ABS(runvar-end_x) < 1.E-8 ) continue_cycle = .false. + ELSE IF ( ABS((runvar-end_x)/end_x) < 1.E-8 ) THEN + ! IF(delta_org.NE.0.0) WRITE (*,*)' FINISHED ITERATION',count1 + continue_cycle = .false. + ELSE IF ( count1 == maxiter ) THEN + WRITE (*,*) ' MAX. NO OF ITERATIONS',count1 + converg = 0 + continue_cycle = .false. + ELSE IF ( ABS(delta_x) < 1.E-5*ABS(delta_org) ) THEN + ! WRITE (*,*) ' CLOSEST APPROACH REACHED',count1 + converg = 0 + continue_cycle = .false. + ELSE + continue_cycle = .true. + val_org = runvar + IF (ABS(runvar+delta_x-end_x) > ABS(runvar-end_x)) delta_x = end_x - runvar ! if end-point passed + val_init(runindex) = runvar + delta_x + IF (running(1:1) == 'x') val_init(runindex) = LOG(runvar+delta_x) + END IF + + IF (ABS(delta_x) < ABS(delta_org) .AND. count2 >= 5) THEN + delta_x = delta_x * 2.0 + count2 = 0 + END IF + +END DO ! continue_cycle + +END SUBROUTINE phase_equilib + +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! + SUBROUTINE new_flash (ph_it) +! + USE BASIC_VARIABLES + IMPLICIT NONE +! +! ---------------------------------------------------------------------- + INTEGER, INTENT(IN) :: ph_it +! +! ---------------------------------------------------------------------- + INTEGER :: i, ph_cal + REAL, DIMENSION(nc) :: ni_1, ni_2 +! ---------------------------------------------------------------------- + + ph_cal = 3 - ph_it ! for two phases only + + DO i = 1, ncomp + IF ( lnx(ph_it,i) < -300.0 ) THEN + ni_2(i) = 0.0 + ELSE + ni_2(i) = EXP( lnx(ph_it,i) ) + END IF + END DO + + DO i = 1, ncomp + ni_1(i) = xif(i)-ni_2(i) + IF ( ni_2(i) > xif(i) ) THEN + ni_2(i) = xif(i) + ni_1(i) = xif(i) * 1.E-20 + ENDIF + END DO + + xi(ph_it,1:ncomp) = ni_2(1:ncomp) / SUM( ni_2(1:ncomp) ) + DO i = 1, ncomp + IF ( xi(ph_it,i) >= 1.E-300 ) lnx(ph_it,i) = LOG( xi(ph_it,i) ) + END DO + xi(ph_cal,1:ncomp) = ni_1(1:ncomp) / SUM( ni_1(1:ncomp) ) + lnx(ph_cal,1:ncomp) = LOG( xi(ph_cal,1:ncomp) ) + +END SUBROUTINE new_flash + + +!>WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +!! SUBROUTINE PHI_EOS +!! +!! This subroutine gives the residual chemical potential: +!! --> mu_i^res(T,p,x)/kT = ln( phi_i ) when ensemble_flag = 'tp' +!! The required input for this case (T, p, x(nc)) and as a starting value +!! eta_start +!! +!! or it gives +!! +!! --> mu_i^res(T,rho,x)/kT when ensemble_flag = 'tv' +!! The required input for this case (T, eta_start, x(nc)). Note that +!! eta_start is the specified density (packing fraction) in this case. +!!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +!! + SUBROUTINE PHI_EOS +! + USE PARAMETERS + USE EOS_VARIABLES + USE EOS_CONSTANTS + + + IMPLICIT NONE +! +! --- local variables--------------------------------------------------- + INTEGER :: i, j, k, ki, l, m + REAL :: z0, z1, z2, z3, z0_rk, z1_rk, z2_rk, z3_rk + REAL :: zms, m_mean + REAL, DIMENSION(nc) :: mhs, mdsp, mhc, myres + REAL, DIMENSION(nc) :: m_rk + REAL :: gij_rk(nc,nc) + REAL :: zres, zges + REAL :: dpdz, dpdz2 + + REAL :: I1, I2, I1_rk, I2_rk + REAL :: ord1_rk, ord2_rk + REAL :: c1_con, c2_con, c1_rk + REAL :: zmr, nmr, zmr_rk, nmr_rk, um_rk + REAL, DIMENSION(nc,0:6) :: ap_rk, bp_rk + + LOGICAL :: assoc + REAL :: ass_s2, m_hbon(nc) + + REAL :: fdd_rk, fqq_rk, fdq_rk + REAL, DIMENSION(nc) :: my_dd, my_qq, my_dq +! ---------------------------------------------------------------------- + +! ---------------------------------------------------------------------- +! obtain parameters and density independent expressions +! ---------------------------------------------------------------------- +CALL PERTURBATION_PARAMETER + + +! ---------------------------------------------------------------------- +! density iteration: (pTx)-ensemble OR p calc.: (pvx)-ensemble +! ---------------------------------------------------------------------- +IF (ensemble_flag == 'tp') THEN + CALL DENSITY_ITERATION +ELSEIF (ensemble_flag == 'tv') THEN + eta = eta_start + CALL P_EOS +ELSE + write (*,*) 'PHI_EOS: define ensemble, ensemble_flag == (pv) or (pt)' + stop +END IF + + +! --- Eq.(A.8) --------------------------------------------------------- +rho = eta / z3t +z0 = z0t * rho +z1 = z1t * rho +z2 = z2t * rho +z3 = z3t * rho + +m_mean = z0t / (PI/6.0) +zms = 1.0 - eta + +! ---------------------------------------------------------------------- +! compressibility factor z = p/(kT*rho) +! ---------------------------------------------------------------------- +zges = (p * 1.d-30) / (KBOL*t*rho) +IF ( ensemble_flag == 'tv' ) zges = (pges * 1.d-30) / (KBOL*t*rho) +zres = zges - 1.0 + + + +! ====================================================================== +! calculate the derivatives of f to mole fraction x ( d(f)/d(x) ) +! ====================================================================== + +DO k = 1, ncomp + + z0_rk = PI/6.0 * mseg(k) + z1_rk = PI/6.0 * mseg(k) * dhs(k) + z2_rk = PI/6.0 * mseg(k) * dhs(k)*dhs(k) + z3_rk = PI/6.0 * mseg(k) * dhs(k)**3 + +! --- derivative d(m_mean)/d(x) ---------------------------------------- + m_rk(k) = ( mseg(k) - m_mean ) / rho + ! lij(1,2)= -0.050 + ! lij(2,1)=lij(1,2) + ! r_m2dx(k)=0.0 + ! m_mean2=0.0 + ! DO i =1,ncomp + ! r_m2dx(k)=r_m2dx(k)+2.0*x(i)*(mseg(i)+mseg(k))/2.0*(1.0-lij(i,k)) + ! DO j =1,ncomp + ! m_mean2=m_mean2+x(i)*x(j)*(mseg(i)+mseg(j))/2.0*(1.0-lij(i,j)) + ! ENDDO + ! ENDDO + + ! -------------------------------------------------------------------- + ! d(f)/d(x) : hard sphere contribution + ! -------------------------------------------------------------------- + mhs(k) = 6.0/PI* ( 3.0*(z1_rk*z2+z1*z2_rk)/zms + 3.0*z1*z2*z3_rk/zms/zms & + + 3.0*z2*z2*z2_rk/z3/zms/zms + z2**3 *z3_rk*(3.0*z3-1.0)/z3/z3/zms**3 & + + ((3.0*z2*z2*z2_rk*z3-2.0*z2**3 *z3_rk)/z3**3 -z0_rk) *LOG(zms) & + + (z0-z2**3 /z3/z3)*z3_rk/zms ) + + ! -------------------------------------------------------------------- + ! d(f)/d(x) : chain term + ! -------------------------------------------------------------------- + DO i = 1, ncomp + DO j = 1, ncomp + gij(i,j) = 1.0/zms + 3.0*dij_ab(i,j)*z2/zms/zms + 2.0*(dij_ab(i,j)*z2)**2 /zms**3 + gij_rk(i,j) = z3_rk/zms/zms & + + 3.0*dij_ab(i,j)*(z2_rk+2.0*z2*z3_rk/zms)/zms/zms & + + dij_ab(i,j)**2 *z2/zms**3 *(4.0*z2_rk+6.0*z2*z3_rk/zms) + END DO + END DO + + mhc(k) = 0.0 + DO i = 1, ncomp + mhc(k) = mhc(k) + x(i)*rho * (1.0-mseg(i)) / gij(i,i) * gij_rk(i,i) + END DO + mhc(k) = mhc(k) + ( 1.0-mseg(k)) * LOG( gij(k,k) ) + + + ! -------------------------------------------------------------------- + ! PC-SAFT: d(f)/d(x) : dispersion contribution + ! -------------------------------------------------------------------- + IF (eos == 1) THEN + + ! --- derivatives of apar, bpar to rho_k --------------------------- + DO m = 0, 6 + ap_rk(k,m) = m_rk(k)/m_mean**2 * ( ap(m,2) + (3.0 -4.0/m_mean) *ap(m,3) ) + bp_rk(k,m) = m_rk(k)/m_mean**2 * ( bp(m,2) + (3.0 -4.0/m_mean) *bp(m,3) ) + END DO + + I1 = 0.0 + I2 = 0.0 + I1_rk = 0.0 + I2_rk = 0.0 + DO m = 0, 6 + I1 = I1 + apar(m)*eta**REAL(m) + I2 = I2 + bpar(m)*eta**REAL(m) + I1_rk = I1_rk + apar(m)*REAL(m)*eta**REAL(m-1)*z3_rk + ap_rk(k,m)*eta**REAL(m) + I2_rk = I2_rk + bpar(m)*REAL(m)*eta**REAL(m-1)*z3_rk + bp_rk(k,m)*eta**REAL(m) + END DO + + ord1_rk = 0.0 + ord2_rk = 0.0 + DO i = 1,ncomp + ord1_rk = ord1_rk + 2.0*mseg(k)*rho*x(i)*mseg(i)*sig_ij(i,k)**3 *uij(i,k)/t + ord2_rk = ord2_rk + 2.0*mseg(k)*rho*x(i)*mseg(i)*sig_ij(i,k)**3 *(uij(i,k)/t)**2 + END DO + + c1_con= 1.0/ ( 1.0 + m_mean*(8.0*z3-2.0*z3*z3)/zms**4 & + + (1.0 - m_mean)*(20.0*z3-27.0*z3*z3 +12.0*z3**3 -2.0*z3**4 ) & + /(zms*(2.0-z3))**2 ) + c2_con= - c1_con*c1_con *( m_mean*(-4.0*z3*z3+20.0*z3+8.0)/zms**5 & + + (1.0 - m_mean) *(2.0*z3**3 +12.0*z3*z3-48.0*z3+40.0) & + /(zms*(2.0-z3))**3 ) + c1_rk= c2_con*z3_rk - c1_con*c1_con*m_rk(k) * ( (8.0*z3-2.0*z3*z3)/zms**4 & + - (-2.0*z3**4 +12.0*z3**3 -27.0*z3*z3+20.0*z3) / (zms*(2.0-z3))**2 ) + + mdsp(k) = -2.0*PI* ( order1*rho*rho*I1_rk + ord1_rk*I1 ) & + - PI* c1_con*m_mean * ( order2*rho*rho*I2_rk + ord2_rk*I2 ) & + - PI* ( c1_con*m_rk(k) + c1_rk*m_mean ) * order2*rho*rho*I2 + + ! -------------------------------------------------------------------- + ! SAFT: d(f)/d(x) : dispersion contribution + ! -------------------------------------------------------------------- + ELSE + + zmr = 0.0 + nmr = 0.0 + zmr_rk = 0.0 + nmr_rk = 0.0 + DO i = 1, ncomp + DO j = 1, ncomp + zmr = zmr + x(i)*x(j)*mseg(i)*mseg(j)*vij(i,j)*uij(i,j) + nmr = nmr + x(i)*x(j)*mseg(i)*mseg(j)*vij(i,j) + END DO + zmr_rk = zmr_rk + 2.0*mseg(k) * x(i)*mseg(i)*vij(k,i)*uij(k,i) + nmr_rk = nmr_rk + 2.0*mseg(k) * x(i)*mseg(i)*vij(k,i) + END DO + + um_rk = 1.0/nmr**2 * ( nmr*zmr_rk - zmr*nmr_rk ) + + mdsp(k) = 0.0 + DO i = 1,4 + DO j = 1,9 + mdsp(k) = mdsp(k) + dnm(i,j)*(um/t)**REAL(i)*(eta/tau)**REAL(j) & + * ( 1.0 + z3_rk*rho/eta*REAL(j) + um_rk*rho/um*REAL(i) ) + END DO + END DO + + END IF + ! --- end of dispersion contribution------------------------------------ + + + ! -------------------------------------------------------------------- + ! TPT-1-association according to Chapman et al. + ! -------------------------------------------------------------------- + m_hbon(k) = 0.0 + assoc = .false. + DO i = 1,ncomp + IF (nhb_typ(i) /= 0) assoc = .true. + END DO + IF (assoc) THEN + + ass_s2 = 0.0 + DO l = 1, nhb_typ(k) + ass_s2 = ass_s2 + nhb_no(k,l) * LOG(mx(k,l)) + END DO + + m_hbon(k)=ass_s2 + DO i = 1, ncomp + DO ki = 1, nhb_typ(i) + DO j = 1, ncomp + DO l = 1, nhb_typ(j) + m_hbon(k)= m_hbon(k) - rho*rho/2.0*x(i)*x(j) *mx(i,ki)*mx(j,l) *nhb_no(i,ki)*nhb_no(j,l) & + * gij_rk(i,j) * ass_d(i,j,ki,l) + END DO + END DO + END DO + END DO + + END IF + ! --- end of TPT-1-association accord. to Chapman -------------------- + + + ! -------------------------------------------------------------------- + ! polar terms + ! -------------------------------------------------------------------- + CALL PHI_POLAR ( k, z3_rk, fdd_rk, fqq_rk, fdq_rk ) + my_dd(k) = fdd_rk + my_qq(k) = fqq_rk + my_dq(k) = fdq_rk + + + ! -------------------------------------------------------------------- + ! d(f)/d(x) : summation of all contributions + ! -------------------------------------------------------------------- + myres(k) = mhs(k) +mhc(k) +mdsp(k) +m_hbon(k) +my_dd(k) +my_qq(k) +my_dq(k) + + + + +END DO + + +! ---------------------------------------------------------------------- +! finally calculate +! mu_i^res(T,p,x)/kT = ln( phi_i ) when ensemble_flag = 'tp' +! mu_i^res(T,rho,x)/kT when ensemble_flag = 'tv' +! ---------------------------------------------------------------------- + +DO k = 1, ncomp + ! write (*,*) k,myres(k) +LOG(rho*x(k)),rho + IF (ensemble_flag == 'tp' ) lnphi(k) = myres(k) - LOG(zges) + IF (ensemble_flag == 'tv' ) lnphi(k) = myres(k) + ! write (*,*) 'in',k,EXP(lnphi(k)),LOG(zges),eta +END DO +!write (*,'(5G18.10)') lnphi(1),rho + +dpdz = pgesdz +dpdz2 = pgesd2 + +END SUBROUTINE PHI_EOS + + + + + + + + +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! SUBROUTINE PHI_EOS +! +! This subroutine gives the residual chemical potential: +! --> mu_i^res(T,p,x)/kT = ln( phi_i ) when ensemble_flag = 'tp' +! The required input for this case (T, p, x(nc)) and as a starting value +! eta_start +! +! or it gives +! +! --> mu_i^res(T,rho,x)/kT when ensemble_flag = 'tv' +! The required input for this case (T, eta_start, x(nc)). Note that +! eta_start is the specified density (packing fraction) in this case. +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! + SUBROUTINE PHI_EOS2 +! + USE PARAMETERS + USE EOS_VARIABLES + USE EOS_CONSTANTS + + + IMPLICIT NONE +! +! --- local variables--------------------------------------------------- + INTEGER :: i, j, k, ki, l, m + REAL :: z0, z1, z2, z3, z0_rk, z1_rk, z2_rk, z3_rk + REAL :: zms, m_mean + REAL, DIMENSION(nc) :: mhs, mdsp, mhc, myres + REAL, DIMENSION(nc) :: m_rk + REAL :: gij_rk(nc,nc) + REAL :: zres, zges + REAL :: dpdz, dpdz2 + + REAL :: I1, I2, I1_rk, I2_rk + REAL :: ord1_rk, ord2_rk + REAL :: c1_con, c2_con, c1_rk + REAL :: zmr, nmr, zmr_rk, nmr_rk, um_rk + REAL, DIMENSION(nc,0:6) :: ap_rk, bp_rk + + LOGICAL :: assoc + REAL :: ass_s2, m_hbon(nc) + + REAL :: fdd_rk, fqq_rk, fdq_rk + REAL, DIMENSION(nc) :: my_dd, my_qq, my_dq +! ---------------------------------------------------------------------- + +! ---------------------------------------------------------------------- +! obtain parameters and density independent expressions +! ---------------------------------------------------------------------- +CALL PERTURBATION_PARAMETER + + +! ---------------------------------------------------------------------- +! density iteration: (pTx)-ensemble OR p calc.: (pvx)-ensemble +! ---------------------------------------------------------------------- +IF (ensemble_flag == 'tp') THEN + CALL DENSITY_ITERATION +ELSEIF (ensemble_flag == 'tv') THEN + eta = eta_start + CALL P_EOS +ELSE + write (*,*) 'PHI_EOS: define ensemble, ensemble_flag == (pv) or (pt)' + stop +END IF + + +! --- Eq.(A.8) --------------------------------------------------------- +rho = eta / z3t +z0 = z0t * rho +z1 = z1t * rho +z2 = z2t * rho +z3 = z3t * rho + +m_mean = z0t / (PI/6.0) +zms = 1.0 - eta + +! ---------------------------------------------------------------------- +! compressibility factor z = p/(kT*rho) +! ---------------------------------------------------------------------- +zges = (p * 1.d-30) / (KBOL*t*rho) +IF ( ensemble_flag == 'tv' ) zges = (pges * 1.d-30) / (KBOL*t*rho) +zres = zges - 1.0 + + + +! ====================================================================== +! calculate the derivatives of f to mole fraction x ( d(f)/d(x) ) +! ====================================================================== + +DO k = 1, ncomp + + z0_rk = PI/6.0 * mseg(k) + z1_rk = PI/6.0 * mseg(k) * dhs(k) + z2_rk = PI/6.0 * mseg(k) * dhs(k)*dhs(k) + z3_rk = PI/6.0 * mseg(k) * dhs(k)**3 + +! --- derivative d(m_mean)/d(x) ---------------------------------------- + m_rk(k) = ( mseg(k) - m_mean ) / rho + ! lij(1,2)= -0.050 + ! lij(2,1)=lij(1,2) + ! r_m2dx(k)=0.0 + ! m_mean2=0.0 + ! DO i =1,ncomp + ! r_m2dx(k)=r_m2dx(k)+2.0*x(i)*(mseg(i)+mseg(k))/2.0*(1.0-lij(i,k)) + ! DO j =1,ncomp + ! m_mean2=m_mean2+x(i)*x(j)*(mseg(i)+mseg(j))/2.0*(1.0-lij(i,j)) + ! ENDDO + ! ENDDO + + ! -------------------------------------------------------------------- + ! d(f)/d(x) : hard sphere contribution + ! -------------------------------------------------------------------- + mhs(k) = 6.0/PI* ( 3.0*(z1_rk*z2+z1*z2_rk)/zms + 3.0*z1*z2*z3_rk/zms/zms & + + 3.0*z2*z2*z2_rk/z3/zms/zms + z2**3 *z3_rk*(3.0*z3-1.0)/z3/z3/zms**3 & + + ((3.0*z2*z2*z2_rk*z3-2.0*z2**3 *z3_rk)/z3**3 -z0_rk) *LOG(zms) & + + (z0-z2**3 /z3/z3)*z3_rk/zms ) + + ! -------------------------------------------------------------------- + ! d(f)/d(x) : chain term + ! -------------------------------------------------------------------- + DO i = 1, ncomp + DO j = 1, ncomp + gij(i,j) = 1.0/zms + 3.0*dij_ab(i,j)*z2/zms/zms + 2.0*(dij_ab(i,j)*z2)**2 /zms**3 + gij_rk(i,j) = z3_rk/zms/zms & + + 3.0*dij_ab(i,j)*(z2_rk+2.0*z2*z3_rk/zms)/zms/zms & + + dij_ab(i,j)**2 *z2/zms**3 *(4.0*z2_rk+6.0*z2*z3_rk/zms) + END DO + END DO + + mhc(k) = 0.0 + DO i = 1, ncomp + mhc(k) = mhc(k) + x(i)*rho * (1.0-mseg(i)) / gij(i,i) * gij_rk(i,i) + END DO + mhc(k) = mhc(k) + ( 1.0-mseg(k)) * LOG( gij(k,k) ) + + + ! -------------------------------------------------------------------- + ! PC-SAFT: d(f)/d(x) : dispersion contribution + ! -------------------------------------------------------------------- + IF (eos == 1) THEN + + ! --- derivatives of apar, bpar to rho_k --------------------------- + DO m = 0, 6 + ap_rk(k,m) = m_rk(k)/m_mean**2 * ( ap(m,2) + (3.0 -4.0/m_mean) *ap(m,3) ) + bp_rk(k,m) = m_rk(k)/m_mean**2 * ( bp(m,2) + (3.0 -4.0/m_mean) *bp(m,3) ) + END DO + + I1 = 0.0 + I2 = 0.0 + I1_rk = 0.0 + I2_rk = 0.0 + DO m = 0, 6 + I1 = I1 + apar(m)*eta**REAL(m) + I2 = I2 + bpar(m)*eta**REAL(m) + I1_rk = I1_rk + apar(m)*REAL(m)*eta**REAL(m-1)*z3_rk + ap_rk(k,m)*eta**REAL(m) + I2_rk = I2_rk + bpar(m)*REAL(m)*eta**REAL(m-1)*z3_rk + bp_rk(k,m)*eta**REAL(m) + END DO + + ord1_rk = 0.0 + ord2_rk = 0.0 + DO i = 1,ncomp + ord1_rk = ord1_rk + 2.0*mseg(k)*rho*x(i)*mseg(i)*sig_ij(i,k)**3 *uij(i,k)/t + ord2_rk = ord2_rk + 2.0*mseg(k)*rho*x(i)*mseg(i)*sig_ij(i,k)**3 *(uij(i,k)/t)**2 + END DO + + c1_con= 1.0/ ( 1.0 + m_mean*(8.0*z3-2.0*z3*z3)/zms**4 & + + (1.0 - m_mean)*(20.0*z3-27.0*z3*z3 +12.0*z3**3 -2.0*z3**4 ) & + /(zms*(2.0-z3))**2 ) + c2_con= - c1_con*c1_con *( m_mean*(-4.0*z3*z3+20.0*z3+8.0)/zms**5 & + + (1.0 - m_mean) *(2.0*z3**3 +12.0*z3*z3-48.0*z3+40.0) & + /(zms*(2.0-z3))**3 ) + c1_rk= c2_con*z3_rk - c1_con*c1_con*m_rk(k) * ( (8.0*z3-2.0*z3*z3)/zms**4 & + - (-2.0*z3**4 +12.0*z3**3 -27.0*z3*z3+20.0*z3) / (zms*(2.0-z3))**2 ) + + mdsp(k) = -2.0*PI* ( order1*rho*rho*I1_rk + ord1_rk*I1 ) & + - PI* c1_con*m_mean * ( order2*rho*rho*I2_rk + ord2_rk*I2 ) & + - PI* ( c1_con*m_rk(k) + c1_rk*m_mean ) * order2*rho*rho*I2 + + ! -------------------------------------------------------------------- + ! SAFT: d(f)/d(x) : dispersion contribution + ! -------------------------------------------------------------------- + ELSE + + zmr = 0.0 + nmr = 0.0 + zmr_rk = 0.0 + nmr_rk = 0.0 + DO i = 1, ncomp + DO j = 1, ncomp + zmr = zmr + x(i)*x(j)*mseg(i)*mseg(j)*vij(i,j)*uij(i,j) + nmr = nmr + x(i)*x(j)*mseg(i)*mseg(j)*vij(i,j) + END DO + zmr_rk = zmr_rk + 2.0*mseg(k) * x(i)*mseg(i)*vij(k,i)*uij(k,i) + nmr_rk = nmr_rk + 2.0*mseg(k) * x(i)*mseg(i)*vij(k,i) + END DO + + um_rk = 1.0/nmr**2 * ( nmr*zmr_rk - zmr*nmr_rk ) + + mdsp(k) = 0.0 + DO i = 1,4 + DO j = 1,9 + mdsp(k) = mdsp(k) + dnm(i,j)*(um/t)**REAL(i)*(eta/tau)**REAL(j) & + * ( 1.0 + z3_rk*rho/eta*REAL(j) + um_rk*rho/um*REAL(i) ) + END DO + END DO + + END IF + ! --- end of dispersion contribution------------------------------------ + + + ! -------------------------------------------------------------------- + ! TPT-1-association according to Chapman et al. + ! -------------------------------------------------------------------- + m_hbon(k) = 0.0 + assoc = .false. + DO i = 1,ncomp + IF (nhb_typ(i) /= 0) assoc = .true. + END DO + IF (assoc) THEN + + ass_s2 = 0.0 + DO l = 1, nhb_typ(k) + ass_s2 = ass_s2 + nhb_no(k,l) * LOG(mx(k,l)) + END DO + + m_hbon(k)=ass_s2 + DO i = 1, ncomp + DO ki = 1, nhb_typ(i) + DO j = 1, ncomp + DO l = 1, nhb_typ(j) + m_hbon(k)= m_hbon(k) - rho*rho/2.0*x(i)*x(j) *mx(i,ki)*mx(j,l) *nhb_no(i,ki)*nhb_no(j,l) & + * gij_rk(i,j) * ass_d(i,j,ki,l) + END DO + END DO + END DO + END DO + + END IF + ! --- end of TPT-1-association accord. to Chapman -------------------- + + + ! -------------------------------------------------------------------- + ! polar terms + ! -------------------------------------------------------------------- + CALL PHI_POLAR ( k, z3_rk, fdd_rk, fqq_rk, fdq_rk ) + my_dd(k) = fdd_rk + my_qq(k) = fqq_rk + my_dq(k) = fdq_rk + + + ! -------------------------------------------------------------------- + ! d(f)/d(x) : summation of all contributions + ! -------------------------------------------------------------------- + myres(k) = mhs(k) +mhc(k) +mdsp(k) +m_hbon(k) +my_dd(k) +my_qq(k) +my_dq(k) + + +END DO + + + + +muhs(1:ncomp) = mhs(1:ncomp) +muhc(1:ncomp) = mhc(1:ncomp) +mudisp(1:ncomp) = mdsp(1:ncomp) + + + + +! ---------------------------------------------------------------------- +! finally calculate +! mu_i^res(T,p,x)/kT = ln( phi_i ) when ensemble_flag = 'tp' +! mu_i^res(T,rho,x)/kT when ensemble_flag = 'tv' +! ---------------------------------------------------------------------- + +DO k = 1, ncomp + ! write (*,*) k,myres(k) +LOG(rho*x(k)),rho + IF (ensemble_flag == 'tp' ) lnphi(k) = myres(k) - LOG(zges) + IF (ensemble_flag == 'tv' ) lnphi(k) = myres(k) + ! write (*,*) 'in',k,EXP(lnphi(k)),LOG(zges),eta +END DO +!write (*,'(5G18.10)') lnphi(1),rho + +dpdz = pgesdz +dpdz2 = pgesd2 + + +write(*,*)'tp?',myres(1), lnphi(1) + +END SUBROUTINE PHI_EOS2 + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! + SUBROUTINE PHI_NUMERICAL +! + USE EOS_VARIABLES + USE EOS_CONSTANTS + USE DFT_MODULE, ONLY: z_ges, fres_temp + IMPLICIT NONE +! +!-----local variables------------------------------------------------- + INTEGER :: k + REAL :: zres, zges + REAL :: fres1, fres2, fres3, fres4, fres5 + REAL :: delta_rho + REAL, DIMENSION(nc) :: myres + REAL, DIMENSION(nc) :: rhoi, rhoi_0 + REAL :: tfr_1, tfr_2, tfr_3, tfr_4, tfr_5 +!----------------------------------------------------------------------- + + +!----------------------------------------------------------------------- +! density iteration or pressure calculation +!----------------------------------------------------------------------- + +IF (ensemble_flag == 'tp') THEN + CALL DENSITY_ITERATION +ELSEIF (ensemble_flag == 'tv') THEN + eta = eta_start + CALL P_NUMERICAL +ELSE + write (*,*) 'PHI_EOS: define ensemble, ensemble_flag == (tv) or (tp)' + stop +END IF + +!----------------------------------------------------------------------- +! compressibility factor z = p/(kT*rho) +!----------------------------------------------------------------------- + +zges = (p * 1.E-30) / (kbol*t*eta/z3t) +IF ( ensemble_flag == 'tv' ) zges = (pges * 1.E-30) / (kbol*t*eta/z3t) +zres = zges - 1.0 +z_ges = zges + +rhoi_0(1:ncomp) = x(1:ncomp) * eta/z3t +rhoi(1:ncomp) = rhoi_0(1:ncomp) + + +!----------------------------------------------------------------------- +! derivative to rho_k (keeping other rho_i's constant +!----------------------------------------------------------------------- + +DO k = 1, ncomp + + IF ( rhoi_0(k) > 1.d-9 ) THEN + delta_rho = 1.E-13 * 10.0**(0.5*(15.0+LOG10(rhoi_0(k)))) + ELSE + delta_rho = 1.E-10 + END IF + + rhoi(k) = rhoi_0(k) + delta_rho + eta = PI/6.0 * SUM( rhoi(1:ncomp)*mseg(1:ncomp)*dhs(1:ncomp)**3 ) + x(1:ncomp) = rhoi(1:ncomp) / SUM( rhoi(1:ncomp) ) + rho = SUM( rhoi(1:ncomp) ) + CALL F_NUMERICAL + fres1 = fres*rho + tfr_1 = tfr*rho + + rhoi(k) = rhoi_0(k) + 0.5 * delta_rho + eta = PI/6.0 * SUM( rhoi(1:ncomp)*mseg(1:ncomp)*dhs(1:ncomp)**3 ) + x(1:ncomp) = rhoi(1:ncomp) / SUM( rhoi(1:ncomp) ) + rho = SUM( rhoi(1:ncomp) ) + CALL F_NUMERICAL + fres2 = fres*rho + tfr_2 = tfr*rho + + IF ( rhoi_0(k) > 1.E-9 ) THEN + rhoi(k) = rhoi_0(k) - 0.5 * delta_rho + eta = PI/6.0 * SUM( rhoi(1:ncomp)*mseg(1:ncomp)*dhs(1:ncomp)**3 ) + x(1:ncomp) = rhoi(1:ncomp) / SUM( rhoi(1:ncomp) ) + rho = SUM( rhoi(1:ncomp) ) + CALL F_NUMERICAL + fres4 = fres*rho + tfr_4 = tfr*rho + + rhoi(k) = rhoi_0(k) - delta_rho + eta = PI/6.0 * SUM( rhoi(1:ncomp)*mseg(1:ncomp)*dhs(1:ncomp)**3 ) + x(1:ncomp) = rhoi(1:ncomp) / SUM( rhoi(1:ncomp) ) + rho = SUM( rhoi(1:ncomp) ) + CALL F_NUMERICAL + fres5 = fres*rho + tfr_5 = tfr*rho + END IF + + rhoi(k) = rhoi_0(k) + eta = PI/6.0 * SUM( rhoi(1:ncomp)*mseg(1:ncomp)*dhs(1:ncomp)**3 ) + x(1:ncomp) = rhoi(1:ncomp) / SUM( rhoi(1:ncomp) ) + rho = SUM( rhoi(1:ncomp) ) + CALL F_NUMERICAL + fres3 = fres*rho + tfr_3 = tfr*rho + + IF ( rhoi_0(k) > 1.E-9 ) THEN + myres(k) = ( fres5 - 8.0*fres4 + 8.0*fres2 - fres1 ) / ( 6.0*delta_rho ) + ELSE + myres(k) = ( -3.0*fres3 + 4.0*fres2 - fres1 ) / delta_rho + END IF + +END DO + + +!----------------------------------------------------------------------- +! residual Helmholtz energy +!----------------------------------------------------------------------- + +fres_temp = fres + +!----------------------------------------------------------------------- +! residual chemical potential +!----------------------------------------------------------------------- + +DO k = 1, ncomp + IF (ensemble_flag == 'tp') lnphi(k) = myres(k) - LOG(zges) + IF (ensemble_flag == 'tv' .AND. eta >= 0.0) lnphi(k) = myres(k) !+LOG(rho) + ! write (*,*) 'in',k,EXP(lnphi(k)),LOG(zges),eta + ! IF (DFT.GE.98) write (*,*) dft + ! write (*,*) 'lnphi',k,LNPHI(k),x(k),MYRES(k), -LOG(ZGES) + ! pause + ! write (*,*) k, myres(k), fres, ZRES +END DO + +END SUBROUTINE PHI_NUMERICAL + + +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW + +! SUBROUTINE H_EOS (phas,h_res,s_res,cp_res,X,T,P,PARAME, +! 1 KIJ,lij,NCOMP,ETA_START,ETA,eos,tfr) +! IMPLICIT NONE +! INTEGER nc +! PARAMETER (nc=20) +! INTEGER phas,ncomp,eos,i +! REAL kij(nc,nc),lij(nc,nc),x(nc),t,p,parame(nc,25) +! REAL eta_start,eta,tfr,h_res,cp_res,s_res + + +! i=1 + +! IF (i.EQ.1) THEN +! CALL H_EOS_1(phas,h_res,s_res,cp_res,X,T,P,PARAME, +! 1 KIJ,lij,NCOMP,ETA_START,ETA,eos,tfr) +! ELSE +! CALL H_EOS_NUM (phas,h_res,s_res,cp_res,X,T,P,PARAME, +! 1 KIJ,lij,NCOMP,ETA_START,ETA,eos,tfr) +! ENDIF + +! RETURN +! END + + +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! + SUBROUTINE H_EOS +! + USE PARAMETERS, ONLY: RGAS + USE EOS_CONSTANTS + USE EOS_VARIABLES + IMPLICIT NONE +! +! ---------------------------------------------------------------------- + REAL :: zges, df_dt, dfdr, ddfdrdr + REAL :: cv_res, df_dt2, df_drdt + REAL :: fact, dist, t_tmp, rho_0 + REAL :: fdr1, fdr2, fdr3, fdr4 + + INTEGER :: i, m + REAL :: dhsdt(nc), dhsdt2(nc) + REAL :: z0, z1, z2, z3, z1tdt, z2tdt, z3tdt + REAL :: z1dt, z2dt, z3dt, zms, gii + REAL :: fhsdt, fhsdt2 + REAL :: fchdt, fchdt2 + REAL :: fdspdt, fdspdt2 + REAL :: fhbdt, fhbdt2 + REAL :: sumseg, I1, I2, I1dt, I2dt, I1dt2, I2dt2 + REAL :: c1_con, c2_con, c3_con, c1_dt, c1_dt2 + REAL :: z1tdt2, z2tdt2, z3tdt2 + REAL :: z1dt2, z2dt2, z3dt2 + + INTEGER :: j, k, l, no, ass_cnt, max_eval + LOGICAL :: assoc + REAL :: dij, dijdt, dijdt2 + REAL :: gij1dt, gij2dt, gij3dt + REAL :: gij1dt2, gij2dt2, gij3dt2 + REAL, DIMENSION(nc,nc) :: gijdt, gijdt2, kap_hb + REAL, DIMENSION(nc,nc,nsite,nsite) :: ass_d_dt, ass_d_dt2, eps_hb, delta, deltadt, deltadt2 + REAL, DIMENSION(nc,nsite) :: mxdt, mxdt2, mx_itr, mx_itrdt, mx_itrdt2 + REAL :: attenu, tol, suma, sumdt, sumdt2, err_sum + + INTEGER :: dipole + REAL :: fdddt, fdddt2 + REAL, DIMENSION(nc) :: my2dd, my0 + REAL, DIMENSION(nc,nc) :: idd2, idd2dt, idd2dt2, idd4, idd4dt, idd4dt2 + REAL, DIMENSION(nc,nc,nc) :: idd3, idd3dt, idd3dt2 + REAL :: factor2, factor3 + REAL :: fdd2, fdd3, fdd2dt, fdd3dt, fdd2dt2, fdd3dt2 + REAL :: eij, xijmt, xijkmt + + INTEGER :: qudpole + REAL :: fqqdt, fqqdt2 + REAL, DIMENSION(nc) :: qq2 + REAL, DIMENSION(nc,nc) :: iqq2, iqq2dt, iqq2dt2, iqq4, iqq4dt, iqq4dt2 + REAL, DIMENSION(nc,nc,nc) :: iqq3, iqq3dt, iqq3dt2 + REAL :: fqq2, fqq2dt, fqq2dt2, fqq3, fqq3dt, fqq3dt2 + + INTEGER :: dip_quad + REAL :: fdqdt, fdqdt2 + REAL, DIMENSION(nc) :: myfac, q_fac + REAL, DIMENSION(nc,nc) :: idq2, idq2dt, idq2dt2, idq4, idq4dt, idq4dt2 + REAL, DIMENSION(nc,nc,nc) :: idq3, idq3dt, idq3dt2 + REAL :: fdq2, fdq2dt, fdq2dt2, fdq3, fdq3dt, fdq3dt2 +! ---------------------------------------------------------------------- + + +! ---------------------------------------------------------------------- +! Initializing +! ---------------------------------------------------------------------- +CALL PERTURBATION_PARAMETER + +rho = eta/z3t +z0 = z0t*rho +z1 = z1t*rho +z2 = z2t*rho +z3 = z3t*rho + +sumseg = z0t / (PI/6.0) +zms = 1.0 - z3 + + +! ---------------------------------------------------------------------- +! first and second derivative of f to density (dfdr,ddfdrdr) +! ---------------------------------------------------------------------- +CALL P_EOS + +zges = (pges * 1.E-30)/(kbol*t*rho) + +dfdr = pges/(eta*rho*(kbol*t)/1.E-30) +ddfdrdr = pgesdz/(eta*rho*(kbol*t)/1.E-30) - dfdr*2.0/eta - 1.0/eta**2 + + +! ---------------------------------------------------------------------- +! Helmholtz Energy f/kT = fres +! ---------------------------------------------------------------------- +CALL F_EOS + + +! ---------------------------------------------------------------------- +! derivative of some auxilliary properties to temperature +! ---------------------------------------------------------------------- +DO i = 1,ncomp + dhsdt(i)=parame(i,2) *(-3.0*parame(i,3)/t/t)*0.12*EXP(-3.0*parame(i,3)/t) + dhsdt2(i) = dhsdt(i)*3.0*parame(i,3)/t/t & + + 6.0*parame(i,2)*parame(i,3)/t**3 *0.12*EXP(-3.0*parame(i,3)/t) +END DO + +z1tdt = 0.0 +z2tdt = 0.0 +z3tdt = 0.0 +DO i = 1,ncomp + z1tdt = z1tdt + x(i) * mseg(i) * dhsdt(i) + z2tdt = z2tdt + x(i) * mseg(i) * 2.0*dhs(i)*dhsdt(i) + z3tdt = z3tdt + x(i) * mseg(i) * 3.0*dhs(i)*dhs(i)*dhsdt(i) +END DO +z1dt = PI / 6.0*z1tdt *rho +z2dt = PI / 6.0*z2tdt *rho +z3dt = PI / 6.0*z3tdt *rho + + +z1tdt2 = 0.0 +z2tdt2 = 0.0 +z3tdt2 = 0.0 +DO i = 1,ncomp + z1tdt2 = z1tdt2 + x(i)*mseg(i)*dhsdt2(i) + z2tdt2 = z2tdt2 + x(i)*mseg(i)*2.0 *( dhsdt(i)*dhsdt(i) +dhs(i)*dhsdt2(i) ) + z3tdt2 = z3tdt2 + x(i)*mseg(i)*3.0 *( 2.0*dhs(i)*dhsdt(i)* & + dhsdt(i) +dhs(i)*dhs(i)*dhsdt2(i) ) +END DO +z1dt2 = PI / 6.0*z1tdt2 *rho +z2dt2 = PI / 6.0*z2tdt2 *rho +z3dt2 = PI / 6.0*z3tdt2 *rho + + +! ---------------------------------------------------------------------- +! 1st & 2nd derivative of f/kT hard spheres to temp. (fhsdt) +! ---------------------------------------------------------------------- +fhsdt = 6.0/PI/rho*( 3.0*(z1dt*z2+z1*z2dt)/zms + 3.0*z1*z2*z3dt/zms/zms & + + 3.0*z2*z2*z2dt/z3/zms/zms & + + z2**3 *(2.0*z3*z3dt-z3dt*zms)/(z3*z3*zms**3 ) & + + (3.0*z2*z2*z2dt*z3-2.0*z2**3 *z3dt)/z3**3 *LOG(zms) & + + (z0-z2**3 /z3/z3)*z3dt/zms ) + +fhsdt2= 6.0/PI/rho*( 3.0*(z1dt2*z2+2.0*z1dt*z2dt+z1*z2dt2)/zms & + + 6.0*(z1dt*z2+z1*z2dt)*z3dt/zms/zms & + + 3.0*z1*z2*z3dt2/zms/zms + 6.0*z1*z2*z3dt*z3dt/zms**3 & + + 3.0*z2*(2.0*z2dt*z2dt+z2*z2dt2)/z3/zms/zms & + - z2*z2*(6.0*z2dt*z3dt+z2*z3dt2)/(z3*z3*zms*zms) & + + 2.0*z2**3 *z3dt*z3dt/(z3**3 *zms*zms) & + - 4.0*z2**3 *z3dt*z3dt/(z3*z3 *zms**3 ) & + + (12.0*z2*z2*z2dt*z3dt+2.0*z2**3 *z3dt2)/(z3*zms**3 ) & + + 6.0*z2**3 *z3dt*z3dt/(z3*zms**4 ) & + - 2.0*(3.0*z2*z2*z2dt/z3/z3-2.0*z2**3 *z3dt/z3**3 ) *z3dt/zms & + -(z2**3 /z3/z3-z0)*(z3dt2/zms+z3dt*z3dt/zms/zms) & + + ( (6.0*z2*z2dt*z2dt+3.0*z2*z2*z2dt2)/z3/z3 & + - (12.0*z2*z2*z2dt*z3dt+2.0*z2**3 *z3dt2)/z3**3 & + + 6.0*z2**3 *z3dt*z3dt/z3**4 )* LOG(zms) ) + + +! ---------------------------------------------------------------------- +! 1st & 2nd derivative of f/kT of chain term to T (fchdt) +! ---------------------------------------------------------------------- +fchdt = 0.0 +fchdt2 = 0.0 +DO i = 1, ncomp + DO j = 1, ncomp + dij=dhs(i)*dhs(j)/(dhs(i)+dhs(j)) + dijdt =(dhsdt(i)*dhs(j) + dhs(i)*dhsdt(j)) / (dhs(i)+dhs(j)) & + - dhs(i)*dhs(j)/(dhs(i)+dhs(j))**2 *(dhsdt(i)+dhsdt(j)) + dijdt2=(dhsdt2(i)*dhs(j) + 2.0*dhsdt(i)*dhsdt(j) & + + dhs(i)*dhsdt2(j)) / (dhs(i)+dhs(j)) & + - 2.0*(dhsdt(i)*dhs(j) + dhs(i)*dhsdt(j)) & + / (dhs(i)+dhs(j))**2 *(dhsdt(i)+dhsdt(j)) & + + 2.0* dhs(i)*dhs(j) / (dhs(i)+dhs(j))**3 & + * (dhsdt(i)+dhsdt(j))**2 & + - dhs(i)*dhs(j)/(dhs(i)+dhs(j))**2 *(dhsdt2(i)+dhsdt2(j)) + gij1dt = z3dt/zms/zms + gij2dt = 3.0*( z2dt*dij+z2*dijdt )/zms/zms +6.0*z2*dij*z3dt/zms**3 + gij3dt = 4.0*(dij*z2)* (dijdt*z2 + dij*z2dt) /zms**3 & + + 6.0*(dij*z2)**2 * z3dt /zms**4 + gij1dt2 = z3dt2/zms/zms +2.0*z3dt*z3dt/zms**3 + gij2dt2 = 3.0*( z2dt2*dij+2.0*z2dt*dijdt+z2*dijdt2 )/zms/zms & + + 6.0*( z2dt*dij+z2*dijdt )/zms**3 * z3dt & + + 6.0*(z2dt*dij*z3dt+z2*dijdt*z3dt+z2*dij*z3dt2) /zms**3 & + + 18.0*z2*dij*z3dt*z3dt/zms**4 + gij3dt2 = 4.0*(dijdt*z2+dij*z2dt)**2 /zms**3 & + + 4.0*(dij*z2)* (dijdt2*z2+2.0*dijdt*z2dt+dij*z2dt2) /zms**3 & + + 24.0*(dij*z2) *(dijdt*z2+dij*z2dt)/zms**4 *z3dt & + + 6.0*(dij*z2)**2 * z3dt2 /zms**4 & + + 24.0*(dij*z2)**2 * z3dt*z3dt /zms**5 + gijdt(i,j) = gij1dt + gij2dt + gij3dt + gijdt2(i,j) = gij1dt2 + gij2dt2 + gij3dt2 + END DO +END DO + +DO i = 1, ncomp + gii = 1.0/zms + 3.0*dhs(i)/2.0*z2/zms/zms + 2.0*dhs(i)*dhs(i)/4.0*z2*z2/zms**3 + fchdt = fchdt + x(i) * (1.0-mseg(i)) * gijdt(i,i) / gii + fchdt2= fchdt2+ x(i) * (1.0-mseg(i)) & + * (gijdt2(i,i) / gii - (gijdt(i,i)/gii)**2 ) +END DO + + +! ---------------------------------------------------------------------- +! 1st & 2nd derivative of f/kT dispersion term to T (fdspdt) +! ---------------------------------------------------------------------- +I1 = 0.0 +I2 = 0.0 +I1dt = 0.0 +I2dt = 0.0 +I1dt2= 0.0 +I2dt2= 0.0 +DO m = 0, 6 + I1 = I1 + apar(m)*z3**REAL(m) + I2 = I2 + bpar(m)*z3**REAL(m) + I1dt = I1dt + apar(m)*z3dt*REAL(m)*z3**REAL(m-1) + I2dt = I2dt + bpar(m)*z3dt*REAL(m)*z3**REAL(m-1) + I1dt2= I1dt2+ apar(m)*z3dt2*REAL(m)*z3**REAL(m-1) & + + apar(m)*z3dt*z3dt *REAL(m)*REAL(m-1)*z3**REAL(m-2) + I2dt2= I2dt2+ bpar(m)*z3dt2*REAL(m)*z3**REAL(m-1) & + + bpar(m)*z3dt*z3dt *REAL(m)*REAL(m-1)*z3**REAL(m-2) +END DO + +c1_con= 1.0/ ( 1.0 + sumseg*(8.0*z3-2.0*z3**2 )/zms**4 & + + (1.0 - sumseg)*(20.0*z3-27.0*z3**2 +12.0*z3**3 -2.0*z3**4 ) & + /(zms*(2.0-z3))**2 ) +c2_con= - c1_con*c1_con *(sumseg*(-4.0*z3**2 +20.0*z3+8.0)/zms**5 & + + (1.0 - sumseg) *(2.0*z3**3 +12.0*z3**2 -48.0*z3+40.0) & + /(zms*(2.0-z3))**3 ) +c3_con= 2.0 * c2_con*c2_con/c1_con - c1_con*c1_con & + *( sumseg*(-12.0*z3**2 +72.0*z3+60.0)/zms**6 + (1.0 - sumseg) & + *(-6.0*z3**4 -48.0*z3**3 +288.0*z3**2 -480.0*z3+264.0) & + /(zms*(2.0-z3))**4 ) +c1_dt = c2_con*z3dt +c1_dt2 = c3_con*z3dt*z3dt + c2_con*z3dt2 + +fdspdt = - 2.0*PI*rho*(I1dt-I1/t)*order1 & + - PI*rho*sumseg*(c1_dt*I2+c1_con*I2dt-2.0*c1_con*I2/t)*order2 + +fdspdt2 = - 2.0*PI*rho*(I1dt2-2.0*I1dt/t+2.0*I1/t/t)*order1 & + - PI*rho*sumseg*order2*( c1_dt2*I2 +2.0*c1_dt*I2dt -4.0*c1_dt*I2/t & + + 6.0*c1_con*I2/t/t -4.0*c1_con*I2dt/t +c1_con*I2dt2) + + +! ---------------------------------------------------------------------- +! 1st & 2nd derivative of f/kT association term to T (fhbdt) +! ---------------------------------------------------------------------- +fhbdt = 0.0 +fhbdt2 = 0.0 +assoc = .false. +DO i = 1,ncomp + IF ( nhb_typ(i) /= 0 ) assoc = .true. +END DO +IF (assoc) THEN + + DO i = 1,ncomp + IF ( nhb_typ(i) /= 0 ) THEN + kap_hb(i,i) = parame(i,13) + no = 0 + DO j = 1,nhb_typ(i) + DO k = 1,nhb_typ(i) + eps_hb(i,i,j,k) = parame(i,(14+no)) + no = no + 1 + END DO + END DO + DO j = 1,nhb_typ(i) + no = no + 1 + END DO + ELSE + kap_hb(i,i) = 0.0 + DO k = 1,nsite + DO l = 1,nsite + eps_hb(i,i,k,l) = 0.0 + END DO + END DO + END IF + END DO + + DO i = 1,ncomp + DO j = 1,ncomp + IF ( i /= j .AND. (nhb_typ(i) /= 0 .AND. nhb_typ(j) /= 0) ) THEN + kap_hb(i,j)= (kap_hb(i,i)*kap_hb(j,j))**0.5 & + *((parame(i,2)*parame(j,2))**3 )**0.5 & + /(0.5*(parame(i,2)+parame(j,2)))**3 + ! kap_hb(i,j)= kap_hb(i,j)*(1.0-k_kij) + DO k = 1,nhb_typ(i) + DO l = 1,nhb_typ(j) + IF (k /= l) THEN + eps_hb(i,j,k,l)=(eps_hb(i,i,k,l)+eps_hb(j,j,l,k))/2.0 + ! eps_hb(i,j,k,l)=eps_hb(i,j,k,l)*(1.0-eps_kij) + END IF + END DO + END DO + END IF + END DO + END DO + IF (nhb_typ(1) == 3) THEN + eps_hb(1,2,3,1)=0.5*(eps_hb(1,1,3,1)+eps_hb(2,2,1,2)) + eps_hb(2,1,1,3) = eps_hb(1,2,3,1) + END IF + IF (nhb_typ(2) == 3) THEN + eps_hb(2,1,3,1)=0.5*(eps_hb(2,2,3,1)+eps_hb(1,1,1,2)) + eps_hb(1,2,1,3) = eps_hb(2,1,3,1) + END IF + + DO i = 1, ncomp + DO k = 1, nhb_typ(i) + DO j = 1, ncomp + DO l = 1, nhb_typ(j) + ! ass_d(i,j,k,l)=kap_hb(i,j) *sig_ij(i,j)**3 *(EXP(eps_hb(i,j,k,l)/t)-1.0) + ass_d_dt(i,j,k,l)= - kap_hb(i,j) *sig_ij(i,j)**3 * eps_hb(i,j,k,l)/t/t*EXP(eps_hb(i,j,k,l)/t) + ass_d_dt2(i,j,k,l)= - kap_hb(i,j) *sig_ij(i,j)**3 & + * eps_hb(i,j,k,l)/t/t*EXP(eps_hb(i,j,k,l)/t) & + * (-2.0/t - eps_hb(i,j,k,l)/t/t) + END DO + END DO + END DO + END DO + + DO i = 1, ncomp + DO k = 1, nhb_typ(i) + DO j = 1, ncomp + DO l = 1, nhb_typ(j) + delta(i,j,k,l)=gij(i,j)*ass_d(i,j,k,l) + deltadt(i,j,k,l) = gijdt(i,j)*ass_d(i,j,k,l) + gij(i,j)*ass_d_dt(i,j,k,l) + deltadt2(i,j,k,l)= gijdt2(i,j)*ass_d(i,j,k,l) & + + 2.0*gijdt(i,j)*ass_d_dt(i,j,k,l) +gij(i,j)*ass_d_dt2(i,j,k,l) + END DO + END DO + END DO + END DO + + +! ------ constants for iteration --------------------------------------- + attenu = 0.7 + tol = 1.E-10 + IF (eta < 0.2) tol = 1.E-11 + IF (eta < 0.01) tol = 1.E-12 + max_eval = 200 + +! ------ initialize mxdt(i,j) ------------------------------------------ + DO i = 1, ncomp + DO k = 1, nhb_typ(i) + mxdt(i,k) = 0.0 + mxdt2(i,k) = 0.0 + END DO + END DO + + +! ------ iterate over all components and all sites --------------------- + DO ass_cnt = 1, max_eval + + DO i = 1, ncomp + DO k = 1, nhb_typ(i) + suma = 0.0 + sumdt = 0.0 + sumdt2= 0.0 + DO j = 1, ncomp + DO l = 1, nhb_typ(j) + suma = suma + x(j)*nhb_no(j,l)* mx(j,l) *delta(i,j,k,l) + sumdt = sumdt + x(j)*nhb_no(j,l)*( mx(j,l) *deltadt(i,j,k,l) & + + mxdt(j,l)*delta(i,j,k,l) ) + sumdt2 = sumdt2 + x(j)*nhb_no(j,l)*( mx(j,l)*deltadt2(i,j,k,l) & + + 2.0*mxdt(j,l)*deltadt(i,j,k,l) + mxdt2(j,l)*delta(i,j,k,l) ) + END DO + END DO + mx_itr(i,k) = 1.0 / (1.0 + suma * rho) + mx_itrdt(i,k)= - mx_itr(i,k)**2 * sumdt*rho + mx_itrdt2(i,k)= +2.0*mx_itr(i,k)**3 * (sumdt*rho)**2 - mx_itr(i,k)**2 *sumdt2*rho + END DO + END DO + + err_sum = 0.0 + DO i = 1, ncomp + DO k = 1, nhb_typ(i) + err_sum = err_sum + ABS(mx_itr(i,k) - mx(i,k)) & + + ABS(mx_itrdt(i,k) - mxdt(i,k)) + ABS(mx_itrdt2(i,k) - mxdt2(i,k)) + mx(i,k) = mx_itr(i,k) * attenu + mx(i,k) * (1.0 - attenu) + mxdt(i,k)=mx_itrdt(i,k)*attenu +mxdt(i,k)* (1.0 - attenu) + mxdt2(i,k)=mx_itrdt2(i,k)*attenu +mxdt2(i,k)* (1.0 - attenu) + END DO + END DO + IF(err_sum <= tol) GO TO 10 + + END DO + WRITE(6,*) 'CAL_PCSAFT: max_eval violated err_sum = ',err_sum,tol + STOP + 10 CONTINUE + + DO i = 1, ncomp + DO k = 1, nhb_typ(i) + ! fhb = fhb + x(i)* nhb_no(i,k)* ( 0.5 * ( 1.0 - mx(i,k) ) + LOG(mx(i,k)) ) + fhbdt = fhbdt + x(i)*nhb_no(i,k) *mxdt(i,k)*(1.0/mx(i,k)-0.5) + fhbdt2= fhbdt2 + x(i)*nhb_no(i,k) *(mxdt2(i,k)*(1.0/mx(i,k)-0.5) & + -(mxdt(i,k)/mx(i,k))**2 ) + END DO + END DO + +END IF + + +! ---------------------------------------------------------------------- +! derivatives of f/kT of dipole-dipole term to temp. (fdddt) +! ---------------------------------------------------------------------- +fdddt = 0.0 +fdddt2 = 0.0 +dipole = 0 +DO i = 1,ncomp + my2dd(i) = 0.0 + IF ( parame(i,6) /= 0.0 .AND. uij(i,i) /= 0.0 ) THEN + dipole = 1 + my2dd(i) = (parame(i,6))**2 *1.E-49 / (uij(i,i)*kbol*mseg(i)*sig_ij(i,i)**3 *1.E-30) + END IF + my0(i) = my2dd(i) ! needed for dipole-quadrupole-term +END DO + +IF (dipole == 1) THEN + DO i = 1,ncomp + DO j = 1,ncomp + idd2(i,j) =0.0 + idd4(i,j) =0.0 + idd2dt(i,j) =0.0 + idd4dt(i,j) =0.0 + idd2dt2(i,j)=0.0 + idd4dt2(i,j)=0.0 + DO m=0,4 + idd2(i,j) = idd2(i,j) +ddp2(i,j,m)*z3**REAL(m) + idd4(i,j) = idd4(i,j) +ddp4(i,j,m)*z3**REAL(m) + idd2dt(i,j)= idd2dt(i,j) +ddp2(i,j,m)*z3dt*REAL(m)*z3**REAL(m-1) + idd4dt(i,j)= idd4dt(i,j) +ddp4(i,j,m)*z3dt*REAL(m)*z3**REAL(m-1) + idd2dt2(i,j)=idd2dt2(i,j)+ddp2(i,j,m)*z3dt2*REAL(m)*z3**REAL(m-1) & + + ddp2(i,j,m)*z3dt**2 *REAL(m)*REAL(m-1)*z3**REAL(m-2) + idd4dt2(i,j)=idd4dt2(i,j)+ddp4(i,j,m)*z3dt2*REAL(m)*z3**REAL(m-1) & + + ddp4(i,j,m)*z3dt**2 *REAL(m)*REAL(m-1)*z3**REAL(m-2) + END DO + DO k = 1,ncomp + idd3(i,j,k) =0.0 + idd3dt(i,j,k) =0.0 + idd3dt2(i,j,k)=0.0 + DO m = 0, 4 + idd3(i,j,k) = idd3(i,j,k) +ddp3(i,j,k,m)*z3**REAL(m) + idd3dt(i,j,k) = idd3dt(i,j,k)+ddp3(i,j,k,m)*z3dt*REAL(m) *z3**REAL(m-1) + idd3dt2(i,j,k)= idd3dt2(i,j,k)+ddp3(i,j,k,m)*z3dt2*REAL(m) & + *z3**REAL(m-1) +ddp3(i,j,k,m)*z3dt**2 *REAL(m)*REAL(m-1) *z3**REAL(m-2) + END DO + END DO + END DO + END DO + + + factor2= -PI *rho + factor3= -4.0/3.0*PI**2 * rho**2 + + fdd2 = 0.0 + fdd3 = 0.0 + fdd2dt= 0.0 + fdd3dt= 0.0 + fdd2dt2= 0.0 + fdd3dt2= 0.0 + DO i = 1, ncomp + DO j = 1, ncomp + xijmt = x(i)*parame(i,3)*parame(i,2)**3 *x(j)*parame(j,3)*parame(j,2)**3 & + / ((parame(i,2)+parame(j,2))/2.0)**3 *my2dd(i)*my2dd(j) + eij = (parame(i,3)*parame(j,3))**0.5 + fdd2 = fdd2 +factor2* xijmt/t/t*(idd2(i,j)+eij/t*idd4(i,j)) + fdd2dt= fdd2dt+ factor2* xijmt/t/t*(idd2dt(i,j)-2.0*idd2(i,j)/t & + +eij/t*idd4dt(i,j)-3.0*eij/t/t*idd4(i,j)) + fdd2dt2=fdd2dt2+factor2*xijmt/t/t*(idd2dt2(i,j)-4.0*idd2dt(i,j)/t & + +6.0*idd2(i,j)/t/t+eij/t*idd4dt2(i,j) & + -6.0*eij/t/t*idd4dt(i,j)+12.0*eij/t**3 *idd4(i,j)) + DO k = 1, ncomp + xijkmt=x(i)*parame(i,3)*parame(i,2)**3 & + *x(j)*parame(j,3)*parame(j,2)**3 & + *x(k)*parame(k,3)*parame(k,2)**3 & + /((parame(i,2)+parame(j,2))/2.0) /((parame(i,2)+parame(k,2))/2.0) & + /((parame(j,2)+parame(k,2))/2.0) *my2dd(i)*my2dd(j)*my2dd(k) + fdd3 =fdd3 +factor3*xijkmt/t**3 *idd3(i,j,k) + fdd3dt =fdd3dt +factor3*xijkmt/t**3 * (idd3dt(i,j,k)-3.0*idd3(i,j,k)/t) + fdd3dt2=fdd3dt2+factor3*xijkmt/t**3 & + *( idd3dt2(i,j,k)-6.0*idd3dt(i,j,k)/t+12.0*idd3(i,j,k)/t/t ) + END DO + END DO + END DO + + IF ( fdd2 < -1.E-100 .AND. fdd3 /= 0.0 ) THEN + fdddt = fdd2* (fdd2*fdd2dt - 2.0*fdd3*fdd2dt+fdd2*fdd3dt) / (fdd2-fdd3)**2 + fdddt2 = ( 2.0*fdd2*fdd2dt*fdd2dt +fdd2*fdd2*fdd2dt2 & + -2.0*fdd2dt**2 *fdd3 -2.0*fdd2*fdd2dt2*fdd3 +fdd2*fdd2*fdd3dt2 ) & + /(fdd2-fdd3)**2 + fdddt * 2.0*(fdd3dt-fdd2dt)/(fdd2-fdd3) + END IF +END IF + + +! ---------------------------------------------------------------------- +! derivatives f/kT of quadrupole-quadrup. term to T (fqqdt) +! ---------------------------------------------------------------------- +fqqdt = 0.0 +fqqdt2 = 0.0 +qudpole = 0 +DO i = 1, ncomp + qq2(i) = (parame(i,7))**2 *1.E-69 / (uij(i,i)*kbol*mseg(i)*sig_ij(i,i)**5 *1.E-50) + IF (qq2(i) /= 0.0) qudpole = 1 +END DO + +IF (qudpole == 1) THEN + + DO i = 1,ncomp + DO j = 1,ncomp + iqq2(i,j) = 0.0 + iqq4(i,j) = 0.0 + iqq2dt(i,j) = 0.0 + iqq4dt(i,j) = 0.0 + iqq2dt2(i,j)= 0.0 + iqq4dt2(i,j)= 0.0 + DO m = 0, 4 + iqq2(i,j) = iqq2(i,j) + qqp2(i,j,m)*z3**REAL(m) + iqq4(i,j) = iqq4(i,j) + qqp4(i,j,m)*z3**REAL(m) + iqq2dt(i,j) = iqq2dt(i,j)+ qqp2(i,j,m)*z3dt*REAL(m)*z3**REAL(m-1) + iqq4dt(i,j) = iqq4dt(i,j)+ qqp4(i,j,m)*z3dt*REAL(m)*z3**REAL(m-1) + iqq2dt2(i,j)= iqq2dt2(i,j)+qqp2(i,j,m)*z3dt2*REAL(m)*z3**REAL(m-1) & + + qqp2(i,j,m)*z3dt**2 *REAL(m)*REAL(m-1)*z3**REAL(m-2) + iqq4dt2(i,j)= iqq4dt2(i,j)+qqp4(i,j,m)*z3dt2*REAL(m)*z3**REAL(m-1) & + + qqp4(i,j,m)*z3dt**2 *REAL(m)*REAL(m-1)*z3**REAL(m-2) + END DO + DO k = 1,ncomp + iqq3(i,j,k) =0.0 + iqq3dt(i,j,k) =0.0 + iqq3dt2(i,j,k)=0.0 + DO m = 0, 4 + iqq3(i,j,k) = iqq3(i,j,k) + qqp3(i,j,k,m)*z3**REAL(m) + iqq3dt(i,j,k) = iqq3dt(i,j,k)+ qqp3(i,j,k,m)*z3dt*REAL(m) * z3**REAL(m-1) + iqq3dt2(i,j,k)= iqq3dt2(i,j,k)+qqp3(i,j,k,m)*z3dt2*REAL(m) * z3**REAL(m-1) & + + qqp3(i,j,k,m)*z3dt**2 *REAL(m)*REAL(m-1)*z3**REAL(m-2) + END DO + END DO + END DO + END DO + + factor2 = -9.0/16.0 * PI *rho + factor3 = 9.0/16.0 * PI**2 * rho**2 + + fqq2 = 0.0 + fqq3 = 0.0 + fqq2dt = 0.0 + fqq3dt = 0.0 + fqq2dt2= 0.0 + fqq3dt2= 0.0 + DO i = 1,ncomp + DO j = 1,ncomp + xijmt = x(i)*uij(i,i)*qq2(i)*sig_ij(i,i)**5 & + * x(j)*uij(j,j)*qq2(j)*sig_ij(j,j)**5 /sig_ij(i,j)**7.0 + eij = (parame(i,3)*parame(j,3))**0.5 + fqq2 = fqq2 +factor2* xijmt/t/t*(iqq2(i,j)+eij/t*iqq4(i,j)) + fqq2dt= fqq2dt +factor2* xijmt/t/t*(iqq2dt(i,j)-2.0*iqq2(i,j)/t & + + eij/t*iqq4dt(i,j)-3.0*eij/t/t*iqq4(i,j)) + fqq2dt2=fqq2dt2+factor2*xijmt/t/t*(iqq2dt2(i,j)-4.0*iqq2dt(i,j)/t & + + 6.0*iqq2(i,j)/t/t+eij/t*iqq4dt2(i,j) & + - 6.0*eij/t/t*iqq4dt(i,j)+12.0*eij/t**3 *iqq4(i,j)) + DO k = 1,ncomp + xijkmt = x(i)*uij(i,i)*qq2(i)*sig_ij(i,i)**5 /sig_ij(i,j)**3 & + * x(j)*uij(j,j)*qq2(j)*sig_ij(j,j)**5 /sig_ij(i,k)**3 & + * x(k)*uij(k,k)*qq2(k)*sig_ij(k,k)**5 /sig_ij(j,k)**3 + fqq3 = fqq3 +factor3*xijkmt/t**3 *iqq3(i,j,k) + fqq3dt = fqq3dt +factor3*xijkmt/t**3 *(iqq3dt(i,j,k)-3.0*iqq3(i,j,k)/t) + fqq3dt2= fqq3dt2+factor3*xijkmt/t**3 & + * ( iqq3dt2(i,j,k)-6.0*iqq3dt(i,j,k)/t+12.0*iqq3(i,j,k)/t/t ) + END DO + END DO + END DO + + IF ( fqq2 /= 0.0 .AND. fqq3 /= 0.0 ) THEN + fqqdt = fqq2* (fqq2*fqq2dt - 2.0*fqq3*fqq2dt+fqq2*fqq3dt) / (fqq2-fqq3)**2 + fqqdt2 = ( 2.0*fqq2*fqq2dt*fqq2dt +fqq2*fqq2*fqq2dt2 & + - 2.0*fqq2dt**2 *fqq3 -2.0*fqq2*fqq2dt2*fqq3 +fqq2*fqq2*fqq3dt2 ) & + / (fqq2-fqq3)**2 + fqqdt * 2.0*(fqq3dt-fqq2dt)/(fqq2-fqq3) + END IF + +END IF + + +! ---------------------------------------------------------------------- +! derivatives f/kT of dipole-quadruppole term to T (fdqdt) +! ---------------------------------------------------------------------- +fdqdt = 0.0 +fdqdt2= 0.0 +dip_quad = 0 +DO i = 1,ncomp + DO j = 1,ncomp + IF (parame(i,6) /= 0.0 .AND. parame(j,7) /= 0.0) dip_quad = 1 + END DO + myfac(i) = parame(i,3)*parame(i,2)**4 *my0(i) + q_fac(i) = parame(i,3)*parame(i,2)**4 *qq2(i) +END DO + +IF (dip_quad == 1) THEN + + DO i = 1,ncomp + DO j = 1,ncomp + idq2(i,j) = 0.0 + idq4(i,j) = 0.0 + idq2dt(i,j) = 0.0 + idq4dt(i,j) = 0.0 + idq2dt2(i,j)= 0.0 + idq4dt2(i,j)= 0.0 + IF ( myfac(i) /= 0.0 .AND. q_fac(j) /= 0.0 ) THEN + DO m = 0, 4 + idq2(i,j) = idq2(i,j) + dqp2(i,j,m)*z3**REAL(m) + idq4(i,j) = idq4(i,j) + dqp4(i,j,m)*z3**REAL(m) + idq2dt(i,j) = idq2dt(i,j)+ dqp2(i,j,m)*z3dt*REAL(m)*z3**REAL(m-1) + idq4dt(i,j) = idq4dt(i,j)+ dqp4(i,j,m)*z3dt*REAL(m)*z3**REAL(m-1) + idq2dt2(i,j)= idq2dt2(i,j)+dqp2(i,j,m)*z3dt2*REAL(m)*z3**REAL(m-1) & + + dqp2(i,j,m)*z3dt**2 *REAL(m)*REAL(m-1)*z3**REAL(m-2) + idq4dt2(i,j)= idq4dt2(i,j)+dqp4(i,j,m)*z3dt2*REAL(m)*z3**REAL(m-1) & + + dqp4(i,j,m)*z3dt**2 *REAL(m)*REAL(m-1)*z3**REAL(m-2) + END DO + + DO k = 1,ncomp + idq3(i,j,k) = 0.0 + idq3dt(i,j,k) = 0.0 + idq3dt2(i,j,k)= 0.0 + IF ( myfac(k) /= 0.0 .OR. q_fac(k) /= 0.0 ) THEN + DO m = 0, 4 + idq3(i,j,k) = idq3(i,j,k) + dqp3(i,j,k,m)*z3**REAL(m) + idq3dt(i,j,k)= idq3dt(i,j,k)+ dqp3(i,j,k,m)*z3dt*REAL(m) *z3**REAL(m-1) + idq3dt2(i,j,k)= idq3dt2(i,j,k)+dqp3(i,j,k,m)*z3dt2*REAL(m) *z3**REAL(m-1) & + + dqp3(i,j,k,m)*z3dt**2 *REAL(m)*REAL(m-1)*z3**REAL(m-2) + END DO + END IF + END DO + END IF + END DO + END DO + + factor2= -9.0/4.0 * PI * rho + factor3= PI**2 * rho**2 + + fdq2 = 0.0 + fdq3 = 0.0 + fdq2dt= 0.0 + fdq3dt= 0.0 + fdq2dt2=0.0 + fdq3dt2=0.0 + DO i = 1,ncomp + DO j = 1,ncomp + IF ( myfac(i) /= 0.0 .AND. q_fac(j) /= 0.0 ) THEN + xijmt = x(i)*myfac(i) * x(j)*q_fac(j) /sig_ij(i,j)**5 + eij = (parame(i,3)*parame(j,3))**0.5 + fdq2 = fdq2 + factor2* xijmt/t/t*(idq2(i,j)+eij/t*idq4(i,j)) + fdq2dt= fdq2dt+ factor2* xijmt/t/t*(idq2dt(i,j)-2.0*idq2(i,j)/t & + + eij/t*idq4dt(i,j)-3.0*eij/t/t*idq4(i,j)) + fdq2dt2 = fdq2dt2+factor2*xijmt/t/t*(idq2dt2(i,j)-4.0*idq2dt(i,j)/t & + + 6.0*idq2(i,j)/t/t+eij/t*idq4dt2(i,j) & + - 6.0*eij/t/t*idq4dt(i,j)+12.0*eij/t**3 *idq4(i,j)) + DO k = 1,ncomp + IF ( myfac(k) /= 0.0 .OR. q_fac(k) /= 0.0 ) THEN + xijkmt= x(i)*x(j)*x(k)/(sig_ij(i,j)*sig_ij(i,k)*sig_ij(j,k))**2 & + * ( myfac(i)*q_fac(j)*myfac(k) & + + myfac(i)*q_fac(j)*q_fac(k)*1.193735 ) + + fdq3 =fdq3 + factor3*xijkmt/t**3 *idq3(i,j,k) + fdq3dt=fdq3dt+ factor3*xijkmt/t**3 * (idq3dt(i,j,k)-3.0*idq3(i,j,k)/t) + fdq3dt2=fdq3dt2+factor3*xijkmt/t**3 & + *( idq3dt2(i,j,k)-6.0*idq3dt(i,j,k)/t+12.0*idq3(i,j,k)/t/t ) + END IF + END DO + END IF + END DO + END DO + + IF (fdq2 /= 0.0 .AND. fdq3 /= 0.0) THEN + fdqdt = fdq2* (fdq2*fdq2dt - 2.0*fdq3*fdq2dt+fdq2*fdq3dt) / (fdq2-fdq3)**2 + fdqdt2 = ( 2.0*fdq2*fdq2dt*fdq2dt +fdq2*fdq2*fdq2dt2 & + - 2.0*fdq2dt**2 *fdq3 -2.0*fdq2*fdq2dt2*fdq3 +fdq2*fdq2*fdq3dt2 ) & + / (fdq2-fdq3)**2 + fdqdt * 2.0*(fdq3dt-fdq2dt)/(fdq2-fdq3) + END IF + +END IF +! ---------------------------------------------------------------------- + + + + +! ---------------------------------------------------------------------- +! total derivative of fres/kT to temperature +! ---------------------------------------------------------------------- + +df_dt = fhsdt + fchdt + fdspdt + fhbdt + fdddt + fqqdt + fdqdt + + + +! ---------------------------------------------------------------------- +! second derivative of fres/kT to T +! ---------------------------------------------------------------------- + +df_dt2 = fhsdt2 +fchdt2 +fdspdt2 +fhbdt2 +fdddt2 +fqqdt2 +fdqdt2 + + + +! ---------------------------------------------------------------------- +! ------ derivatives of fres/kt to density and to T -------------------- +! ---------------------------------------------------------------------- + +! ---------------------------------------------------------------------- +! the analytic derivative of fres/kT to (density and T) (df_drdt) +! is still missing. A numerical differentiation is implemented. +! ---------------------------------------------------------------------- +fact = 1.0 +dist = t * 100.E-5 * fact +t_tmp = t +rho_0 = rho + + +t = t_tmp - 2.0*dist +CALL PERTURBATION_PARAMETER +eta = z3t*rho_0 +CALL P_EOS +fdr1 = pges / (eta*rho_0*(kbol*t)/1.E-30) +t = t_tmp - dist +CALL PERTURBATION_PARAMETER +eta = z3t*rho_0 +CALL P_EOS +fdr2 = pges / (eta*rho_0*(kbol*t)/1.E-30) + +t = t_tmp + dist +CALL PERTURBATION_PARAMETER +eta = z3t*rho_0 +CALL P_EOS +fdr3 = pges / (eta*rho_0*(kbol*t)/1.E-30) + +t = t_tmp + 2.0*dist +CALL PERTURBATION_PARAMETER +eta = z3t*rho_0 +CALL P_EOS +fdr4 = pges / (eta*rho_0*(kbol*t)/1.E-30) + +t = t_tmp +CALL PERTURBATION_PARAMETER +eta = z3t*rho_0 +CALL P_EOS + + +df_drdt = (-fdr4+8.0*fdr3-8.0*fdr2+fdr1)/(12.0*dist) + + + + + +! ---------------------------------------------------------------------- +! thermodynamic properties +! ---------------------------------------------------------------------- + +s_res = ( - df_dt *t - fres )*RGAS + RGAS * LOG(zges) +h_res = ( - t*df_dt + zges-1.0 ) * RGAS *t +cv_res = - ( t*df_dt2 + 2.0*df_dt ) * RGAS*t +cp_res = cv_res - RGAS + RGAS*(zges +eta*t*df_drdt)**2 & + / (1.0 + 2.0*eta*dfdr +eta**2 *ddfdrdr) + +! write (*,*) 'df_... ', df_dt,df_dt2 +! write (*,*) 'kreuz ', zges,eta*t*df_drdt,eta*dfdr, eta**2 *ddfdrdr +! write (*,*) 'h,cv,cp', h_res,cv_res,cp_res + + +END SUBROUTINE H_EOS + + + +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! SUBROUTINE H_EOS_num +! +! This subroutine calculates enthalpies and heat capacities (cp) by +! taking numerical derivatieves. +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! + SUBROUTINE H_EOS_num +! + USE PARAMETERS, ONLY: RGAS + USE EOS_VARIABLES + IMPLICIT NONE +! +!--------------------------------------------------------------------- + REAL :: dist, fact, rho_0 + REAL :: fres1, fres2, fres3, fres4, fres5 + REAL :: f_1, f_2, f_3, f_4 + REAL :: cv_res, t_tmp, zges + REAL :: df_dt, df_dtdt, df_drdt, dfdr, ddfdrdr + +!----------------------------------------------------------------------- + + +CALL PERTURBATION_PARAMETER +rho_0 = eta/z3t + + +fact = 1.0 +dist = t * 100.E-5 * fact + +t_tmp = t + +t = t_tmp - 2.0*dist +CALL PERTURBATION_PARAMETER +eta = z3t*rho_0 +CALL F_EOS +fres1 = fres +t = t_tmp - dist +CALL PERTURBATION_PARAMETER +eta = z3t*rho_0 +CALL F_EOS +fres2 = fres +t = t_tmp + dist +CALL PERTURBATION_PARAMETER +eta = z3t*rho_0 +CALL F_EOS +fres3 = fres +t = t_tmp + 2.0*dist +CALL PERTURBATION_PARAMETER +eta = z3t*rho_0 +CALL F_EOS +fres4 = fres +t = t_tmp +CALL PERTURBATION_PARAMETER +eta = z3t*rho_0 +CALL F_EOS +fres5 = fres +! *(KBOL*T)/1.E-30 + +zges = (p * 1.E-30)/(kbol*t*rho_0) + + +df_dt = (-fres4+8.0*fres3-8.0*fres2+fres1)/(12.0*dist) +df_dtdt = (-fres4+16.0*fres3-3.d1*fres5+16.0*fres2-fres1) & + /(12.0*(dist**2 )) + + +s_res = (- df_dt -fres/t)*RGAS*t + RGAS * LOG(zges) +h_res = ( - t*df_dt + zges-1.0 ) * RGAS*t +cv_res = -( t*df_dtdt + 2.0*df_dt ) * RGAS*t + + + +t = t_tmp - 2.0*dist +CALL PERTURBATION_PARAMETER +eta = z3t*rho_0 +CALL P_EOS +f_1 = pges/(eta*rho_0*(kbol*t)/1.E-30) + +t = t_tmp - dist +CALL PERTURBATION_PARAMETER +eta = z3t*rho_0 +CALL P_EOS +f_2 = pges/(eta*rho_0*(kbol*t)/1.E-30) + +t = t_tmp + dist +CALL PERTURBATION_PARAMETER +eta = z3t*rho_0 +CALL P_EOS +f_3 = pges/(eta*rho_0*(kbol*t)/1.E-30) + +t = t_tmp + 2.0*dist +CALL PERTURBATION_PARAMETER +eta = z3t*rho_0 +CALL P_EOS +f_4 = pges/(eta*rho_0*(kbol*t)/1.E-30) + +t = t_tmp +CALL PERTURBATION_PARAMETER +eta = z3t*rho_0 +CALL P_EOS + +dfdr = pges / (eta*rho_0*(kbol*t)/1.E-30) +ddfdrdr = pgesdz/(eta*rho_0*(kbol*t)/1.E-30) - dfdr*2.0/eta - 1.0/eta**2 + +df_drdt = ( -f_4 +8.0*f_3 -8.0*f_2 +f_1) / (12.0*dist) + +cp_res = cv_res - RGAS +RGAS*(zges+eta*t*df_drdt)**2 & + * 1.0/(1.0 + 2.0*eta*dfdr + eta**2 *ddfdrdr) + +! write (*,*) 'n',df_dt,df_dtdt +! write (*,*) 'kreuz ', zges,eta*t*df_drdt,eta*dfdr, eta**2 *ddfdrdr +! write (*,*) 'h, cv', h_res, cv_res +! write (*,*) h_res - t*s_res +! write (*,*) cv_res,cp_res,eta +! pause + +END SUBROUTINE H_EOS_num + + +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! SUBROUTINE DENSITY_ITERATION +! +! iterates the density until the calculated pressure 'pges' is equal to +! the specified pressure 'p'. A Newton-scheme is used for determining +! the root to the objective function f(eta) = (pges / p ) - 1.0. +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! + SUBROUTINE DENSITY_ITERATION +! + USE BASIC_VARIABLES, ONLY: num + USE EOS_VARIABLES + IMPLICIT NONE +! +! ---------------------------------------------------------------------- + INTEGER :: i, start, max_i + REAL :: eta_iteration + REAL :: error, dydx, acc_i, delta_eta +! ---------------------------------------------------------------------- + + +IF ( densav(phas) /= 0.0 .AND. eta_start == denold(phas) ) THEN + denold(phas) = eta_start + eta_start = densav(phas) +ELSE + denold(phas) = eta_start + densav(phas) = eta_start +END IF + + +acc_i = 1.d-9 +max_i = 30 +density_error(:) = 0.0 + +i = 0 +eta_iteration = eta_start + +! ---------------------------------------------------------------------- +! iterate density until p_calc = p +! ---------------------------------------------------------------------- +iterate_density: DO + + i = i + 1 + eta = eta_iteration + + IF ( num == 0 ) THEN + CALL P_EOS + ELSE IF ( num == 1 ) THEN + CALL P_NUMERICAL + ELSE IF ( num == 2 ) THEN + WRITE(*,*) 'CRITICAL RENORM NOT INCLUDED YET' + !!CALL F_EOS_RN + ELSE + write (*,*) 'define calculation option (num)' + END IF + + error = (pges / p ) - 1.0 + + ! --- instable region correction ------------------------------------- + IF ( pgesdz < 0.0 .AND. i < max_i ) THEN + IF ( error > 0.0 .AND. pgesd2 > 0.0 ) THEN ! no liquid density + CALL PRESSURE_SPINODAL + eta_iteration = eta + error = (pges / p ) - 1.0 + IF ( ((pges/p ) -1.0) > 0.0 ) eta_iteration = 0.001 ! no solution possible + IF ( ((pges/p ) -1.0) <=0.0 ) eta_iteration = eta_iteration * 1.1 ! no solution found so far + ELSE IF ( error < 0.0 .AND. pgesd2 < 0.0 ) THEN ! no vapor density + CALL PRESSURE_SPINODAL + eta_iteration = eta + error = (pges / p ) - 1.0 + IF ( ((pges/p ) -1.0) < 0.0 ) eta_iteration = 0.5 ! no solution possible + IF ( ((pges/p ) -1.0) >=0.0 ) eta_iteration = eta_iteration * 0.9 ! no solution found so far + ELSE + eta_iteration = (eta_iteration + eta_start) / 2.0 + IF (eta_iteration == eta_start) eta_iteration = eta_iteration + 0.2 + END IF + CYCLE iterate_density + END IF + + + dydx = pgesdz/p + delta_eta = error/ dydx + IF ( delta_eta > 0.05 ) delta_eta = 0.05 + IF ( delta_eta < -0.05 ) delta_eta = -0.05 + + eta_iteration = eta_iteration - delta_eta + + IF (eta_iteration > 0.9) eta_iteration = 0.6 + IF (eta_iteration <= 0.0) eta_iteration = 1.E-16 + start = 1 + + IF ( ABS(error*p/pgesdz) < 1.d-12 ) start = 0 + IF ( ABS(error) < acc_i ) start = 0 + IF ( i > max_i ) THEN + start = 0 + density_error(phas) = ABS( error ) + ! write (*,*) 'density iteration failed' + END IF + + IF (start /= 1) EXIT iterate_density + +END DO iterate_density + +eta = eta_iteration + +IF ((eta > 0.3 .AND. densav(phas) > 0.3) .OR. & + (eta < 0.1 .AND. densav(phas) < 0.1)) densav(phas) = eta + +END SUBROUTINE DENSITY_ITERATION + + + + +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! SUBROUTINE F_EOS +! +! calculates the Helmholtz energy f/kT. The input to the subroutine is +! (T,eta,x), where eta is the packing fraction. +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! + SUBROUTINE F_EOS +! + USE PARAMETERS, ONLY: nc, nsite + USE EOS_VARIABLES + USE EOS_CONSTANTS + IMPLICIT NONE +! +! --- local variables -------------------------------------------------- + INTEGER :: i, j, k, l, m, n + REAL :: z0, z1, z2, z3 + REAL :: zms, m_mean ! ,lij(nc,nc) + REAL :: I1,I2, c1_con + REAL :: fhs, fdsp, fhc + + LOGICAL :: assoc + INTEGER :: ass_cnt,max_eval + REAL :: delta(nc,nc,nsite,nsite) + REAL :: mx_itr(nc,nsite), err_sum, sum, attenu, tol, fhb + REAL :: ass_s1, ass_s2 + + REAL :: fdd, fqq, fdq +! ---------------------------------------------------------------------- + + +! ---------------------------------------------------------------------- +! abbreviations +! ---------------------------------------------------------------------- +rho = eta/z3t +z0 = z0t*rho +z1 = z1t*rho +z2 = z2t*rho +z3 = z3t*rho + +m_mean = z0t / ( PI / 6.0 ) +zms = 1.0 - eta + +! m_mean2 = 0.0 +! lij(1,2) = -0.05 +! lij(2,1) = lij(1,2) +! DO i = 1, ncomp +! DO j = 1, ncomp +! m_mean2 = m_mean2 + x(i)*x(j)*(mseg(i)+mseg(j))/2.0*(1.0-lij(i,j)) +! ENDDO +! ENDDO + + +! ---------------------------------------------------------------------- +! radial distr. function at contact, gij +! ---------------------------------------------------------------------- +DO i = 1, ncomp + DO j=1,ncomp + gij(i,j) = 1.0/zms + 3.0*dij_ab(i,j)*z2/zms/zms + 2.0*(dij_ab(i,j)*z2)**2 /zms**3 + END DO +END DO + + +! ---------------------------------------------------------------------- +! Helmholtz energy : hard sphere contribution +! ---------------------------------------------------------------------- +fhs= m_mean*( 3.0*z1*z2/zms + z2**3 /z3/zms/zms + (z2**3 /z3/z3-z0)*LOG(zms) )/z0 + + +! ---------------------------------------------------------------------- +! Helmholtz energy : chain term +! ---------------------------------------------------------------------- +fhc = 0.0 +DO i = 1, ncomp + fhc = fhc + x(i) *(1.0- mseg(i)) *LOG(gij(i,i)) +END DO + + +! ---------------------------------------------------------------------- +! Helmholtz energy : PC-SAFT dispersion contribution +! ---------------------------------------------------------------------- +IF (eos == 1) THEN + + I1 = 0.0 + I2 = 0.0 + DO m = 0, 6 + I1 = I1 + apar(m)*eta**REAL(m) + I2 = I2 + bpar(m)*eta**REAL(m) + END DO + + c1_con= 1.0/ ( 1.0 + m_mean*(8.0*eta-2.0*eta**2 )/zms**4 & + + (1.0 - m_mean)*(20.0*eta-27.0*eta**2 & + + 12.0*eta**3 -2.0*eta**4 ) /(zms*(2.0-eta))**2 ) + + fdsp = -2.0*PI*rho*I1*order1 - PI*rho*c1_con*m_mean*I2*order2 + +! ---------------------------------------------------------------------- +! Helmholtz energy : SAFT (Chen, Kreglewski) dispersion contribution +! ---------------------------------------------------------------------- +ELSE + + fdsp = 0.0 + DO n = 1,4 + DO m = 1,9 + fdsp = fdsp + dnm(n,m) * (um/t)**REAL(n) *(eta/tau)**REAL(m) + END DO + END DO + fdsp = m_mean * fdsp + +END IF + + +! ---------------------------------------------------------------------- +! TPT-1-association according to Chapman et al. +! ---------------------------------------------------------------------- +fhb = 0.0 +assoc = .false. +DO i = 1, ncomp + IF (nhb_typ(i) /= 0) assoc = .true. +END DO +IF (assoc) THEN + + DO i = 1, ncomp + DO k = 1, nhb_typ(i) + IF (mx(i,k) == 0.0) mx(i,k) = 1.0 ! Initialize mx(i,j) + DO j = 1, ncomp + DO l = 1, nhb_typ(j) + delta(i,j,k,l) = gij(i,j) * ass_d(i,j,k,l) + END DO + END DO + END DO + END DO + + +! --- constants for iteration ------------------------------------------ + attenu = 0.70 + tol = 1.d-10 + IF (eta < 0.2) tol = 1.d-12 + IF (eta < 0.01) tol = 1.d-13 + max_eval = 200 + +! --- iterate over all components and all sites ------------------------ + ass_cnt = 0 + iterate_TPT1: DO + + ass_cnt = ass_cnt + 1 + + DO i = 1, ncomp + DO k = 1, nhb_typ(i) + sum = 0.0 + DO j = 1, ncomp + DO l = 1, nhb_typ(j) + sum = sum + x(j)* mx(j,l)*nhb_no(j,l) *delta(i,j,k,l) +! if (ass_cnt == 1) write (*,*) j,l,x(j), mx(j,l) + END DO + END DO + mx_itr(i,k) = 1.0 / (1.0 + sum * rho) +! if (ass_cnt == 1) write (*,*) 'B',ass_cnt,sum, rho + END DO + END DO + + err_sum = 0.0 + DO i = 1, ncomp + DO k = 1, nhb_typ(i) + err_sum = err_sum + ABS(mx_itr(i,k) - mx(i,k)) ! / ABS(mx_itr(i,k)) + mx(i,k) = mx_itr(i,k) * attenu + mx(i,k) * (1.0 - attenu) + END DO + END DO + + IF ( err_sum <= tol .OR. ass_cnt >= max_eval ) THEN + IF (ass_cnt >= max_eval) WRITE(*,'(a,2G15.7)') 'F_EOS: Max_eval violated (mx) Err_Sum = ',err_sum,tol + EXIT iterate_TPT1 + END IF + + END DO iterate_TPT1 + + DO i = 1, ncomp + ass_s1 = 0.0 + ass_s2 = 0.0 + DO k = 1, nhb_typ(i) + ass_s1 = ass_s1 + nhb_no(i,k) * ( 1.0 - mx(i,k) ) + ass_s2 = ass_s2 + nhb_no(i,k) * LOG( mx(i,k) ) + END DO + fhb = fhb + x(i) * ( ass_s2 + ass_s1 / 2.0 ) + END DO + +END IF +! --- TPT-1-association accord. to Chapman ----------------------------- + + +! ---------------------------------------------------------------------- +! polar terms +! ---------------------------------------------------------------------- + CALL F_POLAR ( fdd, fqq, fdq ) + + +! ---------------------------------------------------------------------- +! resid. Helmholtz energy f/kT +! ---------------------------------------------------------------------- +fres = fhs + fhc + fdsp + fhb + fdd + fqq + fdq + +tfr= fres + +END SUBROUTINE F_EOS + + +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! + SUBROUTINE F_NUMERICAL +! + USE EOS_VARIABLES + USE EOS_CONSTANTS + USE EOS_NUMERICAL_DERIVATIVES, ONLY: ideal_gas, hard_sphere, chain_term, & + disp_term, hb_term, LC_term, branch_term, & + II_term, ID_term, subtract1, subtract2 + IMPLICIT NONE +! +!--------------------------------------------------------------------- + +!-----local variables------------------------------------------------- + INTEGER :: i, j + REAL :: m_mean2 + REAL :: fid, fhs, fdsp, fhc + REAL :: fhb, fdd, fqq, fdq + REAL :: fhend, fcc + REAL :: fbr, flc + REAL :: fref + + REAL :: eps_kij, k_kij +!--------------------------------------------------------------------- + +eps_kij = 0.0 +k_kij = 0.0 + +fid = 0.0 +fhs = 0.0 +fhc = 0.0 +fdsp= 0.0 +fhb = 0.0 +fdd = 0.0 +fqq = 0.0 +fdq = 0.0 +fcc = 0.0 +fbr = 0.0 +flc = 0.0 + + +CALL PERTURBATION_PARAMETER + +! ---------------------------------------------------------------------- +! overwrite the standard mixing rules by those published by Tang & Gross +! using an additional lij parameter +! WARNING : the lij parameter is set to lij = - lji in 'para_input' +! ---------------------------------------------------------------------- +order1 = 0.0 +order2 = 0.0 +DO i = 1, ncomp + DO j = 1, ncomp + order1 = order1 + x(i)*x(j)* mseg(i)*mseg(j) * sig_ij(i,j)**3 * uij(i,j)/t + order2 = order2 + x(i)*x(j)* mseg(i)*mseg(j) * sig_ij(i,j)**3 * (uij(i,j)/t)**2 + END DO +END DO +DO i = 1, ncomp + DO j = 1, ncomp + order1 = order1 + x(i)*mseg(i)/t*( x(j)*mseg(j) & + *sig_ij(i,j)*(uij(i,i)*uij(j,j))**(1.0/6.0) )**3 *lij(i,j) + END DO +END DO + + +! ---------------------------------------------------------------------- +! a non-standard mixing rule scaling the hard-sphere term +! WARNING : the lij parameter is set to lij = - lji in 'para_input' +! (uses an additional lij parameter) +! ---------------------------------------------------------------------- +m_mean2 = 0.0 +DO i = 1, ncomp + DO j = 1, ncomp + m_mean2 = m_mean2 + x(i)*x(j)*(mseg(i)+mseg(j))/2.0 + END DO +END DO +DO i = 1, ncomp + DO j = 1, ncomp + ! m_mean2=m_mean2+x(i)*(x(j)*((mseg(i)+mseg(j))*0.5)**(1.0/3.0) *lij(i,j) )**3 + END DO +END DO + +! --- ideal gas contribution ------------------------------------------- +IF ( ideal_gas == 'yes' ) CALL F_IDEAL_GAS ( fid ) +! ---------------------------------------------------------------------- + +! --- hard-sphere contribution ----------------------------------------- +IF ( hard_sphere == 'CSBM' ) CALL F_HARD_SPHERE ( m_mean2, fhs ) +! ---------------------------------------------------------------------- + +! -- chain term -------------------------------------------------------- +IF ( chain_term == 'TPT1' ) CALL F_CHAIN_TPT1 ( fhc ) +IF ( chain_term == 'TPT2' ) CALL F_CHAIN_TPT_D ( fhc ) +IF ( chain_term == 'HuLiu' ) CALL F_CHAIN_HU_LIU ( fhc ) +IF ( chain_term == 'HuLiu_rc' ) CALL F_CHAIN_HU_LIU_RC ( fhs, fhc ) +!!IF ( chain_term == 'SPT' ) CALL F_SPT ( fhs, fhc ) +IF ( chain_term == 'SPT' ) WRITE(*,*) 'SPT NOT INCLUDED YET' +! ---------------------------------------------------------------------- + +! --- dispersive attraction -------------------------------------------- +IF ( disp_term == 'PC-SAFT') CALL F_DISP_PCSAFT ( fdsp ) +IF ( disp_term == 'CK') CALL F_DISP_CKSAFT ( fdsp ) +IF ( disp_term(1:2) == 'PT') CALL F_pert_theory ( fdsp ) +! ---------------------------------------------------------------------- + +! --- H-bonding contribution / Association ----------------------------- +IF ( hb_term == 'TPT1_Chap') CALL F_ASSOCIATION( eps_kij, k_kij, fhb ) +! ---------------------------------------------------------------------- + +! --- polar terms ------------------------------------------------------ + CALL F_POLAR ( fdd, fqq, fdq ) +! ---------------------------------------------------------------------- + +! --- ion-dipole term -------------------------------------------------- +IF ( ID_term == 'TBH') CALL F_ION_DIPOLE_TBH ( fhend ) +! ---------------------------------------------------------------------- + +! --- ion-ion term ----------------------------------------------------- +IF ( II_term == 'primMSA') CALL F_ION_ION_PrimMSA ( fcc ) +IF ( II_term == 'nprMSA') CALL F_ION_ION_nonPrimMSA ( fdd, fqq, fdq, fcc ) +! ---------------------------------------------------------------------- + +! --- liquid-crystal term ---------------------------------------------- +IF ( LC_term == 'MSaupe') CALL F_LC_MayerSaupe ( flc ) + +!!IF ( LC_term == 'OVL') fref = fhs + fhc +IF ( LC_term == 'OVL') WRITE(*,*) 'OVL NOT INCLUDED YET' +!IF ( LC_term == 'OVL') CALL F_LC_OVL ( fref, flc ) +!! IF ( LC_term == 'SPT') fref = fhs + fhc +IF ( LC_term == 'SPT') WRITE(*,*) 'SPT NOT INCLUDED YET' +!!IF ( LC_term == 'SPT') CALL F_LC_SPT( fref, flc ) +! ---------------------------------------------------------------------- + +! ====================================================================== +! SUBTRACT TERMS (local density approximation) FOR DFT +! ====================================================================== + +!IF ( subtract1 == '1PT') CALL F_subtract_local_pert_theory ( subtract1, fdsp ) +!IF ( subtract1 == '2PT') CALL F_subtract_local_pert_theory ( subtract1, fdsp ) +!IF ( subtract2 =='ITTpolar') CALL F_local_ITT_polar ( fdd ) +! ---------------------------------------------------------------------- + +! ---------------------------------------------------------------------- +! residual Helmholtz energy F/(NkT) +! ---------------------------------------------------------------------- +fres = fid + fhs + fhc + fdsp + fhb + fdd + fqq + fdq + fcc + flc + +tfr = 0.0 + +END SUBROUTINE F_NUMERICAL + + + +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! SUBROUTINE P_EOS +! +! calculates the pressure in units (Pa). +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! + SUBROUTINE P_EOS +! +! ---------------------------------------------------------------------- + USE PARAMETERS, ONLY: nc, nsite + USE EOS_VARIABLES + USE EOS_CONSTANTS + IMPLICIT NONE +! +! --- local variables -------------------------------------------------- + INTEGER :: i, j, k, l, m, n + INTEGER :: ass_cnt,max_eval + LOGICAL :: assoc + REAL :: z0, z1, z2, z3 + REAL :: zms, m_mean + REAL :: zges, zgesdz, zgesd2, zgesd3 + REAL :: zhs, zhsdz, zhsd2, zhsd3 + REAL :: zhc, zhcdz, zhcd2, zhcd3 + REAL, DIMENSION(nc,nc) :: dgijdz, dgijd2, dgijd3, dgijd4 + REAL :: zdsp, zdspdz, zdspd2, zdspd3 + REAL :: c1_con, c2_con, c3_con, c4_con, c5_con + REAL :: I2, edI1dz, edI2dz, edI1d2, edI2d2 + REAL :: edI1d3, edI2d3, edI1d4, edI2d4 + REAL :: fdspdz,fdspd2 + REAL :: zhb, zhbdz, zhbd2, zhbd3 + REAL, DIMENSION(nc,nc,nsite,nsite) :: delta, dq_dz, dq_d2, dq_d3, dq_d4 + REAL, DIMENSION(nc,nsite) :: mx_itr, dmx_dz, ndmxdz, dmx_d2, ndmxd2 + REAL, DIMENSION(nc,nsite) :: dmx_d3, ndmxd3, dmx_d4, ndmxd4 + REAL :: err_sum, sum0, sum1, sum2, sum3, sum4, attenu, tol + REAL :: sum_d1, sum_d2, sum_d3, sum_d4 + REAL :: zdd, zddz, zddz2, zddz3 + REAL :: zqq, zqqz, zqqz2, zqqz3 + REAL :: zdq, zdqz, zdqz2, zdqz3 +! ---------------------------------------------------------------------- + + +! ---------------------------------------------------------------------- +! abbreviations +! ---------------------------------------------------------------------- +rho = eta/z3t +z0 = z0t*rho +z1 = z1t*rho +z2 = z2t*rho +z3 = z3t*rho + +m_mean = z0t/(PI/6.0) +zms = 1.0 -eta + +! m_mean2=0.0 +! lij(1,2)= -0.050 +! lij(2,1)=lij(1,2) +! DO i =1,ncomp +! DO j =1,ncomp +! m_mean2=m_mean2+x(i)*x(j) * (mseg(i)+mseg(j))/2.0*(1.0-lij(i,j)) +! ENDDO +! ENDDO + + +! ---------------------------------------------------------------------- +! radial distr. function at contact, gij , and derivatives +! dgijdz=d(gij)/d(eta) and dgijd2 = dd(gij)/d(eta)**2 +! ---------------------------------------------------------------------- +DO i = 1, ncomp + DO j=1,ncomp + ! j=i + gij(i,j) = 1.0/zms + 3.0*dij_ab(i,j)*z2/zms/zms + 2.0*(dij_ab(i,j)*z2)**2 /zms**3 + dgijdz(i,j)= 1.0/zms/zms + 3.0*dij_ab(i,j)*z2*(1.0+z3)/z3/zms**3 & + + (dij_ab(i,j)*z2/zms/zms)**2 *(4.0+2.0*z3)/z3 + dgijd2(i,j) = 2.0/zms**3 & + + 6.0*dij_ab(i,j)*z2/z3/zms**4 *(2.0+z3) & + + (2.0*dij_ab(i,j)*z2/z3)**2 /zms**5 *(1.0+4.0*z3+z3*z3) + dgijd3(i,j) = 6.0/zms**4 & + + 18.0*dij_ab(i,j)*z2/z3/zms**5 *(3.0+z3) & + + 12.0*(dij_ab(i,j)*z2/z3/zms**3 )**2 *(3.0+6.0*z3+z3*z3) + dgijd4(i,j) = 24.0/zms**5 & + + 72.0*dij_ab(i,j)*z2/z3/zms**6 *(4.0+z3) & + + 48.0*(dij_ab(i,j)*z2/z3)**2 /zms**7 *(6.0+8.0*z3+z3*z3) + END DO +END DO + + +! ---------------------------------------------------------------------- +! p : hard sphere contribution +! ---------------------------------------------------------------------- +zhs = m_mean* ( z3/zms + 3.0*z1*z2/z0/zms/zms + z2**3 /z0*(3.0-z3)/zms**3 ) +zhsdz = m_mean*( 1.0/zms/zms + 3.0*z1*z2/z0/z3*(1.0+z3)/zms**3 & + + 6.0*z2**3 /z0/z3/zms**4 ) +zhsd2 = m_mean*( 2.0/zms**3 + 6.0*z1*z2/z0/z3*(2.0+z3)/zms**4 & + + 6.0*z2**3 /z0/z3/z3*(1.0+3.0*z3)/zms**5 ) +zhsd3 = m_mean*( 6.0/zms**4 + 18.0*z1*z2/z0/z3*(3.0+z3)/zms**5 & + + 24.0*z2**3 /z0/z3/z3*(2.0+3.0*z3)/zms**6 ) + + +! ---------------------------------------------------------------------- +! p : chain term +! ---------------------------------------------------------------------- +zhc = 0.0 +zhcdz = 0.0 +zhcd2 = 0.0 +zhcd3 = 0.0 +DO i= 1, ncomp + zhc = zhc + x(i)*(1.0-mseg(i))*eta/gij(i,i)* dgijdz(i,i) + zhcdz = zhcdz + x(i)*(1.0-mseg(i)) *(-eta*(dgijdz(i,i)/gij(i,i))**2 & + + dgijdz(i,i)/gij(i,i) + eta/gij(i,i)*dgijd2(i,i)) + zhcd2 = zhcd2 + x(i)*(1.0-mseg(i)) & + *( 2.0*eta*(dgijdz(i,i)/gij(i,i))**3 & + -2.0*(dgijdz(i,i)/gij(i,i))**2 & + -3.0*eta/gij(i,i)**2 *dgijdz(i,i)*dgijd2(i,i) & + +2.0/gij(i,i)*dgijd2(i,i) +eta/gij(i,i)*dgijd3(i,i) ) + zhcd3 = zhcd3 + x(i)*(1.0-mseg(i)) *( 6.0*(dgijdz(i,i)/gij(i,i))**3 & + -6.0*eta*(dgijdz(i,i)/gij(i,i))**4 & + +12.0*eta/gij(i,i)**3 *dgijdz(i,i)**2 *dgijd2(i,i) & + -9.0/gij(i,i)**2 *dgijdz(i,i)*dgijd2(i,i) +3.0/gij(i,i)*dgijd3(i,i) & + -3.0*eta*(dgijd2(i,i)/gij(i,i))**2 & + -4.0*eta/gij(i,i)**2 *dgijdz(i,i)*dgijd3(i,i) & + +eta/gij(i,i)*dgijd4(i,i) ) +END DO + +! ---------------------------------------------------------------------- +! p : PC-SAFT dispersion contribution +! note: edI1dz is equal to d(eta*I1)/d(eta), analogous for edI2dz +! ---------------------------------------------------------------------- +IF (eos == 1) THEN + + I2 = 0.0 + edI1dz = 0.0 + edI2dz = 0.0 + edI1d2 = 0.0 + edI2d2 = 0.0 + edI1d3 = 0.0 + edI2d3 = 0.0 + edI1d4 = 0.0 + edI2d4 = 0.0 + DO m=0,6 + I2 = I2 + bpar(m)*z3**REAL(m) + edI1dz= edI1dz+apar(m)*REAL(m+1)*z3**REAL(m) + edI2dz= edI2dz+bpar(m)*REAL(m+1)*z3**REAL(m) + edI1d2= edI1d2+apar(m)*REAL((m+1)*m)*z3**REAL(m-1) + edI2d2= edI2d2+bpar(m)*REAL((m+1)*m)*z3**REAL(m-1) + edI1d3= edI1d3+apar(m)*REAL((m+1)*m*(m-1))*z3**REAL(m-2) + edI2d3= edI2d3+bpar(m)*REAL((m+1)*m*(m-1))*z3**REAL(m-2) + edI1d4= edI1d4+apar(m)*REAL((m+1)*m*(m-1)*(m-2))*z3**REAL(m-3) + edI2d4= edI2d4+bpar(m)*REAL((m+1)*m*(m-1)*(m-2))*z3**REAL(m-3) + END DO + + c1_con= 1.0/ ( 1.0 + m_mean*(8.0*eta-2.0*eta**2 )/zms**4 & + + (1.0 - m_mean)*(20.0*eta-27.0*eta**2 & + + 12.0*eta**3 -2.0*eta**4 ) /(zms*(2.0-eta))**2 ) + c2_con= - c1_con*c1_con & + *(m_mean*(-4.0*eta**2 +20.0*eta+8.0)/zms**5 + (1.0 - m_mean) & + *(2.0*eta**3 +12.0*eta**2 -48.0*eta+40.0) & + /(zms*(2.0-eta))**3 ) + c3_con= 2.0 * c2_con*c2_con/c1_con - c1_con*c1_con & + *( m_mean*(-12.0*eta**2 +72.0*eta+60.0)/zms**6 & + + (1.0 - m_mean) & + *(-6.0*eta**4 -48.0*eta**3 +288.0*eta**2 & + -480.0*eta+264.0) /(zms*(2.0-eta))**4 ) + c4_con= 6.0*c2_con*c3_con/c1_con -6.0*c2_con**3 /c1_con**2 & + - c1_con*c1_con & + *( m_mean*(-48.0*eta**2 +336.0*eta+432.0)/zms**7 & + + (1.0 - m_mean) & + *(24.0*eta**5 +240.0*eta**4 -1920.0*eta**3 & + +4800.0*eta**2 -5280.0*eta+2208.0) /(zms*(2.0-eta))**5 ) + c5_con= 6.0*c3_con**2 /c1_con - 36.0*c2_con**2 /c1_con**2 *c3_con & + + 8.0*c2_con/c1_con*c4_con+24.0*c2_con**4 /c1_con**3 & + - c1_con*c1_con & + *( m_mean*(-240.0*eta**2 +1920.0*eta+3360.0)/zms**8 & + + (1.0 - m_mean) & + *(-120.0*eta**6 -1440.0*eta**5 +14400.0*eta**4 & + -48000.0*eta**3 +79200.0*eta**2 -66240.0*eta+22560.0) & + /(zms*(2.0-eta))**6 ) + + zdsp = - 2.0*PI*rho*edI1dz*order1 & + - PI*rho*order2*m_mean*(c2_con*I2*eta + c1_con*edI2dz) + zdspdz= zdsp/eta - 2.0*PI*rho*edI1d2*order1 & + - PI*rho*order2*m_mean*(c3_con*I2*eta & + + 2.0*c2_con*edI2dz + c1_con*edI2d2) + zdspd2= -2.0*zdsp/eta/eta +2.0*zdspdz/eta & + - 2.0*PI*rho*edI1d3*order1 - PI*rho*order2*m_mean*(c4_con*I2*eta & + + 3.0*c3_con*edI2dz +3.0*c2_con*edI2d2 +c1_con*edI2d3) + zdspd3= 6.0*zdsp/eta**3 -6.0*zdspdz/eta/eta & + + 3.0*zdspd2/eta - 2.0*PI*rho*edI1d4*order1 & + - PI*rho*order2*m_mean*(c5_con*I2*eta & + + 4.0*c4_con*edI2dz +6.0*c3_con*edI2d2 & + + 4.0*c2_con*edI2d3 + c1_con*edI2d4) + + +! ---------------------------------------------------------------------- +! p : SAFT (Chen & Kreglewski) dispersion contribution +! ---------------------------------------------------------------------- +ELSE + + fdspdz = 0.0 + fdspd2 = 0.0 + DO n = 1,4 + DO m = 1,9 + fdspdz = fdspdz + m_mean/tau * dnm(n,m) * (um/t)**REAL(n) *REAL(m)*(eta/tau)**REAL(m-1) + END DO + DO m= 2,9 + fdspd2= fdspd2 + m_mean/tau * dnm(n,m)*(um/t)**REAL(n) *REAL(m)*REAL(m-1) & + * (eta/tau)**REAL(m-2) * 1.0/tau + END DO + END DO + zdsp = eta * fdspdz + zdspdz = (2.0*fdspdz + eta*fdspd2) - zdsp/z3 + +END IF +! --- end of dispersion contribution ----------------------------------- + + +! ---------------------------------------------------------------------- +! p: TPT-1-association accord. to Chapman et al. +! ---------------------------------------------------------------------- +zhb = 0.0 +zhbdz = 0.0 +zhbd2 = 0.0 +zhbd3 = 0.0 +assoc = .false. +DO i = 1,ncomp + IF (nhb_typ(i) /= 0) assoc = .true. +END DO +IF (assoc) THEN + + DO j = 1, ncomp + DO i = 1, nhb_typ(j) + DO k = 1, ncomp + DO l = 1, nhb_typ(k) + delta(j,k,i,l) = gij(j,k) * ass_d(j,k,i,l) + dq_dz(j,k,i,l) = dgijdz(j,k) * ass_d(j,k,i,l) + dq_d2(j,k,i,l) = dgijd2(j,k) * ass_d(j,k,i,l) + dq_d3(j,k,i,l) = dgijd3(j,k) * ass_d(j,k,i,l) + dq_d4(j,k,i,l) = dgijd4(j,k) * ass_d(j,k,i,l) + END DO + END DO + END DO + END DO + +! --- constants for iteration ------------------------------------------ + attenu = 0.7 + tol = 1.d-10 + IF ( eta < 0.2 ) tol = 1.d-12 + IF ( eta < 0.01 ) tol = 1.d-13 + IF ( eta < 1.E-6) tol = 1.d-15 + max_eval = 1000 + +! --- initialize mx(i,j) ----------------------------------------------- + DO i = 1, ncomp + DO j = 1, nhb_typ(i) + mx(i,j) = 1.0 + dmx_dz(i,j) = 0.0 + dmx_d2(i,j) = 0.0 + dmx_d3(i,j) = 0.0 + dmx_d4(i,j) = 0.0 + END DO + END DO + +! --- iterate over all components and all sites ------------------------ + ass_cnt = 0 + err_sum = tol + 1.0 + DO WHILE ( err_sum > tol .AND. ass_cnt <= max_eval) + ass_cnt = ass_cnt + 1 + DO i = 1, ncomp + DO j = 1, nhb_typ(i) + sum0 = 0.0 + sum1 = 0.0 + sum2 = 0.0 + sum3 = 0.0 + sum4 = 0.0 + DO k = 1, ncomp + DO l = 1, nhb_typ(k) + sum0 =sum0 +x(k)*nhb_no(k,l)* mx(k,l)* delta(i,k,j,l) + sum1 =sum1 +x(k)*nhb_no(k,l)*( mx(k,l)* dq_dz(i,k,j,l) & + + dmx_dz(k,l)* delta(i,k,j,l)) + sum2 =sum2 +x(k)*nhb_no(k,l)*( mx(k,l)* dq_d2(i,k,j,l) & + + 2.0*dmx_dz(k,l)* dq_dz(i,k,j,l) & + + dmx_d2(k,l)* delta(i,k,j,l)) + sum3 =sum3 +x(k)*nhb_no(k,l)*( mx(k,l)* dq_d3(i,k,j,l) & + + 3.0*dmx_dz(k,l)* dq_d2(i,k,j,l) & + + 3.0*dmx_d2(k,l)* dq_dz(i,k,j,l) & + + dmx_d3(k,l)* delta(i,k,j,l)) + sum4 =sum4 + x(k)*nhb_no(k,l)*( mx(k,l)* dq_d4(i,k,j,l) & + + 4.0*dmx_dz(k,l)* dq_d3(i,k,j,l) & + + 6.0*dmx_d2(k,l)* dq_d2(i,k,j,l) & + + 4.0*dmx_d3(k,l)* dq_dz(i,k,j,l) & + + dmx_d4(k,l)* delta(i,k,j,l)) + END DO + END DO + mx_itr(i,j)= 1.0 / (1.0 + sum0 * rho) + ndmxdz(i,j)= -(mx_itr(i,j)*mx_itr(i,j))* (sum0/z3t +sum1*rho) + ndmxd2(i,j)= + 2.0/mx_itr(i,j)*ndmxdz(i,j)*ndmxdz(i,j) & + - (mx_itr(i,j)*mx_itr(i,j)) * (2.0/z3t*sum1 + rho*sum2) + ndmxd3(i,j)= - 6.0/mx_itr(i,j)**2 *ndmxdz(i,j)**3 & + + 6.0/mx_itr(i,j)*ndmxdz(i,j)*ndmxd2(i,j) - mx_itr(i,j)*mx_itr(i,j) & + * (3.0/z3t*sum2 + rho*sum3) + ndmxd4(i,j)= 24.0/mx_itr(i,j)**3 *ndmxdz(i,j)**4 & + -36.0/mx_itr(i,j)**2 *ndmxdz(i,j)**2 *ndmxd2(i,j) & + +6.0/mx_itr(i,j)*ndmxd2(i,j)**2 & + +8.0/mx_itr(i,j)*ndmxdz(i,j)*ndmxd3(i,j) - mx_itr(i,j)**2 & + *(4.0/z3t*sum3 + rho*sum4) + END DO + END DO + + err_sum = 0.0 + DO i = 1, ncomp + DO j = 1, nhb_typ(i) + err_sum = err_sum + ABS(mx_itr(i,j) - mx(i,j)) & + + ABS(ndmxdz(i,j) - dmx_dz(i,j)) + ABS(ndmxd2(i,j) - dmx_d2(i,j)) + mx(i,j) = mx_itr(i,j)*attenu + mx(i,j) * (1.0-attenu) + dmx_dz(i,j) = ndmxdz(i,j)*attenu + dmx_dz(i,j) * (1.0-attenu) + dmx_d2(i,j) = ndmxd2(i,j)*attenu + dmx_d2(i,j) * (1.0-attenu) + dmx_d3(i,j) = ndmxd3(i,j)*attenu + dmx_d3(i,j) * (1.0-attenu) + dmx_d4(i,j) = ndmxd4(i,j)*attenu + dmx_d4(i,j) * (1.0-attenu) + END DO + END DO + END DO + + IF ( ass_cnt >= max_eval .AND. err_sum > SQRT(tol) ) THEN + WRITE (*,'(a,2G15.7)') 'P_EOS: Max_eval violated (mx) Err_Sum= ',err_sum,tol + ! stop + END IF + + + ! --- calculate the hydrogen-bonding contribution -------------------- + DO i = 1, ncomp + sum_d1 = 0.0 + sum_d2 = 0.0 + sum_d3 = 0.0 + sum_d4 = 0.0 + DO j = 1, nhb_typ(i) + sum_d1= sum_d1 +nhb_no(i,j)* dmx_dz(i,j)*(1.0/mx(i,j)-0.5) + sum_d2= sum_d2 +nhb_no(i,j)*(dmx_d2(i,j)*(1.0/mx(i,j)-0.5) & + -(dmx_dz(i,j)/mx(i,j))**2 ) + sum_d3= sum_d3 +nhb_no(i,j)*(dmx_d3(i,j)*(1.0/mx(i,j)-0.5) & + -3.0/mx(i,j)**2 *dmx_dz(i,j)*dmx_d2(i,j) + 2.0*(dmx_dz(i,j)/mx(i,j))**3 ) + sum_d4= sum_d4 +nhb_no(i,j)*(dmx_d4(i,j)*(1.0/mx(i,j)-0.5) & + -4.0/mx(i,j)**2 *dmx_dz(i,j)*dmx_d3(i,j) & + + 12.0/mx(i,j)**3 *dmx_dz(i,j)**2 *dmx_d2(i,j) & + - 3.0/mx(i,j)**2 *dmx_d2(i,j)**2 - 6.0*(dmx_dz(i,j)/mx(i,j))**4 ) + END DO + zhb = zhb + x(i) * eta * sum_d1 + zhbdz = zhbdz + x(i) * eta * sum_d2 + zhbd2 = zhbd2 + x(i) * eta * sum_d3 + zhbd3 = zhbd3 + x(i) * eta * sum_d4 + END DO + zhbdz = zhbdz + zhb/eta + zhbd2 = zhbd2 + 2.0/eta*zhbdz-2.0/eta**2 *zhb + zhbd3 = zhbd3 - 6.0/eta**2 *zhbdz+3.0/eta*zhbd2 + 6.0/eta**3 *zhb +END IF +! --- TPT-1-association accord. to Chapman ----------------------------- + + +! ---------------------------------------------------------------------- +! p: polar terms +! ---------------------------------------------------------------------- +CALL P_POLAR ( zdd, zddz, zddz2, zddz3, zqq, zqqz, zqqz2, zqqz3, zdq, zdqz, zdqz2, zdqz3 ) + + +! ---------------------------------------------------------------------- +! compressibility factor z and total p +! as well as derivatives d(z)/d(eta) and d(p)/d(eta) with unit [Pa] +! ---------------------------------------------------------------------- +zges = 1.0 + zhs + zhc + zdsp + zhb + zdd + zqq + zdq +zgesdz = zhsdz + zhcdz + zdspdz + zhbdz + zddz + zqqz + zdqz +zgesd2 = zhsd2 + zhcd2 + zdspd2 + zhbd2 + zddz2 +zqqz2+zdqz2 +zgesd3 = zhsd3 + zhcd3 + zdspd3 + zhbd3 + zddz3 +zqqz3+zdqz3 + +pges = zges *rho *(kbol*t)/1.d-30 +pgesdz = ( zgesdz*rho + zges*rho/z3 )*(kbol*t)/1.d-30 +pgesd2 = ( zgesd2*rho + 2.0*zgesdz*rho/z3 )*(kbol*t)/1.d-30 +pgesd3 = ( zgesd3*rho + 3.0*zgesd2*rho/z3 )*(kbol*t)/1.d-30 + +END SUBROUTINE P_EOS + + + + +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! + SUBROUTINE PHI_POLAR ( k, z3_rk, fdd_rk, fqq_rk, fdq_rk ) +! + USE EOS_VARIABLES, ONLY: ncomp, parame, dd_term, qq_term, dq_term + IMPLICIT NONE +! +! ---------------------------------------------------------------------- + INTEGER, INTENT(IN) :: k + REAL, INTENT(IN) :: z3_rk + REAL, INTENT(OUT) :: fdd_rk, fqq_rk, fdq_rk +! +! --- local variables--------------------------------------------------- + INTEGER :: dipole + INTEGER :: quadrupole + INTEGER :: dipole_quad +! ---------------------------------------------------------------------- + + fdd_rk = 0.0 + fqq_rk = 0.0 + fdq_rk = 0.0 + + dipole = 0 + quadrupole = 0 + dipole_quad = 0 + IF ( SUM( parame(1:ncomp,6) ) /= 0.0 ) dipole = 1 + IF ( SUM( parame(1:ncomp,7) ) /= 0.0 ) quadrupole = 1 + IF ( dipole == 1 .AND. quadrupole == 1 ) dipole_quad = 1 + + ! -------------------------------------------------------------------- + ! dipole-dipole term + ! -------------------------------------------------------------------- + IF (dipole == 1) THEN + + IF (dd_term == 'GV') CALL PHI_DD_GROSS_VRABEC( k, z3_rk, fdd_rk ) + ! IF (dd_term == 'SF') CALL PHI_DD_SAAGER_FISCHER( k ) + + IF (dd_term /= 'GV' .AND. dd_term /= 'SF') write (*,*) 'specify dipole term !' + + ENDIF + + ! -------------------------------------------------------------------- + ! quadrupole-quadrupole term + ! -------------------------------------------------------------------- + IF (quadrupole == 1) THEN + + !IF (qq_term == 'SF') CALL PHI_QQ_SAAGER_FISCHER( k ) + IF (qq_term == 'JG') CALL PHI_QQ_GROSS( k, z3_rk, fqq_rk ) + + IF (qq_term /= 'JG' .AND. qq_term /= 'SF') write (*,*) 'specify quadrupole term !' + + ENDIF + + ! -------------------------------------------------------------------- + ! dipole-quadrupole cross term + ! -------------------------------------------------------------------- + IF (dipole_quad == 1) THEN + + IF (dq_term == 'VG') CALL PHI_DQ_VRABEC_GROSS( k, z3_rk, fdq_rk ) + + IF (dq_term /= 'VG' ) write (*,*) 'specify DQ-cross term !' + + ENDIF + +END SUBROUTINE PHI_POLAR + + +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! + SUBROUTINE PHI_DD_GROSS_VRABEC( k, z3_rk, fdd_rk ) +! + USE PARAMETERS, ONLY: PI, KBOL + USE EOS_VARIABLES, ONLY: nc, ncomp, uij, parame, mseg, sig_ij, rho, eta, x, t + USE EOS_CONSTANTS, ONLY: ddp2, ddp3, ddp4 + IMPLICIT NONE +! +! ---------------------------------------------------------------------- + INTEGER, INTENT(IN) :: k + REAL, INTENT(IN) :: z3_rk + REAL, INTENT(IN OUT) :: fdd_rk +! +! --- local variables--------------------------------------------------- + INTEGER :: i, j, l, m + + REAL :: factor2, factor3, z3 + REAL :: xijfa, xijkfa, xijfa_x, xijkf_x, eij + REAL :: fdd2, fdd3, fdd2x, fdd3x + REAL, DIMENSION(nc) :: my2dd + REAL, DIMENSION(nc,nc) :: Idd2, Idd4, Idd2x, Idd4x + REAL, DIMENSION(nc,nc,nc) :: Idd3, Idd3x +! ---------------------------------------------------------------------- + + + fdd_rk = 0.0 + z3 = eta + DO i = 1, ncomp + IF ( uij(i,i) == 0.0 ) write (*,*) 'PHI_DD_GROSS_VRABEC: do not use dimensionless units' + IF ( uij(i,i) == 0.0 ) stop + my2dd(i) = (parame(i,6))**2 *1.E-49 / (uij(i,i)*KBOL*mseg(i)*sig_ij(i,i)**3 *1.E-30) + END DO + + DO i = 1, ncomp + DO j = 1, ncomp + Idd2(i,j) = 0.0 + Idd4(i,j) = 0.0 + Idd2x(i,j) = 0.0 + Idd4x(i,j) = 0.0 + IF (parame(i,6) /= 0.0 .AND. parame(j,6) /= 0.0) THEN + DO m=0,4 + Idd2(i,j) =Idd2(i,j) + ddp2(i,j,m)*z3**m + Idd4(i,j) =Idd4(i,j) + ddp4(i,j,m)*z3**m + Idd2x(i,j) =Idd2x(i,j)+ ddp2(i,j,m)*REAL(m)*z3**(m-1)*z3_rk + Idd4x(i,j) =Idd4x(i,j)+ ddp4(i,j,m)*REAL(m)*z3**(m-1)*z3_rk + END DO + DO l = 1, ncomp + Idd3(i,j,l) = 0.0 + Idd3x(i,j,l) = 0.0 + IF (parame(l,6) /= 0.0) THEN + DO m=0,4 + Idd3(i,j,l) =Idd3(i,j,l) +ddp3(i,j,l,m)*z3**m + Idd3x(i,j,l)=Idd3x(i,j,l)+ddp3(i,j,l,m)*REAL(m)*z3**(m-1)*z3_rk + END DO + END IF + END DO + END IF + END DO + END DO + + factor2= -PI + factor3= -4.0/3.0*PI**2 + + fdd2 = 0.0 + fdd3 = 0.0 + fdd2x = 0.0 + fdd3x = 0.0 + DO i = 1, ncomp + xijfa_x = 2.0*x(i)*rho*uij(i,i)*my2dd(i)*sig_ij(i,i)**3 /t & + *uij(k,k)*my2dd(k)*sig_ij(k,k)**3 /t/sig_ij(i,k)**3 + eij = (parame(i,3)*parame(k,3))**0.5 + fdd2x = fdd2x + factor2*xijfa_x*( Idd2(i,k) + eij/t*Idd4(i,k) ) + DO j = 1, ncomp + IF (parame(i,6) /= 0.0 .AND. parame(j,6) /= 0.0) THEN + xijfa =x(i)*rho*uij(i,i)*my2dd(i)*sig_ij(i,i)**3 /t & + *x(j)*rho*uij(j,j)*my2dd(j)*sig_ij(j,j)**3 /t/sig_ij(i,j)**3 + eij = (parame(i,3)*parame(j,3))**0.5 + fdd2= fdd2 +factor2*xijfa*(Idd2(i,j) +eij/t*Idd4(i,j) ) + fdd2x =fdd2x +factor2*xijfa*(Idd2x(i,j)+eij/t*Idd4x(i,j)) + !--------------------- + xijkf_x=x(i)*rho*uij(i,i)*my2dd(i)*sig_ij(i,i)**3 /t/sig_ij(i,j) & + *x(j)*rho*uij(j,j)*my2dd(j)*sig_ij(j,j)**3 /t/sig_ij(i,k) & + *3.0* uij(k,k)*my2dd(k)*sig_ij(k,k)**3 /t/sig_ij(j,k) + fdd3x=fdd3x+factor3*xijkf_x*Idd3(i,j,k) + DO l=1,ncomp + IF (parame(l,6) /= 0.0) THEN + xijkfa= x(i)*rho*uij(i,i)/t*my2dd(i)*sig_ij(i,i)**3 & + *x(j)*rho*uij(j,j)/t*my2dd(j)*sig_ij(j,j)**3 & + *x(l)*rho*uij(l,l)/t*my2dd(l)*sig_ij(l,l)**3 & + /sig_ij(i,j)/sig_ij(i,l)/sig_ij(j,l) + fdd3 =fdd3 + factor3 * xijkfa *Idd3(i,j,l) + fdd3x =fdd3x + factor3 * xijkfa *Idd3x(i,j,l) + END IF + END DO + END IF + END DO + END DO + + IF (fdd2 < -1.E-50 .AND. fdd3 /= 0.0 .AND. fdd2x /= 0.0 .AND. fdd3x /= 0.0)THEN + + fdd_rk = fdd2* (fdd2*fdd2x - 2.0*fdd3*fdd2x+fdd2*fdd3x) / (fdd2-fdd3)**2 + + END IF + +END SUBROUTINE PHI_DD_GROSS_VRABEC + + + +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! + SUBROUTINE PHI_QQ_GROSS( k, z3_rk, fqq_rk ) +! + USE PARAMETERS, ONLY: PI, KBOL + USE EOS_VARIABLES, ONLY: nc, ncomp, uij, parame, mseg, sig_ij, rho, eta, x, t + USE EOS_CONSTANTS, ONLY: qqp2, qqp3, qqp4 + IMPLICIT NONE +! +! ---------------------------------------------------------------------- + INTEGER, INTENT(IN) :: k + REAL, INTENT(IN) :: z3_rk + REAL, INTENT(IN OUT) :: fqq_rk +! +! --- local variables--------------------------------------------------- + INTEGER :: i, j, l, m + + REAL :: factor2, factor3, z3 + REAL :: xijfa, xijkfa, xijfa_x, xijkf_x, eij + REAL :: fqq2, fqq3, fqq2x, fqq3x + REAL, DIMENSION(nc) :: qq2 + REAL, DIMENSION(nc,nc) :: Iqq2, Iqq4, Iqq2x, Iqq4x + REAL, DIMENSION(nc,nc,nc) :: Iqq3, Iqq3x +! ---------------------------------------------------------------------- + + + fqq_rk = 0.0 + z3 = eta + DO i = 1, ncomp + IF ( uij(i,i) == 0.0 ) write (*,*) 'PHI_QQ_GROSS: do not use dimensionless units' + qq2(i) = (parame(i,7))**2 *1.E-69 / (uij(i,i)*kbol*mseg(i)*sig_ij(i,i)**5 *1.E-50) + END DO + + DO i = 1, ncomp + DO j = 1, ncomp + Iqq2(i,j) = 0.0 + Iqq4(i,j) = 0.0 + Iqq2x(i,j) = 0.0 + Iqq4x(i,j) = 0.0 + IF (parame(i,7) /= 0.0 .AND. parame(j,7) /= 0.0) THEN + DO m = 0, 4 + Iqq2(i,j) = Iqq2(i,j) + qqp2(i,j,m) * z3**m + Iqq4(i,j) = Iqq4(i,j) + qqp4(i,j,m) * z3**m + Iqq2x(i,j) = Iqq2x(i,j) + qqp2(i,j,m) * REAL(m)*z3**(m-1)*z3_rk + Iqq4x(i,j) = Iqq4x(i,j) + qqp4(i,j,m) * REAL(m)*z3**(m-1)*z3_rk + END DO + DO l = 1, ncomp + Iqq3(i,j,l) = 0.0 + Iqq3x(i,j,l) = 0.0 + IF (parame(l,7) /= 0.0) THEN + DO m = 0, 4 + Iqq3(i,j,l) = Iqq3(i,j,l) + qqp3(i,j,l,m)*z3**m + Iqq3x(i,j,l) = Iqq3x(i,j,l) + qqp3(i,j,l,m)*REAL(m) *z3**(m-1)*z3_rk + END DO + END IF + END DO + END IF + END DO + END DO + + factor2= -9.0/16.0*PI + factor3= 9.0/16.0*PI**2 + + fqq2 = 0.0 + fqq3 = 0.0 + fqq2x = 0.0 + fqq3x = 0.0 + DO i = 1, ncomp + xijfa_x = 2.0*x(i)*rho*uij(i,i)*qq2(i)*sig_ij(i,i)**5 /t & + *uij(k,k)*qq2(k)*sig_ij(k,k)**5 /t/sig_ij(i,k)**7.0 + eij = (parame(i,3)*parame(k,3))**0.5 + fqq2x =fqq2x +factor2*xijfa_x*(Iqq2(i,k)+eij/t*Iqq4(i,k)) + DO j=1,ncomp + IF (parame(i,7) /= 0.0 .AND. parame(j,7) /= 0.0) THEN + xijfa =x(i)*rho*uij(i,i)*qq2(i)*sig_ij(i,i)**5 /t & + *x(j)*rho*uij(j,j)*qq2(j)*sig_ij(j,j)**5 /t/sig_ij(i,j)**7.0 + eij = (parame(i,3)*parame(j,3))**0.5 + fqq2= fqq2 +factor2*xijfa*(Iqq2(i,j) +eij/t*Iqq4(i,j) ) + fqq2x =fqq2x +factor2*xijfa*(Iqq2x(i,j)+eij/t*Iqq4x(i,j)) + ! ------------------ + xijkf_x=x(i)*rho*uij(i,i)*qq2(i)*sig_ij(i,i)**5 /t/sig_ij(i,j)**3 & + *x(j)*rho*uij(j,j)*qq2(j)*sig_ij(j,j)**5 /t/sig_ij(i,k)**3 & + *3.0* uij(k,k)*qq2(k)*sig_ij(k,k)**5 /t/sig_ij(j,k)**3 + fqq3x = fqq3x + factor3*xijkf_x*Iqq3(i,j,k) + DO l = 1, ncomp + IF (parame(l,7) /= 0.0) THEN + xijkfa=x(i)*rho*uij(i,i)*qq2(i)*sig_ij(i,i)**5 /t/sig_ij(i,j)**3 & + *x(j)*rho*uij(j,j)*qq2(j)*sig_ij(j,j)**5 /t/sig_ij(i,l)**3 & + *x(l)*rho*uij(l,l)*qq2(l)*sig_ij(l,l)**5 /t/sig_ij(j,l)**3 + fqq3 =fqq3 + factor3 * xijkfa *Iqq3(i,j,l) + fqq3x =fqq3x + factor3 * xijkfa *Iqq3x(i,j,l) + END IF + END DO + END IF + END DO + END DO + + IF (fqq2 < -1.E-50 .AND. fqq3 /= 0.0 .AND. fqq2x /= 0.0 .AND. fqq3x /= 0.0) THEN + fqq_rk = fqq2* (fqq2*fqq2x - 2.0*fqq3*fqq2x+fqq2*fqq3x) / (fqq2-fqq3)**2 + END IF + +END SUBROUTINE PHI_QQ_GROSS + +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! + SUBROUTINE PHI_DQ_VRABEC_GROSS( k, z3_rk, fdq_rk ) +! + USE PARAMETERS, ONLY: PI, KBOL + USE EOS_VARIABLES, ONLY: nc, ncomp, uij, parame, mseg, sig_ij, rho, eta, x, t + USE EOS_CONSTANTS, ONLY: dqp2, dqp3, dqp4 + IMPLICIT NONE +! +! ---------------------------------------------------------------------- + INTEGER, INTENT(IN) :: k + REAL, INTENT(IN) :: z3_rk + REAL, INTENT(IN OUT) :: fdq_rk +! +! --- local variables--------------------------------------------------- + INTEGER :: i, j, l, m + + REAL :: factor2, factor3, z3 + REAL :: xijfa, xijkfa, xijfa_x, xijkf_x, eij + REAL :: fdq2, fdq3, fdq2x, fdq3x + REAL, DIMENSION(nc) :: my2dd, myfac, qq2, q_fac + REAL, DIMENSION(nc,nc) :: Idq2, Idq4, Idq2x, Idq4x + REAL, DIMENSION(nc,nc,nc) :: Idq3, Idq3x +! ---------------------------------------------------------------------- + + fdq_rk = 0.0 + z3 = eta + DO i=1,ncomp + my2dd(i) = (parame(i,6))**2 *1.E-49 / (uij(i,i)*KBOL*mseg(i)*sig_ij(i,i)**3 *1.E-30) + myfac(i) = parame(i,3)/t*parame(i,2)**4 *my2dd(i) + qq2(i) = (parame(i,7))**2 *1.E-69 / (uij(i,i)*kbol*mseg(i)*sig_ij(i,i)**5 *1.E-50) + q_fac(i) = parame(i,3)/t*parame(i,2)**4 *qq2(i) + END DO + + DO i = 1, ncomp + DO j = 1, ncomp + Idq2(i,j) = 0.0 + Idq4(i,j) = 0.0 + Idq2x(i,j) = 0.0 + Idq4x(i,j) = 0.0 + DO m = 0, 4 + Idq2(i,j) = Idq2(i,j) + dqp2(i,j,m)*z3**m + Idq4(i,j) = Idq4(i,j) + dqp4(i,j,m)*z3**m + Idq2x(i,j) = Idq2x(i,j) + dqp2(i,j,m)*REAL(m)*z3**(m-1) *z3_rk + Idq4x(i,j) = Idq4x(i,j) + dqp4(i,j,m)*REAL(m)*z3**(m-1) *z3_rk + END DO + DO l = 1, ncomp + Idq3(i,j,l) = 0.0 + Idq3x(i,j,l) = 0.0 + DO m = 0, 4 + Idq3(i,j,l) =Idq3(i,j,l) +dqp3(i,j,l,m)*z3**m + Idq3x(i,j,l)=Idq3x(i,j,l)+dqp3(i,j,l,m)*REAL(m)*z3**(m-1)*z3_rk + END DO + END DO + END DO + END DO + + factor2= -9.0/4.0*PI + factor3= PI**2 + + fdq2 = 0.0 + fdq3 = 0.0 + fdq2x = 0.0 + fdq3x = 0.0 + DO i = 1, ncomp + xijfa_x = x(i)*rho*( myfac(i)*q_fac(k) + myfac(k)*q_fac(i) ) / sig_ij(i,k)**5 + eij = (parame(i,3)*parame(k,3))**0.5 + fdq2x =fdq2x +factor2*xijfa_x*(Idq2(i,k)+eij/t*Idq4(i,k)) + DO j=1,ncomp + xijfa =x(i)*rho*myfac(i) * x(j)*rho*q_fac(j) /sig_ij(i,j)**5 + eij = (parame(i,3)*parame(j,3))**0.5 + fdq2= fdq2 +factor2*xijfa*(Idq2(i,j) +eij/t*Idq4(i,j) ) + fdq2x =fdq2x +factor2*xijfa*(Idq2x(i,j) +eij/t*Idq4x(i,j)) + !--------------------- + xijkf_x=x(i)*rho*x(j)*rho/(sig_ij(i,j)*sig_ij(i,k)*sig_ij(j,k))**2 & + *( myfac(i)*q_fac(j)*myfac(k) + myfac(i)*q_fac(k)*myfac(j) & + + myfac(k)*q_fac(i)*myfac(j) +myfac(i)*q_fac(j)*q_fac(k)*1.1937350 & + +myfac(i)*q_fac(k)*q_fac(j)*1.193735 & + +myfac(k)*q_fac(i)*q_fac(j)*1.193735 ) + fdq3x = fdq3x + factor3*xijkf_x*Idq3(i,j,k) + DO l = 1, ncomp + xijkfa=x(i)*rho*x(j)*rho*x(l)*rho/(sig_ij(i,j)*sig_ij(i,l)*sig_ij(j,l))**2 & + *( myfac(i)*q_fac(j)*myfac(l) & + +myfac(i)*q_fac(j)*q_fac(l)*1.193735 ) + fdq3 =fdq3 + factor3 * xijkfa *Idq3(i,j,l) + fdq3x =fdq3x + factor3 * xijkfa *Idq3x(i,j,l) + END DO + END DO + END DO + + IF (fdq2 < -1.E-50 .AND. fdq3 /= 0.0 .AND. fdq2x /= 0.0 .AND. fdq3x /= 0.0)THEN + + fdq_rk = fdq2* (fdq2*fdq2x - 2.0*fdq3*fdq2x+fdq2*fdq3x) / (fdq2-fdq3)**2 + + END IF + +END SUBROUTINE PHI_DQ_VRABEC_GROSS + + + +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! + SUBROUTINE P_NUMERICAL +! + USE EOS_VARIABLES + IMPLICIT NONE +! +!-----local variables------------------------------------------------- + REAL :: dzetdv, eta_0, dist, fact + REAL :: fres1, fres2, fres3, fres4, fres5 + REAL :: df_dr, df_drdr, pideal, dpiddz + REAL :: tfr_1, tfr_2, tfr_3, tfr_4, tfr_5 +!----------------------------------------------------------------------- + + +IF (eta > 0.1) THEN + fact = 1.0 +ELSE IF (eta <= 0.1 .AND. eta > 0.01) THEN + fact = 10.0 +ELSE + fact = 10.0 +END IF +dist = eta*3.d-3 *fact +! dist = eta*4.d-3 *fact +!***************************** +! fuer MC simulation: neues dist: +! dist = eta*5.d-3*fact + +eta_0 = eta +eta = eta_0 - 2.0*dist +CALL F_NUMERICAL +fres1 = fres +tfr_1 = tfr +eta = eta_0 - dist +CALL F_NUMERICAL +fres2 = fres +tfr_2 = tfr +eta = eta_0 + dist +CALL F_NUMERICAL +fres3 = fres +tfr_3 = tfr +eta = eta_0 + 2.0*dist +CALL F_NUMERICAL +fres4 = fres +tfr_4 = tfr +eta = eta_0 +CALL F_NUMERICAL +fres5 = fres +tfr_5 = tfr + +!--------------------------------------------------------- +! ptfr = (-tfr_4+8.0*tfr_3-8.0*tfr_2+tfr_1)/(12.0*dist) +! & *dzetdv*(KBOL*T)/1.E-30 +! ztfr =ptfr /( rho * (KBOL*t) / 1.E-30) +! ptfrdz = (-tfr_4+16.0*tfr_3-3.d1*tfr_5+16.0*tfr_2-tfr_1) +! & /(12.0*(dist**2 ))* dzetdv*(KBOL*T)/1.E-30 +! & + (-tfr_4+8.0*tfr_3-8.0*tfr_2+tfr_1) +! & /(12.0*dist) * 2.0 *eta*6.0/PI/D +! & *(KBOL*T)/1.E-30 +! ztfrdz=ptfrdz/( rho*(kbol*T)/1.E-30 ) - ztfr/eta +! write (*,*) eta,ztfr,ztfrdz + +! dtfr_dr = (-tfr_4+8.0*tfr_3-8.0*tfr_2+tfr_1)/(12.0*dist) +! write (*,*) eta,dtfr_dr +! stop +!--------------------------------------------------------- + +df_dr = (-fres4+8.0*fres3-8.0*fres2+fres1) / (12.0*dist) +df_drdr = (-fres4+16.0*fres3-3.d1*fres5+16.0*fres2-fres1) & + /(12.0*(dist**2 )) + + +dzetdv = eta*rho + +pges = (-fres4+8.0*fres3-8.0*fres2+fres1) & + /(12.0*dist) *dzetdv*(kbol*t)/1.E-30 + +dpiddz = 1.0/z3t*(kbol*t)/1.E-30 +pgesdz = (-fres4+16.0*fres3-3.d1*fres5+16.0*fres2-fres1) & + /(12.0*(dist**2 ))* dzetdv*(kbol*t)/1.E-30 & + + (-fres4+8.0*fres3-8.0*fres2+fres1) /(12.0*dist) * 2.0 *rho & + *(kbol*t)/1.E-30 + dpiddz + +pgesd2 = (fres4-2.0*fres3+2.0*fres2-fres1) /(2.0*dist**3 ) & + * dzetdv*(kbol*t)/1.E-30 & + + (-fres4+16.0*fres3-3.d1*fres5+16.0*fres2-fres1) /(12.0*(dist**2 )) & + * 4.0 *rho *(kbol*t)/1.E-30 + (-fres4+8.0*fres3-8.0*fres2+fres1) & + /(12.0*dist) * 2.0 /z3t *(kbol*t)/1.E-30 +pgesd3 = (fres4-4.0*fres3+6.0*fres5-4.0*fres2+fres1) /(dist**4 ) & + * dzetdv*(kbol*t)/1.E-30 + (fres4-2.0*fres3+2.0*fres2-fres1) & + /(2.0*dist**3 ) * 6.0 *rho *(kbol*t)/1.E-30 & + + (-fres4+16.0*fres3-3.d1*fres5+16.0*fres2-fres1) & + /(12.0*dist**2 )* 6.0 /z3t *(kbol*t)/1.E-30 + +!------------------p ideal------------------------------------ +pideal = rho * (kbol*t) / 1.E-30 + +!------------------p summation, p comes out in Pa ------------ +pges = pideal + pges + +END SUBROUTINE P_NUMERICAL + + +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! + SUBROUTINE H_numerical +! + USE PARAMETERS, ONLY: RGAS + USE EOS_VARIABLES + IMPLICIT NONE +! +!--------------------------------------------------------------------- + REAL :: dist, fact, rho_0 + REAL :: fres1,fres2,fres3,fres4,fres5 + REAL :: f_1, f_2, f_3, f_4 + REAL :: cv_res, t_tmp, zges + REAL :: f_dt, f_dtdt, f_dr, f_drdr, f_drdt +!----------------------------------------------------------------------- + + +CALL PERTURBATION_PARAMETER +rho_0 = eta/z3t + + +fact = 1.0 +dist = t * 100.E-5 * fact + +t_tmp = t + +t = t_tmp - 2.0*dist +CALL PERTURBATION_PARAMETER +eta = z3t*rho_0 +CALL F_NUMERICAL +fres1 = fres +t = t_tmp - dist +CALL PERTURBATION_PARAMETER +eta = z3t*rho_0 +CALL F_NUMERICAL +fres2 = fres +t = t_tmp + dist +CALL PERTURBATION_PARAMETER +eta = z3t*rho_0 +CALL F_NUMERICAL +fres3 = fres +t = t_tmp + 2.0*dist +CALL PERTURBATION_PARAMETER +eta = z3t*rho_0 +CALL F_NUMERICAL +fres4 = fres +t = t_tmp +CALL PERTURBATION_PARAMETER +eta = z3t*rho_0 +CALL F_NUMERICAL +fres5 = fres +! *(KBOL*T)/1.E-30 + +zges = (p * 1.E-30)/(kbol*t*rho_0) + + +f_dt = (-fres4+8.0*fres3-8.0*fres2+fres1)/(12.0*dist) +f_dtdt = (-fres4+16.0*fres3-3.d1*fres5+16.0*fres2-fres1) /(12.0*(dist**2 )) + +s_res = (- f_dt -fres/t)*RGAS*t + RGAS * LOG(zges) +h_res = ( - t*f_dt + zges-1.0 ) * RGAS*t +cv_res = -( t*f_dtdt + 2.0*f_dt ) * RGAS*t + + + +t = t_tmp - 2.0*dist +CALL PERTURBATION_PARAMETER +eta = z3t*rho_0 +CALL P_NUMERICAL +f_1 = pges/(eta*rho_0*(KBOL*T)/1.E-30) + +t = t_tmp - dist +CALL PERTURBATION_PARAMETER +eta = z3t*rho_0 +CALL P_NUMERICAL +f_2 = pges/(eta*rho_0*(KBOL*T)/1.E-30) + +t = t_tmp + dist +CALL PERTURBATION_PARAMETER +eta = z3t*rho_0 +CALL P_NUMERICAL +f_3 = pges/(eta*rho_0*(KBOL*T)/1.E-30) + +t = t_tmp + 2.0*dist +CALL PERTURBATION_PARAMETER +eta = z3t*rho_0 +CALL P_NUMERICAL +f_4 = pges/(eta*rho_0*(KBOL*T)/1.E-30) + +t = t_tmp +CALL PERTURBATION_PARAMETER +eta = z3t*rho_0 +CALL P_NUMERICAL + +f_dr = pges / (eta*rho_0*(KBOL*T)/1.E-30) +f_drdr = pgesdz/ (eta*rho_0*(KBOL*T)/1.E-30) - f_dr*2.0/eta - 1.0/eta**2 + +f_drdt = ( - f_4 + 8.0*f_3 - 8.0*f_2 + f_1 ) / ( 12.0*dist ) + +cp_res = cv_res - RGAS + RGAS*( zges + eta*t*f_drdt)**2 / (1.0 + 2.0*eta*f_dr + eta**2 *f_drdr) +! write (*,*) cv_res,cp_res,eta + + +END SUBROUTINE H_numerical + + + + + + + + + + + +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! + SUBROUTINE F_POLAR ( fdd, fqq, fdq ) +! + USE EOS_VARIABLES, ONLY: ncomp, parame, dd_term, qq_term, dq_term + IMPLICIT NONE +! +! ---------------------------------------------------------------------- + REAL, INTENT(OUT) :: fdd, fqq, fdq +! +! --- local variables--------------------------------------------------- + INTEGER :: dipole + INTEGER :: quadrupole + INTEGER :: dipole_quad +! ---------------------------------------------------------------------- + + fdd = 0.0 + fqq = 0.0 + fdq = 0.0 + + dipole = 0 + quadrupole = 0 + dipole_quad = 0 + IF ( SUM( parame(1:ncomp,6) ) /= 0.0 ) dipole = 1 + IF ( SUM( parame(1:ncomp,7) ) /= 0.0 ) quadrupole = 1 + IF ( dipole == 1 .AND. quadrupole == 1 ) dipole_quad = 1 + + ! -------------------------------------------------------------------- + ! dipole-dipole term + ! -------------------------------------------------------------------- + IF (dipole == 1) THEN + + IF (dd_term == 'GV') CALL F_DD_GROSS_VRABEC( fdd ) + ! IF (dd_term == 'SF') CALL F_DD_SAAGER_FISCHER( k ) + IF (dd_term /= 'GV' .AND. dd_term /= 'SF') write (*,*) 'specify dipole term !' + + ENDIF + + ! -------------------------------------------------------------------- + ! quadrupole-quadrupole term + ! -------------------------------------------------------------------- + IF (quadrupole == 1) THEN + + !IF (qq_term == 'SF') CALL F_QQ_SAAGER_FISCHER( k ) + IF (qq_term == 'JG') CALL F_QQ_GROSS( fqq ) + IF (qq_term /= 'JG' .AND. qq_term /= 'SF') write (*,*) 'specify quadrupole term !' + + ENDIF + + ! -------------------------------------------------------------------- + ! dipole-quadrupole cross term + ! -------------------------------------------------------------------- + IF (dipole_quad == 1) THEN + + IF (dq_term == 'VG') CALL F_DQ_VRABEC_GROSS( fdq ) + IF (dq_term /= 'VG' ) write (*,*) 'specify DQ-cross term !' + + ENDIF + +END SUBROUTINE F_POLAR + + + +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! SUBROUTINE PRESSURE_SPINODAL +! +! iterates the density until the derivative of pressure 'pges' to +! density is equal to zero. A Newton-scheme is used for determining +! the root to the objective function. +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! + SUBROUTINE PRESSURE_SPINODAL +! + USE BASIC_VARIABLES, ONLY: num + USE EOS_VARIABLES + IMPLICIT NONE +! +! ---------------------------------------------------------------------- + INTEGER :: i, max_i + REAL :: eta_iteration + REAL :: error, acc_i, delta_eta +! ---------------------------------------------------------------------- + +acc_i = 1.d-6 +max_i = 30 + +i = 0 +eta_iteration = eta_start + +! ---------------------------------------------------------------------- +! iterate density until p_calc = p +! ---------------------------------------------------------------------- + +error = acc_i + 1.0 +DO WHILE ( ABS(error) > acc_i .AND. i < max_i ) + + i = i + 1 + eta = eta_iteration + + IF ( num == 0 ) THEN + CALL P_EOS + ELSE IF ( num == 1 ) THEN + CALL P_NUMERICAL + ELSE IF ( num == 2 ) THEN + WRITE(*,*) 'CRITICAL RENORM NOT INCLUDED YET' + !!CALL F_EOS_RN + ELSE + write (*,*) 'define calculation option (num)' + END IF + + error = pgesdz + + delta_eta = error/ pgesd2 + IF ( delta_eta > 0.02 ) delta_eta = 0.02 + IF ( delta_eta < -0.02 ) delta_eta = -0.02 + + eta_iteration = eta_iteration - delta_eta + ! write (*,'(a,i3,3G18.10)') 'iter',i, error, eta_iteration, pgesdz + + IF (eta_iteration > 0.9) eta_iteration = 0.5 + IF (eta_iteration <= 0.0) eta_iteration = 1.E-16 + +END DO + +eta = eta_iteration + +END SUBROUTINE PRESSURE_SPINODAL + + +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! + SUBROUTINE F_IDEAL_GAS ( fid ) +! + USE EOS_VARIABLES, ONLY: nc, ncomp, t, x, rho, PI, KBOL, NAv + IMPLICIT NONE +! +!--------------------------------------------------------------------- + REAL, INTENT(IN OUT) :: fid +!--------------------------------------------------------------------- + INTEGER :: i + REAL, DIMENSION(nc) :: rhoi +!---------------------------------------------------------------------- + + !h_Planck = 6.62606896E-34 ! Js + DO i = 1, ncomp + rhoi(i) = x(i) * rho + ! debroglie(i) = h_Planck *1d10 & ! in units Angstrom + ! *SQRT( 1.0 / (2.0*PI *1.0 / NAv / 1000.0 * KBOL*T) ) + ! ! *SQRT( 1.0 / (2.0*PI *mm(i) /NAv/1000.0 * KBOL*T) ) + ! fid = fid + x(i) * ( LOG(rhoi(i)*debroglie(i)**3) - 1.0 ) + fid = fid + x(i) * ( LOG(rhoi(i)) - 1.0 ) + END DO + + END SUBROUTINE F_IDEAL_GAS + +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! + SUBROUTINE F_HARD_SPHERE ( m_mean2, fhs ) +! + USE EOS_VARIABLES, ONLY: z0t, z1t, z2t, z3t, eta, rho + IMPLICIT NONE +! +!--------------------------------------------------------------------- + REAL, INTENT(IN) :: m_mean2 + REAL, INTENT(IN OUT) :: fhs +!--------------------------------------------------------------------- + REAL :: z0, z1, z2, z3, zms +!---------------------------------------------------------------------- + + rho = eta / z3t + z0 = z0t * rho + z1 = z1t * rho + z2 = z2t * rho + z3 = z3t * rho + zms = 1.0 - z3 + + fhs= m_mean2*( 3.0*z1*z2/zms + z2**3 /z3/zms/zms + (z2**3 /z3/z3-z0)*LOG(zms) )/z0 + + + END SUBROUTINE F_HARD_SPHERE + +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! + SUBROUTINE F_CHAIN_TPT1 ( fhc ) +! + USE EOS_VARIABLES, ONLY: nc, ncomp, mseg, x, z0t, z1t, z2t, z3t, & + rho, eta, dij_ab, gij + IMPLICIT NONE +! +!--------------------------------------------------------------------- + REAL, INTENT(IN OUT) :: fhc +!--------------------------------------------------------------------- + INTEGER :: i, j + REAL :: z0, z1, z2, z3, zms +!--------------------------------------------------------------------- + + rho = eta / z3t + z0 = z0t * rho + z1 = z1t * rho + z2 = z2t * rho + z3 = z3t * rho + zms = 1.0 - z3 + + DO i = 1, ncomp + DO j = 1, ncomp + gij(i,j) = 1.0/zms + 3.0*dij_ab(i,j)*z2/zms/zms + 2.0*(dij_ab(i,j)*z2)**2 / zms**3 + END DO + END DO + + fhc = 0.0 + DO i = 1, ncomp + fhc = fhc + x(i) *(1.0- mseg(i)) *LOG(gij(i,i)) + END DO + + END SUBROUTINE F_CHAIN_TPT1 + + +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! + SUBROUTINE F_CHAIN_TPT_D ( fhc ) +! + USE EOS_VARIABLES, ONLY: nc, ncomp, mseg, x, z0t, z1t, z2t, z3t, rho, eta, & + dhs, mseg, dij_ab, gij + IMPLICIT NONE +! +!--------------------------------------------------------------------- + REAL, INTENT(OUT) :: fhc +!--------------------------------------------------------------------- + INTEGER :: i, j + REAL, DIMENSION(nc) :: gij_hd + REAL :: z0, z1, z2, z3, zms +!--------------------------------------------------------------------- + + rho = eta / z3t + z0 = z0t * rho + z1 = z1t * rho + z2 = z2t * rho + z3 = z3t * rho + zms = 1.0 - z3 + + DO i = 1, ncomp + DO j = 1, ncomp + gij(i,j) = 1.0/zms + 3.0*dij_ab(i,j)*z2/zms/zms + 2.0*(dij_ab(i,j)*z2)**2 / zms**3 + END DO + END DO + + DO i = 1, ncomp + gij_hd(i) = 1.0/(2.0*zms) + 3.0*dij_ab(i,i)*z2 / zms**2 + END DO + + fhc = 0.0 + DO i = 1, ncomp + IF ( mseg(i) >= 2.0 ) THEN + fhc = fhc - x(i) * ( mseg(i)/2.0 * LOG( gij(i,i) ) + ( mseg(i)/2.0 - 1.0 ) * LOG( gij_hd(i)) ) + ELSE + fhc = fhc + x(i) * ( 1.0 - mseg(i) ) * LOG( gij(i,i) ) + END IF + END DO + + END SUBROUTINE F_CHAIN_TPT_D + + +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! + SUBROUTINE F_CHAIN_HU_LIU ( fhc ) +! + USE EOS_VARIABLES, ONLY: nc, ncomp, mseg, x, rho, eta + IMPLICIT NONE +! +! This subroutine calculates the hard chain contribution of the TPT-Liu-Hu Eos. +!--------------------------------------------------------------------- + REAL, INTENT(OUT) :: fhc +!--------------------------------------------------------------------- + REAL :: a2, b2, c2, a3, b3, c3 + REAL :: a20, b20, c20, a30, b30, c30 + REAL :: sum1, sum2, am, bm, cm + REAL :: zms +!--------------------------------------------------------------------- + + zms = 1.0 - eta + + sum1 = SUM( x(1:ncomp)*(mseg(1:ncomp)-1.0) ) + sum2 = SUM( x(1:ncomp)/mseg(1:ncomp)*(mseg(1:ncomp)-1.0)*(mseg(1:ncomp)-2.0) ) + + a2 = 0.45696 + a3 = -0.74745 + b2 = 2.10386 + b3 = 3.49695 + c2 = 1.75503 + c3 = 4.83207 + a20 = - a2 + b2 - 3.0*c2 + b20 = - a2 - b2 + c2 + c20 = c2 + a30 = - a3 + b3 - 3.0*c3 + b30 = - a3 - b3 + c3 + c30 = c3 + am = (3.0 + a20) * sum1 + a30 * sum2 + bm = (1.0 + b20) * sum1 + b30 * sum2 + cm = (1.0 + c20) * sum1 + c30 * sum2 + + fhc = - ( (am*eta - bm) / (2.0*zms) + bm/2.0/zms**2 - cm *LOG(ZMS) ) + + + END SUBROUTINE F_CHAIN_HU_LIU + +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! + SUBROUTINE F_CHAIN_HU_LIU_RC ( fhs, fhc ) +! + USE EOS_VARIABLES, ONLY: mseg, chiR, eta + IMPLICIT NONE +! +! This subroutine calculates the hard chain contribution of the TPT-Liu-Hu Eos. +!--------------------------------------------------------------------- + REAL, INTENT(IN) :: fhs + REAL, INTENT(OUT) :: fhc +!--------------------------------------------------------------------- + REAL :: a2, b2, c2, a3, b3, c3 + REAL :: para1,para2,para3,para4 + REAL :: aLH,bLH,cLH +!--------------------------------------------------------------------- + +! This routine is only for pure components + + a2 = 0.45696 + b2 = 2.10386 + c2 = 1.75503 + + para1 = -0.74745 + para2 = 0.299154629727814 + para3 = 1.087271036653154 + para4 = -0.708979110326831 + a3 = para1 + para2*chiR(1) + para3*chiR(1)**2 + para4*chiR(1)**3 + b3 = 3.49695 - (3.49695 + 0.317719074806190)*chiR(1) + c3 = 4.83207 - (4.83207 - 3.480163780334421)*chiR(1) + + aLH = mseg(1)*(1.0 + ((mseg(1)-1.0)/mseg(1))*a2 + ((mseg(1)-1.0)/mseg(1))*((mseg(1)-2.0)/mseg(1))*a3 ) + bLH = mseg(1)*(1.0 + ((mseg(1)-1.0)/mseg(1))*b2 + ((mseg(1)-1.0)/mseg(1))*((mseg(1)-2.0)/mseg(1))*b3 ) + cLH = mseg(1)*(1.0 + ((mseg(1)-1.0)/mseg(1))*c2 + ((mseg(1)-1.0)/mseg(1))*((mseg(1)-2.0)/mseg(1))*c3 ) + + fhc = ((3.0 + aLH - bLH + 3.0*cLH)*eta - (1.0 + aLH + bLH - cLH)) / (2.0*(1.0-eta)) + & + (1.0 + aLH + bLH - cLH) / ( 2.0*(1.0-eta)**2 ) + (cLH - 1.0)*LOG(1.0-eta) + + fhc = fhc - fhs + + END SUBROUTINE F_CHAIN_HU_LIU_RC + + + + +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! + SUBROUTINE F_DISP_PCSAFT ( fdsp ) +! + USE EOS_VARIABLES, ONLY: PI, rho, eta, z0t, apar, bpar, order1, order2 + IMPLICIT NONE +! +!--------------------------------------------------------------------- + REAL, INTENT(IN OUT) :: fdsp +!--------------------------------------------------------------------- + INTEGER :: m + REAL :: I1, I2, c1_con, z3, zms, m_mean +!--------------------------------------------------------------------- + + z3 = eta + zms = 1.0 - eta + m_mean = z0t / ( PI / 6.0 ) + + I1 = 0.0 + I2 = 0.0 + DO m = 0, 6 + I1 = I1 + apar(m) * z3**m + I2 = I2 + bpar(m) * z3**m + END DO + + c1_con= 1.0/ ( 1.0 + m_mean*(8.0*z3-2.0*z3**2 )/zms**4 & + + (1.0-m_mean)*( 20.0*z3-27.0*z3**2 +12.0*z3**3 -2.0*z3**4 )/(zms*(2.0-z3))**2 ) + + fdsp = -2.0*PI*rho*I1*order1 - PI*rho*c1_con*m_mean*I2*order2 + + END SUBROUTINE F_DISP_PCSAFT + +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! + SUBROUTINE F_DISP_CKSAFT ( fdsp ) +! + USE EOS_VARIABLES, ONLY: nc, ncomp, PI, TAU, t, rho, eta, x, z0t, mseg, vij, uij, parame, um + USE EOS_CONSTANTS, ONLY: DNM + IMPLICIT NONE +! +!--------------------------------------------------------------------- + REAL, INTENT(IN OUT) :: fdsp +!--------------------------------------------------------------------- + INTEGER :: i, j, n, m + REAL :: zmr, nmr, m_mean +!--------------------------------------------------------------------- + + m_mean = z0t / ( PI / 6.0 ) + + DO i = 1, ncomp + DO j = 1, ncomp + vij(i,j)=(0.5*((parame(i,2)*(1.0-0.12 *EXP(-3.0*parame(i,3)/t))**3 )**(1.0/3.0) & + +(parame(j,2)*(1.0-0.12 *EXP(-3.0*parame(j,3)/t))**3 )**(1.0/3.0)))**3 + END DO + END DO + zmr = 0.0 + nmr = 0.0 + DO i = 1, ncomp + DO j = 1, ncomp + zmr = zmr + x(i)*x(j)*mseg(i)*mseg(j)*vij(i,j)*uij(i,j) + nmr = nmr + x(i)*x(j)*mseg(i)*mseg(j)*vij(i,j) + END DO + END DO + um = zmr / nmr + fdsp = 0.0 + DO n = 1, 4 + DO m = 1, 9 + fdsp = fdsp + DNM(n,m) * (um/t)**n *(eta/TAU)**m + END DO + END DO + fdsp = m_mean * fdsp + + + END SUBROUTINE F_DISP_CKSAFT + +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! + SUBROUTINE F_ASSOCIATION ( eps_kij, k_kij, fhb ) +! + USE EOS_VARIABLES, ONLY: nc, nsite, ncomp, t, z0t, z1t, z2t, z3t, rho, eta, x, & + parame, sig_ij, dij_ab, gij, nhb_typ, mx, nhb_no + IMPLICIT NONE +! +!--------------------------------------------------------------------- + REAL, INTENT(IN) :: eps_kij, k_kij + REAL, INTENT(IN OUT) :: fhb +!--------------------------------------------------------------------- + LOGICAL :: assoc + INTEGER :: i, j, k, l, no, ass_cnt, max_eval + REAL, DIMENSION(nc,nc) :: kap_hb + REAL, DIMENSION(nc,nc,nsite,nsite) :: eps_hb + REAL, DIMENSION(nc,nsite,nc,nsite) :: delta + REAL, DIMENSION(nc,nsite) :: mx_itr + REAL :: err_sum, sum0, amix, tol, ass_s1, ass_s2 + REAL :: z0, z1, z2, z3, zms +!--------------------------------------------------------------------- + + assoc = .false. + DO i = 1,ncomp + IF (NINT(parame(i,12)) /= 0) assoc = .true. + END DO + IF (assoc) THEN + + rho = eta / z3t + z0 = z0t * rho + z1 = z1t * rho + z2 = z2t * rho + z3 = z3t * rho + zms = 1.0 - z3 + + DO i = 1, ncomp + DO j = 1, ncomp + gij(i,j) = 1.0/zms + 3.0*dij_ab(i,j)*z2/zms/zms + 2.0*(dij_ab(i,j)*z2)**2 / zms**3 + END DO + END DO + + + DO i = 1, ncomp + IF ( NINT(parame(i,12)) /= 0 ) THEN + nhb_typ(i) = NINT( parame(i,12) ) + kap_hb(i,i) = parame(i,13) + no = 0 + DO k = 1,nhb_typ(i) + DO l = 1,nhb_typ(i) + eps_hb(i,i,k,l) = parame(i,(14+no)) + no = no + 1 + END DO + END DO + DO k = 1,nhb_typ(i) + nhb_no(i,k) = parame(i,(14+no)) + no = no + 1 + END DO + ELSE + nhb_typ(i) = 0 + kap_hb(i,i)= 0.0 + DO k = 1,nsite + DO l = 1,nsite + eps_hb(i,i,k,l) = 0.0 + END DO + END DO + END IF + END DO + + DO i = 1,ncomp + DO j = 1,ncomp + IF ( i /= j .AND. (nhb_typ(i) /= 0.AND.nhb_typ(j) /= 0) ) THEN + ! kap_hb(i,j)= (kap_hb(i,i)+kap_hb(j,j))/2.0 + ! kap_hb(i,j)= ( ( kap_hb(i,i)**(1.0/3.0) + kap_hb(j,j)**(1.0/3.0) )/2.0 )**3 + kap_hb(i,j) = (kap_hb(i,i)*kap_hb(j,j))**0.5 & + *((parame(i,2)*parame(j,2))**3 )**0.5 & + / (0.5*(parame(i,2)+parame(j,2)))**3 + kap_hb(i,j)= kap_hb(i,j)*(1.0-k_kij) + DO k = 1,nhb_typ(i) + DO l = 1,nhb_typ(j) + IF ( k /= l .AND. nhb_typ(i) >= 2 .AND. nhb_typ(j) >= 2 ) THEN + eps_hb(i,j,k,l) = (eps_hb(i,i,k,l)+eps_hb(j,j,l,k))/2.0 + ! eps_hb(i,j,k,l) = (eps_hb(i,i,k,l)*eps_hb(j,j,l,k))**0.5 + eps_hb(i,j,k,l) = eps_hb(i,j,k,l)*(1.0-eps_kij) + ELSE IF ( nhb_typ(i) == 1 .AND. l > k ) THEN + eps_hb(i,j,k,l) = (eps_hb(i,i,k,k)+eps_hb(j,j,l,k))/2.0 + eps_hb(j,i,l,k) = (eps_hb(i,i,k,k)+eps_hb(j,j,l,k))/2.0 + eps_hb(i,j,k,l) = eps_hb(i,j,k,l)*(1.0-eps_kij) + eps_hb(j,i,l,k) = eps_hb(j,i,l,k)*(1.0-eps_kij) + END IF + END DO + END DO + END IF + END DO + END DO + +!-----setting the self-association to zero for ionic compounds------ + DO i = 1,ncomp + IF ( parame(i,10) /= 0) kap_hb(i,i)=0.0 + DO j = 1,ncomp + IF ( parame(i,10) /= 0 .AND. parame(j,10) /= 0 ) kap_hb(i,j) = 0.0 + END DO + END DO + ! kap_hb(1,2)=0.050 + ! kap_hb(2,1)=0.050 + ! eps_hb(2,1,1,1)=465.0 + ! eps_hb(1,2,1,1)=465.0 + ! nhb_typ(1) = 1 + ! nhb_typ(2) = 1 + ! nhb_no(1,1)= 1.0 + ! nhb_no(2,1)= 1.0 + + + DO i = 1, ncomp + DO k = 1, nhb_typ(i) + DO j = 1, ncomp + DO l = 1, nhb_typ(j) + delta(i,k,j,l)=gij(i,j)*kap_hb(i,j)*(EXP(eps_hb(i,j,k,l)/t)-1.0) *sig_ij(i,j)**3 +!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! +! IF ((i+j).EQ.3) delta(i,k,j,l)=94.0 +!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! + END DO + END DO + IF ( mx(i,k) == 0.0 ) mx(i,k) = 1.0 + END DO + END DO + +!------constants for Iteration --------------------------------------- + amix = 0.7 + tol = 1.E-10 + IF (eta < 0.2) tol = 1.E-11 + IF (eta < 0.01) tol = 1.E-14 + max_eval = 200 + +! --- Iterate over all components and all sites ------------------------ + ass_cnt = 0 + iterate_TPT1: DO + + ass_cnt = ass_cnt + 1 + + DO i = 1, ncomp + DO k = 1, nhb_typ(i) + sum0 = 0.0 + DO j = 1, ncomp + DO l = 1, nhb_typ(j) + sum0 = sum0 + x(j)* mx(j,l)*nhb_no(j,l) *delta(i,k,j,l) + END DO + END DO + mx_itr(i,k) = 1.0 / (1.0 + sum0*rho) + END DO + END DO + + err_sum = 0.0 + DO i = 1, ncomp + DO k = 1, nhb_typ(i) + err_sum = err_sum + ABS( mx_itr(i,k) - mx(i,k) ) ! / ABS(mx_itr(i,k)) + mx(i,k) = mx_itr(i,k) * amix + mx(i,k) * (1.0 - amix) + IF ( mx(i,k) <= 0.0 ) mx(i,k)=1.E-50 + IF ( mx(i,k) > 1.0 ) mx(i,k)=1.0 + END DO + END DO + + IF ( err_sum <= tol .OR. ass_cnt >= max_eval ) THEN + IF ( ass_cnt >= max_eval ) WRITE(*,*) 'F_NUMERICAL: Max_eval violated = ',err_sum,tol + EXIT iterate_TPT1 + END IF + + END DO iterate_TPT1 + + DO i = 1, ncomp + ass_s1 = 0.0 + ass_s2 = 0.0 + DO k = 1, nhb_typ(i) + ass_s1 = ass_s1 + nhb_no(i,k) * ( 1.0 - mx(i,k) ) + ass_s2 = ass_s2 + nhb_no(i,k) * LOG(mx(i,k)) + END DO + fhb = fhb + x(i) * ( ass_s2 + ass_s1/2.0 ) + END DO + + END IF + + END SUBROUTINE F_ASSOCIATION + + +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! + SUBROUTINE F_ION_DIPOLE_TBH ( fhend ) +! + USE EOS_VARIABLES, ONLY: nc, PI, KBOL, NAv, ncomp, t, rho, eta, x, z0t, parame, uij, sig_ij + IMPLICIT NONE +! +!--------------------------------------------------------------------- + REAL, INTENT(IN OUT) :: fhend +!--------------------------------------------------------------------- + INTEGER :: i, dipole, ions + REAL :: m_mean + REAL :: fh32, fh2, fh52, fh3 + REAL :: e_elem, eps_cc0, rho_sol, dielec + REAL :: polabil, ydd, kappa, x_dipol, x_ions + REAL, DIMENSION(nc) :: my2dd, z_ii, e_cd, x_dd, x_ii + REAL :: sig_c, sig_d, sig_cd, r_s + REAL :: I0cc, I1cc, I2cc, Icd, Idd + REAL :: Iccc, Iccd, Icdd, Iddd +!--------------------------------------------------------------------- + +m_mean = z0t / ( PI / 6.0 ) + +!----------------Dieletric Constant of Water-------------------------- +e_elem = 1.602189246E-19 ! in Unit [Coulomb] +eps_cc0 = 8.854187818E-22 ! in Unit [Coulomb**2 /(J*Angstrom)] +! Correlation of M. Uematsu and E. U. Frank +! (Static Dieletric Constant of Water and Steam) +! valid range of conditions 273,15 K <=T<= 823,15 K +! and density <= 1150 kg/m3 (i.e. 0 <= p <= 500 MPa) +rho_sol = rho * 18.015 * 1.E27/ NAv +rho_sol = rho_sol/1000.0 +dielec = 1.0+(7.62571/(t/293.15))*rho_sol +(2.44E2/(t/293.15)-1.41E2 & + + 2.78E1*(t/293.15))*rho_sol**2 & + + (-9.63E1/(t/293.15)+4.18E1*(t/293.15) & + - 1.02E1*(t/293.15)**2 )*rho_sol**3 +(-4.52E1/(t/293.15)**2 & + + 8.46E1/(t/293.15)-3.59E1)*rho_sol**4 + + +! !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! + +dielec = 1.0 + +! !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! + + +!----------------Dipole-Ion Term----------------------------------- +dipole = 0 +ions = 0 +fhend = 0.0 +DO i = 1, ncomp + IF ( parame(i,6) /= 0.0 .AND. uij(i,i) /= 0.0 .AND. x(i) > 0.0 ) THEN + my2dd(i) = (parame(i,6))**2 *1.E-49 / (uij(i,i)*KBOL*sig_ij(i,i)**3 *1.E-30) + dipole = 1 + ELSE + my2dd(i) = 0.0 + END IF + + z_ii(i) = parame(i,10) + IF ( z_ii(i) /= 0.0 .AND. uij(i,i) /= 0.0 .AND. x(i) > 0.0 ) THEN + e_cd(i) = ( parame(i,10)*e_elem* 1.E5 / SQRT(1.11265005) )**2 & + / ( uij(i,i)*kbol*sig_ij(i,i)*1.E-10 ) + ions = 1 + ELSE + e_cd(i) = 0.0 + END IF +END DO + + +IF ( dipole == 1 .AND. ions == 1 ) THEN + + ydd = 0.0 + kappa = 0.0 + x_dipol = 0.0 + x_ions = 0.0 + polabil = 0.0 + DO i = 1, ncomp + ydd = ydd + x(i)*(parame(i,6))**2 *1.E-49/ (kbol*t*1.E-30) + kappa = kappa + x(i) & + *(parame(i,10)*e_elem* 1.E5/SQRT(1.11265005))**2 /(KBOL*t*1.E-10) + IF (parame(i,10) /= 0.0) THEN + x_ions = x_ions + x(i) + ELSE + polabil = polabil + 4.0*PI*x(i)*rho*1.4573 *1.E-30 & + / (sig_ij(3,3)**3 *1.E-30) + END IF + IF (parame(i,6) /= 0.0) x_dipol= x_dipol+ x(i) + END DO + ydd = ydd * 4.0/9.0 * PI * rho + kappa = SQRT( 4.0 * PI * rho * kappa ) + + fh2 = 0.0 + sig_c = 0.0 + sig_d = 0.0 + DO i=1,ncomp + x_ii(i) = 0.0 + x_dd(i) = 0.0 + IF(parame(i,10) /= 0.0 .AND. x_ions /= 0.0) x_ii(i) = x(i)/x_ions + IF(parame(i,6) /= 0.0 .AND. x_dipol /= 0.0) x_dd(i) = x(i)/x_dipol + sig_c = sig_c + x_ii(i)*parame(i,2) + sig_d = sig_d + x_dd(i)*parame(i,2) + END DO + sig_cd = 0.5 * (sig_c + sig_d) + + r_s = 0.0 + ! DO i=1,ncomp + ! r_s=r_s + rho * x(i) * dhs(i)**3 + ! END DO + r_s = eta*6.0 / PI / m_mean + + I0cc = - (1.0 + 0.97743 * r_s + 0.05257*r_s*r_s) & + /(1.0 + 1.43613 * r_s + 0.41580*r_s*r_s) + ! I1cc = - (10.0 - 2.0*z3 + z3*z3) /20.0/(1.0 + 2.0*z3) + I1cc = - (10.0 - 2.0*r_s*pi/6.0 + r_s*r_s*pi/6.0*pi/6.0) & + /20.0/(1.0 + 2.0*r_s*pi/6.0) +!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! + ! I2cc = + (z3-4.0)*(z3*z3+2.0) /24.0/(1.0+2.0*z3) + ! relation of Stell and Lebowitz + I2cc = -0.33331+0.7418*r_s - 1.2047*r_s*r_s & + + 1.6139*r_s**3 - 1.5487*r_s**4 + 0.6626*r_s**5 +!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! + Icd = (1.0 + 0.79576 *r_s + 0.104556 *r_s*r_s) & + /(1.0 + 0.486704*r_s - 0.0222903*r_s*r_s) + Idd = (1.0 + 0.18158*r_s - 0.11467*r_s*r_s) & + /3.0/(1.0 - 0.49303*r_s + 0.06293*r_s*r_s) + Iccc= 3.0*(1.0 - 1.05560*r_s + 0.26591*r_s*r_s) & + /2.0/(1.0 + 0.53892*r_s - 0.94236*r_s*r_s) + Iccd= 11.0*(1.0 + 2.25642 *r_s + 0.05679 *r_s*r_s) & + /6.0/(1.0 + 2.64178 *r_s + 0.79783 *r_s*r_s) + Icdd= 0.94685*(1.0 + 2.97323 *r_s + 3.11931 *r_s*r_s) & + /(1.0 + 2.70186 *r_s + 1.22989 *r_s*r_s) + Iddd= 5.0*(1.0 + 1.12754*r_s + 0.56192*r_s*r_s) & + /24.0/(1.0 - 0.05495*r_s + 0.13332*r_s*r_s) + + IF ( sig_c <= 0.0 ) WRITE (*,*) 'error in Henderson ion term' + + fh32= - kappa**3 /(12.0*pi*rho) + fh2 = - 3.0* kappa**2 * ydd*Icd /(8.0*pi*rho) / sig_cd & + - kappa**4 *sig_c/(16.0*pi*rho)*I0cc + IF (sig_d /= 0.0) fh2 = fh2 - 27.0* ydd * ydd*Idd & + /(8.0*pi*rho) / sig_d**3 + fh52= (3.0*kappa**3 * ydd + kappa**5 *sig_c**2 *I1cc) & + /(8.0*pi*rho) + fh3 = - kappa**6 * sig_c**3 /(8.0*pi*rho) *(I2cc-Iccc/6.0) & + + kappa**4 * ydd *sig_c/(16.0*pi*rho) & + *( (6.0+5.0/3.0*sig_d/sig_c)*I0cc + 3.0*sig_d/sig_c*Iccd ) & + + 3.0*kappa**2 * ydd*ydd /(8.0*pi*rho) / sig_cd & + *( (2.0-3.21555*sig_d/sig_cd)*Icd +3.0*sig_d/sig_cd*Icdd ) + IF (sig_d /= 0.0) fh3 = fh3 + 27.0*ydd**3 & + /(16.0*pi*rho)/sig_d**3 *Iddd + + fhend = ( fh32 + (fh32*fh32*fh3-2.0*fh32*fh2*fh52+fh2**3 ) & + /(fh2*fh2-fh32*fh52) ) & + / ( 1.0 + (fh32*fh3-fh2*fh52) /(fh2*fh2-fh32*fh52) & + - (fh2*fh3-fh52*fh52) /(fh2*fh2-fh32*fh52) ) +!---------- +! fH32= - kappa**3 /(12.0*PI*rho) +! fH2 = - 3.0* kappa**2 * ydd*Icd /(8.0*PI*rho) / sig_cd +! fH52= (3.0*kappa**3 * ydd)/(8.0*PI*rho) +! fH3 = + kappa**4 * ydd *sig_c/(16.0*PI*rho) & +! *( (6.0+5.0/3.0*sig_d/sig_c)*0.0*I0cc + 3.0*sig_d/sig_c*Iccd) & +! + 3.0*kappa**2 * ydd*ydd /(8.0*PI*rho) / sig_cd & +! *( (2.0-3.215550*sig_d/sig_cd)*Icd +3.0*sig_d/sig_cd*Icdd ) + +! fHcd = ( + (fH32*fH32*fH3-2.0*fH32*fH2*fH52+fH2**3 ) & +! /(fH2*fH2-fH32*fH52) ) & +! / ( 1.0 + (fH32*fH3-fH2*fH52) /(fH2*fH2-fH32*fH52) & +! - (fH2*fH3-fH52*fH52) /(fH2*fH2-fH32*fH52) ) + +END IF + + END SUBROUTINE F_ION_DIPOLE_TBH + + +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! + SUBROUTINE F_ION_ION_PrimMSA ( fcc ) +! + USE EOS_VARIABLES, ONLY: nc, PI, KBOL, NAv, ncomp, t, rho, x, parame, mx + IMPLICIT NONE +! +!--------------------------------------------------------------------- + REAL, INTENT(IN OUT) :: fcc +!--------------------------------------------------------------------- + INTEGER :: i, j, cc_it, ions + REAL :: e_elem, eps_cc0, rho_sol, dielec + REAL :: x_ions + REAL :: cc_sig1, cc_sig2, cc_sig3 + REAL, DIMENSION(nc) :: z_ii, x_ii, sigm_i, my2dd + REAL :: alpha_2, kappa, ii_par + REAL :: cc_omeg, p_n, q2_i, cc_q2, cc_gam + REAL :: cc_error(2), cc_delt + REAL :: rhs, lambda, lam_s +!--------------------------------------------------------------------- + +!----------------Dieletric Constant of Water-------------------------- +e_elem = 1.602189246E-19 ! in Unit [Coulomb] +eps_cc0 = 8.854187818E-22 ! in Unit [Coulomb**2 /(J*Angstrom)] +! Correlation of M. Uematsu and E. U. Frank +! (Static Dieletric Constant of Water and Steam) +! valid range of conditions 273,15 K <=T<= 823,15 K +! and density <= 1150 kg/m3 (i.e. 0 <= p <= 500 MPa) +rho_sol = rho * 18.015 * 1.E27/ NAv +rho_sol = rho_sol/1000.0 +dielec = 1.0+(7.62571/(t/293.15))*rho_sol +(2.44E2/(t/293.15)-1.41E2 & + +2.78E1*(t/293.15))*rho_sol**2 & + +(-9.63E1/(t/293.15)+4.18E1*(t/293.15) & + -1.02E1*(t/293.15)**2 )*rho_sol**3 +(-4.52E1/(t/293.15)**2 & + +8.46E1/(t/293.15)-3.59E1)*rho_sol**4 + + +! !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! + +dielec = 1.0 + +! !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! + + +!----------------Ion-Ion: primitive MSA ------------------------------- +! the (dipole moment)**2 [my**2] corresponds to an attraction from +! point charges of [ SUM(xi * zi**2 * e_elem**2) * 3 * di**2 ] + +! parame(ion,6))**2 * 1.E-49 / (kbol*T) +! = (e_elem* 1.E5/SQRT(1.112650050))**2 +! *x(i)*zi**2 *3.0*sig_ij(1,1)**2 *1.E-20 + +! parame(ion,6))**2 = (e_elem* 1.E5/SQRT(1.112650050))**2 /1.E-49 +! *x(i)*zi**2 *3.0*sig_ij(i,i)**2 *1.E-20 + +! with the units +! my**2 [=] D**2 = 1.E-49 J*m3 +! e_elem **2 [=] C**2 = 1.E5 / SQRT(1.112650050) J*m + + +ions = 0 +x_ions = 0.0 +fcc = 0.0 +DO i = 1, ncomp + z_ii(i) = parame(i,10) + IF (z_ii(i) /= 0.0) THEN + sigm_i(i) = parame(i,2) + ELSE + sigm_i(i) = 0.0 + END IF + IF (z_ii(i) /= 0.0) ions = 1 + IF (z_ii(i) /= 0.0) x_ions = x_ions + x(i) +END DO + +IF (ions == 1 .AND. x_ions > 0.0) THEN + + cc_sig1 = 0.0 + cc_sig2 = 0.0 + cc_sig3 = 0.0 + DO i=1,ncomp + IF (z_ii(i) /= 0.0) THEN + x_ii(i) = x(i)/x_ions + ELSE + x_ii(i) =0.0 + END IF + cc_sig1 = cc_sig1 +x_ii(i)*sigm_i(i) + cc_sig2 = cc_sig2 +x_ii(i)*sigm_i(i)**2 + cc_sig3 = cc_sig3 +x_ii(i)*sigm_i(i)**3 + END DO + + + ! alpha_2 = 4.0*PI*e_elem**2 /eps_cc0/dielec/kbol/T + alpha_2 = e_elem**2 /eps_cc0 / dielec / KBOL/t + kappa = 0.0 + DO i = 1, ncomp + kappa = kappa + x(i)*z_ii(i)*z_ii(i)*mx(i,1) + END DO + kappa = SQRT( rho * alpha_2 * kappa ) + ii_par= kappa * cc_sig1 + + ! Temporaer: nach der Arbeit von Krienke verifiziert + ! noch nicht fuer Mischungen mit unterschiedl. Ladung erweitert + ! ii_par = DSQRT( e_elem**2 /eps_cc0/dielec/kbol/T & + ! *rho*(x(1)*Z_ii(1)**2 + x(2)*Z_ii(2)**2 ) )*cc_sig1 + + + cc_gam = kappa/2.0 + + ! noch offen !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! + cc_delt = 0.0 + DO i = 1, ncomp + cc_delt = cc_delt + x(i)*mx(i,1)*rho*sigm_i(i)**3 + END DO + cc_delt= 1.0 - PI/6.0*cc_delt + + cc_it = 0 + 13 CONTINUE + j = 0 + cc_it = cc_it + 1 + 131 CONTINUE + j = j + 1 + cc_omeg = 0.0 + DO i = 1, ncomp + cc_omeg = cc_omeg +x(i)*mx(i,1)*sigm_i(i)**3 /(1.0+cc_gam*sigm_i(i)) + END DO + cc_omeg = 1.0 + PI/2.0 / cc_delt * rho * cc_omeg + p_n = 0.0 + DO i = 1, ncomp + p_n = p_n + x(i)*mx(i,1)*rho / cc_omeg*sigm_i(i)*z_ii(i) / (1.0+cc_gam*sigm_i(i)) + END DO + q2_i = 0.0 + cc_q2= 0.0 + DO i = 1, ncomp + q2_i = q2_i + rho*x(i)*mx(i,1)*( (z_ii(i)-pi/2.0/cc_delt*sigm_i(i)**2 *p_n) & + /(1.0+cc_gam*sigm_i(i)) )**2 + cc_q2 = cc_q2 + x(i)*mx(i,1)*rho*z_ii(i)**2 / (1.0+cc_gam*sigm_i(i)) + END DO + q2_i = q2_i*alpha_2 / 4.0 + + cc_error(j) = cc_gam - SQRT(q2_i) + IF (j == 1) cc_gam = cc_gam*1.000001 + IF (j == 2) cc_gam = cc_gam - cc_error(2)* (cc_gam-cc_gam/1.000001)/(cc_error(2)-cc_error(1)) + + IF ( j == 1 .AND. ABS(cc_error(1)) > 1.E-15 ) GO TO 131 + IF ( cc_it >= 10 ) THEN + WRITE (*,*) ' cc error' + STOP + END IF + IF ( j /= 1 ) GO TO 13 + + fcc= - alpha_2 / PI/4.0 /rho* (cc_gam*cc_q2 & + + pi/2.0/cc_delt *cc_omeg*p_n**2 ) + cc_gam**3 /pi/3.0/rho + ! Restricted Primitive Model + ! fcc=-(3.0*ii_par*ii_par+6.0*ii_par+2.0 & + ! -2.0*(1.0+2.0*ii_par)**1.50) & + ! /(12.0*PI*rho *cc_sig1**3 ) + + ! fcc = x_ions * fcc + + my2dd(3) = (parame(3,6))**2 *1.E-19 /(KBOL*t) + my2dd(3) = (1.84)**2 *1.E-19 /(kbol*t) + + rhs = 12.0 * PI * rho * x(3) * my2dd(3) + lam_s = 1.0 + 12 CONTINUE + lambda = (rhs/((lam_s+2.0)**2 ) + 16.0/((1.0+lam_s)**4 ) )**0.5 + IF ( ABS(lam_s-lambda) > 1.E-10 )THEN + lam_s = ( lambda + lam_s ) / 2.0 + GO TO 12 + END IF + + ! f_cd = -(ii_par*ii_par)/(4.0*PI*rho*m_mean *cc_sig1**3 ) & + ! *(dielec-1.0)/(1.0 + parame(3,2)/cc_sig1/lambda) + ! write (*,*) ' ',f_cd,fcc,x_ions + ! f_cd = f_cd/(1.0 - fcc/f_cd) + ! fcc = 0.0 + +END IF + + +END SUBROUTINE F_ION_ION_PrimMSA + + +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! + SUBROUTINE F_ION_ION_nonPrimMSA ( fdd, fqq, fdq, fcc ) +! + USE EOS_VARIABLES, ONLY: nc, ncomp, t, eta, x, parame, mseg + IMPLICIT NONE +! +!--------------------------------------------------------------------- + REAL, INTENT(IN OUT) :: fdd, fqq, fdq, fcc +!--------------------------------------------------------------------- + INTEGER :: dipole + !REAL :: A_MSA !, A_CC, A_CD, A_DD, U_MSA, chempot + REAL, DIMENSION(nc) :: x_export, msegm +!--------------------------------------------------------------------- + + dipole = 0 + IF ( SUM( parame(1:ncomp,6) ) > 1.E-5 ) dipole = 1 + + IF ( dipole /= 0 ) THEN ! alternatively ions and dipoles = 1 + fdd = 0.0 + fqq = 0.0 + fdq = 0.0 + fcc = 0.0 + msegm(:) = mseg(:) ! the entries of the vector mseg and x are changed + x_export(:) = x(:) ! in SEMIRESTRICTED because the ions should be positioned first + ! that is why dummy vectors msegm and x_export are defined + !CALL SEMIRESTRICTED (A_MSA,A_CC,A_CD,A_DD,U_MSA, & + ! chempot,ncomp,parame,t,eta,x_export,msegm,0) + !fdd = A_MSA + write (*,*) 'why are individual contrib. A_CC,A_CD,A_DD not used' + stop + END IF + + END SUBROUTINE F_ION_ION_nonPrimMSA + + +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! + SUBROUTINE F_LC_MayerSaupe ( flc ) +! + USE EOS_VARIABLES, ONLY: nc, PI, KBOL, NAv, ncomp, phas, t, rho, eta, & + x, mseg, parame, E_lc, S_lc, dhs + IMPLICIT NONE +! +!--------------------------------------------------------------------- + REAL, INTENT(IN OUT) :: flc +!--------------------------------------------------------------------- + INTEGER :: i, j, k + INTEGER :: liq_crystal, count_lc, steps_lc + REAL :: alpha_lc, tolerance, deltay + REAL :: integrand1, integrand2, accel_lc + REAL :: error_lc, u_term, sphase + REAL, DIMENSION(nc) :: z_lc, S_lc1, S_lc2, sumu + REAL, DIMENSION(nc,nc) :: u_lc, klc +!--------------------------------------------------------------------- +INTEGER :: stabil +COMMON /stabil / stabil +!--------------------------------------------------------------------- + + + klc(1,2) = 0.0 + klc(2,1) = klc(1,2) + + alpha_lc = 1.0 + accel_lc = 4.0 + IF ( eta < 0.35 ) accel_lc = 1.3 + IF ( eta < 0.15 ) accel_lc = 1.0 + + liq_crystal = 0 + DO i = 1, ncomp + DO j = 1, ncomp + E_lc(i,j) = (E_lc(i,i)*E_lc(j,j))**0.5 *(1.0-klc(i,j)) !combining rule + ! E_LC(i,j)= ( E_LC(i,i)+E_LC(j,j) ) * 0.5 !combining rule + ! S_LC(i,j)= ( S_LC(i,i)+S_LC(j,j) ) * 0.5 !combining rule + IF (E_lc(i,j) /= 0.0) liq_crystal = 1 + END DO + END DO + ! S_LC(1,2) = 0.0 + ! S_LC(2,1) = S_LC(1,2) + ! E_LC(1,2) = 60.0 + ! E_LC(2,1) = E_LC(1,2) + + IF ( liq_crystal == 1 .AND. phas == 1 .AND. stabil == 0 ) THEN + + count_lc = 0 + tolerance = 1.E-6 + + steps_lc = 200 + deltay = 1.0 / REAL(steps_lc) + + ! --- dimensionless function U_LC repres. anisotr. intermolecular interactions in l.c. + + DO i = 1, ncomp + DO j = 1, ncomp + u_lc(i,j) = 2.0/3.0*pi*mseg(i)*mseg(j) *(0.5*(dhs(i)+dhs(j)))**3 & ! sig_ij(i,j)**3 + *(E_lc(i,j)/t+S_lc(i,j))*rho + END DO + END DO + + + DO i=1,ncomp + ! S_lc2(i) = 0.0 !for isotropic + S_lc2(i) = 0.5 !for nematic + S_lc1(i) = S_lc2(i) + END DO + + 1 CONTINUE + + DO i = 1, ncomp + IF (S_lc2(i) <= 0.3) S_lc1(i) = S_lc2(i) + IF (S_lc2(i) > 0.3) S_lc1(i) = S_lc1(i) + (S_lc2(i)-S_lc1(i))*accel_lc + END DO + + count_lc = count_lc + 1 + + ! --- single-particle orientation partition function Z_LC in liquid crystals + + DO i = 1, ncomp + sumu(i) = 0.0 + DO j = 1, ncomp + sumu(i) = sumu(i) + x(j)*u_lc(i,j)*S_lc1(j) + END DO + END DO + + DO i = 1, ncomp + z_lc(i) = 0.0 + integrand1 = EXP(-0.5*sumu(i)) !eq. for Z_LC with y=0 + DO k = 1, steps_lc + integrand2 = EXP(0.5*sumu(i)*(3.0*(deltay*REAL(k)) **2 -1.0)) + z_lc(i) = z_lc(i) + (integrand1 + integrand2)/2.0*deltay + integrand1 = integrand2 + END DO !k-index integration + END DO !i-index Z_LC(i) calculation + + ! --- order parameter S_lc in liquid crystals ----------------------- + + error_lc = 0.0 + DO i = 1, ncomp + S_lc2(i) = 0.0 + integrand1 = -1.0/z_lc(i)*0.5*EXP(-0.5*sumu(i)) !for S_lc with y=0 + DO k = 1, steps_lc + integrand2 = 1.0/z_lc(i)*0.5*(3.0*(deltay*REAL(k)) & + **2 -1.0)*EXP(0.5*sumu(i)*(3.0 *(deltay*REAL(k))**2 -1.0)) + S_lc2(i) = S_lc2(i) + (integrand1 + integrand2)/2.0*deltay + integrand1 = integrand2 + END DO !k-index integration + error_lc = error_lc + ABS(S_lc2(i)-S_lc1(i)) + END DO !i-index Z_LC(i) calculation + + sphase = 0.0 + DO i = 1, ncomp + sphase = sphase + S_lc2(i) + END DO + IF (sphase < 1.E-4) THEN + error_lc = 0.0 + DO i = 1, ncomp + S_lc2(i)= 0.0 + z_lc(i) = 1.0 + END DO + END IF + + + ! write (*,*) count_LC,S_lc2(1)-S_lc1(1),S_lc2(2)-S_lc1(2) + IF (error_lc > tolerance .AND. count_lc < 400) GO TO 1 + ! write (*,*) 'done',eta,S_lc2(1),S_lc2(2) + + IF (count_lc == 400) WRITE (*,*) 'LC iteration not converg.' + + ! --- the anisotropic contribution to the Helmholtz energy ---------- + + u_term = 0.0 + DO i = 1, ncomp + DO j = 1, ncomp + u_term = u_term + 0.5*x(i)*x(j)*S_lc2(i) *S_lc2(j)*u_lc(i,j) + END DO + END DO + + flc = 0.0 + DO i = 1, ncomp + IF (z_lc(i) /= 0.0) flc = flc - x(i) * LOG(z_lc(i)) + END DO + flc = flc + u_term + ! pause + + END IF + ! write (*,'(i2,i2,4(f15.8))') phas,stabil,flc,eta,S_lc2(1),x(1) + + + END SUBROUTINE F_LC_MayerSaupe + + + +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! + SUBROUTINE P_POLAR ( zdd, zddz, zddz2, zddz3, zqq, zqqz, zqqz2, zqqz3, zdq, zdqz, zdqz2, zdqz3 ) +! + USE EOS_VARIABLES, ONLY: ncomp, parame, dd_term, qq_term, dq_term + IMPLICIT NONE +! +! ---------------------------------------------------------------------- + REAL, INTENT(OUT) :: zdd, zddz, zddz2, zddz3 + REAL, INTENT(OUT) :: zqq, zqqz, zqqz2, zqqz3 + REAL, INTENT(OUT) :: zdq, zdqz, zdqz2, zdqz3 +! +! --- local variables--------------------------------------------------- + INTEGER :: dipole + INTEGER :: quadrupole + INTEGER :: dipole_quad +! ---------------------------------------------------------------------- + + zdd = 0.0 + zddz = 0.0 + zddz2 = 0.0 + zddz3 = 0.0 + zqq = 0.0 + zqqz = 0.0 + zqqz2 = 0.0 + zqqz3 = 0.0 + zdq = 0.0 + zdqz = 0.0 + zdqz2 = 0.0 + zdqz3 = 0.0 + + dipole = 0 + quadrupole = 0 + dipole_quad = 0 + IF ( SUM( parame(1:ncomp,6) ) /= 0.0 ) dipole = 1 + IF ( SUM( parame(1:ncomp,7) ) /= 0.0 ) quadrupole = 1 + IF ( dipole == 1 .AND. quadrupole == 1 ) dipole_quad = 1 + + ! -------------------------------------------------------------------- + ! dipole-dipole term + ! -------------------------------------------------------------------- + IF (dipole == 1) THEN + + IF (dd_term == 'GV') CALL P_DD_GROSS_VRABEC( zdd, zddz, zddz2, zddz3 ) + ! IF (dd_term == 'SF') CALL F_DD_SAAGER_FISCHER( k ) + IF (dd_term /= 'GV' .AND. dd_term /= 'SF') write (*,*) 'specify dipole term !' + + ENDIF + + ! -------------------------------------------------------------------- + ! quadrupole-quadrupole term + ! -------------------------------------------------------------------- + IF (quadrupole == 1) THEN + + !IF (qq_term == 'SF') CALL F_QQ_SAAGER_FISCHER( k ) + IF (qq_term == 'JG') CALL P_QQ_GROSS( zqq, zqqz, zqqz2, zqqz3 ) + IF (qq_term /= 'JG' .AND. qq_term /= 'SF') write (*,*) 'specify quadrupole term !' + + ENDIF + + ! -------------------------------------------------------------------- + ! dipole-quadrupole cross term + ! -------------------------------------------------------------------- + IF (dipole_quad == 1) THEN + + IF (dq_term == 'VG') CALL P_DQ_VRABEC_GROSS( zdq, zdqz, zdqz2, zdqz3 ) + IF (dq_term /= 'VG' ) write (*,*) 'specify DQ-cross term !' + + ENDIF + +END SUBROUTINE P_POLAR + + +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! + SUBROUTINE P_DD_GROSS_VRABEC( zdd, zddz, zddz2, zddz3 ) +! + USE PARAMETERS, ONLY: PI, KBOL + USE EOS_VARIABLES, ONLY: nc, ncomp, uij, parame, mseg, sig_ij, rho, eta, x, t + USE EOS_CONSTANTS, ONLY: ddp2, ddp3, ddp4 + IMPLICIT NONE +! +! ---------------------------------------------------------------------- + REAL, INTENT(IN OUT) :: zdd, zddz, zddz2, zddz3 +! ---------------------------------------------------------------------- + INTEGER :: i, j, k, m + REAL :: factor2, factor3, z3 + REAL :: xijfa, xijkfa, eij + REAL :: fdddr, fddd2, fddd3, fddd4 + REAL :: fdd2, fdd2z, fdd2z2, fdd2z3, fdd2z4 + REAL :: fdd3, fdd3z, fdd3z2, fdd3z3, fdd3z4 + REAL, DIMENSION(nc) :: my2dd + REAL, DIMENSION(nc,nc) :: Idd2, Idd2z, Idd2z2, Idd2z3, Idd2z4 + REAL, DIMENSION(nc,nc) :: Idd4, Idd4z, Idd4z2, Idd4z3, Idd4z4 + REAL, DIMENSION(nc,nc,nc) :: Idd3, Idd3z, Idd3z2, Idd3z3, Idd3z4 +! ---------------------------------------------------------------------- + + + zdd = 0.0 + zddz = 0.0 + zddz2 = 0.0 + zddz3 = 0.0 + z3 = eta + DO i = 1, ncomp + my2dd(i) = (parame(i,6))**2 *1.E-49 / (uij(i,i)*KBOL*mseg(i)*sig_ij(i,i)**3 *1.E-30) + END DO + + DO i = 1, ncomp + DO j = 1, ncomp + Idd2(i,j) = 0.0 + Idd4(i,j) = 0.0 + Idd2z(i,j) = 0.0 + Idd4z(i,j) = 0.0 + Idd2z2(i,j) = 0.0 + Idd4z2(i,j) = 0.0 + Idd2z3(i,j) = 0.0 + Idd4z3(i,j) = 0.0 + Idd2z4(i,j) = 0.0 + Idd4z4(i,j) = 0.0 + ! IF (paramei,6).NE.0.0 .AND. parame(j,6).NE.0.0) THEN + DO m = 0, 4 + Idd2(i,j) =Idd2(i,j) + ddp2(i,j,m) *z3**(m+1) + Idd4(i,j) =Idd4(i,j) + ddp4(i,j,m) *z3**(m+1) + Idd2z(i,j) =Idd2z(i,j) +ddp2(i,j,m)*REAL(m+1) *z3**m + Idd4z(i,j) =Idd4z(i,j) +ddp4(i,j,m)*REAL(m+1) *z3**m + Idd2z2(i,j)=Idd2z2(i,j)+ddp2(i,j,m)*REAL((m+1)*m) *z3**(m-1) + Idd4z2(i,j)=Idd4z2(i,j)+ddp4(i,j,m)*REAL((m+1)*m) *z3**(m-1) + Idd2z3(i,j)=Idd2z3(i,j)+ddp2(i,j,m)*REAL((m+1)*m*(m-1)) *z3**(m-2) + Idd4z3(i,j)=Idd4z3(i,j)+ddp4(i,j,m)*REAL((m+1)*m*(m-1)) *z3**(m-2) + Idd2z4(i,j)=Idd2z4(i,j)+ddp2(i,j,m)*REAL((m+1)*m*(m-1)*(m-2)) *z3**(m-3) + Idd4z4(i,j)=Idd4z4(i,j)+ddp4(i,j,m)*REAL((m+1)*m*(m-1)*(m-2)) *z3**(m-3) + END DO + DO k = 1, ncomp + Idd3(i,j,k) = 0.0 + Idd3z(i,j,k) = 0.0 + Idd3z2(i,j,k) = 0.0 + Idd3z3(i,j,k) = 0.0 + Idd3z4(i,j,k) = 0.0 + ! IF (parame(k,6).NE.0.0) THEN + DO m = 0, 4 + Idd3(i,j,k) =Idd3(i,j,k) +ddp3(i,j,k,m)*z3**(m+2) + Idd3z(i,j,k) =Idd3z(i,j,k) +ddp3(i,j,k,m)*REAL(m+2)*z3**(m+1) + Idd3z2(i,j,k)=Idd3z2(i,j,k)+ddp3(i,j,k,m)*REAL((m+2)*(m+1))*z3**m + Idd3z3(i,j,k)=Idd3z3(i,j,k)+ddp3(i,j,k,m)*REAL((m+2)*(m+1)*m)*z3**(m-1) + Idd3z4(i,j,k)=Idd3z4(i,j,k)+ddp3(i,j,k,m)*REAL((m+2)*(m+1)*m*(m-1)) *z3**(m-2) + END DO + ! ENDIF + END DO + ! ENDIF + END DO + END DO + + factor2= -PI *rho/z3 + factor3= -4.0/3.0*PI**2 * (rho/z3)**2 + + fdd2 = 0.0 + fdd2z = 0.0 + fdd2z2 = 0.0 + fdd2z3 = 0.0 + fdd2z4 = 0.0 + fdd3 = 0.0 + fdd3z = 0.0 + fdd3z2 = 0.0 + fdd3z3 = 0.0 + fdd3z4 = 0.0 + DO i = 1, ncomp + DO j = 1, ncomp + ! IF (parame(i,6).NE.0.0 .AND. parame(j,6).NE.0.0) THEN + xijfa = x(i)*parame(i,3)/t*parame(i,2)**3 *x(j)*parame(j,3)/t*parame(j,2)**3 & + / ((parame(i,2)+parame(j,2))/2.0)**3 *my2dd(i)*my2dd(j) + eij = (parame(i,3)*parame(j,3))**0.5 + fdd2 = fdd2 +factor2*xijfa*(Idd2(i,j) +eij/t*Idd4(i,j)) + fdd2z = fdd2z +factor2*xijfa*(Idd2z(i,j) +eij/t*Idd4z(i,j)) + fdd2z2 = fdd2z2+factor2*xijfa*(Idd2z2(i,j)+eij/t*Idd4z2(i,j)) + fdd2z3 = fdd2z3+factor2*xijfa*(Idd2z3(i,j)+eij/t*Idd4z3(i,j)) + fdd2z4 = fdd2z4+factor2*xijfa*(Idd2z4(i,j)+eij/t*Idd4z4(i,j)) + DO k = 1, ncomp + ! IF (parame(k,6).NE.0.0) THEN + xijkfa= x(i)*parame(i,3)/t*parame(i,2)**3 *x(j)*parame(j,3)/t*parame(j,2)**3 & + *x(k)*parame(k,3)/t*parame(k,2)**3 /((parame(i,2)+parame(j,2))/2.0) & + /((parame(i,2)+parame(k,2))/2.0) /((parame(j,2)+parame(k,2))/2.0) & + *my2dd(i)*my2dd(j)*my2dd(k) + fdd3 = fdd3 + factor3 * xijkfa*Idd3(i,j,k) + fdd3z = fdd3z + factor3 * xijkfa*Idd3z(i,j,k) + fdd3z2 = fdd3z2 + factor3 * xijkfa*Idd3z2(i,j,k) + fdd3z3 = fdd3z3 + factor3 * xijkfa*Idd3z3(i,j,k) + fdd3z4 = fdd3z4 + factor3 * xijkfa*Idd3z4(i,j,k) + ! ENDIF + END DO + ! ENDIF + END DO + END DO + IF (fdd2 < -1.E-50 .AND. fdd3 /= 0.0 .AND. fdd2z /= 0.0 .AND. fdd3z /= 0.0) THEN + + fdddr= fdd2* (fdd2*fdd2z - 2.0*fdd3*fdd2z+fdd2*fdd3z) / (fdd2-fdd3)**2 + fddd2=(2.0*fdd2*fdd2z*fdd2z +fdd2*fdd2*fdd2z2 & + -2.0*fdd2z**2 *fdd3-2.0*fdd2*fdd2z2*fdd3+fdd2*fdd2*fdd3z2) & + /(fdd2-fdd3)**2 + fdddr * 2.0*(fdd3z-fdd2z)/(fdd2-fdd3) + fddd3=(2.0*fdd2z**3 +6.0*fdd2*fdd2z*fdd2z2+fdd2*fdd2*fdd2z3 & + -6.0*fdd2z*fdd2z2*fdd3-2.0*fdd2z**2 *fdd3z & + -2.0*fdd2*fdd2z3*fdd3 -2.0*fdd2*fdd2z2*fdd3z & + +2.0*fdd2*fdd2z*fdd3z2+fdd2*fdd2*fdd3z3) /(fdd2-fdd3)**2 & + + 2.0/(fdd2-fdd3)* ( 2.0*fddd2*(fdd3z-fdd2z) & + + fdddr*(fdd3z2-fdd2z2) & + - fdddr/(fdd2-fdd3)*(fdd3z-fdd2z)**2 ) + fddd4=( 12.0*fdd2z**2 *fdd2z2+6.0*fdd2*fdd2z2**2 & + +8.0*fdd2*fdd2z*fdd2z3+fdd2*fdd2*fdd2z4-6.0*fdd2z2**2 *fdd3 & + -12.0*fdd2z*fdd2z2*fdd3z -8.0*fdd2z*fdd2z3*fdd3 & + -2.0*fdd2*fdd2z4*fdd3-4.0*fdd2*fdd2z3*fdd3z & + +4.0*fdd2*fdd2z*fdd3z3+fdd2**2 *fdd3z4 ) /(fdd2-fdd3)**2 & + + 6.0/(fdd2-fdd3)* ( fddd3*(fdd3z-fdd2z) & + -fddd2/(fdd2-fdd3)*(fdd3z-fdd2z)**2 & + - fdddr/(fdd2-fdd3)*(fdd3z-fdd2z)*(fdd3z2-fdd2z2) & + + fddd2*(fdd3z2-fdd2z2) +1.0/3.0*fdddr*(fdd3z3-fdd2z3) ) + zdd = fdddr*eta + zddz = fddd2*eta + fdddr + zddz2 = fddd3*eta + 2.0* fddd2 + zddz3 = fddd4*eta + 3.0* fddd3 + + END IF + + +END SUBROUTINE P_DD_GROSS_VRABEC + + + +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! + SUBROUTINE P_QQ_GROSS( zqq, zqqz, zqqz2, zqqz3 ) +! + USE PARAMETERS, ONLY: PI, KBOL + USE EOS_VARIABLES, ONLY: nc, ncomp, uij, parame, mseg, sig_ij, rho, eta, x, t + USE EOS_CONSTANTS, ONLY: qqp2, qqp3, qqp4 + IMPLICIT NONE +! +! ---------------------------------------------------------------------- + REAL, INTENT(IN OUT) :: zqq, zqqz, zqqz2, zqqz3 +! ---------------------------------------------------------------------- + INTEGER :: i, j, k, m + REAL :: factor2, factor3, z3 + REAL :: xijfa, xijkfa, eij + REAL :: fqqdr, fqqd2, fqqd3, fqqd4 + REAL :: fqq2, fqq2z, fqq2z2, fqq2z3, fqq2z4 + REAL :: fqq3, fqq3z, fqq3z2, fqq3z3, fqq3z4 + REAL, DIMENSION(nc) :: qq2 + REAL, DIMENSION(nc,nc) :: Iqq2, Iqq2z, Iqq2z2, Iqq2z3, Iqq2z4 + REAL, DIMENSION(nc,nc) :: Iqq4, Iqq4z, Iqq4z2, Iqq4z3, Iqq4z4 + REAL, DIMENSION(nc,nc,nc) :: Iqq3, Iqq3z, Iqq3z2, Iqq3z3, Iqq3z4 +! ---------------------------------------------------------------------- + + zqq = 0.0 + zqqz = 0.0 + zqqz2 = 0.0 + zqqz3 = 0.0 + z3 = eta + DO i=1,ncomp + qq2(i) = (parame(i,7))**2 *1.E-69 / (uij(i,i)*kbol*mseg(i)*sig_ij(i,i)**5 *1.E-50) + END DO + + DO i = 1, ncomp + DO j = 1, ncomp + Iqq2(i,j) = 0.0 + Iqq4(i,j) = 0.0 + Iqq2z(i,j) = 0.0 + Iqq4z(i,j) = 0.0 + Iqq2z2(i,j) = 0.0 + Iqq4z2(i,j) = 0.0 + Iqq2z3(i,j) = 0.0 + Iqq4z3(i,j) = 0.0 + Iqq2z4(i,j) = 0.0 + Iqq4z4(i,j) = 0.0 + IF (parame(i,7) /= 0.0 .AND. parame(j,7) /= 0.0) THEN + DO m = 0, 4 + Iqq2(i,j) =Iqq2(i,j) + qqp2(i,j,m)*z3**(m+1) + Iqq4(i,j) =Iqq4(i,j) + qqp4(i,j,m)*z3**(m+1) + Iqq2z(i,j) =Iqq2z(i,j) +qqp2(i,j,m)*REAL(m+1)*z3**m + Iqq4z(i,j) =Iqq4z(i,j) +qqp4(i,j,m)*REAL(m+1)*z3**m + Iqq2z2(i,j)=Iqq2z2(i,j)+qqp2(i,j,m)*REAL((m+1)*m)*z3**(m-1) + Iqq4z2(i,j)=Iqq4z2(i,j)+qqp4(i,j,m)*REAL((m+1)*m)*z3**(m-1) + Iqq2z3(i,j)=Iqq2z3(i,j)+qqp2(i,j,m)*REAL((m+1)*m*(m-1)) *z3**(m-2) + Iqq4z3(i,j)=Iqq4z3(i,j)+qqp4(i,j,m)*REAL((m+1)*m*(m-1)) *z3**(m-2) + Iqq2z4(i,j)=Iqq2z4(i,j)+qqp2(i,j,m)*REAL((m+1)*m*(m-1)*(m-2)) *z3**(m-3) + Iqq4z4(i,j)=Iqq4z4(i,j)+qqp4(i,j,m)*REAL((m+1)*m*(m-1)*(m-2)) *z3**(m-3) + END DO + DO k=1,ncomp + Iqq3(i,j,k) = 0.0 + Iqq3z(i,j,k) = 0.0 + Iqq3z2(i,j,k) = 0.0 + Iqq3z3(i,j,k) = 0.0 + Iqq3z4(i,j,k) = 0.0 + IF (parame(k,7) /= 0.0) THEN + DO m=0,4 + Iqq3(i,j,k) =Iqq3(i,j,k) + qqp3(i,j,k,m)*z3**(m+2) + Iqq3z(i,j,k)=Iqq3z(i,j,k)+qqp3(i,j,k,m)*REAL(m+2)*z3**(m+1) + Iqq3z2(i,j,k)=Iqq3z2(i,j,k)+qqp3(i,j,k,m)*REAL((m+2)*(m+1)) *z3**m + Iqq3z3(i,j,k)=Iqq3z3(i,j,k)+qqp3(i,j,k,m)*REAL((m+2)*(m+1)*m) *z3**(m-1) + Iqq3z4(i,j,k)=Iqq3z4(i,j,k)+qqp3(i,j,k,m) *REAL((m+2)*(m+1)*m*(m-1)) *z3**(m-2) + END DO + END IF + END DO + + END IF + END DO + END DO + + factor2= -9.0/16.0*PI *rho/z3 + factor3= 9.0/16.0*PI**2 * (rho/z3)**2 + + fqq2 = 0.0 + fqq2z = 0.0 + fqq2z2 = 0.0 + fqq2z3 = 0.0 + fqq2z4 = 0.0 + fqq3 = 0.0 + fqq3z = 0.0 + fqq3z2 = 0.0 + fqq3z3 = 0.0 + fqq3z4 = 0.0 + DO i = 1, ncomp + DO j = 1, ncomp + IF (parame(i,7) /= 0.0 .AND. parame(j,7) /= 0.0) THEN + xijfa =x(i)*uij(i,i)*qq2(i)*sig_ij(i,i)**5 /t & + *x(j)*uij(j,j)*qq2(j)*sig_ij(j,j)**5 /t/sig_ij(i,j)**7.0 + eij = (parame(i,3)*parame(j,3))**0.5 + fqq2= fqq2 +factor2*xijfa*(Iqq2(i,j) +eij/t*Iqq4(i,j) ) + fqq2z =fqq2z +factor2*xijfa*(Iqq2z(i,j) +eij/t*Iqq4z(i,j) ) + fqq2z2=fqq2z2+factor2*xijfa*(Iqq2z2(i,j)+eij/t*Iqq4z2(i,j)) + fqq2z3=fqq2z3+factor2*xijfa*(Iqq2z3(i,j)+eij/t*Iqq4z3(i,j)) + fqq2z4=fqq2z4+factor2*xijfa*(Iqq2z4(i,j)+eij/t*Iqq4z4(i,j)) + DO k = 1, ncomp + IF (parame(k,7) /= 0.0) THEN + xijkfa=x(i)*uij(i,i)*qq2(i)*sig_ij(i,i)**5 /t/sig_ij(i,j)**3 & + *x(j)*uij(j,j)*qq2(j)*sig_ij(j,j)**5 /t/sig_ij(i,k)**3 & + *x(k)*uij(k,k)*qq2(k)*sig_ij(k,k)**5 /t/sig_ij(j,k)**3 + fqq3 = fqq3 + factor3 * xijkfa*Iqq3(i,j,k) + fqq3z = fqq3z + factor3 * xijkfa*Iqq3z(i,j,k) + fqq3z2 = fqq3z2 + factor3 * xijkfa*Iqq3z2(i,j,k) + fqq3z3 = fqq3z3 + factor3 * xijkfa*Iqq3z3(i,j,k) + fqq3z4 = fqq3z4 + factor3 * xijkfa*Iqq3z4(i,j,k) + END IF + END DO + END IF + END DO + END DO + IF (fqq2 < -1.E-50 .AND. fqq3 /= 0.0 .AND. fqq2z /= 0.0 .AND. fqq3z /= 0.0) THEN + fqqdr = fqq2* (fqq2*fqq2z - 2.0*fqq3*fqq2z+fqq2*fqq3z) /(fqq2-fqq3)**2 + fqqd2= (2.0*fqq2*fqq2z*fqq2z +fqq2*fqq2*fqq2z2 & + -2.0*fqq2z**2 *fqq3-2.0*fqq2*fqq2z2*fqq3+fqq2*fqq2*fqq3z2) & + /(fqq2-fqq3)**2 + fqqdr * 2.0*(fqq3z-fqq2z)/(fqq2-fqq3) + fqqd3=(2.0*fqq2z**3 +6.0*fqq2*fqq2z*fqq2z2+fqq2*fqq2*fqq2z3 & + -6.0*fqq2z*fqq2z2*fqq3-2.0*fqq2z**2 *fqq3z & + -2.0*fqq2*fqq2z3*fqq3 -2.0*fqq2*fqq2z2*fqq3z & + +2.0*fqq2*fqq2z*fqq3z2+fqq2*fqq2*fqq3z3) /(fqq2-fqq3)**2 & + + 2.0/(fqq2-fqq3)* ( 2.0*fqqd2*(fqq3z-fqq2z) & + + fqqdr*(fqq3z2-fqq2z2) - fqqdr/(fqq2-fqq3)*(fqq3z-fqq2z)**2 ) + fqqd4=( 12.0*fqq2z**2 *fqq2z2+6.0*fqq2*fqq2z2**2 & + +8.0*fqq2*fqq2z*fqq2z3+fqq2*fqq2*fqq2z4-6.0*fqq2z2**2 *fqq3 & + -12.0*fqq2z*fqq2z2*fqq3z -8.0*fqq2z*fqq2z3*fqq3 & + -2.0*fqq2*fqq2z4*fqq3-4.0*fqq2*fqq2z3*fqq3z & + +4.0*fqq2*fqq2z*fqq3z3+fqq2**2 *fqq3z4 ) /(fqq2-fqq3)**2 & + + 6.0/(fqq2-fqq3)* ( fqqd3*(fqq3z-fqq2z) & + -fqqd2/(fqq2-fqq3)*(fqq3z-fqq2z)**2 & + - fqqdr/(fqq2-fqq3)*(fqq3z-fqq2z)*(fqq3z2-fqq2z2) & + + fqqd2*(fqq3z2-fqq2z2) +1.0/3.0*fqqdr*(fqq3z3-fqq2z3) ) + zqq = fqqdr*eta + zqqz = fqqd2*eta + fqqdr + zqqz2 = fqqd3*eta + 2.0* fqqd2 + zqqz3 = fqqd4*eta + 3.0* fqqd3 + END IF + + +END SUBROUTINE P_QQ_GROSS + +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! + SUBROUTINE P_DQ_VRABEC_GROSS( zdq, zdqz, zdqz2, zdqz3 ) +! + USE PARAMETERS, ONLY: PI, KBOL + USE EOS_VARIABLES, ONLY: nc, ncomp, uij, parame, mseg, sig_ij, rho, eta, x, t + USE EOS_CONSTANTS, ONLY: dqp2, dqp3, dqp4 + IMPLICIT NONE +! +! ---------------------------------------------------------------------- + REAL, INTENT(IN OUT) :: zdq, zdqz, zdqz2, zdqz3 +! ---------------------------------------------------------------------- + INTEGER :: i, j, k, m + REAL :: factor2, factor3, z3 + REAL :: xijfa, xijkfa, eij + REAL :: fdqdr, fdqd2, fdqd3, fdqd4 + REAL :: fdq2, fdq2z, fdq2z2, fdq2z3, fdq2z4 + REAL :: fdq3, fdq3z, fdq3z2, fdq3z3, fdq3z4 + REAL, DIMENSION(nc) :: my2dd, myfac, qq2, q_fac + REAL, DIMENSION(nc,nc) :: Idq2, Idq2z, Idq2z2, Idq2z3, Idq2z4 + REAL, DIMENSION(nc,nc) :: Idq4, Idq4z, Idq4z2, Idq4z3, Idq4z4 + REAL, DIMENSION(nc,nc,nc) :: Idq3, Idq3z, Idq3z2, Idq3z3, Idq3z4 +! ---------------------------------------------------------------------- + + zdq = 0.0 + zdqz = 0.0 + zdqz2 = 0.0 + zdqz3 = 0.0 + z3 = eta + DO i = 1, ncomp + my2dd(i) = (parame(i,6))**2 *1.E-49 / (uij(i,i)*KBOL*mseg(i)*sig_ij(i,i)**3 *1.E-30) + myfac(i) = parame(i,3)/t*parame(i,2)**4 *my2dd(i) + qq2(i) = (parame(i,7))**2 *1.E-69 / (uij(i,i)*kbol*mseg(i)*sig_ij(i,i)**5 *1.E-50) + q_fac(i) = parame(i,3)/t*parame(i,2)**4 *qq2(i) + END DO + + + DO i = 1, ncomp + DO j = 1, ncomp + Idq2(i,j) = 0.0 + Idq4(i,j) = 0.0 + Idq2z(i,j) = 0.0 + Idq4z(i,j) = 0.0 + Idq2z2(i,j) = 0.0 + Idq4z2(i,j) = 0.0 + Idq2z3(i,j) = 0.0 + Idq4z3(i,j) = 0.0 + Idq2z4(i,j) = 0.0 + Idq4z4(i,j) = 0.0 + IF (myfac(i) /= 0.0 .AND. q_fac(j) /= 0.0) THEN + DO m = 0, 4 + Idq2(i,j) =Idq2(i,j) + dqp2(i,j,m)*z3**(m+1) + Idq4(i,j) =Idq4(i,j) + dqp4(i,j,m)*z3**(m+1) + Idq2z(i,j) =Idq2z(i,j) +dqp2(i,j,m)*REAL(m+1)*z3**m + Idq4z(i,j) =Idq4z(i,j) +dqp4(i,j,m)*REAL(m+1)*z3**m + Idq2z2(i,j)=Idq2z2(i,j)+dqp2(i,j,m)*REAL((m+1)*m)*z3**(m-1) + Idq4z2(i,j)=Idq4z2(i,j)+dqp4(i,j,m)*REAL((m+1)*m)*z3**(m-1) + Idq2z3(i,j)=Idq2z3(i,j)+dqp2(i,j,m)*REAL((m+1)*m*(m-1)) *z3**(m-2) + Idq4z3(i,j)=Idq4z3(i,j)+dqp4(i,j,m)*REAL((m+1)*m*(m-1)) *z3**(m-2) + Idq2z4(i,j)=Idq2z4(i,j)+dqp2(i,j,m)*REAL((m+1)*m*(m-1)*(m-2)) *z3**(m-3) + Idq4z4(i,j)=Idq4z4(i,j)+dqp4(i,j,m)*REAL((m+1)*m*(m-1)*(m-2)) *z3**(m-3) + END DO + DO k = 1, ncomp + Idq3(i,j,k) = 0.0 + Idq3z(i,j,k) = 0.0 + Idq3z2(i,j,k) = 0.0 + Idq3z3(i,j,k) = 0.0 + Idq3z4(i,j,k) = 0.0 + IF (myfac(k) /= 0.0.OR.q_fac(k) /= 0.0) THEN + DO m = 0, 4 + Idq3(i,j,k) =Idq3(i,j,k) + dqp3(i,j,k,m)*z3**(m+2) + Idq3z(i,j,k)=Idq3z(i,j,k)+dqp3(i,j,k,m)*REAL(m+2)*z3**(m+1) + Idq3z2(i,j,k)=Idq3z2(i,j,k)+dqp3(i,j,k,m)*REAL((m+2)*(m+1)) *z3**m + Idq3z3(i,j,k)=Idq3z3(i,j,k)+dqp3(i,j,k,m)*REAL((m+2)*(m+1)*m) *z3**(m-1) + Idq3z4(i,j,k)=Idq3z4(i,j,k)+dqp3(i,j,k,m) & + *REAL((m+2)*(m+1)*m*(m-1)) *z3**(m-2) + END DO + END IF + END DO + + END IF + END DO + END DO + + factor2= -9.0/4.0*PI *rho/z3 + factor3= PI**2 * (rho/z3)**2 + + fdq2 = 0.0 + fdq2z = 0.0 + fdq2z2 = 0.0 + fdq2z3 = 0.0 + fdq2z4 = 0.0 + fdq3 = 0.0 + fdq3z = 0.0 + fdq3z2 = 0.0 + fdq3z3 = 0.0 + fdq3z4 = 0.0 + DO i = 1, ncomp + DO j = 1, ncomp + IF (myfac(i) /= 0.0 .AND. q_fac(j) /= 0.0) THEN + xijfa =x(i)*myfac(i) * x(j)*q_fac(j) /sig_ij(i,j)**5 + eij = (parame(i,3)*parame(j,3))**0.5 + fdq2= fdq2 +factor2*xijfa*(Idq2(i,j) +eij/t*Idq4(i,j) ) + fdq2z =fdq2z +factor2*xijfa*(Idq2z(i,j) +eij/t*Idq4z(i,j) ) + fdq2z2=fdq2z2+factor2*xijfa*(Idq2z2(i,j)+eij/t*Idq4z2(i,j)) + fdq2z3=fdq2z3+factor2*xijfa*(Idq2z3(i,j)+eij/t*Idq4z3(i,j)) + fdq2z4=fdq2z4+factor2*xijfa*(Idq2z4(i,j)+eij/t*Idq4z4(i,j)) + DO k = 1, ncomp + IF (myfac(k) /= 0.0.OR.q_fac(k) /= 0.0) THEN + xijkfa=x(i)*x(j)*x(k)/(sig_ij(i,j)*sig_ij(i,k)*sig_ij(j,k))**2 & + *( myfac(i)*q_fac(j)*myfac(k) + myfac(i)*q_fac(j)*q_fac(k)*1.193735 ) + fdq3 =fdq3 + factor3 * xijkfa*Idq3(i,j,k) + fdq3z =fdq3z + factor3 * xijkfa*Idq3z(i,j,k) + fdq3z2=fdq3z2 + factor3 * xijkfa*Idq3z2(i,j,k) + fdq3z3=fdq3z3 + factor3 * xijkfa*Idq3z3(i,j,k) + fdq3z4=fdq3z4 + factor3 * xijkfa*Idq3z4(i,j,k) + END IF + END DO + END IF + END DO + END DO + IF (fdq2 < -1.E-50 .AND. fdq3 /= 0.0 .AND. fdq2z /= 0.0 .AND. fdq3z /= 0.0) THEN + fdqdr = fdq2* (fdq2*fdq2z - 2.0*fdq3*fdq2z+fdq2*fdq3z) /(fdq2-fdq3)**2 + fdqd2= (2.0*fdq2*fdq2z*fdq2z +fdq2*fdq2*fdq2z2 & + -2.0*fdq2z**2 *fdq3-2.0*fdq2*fdq2z2*fdq3+fdq2*fdq2*fdq3z2) & + /(fdq2-fdq3)**2 + fdqdr * 2.0*(fdq3z-fdq2z)/(fdq2-fdq3) + fdqd3=(2.0*fdq2z**3 +6.0*fdq2*fdq2z*fdq2z2+fdq2*fdq2*fdq2z3 & + -6.0*fdq2z*fdq2z2*fdq3-2.0*fdq2z**2 *fdq3z & + -2.0*fdq2*fdq2z3*fdq3 -2.0*fdq2*fdq2z2*fdq3z & + +2.0*fdq2*fdq2z*fdq3z2+fdq2*fdq2*fdq3z3) /(fdq2-fdq3)**2 & + + 2.0/(fdq2-fdq3)* ( 2.0*fdqd2*(fdq3z-fdq2z) & + + fdqdr*(fdq3z2-fdq2z2) - fdqdr/(fdq2-fdq3)*(fdq3z-fdq2z)**2 ) + fdqd4=( 12.0*fdq2z**2 *fdq2z2+6.0*fdq2*fdq2z2**2 & + +8.0*fdq2*fdq2z*fdq2z3+fdq2*fdq2*fdq2z4-6.0*fdq2z2**2 *fdq3 & + -12.0*fdq2z*fdq2z2*fdq3z -8.0*fdq2z*fdq2z3*fdq3 & + -2.0*fdq2*fdq2z4*fdq3-4.0*fdq2*fdq2z3*fdq3z & + +4.0*fdq2*fdq2z*fdq3z3+fdq2**2 *fdq3z4 ) /(fdq2-fdq3)**2 & + + 6.0/(fdq2-fdq3)* ( fdqd3*(fdq3z-fdq2z) & + -fdqd2/(fdq2-fdq3)*(fdq3z-fdq2z)**2 & + - fdqdr/(fdq2-fdq3)*(fdq3z-fdq2z)*(fdq3z2-fdq2z2) & + + fdqd2*(fdq3z2-fdq2z2) +1.0/3.0*fdqdr*(fdq3z3-fdq2z3) ) + zdq = fdqdr*eta + zdqz = fdqd2*eta + fdqdr + zdqz2 = fdqd3*eta + 2.0* fdqd2 + zdqz3 = fdqd4*eta + 3.0* fdqd3 + END IF + + +END SUBROUTINE P_DQ_VRABEC_GROSS + + + +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! + SUBROUTINE F_pert_theory ( fdsp ) +! + USE EOS_VARIABLES, ONLY: nc, PI, ncomp, t, p, rho, eta, & + x, z0t, mseg, parame, order1, order2 + USE EOS_NUMERICAL_DERIVATIVES, ONLY: disp_term + USE DFT_MODULE + IMPLICIT NONE +! +!--------------------------------------------------------------------- + REAL, INTENT(IN OUT) :: fdsp +!--------------------------------------------------------------------- + REAL :: I1, I2 + REAL :: z3, zms, c1_con, m_mean +!--------------------------------------------------------------------- + + ! caution: positive sign of correlation integral is used here ! + ! (the Helmholtz energy terms are written with a negative sign, while I1 and I2 are positive) + + IF (disp_term == 'PT1') THEN + + CALL f_dft ( I1, I2) + c1_con = 0.0 + I2 = 0.0 + fdsp = + ( - 2.0*PI*rho*I1*order1 ) + + ELSEIF (disp_term == 'PT2') THEN + + CALL f_dft ( I1, I2) + z3 = eta + zms = 1.0 - z3 + m_mean = z0t / ( PI / 6.0 ) + c1_con = 1.0/ ( 1.0 + m_mean*(8.0*z3-2.0*z3**2 )/zms**4 & + + (1.0 - m_mean)*( 20.0*z3 -27.0*z3**2 +12.0*z3**3 -2.0*z3**4 ) & + /(zms*(2.0-z3))**2 ) + fdsp = + ( - 2.0*PI*rho*I1*order1 - PI*rho*c1_con*m_mean*I2*order2 ) + + ELSEIF (disp_term == 'PT_MIX') THEN + + CALL f_pert_theory_mix ( fdsp ) + + ELSEIF (disp_term == 'PT_MF') THEN + + ! mean field theory + I1 = - ( - 8.0/9.0 - 4.0/9.0*(rc**(-9) -3.0*rc**(-3) ) - tau_cut/3.0*(rc**3 -1.0) ) + fdsp = + ( - 2.0*PI*rho*I1*order1 ) + write (*,*) 'caution: not thoroughly checked and tested' + + ELSE + write (*,*) 'define the type of perturbation theory' + stop + END IF + + ! I1 = I1 + 4.0/9.0*(2.5**-9 -3.0*2.5**-3 ) + ! fdsp = + ( - 2.0*PI*rho*I1*order1 - PI*rho*c1_con*m_mean*I2*order2 ) + + END SUBROUTINE F_pert_theory + + + + +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! + SUBROUTINE f_pert_theory_mix ( fdsp ) +! + USE EOS_VARIABLES, ONLY: nc, PI, ncomp, t, rho, eta, x, parame, mseg, dhs, sig_ij, uij + USE DFT_MODULE + IMPLICIT NONE +! +! ---------------------------------------------------------------------- + REAL, INTENT(IN OUT) :: fdsp +! +! ---------------------------------------------------------------------- + INTEGER :: k, ih + INTEGER :: l, m + REAL :: z3 + REAL :: ua, ua_c, rm + REAL, DIMENSION(nc,nc) :: I1 + REAL :: int10, int11 + REAL :: d_ij, dzr_local + REAL :: rad, xg, rdf + REAL :: dg_dz3, dg_dr + ! REAL :: intgrid(0:5000),intgri2(0:5000), utri(5000),I1_spline +! ---------------------------------------------------------------------- + +! -----constants-------------------------------------------------------- + ua_c = 4.0 * ( rc**(-12) - rc**(-6) ) + rm = 2.0**(1.0/6.0) + + I1(:,:) = 0.0 + + DO l = 1, ncomp + DO m = 1, ncomp + + rad = rc + + int10 = rc * rc * ua_c + ! intgrid(0)= int10 + + k = 0 + ih = 85 + + DO WHILE ( rad /= 1.0 ) + + dzr_local = dzr + IF ( rad - dzr_local <= 1.0 ) dzr_local = rad - 1.0 + + rad = rad - dzr_local + + k = k + 1 + + d_ij = 0.5*(dhs(l)+dhs(m)) / sig_ij(l,m) ! dimensionless effective hs-diameter d(T)/sig + xg = rad / d_ij + z3 = eta + rdf = 1.0 + dg_dz3 = 0.0 + IF ( rad <= rg ) THEN + IF ( l == 1 .AND. m == 1 ) CALL BI_CUB_SPLINE (z3,xg,ya_11,x1a_11,x2a_11,y1a_11,y2a_11,y12a_11, & + c_bicub_11,rdf,dg_dz3,dg_dr,den_step,ih,k) + IF ( l /= m ) CALL BI_CUB_SPLINE (z3,xg,ya_12,x1a_12,x2a_12,y1a_12,y2a_12,y12a_12, & + c_bicub_12,rdf,dg_dz3,dg_dr,den_step,ih,k) + IF ( l == 2 .AND. m == 2 ) CALL BI_CUB_SPLINE (z3,xg,ya_22,x1a_22,x2a_22,y1a_22,y2a_22,y12a_22, & + c_bicub_22,rdf,dg_dz3,dg_dr,den_step,ih,k) + END IF + + ua = 4.0 * ( rad**(-12) - rad**(-6) ) + + int11 = rdf * rad * rad * ua + I1(l,m) = I1(l,m) + dzr_local * ( int11 + int10 ) / 2.0 + + int10 = int11 + ! intgrid(k)= int11 + + END DO + + ! stepno = k + ! CALL SPLINE_PARA (dzr,intgrid,utri,stepno) + ! CALL SPLINE_INT (I1_spline,dzr,intgrid,utri,stepno) + + + ! caution: 1st order integral is in F_EOS.f defined with negative sign + ! --------------------------------------------------------------- + ! cut-off corrections + ! --------------------------------------------------------------- + ! I1(l,m) = I1(l,m) + ( 4.0/9.0 * rc**-9 - 4.0/3.0 * rc**-3 ) + ! I2(l,m) = I2(l,m) + 16.0/21.0 * rc**-21 - 32.0/15.0 * rc**-15 + 16.0/9.0 * rc**-9 + + END DO + END DO + + + fdsp = 0.0 + DO l = 1, ncomp + DO m = 1, ncomp + fdsp = fdsp + 2.0*PI*rho*x(l)*x(m)* mseg(l)*mseg(m)*sig_ij(l,m)**3 * uij(l,m)/t *I1(l,m) + ! ( 2.0*PI*rho*I1*order1 - PI*rho*c1_con*m_mean*I2*order2 ) + END DO + END DO + + +!!$ IF (disp_term == 'PT1') THEN +!!$ c1_con = 0.0 +!!$ I2 = 0.0 +!!$ ELSEIF (disp_term == 'PT2') THEN +!!$ zms = 1.0 - z3 +!!$ c1_con = 1.0/ ( 1.0 + m_mean*(8.0*z3-2.0*z3**2 )/zms**4 & +!!$ + (1.0 - m_mean)*( 20.0*z3 -27.0*z3**2 +12.0*z3**3 -2.0*z3**4 ) & +!!$ /(zms*(2.0-z3))**2 ) +!!$ ELSE +!!$ write (*,*) 'define the type of perturbation theory' +!!$ stop +!!$ END IF + + +END SUBROUTINE f_pert_theory_mix + + +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! + SUBROUTINE mu_pert_theory_mix ( mu_dsp ) +! + USE EOS_VARIABLES, ONLY: nc, PI, ncomp, t, rho, eta, x, parame, mseg, dhs, sig_ij, uij + USE DFT_MODULE + IMPLICIT NONE +! +! ---------------------------------------------------------------------- + REAL, INTENT(IN OUT) :: mu_dsp(nc) +! +! ---------------------------------------------------------------------- + INTEGER :: k, ih + INTEGER :: l, m + REAL :: z3 + REAL :: ua, ua_c, rm + REAL, DIMENSION(nc,nc) :: I1, I2 + REAL :: int1_0, int1_1, int2_0, int2_1 + REAL :: d_ij, dzr_local + REAL :: rad, xg, rdf + REAL :: dg_dz3, dg_dr + REAL :: term1(nc), term2 + ! REAL :: intgrid(0:5000),intgri2(0:5000), utri(5000),I1_spline +! ---------------------------------------------------------------------- + +! -----constants-------------------------------------------------------- + ua_c = 4.0 * ( rc**(-12) - rc**(-6) ) + rm = 2.0**(1.0/6.0) + + I1(:,:) = 0.0 + I2(:,:) = 0.0 + + DO l = 1, ncomp + + term1(l) = 0.0 + + DO m = 1, ncomp + + rad = rc + + int1_0 = rc * rc * ua_c + int2_0 = 0.0 + + k = 0 + ih = 85 + + DO WHILE ( rad /= 1.0 ) + + dzr_local = dzr + IF ( rad - dzr_local <= 1.0 ) dzr_local = rad - 1.0 + + rad = rad - dzr_local + k = k + 1 + + d_ij = 0.5*(dhs(l)+dhs(m)) / sig_ij(l,m) ! dimensionless effective hs-diameter d(T)/sig + xg = rad / d_ij + z3 = eta + rdf = 1.0 + dg_dz3 = 0.0 + IF ( rad <= rg ) THEN + IF ( l == 1 .AND. m == 1 ) CALL BI_CUB_SPLINE (z3,xg,ya_11,x1a_11,x2a_11,y1a_11,y2a_11,y12a_11, & + c_bicub_11,rdf,dg_dz3,dg_dr,den_step,ih,k) + IF ( l /= m ) CALL BI_CUB_SPLINE (z3,xg,ya_12,x1a_12,x2a_12,y1a_12,y2a_12,y12a_12, & + c_bicub_12,rdf,dg_dz3,dg_dr,den_step,ih,k) + IF ( l == 2 .AND. m == 2 ) CALL BI_CUB_SPLINE (z3,xg,ya_22,x1a_22,x2a_22,y1a_22,y2a_22,y12a_22, & + c_bicub_22,rdf,dg_dz3,dg_dr,den_step,ih,k) + END IF + + ua = 4.0 * ( rad**(-12) - rad**(-6) ) + + int1_1 = rdf * rad * rad * ua + int2_1 = dg_dz3 * rad * rad * ua + I1(l,m) = I1(l,m) + dzr_local * ( int1_1 + int1_0 ) / 2.0 + I2(l,m) = I2(l,m) + dzr_local * ( int2_1 + int2_0 ) / 2.0 + + int1_0 = int1_1 + int2_0 = int2_1 + + term1(l) = term1(l) +4.0*PI*rho*x(m)* mseg(l)*mseg(m) *sig_ij(l,m)**3 *uij(l,m)/t* dzr_local*(int1_1+int1_0)/2.0 + + END DO + + END DO + END DO + + + ! DO l = 1, ncomp + ! term1(l) = 0.0 + ! DO m = 1, ncomp + ! term1(l) = term1(l) + 4.0*PI*rho*x(m)* mseg(l)*mseg(m) * sig_ij(l,m)**3 * uij(l,m)/t *I1(l,m) + ! END DO + ! END DO + + term2 = 0.0 + DO l = 1, ncomp + DO m = 1, ncomp + term2 = term2 + 2.0*PI*rho*x(l) * rho*x(m)* mseg(l)*mseg(m) * sig_ij(l,m)**3 * uij(l,m)/t *I2(l,m) + END DO + END DO + + DO l = 1, ncomp + mu_dsp(l) = term1(l) + term2 * PI/ 6.0 * mseg(l)*dhs(l)**3 + END DO + +END SUBROUTINE mu_pert_theory_mix + + +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! + SUBROUTINE F_DD_GROSS_VRABEC( fdd ) +! + USE PARAMETERS, ONLY: PI, KBOL + USE EOS_VARIABLES, ONLY: nc, ncomp, uij, parame, mseg, sig_ij, rho, eta, x, t + USE EOS_CONSTANTS, ONLY: ddp2, ddp3, ddp4 + IMPLICIT NONE +! +! ---------------------------------------------------------------------- + REAL, INTENT(IN OUT) :: fdd +! ---------------------------------------------------------------------- + INTEGER :: i, j, k, m + INTEGER :: ddit, ddmax + REAL :: factor2, factor3 + REAL :: xijfa, xijkfa, xijf_j, xijkf_j, eij + REAL :: fdd2, fdd3 + REAL, DIMENSION(nc) :: my2dd, my0, alph_tst, z1dd, z2dd, dderror + REAL, DIMENSION(nc) :: fdd2m, fdd3m, fdd2m2, fdd3m2, fddm, fddm2 + REAL, DIMENSION(nc,nc) :: Idd2, Idd4 + REAL, DIMENSION(nc,nc,nc) :: Idd3 +! ---------------------------------------------------------------------- + + fdd = 0.0 + ddit = 0 + ddmax = 0 ! value assigned, if polarizable compound is present + fddm(:) = 0.0 + DO i = 1, ncomp + IF ( uij(i,i) == 0.0 ) write (*,*) 'F_DD_GROSS_VRABEC: do not use dimensionless units' + IF ( uij(i,i) == 0.0 ) stop + my2dd(i) = (parame(i,6))**2 *1.E-49 /(uij(i,i)*kbol* mseg(i)*sig_ij(i,i)**3 *1.E-30) + alph_tst(i) = parame(i,11) / (mseg(i)*sig_ij(i,i)**3 ) * t/parame(i,3) + IF ( alph_Tst(i) /= 0.0 ) ddmax = 25 ! set maximum number of polarizable RGT-iterations + z1dd(i) = my2dd(i) + 3.0*alph_tst(i) + z2dd(i) = 3.0*alph_tst(i) + my0(i) = my2dd(i) + END DO + + DO i = 1, ncomp + DO j = 1, ncomp + Idd2(i,j) = 0.0 + Idd4(i,j) = 0.0 + ! IF (parame(i,6).NE.0.0 .AND. parame(j,6).NE.0.0) THEN + DO m = 0, 4 + Idd2(i,j) = Idd2(i,j) + ddp2(i,j,m)*eta**m + Idd4(i,j) = Idd4(i,j) + ddp4(i,j,m)*eta**m + END DO + DO k = 1, ncomp + Idd3(i,j,k) = 0.0 + ! IF (parame(k,6).NE.0.0) THEN + DO m = 0, 4 + Idd3(i,j,k) = Idd3(i,j,k) + ddp3(i,j,k,m)*eta**m + END DO + ! ENDIF + END DO + ! ENDIF + END DO + END DO + + factor2 = -PI *rho + factor3 = -4.0/3.0*PI**2 * rho**2 + +9 CONTINUE + + fdd2m(:) = 0.0 + fdd2m2(:) = 0.0 + fdd3m(:) = 0.0 + fdd3m2(:) = 0.0 + fdd2 = 0.0 + fdd3 = 0.0 + DO i = 1, ncomp + DO j = 1, ncomp + ! IF (parame(i,6).NE.0.0 .AND. parame(j,6).NE.0.0) THEN + xijfa =x(i)*parame(i,3)/t*parame(i,2)**3 * x(j)*parame(j,3)/t*parame(j,2)**3 & + /((parame(i,2)+parame(j,2))/2.0)**3 * (z1dd(i)*z1dd(j)-z2dd(i)*z2dd(j)) ! * (1.0-lij(i,j)) + eij = (parame(i,3)*parame(j,3))**0.5 + fdd2= fdd2 + factor2 * xijfa * ( Idd2(i,j) + eij/t*Idd4(i,j) ) + xijf_j = parame(i,3)/t*parame(i,2)**3 *x(j)*parame(j,3)/t*parame(j,2)**3 & + /((parame(i,2)+parame(j,2))/2.0)**3 ! * (1.0-lij(i,j)) + fdd2m(i)=fdd2m(i)+4.0*SQRT(my2dd(i))*z1dd(j)*factor2* xijf_j *(Idd2(i,j)+eij/t*Idd4(i,j)) + fdd2m2(i)=fdd2m2(i) + 4.0*z1dd(j)*factor2* xijf_j *(Idd2(i,j)+eij/t*Idd4(i,j)) + IF (j == i) fdd2m2(i) =fdd2m2(i) +8.0*factor2* xijf_j*my2dd(i) *(Idd2(i,j)+eij/t*Idd4(i,j)) + DO k = 1, ncomp + ! IF (parame(k,6).NE.0.0) THEN + xijkfa = x(i)*parame(i,3)/t*parame(i,2)**3 *x(j)*parame(j,3)/t*parame(j,2)**3 & + *x(k)*parame(k,3)/t*parame(k,2)**3 / ((parame(i,2)+parame(j,2))/2.0) & + /((parame(i,2)+parame(k,2))/2.0) / ((parame(j,2)+parame(k,2))/2.0) & + *(z1dd(i)*z1dd(j)*z1dd(k)-z2dd(i)*z2dd(j)*z2dd(k)) + ! *(1.0-lij(i,j))*(1.0-lij(i,k))*(1.0-lij(j,k)) + fdd3 = fdd3 + factor3 * xijkfa * Idd3(i,j,k) + xijkf_j = parame(i,3)/t*parame(i,2)**3 *x(j)*parame(j,3)/t*parame(j,2)**3 & + *x(k)*parame(k,3)/t*parame(k,2)**3 /((parame(i,2)+parame(j,2))/2.0) & + /((parame(i,2)+parame(k,2))/2.0) /((parame(j,2)+parame(k,2))/2.0) + ! *(1.0-lij(i,j))*(1.0-lij(i,k))*(1.0-lij(j,k)) + fdd3m(i)=fdd3m(i)+6.0*factor3*SQRT(my2dd(i))*z1dd(j)*z1dd(k) *xijkf_j*Idd3(i,j,k) + fdd3m2(i)=fdd3m2(i)+6.0*factor3*z1dd(j)*z1dd(k) *xijkf_j*Idd3(i,j,k) + IF(j == i) fdd3m2(i) =fdd3m2(i)+24.0*factor3*my2dd(i)*z1dd(k) *xijkf_j*Idd3(i,j,k) + ! ENDIF + END DO + ! ENDIF + END DO + END DO + + IF (fdd2 < -1.E-50 .AND. fdd3 /= 0.0) THEN + fdd = fdd2 / ( 1.0 - fdd3/fdd2 ) + IF ( ddmax /= 0 ) THEN + DO i = 1, ncomp + ddit = ddit + 1 + fddm(i) =fdd2*(fdd2*fdd2m(i) -2.0*fdd3*fdd2m(i)+fdd2*fdd3m(i)) /(fdd2-fdd3)**2 + fddm2(i) = fdd2m(i) * (fdd2*fdd2m(i)-2.0*fdd3*fdd2m(i) +fdd2*fdd3m(i)) / (fdd2-fdd3)**2 & + + fdd2*(fdd2*fdd2m2(i) -2.0*fdd3*fdd2m2(i)+fdd2m(i)**2 & + -fdd2m(i)*fdd3m(i) +fdd2*fdd3m2(i)) / (fdd2-fdd3)**2 & + - 2.0*fdd2*(fdd2*fdd2m(i) -2.0*fdd3*fdd2m(i) +fdd2*fdd3m(i)) /(fdd2-fdd3)**3 & + *(fdd2m(i)-fdd3m(i)) + dderror(i)= SQRT( my2dd(i) ) - SQRT( my0(i) ) + alph_Tst(i)*fddm(i) + my2dd(i) = ( SQRT( my2dd(i) ) - dderror(i) / (1.0+alph_Tst(i)*fddm2(i)) )**2 + z1dd(i) = my2dd(i) + 3.0 * alph_Tst(i) + ENDDO + DO i = 1, ncomp + IF (ABS(dderror(i)) > 1.E-11 .AND. ddit < ddmax) GOTO 9 + ENDDO + fdd = fdd + SUM( 0.5*x(1:ncomp)*alph_Tst(1:ncomp)*fddm(1:ncomp)**2 ) + ENDIF + END IF + + +END SUBROUTINE F_DD_GROSS_VRABEC + + + +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! + SUBROUTINE F_QQ_GROSS( fqq ) +! + USE PARAMETERS, ONLY: PI, KBOL + USE EOS_VARIABLES, ONLY: nc, ncomp, uij, parame, mseg, sig_ij, rho, eta, x, t + USE EOS_CONSTANTS, ONLY: qqp2, qqp3, qqp4 + IMPLICIT NONE +! +! ---------------------------------------------------------------------- + REAL, INTENT(IN OUT) :: fqq +! ---------------------------------------------------------------------- + INTEGER :: i, j, k, m + REAL :: factor2, factor3 + REAL :: xijfa, xijkfa, eij + REAL :: fqq2, fqq3 + REAL, DIMENSION(nc) :: qq2 + REAL, DIMENSION(nc,nc) :: Iqq2, Iqq4 + REAL, DIMENSION(nc,nc,nc) :: Iqq3 +! ---------------------------------------------------------------------- + + + fqq = 0.0 + DO i = 1, ncomp + qq2(i) = (parame(i,7))**2 *1.E-69 / (uij(i,i)*kbol*mseg(i)*sig_ij(i,i)**5 *1.E-50) + END DO + + DO i = 1, ncomp + DO j = 1, ncomp + Iqq2(i,j) = 0.0 + Iqq4(i,j) = 0.0 + IF (parame(i,7) /= 0.0 .AND. parame(j,7) /= 0.0) THEN + DO m = 0, 4 + Iqq2(i,j) = Iqq2(i,j) + qqp2(i,j,m)*eta**m + Iqq4(i,j) = Iqq4(i,j) + qqp4(i,j,m)*eta**m + END DO + DO k = 1, ncomp + Iqq3(i,j,k) = 0.0 + IF (parame(k,7) /= 0.0) THEN + DO m = 0, 4 + Iqq3(i,j,k) = Iqq3(i,j,k) + qqp3(i,j,k,m)*eta**m + END DO + END IF + END DO + END IF + END DO + END DO + + factor2 = -9.0/16.0*PI *rho + factor3 = 9.0/16.0*PI**2 * rho**2 + + fqq2 = 0.0 + fqq3 = 0.0 + DO i = 1, ncomp + DO j = 1, ncomp + IF (parame(i,7) /= 0.0 .AND. parame(j,7) /= 0.0) THEN + xijfa=x(i)*uij(i,i)*qq2(i)*sig_ij(i,i)**5 /t & + *x(j)*uij(j,j)*qq2(j)*sig_ij(j,j)**5 /t/sig_ij(i,j)**7.0 + eij = (parame(i,3)*parame(j,3))**0.5 + fqq2= fqq2 +factor2* xijfa * (Iqq2(i,j)+eij/t*Iqq4(i,j)) + DO k = 1, ncomp + IF (parame(k,7) /= 0.0) THEN + xijkfa=x(i)*uij(i,i)*qq2(i)*sig_ij(i,i)**5 /t/sig_ij(i,j)**3 & + *x(j)*uij(j,j)*qq2(j)*sig_ij(j,j)**5 /t/sig_ij(i,k)**3 & + *x(k)*uij(k,k)*qq2(k)*sig_ij(k,k)**5 /t/sig_ij(j,k)**3 + fqq3 = fqq3 + factor3 * xijkfa * Iqq3(i,j,k) + END IF + END DO + END IF + END DO + END DO + + IF ( fqq2 < -1.E-50 .AND. fqq3 /= 0.0 ) THEN + fqq = fqq2 / ( 1.0 - fqq3/fqq2 ) + END IF + + + +END SUBROUTINE F_QQ_GROSS + +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! + SUBROUTINE F_DQ_VRABEC_GROSS( fdq ) +! + USE PARAMETERS, ONLY: PI, KBOL + USE EOS_VARIABLES, ONLY: nc, ncomp, uij, parame, mseg, sig_ij, rho, eta, x, t + USE EOS_CONSTANTS, ONLY: dqp2, dqp3, dqp4 + IMPLICIT NONE +! +! ---------------------------------------------------------------------- + REAL, INTENT(IN OUT) :: fdq +! ---------------------------------------------------------------------- + INTEGER :: i, j, k, m + REAL :: factor2, factor3 + REAL :: xijfa, xijkfa, eij + REAL :: fdq2, fdq3 + REAL, DIMENSION(nc) :: my2dd, myfac, qq2, q_fac + REAL, DIMENSION(nc,nc) :: Idq2, Idq4 + REAL, DIMENSION(nc,nc,nc) :: Idq3 +! ---------------------------------------------------------------------- + + + fdq = 0.0 + DO i = 1, ncomp + my2dd(i) = (parame(i,6))**2 *1.E-49 /(uij(i,i)*kbol* mseg(i)*sig_ij(i,i)**3 *1.E-30) + myfac(i) = parame(i,3)/t*parame(i,2)**4 *my2dd(i) + ! myfac(i)=parame(i,3)/T*parame(i,2)**4 *my2dd_renormalized(i) + qq2(i) = (parame(i,7))**2 *1.E-69 / (uij(i,i)*kbol*mseg(i)*sig_ij(i,i)**5 *1.E-50) + q_fac(i) = parame(i,3)/t*parame(i,2)**4 *qq2(i) + END DO + + DO i = 1, ncomp + DO j = 1, ncomp + Idq2(i,j) = 0.0 + Idq4(i,j) = 0.0 + IF (myfac(i) /= 0.0 .AND. q_fac(j) /= 0.0) THEN + DO m = 0, 4 + Idq2(i,j) = Idq2(i,j) + dqp2(i,j,m)*eta**m + Idq4(i,j) = Idq4(i,j) + dqp4(i,j,m)*eta**m + END DO + DO k = 1, ncomp + Idq3(i,j,k) = 0.0 + IF (myfac(k) /= 0.0 .OR. q_fac(k) /= 0.0) THEN + DO m = 0, 4 + Idq3(i,j,k) = Idq3(i,j,k) + dqp3(i,j,k,m)*eta**m + END DO + END IF + END DO + END IF + END DO + END DO + + factor2 = -9.0/4.0 * PI *rho + factor3 = PI**2 * rho**2 + + fdq2 = 0.0 + fdq3 = 0.0 + DO i = 1, ncomp + DO j = 1, ncomp + IF (myfac(i) /= 0.0 .AND. q_fac(j) /= 0.0) THEN + xijfa = x(i)*myfac(i) * x(j)*q_fac(j) /sig_ij(i,j)**5 + eij = (parame(i,3)*parame(j,3))**0.5 + fdq2 = fdq2 +factor2* xijfa*(Idq2(i,j)+eij/t*Idq4(i,j)) + DO k = 1, ncomp + IF (myfac(k) /= 0.0 .OR. q_fac(k) /= 0.0) THEN + xijkfa=x(i)*x(j)*x(k)/(sig_ij(i,j)*sig_ij(i,k)*sig_ij(j,k))**2 & + *( myfac(i)*q_fac(j)*myfac(k) + myfac(i)*q_fac(j)*q_fac(k)*1.1937350 ) + fdq3 = fdq3 + factor3*xijkfa*Idq3(i,j,k) + END IF + END DO + END IF + END DO + END DO + + IF (fdq2 < -1.E-50 .AND. fdq3 /= 0.0) THEN + fdq = fdq2 / ( 1.0 - fdq3/fdq2 ) + END IF + +END SUBROUTINE F_DQ_VRABEC_GROSS + + +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! + SUBROUTINE f_dft ( I1_dft, I2_dft ) +! + USE EOS_VARIABLES, ONLY: nc, PI, ncomp, t, rho, eta, x, mseg, parame + USE DFT_MODULE + IMPLICIT NONE +! +! ---------------------------------------------------------------------- + REAL, INTENT(OUT) :: I1_dft + REAL, INTENT(OUT) :: I2_dft +! +! ---------------------------------------------------------------------- + INTEGER :: k,ih + ! REAL :: z3 + REAL :: ua, ua_c, ua_2, ua_c_2, rm + REAL :: int10, int11, int20, int21 + REAL :: dg_drho + REAL :: rad, xg, rdf, rho_st, msegm + REAL :: sig_ij + REAL :: dg_dr, dzr_org !,rdf_d + ! REAL :: intgrid(0:NDFT),intgri2(0:NDFT) +! ---------------------------------------------------------------------- + +! -----constants-------------------------------------------------------- +msegm = parame(1,1) +rho_st = rho * parame(1,2)**3 + +ua_c = 4.0 * ( rc**(-12) - rc**(-6) ) +ua_c_2 = ua_c * ua_c +rm = 2.0**(1.0/6.0) + +int10 = rc*rc* ua_c +int20 = rc*rc* ua_c_2 +! intgrid(0)= int10 +! intgri2(0)= int20 + + +sig_ij = parame(1,2) + + +I1_dft = 0.0 +I2_dft = 0.0 +rad = rc +!dzr = dzp / 2.0 ! this line is obsolete. dzr is defined in DFT-nMF2 (dimensionless) +dzr_org= dzr +k = 0 +ih = 85 + +DO WHILE ( rad-dzr+1.E-9 >= 1.0 ) + + rad = rad - dzr + ! IF (rad <= 8.0) dzr = dzp + ! IF (rad <= rg) dzr = dzp/2.0 + k = k + 1 + xg = rad / dhs_st + ua = 4.0 * ( rad**(-12) - rad**(-6) ) + ua_2 = ua * ua + rdf = 1.0 + dg_drho = 0.0 + IF ( rad <= rg ) THEN + CALL BI_CUB_SPLINE (rho_st,xg,ya,x1a,x2a,y1a,y2a,y12a, & + c_bicub,rdf,dg_drho,dg_dr,den_step,ih,k) + END IF + + int11 = rdf*rad*rad* ua + int21 = rdf*rad*rad* ua_2 + I1_dft= I1_dft + dzr*(int11+int10)/2.0 + I2_dft= I2_dft + dzr*(int21+int20)/2.0 + int10 = int11 + int20 = int21 + +END DO + +dzr = dzr_org + +! stepno = k +! CALL SPLINE_PARA (dzr,intgrid,utri,stepno) +! CALL SPLINE_INT (I1,dzr,intgrid,utri,stepno) + +! caution: 1st order integral is in F_EOS.f defined with negative sign +I1_dft= - I1_dft - ( 4.0/9.0 * rc**(-9) - 4.0/3.0 * rc**(-3) ) + +! CALL SPLINE_PARA (dzr,intgri2,utri,stepno) +! CALL SPLINE_INT (I2,dzr,intgri2,utri,stepno) + +I2_dft = I2_dft + 16.0/21.0 * rc**(-21) - 32.0/15.0 * rc**(-15) + 16.0/9.0 * rc**(-9) + + +END SUBROUTINE f_dft + + + + +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! + REAL FUNCTION TANGENT_VALUE2 ( optpara, n ) +! SUBROUTINE TANGENT_VALUE ( fmin, optpara, n ) +! + USE BASIC_VARIABLES + USE STARTING_VALUES + IMPLICIT NONE +! +! ---------------------------------------------------------------------- + INTEGER, INTENT(IN) :: n + REAL, INTENT(IN) :: optpara(n) + !REAL, INTENT(IN) :: optpara(:) + !REAL, INTENT(IN OUT) :: fmin +! +! ---------------------------------------------------------------------- + INTEGER :: i + REAL :: lnphi(np,nc),ph_frac, gibbs_full(np),xlnx1,xlnx2 + REAL, DIMENSION(nc) :: ni_1, ni_2 +! ---------------------------------------------------------------------- + + + ! --- setting of mole fractions --------------------------------------- + DO i = 1, ncomp + IF ( optpara(i) < -300.0 ) THEN + ni_2(i) = 0.0 + ELSE + ni_2(i) = EXP( optpara(i) ) + END IF + END DO + + DO i = 1, ncomp + ni_1(i) = xif(i) - ni_2(i) + IF ( ni_2(i) > xif(i) ) THEN + ni_2(i) = xif(i) + ni_1(i) = xif(i) * 1.E-20 + ENDIF + END DO + + xi(2,1:ncomp) = ni_2(1:ncomp) / SUM( ni_2(1:ncomp) ) + lnx(2,1:ncomp) = optpara(1:ncomp) - LOG( SUM( ni_2(1:ncomp) ) ) + + ph_frac = SUM( ni_1(1:ncomp) ) + xi(1,1:ncomp) = ni_1(1:ncomp) / ph_frac + lnx(1,1:ncomp) = LOG( ni_1(1:ncomp) ) - LOG( ph_frac ) + ! write (*,'(a,4G18.8)') 'FF',(xif(i),i=1,ncomp) + ! write (*,'(a,4G18.8)') 'AA',(xi(1,i),i=1,ncomp) + ! write (*,'(a,3G18.8)') 'BB',(xi(2,i),i=1,ncomp) + + CALL fugacity (lnphi) + !CALL enthalpy_etc + + gibbs(1) = SUM( xi(1,1:ncomp) * lnphi(1,1:ncomp) ) ! dimensionless g/RT + gibbs(2) = SUM( xi(2,1:ncomp) * lnphi(2,1:ncomp) ) + + xlnx1 = SUM( xi(1,1:ncomp)*lnx(1,1:ncomp) ) ! dimensionless s/RT + xlnx2 = SUM( xi(2,1:ncomp)*lnx(2,1:ncomp) ) + + gibbs_full(1) = gibbs(1) + xlnx1 + gibbs_full(2) = gibbs(2) + xlnx2 + + TANGENT_VALUE2 = gibbs_full(1)*ph_frac + gibbs_full(2)*(1.0-ph_frac) + !fmin = gibbs_full(1)*ph_frac + gibbs_full(2)*(1.0-ph_frac) + !write (*,'(a,4G18.8)') 'TP',TANGENT_VALUE2,(lnx(1,i),i=1,ncomp) + !write (*,'(a,4G18.8)') 'al',ph_frac,(lnx(2,i), i=1,ncomp) + !write (*,*) ' ' + !pause + +END FUNCTION TANGENT_VALUE2 + + + + + + + + diff --git a/applications/PUfoam/MoDeNaModels/SurfaceTension/src/crit_point_mixtures.F90 b/applications/PUfoam/MoDeNaModels/SurfaceTension/src/crit_point_mixtures.F90 new file mode 100644 index 000000000..3c5dd8218 --- /dev/null +++ b/applications/PUfoam/MoDeNaModels/SurfaceTension/src/crit_point_mixtures.F90 @@ -0,0 +1,474 @@ +!>This file contains the subroutines which determine the critical point of +!!a mixture. + + +SUBROUTINE CRIT_POINT_MIX(tc,user) + +!PETSc module +USE PetscManagement + +!VLE and DFT modules +USE BASIC_VARIABLES + +IMPLICIT NONE + +#include + +type (userctx) user +REAL :: tc +!local +REAL :: tc_L, tc_V, xi_save(np,nc),p_save +PetscErrorCode ierr + + +!!J:save value of pressure because it is changed during the calculation +p_save = p + +! --------------------------------------------------------------------- + ! determine the critical temp. to xi of liquid and to xi of vapor + ! --------------------------------------------------------------------- + + + xi_save(:,:) = xi(:,:) + dense(1) = 0.15 + + !call MPI_Barrier(PETSC_COMM_WORLD,ierr) + + !only proc 0 reads in the estimate and then sends it to all other procs using MPI_Bcast +! IF(user%rank == 0) THEN +! WRITE (*,*) 'provide an estimate of the crit. Temp. of the mixture' +! READ (*,*) t +! END IF + + t = 1.2 * t !initial estimate of critical temperature + + CALL MPI_Bcast(t,1,MPI_DOUBLE_PRECISION,0,PETSC_COMM_WORLD,ierr) + + xiF(1:ncomp) = xi_save(1,1:ncomp) + CALL Heidemann_Khalil + tc_L = t +! IF(user%rank == 0) THEN +! WRITE (*,*) 'critical temperature to xi_liquid',tc_L +! END IF + + xiF(1:ncomp) = xi_save(2,1:ncomp) + ! dense(1) = 0.15 + ! WRITE (*,*) 'provide an estimate of the crit. Temp. of the mixture' + ! READ (*,*) t + CALL Heidemann_Khalil + tc_V = t +! IF(user%rank == 0) THEN +! WRITE (*,*) 'critical temperature to xi_vapor ',tc_V +! END IF + + ! tc_L = 600.0 + ! WRITE (*,*) 'I have tentitativly set tc=700 ' + ! pause + + + !tc = ( tc_L + tc_V ) / 2.0 + tc = tc_L + xi(:,:) = xi_save(:,:) + densta(1:nphas) = val_conv(1:nphas) + dense(1:nphas) = val_conv(1:nphas) + t = val_conv(3) + IF(user%rank == 0) THEN + WRITE (*,*) 'estimate of critical temperature:',tc,'K' + WRITE (*,*) ' ' + END IF + +!!J: set pressure to its regular value +p = p_save + + +END SUBROUTINE CRIT_POINT_MIX + + + + + + + + + +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! SUBROUTINE Heidemann_Khalil +! +! This subroutine .... +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! + SUBROUTINE Heidemann_Khalil +! + USE PARAMETERS, ONLY: PI + USE BASIC_VARIABLES + USE Module_Heidemann_Khalil + USE Solve_NonLin + IMPLICIT NONE +! +! ---------------------------------------------------------------------- + INTERFACE + SUBROUTINE Heidemann_Khalil_obj ( iter_no, y, residu, dummy ) + INTEGER, INTENT(IN) :: iter_no + REAL, INTENT(IN) :: y(iter_no) + REAL, INTENT(OUT) :: residu(iter_no) + INTEGER, INTENT(IN OUT) :: dummy + END SUBROUTINE Heidemann_Khalil_obj + END INTERFACE +! + INTEGER :: info + REAL, ALLOCATABLE :: y(:),diag(:),residu(:) + + INTEGER :: i, count, nphas_save + REAL :: error0, error1, dense0, dfdx, delta_rho + CHARACTER (LEN=2) :: ensemble_save +! ---------------------------------------------------------------------- + + ensemble_save = ensemble_flag + ensemble_flag = 'tv' + + nphas_save = nphas + nphas = 1 + + ! xiF(2) = 0.5 * ( 0.71928411 + 0.72025642 ) + ! xiF(1) = 1.0 - xiF(2) + ! dense(1) = 0.5 * ( 0.159315 + 0.158817 ) + 0.02 + ! t = 500.0 + + dense0 = dense(1) + + info = 1 + n_unkw = ncomp + 1 + acc_a = 5.E-8 + step_a = 1.E-8 + + + ALLOCATE( y(n_unkw), diag(n_unkw), residu(n_unkw) ) + DO i = 1,ncomp + y(i) = 1.0 / SQRT( REAL( ncomp ) ) + END DO + y(ncomp+1) = t + count = 0 + error0 = 1.0 + + DO WHILE ( ABS( error0) > 0.001 .AND. count < 20 ) + count = count + 1 + + dense(1) = dense0 + 0.0001 + CALL hbrd (Heidemann_Khalil_obj, n_unkw, y, residu, step_a, acc_a, info, diag) + error1 = error_condition2 + IF (SUM( ABS( residu(1:n_unkw) ) ) > 1.E-5) write (*,*) 'caution: error 1st inner loop', SUM( ABS( residu(1:n_unkw) ) ) + + dense(1) = dense0 + CALL hbrd (Heidemann_Khalil_obj, n_unkw, y, residu, step_a, acc_a, info, diag) + IF (SUM( ABS( residu(1:n_unkw) ) ) > 1.E-5) write (*,*) 'caution: error 2nd inner loop', SUM( ABS( residu(1:n_unkw) ) ) + error0 = error_condition2 + + ! write (*,'(a,4G18.10)') ' t, p, eta error', t, p, dense(1), error0 + ! pause + dfdx = ( error1 - error0 ) / 0.0001 + delta_rho = MIN( error0 / dfdx, 0.02) + delta_rho = MAX( delta_rho, -0.02) + dense0 = dense0 - delta_rho + dense(1) = dense0 + + END DO + + !tc = t + !pc = p + + DEALLOCATE( y, diag, residu ) + + ensemble_flag = ensemble_save + nphas = nphas_save + IF ( ABS( error_condition2 ) > 1.E-1 ) write (*,*) 'caution: error outer loop', ABS( error_condition2 ) + +END SUBROUTINE Heidemann_Khalil + + +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! SUBROUTINE Heidemann_Khalil +! +! This subroutine .... +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! + SUBROUTINE Heidemann_Khalil_obj ( iter_no, y, residu, dummy ) +! + USE PARAMETERS, ONLY: PI + USE BASIC_VARIABLES + USE Module_Heidemann_Khalil + IMPLICIT NONE +! +! ---------------------------------------------------------------------- + INTEGER, INTENT(IN) :: iter_no + REAL, INTENT(IN) :: y(iter_no) + REAL, INTENT(OUT) :: residu(iter_no) + INTEGER, INTENT(IN OUT) :: dummy +! +! ---------------------------------------------------------------------- + INTEGER :: i, j, k + REAL, DIMENSION(nc) :: dn + REAL, DIMENSION(nc) :: dhs, rhoi00, rhoi0 + REAL :: rho, d_rho + ! REAL :: lnphi(np,nc) + REAL :: qij(nc,nc), qij0(nc,nc), qijk(nc,nc,nc) + ! CHARACTER (LEN=3) :: char_len +! ---------------------------------------------------------------------- + + dn(1:ncomp) = y(1:ncomp) + t = y(ncomp+1) + !dense(1) = y(ncomp+2) + + dhs(1:ncomp) = parame(1:ncomp,2) * ( 1.0 - 0.12 *EXP( -3.0*parame(1:ncomp,3)/t ) ) + rho = dense(1) / SUM( PI/6.0*xiF(1:ncomp)*parame(1:ncomp,1)* dhs(1:ncomp)**3 ) + rhoi00(1:ncomp) = xiF(1:ncomp)*rho + + d_rho = 0.000001 + + DO k = 1, ncomp + + rhoi0(1:ncomp) = rhoi00(1:ncomp) + rhoi0(k) = rhoi00(k) + d_rho + CALL qij_matrix ( rhoi0, dhs, d_rho, qij ) + qij0(:,:) = qij(:,:) + + rhoi0(1:ncomp) = rhoi00(1:ncomp) + CALL qij_matrix ( rhoi0, dhs, d_rho, qij ) + + DO i = 1, ncomp + DO j = 1, ncomp + qijk(i,j,k) = ( qij0(i,j) - qij(i,j) ) / d_rho + ! write(*,*) i,j,k,qijk(i,j,k) + END DO + END DO + + END DO + + ! write (*,'(a,4G18.10)') 'det',qij(2,2)*qij(1,1) - qij(2,1)*qij(1,2) + ! write (*,'(a,3G18.10)') ' t,p,eta ', t, p, dense(1) + DO j = 1, ncomp + residu(j) = SUM( qij(1:ncomp,j)*dn(1:ncomp) ) + END DO + residu(ncomp+1) = 1.0 - SUM( dn(1:ncomp)*dn(1:ncomp) ) + + error_condition2 = 0.0 + DO k = 1, ncomp + DO i = 1, ncomp + DO j = 1, ncomp + error_condition2 = error_condition2 + qijk(i,j,k) * dn(i) * dn(j) * dn(k) + END DO + END DO + END DO + error_condition2 = error_condition2 * 1.E-4 ! the values are scaled down to prevent numerical dominance of this error + !residu(ncomp+2) = error_condition2 + + !write (char_len,'(I3)') ncomp+2 + !write (*,'(a,'//char_len//'G18.10)') ' error',residu(1:ncomp+1) + !write (*,*) ' ' + !pause + +END SUBROUTINE Heidemann_Khalil_obj + + +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! SUBROUTINE Heidemann_Khalil +! +! This subroutine calculates the spinodal for a binary mixture to given +! T, p and for a given starting value of the density vector rhoi +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! + SUBROUTINE binary_tp_spinodal ( rhoi, p_sp ) +! + USE PARAMETERS, ONLY: PI + USE BASIC_VARIABLES + USE Module_Heidemann_Khalil + USE Solve_NonLin + IMPLICIT NONE +! +! ---------------------------------------------------------------------- + INTERFACE + SUBROUTINE binary_spinodal_obj ( iter_no, y, residu, dummy ) + INTEGER, INTENT(IN) :: iter_no + REAL, INTENT(IN) :: y(iter_no) + REAL, INTENT(OUT) :: residu(iter_no) + INTEGER, INTENT(IN OUT) :: dummy + END SUBROUTINE binary_spinodal_obj + END INTERFACE + + REAL, dimension(nc) :: rhoi + REAL :: p_sp +! ---------------------------------------------------------------------- + + INTEGER :: info + REAL, ALLOCATABLE :: y(:), diag(:), residu(:) + + INTEGER :: i, nphas_save + CHARACTER (LEN=2) :: ensemble_save +! ---------------------------------------------------------------------- + + ensemble_save = ensemble_flag + ensemble_flag = 'tv' + + nphas_save = nphas + nphas = 1 + + info = 1 + n_unkw = ncomp + 2 + acc_a = 5.E-8 + step_a = 1.E-8 + + + ALLOCATE( y(n_unkw), diag(n_unkw), residu(n_unkw) ) + DO i = 1, ncomp + y(i) = 1.0 / SQRT( REAL( ncomp ) ) + END DO + DO i = 1, ncomp + y( ncomp + i ) = rhoi( i ) + END DO + + CALL hbrd (binary_spinodal_obj, n_unkw, y, residu, step_a, acc_a, info, diag) + + DO i = 1, ncomp + rhoi( i ) = y( ncomp + i ) + END DO + write (*,*) 'info',info + write (*,*) 'rhoi',rhoi(1:ncomp) + !write (*,*) 'eta',PI / 6.0 * sum( rhoi(1:ncomp)*mseg(1:ncomp)*dhs(1:ncomp)**3 ) + write (*,*) 'x',rhoi(1:ncomp) / sum( rhoi(1:ncomp) ) + + DEALLOCATE( y, diag, residu ) + + ensemble_flag = ensemble_save + nphas = nphas_save + +END SUBROUTINE binary_tp_spinodal + + +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! SUBROUTINE Heidemann_Khalil +! +! This subroutine .... +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! + SUBROUTINE binary_spinodal_obj ( iter_no, y, residu, dummy ) +! + USE PARAMETERS, ONLY: PI + USE BASIC_VARIABLES + USE Module_Heidemann_Khalil + IMPLICIT NONE +! +! ---------------------------------------------------------------------- + INTEGER, INTENT(IN) :: iter_no + REAL, INTENT(IN) :: y(iter_no) + REAL, INTENT(OUT) :: residu(iter_no) + INTEGER, INTENT(IN OUT) :: dummy +! +! ---------------------------------------------------------------------- + INTEGER :: j, k + REAL :: p_calculated, zges, p_sp + REAL :: d_rho + REAL, DIMENSION(nc) :: dn + REAL, DIMENSION(nc) :: dhs, rhoi + REAL, DIMENSION(nc,nc) :: qij +! ---------------------------------------------------------------------- + + dn(1:ncomp) = y(1:ncomp) + rhoi(1:ncomp) = y( (ncomp+1) : (ncomp+ncomp) ) + dhs(1:ncomp) = parame(1:ncomp,2) * ( 1.0 - 0.12 *EXP( -3.0*parame(1:ncomp,3)/t ) ) ! is this calc. needed? + + call p_calc ( p_calculated, zges ) + + d_rho = 0.000001 + + DO k = 1, ncomp + + CALL qij_matrix ( rhoi, dhs, d_rho, qij ) + + END DO + + !write (*,'(a,4G18.10)') 'det',qij(2,2)*qij(1,1) - qij(2,1)*qij(1,2) + write (*,'(a,3G18.10)') ' t,p,eta ', t, p, dense(1) + DO j = 1, ncomp + residu(j) = SUM( qij(1:ncomp,j)*dn(1:ncomp) ) + END DO + residu(ncomp+1) = 1.0 - SUM( dn(1:ncomp)*dn(1:ncomp) ) + write (*,*) 'p_sp has to be handed over to the obj fct properly!' + write (*,*) 'Can I simply set p = p_sp? In other words is p altered during the calculation?' + stop + residu(ncomp+2) = p_sp - p_calculated + + write (*,'(a,4G18.10)') ' error',residu(1:4) + write (*,*) ' ' + pause + +END SUBROUTINE binary_spinodal_obj + + +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! SUBROUTINE Heidemann_Khalil +! +! This subroutine .... +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! + SUBROUTINE qij_matrix ( rhoi0, dhs, d_rho, qij ) +! + USE PARAMETERS, ONLY: PI, KBOL + USE BASIC_VARIABLES + USE EOS_VARIABLES, ONLY: pges + IMPLICIT NONE +! +! ---------------------------------------------------------------------- + REAL, DIMENSION(nc), INTENT(IN) :: rhoi0 + REAL, DIMENSION(nc), INTENT(IN) :: dhs + REAL, INTENT(IN) :: d_rho + REAL, DIMENSION(nc,nc), INTENT(OUT) :: qij +! +! ---------------------------------------------------------------------- + INTEGER :: i + REAL, DIMENSION(nc) :: rhoi, lnf0, lnf1, lnf2 + REAL :: lnphi(np,nc), zges +! ---------------------------------------------------------------------- + + + DO i = 1, ncomp + rhoi(1:ncomp) = rhoi0(1:ncomp) + rhoi(i) = rhoi0(i) + d_rho + dense(1) = SUM( PI/6.0*rhoi(1:ncomp)*parame(1:ncomp,1)* dhs(1:ncomp)**3 ) + densta(1) = dense(1) + xi(1,1:ncomp) = rhoi(1:ncomp) / SUM( rhoi(1:ncomp) ) + CALL FUGACITY ( lnphi ) + p = pges + zges = (pges * 1.d-30) / ( KBOL*t*SUM(rhoi(1:ncomp)) ) + lnf1(1:ncomp) = lnphi(1,1:ncomp) + LOG( rhoi(1:ncomp) ) + + IF (rhoi0(i) - d_rho > 0.0 ) THEN + rhoi(1:ncomp) = rhoi0(1:ncomp) + rhoi(i) = rhoi0(i) - d_rho + dense(1) = SUM( PI/6.0*rhoi(1:ncomp)*parame(1:ncomp,1)* dhs(1:ncomp)**3 ) + densta(1) = dense(1) + xi(1,1:ncomp) = rhoi(1:ncomp) / SUM( rhoi(1:ncomp) ) + CALL FUGACITY ( lnphi ) + p = pges + zges = (pges * 1.d-30) / ( KBOL*t*SUM(rhoi(1:ncomp)) ) + lnf2(1:ncomp) = lnphi(1,1:ncomp) + LOG( rhoi(1:ncomp) ) + END IF + + rhoi(1:ncomp) = rhoi0(1:ncomp) + dense(1) = SUM( PI/6.0*rhoi(1:ncomp)*parame(1:ncomp,1)* dhs(1:ncomp)**3 ) + densta(1) = dense(1) + xi(1,1:ncomp) = rhoi(1:ncomp) / SUM( rhoi(1:ncomp) ) + CALL FUGACITY ( lnphi ) + p = pges + zges = (pges * 1.d-30) / ( KBOL*t*SUM(rhoi(1:ncomp)) ) + lnf0(1:ncomp) = lnphi(1,1:ncomp) + LOG( rhoi(1:ncomp) ) + + IF (rhoi0(i) - d_rho > 0.0 ) THEN + qij(i,1:ncomp) = ( lnf1(1:ncomp) - lnf2(1:ncomp) ) / (2.0*d_rho) ! qij = d(F/V) / (d_rho_i*d_rho_j) + ELSE + qij(i,1:ncomp) = ( lnf1(1:ncomp) - lnf0(1:ncomp) ) / d_rho ! qij = d(F/V) / (d_rho_i*d_rho_j) + END IF + ! write (*,*) i,1,qij(i,1) + ! write (*,*) i,2,qij(i,2) + END DO + +END SUBROUTINE qij_matrix + diff --git a/applications/PUfoam/MoDeNaModels/SurfaceTension/src/fort.40 b/applications/PUfoam/MoDeNaModels/SurfaceTension/src/fort.40 new file mode 100644 index 000000000..b01fbd7fd --- /dev/null +++ b/applications/PUfoam/MoDeNaModels/SurfaceTension/src/fort.40 @@ -0,0 +1 @@ + x1_ph1 x2_ph1 x3_ph1 x1_ph2 x2_ph2 x3_ph2 T P rho1 rho2 diff --git a/applications/PUfoam/MoDeNaModels/SurfaceTension/src/getting_started_subroutines.F90 b/applications/PUfoam/MoDeNaModels/SurfaceTension/src/getting_started_subroutines.F90 new file mode 100644 index 000000000..3de5d08dc --- /dev/null +++ b/applications/PUfoam/MoDeNaModels/SurfaceTension/src/getting_started_subroutines.F90 @@ -0,0 +1,4126 @@ + +!>This file contains auxiliary subroutines. + + + +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! SUBROUTINE eos_const +! +! This subroutine provides the constants of the PC-SAFT EOS. +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! + SUBROUTINE eos_const (ap,bp,dnm) +! + IMPLICIT NONE +! +! ---------------------------------------------------------------------- + REAL, INTENT(OUT) :: ap(0:6,3) + REAL, INTENT(OUT) :: bp(0:6,3) + REAL, INTENT(OUT) :: dnm(4,9) +! ---------------------------------------------------------------------- + + +! --- dispersion term constants ---------------------------------------- +ap(0,1) = 0.91056314451539 +ap(0,2) = -0.30840169182720 +ap(0,3) = -0.09061483509767 +ap(1,1) = 0.63612814494991 +ap(1,2) = 0.18605311591713 +ap(1,3) = 0.45278428063920 +ap(2,1) = 2.68613478913903 +ap(2,2) = -2.50300472586548 +ap(2,3) = 0.59627007280101 +ap(3,1) = -26.5473624914884 +ap(3,2) = 21.4197936296668 +ap(3,3) = -1.72418291311787 +ap(4,1) = 97.7592087835073 +ap(4,2) = -65.2558853303492 +ap(4,3) = -4.13021125311661 +ap(5,1) = -159.591540865600 +ap(5,2) = 83.3186804808856 +ap(5,3) = 13.7766318697211 +ap(6,1) = 91.2977740839123 +ap(6,2) = -33.7469229297323 +ap(6,3) = -8.67284703679646 + +bp(0,1) = 0.72409469413165 +bp(0,2) = -0.57554980753450 +bp(0,3) = 0.09768831158356 +bp(1,1) = 1.11913959304690 *2.0 +bp(1,2) = 0.34975477607218 *2.0 +bp(1,3) = -0.12787874908050 *2.0 +bp(2,1) = -1.33419498282114 *3.0 +bp(2,2) = 1.29752244631769 *3.0 +bp(2,3) = -3.05195205099107 *3.0 +bp(3,1) = -5.25089420371162 *4.0 +bp(3,2) = -4.30386791194303 *4.0 +bp(3,3) = 5.16051899359931 *4.0 +bp(4,1) = 5.37112827253230 *5.0 +bp(4,2) = 38.5344528930499 *5.0 +bp(4,3) = -7.76088601041257 *5.0 +bp(5,1) = 34.4252230677698 *6.0 +bp(5,2) = -26.9710769414608 *6.0 +bp(5,3) = 15.6044623461691 *6.0 +bp(6,1) = -50.8003365888685 *7.0 +bp(6,2) = -23.6010990650801 *7.0 +bp(6,3) = -4.23812936930675 *7.0 + + +! square-well fluid +! ap(1,1)= 0.79152347258784 +! ap(1,2)= -0.62269805320654 +! ap(1,3)= -0.06798823934067 +! ap(2,1)= 1.07120982251709 +! ap(2,2)= 0.48628215731716 +! ap(2,3)= 0.02837828512515 +! ap(3,1)= 0.92084839459226 +! ap(3,2)= 1.11652038059747 +! ap(3,3)= 0.09713202077943 +! ap(4,1)= -7.84708350369249 +! ap(4,2)= -2.04200599876547 +! ap(4,3)= 0.06475764015088 +! ap(5,1)= 25.90284137818050 +! ap(5,2)= 9.27791640100603 +! ap(5,3)= 0.07729792971827 +! ap(6,1)= -57.1528726997640 +! ap(6,2)= -16.8377999920957 +! ap(6,3)= 0.24883598436184 +! ap(7,1)= 42.02314637860930 +! ap(7,2)= 7.62432635016420 +! ap(7,3)= -0.72472024688888 + +! bp(1,1)= 0.79152347258784 +! bp(1,2)= -0.62269805320654 +! bp(1,3)= -0.06798823934067 +! bp(2,1)= 1.07120982251709 *2.0 +! bp(2,2)= 0.48628215731716 *2.0 +! bp(2,3)= 0.02837828512515 *2.0 +! bp(3,1)= 0.92084839459226 *3.0 +! bp(3,2)= 1.11652038059747 *3.0 +! bp(3,3)= 0.09713202077943 *3.0 +! bp(4,1)= -7.84708350369249 *4.0 +! bp(4,2)= -2.04200599876547 *4.0 +! bp(4,3)= 0.06475764015088 *4.0 +! bp(5,1)= 25.90284137818050 *5.0 +! bp(5,2)= 9.27791640100603 *5.0 +! bp(5,3)= 0.07729792971827 *5.0 +! bp(6,1)= -57.1528726997640 *6.0 +! bp(6,2)= -16.8377999920957 *6.0 +! bp(6,3)= 0.24883598436184 *6.0 +! bp(7,1)= 42.02314637860930 *7.0 +! bp(7,2)= 7.62432635016420 *7.0 +! bp(7,3)= -0.72472024688888 *7.0 + + +dnm(1,1) = -8.8043 +dnm(1,2) = +4.1646270 +dnm(1,3) = -48.203555 +dnm(1,4) = +140.43620 +dnm(1,5) = -195.23339 +dnm(1,6) = +113.51500 +dnm(2,1) = +2.9396 +dnm(2,2) = -6.0865383 +dnm(2,3) = +40.137956 +dnm(2,4) = -76.230797 +dnm(2,5) = -133.70055 +dnm(2,6) = +860.25349 +dnm(2,7) = -1535.3224 +dnm(2,8) = +1221.4261 +dnm(2,9) = -409.10539 +dnm(3,1) = -2.8225 +dnm(3,2) = +4.7600148 +dnm(3,3) = +11.257177 +dnm(3,4) = -66.382743 +dnm(3,5) = +69.248785 +dnm(4,1) = +0.3400 +dnm(4,2) = -3.1875014 +dnm(4,3) = +12.231796 +dnm(4,4) = -12.110681 + +END SUBROUTINE eos_const + + + +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! SUBROUTINE dq_const +! +! This subr. provides the constants of the dipole-quadrupole term. +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! + SUBROUTINE dq_const ( dqp2,dqp3,dqp4 ) +! + USE PARAMETERS, ONLY: nc + USE EOS_VARIABLES, ONLY: ncomp, parame + IMPLICIT NONE +! +! ---------------------------------------------------------------------- + REAL, INTENT(OUT) :: dqp2(nc,nc,0:8) + REAL, INTENT(OUT) :: dqp3(nc,nc,nc,0:8) + REAL, INTENT(OUT) :: dqp4(nc,nc,0:8) +! +! ---------------------------------------------------------------------- + INTEGER :: i, j, k + REAL :: mdq(nc) + REAL :: mf1, mf2, msegij +! ---------------------------------------------------------------------- + +DO i=1,ncomp + mdq(i) = parame(i,1) + IF (mdq(i) > 2.0) mdq(i) = 2.0 +END DO + + +DO i=1,ncomp + DO j=1,ncomp + + msegij=(mdq(i)*mdq(j))**0.5 + mf1 = (msegij-1.0)/msegij + mf2 = mf1*(msegij-2.0)/msegij + + dqp2(i,j,0) = 0.697094963 + mf1*(-0.673459279) + mf2*0.670340770 + dqp2(i,j,1) = -0.633554144 + mf1*(-1.425899106) + mf2*(-4.338471826) + dqp2(i,j,2) = 2.945509028 + mf1 * 4.19441392 + mf2*7.234168360 + dqp2(i,j,3) = -1.467027314 + mf1 * 1.0266216 + dqp2(i,j,4) = 0.0 + + dqp4(i,j,0) = -0.484038322 + mf1 * 0.67651011 + mf2*(-1.167560146) + dqp4(i,j,1) = 1.970405465 + mf1*(-3.013867512) + mf2*2.13488432 + dqp4(i,j,2) = -2.118572671 + mf1 * 0.46742656 + dqp4(i,j,3) = 0.0 + dqp4(i,j,4) = 0.0 + + + DO k=1,ncomp + msegij=(mdq(i)*mdq(j)*mdq(k))**(1.0/3.0) + mf1 = (msegij-1.0)/msegij + mf2 = (msegij-2.0)/msegij + dqp3(i,j,k,0) = 0.795009692 + mf1*(-2.099579397) + dqp3(i,j,k,1) = 3.386863396 + mf1*(-5.941376392) + dqp3(i,j,k,2) = 0.475106328 + mf1*(-0.178820384) + dqp3(i,j,k,3) = 0.0 + dqp3(i,j,k,4) = 0.0 + END DO + + END DO +END DO + +END SUBROUTINE dq_const + + +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! SUBROUTINE dd_const +! +! This subroutine provides the constants of the dipole-term. +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! + SUBROUTINE dd_const ( ddp2,ddp3,ddp4 ) +! + USE PARAMETERS, ONLY: nc, PI + USE EOS_VARIABLES, ONLY: ncomp, parame + IMPLICIT NONE +! +! ---------------------------------------------------------------------- + REAL, INTENT(OUT) :: ddp2(nc,nc,0:8) + REAL, INTENT(OUT) :: ddp3(nc,nc,nc,0:8) + REAL, INTENT(OUT) :: ddp4(nc,nc,0:8) +! +! ---------------------------------------------------------------------- + INTEGER :: i, j, k + REAL :: pardd(nc) + REAL :: mf1,mf2,msegij,sin2t +! ---------------------------------------------------------------------- + +sin2t = SIN( 0.0 * PI / 180.0 ) +sin2t = sin2t*sin2t + +DO i = 1, ncomp + pardd(i) = parame(i,1) + IF (pardd(i) > 2.0) pardd(i) = 2.0 +END DO + +DO i=1,ncomp + DO j=1,ncomp +! IF (parame(i,6).NE.0.0.AND.parame(j,6).NE.0.0) THEN + + msegij=(pardd(i)*pardd(j))**0.5 + mf1 = (msegij-1.0)/msegij + mf2 = mf1*(msegij-2.0)/msegij + + ddp2(i,j,0) = 0.30435038064 + mf1*(0.95346405973+0.201436*sin2t) & + + mf2*(-1.16100802773-1.74114*sin2t) + ddp2(i,j,1) = -0.13585877707 + mf1*(-1.83963831920+1.31649*sin2t) & + + mf2*4.52586067320 + ddp2(i,j,2) = 1.44933285154 + mf1 * 2.01311801180 + mf2*0.97512223853 + ddp2(i,j,3) = 0.35569769252 + mf1*(-7.37249576667) + mf2*(-12.2810377713) + ddp2(i,j,4) = -2.06533084541 + mf1 * 8.23741345333 + mf2*5.93975747420 + + ddp4(i,j,0) = 0.21879385627 + mf1*(-0.58731641193) + mf2*3.48695755800 + ddp4(i,j,1) = -1.18964307357 + mf1 * 1.24891317047 + mf2*(-14.9159739347) + ddp4(i,j,2) = 1.16268885692 + mf1*(-0.50852797392) + mf2*15.3720218600 + ddp4(i,j,3) = 0.0 + ddp4(i,j,4) = 0.0 + + DO k=1,ncomp +! IF (parame(k,6).NE.0.0) THEN + msegij=(pardd(i)*pardd(j)*pardd(k))**(1.0/3.0) + mf1 = (msegij-1.0)/msegij + mf2 = mf1*(msegij-2.0)/msegij + ddp3(i,j,k,0) = -0.06467735252 + mf1*(-0.95208758351+0.28503*sin2t) & + + mf2*(-0.62609792333+2.2195*sin2t) + ddp3(i,j,k,1) = 0.19758818347 + mf1 * 2.99242575222 + mf2*1.29246858189 + ddp3(i,j,k,2) = -0.80875619458 + mf1*(-2.38026356489) + mf2*1.65427830900 + ddp3(i,j,k,3) = 0.69028490492 + mf1*(-0.27012609786) + mf2*(-3.43967436378) + ddp3(i,j,k,4) = 0.0 + +! ENDIF + END DO + +! ENDIF + END DO +END DO + +END SUBROUTINE dd_const + + +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! SUBROUTINE qq_const +! +! This subroutine provides the constants of the quadrupole-term. +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! + SUBROUTINE qq_const ( qqp2,qqp3,qqp4 ) +! + USE PARAMETERS, ONLY: nc + USE EOS_VARIABLES, ONLY: ncomp, parame + IMPLICIT NONE +! +! ---------------------------------------------------------------------- + REAL, INTENT(OUT) :: qqp2(nc,nc,0:8) + REAL, INTENT(OUT) :: qqp3(nc,nc,nc,0:8) + REAL, INTENT(OUT) :: qqp4(nc,nc,0:8) +! +! ---------------------------------------------------------------------- + INTEGER :: i, j, k + REAL :: mqq(nc) + REAL :: mf1, mf2, msegij +! ---------------------------------------------------------------------- + +DO i = 1,ncomp + mqq(i) = parame(i,1) + IF (mqq(i) > 2.0) mqq(i) = 2.0 +END DO + +DO i = 1,ncomp + DO j = 1,ncomp + IF (parame(i,7) /= 0.0 .AND. parame(j,7) /= 0.0) THEN + + msegij=(mqq(i)*mqq(j))**0.5 +! msegij=(parame(i,1)*parame(j,1))**0.50 + mf1 = (msegij-1.0)/msegij + mf2 = mf1*(msegij-2.0)/msegij + + qqp2(i,j,0) = 1.237830788 + mf1 * 1.285410878 + mf2*1.794295401 + qqp2(i,j,1) = 2.435503144 + mf1*(-11.46561451) + mf2*0.769510293 + qqp2(i,j,2) = 1.633090469 + mf1 *22.08689285 + mf2*7.264792255 + qqp2(i,j,3) = -1.611815241 + mf1 * 7.46913832 + mf2*94.48669892 + qqp2(i,j,4) = 6.977118504 + mf1*(-17.19777208) + mf2*(-77.1484579) + + qqp4(i,j,0) = 0.454271755 + mf1*(-0.813734006) + mf2*6.868267516 + qqp4(i,j,1) = -4.501626435 + mf1 * 10.06402986 + mf2*(-5.173223765) + qqp4(i,j,2) = 3.585886783 + mf1*(-10.87663092) + mf2*(-17.2402066) + qqp4(i,j,3) = 0.0 + qqp4(i,j,4) = 0.0 + + DO k = 1,ncomp + IF (parame(k,7) /= 0.0) THEN + msegij=(mqq(i)*mqq(j)*mqq(k))**(1.0/3.0) +! msegij=(parame(i,1)*parame(j,1)*parame(k,1))**(1.0/3.0) + mf1 = (msegij-1.0)/msegij + mf2 = mf1*(msegij-2.0)/msegij + qqp3(i,j,k,0) = -0.500043713 + mf1 * 2.000209381 + mf2*3.135827145 + qqp3(i,j,k,1) = 6.531869153 + mf1*(-6.78386584) + mf2*7.247588801 + qqp3(i,j,k,2) = -16.01477983 + mf1 * 20.38324603 + mf2*3.075947834 + qqp3(i,j,k,3) = 14.42597018 + mf1*(-10.89598394) + qqp3(i,j,k,4) = 0.0 + END IF + END DO + + END IF + END DO +END DO + +END SUBROUTINE qq_const + + + + + + + +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! + SUBROUTINE SET_DEFAULT_EOS_NUMERICAL +! + USE EOS_NUMERICAL_DERIVATIVES + IMPLICIT NONE +! +! ---------------------------------------------------------------------- + + ideal_gas = 'no' ! ( yes, no ) + hard_sphere = 'CSBM' ! ( CSBM, no ) + chain_term = 'TPT1' ! ( TPT1, HuLiu, no ) + disp_term = 'PC-SAFT' ! ( PC-SAFT, CK, PT1, PT2, PT_MF, PT_MIX, no ) + hb_term = 'TPT1_Chap' ! ( TPT1_Chap, no ) + LC_term = 'no' ! ( MSaupe, OVL, no ) + branch_term = 'no' ! ( TPT2, no ) + II_term = 'no' + ID_term = 'no' + + subtract1 = 'no' ! (1PT, 2PT, no) + subtract2 = 'no' ! (ITTpolar, no) + +END SUBROUTINE SET_DEFAULT_EOS_NUMERICAL + + + + + + + + + +SUBROUTINE READ_INPUT +! + USE BASIC_VARIABLES + IMPLICIT NONE +! +! ---------------------------------------------------------------------- + INTEGER :: i + REAL :: reading2,reading3,sumfeed + CHARACTER (LEN=4) :: uoutp, uinp + CHARACTER (LEN=1) :: uoutt, uint + CHARACTER (LEN=50) :: filename + CHARACTER (LEN=30) :: reading1 +! ---------------------------------------------------------------------- + + filename='./input_file/INPUT.INP' + CALL file_open(filename,30) + READ (30,*) eos, pol !J: specify by numbers! eos(1=pcsaft, 2=SRK,...) pol (=polar) yes(1) no(0) + READ (30,*) t, uint, p, uinp !J: t: value of temp, uint: unit of temp, p: value of pressure, uinp: unit of pressure + + ncomp = 0 + i = 0 + sumfeed = 0.0 + read_loop: DO + READ (30,*) reading1,reading2,reading3 + IF (reading1 == 'end') EXIT read_loop + ncomp = ncomp + 1 + i = i + 1 + compna(i)= reading1 ! comp.name + mm(i) = reading2 ! molec.mass (mandatory only for polymers) + xif(i) = reading3 !J: molefractions + sumfeed = sumfeed + xif(i) + ENDDO read_loop + + CLOSE (30) + + IF (sumfeed /= 0.0 .AND. sumfeed /= 1.0) THEN !J: in case mole fractions dont sum up to 1?? + xif(1:ncomp) = xif(1:ncomp)/sumfeed + END IF + + uoutt = uint + uoutp = uinp + IF (uint == 'C') THEN !J: unit stuff + u_in_t = 273.15 + ELSE + u_in_t = 0.0 + END IF + IF (uinp == 'bar') THEN + u_in_p = 1.E5 + ELSE IF (uinp == 'mbar') THEN + u_in_p = 1.E2 + ELSE IF (uinp == 'MPa') THEN + u_in_p = 1.E6 + ELSE IF (uinp == 'kPa') THEN + u_in_p = 1.E3 + ELSE + u_in_p = 1.E0 + END IF + + IF (uoutt == 'C') THEN + u_out_t = 273.15 + ELSE + u_out_t = 0.0 + END IF + IF (uoutp == 'bar') THEN + u_out_p = 1.E5 + ELSE IF (uoutp == 'mbar') THEN + u_out_p = 1.E2 + ELSE IF (uoutp == 'MPa') THEN + u_out_p = 1.E6 + ELSE IF (uoutp == 'kPa') THEN + u_out_p = 1.E3 + ELSE + u_out_p = 1.0 + END IF + + t = t + u_in_t !J: calculate temp in Kelvin + p = p * u_in_p !J: calculate pressure in Pascal + + CALL para_input ! retriev pure comp. parameters + + IF (ncomp == 1) THEN + WRITE (40,*) ' T P rho_1 rho_2 h_LV' + ELSE IF (ncomp == 2) THEN + ! WRITE (40,*) ' x2_phase1 x2_phase2 w1_phase1 w2_phase2 T P rho1 rho2' + WRITE (40,*) ' ' + ELSE IF (ncomp == 3) THEN + WRITE (40,*) ' x1_ph1 x2_ph1 x3_ph1 x1_ph2', & + ' x2_ph2 x3_ph2 T P rho1 rho2' + END IF + + END SUBROUTINE READ_INPUT + + + + + +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! SUBROUTINE file_open +! +! This subroutine opens files for reading. Beforehand, it checks +! whether this file is available. +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! + SUBROUTINE file_open(filename,file_number) +! +! ---------------------------------------------------------------------- + CHARACTER (LEN=50) :: filename + INTEGER :: file_number + LOGICAL :: filefound +! ---------------------------------------------------------------------- + +INQUIRE (FILE=filename, EXIST = filefound) +IF (filefound) THEN + OPEN (file_number, FILE = filename) +ELSE + write (*,*) ' FOLLOWING FILE CAN NOT BE OPENED', filename + stop +END IF + +END SUBROUTINE file_open + + + +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! SUBROUTINE para_input +! +! This subroutine provides pure component parameters and kij parameters. +! The following syntax applies: +! +! compna(i) component name +! parame(i,k) pure comp. parameter: +! parame(i,1): segment number [/] +! parame(i,2): segment diameter "sigma" [Angstrom] +! parame(i,3): segment energy param. epsilon/k [K] +! parame(i,4): model parameter; not used for PC-SAFT (=0) +! it is 10K most of the time for SAFT [K] +! parame(i,5): Param. for T-dependent segment diameter [/] +! parame(i,6): dipolar moment [debye] +! parame(i,7): quadrupolar moment [debye] +! parame(i,8): number of segments that are part of a branching 4-mer [/] +! parame(i,9): +! parame(i,10): ionic charge number (positiv or negativ) [/] +! parame(i,11): polarizability [A**3] +! parame(i,12): number of association sites [/] +! parame(i,13): (=kap_hb, see below) [/] +! parame(i,14 to 25): (=eps_hb, see below) [K] +! nhb_typ(i) number of different types of association sites (comp. i) +! nhb_no(i,k) number of association sites of type k +! eps_hb depth of association potential [K] +! kap_hb effective width of assoc. potential (angle-averg.) +! mm molec. mass +! scaling param. for roughly scaling the set of objective functions +! +! As opposed to low-molec mass compounds, the molecular mass of a +! polymer is not obtained from this routine. Rather, it is a +! user-specification given in the file INPUT.INP +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! + SUBROUTINE para_input +! + USE BASIC_VARIABLES + IMPLICIT NONE +! +!---------------------------------------------------------------------- + INTEGER :: i +!---------------------------------------------------------------------- + +IF (eos == 1) THEN + CALL pcsaft_par +ELSE IF (eos == 4 .OR. eos == 5 .OR. eos == 6 .OR. eos == 8) THEN + ! CALL lj_par + write (*,*) 'deactivated this line when making a transition to f90' + stop +ELSE IF (eos == 7) THEN + ! CALL sw_par + write (*,*) 'deactivated this line when making a transition to f90' + stop +ELSE IF (eos == 10) THEN + i = 1 + IF (compna(i) == 'LC_generic' .AND. ncomp == 1 ) THEN + mm(i) = 1.0 + parame(i,1) = 7.0 + parame(i,2) = 1.0 + parame(i,3) = 0.0 + ELSE + write (*,*) 'PARA_INPUT: define the component !' + stop + ENDIF +ELSE + !CALL saft_par +END IF + +DO i = 1, ncomp + IF ( mm(i) >= 1.0 .AND. mm(i) < 45.0 ) THEN + scaling(i) = 10000.0 + ELSE IF( mm(i) >= 45.0 .AND. mm(i) < 90.0 ) THEN + scaling(i) = 1000.0 + ELSE IF( mm(i) >= 90.0 .AND. mm(i) < 150.0 ) THEN + scaling(i) = 100.0 + ELSE IF( mm(i) >= 150.0 .AND. mm(i) < 250.0 ) THEN + scaling(i) = 10.0 + ELSE + scaling(i) = 1.0 + END IF + IF (parame(i,10) /= 0.0) scaling(i) = scaling(i) / 1.E4 ! Electrolytes +END DO + +END SUBROUTINE para_input + + + + +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! SUBROUTINE pcsaft_par +! +! pure component parameters and kij parameters +! (as described in SUBROUTINE para_input) +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! + SUBROUTINE pcsaft_par +! + USE BASIC_VARIABLES + IMPLICIT NONE +! +!---------------------------------------------------------------------- + INTEGER :: i, j, k, no + INTEGER, DIMENSION(nc) :: nhb_typ + INTEGER, DIMENSION(nc,nsite) :: nhb_no + REAL, DIMENSION(nc,nc,nsite,nsite) :: eps_hb + REAL, DIMENSION(nc,nc) :: kap_hb +!---------------------------------------------------------------------- + + +DO i = 1, ncomp + parame(i,4) = 0.0 ! T correct. required for SAFT, not PC-SAFT + parame(i,5) = 0.12 ! Param. for T-dependent segment diameter + parame(i,6) = 0.0 ! dipolar moment + parame(i,7) = 0.0 ! quadrupolar moment + parame(i,8) = 0.0 ! number of segments that are part of a branching 4-mer + parame(i,9) = 0.0 + parame(i,10)= 0.0 ! ionic charge number + parame(i,11)= 0.0 ! polarizability + lli(i) = 0.0 + phi_criti(i)= 0.0 + chap(i) = 0.0 + + nhb_typ(i) = 0 + kap_hb(i,i) = 0.0 + ! irgendwann sollten nhb_typ und kap_hb durch parame(i,12) und (i,13) + ! ersetzt werden. + IF (compna(i) == 'ps') THEN + parame(i,1) = mm(i)*1.9E-2 + parame(i,2) = 4.10705961 + parame(i,3) = 267.0 + ELSE IF (compna(i) == 'ps_J') THEN !from Xu,Diego: DFT for polymer-co2 mixtures: A PC-SAFT approach + parame(i,1) = mm(i)*0.0253 + parame(i,2) = 3.45 + parame(i,3) = 328.1 + ELSE IF (compna(i) == 'co2_J') THEN !from Xu,Diego: DFT for polymer-co2 mixtures: A PC-SAFT approach + parame(i,1) = 2.0 + parame(i,2) = 2.79 + parame(i,3) = 170.5 + + + + ELSE IF (compna(i) == 'pg2') THEN !Polyglycerol 2 + mm(i) = 2000.0 + parame(i,1) = mm(i)*2.37E-2 ! from figure 5 PCSAFT paper + parame(i,2) = 3.8 ! from figure 5 PCSAFT paper + parame(i,3) = 270.0 ! starting value for iteration + ! this is the extra parameter + parame(i,8) = mm(i)*2.37E-2 + + nhb_typ(i) = 2 ! no. of different association sites + nhb_no(i,1) = 27 ! no. of sites of type 1 + nhb_no(i,2) = 27 ! no. of sites of type 2 + eps_hb(i,i,1,2)= 2544.6 ! taken from butanol (same M/OH) + eps_hb(i,i,2,1)= 2544.6 + eps_hb(i,i,1,1)= 0.0 + eps_hb(i,i,2,2)= 0.0 + kap_hb(i,i)= .00489087833 ! taken from butanol (same M/OH) + ELSE IF (compna(i) == 'peva') THEN + parame(i,1) = mm(i)*2.63E-2 + ! -- 0 Gew.% VA------------- + ! parame(i,2) = 4.021767 + ! parame(i,3) = 249.5 + ! -- 7.5 Gew.% VA------------- + ! parame(i,2) = 4.011 + ! parame(i,3) = 248.1864 + ! parame(i,3) = 247.6286 + ! ---12.7 Gew.% VA------------ + ! parame(i,2) = 4.0028 + ! parame(i,3) = 247.2075 + ! parame(i,3) = 246.24454 + ! ---27.3 Gew.% VA------------ + ! parame(i,2) = 3.9762 + ! parame(i,3) = 244.114 + ! parame(i,3) = 241.9345 + ! ---31.8 Gew.% VA------------ + parame(i,2) = 3.9666 + parame(i,3) = 243.0436 + ! parame(i,3) = 240.46 + ! ---42.7 Gew.% VA------------ + ! parame(i,2) = 3.9400 + ! parame(i,3) = 240.184 + ! parame(i,3) = 236.62 + ! --------------- + ELSE IF (compna(i) == 'pp') THEN + parame(i,1) = mm(i)*2.2E-2 + parame(i,2) = 4.2 + parame(i,3) = 220.0 + + parame(i,1) = mm(i)*0.0230487701 + parame(i,2) = 4.1 + parame(i,3) = 217.0 + ELSE IF (compna(i) == 'pe') THEN + parame(i,1) = mm(i)*2.622E-2 + parame(i,2) = 4.021767 + parame(i,3) = 252.0 + ! HDPE: extrapolated from pure comp. param. of n-alkane series! + ! parame(i,1) = mm(i)*2.4346E-2 + ! parame(i,2) = 4.07182 + ! parame(i,3) = 269.67 + !! parame(i,3) = 252.5 + ELSE IF (compna(i) == 'ldpe') THEN + parame(i,1) = mm(i)*2.63E-2 + parame(i,2) = 4.021767 + parame(i,3) = 249.5 + ELSE IF (compna(i) == 'pba') THEN + parame(i,1) = mm(i)*2.5872E-2 + parame(i,2) = 3.95 + parame(i,3) = 229.0 + ELSE IF (compna(i) == 'dextran') THEN + parame(i,1) = mm(i)*2.E-2 + parame(i,2) = 4.0 + parame(i,3) = 300.0 + ELSE IF (compna(i) == 'glycol-ethers') THEN + ! mm(i) = 218.0 + ! parame(i,1) = 7.4044 + ! parame(i,2) = 3.61576 + ! parame(i,3) = 244.0034598 + mm(i) = 222.0 + parame(i,1) = 7.994 + parame(i,2) = 3.445377778 + parame(i,3) = 234.916506 + ELSE IF (compna(i) == 'LJ') THEN + mm(i) = 1.0 + parame(i,1) = 1.0 + parame(i,2) = 1.0 + parame(i,3) = 1.0 + ELSE IF (compna(i) == 'LJ1205') THEN + mm(i) = 1.0 + parame(i,1) = 1.0 + parame(i,2) = 1.0 + parame(i,3) = 140.0 + ELSE IF (compna(i) == 'adamantane') THEN + mm(i) = 136.235000000000 + parame(i,1) = 4.81897145432221 + parame(i,2) = 3.47128575274660 + parame(i,3) = 266.936967922521 + + Else IF (compna(i) == '14-butandiol') THEN + mm(i) = 90.12 + parame(i,1) = 4.35923557 + parame(i,2) = 3.02947364 + parame(i,3) = 197.11998863 + + Else IF(compna(i) == 'po') THEN + mm(i) = 90.12 + parame(i,1) = 4.35923557 + parame(i,2) = 3.02947364 + parame(i,3) = 197.11998863 + + ELSE IF (compna(i) == 'air') THEN + mm(i) = 28.899 !n2 and o2 according to mole fractions + parame(i,1) = 1.18938 !n2 and o2 according to mole fractions (weighted artihm. avg) + parame(i,2) = 3.28694 !n2 and o2 according to mole fractions (weighted artihm. avg) + parame(i,3) = 95.672 !n2 and o2 according to mole fractions (weighted artihm. avg) + + + + Else IF(compna(i) == 'mdi') THEN + mm(i) = 2.50252E+02 + parame(i,1) = mm(i)*0.030769 + parame(i,2) = 2.886003 + parame(i,3) = 283.052778 + + Else IF(compna(i) == 'pu') THEN +! mm(i) = 2042.22 !pu n = 5 +! parame(i,1) = mm(i)*0.008845 +! parame(i,2) = 5.680270 +! parame(i,3) = 497.997594 + mm(i) = 340.37 !pu n = 0 + parame(i,1) = mm(i)*0.043312 + parame(i,2) = 3.008359 + parame(i,3) = 273.445205 +! mm(i) = 680.74 !pu n = 1 +! parame(i,1) = mm(i)*0.024106 +! parame(i,2) = 3.744327 +! parame(i,3) = 321.486386 +! mm(i) = 1021.11 !pu n = 2 +! parame(i,1) = mm(i)*0.015076 +! parame(i,2) = 4.537837 +! parame(i,3) = 400.036950 + + + Else IF(compna(i) == 'tpg') THEN + mm(i) = 192.25 + parame(i,1) = mm(i)*0.01239 + parame(i,2) = 4.549 + parame(i,3) = 148.678 + parame(i,6) = 0.41 + + nhb_typ(i) = 2 ! no. of different association sites + nhb_no(i,1) = 2 ! no. of sites of type 1 + nhb_no(i,2) = 2 ! no. of sites of type 2 + + eps_hb(i,i,1,2)= 5597.844 + eps_hb(i,i,2,1)= 5597.844 + eps_hb(i,i,1,1)= 0.0 + eps_hb(i,i,2,2)= 0.0 + kap_hb(i,i) = 0.03 + + + ELSE IF (compna(i) == 'methane') THEN + mm(i) = 16.043 + parame(i,1) = 1.0 + parame(i,2) = 3.70388767 + parame(i,3) = 150.033987 + ! LLi(i) = 1.185*parame(i,2) + ! phi_criti(i)= 11.141 + ! chap(i) = 0.787 + lli(i) = 1.398*parame(i,2) + phi_criti(i)= 16.01197 + chap(i) = 0.6 + IF (pol == 2) parame(i,11)= 2.593 + ! --- adjusted to Tc, Pc und omega --- + ! mm(i) = 16.0430000000000 + ! parame(i,1) = 1.03353666429362 + ! parame(i,2) = 3.64824920605089 + ! parame(i,3) = 147.903953522994 + lli(i) = 2.254442763775*parame(i,2) + phi_criti(i)= 42.060975627454 + chap(i) = 0.704895924 + lli(i) = 1.935801125833*parame(i,2) + phi_criti(i)= 26.363325937261 + chap(i) = 0.700112854298 + lli(i) = 2.610103087662*parame(i,2) + phi_criti(i)= 38.192854403173 + chap(i) = 0.812100472735 + ! 2.122960316503 34.937141524804 0.734513223627 + ! 2.082897379591 33.036391564859 0.877578492999 + ELSE IF (compna(i) == 'ethane') THEN + mm(i) = 30.070 + parame(i,1) =mm(i)* .0534364758 + parame(i,2) = 3.5205923 + parame(i,3) = 191.423815 + lli(i) = 1.40*parame(i,2) + phi_criti(i)= 15.38 + chap(i) = 0.520 + IF (pol == 2) parame(i,11)= 4.3 + ! --- adjusted to Tc, Pc und omega --- + ! mm(i) = 30.069 + ! parame(i,1) = 1.74034548122 + ! parame(i,2) = 3.4697441893134 + ! parame(i,3) = 181.90770083591 + IF (pol >= 1) mm(i) = 30.0700000000000 + IF (pol >= 1) parame(i,1) = mm(i)* 5.341907666260094E-002 + IF (pol >= 1) parame(i,2) = 3.52104466654628 + IF (pol >= 1) parame(i,3) = 191.449300423694 + IF (pol >= 1) parame(i,7) = 0.650000000000000 + IF (pol >= 1) lli(i) = 0.0 + IF (pol >= 1) phi_criti(i)= 0.0 + IF (pol >= 1) chap(i) = 0.0 + ELSE IF (compna(i) == 'propane') THEN + mm(i) = 44.096 + parame(i,1) = mm(i)* .0453970622 + parame(i,2) = 3.61835302 + parame(i,3) = 208.110116 + lli(i) = 1.8*parame(i,2) + phi_criti(i)= 21.0 + chap(i) = 1.0 + lli(i) = 1.63*parame(i,2) + phi_criti(i)= 20.37 + chap(i) = 0.397 + IF (pol == 2) parame(i,11)= 6.29 + ELSE IF (compna(i) == 'butane_debug') THEN + mm(i) = 58.123 + parame(i,1) = 2.3374 + parame(i,2) = 3.6655 + parame(i,3) = 214.805 + ELSE IF (compna(i) == 'butane') THEN + mm(i) = 58.123 + parame(i,1) = mm(i)* .0401146927 + parame(i,2) = 3.70860139 + parame(i,3) = 222.877405 + lli(i) = 1.75*parame(i,2) + phi_criti(i)= 23.43 + chap(i) = 0.304 + ! LLi(i) = 1.942079633622*parame(i,2) + ! phi_criti(i)= 24.527323443155 + ! chap(i) = 0.734064026277 + ! LLi(i) = 1.515115760477*parame(i,2) + ! phi_criti(i)= 17.682929717796 + ! chap(i) = 0.335848717079 + IF (pol == 2) parame(i,11)= 8.2 + ! --- adjusted to Tc, Pc und omega --- + ! mm(i) = 58.1230000000 + ! parame(i,1) = 2.45352304112 + ! parame(i,2) = 3.74239117802 + ! parame(i,3) = 214.185157925 + ELSE IF (compna(i) == 'pentane') THEN + mm(i) = 72.146 + parame(i,1) = mm(i)* .03727896 + parame(i,2) = 3.77293174 + parame(i,3) = 231.197015 + IF (pol == 2) parame(i,11)= 9.99 + ELSE IF (compna(i) == 'hexane') THEN + mm(i) = 86.177 + parame(i,1) = mm(i)* .0354812325 + parame(i,2) = 3.79829291 + parame(i,3) = 236.769054 + lli(i) = 2.24*parame(i,2) + phi_criti(i)= 33.25 + chap(i) = 0.205 + IF (pol == 2) parame(i,11)= 11.9 + ELSE IF (compna(i) == 'heptane') THEN + mm(i) = 100.203 + parame(i,1) = mm(i)* .034762384 + parame(i,2) = 3.80487025 + parame(i,3) = 238.400913 + lli(i) = 2.35*parame(i,2) + phi_criti(i)= 38.10 + chap(i) = 0.173 + IF (pol == 2) parame(i,11)= 13.61 + ELSE IF (compna(i) == 'octane') THEN + mm(i) = 114.231 + parame(i,1) = mm(i)* .0334228038 + parame(i,2) = 3.83732677 + parame(i,3) = 242.775853 + ! LLi(i) = 2.0*parame(i,2) + ! phi_criti(i)= 18.75 + ! chap(i) = 1.0 + lli(i) = 2.63*parame(i,2) + phi_criti(i)= 42.06 + chap(i) = 0.155 + IF (pol == 2) parame(i,11)= 15.9 + ELSE IF (compna(i) == 'nonane') THEN + mm(i) = 128.25 + parame(i,1) = mm(i)* .0328062594 + parame(i,2) = 3.84483643 + parame(i,3) = 244.508457 + ELSE IF (compna(i) == 'decane') THEN + mm(i) = 142.285 + parame(i,1) = mm(i)* .03277373 + parame(i,2) = 3.8384498 + parame(i,3) = 243.866074 + lli(i) = 1.845*parame(i,2) + phi_criti(i)= 21.27 + chap(i) = 1.0 + lli(i) = 2.68*parame(i,2) + phi_criti(i)= 45.0 + chap(i) = 0.15 + IF (pol == 2) parame(i,11)= 19.1 + ! --- adjusted to Tc, Pc und omega --- + ! parame(i,1) = 4.794137228322 + ! parame(i,2) = 4.030446690586 + ! parame(i,3) = 236.5884493386 + ELSE IF (compna(i) == 'dodecane') THEN + mm(i) = 170.338 + parame(i,1) = mm(i)* .0311484156 + parame(i,2) = 3.89589236 + parame(i,3) = 249.214532 +ELSE IF (compna(i) == 'tetradecane') THEN + mm(i) = 198.39 + parame(i,1) = 5.9002!mm(i)* .0311484156 + parame(i,2) = 3.9396 + parame(i,3) = 254.21 + ELSE IF (compna(i) == 'hexadecane') THEN + mm(i) = 226.446 + parame(i,1) = mm(i)* .0293593045 + parame(i,2) = 3.95516743 + parame(i,3) = 254.700131 + ELSE IF (compna(i) == 'octadecane') THEN + mm(i) = 254.5 + parame(i,1) = 7.3271 + parame(i,2) = 3.9668 + parame(i,3) = 256.20 + IF (pol == 2) parame(i,11)= 30.2 + ! --- adjusted to Tc, Pc und omega --- + ! mm(i) = 226.446000000000 + ! parame(i,1) = 6.66976520488694 + ! parame(i,2) = 4.25025597912511 + ! parame(i,3) = 249.582941976119 + ELSE IF (compna(i) == 'eicosane') THEN + mm(i) = 282.553 + parame(i,1) = mm(i)* .0282572812 + parame(i,2) = 3.98692612 + parame(i,3) = 257.747939 + ELSE IF (compna(i) == 'triacontane') THEN + ! mm(i) = 422.822 ! polyethylene parameters + ! parame(i,1) = mm(i)*2.622E-2 + ! parame(i,2) = 4.021767 + ! parame(i,3) = 252.0 + mm(i) = 422.822 ! param. by extrapolation of n-alkanes + parame(i,1) = mm(i)* 0.026922527 + parame(i,2) = 4.007608009 + parame(i,3) = 262.28622 + ELSE IF (compna(i) == 'octaeicosane') THEN + mm(i) = 395.0 ! param. by extrapolation of n-alkanes (sloppy!!) + parame(i,1) = mm(i)* 0.026922527 + parame(i,2) = 4.007608009 + parame(i,3) = 262.28622 + ELSE IF (compna(i) == 'tetracontane') THEN + ! mm(i) = 563.1 ! polyethylene parameters + ! parame(i,1) = mm(i)*2.622E-2 + ! parame(i,2) = 4.021767 + ! parame(i,3) = 252.0 + mm(i) = 563.1 ! param. by extrapolation of n-alkanes + parame(i,1) = mm(i)*0.026287593 + parame(i,2) = 4.023277 + parame(i,3) = 264.10466 + ELSE IF (compna(i) == 'isobutane') THEN + mm(i) = 58.123 + parame(i,1) = mm(i)* .0389105395 + parame(i,2) = 3.75735249 + parame(i,3) = 216.528584 + ELSE IF (compna(i) == 'isopentane') THEN + mm(i) = 72.15 + parame(i,1) = 2.5620 + parame(i,2) = 3.8296 + parame(i,3) = 230.75 + ELSE IF (compna(i) == '2-methylpentane') THEN + mm(i) = 86.177 + parame(i,1) = mm(i)* .0340166994 + parame(i,2) = 3.85354665 + parame(i,3) = 235.5801 + ELSE IF (compna(i) == '23-dimethylbutane') THEN + mm(i) = 86.177 + parame(i,1) = mm(i)* .0311599207 + parame(i,2) = 3.9544545 + parame(i,3) = 246.068188 + ELSE IF (compna(i) == 'ethylene') THEN + mm(i) = 28.05 + parame(i,1) = mm(i)* .0567939013 + parame(i,2) = 3.44499904 + parame(i,3) = 176.468725 + IF (pol == 2) parame(i,11)= 4.252 +! eigener 3-ter Anlauf. + IF (pol >= 1) parame(i,1) = mm(i)* 5.574644443117726E-002 + IF (pol >= 1) parame(i,2) = 3.43281482228714 + IF (pol >= 1) parame(i,3) = 178.627308564610 + IF (pol >= 1) parame(i,7) = 1.56885870200446 + IF (pol == 2) parame(i,11)= 4.252 + ELSE IF (compna(i) == 'propylene') THEN + mm(i) = 42.081 + parame(i,1) = mm(i)* .0465710324 + parame(i,2) = 3.53559831 + parame(i,3) = 207.189309 + ! --- adjusted to Tc, Pc und omega --- + ! mm(i) = 42.081 + ! parame(i,1) = 2.086735327675 + ! parame(i,2) = 3.536779407969 + ! parame(i,3) = 198.3529810625 + ELSE IF (compna(i) == '1-butene') THEN + mm(i) = 56.107 + parame(i,1) = mm(i)* .0407524782 + parame(i,2) = 3.64305136 + parame(i,3) = 222.002756 + IF (pol == 2) parame(i,11)= 7.97 + ELSE IF (compna(i) == '1-pentene') THEN + mm(i) = 70.134 + parame(i,1) = 2.6006 + parame(i,2) = 3.7399 + parame(i,3) = 231.99 + ELSE IF (compna(i) == '1-hexene') THEN + mm(i) = 84.616 + parame(i,1) = mm(i)* .0352836857 + parame(i,2) = 3.77529612 + parame(i,3) = 236.810973 + ELSE IF (compna(i) == '1-octene') THEN + mm(i) = 112.215 + parame(i,1) = mm(i)* .033345175 + parame(i,2) = 3.81329011 + parame(i,3) = 243.017587 + ELSE IF (compna(i) == 'cyclopentane') THEN + mm(i) = 70.13 + parame(i,1) = mm(i)* .0337262571 + parame(i,2) = 3.71139254 + parame(i,3) = 265.828755 + ELSE IF (compna(i) == 'cyclohexane') THEN + mm(i) = 84.147 + parame(i,1) = mm(i)* .0300695505 + parame(i,2) = 3.84990887 + parame(i,3) = 278.108786 + IF (pol == 2) parame(i,11)= 10.87 + ELSE IF (compna(i) == 'toluene') THEN + mm(i) = 92.141 + parame(i,1) = mm(i)* .0305499338 + parame(i,2) = 3.71689689 + parame(i,3) = 285.68996 + IF (pol == 2) parame(i,11)= 11.8 + ! --- adjusted to Tc, Pc und omega --- + ! mm(i) = 92.141 + ! parame(i,1) = 3.002119827762 + ! parame(i,2) = 3.803702734224 + ! parame(i,3) = 271.9428642880 + ELSE IF (compna(i) == 'm-xylene') THEN + mm(i) = 106.167 + parame(i,1) = mm(i)* .030011086 + parame(i,2) = 3.75625585 + parame(i,3) = 283.977525 + ELSE IF (compna(i) == 'o-xylene') THEN + mm(i) = 106.167 + parame(i,1) = mm(i)* .0295409161 + parame(i,2) = 3.76000631 + parame(i,3) = 291.049123 + ELSE IF (compna(i) == 'thf') THEN + mm(i) = 72.1057000000000 + ! parame(i,1) = mm(i)* 0.34311391E-01 + parame(i,1) = 2.47404685540709 + parame(i,2) = 3.51369375633677 + parame(i,3) = 274.181927093696 + parame(i,6) = 1.63100000000000 + ELSE IF (compna(i) == 'co2') THEN + mm(i) = 44.01 + parame(i,1) = mm(i)* .0470968503 + parame(i,2) = 2.7851954 + parame(i,3) = 169.207418 + IF (pol >= 1) parame(i,1) = mm(i)* 3.438191426159075E-002 + IF (pol >= 1) parame(i,2) = 3.18693935424469 + IF (pol >= 1) parame(i,3) = 163.333232725156 + IF (pol >= 1) parame(i,7) = 4.400000000000 + IF (pol >= 1) lli(i) = 1.472215*parame(i,2) + IF (pol >= 1) phi_criti(i)= 17.706567 + IF (pol >= 1) chap(i) = 0.5 + IF (pol == 2) parame(i,11)= 2.911 + ELSE IF (compna(i) == 'co') THEN + IF (pol /= 1) write (*,*) 'parameters for co missing' + IF (pol /= 1) stop + IF (pol >= 1) mm(i) = 28.01 + IF (pol >= 1) parame(i,1) = mm(i)* 5.126059746332587E-002 ! 1.43580933494776 + IF (pol >= 1) parame(i,2) = 3.13556624711756 + IF (pol >= 1) parame(i,3) = 87.7191028693595 + IF (pol >= 1) parame(i,6) = 0.1098 + ELSE IF (compna(i) == 'n2') THEN + mm(i) = 28.01 + parame(i,1) = mm(i)* .0430301713 + parame(i,2) = 3.3129702 + parame(i,3) = 90.9606924 + IF (pol >= 1) parame(i,1) = mm(i)* 3.971157114787596E-002 + IF (pol >= 1) parame(i,2) = 3.42116853868336 + IF (pol >= 1) parame(i,3) = 92.3972606842862 + IF (pol >= 1) parame(i,7) = 1.52000000000000 + IF (pol >= 1) lli(i) = 1.5188*parame(i,2) + IF (pol >= 1) phi_criti(i)= 19.9247 + IF (pol >= 1) chap(i) = 0.375 + ! better RGT-results came later, with: 1.5822 21.201 0.3972 + ELSE IF (compna(i) == 'o2') THEN + mm(i) = 32.05 + parame(i,1) = mm(i)* .0353671563 + parame(i,2) = 3.19465166 + parame(i,3) = 114.430197 + ELSE IF (compna(i) == 'hydrogen') THEN + mm(i) = 2.016 + parame(i,1) = mm(i)* .258951975 + parame(i,2) = 4.43304935 + parame(i,3) = 29.6509579 + + mm(i) = 2.016 + parame(i,1) = 1.0 + parame(i,2) = 2.915 + parame(i,3) = 38.0 + + ! mm(i) = 2.016 ! Ghosh et al. 2003 + ! parame(i,1) = 1.0 + ! parame(i,2) = 2.986 + ! parame(i,3) = 19.2775 + ELSE IF (compna(i) == 'argon') THEN + ! mm(i) = 39.948 ! adjusted m !! + ! parame(i,1) = 0.9285 + ! parame(i,2) = 3.4784 + ! parame(i,3) = 122.23 + mm(i) = 39.948 ! enforced m=1 !! + parame(i,1) = 1.0 + parame(i,2) = 3.3658 + parame(i,3) = 118.34 + IF (pol == 2) parame(i,11)= 1.6411 + ELSE IF (compna(i) == 'xenon') THEN + mm(i) = 131.29 + parame(i,1) = 1.0 + parame(i,2) = 3.93143 + parame(i,3) = 227.749 + ELSE IF (compna(i) == 'chlorine') THEN ! Cl2 + mm(i) = 70.906 + parame(i,1) = 1.5514 + parame(i,2) = 3.3672 + parame(i,3) = 265.67 + ELSE IF (compna(i) == 'SF6') THEN + mm(i) = 146.056 ! adjusted m !! + parame(i,1) = 2.48191 + parame(i,2) = 3.32727 + parame(i,3) = 161.639 + ! mm(i) = 146.056 ! enforced m=1 !! + ! parame(i,1) = 1.0 + ! parame(i,2) = 4.55222 + ! parame(i,3) = 263.1356 + ELSE IF (compna(i) == 'benzene') THEN + mm(i) = 78.114 + parame(i,1) = mm(i)* .0315590546 + parame(i,2) = 3.64778975 + parame(i,3) = 287.354574 + IF (pol >= 1) mm(i) = 78.114 ! PCP-SAFT with m=2 in QQ term + IF (pol >= 1) parame(i,1) = mm(i)* 2.932783311E-2 ! = 2.29091435590515 + IF (pol >= 1) parame(i,2) = 3.7563854 + IF (pol >= 1) parame(i,3) = 294.06253 + IF (pol >= 1) parame(i,7) = 5.5907 + ELSE IF (compna(i) == 'ethylbenzene') THEN + mm(i) = 106.167 + parame(i,1) = mm(i)* .0290120497 + parame(i,2) = 3.79741116 + parame(i,3) = 287.348098 + IF (pol == 2) parame(i,11)= 13.3 + ELSE IF (compna(i) == 'propylbenzene') THEN + mm(i) = 120.194 + parame(i,1) = mm(i)* .0278171627 + parame(i,2) = 3.8437772 + parame(i,3) = 288.128269 + ELSE IF (compna(i) == 'n-butylbenzene') THEN + mm(i) = 134.221 + parame(i,1) = mm(i)* .0280642225 + parame(i,2) = 3.87267961 + parame(i,3) = 283.072331 + ELSE IF (compna(i) == 'tetralin') THEN + mm(i) = 132.205 + parame(i,1) = mm(i)* .0250640795 + parame(i,2) = 3.87498866 + parame(i,3) = 325.065688 + ELSE IF (compna(i) == 'methylcyclohexane') THEN + mm(i) = 98.182 + parame(i,1) = mm(i)* .0271259953 + parame(i,2) = 3.99931892 + parame(i,3) = 282.334148 + IF (pol == 2) parame(i,11)= 13.1 + ELSE IF (compna(i) == 'methylcyclopentane') THEN + mm(i) = 84.156 + parame(i,1) = mm(i)* .0310459009 + parame(i,2) = 3.82534693 + parame(i,3) = 265.122799 + ELSE IF (compna(i) == 'acetone') THEN + mm(i) = 58.0800000000000 ! PC-SAFT + parame(i,1) = mm(i)* 4.870380408159182E-002 ! =2.82871694105885 + parame(i,2) = 3.24969003020675 + parame(i,3) = 250.262241927379 + lli(i) = 2.0021*parame(i,2) + phi_criti(i)= 21.336 + chap(i) = 0.24931 + IF (pol >= 1) mm(i) = 58.0800000000000 ! PCP-SAFT + IF (pol >= 1) parame(i,1) = mm(i)* 4.725811736856114E-002 ! =2.74475145676603 + IF (pol >= 1) parame(i,2) = 3.27423145271184 + IF (pol >= 1) parame(i,3) = 232.990879135326 + IF (pol >= 1) parame(i,6) = 2.88000000000000 + IF (pol >= 1) lli(i) = 2.0641*parame(i,2) + IF (pol >= 1) phi_criti(i)= 28.1783 + IF (pol >= 1) chap(i) = 0.22695 + IF (pol >= 2) mm(i) = 58.0800000000000 ! PCIP-SAFT + IF (pol >= 2) parame(i,1) = mm(i)* 4.902301475689938E-002 ! =2.84725669708072 + IF (pol >= 2) parame(i,2) = 3.23880349104868 + IF (pol >= 2) parame(i,3) = 220.884202656054 + IF (pol >= 2) parame(i,6) = 2.88000000000000 + IF (pol == 2) parame(i,11)= 6.40000000000000 + ELSE IF (compna(i) == 'butanone') THEN + mm(i) = 72.1066 ! PC-SAFT + parame(i,1) = mm(i)* 4.264192830122321E-002 ! =3.07476446724498 + parame(i,2) = 3.39324011060028 + parame(i,3) = 252.267273608975 + IF (pol >= 1) mm(i) = 72.1066 ! PCP-SAFT + IF (pol >= 1) parame(i,1) = mm(i)* 4.137668924230600E-002 ! =2.98353238051926 + IF (pol >= 1) parame(i,2) = 3.42393701353423 + IF (pol >= 1) parame(i,3) = 244.994381354681 + IF (pol >= 1) parame(i,6) = 2.78000000000000 + IF (pol >= 2) mm(i) = 72.1066 ! PCIP-SAFT + IF (pol >= 2) parame(i,1) = mm(i)* 4.254697075199448E-002 ! =3.06791740122577 + IF (pol >= 2) parame(i,2) = 3.39138375903252 + IF (pol >= 2) parame(i,3) = 236.527763837528 + IF (pol >= 2) parame(i,6) = 2.78000000000000 + IF (pol == 2) parame(i,11)= 8.13000000000000 + ELSE IF (compna(i) == '2-pentanone') THEN + ! mm(i) = 86.134 ! PC-SAFT + ! parame(i,1) = mm(i)* 3.982654501296355E-002 ! =3.43041962814660 + ! parame(i,2) = 3.46877976946838 + ! parame(i,3) = 249.834724442656 + ! mm(i) = 86.134 ! PCP-SAFT + ! parame(i,1) = mm(i)* 3.893594769994072E-002 ! =3.35370891918669 + ! parame(i,2) = 3.49417356096593 + ! parame(i,3) = 246.656329096835 + ! parame(i,6) = 2.70000000000000 + mm(i) = 86.134 ! PCIP-SAFT + parame(i,1) = mm(i)* 3.973160761515879E-002 ! =3.42224229032409 + parame(i,2) = 3.46827593107280 + parame(i,3) = 240.904278156822 + parame(i,6) = 2.70000000000000 + IF (pol == 2) parame(i,11)= 9.93000000000000 + ELSE IF (compna(i) == '3-pentanone') THEN + mm(i) = 86.134 ! PC-SAFT + parame(i,1) = 3.36439508013322 + parame(i,2) = 3.48770251979329 + parame(i,3) = 252.695415552376 + IF (pol >= 1) mm(i) = 86.134 ! PCP-SAFT + IF (pol >= 1) parame(i,1) = 3.27863398611842 + IF (pol >= 1) parame(i,2) = 3.51592571835030 + IF (pol >= 1) parame(i,3) = 248.690775540981 + IF (pol >= 1) parame(i,6) = 2.82000000000000 + IF (pol == 2) mm(i) = 86.134 ! PCIP-SAFT + IF (pol == 2) parame(i,1) = 3.34821857026283 + IF (pol == 2) parame(i,2) = 3.48903345340516 + IF (pol == 2) parame(i,3) = 242.314578558329 + IF (pol == 2) parame(i,6) = 2.82000000000000 + IF (pol == 2) parame(i,11)= 9.93000000000000 + ELSE IF (compna(i) == 'cyclohexanone') THEN ! from DIPPR + ! IF (pol.GE.1) mm(i) = 98.1430 ! PCP-SAFT + ! IF (pol.GE.1) parame(i,1) = 3.084202 + ! IF (pol.GE.1) parame(i,2) = 3.613681 + ! IF (pol.GE.1) parame(i,3) = 286.15865 + ! IF (pol.GE.1) parame(i,6) = 3.087862 + IF (pol >= 1) mm(i) = 98.1500000000000 + IF (pol >= 1) parame(i,1) = 2.72291913132818 + IF (pol >= 1) parame(i,2) = 3.79018433908522 + IF (pol >= 1) parame(i,3) = 314.772193827344 + IF (pol >= 1) parame(i,6) = 3.24600000000000 + IF (pol /= 1) WRITE (*,*) 'no non-polar param. for cyclohexanone' + IF (pol /= 1) STOP + ELSE IF (compna(i) == 'propanal') THEN + mm(i) = 58.08 ! PC-SAFT + parame(i,1) = 2.67564746980910 + parame(i,2) = 3.26295953984941 + parame(i,3) = 251.888982765626 + IF (pol >= 1) mm(i) = 58.08 ! PCP-SAFT + IF (pol >= 1) parame(i,1) = 2.60007872084995 + IF (pol >= 1) parame(i,2) = 3.28720732189761 + IF (pol >= 1) parame(i,3) = 235.205188090107 + IF (pol >= 1) parame(i,6) = 2.72000000000000 + IF (pol >= 2) mm(i) = 58.08 ! PCIP-SAFT + IF (pol >= 2) parame(i,1) = 2.72471167411028 + IF (pol >= 2) parame(i,2) = 3.24781643022922 + IF (pol >= 2) parame(i,3) = 221.642071811094 + IF (pol >= 2) parame(i,6) = 2.72000000000000 + IF (pol >= 2) parame(i,11)= 6.50000000000000 + ELSE IF (compna(i) == 'butanal') THEN + mm(i) = 72.1066000000000 ! PC-SAFT + parame(i,1) = 2.96824823599784 + parame(i,2) = 3.44068916025889 + parame(i,3) = 253.929404992884 + IF (pol >= 1) mm(i) = 72.1066000000000 ! PCP-SAFT + IF (pol >= 1) parame(i,1) = 2.86783706423953 + IF (pol >= 1) parame(i,2) = 3.47737904036296 + IF (pol >= 1) parame(i,3) = 247.543312127310 + IF (pol >= 1) parame(i,6) = 2.72000000000000 + ELSE IF (compna(i) == 'dmso') THEN + mm(i) = 78.1300000000000 ! PC-SAFT + parame(i,1) = 2.92225114054231 + parame(i,2) = 3.27780791606297 + parame(i,3) = 355.688793038512 + IF (pol >= 1) mm(i) = 78.1300000000000 ! PCP-SAFT + IF (pol >= 1) parame(i,1) = 3.02433694138348 + IF (pol >= 1) parame(i,2) = 3.24270742566613 + IF (pol >= 1) parame(i,3) = 309.357476696679 + IF (pol >= 1) parame(i,6) = 3.96000000000000 + IF (pol >= 2) mm(i) = 78.1300000000000 ! PCIP-SAFT + IF (pol >= 2) parame(i,1) = 3.19078234633277 + IF (pol >= 2) parame(i,2) = 3.19778269816832 + IF (pol >= 2) parame(i,3) = 286.337981216861 + IF (pol >= 2) parame(i,6) = 3.96000000000000 + IF (pol >= 2) parame(i,11)= 7.97000000000000 + ELSE IF (compna(i) == 'acetone_JC') THEN ! Jog-Chapman + ! mm(i) = 58.0800000000000 ! Dominik et al.2005 + ! parame(i,1) = 2.221 + ! parame(i,2) = 3.607908 + ! parame(i,3) = 259.99 + ! parame(i,6) = 2.7 + ! parame(i,8) = 0.2258 + ! mm(i) = 58.0800000000000 + ! parame(i,1) = mm(i)* 3.556617369195472E-002 + ! parame(i,2) = 3.58780367502515 + ! parame(i,3) = 273.025100470307 + ! parame(i,6) = 2.70000000000000 + ! parame(i,8) = 0.229800000000000 + + mm(i) = 58.08 ! Tumakaka Sadowski 2004 + parame(i,1) = mm(i)* 3.766E-2 + parame(i,2) = 3.6028 + parame(i,3) = 245.49 + parame(i,6) = 2.72 + parame(i,8) = 0.2969 + ! mm(i) = 58.0800000000000 ! no adjust. DD-param. + ! parame(i,1) = 1.87041620247774 + ! parame(i,2) = 3.79783535570774 + ! parame(i,3) = 208.885730881588 + ! parame(i,6) = 2.88000000000000 + ! parame(i,8) = 1.0/parame(i,1) + WRITE (*,*) 'caution: parame(i,8) is now used for branching' + STOP + kij(1,2) = -0.005 + kij(2,1)=kij(1,2) + ELSE IF (compna(i) == 'acetone_SF') THEN ! Saager-Fischer + mm(i) = 58.08 + parame(i,1) = mm(i)* 4.603296414764944E-002 + parame(i,2) = 3.29454924451643 + parame(i,3) = 221.052649057645 + parame(i,6) = 2.70000000000000 + parame(i,8) = 0.625410000000000 + mm(i) = 58.08 ! form as expected from me - no DD-param adjusted.dat + parame(i,1) = mm(i)* 4.364264724158790E-002 ! =2.53476495179143 + parame(i,2) = 3.37098670735567 + parame(i,3) = 254.366379701851 + parame(i,6) = 2.88000000000000 + ! mm(i) = 58.08 ! form as expected but w/ sumseg/1.5 - no DD-param adjusted.dat + ! parame(i,1) = mm(i)* 4.694644361257521E-002 ! =2.72664944501837 + ! parame(i,2) = 3.27842292595463 + ! parame(i,3) = 238.398883501772 + ! parame(i,6) = 2.88000000000000 + ! mm(i) = 58.08 ! form as expected but w/ sumseg/1.5 and fdd*sumseg- no DD-param adjusted.dat + ! parame(i,1) = mm(i)* 4.458214655521766E-002 ! =2.58933107192704 + ! parame(i,2) = 3.32050824493493 + ! parame(i,3) = 218.285994651271 + ! parame(i,6) = 2.88000000000000 + WRITE (*,*) 'caution: parame(i,8) is now used for branching' + STOP + kij(1,2) = 0.035 + kij(2,1)=kij(1,2) + ELSE IF (compna(i) == 'ethylacetate_JC') THEN ! Jog-Chapman + ! mm(i) = 88.11 + ! parame(i,1) = 2.7481 + ! parame(i,2) = 3.6511 + ! parame(i,3) = 236.99 + ! parame(i,6) = 1.84 + ! parame(i,8) = 0.5458 + mm(i) = 88.1060000000000 + parame(i,1) = mm(i)* 0.03117 ! 2.74626402 + parame(i,2) = 3.6493 + parame(i,3) = 236.75 + parame(i,6) = 1.8 + parame(i,8) = 0.5462 + ELSE IF (compna(i) == 'ethylacetate_SF') THEN ! Saager-Fischer + mm(i) = 88.106 + parame(i,1) = mm(i)* 3.564165384763394E-002 + parame(i,2) = 3.447379322 + parame(i,3) = 226.0930487 + parame(i,6) = 1.8 + parame(i,8) = 0.849967000000000 + WRITE (*,*) 'caution: parame(i,8) is now used for branching' + STOP + ELSE IF (compna(i) == '12po_JC') THEN ! Jog-Chapman + mm(i) = 58.08 + parame(i,1) = 2.0105 + parame(i,2) = 3.6095 + parame(i,3) = 258.82 + parame(i,6) = 2.0 + parame(i,8) = 0.3979 + WRITE (*,*) 'caution: parame(i,8) is now used for branching' + STOP + ELSE IF (compna(i) == '12po_SF') THEN ! Saager-Fischer + mm(i) = 58.08 + parame(i,1) = 2.1341 + parame(i,2) = 3.4739 + parame(i,3) = 252.95 + parame(i,6) = 2.0 + parame(i,8) = 0.916 + WRITE (*,*) 'caution: parame(i,8) is now used for branching' + STOP + ELSE IF (compna(i) == 'acrylonitrile') THEN + IF (pol >= 2) mm(i) = 53.06 ! PCIP-SAFT + IF (pol >= 2) parame(i,1) = 2.168 + IF (pol >= 2) parame(i,2) = 3.575 + IF (pol >= 2) parame(i,3) = 214.83 + IF (pol >= 2) parame(i,6) = 3.91 + IF (pol == 2) parame(i,11)= 8.04 + IF (pol >= 2) mm(i) = 53.0000000000000 ! second parameter set ?? + IF (pol >= 2) parame(i,1) = 2.45403467006041 + IF (pol >= 2) parame(i,2) = 3.41276825781723 + IF (pol >= 2) parame(i,3) = 195.194353082408 + IF (pol >= 2) parame(i,6) = 3.91000000000000 + IF (pol == 2) parame(i,11)= 8.04000000000000 + ELSE IF (compna(i) == 'butyronitrile') THEN + ! mm(i) = 69.11 + ! parame(i,1) = 2.860 + ! parame(i,2) = 3.478 + ! parame(i,3) = 253.21 + ! parame(i,6) = 4.07 + mm(i) = 69.11 + parame(i,1) = 2.989 + parame(i,2) = 3.441 + parame(i,3) = 234.04 + parame(i,6) = 4.07 + IF (pol == 2) parame(i,11)= 8.4 + ELSE IF (compna(i) == 'propionitrile') THEN + mm(i) = 55.079 ! PC-SAFT + parame(i,1) = 2.66211021227108 + parame(i,2) = 3.34032231132738 + parame(i,3) = 294.078737359580 + IF (pol >= 1) mm(i) = 55.079 ! PCP-SAFT + IF (pol >= 1) parame(i,1) = 2.50958981615666 + IF (pol >= 1) parame(i,2) = 3.39806320429568 + IF (pol >= 1) parame(i,3) = 239.152759066148 + IF (pol >= 1) parame(i,6) = 4.05000000000000 + IF (pol >= 2) mm(i) = 55.079 ! PCIP-SAFT + IF (pol >= 2) parame(i,1) = 2.54684827683436 + IF (pol >= 2) parame(i,2) = 3.41240089912190 + IF (pol >= 2) parame(i,3) = 218.299491580335 + IF (pol >= 2) parame(i,6) = 4.05000000000000 + IF (pol == 2) parame(i,11)= 6.24000000000000 + ! IF (pol.GE.2) mm(i) = 55.079 ! PCIP-SAFT my_DD adjusted + ! IF (pol.GE.2) parame(i,1) = 2.61175151088002 + ! IF (pol.GE.2) parame(i,2) = 3.37194293181453 + ! IF (pol.GE.2) parame(i,3) = 233.346110749402 + ! IF (pol.GE.2) parame(i,6) = 3.74682245835235 + ! IF (pol.EQ.2) parame(i,11)= 6.24000000000000 + ELSE IF (compna(i) == 'nitromethane') THEN + mm(i) = 61.04 ! PC-SAFT + parame(i,1) = mm(i)* 4.233767489308791E-002 ! =2.58429167547409 + parame(i,2) = 3.10839592337018 + parame(i,3) = 310.694151426943 + IF (pol >= 1) mm(i) = 61.04 ! PCP-SAFT + IF (pol >= 1) parame(i,1) = mm(i)* 4.191475020685036E-002 ! =2.55847635262615 + IF (pol >= 1) parame(i,2) = 3.10129282495975 + IF (pol >= 1) parame(i,3) = 256.456941430554 + IF (pol >= 1) parame(i,6) = 3.46000000000000 + IF (pol >= 2) mm(i) = 61.04 ! PCIP-SAFT + IF (pol >= 2) parame(i,1) = mm(i)* 4.394323357988009E-002 ! =2.68229497771588 + IF (pol >= 2) parame(i,2) = 3.10654492320028 + IF (pol >= 2) parame(i,3) = 225.973607468282 + IF (pol >= 2) parame(i,6) = 3.46000000000000 + IF (pol >= 2) parame(i,11)= 7.37000000000000 + ELSE IF (compna(i) == 'nitroethane') THEN + mm(i) = 75.067 ! PC-SAFT + parame(i,1) = mm(i)* 4.019977215251163E-002 ! =3.01767629617259 + parame(i,2) = 3.21364231060938 + parame(i,3) = 286.571650044235 + IF (pol >= 1) mm(i) = 75.067 ! PCP-SAFT + IF (pol >= 1) parame(i,1) = mm(i)* 3.928506808347654E-002 ! =2.94901220582233 + IF (pol >= 1) parame(i,2) = 3.23117331990738 + IF (pol >= 1) parame(i,3) = 265.961000131109 + IF (pol >= 1) parame(i,6) = 3.23000000000000 + IF (pol >= 2) mm(i) = 75.067 ! PCIP-SAFT + IF (pol >= 2) parame(i,1) = mm(i)* 4.117677400894779E-002 ! =3.09101689452968 + IF (pol >= 2) parame(i,2) = 3.19364569858756 + IF (pol >= 2) parame(i,3) = 246.676040248662 + IF (pol >= 2) parame(i,6) = 3.23000000000000 + IF (pol >= 2) parame(i,11)= 9.63000000000000 + ELSE IF (compna(i) == 'acetonitrile') THEN + mm(i) = 41.052 ! PC-SAFT + parame(i,1) = mm(i)* 5.673187410405271E-002 ! =2.32895689571957 + parame(i,2) = 3.18980108373791 + parame(i,3) = 311.307486044181 + IF (pol >= 1) mm(i) = 41.052 ! PCP-SAFT + IF (pol >= 1) parame(i,1) = mm(i)* 5.254832931037250E-002 ! =2.15721401484941 + IF (pol >= 1) parame(i,2) = 3.27301469369132 + IF (pol >= 1) parame(i,3) = 216.888948676921 + IF (pol >= 1) parame(i,6) = 3.92520000000000 + IF (pol >= 2) mm(i) = 41.052 ! PCIP-SAFT + IF (pol >= 2) parame(i,1) = mm(i)* 5.125846581157176E-002 ! =2.10426253849664 + IF (pol >= 2) parame(i,2) = 3.39403305120647 + IF (pol >= 2) parame(i,3) = 199.070191065791 + IF (pol >= 2) parame(i,6) = 3.92520000000000 + IF (pol >= 2) parame(i,11)= 4.40000000000000 + ! IF (pol >= 2) mm(i) = 41.052 ! PCIP-SAFT my_DD adjusted + ! IF (pol >= 2) parame(i,1) = mm(i)* 5.755347845863738E-002 ! =2.36268539768398 + ! IF (pol >= 2) parame(i,2) = 3.18554306395900 + ! IF (pol >= 2) parame(i,3) = 225.143934506015 + ! IF (pol >= 2) parame(i,6) = 3.43151866932598 + ! IF (pol >= 2) parame(i,11)= 4.40000000000000 + ! mm(i) = 41.053 ! PCP-SAFT dipole and quadrupole + ! parame(i,1) = 1.79993 + ! parame(i,2) = 3.47366 + ! parame(i,3) = 211.001 + ! parame(i,6) = 3.93800 + ! parame(i,7) = 2.44000 + ! parame(i,11)= 0.0 + ELSE IF (compna(i) == 'dmf') THEN + mm(i) = 73.09 ! PC-SAFT + parame(i,1) = 2.388 + parame(i,2) = 3.658 + parame(i,3) = 363.77 + IF (pol >= 1) mm(i) = 73.09 ! PCP-SAFT + IF (pol >= 1) parame(i,1) = 2.269 + IF (pol >= 1) parame(i,2) = 3.714 + IF (pol >= 1) parame(i,3) = 331.56 + IF (pol >= 1) parame(i,6) = 3.82 + IF (pol >= 2) mm(i) = 73.09 ! PCIP-SAFT + IF (pol >= 2) parame(i,1) = 2.375 + IF (pol >= 2) parame(i,2) = 3.667 + IF (pol >= 2) parame(i,3) = 308.42 + IF (pol >= 2) parame(i,6) = 3.82 + IF (pol >= 2) parame(i,11)= 7.81 + ELSE IF (compna(i) == 'chloroform') THEN + mm(i) = 119.377 ! PCIP-SAFT + parame(i,1) = 2.5957 + parame(i,2) = 3.4299 + parame(i,3) = 264.664 + parame(i,6) = 1.04 + IF (pol == 2) parame(i,11)= 8.23 + ELSE IF (compna(i) == 'dimethyl-ether') THEN + mm(i) = 46.069 ! PC-SAFT + parame(i,1) = mm(i)* 0.049107715 ! =2.26234331 + parame(i,2) = 3.276640534 + parame(i,3) = 212.9343244 + IF (pol >= 1) mm(i) = 46.0690000000000 ! PCP-SAFT + IF (pol >= 1) parame(i,1) = mm(i)* 0.048170452 ! =2.219164566 + IF (pol >= 1) parame(i,2) = 3.296939638 + IF (pol >= 1) parame(i,3) = 212.1048888 + IF (pol >= 1) parame(i,6) = 1.30000000000000 + IF (pol >= 2) mm(i) = 46.0690000000000 ! PCIP-SAFT + IF (pol >= 2) parame(i,1) = mm(i)* 4.939183716945787E-002 ! =2.27543254655976 + IF (pol >= 2) parame(i,2) = 3.26584718800835 + IF (pol >= 2) parame(i,3) = 206.904551967059 + IF (pol >= 2) parame(i,6) = 1.30000000000000 + IF (pol == 2) parame(i,11)= 5.29000000000000 + ELSE IF (compna(i) == 'methyl-ethyl-ether') THEN + mm(i) = 60.096 + parame(i,1) = mm(i)* .0442404671 + parame(i,2) = 3.37282595 + parame(i,3) = 216.010217 + IF (pol >= 1) mm(i) = 60.096 ! PCP-SAFT + IF (pol >= 1) parame(i,1) = mm(i)* 4.3971676124088D-002 ! =2.64252184835325 + IF (pol >= 1) parame(i,2) = 3.37938465390 + IF (pol >= 1) parame(i,3) = 215.787173860 + IF (pol >= 1) parame(i,6) = 1.17000000000 + IF (pol >= 2) mm(i) = 60.096 ! PICP-SAFT + IF (pol >= 2) parame(i,1) = mm(i)* 4.4580196137984D-002 ! =2.67909146710834 + IF (pol >= 2) parame(i,2) = 3.36105342286 + IF (pol >= 2) parame(i,3) = 212.871911999 + IF (pol >= 2) parame(i,6) = 1.17000000000 + IF (pol >= 2) parame(i,11) = 7.93000000000 + ELSE IF (compna(i) == 'diethyl-ether') THEN + mm(i) = 74.123 ! PC-SAFT + parame(i,1) = mm(i)* .0409704089 + parame(i,2) = 3.48569553 + parame(i,3) = 217.64113 + IF (pol >= 1) mm(i) = 74.123 ! PCP-SAFT + IF (pol >= 1) parame(i,1) = mm(i)* 4.0103121403686E-2 ! =2.97256367 + IF (pol >= 1) parame(i,2) = 3.51268687697978 + IF (pol >= 1) parame(i,3) = 219.527376572135 + IF (pol >= 1) parame(i,6) = 1.15000000000000 + IF (pol >= 2) mm(i) = 74.123 ! PCIP-SAFT + IF (pol >= 2) parame(i,1) = mm(i)* 4.04144179873E-2 ! =2.9956379 + IF (pol >= 2) parame(i,2) = 3.501724569 + IF (pol >= 2) parame(i,3) = 217.8941822 + IF (pol >= 2) parame(i,6) = 1.15 + IF (pol == 2) parame(i,11)= 8.73 + ELSE IF (compna(i) == 'vinylacetate') THEN + mm(i) = 86.092 + parame(i,1) = mm(i)* .0374329292 + parame(i,2) = 3.35278602 + parame(i,3) = 240.492049 + ELSE IF (compna(i) == 'chloromethane') THEN ! R40 + mm(i) = 50.488 ! PC-SAFT + parame(i,1) = mm(i)* 0.039418879 ! 1.9902 + parame(i,2) = 3.1974 + parame(i,3) = 237.27 + IF (pol >= 1) mm(i) = 50.488 ! PCP-SAFT + IF (pol >= 1) parame(i,1) = mm(i)* 0.035790801 ! 1.8070 + IF (pol >= 1) parame(i,2) = 3.3034 + IF (pol >= 1) parame(i,3) = 229.97 + IF (pol >= 1) parame(i,6) = 1.8963 + IF (pol >= 1) lli(i) = 1.67703*parame(i,2) + IF (pol >= 1) phi_criti(i)= 20.75417 + IF (pol >= 1) chap(i) = 0.5 + IF (pol >= 2) mm(i) = 50.488 ! PCIP-SAFT + IF (pol >= 2) parame(i,1) = mm(i)* 3.68559992E-2 ! 1.86078 + IF (pol >= 2) parame(i,2) = 3.275186 + IF (pol >= 2) parame(i,3) = 216.4621 + IF (pol >= 2) parame(i,6) = 1.8963 + IF (pol == 2) parame(i,11)= 4.72 + ELSE IF (compna(i) == 'fluoromethane') THEN ! R41 + IF (pol /= 1) write (*,*) 'non-polar parameters missing for fluoromethane' + IF (pol /= 1) stop + IF (pol >= 1) mm(i) = 34.0329000000000 + IF (pol >= 1) parame(i,1) = 1.94494757526896 + IF (pol >= 1) parame(i,2) = 2.96858005012635 + IF (pol >= 1) parame(i,3) = 168.938697391009 + IF (pol >= 1) parame(i,6) = 1.57823038894029 + ELSE IF (compna(i) == 'dichloromethane') THEN ! R30 + mm(i) = 84.932 ! PC-SAFT + parame(i,1) = 2.3117 + parame(i,2) = 3.3161 + parame(i,3) = 270.98 + IF (pol >= 1) mm(i) = 84.932 ! PCP-SAFT + IF (pol >= 1) parame(i,1) = 2.2687 + IF (pol >= 1) parame(i,2) = 3.3373 + IF (pol >= 1) parame(i,3) = 269.08 + IF (pol >= 1) parame(i,6) = 1.6 + IF (pol >= 2) mm(i) = 84.932 ! PCIP-SAFT + IF (pol >= 2) parame(i,1) = 2.3435 + IF (pol >= 2) parame(i,2) = 3.2987 + IF (pol >= 2) parame(i,3) = 260.66 + IF (pol >= 2) parame(i,6) = 1.6 + IF (pol == 2) parame(i,11)= 6.48 + ELSE IF (compna(i) == 'difluoromethane') THEN ! R32 + IF (pol /= 1) write (*,*) 'non-polar parameters missing for difluoromethane' + IF (pol /= 1) stop + IF (pol >= 1) mm(i) = 52.0236 ! PCP-SAFT + IF (pol >= 1) parame(i,1) = mm(i)* 4.814700934384165E-002 ! 2.50478075530028 + IF (pol >= 1) parame(i,2) = 2.79365980535456 + IF (pol >= 1) parame(i,3) = 160.893555378523 + IF (pol >= 1) parame(i,6) = 1.97850000000000 + ELSE IF (compna(i) == 'trifluoromethane') THEN ! R23 + IF (pol /= 1) write (*,*) 'non-polar parameters missing for trifluoromethane' + IF (pol /= 1) stop + IF (pol >= 1) mm(i) = 70.0138000000000 + IF (pol >= 1) parame(i,1) = 2.66039274225485 + IF (pol >= 1) parame(i,2) = 2.82905884530501 + IF (pol >= 1) parame(i,3) = 149.527709542333 + IF (pol >= 1) parame(i,6) = 1.339963415253999E-002 + ELSE IF (compna(i) == 'tetrachloromethane') THEN ! R10 + mm(i) = 153.822 + parame(i,1) = mm(i)* .0150432213 + parame(i,2) = 3.81801454 + parame(i,3) = 292.838632 + ELSE IF (compna(i) == 'trichlorofluoromethane') THEN ! R11 + IF (pol /= 1) write (*,*) 'non-polar parameters missing for trichlorofluoromethane' + IF (pol /= 1) stop + IF (pol >= 1) mm(i) = 137.368000000000 + IF (pol >= 1) parame(i,1) = 2.28793359008803 + IF (pol >= 1) parame(i,2) = 3.69013104930876 + IF (pol >= 1) parame(i,3) = 248.603173885090 + IF (pol >= 1) parame(i,6) = 0.23225538492979 + ELSE IF (compna(i) == 'chlorodifluoromethane') THEN ! R22 ( CHClF2 or CHF2Cl) + IF (pol /= 1) write (*,*) 'non-polar parameters missing for chlorodifluoromethane' + IF (pol /= 1) stop + IF (pol >= 1) mm(i) = 86.4684000000000 + IF (pol >= 1) parame(i,1) = 2.47218586047893 + IF (pol >= 1) parame(i,2) = 3.13845692489930 + IF (pol >= 1) parame(i,3) = 187.666355083434 + IF (pol >= 1) parame(i,6) = 1.04954264812860 + ELSE IF (compna(i) == 'chloroethane') THEN + mm(i) = 64.514 + parame(i,1) = mm(i)* .0350926868 + parame(i,2) = 3.41602397 + parame(i,3) = 245.42626 + ELSE IF (compna(i) == '11difluoroethane') THEN + ! mm(i) = 66.0500000000000 ! PC-SAFT + ! parame(i,1) = mm(i)* 4.109944338817734E-002 + ! parame(i,2) = 3.10257444633546 + ! parame(i,3) = 192.177159144029 + ! mm(i) = 66.05 ! PC-SAFT assoc + ! parame(i,1)= 2.984947188 + ! parame(i,2)= 2.978630027 + ! parame(i,3)= 137.8192282 + ! nhb_typ(i) = 2 + ! nhb_no(i,1)= 1 + ! nhb_no(i,2)= 1 + ! eps_hb(i,i,1,2)= 823.3478288 + ! eps_hb(i,i,2,1)= 823.3478288 + ! eps_hb(i,i,1,1)= 0.0 + ! eps_hb(i,i,2,2)= 0.0 + ! kap_hb(i,i) = 0.96345994 + IF (pol >= 1) mm(i) = 66.0500000000000 ! PCP-SAFT + IF (pol >= 1) parame(i,1) = mm(i)* 3.949665745363346E-002 ! =2.60875422481249 + IF (pol >= 1) parame(i,2) = 3.13758353925036 + IF (pol >= 1) parame(i,3) = 179.517952627836 + IF (pol >= 1) parame(i,6) = 2.27000000000000 + IF (pol >= 1) lli(i) = 2.03907*parame(i,2) + IF (pol >= 1) phi_criti(i)= 26.5 + IF (pol >= 1) chap(i) = 0.4 + IF (pol >= 2) mm(i) = 66.0500000000000 ! PCIP-SAFT + IF (pol >= 2) parame(i,1) = mm(i)* 4.093647666154238E-002 ! =2.70385428349487 + IF (pol >= 2) parame(i,2) = 3.10437129415885 + IF (pol >= 2) parame(i,3) = 170.464400902455 + IF (pol >= 2) parame(i,6) = 2.27000000000000 + IF (pol == 2) parame(i,11)= 5.01000000000000 + ELSE IF (compna(i) == '1-chlorobutane') THEN + mm(i) = 92.568 + parame(i,1) = mm(i)* .0308793201 + parame(i,2) = 3.64240187 + parame(i,3) = 258.655298 + ELSE IF (compna(i) == 'chlorobenzene') THEN + ! mm(i) = 112.558 + ! parame(i,1) = mm(i)* .0235308686 + ! parame(i,2) = 3.75328494 + ! parame(i,3) = 315.039018 + mm(i) = 112.558 ! PCIP-SAFT + parame(i,1) = mm(i)* 0.023824167 ! =2.6816 + parame(i,2) = 3.7352 + parame(i,3) = 308.82 + parame(i,6) = 1.69 + IF (pol == 2) parame(i,11)= 14.1 + ELSE IF (compna(i) == 'styrene') THEN + mm(i) = 104.150 + parame(i,1) = mm(i)* 2.9124104853E-2 + parame(i,2) = 3.760233548 + parame(i,3) = 298.51287564 + ELSE IF (compna(i) == 'methylmethanoate') THEN + mm(i) = 60.053 + parame(i,1) = mm(i)* .0446000264 + parame(i,2) = 3.08753499 + parame(i,3) = 242.626755 + IF (pol >= 1) mm(i) = 60.053 ! PCP-SAFT + IF (pol >= 1) parame(i,1) = mm(i)* 4.366991153963102E-002 ! =2.62250919768946 + IF (pol >= 1) parame(i,2) = 3.10946396964 + IF (pol >= 1) parame(i,3) = 239.051951942 + IF (pol >= 1) parame(i,6) = 1.77 + IF (pol >= 2) mm(i) = 60.053 ! PCIP-SAFT + IF (pol >= 2) parame(i,1) = mm(i)* 4.492572388931002E-2 ! 2.69792449 + IF (pol >= 2) parame(i,2) = 3.078467837 + IF (pol >= 2) parame(i,3) = 232.1842551 + IF (pol >= 2) parame(i,6) = 1.77 + IF (pol == 2) parame(i,11)= 5.05 + ELSE IF (compna(i) == 'ethylmethanoate') THEN + mm(i) = 74.079 ! PC-SAFT + parame(i,1) = mm(i)* .03898009 + parame(i,2) = 3.31087192 + parame(i,3) = 246.465646 + IF (pol >= 1) mm(i) = 74.079 ! PCP-SAFT + IF (pol >= 1) parame(i,1) = mm(i)* 3.825407152074255E-002 ! =2.83382336418509 + IF (pol >= 1) parame(i,2) = 3.33160046679 + IF (pol >= 1) parame(i,3) = 244.495680932 + IF (pol >= 1) parame(i,6) = 1.93000000000 + ELSE IF (compna(i) == 'propylmethanoate') THEN + mm(i) = 88.106 + parame(i,1) = mm(i)* .0364206062 + parame(i,2) = 3.41679642 + parame(i,3) = 246.457732 + IF (pol >= 1) mm(i) = 88.106 + IF (pol >= 1) parame(i,1) = mm(i)* 3.60050739149E-2 ! =3.17226304235232 + IF (pol >= 1) parame(i,2) = 3.42957609309 + IF (pol >= 1) parame(i,3) = 245.637644107 + IF (pol >= 1) parame(i,6) = 1.89 + ELSE IF (compna(i) == 'methylacetate') THEN + mm(i) = 74.079 ! PC-SAFT + parame(i,1) = mm(i)* 4.286817177E-2 ! =3.175631296 + parame(i,2) = 3.18722021277843 + parame(i,3) = 234.106931032456 + IF (pol >= 1) mm(i) = 74.079 ! PCP-SAFT + IF (pol >= 1) parame(i,1) = mm(i)* 4.228922065E-2 ! =3.132743176 + IF (pol >= 1) parame(i,2) = 3.2011401688 + IF (pol >= 1) parame(i,3) = 233.17562886 + IF (pol >= 1) parame(i,6) = 1.72 + IF (pol >= 2) mm(i) = 74.079 ! PCIP-SAFT + IF (pol >= 2) parame(i,1) = mm(i)* 4.298900538E-2 ! =3.18458252 + IF (pol >= 2) parame(i,2) = 3.180642322 + IF (pol >= 2) parame(i,3) = 229.3132680 + IF (pol >= 2) parame(i,6) = 1.72 + IF (pol == 2) parame(i,11)= 6.94 + ELSE IF (compna(i) == 'ethylacetate') THEN + mm(i) = 88.106 ! PC-SAFT + parame(i,1) = mm(i)* .0401464427 ! =3.537142481 + parame(i,2) = 3.30789258 + parame(i,3) = 230.800689 + IF (pol >= 1) mm(i) = 88.106 ! PCP-SAFT + IF (pol >= 1) parame(i,1) = mm(i)* 0.039792575 ! =3.505964572 + IF (pol >= 1) parame(i,2) = 3.317655188 + IF (pol >= 1) parame(i,3) = 230.2434769 + IF (pol >= 1) parame(i,6) = 1.78 + IF (pol >= 2) mm(i) = 88.106 ! PCIP-SAFT + IF (pol >= 2) parame(i,1) = mm(i)* 0.040270267 ! =3.548052143 + IF (pol >= 2) parame(i,2) = 3.302097562 + IF (pol >= 2) parame(i,3) = 227.5026191 + IF (pol >= 2) parame(i,6) = 1.78 + IF (pol == 2) parame(i,11)= 8.62 + ELSE IF (compna(i) == 'ethyl-propanoate') THEN + mm(i) = 102.133 + parame(i,1) = mm(i)* .0375692464 + parame(i,2) = 3.40306071 + parame(i,3) = 232.778374 + ELSE IF (compna(i) == 'propyl-ethanoate') THEN + mm(i) = 102.133 + parame(i,1) = mm(i)* .0370721275 + parame(i,2) = 3.42272266 + parame(i,3) = 235.758378 + IF (pol >= 1) mm(i) = 102.133 ! PCP-SAFT + IF (pol >= 1) parame(i,1) = mm(i)* 3.687149995200072E-2 ! =3.76579690459769 + IF (pol >= 1) parame(i,2) = 3.4289353421006 + IF (pol >= 1) parame(i,3) = 235.41679442910 + IF (pol >= 1) parame(i,6) = 1.78 + ! IF (pol.EQ.2) parame(i,11)= 10.41 + ELSE IF (compna(i) == 'nbutyl-ethanoate') THEN + mm(i) = 116.16 ! PC-SAFT + parame(i,1) = mm(i)* .03427004 + parame(i,2) = 3.54269638 + parame(i,3) = 242.515768 + IF (pol >= 1) mm(i) = 116.16 ! PCP-SAFT + IF (pol >= 1) parame(i,1) = mm(i)* 3.411585209773470E-002 ! =3.96289737967286 + IF (pol >= 1) parame(i,2) = 3.54821589228130 + IF (pol >= 1) parame(i,3) = 242.274388267447 + IF (pol >= 1) parame(i,6) = 1.87000000000000 + IF (pol >= 2) mm(i) = 116.16 ! PCIP-SAFT + IF (pol >= 2) parame(i,1) = mm(i)* 3.442139015733717E-002 ! =3.99838868067629 + IF (pol >= 2) parame(i,2) = 3.53576054452119 + IF (pol >= 2) parame(i,3) = 240.154409609249 + IF (pol >= 2) parame(i,6) = 1.87000000000000 + IF (pol == 2) parame(i,11)= 14.2000000000000 + ELSE IF (compna(i) == 'methyl-octanoate') THEN + mm(i) = 158.24 ! PC-SAFT + parame(i,1) = 5.2074 + parame(i,2) = 3.6069 + parame(i,3) = 244.12 + ELSE IF (compna(i) == 'methyl-decanoate') THEN + mm(i) = 186.2912 ! PC-SAFT + parame(i,1) = 5.8402 + parame(i,2) = 3.6871 + parame(i,3) = 248.27 + + mm(i) = 186.2912 ! PC-SAFT from GC-method Tim + parame(i,1) = 7.716 + parame(i,2) = 3.337303029 + parame(i,3) = 204.250907 + + mm(i) = 186.2912 ! PC-SAFT from GC-method (tightly fit) Tim + parame(i,1) = 7.728 + parame(i,2) = 3.334023322 + parame(i,3) = 206.9099379 + + ! mm(i) = 186.2912 ! PC-SAFT from fit to DIPPR + ! parame(i,1) = 6.285005 + ! parame(i,2) = 3.594888 + ! parame(i,3) = 236.781461 + ! ! parame(i,6) = 2.08056 + + ! mm(i) = 186.291000000000 + ! parame(i,1) = 6.28500485898895 + ! parame(i,2) = 3.59488828061149 + ! parame(i,3) = 236.781461491921 + ! parame(i,6) = 2.08055996894836 + ! parame(i,8) = 1.00000000000000 + mm(i) = 186.291000000000 + parame(i,1) = 6.14436331493372 + parame(i,2) = 3.61977264863944 + parame(i,3) = 242.071887817656 + + ELSE IF (compna(i) == 'methyl-dodecanoate') THEN + mm(i) = 214.344 ! PC-SAFT + parame(i,1) = 6.5153 + parame(i,2) = 3.7406 + parame(i,3) = 250.7 + ELSE IF (compna(i) == 'methyl-tetradecanoate') THEN + mm(i) = 242.398 ! PC-SAFT + parame(i,1) = 7.1197 + parame(i,2) = 3.7968 + parame(i,3) = 253.77 + ELSE IF (compna(i) == 'methyl-hexadecanoate') THEN + mm(i) = 270.451 ! PC-SAFT + parame(i,1) = 7.891 + parame(i,2) = 3.814 + parame(i,3) = 253.71 + ELSE IF (compna(i) == 'methyl-octadecanoate') THEN + mm(i) = 298.504 ! PC-SAFT + parame(i,1) = 8.8759 + parame(i,2) = 3.7932 + parame(i,3) = 250.81 + ELSE IF (compna(i) == 'CH2F2') THEN + mm(i) = 52.02 + parame(i,1) = 3.110084171 + parame(i,2) = 2.8145230485 + parame(i,3) = 158.98060151 + ELSE IF (compna(i) == 'naphthalene') THEN + ! mm(i) = 128.174000000 + ! parame(i,1) = mm(i)* 2.4877834216412E-2 + ! parame(i,2) = 3.82355815011 + ! parame(i,3) = 341.560675334 + + mm(i) = 128.17400000000 + parame(i,1) = mm(i)* 2.6400924157729E-2 + parame(i,2) = 3.8102186020014 + parame(i,3) = 328.96792935903 + ELSE IF (compna(i) == 'h2s') THEN + mm(i) = 34.0820000000000 ! PC-SAFT + parame(i,1) = mm(i)* 4.838886696385162E-002 ! = 1.64918936386199 + parame(i,2) = 3.05478289838459 + parame(i,3) = 229.838873939562 + nhb_typ(i) = 2 + nhb_no(i,1) = 1 + nhb_no(i,2) = 1 + eps_hb(i,i,1,2)= 536.634834731413 + eps_hb(i,i,2,1)= 536.634834731413 + eps_hb(i,i,1,1)= 0.0 + eps_hb(i,i,2,2)= 0.0 + kap_hb(i,i) = 1.000000000000000E-003 +! PC-SAFT from Xiaohua + mm(i) = 34.082 ! PC-SAFT + parame(i,1) = 1.63677 + parame(i,2) = 3.06565 + parame(i,3) = 230.2121 + nhb_typ(i) = 2 + nhb_no(i,1) = 1 + nhb_no(i,2) = 1 + eps_hb(i,i,1,2)= 275.1088 + eps_hb(i,i,2,1)= 275.1088 + eps_hb(i,i,1,1)= 0.0 + eps_hb(i,i,2,2)= 0.0 + kap_hb(i,i) = 1.E-2 + ! IF (pol.GE.1) mm(i) = 34.082 ! PCP-SAFT with quadrupole + ! IF (pol.GE.1) parame(i,1) = mm(i)* 3.03171032558E-2 ! =1.03326751316478 + ! IF (pol.GE.1) parame(i,2) = 3.6868189914018 + ! IF (pol.GE.1) parame(i,3) = 246.862831266172 + ! IF (pol.GE.1) nhb_typ(i) = 2 + ! IF (pol.GE.1) nhb_no(i,1) = 1 + ! IF (pol.GE.1) nhb_no(i,2) = 1 + ! IF (pol.GE.1) eps_hb(i,i,1,2)= 987.4927232 + ! IF (pol.GE.1) eps_hb(i,i,2,1)= 987.4927232 + ! IF (pol.GE.1) eps_hb(i,i,1,1)= 0.0 + ! IF (pol.GE.1) eps_hb(i,i,2,2)= 0.0 + ! IF (pol.GE.1) kap_hb(i,i) = 5.5480659623d-4 + ! IF (pol.GE.1) parame(i,6) = 0.97833 + ! IF (pol.GE.1) parame(i,7) = 3.8623 + ! IF (pol.GE.1) LLi(i) = 1.2737*parame(i,2) + ! IF (pol.GE.1) phi_criti(i)= 14.316 + ! IF (pol.GE.1) chap(i) = 0.4473 + IF (pol >= 1) mm(i) = 34.0820000000000 ! PCP-SAFT no quadrupoLE + IF (pol >= 1) parame(i,1) = mm(i)* 4.646468487062725E-002 ! 1.58360938976072 + IF (pol >= 1) parame(i,2) = 3.10111012646306 + IF (pol >= 1) parame(i,3) = 230.243457544889 + IF (pol >= 1) nhb_typ(i) = 2 + IF (pol >= 1) nhb_no(i,1) = 1 + IF (pol >= 1) nhb_no(i,2) = 1 + IF (pol >= 1) eps_hb(i,i,1,2)= 584.367708701411 + IF (pol >= 1) eps_hb(i,i,2,1)= 584.367708701411 + IF (pol >= 1) eps_hb(i,i,1,1)= 0.0 + IF (pol >= 1) eps_hb(i,i,2,2)= 0.0 + IF (pol >= 1) kap_hb(i,i) = 1.000000000000000E-003 + IF (pol >= 1) parame(i,6) = 0.978330000000000 + + IF (pol >= 1) lli(i) = 1.2737*parame(i,2) + IF (pol >= 1) phi_criti(i)= 14.316 + IF (pol >= 1) chap(i) = 0.4473 + + + IF (pol == 2) parame(i,7) = 0.0 + IF (pol == 2) mm(i) = 34.0820000000000 ! PCIP-SAFT + IF (pol == 2) parame(i,1) = mm(i)* 4.806418212963168E-002 ! 1.63812345534211 + IF (pol == 2) parame(i,2) = 3.06556006883749 + IF (pol == 2) parame(i,3) = 221.746622243054 + IF (pol == 2) nhb_typ(i) = 2 + IF (pol == 2) nhb_no(i,1) = 1 + IF (pol == 2) nhb_no(i,2) = 1 + IF (pol == 2) eps_hb(i,i,1,2)= 672.164783984789 + IF (pol == 2) eps_hb(i,i,2,1)= 672.164783984789 + IF (pol == 2) eps_hb(i,i,1,1)= 0.0 + IF (pol == 2) eps_hb(i,i,2,2)= 0.0 + IF (pol == 2) kap_hb(i,i) = 1.000000000000000E-003 + IF (pol == 2) parame(i,6) = 0.978330000000000 + IF (pol == 2) parame(i,11) = 3.60200000000000 + IF (pol == 2) parame(i,7) = 0.0 + + IF (pol >= 1)mm(i) = 34.0820000000000 !PCP-SAFT D&Q + IF (pol >= 1)parame(i,1) = mm(i)* 3.974667896078737E-002 ! = 1.35464631234155 + IF (pol >= 1)parame(i,2) = 3.30857082333438 + IF (pol >= 1)parame(i,3) = 234.248947273191 + IF (pol >= 1)nhb_typ(i) = 2 + IF (pol >= 1)nhb_no(i,1) = 1 + IF (pol >= 1)nhb_no(i,2) = 1 + IF (pol >= 1)eps_hb(i,i,1,2)= 780.770936834770 + IF (pol >= 1)eps_hb(i,i,2,1)= 780.770936834770 + IF (pol >= 1)eps_hb(i,i,1,1)= 0.0 + IF (pol >= 1)eps_hb(i,i,2,2)= 0.0 + IF (pol >= 1)kap_hb(i,i) = 1.000000000000000E-003 + IF (pol >= 1)parame(i,6) = 0.978330000000000 + IF (pol >= 1)parame(i,7) = 2.93750500000000 + + ELSE IF (compna(i) == 'methanol') THEN + mm(i) = 32.042 ! PC-SAFT + parame(i,1) = mm(i)* .0476100379 + parame(i,2) = 3.23000005 + parame(i,3) = 188.904644 + nhb_typ(i) = 2 + nhb_no(i,1) = 1 ! no. of sites of type 1 + nhb_no(i,2) = 1 ! no. of sites of type 2 + eps_hb(i,i,1,2)= 2899.49055 + eps_hb(i,i,2,1)= 2899.49055 + eps_hb(i,i,1,1)= 0.0 + eps_hb(i,i,2,2)= 0.0 + kap_hb(i,i) = .0351760892 + IF (pol >= 1) mm(i) = 32.042 ! PCP-SAFT + IF (pol >= 1) parame(i,1) = mm(i)* 7.213091821E-2 ! =2.31121888139672 + IF (pol >= 1) parame(i,2) = 2.8270129502 + IF (pol >= 1) parame(i,3) = 176.3760515 + IF (pol >= 1) nhb_typ(i) = 2 + IF (pol >= 1) nhb_no(i,1) = 1 + IF (pol >= 1) nhb_no(i,2) = 1 + IF (pol >= 1) eps_hb(i,i,1,2)= 2332.5845803 + IF (pol >= 1) eps_hb(i,i,2,1)= 2332.5845803 + IF (pol >= 1) eps_hb(i,i,1,1)= 0.0 + IF (pol >= 1) eps_hb(i,i,2,2)= 0.0 + IF (pol >= 1) kap_hb(i,i) = 8.9248658086E-2 + IF (pol >= 1) parame(i,6) = 1.7 + IF (pol >= 1) lli(i) = 1.75*parame(i,2) + IF (pol >= 1) phi_criti(i)= 23.43 + IF (pol >= 1) chap(i) = 0.304 + IF (pol == 2) mm(i) = 32.042 ! PCIP-SAFT + IF (pol == 2) parame(i,1) = 2.0693 + IF (pol == 2) parame(i,2) = 2.9547 + IF (pol == 2) parame(i,3) = 174.51 + IF (pol == 2) nhb_typ(i) = 2 + IF (pol == 2) nhb_no(i,1) = 1 + IF (pol == 2) nhb_no(i,2) = 1 + IF (pol == 2) eps_hb(i,i,1,2)= 2418.5 + IF (pol == 2) eps_hb(i,i,2,1)= 2418.5 + IF (pol == 2) eps_hb(i,i,1,1)= 0.0 + IF (pol == 2) eps_hb(i,i,2,2)= 0.0 + IF (pol == 2) kap_hb(i,i) = 0.06319 + IF (pol == 2) parame(i,6) = 1.7 + IF (pol == 2) parame(i,11)= 3.29 + ! mm(i) = 32.0420000000000 ! PCP-SAFT with adjusted QQ + ! parame(i,1) = mm(i)* 6.241807629559099E-002 + ! ! parame(i,1) = 2.00000000066333 + ! parame(i,2) = 2.97610169698593 + ! parame(i,3) = 163.268505098639 + ! nhb_typ(i) = 2 + ! nhb_no(i,1) = 1 + ! nhb_no(i,2) = 1 + ! eps_hb(i,i,1,2)= 2449.55621933612 + ! eps_hb(i,i,2,1)= 2449.55621933612 + ! eps_hb(i,i,1,1)= 0.0 + ! eps_hb(i,i,2,2)= 0.0 + ! kap_hb(i,i) = 8.431015160393653E-002 + ! parame(i,6) = 1.72000000000000 + ! parame(i,7) = 1.59810028824523 + ELSE IF (compna(i) == 'ethanol') THEN + mm(i) = 46.069 + parame(i,1) = mm(i)* .0517195521 + parame(i,2) = 3.17705595 + parame(i,3) = 198.236542 + nhb_typ(i) = 2 + nhb_no(i,1) = 1 ! no. of sites of type 1 + nhb_no(i,2) = 1 ! no. of sites of type 2 + eps_hb(i,i,1,2)= 2653.38367 + eps_hb(i,i,2,1)= 2653.38367 + eps_hb(i,i,1,1)= 0.0 + eps_hb(i,i,2,2)= 0.0 + kap_hb(i,i) = .0323840159 + IF (pol >= 1) mm(i) = 46.0690000000000 + IF (pol >= 1) parame(i,1) = mm(i)* 4.753626908781145E-002 ! =2.18994838060639 + IF (pol >= 1) parame(i,2) = 3.30120000000000 + IF (pol >= 1) parame(i,3) = 209.824555801706 + IF (pol >= 1) nhb_typ(i) = 2 + IF (pol >= 1) nhb_no(i,1) = 1 + IF (pol >= 1) nhb_no(i,2) = 1 + IF (pol >= 1) eps_hb(i,i,1,2)= 2584.53116785767 + IF (pol >= 1) eps_hb(i,i,2,1)= 2584.53116785767 + IF (pol >= 1) eps_hb(i,i,1,1)= 0.0 + IF (pol >= 1) eps_hb(i,i,2,2)= 0.0 + IF (pol >= 1) kap_hb(i,i) = 2.349382956935725E-002 + IF (pol >= 1) parame(i,6) = 1.69000000000000 + ! mm(i) = 46.0690000000000 + ! parame(i,1) = mm(i)* 5.117957752785066E-002 ! =2.357791957 + ! parame(i,2) = 3.24027031244304 + ! parame(i,3) = 175.657110615456 + ! nhb_typ(i) = 2 + ! nhb_no(i,1) = 1 + ! nhb_no(i,2) = 1 + ! eps_hb(i,i,1,2)= 2273.62670516146 + ! eps_hb(i,i,2,1)= 2273.62670516146 + ! eps_hb(i,i,1,1)= 0.0 + ! eps_hb(i,i,2,2)= 0.0 + ! kap_hb(i,i) = 7.030279197039477E-002 + ! parame(i,6) = 1.69000000000000 + ! parame(i,7) = 3.63701294195013 + IF (pol == 2) mm(i) = 46.0690000000000 + IF (pol == 2) parame(i,1) = mm(i)* 4.733436280008321E-002 ! =2.18064676 + IF (pol == 2) parame(i,2) = 3.31260000000000 + IF (pol == 2) parame(i,3) = 207.594119926613 + IF (pol == 2) nhb_typ(i) = 2 + IF (pol == 2) nhb_no(i,1) = 1 + IF (pol == 2) nhb_no(i,2) = 1 + IF (pol == 2) eps_hb(i,i,1,2)= 2589.68311382661 + IF (pol == 2) eps_hb(i,i,2,1)= 2589.68311382661 + IF (pol == 2) eps_hb(i,i,1,1)= 0.0 + IF (pol == 2) eps_hb(i,i,2,2)= 0.0 + IF (pol == 2) kap_hb(i,i) = 2.132561218631547E-002 + IF (pol == 2) parame(i,6) = 1.69000000000000 + IF (pol == 2) parame(i,7) = 0.0 + IF (pol == 2) parame(i,11)= 5.11000000000000 + ELSE IF (compna(i) == '1-propanol') THEN + mm(i) = 60.096 + parame(i,1) = mm(i)* .0499154461 + parame(i,2) = 3.25221234 + parame(i,3) = 233.396705 + nhb_typ(i) = 2 + nhb_no(i,1) = 1 ! no. of sites of type 1 + nhb_no(i,2) = 1 ! no. of sites of type 2 + eps_hb(i,i,1,2)= 2276.77867 + eps_hb(i,i,2,1)= 2276.77867 + eps_hb(i,i,1,1)= 0.0 + eps_hb(i,i,2,2)= 0.0 + kap_hb(i,i) = .0152683094 + ELSE IF (compna(i) == '1-butanol') THEN + mm(i) = 74.123 + parame(i,1) = mm(i)* .0341065046 + parame(i,2) = 3.72361538 + parame(i,3) = 269.798048 + nhb_typ(i) = 2 + nhb_no(i,1) = 1 ! no. of sites of type 1 + nhb_no(i,2) = 1 ! no. of sites of type 2 + eps_hb(i,i,1,2)= 2661.37119 + eps_hb(i,i,2,1)= 2661.37119 + eps_hb(i,i,1,1)= 0.0 + eps_hb(i,i,2,2)= 0.0 + kap_hb(i,i) = .00489087833 + mm(i) = 74.1230000000000 + parame(i,1) = mm(i)* 3.329202420547412E-002 ! =2.46770471018236 + parame(i,2) = 3.76179376417092 + parame(i,3) = 270.237284242002 + nhb_typ(i) = 2 + nhb_no(i,1) = 1 + nhb_no(i,2) = 1 + eps_hb(i,i,1,2)= 2669.28754983370 + eps_hb(i,i,2,1)= 2669.28754983370 + eps_hb(i,i,1,1)= 0.0 + eps_hb(i,i,2,2)= 0.0 + kap_hb(i,i) = 4.855584122733399E-003 + parame(i,6) = 1.66000000000000 + ELSE IF (compna(i) == '1-pentanol') THEN + mm(i) = 88.15 ! PC-SAFT + parame(i,1) = mm(i)* .041134139 + parame(i,2) = 3.45079143 + parame(i,3) = 247.278748 + nhb_typ(i) = 2 + nhb_no(i,1) = 1 ! no. of sites of type 1 + nhb_no(i,2) = 1 ! no. of sites of type 2 + eps_hb(i,i,1,2)= 2252.09237 + eps_hb(i,i,2,1)= 2252.09237 + eps_hb(i,i,1,1)= 0.0 + eps_hb(i,i,2,2)= 0.0 + kap_hb(i,i) = .0103189939 + IF (pol >= 1) mm(i) = 88.1500000000000 ! PCP-SAFT + IF (pol >= 1) parame(i,1) = mm(i)* 4.138903382168521E-002 ! =3.64844333138155 + IF (pol >= 1) parame(i,2) = 3.44250118689142 + IF (pol >= 1) parame(i,3) = 246.078034174947 + IF (pol >= 1) nhb_typ(i) = 2 + IF (pol >= 1) nhb_no(i,1) = 1 + IF (pol >= 1) nhb_no(i,2) = 1 + IF (pol >= 1) eps_hb(i,i,1,2)= 2236.72830142446 + IF (pol >= 1) eps_hb(i,i,2,1)= 2236.72830142446 + IF (pol >= 1) eps_hb(i,i,1,1)= 0.0 + IF (pol >= 1) eps_hb(i,i,2,2)= 0.0 + IF (pol >= 1) kap_hb(i,i) = 1.040067895187016E-002 + IF (pol >= 1) parame(i,6) = 1.70000000000000 + IF (pol == 2) mm(i) = 88.1500000000000 ! PCIP-SAFT + IF (pol == 2) parame(i,1) = mm(i)* 4.161521814399406E-002 ! =3.66838147939308 + IF (pol == 2) parame(i,2) = 3.43496654431777 + IF (pol == 2) parame(i,3) = 244.177313808431 + IF (pol == 2) nhb_typ(i) = 2 + IF (pol == 2) nhb_no(i,1) = 1 + IF (pol == 2) nhb_no(i,2) = 1 + IF (pol == 2) eps_hb(i,i,1,2)= 2241.27880639096 + IF (pol == 2) eps_hb(i,i,2,1)= 2241.27880639096 + IF (pol == 2) eps_hb(i,i,1,1)= 0.0 + IF (pol == 2) eps_hb(i,i,2,2)= 0.0 + IF (pol == 2) kap_hb(i,i) = 1.049516309928397E-002 + IF (pol == 2) parame(i,6) = 1.70000000000000 + IF (pol == 2) parame(i,11)= 10.8000000000000 + ELSE IF (compna(i) == '1-octanol') THEN + mm(i) = 130.23 + parame(i,1) = mm(i)* .0334446084 + parame(i,2) = 3.714535 + parame(i,3) = 262.740637 + nhb_typ(i) = 2 + nhb_no(i,1) = 1 ! no. of sites of type 1 + nhb_no(i,2) = 1 ! no. of sites of type 2 + eps_hb(i,i,1,2)= 2754.77272 + eps_hb(i,i,2,1)= 2754.77272 + eps_hb(i,i,1,1)= 0.0 + eps_hb(i,i,2,2)= 0.0 + kap_hb(i,i) = .00219656803 + ELSE IF (compna(i) == '1-nonanol') THEN + mm(i) = 144.257 + parame(i,1) = mm(i)* .0324692669 + parame(i,2) = 3.72924286 + parame(i,3) = 263.636673 + nhb_typ(i) = 2 + nhb_no(i,1) = 1 ! no. of sites of type 1 + nhb_no(i,2) = 1 ! no. of sites of type 2 + eps_hb(i,i,1,2)= 2941.9231 + eps_hb(i,i,2,1)= 2941.9231 + eps_hb(i,i,1,1)= 0.0 + eps_hb(i,i,2,2)= 0.0 + kap_hb(i,i) = .00142696883 + ELSE IF (compna(i) == '2-propanol') THEN + mm(i) = 60.096 + parame(i,1) = mm(i)* .0514663133 + parame(i,2) = 3.20845858 + parame(i,3) = 208.420809 + nhb_typ(i) = 2 + nhb_no(i,1) = 1 ! no. of sites of type 1 + nhb_no(i,2) = 1 ! no. of sites of type 2 + eps_hb(i,i,1,2)= 2253.91064 + eps_hb(i,i,2,1)= 2253.91064 + eps_hb(i,i,1,1)= 0.0 + eps_hb(i,i,2,2)= 0.0 + kap_hb(i,i) = .0246746934 + ELSE IF (compna(i) == '2-methyl-2-butanol') THEN + mm(i) = 88.15 + parame(i,1) = mm(i)* .0289135026 + parame(i,2) = 3.90526707 + parame(i,3) = 266.011828 + nhb_typ(i) = 2 + nhb_no(i,1) = 1 ! no. of sites of type 1 + nhb_no(i,2) = 1 ! no. of sites of type 2 + eps_hb(i,i,1,2)= 2618.80124 + eps_hb(i,i,2,1)= 2618.80124 + eps_hb(i,i,1,1)= 0.0 + eps_hb(i,i,2,2)= 0.0 + kap_hb(i,i) = .00186263367 + ELSE IF (compna(i) == 'acetic-acid') THEN + mm(i) = 60.053 + parame(i,1) = mm(i)* .0227076949 + parame(i,2) = 3.79651163 + parame(i,3) = 199.225066 + nhb_typ(i) = 2 + nhb_no(i,1) = 1 ! no. of sites of type 1 + nhb_no(i,2) = 1 ! no. of sites of type 2 + eps_hb(i,i,1,2)= 3092.40109 + eps_hb(i,i,2,1)= 3092.40109 + eps_hb(i,i,1,1)= 0.0 + eps_hb(i,i,2,2)= 0.0 + kap_hb(i,i) = .0870093874 + + + mm(i) = 60.053 + parame(i,1) = mm(i)* .0181797646 + parame(i,2) = 4.13711044 + parame(i,3) = 207.552969 + nhb_typ(i) = 2 + nhb_no(i,1) = 1 ! no. of sites of type 1 + nhb_no(i,2) = 1 ! no. of sites of type 2 + eps_hb(i,i,1,2)= 3198.84362 + eps_hb(i,i,2,1)= 3198.84362 + eps_hb(i,i,1,1)= 0.0 + eps_hb(i,i,2,2)= 0.0 + kap_hb(i,i) = .0586552968 + +! mit gesetztem Dipol-Moment + mm(i) = 60.0530000000000 + parame(i,1) = mm(i)* 1.736420143637533E-002 + parame(i,2) = 4.25220708070687 + parame(i,3) = 190.957247854820 + parame(i,6) = 3.50000000000000 + nhb_typ(i) = 2 + nhb_no(i,1) = 1 ! no. of sites of type 1 + nhb_no(i,2) = 1 ! no. of sites of type 2 + eps_hb(i,i,1,2)= 3096.36190957945 + eps_hb(i,i,2,1)= 3096.36190957945 + eps_hb(i,i,1,1)= 0.0 + eps_hb(i,i,2,2)= 0.0 + kap_hb(i,i) = 6.154307094782551E-002 + + ELSE IF (compna(i) == 'propionic-acid') THEN + mm(i) = 74.0800000000000 + parame(i,1) = mm(i)* 2.359519915877884E-002 + parame(i,2) = 3.99339224153844 + parame(i,3) = 295.947729838532 + nhb_typ(i) = 2 + nhb_no(i,1) = 1 ! no. of sites of type 1 + nhb_no(i,2) = 1 ! no. of sites of type 2 + eps_hb(i,i,1,2)= 2668.97826430874 + eps_hb(i,i,2,1)= 2668.97826430874 + eps_hb(i,i,1,1)= 0.0 + eps_hb(i,i,2,2)= 0.0 + kap_hb(i,i) = 3.660242292423115E-002 + ELSE IF (compna(i) == 'acrylic-acid') THEN + mm(i) = 72.0636 + parame(i,1) = mm(i)* .0430585424 + parame(i,2) = 3.0545415 + parame(i,3) = 164.115604 + nhb_typ(i) = 2 + nhb_no(i,1) = 1 ! no. of sites of type 1 + nhb_no(i,2) = 1 ! no. of sites of type 2 + eps_hb(i,i,1,2)= 3065.40667 + eps_hb(i,i,2,1)= 3065.40667 + eps_hb(i,i,1,1)= 0.0 + eps_hb(i,i,2,2)= 0.0 + kap_hb(i,i) = .336261669 + ELSE IF (compna(i) == 'caproic-acid') THEN + mm(i) = 116.16 + parame(i,1) = 5.87151 + parame(i,2) = 3.0694697 + parame(i,3) = 241.4569 + nhb_typ(i) = 1 + eps_hb(i,i,1,1)= 2871.37 + kap_hb(i,i) = 3.411613D-3 + ELSE IF (compna(i) == 'aniline') THEN + mm(i) = 93.13 + parame(i,1) = mm(i)* .0285695992 + parame(i,2) = 3.70214085 + parame(i,3) = 335.471062 + nhb_typ(i) = 2 + nhb_no(i,1) = 1 ! no. of sites of type 1 + nhb_no(i,2) = 1 ! no. of sites of type 2 + eps_hb(i,i,1,2)= 1351.64234 + eps_hb(i,i,2,1)= 1351.64234 + eps_hb(i,i,1,1)= 0.0 + eps_hb(i,i,2,2)= 0.0 + kap_hb(i,i) = .0748830615 + + mm(i) = 93.1300000000000 + parame(i,1) = mm(i)* 2.834372610192228E-002 ! =2.63965121187202 + parame(i,2) = 3.71326867619433 + parame(i,3) = 332.253796842009 + nhb_typ(i) = 2 + nhb_no(i,1) = 1 + nhb_no(i,2) = 1 + eps_hb(i,i,1,2)= 1392.14266886674 + eps_hb(i,i,2,1)= 1392.14266886674 + eps_hb(i,i,1,1)= 0.0 + eps_hb(i,i,2,2)= 0.0 + kap_hb(i,i) = 7.424612087328866E-002 + parame(i,6) = 1.55000000000000 + IF (pol == 2) parame(i,11)= 12.1000000000000 + ELSE IF (compna(i) == 'HF') THEN + ! mm(i) = 20.006 ! PC-SAFT + ! parame(i,1) = 0.87731 + ! parame(i,2) = 3.0006 + ! parame(i,3) = 112.24 + ! nhb_typ(i) = 2 + ! nhb_no(i,1) = 1 + ! nhb_no(i,2) = 1 + ! eps_hb(i,i,1,2)= 2208.22 + ! eps_hb(i,i,2,1)= 2208.22 + ! eps_hb(i,i,1,1)= 0.0 + ! eps_hb(i,i,2,2)= 0.0 + ! kap_hb(i,i) = 0.71265 + mm(i) = 20.0060000000000 ! PCP-SAFT + parame(i,1) = 1.00030000000000 + parame(i,2) = 3.17603622195029 + parame(i,3) = 331.133373208282 + nhb_typ(i) = 2 + nhb_no(i,1) = 1 + nhb_no(i,2) = 1 + eps_hb(i,i,1,2)= 348.251433080979 + eps_hb(i,i,2,1)= 348.251433080979 + eps_hb(i,i,1,1)= 0.0 + eps_hb(i,i,2,2)= 0.0 + kap_hb(i,i) = 2.868887975449893E-002 + parame(i,6) = 1.82600000000000 + ELSE IF (compna(i) == 'HCl') THEN + ! mm(i) = 36.4610000000000 + ! parame(i,1) = mm(i)* 3.922046741026943E-002 + ! parame(i,2) = 3.08731180727493 + ! parame(i,3) = 203.898845304388 + ! nhb_typ(i) = 2 + ! nhb_no(i,1) = 1 + ! nhb_no(i,2) = 1 + ! eps_hb(i,i,1,2)= 245.462773177367 + ! eps_hb(i,i,2,1)= 245.462773177367 + ! eps_hb(i,i,1,1)= 0.0 + ! eps_hb(i,i,2,2)= 0.0 + ! kap_hb(i,i) = 0.256454187330899 + mm(i) = 36.461 ! PCIP-SAFT + parame(i,1) = 1.6335 + parame(i,2) = 2.9066 + parame(i,3) = 190.17 + parame(i,6) = 1.1086 + IF (pol == 2) parame(i,11)= 2.63 + ELSE IF (compna(i) == 'gen') THEN + mm(i) = 302.0 + parame(i,1) = 8.7563 + parame(i,2) = 3.604243 + parame(i,3) = 255.6434 + nhb_typ(i) = 2 + nhb_no(i,1) = 1 ! no. of sites of type 1 + nhb_no(i,2) = 1 ! no. of sites of type 2 + eps_hb(i,i,1,2)= 0.0 + eps_hb(i,i,2,1)= 0.0 + eps_hb(i,i,1,1)= 0.0 + eps_hb(i,i,2,2)= 0.0 + kap_hb(i,i) = 0.02 + ELSE IF (compna(i) == 'h2o') THEN + mm(i) = 18.015 + parame(i,1) = mm(i)* .05915 + parame(i,2) = 3.00068335 + parame(i,3) = 366.512135 + nhb_typ(i) = 2 + nhb_no(i,1) = 1 ! no. of sites of type 1 + nhb_no(i,2) = 1 ! no. of sites of type 2 + eps_hb(i,i,1,2)= 2500.6706 + eps_hb(i,i,2,1)= 2500.6706 + eps_hb(i,i,1,1)= 0.0 + eps_hb(i,i,2,2)= 0.0 + kap_hb(i,i) = .0348679836 + + ! mm(i) = 18.015 + ! parame(i,1) = 1.706 + ! parame(i,2) = 2.429 + ! parame(i,3) = 242.19 + ! nhb_typ(i) = 2 + ! nhb_no(i,1) = 1 ! no. of sites of type 1 + ! nhb_no(i,2) = 1 ! no. of sites of type 2 + ! eps_hb(i,i,1,2)= 2644.2 + ! eps_hb(i,i,2,1)= 2644.2 + ! eps_hb(i,i,1,1)= 0.0 + ! eps_hb(i,i,2,2)= 0.0 + ! kap_hb(i,i) = 0.153 + + ! mm(i) = 18.015 + ! parame(i,1) = mm(i)* .0588185709 + ! parame(i,2) = 3.02483704 + ! parame(i,3) = 382.086672 + !c! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! + ! nhb_typ(i) = 2 + ! nhb_no(i,1) = 1 ! no. of sites of type 1 + ! nhb_no(i,2) = 2 ! no. of sites of type 2 + !c! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! + ! eps_hb(i,i,1,2)= 2442.49782 + ! eps_hb(i,i,2,1)= 2442.49782 + ! eps_hb(i,i,1,1)=0.0 + ! eps_hb(i,i,2,2)=0.0 + ! kap_hb(i,i) = .0303754635 + + ! mit gefittetem Dipol-Moment - Haarlem-night + ! mm(i) = 18.015 + ! parame(i,1) = mm(i)* 7.0037160952278E-2 + ! parame(i,2) = 2.79276650240763 + ! parame(i,3) = 270.970053834558 + ! nhb_typ(i) = 2 + ! nhb_no(i,1) = 1 ! no. of sites of type 1 + ! nhb_no(i,2) = 1 ! no. of sites of type 2 + ! eps_hb(i,i,1,2)= 1427.8287 + ! eps_hb(i,i,2,1)= 1427.8287 + ! eps_hb(i,i,1,1)=0.0 + ! eps_hb(i,i,2,2)=0.0 + ! kap_hb(i,i) = 4.335167238E-2 + ! parame(i,6) = 3.968686856378 + + IF (pol >= 1) mm(i) = 18.015 ! PCP-SAFT + IF (pol >= 1) parame(i,1) = 0.922688825223317 + IF (pol >= 1) parame(i,2) = 3.17562052023944 + IF (pol >= 1) parame(i,3) = 388.462197714696 + IF (pol >= 1) nhb_typ(i) = 2 + IF (pol >= 1) nhb_no(i,1) = 1 + IF (pol >= 1) nhb_no(i,2) = 1 + IF (pol >= 1) eps_hb(i,i,1,2)= 2000.67247409031 + IF (pol >= 1) eps_hb(i,i,2,1)= 2000.67247409031 + IF (pol >= 1) eps_hb(i,i,1,1)= 0.0 + IF (pol >= 1) eps_hb(i,i,2,2)= 0.0 + IF (pol >= 1) kap_hb(i,i) = 2.040614952751225E-003 + IF (pol >= 1) parame(i,6) = 1.85500000000000 + IF (pol >= 1) parame(i,7) = 2.00000000000000 + ! IF (pol.EQ.2) mm(i) = 18.015 ! PCIP-SAFT - DQ with my=my_RPT + ! IF (pol.EQ.2) parame(i,1) = 1.0 + ! IF (pol.EQ.2) parame(i,2) = 3.14540664928026 + ! IF (pol.EQ.2) parame(i,3) = 320.283823615925 + ! IF (pol.EQ.2) nhb_typ(i) = 2 + ! IF (pol.EQ.2) nhb_no(i,1) = 2 + ! IF (pol.EQ.2) nhb_no(i,2) = 2 + ! IF (pol.EQ.2) eps_hb(i,i,1,2)= 1335.72887678032 + ! IF (pol.EQ.2) eps_hb(i,i,2,1)= 1335.72887678032 + ! IF (pol.EQ.2) eps_hb(i,i,1,1)= 0.0 + ! IF (pol.EQ.2) eps_hb(i,i,2,2)= 0.0 + ! IF (pol.EQ.2) kap_hb(i,i) = 4.162619960844732E-003 + ! IF (pol.EQ.2) parame(i,6) = 1.85500000000000 + ! IF (pol.EQ.2) parame(i,7) = 2.00000000000000 + ! IF (pol.EQ.2) parame(i,11)= 1.45000000000000 + ! mm(i) = 18.0150000000000 + ! parame(i,1) = 1.0 + ! parame(i,2) = 3.11505069470915 + ! parame(i,3) = 320.991387913502 + ! nhb_typ(i) = 2 + ! nhb_no(i,1) = 1 + ! nhb_no(i,2) = 1 + ! eps_hb(i,i,1,2)= 2037.76329812542 + ! eps_hb(i,i,2,1)= 2037.76329812542 + ! eps_hb(i,i,1,1)= 0.0 + ! eps_hb(i,i,2,2)= 0.0 + ! kap_hb(i,i) = 3.763148982832804E-003 + ! parame(i,6) = 1.85500000000000 + ! parame(i,7) = 2.00000000000000 + ! IF (pol.EQ.2) parame(i,11)= 1.45000000000000 + IF (pol == 2) mm(i) = 18.015 ! PCIP-SAFT - DQ with my=my_0 + IF (pol == 2) parame(i,1) = 1.0 + IF (pol == 2) parame(i,2) = 3.11574491885322 + IF (pol == 2) parame(i,3) = 322.699984283499 + IF (pol == 2) nhb_typ(i) = 2 + IF (pol == 2) nhb_no(i,1) = 1 + IF (pol == 2) nhb_no(i,2) = 1 + IF (pol == 2) eps_hb(i,i,1,2)= 2033.87777692450 + IF (pol == 2) eps_hb(i,i,2,1)= 2033.87777692450 + IF (pol == 2) eps_hb(i,i,1,1)= 0.0 + IF (pol == 2) eps_hb(i,i,2,2)= 0.0 + IF (pol == 2) kap_hb(i,i) = 3.815764667176484E-003 + IF (pol == 2) parame(i,6) = 1.85500000000000 + IF (pol == 2) parame(i,7) = 2.00000000000000 + IF (pol == 2) parame(i,11)= 1.45000000000000 + ! mm(i) = 18.015 ! Dortmund + ! parame(i,1) = 0.11065254*mm(i) + ! parame(i,2) = 2.36393615 + ! parame(i,3) = 300.288589 + ! nhb_typ(i) = 2 + ! nhb_no(i,1) = 1 + ! nhb_no(i,2) = 1 + ! eps_hb(i,i,1,2)= 1193.45585 + ! eps_hb(i,i,2,1)= 1193.45585 + ! eps_hb(i,i,1,1)= 0.0 + ! eps_hb(i,i,2,2)= 0.0 + ! kap_hb(i,i) = 0.091203519 + ! parame(i,6) = 1.8546 + ! parame(i,7) = 0.0 + ! parame(i,11)= 0.0 + ELSE IF (compna(i) == 'MBBA') THEN + mm(i) = 267.37 + parame(i,1) = 12.194 + parame(i,2) = 3.064 + parame(i,3) = 270.7 + e_lc(i,i) = 13.7 !Hino & Prausnitz + s_lc(i,i) = 0.176 !Hino & Prausnitz + ELSE IF (compna(i) == 'PCH5') THEN + mm(i) = 255.41 + parame(i,1) = 11.6 + parame(i,2) = 3.2 + parame(i,3) = 270.7 + ! E_LC(i,i) = 16.7 !Hino & Prausnitz + ! S_LC(i,i) = 0.176 !Hino & Prausnitz + e_lc(i,i) = 8.95 + s_lc(i,i) = 0.2 + + ! mm(i) = 255.41 + ! parame(i,1) = 11.6 + ! parame(i,2) = 3.2 + ! parame(i,3) = 290.7 + ! E_LC(i,i) = 7.18 + ! S_LC(i,i) = 0.2 + + ELSE IF (compna(i) == 'Li') THEN + mm(i) = 6.9 + parame(i,1) = 1.0 + parame(i,2) = 1.4 + parame(i,3) = 96.83 + parame(i,10)= 1.0 +! the self-association is set to zero in routine F_EXPL for ions + ! nhb_typ(i) = 1 + ! nhb_no(i,1) = 3 ! no. of sites of type 1 + ! eps_hb(i,i,1,1)= 2000.0 + ! kap_hb(i,i) = 0.008 + ELSE IF (compna(i) == 'Na') THEN + mm(i) = 23.0 + parame(i,1) = 1.0 + parame(i,2) = 1.9 + parame(i,3) = 147.38 + parame(i,10)= 1.0 +! the self-association is set to zero in routine F_EXPL for ions + nhb_typ(i) = 1 + nhb_no(i,1) = 3 ! no. of sites of type 1 + eps_hb(i,i,1,1)= 8946.28257 ! 25C, 3 sites, dG-ref-1 + kap_hb(i,i) = 0.001648933 + ELSE IF (compna(i) == 'Ka') THEN + mm(i) = 39.1 + parame(i,1) = 1.0 + parame(i,2) = 2.66 + parame(i,3) = 221.44 + parame(i,10)= 1.0 + ! the self-association is set to zero in routine F_EXPL for ions + nhb_typ(i) = 1 + nhb_no(i,1) = 3 ! no. of sites of type 1 + eps_hb(i,i,1,1)= 3118.336216 ! 25C, 3 sites, dG-ref-1 + kap_hb(i,i) = 0.00200559 + ELSE IF (compna(i) == 'Cs') THEN + mm(i) = 132.9 + parame(i,1) = 1.0 + parame(i,2) = 3.38 + parame(i,3) = 523.28 + parame(i,10)= 1.0 + ! the self-association is set to zero in routine F_EXPL for ions + ! nhb_typ(i) = 1 + ! nhb_no(i,1) = 3 ! no. of sites of type 1 + ! eps_hb(i,i,1,1)= 2000.0 + ! kap_hb(i,i) = 0.00200559 + ELSE IF (compna(i) == 'Cl') THEN + mm(i) = 35.5 + parame(i,1) = 1.0 + parame(i,2) = 3.62 + parame(i,3) = 225.44 + parame(i,10)= -1.0 +! the self-association is set to zero in routine F_EXPL for ions + nhb_typ(i) = 1 + nhb_no(i,1) = 4 ! no. of sites of type 1 + eps_hb(i,i,1,1)= 6744.12509 ! 25C, 3 sites, dG-ref-1 + kap_hb(i,i) = 0.00155252 + ELSE IF (compna(i) == 'Br') THEN + mm(i) = 79.9 + parame(i,1) = 1.0 + parame(i,2) = 3.9 + parame(i,3) = 330.82 + parame(i,10)= -1.0 +! the self-association is set to zero in routine F_EXPL for ions + nhb_typ(i) = 1 + nhb_no(i,1) = 4 ! no. of sites of type 1 + eps_hb(i,i,1,1)= 4516.033227 ! 25C, 3 sites, dG-ref-1 + kap_hb(i,i) = 0.00200559 + ELSE IF (compna(i) == 'Io') THEN + mm(i) = 126.9 + parame(i,1) = 1.0 + parame(i,2) = 4.4 + parame(i,3) = 380.60 + parame(i,10)= -1.0 +! the self-association is set to zero in routine F_EXPL for ions + nhb_typ(i) = 1 + nhb_no(i,1) = 4 ! no. of sites of type 1 + eps_hb(i,i,1,1)= 1631.203342 ! 25C, 3 sites, dG-ref-1 + kap_hb(i,i) = 0.00200559 + ELSE IF (compna(i) == 'OH') THEN + mm(i) = 17.0 + parame(i,1) = 1.0 + parame(i,2) = 3.06 + parame(i,3) = 217.26 + parame(i,10)= -1.0 + ! the self-association is set to zero in routine F_EXPL for ions + nhb_typ(i) = 1 + nhb_no(i,1) = 4 ! no. of sites of type 1 + eps_hb(i,i,1,1)= 14118.68089 ! 25C, 3 sites, dG-ref-1 + kap_hb(i,i) = 0.00200559 + ELSE IF (compna(i) == 'NO3') THEN + mm(i) = 62.0 + parame(i,1) = 1.0 + parame(i,2) = 4.12 + parame(i,3) = 239.48 + parame(i,10)= -1.0 + ! the self-association is set to zero in routine F_EXPL for ions + ! nhb_typ(i) = 1 + ! nhb_no(i,1) = 4 ! no. of sites of type 1 + ! eps_hb(i,i,1,1)= 2000.0 + ! kap_hb(i,i) = 0.00200559 + ELSE IF (compna(i) == 'bf4') THEN + mm(i) = 86.8 + parame(i,1) = 1.0 + parame(i,2) = 4.51 ! *0.85 + parame(i,3) = 164.7 + parame(i,10)= -1.0 + ELSE IF (compna(i) == 'pf6') THEN + mm(i) = 145.0 + parame(i,1) = 1.0 + parame(i,2) = 5.06 + parame(i,3) = 224.9 + parame(i,10)= -1.0 + ELSE IF (compna(i) == 'emim') THEN + mm(i) = 111.16 + parame(i,1) = 3.11 + parame(i,2) = 4.0 + parame(i,3) = 250.0 + parame(i,10)= 1.0 + ELSE IF (compna(i) == 'bmim') THEN + mm(i) = 139.21 + ! parame(i,1) = 2.81 + ! parame(i,2) = 3.5 + parame(i,1) = 3.81 + parame(i,2) = 4.0 + parame(i,3) = 250.0 + parame(i,6) = 0.0 + parame(i,10)= 1.0 + ELSE IF (compna(i) == 'hmim') THEN + mm(i) = 167.27 + parame(i,1) = 4.53 + parame(i,2) = 4.0 + parame(i,3) = 250.0 + parame(i,10)= 1.0 + ELSE IF (compna(i) == 'omim') THEN + mm(i) = 195.32 + parame(i,1) = 5.30 + parame(i,2) = 4.0 + parame(i,3) = 250.0 + parame(i,10)= 1.0 + ELSE IF (compna(i) == 'sw') THEN + parame(i,1) = 1.0 + parame(i,2) = 1.0 + parame(i,3) = 100.0 + parame(i,4) = 0.0 + parame(i,5) = 0.0 + mm(i) = 1.0 + parame(i,6) = 0.1175015839*2.0 + ! use Temp. in Kelvin in the input-file. For dimensionless quantities + ! (P*=P*sig**3/epsilon, T*=T*kBol/epsilon, rho*=rho*sig**3) calculate + ! P* = P *1E5 * (1.e-10)^3 / (100*8.31441/6.022045E+23) + ! T* = (T+273.15)/100 + ! for rho* go to utilities.f (subroutine SI_DENS) and write + ! density(ph) = dense(ph)*6.0/PI + ELSE IF (compna(i) == 'c8-sim') THEN + mm(i) = 114.231 + parame(i,1) = mm(i)* 4.095944E-2 ! =4.67883774717337 + parame(i,2) = 3.501769 + parame(i,3) = 163.8606 + ! mm(i) = 114.231000000000 + ! parame(i,1) = mm(i)* 3.547001476437745E-002 ! =4.05177525654960 + ! parame(i,2) = 3.70988567055814 + ! parame(i,3) = 192.787548176343 + ELSE IF (compna(i) == 'argon_ge') THEN + mm(i) = 39.948 + parame(i,1) = mm(i)*0.030327 + parame(i,2) = 3.149910 + parame(i,3) = 100.188975 + ELSE IF (compna(i) == 'argon_ge2') THEN + mm(i) = 39.948 + parame(i,1) = mm(i)*0.030327 + parame(i,2) = 3.149910 + parame(i,3) = 0.8*100.188975 + ELSE + WRITE (*,*) ' pure component parameters missing for ',compna(i) + STOP + END IF + + IF (pol == 2.AND.parame(i,11) == 0.0) THEN + WRITE (*,*) ' polarizability missing for comp. ',compna(i) + STOP + END IF + + IF (nhb_typ(i) /= 0) THEN + parame(i,12) = DBLE(nhb_typ(i)) + parame(i,13) = kap_hb(i,i) + no = 0 + DO j=1,nhb_typ(i) + DO k=1,nhb_typ(i) + parame(i,(14+no))=eps_hb(i,i,j,k) + no=no+1 + END DO + END DO + DO j=1,nhb_typ(i) + parame(i,(14+no))=DBLE(nhb_no(i,j)) + no=no+1 + END DO + ELSE + DO k=12,25 + parame(i,k)=0.0 + END DO + END IF + +END DO + + +DO i = 1,ncomp + DO j = 1,ncomp + IF (compna(i) == 'ps'.AND.compna(j) == 'cyclohexane')THEN + kij(i,j) = 0.0075 + ELSE IF(compna(i) == 'peva'.AND.compna(j) == 'ethylene')THEN +! -- 0 Gew.% VA------------- + ! kij(i,j) = 0.039 +! -- 7.5 Gew.% VA------------- + ! kij(i,j) = 0.0377325 + ! kij(i,j) = 0.0374867 +! ---12.7 Gew.% VA------------ + ! kij(i,j) = 0.036854 + ! kij(i,j) = 0.0366508 +! ---27.3 Gew.% VA------------ + ! kij(i,j) = 0.034386 + ! kij(i,j) = 0.0352375 +! ---31.8 Gew.% VA------------ + kij(i,j) = 0.033626 + ! kij(i,j) = 0.0350795 +! ---42.7 Gew.% VA------------ + ! kij(i,j) = 0.031784 + ! kij(i,j) = 0.035239 + ELSE IF(compna(i) == 'ps_J'.AND.compna(j) == 'co2_J')THEN !from: Xu, Diego: DFT for polymer-co2 mixtures: A PC-SAFT approach + kij(i,j) = - 0.00296 + ELSE IF(compna(i) == 'gen'.AND.compna(j) == 'h2o')THEN + kij(i,j) = - 0.2 + ELSE IF(compna(i) == 'peva'.AND.compna(j) == 'vinylacetate')THEN + kij(i,j) = 0.019 + ELSE IF(compna(i) == 'ps'.AND.compna(j) == 'co2') THEN + IF ( pol == 0 ) kij(i,j) = 0.195 + IF ( pol == 1 ) kij(i,j) = 0.06 + ELSE IF(compna(i) == 'ps'.AND.compna(j) == 'acetone') THEN + kij(i,j) = 0.021 + ELSE IF(compna(i) == 'ps'.AND.compna(j) == 'hexane') THEN + kij(i,j) = 0.012 + ELSE IF(compna(i) == 'ps'.AND.compna(j) == 'pentane')THEN + kij(i,j) = 0.005 + ELSE IF(compna(i) == 'ps'.AND.compna(j) == 'methylcyclohexane') THEN + kij(i,j) = 0.0073 + ELSE IF(compna(i) == 'ps'.AND.compna(j) == 'ethylbenzene')THEN + kij(i,j) = 0.008 + ELSE IF(compna(i) == 'pe'.AND.compna(j) == 'co2') THEN + ! kij(i,j) = 0.181 + kij(i,j) = 0.088 + ELSE IF(compna(i) == 'pe'.AND.compna(j) == 'propane') THEN + kij(i,j) = 0.0206 + ELSE IF(compna(i) == 'pe'.AND.compna(j) == 'butane') THEN + kij(i,j) = 0.01 + ELSE IF(compna(i) == 'methane'.AND.compna(j) == 'argon') THEN + kij(i,j) = 0.01 + ELSE IF(compna(i) == 'methane'.AND.compna(j) == 'butane') THEN + kij(i,j) = 0.026 + ELSE IF(compna(i) == 'pe'.AND.compna(j) == 'pentane') THEN + ! kij(i,j) = -0.0195 + ELSE IF(compna(i) == 'pe'.AND.compna(j) == 'hexane') THEN + ! kij(i,j) = 0.008 + kij(i,j) = 0.004 + ELSE IF(compna(i) == 'pe'.AND.compna(j) == 'ethylene') THEN + kij(i,j) = 0.0404 + ! kij(i,j) = 0.0423 + ! kij(i,j) = 0.044 + ELSE IF(compna(i) == 'pe'.AND.compna(j) == 'cyclohexane') THEN + kij(i,j) = -0.1 + ELSE IF(compna(i) == 'ldpe'.AND.compna(j) == 'cyclopentane')THEN + kij(i,j) = -0.016 + ELSE IF(compna(i) == 'pp'.AND.compna(j) == 'propane') THEN + kij(i,j) = 0.0242 + ELSE IF(compna(i) == 'pp'.AND.compna(j) == 'pentane') THEN + kij(i,j) = 0.0137583176 + ELSE IF(compna(i) == 'pp'.AND.compna(j) == 'co2') THEN + kij(i,j) = 0.1767 ! without quadrupol-term + kij(i,j) = 0.063 ! with quadrupol-term + ELSE IF(compna(i) == 'pba'.AND.compna(j) == 'ethylene') THEN + kij(i,j) = 0.026 + ELSE IF(compna(i) == 'decane'.AND.compna(j) == 'ethane') THEN + kij(i,j) = 0.017 + ELSE IF(compna(i) == 'n2'.AND.compna(j) == 'co2') THEN + ! kij(i,j) = -0.04 + ELSE IF(compna(i) == 'methane'.AND.compna(j) == 'co2') THEN + kij(i,j) = 0.051875 ! PC-SAFT + IF (pol == 1) kij(i,j) = -0.0353125 ! PCP-SAFT + ELSE IF(compna(i) == 'methane'.AND.compna(j) == 'co') THEN + ! IF (pol == 1) kij(i,j) = -0.003 ! PCP-SAFT + IF (pol == 1) kij(i,j) = 0.018 ! PCP-SAFT + ELSE IF(compna(i) == 'ethane'.AND.compna(j) == 'co2') THEN + kij(i,j) = 0.095 + kij(i,j) = 0.021 + ! kij(i,j) = 0.024 + ELSE IF(compna(i) == 'propane'.AND.compna(j) == 'co2') THEN + kij(i,j) = 0.042 + ELSE IF(compna(i) == 'argon_ge'.AND.compna(j) == 'argon_ge2') THEN + read (*,*) kij(i,j) + ELSE IF(compna(i) == 'butane'.AND.compna(j) == 'co2') THEN + ! kij(i,j) = 0.115 + ! kij(i,j) = 0.048 + kij(i,j) = 0.036 + ELSE IF(compna(i) == 'pentane'.AND.compna(j) == 'co2') THEN + kij(i,j) = 0.143 ! without quadrupol-term + kij(i,j) = 0.0 ! with quadrupol-term + ELSE IF(compna(i) == 'hexane'.AND.compna(j) == 'co2') THEN + ! kij(i,j) = 0.125 ! without quadrupol-term + kij(i,j) = 0.0495 + ELSE IF(compna(i) == 'heptane'.AND.compna(j) == 'co2') THEN + kij(i,j) = 0.11 ! without quadrupol-term + ! kij(i,j) = 0.05 + ! kij(i,j) = 0.039 ! with quadrupol-term + ELSE IF(compna(i) == 'decane'.AND.compna(j) == 'co2') THEN + ! kij(i,j) = 0.128 ! without quadrupol-term + kij(i,j) = 0.053 ! with quadrupol-term + ELSE IF(compna(i) == 'dodecane'.AND.compna(j) == 'co2') THEN + kij(i,j) = 0.12 ! without quadrupol-term + kij(i,j) = 0.0508 ! with quadrupol-term + ELSE IF(compna(i) == 'benzene'.AND.compna(j) == 'co2') THEN + ! kij(i,j) = 0.087968750000 ! without quadrupol-term + ! kij(i,j) = 0.008203125 ! only co2 quadrupol + kij(i,j) = 0.042 ! both quadrupol + ! kij(i,j) = 0.003 ! both quadrupol + ELSE IF(compna(i) == 'toluene'.AND.compna(j) == 'co2') THEN + ! kij(i,j) = 0.110784912 ! without quadrupol-term + kij(i,j) = 0.0305 ! with quadrupol-term + ELSE IF(compna(i) == 'cyclohexane'.AND.compna(j) == 'co2') THEN + kij(i,j) = 0.13 + lij(i,j) = - 0.00 + ! kij(i,j) = 0.045 + ELSE IF(compna(i) == 'chloromethane'.AND.compna(j) == 'co2')THEN + ! kij(i,j) = 0.04 ! PC-SAFT + kij(i,j) = 0.025 ! PCP-SAFT + ! kij(i,j) = 0.083 ! PCIP-SAFT + ELSE IF(compna(i) == 'acetone'.AND.compna(j) == 'n2')THEN + kij(i,j) = 0.035211 ! PCP-SAFT + lij(i,j) = + 0.013225 ! PCP-SAFT + kij(i,j) = 0.023 ! PCP-SAFT + lij(i,j) = + 0.013225 ! PCP-SAFT + !kij(i,j) = 1.722238535635467E-002 ! PCP-SAFT + !lij(i,j) = 2.815974678394451E-003 ! PCP-SAFT + !kij(i,j) = 1.931522058164026E-002 ! PCP-SAFT + !lij(i,j) = 0.0 ! PCP-SAFT + !kij(i,j) = 1.641053794134795E-002 ! PCP-SAFT + !lij(i,j) = -5.850421759950764E-003 ! PCP-SAFT + if ( num == 0 ) write (*,*) 'calculation with lij only possible with num=1' + if ( num == 0 ) stop + ELSE IF(compna(i) == 'acetone'.AND.compna(j) == 'co2')THEN + kij(i,j) = 0.015 ! PC-SAFT + IF (pol == 1) kij(i,j) = -0.02 ! PCP-SAFT + IF (pol == 2) kij(i,j) = -0.005 ! PCIP-SAFT where DQ with my=my_vacuum + ! IF (pol.EQ.2) kij(i,j) = 0.0 ! PCIP-SAFT where DQ with my=my_RPT + ELSE IF(compna(i) == 'methanol'.AND.compna(j) == 'co2')THEN + ! kij(i,j) = 0.0288 ! PC-SAFT + ! kij(i,j) = - 0.035 ! PCP-SAFT for co2 and PC-SAFT methanol + ! kij(i,j) = - 0.035 ! PCP-SAFT + ! lij(i,j) = 0.3 ! PCP-SAFT + ELSE IF(compna(i) == 'dimethyl-ether'.AND.compna(j) == 'co2')THEN + kij(i,j) = 0.00896894 ! PC-SAFT + ! kij(i,j) = - 0.015 ! PCP-SAFT + ELSE IF(compna(i) == 'dimethyl-ether'.AND.compna(j) == 'h2o')THEN + ! kij(i,j) = -0.134 ! PC-SAFT + ELSE IF(compna(i) == 'dichloromethane'.AND.compna(j) == 'co2')THEN + ! kij(i,j) = 0.06881725 ! PC-SAFT + ! kij(i,j) = 0.05839145 ! PCP-SAFT + kij(i,j) = -0.00944346 ! PCP-SAFT co2 dichloromethane PC-SAFT + ! kij(i,j) = 0.06 ! PCIP-SAFT + ELSE IF(compna(i) == 'h2s'.AND.compna(j) == 'methane')THEN + ! kij(i,j) = 0.0414 ! PC-SAFT + kij(i,j) = 0.0152 ! PCP-SAFT Dipole momnet (d with Q) + ELSE IF(compna(i) == 'butane'.AND.compna(j) == 'h2s')THEN + kij(i,j) = -0.002 ! PCP-SAFT + ELSE IF(compna(i) == 'methanol'.AND.compna(j) == 'h2s')THEN + kij(i,j) = 0.0 ! PCP-SAFT + lij(i,j) = 0.0 ! PCP-SAFT + ELSE IF(compna(i) == 'co2'.AND.compna(j) == 'hydrogen') THEN + ! lij(i,j) = -0.08 !!!!! Lij not kij !!!! + ELSE IF(compna(i) == 'hexane'.AND.compna(j) == 'n2') THEN + kij(i,j) = 0.11 + ELSE IF(compna(i) == 'propane'.AND.compna(j) == 'n2') THEN + kij(i,j) = 0.0251171875 + ELSE IF(compna(i) == 'co2'.AND.compna(j) == 'hexadecane') THEN + ! kij(i,j) = 0.1194 ! PC-SAFT ohne QQ + kij(i,j) = 0.0588 + ELSE IF(compna(i) == 'ethane'.AND.compna(j) == 'acetone') THEN + ! kij(i,j) = 0.065 ! no DD + kij(i,j) = 0.038 ! DD non-polarizable + ! kij(i,j) = 0.025 ! DD polarizable + ELSE IF(compna(i) == 'butane'.AND.compna(j) == 'acetone') THEN + ! kij(i,j) = 0.065 ! no DD + kij(i,j) = 0.037 ! DD non-polarizable + ! kij(i,j) = 0.025 ! DD polarizable + ELSE IF(compna(i) == 'pentane'.AND.compna(j) == 'acetone') THEN + ! kij(i,j) = 0.072 ! no DD + ! kij(i,j) = 0.041 ! DD non-polarizable + kij(i,j) = 0.039 ! DD polarizable + ! kij(i,j) = 0.035 ! DD polarizable + ELSE IF(compna(i) == 'hexane'.AND.compna(j) == 'acetone') THEN + ! kij(i,j) = 0.063 + kij(i,j) = 0.038 ! PCP-SAFT + ! kij(i,j) = 0.036 ! PCIP-SAFT + ELSE IF(compna(i) == 'heptane'.AND.compna(j) == 'acetone') THEN + kij(i,j) = 0.035 ! PCP-SAFT + ELSE IF(compna(i) == 'decane'.AND.compna(j) == 'acetone') THEN + ! kij(i,j) = 0.059 ! no DD + ! kij(i,j) = 0.03281250 ! DD non-polarizable + kij(i,j) = 0.028 ! DD polarizable + ELSE IF(compna(i) == 'hexadecane'.AND.compna(j) == 'acetone') THEN + ! kij(i,j) = 0.07 ! no DD + ! kij(i,j) = 0.0415 ! DD non-polarizable + kij(i,j) = 0.035 ! DD polarizable + ELSE IF(compna(i) == 'hexane'.AND.compna(j) == 'butanone')THEN + kij(i,j) = 0.027 ! PCP-SAFT + ! kij(i,j) = 0.033 ! PCP-SAFT with lij + ! lij(i,j) = 0.13 ! PCP-SAFT + ! kij(i,j) = 0.042 ! PC-SAFT + ELSE IF(compna(i) == 'heptane'.AND.compna(j) == 'butanone')THEN + kij(i,j) = 0.042 ! no DD + ! kij(i,j) = 0.027 ! DD non-polarizable + ELSE IF(compna(i) == 'heptane'.AND.compna(j) == '2-pentanone')THEN + kij(i,j) = 0.041 ! no DD + ! kij(i,j) = 0.031 ! DD non-polarizable + ELSE IF(compna(i) == 'hexane'.AND.compna(j) == '3-pentanone')THEN + kij(i,j) = 0.0 + ELSE IF(compna(i) == 'pentane'.AND.compna(j) == 'propanal')THEN + ! kij(i,j) = 0.055 ! no DD + kij(i,j) = 0.027 ! DD non-polarizable + ! kij(i,j) = 0.026 ! DD polarizable 22 + ELSE IF(compna(i) == 'cyclohexane'.AND.compna(j) == 'propanal')THEN + ! kij(i,j) = 0.06 ! no DD + kij(i,j) = 0.036 ! DD non-polarizable + kij(i,j) = 0.035 ! DD polarizable 22 + ELSE IF(compna(i) == 'heptane'.AND.compna(j) == 'butanal')THEN + kij(i,j) = 0.041 ! no DD + ! kij(i,j) = 0.025 ! DD non-polarizable + ELSE IF(compna(i) == 'hexane'.AND.compna(j) == 'thf')THEN + kij(i,j) = 0.012 ! PCP-SAFT + ELSE IF(compna(i) == 'octane'.AND.compna(j) == 'thf')THEN + kij(i,j) = 0.012 ! PCP-SAFT + ELSE IF(compna(i) == 'decane'.AND.compna(j) == 'thf')THEN + kij(i,j) = 0.012 ! PCP-SAFT + ELSE IF(compna(i) == 'toluene'.AND.compna(j) == 'dmso')THEN + ! kij(i,j) = 0.025 ! no DD + kij(i,j) = - 0.0105 ! DD non-polarizable + ! kij(i,j) = - 0.019 ! DD polarizable + ELSE IF(compna(i) == 'hexane'.AND.compna(j) == 'acrylonitrile')THEN + kij(i,j) = - 0.05 ! DD polarizable + ELSE IF(compna(i) == 'heptane' .AND. compna(j) == 'butyronitrile')THEN + kij(i,j) = - 0.002 ! DD polarizable 11 + kij(i,j) = 0.002 ! DD polarizable 22 + ELSE IF(compna(i) == '1-butene'.AND.compna(j) == 'dmf')THEN + ! kij(i,j) = 0.04 ! no DD + ! kij(i,j) = 0.004 ! DD non-polarizable + kij(i,j) = 0.005 ! DD polarizable 22 + ELSE IF(compna(i) == 'cyclohexane'.AND.compna(j) == 'dmf')THEN + kij(i,j) = 0.0135 ! DD polarizable 11 + kij(i,j) = 0.022 ! DD polarizable 22 + ELSE IF(compna(i) == 'ethylene'.AND.compna(j) == 'dmf')THEN + ! kij(i,j) = - 0.0215 ! DD polarizable 11 + kij(i,j) = - 0.01 ! DD polarizable 22 + ELSE IF(compna(i) == 'nbutyl-ethanoate'.AND.compna(j) == 'dmf')THEN + ! kij(i,j) = 0.016 ! no DD + ! kij(i,j) = -0.01 ! DD non-polarizable + kij(i,j) = - 0.015 ! DD polarizable 22 + ELSE IF(compna(i) == 'methylacetate' .AND. compna(j) == 'cyclohexane')THEN + kij(i,j) = 0.066 ! PC-SAFT + ! kij(i,j) = 0.061 ! PCP-SAFT + ! kij(i,j) = 0.0625 ! PCIP-SAFT + ELSE IF(compna(i) == 'methylacetate'.AND.compna(j) == 'decane')THEN + kij(i,j) = 0.0625 ! PCIP-SAFT + ELSE IF(compna(i) == 'methylacetate' .AND. compna(j) == 'methanol')THEN + ! kij(i,j) = -0.07 ! PCIP-SAFT + ELSE IF(compna(i) == 'pentane' .AND. compna(j) == 'propionitrile')THEN + kij(i,j) = 0.0498 + IF (pol >= 1) kij(i,j) = -0.01 + IF (pol >= 2) kij(i,j) = -0.027 + ELSE IF(compna(i) == 'hexane' .AND. compna(j) == 'propionitrile')THEN + kij(i,j) = 0.05 + IF (pol >= 1) kij(i,j) = 0.0 + IF (pol >= 2) kij(i,j) = -0.03 + ELSE IF(compna(i) == 'octane' .AND. compna(j) == 'propionitrile')THEN + kij(i,j) = 0.0 ! DD polarizable 22 + ELSE IF(compna(i) == 'cyclohexane' .AND. compna(j) == 'nitromethane')THEN + kij(i,j) = 0.14 ! no DD + ! kij(i,j) = 0.07 ! DD non-polarizable + ! kij(i,j) = 0.055 ! DD polarizable 22 + ELSE IF(compna(i) == 'cyclohexane' .AND. compna(j) == 'nitroethane')THEN + ! kij(i,j) = 0.06 ! no DD + kij(i,j) = 0.03 ! DD polarizable 22 + ELSE IF(compna(i) == 'acetone' .AND. compna(j) == 'nitromethane')THEN + ! kij(i,j) = - 0.017 ! no DD + kij(i,j) = - 0.021 ! DD non-polarizable + ! kij(i,j) = - 0.023 ! DD polarizable 22 + ELSE IF(compna(i) == 'acetone' .AND. compna(j) == 'h2o')THEN + kij(i,j) = - 0.2 ! PCP-SAFT (no cross-association) + ELSE IF(compna(i) == 'methylcyclohexane' .AND. compna(j) == 'acetonitrile')THEN + ! kij(i,j) = 0.09 ! no DD + ! kij(i,j) = 0.033 ! DD non-polarizable + ! kij(i,j) = 0.025 ! DD polarizable 22 + kij(i,j) = 0.04 ! DD polarizable 22 und my angepasst + ELSE IF(compna(i) == 'ethylacetate' .AND. compna(j) == 'acetonitrile')THEN + kij(i,j) = 0.007 ! no DD + ! kij(i,j) = -0.045 ! DD polarizable 22 + ELSE IF(compna(i) == 'dimethyl-ether' .AND. compna(j) == 'propane')THEN + ! kij(i,j) = 0.03 ! no DD + kij(i,j) = 0.0225 ! DD non-polarizable + ELSE IF(compna(i) == 'benzene' .AND. compna(j) == 'pentane')THEN + ! kij(i,j) = 0.012968750 ! ohne QQ + ! kij(i,j) = 0.004921875 ! mit QQ=5.6D (gefittet) + ! kij(i,j) = -0.006406250 ! mit QQ=7.45D (Literatur) + ELSE IF(compna(i) == 'benzene' .AND. compna(j) == 'heptane')THEN + kij(i,j) = 0.01328125 + ! kij(i,j) = 0.0038 + ELSE IF(compna(i) == 'benzene' .AND. compna(j) == '1-hexene')THEN + kij(i,j) = 0.0067 + ELSE IF(compna(i) == 'ethylene' .AND. compna(j) == 'co2') THEN + kij(i,j) = 0.04 + kij(i,j) = -0.029 + ELSE IF(compna(i) == 'ethylene' .AND. compna(j) == 'vinylacetate') THEN + kij(i,j) = - 0.013847 + ELSE IF(compna(i) == 'triacontane' .AND. compna(j) == 'ethylene') THEN + kij(i,j) = 0.028 + ELSE IF(compna(i) == 'triacontane' .AND. compna(j) == 'methane')THEN + ! kij(i,j) = 0.061953125 ! polyethylene parameters + kij(i,j) = 0.039609375 ! param. by extrapolation of n-alkanes + ELSE IF(compna(i) == 'tetracontane' .AND. compna(j) == 'methane')THEN + ! kij(i,j) = 0.06515625 ! polyethylene parameters + kij(i,j) = 0.04453125 ! param. by extrapolation of n-alkanes + ! --- kij and lij adjusted ------- + ! kij(i,j) = 0.045786119 ! param. by extrapolation of n-alkanes + ! lij(i,j) = +8.53466437d-4 ! param. by extrapolation of n-alkanes + ELSE IF(compna(i) == 'eicosane' .AND. compna(j) == 'methane')THEN + kij(i,j) = 0.0360134457445 + ELSE IF(compna(i) == 'tetracontane' .AND. compna(j) == 'methane')THEN + kij(i,j) = 0.0360134457445 ! assumed equal to eicosane-C1 + ELSE IF(compna(i) == 'chlorobenzene' .AND. compna(j) == 'cyclohexane') THEN + kij(i,j) = 0.013 + ELSE IF(compna(i) == 'chloroethane' .AND. compna(j) == 'butane')THEN + kij(i,j) = 0.025 + ELSE IF(compna(i) == 'tetrachloromethane' .AND. compna(j) == '2-methylpentane') THEN + kij(i,j) = 0.0070105 + ELSE IF(compna(i) == 'tetrachloromethane' .AND. compna(j) == 'hexane') THEN + kij(i,j) = 0.004 + ELSE IF(compna(i) == 'hydrogen' .AND. compna(j) == 'hexane') THEN + kij(i,j) = 0.1501 + ELSE IF(compna(i) == 'ethanol' .AND. compna(j) == 'co2') THEN + ! kij(i,j) = -0.08 + ELSE IF(compna(i) == 'ethanol' .AND. compna(j) == 'propane') THEN + kij(i,j) = - 0.07 + ELSE IF(compna(i) == 'ethanol' .AND. compna(j) == 'ethane') THEN + kij(i,j) = 0.0 + ELSE IF(compna(i) == 'ethanol' .AND. compna(j) == 'butane') THEN + kij(i,j) = 0.028 + kij(i,j) = 0.016 + ELSE IF(compna(i) == 'ethanol' .AND. compna(j) == 'cyclohexane')THEN + kij(i,j) = 0.037 + ELSE IF(compna(i) == 'ethanol' .AND. compna(j) == '2-methylpentane') THEN + kij(i,j) = 0.028 + ELSE IF(compna(i) == 'ethanol' .AND. compna(j) == '1-octanol')THEN + kij(i,j) = 0.06 + ELSE IF(compna(i) == 'methanol' .AND. compna(j) == 'cyclohexane') THEN + kij(i,j) = 0.0508 + ! kij(i,j) = 0.03 + ELSE IF(compna(i) == 'methanol' .AND. compna(j) == 'heptane')THEN + kij(i,j) = 0.034 + ELSE IF(compna(i) == 'methanol' .AND. compna(j) == 'decane')THEN + ! kij(i,j) = 0.042 ! PC-SAFT + ! kij(i,j) = 0.011 ! PCP-SAFT + kij(i,j) = 0.000 ! PCIP-SAFT + ELSE IF(compna(i) == 'methanol' .AND. compna(j) == 'isobutane') THEN + kij(i,j) = 0.051 + ELSE IF(compna(i) == 'methanol' .AND. compna(j) == '1-octanol') THEN + kij(i,j) = 0.02 + ELSE IF(compna(i) == '1-butanol' .AND. compna(j) == 'butane') THEN + kij(i,j) = 0.015 + ELSE IF(compna(i) == '1-nonanol' .AND. compna(j) == 'co2') THEN + kij(i,j) = 0.076 + kij(i,j) = 0.01443 + ELSE IF(compna(i) == '1-propanol' .AND. compna(j) == 'ethylbenzene') THEN + kij(i,j) = 0.0251757813 + ELSE IF(compna(i) == 'decane'.AND.compna(j) == 'ethanol') THEN + kij(i,j) = 0.085 + ELSE IF(compna(i) == 'hexane'.AND.compna(j) == '1-chlorobutane') THEN + kij(i,j) = 0.017 + ELSE IF(compna(i) == 'aniline'.AND.compna(j) == 'methylcyclopentane') THEN + kij(i,j) = 0.0153 + ELSE IF(compna(i) == 'heptane'.AND.compna(j) == 'nbutyl-ethanoate')THEN + kij(i,j) = 0.027 + ELSE IF(compna(i) == '1-hexene'.AND.compna(j) == 'ethyl-ethanoate')THEN + kij(i,j) = 0.026 + ELSE IF(compna(i) == 'co2'.AND.compna(j) == '1-butanol')THEN + ! kij(i,j) = 0.075 + kij(i,j) = 0.0 + ELSE IF(compna(i) == 'acrylic-acid'.AND.compna(j) == 'co2')THEN + kij(i,j) = -0.1 + ELSE IF(compna(i) == 'bmim'.AND.compna(j) == 'hydrogen')THEN + lij(i,j) = 0.55 !!!!! Lij not kij !!!! + ELSE IF(compna(i) == 'bf4'.AND.compna(j) == 'hydrogen')THEN + lij(i,j) = 0.55 !!!!! Lij not kij !!!! + ELSE IF(compna(i) == 'h2o'.AND.compna(j) == 'butane')THEN !K.R.Hall FPE 2007 254 112-125 kij=0.1850 + kij(i,j) = -0.07 + ELSE IF(compna(i) == 'h2o'.AND.compna(j) == '1-butanol')THEN + kij(i,j) = -0.12 + ELSE IF(compna(i) == 'h2o'.AND.compna(j) == 'aniline')THEN + kij(i,j) = 0.0 + ELSE IF(compna(i) == 'h2o'.AND.compna(j) == 'methanol') THEN + kij(i,j) = -0.02 + ELSE IF(compna(i) == 'h2o'.AND.compna(j) == 'ethanol') THEN + kij(i,j) = -0.027 + ELSE IF(compna(i) == 'h2o'.AND.compna(j) == 'styrene') THEN + kij(i,j) = 0.1 + ELSE IF(compna(i) == 'h2o'.AND.compna(j) == 'propyl-ethanoate') THEN + kij(i,j) = -0.205 + ELSE IF(compna(i) == 'h2o'.AND.compna(j) == 'ethyl-propanoate') THEN + kij(i,j) = 0.0 + ELSE IF(compna(i) == 'h2o'.AND.compna(j) == '1-pentanol') THEN + kij(i,j) = 0.0165 + ! kij(i,j) = 0.0294 + ! kij(i,j) = -0.082 + ELSE IF(compna(i) == 'h2o'.AND.compna(j) == 'methane') THEN + ! kij(i,j) = +0.06 + kij(i,j) = -0.08 + ELSE IF(compna(i) == 'h2o'.AND.compna(j) == 'propane') THEN + kij(i,j) = 0.02 + ELSE IF(compna(i) == 'h2o'.AND.compna(j) == 'hexane') THEN + kij(i,j) = -0.02 + ELSE IF(compna(i) == 'h2o'.AND.compna(j) == 'acetic-acid') THEN + kij(i,j) = -0.0 + ELSE IF(compna(i) == 'h2o'.AND.compna(j) == 'co2') THEN + if (pol == 0) kij(i,j) = 0.0030625 ! for T=50C, according to X.Tang + stop ! very T-dependent + ELSE IF(compna(i) == 'toluene'.AND.compna(j) == 'acetic-acid') THEN + kij(i,j) = -0.1 + ELSE IF(compna(i) == 'caproic-acid'.AND.compna(j) == 'cyclohexane') THEN + kij(i,j) = 0.041531 + ELSE IF(compna(i) == '1-octanol'.AND.compna(j) == 'h2o')THEN + kij(i,j) = 0.07 + ELSE IF(compna(i) == 'acetone'.AND.compna(j) == 'benzene')THEN + kij(i,j) = 0.02132466 ! PC-SAFT + ! kij(i,j) = 0.01495148 ! PCP-SAFT + ! kij(i,j) = -0.00735575 ! PCP-SAFT but non-polar benzene + ELSE IF(compna(i) == '1-propanol'.AND.compna(j) == 'benzene')THEN + kij(i,j) = 0.02017 + ELSE IF(compna(i) == '2-propanol'.AND.compna(j) == 'benzene')THEN + kij(i,j) = 0.021386 + ELSE IF(compna(i) == '1-pentanol'.AND.compna(j) == 'benzene')THEN + kij(i,j) = 0.0129638671875 + ELSE IF(compna(i) == 'CH2F2' .AND. compna(j) == 'co2') THEN + kij(i,j) = 2.2548828125E-2 + ELSE IF(compna(i) == 'dmso' .AND. compna(j) == 'co2') THEN + kij(i,j) = -0.00 + ELSE IF(compna(i) == 'dmf'.AND.compna(j) == 'h2o')THEN + kij(i,j) = -0.0 + ELSE IF(compna(i) == 'decane'.AND.compna(j) == 'h2o')THEN + kij(i,j) = 0.11 + ELSE IF(compna(i) == '11difluoroethane'.AND.compna(j) == 'HF')THEN + kij(i,j) = 0.032 ! association: eps_kij = 0.16 + ELSE IF(compna(i) == '11difluoroethane'.AND.compna(j) == 'co2')THEN + kij(i,j) = -0.004 ! PCP-SAFT (taken from simulation) + ELSE IF(compna(i) == 'difluoromethane'.AND.compna(j) == 'HF')THEN + kij(i,j) = -0.02 + ELSE IF(compna(i) == 'naphthalene'.AND.compna(j) == 'co2')THEN + kij(i,j) = 0.137 ! angepasst an SVLE-Linie (tradition.CO2-Parameter) + kij(i,j) = 0.09 ! angepasst an SVLE-Linie (tradition.CO2-Parameter) + ELSE IF(compna(i) == 'pg2'.AND.compna(j) == 'methanol')THEN + kij(i,j) = 0.03 + ELSE IF(compna(i) == 'pg2'.AND.compna(j) == 'co2')THEN + ! kij(i,j) = 0.05 + ELSE IF(compna(i) == 'PCH5'.AND.compna(j) == 'co2')THEN + ! kij(i,j) = -0.047 + kij(i,j) = +0.055 + ! kij(i,j) = +0.036 + ELSE + END IF + kij(j,i) = kij(i,j) + lij(j,i) = -lij(i,j) + + END DO +END DO + +END SUBROUTINE pcsaft_par + + +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! SUBROUTINE init_vars +! +! This subroutine writes variables from an array "val_init" to the +! system-variables. Those variables +! include some specifications but also some starting values for a +! phase equilibrium calculation. (val_init stands for 'initial value') + +! The array comprises the following elements +! element 0 density of third phase +! element 1 density of first phase +! element 2 density of second phase +! element 3 temperature [K] +! element 4 pressure [Pa] +! element 5,..(5+NCOMP) mole-fraction of comp. i in log. from (phase 1) +! element ... mole-fraction of comp. i in log. from (phase 2) +! element ... mole-fraction of comp. i in log. from (phase 3) +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! + SUBROUTINE init_vars +! + USE BASIC_VARIABLES + IMPLICIT NONE +! + INTEGER :: i, ph +! ---------------------------------------------------------------------- + +densta(3)=val_init(0) +densta(1)=val_init(1) +densta(2)=val_init(2) +t = val_init(3) +p = val_init(4) +DO ph = 1,nphas + DO i = 1,ncomp + lnx(ph,i) = val_init(4+i+(ph-1)*ncomp) + END DO +END DO + +END SUBROUTINE init_vars + + +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! SUBROUTINE converged +! +! Once a converged solution for an equilibrium calculation is found, +! this subroutine writes variables to an array "val_conv". +! (= short for converged values) +! The array comprises the following elements +! element 0 density of third phase +! element 1 density of first phase +! element 2 density of second phase +! element 3 temperature [K] +! element 4 pressure [Pa] +! element 5,..(4+NCOMP) mole-fraction of comp. i in log. from (phase 1) +! element ... mole-fraction of comp. i in log. from (phase 2) +! element ... mole-fraction of comp. i in log. from (phase 3) +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! + SUBROUTINE converged +! + USE BASIC_VARIABLES + IMPLICIT NONE +! + INTEGER :: i, ph +! ---------------------------------------------------------------------- + +val_conv(0) = dense(3) +val_conv(1) = dense(1) +val_conv(2) = dense(2) +val_conv(3) = t +val_conv(4) = p +DO ph = 1,nphas + DO i = 1,ncomp + val_conv(4+i+(ph-1)*ncomp) = lnx(ph,i) + END DO +END DO + +END SUBROUTINE converged + +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! SUBROUTINE PERTURBATION_PARAMETER +! +! calculates density-independent parameters of the equation of state. +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! + SUBROUTINE PERTURBATION_PARAMETER +! + USE PARAMETERS, ONLY: PI, KBOL, RGAS, NAV, TAU + USE EOS_VARIABLES + USE EOS_CONSTANTS + IMPLICIT NONE +! +! --- local variables -------------------------------------------------- + INTEGER :: i, j, k, l, m, no + LOGICAL :: assoc, qudpole, dipole + REAL :: m_mean + REAL, DIMENSION(nc) :: v00, v0, d00, u + REAL, DIMENSION(nc,nc,nsite,nsite) :: eps_hb + REAL, DIMENSION(nc,nc) :: kap_hb + REAL :: zmr, nmr + REAL :: eps_kij, k_kij +! ---------------------------------------------------------------------- + +! ---------------------------------------------------------------------- +! pure component parameters +! ---------------------------------------------------------------------- +DO i = 1, ncomp + u(i) = parame(i,3) * (1.0 + parame(i,4)/t) + mseg(i) = parame(i,1) + IF (eos == 0) THEN + v00(i) = parame(i,2) + v0(i) = v00(i)*(1.0-0.12*EXP(-3.0*parame(i,3)/t))**3 + d00(i) = (1.d30/1.d6 *tau *v00(i)*6.0/PI /NAV)**(1.0/3.0) + dhs(i) = d00(i)*(1.0-0.12*EXP(-3.0*parame(i,3)/t)) + ELSE + dhs(i) = parame(i,2)*(1.0-0.12*EXP(-3.0*parame(i,3)/t)) + d00(i) = parame(i,2) + END IF +END DO + + +! ---------------------------------------------------------------------- +! combination rules +! ---------------------------------------------------------------------- +DO i = 1, ncomp + DO j = 1, ncomp + sig_ij(i,j) = 0.5 * ( d00(i) + d00(j) ) + uij(i,j) = ( 1.0 - kij(i,j) ) * ( u(i)*u(j) )**0.5 + vij(i,j) = ( 0.5*( v0(i)**(1.0/3.0) + v0(j)**(1.0/3.0) ) )**3 + END DO +END DO + + +! ---------------------------------------------------------------------- +! abbreviations +! ---------------------------------------------------------------------- +z0t = PI / 6.0 * SUM( x(1:ncomp) * mseg(1:ncomp) ) +z1t = PI / 6.0 * SUM( x(1:ncomp) * mseg(1:ncomp) * dhs(1:ncomp) ) +z2t = PI / 6.0 * SUM( x(1:ncomp) * mseg(1:ncomp) * dhs(1:ncomp)**2 ) +z3t = PI / 6.0 * SUM( x(1:ncomp) * mseg(1:ncomp) * dhs(1:ncomp)**3 ) + +m_mean = z0t/(PI/6.0) + +DO i = 1, ncomp + DO j = 1, ncomp + dij_ab(i,j) = dhs(i)*dhs(j) / ( dhs(i) + dhs(j) ) + END DO +END DO + +! ---------------------------------------------------------------------- +! dispersion term parameters for chain molecules +! ---------------------------------------------------------------------- +DO m = 0, 6 + apar(m) = ap(m,1) + (1.0-1.0/m_mean)*ap(m,2) & + + (1.0-1.0/m_mean)*(1.0-2.0/m_mean)*ap(m,3) + bpar(m) = bp(m,1) + (1.0-1.0/m_mean)*bp(m,2) & + + (1.0-1.0/m_mean)*(1.0-2.0/m_mean)*bp(m,3) +END DO + + +! ---------------------------------------------------------------------- +! van der Waals mixing rules for perturbation terms +! ---------------------------------------------------------------------- +order1 = 0.0 +order2 = 0.0 +DO i = 1, ncomp + DO j = 1, ncomp + order1 = order1 + x(i)*x(j)* mseg(i)*mseg(j)*sig_ij(i,j)**3 * uij(i,j)/t + order2 = order2 + x(i)*x(j)* mseg(i)*mseg(j)*sig_ij(i,j)**3 * (uij(i,j)/t)**2 + END DO +END DO + + +! ---------------------------------------------------------------------- +! SAFT parameters +! ---------------------------------------------------------------------- +IF (eos == 0) THEN + zmr = 0.0 + nmr = 0.0 + DO i = 1, ncomp + DO j = 1, ncomp + zmr = zmr + x(i)*x(j)*mseg(i)*mseg(j)*vij(i,j)*uij(i,j) + nmr = nmr + x(i)*x(j)*mseg(i)*mseg(j)*vij(i,j) + END DO + END DO + um = zmr / nmr +END IF + + + +! ---------------------------------------------------------------------- +! association and polar parameters +! ---------------------------------------------------------------------- +assoc = .false. +qudpole = .false. +dipole = .false. +DO i = 1, ncomp + IF (NINT(parame(i,12)) /= 0) assoc = .true. + IF (parame(i,7) /= 0.0) qudpole = .true. + IF (parame(i,6) /= 0.0) dipole = .true. +END DO + +! --- dipole and quadrupole constants ---------------------------------- +IF (qudpole) CALL qq_const ( qqp2, qqp3, qqp4 ) +IF (dipole) CALL dd_const ( ddp2, ddp3, ddp4 ) +IF (dipole .AND. qudpole) CALL dq_const ( dqp2, dqp3, dqp4 ) + + +! --- TPT-1-association parameters ------------------------------------- +IF (assoc) THEN + + eps_kij = 0.0 + k_kij = 0.0 + + DO i = 1, ncomp + IF (NINT(parame(i,12)) /= 0) THEN + nhb_typ(i) = NINT(parame(i,12)) + kap_hb(i,i) = parame(i,13) + no = 0 + DO j = 1, nhb_typ(i) + DO k = 1, nhb_typ(i) + eps_hb(i,i,j,k) = parame(i,(14+no)) + no=no+1 + END DO + END DO + DO j = 1, nhb_typ(i) + nhb_no(i,j) = parame(i,(14+no)) + no=no+1 + END DO + ELSE + nhb_typ(i) = 0 + kap_hb(i,i)= 0.0 + DO k = 1, nsite + DO l = 1, nsite + eps_hb(i,i,k,l) = 0.0 + END DO + END DO + END IF + END DO + + DO i = 1, ncomp + DO j = 1, ncomp + IF (i /= j .AND. (nhb_typ(i) /= 0 .AND. nhb_typ(j) /= 0)) THEN + kap_hb(i,j)= (kap_hb(i,i)*kap_hb(j,j))**0.5 & + *((parame(i,2)*parame(j,2))**3 )**0.5 & + /(0.5*(parame(i,2)+parame(j,2)))**3 + kap_hb(i,j)= kap_hb(i,j)*(1.0-k_kij) + DO k = 1, nhb_typ(i) + DO l = 1, nhb_typ(j) + IF (k /= l) THEN + eps_hb(i,j,k,l) = (eps_hb(i,i,k,l)+eps_hb(j,j,l,k))/2.0 + eps_hb(i,j,k,l) = eps_hb(i,j,k,l)*(1.0-eps_kij) + END IF + END DO + END DO + END IF + END DO + END DO + IF (nhb_typ(1) == 3) THEN +! write(*,*)'eps_hb manuell eingegeben' + eps_hb(1,2,3,1) = 0.5*(eps_hb(1,1,3,1)+eps_hb(2,2,1,2)) + eps_hb(2,1,1,3) = eps_hb(1,2,3,1) + END IF + IF (nhb_typ(2) == 3) THEN + eps_hb(2,1,3,1) = 0.5*(eps_hb(2,2,3,1)+eps_hb(1,1,1,2)) + eps_hb(1,2,1,3) = eps_hb(2,1,3,1) + END IF + + DO i = 1, ncomp + DO k = 1, nhb_typ(i) + DO j = 1, ncomp + DO l = 1, nhb_typ(j) + ass_d(i,j,k,l) = kap_hb(i,j) *sig_ij(i,j)**3 *(EXP(eps_hb(i,j,k,l)/t)-1.0) + END DO + END DO + END DO + END DO + +END IF + +END SUBROUTINE PERTURBATION_PARAMETER + + + + +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! SUBROUTINE OUTPUT +! +! The purpose of this subroutine is obvious. +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! + SUBROUTINE OUTPUT +! + USE BASIC_VARIABLES + IMPLICIT NONE +! +! ---------------------------------------------------------------------- + INTEGER :: i + CHARACTER (LEN=4) :: t_ind + CHARACTER (LEN=4) :: p_ind + CHARACTER (LEN=4) :: char_ncomp + REAL :: density(np),w(np,nc) +! ---------------------------------------------------------------------- + + CALL si_dens (density,w) + + IF (u_in_p == 1.E5) THEN + p_ind = ' bar' + ELSE IF (u_in_p == 1.E2) THEN + p_ind = 'mbar' + ELSE IF (u_in_p == 1.E6) THEN + p_ind = ' MPa' + ELSE IF (u_in_p == 1.E3) THEN + p_ind = ' kPa' + ELSE + p_ind = ' Pa' + END IF + IF (u_in_t == 273.15) THEN + t_ind = ' C' + ELSE + t_ind = ' K' + END IF + + WRITE(*,*) '--------------------------------------------------' + WRITE (char_ncomp,'(I3)') ncomp + WRITE(*,'(t2,a,f7.2,2a,f9.4,a)') ' T =',t-u_out_t,t_ind & + ,' P =',p/u_out_p,p_ind + WRITE(*,'(t15,4(a12,1x),10x,a)') (compna(i),i=1,ncomp) + WRITE(*,'(2x,a,'//char_ncomp//'(g13.6,1x))') 'PHASE I w', (w(1,i),i=1,ncomp) + WRITE(*,'(2x,a,'//char_ncomp//'(g13.6,1x))') 'PHASE II w', (w(2,i),i=1,ncomp) + WRITE(*,'(2x,a,'//char_ncomp//'(g13.6,1x))') 'PHASE I x', (EXP(lnx(1,i)),i=1,ncomp) + WRITE(*,'(2x,a,'//char_ncomp//'(g13.6,1x))') 'PHASE II x', (EXP(lnx(2,i)),i=1,ncomp) + WRITE(*,'(2x,a,2(g13.6,1x))') 'DENSITY ', density(1),density(2) + + !-----output to files-------------------------------------------------- + IF (ncomp == 1) THEN + WRITE (40,'(7(2x,f18.8))') t-u_out_t, p/u_out_p, & + density(1), density(2),h_lv,cpres(1),cpres(2) + ! & ,(enthal(2)-enthal(1))/mm(1) + ! WRITE (40,'(4(2x,f15.8))') t, p, 0.3107*dense(1) + ! & /0.1617*(0.689+0.311*(T/1.328)**0.3674),0.3107 + ! & *dense(2)/0.1617*(0.689+0.311*(T/1.328)**0.3674) + ELSE IF (ncomp == 2) THEN + WRITE (40,'(12(2x,G15.8))') 1.0-xi(1,1),1.0-xi(2,1), & + w(1,1),w(2,1),t-u_out_t, p/u_out_p, density(1),density(2) & + ,enthal(1),enthal(2),cpres(1),cpres(2) + ELSE IF (ncomp == 3) THEN + WRITE (40,'(10(2x,f15.8))') xi(1,1),xi(1,2),xi(1,3),xi(2,1),xi(2,2), & + xi(2,3),t-u_out_t, p/u_out_p, density(1),density(2) + END IF + + END SUBROUTINE OUTPUT + + + +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! SUBROUTINE neutr_charge +! +! This subroutine is called for electrolye solutions, where a +! neutral overall-charge has to be enforced in all phases. The basic +! philosophy is similar to the above described routine X_SUMMATION. +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! + SUBROUTINE neutr_charge(i) +! + USE BASIC_VARIABLES + IMPLICIT NONE +! +! ---------------------------------------------------------------------- + INTEGER, INTENT(IN) :: i +! +! ---------------------------------------------------------------------- + INTEGER :: comp_e, ph_e + REAL :: sum_c + CHARACTER (LEN=2) :: phasno + CHARACTER (LEN=2) :: compno +! ---------------------------------------------------------------------- + +phasno = sum_rel(i)(2:2) +READ(phasno,*) ph_e +compno = sum_rel(i)(3:3) +READ(compno,*) comp_e + +sum_c = 0.0 +write (*,*) 'there must be an error in neutr_charge' +stop +! there is an error in the following passage. The index i is an +! argument to this subroutine - I guess it is INTENT(IN), so the +! index in the following loop can not be i. +! +! I have commented the loop until I check the code. +!DO i=1,ncomp +! IF ( comp_e /= i .AND. parame(i,10) /= 0.0) & +! sum_c = sum_c + xi(ph_e,i)*parame(i,10) +!END DO + +xi(ph_e,comp_e) = - sum_c +IF (xi(ph_e,comp_e) < 0.0) xi(ph_e,comp_e)=0.0 +IF (xi(ph_e,comp_e) /= 0.0) THEN + lnx(ph_e,comp_e) = LOG(xi(ph_e,comp_e)) +ELSE + lnx(ph_e,comp_e) = -100000.0 +END IF + +! xi(2,1) = xi(2,2) +! IF (xi(2,1).NE.0.0) lnx(2,1) = LOG(xi(2,1)) + +END SUBROUTINE neutr_charge + + +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! + SUBROUTINE flash_sum +! + USE BASIC_VARIABLES + IMPLICIT NONE +! + INTEGER :: i, j, ph_i, phase1, phase2 +! ---------------------------------------------------------------------- + +phase1=0 +phase2=0 +DO j=1,ncomp + IF (it(j)(2:2) == '1') phase1=phase1+1 + IF (it(j)(2:2) == '2') phase2=phase2+1 +END DO + +IF (phase1 == ncomp-1) THEN + ph_i = 1 +ELSE IF (phase2 == ncomp-1) THEN + ph_i = 2 +ELSE + WRITE (*,*) ' FLASH_SUM: undefined flash-case' + STOP +END IF + + + +IF (ph_i == 1) THEN + DO i=1,ncomp + IF (alpha > DMIN1(1.0,xif(i)/xi(1,i), & + (xif(i)-1.0)/(xi(1,i)-1.0),alpha)) THEN + WRITE (*,*) ' FLASH_SUM: exeeded 1st alpha-bound' + alpha=DMIN1(1.0,xif(i)/xi(1,i),(xif(i)-1.0)/(xi(1,i)-1.0)) + END IF + END DO + DO i=1,ncomp + xi(2,i) = ( xif(i) - alpha*xi(1,i) ) / (1.0-alpha) + IF (xi(2,i) > 0.0) THEN + lnx(2,i) = LOG(xi(2,i)) + ELSE + xi(2,i) = 0.0 + lnx(2,i) = -100000.0 + END IF + END DO +ELSE IF (ph_i == 2) THEN + DO i=1,ncomp + IF (alpha > DMAX1(0.0,(xif(i)-xi(2,i))/(1.0-xi(2,i)), & + 1.0-xif(i)/xi(2,i),alpha)) THEN + WRITE (*,*) ' FLASH_SUM: exeeded 2nd alpha-bound' + WRITE (*,*) 0.0,(xif(i)-xi(2,i))/(1.0-xi(2,i)), 1.0-xif(i)/xi(2,i) + alpha=DMAX1(0.0,(xif(i)-xi(2,i))/(1.0-xi(2,i)), 1.0-xif(i)/xi(2,i)) + END IF + END DO + DO i=1,ncomp + xi(1,i) = ( xif(i) - (1.0-alpha)*xi(2,i) ) / alpha +! write (*,*) 'x1,i',xi(1,i),xi(2,i),alpha + IF (xi(1,i) > 0.0) THEN + lnx(1,i) = LOG(xi(1,i)) + ELSE + xi(1,i) = 0.0 + lnx(1,i) = -100000.0 + END IF + END DO +END IF + +! pause + +RETURN +END SUBROUTINE flash_sum + +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! SUBROUTINE flash_alpha +! +! This subroutine calculates all molefractions of one phase +! from a component balance. What is needed for this calculation +! are all molefractions of the other phase (nphas=2, so far) +! and the phase fraction alpha. +! Alpha is calculated from the mole fraction +! of component {sum_rel(j)(3:3)}. If for example sum_rel(2)='fl3', +! then the alpha is determined from the molefraction of comp. 3 and +! all molefractions of one phase are calculated using that alpha-value. +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! + SUBROUTINE flash_alpha +! + USE BASIC_VARIABLES + IMPLICIT NONE +! +! ---------------------------------------------------------------------- + INTEGER :: i, j, comp_i, phase1, phase2 + CHARACTER (LEN=2) :: compno +! ---------------------------------------------------------------------- + + +! ---------------------------------------------------------------------- +! first calculate the phase fraction alpha from a known composition +! of component sum_rel(j)(3:3). +! ---------------------------------------------------------------------- + +DO j = 1, nphas + IF ( sum_rel(j)(1:2) == 'fl' ) THEN + compno = sum_rel(j)(3:3) + READ(compno,*) comp_i + IF ( (xi(1,comp_i)-xi(2,comp_i)) /= 0.0 ) THEN + alpha = (xif(comp_i)-xi(2,comp_i)) / (xi(1,comp_i)-xi(2,comp_i)) + write (*,*) 'flsh',(xif(comp_i)-xi(2,comp_i)),(xi(1,comp_i)-xi(2,comp_i)) + ELSE + alpha = 0.5 + WRITE (*,*) 'FLASH_ALPHA:error in calc. of phase fraction',comp_i + END IF + ! IF (alpha <= 0.0 .OR. alpha >= 1.0) WRITE(*,*) 'FLASH_ALPHA: error',alpha + IF (alpha > 1.0) alpha = 1.0 + IF (alpha < 0.0) alpha = 0.0 + END IF +END DO + +! ---------------------------------------------------------------------- +! determine which phase is fully determined by iterated molefractions (+ summation relation) +! ---------------------------------------------------------------------- +phase1 = 0 +phase2 = 0 +DO i = 1, ncomp + IF ( it(i)(2:2) == '1' ) phase1 = phase1 + 1 + IF ( it(i)(2:2) == '2' ) phase2 = phase2 + 1 +END DO +DO i = 1, ncomp + IF ( sum_rel(i)(2:2) == '1' ) phase1 = phase1 + 1 + IF ( sum_rel(i)(2:2) == '2' ) phase2 = phase2 + 1 +END DO + + +IF ( phase1 == ncomp ) THEN + ! -------------------------------------------------------------------- + ! phase 1 is defined by iterated molefractions + summation relation + ! phase 2 is determined from componennt balance (using alpha) + ! -------------------------------------------------------------------- + IF ( alpha == 1.0 ) alpha = 1.0 - 1.0E-10 + DO i=1,ncomp + xi(2,i) = ( xif(i) - alpha*xi(1,i) ) / (1.0-alpha) + IF ( xi(2,i) < 0.0 ) xi(2,i) = 0.0 + IF ( xi(2,i) > 1.0 ) xi(2,i) = 1.0 + IF ( xi(2,i) /= 0.0 ) THEN + lnx(2,i) = LOG( xi(2,i) ) + ELSE + lnx(2,i) = -100000.0 + END IF + write (*,*) 'fl_cal ph=2',i,lnx(2,i),xi(2,i) + END DO +ELSE IF ( phase2 == ncomp ) THEN + ! -------------------------------------------------------------------- + ! phase 2 is defined by iterated molefractions + summation relation + ! phase 1 is determined from componennt balance (using alpha) + ! -------------------------------------------------------------------- + DO i = 1, ncomp + xi(1,i) = ( xif(i) - (1.0-alpha)*xi(2,i) ) /alpha + IF ( xi(1,i) < 0.0 ) xi(1,i) = 0.0 + IF ( xi(1,i) > 1.0 ) xi(1,i) = 1.0 + IF ( xi(1,i) /= 0.0 ) THEN + lnx(1,i) = LOG( xi(1,i) ) + ELSE + lnx(1,i) = -100000.0 + END IF + write (*,*) 'fl_cal ph=1',i,lnx(1,i),xi(1,i),alpha + END DO +ELSE + WRITE (*,*) ' FLASH_ALPHA: undefined flash-case' + STOP +END IF + +END SUBROUTINE flash_alpha + + +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! SUBROUTINE SI_DENS (density,w) +! +! This subroutine calculates the (macroskopic) fluid-density in +! units [kg/m3] from the dimensionless density (eta=zeta3). +! Further, mass fractions are calculated from mole fractions. +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! + SUBROUTINE SI_DENS (density,w) +! + USE PARAMETERS, ONLY: pi, nav, tau + USE BASIC_VARIABLES + IMPLICIT NONE +! +! ---------------------------------------------------------------------- + REAL, INTENT(OUT) :: density(np) + REAL, INTENT(OUT) :: w(np,nc) +! +! ---------------------------------------------------------------------- + INTEGER :: i, ph + REAL :: mm_mean, rho, z3t + REAL :: dhs(nc), d00(nc), t_p, pcon, l_st +! ---------------------------------------------------------------------- + + +DO i = 1,ncomp + IF (eos == 1) THEN + dhs(i) = parame(i,2) * ( 1.0 - 0.12 *EXP( -3.0*parame(i,3)/t ) ) + ELSE IF (eos == 0) THEN + d00(i) = ( 1.E30/1.E6*tau*parame(i,2)*6.0/pi/nav )**(1.0/3.0) + dhs(i) = d00(i) * ( 1.0 - 0.12 *EXP( -3.0*parame(i,3)/t ) ) + ELSE IF (eos == 4) THEN + dhs(i) = ( 0.1617/0.3107 / ( 0.689+0.311*(t/parame(i,3)/1.328)**0.3674 ) & + / ( pi/6.0 ) )**(1.0/3.0) * parame(i,2) + ELSE IF (eos == 5.OR.eos == 6) THEN + l_st = parame(1,25) + IF (ncomp /= 1) write (*,*) ' ERROR for EOS = 5' + t_p =((34.037352+17.733741*l_st) /(1.0+0.53237307*l_st+12.860239*l_st**2 ))**0.5 + IF (l_st == 0.0) t_p = t_p/4.0 + IF (eos == 5 .AND. l_st /= 0.0) t_p = t_p/4.0*parame(1,1)**2 + t_p = t/parame(i,3)/t_p + pcon =0.5256+3.2088804*l_st**2 -3.1499114*l_st**2.5 +0.43049357*l_st**4 + dhs(i) = ( pcon/(0.67793+0.32207*(t_p)**0.3674) /(pi/6.0) )**(1.0/3.0) *parame(i,2) + ELSE IF (eos == 8) THEN + dhs(i) = parame(i,2)*(1.0+0.2977*t/parame(i,3)) & + /(1.0+0.33163*t/parame(i,3) +1.0477E-3*(t/parame(i,3))**2 ) + ELSE + write (*,*) 'define EOS in subroutine: SI_DENS' + stop + END IF +END DO + +DO ph = 1,nphas + mm_mean = 0.0 + z3t = 0.0 + DO i = 1, ncomp + mm_mean = mm_mean + xi(ph,i)*mm(i) + z3t = z3t + xi(ph,i) * parame(i,1) * dhs(i)**3 + END DO + z3t = pi/6.0 * z3t + rho = dense(ph)/z3t + density(ph) = rho * mm_mean * 1.E27 /nav + DO i = 1, ncomp + w(ph,i) = xi(ph,i) * mm(i)/mm_mean + END DO +! write (*,*) density(ph),rho,mm_mean,1.d27 /NAV +END DO + +END SUBROUTINE SI_DENS + + + +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! + REAL FUNCTION F_STABILITY ( optpara, n ) +! + USE BASIC_VARIABLES + USE STARTING_VALUES + USE EOS_VARIABLES, ONLY: dhs, PI + IMPLICIT NONE +! +! ---------------------------------------------------------------------- + INTEGER, INTENT(IN) :: n + REAL, INTENT(IN OUT) :: optpara(n) +! +! ---------------------------------------------------------------------- + INTEGER :: i, stabil + REAL :: rhoi(nc),gradterm + REAL :: fden,punish + REAL :: dens +! ---------------------------------------------------------------------- + +COMMON /stabil / stabil + +punish = 0.0 +stabil = 1 + +DO i = 1, n + IF ( optpara(i) < 0.5 ) rhoi(i) = EXP(optpara(i) ) + IF ( optpara(i) >= 0.5) rhoi(i) = EXP(0.5) +END DO + +dens = PI/6.0 * SUM( rhoi(1:ncomp) * parame(1:ncomp,1) * dhs(1:ncomp)**3 ) + +IF (dens > 0.65) THEN + punish = punish + (dens-0.65)*10000.0 + rhoi(1:n) = rhoi(1:n)*0.65/dens +END IF + +CALL fden_calc (fden, rhoi) + +gradterm = sum( grad_fd(1:n) * ( rhoi(1:n) - rhoif(1:n) ) ) + +f_stability = fden - fdenf - gradterm + punish + +! write (*,'(5G16.8)') F_STABILITY,(rhoi(i),i=1,n) +! pause + +stabil = 0 + +END FUNCTION F_STABILITY + + + + +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! SUBROUTINE p_calc (pges_transfer, zges) +! +! This subroutine serves as an iterface to the EOS-routines. The +! system pressure corresponding to given (desity,T,xi) is calculated. +! (Note: the more common interface is SUBROUTINE FUGACITY. This +! routine is only used for one-phase systems, e.g. calculation of +! virial coefficients) +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! + SUBROUTINE p_calc (pges_transfer, zges) +! + USE BASIC_VARIABLES + USE EOS_VARIABLES + IMPLICIT NONE +! +! ---------------------------------------------------------------------- + REAL, INTENT(IN OUT) :: pges_transfer + REAL, INTENT(OUT) :: zges +! ---------------------------------------------------------------------- + +IF (nphas /= 1 ) THEN + write (*,*) 'P_CALC: can only be called for single phases' + stop +ENDIF + +IF (eos < 2) THEN + + phas = 1 + eta = dense(1) + x(1:ncomp) = xi(1,1:ncomp) + + CALL PERTURBATION_PARAMETER + IF (num == 0) CALL P_EOS + IF(num == 1) CALL P_NUMERICAL + !! IF(num == 2) CALL F_EOS_RN + + pges_transfer = pges + rho = eta/z3t + zges = (pges * 1.E-30) / (kbol*t*rho) + +ELSE + write (*,*) ' SUBROUTINE P_CALC not available for cubic EOS' + stop +END IF + +END SUBROUTINE p_calc + + + +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! +SUBROUTINE ONLY_ONE_TERM_EOS_NUMERICAL ( only_term, type_of_term ) +! + USE EOS_NUMERICAL_DERIVATIVES + IMPLICIT NONE +! + character (LEN=9) :: only_term, type_of_term +! ---------------------------------------------------------------------- + + save_eos_terms(1) = ideal_gas + save_eos_terms(2) = hard_sphere + save_eos_terms(3) = chain_term + save_eos_terms(4) = disp_term + save_eos_terms(5) = hb_term + save_eos_terms(6) = LC_term + save_eos_terms(7) = branch_term + save_eos_terms(8) = II_term + save_eos_terms(9) = ID_term + + ideal_gas = 'no' + hard_sphere = 'no' + chain_term = 'no' + disp_term = 'no' + hb_term = 'no' + LC_term = 'no' + branch_term = 'no' + II_term = 'no' + ID_term = 'no' + + IF ( only_term == 'ideal_gas' ) ideal_gas = trim( adjustl( type_of_term ) ) + IF ( only_term == 'hard_sphere' ) hard_sphere = trim( adjustl( type_of_term ) ) + IF ( only_term == 'chain_term' ) chain_term = trim( adjustl( type_of_term ) ) + IF ( only_term == 'disp_term' ) disp_term = trim( adjustl( type_of_term ) ) + IF ( only_term == 'hb_term' ) hb_term = trim( adjustl( type_of_term ) ) + IF ( only_term == 'LC_term' ) LC_term = trim( adjustl( type_of_term ) ) + IF ( only_term == 'branch_term' ) branch_term = trim( adjustl( type_of_term ) ) + IF ( only_term == 'II_term' ) II_term = trim( adjustl( type_of_term ) ) + IF ( only_term == 'ID_term' ) ID_term = trim( adjustl( type_of_term ) ) + +END SUBROUTINE ONLY_ONE_TERM_EOS_NUMERICAL + + +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! +SUBROUTINE RESTORE_PREVIOUS_EOS_NUMERICAL +! + USE EOS_NUMERICAL_DERIVATIVES + IMPLICIT NONE +! +! ---------------------------------------------------------------------- + ideal_gas = trim( adjustl( save_eos_terms(1) ) ) + hard_sphere = trim( adjustl( save_eos_terms(2) ) ) + chain_term = trim( adjustl( save_eos_terms(3) ) ) + disp_term = trim( adjustl( save_eos_terms(4) ) ) + hb_term = trim( adjustl( save_eos_terms(5) ) ) + LC_term = trim( adjustl( save_eos_terms(6) ) ) + branch_term = trim( adjustl( save_eos_terms(7) ) ) + II_term = trim( adjustl( save_eos_terms(8) ) ) + ID_term = trim( adjustl( save_eos_terms(9) ) ) + +END SUBROUTINE RESTORE_PREVIOUS_EOS_NUMERICAL + + + + diff --git a/applications/PUfoam/MoDeNaModels/SurfaceTension/src/gnuplot_script.srp b/applications/PUfoam/MoDeNaModels/SurfaceTension/src/gnuplot_script.srp new file mode 100644 index 000000000..393ce9af6 --- /dev/null +++ b/applications/PUfoam/MoDeNaModels/SurfaceTension/src/gnuplot_script.srp @@ -0,0 +1,55 @@ + + +plotfile = 'ItsTimeNorm.eps' +readfile = 'ItsTimeNorm.dat' +Titel = 'Zeitverlauf der Residuen' +NameX = 'Zeit t' +NameY1 = '|F|' +#NameY2 = 'rho(r)exp(...)-rho(r)' + +set terminal postscript eps +set output plotfile + + +#Set labels +set title Titel +set xlabel NameX +set ylabel NameY1 +#set y2label NameY2 +#set ytics +#set y2tics +#set ytics nomirror + +##Read min and max values to scale the axes +#stats readfile using 2 nooutput +#y1max = STATS_max +#y1min = STATS_min +#stats readfile using 3 nooutput +#y2max = STATS_max +#y2min = STATS_min +#this is needed to get a symmetric plot about 0 where the 0 is at the same height for +#both y axes +#if (abs(y1max) > abs(y1min)) { +# y1range = y1max +# } else { +# y1range = abs(y1min) +# } + +#if (abs(y2max) > abs(y2min)) { +# y2range = y2max +# } else { +# y2range = abs(y2min) +# } + +#set yrange[-1.1*y1range:1.1*y1range] +#set y2range[-1.1*y2range:1.1*y2range] + +#set size square + +#set autoscale y +#set autoscale y2 + + +#plot readfile using 1:2 with lines axes x1y1 title NameY1 , readfile using 1:3 with lines axes x2y2 title NameY2 +plot readfile using 2:3 title NameY1 + diff --git a/applications/PUfoam/MoDeNaModels/SurfaceTension/src/in.txt b/applications/PUfoam/MoDeNaModels/SurfaceTension/src/in.txt new file mode 100644 index 000000000..2d712ecf4 --- /dev/null +++ b/applications/PUfoam/MoDeNaModels/SurfaceTension/src/in.txt @@ -0,0 +1,6 @@ +260.0 +2 +air +thf +0. +0. \ No newline at end of file diff --git a/applications/PUfoam/MoDeNaModels/SurfaceTension/src/makefile b/applications/PUfoam/MoDeNaModels/SurfaceTension/src/makefile new file mode 100644 index 000000000..ab6537b9f --- /dev/null +++ b/applications/PUfoam/MoDeNaModels/SurfaceTension/src/makefile @@ -0,0 +1,344 @@ + +#include /usr/ITT/mhofer/Documents/Diss/NumericalMethods/Libraries/Petsc/petsc-3.4.4/conf/variables +#include /usr/ITT/mhofer/Documents/Diss/NumericalMethods/Libraries/Petsc/petsc-3.4.4/conf/rules + +#include ~/NumLib/PETSc/petsc-3.4.4/conf/variables +#include ~/NumLib/PETSc/petsc-3.4.4/conf/rules + + +include /${PETSC_DIR}/conf/variables +include /${PETSC_DIR}/conf/rules + + + +SOURCE = Modules.F90 \ + mod_PETSc.F90 \ + mod_DFT_FMT.F90 \ + mod_DFT_FMT_d.F90 \ + mod_DFT_CHAIN.F90 \ + mod_DFT_CHAIN_d.F90 \ + mod_DFT_DISP_WDA.F90 \ + mod_DFT_DISP_WDA_d.F90 \ + module_solve_nonlinear.F90 \ + getting_started_subroutines.F90 \ + Helfer_Routinen.F90 \ + Numeric_subroutines.F90 \ + Spline_Integration_d.F90 \ + VLE_main.F90 \ + VLE_subroutines.F90 \ + crit_point_mixtures.F90 \ + Function.F90 \ + AD_Routines.F90 \ + InitialGuess.F90 \ + SolverSetup.F90 \ + Main.F90 \ + +#Object files +OBJECT = $(SOURCE:%.F90=%.o) + +#define target for non-PETSc files +%.o: %.F90 + ${PETSC_FCOMPILE} -fdefault-real-8 -c $< -o $@ + +DFT: $(OBJECT) + -${FLINKER} -o PCSAFT_SurfaceTension $(OBJECT) ${PETSC_SNES_LIB} + +#-------------------------------------------------------------------------- + +#Anzahl Prozessoren +NP = 1 + +#Initial profile: 0: normal, 1-3: add perturbation to regular initial profile +PERT = 0 + +#DFT Settings +NGRID = 800 +CUTOFF = 9.0 +BOXSIZE = 300.0 + +#Solver Settings +ITS_SNES = 20 +ITS_KSP = 15 +E_REL = 1e-08 + +#Its for Anderson Mixing +ITS_SNES_ANDERSON = 100 +#Its for Picard Iterations +ITS_SNES_PICARD = 100 + +#Toleranzen +ATOL_SNES = 1e-08 +RTOL_SNES = 1e-08 +STOL_SNES = 1e-08 + +ATOL_KSP = 1e-08 +RTOL_KSP = 1e-04 + +#D�mpfungsfaktoren +DAMP = 0.3 +DAMP_LBFGS = 1.0 +DAMP_ANDERSON = 0.01 +DAMP_PICARD = 0.01 + +#------------------------------------------------------------------------------ +#1) Inexact-Newton type solvers (iterative solver for linear system) +#------------------------------------------------------------------------------ + +#matrix-free, numerical approximation of directional derivatives (choose between trust region and line search) +run_mf: + -@${MPIEXEC} -n $(NP) ./PCSAFT_SurfaceTension -snes_monitor_short -ksp_monitor_short \ + -nx $(NGRID) \ + -rc $(CUTOFF) \ + -box $(BOXSIZE) \ + -erel $(E_REL) \ + -init_pert $(PERT) \ + -snes_type newtonls -snes_converged_reason \ + -snes_atol $(ATOL_SNES) -snes_rtol $(RTOL_SNES) -snes_stol $(STOL_SNES) -snes_max_it $(ITS_SNES) \ + -ksp_atol $(ATOL_KSP) -ksp_rtol $(RTOL_KSP) -ksp_max_it $(ITS_KSP) -ksp_gmres_restart 50 \ + -snes_linesearch_type bt -snes_linesearch_damping $(DAMP) -snes_linesearch_monitor \ + -snes_max_fail 1 -snes_max_linear_solve_fail 100 \ + -ksp_gmres_cgs_refinement_type refine_always \ + -snes_ksp_ew -snes_ksp_ew_version 1 -snes_ksp_ew_rtol0 0.5 -snes_ksp_ew_rtolmax 0.9 -snes_ksp_ew_threshold 0.1 \ + -jac 0 \ + -pc_type none \ + + + +#matrix-free, AD-calculation directional derivatives (choose between trust region and line search) +run_ad: + -@${MPIEXEC} -n $(NP) ./PCSAFT_SurfaceTension -snes_monitor_short -ksp_monitor_short \ + -nx $(NGRID) \ + -rc $(CUTOFF) \ + -box $(BOXSIZE) \ + -init_pert $(PERT) \ + -snes_type newtonls -snes_converged_reason \ + -snes_atol $(ATOL_SNES) -snes_rtol $(RTOL_SNES) -snes_stol $(STOL_SNES) -snes_max_it $(ITS_SNES) \ + -ksp_atol $(ATOL_KSP) -ksp_rtol $(RTOL_KSP) -ksp_max_it $(ITS_KSP) -ksp_gmres_restart 50 \ + -snes_linesearch_type bt -snes_linesearch_damping $(DAMP) -snes_linesearch_monitor \ + -snes_max_fail 1 -snes_max_linear_solve_fail 100 \ + -ksp_gmres_cgs_refinement_type refine_always \ + -snes_ksp_ew -snes_ksp_ew_version 1 -snes_ksp_ew_rtol0 0.5 -snes_ksp_ew_rtolmax 0.9 -snes_ksp_ew_threshold 0.1 \ + -jac 1 \ +# -pc_type none + +#finite-difference approximation of Jacobi matrix (-> PC can be used!) (choose between trust region and line search) +run_fd: + -@${MPIEXEC} -n $(NP) ./PCSAFT_SurfaceTension -snes_fd -snes_monitor_short -ksp_monitor_short \ + -nx $(NGRID) \ + -rc $(CUTOFF) \ + -box $(BOXSIZE) \ + -init_pert $(PERT) \ + -snes_type newtonls -snes_converged_reason \ + -snes_atol $(ATOL_SNES) -snes_rtol $(RTOL_SNES) -snes_stol $(STOL_SNES) -snes_max_it $(ITS_SNES) \ + -ksp_atol $(ATOL_KSP) -ksp_rtol $(RTOL_KSP) -ksp_max_it $(ITS_KSP) -ksp_gmres_restart 50 \ + -snes_linesearch_type bt -snes_linesearch_damping $(DAMP) -snes_linesearch_monitor \ + -snes_max_fail 1 -snes_max_linear_solve_fail 100 \ + -ksp_gmres_cgs_refinement_type refine_always \ + -snes_ksp_ew -snes_ksp_ew_version 1 -snes_ksp_ew_rtol0 0.5 -snes_ksp_ew_rtolmax 0.9 -snes_ksp_ew_threshold 0.1 \ + -jac 2 \ + -dm_mat_type aij \ +# -pc_type ilu + +#Build complete Jacobi matrix with AD (-> PC can be used!) (choose between trust region and line search) +run_anad: + -@${MPIEXEC} -n $(NP) ./PCSAFT_SurfaceTension -snes_monitor_short -ksp_monitor_short \ + -nx $(NGRID) \ + -rc $(CUTOFF) \ + -box $(BOXSIZE) \ + -init_pert $(PERT) \ + -snes_type newtonls -snes_converged_reason \ + -snes_atol $(ATOL_SNES) -snes_rtol $(RTOL_SNES) -snes_stol $(STOL_SNES) -snes_max_it $(ITS_SNES) \ + -ksp_atol $(ATOL_KSP) -ksp_rtol $(RTOL_KSP) -ksp_max_it $(ITS_KSP) -ksp_gmres_restart 50 \ + -snes_linesearch_type bt -snes_linesearch_damping $(DAMP) -snes_linesearch_monitor \ + -snes_max_fail 1 -snes_max_linear_solve_fail 100 \ + -ksp_gmres_cgs_refinement_type refine_always \ + -snes_ksp_ew -snes_ksp_ew_version 1 -snes_ksp_ew_rtol0 0.5 -snes_ksp_ew_rtolmax 0.9 -snes_ksp_ew_threshold 0.1 \ + -jac 3 \ + + + +#------------------------------------------------------------------------------ +#2) Newton type solvers (direct solver for linear system) +#------------------------------------------------------------------------------ + +#finite-difference approximation of Jacobi matrix (-> PC can be used!) (choose between trust region and line search) +run_fdmumps: + -@${MPIEXEC} -n $(NP) ./PCSAFT_SurfaceTension -snes_monitor_short -ksp_monitor_short \ + -nx $(NGRID) \ + -rc $(CUTOFF) \ + -box $(BOXSIZE) \ + -init_pert $(PERT) \ + -snes_type newtonls -snes_converged_reason \ + -snes_atol $(ATOL_SNES) -snes_rtol $(RTOL_SNES) -snes_stol $(STOL_SNES) -snes_max_it $(ITS_SNES) \ + -snes_linesearch_type bt -snes_linesearch_damping $(DAMP) -snes_linesearch_monitor \ + -snes_max_fail 1 -snes_max_linear_solve_fail 100 \ + -jac 2 \ + -dm_mat_type aij \ + -pc_type lu -pc_factor_mat_solver_package mumps \ + +#Build complete Jacobi matrix with AD (-> PC can be used!) (choose between trust region and line search) +run_anadmumps: + -@${MPIEXEC} -n $(NP) ./PCSAFT_SurfaceTension -snes_monitor_short -ksp_monitor_short \ + -nx $(NGRID) \ + -rc $(CUTOFF) \ + -box $(BOXSIZE) \ + -init_pert $(PERT) \ + -snes_type newtonls -snes_converged_reason \ + -snes_atol $(ATOL_SNES) -snes_rtol $(RTOL_SNES) -snes_stol $(STOL_SNES) -snes_max_it $(ITS_SNES) \ + -snes_linesearch_type bt -snes_linesearch_damping $(DAMP) -snes_linesearch_monitor \ + -snes_max_fail 1 -snes_max_linear_solve_fail 100 \ + -jac 3 \ + -pc_type lu -pc_factor_mat_solver_package mumps \ + + +#------------------------------------------------------------------------------ +#3) Quasi-Newton type solvers (secant updates for approximation to inverse Jacobian) +#------------------------------------------------------------------------------ + +#limitd memory quasi newton with BFGS updates -> choose restart parameter +run_LBFGS: + -@${MPIEXEC} -n $(NP) ./PCSAFT_SurfaceTension -snes_monitor_short -ksp_monitor_short \ + -nx $(NGRID) \ + -rc $(CUTOFF) \ + -box $(BOXSIZE) \ + -init_pert $(PERT) \ + -snes_type qn -snes_qn_type lbfgs \ + -snes_converged_reason \ + -snes_linesearch_type cp -snes_linesearch_damping $(DAMP_LBFGS) \ + -snes_atol $(ATOL_SNES) -snes_rtol $(RTOL_SNES) -snes_stol $(STOL_SNES) -snes_max_it $(ITS_SNES) \ + -snes_ksp_ew -snes_ksp_ew_version 1 -snes_ksp_ew_rtol0 0.5 -snes_ksp_ew_rtolmax 0.9 -snes_ksp_ew_threshold 0.1 \ + -ksp_atol $(ATOL_KSP) -ksp_rtol $(RTOL_KSP) -ksp_max_it $(ITS_KSP) -ksp_gmres_restart 50 \ + -snes_max_fail 1 -snes_max_linear_solve_fail 100 \ + -jac -1 \ + +#limitd memory quasi newton with BFGS updates -> choose restart parameter +#calculate initial jacobian with AD, then use BFGS updates in later iterations + +#anpassen damping, jac 0/1 + +run_LBFGSinitJac: + -@${MPIEXEC} -n $(NP) ./PCSAFT_SurfaceTension -snes_monitor_short -ksp_monitor_short \ + -nx $(NGRID) \ + -rc $(CUTOFF) \ + -box $(BOXSIZE) \ + -init_pert $(PERT) \ + -snes_type qn -snes_qn_type lbfgs -snes_qn_scale_type jacobian \ + -snes_converged_reason \ + -snes_linesearch_type bt -snes_linesearch_damping $(DAMP_LBFGS) \ + -snes_atol $(ATOL_SNES) -snes_rtol $(RTOL_SNES) -snes_stol $(STOL_SNES) -snes_max_it $(ITS_SNES) \ + -snes_ksp_ew -snes_ksp_ew_version 1 -snes_ksp_ew_rtol0 0.5 -snes_ksp_ew_rtolmax 0.9 -snes_ksp_ew_threshold 0.1 \ + -ksp_atol $(ATOL_KSP) -ksp_rtol $(RTOL_KSP) -ksp_max_it $(ITS_KSP) -ksp_gmres_restart 50 \ + -snes_max_fail 1 -snes_max_linear_solve_fail 100 \ + -jac 0 \ + + +#use a direct solver for linear system + +#limitd memory quasi newton with BFGS updates -> choose restart parameter +#calculate initial jacobian with AD, then use BFGS updates in later iterations +run_LBFGSinitJac2: + -@${MPIEXEC} -n $(NP) ./PCSAFT_SurfaceTension -snes_monitor_short -ksp_monitor_short \ + -nx $(NGRID) \ + -rc $(CUTOFF) \ + -box $(BOXSIZE) \ + -init_pert $(PERT) \ + -snes_type qn -snes_qn_type lbfgs -snes_qn_scale_type jacobian \ + -snes_converged_reason \ + -snes_linesearch_type bt -snes_linesearch_damping $(DAMP_LBFGS) \ + -snes_atol $(ATOL_SNES) -snes_rtol $(RTOL_SNES) -snes_stol $(STOL_SNES) -snes_max_it $(ITS_SNES) \ + -ksp_atol $(ATOL_KSP) -ksp_rtol $(RTOL_KSP) -ksp_max_it $(ITS_KSP) -ksp_gmres_restart 50 \ + -snes_max_fail 1 -snes_max_linear_solve_fail 100 \ + -jac 3 \ + + + +#------------------------------------------------------------------------------ +#4) Simple Fixpoint Iterations +#------------------------------------------------------------------------------ + + +#Anderson mixing +run_Anderson: + -@${MPIEXEC} -n $(NP) ./PCSAFT_SurfaceTension -snes_monitor_short -ksp_monitor_short \ + -nx $(NGRID) \ + -rc $(CUTOFF) \ + -box $(BOXSIZE) \ + -init_pert $(PERT) \ + -snes_type anderson \ + -snes_atol $(ATOL_SNES) -snes_rtol $(RTOL_SNES) -snes_stol $(STOL_SNES) -snes_max_it $(ITS_SNES_ANDERSON) \ + -snes_converged_reason \ + -snes_linesearch_type l2 -snes_linesearch_damping $(DAMP_ANDERSON) -snes_linesearch_monitor \ + -jac -1 \ + + +#Picard Iteration +run_Picard: + -@${MPIEXEC} -n $(NP) ./PCSAFT_SurfaceTension -snes_monitor_short -ksp_monitor_short \ + -nx $(NGRID) \ + -rc $(CUTOFF) \ + -box $(BOXSIZE) \ + -init_pert $(PERT) \ + -snes_type nrichardson \ + -snes_atol $(ATOL_SNES) -snes_rtol $(RTOL_SNES) -snes_stol $(STOL_SNES) -snes_max_it $(ITS_SNES_PICARD) \ + -snes_converged_reason \ + -snes_linesearch_type l2 -snes_linesearch_damping $(DAMP_PICARD) -snes_linesearch_monitor \ + -jac -1 \ + + + + +# # #-------------------------------------------------------------------------- +# # +# # #Anzahl Prozessoren +# # NP = 1 +# # +# # +# # #DFT Settings +# # NGRID = 800 +# # CUTOFF = 9.0 +# # BOXSIZE = 10.0 +# # +# # #Solver Settings +# # ITS_SNES = 40 +# # ITS_KSP = 20 +# # E_REL = 1e-11 +# # +# # #Its for Anderson Mixing +# # ITS_SNES_ANDERSON = 250 +# # #Its for Picard Iterations +# # ITS_SNES_PICARD = 250 +# # +# # #Toleranzen +# # ATOL_SNES = 1e-08 +# # RTOL_SNES = 1e-08 +# # STOL_SNES = 1e-08 +# # +# # ATOL_KSP = 1e-08 +# # RTOL_KSP = 1e-04 +# # +# # #D�mpfungsfaktoren +# # DAMP = 0.5 +# # DAMP_LBFGS = 0.5 +# # DAMP_ANDERSON = 0.5 +# # DAMP_PICARD = 0.01 +# # +# # #------------------------------------------------------------------------------ +# # #1) Inexact-Newton type solvers (iterative solver for linear system) +# # #------------------------------------------------------------------------------ +# # +# # #matrix-free, numerical approximation of directional derivatives (choose between trust region and line search) +# # runNLsolver_mf: +# # -@${MPIEXEC} -n $(NP) ./NLsolver -snes_monitor_short -ksp_monitor_short \ +# # -nx $(NGRID) \ +# # -rc $(CUTOFF) \ +# # -box $(BOXSIZE) \ +# # -erel $(E_REL) \ +# # -snes_type newtonls -snes_converged_reason \ +# # -snes_atol $(ATOL_SNES) -snes_rtol $(RTOL_SNES) -snes_stol $(STOL_SNES) -snes_max_it $(ITS_SNES) \ +# # -ksp_atol $(ATOL_KSP) -ksp_rtol $(RTOL_KSP) -ksp_max_it $(ITS_KSP) -ksp_gmres_restart 50 \ +# # -snes_linesearch_type bt -snes_linesearch_damping $(DAMP) -snes_linesearch_monitor \ +# # -snes_max_fail 1 -snes_max_linear_solve_fail 100 \ +# # -ksp_gmres_cgs_refinement_type refine_always \ +# # -snes_ksp_ew -snes_ksp_ew_version 1 -snes_ksp_ew_rtol0 0.5 -snes_ksp_ew_rtolmax 0.9 -snes_ksp_ew_threshold 0.1 \ +# # -jac 0 \ +# # -pc_type none \ diff --git a/applications/PUfoam/MoDeNaModels/SurfaceTension/src/mod_ChemPot.F90 b/applications/PUfoam/MoDeNaModels/SurfaceTension/src/mod_ChemPot.F90 new file mode 100644 index 000000000..6f1b96c1c --- /dev/null +++ b/applications/PUfoam/MoDeNaModels/SurfaceTension/src/mod_ChemPot.F90 @@ -0,0 +1,250 @@ +Module mod_ChemPot + + + +Implicit None + + + +private + +public :: Chemical_Potential +public :: PCSAFT_const +REAL, public, allocatable :: ChemPot_tot(:) +REAL, public, allocatable :: ChemPot_res(:) + + contains + + + + +Subroutine Chemical_Potential + +Use BASIC_VARIABLES +Use EOS_VARIABLES +Use PARAMETERS +USe EOS_CONSTANTS + +Integer :: k,i,j +REAL :: z0t,z1t,z2t,z3t +REAL :: z0,z1,z2,z3,zms +REAL :: z0_rk,z1_rk,z2_rk,z3_rk +REAL, allocatable :: mhs(:), mhc(:) +REAL, allocatable :: gij(:,:), gij_rk(:,:), dij_ab(:,:) + +!DISP HERE!!! +INTEGER :: m +REAL :: m_mean,I1,I2,I1_rk,I2_rk +REAL :: ord1_rk,ord2_rk +REAL :: c1_con,c2_con,c1_rk +REAL :: order1,order2 +REAL :: apar(0:6),bpar(0:6) +REAL, allocatable :: m_rk(:),mdsp(:) +REAL, allocatable :: ap_rk(:,:),bp_rk(:,:) + +Allocate(mdsp(ncomp),m_rk(ncomp),ap_rk(ncomp,0:6),bp_rk(ncomp,0:6)) +Allocate(sig_ij(ncomp,ncomp),uij(ncomp,ncomp)) + +kij = 0.0 + + + +Allocate(mhs(ncomp), mhc(ncomp), ChemPot_res(ncomp), ChemPot_tot(ncomp) ) +Allocate(gij(ncomp,ncomp), gij_rk(ncomp,ncomp), dij_ab(ncomp,ncomp) ) + + +!belege dichteunabh�ngige Parameter (z0z,z1t,z2t,z3t) +z0t = PI / 6.0 * SUM( xx(1:ncomp) * mseg(1:ncomp) ) +z1t = PI / 6.0 * SUM( xx(1:ncomp) * mseg(1:ncomp) * dhs(1:ncomp) ) +z2t = PI / 6.0 * SUM( xx(1:ncomp) * mseg(1:ncomp) * dhs(1:ncomp)**2 ) +z3t = PI / 6.0 * SUM( xx(1:ncomp) * mseg(1:ncomp) * dhs(1:ncomp)**3 ) + + + +! --- Eq.(A.8) --------------------------------------------------------- +rho = eta / z3t !total number density [particles/A^3] +z0 = z0t * rho +z1 = z1t * rho +z2 = z2t * rho +z3 = z3t * rho + +zms = 1.0 - eta + +call PCSAFT_const(ap,bp) !get PCSAFT constants + +DO k = 1, ncomp + + z0_rk = PI/6.0 * mseg(k) + z1_rk = PI/6.0 * mseg(k) * dhs(k) + z2_rk = PI/6.0 * mseg(k) * dhs(k)*dhs(k) + z3_rk = PI/6.0 * mseg(k) * dhs(k)**3 + + ! -------------------------------------------------------------------- + ! d(f)/d(x) : hard sphere contribution + ! -------------------------------------------------------------------- + mhs(k) = 6.0/PI* ( 3.0*(z1_rk*z2+z1*z2_rk)/zms + 3.0*z1*z2*z3_rk/zms/zms & + + 3.0*z2*z2*z2_rk/z3/zms/zms + z2**3 *z3_rk*(3.0*z3-1.0)/z3/z3/zms**3 & + + ((3.0*z2*z2*z2_rk*z3-2.0*z2**3 *z3_rk)/z3**3 -z0_rk) *LOG(zms) & + + (z0-z2**3 /z3/z3)*z3_rk/zms ) + + + ! -------------------------------------------------------------------- + ! d(f)/d(x) : chain term + ! -------------------------------------------------------------------- + DO i = 1, ncomp + DO j = 1, ncomp + dij_ab(i,j) = dhs(i)*dhs(j) / ( dhs(i) + dhs(j) ) + END DO + END DO + + DO i = 1, ncomp + DO j = 1, ncomp + gij(i,j) = 1.0/zms + 3.0*dij_ab(i,j)*z2/zms/zms + 2.0*(dij_ab(i,j)*z2)**2 /zms**3 + gij_rk(i,j) = z3_rk/zms/zms & + + 3.0*dij_ab(i,j)*(z2_rk+2.0*z2*z3_rk/zms)/zms/zms & + + dij_ab(i,j)**2 *z2/zms**3 *(4.0*z2_rk+6.0*z2*z3_rk/zms) + END DO + END DO + + mhc(k) = 0.0 + DO i = 1, ncomp + mhc(k) = mhc(k) + xx(i)*rho * (1.0-mseg(i)) / gij(i,i) * gij_rk(i,i) + END DO + mhc(k) = mhc(k) + ( 1.0-mseg(k)) * LOG( gij(k,k) ) + + ! -------------------------------------------------------------------- + ! PC-SAFT: d(f)/d(x) : dispersion contribution + ! -------------------------------------------------------------------- + + m_mean = z0t / (PI/6.0) + m_rk(k) = ( mseg(k) - m_mean ) / rho + + + DO m = 0, 6 + apar(m) = ap(m,1) + (1.0-1.0/m_mean)*ap(m,2) & + + (1.0-1.0/m_mean)*(1.0-2.0/m_mean)*ap(m,3) + bpar(m) = bp(m,1) + (1.0-1.0/m_mean)*bp(m,2) & + + (1.0-1.0/m_mean)*(1.0-2.0/m_mean)*bp(m,3) + + ! --- derivatives of apar, bpar to rho_k --------------------------- + ap_rk(k,m) = m_rk(k)/m_mean**2 * ( ap(m,2) + (3.0 -4.0/m_mean) *ap(m,3) ) + bp_rk(k,m) = m_rk(k)/m_mean**2 * ( bp(m,2) + (3.0 -4.0/m_mean) *bp(m,3) ) + END DO + + I1 = 0.0 + I2 = 0.0 + I1_rk = 0.0 + I2_rk = 0.0 + DO m = 0, 6 + I1 = I1 + apar(m)*eta**REAL(m) + I2 = I2 + bpar(m)*eta**REAL(m) + I1_rk = I1_rk + apar(m)*REAL(m)*eta**REAL(m-1)*z3_rk + ap_rk(k,m)*eta**REAL(m) + I2_rk = I2_rk + bpar(m)*REAL(m)*eta**REAL(m-1)*z3_rk + bp_rk(k,m)*eta**REAL(m) + END DO + + ord1_rk = 0.0 + ord2_rk = 0.0 + order1 = 0.0 + order2 = 0.0 + DO i = 1,ncomp + sig_ij(i,k) = 0.5 * ( dhs(i) + dhs(k) ) + uij(i,k) = (1.0 - kij(i,k)) * SQRT( eps(i) * eps(k) ) + order1 = order1 + xx(i)*xx(k)* mseg(i)*mseg(k)*sig_ij(i,k)**3 * uij(i,k)/t + order2 = order2 + xx(i)*xx(k)* mseg(i)*mseg(k)*sig_ij(i,k)**3 * (uij(i,k)/t)**2 + ord1_rk = ord1_rk + 2.0*mseg(k)*rho*xx(i)*mseg(i)*sig_ij(i,k)**3 *uij(i,k)/t + ord2_rk = ord2_rk + 2.0*mseg(k)*rho*xx(i)*mseg(i)*sig_ij(i,k)**3 *(uij(i,k)/t)**2 + END DO + + + c1_con= 1.0/ ( 1.0 + m_mean*(8.0*z3-2.0*z3*z3)/zms**4 & + + (1.0 - m_mean)*(20.0*z3-27.0*z3*z3 +12.0*z3**3 -2.0*z3**4 ) & + /(zms*(2.0-z3))**2 ) + c2_con= - c1_con*c1_con *( m_mean*(-4.0*z3*z3+20.0*z3+8.0)/zms**5 & + + (1.0 - m_mean) *(2.0*z3**3 +12.0*z3*z3-48.0*z3+40.0) & + /(zms*(2.0-z3))**3 ) + c1_rk= c2_con*z3_rk - c1_con*c1_con*m_rk(k) * ( (8.0*z3-2.0*z3*z3)/zms**4 & + - (-2.0*z3**4 +12.0*z3**3 -27.0*z3*z3+20.0*z3) / (zms*(2.0-z3))**2 ) + + mdsp(k) = -2.0*PI* ( order1*rho*rho*I1_rk + ord1_rk*I1 ) & + - PI* c1_con*m_mean * ( order2*rho*rho*I2_rk + ord2_rk*I2 ) & + - PI* ( c1_con*m_rk(k) + c1_rk*m_mean ) * order2*rho*rho*I2 + + +End Do + +!residual + ChemPot_res(1:ncomp) = mhs(1:ncomp) + mhc(1:ncomp) + mdsp(1:ncomp) ! /kT [-] +!total + ChemPot_tot(1:ncomp) = ChemPot_res(1:ncomp) + log( xx(1:ncomp)*rho ) ! /kT [-] + +write(*,*)'rhob',xx(1:ncomp)*rho + +End Subroutine Chemical_Potential + + + + + + + + + +Subroutine PCSAFT_const(ap,bp) + +Implicit None + +!passed +REAL, INTENT(OUT) :: ap(0:6,3) +REAL, INTENT(OUT) :: bp(0:6,3) + +! --- dispersion term constants ---------------------------------------- +ap(0,1) = 0.91056314451539 +ap(0,2) = -0.30840169182720 +ap(0,3) = -0.09061483509767 +ap(1,1) = 0.63612814494991 +ap(1,2) = 0.18605311591713 +ap(1,3) = 0.45278428063920 +ap(2,1) = 2.68613478913903 +ap(2,2) = -2.50300472586548 +ap(2,3) = 0.59627007280101 +ap(3,1) = -26.5473624914884 +ap(3,2) = 21.4197936296668 +ap(3,3) = -1.72418291311787 +ap(4,1) = 97.7592087835073 +ap(4,2) = -65.2558853303492 +ap(4,3) = -4.13021125311661 +ap(5,1) = -159.591540865600 +ap(5,2) = 83.3186804808856 +ap(5,3) = 13.7766318697211 +ap(6,1) = 91.2977740839123 +ap(6,2) = -33.7469229297323 +ap(6,3) = -8.67284703679646 + +bp(0,1) = 0.72409469413165 +bp(0,2) = -0.57554980753450 +bp(0,3) = 0.09768831158356 +bp(1,1) = 1.11913959304690 *2.0 +bp(1,2) = 0.34975477607218 *2.0 +bp(1,3) = -0.12787874908050 *2.0 +bp(2,1) = -1.33419498282114 *3.0 +bp(2,2) = 1.29752244631769 *3.0 +bp(2,3) = -3.05195205099107 *3.0 +bp(3,1) = -5.25089420371162 *4.0 +bp(3,2) = -4.30386791194303 *4.0 +bp(3,3) = 5.16051899359931 *4.0 +bp(4,1) = 5.37112827253230 *5.0 +bp(4,2) = 38.5344528930499 *5.0 +bp(4,3) = -7.76088601041257 *5.0 +bp(5,1) = 34.4252230677698 *6.0 +bp(5,2) = -26.9710769414608 *6.0 +bp(5,3) = 15.6044623461691 *6.0 +bp(6,1) = -50.8003365888685 *7.0 +bp(6,2) = -23.6010990650801 *7.0 +bp(6,3) = -4.23812936930675 *7.0 + + +End Subroutine PCSAFT_const + + + +End Module mod_ChemPot diff --git a/applications/PUfoam/MoDeNaModels/SurfaceTension/src/mod_DFT_CHAIN.F90 b/applications/PUfoam/MoDeNaModels/SurfaceTension/src/mod_DFT_CHAIN.F90 new file mode 100644 index 000000000..52cdd475a --- /dev/null +++ b/applications/PUfoam/MoDeNaModels/SurfaceTension/src/mod_DFT_CHAIN.F90 @@ -0,0 +1,351 @@ +!>This file contains the subroutines which calculate the contribution of +!!chain formation to the Helmholtz energy functional. + + +Module mod_DFT_CHAIN + +Implicit None +private + + +public :: Chain_aux +public :: Chain_dFdrho + + + contains + + + +Subroutine Chain_aux(rhop,rhobar,lambda,user) + +Use BASIC_VARIABLES, Only: ncomp +Use EOS_VARIABLES, Only: dhs,rho +Use mod_DFT, Only: zp,dzp,fa + + +!PETSc module +Use PetscManagement + +#include + +!passed +type (userctx) :: user +PetscScalar :: rhop(ncomp,user%gxs:user%gxe) +REAL,INTENT(OUT) :: rhobar(user%gxs:user%gxe,ncomp) +REAL,INTENT(OUT) :: lambda(user%gxs:user%gxe,ncomp) + +!local +INTEGER :: i,j,k +REAL :: dhsk +INTEGER :: fak,n +REAL :: zz,dz,xlo,xhi,integral_lamb,integral_rb +INTEGER, parameter :: NMAX = 800 +REAL,dimension(NMAX) :: x_int, lamb_int, rb_int +REAL,dimension(NMAX) :: y2_lamb, y2_rb +REAL :: rhopjk,rhopjp1k + + +!fak = maxval(fa(1:ncomp)) + +Do k = 1,ncomp + dhsk = dhs(k) + fak = fa(k) + 1 + + Do i = user%xs-fak,user%xe+fak !lambda und rhobar werden bis i+-sig gebraucht -> Schleife bis +- fa + n = 1 !this is the index of the arrays that will be passed to the spline integration routines + x_int = 0.0 + lamb_int = 0.0 + rb_int = 0.0 + + Do j = i-fak,i+fak !um lambda bei i zu berechnen, muss bis +- sig um i integriert werden -> Schleife bis +- fa + rhopjk = rhop(k,j) + rhopjp1k = rhop(k,j+1) + + + If( ( zp(i)-zp(j+1) ) < dhsk .and. ( zp(i) - zp(j) ) >= dhsk ) Then !the position of j+1 is already within i-d while j is still outside this range in this case, the integration steplength (dz) is just the distance, which j+1 overlaps with i-d and what is integrated is the interpolated value of the integrand + + If(n/= 1) stop 'n /=1 in Chain_aux' !here always n=1! + zz = zp(j) - zp(i) !distance between grid points j and i + dz = zp(j+1) - (zp(i) - dhsk) !the part of the intervall between zp(j) and zp(j+1) which is already within i-d + !if(dz < epsilon(dz)) dz = epsilon(dz) !bei unguenstiger Kombination von sig und ngrid kann dz unter Machinengenauigkeit epsilon liegen, dann ist x(2) = x(1) + dz = x(1) -> das fuehrt zu Abbruch in Spline Interpolation + x_int(n) = 0.0 !array containing x-values for spline integration + + lamb_int(n) = rhopjk + (rhopjp1k - rhopjk)/dzp * (dzp-dz) !lineare interpolation analog zum FMT Teil + rb_int(n) = 0.0 !erklärung analog wie bei n3_int in FMT Teil + + + Else If (zp(j) > (zp(i)-dhsk) .and. zp(j) <= (zp(i)+dhsk)) Then !grid point j within i+-d + + n = n + 1 + x_int(n) = x_int(n-1) + dz !first time in this If condition, dz is stil the old value from above! + zz = zp(j) - zp(i) + dz = dzp + lamb_int(n) = rhopjk + rb_int(n) = rhopjk * ( dhsk**2 - zz**2 ) + + If (zp(j) < (zp(i)+dhsk) .and. zp(j+1) >= (zp(i)+dhsk) ) Then !zp(j) is still within zp(i)+d but zp(j+1) is already outside zp(i)+d + + dz = zp(i) + dhsk - zp(j) + !If(dz <= epsilon(dz)) exit !wie oben, kann auch hier bei ungluecklicher Wahl von sig und ngrid dz < eps werden und somit x(n) = x(n-1) -> Abbruch in Spline interpolation. Dann einfach ngrid aendern! + zz = zp(j) - zp(i) + n = n + 1 + x_int(n) = x_int(n-1) + dz + rb_int(n) = 0.0 + lamb_int(n) = rhopjk + (rhopjp1k - rhopjk)/dzp * dz +! If(x_int(n) == x_int(n-1)) Then +! n = n - 1 +! exit +! End If + + End If + End If + End Do + + + + !spline integration + xlo = x_int(1) + xhi = x_int(n) + + If(n > NMAX) stop 'Increase NMAX in Chain_aux (auch in AD Routine!!)' + + call spline ( x_int, lamb_int, n, 1.E30, 1.E30, y2_lamb ) + call spline ( x_int, rb_int, n, 1.E30, 1.E30, y2_rb ) + + call splint_integral ( x_int, lamb_int, y2_lamb, n, xlo, xhi, integral_lamb ) + call splint_integral ( x_int, rb_int, y2_rb, n, xlo, xhi, integral_rb ) + lambda(i,k) = 0.5 * integral_lamb / dhsk + rhobar(i,k) = 0.75 * integral_rb / dhsk**3 + + If(lambda(i,k) < epsilon(dz) ) lambda(i,k) = epsilon(dz) + !If ( lambda(i,k) < 0.5*xx(k)*rho ) write (*,*) 'warning: lambda too low',i,lambda(i,k) + !If ( k == 1 .AND. lambda(i,k) < 0.5*rhob(2,k) ) lambda(i,k) = 0.5*rhob(2,k) + + + End Do + +End Do + + +End Subroutine Chain_aux + + + + + + + + +Subroutine Chain_dFdrho(i,rhop,lambda,rhobar,dF_drho_CHAIN,f_ch,user) + +Use BASIC_VARIABLES, Only: ncomp,parame +Use EOS_VARIABLES, Only: dhs +Use mod_DFT, Only: zp,dzp,fa + +!PETSc module +Use PetscManagement + +#include + +!passed +INTEGER, INTENT(IN) :: i !the grid point to calculate dFdrho at +type (userctx) :: user +PetscScalar :: rhop(ncomp,user%gxs:user%gxe) +REAL,INTENT(IN) :: rhobar(user%gxs:user%gxe,ncomp) +REAL,INTENT(IN) :: lambda(user%gxs:user%gxe,ncomp) +REAL,INTENT(OUT) :: dF_drho_CHAIN(user%xs:user%xe,ncomp) +REAL, INTENT(OUT) :: f_ch + + +!local +INTEGER :: j,k,n +REAL :: dhsk +INTEGER :: fak +REAL :: rhopjk,rhopjp1k,logrho,xlo,xhi +REAL :: ycorr(ncomp),dlny(ncomp,ncomp) +INTEGER, parameter :: NMAX = 800 +REAL,dimension(NMAX) :: x_int, int_1,int_2 !Fehlerwarnung falls 800 ueberschritten einbauen +REAL,dimension(NMAX) :: y2_1, y2_2 +REAL :: dz,zz,integral_1,integral_2 +REAL :: lamy + + + call Cavity_mix(rhobar(i,1:ncomp),ycorr,dlny) + + f_ch = 0.0 + + Do k = 1,ncomp + fak = fa(k) + dhsk = dhs(k) + n = 1 + x_int = 0.0 + int_1 = 0.0 + int_2 = 0.0 + + + Do j = i-fak,i+fak !es muss bis +- sig um i integriert werden + rhopjk = rhop(k,j) + rhopjp1k = rhop(k,j+1) + + If( ( zp(i)-zp(j+1) ) < dhsk .and. ( zp(i) - zp(j) ) >= dhsk ) Then !the position of j+1 is already within i-d while j is still outside this range in this case, the integration steplength (dz) is just the distance, which j+1 overlaps with i-d and what is integrated is the interpolated value of the integrand + + If(n/= 1) stop 'n /=1 in Chain_dFdrho' !here always n=1! + zz = zp(j) - zp(i) !distance between grid points j and i + dz = zp(j+1) - (zp(i) - dhsk) !the part of the intervall between zp(j) and zp(j+1) which is already within i-d + !if(dz < epsilon(dz)) dz = epsilon(dz) !bei unguenstiger Kombination von sig und ngrid kann dz unter Machinengenauigkeit epsilon liegen, dann ist x(2) = x(1) + dz = x(1) -> das fuehrt zu Abbruch in Spline Interpolation + x_int(n) = 0.0 !array containing x-values for spline integration + int_1(n) = 0.0 !erklärung analog wie bei n3_int in FMT Teil + int_2(n) = rhopjk*lambda(j,k) + (rhopjp1k*lambda(j+1,k) - rhopjk*lambda(j,k) )/dzp * (dzp-dz) !lineare interpolation analog zum FMT Teil + + Else If (zp(j) > (zp(i)-dhsk) .and. zp(j) <= (zp(i)+dhsk)) Then !grid point j within i+-d + + n = n + 1 + x_int(n) = x_int(n-1) + dz !first time in this If condition, dz is stil the old value from above! + zz = zp(j) - zp(i) + dz = dzp + int_1(n) = SUM( ( parame(1:ncomp,1)-1.0 ) * rhop(1:ncomp,j)*dlny(1:ncomp,k) ) & + * 0.75/dhsk**3 * (dhsk**2-zz**2) + int_2(n) = rhopjk / lambda(j,k) + + If (zp(j) < (zp(i)+dhsk) .and. zp(j+1) >= (zp(i)+dhsk) ) Then !zp(j) is still within zp(i)+d but zp(j+1) is already outside zp(i)+d + + dz = zp(i) + dhsk - zp(j) + !If(dz <= epsilon(dz)) exit !wie oben, kann auch hier bei ungluecklicher Wahl von sig und ngrid dz < eps werden und somit x(n) = x(n-1) -> Abbruch in Spline interpolation. Dann einfach ngrid aendern! + zz = zp(j) - zp(i) + n = n + 1 + x_int(n) = x_int(n-1) + dz + int_1(n) = 0.0 + int_2(n) = rhopjk*lambda(j,k) + (rhopjp1k*lambda(j+1,k) - rhopjk*lambda(j,k) )/dzp * dz + +! If(x_int(n) == x_int(n-1)) Then +! n = n - 1 +! exit +! End If + + End If + End If + End Do + + !Spline Integration + xlo = x_int(1) + xhi = x_int(n) + + If(n > NMAX) stop 'Increase NMAX in Chain_dFdrho (auch in AD Routine!!)' + + CALL spline ( x_int, int_1, n, 1.E30, 1.E30, y2_1 ) + CALL splint_integral( x_int, int_1, y2_1, n, xlo, xhi, integral_1 ) + CALL spline ( x_int, int_2, n, 1.E30, 1.E30, y2_2 ) + CALL splint_integral( x_int, int_2, y2_2, n, xlo, xhi, integral_2 ) + + If(rhop(k,i) < epsilon(dz)) rhop = epsilon(dz) + + dF_drho_CHAIN(i,k) = (parame(k,1) - 1.0)*log(rhop(k,i)) & + - (parame(k,1) - 1.0) * ( log(ycorr(k)*lambda(i,k))-1.0 + 0.5*integral_2/dhsk ) - integral_1 + + + f_ch = f_ch + ( parame(k,1) - 1.0 ) * rhop(k,i) * ( log(rhop(k,i)) - 1.0 ) & + - ( parame(k,1) - 1.0 ) * rhop(k,i) * ( log(ycorr(k)*lambda(i,k)) - 1.0 ) + + + + + +End Do + + + + + + + + + + + + +End Subroutine Chain_dFdrho + + + + + + + + + + + + + + + + +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! + SUBROUTINE Cavity_mix ( rhoi, ycorr, dlnydr ) +! + USE PARAMETERS, ONLY: PI + USE BASIC_VARIABLES, ONLY: ncomp,parame + USE EOS_VARIABLES, Only: dhs + IMPLICIT NONE +! +! ---------------------------------------------------------------------- + REAL, INTENT(IN) :: rhoi(ncomp) + REAL, INTENT(OUT) :: ycorr(ncomp) + REAL, INTENT(OUT) :: dlnydr(ncomp,ncomp) ! this is: d( ln( yij ) ) / d( rho(k) ) used with i=j +! +! ---------------------------------------------------------------------- + INTEGER :: i, j, k + REAL :: z0, z1, z2, z3, zms, z1_rk, z2_rk, z3_rk + REAL, DIMENSION(ncomp,ncomp) :: dij_ab, gij, gij_rk +! ---------------------------------------------------------------------- + + z0 = PI / 6.0 * SUM( rhoi(1:ncomp) * parame(1:ncomp,1) ) + z1 = PI / 6.0 * SUM( rhoi(1:ncomp) * parame(1:ncomp,1) * dhs(1:ncomp) ) + z2 = PI / 6.0 * SUM( rhoi(1:ncomp) * parame(1:ncomp,1) * dhs(1:ncomp)**2 ) + z3 = PI / 6.0 * SUM( rhoi(1:ncomp) * parame(1:ncomp,1) * dhs(1:ncomp)**3 ) + + zms = 1.0 - z3 + + DO i = 1,ncomp + DO j=1,ncomp + dij_ab(i,j)=dhs(i)*dhs(j)/(dhs(i)+dhs(j)) + ENDDO + END DO + + DO k = 1, ncomp + DO i = 1, ncomp + z1_rk = PI/6.0 * parame(k,1) * dhs(k) + z2_rk = PI/6.0 * parame(k,1) * dhs(k)*dhs(k) + z3_rk = PI/6.0 * parame(k,1) * dhs(k)**3 + !DO j = 1, ncomp + j = i + gij(i,j) = 1.0/zms + 3.0*dij_ab(i,j)*z2/zms/zms & + + 2.0*(dij_ab(i,j)*z2)**2 /zms**3 + !dgijdz(i,j)= 1.0/zms/zms + 3.0*dij_ab(i,j)*z2*(1.0+z3)/z3/zms**3 & + ! + (dij_ab(i,j)*z2/zms/zms)**2 *(4.0+2.0*z3)/z3 + gij_rk(i,j) = z3_rk/zms/zms & + + 3.0*dij_ab(i,j)*(z2_rk+2.0*z2*z3_rk/zms)/zms/zms & + + dij_ab(i,j)**2 *z2/zms**3 *(4.0*z2_rk+6.0*z2*z3_rk/zms) + !END DO + + ycorr(i) = gij(i,i) + dlnydr(i,k) = gij_rk(i,i) / gij(i,i) + + END DO + END DO + +END SUBROUTINE Cavity_mix + + + + + + + + + + +End Module mod_DFT_CHAIN \ No newline at end of file diff --git a/applications/PUfoam/MoDeNaModels/SurfaceTension/src/mod_DFT_CHAIN_d.F90 b/applications/PUfoam/MoDeNaModels/SurfaceTension/src/mod_DFT_CHAIN_d.F90 new file mode 100644 index 000000000..644d8020f --- /dev/null +++ b/applications/PUfoam/MoDeNaModels/SurfaceTension/src/mod_DFT_CHAIN_d.F90 @@ -0,0 +1,431 @@ +!>This file contains the subroutines which calculate the derivatives of the contribution of +!!chain formation to the Helmholtz energy functional. + + + +! Generated by TAPENADE (INRIA, Tropics team) +! Tapenade 3.10 (r5498) - 20 Jan 2015 09:48 +! +MODULE MOD_DFT_CHAIN_D + IMPLICIT NONE + PRIVATE + PUBLIC chain_aux_d + PUBLIC chain_dfdrho_d + +CONTAINS +! Differentiation of chain_aux in forward (tangent) mode: +! variations of useful results: rhobar lambda +! with respect to varying inputs: rhop + SUBROUTINE CHAIN_AUX_D(rhop, rhopd, rhobar, rhobard, lambda, lambdad, & +& user) + USE BASIC_VARIABLES, ONLY : ncomp + USE EOS_VARIABLES, Only: dhs,rho + USE MOD_DFT, ONLY : zp, dzp, fa + + !PETSc module + Use PetscManagement + + IMPLICIT NONE + +#include + + +!passed +type (userctx) :: user +PetscScalar :: rhop(ncomp,user%gxs:user%gxe) +PetscScalar :: rhopd(ncomp,user%gxs:user%gxe) +REAL,INTENT(OUT) :: rhobar(user%gxs:user%gxe,ncomp) +REAL,INTENT(OUT) :: rhobard(user%gxs:user%gxe,ncomp) +REAL,INTENT(OUT) :: lambda(user%gxs:user%gxe,ncomp) +REAL,INTENT(OUT) :: lambdad(user%gxs:user%gxe,ncomp) + +!local + INTEGER :: i, j, k + REAL :: dhsk + INTEGER :: fak, n + REAL :: zz, dz, xlo, xhi, integral_lamb, integral_rb + REAL :: integral_lambd, integral_rbd + INTEGER, parameter :: NMAX = 800 + REAL, DIMENSION(NMAX) :: x_int, lamb_int, rb_int + REAL, DIMENSION(NMAX) :: lamb_intd, rb_intd + REAL, DIMENSION(NMAX) :: y2_lamb, y2_rb + REAL, DIMENSION(NMAX) :: y2_lambd, y2_rbd + REAL :: rhopjk, rhopjp1k + REAL :: rhopjkd, rhopjp1kd + INTRINSIC EPSILON + REAL :: result1 + + + + rhobard = 0.0 + lambdad = 0.0 + y2_rbd = 0.0 + y2_lambd = 0.0 +!fak = maxval(fa(1:ncomp)) + DO k=1,ncomp + dhsk = dhs(k) + fak = fa(k) + 1 + + Do i = user%xs-fak,user%xe+fak !lambda und rhobar werden bis i+-sig gebraucht -> Schleife bis +- fa + n = 1 + x_int = 0.0 + lamb_int = 0.0 + rb_int = 0.0 + rb_intd = 0.0 + lamb_intd = 0.0 +!um lambda bei i zu berechnen, muss bis +- sig um i integriert werden -> Schleife bis +- fa + DO j=i-fak,i+fak + rhopjkd = rhopd(k, j) + rhopjk = rhop(k, j) + rhopjp1kd = rhopd(k, j+1) + rhopjp1k = rhop(k, j+1) + IF (zp(i) - zp(j+1) .LT. dhsk .AND. zp(i) - zp(j) .GE. dhsk) & +& THEN +!the position of j+1 is already within i-d while j is still outside this range in this case, the integration steplength (dz) is j +!ust the distance, which j+1 overlaps with i-d and what is integrated is the interpolated value of the integrand +!here always n=1! + IF (n .NE. 1) THEN + GOTO 100 + ELSE +!distance between grid points j and i + zz = zp(j) - zp(i) +!the part of the intervall between zp(j) and zp(j+1) which is already within i-d + dz = zp(j+1) - (zp(i)-dhsk) +!if(dz < epsilon(dz)) dz = epsilon(dz) !bei unguenstiger Kombination von sig und ngrid kann dz unter Machinengenauigkeit epsilon +!liegen, dann ist x(2) = x(1) + dz = x(1) -> das fuehrt zu Abbruch in Spline Interpolation +!array containing x-values for spline integration + x_int(n) = 0.0 +!lineare interpolation analog zum FMT Teil + lamb_intd(n) = rhopjkd + (dzp-dz)*(rhopjp1kd-rhopjkd)/dzp + lamb_int(n) = rhopjk + (rhopjp1k-rhopjk)/dzp*(dzp-dz) +!erklärung analog wie bei n3_int in FMT Teil + rb_intd(n) = 0.0 + rb_int(n) = 0.0 + END IF + ELSE IF (zp(j) .GT. zp(i) - dhsk .AND. zp(j) .LE. zp(i) + dhsk& +& ) THEN +!grid point j within i+-d + n = n + 1 +!first time in this If condition, dz is stil the old value from above! + x_int(n) = x_int(n-1) + dz + zz = zp(j) - zp(i) + dz = dzp + lamb_intd(n) = rhopjkd + lamb_int(n) = rhopjk + rb_intd(n) = (dhsk**2-zz**2)*rhopjkd + rb_int(n) = rhopjk*(dhsk**2-zz**2) + IF (zp(j) .LT. zp(i) + dhsk .AND. zp(j+1) .GE. zp(i) + dhsk& +& ) THEN +!zp(j) is still within zp(i)+d but zp(j+1) is already outside zp(i)+d + dz = zp(i) + dhsk - zp(j) +!If(dz <= epsilon(dz)) exit !wie oben, kann auch hier bei ungluecklicher Wahl von sig und ngrid dz < eps werden und somit x(n) +!= x(n-1) -> Abbruch in Spline interpolation. Dann einfach ngrid aendern! + zz = zp(j) - zp(i) + n = n + 1 + x_int(n) = x_int(n-1) + dz + rb_intd(n) = 0.0 + rb_int(n) = 0.0 + lamb_intd(n) = rhopjkd + dz*(rhopjp1kd-rhopjkd)/dzp + lamb_int(n) = rhopjk + (rhopjp1k-rhopjk)/dzp*dz +! If(x_int(n) == x_int(n-1)) Then +! n = n - 1 +! exit +! End If + END IF + END IF + END DO +!spline integration + xlo = x_int(1) + xhi = x_int(n) + CALL SPLINE_D(x_int, lamb_int, lamb_intd, n, 1.e30, 1.e30, & +& y2_lamb, y2_lambd) + CALL SPLINE_D(x_int, rb_int, rb_intd, n, 1.e30, 1.e30, y2_rb, & +& y2_rbd) + CALL SPLINT_INTEGRAL_D(x_int, lamb_int, lamb_intd, y2_lamb, & +& y2_lambd, n, xlo, xhi, integral_lamb, & +& integral_lambd) + CALL SPLINT_INTEGRAL_D(x_int, rb_int, rb_intd, y2_rb, y2_rbd, n& +& , xlo, xhi, integral_rb, integral_rbd) + lambdad(i, k) = 0.5*integral_lambd/dhsk + lambda(i, k) = 0.5*integral_lamb/dhsk + rhobard(i, k) = 0.75*integral_rbd/dhsk**3 + rhobar(i, k) = 0.75*integral_rb/dhsk**3 + result1 = EPSILON(dz) + IF (lambda(i, k) .LT. result1) lambda(i, k) = EPSILON(dz) + END DO + END DO + GOTO 110 + 100 STOP + 110 CONTINUE + END SUBROUTINE CHAIN_AUX_D + + + + +! Differentiation of chain_dfdrho in forward (tangent) mode: +! variations of useful results: df_drho_chain rhop +! with respect to varying inputs: rhobar df_drho_chain lambda +! rhop + SUBROUTINE CHAIN_DFDRHO_D(i, rhop, rhopd, lambda, lambdad, rhobar, & +& rhobard, df_drho_chain, df_drho_chaind, user) + USE BASIC_VARIABLES, ONLY : ncomp,parame + USE EOS_VARIABLES, Only: dhs + USE MOD_DFT, ONLY : zp, dzp, fa + + !PETSc module + Use PetscManagement + IMPLICIT NONE + +#include + + +!passed +INTEGER, INTENT(IN) :: i !the grid point to calculate dFdrho at +type (userctx) :: user +PetscScalar :: rhop(ncomp,user%gxs:user%gxe) +PetscScalar :: rhopd(ncomp,user%gxs:user%gxe) +REAL,INTENT(IN) :: rhobar(user%gxs:user%gxe,ncomp) +REAL,INTENT(IN) :: rhobard(user%gxs:user%gxe,ncomp) +REAL,INTENT(IN) :: lambda(user%gxs:user%gxe,ncomp) +REAL,INTENT(IN) :: lambdad(user%gxs:user%gxe,ncomp) + + + +REAL,INTENT(OUT) :: dF_drho_CHAIN(user%xs:user%xe,ncomp) +REAL,INTENT(OUT) :: dF_drho_CHAINd(user%xs:user%xe,ncomp) + + +!local + INTEGER :: j, k, n + REAL :: dhsk + INTEGER :: fak + REAL :: rhopjk, rhopjp1k, logrho, xlo, xhi + REAL :: rhopjkd, rhopjp1kd + REAL :: ycorr(ncomp), dlny(ncomp, ncomp) + REAL :: ycorrd(ncomp), dlnyd(ncomp, ncomp) + INTEGER, parameter :: NMAX = 800 + REAL, DIMENSION(NMAX) :: x_int, int_1, int_2 + REAL, DIMENSION(NMAX) :: int_1d, int_2d + REAL, DIMENSION(NMAX) :: y2_1, y2_2 + REAL, DIMENSION(NMAX) :: y2_1d, y2_2d + REAL :: dz, zz, integral_1, integral_2 + REAL :: integral_1d, integral_2d + REAL :: lamy + INTRINSIC SUM + INTRINSIC EPSILON + INTRINSIC LOG + REAL, DIMENSION(ncomp) :: arg1 + REAL, DIMENSION(ncomp) :: arg1d + REAL :: result1 + REAL :: arg10 + REAL :: arg10d + + + + + + CALL CAVITY_MIX_D(rhobar(i, 1:ncomp), rhobard(i, 1:ncomp), ycorr, & +& ycorrd, dlny, dlnyd) + y2_1d = 0.0 + y2_2d = 0.0 + DO k=1,ncomp + fak = fa(k) + dhsk = dhs(k) + n = 1 + x_int = 0.0 + int_1 = 0.0 + int_2 = 0.0 + int_1d = 0.0 + int_2d = 0.0 +!es muss bis +- sig um i integriert werden + DO j=i-fak,i+fak + rhopjkd = rhopd(k, j) + rhopjk = rhop(k, j) + rhopjp1kd = rhopd(k, j+1) + rhopjp1k = rhop(k, j+1) + IF (zp(i) - zp(j+1) .LT. dhsk .AND. zp(i) - zp(j) .GE. dhsk) & +& THEN +!the position of j+1 is already within i-d while j is still outside this range in this case, the integration steplength (dz) is j +!ust the distance, which j+1 overlaps with i-d and what is integrated is the interpolated value of the integrand +!here always n=1! + IF (n .NE. 1) THEN + GOTO 100 + ELSE +!distance between grid points j and i + zz = zp(j) - zp(i) +!the part of the intervall between zp(j) and zp(j+1) which is already within i-d + dz = zp(j+1) - (zp(i)-dhsk) +!if(dz < epsilon(dz)) dz = epsilon(dz) !bei unguenstiger Kombination von sig und ngrid kann dz unter Machinengenauigkeit epsilon +!liegen, dann ist x(2) = x(1) + dz = x(1) -> das fuehrt zu Abbruch in Spline Interpolation +!array containing x-values for spline integration + x_int(n) = 0.0 +!erklärung analog wie bei n3_int in FMT Teil + int_1d(n) = 0.0 + int_1(n) = 0.0 +!lineare interpolation analog zum FMT Teil + int_2d(n) = rhopjkd*lambda(j, k) + rhopjk*lambdad(j, k) + (& +& dzp-dz)*(rhopjp1kd*lambda(j+1, k)+rhopjp1k*lambdad(j+1, k)& +& -rhopjkd*lambda(j, k)-rhopjk*lambdad(j, k))/dzp + int_2(n) = rhopjk*lambda(j, k) + (rhopjp1k*lambda(j+1, k)-& +& rhopjk*lambda(j, k))/dzp*(dzp-dz) + END IF + ELSE IF (zp(j) .GT. zp(i) - dhsk .AND. zp(j) .LE. zp(i) + dhsk) & +& THEN +!grid point j within i+-d + n = n + 1 +!first time in this If condition, dz is stil the old value from above! + x_int(n) = x_int(n-1) + dz + zz = zp(j) - zp(i) + dz = dzp + arg1d(:) = (parame(1:ncomp,1)-1.0)*(rhopd(1:ncomp, j)*dlny(1:ncomp& +& , k)+rhop(1:ncomp, j)*dlnyd(1:ncomp, k)) + arg1(:) = (parame(1:ncomp,1)-1.0)*rhop(1:ncomp, j)*dlny(1:ncomp, k& +& ) + int_1d(n) = (dhsk**2-zz**2)*0.75*SUM(arg1d(:))/dhsk**3 + int_1(n) = SUM(arg1(:))*0.75/dhsk**3*(dhsk**2-zz**2) + int_2d(n) = (rhopjkd*lambda(j, k)-rhopjk*lambdad(j, k))/lambda& +& (j, k)**2 + int_2(n) = rhopjk/lambda(j, k) + IF (zp(j) .LT. zp(i) + dhsk .AND. zp(j+1) .GE. zp(i) + dhsk) & +& THEN +!zp(j) is still within zp(i)+d but zp(j+1) is already outside zp(i)+d + dz = zp(i) + dhsk - zp(j) +!If(dz <= epsilon(dz)) exit !wie oben, kann auch hier bei ungluecklicher Wahl von sig und ngrid dz < eps werden und somit x(n) +!= x(n-1) -> Abbruch in Spline interpolation. Dann einfach ngrid aendern! + zz = zp(j) - zp(i) + n = n + 1 + x_int(n) = x_int(n-1) + dz + int_1d(n) = 0.0 + int_1(n) = 0.0 + int_2d(n) = rhopjkd*lambda(j, k) + rhopjk*lambdad(j, k) + dz& +& *(rhopjp1kd*lambda(j+1, k)+rhopjp1k*lambdad(j+1, k)-& +& rhopjkd*lambda(j, k)-rhopjk*lambdad(j, k))/dzp + int_2(n) = rhopjk*lambda(j, k) + (rhopjp1k*lambda(j+1, k)-& +& rhopjk*lambda(j, k))/dzp*dz +! If(x_int(n) == x_int(n-1)) Then +! n = n - 1 +! exit +! End If + END IF + END IF + END DO +!Spline Integration + xlo = x_int(1) + xhi = x_int(n) + CALL SPLINE_D(x_int, int_1, int_1d, n, 1.e30, 1.e30, y2_1, y2_1d) + CALL SPLINT_INTEGRAL_D(x_int, int_1, int_1d, y2_1, y2_1d, n, xlo, & +& xhi, integral_1, integral_1d) + CALL SPLINE_D(x_int, int_2, int_2d, n, 1.e30, 1.e30, y2_2, y2_2d) + CALL SPLINT_INTEGRAL_D(x_int, int_2, int_2d, y2_2, y2_2d, n, xlo, & +& xhi, integral_2, integral_2d) + result1 = EPSILON(dz) + IF (rhop(k, i) .LT. result1) THEN + rhop = EPSILON(dz) + rhopd = 0.0 + END IF + arg10d = ycorrd(k)*lambda(i, k) + ycorr(k)*lambdad(i, k) + arg10 = ycorr(k)*lambda(i, k) + df_drho_chaind(i, k) = (parame(k,1)-1.0)*rhopd(k, i)/rhop(k, i) - (& +& parame(k,1)-1.0)*(arg10d/arg10+0.5*integral_2d/dhsk) - integral_1d + df_drho_chain(i, k) = (parame(k,1)-1.0)*LOG(rhop(k, i)) - (parame(k,1)-1.0& +& )*(LOG(arg10)-1.0+0.5*integral_2/dhsk) - integral_1 + END DO + GOTO 110 + 100 STOP + 110 CONTINUE + END SUBROUTINE CHAIN_DFDRHO_D + + + +! Differentiation of cavity_mix in forward (tangent) mode: +! variations of useful results: ycorr dlnydr +! with respect to varying inputs: rhoi +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! + SUBROUTINE CAVITY_MIX_D(rhoi, rhoid, ycorr, ycorrd, dlnydr, dlnydrd) +! + USE PARAMETERS, ONLY : pi + USE BASIC_VARIABLES, ONLY : ncomp,parame + USE EOS_VARIABLES, Only: dhs + IMPLICIT NONE +! +! ---------------------------------------------------------------------- + REAL, INTENT(IN) :: rhoi(ncomp) + REAL, INTENT(IN) :: rhoid(ncomp) + REAL, INTENT(OUT) :: ycorr(ncomp) + REAL, INTENT(OUT) :: ycorrd(ncomp) +! this is: d( ln( yij ) ) / d( rho(k) ) used with i=j + REAL, INTENT(OUT) :: dlnydr(ncomp, ncomp) + REAL, INTENT(OUT) :: dlnydrd(ncomp, ncomp) +! +! ---------------------------------------------------------------------- + INTEGER :: i, j, k + REAL :: z0, z1, z2, z3, zms, z1_rk, z2_rk, z3_rk + REAL :: z2d, z3d, zmsd + REAL, DIMENSION(ncomp, ncomp) :: dij_ab, gij, gij_rk + REAL, DIMENSION(ncomp, ncomp) :: gijd, gij_rkd + INTRINSIC SUM + REAL, DIMENSION(ncomp) :: arg1 + REAL, DIMENSION(ncomp) :: arg1d +! ---------------------------------------------------------------------- + arg1(:) = rhoi(1:ncomp)*parame(1:ncomp,1) + z0 = pi/6.0*SUM(arg1(:)) + arg1(:) = rhoi(1:ncomp)*parame(1:ncomp,1)*dhs(1:ncomp) + z1 = pi/6.0*SUM(arg1(:)) + arg1d(:) = parame(1:ncomp,1)*dhs(1:ncomp)**2*rhoid(1:ncomp) + arg1(:) = rhoi(1:ncomp)*parame(1:ncomp,1)*dhs(1:ncomp)**2 + z2d = pi*SUM(arg1d(:))/6.0 + z2 = pi/6.0*SUM(arg1(:)) + arg1d(:) = parame(1:ncomp,1)*dhs(1:ncomp)**3*rhoid(1:ncomp) + arg1(:) = rhoi(1:ncomp)*parame(1:ncomp,1)*dhs(1:ncomp)**3 + z3d = pi*SUM(arg1d(:))/6.0 + z3 = pi/6.0*SUM(arg1(:)) + zmsd = -z3d + zms = 1.0 - z3 + DO i=1,ncomp + DO j=1,ncomp + dij_ab(i, j) = dhs(i)*dhs(j)/(dhs(i)+dhs(j)) + END DO + END DO + ycorrd = 0.0 + dlnydrd = 0.0 + gij_rkd = 0.0 + gijd = 0.0 + DO k=1,ncomp + DO i=1,ncomp + z1_rk = pi/6.0*parame(k,1)*dhs(k) + z2_rk = pi/6.0*parame(k,1)*dhs(k)*dhs(k) + z3_rk = pi/6.0*parame(k,1)*dhs(k)**3 +!DO j = 1, ncomp + j = i + gijd(i, j) = ((3.0*dij_ab(i, j)*z2d*zms-3.0*dij_ab(i, j)*z2*zmsd& +& )/zms-3.0*dij_ab(i, j)*z2*zmsd/zms)/zms**2 - zmsd/zms**2 + (& +& 2.0*2*dij_ab(i, j)**2*z2*z2d*zms**3-2.0*dij_ab(i, j)**2*z2**2*& +& 3*zms**2*zmsd)/(zms**3)**2 + gij(i, j) = 1.0/zms + 3.0*dij_ab(i, j)*z2/zms/zms + 2.0*(dij_ab(& +& i, j)*z2)**2/zms**3 +!dgijdz(i,j)= 1.0/zms/zms + 3.0*dij_ab(i,j)*z2*(1.0+z3)/z3/zms**3 & +! + (dij_ab(i,j)*z2/zms/zms)**2 *(4.0+2.0*z3)/z3 + gij_rkd(i, j) = (-2)*(z3_rk*zmsd/zms)/zms**2 + ((3.0*dij_ab(i, j& +& )*(2.0*z3_rk*z2d*zms-2.0*z2*z3_rk*zmsd)/zms-3.0*dij_ab(i, j)*(& +& z2_rk+2.0*z2*z3_rk/zms)*zmsd)/zms-3.0*dij_ab(i, j)*(z2_rk+2.0*& +& z2*z3_rk/zms)*zmsd/zms)/zms**2 + (dij_ab(i, j)**2*z2d*zms**3-& +& dij_ab(i, j)**2*z2*3*zms**2*zmsd)*(4.0*z2_rk+6.0*z2*z3_rk/zms)& +& /zms**6 + dij_ab(i, j)**2*z2*(6.0*z3_rk*z2d*zms-6.0*z2*z3_rk*& +& zmsd)/zms**5 + gij_rk(i, j) = z3_rk/zms/zms + 3.0*dij_ab(i, j)*(z2_rk+2.0*z2*& +& z3_rk/zms)/zms/zms + dij_ab(i, j)**2*z2/zms**3*(4.0*z2_rk+6.0*& +& z2*z3_rk/zms) +!END DO + ycorrd(i) = gijd(i, i) + ycorr(i) = gij(i, i) + dlnydrd(i, k) = (gij_rkd(i, i)*gij(i, i)-gij_rk(i, i)*gijd(i, i)& +& )/gij(i, i)**2 + dlnydr(i, k) = gij_rk(i, i)/gij(i, i) + END DO + END DO + END SUBROUTINE CAVITY_MIX_D + +END MODULE MOD_DFT_CHAIN_D diff --git a/applications/PUfoam/MoDeNaModels/SurfaceTension/src/mod_DFT_DISP_WDA.F90 b/applications/PUfoam/MoDeNaModels/SurfaceTension/src/mod_DFT_DISP_WDA.F90 new file mode 100644 index 000000000..15e414b50 --- /dev/null +++ b/applications/PUfoam/MoDeNaModels/SurfaceTension/src/mod_DFT_DISP_WDA.F90 @@ -0,0 +1,697 @@ +!>This file contains the subroutines which calculate the contribution of +!!dispersion to the Helmholtz energy functional. + + + + + + + +Module mod_DFT_DISP_WDA + + +Implicit None + +Private + +Public :: rhoi_disp_wd +Public :: a_disp_pcsaft +Public :: dF_disp_drho_wda + + + + + + Contains + + + + SUBROUTINE rhoi_disp_wd ( discret, fa_psi, fa_psi_max, psi_j, rhop, rhoi_disp,user ) + + + Use PetscManagement + Use basic_variables, ONLY: ncomp, t, parame + Use mod_DFT, Only: zp,dzp + IMPLICIT NONE + +#include + +! +! ---------------------------------------------------------------------- + Type (userctx) :: user + PetscScalar :: rhop(ncomp,user%gxs:user%gxe) + INTEGER, INTENT(IN) :: discret + INTEGER, INTENT(IN) :: fa_psi(ncomp) + INTEGER, INTENT(IN) :: fa_psi_max +! REAL, INTENT(IN) :: dzp + REAL, INTENT(IN) :: psi_j(ncomp) +! REAL, INTENT(IN) :: zp(user%gxs:user%gxe) + REAL, INTENT(OUT) :: rhoi_disp(user%gxs:user%gxe,ncomp) +! ---------------------------------------------------------------------- + INTEGER :: ii, jj, icomp, nn + REAL :: zmin, zl, zr + REAL :: int1, zz1, xl, xh + REAL, DIMENSION(700) :: y2, rx, ry1 +! ---------------------------------------------------------------------- + +!write(*,*)'rhoi_wd' + + zmin = 1d-6 + DO icomp = 1, ncomp + DO ii = (user%xs-fa_psi_max),(user%xe+fa_psi_max)!(-fa_psi_max), (discret+fa_psi_max) + nn = 0 + zl = zp(ii) - psi_j(icomp) + zr = zp(ii) + psi_j(icomp) + DO jj = (ii-fa_psi(icomp)), (ii+fa_psi(icomp)) + IF ( zp(jj+1) > (zl+zmin) ) THEN + ! first position: left side of the sphere: zl. Linear Interpolation of h's + IF ( nn == 0 ) THEN + nn = nn + 1 + rx(1) = zl + ry1(1) = 0.0 ! = 0.75*rhop(ii-fa,icomp)*( d.**2 -d.**2 ) +!write(*,*)'FIRST',nn,rx(nn),ry1(nn) + ! middle position: within the sphere: zl < jj < zr + ELSE + nn = nn + 1 + zz1 = zp(jj)-zp(ii) ! distance z12 between 1 and 2 + rx(nn) = zp(jj) + ry1(nn) = rhop(icomp,jj) * (psi_j(icomp)*psi_j(icomp) - zz1*zz1) +!write(*,*)'MIDDLE',nn,rx(nn),ry1(nn) + ! last position: right side of the sphere: zr. Linear Interpolation of h's + IF ( zp(jj+1) > (zr-zmin) ) THEN + nn = nn + 1 + rx(nn) = zr + ry1(nn) = 0.0 +!write(*,*)'LAST',nn,rx(nn),ry1(nn) + EXIT + END IF + END IF + END IF + END DO + xl = rx(1) + xh = rx(nn) + + if( nn >= 700 ) then + write(*,*) 'rhoi_disp_wd: bigger vectors rx, ry1, ry2, ... required!', nn + pause + end if + + CALL spline ( rx(1:nn), ry1(1:nn), nn, 1.E30, 1.E30, y2(1:nn) ) + CALL splint_integral ( rx(1:nn), ry1(1:nn), y2(1:nn), nn, xl, xh, int1 ) + rhoi_disp(ii,icomp) = int1 * 0.75/psi_j(icomp)**3 + + if ( rhoi_disp(ii,icomp) < 0.0 ) then + rhoi_disp(ii,icomp) = 0.0 + do jj = 2, nn + rhoi_disp(ii,icomp) = rhoi_disp(ii,icomp) + (ry1(jj)+ry1(jj-1))/2.0 *(rx(jj)-rx(jj-1)) + end do + end if + if ( rhoi_disp(ii,icomp) < 0.0 ) rhoi_disp(ii,icomp) = rhop(icomp,ii) + END DO + END DO + + +END SUBROUTINE rhoi_disp_wd + + + + + + + + + +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! SUBROUTINE a_disp_pcsaft +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! + SUBROUTINE a_disp_pcsaft( discret, fa_psi, fa_psi_max, rhoi_disp, rho_disp, adisp, mydisp, dadisp_dr,user ) + + Use PetscManagement +! + USE parameters, ONLY: PI, np, nc + USE basic_variables, ONLY: ncomp, t, parame, xi, densta, ensemble_flag + USE eos_variables, ONLY: dhs, sig_ij, uij + USE eos_constants, ONLY: ap, bp + IMPLICIT NONE + +#include + + + + +! +! ---------------------------------------------------------------------- + Type (userctx) :: user + INTEGER, INTENT(IN) :: discret + INTEGER, INTENT(IN) :: fa_psi(ncomp) + INTEGER, INTENT(IN) :: fa_psi_max + REAL, INTENT(IN) :: rhoi_disp(user%gxs:user%gxe,ncomp) + REAL, INTENT(OUT) :: rho_disp(user%gxs:user%gxe) + REAL, INTENT(OUT) :: adisp(user%gxs:user%gxe) + REAL, INTENT(OUT) :: mydisp(user%gxs:user%gxe,ncomp) + REAL, INTENT(OUT) :: dadisp_dr(user%gxs:user%gxe,ncomp) +! ---------------------------------------------------------------------- + INTEGER :: jj, m + INTEGER :: icomp, jcomp, kcomp + REAL, DIMENSION(ncomp) :: x_disp + REAL :: eta_disp, zms_disp + REAL, DIMENSION(0:6) :: apar, bpar, apar_rk, bpar_rk + REAL :: m_mean, C1, I1, I2 + REAL :: r2_ord1, r2_ord2 + REAL :: eta_rk, m_mean_rk, zms2eta + REAL :: C1_m_mean, C1_eta, C1_rk + REAL :: I1_rk, I2_rk + REAL :: r2_ord1_rk, r2_ord2_rk + REAL :: term1, term2, term3 + INTEGER :: iphas + REAL, DIMENSION(np,nc) :: mydisp2 +! ---------------------------------------------------------------------- + + DO icomp = 1, ncomp + DO jj = (user%xs-fa_psi_max),(user%xe+fa_psi_max)!(-fa_psi_max), (discret+fa_psi_max) + m_mean = 0. + eta_disp = 0. +! rho_disp(jj) = sum( rhop(jj,1:ncomp) ) + rho_disp(jj) = sum( rhoi_disp(jj,1:ncomp) ) + do kcomp=1, ncomp +! x_disp(kcomp) = rhop(jj,kcomp) / rho_disp(jj) + x_disp(kcomp) = rhoi_disp(jj,kcomp) / rho_disp(jj) + m_mean = m_mean + x_disp(kcomp) * parame(kcomp,1) +! eta_disp = eta_disp + rhop(jj,kcomp) * parame(kcomp,1) * dhs(kcomp)**3. + eta_disp = eta_disp + rhoi_disp(jj,kcomp) * parame(kcomp,1) * dhs(kcomp)**3. + end do + eta_disp = eta_disp * PI / 6. + zms_disp = 1. - eta_disp + if( zms_disp <= 0. ) write(*,'(a56,i6,f12.5)') 'system too dense for disp contribution ( jj, eta_disp ):', jj, eta_disp + + + ! quantities of the dispersive free energy contribution + I1 = 0. + I2 = 0. + do m = 0, 6 + apar(m) = ap(m,1) + (1.-1./m_mean)*ap(m,2) + (1.-1./m_mean)*(1.-2./m_mean)*ap(m,3) + bpar(m) = bp(m,1) + (1.-1./m_mean)*bp(m,2) + (1.-1./m_mean)*(1.-2./m_mean)*bp(m,3) + I1 = I1 + apar(m) * eta_disp**m + I2 = I2 + bpar(m) * eta_disp**m + end do + + r2_ord1 = 0. + r2_ord2 = 0. + do kcomp = 1, ncomp + do jcomp = 1, ncomp + r2_ord1 = r2_ord1 + rhoi_disp(jj,kcomp)*rhoi_disp(jj,jcomp)*parame(kcomp,1) & + *parame(jcomp,1)*sig_ij(kcomp,jcomp)**3 * uij(kcomp,jcomp)/t + r2_ord2 = r2_ord2 + rhoi_disp(jj,kcomp)*rhoi_disp(jj,jcomp)*parame(kcomp,1) & + *parame(jcomp,1)*sig_ij(kcomp,jcomp)**3 * (uij(kcomp,jcomp)/t)**2 + end do + end do + + C1 = (1.-m_mean)*(20.*eta_disp-27.*eta_disp**2 +12.*eta_disp**3 -2.*eta_disp**4 )/(zms_disp*(2.-eta_disp))**2 + C1 = 1. + m_mean*(8.*eta_disp-2.*eta_disp**2)/zms_disp**4 + C1 + C1 = 1. / C1 + + + ! dispersive free energy contribution + adisp(jj) = -2.*PI*I1*r2_ord1/rho_disp(jj) - PI*C1*m_mean*I2*r2_ord2/rho_disp(jj) + + + ! quantity-derivatives of the dispersive free energy contribution + m_mean_rk = ( parame(icomp,1) - m_mean ) / rho_disp(jj) + + do m = 0, 6 + apar_rk(m) = m_mean_rk/m_mean**2 * ( ap(m,2) + (3. - 4./m_mean) * ap(m,3) ) + bpar_rk(m) = m_mean_rk/m_mean**2 * ( bp(m,2) + (3. - 4./m_mean) * bp(m,3) ) + end do + eta_rk = parame(icomp,1) * dhs(icomp)**3. * PI / 6. + I1_rk = apar_rk(0) + apar(1)*eta_rk + apar_rk(1)*eta_disp + I2_rk = bpar_rk(0) + bpar(1)*eta_rk + bpar_rk(1)*eta_disp + do m = 2, 6 + I1_rk = I1_rk + apar(m)*REAL(m)*eta_disp**REAL(m-1)*eta_rk + apar_rk(m)*eta_disp**REAL(m) + I2_rk = I2_rk + bpar(m)*REAL(m)*eta_disp**REAL(m-1)*eta_rk + bpar_rk(m)*eta_disp**REAL(m) + end do + + r2_ord1_rk = 0. + r2_ord2_rk = 0. + do kcomp = 1,ncomp + r2_ord1_rk = r2_ord1_rk + rhoi_disp(jj,kcomp) * parame(kcomp,1) * sig_ij(icomp,kcomp)**3 * uij(icomp,kcomp)/t + r2_ord2_rk = r2_ord2_rk + rhoi_disp(jj,kcomp) * parame(kcomp,1) * sig_ij(icomp,kcomp)**3 *(uij(icomp,kcomp)/t)**2 + end do + r2_ord1_rk = 2. * parame(icomp,1) * r2_ord1_rk + r2_ord2_rk = 2. * parame(icomp,1) * r2_ord2_rk + + zms2eta = zms_disp * (2.-eta_disp) + C1_m_mean = ( 8.*eta_disp - 2.*eta_disp*eta_disp ) / zms_disp**4 & + - ( 20.*eta_disp - 27.*eta_disp*eta_disp + 12.*eta_disp**3 - 2.*eta_disp**4 ) / zms2eta**2 + C1_eta = m_mean * ( 8. + 20.*eta_disp - 4.*eta_disp*eta_disp ) / zms_disp**5 & + + (1. - m_mean) * ( 40. - 48.*eta_disp + 12.*eta_disp*eta_disp + 2.*eta_disp**3 ) / zms2eta**3 + C1_rk = - C1 * C1 * ( eta_rk * C1_eta + m_mean_rk * C1_m_mean ) + + + ! chemical potential and derivative of adisp (analytically) + term1 = - 2. * PI * ( I1 * r2_ord1_rk + r2_ord1 * I1_rk ) + term2 = - PI * C1 * m_mean * ( I2 * r2_ord2_rk + r2_ord2 * I2_rk ) + term3 = - PI * I2 * r2_ord2 * ( m_mean * C1_rk + C1 * m_mean_rk ) + mydisp(jj,icomp) = term1 + term2 + term3 + dadisp_dr(jj,icomp) = ( mydisp(jj,icomp) - adisp(jj) ) / rho_disp(jj) + + + ! chemical potential and derivative of adisp (numerically) +! do kcomp=1, ncomp +! xi(1,kcomp) = x_disp(kcomp) +! end do +! iphas = 1 +! ensemble_flag = 'tv' +! densta(1) = eta_disp +! call ONLY_ONE_TERM_EOS_NUMERICAL ( 'disp_term', 'PC-SAFT ' ) +! if( rho_disp(jj) /= 0. ) CALL FUGACITY(mydisp2) +! call RESTORE_PREVIOUS_EOS_NUMERICAL +! mydisp(jj,1:ncomp) = mydisp2(iphas,1:ncomp) +! dadisp_dr(jj,icomp) = ( mydisp(jj,icomp) - adisp(jj) ) / rho_disp(jj) + + + if( rho_disp(jj) == 0. ) then + adisp(jj) = 0. + mydisp(jj,icomp) = 0. + dadisp_dr(jj,icomp) = 0. + end if + + END DO + END DO + + +END SUBROUTINE a_disp_pcsaft + + + + + + + +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! SUBROUTINE dF_disp_drho_wda +!WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW +! + SUBROUTINE dF_disp_drho_wda( ii, WDA_var, fa_psi, psi_j, rhop, rhop_sum, & + rhoi_disp, rho_disp, adisp, mydisp, dadisp_dr, dF_drho_att,user ) + + Use PetscManagement + Use basic_variables, ONLY: ncomp + Use mod_DFT, Only: zp + IMPLICIT NONE + +#include + +! +! ---------------------------------------------------------------------- + Type (userctx) :: user + PetscScalar :: rhop(ncomp,user%gxs:user%gxe) +! +! ---------------------------------------------------------------------- + INTEGER, INTENT(IN) :: ii, WDA_var + INTEGER, INTENT(IN) :: fa_psi(ncomp) + REAL, INTENT(IN) :: psi_j(ncomp) +! REAL, INTENT(IN) :: zp(user%gxs:user%gxe) + REAL, INTENT(IN) :: adisp(user%gxs:user%gxe) + REAL, INTENT(IN) :: mydisp(user%gxs:user%gxe,ncomp) + REAL, INTENT(IN) :: rhop_sum(user%gxs:user%gxe) + REAL, INTENT(IN) :: rhoi_disp(user%gxs:user%gxe,ncomp) + REAL, INTENT(IN) :: rho_disp(user%gxs:user%gxe) + REAL, INTENT(IN) :: dadisp_dr(user%gxs:user%gxe,ncomp) + REAL, INTENT(OUT) :: dF_drho_att(ncomp) +! ---------------------------------------------------------------------- + INTEGER :: jj, icomp, nn + REAL :: int3 + REAL :: zmin, zl, zr, zz1, xl, xh + REAL, DIMENSION(700) :: y2, hx, hy3 +! ---------------------------------------------------------------------- + + zmin = 1d-6 + DO icomp = 1, ncomp + nn = 0 + zl = zp(ii) - psi_j(icomp) + zr = zp(ii) + psi_j(icomp) + DO jj = (ii-fa_psi(icomp)), (ii+fa_psi(icomp)) + IF ( zp(jj+1) > (zl+zmin) ) THEN + ! first position: left side of the sphere: zl. Linear Interpolation of h's + IF ( nn == 0 ) THEN + nn = nn + 1 + hx(1) = zl + hy3(1) = 0. +!write(*,*)'FIRST',nn,hx(nn),hy3(nn) + ! middle position: within the sphere: zl < jj < zr + ELSE + nn = nn + 1 + zz1 = zp(jj) - zp(ii) ! distance z12 between 1 and 2 + hx(nn) = zp(jj) + if(WDA_var == 1) hy3(nn) = mydisp(jj,icomp) * ( psi_j(icomp)*psi_j(icomp) - zz1**2 ) + if(WDA_var == 2) hy3(nn) = rhop_sum(jj) * dadisp_dr(jj,icomp) * ( psi_j(icomp)*psi_j(icomp) - zz1**2 ) +!write(*,*)'MIDDLE',nn,hx(nn),hy3(nn) + ! last position: right side of the sphere: zr. Linear Interpolation of h's + IF ( zp(jj+1) > (zr-zmin) ) THEN + nn = nn + 1 + hx(nn) = zr + hy3(nn) = 0. +!write(*,*)'LAST',nn,hx(nn),hy3(nn) + + EXIT + END IF + END IF + END IF + END DO + xl = hx(1) + xh = hx(nn) + + if( nn >= 700 ) then + write(*,*) 'dF_disp_wd_pcsaft: bigger vectors hx, hy3, ... required!', nn + pause + end if + + CALL spline ( hx(1:nn), hy3(1:nn), nn, 1.E30, 1.E30, y2(1:nn) ) + CALL splint_integral( hx(1:nn), hy3(1:nn), y2(1:nn), nn, xl, xh, int3 ) + + if(WDA_var == 1) dF_drho_att(icomp) = int3 * 0.75 / psi_j(icomp)**3. + if(WDA_var == 2) dF_drho_att(icomp) = int3 * 0.75 / psi_j(icomp)**3. + adisp(ii) + END DO + + +END SUBROUTINE dF_disp_drho_wda + + + +End Module mod_DFT_DISP_WDA + + +! ! ! +! ! ! Subroutine DISP_Weighted_Densities(rhop, rhop_wd, user) +! ! ! +! ! ! Use PetscManagement +! ! ! Use BASIC_VARIABLES, Only: ncomp +! ! ! Use mod_DFT, Only: fa_disp,ab_disp,zp,dzp +! ! ! Implicit None +! ! ! +! ! ! #include +! ! ! +! ! ! !passed +! ! ! Type (userctx) :: user +! ! ! PetscScalar :: rhop(ncomp,user%gxs:user%gxe) +! ! ! REAL, INTENT(OUT) :: rhop_wd(user%gxs:user%gxe,ncomp) +! ! ! +! ! ! +! ! ! !local +! ! ! INTEGER :: i,j,k +! ! ! INTEGER :: n +! ! ! INTEGER, parameter :: NMAX = 800 +! ! ! REAL :: x_int(NMAX),y_int(NMAX),y2(NMAX) !Fehlermeldung einbauen, falls dim > 400!! +! ! ! REAL :: zmin,dz,zz +! ! ! REAL :: xlo,xhi,int1 +! ! ! INTEGER :: fa_disp_max +! ! ! +! ! ! +! ! ! +! ! ! zmin = 1d-6 +! ! ! fa_disp_max = maxval(fa_disp(1:ncomp)) +! ! ! +! ! ! Do k = 1,ncomp +! ! ! +! ! ! Do i = user%xs - fa_disp_max , user%xe + fa_disp_max +! ! ! n = 1 +! ! ! x_int = 0.0 +! ! ! y_int = 0.0 +! ! ! +! ! ! Do j = i-fa_disp(k),i+fa_disp(k) +! ! ! +! ! ! If( ( zp(i)-zp(j+1) ) < ab_disp(k) .and. ( zp(i) - zp(j) ) >= ab_disp(k) ) Then !the position of j+1 is already within i-d/2 while j is still outside this range in this case, the integration steplength (dz) is just the distance, which j+1 overlaps with i-d/2 and what is integrated is the interpolated value of the integrand +! ! ! +! ! ! If(n/= 1) stop 'n /=1 in DISP_Weighted_Densities' !here always n=1! +! ! ! zz = zp(j) - zp(i) !distance between grid points j and i +! ! ! dz = zp(j+1) - (zp(i) - ab_disp(k)) !the part of the intervall between zp(j) and zp(j+1) which is already within i-d/2 +! ! ! !if(dz < epsilon(dz)) dz = epsilon(dz) !bei unguenstiger Kombination von sig und ngrid kann dz unter Machinengenauigkeit epsilon liegen, dann ist x(2) = x(1) + dz = x(1) -> das fuehrt zu Abbruch in Spline Interpolation +! ! ! x_int(n) = 0.0 !array containing x-values for spline integration +! ! ! y_int(n) = 0.0 +! ! ! +! ! ! +! ! ! Else If (zp(j) > (zp(i)-ab_disp(k)) .and. zp(j) <= (zp(i)+ab_disp(k))) Then !grid point j within i+-d2 +! ! ! +! ! ! n = n + 1 +! ! ! x_int(n) = x_int(n-1) + dz !first time in this If condition, dz is stil the old value from above! +! ! ! zz = zp(j) - zp(i) +! ! ! dz = dzp +! ! ! y_int(n) = rhop(k,j) * (ab_disp(k)*ab_disp(k) - zz*zz ) +! ! ! +! ! ! +! ! ! If (zp(j) < (zp(i)+ab_disp(k)) .and. zp(j+1) >= (zp(i)+ab_disp(k)) ) Then !zp(j) is still within zp(i)+d2 but zp(j+1) is already outside zp(i)+d2 +! ! ! dz = zp(i) + ab_disp(k) - zp(j) +! ! ! !If(dz <= epsilon(dz)) exit !wie oben, kann auch hier bei ungluecklicher Wahl von sig und ngrid dz < eps werden und somit x(n) = x(n-1) -> Abbruch in Spline interpolation. Dann einfach ngrid aendern! +! ! ! zz = zp(j) - zp(i) +! ! ! n = n + 1 +! ! ! x_int(n) = x_int(n-1) + dz +! ! ! y_int(n) = 0.0 +! ! ! +! ! ! +! ! ! End If +! ! ! End If +! ! ! End Do +! ! ! +! ! ! +! ! ! xlo = x_int(1) +! ! ! xhi = x_int(n) +! ! ! +! ! ! If(n > NMAX) stop 'Increase NMAX in DISP_Weighted_Densities (auch in AD Routine!!)' +! ! ! +! ! ! write(*,*)'n',n +! ! ! pause +! ! ! write(*,*)'rx',x_int(1:n) +! ! ! pause +! ! ! write(*,*)'ry',y_int(1:n) +! ! ! pause +! ! ! +! ! ! +! ! ! +! ! ! CALL spline( x_int(1:n), y_int(1:n), n, 1.E30, 1.E30, y2(1:n) ) +! ! ! CALL splint_integral ( x_int(1:n), y_int(1:n), y2(1:n), n, xlo, xhi, int1 ) +! ! ! rhop_wd(i,k) = 0.75 * int1 / ab_disp(k)**3 +! ! ! +! ! ! if ( rhop_wd(i,k) < 0.0 ) then +! ! ! rhop_wd(i,k) = 0.0 +! ! ! do j = 2, n +! ! ! rhop_wd(i,k) = rhop_wd(i,k) + (y_int(j)+y_int(j-1))/2.0 *(x_int(j)-x_int(j-1)) +! ! ! end do +! ! ! end if +! ! ! if ( rhop_wd(i,k) < 0.0 ) rhop_wd(i,k) = rhop(k,i) +! ! ! +! ! ! End Do +! ! ! End Do +! ! ! +! ! ! +! ! ! End Subroutine DISP_Weighted_Densities +! ! ! +! ! ! +! ! ! +! ! ! Subroutine DISP_mu(rhop_wd,f_disp,my_disp,df_disp_drk,user) +! ! ! +! ! ! Use PetscManagement +! ! ! Use PARAMETERS, Only: PI +! ! ! Use EOS_CONSTANTS, Only: ap,bp +! ! ! Use BASIC_VARIABLES, Only: ncomp,t,parame +! ! ! Use EOS_VARIABLES, Only: dhs,sig_ij,uij +! ! ! Use mod_DFT, Only: fa_disp +! ! ! Implicit None +! ! ! +! ! ! #include +! ! ! +! ! ! !passed +! ! ! Type (userctx) :: user +! ! ! REAL, INTENT(IN) :: rhop_wd(user%gxs:user%gxe,ncomp) +! ! ! REAL, INTENT(OUT) :: my_disp(user%gxs:user%gxe,ncomp) !chemPot_disp / kT +! ! ! REAL, INTENT(OUT) :: f_disp(user%gxs:user%gxe) !F_disp / NkT +! ! ! REAL, INTENT(OUT) :: df_disp_drk(user%gxs:user%gxe,ncomp) ! d(F/NkT) / drho_k = (mu/kT - F_disp / NkT)/rho +! ! ! +! ! ! ! ! !local +! ! ! ! ! INTEGER :: k,ii,kk,m +! ! ! ! ! REAL :: m_mean, m_rk(ncomp) +! ! ! ! ! REAL :: apar(0:6),bpar(0:6) +! ! ! ! ! REAL :: ap_rk(ncomp,0:6),bp_rk(ncomp,0:6) +! ! ! ! ! REAL :: xi(ncomp),z3 +! ! ! ! ! REAL :: I1,I2,I1_rk,I2_rk +! ! ! ! ! REAL :: order1,order2,ord1_rk,ord2_rk +! ! ! ! ! REAL :: c1_con,c2_con, c1_rk,rho2 +! ! ! ! ! REAL :: rhop_wd_sum, eta_disp, eta_rk, zms +! ! ! ! ! INTEGER :: fa_disp_max +! ! ! ! ! +! ! ! ! ! +! ! ! ! ! fa_disp_max = maxval(fa_disp(1:ncomp)) +! ! ! ! ! +! ! ! ! ! Do k = 1,ncomp +! ! ! ! ! Do ii = user%xs-fa_disp_max,user%xe+fa_disp_max +! ! ! ! ! +! ! ! ! ! rhop_wd_sum = SUM(rhop_wd(ii,1:ncomp)) +! ! ! ! ! +! ! ! ! ! m_mean = 0.0 +! ! ! ! ! eta_disp = 0.0 +! ! ! ! ! Do kk = 1,ncomp +! ! ! ! ! xi(kk) = rhop_wd(ii,kk) / rhop_wd_sum +! ! ! ! ! m_mean = m_mean + xi(kk)*parame(kk,1) +! ! ! ! ! eta_disp = eta_disp + rhop_wd(ii,kk)*parame(kk,1)*dhs(kk)**3 +! ! ! ! ! End Do +! ! ! ! ! +! ! ! ! ! eta_disp = eta_disp * PI / 6.0 +! ! ! ! ! eta_rk = parame(k,1) * dhs(k)**3 * PI / 6.0 +! ! ! ! ! +! ! ! ! ! m_rk(k) = ( parame(k,1) - m_mean ) / rhop_wd_sum +! ! ! ! ! +! ! ! ! ! +! ! ! ! ! DO m = 0, 6 +! ! ! ! ! apar(m) = ap(m,1) + (1.0-1.0/m_mean)*ap(m,2) & +! ! ! ! ! + (1.0-1.0/m_mean)*(1.0-2.0/m_mean)*ap(m,3) +! ! ! ! ! bpar(m) = bp(m,1) + (1.0-1.0/m_mean)*bp(m,2) & +! ! ! ! ! + (1.0-1.0/m_mean)*(1.0-2.0/m_mean)*bp(m,3) +! ! ! ! ! +! ! ! ! ! ! --- derivatives of apar, bpar to rho_k --------------------------- +! ! ! ! ! ap_rk(k,m) = m_rk(k)/m_mean**2 * ( ap(m,2) + (3.0 -4.0/m_mean) *ap(m,3) ) +! ! ! ! ! bp_rk(k,m) = m_rk(k)/m_mean**2 * ( bp(m,2) + (3.0 -4.0/m_mean) *bp(m,3) ) +! ! ! ! ! END DO +! ! ! ! ! +! ! ! ! ! +! ! ! ! ! I1 = 0.0 +! ! ! ! ! I2 = 0.0 +! ! ! ! ! I1_rk = 0.0 +! ! ! ! ! I2_rk = 0.0 +! ! ! ! ! DO m = 0, 6 +! ! ! ! ! I1 = I1 + apar(m)*eta_disp**REAL(m) +! ! ! ! ! I2 = I2 + bpar(m)*eta_disp**REAL(m) +! ! ! ! ! I1_rk = I1_rk + apar(m)*REAL(m)*eta_disp**REAL(m-1)*eta_rk + ap_rk(k,m)*eta_disp**REAL(m) +! ! ! ! ! I2_rk = I2_rk + bpar(m)*REAL(m)*eta_disp**REAL(m-1)*eta_rk + bp_rk(k,m)*eta_disp**REAL(m) +! ! ! ! ! END DO +! ! ! ! ! +! ! ! ! ! +! ! ! ! ! ord1_rk = 0.0 +! ! ! ! ! ord2_rk = 0.0 +! ! ! ! ! order1 = 0.0 +! ! ! ! ! order2 = 0.0 +! ! ! ! ! DO kk = 1,ncomp +! ! ! ! ! !sig_ij(kk,k) = 0.5 * ( dhs(kk) + dhs(k) ) +! ! ! ! ! !uij(kk,k) = (1.0 - kij(kk,k)) * SQRT( eps(kk) * eps(k) ) +! ! ! ! ! order1 = order1 + xi(kk)*xi(k)* parame(kk,1)*parame(k,1)*sig_ij(kk,k)**3 * uij(kk,k)/t +! ! ! ! ! order2 = order2 + xi(kk)*xi(k)* parame(kk,1)*parame(k,1)*sig_ij(kk,k)**3 * (uij(kk,k)/t)**2 +! ! ! ! ! ord1_rk = ord1_rk + 2.0*parame(k,1)*rhop_wd_sum*xi(kk)*parame(kk,1)*sig_ij(kk,k)**3 *uij(kk,k)/t +! ! ! ! ! ord2_rk = ord2_rk + 2.0*parame(k,1)*rhop_wd_sum*xi(kk)*parame(kk,1)*sig_ij(kk,k)**3 *(uij(kk,k)/t)**2 +! ! ! ! ! END DO +! ! ! ! ! +! ! ! ! ! z3 = eta_disp +! ! ! ! ! zms = 1.0 - z3 +! ! ! ! ! +! ! ! ! ! c1_con= 1.0/ ( 1.0 + m_mean*(8.0*z3-2.0*z3*z3)/zms**4 & +! ! ! ! ! + (1.0 - m_mean)*(20.0*z3-27.0*z3*z3 +12.0*z3**3 -2.0*z3**4 ) & +! ! ! ! ! /(zms*(2.0-z3))**2 ) +! ! ! ! ! c2_con= - c1_con*c1_con *( m_mean*(-4.0*z3*z3+20.0*z3+8.0)/zms**5 & +! ! ! ! ! + (1.0 - m_mean) *(2.0*z3**3 +12.0*z3*z3-48.0*z3+40.0) & +! ! ! ! ! /(zms*(2.0-z3))**3 ) +! ! ! ! ! c1_rk= c2_con*eta_rk - c1_con*c1_con*m_rk(k) * ( (8.0*z3-2.0*z3*z3)/zms**4 & +! ! ! ! ! - (-2.0*z3**4 +12.0*z3**3 -27.0*z3*z3+20.0*z3) / (zms*(2.0-z3))**2 ) +! ! ! ! ! +! ! ! ! ! +! ! ! ! ! rho2 = rhop_wd_sum * rhop_wd_sum +! ! ! ! ! +! ! ! ! ! my_disp(ii,k) = -2.0*PI* ( order1*rho2*I1_rk + ord1_rk*I1 ) & +! ! ! ! ! - PI* c1_con*m_mean * ( order2*rho2*I2_rk + ord2_rk*I2 ) & +! ! ! ! ! - PI* ( c1_con*m_rk(k) + c1_rk*m_mean ) * order2*rho2*I2 +! ! ! ! ! +! ! ! ! ! f_disp(ii) = -2.0 * PI * rhop_wd_sum * I1 * order1 & !hier * rho_wd_sum, bei Elmar/rho_wd_sum, da in order1 bei Elmar mit rhoi, hier mit xi!! +! ! ! ! ! -PI * rhop_wd_sum * c1_con * m_mean * I2 * order2 +! ! ! ! ! +! ! ! ! ! df_disp_drk(ii,k) = ( my_disp(ii,k) - f_disp(ii) ) / rhop_wd_sum +! ! ! ! ! +! ! ! ! ! End Do +! ! ! ! ! +! ! ! ! ! End Do +! ! ! +! ! ! +! ! ! End Subroutine DISP_mu +! ! ! +! ! ! +! ! ! +! ! ! Subroutine DISP_dFdrho_wda(ii,rhop,rhop_wd,my_disp,f_disp,df_disp_drk,dF_drho_disp,user) +! ! ! +! ! ! Use PetscManagement +! ! ! +! ! ! Use BASIC_VARIABLES, Only: ncomp +! ! ! Use mod_DFT, Only: zp,dzp,fa_disp,ab_disp +! ! ! +! ! ! Implicit None +! ! ! #include +! ! ! +! ! ! !passed +! ! ! INTEGER, INTENT(IN) :: ii +! ! ! Type (userctx) :: user +! ! ! PetscScalar :: rhop(ncomp,user%gxs:user%gxe) +! ! ! REAL, INTENT(IN) :: rhop_wd(user%gxs:user%gxe,ncomp) +! ! ! REAL, INTENT(IN) :: my_disp(user%gxs:user%gxe,ncomp) !chemPot_disp / kT +! ! ! REAL, INTENT(IN) :: f_disp(user%gxs:user%gxe) !F_disp / NkT +! ! ! REAL, INTENT(IN) :: df_disp_drk(user%gxs:user%gxe,ncomp) ! d(F/NkT) / drho_k = (mu/kT - F_disp / NkT)/rho +! ! ! REAL, INTENT(OUT) :: dF_drho_disp(ncomp) +! ! ! +! ! ! ! ! !local +! ! ! ! ! INTEGER :: n,icomp,jj +! ! ! ! ! REAL :: zmin,zz,dz +! ! ! ! ! INTEGER, parameter :: NMAX = 800 +! ! ! ! ! REAL :: x_int(NMAX), y_int(NMAX), y2(NMAX) +! ! ! ! ! REAL :: xhi,xlo,int2 +! ! ! ! ! REAL :: rhop_sum +! ! ! ! ! +! ! ! ! ! zmin = 1d-6 +! ! ! ! ! DO icomp = 1, ncomp +! ! ! ! ! n = 1 +! ! ! ! ! x_int = 0.0 +! ! ! ! ! y_int = 0.0 +! ! ! ! ! +! ! ! ! ! DO jj = (ii-fa_disp(icomp)), (ii+fa_disp(icomp)) +! ! ! ! ! +! ! ! ! ! !IF ( zp(jj+1) > (zl+zmin) ) THEN +! ! ! ! ! If( ( zp(ii)-zp(jj+1) ) < ab_disp(icomp) .and. ( zp(ii) - zp(jj) ) >= ab_disp(icomp) ) Then !the position of j+1 is already within i-d/2 while j is still outside this range in this case, the integration steplength (dz) is just the distance, which j+1 overlaps with i-d/2 and what is integrated is the interpolated value of the integrand +! ! ! ! ! +! ! ! ! ! If(n/= 1) stop 'n /=1 in DISP_Weighted_Densities' !here always n=1! +! ! ! ! ! zz = zp(jj) - zp(ii) !distance between grid points j and i +! ! ! ! ! dz = zp(jj+1) - (zp(ii) - ab_disp(icomp)) !the part of the intervall between zp(j) and zp(j+1) which is already within i-d/2 +! ! ! ! ! !if(dz < epsilon(dz)) dz = epsilon(dz) !bei unguenstiger Kombination von sig und ngrid kann dz unter Machinengenauigkeit epsilon liegen, dann ist x(2) = x(1) + dz = x(1) -> das fuehrt zu Abbruch in Spline Interpolation +! ! ! ! ! x_int(n) = 0.0 !array containing x-values for spline integration +! ! ! ! ! y_int(n) = 0.0 +! ! ! ! ! +! ! ! ! ! Else If (zp(jj) > (zp(ii)-ab_disp(icomp)) .and. zp(jj) <= (zp(ii)+ab_disp(icomp))) Then !grid point j within i+-d2 +! ! ! ! ! +! ! ! ! ! n = n + 1 +! ! ! ! ! x_int(n) = x_int(n-1) + dz !first time in this If condition, dz is stil the old value from above! +! ! ! ! ! zz = zp(jj) - zp(ii) +! ! ! ! ! dz = dzp +! ! ! ! ! y_int(n) = my_disp(jj,icomp) * (ab_disp(icomp)*ab_disp(icomp) - zz*zz ) +! ! ! ! ! +! ! ! ! ! !rhop_sum = sum(rhop(1:ncomp,jj)) +! ! ! ! ! !y_int(n) = rhop_sum * df_disp_drk(jj,icomp) * (ab_disp(icomp)*ab_disp(icomp) - zz*zz) +! ! ! ! ! +! ! ! ! ! If (zp(jj) < (zp(ii)+ab_disp(icomp)) .and. zp(jj+1) >= (zp(ii)+ab_disp(icomp)) ) Then !zp(j) is still within zp(i)+d2 but zp(j+1) is already outside zp(i)+d2 +! ! ! ! ! dz = zp(ii) + ab_disp(icomp) - zp(jj) +! ! ! ! ! !If(dz <= epsilon(dz)) exit !wie oben, kann auch hier bei ungluecklicher Wahl von sig und ngrid dz < eps werden und somit x(n) = x(n-1) -> Abbruch in Spline interpolation. Dann einfach ngrid aendern! +! ! ! ! ! zz = zp(jj) - zp(ii) +! ! ! ! ! n = n + 1 +! ! ! ! ! x_int(n) = x_int(n-1) + dz +! ! ! ! ! y_int(n) = 0.0 +! ! ! ! ! +! ! ! ! ! End If +! ! ! ! ! End If +! ! ! ! ! END DO +! ! ! ! ! xlo = x_int(1) +! ! ! ! ! xhi = x_int(n) +! ! ! ! ! +! ! ! ! ! If(n > NMAX) stop 'Increase NMAX in DISP_dFdrho_wda (auch in AD Routine!!)' +! ! ! ! ! +! ! ! ! ! CALL spline ( x_int(1:n), y_int(1:n), n, 1.E30, 1.E30, y2(1:n) ) +! ! ! ! ! CALL splint_integral( x_int(1:n), y_int(1:n), y2(1:n), n, xlo, xhi, int2 ) +! ! ! ! ! +! ! ! ! ! dF_drho_disp(icomp) = int2 * 0.75 / ab_disp(icomp)**3 +! ! ! ! ! !dF_drho_disp(icomp) = int2 * 0.75 / ab_disp(icomp)**3 + f_disp(ii) +! ! ! ! ! END DO +! ! ! ! ! +! ! ! +! ! ! End Subroutine DISP_dFdrho_wda +! ! ! + diff --git a/applications/PUfoam/MoDeNaModels/SurfaceTension/src/mod_DFT_DISP_WDA_d.F90 b/applications/PUfoam/MoDeNaModels/SurfaceTension/src/mod_DFT_DISP_WDA_d.F90 new file mode 100644 index 000000000..ded4e3e3c --- /dev/null +++ b/applications/PUfoam/MoDeNaModels/SurfaceTension/src/mod_DFT_DISP_WDA_d.F90 @@ -0,0 +1,513 @@ +!>This file contains the subroutines which calculate the derivatives of th contribution of +!!dispersion to the Helmholtz energy functional. + + + + + + +! Generated by TAPENADE (INRIA, Tropics team) +! Tapenade 3.10 (r5498) - 20 Jan 2015 09:48 +! +MODULE MOD_DFT_DISP_WDA_D + IMPLICIT NONE + PRIVATE + PUBLIC disp_weighted_densities_d + PUBLIC disp_mu_d + PUBLIC disp_dfdrho_wda_d + + CONTAINS + + ! Differentiation of disp_weighted_densities in forward (tangent) mode: +! variations of useful results: rhop_wd +! with respect to varying inputs: rhop + SUBROUTINE DISP_WEIGHTED_DENSITIES_D(rhop, rhopd, rhop_wd, rhop_wdd, & +& user) + Use PetscManagement + USE BASIC_VARIABLES, ONLY : ncomp + USE MOD_DFT, ONLY : fa_disp, ab_disp, zp, dzp + IMPLICIT NONE + +#include + +!passed +Type (userctx) :: user +PetscScalar :: rhop(ncomp,user%gxs:user%gxe) +PetscScalar :: rhopd(ncomp,user%gxs:user%gxe) +REAL, INTENT(OUT) :: rhop_wd(user%gxs:user%gxe,ncomp) +REAL, INTENT(OUT) :: rhop_wdd(user%gxs:user%gxe,ncomp) + + +! ! !local +! ! INTEGER :: i, j, k +! ! INTEGER :: n +! ! !Fehlermeldung einbauen, falls dim > 400!! +! ! REAL :: x_int(400), y_int(400), y2(400) +! ! REAL :: y_intd(400), y2d(400) +! ! REAL :: zmin, dz, zz +! ! REAL :: xlo, xhi, int1 +! ! REAL :: int1d +! ! INTEGER :: fa_disp_max +! ! INTRINSIC MAXVAL +! ! zmin = 1d-6 +! ! fa_disp_max = MAXVAL(fa_disp(1:ncomp)) +! ! rhop_wdd = 0.0 +! ! y2d = 0.0 +! ! DO k=1,ncomp +! ! Do i = user%xs - fa_disp_max , user%xe + fa_disp_max +! ! n = 1 +! ! x_int = 0.0 +! ! y_int = 0.0 +! ! y_intd = 0.0 +! ! DO j=i-fa_disp(k),i+fa_disp(k) +! ! IF (zp(i) - zp(j+1) .LT. ab_disp(k) .AND. zp(i) - zp(j) .GE. & +! ! & ab_disp(k)) THEN +! ! !the position of j+1 is already within i-d/2 while j is still outside this range in this case, the integration steplength (dz) is +! ! ! just the distance, which j+1 overlaps with i-d/2 and what is integrated is the interpolated value of the integrand +! ! !here always n=1! +! ! IF (n .NE. 1) THEN +! ! GOTO 100 +! ! ELSE +! ! !distance between grid points j and i +! ! zz = zp(j) - zp(i) +! ! !the part of the intervall between zp(j) and zp(j+1) which is already within i-d/2 +! ! dz = zp(j+1) - (zp(i)-ab_disp(k)) +! ! !if(dz < epsilon(dz)) dz = epsilon(dz) !bei unguenstiger Kombination von sig und ngrid kann dz unter Machinengenauigkeit epsilon +! ! !liegen, dann ist x(2) = x(1) + dz = x(1) -> das fuehrt zu Abbruch in Spline Interpolation +! ! !array containing x-values for spline integration +! ! x_int(n) = 0.0 +! ! y_intd(n) = 0.0 +! ! y_int(n) = 0.0 +! ! END IF +! ! ELSE IF (zp(j) .GT. zp(i) - ab_disp(k) .AND. zp(j) .LE. zp(i) & +! ! & + ab_disp(k)) THEN +! ! !grid point j within i+-d2 +! ! n = n + 1 +! ! !first time in this If condition, dz is stil the old value from above! +! ! x_int(n) = x_int(n-1) + dz +! ! zz = zp(j) - zp(i) +! ! dz = dzp +! ! y_intd(n) = (ab_disp(k)*ab_disp(k)-zz*zz)*rhopd(k, j) +! ! y_int(n) = rhop(k, j)*(ab_disp(k)*ab_disp(k)-zz*zz) +! ! IF (zp(j) .LT. zp(i) + ab_disp(k) .AND. zp(j+1) .GE. zp(i) +& +! ! & ab_disp(k)) THEN +! ! !zp(j) is still within zp(i)+d2 but zp(j+1) is already outside zp(i)+d2 +! ! dz = zp(i) + ab_disp(k) - zp(j) +! ! !If(dz <= epsilon(dz)) exit !wie oben, kann auch hier bei ungluecklicher Wahl von sig und ngrid dz < eps werden und somit x(n) +! ! != x(n-1) -> Abbruch in Spline interpolation. Dann einfach ngrid aendern! +! ! zz = zp(j) - zp(i) +! ! n = n + 1 +! ! x_int(n) = x_int(n-1) + dz +! ! y_intd(n) = 0.0 +! ! y_int(n) = 0.0 +! ! END IF +! ! END IF +! ! END DO +! ! xlo = x_int(1) +! ! xhi = x_int(n) +! ! CALL SPLINE_D(x_int(1:n), y_int(1:n), y_intd(1:n), n, 1.e30, & +! ! & 1.e30, y2(1:n), y2d(1:n)) +! ! CALL SPLINT_INTEGRAL_D(x_int(1:n), y_int(1:n), y_intd(1:n), y2(1& +! ! & :n), y2d(1:n), n, xlo, xhi, int1, int1d) +! ! rhop_wdd(i, k) = 0.75*int1d/ab_disp(k)**3 +! ! rhop_wd(i, k) = 0.75*int1/ab_disp(k)**3 +! ! IF (rhop_wd(i, k) .LT. 0.0) THEN +! ! rhop_wdd(i, k) = 0.0 +! ! rhop_wd(i, k) = 0.0 +! ! DO j=2,n +! ! rhop_wdd(i, k) = rhop_wdd(i, k) + (x_int(j)-x_int(j-1))*(& +! ! & y_intd(j)+y_intd(j-1))/2.0 +! ! rhop_wd(i, k) = rhop_wd(i, k) + (y_int(j)+y_int(j-1))/2.0*(& +! ! & x_int(j)-x_int(j-1)) +! ! END DO +! ! END IF +! ! IF (rhop_wd(i, k) .LT. 0.0) THEN +! ! rhop_wdd(i, k) = rhopd(k, i) +! ! rhop_wd(i, k) = rhop(k, i) +! ! END IF +! ! END DO +! ! END DO +! ! GOTO 110 +! ! 100 STOP +! ! 110 CONTINUE + END SUBROUTINE DISP_WEIGHTED_DENSITIES_D + + + +! Differentiation of disp_mu in forward (tangent) mode: +! variations of useful results: my_disp +! with respect to varying inputs: rhop_wd + SUBROUTINE DISP_MU_D(rhop_wd, rhop_wdd, f_disp, my_disp, my_dispd, & +& df_disp_drk, user) + + Use PetscManagement + USE PARAMETERS, ONLY : pi + USE EOS_CONSTANTS, ONLY : ap, bp + USE BASIC_VARIABLES, ONLY : ncomp, t, parame + USE EOS_VARIABLES, Only: dhs, sig_ij, uij + USE MOD_DFT, ONLY : fa_disp + IMPLICIT NONE +#include + +!passed +Type (userctx) :: user +REAL, INTENT(IN) :: rhop_wd(user%gxs:user%gxe,ncomp) +REAL, INTENT(IN) :: rhop_wdd(user%gxs:user%gxe,ncomp) +REAL, INTENT(OUT) :: my_disp(user%gxs:user%gxe,ncomp) !chemPot_disp / kT +REAL, INTENT(OUT) :: my_dispd(user%gxs:user%gxe,ncomp) !chemPot_disp / kT +REAL, INTENT(OUT) :: f_disp(user%gxs:user%gxe) !F_disp / NkT +REAL, INTENT(OUT) :: df_disp_drk(user%gxs:user%gxe,ncomp) ! d(F/NkT) / drho_k = (mu/kT - F_disp / NkT)/rho + +! ! !local +! ! INTEGER :: k, ii, kk, m +! ! REAL :: m_mean, m_rk(ncomp) +! ! REAL :: m_meand, m_rkd(ncomp) +! ! REAL :: apar(0:6), bpar(0:6) +! ! REAL :: apard(0:6), bpard(0:6) +! ! REAL :: ap_rk(ncomp, 0:6), bp_rk(ncomp, 0:6) +! ! REAL :: ap_rkd(ncomp, 0:6), bp_rkd(ncomp, 0:6) +! ! REAL :: xi(ncomp), z3 +! ! REAL :: xid(ncomp), z3d +! ! REAL :: i1, i2, i1_rk, i2_rk +! ! REAL :: i1d, i2d, i1_rkd, i2_rkd +! ! REAL :: order1, order2, ord1_rk, ord2_rk +! ! REAL :: order1d, order2d, ord1_rkd, ord2_rkd +! ! REAL :: c1_con, c2_con, c1_rk, rho2 +! ! REAL :: c1_cond, c2_cond, c1_rkd, rho2d +! ! REAL :: rhop_wd_sum, eta_disp, eta_rk, zms +! ! REAL :: rhop_wd_sumd, eta_dispd, zmsd +! ! INTEGER :: fa_disp_max +! ! INTRINSIC MAXVAL +! ! INTRINSIC SUM +! ! INTRINSIC REAL +! ! REAL :: pwy1 +! ! REAL :: pwr1 +! ! REAL :: pwr1d +! ! REAL :: pwy2 +! ! REAL :: pwr2 +! ! REAL :: pwr2d +! ! fa_disp_max = MAXVAL(fa_disp(1:ncomp)) +! ! my_dispd = 0.0 +! ! xid = 0.0 +! ! m_rkd = 0.0 +! ! ap_rkd = 0.0 +! ! bpard = 0.0 +! ! apard = 0.0 +! ! bp_rkd = 0.0 +! ! DO k=1,ncomp +! ! Do ii = user%xs-fa_disp_max,user%xe+fa_disp_max +! ! rhop_wd_sumd = SUM(rhop_wdd(ii, 1:ncomp)) +! ! rhop_wd_sum = SUM(rhop_wd(ii, 1:ncomp)) +! ! m_mean = 0.0 +! ! eta_disp = 0.0 +! ! eta_dispd = 0.0 +! ! m_meand = 0.0 +! ! DO kk=1,ncomp +! ! xid(kk) = (rhop_wdd(ii, kk)*rhop_wd_sum-rhop_wd(ii, kk)*& +! ! & rhop_wd_sumd)/rhop_wd_sum**2 +! ! xi(kk) = rhop_wd(ii, kk)/rhop_wd_sum +! ! m_meand = m_meand + parame(kk,1)*xid(kk) +! ! m_mean = m_mean + xi(kk)*parame(kk,1) +! ! eta_dispd = eta_dispd + parame(kk,1)*dhs(kk)**3*rhop_wdd(ii, kk) +! ! eta_disp = eta_disp + rhop_wd(ii, kk)*parame(kk,1)*dhs(kk)**3 +! ! END DO +! ! eta_dispd = pi*eta_dispd/6.0 +! ! eta_disp = eta_disp*pi/6.0 +! ! eta_rk = parame(k,1)*dhs(k)**3*pi/6.0 +! ! m_rkd(k) = (-(m_meand*rhop_wd_sum)-(parame(k,1)-m_mean)*rhop_wd_sumd& +! ! & )/rhop_wd_sum**2 +! ! m_rk(k) = (parame(k,1)-m_mean)/rhop_wd_sum +! ! DO m=0,6 +! ! apard(m) = ap(m, 2)*m_meand/m_mean**2 + ap(m, 3)*(m_meand*(1.0& +! ! & -2.0/m_mean)/m_mean**2+(1.0-1.0/m_mean)*2.0*m_meand/m_mean**& +! ! & 2) +! ! apar(m) = ap(m, 1) + (1.0-1.0/m_mean)*ap(m, 2) + (1.0-1.0/& +! ! & m_mean)*(1.0-2.0/m_mean)*ap(m, 3) +! ! bpard(m) = bp(m, 2)*m_meand/m_mean**2 + bp(m, 3)*(m_meand*(1.0& +! ! & -2.0/m_mean)/m_mean**2+(1.0-1.0/m_mean)*2.0*m_meand/m_mean**& +! ! & 2) +! ! bpar(m) = bp(m, 1) + (1.0-1.0/m_mean)*bp(m, 2) + (1.0-1.0/& +! ! & m_mean)*(1.0-2.0/m_mean)*bp(m, 3) +! ! ! --- derivatives of apar, bpar to rho_k --------------------------- +! ! ap_rkd(k, m) = (m_rkd(k)*m_mean**2-m_rk(k)*2*m_mean*m_meand)*(& +! ! & ap(m, 2)+(3.0-4.0/m_mean)*ap(m, 3))/m_mean**4 + m_rk(k)*ap(m& +! ! & , 3)*4.0*m_meand/m_mean**4 +! ! ap_rk(k, m) = m_rk(k)/m_mean**2*(ap(m, 2)+(3.0-4.0/m_mean)*ap(& +! ! & m, 3)) +! ! bp_rkd(k, m) = (m_rkd(k)*m_mean**2-m_rk(k)*2*m_mean*m_meand)*(& +! ! & bp(m, 2)+(3.0-4.0/m_mean)*bp(m, 3))/m_mean**4 + m_rk(k)*bp(m& +! ! & , 3)*4.0*m_meand/m_mean**4 +! ! bp_rk(k, m) = m_rk(k)/m_mean**2*(bp(m, 2)+(3.0-4.0/m_mean)*bp(& +! ! & m, 3)) +! ! END DO +! ! i1 = 0.0 +! ! i2 = 0.0 +! ! i1_rk = 0.0 +! ! i2_rk = 0.0 +! ! i1_rkd = 0.0 +! ! i1d = 0.0 +! ! i2d = 0.0 +! ! i2_rkd = 0.0 +! ! DO m=0,6 +! ! pwy1 = REAL(m) +! ! IF (eta_disp .GT. 0.0 .OR. (eta_disp .LT. 0.0 .AND. pwy1 .EQ. & +! ! & INT(pwy1))) THEN +! ! pwr1d = pwy1*eta_disp**(pwy1-1)*eta_dispd +! ! ELSE IF (eta_disp .EQ. 0.0 .AND. pwy1 .EQ. 1.0) THEN +! ! pwr1d = eta_dispd +! ! ELSE +! ! pwr1d = 0.0 +! ! END IF +! ! pwr1 = eta_disp**pwy1 +! ! i1d = i1d + apard(m)*pwr1 + apar(m)*pwr1d +! ! i1 = i1 + apar(m)*pwr1 +! ! pwy1 = REAL(m) +! ! IF (eta_disp .GT. 0.0 .OR. (eta_disp .LT. 0.0 .AND. pwy1 .EQ. & +! ! & INT(pwy1))) THEN +! ! pwr1d = pwy1*eta_disp**(pwy1-1)*eta_dispd +! ! ELSE IF (eta_disp .EQ. 0.0 .AND. pwy1 .EQ. 1.0) THEN +! ! pwr1d = eta_dispd +! ! ELSE +! ! pwr1d = 0.0 +! ! END IF +! ! pwr1 = eta_disp**pwy1 +! ! i2d = i2d + bpard(m)*pwr1 + bpar(m)*pwr1d +! ! i2 = i2 + bpar(m)*pwr1 +! ! pwy1 = REAL(m - 1) +! ! IF (eta_disp .GT. 0.0 .OR. (eta_disp .LT. 0.0 .AND. pwy1 .EQ. & +! ! & INT(pwy1))) THEN +! ! pwr1d = pwy1*eta_disp**(pwy1-1)*eta_dispd +! ! ELSE IF (eta_disp .EQ. 0.0 .AND. pwy1 .EQ. 1.0) THEN +! ! pwr1d = eta_dispd +! ! ELSE +! ! pwr1d = 0.0 +! ! END IF +! ! pwr1 = eta_disp**pwy1 +! ! pwy2 = REAL(m) +! ! IF (eta_disp .GT. 0.0 .OR. (eta_disp .LT. 0.0 .AND. pwy2 .EQ. & +! ! & INT(pwy2))) THEN +! ! pwr2d = pwy2*eta_disp**(pwy2-1)*eta_dispd +! ! ELSE IF (eta_disp .EQ. 0.0 .AND. pwy2 .EQ. 1.0) THEN +! ! pwr2d = eta_dispd +! ! ELSE +! ! pwr2d = 0.0 +! ! END IF +! ! pwr2 = eta_disp**pwy2 +! ! i1_rkd = i1_rkd + REAL(m)*eta_rk*(apard(m)*pwr1+apar(m)*pwr1d)& +! ! & + ap_rkd(k, m)*pwr2 + ap_rk(k, m)*pwr2d +! ! i1_rk = i1_rk + apar(m)*REAL(m)*pwr1*eta_rk + ap_rk(k, m)*pwr2 +! ! pwy1 = REAL(m - 1) +! ! IF (eta_disp .GT. 0.0 .OR. (eta_disp .LT. 0.0 .AND. pwy1 .EQ. & +! ! & INT(pwy1))) THEN +! ! pwr1d = pwy1*eta_disp**(pwy1-1)*eta_dispd +! ! ELSE IF (eta_disp .EQ. 0.0 .AND. pwy1 .EQ. 1.0) THEN +! ! pwr1d = eta_dispd +! ! ELSE +! ! pwr1d = 0.0 +! ! END IF +! ! pwr1 = eta_disp**pwy1 +! ! pwy2 = REAL(m) +! ! IF (eta_disp .GT. 0.0 .OR. (eta_disp .LT. 0.0 .AND. pwy2 .EQ. & +! ! & INT(pwy2))) THEN +! ! pwr2d = pwy2*eta_disp**(pwy2-1)*eta_dispd +! ! ELSE IF (eta_disp .EQ. 0.0 .AND. pwy2 .EQ. 1.0) THEN +! ! pwr2d = eta_dispd +! ! ELSE +! ! pwr2d = 0.0 +! ! END IF +! ! pwr2 = eta_disp**pwy2 +! ! i2_rkd = i2_rkd + REAL(m)*eta_rk*(bpard(m)*pwr1+bpar(m)*pwr1d)& +! ! & + bp_rkd(k, m)*pwr2 + bp_rk(k, m)*pwr2d +! ! i2_rk = i2_rk + bpar(m)*REAL(m)*pwr1*eta_rk + bp_rk(k, m)*pwr2 +! ! END DO +! ! ord1_rk = 0.0 +! ! ord2_rk = 0.0 +! ! order1 = 0.0 +! ! order2 = 0.0 +! ! order1d = 0.0 +! ! order2d = 0.0 +! ! ord2_rkd = 0.0 +! ! ord1_rkd = 0.0 +! ! DO kk=1,ncomp +! ! !sig_ij(kk,k) = 0.5 * ( dhs(kk) + dhs(k) ) +! ! !uij(kk,k) = (1.0 - kij(kk,k)) * SQRT( eps(kk) * eps(k) ) +! ! order1d = order1d + parame(kk,1)*parame(k,1)*sig_ij(kk, k)**3*uij(kk, & +! ! & k)*(xid(kk)*xi(k)+xi(kk)*xid(k))/t +! ! order1 = order1 + xi(kk)*xi(k)*parame(kk,1)*parame(k,1)*sig_ij(kk, k)& +! ! & **3*uij(kk, k)/t +! ! order2d = order2d + parame(kk,1)*parame(k,1)*sig_ij(kk, k)**3*uij(kk, & +! ! & k)**2*(xid(kk)*xi(k)+xi(kk)*xid(k))/t**2 +! ! order2 = order2 + xi(kk)*xi(k)*parame(kk,1)*parame(k,1)*sig_ij(kk, k)& +! ! & **3*(uij(kk, k)/t)**2 +! ! ord1_rkd = ord1_rkd + 2.0*parame(k,1)*parame(kk,1)*sig_ij(kk, k)**3*& +! ! & uij(kk, k)*(rhop_wd_sumd*xi(kk)+rhop_wd_sum*xid(kk))/t +! ! ord1_rk = ord1_rk + 2.0*parame(k,1)*rhop_wd_sum*xi(kk)*parame(kk,1)*& +! ! & sig_ij(kk, k)**3*uij(kk, k)/t +! ! ord2_rkd = ord2_rkd + 2.0*parame(k,1)*parame(kk,1)*sig_ij(kk, k)**3*& +! ! & uij(kk, k)**2*(rhop_wd_sumd*xi(kk)+rhop_wd_sum*xid(kk))/t**2 +! ! ord2_rk = ord2_rk + 2.0*parame(k,1)*rhop_wd_sum*xi(kk)*parame(kk,1)*& +! ! & sig_ij(kk, k)**3*(uij(kk, k)/t)**2 +! ! END DO +! ! z3d = eta_dispd +! ! z3 = eta_disp +! ! zmsd = -z3d +! ! zms = 1.0 - z3 +! ! c1_cond = -((((m_meand*(8.0*z3-2.0*z3*z3)+m_mean*(8.0*z3d-2.0*(& +! ! & z3d*z3+z3*z3d)))*zms**4-m_mean*(8.0*z3-2.0*z3*z3)*4*zms**3*& +! ! & zmsd)/(zms**4)**2+(((1.0-m_mean)*(20.0*z3d-27.0*(z3d*z3+z3*z3d& +! ! & )+12.0*3*z3**2*z3d-2.0*4*z3**3*z3d)-m_meand*(20.0*z3-27.0*z3*& +! ! & z3+12.0*z3**3-2.0*z3**4))*zms**2*(2.0-z3)**2-(1.0-m_mean)*(& +! ! & 20.0*z3-27.0*z3*z3+12.0*z3**3-2.0*z3**4)*2*zms*(2.0-z3)*(zmsd*& +! ! & (2.0-z3)-zms*z3d))/((zms*(2.0-z3))**2)**2)/(1.0+m_mean*(8.0*z3& +! ! & -2.0*z3*z3)/zms**4+(1.0-m_mean)*(20.0*z3-27.0*z3*z3+12.0*z3**3& +! ! & -2.0*z3**4)/(zms*(2.0-z3))**2)**2) +! ! c1_con = 1.0/(1.0+m_mean*(8.0*z3-2.0*z3*z3)/zms**4+(1.0-m_mean)*& +! ! & (20.0*z3-27.0*z3*z3+12.0*z3**3-2.0*z3**4)/(zms*(2.0-z3))**2) +! ! c2_cond = -((c1_cond*c1_con+c1_con*c1_cond)*(m_mean*(-(4.0*z3*z3& +! ! & )+20.0*z3+8.0)/zms**5+(1.0-m_mean)*(2.0*z3**3+12.0*z3*z3-48.0*& +! ! & z3+40.0)/(zms*(2.0-z3))**3)+c1_con**2*(((m_meand*(-(4.0*z3*z3)& +! ! & +20.0*z3+8.0)+m_mean*(20.0*z3d-4.0*(z3d*z3+z3*z3d)))*zms**5-& +! ! & m_mean*(-(4.0*z3*z3)+20.0*z3+8.0)*5*zms**4*zmsd)/(zms**5)**2+(& +! ! & ((1.0-m_mean)*(2.0*3*z3**2*z3d+12.0*(z3d*z3+z3*z3d)-48.0*z3d)-& +! ! & m_meand*(2.0*z3**3+12.0*z3*z3-48.0*z3+40.0))*zms**3*(2.0-z3)**& +! ! & 3-(1.0-m_mean)*(2.0*z3**3+12.0*z3*z3-48.0*z3+40.0)*3*zms**2*(& +! ! & 2.0-z3)**2*(zmsd*(2.0-z3)-zms*z3d))/((zms*(2.0-z3))**3)**2)) +! ! c2_con = -(c1_con*c1_con*(m_mean*(-(4.0*z3*z3)+20.0*z3+8.0)/zms& +! ! & **5+(1.0-m_mean)*(2.0*z3**3+12.0*z3*z3-48.0*z3+40.0)/(zms*(2.0& +! ! & -z3))**3)) +! ! c1_rkd = eta_rk*c2_cond - ((c1_cond*c1_con+c1_con*c1_cond)*m_rk(& +! ! & k)+c1_con**2*m_rkd(k))*((8.0*z3-2.0*z3*z3)/zms**4-(-(2.0*z3**4& +! ! & )+12.0*z3**3-27.0*z3*z3+20.0*z3)/(zms*(2.0-z3))**2) - c1_con**& +! ! & 2*m_rk(k)*(((8.0*z3d-2.0*(z3d*z3+z3*z3d))*zms**4-(8.0*z3-2.0*& +! ! & z3*z3)*4*zms**3*zmsd)/(zms**4)**2-((12.0*3*z3**2*z3d-2.0*4*z3& +! ! & **3*z3d-27.0*(z3d*z3+z3*z3d)+20.0*z3d)*zms**2*(2.0-z3)**2-(-(& +! ! & 2.0*z3**4)+12.0*z3**3-27.0*z3*z3+20.0*z3)*2*zms*(2.0-z3)*(zmsd& +! ! & *(2.0-z3)-zms*z3d))/((zms*(2.0-z3))**2)**2) +! ! c1_rk = c2_con*eta_rk - c1_con*c1_con*m_rk(k)*((8.0*z3-2.0*z3*z3& +! ! & )/zms**4-(-(2.0*z3**4)+12.0*z3**3-27.0*z3*z3+20.0*z3)/(zms*(& +! ! & 2.0-z3))**2) +! ! rho2d = rhop_wd_sumd*rhop_wd_sum + rhop_wd_sum*rhop_wd_sumd +! ! rho2 = rhop_wd_sum*rhop_wd_sum +! ! my_dispd(ii, k) = -(2.0*pi*((order1d*rho2+order1*rho2d)*i1_rk+& +! ! & order1*rho2*i1_rkd+ord1_rkd*i1+ord1_rk*i1d)) - pi*((c1_cond*& +! ! & m_mean+c1_con*m_meand)*(order2*rho2*i2_rk+ord2_rk*i2)+c1_con*& +! ! & m_mean*((order2d*rho2+order2*rho2d)*i2_rk+order2*rho2*i2_rkd+& +! ! & ord2_rkd*i2+ord2_rk*i2d)) - pi*((c1_cond*m_rk(k)+c1_con*m_rkd(& +! ! & k)+c1_rkd*m_mean+c1_rk*m_meand)*order2*rho2*i2+(c1_con*m_rk(k)& +! ! & +c1_rk*m_mean)*((order2d*rho2+order2*rho2d)*i2+order2*rho2*i2d& +! ! & )) +! ! my_disp(ii, k) = -(2.0*pi*(order1*rho2*i1_rk+ord1_rk*i1)) - pi*& +! ! & c1_con*m_mean*(order2*rho2*i2_rk+ord2_rk*i2) - pi*(c1_con*m_rk& +! ! & (k)+c1_rk*m_mean)*order2*rho2*i2 +! ! f_disp(ii) = -(2.0*pi*rhop_wd_sum*i1*order1) - pi*rhop_wd_sum*& +! ! & c1_con*m_mean*i2*order2 +! ! df_disp_drk(ii, k) = (my_disp(ii, k)-f_disp(ii))/rhop_wd_sum +! ! END DO +! ! END DO + END SUBROUTINE DISP_MU_D + + + +! Differentiation of disp_dfdrho_wda in forward (tangent) mode: +! variations of useful results: df_drho_disp +! with respect to varying inputs: my_disp df_drho_disp + SUBROUTINE DISP_DFDRHO_WDA_D(ii, rhop, rhop_wd, my_disp, my_dispd, & +& f_disp, df_disp_drk, df_drho_disp, df_drho_dispd, user) + + Use PetscManagement + USE BASIC_VARIABLES, ONLY : ncomp + USE MOD_DFT, ONLY : zp, dzp, fa_disp, ab_disp + IMPLICIT NONE +#include + +!passed +INTEGER, INTENT(IN) :: ii +Type (userctx) :: user +PetscScalar :: rhop(ncomp,user%gxs:user%gxe) +REAL, INTENT(IN) :: rhop_wd(user%gxs:user%gxe,ncomp) +REAL, INTENT(IN) :: my_disp(user%gxs:user%gxe,ncomp) !chemPot_disp / kT +REAL, INTENT(IN) :: my_dispd(user%gxs:user%gxe,ncomp) !chemPot_disp / kT +REAL, INTENT(IN) :: f_disp(user%gxs:user%gxe) !F_disp / NkT +REAL, INTENT(IN) :: df_disp_drk(user%gxs:user%gxe,ncomp) ! d(F/NkT) / drho_k = (mu/kT - F_disp / NkT)/rho +REAL, INTENT(OUT) :: dF_drho_disp(ncomp) +REAL, INTENT(OUT) :: dF_drho_dispd(ncomp) + +! ! !local +! ! INTEGER :: n, icomp, jj +! ! REAL :: zmin, zz, dz +! ! REAL :: x_int(400), y_int(400), y2(400) +! ! REAL :: y_intd(400), y2d(400) +! ! REAL :: xhi, xlo, int2 +! ! REAL :: int2d +! ! REAL :: rhop_sum +! ! zmin = 1d-6 +! ! y2d = 0.0 +! ! DO icomp=1,ncomp +! ! n = 1 +! ! x_int = 0.0 +! ! y_int = 0.0 +! ! y_intd = 0.0 +! ! DO jj=ii-fa_disp(icomp),ii+fa_disp(icomp) +! ! !IF ( zp(jj+1) > (zl+zmin) ) THEN +! ! IF (zp(ii) - zp(jj+1) .LT. ab_disp(icomp) .AND. zp(ii) - zp(jj) & +! ! & .GE. ab_disp(icomp)) THEN +! ! !the position of j+1 is already within i-d/2 while j is still outside this range in this case, the integration steplength (dz) is +! ! ! just the distance, which j+1 overlaps with i-d/2 and what is integrated is the interpolated value of the integrand +! ! !here always n=1! +! ! IF (n .NE. 1) THEN +! ! GOTO 100 +! ! ELSE +! ! !distance between grid points j and i +! ! zz = zp(jj) - zp(ii) +! ! !the part of the intervall between zp(j) and zp(j+1) which is already within i-d/2 +! ! dz = zp(jj+1) - (zp(ii)-ab_disp(icomp)) +! ! !if(dz < epsilon(dz)) dz = epsilon(dz) !bei unguenstiger Kombination von sig und ngrid kann dz unter Machinengenauigkeit epsilon +! ! !liegen, dann ist x(2) = x(1) + dz = x(1) -> das fuehrt zu Abbruch in Spline Interpolation +! ! !array containing x-values for spline integration +! ! x_int(n) = 0.0 +! ! y_intd(n) = 0.0 +! ! y_int(n) = 0.0 +! ! END IF +! ! ELSE IF (zp(jj) .GT. zp(ii) - ab_disp(icomp) .AND. zp(jj) .LE. & +! ! & zp(ii) + ab_disp(icomp)) THEN +! ! !grid point j within i+-d2 +! ! n = n + 1 +! ! !first time in this If condition, dz is stil the old value from above! +! ! x_int(n) = x_int(n-1) + dz +! ! zz = zp(jj) - zp(ii) +! ! dz = dzp +! ! y_intd(n) = (ab_disp(icomp)*ab_disp(icomp)-zz*zz)*my_dispd(jj& +! ! & , icomp) +! ! y_int(n) = my_disp(jj, icomp)*(ab_disp(icomp)*ab_disp(icomp)-& +! ! & zz*zz) +! ! !rhop_sum = sum(rhop(1:ncomp,jj)) +! ! !y_int(n) = rhop_sum * df_disp_drk(jj,icomp) * (ab_disp(icomp)*ab_disp(icomp) - zz*zz) +! ! IF (zp(jj) .LT. zp(ii) + ab_disp(icomp) .AND. zp(jj+1) .GE. zp& +! ! & (ii) + ab_disp(icomp)) THEN +! ! !zp(j) is still within zp(i)+d2 but zp(j+1) is already outside zp(i)+d2 +! ! dz = zp(ii) + ab_disp(icomp) - zp(jj) +! ! !If(dz <= epsilon(dz)) exit !wie oben, kann auch hier bei ungluecklicher Wahl von sig und ngrid dz < eps werden und somit x(n) +! ! != x(n-1) -> Abbruch in Spline interpolation. Dann einfach ngrid aendern! +! ! zz = zp(jj) - zp(ii) +! ! n = n + 1 +! ! x_int(n) = x_int(n-1) + dz +! ! y_intd(n) = 0.0 +! ! y_int(n) = 0.0 +! ! END IF +! ! END IF +! ! END DO +! ! xlo = x_int(1) +! ! xhi = x_int(n) +! ! CALL SPLINE_D(x_int(1:n), y_int(1:n), y_intd(1:n), n, 1.e30, 1.e30& +! ! & , y2(1:n), y2d(1:n)) +! ! CALL SPLINT_INTEGRAL_D(x_int(1:n), y_int(1:n), y_intd(1:n), y2(1:n& +! ! & ), y2d(1:n), n, xlo, xhi, int2, int2d) +! ! df_drho_dispd(icomp) = 0.75*int2d/ab_disp(icomp)**3 +! ! df_drho_disp(icomp) = int2*0.75/ab_disp(icomp)**3 +! ! END DO +! ! GOTO 110 +! ! 100 STOP +! ! 110 CONTINUE + END SUBROUTINE DISP_DFDRHO_WDA_D + +END MODULE MOD_DFT_DISP_WDA_D diff --git a/applications/PUfoam/MoDeNaModels/SurfaceTension/src/mod_DFT_FMT.F90 b/applications/PUfoam/MoDeNaModels/SurfaceTension/src/mod_DFT_FMT.F90 new file mode 100644 index 000000000..5d6ed7f0c --- /dev/null +++ b/applications/PUfoam/MoDeNaModels/SurfaceTension/src/mod_DFT_FMT.F90 @@ -0,0 +1,344 @@ +!>This file contains the subroutines which calculate the contribution of +!!volume exclusion to the Helmholtz energy functional. + + + + +Module mod_DFT_FMT + +Implicit None + +Private + +Public :: FMT_Weighted_Densities +Public :: FMT_dFdrho + + Contains + + + + + +Subroutine FMT_Weighted_Densities(rhop,n0,n1,n2,n3,nv1,nv2,phi_dn0,phi_dn1,phi_dn2,phi_dn3,phi_dnv1,phi_dnv2,user) + +Use PARAMETERS, ONLY: PI +Use BASIC_VARIABLES, Only: ncomp,parame +Use EOS_VARIABLES, Only: dhs +Use mod_DFT, Only: zp,dzp,fa + +!PETSc module +Use PetscManagement + +#include + +!passed +Type (userctx) :: user +PetscScalar :: rhop(ncomp,user%gxs:user%gxe) +REAL,dimension(user%gxs:user%gxe),Intent(OUT) :: n0,n1,n2,n3,nv1,nv2 !ngp muss groesser als fa+fa/2 sein!! +REAL,dimension(user%gxs:user%gxe),Intent(OUT) :: phi_dn0,phi_dn1,phi_dn2,phi_dn3,phi_dnv1,phi_dnv2 + +!local +Integer :: k,i,j +Integer :: fa2 +REAL :: dz,d2,zz +INTEGER :: n +INTEGER, parameter :: NMAX = 800 +REAL,dimension(NMAX) :: x_int,n2_int,n3_int,nv2_int !Fehlerwarnung falls 200 ueberschritten einbauen +REAL,dimension(NMAX) :: y2_n2, y2_n3,y2_nv2 +REAL :: int_n2,int_n3,int_nv2,xhi,xlo +REAL :: zms,zms2,zms3,logzms +REAL :: nn0,nn1,nn2,nn3,nnv1,nnv2 +REAL :: rhopjk, rhopjp1k + + + n0 = 0.0 + n1 = 0.0 + n2 = 0.0 + n3 = 0.0 + nv1 = 0.0 + nv2 = 0.0 + + fa2 = maxval(fa(1:ncomp) + 5) / 2 + +Do k=1,ncomp + !fa2 = (fa(k) + 5) / 2 !grid points in sig/2 + d2 = dhs(k) / 2.0 !half of dhs [A] + + + Do i=user%xs-fa2,user%xe+fa2 !to evaluate dF/drho at any point, the derivatives dphi/dn have to be evaluated at +-d/2 around this point + n = 1 !this is the index of the arrays that will be passed to the spline integration routines + x_int = 0.0 + n2_int = 0.0 + n3_int = 0.0 + nv2_int = 0.0 + + Do j=i-fa2,i+fa2 !to evaluate dphi/dn at a given point, the weighted densities are needed at +-d/2 around this point + + rhopjk = rhop(k,j) * parame(k,1) + rhopjp1k = rhop(k,j+1) * parame(k,1) + + If( ( zp(i)-zp(j+1) ) < d2 .and. ( zp(i) - zp(j) ) >= d2 ) Then !the position of j+1 is already within i-d/2 while j is still outside this range in this case, the integration steplength (dz) is just the distance, which j+1 overlaps with i-d/2 and what is integrated is the interpolated value of the integrand + + If(n/= 1) stop 'n /=1 in FMT_Weighted_Densities' !here always n=1! + zz = zp(j) - zp(i) !distance between grid points j and i + dz = zp(j+1) - (zp(i) - d2) !the part of the intervall between zp(j) and zp(j+1) which is already within i-d/2 + !if(dz < epsilon(dz)) dz = epsilon(dz) !bei unguenstiger Kombination von sig und ngrid kann dz unter Machinengenauigkeit epsilon liegen, dann ist x(2) = x(1) + dz = x(1) -> das fuehrt zu Abbruch in Spline Interpolation + x_int(n) = 0.0 !array containing x-values for spline integration + n2_int(n) = rhopjk + (rhopjp1k-rhopjk) / (dzp) * (dzp-dz) !integrand f�r n2 (=rhop) linear interpoliert f�r den Punk zp(i)-d/2 + n3_int(n) = 0.0 !integrand f�r n3: rhop*(d2**2 - z'**2), da hier gerade z' = d2 -> integrand wird hier = 0!! + nv2_int(n) = rhopjk*zz +(rhopjp1k*(zp(j+1)-zp(i))-rhopjk*zz)/(dzp)*(dzp-dz) !analog + + + Else If (zp(j) > (zp(i)-d2) .and. zp(j) <= (zp(i)+d2)) Then !grid point j within i+-d2 + + n = n + 1 + x_int(n) = x_int(n-1) + dz !first time in this If condition, dz is stil the old value from above! + zz = zp(j) - zp(i) + dz = dzp + n2_int(n) = rhopjk + n3_int(n) = rhopjk * (d2**2 - zz**2) + nv2_int(n) = rhopjk * zz + + If (zp(j) < (zp(i)+d2) .and. zp(j+1) >= (zp(i)+d2) ) Then !zp(j) is still within zp(i)+d2 but zp(j+1) is already outside zp(i)+d2 + + dz = zp(i) + d2 - zp(j) + !If(dz <= epsilon(dz)) exit !wie oben, kann auch hier bei ungluecklicher Wahl von sig und ngrid dz < eps werden und somit x(n) = x(n-1) -> Abbruch in Spline interpolation. Dann einfach ngrid aendern! + zz = zp(j) - zp(i) + n = n + 1 + x_int(n) = x_int(n-1) + dz +! If(x_int(n) == x_int(n-1)) Then +! n = n - 1 +! exit +! End If + n2_int(n) = rhopjk + (rhopjp1k-rhopjk) / (dzp) * dz + n3_int(n) = 0.0 !Begr�ndung wie oben + nv2_int(n) = rhopjk*zz + (rhopjp1k*(zp(j+1)-zp(i)) - rhopjk*zz) / (dzp) * dz + + End If + + End If + + + End Do + + !spline integration + xlo = x_int(1) + xhi = x_int(n) + + If(n > NMAX) stop 'Increase NMAX in FMT_Weighted_Densities (auch in AD Routine!!)' + + call spline ( x_int, n2_int, n, 1.E30, 1.E30, y2_n2 ) + call spline ( x_int, n3_int, n, 1.E30, 1.E30, y2_n3 ) + call spline ( x_int, nv2_int, n, 1.E30, 1.E30, y2_nv2 ) + + call splint_integral ( x_int, n2_int, y2_n2, n, xlo, xhi, int_n2 ) + call splint_integral ( x_int, n3_int, y2_n3, n, xlo, xhi, int_n3 ) + call splint_integral ( x_int, nv2_int, y2_nv2, n, xlo, xhi, int_nv2 ) + + !weighted densities + n2(i) = n2(i) + PI * dhs(k) * int_n2 + n1(i) = n1(i) + 0.5 * int_n2 + n0(i) = n0(i) + int_n2/dhs(k) + n3(i) = n3(i) + PI * int_n3 + nv2(i) = nv2(i) -2.0 * PI * int_nv2 + nv1(i) = nv1(i) -int_nv2 / dhs(k) + +! If(i < 5) Then +! write(*,*)'i dens',i,nv2(i),n1(i),n0(i) +! write(*,*)'i dens',i,n3(i),nv1(i),nv2(i) +! end if +! +! If(i > 95) then +! write(*,*)'i dens',i,nv2(i),n1(i),n0(i) +! write(*,*)'i dens',i,n3(i),nv1(i),nv2(i) +! End If +! + End Do + + ! pause + +End Do + + +!derivatives of FMT helmholtz energy density w.r.t. weighted densities +Do i=user%xs-maxval((fa(1:ncomp)+1)/2),user%xe+maxval((fa(1:ncomp)+1)/2) + !weils k�rzer ist + nn0 = n0(i) + nn1 = n1(i) + nn2 = n2(i) + nn3 = n3(i) + nnv1 = nv1(i) + nnv2 = nv2(i) + + zms = 1.0 - nn3 + zms2 = zms*zms + zms3 = zms2*zms + logzms = log(zms) + if(isnan(logzms)) stop 'zms < 0, log(zms) undefined FMT_Weighted_Densities' + + phi_dn0(i) = -logzms + phi_dn1(i) = nn2/zms + phi_dn2(i) = nn1/zms + 3.0*(nn2*nn2-nnv2*nnv2) * (nn3+zms2*logzms) / (36.0*PI*nn3*nn3*zms2) + + phi_dn3(i) = nn0/zms + (nn1*nn2-nnv1*nnv2)/zms2 - (nn2**3-3.0*nn2*nnv2*nnv2) * (nn3*(nn3**2-5.0*nn3+2.0)+2.0*zms3*logzms) & + / (36.0*PI*nn3**3*zms3) + + phi_dnv1(i) = -nnv2/zms + + phi_dnv2(i) = -nnv1/zms - 6.0*nn2*nnv2*(nn3+zms2*logzms)/(36.0*PI*nn3**2*zms2) + +End Do + +End Subroutine FMT_Weighted_Densities + + + + + + + +Subroutine FMT_dFdrho(i,fa,user,phi_dn0,phi_dn1,phi_dn2,phi_dn3,phi_dnv1,phi_dnv2,dF_drho_FMT) + +Use BASIC_VARIABLES, Only: ncomp,parame +Use EOS_VARIABLES, Only: dhs +Use mod_DFT, Only: zp,dzp +Use PARAMETERS, ONLY: PI + +!PETSc module +Use PetscManagement + +!passed +INTEGER, INTENT(IN) :: i !the grid point at which to calculate dFdrho +INTEGER, INTENT(IN) :: fa(ncomp) +Type (userctx) :: user +REAL,dimension(user%gxs:user%gxe),INTENT(IN) :: phi_dn0,phi_dn1,phi_dn2,phi_dn3,phi_dnv1,phi_dnv2 +REAL,dimension(user%xs:user%xe,ncomp), INTENT(OUT) :: dF_drho_FMT + + +!local +INTEGER :: j,k,n +INTEGER :: fa2 +REAL :: dz,d2,zz, zz_jp1 +INTEGER, parameter :: NMAX = 800 +REAL,dimension(NMAX) :: x_int,y_int,y0_int,y1_int,y2_int,y3_int,yv1_int,yv2_int,y2 +REAL :: xhi,xlo,integral,int0,int1,int2,int3,intv1,intv2 +REAL :: at_j, at_jp1 + + +!Das Integral (Gleichung A1 in Gross DFT 2009) wird hier in einem Schlag berechnet! +!Falls die einzelnen Terme einzeln integriert werden sollen, einfach die auskommentierte Version verwenden + +Do k=1,ncomp !das einzige, das hier von k abhaengt, sind fa und dhs!! die Ableitungen phi_dn... sind nicht Komponentenspez, da die + !gewichteten Dichten ja uch nicht mehr Komponentenspez sind (n_i = sum n_i(k)) + + n = 1 + fa2 = ( fa(k) + 5 ) / 2 !number of grid points within dhs/2 + d2 = dhs(k)/2.0 + + Do j = i-fa2,i+fa2 + + If( ( zp(i)-zp(j+1) ) < d2 .and. ( zp(i) - zp(j) ) >= d2 ) Then !the position of j+1 is already within i-d/2 while j is still outside this range in this case, the integration steplength (dz) is just the distance, which j+1 overlaps with i-d/2 and what is integrated is the interpolated value of the integrand + x_int(n) = 0.0 + If(n/=1) stop 'error in FMT_dFdrho, n should be 1 here!' + dz = zp(j+1) - (zp(i) - d2) + zz = zp(j) - zp(i) + zz_jp1 = zp(j+1) - zp(i) + at_j = phi_dn0(j)/dhs(k) + 0.5*phi_dn1(j) + PI*dhs(k)*phi_dn2(j) & + + PI*phi_dn3(j)*(d2**2 - zz**2) + phi_dnv1(j)*zz/dhs(k) + 2.0*PI*phi_dnv2(j)*zz + + at_jp1 = phi_dn0(j+1)/dhs(k) + 0.5*phi_dn1(j+1) + PI*dhs(k)*phi_dn2(j+1) & + + PI*phi_dn3(j+1)*(d2**2 - zz_jp1**2) + phi_dnv1(j+1)*zz_jp1/dhs(k) + 2.0*PI*phi_dnv2(j+1)*zz_jp1 + + y_int(n) = at_j + (at_jp1-at_j)/dzp * (dzp-dz) !lineare interpolation genau, wie in FMT_Weighted_Densities +! y0_int(n) = phi_dn0(j) + (phi_dn0(j+1) -phi_dn0(j))/dzp * (dzp-dz) +! y1_int(n) = phi_dn1(j) + (phi_dn1(j+1) -phi_dn1(j))/dzp * (dzp-dz) +! y2_int(n) = phi_dn2(j) + (phi_dn2(j+1) -phi_dn2(j))/dzp * (dzp-dz) +! y3_int(n) = phi_dn3(j)*(d2**2-zz**2) + (phi_dn3(j+1)*(d2**2-zz_jp1**2) - phi_dn3(j)*(d2**2-zz**2) )/dzp * (dzp-dz) +! yv1_int(n) = phi_dnv1(j)*zz + (phi_dnv1(j+1)*zz_jp1 - phi_dnv1(j)*zz)/dzp * (dzp-dz) +! yv2_int(n) = phi_dnv2(j)*zz + (phi_dnv2(j+1)*zz_jp1 - phi_dnv2(j)*zz)/dzp * (dzp-dz) +! + + Else If (zp(j) > (zp(i)-d2) .and. zp(j) <= (zp(i)+d2)) Then !grid points j and j+1 are completely within i+-d2 + + n = n + 1 + zz = zp(j) - zp(i) + x_int(n) = x_int(n-1) + dz + + + y_int(n) = phi_dn0(j)/dhs(k) + 0.5*phi_dn1(j) + PI*dhs(k)*phi_dn2(j) & + + PI*phi_dn3(j)*(d2**2 - zz**2) + phi_dnv1(j)*zz/dhs(k) + 2.0*PI*phi_dnv2(j)*zz + + +! y0_int(n) = phi_dn0(j) +! y1_int(n) = phi_dn1(j) +! y2_int(n) = phi_dn2(j) +! y3_int(n) = phi_dn3(j)*(d2**2-zz**2) +! yv1_int(n) = phi_dnv1(j)*zz +! yv2_int(n) = phi_dnv2(j)*zz +! + + dz = dzp + + If (zp(j) < (zp(i)+d2) .and. zp(j+1) > (zp(i)+d2) ) Then !zp(j) is still within zp(i)+d2 but zp(j+1) is already out side zp(i)+d2 + + n = n + 1 + zz = zp(j) - zp(i) + zz_jp1 = zp(j+1) - zp(i) + dz = zp(i) + d2 - zp(j) + x_int(n) = x_int(n-1) + dz + at_j = phi_dn0(j)/dhs(k) + 0.5*phi_dn1(j) + PI*dhs(k)*phi_dn2(j) & + + PI*phi_dn3(j)*(d2**2 - zz**2) + phi_dnv1(j)*zz/dhs(k) + 2.0*PI*phi_dnv2(j)*zz + at_jp1 = phi_dn0(j+1)/dhs(k) + 0.5*phi_dn1(j+1) + PI*dhs(k)*phi_dn2(j+1) & + + PI*phi_dn3(j+1)*(d2**2 - zz_jp1**2) + phi_dnv1(j+1)*zz_jp1/dhs(k) + 2.0*PI*phi_dnv2(j+1)*zz_jp1 + y_int(n) = at_j + (at_jp1-at_j)/dzp * dz + + +! y0_int(n) = phi_dn0(j) + (phi_dn0(j+1) - phi_dn0(j))/dzp * dz +! y1_int(n) = phi_dn1(j) + (phi_dn1(j+1) - phi_dn1(j))/dzp * dz +! y2_int(n) = phi_dn2(j) + (phi_dn2(j+1) - phi_dn2(j))/dzp * dz +! y3_int(n) = phi_dn3(j)*(d2**2 - zz**2) + (phi_dn3(j+1)*(d2**2 - zz_jp1**2) - phi_dn3(j)*(d2**2 - zz**2))/dzp * dz +! yv1_int(n) = phi_dnv1(j)*zz + (phi_dnv1(j+1)*zz_jp1 - phi_dnv1(j)*zz)/dzp * dz +! yv2_int(n) = phi_dnv2(j)*zz + (phi_dnv2(j+1)*zz_jp1 - phi_dnv2(j)*zz)/dzp * dz +! + + + End If + + End If + + + End Do + + !spline integration + xlo = x_int(1) + xhi = x_int(n) + + If(n > NMAX) stop 'Increase NMAX in FMT_dFdrho (auch in AD Routine!!)' + + call spline(x_int,y_int,n,1.E30,1.E30,y2) + call splint_integral(x_int,y_int,y2,n,xlo,xhi,integral) + +! call spline ( x_int, y0_int, n, 1.E30, 1.E30, y2 ) +! call splint_integral ( x_int, y0_int, y2, n, xlo, xhi, int0 ) +! call spline ( x_int, y1_int, n, 1.E30, 1.E30, y2 ) +! call splint_integral ( x_int, y1_int, y2, n, xlo, xhi, int1 ) +! call spline ( x_int, y2_int, n, 1.E30, 1.E30, y2 ) +! call splint_integral ( x_int, y2_int, y2, n, xlo, xhi, int2 ) +! call spline ( x_int, y3_int, n, 1.E30, 1.E30, y2 ) +! call splint_integral ( x_int, y3_int, y2, n, xlo, xhi, int3 ) +! call spline ( x_int, yv1_int, n, 1.E30, 1.E30, y2 ) +! call splint_integral ( x_int, yv1_int, y2, n, xlo, xhi, intv1 ) +! call spline ( x_int, yv2_int, n, 1.E30, 1.E30, y2 ) +! call splint_integral ( x_int, yv2_int, y2, n, xlo, xhi, intv2 ) +! + + !dF_drho_FMT(i,k) = int0/dhs(k) + 0.5*int1 + PI*dhs(k)*int2 + PI*int3 + intv1/dhs(k) + 2.0*PI*intv2 + dF_drho_FMT(i,k) = integral*parame(k,1) + +End Do + + +End Subroutine FMT_dFdrho + + +End Module mod_DFT_FMT diff --git a/applications/PUfoam/MoDeNaModels/SurfaceTension/src/mod_DFT_FMT_d.F90 b/applications/PUfoam/MoDeNaModels/SurfaceTension/src/mod_DFT_FMT_d.F90 new file mode 100644 index 000000000..75729b74d --- /dev/null +++ b/applications/PUfoam/MoDeNaModels/SurfaceTension/src/mod_DFT_FMT_d.F90 @@ -0,0 +1,464 @@ +!>This file contains the subroutines which calculate the derivatives of the contribution of +!!volume exclusion to the Helmholtz energy functional. + + + + + +! Generated by TAPENADE (INRIA, Tropics team) +! Tapenade 3.10 (r5498) - 20 Jan 2015 09:48 +! +!All equations are taken from the appendix of: +!Gross: 'A density functional theory for vapor-liquid interfaces using the PCP-SAFT eos' +!But: here we dont treat chain-molecules!! -> no multiplications with segment number +MODULE MOD_DFT_FMT_D + IMPLICIT NONE + PRIVATE + PUBLIC fmt_weighted_densities_d + PUBLIC fmt_dfdrho_d + +CONTAINS +! Differentiation of fmt_weighted_densities in forward (tangent) mode: +! variations of useful results: phi_dn0 phi_dn1 phi_dn2 phi_dnv1 +! phi_dn3 phi_dnv2 +! with respect to varying inputs: rhop + SUBROUTINE FMT_WEIGHTED_DENSITIES_D(rhop, rhopd, n0, n1, n2, n3, nv1, & +& nv2, phi_dn0, phi_dn0d, phi_dn1, phi_dn1d, phi_dn2, phi_dn2d, & +& phi_dn3, phi_dn3d, phi_dnv1, phi_dnv1d, phi_dnv2, phi_dnv2d, user) + USE PARAMETERS, ONLY : pi + USE BASIC_VARIABLES, ONLY : ncomp,parame + USE EOS_VARIABLES, Only: dhs + USE MOD_DFT, ONLY : zp, dzp, fa + + +!PETSc module +Use PetscManagement +IMPLICIT NONE + +#include + +!passed +Type (userctx) :: user +PetscScalar :: rhop(ncomp,user%gxs:user%gxe) +PetscScalar :: rhopd(ncomp,user%gxs:user%gxe) +REAL,dimension(user%gxs:user%gxe),Intent(OUT) :: n0,n1,n2,n3,nv1,nv2 !ngp muss groesser als fa+fa/2 sein!! +REAL,dimension(user%gxs:user%gxe),Intent(OUT) :: phi_dn0,phi_dn1,phi_dn2,phi_dn3,phi_dnv1,phi_dnv2 +REAL,dimension(user%gxs:user%gxe),Intent(OUT) :: phi_dn0d,phi_dn1d,phi_dn2d,phi_dn3d,phi_dnv1d,phi_dnv2d + + + + +!local + REAL, DIMENSION(user%gxs:user%gxe) :: n0d,n1d,n2d,n3d,nv1d,nv2d + INTEGER :: k, i, j + INTEGER :: fa2 + REAL :: dz, d2, zz + INTEGER :: n + INTEGER, parameter :: NMAX = 800 + REAL, DIMENSION(NMAX) :: x_int, n2_int, n3_int, nv2_int + REAL, DIMENSION(NMAX) :: n2_intd, n3_intd, nv2_intd + REAL, DIMENSION(NMAX) :: y2_n2, y2_n3, y2_nv2 + REAL, DIMENSION(NMAX) :: y2_n2d, y2_n3d, y2_nv2d + REAL :: int_n2, int_n3, int_nv2, xhi, xlo + REAL :: int_n2d, int_n3d, int_nv2d + REAL :: zms, zms2, zms3, logzms + REAL :: zmsd, zms2d, zms3d, logzmsd + REAL :: nn0, nn1, nn2, nn3, nnv1, nnv2 + REAL :: nn0d, nn1d, nn2d, nn3d, nnv1d, nnv2d + REAL :: rhopjk, rhopjp1k + REAL :: rhopjkd, rhopjp1kd + INTRINSIC MAXVAL + INTRINSIC LOG + REAL :: result1 + + + + n0 = 0.0 + n1 = 0.0 + n2 = 0.0 + n3 = 0.0 + nv1 = 0.0 + nv2 = 0.0 + result1 = MAXVAL(fa(1:ncomp) + 5) + fa2 = result1/2 + nv1d = 0.0 + nv2d = 0.0 + n0d = 0.0 + n1d = 0.0 + n2d = 0.0 + n3d = 0.0 + y2_n2d = 0.0 + y2_n3d = 0.0 + y2_nv2d = 0.0 + DO k=1,ncomp +!fa2 = (fa(k) + 5) / 2 !grid points in sig/2 +!half of dhs [A] + d2 = dhs(k)/2.0 + + + + + Do i=user%xs-fa2,user%xe+fa2 !to evaluate dF/drho at any point, the derivatives dphi/dn have to be evaluated at +-d/2 around this point + + n = 1 + x_int = 0.0 + n2_int = 0.0 + n3_int = 0.0 + nv2_int = 0.0 + n2_intd = 0.0 + nv2_intd = 0.0 + n3_intd = 0.0 +!to evaluate dphi/dn at a given point, the weighted densities are needed at +-d/2 around this point + DO j=i-fa2,i+fa2 + rhopjkd = parame(k,1)*rhopd(k, j) + rhopjk = rhop(k, j)*parame(k,1) + rhopjp1kd = parame(k,1)*rhopd(k, j+1) + rhopjp1k = rhop(k, j+1)*parame(k,1) + IF (zp(i) - zp(j+1) .LT. d2 .AND. zp(i) - zp(j) .GE. d2) THEN +!the position of j+1 is already within i-d/2 while j is still outside this range in this case, the integration steplength (dz) is +! just the distance, which j+1 overlaps with i-d/2 and what is integrated is the interpolated value of the integrand +!here always n=1! + IF (n .NE. 1) THEN + GOTO 100 + ELSE +!distance between grid points j and i + zz = zp(j) - zp(i) +!the part of the intervall between zp(j) and zp(j+1) which is already within i-d/2 + dz = zp(j+1) - (zp(i)-d2) +!if(dz < epsilon(dz)) dz = epsilon(dz) !bei unguenstiger Kombination von sig und ngrid kann dz unter Machinengenauigkeit epsilon +!liegen, dann ist x(2) = x(1) + dz = x(1) -> das fuehrt zu Abbruch in Spline Interpolation +!array containing x-values for spline integration + x_int(n) = 0.0 +!integrand f�r n2 (=rhop) linear interpoliert f�r den Punk zp(i)-d/2 + n2_intd(n) = rhopjkd + (dzp-dz)*(rhopjp1kd-rhopjkd)/dzp + n2_int(n) = rhopjk + (rhopjp1k-rhopjk)/dzp*(dzp-dz) +!integrand f�r n3: rhop*(d2**2 - z'**2), da hier gerade z' = d2 -> integrand wird hier = 0!! + n3_intd(n) = 0.0 + n3_int(n) = 0.0 +!analog + nv2_intd(n) = zz*rhopjkd + (dzp-dz)*((zp(j+1)-zp(i))*& +& rhopjp1kd-zz*rhopjkd)/dzp + nv2_int(n) = rhopjk*zz + (rhopjp1k*(zp(j+1)-zp(i))-rhopjk*& +& zz)/dzp*(dzp-dz) + END IF + ELSE IF (zp(j) .GT. zp(i) - d2 .AND. zp(j) .LE. zp(i) + d2) & +& THEN +!grid point j within i+-d2 + n = n + 1 +!first time in this If condition, dz is stil the old value from above! + x_int(n) = x_int(n-1) + dz + zz = zp(j) - zp(i) + dz = dzp + n2_intd(n) = rhopjkd + n2_int(n) = rhopjk + n3_intd(n) = (d2**2-zz**2)*rhopjkd + n3_int(n) = rhopjk*(d2**2-zz**2) + nv2_intd(n) = zz*rhopjkd + nv2_int(n) = rhopjk*zz + IF (zp(j) .LT. zp(i) + d2 .AND. zp(j+1) .GE. zp(i) + d2) & +& THEN +!zp(j) is still within zp(i)+d2 but zp(j+1) is already outside zp(i)+d2 + dz = zp(i) + d2 - zp(j) +!If(dz <= epsilon(dz)) exit !wie oben, kann auch hier bei ungluecklicher Wahl von sig und ngrid dz < eps werden und somit x(n) +!= x(n-1) -> Abbruch in Spline interpolation. Dann einfach ngrid aendern! + zz = zp(j) - zp(i) + n = n + 1 + x_int(n) = x_int(n-1) + dz +! If(x_int(n) == x_int(n-1)) Then +! n = n - 1 +! exit +! End If + n2_intd(n) = rhopjkd + dz*(rhopjp1kd-rhopjkd)/dzp + n2_int(n) = rhopjk + (rhopjp1k-rhopjk)/dzp*dz +!Begr�ndung wie oben + n3_intd(n) = 0.0 + n3_int(n) = 0.0 + nv2_intd(n) = zz*rhopjkd + dz*((zp(j+1)-zp(i))*rhopjp1kd-& +& zz*rhopjkd)/dzp + nv2_int(n) = rhopjk*zz + (rhopjp1k*(zp(j+1)-zp(i))-rhopjk*& +& zz)/dzp*dz + END IF + END IF + END DO +!spline integration + xlo = x_int(1) + xhi = x_int(n) + CALL SPLINE_D(x_int, n2_int, n2_intd, n, 1.e30, 1.e30, y2_n2, & +& y2_n2d) + CALL SPLINE_D(x_int, n3_int, n3_intd, n, 1.e30, 1.e30, y2_n3, & +& y2_n3d) + CALL SPLINE_D(x_int, nv2_int, nv2_intd, n, 1.e30, 1.e30, y2_nv2& +& , y2_nv2d) + CALL SPLINT_INTEGRAL_D(x_int, n2_int, n2_intd, y2_n2, y2_n2d, n& +& , xlo, xhi, int_n2, int_n2d) + CALL SPLINT_INTEGRAL_D(x_int, n3_int, n3_intd, y2_n3, y2_n3d, n& +& , xlo, xhi, int_n3, int_n3d) + CALL SPLINT_INTEGRAL_D(x_int, nv2_int, nv2_intd, y2_nv2, y2_nv2d& +& , n, xlo, xhi, int_nv2, int_nv2d) +!weighted densities + n2d(i) = n2d(i) + pi*dhs(k)*int_n2d + n2(i) = n2(i) + pi*dhs(k)*int_n2 + n1d(i) = n1d(i) + 0.5*int_n2d + n1(i) = n1(i) + 0.5*int_n2 + n0d(i) = n0d(i) + int_n2d/dhs(k) + n0(i) = n0(i) + int_n2/dhs(k) + n3d(i) = n3d(i) + pi*int_n3d + n3(i) = n3(i) + pi*int_n3 + nv2d(i) = nv2d(i) - 2.0*pi*int_nv2d + nv2(i) = nv2(i) - 2.0*pi*int_nv2 + nv1d(i) = nv1d(i) - int_nv2d/dhs(k) + nv1(i) = nv1(i) - int_nv2/dhs(k) + END DO + END DO + phi_dn0d = 0.0 + phi_dn1d = 0.0 + phi_dn2d = 0.0 + phi_dnv1d = 0.0 + phi_dn3d = 0.0 + phi_dnv2d = 0.0 +! If(i < 5) Then +! write(*,*)'i dens',i,nv2(i),n1(i),n0(i) +! write(*,*)'i dens',i,n3(i),nv1(i),nv2(i) +! end if +! +! If(i > 95) then +! write(*,*)'i dens',i,nv2(i),n1(i),n0(i) +! write(*,*)'i dens',i,n3(i),nv1(i),nv2(i) +! End If +! +! pause + + +!derivatives of FMT helmholtz energy density w.r.t. weighted densities +Do i=user%xs-maxval((fa(1:ncomp)+1)/2),user%xe+maxval((fa(1:ncomp)+1)/2) +!weils k�rzer ist + nn0d = n0d(i) + nn0 = n0(i) + nn1d = n1d(i) + nn1 = n1(i) + nn2d = n2d(i) + nn2 = n2(i) + nn3d = n3d(i) + nn3 = n3(i) + nnv1d = nv1d(i) + nnv1 = nv1(i) + nnv2d = nv2d(i) + nnv2 = nv2(i) + zmsd = -nn3d + zms = 1.0 - nn3 + zms2d = zmsd*zms + zms*zmsd + zms2 = zms*zms + zms3d = zms2d*zms + zms2*zmsd + zms3 = zms2*zms + logzmsd = zmsd/zms + logzms = LOG(zms) +!if(isnan(logzms)) stop 'zms < 0, log(zms) undefined FMT_Weighted_Densities' + phi_dn0d(i) = -logzmsd + phi_dn0(i) = -logzms + phi_dn1d(i) = (nn2d*zms-nn2*zmsd)/zms**2 + phi_dn1(i) = nn2/zms + phi_dn2d(i) = (nn1d*zms-nn1*zmsd)/zms**2 + (3.0*((nn2d*nn2+nn2*& +& nn2d-nnv2d*nnv2-nnv2*nnv2d)*(nn3+zms2*logzms)+(nn2*nn2-nnv2*nnv2& +& )*(nn3d+zms2d*logzms+zms2*logzmsd))*36.0*pi*nn3**2*zms2-3.0*(nn2& +& *nn2-nnv2*nnv2)*(nn3+zms2*logzms)*36.0*pi*((nn3d*nn3+nn3*nn3d)*& +& zms2+nn3**2*zms2d))/(36.0*pi*nn3*nn3*zms2)**2 + phi_dn2(i) = nn1/zms + 3.0*(nn2*nn2-nnv2*nnv2)*(nn3+zms2*logzms)/(& +& 36.0*pi*nn3*nn3*zms2) + phi_dn3d(i) = (nn0d*zms-nn0*zmsd)/zms**2 + ((nn1d*nn2+nn1*nn2d-& +& nnv1d*nnv2-nnv1*nnv2d)*zms2-(nn1*nn2-nnv1*nnv2)*zms2d)/zms2**2 -& +& (((3*nn2**2*nn2d-3.0*((nn2d*nnv2+nn2*nnv2d)*nnv2+nn2*nnv2*nnv2d)& +& )*(nn3*(nn3**2-5.0*nn3+2.0)+2.0*zms3*logzms)+(nn2**3-3.0*nn2*& +& nnv2*nnv2)*(nn3d*(nn3**2-5.0*nn3+2.0)+nn3*(2*nn3*nn3d-5.0*nn3d)+& +& 2.0*(zms3d*logzms+zms3*logzmsd)))*36.0*pi*nn3**3*zms3-(nn2**3-& +& 3.0*nn2*nnv2*nnv2)*(nn3*(nn3**2-5.0*nn3+2.0)+2.0*zms3*logzms)*& +& 36.0*pi*(3*nn3**2*nn3d*zms3+nn3**3*zms3d))/(36.0*pi*nn3**3*zms3)& +& **2 + phi_dn3(i) = nn0/zms + (nn1*nn2-nnv1*nnv2)/zms2 - (nn2**3-3.0*nn2*& +& nnv2*nnv2)*(nn3*(nn3**2-5.0*nn3+2.0)+2.0*zms3*logzms)/(36.0*pi*& +& nn3**3*zms3) + phi_dnv1d(i) = -((nnv2d*zms-nnv2*zmsd)/zms**2) + phi_dnv1(i) = -(nnv2/zms) + phi_dnv2d(i) = -((nnv1d*zms-nnv1*zmsd)/zms**2) - (6.0*((nn2d*nnv2+& +& nn2*nnv2d)*(nn3+zms2*logzms)+nn2*nnv2*(nn3d+zms2d*logzms+zms2*& +& logzmsd))*36.0*pi*nn3**2*zms2-6.0*nn2*nnv2*(nn3+zms2*logzms)*& +& 36.0*pi*(2*nn3*nn3d*zms2+nn3**2*zms2d))/(36.0*pi*nn3**2*zms2)**2 + phi_dnv2(i) = -(nnv1/zms) - 6.0*nn2*nnv2*(nn3+zms2*logzms)/(36.0*& +& pi*nn3**2*zms2) + END DO + GOTO 110 + 100 STOP + 110 CONTINUE + END SUBROUTINE FMT_WEIGHTED_DENSITIES_D + + + +! Differentiation of fmt_dfdrho in forward (tangent) mode: +! variations of useful results: df_drho_fmt +! with respect to varying inputs: df_drho_fmt phi_dn0 phi_dn1 +! phi_dn2 phi_dnv1 phi_dn3 phi_dnv2 + SUBROUTINE FMT_DFDRHO_D(i, fa, user, phi_dn0, phi_dn0d, phi_dn1, & +& phi_dn1d, phi_dn2, phi_dn2d, phi_dn3, phi_dn3d, phi_dnv1, phi_dnv1d& +& , phi_dnv2, phi_dnv2d, df_drho_fmt, df_drho_fmtd) + USE BASIC_VARIABLES, ONLY : ncomp,parame + USE EOS_VARIABLES, Only: dhs + USE MOD_DFT, ONLY : zp, dzp + USE PARAMETERS, ONLY : pi + + +!PETSc module +Use PetscManagement + + IMPLICIT NONE + +!passed +INTEGER, INTENT(IN) :: i !the grid point at which to calculate dFdrho +INTEGER, INTENT(IN) :: fa(ncomp) +Type (userctx) :: user +REAL,dimension(user%gxs:user%gxe),INTENT(IN) :: phi_dn0,phi_dn1,phi_dn2,phi_dn3,phi_dnv1,phi_dnv2 +REAL,dimension(user%gxs:user%gxe),INTENT(IN) :: phi_dn0d,phi_dn1d,phi_dn2d,phi_dn3d,phi_dnv1d,phi_dnv2d + +REAL,dimension(user%xs:user%xe,ncomp), INTENT(OUT) :: dF_drho_FMT +REAL,dimension(user%xs:user%xe,ncomp), INTENT(OUT) :: dF_drho_FMTd + + +!local + INTEGER :: j, k, n + INTEGER :: fa2 + REAL :: dz, d2, zz, zz_jp1 + INTEGER, parameter :: NMAX = 800 + REAL, DIMENSION(NMAX) :: x_int, y_int, y0_int, y1_int, y2_int, y3_int& +& , yv1_int, yv2_int, y2 + REAL, DIMENSION(NMAX) :: y_intd, y2d + REAL :: xhi, xlo, integral, int0, int1, int2, int3, intv1, intv2 + REAL :: integrald + REAL :: at_j, at_jp1 + REAL :: at_jd, at_jp1d + + + y2d = 0.0 + y_intd = 0.0 +!Das Integral (Gleichung A1 in Gross DFT 2009) wird hier in einem Schlag berechnet! +!Falls die einzelnen Terme einzeln integriert werden sollen, einfach die auskommentierte Version verwenden +!das einzige, das hier von k abhaengt, sind fa und dhs!! die Ableitungen phi_dn... sind nicht Komponentenspez, da die + DO k=1,ncomp +!gewichteten Dichten ja uch nicht mehr Komponentenspez sind (n_i = sum n_i(k)) + n = 1 +!number of grid points within dhs/2 + fa2 = (fa(k)+5)/2 + d2 = dhs(k)/2.0 + DO j=i-fa2,i+fa2 + IF (zp(i) - zp(j+1) .LT. d2 .AND. zp(i) - zp(j) .GE. d2) THEN +!the position of j+1 is already within i-d/2 while j is still outside this range in this case, the integration steplength (dz) is +! just the distance, which j+1 overlaps with i-d/2 and what is integrated is the interpolated value of the integrand + x_int(n) = 0.0 + IF (n .NE. 1) THEN + GOTO 100 + ELSE + dz = zp(j+1) - (zp(i)-d2) + zz = zp(j) - zp(i) + zz_jp1 = zp(j+1) - zp(i) + at_jd = phi_dn0d(j)/dhs(k) + 0.5*phi_dn1d(j) + pi*dhs(k)*& +& phi_dn2d(j) + pi*(d2**2-zz**2)*phi_dn3d(j) + zz*phi_dnv1d(& +& j)/dhs(k) + 2.0*pi*zz*phi_dnv2d(j) + at_j = phi_dn0(j)/dhs(k) + 0.5*phi_dn1(j) + pi*dhs(k)*& +& phi_dn2(j) + pi*phi_dn3(j)*(d2**2-zz**2) + phi_dnv1(j)*zz/& +& dhs(k) + 2.0*pi*phi_dnv2(j)*zz + at_jp1d = phi_dn0d(j+1)/dhs(k) + 0.5*phi_dn1d(j+1) + pi*dhs(& +& k)*phi_dn2d(j+1) + pi*(d2**2-zz_jp1**2)*phi_dn3d(j+1) + & +& zz_jp1*phi_dnv1d(j+1)/dhs(k) + 2.0*pi*zz_jp1*phi_dnv2d(j+1& +& ) + at_jp1 = phi_dn0(j+1)/dhs(k) + 0.5*phi_dn1(j+1) + pi*dhs(k)*& +& phi_dn2(j+1) + pi*phi_dn3(j+1)*(d2**2-zz_jp1**2) + & +& phi_dnv1(j+1)*zz_jp1/dhs(k) + 2.0*pi*phi_dnv2(j+1)*zz_jp1 +!lineare interpolation genau, wie in FMT_Weighted_Densities + y_intd(n) = at_jd + (dzp-dz)*(at_jp1d-at_jd)/dzp + y_int(n) = at_j + (at_jp1-at_j)/dzp*(dzp-dz) +! y0_int(n) = phi_dn0(j) + (phi_dn0(j+1) -phi_dn0(j))/dzp * (dzp-dz) +! y1_int(n) = phi_dn1(j) + (phi_dn1(j+1) -phi_dn1(j))/dzp * (dzp-dz) +! y2_int(n) = phi_dn2(j) + (phi_dn2(j+1) -phi_dn2(j))/dzp * (dzp-dz) +! y3_int(n) = phi_dn3(j)*(d2**2-zz**2) + (phi_dn3(j+1)*(d2**2-zz_jp1**2) - phi_dn3(j)*(d2**2-zz**2) )/dzp * (dzp-dz) +! yv1_int(n) = phi_dnv1(j)*zz + (phi_dnv1(j+1)*zz_jp1 - phi_dnv1(j)*zz)/dzp * (dzp-dz) +! yv2_int(n) = phi_dnv2(j)*zz + (phi_dnv2(j+1)*zz_jp1 - phi_dnv2(j)*zz)/dzp * (dzp-dz) +! + END IF + ELSE IF (zp(j) .GT. zp(i) - d2 .AND. zp(j) .LE. zp(i) + d2) THEN +!grid points j and j+1 are completely within i+-d2 + n = n + 1 + zz = zp(j) - zp(i) + x_int(n) = x_int(n-1) + dz + y_intd(n) = phi_dn0d(j)/dhs(k) + 0.5*phi_dn1d(j) + pi*dhs(k)*& +& phi_dn2d(j) + pi*(d2**2-zz**2)*phi_dn3d(j) + zz*phi_dnv1d(j)& +& /dhs(k) + 2.0*pi*zz*phi_dnv2d(j) + y_int(n) = phi_dn0(j)/dhs(k) + 0.5*phi_dn1(j) + pi*dhs(k)*& +& phi_dn2(j) + pi*phi_dn3(j)*(d2**2-zz**2) + phi_dnv1(j)*zz/& +& dhs(k) + 2.0*pi*phi_dnv2(j)*zz +! y0_int(n) = phi_dn0(j) +! y1_int(n) = phi_dn1(j) +! y2_int(n) = phi_dn2(j) +! y3_int(n) = phi_dn3(j)*(d2**2-zz**2) +! yv1_int(n) = phi_dnv1(j)*zz +! yv2_int(n) = phi_dnv2(j)*zz +! + dz = dzp + IF (zp(j) .LT. zp(i) + d2 .AND. zp(j+1) .GT. zp(i) + d2) THEN +!zp(j) is still within zp(i)+d2 but zp(j+1) is already out side zp(i)+d2 + n = n + 1 + zz = zp(j) - zp(i) + zz_jp1 = zp(j+1) - zp(i) + dz = zp(i) + d2 - zp(j) + x_int(n) = x_int(n-1) + dz + at_jd = phi_dn0d(j)/dhs(k) + 0.5*phi_dn1d(j) + pi*dhs(k)*& +& phi_dn2d(j) + pi*(d2**2-zz**2)*phi_dn3d(j) + zz*phi_dnv1d(& +& j)/dhs(k) + 2.0*pi*zz*phi_dnv2d(j) + at_j = phi_dn0(j)/dhs(k) + 0.5*phi_dn1(j) + pi*dhs(k)*& +& phi_dn2(j) + pi*phi_dn3(j)*(d2**2-zz**2) + phi_dnv1(j)*zz/& +& dhs(k) + 2.0*pi*phi_dnv2(j)*zz + at_jp1d = phi_dn0d(j+1)/dhs(k) + 0.5*phi_dn1d(j+1) + pi*dhs(& +& k)*phi_dn2d(j+1) + pi*(d2**2-zz_jp1**2)*phi_dn3d(j+1) + & +& zz_jp1*phi_dnv1d(j+1)/dhs(k) + 2.0*pi*zz_jp1*phi_dnv2d(j+1& +& ) + at_jp1 = phi_dn0(j+1)/dhs(k) + 0.5*phi_dn1(j+1) + pi*dhs(k)*& +& phi_dn2(j+1) + pi*phi_dn3(j+1)*(d2**2-zz_jp1**2) + & +& phi_dnv1(j+1)*zz_jp1/dhs(k) + 2.0*pi*phi_dnv2(j+1)*zz_jp1 + y_intd(n) = at_jd + dz*(at_jp1d-at_jd)/dzp + y_int(n) = at_j + (at_jp1-at_j)/dzp*dz +! y0_int(n) = phi_dn0(j) + (phi_dn0(j+1) - phi_dn0(j))/dzp * dz +! y1_int(n) = phi_dn1(j) + (phi_dn1(j+1) - phi_dn1(j))/dzp * dz +! y2_int(n) = phi_dn2(j) + (phi_dn2(j+1) - phi_dn2(j))/dzp * dz +! y3_int(n) = phi_dn3(j)*(d2**2 - zz**2) + (phi_dn3(j+1)*(d2**2 - zz_jp1**2) - phi_dn3(j)*(d2**2 - zz**2))/dzp * dz +! yv1_int(n) = phi_dnv1(j)*zz + (phi_dnv1(j+1)*zz_jp1 - phi_dnv1(j)*zz)/dzp * dz +! yv2_int(n) = phi_dnv2(j)*zz + (phi_dnv2(j+1)*zz_jp1 - phi_dnv2(j)*zz)/dzp * dz +! + END IF + END IF + END DO +!spline integration + xlo = x_int(1) + xhi = x_int(n) + CALL SPLINE_D(x_int, y_int, y_intd, n, 1.e30, 1.e30, y2, y2d) + CALL SPLINT_INTEGRAL_D(x_int, y_int, y_intd, y2, y2d, n, xlo, xhi& +& , integral, integrald) +! call spline ( x_int, y0_int, n, 1.E30, 1.E30, y2 ) +! call splint_integral ( x_int, y0_int, y2, n, xlo, xhi, int0 ) +! call spline ( x_int, y1_int, n, 1.E30, 1.E30, y2 ) +! call splint_integral ( x_int, y1_int, y2, n, xlo, xhi, int1 ) +! call spline ( x_int, y2_int, n, 1.E30, 1.E30, y2 ) +! call splint_integral ( x_int, y2_int, y2, n, xlo, xhi, int2 ) +! call spline ( x_int, y3_int, n, 1.E30, 1.E30, y2 ) +! call splint_integral ( x_int, y3_int, y2, n, xlo, xhi, int3 ) +! call spline ( x_int, yv1_int, n, 1.E30, 1.E30, y2 ) +! call splint_integral ( x_int, yv1_int, y2, n, xlo, xhi, intv1 ) +! call spline ( x_int, yv2_int, n, 1.E30, 1.E30, y2 ) +! call splint_integral ( x_int, yv2_int, y2, n, xlo, xhi, intv2 ) +! +!dF_drho_FMT(i,k) = int0/dhs(k) + 0.5*int1 + PI*dhs(k)*int2 + PI*int3 + intv1/dhs(k) + 2.0*PI*intv2 + df_drho_fmtd(i, k) = parame(k,1)*integrald + df_drho_fmt(i, k) = integral*parame(k,1) + END DO + GOTO 110 + 100 STOP + 110 CONTINUE + END SUBROUTINE FMT_DFDRHO_D + +END MODULE MOD_DFT_FMT_D + diff --git a/applications/PUfoam/MoDeNaModels/SurfaceTension/src/mod_PETSc.F90 b/applications/PUfoam/MoDeNaModels/SurfaceTension/src/mod_PETSc.F90 new file mode 100644 index 000000000..a9ccaec0f --- /dev/null +++ b/applications/PUfoam/MoDeNaModels/SurfaceTension/src/mod_PETSc.F90 @@ -0,0 +1,69 @@ + + + + +!>In this module, the application context is defined + +Module PetscManagement + + type userctx +#include +#include +#include + PetscInt xs,xe,xm,gxs,gxe,gxm,mx + PetscMPIInt rank + PetscMPIInt num_procs + end type userctx + +End Module + + + +!>This module contains variables associated with the PETSc solver + +Module Global_x +Implicit None +#include +#include +#include + +SNES :: snes !nonlinear solver context +Vec :: x !array of unknowns +Vec :: r !array of residuals +PetscInt :: ngrid !number of grid points +PetscInt :: ngp !number of ghost points + +DOUBLE PRECISION :: timer ! timer +DOUBLE PRECISION :: timer_old ! timer +DOUBLE PRECISION :: total_time ! timer + + +End Module Global_x + + + +Module f90moduleinterfaces +Use PetscManagement +#include + + Interface SNESSetApplicationContext + Subroutine SNESSetApplicationContext(snes,ctx,ierr) + use PetscManagement + SNES snes + type(userctx) ctx + PetscErrorCode ierr + End Subroutine + End Interface SNESSetApplicationContext + + Interface SNESGetApplicationContext + Subroutine SNESGetApplicationContext(snes,ctx,ierr) + use PetscManagement + SNES snes + type(userctx), pointer :: ctx + PetscErrorCode ierr + End Subroutine + End Interface SNESGetApplicationContext + +End Module f90moduleinterfaces + + diff --git a/applications/PUfoam/MoDeNaModels/SurfaceTension/src/module_solve_nonlinear.F90 b/applications/PUfoam/MoDeNaModels/SurfaceTension/src/module_solve_nonlinear.F90 new file mode 100644 index 000000000..7d8f5be52 --- /dev/null +++ b/applications/PUfoam/MoDeNaModels/SurfaceTension/src/module_solve_nonlinear.F90 @@ -0,0 +1,1621 @@ + +MODULE Solve_NonLin + +! Corrections to FUNCTION Enorm - 28 November 2003 + +IMPLICIT NONE +INTEGER, PARAMETER :: dp = SELECTED_REAL_KIND(14, 60) +PRIVATE +PUBLIC :: hbrd, hybrd + + +CONTAINS + + +SUBROUTINE hbrd(fcn, n, x, fvec, epsfcn, tol, info, diag) + +! Code converted using TO_F90 by Alan Miller +! Date: 2003-07-15 Time: 13:27:42 + +INTEGER, INTENT(IN) :: n +REAL (dp), INTENT(IN OUT) :: x(n) +REAL (dp), INTENT(IN OUT) :: fvec(n) +REAL (dp), INTENT(IN) :: epsfcn +REAL (dp), INTENT(IN) :: tol +INTEGER, INTENT(OUT) :: info +REAL (dp), INTENT(OUT) :: diag(n) + +! EXTERNAL fcn +INTERFACE + SUBROUTINE FCN(N, X, FVEC, IFLAG) + IMPLICIT NONE + INTEGER, PARAMETER :: dp = SELECTED_REAL_KIND(14, 60) + INTEGER, INTENT(IN) :: n + REAL (dp), INTENT(IN) :: x(n) + REAL (dp), INTENT(OUT) :: fvec(n) + INTEGER, INTENT(IN OUT) :: iflag + END SUBROUTINE FCN +END INTERFACE + +!> ********** +!! SUBROUTINE HBRD +!! THE PURPOSE OF HBRD IS TO FIND A ZERO OF A SYSTEM OF N NONLINEAR +!! FUNCTIONS IN N VARIABLES BY A MODIFICATION OF THE POWELL HYBRID METHOD. +!! THIS IS DONE BY USING THE MORE GENERAL NONLINEAR EQUATION SOLVER HYBRD. +!! THE USER MUST PROVIDE A SUBROUTINE WHICH CALCULATES THE FUNCTIONS. +!! THE JACOBIAN IS THEN CALCULATED BY A FORWARD-DIFFERENCE APPROXIMATION. +!! THE SUBROUTINE STATEMENT IS +!! SUBROUTINE HBRD(N, X, FVEC, EPSFCN, TOL, INFO, WA, LWA) +!! WHERE +!! FCN IS THE NAME OF THE USER-SUPPLIED SUBROUTINE WHICH CALCULATES +!! THE FUNCTIONS. FCN MUST BE DECLARED IN AN EXTERNAL STATEMENT +!! IN THE USER CALLING PROGRAM, AND SHOULD BE WRITTEN AS FOLLOWS. +!! SUBROUTINE FCN(N, X, FVEC, IFLAG) +!! INTEGER N,IFLAG +!! REAL X(N),FVEC(N) +!! ---------- +!! CALCULATE THE FUNCTIONS AT X AND RETURN THIS VECTOR IN FVEC. +!! --------- +!! RETURN +!! END +!! THE VALUE OF IFLAG NOT BE CHANGED BY FCN UNLESS +!! THE USER WANTS TO TERMINATE THE EXECUTION OF HBRD. +!! IN THIS CASE SET IFLAG TO A NEGATIVE INTEGER. +!! N IS A POSITIVE INTEGER INPUT VARIABLE SET TO THE NUMBER +!! OF FUNCTIONS AND VARIABLES. +!! X IS AN ARRAY OF LENGTH N. ON INPUT X MUST CONTAIN AN INITIAL +!! ESTIMATE OF THE SOLUTION VECTOR. ON OUTPUT X CONTAINS THE +!! FINAL ESTIMATE OF THE SOLUTION VECTOR. +!! FVEC IS AN OUTPUT ARRAY OF LENGTH N WHICH CONTAINS +!! THE FUNCTIONS EVALUATED AT THE OUTPUT X. +!! EPSFCN IS AN INPUT VARIABLE USED IN DETERMINING A SUITABLE STEP LENGTH +!! FOR THE FORWARD-DIFFERENCE APPROXIMATION. THIS APPROXIMATION ASSUMES +!! THAT THE RELATIVE ERRORS IN THE FUNCTIONS ARE OF THE ORDER OF EPSFCN. +!! IF EPSFCN IS LESS THAN THE MACHINE PRECISION, IT IS ASSUMED THAT THE +!! RELATIVE ERRORS IN THE FUNCTIONS ARE OF THE ORDER OF THE MACHINE +!! PRECISION. +!! TOL IS A NONNEGATIVE INPUT VARIABLE. TERMINATION OCCURS WHEN THE +!! ALGORITHM ESTIMATES THAT THE RELATIVE ERROR BETWEEN X AND THE SOLUTION +!! IS AT MOST TOL. +!! INFO IS AN INTEGER OUTPUT VARIABLE. IF THE USER HAS TERMINATED +!! EXECUTION, INFO IS SET TO THE (NEGATIVE) VALUE OF IFLAG. +!! SEE DESCRIPTION OF FCN. OTHERWISE, INFO IS SET AS FOLLOWS. +!! INFO = 0 IMPROPER INPUT PARAMETERS. +!! INFO = 1 ALGORITHM ESTIMATES THAT THE RELATIVE ERROR +!! BETWEEN X AND THE SOLUTION IS AT MOST TOL. +!! INFO = 2 NUMBER OF CALLS TO FCN HAS REACHED OR EXCEEDED 200*(N+1). +!! INFO = 3 TOL IS TOO SMALL. NO FURTHER IMPROVEMENT IN +!! THE APPROXIMATE SOLUTION X IS POSSIBLE. +!! INFO = 4 ITERATION IS NOT MAKING GOOD PROGRESS. +!! SUBPROGRAMS CALLED +!! USER-SUPPLIED ...... FCN +!! MINPACK-SUPPLIED ... HYBRD +!! ARGONNE NATIONAL LABORATORY. MINPACK PROJECT. MARCH 1980. +!! BURTON S. GARBOW, KENNETH E. HILLSTROM, JORGE J. MORE +!! Reference: +!! Powell, M.J.D. 'A hybrid method for nonlinear equations' in Numerical Methods +!! for Nonlinear Algebraic Equations', P.Rabinowitz (editor), Gordon and +!! Breach, London 1970. +!! ********** +INTEGER :: maxfev, ml, mode, mu, nfev, nprint +REAL (dp) :: xtol +REAL (dp), PARAMETER :: factor = 1.0_dp, zero = 0.0_dp + +info = 0 + +! CHECK THE INPUT PARAMETERS FOR ERRORS. + + +IF (n <= 0 .OR. epsfcn < zero .OR. tol < zero) GO TO 20 + +! CALL HYBRD. + +maxfev = 200*(n + 1) +xtol = tol +ml = n - 1 +mu = n - 1 +mode = 2 +nprint = 0 +CALL hybrd(fcn, n, x, fvec, xtol, maxfev, ml, mu, epsfcn, diag, mode, & + factor, nprint, info, nfev) +IF (info == 5) info = 4 +20 RETURN + +! LAST CARD OF SUBROUTINE HBRD. + +END SUBROUTINE hbrd + + + +SUBROUTINE hybrd(fcn, n, x, fvec, xtol, maxfev, ml, mu, epsfcn, diag, mode, & + factor, nprint, info, nfev) + +INTEGER, INTENT(IN) :: n +REAL (dp), INTENT(IN OUT) :: x(n) +REAL (dp), INTENT(IN OUT) :: fvec(n) +REAL (dp), INTENT(IN) :: xtol +INTEGER, INTENT(IN OUT) :: maxfev +INTEGER, INTENT(IN OUT) :: ml +INTEGER, INTENT(IN) :: mu +REAL (dp), INTENT(IN) :: epsfcn +REAL (dp), INTENT(OUT) :: diag(n) +INTEGER, INTENT(IN) :: mode +REAL (dp), INTENT(IN) :: factor +INTEGER, INTENT(IN OUT) :: nprint +INTEGER, INTENT(OUT) :: info +INTEGER, INTENT(OUT) :: nfev + +! EXTERNAL fcn +INTERFACE + SUBROUTINE FCN(N, X, FVEC, IFLAG) + IMPLICIT NONE + INTEGER, PARAMETER :: dp = SELECTED_REAL_KIND(14, 60) + INTEGER, INTENT(IN) :: n + REAL (dp), INTENT(IN) :: x(n) + REAL (dp), INTENT(OUT) :: fvec(n) + INTEGER, INTENT(IN OUT) :: iflag + END SUBROUTINE FCN +END INTERFACE + +! ********** + +! SUBROUTINE HYBRD + +! THE PURPOSE OF HYBRD IS TO FIND A ZERO OF A SYSTEM OF N NONLINEAR +! FUNCTIONS IN N VARIABLES BY A MODIFICATION OF THE POWELL HYBRID METHOD. +! THE USER MUST PROVIDE A SUBROUTINE WHICH CALCULATES THE FUNCTIONS. +! THE JACOBIAN IS THEN CALCULATED BY A FORWARD-DIFFERENCE APPROXIMATION. + +! THE SUBROUTINE STATEMENT IS + +! SUBROUTINE HYBRD(FCN, N, X, FVEC, XTOL, MAXFEV, ML, MU, EPSFCN, +! DIAG, MODE, FACTOR, NPRINT, INFO, NFEV, FJAC, +! LDFJAC, R, LR, QTF, WA1, WA2, WA3, WA4) + +! WHERE + +! FCN IS THE NAME OF THE USER-SUPPLIED SUBROUTINE WHICH CALCULATES +! THE FUNCTIONS. FCN MUST BE DECLARED IN AN EXTERNAL STATEMENT IN +! THE USER CALLING PROGRAM, AND SHOULD BE WRITTEN AS FOLLOWS. + +! SUBROUTINE FCN(N, X, FVEC, IFLAG) +! INTEGER N, IFLAG +! REAL X(N), FVEC(N) +! ---------- +! CALCULATE THE FUNCTIONS AT X AND +! RETURN THIS VECTOR IN FVEC. +! --------- +! RETURN +! END + +! THE VALUE OF IFLAG SHOULD NOT BE CHANGED BY FCN UNLESS +! THE USER WANTS TO TERMINATE EXECUTION OF HYBRD. +! IN THIS CASE SET IFLAG TO A NEGATIVE INTEGER. + +! N IS A POSITIVE INTEGER INPUT VARIABLE SET TO THE NUMBER +! OF FUNCTIONS AND VARIABLES. + +! X IS AN ARRAY OF LENGTH N. ON INPUT X MUST CONTAIN AN INITIAL +! ESTIMATE OF THE SOLUTION VECTOR. ON OUTPUT X CONTAINS THE FINAL +! ESTIMATE OF THE SOLUTION VECTOR. + +! FVEC IS AN OUTPUT ARRAY OF LENGTH N WHICH CONTAINS +! THE FUNCTIONS EVALUATED AT THE OUTPUT X. + +! XTOL IS A NONNEGATIVE INPUT VARIABLE. TERMINATION OCCURS WHEN THE +! RELATIVE ERROR BETWEEN TWO CONSECUTIVE ITERATES IS AT MOST XTOL. + +! MAXFEV IS A POSITIVE INTEGER INPUT VARIABLE. TERMINATION OCCURS WHEN +! THE NUMBER OF CALLS TO FCN IS AT LEAST MAXFEV BY THE END OF AN +! ITERATION. + +! ML IS A NONNEGATIVE INTEGER INPUT VARIABLE WHICH SPECIFIES THE +! NUMBER OF SUBDIAGONALS WITHIN THE BAND OF THE JACOBIAN MATRIX. +! IF THE JACOBIAN IS NOT BANDED, SET ML TO AT LEAST N - 1. + +! MU IS A NONNEGATIVE INTEGER INPUT VARIABLE WHICH SPECIFIES THE NUMBER +! OF SUPERDIAGONALS WITHIN THE BAND OF THE JACOBIAN MATRIX. +! IF THE JACOBIAN IS NOT BANDED, SET MU TO AT LEAST N - 1. + +! EPSFCN IS AN INPUT VARIABLE USED IN DETERMINING A SUITABLE STEP LENGTH +! FOR THE FORWARD-DIFFERENCE APPROXIMATION. THIS APPROXIMATION +! ASSUMES THAT THE RELATIVE ERRORS IN THE FUNCTIONS ARE OF THE ORDER +! OF EPSFCN. IF EPSFCN IS LESS THAN THE MACHINE PRECISION, +! IT IS ASSUMED THAT THE RELATIVE ERRORS IN THE FUNCTIONS ARE OF THE +! ORDER OF THE MACHINE PRECISION. + +! DIAG IS AN ARRAY OF LENGTH N. IF MODE = 1 (SEE BELOW), +! DIAG IS INTERNALLY SET. IF MODE = 2, DIAG MUST CONTAIN POSITIVE +! ENTRIES THAT SERVE AS MULTIPLICATIVE SCALE FACTORS FOR THE +! VARIABLES. + +! MODE IS AN INTEGER INPUT VARIABLE. IF MODE = 1, THE VARIABLES WILL BE +! SCALED INTERNALLY. IF MODE = 2, THE SCALING IS SPECIFIED BY THE +! INPUT DIAG. OTHER VALUES OF MODE ARE EQUIVALENT TO MODE = 1. + +! FACTOR IS A POSITIVE INPUT VARIABLE USED IN DETERMINING THE +! INITIAL STEP BOUND. THIS BOUND IS SET TO THE PRODUCT OF +! FACTOR AND THE EUCLIDEAN NORM OF DIAG*X IF NONZERO, OR ELSE +! TO FACTOR ITSELF. IN MOST CASES FACTOR SHOULD LIE IN THE +! INTERVAL (.1,100.). 100. IS A GENERALLY RECOMMENDED VALUE. + +! NPRINT IS AN INTEGER INPUT VARIABLE THAT ENABLES CONTROLLED +! PRINTING OF ITERATES IF IT IS POSITIVE. IN THIS CASE, +! FCN IS CALLED WITH IFLAG = 0 AT THE BEGINNING OF THE FIRST +! ITERATION AND EVERY NPRINT ITERATIONS THEREAFTER AND +! IMMEDIATELY PRIOR TO RETURN, WITH X AND FVEC AVAILABLE +! FOR PRINTING. IF NPRINT IS NOT POSITIVE, NO SPECIAL CALLS +! OF FCN WITH IFLAG = 0 ARE MADE. + +! INFO IS AN INTEGER OUTPUT VARIABLE. IF THE USER HAS +! TERMINATED EXECUTION, INFO IS SET TO THE (NEGATIVE) +! VALUE OF IFLAG. SEE DESCRIPTION OF FCN. OTHERWISE, +! INFO IS SET AS FOLLOWS. + +! INFO = 0 IMPROPER INPUT PARAMETERS. + +! INFO = 1 RELATIVE ERROR BETWEEN TWO CONSECUTIVE ITERATES +! IS AT MOST XTOL. + +! INFO = 2 NUMBER OF CALLS TO FCN HAS REACHED OR EXCEEDED MAXFEV. + +! INFO = 3 XTOL IS TOO SMALL. NO FURTHER IMPROVEMENT IN +! THE APPROXIMATE SOLUTION X IS POSSIBLE. + +! INFO = 4 ITERATION IS NOT MAKING GOOD PROGRESS, AS +! MEASURED BY THE IMPROVEMENT FROM THE LAST +! FIVE JACOBIAN EVALUATIONS. + +! INFO = 5 ITERATION IS NOT MAKING GOOD PROGRESS, AS MEASURED BY +! THE IMPROVEMENT FROM THE LAST TEN ITERATIONS. + +! NFEV IS AN INTEGER OUTPUT VARIABLE SET TO THE NUMBER OF CALLS TO FCN. + +! FJAC IS AN OUTPUT N BY N ARRAY WHICH CONTAINS THE ORTHOGONAL MATRIX Q +! PRODUCED BY THE QR FACTORIZATION OF THE FINAL APPROXIMATE JACOBIAN. + +! LDFJAC IS A POSITIVE INTEGER INPUT VARIABLE NOT LESS THAN N +! WHICH SPECIFIES THE LEADING DIMENSION OF THE ARRAY FJAC. + +! R IS AN OUTPUT ARRAY OF LENGTH LR WHICH CONTAINS THE +! UPPER TRIANGULAR MATRIX PRODUCED BY THE QR FACTORIZATION +! OF THE FINAL APPROXIMATE JACOBIAN, STORED ROWWISE. + +! LR IS A POSITIVE INTEGER INPUT VARIABLE NOT LESS THAN (N*(N+1))/2. + +! QTF IS AN OUTPUT ARRAY OF LENGTH N WHICH CONTAINS +! THE VECTOR (Q TRANSPOSE)*FVEC. + +! WA1, WA2, WA3, AND WA4 ARE WORK ARRAYS OF LENGTH N. + +! SUBPROGRAMS CALLED + +! USER-SUPPLIED ...... FCN + +! MINPACK-SUPPLIED ... DOGLEG,SPMPAR,ENORM,FDJAC1, +! QFORM,QRFAC,R1MPYQ,R1UPDT + +! FORTRAN-SUPPLIED ... ABS,MAX,MIN,MIN,MOD + +! ARGONNE NATIONAL LABORATORY. MINPACK PROJECT. MARCH 1980. +! BURTON S. GARBOW, KENNETH E. HILLSTROM, JORGE J. MORE + +! ********** + +INTEGER :: i, iflag, iter, j, jm1, l, lr, msum, ncfail, ncsuc, nslow1, & + nslow2 +INTEGER :: iwa(1) +LOGICAL :: jeval, sing +REAL (dp) :: actred, delta, epsmch, fnorm, fnorm1, pnorm, prered, & + ratio, sum, temp, xnorm +REAL (dp), PARAMETER :: one = 1.0_dp, p1 = 0.1_dp, p5 = 0.5_dp, & + p001 = 0.001_dp, p0001 = 0.0001_dp, zero = 0.0_dp + +! The following were workspace arguments +REAL (dp) :: fjac(n,n), r(n*(n+1)/2), qtf(n), wa1(n), wa2(n), & + wa3(n), wa4(n) + +! EPSMCH IS THE MACHINE PRECISION. + +epsmch = EPSILON(1.0_dp) + +info = 0 +iflag = 0 +nfev = 0 +lr = n*(n+1)/2 + +! CHECK THE INPUT PARAMETERS FOR ERRORS. + +IF (n > 0 .AND. xtol >= zero .AND. maxfev > 0 .AND. ml >= 0 .AND. mu >= & + 0 .AND. factor > zero ) THEN +IF (mode == 2) THEN + diag(1:n) = one +END IF + +! EVALUATE THE FUNCTION AT THE STARTING POINT AND CALCULATE ITS NORM. + +iflag = 1 +CALL fcn(n, x, fvec, iflag) +nfev = 1 +IF (iflag >= 0) THEN + fnorm = enorm(n, fvec) + +! DETERMINE THE NUMBER OF CALLS TO FCN NEEDED TO COMPUTE THE JACOBIAN MATRIX. + + msum = MIN(ml+mu+1,n) + +! INITIALIZE ITERATION COUNTER AND MONITORS. + + iter = 1 + ncsuc = 0 + ncfail = 0 + nslow1 = 0 + nslow2 = 0 + +! BEGINNING OF THE OUTER LOOP. + + 20 jeval = .true. + +! CALCULATE THE JACOBIAN MATRIX. + + iflag = 2 + CALL fdjac1(fcn, n, x, fvec, fjac, n, iflag, ml, mu, epsfcn, wa1, wa2) + nfev = nfev + msum + IF (iflag >= 0) THEN + +! COMPUTE THE QR FACTORIZATION OF THE JACOBIAN. + + CALL qrfac(n, n, fjac, n, .false., iwa, 1, wa1, wa2, wa3) + +! ON THE FIRST ITERATION AND IF MODE IS 1, SCALE ACCORDING +! TO THE NORMS OF THE COLUMNS OF THE INITIAL JACOBIAN. + + IF (iter == 1) THEN + IF (mode /= 2) THEN + DO j = 1, n + diag(j) = wa2(j) + IF (wa2(j) == zero) diag(j) = one + END DO + END IF + +! ON THE FIRST ITERATION, CALCULATE THE NORM OF THE SCALED X +! AND INITIALIZE THE STEP BOUND DELTA. + + wa3(1:n) = diag(1:n) * x(1:n) + xnorm = enorm(n, wa3) + delta = factor * xnorm + IF (delta == zero) delta = factor + END IF + +! FORM (Q TRANSPOSE)*FVEC AND STORE IN QTF. + + qtf(1:n) = fvec(1:n) + DO j = 1, n + IF (fjac(j,j) /= zero) THEN + sum = zero + DO i = j, n + sum = sum + fjac(i,j) * qtf(i) + END DO + temp = -sum / fjac(j,j) + DO i = j, n + qtf(i) = qtf(i) + fjac(i,j) * temp + END DO + END IF + END DO + +! COPY THE TRIANGULAR FACTOR OF THE QR FACTORIZATION INTO R. + + sing = .false. + DO j = 1, n + l = j + jm1 = j - 1 + IF (jm1 >= 1) THEN + DO i = 1, jm1 + r(l) = fjac(i,j) + l = l + n - i + END DO + END IF + r(l) = wa1(j) + IF (wa1(j) == zero) sing = .true. + END DO + +! ACCUMULATE THE ORTHOGONAL FACTOR IN FJAC. + + CALL qform(n, n, fjac, n, wa1) + +! RESCALE IF NECESSARY. + + IF (mode /= 2) THEN + DO j = 1, n + diag(j) = MAX(diag(j), wa2(j)) + END DO + END IF + +! BEGINNING OF THE INNER LOOP. + +! IF REQUESTED, CALL FCN TO ENABLE PRINTING OF ITERATES. + + 120 IF (nprint > 0) THEN + iflag = 0 + IF (MOD(iter-1, nprint) == 0) CALL fcn(n, x, fvec, iflag) + IF (iflag < 0) GO TO 190 + END IF + +! DETERMINE THE DIRECTION P. + + CALL dogleg(n, r, lr, diag, qtf, delta, wa1, wa2, wa3) + +! STORE THE DIRECTION P AND X + P. CALCULATE THE NORM OF P. + + DO j = 1, n + wa1(j) = -wa1(j) + wa2(j) = x(j) + wa1(j) + wa3(j) = diag(j) * wa1(j) + END DO + pnorm = enorm(n, wa3) + +! ON THE FIRST ITERATION, ADJUST THE INITIAL STEP BOUND. + + IF (iter == 1) delta = MIN(delta, pnorm) + +! EVALUATE THE FUNCTION AT X + P AND CALCULATE ITS NORM. + + iflag = 1 + CALL fcn(n, wa2, wa4, iflag) + nfev = nfev + 1 + IF (iflag >= 0) THEN + fnorm1 = enorm(n, wa4) + +! COMPUTE THE SCALED ACTUAL REDUCTION. + + actred = -one + IF (fnorm1 < fnorm) actred = one - (fnorm1/fnorm) ** 2 + +! COMPUTE THE SCALED PREDICTED REDUCTION. + + l = 1 + DO i = 1, n + sum = zero + DO j = i, n + sum = sum + r(l) * wa1(j) + l = l + 1 + END DO + wa3(i) = qtf(i) + sum + END DO + temp = enorm(n, wa3) + prered = zero + IF (temp < fnorm) prered = one - (temp/fnorm) ** 2 + +! COMPUTE THE RATIO OF THE ACTUAL TO THE PREDICTED REDUCTION. + + ratio = zero + IF (prered > zero) ratio = actred / prered + +! UPDATE THE STEP BOUND. + + IF (ratio < p1) THEN + ncsuc = 0 + ncfail = ncfail + 1 + delta = p5 * delta + ELSE + ncfail = 0 + ncsuc = ncsuc + 1 + IF (ratio >= p5 .OR. ncsuc > 1) delta = MAX(delta,pnorm/p5) + IF (ABS(ratio-one) <= p1) delta = pnorm / p5 + END IF + +! TEST FOR SUCCESSFUL ITERATION. + + IF (ratio >= p0001) THEN + +! SUCCESSFUL ITERATION. UPDATE X, FVEC, AND THEIR NORMS. + + DO j = 1, n + x(j) = wa2(j) + wa2(j) = diag(j) * x(j) + fvec(j) = wa4(j) + END DO + xnorm = enorm(n, wa2) + fnorm = fnorm1 + iter = iter + 1 + END IF + +! DETERMINE THE PROGRESS OF THE ITERATION. + + nslow1 = nslow1 + 1 + IF (actred >= p001) nslow1 = 0 + IF (jeval) nslow2 = nslow2 + 1 + IF (actred >= p1) nslow2 = 0 + +! TEST FOR CONVERGENCE. + + IF (delta <= xtol*xnorm .OR. fnorm == zero) info = 1 + IF (info == 0) THEN + +! TESTS FOR TERMINATION AND STRINGENT TOLERANCES. + + IF (nfev >= maxfev) info = 2 + IF (p1*MAX(p1*delta, pnorm) <= epsmch*xnorm) info = 3 + IF (nslow2 == 5) info = 4 + IF (nslow1 == 10) info = 5 + IF (info == 0) THEN + +! CRITERION FOR RECALCULATING JACOBIAN APPROXIMATION +! BY FORWARD DIFFERENCES. + + IF (ncfail /= 2) THEN + +! CALCULATE THE RANK ONE MODIFICATION TO THE JACOBIAN +! AND UPDATE QTF IF NECESSARY. + + DO j = 1, n + sum = zero + DO i = 1, n + sum = sum + fjac(i,j) * wa4(i) + END DO + wa2(j) = (sum-wa3(j)) / pnorm + wa1(j) = diag(j) * ((diag(j)*wa1(j))/pnorm) + IF (ratio >= p0001) qtf(j) = sum + END DO + +! COMPUTE THE QR FACTORIZATION OF THE UPDATED JACOBIAN. + + CALL r1updt(n, n, r, lr, wa1, wa2, wa3, sing) + CALL r1mpyq(n, n, fjac, n, wa2, wa3) + CALL r1mpyq(1, n, qtf, 1, wa2, wa3) + +! END OF THE INNER LOOP. + + jeval = .false. + GO TO 120 + END IF + +! END OF THE OUTER LOOP. + + GO TO 20 + END IF + END IF + END IF + END IF +END IF +END IF + +! TERMINATION, EITHER NORMAL OR USER IMPOSED. + +190 IF (iflag < 0) info = iflag +iflag = 0 +IF (nprint > 0) CALL fcn(n, x, fvec, iflag) +RETURN + +! LAST CARD OF SUBROUTINE HYBRD. + +END SUBROUTINE hybrd + + + +SUBROUTINE dogleg(n, r, lr, diag, qtb, delta, x, wa1, wa2) + +INTEGER, INTENT(IN) :: n +INTEGER, INTENT(IN) :: lr +REAL (dp), INTENT(IN) :: r(lr) +REAL (dp), INTENT(IN) :: diag(n) +REAL (dp), INTENT(IN) :: qtb(n) +REAL (dp), INTENT(IN) :: delta +REAL (dp), INTENT(IN OUT) :: x(n) +REAL (dp), INTENT(OUT) :: wa1(n) +REAL (dp), INTENT(OUT) :: wa2(n) + + +! ********** + +! SUBROUTINE DOGLEG + +! GIVEN AN M BY N MATRIX A, AN N BY N NONSINGULAR DIAGONAL +! MATRIX D, AN M-VECTOR B, AND A POSITIVE NUMBER DELTA, THE +! PROBLEM IS TO DETERMINE THE CONVEX COMBINATION X OF THE +! GAUSS-NEWTON AND SCALED GRADIENT DIRECTIONS THAT MINIMIZES +! (A*X - B) IN THE LEAST SQUARES SENSE, SUBJECT TO THE +! RESTRICTION THAT THE EUCLIDEAN NORM OF D*X BE AT MOST DELTA. + +! THIS SUBROUTINE COMPLETES THE SOLUTION OF THE PROBLEM +! IF IT IS PROVIDED WITH THE NECESSARY INFORMATION FROM THE +! QR FACTORIZATION OF A. THAT IS, IF A = Q*R, WHERE Q HAS +! ORTHOGONAL COLUMNS AND R IS AN UPPER TRIANGULAR MATRIX, +! THEN DOGLEG EXPECTS THE FULL UPPER TRIANGLE OF R AND +! THE FIRST N COMPONENTS OF (Q TRANSPOSE)*B. + +! THE SUBROUTINE STATEMENT IS + +! SUBROUTINE DOGLEG(N,R,LR,DIAG,QTB,DELTA,X,WA1,WA2) + +! WHERE + +! N IS A POSITIVE INTEGER INPUT VARIABLE SET TO THE ORDER OF R. + +! R IS AN INPUT ARRAY OF LENGTH LR WHICH MUST CONTAIN THE UPPER +! TRIANGULAR MATRIX R STORED BY ROWS. + +! LR IS A POSITIVE INTEGER INPUT VARIABLE NOT LESS THAN +! (N*(N+1))/2. + +! DIAG IS AN INPUT ARRAY OF LENGTH N WHICH MUST CONTAIN THE +! DIAGONAL ELEMENTS OF THE MATRIX D. + +! QTB IS AN INPUT ARRAY OF LENGTH N WHICH MUST CONTAIN THE FIRST +! N ELEMENTS OF THE VECTOR (Q TRANSPOSE)*B. + +! DELTA IS A POSITIVE INPUT VARIABLE WHICH SPECIFIES AN UPPER +! BOUND ON THE EUCLIDEAN NORM OF D*X. + +! X IS AN OUTPUT ARRAY OF LENGTH N WHICH CONTAINS THE DESIRED +! CONVEX COMBINATION OF THE GAUSS-NEWTON DIRECTION AND THE +! SCALED GRADIENT DIRECTION. + +! WA1 AND WA2 ARE WORK ARRAYS OF LENGTH N. + +! SUBPROGRAMS CALLED + +! MINPACK-SUPPLIED ... SPMPAR,ENORM + +! FORTRAN-SUPPLIED ... ABS,MAX,MIN,SQRT + +! ARGONNE NATIONAL LABORATORY. MINPACK PROJECT. MARCH 1980. +! BURTON S. GARBOW, KENNETH E. HILLSTROM, JORGE J. MORE + +! ********** +INTEGER :: i, j, jj, jp1, k, l +REAL (dp) :: alpha, bnorm, epsmch, gnorm, qnorm, sgnorm, sum, temp + +! EPSMCH IS THE MACHINE PRECISION. + +epsmch = EPSILON(1.0_dp) + +! FIRST, CALCULATE THE GAUSS-NEWTON DIRECTION. + +jj = (n*(n+1)) / 2 + 1 +DO k = 1, n + j = n - k + 1 + jp1 = j + 1 + jj = jj - k + l = jj + 1 + sum = 0.0 + IF (n >= jp1) THEN + DO i = jp1, n + sum = sum + r(l) * x(i) + l = l + 1 + END DO + END IF + temp = r(jj) + IF (temp == 0.0) THEN + l = j + DO i = 1, j + temp = MAX(temp,ABS(r(l))) + l = l + n - i + END DO + temp = epsmch * temp + IF (temp == 0.0) temp = epsmch + END IF + x(j) = (qtb(j)-sum) / temp +END DO + +! TEST WHETHER THE GAUSS-NEWTON DIRECTION IS ACCEPTABLE. + +DO j = 1, n + wa1(j) = 0.0 + wa2(j) = diag(j) * x(j) +END DO +qnorm = enorm(n, wa2) +IF (qnorm > delta) THEN + +! THE GAUSS-NEWTON DIRECTION IS NOT ACCEPTABLE. +! NEXT, CALCULATE THE SCALED GRADIENT DIRECTION. + + l = 1 + DO j = 1, n + temp = qtb(j) + DO i = j, n + wa1(i) = wa1(i) + r(l) * temp + l = l + 1 + END DO + wa1(j) = wa1(j) / diag(j) + END DO + +! CALCULATE THE NORM OF THE SCALED GRADIENT AND TEST FOR +! THE SPECIAL CASE IN WHICH THE SCALED GRADIENT IS ZERO. + + gnorm = enorm(n, wa1) + sgnorm = 0.0 + alpha = delta / qnorm + IF (gnorm /= 0.0) THEN + +! CALCULATE THE POINT ALONG THE SCALED GRADIENT +! AT WHICH THE QUADRATIC IS MINIMIZED. + + DO j = 1, n + wa1(j) = (wa1(j)/gnorm) / diag(j) + END DO + l = 1 + DO j = 1, n + sum = 0.0 + DO i = j, n + sum = sum + r(l) * wa1(i) + l = l + 1 + END DO + wa2(j) = sum + END DO + temp = enorm(n, wa2) + sgnorm = (gnorm/temp) / temp + +! TEST WHETHER THE SCALED GRADIENT DIRECTION IS ACCEPTABLE. + + alpha = 0.0 + IF (sgnorm < delta) THEN + +! THE SCALED GRADIENT DIRECTION IS NOT ACCEPTABLE. +! FINALLY, CALCULATE THE POINT ALONG THE DOGLEG +! AT WHICH THE QUADRATIC IS MINIMIZED. + + bnorm = enorm(n, qtb) + temp = (bnorm/gnorm) * (bnorm/qnorm) * (sgnorm/delta) + temp = temp - (delta/qnorm) * (sgnorm/delta) ** 2 + SQRT(( & + temp-(delta/qnorm))**2+(1.0-(delta/qnorm)**2)*(1.0-( sgnorm/delta)**2)) + alpha = ((delta/qnorm)*(1.0-(sgnorm/delta)**2)) / temp + END IF + END IF + +! FORM APPROPRIATE CONVEX COMBINATION OF THE GAUSS-NEWTON +! DIRECTION AND THE SCALED GRADIENT DIRECTION. + + temp = (1.0-alpha) * MIN(sgnorm,delta) + DO j = 1, n + x(j) = temp * wa1(j) + alpha * x(j) + END DO +END IF +RETURN +END SUBROUTINE dogleg + + +SUBROUTINE fdjac1(fcn, n, x, fvec, fjac, ldfjac, iflag, ml, mu, epsfcn, & + wa1, wa2) + +INTEGER, INTENT(IN) :: n +REAL (dp), INTENT(IN OUT) :: x(n) +REAL (dp), INTENT(IN) :: fvec(n) +INTEGER, INTENT(IN) :: ldfjac +REAL (dp), INTENT(OUT) :: fjac(ldfjac,n) +INTEGER, INTENT(IN OUT) :: iflag +INTEGER, INTENT(IN) :: ml +INTEGER, INTENT(IN) :: mu +REAL (dp), INTENT(IN) :: epsfcn +REAL (dp), INTENT(IN OUT) :: wa1(n) +REAL (dp), INTENT(OUT) :: wa2(n) + +! EXTERNAL fcn +INTERFACE + SUBROUTINE FCN(N, X, FVEC, IFLAG) + IMPLICIT NONE + INTEGER, PARAMETER :: dp = SELECTED_REAL_KIND(14, 60) + INTEGER, INTENT(IN) :: n + REAL (dp), INTENT(IN) :: x(n) + REAL (dp), INTENT(OUT) :: fvec(n) + INTEGER, INTENT(IN OUT) :: iflag + END SUBROUTINE FCN +END INTERFACE + +! ********** + +! SUBROUTINE FDJAC1 + +! THIS SUBROUTINE COMPUTES A FORWARD-DIFFERENCE APPROXIMATION TO THE N BY N +! JACOBIAN MATRIX ASSOCIATED WITH A SPECIFIED PROBLEM OF N FUNCTIONS IN N +! VARIABLES. IF THE JACOBIAN HAS A BANDED FORM, THEN FUNCTION EVALUATIONS +! ARE SAVED BY ONLY APPROXIMATING THE NONZERO TERMS. + +! THE SUBROUTINE STATEMENT IS + +! SUBROUTINE FDJAC1(FCN,N,X,FVEC,FJAC,LDFJAC,IFLAG,ML,MU,EPSFCN, +! WA1,WA2) + +! WHERE + +! FCN IS THE NAME OF THE USER-SUPPLIED SUBROUTINE WHICH CALCULATES +! THE FUNCTIONS. FCN MUST BE DECLARED IN AN EXTERNAL STATEMENT IN +! THE USER CALLING PROGRAM, AND SHOULD BE WRITTEN AS FOLLOWS. + +! SUBROUTINE FCN(N,X,FVEC,IFLAG) +! INTEGER N,IFLAG +! REAL X(N),FVEC(N) +! ---------- +! CALCULATE THE FUNCTIONS AT X AND +! RETURN THIS VECTOR IN FVEC. +! ---------- +! RETURN +! END + +! THE VALUE OF IFLAG SHOULD NOT BE CHANGED BY FCN UNLESS +! THE USER WANTS TO TERMINATE EXECUTION OF FDJAC1. +! IN THIS CASE SET IFLAG TO A NEGATIVE INTEGER. + +! N IS A POSITIVE INTEGER INPUT VARIABLE SET TO THE NUMBER +! OF FUNCTIONS AND VARIABLES. + +! X IS AN INPUT ARRAY OF LENGTH N. + +! FVEC IS AN INPUT ARRAY OF LENGTH N WHICH MUST CONTAIN THE +! FUNCTIONS EVALUATED AT X. + +! FJAC IS AN OUTPUT N BY N ARRAY WHICH CONTAINS THE +! APPROXIMATION TO THE JACOBIAN MATRIX EVALUATED AT X. + +! LDFJAC IS A POSITIVE INTEGER INPUT VARIABLE NOT LESS THAN N +! WHICH SPECIFIES THE LEADING DIMENSION OF THE ARRAY FJAC. + +! IFLAG IS AN INTEGER VARIABLE WHICH CAN BE USED TO TERMINATE +! THE EXECUTION OF FDJAC1. SEE DESCRIPTION OF FCN. + +! ML IS A NONNEGATIVE INTEGER INPUT VARIABLE WHICH SPECIFIES +! THE NUMBER OF SUBDIAGONALS WITHIN THE BAND OF THE +! JACOBIAN MATRIX. IF THE JACOBIAN IS NOT BANDED, SET +! ML TO AT LEAST N - 1. + +! EPSFCN IS AN INPUT VARIABLE USED IN DETERMINING A SUITABLE +! STEP LENGTH FOR THE FORWARD-DIFFERENCE APPROXIMATION. THIS +! APPROXIMATION ASSUMES THAT THE RELATIVE ERRORS IN THE +! FUNCTIONS ARE OF THE ORDER OF EPSFCN. IF EPSFCN IS LESS +! THAN THE MACHINE PRECISION, IT IS ASSUMED THAT THE RELATIVE +! ERRORS IN THE FUNCTIONS ARE OF THE ORDER OF THE MACHINE PRECISION. + +! MU IS A NONNEGATIVE INTEGER INPUT VARIABLE WHICH SPECIFIES +! THE NUMBER OF SUPERDIAGONALS WITHIN THE BAND OF THE +! JACOBIAN MATRIX. IF THE JACOBIAN IS NOT BANDED, SET +! MU TO AT LEAST N - 1. + +! WA1 AND WA2 ARE WORK ARRAYS OF LENGTH N. IF ML + MU + 1 IS AT +! LEAST N, THEN THE JACOBIAN IS CONSIDERED DENSE, AND WA2 IS +! NOT REFERENCED. + +! SUBPROGRAMS CALLED + +! MINPACK-SUPPLIED ... SPMPAR + +! FORTRAN-SUPPLIED ... ABS,MAX,SQRT + +! ARGONNE NATIONAL LABORATORY. MINPACK PROJECT. MARCH 1980. +! BURTON S. GARBOW, KENNETH E. HILLSTROM, JORGE J. MORE + +! ********** +INTEGER :: i, j, k, msum +REAL (dp) :: eps, epsmch, h, temp +REAL (dp), PARAMETER :: zero = 0.0_dp + +! EPSMCH IS THE MACHINE PRECISION. + +epsmch = EPSILON(1.0_dp) + +eps = SQRT(MAX(epsfcn, epsmch)) +msum = ml + mu + 1 +IF (msum >= n) THEN + +! COMPUTATION OF DENSE APPROXIMATE JACOBIAN. + + DO j = 1, n + temp = x(j) + h = eps * ABS(temp) + IF (h == zero) h = eps + x(j) = temp + h + CALL fcn(n, x, wa1, iflag) + IF (iflag < 0) EXIT + x(j) = temp + DO i = 1, n + fjac(i,j) = (wa1(i)-fvec(i)) / h + END DO + END DO +ELSE + +! COMPUTATION OF BANDED APPROXIMATE JACOBIAN. + + DO k = 1, msum + DO j = k, n, msum + wa2(j) = x(j) + h = eps * ABS(wa2(j)) + IF (h == zero) h = eps + x(j) = wa2(j) + h + END DO + CALL fcn(n, x, wa1, iflag) + IF (iflag < 0) EXIT + DO j = k, n, msum + x(j) = wa2(j) + h = eps * ABS(wa2(j)) + IF (h == zero) h = eps + DO i = 1, n + fjac(i,j) = zero + IF (i >= j-mu .AND. i <= j+ml) fjac(i,j) = (wa1(i)-fvec(i)) / h + END DO + END DO + END DO +END IF +RETURN + +! LAST CARD OF SUBROUTINE FDJAC1. + +END SUBROUTINE fdjac1 + + + +SUBROUTINE qform(m, n, q, ldq, wa) + +INTEGER, INTENT(IN) :: m +INTEGER, INTENT(IN) :: n +INTEGER, INTENT(IN) :: ldq +REAL (dp), INTENT(OUT) :: q(ldq,m) +REAL (dp), INTENT(OUT) :: wa(m) + + +! ********** + +! SUBROUTINE QFORM + +! THIS SUBROUTINE PROCEEDS FROM THE COMPUTED QR FACTORIZATION OF AN M BY N +! MATRIX A TO ACCUMULATE THE M BY M ORTHOGONAL MATRIX Q FROM ITS FACTORED FORM. + +! THE SUBROUTINE STATEMENT IS + +! SUBROUTINE QFORM(M,N,Q,LDQ,WA) + +! WHERE + +! M IS A POSITIVE INTEGER INPUT VARIABLE SET TO THE NUMBER +! OF ROWS OF A AND THE ORDER OF Q. + +! N IS A POSITIVE INTEGER INPUT VARIABLE SET TO THE NUMBER OF COLUMNS OF A. + +! Q IS AN M BY M ARRAY. ON INPUT THE FULL LOWER TRAPEZOID IN +! THE FIRST MIN(M,N) COLUMNS OF Q CONTAINS THE FACTORED FORM. +! ON OUTPUT Q HAS BEEN ACCUMULATED INTO A SQUARE MATRIX. + +! LDQ IS A POSITIVE INTEGER INPUT VARIABLE NOT LESS THAN M +! WHICH SPECIFIES THE LEADING DIMENSION OF THE ARRAY Q. + +! WA IS A WORK ARRAY OF LENGTH M. + +! SUBPROGRAMS CALLED + +! FORTRAN-SUPPLIED ... MIN + +! ARGONNE NATIONAL LABORATORY. MINPACK PROJECT. MARCH 1980. +! BURTON S. GARBOW, KENNETH E. HILLSTROM, JORGE J. MORE + +! ********** +INTEGER :: i, j, jm1, k, l, minmn, np1 +REAL (dp) :: sum, temp +REAL (dp), PARAMETER :: one = 1.0_dp, zero = 0.0_dp + +! ZERO OUT UPPER TRIANGLE OF Q IN THE FIRST MIN(M,N) COLUMNS. + +minmn = MIN(m,n) +IF (minmn >= 2) THEN + DO j = 2, minmn + jm1 = j - 1 + DO i = 1, jm1 + q(i,j) = zero + END DO + END DO +END IF + +! INITIALIZE REMAINING COLUMNS TO THOSE OF THE IDENTITY MATRIX. + +np1 = n + 1 +IF (m >= np1) THEN + DO j = np1, m + DO i = 1, m + q(i,j) = zero + END DO + q(j,j) = one + END DO +END IF + +! ACCUMULATE Q FROM ITS FACTORED FORM. + +DO l = 1, minmn + k = minmn - l + 1 + DO i = k, m + wa(i) = q(i,k) + q(i,k) = zero + END DO + q(k,k) = one + IF (wa(k) /= zero) THEN + DO j = k, m + sum = zero + DO i = k, m + sum = sum + q(i,j) * wa(i) + END DO + temp = sum / wa(k) + DO i = k, m + q(i,j) = q(i,j) - temp * wa(i) + END DO + END DO + END IF +END DO +RETURN + +! LAST CARD OF SUBROUTINE QFORM. + +END SUBROUTINE qform + + +SUBROUTINE qrfac(m, n, a, lda, pivot, ipvt, lipvt, rdiag, acnorm, wa) + +INTEGER, INTENT(IN) :: m +INTEGER, INTENT(IN) :: n +INTEGER, INTENT(IN) :: lda +REAL (dp), INTENT(IN OUT) :: a(lda,n) +LOGICAL, INTENT(IN) :: pivot +INTEGER, INTENT(IN) :: lipvt +INTEGER, INTENT(OUT) :: ipvt(lipvt) +REAL (dp), INTENT(OUT) :: rdiag(n) +REAL (dp), INTENT(OUT) :: acnorm(n) +REAL (dp), INTENT(OUT) :: wa(n) + + +! ********** + +! SUBROUTINE QRFAC + +! THIS SUBROUTINE USES HOUSEHOLDER TRANSFORMATIONS WITH COLUMN PIVOTING +! (OPTIONAL) TO COMPUTE A QR FACTORIZATION OF THE M BY N MATRIX A. +! THAT IS, QRFAC DETERMINES AN ORTHOGONAL MATRIX Q, A PERMUTATION MATRIX P, +! AND AN UPPER TRAPEZOIDAL MATRIX R WITH DIAGONAL ELEMENTS OF NONINCREASING +! MAGNITUDE, SUCH THAT A*P = Q*R. THE HOUSEHOLDER TRANSFORMATION FOR +! COLUMN K, K = 1,2,...,MIN(M,N), IS OF THE FORM + +! T +! I - (1/U(K))*U*U + +! WHERE U HAS ZEROS IN THE FIRST K-1 POSITIONS. THE FORM OF THIS +! TRANSFORMATION AND THE METHOD OF PIVOTING FIRST APPEARED IN THE +! CORRESPONDING LINPACK SUBROUTINE. + +! THE SUBROUTINE STATEMENT IS + +! SUBROUTINE QRFAC(M,N,A,LDA,PIVOT,IPVT,LIPVT,RDIAG,ACNORM,WA) + +! WHERE + +! M IS A POSITIVE INTEGER INPUT VARIABLE SET TO THE NUMBER OF ROWS OF A. + +! N IS A POSITIVE INTEGER INPUT VARIABLE SET TO THE NUMBER +! OF COLUMNS OF A. + +! A IS AN M BY N ARRAY. ON INPUT A CONTAINS THE MATRIX FOR WHICH THE +! QR FACTORIZATION IS TO BE COMPUTED. ON OUTPUT THE STRICT UPPER +! TRAPEZOIDAL PART OF A CONTAINS THE STRICT UPPER TRAPEZOIDAL PART OF R, +! AND THE LOWER TRAPEZOIDAL PART OF A CONTAINS A FACTORED FORM OF Q +! (THE NON-TRIVIAL ELEMENTS OF THE U VECTORS DESCRIBED ABOVE). + +! LDA IS A POSITIVE INTEGER INPUT VARIABLE NOT LESS THAN M +! WHICH SPECIFIES THE LEADING DIMENSION OF THE ARRAY A. + +! PIVOT IS A LOGICAL INPUT VARIABLE. IF PIVOT IS SET TRUE, +! THEN COLUMN PIVOTING IS ENFORCED. IF PIVOT IS SET FALSE, +! THEN NO COLUMN PIVOTING IS DONE. + +! IPVT IS AN INTEGER OUTPUT ARRAY OF LENGTH LIPVT. IPVT DEFINES THE +! PERMUTATION MATRIX P SUCH THAT A*P = Q*R. +! COLUMN J OF P IS COLUMN IPVT(J) OF THE IDENTITY MATRIX. +! IF PIVOT IS FALSE, IPVT IS NOT REFERENCED. + +! LIPVT IS A POSITIVE INTEGER INPUT VARIABLE. IF PIVOT IS FALSE, +! THEN LIPVT MAY BE AS SMALL AS 1. IF PIVOT IS TRUE, THEN +! LIPVT MUST BE AT LEAST N. + +! RDIAG IS AN OUTPUT ARRAY OF LENGTH N WHICH CONTAINS THE +! DIAGONAL ELEMENTS OF R. + +! ACNORM IS AN OUTPUT ARRAY OF LENGTH N WHICH CONTAINS THE NORMS OF +! THE CORRESPONDING COLUMNS OF THE INPUT MATRIX A. +! IF THIS INFORMATION IS NOT NEEDED, THEN ACNORM CAN COINCIDE WITH RDIAG. + +! WA IS A WORK ARRAY OF LENGTH N. IF PIVOT IS FALSE, THEN WA +! CAN COINCIDE WITH RDIAG. + +! SUBPROGRAMS CALLED + +! MINPACK-SUPPLIED ... SPMPAR,ENORM + +! FORTRAN-SUPPLIED ... MAX,SQRT,MIN + +! ARGONNE NATIONAL LABORATORY. MINPACK PROJECT. MARCH 1980. +! BURTON S. GARBOW, KENNETH E. HILLSTROM, JORGE J. MORE + +! ********** +INTEGER :: i, j, jp1, k, kmax, minmn +REAL (dp) :: ajnorm, epsmch, sum, temp +REAL (dp), PARAMETER :: one = 1.0_dp, p05 = 0.05_dp, zero = 0.0_dp + +! EPSMCH IS THE MACHINE PRECISION. + +epsmch = EPSILON(1.0_dp) + +! COMPUTE THE INITIAL COLUMN NORMS AND INITIALIZE SEVERAL ARRAYS. + +DO j = 1, n + acnorm(j) = enorm(m, a(1:,j)) + rdiag(j) = acnorm(j) + wa(j) = rdiag(j) + IF (pivot) ipvt(j) = j +END DO + +! REDUCE A TO R WITH HOUSEHOLDER TRANSFORMATIONS. + +minmn = MIN(m,n) +DO j = 1, minmn + IF (pivot) THEN + +! BRING THE COLUMN OF LARGEST NORM INTO THE PIVOT POSITION. + + kmax = j + DO k = j, n + IF (rdiag(k) > rdiag(kmax)) kmax = k + END DO + IF (kmax /= j) THEN + DO i = 1, m + temp = a(i,j) + a(i,j) = a(i,kmax) + a(i,kmax) = temp + END DO + rdiag(kmax) = rdiag(j) + wa(kmax) = wa(j) + k = ipvt(j) + ipvt(j) = ipvt(kmax) + ipvt(kmax) = k + END IF + END IF + +! COMPUTE THE HOUSEHOLDER TRANSFORMATION TO REDUCE THE +! J-TH COLUMN OF A TO A MULTIPLE OF THE J-TH UNIT VECTOR. + + ajnorm = enorm(m-j+1, a(j:,j)) + IF (ajnorm /= zero) THEN + IF (a(j,j) < zero) ajnorm = -ajnorm + DO i = j, m + a(i,j) = a(i,j) / ajnorm + END DO + a(j,j) = a(j,j) + one + +! APPLY THE TRANSFORMATION TO THE REMAINING COLUMNS AND UPDATE THE NORMS. + + jp1 = j + 1 + IF (n >= jp1) THEN + DO k = jp1, n + sum = zero + DO i = j, m + sum = sum + a(i,j) * a(i,k) + END DO + temp = sum / a(j,j) + DO i = j, m + a(i,k) = a(i,k) - temp * a(i,j) + END DO + IF (.NOT.(.NOT.pivot.OR.rdiag(k) == zero)) THEN + temp = a(j,k) / rdiag(k) + rdiag(k) = rdiag(k) * SQRT(MAX(zero,one-temp**2)) + IF (p05*(rdiag(k)/wa(k))**2 <= epsmch) THEN + rdiag(k) = enorm(m-j, a(jp1:,k)) + wa(k) = rdiag(k) + END IF + END IF + END DO + END IF + END IF + rdiag(j) = -ajnorm +END DO +RETURN + +! LAST CARD OF SUBROUTINE QRFAC. + +END SUBROUTINE qrfac + + + +SUBROUTINE r1mpyq(m, n, a, lda, v, w) + +INTEGER, INTENT(IN) :: m +INTEGER, INTENT(IN) :: n +INTEGER, INTENT(IN) :: lda +REAL (dp), INTENT(IN OUT) :: a(lda,n) +REAL (dp), INTENT(IN) :: v(n) +REAL (dp), INTENT(IN) :: w(n) + + +! ********** + +! SUBROUTINE R1MPYQ + +! GIVEN AN M BY N MATRIX A, THIS SUBROUTINE COMPUTES A*Q WHERE +! Q IS THE PRODUCT OF 2*(N - 1) TRANSFORMATIONS + +! GV(N-1)*...*GV(1)*GW(1)*...*GW(N-1) + +! AND GV(I), GW(I) ARE GIVENS ROTATIONS IN THE (I,N) PLANE WHICH +! ELIMINATE ELEMENTS IN THE I-TH AND N-TH PLANES, RESPECTIVELY. +! Q ITSELF IS NOT GIVEN, RATHER THE INFORMATION TO RECOVER THE +! GV, GW ROTATIONS IS SUPPLIED. + +! THE SUBROUTINE STATEMENT IS + +! SUBROUTINE R1MPYQ(M, N, A, LDA, V, W) + +! WHERE + +! M IS A POSITIVE INTEGER INPUT VARIABLE SET TO THE NUMBER OF ROWS OF A. + +! N IS A POSITIVE INTEGER INPUT VARIABLE SET TO THE NUMBER OF COLUMNS OF A. + +! A IS AN M BY N ARRAY. ON INPUT A MUST CONTAIN THE MATRIX TO BE +! POSTMULTIPLIED BY THE ORTHOGONAL MATRIX Q DESCRIBED ABOVE. +! ON OUTPUT A*Q HAS REPLACED A. + +! LDA IS A POSITIVE INTEGER INPUT VARIABLE NOT LESS THAN M +! WHICH SPECIFIES THE LEADING DIMENSION OF THE ARRAY A. + +! V IS AN INPUT ARRAY OF LENGTH N. V(I) MUST CONTAIN THE INFORMATION +! NECESSARY TO RECOVER THE GIVENS ROTATION GV(I) DESCRIBED ABOVE. + +! W IS AN INPUT ARRAY OF LENGTH N. W(I) MUST CONTAIN THE INFORMATION +! NECESSARY TO RECOVER THE GIVENS ROTATION GW(I) DESCRIBED ABOVE. + +! SUBROUTINES CALLED + +! FORTRAN-SUPPLIED ... ABS, SQRT + +! ARGONNE NATIONAL LABORATORY. MINPACK PROJECT. MARCH 1980. +! BURTON S. GARBOW, KENNETH E. HILLSTROM, JORGE J. MORE + +! ********** +INTEGER :: i, j, nmj, nm1 +REAL (dp) :: COS, SIN, temp +REAL (dp), PARAMETER :: one = 1.0_dp + +! APPLY THE FIRST SET OF GIVENS ROTATIONS TO A. + +nm1 = n - 1 +IF (nm1 >= 1) THEN + DO nmj = 1, nm1 + j = n - nmj + IF (ABS(v(j)) > one) COS = one / v(j) + IF (ABS(v(j)) > one) SIN = SQRT(one-COS**2) + IF (ABS(v(j)) <= one) SIN = v(j) + IF (ABS(v(j)) <= one) COS = SQRT(one-SIN**2) + DO i = 1, m + temp = COS * a(i,j) - SIN * a(i,n) + a(i,n) = SIN * a(i,j) + COS * a(i,n) + a(i,j) = temp + END DO + END DO + +! APPLY THE SECOND SET OF GIVENS ROTATIONS TO A. + + DO j = 1, nm1 + IF (ABS(w(j)) > one) COS = one / w(j) + IF (ABS(w(j)) > one) SIN = SQRT(one-COS**2) + IF (ABS(w(j)) <= one) SIN = w(j) + IF (ABS(w(j)) <= one) COS = SQRT(one-SIN**2) + DO i = 1, m + temp = COS * a(i,j) + SIN * a(i,n) + a(i,n) = -SIN * a(i,j) + COS * a(i,n) + a(i,j) = temp + END DO + END DO +END IF +RETURN + +! LAST CARD OF SUBROUTINE R1MPYQ. + +END SUBROUTINE r1mpyq + + + +SUBROUTINE r1updt(m, n, s, ls, u, v, w, sing) + +INTEGER, INTENT(IN) :: m +INTEGER, INTENT(IN) :: n +INTEGER, INTENT(IN) :: ls +REAL (dp), INTENT(IN OUT) :: s(ls) +REAL (dp), INTENT(IN) :: u(m) +REAL (dp), INTENT(IN OUT) :: v(n) +REAL (dp), INTENT(OUT) :: w(m) +LOGICAL, INTENT(OUT) :: sing + + +! ********** + +! SUBROUTINE R1UPDT + +! GIVEN AN M BY N LOWER TRAPEZOIDAL MATRIX S, AN M-VECTOR U, +! AND AN N-VECTOR V, THE PROBLEM IS TO DETERMINE AN +! ORTHOGONAL MATRIX Q SUCH THAT + +! T +! (S + U*V )*Q + +! IS AGAIN LOWER TRAPEZOIDAL. + +! THIS SUBROUTINE DETERMINES Q AS THE PRODUCT OF 2*(N - 1) TRANSFORMATIONS + +! GV(N-1)*...*GV(1)*GW(1)*...*GW(N-1) + +! WHERE GV(I), GW(I) ARE GIVENS ROTATIONS IN THE (I,N) PLANE +! WHICH ELIMINATE ELEMENTS IN THE I-TH AND N-TH PLANES, RESPECTIVELY. +! Q ITSELF IS NOT ACCUMULATED, RATHER THE INFORMATION TO RECOVER THE GV, +! GW ROTATIONS IS RETURNED. + +! THE SUBROUTINE STATEMENT IS + +! SUBROUTINE R1UPDT(M,N,S,LS,U,V,W,SING) + +! WHERE + +! M IS A POSITIVE INTEGER INPUT VARIABLE SET TO THE NUMBER OF ROWS OF S. + +! N IS A POSITIVE INTEGER INPUT VARIABLE SET TO THE NUMBER +! OF COLUMNS OF S. N MUST NOT EXCEED M. + +! S IS AN ARRAY OF LENGTH LS. ON INPUT S MUST CONTAIN THE LOWER +! TRAPEZOIDAL MATRIX S STORED BY COLUMNS. ON OUTPUT S CONTAINS +! THE LOWER TRAPEZOIDAL MATRIX PRODUCED AS DESCRIBED ABOVE. + +! LS IS A POSITIVE INTEGER INPUT VARIABLE NOT LESS THAN +! (N*(2*M-N+1))/2. + +! U IS AN INPUT ARRAY OF LENGTH M WHICH MUST CONTAIN THE VECTOR U. + +! V IS AN ARRAY OF LENGTH N. ON INPUT V MUST CONTAIN THE VECTOR V. +! ON OUTPUT V(I) CONTAINS THE INFORMATION NECESSARY TO +! RECOVER THE GIVENS ROTATION GV(I) DESCRIBED ABOVE. + +! W IS AN OUTPUT ARRAY OF LENGTH M. W(I) CONTAINS INFORMATION +! NECESSARY TO RECOVER THE GIVENS ROTATION GW(I) DESCRIBED ABOVE. + +! SING IS A LOGICAL OUTPUT VARIABLE. SING IS SET TRUE IF ANY OF THE +! DIAGONAL ELEMENTS OF THE OUTPUT S ARE ZERO. OTHERWISE SING IS +! SET FALSE. + +! SUBPROGRAMS CALLED + +! MINPACK-SUPPLIED ... SPMPAR + +! FORTRAN-SUPPLIED ... ABS,SQRT + +! ARGONNE NATIONAL LABORATORY. MINPACK PROJECT. MARCH 1980. +! BURTON S. GARBOW, KENNETH E. HILLSTROM, JORGE J. MORE, JOHN L. NAZARETH + +! ********** +INTEGER :: i, j, jj, l, nmj, nm1 +REAL (dp) :: COS, cotan, giant, SIN, TAN, tau, temp +REAL (dp), PARAMETER :: one = 1.0_dp, p5 = 0.5_dp, p25 = 0.25_dp, zero = 0.0_dp + +! GIANT IS THE LARGEST MAGNITUDE. + +giant = HUGE(1.0_dp) + +! INITIALIZE THE DIAGONAL ELEMENT POINTER. + +jj = (n*(2*m-n+1)) / 2 - (m-n) + +! MOVE THE NONTRIVIAL PART OF THE LAST COLUMN OF S INTO W. + +l = jj +DO i = n, m + w(i) = s(l) + l = l + 1 +END DO + +! ROTATE THE VECTOR V INTO A MULTIPLE OF THE N-TH UNIT VECTOR +! IN SUCH A WAY THAT A SPIKE IS INTRODUCED INTO W. + +nm1 = n - 1 +IF (nm1 >= 1) THEN + DO nmj = 1, nm1 + j = n - nmj + jj = jj - (m-j+1) + w(j) = zero + IF (v(j) /= zero) THEN + +! DETERMINE A GIVENS ROTATION WHICH ELIMINATES THE J-TH ELEMENT OF V. + + IF (ABS(v(n)) < ABS(v(j))) THEN + cotan = v(n) / v(j) + SIN = p5 / SQRT(p25+p25*cotan**2) + COS = SIN * cotan + tau = one + IF (ABS(COS)*giant > one) tau = one / COS + ELSE + TAN = v(j) / v(n) + COS = p5 / SQRT(p25+p25*TAN**2) + SIN = COS * TAN + tau = SIN + END IF + +! APPLY THE TRANSFORMATION TO V AND STORE THE INFORMATION +! NECESSARY TO RECOVER THE GIVENS ROTATION. + + v(n) = SIN * v(j) + COS * v(n) + v(j) = tau + +! APPLY THE TRANSFORMATION TO S AND EXTEND THE SPIKE IN W. + + l = jj + DO i = j, m + temp = COS * s(l) - SIN * w(i) + w(i) = SIN * s(l) + COS * w(i) + s(l) = temp + l = l + 1 + END DO + END IF + END DO +END IF + +! ADD THE SPIKE FROM THE RANK 1 UPDATE TO W. + +DO i = 1, m + w(i) = w(i) + v(n) * u(i) +END DO + +! ELIMINATE THE SPIKE. + +sing = .false. +IF (nm1 >= 1) THEN + DO j = 1, nm1 + IF (w(j) /= zero) THEN + +! DETERMINE A GIVENS ROTATION WHICH ELIMINATES THE +! J-TH ELEMENT OF THE SPIKE. + + IF (ABS(s(jj)) < ABS(w(j))) THEN + cotan = s(jj) / w(j) + SIN = p5 / SQRT(p25 + p25*cotan**2) + COS = SIN * cotan + tau = one + IF (ABS(COS)*giant > one) tau = one / COS + ELSE + TAN = w(j) / s(jj) + COS = p5 / SQRT(p25+p25*TAN**2) + SIN = COS * TAN + tau = SIN + END IF + +! APPLY THE TRANSFORMATION TO S AND REDUCE THE SPIKE IN W. + + l = jj + DO i = j, m + temp = COS * s(l) + SIN * w(i) + w(i) = -SIN * s(l) + COS * w(i) + s(l) = temp + l = l + 1 + END DO + +! STORE THE INFORMATION NECESSARY TO RECOVER THE GIVENS ROTATION. + + w(j) = tau + END IF + +! TEST FOR ZERO DIAGONAL ELEMENTS IN THE OUTPUT S. + + IF (s(jj) == zero) sing = .true. + jj = jj + (m-j+1) + END DO +END IF + +! MOVE W BACK INTO THE LAST COLUMN OF THE OUTPUT S. + +l = jj +DO i = n, m + s(l) = w(i) + l = l + 1 +END DO +IF (s(jj) == zero) sing = .true. +RETURN + +! LAST CARD OF SUBROUTINE R1UPDT. + +END SUBROUTINE r1updt + + +FUNCTION enorm(n, x) RESULT(fn_val) + +INTEGER, INTENT(IN) :: n +REAL (dp), INTENT(IN) :: x(n) +REAL (dp) :: fn_val + +! ********** + +! FUNCTION ENORM + +! GIVEN AN N-VECTOR X, THIS FUNCTION CALCULATES THE EUCLIDEAN NORM OF X. + +! THE EUCLIDEAN NORM IS COMPUTED BY ACCUMULATING THE SUM OF SQUARES IN THREE +! DIFFERENT SUMS. THE SUMS OF SQUARES FOR THE SMALL AND LARGE COMPONENTS +! ARE SCALED SO THAT NO OVERFLOWS OCCUR. NON-DESTRUCTIVE UNDERFLOWS ARE +! PERMITTED. UNDERFLOWS AND OVERFLOWS DO NOT OCCUR IN THE COMPUTATION OF THE UNSCALED +! SUM OF SQUARES FOR THE INTERMEDIATE COMPONENTS. +! THE DEFINITIONS OF SMALL, INTERMEDIATE AND LARGE COMPONENTS DEPEND ON +! TWO CONSTANTS, RDWARF AND RGIANT. THE MAIN RESTRICTIONS ON THESE CONSTANTS +! ARE THAT RDWARF**2 NOT UNDERFLOW AND RGIANT**2 NOT OVERFLOW. +! THE CONSTANTS GIVEN HERE ARE SUITABLE FOR EVERY KNOWN COMPUTER. + +! THE FUNCTION STATEMENT IS + +! REAL FUNCTION ENORM(N, X) + +! WHERE + +! N IS A POSITIVE INTEGER INPUT VARIABLE. + +! X IS AN INPUT ARRAY OF LENGTH N. + +! SUBPROGRAMS CALLED + +! FORTRAN-SUPPLIED ... ABS,SQRT + +! ARGONNE NATIONAL LABORATORY. MINPACK PROJECT. MARCH 1980. +! BURTON S. GARBOW, KENNETH E. HILLSTROM, JORGE J. MORE + +! ********** +INTEGER :: i +REAL (dp) :: agiant, floatn, s1, s2, s3, xabs, x1max, x3max +REAL (dp), PARAMETER :: rdwarf = 1.0D-100, rgiant = 1.0D+100 + +s1 = 0.0_dp +s2 = 0.0_dp +s3 = 0.0_dp +x1max = 0.0_dp +x3max = 0.0_dp +floatn = n +agiant = rgiant / floatn +DO i = 1, n + xabs = ABS(x(i)) + IF (xabs <= rdwarf .OR. xabs >= agiant) THEN + IF (xabs > rdwarf) THEN + +! SUM FOR LARGE COMPONENTS. + + IF (xabs > x1max) THEN + s1 = 1.0_dp + s1 * (x1max/xabs) ** 2 + x1max = xabs + ELSE + s1 = s1 + (xabs/x1max) ** 2 + END IF + ELSE + +! SUM FOR SMALL COMPONENTS. + + IF (xabs > x3max) THEN + s3 = 1.0_dp + s3 * (x3max/xabs) ** 2 + x3max = xabs + ELSE + IF (xabs /= 0.0_dp) s3 = s3 + (xabs/x3max) ** 2 + END IF + END IF + ELSE + +! SUM FOR INTERMEDIATE COMPONENTS. + + s2 = s2 + xabs ** 2 + END IF +END DO + +! CALCULATION OF NORM. + +IF (s1 /= 0.0_dp) THEN + fn_val = x1max * SQRT(s1 + (s2/x1max)/x1max) +ELSE + IF (s2 /= 0.0_dp) THEN + IF (s2 >= x3max) fn_val = SQRT(s2*(1.0_dp + (x3max/s2)*(x3max*s3))) + IF (s2 < x3max) fn_val = SQRT(x3max*((s2/x3max) + (x3max*s3))) + ELSE + fn_val = x3max * SQRT(s3) + END IF +END IF +RETURN +END FUNCTION enorm + +END MODULE Solve_NonLin diff --git a/applications/PUfoam/MoDeNaModels/SurfaceTension/src/out.txt b/applications/PUfoam/MoDeNaModels/SurfaceTension/src/out.txt new file mode 100644 index 000000000..247f493f1 --- /dev/null +++ b/applications/PUfoam/MoDeNaModels/SurfaceTension/src/out.txt @@ -0,0 +1 @@ + 33.518519488031210 diff --git a/applications/PUfoam/MoDeNaModels/US_Solubility_Model/PythonModule_and_DetailedModelCode/PCSAFT_Henry b/applications/PUfoam/MoDeNaModels/US_Solubility_Model/PythonModule_and_DetailedModelCode/PCSAFT_Henry new file mode 100755 index 0000000000000000000000000000000000000000..49b1ded440f4c8dd168243842e4417f9ba9eebc0 GIT 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zri&+BOoX)4mAAoLAsmFOLJTtmbv+cdB;U44Wy={-MFd4`*l0Z3pp>m-NSIj!PUWRo zmF|FD940$UEL{3{yOoS;QT8B_;l^$Z?H*4N7>HF8v?~FBV!|kg#nSg6l)_VWdJf~X z*|(*nvIF&xHK=-%z}CUaDx{M|#@M2w59z2(i>Np9V%p|mA%)0=nL?^~dl2LkOtB1V zAH#-wXl8?zc zOeqURk<>-6x!jCaZHj~vSw`>xkzco{4kAnTFf1-1o#FzzQ|m1~rA>rfQqr_4fjo*r(HEv;V3ws5mEXE)u zu%iF#Q$MF+Y^pX7nm8Pb2ZqxxSvF%+>`;0kj1PETGpo?WfnEH)z6sRg(9G#}{=SCeP>2+=OT51hoY4;pc$N*C@r+I*T`7VAwHSo<>+!Mo}MNC<28F{A|GOP$6gW(frrHx2;C<3b_15+dV~`R$xxtL9-K7FRTV= zH!-RS|2fPzqo*jt2Mu#5nSpsBh@$Jj4c?9d>Z^Ga+}3o$zDSaWL~PxTU#U)TPu zSX|C7R>6ldSntFlLI=d6OBxABl{-_+UyE`oT^H;g?C#QRa&><_1H_dmibxjA%Ypo? zcpr$63>I9i7wdl4Dal)S}t>(qI%It#nhW8!S}BvJ!pJa3g32Mt>>n387KZ$Ak?<-OHa@|us?JF@9l&9v4*>y<@j=7@ zfg_l-8lhDho@qILlh{Fx_Ys_VO_FrW_o<*mRmr724MN>Q%x%m*R+fqe&ZEzQI+rRz*v|(6WDReHDmb8uG`YeF7?AJ|Hl^|lk~oT zkACc@+t2A;eFKjJjt__yR$|Ia+5_h>Luemn+T-}_j`ZwxJj-PFq@$1{(HBN|A18?@j`k08p zVdiQ2H}K~EFHnc@cUc*S*;n|vhBx~V6P_rw;eU;L#4GX3!|bp1vyarZdU#Hq^FR9< z9>2uJ5Z>&=^|6LOC285Knd+1Af2!dP{>}bhpKACQ6p+F3*5I6{zr~0B8+fx%Souv#753?|=5OQg_oy?3 zH~Wdb@ofeF6TGiCJPiHJy&If-6(7@$*>~*4xq`Rr+t+^pEM5ie;LScmpS>phXMpAS zP5)*eu)n+}{GS0!N*Q>w-`U?Z{F@rFh6~L24Ili~>fh{(_OB-|pTBA6?-sn-$J_g^ zg8v;SH#iKO`ThsWhVwW3tlfN1!JnFnx{cF8TRi<7A67B*@1D2)k?#L1zrvHj{c+l# z%CrCAKl?wn?t2N4wc#JdA. + +Description + Python library of FireTasks + +Authors + Henrik Rusche + +Contributors +''' + +from bubbleGrowth import m + diff --git a/applications/PUfoam/MoDeNaModels/bubbleGrowth/bubbleGrowth.py b/applications/PUfoam/MoDeNaModels/bubbleGrowth/bubbleGrowth.py new file mode 100644 index 000000000..4644eba29 --- /dev/null +++ b/applications/PUfoam/MoDeNaModels/bubbleGrowth/bubbleGrowth.py @@ -0,0 +1,45 @@ +'''@cond + + ooo ooooo oooooooooo. ooooo ooo + `88. .888' `888' `Y8b `888b. `8' + 888b d'888 .ooooo. 888 888 .ooooo. 8 `88b. 8 .oooo. + 8 Y88. .P 888 d88' `88b 888 888 d88' `88b 8 `88b. 8 `P )88b + 8 `888' 888 888 888 888 888 888ooo888 8 `88b.8 .oP"888 + 8 Y 888 888 888 888 d88' 888 .o 8 `888 d8( 888 + o8o o888o `Y8bod8P' o888bood8P' `Y8bod8P' o8o `8 `Y888""8o + +Copyright + 2014 MoDeNa Consortium, All rights reserved. + +License + This file is part of Modena. + + Modena is free software; you can redistribute it and/or modify it under + the terms of the GNU General Public License as published by the Free + Software Foundation, either version 3 of the License, or (at your option) + any later version. + + Modena is distributed in the hope that it will be useful, but WITHOUT ANY + WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS + FOR A PARTICULAR PURPOSE. See the GNU General Public License + for more details. + + You should have received a copy of the GNU General Public License along + with Modena. If not, see . +@endcond''' + +""" +@file +Backward mapping Firetask for Bubble growth model. +Contains path to the detailed model executable. + +@author Pavel Ferkl +@copyright 2014-2015, MoDeNa Project. GNU Public License. +@ingroup app_foaming +""" +import os +from modena.Strategy import BackwardMappingScriptTask + +m = BackwardMappingScriptTask( + script=os.path.dirname(os.path.abspath(__file__))+'/src/bblgrExact' +) diff --git a/applications/PUfoam/MoDeNaModels/bubbleGrowth/src/CMakeLists.txt b/applications/PUfoam/MoDeNaModels/bubbleGrowth/src/CMakeLists.txt new file mode 100644 index 000000000..ae2662da8 --- /dev/null +++ b/applications/PUfoam/MoDeNaModels/bubbleGrowth/src/CMakeLists.txt @@ -0,0 +1,20 @@ +cmake_minimum_required (VERSION 2.8) +project (bubbleGrowth C CXX Fortran) + +if( CMAKE_VERSION VERSION_GREATER "3.0" ) + cmake_policy(SET CMP0042 OLD) + cmake_policy(SET CMP0026 OLD) +endif() + +find_package(MODENA REQUIRED) + +include_directories(${MODENA_INCLUDE_DIRS}) +link_directories(${MODENA_LIBRARY_DIRS}) + + +set (CMAKE_Fortran_FLAGS "-ffree-line-length-none -O3") + +set (CMAKE_Fortran_MODULE_DIRECTORY mod) +file (GLOB _sources RELATIVE ${CMAKE_CURRENT_SOURCE_DIR} src/*.f*) +add_executable(bblgrExact ${_sources}) +target_link_libraries(bblgrExact MODENA::modena) diff --git a/applications/PUfoam/MoDeNaModels/bubbleGrowth/src/src/constants.f90 b/applications/PUfoam/MoDeNaModels/bubbleGrowth/src/src/constants.f90 new file mode 100644 index 000000000..bd92051d1 --- /dev/null +++ b/applications/PUfoam/MoDeNaModels/bubbleGrowth/src/src/constants.f90 @@ -0,0 +1,15 @@ +!> @file +!! stores parameters and commonly used variables as globals +!! @author Pavel Ferkl +!! @ingroup bblgr +module constants + use,intrinsic :: iso_fortran_env, only: dp => real64 + implicit none + real(dp), parameter :: & + pi=3.1415926535897932384626433832795028841971693993751058209749445923& + &078164062862089986280348253421170679_dp,& ! @file +!! handles input and output +!! @author Pavel Ferkl +!! @ingroup bblgr +module in_out + use constants + use ioutils, only:newunit,str + implicit none + logical :: inertial_term,solcorr,gelpoint,dilution + integer :: fi1,fi2,fi3,fi4,& + integrator,p,maxts,its,visc_model,rhop_model,itens_model,ngas,co2_pos,& + kin_model,MF,NEQ,& + fceq,& !first concentration equation (index) + fpeq,lpeq,& !first and last pressure equation (index) + req,& !radius equation (index) + teq,& !temperature equation (index) + xOHeq,xWeq,& !conversion equations (indexes) + kineq(12) !kinetics state variable equations (indexes) + real(dp) :: mshco,& !mesh coarsening parameter + Temp0,R0,Sn,OH0,W0,NCO0,AOH,EOH,AW,EW,dHOH,dHW,& + time,radius,eqconc,grrate(2),st,S0,& + T,TEND,RTOL,ATOL,& + eta,maxeta,Aeta,Eeta,Cg,AA,B,& + Pamb,sigma,rhop,cp,cppol,rhobl,& + kinsource(12) !kinetic source term + integer, dimension(:), allocatable :: diff_model,sol_model,fic + real(dp), dimension(:), allocatable :: Y,cbl,xgas,& + D,KH,Mbl,dHv,cpblg,cpbll,& + mb,mb2,mb3,avconc,pressure +contains +!********************************BEGINNING************************************* +!> reads input values from a file +subroutine read_inputs(inputs) + character(len=80),intent(in) :: inputs + integer :: fi + write(*,*) 'loading input file ',TRIM(inputs) + open(newunit(fi),file=inputs) + read(fi,*) integrator !integrator. 1=dlsode,2=dlsodes + read(fi,*) MF !10=nonstiff,22=stiff,automatic Jacobian(dlsode), + ! 222=stiff,automatic Jacobian(dlsodes) + read(fi,*) + read(fi,*) inertial_term !include inertial term in equations (t/f) + read(fi,*) solcorr !use solubility correction on bubble radius (t/f) + read(fi,*) mshco !mesh coarsening parameter + read(fi,*) + read(fi,*) p !number of internal nodes + read(fi,*) T !initial time + read(fi,*) TEND !final time + read(fi,*) its !number of outer integration time steps (how many + ! times are values written) + read(fi,*) maxts !maximum inner time steps between t and t+h + ! (default 500, recommended 50000) + read(fi,*) RTOL !relative tolerance + read(fi,*) ATOL !absolute tolerance + read(fi,*) + read(fi,*) ngas !number of dissolved gases + allocate(D(ngas),cbl(ngas),xgas(ngas+1),KH(ngas),fic(ngas),Mbl(ngas),& + dHv(ngas),mb(ngas),mb2(ngas),mb3(ngas),avconc(ngas),pressure(ngas),& + diff_model(ngas),sol_model(ngas),cpblg(ngas),cpbll(ngas)) + read(fi,*) co2_pos !carbon dioxide position + read(fi,*) Pamb !ambient pressure + read(fi,*) Mbl !blowing agent molar mass (for each dissolved gas) + read(fi,*) cppol !heat capacity of polymer + read(fi,*) cpbll !heat capacity of blowing agent in liquid phase + ! (for each) + read(fi,*) cpblg !heat capacity of blowing agent in gas phase + ! (for each) + read(fi,*) dHv !evaporation heat of blowing agent (for each gas) + read(fi,*) rhobl !density of liquid physical blowing agent + read(fi,*) + read(fi,*) Temp0 !initial temperature + read(fi,*) R0 !initial radius + read(fi,*) Sn !how many times is initial shell larger than initial + ! bubble radius + read(fi,*) OH0 !initial concentration of polyol (don't set to zero - + ! division by zero; if you don't want reaction, set water to zero) + read(fi,*) W0 !initial concentration of water (if you set this to + ! zero, water conversion results are meanigless) + read(fi,*) NCO0 !initial concentration of isocyanate + read(fi,*) cbl !initial concentration of disolved blowing agent + ! (for each dissolved gas) + read(fi,*) xgas !initial molar fraction of gases in the bubble (for + ! air and each dissolved gas) + read(fi,*) + read(fi,*) kin_model !reaction kinetics model. 1=Baser,2=modena + read(fi,*) dilution !use dilution effect + read(fi,*) AOH !frequential factor of gelling reaction + read(fi,*) EOH !activation energy of gelling reaction + read(fi,*) AW !frequential factor of blowing reaction + read(fi,*) EW !activation energy of blowing reaction + read(fi,*) dHOH !gelling reaction enthalpy + read(fi,*) dHW !blowing reaction enthalpy + read(fi,*) + read(fi,*) rhop_model !polymer density model. 1=constant,2=modena + read(fi,*) rhop !polymer density + read(fi,*) + read(fi,*) itens_model !interfacial tension model. 1=constant,2=modena + read(fi,*) sigma !interfacial tension + read(fi,*) + read(fi,*) diff_model !diffusivity model (for each dissolved gas). + ! 1=constant,2=modena + read(fi,*) D !diffusion coefficients (for each dissolved gas) + read(fi,*) + read(fi,*) sol_model !solubility model (for each dissolved gas). + ! 1=constant,2=modena + read(fi,*) KH !Henry constants (for each dissolved gas) + read(fi,*) + read(fi,*) visc_model !viscosity model. 1=constant,2=Castro and + ! Macosko,3=modena + read(fi,*) eta !viscosity (if constant viscosity is used) + read(fi,*) maxeta !maximum viscosity + read(fi,*) Aeta !viscosity constant Aeta + read(fi,*) Eeta !viscosity constant Eeta + read(fi,*) Cg !viscosity constant Cg + read(fi,*) AA !viscosity constant AA + read(fi,*) B !viscosity constant B + close(fi) + write(*,*) 'done: inputs loaded' + write(*,*) +end subroutine read_inputs +!***********************************END**************************************** + + +!********************************BEGINNING************************************* +!> saves parameters of surrogate model +subroutine save_surrogate_parameters(spar) + character(len=80),intent(in) :: spar + integer :: fi,i + write(*,*) 'saving parameters of surrogate model to ',TRIM(spar) + open(newunit(fi),file=spar) + write(fi,*) ngas !number of dissolved gases + write(fi,*) sigma !interfacial tension + do i=1,ngas + write(fi,*) KH(i) !Henry constants (for each dissolved gas) + enddo + close(fi) + write(*,*) 'done: parameters of surrogate model saved' + write(*,*) +end subroutine save_surrogate_parameters +!***********************************END**************************************** + + +!********************************BEGINNING************************************* +!> opens output files and writes a header +subroutine save_integration_header(outputs_1d,outputs_GR,outputs_GR_c,& + outputs_GR_p,concloc) + character(*),intent(in) :: outputs_1d,outputs_GR,outputs_GR_c,outputs_GR_p,& + concloc !file names + integer :: i + open (unit=newunit(fi1), file = outputs_1d) + write(fi1,'(1000A23)') '#time', 'radius','pressure','conversion of polyol',& + 'conversion of water', 'eq. concentration', 'first concentration', & + 'viscosity', 'moles in polymer', 'moles in bubble', 'total moles', & + 'shell thickness', 'temperature', 'foam density', 'weight fraction' + open (unit=newunit(fi2), file = outputs_GR) + write(fi2,'(1000A23)') '#GrowthRate1', 'GrowthRate2', 'temperature', & + 'bubbleRadius', 'KH1','KH2','c1','c2','p1','p2' +end subroutine save_integration_header +!***********************************END**************************************** + + +!********************************BEGINNING************************************* +!> writes an integration step to output file +subroutine save_integration_step + integer :: i + write(fi1,"(1000es23.15)") time,radius, pressure(1), Y(xOHeq), Y(xWeq), & + eqconc,Y(fceq),eta,mb(1),mb2(1),mb3(1),st,Y(teq),(1-radius**3/& + (radius**3+S0**3-R0**3))*rhop,mb(2)*Mbl(2)/(rhop*4*pi/3*(S0**3-R0**3)),& + mb(1)*Mbl(1)/(rhop*4*pi/3*(S0**3-R0**3)) + write(fi2,"(1000es23.15)") grrate, Y(teq), radius, KH, avconc, pressure +end subroutine save_integration_step +!***********************************END**************************************** + + +!********************************BEGINNING************************************* +!> closes output files +subroutine save_integration_close +!***************************DECLARATION****************************** + integer :: i +!******************************BODY********************************** + close(fi1) + close(fi2) +end subroutine save_integration_close +!***********************************END**************************************** +end module in_out diff --git a/applications/PUfoam/MoDeNaModels/bubbleGrowth/src/src/ioutils.f90 b/applications/PUfoam/MoDeNaModels/bubbleGrowth/src/src/ioutils.f90 new file mode 100644 index 000000000..80a5bbb10 --- /dev/null +++ b/applications/PUfoam/MoDeNaModels/bubbleGrowth/src/src/ioutils.f90 @@ -0,0 +1,41 @@ +!> @file +!! i/o utilities +!! @author Pavel Ferkl +!! @ingroup foam_aging +module ioutils + implicit none + private + public newunit,str +contains +!********************************BEGINNING************************************* +!> returns lowest i/o unit number not in use +integer function newunit(unit) result(n) + integer, intent(out), optional :: unit + logical inuse + integer, parameter :: & + nmin=123,& ! avoid lower numbers which are sometimes reserved + nmax=999 ! may be system-dependent + do n = nmin, nmax + inquire(unit=n, opened=inuse) + if (.not. inuse) then + if (present(unit)) unit=n + return + end if + end do + write(*,*) "newunit ERROR: available unit not found." + stop +end function newunit +!***********************************END**************************************** + + + +!********************************BEGINNING************************************* +!> converts integer to string +function str(k) + character(len=20) :: str + integer, intent(in) :: k + write (str, *) k + str = adjustl(str) +end function str +!***********************************END**************************************** +end module ioutils diff --git a/applications/PUfoam/MoDeNaModels/bubbleGrowth/src/src/main.f90 b/applications/PUfoam/MoDeNaModels/bubbleGrowth/src/src/main.f90 new file mode 100644 index 000000000..758a617cf --- /dev/null +++ b/applications/PUfoam/MoDeNaModels/bubbleGrowth/src/src/main.f90 @@ -0,0 +1,11 @@ +!> @file +!! simulation of bubble growth; +!! inspired by [Feng and Bertelo (2004)](http://dx.doi.org/10.1122/1.1645518) +!! and adapted to polyurethanes +!! @author Pavel Ferkl +!! @ingroup bblgr +program singlebubblegrowth + use tests + implicit none + call onegrowth +end program diff --git a/applications/PUfoam/MoDeNaModels/bubbleGrowth/src/src/model.f90 b/applications/PUfoam/MoDeNaModels/bubbleGrowth/src/src/model.f90 new file mode 100644 index 000000000..1143ccfb9 --- /dev/null +++ b/applications/PUfoam/MoDeNaModels/bubbleGrowth/src/src/model.f90 @@ -0,0 +1,491 @@ +!> @file +!! contains model subroutines for bubble growth model +!! @author Pavel Ferkl +!! @ingroup bblgr +module model + use constants + use in_out + use iso_c_binding + use fmodena + use modenastuff + implicit none + integer :: info + real(dp) :: Pair0,timestep,GR,Rold,Told,pold(2),nold(2),Vsh + !time integration variables for lsode + integer :: IOUT, IOPT, ISTATE, ITASK, ITOL, LIW, LRW, NNZ, LENRAT!, MF, NEQ + real(dp) :: JAC,TOUT!,RTOL,ATOL,T + real(dp), dimension(:), allocatable :: RWORK!,Y + integer, dimension(:), allocatable :: IWORK + !mesh variables + real(dp),allocatable :: atri(:),btri(:),ctri(:),rtri(:),utri(:),dz(:) + !needed for selection of subroutine for evaluation of derivatives + abstract interface + subroutine sub (NEQ, T, Y, YDOT) + use constants + INTEGER :: NEQ + real(dp) :: T, Y(NEQ), YDOT(NEQ) + end subroutine sub + end interface + procedure (sub), pointer :: sub_ptr => FEX +contains +!********************************BEGINNING************************************* +!> model supplied to integrator, FVM, nonequidistant mesh +SUBROUTINE FEX (NEQ, T, Y, YDOT) + INTEGER :: NEQ,i,j + real(dp) :: T, Y(NEQ), YDOT(NEQ),z,zw,ze,zww,zee,lamw,lame,cw,ce,cww,cee,& + c,dcw,dce,dil,bll + call molar_balance + YDOT=0 + YDOT(xOHeq) = AOH*exp(-EOH/Rg/Y(teq))*(1-Y(xOHeq))*& + (NCO0-2*W0*Y(xWeq)-OH0*Y(xOHeq)) !polyol conversion + if (kin_model==3) then + if (Y(xOHeq)>0.5_dp .and. Y(xOHeq)<0.87_dp) YDOT(xOHeq)=YDOT(xOHeq)*& + (-2.027_dp*Y(xOHeq)+2.013_dp) !gelling influence on kinetics + if (Y(xOHeq)>0.87_dp) YDOT(xOHeq)=YDOT(xOHeq)*& + (3.461_dp*Y(xOHeq)-2.761_dp) + endif + if (W0>1e-3) then + ! water conversion + ! YDOT(xWeq) = AW*exp(-EW/Rg/Y(teq))*(1-Y(xWeq))*& + ! (NCO0-2*W0*Y(xWeq)-OH0*Y(xOHeq)) 2nd order + YDOT(xWeq) = AW*exp(-EW/Rg/Y(teq))*(1-Y(xWeq)) !1st order + endif + if (dilution) then + if (co2_pos==1) then + bll=mb(2)/Vsh*Mbl(2)/rhop + else + bll=mb(1)/Vsh*Mbl(1)/rhop + endif + dil=1/(1+rhop/rhobl*bll) + YDOT(xOHeq)=YDOT(xOHeq)*dil + YDOT(xWeq)=YDOT(xWeq)*dil + endif + if (kin_model==2) then + call kinModel + do i=1,size(kineq) + YDOT(kineq(i))=kinsource(i) + enddo + YDOT(xOHeq) = -YDOT(kineq(2))/OH0 + YDOT(xWeq) = -YDOT(kineq(3))/W0 + endif + !temperature (enthalpy balance) + YDOT(teq) = -dHOH*OH0/(rhop*cp)*YDOT(xOHeq)-dHW*W0/(rhop*cp)*YDOT(xWeq) + if (kin_model==2) then + YDOT(kineq(12))=YDOT(teq) + endif + do i=1,ngas + YDOT(teq) = YDOT(teq) - dHv(i)*12*pi*Mbl(i)*D(i)*Y(req)**4/& + (rhop*cp*Vsh)*(Y(fceq+i-1)-KH(i)*Y(fpeq+i-1))/(dz(1)/2) + enddo + if (inertial_term) then + YDOT(req) = Y(req+1) !radius (momentum balance) + YDOT(req+1) = (sum(Y(fpeq:lpeq)) + Pair0*R0**3/Y(req)**3 - Pamb - & + 2*sigma/Y(req) - 4*eta*Y(req+1)/Y(req) - & + 3._dp/2*Y(req+1)**2)/(Y(req)*rhop) + else + YDOT(req) = (sum(Y(fpeq:lpeq)) + Pair0*R0**3/Y(req)**3 - Pamb - & + 2*sigma/Y(req))*Y(req)/(4*eta) !radius (momentum balance) + endif + do i=fpeq,lpeq + YDOT(i) = -3*Y(i)*YDOT(req)/Y(req) + Y(i)/Y(teq)*YDOT(teq) + & + 9*Rg*Y(teq)*D(i-fpeq+1)*Y(req)*(Y(fceq+i-fpeq)-KH(i-fpeq+1)*Y(i))/& + (dz(1)/2) !partial pressure (molar balance) + enddo + do j=1,ngas + do i=1,p+1 + if (i==1) then !bubble boundary + zw=0e0_dp + z=dz(i)/2 + ze=dz(i) + zee=ze+dz(i+1)/2 + lame=(ze-z)/(zee-z) + c=Y(fceq+(i-1)*ngas+j-1) + cee=Y(fceq+i*ngas+j-1) + cw=KH(j)*Y(fpeq+j-1) + ce=cee*lame+c*(1-lame) + dcw=(c-cw)/(z-zw) + dce=(cee-c)/(zee-z) + elseif(i==p+1) then !outer boundary + zww=z + zw=ze + z=zee + ze=ze+dz(i) + lamw=(zw-zww)/(z-zww) + cww=Y(fceq+(i-2)*ngas+j-1) + c=Y(fceq+(i-1)*ngas+j-1) + cw=c*lamw+cww*(1-lamw) + ce=c + dcw=(c-cww)/(z-zww) + dce=0e0_dp + else + zww=z + zw=ze + z=zee + ze=ze+dz(i) + zee=ze+dz(i+1)/2 + lamw=(zw-zww)/(z-zww) + lame=(ze-z)/(zee-z) + cww=Y(fceq+(i-2)*ngas+j-1) + c=Y(fceq+(i-1)*ngas+j-1) + cee=Y(fceq+i*ngas+j-1) + cw=c*lamw+cww*(1-lamw) + ce=cee*lame+c*(1-lame) + dcw=(c-cww)/(z-zww) + dce=(cee-c)/(zee-z) + endif + !concentration (molar balance) + YDOT(fceq+(i-1)*ngas+j-1) = 9*D(j)*((ze+Y(req)**3)**(4._dp/3)*dce -& + (zw+Y(req)**3)**(4._dp/3)*dcw)/dz(i) + if (j==co2_pos) YDOT(fceq+(i-1)*ngas+j-1) = & + YDOT(fceq+(i-1)*ngas+j-1) + W0*YDOT(xWeq) !reaction source + enddo + enddo +END subroutine FEX +!***********************************END**************************************** + + +!********************************BEGINNING************************************* +!> calculates values of physical properties +subroutine physical_properties(Y) + real(dp), dimension(:), intent(in) :: Y + integer :: i + if (.not. gelpoint .and. Y(teq)<500) then + select case(visc_model) + case(1) + case(2) + eta=Aeta*exp(Eeta/(Rg*Y(teq)))*(Cg/(Cg-Y(xOHeq)))**(AA+B*Y(xOHeq)) + case(3) + !set input vector + call modena_inputs_set(viscInputs, viscTpos, Y(teq)); + call modena_inputs_set(viscInputs, viscXPos, Y(xOHeq)); + !call model + ret = modena_model_call(viscModena, viscInputs, viscOutputs) + if(ret /= 0) then + call exit(ret) + endif + !fetch results + eta = modena_outputs_get(viscOutputs, 0_c_size_t); + end select + if (eta>maxeta .or. isnan(eta)) then + eta=maxeta + gelpoint=.true. + write(*,'(2x,A,es8.2,A)') 'gel point reached at time t = ',TOUT,' s' + write(*,'(2x,A,es8.2,A)') 'temperature at gel point T = ',Y(teq),' K' + write(*,'(2x,A,es8.2)') 'conversion at gel point X = ',Y(xOHeq) + endif + else + eta=maxeta + endif + select case(itens_model) + case(1) + case(2) + call modena_inputs_set(itensInputs, itensTpos, Y(teq)) + ret = modena_model_call(itensModena, itensInputs, itensOutputs) + if(ret /= 0) then + call exit(ret) + endif + sigma = modena_outputs_get(itensOutputs, 0_c_size_t) + end select + do i=1,ngas + select case(diff_model(i)) + case(1) + case(2) + call modena_inputs_set(diffInputs(i), diffTpos(i), Y(teq)) + ret = modena_model_call(diffModena(i), diffInputs(i), diffOutputs(i)) + if(ret /= 0) then + call exit(ret) + endif + D(i) = modena_outputs_get(diffOutputs(i), 0_c_size_t) + end select + select case(sol_model(i)) + case(1) + case(2) + call modena_inputs_set(solInputs(i), solTpos(i), Y(teq)) + ret = modena_model_call(solModena(i), solInputs(i), solOutputs(i)) + if(ret /= 0) then + call exit(ret) + endif + KH(i) = modena_outputs_get(solOutputs(i), 0_c_size_t) + KH(i)=rhop/Mbl(i)/KH(i) + case(3) + KH(i)=-rhop/Mbl(i)/Pamb*3.3e-4_dp*(exp((2.09e4_dp-67.5_dp*(Y(teq)-& + 35.8_dp*log(Pamb/1e5_dp)))/(8.68e4_dp-(Y(teq)-35.8_dp*& + log(Pamb/1e5_dp))))-1.01_dp)**(-1) + case(4) + KH(i)=rhop/Mbl(i)/Pamb*(0.0064_dp+0.0551_dp*exp(-(Y(teq)-298)**2/& + (2*17.8_dp**2))) + case(5) + KH(i)=rhop/Mbl(i)/Pamb*(0.00001235_dp*Y(teq)**2-0.00912_dp*Y(teq)+& + 1.686_dp) + case(6) + KH(i)=rhop/Mbl(i)/Pamb*(1e-7_dp+4.2934_dp*& + exp(-(Y(teq)-203.3556_dp)**2/(2*40.016_dp**2))) + end select + enddo + if (solcorr) KH=KH*exp(2*sigma*Mbl/(rhop*Rg*Y(teq)*Y(req))) + cp=cppol+sum(cbl*Mbl*cpbll)/rhop +end subroutine physical_properties +!***********************************END**************************************** + + +!********************************BEGINNING************************************* +!> calculates molar amount in bubble and shell and thickness of the shell +subroutine molar_balance + integer :: i,j + call physical_properties(Y) + !numerical integration + mb=0e0_dp + !rectangle rule + do i=1,p+1 + do j=1,ngas + mb(j)=mb(j)+Y(fceq+j-1+(i-1)*ngas)*dz(i) + enddo + enddo + mb=mb*4*pi/3 !moles in polymer + do i=1,ngas + mb2(i)=Y(fpeq+i-1)*Y(req)**3*4*pi/(3*Rg*Y(teq)) !moles in bubble + enddo + mb3=mb+mb2 !total moles + st=(S0**3+Y(req)**3-R0**3)**(1._dp/3)-Y(req) !thickness of the shell +end subroutine molar_balance +!***********************************END**************************************** + + +!********************************BEGINNING************************************* +!> restores dimensional variables +subroutine restoreDV + integer :: i + time=TOUT + radius=Y(req) + eqconc=Y(fpeq)*KH(1) !only first gas + do i=1,ngas + pressure(i)=Y(fpeq+i-1) + grrate(i)=(mb2(i)-nold(i))/timestep + enddo + i=1 + Rold=Y(req) + Told=Y(teq) + do i=1,ngas + pold(i)=Y(fpeq+i-1) + nold(i)=mb2(i) + enddo + avconc=mb/Vsh +end subroutine restoreDV +!***********************************END**************************************** + + +!********************************BEGINNING************************************* +!> evaluates kinetic source terms +subroutine kinModel + call modena_inputs_set(kinInputs, kinNCOPos, Y(kineq(1))); + call modena_inputs_set(kinInputs, kinOHPos, Y(kineq(2))); + call modena_inputs_set(kinInputs, kinH2OPos, Y(kineq(3))); + call modena_inputs_set(kinInputs, kinCO2Pos, Y(kineq(4))); + call modena_inputs_set(kinInputs, kinPentanePos, Y(kineq(5))); + call modena_inputs_set(kinInputs, kinPolymerPos, Y(kineq(6))); + call modena_inputs_set(kinInputs, kinPolymerBlowPos, Y(kineq(7))); + call modena_inputs_set(kinInputs, kinUreaPos, Y(kineq(8))); + call modena_inputs_set(kinInputs, kinR1Pos, Y(kineq(9))); + call modena_inputs_set(kinInputs, kinRmassPos, Y(kineq(10))); + call modena_inputs_set(kinInputs, kinRvolPos, Y(kineq(11))); + call modena_inputs_set(kinInputs, kinRtempPos, Y(kineq(12))); + ret = modena_model_call (kinModena, kinInputs, kinOutputs) + if(ret /= 0) then + call exit(ret) + endif + kinsource(kineq(1)) = modena_outputs_get(kinOutputs, kinSourceNCOPos); + kinsource(kineq(2)) = modena_outputs_get(kinOutputs, kinSourceOHPos); + kinsource(kineq(3)) = modena_outputs_get(kinOutputs, kinSourceH2OPos); + kinsource(kineq(4)) = modena_outputs_get(kinOutputs, kinSourceCO2Pos); + kinsource(kineq(5)) = modena_outputs_get(kinOutputs, kinSourcePentanePos); + kinsource(kineq(6)) = modena_outputs_get(kinOutputs, kinSourcePolymerPos); + kinsource(kineq(7)) = modena_outputs_get(kinOutputs, & + kinSourcePolymerBlowPos); + kinsource(kineq(8)) = modena_outputs_get(kinOutputs, kinSourceUreaPos); + kinsource(kineq(9)) = modena_outputs_get(kinOutputs, kinSourceR1Pos); + kinsource(kineq(10)) = modena_outputs_get(kinOutputs, kinSourceRmassPos); + kinsource(kineq(11)) = modena_outputs_get(kinOutputs, kinSourceRvolPos); + kinsource(kineq(12)) = modena_outputs_get(kinOutputs, kinSourceRtempPos); +end subroutine kinModel +!***********************************END**************************************** + + +!********************************BEGINNING************************************* +!> prepares integration +subroutine bblpreproc + integer :: i,j + write(*,*) 'preparing simulation...' + !determine number of equations and their indexes + NEQ=(p+1)*ngas + NEQ = NEQ+4+ngas + req=1 !radius index + fpeq=2 !pressure index + if (inertial_term) then + NEQ=NEQ+1 + fpeq=fpeq+1 + endif + lpeq=fpeq+ngas-1 + teq=lpeq+1 !temperature index + xOHeq=teq+1 !polyol conversion index + xWeq=xOHeq+1 !water conversion index + fceq = xWeq+1 !concentration index + if (kin_model==2) then + NEQ=NEQ+size(kineq) + do i=1,size(kineq) + kineq(i)=xWeq+i + enddo + fceq=kineq(size(kineq))+1 + endif + + !set initial values + allocate(Y(NEQ)) + Y=0 + Y(req) = R0 !radius + if (inertial_term) Y(req+1) = 0 !velocity + Y(teq) = Temp0 !temperature + Y(xOHeq) = 0 !xOH + Y(xWeq) = 0 !xW + if (kin_model==2) then + Y(kineq(1))=NCO0*1e3_dp + Y(kineq(2))=OH0*1e3_dp + Y(kineq(3))=W0*1e3_dp + endif + do j=1,ngas + do i=1,p+1 + Y(fceq+(i-1)*ngas+j-1) = cbl(j) !blowing agent concentration + enddo + enddo + if (sum(xgas) /= 1) then + write(*,*) 'Sum of initial molar fractions of gases in the bubble is & + not equal to one. Normalizing...' + xgas=xgas/sum(xgas) + write(*,*) 'New initial molar fractions of gases in the bubble' + write(*,*) xgas + endif + call createModenaModels + select case(rhop_model) !density is kept constant, calculate it only once + case(1) + case(2) + call modena_inputs_set(rhopInputs, rhopTpos, Y(teq)) + ret = modena_model_call (rhopModena, rhopInputs, rhopOutputs) + if(ret /= 0) then + call exit(ret) + endif + rhop = modena_outputs_get(rhopOutputs, 0_c_size_t) + call modena_inputs_set(rhopInputs, rhopTpos, Y(teq)+150) + ret = modena_model_call (rhopModena, rhopInputs, rhopOutputs) + if(ret /= 0) then + call exit(ret) + endif + !average density during foaming + rhop=(rhop + modena_outputs_get(rhopOutputs, 0_c_size_t))/2 + end select + call physical_properties(Y) + Pair0=(Pamb+2*sigma/R0)*xgas(1) + do i=1,ngas + Y(fpeq+i-1) = xgas(i+1)*(Pamb+2*sigma/R0) !pressure + if (Y(fpeq+i-1)<1e-16_dp) Y(fpeq+i-1)=1e-16_dp + enddo + Rold=Y(req) + Told=Y(teq) + pold(1)=Y(fpeq) + pold(2)=Y(fpeq+1) + S0=Sn*Y(req) + Vsh=4*pi/3*(S0**3-R0**3) + gelpoint=.false. + timestep=(TEND-T)/its + write(*,'(2x,A,2x,e12.6)') 'NN',Sn**(-3)/(1-Sn**(-3))/& + exp(log(4._dp/3*pi*R0**3)) + + !calculate spatial grid points + allocate(atri(p),btri(p),ctri(p),rtri(p),utri(p),dz(p+1)) + atri=-mshco !lower diagonal + btri=1+mshco !main diagonal + ctri=-1 !upper diagonal + rtri=0 !rhs + rtri(p)=S0**3-R0**3 + utri=rtri + call dgtsl(p,atri,btri,ctri,utri,info) + if ((utri(2)-utri(1))/utri(1)<10*epsilon(utri)) stop 'set smaller mesh & + coarsening parameter' + dz(1)=utri(1)+rtri(1)/mshco + do i=2,p + dz(i)=utri(i)-utri(i-1) + enddo + dz(p+1)=rtri(p)-utri(p) + deallocate(atri,btri,ctri,rtri,utri) + + !choose and set integrator + select case(integrator) + case(1) + select case(MF) + case(10) + allocate(RWORK(20+16*NEQ),IWORK(20)) + case(22) + allocate(RWORK(22+9*NEQ+NEQ**2),IWORK(20+NEQ)) + case default + stop 'unknown MF' + end select + case(2) + select case(MF) + case(10) + allocate(RWORK(20+16*NEQ),IWORK(30)) + case(222) + NNZ=NEQ**2 !Not sure, smaller numbers make problems for low p + LENRAT=2 !depends on dp + allocate(RWORK(int(20+(2+1._dp/LENRAT)*NNZ+(11+9._dp/LENRAT)*NEQ)),& + IWORK(30)) + case default + stop 'unknown MF' + end select + case default + stop 'unknown integrator' + end select + ITASK = 1 + ISTATE = 1 + IOPT = 1 + RWORK(5:10)=0 + IWORK(5:10)=0 + LRW = size(RWORK) + LIW = size(IWORK) + IWORK(6)=maxts + TOUT =T+timestep + ITOL = 1 !don't change, or you must declare ATOL as ATOL(NEQ) + write(*,*) 'done: simulation prepared' + write(*,*) +end subroutine bblpreproc +!***********************************END**************************************** + + +!********************************BEGINNING************************************* +!> performs integration +subroutine bblinteg(outputs_1d,outputs_GR,outputs_GR_c,outputs_GR_p,concloc) + character(*),intent(in) :: outputs_1d,outputs_GR,outputs_GR_c,outputs_GR_p,& + concloc !file names + write(*,*) 'integrating...' + call save_integration_header(outputs_1d,outputs_GR,outputs_GR_c,& + outputs_GR_p,concloc) + DO IOUT = 1,its + select case (integrator) + case(1) + CALL DLSODE (sub_ptr, NEQ, Y, T, TOUT, ITOL, RTOL, ATOL, ITASK, & + ISTATE, IOPT, RWORK, LRW, IWORK, LIW, JAC, MF) + case(2) + call DLSODES (sub_ptr, NEQ, Y, T, TOUT, ITOL, RTOL, ATOL, ITASK, & + ISTATE, IOPT, RWORK, LRW, IWORK, LIW, JAC, MF) + case default + stop 'unknown integrator' + end select + call molar_balance + call restoreDV + call save_integration_step + TOUT = TOUT+timestep + if (eta==maxeta) exit + END DO + call save_integration_close + write(*,*) 'done: integration' + call destroyModenaModels + call exit(0) +end subroutine bblinteg +!***********************************END**************************************** +end module model diff --git a/applications/PUfoam/MoDeNaModels/bubbleGrowth/src/src/modenastuff.f90 b/applications/PUfoam/MoDeNaModels/bubbleGrowth/src/src/modenastuff.f90 new file mode 100644 index 000000000..7f4ab070b --- /dev/null +++ b/applications/PUfoam/MoDeNaModels/bubbleGrowth/src/src/modenastuff.f90 @@ -0,0 +1,218 @@ +!> @file +!! contains definitions of modena variables +!! creates and destroys modena models +!! @author Pavel Ferkl +!! @ingroup bblgr +module modenastuff + use in_out + use iso_c_binding + use fmodena + implicit none + integer(c_int) :: ret + integer(c_size_t) :: viscTpos + integer(c_size_t) :: viscXPos + integer(c_size_t) :: rhopTPos + integer(c_size_t) :: itensTPos + integer(c_size_t) :: diffTPos(2) + integer(c_size_t) :: solTPos(2) + integer(c_size_t) :: kinNCOPos + integer(c_size_t) :: kinOHPos + integer(c_size_t) :: kinH2OPos + integer(c_size_t) :: kinCO2Pos + integer(c_size_t) :: kinPentanePos + integer(c_size_t) :: kinPolymerPos + integer(c_size_t) :: kinPolymerBlowPos + integer(c_size_t) :: kinUreaPos + integer(c_size_t) :: kinR1Pos + integer(c_size_t) :: kinRmassPos + integer(c_size_t) :: kinRvolPos + integer(c_size_t) :: kinRtempPos + integer(c_size_t) :: kinSourceNCOPos + integer(c_size_t) :: kinSourceOHPos + integer(c_size_t) :: kinSourceH2OPos + integer(c_size_t) :: kinSourceCO2Pos + integer(c_size_t) :: kinSourcePentanePos + integer(c_size_t) :: kinSourcePolymerPos + integer(c_size_t) :: kinSourcePolymerBlowPos + integer(c_size_t) :: kinSourceUreaPos + integer(c_size_t) :: kinSourceR1Pos + integer(c_size_t) :: kinSourceRmassPos + integer(c_size_t) :: kinSourceRvolPos + integer(c_size_t) :: kinSourceRtempPos + type(c_ptr) :: viscModena = c_null_ptr + type(c_ptr) :: viscInputs = c_null_ptr + type(c_ptr) :: viscOutputs = c_null_ptr + type(c_ptr) :: rhopModena = c_null_ptr + type(c_ptr) :: rhopInputs = c_null_ptr + type(c_ptr) :: rhopOutputs = c_null_ptr + type(c_ptr) :: itensModena = c_null_ptr + type(c_ptr) :: itensInputs = c_null_ptr + type(c_ptr) :: itensOutputs = c_null_ptr + type(c_ptr) :: diffModena(2) = c_null_ptr + type(c_ptr) :: diffInputs(2) = c_null_ptr + type(c_ptr) :: diffOutputs(2) = c_null_ptr + type(c_ptr) :: solModena(2) = c_null_ptr + type(c_ptr) :: solInputs(2) = c_null_ptr + type(c_ptr) :: solOutputs(2) = c_null_ptr + type(c_ptr) :: kinModena = c_null_ptr + type(c_ptr) :: kinInputs = c_null_ptr + type(c_ptr) :: kinOutputs = c_null_ptr +contains +!********************************BEGINNING************************************* +!> creates Modena models +subroutine createModenaModels + integer :: i + if (visc_model==3) then + viscModena = modena_model_new (c_char_"polymerViscosity"//c_null_char); + viscInputs = modena_inputs_new (viscModena); + viscOutputs = modena_outputs_new (viscModena); + viscTpos = modena_model_inputs_argPos(viscModena, & + c_char_"T"//c_null_char); + viscXPos = modena_model_inputs_argPos(viscModena, & + c_char_"X"//c_null_char); + call modena_model_argPos_check(viscModena) + endif + if (rhop_model==2) then + rhopModena = modena_model_new (c_char_"polymerDensity"//c_null_char); + rhopInputs = modena_inputs_new (rhopModena); + rhopOutputs = modena_outputs_new (rhopModena); + rhopTpos = modena_model_inputs_argPos(rhopModena, & + c_char_"T"//c_null_char); + call modena_model_argPos_check(rhopModena) + endif + if (itens_model==2) then + itensModena = modena_model_new (& + c_char_"interfacialTension"//c_null_char); !TODO: implement + itensInputs = modena_inputs_new (itensModena); + itensOutputs = modena_outputs_new (itensModena); + itensTpos = modena_model_inputs_argPos(& + itensModena, c_char_"T"//c_null_char); + call modena_model_argPos_check(itensModena) + endif + if (diff_model(1)==2) diffModena(1) = modena_model_new (& + c_char_"gas_diffusivity[A=CyP]"//c_null_char); + if (diff_model(2)==2) diffModena(2) = modena_model_new (& + c_char_"gas_diffusivity[A=CO2]"//c_null_char); + do i=1,ngas + if (diff_model(i)==2) then + diffInputs(i) = modena_inputs_new (diffModena(i)); + diffOutputs(i) = modena_outputs_new (diffModena(i)); + diffTpos(i) = modena_model_inputs_argPos(diffModena(i), & + c_char_"T"//c_null_char); + call modena_model_argPos_check(diffModena(i)) + endif + enddo + if (sol_model(1)==2) solModena(1) = modena_model_new (& + c_char_"solubilityRM[A=CyP]"//c_null_char); !TODO: implement + if (sol_model(2)==2) solModena(1) = modena_model_new (& + c_char_"solubilityRM[A=CO2]"//c_null_char); !TODO: implement + do i=1,ngas + if (sol_model(i)==2) then + solInputs(i) = modena_inputs_new (solModena(i)); + solOutputs(i) = modena_outputs_new (solModena(i)); + solTpos(i) = modena_model_inputs_argPos(solModena(i), & + c_char_"T"//c_null_char); + call modena_model_argPos_check(solModena(i)) + endif + enddo + if (kin_model==2) then + kinModena = modena_model_new (c_char_"simpleKinetics"//c_null_char); + kinInputs = modena_inputs_new (kinModena); + kinOutputs = modena_outputs_new (kinModena); + + kinNCOPos = modena_model_inputs_argPos(kinModena, & + c_char_"'EG_NCO'"//c_null_char); + kinOHPos = modena_model_inputs_argPos(kinModena, & + c_char_"'EG_OH'"//c_null_char); + kinH2OPos = modena_model_inputs_argPos(kinModena, & + c_char_"'H2O'"//c_null_char); + kinCO2Pos = modena_model_inputs_argPos(kinModena, & + c_char_"'CO2'"//c_null_char); + kinPentanePos = modena_model_inputs_argPos(kinModena, & + c_char_"'PENTANE'"//c_null_char); + kinPolymerPos = modena_model_inputs_argPos(kinModena, & + c_char_"'POLYMER'"//c_null_char); + kinPolymerBlowPos = modena_model_inputs_argPos(kinModena, & + c_char_"'POLMERBLOW'"//c_null_char); + kinUreaPos = modena_model_inputs_argPos(kinModena, & + c_char_"'UREA'"//c_null_char); + kinR1Pos = modena_model_inputs_argPos(kinModena, & + c_char_"'R_1'"//c_null_char); + kinRmassPos = modena_model_inputs_argPos(kinModena, & + c_char_"'R_1_mass'"//c_null_char); + kinRvolPos = modena_model_inputs_argPos(kinModena, & + c_char_"'R_1_vol'"//c_null_char); + kinRtempPos = modena_model_inputs_argPos(kinModena, & + c_char_"'R_1_temp'"//c_null_char); + + kinSourceNCOPos = modena_model_outputs_argPos(kinModena, & + c_char_"source_EG_NCO"//c_null_char); + kinSourceOHPos = modena_model_outputs_argPos(kinModena, & + c_char_"source_EG_OH"//c_null_char); + kinSourceH2OPos = modena_model_outputs_argPos(kinModena, & + c_char_"source_H2O"//c_null_char); + kinSourceCO2Pos = modena_model_outputs_argPos(kinModena, & + c_char_"source_CO2"//c_null_char); + kinSourcePentanePos = modena_model_outputs_argPos(kinModena, & + c_char_"source_PENTANE"//c_null_char); + kinSourcePolymerPos = modena_model_outputs_argPos(kinModena, & + c_char_"source_POLYMER"//c_null_char); + kinSourcePolymerBlowPos = modena_model_outputs_argPos(kinModena, & + c_char_"source_POLMERBLOW"//c_null_char); + kinSourceUreaPos = modena_model_outputs_argPos(kinModena, & + c_char_"source_UREA"//c_null_char); + kinSourceR1Pos = modena_model_outputs_argPos(kinModena, & + c_char_"source_R_1"//c_null_char); + kinSourceRmassPos = modena_model_outputs_argPos(kinModena, & + c_char_"source_R_1_mass"//c_null_char); + kinSourceRvolPos = modena_model_outputs_argPos(kinModena, & + c_char_"source_R_1_vol"//c_null_char); + kinSourceRtempPos = modena_model_outputs_argPos(kinModena, & + c_char_"source_R_1_temp"//c_null_char); + call modena_model_argPos_check(kinModena) + endif +end subroutine createModenaModels +!***********************************END**************************************** + + +!********************************BEGINNING************************************* +!> destroys Modena models +subroutine destroyModenaModels + integer :: i + if (visc_model==3) then + call modena_inputs_destroy (viscInputs); + call modena_outputs_destroy (viscOutputs); + call modena_model_destroy (viscModena); + endif + if (rhop_model==2) then + call modena_inputs_destroy (rhopInputs); + call modena_outputs_destroy (rhopOutputs); + call modena_model_destroy (rhopModena); + endif + if (itens_model==2) then + call modena_inputs_destroy (itensInputs); + call modena_outputs_destroy (itensOutputs); + call modena_model_destroy (itensModena); + endif + do i=1,ngas + if (diff_model(i)==2) then + call modena_inputs_destroy (diffInputs(i)); + call modena_outputs_destroy (diffOutputs(i)); + call modena_model_destroy (diffModena(i)); + endif + enddo + do i=1,ngas + if (sol_model(i)==2) then + call modena_inputs_destroy (solInputs(i)); + call modena_outputs_destroy (solOutputs(i)); + call modena_model_destroy (solModena(i)); + endif + enddo + if (kin_model==2) then + call modena_inputs_destroy (kinInputs); + call modena_outputs_destroy (kinOutputs); + call modena_model_destroy (kinModena); + endif +end subroutine destroyModenaModels +!***********************************END**************************************** +end module modenastuff diff --git a/applications/PUfoam/MoDeNaModels/bubbleGrowth/src/src/opkda1.f b/applications/PUfoam/MoDeNaModels/bubbleGrowth/src/src/opkda1.f new file mode 100644 index 000000000..89ddd6890 --- /dev/null +++ b/applications/PUfoam/MoDeNaModels/bubbleGrowth/src/src/opkda1.f @@ -0,0 +1,10136 @@ +*DECK DUMACH + DOUBLE PRECISION FUNCTION DUMACH () +C***BEGIN PROLOGUE DUMACH +C***PURPOSE Compute the unit roundoff of the machine. +C***CATEGORY R1 +C***TYPE DOUBLE PRECISION (RUMACH-S, DUMACH-D) +C***KEYWORDS MACHINE CONSTANTS +C***AUTHOR Hindmarsh, Alan C., (LLNL) +C***DESCRIPTION +C *Usage: +C DOUBLE PRECISION A, DUMACH +C A = DUMACH() +C +C *Function Return Values: +C A : the unit roundoff of the machine. +C +C *Description: +C The unit roundoff is defined as the smallest positive machine +C number u such that 1.0 + u .ne. 1.0. This is computed by DUMACH +C in a machine-independent manner. +C +C***REFERENCES (NONE) +C***ROUTINES CALLED DUMSUM +C***REVISION HISTORY (YYYYMMDD) +C 19930216 DATE WRITTEN +C 19930818 Added SLATEC-format prologue. (FNF) +C 20030707 Added DUMSUM to force normal storage of COMP. (ACH) +C***END PROLOGUE DUMACH +C + DOUBLE PRECISION U, COMP +C***FIRST EXECUTABLE STATEMENT DUMACH + U = 1.0D0 + 10 U = U*0.5D0 + CALL DUMSUM(1.0D0, U, COMP) + IF (COMP .NE. 1.0D0) GO TO 10 + DUMACH = U*2.0D0 + RETURN +C----------------------- End of Function DUMACH ------------------------ + END + SUBROUTINE DUMSUM(A,B,C) +C Routine to force normal storing of A + B, for DUMACH. + DOUBLE PRECISION A, B, C + C = A + B + RETURN + END +*DECK DCFODE + SUBROUTINE DCFODE (METH, ELCO, TESCO) +C***BEGIN PROLOGUE DCFODE +C***SUBSIDIARY +C***PURPOSE Set ODE integrator coefficients. +C***TYPE DOUBLE PRECISION (SCFODE-S, DCFODE-D) +C***AUTHOR Hindmarsh, Alan C., (LLNL) +C***DESCRIPTION +C +C DCFODE is called by the integrator routine to set coefficients +C needed there. The coefficients for the current method, as +C given by the value of METH, are set for all orders and saved. +C The maximum order assumed here is 12 if METH = 1 and 5 if METH = 2. +C (A smaller value of the maximum order is also allowed.) +C DCFODE is called once at the beginning of the problem, +C and is not called again unless and until METH is changed. +C +C The ELCO array contains the basic method coefficients. +C The coefficients el(i), 1 .le. i .le. nq+1, for the method of +C order nq are stored in ELCO(i,nq). They are given by a genetrating +C polynomial, i.e., +C l(x) = el(1) + el(2)*x + ... + el(nq+1)*x**nq. +C For the implicit Adams methods, l(x) is given by +C dl/dx = (x+1)*(x+2)*...*(x+nq-1)/factorial(nq-1), l(-1) = 0. +C For the BDF methods, l(x) is given by +C l(x) = (x+1)*(x+2)* ... *(x+nq)/K, +C where K = factorial(nq)*(1 + 1/2 + ... + 1/nq). +C +C The TESCO array contains test constants used for the +C local error test and the selection of step size and/or order. +C At order nq, TESCO(k,nq) is used for the selection of step +C size at order nq - 1 if k = 1, at order nq if k = 2, and at order +C nq + 1 if k = 3. +C +C***SEE ALSO DLSODE +C***ROUTINES CALLED (NONE) +C***REVISION HISTORY (YYMMDD) +C 791129 DATE WRITTEN +C 890501 Modified prologue to SLATEC/LDOC format. (FNF) +C 890503 Minor cosmetic changes. (FNF) +C 930809 Renamed to allow single/double precision versions. (ACH) +C***END PROLOGUE DCFODE +C**End + INTEGER METH + INTEGER I, IB, NQ, NQM1, NQP1 + DOUBLE PRECISION ELCO, TESCO + DOUBLE PRECISION AGAMQ, FNQ, FNQM1, PC, PINT, RAGQ, + 1 RQFAC, RQ1FAC, TSIGN, XPIN + DIMENSION ELCO(13,12), TESCO(3,12) + DIMENSION PC(12) +C +C***FIRST EXECUTABLE STATEMENT DCFODE + GO TO (100, 200), METH +C + 100 ELCO(1,1) = 1.0D0 + ELCO(2,1) = 1.0D0 + TESCO(1,1) = 0.0D0 + TESCO(2,1) = 2.0D0 + TESCO(1,2) = 1.0D0 + TESCO(3,12) = 0.0D0 + PC(1) = 1.0D0 + RQFAC = 1.0D0 + DO 140 NQ = 2,12 +C----------------------------------------------------------------------- +C The PC array will contain the coefficients of the polynomial +C p(x) = (x+1)*(x+2)*...*(x+nq-1). +C Initially, p(x) = 1. +C----------------------------------------------------------------------- + RQ1FAC = RQFAC + RQFAC = RQFAC/NQ + NQM1 = NQ - 1 + FNQM1 = NQM1 + NQP1 = NQ + 1 +C Form coefficients of p(x)*(x+nq-1). ---------------------------------- + PC(NQ) = 0.0D0 + DO 110 IB = 1,NQM1 + I = NQP1 - IB + 110 PC(I) = PC(I-1) + FNQM1*PC(I) + PC(1) = FNQM1*PC(1) +C Compute integral, -1 to 0, of p(x) and x*p(x). ----------------------- + PINT = PC(1) + XPIN = PC(1)/2.0D0 + TSIGN = 1.0D0 + DO 120 I = 2,NQ + TSIGN = -TSIGN + PINT = PINT + TSIGN*PC(I)/I + 120 XPIN = XPIN + TSIGN*PC(I)/(I+1) +C Store coefficients in ELCO and TESCO. -------------------------------- + ELCO(1,NQ) = PINT*RQ1FAC + ELCO(2,NQ) = 1.0D0 + DO 130 I = 2,NQ + 130 ELCO(I+1,NQ) = RQ1FAC*PC(I)/I + AGAMQ = RQFAC*XPIN + RAGQ = 1.0D0/AGAMQ + TESCO(2,NQ) = RAGQ + IF (NQ .LT. 12) TESCO(1,NQP1) = RAGQ*RQFAC/NQP1 + TESCO(3,NQM1) = RAGQ + 140 CONTINUE + RETURN +C + 200 PC(1) = 1.0D0 + RQ1FAC = 1.0D0 + DO 230 NQ = 1,5 +C----------------------------------------------------------------------- +C The PC array will contain the coefficients of the polynomial +C p(x) = (x+1)*(x+2)*...*(x+nq). +C Initially, p(x) = 1. +C----------------------------------------------------------------------- + FNQ = NQ + NQP1 = NQ + 1 +C Form coefficients of p(x)*(x+nq). ------------------------------------ + PC(NQP1) = 0.0D0 + DO 210 IB = 1,NQ + I = NQ + 2 - IB + 210 PC(I) = PC(I-1) + FNQ*PC(I) + PC(1) = FNQ*PC(1) +C Store coefficients in ELCO and TESCO. -------------------------------- + DO 220 I = 1,NQP1 + 220 ELCO(I,NQ) = PC(I)/PC(2) + ELCO(2,NQ) = 1.0D0 + TESCO(1,NQ) = RQ1FAC + TESCO(2,NQ) = NQP1/ELCO(1,NQ) + TESCO(3,NQ) = (NQ+2)/ELCO(1,NQ) + RQ1FAC = RQ1FAC/FNQ + 230 CONTINUE + RETURN +C----------------------- END OF SUBROUTINE DCFODE ---------------------- + END +*DECK DINTDY + SUBROUTINE DINTDY (T, K, YH, NYH, DKY, IFLAG) +C***BEGIN PROLOGUE DINTDY +C***SUBSIDIARY +C***PURPOSE Interpolate solution derivatives. +C***TYPE DOUBLE PRECISION (SINTDY-S, DINTDY-D) +C***AUTHOR Hindmarsh, Alan C., (LLNL) +C***DESCRIPTION +C +C DINTDY computes interpolated values of the K-th derivative of the +C dependent variable vector y, and stores it in DKY. This routine +C is called within the package with K = 0 and T = TOUT, but may +C also be called by the user for any K up to the current order. +C (See detailed instructions in the usage documentation.) +C +C The computed values in DKY are gotten by interpolation using the +C Nordsieck history array YH. This array corresponds uniquely to a +C vector-valued polynomial of degree NQCUR or less, and DKY is set +C to the K-th derivative of this polynomial at T. +C The formula for DKY is: +C q +C DKY(i) = sum c(j,K) * (T - tn)**(j-K) * h**(-j) * YH(i,j+1) +C j=K +C where c(j,K) = j*(j-1)*...*(j-K+1), q = NQCUR, tn = TCUR, h = HCUR. +C The quantities nq = NQCUR, l = nq+1, N = NEQ, tn, and h are +C communicated by COMMON. The above sum is done in reverse order. +C IFLAG is returned negative if either K or T is out of bounds. +C +C***SEE ALSO DLSODE +C***ROUTINES CALLED XERRWD +C***COMMON BLOCKS DLS001 +C***REVISION HISTORY (YYMMDD) +C 791129 DATE WRITTEN +C 890501 Modified prologue to SLATEC/LDOC format. (FNF) +C 890503 Minor cosmetic changes. (FNF) +C 930809 Renamed to allow single/double precision versions. (ACH) +C 010418 Reduced size of Common block /DLS001/. (ACH) +C 031105 Restored 'own' variables to Common block /DLS001/, to +C enable interrupt/restart feature. (ACH) +C 050427 Corrected roundoff decrement in TP. (ACH) +C***END PROLOGUE DINTDY +C**End + INTEGER K, NYH, IFLAG + DOUBLE PRECISION T, YH, DKY + DIMENSION YH(NYH,*), DKY(*) + INTEGER IOWND, IOWNS, + 1 ICF, IERPJ, IERSL, JCUR, JSTART, KFLAG, L, + 2 LYH, LEWT, LACOR, LSAVF, LWM, LIWM, METH, MITER, + 3 MAXORD, MAXCOR, MSBP, MXNCF, N, NQ, NST, NFE, NJE, NQU + DOUBLE PRECISION ROWNS, + 1 CCMAX, EL0, H, HMIN, HMXI, HU, RC, TN, UROUND + COMMON /DLS001/ ROWNS(209), + 1 CCMAX, EL0, H, HMIN, HMXI, HU, RC, TN, UROUND, + 2 IOWND(6), IOWNS(6), + 3 ICF, IERPJ, IERSL, JCUR, JSTART, KFLAG, L, + 4 LYH, LEWT, LACOR, LSAVF, LWM, LIWM, METH, MITER, + 5 MAXORD, MAXCOR, MSBP, MXNCF, N, NQ, NST, NFE, NJE, NQU + INTEGER I, IC, J, JB, JB2, JJ, JJ1, JP1 + DOUBLE PRECISION C, R, S, TP + CHARACTER*80 MSG +C +C***FIRST EXECUTABLE STATEMENT DINTDY + IFLAG = 0 + IF (K .LT. 0 .OR. K .GT. NQ) GO TO 80 + TP = TN - HU - 100.0D0*UROUND*SIGN(ABS(TN) + ABS(HU), HU) + IF ((T-TP)*(T-TN) .GT. 0.0D0) GO TO 90 +C + S = (T - TN)/H + IC = 1 + IF (K .EQ. 0) GO TO 15 + JJ1 = L - K + DO 10 JJ = JJ1,NQ + 10 IC = IC*JJ + 15 C = IC + DO 20 I = 1,N + 20 DKY(I) = C*YH(I,L) + IF (K .EQ. NQ) GO TO 55 + JB2 = NQ - K + DO 50 JB = 1,JB2 + J = NQ - JB + JP1 = J + 1 + IC = 1 + IF (K .EQ. 0) GO TO 35 + JJ1 = JP1 - K + DO 30 JJ = JJ1,J + 30 IC = IC*JJ + 35 C = IC + DO 40 I = 1,N + 40 DKY(I) = C*YH(I,JP1) + S*DKY(I) + 50 CONTINUE + IF (K .EQ. 0) RETURN + 55 R = H**(-K) + DO 60 I = 1,N + 60 DKY(I) = R*DKY(I) + RETURN +C + 80 MSG = 'DINTDY- K (=I1) illegal ' + CALL XERRWD (MSG, 30, 51, 0, 1, K, 0, 0, 0.0D0, 0.0D0) + IFLAG = -1 + RETURN + 90 MSG = 'DINTDY- T (=R1) illegal ' + CALL XERRWD (MSG, 30, 52, 0, 0, 0, 0, 1, T, 0.0D0) + MSG=' T not in interval TCUR - HU (= R1) to TCUR (=R2) ' + CALL XERRWD (MSG, 60, 52, 0, 0, 0, 0, 2, TP, TN) + IFLAG = -2 + RETURN +C----------------------- END OF SUBROUTINE DINTDY ---------------------- + END +*DECK DPREPJ + SUBROUTINE DPREPJ (NEQ, Y, YH, NYH, EWT, FTEM, SAVF, WM, IWM, + 1 F, JAC) +C***BEGIN PROLOGUE DPREPJ +C***SUBSIDIARY +C***PURPOSE Compute and process Newton iteration matrix. +C***TYPE DOUBLE PRECISION (SPREPJ-S, DPREPJ-D) +C***AUTHOR Hindmarsh, Alan C., (LLNL) +C***DESCRIPTION +C +C DPREPJ is called by DSTODE to compute and process the matrix +C P = I - h*el(1)*J , where J is an approximation to the Jacobian. +C Here J is computed by the user-supplied routine JAC if +C MITER = 1 or 4, or by finite differencing if MITER = 2, 3, or 5. +C If MITER = 3, a diagonal approximation to J is used. +C J is stored in WM and replaced by P. If MITER .ne. 3, P is then +C subjected to LU decomposition in preparation for later solution +C of linear systems with P as coefficient matrix. This is done +C by DGEFA if MITER = 1 or 2, and by DGBFA if MITER = 4 or 5. +C +C In addition to variables described in DSTODE and DLSODE prologues, +C communication with DPREPJ uses the following: +C Y = array containing predicted values on entry. +C FTEM = work array of length N (ACOR in DSTODE). +C SAVF = array containing f evaluated at predicted y. +C WM = real work space for matrices. On output it contains the +C inverse diagonal matrix if MITER = 3 and the LU decomposition +C of P if MITER is 1, 2 , 4, or 5. +C Storage of matrix elements starts at WM(3). +C WM also contains the following matrix-related data: +C WM(1) = SQRT(UROUND), used in numerical Jacobian increments. +C WM(2) = H*EL0, saved for later use if MITER = 3. +C IWM = integer work space containing pivot information, starting at +C IWM(21), if MITER is 1, 2, 4, or 5. IWM also contains band +C parameters ML = IWM(1) and MU = IWM(2) if MITER is 4 or 5. +C EL0 = EL(1) (input). +C IERPJ = output error flag, = 0 if no trouble, .gt. 0 if +C P matrix found to be singular. +C JCUR = output flag = 1 to indicate that the Jacobian matrix +C (or approximation) is now current. +C This routine also uses the COMMON variables EL0, H, TN, UROUND, +C MITER, N, NFE, and NJE. +C +C***SEE ALSO DLSODE +C***ROUTINES CALLED DGBFA, DGEFA, DVNORM +C***COMMON BLOCKS DLS001 +C***REVISION HISTORY (YYMMDD) +C 791129 DATE WRITTEN +C 890501 Modified prologue to SLATEC/LDOC format. (FNF) +C 890504 Minor cosmetic changes. (FNF) +C 930809 Renamed to allow single/double precision versions. (ACH) +C 010418 Reduced size of Common block /DLS001/. (ACH) +C 031105 Restored 'own' variables to Common block /DLS001/, to +C enable interrupt/restart feature. (ACH) +C***END PROLOGUE DPREPJ +C**End + EXTERNAL F, JAC + INTEGER NEQ, NYH, IWM + DOUBLE PRECISION Y, YH, EWT, FTEM, SAVF, WM + DIMENSION NEQ(*), Y(*), YH(NYH,*), EWT(*), FTEM(*), SAVF(*), + 1 WM(*), IWM(*) + INTEGER IOWND, IOWNS, + 1 ICF, IERPJ, IERSL, JCUR, JSTART, KFLAG, L, + 2 LYH, LEWT, LACOR, LSAVF, LWM, LIWM, METH, MITER, + 3 MAXORD, MAXCOR, MSBP, MXNCF, N, NQ, NST, NFE, NJE, NQU + DOUBLE PRECISION ROWNS, + 1 CCMAX, EL0, H, HMIN, HMXI, HU, RC, TN, UROUND + COMMON /DLS001/ ROWNS(209), + 1 CCMAX, EL0, H, HMIN, HMXI, HU, RC, TN, UROUND, + 2 IOWND(6), IOWNS(6), + 3 ICF, IERPJ, IERSL, JCUR, JSTART, KFLAG, L, + 4 LYH, LEWT, LACOR, LSAVF, LWM, LIWM, METH, MITER, + 5 MAXORD, MAXCOR, MSBP, MXNCF, N, NQ, NST, NFE, NJE, NQU + INTEGER I, I1, I2, IER, II, J, J1, JJ, LENP, + 1 MBA, MBAND, MEB1, MEBAND, ML, ML3, MU, NP1 + DOUBLE PRECISION CON, DI, FAC, HL0, R, R0, SRUR, YI, YJ, YJJ, + 1 DVNORM +C +C***FIRST EXECUTABLE STATEMENT DPREPJ + NJE = NJE + 1 + IERPJ = 0 + JCUR = 1 + HL0 = H*EL0 + GO TO (100, 200, 300, 400, 500), MITER +C If MITER = 1, call JAC and multiply by scalar. ----------------------- + 100 LENP = N*N + DO 110 I = 1,LENP + 110 WM(I+2) = 0.0D0 + CALL JAC (NEQ, TN, Y, 0, 0, WM(3), N) + CON = -HL0 + DO 120 I = 1,LENP + 120 WM(I+2) = WM(I+2)*CON + GO TO 240 +C If MITER = 2, make N calls to F to approximate J. -------------------- + 200 FAC = DVNORM (N, SAVF, EWT) + R0 = 1000.0D0*ABS(H)*UROUND*N*FAC + IF (R0 .EQ. 0.0D0) R0 = 1.0D0 + SRUR = WM(1) + J1 = 2 + DO 230 J = 1,N + YJ = Y(J) + R = MAX(SRUR*ABS(YJ),R0/EWT(J)) + Y(J) = Y(J) + R + FAC = -HL0/R + CALL F (NEQ, TN, Y, FTEM) + DO 220 I = 1,N + 220 WM(I+J1) = (FTEM(I) - SAVF(I))*FAC + Y(J) = YJ + J1 = J1 + N + 230 CONTINUE + NFE = NFE + N +C Add identity matrix. ------------------------------------------------- + 240 J = 3 + NP1 = N + 1 + DO 250 I = 1,N + WM(J) = WM(J) + 1.0D0 + 250 J = J + NP1 +C Do LU decomposition on P. -------------------------------------------- + CALL DGEFA (WM(3), N, N, IWM(21), IER) + IF (IER .NE. 0) IERPJ = 1 + RETURN +C If MITER = 3, construct a diagonal approximation to J and P. --------- + 300 WM(2) = HL0 + R = EL0*0.1D0 + DO 310 I = 1,N + 310 Y(I) = Y(I) + R*(H*SAVF(I) - YH(I,2)) + CALL F (NEQ, TN, Y, WM(3)) + NFE = NFE + 1 + DO 320 I = 1,N + R0 = H*SAVF(I) - YH(I,2) + DI = 0.1D0*R0 - H*(WM(I+2) - SAVF(I)) + WM(I+2) = 1.0D0 + IF (ABS(R0) .LT. UROUND/EWT(I)) GO TO 320 + IF (ABS(DI) .EQ. 0.0D0) GO TO 330 + WM(I+2) = 0.1D0*R0/DI + 320 CONTINUE + RETURN + 330 IERPJ = 1 + RETURN +C If MITER = 4, call JAC and multiply by scalar. ----------------------- + 400 ML = IWM(1) + MU = IWM(2) + ML3 = ML + 3 + MBAND = ML + MU + 1 + MEBAND = MBAND + ML + LENP = MEBAND*N + DO 410 I = 1,LENP + 410 WM(I+2) = 0.0D0 + CALL JAC (NEQ, TN, Y, ML, MU, WM(ML3), MEBAND) + CON = -HL0 + DO 420 I = 1,LENP + 420 WM(I+2) = WM(I+2)*CON + GO TO 570 +C If MITER = 5, make MBAND calls to F to approximate J. ---------------- + 500 ML = IWM(1) + MU = IWM(2) + MBAND = ML + MU + 1 + MBA = MIN(MBAND,N) + MEBAND = MBAND + ML + MEB1 = MEBAND - 1 + SRUR = WM(1) + FAC = DVNORM (N, SAVF, EWT) + R0 = 1000.0D0*ABS(H)*UROUND*N*FAC + IF (R0 .EQ. 0.0D0) R0 = 1.0D0 + DO 560 J = 1,MBA + DO 530 I = J,N,MBAND + YI = Y(I) + R = MAX(SRUR*ABS(YI),R0/EWT(I)) + 530 Y(I) = Y(I) + R + CALL F (NEQ, TN, Y, FTEM) + DO 550 JJ = J,N,MBAND + Y(JJ) = YH(JJ,1) + YJJ = Y(JJ) + R = MAX(SRUR*ABS(YJJ),R0/EWT(JJ)) + FAC = -HL0/R + I1 = MAX(JJ-MU,1) + I2 = MIN(JJ+ML,N) + II = JJ*MEB1 - ML + 2 + DO 540 I = I1,I2 + 540 WM(II+I) = (FTEM(I) - SAVF(I))*FAC + 550 CONTINUE + 560 CONTINUE + NFE = NFE + MBA +C Add identity matrix. ------------------------------------------------- + 570 II = MBAND + 2 + DO 580 I = 1,N + WM(II) = WM(II) + 1.0D0 + 580 II = II + MEBAND +C Do LU decomposition of P. -------------------------------------------- + CALL DGBFA (WM(3), MEBAND, N, ML, MU, IWM(21), IER) + IF (IER .NE. 0) IERPJ = 1 + RETURN +C----------------------- END OF SUBROUTINE DPREPJ ---------------------- + END +*DECK DSOLSY + SUBROUTINE DSOLSY (WM, IWM, X, TEM) +C***BEGIN PROLOGUE DSOLSY +C***SUBSIDIARY +C***PURPOSE ODEPACK linear system solver. +C***TYPE DOUBLE PRECISION (SSOLSY-S, DSOLSY-D) +C***AUTHOR Hindmarsh, Alan C., (LLNL) +C***DESCRIPTION +C +C This routine manages the solution of the linear system arising from +C a chord iteration. It is called if MITER .ne. 0. +C If MITER is 1 or 2, it calls DGESL to accomplish this. +C If MITER = 3 it updates the coefficient h*EL0 in the diagonal +C matrix, and then computes the solution. +C If MITER is 4 or 5, it calls DGBSL. +C Communication with DSOLSY uses the following variables: +C WM = real work space containing the inverse diagonal matrix if +C MITER = 3 and the LU decomposition of the matrix otherwise. +C Storage of matrix elements starts at WM(3). +C WM also contains the following matrix-related data: +C WM(1) = SQRT(UROUND) (not used here), +C WM(2) = HL0, the previous value of h*EL0, used if MITER = 3. +C IWM = integer work space containing pivot information, starting at +C IWM(21), if MITER is 1, 2, 4, or 5. IWM also contains band +C parameters ML = IWM(1) and MU = IWM(2) if MITER is 4 or 5. +C X = the right-hand side vector on input, and the solution vector +C on output, of length N. +C TEM = vector of work space of length N, not used in this version. +C IERSL = output flag (in COMMON). IERSL = 0 if no trouble occurred. +C IERSL = 1 if a singular matrix arose with MITER = 3. +C This routine also uses the COMMON variables EL0, H, MITER, and N. +C +C***SEE ALSO DLSODE +C***ROUTINES CALLED DGBSL, DGESL +C***COMMON BLOCKS DLS001 +C***REVISION HISTORY (YYMMDD) +C 791129 DATE WRITTEN +C 890501 Modified prologue to SLATEC/LDOC format. (FNF) +C 890503 Minor cosmetic changes. (FNF) +C 930809 Renamed to allow single/double precision versions. (ACH) +C 010418 Reduced size of Common block /DLS001/. (ACH) +C 031105 Restored 'own' variables to Common block /DLS001/, to +C enable interrupt/restart feature. (ACH) +C***END PROLOGUE DSOLSY +C**End + INTEGER IWM + DOUBLE PRECISION WM, X, TEM + DIMENSION WM(*), IWM(*), X(*), TEM(*) + INTEGER IOWND, IOWNS, + 1 ICF, IERPJ, IERSL, JCUR, JSTART, KFLAG, L, + 2 LYH, LEWT, LACOR, LSAVF, LWM, LIWM, METH, MITER, + 3 MAXORD, MAXCOR, MSBP, MXNCF, N, NQ, NST, NFE, NJE, NQU + DOUBLE PRECISION ROWNS, + 1 CCMAX, EL0, H, HMIN, HMXI, HU, RC, TN, UROUND + COMMON /DLS001/ ROWNS(209), + 1 CCMAX, EL0, H, HMIN, HMXI, HU, RC, TN, UROUND, + 2 IOWND(6), IOWNS(6), + 3 ICF, IERPJ, IERSL, JCUR, JSTART, KFLAG, L, + 4 LYH, LEWT, LACOR, LSAVF, LWM, LIWM, METH, MITER, + 5 MAXORD, MAXCOR, MSBP, MXNCF, N, NQ, NST, NFE, NJE, NQU + INTEGER I, MEBAND, ML, MU + DOUBLE PRECISION DI, HL0, PHL0, R +C +C***FIRST EXECUTABLE STATEMENT DSOLSY + IERSL = 0 + GO TO (100, 100, 300, 400, 400), MITER + 100 CALL DGESL (WM(3), N, N, IWM(21), X, 0) + RETURN +C + 300 PHL0 = WM(2) + HL0 = H*EL0 + WM(2) = HL0 + IF (HL0 .EQ. PHL0) GO TO 330 + R = HL0/PHL0 + DO 320 I = 1,N + DI = 1.0D0 - R*(1.0D0 - 1.0D0/WM(I+2)) + IF (ABS(DI) .EQ. 0.0D0) GO TO 390 + 320 WM(I+2) = 1.0D0/DI + 330 DO 340 I = 1,N + 340 X(I) = WM(I+2)*X(I) + RETURN + 390 IERSL = 1 + RETURN +C + 400 ML = IWM(1) + MU = IWM(2) + MEBAND = 2*ML + MU + 1 + CALL DGBSL (WM(3), MEBAND, N, ML, MU, IWM(21), X, 0) + RETURN +C----------------------- END OF SUBROUTINE DSOLSY ---------------------- + END +*DECK DSRCOM + SUBROUTINE DSRCOM (RSAV, ISAV, JOB) +C***BEGIN PROLOGUE DSRCOM +C***SUBSIDIARY +C***PURPOSE Save/restore ODEPACK COMMON blocks. +C***TYPE DOUBLE PRECISION (SSRCOM-S, DSRCOM-D) +C***AUTHOR Hindmarsh, Alan C., (LLNL) +C***DESCRIPTION +C +C This routine saves or restores (depending on JOB) the contents of +C the COMMON block DLS001, which is used internally +C by one or more ODEPACK solvers. +C +C RSAV = real array of length 218 or more. +C ISAV = integer array of length 37 or more. +C JOB = flag indicating to save or restore the COMMON blocks: +C JOB = 1 if COMMON is to be saved (written to RSAV/ISAV) +C JOB = 2 if COMMON is to be restored (read from RSAV/ISAV) +C A call with JOB = 2 presumes a prior call with JOB = 1. +C +C***SEE ALSO DLSODE +C***ROUTINES CALLED (NONE) +C***COMMON BLOCKS DLS001 +C***REVISION HISTORY (YYMMDD) +C 791129 DATE WRITTEN +C 890501 Modified prologue to SLATEC/LDOC format. (FNF) +C 890503 Minor cosmetic changes. (FNF) +C 921116 Deleted treatment of block /EH0001/. (ACH) +C 930801 Reduced Common block length by 2. (ACH) +C 930809 Renamed to allow single/double precision versions. (ACH) +C 010418 Reduced Common block length by 209+12. (ACH) +C 031105 Restored 'own' variables to Common block /DLS001/, to +C enable interrupt/restart feature. (ACH) +C 031112 Added SAVE statement for data-loaded constants. +C***END PROLOGUE DSRCOM +C**End + INTEGER ISAV, JOB + INTEGER ILS + INTEGER I, LENILS, LENRLS + DOUBLE PRECISION RSAV, RLS + DIMENSION RSAV(*), ISAV(*) + SAVE LENRLS, LENILS + COMMON /DLS001/ RLS(218), ILS(37) + DATA LENRLS/218/, LENILS/37/ +C +C***FIRST EXECUTABLE STATEMENT DSRCOM + IF (JOB .EQ. 2) GO TO 100 +C + DO 10 I = 1,LENRLS + 10 RSAV(I) = RLS(I) + DO 20 I = 1,LENILS + 20 ISAV(I) = ILS(I) + RETURN +C + 100 CONTINUE + DO 110 I = 1,LENRLS + 110 RLS(I) = RSAV(I) + DO 120 I = 1,LENILS + 120 ILS(I) = ISAV(I) + RETURN +C----------------------- END OF SUBROUTINE DSRCOM ---------------------- + END +*DECK DSTODE + SUBROUTINE DSTODE (NEQ, Y, YH, NYH, YH1, EWT, SAVF, ACOR, + 1 WM, IWM, F, JAC, PJAC, SLVS) +C***BEGIN PROLOGUE DSTODE +C***SUBSIDIARY +C***PURPOSE Performs one step of an ODEPACK integration. +C***TYPE DOUBLE PRECISION (SSTODE-S, DSTODE-D) +C***AUTHOR Hindmarsh, Alan C., (LLNL) +C***DESCRIPTION +C +C DSTODE performs one step of the integration of an initial value +C problem for a system of ordinary differential equations. +C Note: DSTODE is independent of the value of the iteration method +C indicator MITER, when this is .ne. 0, and hence is independent +C of the type of chord method used, or the Jacobian structure. +C Communication with DSTODE is done with the following variables: +C +C NEQ = integer array containing problem size in NEQ(1), and +C passed as the NEQ argument in all calls to F and JAC. +C Y = an array of length .ge. N used as the Y argument in +C all calls to F and JAC. +C YH = an NYH by LMAX array containing the dependent variables +C and their approximate scaled derivatives, where +C LMAX = MAXORD + 1. YH(i,j+1) contains the approximate +C j-th derivative of y(i), scaled by h**j/factorial(j) +C (j = 0,1,...,NQ). on entry for the first step, the first +C two columns of YH must be set from the initial values. +C NYH = a constant integer .ge. N, the first dimension of YH. +C YH1 = a one-dimensional array occupying the same space as YH. +C EWT = an array of length N containing multiplicative weights +C for local error measurements. Local errors in Y(i) are +C compared to 1.0/EWT(i) in various error tests. +C SAVF = an array of working storage, of length N. +C Also used for input of YH(*,MAXORD+2) when JSTART = -1 +C and MAXORD .lt. the current order NQ. +C ACOR = a work array of length N, used for the accumulated +C corrections. On a successful return, ACOR(i) contains +C the estimated one-step local error in Y(i). +C WM,IWM = real and integer work arrays associated with matrix +C operations in chord iteration (MITER .ne. 0). +C PJAC = name of routine to evaluate and preprocess Jacobian matrix +C and P = I - h*el0*JAC, if a chord method is being used. +C SLVS = name of routine to solve linear system in chord iteration. +C CCMAX = maximum relative change in h*el0 before PJAC is called. +C H = the step size to be attempted on the next step. +C H is altered by the error control algorithm during the +C problem. H can be either positive or negative, but its +C sign must remain constant throughout the problem. +C HMIN = the minimum absolute value of the step size h to be used. +C HMXI = inverse of the maximum absolute value of h to be used. +C HMXI = 0.0 is allowed and corresponds to an infinite hmax. +C HMIN and HMXI may be changed at any time, but will not +C take effect until the next change of h is considered. +C TN = the independent variable. TN is updated on each step taken. +C JSTART = an integer used for input only, with the following +C values and meanings: +C 0 perform the first step. +C .gt.0 take a new step continuing from the last. +C -1 take the next step with a new value of H, MAXORD, +C N, METH, MITER, and/or matrix parameters. +C -2 take the next step with a new value of H, +C but with other inputs unchanged. +C On return, JSTART is set to 1 to facilitate continuation. +C KFLAG = a completion code with the following meanings: +C 0 the step was succesful. +C -1 the requested error could not be achieved. +C -2 corrector convergence could not be achieved. +C -3 fatal error in PJAC or SLVS. +C A return with KFLAG = -1 or -2 means either +C abs(H) = HMIN or 10 consecutive failures occurred. +C On a return with KFLAG negative, the values of TN and +C the YH array are as of the beginning of the last +C step, and H is the last step size attempted. +C MAXORD = the maximum order of integration method to be allowed. +C MAXCOR = the maximum number of corrector iterations allowed. +C MSBP = maximum number of steps between PJAC calls (MITER .gt. 0). +C MXNCF = maximum number of convergence failures allowed. +C METH/MITER = the method flags. See description in driver. +C N = the number of first-order differential equations. +C The values of CCMAX, H, HMIN, HMXI, TN, JSTART, KFLAG, MAXORD, +C MAXCOR, MSBP, MXNCF, METH, MITER, and N are communicated via COMMON. +C +C***SEE ALSO DLSODE +C***ROUTINES CALLED DCFODE, DVNORM +C***COMMON BLOCKS DLS001 +C***REVISION HISTORY (YYMMDD) +C 791129 DATE WRITTEN +C 890501 Modified prologue to SLATEC/LDOC format. (FNF) +C 890503 Minor cosmetic changes. (FNF) +C 930809 Renamed to allow single/double precision versions. (ACH) +C 010418 Reduced size of Common block /DLS001/. (ACH) +C 031105 Restored 'own' variables to Common block /DLS001/, to +C enable interrupt/restart feature. (ACH) +C***END PROLOGUE DSTODE +C**End + EXTERNAL F, JAC, PJAC, SLVS + INTEGER NEQ, NYH, IWM + DOUBLE PRECISION Y, YH, YH1, EWT, SAVF, ACOR, WM + DIMENSION NEQ(*), Y(*), YH(NYH,*), YH1(*), EWT(*), SAVF(*), + 1 ACOR(*), WM(*), IWM(*) + INTEGER IOWND, IALTH, IPUP, LMAX, MEO, NQNYH, NSLP, + 1 ICF, IERPJ, IERSL, JCUR, JSTART, KFLAG, L, + 2 LYH, LEWT, LACOR, LSAVF, LWM, LIWM, METH, MITER, + 3 MAXORD, MAXCOR, MSBP, MXNCF, N, NQ, NST, NFE, NJE, NQU + INTEGER I, I1, IREDO, IRET, J, JB, M, NCF, NEWQ + DOUBLE PRECISION CONIT, CRATE, EL, ELCO, HOLD, RMAX, TESCO, + 2 CCMAX, EL0, H, HMIN, HMXI, HU, RC, TN, UROUND + DOUBLE PRECISION DCON, DDN, DEL, DELP, DSM, DUP, EXDN, EXSM, EXUP, + 1 R, RH, RHDN, RHSM, RHUP, TOLD, DVNORM + COMMON /DLS001/ CONIT, CRATE, EL(13), ELCO(13,12), + 1 HOLD, RMAX, TESCO(3,12), + 2 CCMAX, EL0, H, HMIN, HMXI, HU, RC, TN, UROUND, + 3 IOWND(6), IALTH, IPUP, LMAX, MEO, NQNYH, NSLP, + 3 ICF, IERPJ, IERSL, JCUR, JSTART, KFLAG, L, + 4 LYH, LEWT, LACOR, LSAVF, LWM, LIWM, METH, MITER, + 5 MAXORD, MAXCOR, MSBP, MXNCF, N, NQ, NST, NFE, NJE, NQU +C +C***FIRST EXECUTABLE STATEMENT DSTODE + KFLAG = 0 + TOLD = TN + NCF = 0 + IERPJ = 0 + IERSL = 0 + JCUR = 0 + ICF = 0 + DELP = 0.0D0 + IF (JSTART .GT. 0) GO TO 200 + IF (JSTART .EQ. -1) GO TO 100 + IF (JSTART .EQ. -2) GO TO 160 +C----------------------------------------------------------------------- +C On the first call, the order is set to 1, and other variables are +C initialized. RMAX is the maximum ratio by which H can be increased +C in a single step. It is initially 1.E4 to compensate for the small +C initial H, but then is normally equal to 10. If a failure +C occurs (in corrector convergence or error test), RMAX is set to 2 +C for the next increase. +C----------------------------------------------------------------------- + LMAX = MAXORD + 1 + NQ = 1 + L = 2 + IALTH = 2 + RMAX = 10000.0D0 + RC = 0.0D0 + EL0 = 1.0D0 + CRATE = 0.7D0 + HOLD = H + MEO = METH + NSLP = 0 + IPUP = MITER + IRET = 3 + GO TO 140 +C----------------------------------------------------------------------- +C The following block handles preliminaries needed when JSTART = -1. +C IPUP is set to MITER to force a matrix update. +C If an order increase is about to be considered (IALTH = 1), +C IALTH is reset to 2 to postpone consideration one more step. +C If the caller has changed METH, DCFODE is called to reset +C the coefficients of the method. +C If the caller has changed MAXORD to a value less than the current +C order NQ, NQ is reduced to MAXORD, and a new H chosen accordingly. +C If H is to be changed, YH must be rescaled. +C If H or METH is being changed, IALTH is reset to L = NQ + 1 +C to prevent further changes in H for that many steps. +C----------------------------------------------------------------------- + 100 IPUP = MITER + LMAX = MAXORD + 1 + IF (IALTH .EQ. 1) IALTH = 2 + IF (METH .EQ. MEO) GO TO 110 + CALL DCFODE (METH, ELCO, TESCO) + MEO = METH + IF (NQ .GT. MAXORD) GO TO 120 + IALTH = L + IRET = 1 + GO TO 150 + 110 IF (NQ .LE. MAXORD) GO TO 160 + 120 NQ = MAXORD + L = LMAX + DO 125 I = 1,L + 125 EL(I) = ELCO(I,NQ) + NQNYH = NQ*NYH + RC = RC*EL(1)/EL0 + EL0 = EL(1) + CONIT = 0.5D0/(NQ+2) + DDN = DVNORM (N, SAVF, EWT)/TESCO(1,L) + EXDN = 1.0D0/L + RHDN = 1.0D0/(1.3D0*DDN**EXDN + 0.0000013D0) + RH = MIN(RHDN,1.0D0) + IREDO = 3 + IF (H .EQ. HOLD) GO TO 170 + RH = MIN(RH,ABS(H/HOLD)) + H = HOLD + GO TO 175 +C----------------------------------------------------------------------- +C DCFODE is called to get all the integration coefficients for the +C current METH. Then the EL vector and related constants are reset +C whenever the order NQ is changed, or at the start of the problem. +C----------------------------------------------------------------------- + 140 CALL DCFODE (METH, ELCO, TESCO) + 150 DO 155 I = 1,L + 155 EL(I) = ELCO(I,NQ) + NQNYH = NQ*NYH + RC = RC*EL(1)/EL0 + EL0 = EL(1) + CONIT = 0.5D0/(NQ+2) + GO TO (160, 170, 200), IRET +C----------------------------------------------------------------------- +C If H is being changed, the H ratio RH is checked against +C RMAX, HMIN, and HMXI, and the YH array rescaled. IALTH is set to +C L = NQ + 1 to prevent a change of H for that many steps, unless +C forced by a convergence or error test failure. +C----------------------------------------------------------------------- + 160 IF (H .EQ. HOLD) GO TO 200 + RH = H/HOLD + H = HOLD + IREDO = 3 + GO TO 175 + 170 RH = MAX(RH,HMIN/ABS(H)) + 175 RH = MIN(RH,RMAX) + RH = RH/MAX(1.0D0,ABS(H)*HMXI*RH) + R = 1.0D0 + DO 180 J = 2,L + R = R*RH + DO 180 I = 1,N + 180 YH(I,J) = YH(I,J)*R + H = H*RH + RC = RC*RH + IALTH = L + IF (IREDO .EQ. 0) GO TO 690 +C----------------------------------------------------------------------- +C This section computes the predicted values by effectively +C multiplying the YH array by the Pascal Triangle matrix. +C RC is the ratio of new to old values of the coefficient H*EL(1). +C When RC differs from 1 by more than CCMAX, IPUP is set to MITER +C to force PJAC to be called, if a Jacobian is involved. +C In any case, PJAC is called at least every MSBP steps. +C----------------------------------------------------------------------- + 200 IF (ABS(RC-1.0D0) .GT. CCMAX) IPUP = MITER + IF (NST .GE. NSLP+MSBP) IPUP = MITER + TN = TN + H + I1 = NQNYH + 1 + DO 215 JB = 1,NQ + I1 = I1 - NYH +Cdir$ ivdep + DO 210 I = I1,NQNYH + 210 YH1(I) = YH1(I) + YH1(I+NYH) + 215 CONTINUE +C----------------------------------------------------------------------- +C Up to MAXCOR corrector iterations are taken. A convergence test is +C made on the R.M.S. norm of each correction, weighted by the error +C weight vector EWT. The sum of the corrections is accumulated in the +C vector ACOR(i). The YH array is not altered in the corrector loop. +C----------------------------------------------------------------------- + 220 M = 0 + DO 230 I = 1,N + 230 Y(I) = YH(I,1) + CALL F (NEQ, TN, Y, SAVF) + NFE = NFE + 1 + IF (IPUP .LE. 0) GO TO 250 +C----------------------------------------------------------------------- +C If indicated, the matrix P = I - h*el(1)*J is reevaluated and +C preprocessed before starting the corrector iteration. IPUP is set +C to 0 as an indicator that this has been done. +C----------------------------------------------------------------------- + CALL PJAC (NEQ, Y, YH, NYH, EWT, ACOR, SAVF, WM, IWM, F, JAC) + IPUP = 0 + RC = 1.0D0 + NSLP = NST + CRATE = 0.7D0 + IF (IERPJ .NE. 0) GO TO 430 + 250 DO 260 I = 1,N + 260 ACOR(I) = 0.0D0 + 270 IF (MITER .NE. 0) GO TO 350 +C----------------------------------------------------------------------- +C In the case of functional iteration, update Y directly from +C the result of the last function evaluation. +C----------------------------------------------------------------------- + DO 290 I = 1,N + SAVF(I) = H*SAVF(I) - YH(I,2) + 290 Y(I) = SAVF(I) - ACOR(I) + DEL = DVNORM (N, Y, EWT) + DO 300 I = 1,N + Y(I) = YH(I,1) + EL(1)*SAVF(I) + 300 ACOR(I) = SAVF(I) + GO TO 400 +C----------------------------------------------------------------------- +C In the case of the chord method, compute the corrector error, +C and solve the linear system with that as right-hand side and +C P as coefficient matrix. +C----------------------------------------------------------------------- + 350 DO 360 I = 1,N + 360 Y(I) = H*SAVF(I) - (YH(I,2) + ACOR(I)) + CALL SLVS (WM, IWM, Y, SAVF) + IF (IERSL .LT. 0) GO TO 430 + IF (IERSL .GT. 0) GO TO 410 + DEL = DVNORM (N, Y, EWT) + DO 380 I = 1,N + ACOR(I) = ACOR(I) + Y(I) + 380 Y(I) = YH(I,1) + EL(1)*ACOR(I) +C----------------------------------------------------------------------- +C Test for convergence. If M.gt.0, an estimate of the convergence +C rate constant is stored in CRATE, and this is used in the test. +C----------------------------------------------------------------------- + 400 IF (M .NE. 0) CRATE = MAX(0.2D0*CRATE,DEL/DELP) + DCON = DEL*MIN(1.0D0,1.5D0*CRATE)/(TESCO(2,NQ)*CONIT) + IF (DCON .LE. 1.0D0) GO TO 450 + M = M + 1 + IF (M .EQ. MAXCOR) GO TO 410 + IF (M .GE. 2 .AND. DEL .GT. 2.0D0*DELP) GO TO 410 + DELP = DEL + CALL F (NEQ, TN, Y, SAVF) + NFE = NFE + 1 + GO TO 270 +C----------------------------------------------------------------------- +C The corrector iteration failed to converge. +C If MITER .ne. 0 and the Jacobian is out of date, PJAC is called for +C the next try. Otherwise the YH array is retracted to its values +C before prediction, and H is reduced, if possible. If H cannot be +C reduced or MXNCF failures have occurred, exit with KFLAG = -2. +C----------------------------------------------------------------------- + 410 IF (MITER .EQ. 0 .OR. JCUR .EQ. 1) GO TO 430 + ICF = 1 + IPUP = MITER + GO TO 220 + 430 ICF = 2 + NCF = NCF + 1 + RMAX = 2.0D0 + TN = TOLD + I1 = NQNYH + 1 + DO 445 JB = 1,NQ + I1 = I1 - NYH +Cdir$ ivdep + DO 440 I = I1,NQNYH + 440 YH1(I) = YH1(I) - YH1(I+NYH) + 445 CONTINUE + IF (IERPJ .LT. 0 .OR. IERSL .LT. 0) GO TO 680 + IF (ABS(H) .LE. HMIN*1.00001D0) GO TO 670 + IF (NCF .EQ. MXNCF) GO TO 670 + RH = 0.25D0 + IPUP = MITER + IREDO = 1 + GO TO 170 +C----------------------------------------------------------------------- +C The corrector has converged. JCUR is set to 0 +C to signal that the Jacobian involved may need updating later. +C The local error test is made and control passes to statement 500 +C if it fails. +C----------------------------------------------------------------------- + 450 JCUR = 0 + IF (M .EQ. 0) DSM = DEL/TESCO(2,NQ) + IF (M .GT. 0) DSM = DVNORM (N, ACOR, EWT)/TESCO(2,NQ) + IF (DSM .GT. 1.0D0) GO TO 500 +C----------------------------------------------------------------------- +C After a successful step, update the YH array. +C Consider changing H if IALTH = 1. Otherwise decrease IALTH by 1. +C If IALTH is then 1 and NQ .lt. MAXORD, then ACOR is saved for +C use in a possible order increase on the next step. +C If a change in H is considered, an increase or decrease in order +C by one is considered also. A change in H is made only if it is by a +C factor of at least 1.1. If not, IALTH is set to 3 to prevent +C testing for that many steps. +C----------------------------------------------------------------------- + KFLAG = 0 + IREDO = 0 + NST = NST + 1 + HU = H + NQU = NQ + DO 470 J = 1,L + DO 470 I = 1,N + 470 YH(I,J) = YH(I,J) + EL(J)*ACOR(I) + IALTH = IALTH - 1 + IF (IALTH .EQ. 0) GO TO 520 + IF (IALTH .GT. 1) GO TO 700 + IF (L .EQ. LMAX) GO TO 700 + DO 490 I = 1,N + 490 YH(I,LMAX) = ACOR(I) + GO TO 700 +C----------------------------------------------------------------------- +C The error test failed. KFLAG keeps track of multiple failures. +C Restore TN and the YH array to their previous values, and prepare +C to try the step again. Compute the optimum step size for this or +C one lower order. After 2 or more failures, H is forced to decrease +C by a factor of 0.2 or less. +C----------------------------------------------------------------------- + 500 KFLAG = KFLAG - 1 + TN = TOLD + I1 = NQNYH + 1 + DO 515 JB = 1,NQ + I1 = I1 - NYH +Cdir$ ivdep + DO 510 I = I1,NQNYH + 510 YH1(I) = YH1(I) - YH1(I+NYH) + 515 CONTINUE + RMAX = 2.0D0 + IF (ABS(H) .LE. HMIN*1.00001D0) GO TO 660 + IF (KFLAG .LE. -3) GO TO 640 + IREDO = 2 + RHUP = 0.0D0 + GO TO 540 +C----------------------------------------------------------------------- +C Regardless of the success or failure of the step, factors +C RHDN, RHSM, and RHUP are computed, by which H could be multiplied +C at order NQ - 1, order NQ, or order NQ + 1, respectively. +C In the case of failure, RHUP = 0.0 to avoid an order increase. +C The largest of these is determined and the new order chosen +C accordingly. If the order is to be increased, we compute one +C additional scaled derivative. +C----------------------------------------------------------------------- + 520 RHUP = 0.0D0 + IF (L .EQ. LMAX) GO TO 540 + DO 530 I = 1,N + 530 SAVF(I) = ACOR(I) - YH(I,LMAX) + DUP = DVNORM (N, SAVF, EWT)/TESCO(3,NQ) + EXUP = 1.0D0/(L+1) + RHUP = 1.0D0/(1.4D0*DUP**EXUP + 0.0000014D0) + 540 EXSM = 1.0D0/L + RHSM = 1.0D0/(1.2D0*DSM**EXSM + 0.0000012D0) + RHDN = 0.0D0 + IF (NQ .EQ. 1) GO TO 560 + DDN = DVNORM (N, YH(1,L), EWT)/TESCO(1,NQ) + EXDN = 1.0D0/NQ + RHDN = 1.0D0/(1.3D0*DDN**EXDN + 0.0000013D0) + 560 IF (RHSM .GE. RHUP) GO TO 570 + IF (RHUP .GT. RHDN) GO TO 590 + GO TO 580 + 570 IF (RHSM .LT. RHDN) GO TO 580 + NEWQ = NQ + RH = RHSM + GO TO 620 + 580 NEWQ = NQ - 1 + RH = RHDN + IF (KFLAG .LT. 0 .AND. RH .GT. 1.0D0) RH = 1.0D0 + GO TO 620 + 590 NEWQ = L + RH = RHUP + IF (RH .LT. 1.1D0) GO TO 610 + R = EL(L)/L + DO 600 I = 1,N + 600 YH(I,NEWQ+1) = ACOR(I)*R + GO TO 630 + 610 IALTH = 3 + GO TO 700 + 620 IF ((KFLAG .EQ. 0) .AND. (RH .LT. 1.1D0)) GO TO 610 + IF (KFLAG .LE. -2) RH = MIN(RH,0.2D0) +C----------------------------------------------------------------------- +C If there is a change of order, reset NQ, l, and the coefficients. +C In any case H is reset according to RH and the YH array is rescaled. +C Then exit from 690 if the step was OK, or redo the step otherwise. +C----------------------------------------------------------------------- + IF (NEWQ .EQ. NQ) GO TO 170 + 630 NQ = NEWQ + L = NQ + 1 + IRET = 2 + GO TO 150 +C----------------------------------------------------------------------- +C Control reaches this section if 3 or more failures have occured. +C If 10 failures have occurred, exit with KFLAG = -1. +C It is assumed that the derivatives that have accumulated in the +C YH array have errors of the wrong order. Hence the first +C derivative is recomputed, and the order is set to 1. Then +C H is reduced by a factor of 10, and the step is retried, +C until it succeeds or H reaches HMIN. +C----------------------------------------------------------------------- + 640 IF (KFLAG .EQ. -10) GO TO 660 + RH = 0.1D0 + RH = MAX(HMIN/ABS(H),RH) + H = H*RH + DO 645 I = 1,N + 645 Y(I) = YH(I,1) + CALL F (NEQ, TN, Y, SAVF) + NFE = NFE + 1 + DO 650 I = 1,N + 650 YH(I,2) = H*SAVF(I) + IPUP = MITER + IALTH = 5 + IF (NQ .EQ. 1) GO TO 200 + NQ = 1 + L = 2 + IRET = 3 + GO TO 150 +C----------------------------------------------------------------------- +C All returns are made through this section. H is saved in HOLD +C to allow the caller to change H on the next step. +C----------------------------------------------------------------------- + 660 KFLAG = -1 + GO TO 720 + 670 KFLAG = -2 + GO TO 720 + 680 KFLAG = -3 + GO TO 720 + 690 RMAX = 10.0D0 + 700 R = 1.0D0/TESCO(2,NQU) + DO 710 I = 1,N + 710 ACOR(I) = ACOR(I)*R + 720 HOLD = H + JSTART = 1 + RETURN +C----------------------- END OF SUBROUTINE DSTODE ---------------------- + END +*DECK DEWSET + SUBROUTINE DEWSET (N, ITOL, RTOL, ATOL, YCUR, EWT) +C***BEGIN PROLOGUE DEWSET +C***SUBSIDIARY +C***PURPOSE Set error weight vector. +C***TYPE DOUBLE PRECISION (SEWSET-S, DEWSET-D) +C***AUTHOR Hindmarsh, Alan C., (LLNL) +C***DESCRIPTION +C +C This subroutine sets the error weight vector EWT according to +C EWT(i) = RTOL(i)*ABS(YCUR(i)) + ATOL(i), i = 1,...,N, +C with the subscript on RTOL and/or ATOL possibly replaced by 1 above, +C depending on the value of ITOL. +C +C***SEE ALSO DLSODE +C***ROUTINES CALLED (NONE) +C***REVISION HISTORY (YYMMDD) +C 791129 DATE WRITTEN +C 890501 Modified prologue to SLATEC/LDOC format. (FNF) +C 890503 Minor cosmetic changes. (FNF) +C 930809 Renamed to allow single/double precision versions. (ACH) +C***END PROLOGUE DEWSET +C**End + INTEGER N, ITOL + INTEGER I + DOUBLE PRECISION RTOL, ATOL, YCUR, EWT + DIMENSION RTOL(*), ATOL(*), YCUR(N), EWT(N) +C +C***FIRST EXECUTABLE STATEMENT DEWSET + GO TO (10, 20, 30, 40), ITOL + 10 CONTINUE + DO 15 I = 1,N + 15 EWT(I) = RTOL(1)*ABS(YCUR(I)) + ATOL(1) + RETURN + 20 CONTINUE + DO 25 I = 1,N + 25 EWT(I) = RTOL(1)*ABS(YCUR(I)) + ATOL(I) + RETURN + 30 CONTINUE + DO 35 I = 1,N + 35 EWT(I) = RTOL(I)*ABS(YCUR(I)) + ATOL(1) + RETURN + 40 CONTINUE + DO 45 I = 1,N + 45 EWT(I) = RTOL(I)*ABS(YCUR(I)) + ATOL(I) + RETURN +C----------------------- END OF SUBROUTINE DEWSET ---------------------- + END +*DECK DVNORM + DOUBLE PRECISION FUNCTION DVNORM (N, V, W) +C***BEGIN PROLOGUE DVNORM +C***SUBSIDIARY +C***PURPOSE Weighted root-mean-square vector norm. +C***TYPE DOUBLE PRECISION (SVNORM-S, DVNORM-D) +C***AUTHOR Hindmarsh, Alan C., (LLNL) +C***DESCRIPTION +C +C This function routine computes the weighted root-mean-square norm +C of the vector of length N contained in the array V, with weights +C contained in the array W of length N: +C DVNORM = SQRT( (1/N) * SUM( V(i)*W(i) )**2 ) +C +C***SEE ALSO DLSODE +C***ROUTINES CALLED (NONE) +C***REVISION HISTORY (YYMMDD) +C 791129 DATE WRITTEN +C 890501 Modified prologue to SLATEC/LDOC format. (FNF) +C 890503 Minor cosmetic changes. (FNF) +C 930809 Renamed to allow single/double precision versions. (ACH) +C***END PROLOGUE DVNORM +C**End + INTEGER N, I + DOUBLE PRECISION V, W, SUM + DIMENSION V(N), W(N) +C +C***FIRST EXECUTABLE STATEMENT DVNORM + SUM = 0.0D0 + DO 10 I = 1,N + 10 SUM = SUM + (V(I)*W(I))**2 + DVNORM = SQRT(SUM/N) + RETURN +C----------------------- END OF FUNCTION DVNORM ------------------------ + END +*DECK DIPREP + SUBROUTINE DIPREP (NEQ, Y, RWORK, IA, JA, IPFLAG, F, JAC) + EXTERNAL F, JAC + INTEGER NEQ, IA, JA, IPFLAG + DOUBLE PRECISION Y, RWORK + DIMENSION NEQ(*), Y(*), RWORK(*), IA(*), JA(*) + INTEGER IOWND, IOWNS, + 1 ICF, IERPJ, IERSL, JCUR, JSTART, KFLAG, L, + 2 LYH, LEWT, LACOR, LSAVF, LWM, LIWM, METH, MITER, + 3 MAXORD, MAXCOR, MSBP, MXNCF, N, NQ, NST, NFE, NJE, NQU + INTEGER IPLOST, IESP, ISTATC, IYS, IBA, IBIAN, IBJAN, IBJGP, + 1 IPIAN, IPJAN, IPJGP, IPIGP, IPR, IPC, IPIC, IPISP, IPRSP, IPA, + 2 LENYH, LENYHM, LENWK, LREQ, LRAT, LREST, LWMIN, MOSS, MSBJ, + 3 NSLJ, NGP, NLU, NNZ, NSP, NZL, NZU + DOUBLE PRECISION ROWNS, + 1 CCMAX, EL0, H, HMIN, HMXI, HU, RC, TN, UROUND + DOUBLE PRECISION RLSS + COMMON /DLS001/ ROWNS(209), + 1 CCMAX, EL0, H, HMIN, HMXI, HU, RC, TN, UROUND, + 2 IOWND(6), IOWNS(6), + 3 ICF, IERPJ, IERSL, JCUR, JSTART, KFLAG, L, + 4 LYH, LEWT, LACOR, LSAVF, LWM, LIWM, METH, MITER, + 5 MAXORD, MAXCOR, MSBP, MXNCF, N, NQ, NST, NFE, NJE, NQU + COMMON /DLSS01/ RLSS(6), + 1 IPLOST, IESP, ISTATC, IYS, IBA, IBIAN, IBJAN, IBJGP, + 2 IPIAN, IPJAN, IPJGP, IPIGP, IPR, IPC, IPIC, IPISP, IPRSP, IPA, + 3 LENYH, LENYHM, LENWK, LREQ, LRAT, LREST, LWMIN, MOSS, MSBJ, + 4 NSLJ, NGP, NLU, NNZ, NSP, NZL, NZU + INTEGER I, IMAX, LEWTN, LYHD, LYHN +C----------------------------------------------------------------------- +C This routine serves as an interface between the driver and +C Subroutine DPREP. It is called only if MITER is 1 or 2. +C Tasks performed here are: +C * call DPREP, +C * reset the required WM segment length LENWK, +C * move YH back to its final location (following WM in RWORK), +C * reset pointers for YH, SAVF, EWT, and ACOR, and +C * move EWT to its new position if ISTATE = 1. +C IPFLAG is an output error indication flag. IPFLAG = 0 if there was +C no trouble, and IPFLAG is the value of the DPREP error flag IPPER +C if there was trouble in Subroutine DPREP. +C----------------------------------------------------------------------- + IPFLAG = 0 +C Call DPREP to do matrix preprocessing operations. -------------------- + CALL DPREP (NEQ, Y, RWORK(LYH), RWORK(LSAVF), RWORK(LEWT), + 1 RWORK(LACOR), IA, JA, RWORK(LWM), RWORK(LWM), IPFLAG, F, JAC) + LENWK = MAX(LREQ,LWMIN) + IF (IPFLAG .LT. 0) RETURN +C If DPREP was successful, move YH to end of required space for WM. ---- + LYHN = LWM + LENWK + IF (LYHN .GT. LYH) RETURN + LYHD = LYH - LYHN + IF (LYHD .EQ. 0) GO TO 20 + IMAX = LYHN - 1 + LENYHM + DO 10 I = LYHN,IMAX + 10 RWORK(I) = RWORK(I+LYHD) + LYH = LYHN +C Reset pointers for SAVF, EWT, and ACOR. ------------------------------ + 20 LSAVF = LYH + LENYH + LEWTN = LSAVF + N + LACOR = LEWTN + N + IF (ISTATC .EQ. 3) GO TO 40 +C If ISTATE = 1, move EWT (left) to its new position. ------------------ + IF (LEWTN .GT. LEWT) RETURN + DO 30 I = 1,N + 30 RWORK(I+LEWTN-1) = RWORK(I+LEWT-1) + 40 LEWT = LEWTN + RETURN +C----------------------- End of Subroutine DIPREP ---------------------- + END +*DECK DPREP + SUBROUTINE DPREP (NEQ, Y, YH, SAVF, EWT, FTEM, IA, JA, + 1 WK, IWK, IPPER, F, JAC) + EXTERNAL F,JAC + INTEGER NEQ, IA, JA, IWK, IPPER + DOUBLE PRECISION Y, YH, SAVF, EWT, FTEM, WK + DIMENSION NEQ(*), Y(*), YH(*), SAVF(*), EWT(*), FTEM(*), + 1 IA(*), JA(*), WK(*), IWK(*) + INTEGER IOWND, IOWNS, + 1 ICF, IERPJ, IERSL, JCUR, JSTART, KFLAG, L, + 2 LYH, LEWT, LACOR, LSAVF, LWM, LIWM, METH, MITER, + 3 MAXORD, MAXCOR, MSBP, MXNCF, N, NQ, NST, NFE, NJE, NQU + INTEGER IPLOST, IESP, ISTATC, IYS, IBA, IBIAN, IBJAN, IBJGP, + 1 IPIAN, IPJAN, IPJGP, IPIGP, IPR, IPC, IPIC, IPISP, IPRSP, IPA, + 2 LENYH, LENYHM, LENWK, LREQ, LRAT, LREST, LWMIN, MOSS, MSBJ, + 3 NSLJ, NGP, NLU, NNZ, NSP, NZL, NZU + DOUBLE PRECISION ROWNS, + 1 CCMAX, EL0, H, HMIN, HMXI, HU, RC, TN, UROUND + DOUBLE PRECISION CON0, CONMIN, CCMXJ, PSMALL, RBIG, SETH + COMMON /DLS001/ ROWNS(209), + 1 CCMAX, EL0, H, HMIN, HMXI, HU, RC, TN, UROUND, + 2 IOWND(6), IOWNS(6), + 3 ICF, IERPJ, IERSL, JCUR, JSTART, KFLAG, L, + 4 LYH, LEWT, LACOR, LSAVF, LWM, LIWM, METH, MITER, + 5 MAXORD, MAXCOR, MSBP, MXNCF, N, NQ, NST, NFE, NJE, NQU + COMMON /DLSS01/ CON0, CONMIN, CCMXJ, PSMALL, RBIG, SETH, + 1 IPLOST, IESP, ISTATC, IYS, IBA, IBIAN, IBJAN, IBJGP, + 2 IPIAN, IPJAN, IPJGP, IPIGP, IPR, IPC, IPIC, IPISP, IPRSP, IPA, + 3 LENYH, LENYHM, LENWK, LREQ, LRAT, LREST, LWMIN, MOSS, MSBJ, + 4 NSLJ, NGP, NLU, NNZ, NSP, NZL, NZU + INTEGER I, IBR, IER, IPIL, IPIU, IPTT1, IPTT2, J, JFOUND, K, + 1 KNEW, KMAX, KMIN, LDIF, LENIGP, LIWK, MAXG, NP1, NZSUT + DOUBLE PRECISION DQ, DYJ, ERWT, FAC, YJ +C----------------------------------------------------------------------- +C This routine performs preprocessing related to the sparse linear +C systems that must be solved if MITER = 1 or 2. +C The operations that are performed here are: +C * compute sparseness structure of Jacobian according to MOSS, +C * compute grouping of column indices (MITER = 2), +C * compute a new ordering of rows and columns of the matrix, +C * reorder JA corresponding to the new ordering, +C * perform a symbolic LU factorization of the matrix, and +C * set pointers for segments of the IWK/WK array. +C In addition to variables described previously, DPREP uses the +C following for communication: +C YH = the history array. Only the first column, containing the +C current Y vector, is used. Used only if MOSS .ne. 0. +C SAVF = a work array of length NEQ, used only if MOSS .ne. 0. +C EWT = array of length NEQ containing (inverted) error weights. +C Used only if MOSS = 2 or if ISTATE = MOSS = 1. +C FTEM = a work array of length NEQ, identical to ACOR in the driver, +C used only if MOSS = 2. +C WK = a real work array of length LENWK, identical to WM in +C the driver. +C IWK = integer work array, assumed to occupy the same space as WK. +C LENWK = the length of the work arrays WK and IWK. +C ISTATC = a copy of the driver input argument ISTATE (= 1 on the +C first call, = 3 on a continuation call). +C IYS = flag value from ODRV or CDRV. +C IPPER = output error flag with the following values and meanings: +C 0 no error. +C -1 insufficient storage for internal structure pointers. +C -2 insufficient storage for JGROUP. +C -3 insufficient storage for ODRV. +C -4 other error flag from ODRV (should never occur). +C -5 insufficient storage for CDRV. +C -6 other error flag from CDRV. +C----------------------------------------------------------------------- + IBIAN = LRAT*2 + IPIAN = IBIAN + 1 + NP1 = N + 1 + IPJAN = IPIAN + NP1 + IBJAN = IPJAN - 1 + LIWK = LENWK*LRAT + IF (IPJAN+N-1 .GT. LIWK) GO TO 210 + IF (MOSS .EQ. 0) GO TO 30 +C + IF (ISTATC .EQ. 3) GO TO 20 +C ISTATE = 1 and MOSS .ne. 0. Perturb Y for structure determination. -- + DO 10 I = 1,N + ERWT = 1.0D0/EWT(I) + FAC = 1.0D0 + 1.0D0/(I + 1.0D0) + Y(I) = Y(I) + FAC*SIGN(ERWT,Y(I)) + 10 CONTINUE + GO TO (70, 100), MOSS +C + 20 CONTINUE +C ISTATE = 3 and MOSS .ne. 0. Load Y from YH(*,1). -------------------- + DO 25 I = 1,N + 25 Y(I) = YH(I) + GO TO (70, 100), MOSS +C +C MOSS = 0. Process user's IA,JA. Add diagonal entries if necessary. - + 30 KNEW = IPJAN + KMIN = IA(1) + IWK(IPIAN) = 1 + DO 60 J = 1,N + JFOUND = 0 + KMAX = IA(J+1) - 1 + IF (KMIN .GT. KMAX) GO TO 45 + DO 40 K = KMIN,KMAX + I = JA(K) + IF (I .EQ. J) JFOUND = 1 + IF (KNEW .GT. LIWK) GO TO 210 + IWK(KNEW) = I + KNEW = KNEW + 1 + 40 CONTINUE + IF (JFOUND .EQ. 1) GO TO 50 + 45 IF (KNEW .GT. LIWK) GO TO 210 + IWK(KNEW) = J + KNEW = KNEW + 1 + 50 IWK(IPIAN+J) = KNEW + 1 - IPJAN + KMIN = KMAX + 1 + 60 CONTINUE + GO TO 140 +C +C MOSS = 1. Compute structure from user-supplied Jacobian routine JAC. + 70 CONTINUE +C A dummy call to F allows user to create temporaries for use in JAC. -- + CALL F (NEQ, TN, Y, SAVF) + K = IPJAN + IWK(IPIAN) = 1 + DO 90 J = 1,N + IF (K .GT. LIWK) GO TO 210 + IWK(K) = J + K = K + 1 + DO 75 I = 1,N + 75 SAVF(I) = 0.0D0 + CALL JAC (NEQ, TN, Y, J, IWK(IPIAN), IWK(IPJAN), SAVF) + DO 80 I = 1,N + IF (ABS(SAVF(I)) .LE. SETH) GO TO 80 + IF (I .EQ. J) GO TO 80 + IF (K .GT. LIWK) GO TO 210 + IWK(K) = I + K = K + 1 + 80 CONTINUE + IWK(IPIAN+J) = K + 1 - IPJAN + 90 CONTINUE + GO TO 140 +C +C MOSS = 2. Compute structure from results of N + 1 calls to F. ------- + 100 K = IPJAN + IWK(IPIAN) = 1 + CALL F (NEQ, TN, Y, SAVF) + DO 120 J = 1,N + IF (K .GT. LIWK) GO TO 210 + IWK(K) = J + K = K + 1 + YJ = Y(J) + ERWT = 1.0D0/EWT(J) + DYJ = SIGN(ERWT,YJ) + Y(J) = YJ + DYJ + CALL F (NEQ, TN, Y, FTEM) + Y(J) = YJ + DO 110 I = 1,N + DQ = (FTEM(I) - SAVF(I))/DYJ + IF (ABS(DQ) .LE. SETH) GO TO 110 + IF (I .EQ. J) GO TO 110 + IF (K .GT. LIWK) GO TO 210 + IWK(K) = I + K = K + 1 + 110 CONTINUE + IWK(IPIAN+J) = K + 1 - IPJAN + 120 CONTINUE +C + 140 CONTINUE + IF (MOSS .EQ. 0 .OR. ISTATC .NE. 1) GO TO 150 +C If ISTATE = 1 and MOSS .ne. 0, restore Y from YH. -------------------- + DO 145 I = 1,N + 145 Y(I) = YH(I) + 150 NNZ = IWK(IPIAN+N) - 1 + LENIGP = 0 + IPIGP = IPJAN + NNZ + IF (MITER .NE. 2) GO TO 160 +C +C Compute grouping of column indices (MITER = 2). ---------------------- + MAXG = NP1 + IPJGP = IPJAN + NNZ + IBJGP = IPJGP - 1 + IPIGP = IPJGP + N + IPTT1 = IPIGP + NP1 + IPTT2 = IPTT1 + N + LREQ = IPTT2 + N - 1 + IF (LREQ .GT. LIWK) GO TO 220 + CALL JGROUP (N, IWK(IPIAN), IWK(IPJAN), MAXG, NGP, IWK(IPIGP), + 1 IWK(IPJGP), IWK(IPTT1), IWK(IPTT2), IER) + IF (IER .NE. 0) GO TO 220 + LENIGP = NGP + 1 +C +C Compute new ordering of rows/columns of Jacobian. -------------------- + 160 IPR = IPIGP + LENIGP + IPC = IPR + IPIC = IPC + N + IPISP = IPIC + N + IPRSP = (IPISP - 2)/LRAT + 2 + IESP = LENWK + 1 - IPRSP + IF (IESP .LT. 0) GO TO 230 + IBR = IPR - 1 + DO 170 I = 1,N + 170 IWK(IBR+I) = I + NSP = LIWK + 1 - IPISP + CALL ODRV (N, IWK(IPIAN), IWK(IPJAN), WK, IWK(IPR), IWK(IPIC), + 1 NSP, IWK(IPISP), 1, IYS) + IF (IYS .EQ. 11*N+1) GO TO 240 + IF (IYS .NE. 0) GO TO 230 +C +C Reorder JAN and do symbolic LU factorization of matrix. -------------- + IPA = LENWK + 1 - NNZ + NSP = IPA - IPRSP + LREQ = MAX(12*N/LRAT, 6*N/LRAT+2*N+NNZ) + 3 + LREQ = LREQ + IPRSP - 1 + NNZ + IF (LREQ .GT. LENWK) GO TO 250 + IBA = IPA - 1 + DO 180 I = 1,NNZ + 180 WK(IBA+I) = 0.0D0 + IPISP = LRAT*(IPRSP - 1) + 1 + CALL CDRV (N,IWK(IPR),IWK(IPC),IWK(IPIC),IWK(IPIAN),IWK(IPJAN), + 1 WK(IPA),WK(IPA),WK(IPA),NSP,IWK(IPISP),WK(IPRSP),IESP,5,IYS) + LREQ = LENWK - IESP + IF (IYS .EQ. 10*N+1) GO TO 250 + IF (IYS .NE. 0) GO TO 260 + IPIL = IPISP + IPIU = IPIL + 2*N + 1 + NZU = IWK(IPIL+N) - IWK(IPIL) + NZL = IWK(IPIU+N) - IWK(IPIU) + IF (LRAT .GT. 1) GO TO 190 + CALL ADJLR (N, IWK(IPISP), LDIF) + LREQ = LREQ + LDIF + 190 CONTINUE + IF (LRAT .EQ. 2 .AND. NNZ .EQ. N) LREQ = LREQ + 1 + NSP = NSP + LREQ - LENWK + IPA = LREQ + 1 - NNZ + IBA = IPA - 1 + IPPER = 0 + RETURN +C + 210 IPPER = -1 + LREQ = 2 + (2*N + 1)/LRAT + LREQ = MAX(LENWK+1,LREQ) + RETURN +C + 220 IPPER = -2 + LREQ = (LREQ - 1)/LRAT + 1 + RETURN +C + 230 IPPER = -3 + CALL CNTNZU (N, IWK(IPIAN), IWK(IPJAN), NZSUT) + LREQ = LENWK - IESP + (3*N + 4*NZSUT - 1)/LRAT + 1 + RETURN +C + 240 IPPER = -4 + RETURN +C + 250 IPPER = -5 + RETURN +C + 260 IPPER = -6 + LREQ = LENWK + RETURN +C----------------------- End of Subroutine DPREP ----------------------- + END +*DECK JGROUP + SUBROUTINE JGROUP (N,IA,JA,MAXG,NGRP,IGP,JGP,INCL,JDONE,IER) + INTEGER N, IA, JA, MAXG, NGRP, IGP, JGP, INCL, JDONE, IER + DIMENSION IA(*), JA(*), IGP(*), JGP(*), INCL(*), JDONE(*) +C----------------------------------------------------------------------- +C This subroutine constructs groupings of the column indices of +C the Jacobian matrix, used in the numerical evaluation of the +C Jacobian by finite differences. +C +C Input: +C N = the order of the matrix. +C IA,JA = sparse structure descriptors of the matrix by rows. +C MAXG = length of available storage in the IGP array. +C +C Output: +C NGRP = number of groups. +C JGP = array of length N containing the column indices by groups. +C IGP = pointer array of length NGRP + 1 to the locations in JGP +C of the beginning of each group. +C IER = error indicator. IER = 0 if no error occurred, or 1 if +C MAXG was insufficient. +C +C INCL and JDONE are working arrays of length N. +C----------------------------------------------------------------------- + INTEGER I, J, K, KMIN, KMAX, NCOL, NG +C + IER = 0 + DO 10 J = 1,N + 10 JDONE(J) = 0 + NCOL = 1 + DO 60 NG = 1,MAXG + IGP(NG) = NCOL + DO 20 I = 1,N + 20 INCL(I) = 0 + DO 50 J = 1,N +C Reject column J if it is already in a group.-------------------------- + IF (JDONE(J) .EQ. 1) GO TO 50 + KMIN = IA(J) + KMAX = IA(J+1) - 1 + DO 30 K = KMIN,KMAX +C Reject column J if it overlaps any column already in this group.------ + I = JA(K) + IF (INCL(I) .EQ. 1) GO TO 50 + 30 CONTINUE +C Accept column J into group NG.---------------------------------------- + JGP(NCOL) = J + NCOL = NCOL + 1 + JDONE(J) = 1 + DO 40 K = KMIN,KMAX + I = JA(K) + 40 INCL(I) = 1 + 50 CONTINUE +C Stop if this group is empty (grouping is complete).------------------- + IF (NCOL .EQ. IGP(NG)) GO TO 70 + 60 CONTINUE +C Error return if not all columns were chosen (MAXG too small).--------- + IF (NCOL .LE. N) GO TO 80 + NG = MAXG + 70 NGRP = NG - 1 + RETURN + 80 IER = 1 + RETURN +C----------------------- End of Subroutine JGROUP ---------------------- + END +*DECK ADJLR + SUBROUTINE ADJLR (N, ISP, LDIF) + INTEGER N, ISP, LDIF + DIMENSION ISP(*) +C----------------------------------------------------------------------- +C This routine computes an adjustment, LDIF, to the required +C integer storage space in IWK (sparse matrix work space). +C It is called only if the word length ratio is LRAT = 1. +C This is to account for the possibility that the symbolic LU phase +C may require more storage than the numerical LU and solution phases. +C----------------------------------------------------------------------- + INTEGER IP, JLMAX, JUMAX, LNFC, LSFC, NZLU +C + IP = 2*N + 1 +C Get JLMAX = IJL(N) and JUMAX = IJU(N) (sizes of JL and JU). ---------- + JLMAX = ISP(IP) + JUMAX = ISP(IP+IP) +C NZLU = (size of L) + (size of U) = (IL(N+1)-IL(1)) + (IU(N+1)-IU(1)). + NZLU = ISP(N+1) - ISP(1) + ISP(IP+N+1) - ISP(IP+1) + LSFC = 12*N + 3 + 2*MAX(JLMAX,JUMAX) + LNFC = 9*N + 2 + JLMAX + JUMAX + NZLU + LDIF = MAX(0, LSFC - LNFC) + RETURN +C----------------------- End of Subroutine ADJLR ----------------------- + END +*DECK CNTNZU + SUBROUTINE CNTNZU (N, IA, JA, NZSUT) + INTEGER N, IA, JA, NZSUT + DIMENSION IA(*), JA(*) +C----------------------------------------------------------------------- +C This routine counts the number of nonzero elements in the strict +C upper triangle of the matrix M + M(transpose), where the sparsity +C structure of M is given by pointer arrays IA and JA. +C This is needed to compute the storage requirements for the +C sparse matrix reordering operation in ODRV. +C----------------------------------------------------------------------- + INTEGER II, JJ, J, JMIN, JMAX, K, KMIN, KMAX, NUM +C + NUM = 0 + DO 50 II = 1,N + JMIN = IA(II) + JMAX = IA(II+1) - 1 + IF (JMIN .GT. JMAX) GO TO 50 + DO 40 J = JMIN,JMAX + IF (JA(J) - II) 10, 40, 30 + 10 JJ =JA(J) + KMIN = IA(JJ) + KMAX = IA(JJ+1) - 1 + IF (KMIN .GT. KMAX) GO TO 30 + DO 20 K = KMIN,KMAX + IF (JA(K) .EQ. II) GO TO 40 + 20 CONTINUE + 30 NUM = NUM + 1 + 40 CONTINUE + 50 CONTINUE + NZSUT = NUM + RETURN +C----------------------- End of Subroutine CNTNZU ---------------------- + END +*DECK DPRJS + SUBROUTINE DPRJS (NEQ,Y,YH,NYH,EWT,FTEM,SAVF,WK,IWK,F,JAC) + EXTERNAL F,JAC + INTEGER NEQ, NYH, IWK + DOUBLE PRECISION Y, YH, EWT, FTEM, SAVF, WK + DIMENSION NEQ(*), Y(*), YH(NYH,*), EWT(*), FTEM(*), SAVF(*), + 1 WK(*), IWK(*) + INTEGER IOWND, IOWNS, + 1 ICF, IERPJ, IERSL, JCUR, JSTART, KFLAG, L, + 2 LYH, LEWT, LACOR, LSAVF, LWM, LIWM, METH, MITER, + 3 MAXORD, MAXCOR, MSBP, MXNCF, N, NQ, NST, NFE, NJE, NQU + INTEGER IPLOST, IESP, ISTATC, IYS, IBA, IBIAN, IBJAN, IBJGP, + 1 IPIAN, IPJAN, IPJGP, IPIGP, IPR, IPC, IPIC, IPISP, IPRSP, IPA, + 2 LENYH, LENYHM, LENWK, LREQ, LRAT, LREST, LWMIN, MOSS, MSBJ, + 3 NSLJ, NGP, NLU, NNZ, NSP, NZL, NZU + DOUBLE PRECISION ROWNS, + 1 CCMAX, EL0, H, HMIN, HMXI, HU, RC, TN, UROUND + DOUBLE PRECISION CON0, CONMIN, CCMXJ, PSMALL, RBIG, SETH + COMMON /DLS001/ ROWNS(209), + 1 CCMAX, EL0, H, HMIN, HMXI, HU, RC, TN, UROUND, + 2 IOWND(6), IOWNS(6), + 3 ICF, IERPJ, IERSL, JCUR, JSTART, KFLAG, L, + 4 LYH, LEWT, LACOR, LSAVF, LWM, LIWM, METH, MITER, + 5 MAXORD, MAXCOR, MSBP, MXNCF, N, NQ, NST, NFE, NJE, NQU + COMMON /DLSS01/ CON0, CONMIN, CCMXJ, PSMALL, RBIG, SETH, + 1 IPLOST, IESP, ISTATC, IYS, IBA, IBIAN, IBJAN, IBJGP, + 2 IPIAN, IPJAN, IPJGP, IPIGP, IPR, IPC, IPIC, IPISP, IPRSP, IPA, + 3 LENYH, LENYHM, LENWK, LREQ, LRAT, LREST, LWMIN, MOSS, MSBJ, + 4 NSLJ, NGP, NLU, NNZ, NSP, NZL, NZU + INTEGER I, IMUL, J, JJ, JOK, JMAX, JMIN, K, KMAX, KMIN, NG + DOUBLE PRECISION CON, DI, FAC, HL0, PIJ, R, R0, RCON, RCONT, + 1 SRUR, DVNORM +C----------------------------------------------------------------------- +C DPRJS is called to compute and process the matrix +C P = I - H*EL(1)*J , where J is an approximation to the Jacobian. +C J is computed by columns, either by the user-supplied routine JAC +C if MITER = 1, or by finite differencing if MITER = 2. +C if MITER = 3, a diagonal approximation to J is used. +C if MITER = 1 or 2, and if the existing value of the Jacobian +C (as contained in P) is considered acceptable, then a new value of +C P is reconstructed from the old value. In any case, when MITER +C is 1 or 2, the P matrix is subjected to LU decomposition in CDRV. +C P and its LU decomposition are stored (separately) in WK. +C +C In addition to variables described previously, communication +C with DPRJS uses the following: +C Y = array containing predicted values on entry. +C FTEM = work array of length N (ACOR in DSTODE). +C SAVF = array containing f evaluated at predicted y. +C WK = real work space for matrices. On output it contains the +C inverse diagonal matrix if MITER = 3, and P and its sparse +C LU decomposition if MITER is 1 or 2. +C Storage of matrix elements starts at WK(3). +C WK also contains the following matrix-related data: +C WK(1) = SQRT(UROUND), used in numerical Jacobian increments. +C WK(2) = H*EL0, saved for later use if MITER = 3. +C IWK = integer work space for matrix-related data, assumed to +C be equivalenced to WK. In addition, WK(IPRSP) and IWK(IPISP) +C are assumed to have identical locations. +C EL0 = EL(1) (input). +C IERPJ = output error flag (in Common). +C = 0 if no error. +C = 1 if zero pivot found in CDRV. +C = 2 if a singular matrix arose with MITER = 3. +C = -1 if insufficient storage for CDRV (should not occur here). +C = -2 if other error found in CDRV (should not occur here). +C JCUR = output flag showing status of (approximate) Jacobian matrix: +C = 1 to indicate that the Jacobian is now current, or +C = 0 to indicate that a saved value was used. +C This routine also uses other variables in Common. +C----------------------------------------------------------------------- + HL0 = H*EL0 + CON = -HL0 + IF (MITER .EQ. 3) GO TO 300 +C See whether J should be reevaluated (JOK = 0) or not (JOK = 1). ------ + JOK = 1 + IF (NST .EQ. 0 .OR. NST .GE. NSLJ+MSBJ) JOK = 0 + IF (ICF .EQ. 1 .AND. ABS(RC - 1.0D0) .LT. CCMXJ) JOK = 0 + IF (ICF .EQ. 2) JOK = 0 + IF (JOK .EQ. 1) GO TO 250 +C +C MITER = 1 or 2, and the Jacobian is to be reevaluated. --------------- + 20 JCUR = 1 + NJE = NJE + 1 + NSLJ = NST + IPLOST = 0 + CONMIN = ABS(CON) + GO TO (100, 200), MITER +C +C If MITER = 1, call JAC, multiply by scalar, and add identity. -------- + 100 CONTINUE + KMIN = IWK(IPIAN) + DO 130 J = 1, N + KMAX = IWK(IPIAN+J) - 1 + DO 110 I = 1,N + 110 FTEM(I) = 0.0D0 + CALL JAC (NEQ, TN, Y, J, IWK(IPIAN), IWK(IPJAN), FTEM) + DO 120 K = KMIN, KMAX + I = IWK(IBJAN+K) + WK(IBA+K) = FTEM(I)*CON + IF (I .EQ. J) WK(IBA+K) = WK(IBA+K) + 1.0D0 + 120 CONTINUE + KMIN = KMAX + 1 + 130 CONTINUE + GO TO 290 +C +C If MITER = 2, make NGP calls to F to approximate J and P. ------------ + 200 CONTINUE + FAC = DVNORM(N, SAVF, EWT) + R0 = 1000.0D0 * ABS(H) * UROUND * N * FAC + IF (R0 .EQ. 0.0D0) R0 = 1.0D0 + SRUR = WK(1) + JMIN = IWK(IPIGP) + DO 240 NG = 1,NGP + JMAX = IWK(IPIGP+NG) - 1 + DO 210 J = JMIN,JMAX + JJ = IWK(IBJGP+J) + R = MAX(SRUR*ABS(Y(JJ)),R0/EWT(JJ)) + 210 Y(JJ) = Y(JJ) + R + CALL F (NEQ, TN, Y, FTEM) + DO 230 J = JMIN,JMAX + JJ = IWK(IBJGP+J) + Y(JJ) = YH(JJ,1) + R = MAX(SRUR*ABS(Y(JJ)),R0/EWT(JJ)) + FAC = -HL0/R + KMIN =IWK(IBIAN+JJ) + KMAX =IWK(IBIAN+JJ+1) - 1 + DO 220 K = KMIN,KMAX + I = IWK(IBJAN+K) + WK(IBA+K) = (FTEM(I) - SAVF(I))*FAC + IF (I .EQ. JJ) WK(IBA+K) = WK(IBA+K) + 1.0D0 + 220 CONTINUE + 230 CONTINUE + JMIN = JMAX + 1 + 240 CONTINUE + NFE = NFE + NGP + GO TO 290 +C +C If JOK = 1, reconstruct new P from old P. ---------------------------- + 250 JCUR = 0 + RCON = CON/CON0 + RCONT = ABS(CON)/CONMIN + IF (RCONT .GT. RBIG .AND. IPLOST .EQ. 1) GO TO 20 + KMIN = IWK(IPIAN) + DO 275 J = 1,N + KMAX = IWK(IPIAN+J) - 1 + DO 270 K = KMIN,KMAX + I = IWK(IBJAN+K) + PIJ = WK(IBA+K) + IF (I .NE. J) GO TO 260 + PIJ = PIJ - 1.0D0 + IF (ABS(PIJ) .GE. PSMALL) GO TO 260 + IPLOST = 1 + CONMIN = MIN(ABS(CON0),CONMIN) + 260 PIJ = PIJ*RCON + IF (I .EQ. J) PIJ = PIJ + 1.0D0 + WK(IBA+K) = PIJ + 270 CONTINUE + KMIN = KMAX + 1 + 275 CONTINUE +C +C Do numerical factorization of P matrix. ------------------------------ + 290 NLU = NLU + 1 + CON0 = CON + IERPJ = 0 + DO 295 I = 1,N + 295 FTEM(I) = 0.0D0 + CALL CDRV (N,IWK(IPR),IWK(IPC),IWK(IPIC),IWK(IPIAN),IWK(IPJAN), + 1 WK(IPA),FTEM,FTEM,NSP,IWK(IPISP),WK(IPRSP),IESP,2,IYS) + IF (IYS .EQ. 0) RETURN + IMUL = (IYS - 1)/N + IERPJ = -2 + IF (IMUL .EQ. 8) IERPJ = 1 + IF (IMUL .EQ. 10) IERPJ = -1 + RETURN +C +C If MITER = 3, construct a diagonal approximation to J and P. --------- + 300 CONTINUE + JCUR = 1 + NJE = NJE + 1 + WK(2) = HL0 + IERPJ = 0 + R = EL0*0.1D0 + DO 310 I = 1,N + 310 Y(I) = Y(I) + R*(H*SAVF(I) - YH(I,2)) + CALL F (NEQ, TN, Y, WK(3)) + NFE = NFE + 1 + DO 320 I = 1,N + R0 = H*SAVF(I) - YH(I,2) + DI = 0.1D0*R0 - H*(WK(I+2) - SAVF(I)) + WK(I+2) = 1.0D0 + IF (ABS(R0) .LT. UROUND/EWT(I)) GO TO 320 + IF (ABS(DI) .EQ. 0.0D0) GO TO 330 + WK(I+2) = 0.1D0*R0/DI + 320 CONTINUE + RETURN + 330 IERPJ = 2 + RETURN +C----------------------- End of Subroutine DPRJS ----------------------- + END +*DECK DSOLSS + SUBROUTINE DSOLSS (WK, IWK, X, TEM) + INTEGER IWK + DOUBLE PRECISION WK, X, TEM + DIMENSION WK(*), IWK(*), X(*), TEM(*) + INTEGER IOWND, IOWNS, + 1 ICF, IERPJ, IERSL, JCUR, JSTART, KFLAG, L, + 2 LYH, LEWT, LACOR, LSAVF, LWM, LIWM, METH, MITER, + 3 MAXORD, MAXCOR, MSBP, MXNCF, N, NQ, NST, NFE, NJE, NQU + INTEGER IPLOST, IESP, ISTATC, IYS, IBA, IBIAN, IBJAN, IBJGP, + 1 IPIAN, IPJAN, IPJGP, IPIGP, IPR, IPC, IPIC, IPISP, IPRSP, IPA, + 2 LENYH, LENYHM, LENWK, LREQ, LRAT, LREST, LWMIN, MOSS, MSBJ, + 3 NSLJ, NGP, NLU, NNZ, NSP, NZL, NZU + DOUBLE PRECISION ROWNS, + 1 CCMAX, EL0, H, HMIN, HMXI, HU, RC, TN, UROUND + DOUBLE PRECISION RLSS + COMMON /DLS001/ ROWNS(209), + 1 CCMAX, EL0, H, HMIN, HMXI, HU, RC, TN, UROUND, + 2 IOWND(6), IOWNS(6), + 3 ICF, IERPJ, IERSL, JCUR, JSTART, KFLAG, L, + 4 LYH, LEWT, LACOR, LSAVF, LWM, LIWM, METH, MITER, + 5 MAXORD, MAXCOR, MSBP, MXNCF, N, NQ, NST, NFE, NJE, NQU + COMMON /DLSS01/ RLSS(6), + 1 IPLOST, IESP, ISTATC, IYS, IBA, IBIAN, IBJAN, IBJGP, + 2 IPIAN, IPJAN, IPJGP, IPIGP, IPR, IPC, IPIC, IPISP, IPRSP, IPA, + 3 LENYH, LENYHM, LENWK, LREQ, LRAT, LREST, LWMIN, MOSS, MSBJ, + 4 NSLJ, NGP, NLU, NNZ, NSP, NZL, NZU + INTEGER I + DOUBLE PRECISION DI, HL0, PHL0, R +C----------------------------------------------------------------------- +C This routine manages the solution of the linear system arising from +C a chord iteration. It is called if MITER .ne. 0. +C If MITER is 1 or 2, it calls CDRV to accomplish this. +C If MITER = 3 it updates the coefficient H*EL0 in the diagonal +C matrix, and then computes the solution. +C communication with DSOLSS uses the following variables: +C WK = real work space containing the inverse diagonal matrix if +C MITER = 3 and the LU decomposition of the matrix otherwise. +C Storage of matrix elements starts at WK(3). +C WK also contains the following matrix-related data: +C WK(1) = SQRT(UROUND) (not used here), +C WK(2) = HL0, the previous value of H*EL0, used if MITER = 3. +C IWK = integer work space for matrix-related data, assumed to +C be equivalenced to WK. In addition, WK(IPRSP) and IWK(IPISP) +C are assumed to have identical locations. +C X = the right-hand side vector on input, and the solution vector +C on output, of length N. +C TEM = vector of work space of length N, not used in this version. +C IERSL = output flag (in Common). +C IERSL = 0 if no trouble occurred. +C IERSL = -1 if CDRV returned an error flag (MITER = 1 or 2). +C This should never occur and is considered fatal. +C IERSL = 1 if a singular matrix arose with MITER = 3. +C This routine also uses other variables in Common. +C----------------------------------------------------------------------- + IERSL = 0 + GO TO (100, 100, 300), MITER + 100 CALL CDRV (N,IWK(IPR),IWK(IPC),IWK(IPIC),IWK(IPIAN),IWK(IPJAN), + 1 WK(IPA),X,X,NSP,IWK(IPISP),WK(IPRSP),IESP,4,IERSL) + IF (IERSL .NE. 0) IERSL = -1 + RETURN +C + 300 PHL0 = WK(2) + HL0 = H*EL0 + WK(2) = HL0 + IF (HL0 .EQ. PHL0) GO TO 330 + R = HL0/PHL0 + DO 320 I = 1,N + DI = 1.0D0 - R*(1.0D0 - 1.0D0/WK(I+2)) + IF (ABS(DI) .EQ. 0.0D0) GO TO 390 + 320 WK(I+2) = 1.0D0/DI + 330 DO 340 I = 1,N + 340 X(I) = WK(I+2)*X(I) + RETURN + 390 IERSL = 1 + RETURN +C +C----------------------- End of Subroutine DSOLSS ---------------------- + END +*DECK DSRCMS + SUBROUTINE DSRCMS (RSAV, ISAV, JOB) +C----------------------------------------------------------------------- +C This routine saves or restores (depending on JOB) the contents of +C the Common blocks DLS001, DLSS01, which are used +C internally by one or more ODEPACK solvers. +C +C RSAV = real array of length 224 or more. +C ISAV = integer array of length 71 or more. +C JOB = flag indicating to save or restore the Common blocks: +C JOB = 1 if Common is to be saved (written to RSAV/ISAV) +C JOB = 2 if Common is to be restored (read from RSAV/ISAV) +C A call with JOB = 2 presumes a prior call with JOB = 1. +C----------------------------------------------------------------------- + INTEGER ISAV, JOB + INTEGER ILS, ILSS + INTEGER I, LENILS, LENISS, LENRLS, LENRSS + DOUBLE PRECISION RSAV, RLS, RLSS + DIMENSION RSAV(*), ISAV(*) + SAVE LENRLS, LENILS, LENRSS, LENISS + COMMON /DLS001/ RLS(218), ILS(37) + COMMON /DLSS01/ RLSS(6), ILSS(34) + DATA LENRLS/218/, LENILS/37/, LENRSS/6/, LENISS/34/ +C + IF (JOB .EQ. 2) GO TO 100 + DO 10 I = 1,LENRLS + 10 RSAV(I) = RLS(I) + DO 15 I = 1,LENRSS + 15 RSAV(LENRLS+I) = RLSS(I) +C + DO 20 I = 1,LENILS + 20 ISAV(I) = ILS(I) + DO 25 I = 1,LENISS + 25 ISAV(LENILS+I) = ILSS(I) +C + RETURN +C + 100 CONTINUE + DO 110 I = 1,LENRLS + 110 RLS(I) = RSAV(I) + DO 115 I = 1,LENRSS + 115 RLSS(I) = RSAV(LENRLS+I) +C + DO 120 I = 1,LENILS + 120 ILS(I) = ISAV(I) + DO 125 I = 1,LENISS + 125 ILSS(I) = ISAV(LENILS+I) +C + RETURN +C----------------------- End of Subroutine DSRCMS ---------------------- + END +*DECK ODRV + subroutine odrv + * (n, ia,ja,a, p,ip, nsp,isp, path, flag) +c 5/2/83 +c*********************************************************************** +c odrv -- driver for sparse matrix reordering routines +c*********************************************************************** +c +c description +c +c odrv finds a minimum degree ordering of the rows and columns +c of a matrix m stored in (ia,ja,a) format (see below). for the +c reordered matrix, the work and storage required to perform +c gaussian elimination is (usually) significantly less. +c +c note.. odrv and its subordinate routines have been modified to +c compute orderings for general matrices, not necessarily having any +c symmetry. the miminum degree ordering is computed for the +c structure of the symmetric matrix m + m-transpose. +c modifications to the original odrv module have been made in +c the coding in subroutine mdi, and in the initial comments in +c subroutines odrv and md. +c +c if only the nonzero entries in the upper triangle of m are being +c stored, then odrv symmetrically reorders (ia,ja,a), (optionally) +c with the diagonal entries placed first in each row. this is to +c ensure that if m(i,j) will be in the upper triangle of m with +c respect to the new ordering, then m(i,j) is stored in row i (and +c thus m(j,i) is not stored), whereas if m(i,j) will be in the +c strict lower triangle of m, then m(j,i) is stored in row j (and +c thus m(i,j) is not stored). +c +c +c storage of sparse matrices +c +c the nonzero entries of the matrix m are stored row-by-row in the +c array a. to identify the individual nonzero entries in each row, +c we need to know in which column each entry lies. these column +c indices are stored in the array ja. i.e., if a(k) = m(i,j), then +c ja(k) = j. to identify the individual rows, we need to know where +c each row starts. these row pointers are stored in the array ia. +c i.e., if m(i,j) is the first nonzero entry (stored) in the i-th row +c and a(k) = m(i,j), then ia(i) = k. moreover, ia(n+1) points to +c the first location following the last element in the last row. +c thus, the number of entries in the i-th row is ia(i+1) - ia(i), +c the nonzero entries in the i-th row are stored consecutively in +c +c a(ia(i)), a(ia(i)+1), ..., a(ia(i+1)-1), +c +c and the corresponding column indices are stored consecutively in +c +c ja(ia(i)), ja(ia(i)+1), ..., ja(ia(i+1)-1). +c +c when the coefficient matrix is symmetric, only the nonzero entries +c in the upper triangle need be stored. for example, the matrix +c +c ( 1 0 2 3 0 ) +c ( 0 4 0 0 0 ) +c m = ( 2 0 5 6 0 ) +c ( 3 0 6 7 8 ) +c ( 0 0 0 8 9 ) +c +c could be stored as +c +c - 1 2 3 4 5 6 7 8 9 10 11 12 13 +c ---+-------------------------------------- +c ia - 1 4 5 8 12 14 +c ja - 1 3 4 2 1 3 4 1 3 4 5 4 5 +c a - 1 2 3 4 2 5 6 3 6 7 8 8 9 +c +c or (symmetrically) as +c +c - 1 2 3 4 5 6 7 8 9 +c ---+-------------------------- +c ia - 1 4 5 7 9 10 +c ja - 1 3 4 2 3 4 4 5 5 +c a - 1 2 3 4 5 6 7 8 9 . +c +c +c parameters +c +c n - order of the matrix +c +c ia - integer one-dimensional array containing pointers to delimit +c rows in ja and a. dimension = n+1 +c +c ja - integer one-dimensional array containing the column indices +c corresponding to the elements of a. dimension = number of +c nonzero entries in (the upper triangle of) m +c +c a - real one-dimensional array containing the nonzero entries in +c (the upper triangle of) m, stored by rows. dimension = +c number of nonzero entries in (the upper triangle of) m +c +c p - integer one-dimensional array used to return the permutation +c of the rows and columns of m corresponding to the minimum +c degree ordering. dimension = n +c +c ip - integer one-dimensional array used to return the inverse of +c the permutation returned in p. dimension = n +c +c nsp - declared dimension of the one-dimensional array isp. nsp +c must be at least 3n+4k, where k is the number of nonzeroes +c in the strict upper triangle of m +c +c isp - integer one-dimensional array used for working storage. +c dimension = nsp +c +c path - integer path specification. values and their meanings are - +c 1 find minimum degree ordering only +c 2 find minimum degree ordering and reorder symmetrically +c stored matrix (used when only the nonzero entries in +c the upper triangle of m are being stored) +c 3 reorder symmetrically stored matrix as specified by +c input permutation (used when an ordering has already +c been determined and only the nonzero entries in the +c upper triangle of m are being stored) +c 4 same as 2 but put diagonal entries at start of each row +c 5 same as 3 but put diagonal entries at start of each row +c +c flag - integer error flag. values and their meanings are - +c 0 no errors detected +c 9n+k insufficient storage in md +c 10n+1 insufficient storage in odrv +c 11n+1 illegal path specification +c +c +c conversion from real to double precision +c +c change the real declarations in odrv and sro to double precision +c declarations. +c +c----------------------------------------------------------------------- +c + integer ia(*), ja(*), p(*), ip(*), isp(*), path, flag, + * v, l, head, tmp, q +c... real a(*) + double precision a(*) + logical dflag +c +c----initialize error flag and validate path specification + flag = 0 + if (path.lt.1 .or. 5.lt.path) go to 111 +c +c----allocate storage and find minimum degree ordering + if ((path-1) * (path-2) * (path-4) .ne. 0) go to 1 + max = (nsp-n)/2 + v = 1 + l = v + max + head = l + max + next = head + n + if (max.lt.n) go to 110 +c + call md + * (n, ia,ja, max,isp(v),isp(l), isp(head),p,ip, isp(v), flag) + if (flag.ne.0) go to 100 +c +c----allocate storage and symmetrically reorder matrix + 1 if ((path-2) * (path-3) * (path-4) * (path-5) .ne. 0) go to 2 + tmp = (nsp+1) - n + q = tmp - (ia(n+1)-1) + if (q.lt.1) go to 110 +c + dflag = path.eq.4 .or. path.eq.5 + call sro + * (n, ip, ia, ja, a, isp(tmp), isp(q), dflag) +c + 2 return +c +c ** error -- error detected in md + 100 return +c ** error -- insufficient storage + 110 flag = 10*n + 1 + return +c ** error -- illegal path specified + 111 flag = 11*n + 1 + return + end + subroutine md + * (n, ia,ja, max, v,l, head,last,next, mark, flag) +c*********************************************************************** +c md -- minimum degree algorithm (based on element model) +c*********************************************************************** +c +c description +c +c md finds a minimum degree ordering of the rows and columns of a +c general sparse matrix m stored in (ia,ja,a) format. +c when the structure of m is nonsymmetric, the ordering is that +c obtained for the symmetric matrix m + m-transpose. +c +c +c additional parameters +c +c max - declared dimension of the one-dimensional arrays v and l. +c max must be at least n+2k, where k is the number of +c nonzeroes in the strict upper triangle of m + m-transpose +c +c v - integer one-dimensional work array. dimension = max +c +c l - integer one-dimensional work array. dimension = max +c +c head - integer one-dimensional work array. dimension = n +c +c last - integer one-dimensional array used to return the permutation +c of the rows and columns of m corresponding to the minimum +c degree ordering. dimension = n +c +c next - integer one-dimensional array used to return the inverse of +c the permutation returned in last. dimension = n +c +c mark - integer one-dimensional work array (may be the same as v). +c dimension = n +c +c flag - integer error flag. values and their meanings are - +c 0 no errors detected +c 9n+k insufficient storage in md +c +c +c definitions of internal parameters +c +c ---------+--------------------------------------------------------- +c v(s) - value field of list entry +c ---------+--------------------------------------------------------- +c l(s) - link field of list entry (0 =) end of list) +c ---------+--------------------------------------------------------- +c l(vi) - pointer to element list of uneliminated vertex vi +c ---------+--------------------------------------------------------- +c l(ej) - pointer to boundary list of active element ej +c ---------+--------------------------------------------------------- +c head(d) - vj =) vj head of d-list d +c - 0 =) no vertex in d-list d +c +c +c - vi uneliminated vertex +c - vi in ek - vi not in ek +c ---------+-----------------------------+--------------------------- +c next(vi) - undefined but nonnegative - vj =) vj next in d-list +c - - 0 =) vi tail of d-list +c ---------+-----------------------------+--------------------------- +c last(vi) - (not set until mdp) - -d =) vi head of d-list d +c --vk =) compute degree - vj =) vj last in d-list +c - ej =) vi prototype of ej - 0 =) vi not in any d-list +c - 0 =) do not compute degree - +c ---------+-----------------------------+--------------------------- +c mark(vi) - mark(vk) - nonneg. tag .lt. mark(vk) +c +c +c - vi eliminated vertex +c - ei active element - otherwise +c ---------+-----------------------------+--------------------------- +c next(vi) - -j =) vi was j-th vertex - -j =) vi was j-th vertex +c - to be eliminated - to be eliminated +c ---------+-----------------------------+--------------------------- +c last(vi) - m =) size of ei = m - undefined +c ---------+-----------------------------+--------------------------- +c mark(vi) - -m =) overlap count of ei - undefined +c - with ek = m - +c - otherwise nonnegative tag - +c - .lt. mark(vk) - +c +c----------------------------------------------------------------------- +c + integer ia(*), ja(*), v(*), l(*), head(*), last(*), next(*), + * mark(*), flag, tag, dmin, vk,ek, tail + equivalence (vk,ek) +c +c----initialization + tag = 0 + call mdi + * (n, ia,ja, max,v,l, head,last,next, mark,tag, flag) + if (flag.ne.0) return +c + k = 0 + dmin = 1 +c +c----while k .lt. n do + 1 if (k.ge.n) go to 4 +c +c------search for vertex of minimum degree + 2 if (head(dmin).gt.0) go to 3 + dmin = dmin + 1 + go to 2 +c +c------remove vertex vk of minimum degree from degree list + 3 vk = head(dmin) + head(dmin) = next(vk) + if (head(dmin).gt.0) last(head(dmin)) = -dmin +c +c------number vertex vk, adjust tag, and tag vk + k = k+1 + next(vk) = -k + last(ek) = dmin - 1 + tag = tag + last(ek) + mark(vk) = tag +c +c------form element ek from uneliminated neighbors of vk + call mdm + * (vk,tail, v,l, last,next, mark) +c +c------purge inactive elements and do mass elimination + call mdp + * (k,ek,tail, v,l, head,last,next, mark) +c +c------update degrees of uneliminated vertices in ek + call mdu + * (ek,dmin, v,l, head,last,next, mark) +c + go to 1 +c +c----generate inverse permutation from permutation + 4 do 5 k=1,n + next(k) = -next(k) + 5 last(next(k)) = k +c + return + end + subroutine mdi + * (n, ia,ja, max,v,l, head,last,next, mark,tag, flag) +c*********************************************************************** +c mdi -- initialization +c*********************************************************************** + integer ia(*), ja(*), v(*), l(*), head(*), last(*), next(*), + * mark(*), tag, flag, sfs, vi,dvi, vj +c +c----initialize degrees, element lists, and degree lists + do 1 vi=1,n + mark(vi) = 1 + l(vi) = 0 + 1 head(vi) = 0 + sfs = n+1 +c +c----create nonzero structure +c----for each nonzero entry a(vi,vj) + do 6 vi=1,n + jmin = ia(vi) + jmax = ia(vi+1) - 1 + if (jmin.gt.jmax) go to 6 + do 5 j=jmin,jmax + vj = ja(j) + if (vj-vi) 2, 5, 4 +c +c------if a(vi,vj) is in strict lower triangle +c------check for previous occurrence of a(vj,vi) + 2 lvk = vi + kmax = mark(vi) - 1 + if (kmax .eq. 0) go to 4 + do 3 k=1,kmax + lvk = l(lvk) + if (v(lvk).eq.vj) go to 5 + 3 continue +c----for unentered entries a(vi,vj) + 4 if (sfs.ge.max) go to 101 +c +c------enter vj in element list for vi + mark(vi) = mark(vi) + 1 + v(sfs) = vj + l(sfs) = l(vi) + l(vi) = sfs + sfs = sfs+1 +c +c------enter vi in element list for vj + mark(vj) = mark(vj) + 1 + v(sfs) = vi + l(sfs) = l(vj) + l(vj) = sfs + sfs = sfs+1 + 5 continue + 6 continue +c +c----create degree lists and initialize mark vector + do 7 vi=1,n + dvi = mark(vi) + next(vi) = head(dvi) + head(dvi) = vi + last(vi) = -dvi + nextvi = next(vi) + if (nextvi.gt.0) last(nextvi) = vi + 7 mark(vi) = tag +c + return +c +c ** error- insufficient storage + 101 flag = 9*n + vi + return + end + subroutine mdm + * (vk,tail, v,l, last,next, mark) +c*********************************************************************** +c mdm -- form element from uneliminated neighbors of vk +c*********************************************************************** + integer vk, tail, v(*), l(*), last(*), next(*), mark(*), + * tag, s,ls,vs,es, b,lb,vb, blp,blpmax + equivalence (vs, es) +c +c----initialize tag and list of uneliminated neighbors + tag = mark(vk) + tail = vk +c +c----for each vertex/element vs/es in element list of vk + ls = l(vk) + 1 s = ls + if (s.eq.0) go to 5 + ls = l(s) + vs = v(s) + if (next(vs).lt.0) go to 2 +c +c------if vs is uneliminated vertex, then tag and append to list of +c------uneliminated neighbors + mark(vs) = tag + l(tail) = s + tail = s + go to 4 +c +c------if es is active element, then ... +c--------for each vertex vb in boundary list of element es + 2 lb = l(es) + blpmax = last(es) + do 3 blp=1,blpmax + b = lb + lb = l(b) + vb = v(b) +c +c----------if vb is untagged vertex, then tag and append to list of +c----------uneliminated neighbors + if (mark(vb).ge.tag) go to 3 + mark(vb) = tag + l(tail) = b + tail = b + 3 continue +c +c--------mark es inactive + mark(es) = tag +c + 4 go to 1 +c +c----terminate list of uneliminated neighbors + 5 l(tail) = 0 +c + return + end + subroutine mdp + * (k,ek,tail, v,l, head,last,next, mark) +c*********************************************************************** +c mdp -- purge inactive elements and do mass elimination +c*********************************************************************** + integer ek, tail, v(*), l(*), head(*), last(*), next(*), + * mark(*), tag, free, li,vi,lvi,evi, s,ls,es, ilp,ilpmax +c +c----initialize tag + tag = mark(ek) +c +c----for each vertex vi in ek + li = ek + ilpmax = last(ek) + if (ilpmax.le.0) go to 12 + do 11 ilp=1,ilpmax + i = li + li = l(i) + vi = v(li) +c +c------remove vi from degree list + if (last(vi).eq.0) go to 3 + if (last(vi).gt.0) go to 1 + head(-last(vi)) = next(vi) + go to 2 + 1 next(last(vi)) = next(vi) + 2 if (next(vi).gt.0) last(next(vi)) = last(vi) +c +c------remove inactive items from element list of vi + 3 ls = vi + 4 s = ls + ls = l(s) + if (ls.eq.0) go to 6 + es = v(ls) + if (mark(es).lt.tag) go to 5 + free = ls + l(s) = l(ls) + ls = s + 5 go to 4 +c +c------if vi is interior vertex, then remove from list and eliminate + 6 lvi = l(vi) + if (lvi.ne.0) go to 7 + l(i) = l(li) + li = i +c + k = k+1 + next(vi) = -k + last(ek) = last(ek) - 1 + go to 11 +c +c------else ... +c--------classify vertex vi + 7 if (l(lvi).ne.0) go to 9 + evi = v(lvi) + if (next(evi).ge.0) go to 9 + if (mark(evi).lt.0) go to 8 +c +c----------if vi is prototype vertex, then mark as such, initialize +c----------overlap count for corresponding element, and move vi to end +c----------of boundary list + last(vi) = evi + mark(evi) = -1 + l(tail) = li + tail = li + l(i) = l(li) + li = i + go to 10 +c +c----------else if vi is duplicate vertex, then mark as such and adjust +c----------overlap count for corresponding element + 8 last(vi) = 0 + mark(evi) = mark(evi) - 1 + go to 10 +c +c----------else mark vi to compute degree + 9 last(vi) = -ek +c +c--------insert ek in element list of vi + 10 v(free) = ek + l(free) = l(vi) + l(vi) = free + 11 continue +c +c----terminate boundary list + 12 l(tail) = 0 +c + return + end + subroutine mdu + * (ek,dmin, v,l, head,last,next, mark) +c*********************************************************************** +c mdu -- update degrees of uneliminated vertices in ek +c*********************************************************************** + integer ek, dmin, v(*), l(*), head(*), last(*), next(*), + * mark(*), tag, vi,evi,dvi, s,vs,es, b,vb, ilp,ilpmax, + * blp,blpmax + equivalence (vs, es) +c +c----initialize tag + tag = mark(ek) - last(ek) +c +c----for each vertex vi in ek + i = ek + ilpmax = last(ek) + if (ilpmax.le.0) go to 11 + do 10 ilp=1,ilpmax + i = l(i) + vi = v(i) + if (last(vi)) 1, 10, 8 +c +c------if vi neither prototype nor duplicate vertex, then merge elements +c------to compute degree + 1 tag = tag + 1 + dvi = last(ek) +c +c--------for each vertex/element vs/es in element list of vi + s = l(vi) + 2 s = l(s) + if (s.eq.0) go to 9 + vs = v(s) + if (next(vs).lt.0) go to 3 +c +c----------if vs is uneliminated vertex, then tag and adjust degree + mark(vs) = tag + dvi = dvi + 1 + go to 5 +c +c----------if es is active element, then expand +c------------check for outmatched vertex + 3 if (mark(es).lt.0) go to 6 +c +c------------for each vertex vb in es + b = es + blpmax = last(es) + do 4 blp=1,blpmax + b = l(b) + vb = v(b) +c +c--------------if vb is untagged, then tag and adjust degree + if (mark(vb).ge.tag) go to 4 + mark(vb) = tag + dvi = dvi + 1 + 4 continue +c + 5 go to 2 +c +c------else if vi is outmatched vertex, then adjust overlaps but do not +c------compute degree + 6 last(vi) = 0 + mark(es) = mark(es) - 1 + 7 s = l(s) + if (s.eq.0) go to 10 + es = v(s) + if (mark(es).lt.0) mark(es) = mark(es) - 1 + go to 7 +c +c------else if vi is prototype vertex, then calculate degree by +c------inclusion/exclusion and reset overlap count + 8 evi = last(vi) + dvi = last(ek) + last(evi) + mark(evi) + mark(evi) = 0 +c +c------insert vi in appropriate degree list + 9 next(vi) = head(dvi) + head(dvi) = vi + last(vi) = -dvi + if (next(vi).gt.0) last(next(vi)) = vi + if (dvi.lt.dmin) dmin = dvi +c + 10 continue +c + 11 return + end + subroutine sro + * (n, ip, ia,ja,a, q, r, dflag) +c*********************************************************************** +c sro -- symmetric reordering of sparse symmetric matrix +c*********************************************************************** +c +c description +c +c the nonzero entries of the matrix m are assumed to be stored +c symmetrically in (ia,ja,a) format (i.e., not both m(i,j) and m(j,i) +c are stored if i ne j). +c +c sro does not rearrange the order of the rows, but does move +c nonzeroes from one row to another to ensure that if m(i,j) will be +c in the upper triangle of m with respect to the new ordering, then +c m(i,j) is stored in row i (and thus m(j,i) is not stored), whereas +c if m(i,j) will be in the strict lower triangle of m, then m(j,i) is +c stored in row j (and thus m(i,j) is not stored). +c +c +c additional parameters +c +c q - integer one-dimensional work array. dimension = n +c +c r - integer one-dimensional work array. dimension = number of +c nonzero entries in the upper triangle of m +c +c dflag - logical variable. if dflag = .true., then store nonzero +c diagonal elements at the beginning of the row +c +c----------------------------------------------------------------------- +c + integer ip(*), ia(*), ja(*), q(*), r(*) +c... real a(*), ak + double precision a(*), ak + logical dflag +c +c +c--phase 1 -- find row in which to store each nonzero +c----initialize count of nonzeroes to be stored in each row + do 1 i=1,n + 1 q(i) = 0 +c +c----for each nonzero element a(j) + do 3 i=1,n + jmin = ia(i) + jmax = ia(i+1) - 1 + if (jmin.gt.jmax) go to 3 + do 2 j=jmin,jmax +c +c--------find row (=r(j)) and column (=ja(j)) in which to store a(j) ... + k = ja(j) + if (ip(k).lt.ip(i)) ja(j) = i + if (ip(k).ge.ip(i)) k = i + r(j) = k +c +c--------... and increment count of nonzeroes (=q(r(j)) in that row + 2 q(k) = q(k) + 1 + 3 continue +c +c +c--phase 2 -- find new ia and permutation to apply to (ja,a) +c----determine pointers to delimit rows in permuted (ja,a) + do 4 i=1,n + ia(i+1) = ia(i) + q(i) + 4 q(i) = ia(i+1) +c +c----determine where each (ja(j),a(j)) is stored in permuted (ja,a) +c----for each nonzero element (in reverse order) + ilast = 0 + jmin = ia(1) + jmax = ia(n+1) - 1 + j = jmax + do 6 jdummy=jmin,jmax + i = r(j) + if (.not.dflag .or. ja(j).ne.i .or. i.eq.ilast) go to 5 +c +c------if dflag, then put diagonal nonzero at beginning of row + r(j) = ia(i) + ilast = i + go to 6 +c +c------put (off-diagonal) nonzero in last unused location in row + 5 q(i) = q(i) - 1 + r(j) = q(i) +c + 6 j = j-1 +c +c +c--phase 3 -- permute (ja,a) to upper triangular form (wrt new ordering) + do 8 j=jmin,jmax + 7 if (r(j).eq.j) go to 8 + k = r(j) + r(j) = r(k) + r(k) = k + jak = ja(k) + ja(k) = ja(j) + ja(j) = jak + ak = a(k) + a(k) = a(j) + a(j) = ak + go to 7 + 8 continue +c + return + end +*DECK CDRV + subroutine cdrv + * (n, r,c,ic, ia,ja,a, b, z, nsp,isp,rsp,esp, path, flag) +c*** subroutine cdrv +c*** driver for subroutines for solving sparse nonsymmetric systems of +c linear equations (compressed pointer storage) +c +c +c parameters +c class abbreviations are-- +c n - integer variable +c f - real variable +c v - supplies a value to the driver +c r - returns a result from the driver +c i - used internally by the driver +c a - array +c +c class - parameter +c ------+---------- +c - +c the nonzero entries of the coefficient matrix m are stored +c row-by-row in the array a. to identify the individual nonzero +c entries in each row, we need to know in which column each entry +c lies. the column indices which correspond to the nonzero entries +c of m are stored in the array ja. i.e., if a(k) = m(i,j), then +c ja(k) = j. in addition, we need to know where each row starts and +c how long it is. the index positions in ja and a where the rows of +c m begin are stored in the array ia. i.e., if m(i,j) is the first +c nonzero entry (stored) in the i-th row and a(k) = m(i,j), then +c ia(i) = k. moreover, the index in ja and a of the first location +c following the last element in the last row is stored in ia(n+1). +c thus, the number of entries in the i-th row is given by +c ia(i+1) - ia(i), the nonzero entries of the i-th row are stored +c consecutively in +c a(ia(i)), a(ia(i)+1), ..., a(ia(i+1)-1), +c and the corresponding column indices are stored consecutively in +c ja(ia(i)), ja(ia(i)+1), ..., ja(ia(i+1)-1). +c for example, the 5 by 5 matrix +c ( 1. 0. 2. 0. 0.) +c ( 0. 3. 0. 0. 0.) +c m = ( 0. 4. 5. 6. 0.) +c ( 0. 0. 0. 7. 0.) +c ( 0. 0. 0. 8. 9.) +c would be stored as +c - 1 2 3 4 5 6 7 8 9 +c ---+-------------------------- +c ia - 1 3 4 7 8 10 +c ja - 1 3 2 2 3 4 4 4 5 +c a - 1. 2. 3. 4. 5. 6. 7. 8. 9. . +c +c nv - n - number of variables/equations. +c fva - a - nonzero entries of the coefficient matrix m, stored +c - by rows. +c - size = number of nonzero entries in m. +c nva - ia - pointers to delimit the rows in a. +c - size = n+1. +c nva - ja - column numbers corresponding to the elements of a. +c - size = size of a. +c fva - b - right-hand side b. b and z can the same array. +c - size = n. +c fra - z - solution x. b and z can be the same array. +c - size = n. +c +c the rows and columns of the original matrix m can be +c reordered (e.g., to reduce fillin or ensure numerical stability) +c before calling the driver. if no reordering is done, then set +c r(i) = c(i) = ic(i) = i for i=1,...,n. the solution z is returned +c in the original order. +c if the columns have been reordered (i.e., c(i).ne.i for some +c i), then the driver will call a subroutine (nroc) which rearranges +c each row of ja and a, leaving the rows in the original order, but +c placing the elements of each row in increasing order with respect +c to the new ordering. if path.ne.1, then nroc is assumed to have +c been called already. +c +c nva - r - ordering of the rows of m. +c - size = n. +c nva - c - ordering of the columns of m. +c - size = n. +c nva - ic - inverse of the ordering of the columns of m. i.e., +c - ic(c(i)) = i for i=1,...,n. +c - size = n. +c +c the solution of the system of linear equations is divided into +c three stages -- +c nsfc -- the matrix m is processed symbolically to determine where +c fillin will occur during the numeric factorization. +c nnfc -- the matrix m is factored numerically into the product ldu +c of a unit lower triangular matrix l, a diagonal matrix +c d, and a unit upper triangular matrix u, and the system +c mx = b is solved. +c nnsc -- the linear system mx = b is solved using the ldu +c or factorization from nnfc. +c nntc -- the transposed linear system mt x = b is solved using +c the ldu factorization from nnf. +c for several systems whose coefficient matrices have the same +c nonzero structure, nsfc need be done only once (for the first +c system). then nnfc is done once for each additional system. for +c several systems with the same coefficient matrix, nsfc and nnfc +c need be done only once (for the first system). then nnsc or nntc +c is done once for each additional right-hand side. +c +c nv - path - path specification. values and their meanings are -- +c - 1 perform nroc, nsfc, and nnfc. +c - 2 perform nnfc only (nsfc is assumed to have been +c - done in a manner compatible with the storage +c - allocation used in the driver). +c - 3 perform nnsc only (nsfc and nnfc are assumed to +c - have been done in a manner compatible with the +c - storage allocation used in the driver). +c - 4 perform nntc only (nsfc and nnfc are assumed to +c - have been done in a manner compatible with the +c - storage allocation used in the driver). +c - 5 perform nroc and nsfc. +c +c various errors are detected by the driver and the individual +c subroutines. +c +c nr - flag - error flag. values and their meanings are -- +c - 0 no errors detected +c - n+k null row in a -- row = k +c - 2n+k duplicate entry in a -- row = k +c - 3n+k insufficient storage in nsfc -- row = k +c - 4n+1 insufficient storage in nnfc +c - 5n+k null pivot -- row = k +c - 6n+k insufficient storage in nsfc -- row = k +c - 7n+1 insufficient storage in nnfc +c - 8n+k zero pivot -- row = k +c - 10n+1 insufficient storage in cdrv +c - 11n+1 illegal path specification +c +c working storage is needed for the factored form of the matrix +c m plus various temporary vectors. the arrays isp and rsp should be +c equivalenced. integer storage is allocated from the beginning of +c isp and real storage from the end of rsp. +c +c nv - nsp - declared dimension of rsp. nsp generally must +c - be larger than 8n+2 + 2k (where k = (number of +c - nonzero entries in m)). +c nvira - isp - integer working storage divided up into various arrays +c - needed by the subroutines. isp and rsp should be +c - equivalenced. +c - size = lratio*nsp. +c fvira - rsp - real working storage divided up into various arrays +c - needed by the subroutines. isp and rsp should be +c - equivalenced. +c - size = nsp. +c nr - esp - if sufficient storage was available to perform the +c - symbolic factorization (nsfc), then esp is set to +c - the amount of excess storage provided (negative if +c - insufficient storage was available to perform the +c - numeric factorization (nnfc)). +c +c +c conversion to double precision +c +c to convert these routines for double precision arrays.. +c (1) use the double precision declarations in place of the real +c declarations in each subprogram, as given in comment cards. +c (2) change the data-loaded value of the integer lratio +c in subroutine cdrv, as indicated below. +c (3) change e0 to d0 in the constants in statement number 10 +c in subroutine nnfc and the line following that. +c + integer r(*), c(*), ic(*), ia(*), ja(*), isp(*), esp, path, + * flag, d, u, q, row, tmp, ar, umax +c real a(*), b(*), z(*), rsp(*) + double precision a(*), b(*), z(*), rsp(*) +c +c set lratio equal to the ratio between the length of floating point +c and integer array data. e. g., lratio = 1 for (real, integer), +c lratio = 2 for (double precision, integer) +c + data lratio/2/ +c + if (path.lt.1 .or. 5.lt.path) go to 111 +c******initialize and divide up temporary storage ******************* + il = 1 + ijl = il + (n+1) + iu = ijl + n + iju = iu + (n+1) + irl = iju + n + jrl = irl + n + jl = jrl + n +c +c ****** reorder a if necessary, call nsfc if flag is set *********** + if ((path-1) * (path-5) .ne. 0) go to 5 + max = (lratio*nsp + 1 - jl) - (n+1) - 5*n + jlmax = max/2 + q = jl + jlmax + ira = q + (n+1) + jra = ira + n + irac = jra + n + iru = irac + n + jru = iru + n + jutmp = jru + n + jumax = lratio*nsp + 1 - jutmp + esp = max/lratio + if (jlmax.le.0 .or. jumax.le.0) go to 110 +c + do 1 i=1,n + if (c(i).ne.i) go to 2 + 1 continue + go to 3 + 2 ar = nsp + 1 - n + call nroc + * (n, ic, ia,ja,a, isp(il), rsp(ar), isp(iu), flag) + if (flag.ne.0) go to 100 +c + 3 call nsfc + * (n, r, ic, ia,ja, + * jlmax, isp(il), isp(jl), isp(ijl), + * jumax, isp(iu), isp(jutmp), isp(iju), + * isp(q), isp(ira), isp(jra), isp(irac), + * isp(irl), isp(jrl), isp(iru), isp(jru), flag) + if(flag .ne. 0) go to 100 +c ****** move ju next to jl ***************************************** + jlmax = isp(ijl+n-1) + ju = jl + jlmax + jumax = isp(iju+n-1) + if (jumax.le.0) go to 5 + do 4 j=1,jumax + 4 isp(ju+j-1) = isp(jutmp+j-1) +c +c ****** call remaining subroutines ********************************* + 5 jlmax = isp(ijl+n-1) + ju = jl + jlmax + jumax = isp(iju+n-1) + l = (ju + jumax - 2 + lratio) / lratio + 1 + lmax = isp(il+n) - 1 + d = l + lmax + u = d + n + row = nsp + 1 - n + tmp = row - n + umax = tmp - u + esp = umax - (isp(iu+n) - 1) +c + if ((path-1) * (path-2) .ne. 0) go to 6 + if (umax.lt.0) go to 110 + call nnfc + * (n, r, c, ic, ia, ja, a, z, b, + * lmax, isp(il), isp(jl), isp(ijl), rsp(l), rsp(d), + * umax, isp(iu), isp(ju), isp(iju), rsp(u), + * rsp(row), rsp(tmp), isp(irl), isp(jrl), flag) + if(flag .ne. 0) go to 100 +c + 6 if ((path-3) .ne. 0) go to 7 + call nnsc + * (n, r, c, isp(il), isp(jl), isp(ijl), rsp(l), + * rsp(d), isp(iu), isp(ju), isp(iju), rsp(u), + * z, b, rsp(tmp)) +c + 7 if ((path-4) .ne. 0) go to 8 + call nntc + * (n, r, c, isp(il), isp(jl), isp(ijl), rsp(l), + * rsp(d), isp(iu), isp(ju), isp(iju), rsp(u), + * z, b, rsp(tmp)) + 8 return +c +c ** error.. error detected in nroc, nsfc, nnfc, or nnsc + 100 return +c ** error.. insufficient storage + 110 flag = 10*n + 1 + return +c ** error.. illegal path specification + 111 flag = 11*n + 1 + return + end + subroutine nroc (n, ic, ia, ja, a, jar, ar, p, flag) +c +c ---------------------------------------------------------------- +c +c yale sparse matrix package - nonsymmetric codes +c solving the system of equations mx = b +c +c i. calling sequences +c the coefficient matrix can be processed by an ordering routine +c (e.g., to reduce fillin or ensure numerical stability) before using +c the remaining subroutines. if no reordering is done, then set +c r(i) = c(i) = ic(i) = i for i=1,...,n. if an ordering subroutine +c is used, then nroc should be used to reorder the coefficient matrix +c the calling sequence is -- +c ( (matrix ordering)) +c (nroc (matrix reordering)) +c nsfc (symbolic factorization to determine where fillin will +c occur during numeric factorization) +c nnfc (numeric factorization into product ldu of unit lower +c triangular matrix l, diagonal matrix d, and unit +c upper triangular matrix u, and solution of linear +c system) +c nnsc (solution of linear system for additional right-hand +c side using ldu factorization from nnfc) +c (if only one system of equations is to be solved, then the +c subroutine trk should be used.) +c +c ii. storage of sparse matrices +c the nonzero entries of the coefficient matrix m are stored +c row-by-row in the array a. to identify the individual nonzero +c entries in each row, we need to know in which column each entry +c lies. the column indices which correspond to the nonzero entries +c of m are stored in the array ja. i.e., if a(k) = m(i,j), then +c ja(k) = j. in addition, we need to know where each row starts and +c how long it is. the index positions in ja and a where the rows of +c m begin are stored in the array ia. i.e., if m(i,j) is the first +c (leftmost) entry in the i-th row and a(k) = m(i,j), then +c ia(i) = k. moreover, the index in ja and a of the first location +c following the last element in the last row is stored in ia(n+1). +c thus, the number of entries in the i-th row is given by +c ia(i+1) - ia(i), the nonzero entries of the i-th row are stored +c consecutively in +c a(ia(i)), a(ia(i)+1), ..., a(ia(i+1)-1), +c and the corresponding column indices are stored consecutively in +c ja(ia(i)), ja(ia(i)+1), ..., ja(ia(i+1)-1). +c for example, the 5 by 5 matrix +c ( 1. 0. 2. 0. 0.) +c ( 0. 3. 0. 0. 0.) +c m = ( 0. 4. 5. 6. 0.) +c ( 0. 0. 0. 7. 0.) +c ( 0. 0. 0. 8. 9.) +c would be stored as +c - 1 2 3 4 5 6 7 8 9 +c ---+-------------------------- +c ia - 1 3 4 7 8 10 +c ja - 1 3 2 2 3 4 4 4 5 +c a - 1. 2. 3. 4. 5. 6. 7. 8. 9. . +c +c the strict upper (lower) triangular portion of the matrix +c u (l) is stored in a similar fashion using the arrays iu, ju, u +c (il, jl, l) except that an additional array iju (ijl) is used to +c compress storage of ju (jl) by allowing some sequences of column +c (row) indices to used for more than one row (column) (n.b., l is +c stored by columns). iju(k) (ijl(k)) points to the starting +c location in ju (jl) of entries for the kth row (column). +c compression in ju (jl) occurs in two ways. first, if a row +c (column) i was merged into the current row (column) k, and the +c number of elements merged in from (the tail portion of) row +c (column) i is the same as the final length of row (column) k, then +c the kth row (column) and the tail of row (column) i are identical +c and iju(k) (ijl(k)) points to the start of the tail. second, if +c some tail portion of the (k-1)st row (column) is identical to the +c head of the kth row (column), then iju(k) (ijl(k)) points to the +c start of that tail portion. for example, the nonzero structure of +c the strict upper triangular part of the matrix +c d 0 x x x +c 0 d 0 x x +c 0 0 d x 0 +c 0 0 0 d x +c 0 0 0 0 d +c would be represented as +c - 1 2 3 4 5 6 +c ----+------------ +c iu - 1 4 6 7 8 8 +c ju - 3 4 5 4 +c iju - 1 2 4 3 . +c the diagonal entries of l and u are assumed to be equal to one and +c are not stored. the array d contains the reciprocals of the +c diagonal entries of the matrix d. +c +c iii. additional storage savings +c in nsfc, r and ic can be the same array in the calling +c sequence if no reordering of the coefficient matrix has been done. +c in nnfc, r, c, and ic can all be the same array if no +c reordering has been done. if only the rows have been reordered, +c then c and ic can be the same array. if the row and column +c orderings are the same, then r and c can be the same array. z and +c row can be the same array. +c in nnsc or nntc, r and c can be the same array if no +c reordering has been done or if the row and column orderings are the +c same. z and b can be the same array. however, then b will be +c destroyed. +c +c iv. parameters +c following is a list of parameters to the programs. names are +c uniform among the various subroutines. class abbreviations are -- +c n - integer variable +c f - real variable +c v - supplies a value to a subroutine +c r - returns a result from a subroutine +c i - used internally by a subroutine +c a - array +c +c class - parameter +c ------+---------- +c fva - a - nonzero entries of the coefficient matrix m, stored +c - by rows. +c - size = number of nonzero entries in m. +c fva - b - right-hand side b. +c - size = n. +c nva - c - ordering of the columns of m. +c - size = n. +c fvra - d - reciprocals of the diagonal entries of the matrix d. +c - size = n. +c nr - flag - error flag. values and their meanings are -- +c - 0 no errors detected +c - n+k null row in a -- row = k +c - 2n+k duplicate entry in a -- row = k +c - 3n+k insufficient storage for jl -- row = k +c - 4n+1 insufficient storage for l +c - 5n+k null pivot -- row = k +c - 6n+k insufficient storage for ju -- row = k +c - 7n+1 insufficient storage for u +c - 8n+k zero pivot -- row = k +c nva - ia - pointers to delimit the rows of a. +c - size = n+1. +c nvra - ijl - pointers to the first element in each column in jl, +c - used to compress storage in jl. +c - size = n. +c nvra - iju - pointers to the first element in each row in ju, used +c - to compress storage in ju. +c - size = n. +c nvra - il - pointers to delimit the columns of l. +c - size = n+1. +c nvra - iu - pointers to delimit the rows of u. +c - size = n+1. +c nva - ja - column numbers corresponding to the elements of a. +c - size = size of a. +c nvra - jl - row numbers corresponding to the elements of l. +c - size = jlmax. +c nv - jlmax - declared dimension of jl. jlmax must be larger than +c - the number of nonzeros in the strict lower triangle +c - of m plus fillin minus compression. +c nvra - ju - column numbers corresponding to the elements of u. +c - size = jumax. +c nv - jumax - declared dimension of ju. jumax must be larger than +c - the number of nonzeros in the strict upper triangle +c - of m plus fillin minus compression. +c fvra - l - nonzero entries in the strict lower triangular portion +c - of the matrix l, stored by columns. +c - size = lmax. +c nv - lmax - declared dimension of l. lmax must be larger than +c - the number of nonzeros in the strict lower triangle +c - of m plus fillin (il(n+1)-1 after nsfc). +c nv - n - number of variables/equations. +c nva - r - ordering of the rows of m. +c - size = n. +c fvra - u - nonzero entries in the strict upper triangular portion +c - of the matrix u, stored by rows. +c - size = umax. +c nv - umax - declared dimension of u. umax must be larger than +c - the number of nonzeros in the strict upper triangle +c - of m plus fillin (iu(n+1)-1 after nsfc). +c fra - z - solution x. +c - size = n. +c +c ---------------------------------------------------------------- +c +c*** subroutine nroc +c*** reorders rows of a, leaving row order unchanged +c +c +c input parameters.. n, ic, ia, ja, a +c output parameters.. ja, a, flag +c +c parameters used internally.. +c nia - p - at the kth step, p is a linked list of the reordered +c - column indices of the kth row of a. p(n+1) points +c - to the first entry in the list. +c - size = n+1. +c nia - jar - at the kth step,jar contains the elements of the +c - reordered column indices of a. +c - size = n. +c fia - ar - at the kth step, ar contains the elements of the +c - reordered row of a. +c - size = n. +c + integer ic(*), ia(*), ja(*), jar(*), p(*), flag +c real a(*), ar(*) + double precision a(*), ar(*) +c +c ****** for each nonempty row ******************************* + do 5 k=1,n + jmin = ia(k) + jmax = ia(k+1) - 1 + if(jmin .gt. jmax) go to 5 + p(n+1) = n + 1 +c ****** insert each element in the list ********************* + do 3 j=jmin,jmax + newj = ic(ja(j)) + i = n + 1 + 1 if(p(i) .ge. newj) go to 2 + i = p(i) + go to 1 + 2 if(p(i) .eq. newj) go to 102 + p(newj) = p(i) + p(i) = newj + jar(newj) = ja(j) + ar(newj) = a(j) + 3 continue +c ****** replace old row in ja and a ************************* + i = n + 1 + do 4 j=jmin,jmax + i = p(i) + ja(j) = jar(i) + 4 a(j) = ar(i) + 5 continue + flag = 0 + return +c +c ** error.. duplicate entry in a + 102 flag = n + k + return + end + subroutine nsfc + * (n, r, ic, ia,ja, jlmax,il,jl,ijl, jumax,iu,ju,iju, + * q, ira,jra, irac, irl,jrl, iru,jru, flag) +c*** subroutine nsfc +c*** symbolic ldu-factorization of nonsymmetric sparse matrix +c (compressed pointer storage) +c +c +c input variables.. n, r, ic, ia, ja, jlmax, jumax. +c output variables.. il, jl, ijl, iu, ju, iju, flag. +c +c parameters used internally.. +c nia - q - suppose m* is the result of reordering m. if +c - processing of the ith row of m* (hence the ith +c - row of u) is being done, q(j) is initially +c - nonzero if m*(i,j) is nonzero (j.ge.i). since +c - values need not be stored, each entry points to the +c - next nonzero and q(n+1) points to the first. n+1 +c - indicates the end of the list. for example, if n=9 +c - and the 5th row of m* is +c - 0 x x 0 x 0 0 x 0 +c - then q will initially be +c - a a a a 8 a a 10 5 (a - arbitrary). +c - as the algorithm proceeds, other elements of q +c - are inserted in the list because of fillin. +c - q is used in an analogous manner to compute the +c - ith column of l. +c - size = n+1. +c nia - ira, - vectors used to find the columns of m. at the kth +c nia - jra, step of the factorization, irac(k) points to the +c nia - irac head of a linked list in jra of row indices i +c - such that i .ge. k and m(i,k) is nonzero. zero +c - indicates the end of the list. ira(i) (i.ge.k) +c - points to the smallest j such that j .ge. k and +c - m(i,j) is nonzero. +c - size of each = n. +c nia - irl, - vectors used to find the rows of l. at the kth step +c nia - jrl of the factorization, jrl(k) points to the head +c - of a linked list in jrl of column indices j +c - such j .lt. k and l(k,j) is nonzero. zero +c - indicates the end of the list. irl(j) (j.lt.k) +c - points to the smallest i such that i .ge. k and +c - l(i,j) is nonzero. +c - size of each = n. +c nia - iru, - vectors used in a manner analogous to irl and jrl +c nia - jru to find the columns of u. +c - size of each = n. +c +c internal variables.. +c jlptr - points to the last position used in jl. +c juptr - points to the last position used in ju. +c jmin,jmax - are the indices in a or u of the first and last +c elements to be examined in a given row. +c for example, jmin=ia(k), jmax=ia(k+1)-1. +c + integer cend, qm, rend, rk, vj + integer ia(*), ja(*), ira(*), jra(*), il(*), jl(*), ijl(*) + integer iu(*), ju(*), iju(*), irl(*), jrl(*), iru(*), jru(*) + integer r(*), ic(*), q(*), irac(*), flag +c +c ****** initialize pointers **************************************** + np1 = n + 1 + jlmin = 1 + jlptr = 0 + il(1) = 1 + jumin = 1 + juptr = 0 + iu(1) = 1 + do 1 k=1,n + irac(k) = 0 + jra(k) = 0 + jrl(k) = 0 + 1 jru(k) = 0 +c ****** initialize column pointers for a *************************** + do 2 k=1,n + rk = r(k) + iak = ia(rk) + if (iak .ge. ia(rk+1)) go to 101 + jaiak = ic(ja(iak)) + if (jaiak .gt. k) go to 105 + jra(k) = irac(jaiak) + irac(jaiak) = k + 2 ira(k) = iak +c +c ****** for each column of l and row of u ************************** + do 41 k=1,n +c +c ****** initialize q for computing kth column of l ***************** + q(np1) = np1 + luk = -1 +c ****** by filling in kth column of a ****************************** + vj = irac(k) + if (vj .eq. 0) go to 5 + 3 qm = np1 + 4 m = qm + qm = q(m) + if (qm .lt. vj) go to 4 + if (qm .eq. vj) go to 102 + luk = luk + 1 + q(m) = vj + q(vj) = qm + vj = jra(vj) + if (vj .ne. 0) go to 3 +c ****** link through jru ******************************************* + 5 lastid = 0 + lasti = 0 + ijl(k) = jlptr + i = k + 6 i = jru(i) + if (i .eq. 0) go to 10 + qm = np1 + jmin = irl(i) + jmax = ijl(i) + il(i+1) - il(i) - 1 + long = jmax - jmin + if (long .lt. 0) go to 6 + jtmp = jl(jmin) + if (jtmp .ne. k) long = long + 1 + if (jtmp .eq. k) r(i) = -r(i) + if (lastid .ge. long) go to 7 + lasti = i + lastid = long +c ****** and merge the corresponding columns into the kth column **** + 7 do 9 j=jmin,jmax + vj = jl(j) + 8 m = qm + qm = q(m) + if (qm .lt. vj) go to 8 + if (qm .eq. vj) go to 9 + luk = luk + 1 + q(m) = vj + q(vj) = qm + qm = vj + 9 continue + go to 6 +c ****** lasti is the longest column merged into the kth ************ +c ****** see if it equals the entire kth column ********************* + 10 qm = q(np1) + if (qm .ne. k) go to 105 + if (luk .eq. 0) go to 17 + if (lastid .ne. luk) go to 11 +c ****** if so, jl can be compressed ******************************** + irll = irl(lasti) + ijl(k) = irll + 1 + if (jl(irll) .ne. k) ijl(k) = ijl(k) - 1 + go to 17 +c ****** if not, see if kth column can overlap the previous one ***** + 11 if (jlmin .gt. jlptr) go to 15 + qm = q(qm) + do 12 j=jlmin,jlptr + if (jl(j) - qm) 12, 13, 15 + 12 continue + go to 15 + 13 ijl(k) = j + do 14 i=j,jlptr + if (jl(i) .ne. qm) go to 15 + qm = q(qm) + if (qm .gt. n) go to 17 + 14 continue + jlptr = j - 1 +c ****** move column indices from q to jl, update vectors *********** + 15 jlmin = jlptr + 1 + ijl(k) = jlmin + if (luk .eq. 0) go to 17 + jlptr = jlptr + luk + if (jlptr .gt. jlmax) go to 103 + qm = q(np1) + do 16 j=jlmin,jlptr + qm = q(qm) + 16 jl(j) = qm + 17 irl(k) = ijl(k) + il(k+1) = il(k) + luk +c +c ****** initialize q for computing kth row of u ******************** + q(np1) = np1 + luk = -1 +c ****** by filling in kth row of reordered a *********************** + rk = r(k) + jmin = ira(k) + jmax = ia(rk+1) - 1 + if (jmin .gt. jmax) go to 20 + do 19 j=jmin,jmax + vj = ic(ja(j)) + qm = np1 + 18 m = qm + qm = q(m) + if (qm .lt. vj) go to 18 + if (qm .eq. vj) go to 102 + luk = luk + 1 + q(m) = vj + q(vj) = qm + 19 continue +c ****** link through jrl, ****************************************** + 20 lastid = 0 + lasti = 0 + iju(k) = juptr + i = k + i1 = jrl(k) + 21 i = i1 + if (i .eq. 0) go to 26 + i1 = jrl(i) + qm = np1 + jmin = iru(i) + jmax = iju(i) + iu(i+1) - iu(i) - 1 + long = jmax - jmin + if (long .lt. 0) go to 21 + jtmp = ju(jmin) + if (jtmp .eq. k) go to 22 +c ****** update irl and jrl, ***************************************** + long = long + 1 + cend = ijl(i) + il(i+1) - il(i) + irl(i) = irl(i) + 1 + if (irl(i) .ge. cend) go to 22 + j = jl(irl(i)) + jrl(i) = jrl(j) + jrl(j) = i + 22 if (lastid .ge. long) go to 23 + lasti = i + lastid = long +c ****** and merge the corresponding rows into the kth row ********** + 23 do 25 j=jmin,jmax + vj = ju(j) + 24 m = qm + qm = q(m) + if (qm .lt. vj) go to 24 + if (qm .eq. vj) go to 25 + luk = luk + 1 + q(m) = vj + q(vj) = qm + qm = vj + 25 continue + go to 21 +c ****** update jrl(k) and irl(k) *********************************** + 26 if (il(k+1) .le. il(k)) go to 27 + j = jl(irl(k)) + jrl(k) = jrl(j) + jrl(j) = k +c ****** lasti is the longest row merged into the kth *************** +c ****** see if it equals the entire kth row ************************ + 27 qm = q(np1) + if (qm .ne. k) go to 105 + if (luk .eq. 0) go to 34 + if (lastid .ne. luk) go to 28 +c ****** if so, ju can be compressed ******************************** + irul = iru(lasti) + iju(k) = irul + 1 + if (ju(irul) .ne. k) iju(k) = iju(k) - 1 + go to 34 +c ****** if not, see if kth row can overlap the previous one ******** + 28 if (jumin .gt. juptr) go to 32 + qm = q(qm) + do 29 j=jumin,juptr + if (ju(j) - qm) 29, 30, 32 + 29 continue + go to 32 + 30 iju(k) = j + do 31 i=j,juptr + if (ju(i) .ne. qm) go to 32 + qm = q(qm) + if (qm .gt. n) go to 34 + 31 continue + juptr = j - 1 +c ****** move row indices from q to ju, update vectors ************** + 32 jumin = juptr + 1 + iju(k) = jumin + if (luk .eq. 0) go to 34 + juptr = juptr + luk + if (juptr .gt. jumax) go to 106 + qm = q(np1) + do 33 j=jumin,juptr + qm = q(qm) + 33 ju(j) = qm + 34 iru(k) = iju(k) + iu(k+1) = iu(k) + luk +c +c ****** update iru, jru ******************************************** + i = k + 35 i1 = jru(i) + if (r(i) .lt. 0) go to 36 + rend = iju(i) + iu(i+1) - iu(i) + if (iru(i) .ge. rend) go to 37 + j = ju(iru(i)) + jru(i) = jru(j) + jru(j) = i + go to 37 + 36 r(i) = -r(i) + 37 i = i1 + if (i .eq. 0) go to 38 + iru(i) = iru(i) + 1 + go to 35 +c +c ****** update ira, jra, irac ************************************** + 38 i = irac(k) + if (i .eq. 0) go to 41 + 39 i1 = jra(i) + ira(i) = ira(i) + 1 + if (ira(i) .ge. ia(r(i)+1)) go to 40 + irai = ira(i) + jairai = ic(ja(irai)) + if (jairai .gt. i) go to 40 + jra(i) = irac(jairai) + irac(jairai) = i + 40 i = i1 + if (i .ne. 0) go to 39 + 41 continue +c + ijl(n) = jlptr + iju(n) = juptr + flag = 0 + return +c +c ** error.. null row in a + 101 flag = n + rk + return +c ** error.. duplicate entry in a + 102 flag = 2*n + rk + return +c ** error.. insufficient storage for jl + 103 flag = 3*n + k + return +c ** error.. null pivot + 105 flag = 5*n + k + return +c ** error.. insufficient storage for ju + 106 flag = 6*n + k + return + end + subroutine nnfc + * (n, r,c,ic, ia,ja,a, z, b, + * lmax,il,jl,ijl,l, d, umax,iu,ju,iju,u, + * row, tmp, irl,jrl, flag) +c*** subroutine nnfc +c*** numerical ldu-factorization of sparse nonsymmetric matrix and +c solution of system of linear equations (compressed pointer +c storage) +c +c +c input variables.. n, r, c, ic, ia, ja, a, b, +c il, jl, ijl, lmax, iu, ju, iju, umax +c output variables.. z, l, d, u, flag +c +c parameters used internally.. +c nia - irl, - vectors used to find the rows of l. at the kth step +c nia - jrl of the factorization, jrl(k) points to the head +c - of a linked list in jrl of column indices j +c - such j .lt. k and l(k,j) is nonzero. zero +c - indicates the end of the list. irl(j) (j.lt.k) +c - points to the smallest i such that i .ge. k and +c - l(i,j) is nonzero. +c - size of each = n. +c fia - row - holds intermediate values in calculation of u and l. +c - size = n. +c fia - tmp - holds new right-hand side b* for solution of the +c - equation ux = b*. +c - size = n. +c +c internal variables.. +c jmin, jmax - indices of the first and last positions in a row to +c be examined. +c sum - used in calculating tmp. +c + integer rk,umax + integer r(*), c(*), ic(*), ia(*), ja(*), il(*), jl(*), ijl(*) + integer iu(*), ju(*), iju(*), irl(*), jrl(*), flag +c real a(*), l(*), d(*), u(*), z(*), b(*), row(*) +c real tmp(*), lki, sum, dk + double precision a(*), l(*), d(*), u(*), z(*), b(*), row(*) + double precision tmp(*), lki, sum, dk +c +c ****** initialize pointers and test storage *********************** + if(il(n+1)-1 .gt. lmax) go to 104 + if(iu(n+1)-1 .gt. umax) go to 107 + do 1 k=1,n + irl(k) = il(k) + jrl(k) = 0 + 1 continue +c +c ****** for each row *********************************************** + do 19 k=1,n +c ****** reverse jrl and zero row where kth row of l will fill in *** + row(k) = 0 + i1 = 0 + if (jrl(k) .eq. 0) go to 3 + i = jrl(k) + 2 i2 = jrl(i) + jrl(i) = i1 + i1 = i + row(i) = 0 + i = i2 + if (i .ne. 0) go to 2 +c ****** set row to zero where u will fill in *********************** + 3 jmin = iju(k) + jmax = jmin + iu(k+1) - iu(k) - 1 + if (jmin .gt. jmax) go to 5 + do 4 j=jmin,jmax + 4 row(ju(j)) = 0 +c ****** place kth row of a in row ********************************** + 5 rk = r(k) + jmin = ia(rk) + jmax = ia(rk+1) - 1 + do 6 j=jmin,jmax + row(ic(ja(j))) = a(j) + 6 continue +c ****** initialize sum, and link through jrl *********************** + sum = b(rk) + i = i1 + if (i .eq. 0) go to 10 +c ****** assign the kth row of l and adjust row, sum **************** + 7 lki = -row(i) +c ****** if l is not required, then comment out the following line ** + l(irl(i)) = -lki + sum = sum + lki * tmp(i) + jmin = iu(i) + jmax = iu(i+1) - 1 + if (jmin .gt. jmax) go to 9 + mu = iju(i) - jmin + do 8 j=jmin,jmax + 8 row(ju(mu+j)) = row(ju(mu+j)) + lki * u(j) + 9 i = jrl(i) + if (i .ne. 0) go to 7 +c +c ****** assign kth row of u and diagonal d, set tmp(k) ************* + 10 if (row(k) .eq. 0.0d0) go to 108 + dk = 1.0d0 / row(k) + d(k) = dk + tmp(k) = sum * dk + if (k .eq. n) go to 19 + jmin = iu(k) + jmax = iu(k+1) - 1 + if (jmin .gt. jmax) go to 12 + mu = iju(k) - jmin + do 11 j=jmin,jmax + 11 u(j) = row(ju(mu+j)) * dk + 12 continue +c +c ****** update irl and jrl, keeping jrl in decreasing order ******** + i = i1 + if (i .eq. 0) go to 18 + 14 irl(i) = irl(i) + 1 + i1 = jrl(i) + if (irl(i) .ge. il(i+1)) go to 17 + ijlb = irl(i) - il(i) + ijl(i) + j = jl(ijlb) + 15 if (i .gt. jrl(j)) go to 16 + j = jrl(j) + go to 15 + 16 jrl(i) = jrl(j) + jrl(j) = i + 17 i = i1 + if (i .ne. 0) go to 14 + 18 if (irl(k) .ge. il(k+1)) go to 19 + j = jl(ijl(k)) + jrl(k) = jrl(j) + jrl(j) = k + 19 continue +c +c ****** solve ux = tmp by back substitution ********************** + k = n + do 22 i=1,n + sum = tmp(k) + jmin = iu(k) + jmax = iu(k+1) - 1 + if (jmin .gt. jmax) go to 21 + mu = iju(k) - jmin + do 20 j=jmin,jmax + 20 sum = sum - u(j) * tmp(ju(mu+j)) + 21 tmp(k) = sum + z(c(k)) = sum + 22 k = k-1 + flag = 0 + return +c +c ** error.. insufficient storage for l + 104 flag = 4*n + 1 + return +c ** error.. insufficient storage for u + 107 flag = 7*n + 1 + return +c ** error.. zero pivot + 108 flag = 8*n + k + return + end + subroutine nnsc + * (n, r, c, il, jl, ijl, l, d, iu, ju, iju, u, z, b, tmp) +c*** subroutine nnsc +c*** numerical solution of sparse nonsymmetric system of linear +c equations given ldu-factorization (compressed pointer storage) +c +c +c input variables.. n, r, c, il, jl, ijl, l, d, iu, ju, iju, u, b +c output variables.. z +c +c parameters used internally.. +c fia - tmp - temporary vector which gets result of solving ly = b. +c - size = n. +c +c internal variables.. +c jmin, jmax - indices of the first and last positions in a row of +c u or l to be used. +c + integer r(*), c(*), il(*), jl(*), ijl(*), iu(*), ju(*), iju(*) +c real l(*), d(*), u(*), b(*), z(*), tmp(*), tmpk, sum + double precision l(*), d(*), u(*), b(*), z(*), tmp(*), tmpk,sum +c +c ****** set tmp to reordered b ************************************* + do 1 k=1,n + 1 tmp(k) = b(r(k)) +c ****** solve ly = b by forward substitution ********************* + do 3 k=1,n + jmin = il(k) + jmax = il(k+1) - 1 + tmpk = -d(k) * tmp(k) + tmp(k) = -tmpk + if (jmin .gt. jmax) go to 3 + ml = ijl(k) - jmin + do 2 j=jmin,jmax + 2 tmp(jl(ml+j)) = tmp(jl(ml+j)) + tmpk * l(j) + 3 continue +c ****** solve ux = y by back substitution ************************ + k = n + do 6 i=1,n + sum = -tmp(k) + jmin = iu(k) + jmax = iu(k+1) - 1 + if (jmin .gt. jmax) go to 5 + mu = iju(k) - jmin + do 4 j=jmin,jmax + 4 sum = sum + u(j) * tmp(ju(mu+j)) + 5 tmp(k) = -sum + z(c(k)) = -sum + k = k - 1 + 6 continue + return + end + subroutine nntc + * (n, r, c, il, jl, ijl, l, d, iu, ju, iju, u, z, b, tmp) +c*** subroutine nntc +c*** numeric solution of the transpose of a sparse nonsymmetric system +c of linear equations given lu-factorization (compressed pointer +c storage) +c +c +c input variables.. n, r, c, il, jl, ijl, l, d, iu, ju, iju, u, b +c output variables.. z +c +c parameters used internally.. +c fia - tmp - temporary vector which gets result of solving ut y = b +c - size = n. +c +c internal variables.. +c jmin, jmax - indices of the first and last positions in a row of +c u or l to be used. +c + integer r(*), c(*), il(*), jl(*), ijl(*), iu(*), ju(*), iju(*) +c real l(*), d(*), u(*), b(*), z(*), tmp(*), tmpk,sum + double precision l(*), d(*), u(*), b(*), z(*), tmp(*), tmpk,sum +c +c ****** set tmp to reordered b ************************************* + do 1 k=1,n + 1 tmp(k) = b(c(k)) +c ****** solve ut y = b by forward substitution ******************* + do 3 k=1,n + jmin = iu(k) + jmax = iu(k+1) - 1 + tmpk = -tmp(k) + if (jmin .gt. jmax) go to 3 + mu = iju(k) - jmin + do 2 j=jmin,jmax + 2 tmp(ju(mu+j)) = tmp(ju(mu+j)) + tmpk * u(j) + 3 continue +c ****** solve lt x = y by back substitution ********************** + k = n + do 6 i=1,n + sum = -tmp(k) + jmin = il(k) + jmax = il(k+1) - 1 + if (jmin .gt. jmax) go to 5 + ml = ijl(k) - jmin + do 4 j=jmin,jmax + 4 sum = sum + l(j) * tmp(jl(ml+j)) + 5 tmp(k) = -sum * d(k) + z(r(k)) = tmp(k) + k = k - 1 + 6 continue + return + end +*DECK DSTODA + SUBROUTINE DSTODA (NEQ, Y, YH, NYH, YH1, EWT, SAVF, ACOR, + 1 WM, IWM, F, JAC, PJAC, SLVS) + EXTERNAL F, JAC, PJAC, SLVS + INTEGER NEQ, NYH, IWM + DOUBLE PRECISION Y, YH, YH1, EWT, SAVF, ACOR, WM + DIMENSION NEQ(*), Y(*), YH(NYH,*), YH1(*), EWT(*), SAVF(*), + 1 ACOR(*), WM(*), IWM(*) + INTEGER IOWND, IALTH, IPUP, LMAX, MEO, NQNYH, NSLP, + 1 ICF, IERPJ, IERSL, JCUR, JSTART, KFLAG, L, + 2 LYH, LEWT, LACOR, LSAVF, LWM, LIWM, METH, MITER, + 3 MAXORD, MAXCOR, MSBP, MXNCF, N, NQ, NST, NFE, NJE, NQU + INTEGER IOWND2, ICOUNT, IRFLAG, JTYP, MUSED, MXORDN, MXORDS + DOUBLE PRECISION CONIT, CRATE, EL, ELCO, HOLD, RMAX, TESCO, + 2 CCMAX, EL0, H, HMIN, HMXI, HU, RC, TN, UROUND + DOUBLE PRECISION ROWND2, CM1, CM2, PDEST, PDLAST, RATIO, + 1 PDNORM + COMMON /DLS001/ CONIT, CRATE, EL(13), ELCO(13,12), + 1 HOLD, RMAX, TESCO(3,12), + 2 CCMAX, EL0, H, HMIN, HMXI, HU, RC, TN, UROUND, + 3 IOWND(6), IALTH, IPUP, LMAX, MEO, NQNYH, NSLP, + 4 ICF, IERPJ, IERSL, JCUR, JSTART, KFLAG, L, + 5 LYH, LEWT, LACOR, LSAVF, LWM, LIWM, METH, MITER, + 6 MAXORD, MAXCOR, MSBP, MXNCF, N, NQ, NST, NFE, NJE, NQU + COMMON /DLSA01/ ROWND2, CM1(12), CM2(5), PDEST, PDLAST, RATIO, + 1 PDNORM, + 2 IOWND2(3), ICOUNT, IRFLAG, JTYP, MUSED, MXORDN, MXORDS + INTEGER I, I1, IREDO, IRET, J, JB, M, NCF, NEWQ + INTEGER LM1, LM1P1, LM2, LM2P1, NQM1, NQM2 + DOUBLE PRECISION DCON, DDN, DEL, DELP, DSM, DUP, EXDN, EXSM, EXUP, + 1 R, RH, RHDN, RHSM, RHUP, TOLD, DMNORM + DOUBLE PRECISION ALPHA, DM1,DM2, EXM1,EXM2, + 1 PDH, PNORM, RATE, RH1, RH1IT, RH2, RM, SM1(12) + SAVE SM1 + DATA SM1/0.5D0, 0.575D0, 0.55D0, 0.45D0, 0.35D0, 0.25D0, + 1 0.20D0, 0.15D0, 0.10D0, 0.075D0, 0.050D0, 0.025D0/ +C----------------------------------------------------------------------- +C DSTODA performs one step of the integration of an initial value +C problem for a system of ordinary differential equations. +C Note: DSTODA is independent of the value of the iteration method +C indicator MITER, when this is .ne. 0, and hence is independent +C of the type of chord method used, or the Jacobian structure. +C Communication with DSTODA is done with the following variables: +C +C Y = an array of length .ge. N used as the Y argument in +C all calls to F and JAC. +C NEQ = integer array containing problem size in NEQ(1), and +C passed as the NEQ argument in all calls to F and JAC. +C YH = an NYH by LMAX array containing the dependent variables +C and their approximate scaled derivatives, where +C LMAX = MAXORD + 1. YH(i,j+1) contains the approximate +C j-th derivative of y(i), scaled by H**j/factorial(j) +C (j = 0,1,...,NQ). On entry for the first step, the first +C two columns of YH must be set from the initial values. +C NYH = a constant integer .ge. N, the first dimension of YH. +C YH1 = a one-dimensional array occupying the same space as YH. +C EWT = an array of length N containing multiplicative weights +C for local error measurements. Local errors in y(i) are +C compared to 1.0/EWT(i) in various error tests. +C SAVF = an array of working storage, of length N. +C ACOR = a work array of length N, used for the accumulated +C corrections. On a successful return, ACOR(i) contains +C the estimated one-step local error in y(i). +C WM,IWM = real and integer work arrays associated with matrix +C operations in chord iteration (MITER .ne. 0). +C PJAC = name of routine to evaluate and preprocess Jacobian matrix +C and P = I - H*EL0*Jac, if a chord method is being used. +C It also returns an estimate of norm(Jac) in PDNORM. +C SLVS = name of routine to solve linear system in chord iteration. +C CCMAX = maximum relative change in H*EL0 before PJAC is called. +C H = the step size to be attempted on the next step. +C H is altered by the error control algorithm during the +C problem. H can be either positive or negative, but its +C sign must remain constant throughout the problem. +C HMIN = the minimum absolute value of the step size H to be used. +C HMXI = inverse of the maximum absolute value of H to be used. +C HMXI = 0.0 is allowed and corresponds to an infinite HMAX. +C HMIN and HMXI may be changed at any time, but will not +C take effect until the next change of H is considered. +C TN = the independent variable. TN is updated on each step taken. +C JSTART = an integer used for input only, with the following +C values and meanings: +C 0 perform the first step. +C .gt.0 take a new step continuing from the last. +C -1 take the next step with a new value of H, +C N, METH, MITER, and/or matrix parameters. +C -2 take the next step with a new value of H, +C but with other inputs unchanged. +C On return, JSTART is set to 1 to facilitate continuation. +C KFLAG = a completion code with the following meanings: +C 0 the step was succesful. +C -1 the requested error could not be achieved. +C -2 corrector convergence could not be achieved. +C -3 fatal error in PJAC or SLVS. +C A return with KFLAG = -1 or -2 means either +C ABS(H) = HMIN or 10 consecutive failures occurred. +C On a return with KFLAG negative, the values of TN and +C the YH array are as of the beginning of the last +C step, and H is the last step size attempted. +C MAXORD = the maximum order of integration method to be allowed. +C MAXCOR = the maximum number of corrector iterations allowed. +C MSBP = maximum number of steps between PJAC calls (MITER .gt. 0). +C MXNCF = maximum number of convergence failures allowed. +C METH = current method. +C METH = 1 means Adams method (nonstiff) +C METH = 2 means BDF method (stiff) +C METH may be reset by DSTODA. +C MITER = corrector iteration method. +C MITER = 0 means functional iteration. +C MITER = JT .gt. 0 means a chord iteration corresponding +C to Jacobian type JT. (The DLSODA/DLSODAR argument JT is +C communicated here as JTYP, but is not used in DSTODA +C except to load MITER following a method switch.) +C MITER may be reset by DSTODA. +C N = the number of first-order differential equations. +C----------------------------------------------------------------------- + KFLAG = 0 + TOLD = TN + NCF = 0 + IERPJ = 0 + IERSL = 0 + JCUR = 0 + ICF = 0 + DELP = 0.0D0 + IF (JSTART .GT. 0) GO TO 200 + IF (JSTART .EQ. -1) GO TO 100 + IF (JSTART .EQ. -2) GO TO 160 +C----------------------------------------------------------------------- +C On the first call, the order is set to 1, and other variables are +C initialized. RMAX is the maximum ratio by which H can be increased +C in a single step. It is initially 1.E4 to compensate for the small +C initial H, but then is normally equal to 10. If a failure +C occurs (in corrector convergence or error test), RMAX is set at 2 +C for the next increase. +C DCFODE is called to get the needed coefficients for both methods. +C----------------------------------------------------------------------- + LMAX = MAXORD + 1 + NQ = 1 + L = 2 + IALTH = 2 + RMAX = 10000.0D0 + RC = 0.0D0 + EL0 = 1.0D0 + CRATE = 0.7D0 + HOLD = H + NSLP = 0 + IPUP = MITER + IRET = 3 +C Initialize switching parameters. METH = 1 is assumed initially. ----- + ICOUNT = 20 + IRFLAG = 0 + PDEST = 0.0D0 + PDLAST = 0.0D0 + RATIO = 5.0D0 + CALL DCFODE (2, ELCO, TESCO) + DO 10 I = 1,5 + 10 CM2(I) = TESCO(2,I)*ELCO(I+1,I) + CALL DCFODE (1, ELCO, TESCO) + DO 20 I = 1,12 + 20 CM1(I) = TESCO(2,I)*ELCO(I+1,I) + GO TO 150 +C----------------------------------------------------------------------- +C The following block handles preliminaries needed when JSTART = -1. +C IPUP is set to MITER to force a matrix update. +C If an order increase is about to be considered (IALTH = 1), +C IALTH is reset to 2 to postpone consideration one more step. +C If the caller has changed METH, DCFODE is called to reset +C the coefficients of the method. +C If H is to be changed, YH must be rescaled. +C If H or METH is being changed, IALTH is reset to L = NQ + 1 +C to prevent further changes in H for that many steps. +C----------------------------------------------------------------------- + 100 IPUP = MITER + LMAX = MAXORD + 1 + IF (IALTH .EQ. 1) IALTH = 2 + IF (METH .EQ. MUSED) GO TO 160 + CALL DCFODE (METH, ELCO, TESCO) + IALTH = L + IRET = 1 +C----------------------------------------------------------------------- +C The el vector and related constants are reset +C whenever the order NQ is changed, or at the start of the problem. +C----------------------------------------------------------------------- + 150 DO 155 I = 1,L + 155 EL(I) = ELCO(I,NQ) + NQNYH = NQ*NYH + RC = RC*EL(1)/EL0 + EL0 = EL(1) + CONIT = 0.5D0/(NQ+2) + GO TO (160, 170, 200), IRET +C----------------------------------------------------------------------- +C If H is being changed, the H ratio RH is checked against +C RMAX, HMIN, and HMXI, and the YH array rescaled. IALTH is set to +C L = NQ + 1 to prevent a change of H for that many steps, unless +C forced by a convergence or error test failure. +C----------------------------------------------------------------------- + 160 IF (H .EQ. HOLD) GO TO 200 + RH = H/HOLD + H = HOLD + IREDO = 3 + GO TO 175 + 170 RH = MAX(RH,HMIN/ABS(H)) + 175 RH = MIN(RH,RMAX) + RH = RH/MAX(1.0D0,ABS(H)*HMXI*RH) +C----------------------------------------------------------------------- +C If METH = 1, also restrict the new step size by the stability region. +C If this reduces H, set IRFLAG to 1 so that if there are roundoff +C problems later, we can assume that is the cause of the trouble. +C----------------------------------------------------------------------- + IF (METH .EQ. 2) GO TO 178 + IRFLAG = 0 + PDH = MAX(ABS(H)*PDLAST,0.000001D0) + IF (RH*PDH*1.00001D0 .LT. SM1(NQ)) GO TO 178 + RH = SM1(NQ)/PDH + IRFLAG = 1 + 178 CONTINUE + R = 1.0D0 + DO 180 J = 2,L + R = R*RH + DO 180 I = 1,N + 180 YH(I,J) = YH(I,J)*R + H = H*RH + RC = RC*RH + IALTH = L + IF (IREDO .EQ. 0) GO TO 690 +C----------------------------------------------------------------------- +C This section computes the predicted values by effectively +C multiplying the YH array by the Pascal triangle matrix. +C RC is the ratio of new to old values of the coefficient H*EL(1). +C When RC differs from 1 by more than CCMAX, IPUP is set to MITER +C to force PJAC to be called, if a Jacobian is involved. +C In any case, PJAC is called at least every MSBP steps. +C----------------------------------------------------------------------- + 200 IF (ABS(RC-1.0D0) .GT. CCMAX) IPUP = MITER + IF (NST .GE. NSLP+MSBP) IPUP = MITER + TN = TN + H + I1 = NQNYH + 1 + DO 215 JB = 1,NQ + I1 = I1 - NYH +CDIR$ IVDEP + DO 210 I = I1,NQNYH + 210 YH1(I) = YH1(I) + YH1(I+NYH) + 215 CONTINUE + PNORM = DMNORM (N, YH1, EWT) +C----------------------------------------------------------------------- +C Up to MAXCOR corrector iterations are taken. A convergence test is +C made on the RMS-norm of each correction, weighted by the error +C weight vector EWT. The sum of the corrections is accumulated in the +C vector ACOR(i). The YH array is not altered in the corrector loop. +C----------------------------------------------------------------------- + 220 M = 0 + RATE = 0.0D0 + DEL = 0.0D0 + DO 230 I = 1,N + 230 Y(I) = YH(I,1) + CALL F (NEQ, TN, Y, SAVF) + NFE = NFE + 1 + IF (IPUP .LE. 0) GO TO 250 +C----------------------------------------------------------------------- +C If indicated, the matrix P = I - H*EL(1)*J is reevaluated and +C preprocessed before starting the corrector iteration. IPUP is set +C to 0 as an indicator that this has been done. +C----------------------------------------------------------------------- + CALL PJAC (NEQ, Y, YH, NYH, EWT, ACOR, SAVF, WM, IWM, F, JAC) + IPUP = 0 + RC = 1.0D0 + NSLP = NST + CRATE = 0.7D0 + IF (IERPJ .NE. 0) GO TO 430 + 250 DO 260 I = 1,N + 260 ACOR(I) = 0.0D0 + 270 IF (MITER .NE. 0) GO TO 350 +C----------------------------------------------------------------------- +C In the case of functional iteration, update Y directly from +C the result of the last function evaluation. +C----------------------------------------------------------------------- + DO 290 I = 1,N + SAVF(I) = H*SAVF(I) - YH(I,2) + 290 Y(I) = SAVF(I) - ACOR(I) + DEL = DMNORM (N, Y, EWT) + DO 300 I = 1,N + Y(I) = YH(I,1) + EL(1)*SAVF(I) + 300 ACOR(I) = SAVF(I) + GO TO 400 +C----------------------------------------------------------------------- +C In the case of the chord method, compute the corrector error, +C and solve the linear system with that as right-hand side and +C P as coefficient matrix. +C----------------------------------------------------------------------- + 350 DO 360 I = 1,N + 360 Y(I) = H*SAVF(I) - (YH(I,2) + ACOR(I)) + CALL SLVS (WM, IWM, Y, SAVF) + IF (IERSL .LT. 0) GO TO 430 + IF (IERSL .GT. 0) GO TO 410 + DEL = DMNORM (N, Y, EWT) + DO 380 I = 1,N + ACOR(I) = ACOR(I) + Y(I) + 380 Y(I) = YH(I,1) + EL(1)*ACOR(I) +C----------------------------------------------------------------------- +C Test for convergence. If M .gt. 0, an estimate of the convergence +C rate constant is stored in CRATE, and this is used in the test. +C +C We first check for a change of iterates that is the size of +C roundoff error. If this occurs, the iteration has converged, and a +C new rate estimate is not formed. +C In all other cases, force at least two iterations to estimate a +C local Lipschitz constant estimate for Adams methods. +C On convergence, form PDEST = local maximum Lipschitz constant +C estimate. PDLAST is the most recent nonzero estimate. +C----------------------------------------------------------------------- + 400 CONTINUE + IF (DEL .LE. 100.0D0*PNORM*UROUND) GO TO 450 + IF (M .EQ. 0 .AND. METH .EQ. 1) GO TO 405 + IF (M .EQ. 0) GO TO 402 + RM = 1024.0D0 + IF (DEL .LE. 1024.0D0*DELP) RM = DEL/DELP + RATE = MAX(RATE,RM) + CRATE = MAX(0.2D0*CRATE,RM) + 402 DCON = DEL*MIN(1.0D0,1.5D0*CRATE)/(TESCO(2,NQ)*CONIT) + IF (DCON .GT. 1.0D0) GO TO 405 + PDEST = MAX(PDEST,RATE/ABS(H*EL(1))) + IF (PDEST .NE. 0.0D0) PDLAST = PDEST + GO TO 450 + 405 CONTINUE + M = M + 1 + IF (M .EQ. MAXCOR) GO TO 410 + IF (M .GE. 2 .AND. DEL .GT. 2.0D0*DELP) GO TO 410 + DELP = DEL + CALL F (NEQ, TN, Y, SAVF) + NFE = NFE + 1 + GO TO 270 +C----------------------------------------------------------------------- +C The corrector iteration failed to converge. +C If MITER .ne. 0 and the Jacobian is out of date, PJAC is called for +C the next try. Otherwise the YH array is retracted to its values +C before prediction, and H is reduced, if possible. If H cannot be +C reduced or MXNCF failures have occurred, exit with KFLAG = -2. +C----------------------------------------------------------------------- + 410 IF (MITER .EQ. 0 .OR. JCUR .EQ. 1) GO TO 430 + ICF = 1 + IPUP = MITER + GO TO 220 + 430 ICF = 2 + NCF = NCF + 1 + RMAX = 2.0D0 + TN = TOLD + I1 = NQNYH + 1 + DO 445 JB = 1,NQ + I1 = I1 - NYH +CDIR$ IVDEP + DO 440 I = I1,NQNYH + 440 YH1(I) = YH1(I) - YH1(I+NYH) + 445 CONTINUE + IF (IERPJ .LT. 0 .OR. IERSL .LT. 0) GO TO 680 + IF (ABS(H) .LE. HMIN*1.00001D0) GO TO 670 + IF (NCF .EQ. MXNCF) GO TO 670 + RH = 0.25D0 + IPUP = MITER + IREDO = 1 + GO TO 170 +C----------------------------------------------------------------------- +C The corrector has converged. JCUR is set to 0 +C to signal that the Jacobian involved may need updating later. +C The local error test is made and control passes to statement 500 +C if it fails. +C----------------------------------------------------------------------- + 450 JCUR = 0 + IF (M .EQ. 0) DSM = DEL/TESCO(2,NQ) + IF (M .GT. 0) DSM = DMNORM (N, ACOR, EWT)/TESCO(2,NQ) + IF (DSM .GT. 1.0D0) GO TO 500 +C----------------------------------------------------------------------- +C After a successful step, update the YH array. +C Decrease ICOUNT by 1, and if it is -1, consider switching methods. +C If a method switch is made, reset various parameters, +C rescale the YH array, and exit. If there is no switch, +C consider changing H if IALTH = 1. Otherwise decrease IALTH by 1. +C If IALTH is then 1 and NQ .lt. MAXORD, then ACOR is saved for +C use in a possible order increase on the next step. +C If a change in H is considered, an increase or decrease in order +C by one is considered also. A change in H is made only if it is by a +C factor of at least 1.1. If not, IALTH is set to 3 to prevent +C testing for that many steps. +C----------------------------------------------------------------------- + KFLAG = 0 + IREDO = 0 + NST = NST + 1 + HU = H + NQU = NQ + MUSED = METH + DO 460 J = 1,L + DO 460 I = 1,N + 460 YH(I,J) = YH(I,J) + EL(J)*ACOR(I) + ICOUNT = ICOUNT - 1 + IF (ICOUNT .GE. 0) GO TO 488 + IF (METH .EQ. 2) GO TO 480 +C----------------------------------------------------------------------- +C We are currently using an Adams method. Consider switching to BDF. +C If the current order is greater than 5, assume the problem is +C not stiff, and skip this section. +C If the Lipschitz constant and error estimate are not polluted +C by roundoff, go to 470 and perform the usual test. +C Otherwise, switch to the BDF methods if the last step was +C restricted to insure stability (irflag = 1), and stay with Adams +C method if not. When switching to BDF with polluted error estimates, +C in the absence of other information, double the step size. +C +C When the estimates are OK, we make the usual test by computing +C the step size we could have (ideally) used on this step, +C with the current (Adams) method, and also that for the BDF. +C If NQ .gt. MXORDS, we consider changing to order MXORDS on switching. +C Compare the two step sizes to decide whether to switch. +C The step size advantage must be at least RATIO = 5 to switch. +C----------------------------------------------------------------------- + IF (NQ .GT. 5) GO TO 488 + IF (DSM .GT. 100.0D0*PNORM*UROUND .AND. PDEST .NE. 0.0D0) + 1 GO TO 470 + IF (IRFLAG .EQ. 0) GO TO 488 + RH2 = 2.0D0 + NQM2 = MIN(NQ,MXORDS) + GO TO 478 + 470 CONTINUE + EXSM = 1.0D0/L + RH1 = 1.0D0/(1.2D0*DSM**EXSM + 0.0000012D0) + RH1IT = 2.0D0*RH1 + PDH = PDLAST*ABS(H) + IF (PDH*RH1 .GT. 0.00001D0) RH1IT = SM1(NQ)/PDH + RH1 = MIN(RH1,RH1IT) + IF (NQ .LE. MXORDS) GO TO 474 + NQM2 = MXORDS + LM2 = MXORDS + 1 + EXM2 = 1.0D0/LM2 + LM2P1 = LM2 + 1 + DM2 = DMNORM (N, YH(1,LM2P1), EWT)/CM2(MXORDS) + RH2 = 1.0D0/(1.2D0*DM2**EXM2 + 0.0000012D0) + GO TO 476 + 474 DM2 = DSM*(CM1(NQ)/CM2(NQ)) + RH2 = 1.0D0/(1.2D0*DM2**EXSM + 0.0000012D0) + NQM2 = NQ + 476 CONTINUE + IF (RH2 .LT. RATIO*RH1) GO TO 488 +C THE SWITCH TEST PASSED. RESET RELEVANT QUANTITIES FOR BDF. ---------- + 478 RH = RH2 + ICOUNT = 20 + METH = 2 + MITER = JTYP + PDLAST = 0.0D0 + NQ = NQM2 + L = NQ + 1 + GO TO 170 +C----------------------------------------------------------------------- +C We are currently using a BDF method. Consider switching to Adams. +C Compute the step size we could have (ideally) used on this step, +C with the current (BDF) method, and also that for the Adams. +C If NQ .gt. MXORDN, we consider changing to order MXORDN on switching. +C Compare the two step sizes to decide whether to switch. +C The step size advantage must be at least 5/RATIO = 1 to switch. +C If the step size for Adams would be so small as to cause +C roundoff pollution, we stay with BDF. +C----------------------------------------------------------------------- + 480 CONTINUE + EXSM = 1.0D0/L + IF (MXORDN .GE. NQ) GO TO 484 + NQM1 = MXORDN + LM1 = MXORDN + 1 + EXM1 = 1.0D0/LM1 + LM1P1 = LM1 + 1 + DM1 = DMNORM (N, YH(1,LM1P1), EWT)/CM1(MXORDN) + RH1 = 1.0D0/(1.2D0*DM1**EXM1 + 0.0000012D0) + GO TO 486 + 484 DM1 = DSM*(CM2(NQ)/CM1(NQ)) + RH1 = 1.0D0/(1.2D0*DM1**EXSM + 0.0000012D0) + NQM1 = NQ + EXM1 = EXSM + 486 RH1IT = 2.0D0*RH1 + PDH = PDNORM*ABS(H) + IF (PDH*RH1 .GT. 0.00001D0) RH1IT = SM1(NQM1)/PDH + RH1 = MIN(RH1,RH1IT) + RH2 = 1.0D0/(1.2D0*DSM**EXSM + 0.0000012D0) + IF (RH1*RATIO .LT. 5.0D0*RH2) GO TO 488 + ALPHA = MAX(0.001D0,RH1) + DM1 = (ALPHA**EXM1)*DM1 + IF (DM1 .LE. 1000.0D0*UROUND*PNORM) GO TO 488 +C The switch test passed. Reset relevant quantities for Adams. -------- + RH = RH1 + ICOUNT = 20 + METH = 1 + MITER = 0 + PDLAST = 0.0D0 + NQ = NQM1 + L = NQ + 1 + GO TO 170 +C +C No method switch is being made. Do the usual step/order selection. -- + 488 CONTINUE + IALTH = IALTH - 1 + IF (IALTH .EQ. 0) GO TO 520 + IF (IALTH .GT. 1) GO TO 700 + IF (L .EQ. LMAX) GO TO 700 + DO 490 I = 1,N + 490 YH(I,LMAX) = ACOR(I) + GO TO 700 +C----------------------------------------------------------------------- +C The error test failed. KFLAG keeps track of multiple failures. +C Restore TN and the YH array to their previous values, and prepare +C to try the step again. Compute the optimum step size for this or +C one lower order. After 2 or more failures, H is forced to decrease +C by a factor of 0.2 or less. +C----------------------------------------------------------------------- + 500 KFLAG = KFLAG - 1 + TN = TOLD + I1 = NQNYH + 1 + DO 515 JB = 1,NQ + I1 = I1 - NYH +CDIR$ IVDEP + DO 510 I = I1,NQNYH + 510 YH1(I) = YH1(I) - YH1(I+NYH) + 515 CONTINUE + RMAX = 2.0D0 + IF (ABS(H) .LE. HMIN*1.00001D0) GO TO 660 + IF (KFLAG .LE. -3) GO TO 640 + IREDO = 2 + RHUP = 0.0D0 + GO TO 540 +C----------------------------------------------------------------------- +C Regardless of the success or failure of the step, factors +C RHDN, RHSM, and RHUP are computed, by which H could be multiplied +C at order NQ - 1, order NQ, or order NQ + 1, respectively. +C In the case of failure, RHUP = 0.0 to avoid an order increase. +C The largest of these is determined and the new order chosen +C accordingly. If the order is to be increased, we compute one +C additional scaled derivative. +C----------------------------------------------------------------------- + 520 RHUP = 0.0D0 + IF (L .EQ. LMAX) GO TO 540 + DO 530 I = 1,N + 530 SAVF(I) = ACOR(I) - YH(I,LMAX) + DUP = DMNORM (N, SAVF, EWT)/TESCO(3,NQ) + EXUP = 1.0D0/(L+1) + RHUP = 1.0D0/(1.4D0*DUP**EXUP + 0.0000014D0) + 540 EXSM = 1.0D0/L + RHSM = 1.0D0/(1.2D0*DSM**EXSM + 0.0000012D0) + RHDN = 0.0D0 + IF (NQ .EQ. 1) GO TO 550 + DDN = DMNORM (N, YH(1,L), EWT)/TESCO(1,NQ) + EXDN = 1.0D0/NQ + RHDN = 1.0D0/(1.3D0*DDN**EXDN + 0.0000013D0) +C If METH = 1, limit RH according to the stability region also. -------- + 550 IF (METH .EQ. 2) GO TO 560 + PDH = MAX(ABS(H)*PDLAST,0.000001D0) + IF (L .LT. LMAX) RHUP = MIN(RHUP,SM1(L)/PDH) + RHSM = MIN(RHSM,SM1(NQ)/PDH) + IF (NQ .GT. 1) RHDN = MIN(RHDN,SM1(NQ-1)/PDH) + PDEST = 0.0D0 + 560 IF (RHSM .GE. RHUP) GO TO 570 + IF (RHUP .GT. RHDN) GO TO 590 + GO TO 580 + 570 IF (RHSM .LT. RHDN) GO TO 580 + NEWQ = NQ + RH = RHSM + GO TO 620 + 580 NEWQ = NQ - 1 + RH = RHDN + IF (KFLAG .LT. 0 .AND. RH .GT. 1.0D0) RH = 1.0D0 + GO TO 620 + 590 NEWQ = L + RH = RHUP + IF (RH .LT. 1.1D0) GO TO 610 + R = EL(L)/L + DO 600 I = 1,N + 600 YH(I,NEWQ+1) = ACOR(I)*R + GO TO 630 + 610 IALTH = 3 + GO TO 700 +C If METH = 1 and H is restricted by stability, bypass 10 percent test. + 620 IF (METH .EQ. 2) GO TO 622 + IF (RH*PDH*1.00001D0 .GE. SM1(NEWQ)) GO TO 625 + 622 IF (KFLAG .EQ. 0 .AND. RH .LT. 1.1D0) GO TO 610 + 625 IF (KFLAG .LE. -2) RH = MIN(RH,0.2D0) +C----------------------------------------------------------------------- +C If there is a change of order, reset NQ, L, and the coefficients. +C In any case H is reset according to RH and the YH array is rescaled. +C Then exit from 690 if the step was OK, or redo the step otherwise. +C----------------------------------------------------------------------- + IF (NEWQ .EQ. NQ) GO TO 170 + 630 NQ = NEWQ + L = NQ + 1 + IRET = 2 + GO TO 150 +C----------------------------------------------------------------------- +C Control reaches this section if 3 or more failures have occured. +C If 10 failures have occurred, exit with KFLAG = -1. +C It is assumed that the derivatives that have accumulated in the +C YH array have errors of the wrong order. Hence the first +C derivative is recomputed, and the order is set to 1. Then +C H is reduced by a factor of 10, and the step is retried, +C until it succeeds or H reaches HMIN. +C----------------------------------------------------------------------- + 640 IF (KFLAG .EQ. -10) GO TO 660 + RH = 0.1D0 + RH = MAX(HMIN/ABS(H),RH) + H = H*RH + DO 645 I = 1,N + 645 Y(I) = YH(I,1) + CALL F (NEQ, TN, Y, SAVF) + NFE = NFE + 1 + DO 650 I = 1,N + 650 YH(I,2) = H*SAVF(I) + IPUP = MITER + IALTH = 5 + IF (NQ .EQ. 1) GO TO 200 + NQ = 1 + L = 2 + IRET = 3 + GO TO 150 +C----------------------------------------------------------------------- +C All returns are made through this section. H is saved in HOLD +C to allow the caller to change H on the next step. +C----------------------------------------------------------------------- + 660 KFLAG = -1 + GO TO 720 + 670 KFLAG = -2 + GO TO 720 + 680 KFLAG = -3 + GO TO 720 + 690 RMAX = 10.0D0 + 700 R = 1.0D0/TESCO(2,NQU) + DO 710 I = 1,N + 710 ACOR(I) = ACOR(I)*R + 720 HOLD = H + JSTART = 1 + RETURN +C----------------------- End of Subroutine DSTODA ---------------------- + END +*DECK DPRJA + SUBROUTINE DPRJA (NEQ, Y, YH, NYH, EWT, FTEM, SAVF, WM, IWM, + 1 F, JAC) + EXTERNAL F, JAC + INTEGER NEQ, NYH, IWM + DOUBLE PRECISION Y, YH, EWT, FTEM, SAVF, WM + DIMENSION NEQ(*), Y(*), YH(NYH,*), EWT(*), FTEM(*), SAVF(*), + 1 WM(*), IWM(*) + INTEGER IOWND, IOWNS, + 1 ICF, IERPJ, IERSL, JCUR, JSTART, KFLAG, L, + 2 LYH, LEWT, LACOR, LSAVF, LWM, LIWM, METH, MITER, + 3 MAXORD, MAXCOR, MSBP, MXNCF, N, NQ, NST, NFE, NJE, NQU + INTEGER IOWND2, IOWNS2, JTYP, MUSED, MXORDN, MXORDS + DOUBLE PRECISION ROWNS, + 1 CCMAX, EL0, H, HMIN, HMXI, HU, RC, TN, UROUND + DOUBLE PRECISION ROWND2, ROWNS2, PDNORM + COMMON /DLS001/ ROWNS(209), + 1 CCMAX, EL0, H, HMIN, HMXI, HU, RC, TN, UROUND, + 2 IOWND(6), IOWNS(6), + 3 ICF, IERPJ, IERSL, JCUR, JSTART, KFLAG, L, + 4 LYH, LEWT, LACOR, LSAVF, LWM, LIWM, METH, MITER, + 5 MAXORD, MAXCOR, MSBP, MXNCF, N, NQ, NST, NFE, NJE, NQU + COMMON /DLSA01/ ROWND2, ROWNS2(20), PDNORM, + 1 IOWND2(3), IOWNS2(2), JTYP, MUSED, MXORDN, MXORDS + INTEGER I, I1, I2, IER, II, J, J1, JJ, LENP, + 1 MBA, MBAND, MEB1, MEBAND, ML, ML3, MU, NP1 + DOUBLE PRECISION CON, FAC, HL0, R, R0, SRUR, YI, YJ, YJJ, + 1 DMNORM, DFNORM, DBNORM +C----------------------------------------------------------------------- +C DPRJA is called by DSTODA to compute and process the matrix +C P = I - H*EL(1)*J , where J is an approximation to the Jacobian. +C Here J is computed by the user-supplied routine JAC if +C MITER = 1 or 4 or by finite differencing if MITER = 2 or 5. +C J, scaled by -H*EL(1), is stored in WM. Then the norm of J (the +C matrix norm consistent with the weighted max-norm on vectors given +C by DMNORM) is computed, and J is overwritten by P. P is then +C subjected to LU decomposition in preparation for later solution +C of linear systems with P as coefficient matrix. This is done +C by DGEFA if MITER = 1 or 2, and by DGBFA if MITER = 4 or 5. +C +C In addition to variables described previously, communication +C with DPRJA uses the following: +C Y = array containing predicted values on entry. +C FTEM = work array of length N (ACOR in DSTODA). +C SAVF = array containing f evaluated at predicted y. +C WM = real work space for matrices. On output it contains the +C LU decomposition of P. +C Storage of matrix elements starts at WM(3). +C WM also contains the following matrix-related data: +C WM(1) = SQRT(UROUND), used in numerical Jacobian increments. +C IWM = integer work space containing pivot information, starting at +C IWM(21). IWM also contains the band parameters +C ML = IWM(1) and MU = IWM(2) if MITER is 4 or 5. +C EL0 = EL(1) (input). +C PDNORM= norm of Jacobian matrix. (Output). +C IERPJ = output error flag, = 0 if no trouble, .gt. 0 if +C P matrix found to be singular. +C JCUR = output flag = 1 to indicate that the Jacobian matrix +C (or approximation) is now current. +C This routine also uses the Common variables EL0, H, TN, UROUND, +C MITER, N, NFE, and NJE. +C----------------------------------------------------------------------- + NJE = NJE + 1 + IERPJ = 0 + JCUR = 1 + HL0 = H*EL0 + GO TO (100, 200, 300, 400, 500), MITER +C If MITER = 1, call JAC and multiply by scalar. ----------------------- + 100 LENP = N*N + DO 110 I = 1,LENP + 110 WM(I+2) = 0.0D0 + CALL JAC (NEQ, TN, Y, 0, 0, WM(3), N) + CON = -HL0 + DO 120 I = 1,LENP + 120 WM(I+2) = WM(I+2)*CON + GO TO 240 +C If MITER = 2, make N calls to F to approximate J. -------------------- + 200 FAC = DMNORM (N, SAVF, EWT) + R0 = 1000.0D0*ABS(H)*UROUND*N*FAC + IF (R0 .EQ. 0.0D0) R0 = 1.0D0 + SRUR = WM(1) + J1 = 2 + DO 230 J = 1,N + YJ = Y(J) + R = MAX(SRUR*ABS(YJ),R0/EWT(J)) + Y(J) = Y(J) + R + FAC = -HL0/R + CALL F (NEQ, TN, Y, FTEM) + DO 220 I = 1,N + 220 WM(I+J1) = (FTEM(I) - SAVF(I))*FAC + Y(J) = YJ + J1 = J1 + N + 230 CONTINUE + NFE = NFE + N + 240 CONTINUE +C Compute norm of Jacobian. -------------------------------------------- + PDNORM = DFNORM (N, WM(3), EWT)/ABS(HL0) +C Add identity matrix. ------------------------------------------------- + J = 3 + NP1 = N + 1 + DO 250 I = 1,N + WM(J) = WM(J) + 1.0D0 + 250 J = J + NP1 +C Do LU decomposition on P. -------------------------------------------- + CALL DGEFA (WM(3), N, N, IWM(21), IER) + IF (IER .NE. 0) IERPJ = 1 + RETURN +C Dummy block only, since MITER is never 3 in this routine. ------------ + 300 RETURN +C If MITER = 4, call JAC and multiply by scalar. ----------------------- + 400 ML = IWM(1) + MU = IWM(2) + ML3 = ML + 3 + MBAND = ML + MU + 1 + MEBAND = MBAND + ML + LENP = MEBAND*N + DO 410 I = 1,LENP + 410 WM(I+2) = 0.0D0 + CALL JAC (NEQ, TN, Y, ML, MU, WM(ML3), MEBAND) + CON = -HL0 + DO 420 I = 1,LENP + 420 WM(I+2) = WM(I+2)*CON + GO TO 570 +C If MITER = 5, make MBAND calls to F to approximate J. ---------------- + 500 ML = IWM(1) + MU = IWM(2) + MBAND = ML + MU + 1 + MBA = MIN(MBAND,N) + MEBAND = MBAND + ML + MEB1 = MEBAND - 1 + SRUR = WM(1) + FAC = DMNORM (N, SAVF, EWT) + R0 = 1000.0D0*ABS(H)*UROUND*N*FAC + IF (R0 .EQ. 0.0D0) R0 = 1.0D0 + DO 560 J = 1,MBA + DO 530 I = J,N,MBAND + YI = Y(I) + R = MAX(SRUR*ABS(YI),R0/EWT(I)) + 530 Y(I) = Y(I) + R + CALL F (NEQ, TN, Y, FTEM) + DO 550 JJ = J,N,MBAND + Y(JJ) = YH(JJ,1) + YJJ = Y(JJ) + R = MAX(SRUR*ABS(YJJ),R0/EWT(JJ)) + FAC = -HL0/R + I1 = MAX(JJ-MU,1) + I2 = MIN(JJ+ML,N) + II = JJ*MEB1 - ML + 2 + DO 540 I = I1,I2 + 540 WM(II+I) = (FTEM(I) - SAVF(I))*FAC + 550 CONTINUE + 560 CONTINUE + NFE = NFE + MBA + 570 CONTINUE +C Compute norm of Jacobian. -------------------------------------------- + PDNORM = DBNORM (N, WM(ML+3), MEBAND, ML, MU, EWT)/ABS(HL0) +C Add identity matrix. ------------------------------------------------- + II = MBAND + 2 + DO 580 I = 1,N + WM(II) = WM(II) + 1.0D0 + 580 II = II + MEBAND +C Do LU decomposition of P. -------------------------------------------- + CALL DGBFA (WM(3), MEBAND, N, ML, MU, IWM(21), IER) + IF (IER .NE. 0) IERPJ = 1 + RETURN +C----------------------- End of Subroutine DPRJA ----------------------- + END +*DECK DMNORM + DOUBLE PRECISION FUNCTION DMNORM (N, V, W) +C----------------------------------------------------------------------- +C This function routine computes the weighted max-norm +C of the vector of length N contained in the array V, with weights +C contained in the array w of length N: +C DMNORM = MAX(i=1,...,N) ABS(V(i))*W(i) +C----------------------------------------------------------------------- + INTEGER N, I + DOUBLE PRECISION V, W, VM + DIMENSION V(N), W(N) + VM = 0.0D0 + DO 10 I = 1,N + 10 VM = MAX(VM,ABS(V(I))*W(I)) + DMNORM = VM + RETURN +C----------------------- End of Function DMNORM ------------------------ + END +*DECK DFNORM + DOUBLE PRECISION FUNCTION DFNORM (N, A, W) +C----------------------------------------------------------------------- +C This function computes the norm of a full N by N matrix, +C stored in the array A, that is consistent with the weighted max-norm +C on vectors, with weights stored in the array W: +C DFNORM = MAX(i=1,...,N) ( W(i) * Sum(j=1,...,N) ABS(a(i,j))/W(j) ) +C----------------------------------------------------------------------- + INTEGER N, I, J + DOUBLE PRECISION A, W, AN, SUM + DIMENSION A(N,N), W(N) + AN = 0.0D0 + DO 20 I = 1,N + SUM = 0.0D0 + DO 10 J = 1,N + 10 SUM = SUM + ABS(A(I,J))/W(J) + AN = MAX(AN,SUM*W(I)) + 20 CONTINUE + DFNORM = AN + RETURN +C----------------------- End of Function DFNORM ------------------------ + END +*DECK DBNORM + DOUBLE PRECISION FUNCTION DBNORM (N, A, NRA, ML, MU, W) +C----------------------------------------------------------------------- +C This function computes the norm of a banded N by N matrix, +C stored in the array A, that is consistent with the weighted max-norm +C on vectors, with weights stored in the array W. +C ML and MU are the lower and upper half-bandwidths of the matrix. +C NRA is the first dimension of the A array, NRA .ge. ML+MU+1. +C In terms of the matrix elements a(i,j), the norm is given by: +C DBNORM = MAX(i=1,...,N) ( W(i) * Sum(j=1,...,N) ABS(a(i,j))/W(j) ) +C----------------------------------------------------------------------- + INTEGER N, NRA, ML, MU + INTEGER I, I1, JLO, JHI, J + DOUBLE PRECISION A, W + DOUBLE PRECISION AN, SUM + DIMENSION A(NRA,N), W(N) + AN = 0.0D0 + DO 20 I = 1,N + SUM = 0.0D0 + I1 = I + MU + 1 + JLO = MAX(I-ML,1) + JHI = MIN(I+MU,N) + DO 10 J = JLO,JHI + 10 SUM = SUM + ABS(A(I1-J,J))/W(J) + AN = MAX(AN,SUM*W(I)) + 20 CONTINUE + DBNORM = AN + RETURN +C----------------------- End of Function DBNORM ------------------------ + END +*DECK DSRCMA + SUBROUTINE DSRCMA (RSAV, ISAV, JOB) +C----------------------------------------------------------------------- +C This routine saves or restores (depending on JOB) the contents of +C the Common blocks DLS001, DLSA01, which are used +C internally by one or more ODEPACK solvers. +C +C RSAV = real array of length 240 or more. +C ISAV = integer array of length 46 or more. +C JOB = flag indicating to save or restore the Common blocks: +C JOB = 1 if Common is to be saved (written to RSAV/ISAV) +C JOB = 2 if Common is to be restored (read from RSAV/ISAV) +C A call with JOB = 2 presumes a prior call with JOB = 1. +C----------------------------------------------------------------------- + INTEGER ISAV, JOB + INTEGER ILS, ILSA + INTEGER I, LENRLS, LENILS, LENRLA, LENILA + DOUBLE PRECISION RSAV + DOUBLE PRECISION RLS, RLSA + DIMENSION RSAV(*), ISAV(*) + SAVE LENRLS, LENILS, LENRLA, LENILA + COMMON /DLS001/ RLS(218), ILS(37) + COMMON /DLSA01/ RLSA(22), ILSA(9) + DATA LENRLS/218/, LENILS/37/, LENRLA/22/, LENILA/9/ +C + IF (JOB .EQ. 2) GO TO 100 + DO 10 I = 1,LENRLS + 10 RSAV(I) = RLS(I) + DO 15 I = 1,LENRLA + 15 RSAV(LENRLS+I) = RLSA(I) +C + DO 20 I = 1,LENILS + 20 ISAV(I) = ILS(I) + DO 25 I = 1,LENILA + 25 ISAV(LENILS+I) = ILSA(I) +C + RETURN +C + 100 CONTINUE + DO 110 I = 1,LENRLS + 110 RLS(I) = RSAV(I) + DO 115 I = 1,LENRLA + 115 RLSA(I) = RSAV(LENRLS+I) +C + DO 120 I = 1,LENILS + 120 ILS(I) = ISAV(I) + DO 125 I = 1,LENILA + 125 ILSA(I) = ISAV(LENILS+I) +C + RETURN +C----------------------- End of Subroutine DSRCMA ---------------------- + END +*DECK DRCHEK + SUBROUTINE DRCHEK (JOB, G, NEQ, Y, YH,NYH, G0, G1, GX, JROOT, IRT) + EXTERNAL G + INTEGER JOB, NEQ, NYH, JROOT, IRT + DOUBLE PRECISION Y, YH, G0, G1, GX + DIMENSION NEQ(*), Y(*), YH(NYH,*), G0(*), G1(*), GX(*), JROOT(*) + INTEGER IOWND, IOWNS, + 1 ICF, IERPJ, IERSL, JCUR, JSTART, KFLAG, L, + 2 LYH, LEWT, LACOR, LSAVF, LWM, LIWM, METH, MITER, + 3 MAXORD, MAXCOR, MSBP, MXNCF, N, NQ, NST, NFE, NJE, NQU + INTEGER IOWND3, IOWNR3, IRFND, ITASKC, NGC, NGE + DOUBLE PRECISION ROWNS, + 1 CCMAX, EL0, H, HMIN, HMXI, HU, RC, TN, UROUND + DOUBLE PRECISION ROWNR3, T0, TLAST, TOUTC + COMMON /DLS001/ ROWNS(209), + 1 CCMAX, EL0, H, HMIN, HMXI, HU, RC, TN, UROUND, + 2 IOWND(6), IOWNS(6), + 3 ICF, IERPJ, IERSL, JCUR, JSTART, KFLAG, L, + 4 LYH, LEWT, LACOR, LSAVF, LWM, LIWM, METH, MITER, + 5 MAXORD, MAXCOR, MSBP, MXNCF, N, NQ, NST, NFE, NJE, NQU + COMMON /DLSR01/ ROWNR3(2), T0, TLAST, TOUTC, + 1 IOWND3(3), IOWNR3(2), IRFND, ITASKC, NGC, NGE + INTEGER I, IFLAG, JFLAG + DOUBLE PRECISION HMING, T1, TEMP1, TEMP2, X + LOGICAL ZROOT +C----------------------------------------------------------------------- +C This routine checks for the presence of a root in the vicinity of +C the current T, in a manner depending on the input flag JOB. It calls +C Subroutine DROOTS to locate the root as precisely as possible. +C +C In addition to variables described previously, DRCHEK +C uses the following for communication: +C JOB = integer flag indicating type of call: +C JOB = 1 means the problem is being initialized, and DRCHEK +C is to look for a root at or very near the initial T. +C JOB = 2 means a continuation call to the solver was just +C made, and DRCHEK is to check for a root in the +C relevant part of the step last taken. +C JOB = 3 means a successful step was just taken, and DRCHEK +C is to look for a root in the interval of the step. +C G0 = array of length NG, containing the value of g at T = T0. +C G0 is input for JOB .ge. 2, and output in all cases. +C G1,GX = arrays of length NG for work space. +C IRT = completion flag: +C IRT = 0 means no root was found. +C IRT = -1 means JOB = 1 and a root was found too near to T. +C IRT = 1 means a legitimate root was found (JOB = 2 or 3). +C On return, T0 is the root location, and Y is the +C corresponding solution vector. +C T0 = value of T at one endpoint of interval of interest. Only +C roots beyond T0 in the direction of integration are sought. +C T0 is input if JOB .ge. 2, and output in all cases. +C T0 is updated by DRCHEK, whether a root is found or not. +C TLAST = last value of T returned by the solver (input only). +C TOUTC = copy of TOUT (input only). +C IRFND = input flag showing whether the last step taken had a root. +C IRFND = 1 if it did, = 0 if not. +C ITASKC = copy of ITASK (input only). +C NGC = copy of NG (input only). +C----------------------------------------------------------------------- + IRT = 0 + DO 10 I = 1,NGC + 10 JROOT(I) = 0 + HMING = (ABS(TN) + ABS(H))*UROUND*100.0D0 +C + GO TO (100, 200, 300), JOB +C +C Evaluate g at initial T, and check for zero values. ------------------ + 100 CONTINUE + T0 = TN + CALL G (NEQ, T0, Y, NGC, G0) + NGE = 1 + ZROOT = .FALSE. + DO 110 I = 1,NGC + 110 IF (ABS(G0(I)) .LE. 0.0D0) ZROOT = .TRUE. + IF (.NOT. ZROOT) GO TO 190 +C g has a zero at T. Look at g at T + (small increment). -------------- + TEMP2 = MAX(HMING/ABS(H), 0.1D0) + TEMP1 = TEMP2*H + T0 = T0 + TEMP1 + DO 120 I = 1,N + 120 Y(I) = Y(I) + TEMP2*YH(I,2) + CALL G (NEQ, T0, Y, NGC, G0) + NGE = NGE + 1 + ZROOT = .FALSE. + DO 130 I = 1,NGC + 130 IF (ABS(G0(I)) .LE. 0.0D0) ZROOT = .TRUE. + IF (.NOT. ZROOT) GO TO 190 +C g has a zero at T and also close to T. Take error return. ----------- + IRT = -1 + RETURN +C + 190 CONTINUE + RETURN +C +C + 200 CONTINUE + IF (IRFND .EQ. 0) GO TO 260 +C If a root was found on the previous step, evaluate G0 = g(T0). ------- + CALL DINTDY (T0, 0, YH, NYH, Y, IFLAG) + CALL G (NEQ, T0, Y, NGC, G0) + NGE = NGE + 1 + ZROOT = .FALSE. + DO 210 I = 1,NGC + 210 IF (ABS(G0(I)) .LE. 0.0D0) ZROOT = .TRUE. + IF (.NOT. ZROOT) GO TO 260 +C g has a zero at T0. Look at g at T + (small increment). ------------- + TEMP1 = SIGN(HMING,H) + T0 = T0 + TEMP1 + IF ((T0 - TN)*H .LT. 0.0D0) GO TO 230 + TEMP2 = TEMP1/H + DO 220 I = 1,N + 220 Y(I) = Y(I) + TEMP2*YH(I,2) + GO TO 240 + 230 CALL DINTDY (T0, 0, YH, NYH, Y, IFLAG) + 240 CALL G (NEQ, T0, Y, NGC, G0) + NGE = NGE + 1 + ZROOT = .FALSE. + DO 250 I = 1,NGC + IF (ABS(G0(I)) .GT. 0.0D0) GO TO 250 + JROOT(I) = 1 + ZROOT = .TRUE. + 250 CONTINUE + IF (.NOT. ZROOT) GO TO 260 +C g has a zero at T0 and also close to T0. Return root. --------------- + IRT = 1 + RETURN +C G0 has no zero components. Proceed to check relevant interval. ------ + 260 IF (TN .EQ. TLAST) GO TO 390 +C + 300 CONTINUE +C Set T1 to TN or TOUTC, whichever comes first, and get g at T1. ------- + IF (ITASKC.EQ.2 .OR. ITASKC.EQ.3 .OR. ITASKC.EQ.5) GO TO 310 + IF ((TOUTC - TN)*H .GE. 0.0D0) GO TO 310 + T1 = TOUTC + IF ((T1 - T0)*H .LE. 0.0D0) GO TO 390 + CALL DINTDY (T1, 0, YH, NYH, Y, IFLAG) + GO TO 330 + 310 T1 = TN + DO 320 I = 1,N + 320 Y(I) = YH(I,1) + 330 CALL G (NEQ, T1, Y, NGC, G1) + NGE = NGE + 1 +C Call DROOTS to search for root in interval from T0 to T1. ------------ + JFLAG = 0 + 350 CONTINUE + CALL DROOTS (NGC, HMING, JFLAG, T0, T1, G0, G1, GX, X, JROOT) + IF (JFLAG .GT. 1) GO TO 360 + CALL DINTDY (X, 0, YH, NYH, Y, IFLAG) + CALL G (NEQ, X, Y, NGC, GX) + NGE = NGE + 1 + GO TO 350 + 360 T0 = X + CALL DCOPY (NGC, GX, 1, G0, 1) + IF (JFLAG .EQ. 4) GO TO 390 +C Found a root. Interpolate to X and return. -------------------------- + CALL DINTDY (X, 0, YH, NYH, Y, IFLAG) + IRT = 1 + RETURN +C + 390 CONTINUE + RETURN +C----------------------- End of Subroutine DRCHEK ---------------------- + END +*DECK DROOTS + SUBROUTINE DROOTS (NG, HMIN, JFLAG, X0, X1, G0, G1, GX, X, JROOT) + INTEGER NG, JFLAG, JROOT + DOUBLE PRECISION HMIN, X0, X1, G0, G1, GX, X + DIMENSION G0(NG), G1(NG), GX(NG), JROOT(NG) + INTEGER IOWND3, IMAX, LAST, IDUM3 + DOUBLE PRECISION ALPHA, X2, RDUM3 + COMMON /DLSR01/ ALPHA, X2, RDUM3(3), + 1 IOWND3(3), IMAX, LAST, IDUM3(4) +C----------------------------------------------------------------------- +C This subroutine finds the leftmost root of a set of arbitrary +C functions gi(x) (i = 1,...,NG) in an interval (X0,X1). Only roots +C of odd multiplicity (i.e. changes of sign of the gi) are found. +C Here the sign of X1 - X0 is arbitrary, but is constant for a given +C problem, and -leftmost- means nearest to X0. +C The values of the vector-valued function g(x) = (gi, i=1...NG) +C are communicated through the call sequence of DROOTS. +C The method used is the Illinois algorithm. +C +C Reference: +C Kathie L. Hiebert and Lawrence F. Shampine, Implicitly Defined +C Output Points for Solutions of ODEs, Sandia Report SAND80-0180, +C February 1980. +C +C Description of parameters. +C +C NG = number of functions gi, or the number of components of +C the vector valued function g(x). Input only. +C +C HMIN = resolution parameter in X. Input only. When a root is +C found, it is located only to within an error of HMIN in X. +C Typically, HMIN should be set to something on the order of +C 100 * UROUND * MAX(ABS(X0),ABS(X1)), +C where UROUND is the unit roundoff of the machine. +C +C JFLAG = integer flag for input and output communication. +C +C On input, set JFLAG = 0 on the first call for the problem, +C and leave it unchanged until the problem is completed. +C (The problem is completed when JFLAG .ge. 2 on return.) +C +C On output, JFLAG has the following values and meanings: +C JFLAG = 1 means DROOTS needs a value of g(x). Set GX = g(X) +C and call DROOTS again. +C JFLAG = 2 means a root has been found. The root is +C at X, and GX contains g(X). (Actually, X is the +C rightmost approximation to the root on an interval +C (X0,X1) of size HMIN or less.) +C JFLAG = 3 means X = X1 is a root, with one or more of the gi +C being zero at X1 and no sign changes in (X0,X1). +C GX contains g(X) on output. +C JFLAG = 4 means no roots (of odd multiplicity) were +C found in (X0,X1) (no sign changes). +C +C X0,X1 = endpoints of the interval where roots are sought. +C X1 and X0 are input when JFLAG = 0 (first call), and +C must be left unchanged between calls until the problem is +C completed. X0 and X1 must be distinct, but X1 - X0 may be +C of either sign. However, the notion of -left- and -right- +C will be used to mean nearer to X0 or X1, respectively. +C When JFLAG .ge. 2 on return, X0 and X1 are output, and +C are the endpoints of the relevant interval. +C +C G0,G1 = arrays of length NG containing the vectors g(X0) and g(X1), +C respectively. When JFLAG = 0, G0 and G1 are input and +C none of the G0(i) should be zero. +C When JFLAG .ge. 2 on return, G0 and G1 are output. +C +C GX = array of length NG containing g(X). GX is input +C when JFLAG = 1, and output when JFLAG .ge. 2. +C +C X = independent variable value. Output only. +C When JFLAG = 1 on output, X is the point at which g(x) +C is to be evaluated and loaded into GX. +C When JFLAG = 2 or 3, X is the root. +C When JFLAG = 4, X is the right endpoint of the interval, X1. +C +C JROOT = integer array of length NG. Output only. +C When JFLAG = 2 or 3, JROOT indicates which components +C of g(x) have a root at X. JROOT(i) is 1 if the i-th +C component has a root, and JROOT(i) = 0 otherwise. +C----------------------------------------------------------------------- + INTEGER I, IMXOLD, NXLAST + DOUBLE PRECISION T2, TMAX, FRACINT, FRACSUB, ZERO,HALF,TENTH,FIVE + LOGICAL ZROOT, SGNCHG, XROOT + SAVE ZERO, HALF, TENTH, FIVE + DATA ZERO/0.0D0/, HALF/0.5D0/, TENTH/0.1D0/, FIVE/5.0D0/ +C + IF (JFLAG .EQ. 1) GO TO 200 +C JFLAG .ne. 1. Check for change in sign of g or zero at X1. ---------- + IMAX = 0 + TMAX = ZERO + ZROOT = .FALSE. + DO 120 I = 1,NG + IF (ABS(G1(I)) .GT. ZERO) GO TO 110 + ZROOT = .TRUE. + GO TO 120 +C At this point, G0(i) has been checked and cannot be zero. ------------ + 110 IF (SIGN(1.0D0,G0(I)) .EQ. SIGN(1.0D0,G1(I))) GO TO 120 + T2 = ABS(G1(I)/(G1(I)-G0(I))) + IF (T2 .LE. TMAX) GO TO 120 + TMAX = T2 + IMAX = I + 120 CONTINUE + IF (IMAX .GT. 0) GO TO 130 + SGNCHG = .FALSE. + GO TO 140 + 130 SGNCHG = .TRUE. + 140 IF (.NOT. SGNCHG) GO TO 400 +C There is a sign change. Find the first root in the interval. -------- + XROOT = .FALSE. + NXLAST = 0 + LAST = 1 +C +C Repeat until the first root in the interval is found. Loop point. --- + 150 CONTINUE + IF (XROOT) GO TO 300 + IF (NXLAST .EQ. LAST) GO TO 160 + ALPHA = 1.0D0 + GO TO 180 + 160 IF (LAST .EQ. 0) GO TO 170 + ALPHA = 0.5D0*ALPHA + GO TO 180 + 170 ALPHA = 2.0D0*ALPHA + 180 X2 = X1 - (X1 - X0)*G1(IMAX) / (G1(IMAX) - ALPHA*G0(IMAX)) +C If X2 is too close to X0 or X1, adjust it inward, by a fractional ---- +C distance that is between 0.1 and 0.5. -------------------------------- + IF (ABS(X2 - X0) < HALF*HMIN) THEN + FRACINT = ABS(X1 - X0)/HMIN + FRACSUB = TENTH + IF (FRACINT .LE. FIVE) FRACSUB = HALF/FRACINT + X2 = X0 + FRACSUB*(X1 - X0) + ENDIF + IF (ABS(X1 - X2) < HALF*HMIN) THEN + FRACINT = ABS(X1 - X0)/HMIN + FRACSUB = TENTH + IF (FRACINT .LE. FIVE) FRACSUB = HALF/FRACINT + X2 = X1 - FRACSUB*(X1 - X0) + ENDIF + JFLAG = 1 + X = X2 +C Return to the calling routine to get a value of GX = g(X). ----------- + RETURN +C Check to see in which interval g changes sign. ----------------------- + 200 IMXOLD = IMAX + IMAX = 0 + TMAX = ZERO + ZROOT = .FALSE. + DO 220 I = 1,NG + IF (ABS(GX(I)) .GT. ZERO) GO TO 210 + ZROOT = .TRUE. + GO TO 220 +C Neither G0(i) nor GX(i) can be zero at this point. ------------------- + 210 IF (SIGN(1.0D0,G0(I)) .EQ. SIGN(1.0D0,GX(I))) GO TO 220 + T2 = ABS(GX(I)/(GX(I) - G0(I))) + IF (T2 .LE. TMAX) GO TO 220 + TMAX = T2 + IMAX = I + 220 CONTINUE + IF (IMAX .GT. 0) GO TO 230 + SGNCHG = .FALSE. + IMAX = IMXOLD + GO TO 240 + 230 SGNCHG = .TRUE. + 240 NXLAST = LAST + IF (.NOT. SGNCHG) GO TO 250 +C Sign change between X0 and X2, so replace X1 with X2. ---------------- + X1 = X2 + CALL DCOPY (NG, GX, 1, G1, 1) + LAST = 1 + XROOT = .FALSE. + GO TO 270 + 250 IF (.NOT. ZROOT) GO TO 260 +C Zero value at X2 and no sign change in (X0,X2), so X2 is a root. ----- + X1 = X2 + CALL DCOPY (NG, GX, 1, G1, 1) + XROOT = .TRUE. + GO TO 270 +C No sign change between X0 and X2. Replace X0 with X2. --------------- + 260 CONTINUE + CALL DCOPY (NG, GX, 1, G0, 1) + X0 = X2 + LAST = 0 + XROOT = .FALSE. + 270 IF (ABS(X1-X0) .LE. HMIN) XROOT = .TRUE. + GO TO 150 +C +C Return with X1 as the root. Set JROOT. Set X = X1 and GX = G1. ----- + 300 JFLAG = 2 + X = X1 + CALL DCOPY (NG, G1, 1, GX, 1) + DO 320 I = 1,NG + JROOT(I) = 0 + IF (ABS(G1(I)) .GT. ZERO) GO TO 310 + JROOT(I) = 1 + GO TO 320 + 310 IF (SIGN(1.0D0,G0(I)) .NE. SIGN(1.0D0,G1(I))) JROOT(I) = 1 + 320 CONTINUE + RETURN +C +C No sign change in the interval. Check for zero at right endpoint. --- + 400 IF (.NOT. ZROOT) GO TO 420 +C +C Zero value at X1 and no sign change in (X0,X1). Return JFLAG = 3. --- + X = X1 + CALL DCOPY (NG, G1, 1, GX, 1) + DO 410 I = 1,NG + JROOT(I) = 0 + IF (ABS(G1(I)) .LE. ZERO) JROOT (I) = 1 + 410 CONTINUE + JFLAG = 3 + RETURN +C +C No sign changes in this interval. Set X = X1, return JFLAG = 4. ----- + 420 CALL DCOPY (NG, G1, 1, GX, 1) + X = X1 + JFLAG = 4 + RETURN +C----------------------- End of Subroutine DROOTS ---------------------- + END +*DECK DSRCAR + SUBROUTINE DSRCAR (RSAV, ISAV, JOB) +C----------------------------------------------------------------------- +C This routine saves or restores (depending on JOB) the contents of +C the Common blocks DLS001, DLSA01, DLSR01, which are used +C internally by one or more ODEPACK solvers. +C +C RSAV = real array of length 245 or more. +C ISAV = integer array of length 55 or more. +C JOB = flag indicating to save or restore the Common blocks: +C JOB = 1 if Common is to be saved (written to RSAV/ISAV) +C JOB = 2 if Common is to be restored (read from RSAV/ISAV) +C A call with JOB = 2 presumes a prior call with JOB = 1. +C----------------------------------------------------------------------- + INTEGER ISAV, JOB + INTEGER ILS, ILSA, ILSR + INTEGER I, IOFF, LENRLS, LENILS, LENRLA, LENILA, LENRLR, LENILR + DOUBLE PRECISION RSAV + DOUBLE PRECISION RLS, RLSA, RLSR + DIMENSION RSAV(*), ISAV(*) + SAVE LENRLS, LENILS, LENRLA, LENILA, LENRLR, LENILR + COMMON /DLS001/ RLS(218), ILS(37) + COMMON /DLSA01/ RLSA(22), ILSA(9) + COMMON /DLSR01/ RLSR(5), ILSR(9) + DATA LENRLS/218/, LENILS/37/, LENRLA/22/, LENILA/9/ + DATA LENRLR/5/, LENILR/9/ +C + IF (JOB .EQ. 2) GO TO 100 + DO 10 I = 1,LENRLS + 10 RSAV(I) = RLS(I) + DO 15 I = 1,LENRLA + 15 RSAV(LENRLS+I) = RLSA(I) + IOFF = LENRLS + LENRLA + DO 20 I = 1,LENRLR + 20 RSAV(IOFF+I) = RLSR(I) +C + DO 30 I = 1,LENILS + 30 ISAV(I) = ILS(I) + DO 35 I = 1,LENILA + 35 ISAV(LENILS+I) = ILSA(I) + IOFF = LENILS + LENILA + DO 40 I = 1,LENILR + 40 ISAV(IOFF+I) = ILSR(I) +C + RETURN +C + 100 CONTINUE + DO 110 I = 1,LENRLS + 110 RLS(I) = RSAV(I) + DO 115 I = 1,LENRLA + 115 RLSA(I) = RSAV(LENRLS+I) + IOFF = LENRLS + LENRLA + DO 120 I = 1,LENRLR + 120 RLSR(I) = RSAV(IOFF+I) +C + DO 130 I = 1,LENILS + 130 ILS(I) = ISAV(I) + DO 135 I = 1,LENILA + 135 ILSA(I) = ISAV(LENILS+I) + IOFF = LENILS + LENILA + DO 140 I = 1,LENILR + 140 ILSR(I) = ISAV(IOFF+I) +C + RETURN +C----------------------- End of Subroutine DSRCAR ---------------------- + END +*DECK DSTODPK + SUBROUTINE DSTODPK (NEQ, Y, YH, NYH, YH1, EWT, SAVF, SAVX, ACOR, + 1 WM, IWM, F, JAC, PSOL) + EXTERNAL F, JAC, PSOL + INTEGER NEQ, NYH, IWM + DOUBLE PRECISION Y, YH, YH1, EWT, SAVF, SAVX, ACOR, WM + DIMENSION NEQ(*), Y(*), YH(NYH,*), YH1(*), EWT(*), SAVF(*), + 1 SAVX(*), ACOR(*), WM(*), IWM(*) + INTEGER IOWND, IALTH, IPUP, LMAX, MEO, NQNYH, NSLP, + 1 ICF, IERPJ, IERSL, JCUR, JSTART, KFLAG, L, + 2 LYH, LEWT, LACOR, LSAVF, LWM, LIWM, METH, MITER, + 3 MAXORD, MAXCOR, MSBP, MXNCF, N, NQ, NST, NFE, NJE, NQU + INTEGER JPRE, JACFLG, LOCWP, LOCIWP, LSAVX, KMP, MAXL, MNEWT, + 1 NNI, NLI, NPS, NCFN, NCFL + DOUBLE PRECISION CONIT, CRATE, EL, ELCO, HOLD, RMAX, TESCO, + 2 CCMAX, EL0, H, HMIN, HMXI, HU, RC, TN, UROUND + DOUBLE PRECISION DELT, EPCON, SQRTN, RSQRTN + COMMON /DLS001/ CONIT, CRATE, EL(13), ELCO(13,12), + 1 HOLD, RMAX, TESCO(3,12), + 2 CCMAX, EL0, H, HMIN, HMXI, HU, RC, TN, UROUND, + 3 IOWND(6), IALTH, IPUP, LMAX, MEO, NQNYH, NSLP, + 3 ICF, IERPJ, IERSL, JCUR, JSTART, KFLAG, L, + 4 LYH, LEWT, LACOR, LSAVF, LWM, LIWM, METH, MITER, + 5 MAXORD, MAXCOR, MSBP, MXNCF, N, NQ, NST, NFE, NJE, NQU + COMMON /DLPK01/ DELT, EPCON, SQRTN, RSQRTN, + 1 JPRE, JACFLG, LOCWP, LOCIWP, LSAVX, KMP, MAXL, MNEWT, + 2 NNI, NLI, NPS, NCFN, NCFL +C----------------------------------------------------------------------- +C DSTODPK performs one step of the integration of an initial value +C problem for a system of Ordinary Differential Equations. +C----------------------------------------------------------------------- +C The following changes were made to generate Subroutine DSTODPK +C from Subroutine DSTODE: +C 1. The array SAVX was added to the call sequence. +C 2. PJAC and SLVS were replaced by PSOL in the call sequence. +C 3. The Common block /DLPK01/ was added for communication. +C 4. The test constant EPCON is loaded into Common below statement +C numbers 125 and 155, and used below statement 400. +C 5. The Newton iteration counter MNEWT is set below 220 and 400. +C 6. The call to PJAC was replaced with a call to DPKSET (fixed name), +C with a longer call sequence, called depending on JACFLG. +C 7. The corrector residual is stored in SAVX (not Y) at 360, +C and the solution vector is in SAVX in the 380 loop. +C 8. SLVS was renamed DSOLPK and includes NEQ, SAVX, EWT, F, and JAC. +C SAVX was added because DSOLPK now needs Y and SAVF undisturbed. +C 9. The nonlinear convergence failure count NCFN is set at 430. +C----------------------------------------------------------------------- +C Note: DSTODPK is independent of the value of the iteration method +C indicator MITER, when this is .ne. 0, and hence is independent +C of the type of chord method used, or the Jacobian structure. +C Communication with DSTODPK is done with the following variables: +C +C NEQ = integer array containing problem size in NEQ(1), and +C passed as the NEQ argument in all calls to F and JAC. +C Y = an array of length .ge. N used as the Y argument in +C all calls to F and JAC. +C YH = an NYH by LMAX array containing the dependent variables +C and their approximate scaled derivatives, where +C LMAX = MAXORD + 1. YH(i,j+1) contains the approximate +C j-th derivative of y(i), scaled by H**j/factorial(j) +C (j = 0,1,...,NQ). On entry for the first step, the first +C two columns of YH must be set from the initial values. +C NYH = a constant integer .ge. N, the first dimension of YH. +C YH1 = a one-dimensional array occupying the same space as YH. +C EWT = an array of length N containing multiplicative weights +C for local error measurements. Local errors in y(i) are +C compared to 1.0/EWT(i) in various error tests. +C SAVF = an array of working storage, of length N. +C Also used for input of YH(*,MAXORD+2) when JSTART = -1 +C and MAXORD .lt. the current order NQ. +C SAVX = an array of working storage, of length N. +C ACOR = a work array of length N, used for the accumulated +C corrections. On a successful return, ACOR(i) contains +C the estimated one-step local error in y(i). +C WM,IWM = real and integer work arrays associated with matrix +C operations in chord iteration (MITER .ne. 0). +C CCMAX = maximum relative change in H*EL0 before DPKSET is called. +C H = the step size to be attempted on the next step. +C H is altered by the error control algorithm during the +C problem. H can be either positive or negative, but its +C sign must remain constant throughout the problem. +C HMIN = the minimum absolute value of the step size H to be used. +C HMXI = inverse of the maximum absolute value of H to be used. +C HMXI = 0.0 is allowed and corresponds to an infinite HMAX. +C HMIN and HMXI may be changed at any time, but will not +C take effect until the next change of H is considered. +C TN = the independent variable. TN is updated on each step taken. +C JSTART = an integer used for input only, with the following +C values and meanings: +C 0 perform the first step. +C .gt.0 take a new step continuing from the last. +C -1 take the next step with a new value of H, MAXORD, +C N, METH, MITER, and/or matrix parameters. +C -2 take the next step with a new value of H, +C but with other inputs unchanged. +C On return, JSTART is set to 1 to facilitate continuation. +C KFLAG = a completion code with the following meanings: +C 0 the step was succesful. +C -1 the requested error could not be achieved. +C -2 corrector convergence could not be achieved. +C -3 fatal error in DPKSET or DSOLPK. +C A return with KFLAG = -1 or -2 means either +C ABS(H) = HMIN or 10 consecutive failures occurred. +C On a return with KFLAG negative, the values of TN and +C the YH array are as of the beginning of the last +C step, and H is the last step size attempted. +C MAXORD = the maximum order of integration method to be allowed. +C MAXCOR = the maximum number of corrector iterations allowed. +C MSBP = maximum number of steps between DPKSET calls (MITER .gt. 0). +C MXNCF = maximum number of convergence failures allowed. +C METH/MITER = the method flags. See description in driver. +C N = the number of first-order differential equations. +C----------------------------------------------------------------------- + INTEGER I, I1, IREDO, IRET, J, JB, M, NCF, NEWQ + DOUBLE PRECISION DCON, DDN, DEL, DELP, DSM, DUP, EXDN, EXSM, EXUP, + 1 R, RH, RHDN, RHSM, RHUP, TOLD, DVNORM +C + KFLAG = 0 + TOLD = TN + NCF = 0 + IERPJ = 0 + IERSL = 0 + JCUR = 0 + ICF = 0 + DELP = 0.0D0 + IF (JSTART .GT. 0) GO TO 200 + IF (JSTART .EQ. -1) GO TO 100 + IF (JSTART .EQ. -2) GO TO 160 +C----------------------------------------------------------------------- +C On the first call, the order is set to 1, and other variables are +C initialized. RMAX is the maximum ratio by which H can be increased +C in a single step. It is initially 1.E4 to compensate for the small +C initial H, but then is normally equal to 10. If a failure +C occurs (in corrector convergence or error test), RMAX is set at 2 +C for the next increase. +C----------------------------------------------------------------------- + LMAX = MAXORD + 1 + NQ = 1 + L = 2 + IALTH = 2 + RMAX = 10000.0D0 + RC = 0.0D0 + EL0 = 1.0D0 + CRATE = 0.7D0 + HOLD = H + MEO = METH + NSLP = 0 + IPUP = MITER + IRET = 3 + GO TO 140 +C----------------------------------------------------------------------- +C The following block handles preliminaries needed when JSTART = -1. +C IPUP is set to MITER to force a matrix update. +C If an order increase is about to be considered (IALTH = 1), +C IALTH is reset to 2 to postpone consideration one more step. +C If the caller has changed METH, DCFODE is called to reset +C the coefficients of the method. +C If the caller has changed MAXORD to a value less than the current +C order NQ, NQ is reduced to MAXORD, and a new H chosen accordingly. +C If H is to be changed, YH must be rescaled. +C If H or METH is being changed, IALTH is reset to L = NQ + 1 +C to prevent further changes in H for that many steps. +C----------------------------------------------------------------------- + 100 IPUP = MITER + LMAX = MAXORD + 1 + IF (IALTH .EQ. 1) IALTH = 2 + IF (METH .EQ. MEO) GO TO 110 + CALL DCFODE (METH, ELCO, TESCO) + MEO = METH + IF (NQ .GT. MAXORD) GO TO 120 + IALTH = L + IRET = 1 + GO TO 150 + 110 IF (NQ .LE. MAXORD) GO TO 160 + 120 NQ = MAXORD + L = LMAX + DO 125 I = 1,L + 125 EL(I) = ELCO(I,NQ) + NQNYH = NQ*NYH + RC = RC*EL(1)/EL0 + EL0 = EL(1) + CONIT = 0.5D0/(NQ+2) + EPCON = CONIT*TESCO(2,NQ) + DDN = DVNORM (N, SAVF, EWT)/TESCO(1,L) + EXDN = 1.0D0/L + RHDN = 1.0D0/(1.3D0*DDN**EXDN + 0.0000013D0) + RH = MIN(RHDN,1.0D0) + IREDO = 3 + IF (H .EQ. HOLD) GO TO 170 + RH = MIN(RH,ABS(H/HOLD)) + H = HOLD + GO TO 175 +C----------------------------------------------------------------------- +C DCFODE is called to get all the integration coefficients for the +C current METH. Then the EL vector and related constants are reset +C whenever the order NQ is changed, or at the start of the problem. +C----------------------------------------------------------------------- + 140 CALL DCFODE (METH, ELCO, TESCO) + 150 DO 155 I = 1,L + 155 EL(I) = ELCO(I,NQ) + NQNYH = NQ*NYH + RC = RC*EL(1)/EL0 + EL0 = EL(1) + CONIT = 0.5D0/(NQ+2) + EPCON = CONIT*TESCO(2,NQ) + GO TO (160, 170, 200), IRET +C----------------------------------------------------------------------- +C If H is being changed, the H ratio RH is checked against +C RMAX, HMIN, and HMXI, and the YH array rescaled. IALTH is set to +C L = NQ + 1 to prevent a change of H for that many steps, unless +C forced by a convergence or error test failure. +C----------------------------------------------------------------------- + 160 IF (H .EQ. HOLD) GO TO 200 + RH = H/HOLD + H = HOLD + IREDO = 3 + GO TO 175 + 170 RH = MAX(RH,HMIN/ABS(H)) + 175 RH = MIN(RH,RMAX) + RH = RH/MAX(1.0D0,ABS(H)*HMXI*RH) + R = 1.0D0 + DO 180 J = 2,L + R = R*RH + DO 180 I = 1,N + 180 YH(I,J) = YH(I,J)*R + H = H*RH + RC = RC*RH + IALTH = L + IF (IREDO .EQ. 0) GO TO 690 +C----------------------------------------------------------------------- +C This section computes the predicted values by effectively +C multiplying the YH array by the Pascal triangle matrix. +C The flag IPUP is set according to whether matrix data is involved +C (JACFLG .ne. 0) or not (JACFLG = 0), to trigger a call to DPKSET. +C IPUP is set to MITER when RC differs from 1 by more than CCMAX, +C and at least every MSBP steps, when JACFLG = 1. +C RC is the ratio of new to old values of the coefficient H*EL(1). +C----------------------------------------------------------------------- + 200 IF (JACFLG .NE. 0) GO TO 202 + IPUP = 0 + CRATE = 0.7D0 + GO TO 205 + 202 IF (ABS(RC-1.0D0) .GT. CCMAX) IPUP = MITER + IF (NST .GE. NSLP+MSBP) IPUP = MITER + 205 TN = TN + H + I1 = NQNYH + 1 + DO 215 JB = 1,NQ + I1 = I1 - NYH +CDIR$ IVDEP + DO 210 I = I1,NQNYH + 210 YH1(I) = YH1(I) + YH1(I+NYH) + 215 CONTINUE +C----------------------------------------------------------------------- +C Up to MAXCOR corrector iterations are taken. A convergence test is +C made on the RMS-norm of each correction, weighted by the error +C weight vector EWT. The sum of the corrections is accumulated in the +C vector ACOR(i). The YH array is not altered in the corrector loop. +C----------------------------------------------------------------------- + 220 M = 0 + MNEWT = 0 + DO 230 I = 1,N + 230 Y(I) = YH(I,1) + CALL F (NEQ, TN, Y, SAVF) + NFE = NFE + 1 + IF (IPUP .LE. 0) GO TO 250 +C----------------------------------------------------------------------- +C If indicated, DPKSET is called to update any matrix data needed, +C before starting the corrector iteration. +C IPUP is set to 0 as an indicator that this has been done. +C----------------------------------------------------------------------- + CALL DPKSET (NEQ, Y, YH1, EWT, ACOR, SAVF, WM, IWM, F, JAC) + IPUP = 0 + RC = 1.0D0 + NSLP = NST + CRATE = 0.7D0 + IF (IERPJ .NE. 0) GO TO 430 + 250 DO 260 I = 1,N + 260 ACOR(I) = 0.0D0 + 270 IF (MITER .NE. 0) GO TO 350 +C----------------------------------------------------------------------- +C In the case of functional iteration, update Y directly from +C the result of the last function evaluation. +C----------------------------------------------------------------------- + DO 290 I = 1,N + SAVF(I) = H*SAVF(I) - YH(I,2) + 290 Y(I) = SAVF(I) - ACOR(I) + DEL = DVNORM (N, Y, EWT) + DO 300 I = 1,N + Y(I) = YH(I,1) + EL(1)*SAVF(I) + 300 ACOR(I) = SAVF(I) + GO TO 400 +C----------------------------------------------------------------------- +C In the case of the chord method, compute the corrector error, +C and solve the linear system with that as right-hand side and +C P as coefficient matrix. +C----------------------------------------------------------------------- + 350 DO 360 I = 1,N + 360 SAVX(I) = H*SAVF(I) - (YH(I,2) + ACOR(I)) + CALL DSOLPK (NEQ, Y, SAVF, SAVX, EWT, WM, IWM, F, PSOL) + IF (IERSL .LT. 0) GO TO 430 + IF (IERSL .GT. 0) GO TO 410 + DEL = DVNORM (N, SAVX, EWT) + DO 380 I = 1,N + ACOR(I) = ACOR(I) + SAVX(I) + 380 Y(I) = YH(I,1) + EL(1)*ACOR(I) +C----------------------------------------------------------------------- +C Test for convergence. If M .gt. 0, an estimate of the convergence +C rate constant is stored in CRATE, and this is used in the test. +C----------------------------------------------------------------------- + 400 IF (M .NE. 0) CRATE = MAX(0.2D0*CRATE,DEL/DELP) + DCON = DEL*MIN(1.0D0,1.5D0*CRATE)/EPCON + IF (DCON .LE. 1.0D0) GO TO 450 + M = M + 1 + IF (M .EQ. MAXCOR) GO TO 410 + IF (M .GE. 2 .AND. DEL .GT. 2.0D0*DELP) GO TO 410 + MNEWT = M + DELP = DEL + CALL F (NEQ, TN, Y, SAVF) + NFE = NFE + 1 + GO TO 270 +C----------------------------------------------------------------------- +C The corrector iteration failed to converge. +C If MITER .ne. 0 and the Jacobian is out of date, DPKSET is called for +C the next try. Otherwise the YH array is retracted to its values +C before prediction, and H is reduced, if possible. If H cannot be +C reduced or MXNCF failures have occurred, exit with KFLAG = -2. +C----------------------------------------------------------------------- + 410 IF (MITER.EQ.0 .OR. JCUR.EQ.1 .OR. JACFLG.EQ.0) GO TO 430 + ICF = 1 + IPUP = MITER + GO TO 220 + 430 ICF = 2 + NCF = NCF + 1 + NCFN = NCFN + 1 + RMAX = 2.0D0 + TN = TOLD + I1 = NQNYH + 1 + DO 445 JB = 1,NQ + I1 = I1 - NYH +CDIR$ IVDEP + DO 440 I = I1,NQNYH + 440 YH1(I) = YH1(I) - YH1(I+NYH) + 445 CONTINUE + IF (IERPJ .LT. 0 .OR. IERSL .LT. 0) GO TO 680 + IF (ABS(H) .LE. HMIN*1.00001D0) GO TO 670 + IF (NCF .EQ. MXNCF) GO TO 670 + RH = 0.5D0 + IPUP = MITER + IREDO = 1 + GO TO 170 +C----------------------------------------------------------------------- +C The corrector has converged. JCUR is set to 0 +C to signal that the Jacobian involved may need updating later. +C The local error test is made and control passes to statement 500 +C if it fails. +C----------------------------------------------------------------------- + 450 JCUR = 0 + IF (M .EQ. 0) DSM = DEL/TESCO(2,NQ) + IF (M .GT. 0) DSM = DVNORM (N, ACOR, EWT)/TESCO(2,NQ) + IF (DSM .GT. 1.0D0) GO TO 500 +C----------------------------------------------------------------------- +C After a successful step, update the YH array. +C Consider changing H if IALTH = 1. Otherwise decrease IALTH by 1. +C If IALTH is then 1 and NQ .lt. MAXORD, then ACOR is saved for +C use in a possible order increase on the next step. +C If a change in H is considered, an increase or decrease in order +C by one is considered also. A change in H is made only if it is by a +C factor of at least 1.1. If not, IALTH is set to 3 to prevent +C testing for that many steps. +C----------------------------------------------------------------------- + KFLAG = 0 + IREDO = 0 + NST = NST + 1 + HU = H + NQU = NQ + DO 470 J = 1,L + DO 470 I = 1,N + 470 YH(I,J) = YH(I,J) + EL(J)*ACOR(I) + IALTH = IALTH - 1 + IF (IALTH .EQ. 0) GO TO 520 + IF (IALTH .GT. 1) GO TO 700 + IF (L .EQ. LMAX) GO TO 700 + DO 490 I = 1,N + 490 YH(I,LMAX) = ACOR(I) + GO TO 700 +C----------------------------------------------------------------------- +C The error test failed. KFLAG keeps track of multiple failures. +C Restore TN and the YH array to their previous values, and prepare +C to try the step again. Compute the optimum step size for this or +C one lower order. After 2 or more failures, H is forced to decrease +C by a factor of 0.2 or less. +C----------------------------------------------------------------------- + 500 KFLAG = KFLAG - 1 + TN = TOLD + I1 = NQNYH + 1 + DO 515 JB = 1,NQ + I1 = I1 - NYH +CDIR$ IVDEP + DO 510 I = I1,NQNYH + 510 YH1(I) = YH1(I) - YH1(I+NYH) + 515 CONTINUE + RMAX = 2.0D0 + IF (ABS(H) .LE. HMIN*1.00001D0) GO TO 660 + IF (KFLAG .LE. -3) GO TO 640 + IREDO = 2 + RHUP = 0.0D0 + GO TO 540 +C----------------------------------------------------------------------- +C Regardless of the success or failure of the step, factors +C RHDN, RHSM, and RHUP are computed, by which H could be multiplied +C at order NQ - 1, order NQ, or order NQ + 1, respectively. +C In the case of failure, RHUP = 0.0 to avoid an order increase. +C the largest of these is determined and the new order chosen +C accordingly. If the order is to be increased, we compute one +C additional scaled derivative. +C----------------------------------------------------------------------- + 520 RHUP = 0.0D0 + IF (L .EQ. LMAX) GO TO 540 + DO 530 I = 1,N + 530 SAVF(I) = ACOR(I) - YH(I,LMAX) + DUP = DVNORM (N, SAVF, EWT)/TESCO(3,NQ) + EXUP = 1.0D0/(L+1) + RHUP = 1.0D0/(1.4D0*DUP**EXUP + 0.0000014D0) + 540 EXSM = 1.0D0/L + RHSM = 1.0D0/(1.2D0*DSM**EXSM + 0.0000012D0) + RHDN = 0.0D0 + IF (NQ .EQ. 1) GO TO 560 + DDN = DVNORM (N, YH(1,L), EWT)/TESCO(1,NQ) + EXDN = 1.0D0/NQ + RHDN = 1.0D0/(1.3D0*DDN**EXDN + 0.0000013D0) + 560 IF (RHSM .GE. RHUP) GO TO 570 + IF (RHUP .GT. RHDN) GO TO 590 + GO TO 580 + 570 IF (RHSM .LT. RHDN) GO TO 580 + NEWQ = NQ + RH = RHSM + GO TO 620 + 580 NEWQ = NQ - 1 + RH = RHDN + IF (KFLAG .LT. 0 .AND. RH .GT. 1.0D0) RH = 1.0D0 + GO TO 620 + 590 NEWQ = L + RH = RHUP + IF (RH .LT. 1.1D0) GO TO 610 + R = EL(L)/L + DO 600 I = 1,N + 600 YH(I,NEWQ+1) = ACOR(I)*R + GO TO 630 + 610 IALTH = 3 + GO TO 700 + 620 IF ((KFLAG .EQ. 0) .AND. (RH .LT. 1.1D0)) GO TO 610 + IF (KFLAG .LE. -2) RH = MIN(RH,0.2D0) +C----------------------------------------------------------------------- +C If there is a change of order, reset NQ, L, and the coefficients. +C In any case H is reset according to RH and the YH array is rescaled. +C Then exit from 690 if the step was OK, or redo the step otherwise. +C----------------------------------------------------------------------- + IF (NEWQ .EQ. NQ) GO TO 170 + 630 NQ = NEWQ + L = NQ + 1 + IRET = 2 + GO TO 150 +C----------------------------------------------------------------------- +C Control reaches this section if 3 or more failures have occured. +C If 10 failures have occurred, exit with KFLAG = -1. +C It is assumed that the derivatives that have accumulated in the +C YH array have errors of the wrong order. Hence the first +C derivative is recomputed, and the order is set to 1. Then +C H is reduced by a factor of 10, and the step is retried, +C until it succeeds or H reaches HMIN. +C----------------------------------------------------------------------- + 640 IF (KFLAG .EQ. -10) GO TO 660 + RH = 0.1D0 + RH = MAX(HMIN/ABS(H),RH) + H = H*RH + DO 645 I = 1,N + 645 Y(I) = YH(I,1) + CALL F (NEQ, TN, Y, SAVF) + NFE = NFE + 1 + DO 650 I = 1,N + 650 YH(I,2) = H*SAVF(I) + IPUP = MITER + IALTH = 5 + IF (NQ .EQ. 1) GO TO 200 + NQ = 1 + L = 2 + IRET = 3 + GO TO 150 +C----------------------------------------------------------------------- +C All returns are made through this section. H is saved in HOLD +C to allow the caller to change H on the next step. +C----------------------------------------------------------------------- + 660 KFLAG = -1 + GO TO 720 + 670 KFLAG = -2 + GO TO 720 + 680 KFLAG = -3 + GO TO 720 + 690 RMAX = 10.0D0 + 700 R = 1.0D0/TESCO(2,NQU) + DO 710 I = 1,N + 710 ACOR(I) = ACOR(I)*R + 720 HOLD = H + JSTART = 1 + RETURN +C----------------------- End of Subroutine DSTODPK --------------------- + END +*DECK DPKSET + SUBROUTINE DPKSET (NEQ, Y, YSV, EWT, FTEM, SAVF, WM, IWM, F, JAC) + EXTERNAL F, JAC + INTEGER NEQ, IWM + DOUBLE PRECISION Y, YSV, EWT, FTEM, SAVF, WM + DIMENSION NEQ(*), Y(*), YSV(*), EWT(*), FTEM(*), SAVF(*), + 1 WM(*), IWM(*) + INTEGER IOWND, IOWNS, + 1 ICF, IERPJ, IERSL, JCUR, JSTART, KFLAG, L, + 2 LYH, LEWT, LACOR, LSAVF, LWM, LIWM, METH, MITER, + 3 MAXORD, MAXCOR, MSBP, MXNCF, N, NQ, NST, NFE, NJE, NQU + INTEGER JPRE, JACFLG, LOCWP, LOCIWP, LSAVX, KMP, MAXL, MNEWT, + 1 NNI, NLI, NPS, NCFN, NCFL + DOUBLE PRECISION ROWNS, + 1 CCMAX, EL0, H, HMIN, HMXI, HU, RC, TN, UROUND + DOUBLE PRECISION DELT, EPCON, SQRTN, RSQRTN + COMMON /DLS001/ ROWNS(209), + 1 CCMAX, EL0, H, HMIN, HMXI, HU, RC, TN, UROUND, + 2 IOWND(6), IOWNS(6), + 3 ICF, IERPJ, IERSL, JCUR, JSTART, KFLAG, L, + 4 LYH, LEWT, LACOR, LSAVF, LWM, LIWM, METH, MITER, + 5 MAXORD, MAXCOR, MSBP, MXNCF, N, NQ, NST, NFE, NJE, NQU + COMMON /DLPK01/ DELT, EPCON, SQRTN, RSQRTN, + 1 JPRE, JACFLG, LOCWP, LOCIWP, LSAVX, KMP, MAXL, MNEWT, + 2 NNI, NLI, NPS, NCFN, NCFL +C----------------------------------------------------------------------- +C DPKSET is called by DSTODPK to interface with the user-supplied +C routine JAC, to compute and process relevant parts of +C the matrix P = I - H*EL(1)*J , where J is the Jacobian df/dy, +C as need for preconditioning matrix operations later. +C +C In addition to variables described previously, communication +C with DPKSET uses the following: +C Y = array containing predicted values on entry. +C YSV = array containing predicted y, to be saved (YH1 in DSTODPK). +C FTEM = work array of length N (ACOR in DSTODPK). +C SAVF = array containing f evaluated at predicted y. +C WM = real work space for matrices. +C Space for preconditioning data starts at WM(LOCWP). +C IWM = integer work space. +C Space for preconditioning data starts at IWM(LOCIWP). +C IERPJ = output error flag, = 0 if no trouble, .gt. 0 if +C JAC returned an error flag. +C JCUR = output flag = 1 to indicate that the Jacobian matrix +C (or approximation) is now current. +C This routine also uses Common variables EL0, H, TN, IERPJ, JCUR, NJE. +C----------------------------------------------------------------------- + INTEGER IER + DOUBLE PRECISION HL0 +C + IERPJ = 0 + JCUR = 1 + HL0 = EL0*H + CALL JAC (F, NEQ, TN, Y, YSV, EWT, SAVF, FTEM, HL0, + 1 WM(LOCWP), IWM(LOCIWP), IER) + NJE = NJE + 1 + IF (IER .EQ. 0) RETURN + IERPJ = 1 + RETURN +C----------------------- End of Subroutine DPKSET ---------------------- + END +*DECK DSOLPK + SUBROUTINE DSOLPK (NEQ, Y, SAVF, X, EWT, WM, IWM, F, PSOL) + EXTERNAL F, PSOL + INTEGER NEQ, IWM + DOUBLE PRECISION Y, SAVF, X, EWT, WM + DIMENSION NEQ(*), Y(*), SAVF(*), X(*), EWT(*), WM(*), IWM(*) + INTEGER IOWND, IOWNS, + 1 ICF, IERPJ, IERSL, JCUR, JSTART, KFLAG, L, + 2 LYH, LEWT, LACOR, LSAVF, LWM, LIWM, METH, MITER, + 3 MAXORD, MAXCOR, MSBP, MXNCF, N, NQ, NST, NFE, NJE, NQU + INTEGER JPRE, JACFLG, LOCWP, LOCIWP, LSAVX, KMP, MAXL, MNEWT, + 1 NNI, NLI, NPS, NCFN, NCFL + DOUBLE PRECISION ROWNS, + 1 CCMAX, EL0, H, HMIN, HMXI, HU, RC, TN, UROUND + DOUBLE PRECISION DELT, EPCON, SQRTN, RSQRTN + COMMON /DLS001/ ROWNS(209), + 1 CCMAX, EL0, H, HMIN, HMXI, HU, RC, TN, UROUND, + 2 IOWND(6), IOWNS(6), + 3 ICF, IERPJ, IERSL, JCUR, JSTART, KFLAG, L, + 4 LYH, LEWT, LACOR, LSAVF, LWM, LIWM, METH, MITER, + 5 MAXORD, MAXCOR, MSBP, MXNCF, N, NQ, NST, NFE, NJE, NQU + COMMON /DLPK01/ DELT, EPCON, SQRTN, RSQRTN, + 1 JPRE, JACFLG, LOCWP, LOCIWP, LSAVX, KMP, MAXL, MNEWT, + 2 NNI, NLI, NPS, NCFN, NCFL +C----------------------------------------------------------------------- +C This routine interfaces to one of DSPIOM, DSPIGMR, DPCG, DPCGS, or +C DUSOL, for the solution of the linear system arising from a Newton +C iteration. It is called if MITER .ne. 0. +C In addition to variables described elsewhere, +C communication with DSOLPK uses the following variables: +C WM = real work space containing data for the algorithm +C (Krylov basis vectors, Hessenberg matrix, etc.) +C IWM = integer work space containing data for the algorithm +C X = the right-hand side vector on input, and the solution vector +C on output, of length N. +C IERSL = output flag (in Common): +C IERSL = 0 means no trouble occurred. +C IERSL = 1 means the iterative method failed to converge. +C If the preconditioner is out of date, the step +C is repeated with a new preconditioner. +C Otherwise, the stepsize is reduced (forcing a +C new evaluation of the preconditioner) and the +C step is repeated. +C IERSL = -1 means there was a nonrecoverable error in the +C iterative solver, and an error exit occurs. +C This routine also uses the Common variables TN, EL0, H, N, MITER, +C DELT, EPCON, SQRTN, RSQRTN, MAXL, KMP, MNEWT, NNI, NLI, NPS, NCFL, +C LOCWP, LOCIWP. +C----------------------------------------------------------------------- + INTEGER IFLAG, LB, LDL, LHES, LIOM, LGMR, LPCG, LP, LQ, LR, + 1 LV, LW, LWK, LZ, MAXLP1, NPSL + DOUBLE PRECISION DELTA, HL0 +C + IERSL = 0 + HL0 = H*EL0 + DELTA = DELT*EPCON + GO TO (100, 200, 300, 400, 900, 900, 900, 900, 900), MITER +C----------------------------------------------------------------------- +C Use the SPIOM algorithm to solve the linear system P*x = -f. +C----------------------------------------------------------------------- + 100 CONTINUE + LV = 1 + LB = LV + N*MAXL + LHES = LB + N + LWK = LHES + MAXL*MAXL + CALL DCOPY (N, X, 1, WM(LB), 1) + CALL DSCAL (N, RSQRTN, EWT, 1) + CALL DSPIOM (NEQ, TN, Y, SAVF, WM(LB), EWT, N, MAXL, KMP, DELTA, + 1 HL0, JPRE, MNEWT, F, PSOL, NPSL, X, WM(LV), WM(LHES), IWM, + 2 LIOM, WM(LOCWP), IWM(LOCIWP), WM(LWK), IFLAG) + NNI = NNI + 1 + NLI = NLI + LIOM + NPS = NPS + NPSL + CALL DSCAL (N, SQRTN, EWT, 1) + IF (IFLAG .NE. 0) NCFL = NCFL + 1 + IF (IFLAG .GE. 2) IERSL = 1 + IF (IFLAG .LT. 0) IERSL = -1 + RETURN +C----------------------------------------------------------------------- +C Use the SPIGMR algorithm to solve the linear system P*x = -f. +C----------------------------------------------------------------------- + 200 CONTINUE + MAXLP1 = MAXL + 1 + LV = 1 + LB = LV + N*MAXL + LHES = LB + N + 1 + LQ = LHES + MAXL*MAXLP1 + LWK = LQ + 2*MAXL + LDL = LWK + MIN(1,MAXL-KMP)*N + CALL DCOPY (N, X, 1, WM(LB), 1) + CALL DSCAL (N, RSQRTN, EWT, 1) + CALL DSPIGMR (NEQ, TN, Y, SAVF, WM(LB), EWT, N, MAXL, MAXLP1, KMP, + 1 DELTA, HL0, JPRE, MNEWT, F, PSOL, NPSL, X, WM(LV), WM(LHES), + 2 WM(LQ), LGMR, WM(LOCWP), IWM(LOCIWP), WM(LWK), WM(LDL), IFLAG) + NNI = NNI + 1 + NLI = NLI + LGMR + NPS = NPS + NPSL + CALL DSCAL (N, SQRTN, EWT, 1) + IF (IFLAG .NE. 0) NCFL = NCFL + 1 + IF (IFLAG .GE. 2) IERSL = 1 + IF (IFLAG .LT. 0) IERSL = -1 + RETURN +C----------------------------------------------------------------------- +C Use DPCG to solve the linear system P*x = -f +C----------------------------------------------------------------------- + 300 CONTINUE + LR = 1 + LP = LR + N + LW = LP + N + LZ = LW + N + LWK = LZ + N + CALL DCOPY (N, X, 1, WM(LR), 1) + CALL DPCG (NEQ, TN, Y, SAVF, WM(LR), EWT, N, MAXL, DELTA, HL0, + 1 JPRE, MNEWT, F, PSOL, NPSL, X, WM(LP), WM(LW), WM(LZ), + 2 LPCG, WM(LOCWP), IWM(LOCIWP), WM(LWK), IFLAG) + NNI = NNI + 1 + NLI = NLI + LPCG + NPS = NPS + NPSL + IF (IFLAG .NE. 0) NCFL = NCFL + 1 + IF (IFLAG .GE. 2) IERSL = 1 + IF (IFLAG .LT. 0) IERSL = -1 + RETURN +C----------------------------------------------------------------------- +C Use DPCGS to solve the linear system P*x = -f +C----------------------------------------------------------------------- + 400 CONTINUE + LR = 1 + LP = LR + N + LW = LP + N + LZ = LW + N + LWK = LZ + N + CALL DCOPY (N, X, 1, WM(LR), 1) + CALL DPCGS (NEQ, TN, Y, SAVF, WM(LR), EWT, N, MAXL, DELTA, HL0, + 1 JPRE, MNEWT, F, PSOL, NPSL, X, WM(LP), WM(LW), WM(LZ), + 2 LPCG, WM(LOCWP), IWM(LOCIWP), WM(LWK), IFLAG) + NNI = NNI + 1 + NLI = NLI + LPCG + NPS = NPS + NPSL + IF (IFLAG .NE. 0) NCFL = NCFL + 1 + IF (IFLAG .GE. 2) IERSL = 1 + IF (IFLAG .LT. 0) IERSL = -1 + RETURN +C----------------------------------------------------------------------- +C Use DUSOL, which interfaces to PSOL, to solve the linear system +C (no Krylov iteration). +C----------------------------------------------------------------------- + 900 CONTINUE + LB = 1 + LWK = LB + N + CALL DCOPY (N, X, 1, WM(LB), 1) + CALL DUSOL (NEQ, TN, Y, SAVF, WM(LB), EWT, N, DELTA, HL0, MNEWT, + 1 PSOL, NPSL, X, WM(LOCWP), IWM(LOCIWP), WM(LWK), IFLAG) + NNI = NNI + 1 + NPS = NPS + NPSL + IF (IFLAG .NE. 0) NCFL = NCFL + 1 + IF (IFLAG .EQ. 3) IERSL = 1 + IF (IFLAG .LT. 0) IERSL = -1 + RETURN +C----------------------- End of Subroutine DSOLPK ---------------------- + END +*DECK DSPIOM + SUBROUTINE DSPIOM (NEQ, TN, Y, SAVF, B, WGHT, N, MAXL, KMP, DELTA, + 1 HL0, JPRE, MNEWT, F, PSOL, NPSL, X, V, HES, IPVT, + 2 LIOM, WP, IWP, WK, IFLAG) + EXTERNAL F, PSOL + INTEGER NEQ,N,MAXL,KMP,JPRE,MNEWT,NPSL,IPVT,LIOM,IWP,IFLAG + DOUBLE PRECISION TN,Y,SAVF,B,WGHT,DELTA,HL0,X,V,HES,WP,WK + DIMENSION NEQ(*), Y(*), SAVF(*), B(*), WGHT(*), X(*), V(N,*), + 1 HES(MAXL,MAXL), IPVT(*), WP(*), IWP(*), WK(*) +C----------------------------------------------------------------------- +C This routine solves the linear system A * x = b using a scaled +C preconditioned version of the Incomplete Orthogonalization Method. +C An initial guess of x = 0 is assumed. +C----------------------------------------------------------------------- +C +C On entry +C +C NEQ = problem size, passed to F and PSOL (NEQ(1) = N). +C +C TN = current value of t. +C +C Y = array containing current dependent variable vector. +C +C SAVF = array containing current value of f(t,y). +C +C B = the right hand side of the system A*x = b. +C B is also used as work space when computing the +C final approximation. +C (B is the same as V(*,MAXL+1) in the call to DSPIOM.) +C +C WGHT = array of length N containing scale factors. +C 1/WGHT(i) are the diagonal elements of the diagonal +C scaling matrix D. +C +C N = the order of the matrix A, and the lengths +C of the vectors Y, SAVF, B, WGHT, and X. +C +C MAXL = the maximum allowable order of the matrix HES. +C +C KMP = the number of previous vectors the new vector VNEW +C must be made orthogonal to. KMP .le. MAXL. +C +C DELTA = tolerance on residuals b - A*x in weighted RMS-norm. +C +C HL0 = current value of (step size h) * (coefficient l0). +C +C JPRE = preconditioner type flag. +C +C MNEWT = Newton iteration counter (.ge. 0). +C +C WK = real work array of length N used by DATV and PSOL. +C +C WP = real work array used by preconditioner PSOL. +C +C IWP = integer work array used by preconditioner PSOL. +C +C On return +C +C X = the final computed approximation to the solution +C of the system A*x = b. +C +C V = the N by (LIOM+1) array containing the LIOM +C orthogonal vectors V(*,1) to V(*,LIOM). +C +C HES = the LU factorization of the LIOM by LIOM upper +C Hessenberg matrix whose entries are the +C scaled inner products of A*V(*,k) and V(*,i). +C +C IPVT = an integer array containg pivoting information. +C It is loaded in DHEFA and used in DHESL. +C +C LIOM = the number of iterations performed, and current +C order of the upper Hessenberg matrix HES. +C +C NPSL = the number of calls to PSOL. +C +C IFLAG = integer error flag: +C 0 means convergence in LIOM iterations, LIOM.le.MAXL. +C 1 means the convergence test did not pass in MAXL +C iterations, but the residual norm is .lt. 1, +C or .lt. norm(b) if MNEWT = 0, and so X is computed. +C 2 means the convergence test did not pass in MAXL +C iterations, residual .gt. 1, and X is undefined. +C 3 means there was a recoverable error in PSOL +C caused by the preconditioner being out of date. +C -1 means there was a nonrecoverable error in PSOL. +C +C----------------------------------------------------------------------- + INTEGER I, IER, INFO, J, K, LL, LM1 + DOUBLE PRECISION BNRM, BNRM0, PROD, RHO, SNORMW, DNRM2, TEM +C + IFLAG = 0 + LIOM = 0 + NPSL = 0 +C----------------------------------------------------------------------- +C The initial residual is the vector b. Apply scaling to b, and test +C for an immediate return with X = 0 or X = b. +C----------------------------------------------------------------------- + DO 10 I = 1,N + 10 V(I,1) = B(I)*WGHT(I) + BNRM0 = DNRM2 (N, V, 1) + BNRM = BNRM0 + IF (BNRM0 .GT. DELTA) GO TO 30 + IF (MNEWT .GT. 0) GO TO 20 + CALL DCOPY (N, B, 1, X, 1) + RETURN + 20 DO 25 I = 1,N + 25 X(I) = 0.0D0 + RETURN + 30 CONTINUE +C Apply inverse of left preconditioner to vector b. -------------------- + IER = 0 + IF (JPRE .EQ. 0 .OR. JPRE .EQ. 2) GO TO 55 + CALL PSOL (NEQ, TN, Y, SAVF, WK, HL0, WP, IWP, B, 1, IER) + NPSL = 1 + IF (IER .NE. 0) GO TO 300 +C Calculate norm of scaled vector V(*,1) and normalize it. ------------- + DO 50 I = 1,N + 50 V(I,1) = B(I)*WGHT(I) + BNRM = DNRM2(N, V, 1) + DELTA = DELTA*(BNRM/BNRM0) + 55 TEM = 1.0D0/BNRM + CALL DSCAL (N, TEM, V(1,1), 1) +C Zero out the HES array. ---------------------------------------------- + DO 65 J = 1,MAXL + DO 60 I = 1,MAXL + 60 HES(I,J) = 0.0D0 + 65 CONTINUE +C----------------------------------------------------------------------- +C Main loop on LL = l to compute the vectors V(*,2) to V(*,MAXL). +C The running product PROD is needed for the convergence test. +C----------------------------------------------------------------------- + PROD = 1.0D0 + DO 90 LL = 1,MAXL + LIOM = LL +C----------------------------------------------------------------------- +C Call routine DATV to compute VNEW = Abar*v(l), where Abar is +C the matrix A with scaling and inverse preconditioner factors applied. +C Call routine DORTHOG to orthogonalize the new vector vnew = V(*,l+1). +C Call routine DHEFA to update the factors of HES. +C----------------------------------------------------------------------- + CALL DATV (NEQ, Y, SAVF, V(1,LL), WGHT, X, F, PSOL, V(1,LL+1), + 1 WK, WP, IWP, HL0, JPRE, IER, NPSL) + IF (IER .NE. 0) GO TO 300 + CALL DORTHOG (V(1,LL+1), V, HES, N, LL, MAXL, KMP, SNORMW) + CALL DHEFA (HES, MAXL, LL, IPVT, INFO, LL) + LM1 = LL - 1 + IF (LL .GT. 1 .AND. IPVT(LM1) .EQ. LM1) PROD = PROD*HES(LL,LM1) + IF (INFO .NE. LL) GO TO 70 +C----------------------------------------------------------------------- +C The last pivot in HES was found to be zero. +C If vnew = 0 or l = MAXL, take an error return with IFLAG = 2. +C otherwise, continue the iteration without a convergence test. +C----------------------------------------------------------------------- + IF (SNORMW .EQ. 0.0D0) GO TO 120 + IF (LL .EQ. MAXL) GO TO 120 + GO TO 80 +C----------------------------------------------------------------------- +C Update RHO, the estimate of the norm of the residual b - A*x(l). +C test for convergence. If passed, compute approximation x(l). +C If failed and l .lt. MAXL, then continue iterating. +C----------------------------------------------------------------------- + 70 CONTINUE + RHO = BNRM*SNORMW*ABS(PROD/HES(LL,LL)) + IF (RHO .LE. DELTA) GO TO 200 + IF (LL .EQ. MAXL) GO TO 100 +C If l .lt. MAXL, store HES(l+1,l) and normalize the vector v(*,l+1). + 80 CONTINUE + HES(LL+1,LL) = SNORMW + TEM = 1.0D0/SNORMW + CALL DSCAL (N, TEM, V(1,LL+1), 1) + 90 CONTINUE +C----------------------------------------------------------------------- +C l has reached MAXL without passing the convergence test: +C If RHO is not too large, compute a solution anyway and return with +C IFLAG = 1. Otherwise return with IFLAG = 2. +C----------------------------------------------------------------------- + 100 CONTINUE + IF (RHO .LE. 1.0D0) GO TO 150 + IF (RHO .LE. BNRM .AND. MNEWT .EQ. 0) GO TO 150 + 120 CONTINUE + IFLAG = 2 + RETURN + 150 IFLAG = 1 +C----------------------------------------------------------------------- +C Compute the approximation x(l) to the solution. +C Since the vector X was used as work space, and the initial guess +C of the Newton correction is zero, X must be reset to zero. +C----------------------------------------------------------------------- + 200 CONTINUE + LL = LIOM + DO 210 K = 1,LL + 210 B(K) = 0.0D0 + B(1) = BNRM + CALL DHESL (HES, MAXL, LL, IPVT, B) + DO 220 K = 1,N + 220 X(K) = 0.0D0 + DO 230 I = 1,LL + CALL DAXPY (N, B(I), V(1,I), 1, X, 1) + 230 CONTINUE + DO 240 I = 1,N + 240 X(I) = X(I)/WGHT(I) + IF (JPRE .LE. 1) RETURN + CALL PSOL (NEQ, TN, Y, SAVF, WK, HL0, WP, IWP, X, 2, IER) + NPSL = NPSL + 1 + IF (IER .NE. 0) GO TO 300 + RETURN +C----------------------------------------------------------------------- +C This block handles error returns forced by routine PSOL. +C----------------------------------------------------------------------- + 300 CONTINUE + IF (IER .LT. 0) IFLAG = -1 + IF (IER .GT. 0) IFLAG = 3 + RETURN +C----------------------- End of Subroutine DSPIOM ---------------------- + END +*DECK DATV + SUBROUTINE DATV (NEQ, Y, SAVF, V, WGHT, FTEM, F, PSOL, Z, VTEM, + 1 WP, IWP, HL0, JPRE, IER, NPSL) + EXTERNAL F, PSOL + INTEGER NEQ, IWP, JPRE, IER, NPSL + DOUBLE PRECISION Y, SAVF, V, WGHT, FTEM, Z, VTEM, WP, HL0 + DIMENSION NEQ(*), Y(*), SAVF(*), V(*), WGHT(*), FTEM(*), Z(*), + 1 VTEM(*), WP(*), IWP(*) + INTEGER IOWND, IOWNS, + 1 ICF, IERPJ, IERSL, JCUR, JSTART, KFLAG, L, + 2 LYH, LEWT, LACOR, LSAVF, LWM, LIWM, METH, MITER, + 3 MAXORD, MAXCOR, MSBP, MXNCF, N, NQ, NST, NFE, NJE, NQU + DOUBLE PRECISION ROWNS, + 1 CCMAX, EL0, H, HMIN, HMXI, HU, RC, TN, UROUND + COMMON /DLS001/ ROWNS(209), + 1 CCMAX, EL0, H, HMIN, HMXI, HU, RC, TN, UROUND, + 2 IOWND(6), IOWNS(6), + 3 ICF, IERPJ, IERSL, JCUR, JSTART, KFLAG, L, + 4 LYH, LEWT, LACOR, LSAVF, LWM, LIWM, METH, MITER, + 5 MAXORD, MAXCOR, MSBP, MXNCF, N, NQ, NST, NFE, NJE, NQU +C----------------------------------------------------------------------- +C This routine computes the product +C +C (D-inverse)*(P1-inverse)*(I - hl0*df/dy)*(P2-inverse)*(D*v), +C +C where D is a diagonal scaling matrix, and P1 and P2 are the +C left and right preconditioning matrices, respectively. +C v is assumed to have WRMS norm equal to 1. +C The product is stored in z. This is computed by a +C difference quotient, a call to F, and two calls to PSOL. +C----------------------------------------------------------------------- +C +C On entry +C +C NEQ = problem size, passed to F and PSOL (NEQ(1) = N). +C +C Y = array containing current dependent variable vector. +C +C SAVF = array containing current value of f(t,y). +C +C V = real array of length N (can be the same array as Z). +C +C WGHT = array of length N containing scale factors. +C 1/WGHT(i) are the diagonal elements of the matrix D. +C +C FTEM = work array of length N. +C +C VTEM = work array of length N used to store the +C unscaled version of V. +C +C WP = real work array used by preconditioner PSOL. +C +C IWP = integer work array used by preconditioner PSOL. +C +C HL0 = current value of (step size h) * (coefficient l0). +C +C JPRE = preconditioner type flag. +C +C +C On return +C +C Z = array of length N containing desired scaled +C matrix-vector product. +C +C IER = error flag from PSOL. +C +C NPSL = the number of calls to PSOL. +C +C In addition, this routine uses the Common variables TN, N, NFE. +C----------------------------------------------------------------------- + INTEGER I + DOUBLE PRECISION FAC, RNORM, DNRM2, TEMPN +C +C Set VTEM = D * V. + DO 10 I = 1,N + 10 VTEM(I) = V(I)/WGHT(I) + IER = 0 + IF (JPRE .GE. 2) GO TO 30 +C +C JPRE = 0 or 1. Save Y in Z and increment Y by VTEM. + CALL DCOPY (N, Y, 1, Z, 1) + DO 20 I = 1,N + 20 Y(I) = Z(I) + VTEM(I) + FAC = HL0 + GO TO 60 +C +C JPRE = 2 or 3. Apply inverse of right preconditioner to VTEM. + 30 CONTINUE + CALL PSOL (NEQ, TN, Y, SAVF, FTEM, HL0, WP, IWP, VTEM, 2, IER) + NPSL = NPSL + 1 + IF (IER .NE. 0) RETURN +C Calculate L-2 norm of (D-inverse) * VTEM. + DO 40 I = 1,N + 40 Z(I) = VTEM(I)*WGHT(I) + TEMPN = DNRM2 (N, Z, 1) + RNORM = 1.0D0/TEMPN +C Save Y in Z and increment Y by VTEM/norm. + CALL DCOPY (N, Y, 1, Z, 1) + DO 50 I = 1,N + 50 Y(I) = Z(I) + VTEM(I)*RNORM + FAC = HL0*TEMPN +C +C For all JPRE, call F with incremented Y argument, and restore Y. + 60 CONTINUE + CALL F (NEQ, TN, Y, FTEM) + NFE = NFE + 1 + CALL DCOPY (N, Z, 1, Y, 1) +C Set Z = (identity - hl0*Jacobian) * VTEM, using difference quotient. + DO 70 I = 1,N + 70 Z(I) = FTEM(I) - SAVF(I) + DO 80 I = 1,N + 80 Z(I) = VTEM(I) - FAC*Z(I) +C Apply inverse of left preconditioner to Z, if nontrivial. + IF (JPRE .EQ. 0 .OR. JPRE .EQ. 2) GO TO 85 + CALL PSOL (NEQ, TN, Y, SAVF, FTEM, HL0, WP, IWP, Z, 1, IER) + NPSL = NPSL + 1 + IF (IER .NE. 0) RETURN + 85 CONTINUE +C Apply D-inverse to Z and return. + DO 90 I = 1,N + 90 Z(I) = Z(I)*WGHT(I) + RETURN +C----------------------- End of Subroutine DATV ------------------------ + END +*DECK DORTHOG + SUBROUTINE DORTHOG (VNEW, V, HES, N, LL, LDHES, KMP, SNORMW) + INTEGER N, LL, LDHES, KMP + DOUBLE PRECISION VNEW, V, HES, SNORMW + DIMENSION VNEW(*), V(N,*), HES(LDHES,*) +C----------------------------------------------------------------------- +C This routine orthogonalizes the vector VNEW against the previous +C KMP vectors in the V array. It uses a modified Gram-Schmidt +C orthogonalization procedure with conditional reorthogonalization. +C This is the version of 28 may 1986. +C----------------------------------------------------------------------- +C +C On entry +C +C VNEW = the vector of length N containing a scaled product +C of the Jacobian and the vector V(*,LL). +C +C V = the N x l array containing the previous LL +C orthogonal vectors v(*,1) to v(*,LL). +C +C HES = an LL x LL upper Hessenberg matrix containing, +C in HES(i,k), k.lt.LL, scaled inner products of +C A*V(*,k) and V(*,i). +C +C LDHES = the leading dimension of the HES array. +C +C N = the order of the matrix A, and the length of VNEW. +C +C LL = the current order of the matrix HES. +C +C KMP = the number of previous vectors the new vector VNEW +C must be made orthogonal to (KMP .le. MAXL). +C +C +C On return +C +C VNEW = the new vector orthogonal to V(*,i0) to V(*,LL), +C where i0 = MAX(1, LL-KMP+1). +C +C HES = upper Hessenberg matrix with column LL filled in with +C scaled inner products of A*V(*,LL) and V(*,i). +C +C SNORMW = L-2 norm of VNEW. +C +C----------------------------------------------------------------------- + INTEGER I, I0 + DOUBLE PRECISION ARG, DDOT, DNRM2, SUMDSQ, TEM, VNRM +C +C Get norm of unaltered VNEW for later use. ---------------------------- + VNRM = DNRM2 (N, VNEW, 1) +C----------------------------------------------------------------------- +C Do modified Gram-Schmidt on VNEW = A*v(LL). +C Scaled inner products give new column of HES. +C Projections of earlier vectors are subtracted from VNEW. +C----------------------------------------------------------------------- + I0 = MAX(1,LL-KMP+1) + DO 10 I = I0,LL + HES(I,LL) = DDOT (N, V(1,I), 1, VNEW, 1) + TEM = -HES(I,LL) + CALL DAXPY (N, TEM, V(1,I), 1, VNEW, 1) + 10 CONTINUE +C----------------------------------------------------------------------- +C Compute SNORMW = norm of VNEW. +C If VNEW is small compared to its input value (in norm), then +C reorthogonalize VNEW to V(*,1) through V(*,LL). +C Correct if relative correction exceeds 1000*(unit roundoff). +C finally, correct SNORMW using the dot products involved. +C----------------------------------------------------------------------- + SNORMW = DNRM2 (N, VNEW, 1) + IF (VNRM + 0.001D0*SNORMW .NE. VNRM) RETURN + SUMDSQ = 0.0D0 + DO 30 I = I0,LL + TEM = -DDOT (N, V(1,I), 1, VNEW, 1) + IF (HES(I,LL) + 0.001D0*TEM .EQ. HES(I,LL)) GO TO 30 + HES(I,LL) = HES(I,LL) - TEM + CALL DAXPY (N, TEM, V(1,I), 1, VNEW, 1) + SUMDSQ = SUMDSQ + TEM**2 + 30 CONTINUE + IF (SUMDSQ .EQ. 0.0D0) RETURN + ARG = MAX(0.0D0,SNORMW**2 - SUMDSQ) + SNORMW = SQRT(ARG) +C + RETURN +C----------------------- End of Subroutine DORTHOG --------------------- + END +*DECK DSPIGMR + SUBROUTINE DSPIGMR (NEQ, TN, Y, SAVF, B, WGHT, N, MAXL, MAXLP1, + 1 KMP, DELTA, HL0, JPRE, MNEWT, F, PSOL, NPSL, X, V, HES, Q, + 2 LGMR, WP, IWP, WK, DL, IFLAG) + EXTERNAL F, PSOL + INTEGER NEQ,N,MAXL,MAXLP1,KMP,JPRE,MNEWT,NPSL,LGMR,IWP,IFLAG + DOUBLE PRECISION TN,Y,SAVF,B,WGHT,DELTA,HL0,X,V,HES,Q,WP,WK,DL + DIMENSION NEQ(*), Y(*), SAVF(*), B(*), WGHT(*), X(*), V(N,*), + 1 HES(MAXLP1,*), Q(*), WP(*), IWP(*), WK(*), DL(*) +C----------------------------------------------------------------------- +C This routine solves the linear system A * x = b using a scaled +C preconditioned version of the Generalized Minimal Residual method. +C An initial guess of x = 0 is assumed. +C----------------------------------------------------------------------- +C +C On entry +C +C NEQ = problem size, passed to F and PSOL (NEQ(1) = N). +C +C TN = current value of t. +C +C Y = array containing current dependent variable vector. +C +C SAVF = array containing current value of f(t,y). +C +C B = the right hand side of the system A*x = b. +C B is also used as work space when computing +C the final approximation. +C (B is the same as V(*,MAXL+1) in the call to DSPIGMR.) +C +C WGHT = the vector of length N containing the nonzero +C elements of the diagonal scaling matrix. +C +C N = the order of the matrix A, and the lengths +C of the vectors WGHT, B and X. +C +C MAXL = the maximum allowable order of the matrix HES. +C +C MAXLP1 = MAXL + 1, used for dynamic dimensioning of HES. +C +C KMP = the number of previous vectors the new vector VNEW +C must be made orthogonal to. KMP .le. MAXL. +C +C DELTA = tolerance on residuals b - A*x in weighted RMS-norm. +C +C HL0 = current value of (step size h) * (coefficient l0). +C +C JPRE = preconditioner type flag. +C +C MNEWT = Newton iteration counter (.ge. 0). +C +C WK = real work array used by routine DATV and PSOL. +C +C DL = real work array used for calculation of the residual +C norm RHO when the method is incomplete (KMP .lt. MAXL). +C Not needed or referenced in complete case (KMP = MAXL). +C +C WP = real work array used by preconditioner PSOL. +C +C IWP = integer work array used by preconditioner PSOL. +C +C On return +C +C X = the final computed approximation to the solution +C of the system A*x = b. +C +C LGMR = the number of iterations performed and +C the current order of the upper Hessenberg +C matrix HES. +C +C NPSL = the number of calls to PSOL. +C +C V = the N by (LGMR+1) array containing the LGMR +C orthogonal vectors V(*,1) to V(*,LGMR). +C +C HES = the upper triangular factor of the QR decomposition +C of the (LGMR+1) by lgmr upper Hessenberg matrix whose +C entries are the scaled inner-products of A*V(*,i) +C and V(*,k). +C +C Q = real array of length 2*MAXL containing the components +C of the Givens rotations used in the QR decomposition +C of HES. It is loaded in DHEQR and used in DHELS. +C +C IFLAG = integer error flag: +C 0 means convergence in LGMR iterations, LGMR .le. MAXL. +C 1 means the convergence test did not pass in MAXL +C iterations, but the residual norm is .lt. 1, +C or .lt. norm(b) if MNEWT = 0, and so x is computed. +C 2 means the convergence test did not pass in MAXL +C iterations, residual .gt. 1, and X is undefined. +C 3 means there was a recoverable error in PSOL +C caused by the preconditioner being out of date. +C -1 means there was a nonrecoverable error in PSOL. +C +C----------------------------------------------------------------------- + INTEGER I, IER, INFO, IP1, I2, J, K, LL, LLP1 + DOUBLE PRECISION BNRM,BNRM0,C,DLNRM,PROD,RHO,S,SNORMW,DNRM2,TEM +C + IFLAG = 0 + LGMR = 0 + NPSL = 0 +C----------------------------------------------------------------------- +C The initial residual is the vector b. Apply scaling to b, and test +C for an immediate return with X = 0 or X = b. +C----------------------------------------------------------------------- + DO 10 I = 1,N + 10 V(I,1) = B(I)*WGHT(I) + BNRM0 = DNRM2 (N, V, 1) + BNRM = BNRM0 + IF (BNRM0 .GT. DELTA) GO TO 30 + IF (MNEWT .GT. 0) GO TO 20 + CALL DCOPY (N, B, 1, X, 1) + RETURN + 20 DO 25 I = 1,N + 25 X(I) = 0.0D0 + RETURN + 30 CONTINUE +C Apply inverse of left preconditioner to vector b. -------------------- + IER = 0 + IF (JPRE .EQ. 0 .OR. JPRE .EQ. 2) GO TO 55 + CALL PSOL (NEQ, TN, Y, SAVF, WK, HL0, WP, IWP, B, 1, IER) + NPSL = 1 + IF (IER .NE. 0) GO TO 300 +C Calculate norm of scaled vector V(*,1) and normalize it. ------------- + DO 50 I = 1,N + 50 V(I,1) = B(I)*WGHT(I) + BNRM = DNRM2 (N, V, 1) + DELTA = DELTA*(BNRM/BNRM0) + 55 TEM = 1.0D0/BNRM + CALL DSCAL (N, TEM, V(1,1), 1) +C Zero out the HES array. ---------------------------------------------- + DO 65 J = 1,MAXL + DO 60 I = 1,MAXLP1 + 60 HES(I,J) = 0.0D0 + 65 CONTINUE +C----------------------------------------------------------------------- +C Main loop to compute the vectors V(*,2) to V(*,MAXL). +C The running product PROD is needed for the convergence test. +C----------------------------------------------------------------------- + PROD = 1.0D0 + DO 90 LL = 1,MAXL + LGMR = LL +C----------------------------------------------------------------------- +C Call routine DATV to compute VNEW = Abar*v(ll), where Abar is +C the matrix A with scaling and inverse preconditioner factors applied. +C Call routine DORTHOG to orthogonalize the new vector VNEW = V(*,LL+1). +C Call routine DHEQR to update the factors of HES. +C----------------------------------------------------------------------- + CALL DATV (NEQ, Y, SAVF, V(1,LL), WGHT, X, F, PSOL, V(1,LL+1), + 1 WK, WP, IWP, HL0, JPRE, IER, NPSL) + IF (IER .NE. 0) GO TO 300 + CALL DORTHOG (V(1,LL+1), V, HES, N, LL, MAXLP1, KMP, SNORMW) + HES(LL+1,LL) = SNORMW + CALL DHEQR (HES, MAXLP1, LL, Q, INFO, LL) + IF (INFO .EQ. LL) GO TO 120 +C----------------------------------------------------------------------- +C Update RHO, the estimate of the norm of the residual b - A*xl. +C If KMP .lt. MAXL, then the vectors V(*,1),...,V(*,LL+1) are not +C necessarily orthogonal for LL .gt. KMP. The vector DL must then +C be computed, and its norm used in the calculation of RHO. +C----------------------------------------------------------------------- + PROD = PROD*Q(2*LL) + RHO = ABS(PROD*BNRM) + IF ((LL.GT.KMP) .AND. (KMP.LT.MAXL)) THEN + IF (LL .EQ. KMP+1) THEN + CALL DCOPY (N, V(1,1), 1, DL, 1) + DO 75 I = 1,KMP + IP1 = I + 1 + I2 = I*2 + S = Q(I2) + C = Q(I2-1) + DO 70 K = 1,N + 70 DL(K) = S*DL(K) + C*V(K,IP1) + 75 CONTINUE + ENDIF + S = Q(2*LL) + C = Q(2*LL-1)/SNORMW + LLP1 = LL + 1 + DO 80 K = 1,N + 80 DL(K) = S*DL(K) + C*V(K,LLP1) + DLNRM = DNRM2 (N, DL, 1) + RHO = RHO*DLNRM + ENDIF +C----------------------------------------------------------------------- +C Test for convergence. If passed, compute approximation xl. +C if failed and LL .lt. MAXL, then continue iterating. +C----------------------------------------------------------------------- + IF (RHO .LE. DELTA) GO TO 200 + IF (LL .EQ. MAXL) GO TO 100 +C----------------------------------------------------------------------- +C Rescale so that the norm of V(1,LL+1) is one. +C----------------------------------------------------------------------- + TEM = 1.0D0/SNORMW + CALL DSCAL (N, TEM, V(1,LL+1), 1) + 90 CONTINUE + 100 CONTINUE + IF (RHO .LE. 1.0D0) GO TO 150 + IF (RHO .LE. BNRM .AND. MNEWT .EQ. 0) GO TO 150 + 120 CONTINUE + IFLAG = 2 + RETURN + 150 IFLAG = 1 +C----------------------------------------------------------------------- +C Compute the approximation xl to the solution. +C Since the vector X was used as work space, and the initial guess +C of the Newton correction is zero, X must be reset to zero. +C----------------------------------------------------------------------- + 200 CONTINUE + LL = LGMR + LLP1 = LL + 1 + DO 210 K = 1,LLP1 + 210 B(K) = 0.0D0 + B(1) = BNRM + CALL DHELS (HES, MAXLP1, LL, Q, B) + DO 220 K = 1,N + 220 X(K) = 0.0D0 + DO 230 I = 1,LL + CALL DAXPY (N, B(I), V(1,I), 1, X, 1) + 230 CONTINUE + DO 240 I = 1,N + 240 X(I) = X(I)/WGHT(I) + IF (JPRE .LE. 1) RETURN + CALL PSOL (NEQ, TN, Y, SAVF, WK, HL0, WP, IWP, X, 2, IER) + NPSL = NPSL + 1 + IF (IER .NE. 0) GO TO 300 + RETURN +C----------------------------------------------------------------------- +C This block handles error returns forced by routine PSOL. +C----------------------------------------------------------------------- + 300 CONTINUE + IF (IER .LT. 0) IFLAG = -1 + IF (IER .GT. 0) IFLAG = 3 +C + RETURN +C----------------------- End of Subroutine DSPIGMR --------------------- + END +*DECK DPCG + SUBROUTINE DPCG (NEQ, TN, Y, SAVF, R, WGHT, N, MAXL, DELTA, HL0, + 1 JPRE, MNEWT, F, PSOL, NPSL, X, P, W, Z, LPCG, WP, IWP, WK, IFLAG) + EXTERNAL F, PSOL + INTEGER NEQ, N, MAXL, JPRE, MNEWT, NPSL, LPCG, IWP, IFLAG + DOUBLE PRECISION TN,Y,SAVF,R,WGHT,DELTA,HL0,X,P,W,Z,WP,WK + DIMENSION NEQ(*), Y(*), SAVF(*), R(*), WGHT(*), X(*), P(*), W(*), + 1 Z(*), WP(*), IWP(*), WK(*) +C----------------------------------------------------------------------- +C This routine computes the solution to the system A*x = b using a +C preconditioned version of the Conjugate Gradient algorithm. +C It is assumed here that the matrix A and the preconditioner +C matrix M are symmetric positive definite or nearly so. +C----------------------------------------------------------------------- +C +C On entry +C +C NEQ = problem size, passed to F and PSOL (NEQ(1) = N). +C +C TN = current value of t. +C +C Y = array containing current dependent variable vector. +C +C SAVF = array containing current value of f(t,y). +C +C R = the right hand side of the system A*x = b. +C +C WGHT = array of length N containing scale factors. +C 1/WGHT(i) are the diagonal elements of the diagonal +C scaling matrix D. +C +C N = the order of the matrix A, and the lengths +C of the vectors Y, SAVF, R, WGHT, P, W, Z, WK, and X. +C +C MAXL = the maximum allowable number of iterates. +C +C DELTA = tolerance on residuals b - A*x in weighted RMS-norm. +C +C HL0 = current value of (step size h) * (coefficient l0). +C +C JPRE = preconditioner type flag. +C +C MNEWT = Newton iteration counter (.ge. 0). +C +C WK = real work array used by routine DATP. +C +C WP = real work array used by preconditioner PSOL. +C +C IWP = integer work array used by preconditioner PSOL. +C +C On return +C +C X = the final computed approximation to the solution +C of the system A*x = b. +C +C LPCG = the number of iterations performed, and current +C order of the upper Hessenberg matrix HES. +C +C NPSL = the number of calls to PSOL. +C +C IFLAG = integer error flag: +C 0 means convergence in LPCG iterations, LPCG .le. MAXL. +C 1 means the convergence test did not pass in MAXL +C iterations, but the residual norm is .lt. 1, +C or .lt. norm(b) if MNEWT = 0, and so X is computed. +C 2 means the convergence test did not pass in MAXL +C iterations, residual .gt. 1, and X is undefined. +C 3 means there was a recoverable error in PSOL +C caused by the preconditioner being out of date. +C 4 means there was a zero denominator in the algorithm. +C The system matrix or preconditioner matrix is not +C sufficiently close to being symmetric pos. definite. +C -1 means there was a nonrecoverable error in PSOL. +C +C----------------------------------------------------------------------- + INTEGER I, IER + DOUBLE PRECISION ALPHA,BETA,BNRM,PTW,RNRM,DDOT,DVNORM,ZTR,ZTR0 +C + IFLAG = 0 + NPSL = 0 + LPCG = 0 + DO 10 I = 1,N + 10 X(I) = 0.0D0 + BNRM = DVNORM (N, R, WGHT) +C Test for immediate return with X = 0 or X = b. ----------------------- + IF (BNRM .GT. DELTA) GO TO 20 + IF (MNEWT .GT. 0) RETURN + CALL DCOPY (N, R, 1, X, 1) + RETURN +C + 20 ZTR = 0.0D0 +C Loop point for PCG iterations. --------------------------------------- + 30 CONTINUE + LPCG = LPCG + 1 + CALL DCOPY (N, R, 1, Z, 1) + IER = 0 + IF (JPRE .EQ. 0) GO TO 40 + CALL PSOL (NEQ, TN, Y, SAVF, WK, HL0, WP, IWP, Z, 3, IER) + NPSL = NPSL + 1 + IF (IER .NE. 0) GO TO 100 + 40 CONTINUE + ZTR0 = ZTR + ZTR = DDOT (N, Z, 1, R, 1) + IF (LPCG .NE. 1) GO TO 50 + CALL DCOPY (N, Z, 1, P, 1) + GO TO 70 + 50 CONTINUE + IF (ZTR0 .EQ. 0.0D0) GO TO 200 + BETA = ZTR/ZTR0 + DO 60 I = 1,N + 60 P(I) = Z(I) + BETA*P(I) + 70 CONTINUE +C----------------------------------------------------------------------- +C Call DATP to compute A*p and return the answer in W. +C----------------------------------------------------------------------- + CALL DATP (NEQ, Y, SAVF, P, WGHT, HL0, WK, F, W) +C + PTW = DDOT (N, P, 1, W, 1) + IF (PTW .EQ. 0.0D0) GO TO 200 + ALPHA = ZTR/PTW + CALL DAXPY (N, ALPHA, P, 1, X, 1) + ALPHA = -ALPHA + CALL DAXPY (N, ALPHA, W, 1, R, 1) + RNRM = DVNORM (N, R, WGHT) + IF (RNRM .LE. DELTA) RETURN + IF (LPCG .LT. MAXL) GO TO 30 + IFLAG = 2 + IF (RNRM .LE. 1.0D0) IFLAG = 1 + IF (RNRM .LE. BNRM .AND. MNEWT .EQ. 0) IFLAG = 1 + RETURN +C----------------------------------------------------------------------- +C This block handles error returns from PSOL. +C----------------------------------------------------------------------- + 100 CONTINUE + IF (IER .LT. 0) IFLAG = -1 + IF (IER .GT. 0) IFLAG = 3 + RETURN +C----------------------------------------------------------------------- +C This block handles division by zero errors. +C----------------------------------------------------------------------- + 200 CONTINUE + IFLAG = 4 + RETURN +C----------------------- End of Subroutine DPCG ------------------------ + END +*DECK DPCGS + SUBROUTINE DPCGS (NEQ, TN, Y, SAVF, R, WGHT, N, MAXL, DELTA, HL0, + 1 JPRE, MNEWT, F, PSOL, NPSL, X, P, W, Z, LPCG, WP, IWP, WK, IFLAG) + EXTERNAL F, PSOL + INTEGER NEQ, N, MAXL, JPRE, MNEWT, NPSL, LPCG, IWP, IFLAG + DOUBLE PRECISION TN,Y,SAVF,R,WGHT,DELTA,HL0,X,P,W,Z,WP,WK + DIMENSION NEQ(*), Y(*), SAVF(*), R(*), WGHT(*), X(*), P(*), W(*), + 1 Z(*), WP(*), IWP(*), WK(*) +C----------------------------------------------------------------------- +C This routine computes the solution to the system A*x = b using a +C scaled preconditioned version of the Conjugate Gradient algorithm. +C It is assumed here that the scaled matrix D**-1 * A * D and the +C scaled preconditioner D**-1 * M * D are close to being +C symmetric positive definite. +C----------------------------------------------------------------------- +C +C On entry +C +C NEQ = problem size, passed to F and PSOL (NEQ(1) = N). +C +C TN = current value of t. +C +C Y = array containing current dependent variable vector. +C +C SAVF = array containing current value of f(t,y). +C +C R = the right hand side of the system A*x = b. +C +C WGHT = array of length N containing scale factors. +C 1/WGHT(i) are the diagonal elements of the diagonal +C scaling matrix D. +C +C N = the order of the matrix A, and the lengths +C of the vectors Y, SAVF, R, WGHT, P, W, Z, WK, and X. +C +C MAXL = the maximum allowable number of iterates. +C +C DELTA = tolerance on residuals b - A*x in weighted RMS-norm. +C +C HL0 = current value of (step size h) * (coefficient l0). +C +C JPRE = preconditioner type flag. +C +C MNEWT = Newton iteration counter (.ge. 0). +C +C WK = real work array used by routine DATP. +C +C WP = real work array used by preconditioner PSOL. +C +C IWP = integer work array used by preconditioner PSOL. +C +C On return +C +C X = the final computed approximation to the solution +C of the system A*x = b. +C +C LPCG = the number of iterations performed, and current +C order of the upper Hessenberg matrix HES. +C +C NPSL = the number of calls to PSOL. +C +C IFLAG = integer error flag: +C 0 means convergence in LPCG iterations, LPCG .le. MAXL. +C 1 means the convergence test did not pass in MAXL +C iterations, but the residual norm is .lt. 1, +C or .lt. norm(b) if MNEWT = 0, and so X is computed. +C 2 means the convergence test did not pass in MAXL +C iterations, residual .gt. 1, and X is undefined. +C 3 means there was a recoverable error in PSOL +C caused by the preconditioner being out of date. +C 4 means there was a zero denominator in the algorithm. +C the scaled matrix or scaled preconditioner is not +C sufficiently close to being symmetric pos. definite. +C -1 means there was a nonrecoverable error in PSOL. +C +C----------------------------------------------------------------------- + INTEGER I, IER + DOUBLE PRECISION ALPHA, BETA, BNRM, PTW, RNRM, DVNORM, ZTR, ZTR0 +C + IFLAG = 0 + NPSL = 0 + LPCG = 0 + DO 10 I = 1,N + 10 X(I) = 0.0D0 + BNRM = DVNORM (N, R, WGHT) +C Test for immediate return with X = 0 or X = b. ----------------------- + IF (BNRM .GT. DELTA) GO TO 20 + IF (MNEWT .GT. 0) RETURN + CALL DCOPY (N, R, 1, X, 1) + RETURN +C + 20 ZTR = 0.0D0 +C Loop point for PCG iterations. --------------------------------------- + 30 CONTINUE + LPCG = LPCG + 1 + CALL DCOPY (N, R, 1, Z, 1) + IER = 0 + IF (JPRE .EQ. 0) GO TO 40 + CALL PSOL (NEQ, TN, Y, SAVF, WK, HL0, WP, IWP, Z, 3, IER) + NPSL = NPSL + 1 + IF (IER .NE. 0) GO TO 100 + 40 CONTINUE + ZTR0 = ZTR + ZTR = 0.0D0 + DO 45 I = 1,N + 45 ZTR = ZTR + Z(I)*R(I)*WGHT(I)**2 + IF (LPCG .NE. 1) GO TO 50 + CALL DCOPY (N, Z, 1, P, 1) + GO TO 70 + 50 CONTINUE + IF (ZTR0 .EQ. 0.0D0) GO TO 200 + BETA = ZTR/ZTR0 + DO 60 I = 1,N + 60 P(I) = Z(I) + BETA*P(I) + 70 CONTINUE +C----------------------------------------------------------------------- +C Call DATP to compute A*p and return the answer in W. +C----------------------------------------------------------------------- + CALL DATP (NEQ, Y, SAVF, P, WGHT, HL0, WK, F, W) +C + PTW = 0.0D0 + DO 80 I = 1,N + 80 PTW = PTW + P(I)*W(I)*WGHT(I)**2 + IF (PTW .EQ. 0.0D0) GO TO 200 + ALPHA = ZTR/PTW + CALL DAXPY (N, ALPHA, P, 1, X, 1) + ALPHA = -ALPHA + CALL DAXPY (N, ALPHA, W, 1, R, 1) + RNRM = DVNORM (N, R, WGHT) + IF (RNRM .LE. DELTA) RETURN + IF (LPCG .LT. MAXL) GO TO 30 + IFLAG = 2 + IF (RNRM .LE. 1.0D0) IFLAG = 1 + IF (RNRM .LE. BNRM .AND. MNEWT .EQ. 0) IFLAG = 1 + RETURN +C----------------------------------------------------------------------- +C This block handles error returns from PSOL. +C----------------------------------------------------------------------- + 100 CONTINUE + IF (IER .LT. 0) IFLAG = -1 + IF (IER .GT. 0) IFLAG = 3 + RETURN +C----------------------------------------------------------------------- +C This block handles division by zero errors. +C----------------------------------------------------------------------- + 200 CONTINUE + IFLAG = 4 + RETURN +C----------------------- End of Subroutine DPCGS ----------------------- + END +*DECK DATP + SUBROUTINE DATP (NEQ, Y, SAVF, P, WGHT, HL0, WK, F, W) + EXTERNAL F + INTEGER NEQ + DOUBLE PRECISION Y, SAVF, P, WGHT, HL0, WK, W + DIMENSION NEQ(*), Y(*), SAVF(*), P(*), WGHT(*), WK(*), W(*) + INTEGER IOWND, IOWNS, + 1 ICF, IERPJ, IERSL, JCUR, JSTART, KFLAG, L, + 2 LYH, LEWT, LACOR, LSAVF, LWM, LIWM, METH, MITER, + 3 MAXORD, MAXCOR, MSBP, MXNCF, N, NQ, NST, NFE, NJE, NQU + DOUBLE PRECISION ROWNS, + 1 CCMAX, EL0, H, HMIN, HMXI, HU, RC, TN, UROUND + COMMON /DLS001/ ROWNS(209), + 1 CCMAX, EL0, H, HMIN, HMXI, HU, RC, TN, UROUND, + 2 IOWND(6), IOWNS(6), + 3 ICF, IERPJ, IERSL, JCUR, JSTART, KFLAG, L, + 4 LYH, LEWT, LACOR, LSAVF, LWM, LIWM, METH, MITER, + 5 MAXORD, MAXCOR, MSBP, MXNCF, N, NQ, NST, NFE, NJE, NQU +C----------------------------------------------------------------------- +C This routine computes the product +C +C w = (I - hl0*df/dy)*p +C +C This is computed by a call to F and a difference quotient. +C----------------------------------------------------------------------- +C +C On entry +C +C NEQ = problem size, passed to F and PSOL (NEQ(1) = N). +C +C Y = array containing current dependent variable vector. +C +C SAVF = array containing current value of f(t,y). +C +C P = real array of length N. +C +C WGHT = array of length N containing scale factors. +C 1/WGHT(i) are the diagonal elements of the matrix D. +C +C WK = work array of length N. +C +C On return +C +C +C W = array of length N containing desired +C matrix-vector product. +C +C In addition, this routine uses the Common variables TN, N, NFE. +C----------------------------------------------------------------------- + INTEGER I + DOUBLE PRECISION FAC, PNRM, RPNRM, DVNORM +C + PNRM = DVNORM (N, P, WGHT) + RPNRM = 1.0D0/PNRM + CALL DCOPY (N, Y, 1, W, 1) + DO 20 I = 1,N + 20 Y(I) = W(I) + P(I)*RPNRM + CALL F (NEQ, TN, Y, WK) + NFE = NFE + 1 + CALL DCOPY (N, W, 1, Y, 1) + FAC = HL0*PNRM + DO 40 I = 1,N + 40 W(I) = P(I) - FAC*(WK(I) - SAVF(I)) + RETURN +C----------------------- End of Subroutine DATP ------------------------ + END +*DECK DUSOL + SUBROUTINE DUSOL (NEQ, TN, Y, SAVF, B, WGHT, N, DELTA, HL0, MNEWT, + 1 PSOL, NPSL, X, WP, IWP, WK, IFLAG) + EXTERNAL PSOL + INTEGER NEQ, N, MNEWT, NPSL, IWP, IFLAG + DOUBLE PRECISION TN, Y, SAVF, B, WGHT, DELTA, HL0, X, WP, WK + DIMENSION NEQ(*), Y(*), SAVF(*), B(*), WGHT(*), X(*), + 1 WP(*), IWP(*), WK(*) +C----------------------------------------------------------------------- +C This routine solves the linear system A * x = b using only a call +C to the user-supplied routine PSOL (no Krylov iteration). +C If the norm of the right-hand side vector b is smaller than DELTA, +C the vector X returned is X = b (if MNEWT = 0) or X = 0 otherwise. +C PSOL is called with an LR argument of 0. +C----------------------------------------------------------------------- +C +C On entry +C +C NEQ = problem size, passed to F and PSOL (NEQ(1) = N). +C +C TN = current value of t. +C +C Y = array containing current dependent variable vector. +C +C SAVF = array containing current value of f(t,y). +C +C B = the right hand side of the system A*x = b. +C +C WGHT = the vector of length N containing the nonzero +C elements of the diagonal scaling matrix. +C +C N = the order of the matrix A, and the lengths +C of the vectors WGHT, B and X. +C +C DELTA = tolerance on residuals b - A*x in weighted RMS-norm. +C +C HL0 = current value of (step size h) * (coefficient l0). +C +C MNEWT = Newton iteration counter (.ge. 0). +C +C WK = real work array used by PSOL. +C +C WP = real work array used by preconditioner PSOL. +C +C IWP = integer work array used by preconditioner PSOL. +C +C On return +C +C X = the final computed approximation to the solution +C of the system A*x = b. +C +C NPSL = the number of calls to PSOL. +C +C IFLAG = integer error flag: +C 0 means no trouble occurred. +C 3 means there was a recoverable error in PSOL +C caused by the preconditioner being out of date. +C -1 means there was a nonrecoverable error in PSOL. +C +C----------------------------------------------------------------------- + INTEGER I, IER + DOUBLE PRECISION BNRM, DVNORM +C + IFLAG = 0 + NPSL = 0 +C----------------------------------------------------------------------- +C Test for an immediate return with X = 0 or X = b. +C----------------------------------------------------------------------- + BNRM = DVNORM (N, B, WGHT) + IF (BNRM .GT. DELTA) GO TO 30 + IF (MNEWT .GT. 0) GO TO 10 + CALL DCOPY (N, B, 1, X, 1) + RETURN + 10 DO 20 I = 1,N + 20 X(I) = 0.0D0 + RETURN +C Make call to PSOL and copy result from B to X. ----------------------- + 30 IER = 0 + CALL PSOL (NEQ, TN, Y, SAVF, WK, HL0, WP, IWP, B, 0, IER) + NPSL = 1 + IF (IER .NE. 0) GO TO 100 + CALL DCOPY (N, B, 1, X, 1) + RETURN +C----------------------------------------------------------------------- +C This block handles error returns forced by routine PSOL. +C----------------------------------------------------------------------- + 100 CONTINUE + IF (IER .LT. 0) IFLAG = -1 + IF (IER .GT. 0) IFLAG = 3 + RETURN +C----------------------- End of Subroutine DUSOL ----------------------- + END +*DECK DSRCPK + SUBROUTINE DSRCPK (RSAV, ISAV, JOB) +C----------------------------------------------------------------------- +C This routine saves or restores (depending on JOB) the contents of +C the Common blocks DLS001, DLPK01, which are used +C internally by the DLSODPK solver. +C +C RSAV = real array of length 222 or more. +C ISAV = integer array of length 50 or more. +C JOB = flag indicating to save or restore the Common blocks: +C JOB = 1 if Common is to be saved (written to RSAV/ISAV) +C JOB = 2 if Common is to be restored (read from RSAV/ISAV) +C A call with JOB = 2 presumes a prior call with JOB = 1. +C----------------------------------------------------------------------- + INTEGER ISAV, JOB + INTEGER ILS, ILSP + INTEGER I, LENILP, LENRLP, LENILS, LENRLS + DOUBLE PRECISION RSAV, RLS, RLSP + DIMENSION RSAV(*), ISAV(*) + SAVE LENRLS, LENILS, LENRLP, LENILP + COMMON /DLS001/ RLS(218), ILS(37) + COMMON /DLPK01/ RLSP(4), ILSP(13) + DATA LENRLS/218/, LENILS/37/, LENRLP/4/, LENILP/13/ +C + IF (JOB .EQ. 2) GO TO 100 + CALL DCOPY (LENRLS, RLS, 1, RSAV, 1) + CALL DCOPY (LENRLP, RLSP, 1, RSAV(LENRLS+1), 1) + DO 20 I = 1,LENILS + 20 ISAV(I) = ILS(I) + DO 40 I = 1,LENILP + 40 ISAV(LENILS+I) = ILSP(I) + RETURN +C + 100 CONTINUE + CALL DCOPY (LENRLS, RSAV, 1, RLS, 1) + CALL DCOPY (LENRLP, RSAV(LENRLS+1), 1, RLSP, 1) + DO 120 I = 1,LENILS + 120 ILS(I) = ISAV(I) + DO 140 I = 1,LENILP + 140 ILSP(I) = ISAV(LENILS+I) + RETURN +C----------------------- End of Subroutine DSRCPK ---------------------- + END +*DECK DHEFA + SUBROUTINE DHEFA (A, LDA, N, IPVT, INFO, JOB) + INTEGER LDA, N, IPVT(*), INFO, JOB + DOUBLE PRECISION A(LDA,*) +C----------------------------------------------------------------------- +C This routine is a modification of the LINPACK routine DGEFA and +C performs an LU decomposition of an upper Hessenberg matrix A. +C There are two options available: +C +C (1) performing a fresh factorization +C (2) updating the LU factors by adding a row and a +C column to the matrix A. +C----------------------------------------------------------------------- +C DHEFA factors an upper Hessenberg matrix by elimination. +C +C On entry +C +C A DOUBLE PRECISION(LDA, N) +C the matrix to be factored. +C +C LDA INTEGER +C the leading dimension of the array A . +C +C N INTEGER +C the order of the matrix A . +C +C JOB INTEGER +C JOB = 1 means that a fresh factorization of the +C matrix A is desired. +C JOB .ge. 2 means that the current factorization of A +C will be updated by the addition of a row +C and a column. +C +C On return +C +C A an upper triangular matrix and the multipliers +C which were used to obtain it. +C The factorization can be written A = L*U where +C L is a product of permutation and unit lower +C triangular matrices and U is upper triangular. +C +C IPVT INTEGER(N) +C an integer vector of pivot indices. +C +C INFO INTEGER +C = 0 normal value. +C = k if U(k,k) .eq. 0.0 . This is not an error +C condition for this subroutine, but it does +C indicate that DHESL will divide by zero if called. +C +C Modification of LINPACK, by Peter Brown, LLNL. +C Written 7/20/83. This version dated 6/20/01. +C +C BLAS called: DAXPY, IDAMAX +C----------------------------------------------------------------------- + INTEGER IDAMAX, J, K, KM1, KP1, L, NM1 + DOUBLE PRECISION T +C + IF (JOB .GT. 1) GO TO 80 +C +C A new facorization is desired. This is essentially the LINPACK +C code with the exception that we know there is only one nonzero +C element below the main diagonal. +C +C Gaussian elimination with partial pivoting +C + INFO = 0 + NM1 = N - 1 + IF (NM1 .LT. 1) GO TO 70 + DO 60 K = 1, NM1 + KP1 = K + 1 +C +C Find L = pivot index +C + L = IDAMAX (2, A(K,K), 1) + K - 1 + IPVT(K) = L +C +C Zero pivot implies this column already triangularized +C + IF (A(L,K) .EQ. 0.0D0) GO TO 40 +C +C Interchange if necessary +C + IF (L .EQ. K) GO TO 10 + T = A(L,K) + A(L,K) = A(K,K) + A(K,K) = T + 10 CONTINUE +C +C Compute multipliers +C + T = -1.0D0/A(K,K) + A(K+1,K) = A(K+1,K)*T +C +C Row elimination with column indexing +C + DO 30 J = KP1, N + T = A(L,J) + IF (L .EQ. K) GO TO 20 + A(L,J) = A(K,J) + A(K,J) = T + 20 CONTINUE + CALL DAXPY (N-K, T, A(K+1,K), 1, A(K+1,J), 1) + 30 CONTINUE + GO TO 50 + 40 CONTINUE + INFO = K + 50 CONTINUE + 60 CONTINUE + 70 CONTINUE + IPVT(N) = N + IF (A(N,N) .EQ. 0.0D0) INFO = N + RETURN +C +C The old factorization of A will be updated. A row and a column +C has been added to the matrix A. +C N-1 is now the old order of the matrix. +C + 80 CONTINUE + NM1 = N - 1 +C +C Perform row interchanges on the elements of the new column, and +C perform elimination operations on the elements using the multipliers. +C + IF (NM1 .LE. 1) GO TO 105 + DO 100 K = 2,NM1 + KM1 = K - 1 + L = IPVT(KM1) + T = A(L,N) + IF (L .EQ. KM1) GO TO 90 + A(L,N) = A(KM1,N) + A(KM1,N) = T + 90 CONTINUE + A(K,N) = A(K,N) + A(K,KM1)*T + 100 CONTINUE + 105 CONTINUE +C +C Complete update of factorization by decomposing last 2x2 block. +C + INFO = 0 +C +C Find L = pivot index +C + L = IDAMAX (2, A(NM1,NM1), 1) + NM1 - 1 + IPVT(NM1) = L +C +C Zero pivot implies this column already triangularized +C + IF (A(L,NM1) .EQ. 0.0D0) GO TO 140 +C +C Interchange if necessary +C + IF (L .EQ. NM1) GO TO 110 + T = A(L,NM1) + A(L,NM1) = A(NM1,NM1) + A(NM1,NM1) = T + 110 CONTINUE +C +C Compute multipliers +C + T = -1.0D0/A(NM1,NM1) + A(N,NM1) = A(N,NM1)*T +C +C Row elimination with column indexing +C + T = A(L,N) + IF (L .EQ. NM1) GO TO 120 + A(L,N) = A(NM1,N) + A(NM1,N) = T + 120 CONTINUE + A(N,N) = A(N,N) + T*A(N,NM1) + GO TO 150 + 140 CONTINUE + INFO = NM1 + 150 CONTINUE + IPVT(N) = N + IF (A(N,N) .EQ. 0.0D0) INFO = N + RETURN +C----------------------- End of Subroutine DHEFA ----------------------- + END +*DECK DHESL + SUBROUTINE DHESL (A, LDA, N, IPVT, B) + INTEGER LDA, N, IPVT(*) + DOUBLE PRECISION A(LDA,*), B(*) +C----------------------------------------------------------------------- +C This is essentially the LINPACK routine DGESL except for changes +C due to the fact that A is an upper Hessenberg matrix. +C----------------------------------------------------------------------- +C DHESL solves the real system A * x = b +C using the factors computed by DHEFA. +C +C On entry +C +C A DOUBLE PRECISION(LDA, N) +C the output from DHEFA. +C +C LDA INTEGER +C the leading dimension of the array A . +C +C N INTEGER +C the order of the matrix A . +C +C IPVT INTEGER(N) +C the pivot vector from DHEFA. +C +C B DOUBLE PRECISION(N) +C the right hand side vector. +C +C On return +C +C B the solution vector x . +C +C Modification of LINPACK, by Peter Brown, LLNL. +C Written 7/20/83. This version dated 6/20/01. +C +C BLAS called: DAXPY +C----------------------------------------------------------------------- + INTEGER K, KB, L, NM1 + DOUBLE PRECISION T +C + NM1 = N - 1 +C +C Solve A * x = b +C First solve L*y = b +C + IF (NM1 .LT. 1) GO TO 30 + DO 20 K = 1, NM1 + L = IPVT(K) + T = B(L) + IF (L .EQ. K) GO TO 10 + B(L) = B(K) + B(K) = T + 10 CONTINUE + B(K+1) = B(K+1) + T*A(K+1,K) + 20 CONTINUE + 30 CONTINUE +C +C Now solve U*x = y +C + DO 40 KB = 1, N + K = N + 1 - KB + B(K) = B(K)/A(K,K) + T = -B(K) + CALL DAXPY (K-1, T, A(1,K), 1, B(1), 1) + 40 CONTINUE + RETURN +C----------------------- End of Subroutine DHESL ----------------------- + END +*DECK DHEQR + SUBROUTINE DHEQR (A, LDA, N, Q, INFO, IJOB) + INTEGER LDA, N, INFO, IJOB + DOUBLE PRECISION A(LDA,*), Q(*) +C----------------------------------------------------------------------- +C This routine performs a QR decomposition of an upper +C Hessenberg matrix A. There are two options available: +C +C (1) performing a fresh decomposition +C (2) updating the QR factors by adding a row and a +C column to the matrix A. +C----------------------------------------------------------------------- +C DHEQR decomposes an upper Hessenberg matrix by using Givens +C rotations. +C +C On entry +C +C A DOUBLE PRECISION(LDA, N) +C the matrix to be decomposed. +C +C LDA INTEGER +C the leading dimension of the array A . +C +C N INTEGER +C A is an (N+1) by N Hessenberg matrix. +C +C IJOB INTEGER +C = 1 means that a fresh decomposition of the +C matrix A is desired. +C .ge. 2 means that the current decomposition of A +C will be updated by the addition of a row +C and a column. +C On return +C +C A the upper triangular matrix R. +C The factorization can be written Q*A = R, where +C Q is a product of Givens rotations and R is upper +C triangular. +C +C Q DOUBLE PRECISION(2*N) +C the factors c and s of each Givens rotation used +C in decomposing A. +C +C INFO INTEGER +C = 0 normal value. +C = k if A(k,k) .eq. 0.0 . This is not an error +C condition for this subroutine, but it does +C indicate that DHELS will divide by zero +C if called. +C +C Modification of LINPACK, by Peter Brown, LLNL. +C Written 1/13/86. This version dated 6/20/01. +C----------------------------------------------------------------------- + INTEGER I, IQ, J, K, KM1, KP1, NM1 + DOUBLE PRECISION C, S, T, T1, T2 +C + IF (IJOB .GT. 1) GO TO 70 +C +C A new facorization is desired. +C +C QR decomposition without pivoting +C + INFO = 0 + DO 60 K = 1, N + KM1 = K - 1 + KP1 = K + 1 +C +C Compute kth column of R. +C First, multiply the kth column of A by the previous +C k-1 Givens rotations. +C + IF (KM1 .LT. 1) GO TO 20 + DO 10 J = 1, KM1 + I = 2*(J-1) + 1 + T1 = A(J,K) + T2 = A(J+1,K) + C = Q(I) + S = Q(I+1) + A(J,K) = C*T1 - S*T2 + A(J+1,K) = S*T1 + C*T2 + 10 CONTINUE +C +C Compute Givens components c and s +C + 20 CONTINUE + IQ = 2*KM1 + 1 + T1 = A(K,K) + T2 = A(KP1,K) + IF (T2 .NE. 0.0D0) GO TO 30 + C = 1.0D0 + S = 0.0D0 + GO TO 50 + 30 CONTINUE + IF (ABS(T2) .LT. ABS(T1)) GO TO 40 + T = T1/T2 + S = -1.0D0/SQRT(1.0D0+T*T) + C = -S*T + GO TO 50 + 40 CONTINUE + T = T2/T1 + C = 1.0D0/SQRT(1.0D0+T*T) + S = -C*T + 50 CONTINUE + Q(IQ) = C + Q(IQ+1) = S + A(K,K) = C*T1 - S*T2 + IF (A(K,K) .EQ. 0.0D0) INFO = K + 60 CONTINUE + RETURN +C +C The old factorization of A will be updated. A row and a column +C has been added to the matrix A. +C N by N-1 is now the old size of the matrix. +C + 70 CONTINUE + NM1 = N - 1 +C +C Multiply the new column by the N previous Givens rotations. +C + DO 100 K = 1,NM1 + I = 2*(K-1) + 1 + T1 = A(K,N) + T2 = A(K+1,N) + C = Q(I) + S = Q(I+1) + A(K,N) = C*T1 - S*T2 + A(K+1,N) = S*T1 + C*T2 + 100 CONTINUE +C +C Complete update of decomposition by forming last Givens rotation, +C and multiplying it times the column vector (A(N,N), A(N+1,N)). +C + INFO = 0 + T1 = A(N,N) + T2 = A(N+1,N) + IF (T2 .NE. 0.0D0) GO TO 110 + C = 1.0D0 + S = 0.0D0 + GO TO 130 + 110 CONTINUE + IF (ABS(T2) .LT. ABS(T1)) GO TO 120 + T = T1/T2 + S = -1.0D0/SQRT(1.0D0+T*T) + C = -S*T + GO TO 130 + 120 CONTINUE + T = T2/T1 + C = 1.0D0/SQRT(1.0D0+T*T) + S = -C*T + 130 CONTINUE + IQ = 2*N - 1 + Q(IQ) = C + Q(IQ+1) = S + A(N,N) = C*T1 - S*T2 + IF (A(N,N) .EQ. 0.0D0) INFO = N + RETURN +C----------------------- End of Subroutine DHEQR ----------------------- + END +*DECK DHELS + SUBROUTINE DHELS (A, LDA, N, Q, B) + INTEGER LDA, N + DOUBLE PRECISION A(LDA,*), B(*), Q(*) +C----------------------------------------------------------------------- +C This is part of the LINPACK routine DGESL with changes +C due to the fact that A is an upper Hessenberg matrix. +C----------------------------------------------------------------------- +C DHELS solves the least squares problem +C +C min (b-A*x, b-A*x) +C +C using the factors computed by DHEQR. +C +C On entry +C +C A DOUBLE PRECISION(LDA, N) +C the output from DHEQR which contains the upper +C triangular factor R in the QR decomposition of A. +C +C LDA INTEGER +C the leading dimension of the array A . +C +C N INTEGER +C A is originally an (N+1) by N matrix. +C +C Q DOUBLE PRECISION(2*N) +C The coefficients of the N givens rotations +C used in the QR factorization of A. +C +C B DOUBLE PRECISION(N+1) +C the right hand side vector. +C +C On return +C +C B the solution vector x . +C +C Modification of LINPACK, by Peter Brown, LLNL. +C Written 1/13/86. This version dated 6/20/01. +C +C BLAS called: DAXPY +C----------------------------------------------------------------------- + INTEGER IQ, K, KB, KP1 + DOUBLE PRECISION C, S, T, T1, T2 +C +C Minimize (b-A*x, b-A*x) +C First form Q*b. +C + DO 20 K = 1, N + KP1 = K + 1 + IQ = 2*(K-1) + 1 + C = Q(IQ) + S = Q(IQ+1) + T1 = B(K) + T2 = B(KP1) + B(K) = C*T1 - S*T2 + B(KP1) = S*T1 + C*T2 + 20 CONTINUE +C +C Now solve R*x = Q*b. +C + DO 40 KB = 1, N + K = N + 1 - KB + B(K) = B(K)/A(K,K) + T = -B(K) + CALL DAXPY (K-1, T, A(1,K), 1, B(1), 1) + 40 CONTINUE + RETURN +C----------------------- End of Subroutine DHELS ----------------------- + END +*DECK DLHIN + SUBROUTINE DLHIN (NEQ, N, T0, Y0, YDOT, F, TOUT, UROUND, + 1 EWT, ITOL, ATOL, Y, TEMP, H0, NITER, IER) + EXTERNAL F + DOUBLE PRECISION T0, Y0, YDOT, TOUT, UROUND, EWT, ATOL, Y, + 1 TEMP, H0 + INTEGER NEQ, N, ITOL, NITER, IER + DIMENSION NEQ(*), Y0(*), YDOT(*), EWT(*), ATOL(*), Y(*), TEMP(*) +C----------------------------------------------------------------------- +C Call sequence input -- NEQ, N, T0, Y0, YDOT, F, TOUT, UROUND, +C EWT, ITOL, ATOL, Y, TEMP +C Call sequence output -- H0, NITER, IER +C Common block variables accessed -- None +C +C Subroutines called by DLHIN: F, DCOPY +C Function routines called by DLHIN: DVNORM +C----------------------------------------------------------------------- +C This routine computes the step size, H0, to be attempted on the +C first step, when the user has not supplied a value for this. +C +C First we check that TOUT - T0 differs significantly from zero. Then +C an iteration is done to approximate the initial second derivative +C and this is used to define H from WRMS-norm(H**2 * yddot / 2) = 1. +C A bias factor of 1/2 is applied to the resulting h. +C The sign of H0 is inferred from the initial values of TOUT and T0. +C +C Communication with DLHIN is done with the following variables: +C +C NEQ = NEQ array of solver, passed to F. +C N = size of ODE system, input. +C T0 = initial value of independent variable, input. +C Y0 = vector of initial conditions, input. +C YDOT = vector of initial first derivatives, input. +C F = name of subroutine for right-hand side f(t,y), input. +C TOUT = first output value of independent variable +C UROUND = machine unit roundoff +C EWT, ITOL, ATOL = error weights and tolerance parameters +C as described in the driver routine, input. +C Y, TEMP = work arrays of length N. +C H0 = step size to be attempted, output. +C NITER = number of iterations (and of f evaluations) to compute H0, +C output. +C IER = the error flag, returned with the value +C IER = 0 if no trouble occurred, or +C IER = -1 if TOUT and t0 are considered too close to proceed. +C----------------------------------------------------------------------- +C +C Type declarations for local variables -------------------------------- +C + DOUBLE PRECISION AFI, ATOLI, DELYI, HALF, HG, HLB, HNEW, HRAT, + 1 HUB, HUN, PT1, T1, TDIST, TROUND, TWO, DVNORM, YDDNRM + INTEGER I, ITER +C----------------------------------------------------------------------- +C The following Fortran-77 declaration is to cause the values of the +C listed (local) variables to be saved between calls to this integrator. +C----------------------------------------------------------------------- + SAVE HALF, HUN, PT1, TWO + DATA HALF /0.5D0/, HUN /100.0D0/, PT1 /0.1D0/, TWO /2.0D0/ +C + NITER = 0 + TDIST = ABS(TOUT - T0) + TROUND = UROUND*MAX(ABS(T0),ABS(TOUT)) + IF (TDIST .LT. TWO*TROUND) GO TO 100 +C +C Set a lower bound on H based on the roundoff level in T0 and TOUT. --- + HLB = HUN*TROUND +C Set an upper bound on H based on TOUT-T0 and the initial Y and YDOT. - + HUB = PT1*TDIST + ATOLI = ATOL(1) + DO 10 I = 1,N + IF (ITOL .EQ. 2 .OR. ITOL .EQ. 4) ATOLI = ATOL(I) + DELYI = PT1*ABS(Y0(I)) + ATOLI + AFI = ABS(YDOT(I)) + IF (AFI*HUB .GT. DELYI) HUB = DELYI/AFI + 10 CONTINUE +C +C Set initial guess for H as geometric mean of upper and lower bounds. - + ITER = 0 + HG = SQRT(HLB*HUB) +C If the bounds have crossed, exit with the mean value. ---------------- + IF (HUB .LT. HLB) THEN + H0 = HG + GO TO 90 + ENDIF +C +C Looping point for iteration. ----------------------------------------- + 50 CONTINUE +C Estimate the second derivative as a difference quotient in f. -------- + T1 = T0 + HG + DO 60 I = 1,N + 60 Y(I) = Y0(I) + HG*YDOT(I) + CALL F (NEQ, T1, Y, TEMP) + DO 70 I = 1,N + 70 TEMP(I) = (TEMP(I) - YDOT(I))/HG + YDDNRM = DVNORM (N, TEMP, EWT) +C Get the corresponding new value of H. -------------------------------- + IF (YDDNRM*HUB*HUB .GT. TWO) THEN + HNEW = SQRT(TWO/YDDNRM) + ELSE + HNEW = SQRT(HG*HUB) + ENDIF + ITER = ITER + 1 +C----------------------------------------------------------------------- +C Test the stopping conditions. +C Stop if the new and previous H values differ by a factor of .lt. 2. +C Stop if four iterations have been done. Also, stop with previous H +C if hnew/hg .gt. 2 after first iteration, as this probably means that +C the second derivative value is bad because of cancellation error. +C----------------------------------------------------------------------- + IF (ITER .GE. 4) GO TO 80 + HRAT = HNEW/HG + IF ( (HRAT .GT. HALF) .AND. (HRAT .LT. TWO) ) GO TO 80 + IF ( (ITER .GE. 2) .AND. (HNEW .GT. TWO*HG) ) THEN + HNEW = HG + GO TO 80 + ENDIF + HG = HNEW + GO TO 50 +C +C Iteration done. Apply bounds, bias factor, and sign. ---------------- + 80 H0 = HNEW*HALF + IF (H0 .LT. HLB) H0 = HLB + IF (H0 .GT. HUB) H0 = HUB + 90 H0 = SIGN(H0, TOUT - T0) +C Restore Y array from Y0, then exit. ---------------------------------- + CALL DCOPY (N, Y0, 1, Y, 1) + NITER = ITER + IER = 0 + RETURN +C Error return for TOUT - T0 too small. -------------------------------- + 100 IER = -1 + RETURN +C----------------------- End of Subroutine DLHIN ----------------------- + END +*DECK DSTOKA + SUBROUTINE DSTOKA (NEQ, Y, YH, NYH, YH1, EWT, SAVF, SAVX, ACOR, + 1 WM, IWM, F, JAC, PSOL) + EXTERNAL F, JAC, PSOL + INTEGER NEQ, NYH, IWM + DOUBLE PRECISION Y, YH, YH1, EWT, SAVF, SAVX, ACOR, WM + DIMENSION NEQ(*), Y(*), YH(NYH,*), YH1(*), EWT(*), SAVF(*), + 1 SAVX(*), ACOR(*), WM(*), IWM(*) + INTEGER IOWND, IALTH, IPUP, LMAX, MEO, NQNYH, NSLP, + 1 ICF, IERPJ, IERSL, JCUR, JSTART, KFLAG, L, + 2 LYH, LEWT, LACOR, LSAVF, LWM, LIWM, METH, MITER, + 3 MAXORD, MAXCOR, MSBP, MXNCF, N, NQ, NST, NFE, NJE, NQU + INTEGER NEWT, NSFI, NSLJ, NJEV + INTEGER JPRE, JACFLG, LOCWP, LOCIWP, LSAVX, KMP, MAXL, MNEWT, + 1 NNI, NLI, NPS, NCFN, NCFL + DOUBLE PRECISION CONIT, CRATE, EL, ELCO, HOLD, RMAX, TESCO, + 2 CCMAX, EL0, H, HMIN, HMXI, HU, RC, TN, UROUND + DOUBLE PRECISION STIFR + DOUBLE PRECISION DELT, EPCON, SQRTN, RSQRTN + COMMON /DLS001/ CONIT, CRATE, EL(13), ELCO(13,12), + 1 HOLD, RMAX, TESCO(3,12), + 2 CCMAX, EL0, H, HMIN, HMXI, HU, RC, TN, UROUND, + 3 IOWND(6), IALTH, IPUP, LMAX, MEO, NQNYH, NSLP, + 3 ICF, IERPJ, IERSL, JCUR, JSTART, KFLAG, L, + 4 LYH, LEWT, LACOR, LSAVF, LWM, LIWM, METH, MITER, + 5 MAXORD, MAXCOR, MSBP, MXNCF, N, NQ, NST, NFE, NJE, NQU + COMMON /DLS002/ STIFR, NEWT, NSFI, NSLJ, NJEV + COMMON /DLPK01/ DELT, EPCON, SQRTN, RSQRTN, + 1 JPRE, JACFLG, LOCWP, LOCIWP, LSAVX, KMP, MAXL, MNEWT, + 2 NNI, NLI, NPS, NCFN, NCFL +C----------------------------------------------------------------------- +C DSTOKA performs one step of the integration of an initial value +C problem for a system of Ordinary Differential Equations. +C +C This routine was derived from Subroutine DSTODPK in the DLSODPK +C package by the addition of automatic functional/Newton iteration +C switching and logic for re-use of Jacobian data. +C----------------------------------------------------------------------- +C Note: DSTOKA is independent of the value of the iteration method +C indicator MITER, when this is .ne. 0, and hence is independent +C of the type of chord method used, or the Jacobian structure. +C Communication with DSTOKA is done with the following variables: +C +C NEQ = integer array containing problem size in NEQ(1), and +C passed as the NEQ argument in all calls to F and JAC. +C Y = an array of length .ge. N used as the Y argument in +C all calls to F and JAC. +C YH = an NYH by LMAX array containing the dependent variables +C and their approximate scaled derivatives, where +C LMAX = MAXORD + 1. YH(i,j+1) contains the approximate +C j-th derivative of y(i), scaled by H**j/factorial(j) +C (j = 0,1,...,NQ). On entry for the first step, the first +C two columns of YH must be set from the initial values. +C NYH = a constant integer .ge. N, the first dimension of YH. +C YH1 = a one-dimensional array occupying the same space as YH. +C EWT = an array of length N containing multiplicative weights +C for local error measurements. Local errors in y(i) are +C compared to 1.0/EWT(i) in various error tests. +C SAVF = an array of working storage, of length N. +C Also used for input of YH(*,MAXORD+2) when JSTART = -1 +C and MAXORD .lt. the current order NQ. +C SAVX = an array of working storage, of length N. +C ACOR = a work array of length N, used for the accumulated +C corrections. On a successful return, ACOR(i) contains +C the estimated one-step local error in y(i). +C WM,IWM = real and integer work arrays associated with matrix +C operations in chord iteration (MITER .ne. 0). +C CCMAX = maximum relative change in H*EL0 before DSETPK is called. +C H = the step size to be attempted on the next step. +C H is altered by the error control algorithm during the +C problem. H can be either positive or negative, but its +C sign must remain constant throughout the problem. +C HMIN = the minimum absolute value of the step size H to be used. +C HMXI = inverse of the maximum absolute value of H to be used. +C HMXI = 0.0 is allowed and corresponds to an infinite HMAX. +C HMIN and HMXI may be changed at any time, but will not +C take effect until the next change of H is considered. +C TN = the independent variable. TN is updated on each step taken. +C JSTART = an integer used for input only, with the following +C values and meanings: +C 0 perform the first step. +C .gt.0 take a new step continuing from the last. +C -1 take the next step with a new value of H, MAXORD, +C N, METH, MITER, and/or matrix parameters. +C -2 take the next step with a new value of H, +C but with other inputs unchanged. +C On return, JSTART is set to 1 to facilitate continuation. +C KFLAG = a completion code with the following meanings: +C 0 the step was succesful. +C -1 the requested error could not be achieved. +C -2 corrector convergence could not be achieved. +C -3 fatal error in DSETPK or DSOLPK. +C A return with KFLAG = -1 or -2 means either +C ABS(H) = HMIN or 10 consecutive failures occurred. +C On a return with KFLAG negative, the values of TN and +C the YH array are as of the beginning of the last +C step, and H is the last step size attempted. +C MAXORD = the maximum order of integration method to be allowed. +C MAXCOR = the maximum number of corrector iterations allowed. +C MSBP = maximum number of steps between DSETPK calls (MITER .gt. 0). +C MXNCF = maximum number of convergence failures allowed. +C METH/MITER = the method flags. See description in driver. +C N = the number of first-order differential equations. +C----------------------------------------------------------------------- + INTEGER I, I1, IREDO, IRET, J, JB, JOK, M, NCF, NEWQ, NSLOW + DOUBLE PRECISION DCON, DDN, DEL, DELP, DRC, DSM, DUP, EXDN, EXSM, + 1 EXUP, DFNORM, R, RH, RHDN, RHSM, RHUP, ROC, STIFF, TOLD, DVNORM +C + KFLAG = 0 + TOLD = TN + NCF = 0 + IERPJ = 0 + IERSL = 0 + JCUR = 0 + ICF = 0 + DELP = 0.0D0 + IF (JSTART .GT. 0) GO TO 200 + IF (JSTART .EQ. -1) GO TO 100 + IF (JSTART .EQ. -2) GO TO 160 +C----------------------------------------------------------------------- +C On the first call, the order is set to 1, and other variables are +C initialized. RMAX is the maximum ratio by which H can be increased +C in a single step. It is initially 1.E4 to compensate for the small +C initial H, but then is normally equal to 10. If a failure +C occurs (in corrector convergence or error test), RMAX is set at 2 +C for the next increase. +C----------------------------------------------------------------------- + LMAX = MAXORD + 1 + NQ = 1 + L = 2 + IALTH = 2 + RMAX = 10000.0D0 + RC = 0.0D0 + EL0 = 1.0D0 + CRATE = 0.7D0 + HOLD = H + MEO = METH + NSLP = 0 + NSLJ = 0 + IPUP = 0 + IRET = 3 + NEWT = 0 + STIFR = 0.0D0 + GO TO 140 +C----------------------------------------------------------------------- +C The following block handles preliminaries needed when JSTART = -1. +C IPUP is set to MITER to force a matrix update. +C If an order increase is about to be considered (IALTH = 1), +C IALTH is reset to 2 to postpone consideration one more step. +C If the caller has changed METH, DCFODE is called to reset +C the coefficients of the method. +C If the caller has changed MAXORD to a value less than the current +C order NQ, NQ is reduced to MAXORD, and a new H chosen accordingly. +C If H is to be changed, YH must be rescaled. +C If H or METH is being changed, IALTH is reset to L = NQ + 1 +C to prevent further changes in H for that many steps. +C----------------------------------------------------------------------- + 100 IPUP = MITER + LMAX = MAXORD + 1 + IF (IALTH .EQ. 1) IALTH = 2 + IF (METH .EQ. MEO) GO TO 110 + CALL DCFODE (METH, ELCO, TESCO) + MEO = METH + IF (NQ .GT. MAXORD) GO TO 120 + IALTH = L + IRET = 1 + GO TO 150 + 110 IF (NQ .LE. MAXORD) GO TO 160 + 120 NQ = MAXORD + L = LMAX + DO 125 I = 1,L + 125 EL(I) = ELCO(I,NQ) + NQNYH = NQ*NYH + RC = RC*EL(1)/EL0 + EL0 = EL(1) + CONIT = 0.5D0/(NQ+2) + EPCON = CONIT*TESCO(2,NQ) + DDN = DVNORM (N, SAVF, EWT)/TESCO(1,L) + EXDN = 1.0D0/L + RHDN = 1.0D0/(1.3D0*DDN**EXDN + 0.0000013D0) + RH = MIN(RHDN,1.0D0) + IREDO = 3 + IF (H .EQ. HOLD) GO TO 170 + RH = MIN(RH,ABS(H/HOLD)) + H = HOLD + GO TO 175 +C----------------------------------------------------------------------- +C DCFODE is called to get all the integration coefficients for the +C current METH. Then the EL vector and related constants are reset +C whenever the order NQ is changed, or at the start of the problem. +C----------------------------------------------------------------------- + 140 CALL DCFODE (METH, ELCO, TESCO) + 150 DO 155 I = 1,L + 155 EL(I) = ELCO(I,NQ) + NQNYH = NQ*NYH + RC = RC*EL(1)/EL0 + EL0 = EL(1) + CONIT = 0.5D0/(NQ+2) + EPCON = CONIT*TESCO(2,NQ) + GO TO (160, 170, 200), IRET +C----------------------------------------------------------------------- +C If H is being changed, the H ratio RH is checked against +C RMAX, HMIN, and HMXI, and the YH array rescaled. IALTH is set to +C L = NQ + 1 to prevent a change of H for that many steps, unless +C forced by a convergence or error test failure. +C----------------------------------------------------------------------- + 160 IF (H .EQ. HOLD) GO TO 200 + RH = H/HOLD + H = HOLD + IREDO = 3 + GO TO 175 + 170 RH = MAX(RH,HMIN/ABS(H)) + 175 RH = MIN(RH,RMAX) + RH = RH/MAX(1.0D0,ABS(H)*HMXI*RH) + R = 1.0D0 + DO 180 J = 2,L + R = R*RH + DO 180 I = 1,N + 180 YH(I,J) = YH(I,J)*R + H = H*RH + RC = RC*RH + IALTH = L + IF (IREDO .EQ. 0) GO TO 690 +C----------------------------------------------------------------------- +C This section computes the predicted values by effectively +C multiplying the YH array by the Pascal triangle matrix. +C The flag IPUP is set according to whether matrix data is involved +C (NEWT .gt. 0 .and. JACFLG .ne. 0) or not, to trigger a call to DSETPK. +C IPUP is set to MITER when RC differs from 1 by more than CCMAX, +C and at least every MSBP steps, when JACFLG = 1. +C RC is the ratio of new to old values of the coefficient H*EL(1). +C----------------------------------------------------------------------- + 200 IF (NEWT .EQ. 0 .OR. JACFLG .EQ. 0) THEN + DRC = 0.0D0 + IPUP = 0 + CRATE = 0.7D0 + ELSE + DRC = ABS(RC - 1.0D0) + IF (DRC .GT. CCMAX) IPUP = MITER + IF (NST .GE. NSLP+MSBP) IPUP = MITER + ENDIF + TN = TN + H + I1 = NQNYH + 1 + DO 215 JB = 1,NQ + I1 = I1 - NYH +CDIR$ IVDEP + DO 210 I = I1,NQNYH + 210 YH1(I) = YH1(I) + YH1(I+NYH) + 215 CONTINUE +C----------------------------------------------------------------------- +C Up to MAXCOR corrector iterations are taken. A convergence test is +C made on the RMS-norm of each correction, weighted by the error +C weight vector EWT. The sum of the corrections is accumulated in the +C vector ACOR(i). The YH array is not altered in the corrector loop. +C Within the corrector loop, an estimated rate of convergence (ROC) +C and a stiffness ratio estimate (STIFF) are kept. Corresponding +C global estimates are kept as CRATE and stifr. +C----------------------------------------------------------------------- + 220 M = 0 + MNEWT = 0 + STIFF = 0.0D0 + ROC = 0.05D0 + NSLOW = 0 + DO 230 I = 1,N + 230 Y(I) = YH(I,1) + CALL F (NEQ, TN, Y, SAVF) + NFE = NFE + 1 + IF (NEWT .EQ. 0 .OR. IPUP .LE. 0) GO TO 250 +C----------------------------------------------------------------------- +C If indicated, DSETPK is called to update any matrix data needed, +C before starting the corrector iteration. +C JOK is set to indicate if the matrix data need not be recomputed. +C IPUP is set to 0 as an indicator that the matrix data is up to date. +C----------------------------------------------------------------------- + JOK = 1 + IF (NST .EQ. 0 .OR. NST .GT. NSLJ+50) JOK = -1 + IF (ICF .EQ. 1 .AND. DRC .LT. 0.2D0) JOK = -1 + IF (ICF .EQ. 2) JOK = -1 + IF (JOK .EQ. -1) THEN + NSLJ = NST + NJEV = NJEV + 1 + ENDIF + CALL DSETPK (NEQ, Y, YH1, EWT, ACOR, SAVF, JOK, WM, IWM, F, JAC) + IPUP = 0 + RC = 1.0D0 + DRC = 0.0D0 + NSLP = NST + CRATE = 0.7D0 + IF (IERPJ .NE. 0) GO TO 430 + 250 DO 260 I = 1,N + 260 ACOR(I) = 0.0D0 + 270 IF (NEWT .NE. 0) GO TO 350 +C----------------------------------------------------------------------- +C In the case of functional iteration, update Y directly from +C the result of the last function evaluation, and STIFF is set to 1.0. +C----------------------------------------------------------------------- + DO 290 I = 1,N + SAVF(I) = H*SAVF(I) - YH(I,2) + 290 Y(I) = SAVF(I) - ACOR(I) + DEL = DVNORM (N, Y, EWT) + DO 300 I = 1,N + Y(I) = YH(I,1) + EL(1)*SAVF(I) + 300 ACOR(I) = SAVF(I) + STIFF = 1.0D0 + GO TO 400 +C----------------------------------------------------------------------- +C In the case of the chord method, compute the corrector error, +C and solve the linear system with that as right-hand side and +C P as coefficient matrix. STIFF is set to the ratio of the norms +C of the residual and the correction vector. +C----------------------------------------------------------------------- + 350 DO 360 I = 1,N + 360 SAVX(I) = H*SAVF(I) - (YH(I,2) + ACOR(I)) + DFNORM = DVNORM (N, SAVX, EWT) + CALL DSOLPK (NEQ, Y, SAVF, SAVX, EWT, WM, IWM, F, PSOL) + IF (IERSL .LT. 0) GO TO 430 + IF (IERSL .GT. 0) GO TO 410 + DEL = DVNORM (N, SAVX, EWT) + IF (DEL .GT. 1.0D-8) STIFF = MAX(STIFF, DFNORM/DEL) + DO 380 I = 1,N + ACOR(I) = ACOR(I) + SAVX(I) + 380 Y(I) = YH(I,1) + EL(1)*ACOR(I) +C----------------------------------------------------------------------- +C Test for convergence. If M .gt. 0, an estimate of the convergence +C rate constant is made for the iteration switch, and is also used +C in the convergence test. If the iteration seems to be diverging or +C converging at a slow rate (.gt. 0.8 more than once), it is stopped. +C----------------------------------------------------------------------- + 400 IF (M .NE. 0) THEN + ROC = MAX(0.05D0, DEL/DELP) + CRATE = MAX(0.2D0*CRATE,ROC) + ENDIF + DCON = DEL*MIN(1.0D0,1.5D0*CRATE)/EPCON + IF (DCON .LE. 1.0D0) GO TO 450 + M = M + 1 + IF (M .EQ. MAXCOR) GO TO 410 + IF (M .GE. 2 .AND. DEL .GT. 2.0D0*DELP) GO TO 410 + IF (ROC .GT. 10.0D0) GO TO 410 + IF (ROC .GT. 0.8D0) NSLOW = NSLOW + 1 + IF (NSLOW .GE. 2) GO TO 410 + MNEWT = M + DELP = DEL + CALL F (NEQ, TN, Y, SAVF) + NFE = NFE + 1 + GO TO 270 +C----------------------------------------------------------------------- +C The corrector iteration failed to converge. +C If functional iteration is being done (NEWT = 0) and MITER .gt. 0 +C (and this is not the first step), then switch to Newton +C (NEWT = MITER), and retry the step. (Setting STIFR = 1023 insures +C that a switch back will not occur for 10 step attempts.) +C If Newton iteration is being done, but using a preconditioner that +C is out of date (JACFLG .ne. 0 .and. JCUR = 0), then signal for a +C re-evalutation of the preconditioner, and retry the step. +C In all other cases, the YH array is retracted to its values +C before prediction, and H is reduced, if possible. If H cannot be +C reduced or MXNCF failures have occurred, exit with KFLAG = -2. +C----------------------------------------------------------------------- + 410 ICF = 1 + IF (NEWT .EQ. 0) THEN + IF (NST .EQ. 0) GO TO 430 + IF (MITER .EQ. 0) GO TO 430 + NEWT = MITER + STIFR = 1023.0D0 + IPUP = MITER + GO TO 220 + ENDIF + IF (JCUR.EQ.1 .OR. JACFLG.EQ.0) GO TO 430 + IPUP = MITER + GO TO 220 + 430 ICF = 2 + NCF = NCF + 1 + NCFN = NCFN + 1 + RMAX = 2.0D0 + TN = TOLD + I1 = NQNYH + 1 + DO 445 JB = 1,NQ + I1 = I1 - NYH +CDIR$ IVDEP + DO 440 I = I1,NQNYH + 440 YH1(I) = YH1(I) - YH1(I+NYH) + 445 CONTINUE + IF (IERPJ .LT. 0 .OR. IERSL .LT. 0) GO TO 680 + IF (ABS(H) .LE. HMIN*1.00001D0) GO TO 670 + IF (NCF .EQ. MXNCF) GO TO 670 + RH = 0.5D0 + IPUP = MITER + IREDO = 1 + GO TO 170 +C----------------------------------------------------------------------- +C The corrector has converged. JCUR is set to 0 to signal that the +C preconditioner involved may need updating later. +C The stiffness ratio STIFR is updated using the latest STIFF value. +C The local error test is made and control passes to statement 500 +C if it fails. +C----------------------------------------------------------------------- + 450 JCUR = 0 + IF (NEWT .GT. 0) STIFR = 0.5D0*(STIFR + STIFF) + IF (M .EQ. 0) DSM = DEL/TESCO(2,NQ) + IF (M .GT. 0) DSM = DVNORM (N, ACOR, EWT)/TESCO(2,NQ) + IF (DSM .GT. 1.0D0) GO TO 500 +C----------------------------------------------------------------------- +C After a successful step, update the YH array. +C If Newton iteration is being done and STIFR is less than 1.5, +C then switch to functional iteration. +C Consider changing H if IALTH = 1. Otherwise decrease IALTH by 1. +C If IALTH is then 1 and NQ .lt. MAXORD, then ACOR is saved for +C use in a possible order increase on the next step. +C If a change in H is considered, an increase or decrease in order +C by one is considered also. A change in H is made only if it is by a +C factor of at least 1.1. If not, IALTH is set to 3 to prevent +C testing for that many steps. +C----------------------------------------------------------------------- + KFLAG = 0 + IREDO = 0 + NST = NST + 1 + IF (NEWT .EQ. 0) NSFI = NSFI + 1 + IF (NEWT .GT. 0 .AND. STIFR .LT. 1.5D0) NEWT = 0 + HU = H + NQU = NQ + DO 470 J = 1,L + DO 470 I = 1,N + 470 YH(I,J) = YH(I,J) + EL(J)*ACOR(I) + IALTH = IALTH - 1 + IF (IALTH .EQ. 0) GO TO 520 + IF (IALTH .GT. 1) GO TO 700 + IF (L .EQ. LMAX) GO TO 700 + DO 490 I = 1,N + 490 YH(I,LMAX) = ACOR(I) + GO TO 700 +C----------------------------------------------------------------------- +C The error test failed. KFLAG keeps track of multiple failures. +C Restore TN and the YH array to their previous values, and prepare +C to try the step again. Compute the optimum step size for this or +C one lower order. After 2 or more failures, H is forced to decrease +C by a factor of 0.2 or less. +C----------------------------------------------------------------------- + 500 KFLAG = KFLAG - 1 + TN = TOLD + I1 = NQNYH + 1 + DO 515 JB = 1,NQ + I1 = I1 - NYH +CDIR$ IVDEP + DO 510 I = I1,NQNYH + 510 YH1(I) = YH1(I) - YH1(I+NYH) + 515 CONTINUE + RMAX = 2.0D0 + IF (ABS(H) .LE. HMIN*1.00001D0) GO TO 660 + IF (KFLAG .LE. -3) GO TO 640 + IREDO = 2 + RHUP = 0.0D0 + GO TO 540 +C----------------------------------------------------------------------- +C Regardless of the success or failure of the step, factors +C RHDN, RHSM, and RHUP are computed, by which H could be multiplied +C at order NQ - 1, order NQ, or order NQ + 1, respectively. +C in the case of failure, RHUP = 0.0 to avoid an order increase. +C the largest of these is determined and the new order chosen +C accordingly. If the order is to be increased, we compute one +C additional scaled derivative. +C----------------------------------------------------------------------- + 520 RHUP = 0.0D0 + IF (L .EQ. LMAX) GO TO 540 + DO 530 I = 1,N + 530 SAVF(I) = ACOR(I) - YH(I,LMAX) + DUP = DVNORM (N, SAVF, EWT)/TESCO(3,NQ) + EXUP = 1.0D0/(L+1) + RHUP = 1.0D0/(1.4D0*DUP**EXUP + 0.0000014D0) + 540 EXSM = 1.0D0/L + RHSM = 1.0D0/(1.2D0*DSM**EXSM + 0.0000012D0) + RHDN = 0.0D0 + IF (NQ .EQ. 1) GO TO 560 + DDN = DVNORM (N, YH(1,L), EWT)/TESCO(1,NQ) + EXDN = 1.0D0/NQ + RHDN = 1.0D0/(1.3D0*DDN**EXDN + 0.0000013D0) + 560 IF (RHSM .GE. RHUP) GO TO 570 + IF (RHUP .GT. RHDN) GO TO 590 + GO TO 580 + 570 IF (RHSM .LT. RHDN) GO TO 580 + NEWQ = NQ + RH = RHSM + GO TO 620 + 580 NEWQ = NQ - 1 + RH = RHDN + IF (KFLAG .LT. 0 .AND. RH .GT. 1.0D0) RH = 1.0D0 + GO TO 620 + 590 NEWQ = L + RH = RHUP + IF (RH .LT. 1.1D0) GO TO 610 + R = EL(L)/L + DO 600 I = 1,N + 600 YH(I,NEWQ+1) = ACOR(I)*R + GO TO 630 + 610 IALTH = 3 + GO TO 700 + 620 IF ((KFLAG .EQ. 0) .AND. (RH .LT. 1.1D0)) GO TO 610 + IF (KFLAG .LE. -2) RH = MIN(RH,0.2D0) +C----------------------------------------------------------------------- +C If there is a change of order, reset NQ, L, and the coefficients. +C In any case H is reset according to RH and the YH array is rescaled. +C Then exit from 690 if the step was OK, or redo the step otherwise. +C----------------------------------------------------------------------- + IF (NEWQ .EQ. NQ) GO TO 170 + 630 NQ = NEWQ + L = NQ + 1 + IRET = 2 + GO TO 150 +C----------------------------------------------------------------------- +C Control reaches this section if 3 or more failures have occured. +C If 10 failures have occurred, exit with KFLAG = -1. +C It is assumed that the derivatives that have accumulated in the +C YH array have errors of the wrong order. Hence the first +C derivative is recomputed, and the order is set to 1. Then +C H is reduced by a factor of 10, and the step is retried, +C until it succeeds or H reaches HMIN. +C----------------------------------------------------------------------- + 640 IF (KFLAG .EQ. -10) GO TO 660 + RH = 0.1D0 + RH = MAX(HMIN/ABS(H),RH) + H = H*RH + DO 645 I = 1,N + 645 Y(I) = YH(I,1) + CALL F (NEQ, TN, Y, SAVF) + NFE = NFE + 1 + DO 650 I = 1,N + 650 YH(I,2) = H*SAVF(I) + IPUP = MITER + IALTH = 5 + IF (NQ .EQ. 1) GO TO 200 + NQ = 1 + L = 2 + IRET = 3 + GO TO 150 +C----------------------------------------------------------------------- +C All returns are made through this section. H is saved in HOLD +C to allow the caller to change H on the next step. +C----------------------------------------------------------------------- + 660 KFLAG = -1 + GO TO 720 + 670 KFLAG = -2 + GO TO 720 + 680 KFLAG = -3 + GO TO 720 + 690 RMAX = 10.0D0 + 700 R = 1.0D0/TESCO(2,NQU) + DO 710 I = 1,N + 710 ACOR(I) = ACOR(I)*R + 720 HOLD = H + JSTART = 1 + RETURN +C----------------------- End of Subroutine DSTOKA ---------------------- + END +*DECK DSETPK + SUBROUTINE DSETPK (NEQ, Y, YSV, EWT, FTEM, SAVF, JOK, WM, IWM, + 1 F, JAC) + EXTERNAL F, JAC + INTEGER NEQ, JOK, IWM + DOUBLE PRECISION Y, YSV, EWT, FTEM, SAVF, WM + DIMENSION NEQ(*), Y(*), YSV(*), EWT(*), FTEM(*), SAVF(*), + 1 WM(*), IWM(*) + INTEGER IOWND, IOWNS, + 1 ICF, IERPJ, IERSL, JCUR, JSTART, KFLAG, L, + 2 LYH, LEWT, LACOR, LSAVF, LWM, LIWM, METH, MITER, + 3 MAXORD, MAXCOR, MSBP, MXNCF, N, NQ, NST, NFE, NJE, NQU + INTEGER JPRE, JACFLG, LOCWP, LOCIWP, LSAVX, KMP, MAXL, MNEWT, + 1 NNI, NLI, NPS, NCFN, NCFL + DOUBLE PRECISION ROWNS, + 1 CCMAX, EL0, H, HMIN, HMXI, HU, RC, TN, UROUND + DOUBLE PRECISION DELT, EPCON, SQRTN, RSQRTN + COMMON /DLS001/ ROWNS(209), + 1 CCMAX, EL0, H, HMIN, HMXI, HU, RC, TN, UROUND, + 2 IOWND(6), IOWNS(6), + 3 ICF, IERPJ, IERSL, JCUR, JSTART, KFLAG, L, + 4 LYH, LEWT, LACOR, LSAVF, LWM, LIWM, METH, MITER, + 5 MAXORD, MAXCOR, MSBP, MXNCF, N, NQ, NST, NFE, NJE, NQU + COMMON /DLPK01/ DELT, EPCON, SQRTN, RSQRTN, + 1 JPRE, JACFLG, LOCWP, LOCIWP, LSAVX, KMP, MAXL, MNEWT, + 2 NNI, NLI, NPS, NCFN, NCFL +C----------------------------------------------------------------------- +C DSETPK is called by DSTOKA to interface with the user-supplied +C routine JAC, to compute and process relevant parts of +C the matrix P = I - H*EL(1)*J , where J is the Jacobian df/dy, +C as need for preconditioning matrix operations later. +C +C In addition to variables described previously, communication +C with DSETPK uses the following: +C Y = array containing predicted values on entry. +C YSV = array containing predicted y, to be saved (YH1 in DSTOKA). +C FTEM = work array of length N (ACOR in DSTOKA). +C SAVF = array containing f evaluated at predicted y. +C JOK = input flag showing whether it was judged that Jacobian matrix +C data need not be recomputed (JOK = 1) or needs to be +C (JOK = -1). +C WM = real work space for matrices. +C Space for preconditioning data starts at WM(LOCWP). +C IWM = integer work space. +C Space for preconditioning data starts at IWM(LOCIWP). +C IERPJ = output error flag, = 0 if no trouble, .gt. 0 if +C JAC returned an error flag. +C JCUR = output flag to indicate whether the matrix data involved +C is now current (JCUR = 1) or not (JCUR = 0). +C This routine also uses Common variables EL0, H, TN, IERPJ, JCUR, NJE. +C----------------------------------------------------------------------- + INTEGER IER + DOUBLE PRECISION HL0 +C + IERPJ = 0 + JCUR = 0 + IF (JOK .EQ. -1) JCUR = 1 + HL0 = EL0*H + CALL JAC (F, NEQ, TN, Y, YSV, EWT, SAVF, FTEM, HL0, JOK, + 1 WM(LOCWP), IWM(LOCIWP), IER) + NJE = NJE + 1 + IF (IER .EQ. 0) RETURN + IERPJ = 1 + RETURN +C----------------------- End of Subroutine DSETPK ---------------------- + END +*DECK DSRCKR + SUBROUTINE DSRCKR (RSAV, ISAV, JOB) +C----------------------------------------------------------------------- +C This routine saves or restores (depending on JOB) the contents of +C the Common blocks DLS001, DLS002, DLSR01, DLPK01, which +C are used internally by the DLSODKR solver. +C +C RSAV = real array of length 228 or more. +C ISAV = integer array of length 63 or more. +C JOB = flag indicating to save or restore the Common blocks: +C JOB = 1 if Common is to be saved (written to RSAV/ISAV) +C JOB = 2 if Common is to be restored (read from RSAV/ISAV) +C A call with JOB = 2 presumes a prior call with JOB = 1. +C----------------------------------------------------------------------- + INTEGER ISAV, JOB + INTEGER ILS, ILS2, ILSR, ILSP + INTEGER I, IOFF, LENILP, LENRLP, LENILS, LENRLS, LENILR, LENRLR + DOUBLE PRECISION RSAV, RLS, RLS2, RLSR, RLSP + DIMENSION RSAV(*), ISAV(*) + SAVE LENRLS, LENILS, LENRLP, LENILP, LENRLR, LENILR + COMMON /DLS001/ RLS(218), ILS(37) + COMMON /DLS002/ RLS2, ILS2(4) + COMMON /DLSR01/ RLSR(5), ILSR(9) + COMMON /DLPK01/ RLSP(4), ILSP(13) + DATA LENRLS/218/, LENILS/37/, LENRLP/4/, LENILP/13/ + DATA LENRLR/5/, LENILR/9/ +C + IF (JOB .EQ. 2) GO TO 100 + CALL DCOPY (LENRLS, RLS, 1, RSAV, 1) + RSAV(LENRLS+1) = RLS2 + CALL DCOPY (LENRLR, RLSR, 1, RSAV(LENRLS+2), 1) + CALL DCOPY (LENRLP, RLSP, 1, RSAV(LENRLS+LENRLR+2), 1) + DO 20 I = 1,LENILS + 20 ISAV(I) = ILS(I) + ISAV(LENILS+1) = ILS2(1) + ISAV(LENILS+2) = ILS2(2) + ISAV(LENILS+3) = ILS2(3) + ISAV(LENILS+4) = ILS2(4) + IOFF = LENILS + 2 + DO 30 I = 1,LENILR + 30 ISAV(IOFF+I) = ILSR(I) + IOFF = IOFF + LENILR + DO 40 I = 1,LENILP + 40 ISAV(IOFF+I) = ILSP(I) + RETURN +C + 100 CONTINUE + CALL DCOPY (LENRLS, RSAV, 1, RLS, 1) + RLS2 = RSAV(LENRLS+1) + CALL DCOPY (LENRLR, RSAV(LENRLS+2), 1, RLSR, 1) + CALL DCOPY (LENRLP, RSAV(LENRLS+LENRLR+2), 1, RLSP, 1) + DO 120 I = 1,LENILS + 120 ILS(I) = ISAV(I) + ILS2(1) = ISAV(LENILS+1) + ILS2(2) = ISAV(LENILS+2) + ILS2(3) = ISAV(LENILS+3) + ILS2(4) = ISAV(LENILS+4) + IOFF = LENILS + 2 + DO 130 I = 1,LENILR + 130 ILSR(I) = ISAV(IOFF+I) + IOFF = IOFF + LENILR + DO 140 I = 1,LENILP + 140 ILSP(I) = ISAV(IOFF+I) + RETURN +C----------------------- End of Subroutine DSRCKR ---------------------- + END +*DECK DAINVG + SUBROUTINE DAINVG (RES, ADDA, NEQ, T, Y, YDOT, MITER, + 1 ML, MU, PW, IPVT, IER ) + EXTERNAL RES, ADDA + INTEGER NEQ, MITER, ML, MU, IPVT, IER + INTEGER I, LENPW, MLP1, NROWPW + DOUBLE PRECISION T, Y, YDOT, PW + DIMENSION Y(*), YDOT(*), PW(*), IPVT(*) +C----------------------------------------------------------------------- +C This subroutine computes the initial value +C of the vector YDOT satisfying +C A * YDOT = g(t,y) +C when A is nonsingular. It is called by DLSODI for +C initialization only, when ISTATE = 0 . +C DAINVG returns an error flag IER: +C IER = 0 means DAINVG was successful. +C IER .ge. 2 means RES returned an error flag IRES = IER. +C IER .lt. 0 means the a-matrix was found to be singular. +C----------------------------------------------------------------------- +C + IF (MITER .GE. 4) GO TO 100 +C +C Full matrix case ----------------------------------------------------- +C + LENPW = NEQ*NEQ + DO 10 I = 1, LENPW + 10 PW(I) = 0.0D0 +C + IER = 1 + CALL RES ( NEQ, T, Y, PW, YDOT, IER ) + IF (IER .GT. 1) RETURN +C + CALL ADDA ( NEQ, T, Y, 0, 0, PW, NEQ ) + CALL DGEFA ( PW, NEQ, NEQ, IPVT, IER ) + IF (IER .EQ. 0) GO TO 20 + IER = -IER + RETURN + 20 CALL DGESL ( PW, NEQ, NEQ, IPVT, YDOT, 0 ) + RETURN +C +C Band matrix case ----------------------------------------------------- +C + 100 CONTINUE + NROWPW = 2*ML + MU + 1 + LENPW = NEQ * NROWPW + DO 110 I = 1, LENPW + 110 PW(I) = 0.0D0 +C + IER = 1 + CALL RES ( NEQ, T, Y, PW, YDOT, IER ) + IF (IER .GT. 1) RETURN +C + MLP1 = ML + 1 + CALL ADDA ( NEQ, T, Y, ML, MU, PW(MLP1), NROWPW ) + CALL DGBFA ( PW, NROWPW, NEQ, ML, MU, IPVT, IER ) + IF (IER .EQ. 0) GO TO 120 + IER = -IER + RETURN + 120 CALL DGBSL ( PW, NROWPW, NEQ, ML, MU, IPVT, YDOT, 0 ) + RETURN +C----------------------- End of Subroutine DAINVG ---------------------- + END +*DECK DSTODI + SUBROUTINE DSTODI (NEQ, Y, YH, NYH, YH1, EWT, SAVF, SAVR, + 1 ACOR, WM, IWM, RES, ADDA, JAC, PJAC, SLVS ) + EXTERNAL RES, ADDA, JAC, PJAC, SLVS + INTEGER NEQ, NYH, IWM + DOUBLE PRECISION Y, YH, YH1, EWT, SAVF, SAVR, ACOR, WM + DIMENSION NEQ(*), Y(*), YH(NYH,*), YH1(*), EWT(*), SAVF(*), + 1 SAVR(*), ACOR(*), WM(*), IWM(*) + INTEGER IOWND, IALTH, IPUP, LMAX, MEO, NQNYH, NSLP, + 1 ICF, IERPJ, IERSL, JCUR, JSTART, KFLAG, L, + 2 LYH, LEWT, LACOR, LSAVF, LWM, LIWM, METH, MITER, + 3 MAXORD, MAXCOR, MSBP, MXNCF, N, NQ, NST, NFE, NJE, NQU + DOUBLE PRECISION CONIT, CRATE, EL, ELCO, HOLD, RMAX, TESCO, + 2 CCMAX, EL0, H, HMIN, HMXI, HU, RC, TN, UROUND + COMMON /DLS001/ CONIT, CRATE, EL(13), ELCO(13,12), + 1 HOLD, RMAX, TESCO(3,12), + 2 CCMAX, EL0, H, HMIN, HMXI, HU, RC, TN, UROUND, + 3 IOWND(6), IALTH, IPUP, LMAX, MEO, NQNYH, NSLP, + 3 ICF, IERPJ, IERSL, JCUR, JSTART, KFLAG, L, + 4 LYH, LEWT, LACOR, LSAVF, LWM, LIWM, METH, MITER, + 5 MAXORD, MAXCOR, MSBP, MXNCF, N, NQ, NST, NFE, NJE, NQU + INTEGER I, I1, IREDO, IRES, IRET, J, JB, KGO, M, NCF, NEWQ + DOUBLE PRECISION DCON, DDN, DEL, DELP, DSM, DUP, + 1 ELJH, EL1H, EXDN, EXSM, EXUP, + 2 R, RH, RHDN, RHSM, RHUP, TOLD, DVNORM +C----------------------------------------------------------------------- +C DSTODI performs one step of the integration of an initial value +C problem for a system of Ordinary Differential Equations. +C Note: DSTODI is independent of the value of the iteration method +C indicator MITER, and hence is independent +C of the type of chord method used, or the Jacobian structure. +C Communication with DSTODI is done with the following variables: +C +C NEQ = integer array containing problem size in NEQ(1), and +C passed as the NEQ argument in all calls to RES, ADDA, +C and JAC. +C Y = an array of length .ge. N used as the Y argument in +C all calls to RES, JAC, and ADDA. +C NEQ = integer array containing problem size in NEQ(1), and +C passed as the NEQ argument in all calls tO RES, G, ADDA, +C and JAC. +C YH = an NYH by LMAX array containing the dependent variables +C and their approximate scaled derivatives, where +C LMAX = MAXORD + 1. YH(i,j+1) contains the approximate +C j-th derivative of y(i), scaled by H**j/factorial(j) +C (j = 0,1,...,NQ). On entry for the first step, the first +C two columns of YH must be set from the initial values. +C NYH = a constant integer .ge. N, the first dimension of YH. +C YH1 = a one-dimensional array occupying the same space as YH. +C EWT = an array of length N containing multiplicative weights +C for local error measurements. Local errors in y(i) are +C compared to 1.0/EWT(i) in various error tests. +C SAVF = an array of working storage, of length N. also used for +C input of YH(*,MAXORD+2) when JSTART = -1 and MAXORD is less +C than the current order NQ. +C Same as YDOTI in the driver. +C SAVR = an array of working storage, of length N. +C ACOR = a work array of length N used for the accumulated +C corrections. On a succesful return, ACOR(i) contains +C the estimated one-step local error in y(i). +C WM,IWM = real and integer work arrays associated with matrix +C operations in chord iteration. +C PJAC = name of routine to evaluate and preprocess Jacobian matrix. +C SLVS = name of routine to solve linear system in chord iteration. +C CCMAX = maximum relative change in H*EL0 before PJAC is called. +C H = the step size to be attempted on the next step. +C H is altered by the error control algorithm during the +C problem. H can be either positive or negative, but its +C sign must remain constant throughout the problem. +C HMIN = the minimum absolute value of the step size H to be used. +C HMXI = inverse of the maximum absolute value of H to be used. +C HMXI = 0.0 is allowed and corresponds to an infinite HMAX. +C HMIN and HMXI may be changed at any time, but will not +C take effect until the next change of H is considered. +C TN = the independent variable. TN is updated on each step taken. +C JSTART = an integer used for input only, with the following +C values and meanings: +C 0 perform the first step. +C .gt.0 take a new step continuing from the last. +C -1 take the next step with a new value of H, MAXORD, +C N, METH, MITER, and/or matrix parameters. +C -2 take the next step with a new value of H, +C but with other inputs unchanged. +C On return, JSTART is set to 1 to facilitate continuation. +C KFLAG = a completion code with the following meanings: +C 0 the step was succesful. +C -1 the requested error could not be achieved. +C -2 corrector convergence could not be achieved. +C -3 RES ordered immediate return. +C -4 error condition from RES could not be avoided. +C -5 fatal error in PJAC or SLVS. +C A return with KFLAG = -1, -2, or -4 means either +C ABS(H) = HMIN or 10 consecutive failures occurred. +C On a return with KFLAG negative, the values of TN and +C the YH array are as of the beginning of the last +C step, and H is the last step size attempted. +C MAXORD = the maximum order of integration method to be allowed. +C MAXCOR = the maximum number of corrector iterations allowed. +C MSBP = maximum number of steps between PJAC calls. +C MXNCF = maximum number of convergence failures allowed. +C METH/MITER = the method flags. See description in driver. +C N = the number of first-order differential equations. +C----------------------------------------------------------------------- + KFLAG = 0 + TOLD = TN + NCF = 0 + IERPJ = 0 + IERSL = 0 + JCUR = 0 + ICF = 0 + DELP = 0.0D0 + IF (JSTART .GT. 0) GO TO 200 + IF (JSTART .EQ. -1) GO TO 100 + IF (JSTART .EQ. -2) GO TO 160 +C----------------------------------------------------------------------- +C On the first call, the order is set to 1, and other variables are +C initialized. RMAX is the maximum ratio by which H can be increased +C in a single step. It is initially 1.E4 to compensate for the small +C initial H, but then is normally equal to 10. If a failure +C occurs (in corrector convergence or error test), RMAX is set at 2 +C for the next increase. +C----------------------------------------------------------------------- + LMAX = MAXORD + 1 + NQ = 1 + L = 2 + IALTH = 2 + RMAX = 10000.0D0 + RC = 0.0D0 + EL0 = 1.0D0 + CRATE = 0.7D0 + HOLD = H + MEO = METH + NSLP = 0 + IPUP = MITER + IRET = 3 + GO TO 140 +C----------------------------------------------------------------------- +C The following block handles preliminaries needed when JSTART = -1. +C IPUP is set to MITER to force a matrix update. +C If an order increase is about to be considered (IALTH = 1), +C IALTH is reset to 2 to postpone consideration one more step. +C If the caller has changed METH, DCFODE is called to reset +C the coefficients of the method. +C If the caller has changed MAXORD to a value less than the current +C order NQ, NQ is reduced to MAXORD, and a new H chosen accordingly. +C If H is to be changed, YH must be rescaled. +C If H or METH is being changed, IALTH is reset to L = NQ + 1 +C to prevent further changes in H for that many steps. +C----------------------------------------------------------------------- + 100 IPUP = MITER + LMAX = MAXORD + 1 + IF (IALTH .EQ. 1) IALTH = 2 + IF (METH .EQ. MEO) GO TO 110 + CALL DCFODE (METH, ELCO, TESCO) + MEO = METH + IF (NQ .GT. MAXORD) GO TO 120 + IALTH = L + IRET = 1 + GO TO 150 + 110 IF (NQ .LE. MAXORD) GO TO 160 + 120 NQ = MAXORD + L = LMAX + DO 125 I = 1,L + 125 EL(I) = ELCO(I,NQ) + NQNYH = NQ*NYH + RC = RC*EL(1)/EL0 + EL0 = EL(1) + CONIT = 0.5D0/(NQ+2) + DDN = DVNORM (N, SAVF, EWT)/TESCO(1,L) + EXDN = 1.0D0/L + RHDN = 1.0D0/(1.3D0*DDN**EXDN + 0.0000013D0) + RH = MIN(RHDN,1.0D0) + IREDO = 3 + IF (H .EQ. HOLD) GO TO 170 + RH = MIN(RH,ABS(H/HOLD)) + H = HOLD + GO TO 175 +C----------------------------------------------------------------------- +C DCFODE is called to get all the integration coefficients for the +C current METH. Then the EL vector and related constants are reset +C whenever the order NQ is changed, or at the start of the problem. +C----------------------------------------------------------------------- + 140 CALL DCFODE (METH, ELCO, TESCO) + 150 DO 155 I = 1,L + 155 EL(I) = ELCO(I,NQ) + NQNYH = NQ*NYH + RC = RC*EL(1)/EL0 + EL0 = EL(1) + CONIT = 0.5D0/(NQ+2) + GO TO (160, 170, 200), IRET +C----------------------------------------------------------------------- +C If H is being changed, the H ratio RH is checked against +C RMAX, HMIN, and HMXI, and the YH array rescaled. IALTH is set to +C L = NQ + 1 to prevent a change of H for that many steps, unless +C forced by a convergence or error test failure. +C----------------------------------------------------------------------- + 160 IF (H .EQ. HOLD) GO TO 200 + RH = H/HOLD + H = HOLD + IREDO = 3 + GO TO 175 + 170 RH = MAX(RH,HMIN/ABS(H)) + 175 RH = MIN(RH,RMAX) + RH = RH/MAX(1.0D0,ABS(H)*HMXI*RH) + R = 1.0D0 + DO 180 J = 2,L + R = R*RH + DO 180 I = 1,N + 180 YH(I,J) = YH(I,J)*R + H = H*RH + RC = RC*RH + IALTH = L + IF (IREDO .EQ. 0) GO TO 690 +C----------------------------------------------------------------------- +C This section computes the predicted values by effectively +C multiplying the YH array by the Pascal triangle matrix. +C RC is the ratio of new to old values of the coefficient H*EL(1). +C When RC differs from 1 by more than CCMAX, IPUP is set to MITER +C to force PJAC to be called. +C In any case, PJAC is called at least every MSBP steps. +C----------------------------------------------------------------------- + 200 IF (ABS(RC-1.0D0) .GT. CCMAX) IPUP = MITER + IF (NST .GE. NSLP+MSBP) IPUP = MITER + TN = TN + H + I1 = NQNYH + 1 + DO 215 JB = 1,NQ + I1 = I1 - NYH +CDIR$ IVDEP + DO 210 I = I1,NQNYH + 210 YH1(I) = YH1(I) + YH1(I+NYH) + 215 CONTINUE +C----------------------------------------------------------------------- +C Up to MAXCOR corrector iterations are taken. A convergence test is +C made on the RMS-norm of each correction, weighted by H and the +C error weight vector EWT. The sum of the corrections is accumulated +C in ACOR(i). The YH array is not altered in the corrector loop. +C----------------------------------------------------------------------- + 220 M = 0 + DO 230 I = 1,N + SAVF(I) = YH(I,2) / H + 230 Y(I) = YH(I,1) + IF (IPUP .LE. 0) GO TO 240 +C----------------------------------------------------------------------- +C If indicated, the matrix P = A - H*EL(1)*dr/dy is reevaluated and +C preprocessed before starting the corrector iteration. IPUP is set +C to 0 as an indicator that this has been done. +C----------------------------------------------------------------------- + CALL PJAC (NEQ, Y, YH, NYH, EWT, ACOR, SAVR, SAVF, WM, IWM, + 1 RES, JAC, ADDA ) + IPUP = 0 + RC = 1.0D0 + NSLP = NST + CRATE = 0.7D0 + IF (IERPJ .EQ. 0) GO TO 250 + IF (IERPJ .LT. 0) GO TO 435 + IRES = IERPJ + GO TO (430, 435, 430), IRES +C Get residual at predicted values, if not already done in PJAC. ------- + 240 IRES = 1 + CALL RES ( NEQ, TN, Y, SAVF, SAVR, IRES ) + NFE = NFE + 1 + KGO = ABS(IRES) + GO TO ( 250, 435, 430 ) , KGO + 250 DO 260 I = 1,N + 260 ACOR(I) = 0.0D0 +C----------------------------------------------------------------------- +C Solve the linear system with the current residual as +C right-hand side and P as coefficient matrix. +C----------------------------------------------------------------------- + 270 CONTINUE + CALL SLVS (WM, IWM, SAVR, SAVF) + IF (IERSL .LT. 0) GO TO 430 + IF (IERSL .GT. 0) GO TO 410 + EL1H = EL(1) * H + DEL = DVNORM (N, SAVR, EWT) * ABS(H) + DO 380 I = 1,N + ACOR(I) = ACOR(I) + SAVR(I) + SAVF(I) = ACOR(I) + YH(I,2)/H + 380 Y(I) = YH(I,1) + EL1H*ACOR(I) +C----------------------------------------------------------------------- +C Test for convergence. If M .gt. 0, an estimate of the convergence +C rate constant is stored in CRATE, and this is used in the test. +C----------------------------------------------------------------------- + IF (M .NE. 0) CRATE = MAX(0.2D0*CRATE,DEL/DELP) + DCON = DEL*MIN(1.0D0,1.5D0*CRATE)/(TESCO(2,NQ)*CONIT) + IF (DCON .LE. 1.0D0) GO TO 460 + M = M + 1 + IF (M .EQ. MAXCOR) GO TO 410 + IF (M .GE. 2 .AND. DEL .GT. 2.0D0*DELP) GO TO 410 + DELP = DEL + IRES = 1 + CALL RES ( NEQ, TN, Y, SAVF, SAVR, IRES ) + NFE = NFE + 1 + KGO = ABS(IRES) + GO TO ( 270, 435, 410 ) , KGO +C----------------------------------------------------------------------- +C The correctors failed to converge, or RES has returned abnormally. +C on a convergence failure, if the Jacobian is out of date, PJAC is +C called for the next try. Otherwise the YH array is retracted to its +C values before prediction, and H is reduced, if possible. +C take an error exit if IRES = 2, or H cannot be reduced, or MXNCF +C failures have occurred, or a fatal error occurred in PJAC or SLVS. +C----------------------------------------------------------------------- + 410 ICF = 1 + IF (JCUR .EQ. 1) GO TO 430 + IPUP = MITER + GO TO 220 + 430 ICF = 2 + NCF = NCF + 1 + RMAX = 2.0D0 + 435 TN = TOLD + I1 = NQNYH + 1 + DO 445 JB = 1,NQ + I1 = I1 - NYH +CDIR$ IVDEP + DO 440 I = I1,NQNYH + 440 YH1(I) = YH1(I) - YH1(I+NYH) + 445 CONTINUE + IF (IRES .EQ. 2) GO TO 680 + IF (IERPJ .LT. 0 .OR. IERSL .LT. 0) GO TO 685 + IF (ABS(H) .LE. HMIN*1.00001D0) GO TO 450 + IF (NCF .EQ. MXNCF) GO TO 450 + RH = 0.25D0 + IPUP = MITER + IREDO = 1 + GO TO 170 + 450 IF (IRES .EQ. 3) GO TO 680 + GO TO 670 +C----------------------------------------------------------------------- +C The corrector has converged. JCUR is set to 0 +C to signal that the Jacobian involved may need updating later. +C The local error test is made and control passes to statement 500 +C if it fails. +C----------------------------------------------------------------------- + 460 JCUR = 0 + IF (M .EQ. 0) DSM = DEL/TESCO(2,NQ) + IF (M .GT. 0) DSM = ABS(H) * DVNORM (N, ACOR, EWT)/TESCO(2,NQ) + IF (DSM .GT. 1.0D0) GO TO 500 +C----------------------------------------------------------------------- +C After a successful step, update the YH array. +C Consider changing H if IALTH = 1. Otherwise decrease IALTH by 1. +C If IALTH is then 1 and NQ .lt. MAXORD, then ACOR is saved for +C use in a possible order increase on the next step. +C If a change in H is considered, an increase or decrease in order +C by one is considered also. A change in H is made only if it is by a +C factor of at least 1.1. If not, IALTH is set to 3 to prevent +C testing for that many steps. +C----------------------------------------------------------------------- + KFLAG = 0 + IREDO = 0 + NST = NST + 1 + HU = H + NQU = NQ + DO 470 J = 1,L + ELJH = EL(J)*H + DO 470 I = 1,N + 470 YH(I,J) = YH(I,J) + ELJH*ACOR(I) + IALTH = IALTH - 1 + IF (IALTH .EQ. 0) GO TO 520 + IF (IALTH .GT. 1) GO TO 700 + IF (L .EQ. LMAX) GO TO 700 + DO 490 I = 1,N + 490 YH(I,LMAX) = ACOR(I) + GO TO 700 +C----------------------------------------------------------------------- +C The error test failed. KFLAG keeps track of multiple failures. +C restore TN and the YH array to their previous values, and prepare +C to try the step again. Compute the optimum step size for this or +C one lower order. After 2 or more failures, H is forced to decrease +C by a factor of 0.1 or less. +C----------------------------------------------------------------------- + 500 KFLAG = KFLAG - 1 + TN = TOLD + I1 = NQNYH + 1 + DO 515 JB = 1,NQ + I1 = I1 - NYH +CDIR$ IVDEP + DO 510 I = I1,NQNYH + 510 YH1(I) = YH1(I) - YH1(I+NYH) + 515 CONTINUE + RMAX = 2.0D0 + IF (ABS(H) .LE. HMIN*1.00001D0) GO TO 660 + IF (KFLAG .LE. -7) GO TO 660 + IREDO = 2 + RHUP = 0.0D0 + GO TO 540 +C----------------------------------------------------------------------- +C Regardless of the success or failure of the step, factors +C RHDN, RHSM, and RHUP are computed, by which H could be multiplied +C at order NQ - 1, order NQ, or order NQ + 1, respectively. +C In the case of failure, RHUP = 0.0 to avoid an order increase. +C The largest of these is determined and the new order chosen +C accordingly. If the order is to be increased, we compute one +C additional scaled derivative. +C----------------------------------------------------------------------- + 520 RHUP = 0.0D0 + IF (L .EQ. LMAX) GO TO 540 + DO 530 I = 1,N + 530 SAVF(I) = ACOR(I) - YH(I,LMAX) + DUP = ABS(H) * DVNORM (N, SAVF, EWT)/TESCO(3,NQ) + EXUP = 1.0D0/(L+1) + RHUP = 1.0D0/(1.4D0*DUP**EXUP + 0.0000014D0) + 540 EXSM = 1.0D0/L + RHSM = 1.0D0/(1.2D0*DSM**EXSM + 0.0000012D0) + RHDN = 0.0D0 + IF (NQ .EQ. 1) GO TO 560 + DDN = DVNORM (N, YH(1,L), EWT)/TESCO(1,NQ) + EXDN = 1.0D0/NQ + RHDN = 1.0D0/(1.3D0*DDN**EXDN + 0.0000013D0) + 560 IF (RHSM .GE. RHUP) GO TO 570 + IF (RHUP .GT. RHDN) GO TO 590 + GO TO 580 + 570 IF (RHSM .LT. RHDN) GO TO 580 + NEWQ = NQ + RH = RHSM + GO TO 620 + 580 NEWQ = NQ - 1 + RH = RHDN + IF (KFLAG .LT. 0 .AND. RH .GT. 1.0D0) RH = 1.0D0 + GO TO 620 + 590 NEWQ = L + RH = RHUP + IF (RH .LT. 1.1D0) GO TO 610 + R = H*EL(L)/L + DO 600 I = 1,N + 600 YH(I,NEWQ+1) = ACOR(I)*R + GO TO 630 + 610 IALTH = 3 + GO TO 700 + 620 IF ((KFLAG .EQ. 0) .AND. (RH .LT. 1.1D0)) GO TO 610 + IF (KFLAG .LE. -2) RH = MIN(RH,0.1D0) +C----------------------------------------------------------------------- +C If there is a change of order, reset NQ, L, and the coefficients. +C In any case H is reset according to RH and the YH array is rescaled. +C Then exit from 690 if the step was OK, or redo the step otherwise. +C----------------------------------------------------------------------- + IF (NEWQ .EQ. NQ) GO TO 170 + 630 NQ = NEWQ + L = NQ + 1 + IRET = 2 + GO TO 150 +C----------------------------------------------------------------------- +C All returns are made through this section. H is saved in HOLD +C to allow the caller to change H on the next step. +C----------------------------------------------------------------------- + 660 KFLAG = -1 + GO TO 720 + 670 KFLAG = -2 + GO TO 720 + 680 KFLAG = -1 - IRES + GO TO 720 + 685 KFLAG = -5 + GO TO 720 + 690 RMAX = 10.0D0 + 700 R = H/TESCO(2,NQU) + DO 710 I = 1,N + 710 ACOR(I) = ACOR(I)*R + 720 HOLD = H + JSTART = 1 + RETURN +C----------------------- End of Subroutine DSTODI ---------------------- + END +*DECK DPREPJI + SUBROUTINE DPREPJI (NEQ, Y, YH, NYH, EWT, RTEM, SAVR, S, WM, IWM, + 1 RES, JAC, ADDA) + EXTERNAL RES, JAC, ADDA + INTEGER NEQ, NYH, IWM + DOUBLE PRECISION Y, YH, EWT, RTEM, SAVR, S, WM + DIMENSION NEQ(*), Y(*), YH(NYH,*), EWT(*), RTEM(*), + 1 S(*), SAVR(*), WM(*), IWM(*) + INTEGER IOWND, IOWNS, + 1 ICF, IERPJ, IERSL, JCUR, JSTART, KFLAG, L, + 2 LYH, LEWT, LACOR, LSAVF, LWM, LIWM, METH, MITER, + 3 MAXORD, MAXCOR, MSBP, MXNCF, N, NQ, NST, NFE, NJE, NQU + DOUBLE PRECISION ROWNS, + 1 CCMAX, EL0, H, HMIN, HMXI, HU, RC, TN, UROUND + COMMON /DLS001/ ROWNS(209), + 1 CCMAX, EL0, H, HMIN, HMXI, HU, RC, TN, UROUND, + 2 IOWND(6), IOWNS(6), + 3 ICF, IERPJ, IERSL, JCUR, JSTART, KFLAG, L, + 4 LYH, LEWT, LACOR, LSAVF, LWM, LIWM, METH, MITER, + 5 MAXORD, MAXCOR, MSBP, MXNCF, N, NQ, NST, NFE, NJE, NQU + INTEGER I, I1, I2, IER, II, IRES, J, J1, JJ, LENP, + 1 MBA, MBAND, MEB1, MEBAND, ML, ML3, MU + DOUBLE PRECISION CON, FAC, HL0, R, SRUR, YI, YJ, YJJ +C----------------------------------------------------------------------- +C DPREPJI is called by DSTODI to compute and process the matrix +C P = A - H*EL(1)*J , where J is an approximation to the Jacobian dr/dy, +C where r = g(t,y) - A(t,y)*s. Here J is computed by the user-supplied +C routine JAC if MITER = 1 or 4, or by finite differencing if MITER = +C 2 or 5. J is stored in WM, rescaled, and ADDA is called to generate +C P. P is then subjected to LU decomposition in preparation +C for later solution of linear systems with P as coefficient +C matrix. This is done by DGEFA if MITER = 1 or 2, and by +C DGBFA if MITER = 4 or 5. +C +C In addition to variables described previously, communication +C with DPREPJI uses the following: +C Y = array containing predicted values on entry. +C RTEM = work array of length N (ACOR in DSTODI). +C SAVR = array used for output only. On output it contains the +C residual evaluated at current values of t and y. +C S = array containing predicted values of dy/dt (SAVF in DSTODI). +C WM = real work space for matrices. On output it contains the +C LU decomposition of P. +C Storage of matrix elements starts at WM(3). +C WM also contains the following matrix-related data: +C WM(1) = SQRT(UROUND), used in numerical Jacobian increments. +C IWM = integer work space containing pivot information, starting at +C IWM(21). IWM also contains the band parameters +C ML = IWM(1) and MU = IWM(2) if MITER is 4 or 5. +C EL0 = el(1) (input). +C IERPJ = output error flag. +C = 0 if no trouble occurred, +C = 1 if the P matrix was found to be singular, +C = IRES (= 2 or 3) if RES returned IRES = 2 or 3. +C JCUR = output flag = 1 to indicate that the Jacobian matrix +C (or approximation) is now current. +C This routine also uses the Common variables EL0, H, TN, UROUND, +C MITER, N, NFE, and NJE. +C----------------------------------------------------------------------- + NJE = NJE + 1 + HL0 = H*EL0 + IERPJ = 0 + JCUR = 1 + GO TO (100, 200, 300, 400, 500), MITER +C If MITER = 1, call RES, then JAC, and multiply by scalar. ------------ + 100 IRES = 1 + CALL RES (NEQ, TN, Y, S, SAVR, IRES) + NFE = NFE + 1 + IF (IRES .GT. 1) GO TO 600 + LENP = N*N + DO 110 I = 1,LENP + 110 WM(I+2) = 0.0D0 + CALL JAC ( NEQ, TN, Y, S, 0, 0, WM(3), N ) + CON = -HL0 + DO 120 I = 1,LENP + 120 WM(I+2) = WM(I+2)*CON + GO TO 240 +C If MITER = 2, make N + 1 calls to RES to approximate J. -------------- + 200 CONTINUE + IRES = -1 + CALL RES (NEQ, TN, Y, S, SAVR, IRES) + NFE = NFE + 1 + IF (IRES .GT. 1) GO TO 600 + SRUR = WM(1) + J1 = 2 + DO 230 J = 1,N + YJ = Y(J) + R = MAX(SRUR*ABS(YJ),0.01D0/EWT(J)) + Y(J) = Y(J) + R + FAC = -HL0/R + CALL RES ( NEQ, TN, Y, S, RTEM, IRES ) + NFE = NFE + 1 + IF (IRES .GT. 1) GO TO 600 + DO 220 I = 1,N + 220 WM(I+J1) = (RTEM(I) - SAVR(I))*FAC + Y(J) = YJ + J1 = J1 + N + 230 CONTINUE + IRES = 1 + CALL RES (NEQ, TN, Y, S, SAVR, IRES) + NFE = NFE + 1 + IF (IRES .GT. 1) GO TO 600 +C Add matrix A. -------------------------------------------------------- + 240 CONTINUE + CALL ADDA(NEQ, TN, Y, 0, 0, WM(3), N) +C Do LU decomposition on P. -------------------------------------------- + CALL DGEFA (WM(3), N, N, IWM(21), IER) + IF (IER .NE. 0) IERPJ = 1 + RETURN +C Dummy section for MITER = 3 + 300 RETURN +C If MITER = 4, call RES, then JAC, and multiply by scalar. ------------ + 400 IRES = 1 + CALL RES (NEQ, TN, Y, S, SAVR, IRES) + NFE = NFE + 1 + IF (IRES .GT. 1) GO TO 600 + ML = IWM(1) + MU = IWM(2) + ML3 = ML + 3 + MBAND = ML + MU + 1 + MEBAND = MBAND + ML + LENP = MEBAND*N + DO 410 I = 1,LENP + 410 WM(I+2) = 0.0D0 + CALL JAC ( NEQ, TN, Y, S, ML, MU, WM(ML3), MEBAND) + CON = -HL0 + DO 420 I = 1,LENP + 420 WM(I+2) = WM(I+2)*CON + GO TO 570 +C If MITER = 5, make ML + MU + 2 calls to RES to approximate J. -------- + 500 CONTINUE + IRES = -1 + CALL RES (NEQ, TN, Y, S, SAVR, IRES) + NFE = NFE + 1 + IF (IRES .GT. 1) GO TO 600 + ML = IWM(1) + MU = IWM(2) + ML3 = ML + 3 + MBAND = ML + MU + 1 + MBA = MIN(MBAND,N) + MEBAND = MBAND + ML + MEB1 = MEBAND - 1 + SRUR = WM(1) + DO 560 J = 1,MBA + DO 530 I = J,N,MBAND + YI = Y(I) + R = MAX(SRUR*ABS(YI),0.01D0/EWT(I)) + 530 Y(I) = Y(I) + R + CALL RES ( NEQ, TN, Y, S, RTEM, IRES) + NFE = NFE + 1 + IF (IRES .GT. 1) GO TO 600 + DO 550 JJ = J,N,MBAND + Y(JJ) = YH(JJ,1) + YJJ = Y(JJ) + R = MAX(SRUR*ABS(YJJ),0.01D0/EWT(JJ)) + FAC = -HL0/R + I1 = MAX(JJ-MU,1) + I2 = MIN(JJ+ML,N) + II = JJ*MEB1 - ML + 2 + DO 540 I = I1,I2 + 540 WM(II+I) = (RTEM(I) - SAVR(I))*FAC + 550 CONTINUE + 560 CONTINUE + IRES = 1 + CALL RES (NEQ, TN, Y, S, SAVR, IRES) + NFE = NFE + 1 + IF (IRES .GT. 1) GO TO 600 +C Add matrix A. -------------------------------------------------------- + 570 CONTINUE + CALL ADDA(NEQ, TN, Y, ML, MU, WM(ML3), MEBAND) +C Do LU decomposition of P. -------------------------------------------- + CALL DGBFA (WM(3), MEBAND, N, ML, MU, IWM(21), IER) + IF (IER .NE. 0) IERPJ = 1 + RETURN +C Error return for IRES = 2 or IRES = 3 return from RES. --------------- + 600 IERPJ = IRES + RETURN +C----------------------- End of Subroutine DPREPJI --------------------- + END +*DECK DAIGBT + SUBROUTINE DAIGBT (RES, ADDA, NEQ, T, Y, YDOT, + 1 MB, NB, PW, IPVT, IER ) + EXTERNAL RES, ADDA + INTEGER NEQ, MB, NB, IPVT, IER + INTEGER I, LENPW, LBLOX, LPB, LPC + DOUBLE PRECISION T, Y, YDOT, PW + DIMENSION Y(*), YDOT(*), PW(*), IPVT(*), NEQ(*) +C----------------------------------------------------------------------- +C This subroutine computes the initial value +C of the vector YDOT satisfying +C A * YDOT = g(t,y) +C when A is nonsingular. It is called by DLSOIBT for +C initialization only, when ISTATE = 0 . +C DAIGBT returns an error flag IER: +C IER = 0 means DAIGBT was successful. +C IER .ge. 2 means RES returned an error flag IRES = IER. +C IER .lt. 0 means the A matrix was found to have a singular +C diagonal block (hence YDOT could not be solved for). +C----------------------------------------------------------------------- + LBLOX = MB*MB*NB + LPB = 1 + LBLOX + LPC = LPB + LBLOX + LENPW = 3*LBLOX + DO 10 I = 1,LENPW + 10 PW(I) = 0.0D0 + IER = 1 + CALL RES (NEQ, T, Y, PW, YDOT, IER) + IF (IER .GT. 1) RETURN + CALL ADDA (NEQ, T, Y, MB, NB, PW(1), PW(LPB), PW(LPC) ) + CALL DDECBT (MB, NB, PW, PW(LPB), PW(LPC), IPVT, IER) + IF (IER .EQ. 0) GO TO 20 + IER = -IER + RETURN + 20 CALL DSOLBT (MB, NB, PW, PW(LPB), PW(LPC), YDOT, IPVT) + RETURN +C----------------------- End of Subroutine DAIGBT ---------------------- + END +*DECK DPJIBT + SUBROUTINE DPJIBT (NEQ, Y, YH, NYH, EWT, RTEM, SAVR, S, WM, IWM, + 1 RES, JAC, ADDA) + EXTERNAL RES, JAC, ADDA + INTEGER NEQ, NYH, IWM + DOUBLE PRECISION Y, YH, EWT, RTEM, SAVR, S, WM + DIMENSION NEQ(*), Y(*), YH(NYH,*), EWT(*), RTEM(*), + 1 S(*), SAVR(*), WM(*), IWM(*) + INTEGER IOWND, IOWNS, + 1 ICF, IERPJ, IERSL, JCUR, JSTART, KFLAG, L, + 2 LYH, LEWT, LACOR, LSAVF, LWM, LIWM, METH, MITER, + 3 MAXORD, MAXCOR, MSBP, MXNCF, N, NQ, NST, NFE, NJE, NQU + DOUBLE PRECISION ROWNS, + 1 CCMAX, EL0, H, HMIN, HMXI, HU, RC, TN, UROUND + COMMON /DLS001/ ROWNS(209), + 1 CCMAX, EL0, H, HMIN, HMXI, HU, RC, TN, UROUND, + 2 IOWND(6), IOWNS(6), + 3 ICF, IERPJ, IERSL, JCUR, JSTART, KFLAG, L, + 4 LYH, LEWT, LACOR, LSAVF, LWM, LIWM, METH, MITER, + 5 MAXORD, MAXCOR, MSBP, MXNCF, N, NQ, NST, NFE, NJE, NQU + INTEGER I, IER, IIA, IIB, IIC, IPA, IPB, IPC, IRES, J, J1, J2, + 1 K, K1, LENP, LBLOX, LPB, LPC, MB, MBSQ, MWID, NB + DOUBLE PRECISION CON, FAC, HL0, R, SRUR +C----------------------------------------------------------------------- +C DPJIBT is called by DSTODI to compute and process the matrix +C P = A - H*EL(1)*J , where J is an approximation to the Jacobian dr/dy, +C and r = g(t,y) - A(t,y)*s. Here J is computed by the user-supplied +C routine JAC if MITER = 1, or by finite differencing if MITER = 2. +C J is stored in WM, rescaled, and ADDA is called to generate P. +C P is then subjected to LU decomposition by DDECBT in preparation +C for later solution of linear systems with P as coefficient matrix. +C +C In addition to variables described previously, communication +C with DPJIBT uses the following: +C Y = array containing predicted values on entry. +C RTEM = work array of length N (ACOR in DSTODI). +C SAVR = array used for output only. On output it contains the +C residual evaluated at current values of t and y. +C S = array containing predicted values of dy/dt (SAVF in DSTODI). +C WM = real work space for matrices. On output it contains the +C LU decomposition of P. +C Storage of matrix elements starts at WM(3). +C WM also contains the following matrix-related data: +C WM(1) = SQRT(UROUND), used in numerical Jacobian increments. +C IWM = integer work space containing pivot information, starting at +C IWM(21). IWM also contains block structure parameters +C MB = IWM(1) and NB = IWM(2). +C EL0 = EL(1) (input). +C IERPJ = output error flag. +C = 0 if no trouble occurred, +C = 1 if the P matrix was found to be unfactorable, +C = IRES (= 2 or 3) if RES returned IRES = 2 or 3. +C JCUR = output flag = 1 to indicate that the Jacobian matrix +C (or approximation) is now current. +C This routine also uses the Common variables EL0, H, TN, UROUND, +C MITER, N, NFE, and NJE. +C----------------------------------------------------------------------- + NJE = NJE + 1 + HL0 = H*EL0 + IERPJ = 0 + JCUR = 1 + MB = IWM(1) + NB = IWM(2) + MBSQ = MB*MB + LBLOX = MBSQ*NB + LPB = 3 + LBLOX + LPC = LPB + LBLOX + LENP = 3*LBLOX + GO TO (100, 200), MITER +C If MITER = 1, call RES, then JAC, and multiply by scalar. ------------ + 100 IRES = 1 + CALL RES (NEQ, TN, Y, S, SAVR, IRES) + NFE = NFE + 1 + IF (IRES .GT. 1) GO TO 600 + DO 110 I = 1,LENP + 110 WM(I+2) = 0.0D0 + CALL JAC (NEQ, TN, Y, S, MB, NB, WM(3), WM(LPB), WM(LPC)) + CON = -HL0 + DO 120 I = 1,LENP + 120 WM(I+2) = WM(I+2)*CON + GO TO 260 +C +C If MITER = 2, make 3*MB + 1 calls to RES to approximate J. ----------- + 200 CONTINUE + IRES = -1 + CALL RES (NEQ, TN, Y, S, SAVR, IRES) + NFE = NFE + 1 + IF (IRES .GT. 1) GO TO 600 + MWID = 3*MB + SRUR = WM(1) + DO 205 I = 1,LENP + 205 WM(2+I) = 0.0D0 + DO 250 K = 1,3 + DO 240 J = 1,MB +C Increment Y(I) for group of column indices, and call RES. ---- + J1 = J+(K-1)*MB + DO 210 I = J1,N,MWID + R = MAX(SRUR*ABS(Y(I)),0.01D0/EWT(I)) + Y(I) = Y(I) + R + 210 CONTINUE + CALL RES (NEQ, TN, Y, S, RTEM, IRES) + NFE = NFE + 1 + IF (IRES .GT. 1) GO TO 600 + DO 215 I = 1,N + 215 RTEM(I) = RTEM(I) - SAVR(I) + K1 = K + DO 230 I = J1,N,MWID +C Get Jacobian elements in column I (block-column K1). ------- + Y(I) = YH(I,1) + R = MAX(SRUR*ABS(Y(I)),0.01D0/EWT(I)) + FAC = -HL0/R +C Compute and load elements PA(*,J,K1). ---------------------- + IIA = I - J + IPA = 2 + (J-1)*MB + (K1-1)*MBSQ + DO 221 J2 = 1,MB + 221 WM(IPA+J2) = RTEM(IIA+J2)*FAC + IF (K1 .LE. 1) GO TO 223 +C Compute and load elements PB(*,J,K1-1). -------------------- + IIB = IIA - MB + IPB = IPA + LBLOX - MBSQ + DO 222 J2 = 1,MB + 222 WM(IPB+J2) = RTEM(IIB+J2)*FAC + 223 CONTINUE + IF (K1 .GE. NB) GO TO 225 +C Compute and load elements PC(*,J,K1+1). -------------------- + IIC = IIA + MB + IPC = IPA + 2*LBLOX + MBSQ + DO 224 J2 = 1,MB + 224 WM(IPC+J2) = RTEM(IIC+J2)*FAC + 225 CONTINUE + IF (K1 .NE. 3) GO TO 227 +C Compute and load elements PC(*,J,1). ----------------------- + IPC = IPA - 2*MBSQ + 2*LBLOX + DO 226 J2 = 1,MB + 226 WM(IPC+J2) = RTEM(J2)*FAC + 227 CONTINUE + IF (K1 .NE. NB-2) GO TO 229 +C Compute and load elements PB(*,J,NB). ---------------------- + IIB = N - MB + IPB = IPA + 2*MBSQ + LBLOX + DO 228 J2 = 1,MB + 228 WM(IPB+J2) = RTEM(IIB+J2)*FAC + 229 K1 = K1 + 3 + 230 CONTINUE + 240 CONTINUE + 250 CONTINUE +C RES call for first corrector iteration. ------------------------------ + IRES = 1 + CALL RES (NEQ, TN, Y, S, SAVR, IRES) + NFE = NFE + 1 + IF (IRES .GT. 1) GO TO 600 +C Add matrix A. -------------------------------------------------------- + 260 CONTINUE + CALL ADDA (NEQ, TN, Y, MB, NB, WM(3), WM(LPB), WM(LPC)) +C Do LU decomposition on P. -------------------------------------------- + CALL DDECBT (MB, NB, WM(3), WM(LPB), WM(LPC), IWM(21), IER) + IF (IER .NE. 0) IERPJ = 1 + RETURN +C Error return for IRES = 2 or IRES = 3 return from RES. --------------- + 600 IERPJ = IRES + RETURN +C----------------------- End of Subroutine DPJIBT ---------------------- + END +*DECK DSLSBT + SUBROUTINE DSLSBT (WM, IWM, X, TEM) + INTEGER IWM + INTEGER LBLOX, LPB, LPC, MB, NB + DOUBLE PRECISION WM, X, TEM + DIMENSION WM(*), IWM(*), X(*), TEM(*) +C----------------------------------------------------------------------- +C This routine acts as an interface between the core integrator +C routine and the DSOLBT routine for the solution of the linear system +C arising from chord iteration. +C Communication with DSLSBT uses the following variables: +C WM = real work space containing the LU decomposition, +C starting at WM(3). +C IWM = integer work space containing pivot information, starting at +C IWM(21). IWM also contains block structure parameters +C MB = IWM(1) and NB = IWM(2). +C X = the right-hand side vector on input, and the solution vector +C on output, of length N. +C TEM = vector of work space of length N, not used in this version. +C----------------------------------------------------------------------- + MB = IWM(1) + NB = IWM(2) + LBLOX = MB*MB*NB + LPB = 3 + LBLOX + LPC = LPB + LBLOX + CALL DSOLBT (MB, NB, WM(3), WM(LPB), WM(LPC), X, IWM(21)) + RETURN +C----------------------- End of Subroutine DSLSBT ---------------------- + END +*DECK DDECBT + SUBROUTINE DDECBT (M, N, A, B, C, IP, IER) + INTEGER M, N, IP(M,N), IER + DOUBLE PRECISION A(M,M,N), B(M,M,N), C(M,M,N) +C----------------------------------------------------------------------- +C Block-tridiagonal matrix decomposition routine. +C Written by A. C. Hindmarsh. +C Latest revision: November 10, 1983 (ACH) +C Reference: UCID-30150 +C Solution of Block-Tridiagonal Systems of Linear +C Algebraic Equations +C A.C. Hindmarsh +C February 1977 +C The input matrix contains three blocks of elements in each block-row, +C including blocks in the (1,3) and (N,N-2) block positions. +C DDECBT uses block Gauss elimination and Subroutines DGEFA and DGESL +C for solution of blocks. Partial pivoting is done within +C block-rows only. +C +C Note: this version uses LINPACK routines DGEFA/DGESL instead of +C of dec/sol for solution of blocks, and it uses the BLAS routine DDOT +C for dot product calculations. +C +C Input: +C M = order of each block. +C N = number of blocks in each direction of the matrix. +C N must be 4 or more. The complete matrix has order M*N. +C A = M by M by N array containing diagonal blocks. +C A(i,j,k) contains the (i,j) element of the k-th block. +C B = M by M by N array containing the super-diagonal blocks +C (in B(*,*,k) for k = 1,...,N-1) and the block in the (N,N-2) +C block position (in B(*,*,N)). +C C = M by M by N array containing the subdiagonal blocks +C (in C(*,*,k) for k = 2,3,...,N) and the block in the +C (1,3) block position (in C(*,*,1)). +C IP = integer array of length M*N for working storage. +C Output: +C A,B,C = M by M by N arrays containing the block-LU decomposition +C of the input matrix. +C IP = M by N array of pivot information. IP(*,k) contains +C information for the k-th digonal block. +C IER = 0 if no trouble occurred, or +C = -1 if the input value of M or N was illegal, or +C = k if a singular matrix was found in the k-th diagonal block. +C Use DSOLBT to solve the associated linear system. +C +C External routines required: DGEFA and DGESL (from LINPACK) and +C DDOT (from the BLAS, or Basic Linear Algebra package). +C----------------------------------------------------------------------- + INTEGER NM1, NM2, KM1, I, J, K + DOUBLE PRECISION DP, DDOT + IF (M .LT. 1 .OR. N .LT. 4) GO TO 210 + NM1 = N - 1 + NM2 = N - 2 +C Process the first block-row. ----------------------------------------- + CALL DGEFA (A, M, M, IP, IER) + K = 1 + IF (IER .NE. 0) GO TO 200 + DO 10 J = 1,M + CALL DGESL (A, M, M, IP, B(1,J,1), 0) + CALL DGESL (A, M, M, IP, C(1,J,1), 0) + 10 CONTINUE +C Adjust B(*,*,2). ----------------------------------------------------- + DO 40 J = 1,M + DO 30 I = 1,M + DP = DDOT (M, C(I,1,2), M, C(1,J,1), 1) + B(I,J,2) = B(I,J,2) - DP + 30 CONTINUE + 40 CONTINUE +C Main loop. Process block-rows 2 to N-1. ----------------------------- + DO 100 K = 2,NM1 + KM1 = K - 1 + DO 70 J = 1,M + DO 60 I = 1,M + DP = DDOT (M, C(I,1,K), M, B(1,J,KM1), 1) + A(I,J,K) = A(I,J,K) - DP + 60 CONTINUE + 70 CONTINUE + CALL DGEFA (A(1,1,K), M, M, IP(1,K), IER) + IF (IER .NE. 0) GO TO 200 + DO 80 J = 1,M + 80 CALL DGESL (A(1,1,K), M, M, IP(1,K), B(1,J,K), 0) + 100 CONTINUE +C Process last block-row and return. ----------------------------------- + DO 130 J = 1,M + DO 120 I = 1,M + DP = DDOT (M, B(I,1,N), M, B(1,J,NM2), 1) + C(I,J,N) = C(I,J,N) - DP + 120 CONTINUE + 130 CONTINUE + DO 160 J = 1,M + DO 150 I = 1,M + DP = DDOT (M, C(I,1,N), M, B(1,J,NM1), 1) + A(I,J,N) = A(I,J,N) - DP + 150 CONTINUE + 160 CONTINUE + CALL DGEFA (A(1,1,N), M, M, IP(1,N), IER) + K = N + IF (IER .NE. 0) GO TO 200 + RETURN +C Error returns. ------------------------------------------------------- + 200 IER = K + RETURN + 210 IER = -1 + RETURN +C----------------------- End of Subroutine DDECBT ---------------------- + END +*DECK DSOLBT + SUBROUTINE DSOLBT (M, N, A, B, C, Y, IP) + INTEGER M, N, IP(M,N) + DOUBLE PRECISION A(M,M,N), B(M,M,N), C(M,M,N), Y(M,N) +C----------------------------------------------------------------------- +C Solution of block-tridiagonal linear system. +C Coefficient matrix must have been previously processed by DDECBT. +C M, N, A,B,C, and IP must not have been changed since call to DDECBT. +C Written by A. C. Hindmarsh. +C Input: +C M = order of each block. +C N = number of blocks in each direction of matrix. +C A,B,C = M by M by N arrays containing block LU decomposition +C of coefficient matrix from DDECBT. +C IP = M by N integer array of pivot information from DDECBT. +C Y = array of length M*N containg the right-hand side vector +C (treated as an M by N array here). +C Output: +C Y = solution vector, of length M*N. +C +C External routines required: DGESL (LINPACK) and DDOT (BLAS). +C----------------------------------------------------------------------- +C + INTEGER NM1, NM2, I, K, KB, KM1, KP1 + DOUBLE PRECISION DP, DDOT + NM1 = N - 1 + NM2 = N - 2 +C Forward solution sweep. ---------------------------------------------- + CALL DGESL (A, M, M, IP, Y, 0) + DO 30 K = 2,NM1 + KM1 = K - 1 + DO 20 I = 1,M + DP = DDOT (M, C(I,1,K), M, Y(1,KM1), 1) + Y(I,K) = Y(I,K) - DP + 20 CONTINUE + CALL DGESL (A(1,1,K), M, M, IP(1,K), Y(1,K), 0) + 30 CONTINUE + DO 50 I = 1,M + DP = DDOT (M, C(I,1,N), M, Y(1,NM1), 1) + 1 + DDOT (M, B(I,1,N), M, Y(1,NM2), 1) + Y(I,N) = Y(I,N) - DP + 50 CONTINUE + CALL DGESL (A(1,1,N), M, M, IP(1,N), Y(1,N), 0) +C Backward solution sweep. --------------------------------------------- + DO 80 KB = 1,NM1 + K = N - KB + KP1 = K + 1 + DO 70 I = 1,M + DP = DDOT (M, B(I,1,K), M, Y(1,KP1), 1) + Y(I,K) = Y(I,K) - DP + 70 CONTINUE + 80 CONTINUE + DO 100 I = 1,M + DP = DDOT (M, C(I,1,1), M, Y(1,3), 1) + Y(I,1) = Y(I,1) - DP + 100 CONTINUE + RETURN +C----------------------- End of Subroutine DSOLBT ---------------------- + END +*DECK DIPREPI + SUBROUTINE DIPREPI (NEQ, Y, S, RWORK, IA, JA, IC, JC, IPFLAG, + 1 RES, JAC, ADDA) + EXTERNAL RES, JAC, ADDA + INTEGER NEQ, IA, JA, IC, JC, IPFLAG + DOUBLE PRECISION Y, S, RWORK + DIMENSION NEQ(*), Y(*), S(*), RWORK(*), IA(*), JA(*), IC(*), JC(*) + INTEGER IOWND, IOWNS, + 1 ICF, IERPJ, IERSL, JCUR, JSTART, KFLAG, L, + 2 LYH, LEWT, LACOR, LSAVF, LWM, LIWM, METH, MITER, + 3 MAXORD, MAXCOR, MSBP, MXNCF, N, NQ, NST, NFE, NJE, NQU + INTEGER IPLOST, IESP, ISTATC, IYS, IBA, IBIAN, IBJAN, IBJGP, + 1 IPIAN, IPJAN, IPJGP, IPIGP, IPR, IPC, IPIC, IPISP, IPRSP, IPA, + 2 LENYH, LENYHM, LENWK, LREQ, LRAT, LREST, LWMIN, MOSS, MSBJ, + 3 NSLJ, NGP, NLU, NNZ, NSP, NZL, NZU + DOUBLE PRECISION ROWNS, + 1 CCMAX, EL0, H, HMIN, HMXI, HU, RC, TN, UROUND + DOUBLE PRECISION RLSS + COMMON /DLS001/ ROWNS(209), + 1 CCMAX, EL0, H, HMIN, HMXI, HU, RC, TN, UROUND, + 2 IOWND(6), IOWNS(6), + 3 ICF, IERPJ, IERSL, JCUR, JSTART, KFLAG, L, + 4 LYH, LEWT, LACOR, LSAVF, LWM, LIWM, METH, MITER, + 5 MAXORD, MAXCOR, MSBP, MXNCF, N, NQ, NST, NFE, NJE, NQU + COMMON /DLSS01/ RLSS(6), + 1 IPLOST, IESP, ISTATC, IYS, IBA, IBIAN, IBJAN, IBJGP, + 2 IPIAN, IPJAN, IPJGP, IPIGP, IPR, IPC, IPIC, IPISP, IPRSP, IPA, + 3 LENYH, LENYHM, LENWK, LREQ, LRAT, LREST, LWMIN, MOSS, MSBJ, + 4 NSLJ, NGP, NLU, NNZ, NSP, NZL, NZU + INTEGER I, IMAX, LEWTN, LYHD, LYHN +C----------------------------------------------------------------------- +C This routine serves as an interface between the driver and +C Subroutine DPREPI. Tasks performed here are: +C * call DPREPI, +C * reset the required WM segment length LENWK, +C * move YH back to its final location (following WM in RWORK), +C * reset pointers for YH, SAVR, EWT, and ACOR, and +C * move EWT to its new position if ISTATE = 0 or 1. +C IPFLAG is an output error indication flag. IPFLAG = 0 if there was +C no trouble, and IPFLAG is the value of the DPREPI error flag IPPER +C if there was trouble in Subroutine DPREPI. +C----------------------------------------------------------------------- + IPFLAG = 0 +C Call DPREPI to do matrix preprocessing operations. ------------------- + CALL DPREPI (NEQ, Y, S, RWORK(LYH), RWORK(LSAVF), RWORK(LEWT), + 1 RWORK(LACOR), IA, JA, IC, JC, RWORK(LWM), RWORK(LWM), IPFLAG, + 2 RES, JAC, ADDA) + LENWK = MAX(LREQ,LWMIN) + IF (IPFLAG .LT. 0) RETURN +C If DPREPI was successful, move YH to end of required space for WM. --- + LYHN = LWM + LENWK + IF (LYHN .GT. LYH) RETURN + LYHD = LYH - LYHN + IF (LYHD .EQ. 0) GO TO 20 + IMAX = LYHN - 1 + LENYHM + DO 10 I=LYHN,IMAX + 10 RWORK(I) = RWORK(I+LYHD) + LYH = LYHN +C Reset pointers for SAVR, EWT, and ACOR. ------------------------------ + 20 LSAVF = LYH + LENYH + LEWTN = LSAVF + N + LACOR = LEWTN + N + IF (ISTATC .EQ. 3) GO TO 40 +C If ISTATE = 1, move EWT (left) to its new position. ------------------ + IF (LEWTN .GT. LEWT) RETURN + DO 30 I=1,N + 30 RWORK(I+LEWTN-1) = RWORK(I+LEWT-1) + 40 LEWT = LEWTN + RETURN +C----------------------- End of Subroutine DIPREPI --------------------- + END +*DECK DPREPI + SUBROUTINE DPREPI (NEQ, Y, S, YH, SAVR, EWT, RTEM, IA, JA, IC, JC, + 1 WK, IWK, IPPER, RES, JAC, ADDA) + EXTERNAL RES, JAC, ADDA + INTEGER NEQ, IA, JA, IC, JC, IWK, IPPER + DOUBLE PRECISION Y, S, YH, SAVR, EWT, RTEM, WK + DIMENSION NEQ(*), Y(*), S(*), YH(*), SAVR(*), EWT(*), RTEM(*), + 1 IA(*), JA(*), IC(*), JC(*), WK(*), IWK(*) + INTEGER IOWND, IOWNS, + 1 ICF, IERPJ, IERSL, JCUR, JSTART, KFLAG, L, + 2 LYH, LEWT, LACOR, LSAVF, LWM, LIWM, METH, MITER, + 3 MAXORD, MAXCOR, MSBP, MXNCF, N, NQ, NST, NFE, NJE, NQU + INTEGER IPLOST, IESP, ISTATC, IYS, IBA, IBIAN, IBJAN, IBJGP, + 1 IPIAN, IPJAN, IPJGP, IPIGP, IPR, IPC, IPIC, IPISP, IPRSP, IPA, + 2 LENYH, LENYHM, LENWK, LREQ, LRAT, LREST, LWMIN, MOSS, MSBJ, + 3 NSLJ, NGP, NLU, NNZ, NSP, NZL, NZU + DOUBLE PRECISION ROWNS, + 1 CCMAX, EL0, H, HMIN, HMXI, HU, RC, TN, UROUND + DOUBLE PRECISION RLSS + COMMON /DLS001/ ROWNS(209), + 1 CCMAX, EL0, H, HMIN, HMXI, HU, RC, TN, UROUND, + 2 IOWND(6), IOWNS(6), + 3 ICF, IERPJ, IERSL, JCUR, JSTART, KFLAG, L, + 4 LYH, LEWT, LACOR, LSAVF, LWM, LIWM, METH, MITER, + 5 MAXORD, MAXCOR, MSBP, MXNCF, N, NQ, NST, NFE, NJE, NQU + COMMON /DLSS01/ RLSS(6), + 1 IPLOST, IESP, ISTATC, IYS, IBA, IBIAN, IBJAN, IBJGP, + 2 IPIAN, IPJAN, IPJGP, IPIGP, IPR, IPC, IPIC, IPISP, IPRSP, IPA, + 3 LENYH, LENYHM, LENWK, LREQ, LRAT, LREST, LWMIN, MOSS, MSBJ, + 4 NSLJ, NGP, NLU, NNZ, NSP, NZL, NZU + INTEGER I, IBR, IER, IPIL, IPIU, IPTT1, IPTT2, J, K, KNEW, KAMAX, + 1 KAMIN, KCMAX, KCMIN, LDIF, LENIGP, LENWK1, LIWK, LJFO, MAXG, + 2 NP1, NZSUT + DOUBLE PRECISION ERWT, FAC, YJ +C----------------------------------------------------------------------- +C This routine performs preprocessing related to the sparse linear +C systems that must be solved. +C The operations that are performed here are: +C * compute sparseness structure of the iteration matrix +C P = A - con*J according to MOSS, +C * compute grouping of column indices (MITER = 2), +C * compute a new ordering of rows and columns of the matrix, +C * reorder JA corresponding to the new ordering, +C * perform a symbolic LU factorization of the matrix, and +C * set pointers for segments of the IWK/WK array. +C In addition to variables described previously, DPREPI uses the +C following for communication: +C YH = the history array. Only the first column, containing the +C current Y vector, is used. Used only if MOSS .ne. 0. +C S = array of length NEQ, identical to YDOTI in the driver, used +C only if MOSS .ne. 0. +C SAVR = a work array of length NEQ, used only if MOSS .ne. 0. +C EWT = array of length NEQ containing (inverted) error weights. +C Used only if MOSS = 2 or 4 or if ISTATE = MOSS = 1. +C RTEM = a work array of length NEQ, identical to ACOR in the driver, +C used only if MOSS = 2 or 4. +C WK = a real work array of length LENWK, identical to WM in +C the driver. +C IWK = integer work array, assumed to occupy the same space as WK. +C LENWK = the length of the work arrays WK and IWK. +C ISTATC = a copy of the driver input argument ISTATE (= 1 on the +C first call, = 3 on a continuation call). +C IYS = flag value from ODRV or CDRV. +C IPPER = output error flag , with the following values and meanings: +C = 0 no error. +C = -1 insufficient storage for internal structure pointers. +C = -2 insufficient storage for JGROUP. +C = -3 insufficient storage for ODRV. +C = -4 other error flag from ODRV (should never occur). +C = -5 insufficient storage for CDRV. +C = -6 other error flag from CDRV. +C = -7 if the RES routine returned error flag IRES = IER = 2. +C = -8 if the RES routine returned error flag IRES = IER = 3. +C----------------------------------------------------------------------- + IBIAN = LRAT*2 + IPIAN = IBIAN + 1 + NP1 = N + 1 + IPJAN = IPIAN + NP1 + IBJAN = IPJAN - 1 + LENWK1 = LENWK - N + LIWK = LENWK*LRAT + IF (MOSS .EQ. 0) LIWK = LIWK - N + IF (MOSS .EQ. 1 .OR. MOSS .EQ. 2) LIWK = LENWK1*LRAT + IF (IPJAN+N-1 .GT. LIWK) GO TO 310 + IF (MOSS .EQ. 0) GO TO 30 +C + IF (ISTATC .EQ. 3) GO TO 20 +C ISTATE = 1 and MOSS .ne. 0. Perturb Y for structure determination. +C Initialize S with random nonzero elements for structure determination. + DO 10 I=1,N + ERWT = 1.0D0/EWT(I) + FAC = 1.0D0 + 1.0D0/(I + 1.0D0) + Y(I) = Y(I) + FAC*SIGN(ERWT,Y(I)) + S(I) = 1.0D0 + FAC*ERWT + 10 CONTINUE + GO TO (70, 100, 150, 200), MOSS +C + 20 CONTINUE +C ISTATE = 3 and MOSS .ne. 0. Load Y from YH(*,1) and S from YH(*,2). -- + DO 25 I = 1,N + Y(I) = YH(I) + 25 S(I) = YH(N+I) + GO TO (70, 100, 150, 200), MOSS +C +C MOSS = 0. Process user's IA,JA and IC,JC. ---------------------------- + 30 KNEW = IPJAN + KAMIN = IA(1) + KCMIN = IC(1) + IWK(IPIAN) = 1 + DO 60 J = 1,N + DO 35 I = 1,N + 35 IWK(LIWK+I) = 0 + KAMAX = IA(J+1) - 1 + IF (KAMIN .GT. KAMAX) GO TO 45 + DO 40 K = KAMIN,KAMAX + I = JA(K) + IWK(LIWK+I) = 1 + IF (KNEW .GT. LIWK) GO TO 310 + IWK(KNEW) = I + KNEW = KNEW + 1 + 40 CONTINUE + 45 KAMIN = KAMAX + 1 + KCMAX = IC(J+1) - 1 + IF (KCMIN .GT. KCMAX) GO TO 55 + DO 50 K = KCMIN,KCMAX + I = JC(K) + IF (IWK(LIWK+I) .NE. 0) GO TO 50 + IF (KNEW .GT. LIWK) GO TO 310 + IWK(KNEW) = I + KNEW = KNEW + 1 + 50 CONTINUE + 55 IWK(IPIAN+J) = KNEW + 1 - IPJAN + KCMIN = KCMAX + 1 + 60 CONTINUE + GO TO 240 +C +C MOSS = 1. Compute structure from user-supplied Jacobian routine JAC. - + 70 CONTINUE +C A dummy call to RES allows user to create temporaries for use in JAC. + IER = 1 + CALL RES (NEQ, TN, Y, S, SAVR, IER) + IF (IER .GT. 1) GO TO 370 + DO 75 I = 1,N + SAVR(I) = 0.0D0 + 75 WK(LENWK1+I) = 0.0D0 + K = IPJAN + IWK(IPIAN) = 1 + DO 95 J = 1,N + CALL ADDA (NEQ, TN, Y, J, IWK(IPIAN), IWK(IPJAN), WK(LENWK1+1)) + CALL JAC (NEQ, TN, Y, S, J, IWK(IPIAN), IWK(IPJAN), SAVR) + DO 90 I = 1,N + LJFO = LENWK1 + I + IF (WK(LJFO) .EQ. 0.0D0) GO TO 80 + WK(LJFO) = 0.0D0 + SAVR(I) = 0.0D0 + GO TO 85 + 80 IF (SAVR(I) .EQ. 0.0D0) GO TO 90 + SAVR(I) = 0.0D0 + 85 IF (K .GT. LIWK) GO TO 310 + IWK(K) = I + K = K+1 + 90 CONTINUE + IWK(IPIAN+J) = K + 1 - IPJAN + 95 CONTINUE + GO TO 240 +C +C MOSS = 2. Compute structure from results of N + 1 calls to RES. ------ + 100 DO 105 I = 1,N + 105 WK(LENWK1+I) = 0.0D0 + K = IPJAN + IWK(IPIAN) = 1 + IER = -1 + IF (MITER .EQ. 1) IER = 1 + CALL RES (NEQ, TN, Y, S, SAVR, IER) + IF (IER .GT. 1) GO TO 370 + DO 130 J = 1,N + CALL ADDA (NEQ, TN, Y, J, IWK(IPIAN), IWK(IPJAN), WK(LENWK1+1)) + YJ = Y(J) + ERWT = 1.0D0/EWT(J) + Y(J) = YJ + SIGN(ERWT,YJ) + CALL RES (NEQ, TN, Y, S, RTEM, IER) + IF (IER .GT. 1) RETURN + Y(J) = YJ + DO 120 I = 1,N + LJFO = LENWK1 + I + IF (WK(LJFO) .EQ. 0.0D0) GO TO 110 + WK(LJFO) = 0.0D0 + GO TO 115 + 110 IF (RTEM(I) .EQ. SAVR(I)) GO TO 120 + 115 IF (K .GT. LIWK) GO TO 310 + IWK(K) = I + K = K + 1 + 120 CONTINUE + IWK(IPIAN+J) = K + 1 - IPJAN + 130 CONTINUE + GO TO 240 +C +C MOSS = 3. Compute structure from the user's IA/JA and JAC routine. --- + 150 CONTINUE +C A dummy call to RES allows user to create temporaries for use in JAC. + IER = 1 + CALL RES (NEQ, TN, Y, S, SAVR, IER) + IF (IER .GT. 1) GO TO 370 + DO 155 I = 1,N + 155 SAVR(I) = 0.0D0 + KNEW = IPJAN + KAMIN = IA(1) + IWK(IPIAN) = 1 + DO 190 J = 1,N + CALL JAC (NEQ, TN, Y, S, J, IWK(IPIAN), IWK(IPJAN), SAVR) + KAMAX = IA(J+1) - 1 + IF (KAMIN .GT. KAMAX) GO TO 170 + DO 160 K = KAMIN,KAMAX + I = JA(K) + SAVR(I) = 0.0D0 + IF (KNEW .GT. LIWK) GO TO 310 + IWK(KNEW) = I + KNEW = KNEW + 1 + 160 CONTINUE + 170 KAMIN = KAMAX + 1 + DO 180 I = 1,N + IF (SAVR(I) .EQ. 0.0D0) GO TO 180 + SAVR(I) = 0.0D0 + IF (KNEW .GT. LIWK) GO TO 310 + IWK(KNEW) = I + KNEW = KNEW + 1 + 180 CONTINUE + IWK(IPIAN+J) = KNEW + 1 - IPJAN + 190 CONTINUE + GO TO 240 +C +C MOSS = 4. Compute structure from user's IA/JA and N + 1 RES calls. --- + 200 KNEW = IPJAN + KAMIN = IA(1) + IWK(IPIAN) = 1 + IER = -1 + IF (MITER .EQ. 1) IER = 1 + CALL RES (NEQ, TN, Y, S, SAVR, IER) + IF (IER .GT. 1) GO TO 370 + DO 235 J = 1,N + YJ = Y(J) + ERWT = 1.0D0/EWT(J) + Y(J) = YJ + SIGN(ERWT,YJ) + CALL RES (NEQ, TN, Y, S, RTEM, IER) + IF (IER .GT. 1) RETURN + Y(J) = YJ + KAMAX = IA(J+1) - 1 + IF (KAMIN .GT. KAMAX) GO TO 225 + DO 220 K = KAMIN,KAMAX + I = JA(K) + RTEM(I) = SAVR(I) + IF (KNEW .GT. LIWK) GO TO 310 + IWK(KNEW) = I + KNEW = KNEW + 1 + 220 CONTINUE + 225 KAMIN = KAMAX + 1 + DO 230 I = 1,N + IF (RTEM(I) .EQ. SAVR(I)) GO TO 230 + IF (KNEW .GT. LIWK) GO TO 310 + IWK(KNEW) = I + KNEW = KNEW + 1 + 230 CONTINUE + IWK(IPIAN+J) = KNEW + 1 - IPJAN + 235 CONTINUE +C + 240 CONTINUE + IF (MOSS .EQ. 0 .OR. ISTATC .EQ. 3) GO TO 250 +C If ISTATE = 0 or 1 and MOSS .ne. 0, restore Y from YH. --------------- + DO 245 I = 1,N + 245 Y(I) = YH(I) + 250 NNZ = IWK(IPIAN+N) - 1 + IPPER = 0 + NGP = 0 + LENIGP = 0 + IPIGP = IPJAN + NNZ + IF (MITER .NE. 2) GO TO 260 +C +C Compute grouping of column indices (MITER = 2). ---------------------- +C + MAXG = NP1 + IPJGP = IPJAN + NNZ + IBJGP = IPJGP - 1 + IPIGP = IPJGP + N + IPTT1 = IPIGP + NP1 + IPTT2 = IPTT1 + N + LREQ = IPTT2 + N - 1 + IF (LREQ .GT. LIWK) GO TO 320 + CALL JGROUP (N, IWK(IPIAN), IWK(IPJAN), MAXG, NGP, IWK(IPIGP), + 1 IWK(IPJGP), IWK(IPTT1), IWK(IPTT2), IER) + IF (IER .NE. 0) GO TO 320 + LENIGP = NGP + 1 +C +C Compute new ordering of rows/columns of Jacobian. -------------------- + 260 IPR = IPIGP + LENIGP + IPC = IPR + IPIC = IPC + N + IPISP = IPIC + N + IPRSP = (IPISP-2)/LRAT + 2 + IESP = LENWK + 1 - IPRSP + IF (IESP .LT. 0) GO TO 330 + IBR = IPR - 1 + DO 270 I = 1,N + 270 IWK(IBR+I) = I + NSP = LIWK + 1 - IPISP + CALL ODRV(N, IWK(IPIAN), IWK(IPJAN), WK, IWK(IPR), IWK(IPIC), NSP, + 1 IWK(IPISP), 1, IYS) + IF (IYS .EQ. 11*N+1) GO TO 340 + IF (IYS .NE. 0) GO TO 330 +C +C Reorder JAN and do symbolic LU factorization of matrix. -------------- + IPA = LENWK + 1 - NNZ + NSP = IPA - IPRSP + LREQ = MAX(12*N/LRAT, 6*N/LRAT+2*N+NNZ) + 3 + LREQ = LREQ + IPRSP - 1 + NNZ + IF (LREQ .GT. LENWK) GO TO 350 + IBA = IPA - 1 + DO 280 I = 1,NNZ + 280 WK(IBA+I) = 0.0D0 + IPISP = LRAT*(IPRSP - 1) + 1 + CALL CDRV(N,IWK(IPR),IWK(IPC),IWK(IPIC),IWK(IPIAN),IWK(IPJAN), + 1 WK(IPA),WK(IPA),WK(IPA),NSP,IWK(IPISP),WK(IPRSP),IESP,5,IYS) + LREQ = LENWK - IESP + IF (IYS .EQ. 10*N+1) GO TO 350 + IF (IYS .NE. 0) GO TO 360 + IPIL = IPISP + IPIU = IPIL + 2*N + 1 + NZU = IWK(IPIL+N) - IWK(IPIL) + NZL = IWK(IPIU+N) - IWK(IPIU) + IF (LRAT .GT. 1) GO TO 290 + CALL ADJLR (N, IWK(IPISP), LDIF) + LREQ = LREQ + LDIF + 290 CONTINUE + IF (LRAT .EQ. 2 .AND. NNZ .EQ. N) LREQ = LREQ + 1 + NSP = NSP + LREQ - LENWK + IPA = LREQ + 1 - NNZ + IBA = IPA - 1 + IPPER = 0 + RETURN +C + 310 IPPER = -1 + LREQ = 2 + (2*N + 1)/LRAT + LREQ = MAX(LENWK+1,LREQ) + RETURN +C + 320 IPPER = -2 + LREQ = (LREQ - 1)/LRAT + 1 + RETURN +C + 330 IPPER = -3 + CALL CNTNZU (N, IWK(IPIAN), IWK(IPJAN), NZSUT) + LREQ = LENWK - IESP + (3*N + 4*NZSUT - 1)/LRAT + 1 + RETURN +C + 340 IPPER = -4 + RETURN +C + 350 IPPER = -5 + RETURN +C + 360 IPPER = -6 + LREQ = LENWK + RETURN +C + 370 IPPER = -IER - 5 + LREQ = 2 + (2*N + 1)/LRAT + RETURN +C----------------------- End of Subroutine DPREPI ---------------------- + END +*DECK DAINVGS + SUBROUTINE DAINVGS (NEQ, T, Y, WK, IWK, TEM, YDOT, IER, RES, ADDA) + EXTERNAL RES, ADDA + INTEGER NEQ, IWK, IER + INTEGER IPLOST, IESP, ISTATC, IYS, IBA, IBIAN, IBJAN, IBJGP, + 1 IPIAN, IPJAN, IPJGP, IPIGP, IPR, IPC, IPIC, IPISP, IPRSP, IPA, + 2 LENYH, LENYHM, LENWK, LREQ, LRAT, LREST, LWMIN, MOSS, MSBJ, + 3 NSLJ, NGP, NLU, NNZ, NSP, NZL, NZU + INTEGER I, IMUL, J, K, KMIN, KMAX + DOUBLE PRECISION T, Y, WK, TEM, YDOT + DOUBLE PRECISION RLSS + DIMENSION Y(*), WK(*), IWK(*), TEM(*), YDOT(*) + COMMON /DLSS01/ RLSS(6), + 1 IPLOST, IESP, ISTATC, IYS, IBA, IBIAN, IBJAN, IBJGP, + 2 IPIAN, IPJAN, IPJGP, IPIGP, IPR, IPC, IPIC, IPISP, IPRSP, IPA, + 3 LENYH, LENYHM, LENWK, LREQ, LRAT, LREST, LWMIN, MOSS, MSBJ, + 4 NSLJ, NGP, NLU, NNZ, NSP, NZL, NZU +C----------------------------------------------------------------------- +C This subroutine computes the initial value of the vector YDOT +C satisfying +C A * YDOT = g(t,y) +C when A is nonsingular. It is called by DLSODIS for initialization +C only, when ISTATE = 0. The matrix A is subjected to LU +C decomposition in CDRV. Then the system A*YDOT = g(t,y) is solved +C in CDRV. +C In addition to variables described previously, communication +C with DAINVGS uses the following: +C Y = array of initial values. +C WK = real work space for matrices. On output it contains A and +C its LU decomposition. The LU decomposition is not entirely +C sparse unless the structure of the matrix A is identical to +C the structure of the Jacobian matrix dr/dy. +C Storage of matrix elements starts at WK(3). +C WK(1) = SQRT(UROUND), not used here. +C IWK = integer work space for matrix-related data, assumed to +C be equivalenced to WK. In addition, WK(IPRSP) and WK(IPISP) +C are assumed to have identical locations. +C TEM = vector of work space of length N (ACOR in DSTODI). +C YDOT = output vector containing the initial dy/dt. YDOT(i) contains +C dy(i)/dt when the matrix A is non-singular. +C IER = output error flag with the following values and meanings: +C = 0 if DAINVGS was successful. +C = 1 if the A-matrix was found to be singular. +C = 2 if RES returned an error flag IRES = IER = 2. +C = 3 if RES returned an error flag IRES = IER = 3. +C = 4 if insufficient storage for CDRV (should not occur here). +C = 5 if other error found in CDRV (should not occur here). +C----------------------------------------------------------------------- +C + DO 10 I = 1,NNZ + 10 WK(IBA+I) = 0.0D0 +C + IER = 1 + CALL RES (NEQ, T, Y, WK(IPA), YDOT, IER) + IF (IER .GT. 1) RETURN +C + KMIN = IWK(IPIAN) + DO 30 J = 1,NEQ + KMAX = IWK(IPIAN+J) - 1 + DO 15 K = KMIN,KMAX + I = IWK(IBJAN+K) + 15 TEM(I) = 0.0D0 + CALL ADDA (NEQ, T, Y, J, IWK(IPIAN), IWK(IPJAN), TEM) + DO 20 K = KMIN,KMAX + I = IWK(IBJAN+K) + 20 WK(IBA+K) = TEM(I) + KMIN = KMAX + 1 + 30 CONTINUE + NLU = NLU + 1 + IER = 0 + DO 40 I = 1,NEQ + 40 TEM(I) = 0.0D0 +C +C Numerical factorization of matrix A. --------------------------------- + CALL CDRV (NEQ,IWK(IPR),IWK(IPC),IWK(IPIC),IWK(IPIAN),IWK(IPJAN), + 1 WK(IPA),TEM,TEM,NSP,IWK(IPISP),WK(IPRSP),IESP,2,IYS) + IF (IYS .EQ. 0) GO TO 50 + IMUL = (IYS - 1)/NEQ + IER = 5 + IF (IMUL .EQ. 8) IER = 1 + IF (IMUL .EQ. 10) IER = 4 + RETURN +C +C Solution of the linear system. --------------------------------------- + 50 CALL CDRV (NEQ,IWK(IPR),IWK(IPC),IWK(IPIC),IWK(IPIAN),IWK(IPJAN), + 1 WK(IPA),YDOT,YDOT,NSP,IWK(IPISP),WK(IPRSP),IESP,4,IYS) + IF (IYS .NE. 0) IER = 5 + RETURN +C----------------------- End of Subroutine DAINVGS --------------------- + END +*DECK DPRJIS + SUBROUTINE DPRJIS (NEQ, Y, YH, NYH, EWT, RTEM, SAVR, S, WK, IWK, + 1 RES, JAC, ADDA) + EXTERNAL RES, JAC, ADDA + INTEGER NEQ, NYH, IWK + DOUBLE PRECISION Y, YH, EWT, RTEM, SAVR, S, WK + DIMENSION NEQ(*), Y(*), YH(NYH,*), EWT(*), RTEM(*), + 1 S(*), SAVR(*), WK(*), IWK(*) + INTEGER IOWND, IOWNS, + 1 ICF, IERPJ, IERSL, JCUR, JSTART, KFLAG, L, + 2 LYH, LEWT, LACOR, LSAVF, LWM, LIWM, METH, MITER, + 3 MAXORD, MAXCOR, MSBP, MXNCF, N, NQ, NST, NFE, NJE, NQU + INTEGER IPLOST, IESP, ISTATC, IYS, IBA, IBIAN, IBJAN, IBJGP, + 1 IPIAN, IPJAN, IPJGP, IPIGP, IPR, IPC, IPIC, IPISP, IPRSP, IPA, + 2 LENYH, LENYHM, LENWK, LREQ, LRAT, LREST, LWMIN, MOSS, MSBJ, + 3 NSLJ, NGP, NLU, NNZ, NSP, NZL, NZU + DOUBLE PRECISION ROWNS, + 1 CCMAX, EL0, H, HMIN, HMXI, HU, RC, TN, UROUND + DOUBLE PRECISION RLSS + COMMON /DLS001/ ROWNS(209), + 1 CCMAX, EL0, H, HMIN, HMXI, HU, RC, TN, UROUND, + 2 IOWND(6), IOWNS(6), + 3 ICF, IERPJ, IERSL, JCUR, JSTART, KFLAG, L, + 4 LYH, LEWT, LACOR, LSAVF, LWM, LIWM, METH, MITER, + 5 MAXORD, MAXCOR, MSBP, MXNCF, N, NQ, NST, NFE, NJE, NQU + COMMON /DLSS01/ RLSS(6), + 1 IPLOST, IESP, ISTATC, IYS, IBA, IBIAN, IBJAN, IBJGP, + 2 IPIAN, IPJAN, IPJGP, IPIGP, IPR, IPC, IPIC, IPISP, IPRSP, IPA, + 3 LENYH, LENYHM, LENWK, LREQ, LRAT, LREST, LWMIN, MOSS, MSBJ, + 4 NSLJ, NGP, NLU, NNZ, NSP, NZL, NZU + INTEGER I, IMUL, IRES, J, JJ, JMAX, JMIN, K, KMAX, KMIN, NG + DOUBLE PRECISION CON, FAC, HL0, R, SRUR +C----------------------------------------------------------------------- +C DPRJIS is called to compute and process the matrix +C P = A - H*EL(1)*J, where J is an approximation to the Jacobian dr/dy, +C where r = g(t,y) - A(t,y)*s. J is computed by columns, either by +C the user-supplied routine JAC if MITER = 1, or by finite differencing +C if MITER = 2. J is stored in WK, rescaled, and ADDA is called to +C generate P. The matrix P is subjected to LU decomposition in CDRV. +C P and its LU decomposition are stored separately in WK. +C +C In addition to variables described previously, communication +C with DPRJIS uses the following: +C Y = array containing predicted values on entry. +C RTEM = work array of length N (ACOR in DSTODI). +C SAVR = array containing r evaluated at predicted y. On output it +C contains the residual evaluated at current values of t and y. +C S = array containing predicted values of dy/dt (SAVF in DSTODI). +C WK = real work space for matrices. On output it contains P and +C its sparse LU decomposition. Storage of matrix elements +C starts at WK(3). +C WK also contains the following matrix-related data. +C WK(1) = SQRT(UROUND), used in numerical Jacobian increments. +C IWK = integer work space for matrix-related data, assumed to be +C equivalenced to WK. In addition, WK(IPRSP) and IWK(IPISP) +C are assumed to have identical locations. +C EL0 = EL(1) (input). +C IERPJ = output error flag (in COMMON). +C = 0 if no error. +C = 1 if zero pivot found in CDRV. +C = IRES (= 2 or 3) if RES returned IRES = 2 or 3. +C = -1 if insufficient storage for CDRV (should not occur). +C = -2 if other error found in CDRV (should not occur here). +C JCUR = output flag = 1 to indicate that the Jacobian matrix +C (or approximation) is now current. +C This routine also uses other variables in Common. +C----------------------------------------------------------------------- + HL0 = H*EL0 + CON = -HL0 + JCUR = 1 + NJE = NJE + 1 + GO TO (100, 200), MITER +C +C If MITER = 1, call RES, then call JAC and ADDA for each column. ------ + 100 IRES = 1 + CALL RES (NEQ, TN, Y, S, SAVR, IRES) + NFE = NFE + 1 + IF (IRES .GT. 1) GO TO 600 + KMIN = IWK(IPIAN) + DO 130 J = 1,N + KMAX = IWK(IPIAN+J)-1 + DO 110 I = 1,N + 110 RTEM(I) = 0.0D0 + CALL JAC (NEQ, TN, Y, S, J, IWK(IPIAN), IWK(IPJAN), RTEM) + DO 120 I = 1,N + 120 RTEM(I) = RTEM(I)*CON + CALL ADDA (NEQ, TN, Y, J, IWK(IPIAN), IWK(IPJAN), RTEM) + DO 125 K = KMIN,KMAX + I = IWK(IBJAN+K) + WK(IBA+K) = RTEM(I) + 125 CONTINUE + KMIN = KMAX + 1 + 130 CONTINUE + GO TO 290 +C +C If MITER = 2, make NGP + 1 calls to RES to approximate J and P. ------ + 200 CONTINUE + IRES = -1 + CALL RES (NEQ, TN, Y, S, SAVR, IRES) + NFE = NFE + 1 + IF (IRES .GT. 1) GO TO 600 + SRUR = WK(1) + JMIN = IWK(IPIGP) + DO 240 NG = 1,NGP + JMAX = IWK(IPIGP+NG) - 1 + DO 210 J = JMIN,JMAX + JJ = IWK(IBJGP+J) + R = MAX(SRUR*ABS(Y(JJ)),0.01D0/EWT(JJ)) + 210 Y(JJ) = Y(JJ) + R + CALL RES (NEQ,TN,Y,S,RTEM,IRES) + NFE = NFE + 1 + IF (IRES .GT. 1) GO TO 600 + DO 230 J = JMIN,JMAX + JJ = IWK(IBJGP+J) + Y(JJ) = YH(JJ,1) + R = MAX(SRUR*ABS(Y(JJ)),0.01D0/EWT(JJ)) + FAC = -HL0/R + KMIN = IWK(IBIAN+JJ) + KMAX = IWK(IBIAN+JJ+1) - 1 + DO 220 K = KMIN,KMAX + I = IWK(IBJAN+K) + RTEM(I) = (RTEM(I) - SAVR(I))*FAC + 220 CONTINUE + CALL ADDA (NEQ, TN, Y, JJ, IWK(IPIAN), IWK(IPJAN), RTEM) + DO 225 K = KMIN,KMAX + I = IWK(IBJAN+K) + WK(IBA+K) = RTEM(I) + 225 CONTINUE + 230 CONTINUE + JMIN = JMAX + 1 + 240 CONTINUE + IRES = 1 + CALL RES (NEQ, TN, Y, S, SAVR, IRES) + NFE = NFE + 1 + IF (IRES .GT. 1) GO TO 600 +C +C Do numerical factorization of P matrix. ------------------------------ + 290 NLU = NLU + 1 + IERPJ = 0 + DO 295 I = 1,N + 295 RTEM(I) = 0.0D0 + CALL CDRV (N,IWK(IPR),IWK(IPC),IWK(IPIC),IWK(IPIAN),IWK(IPJAN), + 1 WK(IPA),RTEM,RTEM,NSP,IWK(IPISP),WK(IPRSP),IESP,2,IYS) + IF (IYS .EQ. 0) RETURN + IMUL = (IYS - 1)/N + IERPJ = -2 + IF (IMUL .EQ. 8) IERPJ = 1 + IF (IMUL .EQ. 10) IERPJ = -1 + RETURN +C Error return for IRES = 2 or IRES = 3 return from RES. --------------- + 600 IERPJ = IRES + RETURN +C----------------------- End of Subroutine DPRJIS ---------------------- + END + diff --git a/applications/PUfoam/MoDeNaModels/bubbleGrowth/src/src/opkda2.f b/applications/PUfoam/MoDeNaModels/bubbleGrowth/src/src/opkda2.f new file mode 100644 index 000000000..c4b4ff0d0 --- /dev/null +++ b/applications/PUfoam/MoDeNaModels/bubbleGrowth/src/src/opkda2.f @@ -0,0 +1,1441 @@ +*DECK DGEFA + SUBROUTINE DGEFA (A, LDA, N, IPVT, INFO) +C***BEGIN PROLOGUE DGEFA +C***PURPOSE Factor a matrix using Gaussian elimination. +C***CATEGORY D2A1 +C***TYPE DOUBLE PRECISION (SGEFA-S, DGEFA-D, CGEFA-C) +C***KEYWORDS GENERAL MATRIX, LINEAR ALGEBRA, LINPACK, +C MATRIX FACTORIZATION +C***AUTHOR Moler, C. B., (U. of New Mexico) +C***DESCRIPTION +C +C DGEFA factors a double precision matrix by Gaussian elimination. +C +C DGEFA is usually called by DGECO, but it can be called +C directly with a saving in time if RCOND is not needed. +C (Time for DGECO) = (1 + 9/N)*(Time for DGEFA) . +C +C On Entry +C +C A DOUBLE PRECISION(LDA, N) +C the matrix to be factored. +C +C LDA INTEGER +C the leading dimension of the array A . +C +C N INTEGER +C the order of the matrix A . +C +C On Return +C +C A an upper triangular matrix and the multipliers +C which were used to obtain it. +C The factorization can be written A = L*U where +C L is a product of permutation and unit lower +C triangular matrices and U is upper triangular. +C +C IPVT INTEGER(N) +C an integer vector of pivot indices. +C +C INFO INTEGER +C = 0 normal value. +C = K if U(K,K) .EQ. 0.0 . This is not an error +C condition for this subroutine, but it does +C indicate that DGESL or DGEDI will divide by zero +C if called. Use RCOND in DGECO for a reliable +C indication of singularity. +C +C***REFERENCES J. J. Dongarra, J. R. Bunch, C. B. Moler, and G. W. +C Stewart, LINPACK Users' Guide, SIAM, 1979. +C***ROUTINES CALLED DAXPY, DSCAL, IDAMAX +C***REVISION HISTORY (YYMMDD) +C 780814 DATE WRITTEN +C 890831 Modified array declarations. (WRB) +C 890831 REVISION DATE from Version 3.2 +C 891214 Prologue converted to Version 4.0 format. (BAB) +C 900326 Removed duplicate information from DESCRIPTION section. +C (WRB) +C 920501 Reformatted the REFERENCES section. (WRB) +C***END PROLOGUE DGEFA + INTEGER LDA,N,IPVT(*),INFO + DOUBLE PRECISION A(LDA,*) +C + DOUBLE PRECISION T + INTEGER IDAMAX,J,K,KP1,L,NM1 +C +C GAUSSIAN ELIMINATION WITH PARTIAL PIVOTING +C +C***FIRST EXECUTABLE STATEMENT DGEFA + INFO = 0 + NM1 = N - 1 + IF (NM1 .LT. 1) GO TO 70 + DO 60 K = 1, NM1 + KP1 = K + 1 +C +C FIND L = PIVOT INDEX +C + L = IDAMAX(N-K+1,A(K,K),1) + K - 1 + IPVT(K) = L +C +C ZERO PIVOT IMPLIES THIS COLUMN ALREADY TRIANGULARIZED +C + IF (A(L,K) .EQ. 0.0D0) GO TO 40 +C +C INTERCHANGE IF NECESSARY +C + IF (L .EQ. K) GO TO 10 + T = A(L,K) + A(L,K) = A(K,K) + A(K,K) = T + 10 CONTINUE +C +C COMPUTE MULTIPLIERS +C + T = -1.0D0/A(K,K) + CALL DSCAL(N-K,T,A(K+1,K),1) +C +C ROW ELIMINATION WITH COLUMN INDEXING +C + DO 30 J = KP1, N + T = A(L,J) + IF (L .EQ. K) GO TO 20 + A(L,J) = A(K,J) + A(K,J) = T + 20 CONTINUE + CALL DAXPY(N-K,T,A(K+1,K),1,A(K+1,J),1) + 30 CONTINUE + GO TO 50 + 40 CONTINUE + INFO = K + 50 CONTINUE + 60 CONTINUE + 70 CONTINUE + IPVT(N) = N + IF (A(N,N) .EQ. 0.0D0) INFO = N + RETURN + END +*DECK DGESL + SUBROUTINE DGESL (A, LDA, N, IPVT, B, JOB) +C***BEGIN PROLOGUE DGESL +C***PURPOSE Solve the real system A*X=B or TRANS(A)*X=B using the +C factors computed by DGECO or DGEFA. +C***CATEGORY D2A1 +C***TYPE DOUBLE PRECISION (SGESL-S, DGESL-D, CGESL-C) +C***KEYWORDS LINEAR ALGEBRA, LINPACK, MATRIX, SOLVE +C***AUTHOR Moler, C. B., (U. of New Mexico) +C***DESCRIPTION +C +C DGESL solves the double precision system +C A * X = B or TRANS(A) * X = B +C using the factors computed by DGECO or DGEFA. +C +C On Entry +C +C A DOUBLE PRECISION(LDA, N) +C the output from DGECO or DGEFA. +C +C LDA INTEGER +C the leading dimension of the array A . +C +C N INTEGER +C the order of the matrix A . +C +C IPVT INTEGER(N) +C the pivot vector from DGECO or DGEFA. +C +C B DOUBLE PRECISION(N) +C the right hand side vector. +C +C JOB INTEGER +C = 0 to solve A*X = B , +C = nonzero to solve TRANS(A)*X = B where +C TRANS(A) is the transpose. +C +C On Return +C +C B the solution vector X . +C +C Error Condition +C +C A division by zero will occur if the input factor contains a +C zero on the diagonal. Technically this indicates singularity +C but it is often caused by improper arguments or improper +C setting of LDA . It will not occur if the subroutines are +C called correctly and if DGECO has set RCOND .GT. 0.0 +C or DGEFA has set INFO .EQ. 0 . +C +C To compute INVERSE(A) * C where C is a matrix +C with P columns +C CALL DGECO(A,LDA,N,IPVT,RCOND,Z) +C IF (RCOND is too small) GO TO ... +C DO 10 J = 1, P +C CALL DGESL(A,LDA,N,IPVT,C(1,J),0) +C 10 CONTINUE +C +C***REFERENCES J. J. Dongarra, J. R. Bunch, C. B. Moler, and G. W. +C Stewart, LINPACK Users' Guide, SIAM, 1979. +C***ROUTINES CALLED DAXPY, DDOT +C***REVISION HISTORY (YYMMDD) +C 780814 DATE WRITTEN +C 890831 Modified array declarations. (WRB) +C 890831 REVISION DATE from Version 3.2 +C 891214 Prologue converted to Version 4.0 format. (BAB) +C 900326 Removed duplicate information from DESCRIPTION section. +C (WRB) +C 920501 Reformatted the REFERENCES section. (WRB) +C***END PROLOGUE DGESL + INTEGER LDA,N,IPVT(*),JOB + DOUBLE PRECISION A(LDA,*),B(*) +C + DOUBLE PRECISION DDOT,T + INTEGER K,KB,L,NM1 +C***FIRST EXECUTABLE STATEMENT DGESL + NM1 = N - 1 + IF (JOB .NE. 0) GO TO 50 +C +C JOB = 0 , SOLVE A * X = B +C FIRST SOLVE L*Y = B +C + IF (NM1 .LT. 1) GO TO 30 + DO 20 K = 1, NM1 + L = IPVT(K) + T = B(L) + IF (L .EQ. K) GO TO 10 + B(L) = B(K) + B(K) = T + 10 CONTINUE + CALL DAXPY(N-K,T,A(K+1,K),1,B(K+1),1) + 20 CONTINUE + 30 CONTINUE +C +C NOW SOLVE U*X = Y +C + DO 40 KB = 1, N + K = N + 1 - KB + B(K) = B(K)/A(K,K) + T = -B(K) + CALL DAXPY(K-1,T,A(1,K),1,B(1),1) + 40 CONTINUE + GO TO 100 + 50 CONTINUE +C +C JOB = NONZERO, SOLVE TRANS(A) * X = B +C FIRST SOLVE TRANS(U)*Y = B +C + DO 60 K = 1, N + T = DDOT(K-1,A(1,K),1,B(1),1) + B(K) = (B(K) - T)/A(K,K) + 60 CONTINUE +C +C NOW SOLVE TRANS(L)*X = Y +C + IF (NM1 .LT. 1) GO TO 90 + DO 80 KB = 1, NM1 + K = N - KB + B(K) = B(K) + DDOT(N-K,A(K+1,K),1,B(K+1),1) + L = IPVT(K) + IF (L .EQ. K) GO TO 70 + T = B(L) + B(L) = B(K) + B(K) = T + 70 CONTINUE + 80 CONTINUE + 90 CONTINUE + 100 CONTINUE + RETURN + END +*DECK DGBFA + SUBROUTINE DGBFA (ABD, LDA, N, ML, MU, IPVT, INFO) +C***BEGIN PROLOGUE DGBFA +C***PURPOSE Factor a band matrix using Gaussian elimination. +C***CATEGORY D2A2 +C***TYPE DOUBLE PRECISION (SGBFA-S, DGBFA-D, CGBFA-C) +C***KEYWORDS BANDED, LINEAR ALGEBRA, LINPACK, MATRIX FACTORIZATION +C***AUTHOR Moler, C. B., (U. of New Mexico) +C***DESCRIPTION +C +C DGBFA factors a double precision band matrix by elimination. +C +C DGBFA is usually called by DGBCO, but it can be called +C directly with a saving in time if RCOND is not needed. +C +C On Entry +C +C ABD DOUBLE PRECISION(LDA, N) +C contains the matrix in band storage. The columns +C of the matrix are stored in the columns of ABD and +C the diagonals of the matrix are stored in rows +C ML+1 through 2*ML+MU+1 of ABD . +C See the comments below for details. +C +C LDA INTEGER +C the leading dimension of the array ABD . +C LDA must be .GE. 2*ML + MU + 1 . +C +C N INTEGER +C the order of the original matrix. +C +C ML INTEGER +C number of diagonals below the main diagonal. +C 0 .LE. ML .LT. N . +C +C MU INTEGER +C number of diagonals above the main diagonal. +C 0 .LE. MU .LT. N . +C More efficient if ML .LE. MU . +C On Return +C +C ABD an upper triangular matrix in band storage and +C the multipliers which were used to obtain it. +C The factorization can be written A = L*U where +C L is a product of permutation and unit lower +C triangular matrices and U is upper triangular. +C +C IPVT INTEGER(N) +C an integer vector of pivot indices. +C +C INFO INTEGER +C = 0 normal value. +C = K if U(K,K) .EQ. 0.0 . This is not an error +C condition for this subroutine, but it does +C indicate that DGBSL will divide by zero if +C called. Use RCOND in DGBCO for a reliable +C indication of singularity. +C +C Band Storage +C +C If A is a band matrix, the following program segment +C will set up the input. +C +C ML = (band width below the diagonal) +C MU = (band width above the diagonal) +C M = ML + MU + 1 +C DO 20 J = 1, N +C I1 = MAX(1, J-MU) +C I2 = MIN(N, J+ML) +C DO 10 I = I1, I2 +C K = I - J + M +C ABD(K,J) = A(I,J) +C 10 CONTINUE +C 20 CONTINUE +C +C This uses rows ML+1 through 2*ML+MU+1 of ABD . +C In addition, the first ML rows in ABD are used for +C elements generated during the triangularization. +C The total number of rows needed in ABD is 2*ML+MU+1 . +C The ML+MU by ML+MU upper left triangle and the +C ML by ML lower right triangle are not referenced. +C +C***REFERENCES J. J. Dongarra, J. R. Bunch, C. B. Moler, and G. W. +C Stewart, LINPACK Users' Guide, SIAM, 1979. +C***ROUTINES CALLED DAXPY, DSCAL, IDAMAX +C***REVISION HISTORY (YYMMDD) +C 780814 DATE WRITTEN +C 890531 Changed all specific intrinsics to generic. (WRB) +C 890831 Modified array declarations. (WRB) +C 890831 REVISION DATE from Version 3.2 +C 891214 Prologue converted to Version 4.0 format. (BAB) +C 900326 Removed duplicate information from DESCRIPTION section. +C (WRB) +C 920501 Reformatted the REFERENCES section. (WRB) +C***END PROLOGUE DGBFA + INTEGER LDA,N,ML,MU,IPVT(*),INFO + DOUBLE PRECISION ABD(LDA,*) +C + DOUBLE PRECISION T + INTEGER I,IDAMAX,I0,J,JU,JZ,J0,J1,K,KP1,L,LM,M,MM,NM1 +C +C***FIRST EXECUTABLE STATEMENT DGBFA + M = ML + MU + 1 + INFO = 0 +C +C ZERO INITIAL FILL-IN COLUMNS +C + J0 = MU + 2 + J1 = MIN(N,M) - 1 + IF (J1 .LT. J0) GO TO 30 + DO 20 JZ = J0, J1 + I0 = M + 1 - JZ + DO 10 I = I0, ML + ABD(I,JZ) = 0.0D0 + 10 CONTINUE + 20 CONTINUE + 30 CONTINUE + JZ = J1 + JU = 0 +C +C GAUSSIAN ELIMINATION WITH PARTIAL PIVOTING +C + NM1 = N - 1 + IF (NM1 .LT. 1) GO TO 130 + DO 120 K = 1, NM1 + KP1 = K + 1 +C +C ZERO NEXT FILL-IN COLUMN +C + JZ = JZ + 1 + IF (JZ .GT. N) GO TO 50 + IF (ML .LT. 1) GO TO 50 + DO 40 I = 1, ML + ABD(I,JZ) = 0.0D0 + 40 CONTINUE + 50 CONTINUE +C +C FIND L = PIVOT INDEX +C + LM = MIN(ML,N-K) + L = IDAMAX(LM+1,ABD(M,K),1) + M - 1 + IPVT(K) = L + K - M +C +C ZERO PIVOT IMPLIES THIS COLUMN ALREADY TRIANGULARIZED +C + IF (ABD(L,K) .EQ. 0.0D0) GO TO 100 +C +C INTERCHANGE IF NECESSARY +C + IF (L .EQ. M) GO TO 60 + T = ABD(L,K) + ABD(L,K) = ABD(M,K) + ABD(M,K) = T + 60 CONTINUE +C +C COMPUTE MULTIPLIERS +C + T = -1.0D0/ABD(M,K) + CALL DSCAL(LM,T,ABD(M+1,K),1) +C +C ROW ELIMINATION WITH COLUMN INDEXING +C + JU = MIN(MAX(JU,MU+IPVT(K)),N) + MM = M + IF (JU .LT. KP1) GO TO 90 + DO 80 J = KP1, JU + L = L - 1 + MM = MM - 1 + T = ABD(L,J) + IF (L .EQ. MM) GO TO 70 + ABD(L,J) = ABD(MM,J) + ABD(MM,J) = T + 70 CONTINUE + CALL DAXPY(LM,T,ABD(M+1,K),1,ABD(MM+1,J),1) + 80 CONTINUE + 90 CONTINUE + GO TO 110 + 100 CONTINUE + INFO = K + 110 CONTINUE + 120 CONTINUE + 130 CONTINUE + IPVT(N) = N + IF (ABD(M,N) .EQ. 0.0D0) INFO = N + RETURN + END +*DECK DGBSL + SUBROUTINE DGBSL (ABD, LDA, N, ML, MU, IPVT, B, JOB) +C***BEGIN PROLOGUE DGBSL +C***PURPOSE Solve the real band system A*X=B or TRANS(A)*X=B using +C the factors computed by DGBCO or DGBFA. +C***CATEGORY D2A2 +C***TYPE DOUBLE PRECISION (SGBSL-S, DGBSL-D, CGBSL-C) +C***KEYWORDS BANDED, LINEAR ALGEBRA, LINPACK, MATRIX, SOLVE +C***AUTHOR Moler, C. B., (U. of New Mexico) +C***DESCRIPTION +C +C DGBSL solves the double precision band system +C A * X = B or TRANS(A) * X = B +C using the factors computed by DGBCO or DGBFA. +C +C On Entry +C +C ABD DOUBLE PRECISION(LDA, N) +C the output from DGBCO or DGBFA. +C +C LDA INTEGER +C the leading dimension of the array ABD . +C +C N INTEGER +C the order of the original matrix. +C +C ML INTEGER +C number of diagonals below the main diagonal. +C +C MU INTEGER +C number of diagonals above the main diagonal. +C +C IPVT INTEGER(N) +C the pivot vector from DGBCO or DGBFA. +C +C B DOUBLE PRECISION(N) +C the right hand side vector. +C +C JOB INTEGER +C = 0 to solve A*X = B , +C = nonzero to solve TRANS(A)*X = B , where +C TRANS(A) is the transpose. +C +C On Return +C +C B the solution vector X . +C +C Error Condition +C +C A division by zero will occur if the input factor contains a +C zero on the diagonal. Technically this indicates singularity +C but it is often caused by improper arguments or improper +C setting of LDA . It will not occur if the subroutines are +C called correctly and if DGBCO has set RCOND .GT. 0.0 +C or DGBFA has set INFO .EQ. 0 . +C +C To compute INVERSE(A) * C where C is a matrix +C with P columns +C CALL DGBCO(ABD,LDA,N,ML,MU,IPVT,RCOND,Z) +C IF (RCOND is too small) GO TO ... +C DO 10 J = 1, P +C CALL DGBSL(ABD,LDA,N,ML,MU,IPVT,C(1,J),0) +C 10 CONTINUE +C +C***REFERENCES J. J. Dongarra, J. R. Bunch, C. B. Moler, and G. W. +C Stewart, LINPACK Users' Guide, SIAM, 1979. +C***ROUTINES CALLED DAXPY, DDOT +C***REVISION HISTORY (YYMMDD) +C 780814 DATE WRITTEN +C 890531 Changed all specific intrinsics to generic. (WRB) +C 890831 Modified array declarations. (WRB) +C 890831 REVISION DATE from Version 3.2 +C 891214 Prologue converted to Version 4.0 format. (BAB) +C 900326 Removed duplicate information from DESCRIPTION section. +C (WRB) +C 920501 Reformatted the REFERENCES section. (WRB) +C***END PROLOGUE DGBSL + INTEGER LDA,N,ML,MU,IPVT(*),JOB + DOUBLE PRECISION ABD(LDA,*),B(*) +C + DOUBLE PRECISION DDOT,T + INTEGER K,KB,L,LA,LB,LM,M,NM1 +C***FIRST EXECUTABLE STATEMENT DGBSL + M = MU + ML + 1 + NM1 = N - 1 + IF (JOB .NE. 0) GO TO 50 +C +C JOB = 0 , SOLVE A * X = B +C FIRST SOLVE L*Y = B +C + IF (ML .EQ. 0) GO TO 30 + IF (NM1 .LT. 1) GO TO 30 + DO 20 K = 1, NM1 + LM = MIN(ML,N-K) + L = IPVT(K) + T = B(L) + IF (L .EQ. K) GO TO 10 + B(L) = B(K) + B(K) = T + 10 CONTINUE + CALL DAXPY(LM,T,ABD(M+1,K),1,B(K+1),1) + 20 CONTINUE + 30 CONTINUE +C +C NOW SOLVE U*X = Y +C + DO 40 KB = 1, N + K = N + 1 - KB + B(K) = B(K)/ABD(M,K) + LM = MIN(K,M) - 1 + LA = M - LM + LB = K - LM + T = -B(K) + CALL DAXPY(LM,T,ABD(LA,K),1,B(LB),1) + 40 CONTINUE + GO TO 100 + 50 CONTINUE +C +C JOB = NONZERO, SOLVE TRANS(A) * X = B +C FIRST SOLVE TRANS(U)*Y = B +C + DO 60 K = 1, N + LM = MIN(K,M) - 1 + LA = M - LM + LB = K - LM + T = DDOT(LM,ABD(LA,K),1,B(LB),1) + B(K) = (B(K) - T)/ABD(M,K) + 60 CONTINUE +C +C NOW SOLVE TRANS(L)*X = Y +C + IF (ML .EQ. 0) GO TO 90 + IF (NM1 .LT. 1) GO TO 90 + DO 80 KB = 1, NM1 + K = N - KB + LM = MIN(ML,N-K) + B(K) = B(K) + DDOT(LM,ABD(M+1,K),1,B(K+1),1) + L = IPVT(K) + IF (L .EQ. K) GO TO 70 + T = B(L) + B(L) = B(K) + B(K) = T + 70 CONTINUE + 80 CONTINUE + 90 CONTINUE + 100 CONTINUE + RETURN + END +*DECK DAXPY + SUBROUTINE DAXPY (N, DA, DX, INCX, DY, INCY) +C***BEGIN PROLOGUE DAXPY +C***PURPOSE Compute a constant times a vector plus a vector. +C***CATEGORY D1A7 +C***TYPE DOUBLE PRECISION (SAXPY-S, DAXPY-D, CAXPY-C) +C***KEYWORDS BLAS, LINEAR ALGEBRA, TRIAD, VECTOR +C***AUTHOR Lawson, C. L., (JPL) +C Hanson, R. J., (SNLA) +C Kincaid, D. R., (U. of Texas) +C Krogh, F. T., (JPL) +C***DESCRIPTION +C +C B L A S Subprogram +C Description of Parameters +C +C --Input-- +C N number of elements in input vector(s) +C DA double precision scalar multiplier +C DX double precision vector with N elements +C INCX storage spacing between elements of DX +C DY double precision vector with N elements +C INCY storage spacing between elements of DY +C +C --Output-- +C DY double precision result (unchanged if N .LE. 0) +C +C Overwrite double precision DY with double precision DA*DX + DY. +C For I = 0 to N-1, replace DY(LY+I*INCY) with DA*DX(LX+I*INCX) + +C DY(LY+I*INCY), +C where LX = 1 if INCX .GE. 0, else LX = 1+(1-N)*INCX, and LY is +C defined in a similar way using INCY. +C +C***REFERENCES C. L. Lawson, R. J. Hanson, D. R. Kincaid and F. T. +C Krogh, Basic linear algebra subprograms for Fortran +C usage, Algorithm No. 539, Transactions on Mathematical +C Software 5, 3 (September 1979), pp. 308-323. +C***ROUTINES CALLED (NONE) +C***REVISION HISTORY (YYMMDD) +C 791001 DATE WRITTEN +C 890831 Modified array declarations. (WRB) +C 890831 REVISION DATE from Version 3.2 +C 891214 Prologue converted to Version 4.0 format. (BAB) +C 920310 Corrected definition of LX in DESCRIPTION. (WRB) +C 920501 Reformatted the REFERENCES section. (WRB) +C***END PROLOGUE DAXPY + DOUBLE PRECISION DX(*), DY(*), DA +C***FIRST EXECUTABLE STATEMENT DAXPY + IF (N.LE.0 .OR. DA.EQ.0.0D0) RETURN + IF (INCX .EQ. INCY) IF (INCX-1) 5,20,60 +C +C Code for unequal or nonpositive increments. +C + 5 IX = 1 + IY = 1 + IF (INCX .LT. 0) IX = (-N+1)*INCX + 1 + IF (INCY .LT. 0) IY = (-N+1)*INCY + 1 + DO 10 I = 1,N + DY(IY) = DY(IY) + DA*DX(IX) + IX = IX + INCX + IY = IY + INCY + 10 CONTINUE + RETURN +C +C Code for both increments equal to 1. +C +C Clean-up loop so remaining vector length is a multiple of 4. +C + 20 M = MOD(N,4) + IF (M .EQ. 0) GO TO 40 + DO 30 I = 1,M + DY(I) = DY(I) + DA*DX(I) + 30 CONTINUE + IF (N .LT. 4) RETURN + 40 MP1 = M + 1 + DO 50 I = MP1,N,4 + DY(I) = DY(I) + DA*DX(I) + DY(I+1) = DY(I+1) + DA*DX(I+1) + DY(I+2) = DY(I+2) + DA*DX(I+2) + DY(I+3) = DY(I+3) + DA*DX(I+3) + 50 CONTINUE + RETURN +C +C Code for equal, positive, non-unit increments. +C + 60 NS = N*INCX + DO 70 I = 1,NS,INCX + DY(I) = DA*DX(I) + DY(I) + 70 CONTINUE + RETURN + END +*DECK DCOPY + SUBROUTINE DCOPY (N, DX, INCX, DY, INCY) +C***BEGIN PROLOGUE DCOPY +C***PURPOSE Copy a vector. +C***CATEGORY D1A5 +C***TYPE DOUBLE PRECISION (SCOPY-S, DCOPY-D, CCOPY-C, ICOPY-I) +C***KEYWORDS BLAS, COPY, LINEAR ALGEBRA, VECTOR +C***AUTHOR Lawson, C. L., (JPL) +C Hanson, R. J., (SNLA) +C Kincaid, D. R., (U. of Texas) +C Krogh, F. T., (JPL) +C***DESCRIPTION +C +C B L A S Subprogram +C Description of Parameters +C +C --Input-- +C N number of elements in input vector(s) +C DX double precision vector with N elements +C INCX storage spacing between elements of DX +C DY double precision vector with N elements +C INCY storage spacing between elements of DY +C +C --Output-- +C DY copy of vector DX (unchanged if N .LE. 0) +C +C Copy double precision DX to double precision DY. +C For I = 0 to N-1, copy DX(LX+I*INCX) to DY(LY+I*INCY), +C where LX = 1 if INCX .GE. 0, else LX = 1+(1-N)*INCX, and LY is +C defined in a similar way using INCY. +C +C***REFERENCES C. L. Lawson, R. J. Hanson, D. R. Kincaid and F. T. +C Krogh, Basic linear algebra subprograms for Fortran +C usage, Algorithm No. 539, Transactions on Mathematical +C Software 5, 3 (September 1979), pp. 308-323. +C***ROUTINES CALLED (NONE) +C***REVISION HISTORY (YYMMDD) +C 791001 DATE WRITTEN +C 890831 Modified array declarations. (WRB) +C 890831 REVISION DATE from Version 3.2 +C 891214 Prologue converted to Version 4.0 format. (BAB) +C 920310 Corrected definition of LX in DESCRIPTION. (WRB) +C 920501 Reformatted the REFERENCES section. (WRB) +C***END PROLOGUE DCOPY + DOUBLE PRECISION DX(*), DY(*) +C***FIRST EXECUTABLE STATEMENT DCOPY + IF (N .LE. 0) RETURN + IF (INCX .EQ. INCY) IF (INCX-1) 5,20,60 +C +C Code for unequal or nonpositive increments. +C + 5 IX = 1 + IY = 1 + IF (INCX .LT. 0) IX = (-N+1)*INCX + 1 + IF (INCY .LT. 0) IY = (-N+1)*INCY + 1 + DO 10 I = 1,N + DY(IY) = DX(IX) + IX = IX + INCX + IY = IY + INCY + 10 CONTINUE + RETURN +C +C Code for both increments equal to 1. +C +C Clean-up loop so remaining vector length is a multiple of 7. +C + 20 M = MOD(N,7) + IF (M .EQ. 0) GO TO 40 + DO 30 I = 1,M + DY(I) = DX(I) + 30 CONTINUE + IF (N .LT. 7) RETURN + 40 MP1 = M + 1 + DO 50 I = MP1,N,7 + DY(I) = DX(I) + DY(I+1) = DX(I+1) + DY(I+2) = DX(I+2) + DY(I+3) = DX(I+3) + DY(I+4) = DX(I+4) + DY(I+5) = DX(I+5) + DY(I+6) = DX(I+6) + 50 CONTINUE + RETURN +C +C Code for equal, positive, non-unit increments. +C + 60 NS = N*INCX + DO 70 I = 1,NS,INCX + DY(I) = DX(I) + 70 CONTINUE + RETURN + END +*DECK DDOT + DOUBLE PRECISION FUNCTION DDOT (N, DX, INCX, DY, INCY) +C***BEGIN PROLOGUE DDOT +C***PURPOSE Compute the inner product of two vectors. +C***CATEGORY D1A4 +C***TYPE DOUBLE PRECISION (SDOT-S, DDOT-D, CDOTU-C) +C***KEYWORDS BLAS, INNER PRODUCT, LINEAR ALGEBRA, VECTOR +C***AUTHOR Lawson, C. L., (JPL) +C Hanson, R. J., (SNLA) +C Kincaid, D. R., (U. of Texas) +C Krogh, F. T., (JPL) +C***DESCRIPTION +C +C B L A S Subprogram +C Description of Parameters +C +C --Input-- +C N number of elements in input vector(s) +C DX double precision vector with N elements +C INCX storage spacing between elements of DX +C DY double precision vector with N elements +C INCY storage spacing between elements of DY +C +C --Output-- +C DDOT double precision dot product (zero if N .LE. 0) +C +C Returns the dot product of double precision DX and DY. +C DDOT = sum for I = 0 to N-1 of DX(LX+I*INCX) * DY(LY+I*INCY), +C where LX = 1 if INCX .GE. 0, else LX = 1+(1-N)*INCX, and LY is +C defined in a similar way using INCY. +C +C***REFERENCES C. L. Lawson, R. J. Hanson, D. R. Kincaid and F. T. +C Krogh, Basic linear algebra subprograms for Fortran +C usage, Algorithm No. 539, Transactions on Mathematical +C Software 5, 3 (September 1979), pp. 308-323. +C***ROUTINES CALLED (NONE) +C***REVISION HISTORY (YYMMDD) +C 791001 DATE WRITTEN +C 890831 Modified array declarations. (WRB) +C 890831 REVISION DATE from Version 3.2 +C 891214 Prologue converted to Version 4.0 format. (BAB) +C 920310 Corrected definition of LX in DESCRIPTION. (WRB) +C 920501 Reformatted the REFERENCES section. (WRB) +C***END PROLOGUE DDOT + DOUBLE PRECISION DX(*), DY(*) +C***FIRST EXECUTABLE STATEMENT DDOT + DDOT = 0.0D0 + IF (N .LE. 0) RETURN + IF (INCX .EQ. INCY) IF (INCX-1) 5,20,60 +C +C Code for unequal or nonpositive increments. +C + 5 IX = 1 + IY = 1 + IF (INCX .LT. 0) IX = (-N+1)*INCX + 1 + IF (INCY .LT. 0) IY = (-N+1)*INCY + 1 + DO 10 I = 1,N + DDOT = DDOT + DX(IX)*DY(IY) + IX = IX + INCX + IY = IY + INCY + 10 CONTINUE + RETURN +C +C Code for both increments equal to 1. +C +C Clean-up loop so remaining vector length is a multiple of 5. +C + 20 M = MOD(N,5) + IF (M .EQ. 0) GO TO 40 + DO 30 I = 1,M + DDOT = DDOT + DX(I)*DY(I) + 30 CONTINUE + IF (N .LT. 5) RETURN + 40 MP1 = M + 1 + DO 50 I = MP1,N,5 + DDOT = DDOT + DX(I)*DY(I) + DX(I+1)*DY(I+1) + DX(I+2)*DY(I+2) + + 1 DX(I+3)*DY(I+3) + DX(I+4)*DY(I+4) + 50 CONTINUE + RETURN +C +C Code for equal, positive, non-unit increments. +C + 60 NS = N*INCX + DO 70 I = 1,NS,INCX + DDOT = DDOT + DX(I)*DY(I) + 70 CONTINUE + RETURN + END +*DECK DNRM2 + DOUBLE PRECISION FUNCTION DNRM2 (N, DX, INCX) +C***BEGIN PROLOGUE DNRM2 +C***PURPOSE Compute the Euclidean length (L2 norm) of a vector. +C***CATEGORY D1A3B +C***TYPE DOUBLE PRECISION (SNRM2-S, DNRM2-D, SCNRM2-C) +C***KEYWORDS BLAS, EUCLIDEAN LENGTH, EUCLIDEAN NORM, L2, +C LINEAR ALGEBRA, UNITARY, VECTOR +C***AUTHOR Lawson, C. L., (JPL) +C Hanson, R. J., (SNLA) +C Kincaid, D. R., (U. of Texas) +C Krogh, F. T., (JPL) +C***DESCRIPTION +C +C B L A S Subprogram +C Description of parameters +C +C --Input-- +C N number of elements in input vector(s) +C DX double precision vector with N elements +C INCX storage spacing between elements of DX +C +C --Output-- +C DNRM2 double precision result (zero if N .LE. 0) +C +C Euclidean norm of the N-vector stored in DX with storage +C increment INCX. +C If N .LE. 0, return with result = 0. +C If N .GE. 1, then INCX must be .GE. 1 +C +C Four phase method using two built-in constants that are +C hopefully applicable to all machines. +C CUTLO = maximum of SQRT(U/EPS) over all known machines. +C CUTHI = minimum of SQRT(V) over all known machines. +C where +C EPS = smallest no. such that EPS + 1. .GT. 1. +C U = smallest positive no. (underflow limit) +C V = largest no. (overflow limit) +C +C Brief outline of algorithm. +C +C Phase 1 scans zero components. +C move to phase 2 when a component is nonzero and .LE. CUTLO +C move to phase 3 when a component is .GT. CUTLO +C move to phase 4 when a component is .GE. CUTHI/M +C where M = N for X() real and M = 2*N for complex. +C +C Values for CUTLO and CUTHI. +C From the environmental parameters listed in the IMSL converter +C document the limiting values are as follows: +C CUTLO, S.P. U/EPS = 2**(-102) for Honeywell. Close seconds are +C Univac and DEC at 2**(-103) +C Thus CUTLO = 2**(-51) = 4.44089E-16 +C CUTHI, S.P. V = 2**127 for Univac, Honeywell, and DEC. +C Thus CUTHI = 2**(63.5) = 1.30438E19 +C CUTLO, D.P. U/EPS = 2**(-67) for Honeywell and DEC. +C Thus CUTLO = 2**(-33.5) = 8.23181D-11 +C CUTHI, D.P. same as S.P. CUTHI = 1.30438D19 +C DATA CUTLO, CUTHI /8.232D-11, 1.304D19/ +C DATA CUTLO, CUTHI /4.441E-16, 1.304E19/ +C +C***REFERENCES C. L. Lawson, R. J. Hanson, D. R. Kincaid and F. T. +C Krogh, Basic linear algebra subprograms for Fortran +C usage, Algorithm No. 539, Transactions on Mathematical +C Software 5, 3 (September 1979), pp. 308-323. +C***ROUTINES CALLED (NONE) +C***REVISION HISTORY (YYMMDD) +C 791001 DATE WRITTEN +C 890531 Changed all specific intrinsics to generic. (WRB) +C 890831 Modified array declarations. (WRB) +C 890831 REVISION DATE from Version 3.2 +C 891214 Prologue converted to Version 4.0 format. (BAB) +C 920501 Reformatted the REFERENCES section. (WRB) +C***END PROLOGUE DNRM2 + INTEGER NEXT + DOUBLE PRECISION DX(*), CUTLO, CUTHI, HITEST, SUM, XMAX, ZERO, + + ONE + SAVE CUTLO, CUTHI, ZERO, ONE + DATA ZERO, ONE /0.0D0, 1.0D0/ +C + DATA CUTLO, CUTHI /8.232D-11, 1.304D19/ +C***FIRST EXECUTABLE STATEMENT DNRM2 + IF (N .GT. 0) GO TO 10 + DNRM2 = ZERO + GO TO 300 +C + 10 ASSIGN 30 TO NEXT + SUM = ZERO + NN = N * INCX +C +C BEGIN MAIN LOOP +C + I = 1 + 20 GO TO NEXT,(30, 50, 70, 110) + 30 IF (ABS(DX(I)) .GT. CUTLO) GO TO 85 + ASSIGN 50 TO NEXT + XMAX = ZERO +C +C PHASE 1. SUM IS ZERO +C + 50 IF (DX(I) .EQ. ZERO) GO TO 200 + IF (ABS(DX(I)) .GT. CUTLO) GO TO 85 +C +C PREPARE FOR PHASE 2. +C + ASSIGN 70 TO NEXT + GO TO 105 +C +C PREPARE FOR PHASE 4. +C + 100 I = J + ASSIGN 110 TO NEXT + SUM = (SUM / DX(I)) / DX(I) + 105 XMAX = ABS(DX(I)) + GO TO 115 +C +C PHASE 2. SUM IS SMALL. +C SCALE TO AVOID DESTRUCTIVE UNDERFLOW. +C + 70 IF (ABS(DX(I)) .GT. CUTLO) GO TO 75 +C +C COMMON CODE FOR PHASES 2 AND 4. +C IN PHASE 4 SUM IS LARGE. SCALE TO AVOID OVERFLOW. +C + 110 IF (ABS(DX(I)) .LE. XMAX) GO TO 115 + SUM = ONE + SUM * (XMAX / DX(I))**2 + XMAX = ABS(DX(I)) + GO TO 200 +C + 115 SUM = SUM + (DX(I)/XMAX)**2 + GO TO 200 +C +C PREPARE FOR PHASE 3. +C + 75 SUM = (SUM * XMAX) * XMAX +C +C FOR REAL OR D.P. SET HITEST = CUTHI/N +C FOR COMPLEX SET HITEST = CUTHI/(2*N) +C + 85 HITEST = CUTHI / N +C +C PHASE 3. SUM IS MID-RANGE. NO SCALING. +C + DO 95 J = I,NN,INCX + IF (ABS(DX(J)) .GE. HITEST) GO TO 100 + 95 SUM = SUM + DX(J)**2 + DNRM2 = SQRT(SUM) + GO TO 300 +C + 200 CONTINUE + I = I + INCX + IF (I .LE. NN) GO TO 20 +C +C END OF MAIN LOOP. +C +C COMPUTE SQUARE ROOT AND ADJUST FOR SCALING. +C + DNRM2 = XMAX * SQRT(SUM) + 300 CONTINUE + RETURN + END +*DECK DSCAL + SUBROUTINE DSCAL (N, DA, DX, INCX) +C***BEGIN PROLOGUE DSCAL +C***PURPOSE Multiply a vector by a constant. +C***CATEGORY D1A6 +C***TYPE DOUBLE PRECISION (SSCAL-S, DSCAL-D, CSCAL-C) +C***KEYWORDS BLAS, LINEAR ALGEBRA, SCALE, VECTOR +C***AUTHOR Lawson, C. L., (JPL) +C Hanson, R. J., (SNLA) +C Kincaid, D. R., (U. of Texas) +C Krogh, F. T., (JPL) +C***DESCRIPTION +C +C B L A S Subprogram +C Description of Parameters +C +C --Input-- +C N number of elements in input vector(s) +C DA double precision scale factor +C DX double precision vector with N elements +C INCX storage spacing between elements of DX +C +C --Output-- +C DX double precision result (unchanged if N.LE.0) +C +C Replace double precision DX by double precision DA*DX. +C For I = 0 to N-1, replace DX(IX+I*INCX) with DA * DX(IX+I*INCX), +C where IX = 1 if INCX .GE. 0, else IX = 1+(1-N)*INCX. +C +C***REFERENCES C. L. Lawson, R. J. Hanson, D. R. Kincaid and F. T. +C Krogh, Basic linear algebra subprograms for Fortran +C usage, Algorithm No. 539, Transactions on Mathematical +C Software 5, 3 (September 1979), pp. 308-323. +C***ROUTINES CALLED (NONE) +C***REVISION HISTORY (YYMMDD) +C 791001 DATE WRITTEN +C 890831 Modified array declarations. (WRB) +C 890831 REVISION DATE from Version 3.2 +C 891214 Prologue converted to Version 4.0 format. (BAB) +C 900821 Modified to correct problem with a negative increment. +C (WRB) +C 920501 Reformatted the REFERENCES section. (WRB) +C***END PROLOGUE DSCAL + DOUBLE PRECISION DA, DX(*) + INTEGER I, INCX, IX, M, MP1, N +C***FIRST EXECUTABLE STATEMENT DSCAL + IF (N .LE. 0) RETURN + IF (INCX .EQ. 1) GOTO 20 +C +C Code for increment not equal to 1. +C + IX = 1 + IF (INCX .LT. 0) IX = (-N+1)*INCX + 1 + DO 10 I = 1,N + DX(IX) = DA*DX(IX) + IX = IX + INCX + 10 CONTINUE + RETURN +C +C Code for increment equal to 1. +C +C Clean-up loop so remaining vector length is a multiple of 5. +C + 20 M = MOD(N,5) + IF (M .EQ. 0) GOTO 40 + DO 30 I = 1,M + DX(I) = DA*DX(I) + 30 CONTINUE + IF (N .LT. 5) RETURN + 40 MP1 = M + 1 + DO 50 I = MP1,N,5 + DX(I) = DA*DX(I) + DX(I+1) = DA*DX(I+1) + DX(I+2) = DA*DX(I+2) + DX(I+3) = DA*DX(I+3) + DX(I+4) = DA*DX(I+4) + 50 CONTINUE + RETURN + END +*DECK IDAMAX + INTEGER FUNCTION IDAMAX (N, DX, INCX) +C***BEGIN PROLOGUE IDAMAX +C***PURPOSE Find the smallest index of that component of a vector +C having the maximum magnitude. +C***CATEGORY D1A2 +C***TYPE DOUBLE PRECISION (ISAMAX-S, IDAMAX-D, ICAMAX-C) +C***KEYWORDS BLAS, LINEAR ALGEBRA, MAXIMUM COMPONENT, VECTOR +C***AUTHOR Lawson, C. L., (JPL) +C Hanson, R. J., (SNLA) +C Kincaid, D. R., (U. of Texas) +C Krogh, F. T., (JPL) +C***DESCRIPTION +C +C B L A S Subprogram +C Description of Parameters +C +C --Input-- +C N number of elements in input vector(s) +C DX double precision vector with N elements +C INCX storage spacing between elements of DX +C +C --Output-- +C IDAMAX smallest index (zero if N .LE. 0) +C +C Find smallest index of maximum magnitude of double precision DX. +C IDAMAX = first I, I = 1 to N, to maximize ABS(DX(IX+(I-1)*INCX)), +C where IX = 1 if INCX .GE. 0, else IX = 1+(1-N)*INCX. +C +C***REFERENCES C. L. Lawson, R. J. Hanson, D. R. Kincaid and F. T. +C Krogh, Basic linear algebra subprograms for Fortran +C usage, Algorithm No. 539, Transactions on Mathematical +C Software 5, 3 (September 1979), pp. 308-323. +C***ROUTINES CALLED (NONE) +C***REVISION HISTORY (YYMMDD) +C 791001 DATE WRITTEN +C 890531 Changed all specific intrinsics to generic. (WRB) +C 890531 REVISION DATE from Version 3.2 +C 891214 Prologue converted to Version 4.0 format. (BAB) +C 900821 Modified to correct problem with a negative increment. +C (WRB) +C 920501 Reformatted the REFERENCES section. (WRB) +C***END PROLOGUE IDAMAX + DOUBLE PRECISION DX(*), DMAX, XMAG + INTEGER I, INCX, IX, N +C***FIRST EXECUTABLE STATEMENT IDAMAX + IDAMAX = 0 + IF (N .LE. 0) RETURN + IDAMAX = 1 + IF (N .EQ. 1) RETURN +C + IF (INCX .EQ. 1) GOTO 20 +C +C Code for increments not equal to 1. +C + IX = 1 + IF (INCX .LT. 0) IX = (-N+1)*INCX + 1 + DMAX = ABS(DX(IX)) + IX = IX + INCX + DO 10 I = 2,N + XMAG = ABS(DX(IX)) + IF (XMAG .GT. DMAX) THEN + IDAMAX = I + DMAX = XMAG + ENDIF + IX = IX + INCX + 10 CONTINUE + RETURN +C +C Code for increments equal to 1. +C + 20 DMAX = ABS(DX(1)) + DO 30 I = 2,N + XMAG = ABS(DX(I)) + IF (XMAG .GT. DMAX) THEN + IDAMAX = I + DMAX = XMAG + ENDIF + 30 CONTINUE + RETURN + END +*DECK XERRWD + SUBROUTINE XERRWD (MSG, NMES, NERR, LEVEL, NI, I1, I2, NR, R1, R2) +C***BEGIN PROLOGUE XERRWD +C***SUBSIDIARY +C***PURPOSE Write error message with values. +C***CATEGORY R3C +C***TYPE DOUBLE PRECISION (XERRWV-S, XERRWD-D) +C***AUTHOR Hindmarsh, Alan C., (LLNL) +C***DESCRIPTION +C +C Subroutines XERRWD, XSETF, XSETUN, and the function routine IXSAV, +C as given here, constitute a simplified version of the SLATEC error +C handling package. +C +C All arguments are input arguments. +C +C MSG = The message (character array). +C NMES = The length of MSG (number of characters). +C NERR = The error number (not used). +C LEVEL = The error level.. +C 0 or 1 means recoverable (control returns to caller). +C 2 means fatal (run is aborted--see note below). +C NI = Number of integers (0, 1, or 2) to be printed with message. +C I1,I2 = Integers to be printed, depending on NI. +C NR = Number of reals (0, 1, or 2) to be printed with message. +C R1,R2 = Reals to be printed, depending on NR. +C +C Note.. this routine is machine-dependent and specialized for use +C in limited context, in the following ways.. +C 1. The argument MSG is assumed to be of type CHARACTER, and +C the message is printed with a format of (1X,A). +C 2. The message is assumed to take only one line. +C Multi-line messages are generated by repeated calls. +C 3. If LEVEL = 2, control passes to the statement STOP +C to abort the run. This statement may be machine-dependent. +C 4. R1 and R2 are assumed to be in double precision and are printed +C in D21.13 format. +C +C***ROUTINES CALLED IXSAV +C***REVISION HISTORY (YYMMDD) +C 920831 DATE WRITTEN +C 921118 Replaced MFLGSV/LUNSAV by IXSAV. (ACH) +C 930329 Modified prologue to SLATEC format. (FNF) +C 930407 Changed MSG from CHARACTER*1 array to variable. (FNF) +C 930922 Minor cosmetic change. (FNF) +C***END PROLOGUE XERRWD +C +C*Internal Notes: +C +C For a different default logical unit number, IXSAV (or a subsidiary +C routine that it calls) will need to be modified. +C For a different run-abort command, change the statement following +C statement 100 at the end. +C----------------------------------------------------------------------- +C Subroutines called by XERRWD.. None +C Function routine called by XERRWD.. IXSAV +C----------------------------------------------------------------------- +C**End +C +C Declare arguments. +C + DOUBLE PRECISION R1, R2 + INTEGER NMES, NERR, LEVEL, NI, I1, I2, NR + CHARACTER*(*) MSG +C +C Declare local variables. +C + INTEGER LUNIT, IXSAV, MESFLG +C +C Get logical unit number and message print flag. +C +C***FIRST EXECUTABLE STATEMENT XERRWD + LUNIT = IXSAV (1, 0, .FALSE.) + MESFLG = IXSAV (2, 0, .FALSE.) + IF (MESFLG .EQ. 0) GO TO 100 +C +C Write the message. +C + WRITE (LUNIT,10) MSG + 10 FORMAT(1X,A) + IF (NI .EQ. 1) WRITE (LUNIT, 20) I1 + 20 FORMAT(6X,'In above message, I1 =',I10) + IF (NI .EQ. 2) WRITE (LUNIT, 30) I1,I2 + 30 FORMAT(6X,'In above message, I1 =',I10,3X,'I2 =',I10) + IF (NR .EQ. 1) WRITE (LUNIT, 40) R1 + 40 FORMAT(6X,'In above message, R1 =',D21.13) + IF (NR .EQ. 2) WRITE (LUNIT, 50) R1,R2 + 50 FORMAT(6X,'In above, R1 =',D21.13,3X,'R2 =',D21.13) +C +C Abort the run if LEVEL = 2. +C + 100 IF (LEVEL .NE. 2) RETURN + STOP +C----------------------- End of Subroutine XERRWD ---------------------- + END +*DECK XSETF + SUBROUTINE XSETF (MFLAG) +C***BEGIN PROLOGUE XSETF +C***PURPOSE Reset the error print control flag. +C***CATEGORY R3A +C***TYPE ALL (XSETF-A) +C***KEYWORDS ERROR CONTROL +C***AUTHOR Hindmarsh, Alan C., (LLNL) +C***DESCRIPTION +C +C XSETF sets the error print control flag to MFLAG: +C MFLAG=1 means print all messages (the default). +C MFLAG=0 means no printing. +C +C***SEE ALSO XERRWD, XERRWV +C***REFERENCES (NONE) +C***ROUTINES CALLED IXSAV +C***REVISION HISTORY (YYMMDD) +C 921118 DATE WRITTEN +C 930329 Added SLATEC format prologue. (FNF) +C 930407 Corrected SEE ALSO section. (FNF) +C 930922 Made user-callable, and other cosmetic changes. (FNF) +C***END PROLOGUE XSETF +C +C Subroutines called by XSETF.. None +C Function routine called by XSETF.. IXSAV +C----------------------------------------------------------------------- +C**End + INTEGER MFLAG, JUNK, IXSAV +C +C***FIRST EXECUTABLE STATEMENT XSETF + IF (MFLAG .EQ. 0 .OR. MFLAG .EQ. 1) JUNK = IXSAV (2,MFLAG,.TRUE.) + RETURN +C----------------------- End of Subroutine XSETF ----------------------- + END +*DECK XSETUN + SUBROUTINE XSETUN (LUN) +C***BEGIN PROLOGUE XSETUN +C***PURPOSE Reset the logical unit number for error messages. +C***CATEGORY R3B +C***TYPE ALL (XSETUN-A) +C***KEYWORDS ERROR CONTROL +C***DESCRIPTION +C +C XSETUN sets the logical unit number for error messages to LUN. +C +C***AUTHOR Hindmarsh, Alan C., (LLNL) +C***SEE ALSO XERRWD, XERRWV +C***REFERENCES (NONE) +C***ROUTINES CALLED IXSAV +C***REVISION HISTORY (YYMMDD) +C 921118 DATE WRITTEN +C 930329 Added SLATEC format prologue. (FNF) +C 930407 Corrected SEE ALSO section. (FNF) +C 930922 Made user-callable, and other cosmetic changes. (FNF) +C***END PROLOGUE XSETUN +C +C Subroutines called by XSETUN.. None +C Function routine called by XSETUN.. IXSAV +C----------------------------------------------------------------------- +C**End + INTEGER LUN, JUNK, IXSAV +C +C***FIRST EXECUTABLE STATEMENT XSETUN + IF (LUN .GT. 0) JUNK = IXSAV (1,LUN,.TRUE.) + RETURN +C----------------------- End of Subroutine XSETUN ---------------------- + END +*DECK IXSAV + INTEGER FUNCTION IXSAV (IPAR, IVALUE, ISET) +C***BEGIN PROLOGUE IXSAV +C***SUBSIDIARY +C***PURPOSE Save and recall error message control parameters. +C***CATEGORY R3C +C***TYPE ALL (IXSAV-A) +C***AUTHOR Hindmarsh, Alan C., (LLNL) +C***DESCRIPTION +C +C IXSAV saves and recalls one of two error message parameters: +C LUNIT, the logical unit number to which messages are printed, and +C MESFLG, the message print flag. +C This is a modification of the SLATEC library routine J4SAVE. +C +C Saved local variables.. +C LUNIT = Logical unit number for messages. The default is obtained +C by a call to IUMACH (may be machine-dependent). +C MESFLG = Print control flag.. +C 1 means print all messages (the default). +C 0 means no printing. +C +C On input.. +C IPAR = Parameter indicator (1 for LUNIT, 2 for MESFLG). +C IVALUE = The value to be set for the parameter, if ISET = .TRUE. +C ISET = Logical flag to indicate whether to read or write. +C If ISET = .TRUE., the parameter will be given +C the value IVALUE. If ISET = .FALSE., the parameter +C will be unchanged, and IVALUE is a dummy argument. +C +C On return.. +C IXSAV = The (old) value of the parameter. +C +C***SEE ALSO XERRWD, XERRWV +C***ROUTINES CALLED IUMACH +C***REVISION HISTORY (YYMMDD) +C 921118 DATE WRITTEN +C 930329 Modified prologue to SLATEC format. (FNF) +C 930915 Added IUMACH call to get default output unit. (ACH) +C 930922 Minor cosmetic changes. (FNF) +C 010425 Type declaration for IUMACH added. (ACH) +C***END PROLOGUE IXSAV +C +C Subroutines called by IXSAV.. None +C Function routine called by IXSAV.. IUMACH +C----------------------------------------------------------------------- +C**End + LOGICAL ISET + INTEGER IPAR, IVALUE +C----------------------------------------------------------------------- + INTEGER IUMACH, LUNIT, MESFLG +C----------------------------------------------------------------------- +C The following Fortran-77 declaration is to cause the values of the +C listed (local) variables to be saved between calls to this routine. +C----------------------------------------------------------------------- + SAVE LUNIT, MESFLG + DATA LUNIT/-1/, MESFLG/1/ +C +C***FIRST EXECUTABLE STATEMENT IXSAV + IF (IPAR .EQ. 1) THEN + IF (LUNIT .EQ. -1) LUNIT = IUMACH() + IXSAV = LUNIT + IF (ISET) LUNIT = IVALUE + ENDIF +C + IF (IPAR .EQ. 2) THEN + IXSAV = MESFLG + IF (ISET) MESFLG = IVALUE + ENDIF +C + RETURN +C----------------------- End of Function IXSAV ------------------------- + END +*DECK IUMACH + INTEGER FUNCTION IUMACH() +C***BEGIN PROLOGUE IUMACH +C***PURPOSE Provide standard output unit number. +C***CATEGORY R1 +C***TYPE INTEGER (IUMACH-I) +C***KEYWORDS MACHINE CONSTANTS +C***AUTHOR Hindmarsh, Alan C., (LLNL) +C***DESCRIPTION +C *Usage: +C INTEGER LOUT, IUMACH +C LOUT = IUMACH() +C +C *Function Return Values: +C LOUT : the standard logical unit for Fortran output. +C +C***REFERENCES (NONE) +C***ROUTINES CALLED (NONE) +C***REVISION HISTORY (YYMMDD) +C 930915 DATE WRITTEN +C 930922 Made user-callable, and other cosmetic changes. (FNF) +C***END PROLOGUE IUMACH +C +C*Internal Notes: +C The built-in value of 6 is standard on a wide range of Fortran +C systems. This may be machine-dependent. +C**End +C***FIRST EXECUTABLE STATEMENT IUMACH + IUMACH = 6 +C + RETURN +C----------------------- End of Function IUMACH ------------------------ + END diff --git a/applications/PUfoam/MoDeNaModels/bubbleGrowth/src/src/opkdmain.f b/applications/PUfoam/MoDeNaModels/bubbleGrowth/src/src/opkdmain.f new file mode 100644 index 000000000..d879ee498 --- /dev/null +++ b/applications/PUfoam/MoDeNaModels/bubbleGrowth/src/src/opkdmain.f @@ -0,0 +1,16587 @@ +*DECK DLSODE + SUBROUTINE DLSODE (F, NEQ, Y, T, TOUT, ITOL, RTOL, ATOL, ITASK, + 1 ISTATE, IOPT, RWORK, LRW, IWORK, LIW, JAC, MF) + EXTERNAL F, JAC + INTEGER NEQ, ITOL, ITASK, ISTATE, IOPT, LRW, IWORK, LIW, MF + DOUBLE PRECISION Y, T, TOUT, RTOL, ATOL, RWORK + DIMENSION NEQ(*), Y(*), RTOL(*), ATOL(*), RWORK(LRW), IWORK(LIW) +C***BEGIN PROLOGUE DLSODE +C***PURPOSE Livermore Solver for Ordinary Differential Equations. +C DLSODE solves the initial-value problem for stiff or +C nonstiff systems of first-order ODE's, +C dy/dt = f(t,y), or, in component form, +C dy(i)/dt = f(i) = f(i,t,y(1),y(2),...,y(N)), i=1,...,N. +C***CATEGORY I1A +C***TYPE DOUBLE PRECISION (SLSODE-S, DLSODE-D) +C***KEYWORDS ORDINARY DIFFERENTIAL EQUATIONS, INITIAL VALUE PROBLEM, +C STIFF, NONSTIFF +C***AUTHOR Hindmarsh, Alan C., (LLNL) +C Center for Applied Scientific Computing, L-561 +C Lawrence Livermore National Laboratory +C Livermore, CA 94551. +C***DESCRIPTION +C +C NOTE: The "Usage" and "Arguments" sections treat only a subset of +C available options, in condensed fashion. The options +C covered and the information supplied will support most +C standard uses of DLSODE. +C +C For more sophisticated uses, full details on all options are +C given in the concluding section, headed "Long Description." +C A synopsis of the DLSODE Long Description is provided at the +C beginning of that section; general topics covered are: +C - Elements of the call sequence; optional input and output +C - Optional supplemental routines in the DLSODE package +C - internal COMMON block +C +C *Usage: +C Communication between the user and the DLSODE package, for normal +C situations, is summarized here. This summary describes a subset +C of the available options. See "Long Description" for complete +C details, including optional communication, nonstandard options, +C and instructions for special situations. +C +C A sample program is given in the "Examples" section. +C +C Refer to the argument descriptions for the definitions of the +C quantities that appear in the following sample declarations. +C +C For MF = 10, +C PARAMETER (LRW = 20 + 16*NEQ, LIW = 20) +C For MF = 21 or 22, +C PARAMETER (LRW = 22 + 9*NEQ + NEQ**2, LIW = 20 + NEQ) +C For MF = 24 or 25, +C PARAMETER (LRW = 22 + 10*NEQ + (2*ML+MU)*NEQ, +C * LIW = 20 + NEQ) +C +C EXTERNAL F, JAC +C INTEGER NEQ, ITOL, ITASK, ISTATE, IOPT, LRW, IWORK(LIW), +C * LIW, MF +C DOUBLE PRECISION Y(NEQ), T, TOUT, RTOL, ATOL(ntol), RWORK(LRW) +C +C CALL DLSODE (F, NEQ, Y, T, TOUT, ITOL, RTOL, ATOL, ITASK, +C * ISTATE, IOPT, RWORK, LRW, IWORK, LIW, JAC, MF) +C +C *Arguments: +C F :EXT Name of subroutine for right-hand-side vector f. +C This name must be declared EXTERNAL in calling +C program. The form of F must be: +C +C SUBROUTINE F (NEQ, T, Y, YDOT) +C INTEGER NEQ +C DOUBLE PRECISION T, Y(*), YDOT(*) +C +C The inputs are NEQ, T, Y. F is to set +C +C YDOT(i) = f(i,T,Y(1),Y(2),...,Y(NEQ)), +C i = 1, ..., NEQ . +C +C NEQ :IN Number of first-order ODE's. +C +C Y :INOUT Array of values of the y(t) vector, of length NEQ. +C Input: For the first call, Y should contain the +C values of y(t) at t = T. (Y is an input +C variable only if ISTATE = 1.) +C Output: On return, Y will contain the values at the +C new t-value. +C +C T :INOUT Value of the independent variable. On return it +C will be the current value of t (normally TOUT). +C +C TOUT :IN Next point where output is desired (.NE. T). +C +C ITOL :IN 1 or 2 according as ATOL (below) is a scalar or +C an array. +C +C RTOL :IN Relative tolerance parameter (scalar). +C +C ATOL :IN Absolute tolerance parameter (scalar or array). +C If ITOL = 1, ATOL need not be dimensioned. +C If ITOL = 2, ATOL must be dimensioned at least NEQ. +C +C The estimated local error in Y(i) will be controlled +C so as to be roughly less (in magnitude) than +C +C EWT(i) = RTOL*ABS(Y(i)) + ATOL if ITOL = 1, or +C EWT(i) = RTOL*ABS(Y(i)) + ATOL(i) if ITOL = 2. +C +C Thus the local error test passes if, in each +C component, either the absolute error is less than +C ATOL (or ATOL(i)), or the relative error is less +C than RTOL. +C +C Use RTOL = 0.0 for pure absolute error control, and +C use ATOL = 0.0 (or ATOL(i) = 0.0) for pure relative +C error control. Caution: Actual (global) errors may +C exceed these local tolerances, so choose them +C conservatively. +C +C ITASK :IN Flag indicating the task DLSODE is to perform. +C Use ITASK = 1 for normal computation of output +C values of y at t = TOUT. +C +C ISTATE:INOUT Index used for input and output to specify the state +C of the calculation. +C Input: +C 1 This is the first call for a problem. +C 2 This is a subsequent call. +C Output: +C 1 Nothing was done, because TOUT was equal to T. +C 2 DLSODE was successful (otherwise, negative). +C Note that ISTATE need not be modified after a +C successful return. +C -1 Excess work done on this call (perhaps wrong +C MF). +C -2 Excess accuracy requested (tolerances too +C small). +C -3 Illegal input detected (see printed message). +C -4 Repeated error test failures (check all +C inputs). +C -5 Repeated convergence failures (perhaps bad +C Jacobian supplied or wrong choice of MF or +C tolerances). +C -6 Error weight became zero during problem +C (solution component i vanished, and ATOL or +C ATOL(i) = 0.). +C +C IOPT :IN Flag indicating whether optional inputs are used: +C 0 No. +C 1 Yes. (See "Optional inputs" under "Long +C Description," Part 1.) +C +C RWORK :WORK Real work array of length at least: +C 20 + 16*NEQ for MF = 10, +C 22 + 9*NEQ + NEQ**2 for MF = 21 or 22, +C 22 + 10*NEQ + (2*ML + MU)*NEQ for MF = 24 or 25. +C +C LRW :IN Declared length of RWORK (in user's DIMENSION +C statement). +C +C IWORK :WORK Integer work array of length at least: +C 20 for MF = 10, +C 20 + NEQ for MF = 21, 22, 24, or 25. +C +C If MF = 24 or 25, input in IWORK(1),IWORK(2) the +C lower and upper Jacobian half-bandwidths ML,MU. +C +C On return, IWORK contains information that may be +C of interest to the user: +C +C Name Location Meaning +C ----- --------- ----------------------------------------- +C NST IWORK(11) Number of steps taken for the problem so +C far. +C NFE IWORK(12) Number of f evaluations for the problem +C so far. +C NJE IWORK(13) Number of Jacobian evaluations (and of +C matrix LU decompositions) for the problem +C so far. +C NQU IWORK(14) Method order last used (successfully). +C LENRW IWORK(17) Length of RWORK actually required. This +C is defined on normal returns and on an +C illegal input return for insufficient +C storage. +C LENIW IWORK(18) Length of IWORK actually required. This +C is defined on normal returns and on an +C illegal input return for insufficient +C storage. +C +C LIW :IN Declared length of IWORK (in user's DIMENSION +C statement). +C +C JAC :EXT Name of subroutine for Jacobian matrix (MF = +C 21 or 24). If used, this name must be declared +C EXTERNAL in calling program. If not used, pass a +C dummy name. The form of JAC must be: +C +C SUBROUTINE JAC (NEQ, T, Y, ML, MU, PD, NROWPD) +C INTEGER NEQ, ML, MU, NROWPD +C DOUBLE PRECISION T, Y(*), PD(NROWPD,*) +C +C See item c, under "Description" below for more +C information about JAC. +C +C MF :IN Method flag. Standard values are: +C 10 Nonstiff (Adams) method, no Jacobian used. +C 21 Stiff (BDF) method, user-supplied full Jacobian. +C 22 Stiff method, internally generated full +C Jacobian. +C 24 Stiff method, user-supplied banded Jacobian. +C 25 Stiff method, internally generated banded +C Jacobian. +C +C *Description: +C DLSODE solves the initial value problem for stiff or nonstiff +C systems of first-order ODE's, +C +C dy/dt = f(t,y) , +C +C or, in component form, +C +C dy(i)/dt = f(i) = f(i,t,y(1),y(2),...,y(NEQ)) +C (i = 1, ..., NEQ) . +C +C DLSODE is a package based on the GEAR and GEARB packages, and on +C the October 23, 1978, version of the tentative ODEPACK user +C interface standard, with minor modifications. +C +C The steps in solving such a problem are as follows. +C +C a. First write a subroutine of the form +C +C SUBROUTINE F (NEQ, T, Y, YDOT) +C INTEGER NEQ +C DOUBLE PRECISION T, Y(*), YDOT(*) +C +C which supplies the vector function f by loading YDOT(i) with +C f(i). +C +C b. Next determine (or guess) whether or not the problem is stiff. +C Stiffness occurs when the Jacobian matrix df/dy has an +C eigenvalue whose real part is negative and large in magnitude +C compared to the reciprocal of the t span of interest. If the +C problem is nonstiff, use method flag MF = 10. If it is stiff, +C there are four standard choices for MF, and DLSODE requires the +C Jacobian matrix in some form. This matrix is regarded either +C as full (MF = 21 or 22), or banded (MF = 24 or 25). In the +C banded case, DLSODE requires two half-bandwidth parameters ML +C and MU. These are, respectively, the widths of the lower and +C upper parts of the band, excluding the main diagonal. Thus the +C band consists of the locations (i,j) with +C +C i - ML <= j <= i + MU , +C +C and the full bandwidth is ML + MU + 1 . +C +C c. If the problem is stiff, you are encouraged to supply the +C Jacobian directly (MF = 21 or 24), but if this is not feasible, +C DLSODE will compute it internally by difference quotients (MF = +C 22 or 25). If you are supplying the Jacobian, write a +C subroutine of the form +C +C SUBROUTINE JAC (NEQ, T, Y, ML, MU, PD, NROWPD) +C INTEGER NEQ, ML, MU, NRWOPD +C DOUBLE PRECISION T, Y(*), PD(NROWPD,*) +C +C which provides df/dy by loading PD as follows: +C - For a full Jacobian (MF = 21), load PD(i,j) with df(i)/dy(j), +C the partial derivative of f(i) with respect to y(j). (Ignore +C the ML and MU arguments in this case.) +C - For a banded Jacobian (MF = 24), load PD(i-j+MU+1,j) with +C df(i)/dy(j); i.e., load the diagonal lines of df/dy into the +C rows of PD from the top down. +C - In either case, only nonzero elements need be loaded. +C +C d. Write a main program that calls subroutine DLSODE once for each +C point at which answers are desired. This should also provide +C for possible use of logical unit 6 for output of error messages +C by DLSODE. +C +C Before the first call to DLSODE, set ISTATE = 1, set Y and T to +C the initial values, and set TOUT to the first output point. To +C continue the integration after a successful return, simply +C reset TOUT and call DLSODE again. No other parameters need be +C reset. +C +C *Examples: +C The following is a simple example problem, with the coding needed +C for its solution by DLSODE. The problem is from chemical kinetics, +C and consists of the following three rate equations: +C +C dy1/dt = -.04*y1 + 1.E4*y2*y3 +C dy2/dt = .04*y1 - 1.E4*y2*y3 - 3.E7*y2**2 +C dy3/dt = 3.E7*y2**2 +C +C on the interval from t = 0.0 to t = 4.E10, with initial conditions +C y1 = 1.0, y2 = y3 = 0. The problem is stiff. +C +C The following coding solves this problem with DLSODE, using +C MF = 21 and printing results at t = .4, 4., ..., 4.E10. It uses +C ITOL = 2 and ATOL much smaller for y2 than for y1 or y3 because y2 +C has much smaller values. At the end of the run, statistical +C quantities of interest are printed. +C +C EXTERNAL FEX, JEX +C INTEGER IOPT, IOUT, ISTATE, ITASK, ITOL, IWORK(23), LIW, LRW, +C * MF, NEQ +C DOUBLE PRECISION ATOL(3), RTOL, RWORK(58), T, TOUT, Y(3) +C NEQ = 3 +C Y(1) = 1.D0 +C Y(2) = 0.D0 +C Y(3) = 0.D0 +C T = 0.D0 +C TOUT = .4D0 +C ITOL = 2 +C RTOL = 1.D-4 +C ATOL(1) = 1.D-6 +C ATOL(2) = 1.D-10 +C ATOL(3) = 1.D-6 +C ITASK = 1 +C ISTATE = 1 +C IOPT = 0 +C LRW = 58 +C LIW = 23 +C MF = 21 +C DO 40 IOUT = 1,12 +C CALL DLSODE (FEX, NEQ, Y, T, TOUT, ITOL, RTOL, ATOL, ITASK, +C * ISTATE, IOPT, RWORK, LRW, IWORK, LIW, JEX, MF) +C WRITE(6,20) T, Y(1), Y(2), Y(3) +C 20 FORMAT(' At t =',D12.4,' y =',3D14.6) +C IF (ISTATE .LT. 0) GO TO 80 +C 40 TOUT = TOUT*10.D0 +C WRITE(6,60) IWORK(11), IWORK(12), IWORK(13) +C 60 FORMAT(/' No. steps =',i4,', No. f-s =',i4,', No. J-s =',i4) +C STOP +C 80 WRITE(6,90) ISTATE +C 90 FORMAT(///' Error halt.. ISTATE =',I3) +C STOP +C END +C +C SUBROUTINE FEX (NEQ, T, Y, YDOT) +C INTEGER NEQ +C DOUBLE PRECISION T, Y(3), YDOT(3) +C YDOT(1) = -.04D0*Y(1) + 1.D4*Y(2)*Y(3) +C YDOT(3) = 3.D7*Y(2)*Y(2) +C YDOT(2) = -YDOT(1) - YDOT(3) +C RETURN +C END +C +C SUBROUTINE JEX (NEQ, T, Y, ML, MU, PD, NRPD) +C INTEGER NEQ, ML, MU, NRPD +C DOUBLE PRECISION T, Y(3), PD(NRPD,3) +C PD(1,1) = -.04D0 +C PD(1,2) = 1.D4*Y(3) +C PD(1,3) = 1.D4*Y(2) +C PD(2,1) = .04D0 +C PD(2,3) = -PD(1,3) +C PD(3,2) = 6.D7*Y(2) +C PD(2,2) = -PD(1,2) - PD(3,2) +C RETURN +C END +C +C The output from this program (on a Cray-1 in single precision) +C is as follows. +C +C At t = 4.0000e-01 y = 9.851726e-01 3.386406e-05 1.479357e-02 +C At t = 4.0000e+00 y = 9.055142e-01 2.240418e-05 9.446344e-02 +C At t = 4.0000e+01 y = 7.158050e-01 9.184616e-06 2.841858e-01 +C At t = 4.0000e+02 y = 4.504846e-01 3.222434e-06 5.495122e-01 +C At t = 4.0000e+03 y = 1.831701e-01 8.940379e-07 8.168290e-01 +C At t = 4.0000e+04 y = 3.897016e-02 1.621193e-07 9.610297e-01 +C At t = 4.0000e+05 y = 4.935213e-03 1.983756e-08 9.950648e-01 +C At t = 4.0000e+06 y = 5.159269e-04 2.064759e-09 9.994841e-01 +C At t = 4.0000e+07 y = 5.306413e-05 2.122677e-10 9.999469e-01 +C At t = 4.0000e+08 y = 5.494530e-06 2.197825e-11 9.999945e-01 +C At t = 4.0000e+09 y = 5.129458e-07 2.051784e-12 9.999995e-01 +C At t = 4.0000e+10 y = -7.170603e-08 -2.868241e-13 1.000000e+00 +C +C No. steps = 330, No. f-s = 405, No. J-s = 69 +C +C *Accuracy: +C The accuracy of the solution depends on the choice of tolerances +C RTOL and ATOL. Actual (global) errors may exceed these local +C tolerances, so choose them conservatively. +C +C *Cautions: +C The work arrays should not be altered between calls to DLSODE for +C the same problem, except possibly for the conditional and optional +C inputs. +C +C *Portability: +C Since NEQ is dimensioned inside DLSODE, some compilers may object +C to a call to DLSODE with NEQ a scalar variable. In this event, +C use DIMENSION NEQ(1). Similar remarks apply to RTOL and ATOL. +C +C Note to Cray users: +C For maximum efficiency, use the CFT77 compiler. Appropriate +C compiler optimization directives have been inserted for CFT77. +C +C *Reference: +C Alan C. Hindmarsh, "ODEPACK, A Systematized Collection of ODE +C Solvers," in Scientific Computing, R. S. Stepleman, et al., Eds. +C (North-Holland, Amsterdam, 1983), pp. 55-64. +C +C *Long Description: +C The following complete description of the user interface to +C DLSODE consists of four parts: +C +C 1. The call sequence to subroutine DLSODE, which is a driver +C routine for the solver. This includes descriptions of both +C the call sequence arguments and user-supplied routines. +C Following these descriptions is a description of optional +C inputs available through the call sequence, and then a +C description of optional outputs in the work arrays. +C +C 2. Descriptions of other routines in the DLSODE package that may +C be (optionally) called by the user. These provide the ability +C to alter error message handling, save and restore the internal +C COMMON, and obtain specified derivatives of the solution y(t). +C +C 3. Descriptions of COMMON block to be declared in overlay or +C similar environments, or to be saved when doing an interrupt +C of the problem and continued solution later. +C +C 4. Description of two routines in the DLSODE package, either of +C which the user may replace with his own version, if desired. +C These relate to the measurement of errors. +C +C +C Part 1. Call Sequence +C ---------------------- +C +C Arguments +C --------- +C The call sequence parameters used for input only are +C +C F, NEQ, TOUT, ITOL, RTOL, ATOL, ITASK, IOPT, LRW, LIW, JAC, MF, +C +C and those used for both input and output are +C +C Y, T, ISTATE. +C +C The work arrays RWORK and IWORK are also used for conditional and +C optional inputs and optional outputs. (The term output here +C refers to the return from subroutine DLSODE to the user's calling +C program.) +C +C The legality of input parameters will be thoroughly checked on the +C initial call for the problem, but not checked thereafter unless a +C change in input parameters is flagged by ISTATE = 3 on input. +C +C The descriptions of the call arguments are as follows. +C +C F The name of the user-supplied subroutine defining the ODE +C system. The system must be put in the first-order form +C dy/dt = f(t,y), where f is a vector-valued function of +C the scalar t and the vector y. Subroutine F is to compute +C the function f. It is to have the form +C +C SUBROUTINE F (NEQ, T, Y, YDOT) +C DOUBLE PRECISION T, Y(*), YDOT(*) +C +C where NEQ, T, and Y are input, and the array YDOT = +C f(T,Y) is output. Y and YDOT are arrays of length NEQ. +C Subroutine F should not alter Y(1),...,Y(NEQ). F must be +C declared EXTERNAL in the calling program. +C +C Subroutine F may access user-defined quantities in +C NEQ(2),... and/or in Y(NEQ(1)+1),..., if NEQ is an array +C (dimensioned in F) and/or Y has length exceeding NEQ(1). +C See the descriptions of NEQ and Y below. +C +C If quantities computed in the F routine are needed +C externally to DLSODE, an extra call to F should be made +C for this purpose, for consistent and accurate results. +C If only the derivative dy/dt is needed, use DINTDY +C instead. +C +C NEQ The size of the ODE system (number of first-order +C ordinary differential equations). Used only for input. +C NEQ may be decreased, but not increased, during the +C problem. If NEQ is decreased (with ISTATE = 3 on input), +C the remaining components of Y should be left undisturbed, +C if these are to be accessed in F and/or JAC. +C +C Normally, NEQ is a scalar, and it is generally referred +C to as a scalar in this user interface description. +C However, NEQ may be an array, with NEQ(1) set to the +C system size. (The DLSODE package accesses only NEQ(1).) +C In either case, this parameter is passed as the NEQ +C argument in all calls to F and JAC. Hence, if it is an +C array, locations NEQ(2),... may be used to store other +C integer data and pass it to F and/or JAC. Subroutines +C F and/or JAC must include NEQ in a DIMENSION statement +C in that case. +C +C Y A real array for the vector of dependent variables, of +C length NEQ or more. Used for both input and output on +C the first call (ISTATE = 1), and only for output on +C other calls. On the first call, Y must contain the +C vector of initial values. On output, Y contains the +C computed solution vector, evaluated at T. If desired, +C the Y array may be used for other purposes between +C calls to the solver. +C +C This array is passed as the Y argument in all calls to F +C and JAC. Hence its length may exceed NEQ, and locations +C Y(NEQ+1),... may be used to store other real data and +C pass it to F and/or JAC. (The DLSODE package accesses +C only Y(1),...,Y(NEQ).) +C +C T The independent variable. On input, T is used only on +C the first call, as the initial point of the integration. +C On output, after each call, T is the value at which a +C computed solution Y is evaluated (usually the same as +C TOUT). On an error return, T is the farthest point +C reached. +C +C TOUT The next value of T at which a computed solution is +C desired. Used only for input. +C +C When starting the problem (ISTATE = 1), TOUT may be equal +C to T for one call, then should not equal T for the next +C call. For the initial T, an input value of TOUT .NE. T +C is used in order to determine the direction of the +C integration (i.e., the algebraic sign of the step sizes) +C and the rough scale of the problem. Integration in +C either direction (forward or backward in T) is permitted. +C +C If ITASK = 2 or 5 (one-step modes), TOUT is ignored +C after the first call (i.e., the first call with +C TOUT .NE. T). Otherwise, TOUT is required on every call. +C +C If ITASK = 1, 3, or 4, the values of TOUT need not be +C monotone, but a value of TOUT which backs up is limited +C to the current internal T interval, whose endpoints are +C TCUR - HU and TCUR. (See "Optional Outputs" below for +C TCUR and HU.) +C +C +C ITOL An indicator for the type of error control. See +C description below under ATOL. Used only for input. +C +C RTOL A relative error tolerance parameter, either a scalar or +C an array of length NEQ. See description below under +C ATOL. Input only. +C +C ATOL An absolute error tolerance parameter, either a scalar or +C an array of length NEQ. Input only. +C +C The input parameters ITOL, RTOL, and ATOL determine the +C error control performed by the solver. The solver will +C control the vector e = (e(i)) of estimated local errors +C in Y, according to an inequality of the form +C +C rms-norm of ( e(i)/EWT(i) ) <= 1, +C +C where +C +C EWT(i) = RTOL(i)*ABS(Y(i)) + ATOL(i), +C +C and the rms-norm (root-mean-square norm) here is +C +C rms-norm(v) = SQRT(sum v(i)**2 / NEQ). +C +C Here EWT = (EWT(i)) is a vector of weights which must +C always be positive, and the values of RTOL and ATOL +C should all be nonnegative. The following table gives the +C types (scalar/array) of RTOL and ATOL, and the +C corresponding form of EWT(i). +C +C ITOL RTOL ATOL EWT(i) +C ---- ------ ------ ----------------------------- +C 1 scalar scalar RTOL*ABS(Y(i)) + ATOL +C 2 scalar array RTOL*ABS(Y(i)) + ATOL(i) +C 3 array scalar RTOL(i)*ABS(Y(i)) + ATOL +C 4 array array RTOL(i)*ABS(Y(i)) + ATOL(i) +C +C When either of these parameters is a scalar, it need not +C be dimensioned in the user's calling program. +C +C If none of the above choices (with ITOL, RTOL, and ATOL +C fixed throughout the problem) is suitable, more general +C error controls can be obtained by substituting +C user-supplied routines for the setting of EWT and/or for +C the norm calculation. See Part 4 below. +C +C If global errors are to be estimated by making a repeated +C run on the same problem with smaller tolerances, then all +C components of RTOL and ATOL (i.e., of EWT) should be +C scaled down uniformly. +C +C ITASK An index specifying the task to be performed. Input +C only. ITASK has the following values and meanings: +C 1 Normal computation of output values of y(t) at +C t = TOUT (by overshooting and interpolating). +C 2 Take one step only and return. +C 3 Stop at the first internal mesh point at or beyond +C t = TOUT and return. +C 4 Normal computation of output values of y(t) at +C t = TOUT but without overshooting t = TCRIT. TCRIT +C must be input as RWORK(1). TCRIT may be equal to or +C beyond TOUT, but not behind it in the direction of +C integration. This option is useful if the problem +C has a singularity at or beyond t = TCRIT. +C 5 Take one step, without passing TCRIT, and return. +C TCRIT must be input as RWORK(1). +C +C Note: If ITASK = 4 or 5 and the solver reaches TCRIT +C (within roundoff), it will return T = TCRIT (exactly) to +C indicate this (unless ITASK = 4 and TOUT comes before +C TCRIT, in which case answers at T = TOUT are returned +C first). +C +C ISTATE An index used for input and output to specify the state +C of the calculation. +C +C On input, the values of ISTATE are as follows: +C 1 This is the first call for the problem +C (initializations will be done). See "Note" below. +C 2 This is not the first call, and the calculation is to +C continue normally, with no change in any input +C parameters except possibly TOUT and ITASK. (If ITOL, +C RTOL, and/or ATOL are changed between calls with +C ISTATE = 2, the new values will be used but not +C tested for legality.) +C 3 This is not the first call, and the calculation is to +C continue normally, but with a change in input +C parameters other than TOUT and ITASK. Changes are +C allowed in NEQ, ITOL, RTOL, ATOL, IOPT, LRW, LIW, MF, +C ML, MU, and any of the optional inputs except H0. +C (See IWORK description for ML and MU.) +C +C Note: A preliminary call with TOUT = T is not counted as +C a first call here, as no initialization or checking of +C input is done. (Such a call is sometimes useful for the +C purpose of outputting the initial conditions.) Thus the +C first call for which TOUT .NE. T requires ISTATE = 1 on +C input. +C +C On output, ISTATE has the following values and meanings: +C 1 Nothing was done, as TOUT was equal to T with +C ISTATE = 1 on input. +C 2 The integration was performed successfully. +C -1 An excessive amount of work (more than MXSTEP steps) +C was done on this call, before completing the +C requested task, but the integration was otherwise +C successful as far as T. (MXSTEP is an optional input +C and is normally 500.) To continue, the user may +C simply reset ISTATE to a value >1 and call again (the +C excess work step counter will be reset to 0). In +C addition, the user may increase MXSTEP to avoid this +C error return; see "Optional Inputs" below. +C -2 Too much accuracy was requested for the precision of +C the machine being used. This was detected before +C completing the requested task, but the integration +C was successful as far as T. To continue, the +C tolerance parameters must be reset, and ISTATE must +C be set to 3. The optional output TOLSF may be used +C for this purpose. (Note: If this condition is +C detected before taking any steps, then an illegal +C input return (ISTATE = -3) occurs instead.) +C -3 Illegal input was detected, before taking any +C integration steps. See written message for details. +C (Note: If the solver detects an infinite loop of +C calls to the solver with illegal input, it will cause +C the run to stop.) +C -4 There were repeated error-test failures on one +C attempted step, before completing the requested task, +C but the integration was successful as far as T. The +C problem may have a singularity, or the input may be +C inappropriate. +C -5 There were repeated convergence-test failures on one +C attempted step, before completing the requested task, +C but the integration was successful as far as T. This +C may be caused by an inaccurate Jacobian matrix, if +C one is being used. +C -6 EWT(i) became zero for some i during the integration. +C Pure relative error control (ATOL(i)=0.0) was +C requested on a variable which has now vanished. The +C integration was successful as far as T. +C +C Note: Since the normal output value of ISTATE is 2, it +C does not need to be reset for normal continuation. Also, +C since a negative input value of ISTATE will be regarded +C as illegal, a negative output value requires the user to +C change it, and possibly other inputs, before calling the +C solver again. +C +C IOPT An integer flag to specify whether any optional inputs +C are being used on this call. Input only. The optional +C inputs are listed under a separate heading below. +C 0 No optional inputs are being used. Default values +C will be used in all cases. +C 1 One or more optional inputs are being used. +C +C RWORK A real working array (double precision). The length of +C RWORK must be at least +C +C 20 + NYH*(MAXORD + 1) + 3*NEQ + LWM +C +C where +C NYH = the initial value of NEQ, +C MAXORD = 12 (if METH = 1) or 5 (if METH = 2) (unless a +C smaller value is given as an optional input), +C LWM = 0 if MITER = 0, +C LWM = NEQ**2 + 2 if MITER = 1 or 2, +C LWM = NEQ + 2 if MITER = 3, and +C LWM = (2*ML + MU + 1)*NEQ + 2 +C if MITER = 4 or 5. +C (See the MF description below for METH and MITER.) +C +C Thus if MAXORD has its default value and NEQ is constant, +C this length is: +C 20 + 16*NEQ for MF = 10, +C 22 + 16*NEQ + NEQ**2 for MF = 11 or 12, +C 22 + 17*NEQ for MF = 13, +C 22 + 17*NEQ + (2*ML + MU)*NEQ for MF = 14 or 15, +C 20 + 9*NEQ for MF = 20, +C 22 + 9*NEQ + NEQ**2 for MF = 21 or 22, +C 22 + 10*NEQ for MF = 23, +C 22 + 10*NEQ + (2*ML + MU)*NEQ for MF = 24 or 25. +C +C The first 20 words of RWORK are reserved for conditional +C and optional inputs and optional outputs. +C +C The following word in RWORK is a conditional input: +C RWORK(1) = TCRIT, the critical value of t which the +C solver is not to overshoot. Required if ITASK +C is 4 or 5, and ignored otherwise. See ITASK. +C +C LRW The length of the array RWORK, as declared by the user. +C (This will be checked by the solver.) +C +C IWORK An integer work array. Its length must be at least +C 20 if MITER = 0 or 3 (MF = 10, 13, 20, 23), or +C 20 + NEQ otherwise (MF = 11, 12, 14, 15, 21, 22, 24, 25). +C (See the MF description below for MITER.) The first few +C words of IWORK are used for conditional and optional +C inputs and optional outputs. +C +C The following two words in IWORK are conditional inputs: +C IWORK(1) = ML These are the lower and upper half- +C IWORK(2) = MU bandwidths, respectively, of the banded +C Jacobian, excluding the main diagonal. +C The band is defined by the matrix locations +C (i,j) with i - ML <= j <= i + MU. ML and MU +C must satisfy 0 <= ML,MU <= NEQ - 1. These are +C required if MITER is 4 or 5, and ignored +C otherwise. ML and MU may in fact be the band +C parameters for a matrix to which df/dy is only +C approximately equal. +C +C LIW The length of the array IWORK, as declared by the user. +C (This will be checked by the solver.) +C +C Note: The work arrays must not be altered between calls to DLSODE +C for the same problem, except possibly for the conditional and +C optional inputs, and except for the last 3*NEQ words of RWORK. +C The latter space is used for internal scratch space, and so is +C available for use by the user outside DLSODE between calls, if +C desired (but not for use by F or JAC). +C +C JAC The name of the user-supplied routine (MITER = 1 or 4) to +C compute the Jacobian matrix, df/dy, as a function of the +C scalar t and the vector y. (See the MF description below +C for MITER.) It is to have the form +C +C SUBROUTINE JAC (NEQ, T, Y, ML, MU, PD, NROWPD) +C DOUBLE PRECISION T, Y(*), PD(NROWPD,*) +C +C where NEQ, T, Y, ML, MU, and NROWPD are input and the +C array PD is to be loaded with partial derivatives +C (elements of the Jacobian matrix) on output. PD must be +C given a first dimension of NROWPD. T and Y have the same +C meaning as in subroutine F. +C +C In the full matrix case (MITER = 1), ML and MU are +C ignored, and the Jacobian is to be loaded into PD in +C columnwise manner, with df(i)/dy(j) loaded into PD(i,j). +C +C In the band matrix case (MITER = 4), the elements within +C the band are to be loaded into PD in columnwise manner, +C with diagonal lines of df/dy loaded into the rows of PD. +C Thus df(i)/dy(j) is to be loaded into PD(i-j+MU+1,j). ML +C and MU are the half-bandwidth parameters (see IWORK). +C The locations in PD in the two triangular areas which +C correspond to nonexistent matrix elements can be ignored +C or loaded arbitrarily, as they are overwritten by DLSODE. +C +C JAC need not provide df/dy exactly. A crude approximation +C (possibly with a smaller bandwidth) will do. +C +C In either case, PD is preset to zero by the solver, so +C that only the nonzero elements need be loaded by JAC. +C Each call to JAC is preceded by a call to F with the same +C arguments NEQ, T, and Y. Thus to gain some efficiency, +C intermediate quantities shared by both calculations may +C be saved in a user COMMON block by F and not recomputed +C by JAC, if desired. Also, JAC may alter the Y array, if +C desired. JAC must be declared EXTERNAL in the calling +C program. +C +C Subroutine JAC may access user-defined quantities in +C NEQ(2),... and/or in Y(NEQ(1)+1),... if NEQ is an array +C (dimensioned in JAC) and/or Y has length exceeding +C NEQ(1). See the descriptions of NEQ and Y above. +C +C MF The method flag. Used only for input. The legal values +C of MF are 10, 11, 12, 13, 14, 15, 20, 21, 22, 23, 24, +C and 25. MF has decimal digits METH and MITER: +C MF = 10*METH + MITER . +C +C METH indicates the basic linear multistep method: +C 1 Implicit Adams method. +C 2 Method based on backward differentiation formulas +C (BDF's). +C +C MITER indicates the corrector iteration method: +C 0 Functional iteration (no Jacobian matrix is +C involved). +C 1 Chord iteration with a user-supplied full (NEQ by +C NEQ) Jacobian. +C 2 Chord iteration with an internally generated +C (difference quotient) full Jacobian (using NEQ +C extra calls to F per df/dy value). +C 3 Chord iteration with an internally generated +C diagonal Jacobian approximation (using one extra call +C to F per df/dy evaluation). +C 4 Chord iteration with a user-supplied banded Jacobian. +C 5 Chord iteration with an internally generated banded +C Jacobian (using ML + MU + 1 extra calls to F per +C df/dy evaluation). +C +C If MITER = 1 or 4, the user must supply a subroutine JAC +C (the name is arbitrary) as described above under JAC. +C For other values of MITER, a dummy argument can be used. +C +C Optional Inputs +C --------------- +C The following is a list of the optional inputs provided for in the +C call sequence. (See also Part 2.) For each such input variable, +C this table lists its name as used in this documentation, its +C location in the call sequence, its meaning, and the default value. +C The use of any of these inputs requires IOPT = 1, and in that case +C all of these inputs are examined. A value of zero for any of +C these optional inputs will cause the default value to be used. +C Thus to use a subset of the optional inputs, simply preload +C locations 5 to 10 in RWORK and IWORK to 0.0 and 0 respectively, +C and then set those of interest to nonzero values. +C +C Name Location Meaning and default value +C ------ --------- ----------------------------------------------- +C H0 RWORK(5) Step size to be attempted on the first step. +C The default value is determined by the solver. +C HMAX RWORK(6) Maximum absolute step size allowed. The +C default value is infinite. +C HMIN RWORK(7) Minimum absolute step size allowed. The +C default value is 0. (This lower bound is not +C enforced on the final step before reaching +C TCRIT when ITASK = 4 or 5.) +C MAXORD IWORK(5) Maximum order to be allowed. The default value +C is 12 if METH = 1, and 5 if METH = 2. (See the +C MF description above for METH.) If MAXORD +C exceeds the default value, it will be reduced +C to the default value. If MAXORD is changed +C during the problem, it may cause the current +C order to be reduced. +C MXSTEP IWORK(6) Maximum number of (internally defined) steps +C allowed during one call to the solver. The +C default value is 500. +C MXHNIL IWORK(7) Maximum number of messages printed (per +C problem) warning that T + H = T on a step +C (H = step size). This must be positive to +C result in a nondefault value. The default +C value is 10. +C +C Optional Outputs +C ---------------- +C As optional additional output from DLSODE, the variables listed +C below are quantities related to the performance of DLSODE which +C are available to the user. These are communicated by way of the +C work arrays, but also have internal mnemonic names as shown. +C Except where stated otherwise, all of these outputs are defined on +C any successful return from DLSODE, and on any return with ISTATE = +C -1, -2, -4, -5, or -6. On an illegal input return (ISTATE = -3), +C they will be unchanged from their existing values (if any), except +C possibly for TOLSF, LENRW, and LENIW. On any error return, +C outputs relevant to the error will be defined, as noted below. +C +C Name Location Meaning +C ----- --------- ------------------------------------------------ +C HU RWORK(11) Step size in t last used (successfully). +C HCUR RWORK(12) Step size to be attempted on the next step. +C TCUR RWORK(13) Current value of the independent variable which +C the solver has actually reached, i.e., the +C current internal mesh point in t. On output, +C TCUR will always be at least as far as the +C argument T, but may be farther (if interpolation +C was done). +C TOLSF RWORK(14) Tolerance scale factor, greater than 1.0, +C computed when a request for too much accuracy +C was detected (ISTATE = -3 if detected at the +C start of the problem, ISTATE = -2 otherwise). +C If ITOL is left unaltered but RTOL and ATOL are +C uniformly scaled up by a factor of TOLSF for the +C next call, then the solver is deemed likely to +C succeed. (The user may also ignore TOLSF and +C alter the tolerance parameters in any other way +C appropriate.) +C NST IWORK(11) Number of steps taken for the problem so far. +C NFE IWORK(12) Number of F evaluations for the problem so far. +C NJE IWORK(13) Number of Jacobian evaluations (and of matrix LU +C decompositions) for the problem so far. +C NQU IWORK(14) Method order last used (successfully). +C NQCUR IWORK(15) Order to be attempted on the next step. +C IMXER IWORK(16) Index of the component of largest magnitude in +C the weighted local error vector ( e(i)/EWT(i) ), +C on an error return with ISTATE = -4 or -5. +C LENRW IWORK(17) Length of RWORK actually required. This is +C defined on normal returns and on an illegal +C input return for insufficient storage. +C LENIW IWORK(18) Length of IWORK actually required. This is +C defined on normal returns and on an illegal +C input return for insufficient storage. +C +C The following two arrays are segments of the RWORK array which may +C also be of interest to the user as optional outputs. For each +C array, the table below gives its internal name, its base address +C in RWORK, and its description. +C +C Name Base address Description +C ---- ------------ ---------------------------------------------- +C YH 21 The Nordsieck history array, of size NYH by +C (NQCUR + 1), where NYH is the initial value of +C NEQ. For j = 0,1,...,NQCUR, column j + 1 of +C YH contains HCUR**j/factorial(j) times the jth +C derivative of the interpolating polynomial +C currently representing the solution, evaluated +C at t = TCUR. +C ACOR LENRW-NEQ+1 Array of size NEQ used for the accumulated +C corrections on each step, scaled on output to +C represent the estimated local error in Y on +C the last step. This is the vector e in the +C description of the error control. It is +C defined only on successful return from DLSODE. +C +C +C Part 2. Other Callable Routines +C -------------------------------- +C +C The following are optional calls which the user may make to gain +C additional capabilities in conjunction with DLSODE. +C +C Form of call Function +C ------------------------ ---------------------------------------- +C CALL XSETUN(LUN) Set the logical unit number, LUN, for +C output of messages from DLSODE, if the +C default is not desired. The default +C value of LUN is 6. This call may be made +C at any time and will take effect +C immediately. +C CALL XSETF(MFLAG) Set a flag to control the printing of +C messages by DLSODE. MFLAG = 0 means do +C not print. (Danger: this risks losing +C valuable information.) MFLAG = 1 means +C print (the default). This call may be +C made at any time and will take effect +C immediately. +C CALL DSRCOM(RSAV,ISAV,JOB) Saves and restores the contents of the +C internal COMMON blocks used by DLSODE +C (see Part 3 below). RSAV must be a +C real array of length 218 or more, and +C ISAV must be an integer array of length +C 37 or more. JOB = 1 means save COMMON +C into RSAV/ISAV. JOB = 2 means restore +C COMMON from same. DSRCOM is useful if +C one is interrupting a run and restarting +C later, or alternating between two or +C more problems solved with DLSODE. +C CALL DINTDY(,,,,,) Provide derivatives of y, of various +C (see below) orders, at a specified point t, if +C desired. It may be called only after a +C successful return from DLSODE. Detailed +C instructions follow. +C +C Detailed instructions for using DINTDY +C -------------------------------------- +C The form of the CALL is: +C +C CALL DINTDY (T, K, RWORK(21), NYH, DKY, IFLAG) +C +C The input parameters are: +C +C T Value of independent variable where answers are +C desired (normally the same as the T last returned by +C DLSODE). For valid results, T must lie between +C TCUR - HU and TCUR. (See "Optional Outputs" above +C for TCUR and HU.) +C K Integer order of the derivative desired. K must +C satisfy 0 <= K <= NQCUR, where NQCUR is the current +C order (see "Optional Outputs"). The capability +C corresponding to K = 0, i.e., computing y(t), is +C already provided by DLSODE directly. Since +C NQCUR >= 1, the first derivative dy/dt is always +C available with DINTDY. +C RWORK(21) The base address of the history array YH. +C NYH Column length of YH, equal to the initial value of NEQ. +C +C The output parameters are: +C +C DKY Real array of length NEQ containing the computed value +C of the Kth derivative of y(t). +C IFLAG Integer flag, returned as 0 if K and T were legal, +C -1 if K was illegal, and -2 if T was illegal. +C On an error return, a message is also written. +C +C +C Part 3. Common Blocks +C ---------------------- +C +C If DLSODE is to be used in an overlay situation, the user must +C declare, in the primary overlay, the variables in: +C (1) the call sequence to DLSODE, +C (2) the internal COMMON block /DLS001/, of length 255 +C (218 double precision words followed by 37 integer words). +C +C If DLSODE is used on a system in which the contents of internal +C COMMON blocks are not preserved between calls, the user should +C declare the above COMMON block in his main program to insure that +C its contents are preserved. +C +C If the solution of a given problem by DLSODE is to be interrupted +C and then later continued, as when restarting an interrupted run or +C alternating between two or more problems, the user should save, +C following the return from the last DLSODE call prior to the +C interruption, the contents of the call sequence variables and the +C internal COMMON block, and later restore these values before the +C next DLSODE call for that problem. In addition, if XSETUN and/or +C XSETF was called for non-default handling of error messages, then +C these calls must be repeated. To save and restore the COMMON +C block, use subroutine DSRCOM (see Part 2 above). +C +C +C Part 4. Optionally Replaceable Solver Routines +C ----------------------------------------------- +C +C Below are descriptions of two routines in the DLSODE package which +C relate to the measurement of errors. Either routine can be +C replaced by a user-supplied version, if desired. However, since +C such a replacement may have a major impact on performance, it +C should be done only when absolutely necessary, and only with great +C caution. (Note: The means by which the package version of a +C routine is superseded by the user's version may be system- +C dependent.) +C +C DEWSET +C ------ +C The following subroutine is called just before each internal +C integration step, and sets the array of error weights, EWT, as +C described under ITOL/RTOL/ATOL above: +C +C SUBROUTINE DEWSET (NEQ, ITOL, RTOL, ATOL, YCUR, EWT) +C +C where NEQ, ITOL, RTOL, and ATOL are as in the DLSODE call +C sequence, YCUR contains the current dependent variable vector, +C and EWT is the array of weights set by DEWSET. +C +C If the user supplies this subroutine, it must return in EWT(i) +C (i = 1,...,NEQ) a positive quantity suitable for comparing errors +C in Y(i) to. The EWT array returned by DEWSET is passed to the +C DVNORM routine (see below), and also used by DLSODE in the +C computation of the optional output IMXER, the diagonal Jacobian +C approximation, and the increments for difference quotient +C Jacobians. +C +C In the user-supplied version of DEWSET, it may be desirable to use +C the current values of derivatives of y. Derivatives up to order NQ +C are available from the history array YH, described above under +C optional outputs. In DEWSET, YH is identical to the YCUR array, +C extended to NQ + 1 columns with a column length of NYH and scale +C factors of H**j/factorial(j). On the first call for the problem, +C given by NST = 0, NQ is 1 and H is temporarily set to 1.0. +C NYH is the initial value of NEQ. The quantities NQ, H, and NST +C can be obtained by including in SEWSET the statements: +C DOUBLE PRECISION RLS +C COMMON /DLS001/ RLS(218),ILS(37) +C NQ = ILS(33) +C NST = ILS(34) +C H = RLS(212) +C Thus, for example, the current value of dy/dt can be obtained as +C YCUR(NYH+i)/H (i=1,...,NEQ) (and the division by H is unnecessary +C when NST = 0). +C +C DVNORM +C ------ +C DVNORM is a real function routine which computes the weighted +C root-mean-square norm of a vector v: +C +C d = DVNORM (n, v, w) +C +C where: +C n = the length of the vector, +C v = real array of length n containing the vector, +C w = real array of length n containing weights, +C d = SQRT( (1/n) * sum(v(i)*w(i))**2 ). +C +C DVNORM is called with n = NEQ and with w(i) = 1.0/EWT(i), where +C EWT is as set by subroutine DEWSET. +C +C If the user supplies this function, it should return a nonnegative +C value of DVNORM suitable for use in the error control in DLSODE. +C None of the arguments should be altered by DVNORM. For example, a +C user-supplied DVNORM routine might: +C - Substitute a max-norm of (v(i)*w(i)) for the rms-norm, or +C - Ignore some components of v in the norm, with the effect of +C suppressing the error control on those components of Y. +C --------------------------------------------------------------------- +C***ROUTINES CALLED DEWSET, DINTDY, DUMACH, DSTODE, DVNORM, XERRWD +C***COMMON BLOCKS DLS001 +C***REVISION HISTORY (YYYYMMDD) +C 19791129 DATE WRITTEN +C 19791213 Minor changes to declarations; DELP init. in STODE. +C 19800118 Treat NEQ as array; integer declarations added throughout; +C minor changes to prologue. +C 19800306 Corrected TESCO(1,NQP1) setting in CFODE. +C 19800519 Corrected access of YH on forced order reduction; +C numerous corrections to prologues and other comments. +C 19800617 In main driver, added loading of SQRT(UROUND) in RWORK; +C minor corrections to main prologue. +C 19800923 Added zero initialization of HU and NQU. +C 19801218 Revised XERRWD routine; minor corrections to main prologue. +C 19810401 Minor changes to comments and an error message. +C 19810814 Numerous revisions: replaced EWT by 1/EWT; used flags +C JCUR, ICF, IERPJ, IERSL between STODE and subordinates; +C added tuning parameters CCMAX, MAXCOR, MSBP, MXNCF; +C reorganized returns from STODE; reorganized type decls.; +C fixed message length in XERRWD; changed default LUNIT to 6; +C changed Common lengths; changed comments throughout. +C 19870330 Major update by ACH: corrected comments throughout; +C removed TRET from Common; rewrote EWSET with 4 loops; +C fixed t test in INTDY; added Cray directives in STODE; +C in STODE, fixed DELP init. and logic around PJAC call; +C combined routines to save/restore Common; +C passed LEVEL = 0 in error message calls (except run abort). +C 19890426 Modified prologue to SLATEC/LDOC format. (FNF) +C 19890501 Many improvements to prologue. (FNF) +C 19890503 A few final corrections to prologue. (FNF) +C 19890504 Minor cosmetic changes. (FNF) +C 19890510 Corrected description of Y in Arguments section. (FNF) +C 19890517 Minor corrections to prologue. (FNF) +C 19920514 Updated with prologue edited 891025 by G. Shaw for manual. +C 19920515 Converted source lines to upper case. (FNF) +C 19920603 Revised XERRWD calls using mixed upper-lower case. (ACH) +C 19920616 Revised prologue comment regarding CFT. (ACH) +C 19921116 Revised prologue comments regarding Common. (ACH). +C 19930326 Added comment about non-reentrancy. (FNF) +C 19930723 Changed D1MACH to DUMACH. (FNF) +C 19930801 Removed ILLIN and NTREP from Common (affects driver logic); +C minor changes to prologue and internal comments; +C changed Hollerith strings to quoted strings; +C changed internal comments to mixed case; +C replaced XERRWD with new version using character type; +C changed dummy dimensions from 1 to *. (ACH) +C 19930809 Changed to generic intrinsic names; changed names of +C subprograms and Common blocks to DLSODE etc. (ACH) +C 19930929 Eliminated use of REAL intrinsic; other minor changes. (ACH) +C 20010412 Removed all 'own' variables from Common block /DLS001/ +C (affects declarations in 6 routines). (ACH) +C 20010509 Minor corrections to prologue. (ACH) +C 20031105 Restored 'own' variables to Common block /DLS001/, to +C enable interrupt/restart feature. (ACH) +C 20031112 Added SAVE statements for data-loaded constants. +C +C***END PROLOGUE DLSODE +C +C*Internal Notes: +C +C Other Routines in the DLSODE Package. +C +C In addition to Subroutine DLSODE, the DLSODE package includes the +C following subroutines and function routines: +C DINTDY computes an interpolated value of the y vector at t = TOUT. +C DSTODE is the core integrator, which does one step of the +C integration and the associated error control. +C DCFODE sets all method coefficients and test constants. +C DPREPJ computes and preprocesses the Jacobian matrix J = df/dy +C and the Newton iteration matrix P = I - h*l0*J. +C DSOLSY manages solution of linear system in chord iteration. +C DEWSET sets the error weight vector EWT before each step. +C DVNORM computes the weighted R.M.S. norm of a vector. +C DSRCOM is a user-callable routine to save and restore +C the contents of the internal Common block. +C DGEFA and DGESL are routines from LINPACK for solving full +C systems of linear algebraic equations. +C DGBFA and DGBSL are routines from LINPACK for solving banded +C linear systems. +C DUMACH computes the unit roundoff in a machine-independent manner. +C XERRWD, XSETUN, XSETF, IXSAV, IUMACH handle the printing of all +C error messages and warnings. XERRWD is machine-dependent. +C Note: DVNORM, DUMACH, IXSAV, and IUMACH are function routines. +C All the others are subroutines. +C +C**End +C +C Declare externals. + EXTERNAL DPREPJ, DSOLSY + DOUBLE PRECISION DUMACH, DVNORM +C +C Declare all other variables. + INTEGER INIT, MXSTEP, MXHNIL, NHNIL, NSLAST, NYH, IOWNS, + 1 ICF, IERPJ, IERSL, JCUR, JSTART, KFLAG, L, + 2 LYH, LEWT, LACOR, LSAVF, LWM, LIWM, METH, MITER, + 3 MAXORD, MAXCOR, MSBP, MXNCF, N, NQ, NST, NFE, NJE, NQU + INTEGER I, I1, I2, IFLAG, IMXER, KGO, LF0, + 1 LENIW, LENRW, LENWM, ML, MORD, MU, MXHNL0, MXSTP0 + DOUBLE PRECISION ROWNS, + 1 CCMAX, EL0, H, HMIN, HMXI, HU, RC, TN, UROUND + DOUBLE PRECISION ATOLI, AYI, BIG, EWTI, H0, HMAX, HMX, RH, RTOLI, + 1 TCRIT, TDIST, TNEXT, TOL, TOLSF, TP, SIZE, SUM, W0 + DIMENSION MORD(2) + LOGICAL IHIT + CHARACTER*80 MSG + SAVE MORD, MXSTP0, MXHNL0 +C----------------------------------------------------------------------- +C The following internal Common block contains +C (a) variables which are local to any subroutine but whose values must +C be preserved between calls to the routine ("own" variables), and +C (b) variables which are communicated between subroutines. +C The block DLS001 is declared in subroutines DLSODE, DINTDY, DSTODE, +C DPREPJ, and DSOLSY. +C Groups of variables are replaced by dummy arrays in the Common +C declarations in routines where those variables are not used. +C----------------------------------------------------------------------- + COMMON /DLS001/ ROWNS(209), + 1 CCMAX, EL0, H, HMIN, HMXI, HU, RC, TN, UROUND, + 2 INIT, MXSTEP, MXHNIL, NHNIL, NSLAST, NYH, IOWNS(6), + 3 ICF, IERPJ, IERSL, JCUR, JSTART, KFLAG, L, + 4 LYH, LEWT, LACOR, LSAVF, LWM, LIWM, METH, MITER, + 5 MAXORD, MAXCOR, MSBP, MXNCF, N, NQ, NST, NFE, NJE, NQU +C + DATA MORD(1),MORD(2)/12,5/, MXSTP0/500/, MXHNL0/10/ +C----------------------------------------------------------------------- +C Block A. +C This code block is executed on every call. +C It tests ISTATE and ITASK for legality and branches appropriately. +C If ISTATE .GT. 1 but the flag INIT shows that initialization has +C not yet been done, an error return occurs. +C If ISTATE = 1 and TOUT = T, return immediately. +C----------------------------------------------------------------------- +C +C***FIRST EXECUTABLE STATEMENT DLSODE + IF (ISTATE .LT. 1 .OR. ISTATE .GT. 3) GO TO 601 + IF (ITASK .LT. 1 .OR. ITASK .GT. 5) GO TO 602 + IF (ISTATE .EQ. 1) GO TO 10 + IF (INIT .EQ. 0) GO TO 603 + IF (ISTATE .EQ. 2) GO TO 200 + GO TO 20 + 10 INIT = 0 + IF (TOUT .EQ. T) RETURN +C----------------------------------------------------------------------- +C Block B. +C The next code block is executed for the initial call (ISTATE = 1), +C or for a continuation call with parameter changes (ISTATE = 3). +C It contains checking of all inputs and various initializations. +C +C First check legality of the non-optional inputs NEQ, ITOL, IOPT, +C MF, ML, and MU. +C----------------------------------------------------------------------- + 20 IF (NEQ(1) .LE. 0) GO TO 604 + IF (ISTATE .EQ. 1) GO TO 25 + IF (NEQ(1) .GT. N) GO TO 605 + 25 N = NEQ(1) + IF (ITOL .LT. 1 .OR. ITOL .GT. 4) GO TO 606 + IF (IOPT .LT. 0 .OR. IOPT .GT. 1) GO TO 607 + METH = MF/10 + MITER = MF - 10*METH + IF (METH .LT. 1 .OR. METH .GT. 2) GO TO 608 + IF (MITER .LT. 0 .OR. MITER .GT. 5) GO TO 608 + IF (MITER .LE. 3) GO TO 30 + ML = IWORK(1) + MU = IWORK(2) + IF (ML .LT. 0 .OR. ML .GE. N) GO TO 609 + IF (MU .LT. 0 .OR. MU .GE. N) GO TO 610 + 30 CONTINUE +C Next process and check the optional inputs. -------------------------- + IF (IOPT .EQ. 1) GO TO 40 + MAXORD = MORD(METH) + MXSTEP = MXSTP0 + MXHNIL = MXHNL0 + IF (ISTATE .EQ. 1) H0 = 0.0D0 + HMXI = 0.0D0 + HMIN = 0.0D0 + GO TO 60 + 40 MAXORD = IWORK(5) + IF (MAXORD .LT. 0) GO TO 611 + IF (MAXORD .EQ. 0) MAXORD = 100 + MAXORD = MIN(MAXORD,MORD(METH)) + MXSTEP = IWORK(6) + IF (MXSTEP .LT. 0) GO TO 612 + IF (MXSTEP .EQ. 0) MXSTEP = MXSTP0 + MXHNIL = IWORK(7) + IF (MXHNIL .LT. 0) GO TO 613 + IF (MXHNIL .EQ. 0) MXHNIL = MXHNL0 + IF (ISTATE .NE. 1) GO TO 50 + H0 = RWORK(5) + IF ((TOUT - T)*H0 .LT. 0.0D0) GO TO 614 + 50 HMAX = RWORK(6) + IF (HMAX .LT. 0.0D0) GO TO 615 + HMXI = 0.0D0 + IF (HMAX .GT. 0.0D0) HMXI = 1.0D0/HMAX + HMIN = RWORK(7) + IF (HMIN .LT. 0.0D0) GO TO 616 +C----------------------------------------------------------------------- +C Set work array pointers and check lengths LRW and LIW. +C Pointers to segments of RWORK and IWORK are named by prefixing L to +C the name of the segment. E.g., the segment YH starts at RWORK(LYH). +C Segments of RWORK (in order) are denoted YH, WM, EWT, SAVF, ACOR. +C----------------------------------------------------------------------- + 60 LYH = 21 + IF (ISTATE .EQ. 1) NYH = N + LWM = LYH + (MAXORD + 1)*NYH + IF (MITER .EQ. 0) LENWM = 0 + IF (MITER .EQ. 1 .OR. MITER .EQ. 2) LENWM = N*N + 2 + IF (MITER .EQ. 3) LENWM = N + 2 + IF (MITER .GE. 4) LENWM = (2*ML + MU + 1)*N + 2 + LEWT = LWM + LENWM + LSAVF = LEWT + N + LACOR = LSAVF + N + LENRW = LACOR + N - 1 + IWORK(17) = LENRW + LIWM = 1 + LENIW = 20 + N + IF (MITER .EQ. 0 .OR. MITER .EQ. 3) LENIW = 20 + IWORK(18) = LENIW + IF (LENRW .GT. LRW) GO TO 617 + IF (LENIW .GT. LIW) GO TO 618 +C Check RTOL and ATOL for legality. ------------------------------------ + RTOLI = RTOL(1) + ATOLI = ATOL(1) + DO 70 I = 1,N + IF (ITOL .GE. 3) RTOLI = RTOL(I) + IF (ITOL .EQ. 2 .OR. ITOL .EQ. 4) ATOLI = ATOL(I) + IF (RTOLI .LT. 0.0D0) GO TO 619 + IF (ATOLI .LT. 0.0D0) GO TO 620 + 70 CONTINUE + IF (ISTATE .EQ. 1) GO TO 100 +C If ISTATE = 3, set flag to signal parameter changes to DSTODE. ------- + JSTART = -1 + IF (NQ .LE. MAXORD) GO TO 90 +C MAXORD was reduced below NQ. Copy YH(*,MAXORD+2) into SAVF. --------- + DO 80 I = 1,N + 80 RWORK(I+LSAVF-1) = RWORK(I+LWM-1) +C Reload WM(1) = RWORK(LWM), since LWM may have changed. --------------- + 90 IF (MITER .GT. 0) RWORK(LWM) = SQRT(UROUND) + IF (N .EQ. NYH) GO TO 200 +C NEQ was reduced. Zero part of YH to avoid undefined references. ----- + I1 = LYH + L*NYH + I2 = LYH + (MAXORD + 1)*NYH - 1 + IF (I1 .GT. I2) GO TO 200 + DO 95 I = I1,I2 + 95 RWORK(I) = 0.0D0 + GO TO 200 +C----------------------------------------------------------------------- +C Block C. +C The next block is for the initial call only (ISTATE = 1). +C It contains all remaining initializations, the initial call to F, +C and the calculation of the initial step size. +C The error weights in EWT are inverted after being loaded. +C----------------------------------------------------------------------- + 100 UROUND = DUMACH() + TN = T + IF (ITASK .NE. 4 .AND. ITASK .NE. 5) GO TO 110 + TCRIT = RWORK(1) + IF ((TCRIT - TOUT)*(TOUT - T) .LT. 0.0D0) GO TO 625 + IF (H0 .NE. 0.0D0 .AND. (T + H0 - TCRIT)*H0 .GT. 0.0D0) + 1 H0 = TCRIT - T + 110 JSTART = 0 + IF (MITER .GT. 0) RWORK(LWM) = SQRT(UROUND) + NHNIL = 0 + NST = 0 + NJE = 0 + NSLAST = 0 + HU = 0.0D0 + NQU = 0 + CCMAX = 0.3D0 + MAXCOR = 3 + MSBP = 20 + MXNCF = 10 +C Initial call to F. (LF0 points to YH(*,2).) ------------------------- + LF0 = LYH + NYH + CALL F (NEQ, T, Y, RWORK(LF0)) + NFE = 1 +C Load the initial value vector in YH. --------------------------------- + DO 115 I = 1,N + 115 RWORK(I+LYH-1) = Y(I) +C Load and invert the EWT array. (H is temporarily set to 1.0.) ------- + NQ = 1 + H = 1.0D0 + CALL DEWSET (N, ITOL, RTOL, ATOL, RWORK(LYH), RWORK(LEWT)) + DO 120 I = 1,N + IF (RWORK(I+LEWT-1) .LE. 0.0D0) GO TO 621 + 120 RWORK(I+LEWT-1) = 1.0D0/RWORK(I+LEWT-1) +C----------------------------------------------------------------------- +C The coding below computes the step size, H0, to be attempted on the +C first step, unless the user has supplied a value for this. +C First check that TOUT - T differs significantly from zero. +C A scalar tolerance quantity TOL is computed, as MAX(RTOL(I)) +C if this is positive, or MAX(ATOL(I)/ABS(Y(I))) otherwise, adjusted +C so as to be between 100*UROUND and 1.0E-3. +C Then the computed value H0 is given by.. +C NEQ +C H0**2 = TOL / ( w0**-2 + (1/NEQ) * SUM ( f(i)/ywt(i) )**2 ) +C 1 +C where w0 = MAX ( ABS(T), ABS(TOUT) ), +C f(i) = i-th component of initial value of f, +C ywt(i) = EWT(i)/TOL (a weight for y(i)). +C The sign of H0 is inferred from the initial values of TOUT and T. +C----------------------------------------------------------------------- + IF (H0 .NE. 0.0D0) GO TO 180 + TDIST = ABS(TOUT - T) + W0 = MAX(ABS(T),ABS(TOUT)) + IF (TDIST .LT. 2.0D0*UROUND*W0) GO TO 622 + TOL = RTOL(1) + IF (ITOL .LE. 2) GO TO 140 + DO 130 I = 1,N + 130 TOL = MAX(TOL,RTOL(I)) + 140 IF (TOL .GT. 0.0D0) GO TO 160 + ATOLI = ATOL(1) + DO 150 I = 1,N + IF (ITOL .EQ. 2 .OR. ITOL .EQ. 4) ATOLI = ATOL(I) + AYI = ABS(Y(I)) + IF (AYI .NE. 0.0D0) TOL = MAX(TOL,ATOLI/AYI) + 150 CONTINUE + 160 TOL = MAX(TOL,100.0D0*UROUND) + TOL = MIN(TOL,0.001D0) + SUM = DVNORM (N, RWORK(LF0), RWORK(LEWT)) + SUM = 1.0D0/(TOL*W0*W0) + TOL*SUM**2 + H0 = 1.0D0/SQRT(SUM) + H0 = MIN(H0,TDIST) + H0 = SIGN(H0,TOUT-T) +C Adjust H0 if necessary to meet HMAX bound. --------------------------- + 180 RH = ABS(H0)*HMXI + IF (RH .GT. 1.0D0) H0 = H0/RH +C Load H with H0 and scale YH(*,2) by H0. ------------------------------ + H = H0 + DO 190 I = 1,N + 190 RWORK(I+LF0-1) = H0*RWORK(I+LF0-1) + GO TO 270 +C----------------------------------------------------------------------- +C Block D. +C The next code block is for continuation calls only (ISTATE = 2 or 3) +C and is to check stop conditions before taking a step. +C----------------------------------------------------------------------- + 200 NSLAST = NST + GO TO (210, 250, 220, 230, 240), ITASK + 210 IF ((TN - TOUT)*H .LT. 0.0D0) GO TO 250 + CALL DINTDY (TOUT, 0, RWORK(LYH), NYH, Y, IFLAG) + IF (IFLAG .NE. 0) GO TO 627 + T = TOUT + GO TO 420 + 220 TP = TN - HU*(1.0D0 + 100.0D0*UROUND) + IF ((TP - TOUT)*H .GT. 0.0D0) GO TO 623 + IF ((TN - TOUT)*H .LT. 0.0D0) GO TO 250 + GO TO 400 + 230 TCRIT = RWORK(1) + IF ((TN - TCRIT)*H .GT. 0.0D0) GO TO 624 + IF ((TCRIT - TOUT)*H .LT. 0.0D0) GO TO 625 + IF ((TN - TOUT)*H .LT. 0.0D0) GO TO 245 + CALL DINTDY (TOUT, 0, RWORK(LYH), NYH, Y, IFLAG) + IF (IFLAG .NE. 0) GO TO 627 + T = TOUT + GO TO 420 + 240 TCRIT = RWORK(1) + IF ((TN - TCRIT)*H .GT. 0.0D0) GO TO 624 + 245 HMX = ABS(TN) + ABS(H) + IHIT = ABS(TN - TCRIT) .LE. 100.0D0*UROUND*HMX + IF (IHIT) GO TO 400 + TNEXT = TN + H*(1.0D0 + 4.0D0*UROUND) + IF ((TNEXT - TCRIT)*H .LE. 0.0D0) GO TO 250 + H = (TCRIT - TN)*(1.0D0 - 4.0D0*UROUND) + IF (ISTATE .EQ. 2) JSTART = -2 +C----------------------------------------------------------------------- +C Block E. +C The next block is normally executed for all calls and contains +C the call to the one-step core integrator DSTODE. +C +C This is a looping point for the integration steps. +C +C First check for too many steps being taken, update EWT (if not at +C start of problem), check for too much accuracy being requested, and +C check for H below the roundoff level in T. +C----------------------------------------------------------------------- + 250 CONTINUE + IF ((NST-NSLAST) .GE. MXSTEP) GO TO 500 + CALL DEWSET (N, ITOL, RTOL, ATOL, RWORK(LYH), RWORK(LEWT)) + DO 260 I = 1,N + IF (RWORK(I+LEWT-1) .LE. 0.0D0) GO TO 510 + 260 RWORK(I+LEWT-1) = 1.0D0/RWORK(I+LEWT-1) + 270 TOLSF = UROUND*DVNORM (N, RWORK(LYH), RWORK(LEWT)) + IF (TOLSF .LE. 1.0D0) GO TO 280 + TOLSF = TOLSF*2.0D0 + IF (NST .EQ. 0) GO TO 626 + GO TO 520 + 280 IF ((TN + H) .NE. TN) GO TO 290 + NHNIL = NHNIL + 1 + IF (NHNIL .GT. MXHNIL) GO TO 290 + MSG = 'DLSODE- Warning..internal T (=R1) and H (=R2) are' + CALL XERRWD (MSG, 50, 101, 0, 0, 0, 0, 0, 0.0D0, 0.0D0) + MSG=' such that in the machine, T + H = T on the next step ' + CALL XERRWD (MSG, 60, 101, 0, 0, 0, 0, 0, 0.0D0, 0.0D0) + MSG = ' (H = step size). Solver will continue anyway' + CALL XERRWD (MSG, 50, 101, 0, 0, 0, 0, 2, TN, H) + IF (NHNIL .LT. MXHNIL) GO TO 290 + MSG = 'DLSODE- Above warning has been issued I1 times. ' + CALL XERRWD (MSG, 50, 102, 0, 0, 0, 0, 0, 0.0D0, 0.0D0) + MSG = ' It will not be issued again for this problem' + CALL XERRWD (MSG, 50, 102, 0, 1, MXHNIL, 0, 0, 0.0D0, 0.0D0) + 290 CONTINUE +C----------------------------------------------------------------------- +C CALL DSTODE(NEQ,Y,YH,NYH,YH,EWT,SAVF,ACOR,WM,IWM,F,JAC,DPREPJ,DSOLSY) +C----------------------------------------------------------------------- + CALL DSTODE (NEQ, Y, RWORK(LYH), NYH, RWORK(LYH), RWORK(LEWT), + 1 RWORK(LSAVF), RWORK(LACOR), RWORK(LWM), IWORK(LIWM), + 2 F, JAC, DPREPJ, DSOLSY) + KGO = 1 - KFLAG + GO TO (300, 530, 540), KGO +C----------------------------------------------------------------------- +C Block F. +C The following block handles the case of a successful return from the +C core integrator (KFLAG = 0). Test for stop conditions. +C----------------------------------------------------------------------- + 300 INIT = 1 + GO TO (310, 400, 330, 340, 350), ITASK +C ITASK = 1. If TOUT has been reached, interpolate. ------------------- + 310 IF ((TN - TOUT)*H .LT. 0.0D0) GO TO 250 + CALL DINTDY (TOUT, 0, RWORK(LYH), NYH, Y, IFLAG) + T = TOUT + GO TO 420 +C ITASK = 3. Jump to exit if TOUT was reached. ------------------------ + 330 IF ((TN - TOUT)*H .GE. 0.0D0) GO TO 400 + GO TO 250 +C ITASK = 4. See if TOUT or TCRIT was reached. Adjust H if necessary. + 340 IF ((TN - TOUT)*H .LT. 0.0D0) GO TO 345 + CALL DINTDY (TOUT, 0, RWORK(LYH), NYH, Y, IFLAG) + T = TOUT + GO TO 420 + 345 HMX = ABS(TN) + ABS(H) + IHIT = ABS(TN - TCRIT) .LE. 100.0D0*UROUND*HMX + IF (IHIT) GO TO 400 + TNEXT = TN + H*(1.0D0 + 4.0D0*UROUND) + IF ((TNEXT - TCRIT)*H .LE. 0.0D0) GO TO 250 + H = (TCRIT - TN)*(1.0D0 - 4.0D0*UROUND) + JSTART = -2 + GO TO 250 +C ITASK = 5. See if TCRIT was reached and jump to exit. --------------- + 350 HMX = ABS(TN) + ABS(H) + IHIT = ABS(TN - TCRIT) .LE. 100.0D0*UROUND*HMX +C----------------------------------------------------------------------- +C Block G. +C The following block handles all successful returns from DLSODE. +C If ITASK .NE. 1, Y is loaded from YH and T is set accordingly. +C ISTATE is set to 2, and the optional outputs are loaded into the +C work arrays before returning. +C----------------------------------------------------------------------- + 400 DO 410 I = 1,N + 410 Y(I) = RWORK(I+LYH-1) + T = TN + IF (ITASK .NE. 4 .AND. ITASK .NE. 5) GO TO 420 + IF (IHIT) T = TCRIT + 420 ISTATE = 2 + RWORK(11) = HU + RWORK(12) = H + RWORK(13) = TN + IWORK(11) = NST + IWORK(12) = NFE + IWORK(13) = NJE + IWORK(14) = NQU + IWORK(15) = NQ + RETURN +C----------------------------------------------------------------------- +C Block H. +C The following block handles all unsuccessful returns other than +C those for illegal input. First the error message routine is called. +C If there was an error test or convergence test failure, IMXER is set. +C Then Y is loaded from YH and T is set to TN. The optional outputs +C are loaded into the work arrays before returning. +C----------------------------------------------------------------------- +C The maximum number of steps was taken before reaching TOUT. ---------- + 500 MSG = 'DLSODE- At current T (=R1), MXSTEP (=I1) steps ' + CALL XERRWD (MSG, 50, 201, 0, 0, 0, 0, 0, 0.0D0, 0.0D0) + MSG = ' taken on this call before reaching TOUT ' + CALL XERRWD (MSG, 50, 201, 0, 1, MXSTEP, 0, 1, TN, 0.0D0) + ISTATE = -1 + GO TO 580 +C EWT(I) .LE. 0.0 for some I (not at start of problem). ---------------- + 510 EWTI = RWORK(LEWT+I-1) + MSG = 'DLSODE- At T (=R1), EWT(I1) has become R2 .LE. 0.' + CALL XERRWD (MSG, 50, 202, 0, 1, I, 0, 2, TN, EWTI) + ISTATE = -6 + GO TO 580 +C Too much accuracy requested for machine precision. ------------------- + 520 MSG = 'DLSODE- At T (=R1), too much accuracy requested ' + CALL XERRWD (MSG, 50, 203, 0, 0, 0, 0, 0, 0.0D0, 0.0D0) + MSG = ' for precision of machine.. see TOLSF (=R2) ' + CALL XERRWD (MSG, 50, 203, 0, 0, 0, 0, 2, TN, TOLSF) + RWORK(14) = TOLSF + ISTATE = -2 + GO TO 580 +C KFLAG = -1. Error test failed repeatedly or with ABS(H) = HMIN. ----- + 530 MSG = 'DLSODE- At T(=R1) and step size H(=R2), the error' + CALL XERRWD (MSG, 50, 204, 0, 0, 0, 0, 0, 0.0D0, 0.0D0) + MSG = ' test failed repeatedly or with ABS(H) = HMIN' + CALL XERRWD (MSG, 50, 204, 0, 0, 0, 0, 2, TN, H) + ISTATE = -4 + GO TO 560 +C KFLAG = -2. Convergence failed repeatedly or with ABS(H) = HMIN. ---- + 540 MSG = 'DLSODE- At T (=R1) and step size H (=R2), the ' + CALL XERRWD (MSG, 50, 205, 0, 0, 0, 0, 0, 0.0D0, 0.0D0) + MSG = ' corrector convergence failed repeatedly ' + CALL XERRWD (MSG, 50, 205, 0, 0, 0, 0, 0, 0.0D0, 0.0D0) + MSG = ' or with ABS(H) = HMIN ' + CALL XERRWD (MSG, 30, 205, 0, 0, 0, 0, 2, TN, H) + ISTATE = -5 +C Compute IMXER if relevant. ------------------------------------------- + 560 BIG = 0.0D0 + IMXER = 1 + DO 570 I = 1,N + SIZE = ABS(RWORK(I+LACOR-1)*RWORK(I+LEWT-1)) + IF (BIG .GE. SIZE) GO TO 570 + BIG = SIZE + IMXER = I + 570 CONTINUE + IWORK(16) = IMXER +C Set Y vector, T, and optional outputs. ------------------------------- + 580 DO 590 I = 1,N + 590 Y(I) = RWORK(I+LYH-1) + T = TN + RWORK(11) = HU + RWORK(12) = H + RWORK(13) = TN + IWORK(11) = NST + IWORK(12) = NFE + IWORK(13) = NJE + IWORK(14) = NQU + IWORK(15) = NQ + RETURN +C----------------------------------------------------------------------- +C Block I. +C The following block handles all error returns due to illegal input +C (ISTATE = -3), as detected before calling the core integrator. +C First the error message routine is called. If the illegal input +C is a negative ISTATE, the run is aborted (apparent infinite loop). +C----------------------------------------------------------------------- + 601 MSG = 'DLSODE- ISTATE (=I1) illegal ' + CALL XERRWD (MSG, 30, 1, 0, 1, ISTATE, 0, 0, 0.0D0, 0.0D0) + IF (ISTATE .LT. 0) GO TO 800 + GO TO 700 + 602 MSG = 'DLSODE- ITASK (=I1) illegal ' + CALL XERRWD (MSG, 30, 2, 0, 1, ITASK, 0, 0, 0.0D0, 0.0D0) + GO TO 700 + 603 MSG = 'DLSODE- ISTATE .GT. 1 but DLSODE not initialized ' + CALL XERRWD (MSG, 50, 3, 0, 0, 0, 0, 0, 0.0D0, 0.0D0) + GO TO 700 + 604 MSG = 'DLSODE- NEQ (=I1) .LT. 1 ' + CALL XERRWD (MSG, 30, 4, 0, 1, NEQ(1), 0, 0, 0.0D0, 0.0D0) + GO TO 700 + 605 MSG = 'DLSODE- ISTATE = 3 and NEQ increased (I1 to I2) ' + CALL XERRWD (MSG, 50, 5, 0, 2, N, NEQ(1), 0, 0.0D0, 0.0D0) + GO TO 700 + 606 MSG = 'DLSODE- ITOL (=I1) illegal ' + CALL XERRWD (MSG, 30, 6, 0, 1, ITOL, 0, 0, 0.0D0, 0.0D0) + GO TO 700 + 607 MSG = 'DLSODE- IOPT (=I1) illegal ' + CALL XERRWD (MSG, 30, 7, 0, 1, IOPT, 0, 0, 0.0D0, 0.0D0) + GO TO 700 + 608 MSG = 'DLSODE- MF (=I1) illegal ' + CALL XERRWD (MSG, 30, 8, 0, 1, MF, 0, 0, 0.0D0, 0.0D0) + GO TO 700 + 609 MSG = 'DLSODE- ML (=I1) illegal.. .LT.0 or .GE.NEQ (=I2)' + CALL XERRWD (MSG, 50, 9, 0, 2, ML, NEQ(1), 0, 0.0D0, 0.0D0) + GO TO 700 + 610 MSG = 'DLSODE- MU (=I1) illegal.. .LT.0 or .GE.NEQ (=I2)' + CALL XERRWD (MSG, 50, 10, 0, 2, MU, NEQ(1), 0, 0.0D0, 0.0D0) + GO TO 700 + 611 MSG = 'DLSODE- MAXORD (=I1) .LT. 0 ' + CALL XERRWD (MSG, 30, 11, 0, 1, MAXORD, 0, 0, 0.0D0, 0.0D0) + GO TO 700 + 612 MSG = 'DLSODE- MXSTEP (=I1) .LT. 0 ' + CALL XERRWD (MSG, 30, 12, 0, 1, MXSTEP, 0, 0, 0.0D0, 0.0D0) + GO TO 700 + 613 MSG = 'DLSODE- MXHNIL (=I1) .LT. 0 ' + CALL XERRWD (MSG, 30, 13, 0, 1, MXHNIL, 0, 0, 0.0D0, 0.0D0) + GO TO 700 + 614 MSG = 'DLSODE- TOUT (=R1) behind T (=R2) ' + CALL XERRWD (MSG, 40, 14, 0, 0, 0, 0, 2, TOUT, T) + MSG = ' Integration direction is given by H0 (=R1) ' + CALL XERRWD (MSG, 50, 14, 0, 0, 0, 0, 1, H0, 0.0D0) + GO TO 700 + 615 MSG = 'DLSODE- HMAX (=R1) .LT. 0.0 ' + CALL XERRWD (MSG, 30, 15, 0, 0, 0, 0, 1, HMAX, 0.0D0) + GO TO 700 + 616 MSG = 'DLSODE- HMIN (=R1) .LT. 0.0 ' + CALL XERRWD (MSG, 30, 16, 0, 0, 0, 0, 1, HMIN, 0.0D0) + GO TO 700 + 617 CONTINUE + MSG='DLSODE- RWORK length needed, LENRW (=I1), exceeds LRW (=I2)' + CALL XERRWD (MSG, 60, 17, 0, 2, LENRW, LRW, 0, 0.0D0, 0.0D0) + GO TO 700 + 618 CONTINUE + MSG='DLSODE- IWORK length needed, LENIW (=I1), exceeds LIW (=I2)' + CALL XERRWD (MSG, 60, 18, 0, 2, LENIW, LIW, 0, 0.0D0, 0.0D0) + GO TO 700 + 619 MSG = 'DLSODE- RTOL(I1) is R1 .LT. 0.0 ' + CALL XERRWD (MSG, 40, 19, 0, 1, I, 0, 1, RTOLI, 0.0D0) + GO TO 700 + 620 MSG = 'DLSODE- ATOL(I1) is R1 .LT. 0.0 ' + CALL XERRWD (MSG, 40, 20, 0, 1, I, 0, 1, ATOLI, 0.0D0) + GO TO 700 + 621 EWTI = RWORK(LEWT+I-1) + MSG = 'DLSODE- EWT(I1) is R1 .LE. 0.0 ' + CALL XERRWD (MSG, 40, 21, 0, 1, I, 0, 1, EWTI, 0.0D0) + GO TO 700 + 622 CONTINUE + MSG='DLSODE- TOUT (=R1) too close to T(=R2) to start integration' + CALL XERRWD (MSG, 60, 22, 0, 0, 0, 0, 2, TOUT, T) + GO TO 700 + 623 CONTINUE + MSG='DLSODE- ITASK = I1 and TOUT (=R1) behind TCUR - HU (= R2) ' + CALL XERRWD (MSG, 60, 23, 0, 1, ITASK, 0, 2, TOUT, TP) + GO TO 700 + 624 CONTINUE + MSG='DLSODE- ITASK = 4 OR 5 and TCRIT (=R1) behind TCUR (=R2) ' + CALL XERRWD (MSG, 60, 24, 0, 0, 0, 0, 2, TCRIT, TN) + GO TO 700 + 625 CONTINUE + MSG='DLSODE- ITASK = 4 or 5 and TCRIT (=R1) behind TOUT (=R2) ' + CALL XERRWD (MSG, 60, 25, 0, 0, 0, 0, 2, TCRIT, TOUT) + GO TO 700 + 626 MSG = 'DLSODE- At start of problem, too much accuracy ' + CALL XERRWD (MSG, 50, 26, 0, 0, 0, 0, 0, 0.0D0, 0.0D0) + MSG=' requested for precision of machine.. See TOLSF (=R1) ' + CALL XERRWD (MSG, 60, 26, 0, 0, 0, 0, 1, TOLSF, 0.0D0) + RWORK(14) = TOLSF + GO TO 700 + 627 MSG = 'DLSODE- Trouble in DINTDY. ITASK = I1, TOUT = R1' + CALL XERRWD (MSG, 50, 27, 0, 1, ITASK, 0, 1, TOUT, 0.0D0) +C + 700 ISTATE = -3 + RETURN +C + 800 MSG = 'DLSODE- Run aborted.. apparent infinite loop ' + CALL XERRWD (MSG, 50, 303, 2, 0, 0, 0, 0, 0.0D0, 0.0D0) + RETURN +C----------------------- END OF SUBROUTINE DLSODE ---------------------- + END +*DECK DLSODES + SUBROUTINE DLSODES (F, NEQ, Y, T, TOUT, ITOL, RTOL, ATOL, ITASK, + 1 ISTATE, IOPT, RWORK, LRW, IWORK, LIW, JAC, MF) + EXTERNAL F, JAC + INTEGER NEQ, ITOL, ITASK, ISTATE, IOPT, LRW, IWORK, LIW, MF + DOUBLE PRECISION Y, T, TOUT, RTOL, ATOL, RWORK + DIMENSION NEQ(*), Y(*), RTOL(*), ATOL(*), RWORK(LRW), IWORK(LIW) +C----------------------------------------------------------------------- +C This is the 12 November 2003 version of +C DLSODES: Livermore Solver for Ordinary Differential Equations +C with general Sparse Jacobian matrix. +C +C This version is in double precision. +C +C DLSODES solves the initial value problem for stiff or nonstiff +C systems of first order ODEs, +C dy/dt = f(t,y) , or, in component form, +C dy(i)/dt = f(i) = f(i,t,y(1),y(2),...,y(NEQ)) (i = 1,...,NEQ). +C DLSODES is a variant of the DLSODE package, and is intended for +C problems in which the Jacobian matrix df/dy has an arbitrary +C sparse structure (when the problem is stiff). +C +C Authors: Alan C. Hindmarsh +C Center for Applied Scientific Computing, L-561 +C Lawrence Livermore National Laboratory +C Livermore, CA 94551 +C and +C Andrew H. Sherman +C J. S. Nolen and Associates +C Houston, TX 77084 +C----------------------------------------------------------------------- +C References: +C 1. Alan C. Hindmarsh, ODEPACK, A Systematized Collection of ODE +C Solvers, in Scientific Computing, R. S. Stepleman et al. (Eds.), +C North-Holland, Amsterdam, 1983, pp. 55-64. +C +C 2. S. C. Eisenstat, M. C. Gursky, M. H. Schultz, and A. H. Sherman, +C Yale Sparse Matrix Package: I. The Symmetric Codes, +C Int. J. Num. Meth. Eng., 18 (1982), pp. 1145-1151. +C +C 3. S. C. Eisenstat, M. C. Gursky, M. H. Schultz, and A. H. Sherman, +C Yale Sparse Matrix Package: II. The Nonsymmetric Codes, +C Research Report No. 114, Dept. of Computer Sciences, Yale +C University, 1977. +C----------------------------------------------------------------------- +C Summary of Usage. +C +C Communication between the user and the DLSODES package, for normal +C situations, is summarized here. This summary describes only a subset +C of the full set of options available. See the full description for +C details, including optional communication, nonstandard options, +C and instructions for special situations. See also the example +C problem (with program and output) following this summary. +C +C A. First provide a subroutine of the form: +C SUBROUTINE F (NEQ, T, Y, YDOT) +C DOUBLE PRECISION T, Y(*), YDOT(*) +C which supplies the vector function f by loading YDOT(i) with f(i). +C +C B. Next determine (or guess) whether or not the problem is stiff. +C Stiffness occurs when the Jacobian matrix df/dy has an eigenvalue +C whose real part is negative and large in magnitude, compared to the +C reciprocal of the t span of interest. If the problem is nonstiff, +C use a method flag MF = 10. If it is stiff, there are two standard +C choices for the method flag, MF = 121 and MF = 222. In both cases, +C DLSODES requires the Jacobian matrix in some form, and it treats this +C matrix in general sparse form, with sparsity structure determined +C internally. (For options where the user supplies the sparsity +C structure, see the full description of MF below.) +C +C C. If the problem is stiff, you are encouraged to supply the Jacobian +C directly (MF = 121), but if this is not feasible, DLSODES will +C compute it internally by difference quotients (MF = 222). +C If you are supplying the Jacobian, provide a subroutine of the form: +C SUBROUTINE JAC (NEQ, T, Y, J, IAN, JAN, PDJ) +C DOUBLE PRECISION T, Y(*), IAN(*), JAN(*), PDJ(*) +C Here NEQ, T, Y, and J are input arguments, and the JAC routine is to +C load the array PDJ (of length NEQ) with the J-th column of df/dy. +C I.e., load PDJ(i) with df(i)/dy(J) for all relevant values of i. +C The arguments IAN and JAN should be ignored for normal situations. +C DLSODES will call the JAC routine with J = 1,2,...,NEQ. +C Only nonzero elements need be loaded. Usually, a crude approximation +C to df/dy, possibly with fewer nonzero elements, will suffice. +C +C D. Write a main program which calls Subroutine DLSODES once for +C each point at which answers are desired. This should also provide +C for possible use of logical unit 6 for output of error messages by +C DLSODES. On the first call to DLSODES, supply arguments as follows: +C F = name of subroutine for right-hand side vector f. +C This name must be declared External in calling program. +C NEQ = number of first order ODEs. +C Y = array of initial values, of length NEQ. +C T = the initial value of the independent variable t. +C TOUT = first point where output is desired (.ne. T). +C ITOL = 1 or 2 according as ATOL (below) is a scalar or array. +C RTOL = relative tolerance parameter (scalar). +C ATOL = absolute tolerance parameter (scalar or array). +C The estimated local error in Y(i) will be controlled so as +C to be roughly less (in magnitude) than +C EWT(i) = RTOL*ABS(Y(i)) + ATOL if ITOL = 1, or +C EWT(i) = RTOL*ABS(Y(i)) + ATOL(i) if ITOL = 2. +C Thus the local error test passes if, in each component, +C either the absolute error is less than ATOL (or ATOL(i)), +C or the relative error is less than RTOL. +C Use RTOL = 0.0 for pure absolute error control, and +C use ATOL = 0.0 (or ATOL(i) = 0.0) for pure relative error +C control. Caution: actual (global) errors may exceed these +C local tolerances, so choose them conservatively. +C ITASK = 1 for normal computation of output values of Y at t = TOUT. +C ISTATE = integer flag (input and output). Set ISTATE = 1. +C IOPT = 0 to indicate no optional inputs used. +C RWORK = real work array of length at least: +C 20 + 16*NEQ for MF = 10, +C 20 + (2 + 1./LENRAT)*NNZ + (11 + 9./LENRAT)*NEQ +C for MF = 121 or 222, +C where: +C NNZ = the number of nonzero elements in the sparse +C Jacobian (if this is unknown, use an estimate), and +C LENRAT = the real to integer wordlength ratio (usually 1 in +C single precision and 2 in double precision). +C In any case, the required size of RWORK cannot generally +C be predicted in advance if MF = 121 or 222, and the value +C above is a rough estimate of a crude lower bound. Some +C experimentation with this size may be necessary. +C (When known, the correct required length is an optional +C output, available in IWORK(17).) +C LRW = declared length of RWORK (in user dimension). +C IWORK = integer work array of length at least 30. +C LIW = declared length of IWORK (in user dimension). +C JAC = name of subroutine for Jacobian matrix (MF = 121). +C If used, this name must be declared External in calling +C program. If not used, pass a dummy name. +C MF = method flag. Standard values are: +C 10 for nonstiff (Adams) method, no Jacobian used +C 121 for stiff (BDF) method, user-supplied sparse Jacobian +C 222 for stiff method, internally generated sparse Jacobian +C Note that the main program must declare arrays Y, RWORK, IWORK, +C and possibly ATOL. +C +C E. The output from the first call (or any call) is: +C Y = array of computed values of y(t) vector. +C T = corresponding value of independent variable (normally TOUT). +C ISTATE = 2 if DLSODES was successful, negative otherwise. +C -1 means excess work done on this call (perhaps wrong MF). +C -2 means excess accuracy requested (tolerances too small). +C -3 means illegal input detected (see printed message). +C -4 means repeated error test failures (check all inputs). +C -5 means repeated convergence failures (perhaps bad Jacobian +C supplied or wrong choice of MF or tolerances).lsodes +C -6 means error weight became zero during problem. (Solution +C component i vanished, and ATOL or ATOL(i) = 0.) +C -7 means a fatal error return flag came from sparse solver +C CDRV by way of DPRJS or DSOLSS. Should never happen. +C A return with ISTATE = -1, -4, or -5 may result from using +C an inappropriate sparsity structure, one that is quite +C different from the initial structure. Consider calling +C DLSODES again with ISTATE = 3 to force the structure to be +C reevaluated. See the full description of ISTATE below. +C +C F. To continue the integration after a successful return, simply +C reset TOUT and call DLSODES again. No other parameters need be reset. +C +C----------------------------------------------------------------------- +C Example Problem. +C +C The following is a simple example problem, with the coding +C needed for its solution by DLSODES. The problem is from chemical +C kinetics, and consists of the following 12 rate equations: +C dy1/dt = -rk1*y1 +C dy2/dt = rk1*y1 + rk11*rk14*y4 + rk19*rk14*y5 +C - rk3*y2*y3 - rk15*y2*y12 - rk2*y2 +C dy3/dt = rk2*y2 - rk5*y3 - rk3*y2*y3 - rk7*y10*y3 +C + rk11*rk14*y4 + rk12*rk14*y6 +C dy4/dt = rk3*y2*y3 - rk11*rk14*y4 - rk4*y4 +C dy5/dt = rk15*y2*y12 - rk19*rk14*y5 - rk16*y5 +C dy6/dt = rk7*y10*y3 - rk12*rk14*y6 - rk8*y6 +C dy7/dt = rk17*y10*y12 - rk20*rk14*y7 - rk18*y7 +C dy8/dt = rk9*y10 - rk13*rk14*y8 - rk10*y8 +C dy9/dt = rk4*y4 + rk16*y5 + rk8*y6 + rk18*y7 +C dy10/dt = rk5*y3 + rk12*rk14*y6 + rk20*rk14*y7 +C + rk13*rk14*y8 - rk7*y10*y3 - rk17*y10*y12 +C - rk6*y10 - rk9*y10 +C dy11/dt = rk10*y8 +C dy12/dt = rk6*y10 + rk19*rk14*y5 + rk20*rk14*y7 +C - rk15*y2*y12 - rk17*y10*y12 +C +C with rk1 = rk5 = 0.1, rk4 = rk8 = rk16 = rk18 = 2.5, +C rk10 = 5.0, rk2 = rk6 = 10.0, rk14 = 30.0, +C rk3 = rk7 = rk9 = rk11 = rk12 = rk13 = rk19 = rk20 = 50.0, +C rk15 = rk17 = 100.0. +C +C The t interval is from 0 to 1000, and the initial conditions +C are y1 = 1, y2 = y3 = ... = y12 = 0. The problem is stiff. +C +C The following coding solves this problem with DLSODES, using MF = 121 +C and printing results at t = .1, 1., 10., 100., 1000. It uses +C ITOL = 1 and mixed relative/absolute tolerance controls. +C During the run and at the end, statistical quantities of interest +C are printed (see optional outputs in the full description below). +C +C EXTERNAL FEX, JEX +C DOUBLE PRECISION ATOL, RTOL, RWORK, T, TOUT, Y +C DIMENSION Y(12), RWORK(500), IWORK(30) +C DATA LRW/500/, LIW/30/ +C NEQ = 12 +C DO 10 I = 1,NEQ +C 10 Y(I) = 0.0D0 +C Y(1) = 1.0D0 +C T = 0.0D0 +C TOUT = 0.1D0 +C ITOL = 1 +C RTOL = 1.0D-4 +C ATOL = 1.0D-6 +C ITASK = 1 +C ISTATE = 1 +C IOPT = 0 +C MF = 121 +C DO 40 IOUT = 1,5 +C CALL DLSODES (FEX, NEQ, Y, T, TOUT, ITOL, RTOL, ATOL, +C 1 ITASK, ISTATE, IOPT, RWORK, LRW, IWORK, LIW, JEX, MF) +C WRITE(6,30)T,IWORK(11),RWORK(11),(Y(I),I=1,NEQ) +C 30 FORMAT(//' At t =',D11.3,4X, +C 1 ' No. steps =',I5,4X,' Last step =',D11.3/ +C 2 ' Y array = ',4D14.5/13X,4D14.5/13X,4D14.5) +C IF (ISTATE .LT. 0) GO TO 80 +C TOUT = TOUT*10.0D0 +C 40 CONTINUE +C LENRW = IWORK(17) +C LENIW = IWORK(18) +C NST = IWORK(11) +C NFE = IWORK(12) +C NJE = IWORK(13) +C NLU = IWORK(21) +C NNZ = IWORK(19) +C NNZLU = IWORK(25) + IWORK(26) + NEQ +C WRITE (6,70) LENRW,LENIW,NST,NFE,NJE,NLU,NNZ,NNZLU +C 70 FORMAT(//' Required RWORK size =',I4,' IWORK size =',I4/ +C 1 ' No. steps =',I4,' No. f-s =',I4,' No. J-s =',I4, +C 2 ' No. LU-s =',I4/' No. of nonzeros in J =',I5, +C 3 ' No. of nonzeros in LU =',I5) +C STOP +C 80 WRITE(6,90)ISTATE +C 90 FORMAT(///' Error halt.. ISTATE =',I3) +C STOP +C END +C +C SUBROUTINE FEX (NEQ, T, Y, YDOT) +C DOUBLE PRECISION T, Y, YDOT +C DOUBLE PRECISION RK1, RK2, RK3, RK4, RK5, RK6, RK7, RK8, RK9, +C 1 RK10, RK11, RK12, RK13, RK14, RK15, RK16, RK17 +C DIMENSION Y(12), YDOT(12) +C DATA RK1/0.1D0/, RK2/10.0D0/, RK3/50.0D0/, RK4/2.5D0/, RK5/0.1D0/, +C 1 RK6/10.0D0/, RK7/50.0D0/, RK8/2.5D0/, RK9/50.0D0/, RK10/5.0D0/, +C 2 RK11/50.0D0/, RK12/50.0D0/, RK13/50.0D0/, RK14/30.0D0/, +C 3 RK15/100.0D0/, RK16/2.5D0/, RK17/100.0D0/, RK18/2.5D0/, +C 4 RK19/50.0D0/, RK20/50.0D0/ +C YDOT(1) = -RK1*Y(1) +C YDOT(2) = RK1*Y(1) + RK11*RK14*Y(4) + RK19*RK14*Y(5) +C 1 - RK3*Y(2)*Y(3) - RK15*Y(2)*Y(12) - RK2*Y(2) +C YDOT(3) = RK2*Y(2) - RK5*Y(3) - RK3*Y(2)*Y(3) - RK7*Y(10)*Y(3) +C 1 + RK11*RK14*Y(4) + RK12*RK14*Y(6) +C YDOT(4) = RK3*Y(2)*Y(3) - RK11*RK14*Y(4) - RK4*Y(4) +C YDOT(5) = RK15*Y(2)*Y(12) - RK19*RK14*Y(5) - RK16*Y(5) +C YDOT(6) = RK7*Y(10)*Y(3) - RK12*RK14*Y(6) - RK8*Y(6) +C YDOT(7) = RK17*Y(10)*Y(12) - RK20*RK14*Y(7) - RK18*Y(7) +C YDOT(8) = RK9*Y(10) - RK13*RK14*Y(8) - RK10*Y(8) +C YDOT(9) = RK4*Y(4) + RK16*Y(5) + RK8*Y(6) + RK18*Y(7) +C YDOT(10) = RK5*Y(3) + RK12*RK14*Y(6) + RK20*RK14*Y(7) +C 1 + RK13*RK14*Y(8) - RK7*Y(10)*Y(3) - RK17*Y(10)*Y(12) +C 2 - RK6*Y(10) - RK9*Y(10) +C YDOT(11) = RK10*Y(8) +C YDOT(12) = RK6*Y(10) + RK19*RK14*Y(5) + RK20*RK14*Y(7) +C 1 - RK15*Y(2)*Y(12) - RK17*Y(10)*Y(12) +C RETURN +C END +C +C SUBROUTINE JEX (NEQ, T, Y, J, IA, JA, PDJ) +C DOUBLE PRECISION T, Y, PDJ +C DOUBLE PRECISION RK1, RK2, RK3, RK4, RK5, RK6, RK7, RK8, RK9, +C 1 RK10, RK11, RK12, RK13, RK14, RK15, RK16, RK17 +C DIMENSION Y(12), IA(*), JA(*), PDJ(12) +C DATA RK1/0.1D0/, RK2/10.0D0/, RK3/50.0D0/, RK4/2.5D0/, RK5/0.1D0/, +C 1 RK6/10.0D0/, RK7/50.0D0/, RK8/2.5D0/, RK9/50.0D0/, RK10/5.0D0/, +C 2 RK11/50.0D0/, RK12/50.0D0/, RK13/50.0D0/, RK14/30.0D0/, +C 3 RK15/100.0D0/, RK16/2.5D0/, RK17/100.0D0/, RK18/2.5D0/, +C 4 RK19/50.0D0/, RK20/50.0D0/ +C GO TO (1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12), J +C 1 PDJ(1) = -RK1 +C PDJ(2) = RK1 +C RETURN +C 2 PDJ(2) = -RK3*Y(3) - RK15*Y(12) - RK2 +C PDJ(3) = RK2 - RK3*Y(3) +C PDJ(4) = RK3*Y(3) +C PDJ(5) = RK15*Y(12) +C PDJ(12) = -RK15*Y(12) +C RETURN +C 3 PDJ(2) = -RK3*Y(2) +C PDJ(3) = -RK5 - RK3*Y(2) - RK7*Y(10) +C PDJ(4) = RK3*Y(2) +C PDJ(6) = RK7*Y(10) +C PDJ(10) = RK5 - RK7*Y(10) +C RETURN +C 4 PDJ(2) = RK11*RK14 +C PDJ(3) = RK11*RK14 +C PDJ(4) = -RK11*RK14 - RK4 +C PDJ(9) = RK4 +C RETURN +C 5 PDJ(2) = RK19*RK14 +C PDJ(5) = -RK19*RK14 - RK16 +C PDJ(9) = RK16 +C PDJ(12) = RK19*RK14 +C RETURN +C 6 PDJ(3) = RK12*RK14 +C PDJ(6) = -RK12*RK14 - RK8 +C PDJ(9) = RK8 +C PDJ(10) = RK12*RK14 +C RETURN +C 7 PDJ(7) = -RK20*RK14 - RK18 +C PDJ(9) = RK18 +C PDJ(10) = RK20*RK14 +C PDJ(12) = RK20*RK14 +C RETURN +C 8 PDJ(8) = -RK13*RK14 - RK10 +C PDJ(10) = RK13*RK14 +C PDJ(11) = RK10 +C 9 RETURN +C 10 PDJ(3) = -RK7*Y(3) +C PDJ(6) = RK7*Y(3) +C PDJ(7) = RK17*Y(12) +C PDJ(8) = RK9 +C PDJ(10) = -RK7*Y(3) - RK17*Y(12) - RK6 - RK9 +C PDJ(12) = RK6 - RK17*Y(12) +C 11 RETURN +C 12 PDJ(2) = -RK15*Y(2) +C PDJ(5) = RK15*Y(2) +C PDJ(7) = RK17*Y(10) +C PDJ(10) = -RK17*Y(10) +C PDJ(12) = -RK15*Y(2) - RK17*Y(10) +C RETURN +C END +C +C The output of this program (on a Cray-1 in single precision) +C is as follows: +C +C +C At t = 1.000e-01 No. steps = 12 Last step = 1.515e-02 +C Y array = 9.90050e-01 6.28228e-03 3.65313e-03 7.51934e-07 +C 1.12167e-09 1.18458e-09 1.77291e-12 3.26476e-07 +C 5.46720e-08 9.99500e-06 4.48483e-08 2.76398e-06 +C +C +C At t = 1.000e+00 No. steps = 33 Last step = 7.880e-02 +C Y array = 9.04837e-01 9.13105e-03 8.20622e-02 2.49177e-05 +C 1.85055e-06 1.96797e-06 1.46157e-07 2.39557e-05 +C 3.26306e-05 7.21621e-04 5.06433e-05 3.05010e-03 +C +C +C At t = 1.000e+01 No. steps = 48 Last step = 1.239e+00 +C Y array = 3.67876e-01 3.68958e-03 3.65133e-01 4.48325e-05 +C 6.10798e-05 4.33148e-05 5.90211e-05 1.18449e-04 +C 3.15235e-03 3.56531e-03 4.15520e-03 2.48741e-01 +C +C +C At t = 1.000e+02 No. steps = 91 Last step = 3.764e+00 +C Y array = 4.44981e-05 4.42666e-07 4.47273e-04 -3.53257e-11 +C 2.81577e-08 -9.67741e-11 2.77615e-07 1.45322e-07 +C 1.56230e-02 4.37394e-06 1.60104e-02 9.52246e-01 +C +C +C At t = 1.000e+03 No. steps = 111 Last step = 4.156e+02 +C Y array = -2.65492e-13 2.60539e-14 -8.59563e-12 6.29355e-14 +C -1.78066e-13 5.71471e-13 -1.47561e-12 4.58078e-15 +C 1.56314e-02 1.37878e-13 1.60184e-02 9.52719e-01 +C +C +C Required RWORK size = 442 IWORK size = 30 +C No. steps = 111 No. f-s = 142 No. J-s = 2 No. LU-s = 20 +C No. of nonzeros in J = 44 No. of nonzeros in LU = 50 +C +C----------------------------------------------------------------------- +C Full Description of User Interface to DLSODES. +C +C The user interface to DLSODES consists of the following parts. +C +C 1. The call sequence to Subroutine DLSODES, which is a driver +C routine for the solver. This includes descriptions of both +C the call sequence arguments and of user-supplied routines. +C Following these descriptions is a description of +C optional inputs available through the call sequence, and then +C a description of optional outputs (in the work arrays). +C +C 2. Descriptions of other routines in the DLSODES package that may be +C (optionally) called by the user. These provide the ability to +C alter error message handling, save and restore the internal +C Common, and obtain specified derivatives of the solution y(t). +C +C 3. Descriptions of Common blocks to be declared in overlay +C or similar environments, or to be saved when doing an interrupt +C of the problem and continued solution later. +C +C 4. Description of two routines in the DLSODES package, either of +C which the user may replace with his/her own version, if desired. +C These relate to the measurement of errors. +C +C----------------------------------------------------------------------- +C Part 1. Call Sequence. +C +C The call sequence parameters used for input only are +C F, NEQ, TOUT, ITOL, RTOL, ATOL, ITASK, IOPT, LRW, LIW, JAC, MF, +C and those used for both input and output are +C Y, T, ISTATE. +C The work arrays RWORK and IWORK are also used for conditional and +C optional inputs and optional outputs. (The term output here refers +C to the return from Subroutine DLSODES to the user's calling program.) +C +C The legality of input parameters will be thoroughly checked on the +C initial call for the problem, but not checked thereafter unless a +C change in input parameters is flagged by ISTATE = 3 on input. +C +C The descriptions of the call arguments are as follows. +C +C F = the name of the user-supplied subroutine defining the +C ODE system. The system must be put in the first-order +C form dy/dt = f(t,y), where f is a vector-valued function +C of the scalar t and the vector y. Subroutine F is to +C compute the function f. It is to have the form +C SUBROUTINE F (NEQ, T, Y, YDOT) +C DOUBLE PRECISION T, Y(*), YDOT(*) +C where NEQ, T, and Y are input, and the array YDOT = f(t,y) +C is output. Y and YDOT are arrays of length NEQ. +C Subroutine F should not alter y(1),...,y(NEQ). +C F must be declared External in the calling program. +C +C Subroutine F may access user-defined quantities in +C NEQ(2),... and/or in Y(NEQ(1)+1),... if NEQ is an array +C (dimensioned in F) and/or Y has length exceeding NEQ(1). +C See the descriptions of NEQ and Y below. +C +C If quantities computed in the F routine are needed +C externally to DLSODES, an extra call to F should be made +C for this purpose, for consistent and accurate results. +C If only the derivative dy/dt is needed, use DINTDY instead. +C +C NEQ = the size of the ODE system (number of first order +C ordinary differential equations). Used only for input. +C NEQ may be decreased, but not increased, during the problem. +C If NEQ is decreased (with ISTATE = 3 on input), the +C remaining components of Y should be left undisturbed, if +C these are to be accessed in F and/or JAC. +C +C Normally, NEQ is a scalar, and it is generally referred to +C as a scalar in this user interface description. However, +C NEQ may be an array, with NEQ(1) set to the system size. +C (The DLSODES package accesses only NEQ(1).) In either case, +C this parameter is passed as the NEQ argument in all calls +C to F and JAC. Hence, if it is an array, locations +C NEQ(2),... may be used to store other integer data and pass +C it to F and/or JAC. Subroutines F and/or JAC must include +C NEQ in a Dimension statement in that case. +C +C Y = a real array for the vector of dependent variables, of +C length NEQ or more. Used for both input and output on the +C first call (ISTATE = 1), and only for output on other calls. +C on the first call, Y must contain the vector of initial +C values. On output, Y contains the computed solution vector, +C evaluated at T. If desired, the Y array may be used +C for other purposes between calls to the solver. +C +C This array is passed as the Y argument in all calls to +C F and JAC. Hence its length may exceed NEQ, and locations +C Y(NEQ+1),... may be used to store other real data and +C pass it to F and/or JAC. (The DLSODES package accesses only +C Y(1),...,Y(NEQ).) +C +C T = the independent variable. On input, T is used only on the +C first call, as the initial point of the integration. +C on output, after each call, T is the value at which a +C computed solution Y is evaluated (usually the same as TOUT). +C On an error return, T is the farthest point reached. +C +C TOUT = the next value of t at which a computed solution is desired. +C Used only for input. +C +C When starting the problem (ISTATE = 1), TOUT may be equal +C to T for one call, then should .ne. T for the next call. +C For the initial T, an input value of TOUT .ne. T is used +C in order to determine the direction of the integration +C (i.e. the algebraic sign of the step sizes) and the rough +C scale of the problem. Integration in either direction +C (forward or backward in t) is permitted. +C +C If ITASK = 2 or 5 (one-step modes), TOUT is ignored after +C the first call (i.e. the first call with TOUT .ne. T). +C Otherwise, TOUT is required on every call. +C +C If ITASK = 1, 3, or 4, the values of TOUT need not be +C monotone, but a value of TOUT which backs up is limited +C to the current internal T interval, whose endpoints are +C TCUR - HU and TCUR (see optional outputs, below, for +C TCUR and HU). +C +C ITOL = an indicator for the type of error control. See +C description below under ATOL. Used only for input. +C +C RTOL = a relative error tolerance parameter, either a scalar or +C an array of length NEQ. See description below under ATOL. +C Input only. +C +C ATOL = an absolute error tolerance parameter, either a scalar or +C an array of length NEQ. Input only. +C +C The input parameters ITOL, RTOL, and ATOL determine +C the error control performed by the solver. The solver will +C control the vector E = (E(i)) of estimated local errors +C in y, according to an inequality of the form +C RMS-norm of ( E(i)/EWT(i) ) .le. 1, +C where EWT(i) = RTOL(i)*ABS(Y(i)) + ATOL(i), +C and the RMS-norm (root-mean-square norm) here is +C RMS-norm(v) = SQRT(sum v(i)**2 / NEQ). Here EWT = (EWT(i)) +C is a vector of weights which must always be positive, and +C the values of RTOL and ATOL should all be non-negative. +C The following table gives the types (scalar/array) of +C RTOL and ATOL, and the corresponding form of EWT(i). +C +C ITOL RTOL ATOL EWT(i) +C 1 scalar scalar RTOL*ABS(Y(i)) + ATOL +C 2 scalar array RTOL*ABS(Y(i)) + ATOL(i) +C 3 array scalar RTOL(i)*ABS(Y(i)) + ATOL +C 4 array array RTOL(i)*ABS(Y(i)) + ATOL(i) +C +C When either of these parameters is a scalar, it need not +C be dimensioned in the user's calling program. +C +C If none of the above choices (with ITOL, RTOL, and ATOL +C fixed throughout the problem) is suitable, more general +C error controls can be obtained by substituting +C user-supplied routines for the setting of EWT and/or for +C the norm calculation. See Part 4 below. +C +C If global errors are to be estimated by making a repeated +C run on the same problem with smaller tolerances, then all +C components of RTOL and ATOL (i.e. of EWT) should be scaled +C down uniformly. +C +C ITASK = an index specifying the task to be performed. +C Input only. ITASK has the following values and meanings. +C 1 means normal computation of output values of y(t) at +C t = TOUT (by overshooting and interpolating). +C 2 means take one step only and return. +C 3 means stop at the first internal mesh point at or +C beyond t = TOUT and return. +C 4 means normal computation of output values of y(t) at +C t = TOUT but without overshooting t = TCRIT. +C TCRIT must be input as RWORK(1). TCRIT may be equal to +C or beyond TOUT, but not behind it in the direction of +C integration. This option is useful if the problem +C has a singularity at or beyond t = TCRIT. +C 5 means take one step, without passing TCRIT, and return. +C TCRIT must be input as RWORK(1). +C +C Note: If ITASK = 4 or 5 and the solver reaches TCRIT +C (within roundoff), it will return T = TCRIT (exactly) to +C indicate this (unless ITASK = 4 and TOUT comes before TCRIT, +C in which case answers at t = TOUT are returned first). +C +C ISTATE = an index used for input and output to specify the +C the state of the calculation. +C +C On input, the values of ISTATE are as follows. +C 1 means this is the first call for the problem +C (initializations will be done). See note below. +C 2 means this is not the first call, and the calculation +C is to continue normally, with no change in any input +C parameters except possibly TOUT and ITASK. +C (If ITOL, RTOL, and/or ATOL are changed between calls +C with ISTATE = 2, the new values will be used but not +C tested for legality.) +C 3 means this is not the first call, and the +C calculation is to continue normally, but with +C a change in input parameters other than +C TOUT and ITASK. Changes are allowed in +C NEQ, ITOL, RTOL, ATOL, IOPT, LRW, LIW, MF, +C the conditional inputs IA and JA, +C and any of the optional inputs except H0. +C In particular, if MITER = 1 or 2, a call with ISTATE = 3 +C will cause the sparsity structure of the problem to be +C recomputed (or reread from IA and JA if MOSS = 0). +C Note: a preliminary call with TOUT = T is not counted +C as a first call here, as no initialization or checking of +C input is done. (Such a call is sometimes useful for the +C purpose of outputting the initial conditions.) +C Thus the first call for which TOUT .ne. T requires +C ISTATE = 1 on input. +C +C On output, ISTATE has the following values and meanings. +C 1 means nothing was done; TOUT = T and ISTATE = 1 on input. +C 2 means the integration was performed successfully. +C -1 means an excessive amount of work (more than MXSTEP +C steps) was done on this call, before completing the +C requested task, but the integration was otherwise +C successful as far as T. (MXSTEP is an optional input +C and is normally 500.) To continue, the user may +C simply reset ISTATE to a value .gt. 1 and call again +C (the excess work step counter will be reset to 0). +C In addition, the user may increase MXSTEP to avoid +C this error return (see below on optional inputs). +C -2 means too much accuracy was requested for the precision +C of the machine being used. This was detected before +C completing the requested task, but the integration +C was successful as far as T. To continue, the tolerance +C parameters must be reset, and ISTATE must be set +C to 3. The optional output TOLSF may be used for this +C purpose. (Note: If this condition is detected before +C taking any steps, then an illegal input return +C (ISTATE = -3) occurs instead.) +C -3 means illegal input was detected, before taking any +C integration steps. See written message for details. +C Note: If the solver detects an infinite loop of calls +C to the solver with illegal input, it will cause +C the run to stop. +C -4 means there were repeated error test failures on +C one attempted step, before completing the requested +C task, but the integration was successful as far as T. +C The problem may have a singularity, or the input +C may be inappropriate. +C -5 means there were repeated convergence test failures on +C one attempted step, before completing the requested +C task, but the integration was successful as far as T. +C This may be caused by an inaccurate Jacobian matrix, +C if one is being used. +C -6 means EWT(i) became zero for some i during the +C integration. Pure relative error control (ATOL(i)=0.0) +C was requested on a variable which has now vanished. +C The integration was successful as far as T. +C -7 means a fatal error return flag came from the sparse +C solver CDRV by way of DPRJS or DSOLSS (numerical +C factorization or backsolve). This should never happen. +C The integration was successful as far as T. +C +C Note: an error return with ISTATE = -1, -4, or -5 and with +C MITER = 1 or 2 may mean that the sparsity structure of the +C problem has changed significantly since it was last +C determined (or input). In that case, one can attempt to +C complete the integration by setting ISTATE = 3 on the next +C call, so that a new structure determination is done. +C +C Note: since the normal output value of ISTATE is 2, +C it does not need to be reset for normal continuation. +C Also, since a negative input value of ISTATE will be +C regarded as illegal, a negative output value requires the +C user to change it, and possibly other inputs, before +C calling the solver again. +C +C IOPT = an integer flag to specify whether or not any optional +C inputs are being used on this call. Input only. +C The optional inputs are listed separately below. +C IOPT = 0 means no optional inputs are being used. +C Default values will be used in all cases. +C IOPT = 1 means one or more optional inputs are being used. +C +C RWORK = a work array used for a mixture of real (double precision) +C and integer work space. +C The length of RWORK (in real words) must be at least +C 20 + NYH*(MAXORD + 1) + 3*NEQ + LWM where +C NYH = the initial value of NEQ, +C MAXORD = 12 (if METH = 1) or 5 (if METH = 2) (unless a +C smaller value is given as an optional input), +C LWM = 0 if MITER = 0, +C LWM = 2*NNZ + 2*NEQ + (NNZ+9*NEQ)/LENRAT if MITER = 1, +C LWM = 2*NNZ + 2*NEQ + (NNZ+10*NEQ)/LENRAT if MITER = 2, +C LWM = NEQ + 2 if MITER = 3. +C In the above formulas, +C NNZ = number of nonzero elements in the Jacobian matrix. +C LENRAT = the real to integer wordlength ratio (usually 1 in +C single precision and 2 in double precision). +C (See the MF description for METH and MITER.) +C Thus if MAXORD has its default value and NEQ is constant, +C the minimum length of RWORK is: +C 20 + 16*NEQ for MF = 10, +C 20 + 16*NEQ + LWM for MF = 11, 111, 211, 12, 112, 212, +C 22 + 17*NEQ for MF = 13, +C 20 + 9*NEQ for MF = 20, +C 20 + 9*NEQ + LWM for MF = 21, 121, 221, 22, 122, 222, +C 22 + 10*NEQ for MF = 23. +C If MITER = 1 or 2, the above formula for LWM is only a +C crude lower bound. The required length of RWORK cannot +C be readily predicted in general, as it depends on the +C sparsity structure of the problem. Some experimentation +C may be necessary. +C +C The first 20 words of RWORK are reserved for conditional +C and optional inputs and optional outputs. +C +C The following word in RWORK is a conditional input: +C RWORK(1) = TCRIT = critical value of t which the solver +C is not to overshoot. Required if ITASK is +C 4 or 5, and ignored otherwise. (See ITASK.) +C +C LRW = the length of the array RWORK, as declared by the user. +C (This will be checked by the solver.) +C +C IWORK = an integer work array. The length of IWORK must be at least +C 31 + NEQ + NNZ if MOSS = 0 and MITER = 1 or 2, or +C 30 otherwise. +C (NNZ is the number of nonzero elements in df/dy.) +C +C In DLSODES, IWORK is used only for conditional and +C optional inputs and optional outputs. +C +C The following two blocks of words in IWORK are conditional +C inputs, required if MOSS = 0 and MITER = 1 or 2, but not +C otherwise (see the description of MF for MOSS). +C IWORK(30+j) = IA(j) (j=1,...,NEQ+1) +C IWORK(31+NEQ+k) = JA(k) (k=1,...,NNZ) +C The two arrays IA and JA describe the sparsity structure +C to be assumed for the Jacobian matrix. JA contains the row +C indices where nonzero elements occur, reading in columnwise +C order, and IA contains the starting locations in JA of the +C descriptions of columns 1,...,NEQ, in that order, with +C IA(1) = 1. Thus, for each column index j = 1,...,NEQ, the +C values of the row index i in column j where a nonzero +C element may occur are given by +C i = JA(k), where IA(j) .le. k .lt. IA(j+1). +C If NNZ is the total number of nonzero locations assumed, +C then the length of the JA array is NNZ, and IA(NEQ+1) must +C be NNZ + 1. Duplicate entries are not allowed. +C +C LIW = the length of the array IWORK, as declared by the user. +C (This will be checked by the solver.) +C +C Note: The work arrays must not be altered between calls to DLSODES +C for the same problem, except possibly for the conditional and +C optional inputs, and except for the last 3*NEQ words of RWORK. +C The latter space is used for internal scratch space, and so is +C available for use by the user outside DLSODES between calls, if +C desired (but not for use by F or JAC). +C +C JAC = name of user-supplied routine (MITER = 1 or MOSS = 1) to +C compute the Jacobian matrix, df/dy, as a function of +C the scalar t and the vector y. It is to have the form +C SUBROUTINE JAC (NEQ, T, Y, J, IAN, JAN, PDJ) +C DOUBLE PRECISION T, Y(*), IAN(*), JAN(*), PDJ(*) +C where NEQ, T, Y, J, IAN, and JAN are input, and the array +C PDJ, of length NEQ, is to be loaded with column J +C of the Jacobian on output. Thus df(i)/dy(J) is to be +C loaded into PDJ(i) for all relevant values of i. +C Here T and Y have the same meaning as in Subroutine F, +C and J is a column index (1 to NEQ). IAN and JAN are +C undefined in calls to JAC for structure determination +C (MOSS = 1). otherwise, IAN and JAN are structure +C descriptors, as defined under optional outputs below, and +C so can be used to determine the relevant row indices i, if +C desired. +C JAC need not provide df/dy exactly. A crude +C approximation (possibly with greater sparsity) will do. +C In any case, PDJ is preset to zero by the solver, +C so that only the nonzero elements need be loaded by JAC. +C Calls to JAC are made with J = 1,...,NEQ, in that order, and +C each such set of calls is preceded by a call to F with the +C same arguments NEQ, T, and Y. Thus to gain some efficiency, +C intermediate quantities shared by both calculations may be +C saved in a user Common block by F and not recomputed by JAC, +C if desired. JAC must not alter its input arguments. +C JAC must be declared External in the calling program. +C Subroutine JAC may access user-defined quantities in +C NEQ(2),... and/or in Y(NEQ(1)+1),... if NEQ is an array +C (dimensioned in JAC) and/or Y has length exceeding NEQ(1). +C See the descriptions of NEQ and Y above. +C +C MF = the method flag. Used only for input. +C MF has three decimal digits-- MOSS, METH, MITER-- +C MF = 100*MOSS + 10*METH + MITER. +C MOSS indicates the method to be used to obtain the sparsity +C structure of the Jacobian matrix if MITER = 1 or 2: +C MOSS = 0 means the user has supplied IA and JA +C (see descriptions under IWORK above). +C MOSS = 1 means the user has supplied JAC (see below) +C and the structure will be obtained from NEQ +C initial calls to JAC. +C MOSS = 2 means the structure will be obtained from NEQ+1 +C initial calls to F. +C METH indicates the basic linear multistep method: +C METH = 1 means the implicit Adams method. +C METH = 2 means the method based on Backward +C Differentiation Formulas (BDFs). +C MITER indicates the corrector iteration method: +C MITER = 0 means functional iteration (no Jacobian matrix +C is involved). +C MITER = 1 means chord iteration with a user-supplied +C sparse Jacobian, given by Subroutine JAC. +C MITER = 2 means chord iteration with an internally +C generated (difference quotient) sparse Jacobian +C (using NGP extra calls to F per df/dy value, +C where NGP is an optional output described below.) +C MITER = 3 means chord iteration with an internally +C generated diagonal Jacobian approximation +C (using 1 extra call to F per df/dy evaluation). +C If MITER = 1 or MOSS = 1, the user must supply a Subroutine +C JAC (the name is arbitrary) as described above under JAC. +C Otherwise, a dummy argument can be used. +C +C The standard choices for MF are: +C MF = 10 for a nonstiff problem, +C MF = 21 or 22 for a stiff problem with IA/JA supplied +C (21 if JAC is supplied, 22 if not), +C MF = 121 for a stiff problem with JAC supplied, +C but not IA/JA, +C MF = 222 for a stiff problem with neither IA/JA nor +C JAC supplied. +C The sparseness structure can be changed during the +C problem by making a call to DLSODES with ISTATE = 3. +C----------------------------------------------------------------------- +C Optional Inputs. +C +C The following is a list of the optional inputs provided for in the +C call sequence. (See also Part 2.) For each such input variable, +C this table lists its name as used in this documentation, its +C location in the call sequence, its meaning, and the default value. +C The use of any of these inputs requires IOPT = 1, and in that +C case all of these inputs are examined. A value of zero for any +C of these optional inputs will cause the default value to be used. +C Thus to use a subset of the optional inputs, simply preload +C locations 5 to 10 in RWORK and IWORK to 0.0 and 0 respectively, and +C then set those of interest to nonzero values. +C +C Name Location Meaning and Default Value +C +C H0 RWORK(5) the step size to be attempted on the first step. +C The default value is determined by the solver. +C +C HMAX RWORK(6) the maximum absolute step size allowed. +C The default value is infinite. +C +C HMIN RWORK(7) the minimum absolute step size allowed. +C The default value is 0. (This lower bound is not +C enforced on the final step before reaching TCRIT +C when ITASK = 4 or 5.) +C +C SETH RWORK(8) the element threshhold for sparsity determination +C when MOSS = 1 or 2. If the absolute value of +C an estimated Jacobian element is .le. SETH, it +C will be assumed to be absent in the structure. +C The default value of SETH is 0. +C +C MAXORD IWORK(5) the maximum order to be allowed. The default +C value is 12 if METH = 1, and 5 if METH = 2. +C If MAXORD exceeds the default value, it will +C be reduced to the default value. +C If MAXORD is changed during the problem, it may +C cause the current order to be reduced. +C +C MXSTEP IWORK(6) maximum number of (internally defined) steps +C allowed during one call to the solver. +C The default value is 500. +C +C MXHNIL IWORK(7) maximum number of messages printed (per problem) +C warning that T + H = T on a step (H = step size). +C This must be positive to result in a non-default +C value. The default value is 10. +C----------------------------------------------------------------------- +C Optional Outputs. +C +C As optional additional output from DLSODES, the variables listed +C below are quantities related to the performance of DLSODES +C which are available to the user. These are communicated by way of +C the work arrays, but also have internal mnemonic names as shown. +C Except where stated otherwise, all of these outputs are defined +C on any successful return from DLSODES, and on any return with +C ISTATE = -1, -2, -4, -5, or -6. On an illegal input return +C (ISTATE = -3), they will be unchanged from their existing values +C (if any), except possibly for TOLSF, LENRW, and LENIW. +C On any error return, outputs relevant to the error will be defined, +C as noted below. +C +C Name Location Meaning +C +C HU RWORK(11) the step size in t last used (successfully). +C +C HCUR RWORK(12) the step size to be attempted on the next step. +C +C TCUR RWORK(13) the current value of the independent variable +C which the solver has actually reached, i.e. the +C current internal mesh point in t. On output, TCUR +C will always be at least as far as the argument +C T, but may be farther (if interpolation was done). +C +C TOLSF RWORK(14) a tolerance scale factor, greater than 1.0, +C computed when a request for too much accuracy was +C detected (ISTATE = -3 if detected at the start of +C the problem, ISTATE = -2 otherwise). If ITOL is +C left unaltered but RTOL and ATOL are uniformly +C scaled up by a factor of TOLSF for the next call, +C then the solver is deemed likely to succeed. +C (The user may also ignore TOLSF and alter the +C tolerance parameters in any other way appropriate.) +C +C NST IWORK(11) the number of steps taken for the problem so far. +C +C NFE IWORK(12) the number of f evaluations for the problem so far, +C excluding those for structure determination +C (MOSS = 2). +C +C NJE IWORK(13) the number of Jacobian evaluations for the problem +C so far, excluding those for structure determination +C (MOSS = 1). +C +C NQU IWORK(14) the method order last used (successfully). +C +C NQCUR IWORK(15) the order to be attempted on the next step. +C +C IMXER IWORK(16) the index of the component of largest magnitude in +C the weighted local error vector ( E(i)/EWT(i) ), +C on an error return with ISTATE = -4 or -5. +C +C LENRW IWORK(17) the length of RWORK actually required. +C This is defined on normal returns and on an illegal +C input return for insufficient storage. +C +C LENIW IWORK(18) the length of IWORK actually required. +C This is defined on normal returns and on an illegal +C input return for insufficient storage. +C +C NNZ IWORK(19) the number of nonzero elements in the Jacobian +C matrix, including the diagonal (MITER = 1 or 2). +C (This may differ from that given by IA(NEQ+1)-1 +C if MOSS = 0, because of added diagonal entries.) +C +C NGP IWORK(20) the number of groups of column indices, used in +C difference quotient Jacobian aproximations if +C MITER = 2. This is also the number of extra f +C evaluations needed for each Jacobian evaluation. +C +C NLU IWORK(21) the number of sparse LU decompositions for the +C problem so far. +C +C LYH IWORK(22) the base address in RWORK of the history array YH, +C described below in this list. +C +C IPIAN IWORK(23) the base address of the structure descriptor array +C IAN, described below in this list. +C +C IPJAN IWORK(24) the base address of the structure descriptor array +C JAN, described below in this list. +C +C NZL IWORK(25) the number of nonzero elements in the strict lower +C triangle of the LU factorization used in the chord +C iteration (MITER = 1 or 2). +C +C NZU IWORK(26) the number of nonzero elements in the strict upper +C triangle of the LU factorization used in the chord +C iteration (MITER = 1 or 2). +C The total number of nonzeros in the factorization +C is therefore NZL + NZU + NEQ. +C +C The following four arrays are segments of the RWORK array which +C may also be of interest to the user as optional outputs. +C For each array, the table below gives its internal name, +C its base address, and its description. +C For YH and ACOR, the base addresses are in RWORK (a real array). +C The integer arrays IAN and JAN are to be obtained by declaring an +C integer array IWK and identifying IWK(1) with RWORK(21), using either +C an equivalence statement or a subroutine call. Then the base +C addresses IPIAN (of IAN) and IPJAN (of JAN) in IWK are to be obtained +C as optional outputs IWORK(23) and IWORK(24), respectively. +C Thus IAN(1) is IWK(IPIAN), etc. +C +C Name Base Address Description +C +C IAN IPIAN (in IWK) structure descriptor array of size NEQ + 1. +C JAN IPJAN (in IWK) structure descriptor array of size NNZ. +C (see above) IAN and JAN together describe the sparsity +C structure of the Jacobian matrix, as used by +C DLSODES when MITER = 1 or 2. +C JAN contains the row indices of the nonzero +C locations, reading in columnwise order, and +C IAN contains the starting locations in JAN of +C the descriptions of columns 1,...,NEQ, in +C that order, with IAN(1) = 1. Thus for each +C j = 1,...,NEQ, the row indices i of the +C nonzero locations in column j are +C i = JAN(k), IAN(j) .le. k .lt. IAN(j+1). +C Note that IAN(NEQ+1) = NNZ + 1. +C (If MOSS = 0, IAN/JAN may differ from the +C input IA/JA because of a different ordering +C in each column, and added diagonal entries.) +C +C YH LYH the Nordsieck history array, of size NYH by +C (optional (NQCUR + 1), where NYH is the initial value +C output) of NEQ. For j = 0,1,...,NQCUR, column j+1 +C of YH contains HCUR**j/factorial(j) times +C the j-th derivative of the interpolating +C polynomial currently representing the solution, +C evaluated at t = TCUR. The base address LYH +C is another optional output, listed above. +C +C ACOR LENRW-NEQ+1 array of size NEQ used for the accumulated +C corrections on each step, scaled on output +C to represent the estimated local error in y +C on the last step. This is the vector E in +C the description of the error control. It is +C defined only on a successful return from +C DLSODES. +C +C----------------------------------------------------------------------- +C Part 2. Other Routines Callable. +C +C The following are optional calls which the user may make to +C gain additional capabilities in conjunction with DLSODES. +C (The routines XSETUN and XSETF are designed to conform to the +C SLATEC error handling package.) +C +C Form of Call Function +C CALL XSETUN(LUN) Set the logical unit number, LUN, for +C output of messages from DLSODES, if +C the default is not desired. +C The default value of LUN is 6. +C +C CALL XSETF(MFLAG) Set a flag to control the printing of +C messages by DLSODES. +C MFLAG = 0 means do not print. (Danger: +C This risks losing valuable information.) +C MFLAG = 1 means print (the default). +C +C Either of the above calls may be made at +C any time and will take effect immediately. +C +C CALL DSRCMS(RSAV,ISAV,JOB) saves and restores the contents of +C the internal Common blocks used by +C DLSODES (see Part 3 below). +C RSAV must be a real array of length 224 +C or more, and ISAV must be an integer +C array of length 71 or more. +C JOB=1 means save Common into RSAV/ISAV. +C JOB=2 means restore Common from RSAV/ISAV. +C DSRCMS is useful if one is +C interrupting a run and restarting +C later, or alternating between two or +C more problems solved with DLSODES. +C +C CALL DINTDY(,,,,,) Provide derivatives of y, of various +C (see below) orders, at a specified point t, if +C desired. It may be called only after +C a successful return from DLSODES. +C +C The detailed instructions for using DINTDY are as follows. +C The form of the call is: +C +C LYH = IWORK(22) +C CALL DINTDY (T, K, RWORK(LYH), NYH, DKY, IFLAG) +C +C The input parameters are: +C +C T = value of independent variable where answers are desired +C (normally the same as the T last returned by DLSODES). +C For valid results, T must lie between TCUR - HU and TCUR. +C (See optional outputs for TCUR and HU.) +C K = integer order of the derivative desired. K must satisfy +C 0 .le. K .le. NQCUR, where NQCUR is the current order +C (See optional outputs). The capability corresponding +C to K = 0, i.e. computing y(T), is already provided +C by DLSODES directly. Since NQCUR .ge. 1, the first +C derivative dy/dt is always available with DINTDY. +C LYH = the base address of the history array YH, obtained +C as an optional output as shown above. +C NYH = column length of YH, equal to the initial value of NEQ. +C +C The output parameters are: +C +C DKY = a real array of length NEQ containing the computed value +C of the K-th derivative of y(t). +C IFLAG = integer flag, returned as 0 if K and T were legal, +C -1 if K was illegal, and -2 if T was illegal. +C On an error return, a message is also written. +C----------------------------------------------------------------------- +C Part 3. Common Blocks. +C +C If DLSODES is to be used in an overlay situation, the user +C must declare, in the primary overlay, the variables in: +C (1) the call sequence to DLSODES, and +C (2) the two internal Common blocks +C /DLS001/ of length 255 (218 double precision words +C followed by 37 integer words), +C /DLSS01/ of length 40 (6 double precision words +C followed by 34 integer words), +C +C If DLSODES is used on a system in which the contents of internal +C Common blocks are not preserved between calls, the user should +C declare the above Common blocks in the calling program to insure +C that their contents are preserved. +C +C If the solution of a given problem by DLSODES is to be interrupted +C and then later continued, such as when restarting an interrupted run +C or alternating between two or more problems, the user should save, +C following the return from the last DLSODES call prior to the +C interruption, the contents of the call sequence variables and the +C internal Common blocks, and later restore these values before the +C next DLSODES call for that problem. To save and restore the Common +C blocks, use Subroutine DSRCMS (see Part 2 above). +C +C----------------------------------------------------------------------- +C Part 4. Optionally Replaceable Solver Routines. +C +C Below are descriptions of two routines in the DLSODES package which +C relate to the measurement of errors. Either routine can be +C replaced by a user-supplied version, if desired. However, since such +C a replacement may have a major impact on performance, it should be +C done only when absolutely necessary, and only with great caution. +C (Note: The means by which the package version of a routine is +C superseded by the user's version may be system-dependent.) +C +C (a) DEWSET. +C The following subroutine is called just before each internal +C integration step, and sets the array of error weights, EWT, as +C described under ITOL/RTOL/ATOL above: +C Subroutine DEWSET (NEQ, ITOL, RTOL, ATOL, YCUR, EWT) +C where NEQ, ITOL, RTOL, and ATOL are as in the DLSODES call sequence, +C YCUR contains the current dependent variable vector, and +C EWT is the array of weights set by DEWSET. +C +C If the user supplies this subroutine, it must return in EWT(i) +C (i = 1,...,NEQ) a positive quantity suitable for comparing errors +C in y(i) to. The EWT array returned by DEWSET is passed to the DVNORM +C routine (see below), and also used by DLSODES in the computation +C of the optional output IMXER, the diagonal Jacobian approximation, +C and the increments for difference quotient Jacobians. +C +C In the user-supplied version of DEWSET, it may be desirable to use +C the current values of derivatives of y. Derivatives up to order NQ +C are available from the history array YH, described above under +C optional outputs. In DEWSET, YH is identical to the YCUR array, +C extended to NQ + 1 columns with a column length of NYH and scale +C factors of H**j/factorial(j). On the first call for the problem, +C given by NST = 0, NQ is 1 and H is temporarily set to 1.0. +C NYH is the initial value of NEQ. The quantities NQ, H, and NST +C can be obtained by including in DEWSET the statements: +C DOUBLE PRECISION RLS +C COMMON /DLS001/ RLS(218),ILS(37) +C NQ = ILS(33) +C NST = ILS(34) +C H = RLS(212) +C Thus, for example, the current value of dy/dt can be obtained as +C YCUR(NYH+i)/H (i=1,...,NEQ) (and the division by H is +C unnecessary when NST = 0). +C +C (b) DVNORM. +C The following is a real function routine which computes the weighted +C root-mean-square norm of a vector v: +C D = DVNORM (N, V, W) +C where +C N = the length of the vector, +C V = real array of length N containing the vector, +C W = real array of length N containing weights, +C D = SQRT( (1/N) * sum(V(i)*W(i))**2 ). +C DVNORM is called with N = NEQ and with W(i) = 1.0/EWT(i), where +C EWT is as set by Subroutine DEWSET. +C +C If the user supplies this function, it should return a non-negative +C value of DVNORM suitable for use in the error control in DLSODES. +C None of the arguments should be altered by DVNORM. +C For example, a user-supplied DVNORM routine might: +C -substitute a max-norm of (V(i)*W(i)) for the RMS-norm, or +C -ignore some components of V in the norm, with the effect of +C suppressing the error control on those components of y. +C----------------------------------------------------------------------- +C +C***REVISION HISTORY (YYYYMMDD) +C 19810120 DATE WRITTEN +C 19820315 Upgraded MDI in ODRV package: operates on M + M-transpose. +C 19820426 Numerous revisions in use of work arrays; +C use wordlength ratio LENRAT; added IPISP & LRAT to Common; +C added optional outputs IPIAN/IPJAN; +C numerous corrections to comments. +C 19830503 Added routine CNTNZU; added NZL and NZU to /LSS001/; +C changed ADJLR call logic; added optional outputs NZL & NZU; +C revised counter initializations; revised PREP stmt. numbers; +C corrections to comments throughout. +C 19870320 Corrected jump on test of umax in CDRV routine; +C added ISTATE = -7 return. +C 19870330 Major update: corrected comments throughout; +C removed TRET from Common; rewrote EWSET with 4 loops; +C fixed t test in INTDY; added Cray directives in STODE; +C in STODE, fixed DELP init. and logic around PJAC call; +C combined routines to save/restore Common; +C passed LEVEL = 0 in error message calls (except run abort). +C 20010425 Major update: convert source lines to upper case; +C added *DECK lines; changed from 1 to * in dummy dimensions; +C changed names R1MACH/D1MACH to RUMACH/DUMACH; +C renamed routines for uniqueness across single/double prec.; +C converted intrinsic names to generic form; +C removed ILLIN and NTREP (data loaded) from Common; +C removed all 'own' variables from Common; +C changed error messages to quoted strings; +C replaced XERRWV/XERRWD with 1993 revised version; +C converted prologues, comments, error messages to mixed case; +C converted arithmetic IF statements to logical IF statements; +C numerous corrections to prologues and internal comments. +C 20010507 Converted single precision source to double precision. +C 20020502 Corrected declarations in descriptions of user routines. +C 20031105 Restored 'own' variables to Common blocks, to enable +C interrupt/restart feature. +C 20031112 Added SAVE statements for data-loaded constants. +C +C----------------------------------------------------------------------- +C Other routines in the DLSODES package. +C +C In addition to Subroutine DLSODES, the DLSODES package includes the +C following subroutines and function routines: +C DIPREP acts as an iterface between DLSODES and DPREP, and also does +C adjusting of work space pointers and work arrays. +C DPREP is called by DIPREP to compute sparsity and do sparse matrix +C preprocessing if MITER = 1 or 2. +C JGROUP is called by DPREP to compute groups of Jacobian column +C indices for use when MITER = 2. +C ADJLR adjusts the length of required sparse matrix work space. +C It is called by DPREP. +C CNTNZU is called by DPREP and counts the nonzero elements in the +C strict upper triangle of J + J-transpose, where J = df/dy. +C DINTDY computes an interpolated value of the y vector at t = TOUT. +C DSTODE is the core integrator, which does one step of the +C integration and the associated error control. +C DCFODE sets all method coefficients and test constants. +C DPRJS computes and preprocesses the Jacobian matrix J = df/dy +C and the Newton iteration matrix P = I - h*l0*J. +C DSOLSS manages solution of linear system in chord iteration. +C DEWSET sets the error weight vector EWT before each step. +C DVNORM computes the weighted RMS-norm of a vector. +C DSRCMS is a user-callable routine to save and restore +C the contents of the internal Common blocks. +C ODRV constructs a reordering of the rows and columns of +C a matrix by the minimum degree algorithm. ODRV is a +C driver routine which calls Subroutines MD, MDI, MDM, +C MDP, MDU, and SRO. See Ref. 2 for details. (The ODRV +C module has been modified since Ref. 2, however.) +C CDRV performs reordering, symbolic factorization, numerical +C factorization, or linear system solution operations, +C depending on a path argument ipath. CDRV is a +C driver routine which calls Subroutines NROC, NSFC, +C NNFC, NNSC, and NNTC. See Ref. 3 for details. +C DLSODES uses CDRV to solve linear systems in which the +C coefficient matrix is P = I - con*J, where I is the +C identity, con is a scalar, and J is an approximation to +C the Jacobian df/dy. Because CDRV deals with rowwise +C sparsity descriptions, CDRV works with P-transpose, not P. +C DUMACH computes the unit roundoff in a machine-independent manner. +C XERRWD, XSETUN, XSETF, IXSAV, and IUMACH handle the printing of all +C error messages and warnings. XERRWD is machine-dependent. +C Note: DVNORM, DUMACH, IXSAV, and IUMACH are function routines. +C All the others are subroutines. +C +C----------------------------------------------------------------------- + EXTERNAL DPRJS, DSOLSS + DOUBLE PRECISION DUMACH, DVNORM + INTEGER INIT, MXSTEP, MXHNIL, NHNIL, NSLAST, NYH, IOWNS, + 1 ICF, IERPJ, IERSL, JCUR, JSTART, KFLAG, L, + 2 LYH, LEWT, LACOR, LSAVF, LWM, LIWM, METH, MITER, + 3 MAXORD, MAXCOR, MSBP, MXNCF, N, NQ, NST, NFE, NJE, NQU + INTEGER IPLOST, IESP, ISTATC, IYS, IBA, IBIAN, IBJAN, IBJGP, + 1 IPIAN, IPJAN, IPJGP, IPIGP, IPR, IPC, IPIC, IPISP, IPRSP, IPA, + 2 LENYH, LENYHM, LENWK, LREQ, LRAT, LREST, LWMIN, MOSS, MSBJ, + 3 NSLJ, NGP, NLU, NNZ, NSP, NZL, NZU + INTEGER I, I1, I2, IFLAG, IMAX, IMUL, IMXER, IPFLAG, IPGO, IREM, + 1 J, KGO, LENRAT, LENYHT, LENIW, LENRW, LF0, LIA, LJA, + 2 LRTEM, LWTEM, LYHD, LYHN, MF1, MORD, MXHNL0, MXSTP0, NCOLM + DOUBLE PRECISION ROWNS, + 1 CCMAX, EL0, H, HMIN, HMXI, HU, RC, TN, UROUND + DOUBLE PRECISION CON0, CONMIN, CCMXJ, PSMALL, RBIG, SETH + DOUBLE PRECISION ATOLI, AYI, BIG, EWTI, H0, HMAX, HMX, RH, RTOLI, + 1 TCRIT, TDIST, TNEXT, TOL, TOLSF, TP, SIZE, SUM, W0 + DIMENSION MORD(2) + LOGICAL IHIT + CHARACTER*60 MSG + SAVE LENRAT, MORD, MXSTP0, MXHNL0 +C----------------------------------------------------------------------- +C The following two internal Common blocks contain +C (a) variables which are local to any subroutine but whose values must +C be preserved between calls to the routine ("own" variables), and +C (b) variables which are communicated between subroutines. +C The block DLS001 is declared in subroutines DLSODES, DIPREP, DPREP, +C DINTDY, DSTODE, DPRJS, and DSOLSS. +C The block DLSS01 is declared in subroutines DLSODES, DIPREP, DPREP, +C DPRJS, and DSOLSS. +C Groups of variables are replaced by dummy arrays in the Common +C declarations in routines where those variables are not used. +C----------------------------------------------------------------------- + COMMON /DLS001/ ROWNS(209), + 1 CCMAX, EL0, H, HMIN, HMXI, HU, RC, TN, UROUND, + 2 INIT, MXSTEP, MXHNIL, NHNIL, NSLAST, NYH, IOWNS(6), + 3 ICF, IERPJ, IERSL, JCUR, JSTART, KFLAG, L, + 4 LYH, LEWT, LACOR, LSAVF, LWM, LIWM, METH, MITER, + 5 MAXORD, MAXCOR, MSBP, MXNCF, N, NQ, NST, NFE, NJE, NQU +C + COMMON /DLSS01/ CON0, CONMIN, CCMXJ, PSMALL, RBIG, SETH, + 1 IPLOST, IESP, ISTATC, IYS, IBA, IBIAN, IBJAN, IBJGP, + 2 IPIAN, IPJAN, IPJGP, IPIGP, IPR, IPC, IPIC, IPISP, IPRSP, IPA, + 3 LENYH, LENYHM, LENWK, LREQ, LRAT, LREST, LWMIN, MOSS, MSBJ, + 4 NSLJ, NGP, NLU, NNZ, NSP, NZL, NZU +C + DATA MORD(1),MORD(2)/12,5/, MXSTP0/500/, MXHNL0/10/ +C----------------------------------------------------------------------- +C In the Data statement below, set LENRAT equal to the ratio of +C the wordlength for a real number to that for an integer. Usually, +C LENRAT = 1 for single precision and 2 for double precision. If the +C true ratio is not an integer, use the next smaller integer (.ge. 1). +C----------------------------------------------------------------------- + DATA LENRAT/2/ +C----------------------------------------------------------------------- +C Block A. +C This code block is executed on every call. +C It tests ISTATE and ITASK for legality and branches appropriately. +C If ISTATE .gt. 1 but the flag INIT shows that initialization has +C not yet been done, an error return occurs. +C If ISTATE = 1 and TOUT = T, return immediately. +C----------------------------------------------------------------------- + IF (ISTATE .LT. 1 .OR. ISTATE .GT. 3) GO TO 601 + IF (ITASK .LT. 1 .OR. ITASK .GT. 5) GO TO 602 + IF (ISTATE .EQ. 1) GO TO 10 + IF (INIT .EQ. 0) GO TO 603 + IF (ISTATE .EQ. 2) GO TO 200 + GO TO 20 + 10 INIT = 0 + IF (TOUT .EQ. T) RETURN +C----------------------------------------------------------------------- +C Block B. +C The next code block is executed for the initial call (ISTATE = 1), +C or for a continuation call with parameter changes (ISTATE = 3). +C It contains checking of all inputs and various initializations. +C If ISTATE = 1, the final setting of work space pointers, the matrix +C preprocessing, and other initializations are done in Block C. +C +C First check legality of the non-optional inputs NEQ, ITOL, IOPT, +C MF, ML, and MU. +C----------------------------------------------------------------------- + 20 IF (NEQ(1) .LE. 0) GO TO 604 + IF (ISTATE .EQ. 1) GO TO 25 + IF (NEQ(1) .GT. N) GO TO 605 + 25 N = NEQ(1) + IF (ITOL .LT. 1 .OR. ITOL .GT. 4) GO TO 606 + IF (IOPT .LT. 0 .OR. IOPT .GT. 1) GO TO 607 + MOSS = MF/100 + MF1 = MF - 100*MOSS + METH = MF1/10 + MITER = MF1 - 10*METH + IF (MOSS .LT. 0 .OR. MOSS .GT. 2) GO TO 608 + IF (METH .LT. 1 .OR. METH .GT. 2) GO TO 608 + IF (MITER .LT. 0 .OR. MITER .GT. 3) GO TO 608 + IF (MITER .EQ. 0 .OR. MITER .EQ. 3) MOSS = 0 +C Next process and check the optional inputs. -------------------------- + IF (IOPT .EQ. 1) GO TO 40 + MAXORD = MORD(METH) + MXSTEP = MXSTP0 + MXHNIL = MXHNL0 + IF (ISTATE .EQ. 1) H0 = 0.0D0 + HMXI = 0.0D0 + HMIN = 0.0D0 + SETH = 0.0D0 + GO TO 60 + 40 MAXORD = IWORK(5) + IF (MAXORD .LT. 0) GO TO 611 + IF (MAXORD .EQ. 0) MAXORD = 100 + MAXORD = MIN(MAXORD,MORD(METH)) + MXSTEP = IWORK(6) + IF (MXSTEP .LT. 0) GO TO 612 + IF (MXSTEP .EQ. 0) MXSTEP = MXSTP0 + MXHNIL = IWORK(7) + IF (MXHNIL .LT. 0) GO TO 613 + IF (MXHNIL .EQ. 0) MXHNIL = MXHNL0 + IF (ISTATE .NE. 1) GO TO 50 + H0 = RWORK(5) + IF ((TOUT - T)*H0 .LT. 0.0D0) GO TO 614 + 50 HMAX = RWORK(6) + IF (HMAX .LT. 0.0D0) GO TO 615 + HMXI = 0.0D0 + IF (HMAX .GT. 0.0D0) HMXI = 1.0D0/HMAX + HMIN = RWORK(7) + IF (HMIN .LT. 0.0D0) GO TO 616 + SETH = RWORK(8) + IF (SETH .LT. 0.0D0) GO TO 609 +C Check RTOL and ATOL for legality. ------------------------------------ + 60 RTOLI = RTOL(1) + ATOLI = ATOL(1) + DO 65 I = 1,N + IF (ITOL .GE. 3) RTOLI = RTOL(I) + IF (ITOL .EQ. 2 .OR. ITOL .EQ. 4) ATOLI = ATOL(I) + IF (RTOLI .LT. 0.0D0) GO TO 619 + IF (ATOLI .LT. 0.0D0) GO TO 620 + 65 CONTINUE +C----------------------------------------------------------------------- +C Compute required work array lengths, as far as possible, and test +C these against LRW and LIW. Then set tentative pointers for work +C arrays. Pointers to RWORK/IWORK segments are named by prefixing L to +C the name of the segment. E.g., the segment YH starts at RWORK(LYH). +C Segments of RWORK (in order) are denoted WM, YH, SAVF, EWT, ACOR. +C If MITER = 1 or 2, the required length of the matrix work space WM +C is not yet known, and so a crude minimum value is used for the +C initial tests of LRW and LIW, and YH is temporarily stored as far +C to the right in RWORK as possible, to leave the maximum amount +C of space for WM for matrix preprocessing. Thus if MITER = 1 or 2 +C and MOSS .ne. 2, some of the segments of RWORK are temporarily +C omitted, as they are not needed in the preprocessing. These +C omitted segments are: ACOR if ISTATE = 1, EWT and ACOR if ISTATE = 3 +C and MOSS = 1, and SAVF, EWT, and ACOR if ISTATE = 3 and MOSS = 0. +C----------------------------------------------------------------------- + LRAT = LENRAT + IF (ISTATE .EQ. 1) NYH = N + LWMIN = 0 + IF (MITER .EQ. 1) LWMIN = 4*N + 10*N/LRAT + IF (MITER .EQ. 2) LWMIN = 4*N + 11*N/LRAT + IF (MITER .EQ. 3) LWMIN = N + 2 + LENYH = (MAXORD+1)*NYH + LREST = LENYH + 3*N + LENRW = 20 + LWMIN + LREST + IWORK(17) = LENRW + LENIW = 30 + IF (MOSS .EQ. 0 .AND. MITER .NE. 0 .AND. MITER .NE. 3) + 1 LENIW = LENIW + N + 1 + IWORK(18) = LENIW + IF (LENRW .GT. LRW) GO TO 617 + IF (LENIW .GT. LIW) GO TO 618 + LIA = 31 + IF (MOSS .EQ. 0 .AND. MITER .NE. 0 .AND. MITER .NE. 3) + 1 LENIW = LENIW + IWORK(LIA+N) - 1 + IWORK(18) = LENIW + IF (LENIW .GT. LIW) GO TO 618 + LJA = LIA + N + 1 + LIA = MIN(LIA,LIW) + LJA = MIN(LJA,LIW) + LWM = 21 + IF (ISTATE .EQ. 1) NQ = 1 + NCOLM = MIN(NQ+1,MAXORD+2) + LENYHM = NCOLM*NYH + LENYHT = LENYH + IF (MITER .EQ. 1 .OR. MITER .EQ. 2) LENYHT = LENYHM + IMUL = 2 + IF (ISTATE .EQ. 3) IMUL = MOSS + IF (MOSS .EQ. 2) IMUL = 3 + LRTEM = LENYHT + IMUL*N + LWTEM = LWMIN + IF (MITER .EQ. 1 .OR. MITER .EQ. 2) LWTEM = LRW - 20 - LRTEM + LENWK = LWTEM + LYHN = LWM + LWTEM + LSAVF = LYHN + LENYHT + LEWT = LSAVF + N + LACOR = LEWT + N + ISTATC = ISTATE + IF (ISTATE .EQ. 1) GO TO 100 +C----------------------------------------------------------------------- +C ISTATE = 3. Move YH to its new location. +C Note that only the part of YH needed for the next step, namely +C MIN(NQ+1,MAXORD+2) columns, is actually moved. +C A temporary error weight array EWT is loaded if MOSS = 2. +C Sparse matrix processing is done in DIPREP/DPREP if MITER = 1 or 2. +C If MAXORD was reduced below NQ, then the pointers are finally set +C so that SAVF is identical to YH(*,MAXORD+2). +C----------------------------------------------------------------------- + LYHD = LYH - LYHN + IMAX = LYHN - 1 + LENYHM +C Move YH. Move right if LYHD < 0; move left if LYHD > 0. ------------- + IF (LYHD .LT. 0) THEN + DO 72 I = LYHN,IMAX + J = IMAX + LYHN - I + 72 RWORK(J) = RWORK(J+LYHD) + ENDIF + IF (LYHD .GT. 0) THEN + DO 76 I = LYHN,IMAX + 76 RWORK(I) = RWORK(I+LYHD) + ENDIF + 80 LYH = LYHN + IWORK(22) = LYH + IF (MITER .EQ. 0 .OR. MITER .EQ. 3) GO TO 92 + IF (MOSS .NE. 2) GO TO 85 +C Temporarily load EWT if MITER = 1 or 2 and MOSS = 2. ----------------- + CALL DEWSET (N, ITOL, RTOL, ATOL, RWORK(LYH), RWORK(LEWT)) + DO 82 I = 1,N + IF (RWORK(I+LEWT-1) .LE. 0.0D0) GO TO 621 + 82 RWORK(I+LEWT-1) = 1.0D0/RWORK(I+LEWT-1) + 85 CONTINUE +C DIPREP and DPREP do sparse matrix preprocessing if MITER = 1 or 2. --- + LSAVF = MIN(LSAVF,LRW) + LEWT = MIN(LEWT,LRW) + LACOR = MIN(LACOR,LRW) + CALL DIPREP (NEQ, Y, RWORK, IWORK(LIA),IWORK(LJA), IPFLAG, F, JAC) + LENRW = LWM - 1 + LENWK + LREST + IWORK(17) = LENRW + IF (IPFLAG .NE. -1) IWORK(23) = IPIAN + IF (IPFLAG .NE. -1) IWORK(24) = IPJAN + IPGO = -IPFLAG + 1 + GO TO (90, 628, 629, 630, 631, 632, 633), IPGO + 90 IWORK(22) = LYH + IF (LENRW .GT. LRW) GO TO 617 +C Set flag to signal parameter changes to DSTODE. ---------------------- + 92 JSTART = -1 + IF (N .EQ. NYH) GO TO 200 +C NEQ was reduced. Zero part of YH to avoid undefined references. ----- + I1 = LYH + L*NYH + I2 = LYH + (MAXORD + 1)*NYH - 1 + IF (I1 .GT. I2) GO TO 200 + DO 95 I = I1,I2 + 95 RWORK(I) = 0.0D0 + GO TO 200 +C----------------------------------------------------------------------- +C Block C. +C The next block is for the initial call only (ISTATE = 1). +C It contains all remaining initializations, the initial call to F, +C the sparse matrix preprocessing (MITER = 1 or 2), and the +C calculation of the initial step size. +C The error weights in EWT are inverted after being loaded. +C----------------------------------------------------------------------- + 100 CONTINUE + LYH = LYHN + IWORK(22) = LYH + TN = T + NST = 0 + H = 1.0D0 + NNZ = 0 + NGP = 0 + NZL = 0 + NZU = 0 +C Load the initial value vector in YH. --------------------------------- + DO 105 I = 1,N + 105 RWORK(I+LYH-1) = Y(I) +C Initial call to F. (LF0 points to YH(*,2).) ------------------------- + LF0 = LYH + NYH + CALL F (NEQ, T, Y, RWORK(LF0)) + NFE = 1 +C Load and invert the EWT array. (H is temporarily set to 1.0.) ------- + CALL DEWSET (N, ITOL, RTOL, ATOL, RWORK(LYH), RWORK(LEWT)) + DO 110 I = 1,N + IF (RWORK(I+LEWT-1) .LE. 0.0D0) GO TO 621 + 110 RWORK(I+LEWT-1) = 1.0D0/RWORK(I+LEWT-1) + IF (MITER .EQ. 0 .OR. MITER .EQ. 3) GO TO 120 +C DIPREP and DPREP do sparse matrix preprocessing if MITER = 1 or 2. --- + LACOR = MIN(LACOR,LRW) + CALL DIPREP (NEQ, Y, RWORK, IWORK(LIA),IWORK(LJA), IPFLAG, F, JAC) + LENRW = LWM - 1 + LENWK + LREST + IWORK(17) = LENRW + IF (IPFLAG .NE. -1) IWORK(23) = IPIAN + IF (IPFLAG .NE. -1) IWORK(24) = IPJAN + IPGO = -IPFLAG + 1 + GO TO (115, 628, 629, 630, 631, 632, 633), IPGO + 115 IWORK(22) = LYH + IF (LENRW .GT. LRW) GO TO 617 +C Check TCRIT for legality (ITASK = 4 or 5). --------------------------- + 120 CONTINUE + IF (ITASK .NE. 4 .AND. ITASK .NE. 5) GO TO 125 + TCRIT = RWORK(1) + IF ((TCRIT - TOUT)*(TOUT - T) .LT. 0.0D0) GO TO 625 + IF (H0 .NE. 0.0D0 .AND. (T + H0 - TCRIT)*H0 .GT. 0.0D0) + 1 H0 = TCRIT - T +C Initialize all remaining parameters. --------------------------------- + 125 UROUND = DUMACH() + JSTART = 0 + IF (MITER .NE. 0) RWORK(LWM) = SQRT(UROUND) + MSBJ = 50 + NSLJ = 0 + CCMXJ = 0.2D0 + PSMALL = 1000.0D0*UROUND + RBIG = 0.01D0/PSMALL + NHNIL = 0 + NJE = 0 + NLU = 0 + NSLAST = 0 + HU = 0.0D0 + NQU = 0 + CCMAX = 0.3D0 + MAXCOR = 3 + MSBP = 20 + MXNCF = 10 +C----------------------------------------------------------------------- +C The coding below computes the step size, H0, to be attempted on the +C first step, unless the user has supplied a value for this. +C First check that TOUT - T differs significantly from zero. +C A scalar tolerance quantity TOL is computed, as MAX(RTOL(i)) +C if this is positive, or MAX(ATOL(i)/ABS(Y(i))) otherwise, adjusted +C so as to be between 100*UROUND and 1.0E-3. +C Then the computed value H0 is given by.. +C NEQ +C H0**2 = TOL / ( w0**-2 + (1/NEQ) * Sum ( f(i)/ywt(i) )**2 ) +C 1 +C where w0 = MAX ( ABS(T), ABS(TOUT) ), +C f(i) = i-th component of initial value of f, +C ywt(i) = EWT(i)/TOL (a weight for y(i)). +C The sign of H0 is inferred from the initial values of TOUT and T. +C ABS(H0) is made .le. ABS(TOUT-T) in any case. +C----------------------------------------------------------------------- + LF0 = LYH + NYH + IF (H0 .NE. 0.0D0) GO TO 180 + TDIST = ABS(TOUT - T) + W0 = MAX(ABS(T),ABS(TOUT)) + IF (TDIST .LT. 2.0D0*UROUND*W0) GO TO 622 + TOL = RTOL(1) + IF (ITOL .LE. 2) GO TO 140 + DO 130 I = 1,N + 130 TOL = MAX(TOL,RTOL(I)) + 140 IF (TOL .GT. 0.0D0) GO TO 160 + ATOLI = ATOL(1) + DO 150 I = 1,N + IF (ITOL .EQ. 2 .OR. ITOL .EQ. 4) ATOLI = ATOL(I) + AYI = ABS(Y(I)) + IF (AYI .NE. 0.0D0) TOL = MAX(TOL,ATOLI/AYI) + 150 CONTINUE + 160 TOL = MAX(TOL,100.0D0*UROUND) + TOL = MIN(TOL,0.001D0) + SUM = DVNORM (N, RWORK(LF0), RWORK(LEWT)) + SUM = 1.0D0/(TOL*W0*W0) + TOL*SUM**2 + H0 = 1.0D0/SQRT(SUM) + H0 = MIN(H0,TDIST) + H0 = SIGN(H0,TOUT-T) +C Adjust H0 if necessary to meet HMAX bound. --------------------------- + 180 RH = ABS(H0)*HMXI + IF (RH .GT. 1.0D0) H0 = H0/RH +C Load H with H0 and scale YH(*,2) by H0. ------------------------------ + H = H0 + DO 190 I = 1,N + 190 RWORK(I+LF0-1) = H0*RWORK(I+LF0-1) + GO TO 270 +C----------------------------------------------------------------------- +C Block D. +C The next code block is for continuation calls only (ISTATE = 2 or 3) +C and is to check stop conditions before taking a step. +C----------------------------------------------------------------------- + 200 NSLAST = NST + GO TO (210, 250, 220, 230, 240), ITASK + 210 IF ((TN - TOUT)*H .LT. 0.0D0) GO TO 250 + CALL DINTDY (TOUT, 0, RWORK(LYH), NYH, Y, IFLAG) + IF (IFLAG .NE. 0) GO TO 627 + T = TOUT + GO TO 420 + 220 TP = TN - HU*(1.0D0 + 100.0D0*UROUND) + IF ((TP - TOUT)*H .GT. 0.0D0) GO TO 623 + IF ((TN - TOUT)*H .LT. 0.0D0) GO TO 250 + GO TO 400 + 230 TCRIT = RWORK(1) + IF ((TN - TCRIT)*H .GT. 0.0D0) GO TO 624 + IF ((TCRIT - TOUT)*H .LT. 0.0D0) GO TO 625 + IF ((TN - TOUT)*H .LT. 0.0D0) GO TO 245 + CALL DINTDY (TOUT, 0, RWORK(LYH), NYH, Y, IFLAG) + IF (IFLAG .NE. 0) GO TO 627 + T = TOUT + GO TO 420 + 240 TCRIT = RWORK(1) + IF ((TN - TCRIT)*H .GT. 0.0D0) GO TO 624 + 245 HMX = ABS(TN) + ABS(H) + IHIT = ABS(TN - TCRIT) .LE. 100.0D0*UROUND*HMX + IF (IHIT) GO TO 400 + TNEXT = TN + H*(1.0D0 + 4.0D0*UROUND) + IF ((TNEXT - TCRIT)*H .LE. 0.0D0) GO TO 250 + H = (TCRIT - TN)*(1.0D0 - 4.0D0*UROUND) + IF (ISTATE .EQ. 2) JSTART = -2 +C----------------------------------------------------------------------- +C Block E. +C The next block is normally executed for all calls and contains +C the call to the one-step core integrator DSTODE. +C +C This is a looping point for the integration steps. +C +C First check for too many steps being taken, update EWT (if not at +C start of problem), check for too much accuracy being requested, and +C check for H below the roundoff level in T. +C----------------------------------------------------------------------- + 250 CONTINUE + IF ((NST-NSLAST) .GE. MXSTEP) GO TO 500 + CALL DEWSET (N, ITOL, RTOL, ATOL, RWORK(LYH), RWORK(LEWT)) + DO 260 I = 1,N + IF (RWORK(I+LEWT-1) .LE. 0.0D0) GO TO 510 + 260 RWORK(I+LEWT-1) = 1.0D0/RWORK(I+LEWT-1) + 270 TOLSF = UROUND*DVNORM (N, RWORK(LYH), RWORK(LEWT)) + IF (TOLSF .LE. 1.0D0) GO TO 280 + TOLSF = TOLSF*2.0D0 + IF (NST .EQ. 0) GO TO 626 + GO TO 520 + 280 IF ((TN + H) .NE. TN) GO TO 290 + NHNIL = NHNIL + 1 + IF (NHNIL .GT. MXHNIL) GO TO 290 + MSG = 'DLSODES- Warning..Internal T (=R1) and H (=R2) are' + CALL XERRWD (MSG, 50, 101, 0, 0, 0, 0, 0, 0.0D0, 0.0D0) + MSG=' such that in the machine, T + H = T on the next step ' + CALL XERRWD (MSG, 60, 101, 0, 0, 0, 0, 0, 0.0D0, 0.0D0) + MSG = ' (H = step size). Solver will continue anyway.' + CALL XERRWD (MSG, 50, 101, 0, 0, 0, 0, 2, TN, H) + IF (NHNIL .LT. MXHNIL) GO TO 290 + MSG = 'DLSODES- Above warning has been issued I1 times. ' + CALL XERRWD (MSG, 50, 102, 0, 0, 0, 0, 0, 0.0D0, 0.0D0) + MSG = ' It will not be issued again for this problem.' + CALL XERRWD (MSG, 50, 102, 0, 1, MXHNIL, 0, 0, 0.0D0, 0.0D0) + 290 CONTINUE +C----------------------------------------------------------------------- +C CALL DSTODE(NEQ,Y,YH,NYH,YH,EWT,SAVF,ACOR,WM,WM,F,JAC,DPRJS,DSOLSS) +C----------------------------------------------------------------------- + CALL DSTODE (NEQ, Y, RWORK(LYH), NYH, RWORK(LYH), RWORK(LEWT), + 1 RWORK(LSAVF), RWORK(LACOR), RWORK(LWM), RWORK(LWM), + 2 F, JAC, DPRJS, DSOLSS) + KGO = 1 - KFLAG + GO TO (300, 530, 540, 550), KGO +C----------------------------------------------------------------------- +C Block F. +C The following block handles the case of a successful return from the +C core integrator (KFLAG = 0). Test for stop conditions. +C----------------------------------------------------------------------- + 300 INIT = 1 + GO TO (310, 400, 330, 340, 350), ITASK +C ITASK = 1. if TOUT has been reached, interpolate. ------------------- + 310 IF ((TN - TOUT)*H .LT. 0.0D0) GO TO 250 + CALL DINTDY (TOUT, 0, RWORK(LYH), NYH, Y, IFLAG) + T = TOUT + GO TO 420 +C ITASK = 3. Jump to exit if TOUT was reached. ------------------------ + 330 IF ((TN - TOUT)*H .GE. 0.0D0) GO TO 400 + GO TO 250 +C ITASK = 4. See if TOUT or TCRIT was reached. Adjust H if necessary. + 340 IF ((TN - TOUT)*H .LT. 0.0D0) GO TO 345 + CALL DINTDY (TOUT, 0, RWORK(LYH), NYH, Y, IFLAG) + T = TOUT + GO TO 420 + 345 HMX = ABS(TN) + ABS(H) + IHIT = ABS(TN - TCRIT) .LE. 100.0D0*UROUND*HMX + IF (IHIT) GO TO 400 + TNEXT = TN + H*(1.0D0 + 4.0D0*UROUND) + IF ((TNEXT - TCRIT)*H .LE. 0.0D0) GO TO 250 + H = (TCRIT - TN)*(1.0D0 - 4.0D0*UROUND) + JSTART = -2 + GO TO 250 +C ITASK = 5. See if TCRIT was reached and jump to exit. --------------- + 350 HMX = ABS(TN) + ABS(H) + IHIT = ABS(TN - TCRIT) .LE. 100.0D0*UROUND*HMX +C----------------------------------------------------------------------- +C Block G. +C The following block handles all successful returns from DLSODES. +C If ITASK .ne. 1, Y is loaded from YH and T is set accordingly. +C ISTATE is set to 2, and the optional outputs are loaded into the +C work arrays before returning. +C----------------------------------------------------------------------- + 400 DO 410 I = 1,N + 410 Y(I) = RWORK(I+LYH-1) + T = TN + IF (ITASK .NE. 4 .AND. ITASK .NE. 5) GO TO 420 + IF (IHIT) T = TCRIT + 420 ISTATE = 2 + RWORK(11) = HU + RWORK(12) = H + RWORK(13) = TN + IWORK(11) = NST + IWORK(12) = NFE + IWORK(13) = NJE + IWORK(14) = NQU + IWORK(15) = NQ + IWORK(19) = NNZ + IWORK(20) = NGP + IWORK(21) = NLU + IWORK(25) = NZL + IWORK(26) = NZU + RETURN +C----------------------------------------------------------------------- +C Block H. +C The following block handles all unsuccessful returns other than +C those for illegal input. First the error message routine is called. +C If there was an error test or convergence test failure, IMXER is set. +C Then Y is loaded from YH and T is set to TN. +C The optional outputs are loaded into the work arrays before returning. +C----------------------------------------------------------------------- +C The maximum number of steps was taken before reaching TOUT. ---------- + 500 MSG = 'DLSODES- At current T (=R1), MXSTEP (=I1) steps ' + CALL XERRWD (MSG, 50, 201, 0, 0, 0, 0, 0, 0.0D0, 0.0D0) + MSG = ' taken on this call before reaching TOUT ' + CALL XERRWD (MSG, 50, 201, 0, 1, MXSTEP, 0, 1, TN, 0.0D0) + ISTATE = -1 + GO TO 580 +C EWT(i) .le. 0.0 for some i (not at start of problem). ---------------- + 510 EWTI = RWORK(LEWT+I-1) + MSG = 'DLSODES- At T (=R1), EWT(I1) has become R2 .le. 0.' + CALL XERRWD (MSG, 50, 202, 0, 1, I, 0, 2, TN, EWTI) + ISTATE = -6 + GO TO 580 +C Too much accuracy requested for machine precision. ------------------- + 520 MSG = 'DLSODES- At T (=R1), too much accuracy requested ' + CALL XERRWD (MSG, 50, 203, 0, 0, 0, 0, 0, 0.0D0, 0.0D0) + MSG = ' for precision of machine.. See TOLSF (=R2) ' + CALL XERRWD (MSG, 50, 203, 0, 0, 0, 0, 2, TN, TOLSF) + RWORK(14) = TOLSF + ISTATE = -2 + GO TO 580 +C KFLAG = -1. Error test failed repeatedly or with ABS(H) = HMIN. ----- + 530 MSG = 'DLSODES- At T(=R1) and step size H(=R2), the error' + CALL XERRWD (MSG, 50, 204, 0, 0, 0, 0, 0, 0.0D0, 0.0D0) + MSG = ' test failed repeatedly or with ABS(H) = HMIN' + CALL XERRWD (MSG, 50, 204, 0, 0, 0, 0, 2, TN, H) + ISTATE = -4 + GO TO 560 +C KFLAG = -2. Convergence failed repeatedly or with ABS(H) = HMIN. ---- + 540 MSG = 'DLSODES- At T (=R1) and step size H (=R2), the ' + CALL XERRWD (MSG, 50, 205, 0, 0, 0, 0, 0, 0.0D0, 0.0D0) + MSG = ' corrector convergence failed repeatedly ' + CALL XERRWD (MSG, 50, 205, 0, 0, 0, 0, 0, 0.0D0, 0.0D0) + MSG = ' or with ABS(H) = HMIN ' + CALL XERRWD (MSG, 30, 205, 0, 0, 0, 0, 2, TN, H) + ISTATE = -5 + GO TO 560 +C KFLAG = -3. Fatal error flag returned by DPRJS or DSOLSS (CDRV). ---- + 550 MSG = 'DLSODES- At T (=R1) and step size H (=R2), a fatal' + CALL XERRWD (MSG, 50, 207, 0, 0, 0, 0, 0, 0.0D0, 0.0D0) + MSG = ' error flag was returned by CDRV (by way of ' + CALL XERRWD (MSG, 50, 207, 0, 0, 0, 0, 0, 0.0D0, 0.0D0) + MSG = ' Subroutine DPRJS or DSOLSS) ' + CALL XERRWD (MSG, 40, 207, 0, 0, 0, 0, 2, TN, H) + ISTATE = -7 + GO TO 580 +C Compute IMXER if relevant. ------------------------------------------- + 560 BIG = 0.0D0 + IMXER = 1 + DO 570 I = 1,N + SIZE = ABS(RWORK(I+LACOR-1)*RWORK(I+LEWT-1)) + IF (BIG .GE. SIZE) GO TO 570 + BIG = SIZE + IMXER = I + 570 CONTINUE + IWORK(16) = IMXER +C Set Y vector, T, and optional outputs. ------------------------------- + 580 DO 590 I = 1,N + 590 Y(I) = RWORK(I+LYH-1) + T = TN + RWORK(11) = HU + RWORK(12) = H + RWORK(13) = TN + IWORK(11) = NST + IWORK(12) = NFE + IWORK(13) = NJE + IWORK(14) = NQU + IWORK(15) = NQ + IWORK(19) = NNZ + IWORK(20) = NGP + IWORK(21) = NLU + IWORK(25) = NZL + IWORK(26) = NZU + RETURN +C----------------------------------------------------------------------- +C Block I. +C The following block handles all error returns due to illegal input +C (ISTATE = -3), as detected before calling the core integrator. +C First the error message routine is called. If the illegal input +C is a negative ISTATE, the run is aborted (apparent infinite loop). +C----------------------------------------------------------------------- + 601 MSG = 'DLSODES- ISTATE (=I1) illegal.' + CALL XERRWD (MSG, 30, 1, 0, 1, ISTATE, 0, 0, 0.0D0, 0.0D0) + IF (ISTATE .LT. 0) GO TO 800 + GO TO 700 + 602 MSG = 'DLSODES- ITASK (=I1) illegal. ' + CALL XERRWD (MSG, 30, 2, 0, 1, ITASK, 0, 0, 0.0D0, 0.0D0) + GO TO 700 + 603 MSG = 'DLSODES- ISTATE.gt.1 but DLSODES not initialized. ' + CALL XERRWD (MSG, 50, 3, 0, 0, 0, 0, 0, 0.0D0, 0.0D0) + GO TO 700 + 604 MSG = 'DLSODES- NEQ (=I1) .lt. 1 ' + CALL XERRWD (MSG, 30, 4, 0, 1, NEQ(1), 0, 0, 0.0D0, 0.0D0) + GO TO 700 + 605 MSG = 'DLSODES- ISTATE = 3 and NEQ increased (I1 to I2). ' + CALL XERRWD (MSG, 50, 5, 0, 2, N, NEQ(1), 0, 0.0D0, 0.0D0) + GO TO 700 + 606 MSG = 'DLSODES- ITOL (=I1) illegal. ' + CALL XERRWD (MSG, 30, 6, 0, 1, ITOL, 0, 0, 0.0D0, 0.0D0) + GO TO 700 + 607 MSG = 'DLSODES- IOPT (=I1) illegal. ' + CALL XERRWD (MSG, 30, 7, 0, 1, IOPT, 0, 0, 0.0D0, 0.0D0) + GO TO 700 + 608 MSG = 'DLSODES- MF (=I1) illegal. ' + CALL XERRWD (MSG, 30, 8, 0, 1, MF, 0, 0, 0.0D0, 0.0D0) + GO TO 700 + 609 MSG = 'DLSODES- SETH (=R1) .lt. 0.0 ' + CALL XERRWD (MSG, 30, 9, 0, 0, 0, 0, 1, SETH, 0.0D0) + GO TO 700 + 611 MSG = 'DLSODES- MAXORD (=I1) .lt. 0 ' + CALL XERRWD (MSG, 30, 11, 0, 1, MAXORD, 0, 0, 0.0D0, 0.0D0) + GO TO 700 + 612 MSG = 'DLSODES- MXSTEP (=I1) .lt. 0 ' + CALL XERRWD (MSG, 30, 12, 0, 1, MXSTEP, 0, 0, 0.0D0, 0.0D0) + GO TO 700 + 613 MSG = 'DLSODES- MXHNIL (=I1) .lt. 0 ' + CALL XERRWD (MSG, 30, 13, 0, 1, MXHNIL, 0, 0, 0.0D0, 0.0D0) + GO TO 700 + 614 MSG = 'DLSODES- TOUT (=R1) behind T (=R2) ' + CALL XERRWD (MSG, 40, 14, 0, 0, 0, 0, 2, TOUT, T) + MSG = ' Integration direction is given by H0 (=R1) ' + CALL XERRWD (MSG, 50, 14, 0, 0, 0, 0, 1, H0, 0.0D0) + GO TO 700 + 615 MSG = 'DLSODES- HMAX (=R1) .lt. 0.0 ' + CALL XERRWD (MSG, 30, 15, 0, 0, 0, 0, 1, HMAX, 0.0D0) + GO TO 700 + 616 MSG = 'DLSODES- HMIN (=R1) .lt. 0.0 ' + CALL XERRWD (MSG, 30, 16, 0, 0, 0, 0, 1, HMIN, 0.0D0) + GO TO 700 + 617 MSG = 'DLSODES- RWORK length is insufficient to proceed. ' + CALL XERRWD (MSG, 50, 17, 0, 0, 0, 0, 0, 0.0D0, 0.0D0) + MSG=' Length needed is .ge. LENRW (=I1), exceeds LRW (=I2)' + CALL XERRWD (MSG, 60, 17, 0, 2, LENRW, LRW, 0, 0.0D0, 0.0D0) + GO TO 700 + 618 MSG = 'DLSODES- IWORK length is insufficient to proceed. ' + CALL XERRWD (MSG, 50, 18, 0, 0, 0, 0, 0, 0.0D0, 0.0D0) + MSG=' Length needed is .ge. LENIW (=I1), exceeds LIW (=I2)' + CALL XERRWD (MSG, 60, 18, 0, 2, LENIW, LIW, 0, 0.0D0, 0.0D0) + GO TO 700 + 619 MSG = 'DLSODES- RTOL(I1) is R1 .lt. 0.0 ' + CALL XERRWD (MSG, 40, 19, 0, 1, I, 0, 1, RTOLI, 0.0D0) + GO TO 700 + 620 MSG = 'DLSODES- ATOL(I1) is R1 .lt. 0.0 ' + CALL XERRWD (MSG, 40, 20, 0, 1, I, 0, 1, ATOLI, 0.0D0) + GO TO 700 + 621 EWTI = RWORK(LEWT+I-1) + MSG = 'DLSODES- EWT(I1) is R1 .le. 0.0 ' + CALL XERRWD (MSG, 40, 21, 0, 1, I, 0, 1, EWTI, 0.0D0) + GO TO 700 + 622 MSG='DLSODES- TOUT(=R1) too close to T(=R2) to start integration.' + CALL XERRWD (MSG, 60, 22, 0, 0, 0, 0, 2, TOUT, T) + GO TO 700 + 623 MSG='DLSODES- ITASK = I1 and TOUT (=R1) behind TCUR - HU (= R2) ' + CALL XERRWD (MSG, 60, 23, 0, 1, ITASK, 0, 2, TOUT, TP) + GO TO 700 + 624 MSG='DLSODES- ITASK = 4 or 5 and TCRIT (=R1) behind TCUR (=R2) ' + CALL XERRWD (MSG, 60, 24, 0, 0, 0, 0, 2, TCRIT, TN) + GO TO 700 + 625 MSG='DLSODES- ITASK = 4 or 5 and TCRIT (=R1) behind TOUT (=R2) ' + CALL XERRWD (MSG, 60, 25, 0, 0, 0, 0, 2, TCRIT, TOUT) + GO TO 700 + 626 MSG = 'DLSODES- At start of problem, too much accuracy ' + CALL XERRWD (MSG, 50, 26, 0, 0, 0, 0, 0, 0.0D0, 0.0D0) + MSG=' requested for precision of machine.. See TOLSF (=R1) ' + CALL XERRWD (MSG, 60, 26, 0, 0, 0, 0, 1, TOLSF, 0.0D0) + RWORK(14) = TOLSF + GO TO 700 + 627 MSG = 'DLSODES- Trouble in DINTDY. ITASK = I1, TOUT = R1' + CALL XERRWD (MSG, 50, 27, 0, 1, ITASK, 0, 1, TOUT, 0.0D0) + GO TO 700 + 628 MSG='DLSODES- RWORK length insufficient (for Subroutine DPREP). ' + CALL XERRWD (MSG, 60, 28, 0, 0, 0, 0, 0, 0.0D0, 0.0D0) + MSG=' Length needed is .ge. LENRW (=I1), exceeds LRW (=I2)' + CALL XERRWD (MSG, 60, 28, 0, 2, LENRW, LRW, 0, 0.0D0, 0.0D0) + GO TO 700 + 629 MSG='DLSODES- RWORK length insufficient (for Subroutine JGROUP). ' + CALL XERRWD (MSG, 60, 29, 0, 0, 0, 0, 0, 0.0D0, 0.0D0) + MSG=' Length needed is .ge. LENRW (=I1), exceeds LRW (=I2)' + CALL XERRWD (MSG, 60, 29, 0, 2, LENRW, LRW, 0, 0.0D0, 0.0D0) + GO TO 700 + 630 MSG='DLSODES- RWORK length insufficient (for Subroutine ODRV). ' + CALL XERRWD (MSG, 60, 30, 0, 0, 0, 0, 0, 0.0D0, 0.0D0) + MSG=' Length needed is .ge. LENRW (=I1), exceeds LRW (=I2)' + CALL XERRWD (MSG, 60, 30, 0, 2, LENRW, LRW, 0, 0.0D0, 0.0D0) + GO TO 700 + 631 MSG='DLSODES- Error from ODRV in Yale Sparse Matrix Package. ' + CALL XERRWD (MSG, 60, 31, 0, 0, 0, 0, 0, 0.0D0, 0.0D0) + IMUL = (IYS - 1)/N + IREM = IYS - IMUL*N + MSG=' At T (=R1), ODRV returned error flag = I1*NEQ + I2. ' + CALL XERRWD (MSG, 60, 31, 0, 2, IMUL, IREM, 1, TN, 0.0D0) + GO TO 700 + 632 MSG='DLSODES- RWORK length insufficient (for Subroutine CDRV). ' + CALL XERRWD (MSG, 60, 32, 0, 0, 0, 0, 0, 0.0D0, 0.0D0) + MSG=' Length needed is .ge. LENRW (=I1), exceeds LRW (=I2)' + CALL XERRWD (MSG, 60, 32, 0, 2, LENRW, LRW, 0, 0.0D0, 0.0D0) + GO TO 700 + 633 MSG='DLSODES- Error from CDRV in Yale Sparse Matrix Package. ' + CALL XERRWD (MSG, 60, 33, 0, 0, 0, 0, 0, 0.0D0, 0.0D0) + IMUL = (IYS - 1)/N + IREM = IYS - IMUL*N + MSG=' At T (=R1), CDRV returned error flag = I1*NEQ + I2. ' + CALL XERRWD (MSG, 60, 33, 0, 2, IMUL, IREM, 1, TN, 0.0D0) + IF (IMUL .EQ. 2) THEN + MSG=' Duplicate entry in sparsity structure descriptors. ' + CALL XERRWD (MSG, 60, 33, 0, 0, 0, 0, 0, 0.0D0, 0.0D0) + ENDIF + IF (IMUL .EQ. 3 .OR. IMUL .EQ. 6) THEN + MSG=' Insufficient storage for NSFC (called by CDRV). ' + CALL XERRWD (MSG, 60, 33, 0, 0, 0, 0, 0, 0.0D0, 0.0D0) + ENDIF +C + 700 ISTATE = -3 + RETURN +C + 800 MSG = 'DLSODES- Run aborted.. apparent infinite loop. ' + CALL XERRWD (MSG, 50, 303, 2, 0, 0, 0, 0, 0.0D0, 0.0D0) + RETURN +C----------------------- End of Subroutine DLSODES --------------------- + END +*DECK DLSODA + SUBROUTINE DLSODA (F, NEQ, Y, T, TOUT, ITOL, RTOL, ATOL, ITASK, + 1 ISTATE, IOPT, RWORK, LRW, IWORK, LIW, JAC, JT) + EXTERNAL F, JAC + INTEGER NEQ, ITOL, ITASK, ISTATE, IOPT, LRW, IWORK, LIW, JT + DOUBLE PRECISION Y, T, TOUT, RTOL, ATOL, RWORK + DIMENSION NEQ(*), Y(*), RTOL(*), ATOL(*), RWORK(LRW), IWORK(LIW) +C----------------------------------------------------------------------- +C This is the 12 November 2003 version of +C DLSODA: Livermore Solver for Ordinary Differential Equations, with +C Automatic method switching for stiff and nonstiff problems. +C +C This version is in double precision. +C +C DLSODA solves the initial value problem for stiff or nonstiff +C systems of first order ODEs, +C dy/dt = f(t,y) , or, in component form, +C dy(i)/dt = f(i) = f(i,t,y(1),y(2),...,y(NEQ)) (i = 1,...,NEQ). +C +C This a variant version of the DLSODE package. +C It switches automatically between stiff and nonstiff methods. +C This means that the user does not have to determine whether the +C problem is stiff or not, and the solver will automatically choose the +C appropriate method. It always starts with the nonstiff method. +C +C Authors: Alan C. Hindmarsh +C Center for Applied Scientific Computing, L-561 +C Lawrence Livermore National Laboratory +C Livermore, CA 94551 +C and +C Linda R. Petzold +C Univ. of California at Santa Barbara +C Dept. of Computer Science +C Santa Barbara, CA 93106 +C +C References: +C 1. Alan C. Hindmarsh, ODEPACK, A Systematized Collection of ODE +C Solvers, in Scientific Computing, R. S. Stepleman et al. (Eds.), +C North-Holland, Amsterdam, 1983, pp. 55-64. +C 2. Linda R. Petzold, Automatic Selection of Methods for Solving +C Stiff and Nonstiff Systems of Ordinary Differential Equations, +C Siam J. Sci. Stat. Comput. 4 (1983), pp. 136-148. +C----------------------------------------------------------------------- +C Summary of Usage. +C +C Communication between the user and the DLSODA package, for normal +C situations, is summarized here. This summary describes only a subset +C of the full set of options available. See the full description for +C details, including alternative treatment of the Jacobian matrix, +C optional inputs and outputs, nonstandard options, and +C instructions for special situations. See also the example +C problem (with program and output) following this summary. +C +C A. First provide a subroutine of the form: +C SUBROUTINE F (NEQ, T, Y, YDOT) +C DOUBLE PRECISION T, Y(*), YDOT(*) +C which supplies the vector function f by loading YDOT(i) with f(i). +C +C B. Write a main program which calls Subroutine DLSODA once for +C each point at which answers are desired. This should also provide +C for possible use of logical unit 6 for output of error messages +C by DLSODA. On the first call to DLSODA, supply arguments as follows: +C F = name of subroutine for right-hand side vector f. +C This name must be declared External in calling program. +C NEQ = number of first order ODEs. +C Y = array of initial values, of length NEQ. +C T = the initial value of the independent variable. +C TOUT = first point where output is desired (.ne. T). +C ITOL = 1 or 2 according as ATOL (below) is a scalar or array. +C RTOL = relative tolerance parameter (scalar). +C ATOL = absolute tolerance parameter (scalar or array). +C the estimated local error in y(i) will be controlled so as +C to be less than +C EWT(i) = RTOL*ABS(Y(i)) + ATOL if ITOL = 1, or +C EWT(i) = RTOL*ABS(Y(i)) + ATOL(i) if ITOL = 2. +C Thus the local error test passes if, in each component, +C either the absolute error is less than ATOL (or ATOL(i)), +C or the relative error is less than RTOL. +C Use RTOL = 0.0 for pure absolute error control, and +C use ATOL = 0.0 (or ATOL(i) = 0.0) for pure relative error +C control. Caution: actual (global) errors may exceed these +C local tolerances, so choose them conservatively. +C ITASK = 1 for normal computation of output values of y at t = TOUT. +C ISTATE = integer flag (input and output). Set ISTATE = 1. +C IOPT = 0 to indicate no optional inputs used. +C RWORK = real work array of length at least: +C 22 + NEQ * MAX(16, NEQ + 9). +C See also Paragraph E below. +C LRW = declared length of RWORK (in user's dimension). +C IWORK = integer work array of length at least 20 + NEQ. +C LIW = declared length of IWORK (in user's dimension). +C JAC = name of subroutine for Jacobian matrix. +C Use a dummy name. See also Paragraph E below. +C JT = Jacobian type indicator. Set JT = 2. +C See also Paragraph E below. +C Note that the main program must declare arrays Y, RWORK, IWORK, +C and possibly ATOL. +C +C C. The output from the first call (or any call) is: +C Y = array of computed values of y(t) vector. +C T = corresponding value of independent variable (normally TOUT). +C ISTATE = 2 if DLSODA was successful, negative otherwise. +C -1 means excess work done on this call (perhaps wrong JT). +C -2 means excess accuracy requested (tolerances too small). +C -3 means illegal input detected (see printed message). +C -4 means repeated error test failures (check all inputs). +C -5 means repeated convergence failures (perhaps bad Jacobian +C supplied or wrong choice of JT or tolerances). +C -6 means error weight became zero during problem. (Solution +C component i vanished, and ATOL or ATOL(i) = 0.) +C -7 means work space insufficient to finish (see messages). +C +C D. To continue the integration after a successful return, simply +C reset TOUT and call DLSODA again. No other parameters need be reset. +C +C E. Note: If and when DLSODA regards the problem as stiff, and +C switches methods accordingly, it must make use of the NEQ by NEQ +C Jacobian matrix, J = df/dy. For the sake of simplicity, the +C inputs to DLSODA recommended in Paragraph B above cause DLSODA to +C treat J as a full matrix, and to approximate it internally by +C difference quotients. Alternatively, J can be treated as a band +C matrix (with great potential reduction in the size of the RWORK +C array). Also, in either the full or banded case, the user can supply +C J in closed form, with a routine whose name is passed as the JAC +C argument. These alternatives are described in the paragraphs on +C RWORK, JAC, and JT in the full description of the call sequence below. +C +C----------------------------------------------------------------------- +C Example Problem. +C +C The following is a simple example problem, with the coding +C needed for its solution by DLSODA. The problem is from chemical +C kinetics, and consists of the following three rate equations: +C dy1/dt = -.04*y1 + 1.e4*y2*y3 +C dy2/dt = .04*y1 - 1.e4*y2*y3 - 3.e7*y2**2 +C dy3/dt = 3.e7*y2**2 +C on the interval from t = 0.0 to t = 4.e10, with initial conditions +C y1 = 1.0, y2 = y3 = 0. The problem is stiff. +C +C The following coding solves this problem with DLSODA, +C printing results at t = .4, 4., ..., 4.e10. It uses +C ITOL = 2 and ATOL much smaller for y2 than y1 or y3 because +C y2 has much smaller values. +C At the end of the run, statistical quantities of interest are +C printed (see optional outputs in the full description below). +C +C EXTERNAL FEX +C DOUBLE PRECISION ATOL, RTOL, RWORK, T, TOUT, Y +C DIMENSION Y(3), ATOL(3), RWORK(70), IWORK(23) +C NEQ = 3 +C Y(1) = 1. +C Y(2) = 0. +C Y(3) = 0. +C T = 0. +C TOUT = .4 +C ITOL = 2 +C RTOL = 1.D-4 +C ATOL(1) = 1.D-6 +C ATOL(2) = 1.D-10 +C ATOL(3) = 1.D-6 +C ITASK = 1 +C ISTATE = 1 +C IOPT = 0 +C LRW = 70 +C LIW = 23 +C JT = 2 +C DO 40 IOUT = 1,12 +C CALL DLSODA(FEX,NEQ,Y,T,TOUT,ITOL,RTOL,ATOL,ITASK,ISTATE, +C 1 IOPT,RWORK,LRW,IWORK,LIW,JDUM,JT) +C WRITE(6,20)T,Y(1),Y(2),Y(3) +C 20 FORMAT(' At t =',D12.4,' Y =',3D14.6) +C IF (ISTATE .LT. 0) GO TO 80 +C 40 TOUT = TOUT*10. +C WRITE(6,60)IWORK(11),IWORK(12),IWORK(13),IWORK(19),RWORK(15) +C 60 FORMAT(/' No. steps =',I4,' No. f-s =',I4,' No. J-s =',I4/ +C 1 ' Method last used =',I2,' Last switch was at t =',D12.4) +C STOP +C 80 WRITE(6,90)ISTATE +C 90 FORMAT(///' Error halt.. ISTATE =',I3) +C STOP +C END +C +C SUBROUTINE FEX (NEQ, T, Y, YDOT) +C DOUBLE PRECISION T, Y, YDOT +C DIMENSION Y(3), YDOT(3) +C YDOT(1) = -.04*Y(1) + 1.D4*Y(2)*Y(3) +C YDOT(3) = 3.D7*Y(2)*Y(2) +C YDOT(2) = -YDOT(1) - YDOT(3) +C RETURN +C END +C +C The output of this program (on a CDC-7600 in single precision) +C is as follows: +C +C At t = 4.0000e-01 y = 9.851712e-01 3.386380e-05 1.479493e-02 +C At t = 4.0000e+00 Y = 9.055333e-01 2.240655e-05 9.444430e-02 +C At t = 4.0000e+01 Y = 7.158403e-01 9.186334e-06 2.841505e-01 +C At t = 4.0000e+02 Y = 4.505250e-01 3.222964e-06 5.494717e-01 +C At t = 4.0000e+03 Y = 1.831975e-01 8.941774e-07 8.168016e-01 +C At t = 4.0000e+04 Y = 3.898730e-02 1.621940e-07 9.610125e-01 +C At t = 4.0000e+05 Y = 4.936363e-03 1.984221e-08 9.950636e-01 +C At t = 4.0000e+06 Y = 5.161831e-04 2.065786e-09 9.994838e-01 +C At t = 4.0000e+07 Y = 5.179817e-05 2.072032e-10 9.999482e-01 +C At t = 4.0000e+08 Y = 5.283401e-06 2.113371e-11 9.999947e-01 +C At t = 4.0000e+09 Y = 4.659031e-07 1.863613e-12 9.999995e-01 +C At t = 4.0000e+10 Y = 1.404280e-08 5.617126e-14 1.000000e+00 +C +C No. steps = 361 No. f-s = 693 No. J-s = 64 +C Method last used = 2 Last switch was at t = 6.0092e-03 +C----------------------------------------------------------------------- +C Full description of user interface to DLSODA. +C +C The user interface to DLSODA consists of the following parts. +C +C 1. The call sequence to Subroutine DLSODA, which is a driver +C routine for the solver. This includes descriptions of both +C the call sequence arguments and of user-supplied routines. +C following these descriptions is a description of +C optional inputs available through the call sequence, and then +C a description of optional outputs (in the work arrays). +C +C 2. Descriptions of other routines in the DLSODA package that may be +C (optionally) called by the user. These provide the ability to +C alter error message handling, save and restore the internal +C Common, and obtain specified derivatives of the solution y(t). +C +C 3. Descriptions of Common blocks to be declared in overlay +C or similar environments, or to be saved when doing an interrupt +C of the problem and continued solution later. +C +C 4. Description of a subroutine in the DLSODA package, +C which the user may replace with his/her own version, if desired. +C this relates to the measurement of errors. +C +C----------------------------------------------------------------------- +C Part 1. Call Sequence. +C +C The call sequence parameters used for input only are +C F, NEQ, TOUT, ITOL, RTOL, ATOL, ITASK, IOPT, LRW, LIW, JAC, JT, +C and those used for both input and output are +C Y, T, ISTATE. +C The work arrays RWORK and IWORK are also used for conditional and +C optional inputs and optional outputs. (The term output here refers +C to the return from Subroutine DLSODA to the user's calling program.) +C +C The legality of input parameters will be thoroughly checked on the +C initial call for the problem, but not checked thereafter unless a +C change in input parameters is flagged by ISTATE = 3 on input. +C +C The descriptions of the call arguments are as follows. +C +C F = the name of the user-supplied subroutine defining the +C ODE system. The system must be put in the first-order +C form dy/dt = f(t,y), where f is a vector-valued function +C of the scalar t and the vector y. Subroutine F is to +C compute the function f. It is to have the form +C SUBROUTINE F (NEQ, T, Y, YDOT) +C DOUBLE PRECISION T, Y(*), YDOT(*) +C where NEQ, T, and Y are input, and the array YDOT = f(t,y) +C is output. Y and YDOT are arrays of length NEQ. +C Subroutine F should not alter Y(1),...,Y(NEQ). +C F must be declared External in the calling program. +C +C Subroutine F may access user-defined quantities in +C NEQ(2),... and/or in Y(NEQ(1)+1),... if NEQ is an array +C (dimensioned in F) and/or Y has length exceeding NEQ(1). +C See the descriptions of NEQ and Y below. +C +C If quantities computed in the F routine are needed +C externally to DLSODA, an extra call to F should be made +C for this purpose, for consistent and accurate results. +C If only the derivative dy/dt is needed, use DINTDY instead. +C +C NEQ = the size of the ODE system (number of first order +C ordinary differential equations). Used only for input. +C NEQ may be decreased, but not increased, during the problem. +C If NEQ is decreased (with ISTATE = 3 on input), the +C remaining components of Y should be left undisturbed, if +C these are to be accessed in F and/or JAC. +C +C Normally, NEQ is a scalar, and it is generally referred to +C as a scalar in this user interface description. However, +C NEQ may be an array, with NEQ(1) set to the system size. +C (The DLSODA package accesses only NEQ(1).) In either case, +C this parameter is passed as the NEQ argument in all calls +C to F and JAC. Hence, if it is an array, locations +C NEQ(2),... may be used to store other integer data and pass +C it to F and/or JAC. Subroutines F and/or JAC must include +C NEQ in a Dimension statement in that case. +C +C Y = a real array for the vector of dependent variables, of +C length NEQ or more. Used for both input and output on the +C first call (ISTATE = 1), and only for output on other calls. +C On the first call, Y must contain the vector of initial +C values. On output, Y contains the computed solution vector, +C evaluated at T. If desired, the Y array may be used +C for other purposes between calls to the solver. +C +C This array is passed as the Y argument in all calls to +C F and JAC. Hence its length may exceed NEQ, and locations +C Y(NEQ+1),... may be used to store other real data and +C pass it to F and/or JAC. (The DLSODA package accesses only +C Y(1),...,Y(NEQ).) +C +C T = the independent variable. On input, T is used only on the +C first call, as the initial point of the integration. +C on output, after each call, T is the value at which a +C computed solution Y is evaluated (usually the same as TOUT). +C on an error return, T is the farthest point reached. +C +C TOUT = the next value of t at which a computed solution is desired. +C Used only for input. +C +C When starting the problem (ISTATE = 1), TOUT may be equal +C to T for one call, then should .ne. T for the next call. +C For the initial t, an input value of TOUT .ne. T is used +C in order to determine the direction of the integration +C (i.e. the algebraic sign of the step sizes) and the rough +C scale of the problem. Integration in either direction +C (forward or backward in t) is permitted. +C +C If ITASK = 2 or 5 (one-step modes), TOUT is ignored after +C the first call (i.e. the first call with TOUT .ne. T). +C Otherwise, TOUT is required on every call. +C +C If ITASK = 1, 3, or 4, the values of TOUT need not be +C monotone, but a value of TOUT which backs up is limited +C to the current internal T interval, whose endpoints are +C TCUR - HU and TCUR (see optional outputs, below, for +C TCUR and HU). +C +C ITOL = an indicator for the type of error control. See +C description below under ATOL. Used only for input. +C +C RTOL = a relative error tolerance parameter, either a scalar or +C an array of length NEQ. See description below under ATOL. +C Input only. +C +C ATOL = an absolute error tolerance parameter, either a scalar or +C an array of length NEQ. Input only. +C +C The input parameters ITOL, RTOL, and ATOL determine +C the error control performed by the solver. The solver will +C control the vector E = (E(i)) of estimated local errors +C in y, according to an inequality of the form +C max-norm of ( E(i)/EWT(i) ) .le. 1, +C where EWT = (EWT(i)) is a vector of positive error weights. +C The values of RTOL and ATOL should all be non-negative. +C The following table gives the types (scalar/array) of +C RTOL and ATOL, and the corresponding form of EWT(i). +C +C ITOL RTOL ATOL EWT(i) +C 1 scalar scalar RTOL*ABS(Y(i)) + ATOL +C 2 scalar array RTOL*ABS(Y(i)) + ATOL(i) +C 3 array scalar RTOL(i)*ABS(Y(i)) + ATOL +C 4 array array RTOL(i)*ABS(Y(i)) + ATOL(i) +C +C When either of these parameters is a scalar, it need not +C be dimensioned in the user's calling program. +C +C If none of the above choices (with ITOL, RTOL, and ATOL +C fixed throughout the problem) is suitable, more general +C error controls can be obtained by substituting a +C user-supplied routine for the setting of EWT. +C See Part 4 below. +C +C If global errors are to be estimated by making a repeated +C run on the same problem with smaller tolerances, then all +C components of RTOL and ATOL (i.e. of EWT) should be scaled +C down uniformly. +C +C ITASK = an index specifying the task to be performed. +C Input only. ITASK has the following values and meanings. +C 1 means normal computation of output values of y(t) at +C t = TOUT (by overshooting and interpolating). +C 2 means take one step only and return. +C 3 means stop at the first internal mesh point at or +C beyond t = TOUT and return. +C 4 means normal computation of output values of y(t) at +C t = TOUT but without overshooting t = TCRIT. +C TCRIT must be input as RWORK(1). TCRIT may be equal to +C or beyond TOUT, but not behind it in the direction of +C integration. This option is useful if the problem +C has a singularity at or beyond t = TCRIT. +C 5 means take one step, without passing TCRIT, and return. +C TCRIT must be input as RWORK(1). +C +C Note: If ITASK = 4 or 5 and the solver reaches TCRIT +C (within roundoff), it will return T = TCRIT (exactly) to +C indicate this (unless ITASK = 4 and TOUT comes before TCRIT, +C in which case answers at t = TOUT are returned first). +C +C ISTATE = an index used for input and output to specify the +C the state of the calculation. +C +C On input, the values of ISTATE are as follows. +C 1 means this is the first call for the problem +C (initializations will be done). See note below. +C 2 means this is not the first call, and the calculation +C is to continue normally, with no change in any input +C parameters except possibly TOUT and ITASK. +C (If ITOL, RTOL, and/or ATOL are changed between calls +C with ISTATE = 2, the new values will be used but not +C tested for legality.) +C 3 means this is not the first call, and the +C calculation is to continue normally, but with +C a change in input parameters other than +C TOUT and ITASK. Changes are allowed in +C NEQ, ITOL, RTOL, ATOL, IOPT, LRW, LIW, JT, ML, MU, +C and any optional inputs except H0, MXORDN, and MXORDS. +C (See IWORK description for ML and MU.) +C Note: A preliminary call with TOUT = T is not counted +C as a first call here, as no initialization or checking of +C input is done. (Such a call is sometimes useful for the +C purpose of outputting the initial conditions.) +C Thus the first call for which TOUT .ne. T requires +C ISTATE = 1 on input. +C +C On output, ISTATE has the following values and meanings. +C 1 means nothing was done; TOUT = T and ISTATE = 1 on input. +C 2 means the integration was performed successfully. +C -1 means an excessive amount of work (more than MXSTEP +C steps) was done on this call, before completing the +C requested task, but the integration was otherwise +C successful as far as T. (MXSTEP is an optional input +C and is normally 500.) To continue, the user may +C simply reset ISTATE to a value .gt. 1 and call again +C (the excess work step counter will be reset to 0). +C In addition, the user may increase MXSTEP to avoid +C this error return (see below on optional inputs). +C -2 means too much accuracy was requested for the precision +C of the machine being used. This was detected before +C completing the requested task, but the integration +C was successful as far as T. To continue, the tolerance +C parameters must be reset, and ISTATE must be set +C to 3. The optional output TOLSF may be used for this +C purpose. (Note: If this condition is detected before +C taking any steps, then an illegal input return +C (ISTATE = -3) occurs instead.) +C -3 means illegal input was detected, before taking any +C integration steps. See written message for details. +C Note: If the solver detects an infinite loop of calls +C to the solver with illegal input, it will cause +C the run to stop. +C -4 means there were repeated error test failures on +C one attempted step, before completing the requested +C task, but the integration was successful as far as T. +C The problem may have a singularity, or the input +C may be inappropriate. +C -5 means there were repeated convergence test failures on +C one attempted step, before completing the requested +C task, but the integration was successful as far as T. +C This may be caused by an inaccurate Jacobian matrix, +C if one is being used. +C -6 means EWT(i) became zero for some i during the +C integration. Pure relative error control (ATOL(i)=0.0) +C was requested on a variable which has now vanished. +C The integration was successful as far as T. +C -7 means the length of RWORK and/or IWORK was too small to +C proceed, but the integration was successful as far as T. +C This happens when DLSODA chooses to switch methods +C but LRW and/or LIW is too small for the new method. +C +C Note: Since the normal output value of ISTATE is 2, +C it does not need to be reset for normal continuation. +C Also, since a negative input value of ISTATE will be +C regarded as illegal, a negative output value requires the +C user to change it, and possibly other inputs, before +C calling the solver again. +C +C IOPT = an integer flag to specify whether or not any optional +C inputs are being used on this call. Input only. +C The optional inputs are listed separately below. +C IOPT = 0 means no optional inputs are being used. +C default values will be used in all cases. +C IOPT = 1 means one or more optional inputs are being used. +C +C RWORK = a real array (double precision) for work space, and (in the +C first 20 words) for conditional and optional inputs and +C optional outputs. +C As DLSODA switches automatically between stiff and nonstiff +C methods, the required length of RWORK can change during the +C problem. Thus the RWORK array passed to DLSODA can either +C have a static (fixed) length large enough for both methods, +C or have a dynamic (changing) length altered by the calling +C program in response to output from DLSODA. +C +C --- Fixed Length Case --- +C If the RWORK length is to be fixed, it should be at least +C MAX (LRN, LRS), +C where LRN and LRS are the RWORK lengths required when the +C current method is nonstiff or stiff, respectively. +C +C The separate RWORK length requirements LRN and LRS are +C as follows: +C IF NEQ is constant and the maximum method orders have +C their default values, then +C LRN = 20 + 16*NEQ, +C LRS = 22 + 9*NEQ + NEQ**2 if JT = 1 or 2, +C LRS = 22 + 10*NEQ + (2*ML+MU)*NEQ if JT = 4 or 5. +C Under any other conditions, LRN and LRS are given by: +C LRN = 20 + NYH*(MXORDN+1) + 3*NEQ, +C LRS = 20 + NYH*(MXORDS+1) + 3*NEQ + LMAT, +C where +C NYH = the initial value of NEQ, +C MXORDN = 12, unless a smaller value is given as an +C optional input, +C MXORDS = 5, unless a smaller value is given as an +C optional input, +C LMAT = length of matrix work space: +C LMAT = NEQ**2 + 2 if JT = 1 or 2, +C LMAT = (2*ML + MU + 1)*NEQ + 2 if JT = 4 or 5. +C +C --- Dynamic Length Case --- +C If the length of RWORK is to be dynamic, then it should +C be at least LRN or LRS, as defined above, depending on the +C current method. Initially, it must be at least LRN (since +C DLSODA starts with the nonstiff method). On any return +C from DLSODA, the optional output MCUR indicates the current +C method. If MCUR differs from the value it had on the +C previous return, or if there has only been one call to +C DLSODA and MCUR is now 2, then DLSODA has switched +C methods during the last call, and the length of RWORK +C should be reset (to LRN if MCUR = 1, or to LRS if +C MCUR = 2). (An increase in the RWORK length is required +C if DLSODA returned ISTATE = -7, but not otherwise.) +C After resetting the length, call DLSODA with ISTATE = 3 +C to signal that change. +C +C LRW = the length of the array RWORK, as declared by the user. +C (This will be checked by the solver.) +C +C IWORK = an integer array for work space. +C As DLSODA switches automatically between stiff and nonstiff +C methods, the required length of IWORK can change during +C problem, between +C LIS = 20 + NEQ and LIN = 20, +C respectively. Thus the IWORK array passed to DLSODA can +C either have a fixed length of at least 20 + NEQ, or have a +C dynamic length of at least LIN or LIS, depending on the +C current method. The comments on dynamic length under +C RWORK above apply here. Initially, this length need +C only be at least LIN = 20. +C +C The first few words of IWORK are used for conditional and +C optional inputs and optional outputs. +C +C The following 2 words in IWORK are conditional inputs: +C IWORK(1) = ML these are the lower and upper +C IWORK(2) = MU half-bandwidths, respectively, of the +C banded Jacobian, excluding the main diagonal. +C The band is defined by the matrix locations +C (i,j) with i-ML .le. j .le. i+MU. ML and MU +C must satisfy 0 .le. ML,MU .le. NEQ-1. +C These are required if JT is 4 or 5, and +C ignored otherwise. ML and MU may in fact be +C the band parameters for a matrix to which +C df/dy is only approximately equal. +C +C LIW = the length of the array IWORK, as declared by the user. +C (This will be checked by the solver.) +C +C Note: The base addresses of the work arrays must not be +C altered between calls to DLSODA for the same problem. +C The contents of the work arrays must not be altered +C between calls, except possibly for the conditional and +C optional inputs, and except for the last 3*NEQ words of RWORK. +C The latter space is used for internal scratch space, and so is +C available for use by the user outside DLSODA between calls, if +C desired (but not for use by F or JAC). +C +C JAC = the name of the user-supplied routine to compute the +C Jacobian matrix, df/dy, if JT = 1 or 4. The JAC routine +C is optional, but if the problem is expected to be stiff much +C of the time, you are encouraged to supply JAC, for the sake +C of efficiency. (Alternatively, set JT = 2 or 5 to have +C DLSODA compute df/dy internally by difference quotients.) +C If and when DLSODA uses df/dy, it treats this NEQ by NEQ +C matrix either as full (JT = 1 or 2), or as banded (JT = +C 4 or 5) with half-bandwidths ML and MU (discussed under +C IWORK above). In either case, if JT = 1 or 4, the JAC +C routine must compute df/dy as a function of the scalar t +C and the vector y. It is to have the form +C SUBROUTINE JAC (NEQ, T, Y, ML, MU, PD, NROWPD) +C DOUBLE PRECISION T, Y(*), PD(NROWPD,*) +C where NEQ, T, Y, ML, MU, and NROWPD are input and the array +C PD is to be loaded with partial derivatives (elements of +C the Jacobian matrix) on output. PD must be given a first +C dimension of NROWPD. T and Y have the same meaning as in +C Subroutine F. +C In the full matrix case (JT = 1), ML and MU are +C ignored, and the Jacobian is to be loaded into PD in +C columnwise manner, with df(i)/dy(j) loaded into PD(i,j). +C In the band matrix case (JT = 4), the elements +C within the band are to be loaded into PD in columnwise +C manner, with diagonal lines of df/dy loaded into the rows +C of PD. Thus df(i)/dy(j) is to be loaded into PD(i-j+MU+1,j). +C ML and MU are the half-bandwidth parameters (see IWORK). +C The locations in PD in the two triangular areas which +C correspond to nonexistent matrix elements can be ignored +C or loaded arbitrarily, as they are overwritten by DLSODA. +C JAC need not provide df/dy exactly. A crude +C approximation (possibly with a smaller bandwidth) will do. +C In either case, PD is preset to zero by the solver, +C so that only the nonzero elements need be loaded by JAC. +C Each call to JAC is preceded by a call to F with the same +C arguments NEQ, T, and Y. Thus to gain some efficiency, +C intermediate quantities shared by both calculations may be +C saved in a user Common block by F and not recomputed by JAC, +C if desired. Also, JAC may alter the Y array, if desired. +C JAC must be declared External in the calling program. +C Subroutine JAC may access user-defined quantities in +C NEQ(2),... and/or in Y(NEQ(1)+1),... if NEQ is an array +C (dimensioned in JAC) and/or Y has length exceeding NEQ(1). +C See the descriptions of NEQ and Y above. +C +C JT = Jacobian type indicator. Used only for input. +C JT specifies how the Jacobian matrix df/dy will be +C treated, if and when DLSODA requires this matrix. +C JT has the following values and meanings: +C 1 means a user-supplied full (NEQ by NEQ) Jacobian. +C 2 means an internally generated (difference quotient) full +C Jacobian (using NEQ extra calls to F per df/dy value). +C 4 means a user-supplied banded Jacobian. +C 5 means an internally generated banded Jacobian (using +C ML+MU+1 extra calls to F per df/dy evaluation). +C If JT = 1 or 4, the user must supply a Subroutine JAC +C (the name is arbitrary) as described above under JAC. +C If JT = 2 or 5, a dummy argument can be used. +C----------------------------------------------------------------------- +C Optional Inputs. +C +C The following is a list of the optional inputs provided for in the +C call sequence. (See also Part 2.) For each such input variable, +C this table lists its name as used in this documentation, its +C location in the call sequence, its meaning, and the default value. +C The use of any of these inputs requires IOPT = 1, and in that +C case all of these inputs are examined. A value of zero for any +C of these optional inputs will cause the default value to be used. +C Thus to use a subset of the optional inputs, simply preload +C locations 5 to 10 in RWORK and IWORK to 0.0 and 0 respectively, and +C then set those of interest to nonzero values. +C +C Name Location Meaning and Default Value +C +C H0 RWORK(5) the step size to be attempted on the first step. +C The default value is determined by the solver. +C +C HMAX RWORK(6) the maximum absolute step size allowed. +C The default value is infinite. +C +C HMIN RWORK(7) the minimum absolute step size allowed. +C The default value is 0. (This lower bound is not +C enforced on the final step before reaching TCRIT +C when ITASK = 4 or 5.) +C +C IXPR IWORK(5) flag to generate extra printing at method switches. +C IXPR = 0 means no extra printing (the default). +C IXPR = 1 means print data on each switch. +C T, H, and NST will be printed on the same logical +C unit as used for error messages. +C +C MXSTEP IWORK(6) maximum number of (internally defined) steps +C allowed during one call to the solver. +C The default value is 500. +C +C MXHNIL IWORK(7) maximum number of messages printed (per problem) +C warning that T + H = T on a step (H = step size). +C This must be positive to result in a non-default +C value. The default value is 10. +C +C MXORDN IWORK(8) the maximum order to be allowed for the nonstiff +C (Adams) method. the default value is 12. +C if MXORDN exceeds the default value, it will +C be reduced to the default value. +C MXORDN is held constant during the problem. +C +C MXORDS IWORK(9) the maximum order to be allowed for the stiff +C (BDF) method. The default value is 5. +C If MXORDS exceeds the default value, it will +C be reduced to the default value. +C MXORDS is held constant during the problem. +C----------------------------------------------------------------------- +C Optional Outputs. +C +C As optional additional output from DLSODA, the variables listed +C below are quantities related to the performance of DLSODA +C which are available to the user. These are communicated by way of +C the work arrays, but also have internal mnemonic names as shown. +C except where stated otherwise, all of these outputs are defined +C on any successful return from DLSODA, and on any return with +C ISTATE = -1, -2, -4, -5, or -6. On an illegal input return +C (ISTATE = -3), they will be unchanged from their existing values +C (if any), except possibly for TOLSF, LENRW, and LENIW. +C On any error return, outputs relevant to the error will be defined, +C as noted below. +C +C Name Location Meaning +C +C HU RWORK(11) the step size in t last used (successfully). +C +C HCUR RWORK(12) the step size to be attempted on the next step. +C +C TCUR RWORK(13) the current value of the independent variable +C which the solver has actually reached, i.e. the +C current internal mesh point in t. On output, TCUR +C will always be at least as far as the argument +C T, but may be farther (if interpolation was done). +C +C TOLSF RWORK(14) a tolerance scale factor, greater than 1.0, +C computed when a request for too much accuracy was +C detected (ISTATE = -3 if detected at the start of +C the problem, ISTATE = -2 otherwise). If ITOL is +C left unaltered but RTOL and ATOL are uniformly +C scaled up by a factor of TOLSF for the next call, +C then the solver is deemed likely to succeed. +C (The user may also ignore TOLSF and alter the +C tolerance parameters in any other way appropriate.) +C +C TSW RWORK(15) the value of t at the time of the last method +C switch, if any. +C +C NST IWORK(11) the number of steps taken for the problem so far. +C +C NFE IWORK(12) the number of f evaluations for the problem so far. +C +C NJE IWORK(13) the number of Jacobian evaluations (and of matrix +C LU decompositions) for the problem so far. +C +C NQU IWORK(14) the method order last used (successfully). +C +C NQCUR IWORK(15) the order to be attempted on the next step. +C +C IMXER IWORK(16) the index of the component of largest magnitude in +C the weighted local error vector ( E(i)/EWT(i) ), +C on an error return with ISTATE = -4 or -5. +C +C LENRW IWORK(17) the length of RWORK actually required, assuming +C that the length of RWORK is to be fixed for the +C rest of the problem, and that switching may occur. +C This is defined on normal returns and on an illegal +C input return for insufficient storage. +C +C LENIW IWORK(18) the length of IWORK actually required, assuming +C that the length of IWORK is to be fixed for the +C rest of the problem, and that switching may occur. +C This is defined on normal returns and on an illegal +C input return for insufficient storage. +C +C MUSED IWORK(19) the method indicator for the last successful step: +C 1 means Adams (nonstiff), 2 means BDF (stiff). +C +C MCUR IWORK(20) the current method indicator: +C 1 means Adams (nonstiff), 2 means BDF (stiff). +C This is the method to be attempted +C on the next step. Thus it differs from MUSED +C only if a method switch has just been made. +C +C The following two arrays are segments of the RWORK array which +C may also be of interest to the user as optional outputs. +C For each array, the table below gives its internal name, +C its base address in RWORK, and its description. +C +C Name Base Address Description +C +C YH 21 the Nordsieck history array, of size NYH by +C (NQCUR + 1), where NYH is the initial value +C of NEQ. For j = 0,1,...,NQCUR, column j+1 +C of YH contains HCUR**j/factorial(j) times +C the j-th derivative of the interpolating +C polynomial currently representing the solution, +C evaluated at T = TCUR. +C +C ACOR LACOR array of size NEQ used for the accumulated +C (from Common corrections on each step, scaled on output +C as noted) to represent the estimated local error in y +C on the last step. This is the vector E in +C the description of the error control. It is +C defined only on a successful return from +C DLSODA. The base address LACOR is obtained by +C including in the user's program the +C following 2 lines: +C COMMON /DLS001/ RLS(218), ILS(37) +C LACOR = ILS(22) +C +C----------------------------------------------------------------------- +C Part 2. Other Routines Callable. +C +C The following are optional calls which the user may make to +C gain additional capabilities in conjunction with DLSODA. +C (The routines XSETUN and XSETF are designed to conform to the +C SLATEC error handling package.) +C +C Form of Call Function +C CALL XSETUN(LUN) set the logical unit number, LUN, for +C output of messages from DLSODA, if +C the default is not desired. +C The default value of LUN is 6. +C +C CALL XSETF(MFLAG) set a flag to control the printing of +C messages by DLSODA. +C MFLAG = 0 means do not print. (Danger: +C This risks losing valuable information.) +C MFLAG = 1 means print (the default). +C +C Either of the above calls may be made at +C any time and will take effect immediately. +C +C CALL DSRCMA(RSAV,ISAV,JOB) saves and restores the contents of +C the internal Common blocks used by +C DLSODA (see Part 3 below). +C RSAV must be a real array of length 240 +C or more, and ISAV must be an integer +C array of length 46 or more. +C JOB=1 means save Common into RSAV/ISAV. +C JOB=2 means restore Common from RSAV/ISAV. +C DSRCMA is useful if one is +C interrupting a run and restarting +C later, or alternating between two or +C more problems solved with DLSODA. +C +C CALL DINTDY(,,,,,) provide derivatives of y, of various +C (see below) orders, at a specified point t, if +C desired. It may be called only after +C a successful return from DLSODA. +C +C The detailed instructions for using DINTDY are as follows. +C The form of the call is: +C +C CALL DINTDY (T, K, RWORK(21), NYH, DKY, IFLAG) +C +C The input parameters are: +C +C T = value of independent variable where answers are desired +C (normally the same as the T last returned by DLSODA). +C For valid results, T must lie between TCUR - HU and TCUR. +C (See optional outputs for TCUR and HU.) +C K = integer order of the derivative desired. K must satisfy +C 0 .le. K .le. NQCUR, where NQCUR is the current order +C (see optional outputs). The capability corresponding +C to K = 0, i.e. computing y(T), is already provided +C by DLSODA directly. Since NQCUR .ge. 1, the first +C derivative dy/dt is always available with DINTDY. +C RWORK(21) = the base address of the history array YH. +C NYH = column length of YH, equal to the initial value of NEQ. +C +C The output parameters are: +C +C DKY = a real array of length NEQ containing the computed value +C of the K-th derivative of y(t). +C IFLAG = integer flag, returned as 0 if K and T were legal, +C -1 if K was illegal, and -2 if T was illegal. +C On an error return, a message is also written. +C----------------------------------------------------------------------- +C Part 3. Common Blocks. +C +C If DLSODA is to be used in an overlay situation, the user +C must declare, in the primary overlay, the variables in: +C (1) the call sequence to DLSODA, and +C (2) the two internal Common blocks +C /DLS001/ of length 255 (218 double precision words +C followed by 37 integer words), +C /DLSA01/ of length 31 (22 double precision words +C followed by 9 integer words). +C +C If DLSODA is used on a system in which the contents of internal +C Common blocks are not preserved between calls, the user should +C declare the above Common blocks in the calling program to insure +C that their contents are preserved. +C +C If the solution of a given problem by DLSODA is to be interrupted +C and then later continued, such as when restarting an interrupted run +C or alternating between two or more problems, the user should save, +C following the return from the last DLSODA call prior to the +C interruption, the contents of the call sequence variables and the +C internal Common blocks, and later restore these values before the +C next DLSODA call for that problem. To save and restore the Common +C blocks, use Subroutine DSRCMA (see Part 2 above). +C +C----------------------------------------------------------------------- +C Part 4. Optionally Replaceable Solver Routines. +C +C Below is a description of a routine in the DLSODA package which +C relates to the measurement of errors, and can be +C replaced by a user-supplied version, if desired. However, since such +C a replacement may have a major impact on performance, it should be +C done only when absolutely necessary, and only with great caution. +C (Note: The means by which the package version of a routine is +C superseded by the user's version may be system-dependent.) +C +C (a) DEWSET. +C The following subroutine is called just before each internal +C integration step, and sets the array of error weights, EWT, as +C described under ITOL/RTOL/ATOL above: +C Subroutine DEWSET (NEQ, ITOL, RTOL, ATOL, YCUR, EWT) +C where NEQ, ITOL, RTOL, and ATOL are as in the DLSODA call sequence, +C YCUR contains the current dependent variable vector, and +C EWT is the array of weights set by DEWSET. +C +C If the user supplies this subroutine, it must return in EWT(i) +C (i = 1,...,NEQ) a positive quantity suitable for comparing errors +C in y(i) to. The EWT array returned by DEWSET is passed to the +C DMNORM routine, and also used by DLSODA in the computation +C of the optional output IMXER, and the increments for difference +C quotient Jacobians. +C +C In the user-supplied version of DEWSET, it may be desirable to use +C the current values of derivatives of y. Derivatives up to order NQ +C are available from the history array YH, described above under +C optional outputs. In DEWSET, YH is identical to the YCUR array, +C extended to NQ + 1 columns with a column length of NYH and scale +C factors of H**j/factorial(j). On the first call for the problem, +C given by NST = 0, NQ is 1 and H is temporarily set to 1.0. +C NYH is the initial value of NEQ. The quantities NQ, H, and NST +C can be obtained by including in DEWSET the statements: +C DOUBLE PRECISION RLS +C COMMON /DLS001/ RLS(218),ILS(37) +C NQ = ILS(33) +C NST = ILS(34) +C H = RLS(212) +C Thus, for example, the current value of dy/dt can be obtained as +C YCUR(NYH+i)/H (i=1,...,NEQ) (and the division by H is +C unnecessary when NST = 0). +C----------------------------------------------------------------------- +C +C***REVISION HISTORY (YYYYMMDD) +C 19811102 DATE WRITTEN +C 19820126 Fixed bug in tests of work space lengths; +C minor corrections in main prologue and comments. +C 19870330 Major update: corrected comments throughout; +C removed TRET from Common; rewrote EWSET with 4 loops; +C fixed t test in INTDY; added Cray directives in STODA; +C in STODA, fixed DELP init. and logic around PJAC call; +C combined routines to save/restore Common; +C passed LEVEL = 0 in error message calls (except run abort). +C 19970225 Fixed lines setting JSTART = -2 in Subroutine LSODA. +C 20010425 Major update: convert source lines to upper case; +C added *DECK lines; changed from 1 to * in dummy dimensions; +C changed names R1MACH/D1MACH to RUMACH/DUMACH; +C renamed routines for uniqueness across single/double prec.; +C converted intrinsic names to generic form; +C removed ILLIN and NTREP (data loaded) from Common; +C removed all 'own' variables from Common; +C changed error messages to quoted strings; +C replaced XERRWV/XERRWD with 1993 revised version; +C converted prologues, comments, error messages to mixed case; +C numerous corrections to prologues and internal comments. +C 20010507 Converted single precision source to double precision. +C 20010613 Revised excess accuracy test (to match rest of ODEPACK). +C 20010808 Fixed bug in DPRJA (matrix in DBNORM call). +C 20020502 Corrected declarations in descriptions of user routines. +C 20031105 Restored 'own' variables to Common blocks, to enable +C interrupt/restart feature. +C 20031112 Added SAVE statements for data-loaded constants. +C +C----------------------------------------------------------------------- +C Other routines in the DLSODA package. +C +C In addition to Subroutine DLSODA, the DLSODA package includes the +C following subroutines and function routines: +C DINTDY computes an interpolated value of the y vector at t = TOUT. +C DSTODA is the core integrator, which does one step of the +C integration and the associated error control. +C DCFODE sets all method coefficients and test constants. +C DPRJA computes and preprocesses the Jacobian matrix J = df/dy +C and the Newton iteration matrix P = I - h*l0*J. +C DSOLSY manages solution of linear system in chord iteration. +C DEWSET sets the error weight vector EWT before each step. +C DMNORM computes the weighted max-norm of a vector. +C DFNORM computes the norm of a full matrix consistent with the +C weighted max-norm on vectors. +C DBNORM computes the norm of a band matrix consistent with the +C weighted max-norm on vectors. +C DSRCMA is a user-callable routine to save and restore +C the contents of the internal Common blocks. +C DGEFA and DGESL are routines from LINPACK for solving full +C systems of linear algebraic equations. +C DGBFA and DGBSL are routines from LINPACK for solving banded +C linear systems. +C DUMACH computes the unit roundoff in a machine-independent manner. +C XERRWD, XSETUN, XSETF, IXSAV, and IUMACH handle the printing of all +C error messages and warnings. XERRWD is machine-dependent. +C Note: DMNORM, DFNORM, DBNORM, DUMACH, IXSAV, and IUMACH are +C function routines. All the others are subroutines. +C +C----------------------------------------------------------------------- + EXTERNAL DPRJA, DSOLSY + DOUBLE PRECISION DUMACH, DMNORM + INTEGER INIT, MXSTEP, MXHNIL, NHNIL, NSLAST, NYH, IOWNS, + 1 ICF, IERPJ, IERSL, JCUR, JSTART, KFLAG, L, + 2 LYH, LEWT, LACOR, LSAVF, LWM, LIWM, METH, MITER, + 3 MAXORD, MAXCOR, MSBP, MXNCF, N, NQ, NST, NFE, NJE, NQU + INTEGER INSUFR, INSUFI, IXPR, IOWNS2, JTYP, MUSED, MXORDN, MXORDS + INTEGER I, I1, I2, IFLAG, IMXER, KGO, LF0, + 1 LENIW, LENRW, LENWM, ML, MORD, MU, MXHNL0, MXSTP0 + INTEGER LEN1, LEN1C, LEN1N, LEN1S, LEN2, LENIWC, LENRWC + DOUBLE PRECISION ROWNS, + 1 CCMAX, EL0, H, HMIN, HMXI, HU, RC, TN, UROUND + DOUBLE PRECISION TSW, ROWNS2, PDNORM + DOUBLE PRECISION ATOLI, AYI, BIG, EWTI, H0, HMAX, HMX, RH, RTOLI, + 1 TCRIT, TDIST, TNEXT, TOL, TOLSF, TP, SIZE, SUM, W0 + DIMENSION MORD(2) + LOGICAL IHIT + CHARACTER*60 MSG + SAVE MORD, MXSTP0, MXHNL0 +C----------------------------------------------------------------------- +C The following two internal Common blocks contain +C (a) variables which are local to any subroutine but whose values must +C be preserved between calls to the routine ("own" variables), and +C (b) variables which are communicated between subroutines. +C The block DLS001 is declared in subroutines DLSODA, DINTDY, DSTODA, +C DPRJA, and DSOLSY. +C The block DLSA01 is declared in subroutines DLSODA, DSTODA, and DPRJA. +C Groups of variables are replaced by dummy arrays in the Common +C declarations in routines where those variables are not used. +C----------------------------------------------------------------------- + COMMON /DLS001/ ROWNS(209), + 1 CCMAX, EL0, H, HMIN, HMXI, HU, RC, TN, UROUND, + 2 INIT, MXSTEP, MXHNIL, NHNIL, NSLAST, NYH, IOWNS(6), + 3 ICF, IERPJ, IERSL, JCUR, JSTART, KFLAG, L, + 4 LYH, LEWT, LACOR, LSAVF, LWM, LIWM, METH, MITER, + 5 MAXORD, MAXCOR, MSBP, MXNCF, N, NQ, NST, NFE, NJE, NQU +C + COMMON /DLSA01/ TSW, ROWNS2(20), PDNORM, + 1 INSUFR, INSUFI, IXPR, IOWNS2(2), JTYP, MUSED, MXORDN, MXORDS +C + DATA MORD(1),MORD(2)/12,5/, MXSTP0/500/, MXHNL0/10/ +C----------------------------------------------------------------------- +C Block A. +C This code block is executed on every call. +C It tests ISTATE and ITASK for legality and branches appropriately. +C If ISTATE .gt. 1 but the flag INIT shows that initialization has +C not yet been done, an error return occurs. +C If ISTATE = 1 and TOUT = T, return immediately. +C----------------------------------------------------------------------- + IF (ISTATE .LT. 1 .OR. ISTATE .GT. 3) GO TO 601 + IF (ITASK .LT. 1 .OR. ITASK .GT. 5) GO TO 602 + IF (ISTATE .EQ. 1) GO TO 10 + IF (INIT .EQ. 0) GO TO 603 + IF (ISTATE .EQ. 2) GO TO 200 + GO TO 20 + 10 INIT = 0 + IF (TOUT .EQ. T) RETURN +C----------------------------------------------------------------------- +C Block B. +C The next code block is executed for the initial call (ISTATE = 1), +C or for a continuation call with parameter changes (ISTATE = 3). +C It contains checking of all inputs and various initializations. +C +C First check legality of the non-optional inputs NEQ, ITOL, IOPT, +C JT, ML, and MU. +C----------------------------------------------------------------------- + 20 IF (NEQ(1) .LE. 0) GO TO 604 + IF (ISTATE .EQ. 1) GO TO 25 + IF (NEQ(1) .GT. N) GO TO 605 + 25 N = NEQ(1) + IF (ITOL .LT. 1 .OR. ITOL .GT. 4) GO TO 606 + IF (IOPT .LT. 0 .OR. IOPT .GT. 1) GO TO 607 + IF (JT .EQ. 3 .OR. JT .LT. 1 .OR. JT .GT. 5) GO TO 608 + JTYP = JT + IF (JT .LE. 2) GO TO 30 + ML = IWORK(1) + MU = IWORK(2) + IF (ML .LT. 0 .OR. ML .GE. N) GO TO 609 + IF (MU .LT. 0 .OR. MU .GE. N) GO TO 610 + 30 CONTINUE +C Next process and check the optional inputs. -------------------------- + IF (IOPT .EQ. 1) GO TO 40 + IXPR = 0 + MXSTEP = MXSTP0 + MXHNIL = MXHNL0 + HMXI = 0.0D0 + HMIN = 0.0D0 + IF (ISTATE .NE. 1) GO TO 60 + H0 = 0.0D0 + MXORDN = MORD(1) + MXORDS = MORD(2) + GO TO 60 + 40 IXPR = IWORK(5) + IF (IXPR .LT. 0 .OR. IXPR .GT. 1) GO TO 611 + MXSTEP = IWORK(6) + IF (MXSTEP .LT. 0) GO TO 612 + IF (MXSTEP .EQ. 0) MXSTEP = MXSTP0 + MXHNIL = IWORK(7) + IF (MXHNIL .LT. 0) GO TO 613 + IF (MXHNIL .EQ. 0) MXHNIL = MXHNL0 + IF (ISTATE .NE. 1) GO TO 50 + H0 = RWORK(5) + MXORDN = IWORK(8) + IF (MXORDN .LT. 0) GO TO 628 + IF (MXORDN .EQ. 0) MXORDN = 100 + MXORDN = MIN(MXORDN,MORD(1)) + MXORDS = IWORK(9) + IF (MXORDS .LT. 0) GO TO 629 + IF (MXORDS .EQ. 0) MXORDS = 100 + MXORDS = MIN(MXORDS,MORD(2)) + IF ((TOUT - T)*H0 .LT. 0.0D0) GO TO 614 + 50 HMAX = RWORK(6) + IF (HMAX .LT. 0.0D0) GO TO 615 + HMXI = 0.0D0 + IF (HMAX .GT. 0.0D0) HMXI = 1.0D0/HMAX + HMIN = RWORK(7) + IF (HMIN .LT. 0.0D0) GO TO 616 +C----------------------------------------------------------------------- +C Set work array pointers and check lengths LRW and LIW. +C If ISTATE = 1, METH is initialized to 1 here to facilitate the +C checking of work space lengths. +C Pointers to segments of RWORK and IWORK are named by prefixing L to +C the name of the segment. E.g., the segment YH starts at RWORK(LYH). +C Segments of RWORK (in order) are denoted YH, WM, EWT, SAVF, ACOR. +C If the lengths provided are insufficient for the current method, +C an error return occurs. This is treated as illegal input on the +C first call, but as a problem interruption with ISTATE = -7 on a +C continuation call. If the lengths are sufficient for the current +C method but not for both methods, a warning message is sent. +C----------------------------------------------------------------------- + 60 IF (ISTATE .EQ. 1) METH = 1 + IF (ISTATE .EQ. 1) NYH = N + LYH = 21 + LEN1N = 20 + (MXORDN + 1)*NYH + LEN1S = 20 + (MXORDS + 1)*NYH + LWM = LEN1S + 1 + IF (JT .LE. 2) LENWM = N*N + 2 + IF (JT .GE. 4) LENWM = (2*ML + MU + 1)*N + 2 + LEN1S = LEN1S + LENWM + LEN1C = LEN1N + IF (METH .EQ. 2) LEN1C = LEN1S + LEN1 = MAX(LEN1N,LEN1S) + LEN2 = 3*N + LENRW = LEN1 + LEN2 + LENRWC = LEN1C + LEN2 + IWORK(17) = LENRW + LIWM = 1 + LENIW = 20 + N + LENIWC = 20 + IF (METH .EQ. 2) LENIWC = LENIW + IWORK(18) = LENIW + IF (ISTATE .EQ. 1 .AND. LRW .LT. LENRWC) GO TO 617 + IF (ISTATE .EQ. 1 .AND. LIW .LT. LENIWC) GO TO 618 + IF (ISTATE .EQ. 3 .AND. LRW .LT. LENRWC) GO TO 550 + IF (ISTATE .EQ. 3 .AND. LIW .LT. LENIWC) GO TO 555 + LEWT = LEN1 + 1 + INSUFR = 0 + IF (LRW .GE. LENRW) GO TO 65 + INSUFR = 2 + LEWT = LEN1C + 1 + MSG='DLSODA- Warning.. RWORK length is sufficient for now, but ' + CALL XERRWD (MSG, 60, 103, 0, 0, 0, 0, 0, 0.0D0, 0.0D0) + MSG=' may not be later. Integration will proceed anyway. ' + CALL XERRWD (MSG, 60, 103, 0, 0, 0, 0, 0, 0.0D0, 0.0D0) + MSG = ' Length needed is LENRW = I1, while LRW = I2.' + CALL XERRWD (MSG, 50, 103, 0, 2, LENRW, LRW, 0, 0.0D0, 0.0D0) + 65 LSAVF = LEWT + N + LACOR = LSAVF + N + INSUFI = 0 + IF (LIW .GE. LENIW) GO TO 70 + INSUFI = 2 + MSG='DLSODA- Warning.. IWORK length is sufficient for now, but ' + CALL XERRWD (MSG, 60, 104, 0, 0, 0, 0, 0, 0.0D0, 0.0D0) + MSG=' may not be later. Integration will proceed anyway. ' + CALL XERRWD (MSG, 60, 104, 0, 0, 0, 0, 0, 0.0D0, 0.0D0) + MSG = ' Length needed is LENIW = I1, while LIW = I2.' + CALL XERRWD (MSG, 50, 104, 0, 2, LENIW, LIW, 0, 0.0D0, 0.0D0) + 70 CONTINUE +C Check RTOL and ATOL for legality. ------------------------------------ + RTOLI = RTOL(1) + ATOLI = ATOL(1) + DO 75 I = 1,N + IF (ITOL .GE. 3) RTOLI = RTOL(I) + IF (ITOL .EQ. 2 .OR. ITOL .EQ. 4) ATOLI = ATOL(I) + IF (RTOLI .LT. 0.0D0) GO TO 619 + IF (ATOLI .LT. 0.0D0) GO TO 620 + 75 CONTINUE + IF (ISTATE .EQ. 1) GO TO 100 +C If ISTATE = 3, set flag to signal parameter changes to DSTODA. ------- + JSTART = -1 + IF (N .EQ. NYH) GO TO 200 +C NEQ was reduced. Zero part of YH to avoid undefined references. ----- + I1 = LYH + L*NYH + I2 = LYH + (MAXORD + 1)*NYH - 1 + IF (I1 .GT. I2) GO TO 200 + DO 95 I = I1,I2 + 95 RWORK(I) = 0.0D0 + GO TO 200 +C----------------------------------------------------------------------- +C Block C. +C The next block is for the initial call only (ISTATE = 1). +C It contains all remaining initializations, the initial call to F, +C and the calculation of the initial step size. +C The error weights in EWT are inverted after being loaded. +C----------------------------------------------------------------------- + 100 UROUND = DUMACH() + TN = T + TSW = T + MAXORD = MXORDN + IF (ITASK .NE. 4 .AND. ITASK .NE. 5) GO TO 110 + TCRIT = RWORK(1) + IF ((TCRIT - TOUT)*(TOUT - T) .LT. 0.0D0) GO TO 625 + IF (H0 .NE. 0.0D0 .AND. (T + H0 - TCRIT)*H0 .GT. 0.0D0) + 1 H0 = TCRIT - T + 110 JSTART = 0 + NHNIL = 0 + NST = 0 + NJE = 0 + NSLAST = 0 + HU = 0.0D0 + NQU = 0 + MUSED = 0 + MITER = 0 + CCMAX = 0.3D0 + MAXCOR = 3 + MSBP = 20 + MXNCF = 10 +C Initial call to F. (LF0 points to YH(*,2).) ------------------------- + LF0 = LYH + NYH + CALL F (NEQ, T, Y, RWORK(LF0)) + NFE = 1 +C Load the initial value vector in YH. --------------------------------- + DO 115 I = 1,N + 115 RWORK(I+LYH-1) = Y(I) +C Load and invert the EWT array. (H is temporarily set to 1.0.) ------- + NQ = 1 + H = 1.0D0 + CALL DEWSET (N, ITOL, RTOL, ATOL, RWORK(LYH), RWORK(LEWT)) + DO 120 I = 1,N + IF (RWORK(I+LEWT-1) .LE. 0.0D0) GO TO 621 + 120 RWORK(I+LEWT-1) = 1.0D0/RWORK(I+LEWT-1) +C----------------------------------------------------------------------- +C The coding below computes the step size, H0, to be attempted on the +C first step, unless the user has supplied a value for this. +C First check that TOUT - T differs significantly from zero. +C A scalar tolerance quantity TOL is computed, as MAX(RTOL(i)) +C if this is positive, or MAX(ATOL(i)/ABS(Y(i))) otherwise, adjusted +C so as to be between 100*UROUND and 1.0E-3. +C Then the computed value H0 is given by: +C +C H0**(-2) = 1./(TOL * w0**2) + TOL * (norm(F))**2 +C +C where w0 = MAX ( ABS(T), ABS(TOUT) ), +C F = the initial value of the vector f(t,y), and +C norm() = the weighted vector norm used throughout, given by +C the DMNORM function routine, and weighted by the +C tolerances initially loaded into the EWT array. +C The sign of H0 is inferred from the initial values of TOUT and T. +C ABS(H0) is made .le. ABS(TOUT-T) in any case. +C----------------------------------------------------------------------- + IF (H0 .NE. 0.0D0) GO TO 180 + TDIST = ABS(TOUT - T) + W0 = MAX(ABS(T),ABS(TOUT)) + IF (TDIST .LT. 2.0D0*UROUND*W0) GO TO 622 + TOL = RTOL(1) + IF (ITOL .LE. 2) GO TO 140 + DO 130 I = 1,N + 130 TOL = MAX(TOL,RTOL(I)) + 140 IF (TOL .GT. 0.0D0) GO TO 160 + ATOLI = ATOL(1) + DO 150 I = 1,N + IF (ITOL .EQ. 2 .OR. ITOL .EQ. 4) ATOLI = ATOL(I) + AYI = ABS(Y(I)) + IF (AYI .NE. 0.0D0) TOL = MAX(TOL,ATOLI/AYI) + 150 CONTINUE + 160 TOL = MAX(TOL,100.0D0*UROUND) + TOL = MIN(TOL,0.001D0) + SUM = DMNORM (N, RWORK(LF0), RWORK(LEWT)) + SUM = 1.0D0/(TOL*W0*W0) + TOL*SUM**2 + H0 = 1.0D0/SQRT(SUM) + H0 = MIN(H0,TDIST) + H0 = SIGN(H0,TOUT-T) +C Adjust H0 if necessary to meet HMAX bound. --------------------------- + 180 RH = ABS(H0)*HMXI + IF (RH .GT. 1.0D0) H0 = H0/RH +C Load H with H0 and scale YH(*,2) by H0. ------------------------------ + H = H0 + DO 190 I = 1,N + 190 RWORK(I+LF0-1) = H0*RWORK(I+LF0-1) + GO TO 270 +C----------------------------------------------------------------------- +C Block D. +C The next code block is for continuation calls only (ISTATE = 2 or 3) +C and is to check stop conditions before taking a step. +C----------------------------------------------------------------------- + 200 NSLAST = NST + GO TO (210, 250, 220, 230, 240), ITASK + 210 IF ((TN - TOUT)*H .LT. 0.0D0) GO TO 250 + CALL DINTDY (TOUT, 0, RWORK(LYH), NYH, Y, IFLAG) + IF (IFLAG .NE. 0) GO TO 627 + T = TOUT + GO TO 420 + 220 TP = TN - HU*(1.0D0 + 100.0D0*UROUND) + IF ((TP - TOUT)*H .GT. 0.0D0) GO TO 623 + IF ((TN - TOUT)*H .LT. 0.0D0) GO TO 250 + T = TN + GO TO 400 + 230 TCRIT = RWORK(1) + IF ((TN - TCRIT)*H .GT. 0.0D0) GO TO 624 + IF ((TCRIT - TOUT)*H .LT. 0.0D0) GO TO 625 + IF ((TN - TOUT)*H .LT. 0.0D0) GO TO 245 + CALL DINTDY (TOUT, 0, RWORK(LYH), NYH, Y, IFLAG) + IF (IFLAG .NE. 0) GO TO 627 + T = TOUT + GO TO 420 + 240 TCRIT = RWORK(1) + IF ((TN - TCRIT)*H .GT. 0.0D0) GO TO 624 + 245 HMX = ABS(TN) + ABS(H) + IHIT = ABS(TN - TCRIT) .LE. 100.0D0*UROUND*HMX + IF (IHIT) T = TCRIT + IF (IHIT) GO TO 400 + TNEXT = TN + H*(1.0D0 + 4.0D0*UROUND) + IF ((TNEXT - TCRIT)*H .LE. 0.0D0) GO TO 250 + H = (TCRIT - TN)*(1.0D0 - 4.0D0*UROUND) + IF (ISTATE .EQ. 2 .AND. JSTART .GE. 0) JSTART = -2 +C----------------------------------------------------------------------- +C Block E. +C The next block is normally executed for all calls and contains +C the call to the one-step core integrator DSTODA. +C +C This is a looping point for the integration steps. +C +C First check for too many steps being taken, update EWT (if not at +C start of problem), check for too much accuracy being requested, and +C check for H below the roundoff level in T. +C----------------------------------------------------------------------- + 250 CONTINUE + IF (METH .EQ. MUSED) GO TO 255 + IF (INSUFR .EQ. 1) GO TO 550 + IF (INSUFI .EQ. 1) GO TO 555 + 255 IF ((NST-NSLAST) .GE. MXSTEP) GO TO 500 + CALL DEWSET (N, ITOL, RTOL, ATOL, RWORK(LYH), RWORK(LEWT)) + DO 260 I = 1,N + IF (RWORK(I+LEWT-1) .LE. 0.0D0) GO TO 510 + 260 RWORK(I+LEWT-1) = 1.0D0/RWORK(I+LEWT-1) + 270 TOLSF = UROUND*DMNORM (N, RWORK(LYH), RWORK(LEWT)) + IF (TOLSF .LE. 1.0D0) GO TO 280 + TOLSF = TOLSF*2.0D0 + IF (NST .EQ. 0) GO TO 626 + GO TO 520 + 280 IF ((TN + H) .NE. TN) GO TO 290 + NHNIL = NHNIL + 1 + IF (NHNIL .GT. MXHNIL) GO TO 290 + MSG = 'DLSODA- Warning..Internal T (=R1) and H (=R2) are' + CALL XERRWD (MSG, 50, 101, 0, 0, 0, 0, 0, 0.0D0, 0.0D0) + MSG=' such that in the machine, T + H = T on the next step ' + CALL XERRWD (MSG, 60, 101, 0, 0, 0, 0, 0, 0.0D0, 0.0D0) + MSG = ' (H = step size). Solver will continue anyway.' + CALL XERRWD (MSG, 50, 101, 0, 0, 0, 0, 2, TN, H) + IF (NHNIL .LT. MXHNIL) GO TO 290 + MSG = 'DLSODA- Above warning has been issued I1 times. ' + CALL XERRWD (MSG, 50, 102, 0, 0, 0, 0, 0, 0.0D0, 0.0D0) + MSG = ' It will not be issued again for this problem.' + CALL XERRWD (MSG, 50, 102, 0, 1, MXHNIL, 0, 0, 0.0D0, 0.0D0) + 290 CONTINUE +C----------------------------------------------------------------------- +C CALL DSTODA(NEQ,Y,YH,NYH,YH,EWT,SAVF,ACOR,WM,IWM,F,JAC,DPRJA,DSOLSY) +C----------------------------------------------------------------------- + CALL DSTODA (NEQ, Y, RWORK(LYH), NYH, RWORK(LYH), RWORK(LEWT), + 1 RWORK(LSAVF), RWORK(LACOR), RWORK(LWM), IWORK(LIWM), + 2 F, JAC, DPRJA, DSOLSY) + KGO = 1 - KFLAG + GO TO (300, 530, 540), KGO +C----------------------------------------------------------------------- +C Block F. +C The following block handles the case of a successful return from the +C core integrator (KFLAG = 0). +C If a method switch was just made, record TSW, reset MAXORD, +C set JSTART to -1 to signal DSTODA to complete the switch, +C and do extra printing of data if IXPR = 1. +C Then, in any case, check for stop conditions. +C----------------------------------------------------------------------- + 300 INIT = 1 + IF (METH .EQ. MUSED) GO TO 310 + TSW = TN + MAXORD = MXORDN + IF (METH .EQ. 2) MAXORD = MXORDS + IF (METH .EQ. 2) RWORK(LWM) = SQRT(UROUND) + INSUFR = MIN(INSUFR,1) + INSUFI = MIN(INSUFI,1) + JSTART = -1 + IF (IXPR .EQ. 0) GO TO 310 + IF (METH .EQ. 2) THEN + MSG='DLSODA- A switch to the BDF (stiff) method has occurred ' + CALL XERRWD (MSG, 60, 105, 0, 0, 0, 0, 0, 0.0D0, 0.0D0) + ENDIF + IF (METH .EQ. 1) THEN + MSG='DLSODA- A switch to the Adams (nonstiff) method has occurred' + CALL XERRWD (MSG, 60, 106, 0, 0, 0, 0, 0, 0.0D0, 0.0D0) + ENDIF + MSG=' at T = R1, tentative step size H = R2, step NST = I1 ' + CALL XERRWD (MSG, 60, 107, 0, 1, NST, 0, 2, TN, H) + 310 GO TO (320, 400, 330, 340, 350), ITASK +C ITASK = 1. If TOUT has been reached, interpolate. ------------------- + 320 IF ((TN - TOUT)*H .LT. 0.0D0) GO TO 250 + CALL DINTDY (TOUT, 0, RWORK(LYH), NYH, Y, IFLAG) + T = TOUT + GO TO 420 +C ITASK = 3. Jump to exit if TOUT was reached. ------------------------ + 330 IF ((TN - TOUT)*H .GE. 0.0D0) GO TO 400 + GO TO 250 +C ITASK = 4. See if TOUT or TCRIT was reached. Adjust H if necessary. + 340 IF ((TN - TOUT)*H .LT. 0.0D0) GO TO 345 + CALL DINTDY (TOUT, 0, RWORK(LYH), NYH, Y, IFLAG) + T = TOUT + GO TO 420 + 345 HMX = ABS(TN) + ABS(H) + IHIT = ABS(TN - TCRIT) .LE. 100.0D0*UROUND*HMX + IF (IHIT) GO TO 400 + TNEXT = TN + H*(1.0D0 + 4.0D0*UROUND) + IF ((TNEXT - TCRIT)*H .LE. 0.0D0) GO TO 250 + H = (TCRIT - TN)*(1.0D0 - 4.0D0*UROUND) + IF (JSTART .GE. 0) JSTART = -2 + GO TO 250 +C ITASK = 5. See if TCRIT was reached and jump to exit. --------------- + 350 HMX = ABS(TN) + ABS(H) + IHIT = ABS(TN - TCRIT) .LE. 100.0D0*UROUND*HMX +C----------------------------------------------------------------------- +C Block G. +C The following block handles all successful returns from DLSODA. +C If ITASK .ne. 1, Y is loaded from YH and T is set accordingly. +C ISTATE is set to 2, and the optional outputs are loaded into the +C work arrays before returning. +C----------------------------------------------------------------------- + 400 DO 410 I = 1,N + 410 Y(I) = RWORK(I+LYH-1) + T = TN + IF (ITASK .NE. 4 .AND. ITASK .NE. 5) GO TO 420 + IF (IHIT) T = TCRIT + 420 ISTATE = 2 + RWORK(11) = HU + RWORK(12) = H + RWORK(13) = TN + RWORK(15) = TSW + IWORK(11) = NST + IWORK(12) = NFE + IWORK(13) = NJE + IWORK(14) = NQU + IWORK(15) = NQ + IWORK(19) = MUSED + IWORK(20) = METH + RETURN +C----------------------------------------------------------------------- +C Block H. +C The following block handles all unsuccessful returns other than +C those for illegal input. First the error message routine is called. +C If there was an error test or convergence test failure, IMXER is set. +C Then Y is loaded from YH and T is set to TN. +C The optional outputs are loaded into the work arrays before returning. +C----------------------------------------------------------------------- +C The maximum number of steps was taken before reaching TOUT. ---------- + 500 MSG = 'DLSODA- At current T (=R1), MXSTEP (=I1) steps ' + CALL XERRWD (MSG, 50, 201, 0, 0, 0, 0, 0, 0.0D0, 0.0D0) + MSG = ' taken on this call before reaching TOUT ' + CALL XERRWD (MSG, 50, 201, 0, 1, MXSTEP, 0, 1, TN, 0.0D0) + ISTATE = -1 + GO TO 580 +C EWT(i) .le. 0.0 for some i (not at start of problem). ---------------- + 510 EWTI = RWORK(LEWT+I-1) + MSG = 'DLSODA- At T (=R1), EWT(I1) has become R2 .le. 0.' + CALL XERRWD (MSG, 50, 202, 0, 1, I, 0, 2, TN, EWTI) + ISTATE = -6 + GO TO 580 +C Too much accuracy requested for machine precision. ------------------- + 520 MSG = 'DLSODA- At T (=R1), too much accuracy requested ' + CALL XERRWD (MSG, 50, 203, 0, 0, 0, 0, 0, 0.0D0, 0.0D0) + MSG = ' for precision of machine.. See TOLSF (=R2) ' + CALL XERRWD (MSG, 50, 203, 0, 0, 0, 0, 2, TN, TOLSF) + RWORK(14) = TOLSF + ISTATE = -2 + GO TO 580 +C KFLAG = -1. Error test failed repeatedly or with ABS(H) = HMIN. ----- + 530 MSG = 'DLSODA- At T(=R1) and step size H(=R2), the error' + CALL XERRWD (MSG, 50, 204, 0, 0, 0, 0, 0, 0.0D0, 0.0D0) + MSG = ' test failed repeatedly or with ABS(H) = HMIN' + CALL XERRWD (MSG, 50, 204, 0, 0, 0, 0, 2, TN, H) + ISTATE = -4 + GO TO 560 +C KFLAG = -2. Convergence failed repeatedly or with ABS(H) = HMIN. ---- + 540 MSG = 'DLSODA- At T (=R1) and step size H (=R2), the ' + CALL XERRWD (MSG, 50, 205, 0, 0, 0, 0, 0, 0.0D0, 0.0D0) + MSG = ' corrector convergence failed repeatedly ' + CALL XERRWD (MSG, 50, 205, 0, 0, 0, 0, 0, 0.0D0, 0.0D0) + MSG = ' or with ABS(H) = HMIN ' + CALL XERRWD (MSG, 30, 205, 0, 0, 0, 0, 2, TN, H) + ISTATE = -5 + GO TO 560 +C RWORK length too small to proceed. ----------------------------------- + 550 MSG = 'DLSODA- At current T(=R1), RWORK length too small' + CALL XERRWD (MSG, 50, 206, 0, 0, 0, 0, 0, 0.0D0, 0.0D0) + MSG=' to proceed. The integration was otherwise successful.' + CALL XERRWD (MSG, 60, 206, 0, 0, 0, 0, 1, TN, 0.0D0) + ISTATE = -7 + GO TO 580 +C IWORK length too small to proceed. ----------------------------------- + 555 MSG = 'DLSODA- At current T(=R1), IWORK length too small' + CALL XERRWD (MSG, 50, 207, 0, 0, 0, 0, 0, 0.0D0, 0.0D0) + MSG=' to proceed. The integration was otherwise successful.' + CALL XERRWD (MSG, 60, 207, 0, 0, 0, 0, 1, TN, 0.0D0) + ISTATE = -7 + GO TO 580 +C Compute IMXER if relevant. ------------------------------------------- + 560 BIG = 0.0D0 + IMXER = 1 + DO 570 I = 1,N + SIZE = ABS(RWORK(I+LACOR-1)*RWORK(I+LEWT-1)) + IF (BIG .GE. SIZE) GO TO 570 + BIG = SIZE + IMXER = I + 570 CONTINUE + IWORK(16) = IMXER +C Set Y vector, T, and optional outputs. ------------------------------- + 580 DO 590 I = 1,N + 590 Y(I) = RWORK(I+LYH-1) + T = TN + RWORK(11) = HU + RWORK(12) = H + RWORK(13) = TN + RWORK(15) = TSW + IWORK(11) = NST + IWORK(12) = NFE + IWORK(13) = NJE + IWORK(14) = NQU + IWORK(15) = NQ + IWORK(19) = MUSED + IWORK(20) = METH + RETURN +C----------------------------------------------------------------------- +C Block I. +C The following block handles all error returns due to illegal input +C (ISTATE = -3), as detected before calling the core integrator. +C First the error message routine is called. If the illegal input +C is a negative ISTATE, the run is aborted (apparent infinite loop). +C----------------------------------------------------------------------- + 601 MSG = 'DLSODA- ISTATE (=I1) illegal.' + CALL XERRWD (MSG, 30, 1, 0, 1, ISTATE, 0, 0, 0.0D0, 0.0D0) + IF (ISTATE .LT. 0) GO TO 800 + GO TO 700 + 602 MSG = 'DLSODA- ITASK (=I1) illegal. ' + CALL XERRWD (MSG, 30, 2, 0, 1, ITASK, 0, 0, 0.0D0, 0.0D0) + GO TO 700 + 603 MSG = 'DLSODA- ISTATE .gt. 1 but DLSODA not initialized.' + CALL XERRWD (MSG, 50, 3, 0, 0, 0, 0, 0, 0.0D0, 0.0D0) + GO TO 700 + 604 MSG = 'DLSODA- NEQ (=I1) .lt. 1 ' + CALL XERRWD (MSG, 30, 4, 0, 1, NEQ(1), 0, 0, 0.0D0, 0.0D0) + GO TO 700 + 605 MSG = 'DLSODA- ISTATE = 3 and NEQ increased (I1 to I2). ' + CALL XERRWD (MSG, 50, 5, 0, 2, N, NEQ(1), 0, 0.0D0, 0.0D0) + GO TO 700 + 606 MSG = 'DLSODA- ITOL (=I1) illegal. ' + CALL XERRWD (MSG, 30, 6, 0, 1, ITOL, 0, 0, 0.0D0, 0.0D0) + GO TO 700 + 607 MSG = 'DLSODA- IOPT (=I1) illegal. ' + CALL XERRWD (MSG, 30, 7, 0, 1, IOPT, 0, 0, 0.0D0, 0.0D0) + GO TO 700 + 608 MSG = 'DLSODA- JT (=I1) illegal. ' + CALL XERRWD (MSG, 30, 8, 0, 1, JT, 0, 0, 0.0D0, 0.0D0) + GO TO 700 + 609 MSG = 'DLSODA- ML (=I1) illegal: .lt.0 or .ge.NEQ (=I2) ' + CALL XERRWD (MSG, 50, 9, 0, 2, ML, NEQ(1), 0, 0.0D0, 0.0D0) + GO TO 700 + 610 MSG = 'DLSODA- MU (=I1) illegal: .lt.0 or .ge.NEQ (=I2) ' + CALL XERRWD (MSG, 50, 10, 0, 2, MU, NEQ(1), 0, 0.0D0, 0.0D0) + GO TO 700 + 611 MSG = 'DLSODA- IXPR (=I1) illegal. ' + CALL XERRWD (MSG, 30, 11, 0, 1, IXPR, 0, 0, 0.0D0, 0.0D0) + GO TO 700 + 612 MSG = 'DLSODA- MXSTEP (=I1) .lt. 0 ' + CALL XERRWD (MSG, 30, 12, 0, 1, MXSTEP, 0, 0, 0.0D0, 0.0D0) + GO TO 700 + 613 MSG = 'DLSODA- MXHNIL (=I1) .lt. 0 ' + CALL XERRWD (MSG, 30, 13, 0, 1, MXHNIL, 0, 0, 0.0D0, 0.0D0) + GO TO 700 + 614 MSG = 'DLSODA- TOUT (=R1) behind T (=R2) ' + CALL XERRWD (MSG, 40, 14, 0, 0, 0, 0, 2, TOUT, T) + MSG = ' Integration direction is given by H0 (=R1) ' + CALL XERRWD (MSG, 50, 14, 0, 0, 0, 0, 1, H0, 0.0D0) + GO TO 700 + 615 MSG = 'DLSODA- HMAX (=R1) .lt. 0.0 ' + CALL XERRWD (MSG, 30, 15, 0, 0, 0, 0, 1, HMAX, 0.0D0) + GO TO 700 + 616 MSG = 'DLSODA- HMIN (=R1) .lt. 0.0 ' + CALL XERRWD (MSG, 30, 16, 0, 0, 0, 0, 1, HMIN, 0.0D0) + GO TO 700 + 617 MSG='DLSODA- RWORK length needed, LENRW (=I1), exceeds LRW (=I2)' + CALL XERRWD (MSG, 60, 17, 0, 2, LENRW, LRW, 0, 0.0D0, 0.0D0) + GO TO 700 + 618 MSG='DLSODA- IWORK length needed, LENIW (=I1), exceeds LIW (=I2)' + CALL XERRWD (MSG, 60, 18, 0, 2, LENIW, LIW, 0, 0.0D0, 0.0D0) + GO TO 700 + 619 MSG = 'DLSODA- RTOL(I1) is R1 .lt. 0.0 ' + CALL XERRWD (MSG, 40, 19, 0, 1, I, 0, 1, RTOLI, 0.0D0) + GO TO 700 + 620 MSG = 'DLSODA- ATOL(I1) is R1 .lt. 0.0 ' + CALL XERRWD (MSG, 40, 20, 0, 1, I, 0, 1, ATOLI, 0.0D0) + GO TO 700 + 621 EWTI = RWORK(LEWT+I-1) + MSG = 'DLSODA- EWT(I1) is R1 .le. 0.0 ' + CALL XERRWD (MSG, 40, 21, 0, 1, I, 0, 1, EWTI, 0.0D0) + GO TO 700 + 622 MSG='DLSODA- TOUT(=R1) too close to T(=R2) to start integration.' + CALL XERRWD (MSG, 60, 22, 0, 0, 0, 0, 2, TOUT, T) + GO TO 700 + 623 MSG='DLSODA- ITASK = I1 and TOUT (=R1) behind TCUR - HU (= R2) ' + CALL XERRWD (MSG, 60, 23, 0, 1, ITASK, 0, 2, TOUT, TP) + GO TO 700 + 624 MSG='DLSODA- ITASK = 4 or 5 and TCRIT (=R1) behind TCUR (=R2) ' + CALL XERRWD (MSG, 60, 24, 0, 0, 0, 0, 2, TCRIT, TN) + GO TO 700 + 625 MSG='DLSODA- ITASK = 4 or 5 and TCRIT (=R1) behind TOUT (=R2) ' + CALL XERRWD (MSG, 60, 25, 0, 0, 0, 0, 2, TCRIT, TOUT) + GO TO 700 + 626 MSG = 'DLSODA- At start of problem, too much accuracy ' + CALL XERRWD (MSG, 50, 26, 0, 0, 0, 0, 0, 0.0D0, 0.0D0) + MSG=' requested for precision of machine.. See TOLSF (=R1) ' + CALL XERRWD (MSG, 60, 26, 0, 0, 0, 0, 1, TOLSF, 0.0D0) + RWORK(14) = TOLSF + GO TO 700 + 627 MSG = 'DLSODA- Trouble in DINTDY. ITASK = I1, TOUT = R1' + CALL XERRWD (MSG, 50, 27, 0, 1, ITASK, 0, 1, TOUT, 0.0D0) + GO TO 700 + 628 MSG = 'DLSODA- MXORDN (=I1) .lt. 0 ' + CALL XERRWD (MSG, 30, 28, 0, 1, MXORDN, 0, 0, 0.0D0, 0.0D0) + GO TO 700 + 629 MSG = 'DLSODA- MXORDS (=I1) .lt. 0 ' + CALL XERRWD (MSG, 30, 29, 0, 1, MXORDS, 0, 0, 0.0D0, 0.0D0) +C + 700 ISTATE = -3 + RETURN +C + 800 MSG = 'DLSODA- Run aborted.. apparent infinite loop. ' + CALL XERRWD (MSG, 50, 303, 2, 0, 0, 0, 0, 0.0D0, 0.0D0) + RETURN +C----------------------- End of Subroutine DLSODA ---------------------- + END +*DECK DLSODAR + SUBROUTINE DLSODAR (F, NEQ, Y, T, TOUT, ITOL, RTOL, ATOL, ITASK, + 1 ISTATE, IOPT, RWORK, LRW, IWORK, LIW, JAC, JT, + 2 G, NG, JROOT) + EXTERNAL F, JAC, G + INTEGER NEQ, ITOL, ITASK, ISTATE, IOPT, LRW, IWORK, LIW, JT, + 1 NG, JROOT + DOUBLE PRECISION Y, T, TOUT, RTOL, ATOL, RWORK + DIMENSION NEQ(*), Y(*), RTOL(*), ATOL(*), RWORK(LRW), IWORK(LIW), + 1 JROOT(NG) +C----------------------------------------------------------------------- +C This is the 12 November 2003 version of +C DLSODAR: Livermore Solver for Ordinary Differential Equations, with +C Automatic method switching for stiff and nonstiff problems, +C and with Root-finding. +C +C This version is in double precision. +C +C DLSODAR solves the initial value problem for stiff or nonstiff +C systems of first order ODEs, +C dy/dt = f(t,y) , or, in component form, +C dy(i)/dt = f(i) = f(i,t,y(1),y(2),...,y(NEQ)) (i = 1,...,NEQ). +C At the same time, it locates the roots of any of a set of functions +C g(i) = g(i,t,y(1),...,y(NEQ)) (i = 1,...,ng). +C +C This a variant version of the DLSODE package. It differs from it +C in two ways: +C (a) It switches automatically between stiff and nonstiff methods. +C This means that the user does not have to determine whether the +C problem is stiff or not, and the solver will automatically choose the +C appropriate method. It always starts with the nonstiff method. +C (b) It finds the root of at least one of a set of constraint +C functions g(i) of the independent and dependent variables. +C It finds only those roots for which some g(i), as a function +C of t, changes sign in the interval of integration. +C It then returns the solution at the root, if that occurs +C sooner than the specified stop condition, and otherwise returns +C the solution according the specified stop condition. +C +C Authors: Alan C. Hindmarsh, +C Center for Applied Scientific Computing, L-561 +C Lawrence Livermore National Laboratory +C Livermore, CA 94551 +C and +C Linda R. Petzold +C Univ. of California at Santa Barbara +C Dept. of Computer Science +C Santa Barbara, CA 93106 +C +C References: +C 1. Alan C. Hindmarsh, ODEPACK, A Systematized Collection of ODE +C Solvers, in Scientific Computing, R. S. Stepleman et al. (Eds.), +C North-Holland, Amsterdam, 1983, pp. 55-64. +C 2. Linda R. Petzold, Automatic Selection of Methods for Solving +C Stiff and Nonstiff Systems of Ordinary Differential Equations, +C Siam J. Sci. Stat. Comput. 4 (1983), pp. 136-148. +C 3. Kathie L. Hiebert and Lawrence F. Shampine, Implicitly Defined +C Output Points for Solutions of ODEs, Sandia Report SAND80-0180, +C February 1980. +C----------------------------------------------------------------------- +C Summary of Usage. +C +C Communication between the user and the DLSODAR package, for normal +C situations, is summarized here. This summary describes only a subset +C of the full set of options available. See the full description for +C details, including alternative treatment of the Jacobian matrix, +C optional inputs and outputs, nonstandard options, and +C instructions for special situations. See also the example +C problem (with program and output) following this summary. +C +C A. First provide a subroutine of the form: +C SUBROUTINE F (NEQ, T, Y, YDOT) +C DOUBLE PRECISION T, Y(*), YDOT(*) +C which supplies the vector function f by loading YDOT(i) with f(i). +C +C B. Provide a subroutine of the form: +C SUBROUTINE G (NEQ, T, Y, NG, GOUT) +C DOUBLE PRECISION T, Y(*), GOUT(NG) +C which supplies the vector function g by loading GOUT(i) with +C g(i), the i-th constraint function whose root is sought. +C +C C. Write a main program which calls Subroutine DLSODAR once for +C each point at which answers are desired. This should also provide +C for possible use of logical unit 6 for output of error messages by +C DLSODAR. On the first call to DLSODAR, supply arguments as follows: +C F = name of subroutine for right-hand side vector f. +C This name must be declared External in calling program. +C NEQ = number of first order ODEs. +C Y = array of initial values, of length NEQ. +C T = the initial value of the independent variable. +C TOUT = first point where output is desired (.ne. T). +C ITOL = 1 or 2 according as ATOL (below) is a scalar or array. +C RTOL = relative tolerance parameter (scalar). +C ATOL = absolute tolerance parameter (scalar or array). +C the estimated local error in y(i) will be controlled so as +C to be less than +C EWT(i) = RTOL*ABS(Y(i)) + ATOL if ITOL = 1, or +C EWT(i) = RTOL*ABS(Y(i)) + ATOL(i) if ITOL = 2. +C Thus the local error test passes if, in each component, +C either the absolute error is less than ATOL (or ATOL(i)), +C or the relative error is less than RTOL. +C Use RTOL = 0.0 for pure absolute error control, and +C use ATOL = 0.0 (or ATOL(i) = 0.0) for pure relative error +C control. Caution: actual (global) errors may exceed these +C local tolerances, so choose them conservatively. +C ITASK = 1 for normal computation of output values of y at t = TOUT. +C ISTATE = integer flag (input and output). Set ISTATE = 1. +C IOPT = 0 to indicate no optional inputs used. +C RWORK = real work array of length at least: +C 22 + NEQ * MAX(16, NEQ + 9) + 3*NG. +C See also Paragraph F below. +C LRW = declared length of RWORK (in user's dimension). +C IWORK = integer work array of length at least 20 + NEQ. +C LIW = declared length of IWORK (in user's dimension). +C JAC = name of subroutine for Jacobian matrix. +C Use a dummy name. See also Paragraph F below. +C JT = Jacobian type indicator. Set JT = 2. +C See also Paragraph F below. +C G = name of subroutine for constraint functions, whose +C roots are desired during the integration. +C This name must be declared External in calling program. +C NG = number of constraint functions g(i). If there are none, +C set NG = 0, and pass a dummy name for G. +C JROOT = integer array of length NG for output of root information. +C See next paragraph. +C Note that the main program must declare arrays Y, RWORK, IWORK, +C JROOT, and possibly ATOL. +C +C D. The output from the first call (or any call) is: +C Y = array of computed values of y(t) vector. +C T = corresponding value of independent variable. This is +C TOUT if ISTATE = 2, or the root location if ISTATE = 3, +C or the farthest point reached if DLSODAR was unsuccessful. +C ISTATE = 2 or 3 if DLSODAR was successful, negative otherwise. +C 2 means no root was found, and TOUT was reached as desired. +C 3 means a root was found prior to reaching TOUT. +C -1 means excess work done on this call (perhaps wrong JT). +C -2 means excess accuracy requested (tolerances too small). +C -3 means illegal input detected (see printed message). +C -4 means repeated error test failures (check all inputs). +C -5 means repeated convergence failures (perhaps bad Jacobian +C supplied or wrong choice of JT or tolerances). +C -6 means error weight became zero during problem. (Solution +C component i vanished, and ATOL or ATOL(i) = 0.) +C -7 means work space insufficient to finish (see messages). +C JROOT = array showing roots found if ISTATE = 3 on return. +C JROOT(i) = 1 if g(i) has a root at t, or 0 otherwise. +C +C E. To continue the integration after a successful return, proceed +C as follows: +C (a) If ISTATE = 2 on return, reset TOUT and call DLSODAR again. +C (b) If ISTATE = 3 on return, reset ISTATE to 2, call DLSODAR again. +C In either case, no other parameters need be reset. +C +C F. Note: If and when DLSODAR regards the problem as stiff, and +C switches methods accordingly, it must make use of the NEQ by NEQ +C Jacobian matrix, J = df/dy. For the sake of simplicity, the +C inputs to DLSODAR recommended in Paragraph C above cause DLSODAR to +C treat J as a full matrix, and to approximate it internally by +C difference quotients. Alternatively, J can be treated as a band +C matrix (with great potential reduction in the size of the RWORK +C array). Also, in either the full or banded case, the user can supply +C J in closed form, with a routine whose name is passed as the JAC +C argument. These alternatives are described in the paragraphs on +C RWORK, JAC, and JT in the full description of the call sequence below. +C +C----------------------------------------------------------------------- +C Example Problem. +C +C The following is a simple example problem, with the coding +C needed for its solution by DLSODAR. The problem is from chemical +C kinetics, and consists of the following three rate equations: +C dy1/dt = -.04*y1 + 1.e4*y2*y3 +C dy2/dt = .04*y1 - 1.e4*y2*y3 - 3.e7*y2**2 +C dy3/dt = 3.e7*y2**2 +C on the interval from t = 0.0 to t = 4.e10, with initial conditions +C y1 = 1.0, y2 = y3 = 0. The problem is stiff. +C In addition, we want to find the values of t, y1, y2, and y3 at which +C (1) y1 reaches the value 1.e-4, and +C (2) y3 reaches the value 1.e-2. +C +C The following coding solves this problem with DLSODAR, +C printing results at t = .4, 4., ..., 4.e10, and at the computed +C roots. It uses ITOL = 2 and ATOL much smaller for y2 than y1 or y3 +C because y2 has much smaller values. +C At the end of the run, statistical quantities of interest are +C printed (see optional outputs in the full description below). +C +C EXTERNAL FEX, GEX +C DOUBLE PRECISION ATOL, RTOL, RWORK, T, TOUT, Y +C DIMENSION Y(3), ATOL(3), RWORK(76), IWORK(23), JROOT(2) +C NEQ = 3 +C Y(1) = 1. +C Y(2) = 0. +C Y(3) = 0. +C T = 0. +C TOUT = .4 +C ITOL = 2 +C RTOL = 1.D-4 +C ATOL(1) = 1.D-6 +C ATOL(2) = 1.D-10 +C ATOL(3) = 1.D-6 +C ITASK = 1 +C ISTATE = 1 +C IOPT = 0 +C LRW = 76 +C LIW = 23 +C JT = 2 +C NG = 2 +C DO 40 IOUT = 1,12 +C 10 CALL DLSODAR(FEX,NEQ,Y,T,TOUT,ITOL,RTOL,ATOL,ITASK,ISTATE, +C 1 IOPT,RWORK,LRW,IWORK,LIW,JDUM,JT,GEX,NG,JROOT) +C WRITE(6,20)T,Y(1),Y(2),Y(3) +C 20 FORMAT(' At t =',D12.4,' Y =',3D14.6) +C IF (ISTATE .LT. 0) GO TO 80 +C IF (ISTATE .EQ. 2) GO TO 40 +C WRITE(6,30)JROOT(1),JROOT(2) +C 30 FORMAT(5X,' The above line is a root, JROOT =',2I5) +C ISTATE = 2 +C GO TO 10 +C 40 TOUT = TOUT*10. +C WRITE(6,60)IWORK(11),IWORK(12),IWORK(13),IWORK(10), +C 1 IWORK(19),RWORK(15) +C 60 FORMAT(/' No. steps =',I4,' No. f-s =',I4,' No. J-s =',I4, +C 1 ' No. g-s =',I4/ +C 2 ' Method last used =',I2,' Last switch was at t =',D12.4) +C STOP +C 80 WRITE(6,90)ISTATE +C 90 FORMAT(///' Error halt.. ISTATE =',I3) +C STOP +C END +C +C SUBROUTINE FEX (NEQ, T, Y, YDOT) +C DOUBLE PRECISION T, Y, YDOT +C DIMENSION Y(3), YDOT(3) +C YDOT(1) = -.04*Y(1) + 1.D4*Y(2)*Y(3) +C YDOT(3) = 3.D7*Y(2)*Y(2) +C YDOT(2) = -YDOT(1) - YDOT(3) +C RETURN +C END +C +C SUBROUTINE GEX (NEQ, T, Y, NG, GOUT) +C DOUBLE PRECISION T, Y, GOUT +C DIMENSION Y(3), GOUT(2) +C GOUT(1) = Y(1) - 1.D-4 +C GOUT(2) = Y(3) - 1.D-2 +C RETURN +C END +C +C The output of this program (on a CDC-7600 in single precision) +C is as follows: +C +C At t = 2.6400e-01 y = 9.899653e-01 3.470563e-05 1.000000e-02 +C The above line is a root, JROOT = 0 1 +C At t = 4.0000e-01 Y = 9.851712e-01 3.386380e-05 1.479493e-02 +C At t = 4.0000e+00 Y = 9.055333e-01 2.240655e-05 9.444430e-02 +C At t = 4.0000e+01 Y = 7.158403e-01 9.186334e-06 2.841505e-01 +C At t = 4.0000e+02 Y = 4.505250e-01 3.222964e-06 5.494717e-01 +C At t = 4.0000e+03 Y = 1.831975e-01 8.941774e-07 8.168016e-01 +C At t = 4.0000e+04 Y = 3.898730e-02 1.621940e-07 9.610125e-01 +C At t = 4.0000e+05 Y = 4.936363e-03 1.984221e-08 9.950636e-01 +C At t = 4.0000e+06 Y = 5.161831e-04 2.065786e-09 9.994838e-01 +C At t = 2.0745e+07 Y = 1.000000e-04 4.000395e-10 9.999000e-01 +C The above line is a root, JROOT = 1 0 +C At t = 4.0000e+07 Y = 5.179817e-05 2.072032e-10 9.999482e-01 +C At t = 4.0000e+08 Y = 5.283401e-06 2.113371e-11 9.999947e-01 +C At t = 4.0000e+09 Y = 4.659031e-07 1.863613e-12 9.999995e-01 +C At t = 4.0000e+10 Y = 1.404280e-08 5.617126e-14 1.000000e+00 +C +C No. steps = 361 No. f-s = 693 No. J-s = 64 No. g-s = 390 +C Method last used = 2 Last switch was at t = 6.0092e-03 +C +C----------------------------------------------------------------------- +C Full Description of User Interface to DLSODAR. +C +C The user interface to DLSODAR consists of the following parts. +C +C 1. The call sequence to Subroutine DLSODAR, which is a driver +C routine for the solver. This includes descriptions of both +C the call sequence arguments and of user-supplied routines. +C Following these descriptions is a description of +C optional inputs available through the call sequence, and then +C a description of optional outputs (in the work arrays). +C +C 2. Descriptions of other routines in the DLSODAR package that may be +C (optionally) called by the user. These provide the ability to +C alter error message handling, save and restore the internal +C Common, and obtain specified derivatives of the solution y(t). +C +C 3. Descriptions of Common blocks to be declared in overlay +C or similar environments, or to be saved when doing an interrupt +C of the problem and continued solution later. +C +C 4. Description of a subroutine in the DLSODAR package, +C which the user may replace with his/her own version, if desired. +C this relates to the measurement of errors. +C +C----------------------------------------------------------------------- +C Part 1. Call Sequence. +C +C The call sequence parameters used for input only are +C F, NEQ, TOUT, ITOL, RTOL, ATOL, ITASK, IOPT, LRW, LIW, JAC, +C JT, G, and NG, +C that used only for output is JROOT, +C and those used for both input and output are +C Y, T, ISTATE. +C The work arrays RWORK and IWORK are also used for conditional and +C optional inputs and optional outputs. (The term output here refers +C to the return from Subroutine DLSODAR to the user's calling program.) +C +C The legality of input parameters will be thoroughly checked on the +C initial call for the problem, but not checked thereafter unless a +C change in input parameters is flagged by ISTATE = 3 on input. +C +C The descriptions of the call arguments are as follows. +C +C F = the name of the user-supplied subroutine defining the +C ODE system. The system must be put in the first-order +C form dy/dt = f(t,y), where f is a vector-valued function +C of the scalar t and the vector y. Subroutine F is to +C compute the function f. It is to have the form +C SUBROUTINE F (NEQ, T, Y, YDOT) +C DOUBLE PRECISION T, Y(*), YDOT(*) +C where NEQ, T, and Y are input, and the array YDOT = f(t,y) +C is output. Y and YDOT are arrays of length NEQ. +C Subroutine F should not alter Y(1),...,Y(NEQ). +C F must be declared External in the calling program. +C +C Subroutine F may access user-defined quantities in +C NEQ(2),... and/or in Y(NEQ(1)+1),... if NEQ is an array +C (dimensioned in F) and/or Y has length exceeding NEQ(1). +C See the descriptions of NEQ and Y below. +C +C If quantities computed in the F routine are needed +C externally to DLSODAR, an extra call to F should be made +C for this purpose, for consistent and accurate results. +C If only the derivative dy/dt is needed, use DINTDY instead. +C +C NEQ = the size of the ODE system (number of first order +C ordinary differential equations). Used only for input. +C NEQ may be decreased, but not increased, during the problem. +C If NEQ is decreased (with ISTATE = 3 on input), the +C remaining components of Y should be left undisturbed, if +C these are to be accessed in F and/or JAC. +C +C Normally, NEQ is a scalar, and it is generally referred to +C as a scalar in this user interface description. However, +C NEQ may be an array, with NEQ(1) set to the system size. +C (The DLSODAR package accesses only NEQ(1).) In either case, +C this parameter is passed as the NEQ argument in all calls +C to F, JAC, and G. Hence, if it is an array, locations +C NEQ(2),... may be used to store other integer data and pass +C it to F, JAC, and G. Each such subroutine must include +C NEQ in a Dimension statement in that case. +C +C Y = a real array for the vector of dependent variables, of +C length NEQ or more. Used for both input and output on the +C first call (ISTATE = 1), and only for output on other calls. +C On the first call, Y must contain the vector of initial +C values. On output, Y contains the computed solution vector, +C evaluated at T. If desired, the Y array may be used +C for other purposes between calls to the solver. +C +C This array is passed as the Y argument in all calls to F, +C JAC, and G. Hence its length may exceed NEQ, and locations +C Y(NEQ+1),... may be used to store other real data and +C pass it to F, JAC, and G. (The DLSODAR package accesses only +C Y(1),...,Y(NEQ).) +C +C T = the independent variable. On input, T is used only on the +C first call, as the initial point of the integration. +C On output, after each call, T is the value at which a +C computed solution y is evaluated (usually the same as TOUT). +C If a root was found, T is the computed location of the +C root reached first, on output. +C On an error return, T is the farthest point reached. +C +C TOUT = the next value of t at which a computed solution is desired. +C Used only for input. +C +C When starting the problem (ISTATE = 1), TOUT may be equal +C to T for one call, then should .ne. T for the next call. +C For the initial T, an input value of TOUT .ne. T is used +C in order to determine the direction of the integration +C (i.e. the algebraic sign of the step sizes) and the rough +C scale of the problem. Integration in either direction +C (forward or backward in t) is permitted. +C +C If ITASK = 2 or 5 (one-step modes), TOUT is ignored after +C the first call (i.e. the first call with TOUT .ne. T). +C Otherwise, TOUT is required on every call. +C +C If ITASK = 1, 3, or 4, the values of TOUT need not be +C monotone, but a value of TOUT which backs up is limited +C to the current internal T interval, whose endpoints are +C TCUR - HU and TCUR (see optional outputs, below, for +C TCUR and HU). +C +C ITOL = an indicator for the type of error control. See +C description below under ATOL. Used only for input. +C +C RTOL = a relative error tolerance parameter, either a scalar or +C an array of length NEQ. See description below under ATOL. +C Input only. +C +C ATOL = an absolute error tolerance parameter, either a scalar or +C an array of length NEQ. Input only. +C +C The input parameters ITOL, RTOL, and ATOL determine +C the error control performed by the solver. The solver will +C control the vector E = (E(i)) of estimated local errors +C in y, according to an inequality of the form +C max-norm of ( E(i)/EWT(i) ) .le. 1, +C where EWT = (EWT(i)) is a vector of positive error weights. +C The values of RTOL and ATOL should all be non-negative. +C The following table gives the types (scalar/array) of +C RTOL and ATOL, and the corresponding form of EWT(i). +C +C ITOL RTOL ATOL EWT(i) +C 1 scalar scalar RTOL*ABS(Y(i)) + ATOL +C 2 scalar array RTOL*ABS(Y(i)) + ATOL(i) +C 3 array scalar RTOL(i)*ABS(Y(i)) + ATOL +C 4 array array RTOL(i)*ABS(Y(i)) + ATOL(i) +C +C When either of these parameters is a scalar, it need not +C be dimensioned in the user's calling program. +C +C If none of the above choices (with ITOL, RTOL, and ATOL +C fixed throughout the problem) is suitable, more general +C error controls can be obtained by substituting a +C user-supplied routine for the setting of EWT. +C See Part 4 below. +C +C If global errors are to be estimated by making a repeated +C run on the same problem with smaller tolerances, then all +C components of RTOL and ATOL (i.e. of EWT) should be scaled +C down uniformly. +C +C ITASK = an index specifying the task to be performed. +C input only. ITASK has the following values and meanings. +C 1 means normal computation of output values of y(t) at +C t = TOUT (by overshooting and interpolating). +C 2 means take one step only and return. +C 3 means stop at the first internal mesh point at or +C beyond t = TOUT and return. +C 4 means normal computation of output values of y(t) at +C t = TOUT but without overshooting t = TCRIT. +C TCRIT must be input as RWORK(1). TCRIT may be equal to +C or beyond TOUT, but not behind it in the direction of +C integration. This option is useful if the problem +C has a singularity at or beyond t = TCRIT. +C 5 means take one step, without passing TCRIT, and return. +C TCRIT must be input as RWORK(1). +C +C Note: If ITASK = 4 or 5 and the solver reaches TCRIT +C (within roundoff), it will return T = TCRIT (exactly) to +C indicate this (unless ITASK = 4 and TOUT comes before TCRIT, +C in which case answers at t = TOUT are returned first). +C +C ISTATE = an index used for input and output to specify the +C the state of the calculation. +C +C On input, the values of ISTATE are as follows. +C 1 means this is the first call for the problem +C (initializations will be done). See note below. +C 2 means this is not the first call, and the calculation +C is to continue normally, with no change in any input +C parameters except possibly TOUT and ITASK. +C (If ITOL, RTOL, and/or ATOL are changed between calls +C with ISTATE = 2, the new values will be used but not +C tested for legality.) +C 3 means this is not the first call, and the +C calculation is to continue normally, but with +C a change in input parameters other than +C TOUT and ITASK. Changes are allowed in +C NEQ, ITOL, RTOL, ATOL, IOPT, LRW, LIW, JT, ML, MU, +C and any optional inputs except H0, MXORDN, and MXORDS. +C (See IWORK description for ML and MU.) +C In addition, immediately following a return with +C ISTATE = 3 (root found), NG and G may be changed. +C (But changing NG from 0 to .gt. 0 is not allowed.) +C Note: A preliminary call with TOUT = T is not counted +C as a first call here, as no initialization or checking of +C input is done. (Such a call is sometimes useful for the +C purpose of outputting the initial conditions.) +C Thus the first call for which TOUT .ne. T requires +C ISTATE = 1 on input. +C +C On output, ISTATE has the following values and meanings. +C 1 means nothing was done; TOUT = t and ISTATE = 1 on input. +C 2 means the integration was performed successfully, and +C no roots were found. +C 3 means the integration was successful, and one or more +C roots were found before satisfying the stop condition +C specified by ITASK. See JROOT. +C -1 means an excessive amount of work (more than MXSTEP +C steps) was done on this call, before completing the +C requested task, but the integration was otherwise +C successful as far as T. (MXSTEP is an optional input +C and is normally 500.) To continue, the user may +C simply reset ISTATE to a value .gt. 1 and call again +C (the excess work step counter will be reset to 0). +C In addition, the user may increase MXSTEP to avoid +C this error return (see below on optional inputs). +C -2 means too much accuracy was requested for the precision +C of the machine being used. This was detected before +C completing the requested task, but the integration +C was successful as far as T. To continue, the tolerance +C parameters must be reset, and ISTATE must be set +C to 3. The optional output TOLSF may be used for this +C purpose. (Note: If this condition is detected before +C taking any steps, then an illegal input return +C (ISTATE = -3) occurs instead.) +C -3 means illegal input was detected, before taking any +C integration steps. See written message for details. +C Note: If the solver detects an infinite loop of calls +C to the solver with illegal input, it will cause +C the run to stop. +C -4 means there were repeated error test failures on +C one attempted step, before completing the requested +C task, but the integration was successful as far as T. +C The problem may have a singularity, or the input +C may be inappropriate. +C -5 means there were repeated convergence test failures on +C one attempted step, before completing the requested +C task, but the integration was successful as far as T. +C This may be caused by an inaccurate Jacobian matrix, +C if one is being used. +C -6 means EWT(i) became zero for some i during the +C integration. Pure relative error control (ATOL(i)=0.0) +C was requested on a variable which has now vanished. +C The integration was successful as far as T. +C -7 means the length of RWORK and/or IWORK was too small to +C proceed, but the integration was successful as far as T. +C This happens when DLSODAR chooses to switch methods +C but LRW and/or LIW is too small for the new method. +C +C Note: Since the normal output value of ISTATE is 2, +C it does not need to be reset for normal continuation. +C Also, since a negative input value of ISTATE will be +C regarded as illegal, a negative output value requires the +C user to change it, and possibly other inputs, before +C calling the solver again. +C +C IOPT = an integer flag to specify whether or not any optional +C inputs are being used on this call. Input only. +C The optional inputs are listed separately below. +C IOPT = 0 means no optional inputs are being used. +C Default values will be used in all cases. +C IOPT = 1 means one or more optional inputs are being used. +C +C RWORK = a real array (double precision) for work space, and (in the +C first 20 words) for conditional and optional inputs and +C optional outputs. +C As DLSODAR switches automatically between stiff and nonstiff +C methods, the required length of RWORK can change during the +C problem. Thus the RWORK array passed to DLSODAR can either +C have a static (fixed) length large enough for both methods, +C or have a dynamic (changing) length altered by the calling +C program in response to output from DLSODAR. +C +C --- Fixed Length Case --- +C If the RWORK length is to be fixed, it should be at least +C max (LRN, LRS), +C where LRN and LRS are the RWORK lengths required when the +C current method is nonstiff or stiff, respectively. +C +C The separate RWORK length requirements LRN and LRS are +C as follows: +C If NEQ is constant and the maximum method orders have +C their default values, then +C LRN = 20 + 16*NEQ + 3*NG, +C LRS = 22 + 9*NEQ + NEQ**2 + 3*NG (JT = 1 or 2), +C LRS = 22 + 10*NEQ + (2*ML+MU)*NEQ + 3*NG (JT = 4 or 5). +C Under any other conditions, LRN and LRS are given by: +C LRN = 20 + NYH*(MXORDN+1) + 3*NEQ + 3*NG, +C LRS = 20 + NYH*(MXORDS+1) + 3*NEQ + LMAT + 3*NG, +C where +C NYH = the initial value of NEQ, +C MXORDN = 12, unless a smaller value is given as an +C optional input, +C MXORDS = 5, unless a smaller value is given as an +C optional input, +C LMAT = length of matrix work space: +C LMAT = NEQ**2 + 2 if JT = 1 or 2, +C LMAT = (2*ML + MU + 1)*NEQ + 2 if JT = 4 or 5. +C +C --- Dynamic Length Case --- +C If the length of RWORK is to be dynamic, then it should +C be at least LRN or LRS, as defined above, depending on the +C current method. Initially, it must be at least LRN (since +C DLSODAR starts with the nonstiff method). On any return +C from DLSODAR, the optional output MCUR indicates the current +C method. If MCUR differs from the value it had on the +C previous return, or if there has only been one call to +C DLSODAR and MCUR is now 2, then DLSODAR has switched +C methods during the last call, and the length of RWORK +C should be reset (to LRN if MCUR = 1, or to LRS if +C MCUR = 2). (An increase in the RWORK length is required +C if DLSODAR returned ISTATE = -7, but not otherwise.) +C After resetting the length, call DLSODAR with ISTATE = 3 +C to signal that change. +C +C LRW = the length of the array RWORK, as declared by the user. +C (This will be checked by the solver.) +C +C IWORK = an integer array for work space. +C As DLSODAR switches automatically between stiff and nonstiff +C methods, the required length of IWORK can change during +C problem, between +C LIS = 20 + NEQ and LIN = 20, +C respectively. Thus the IWORK array passed to DLSODAR can +C either have a fixed length of at least 20 + NEQ, or have a +C dynamic length of at least LIN or LIS, depending on the +C current method. The comments on dynamic length under +C RWORK above apply here. Initially, this length need +C only be at least LIN = 20. +C +C The first few words of IWORK are used for conditional and +C optional inputs and optional outputs. +C +C The following 2 words in IWORK are conditional inputs: +C IWORK(1) = ML These are the lower and upper +C IWORK(2) = MU half-bandwidths, respectively, of the +C banded Jacobian, excluding the main diagonal. +C The band is defined by the matrix locations +C (i,j) with i-ML .le. j .le. i+MU. ML and MU +C must satisfy 0 .le. ML,MU .le. NEQ-1. +C These are required if JT is 4 or 5, and +C ignored otherwise. ML and MU may in fact be +C the band parameters for a matrix to which +C df/dy is only approximately equal. +C +C LIW = the length of the array IWORK, as declared by the user. +C (This will be checked by the solver.) +C +C Note: The base addresses of the work arrays must not be +C altered between calls to DLSODAR for the same problem. +C The contents of the work arrays must not be altered +C between calls, except possibly for the conditional and +C optional inputs, and except for the last 3*NEQ words of RWORK. +C The latter space is used for internal scratch space, and so is +C available for use by the user outside DLSODAR between calls, if +C desired (but not for use by F, JAC, or G). +C +C JAC = the name of the user-supplied routine to compute the +C Jacobian matrix, df/dy, if JT = 1 or 4. The JAC routine +C is optional, but if the problem is expected to be stiff much +C of the time, you are encouraged to supply JAC, for the sake +C of efficiency. (Alternatively, set JT = 2 or 5 to have +C DLSODAR compute df/dy internally by difference quotients.) +C If and when DLSODAR uses df/dy, it treats this NEQ by NEQ +C matrix either as full (JT = 1 or 2), or as banded (JT = +C 4 or 5) with half-bandwidths ML and MU (discussed under +C IWORK above). In either case, if JT = 1 or 4, the JAC +C routine must compute df/dy as a function of the scalar t +C and the vector y. It is to have the form +C SUBROUTINE JAC (NEQ, T, Y, ML, MU, PD, NROWPD) +C DOUBLE PRECISION T, Y(*), PD(NROWPD,*) +C where NEQ, T, Y, ML, MU, and NROWPD are input and the array +C PD is to be loaded with partial derivatives (elements of +C the Jacobian matrix) on output. PD must be given a first +C dimension of NROWPD. T and Y have the same meaning as in +C Subroutine F. +C In the full matrix case (JT = 1), ML and MU are +C ignored, and the Jacobian is to be loaded into PD in +C columnwise manner, with df(i)/dy(j) loaded into pd(i,j). +C In the band matrix case (JT = 4), the elements +C within the band are to be loaded into PD in columnwise +C manner, with diagonal lines of df/dy loaded into the rows +C of PD. Thus df(i)/dy(j) is to be loaded into PD(i-j+MU+1,j). +C ML and MU are the half-bandwidth parameters (see IWORK). +C The locations in PD in the two triangular areas which +C correspond to nonexistent matrix elements can be ignored +C or loaded arbitrarily, as they are overwritten by DLSODAR. +C JAC need not provide df/dy exactly. A crude +C approximation (possibly with a smaller bandwidth) will do. +C In either case, PD is preset to zero by the solver, +C so that only the nonzero elements need be loaded by JAC. +C Each call to JAC is preceded by a call to F with the same +C arguments NEQ, T, and Y. Thus to gain some efficiency, +C intermediate quantities shared by both calculations may be +C saved in a user Common block by F and not recomputed by JAC, +C if desired. Also, JAC may alter the Y array, if desired. +C JAC must be declared External in the calling program. +C Subroutine JAC may access user-defined quantities in +C NEQ(2),... and/or in Y(NEQ(1)+1),... if NEQ is an array +C (dimensioned in JAC) and/or Y has length exceeding NEQ(1). +C See the descriptions of NEQ and Y above. +C +C JT = Jacobian type indicator. Used only for input. +C JT specifies how the Jacobian matrix df/dy will be +C treated, if and when DLSODAR requires this matrix. +C JT has the following values and meanings: +C 1 means a user-supplied full (NEQ by NEQ) Jacobian. +C 2 means an internally generated (difference quotient) full +C Jacobian (using NEQ extra calls to F per df/dy value). +C 4 means a user-supplied banded Jacobian. +C 5 means an internally generated banded Jacobian (using +C ML+MU+1 extra calls to F per df/dy evaluation). +C If JT = 1 or 4, the user must supply a Subroutine JAC +C (the name is arbitrary) as described above under JAC. +C If JT = 2 or 5, a dummy argument can be used. +C +C G = the name of subroutine for constraint functions, whose +C roots are desired during the integration. It is to have +C the form +C SUBROUTINE G (NEQ, T, Y, NG, GOUT) +C DOUBLE PRECISION T, Y(*), GOUT(NG) +C where NEQ, T, Y, and NG are input, and the array GOUT +C is output. NEQ, T, and Y have the same meaning as in +C the F routine, and GOUT is an array of length NG. +C For i = 1,...,NG, this routine is to load into GOUT(i) +C the value at (T,Y) of the i-th constraint function g(i). +C DLSODAR will find roots of the g(i) of odd multiplicity +C (i.e. sign changes) as they occur during the integration. +C G must be declared External in the calling program. +C +C Caution: Because of numerical errors in the functions +C g(i) due to roundoff and integration error, DLSODAR may +C return false roots, or return the same root at two or more +C nearly equal values of t. If such false roots are +C suspected, the user should consider smaller error tolerances +C and/or higher precision in the evaluation of the g(i). +C +C If a root of some g(i) defines the end of the problem, +C the input to DLSODAR should nevertheless allow integration +C to a point slightly past that root, so that DLSODAR can +C locate the root by interpolation. +C +C Subroutine G may access user-defined quantities in +C NEQ(2),... and Y(NEQ(1)+1),... if NEQ is an array +C (dimensioned in G) and/or Y has length exceeding NEQ(1). +C See the descriptions of NEQ and Y above. +C +C NG = number of constraint functions g(i). If there are none, +C set NG = 0, and pass a dummy name for G. +C +C JROOT = integer array of length NG. Used only for output. +C On a return with ISTATE = 3 (one or more roots found), +C JROOT(i) = 1 if g(i) has a root at T, or JROOT(i) = 0 if not. +C----------------------------------------------------------------------- +C Optional Inputs. +C +C The following is a list of the optional inputs provided for in the +C call sequence. (See also Part 2.) For each such input variable, +C this table lists its name as used in this documentation, its +C location in the call sequence, its meaning, and the default value. +C The use of any of these inputs requires IOPT = 1, and in that +C case all of these inputs are examined. A value of zero for any +C of these optional inputs will cause the default value to be used. +C Thus to use a subset of the optional inputs, simply preload +C locations 5 to 10 in RWORK and IWORK to 0.0 and 0 respectively, and +C then set those of interest to nonzero values. +C +C Name Location Meaning and Default Value +C +C H0 RWORK(5) the step size to be attempted on the first step. +C The default value is determined by the solver. +C +C HMAX RWORK(6) the maximum absolute step size allowed. +C The default value is infinite. +C +C HMIN RWORK(7) the minimum absolute step size allowed. +C The default value is 0. (This lower bound is not +C enforced on the final step before reaching TCRIT +C when ITASK = 4 or 5.) +C +C IXPR IWORK(5) flag to generate extra printing at method switches. +C IXPR = 0 means no extra printing (the default). +C IXPR = 1 means print data on each switch. +C T, H, and NST will be printed on the same logical +C unit as used for error messages. +C +C MXSTEP IWORK(6) maximum number of (internally defined) steps +C allowed during one call to the solver. +C The default value is 500. +C +C MXHNIL IWORK(7) maximum number of messages printed (per problem) +C warning that T + H = T on a step (H = step size). +C This must be positive to result in a non-default +C value. The default value is 10. +C +C MXORDN IWORK(8) the maximum order to be allowed for the nonstiff +C (Adams) method. The default value is 12. +C If MXORDN exceeds the default value, it will +C be reduced to the default value. +C MXORDN is held constant during the problem. +C +C MXORDS IWORK(9) the maximum order to be allowed for the stiff +C (BDF) method. The default value is 5. +C If MXORDS exceeds the default value, it will +C be reduced to the default value. +C MXORDS is held constant during the problem. +C----------------------------------------------------------------------- +C Optional Outputs. +C +C As optional additional output from DLSODAR, the variables listed +C below are quantities related to the performance of DLSODAR +C which are available to the user. These are communicated by way of +C the work arrays, but also have internal mnemonic names as shown. +C Except where stated otherwise, all of these outputs are defined +C on any successful return from DLSODAR, and on any return with +C ISTATE = -1, -2, -4, -5, or -6. On an illegal input return +C (ISTATE = -3), they will be unchanged from their existing values +C (if any), except possibly for TOLSF, LENRW, and LENIW. +C On any error return, outputs relevant to the error will be defined, +C as noted below. +C +C Name Location Meaning +C +C HU RWORK(11) the step size in t last used (successfully). +C +C HCUR RWORK(12) the step size to be attempted on the next step. +C +C TCUR RWORK(13) the current value of the independent variable +C which the solver has actually reached, i.e. the +C current internal mesh point in t. On output, TCUR +C will always be at least as far as the argument +C T, but may be farther (if interpolation was done). +C +C TOLSF RWORK(14) a tolerance scale factor, greater than 1.0, +C computed when a request for too much accuracy was +C detected (ISTATE = -3 if detected at the start of +C the problem, ISTATE = -2 otherwise). If ITOL is +C left unaltered but RTOL and ATOL are uniformly +C scaled up by a factor of TOLSF for the next call, +C then the solver is deemed likely to succeed. +C (The user may also ignore TOLSF and alter the +C tolerance parameters in any other way appropriate.) +C +C TSW RWORK(15) the value of t at the time of the last method +C switch, if any. +C +C NGE IWORK(10) the number of g evaluations for the problem so far. +C +C NST IWORK(11) the number of steps taken for the problem so far. +C +C NFE IWORK(12) the number of f evaluations for the problem so far. +C +C NJE IWORK(13) the number of Jacobian evaluations (and of matrix +C LU decompositions) for the problem so far. +C +C NQU IWORK(14) the method order last used (successfully). +C +C NQCUR IWORK(15) the order to be attempted on the next step. +C +C IMXER IWORK(16) the index of the component of largest magnitude in +C the weighted local error vector ( E(i)/EWT(i) ), +C on an error return with ISTATE = -4 or -5. +C +C LENRW IWORK(17) the length of RWORK actually required, assuming +C that the length of RWORK is to be fixed for the +C rest of the problem, and that switching may occur. +C This is defined on normal returns and on an illegal +C input return for insufficient storage. +C +C LENIW IWORK(18) the length of IWORK actually required, assuming +C that the length of IWORK is to be fixed for the +C rest of the problem, and that switching may occur. +C This is defined on normal returns and on an illegal +C input return for insufficient storage. +C +C MUSED IWORK(19) the method indicator for the last successful step: +C 1 means Adams (nonstiff), 2 means BDF (stiff). +C +C MCUR IWORK(20) the current method indicator: +C 1 means Adams (nonstiff), 2 means BDF (stiff). +C This is the method to be attempted +C on the next step. Thus it differs from MUSED +C only if a method switch has just been made. +C +C The following two arrays are segments of the RWORK array which +C may also be of interest to the user as optional outputs. +C For each array, the table below gives its internal name, +C its base address in RWORK, and its description. +C +C Name Base Address Description +C +C YH 21 + 3*NG the Nordsieck history array, of size NYH by +C (NQCUR + 1), where NYH is the initial value +C of NEQ. For j = 0,1,...,NQCUR, column j+1 +C of YH contains HCUR**j/factorial(j) times +C the j-th derivative of the interpolating +C polynomial currently representing the solution, +C evaluated at t = TCUR. +C +C ACOR LACOR array of size NEQ used for the accumulated +C (from Common corrections on each step, scaled on output +C as noted) to represent the estimated local error in y +C on the last step. This is the vector E in +C the description of the error control. It is +C defined only on a successful return from +C DLSODAR. The base address LACOR is obtained by +C including in the user's program the +C following 2 lines: +C COMMON /DLS001/ RLS(218), ILS(37) +C LACOR = ILS(22) +C +C----------------------------------------------------------------------- +C Part 2. Other Routines Callable. +C +C The following are optional calls which the user may make to +C gain additional capabilities in conjunction with DLSODAR. +C (The routines XSETUN and XSETF are designed to conform to the +C SLATEC error handling package.) +C +C Form of Call Function +C CALL XSETUN(LUN) Set the logical unit number, LUN, for +C output of messages from DLSODAR, if +C the default is not desired. +C The default value of LUN is 6. +C +C CALL XSETF(MFLAG) Set a flag to control the printing of +C messages by DLSODAR. +C MFLAG = 0 means do not print. (Danger: +C This risks losing valuable information.) +C MFLAG = 1 means print (the default). +C +C Either of the above calls may be made at +C any time and will take effect immediately. +C +C CALL DSRCAR(RSAV,ISAV,JOB) saves and restores the contents of +C the internal Common blocks used by +C DLSODAR (see Part 3 below). +C RSAV must be a real array of length 245 +C or more, and ISAV must be an integer +C array of length 55 or more. +C JOB=1 means save Common into RSAV/ISAV. +C JOB=2 means restore Common from RSAV/ISAV. +C DSRCAR is useful if one is +C interrupting a run and restarting +C later, or alternating between two or +C more problems solved with DLSODAR. +C +C CALL DINTDY(,,,,,) Provide derivatives of y, of various +C (see below) orders, at a specified point t, if +C desired. It may be called only after +C a successful return from DLSODAR. +C +C The detailed instructions for using DINTDY are as follows. +C The form of the call is: +C +C LYH = 21 + 3*NG +C CALL DINTDY (T, K, RWORK(LYH), NYH, DKY, IFLAG) +C +C The input parameters are: +C +C T = value of independent variable where answers are desired +C (normally the same as the T last returned by DLSODAR). +C For valid results, T must lie between TCUR - HU and TCUR. +C (See optional outputs for TCUR and HU.) +C K = integer order of the derivative desired. K must satisfy +C 0 .le. K .le. NQCUR, where NQCUR is the current order +C (see optional outputs). The capability corresponding +C to K = 0, i.e. computing y(t), is already provided +C by DLSODAR directly. Since NQCUR .ge. 1, the first +C derivative dy/dt is always available with DINTDY. +C LYH = 21 + 3*NG = base address in RWORK of the history array YH. +C NYH = column length of YH, equal to the initial value of NEQ. +C +C The output parameters are: +C +C DKY = a real array of length NEQ containing the computed value +C of the K-th derivative of y(t). +C IFLAG = integer flag, returned as 0 if K and T were legal, +C -1 if K was illegal, and -2 if T was illegal. +C On an error return, a message is also written. +C----------------------------------------------------------------------- +C Part 3. Common Blocks. +C +C If DLSODAR is to be used in an overlay situation, the user +C must declare, in the primary overlay, the variables in: +C (1) the call sequence to DLSODAR, and +C (2) the three internal Common blocks +C /DLS001/ of length 255 (218 double precision words +C followed by 37 integer words), +C /DLSA01/ of length 31 (22 double precision words +C followed by 9 integer words). +C /DLSR01/ of length 7 (3 double precision words +C followed by 4 integer words). +C +C If DLSODAR is used on a system in which the contents of internal +C Common blocks are not preserved between calls, the user should +C declare the above Common blocks in the calling program to insure +C that their contents are preserved. +C +C If the solution of a given problem by DLSODAR is to be interrupted +C and then later continued, such as when restarting an interrupted run +C or alternating between two or more problems, the user should save, +C following the return from the last DLSODAR call prior to the +C interruption, the contents of the call sequence variables and the +C internal Common blocks, and later restore these values before the +C next DLSODAR call for that problem. To save and restore the Common +C blocks, use Subroutine DSRCAR (see Part 2 above). +C +C----------------------------------------------------------------------- +C Part 4. Optionally Replaceable Solver Routines. +C +C Below is a description of a routine in the DLSODAR package which +C relates to the measurement of errors, and can be +C replaced by a user-supplied version, if desired. However, since such +C a replacement may have a major impact on performance, it should be +C done only when absolutely necessary, and only with great caution. +C (Note: The means by which the package version of a routine is +C superseded by the user's version may be system-dependent.) +C +C (a) DEWSET. +C The following subroutine is called just before each internal +C integration step, and sets the array of error weights, EWT, as +C described under ITOL/RTOL/ATOL above: +C Subroutine DEWSET (NEQ, ITOL, RTOL, ATOL, YCUR, EWT) +C where NEQ, ITOL, RTOL, and ATOL are as in the DLSODAR call sequence, +C YCUR contains the current dependent variable vector, and +C EWT is the array of weights set by DEWSET. +C +C If the user supplies this subroutine, it must return in EWT(i) +C (i = 1,...,NEQ) a positive quantity suitable for comparing errors +C in y(i) to. The EWT array returned by DEWSET is passed to the +C DMNORM routine, and also used by DLSODAR in the computation +C of the optional output IMXER, and the increments for difference +C quotient Jacobians. +C +C In the user-supplied version of DEWSET, it may be desirable to use +C the current values of derivatives of y. Derivatives up to order NQ +C are available from the history array YH, described above under +C optional outputs. In DEWSET, YH is identical to the YCUR array, +C extended to NQ + 1 columns with a column length of NYH and scale +C factors of H**j/factorial(j). On the first call for the problem, +C given by NST = 0, NQ is 1 and H is temporarily set to 1.0. +C NYH is the initial value of NEQ. The quantities NQ, H, and NST +C can be obtained by including in DEWSET the statements: +C DOUBLE PRECISION RLS +C COMMON /DLS001/ RLS(218),ILS(37) +C NQ = ILS(33) +C NST = ILS(34) +C H = RLS(212) +C Thus, for example, the current value of dy/dt can be obtained as +C YCUR(NYH+i)/H (i=1,...,NEQ) (and the division by H is +C unnecessary when NST = 0). +C----------------------------------------------------------------------- +C +C***REVISION HISTORY (YYYYMMDD) +C 19811102 DATE WRITTEN +C 19820126 Fixed bug in tests of work space lengths; +C minor corrections in main prologue and comments. +C 19820507 Fixed bug in RCHEK in setting HMING. +C 19870330 Major update: corrected comments throughout; +C removed TRET from Common; rewrote EWSET with 4 loops; +C fixed t test in INTDY; added Cray directives in STODA; +C in STODA, fixed DELP init. and logic around PJAC call; +C combined routines to save/restore Common; +C passed LEVEL = 0 in error message calls (except run abort). +C 19970225 Fixed lines setting JSTART = -2 in Subroutine LSODAR. +C 20010425 Major update: convert source lines to upper case; +C added *DECK lines; changed from 1 to * in dummy dimensions; +C changed names R1MACH/D1MACH to RUMACH/DUMACH; +C renamed routines for uniqueness across single/double prec.; +C converted intrinsic names to generic form; +C removed ILLIN and NTREP (data loaded) from Common; +C removed all 'own' variables from Common; +C changed error messages to quoted strings; +C replaced XERRWV/XERRWD with 1993 revised version; +C converted prologues, comments, error messages to mixed case; +C numerous corrections to prologues and internal comments. +C 20010507 Converted single precision source to double precision. +C 20010613 Revised excess accuracy test (to match rest of ODEPACK). +C 20010808 Fixed bug in DPRJA (matrix in DBNORM call). +C 20020502 Corrected declarations in descriptions of user routines. +C 20031105 Restored 'own' variables to Common blocks, to enable +C interrupt/restart feature. +C 20031112 Added SAVE statements for data-loaded constants. +C +C----------------------------------------------------------------------- +C Other routines in the DLSODAR package. +C +C In addition to Subroutine DLSODAR, the DLSODAR package includes the +C following subroutines and function routines: +C DRCHEK does preliminary checking for roots, and serves as an +C interface between Subroutine DLSODAR and Subroutine DROOTS. +C DROOTS finds the leftmost root of a set of functions. +C DINTDY computes an interpolated value of the y vector at t = TOUT. +C DSTODA is the core integrator, which does one step of the +C integration and the associated error control. +C DCFODE sets all method coefficients and test constants. +C DPRJA computes and preprocesses the Jacobian matrix J = df/dy +C and the Newton iteration matrix P = I - h*l0*J. +C DSOLSY manages solution of linear system in chord iteration. +C DEWSET sets the error weight vector EWT before each step. +C DMNORM computes the weighted max-norm of a vector. +C DFNORM computes the norm of a full matrix consistent with the +C weighted max-norm on vectors. +C DBNORM computes the norm of a band matrix consistent with the +C weighted max-norm on vectors. +C DSRCAR is a user-callable routine to save and restore +C the contents of the internal Common blocks. +C DGEFA and DGESL are routines from LINPACK for solving full +C systems of linear algebraic equations. +C DGBFA and DGBSL are routines from LINPACK for solving banded +C linear systems. +C DCOPY is one of the basic linear algebra modules (BLAS). +C DUMACH computes the unit roundoff in a machine-independent manner. +C XERRWD, XSETUN, XSETF, IXSAV, and IUMACH handle the printing of all +C error messages and warnings. XERRWD is machine-dependent. +C Note: DMNORM, DFNORM, DBNORM, DUMACH, IXSAV, and IUMACH are +C function routines. All the others are subroutines. +C +C----------------------------------------------------------------------- + EXTERNAL DPRJA, DSOLSY + DOUBLE PRECISION DUMACH, DMNORM + INTEGER INIT, MXSTEP, MXHNIL, NHNIL, NSLAST, NYH, IOWNS, + 1 ICF, IERPJ, IERSL, JCUR, JSTART, KFLAG, L, + 2 LYH, LEWT, LACOR, LSAVF, LWM, LIWM, METH, MITER, + 3 MAXORD, MAXCOR, MSBP, MXNCF, N, NQ, NST, NFE, NJE, NQU + INTEGER INSUFR, INSUFI, IXPR, IOWNS2, JTYP, MUSED, MXORDN, MXORDS + INTEGER LG0, LG1, LGX, IOWNR3, IRFND, ITASKC, NGC, NGE + INTEGER I, I1, I2, IFLAG, IMXER, KGO, LENIW, + 1 LENRW, LENWM, LF0, ML, MORD, MU, MXHNL0, MXSTP0 + INTEGER LEN1, LEN1C, LEN1N, LEN1S, LEN2, LENIWC, LENRWC + INTEGER IRFP, IRT, LENYH, LYHNEW + DOUBLE PRECISION ROWNS, + 1 CCMAX, EL0, H, HMIN, HMXI, HU, RC, TN, UROUND + DOUBLE PRECISION TSW, ROWNS2, PDNORM + DOUBLE PRECISION ROWNR3, T0, TLAST, TOUTC + DOUBLE PRECISION ATOLI, AYI, BIG, EWTI, H0, HMAX, HMX, RH, RTOLI, + 1 TCRIT, TDIST, TNEXT, TOL, TOLSF, TP, SIZE, SUM, W0 + DIMENSION MORD(2) + LOGICAL IHIT + CHARACTER*60 MSG + SAVE MORD, MXSTP0, MXHNL0 +C----------------------------------------------------------------------- +C The following three internal Common blocks contain +C (a) variables which are local to any subroutine but whose values must +C be preserved between calls to the routine ("own" variables), and +C (b) variables which are communicated between subroutines. +C The block DLS001 is declared in subroutines DLSODAR, DINTDY, DSTODA, +C DPRJA, and DSOLSY. +C The block DLSA01 is declared in subroutines DLSODAR, DSTODA, DPRJA. +C The block DLSR01 is declared in subroutines DLSODAR, DRCHEK, DROOTS. +C Groups of variables are replaced by dummy arrays in the Common +C declarations in routines where those variables are not used. +C----------------------------------------------------------------------- + COMMON /DLS001/ ROWNS(209), + 1 CCMAX, EL0, H, HMIN, HMXI, HU, RC, TN, UROUND, + 2 INIT, MXSTEP, MXHNIL, NHNIL, NSLAST, NYH, IOWNS(6), + 3 ICF, IERPJ, IERSL, JCUR, JSTART, KFLAG, L, + 4 LYH, LEWT, LACOR, LSAVF, LWM, LIWM, METH, MITER, + 5 MAXORD, MAXCOR, MSBP, MXNCF, N, NQ, NST, NFE, NJE, NQU +C + COMMON /DLSA01/ TSW, ROWNS2(20), PDNORM, + 1 INSUFR, INSUFI, IXPR, IOWNS2(2), JTYP, MUSED, MXORDN, MXORDS +C + COMMON /DLSR01/ ROWNR3(2), T0, TLAST, TOUTC, + 1 LG0, LG1, LGX, IOWNR3(2), IRFND, ITASKC, NGC, NGE +C + DATA MORD(1),MORD(2)/12,5/, MXSTP0/500/, MXHNL0/10/ +C----------------------------------------------------------------------- +C Block A. +C This code block is executed on every call. +C It tests ISTATE and ITASK for legality and branches appropriately. +C If ISTATE .gt. 1 but the flag INIT shows that initialization has +C not yet been done, an error return occurs. +C If ISTATE = 1 and TOUT = T, return immediately. +C----------------------------------------------------------------------- + IF (ISTATE .LT. 1 .OR. ISTATE .GT. 3) GO TO 601 + IF (ITASK .LT. 1 .OR. ITASK .GT. 5) GO TO 602 + ITASKC = ITASK + IF (ISTATE .EQ. 1) GO TO 10 + IF (INIT .EQ. 0) GO TO 603 + IF (ISTATE .EQ. 2) GO TO 200 + GO TO 20 + 10 INIT = 0 + IF (TOUT .EQ. T) RETURN +C----------------------------------------------------------------------- +C Block B. +C The next code block is executed for the initial call (ISTATE = 1), +C or for a continuation call with parameter changes (ISTATE = 3). +C It contains checking of all inputs and various initializations. +C +C First check legality of the non-optional inputs NEQ, ITOL, IOPT, +C JT, ML, MU, and NG. +C----------------------------------------------------------------------- + 20 IF (NEQ(1) .LE. 0) GO TO 604 + IF (ISTATE .EQ. 1) GO TO 25 + IF (NEQ(1) .GT. N) GO TO 605 + 25 N = NEQ(1) + IF (ITOL .LT. 1 .OR. ITOL .GT. 4) GO TO 606 + IF (IOPT .LT. 0 .OR. IOPT .GT. 1) GO TO 607 + IF (JT .EQ. 3 .OR. JT .LT. 1 .OR. JT .GT. 5) GO TO 608 + JTYP = JT + IF (JT .LE. 2) GO TO 30 + ML = IWORK(1) + MU = IWORK(2) + IF (ML .LT. 0 .OR. ML .GE. N) GO TO 609 + IF (MU .LT. 0 .OR. MU .GE. N) GO TO 610 + 30 CONTINUE + IF (NG .LT. 0) GO TO 630 + IF (ISTATE .EQ. 1) GO TO 35 + IF (IRFND .EQ. 0 .AND. NG .NE. NGC) GO TO 631 + 35 NGC = NG +C Next process and check the optional inputs. -------------------------- + IF (IOPT .EQ. 1) GO TO 40 + IXPR = 0 + MXSTEP = MXSTP0 + MXHNIL = MXHNL0 + HMXI = 0.0D0 + HMIN = 0.0D0 + IF (ISTATE .NE. 1) GO TO 60 + H0 = 0.0D0 + MXORDN = MORD(1) + MXORDS = MORD(2) + GO TO 60 + 40 IXPR = IWORK(5) + IF (IXPR .LT. 0 .OR. IXPR .GT. 1) GO TO 611 + MXSTEP = IWORK(6) + IF (MXSTEP .LT. 0) GO TO 612 + IF (MXSTEP .EQ. 0) MXSTEP = MXSTP0 + MXHNIL = IWORK(7) + IF (MXHNIL .LT. 0) GO TO 613 + IF (MXHNIL .EQ. 0) MXHNIL = MXHNL0 + IF (ISTATE .NE. 1) GO TO 50 + H0 = RWORK(5) + MXORDN = IWORK(8) + IF (MXORDN .LT. 0) GO TO 628 + IF (MXORDN .EQ. 0) MXORDN = 100 + MXORDN = MIN(MXORDN,MORD(1)) + MXORDS = IWORK(9) + IF (MXORDS .LT. 0) GO TO 629 + IF (MXORDS .EQ. 0) MXORDS = 100 + MXORDS = MIN(MXORDS,MORD(2)) + IF ((TOUT - T)*H0 .LT. 0.0D0) GO TO 614 + 50 HMAX = RWORK(6) + IF (HMAX .LT. 0.0D0) GO TO 615 + HMXI = 0.0D0 + IF (HMAX .GT. 0.0D0) HMXI = 1.0D0/HMAX + HMIN = RWORK(7) + IF (HMIN .LT. 0.0D0) GO TO 616 +C----------------------------------------------------------------------- +C Set work array pointers and check lengths LRW and LIW. +C If ISTATE = 1, METH is initialized to 1 here to facilitate the +C checking of work space lengths. +C Pointers to segments of RWORK and IWORK are named by prefixing L to +C the name of the segment. E.g., the segment YH starts at RWORK(LYH). +C Segments of RWORK (in order) are denoted G0, G1, GX, YH, WM, +C EWT, SAVF, ACOR. +C If the lengths provided are insufficient for the current method, +C an error return occurs. This is treated as illegal input on the +C first call, but as a problem interruption with ISTATE = -7 on a +C continuation call. If the lengths are sufficient for the current +C method but not for both methods, a warning message is sent. +C----------------------------------------------------------------------- + 60 IF (ISTATE .EQ. 1) METH = 1 + IF (ISTATE .EQ. 1) NYH = N + LG0 = 21 + LG1 = LG0 + NG + LGX = LG1 + NG + LYHNEW = LGX + NG + IF (ISTATE .EQ. 1) LYH = LYHNEW + IF (LYHNEW .EQ. LYH) GO TO 62 +C If ISTATE = 3 and NG was changed, shift YH to its new location. ------ + LENYH = L*NYH + IF (LRW .LT. LYHNEW-1+LENYH) GO TO 62 + I1 = 1 + IF (LYHNEW .GT. LYH) I1 = -1 + CALL DCOPY (LENYH, RWORK(LYH), I1, RWORK(LYHNEW), I1) + LYH = LYHNEW + 62 CONTINUE + LEN1N = LYHNEW - 1 + (MXORDN + 1)*NYH + LEN1S = LYHNEW - 1 + (MXORDS + 1)*NYH + LWM = LEN1S + 1 + IF (JT .LE. 2) LENWM = N*N + 2 + IF (JT .GE. 4) LENWM = (2*ML + MU + 1)*N + 2 + LEN1S = LEN1S + LENWM + LEN1C = LEN1N + IF (METH .EQ. 2) LEN1C = LEN1S + LEN1 = MAX(LEN1N,LEN1S) + LEN2 = 3*N + LENRW = LEN1 + LEN2 + LENRWC = LEN1C + LEN2 + IWORK(17) = LENRW + LIWM = 1 + LENIW = 20 + N + LENIWC = 20 + IF (METH .EQ. 2) LENIWC = LENIW + IWORK(18) = LENIW + IF (ISTATE .EQ. 1 .AND. LRW .LT. LENRWC) GO TO 617 + IF (ISTATE .EQ. 1 .AND. LIW .LT. LENIWC) GO TO 618 + IF (ISTATE .EQ. 3 .AND. LRW .LT. LENRWC) GO TO 550 + IF (ISTATE .EQ. 3 .AND. LIW .LT. LENIWC) GO TO 555 + LEWT = LEN1 + 1 + INSUFR = 0 + IF (LRW .GE. LENRW) GO TO 65 + INSUFR = 2 + LEWT = LEN1C + 1 + MSG='DLSODAR- Warning.. RWORK length is sufficient for now, but ' + CALL XERRWD (MSG, 60, 103, 0, 0, 0, 0, 0, 0.0D0, 0.0D0) + MSG=' may not be later. Integration will proceed anyway. ' + CALL XERRWD (MSG, 60, 103, 0, 0, 0, 0, 0, 0.0D0, 0.0D0) + MSG = ' Length needed is LENRW = I1, while LRW = I2.' + CALL XERRWD (MSG, 50, 103, 0, 2, LENRW, LRW, 0, 0.0D0, 0.0D0) + 65 LSAVF = LEWT + N + LACOR = LSAVF + N + INSUFI = 0 + IF (LIW .GE. LENIW) GO TO 70 + INSUFI = 2 + MSG='DLSODAR- Warning.. IWORK length is sufficient for now, but ' + CALL XERRWD (MSG, 60, 104, 0, 0, 0, 0, 0, 0.0D0, 0.0D0) + MSG=' may not be later. Integration will proceed anyway. ' + CALL XERRWD (MSG, 60, 104, 0, 0, 0, 0, 0, 0.0D0, 0.0D0) + MSG = ' Length needed is LENIW = I1, while LIW = I2.' + CALL XERRWD (MSG, 50, 104, 0, 2, LENIW, LIW, 0, 0.0D0, 0.0D0) + 70 CONTINUE +C Check RTOL and ATOL for legality. ------------------------------------ + RTOLI = RTOL(1) + ATOLI = ATOL(1) + DO 75 I = 1,N + IF (ITOL .GE. 3) RTOLI = RTOL(I) + IF (ITOL .EQ. 2 .OR. ITOL .EQ. 4) ATOLI = ATOL(I) + IF (RTOLI .LT. 0.0D0) GO TO 619 + IF (ATOLI .LT. 0.0D0) GO TO 620 + 75 CONTINUE + IF (ISTATE .EQ. 1) GO TO 100 +C if ISTATE = 3, set flag to signal parameter changes to DSTODA. ------- + JSTART = -1 + IF (N .EQ. NYH) GO TO 200 +C NEQ was reduced. zero part of yh to avoid undefined references. ----- + I1 = LYH + L*NYH + I2 = LYH + (MAXORD + 1)*NYH - 1 + IF (I1 .GT. I2) GO TO 200 + DO 95 I = I1,I2 + 95 RWORK(I) = 0.0D0 + GO TO 200 +C----------------------------------------------------------------------- +C Block C. +C The next block is for the initial call only (ISTATE = 1). +C It contains all remaining initializations, the initial call to F, +C and the calculation of the initial step size. +C The error weights in EWT are inverted after being loaded. +C----------------------------------------------------------------------- + 100 UROUND = DUMACH() + TN = T + TSW = T + MAXORD = MXORDN + IF (ITASK .NE. 4 .AND. ITASK .NE. 5) GO TO 110 + TCRIT = RWORK(1) + IF ((TCRIT - TOUT)*(TOUT - T) .LT. 0.0D0) GO TO 625 + IF (H0 .NE. 0.0D0 .AND. (T + H0 - TCRIT)*H0 .GT. 0.0D0) + 1 H0 = TCRIT - T + 110 JSTART = 0 + NHNIL = 0 + NST = 0 + NJE = 0 + NSLAST = 0 + HU = 0.0D0 + NQU = 0 + MUSED = 0 + MITER = 0 + CCMAX = 0.3D0 + MAXCOR = 3 + MSBP = 20 + MXNCF = 10 +C Initial call to F. (LF0 points to YH(*,2).) ------------------------- + LF0 = LYH + NYH + CALL F (NEQ, T, Y, RWORK(LF0)) + NFE = 1 +C Load the initial value vector in YH. --------------------------------- + DO 115 I = 1,N + 115 RWORK(I+LYH-1) = Y(I) +C Load and invert the EWT array. (H is temporarily set to 1.0.) ------- + NQ = 1 + H = 1.0D0 + CALL DEWSET (N, ITOL, RTOL, ATOL, RWORK(LYH), RWORK(LEWT)) + DO 120 I = 1,N + IF (RWORK(I+LEWT-1) .LE. 0.0D0) GO TO 621 + 120 RWORK(I+LEWT-1) = 1.0D0/RWORK(I+LEWT-1) +C----------------------------------------------------------------------- +C The coding below computes the step size, H0, to be attempted on the +C first step, unless the user has supplied a value for this. +C First check that TOUT - T differs significantly from zero. +C A scalar tolerance quantity TOL is computed, as MAX(RTOL(i)) +C if this is positive, or MAX(ATOL(i)/ABS(Y(i))) otherwise, adjusted +C so as to be between 100*UROUND and 1.0E-3. +C Then the computed value H0 is given by: +C +C H0**(-2) = 1./(TOL * w0**2) + TOL * (norm(F))**2 +C +C where w0 = MAX ( ABS(T), ABS(TOUT) ), +C F = the initial value of the vector f(t,y), and +C norm() = the weighted vector norm used throughout, given by +C the DMNORM function routine, and weighted by the +C tolerances initially loaded into the EWT array. +C The sign of H0 is inferred from the initial values of TOUT and T. +C ABS(H0) is made .le. ABS(TOUT-T) in any case. +C----------------------------------------------------------------------- + IF (H0 .NE. 0.0D0) GO TO 180 + TDIST = ABS(TOUT - T) + W0 = MAX(ABS(T),ABS(TOUT)) + IF (TDIST .LT. 2.0D0*UROUND*W0) GO TO 622 + TOL = RTOL(1) + IF (ITOL .LE. 2) GO TO 140 + DO 130 I = 1,N + 130 TOL = MAX(TOL,RTOL(I)) + 140 IF (TOL .GT. 0.0D0) GO TO 160 + ATOLI = ATOL(1) + DO 150 I = 1,N + IF (ITOL .EQ. 2 .OR. ITOL .EQ. 4) ATOLI = ATOL(I) + AYI = ABS(Y(I)) + IF (AYI .NE. 0.0D0) TOL = MAX(TOL,ATOLI/AYI) + 150 CONTINUE + 160 TOL = MAX(TOL,100.0D0*UROUND) + TOL = MIN(TOL,0.001D0) + SUM = DMNORM (N, RWORK(LF0), RWORK(LEWT)) + SUM = 1.0D0/(TOL*W0*W0) + TOL*SUM**2 + H0 = 1.0D0/SQRT(SUM) + H0 = MIN(H0,TDIST) + H0 = SIGN(H0,TOUT-T) +C Adjust H0 if necessary to meet HMAX bound. --------------------------- + 180 RH = ABS(H0)*HMXI + IF (RH .GT. 1.0D0) H0 = H0/RH +C Load H with H0 and scale YH(*,2) by H0. ------------------------------ + H = H0 + DO 190 I = 1,N + 190 RWORK(I+LF0-1) = H0*RWORK(I+LF0-1) +C +C Check for a zero of g at T. ------------------------------------------ + IRFND = 0 + TOUTC = TOUT + IF (NGC .EQ. 0) GO TO 270 + CALL DRCHEK (1, G, NEQ, Y, RWORK(LYH), NYH, + 1 RWORK(LG0), RWORK(LG1), RWORK(LGX), JROOT, IRT) + IF (IRT .EQ. 0) GO TO 270 + GO TO 632 +C----------------------------------------------------------------------- +C Block D. +C The next code block is for continuation calls only (ISTATE = 2 or 3) +C and is to check stop conditions before taking a step. +C First, DRCHEK is called to check for a root within the last step +C taken, other than the last root found there, if any. +C If ITASK = 2 or 5, and y(TN) has not yet been returned to the user +C because of an intervening root, return through Block G. +C----------------------------------------------------------------------- + 200 NSLAST = NST +C + IRFP = IRFND + IF (NGC .EQ. 0) GO TO 205 + IF (ITASK .EQ. 1 .OR. ITASK .EQ. 4) TOUTC = TOUT + CALL DRCHEK (2, G, NEQ, Y, RWORK(LYH), NYH, + 1 RWORK(LG0), RWORK(LG1), RWORK(LGX), JROOT, IRT) + IF (IRT .NE. 1) GO TO 205 + IRFND = 1 + ISTATE = 3 + T = T0 + GO TO 425 + 205 CONTINUE + IRFND = 0 + IF (IRFP .EQ. 1 .AND. TLAST .NE. TN .AND. ITASK .EQ. 2) GO TO 400 +C + GO TO (210, 250, 220, 230, 240), ITASK + 210 IF ((TN - TOUT)*H .LT. 0.0D0) GO TO 250 + CALL DINTDY (TOUT, 0, RWORK(LYH), NYH, Y, IFLAG) + IF (IFLAG .NE. 0) GO TO 627 + T = TOUT + GO TO 420 + 220 TP = TN - HU*(1.0D0 + 100.0D0*UROUND) + IF ((TP - TOUT)*H .GT. 0.0D0) GO TO 623 + IF ((TN - TOUT)*H .LT. 0.0D0) GO TO 250 + T = TN + GO TO 400 + 230 TCRIT = RWORK(1) + IF ((TN - TCRIT)*H .GT. 0.0D0) GO TO 624 + IF ((TCRIT - TOUT)*H .LT. 0.0D0) GO TO 625 + IF ((TN - TOUT)*H .LT. 0.0D0) GO TO 245 + CALL DINTDY (TOUT, 0, RWORK(LYH), NYH, Y, IFLAG) + IF (IFLAG .NE. 0) GO TO 627 + T = TOUT + GO TO 420 + 240 TCRIT = RWORK(1) + IF ((TN - TCRIT)*H .GT. 0.0D0) GO TO 624 + 245 HMX = ABS(TN) + ABS(H) + IHIT = ABS(TN - TCRIT) .LE. 100.0D0*UROUND*HMX + IF (IHIT) T = TCRIT + IF (IRFP .EQ. 1 .AND. TLAST .NE. TN .AND. ITASK .EQ. 5) GO TO 400 + IF (IHIT) GO TO 400 + TNEXT = TN + H*(1.0D0 + 4.0D0*UROUND) + IF ((TNEXT - TCRIT)*H .LE. 0.0D0) GO TO 250 + H = (TCRIT - TN)*(1.0D0 - 4.0D0*UROUND) + IF (ISTATE .EQ. 2 .AND. JSTART .GE. 0) JSTART = -2 +C----------------------------------------------------------------------- +C Block E. +C The next block is normally executed for all calls and contains +C the call to the one-step core integrator DSTODA. +C +C This is a looping point for the integration steps. +C +C First check for too many steps being taken, update EWT (if not at +C start of problem), check for too much accuracy being requested, and +C check for H below the roundoff level in T. +C----------------------------------------------------------------------- + 250 CONTINUE + IF (METH .EQ. MUSED) GO TO 255 + IF (INSUFR .EQ. 1) GO TO 550 + IF (INSUFI .EQ. 1) GO TO 555 + 255 IF ((NST-NSLAST) .GE. MXSTEP) GO TO 500 + CALL DEWSET (N, ITOL, RTOL, ATOL, RWORK(LYH), RWORK(LEWT)) + DO 260 I = 1,N + IF (RWORK(I+LEWT-1) .LE. 0.0D0) GO TO 510 + 260 RWORK(I+LEWT-1) = 1.0D0/RWORK(I+LEWT-1) + 270 TOLSF = UROUND*DMNORM (N, RWORK(LYH), RWORK(LEWT)) + IF (TOLSF .LE. 1.0D0) GO TO 280 + TOLSF = TOLSF*2.0D0 + IF (NST .EQ. 0) GO TO 626 + GO TO 520 + 280 IF ((TN + H) .NE. TN) GO TO 290 + NHNIL = NHNIL + 1 + IF (NHNIL .GT. MXHNIL) GO TO 290 + MSG = 'DLSODAR- Warning..Internal T(=R1) and H(=R2) are ' + CALL XERRWD (MSG, 50, 101, 0, 0, 0, 0, 0, 0.0D0, 0.0D0) + MSG=' such that in the machine, T + H = T on the next step ' + CALL XERRWD (MSG, 60, 101, 0, 0, 0, 0, 0, 0.0D0, 0.0D0) + MSG = ' (H = step size). Solver will continue anyway.' + CALL XERRWD (MSG, 50, 101, 0, 0, 0, 0, 2, TN, H) + IF (NHNIL .LT. MXHNIL) GO TO 290 + MSG = 'DLSODAR- Above warning has been issued I1 times. ' + CALL XERRWD (MSG, 50, 102, 0, 0, 0, 0, 0, 0.0D0, 0.0D0) + MSG = ' It will not be issued again for this problem.' + CALL XERRWD (MSG, 50, 102, 0, 1, MXHNIL, 0, 0, 0.0D0, 0.0D0) + 290 CONTINUE +C----------------------------------------------------------------------- +C CALL DSTODA(NEQ,Y,YH,NYH,YH,EWT,SAVF,ACOR,WM,IWM,F,JAC,DPRJA,DSOLSY) +C----------------------------------------------------------------------- + CALL DSTODA (NEQ, Y, RWORK(LYH), NYH, RWORK(LYH), RWORK(LEWT), + 1 RWORK(LSAVF), RWORK(LACOR), RWORK(LWM), IWORK(LIWM), + 2 F, JAC, DPRJA, DSOLSY) + KGO = 1 - KFLAG + GO TO (300, 530, 540), KGO +C----------------------------------------------------------------------- +C Block F. +C The following block handles the case of a successful return from the +C core integrator (KFLAG = 0). +C If a method switch was just made, record TSW, reset MAXORD, +C set JSTART to -1 to signal DSTODA to complete the switch, +C and do extra printing of data if IXPR = 1. +C Then call DRCHEK to check for a root within the last step. +C Then, if no root was found, check for stop conditions. +C----------------------------------------------------------------------- + 300 INIT = 1 + IF (METH .EQ. MUSED) GO TO 310 + TSW = TN + MAXORD = MXORDN + IF (METH .EQ. 2) MAXORD = MXORDS + IF (METH .EQ. 2) RWORK(LWM) = SQRT(UROUND) + INSUFR = MIN(INSUFR,1) + INSUFI = MIN(INSUFI,1) + JSTART = -1 + IF (IXPR .EQ. 0) GO TO 310 + IF (METH .EQ. 2) THEN + MSG='DLSODAR- A switch to the BDF (stiff) method has occurred ' + CALL XERRWD (MSG, 60, 105, 0, 0, 0, 0, 0, 0.0D0, 0.0D0) + ENDIF + IF (METH .EQ. 1) THEN + MSG='DLSODAR- A switch to the Adams (nonstiff) method occurred ' + CALL XERRWD (MSG, 60, 106, 0, 0, 0, 0, 0, 0.0D0, 0.0D0) + ENDIF + MSG=' at T = R1, tentative step size H = R2, step NST = I1 ' + CALL XERRWD (MSG, 60, 107, 0, 1, NST, 0, 2, TN, H) + 310 CONTINUE +C + IF (NGC .EQ. 0) GO TO 315 + CALL DRCHEK (3, G, NEQ, Y, RWORK(LYH), NYH, + 1 RWORK(LG0), RWORK(LG1), RWORK(LGX), JROOT, IRT) + IF (IRT .NE. 1) GO TO 315 + IRFND = 1 + ISTATE = 3 + T = T0 + GO TO 425 + 315 CONTINUE +C + GO TO (320, 400, 330, 340, 350), ITASK +C ITASK = 1. If TOUT has been reached, interpolate. ------------------- + 320 IF ((TN - TOUT)*H .LT. 0.0D0) GO TO 250 + CALL DINTDY (TOUT, 0, RWORK(LYH), NYH, Y, IFLAG) + T = TOUT + GO TO 420 +C ITASK = 3. Jump to exit if TOUT was reached. ------------------------ + 330 IF ((TN - TOUT)*H .GE. 0.0D0) GO TO 400 + GO TO 250 +C ITASK = 4. See if TOUT or TCRIT was reached. Adjust H if necessary. + 340 IF ((TN - TOUT)*H .LT. 0.0D0) GO TO 345 + CALL DINTDY (TOUT, 0, RWORK(LYH), NYH, Y, IFLAG) + T = TOUT + GO TO 420 + 345 HMX = ABS(TN) + ABS(H) + IHIT = ABS(TN - TCRIT) .LE. 100.0D0*UROUND*HMX + IF (IHIT) GO TO 400 + TNEXT = TN + H*(1.0D0 + 4.0D0*UROUND) + IF ((TNEXT - TCRIT)*H .LE. 0.0D0) GO TO 250 + H = (TCRIT - TN)*(1.0D0 - 4.0D0*UROUND) + IF (JSTART .GE. 0) JSTART = -2 + GO TO 250 +C ITASK = 5. See if TCRIT was reached and jump to exit. --------------- + 350 HMX = ABS(TN) + ABS(H) + IHIT = ABS(TN - TCRIT) .LE. 100.0D0*UROUND*HMX +C----------------------------------------------------------------------- +C Block G. +C The following block handles all successful returns from DLSODAR. +C If ITASK .ne. 1, Y is loaded from YH and T is set accordingly. +C ISTATE is set to 2, and the optional outputs are loaded into the +C work arrays before returning. +C----------------------------------------------------------------------- + 400 DO 410 I = 1,N + 410 Y(I) = RWORK(I+LYH-1) + T = TN + IF (ITASK .NE. 4 .AND. ITASK .NE. 5) GO TO 420 + IF (IHIT) T = TCRIT + 420 ISTATE = 2 + 425 CONTINUE + RWORK(11) = HU + RWORK(12) = H + RWORK(13) = TN + RWORK(15) = TSW + IWORK(11) = NST + IWORK(12) = NFE + IWORK(13) = NJE + IWORK(14) = NQU + IWORK(15) = NQ + IWORK(19) = MUSED + IWORK(20) = METH + IWORK(10) = NGE + TLAST = T + RETURN +C----------------------------------------------------------------------- +C Block H. +C The following block handles all unsuccessful returns other than +C those for illegal input. First the error message routine is called. +C If there was an error test or convergence test failure, IMXER is set. +C Then Y is loaded from YH and T is set to TN. +C The optional outputs are loaded into the work arrays before returning. +C----------------------------------------------------------------------- +C The maximum number of steps was taken before reaching TOUT. ---------- + 500 MSG = 'DLSODAR- At current T (=R1), MXSTEP (=I1) steps ' + CALL XERRWD (MSG, 50, 201, 0, 0, 0, 0, 0, 0.0D0, 0.0D0) + MSG = ' taken on this call before reaching TOUT ' + CALL XERRWD (MSG, 50, 201, 0, 1, MXSTEP, 0, 1, TN, 0.0D0) + ISTATE = -1 + GO TO 580 +C EWT(i) .le. 0.0 for some i (not at start of problem). ---------------- + 510 EWTI = RWORK(LEWT+I-1) + MSG = 'DLSODAR- At T(=R1), EWT(I1) has become R2 .le. 0.' + CALL XERRWD (MSG, 50, 202, 0, 1, I, 0, 2, TN, EWTI) + ISTATE = -6 + GO TO 580 +C Too much accuracy requested for machine precision. ------------------- + 520 MSG = 'DLSODAR- At T (=R1), too much accuracy requested ' + CALL XERRWD (MSG, 50, 203, 0, 0, 0, 0, 0, 0.0D0, 0.0D0) + MSG = ' for precision of machine.. See TOLSF (=R2) ' + CALL XERRWD (MSG, 50, 203, 0, 0, 0, 0, 2, TN, TOLSF) + RWORK(14) = TOLSF + ISTATE = -2 + GO TO 580 +C KFLAG = -1. Error test failed repeatedly or with ABS(H) = HMIN. ----- + 530 MSG = 'DLSODAR- At T(=R1), step size H(=R2), the error ' + CALL XERRWD (MSG, 50, 204, 0, 0, 0, 0, 0, 0.0D0, 0.0D0) + MSG = ' test failed repeatedly or with ABS(H) = HMIN' + CALL XERRWD (MSG, 50, 204, 0, 0, 0, 0, 2, TN, H) + ISTATE = -4 + GO TO 560 +C KFLAG = -2. Convergence failed repeatedly or with ABS(H) = HMIN. ---- + 540 MSG = 'DLSODAR- At T (=R1) and step size H (=R2), the ' + CALL XERRWD (MSG, 50, 205, 0, 0, 0, 0, 0, 0.0D0, 0.0D0) + MSG = ' corrector convergence failed repeatedly ' + CALL XERRWD (MSG, 50, 205, 0, 0, 0, 0, 0, 0.0D0, 0.0D0) + MSG = ' or with ABS(H) = HMIN ' + CALL XERRWD (MSG, 30, 205, 0, 0, 0, 0, 2, TN, H) + ISTATE = -5 + GO TO 560 +C RWORK length too small to proceed. ----------------------------------- + 550 MSG = 'DLSODAR- At current T(=R1), RWORK length too small' + CALL XERRWD (MSG, 50, 206, 0, 0, 0, 0, 0, 0.0D0, 0.0D0) + MSG=' to proceed. The integration was otherwise successful.' + CALL XERRWD (MSG, 60, 206, 0, 0, 0, 0, 1, TN, 0.0D0) + ISTATE = -7 + GO TO 580 +C IWORK length too small to proceed. ----------------------------------- + 555 MSG = 'DLSODAR- At current T(=R1), IWORK length too small' + CALL XERRWD (MSG, 50, 207, 0, 0, 0, 0, 0, 0.0D0, 0.0D0) + MSG=' to proceed. The integration was otherwise successful.' + CALL XERRWD (MSG, 60, 207, 0, 0, 0, 0, 1, TN, 0.0D0) + ISTATE = -7 + GO TO 580 +C Compute IMXER if relevant. ------------------------------------------- + 560 BIG = 0.0D0 + IMXER = 1 + DO 570 I = 1,N + SIZE = ABS(RWORK(I+LACOR-1)*RWORK(I+LEWT-1)) + IF (BIG .GE. SIZE) GO TO 570 + BIG = SIZE + IMXER = I + 570 CONTINUE + IWORK(16) = IMXER +C Set Y vector, T, and optional outputs. ------------------------------- + 580 DO 590 I = 1,N + 590 Y(I) = RWORK(I+LYH-1) + T = TN + RWORK(11) = HU + RWORK(12) = H + RWORK(13) = TN + RWORK(15) = TSW + IWORK(11) = NST + IWORK(12) = NFE + IWORK(13) = NJE + IWORK(14) = NQU + IWORK(15) = NQ + IWORK(19) = MUSED + IWORK(20) = METH + IWORK(10) = NGE + TLAST = T + RETURN +C----------------------------------------------------------------------- +C Block I. +C The following block handles all error returns due to illegal input +C (ISTATE = -3), as detected before calling the core integrator. +C First the error message routine is called. If the illegal input +C is a negative ISTATE, the run is aborted (apparent infinite loop). +C----------------------------------------------------------------------- + 601 MSG = 'DLSODAR- ISTATE(=I1) illegal.' + CALL XERRWD (MSG, 30, 1, 0, 1, ISTATE, 0, 0, 0.0D0, 0.0D0) + IF (ISTATE .LT. 0) GO TO 800 + GO TO 700 + 602 MSG = 'DLSODAR- ITASK (=I1) illegal.' + CALL XERRWD (MSG, 30, 2, 0, 1, ITASK, 0, 0, 0.0D0, 0.0D0) + GO TO 700 + 603 MSG = 'DLSODAR- ISTATE.gt.1 but DLSODAR not initialized.' + CALL XERRWD (MSG, 50, 3, 0, 0, 0, 0, 0, 0.0D0, 0.0D0) + GO TO 700 + 604 MSG = 'DLSODAR- NEQ (=I1) .lt. 1 ' + CALL XERRWD (MSG, 30, 4, 0, 1, NEQ(1), 0, 0, 0.0D0, 0.0D0) + GO TO 700 + 605 MSG = 'DLSODAR- ISTATE = 3 and NEQ increased (I1 to I2).' + CALL XERRWD (MSG, 50, 5, 0, 2, N, NEQ(1), 0, 0.0D0, 0.0D0) + GO TO 700 + 606 MSG = 'DLSODAR- ITOL (=I1) illegal. ' + CALL XERRWD (MSG, 30, 6, 0, 1, ITOL, 0, 0, 0.0D0, 0.0D0) + GO TO 700 + 607 MSG = 'DLSODAR- IOPT (=I1) illegal. ' + CALL XERRWD (MSG, 30, 7, 0, 1, IOPT, 0, 0, 0.0D0, 0.0D0) + GO TO 700 + 608 MSG = 'DLSODAR- JT (=I1) illegal. ' + CALL XERRWD (MSG, 30, 8, 0, 1, JT, 0, 0, 0.0D0, 0.0D0) + GO TO 700 + 609 MSG = 'DLSODAR- ML (=I1) illegal: .lt.0 or .ge.NEQ (=I2)' + CALL XERRWD (MSG, 50, 9, 0, 2, ML, NEQ(1), 0, 0.0D0, 0.0D0) + GO TO 700 + 610 MSG = 'DLSODAR- MU (=I1) illegal: .lt.0 or .ge.NEQ (=I2)' + CALL XERRWD (MSG, 50, 10, 0, 2, MU, NEQ(1), 0, 0.0D0, 0.0D0) + GO TO 700 + 611 MSG = 'DLSODAR- IXPR (=I1) illegal. ' + CALL XERRWD (MSG, 30, 11, 0, 1, IXPR, 0, 0, 0.0D0, 0.0D0) + GO TO 700 + 612 MSG = 'DLSODAR- MXSTEP (=I1) .lt. 0 ' + CALL XERRWD (MSG, 30, 12, 0, 1, MXSTEP, 0, 0, 0.0D0, 0.0D0) + GO TO 700 + 613 MSG = 'DLSODAR- MXHNIL (=I1) .lt. 0 ' + CALL XERRWD (MSG, 30, 13, 0, 1, MXHNIL, 0, 0, 0.0D0, 0.0D0) + GO TO 700 + 614 MSG = 'DLSODAR- TOUT (=R1) behind T (=R2) ' + CALL XERRWD (MSG, 40, 14, 0, 0, 0, 0, 2, TOUT, T) + MSG = ' Integration direction is given by H0 (=R1) ' + CALL XERRWD (MSG, 50, 14, 0, 0, 0, 0, 1, H0, 0.0D0) + GO TO 700 + 615 MSG = 'DLSODAR- HMAX (=R1) .lt. 0.0 ' + CALL XERRWD (MSG, 30, 15, 0, 0, 0, 0, 1, HMAX, 0.0D0) + GO TO 700 + 616 MSG = 'DLSODAR- HMIN (=R1) .lt. 0.0 ' + CALL XERRWD (MSG, 30, 16, 0, 0, 0, 0, 1, HMIN, 0.0D0) + GO TO 700 + 617 MSG='DLSODAR- RWORK length needed, LENRW(=I1), exceeds LRW(=I2) ' + CALL XERRWD (MSG, 60, 17, 0, 2, LENRW, LRW, 0, 0.0D0, 0.0D0) + GO TO 700 + 618 MSG='DLSODAR- IWORK length needed, LENIW(=I1), exceeds LIW(=I2) ' + CALL XERRWD (MSG, 60, 18, 0, 2, LENIW, LIW, 0, 0.0D0, 0.0D0) + GO TO 700 + 619 MSG = 'DLSODAR- RTOL(I1) is R1 .lt. 0.0 ' + CALL XERRWD (MSG, 40, 19, 0, 1, I, 0, 1, RTOLI, 0.0D0) + GO TO 700 + 620 MSG = 'DLSODAR- ATOL(I1) is R1 .lt. 0.0 ' + CALL XERRWD (MSG, 40, 20, 0, 1, I, 0, 1, ATOLI, 0.0D0) + GO TO 700 + 621 EWTI = RWORK(LEWT+I-1) + MSG = 'DLSODAR- EWT(I1) is R1 .le. 0.0 ' + CALL XERRWD (MSG, 40, 21, 0, 1, I, 0, 1, EWTI, 0.0D0) + GO TO 700 + 622 MSG='DLSODAR- TOUT(=R1) too close to T(=R2) to start integration.' + CALL XERRWD (MSG, 60, 22, 0, 0, 0, 0, 2, TOUT, T) + GO TO 700 + 623 MSG='DLSODAR- ITASK = I1 and TOUT (=R1) behind TCUR - HU (= R2) ' + CALL XERRWD (MSG, 60, 23, 0, 1, ITASK, 0, 2, TOUT, TP) + GO TO 700 + 624 MSG='DLSODAR- ITASK = 4 or 5 and TCRIT (=R1) behind TCUR (=R2) ' + CALL XERRWD (MSG, 60, 24, 0, 0, 0, 0, 2, TCRIT, TN) + GO TO 700 + 625 MSG='DLSODAR- ITASK = 4 or 5 and TCRIT (=R1) behind TOUT (=R2) ' + CALL XERRWD (MSG, 60, 25, 0, 0, 0, 0, 2, TCRIT, TOUT) + GO TO 700 + 626 MSG = 'DLSODAR- At start of problem, too much accuracy ' + CALL XERRWD (MSG, 50, 26, 0, 0, 0, 0, 0, 0.0D0, 0.0D0) + MSG=' requested for precision of machine.. See TOLSF (=R1) ' + CALL XERRWD (MSG, 60, 26, 0, 0, 0, 0, 1, TOLSF, 0.0D0) + RWORK(14) = TOLSF + GO TO 700 + 627 MSG = 'DLSODAR- Trouble in DINTDY. ITASK = I1, TOUT = R1' + CALL XERRWD (MSG, 50, 27, 0, 1, ITASK, 0, 1, TOUT, 0.0D0) + GO TO 700 + 628 MSG = 'DLSODAR- MXORDN (=I1) .lt. 0 ' + CALL XERRWD (MSG, 30, 28, 0, 1, MXORDN, 0, 0, 0.0D0, 0.0D0) + GO TO 700 + 629 MSG = 'DLSODAR- MXORDS (=I1) .lt. 0 ' + CALL XERRWD (MSG, 30, 29, 0, 1, MXORDS, 0, 0, 0.0D0, 0.0D0) + GO TO 700 + 630 MSG = 'DLSODAR- NG (=I1) .lt. 0 ' + CALL XERRWD (MSG, 30, 30, 0, 1, NG, 0, 0, 0.0D0, 0.0D0) + GO TO 700 + 631 MSG = 'DLSODAR- NG changed (from I1 to I2) illegally, ' + CALL XERRWD (MSG, 50, 31, 0, 0, 0, 0, 0, 0.0D0, 0.0D0) + MSG = ' i.e. not immediately after a root was found.' + CALL XERRWD (MSG, 50, 31, 0, 2, NGC, NG, 0, 0.0D0, 0.0D0) + GO TO 700 + 632 MSG = 'DLSODAR- One or more components of g has a root ' + CALL XERRWD (MSG, 50, 32, 0, 0, 0, 0, 0, 0.0D0, 0.0D0) + MSG = ' too near to the initial point. ' + CALL XERRWD (MSG, 40, 32, 0, 0, 0, 0, 0, 0.0D0, 0.0D0) +C + 700 ISTATE = -3 + RETURN +C + 800 MSG = 'DLSODAR- Run aborted.. apparent infinite loop. ' + CALL XERRWD (MSG, 50, 303, 2, 0, 0, 0, 0, 0.0D0, 0.0D0) + RETURN +C----------------------- End of Subroutine DLSODAR --------------------- + END +*DECK DLSODPK + SUBROUTINE DLSODPK (F, NEQ, Y, T, TOUT, ITOL, RTOL, ATOL, ITASK, + 1 ISTATE, IOPT, RWORK, LRW, IWORK, LIW, JAC, PSOL, MF) + EXTERNAL F, JAC, PSOL + INTEGER NEQ, ITOL, ITASK, ISTATE, IOPT, LRW, IWORK, LIW, MF + DOUBLE PRECISION Y, T, TOUT, RTOL, ATOL, RWORK + DIMENSION NEQ(*), Y(*), RTOL(*), ATOL(*), RWORK(LRW), IWORK(LIW) +C----------------------------------------------------------------------- +C This is the 18 November 2003 version of +C DLSODPK: Livermore Solver for Ordinary Differential equations, +C with Preconditioned Krylov iteration methods for the +C Newton correction linear systems. +C +C This version is in double precision. +C +C DLSODPK solves the initial value problem for stiff or nonstiff +C systems of first order ODEs, +C dy/dt = f(t,y) , or, in component form, +C dy(i)/dt = f(i) = f(i,t,y(1),y(2),...,y(NEQ)) (i = 1,...,NEQ). +C----------------------------------------------------------------------- +C Introduction. +C +C This is a modification of the DLSODE package which incorporates +C various preconditioned Krylov subspace iteration methods for the +C linear algebraic systems that arise in the case of stiff systems. +C +C The linear systems that must be solved have the form +C A * x = b , where A = identity - hl0 * (df/dy) . +C Here hl0 is a scalar, and df/dy is the Jacobian matrix of partial +C derivatives of f (NEQ by NEQ). +C +C The particular Krylov method is chosen by setting the second digit, +C MITER, in the method flag MF. +C Currently, the values of MITER have the following meanings: +C +C MITER = 1 means the preconditioned Scaled Incomplete +C Orthogonalization Method (SPIOM). +C +C 2 means an incomplete version of the Preconditioned Scaled +C Generalized Minimal Residual method (SPIGMR). +C This is the best choice in general. +C +C 3 means the Preconditioned Conjugate Gradient method (PCG). +C Recommended only when df/dy is symmetric or nearly so. +C +C 4 means the scaled Preconditioned Conjugate Gradient method +C (PCGS). Recommended only when D-inverse * df/dy * D is +C symmetric or nearly so, where D is the diagonal scaling +C matrix with elements 1/EWT(i) (see RTOL/ATOL description). +C +C 9 means that only a user-supplied matrix P (approximating A) +C will be used, with no Krylov iteration done. This option +C allows the user to provide the complete linear system +C solution algorithm, if desired. +C +C The user can apply preconditioning to the linear system A*x = b, +C by means of arbitrary matrices (the preconditioners). +C In the case of SPIOM and SPIGMR, one can apply left and right +C preconditioners P1 and P2, and the basic iterative method is then +C applied to the matrix (P1-inverse)*A*(P2-inverse) instead of to the +C matrix A. The product P1*P2 should be an approximation to matrix A +C such that linear systems with P1 or P2 are easier to solve than with +C A. Preconditioning from the left only or right only means using +C P2 = identity or P1 = identity, respectively. +C In the case of the PCG and PCGS methods, there is only one +C preconditioner matrix P (but it can be the product of more than one). +C It should approximate the matrix A but allow for relatively +C easy solution of linear systems with coefficient matrix P. +C For PCG, P should be positive definite symmetric, or nearly so, +C and for PCGS, the scaled preconditioner D-inverse * P * D +C should be symmetric or nearly so. +C If the Jacobian J = df/dy splits in a natural way into a sum +C J = J1 + J2, then one possible choice of preconditioners is +C P1 = identity - hl0 * J1 and P2 = identity - hl0 * J2 +C provided each of these is easy to solve (or approximately solve). +C +C----------------------------------------------------------------------- +C References: +C 1. Peter N. Brown and Alan C. Hindmarsh, Reduced Storage Matrix +C Methods in Stiff ODE Systems, J. Appl. Math. & Comp., 31 (1989), +C pp. 40-91; also L.L.N.L. Report UCRL-95088, Rev. 1, June 1987. +C 2. Alan C. Hindmarsh, ODEPACK, A Systematized Collection of ODE +C Solvers, in Scientific Computing, R. S. Stepleman et al. (Eds.), +C North-Holland, Amsterdam, 1983, pp. 55-64. +C----------------------------------------------------------------------- +C Authors: Alan C. Hindmarsh and Peter N. Brown +C Center for Applied Scientific Computing, L-561 +C Lawrence Livermore National Laboratory +C Livermore, CA 94551 +C----------------------------------------------------------------------- +C Summary of Usage. +C +C Communication between the user and the DLSODPK package, for normal +C situations, is summarized here. This summary describes only a subset +C of the full set of options available. See the full description for +C details, including optional communication, nonstandard options, +C and instructions for special situations. See also the demonstration +C program distributed with this solver. +C +C A. First provide a subroutine of the form: +C SUBROUTINE F (NEQ, T, Y, YDOT) +C DOUBLE PRECISION T, Y(*), YDOT(*) +C which supplies the vector function f by loading YDOT(i) with f(i). +C +C B. Next determine (or guess) whether or not the problem is stiff. +C Stiffness occurs when the Jacobian matrix df/dy has an eigenvalue +C whose real part is negative and large in magnitude, compared to the +C reciprocal of the t span of interest. If the problem is nonstiff, +C use a method flag MF = 10. If it is stiff, MF should be between 21 +C and 24, or possibly 29. MF = 22 is generally the best choice. +C Use 23 or 24 only if symmetry is present. Use MF = 29 if the +C complete linear system solution is to be provided by the user. +C The following four parameters must also be set. +C IWORK(1) = LWP = length of real array WP for preconditioning. +C IWORK(2) = LIWP = length of integer array IWP for preconditioning. +C IWORK(3) = JPRE = preconditioner type flag: +C = 0 for no preconditioning (P1 = P2 = P = identity) +C = 1 for left-only preconditioning (P2 = identity) +C = 2 for right-only preconditioning (P1 = identity) +C = 3 for two-sided preconditioning (and PCG or PCGS) +C IWORK(4) = JACFLG = flag for whether JAC is called. +C = 0 if JAC is not to be called, +C = 1 if JAC is to be called. +C Use JACFLG = 1 if JAC computes any nonconstant data for use in +C preconditioning, such as Jacobian elements. +C The arrays WP and IWP are work arrays under the user's control, +C for use in the routines that perform preconditioning operations. +C +C C. If the problem is stiff, you must supply two routines that deal +C with the preconditioning of the linear systems to be solved. +C These are as follows: +C +C SUBROUTINE JAC (F, NEQ, T, Y, YSV, REWT, FTY, V, HL0, WP,IWP, IER) +C DOUBLE PRECISION T, Y(*),YSV(*), REWT(*), FTY(*), V(*), HL0, WP(*) +C INTEGER IWP(*) +C This routine must evaluate and preprocess any parts of the +C Jacobian matrix df/dy involved in the preconditioners P1, P2, P. +C The Y and FTY arrays contain the current values of y and f(t,y), +C respectively, and YSV also contains the current value of y. +C The array V is work space of length NEQ. +C JAC must multiply all computed Jacobian elements by the scalar +C -HL0, add the identity matrix, and do any factorization +C operations called for, in preparation for solving linear systems +C with a coefficient matrix of P1, P2, or P. The matrix P1*P2 or P +C should be an approximation to identity - HL0 * (df/dy). +C JAC should return IER = 0 if successful, and IER .ne. 0 if not. +C (If IER .ne. 0, a smaller time step will be tried.) +C +C SUBROUTINE PSOL (NEQ, T, Y, FTY, WK, HL0, WP, IWP, B, LR, IER) +C DOUBLE PRECISION T, Y(*), FTY(*), WK(*), HL0, WP(*), B(*) +C INTEGER IWP(*) +C This routine must solve a linear system with B as right-hand +C side and one of the preconditioning matrices, P1, P2, or P, as +C coefficient matrix, and return the solution vector in B. +C LR is a flag concerning left vs right preconditioning, input +C to PSOL. PSOL is to use P1 if LR = 1 and P2 if LR = 2. +C In the case of the PCG or PCGS method, LR will be 3, and PSOL +C should solve the system P*x = B with the preconditioner matrix P. +C In the case MF = 29 (no Krylov iteration), LR will be 0, +C and PSOL is to return in B the desired approximate solution +C to A * x = B, where A = identity - HL0 * (df/dy). +C PSOL can use data generated in the JAC routine and stored in +C WP and IWP. WK is a work array of length NEQ. +C The argument HL0 is the current value of the scalar appearing +C in the linear system. If the old value, at the time of the last +C JAC call, is needed, it must have been saved by JAC in WP. +C On return, PSOL should set the error flag IER as follows: +C IER = 0 if PSOL was successful, +C IER .gt. 0 if a recoverable error occurred, meaning that the +C time step will be retried, +C IER .lt. 0 if an unrecoverable error occurred, meaning that the +C solver is to stop immediately. +C +C D. Write a main program which calls Subroutine DLSODPK once for +C each point at which answers are desired. This should also provide +C for possible use of logical unit 6 for output of error messages by +C DLSODPK. On the first call to DLSODPK, supply arguments as follows: +C F = name of subroutine for right-hand side vector f. +C This name must be declared External in calling program. +C NEQ = number of first order ODEs. +C Y = array of initial values, of length NEQ. +C T = the initial value of the independent variable. +C TOUT = first point where output is desired (.ne. T). +C ITOL = 1 or 2 according as ATOL (below) is a scalar or array. +C RTOL = relative tolerance parameter (scalar). +C ATOL = absolute tolerance parameter (scalar or array). +C the estimated local error in y(i) will be controlled so as +C to be roughly less (in magnitude) than +C EWT(i) = RTOL*ABS(Y(i)) + ATOL if ITOL = 1, or +C EWT(i) = RTOL*ABS(Y(i)) + ATOL(i) if ITOL = 2. +C Thus the local error test passes if, in each component, +C either the absolute error is less than ATOL (or ATOL(i)), +C or the relative error is less than RTOL. +C Use RTOL = 0.0 for pure absolute error control, and +C use ATOL = 0.0 (or ATOL(i) = 0.0) for pure relative error +C control. Caution: Actual (global) errors may exceed these +C local tolerances, so choose them conservatively. +C ITASK = 1 for normal computation of output values of y at t = TOUT. +C ISTATE = integer flag (input and output). Set ISTATE = 1. +C IOPT = 0 to indicate no optional inputs used. +C RWORK = real work array of length at least: +C 20 + 16*NEQ for MF = 10, +C 45 + 17*NEQ + LWP for MF = 21, +C 61 + 17*NEQ + LWP for MF = 22, +C 20 + 15*NEQ + LWP for MF = 23 or 24, +C 20 + 12*NEQ + LWP for MF = 29. +C LRW = declared length of RWORK (in user's dimension). +C IWORK = integer work array of length at least: +C 30 for MF = 10, +C 35 + LIWP for MF = 21, +C 30 + LIWP for MF = 22, 23, 24, or 29. +C LIW = declared length of IWORK (in user's dimension). +C JAC,PSOL = names of subroutines for preconditioning. +C These names must be declared External in the calling program. +C MF = method flag. Standard values are: +C 10 for nonstiff (Adams) method. +C 21 for stiff (BDF) method, with preconditioned SIOM. +C 22 for stiff method, with preconditioned GMRES method. +C 23 for stiff method, with preconditioned CG method. +C 24 for stiff method, with scaled preconditioned CG method. +C 29 for stiff method, with user's PSOL routine only. +C Note that the main program must declare arrays Y, RWORK, IWORK, +C and possibly ATOL. +C +C E. The output from the first call (or any call) is: +C Y = array of computed values of y(t) vector. +C T = corresponding value of independent variable (normally TOUT). +C ISTATE = 2 if DLSODPK was successful, negative otherwise. +C -1 means excess work done on this call (perhaps wrong MF). +C -2 means excess accuracy requested (tolerances too small). +C -3 means illegal input detected (see printed message). +C -4 means repeated error test failures (check all inputs). +C -5 means repeated convergence failures (perhaps bad JAC +C or PSOL routine supplied or wrong choice of MF or +C tolerances, or this solver is inappropriate). +C -6 means error weight became zero during problem. (Solution +C component i vanished, and ATOL or ATOL(i) = 0.) +C -7 means an unrecoverable error occurred in PSOL. +C +C F. To continue the integration after a successful return, simply +C reset TOUT and call DLSODPK again. No other parameters need be reset. +C +C----------------------------------------------------------------------- +C----------------------------------------------------------------------- +C Full Description of User Interface to DLSODPK. +C +C The user interface to DLSODPK consists of the following parts. +C +C 1. The call sequence to Subroutine DLSODPK, which is a driver +C routine for the solver. This includes descriptions of both +C the call sequence arguments and of user-supplied routines. +C Following these descriptions is a description of +C optional inputs available through the call sequence, and then +C a description of optional outputs (in the work arrays). +C +C 2. Descriptions of other routines in the DLSODPK package that may be +C (optionally) called by the user. These provide the ability to +C alter error message handling, save and restore the internal +C Common, and obtain specified derivatives of the solution y(t). +C +C 3. Descriptions of Common blocks to be declared in overlay +C or similar environments, or to be saved when doing an interrupt +C of the problem and continued solution later. +C +C 4. Description of two routines in the DLSODPK package, either of +C which the user may replace with his/her own version, if desired. +C These relate to the measurement of errors. +C +C----------------------------------------------------------------------- +C Part 1. Call Sequence. +C +C The call sequence parameters used for input only are +C F, NEQ, TOUT, ITOL, RTOL, ATOL, ITASK, IOPT, LRW, LIW, JAC, PSOL, MF, +C and those used for both input and output are +C Y, T, ISTATE. +C The work arrays RWORK and IWORK are also used for conditional and +C optional inputs and optional outputs. (The term output here refers +C to the return from Subroutine DLSODPK to the user's calling program.) +C +C The legality of input parameters will be thoroughly checked on the +C initial call for the problem, but not checked thereafter unless a +C change in input parameters is flagged by ISTATE = 3 on input. +C +C The descriptions of the call arguments are as follows. +C +C F = the name of the user-supplied subroutine defining the +C ODE system. The system must be put in the first-order +C form dy/dt = f(t,y), where f is a vector-valued function +C of the scalar t and the vector y. Subroutine F is to +C compute the function f. It is to have the form +C SUBROUTINE F (NEQ, T, Y, YDOT) +C DOUBLE PRECISION T, Y(*), YDOT(*) +C where NEQ, T, and Y are input, and the array YDOT = f(t,y) +C is output. Y and YDOT are arrays of length NEQ. +C Subroutine F should not alter Y(1),...,Y(NEQ). +C F must be declared External in the calling program. +C +C Subroutine F may access user-defined quantities in +C NEQ(2),... and/or in Y(NEQ(1)+1),... if NEQ is an array +C (dimensioned in F) and/or Y has length exceeding NEQ(1). +C See the descriptions of NEQ and Y below. +C +C If quantities computed in the F routine are needed +C externally to DLSODPK, an extra call to F should be made +C for this purpose, for consistent and accurate results. +C If only the derivative dy/dt is needed, use DINTDY instead. +C +C NEQ = the size of the ODE system (number of first order +C ordinary differential equations). Used only for input. +C NEQ may be decreased, but not increased, during the problem. +C If NEQ is decreased (with ISTATE = 3 on input), the +C remaining components of Y should be left undisturbed, if +C these are to be accessed in the user-supplied subroutines. +C +C Normally, NEQ is a scalar, and it is generally referred to +C as a scalar in this user interface description. However, +C NEQ may be an array, with NEQ(1) set to the system size. +C (The DLSODPK package accesses only NEQ(1).) In either case, +C this parameter is passed as the NEQ argument in all calls +C to F, JAC, and PSOL. Hence, if it is an array, locations +C NEQ(2),... may be used to store other integer data and pass +C it to the user-supplied subroutines. Each such routine must +C include NEQ in a Dimension statement in that case. +C +C Y = a real array for the vector of dependent variables, of +C length NEQ or more. Used for both input and output on the +C first call (ISTATE = 1), and only for output on other calls. +C On the first call, Y must contain the vector of initial +C values. On output, Y contains the computed solution vector, +C evaluated at T. If desired, the Y array may be used +C for other purposes between calls to the solver. +C +C This array is passed as the Y argument in all calls to F, +C JAC, and PSOL. Hence its length may exceed NEQ, and locations +C Y(NEQ+1),... may be used to store other real data and +C pass it to the user-supplied subroutines. (The DLSODPK +C package accesses only Y(1),...,Y(NEQ).) +C +C T = the independent variable. On input, T is used only on the +C first call, as the initial point of the integration. +C On output, after each call, T is the value at which a +C computed solution y is evaluated (usually the same as TOUT). +C On an error return, T is the farthest point reached. +C +C TOUT = the next value of t at which a computed solution is desired. +C Used only for input. +C +C When starting the problem (ISTATE = 1), TOUT may be equal +C to T for one call, then should .ne. T for the next call. +C For the initial T, an input value of TOUT .ne. T is used +C in order to determine the direction of the integration +C (i.e. the algebraic sign of the step sizes) and the rough +C scale of the problem. Integration in either direction +C (forward or backward in t) is permitted. +C +C If ITASK = 2 or 5 (one-step modes), TOUT is ignored after +C the first call (i.e. the first call with TOUT .ne. T). +C Otherwise, TOUT is required on every call. +C +C If ITASK = 1, 3, or 4, the values of TOUT need not be +C monotone, but a value of TOUT which backs up is limited +C to the current internal T interval, whose endpoints are +C TCUR - HU and TCUR (see optional outputs, below, for +C TCUR and HU). +C +C ITOL = an indicator for the type of error control. See +C description below under ATOL. Used only for input. +C +C RTOL = a relative error tolerance parameter, either a scalar or +C an array of length NEQ. See description below under ATOL. +C Input only. +C +C ATOL = an absolute error tolerance parameter, either a scalar or +C an array of length NEQ. Input only. +C +C The input parameters ITOL, RTOL, and ATOL determine +C the error control performed by the solver. The solver will +C control the vector E = (E(i)) of estimated local errors +C in y, according to an inequality of the form +C RMS-norm of ( E(i)/EWT(i) ) .le. 1, +C where EWT(i) = RTOL(i)*ABS(Y(i)) + ATOL(i), +C and the RMS-norm (root-mean-square norm) here is +C RMS-norm(v) = SQRT(sum v(i)**2 / NEQ). Here EWT = (EWT(i)) +C is a vector of weights which must always be positive, and +C the values of RTOL and ATOL should all be non-negative. +C the following table gives the types (scalar/array) of +C RTOL and ATOL, and the corresponding form of EWT(i). +C +C ITOL RTOL ATOL EWT(i) +C 1 scalar scalar RTOL*ABS(Y(i)) + ATOL +C 2 scalar array RTOL*ABS(Y(i)) + ATOL(i) +C 3 array scalar RTOL(i)*ABS(Y(i)) + ATOL +C 4 array array RTOL(i)*ABS(Y(i)) + ATOL(i) +C +C When either of these parameters is a scalar, it need not +C be dimensioned in the user's calling program. +C +C If none of the above choices (with ITOL, RTOL, and ATOL +C fixed throughout the problem) is suitable, more general +C error controls can be obtained by substituting +C user-supplied routines for the setting of EWT and/or for +C the norm calculation. See Part 4 below. +C +C If global errors are to be estimated by making a repeated +C run on the same problem with smaller tolerances, then all +C components of RTOL and ATOL (i.e. of EWT) should be scaled +C down uniformly. +C +C ITASK = an index specifying the task to be performed. +C Input only. ITASK has the following values and meanings. +C 1 means normal computation of output values of y(t) at +C t = TOUT (by overshooting and interpolating). +C 2 means take one step only and return. +C 3 means stop at the first internal mesh point at or +C beyond t = TOUT and return. +C 4 means normal computation of output values of y(t) at +C t = TOUT but without overshooting t = TCRIT. +C TCRIT must be input as RWORK(1). TCRIT may be equal to +C or beyond TOUT, but not behind it in the direction of +C integration. This option is useful if the problem +C has a singularity at or beyond t = TCRIT. +C 5 means take one step, without passing TCRIT, and return. +C TCRIT must be input as RWORK(1). +C +C Note: If ITASK = 4 or 5 and the solver reaches TCRIT +C (within roundoff), it will return T = TCRIT (exactly) to +C indicate this (unless ITASK = 4 and TOUT comes before TCRIT, +C in which case answers at t = TOUT are returned first). +C +C ISTATE = an index used for input and output to specify the +C the state of the calculation. +C +C On input, the values of ISTATE are as follows. +C 1 means this is the first call for the problem +C (initializations will be done). See note below. +C 2 means this is not the first call, and the calculation +C is to continue normally, with no change in any input +C parameters except possibly TOUT and ITASK. +C (If ITOL, RTOL, and/or ATOL are changed between calls +C with ISTATE = 2, the new values will be used but not +C tested for legality.) +C 3 means this is not the first call, and the +C calculation is to continue normally, but with +C a change in input parameters other than +C TOUT and ITASK. Changes are allowed in +C NEQ, ITOL, RTOL, ATOL, IOPT, LRW, LIW, MF, +C and any of the optional inputs except H0. +C Note: A preliminary call with TOUT = T is not counted +C as a first call here, as no initialization or checking of +C input is done. (Such a call is sometimes useful for the +C purpose of outputting the initial conditions.) +C Thus the first call for which TOUT .ne. T requires +C ISTATE = 1 on input. +C +C On output, ISTATE has the following values and meanings. +C 1 means nothing was done; TOUT = T and ISTATE = 1 on input. +C 2 means the integration was performed successfully. +C -1 means an excessive amount of work (more than MXSTEP +C steps) was done on this call, before completing the +C requested task, but the integration was otherwise +C successful as far as T. (MXSTEP is an optional input +C and is normally 500.) To continue, the user may +C simply reset ISTATE to a value .gt. 1 and call again +C (the excess work step counter will be reset to 0). +C In addition, the user may increase MXSTEP to avoid +C this error return (see below on optional inputs). +C -2 means too much accuracy was requested for the precision +C of the machine being used. This was detected before +C completing the requested task, but the integration +C was successful as far as T. To continue, the tolerance +C parameters must be reset, and ISTATE must be set +C to 3. The optional output TOLSF may be used for this +C purpose. (Note: If this condition is detected before +C taking any steps, then an illegal input return +C (ISTATE = -3) occurs instead.) +C -3 means illegal input was detected, before taking any +C integration steps. See written message for details. +C Note: If the solver detects an infinite loop of calls +C to the solver with illegal input, it will cause +C the run to stop. +C -4 means there were repeated error test failures on +C one attempted step, before completing the requested +C task, but the integration was successful as far as T. +C The problem may have a singularity, or the input +C may be inappropriate. +C -5 means there were repeated convergence test failures on +C one attempted step, before completing the requested +C task, but the integration was successful as far as T. +C -6 means EWT(i) became zero for some i during the +C integration. Pure relative error control (ATOL(i)=0.0) +C was requested on a variable which has now vanished. +C The integration was successful as far as T. +C -7 means the PSOL routine returned an unrecoverable error +C flag (IER .lt. 0). The integration was successful as +C far as T. +C +C Note: since the normal output value of ISTATE is 2, +C it does not need to be reset for normal continuation. +C Also, since a negative input value of ISTATE will be +C regarded as illegal, a negative output value requires the +C user to change it, and possibly other inputs, before +C calling the solver again. +C +C IOPT = an integer flag to specify whether or not any optional +C inputs are being used on this call. Input only. +C The optional inputs are listed separately below. +C IOPT = 0 means no optional inputs are being used. +C Default values will be used in all cases. +C IOPT = 1 means one or more optional inputs are being used. +C +C RWORK = a real working array (double precision). +C The length of RWORK must be at least +C 20 + NYH*(MAXORD + 1) + 3*NEQ + LENLS + LWP where +C NYH = the initial value of NEQ, +C MAXORD = 12 (if METH = 1) or 5 (if METH = 2) (unless a +C smaller value is given as an optional input), +C LENLS = length of work space for linear system (Krylov) +C method, excluding preconditioning: +C LENLS = 0 if MITER = 0, +C LENLS = NEQ*(MAXL+3) + MAXL**2 if MITER = 1, +C LENLS = NEQ*(MAXL+3+MIN(1,MAXL-KMP)) +C + (MAXL+3)*MAXL + 1 if MITER = 2, +C LENLS = 6*NEQ if MITER = 3 or 4, +C LENLS = 3*NEQ if MITER = 9. +C (See the MF description for METH and MITER, and the +C list of optional inputs for MAXL and KMP.) +C LWP = length of real user work space for preconditioning +C (see JAC/PSOL). +C Thus if default values are used and NEQ is constant, +C this length is: +C 20 + 16*NEQ for MF = 10, +C 45 + 24*NEQ + LWP FOR MF = 11, +C 61 + 24*NEQ + LWP FOR MF = 12, +C 20 + 22*NEQ + LWP FOR MF = 13 OR 14, +C 20 + 19*NEQ + LWP FOR MF = 19, +C 20 + 9*NEQ FOR MF = 20, +C 45 + 17*NEQ + LWP FOR MF = 21, +C 61 + 17*NEQ + LWP FOR MF = 22, +C 20 + 15*NEQ + LWP FOR MF = 23 OR 24, +C 20 + 12*NEQ + LWP for MF = 29. +C The first 20 words of RWORK are reserved for conditional +C and optional inputs and optional outputs. +C +C The following word in RWORK is a conditional input: +C RWORK(1) = TCRIT = critical value of t which the solver +C is not to overshoot. Required if ITASK is +C 4 or 5, and ignored otherwise. (See ITASK.) +C +C LRW = the length of the array RWORK, as declared by the user. +C (This will be checked by the solver.) +C +C IWORK = an integer work array. The length of IWORK must be at least +C 30 if MITER = 0 (MF = 10 or 20), +C 30 + MAXL + LIWP if MITER = 1 (MF = 11, 21), +C 30 + LIWP if MITER = 2, 3, 4, or 9. +C MAXL = 5 unless a different optional input value is given. +C LIWP = length of integer user work space for preconditioning +C (see conditional input list following). +C The first few words of IWORK are used for conditional and +C optional inputs and optional outputs. +C +C The following 4 words in IWORK are conditional inputs, +C required if MITER .ge. 1: +C IWORK(1) = LWP = length of real array WP for use in +C preconditioning (part of RWORK array). +C IWORK(2) = LIWP = length of integer array IWP for use in +C preconditioning (part of IWORK array). +C The arrays WP and IWP are work arrays under the +C user's control, for use in the routines that +C perform preconditioning operations (JAC and PSOL). +C IWORK(3) = JPRE = preconditioner type flag: +C = 0 for no preconditioning (P1 = P2 = P = identity) +C = 1 for left-only preconditioning (P2 = identity) +C = 2 for right-only preconditioning (P1 = identity) +C = 3 for two-sided preconditioning (and PCG or PCGS) +C IWORK(4) = JACFLG = flag for whether JAC is called. +C = 0 if JAC is not to be called, +C = 1 if JAC is to be called. +C Use JACFLG = 1 if JAC computes any nonconstant +C data needed in preconditioning operations, +C such as some of the Jacobian elements. +C +C LIW = the length of the array IWORK, as declared by the user. +C (This will be checked by the solver.) +C +C Note: The work arrays must not be altered between calls to DLSODPK +C for the same problem, except possibly for the conditional and +C optional inputs, and except for the last 3*NEQ words of RWORK. +C The latter space is used for internal scratch space, and so is +C available for use by the user outside DLSODPK between calls, if +C desired (but not for use by any of the user-supplied subroutines). +C +C JAC = the name of the user-supplied routine to compute any +C Jacobian elements (or approximations) involved in the +C matrix preconditioning operations (MITER .ge. 1). +C It is to have the form +C SUBROUTINE JAC (F, NEQ, T, Y, YSV, REWT, FTY, V, +C 1 HL0, WP, IWP, IER) +C DOUBLE PRECISION T, Y(*),YSV(*), REWT(*), FTY(*), V(*), +C 1 HL0, WP(*) +C INTEGER IWP(*) +C This routine must evaluate and preprocess any parts of the +C Jacobian matrix df/dy used in the preconditioners P1, P2, P. +C the Y and FTY arrays contain the current values of y and +C f(t,y), respectively, and YSV also contains the current +C value of y. The array V is work space of length +C NEQ for use by JAC. REWT is the array of reciprocal error +C weights (1/EWT). JAC must multiply all computed Jacobian +C elements by the scalar -HL0, add the identity matrix, and do +C any factorization operations called for, in preparation +C for solving linear systems with a coefficient matrix of +C P1, P2, or P. The matrix P1*P2 or P should be an +C approximation to identity - HL0 * (df/dy). JAC should +C return IER = 0 if successful, and IER .ne. 0 if not. +C (If IER .ne. 0, a smaller time step will be tried.) +C The arrays WP (of length LWP) and IWP (of length LIWP) +C are for use by JAC and PSOL for work space and for storage +C of data needed for the solution of the preconditioner +C linear systems. Their lengths and contents are under the +C user's control. +C The JAC routine may save relevant Jacobian elements (or +C approximations) used in the preconditioners, along with the +C value of HL0, and use these to reconstruct preconditioner +C matrices later without reevaluationg those elements. +C This may be cost-effective if JAC is called with HL0 +C considerably different from its earlier value, indicating +C that a corrector convergence failure has occurred because +C of the change in HL0, not because of changes in the +C value of the Jacobian. In doing this, use the saved and +C current values of HL0 to decide whether to use saved +C or reevaluated elements. +C JAC may alter V, but may not alter Y, YSV, REWT, FTY, or HL0. +C JAC must be declared External in the calling program. +C Subroutine JAC may access user-defined quantities in +C NEQ(2),... and/or in Y(NEQ(1)+1),... if NEQ is an array +C (dimensioned in JAC) and/or Y has length exceeding NEQ(1). +C See the descriptions of NEQ and Y above. +C +C PSOL = the name of the user-supplied routine for the +C solution of preconditioner linear systems. +C It is to have the form +C SUBROUTINE PSOL (NEQ, T, Y, FTY, WK,HL0, WP,IWP, B, LR,IER) +C DOUBLE PRECISION T, Y(*), FTY(*), WK(*), HL0, WP(*), B(*) +C INTEGER IWP(*) +C This routine must solve a linear system with B as right-hand +C side and one of the preconditioning matrices, P1, P2, or P, +C as coefficient matrix, and return the solution vector in B. +C LR is a flag concerning left vs right preconditioning, input +C to PSOL. PSOL is to use P1 if LR = 1 and P2 if LR = 2. +C In the case of the PCG or PCGS method, LR will be 3, and PSOL +C should solve the system P*x = B with the preconditioner P. +C In the case MITER = 9 (no Krylov iteration), LR will be 0, +C and PSOL is to return in B the desired approximate solution +C to A * x = B, where A = identity - HL0 * (df/dy). +C PSOL can use data generated in the JAC routine and stored in +C WP and IWP. +C The Y and FTY arrays contain the current values of y and +C f(t,y), respectively. The array WK is work space of length +C NEQ for use by PSOL. +C The argument HL0 is the current value of the scalar appearing +C in the linear system. If the old value, as of the last +C JAC call, is needed, it must have been saved by JAC in WP. +C On return, PSOL should set the error flag IER as follows: +C IER = 0 if PSOL was successful, +C IER .gt. 0 on a recoverable error, meaning that the +C time step will be retried, +C IER .lt. 0 on an unrecoverable error, meaning that the +C solver is to stop immediately. +C PSOL may not alter Y, FTY, or HL0. +C PSOL must be declared External in the calling program. +C Subroutine PSOL may access user-defined quantities in +C NEQ(2),... and Y(NEQ(1)+1),... if NEQ is an array +C (dimensioned in PSOL) and/or Y has length exceeding NEQ(1). +C See the descriptions of NEQ and Y above. +C +C MF = the method flag. Used only for input. The legal values of +C MF are 10, 11, 12, 13, 14, 19, 20, 21, 22, 23, 24, and 29. +C MF has decimal digits METH and MITER: MF = 10*METH + MITER. +C METH indicates the basic linear multistep method: +C METH = 1 means the implicit Adams method. +C METH = 2 means the method based on Backward +C Differentiation Formulas (BDFs). +C MITER indicates the corrector iteration method: +C MITER = 0 means functional iteration (no linear system +C is involved). +C MITER = 1 means Newton iteration with Scaled Preconditioned +C Incomplete Orthogonalization Method (SPIOM) +C for the linear systems. +C MITER = 2 means Newton iteration with Scaled Preconditioned +C Generalized Minimal Residual method (SPIGMR) +C for the linear systems. +C MITER = 3 means Newton iteration with Preconditioned +C Conjugate Gradient method (PCG) +C for the linear systems. +C MITER = 4 means Newton iteration with scaled Preconditioned +C Conjugate Gradient method (PCGS) +C for the linear systems. +C MITER = 9 means Newton iteration with only the +C user-supplied PSOL routine called (no Krylov +C iteration) for the linear systems. +C JPRE is ignored, and PSOL is called with LR = 0. +C See comments in the introduction about the choice of MITER. +C If MITER .ge. 1, the user must supply routines JAC and PSOL +C (the names are arbitrary) as described above. +C For MITER = 0, dummy arguments can be used. +C----------------------------------------------------------------------- +C Optional Inputs. +C +C The following is a list of the optional inputs provided for in the +C call sequence. (See also Part 2.) For each such input variable, +C this table lists its name as used in this documentation, its +C location in the call sequence, its meaning, and the default value. +C The use of any of these inputs requires IOPT = 1, and in that +C case all of these inputs are examined. A value of zero for any +C of these optional inputs will cause the default value to be used. +C Thus to use a subset of the optional inputs, simply preload +C locations 5 to 10 in RWORK and IWORK to 0.0 and 0 respectively, and +C then set those of interest to nonzero values. +C +C Name Location Meaning and Default Value +C +C H0 RWORK(5) the step size to be attempted on the first step. +C The default value is determined by the solver. +C +C HMAX RWORK(6) the maximum absolute step size allowed. +C The default value is infinite. +C +C HMIN RWORK(7) the minimum absolute step size allowed. +C The default value is 0. (This lower bound is not +C enforced on the final step before reaching TCRIT +C when ITASK = 4 or 5.) +C +C DELT RWORK(8) convergence test constant in Krylov iteration +C algorithm. The default is .05. +C +C MAXORD IWORK(5) the maximum order to be allowed. The default +C value is 12 if METH = 1, and 5 if METH = 2. +C If MAXORD exceeds the default value, it will +C be reduced to the default value. +C If MAXORD is changed during the problem, it may +C cause the current order to be reduced. +C +C MXSTEP IWORK(6) maximum number of (internally defined) steps +C allowed during one call to the solver. +C The default value is 500. +C +C MXHNIL IWORK(7) maximum number of messages printed (per problem) +C warning that T + H = T on a step (H = step size). +C This must be positive to result in a non-default +C value. The default value is 10. +C +C MAXL IWORK(8) maximum number of iterations in the SPIOM, SPIGMR, +C PCG, or PCGS algorithm (.le. NEQ). +C The default is MAXL = MIN(5,NEQ). +C +C KMP IWORK(9) number of vectors on which orthogonalization +C is done in SPIOM or SPIGMR algorithm (.le. MAXL). +C The default is KMP = MAXL. +C Note: When KMP .lt. MAXL and MF = 22, the length +C of RWORK must be defined accordingly. See +C the definition of RWORK above. +C----------------------------------------------------------------------- +C Optional Outputs. +C +C As optional additional output from DLSODPK, the variables listed +C below are quantities related to the performance of DLSODPK +C which are available to the user. These are communicated by way of +C the work arrays, but also have internal mnemonic names as shown. +C Except where stated otherwise, all of these outputs are defined +C on any successful return from DLSODPK, and on any return with +C ISTATE = -1, -2, -4, -5, -6, or -7. On an illegal input return +C (ISTATE = -3), they will be unchanged from their existing values +C (if any), except possibly for TOLSF, LENRW, and LENIW. +C On any error return, outputs relevant to the error will be defined, +C as noted below. +C +C Name Location Meaning +C +C HU RWORK(11) the step size in t last used (successfully). +C +C HCUR RWORK(12) the step size to be attempted on the next step. +C +C TCUR RWORK(13) the current value of the independent variable +C which the solver has actually reached, i.e. the +C current internal mesh point in t. On output, TCUR +C will always be at least as far as the argument +C T, but may be farther (if interpolation was done). +C +C TOLSF RWORK(14) a tolerance scale factor, greater than 1.0, +C computed when a request for too much accuracy was +C detected (ISTATE = -3 if detected at the start of +C the problem, ISTATE = -2 otherwise). If ITOL is +C left unaltered but RTOL and ATOL are uniformly +C scaled up by a factor of TOLSF for the next call, +C then the solver is deemed likely to succeed. +C (The user may also ignore TOLSF and alter the +C tolerance parameters in any other way appropriate.) +C +C NST IWORK(11) the number of steps taken for the problem so far. +C +C NFE IWORK(12) the number of f evaluations for the problem so far. +C +C NPE IWORK(13) the number of calls to JAC so far (for Jacobian +C evaluation associated with preconditioning). +C +C NQU IWORK(14) the method order last used (successfully). +C +C NQCUR IWORK(15) the order to be attempted on the next step. +C +C IMXER IWORK(16) the index of the component of largest magnitude in +C the weighted local error vector ( E(i)/EWT(i) ), +C on an error return with ISTATE = -4 or -5. +C +C LENRW IWORK(17) the length of RWORK actually required. +C This is defined on normal returns and on an illegal +C input return for insufficient storage. +C +C LENIW IWORK(18) the length of IWORK actually required. +C This is defined on normal returns and on an illegal +C input return for insufficient storage. +C +C NNI IWORK(19) number of nonlinear iterations so far (each of +C which calls an iterative linear solver). +C +C NLI IWORK(20) number of linear iterations so far. +C Note: A measure of the success of algorithm is +C the average number of linear iterations per +C nonlinear iteration, given by NLI/NNI. +C If this is close to MAXL, MAXL may be too small. +C +C NPS IWORK(21) number of preconditioning solve operations +C (PSOL calls) so far. +C +C NCFN IWORK(22) number of convergence failures of the nonlinear +C (Newton) iteration so far. +C Note: A measure of success is the overall +C rate of nonlinear convergence failures, NCFN/NST. +C +C NCFL IWORK(23) number of convergence failures of the linear +C iteration so far. +C Note: A measure of success is the overall +C rate of linear convergence failures, NCFL/NNI. +C +C The following two arrays are segments of the RWORK array which +C may also be of interest to the user as optional outputs. +C For each array, the table below gives its internal name, +C its base address in RWORK, and its description. +C +C Name Base Address Description +C +C YH 21 the Nordsieck history array, of size NYH by +C (NQCUR + 1), where NYH is the initial value +C of NEQ. For j = 0,1,...,NQCUR, column j+1 +C of YH contains HCUR**j/factorial(j) times +C the j-th derivative of the interpolating +C polynomial currently representing the solution, +C evaluated at t = TCUR. +C +C ACOR LENRW-NEQ+1 array of size NEQ used for the accumulated +C corrections on each step, scaled on output +C to represent the estimated local error in y +C on the last step. This is the vector E in +C the description of the error control. It is +C defined only on a successful return from +C DLSODPK. +C +C----------------------------------------------------------------------- +C Part 2. Other Routines Callable. +C +C The following are optional calls which the user may make to +C gain additional capabilities in conjunction with DLSODPK. +C (The routines XSETUN and XSETF are designed to conform to the +C SLATEC error handling package.) +C +C Form of Call Function +C CALL XSETUN(LUN) Set the logical unit number, LUN, for +C output of messages from DLSODPK, if +C the default is not desired. +C The default value of lun is 6. +C +C CALL XSETF(MFLAG) Set a flag to control the printing of +C messages by DLSODPK. +C MFLAG = 0 means do not print. (Danger: +C This risks losing valuable information.) +C MFLAG = 1 means print (the default). +C +C Either of the above calls may be made at +C any time and will take effect immediately. +C +C CALL DSRCPK(RSAV,ISAV,JOB) saves and restores the contents of +C the internal Common blocks used by +C DLSODPK (see Part 3 below). +C RSAV must be a real array of length 222 +C or more, and ISAV must be an integer +C array of length 50 or more. +C JOB=1 means save Common into RSAV/ISAV. +C JOB=2 means restore Common from RSAV/ISAV. +C DSRCPK is useful if one is +C interrupting a run and restarting +C later, or alternating between two or +C more problems solved with DLSODPK. +C +C CALL DINTDY(,,,,,) Provide derivatives of y, of various +C (See below) orders, at a specified point t, if +C desired. It may be called only after +C a successful return from DLSODPK. +C +C The detailed instructions for using DINTDY are as follows. +C The form of the call is: +C +C CALL DINTDY (T, K, RWORK(21), NYH, DKY, IFLAG) +C +C The input parameters are: +C +C T = value of independent variable where answers are desired +C (normally the same as the T last returned by DLSODPK). +C for valid results, T must lie between TCUR - HU and TCUR. +C (See optional outputs for TCUR and HU.) +C K = integer order of the derivative desired. K must satisfy +C 0 .le. K .le. NQCUR, where NQCUR is the current order +C (see optional outputs). The capability corresponding +C to K = 0, i.e. computing y(T), is already provided +C by DLSODPK directly. Since NQCUR .ge. 1, the first +C derivative dy/dt is always available with DINTDY. +C RWORK(21) = the base address of the history array YH. +C NYH = column length of YH, equal to the initial value of NEQ. +C +C The output parameters are: +C +C DKY = a real array of length NEQ containing the computed value +C of the K-th derivative of y(t). +C IFLAG = integer flag, returned as 0 if K and T were legal, +C -1 if K was illegal, and -2 if T was illegal. +C On an error return, a message is also written. +C----------------------------------------------------------------------- +C Part 3. Common Blocks. +C +C If DLSODPK is to be used in an overlay situation, the user +C must declare, in the primary overlay, the variables in: +C (1) the call sequence to DLSODPK, and +C (2) the two internal Common blocks +C /DLS001/ of length 255 (218 double precision words +C followed by 37 integer words), +C /DLPK01/ of length 17 (4 double precision words +C followed by 13 integer words). +C +C If DLSODPK is used on a system in which the contents of internal +C Common blocks are not preserved between calls, the user should +C declare the above Common blocks in the calling program to insure +C that their contents are preserved. +C +C If the solution of a given problem by DLSODPK is to be interrupted +C and then later continued, such as when restarting an interrupted run +C or alternating between two or more problems, the user should save, +C following the return from the last DLSODPK call prior to the +C interruption, the contents of the call sequence variables and the +C internal Common blocks, and later restore these values before the +C next DLSODPK call for that problem. To save and restore the Common +C blocks, use Subroutine DSRCPK (see Part 2 above). +C +C----------------------------------------------------------------------- +C Part 4. Optionally Replaceable Solver Routines. +C +C below are descriptions of two routines in the DLSODPK package which +C relate to the measurement of errors. Either routine can be +C replaced by a user-supplied version, if desired. However, since such +C a replacement may have a major impact on performance, it should be +C done only when absolutely necessary, and only with great caution. +C (Note: The means by which the package version of a routine is +C superseded by the user's version may be system-dependent.) +C +C (a) DEWSET. +C The following subroutine is called just before each internal +C integration step, and sets the array of error weights, EWT, as +C described under ITOL/RTOL/ATOL above: +C SUBROUTINE DEWSET (NEQ, ITOL, RTOL, ATOL, YCUR, EWT) +C where NEQ, ITOL, RTOL, and ATOL are as in the DLSODPK call sequence, +C YCUR contains the current dependent variable vector, and +C EWT is the array of weights set by DEWSET. +C +C If the user supplies this subroutine, it must return in EWT(i) +C (i = 1,...,NEQ) a positive quantity suitable for comparing errors +C in y(i) to. The EWT array returned by DEWSET is passed to the DVNORM +C routine (see below), and also used by DLSODPK in the computation +C of the optional output IMXER, the diagonal Jacobian approximation, +C and the increments for difference quotient Jacobians. +C +C In the user-supplied version of DEWSET, it may be desirable to use +C the current values of derivatives of y. Derivatives up to order NQ +C are available from the history array YH, described above under +C optional outputs. In DEWSET, YH is identical to the YCUR array, +C extended to NQ + 1 columns with a column length of NYH and scale +C factors of H**j/factorial(j). On the first call for the problem, +C given by NST = 0, NQ is 1 and H is temporarily set to 1.0. +C NYH is the initial value of NEQ. The quantities NQ, H, and NST +C can be obtained by including in DEWSET the statements: +C DOUBLE PRECISION RLS +C COMMON /DLS001/ RLS(218),ILS(37) +C NQ = ILS(33) +C NST = ILS(34) +C H = RLS(212) +C Thus, for example, the current value of dy/dt can be obtained as +C YCUR(NYH+i)/H (i=1,...,NEQ) (and the division by H is +C unnecessary when NST = 0). +C +C (b) DVNORM. +C The following is a real function routine which computes the weighted +C root-mean-square norm of a vector v: +C D = DVNORM (N, V, W) +C where: +C N = the length of the vector, +C V = real array of length N containing the vector, +C W = real array of length N containing weights, +C D = SQRT( (1/N) * sum(V(i)*W(i))**2 ). +C DVNORM is called with N = NEQ and with W(i) = 1.0/EWT(i), where +C EWT is as set by Subroutine DEWSET. +C +C If the user supplies this function, it should return a non-negative +C value of DVNORM suitable for use in the error control in DLSODPK. +C None of the arguments should be altered by DVNORM. +C For example, a user-supplied DVNORM routine might: +C -substitute a max-norm of (V(i)*W(i)) for the RMS-norm, or +C -ignore some components of V in the norm, with the effect of +C suppressing the error control on those components of y. +C----------------------------------------------------------------------- +C +C***REVISION HISTORY (YYYYMMDD) +C 19860901 DATE WRITTEN +C 19861010 Numerous minor revisions to SPIOM and SPGMR routines; +C minor corrections to prologues and comments. +C 19870114 Changed name SPGMR to SPIGMR; revised residual norm +C calculation in SPIGMR (for incomplete case); +C revised error return logic in SPIGMR; +C 19870330 Major update: corrected comments throughout; +C removed TRET from Common; rewrote EWSET with 4 loops; +C fixed t test in INTDY; added Cray directives in STODPK; +C in STODPK, fixed DELP init. and logic around PJAC call; +C combined routines to save/restore Common; +C passed LEVEL = 0 in error message calls (except run abort). +C 19871130 Added option MITER = 9; shortened WM array by 2; +C revised early return from SPIOM and SPIGMR; +C replaced copy loops with SCOPY/DCOPY calls; +C minor corrections/revisions to SOLPK, SPIGMR, ATV, ATP; +C corrections to main prologue and internal comments. +C 19880304 Corrections to type declarations in SOLPK, SPIOM, USOL. +C 19891025 Added ISTATE = -7 return; minor revisions to USOL; +C added initialization of JACFLG in main driver; +C removed YH and NYH from PKSET call list; +C minor revisions to SPIOM and SPIGMR; +C corrections to main prologue and internal comments. +C 19900803 Added YSV to JAC call list; minor comment corrections. +C 20010425 Major update: convert source lines to upper case; +C added *DECK lines; changed from 1 to * in dummy dimensions; +C changed names R1MACH/D1MACH to RUMACH/DUMACH; +C renamed routines for uniqueness across single/double prec.; +C converted intrinsic names to generic form; +C removed ILLIN and NTREP (data loaded) from Common; +C removed all 'own' variables from Common; +C changed error messages to quoted strings; +C replaced XERRWV/XERRWD with 1993 revised version; +C converted prologues, comments, error messages to mixed case; +C numerous corrections to prologues and internal comments. +C 20010507 Converted single precision source to double precision. +C 20020502 Corrected declarations in descriptions of user routines. +C 20030603 Corrected duplicate type declaration for DUMACH. +C 20031105 Restored 'own' variables to Common blocks, to enable +C interrupt/restart feature. +C 20031112 Added SAVE statements for data-loaded constants. +C 20031117 Changed internal name NPE to NJE. +C +C----------------------------------------------------------------------- +C Other routines in the DLSODPK package. +C +C In addition to Subroutine DLSODPK, the DLSODPK package includes the +C following subroutines and function routines: +C DINTDY computes an interpolated value of the y vector at t = TOUT. +C DEWSET sets the error weight vector EWT before each step. +C DVNORM computes the weighted RMS-norm of a vector. +C DSTODPK is the core integrator, which does one step of the +C integration and the associated error control. +C DCFODE sets all method coefficients and test constants. +C DPKSET interfaces between DSTODPK and the JAC routine. +C DSOLPK manages solution of linear system in Newton iteration. +C DSPIOM performs the SPIOM algorithm. +C DATV computes a scaled, preconditioned product (I-hl0*J)*v. +C DORTHOG orthogonalizes a vector against previous basis vectors. +C DHEFA generates an LU factorization of a Hessenberg matrix. +C DHESL solves a Hessenberg square linear system. +C DSPIGMR performs the SPIGMR algorithm. +C DHEQR generates a QR factorization of a Hessenberg matrix. +C DHELS finds the least squares solution of a Hessenberg system. +C DPCG performs Preconditioned Conjugate Gradient algorithm (PCG). +C DPCGS performs the PCGS algorithm. +C DATP computes the product A*p, where A = I - hl0*df/dy. +C DUSOL interfaces to the user's PSOL routine (MITER = 9). +C DSRCPK is a user-callable routine to save and restore +C the contents of the internal Common blocks. +C DAXPY, DCOPY, DDOT, DNRM2, and DSCAL are basic linear +C algebra modules (from the BLAS collection). +C DUMACH computes the unit roundoff in a machine-independent manner. +C XERRWD, XSETUN, XSETF, IXSAV, and IUMACH handle the printing of all +C error messages and warnings. XERRWD is machine-dependent. +C Note: DVNORM, DDOT, DNRM2, DUMACH, IXSAV, and IUMACH are function +C routines. All the others are subroutines. +C +C----------------------------------------------------------------------- + DOUBLE PRECISION DUMACH, DVNORM + INTEGER INIT, MXSTEP, MXHNIL, NHNIL, NSLAST, NYH, IOWNS, + 1 ICF, IERPJ, IERSL, JCUR, JSTART, KFLAG, L, + 2 LYH, LEWT, LACOR, LSAVF, LWM, LIWM, METH, MITER, + 3 MAXORD, MAXCOR, MSBP, MXNCF, N, NQ, NST, NFE, NJE, NQU + INTEGER JPRE, JACFLG, LOCWP, LOCIWP, LSAVX, KMP, MAXL, MNEWT, + 1 NNI, NLI, NPS, NCFN, NCFL + INTEGER I, I1, I2, IFLAG, IMXER, KGO, LF0, LENIW, + 1 LENIWK, LENRW, LENWM, LENWK, LIWP, LWP, MORD, MXHNL0, MXSTP0, + 2 NCFN0, NCFL0, NLI0, NNI0, NNID, NSTD, NWARN + DOUBLE PRECISION ROWNS, + 1 CCMAX, EL0, H, HMIN, HMXI, HU, RC, TN, UROUND + DOUBLE PRECISION DELT, EPCON, SQRTN, RSQRTN + DOUBLE PRECISION ATOLI, AVDIM, AYI, BIG, EWTI, H0, HMAX, HMX, + 1 RCFL, RCFN, RH, RTOLI, TCRIT, + 2 TDIST, TNEXT, TOL, TOLSF, TP, SIZE, SUM, W0 + DIMENSION MORD(2) + LOGICAL IHIT, LAVD, LCFN, LCFL, LWARN + CHARACTER*60 MSG + SAVE MORD, MXSTP0, MXHNL0 +C----------------------------------------------------------------------- +C The following two internal Common blocks contain +C (a) variables which are local to any subroutine but whose values must +C be preserved between calls to the routine ("own" variables), and +C (b) variables which are communicated between subroutines. +C The block DLS001 is declared in subroutines DLSODPK, DINTDY, DSTODPK, +C DSOLPK, and DATV. +C The block DLPK01 is declared in subroutines DLSODPK, DSTODPK, DPKSET, +C and DSOLPK. +C Groups of variables are replaced by dummy arrays in the Common +C declarations in routines where those variables are not used. +C----------------------------------------------------------------------- + COMMON /DLS001/ ROWNS(209), + 1 CCMAX, EL0, H, HMIN, HMXI, HU, RC, TN, UROUND, + 2 INIT, MXSTEP, MXHNIL, NHNIL, NSLAST, NYH, IOWNS(6), + 3 ICF, IERPJ, IERSL, JCUR, JSTART, KFLAG, L, + 4 LYH, LEWT, LACOR, LSAVF, LWM, LIWM, METH, MITER, + 5 MAXORD, MAXCOR, MSBP, MXNCF, N, NQ, NST, NFE, NJE, NQU +C + COMMON /DLPK01/ DELT, EPCON, SQRTN, RSQRTN, + 1 JPRE, JACFLG, LOCWP, LOCIWP, LSAVX, KMP, MAXL, MNEWT, + 2 NNI, NLI, NPS, NCFN, NCFL +C + DATA MORD(1),MORD(2)/12,5/, MXSTP0/500/, MXHNL0/10/ +C----------------------------------------------------------------------- +C Block A. +C This code block is executed on every call. +C It tests ISTATE and ITASK for legality and branches appropriately. +C If ISTATE .gt. 1 but the flag INIT shows that initialization has +C not yet been done, an error return occurs. +C If ISTATE = 1 and TOUT = T, return immediately. +C----------------------------------------------------------------------- + IF (ISTATE .LT. 1 .OR. ISTATE .GT. 3) GO TO 601 + IF (ITASK .LT. 1 .OR. ITASK .GT. 5) GO TO 602 + IF (ISTATE .EQ. 1) GO TO 10 + IF (INIT .EQ. 0) GO TO 603 + IF (ISTATE .EQ. 2) GO TO 200 + GO TO 20 + 10 INIT = 0 + IF (TOUT .EQ. T) RETURN +C----------------------------------------------------------------------- +C Block B. +C The next code block is executed for the initial call (ISTATE = 1), +C or for a continuation call with parameter changes (ISTATE = 3). +C It contains checking of all inputs and various initializations. +C +C First check legality of the non-optional inputs NEQ, ITOL, IOPT, MF. +C----------------------------------------------------------------------- + 20 IF (NEQ(1) .LE. 0) GO TO 604 + IF (ISTATE .EQ. 1) GO TO 25 + IF (NEQ(1) .GT. N) GO TO 605 + 25 N = NEQ(1) + IF (ITOL .LT. 1 .OR. ITOL .GT. 4) GO TO 606 + IF (IOPT .LT. 0 .OR. IOPT .GT. 1) GO TO 607 + METH = MF/10 + MITER = MF - 10*METH + IF (METH .LT. 1 .OR. METH .GT. 2) GO TO 608 + IF (MITER .LT. 0) GO TO 608 + IF (MITER .GT. 4 .AND. MITER .LT. 9) GO TO 608 + IF (MITER .GE. 1) JPRE = IWORK(3) + JACFLG = 0 + IF (MITER .GE. 1) JACFLG = IWORK(4) +C Next process and check the optional inputs. -------------------------- + IF (IOPT .EQ. 1) GO TO 40 + MAXORD = MORD(METH) + MXSTEP = MXSTP0 + MXHNIL = MXHNL0 + IF (ISTATE .EQ. 1) H0 = 0.0D0 + HMXI = 0.0D0 + HMIN = 0.0D0 + MAXL = MIN(5,N) + KMP = MAXL + DELT = 0.05D0 + GO TO 60 + 40 MAXORD = IWORK(5) + IF (MAXORD .LT. 0) GO TO 611 + IF (MAXORD .EQ. 0) MAXORD = 100 + MAXORD = MIN(MAXORD,MORD(METH)) + MXSTEP = IWORK(6) + IF (MXSTEP .LT. 0) GO TO 612 + IF (MXSTEP .EQ. 0) MXSTEP = MXSTP0 + MXHNIL = IWORK(7) + IF (MXHNIL .LT. 0) GO TO 613 + IF (MXHNIL .EQ. 0) MXHNIL = MXHNL0 + IF (ISTATE .NE. 1) GO TO 50 + H0 = RWORK(5) + IF ((TOUT - T)*H0 .LT. 0.0D0) GO TO 614 + 50 HMAX = RWORK(6) + IF (HMAX .LT. 0.0D0) GO TO 615 + HMXI = 0.0D0 + IF (HMAX .GT. 0.0D0) HMXI = 1.0D0/HMAX + HMIN = RWORK(7) + IF (HMIN .LT. 0.0D0) GO TO 616 + MAXL = IWORK(8) + IF (MAXL .EQ. 0) MAXL = 5 + MAXL = MIN(MAXL,N) + KMP = IWORK(9) + IF (KMP .EQ. 0 .OR. KMP .GT. MAXL) KMP = MAXL + DELT = RWORK(8) + IF (DELT .EQ. 0.0D0) DELT = 0.05D0 +C----------------------------------------------------------------------- +C Set work array pointers and check lengths LRW and LIW. +C Pointers to segments of RWORK and IWORK are named by prefixing L to +C the name of the segment. E.g., the segment YH starts at RWORK(LYH). +C RWORK segments (in order) are denoted YH, WM, EWT, SAVF, SAVX, ACOR. +C----------------------------------------------------------------------- + 60 LYH = 21 + IF (ISTATE .EQ. 1) NYH = N + LWM = LYH + (MAXORD + 1)*NYH + IF (MITER .EQ. 0) LENWK = 0 + IF (MITER .EQ. 1) LENWK = N*(MAXL+2) + MAXL*MAXL + IF (MITER .EQ. 2) + 1 LENWK = N*(MAXL+2+MIN(1,MAXL-KMP)) + (MAXL+3)*MAXL + 1 + IF (MITER .EQ. 3 .OR. MITER .EQ. 4) LENWK = 5*N + IF (MITER .EQ. 9) LENWK = 2*N + LWP = 0 + IF (MITER .GE. 1) LWP = IWORK(1) + LENWM = LENWK + LWP + LOCWP = LENWK + 1 + LEWT = LWM + LENWM + LSAVF = LEWT + N + LSAVX = LSAVF + N + LACOR = LSAVX + N + IF (MITER .EQ. 0) LACOR = LSAVF + N + LENRW = LACOR + N - 1 + IWORK(17) = LENRW + LIWM = 31 + LENIWK = 0 + IF (MITER .EQ. 1) LENIWK = MAXL + LIWP = 0 + IF (MITER .GE. 1) LIWP = IWORK(2) + LENIW = 30 + LENIWK + LIWP + LOCIWP = LENIWK + 1 + IWORK(18) = LENIW + IF (LENRW .GT. LRW) GO TO 617 + IF (LENIW .GT. LIW) GO TO 618 +C Check RTOL and ATOL for legality. ------------------------------------ + RTOLI = RTOL(1) + ATOLI = ATOL(1) + DO 70 I = 1,N + IF (ITOL .GE. 3) RTOLI = RTOL(I) + IF (ITOL .EQ. 2 .OR. ITOL .EQ. 4) ATOLI = ATOL(I) + IF (RTOLI .LT. 0.0D0) GO TO 619 + IF (ATOLI .LT. 0.0D0) GO TO 620 + 70 CONTINUE +C Load SQRT(N) and its reciprocal in Common. --------------------------- + SQRTN = SQRT(REAL(N)) + RSQRTN = 1.0D0/SQRTN + IF (ISTATE .EQ. 1) GO TO 100 +C If ISTATE = 3, set flag to signal parameter changes to DSTODPK. ------ + JSTART = -1 + IF (NQ .LE. MAXORD) GO TO 90 +C MAXORD was reduced below NQ. Copy YH(*,MAXORD+2) into SAVF. --------- + DO 80 I = 1,N + 80 RWORK(I+LSAVF-1) = RWORK(I+LWM-1) + 90 CONTINUE + IF (N .EQ. NYH) GO TO 200 +C NEQ was reduced. Zero part of YH to avoid undefined references. ----- + I1 = LYH + L*NYH + I2 = LYH + (MAXORD + 1)*NYH - 1 + IF (I1 .GT. I2) GO TO 200 + DO 95 I = I1,I2 + 95 RWORK(I) = 0.0D0 + GO TO 200 +C----------------------------------------------------------------------- +C Block C. +C The next block is for the initial call only (ISTATE = 1). +C It contains all remaining initializations, the initial call to F, +C and the calculation of the initial step size. +C The error weights in EWT are inverted after being loaded. +C----------------------------------------------------------------------- + 100 UROUND = DUMACH() + TN = T + IF (ITASK .NE. 4 .AND. ITASK .NE. 5) GO TO 110 + TCRIT = RWORK(1) + IF ((TCRIT - TOUT)*(TOUT - T) .LT. 0.0D0) GO TO 625 + IF (H0 .NE. 0.0D0 .AND. (T + H0 - TCRIT)*H0 .GT. 0.0D0) + 1 H0 = TCRIT - T + 110 JSTART = 0 + NHNIL = 0 + NST = 0 + NJE = 0 + NSLAST = 0 + NLI0 = 0 + NNI0 = 0 + NCFN0 = 0 + NCFL0 = 0 + NWARN = 0 + HU = 0.0D0 + NQU = 0 + CCMAX = 0.3D0 + MAXCOR = 3 + MSBP = 20 + MXNCF = 10 + NNI = 0 + NLI = 0 + NPS = 0 + NCFN = 0 + NCFL = 0 +C Initial call to F. (LF0 points to YH(*,2).) ------------------------- + LF0 = LYH + NYH + CALL F (NEQ, T, Y, RWORK(LF0)) + NFE = 1 +C Load the initial value vector in YH. --------------------------------- + DO 115 I = 1,N + 115 RWORK(I+LYH-1) = Y(I) +C Load and invert the EWT array. (H is temporarily set to 1.0.) ------- + NQ = 1 + H = 1.0D0 + CALL DEWSET (N, ITOL, RTOL, ATOL, RWORK(LYH), RWORK(LEWT)) + DO 120 I = 1,N + IF (RWORK(I+LEWT-1) .LE. 0.0D0) GO TO 621 + 120 RWORK(I+LEWT-1) = 1.0D0/RWORK(I+LEWT-1) +C----------------------------------------------------------------------- +C The coding below computes the step size, H0, to be attempted on the +C first step, unless the user has supplied a value for this. +C First check that TOUT - T differs significantly from zero. +C A scalar tolerance quantity TOL is computed, as MAX(RTOL(i)) +C if this is positive, or MAX(ATOL(i)/ABS(Y(i))) otherwise, adjusted +C so as to be between 100*UROUND and 1.0E-3. +C Then the computed value H0 is given by.. +C NEQ +C H0**2 = TOL / ( w0**-2 + (1/NEQ) * Sum ( f(i)/ywt(i) )**2 ) +C 1 +C where w0 = MAX ( ABS(T), ABS(TOUT) ), +C f(i) = i-th component of initial value of f, +C ywt(i) = EWT(i)/TOL (a weight for y(i)). +C The sign of H0 is inferred from the initial values of TOUT and T. +C----------------------------------------------------------------------- + IF (H0 .NE. 0.0D0) GO TO 180 + TDIST = ABS(TOUT - T) + W0 = MAX(ABS(T),ABS(TOUT)) + IF (TDIST .LT. 2.0D0*UROUND*W0) GO TO 622 + TOL = RTOL(1) + IF (ITOL .LE. 2) GO TO 140 + DO 130 I = 1,N + 130 TOL = MAX(TOL,RTOL(I)) + 140 IF (TOL .GT. 0.0D0) GO TO 160 + ATOLI = ATOL(1) + DO 150 I = 1,N + IF (ITOL .EQ. 2 .OR. ITOL .EQ. 4) ATOLI = ATOL(I) + AYI = ABS(Y(I)) + IF (AYI .NE. 0.0D0) TOL = MAX(TOL,ATOLI/AYI) + 150 CONTINUE + 160 TOL = MAX(TOL,100.0D0*UROUND) + TOL = MIN(TOL,0.001D0) + SUM = DVNORM (N, RWORK(LF0), RWORK(LEWT)) + SUM = 1.0D0/(TOL*W0*W0) + TOL*SUM**2 + H0 = 1.0D0/SQRT(SUM) + H0 = MIN(H0,TDIST) + H0 = SIGN(H0,TOUT-T) +C Adjust H0 if necessary to meet HMAX bound. --------------------------- + 180 RH = ABS(H0)*HMXI + IF (RH .GT. 1.0D0) H0 = H0/RH +C Load H with H0 and scale YH(*,2) by H0. ------------------------------ + H = H0 + DO 190 I = 1,N + 190 RWORK(I+LF0-1) = H0*RWORK(I+LF0-1) + GO TO 270 +C----------------------------------------------------------------------- +C Block D. +C The next code block is for continuation calls only (ISTATE = 2 or 3) +C and is to check stop conditions before taking a step. +C----------------------------------------------------------------------- + 200 NSLAST = NST + NLI0 = NLI + NNI0 = NNI + NCFN0 = NCFN + NCFL0 = NCFL + NWARN = 0 + GO TO (210, 250, 220, 230, 240), ITASK + 210 IF ((TN - TOUT)*H .LT. 0.0D0) GO TO 250 + CALL DINTDY (TOUT, 0, RWORK(LYH), NYH, Y, IFLAG) + IF (IFLAG .NE. 0) GO TO 627 + T = TOUT + GO TO 420 + 220 TP = TN - HU*(1.0D0 + 100.0D0*UROUND) + IF ((TP - TOUT)*H .GT. 0.0D0) GO TO 623 + IF ((TN - TOUT)*H .LT. 0.0D0) GO TO 250 + GO TO 400 + 230 TCRIT = RWORK(1) + IF ((TN - TCRIT)*H .GT. 0.0D0) GO TO 624 + IF ((TCRIT - TOUT)*H .LT. 0.0D0) GO TO 625 + IF ((TN - TOUT)*H .LT. 0.0D0) GO TO 245 + CALL DINTDY (TOUT, 0, RWORK(LYH), NYH, Y, IFLAG) + IF (IFLAG .NE. 0) GO TO 627 + T = TOUT + GO TO 420 + 240 TCRIT = RWORK(1) + IF ((TN - TCRIT)*H .GT. 0.0D0) GO TO 624 + 245 HMX = ABS(TN) + ABS(H) + IHIT = ABS(TN - TCRIT) .LE. 100.0D0*UROUND*HMX + IF (IHIT) GO TO 400 + TNEXT = TN + H*(1.0D0 + 4.0D0*UROUND) + IF ((TNEXT - TCRIT)*H .LE. 0.0D0) GO TO 250 + H = (TCRIT - TN)*(1.0D0 - 4.0D0*UROUND) + IF (ISTATE .EQ. 2) JSTART = -2 +C----------------------------------------------------------------------- +C Block E. +C The next block is normally executed for all calls and contains +C the call to the one-step core integrator DSTODPK. +C +C This is a looping point for the integration steps. +C +C First check for too many steps being taken, +C Check for poor Newton/Krylov method performance, update EWT (if not +C at start of problem), check for too much accuracy being requested, +C and check for H below the roundoff level in T. +C----------------------------------------------------------------------- + 250 CONTINUE + IF ((NST-NSLAST) .GE. MXSTEP) GO TO 500 + NSTD = NST - NSLAST + NNID = NNI - NNI0 + IF (NSTD .LT. 10 .OR. NNID .EQ. 0) GO TO 255 + AVDIM = REAL(NLI - NLI0)/REAL(NNID) + RCFN = REAL(NCFN - NCFN0)/REAL(NSTD) + RCFL = REAL(NCFL - NCFL0)/REAL(NNID) + LAVD = AVDIM .GT. (MAXL - 0.05D0) + LCFN = RCFN .GT. 0.9D0 + LCFL = RCFL .GT. 0.9D0 + LWARN = LAVD .OR. LCFN .OR. LCFL + IF (.NOT.LWARN) GO TO 255 + NWARN = NWARN + 1 + IF (NWARN .GT. 10) GO TO 255 + IF (LAVD) THEN + MSG='DLSODPK- Warning. Poor iterative algorithm performance seen ' + CALL XERRWD (MSG, 60, 111, 0, 0, 0, 0, 0, 0.0D0, 0.0D0) + ENDIF + IF (LAVD) THEN + MSG=' at T = R1 by average no. of linear iterations = R2 ' + CALL XERRWD (MSG, 60, 111, 0, 0, 0, 0, 2, TN, AVDIM) + ENDIF + IF (LCFN) THEN + MSG='DLSODPK- Warning. Poor iterative algorithm performance seen ' + CALL XERRWD (MSG, 60, 112, 0, 0, 0, 0, 0, 0.0D0, 0.0D0) + ENDIF + IF (LCFN) THEN + MSG=' at T = R1 by nonlinear convergence failure rate = R2 ' + CALL XERRWD (MSG, 60, 112, 0, 0, 0, 0, 2, TN, RCFN) + ENDIF + IF (LCFL) THEN + MSG='DLSODPK- Warning. Poor iterative algorithm performance seen ' + CALL XERRWD (MSG, 60, 113, 0, 0, 0, 0, 0, 0.0D0, 0.0D0) + ENDIF + IF (LCFL) THEN + MSG=' at T = R1 by linear convergence failure rate = R2 ' + CALL XERRWD (MSG, 60, 113, 0, 0, 0, 0, 2, TN, RCFL) + ENDIF + 255 CONTINUE + CALL DEWSET (N, ITOL, RTOL, ATOL, RWORK(LYH), RWORK(LEWT)) + DO 260 I = 1,N + IF (RWORK(I+LEWT-1) .LE. 0.0D0) GO TO 510 + 260 RWORK(I+LEWT-1) = 1.0D0/RWORK(I+LEWT-1) + 270 TOLSF = UROUND*DVNORM (N, RWORK(LYH), RWORK(LEWT)) + IF (TOLSF .LE. 1.0D0) GO TO 280 + TOLSF = TOLSF*2.0D0 + IF (NST .EQ. 0) GO TO 626 + GO TO 520 + 280 IF ((TN + H) .NE. TN) GO TO 290 + NHNIL = NHNIL + 1 + IF (NHNIL .GT. MXHNIL) GO TO 290 + MSG = 'DLSODPK- Warning..Internal T(=R1) and H(=R2) are ' + CALL XERRWD (MSG, 50, 101, 0, 0, 0, 0, 0, 0.0D0, 0.0D0) + MSG=' such that in the machine, T + H = T on the next step ' + CALL XERRWD (MSG, 60, 101, 0, 0, 0, 0, 0, 0.0D0, 0.0D0) + MSG = ' (H = step size). Solver will continue anyway.' + CALL XERRWD (MSG, 50, 101, 0, 0, 0, 0, 2, TN, H) + IF (NHNIL .LT. MXHNIL) GO TO 290 + MSG = 'DLSODPK- Above warning has been issued I1 times. ' + CALL XERRWD (MSG, 50, 102, 0, 0, 0, 0, 0, 0.0D0, 0.0D0) + MSG = ' It will not be issued again for this problem.' + CALL XERRWD (MSG, 50, 102, 0, 1, MXHNIL, 0, 0, 0.0D0, 0.0D0) + 290 CONTINUE +C----------------------------------------------------------------------- +C CALL DSTODPK(NEQ,Y,YH,NYH,YH,EWT,SAVF,SAVX,ACOR,WM,IWM,F,JAC,PSOL) +C----------------------------------------------------------------------- + CALL DSTODPK (NEQ, Y, RWORK(LYH), NYH, RWORK(LYH), RWORK(LEWT), + 1 RWORK(LSAVF), RWORK(LSAVX), RWORK(LACOR), RWORK(LWM), + 2 IWORK(LIWM), F, JAC, PSOL) + KGO = 1 - KFLAG + GO TO (300, 530, 540, 550), KGO +C----------------------------------------------------------------------- +C Block F. +C The following block handles the case of a successful return from the +C core integrator (KFLAG = 0). Test for stop conditions. +C----------------------------------------------------------------------- + 300 INIT = 1 + GO TO (310, 400, 330, 340, 350), ITASK +C ITASK = 1. If TOUT has been reached, interpolate. ------------------- + 310 IF ((TN - TOUT)*H .LT. 0.0D0) GO TO 250 + CALL DINTDY (TOUT, 0, RWORK(LYH), NYH, Y, IFLAG) + T = TOUT + GO TO 420 +C ITASK = 3. Jump to exit if TOUT was reached. ------------------------ + 330 IF ((TN - TOUT)*H .GE. 0.0D0) GO TO 400 + GO TO 250 +C ITASK = 4. See if TOUT or TCRIT was reached. Adjust H if necessary. + 340 IF ((TN - TOUT)*H .LT. 0.0D0) GO TO 345 + CALL DINTDY (TOUT, 0, RWORK(LYH), NYH, Y, IFLAG) + T = TOUT + GO TO 420 + 345 HMX = ABS(TN) + ABS(H) + IHIT = ABS(TN - TCRIT) .LE. 100.0D0*UROUND*HMX + IF (IHIT) GO TO 400 + TNEXT = TN + H*(1.0D0 + 4.0D0*UROUND) + IF ((TNEXT - TCRIT)*H .LE. 0.0D0) GO TO 250 + H = (TCRIT - TN)*(1.0D0 - 4.0D0*UROUND) + JSTART = -2 + GO TO 250 +C ITASK = 5. see if TCRIT was reached and jump to exit. --------------- + 350 HMX = ABS(TN) + ABS(H) + IHIT = ABS(TN - TCRIT) .LE. 100.0D0*UROUND*HMX +C----------------------------------------------------------------------- +C Block G. +C The following block handles all successful returns from DLSODPK. +C If ITASK .ne. 1, Y is loaded from YH and T is set accordingly. +C ISTATE is set to 2, and the optional outputs are loaded into the +C work arrays before returning. +C----------------------------------------------------------------------- + 400 DO 410 I = 1,N + 410 Y(I) = RWORK(I+LYH-1) + T = TN + IF (ITASK .NE. 4 .AND. ITASK .NE. 5) GO TO 420 + IF (IHIT) T = TCRIT + 420 ISTATE = 2 + RWORK(11) = HU + RWORK(12) = H + RWORK(13) = TN + IWORK(11) = NST + IWORK(12) = NFE + IWORK(13) = NJE + IWORK(14) = NQU + IWORK(15) = NQ + IWORK(19) = NNI + IWORK(20) = NLI + IWORK(21) = NPS + IWORK(22) = NCFN + IWORK(23) = NCFL + RETURN +C----------------------------------------------------------------------- +C Block H. +C The following block handles all unsuccessful returns other than +C those for illegal input. First the error message routine is called. +C If there was an error test or convergence test failure, IMXER is set. +C Then Y is loaded from YH and T is set to TN. +C The optional outputs are loaded into the work arrays before returning. +C----------------------------------------------------------------------- +C The maximum number of steps was taken before reaching TOUT. ---------- + 500 MSG = 'DLSODPK- At current T (=R1), MXSTEP (=I1) steps ' + CALL XERRWD (MSG, 50, 201, 0, 0, 0, 0, 0, 0.0D0, 0.0D0) + MSG = ' taken on this call before reaching TOUT ' + CALL XERRWD (MSG, 50, 201, 0, 1, MXSTEP, 0, 1, TN, 0.0D0) + ISTATE = -1 + GO TO 580 +C EWT(i) .le. 0.0 for some i (not at start of problem). ---------------- + 510 EWTI = RWORK(LEWT+I-1) + MSG = 'DLSODPK- At T (=R1), EWT(I1) has become R2.le.0. ' + CALL XERRWD (MSG, 50, 202, 0, 1, I, 0, 2, TN, EWTI) + ISTATE = -6 + GO TO 580 +C Too much accuracy requested for machine precision. ------------------- + 520 MSG = 'DLSODPK- At T (=R1), too much accuracy requested ' + CALL XERRWD (MSG, 50, 203, 0, 0, 0, 0, 0, 0.0D0, 0.0D0) + MSG = ' for precision of machine.. See TOLSF (=R2) ' + CALL XERRWD (MSG, 50, 203, 0, 0, 0, 0, 2, TN, TOLSF) + RWORK(14) = TOLSF + ISTATE = -2 + GO TO 580 +C KFLAG = -1. Error test failed repeatedly or with ABS(H) = HMIN. ----- + 530 MSG = 'DLSODPK- At T(=R1), step size H(=R2), the error ' + CALL XERRWD (MSG, 50, 204, 0, 0, 0, 0, 0, 0.0D0, 0.0D0) + MSG = ' test failed repeatedly or with ABS(H) = HMIN' + CALL XERRWD (MSG, 50, 204, 0, 0, 0, 0, 2, TN, H) + ISTATE = -4 + GO TO 560 +C KFLAG = -2. Convergence failed repeatedly or with ABS(H) = HMIN. ---- + 540 MSG = 'DLSODPK- At T (=R1) and step size H (=R2), the ' + CALL XERRWD (MSG, 50, 205, 0, 0, 0, 0, 0, 0.0D0, 0.0D0) + MSG = ' corrector convergence failed repeatedly ' + CALL XERRWD (MSG, 50, 205, 0, 0, 0, 0, 0, 0.0D0, 0.0D0) + MSG = ' or with ABS(H) = HMIN ' + CALL XERRWD (MSG, 30, 205, 0, 0, 0, 0, 2, TN, H) + ISTATE = -5 + GO TO 560 +C KFLAG = -3. Unrecoverable error from PSOL. -------------------------- + 550 MSG = 'DLSODPK- At T (=R1) an unrecoverable error return' + CALL XERRWD (MSG, 50, 205, 0, 0, 0, 0, 0, 0.0D0, 0.0D0) + MSG = ' was made from Subroutine PSOL ' + CALL XERRWD (MSG, 40, 205, 0, 0, 0, 0, 1, TN, 0.0D0) + ISTATE = -7 + GO TO 580 +C Compute IMXER if relevant. ------------------------------------------- + 560 BIG = 0.0D0 + IMXER = 1 + DO 570 I = 1,N + SIZE = ABS(RWORK(I+LACOR-1)*RWORK(I+LEWT-1)) + IF (BIG .GE. SIZE) GO TO 570 + BIG = SIZE + IMXER = I + 570 CONTINUE + IWORK(16) = IMXER +C Set Y vector, T, and optional outputs. ------------------------------- + 580 DO 590 I = 1,N + 590 Y(I) = RWORK(I+LYH-1) + T = TN + RWORK(11) = HU + RWORK(12) = H + RWORK(13) = TN + IWORK(11) = NST + IWORK(12) = NFE + IWORK(13) = NJE + IWORK(14) = NQU + IWORK(15) = NQ + IWORK(19) = NNI + IWORK(20) = NLI + IWORK(21) = NPS + IWORK(22) = NCFN + IWORK(23) = NCFL + RETURN +C----------------------------------------------------------------------- +C Block I. +C The following block handles all error returns due to illegal input +C (ISTATE = -3), as detected before calling the core integrator. +C First the error message routine is called. If the illegal input +C is a negative ISTATE, the run is aborted (apparent infinite loop). +C----------------------------------------------------------------------- + 601 MSG = 'DLSODPK- ISTATE(=I1) illegal.' + CALL XERRWD (MSG, 30, 1, 0, 1, ISTATE, 0, 0, 0.0D0, 0.0D0) + IF (ISTATE .LT. 0) GO TO 800 + GO TO 700 + 602 MSG = 'DLSODPK- ITASK (=I1) illegal.' + CALL XERRWD (MSG, 30, 2, 0, 1, ITASK, 0, 0, 0.0D0, 0.0D0) + GO TO 700 + 603 MSG = 'DLSODPK- ISTATE.gt.1 but DLSODPK not initialized.' + CALL XERRWD (MSG, 50, 3, 0, 0, 0, 0, 0, 0.0D0, 0.0D0) + GO TO 700 + 604 MSG = 'DLSODPK- NEQ (=I1) .lt. 1 ' + CALL XERRWD (MSG, 30, 4, 0, 1, NEQ(1), 0, 0, 0.0D0, 0.0D0) + GO TO 700 + 605 MSG = 'DLSODPK- ISTATE = 3 and NEQ increased (I1 to I2).' + CALL XERRWD (MSG, 50, 5, 0, 2, N, NEQ(1), 0, 0.0D0, 0.0D0) + GO TO 700 + 606 MSG = 'DLSODPK- ITOL (=I1) illegal. ' + CALL XERRWD (MSG, 30, 6, 0, 1, ITOL, 0, 0, 0.0D0, 0.0D0) + GO TO 700 + 607 MSG = 'DLSODPK- IOPT (=I1) illegal. ' + CALL XERRWD (MSG, 30, 7, 0, 1, IOPT, 0, 0, 0.0D0, 0.0D0) + GO TO 700 + 608 MSG = 'DLSODPK- MF (=I1) illegal. ' + CALL XERRWD (MSG, 30, 8, 0, 1, MF, 0, 0, 0.0D0, 0.0D0) + GO TO 700 + 611 MSG = 'DLSODPK- MAXORD (=I1) .lt. 0 ' + CALL XERRWD (MSG, 30, 11, 0, 1, MAXORD, 0, 0, 0.0D0, 0.0D0) + GO TO 700 + 612 MSG = 'DLSODPK- MXSTEP (=I1) .lt. 0 ' + CALL XERRWD (MSG, 30, 12, 0, 1, MXSTEP, 0, 0, 0.0D0, 0.0D0) + GO TO 700 + 613 MSG = 'DLSODPK- MXHNIL (=I1) .lt. 0 ' + CALL XERRWD (MSG, 30, 13, 0, 1, MXHNIL, 0, 0, 0.0D0, 0.0D0) + GO TO 700 + 614 MSG = 'DLSODPK- TOUT (=R1) behind T (=R2) ' + CALL XERRWD (MSG, 40, 14, 0, 0, 0, 0, 2, TOUT, T) + MSG = ' Integration direction is given by H0 (=R1) ' + CALL XERRWD (MSG, 50, 14, 0, 0, 0, 0, 1, H0, 0.0D0) + GO TO 700 + 615 MSG = 'DLSODPK- HMAX (=R1) .lt. 0.0 ' + CALL XERRWD (MSG, 30, 15, 0, 0, 0, 0, 1, HMAX, 0.0D0) + GO TO 700 + 616 MSG = 'DLSODPK- HMIN (=R1) .lt. 0.0 ' + CALL XERRWD (MSG, 30, 16, 0, 0, 0, 0, 1, HMIN, 0.0D0) + GO TO 700 + 617 MSG='DLSODPK- RWORK length needed, LENRW(=I1), exceeds LRW(=I2) ' + CALL XERRWD (MSG, 60, 17, 0, 2, LENRW, LRW, 0, 0.0D0, 0.0D0) + GO TO 700 + 618 MSG='DLSODPK- IWORK length needed, LENIW(=I1), exceeds LIW(=I2) ' + CALL XERRWD (MSG, 60, 18, 0, 2, LENIW, LIW, 0, 0.0D0, 0.0D0) + GO TO 700 + 619 MSG = 'DLSODPK- RTOL(I1) is R1 .lt. 0.0 ' + CALL XERRWD (MSG, 40, 19, 0, 1, I, 0, 1, RTOLI, 0.0D0) + GO TO 700 + 620 MSG = 'DLSODPK- ATOL(I1) is R1 .lt. 0.0 ' + CALL XERRWD (MSG, 40, 20, 0, 1, I, 0, 1, ATOLI, 0.0D0) + GO TO 700 + 621 EWTI = RWORK(LEWT+I-1) + MSG = 'DLSODPK- EWT(I1) is R1 .le. 0.0 ' + CALL XERRWD (MSG, 40, 21, 0, 1, I, 0, 1, EWTI, 0.0D0) + GO TO 700 + 622 MSG='DLSODPK- TOUT(=R1) too close to T(=R2) to start integration.' + CALL XERRWD (MSG, 60, 22, 0, 0, 0, 0, 2, TOUT, T) + GO TO 700 + 623 MSG='DLSODPK- ITASK = I1 and TOUT (=R1) behind TCUR - HU (= R2) ' + CALL XERRWD (MSG, 60, 23, 0, 1, ITASK, 0, 2, TOUT, TP) + GO TO 700 + 624 MSG='DLSODPK- ITASK = 4 or 5 and TCRIT (=R1) behind TCUR (=R2) ' + CALL XERRWD (MSG, 60, 24, 0, 0, 0, 0, 2, TCRIT, TN) + GO TO 700 + 625 MSG='DLSODPK- ITASK = 4 or 5 and TCRIT (=R1) behind TOUT (=R2) ' + CALL XERRWD (MSG, 60, 25, 0, 0, 0, 0, 2, TCRIT, TOUT) + GO TO 700 + 626 MSG = 'DLSODPK- At start of problem, too much accuracy ' + CALL XERRWD (MSG, 50, 26, 0, 0, 0, 0, 0, 0.0D0, 0.0D0) + MSG=' requested for precision of machine.. See TOLSF (=R1) ' + CALL XERRWD (MSG, 60, 26, 0, 0, 0, 0, 1, TOLSF, 0.0D0) + RWORK(14) = TOLSF + GO TO 700 + 627 MSG = 'DLSODPK- Trouble in DINTDY. ITASK = I1, TOUT = R1' + CALL XERRWD (MSG, 50, 27, 0, 1, ITASK, 0, 1, TOUT, 0.0D0) +C + 700 ISTATE = -3 + RETURN +C + 800 MSG = 'DLSODPK- Run aborted.. apparent infinite loop. ' + CALL XERRWD (MSG, 50, 303, 2, 0, 0, 0, 0, 0.0D0, 0.0D0) + RETURN +C----------------------- End of Subroutine DLSODPK --------------------- + END +*DECK DLSODKR + SUBROUTINE DLSODKR (F, NEQ, Y, T, TOUT, ITOL, RTOL, ATOL, ITASK, + 1 ISTATE, IOPT, RWORK, LRW, IWORK, LIW, JAC, PSOL, + 2 MF, G, NG, JROOT) + EXTERNAL F, JAC, PSOL, G + INTEGER NEQ, ITOL, ITASK, ISTATE, IOPT, LRW, IWORK, LIW, MF, + 1 NG, JROOT + DOUBLE PRECISION Y, T, TOUT, RTOL, ATOL, RWORK + DIMENSION NEQ(*), Y(*), RTOL(*), ATOL(*), RWORK(LRW), IWORK(LIW), + 1 JROOT(*) +C----------------------------------------------------------------------- +C This is the 18 November 2003 version of +C DLSODKR: Livermore Solver for Ordinary Differential equations, +C with preconditioned Krylov iteration methods for the +C Newton correction linear systems, and with Rootfinding. +C +C This version is in double precision. +C +C DLSODKR solves the initial value problem for stiff or nonstiff +C systems of first order ODEs, +C dy/dt = f(t,y) , or, in component form, +C dy(i)/dt = f(i) = f(i,t,y(1),y(2),...,y(NEQ)) (i = 1,...,NEQ). +C At the same time, it locates the roots of any of a set of functions +C g(i) = g(i,t,y(1),...,y(NEQ)) (i = 1,...,ng). +C +C----------------------------------------------------------------------- +C Introduction. +C +C This is a modification of the DLSODE package, and differs from it +C in five ways: +C (a) It uses various preconditioned Krylov subspace iteration methods +C for the linear algebraic systems that arise in the case of stiff +C systems. See the introductory notes below. +C (b) It does automatic switching between functional (fixpoint) +C iteration and Newton iteration in the corrector iteration. +C (c) It finds the root of at least one of a set of constraint +C functions g(i) of the independent and dependent variables. +C It finds only those roots for which some g(i), as a function +C of t, changes sign in the interval of integration. +C It then returns the solution at the root, if that occurs +C sooner than the specified stop condition, and otherwise returns +C the solution according the specified stop condition. +C (d) It supplies to JAC an input flag, JOK, which indicates whether +C JAC may (optionally) bypass the evaluation of Jacobian matrix data +C and instead process saved data (with the current value of scalar hl0). +C (e) It contains a new subroutine that calculates the initial step +C size to be attempted. +C +C +C Introduction to the Krylov methods in DLSODKR: +C +C The linear systems that must be solved have the form +C A * x = b , where A = identity - hl0 * (df/dy) . +C Here hl0 is a scalar, and df/dy is the Jacobian matrix of partial +C derivatives of f (NEQ by NEQ). +C +C The particular Krylov method is chosen by setting the second digit, +C MITER, in the method flag MF. +C Currently, the values of MITER have the following meanings: +C +C MITER = 1 means the Scaled Preconditioned Incomplete +C Orthogonalization Method (SPIOM). +C +C 2 means an incomplete version of the preconditioned scaled +C Generalized Minimal Residual method (SPIGMR). +C This is the best choice in general. +C +C 3 means the Preconditioned Conjugate Gradient method (PCG). +C Recommended only when df/dy is symmetric or nearly so. +C +C 4 means the scaled Preconditioned Conjugate Gradient method +C (PCGS). Recommended only when D-inverse * df/dy * D is +C symmetric or nearly so, where D is the diagonal scaling +C matrix with elements 1/EWT(i) (see RTOL/ATOL description). +C +C 9 means that only a user-supplied matrix P (approximating A) +C will be used, with no Krylov iteration done. This option +C allows the user to provide the complete linear system +C solution algorithm, if desired. +C +C The user can apply preconditioning to the linear system A*x = b, +C by means of arbitrary matrices (the preconditioners). +C In the case of SPIOM and SPIGMR, one can apply left and right +C preconditioners P1 and P2, and the basic iterative method is then +C applied to the matrix (P1-inverse)*A*(P2-inverse) instead of to the +C matrix A. The product P1*P2 should be an approximation to matrix A +C such that linear systems with P1 or P2 are easier to solve than with +C A. Preconditioning from the left only or right only means using +C P2 = identity or P1 = identity, respectively. +C In the case of the PCG and PCGS methods, there is only one +C preconditioner matrix P (but it can be the product of more than one). +C It should approximate the matrix A but allow for relatively +C easy solution of linear systems with coefficient matrix P. +C For PCG, P should be positive definite symmetric, or nearly so, +C and for PCGS, the scaled preconditioner D-inverse * P * D +C should be symmetric or nearly so. +C If the Jacobian J = df/dy splits in a natural way into a sum +C J = J1 + J2, then one possible choice of preconditioners is +C P1 = identity - hl0 * J1 and P2 = identity - hl0 * J2 +C provided each of these is easy to solve (or approximately solve). +C +C----------------------------------------------------------------------- +C References: +C 1. Peter N. Brown and Alan C. Hindmarsh, Reduced Storage Matrix +C Methods in Stiff ODE Systems, J. Appl. Math. & Comp., 31 (1989), +C pp. 40-91; also L.L.N.L. Report UCRL-95088, Rev. 1, June 1987. +C 2. Alan C. Hindmarsh, ODEPACK, A Systematized Collection of ODE +C Solvers, in Scientific Computing, R. S. Stepleman et al. (Eds.), +C North-Holland, Amsterdam, 1983, pp. 55-64. +C----------------------------------------------------------------------- +C Authors: Alan C. Hindmarsh and Peter N. Brown +C Center for Applied Scientific Computing, L-561 +C Lawrence Livermore National Laboratory +C Livermore, CA 94551 +C----------------------------------------------------------------------- +C Summary of Usage. +C +C Communication between the user and the DLSODKR package, for normal +C situations, is summarized here. This summary describes only a subset +C of the full set of options available. See the full description for +C details, including optional communication, nonstandard options, +C and instructions for special situations. See also the demonstration +C program distributed with this solver. +C +C A. First provide a subroutine of the form: +C SUBROUTINE F (NEQ, T, Y, YDOT) +C DOUBLE PRECISION T, Y(*), YDOT(*) +C which supplies the vector function f by loading YDOT(i) with f(i). +C +C B. Provide a subroutine of the form: +C SUBROUTINE G (NEQ, T, Y, NG, GOUT) +C DOUBLE PRECISION T, Y(*), GOUT(NG) +C which supplies the vector function g by loading GOUT(i) with +C g(i), the i-th constraint function whose root is sought. +C +C C. Next determine (or guess) whether or not the problem is stiff. +C Stiffness occurs when the Jacobian matrix df/dy has an eigenvalue +C whose real part is negative and large in magnitude, compared to the +C reciprocal of the t span of interest. If the problem is nonstiff, +C use a method flag MF = 10. If it is stiff, MF should be between 21 +C and 24, or possibly 29. MF = 22 is generally the best choice. +C Use 23 or 24 only if symmetry is present. Use MF = 29 if the +C complete linear system solution is to be provided by the user. +C The following four parameters must also be set. +C IWORK(1) = LWP = length of real array WP for preconditioning. +C IWORK(2) = LIWP = length of integer array IWP for preconditioning. +C IWORK(3) = JPRE = preconditioner type flag: +C = 0 for no preconditioning (P1 = P2 = P = identity) +C = 1 for left-only preconditioning (P2 = identity) +C = 2 for right-only preconditioning (P1 = identity) +C = 3 for two-sided preconditioning (and PCG or PCGS) +C IWORK(4) = JACFLG = flag for whether JAC is called. +C = 0 if JAC is not to be called, +C = 1 if JAC is to be called. +C Use JACFLG = 1 if JAC computes any nonconstant data for use in +C preconditioning, such as Jacobian elements. +C The arrays WP and IWP are work arrays under the user's control, +C for use in the routines that perform preconditioning operations. +C +C D. If the problem is stiff, you must supply two routines that deal +C with the preconditioning of the linear systems to be solved. +C These are as follows: +C +C SUBROUTINE JAC (F, NEQ, T, Y, YSV, REWT, FTY,V,HL0,JOK,WP,IWP,IER) +C DOUBLE PRECISION T, Y(*), YSV(*), REWT(*), FTY(*), V(*), HL0,WP(*) +C INTEGER IWP(*) +C This routine must evaluate and preprocess any parts of the +C Jacobian matrix df/dy involved in the preconditioners P1, P2, P. +C The Y and FTY arrays contain the current values of y and f(t,y), +C respectively, and YSV also contains the current value of y. +C The array V is work space of length NEQ. +C JAC must multiply all computed Jacobian elements by the scalar +C -HL0, add the identity matrix, and do any factorization +C operations called for, in preparation for solving linear systems +C with a coefficient matrix of P1, P2, or P. The matrix P1*P2 or P +C should be an approximation to identity - hl0 * (df/dy). +C JAC should return IER = 0 if successful, and IER .ne. 0 if not. +C (If IER .ne. 0, a smaller time step will be tried.) +C JAC may alter Y and V, but not YSV, REWT, FTY, or HL0. +C The JOK argument can be ignored (or see full description below). +C +C SUBROUTINE PSOL (NEQ, T, Y, FTY, WK, HL0, WP, IWP, B, LR, IER) +C DOUBLE PRECISION T, Y(*), FTY(*), WK(*), HL0, WP(*), B(*) +C INTEGER IWP(*) +C This routine must solve a linear system with B as right-hand +C side and one of the preconditioning matrices, P1, P2, or P, as +C coefficient matrix, and return the solution vector in B. +C LR is a flag concerning left vs right preconditioning, input +C to PSOL. PSOL is to use P1 if LR = 1 and P2 if LR = 2. +C In the case of the PCG or PCGS method, LR will be 3, and PSOL +C should solve the system P*x = B with the preconditioner matrix P. +C In the case MF = 29 (no Krylov iteration), LR will be 0, +C and PSOL is to return in B the desired approximate solution +C to A * x = B, where A = identity - hl0 * (df/dy). +C PSOL can use data generated in the JAC routine and stored in +C WP and IWP. WK is a work array of length NEQ. +C The argument HL0 is the current value of the scalar appearing +C in the linear system. If the old value, at the time of the last +C JAC call, is needed, it must have been saved by JAC in WP. +C on return, PSOL should set the error flag IER as follows: +C IER = 0 if PSOL was successful, +C IER .gt. 0 if a recoverable error occurred, meaning that the +C time step will be retried, +C IER .lt. 0 if an unrecoverable error occurred, meaning that the +C solver is to stop immediately. +C +C E. Write a main program which calls Subroutine DLSODKR once for +C each point at which answers are desired. This should also provide +C for possible use of logical unit 6 for output of error messages +C by DLSODKR. On the first call to DLSODKR, supply arguments as +C follows: +C F = name of subroutine for right-hand side vector f. +C This name must be declared External in calling program. +C NEQ = number of first order ODEs. +C Y = array of initial values, of length NEQ. +C T = the initial value of the independent variable. +C TOUT = first point where output is desired (.ne. T). +C ITOL = 1 or 2 according as ATOL (below) is a scalar or array. +C RTOL = relative tolerance parameter (scalar). +C ATOL = absolute tolerance parameter (scalar or array). +C The estimated local error in y(i) will be controlled so as +C to be roughly less (in magnitude) than +C EWT(i) = RTOL*ABS(Y(i)) + ATOL if ITOL = 1, or +C EWT(i) = RTOL*ABS(Y(i)) + ATOL(i) if ITOL = 2. +C Thus the local error test passes if, in each component, +C either the absolute error is less than ATOL (or ATOL(i)), +C or the relative error is less than RTOL. +C Use RTOL = 0.0 for pure absolute error control, and +C use ATOL = 0.0 (or ATOL(i) = 0.0) for pure relative error +C control. Caution: Actual (global) errors may exceed these +C local tolerances, so choose them conservatively. +C ITASK = 1 for normal computation of output values of y at t = TOUT. +C ISTATE = integer flag (input and output). Set ISTATE = 1. +C IOPT = 0 to indicate no optional inputs used. +C RWORK = real work array of length at least: +C 20 + 16*NEQ + 3*NG for MF = 10, +C 45 + 17*NEQ + 3*NG + LWP for MF = 21, +C 61 + 17*NEQ + 3*NG + LWP for MF = 22, +C 20 + 15*NEQ + 3*NG + LWP for MF = 23 or 24, +C 20 + 12*NEQ + 3*NG + LWP for MF = 29. +C LRW = declared length of RWORK (in user's dimension). +C IWORK = integer work array of length at least: +C 30 for MF = 10, +C 35 + LIWP for MF = 21, +C 30 + LIWP for MF = 22, 23, 24, or 29. +C LIW = declared length of IWORK (in user's dimension). +C JAC,PSOL = names of subroutines for preconditioning. +C These names must be declared External in the calling program. +C MF = method flag. Standard values are: +C 10 for nonstiff (Adams) method. +C 21 for stiff (BDF) method, with preconditioned SIOM. +C 22 for stiff method, with preconditioned GMRES method. +C 23 for stiff method, with preconditioned CG method. +C 24 for stiff method, with scaled preconditioned CG method. +C 29 for stiff method, with user's PSOL routine only. +C G = name of subroutine for constraint functions, whose +C roots are desired during the integration. +C This name must be declared External in calling program. +C NG = number of constraint functions g(i). If there are none, +C set NG = 0, and pass a dummy name for G. +C JROOT = integer array of length NG for output of root information. +C See next paragraph. +C Note that the main program must declare arrays Y, RWORK, IWORK, +C JROOT, and possibly ATOL. +C +C F. The output from the first call (or any call) is: +C Y = array of computed values of y(t) vector. +C T = corresponding value of independent variable (normally TOUT). +C ISTATE = 2 or 3 if DLSODKR was successful, negative otherwise. +C 2 means no root was found, and TOUT was reached as desired. +C 3 means a root was found prior to reaching TOUT. +C -1 means excess work done on this call (perhaps wrong MF). +C -2 means excess accuracy requested (tolerances too small). +C -3 means illegal input detected (see printed message). +C -4 means repeated error test failures (check all inputs). +C -5 means repeated convergence failures (perhaps bad JAC +C or PSOL routine supplied or wrong choice of MF or +C tolerances, or this solver is inappropriate). +C -6 means error weight became zero during problem. (Solution +C component i vanished, and ATOL or ATOL(i) = 0.) +C -7 means an unrecoverable error occurred in PSOL. +C JROOT = array showing roots found if ISTATE = 3 on return. +C JROOT(i) = 1 if g(i) has a root at T, or 0 otherwise. +C +C G. To continue the integration after a successful return, proceed +C as follows: +C (a) If ISTATE = 2 on return, reset TOUT and call DLSODKR again. +C (b) If ISTATE = 3 on return, reset ISTATE to 2 and call DLSODKR again. +C In either case, no other parameters need be reset. +C +C----------------------------------------------------------------------- +C----------------------------------------------------------------------- +C Full Description of User Interface to DLSODKR. +C +C The user interface to DLSODKR consists of the following parts. +C +C 1. The call sequence to Subroutine DLSODKR, which is a driver +C routine for the solver. This includes descriptions of both +C the call sequence arguments and of user-supplied routines. +C Following these descriptions is a description of +C optional inputs available through the call sequence, and then +C a description of optional outputs (in the work arrays). +C +C 2. Descriptions of other routines in the DLSODKR package that may be +C (optionally) called by the user. These provide the ability to +C alter error message handling, save and restore the internal +C Common, and obtain specified derivatives of the solution y(t). +C +C 3. Descriptions of Common blocks to be declared in overlay +C or similar environments, or to be saved when doing an interrupt +C of the problem and continued solution later. +C +C 4. Description of two routines in the DLSODKR package, either of +C which the user may replace with his/her own version, if desired. +C These relate to the measurement of errors. +C +C----------------------------------------------------------------------- +C Part 1. Call Sequence. +C +C The call sequence parameters used for input only are +C F, NEQ, TOUT, ITOL, RTOL, ATOL, ITASK, IOPT, LRW, LIW, JAC, PSOL, MF, +C G, and NG, +C that used only for output is JROOT, +C and those used for both input and output are +C Y, T, ISTATE. +C The work arrays RWORK and IWORK are also used for conditional and +C optional inputs and optional outputs. (The term output here refers +C to the return from Subroutine DLSODKR to the user's calling program.) +C +C The legality of input parameters will be thoroughly checked on the +C initial call for the problem, but not checked thereafter unless a +C change in input parameters is flagged by ISTATE = 3 on input. +C +C The descriptions of the call arguments are as follows. +C +C F = the name of the user-supplied subroutine defining the +C ODE system. The system must be put in the first-order +C form dy/dt = f(t,y), where f is a vector-valued function +C of the scalar t and the vector y. Subroutine F is to +C compute the function f. It is to have the form +C SUBROUTINE F (NEQ, T, Y, YDOT) +C DOUBLE PRECISION T, Y(*), YDOT(*) +C where NEQ, T, and Y are input, and the array YDOT = f(t,y) +C is output. Y and YDOT are arrays of length NEQ. +C Subroutine F should not alter Y(1),...,Y(NEQ). +C F must be declared External in the calling program. +C +C Subroutine F may access user-defined quantities in +C NEQ(2),... and/or in Y(NEQ(1)+1),... if NEQ is an array +C (dimensioned in F) and/or Y has length exceeding NEQ(1). +C See the descriptions of NEQ and Y below. +C +C If quantities computed in the F routine are needed +C externally to DLSODKR, an extra call to F should be made +C for this purpose, for consistent and accurate results. +C If only the derivative dy/dt is needed, use DINTDY instead. +C +C NEQ = the size of the ODE system (number of first order +C ordinary differential equations). Used only for input. +C NEQ may be decreased, but not increased, during the problem. +C If NEQ is decreased (with ISTATE = 3 on input), the +C remaining components of Y should be left undisturbed, if +C these are to be accessed in the user-supplied routines. +C +C Normally, NEQ is a scalar, and it is generally referred to +C as a scalar in this user interface description. However, +C NEQ may be an array, with NEQ(1) set to the system size. +C (The DLSODKR package accesses only NEQ(1).) In either case, +C this parameter is passed as the NEQ argument in all calls +C to the user-supplied routines. Hence, if it is an array, +C locations NEQ(2),... may be used to store other integer data +C and pass it to the user-supplied routines. Each such routine +C must include NEQ in a Dimension statement in that case. +C +C Y = a real array for the vector of dependent variables, of +C length NEQ or more. Used for both input and output on the +C first call (ISTATE = 1), and only for output on other calls. +C On the first call, Y must contain the vector of initial +C values. On output, Y contains the computed solution vector, +C evaluated at T. If desired, the Y array may be used +C for other purposes between calls to the solver. +C +C This array is passed as the Y argument in all calls to F, G, +C JAC, and PSOL. Hence its length may exceed NEQ, and +C locations Y(NEQ+1),... may be used to store other real data +C and pass it to the user-supplied routines. +C (The DLSODKR package accesses only Y(1),...,Y(NEQ).) +C +C T = the independent variable. On input, T is used only on the +C first call, as the initial point of the integration. +C On output, after each call, T is the value at which a +C computed solution y is evaluated (usually the same as TOUT). +C If a root was found, T is the computed location of the +C root reached first, on output. +C On an error return, T is the farthest point reached. +C +C TOUT = the next value of t at which a computed solution is desired. +C Used only for input. +C +C When starting the problem (ISTATE = 1), TOUT may be equal +C to T for one call, then should .ne. T for the next call. +C For the initial T, an input value of TOUT .ne. T is used +C in order to determine the direction of the integration +C (i.e. the algebraic sign of the step sizes) and the rough +C scale of the problem. Integration in either direction +C (forward or backward in t) is permitted. +C +C If ITASK = 2 or 5 (one-step modes), TOUT is ignored after +C the first call (i.e. the first call with TOUT .ne. T). +C Otherwise, TOUT is required on every call. +C +C If ITASK = 1, 3, or 4, the values of TOUT need not be +C monotone, but a value of TOUT which backs up is limited +C to the current internal T interval, whose endpoints are +C TCUR - HU and TCUR (see optional outputs, below, for +C TCUR and HU). +C +C ITOL = an indicator for the type of error control. See +C description below under ATOL. Used only for input. +C +C RTOL = a relative error tolerance parameter, either a scalar or +C an array of length NEQ. See description below under ATOL. +C Input only. +C +C ATOL = an absolute error tolerance parameter, either a scalar or +C an array of length NEQ. Input only. +C +C The input parameters ITOL, RTOL, and ATOL determine +C the error control performed by the solver. The solver will +C control the vector E = (E(i)) of estimated local errors +C in y, according to an inequality of the form +C RMS-norm of ( E(i)/EWT(i) ) .le. 1, +C where EWT(i) = RTOL(i)*ABS(Y(i)) + ATOL(i), +C and the RMS-norm (root-mean-square norm) here is +C RMS-norm(v) = SQRT(sum v(i)**2 / NEQ). Here EWT = (EWT(i)) +C is a vector of weights which must always be positive, and +C the values of RTOL and ATOL should all be non-negative. +C The following table gives the types (scalar/array) of +C RTOL and ATOL, and the corresponding form of EWT(i). +C +C ITOL RTOL ATOL EWT(i) +C 1 scalar scalar RTOL*ABS(Y(i)) + ATOL +C 2 scalar array RTOL*ABS(Y(i)) + ATOL(i) +C 3 array scalar RTOL(i)*ABS(Y(i)) + ATOL +C 4 array array RTOL(i)*ABS(Y(i)) + ATOL(i) +C +C When either of these parameters is a scalar, it need not +C be dimensioned in the user's calling program. +C +C If none of the above choices (with ITOL, RTOL, and ATOL +C fixed throughout the problem) is suitable, more general +C error controls can be obtained by substituting +C user-supplied routines for the setting of EWT and/or for +C the norm calculation. See Part 4 below. +C +C If global errors are to be estimated by making a repeated +C run on the same problem with smaller tolerances, then all +C components of RTOL and ATOL (i.e. of EWT) should be scaled +C down uniformly. +C +C ITASK = an index specifying the task to be performed. +C Input only. ITASK has the following values and meanings. +C 1 means normal computation of output values of y(t) at +C t = TOUT (by overshooting and interpolating). +C 2 means take one step only and return. +C 3 means stop at the first internal mesh point at or +C beyond t = TOUT and return. +C 4 means normal computation of output values of y(t) at +C t = TOUT but without overshooting t = TCRIT. +C TCRIT must be input as RWORK(1). TCRIT may be equal to +C or beyond TOUT, but not behind it in the direction of +C integration. This option is useful if the problem +C has a singularity at or beyond t = TCRIT. +C 5 means take one step, without passing TCRIT, and return. +C TCRIT must be input as RWORK(1). +C +C Note: If ITASK = 4 or 5 and the solver reaches TCRIT +C (within roundoff), it will return T = TCRIT (exactly) to +C indicate this (unless ITASK = 4 and TOUT comes before TCRIT, +C in which case answers at T = TOUT are returned first). +C +C ISTATE = an index used for input and output to specify the +C the state of the calculation. +C +C On input, the values of ISTATE are as follows. +C 1 means this is the first call for the problem +C (initializations will be done). See note below. +C 2 means this is not the first call, and the calculation +C is to continue normally, with no change in any input +C parameters except possibly TOUT and ITASK. +C (If ITOL, RTOL, and/or ATOL are changed between calls +C with ISTATE = 2, the new values will be used but not +C tested for legality.) +C 3 means this is not the first call, and the +C calculation is to continue normally, but with +C a change in input parameters other than +C TOUT and ITASK. Changes are allowed in +C NEQ, ITOL, RTOL, ATOL, IOPT, LRW, LIW, MF, +C and any of the optional inputs except H0. +C In addition, immediately following a return with +C ISTATE = 3 (root found), NG and G may be changed. +C (But changing NG from 0 to .gt. 0 is not allowed.) +C Note: A preliminary call with TOUT = T is not counted +C as a first call here, as no initialization or checking of +C input is done. (Such a call is sometimes useful for the +C purpose of outputting the initial conditions.) +C Thus the first call for which TOUT .ne. T requires +C ISTATE = 1 on input. +C +C On output, ISTATE has the following values and meanings. +C 1 means nothing was done; TOUT = T and ISTATE = 1 on input. +C 2 means the integration was performed successfully. +C 3 means the integration was successful, and one or more +C roots were found before satisfying the stop condition +C specified by ITASK. See JROOT. +C -1 means an excessive amount of work (more than MXSTEP +C steps) was done on this call, before completing the +C requested task, but the integration was otherwise +C successful as far as T. (MXSTEP is an optional input +C and is normally 500.) To continue, the user may +C simply reset ISTATE to a value .gt. 1 and call again +C (the excess work step counter will be reset to 0). +C In addition, the user may increase MXSTEP to avoid +C this error return (see below on optional inputs). +C -2 means too much accuracy was requested for the precision +C of the machine being used. This was detected before +C completing the requested task, but the integration +C was successful as far as T. To continue, the tolerance +C parameters must be reset, and ISTATE must be set +C to 3. The optional output TOLSF may be used for this +C purpose. (Note: If this condition is detected before +C taking any steps, then an illegal input return +C (ISTATE = -3) occurs instead.) +C -3 means illegal input was detected, before taking any +C integration steps. See written message for details. +C Note: If the solver detects an infinite loop of calls +C to the solver with illegal input, it will cause +C the run to stop. +C -4 means there were repeated error test failures on +C one attempted step, before completing the requested +C task, but the integration was successful as far as T. +C The problem may have a singularity, or the input +C may be inappropriate. +C -5 means there were repeated convergence test failures on +C one attempted step, before completing the requested +C task, but the integration was successful as far as T. +C -6 means EWT(i) became zero for some i during the +C integration. Pure relative error control (ATOL(i)=0.0) +C was requested on a variable which has now vanished. +C The integration was successful as far as T. +C -7 means the PSOL routine returned an unrecoverable error +C flag (IER .lt. 0). The integration was successful as +C far as T. +C +C Note: Since the normal output value of ISTATE is 2, +C it does not need to be reset for normal continuation. +C Also, since a negative input value of ISTATE will be +C regarded as illegal, a negative output value requires the +C user to change it, and possibly other inputs, before +C calling the solver again. +C +C IOPT = an integer flag to specify whether or not any optional +C inputs are being used on this call. Input only. +C The optional inputs are listed separately below. +C IOPT = 0 means no optional inputs are being used. +C Default values will be used in all cases. +C IOPT = 1 means one or more optional inputs are being used. +C +C RWORK = a real working array (double precision). +C The length of RWORK must be at least +C 20 + NYH*(MAXORD+1) + 3*NEQ + 3*NG + LENLS + LWP where +C NYH = the initial value of NEQ, +C MAXORD = 12 (if METH = 1) or 5 (if METH = 2) (unless a +C smaller value is given as an optional input), +C LENLS = length of work space for linear system (Krylov) +C method, excluding preconditioning: +C LENLS = 0 if MITER = 0, +C LENLS = NEQ*(MAXL+3) + MAXL**2 if MITER = 1, +C LENLS = NEQ*(MAXL+3+MIN(1,MAXL-KMP)) +C + (MAXL+3)*MAXL + 1 if MITER = 2, +C LENLS = 6*NEQ if MITER = 3 or 4, +C LENLS = 3*NEQ if MITER = 9. +C (See the MF description for METH and MITER, and the +C list of optional inputs for MAXL and KMP.) +C LWP = length of real user work space for preconditioning +C (see JAC/PSOL). +C Thus if default values are used and NEQ is constant, +C this length is: +C 20 + 16*NEQ + 3*NG for MF = 10, +C 45 + 24*NEQ + 3*NG + LWP for MF = 11, +C 61 + 24*NEQ + 3*NG + LWP for MF = 12, +C 20 + 22*NEQ + 3*NG + LWP for MF = 13 or 14, +C 20 + 19*NEQ + 3*NG + LWP for MF = 19, +C 20 + 9*NEQ + 3*NG for MF = 20, +C 45 + 17*NEQ + 3*NG + LWP for MF = 21, +C 61 + 17*NEQ + 3*NG + LWP for MF = 22, +C 20 + 15*NEQ + 3*NG + LWP for MF = 23 or 24, +C 20 + 12*NEQ + 3*NG + LWP for MF = 29. +C The first 20 words of RWORK are reserved for conditional +C and optional inputs and optional outputs. +C +C The following word in RWORK is a conditional input: +C RWORK(1) = TCRIT = critical value of t which the solver +C is not to overshoot. Required if ITASK is +C 4 or 5, and ignored otherwise. (See ITASK.) +C +C LRW = the length of the array RWORK, as declared by the user. +C (This will be checked by the solver.) +C +C IWORK = an integer work array. The length of IWORK must be at least +C 30 if MITER = 0 (MF = 10 or 20), +C 30 + MAXL + LIWP if MITER = 1 (MF = 11, 21), +C 30 + LIWP if MITER = 2, 3, 4, or 9. +C MAXL = 5 unless a different optional input value is given. +C LIWP = length of integer user work space for preconditioning +C (see conditional input list following). +C The first few words of IWORK are used for conditional and +C optional inputs and optional outputs. +C +C The following 4 words in IWORK are conditional inputs, +C required if MITER .ge. 1: +C IWORK(1) = LWP = length of real array WP for use in +C preconditioning (part of RWORK array). +C IWORK(2) = LIWP = length of integer array IWP for use in +C preconditioning (part of IWORK array). +C The arrays WP and IWP are work arrays under the +C user's control, for use in the routines that +C perform preconditioning operations (JAC and PSOL). +C IWORK(3) = JPRE = preconditioner type flag: +C = 0 for no preconditioning (P1 = P2 = P = identity) +C = 1 for left-only preconditioning (P2 = identity) +C = 2 for right-only preconditioning (P1 = identity) +C = 3 for two-sided preconditioning (and PCG or PCGS) +C IWORK(4) = JACFLG = flag for whether JAC is called. +C = 0 if JAC is not to be called, +C = 1 if JAC is to be called. +C Use JACFLG = 1 if JAC computes any nonconstant +C data needed in preconditioning operations, +C such as some of the Jacobian elements. +C +C LIW = the length of the array IWORK, as declared by the user. +C (This will be checked by the solver.) +C +C Note: The work arrays must not be altered between calls to DLSODKR +C for the same problem, except possibly for the conditional and +C optional inputs, and except for the last 3*NEQ words of RWORK. +C The latter space is used for internal scratch space, and so is +C available for use by the user outside DLSODKR between calls, if +C desired (but not for use by any of the user-supplied routines). +C +C JAC = the name of the user-supplied routine to compute any +C Jacobian elements (or approximations) involved in the +C matrix preconditioning operations (MITER .ge. 1). +C It is to have the form +C SUBROUTINE JAC (F, NEQ, T, Y, YSV, REWT, FTY, V, +C 1 HL0, JOK, WP, IWP, IER) +C DOUBLE PRECISION T, Y(*), YSV(*), REWT(*), FTY(*), V(*), +C 1 HL0, WP(*) +C INTEGER IWP(*) +C This routine must evaluate and preprocess any parts of the +C Jacobian matrix df/dy used in the preconditioners P1, P2, P. +C The Y and FTY arrays contain the current values of y and +C f(t,y), respectively, and the YSV array also contains +C the current y vector. The array V is work space of length +C NEQ for use by JAC. REWT is the array of reciprocal error +C weights (1/EWT). JAC must multiply all computed Jacobian +C elements by the scalar -HL0, add the identity matrix, and do +C any factorization operations called for, in preparation +C for solving linear systems with a coefficient matrix of +C P1, P2, or P. The matrix P1*P2 or P should be an +C approximation to identity - hl0 * (df/dy). JAC should +C return IER = 0 if successful, and IER .ne. 0 if not. +C (If IER .ne. 0, a smaller time step will be tried.) +C The arrays WP (of length LWP) and IWP (of length LIWP) +C are for use by JAC and PSOL for work space and for storage +C of data needed for the solution of the preconditioner +C linear systems. Their lengths and contents are under the +C user's control. +C The argument JOK is an input flag for optional use +C by JAC in deciding whether to recompute Jacobian elements +C or use saved values. If JOK = -1, then JAC must compute +C any relevant Jacobian elements (or approximations) used in +C the preconditioners. Optionally, JAC may also save these +C elements for later reuse. If JOK = 1, the integrator has +C made a judgement (based on the convergence history and the +C value of HL0) that JAC need not recompute Jacobian elements, +C but instead use saved values, and the current value of HL0, +C to reconstruct the preconditioner matrices, followed by +C any required factorizations. This may be cost-effective if +C Jacobian elements are costly and storage is available. +C JAC may alter Y and V, but not YSV, REWT, FTY, or HL0. +C JAC must be declared External in the calling program. +C Subroutine JAC may access user-defined quantities in +C NEQ(2),... and/or in Y(NEQ(1)+1),... if NEQ is an array +C (dimensioned in JAC) and/or Y has length exceeding NEQ(1). +C See the descriptions of NEQ and Y above. +C +C PSOL = the name of the user-supplied routine for the +C solution of preconditioner linear systems. +C It is to have the form +C SUBROUTINE PSOL (NEQ, T, Y, FTY, WK,HL0, WP,IWP, B, LR,IER) +C DOUBLE PRECISION T, Y(*), FTY(*), WK(*), HL0, WP(*), B(*) +C INTEGER IWP(*) +C This routine must solve a linear system with B as right-hand +C side and one of the preconditioning matrices, P1, P2, or P, +C as coefficient matrix, and return the solution vector in B. +C LR is a flag concerning left vs right preconditioning, input +C to PSOL. PSOL is to use P1 if LR = 1 and P2 if LR = 2. +C In the case of the PCG or PCGS method, LR will be 3, and PSOL +C should solve the system P*x = B with the preconditioner P. +C In the case MITER = 9 (no Krylov iteration), LR will be 0, +C and PSOL is to return in B the desired approximate solution +C to A * x = B, where A = identity - hl0 * (df/dy). +C PSOL can use data generated in the JAC routine and stored in +C WP and IWP. +C The Y and FTY arrays contain the current values of y and +C f(t,y), respectively. The array WK is work space of length +C NEQ for use by PSOL. +C The argument HL0 is the current value of the scalar appearing +C in the linear system. If the old value, as of the last +C JAC call, is needed, it must have been saved by JAC in WP. +C On return, PSOL should set the error flag IER as follows: +C IER = 0 if PSOL was successful, +C IER .gt. 0 on a recoverable error, meaning that the +C time step will be retried, +C IER .lt. 0 on an unrecoverable error, meaning that the +C solver is to stop immediately. +C PSOL may not alter Y, FTY, or HL0. +C PSOL must be declared External in the calling program. +C Subroutine PSOL may access user-defined quantities in +C NEQ(2),... and Y(NEQ(1)+1),... if NEQ is an array +C (dimensioned in PSOL) and/or Y has length exceeding NEQ(1). +C See the descriptions of NEQ and Y above. +C +C MF = the method flag. Used only for input. The legal values of +C MF are 10, 11, 12, 13, 14, 19, 20, 21, 22, 23, 24, and 29. +C MF has decimal digits METH and MITER: MF = 10*METH + MITER. +C METH indicates the basic linear multistep method: +C METH = 1 means the implicit Adams method. +C METH = 2 means the method based on Backward +C Differentiation Formulas (BDFs). +C MITER indicates the corrector iteration method: +C MITER = 0 means functional iteration (no linear system +C is involved). +C MITER = 1 means Newton iteration with Scaled Preconditioned +C Incomplete Orthogonalization Method (SPIOM) +C for the linear systems. +C MITER = 2 means Newton iteration with Scaled Preconditioned +C Incomplete Generalized Minimal Residual method +C (SPIGMR) for the linear systems. +C MITER = 3 means Newton iteration with Preconditioned +C Conjugate Gradient method (PCG) +C for the linear systems. +C MITER = 4 means Newton iteration with scaled preconditioned +C Conjugate Gradient method (PCGS) +C for the linear systems. +C MITER = 9 means Newton iteration with only the +C user-supplied PSOL routine called (no Krylov +C iteration) for the linear systems. +C JPRE is ignored, and PSOL is called with LR = 0. +C See comments in the introduction about the choice of MITER. +C If MITER .ge. 1, the user must supply routines JAC and PSOL +C (the names are arbitrary) as described above. +C For MITER = 0, a dummy argument can be used. +C +C G = the name of subroutine for constraint functions, whose +C roots are desired during the integration. It is to have +C the form +C SUBROUTINE G (NEQ, T, Y, NG, GOUT) +C DOUBLE PRECISION T, Y(*), GOUT(NG) +C where NEQ, T, Y, and NG are input, and the array GOUT +C is output. NEQ, T, and Y have the same meaning as in +C the F routine, and GOUT is an array of length NG. +C For i = 1,...,NG, this routine is to load into GOUT(i) +C the value at (t,y) of the i-th constraint function g(i). +C DLSODKR will find roots of the g(i) of odd multiplicity +C (i.e. sign changes) as they occur during the integration. +C G must be declared External in the calling program. +C +C Caution: Because of numerical errors in the functions +C g(i) due to roundoff and integration error, DLSODKR may +C return false roots, or return the same root at two or more +C nearly equal values of t. If such false roots are +C suspected, the user should consider smaller error tolerances +C and/or higher precision in the evaluation of the g(i). +C +C If a root of some g(i) defines the end of the problem, +C the input to DLSODKR should nevertheless allow integration +C to a point slightly past that root, so that DLSODKR can +C locate the root by interpolation. +C +C Subroutine G may access user-defined quantities in +C NEQ(2),... and Y(NEQ(1)+1),... if NEQ is an array +C (dimensioned in G) and/or Y has length exceeding NEQ(1). +C See the descriptions of NEQ and Y above. +C +C NG = number of constraint functions g(i). If there are none, +C set NG = 0, and pass a dummy name for G. +C +C JROOT = integer array of length NG. Used only for output. +C On a return with ISTATE = 3 (one or more roots found), +C JROOT(i) = 1 if g(i) has a root at t, or JROOT(i) = 0 if not. +C----------------------------------------------------------------------- +C Optional Inputs. +C +C The following is a list of the optional inputs provided for in the +C call sequence. (See also Part 2.) For each such input variable, +C this table lists its name as used in this documentation, its +C location in the call sequence, its meaning, and the default value. +C The use of any of these inputs requires IOPT = 1, and in that +C case all of these inputs are examined. A value of zero for any +C of these optional inputs will cause the default value to be used. +C Thus to use a subset of the optional inputs, simply preload +C locations 5 to 10 in RWORK and IWORK to 0.0 and 0 respectively, and +C then set those of interest to nonzero values. +C +C Name Location Meaning and Default Value +C +C H0 RWORK(5) the step size to be attempted on the first step. +C The default value is determined by the solver. +C +C HMAX RWORK(6) the maximum absolute step size allowed. +C The default value is infinite. +C +C HMIN RWORK(7) the minimum absolute step size allowed. +C The default value is 0. (This lower bound is not +C enforced on the final step before reaching TCRIT +C when ITASK = 4 or 5.) +C +C DELT RWORK(8) convergence test constant in Krylov iteration +C algorithm. The default is .05. +C +C MAXORD IWORK(5) the maximum order to be allowed. The default +C value is 12 if METH = 1, and 5 if METH = 2. +C If MAXORD exceeds the default value, it will +C be reduced to the default value. +C If MAXORD is changed during the problem, it may +C cause the current order to be reduced. +C +C MXSTEP IWORK(6) maximum number of (internally defined) steps +C allowed during one call to the solver. +C The default value is 500. +C +C MXHNIL IWORK(7) maximum number of messages printed (per problem) +C warning that T + H = T on a step (H = step size). +C This must be positive to result in a non-default +C value. The default value is 10. +C +C MAXL IWORK(8) maximum number of iterations in the SPIOM, SPIGMR, +C PCG, or PCGS algorithm (.le. NEQ). +C The default is MAXL = MIN(5,NEQ). +C +C KMP IWORK(9) number of vectors on which orthogonalization +C is done in SPIOM or SPIGMR algorithm (.le. MAXL). +C The default is KMP = MAXL. +C Note: When KMP .lt. MAXL and MF = 22, the length +C of RWORK must be defined accordingly. See +C the definition of RWORK above. +C----------------------------------------------------------------------- +C Optional Outputs. +C +C As optional additional output from DLSODKR, the variables listed +C below are quantities related to the performance of DLSODKR +C which are available to the user. These are communicated by way of +C the work arrays, but also have internal mnemonic names as shown. +C Except where stated otherwise, all of these outputs are defined +C on any successful return from DLSODKR, and on any return with +C ISTATE = -1, -2, -4, -5, -6, or -7. On an illegal input return +C (ISTATE = -3), they will be unchanged from their existing values +C (if any), except possibly for TOLSF, LENRW, and LENIW. +C On any error return, outputs relevant to the error will be defined, +C as noted below. +C +C Name Location Meaning +C +C HU RWORK(11) the step size in t last used (successfully). +C +C HCUR RWORK(12) the step size to be attempted on the next step. +C +C TCUR RWORK(13) the current value of the independent variable +C which the solver has actually reached, i.e. the +C current internal mesh point in t. On output, TCUR +C will always be at least as far as the argument +C T, but may be farther (if interpolation was done). +C +C TOLSF RWORK(14) a tolerance scale factor, greater than 1.0, +C computed when a request for too much accuracy was +C detected (ISTATE = -3 if detected at the start of +C the problem, ISTATE = -2 otherwise). If ITOL is +C left unaltered but RTOL and ATOL are uniformly +C scaled up by a factor of TOLSF for the next call, +C then the solver is deemed likely to succeed. +C (The user may also ignore TOLSF and alter the +C tolerance parameters in any other way appropriate.) +C +C NGE IWORK(10) the number of g evaluations for the problem so far. +C +C NST IWORK(11) the number of steps taken for the problem so far. +C +C NFE IWORK(12) the number of f evaluations for the problem so far. +C +C NPE IWORK(13) the number of calls to JAC so far (for evaluation +C of preconditioners). +C +C NQU IWORK(14) the method order last used (successfully). +C +C NQCUR IWORK(15) the order to be attempted on the next step. +C +C IMXER IWORK(16) the index of the component of largest magnitude in +C the weighted local error vector ( E(i)/EWT(i) ), +C on an error return with ISTATE = -4 or -5. +C +C LENRW IWORK(17) the length of RWORK actually required. +C This is defined on normal returns and on an illegal +C input return for insufficient storage. +C +C LENIW IWORK(18) the length of IWORK actually required. +C This is defined on normal returns and on an illegal +C input return for insufficient storage. +C +C NNI IWORK(19) number of nonlinear iterations so far (each of +C which calls an iterative linear solver). +C +C NLI IWORK(20) number of linear iterations so far. +C Note: A measure of the success of algorithm is +C the average number of linear iterations per +C nonlinear iteration, given by NLI/NNI. +C If this is close to MAXL, MAXL may be too small. +C +C NPS IWORK(21) number of preconditioning solve operations +C (PSOL calls) so far. +C +C NCFN IWORK(22) number of convergence failures of the nonlinear +C (Newton) iteration so far. +C Note: A measure of success is the overall +C rate of nonlinear convergence failures, NCFN/NST. +C +C NCFL IWORK(23) number of convergence failures of the linear +C iteration so far. +C Note: A measure of success is the overall +C rate of linear convergence failures, NCFL/NNI. +C +C NSFI IWORK(24) number of functional iteration steps so far. +C Note: A measure of the extent to which the +C problem is nonstiff is the ratio NSFI/NST. +C +C NJEV IWORK(25) number of JAC calls with JOK = -1 so far +C (number of evaluations of Jacobian data). +C +C The following two arrays are segments of the RWORK array which +C may also be of interest to the user as optional outputs. +C For each array, the table below gives its internal name, +C its base address in RWORK, and its description. +C +C Name Base Address Description +C +C YH 21 + 3*NG the Nordsieck history array, of size NYH by +C (NQCUR + 1), where NYH is the initial value +C of NEQ. For j = 0,1,...,NQCUR, column j+1 +C of YH contains HCUR**j/factorial(j) times +C the j-th derivative of the interpolating +C polynomial currently representing the solution, +C evaluated at t = TCUR. +C +C ACOR LENRW-NEQ+1 array of size NEQ used for the accumulated +C corrections on each step, scaled on output +C to represent the estimated local error in y +C on the last step. This is the vector E in +C the description of the error control. It is +C defined only on a successful return from +C DLSODKR. +C +C----------------------------------------------------------------------- +C Part 2. Other Routines Callable. +C +C The following are optional calls which the user may make to +C gain additional capabilities in conjunction with DLSODKR. +C (The routines XSETUN and XSETF are designed to conform to the +C SLATEC error handling package.) +C +C Form of Call Function +C CALL XSETUN(LUN) Set the logical unit number, LUN, for +C output of messages from DLSODKR, if +C the default is not desired. +C The default value of LUN is 6. +C +C CALL XSETF(MFLAG) Set a flag to control the printing of +C messages by DLSODKR. +C MFLAG = 0 means do not print. (Danger: +C This risks losing valuable information.) +C MFLAG = 1 means print (the default). +C +C Either of the above calls may be made at +C any time and will take effect immediately. +C +C CALL DSRCKR(RSAV,ISAV,JOB) saves and restores the contents of +C the internal Common blocks used by +C DLSODKR (see Part 3 below). +C RSAV must be a real array of length 228 +C or more, and ISAV must be an integer +C array of length 63 or more. +C JOB=1 means save Common into RSAV/ISAV. +C JOB=2 means restore Common from RSAV/ISAV. +C DSRCKR is useful if one is +C interrupting a run and restarting +C later, or alternating between two or +C more problems solved with DLSODKR. +C +C CALL DINTDY(,,,,,) Provide derivatives of y, of various +C (see below) orders, at a specified point t, if +C desired. It may be called only after +C a successful return from DLSODKR. +C +C The detailed instructions for using DINTDY are as follows. +C The form of the call is: +C +C LYH = 21 + 3*NG +C CALL DINTDY (T, K, RWORK(LYH), NYH, DKY, IFLAG) +C +C The input parameters are: +C +C T = value of independent variable where answers are desired +C (normally the same as the T last returned by DLSODKR). +C For valid results, T must lie between TCUR - HU and TCUR. +C (See optional outputs for TCUR and HU.) +C K = integer order of the derivative desired. K must satisfy +C 0 .le. K .le. NQCUR, where NQCUR is the current order +C (see optional outputs). The capability corresponding +C to K = 0, i.e. computing y(T), is already provided +C by DLSODKR directly. Since NQCUR .ge. 1, the first +C derivative dy/dt is always available with DINTDY. +C LYH = 21 + 3*NG = base address in RWORK of the history array YH. +C NYH = column length of YH, equal to the initial value of NEQ. +C +C The output parameters are: +C +C DKY = a real array of length NEQ containing the computed value +C of the K-th derivative of y(t). +C IFLAG = integer flag, returned as 0 if K and T were legal, +C -1 if K was illegal, and -2 if T was illegal. +C On an error return, a message is also written. +C----------------------------------------------------------------------- +C Part 3. Common Blocks. +C +C If DLSODKR is to be used in an overlay situation, the user +C must declare, in the primary overlay, the variables in: +C (1) the call sequence to DLSODKR, and +C (2) the four internal Common blocks +C /DLS001/ of length 255 (218 double precision words +C followed by 37 integer words), +C /DLS002/ of length 5 (1 double precision word +C followed by 4 integer words), +C /DLPK01/ of length 17 (4 double precision words +C followed by 13 integer words), +C /DLSR01/ of length 14 (5 double precision words +C followed by 9 integer words). +C +C If DLSODKR is used on a system in which the contents of internal +C Common blocks are not preserved between calls, the user should +C declare the above Common blocks in the calling program to insure +C that their contents are preserved. +C +C If the solution of a given problem by DLSODKR is to be interrupted +C and then later continued, such as when restarting an interrupted run +C or alternating between two or more problems, the user should save, +C following the return from the last DLSODKR call prior to the +C interruption, the contents of the call sequence variables and the +C internal Common blocks, and later restore these values before the +C next DLSODKR call for that problem. To save and restore the Common +C blocks, use Subroutine DSRCKR (see Part 2 above). +C +C----------------------------------------------------------------------- +C Part 4. Optionally Replaceable Solver Routines. +C +C Below are descriptions of two routines in the DLSODKR package which +C relate to the measurement of errors. Either routine can be +C replaced by a user-supplied version, if desired. However, since such +C a replacement may have a major impact on performance, it should be +C done only when absolutely necessary, and only with great caution. +C (Note: The means by which the package version of a routine is +C superseded by the user's version may be system-dependent.) +C +C (a) DEWSET. +C The following subroutine is called just before each internal +C integration step, and sets the array of error weights, EWT, as +C described under ITOL/RTOL/ATOL above: +C SUBROUTINE DEWSET (NEQ, ITOL, RTOL, ATOL, YCUR, EWT) +C where NEQ, ITOL, RTOL, and ATOL are as in the DLSODKR call sequence, +C YCUR contains the current dependent variable vector, and +C EWT is the array of weights set by DEWSET. +C +C If the user supplies this subroutine, it must return in EWT(i) +C (i = 1,...,NEQ) a positive quantity suitable for comparing errors +C in y(i) to. The EWT array returned by DEWSET is passed to the DVNORM +C routine (see below), and also used by DLSODKR in the computation +C of the optional output IMXER, the diagonal Jacobian approximation, +C and the increments for difference quotient Jacobians. +C +C In the user-supplied version of DEWSET, it may be desirable to use +C the current values of derivatives of y. Derivatives up to order NQ +C are available from the history array YH, described above under +C optional outputs. In DEWSET, YH is identical to the YCUR array, +C extended to NQ + 1 columns with a column length of NYH and scale +C factors of H**j/factorial(j). On the first call for the problem, +C given by NST = 0, NQ is 1 and H is temporarily set to 1.0. +C NYH is the initial value of NEQ. The quantities NQ, H, and NST +C can be obtained by including in DEWSET the statements: +C DOUBLE PRECISION RLS +C COMMON /DLS001/ RLS(218),ILS(37) +C NQ = ILS(33) +C NST = ILS(34) +C H = RLS(212) +C Thus, for example, the current value of dy/dt can be obtained as +C YCUR(NYH+i)/H (i=1,...,NEQ) (and the division by H is +C unnecessary when NST = 0). +C +C (b) DVNORM. +C The following is a real function routine which computes the weighted +C root-mean-square norm of a vector v: +C D = DVNORM (N, V, W) +C where: +C N = the length of the vector, +C V = real array of length N containing the vector, +C W = real array of length N containing weights, +C D = SQRT( (1/N) * sum(V(i)*W(i))**2 ). +C DVNORM is called with N = NEQ and with W(i) = 1.0/EWT(i), where +C EWT is as set by Subroutine DEWSET. +C +C If the user supplies this function, it should return a non-negative +C value of DVNORM suitable for use in the error control in DLSODKR. +C None of the arguments should be altered by DVNORM. +C For example, a user-supplied DVNORM routine might: +C -substitute a max-norm of (V(i)*W(i)) for the RMS-norm, or +C -ignore some components of V in the norm, with the effect of +C suppressing the error control on those components of y. +C----------------------------------------------------------------------- +C +C***REVISION HISTORY (YYYYMMDD) +C 19900117 DATE WRITTEN +C 19900503 Added iteration switching (functional/Newton). +C 19900802 Added flag for Jacobian-saving in user preconditioner. +C 19900910 Added new initial stepsize routine LHIN. +C 19901019 Corrected LHIN - y array restored. +C 19910909 Changed names STOPK to STOKA, PKSET to SETPK; +C removed unused variables in driver declarations; +C minor corrections to main prologue. +C 20010425 Major update: convert source lines to upper case; +C added *DECK lines; changed from 1 to * in dummy dimensions; +C changed names R1MACH/D1MACH to RUMACH/DUMACH; +C renamed routines for uniqueness across single/double prec.; +C converted intrinsic names to generic form; +C removed ILLIN and NTREP (data loaded) from Common; +C removed all 'own' variables from Common; +C changed error messages to quoted strings; +C replaced XERRWV/XERRWD with 1993 revised version; +C converted prologues, comments, error messages to mixed case; +C numerous corrections to prologues and internal comments. +C 20010507 Converted single precision source to double precision. +C 20020502 Corrected declarations in descriptions of user routines. +C 20030603 Corrected duplicate type declaration for DUMACH. +C 20031105 Restored 'own' variables to Common blocks, to enable +C interrupt/restart feature. +C 20031112 Added SAVE statements for data-loaded constants. +C 20031117 Changed internal name NPE to NJE. +C +C----------------------------------------------------------------------- +C Other routines in the DLSODKR package. +C +C In addition to Subroutine DLSODKR, the DLSODKR package includes the +C following subroutines and function routines: +C DLHIN calculates a step size to be attempted initially. +C DRCHEK does preliminary checking for roots, and serves as an +C interface between Subroutine DLSODKR and Subroutine DROOTS. +C DROOTS finds the leftmost root of a set of functions. +C DINTDY computes an interpolated value of the y vector at t = TOUT. +C DEWSET sets the error weight vector EWT before each step. +C DVNORM computes the weighted RMS-norm of a vector. +C DSTOKA is the core integrator, which does one step of the +C integration and the associated error control. +C DCFODE sets all method coefficients and test constants. +C DSETPK interfaces between DSTOKA and the JAC routine. +C DSOLPK manages solution of linear system in Newton iteration. +C DSPIOM performs the SPIOM algorithm. +C DATV computes a scaled, preconditioned product (I-hl0*J)*v. +C DORTHOG orthogonalizes a vector against previous basis vectors. +C DHEFA generates an LU factorization of a Hessenberg matrix. +C DHESL solves a Hessenberg square linear system. +C DSPIGMR performs the SPIGMR algorithm. +C DHEQR generates a QR factorization of a Hessenberg matrix. +C DHELS finds the least squares solution of a Hessenberg system. +C DPCG performs preconditioned conjugate gradient algorithm (PCG). +C DPCGS performs the PCGS algorithm. +C DATP computes the product A*p, where A = I - hl0*df/dy. +C DUSOL interfaces to the user's PSOL routine (MITER = 9). +C DSRCKR is a user-callable routine to save and restore +C the contents of the internal Common blocks. +C DAXPY, DCOPY, DDOT, DNRM2, and DSCAL are basic linear +C algebra modules (from the BLAS collection). +C DUMACH computes the unit roundoff in a machine-independent manner. +C XERRWD, XSETUN, XSETF, IXSAV, and IUMACH handle the printing of all +C error messages and warnings. XERRWD is machine-dependent. +C Note: DVNORM, DDOT, DNRM2, DUMACH, IXSAV, and IUMACH are function +C routines. All the others are subroutines. +C +C----------------------------------------------------------------------- + DOUBLE PRECISION DUMACH, DVNORM + INTEGER INIT, MXSTEP, MXHNIL, NHNIL, NSLAST, NYH, IOWNS, + 1 ICF, IERPJ, IERSL, JCUR, JSTART, KFLAG, L, + 2 LYH, LEWT, LACOR, LSAVF, LWM, LIWM, METH, MITER, + 3 MAXORD, MAXCOR, MSBP, MXNCF, N, NQ, NST, NFE, NJE, NQU + INTEGER NEWT, NSFI, NSLJ, NJEV + INTEGER LG0, LG1, LGX, IOWNR3, IRFND, ITASKC, NGC, NGE + INTEGER JPRE, JACFLG, LOCWP, LOCIWP, LSAVX, KMP, MAXL, MNEWT, + 1 NNI, NLI, NPS, NCFN, NCFL + INTEGER I, I1, I2, IER, IFLAG, IMXER, KGO, LF0, + 1 LENIW, LENIWK, LENRW, LENWM, LENWK, LIWP, LWP, MORD, MXHNL0, + 2 MXSTP0, NCFN0, NCFL0, NITER, NLI0, NNI0, NNID, NSTD, NWARN + INTEGER IRFP, IRT, LENYH, LYHNEW + DOUBLE PRECISION ROWNS, + 1 CCMAX, EL0, H, HMIN, HMXI, HU, RC, TN, UROUND + DOUBLE PRECISION STIFR + DOUBLE PRECISION ROWNR3, T0, TLAST, TOUTC + DOUBLE PRECISION DELT, EPCON, SQRTN, RSQRTN + DOUBLE PRECISION ATOLI, AVDIM, BIG, EWTI, H0, HMAX, HMX, RCFL, + 1 RCFN, RH, RTOLI, TCRIT, TNEXT, TOLSF, TP, SIZE + DIMENSION MORD(2) + LOGICAL IHIT, LAVD, LCFN, LCFL, LWARN + CHARACTER*60 MSG + SAVE MORD, MXSTP0, MXHNL0 +C----------------------------------------------------------------------- +C The following four internal Common blocks contain +C (a) variables which are local to any subroutine but whose values must +C be preserved between calls to the routine ("own" variables), and +C (b) variables which are communicated between subroutines. +C The block DLS001 is declared in subroutines DLSODKR, DINTDY, +C DSTOKA, DSOLPK, and DATV. +C The block DLS002 is declared in subroutines DLSODKR and DSTOKA. +C The block DLSR01 is declared in subroutines DLSODKR, DRCHEK, DROOTS. +C The block DLPK01 is declared in subroutines DLSODKR, DSTOKA, DSETPK, +C and DSOLPK. +C Groups of variables are replaced by dummy arrays in the Common +C declarations in routines where those variables are not used. +C----------------------------------------------------------------------- + COMMON /DLS001/ ROWNS(209), + 1 CCMAX, EL0, H, HMIN, HMXI, HU, RC, TN, UROUND, + 2 INIT, MXSTEP, MXHNIL, NHNIL, NSLAST, NYH, IOWNS(6), + 3 ICF, IERPJ, IERSL, JCUR, JSTART, KFLAG, L, + 4 LYH, LEWT, LACOR, LSAVF, LWM, LIWM, METH, MITER, + 5 MAXORD, MAXCOR, MSBP, MXNCF, N, NQ, NST, NFE, NJE, NQU +C + COMMON /DLS002/ STIFR, NEWT, NSFI, NSLJ, NJEV +C + COMMON /DLSR01/ ROWNR3(2), T0, TLAST, TOUTC, + 1 LG0, LG1, LGX, IOWNR3(2), IRFND, ITASKC, NGC, NGE +C + COMMON /DLPK01/ DELT, EPCON, SQRTN, RSQRTN, + 1 JPRE, JACFLG, LOCWP, LOCIWP, LSAVX, KMP, MAXL, MNEWT, + 2 NNI, NLI, NPS, NCFN, NCFL +C + DATA MORD(1),MORD(2)/12,5/, MXSTP0/500/, MXHNL0/10/ +C----------------------------------------------------------------------- +C Block A. +C This code block is executed on every call. +C It tests ISTATE and ITASK for legality and branches appropriately. +C If ISTATE .gt. 1 but the flag INIT shows that initialization has +C not yet been done, an error return occurs. +C If ISTATE = 1 and TOUT = T, return immediately. +C----------------------------------------------------------------------- + IF (ISTATE .LT. 1 .OR. ISTATE .GT. 3) GO TO 601 + IF (ITASK .LT. 1 .OR. ITASK .GT. 5) GO TO 602 + ITASKC = ITASK + IF (ISTATE .EQ. 1) GO TO 10 + IF (INIT .EQ. 0) GO TO 603 + IF (ISTATE .EQ. 2) GO TO 200 + GO TO 20 + 10 INIT = 0 + IF (TOUT .EQ. T) RETURN +C----------------------------------------------------------------------- +C Block B. +C The next code block is executed for the initial call (ISTATE = 1), +C or for a continuation call with parameter changes (ISTATE = 3). +C It contains checking of all inputs and various initializations. +C +C First check legality of the non-optional inputs NEQ, ITOL, IOPT, MF, +C and NG. +C----------------------------------------------------------------------- + 20 IF (NEQ(1) .LE. 0) GO TO 604 + IF (ISTATE .EQ. 1) GO TO 25 + IF (NEQ(1) .GT. N) GO TO 605 + 25 N = NEQ(1) + IF (ITOL .LT. 1 .OR. ITOL .GT. 4) GO TO 606 + IF (IOPT .LT. 0 .OR. IOPT .GT. 1) GO TO 607 + METH = MF/10 + MITER = MF - 10*METH + IF (METH .LT. 1 .OR. METH .GT. 2) GO TO 608 + IF (MITER .LT. 0) GO TO 608 + IF (MITER .GT. 4 .AND. MITER .LT. 9) GO TO 608 + IF (MITER .GE. 1) JPRE = IWORK(3) + JACFLG = 0 + IF (MITER .GE. 1) JACFLG = IWORK(4) + IF (NG .LT. 0) GO TO 630 + IF (ISTATE .EQ. 1) GO TO 35 + IF (IRFND .EQ. 0 .AND. NG .NE. NGC) GO TO 631 + 35 NGC = NG +C Next process and check the optional inputs. -------------------------- + IF (IOPT .EQ. 1) GO TO 40 + MAXORD = MORD(METH) + MXSTEP = MXSTP0 + MXHNIL = MXHNL0 + IF (ISTATE .EQ. 1) H0 = 0.0D0 + HMXI = 0.0D0 + HMIN = 0.0D0 + MAXL = MIN(5,N) + KMP = MAXL + DELT = 0.05D0 + GO TO 60 + 40 MAXORD = IWORK(5) + IF (MAXORD .LT. 0) GO TO 611 + IF (MAXORD .EQ. 0) MAXORD = 100 + MAXORD = MIN(MAXORD,MORD(METH)) + MXSTEP = IWORK(6) + IF (MXSTEP .LT. 0) GO TO 612 + IF (MXSTEP .EQ. 0) MXSTEP = MXSTP0 + MXHNIL = IWORK(7) + IF (MXHNIL .LT. 0) GO TO 613 + IF (MXHNIL .EQ. 0) MXHNIL = MXHNL0 + IF (ISTATE .NE. 1) GO TO 50 + H0 = RWORK(5) + IF ((TOUT - T)*H0 .LT. 0.0D0) GO TO 614 + 50 HMAX = RWORK(6) + IF (HMAX .LT. 0.0D0) GO TO 615 + HMXI = 0.0D0 + IF (HMAX .GT. 0.0D0) HMXI = 1.0D0/HMAX + HMIN = RWORK(7) + IF (HMIN .LT. 0.0D0) GO TO 616 + MAXL = IWORK(8) + IF (MAXL .EQ. 0) MAXL = 5 + MAXL = MIN(MAXL,N) + KMP = IWORK(9) + IF (KMP .EQ. 0 .OR. KMP .GT. MAXL) KMP = MAXL + DELT = RWORK(8) + IF (DELT .EQ. 0.0D0) DELT = 0.05D0 +C----------------------------------------------------------------------- +C Set work array pointers and check lengths LRW and LIW. +C Pointers to segments of RWORK and IWORK are named by prefixing L to +C the name of the segment. E.g., the segment YH starts at RWORK(LYH). +C RWORK segments (in order) are denoted G0, G1, GX, YH, WM, +C EWT, SAVF, SAVX, ACOR. +C----------------------------------------------------------------------- + 60 IF (ISTATE .EQ. 1) NYH = N + LG0 = 21 + LG1 = LG0 + NG + LGX = LG1 + NG + LYHNEW = LGX + NG + IF (ISTATE .EQ. 1) LYH = LYHNEW + IF (LYHNEW .EQ. LYH) GO TO 62 +C If ISTATE = 3 and NG was changed, shift YH to its new location. ------ + LENYH = L*NYH + IF (LRW .LT. LYHNEW-1+LENYH) GO TO 62 + I1 = 1 + IF (LYHNEW .GT. LYH) I1 = -1 + CALL DCOPY (LENYH, RWORK(LYH), I1, RWORK(LYHNEW), I1) + LYH = LYHNEW + 62 CONTINUE + LWM = LYH + (MAXORD + 1)*NYH + IF (MITER .EQ. 0) LENWK = 0 + IF (MITER .EQ. 1) LENWK = N*(MAXL+2) + MAXL*MAXL + IF (MITER .EQ. 2) + 1 LENWK = N*(MAXL+2+MIN(1,MAXL-KMP)) + (MAXL+3)*MAXL + 1 + IF (MITER .EQ. 3 .OR. MITER .EQ. 4) LENWK = 5*N + IF (MITER .EQ. 9) LENWK = 2*N + LWP = 0 + IF (MITER .GE. 1) LWP = IWORK(1) + LENWM = LENWK + LWP + LOCWP = LENWK + 1 + LEWT = LWM + LENWM + LSAVF = LEWT + N + LSAVX = LSAVF + N + LACOR = LSAVX + N + IF (MITER .EQ. 0) LACOR = LSAVF + N + LENRW = LACOR + N - 1 + IWORK(17) = LENRW + LIWM = 31 + LENIWK = 0 + IF (MITER .EQ. 1) LENIWK = MAXL + LIWP = 0 + IF (MITER .GE. 1) LIWP = IWORK(2) + LENIW = 30 + LENIWK + LIWP + LOCIWP = LENIWK + 1 + IWORK(18) = LENIW + IF (LENRW .GT. LRW) GO TO 617 + IF (LENIW .GT. LIW) GO TO 618 +C Check RTOL and ATOL for legality. ------------------------------------ + RTOLI = RTOL(1) + ATOLI = ATOL(1) + DO 70 I = 1,N + IF (ITOL .GE. 3) RTOLI = RTOL(I) + IF (ITOL .EQ. 2 .OR. ITOL .EQ. 4) ATOLI = ATOL(I) + IF (RTOLI .LT. 0.0D0) GO TO 619 + IF (ATOLI .LT. 0.0D0) GO TO 620 + 70 CONTINUE +C Load SQRT(N) and its reciprocal in Common. --------------------------- + SQRTN = SQRT(REAL(N)) + RSQRTN = 1.0D0/SQRTN + IF (ISTATE .EQ. 1) GO TO 100 +C If ISTATE = 3, set flag to signal parameter changes to DSTOKA.-------- + JSTART = -1 + IF (NQ .LE. MAXORD) GO TO 90 +C MAXORD was reduced below NQ. Copy YH(*,MAXORD+2) into SAVF. --------- + DO 80 I = 1,N + 80 RWORK(I+LSAVF-1) = RWORK(I+LWM-1) + 90 CONTINUE + IF (N .EQ. NYH) GO TO 200 +C NEQ was reduced. Zero part of YH to avoid undefined references. ----- + I1 = LYH + L*NYH + I2 = LYH + (MAXORD + 1)*NYH - 1 + IF (I1 .GT. I2) GO TO 200 + DO 95 I = I1,I2 + 95 RWORK(I) = 0.0D0 + GO TO 200 +C----------------------------------------------------------------------- +C Block C. +C The next block is for the initial call only (ISTATE = 1). +C It contains all remaining initializations, the initial call to F, +C and the calculation of the initial step size. +C The error weights in EWT are inverted after being loaded. +C----------------------------------------------------------------------- + 100 UROUND = DUMACH() + TN = T + IF (ITASK .NE. 4 .AND. ITASK .NE. 5) GO TO 110 + TCRIT = RWORK(1) + IF ((TCRIT - TOUT)*(TOUT - T) .LT. 0.0D0) GO TO 625 + IF (H0 .NE. 0.0D0 .AND. (T + H0 - TCRIT)*H0 .GT. 0.0D0) + 1 H0 = TCRIT - T + 110 JSTART = 0 + NHNIL = 0 + NST = 0 + NJE = 0 + NSLAST = 0 + NLI0 = 0 + NNI0 = 0 + NCFN0 = 0 + NCFL0 = 0 + NWARN = 0 + HU = 0.0D0 + NQU = 0 + CCMAX = 0.3D0 + MAXCOR = 3 + MSBP = 20 + MXNCF = 10 + NNI = 0 + NLI = 0 + NPS = 0 + NCFN = 0 + NCFL = 0 + NSFI = 0 + NJEV = 0 +C Initial call to F. (LF0 points to YH(*,2).) ------------------------- + LF0 = LYH + NYH + CALL F (NEQ, T, Y, RWORK(LF0)) + NFE = 1 +C Load the initial value vector in YH. --------------------------------- + DO 115 I = 1,N + 115 RWORK(I+LYH-1) = Y(I) +C Load and invert the EWT array. (H is temporarily set to 1.0.) ------- + NQ = 1 + H = 1.0D0 + CALL DEWSET (N, ITOL, RTOL, ATOL, RWORK(LYH), RWORK(LEWT)) + DO 120 I = 1,N + IF (RWORK(I+LEWT-1) .LE. 0.0D0) GO TO 621 + 120 RWORK(I+LEWT-1) = 1.0D0/RWORK(I+LEWT-1) + IF (H0 .NE. 0.0D0) GO TO 180 +C Call DLHIN to set initial step size H0 to be attempted. -------------- + CALL DLHIN (NEQ, N, T, RWORK(LYH), RWORK(LF0), F, TOUT, UROUND, + 1 RWORK(LEWT), ITOL, ATOL, Y, RWORK(LACOR), H0, NITER, IER) + NFE = NFE + NITER + IF (IER .NE. 0) GO TO 622 +C Adjust H0 if necessary to meet HMAX bound. --------------------------- + 180 RH = ABS(H0)*HMXI + IF (RH .GT. 1.0D0) H0 = H0/RH +C Load H with H0 and scale YH(*,2) by H0. ------------------------------ + H = H0 + DO 190 I = 1,N + 190 RWORK(I+LF0-1) = H0*RWORK(I+LF0-1) +C Check for a zero of g at T. ------------------------------------------ + IRFND = 0 + TOUTC = TOUT + IF (NGC .EQ. 0) GO TO 270 + CALL DRCHEK (1, G, NEQ, Y, RWORK(LYH), NYH, + 1 RWORK(LG0), RWORK(LG1), RWORK(LGX), JROOT, IRT) + IF (IRT .EQ. 0) GO TO 270 + GO TO 632 +C----------------------------------------------------------------------- +C Block D. +C The next code block is for continuation calls only (ISTATE = 2 or 3) +C and is to check stop conditions before taking a step. +C First, DRCHEK is called to check for a root within the last step +C taken, other than the last root found there, if any. +C If ITASK = 2 or 5, and y(TN) has not yet been returned to the user +C because of an intervening root, return through Block G. +C----------------------------------------------------------------------- + 200 NSLAST = NST +C + IRFP = IRFND + IF (NGC .EQ. 0) GO TO 205 + IF (ITASK .EQ. 1 .OR. ITASK .EQ. 4) TOUTC = TOUT + CALL DRCHEK (2, G, NEQ, Y, RWORK(LYH), NYH, + 1 RWORK(LG0), RWORK(LG1), RWORK(LGX), JROOT, IRT) + IF (IRT .NE. 1) GO TO 205 + IRFND = 1 + ISTATE = 3 + T = T0 + GO TO 425 + 205 CONTINUE + IRFND = 0 + IF (IRFP .EQ. 1 .AND. TLAST .NE. TN .AND. ITASK .EQ. 2) GO TO 400 +C + NLI0 = NLI + NNI0 = NNI + NCFN0 = NCFN + NCFL0 = NCFL + NWARN = 0 + GO TO (210, 250, 220, 230, 240), ITASK + 210 IF ((TN - TOUT)*H .LT. 0.0D0) GO TO 250 + CALL DINTDY (TOUT, 0, RWORK(LYH), NYH, Y, IFLAG) + IF (IFLAG .NE. 0) GO TO 627 + T = TOUT + GO TO 420 + 220 TP = TN - HU*(1.0D0 + 100.0D0*UROUND) + IF ((TP - TOUT)*H .GT. 0.0D0) GO TO 623 + IF ((TN - TOUT)*H .LT. 0.0D0) GO TO 250 + GO TO 400 + 230 TCRIT = RWORK(1) + IF ((TN - TCRIT)*H .GT. 0.0D0) GO TO 624 + IF ((TCRIT - TOUT)*H .LT. 0.0D0) GO TO 625 + IF ((TN - TOUT)*H .LT. 0.0D0) GO TO 245 + CALL DINTDY (TOUT, 0, RWORK(LYH), NYH, Y, IFLAG) + IF (IFLAG .NE. 0) GO TO 627 + T = TOUT + GO TO 420 + 240 TCRIT = RWORK(1) + IF ((TN - TCRIT)*H .GT. 0.0D0) GO TO 624 + 245 HMX = ABS(TN) + ABS(H) + IHIT = ABS(TN - TCRIT) .LE. 100.0D0*UROUND*HMX + IF (IHIT) T = TCRIT + IF (IRFP .EQ. 1 .AND. TLAST .NE. TN .AND. ITASK .EQ. 5) GO TO 400 + IF (IHIT) GO TO 400 + TNEXT = TN + H*(1.0D0 + 4.0D0*UROUND) + IF ((TNEXT - TCRIT)*H .LE. 0.0D0) GO TO 250 + H = (TCRIT - TN)*(1.0D0 - 4.0D0*UROUND) + IF (ISTATE .EQ. 2) JSTART = -2 +C----------------------------------------------------------------------- +C Block E. +C The next block is normally executed for all calls and contains +C the call to the one-step core integrator DSTOKA. +C +C This is a looping point for the integration steps. +C +C First check for too many steps being taken, +C check for poor Newton/Krylov method performance, update EWT (if not +C at start of problem), check for too much accuracy being requested, +C and check for H below the roundoff level in T. +C----------------------------------------------------------------------- + 250 CONTINUE + IF ((NST-NSLAST) .GE. MXSTEP) GO TO 500 + NSTD = NST - NSLAST + NNID = NNI - NNI0 + IF (NSTD .LT. 10 .OR. NNID .EQ. 0) GO TO 255 + AVDIM = REAL(NLI - NLI0)/REAL(NNID) + RCFN = REAL(NCFN - NCFN0)/REAL(NSTD) + RCFL = REAL(NCFL - NCFL0)/REAL(NNID) + LAVD = AVDIM .GT. (MAXL - 0.05D0) + LCFN = RCFN .GT. 0.9D0 + LCFL = RCFL .GT. 0.9D0 + LWARN = LAVD .OR. LCFN .OR. LCFL + IF (.NOT.LWARN) GO TO 255 + NWARN = NWARN + 1 + IF (NWARN .GT. 10) GO TO 255 + IF (LAVD) THEN + MSG='DLSODKR- Warning. Poor iterative algorithm performance seen ' + CALL XERRWD (MSG, 60, 111, 0, 0, 0, 0, 0, 0.0D0, 0.0D0) + ENDIF + IF (LAVD) THEN + MSG=' at T = R1 by average no. of linear iterations = R2 ' + CALL XERRWD (MSG, 60, 111, 0, 0, 0, 0, 2, TN, AVDIM) + ENDIF + IF (LCFN) THEN + MSG='DLSODKR- Warning. Poor iterative algorithm performance seen ' + CALL XERRWD (MSG, 60, 112, 0, 0, 0, 0, 0, 0.0D0, 0.0D0) + ENDIF + IF (LCFN) THEN + MSG=' at T = R1 by nonlinear convergence failure rate = R2 ' + CALL XERRWD (MSG, 60, 112, 0, 0, 0, 0, 2, TN, RCFN) + ENDIF + IF (LCFL) THEN + MSG='DLSODKR- Warning. Poor iterative algorithm performance seen ' + CALL XERRWD (MSG, 60, 113, 0, 0, 0, 0, 0, 0.0D0, 0.0D0) + ENDIF + IF (LCFL) THEN + MSG=' at T = R1 by linear convergence failure rate = R2 ' + CALL XERRWD (MSG, 60, 113, 0, 0, 0, 0, 2, TN, RCFL) + ENDIF + 255 CONTINUE + CALL DEWSET (N, ITOL, RTOL, ATOL, RWORK(LYH), RWORK(LEWT)) + DO 260 I = 1,N + IF (RWORK(I+LEWT-1) .LE. 0.0D0) GO TO 510 + 260 RWORK(I+LEWT-1) = 1.0D0/RWORK(I+LEWT-1) + 270 TOLSF = UROUND*DVNORM (N, RWORK(LYH), RWORK(LEWT)) + IF (TOLSF .LE. 1.0D0) GO TO 280 + TOLSF = TOLSF*2.0D0 + IF (NST .EQ. 0) GO TO 626 + GO TO 520 + 280 IF ((TN + H) .NE. TN) GO TO 290 + NHNIL = NHNIL + 1 + IF (NHNIL .GT. MXHNIL) GO TO 290 + MSG = 'DLSODKR- Warning.. Internal T(=R1) and H(=R2) are' + CALL XERRWD (MSG, 50, 101, 0, 0, 0, 0, 0, 0.0D0, 0.0D0) + MSG=' such that in the machine, T + H = T on the next step ' + CALL XERRWD (MSG, 60, 101, 0, 0, 0, 0, 0, 0.0D0, 0.0D0) + MSG = ' (H = step size). Solver will continue anyway.' + CALL XERRWD (MSG, 50, 101, 0, 0, 0, 0, 2, TN, H) + IF (NHNIL .LT. MXHNIL) GO TO 290 + MSG = 'DLSODKR- Above warning has been issued I1 times. ' + CALL XERRWD (MSG, 50, 102, 0, 0, 0, 0, 0, 0.0D0, 0.0D0) + MSG = ' It will not be issued again for this problem.' + CALL XERRWD (MSG, 50, 102, 0, 1, MXHNIL, 0, 0, 0.0D0, 0.0D0) + 290 CONTINUE +C----------------------------------------------------------------------- +C CALL DSTOKA(NEQ,Y,YH,NYH,YH,EWT,SAVF,SAVX,ACOR,WM,IWM,F,JAC,PSOL) +C----------------------------------------------------------------------- + CALL DSTOKA (NEQ, Y, RWORK(LYH), NYH, RWORK(LYH), RWORK(LEWT), + 1 RWORK(LSAVF), RWORK(LSAVX), RWORK(LACOR), RWORK(LWM), + 2 IWORK(LIWM), F, JAC, PSOL) + KGO = 1 - KFLAG + GO TO (300, 530, 540, 550), KGO +C----------------------------------------------------------------------- +C Block F. +C The following block handles the case of a successful return from the +C core integrator (KFLAG = 0). +C Call DRCHEK to check for a root within the last step. +C Then, if no root was found, check for stop conditions. +C----------------------------------------------------------------------- + 300 INIT = 1 +C + IF (NGC .EQ. 0) GO TO 315 + CALL DRCHEK (3, G, NEQ, Y, RWORK(LYH), NYH, + 1 RWORK(LG0), RWORK(LG1), RWORK(LGX), JROOT, IRT) + IF (IRT .NE. 1) GO TO 315 + IRFND = 1 + ISTATE = 3 + T = T0 + GO TO 425 + 315 CONTINUE +C + GO TO (310, 400, 330, 340, 350), ITASK +C ITASK = 1. If TOUT has been reached, interpolate. ------------------- + 310 IF ((TN - TOUT)*H .LT. 0.0D0) GO TO 250 + CALL DINTDY (TOUT, 0, RWORK(LYH), NYH, Y, IFLAG) + T = TOUT + GO TO 420 +C ITASK = 3. Jump to exit if TOUT was reached. ------------------------ + 330 IF ((TN - TOUT)*H .GE. 0.0D0) GO TO 400 + GO TO 250 +C ITASK = 4. See if TOUT or TCRIT was reached. Adjust H if necessary. + 340 IF ((TN - TOUT)*H .LT. 0.0D0) GO TO 345 + CALL DINTDY (TOUT, 0, RWORK(LYH), NYH, Y, IFLAG) + T = TOUT + GO TO 420 + 345 HMX = ABS(TN) + ABS(H) + IHIT = ABS(TN - TCRIT) .LE. 100.0D0*UROUND*HMX + IF (IHIT) GO TO 400 + TNEXT = TN + H*(1.0D0 + 4.0D0*UROUND) + IF ((TNEXT - TCRIT)*H .LE. 0.0D0) GO TO 250 + H = (TCRIT - TN)*(1.0D0 - 4.0D0*UROUND) + JSTART = -2 + GO TO 250 +C ITASK = 5. See if TCRIT was reached and jump to exit. --------------- + 350 HMX = ABS(TN) + ABS(H) + IHIT = ABS(TN - TCRIT) .LE. 100.0D0*UROUND*HMX +C----------------------------------------------------------------------- +C Block G. +C The following block handles all successful returns from DLSODKR. +C If ITASK .ne. 1, Y is loaded from YH and T is set accordingly. +C ISTATE is set to 2, and the optional outputs are loaded into the +C work arrays before returning. +C----------------------------------------------------------------------- + 400 DO 410 I = 1,N + 410 Y(I) = RWORK(I+LYH-1) + T = TN + IF (ITASK .NE. 4 .AND. ITASK .NE. 5) GO TO 420 + IF (IHIT) T = TCRIT + 420 ISTATE = 2 + 425 CONTINUE + RWORK(11) = HU + RWORK(12) = H + RWORK(13) = TN + IWORK(11) = NST + IWORK(12) = NFE + IWORK(13) = NJE + IWORK(14) = NQU + IWORK(15) = NQ + IWORK(19) = NNI + IWORK(20) = NLI + IWORK(21) = NPS + IWORK(22) = NCFN + IWORK(23) = NCFL + IWORK(24) = NSFI + IWORK(25) = NJEV + IWORK(10) = NGE + TLAST = T + RETURN +C----------------------------------------------------------------------- +C Block H. +C The following block handles all unsuccessful returns other than +C those for illegal input. First the error message routine is called. +C If there was an error test or convergence test failure, IMXER is set. +C Then Y is loaded from YH and T is set to TN. +C The optional outputs are loaded into the work arrays before returning. +C----------------------------------------------------------------------- +C The maximum number of steps was taken before reaching TOUT. ---------- + 500 MSG = 'DLSODKR- At current T (=R1), MXSTEP (=I1) steps ' + CALL XERRWD (MSG, 50, 201, 0, 0, 0, 0, 0, 0.0D0, 0.0D0) + MSG = ' taken on this call before reaching TOUT ' + CALL XERRWD (MSG, 50, 201, 0, 1, MXSTEP, 0, 1, TN, 0.0D0) + ISTATE = -1 + GO TO 580 +C EWT(i) .le. 0.0 for some i (not at start of problem). ---------------- + 510 EWTI = RWORK(LEWT+I-1) + MSG = 'DLSODKR- At T(=R1), EWT(I1) has become R2 .le. 0.' + CALL XERRWD (MSG, 50, 202, 0, 1, I, 0, 2, TN, EWTI) + ISTATE = -6 + GO TO 580 +C Too much accuracy requested for machine precision. ------------------- + 520 MSG = 'DLSODKR- At T (=R1), too much accuracy requested ' + CALL XERRWD (MSG, 50, 203, 0, 0, 0, 0, 0, 0.0D0, 0.0D0) + MSG = ' for precision of machine.. See TOLSF (=R2) ' + CALL XERRWD (MSG, 50, 203, 0, 0, 0, 0, 2, TN, TOLSF) + RWORK(14) = TOLSF + ISTATE = -2 + GO TO 580 +C KFLAG = -1. Error test failed repeatedly or with ABS(H) = HMIN. ----- + 530 MSG = 'DLSODKR- At T(=R1) and step size H(=R2), the error' + CALL XERRWD (MSG, 50, 204, 0, 0, 0, 0, 0, 0.0D0, 0.0D0) + MSG = ' test failed repeatedly or with ABS(H) = HMIN' + CALL XERRWD (MSG, 50, 204, 0, 0, 0, 0, 2, TN, H) + ISTATE = -4 + GO TO 560 +C KFLAG = -2. Convergence failed repeatedly or with ABS(H) = HMIN. ---- + 540 MSG = 'DLSODKR- At T (=R1) and step size H (=R2), the ' + CALL XERRWD (MSG, 50, 205, 0, 0, 0, 0, 0, 0.0D0, 0.0D0) + MSG = ' corrector convergence failed repeatedly ' + CALL XERRWD (MSG, 50, 205, 0, 0, 0, 0, 0, 0.0D0, 0.0D0) + MSG = ' or with ABS(H) = HMIN ' + CALL XERRWD (MSG, 30, 205, 0, 0, 0, 0, 2, TN, H) + ISTATE = -5 + GO TO 580 +C KFLAG = -3. Unrecoverable error from PSOL. -------------------------- + 550 MSG = 'DLSODKR- At T (=R1) an unrecoverable error return' + CALL XERRWD (MSG, 50, 206, 0, 0, 0, 0, 0, 0.0D0, 0.0D0) + MSG = ' was made from Subroutine PSOL ' + CALL XERRWD (MSG, 40, 206, 0, 0, 0, 0, 1, TN, 0.0D0) + ISTATE = -7 + GO TO 580 +C Compute IMXER if relevant. ------------------------------------------- + 560 BIG = 0.0D0 + IMXER = 1 + DO 570 I = 1,N + SIZE = ABS(RWORK(I+LACOR-1)*RWORK(I+LEWT-1)) + IF (BIG .GE. SIZE) GO TO 570 + BIG = SIZE + IMXER = I + 570 CONTINUE + IWORK(16) = IMXER +C Set Y vector, T, and optional outputs. ------------------------------- + 580 DO 590 I = 1,N + 590 Y(I) = RWORK(I+LYH-1) + T = TN + RWORK(11) = HU + RWORK(12) = H + RWORK(13) = TN + IWORK(11) = NST + IWORK(12) = NFE + IWORK(13) = NJE + IWORK(14) = NQU + IWORK(15) = NQ + IWORK(19) = NNI + IWORK(20) = NLI + IWORK(21) = NPS + IWORK(22) = NCFN + IWORK(23) = NCFL + IWORK(24) = NSFI + IWORK(25) = NJEV + IWORK(10) = NGE + TLAST = T + RETURN +C----------------------------------------------------------------------- +C Block I. +C The following block handles all error returns due to illegal input +C (ISTATE = -3), as detected before calling the core integrator. +C First the error message routine is called. If the illegal input +C is a negative ISTATE, the run is aborted (apparent infinite loop). +C----------------------------------------------------------------------- + 601 MSG = 'DLSODKR- ISTATE(=I1) illegal.' + CALL XERRWD (MSG, 30, 1, 0, 1, ISTATE, 0, 0, 0.0D0, 0.0D0) + IF (ISTATE .LT. 0) GO TO 800 + GO TO 700 + 602 MSG = 'DLSODKR- ITASK (=I1) illegal.' + CALL XERRWD (MSG, 30, 2, 0, 1, ITASK, 0, 0, 0.0D0, 0.0D0) + GO TO 700 + 603 MSG = 'DLSODKR- ISTATE.gt.1 but DLSODKR not initialized. ' + CALL XERRWD (MSG, 50, 3, 0, 0, 0, 0, 0, 0.0D0, 0.0D0) + GO TO 700 + 604 MSG = 'DLSODKR- NEQ (=I1) .lt. 1 ' + CALL XERRWD (MSG, 30, 4, 0, 1, NEQ(1), 0, 0, 0.0D0, 0.0D0) + GO TO 700 + 605 MSG = 'DLSODKR- ISTATE = 3 and NEQ increased (I1 to I2).' + CALL XERRWD (MSG, 50, 5, 0, 2, N, NEQ(1), 0, 0.0D0, 0.0D0) + GO TO 700 + 606 MSG = 'DLSODKR- ITOL (=I1) illegal. ' + CALL XERRWD (MSG, 30, 6, 0, 1, ITOL, 0, 0, 0.0D0, 0.0D0) + GO TO 700 + 607 MSG = 'DLSODKR- IOPT (=I1) illegal. ' + CALL XERRWD (MSG, 30, 7, 0, 1, IOPT, 0, 0, 0.0D0, 0.0D0) + GO TO 700 + 608 MSG = 'DLSODKR- MF (=I1) illegal. ' + CALL XERRWD (MSG, 30, 8, 0, 1, MF, 0, 0, 0.0D0, 0.0D0) + GO TO 700 + 611 MSG = 'DLSODKR- MAXORD (=I1) .lt. 0 ' + CALL XERRWD (MSG, 30, 11, 0, 1, MAXORD, 0, 0, 0.0D0, 0.0D0) + GO TO 700 + 612 MSG = 'DLSODKR- MXSTEP (=I1) .lt. 0 ' + CALL XERRWD (MSG, 30, 12, 0, 1, MXSTEP, 0, 0, 0.0D0, 0.0D0) + GO TO 700 + 613 MSG = 'DLSODKR- MXHNIL (=I1) .lt. 0 ' + CALL XERRWD (MSG, 30, 13, 0, 1, MXHNIL, 0, 0, 0.0D0, 0.0D0) + GO TO 700 + 614 MSG = 'DLSODKR- TOUT (=R1) behind T (=R2) ' + CALL XERRWD (MSG, 40, 14, 0, 0, 0, 0, 2, TOUT, T) + MSG = ' Integration direction is given by H0 (=R1) ' + CALL XERRWD (MSG, 50, 14, 0, 0, 0, 0, 1, H0, 0.0D0) + GO TO 700 + 615 MSG = 'DLSODKR- HMAX (=R1) .lt. 0.0 ' + CALL XERRWD (MSG, 30, 15, 0, 0, 0, 0, 1, HMAX, 0.0D0) + GO TO 700 + 616 MSG = 'DLSODKR- HMIN (=R1) .lt. 0.0 ' + CALL XERRWD (MSG, 30, 16, 0, 0, 0, 0, 1, HMIN, 0.0D0) + GO TO 700 + 617 MSG='DLSODKR- RWORK length needed, LENRW(=I1), exceeds LRW(=I2) ' + CALL XERRWD (MSG, 60, 17, 0, 2, LENRW, LRW, 0, 0.0D0, 0.0D0) + GO TO 700 + 618 MSG='DLSODKR- IWORK length needed, LENIW(=I1), exceeds LIW(=I2) ' + CALL XERRWD (MSG, 60, 18, 0, 2, LENIW, LIW, 0, 0.0D0, 0.0D0) + GO TO 700 + 619 MSG = 'DLSODKR- RTOL(I1) is R1 .lt. 0.0 ' + CALL XERRWD (MSG, 40, 19, 0, 1, I, 0, 1, RTOLI, 0.0D0) + GO TO 700 + 620 MSG = 'DLSODKR- ATOL(I1) is R1 .lt. 0.0 ' + CALL XERRWD (MSG, 40, 20, 0, 1, I, 0, 1, ATOLI, 0.0D0) + GO TO 700 + 621 EWTI = RWORK(LEWT+I-1) + MSG = 'DLSODKR- EWT(I1) is R1 .le. 0.0 ' + CALL XERRWD (MSG, 40, 21, 0, 1, I, 0, 1, EWTI, 0.0D0) + GO TO 700 + 622 MSG='DLSODKR- TOUT(=R1) too close to T(=R2) to start integration.' + CALL XERRWD (MSG, 60, 22, 0, 0, 0, 0, 2, TOUT, T) + GO TO 700 + 623 MSG='DLSODKR- ITASK = I1 and TOUT (=R1) behind TCUR - HU (= R2) ' + CALL XERRWD (MSG, 60, 23, 0, 1, ITASK, 0, 2, TOUT, TP) + GO TO 700 + 624 MSG='DLSODKR- ITASK = 4 or 5 and TCRIT (=R1) behind TCUR (=R2) ' + CALL XERRWD (MSG, 60, 24, 0, 0, 0, 0, 2, TCRIT, TN) + GO TO 700 + 625 MSG='DLSODKR- ITASK = 4 or 5 and TCRIT (=R1) behind TOUT (=R2) ' + CALL XERRWD (MSG, 60, 25, 0, 0, 0, 0, 2, TCRIT, TOUT) + GO TO 700 + 626 MSG = 'DLSODKR- At start of problem, too much accuracy ' + CALL XERRWD (MSG, 50, 26, 0, 0, 0, 0, 0, 0.0D0, 0.0D0) + MSG=' requested for precision of machine.. See TOLSF (=R1) ' + CALL XERRWD (MSG, 60, 26, 0, 0, 0, 0, 1, TOLSF, 0.0D0) + RWORK(14) = TOLSF + GO TO 700 + 627 MSG = 'DLSODKR- Trouble in DINTDY. ITASK = I1, TOUT = R1' + CALL XERRWD (MSG, 50, 27, 0, 1, ITASK, 0, 1, TOUT, 0.0D0) + GO TO 700 + 630 MSG = 'DLSODKR- NG (=I1) .lt. 0 ' + CALL XERRWD (MSG, 30, 30, 0, 1, NG, 0, 0, 0.0D0, 0.0D0) + GO TO 700 + 631 MSG = 'DLSODKR- NG changed (from I1 to I2) illegally, ' + CALL XERRWD (MSG, 50, 31, 0, 0, 0, 0, 0, 0.0D0, 0.0D0) + MSG = ' i.e. not immediately after a root was found.' + CALL XERRWD (MSG, 50, 31, 0, 2, NGC, NG, 0, 0.0D0, 0.0D0) + GO TO 700 + 632 MSG = 'DLSODKR- One or more components of g has a root ' + CALL XERRWD (MSG, 50, 32, 0, 0, 0, 0, 0, 0.0D0, 0.0D0) + MSG = ' too near to the initial point. ' + CALL XERRWD (MSG, 40, 32, 0, 0, 0, 0, 0, 0.0D0, 0.0D0) +C + 700 ISTATE = -3 + RETURN +C + 800 MSG = 'DLSODKR- Run aborted.. apparent infinite loop. ' + CALL XERRWD (MSG, 50, 303, 2, 0, 0, 0, 0, 0.0D0, 0.0D0) + RETURN +C----------------------- End of Subroutine DLSODKR --------------------- + END +*DECK DLSODI + SUBROUTINE DLSODI (RES, ADDA, JAC, NEQ, Y, YDOTI, T, TOUT, ITOL, + 1 RTOL, ATOL, ITASK, ISTATE, IOPT, RWORK, LRW, IWORK, LIW, MF ) + EXTERNAL RES, ADDA, JAC + INTEGER NEQ, ITOL, ITASK, ISTATE, IOPT, LRW, IWORK, LIW, MF + DOUBLE PRECISION Y, YDOTI, T, TOUT, RTOL, ATOL, RWORK + DIMENSION NEQ(*), Y(*), YDOTI(*), RTOL(*), ATOL(*), RWORK(LRW), + 1 IWORK(LIW) +C----------------------------------------------------------------------- +C This is the 18 November 2003 version of +C DLSODI: Livermore Solver for Ordinary Differential Equations +C (Implicit form). +C +C This version is in double precision. +C +C DLSODI solves the initial value problem for linearly implicit +C systems of first order ODEs, +C A(t,y) * dy/dt = g(t,y) , where A(t,y) is a square matrix, +C or, in component form, +C ( a * ( dy / dt )) + ... + ( a * ( dy / dt )) = +C i,1 1 i,NEQ NEQ +C +C = g ( t, y , y ,..., y ) ( i = 1,...,NEQ ) +C i 1 2 NEQ +C +C If A is singular, this is a differential-algebraic system. +C +C DLSODI is a variant version of the DLSODE package. +C----------------------------------------------------------------------- +C Reference: +C Alan C. Hindmarsh, ODEPACK, A Systematized Collection of ODE +C Solvers, in Scientific Computing, R. S. Stepleman et al. (Eds.), +C North-Holland, Amsterdam, 1983, pp. 55-64. +C----------------------------------------------------------------------- +C Authors: Alan C. Hindmarsh and Jeffrey F. Painter +C Center for Applied Scientific Computing, L-561 +C Lawrence Livermore National Laboratory +C Livermore, CA 94551 +C----------------------------------------------------------------------- +C Summary of Usage. +C +C Communication between the user and the DLSODI package, for normal +C situations, is summarized here. This summary describes only a subset +C of the full set of options available. See the full description for +C details, including optional communication, nonstandard options, +C and instructions for special situations. See also the example +C problem (with program and output) following this summary. +C +C A. First, provide a subroutine of the form: +C SUBROUTINE RES (NEQ, T, Y, S, R, IRES) +C DOUBLE PRECISION T, Y(*), S(*), R(*) +C which computes the residual function +C r = g(t,y) - A(t,y) * s , +C as a function of t and the vectors y and s. (s is an internally +C generated approximation to dy/dt.) The arrays Y and S are inputs +C to the RES routine and should not be altered. The residual +C vector is to be stored in the array R. The argument IRES should be +C ignored for casual use of DLSODI. (For uses of IRES, see the +C paragraph on RES in the full description below.) +C +C B. Next, decide whether full or banded form is more economical +C for the storage of matrices. DLSODI must deal internally with the +C matrices A and dr/dy, where r is the residual function defined above. +C DLSODI generates a linear combination of these two matrices, and +C this is treated in either full or banded form. +C The matrix structure is communicated by a method flag MF, +C which is 21 or 22 for the full case, and 24 or 25 in the band case. +C In the banded case, DLSODI requires two half-bandwidth +C parameters ML and MU. These are, respectively, the widths of the +C lower and upper parts of the band, excluding the main diagonal. +C Thus the band consists of the locations (i,j) with +C i-ML .le. j .le. i+MU, and the full bandwidth is ML+MU+1. +C Note that the band must accommodate the nonzero elements of +C A(t,y), dg/dy, and d(A*s)/dy (s fixed). Alternatively, one +C can define a band that encloses only the elements that are relatively +C large in magnitude, and gain some economy in storage and possibly +C also efficiency, although the appropriate threshhold for +C retaining matrix elements is highly problem-dependent. +C +C C. You must also provide a subroutine of the form: +C SUBROUTINE ADDA (NEQ, T, Y, ML, MU, P, NROWP) +C DOUBLE PRECISION T, Y(*), P(NROWP,*) +C which adds the matrix A = A(t,y) to the contents of the array P. +C T and the Y array are input and should not be altered. +C In the full matrix case, this routine should add elements of +C to P in the usual order. I.e., add A(i,j) to P(i,j). (Ignore the +C ML and MU arguments in this case.) +C In the band matrix case, this routine should add element A(i,j) +C to P(i-j+MU+1,j). I.e., add the diagonal lines of A to the rows of +C P from the top down (the top line of A added to the first row of P). +C +C D. For the sake of efficiency, you are encouraged to supply the +C Jacobian matrix dr/dy in closed form, where r = g(t,y) - A(t,y)*s +C (s = a fixed vector) as above. If dr/dy is being supplied, +C use MF = 21 or 24, and provide a subroutine of the form: +C SUBROUTINE JAC (NEQ, T, Y, S, ML, MU, P, NROWP) +C DOUBLE PRECISION T, Y(*), S(*), P(NROWP,*) +C which computes dr/dy as a function of t, y, and s. Here T, Y, and +C S are inputs, and the routine is to load dr/dy into P as follows: +C In the full matrix case (MF = 21), load P(i,j) with dr(i)/dy(j), +C the partial derivative of r(i) with respect to y(j). (Ignore the +C ML and MU arguments in this case.) +C In the band matrix case (MF = 24), load P(i-j+mu+1,j) with +C dr(i)/dy(j), i.e. load the diagonal lines of dr/dy into the rows of +C P from the top down. +C In either case, only nonzero elements need be loaded, and the +C indexing of P is the same as in the ADDA routine. +C Note that if A is independent of y (or this dependence +C is weak enough to be ignored) then JAC is to compute dg/dy. +C If it is not feasible to provide a JAC routine, use +C MF = 22 or 25, and DLSODI will compute an approximate Jacobian +C internally by difference quotients. +C +C E. Next decide whether or not to provide the initial value of the +C derivative vector dy/dt. If the initial value of A(t,y) is +C nonsingular (and not too ill-conditioned), you may let DLSODI compute +C this vector (ISTATE = 0). (DLSODI will solve the system A*s = g for +C s, with initial values of A and g.) If A(t,y) is initially +C singular, then the system is a differential-algebraic system, and +C you must make use of the particular form of the system to compute the +C initial values of y and dy/dt. In that case, use ISTATE = 1 and +C load the initial value of dy/dt into the array YDOTI. +C The input array YDOTI and the initial Y array must be consistent with +C the equations A*dy/dt = g. This implies that the initial residual +C r = g(t,y) - A(t,y)*YDOTI must be approximately zero. +C +C F. Write a main program which calls Subroutine DLSODI once for +C each point at which answers are desired. This should also provide +C for possible use of logical unit 6 for output of error messages +C by DLSODI. On the first call to DLSODI, supply arguments as follows: +C RES = name of user subroutine for residual function r. +C ADDA = name of user subroutine for computing and adding A(t,y). +C JAC = name of user subroutine for Jacobian matrix dr/dy +C (MF = 21 or 24). If not used, pass a dummy name. +C Note: the names for the RES and ADDA routines and (if used) the +C JAC routine must be declared External in the calling program. +C NEQ = number of scalar equations in the system. +C Y = array of initial values, of length NEQ. +C YDOTI = array of length NEQ (containing initial dy/dt if ISTATE = 1). +C T = the initial value of the independent variable. +C TOUT = first point where output is desired (.ne. T). +C ITOL = 1 or 2 according as ATOL (below) is a scalar or array. +C RTOL = relative tolerance parameter (scalar). +C ATOL = absolute tolerance parameter (scalar or array). +C the estimated local error in y(i) will be controlled so as +C to be roughly less (in magnitude) than +C EWT(i) = RTOL*ABS(Y(i)) + ATOL if ITOL = 1, or +C EWT(i) = RTOL*ABS(Y(i)) + ATOL(i) if ITOL = 2. +C Thus the local error test passes if, in each component, +C either the absolute error is less than ATOL (or ATOL(i)), +C or the relative error is less than RTOL. +C Use RTOL = 0.0 for pure absolute error control, and +C use ATOL = 0.0 (or ATOL(i) = 0.0) for pure relative error +C control. Caution: Actual (global) errors may exceed these +C local tolerances, so choose them conservatively. +C ITASK = 1 for normal computation of output values of y at t = TOUT. +C ISTATE = integer flag (input and output). Set ISTATE = 1 if the +C initial dy/dt is supplied, and 0 otherwise. +C IOPT = 0 to indicate no optional inputs used. +C RWORK = real work array of length at least: +C 22 + 9*NEQ + NEQ**2 for MF = 21 or 22, +C 22 + 10*NEQ + (2*ML + MU)*NEQ for MF = 24 or 25. +C LRW = declared length of RWORK (in user's dimension). +C IWORK = integer work array of length at least 20 + NEQ. +C If MF = 24 or 25, input in IWORK(1),IWORK(2) the lower +C and upper half-bandwidths ML,MU. +C LIW = declared length of IWORK (in user's dimension). +C MF = method flag. Standard values are: +C 21 for a user-supplied full Jacobian. +C 22 for an internally generated full Jacobian. +C 24 for a user-supplied banded Jacobian. +C 25 for an internally generated banded Jacobian. +C for other choices of MF, see the paragraph on MF in +C the full description below. +C Note that the main program must declare arrays Y, YDOTI, RWORK, IWORK, +C and possibly ATOL. +C +C G. The output from the first call (or any call) is: +C Y = array of computed values of y(t) vector. +C T = corresponding value of independent variable (normally TOUT). +C ISTATE = 2 if DLSODI was successful, negative otherwise. +C -1 means excess work done on this call (check all inputs). +C -2 means excess accuracy requested (tolerances too small). +C -3 means illegal input detected (see printed message). +C -4 means repeated error test failures (check all inputs). +C -5 means repeated convergence failures (perhaps bad Jacobian +C supplied or wrong choice of tolerances). +C -6 means error weight became zero during problem. (Solution +C component i vanished, and ATOL or ATOL(i) = 0.) +C -7 cannot occur in casual use. +C -8 means DLSODI was unable to compute the initial dy/dt. +C In casual use, this means A(t,y) is initially singular. +C Supply YDOTI and use ISTATE = 1 on the first call. +C +C If DLSODI returns ISTATE = -1, -4, or -5, then the output of +C DLSODI also includes YDOTI = array containing residual vector +C r = g - A * dy/dt evaluated at the current t, y, and dy/dt. +C +C H. To continue the integration after a successful return, simply +C reset TOUT and call DLSODI again. No other parameters need be reset. +C +C----------------------------------------------------------------------- +C Example Problem. +C +C The following is a simple example problem, with the coding +C needed for its solution by DLSODI. The problem is from chemical +C kinetics, and consists of the following three equations: +C dy1/dt = -.04*y1 + 1.e4*y2*y3 +C dy2/dt = .04*y1 - 1.e4*y2*y3 - 3.e7*y2**2 +C 0. = y1 + y2 + y3 - 1. +C on the interval from t = 0.0 to t = 4.e10, with initial conditions +C y1 = 1.0, y2 = y3 = 0. +C +C The following coding solves this problem with DLSODI, using MF = 21 +C and printing results at t = .4, 4., ..., 4.e10. It uses +C ITOL = 2 and ATOL much smaller for y2 than y1 or y3 because +C y2 has much smaller values. dy/dt is supplied in YDOTI. We had +C obtained the initial value of dy3/dt by differentiating the +C third equation and evaluating the first two at t = 0. +C At the end of the run, statistical quantities of interest are +C printed (see optional outputs in the full description below). +C +C EXTERNAL RESID, APLUSP, DGBYDY +C DOUBLE PRECISION ATOL, RTOL, RWORK, T, TOUT, Y, YDOTI +C DIMENSION Y(3), YDOTI(3), ATOL(3), RWORK(58), IWORK(23) +C NEQ = 3 +C Y(1) = 1. +C Y(2) = 0. +C Y(3) = 0. +C YDOTI(1) = -.04 +C YDOTI(2) = .04 +C YDOTI(3) = 0. +C T = 0. +C TOUT = .4 +C ITOL = 2 +C RTOL = 1.D-4 +C ATOL(1) = 1.D-6 +C ATOL(2) = 1.D-10 +C ATOL(3) = 1.D-6 +C ITASK = 1 +C ISTATE = 1 +C IOPT = 0 +C LRW = 58 +C LIW = 23 +C MF = 21 +C DO 40 IOUT = 1,12 +C CALL DLSODI(RESID, APLUSP, DGBYDY, NEQ, Y, YDOTI, T, TOUT, ITOL, +C 1 RTOL, ATOL, ITASK, ISTATE, IOPT, RWORK, LRW, IWORK, LIW, MF) +C WRITE (6,20) T, Y(1), Y(2), Y(3) +C 20 FORMAT(' At t =',D12.4,' Y =',3D14.6) +C IF (ISTATE .LT. 0 ) GO TO 80 +C 40 TOUT = TOUT*10. +C WRITE (6,60) IWORK(11), IWORK(12), IWORK(13) +C 60 FORMAT(/' No. steps =',I4,' No. r-s =',I4,' No. J-s =',I4) +C STOP +C 80 WRITE (6,90) ISTATE +C 90 FORMAT(///' Error halt.. ISTATE =',I3) +C STOP +C END +C +C SUBROUTINE RESID(NEQ, T, Y, S, R, IRES) +C DOUBLE PRECISION T, Y, S, R +C DIMENSION Y(3), S(3), R(3) +C R(1) = -.04*Y(1) + 1.D4*Y(2)*Y(3) - S(1) +C R(2) = .04*Y(1) - 1.D4*Y(2)*Y(3) - 3.D7*Y(2)*Y(2) - S(2) +C R(3) = Y(1) + Y(2) + Y(3) - 1. +C RETURN +C END +C +C SUBROUTINE APLUSP(NEQ, T, Y, ML, MU, P, NROWP) +C DOUBLE PRECISION T, Y, P +C DIMENSION Y(3), P(NROWP,3) +C P(1,1) = P(1,1) + 1. +C P(2,2) = P(2,2) + 1. +C RETURN +C END +C +C SUBROUTINE DGBYDY(NEQ, T, Y, S, ML, MU, P, NROWP) +C DOUBLE PRECISION T, Y, S, P +C DIMENSION Y(3), S(3), P(NROWP,3) +C P(1,1) = -.04 +C P(1,2) = 1.D4*Y(3) +C P(1,3) = 1.D4*Y(2) +C P(2,1) = .04 +C P(2,2) = -1.D4*Y(3) - 6.D7*Y(2) +C P(2,3) = -1.D4*Y(2) +C P(3,1) = 1. +C P(3,2) = 1. +C P(3,3) = 1. +C RETURN +C END +C +C The output of this program (on a CDC-7600 in single precision) +C is as follows: +C +C At t = 4.0000e-01 Y = 9.851726e-01 3.386406e-05 1.479357e-02 +C At t = 4.0000e+00 Y = 9.055142e-01 2.240418e-05 9.446344e-02 +C At t = 4.0000e+01 Y = 7.158050e-01 9.184616e-06 2.841858e-01 +C At t = 4.0000e+02 Y = 4.504846e-01 3.222434e-06 5.495122e-01 +C At t = 4.0000e+03 Y = 1.831701e-01 8.940379e-07 8.168290e-01 +C At t = 4.0000e+04 Y = 3.897016e-02 1.621193e-07 9.610297e-01 +C At t = 4.0000e+05 Y = 4.935213e-03 1.983756e-08 9.950648e-01 +C At t = 4.0000e+06 Y = 5.159269e-04 2.064759e-09 9.994841e-01 +C At t = 4.0000e+07 Y = 5.306413e-05 2.122677e-10 9.999469e-01 +C At t = 4.0000e+08 Y = 5.494532e-06 2.197826e-11 9.999945e-01 +C At t = 4.0000e+09 Y = 5.129457e-07 2.051784e-12 9.999995e-01 +C At t = 4.0000e+10 Y = -7.170472e-08 -2.868188e-13 1.000000e+00 +C +C No. steps = 330 No. r-s = 404 No. J-s = 69 +C +C----------------------------------------------------------------------- +C Full Description of User Interface to DLSODI. +C +C The user interface to DLSODI consists of the following parts. +C +C 1. The call sequence to Subroutine DLSODI, which is a driver +C routine for the solver. This includes descriptions of both +C the call sequence arguments and of user-supplied routines. +C Following these descriptions is a description of +C optional inputs available through the call sequence, and then +C a description of optional outputs (in the work arrays). +C +C 2. Descriptions of other routines in the DLSODI package that may be +C (optionally) called by the user. These provide the ability to +C alter error message handling, save and restore the internal +C Common, and obtain specified derivatives of the solution y(t). +C +C 3. Descriptions of Common blocks to be declared in overlay +C or similar environments, or to be saved when doing an interrupt +C of the problem and continued solution later. +C +C 4. Description of two routines in the DLSODI package, either of +C which the user may replace with his/her own version, if desired. +C These relate to the measurement of errors. +C +C----------------------------------------------------------------------- +C Part 1. Call Sequence. +C +C The call sequence parameters used for input only are +C RES, ADDA, JAC, NEQ, TOUT, ITOL, RTOL, ATOL, ITASK, +C IOPT, LRW, LIW, MF, +C and those used for both input and output are +C Y, T, ISTATE, YDOTI. +C The work arrays RWORK and IWORK are also used for conditional and +C optional inputs and optional outputs. (The term output here refers +C to the return from Subroutine DLSODI to the user's calling program.) +C +C The legality of input parameters will be thoroughly checked on the +C initial call for the problem, but not checked thereafter unless a +C change in input parameters is flagged by ISTATE = 3 on input. +C +C The descriptions of the call arguments are as follows. +C +C RES = the name of the user-supplied subroutine which supplies +C the residual vector for the ODE system, defined by +C r = g(t,y) - A(t,y) * s +C as a function of the scalar t and the vectors +C s and y (s approximates dy/dt). This subroutine +C is to have the form +C SUBROUTINE RES (NEQ, T, Y, S, R, IRES) +C DOUBLE PRECISION T, Y(*), S(*), R(*) +C where NEQ, T, Y, S, and IRES are input, and R and +C IRES are output. Y, S, and R are arrays of length NEQ. +C On input, IRES indicates how DLSODI will use the +C returned array R, as follows: +C IRES = 1 means that DLSODI needs the full residual, +C r = g - A*s, exactly. +C IRES = -1 means that DLSODI is using R only to compute +C the Jacobian dr/dy by difference quotients. +C The RES routine can ignore IRES, or it can omit some terms +C if IRES = -1. If A does not depend on y, then RES can +C just return R = g when IRES = -1. If g - A*s contains other +C additive terms that are independent of y, these can also be +C dropped, if done consistently, when IRES = -1. +C The subroutine should set the flag IRES if it +C encounters a halt condition or illegal input. +C Otherwise, it should not reset IRES. On output, +C IRES = 1 or -1 represents a normal return, and +C DLSODI continues integrating the ODE. Leave IRES +C unchanged from its input value. +C IRES = 2 tells DLSODI to immediately return control +C to the calling program, with ISTATE = 3. This lets +C the calling program change parameters of the problem, +C if necessary. +C IRES = 3 represents an error condition (for example, an +C illegal value of y). DLSODI tries to integrate the system +C without getting IRES = 3 from RES. If it cannot, DLSODI +C returns with ISTATE = -7 or -1. +C On an DLSODI return with ISTATE = 3, -1, or -7, the values +C of T and Y returned correspond to the last point reached +C successfully without getting the flag IRES = 2 or 3. +C The flag values IRES = 2 and 3 should not be used to +C handle switches or root-stop conditions. This is better +C done by calling DLSODI in a one-step mode and checking the +C stopping function for a sign change at each step. +C If quantities computed in the RES routine are needed +C externally to DLSODI, an extra call to RES should be made +C for this purpose, for consistent and accurate results. +C To get the current dy/dt for the S argument, use DINTDY. +C RES must be declared External in the calling +C program. See note below for more about RES. +C +C ADDA = the name of the user-supplied subroutine which adds the +C matrix A = A(t,y) to another matrix stored in the same form +C as A. The storage form is determined by MITER (see MF). +C This subroutine is to have the form +C SUBROUTINE ADDA (NEQ, T, Y, ML, MU, P, NROWP) +C DOUBLE PRECISION T, Y(*), P(NROWP,*) +C where NEQ, T, Y, ML, MU, and NROWP are input and P is +C output. Y is an array of length NEQ, and the matrix P is +C stored in an NROWP by NEQ array. +C In the full matrix case ( MITER = 1 or 2) ADDA should +C add A to P(i,j). ML and MU are ignored. +C i,j +C In the band matrix case ( MITER = 4 or 5) ADDA should +C add A to P(i-j+MU+1,j). +C i,j +C See JAC for details on this band storage form. +C ADDA must be declared External in the calling program. +C See note below for more information about ADDA. +C +C JAC = the name of the user-supplied subroutine which supplies the +C Jacobian matrix, dr/dy, where r = g - A*s. The form of the +C Jacobian matrix is determined by MITER. JAC is required +C if MITER = 1 or 4 -- otherwise a dummy name can be +C passed. This subroutine is to have the form +C SUBROUTINE JAC ( NEQ, T, Y, S, ML, MU, P, NROWP ) +C DOUBLE PRECISION T, Y(*), S(*), P(NROWP,*) +C where NEQ, T, Y, S, ML, MU, and NROWP are input and P +C is output. Y and S are arrays of length NEQ, and the +C matrix P is stored in an NROWP by NEQ array. +C P is to be loaded with partial derivatives (elements +C of the Jacobian matrix) on output. +C In the full matrix case (MITER = 1), ML and MU +C are ignored and the Jacobian is to be loaded into P +C by columns-- i.e., dr(i)/dy(j) is loaded into P(i,j). +C In the band matrix case (MITER = 4), the elements +C within the band are to be loaded into P by columns, +C with diagonal lines of dr/dy loaded into the +C rows of P. Thus dr(i)/dy(j) is to be loaded +C into P(i-j+MU+1,j). The locations in P in the two +C triangular areas which correspond to nonexistent matrix +C elements can be ignored or loaded arbitrarily, as they +C they are overwritten by DLSODI. ML and MU are the +C half-bandwidth parameters (see IWORK). +C In either case, P is preset to zero by the solver, +C so that only the nonzero elements need be loaded by JAC. +C Each call to JAC is preceded by a call to RES with the same +C arguments NEQ, T, Y, and S. Thus to gain some efficiency, +C intermediate quantities shared by both calculations may be +C saved in a user Common block by RES and not recomputed by JAC +C if desired. Also, JAC may alter the Y array, if desired. +C JAC need not provide dr/dy exactly. A crude +C approximation (possibly with a smaller bandwidth) will do. +C JAC must be declared External in the calling program. +C See note below for more about JAC. +C +C Note on RES, ADDA, and JAC: +C These subroutines may access user-defined quantities in +C NEQ(2),... and/or in Y(NEQ(1)+1),... if NEQ is an array +C (dimensioned in the subroutines) and/or Y has length +C exceeding NEQ(1). However, these routines should not alter +C NEQ(1), Y(1),...,Y(NEQ) or any other input variables. +C See the descriptions of NEQ and Y below. +C +C NEQ = the size of the system (number of first order ordinary +C differential equations or scalar algebraic equations). +C Used only for input. +C NEQ may be decreased, but not increased, during the problem. +C If NEQ is decreased (with ISTATE = 3 on input), the +C remaining components of Y should be left undisturbed, if +C these are to be accessed in RES, ADDA, or JAC. +C +C Normally, NEQ is a scalar, and it is generally referred to +C as a scalar in this user interface description. However, +C NEQ may be an array, with NEQ(1) set to the system size. +C (The DLSODI package accesses only NEQ(1).) In either case, +C this parameter is passed as the NEQ argument in all calls +C to RES, ADDA, and JAC. Hence, if it is an array, +C locations NEQ(2),... may be used to store other integer data +C and pass it to RES, ADDA, or JAC. Each such subroutine +C must include NEQ in a Dimension statement in that case. +C +C Y = a real array for the vector of dependent variables, of +C length NEQ or more. Used for both input and output on the +C first call (ISTATE = 0 or 1), and only for output on other +C calls. On the first call, Y must contain the vector of +C initial values. On output, Y contains the computed solution +C vector, evaluated at T. If desired, the Y array may be used +C for other purposes between calls to the solver. +C +C This array is passed as the Y argument in all calls to RES, +C ADDA, and JAC. Hence its length may exceed NEQ, +C and locations Y(NEQ+1),... may be used to store other real +C data and pass it to RES, ADDA, or JAC. (The DLSODI +C package accesses only Y(1),...,Y(NEQ). ) +C +C YDOTI = a real array for the initial value of the vector +C dy/dt and for work space, of dimension at least NEQ. +C +C On input: +C If ISTATE = 0, then DLSODI will compute the initial value +C of dy/dt, if A is nonsingular. Thus YDOTI will +C serve only as work space and may have any value. +C If ISTATE = 1, then YDOTI must contain the initial value +C of dy/dt. +C If ISTATE = 2 or 3 (continuation calls), then YDOTI +C may have any value. +C Note: If the initial value of A is singular, then +C DLSODI cannot compute the initial value of dy/dt, so +C it must be provided in YDOTI, with ISTATE = 1. +C +C On output, when DLSODI terminates abnormally with ISTATE = +C -1, -4, or -5, YDOTI will contain the residual +C r = g(t,y) - A(t,y)*(dy/dt). If r is large, t is near +C its initial value, and YDOTI is supplied with ISTATE = 1, +C then there may have been an incorrect input value of +C YDOTI = dy/dt, or the problem (as given to DLSODI) +C may not have a solution. +C +C If desired, the YDOTI array may be used for other +C purposes between calls to the solver. +C +C T = the independent variable. On input, T is used only on the +C first call, as the initial point of the integration. +C On output, after each call, T is the value at which a +C computed solution Y is evaluated (usually the same as TOUT). +C on an error return, T is the farthest point reached. +C +C TOUT = the next value of t at which a computed solution is desired. +C Used only for input. +C +C When starting the problem (ISTATE = 0 or 1), TOUT may be +C equal to T for one call, then should .ne. T for the next +C call. For the initial T, an input value of TOUT .ne. T is +C used in order to determine the direction of the integration +C (i.e. the algebraic sign of the step sizes) and the rough +C scale of the problem. Integration in either direction +C (forward or backward in t) is permitted. +C +C If ITASK = 2 or 5 (one-step modes), TOUT is ignored after +C the first call (i.e. the first call with TOUT .ne. T). +C Otherwise, TOUT is required on every call. +C +C If ITASK = 1, 3, or 4, the values of TOUT need not be +C monotone, but a value of TOUT which backs up is limited +C to the current internal T interval, whose endpoints are +C TCUR - HU and TCUR (see optional outputs, below, for +C TCUR and HU). +C +C ITOL = an indicator for the type of error control. See +C description below under ATOL. Used only for input. +C +C RTOL = a relative error tolerance parameter, either a scalar or +C an array of length NEQ. See description below under ATOL. +C Input only. +C +C ATOL = an absolute error tolerance parameter, either a scalar or +C an array of length NEQ. Input only. +C +C The input parameters ITOL, RTOL, and ATOL determine +C the error control performed by the solver. The solver will +C control the vector E = (E(i)) of estimated local errors +C in y, according to an inequality of the form +C RMS-norm of ( E(i)/EWT(i) ) .le. 1, +C where EWT(i) = RTOL(i)*ABS(Y(i)) + ATOL(i), +C and the RMS-norm (root-mean-square norm) here is +C RMS-norm(v) = SQRT(sum v(i)**2 / NEQ). Here EWT = (EWT(i)) +C is a vector of weights which must always be positive, and +C the values of RTOL and ATOL should all be non-negative. +C The following table gives the types (scalar/array) of +C RTOL and ATOL, and the corresponding form of EWT(i). +C +C ITOL RTOL ATOL EWT(i) +C 1 scalar scalar RTOL*ABS(Y(i)) + ATOL +C 2 scalar array RTOL*ABS(Y(i)) + ATOL(i) +C 3 array scalar RTOL(i)*ABS(Y(i)) + ATOL +C 4 array scalar RTOL(i)*ABS(Y(i)) + ATOL(i) +C +C When either of these parameters is a scalar, it need not +C be dimensioned in the user's calling program. +C +C If none of the above choices (with ITOL, RTOL, and ATOL +C fixed throughout the problem) is suitable, more general +C error controls can be obtained by substituting +C user-supplied routines for the setting of EWT and/or for +C the norm calculation. See Part 4 below. +C +C If global errors are to be estimated by making a repeated +C run on the same problem with smaller tolerances, then all +C components of RTOL and ATOL (i.e. of EWT) should be scaled +C down uniformly. +C +C ITASK = an index specifying the task to be performed. +C Input only. ITASK has the following values and meanings. +C 1 means normal computation of output values of y(t) at +C t = TOUT (by overshooting and interpolating). +C 2 means take one step only and return. +C 3 means stop at the first internal mesh point at or +C beyond t = TOUT and return. +C 4 means normal computation of output values of y(t) at +C t = TOUT but without overshooting t = TCRIT. +C TCRIT must be input as RWORK(1). TCRIT may be equal to +C or beyond TOUT, but not behind it in the direction of +C integration. This option is useful if the problem +C has a singularity at or beyond t = TCRIT. +C 5 means take one step, without passing TCRIT, and return. +C TCRIT must be input as RWORK(1). +C +C Note: If ITASK = 4 or 5 and the solver reaches TCRIT +C (within roundoff), it will return T = TCRIT (exactly) to +C indicate this (unless ITASK = 4 and TOUT comes before TCRIT, +C in which case answers at t = TOUT are returned first). +C +C ISTATE = an index used for input and output to specify the +C state of the calculation. +C +C On input, the values of ISTATE are as follows. +C 0 means this is the first call for the problem, and +C DLSODI is to compute the initial value of dy/dt +C (while doing other initializations). See note below. +C 1 means this is the first call for the problem, and +C the initial value of dy/dt has been supplied in +C YDOTI (DLSODI will do other initializations). See note +C below. +C 2 means this is not the first call, and the calculation +C is to continue normally, with no change in any input +C parameters except possibly TOUT and ITASK. +C (If ITOL, RTOL, and/or ATOL are changed between calls +C with ISTATE = 2, the new values will be used but not +C tested for legality.) +C 3 means this is not the first call, and the +C calculation is to continue normally, but with +C a change in input parameters other than +C TOUT and ITASK. Changes are allowed in +C NEQ, ITOL, RTOL, ATOL, IOPT, LRW, LIW, MF, ML, MU, +C and any of the optional inputs except H0. +C (See IWORK description for ML and MU.) +C Note: A preliminary call with TOUT = T is not counted +C as a first call here, as no initialization or checking of +C input is done. (Such a call is sometimes useful for the +C purpose of outputting the initial conditions.) +C Thus the first call for which TOUT .ne. T requires +C ISTATE = 0 or 1 on input. +C +C On output, ISTATE has the following values and meanings. +C 0 or 1 means nothing was done; TOUT = t and +C ISTATE = 0 or 1 on input. +C 2 means that the integration was performed successfully. +C 3 means that the user-supplied Subroutine RES signalled +C DLSODI to halt the integration and return (IRES = 2). +C Integration as far as T was achieved with no occurrence +C of IRES = 2, but this flag was set on attempting the +C next step. +C -1 means an excessive amount of work (more than MXSTEP +C steps) was done on this call, before completing the +C requested task, but the integration was otherwise +C successful as far as T. (MXSTEP is an optional input +C and is normally 500.) To continue, the user may +C simply reset ISTATE to a value .gt. 1 and call again +C (the excess work step counter will be reset to 0). +C In addition, the user may increase MXSTEP to avoid +C this error return (see below on optional inputs). +C -2 means too much accuracy was requested for the precision +C of the machine being used. This was detected before +C completing the requested task, but the integration +C was successful as far as T. To continue, the tolerance +C parameters must be reset, and ISTATE must be set +C to 3. The optional output TOLSF may be used for this +C purpose. (Note: If this condition is detected before +C taking any steps, then an illegal input return +C (ISTATE = -3) occurs instead.) +C -3 means illegal input was detected, before taking any +C integration steps. See written message for details. +C Note: If the solver detects an infinite loop of calls +C to the solver with illegal input, it will cause +C the run to stop. +C -4 means there were repeated error test failures on +C one attempted step, before completing the requested +C task, but the integration was successful as far as T. +C The problem may have a singularity, or the input +C may be inappropriate. +C -5 means there were repeated convergence test failures on +C one attempted step, before completing the requested +C task, but the integration was successful as far as T. +C This may be caused by an inaccurate Jacobian matrix. +C -6 means EWT(i) became zero for some i during the +C integration. pure relative error control (ATOL(i)=0.0) +C was requested on a variable which has now vanished. +C the integration was successful as far as T. +C -7 means that the user-supplied Subroutine RES set +C its error flag (IRES = 3) despite repeated tries by +C DLSODI to avoid that condition. +C -8 means that ISTATE was 0 on input but DLSODI was unable +C to compute the initial value of dy/dt. See the +C printed message for details. +C +C Note: Since the normal output value of ISTATE is 2, +C it does not need to be reset for normal continuation. +C Similarly, ISTATE (= 3) need not be reset if RES told +C DLSODI to return because the calling program must change +C the parameters of the problem. +C Also, since a negative input value of ISTATE will be +C regarded as illegal, a negative output value requires the +C user to change it, and possibly other inputs, before +C calling the solver again. +C +C IOPT = an integer flag to specify whether or not any optional +C inputs are being used on this call. Input only. +C The optional inputs are listed separately below. +C IOPT = 0 means no optional inputs are being used. +C Default values will be used in all cases. +C IOPT = 1 means one or more optional inputs are being used. +C +C RWORK = a real working array (double precision). +C The length of RWORK must be at least +C 20 + NYH*(MAXORD + 1) + 3*NEQ + LENWM where +C NYH = the initial value of NEQ, +C MAXORD = 12 (if METH = 1) or 5 (if METH = 2) (unless a +C smaller value is given as an optional input), +C LENWM = NEQ**2 + 2 if MITER is 1 or 2, and +C LENWM = (2*ML+MU+1)*NEQ + 2 if MITER is 4 or 5. +C (See MF description for the definition of METH and MITER.) +C Thus if MAXORD has its default value and NEQ is constant, +C this length is +C 22 + 16*NEQ + NEQ**2 for MF = 11 or 12, +C 22 + 17*NEQ + (2*ML+MU)*NEQ for MF = 14 or 15, +C 22 + 9*NEQ + NEQ**2 for MF = 21 or 22, +C 22 + 10*NEQ + (2*ML+MU)*NEQ for MF = 24 or 25. +C The first 20 words of RWORK are reserved for conditional +C and optional inputs and optional outputs. +C +C The following word in RWORK is a conditional input: +C RWORK(1) = TCRIT = critical value of t which the solver +C is not to overshoot. Required if ITASK is +C 4 or 5, and ignored otherwise. (See ITASK.) +C +C LRW = the length of the array RWORK, as declared by the user. +C (This will be checked by the solver.) +C +C IWORK = an integer work array. The length of IWORK must be at least +C 20 + NEQ . The first few words of IWORK are used for +C conditional and optional inputs and optional outputs. +C +C The following 2 words in IWORK are conditional inputs: +C IWORK(1) = ML These are the lower and upper +C IWORK(2) = MU half-bandwidths, respectively, of the +C matrices in the problem-- the Jacobian dr/dy +C and the left-hand side matrix A. These +C half-bandwidths exclude the main diagonal, +C so the total bandwidth is ML + MU + 1 . +C The band is defined by the matrix locations +C (i,j) with i-ML .le. j .le. i+MU. ML and MU +C must satisfy 0 .le. ML,MU .le. NEQ-1. +C These are required if MITER is 4 or 5, and +C ignored otherwise. +C ML and MU may in fact be the band parameters +C for matrices to which dr/dy and A are only +C approximately equal. +C +C LIW = the length of the array IWORK, as declared by the user. +C (This will be checked by the solver.) +C +C Note: The work arrays must not be altered between calls to DLSODI +C for the same problem, except possibly for the conditional and +C optional inputs, and except for the last 3*NEQ words of RWORK. +C The latter space is used for internal scratch space, and so is +C available for use by the user outside DLSODI between calls, if +C desired (but not for use by RES, ADDA, or JAC). +C +C MF = the method flag. Used only for input. The legal values of +C MF are 11, 12, 14, 15, 21, 22, 24, and 25. +C MF has decimal digits METH and MITER: MF = 10*METH + MITER. +C METH indicates the basic linear multistep method: +C METH = 1 means the implicit Adams method. +C METH = 2 means the method based on Backward +C Differentiation Formulas (BDFs). +C The BDF method is strongly preferred for stiff +C problems, while the Adams method is preferred when +C the problem is not stiff. If the matrix A(t,y) is +C nonsingular, stiffness here can be taken to mean that of +C the explicit ODE system dy/dt = A-inverse * g. If A is +C singular, the concept of stiffness is not well defined. +C If you do not know whether the problem is stiff, we +C recommend using METH = 2. If it is stiff, the advantage +C of METH = 2 over METH = 1 will be great, while if it is +C not stiff, the advantage of METH = 1 will be slight. +C If maximum efficiency is important, some experimentation +C with METH may be necessary. +C MITER indicates the corrector iteration method: +C MITER = 1 means chord iteration with a user-supplied +C full (NEQ by NEQ) Jacobian. +C MITER = 2 means chord iteration with an internally +C generated (difference quotient) full Jacobian. +C This uses NEQ+1 extra calls to RES per dr/dy +C evaluation. +C MITER = 4 means chord iteration with a user-supplied +C banded Jacobian. +C MITER = 5 means chord iteration with an internally +C generated banded Jacobian (using ML+MU+2 +C extra calls to RES per dr/dy evaluation). +C If MITER = 1 or 4, the user must supply a Subroutine JAC +C (the name is arbitrary) as described above under JAC. +C For other values of MITER, a dummy argument can be used. +C----------------------------------------------------------------------- +C Optional Inputs. +C +C The following is a list of the optional inputs provided for in the +C call sequence. (See also Part 2.) For each such input variable, +C this table lists its name as used in this documentation, its +C location in the call sequence, its meaning, and the default value. +C the use of any of these inputs requires IOPT = 1, and in that +C case all of these inputs are examined. A value of zero for any +C of these optional inputs will cause the default value to be used. +C Thus to use a subset of the optional inputs, simply preload +C locations 5 to 10 in RWORK and IWORK to 0.0 and 0 respectively, and +C then set those of interest to nonzero values. +C +C Name Location Meaning and Default Value +C +C H0 RWORK(5) the step size to be attempted on the first step. +C The default value is determined by the solver. +C +C HMAX RWORK(6) the maximum absolute step size allowed. +C The default value is infinite. +C +C HMIN RWORK(7) the minimum absolute step size allowed. +C The default value is 0. (This lower bound is not +C enforced on the final step before reaching TCRIT +C when ITASK = 4 or 5.) +C +C MAXORD IWORK(5) the maximum order to be allowed. The default +C value is 12 if METH = 1, and 5 if METH = 2. +C If MAXORD exceeds the default value, it will +C be reduced to the default value. +C If MAXORD is changed during the problem, it may +C cause the current order to be reduced. +C +C MXSTEP IWORK(6) maximum number of (internally defined) steps +C allowed during one call to the solver. +C The default value is 500. +C +C MXHNIL IWORK(7) maximum number of messages printed (per problem) +C warning that T + H = T on a step (H = step size). +C This must be positive to result in a non-default +C value. The default value is 10. +C----------------------------------------------------------------------- +C Optional Outputs. +C +C As optional additional output from DLSODI, the variables listed +C below are quantities related to the performance of DLSODI +C which are available to the user. These are communicated by way of +C the work arrays, but also have internal mnemonic names as shown. +C Except where stated otherwise, all of these outputs are defined +C on any successful return from DLSODI, and on any return with +C ISTATE = -1, -2, -4, -5, -6, or -7. On a return with -3 (illegal +C input) or -8, they will be unchanged from their existing values +C (if any), except possibly for TOLSF, LENRW, and LENIW. +C On any error return, outputs relevant to the error will be defined, +C as noted below. +C +C Name Location Meaning +C +C HU RWORK(11) the step size in t last used (successfully). +C +C HCUR RWORK(12) the step size to be attempted on the next step. +C +C TCUR RWORK(13) the current value of the independent variable +C which the solver has actually reached, i.e. the +C current internal mesh point in t. On output, TCUR +C will always be at least as far as the argument +C T, but may be farther (if interpolation was done). +C +C TOLSF RWORK(14) a tolerance scale factor, greater than 1.0, +C computed when a request for too much accuracy was +C detected (ISTATE = -3 if detected at the start of +C the problem, ISTATE = -2 otherwise). If ITOL is +C left unaltered but RTOL and ATOL are uniformly +C scaled up by a factor of TOLSF for the next call, +C then the solver is deemed likely to succeed. +C (The user may also ignore TOLSF and alter the +C tolerance parameters in any other way appropriate.) +C +C NST IWORK(11) the number of steps taken for the problem so far. +C +C NRE IWORK(12) the number of residual evaluations (RES calls) +C for the problem so far. +C +C NJE IWORK(13) the number of Jacobian evaluations (each involving +C an evaluation of A and dr/dy) for the problem so +C far. This equals the number of calls to ADDA and +C (if MITER = 1 or 4) JAC, and the number of matrix +C LU decompositions. +C +C NQU IWORK(14) the method order last used (successfully). +C +C NQCUR IWORK(15) the order to be attempted on the next step. +C +C IMXER IWORK(16) the index of the component of largest magnitude in +C the weighted local error vector ( E(i)/EWT(i) ), +C on an error return with ISTATE = -4 or -5. +C +C LENRW IWORK(17) the length of RWORK actually required. +C This is defined on normal returns and on an illegal +C input return for insufficient storage. +C +C LENIW IWORK(18) the length of IWORK actually required. +C This is defined on normal returns and on an illegal +C input return for insufficient storage. +C +C +C The following two arrays are segments of the RWORK array which +C may also be of interest to the user as optional outputs. +C For each array, the table below gives its internal name, +C its base address in RWORK, and its description. +C +C Name Base Address Description +C +C YH 21 the Nordsieck history array, of size NYH by +C (NQCUR + 1), where NYH is the initial value +C of NEQ. For j = 0,1,...,NQCUR, column j+1 +C of YH contains HCUR**j/factorial(j) times +C the j-th derivative of the interpolating +C polynomial currently representing the solution, +C evaluated at t = TCUR. +C +C ACOR LENRW-NEQ+1 array of size NEQ used for the accumulated +C corrections on each step, scaled on output to +C represent the estimated local error in y on the +C last step. This is the vector E in the descrip- +C tion of the error control. It is defined only +C on a return from DLSODI with ISTATE = 2. +C +C----------------------------------------------------------------------- +C Part 2. Other Routines Callable. +C +C The following are optional calls which the user may make to +C gain additional capabilities in conjunction with DLSODI. +C (The routines XSETUN and XSETF are designed to conform to the +C SLATEC error handling package.) +C +C Form of Call Function +C CALL XSETUN(LUN) Set the logical unit number, LUN, for +C output of messages from DLSODI, if +C the default is not desired. +C The default value of LUN is 6. +C +C CALL XSETF(MFLAG) Set a flag to control the printing of +C messages by DLSODI. +C MFLAG = 0 means do not print. (Danger: +C This risks losing valuable information.) +C MFLAG = 1 means print (the default). +C +C Either of the above calls may be made at +C any time and will take effect immediately. +C +C CALL DSRCOM(RSAV,ISAV,JOB) saves and restores the contents of +C the internal Common blocks used by +C DLSODI (see Part 3 below). +C RSAV must be a real array of length 218 +C or more, and ISAV must be an integer +C array of length 37 or more. +C JOB=1 means save Common into RSAV/ISAV. +C JOB=2 means restore Common from RSAV/ISAV. +C DSRCOM is useful if one is +C interrupting a run and restarting +C later, or alternating between two or +C more problems solved with DLSODI. +C +C CALL DINTDY(,,,,,) Provide derivatives of y, of various +C (see below) orders, at a specified point t, if +C desired. It may be called only after +C a successful return from DLSODI. +C +C The detailed instructions for using DINTDY are as follows. +C The form of the call is: +C +C CALL DINTDY (T, K, RWORK(21), NYH, DKY, IFLAG) +C +C The input parameters are: +C +C T = value of independent variable where answers are desired +C (normally the same as the T last returned by DLSODI). +C For valid results, T must lie between TCUR - HU and TCUR. +C (See optional outputs for TCUR and HU.) +C K = integer order of the derivative desired. K must satisfy +C 0 .le. K .le. NQCUR, where NQCUR is the current order +C (see optional outputs). The capability corresponding +C to K = 0, i.e. computing y(T), is already provided +C by DLSODI directly. Since NQCUR .ge. 1, the first +C derivative dy/dt is always available with DINTDY. +C RWORK(21) = the base address of the history array YH. +C NYH = column length of YH, equal to the initial value of NEQ. +C +C The output parameters are: +C +C DKY = a real array of length NEQ containing the computed value +C of the K-th derivative of y(t). +C IFLAG = integer flag, returned as 0 if K and T were legal, +C -1 if K was illegal, and -2 if T was illegal. +C On an error return, a message is also written. +C----------------------------------------------------------------------- +C Part 3. Common Blocks. +C +C If DLSODI is to be used in an overlay situation, the user +C must declare, in the primary overlay, the variables in: +C (1) the call sequence to DLSODI, and +C (2) the internal Common block +C /DLS001/ of length 255 (218 double precision words +C followed by 37 integer words), +C +C If DLSODI is used on a system in which the contents of internal +C Common blocks are not preserved between calls, the user should +C declare the above Common block in the calling program to insure +C that their contents are preserved. +C +C If the solution of a given problem by DLSODI is to be interrupted +C and then later continued, such as when restarting an interrupted run +C or alternating between two or more problems, the user should save, +C following the return from the last DLSODI call prior to the +C interruption, the contents of the call sequence variables and the +C internal Common blocks, and later restore these values before the +C next DLSODI call for that problem. To save and restore the Common +C blocks, use Subroutine DSRCOM (see Part 2 above). +C +C----------------------------------------------------------------------- +C Part 4. Optionally Replaceable Solver Routines. +C +C Below are descriptions of two routines in the DLSODI package which +C relate to the measurement of errors. Either routine can be +C replaced by a user-supplied version, if desired. However, since such +C a replacement may have a major impact on performance, it should be +C done only when absolutely necessary, and only with great caution. +C (Note: The means by which the package version of a routine is +C superseded by the user's version may be system-dependent.) +C +C (a) DEWSET. +C The following subroutine is called just before each internal +C integration step, and sets the array of error weights, EWT, as +C described under ITOL/RTOL/ATOL above: +C SUBROUTINE DEWSET (NEQ, ITOL, RTOL, ATOL, YCUR, EWT) +C where NEQ, ITOL, RTOL, and ATOL are as in the DLSODI call sequence, +C YCUR contains the current dependent variable vector, and +C EWT is the array of weights set by DEWSET. +C +C If the user supplies this subroutine, it must return in EWT(i) +C (i = 1,...,NEQ) a positive quantity suitable for comparing errors +C in y(i) to. The EWT array returned by DEWSET is passed to the DVNORM +C routine (see below), and also used by DLSODI in the computation +C of the optional output IMXER, the diagonal Jacobian approximation, +C and the increments for difference quotient Jacobians. +C +C In the user-supplied version of DEWSET, it may be desirable to use +C the current values of derivatives of y. Derivatives up to order NQ +C are available from the history array YH, described above under +C optional outputs. In DEWSET, YH is identical to the YCUR array, +C extended to NQ + 1 columns with a column length of NYH and scale +C factors of H**j/factorial(j). On the first call for the problem, +C given by NST = 0, NQ is 1 and H is temporarily set to 1.0. +C NYH is the initial value of NEQ. The quantities NQ, H, and NST +C can be obtained by including in DEWSET the statements: +C DOUBLE PRECISION RLS +C COMMON /DLS001/ RLS(218),ILS(37) +C NQ = ILS(33) +C NST = ILS(34) +C H = RLS(212) +C Thus, for example, the current value of dy/dt can be obtained as +C YCUR(NYH+i)/H (i=1,...,NEQ) (and the division by H is +C unnecessary when NST = 0). +C +C (b) DVNORM. +C The following is a real function routine which computes the weighted +C root-mean-square norm of a vector v: +C D = DVNORM (N, V, W) +C where: +C N = the length of the vector, +C V = real array of length N containing the vector, +C W = real array of length N containing weights, +C D = SQRT( (1/N) * sum(V(i)*W(i))**2 ). +C DVNORM is called with N = NEQ and with W(i) = 1.0/EWT(i), where +C EWT is as set by Subroutine DEWSET. +C +C If the user supplies this function, it should return a non-negative +C value of DVNORM suitable for use in the error control in DLSODI. +C None of the arguments should be altered by DVNORM. +C For example, a user-supplied DVNORM routine might: +C -substitute a max-norm of (V(i)*W(i)) for the RMS-norm, or +C -ignore some components of V in the norm, with the effect of +C suppressing the error control on those components of y. +C----------------------------------------------------------------------- +C +C***REVISION HISTORY (YYYYMMDD) +C 19800424 DATE WRITTEN +C 19800519 Corrected access of YH on forced order reduction; +C numerous corrections to prologues and other comments. +C 19800617 In main driver, added loading of SQRT(UROUND) in RWORK; +C minor corrections to main prologue. +C 19800903 Corrected ISTATE logic; minor changes in prologue. +C 19800923 Added zero initialization of HU and NQU. +C 19801028 Reorganized RES calls in AINVG, STODI, and PREPJI; +C in LSODI, corrected NRE increment and reset LDY0 at 580; +C numerous corrections to main prologue. +C 19801218 Revised XERRWD routine; minor corrections to main prologue. +C 19810330 Added Common block /LSI001/; use LSODE's INTDY and SOLSY; +C minor corrections to XERRWD and error message at 604; +C minor corrections to declarations; corrections to prologues. +C 19810818 Numerous revisions: replaced EWT by 1/EWT; used flags +C JCUR, ICF, IERPJ, IERSL between STODI and subordinates; +C added tuning parameters CCMAX, MAXCOR, MSBP, MXNCF; +C reorganized returns from STODI; reorganized type decls.; +C fixed message length in XERRWD; changed default LUNIT to 6; +C changed Common lengths; changed comments throughout. +C 19820906 Corrected use of ABS(H) in STODI; minor comment fixes. +C 19830510 Numerous revisions: revised diff. quotient increment; +C eliminated block /LSI001/, using IERPJ flag; +C revised STODI logic after PJAC return; +C revised tuning of H change and step attempts in STODI; +C corrections to main prologue and internal comments. +C 19870330 Major update: corrected comments throughout; +C removed TRET from Common; rewrote EWSET with 4 loops; +C fixed t test in INTDY; added Cray directives in STODI; +C in STODI, fixed DELP init. and logic around PJAC call; +C combined routines to save/restore Common; +C passed LEVEL = 0 in error message calls (except run abort). +C 20010425 Major update: convert source lines to upper case; +C added *DECK lines; changed from 1 to * in dummy dimensions; +C changed names R1MACH/D1MACH to RUMACH/DUMACH; +C renamed routines for uniqueness across single/double prec.; +C converted intrinsic names to generic form; +C removed ILLIN and NTREP (data loaded) from Common; +C removed all 'own' variables from Common; +C changed error messages to quoted strings; +C replaced XERRWV/XERRWD with 1993 revised version; +C converted prologues, comments, error messages to mixed case; +C converted arithmetic IF statements to logical IF statements; +C numerous corrections to prologues and internal comments. +C 20010507 Converted single precision source to double precision. +C 20020502 Corrected declarations in descriptions of user routines. +C 20031105 Restored 'own' variables to Common block, to enable +C interrupt/restart feature. +C 20031112 Added SAVE statements for data-loaded constants. +C 20031117 Changed internal names NRE, LSAVR to NFE, LSAVF resp. +C +C----------------------------------------------------------------------- +C Other routines in the DLSODI package. +C +C In addition to Subroutine DLSODI, the DLSODI package includes the +C following subroutines and function routines: +C DAINVG computes the initial value of the vector +C dy/dt = A-inverse * g +C DINTDY computes an interpolated value of the y vector at t = TOUT. +C DSTODI is the core integrator, which does one step of the +C integration and the associated error control. +C DCFODE sets all method coefficients and test constants. +C DPREPJI computes and preprocesses the Jacobian matrix +C and the Newton iteration matrix P. +C DSOLSY manages solution of linear system in chord iteration. +C DEWSET sets the error weight vector EWT before each step. +C DVNORM computes the weighted RMS-norm of a vector. +C DSRCOM is a user-callable routine to save and restore +C the contents of the internal Common blocks. +C DGEFA and DGESL are routines from LINPACK for solving full +C systems of linear algebraic equations. +C DGBFA and DGBSL are routines from LINPACK for solving banded +C linear systems. +C DUMACH computes the unit roundoff in a machine-independent manner. +C XERRWD, XSETUN, XSETF, IXSAV, and IUMACH handle the printing of all +C error messages and warnings. XERRWD is machine-dependent. +C Note: DVNORM, DUMACH, IXSAV, and IUMACH are function routines. +C All the others are subroutines. +C +C----------------------------------------------------------------------- + EXTERNAL DPREPJI, DSOLSY + DOUBLE PRECISION DUMACH, DVNORM + INTEGER INIT, MXSTEP, MXHNIL, NHNIL, NSLAST, NYH, IOWNS, + 1 ICF, IERPJ, IERSL, JCUR, JSTART, KFLAG, L, + 2 LYH, LEWT, LACOR, LSAVF, LWM, LIWM, METH, MITER, + 3 MAXORD, MAXCOR, MSBP, MXNCF, N, NQ, NST, NFE, NJE, NQU + INTEGER I, I1, I2, IER, IFLAG, IMXER, IRES, KGO, + 1 LENIW, LENRW, LENWM, LP, LYD0, ML, MORD, MU, MXHNL0, MXSTP0 + DOUBLE PRECISION ROWNS, + 1 CCMAX, EL0, H, HMIN, HMXI, HU, RC, TN, UROUND + DOUBLE PRECISION ATOLI, AYI, BIG, EWTI, H0, HMAX, HMX, RH, RTOLI, + 1 TCRIT, TDIST, TNEXT, TOL, TOLSF, TP, SIZE, SUM, W0 + DIMENSION MORD(2) + LOGICAL IHIT + CHARACTER*60 MSG + SAVE MORD, MXSTP0, MXHNL0 +C----------------------------------------------------------------------- +C The following internal Common block contains +C (a) variables which are local to any subroutine but whose values must +C be preserved between calls to the routine ("own" variables), and +C (b) variables which are communicated between subroutines. +C The block DLS001 is declared in subroutines DLSODI, DINTDY, DSTODI, +C DPREPJI, and DSOLSY. +C Groups of variables are replaced by dummy arrays in the Common +C declarations in routines where those variables are not used. +C----------------------------------------------------------------------- + COMMON /DLS001/ ROWNS(209), + 1 CCMAX, EL0, H, HMIN, HMXI, HU, RC, TN, UROUND, + 2 INIT, MXSTEP, MXHNIL, NHNIL, NSLAST, NYH, IOWNS(6), + 3 ICF, IERPJ, IERSL, JCUR, JSTART, KFLAG, L, + 4 LYH, LEWT, LACOR, LSAVF, LWM, LIWM, METH, MITER, + 5 MAXORD, MAXCOR, MSBP, MXNCF, N, NQ, NST, NFE, NJE, NQU +C + DATA MORD(1),MORD(2)/12,5/, MXSTP0/500/, MXHNL0/10/ +C----------------------------------------------------------------------- +C Block A. +C This code block is executed on every call. +C It tests ISTATE and ITASK for legality and branches appropriately. +C If ISTATE .gt. 1 but the flag INIT shows that initialization has +C not yet been done, an error return occurs. +C If ISTATE = 0 or 1 and TOUT = T, return immediately. +C----------------------------------------------------------------------- + IF (ISTATE .LT. 0 .OR. ISTATE .GT. 3) GO TO 601 + IF (ITASK .LT. 1 .OR. ITASK .GT. 5) GO TO 602 + IF (ISTATE .LE. 1) GO TO 10 + IF (INIT .EQ. 0) GO TO 603 + IF (ISTATE .EQ. 2) GO TO 200 + GO TO 20 + 10 INIT = 0 + IF (TOUT .EQ. T) RETURN +C----------------------------------------------------------------------- +C Block B. +C The next code block is executed for the initial call (ISTATE = 0 or 1) +C or for a continuation call with parameter changes (ISTATE = 3). +C It contains checking of all inputs and various initializations. +C +C First check legality of the non-optional inputs NEQ, ITOL, IOPT, +C MF, ML, and MU. +C----------------------------------------------------------------------- + 20 IF (NEQ(1) .LE. 0) GO TO 604 + IF (ISTATE .LE. 1) GO TO 25 + IF (NEQ(1) .GT. N) GO TO 605 + 25 N = NEQ(1) + IF (ITOL .LT. 1 .OR. ITOL .GT. 4) GO TO 606 + IF (IOPT .LT. 0 .OR. IOPT .GT. 1) GO TO 607 + METH = MF/10 + MITER = MF - 10*METH + IF (METH .LT. 1 .OR. METH .GT. 2) GO TO 608 + IF (MITER .LE. 0 .OR. MITER .GT. 5) GO TO 608 + IF (MITER .EQ. 3) GO TO 608 + IF (MITER .LT. 3) GO TO 30 + ML = IWORK(1) + MU = IWORK(2) + IF (ML .LT. 0 .OR. ML .GE. N) GO TO 609 + IF (MU .LT. 0 .OR. MU .GE. N) GO TO 610 + 30 CONTINUE +C Next process and check the optional inputs. -------------------------- + IF (IOPT .EQ. 1) GO TO 40 + MAXORD = MORD(METH) + MXSTEP = MXSTP0 + MXHNIL = MXHNL0 + IF (ISTATE .LE. 1) H0 = 0.0D0 + HMXI = 0.0D0 + HMIN = 0.0D0 + GO TO 60 + 40 MAXORD = IWORK(5) + IF (MAXORD .LT. 0) GO TO 611 + IF (MAXORD .EQ. 0) MAXORD = 100 + MAXORD = MIN(MAXORD,MORD(METH)) + MXSTEP = IWORK(6) + IF (MXSTEP .LT. 0) GO TO 612 + IF (MXSTEP .EQ. 0) MXSTEP = MXSTP0 + MXHNIL = IWORK(7) + IF (MXHNIL .LT. 0) GO TO 613 + IF (MXHNIL .EQ. 0) MXHNIL = MXHNL0 + IF (ISTATE .GT. 1) GO TO 50 + H0 = RWORK(5) + IF ((TOUT - T)*H0 .LT. 0.0D0) GO TO 614 + 50 HMAX = RWORK(6) + IF (HMAX .LT. 0.0D0) GO TO 615 + HMXI = 0.0D0 + IF (HMAX .GT. 0.0D0) HMXI = 1.0D0/HMAX + HMIN = RWORK(7) + IF (HMIN .LT. 0.0D0) GO TO 616 +C----------------------------------------------------------------------- +C Set work array pointers and check lengths LRW and LIW. +C Pointers to segments of RWORK and IWORK are named by prefixing L to +C the name of the segment. E.g., the segment YH starts at RWORK(LYH). +C Segments of RWORK (in order) are denoted YH, WM, EWT, SAVR, ACOR. +C----------------------------------------------------------------------- + 60 LYH = 21 + IF (ISTATE .LE. 1) NYH = N + LWM = LYH + (MAXORD + 1)*NYH + IF (MITER .LE. 2) LENWM = N*N + 2 + IF (MITER .GE. 4) LENWM = (2*ML + MU + 1)*N + 2 + LEWT = LWM + LENWM + LSAVF = LEWT + N + LACOR = LSAVF + N + LENRW = LACOR + N - 1 + IWORK(17) = LENRW + LIWM = 1 + LENIW = 20 + N + IWORK(18) = LENIW + IF (LENRW .GT. LRW) GO TO 617 + IF (LENIW .GT. LIW) GO TO 618 +C Check RTOL and ATOL for legality. ------------------------------------ + RTOLI = RTOL(1) + ATOLI = ATOL(1) + DO 70 I = 1,N + IF (ITOL .GE. 3) RTOLI = RTOL(I) + IF (ITOL .EQ. 2 .OR. ITOL .EQ. 4) ATOLI = ATOL(I) + IF (RTOLI .LT. 0.0D0) GO TO 619 + IF (ATOLI .LT. 0.0D0) GO TO 620 + 70 CONTINUE + IF (ISTATE .LE. 1) GO TO 100 +C If ISTATE = 3, set flag to signal parameter changes to DSTODI. ------- + JSTART = -1 + IF (NQ .LE. MAXORD) GO TO 90 +C MAXORD was reduced below NQ. Copy YH(*,MAXORD+2) into YDOTI.--------- + DO 80 I = 1,N + 80 YDOTI(I) = RWORK(I+LWM-1) +C Reload WM(1) = RWORK(lWM), since lWM may have changed. --------------- + 90 RWORK(LWM) = SQRT(UROUND) + IF (N .EQ. NYH) GO TO 200 +C NEQ was reduced. Zero part of YH to avoid undefined references. ----- + I1 = LYH + L*NYH + I2 = LYH + (MAXORD + 1)*NYH - 1 + IF (I1 .GT. I2) GO TO 200 + DO 95 I = I1,I2 + 95 RWORK(I) = 0.0D0 + GO TO 200 +C----------------------------------------------------------------------- +C Block C. +C The next block is for the initial call only (ISTATE = 0 or 1). +C It contains all remaining initializations, the call to DAINVG +C (if ISTATE = 1), and the calculation of the initial step size. +C The error weights in EWT are inverted after being loaded. +C----------------------------------------------------------------------- + 100 UROUND = DUMACH() + TN = T + IF (ITASK .NE. 4 .AND. ITASK .NE. 5) GO TO 105 + TCRIT = RWORK(1) + IF ((TCRIT - TOUT)*(TOUT - T) .LT. 0.0D0) GO TO 625 + IF (H0 .NE. 0.0D0 .AND. (T + H0 - TCRIT)*H0 .GT. 0.0D0) + 1 H0 = TCRIT - T + 105 JSTART = 0 + RWORK(LWM) = SQRT(UROUND) + NHNIL = 0 + NST = 0 + NFE = 0 + NJE = 0 + NSLAST = 0 + HU = 0.0D0 + NQU = 0 + CCMAX = 0.3D0 + MAXCOR = 3 + MSBP = 20 + MXNCF = 10 +C Compute initial dy/dt, if necessary, and load it and initial Y into YH + LYD0 = LYH + NYH + LP = LWM + 1 + IF (ISTATE .EQ. 1) GO TO 120 +C DLSODI must compute initial dy/dt (LYD0 points to YH(*,2)). ---------- + CALL DAINVG( RES, ADDA, NEQ, T, Y, RWORK(LYD0), MITER, + 1 ML, MU, RWORK(LP), IWORK(21), IER ) + NFE = NFE + 1 + IF (IER .LT. 0) GO TO 560 + IF (IER .GT. 0) GO TO 565 + DO 115 I = 1,N + 115 RWORK(I+LYH-1) = Y(I) + GO TO 130 +C Initial dy/dt was supplied. Load into YH (LYD0 points to YH(*,2).). - + 120 DO 125 I = 1,N + RWORK(I+LYH-1) = Y(I) + 125 RWORK(I+LYD0-1) = YDOTI(I) +C Load and invert the EWT array. (H is temporarily set to 1.0.) ------- + 130 CONTINUE + NQ = 1 + H = 1.0D0 + CALL DEWSET (N, ITOL, RTOL, ATOL, RWORK(LYH), RWORK(LEWT)) + DO 135 I = 1,N + IF (RWORK(I+LEWT-1) .LE. 0.0D0) GO TO 621 + 135 RWORK(I+LEWT-1) = 1.0D0/RWORK(I+LEWT-1) +C----------------------------------------------------------------------- +C The coding below computes the step size, H0, to be attempted on the +C first step, unless the user has supplied a value for this. +C First check that TOUT - T differs significantly from zero. +C A scalar tolerance quantity TOL is computed, as MAX(RTOL(i)) +C if this is positive, or MAX(ATOL(i)/ABS(Y(i))) otherwise, adjusted +C so as to be between 100*UROUND and 1.0E-3. +C Then the computed value H0 is given by.. +C NEQ +C H0**2 = TOL / ( w0**-2 + (1/NEQ) * Sum ( YDOT(i)/ywt(i) )**2 ) +C 1 +C where w0 = MAX ( ABS(T), ABS(TOUT) ), +C YDOT(i) = i-th component of initial value of dy/dt, +C ywt(i) = EWT(i)/TOL (a weight for y(i)). +C The sign of H0 is inferred from the initial values of TOUT and T. +C----------------------------------------------------------------------- + IF (H0 .NE. 0.0D0) GO TO 180 + TDIST = ABS(TOUT - T) + W0 = MAX(ABS(T),ABS(TOUT)) + IF (TDIST .LT. 2.0D0*UROUND*W0) GO TO 622 + TOL = RTOL(1) + IF (ITOL .LE. 2) GO TO 145 + DO 140 I = 1,N + 140 TOL = MAX(TOL,RTOL(I)) + 145 IF (TOL .GT. 0.0D0) GO TO 160 + ATOLI = ATOL(1) + DO 150 I = 1,N + IF (ITOL .EQ. 2 .OR. ITOL .EQ. 4) ATOLI = ATOL(I) + AYI = ABS(Y(I)) + IF (AYI .NE. 0.0D0) TOL = MAX(TOL,ATOLI/AYI) + 150 CONTINUE + 160 TOL = MAX(TOL,100.0D0*UROUND) + TOL = MIN(TOL,0.001D0) + SUM = DVNORM (N, RWORK(LYD0), RWORK(LEWT)) + SUM = 1.0D0/(TOL*W0*W0) + TOL*SUM**2 + H0 = 1.0D0/SQRT(SUM) + H0 = MIN(H0,TDIST) + H0 = SIGN(H0,TOUT-T) +C Adjust H0 if necessary to meet HMAX bound. --------------------------- + 180 RH = ABS(H0)*HMXI + IF (RH .GT. 1.0D0) H0 = H0/RH +C Load H with H0 and scale YH(*,2) by H0. ------------------------------ + H = H0 + DO 190 I = 1,N + 190 RWORK(I+LYD0-1) = H0*RWORK(I+LYD0-1) + GO TO 270 +C----------------------------------------------------------------------- +C Block D. +C The next code block is for continuation calls only (ISTATE = 2 or 3) +C and is to check stop conditions before taking a step. +C----------------------------------------------------------------------- + 200 NSLAST = NST + GO TO (210, 250, 220, 230, 240), ITASK + 210 IF ((TN - TOUT)*H .LT. 0.0D0) GO TO 250 + CALL DINTDY (TOUT, 0, RWORK(LYH), NYH, Y, IFLAG) + IF (IFLAG .NE. 0) GO TO 627 + T = TOUT + GO TO 420 + 220 TP = TN - HU*(1.0D0 + 100.0D0*UROUND) + IF ((TP - TOUT)*H .GT. 0.0D0) GO TO 623 + IF ((TN - TOUT)*H .LT. 0.0D0) GO TO 250 + GO TO 400 + 230 TCRIT = RWORK(1) + IF ((TN - TCRIT)*H .GT. 0.0D0) GO TO 624 + IF ((TCRIT - TOUT)*H .LT. 0.0D0) GO TO 625 + IF ((TN - TOUT)*H .LT. 0.0D0) GO TO 245 + CALL DINTDY (TOUT, 0, RWORK(LYH), NYH, Y, IFLAG) + IF (IFLAG .NE. 0) GO TO 627 + T = TOUT + GO TO 420 + 240 TCRIT = RWORK(1) + IF ((TN - TCRIT)*H .GT. 0.0D0) GO TO 624 + 245 HMX = ABS(TN) + ABS(H) + IHIT = ABS(TN - TCRIT) .LE. 100.0D0*UROUND*HMX + IF (IHIT) GO TO 400 + TNEXT = TN + H*(1.0D0 + 4.0D0*UROUND) + IF ((TNEXT - TCRIT)*H .LE. 0.0D0) GO TO 250 + H = (TCRIT - TN)*(1.0D0 - 4.0D0*UROUND) + IF (ISTATE .EQ. 2) JSTART = -2 +C----------------------------------------------------------------------- +C Block E. +C The next block is normally executed for all calls and contains +C the call to the one-step core integrator DSTODI. +C +C This is a looping point for the integration steps. +C +C First check for too many steps being taken, update EWT (if not at +C start of problem), check for too much accuracy being requested, and +C check for H below the roundoff level in T. +C----------------------------------------------------------------------- + 250 CONTINUE + IF ((NST-NSLAST) .GE. MXSTEP) GO TO 500 + CALL DEWSET (N, ITOL, RTOL, ATOL, RWORK(LYH), RWORK(LEWT)) + DO 260 I = 1,N + IF (RWORK(I+LEWT-1) .LE. 0.0D0) GO TO 510 + 260 RWORK(I+LEWT-1) = 1.0D0/RWORK(I+LEWT-1) + 270 TOLSF = UROUND*DVNORM (N, RWORK(LYH), RWORK(LEWT)) + IF (TOLSF .LE. 1.0D0) GO TO 280 + TOLSF = TOLSF*2.0D0 + IF (NST .EQ. 0) GO TO 626 + GO TO 520 + 280 IF ((TN + H) .NE. TN) GO TO 290 + NHNIL = NHNIL + 1 + IF (NHNIL .GT. MXHNIL) GO TO 290 + MSG = 'DLSODI- Warning..Internal T (=R1) and H (=R2) are' + CALL XERRWD (MSG, 50, 101, 0, 0, 0, 0, 0, 0.0D0, 0.0D0) + MSG=' such that in the machine, T + H = T on the next step ' + CALL XERRWD (MSG, 60, 101, 0, 0, 0, 0, 0, 0.0D0, 0.0D0) + MSG = ' (H = step size). Solver will continue anyway.' + CALL XERRWD (MSG, 50, 101, 0, 0, 0, 0, 2, TN, H) + IF (NHNIL .LT. MXHNIL) GO TO 290 + MSG = 'DLSODI- Above warning has been issued I1 times. ' + CALL XERRWD (MSG, 50, 102, 0, 0, 0, 0, 0, 0.0D0, 0.0D0) + MSG = ' It will not be issued again for this problem.' + CALL XERRWD (MSG, 50, 102, 0, 1, MXHNIL, 0, 0, 0.0D0, 0.0D0) + 290 CONTINUE +C----------------------------------------------------------------------- +C CALL DSTODI(NEQ,Y,YH,NYH,YH1,EWT,SAVF,SAVR,ACOR,WM,IWM,RES, +C ADDA,JAC,DPREPJI,DSOLSY) +C Note: SAVF in DSTODI occupies the same space as YDOTI in DLSODI. +C----------------------------------------------------------------------- + CALL DSTODI (NEQ, Y, RWORK(LYH), NYH, RWORK(LYH), RWORK(LEWT), + 1 YDOTI, RWORK(LSAVF), RWORK(LACOR), RWORK(LWM), + 2 IWORK(LIWM), RES, ADDA, JAC, DPREPJI, DSOLSY ) + KGO = 1 - KFLAG + GO TO (300, 530, 540, 400, 550), KGO +C +C KGO = 1:success; 2:error test failure; 3:convergence failure; +C 4:RES ordered return. 5:RES returned error. +C----------------------------------------------------------------------- +C Block F. +C The following block handles the case of a successful return from the +C core integrator (KFLAG = 0). Test for stop conditions. +C----------------------------------------------------------------------- + 300 INIT = 1 + GO TO (310, 400, 330, 340, 350), ITASK +C ITASK = 1. If TOUT has been reached, interpolate. ------------------- + 310 IF ((TN - TOUT)*H .LT. 0.0D0) GO TO 250 + CALL DINTDY (TOUT, 0, RWORK(LYH), NYH, Y, IFLAG) + T = TOUT + GO TO 420 +C ITASK = 3. Jump to exit if TOUT was reached. ------------------------ + 330 IF ((TN - TOUT)*H .GE. 0.0D0) GO TO 400 + GO TO 250 +C ITASK = 4. see if TOUT or TCRIT was reached. adjust h if necessary. + 340 IF ((TN - TOUT)*H .LT. 0.0D0) GO TO 345 + CALL DINTDY (TOUT, 0, RWORK(LYH), NYH, Y, IFLAG) + T = TOUT + GO TO 420 + 345 HMX = ABS(TN) + ABS(H) + IHIT = ABS(TN - TCRIT) .LE. 100.0D0*UROUND*HMX + IF (IHIT) GO TO 400 + TNEXT = TN + H*(1.0D0 + 4.0D0*UROUND) + IF ((TNEXT - TCRIT)*H .LE. 0.0D0) GO TO 250 + H = (TCRIT - TN)*(1.0D0 - 4.0D0*UROUND) + JSTART = -2 + GO TO 250 +C ITASK = 5. See if TCRIT was reached and jump to exit. --------------- + 350 HMX = ABS(TN) + ABS(H) + IHIT = ABS(TN - TCRIT) .LE. 100.0D0*UROUND*HMX +C----------------------------------------------------------------------- +C Block G. +C The following block handles all successful returns from DLSODI. +C if ITASK .ne. 1, Y is loaded from YH and T is set accordingly. +C ISTATE is set to 2, and the optional outputs are loaded into the +C work arrays before returning. +C----------------------------------------------------------------------- + 400 DO 410 I = 1,N + 410 Y(I) = RWORK(I+LYH-1) + T = TN + IF (ITASK .NE. 4 .AND. ITASK .NE. 5) GO TO 420 + IF (IHIT) T = TCRIT + 420 ISTATE = 2 + IF (KFLAG .EQ. -3) ISTATE = 3 + RWORK(11) = HU + RWORK(12) = H + RWORK(13) = TN + IWORK(11) = NST + IWORK(12) = NFE + IWORK(13) = NJE + IWORK(14) = NQU + IWORK(15) = NQ + RETURN +C----------------------------------------------------------------------- +C Block H. +C The following block handles all unsuccessful returns other than +C those for illegal input. First the error message routine is called. +C If there was an error test or convergence test failure, IMXER is set. +C Then Y is loaded from YH and T is set to TN. +C The optional outputs are loaded into the work arrays before returning. +C----------------------------------------------------------------------- +C The maximum number of steps was taken before reaching TOUT. ---------- + 500 MSG = 'DLSODI- At current T (=R1), MXSTEP (=I1) steps ' + CALL XERRWD (MSG, 50, 201, 0, 0, 0, 0, 0, 0.0D0, 0.0D0) + MSG = ' taken on this call before reaching TOUT ' + CALL XERRWD (MSG, 50, 201, 0, 1, MXSTEP, 0, 1, TN, 0.0D0) + ISTATE = -1 + GO TO 580 +C EWT(i) .le. 0.0 for some i (not at start of problem). ---------------- + 510 EWTI = RWORK(LEWT+I-1) + MSG = 'DLSODI- At T (=R1), EWT(I1) has become R2 .le. 0.' + CALL XERRWD (MSG, 50, 202, 0, 1, I, 0, 2, TN, EWTI) + ISTATE = -6 + GO TO 590 +C Too much accuracy requested for machine precision. ------------------- + 520 MSG = 'DLSODI- At T (=R1), too much accuracy requested ' + CALL XERRWD (MSG, 50, 203, 0, 0, 0, 0, 0, 0.0D0, 0.0D0) + MSG = ' for precision of machine.. See TOLSF (=R2) ' + CALL XERRWD (MSG, 50, 203, 0, 0, 0, 0, 2, TN, TOLSF) + RWORK(14) = TOLSF + ISTATE = -2 + GO TO 590 +C KFLAG = -1. Error test failed repeatedly or with ABS(H) = HMIN. ----- + 530 MSG = 'DLSODI- At T(=R1) and step size H(=R2), the error' + CALL XERRWD (MSG, 50, 204, 0, 0, 0, 0, 0, 0.0D0, 0.0D0) + MSG = ' test failed repeatedly or with ABS(H) = HMIN' + CALL XERRWD (MSG, 50, 204, 0, 0, 0, 0, 2, TN, H) + ISTATE = -4 + GO TO 570 +C KFLAG = -2. Convergence failed repeatedly or with ABS(H) = HMIN. ---- + 540 MSG = 'DLSODI- At T (=R1) and step size H (=R2), the ' + CALL XERRWD (MSG, 50, 205, 0, 0, 0, 0, 0, 0.0D0, 0.0D0) + MSG = ' corrector convergence failed repeatedly ' + CALL XERRWD (MSG, 50, 205, 0, 0, 0, 0, 0, 0.0D0, 0.0D0) + MSG = ' or with ABS(H) = HMIN ' + CALL XERRWD (MSG, 30, 205, 0, 0, 0, 0, 2, TN, H) + ISTATE = -5 + GO TO 570 +C IRES = 3 returned by RES, despite retries by DSTODI. ----------------- + 550 MSG = 'DLSODI- At T (=R1) residual routine returned ' + CALL XERRWD (MSG, 50, 206, 0, 0, 0, 0, 0, 0.0D0, 0.0D0) + MSG = ' error IRES = 3 repeatedly. ' + CALL XERRWD (MSG, 40, 206, 0, 0, 0, 0, 1, TN, 0.0D0) + ISTATE = -7 + GO TO 590 +C DAINVG failed because matrix A was singular. ------------------------- + 560 IER = -IER + MSG='DLSODI- Attempt to initialize dy/dt failed: Matrix A is ' + CALL XERRWD (MSG, 60, 207, 0, 0, 0, 0, 0, 0.0D0, 0.0D0) + MSG = ' singular. DGEFA or DGBFA returned INFO = I1' + CALL XERRWD (MSG, 50, 207, 0, 1, IER, 0, 0, 0.0D0, 0.0D0) + ISTATE = -8 + RETURN +C DAINVG failed because RES set IRES to 2 or 3. ------------------------ + 565 MSG = 'DLSODI- Attempt to initialize dy/dt failed ' + CALL XERRWD (MSG, 50, 208, 0, 0, 0, 0, 0, 0.0D0, 0.0D0) + MSG = ' because residual routine set its error flag ' + CALL XERRWD (MSG, 50, 208, 0, 0, 0, 0, 0, 0.0D0, 0.0D0) + MSG = ' to IRES = (I1)' + CALL XERRWD (MSG, 20, 208, 0, 1, IER, 0, 0, 0.0D0, 0.0D0) + ISTATE = -8 + RETURN +C Compute IMXER if relevant. ------------------------------------------- + 570 BIG = 0.0D0 + IMXER = 1 + DO 575 I = 1,N + SIZE = ABS(RWORK(I+LACOR-1)*RWORK(I+LEWT-1)) + IF (BIG .GE. SIZE) GO TO 575 + BIG = SIZE + IMXER = I + 575 CONTINUE + IWORK(16) = IMXER +C Compute residual if relevant. ---------------------------------------- + 580 LYD0 = LYH + NYH + DO 585 I = 1,N + RWORK(I+LSAVF-1) = RWORK(I+LYD0-1)/H + 585 Y(I) = RWORK(I+LYH-1) + IRES = 1 + CALL RES (NEQ, TN, Y, RWORK(LSAVF), YDOTI, IRES ) + NFE = NFE + 1 + IF (IRES .LE. 1) GO TO 595 + MSG = 'DLSODI- Residual routine set its flag IRES ' + CALL XERRWD (MSG, 50, 210, 0, 0, 0, 0, 0, 0.0D0, 0.0D0) + MSG = ' to (I1) when called for final output. ' + CALL XERRWD (MSG, 50, 210, 0, 1, IRES, 0, 0, 0.0D0, 0.0D0) + GO TO 595 +C Set Y vector, T, and optional outputs. ------------------------------- + 590 DO 592 I = 1,N + 592 Y(I) = RWORK(I+LYH-1) + 595 T = TN + RWORK(11) = HU + RWORK(12) = H + RWORK(13) = TN + IWORK(11) = NST + IWORK(12) = NFE + IWORK(13) = NJE + IWORK(14) = NQU + IWORK(15) = NQ + RETURN +C----------------------------------------------------------------------- +C Block I. +C The following block handles all error returns due to illegal input +C (ISTATE = -3), as detected before calling the core integrator. +C First the error message routine is called. If the illegal input +C is a negative ISTATE, the run is aborted (apparent infinite loop). +C----------------------------------------------------------------------- + 601 MSG = 'DLSODI- ISTATE (=I1) illegal.' + CALL XERRWD (MSG, 30, 1, 0, 1, ISTATE, 0, 0, 0.0D0, 0.0D0) + IF (ISTATE .LT. 0) GO TO 800 + GO TO 700 + 602 MSG = 'DLSODI- ITASK (=I1) illegal. ' + CALL XERRWD (MSG, 30, 2, 0, 1, ITASK, 0, 0, 0.0D0, 0.0D0) + GO TO 700 + 603 MSG = 'DLSODI- ISTATE .gt. 1 but DLSODI not initialized.' + CALL XERRWD (MSG, 50, 3, 0, 0, 0, 0, 0, 0.0D0, 0.0D0) + GO TO 700 + 604 MSG = 'DLSODI- NEQ (=I1) .lt. 1 ' + CALL XERRWD (MSG, 30, 4, 0, 1, NEQ(1), 0, 0, 0.0D0, 0.0D0) + GO TO 700 + 605 MSG = 'DLSODI- ISTATE = 3 and NEQ increased (I1 to I2). ' + CALL XERRWD (MSG, 50, 5, 0, 2, N, NEQ(1), 0, 0.0D0, 0.0D0) + GO TO 700 + 606 MSG = 'DLSODI- ITOL (=I1) illegal. ' + CALL XERRWD (MSG, 30, 6, 0, 1, ITOL, 0, 0, 0.0D0, 0.0D0) + GO TO 700 + 607 MSG = 'DLSODI- IOPT (=I1) illegal. ' + CALL XERRWD (MSG, 30, 7, 0, 1, IOPT, 0, 0, 0.0D0, 0.0D0) + GO TO 700 + 608 MSG = 'DLSODI- MF (=I1) illegal. ' + CALL XERRWD (MSG, 30, 8, 0, 1, MF, 0, 0, 0.0D0, 0.0D0) + GO TO 700 + 609 MSG = 'DLSODI- ML(=I1) illegal: .lt. 0 or .ge. NEQ(=I2) ' + CALL XERRWD (MSG, 50, 9, 0, 2, ML, NEQ(1), 0, 0.0D0, 0.0D0) + GO TO 700 + 610 MSG = 'DLSODI- MU(=I1) illegal: .lt. 0 or .ge. NEQ(=I2) ' + CALL XERRWD (MSG, 50, 10, 0, 2, MU, NEQ(1), 0, 0.0D0, 0.0D0) + GO TO 700 + 611 MSG = 'DLSODI- MAXORD (=I1) .lt. 0 ' + CALL XERRWD (MSG, 30, 11, 0, 1, MAXORD, 0, 0, 0.0D0, 0.0D0) + GO TO 700 + 612 MSG = 'DLSODI- MXSTEP (=I1) .lt. 0 ' + CALL XERRWD (MSG, 30, 12, 0, 1, MXSTEP, 0, 0, 0.0D0, 0.0D0) + GO TO 700 + 613 MSG = 'DLSODI- MXHNIL (=I1) .lt. 0 ' + CALL XERRWD (MSG, 30, 13, 0, 1, MXHNIL, 0, 0, 0.0D0, 0.0D0) + GO TO 700 + 614 MSG = 'DLSODI- TOUT (=R1) behind T (=R2) ' + CALL XERRWD (MSG, 40, 14, 0, 0, 0, 0, 2, TOUT, T) + MSG = ' Integration direction is given by H0 (=R1) ' + CALL XERRWD (MSG, 50, 14, 0, 0, 0, 0, 1, H0, 0.0D0) + GO TO 700 + 615 MSG = 'DLSODI- HMAX (=R1) .lt. 0.0 ' + CALL XERRWD (MSG, 30, 15, 0, 0, 0, 0, 1, HMAX, 0.0D0) + GO TO 700 + 616 MSG = 'DLSODI- HMIN (=R1) .lt. 0.0 ' + CALL XERRWD (MSG, 30, 16, 0, 0, 0, 0, 1, HMIN, 0.0D0) + GO TO 700 + 617 MSG='DLSODI- RWORK length needed, LENRW (=I1), exceeds LRW (=I2)' + CALL XERRWD (MSG, 60, 17, 0, 2, LENRW, LRW, 0, 0.0D0, 0.0D0) + GO TO 700 + 618 MSG='DLSODI- IWORK length needed, LENIW (=I1), exceeds LIW (=I2)' + CALL XERRWD (MSG, 60, 18, 0, 2, LENIW, LIW, 0, 0.0D0, 0.0D0) + GO TO 700 + 619 MSG = 'DLSODI- RTOL(=I1) is R1 .lt. 0.0 ' + CALL XERRWD (MSG, 40, 19, 0, 1, I, 0, 1, RTOLI, 0.0D0) + GO TO 700 + 620 MSG = 'DLSODI- ATOL(=I1) is R1 .lt. 0.0 ' + CALL XERRWD (MSG, 40, 20, 0, 1, I, 0, 1, ATOLI, 0.0D0) + GO TO 700 + 621 EWTI = RWORK(LEWT+I-1) + MSG = 'DLSODI- EWT(I1) is R1 .le. 0.0 ' + CALL XERRWD (MSG, 40, 21, 0, 1, I, 0, 1, EWTI, 0.0D0) + GO TO 700 + 622 MSG='DLSODI- TOUT(=R1) too close to T(=R2) to start integration.' + CALL XERRWD (MSG, 60, 22, 0, 0, 0, 0, 2, TOUT, T) + GO TO 700 + 623 MSG='DLSODI- ITASK = I1 and TOUT (=R1) behind TCUR - HU (= R2) ' + CALL XERRWD (MSG, 60, 23, 0, 1, ITASK, 0, 2, TOUT, TP) + GO TO 700 + 624 MSG='DLSODI- ITASK = 4 or 5 and TCRIT (=R1) behind TCUR (=R2) ' + CALL XERRWD (MSG, 60, 24, 0, 0, 0, 0, 2, TCRIT, TN) + GO TO 700 + 625 MSG='DLSODI- ITASK = 4 or 5 and TCRIT (=R1) behind TOUT (=R2) ' + CALL XERRWD (MSG, 60, 25, 0, 0, 0, 0, 2, TCRIT, TOUT) + GO TO 700 + 626 MSG = 'DLSODI- At start of problem, too much accuracy ' + CALL XERRWD (MSG, 50, 26, 0, 0, 0, 0, 0, 0.0D0, 0.0D0) + MSG=' requested for precision of machine.. See TOLSF (=R1) ' + CALL XERRWD (MSG, 60, 26, 0, 0, 0, 0, 1, TOLSF, 0.0D0) + RWORK(14) = TOLSF + GO TO 700 + 627 MSG = 'DLSODI- Trouble in DINTDY. ITASK = I1, TOUT = R1' + CALL XERRWD (MSG, 50, 27, 0, 1, ITASK, 0, 1, TOUT, 0.0D0) +C + 700 ISTATE = -3 + RETURN +C + 800 MSG = 'DLSODI- Run aborted.. apparent infinite loop. ' + CALL XERRWD (MSG, 50, 303, 2, 0, 0, 0, 0, 0.0D0, 0.0D0) + RETURN +C----------------------- End of Subroutine DLSODI ---------------------- + END +*DECK DLSOIBT + SUBROUTINE DLSOIBT (RES, ADDA, JAC, NEQ, Y, YDOTI, T, TOUT, ITOL, + 1 RTOL, ATOL, ITASK, ISTATE, IOPT, RWORK, LRW, IWORK, LIW, MF ) + EXTERNAL RES, ADDA, JAC + INTEGER NEQ, ITOL, ITASK, ISTATE, IOPT, LRW, IWORK, LIW, MF + DOUBLE PRECISION Y, YDOTI, T, TOUT, RTOL, ATOL, RWORK + DIMENSION NEQ(*), Y(*), YDOTI(*), RTOL(*), ATOL(*), RWORK(LRW), + 1 IWORK(LIW) +C----------------------------------------------------------------------- +C This is the 18 November 2003 version of +C DLSOIBT: Livermore Solver for Ordinary differential equations given +C in Implicit form, with Block-Tridiagonal Jacobian treatment. +C +C This version is in double precision. +C +C DLSOIBT solves the initial value problem for linearly implicit +C systems of first order ODEs, +C A(t,y) * dy/dt = g(t,y) , where A(t,y) is a square matrix, +C or, in component form, +C ( a * ( dy / dt )) + ... + ( a * ( dy / dt )) = +C i,1 1 i,NEQ NEQ +C +C = g ( t, y , y ,..., y ) ( i = 1,...,NEQ ) +C i 1 2 NEQ +C +C If A is singular, this is a differential-algebraic system. +C +C DLSOIBT is a variant version of the DLSODI package, for the case where +C the matrices A, dg/dy, and d(A*s)/dy are all block-tridiagonal. +C----------------------------------------------------------------------- +C Reference: +C Alan C. Hindmarsh, ODEPACK, A Systematized Collection of ODE +C Solvers, in Scientific Computing, R. S. Stepleman et al. (Eds.), +C North-Holland, Amsterdam, 1983, pp. 55-64. +C----------------------------------------------------------------------- +C Authors: Alan C. Hindmarsh and Jeffrey F. Painter +C Center for Applied Scientific Computing, L-561 +C Lawrence Livermore National Laboratory +C Livermore, CA 94551 +C and +C Charles S. Kenney +C formerly at: Naval Weapons Center +C China Lake, CA 93555 +C----------------------------------------------------------------------- +C Summary of Usage. +C +C Communication between the user and the DLSOIBT package, for normal +C situations, is summarized here. This summary describes only a subset +C of the full set of options available. See the full description for +C details, including optional communication, nonstandard options, +C and instructions for special situations. See also the example +C problem (with program and output) following this summary. +C +C A. First, provide a subroutine of the form: +C SUBROUTINE RES (NEQ, T, Y, S, R, IRES) +C DOUBLE PRECISION T, Y(*), S(*), R(*) +C which computes the residual function +C r = g(t,y) - A(t,y) * s , +C as a function of t and the vectors y and s. (s is an internally +C generated approximation to dy/dt.) The arrays Y and S are inputs +C to the RES routine and should not be altered. The residual +C vector is to be stored in the array R. The argument IRES should be +C ignored for casual use of DLSOIBT. (For uses of IRES, see the +C paragraph on RES in the full description below.) +C +C B. Next, identify the block structure of the matrices A = A(t,y) and +C dr/dy. DLSOIBT must deal internally with a linear combination, P, of +C these two matrices. The matrix P (hence both A and dr/dy) must have +C a block-tridiagonal form with fixed structure parameters +C MB = block size, MB .ge. 1, and +C NB = number of blocks in each direction, NB .ge. 4, +C with MB*NB = NEQ. In each of the NB block-rows of the matrix P +C (each consisting of MB consecutive rows), the nonzero elements are +C to lie in three consecutive MB by MB blocks. In block-rows +C 2 through NB - 1, these are centered about the main diagonal. +C in block-rows 1 and NB, they are the diagonal blocks and the two +C blocks adjacent to the diagonal block. (Thus block positions (1,3) +C and (NB,NB-2) can be nonzero.) +C Alternatively, P (hence A and dr/dy) may be only approximately +C equal to matrices with this form, and DLSOIBT should still succeed. +C The block-tridiagonal matrix P is described by three arrays, +C each of size MB by MB by NB: +C PA = array of diagonal blocks, +C PB = array of superdiagonal (and one subdiagonal) blocks, and +C PC = array of subdiagonal (and one superdiagonal) blocks. +C Specifically, the three MB by MB blocks in the k-th block-row of P +C are stored in (reading across): +C PC(*,*,k) = block to the left of the diagonal block, +C PA(*,*,k) = diagonal block, and +C PB(*,*,k) = block to the right of the diagonal block, +C except for k = 1, where the three blocks (reading across) are +C PA(*,*,1) (= diagonal block), PB(*,*,1), and PC(*,*,1), +C and k = NB, where they are +C PB(*,*,NB), PC(*,*,NB), and PA(*,*,NB) (= diagonal block). +C (Each asterisk * stands for an index that ranges from 1 to MB.) +C +C C. You must also provide a subroutine of the form: +C SUBROUTINE ADDA (NEQ, T, Y, MB, NB, PA, PB, PC) +C DOUBLE PRECISION T, Y(*), PA(MB,MB,NB), PB(MB,MB,NB), PC(MB,MB,NB) +C which adds the nonzero blocks of the matrix A = A(t,y) to the +C contents of the arrays PA, PB, and PC, following the structure +C description in Paragraph B above. +C T and the Y array are input and should not be altered. +C Thus the affect of ADDA should be the following: +C DO 30 K = 1,NB +C DO 20 J = 1,MB +C DO 10 I = 1,MB +C PA(I,J,K) = PA(I,J,K) + +C ( (I,J) element of K-th diagonal block of A) +C PB(I,J,K) = PB(I,J,K) + +C ( (I,J) element of block in block position (K,K+1) of A, +C or in block position (NB,NB-2) if K = NB) +C PC(I,J,K) = PC(I,J,K) + +C ( (I,J) element of block in block position (K,K-1) of A, +C or in block position (1,3) if K = 1) +C 10 CONTINUE +C 20 CONTINUE +C 30 CONTINUE +C +C D. For the sake of efficiency, you are encouraged to supply the +C Jacobian matrix dr/dy in closed form, where r = g(t,y) - A(t,y)*s +C (s = a fixed vector) as above. If dr/dy is being supplied, +C use MF = 21, and provide a subroutine of the form: +C SUBROUTINE JAC (NEQ, T, Y, S, MB, NB, PA, PB, PC) +C DOUBLE PRECISION T, Y(*), S(*), PA(MB,MB,NB), PB(MB,MB,NB), +C 1 PC(MB,MB,NB) +C which computes dr/dy as a function of t, y, and s. Here T, Y, and +C S are inputs, and the routine is to load dr/dy into PA, PB, PC, +C according to the structure description in Paragraph B above. +C That is, load the diagonal blocks into PA, the superdiagonal blocks +C (and block (NB,NB-2) ) into PB, and the subdiagonal blocks (and +C block (1,3) ) into PC. The blocks in block-row k of dr/dy are to +C be loaded into PA(*,*,k), PB(*,*,k), and PC(*,*,k). +C Only nonzero elements need be loaded, and the indexing +C of PA, PB, and PC is the same as in the ADDA routine. +C Note that if A is independent of Y (or this dependence +C is weak enough to be ignored) then JAC is to compute dg/dy. +C If it is not feasible to provide a JAC routine, use +C MF = 22, and DLSOIBT will compute an approximate Jacobian +C internally by difference quotients. +C +C E. Next decide whether or not to provide the initial value of the +C derivative vector dy/dt. If the initial value of A(t,y) is +C nonsingular (and not too ill-conditioned), you may let DLSOIBT compute +C this vector (ISTATE = 0). (DLSOIBT will solve the system A*s = g for +C s, with initial values of A and g.) If A(t,y) is initially +C singular, then the system is a differential-algebraic system, and +C you must make use of the particular form of the system to compute the +C initial values of y and dy/dt. In that case, use ISTATE = 1 and +C load the initial value of dy/dt into the array YDOTI. +C The input array YDOTI and the initial Y array must be consistent with +C the equations A*dy/dt = g. This implies that the initial residual +C r = g(t,y) - A(t,y)*YDOTI must be approximately zero. +C +C F. Write a main program which calls Subroutine DLSOIBT once for +C each point at which answers are desired. This should also provide +C for possible use of logical unit 6 for output of error messages by +C DLSOIBT. on the first call to DLSOIBT, supply arguments as follows: +C RES = name of user subroutine for residual function r. +C ADDA = name of user subroutine for computing and adding A(t,y). +C JAC = name of user subroutine for Jacobian matrix dr/dy +C (MF = 21). If not used, pass a dummy name. +C Note: the names for the RES and ADDA routines and (if used) the +C JAC routine must be declared External in the calling program. +C NEQ = number of scalar equations in the system. +C Y = array of initial values, of length NEQ. +C YDOTI = array of length NEQ (containing initial dy/dt if ISTATE = 1). +C T = the initial value of the independent variable. +C TOUT = first point where output is desired (.ne. T). +C ITOL = 1 or 2 according as ATOL (below) is a scalar or array. +C RTOL = relative tolerance parameter (scalar). +C ATOL = absolute tolerance parameter (scalar or array). +C the estimated local error in y(i) will be controlled so as +C to be roughly less (in magnitude) than +C EWT(i) = RTOL*ABS(Y(i)) + ATOL if ITOL = 1, or +C EWT(i) = RTOL*ABS(Y(i)) + ATOL(i) if ITOL = 2. +C Thus the local error test passes if, in each component, +C either the absolute error is less than ATOL (or ATOL(i)), +C or the relative error is less than RTOL. +C Use RTOL = 0.0 for pure absolute error control, and +C use ATOL = 0.0 (or ATOL(i) = 0.0) for pure relative error +C control. Caution: Actual (global) errors may exceed these +C local tolerances, so choose them conservatively. +C ITASK = 1 for normal computation of output values of y at t = TOUT. +C ISTATE = integer flag (input and output). Set ISTATE = 1 if the +C initial dy/dt is supplied, and 0 otherwise. +C IOPT = 0 to indicate no optional inputs used. +C RWORK = real work array of length at least: +C 22 + 9*NEQ + 3*MB*MB*NB for MF = 21 or 22. +C LRW = declared length of RWORK (in user's dimension). +C IWORK = integer work array of length at least 20 + NEQ. +C Input in IWORK(1) the block size MB and in IWORK(2) the +C number NB of blocks in each direction along the matrix A. +C These must satisfy MB .ge. 1, NB .ge. 4, and MB*NB = NEQ. +C LIW = declared length of IWORK (in user's dimension). +C MF = method flag. Standard values are: +C 21 for a user-supplied Jacobian. +C 22 for an internally generated Jacobian. +C For other choices of MF, see the paragraph on MF in +C the full description below. +C Note that the main program must declare arrays Y, YDOTI, RWORK, IWORK, +C and possibly ATOL. +C +C G. The output from the first call (or any call) is: +C Y = array of computed values of y(t) vector. +C T = corresponding value of independent variable (normally TOUT). +C ISTATE = 2 if DLSOIBT was successful, negative otherwise. +C -1 means excess work done on this call (check all inputs). +C -2 means excess accuracy requested (tolerances too small). +C -3 means illegal input detected (see printed message). +C -4 means repeated error test failures (check all inputs). +C -5 means repeated convergence failures (perhaps bad Jacobian +C supplied or wrong choice of tolerances). +C -6 means error weight became zero during problem. (Solution +C component i vanished, and ATOL or ATOL(i) = 0.) +C -7 cannot occur in casual use. +C -8 means DLSOIBT was unable to compute the initial dy/dt. +C In casual use, this means A(t,y) is initially singular. +C Supply YDOTI and use ISTATE = 1 on the first call. +C +C If DLSOIBT returns ISTATE = -1, -4, or -5, then the output of +C DLSOIBT also includes YDOTI = array containing residual vector +C r = g - A * dy/dt evaluated at the current t, y, and dy/dt. +C +C H. To continue the integration after a successful return, simply +C reset TOUT and call DLSOIBT again. No other parameters need be reset. +C +C----------------------------------------------------------------------- +C Example Problem. +C +C The following is an example problem, with the coding needed +C for its solution by DLSOIBT. The problem comes from the partial +C differential equation (the Burgers equation) +C du/dt = - u * du/dx + eta * d**2 u/dx**2, eta = .05, +C on -1 .le. x .le. 1. The boundary conditions are +C du/dx = 0 at x = -1 and at x = 1. +C The initial profile is a square wave, +C u = 1 in ABS(x) .lt. .5, u = .5 at ABS(x) = .5, u = 0 elsewhere. +C The PDE is discretized in x by a simplified Galerkin method, +C using piecewise linear basis functions, on a grid of 40 intervals. +C The equations at x = -1 and 1 use a 3-point difference approximation +C for the right-hand side. The result is a system A * dy/dt = g(y), +C of size NEQ = 41, where y(i) is the approximation to u at x = x(i), +C with x(i) = -1 + (i-1)*delx, delx = 2/(NEQ-1) = .05. The individual +C equations in the system are +C dy(1)/dt = ( y(3) - 2*y(2) + y(1) ) * eta / delx**2, +C dy(NEQ)/dt = ( y(NEQ-2) - 2*y(NEQ-1) + y(NEQ) ) * eta / delx**2, +C and for i = 2, 3, ..., NEQ-1, +C (1/6) dy(i-1)/dt + (4/6) dy(i)/dt + (1/6) dy(i+1)/dt +C = ( y(i-1)**2 - y(i+1)**2 ) / (4*delx) +C + ( y(i+1) - 2*y(i) + y(i-1) ) * eta / delx**2. +C The following coding solves the problem with MF = 21, with output +C of solution statistics at t = .1, .2, .3, and .4, and of the +C solution vector at t = .4. Here the block size is just MB = 1. +C +C EXTERNAL RESID, ADDABT, JACBT +C DOUBLE PRECISION ATOL, RTOL, RWORK, T, TOUT, Y, YDOTI +C DIMENSION Y(41), YDOTI(41), RWORK(514), IWORK(61) +C NEQ = 41 +C DO 10 I = 1,NEQ +C 10 Y(I) = 0.0 +C Y(11) = 0.5 +C DO 20 I = 12,30 +C 20 Y(I) = 1.0 +C Y(31) = 0.5 +C T = 0.0 +C TOUT = 0.1 +C ITOL = 1 +C RTOL = 1.0D-4 +C ATOL = 1.0D-5 +C ITASK = 1 +C ISTATE = 0 +C IOPT = 0 +C LRW = 514 +C LIW = 61 +C IWORK(1) = 1 +C IWORK(2) = NEQ +C MF = 21 +C DO 40 IO = 1,4 +C CALL DLSOIBT (RESID, ADDABT, JACBT, NEQ, Y, YDOTI, T, TOUT, +C 1 ITOL,RTOL,ATOL, ITASK, ISTATE, IOPT, RWORK,LRW,IWORK,LIW, MF) +C WRITE (6,30) T, IWORK(11), IWORK(12), IWORK(13) +C 30 FORMAT(' At t =',F5.2,' No. steps =',I4,' No. r-s =',I4, +C 1 ' No. J-s =',I3) +C IF (ISTATE .NE. 2) GO TO 90 +C TOUT = TOUT + 0.1 +C 40 CONTINUE +C WRITE(6,50) (Y(I),I=1,NEQ) +C 50 FORMAT(/' Final solution values..'/9(5D12.4/)) +C STOP +C 90 WRITE(6,95) ISTATE +C 95 FORMAT(///' Error halt.. ISTATE =',I3) +C STOP +C END +C +C SUBROUTINE RESID (N, T, Y, S, R, IRES) +C DOUBLE PRECISION T, Y, S, R, ETA, DELX, EODSQ +C DIMENSION Y(N), S(N), R(N) +C DATA ETA/0.05/, DELX/0.05/ +C EODSQ = ETA/DELX**2 +C R(1) = EODSQ*(Y(3) - 2.0*Y(2) + Y(1)) - S(1) +C NM1 = N - 1 +C DO 10 I = 2,NM1 +C R(I) = (Y(I-1)**2 - Y(I+1)**2)/(4.0*DELX) +C 1 + EODSQ*(Y(I+1) - 2.0*Y(I) + Y(I-1)) +C 2 - (S(I-1) + 4.0*S(I) + S(I+1))/6.0 +C 10 CONTINUE +C R(N) = EODSQ*(Y(N-2) - 2.0*Y(NM1) + Y(N)) - S(N) +C RETURN +C END +C +C SUBROUTINE ADDABT (N, T, Y, MB, NB, PA, PB, PC) +C DOUBLE PRECISION T, Y, PA, PB, PC +C DIMENSION Y(N), PA(MB,MB,NB), PB(MB,MB,NB), PC(MB,MB,NB) +C PA(1,1,1) = PA(1,1,1) + 1.0 +C NM1 = N - 1 +C DO 10 K = 2,NM1 +C PA(1,1,K) = PA(1,1,K) + (4.0/6.0) +C PB(1,1,K) = PB(1,1,K) + (1.0/6.0) +C PC(1,1,K) = PC(1,1,K) + (1.0/6.0) +C 10 CONTINUE +C PA(1,1,N) = PA(1,1,N) + 1.0 +C RETURN +C END +C +C SUBROUTINE JACBT (N, T, Y, S, MB, NB, PA, PB, PC) +C DOUBLE PRECISION T, Y, S, PA, PB, PC, ETA, DELX, EODSQ +C DIMENSION Y(N), S(N), PA(MB,MB,NB),PB(MB,MB,NB),PC(MB,MB,NB) +C DATA ETA/0.05/, DELX/0.05/ +C EODSQ = ETA/DELX**2 +C PA(1,1,1) = EODSQ +C PB(1,1,1) = -2.0*EODSQ +C PC(1,1,1) = EODSQ +C DO 10 K = 2,N +C PA(1,1,K) = -2.0*EODSQ +C PB(1,1,K) = -Y(K+1)*(0.5/DELX) + EODSQ +C PC(1,1,K) = Y(K-1)*(0.5/DELX) + EODSQ +C 10 CONTINUE +C PB(1,1,N) = EODSQ +C PC(1,1,N) = -2.0*EODSQ +C PA(1,1,N) = EODSQ +C RETURN +C END +C +C The output of this program (on a CDC-7600 in single precision) +C is as follows: +C +C At t = 0.10 No. steps = 35 No. r-s = 45 No. J-s = 9 +C At t = 0.20 No. steps = 43 No. r-s = 54 No. J-s = 10 +C At t = 0.30 No. steps = 48 No. r-s = 60 No. J-s = 11 +C At t = 0.40 No. steps = 51 No. r-s = 64 No. J-s = 12 +C +C Final solution values.. +C 1.2747e-02 1.1997e-02 1.5560e-02 2.3767e-02 3.7224e-02 +C 5.6646e-02 8.2645e-02 1.1557e-01 1.5541e-01 2.0177e-01 +C 2.5397e-01 3.1104e-01 3.7189e-01 4.3530e-01 5.0000e-01 +C 5.6472e-01 6.2816e-01 6.8903e-01 7.4612e-01 7.9829e-01 +C 8.4460e-01 8.8438e-01 9.1727e-01 9.4330e-01 9.6281e-01 +C 9.7632e-01 9.8426e-01 9.8648e-01 9.8162e-01 9.6617e-01 +C 9.3374e-01 8.7535e-01 7.8236e-01 6.5321e-01 5.0003e-01 +C 3.4709e-01 2.1876e-01 1.2771e-01 7.3671e-02 5.0642e-02 +C 5.4496e-02 +C +C----------------------------------------------------------------------- +C Full Description of User Interface to DLSOIBT. +C +C The user interface to DLSOIBT consists of the following parts. +C +C 1. The call sequence to Subroutine DLSOIBT, which is a driver +C routine for the solver. This includes descriptions of both +C the call sequence arguments and of user-supplied routines. +C Following these descriptions is a description of +C optional inputs available through the call sequence, and then +C a description of optional outputs (in the work arrays). +C +C 2. Descriptions of other routines in the DLSOIBT package that may be +C (optionally) called by the user. These provide the ability to +C alter error message handling, save and restore the internal +C Common, and obtain specified derivatives of the solution y(t). +C +C 3. Descriptions of Common blocks to be declared in overlay +C or similar environments, or to be saved when doing an interrupt +C of the problem and continued solution later. +C +C 4. Description of two routines in the DLSOIBT package, either of +C which the user may replace with his/her own version, if desired. +C These relate to the measurement of errors. +C +C----------------------------------------------------------------------- +C Part 1. Call Sequence. +C +C The call sequence parameters used for input only are +C RES, ADDA, JAC, NEQ, TOUT, ITOL, RTOL, ATOL, ITASK, +C IOPT, LRW, LIW, MF, +C and those used for both input and output are +C Y, T, ISTATE, YDOTI. +C The work arrays RWORK and IWORK are also used for additional and +C optional inputs and optional outputs. (The term output here refers +C to the return from Subroutine DLSOIBT to the user's calling program.) +C +C The legality of input parameters will be thoroughly checked on the +C initial call for the problem, but not checked thereafter unless a +C change in input parameters is flagged by ISTATE = 3 on input. +C +C The descriptions of the call arguments are as follows. +C +C RES = the name of the user-supplied subroutine which supplies +C the residual vector for the ODE system, defined by +C r = g(t,y) - A(t,y) * s +C as a function of the scalar t and the vectors +C s and y (s approximates dy/dt). This subroutine +C is to have the form +C SUBROUTINE RES (NEQ, T, Y, S, R, IRES) +C DOUBLE PRECISION T, Y(*), S(*), R(*) +C where NEQ, T, Y, S, and IRES are input, and R and +C IRES are output. Y, S, and R are arrays of length NEQ. +C On input, IRES indicates how DLSOIBT will use the +C returned array R, as follows: +C IRES = 1 means that DLSOIBT needs the full residual, +C r = g - A*s, exactly. +C IRES = -1 means that DLSOIBT is using R only to compute +C the Jacobian dr/dy by difference quotients. +C The RES routine can ignore IRES, or it can omit some terms +C if IRES = -1. If A does not depend on y, then RES can +C just return R = g when IRES = -1. If g - A*s contains other +C additive terms that are independent of y, these can also be +C dropped, if done consistently, when IRES = -1. +C The subroutine should set the flag IRES if it +C encounters a halt condition or illegal input. +C Otherwise, it should not reset IRES. On output, +C IRES = 1 or -1 represents a normal return, and +C DLSOIBT continues integrating the ODE. Leave IRES +C unchanged from its input value. +C IRES = 2 tells DLSOIBT to immediately return control +C to the calling program, with ISTATE = 3. This lets +C the calling program change parameters of the problem +C if necessary. +C IRES = 3 represents an error condition (for example, an +C illegal value of y). DLSOIBT tries to integrate the system +C without getting IRES = 3 from RES. If it cannot, DLSOIBT +C returns with ISTATE = -7 or -1. +C On an DLSOIBT return with ISTATE = 3, -1, or -7, the +C values of T and Y returned correspond to the last point +C reached successfully without getting the flag IRES = 2 or 3. +C The flag values IRES = 2 and 3 should not be used to +C handle switches or root-stop conditions. This is better +C done by calling DLSOIBT in a one-step mode and checking the +C stopping function for a sign change at each step. +C If quantities computed in the RES routine are needed +C externally to DLSOIBT, an extra call to RES should be made +C for this purpose, for consistent and accurate results. +C To get the current dy/dt for the S argument, use DINTDY. +C RES must be declared External in the calling +C program. See note below for more about RES. +C +C ADDA = the name of the user-supplied subroutine which adds the +C matrix A = A(t,y) to another matrix, P, stored in +C block-tridiagonal form. This routine is to have the form +C SUBROUTINE ADDA (NEQ, T, Y, MB, NB, PA, PB, PC) +C DOUBLE PRECISION T, Y(*), PA(MB,MB,NB), PB(MB,MB,NB), +C 1 PC(MB,MB,NB) +C where NEQ, T, Y, MB, NB, and the arrays PA, PB, and PC +C are input, and the arrays PA, PB, and PC are output. +C Y is an array of length NEQ, and the arrays PA, PB, PC +C are all MB by MB by NB. +C Here a block-tridiagonal structure is assumed for A(t,y), +C and also for the matrix P to which A is added here, +C as described in Paragraph B of the Summary of Usage above. +C Thus the affect of ADDA should be the following: +C DO 30 K = 1,NB +C DO 20 J = 1,MB +C DO 10 I = 1,MB +C PA(I,J,K) = PA(I,J,K) + +C ( (I,J) element of K-th diagonal block of A) +C PB(I,J,K) = PB(I,J,K) + +C ( (I,J) element of block (K,K+1) of A, +C or block (NB,NB-2) if K = NB) +C PC(I,J,K) = PC(I,J,K) + +C ( (I,J) element of block (K,K-1) of A, +C or block (1,3) if K = 1) +C 10 CONTINUE +C 20 CONTINUE +C 30 CONTINUE +C ADDA must be declared External in the calling program. +C See note below for more information about ADDA. +C +C JAC = the name of the user-supplied subroutine which supplies +C the Jacobian matrix, dr/dy, where r = g - A*s. JAC is +C required if MITER = 1. Otherwise a dummy name can be +C passed. This subroutine is to have the form +C SUBROUTINE JAC (NEQ, T, Y, S, MB, NB, PA, PB, PC) +C DOUBLE PRECISION T, Y(*), S(*), PA(MB,MB,NB), +C 1 PB(MB,MB,NB), PC(MB,MB,NB) +C where NEQ, T, Y, S, MB, NB, and the arrays PA, PB, and PC +C are input, and the arrays PA, PB, and PC are output. +C Y and S are arrays of length NEQ, and the arrays PA, PB, PC +C are all MB by MB by NB. +C PA, PB, and PC are to be loaded with partial derivatives +C (elements of the Jacobian matrix) on output, in terms of the +C block-tridiagonal structure assumed, as described +C in Paragraph B of the Summary of Usage above. +C That is, load the diagonal blocks into PA, the +C superdiagonal blocks (and block (NB,NB-2) ) into PB, and +C the subdiagonal blocks (and block (1,3) ) into PC. +C The blocks in block-row k of dr/dy are to be loaded into +C PA(*,*,k), PB(*,*,k), and PC(*,*,k). +C Thus the affect of JAC should be the following: +C DO 30 K = 1,NB +C DO 20 J = 1,MB +C DO 10 I = 1,MB +C PA(I,J,K) = ( (I,J) element of +C K-th diagonal block of dr/dy) +C PB(I,J,K) = ( (I,J) element of block (K,K+1) +C of dr/dy, or block (NB,NB-2) if K = NB) +C PC(I,J,K) = ( (I,J) element of block (K,K-1) +C of dr/dy, or block (1,3) if K = 1) +C 10 CONTINUE +C 20 CONTINUE +C 30 CONTINUE +C PA, PB, and PC are preset to zero by the solver, +C so that only the nonzero elements need be loaded by JAC. +C Each call to JAC is preceded by a call to RES with the same +C arguments NEQ, T, Y, and S. Thus to gain some efficiency, +C intermediate quantities shared by both calculations may be +C saved in a user Common block by RES and not recomputed by JAC +C if desired. Also, JAC may alter the Y array, if desired. +C JAC need not provide dr/dy exactly. A crude +C approximation will do, so that DLSOIBT may be used when +C A and dr/dy are not really block-tridiagonal, but are close +C to matrices that are. +C JAC must be declared External in the calling program. +C See note below for more about JAC. +C +C Note on RES, ADDA, and JAC: +C These subroutines may access user-defined quantities in +C NEQ(2),... and/or in Y(NEQ(1)+1),... if NEQ is an array +C (dimensioned in the subroutines) and/or Y has length +C exceeding NEQ(1). However, these routines should not alter +C NEQ(1), Y(1),...,Y(NEQ) or any other input variables. +C See the descriptions of NEQ and Y below. +C +C NEQ = the size of the system (number of first order ordinary +C differential equations or scalar algebraic equations). +C Used only for input. +C NEQ may be decreased, but not increased, during the problem. +C If NEQ is decreased (with ISTATE = 3 on input), the +C remaining components of Y should be left undisturbed, if +C these are to be accessed in RES, ADDA, or JAC. +C +C Normally, NEQ is a scalar, and it is generally referred to +C as a scalar in this user interface description. However, +C NEQ may be an array, with NEQ(1) set to the system size. +C (The DLSOIBT package accesses only NEQ(1).) In either case, +C this parameter is passed as the NEQ argument in all calls +C to RES, ADDA, and JAC. Hence, if it is an array, +C locations NEQ(2),... may be used to store other integer data +C and pass it to RES, ADDA, or JAC. Each such subroutine +C must include NEQ in a Dimension statement in that case. +C +C Y = a real array for the vector of dependent variables, of +C length NEQ or more. Used for both input and output on the +C first call (ISTATE = 0 or 1), and only for output on other +C calls. On the first call, Y must contain the vector of +C initial values. On output, Y contains the computed solution +C vector, evaluated at t. If desired, the Y array may be used +C for other purposes between calls to the solver. +C +C This array is passed as the Y argument in all calls to RES, +C ADDA, and JAC. Hence its length may exceed NEQ, +C and locations Y(NEQ+1),... may be used to store other real +C data and pass it to RES, ADDA, or JAC. (The DLSOIBT +C package accesses only Y(1),...,Y(NEQ). ) +C +C YDOTI = a real array for the initial value of the vector +C dy/dt and for work space, of dimension at least NEQ. +C +C On input: +C If ISTATE = 0 then DLSOIBT will compute the initial value +C of dy/dt, if A is nonsingular. Thus YDOTI will +C serve only as work space and may have any value. +C If ISTATE = 1 then YDOTI must contain the initial value +C of dy/dt. +C If ISTATE = 2 or 3 (continuation calls) then YDOTI +C may have any value. +C Note: If the initial value of A is singular, then +C DLSOIBT cannot compute the initial value of dy/dt, so +C it must be provided in YDOTI, with ISTATE = 1. +C +C On output, when DLSOIBT terminates abnormally with ISTATE = +C -1, -4, or -5, YDOTI will contain the residual +C r = g(t,y) - A(t,y)*(dy/dt). If r is large, t is near +C its initial value, and YDOTI is supplied with ISTATE = 1, +C there may have been an incorrect input value of +C YDOTI = dy/dt, or the problem (as given to DLSOIBT) +C may not have a solution. +C +C If desired, the YDOTI array may be used for other +C purposes between calls to the solver. +C +C T = the independent variable. On input, T is used only on the +C first call, as the initial point of the integration. +C On output, after each call, T is the value at which a +C computed solution y is evaluated (usually the same as TOUT). +C On an error return, T is the farthest point reached. +C +C TOUT = the next value of t at which a computed solution is desired. +C Used only for input. +C +C When starting the problem (ISTATE = 0 or 1), TOUT may be +C equal to T for one call, then should .ne. T for the next +C call. For the initial T, an input value of TOUT .ne. T is +C used in order to determine the direction of the integration +C (i.e. the algebraic sign of the step sizes) and the rough +C scale of the problem. Integration in either direction +C (forward or backward in t) is permitted. +C +C If ITASK = 2 or 5 (one-step modes), TOUT is ignored after +C the first call (i.e. the first call with TOUT .ne. T). +C Otherwise, TOUT is required on every call. +C +C If ITASK = 1, 3, or 4, the values of TOUT need not be +C monotone, but a value of TOUT which backs up is limited +C to the current internal T interval, whose endpoints are +C TCUR - HU and TCUR (see optional outputs, below, for +C TCUR and HU). +C +C ITOL = an indicator for the type of error control. See +C description below under ATOL. Used only for input. +C +C RTOL = a relative error tolerance parameter, either a scalar or +C an array of length NEQ. See description below under ATOL. +C Input only. +C +C ATOL = an absolute error tolerance parameter, either a scalar or +C an array of length NEQ. Input only. +C +C The input parameters ITOL, RTOL, and ATOL determine +C the error control performed by the solver. The solver will +C control the vector E = (E(i)) of estimated local errors +C in y, according to an inequality of the form +C RMS-norm of ( E(i)/EWT(i) ) .le. 1, +C where EWT(i) = RTOL(i)*ABS(Y(i)) + ATOL(i), +C and the RMS-norm (root-mean-square norm) here is +C RMS-norm(v) = SQRT(sum v(i)**2 / NEQ). Here EWT = (EWT(i)) +C is a vector of weights which must always be positive, and +C the values of RTOL and ATOL should all be non-negative. +C The following table gives the types (scalar/array) of +C RTOL and ATOL, and the corresponding form of EWT(i). +C +C ITOL RTOL ATOL EWT(i) +C 1 scalar scalar RTOL*ABS(Y(i)) + ATOL +C 2 scalar array RTOL*ABS(Y(i)) + ATOL(i) +C 3 array scalar RTOL(i)*ABS(Y(i)) + ATOL +C 4 array scalar RTOL(i)*ABS(Y(i)) + ATOL(i) +C +C When either of these parameters is a scalar, it need not +C be dimensioned in the user's calling program. +C +C If none of the above choices (with ITOL, RTOL, and ATOL +C fixed throughout the problem) is suitable, more general +C error controls can be obtained by substituting +C user-supplied routines for the setting of EWT and/or for +C the norm calculation. See Part 4 below. +C +C If global errors are to be estimated by making a repeated +C run on the same problem with smaller tolerances, then all +C components of RTOL and ATOL (i.e. of EWT) should be scaled +C down uniformly. +C +C ITASK = an index specifying the task to be performed. +C Input only. ITASK has the following values and meanings. +C 1 means normal computation of output values of y(t) at +C t = TOUT (by overshooting and interpolating). +C 2 means take one step only and return. +C 3 means stop at the first internal mesh point at or +C beyond t = TOUT and return. +C 4 means normal computation of output values of y(t) at +C t = TOUT but without overshooting t = TCRIT. +C TCRIT must be input as RWORK(1). TCRIT may be equal to +C or beyond TOUT, but not behind it in the direction of +C integration. This option is useful if the problem +C has a singularity at or beyond t = TCRIT. +C 5 means take one step, without passing TCRIT, and return. +C TCRIT must be input as RWORK(1). +C +C Note: If ITASK = 4 or 5 and the solver reaches TCRIT +C (within roundoff), it will return T = TCRIT (exactly) to +C indicate this (unless ITASK = 4 and TOUT comes before TCRIT, +C in which case answers at t = TOUT are returned first). +C +C ISTATE = an index used for input and output to specify the +C state of the calculation. +C +C On input, the values of ISTATE are as follows. +C 0 means this is the first call for the problem, and +C DLSOIBT is to compute the initial value of dy/dt +C (while doing other initializations). See note below. +C 1 means this is the first call for the problem, and +C the initial value of dy/dt has been supplied in +C YDOTI (DLSOIBT will do other initializations). +C See note below. +C 2 means this is not the first call, and the calculation +C is to continue normally, with no change in any input +C parameters except possibly TOUT and ITASK. +C (If ITOL, RTOL, and/or ATOL are changed between calls +C with ISTATE = 2, the new values will be used but not +C tested for legality.) +C 3 means this is not the first call, and the +C calculation is to continue normally, but with +C a change in input parameters other than +C TOUT and ITASK. Changes are allowed in +C NEQ, ITOL, RTOL, ATOL, IOPT, LRW, LIW, MF, MB, NB, +C and any of the optional inputs except H0. +C (See IWORK description for MB and NB.) +C Note: A preliminary call with TOUT = T is not counted +C as a first call here, as no initialization or checking of +C input is done. (Such a call is sometimes useful for the +C purpose of outputting the initial conditions.) +C Thus the first call for which TOUT .ne. T requires +C ISTATE = 0 or 1 on input. +C +C On output, ISTATE has the following values and meanings. +C 0 or 1 means nothing was done; TOUT = t and +C ISTATE = 0 or 1 on input. +C 2 means that the integration was performed successfully. +C 3 means that the user-supplied Subroutine RES signalled +C DLSOIBT to halt the integration and return (IRES = 2). +C Integration as far as T was achieved with no occurrence +C of IRES = 2, but this flag was set on attempting the +C next step. +C -1 means an excessive amount of work (more than MXSTEP +C steps) was done on this call, before completing the +C requested task, but the integration was otherwise +C successful as far as T. (MXSTEP is an optional input +C and is normally 500.) To continue, the user may +C simply reset ISTATE to a value .gt. 1 and call again +C (the excess work step counter will be reset to 0). +C In addition, the user may increase MXSTEP to avoid +C this error return (see below on optional inputs). +C -2 means too much accuracy was requested for the precision +C of the machine being used. This was detected before +C completing the requested task, but the integration +C was successful as far as T. To continue, the tolerance +C parameters must be reset, and ISTATE must be set +C to 3. The optional output TOLSF may be used for this +C purpose. (Note: If this condition is detected before +C taking any steps, then an illegal input return +C (ISTATE = -3) occurs instead.) +C -3 means illegal input was detected, before taking any +C integration steps. See written message for details. +C Note: If the solver detects an infinite loop of calls +C to the solver with illegal input, it will cause +C the run to stop. +C -4 means there were repeated error test failures on +C one attempted step, before completing the requested +C task, but the integration was successful as far as T. +C The problem may have a singularity, or the input +C may be inappropriate. +C -5 means there were repeated convergence test failures on +C one attempted step, before completing the requested +C task, but the integration was successful as far as T. +C This may be caused by an inaccurate Jacobian matrix. +C -6 means EWT(i) became zero for some i during the +C integration. Pure relative error control (ATOL(i) = 0.0) +C was requested on a variable which has now vanished. +C The integration was successful as far as T. +C -7 means that the user-supplied Subroutine RES set +C its error flag (IRES = 3) despite repeated tries by +C DLSOIBT to avoid that condition. +C -8 means that ISTATE was 0 on input but DLSOIBT was unable +C to compute the initial value of dy/dt. See the +C printed message for details. +C +C Note: Since the normal output value of ISTATE is 2, +C it does not need to be reset for normal continuation. +C Similarly, ISTATE (= 3) need not be reset if RES told +C DLSOIBT to return because the calling program must change +C the parameters of the problem. +C Also, since a negative input value of ISTATE will be +C regarded as illegal, a negative output value requires the +C user to change it, and possibly other inputs, before +C calling the solver again. +C +C IOPT = an integer flag to specify whether or not any optional +C inputs are being used on this call. Input only. +C The optional inputs are listed separately below. +C IOPT = 0 means no optional inputs are being used. +C Default values will be used in all cases. +C IOPT = 1 means one or more optional inputs are being used. +C +C RWORK = a real working array (double precision). +C The length of RWORK must be at least +C 20 + NYH*(MAXORD + 1) + 3*NEQ + LENWM where +C NYH = the initial value of NEQ, +C MAXORD = 12 (if METH = 1) or 5 (if METH = 2) (unless a +C smaller value is given as an optional input), +C LENWM = 3*MB*MB*NB + 2. +C (See MF description for the definition of METH.) +C Thus if MAXORD has its default value and NEQ is constant, +C this length is +C 22 + 16*NEQ + 3*MB*MB*NB for MF = 11 or 12, +C 22 + 9*NEQ + 3*MB*MB*NB for MF = 21 or 22. +C The first 20 words of RWORK are reserved for conditional +C and optional inputs and optional outputs. +C +C The following word in RWORK is a conditional input: +C RWORK(1) = TCRIT = critical value of t which the solver +C is not to overshoot. Required if ITASK is +C 4 or 5, and ignored otherwise. (See ITASK.) +C +C LRW = the length of the array RWORK, as declared by the user. +C (This will be checked by the solver.) +C +C IWORK = an integer work array. The length of IWORK must be at least +C 20 + NEQ . The first few words of IWORK are used for +C additional and optional inputs and optional outputs. +C +C The following 2 words in IWORK are additional required +C inputs to DLSOIBT: +C IWORK(1) = MB = block size +C IWORK(2) = NB = number of blocks in the main diagonal +C These must satisfy MB .ge. 1, NB .ge. 4, and MB*NB = NEQ. +C +C LIW = the length of the array IWORK, as declared by the user. +C (This will be checked by the solver.) +C +C Note: The work arrays must not be altered between calls to DLSOIBT +C for the same problem, except possibly for the additional and +C optional inputs, and except for the last 3*NEQ words of RWORK. +C The latter space is used for internal scratch space, and so is +C available for use by the user outside DLSOIBT between calls, if +C desired (but not for use by RES, ADDA, or JAC). +C +C MF = the method flag. used only for input. The legal values of +C MF are 11, 12, 21, and 22. +C MF has decimal digits METH and MITER: MF = 10*METH + MITER. +C METH indicates the basic linear multistep method: +C METH = 1 means the implicit Adams method. +C METH = 2 means the method based on Backward +C Differentiation Formulas (BDFS). +C The BDF method is strongly preferred for stiff +C problems, while the Adams method is preferred when the +C problem is not stiff. If the matrix A(t,y) is +C nonsingular, stiffness here can be taken to mean that of +C the explicit ODE system dy/dt = A-inverse * g. If A is +C singular, the concept of stiffness is not well defined. +C If you do not know whether the problem is stiff, we +C recommend using METH = 2. If it is stiff, the advantage +C of METH = 2 over METH = 1 will be great, while if it is +C not stiff, the advantage of METH = 1 will be slight. +C If maximum efficiency is important, some experimentation +C with METH may be necessary. +C MITER indicates the corrector iteration method: +C MITER = 1 means chord iteration with a user-supplied +C block-tridiagonal Jacobian. +C MITER = 2 means chord iteration with an internally +C generated (difference quotient) block- +C tridiagonal Jacobian approximation, using +C 3*MB+1 extra calls to RES per dr/dy evaluation. +C If MITER = 1, the user must supply a Subroutine JAC +C (the name is arbitrary) as described above under JAC. +C For MITER = 2, a dummy argument can be used. +C----------------------------------------------------------------------- +C Optional Inputs. +C +C The following is a list of the optional inputs provided for in the +C call sequence. (See also Part 2.) For each such input variable, +C this table lists its name as used in this documentation, its +C location in the call sequence, its meaning, and the default value. +C The use of any of these inputs requires IOPT = 1, and in that +C case all of these inputs are examined. A value of zero for any +C of these optional inputs will cause the default value to be used. +C Thus to use a subset of the optional inputs, simply preload +C locations 5 to 10 in RWORK and IWORK to 0.0 and 0 respectively, and +C then set those of interest to nonzero values. +C +C Name Location Meaning and Default Value +C +C H0 RWORK(5) the step size to be attempted on the first step. +C The default value is determined by the solver. +C +C HMAX RWORK(6) the maximum absolute step size allowed. +C The default value is infinite. +C +C HMIN RWORK(7) the minimum absolute step size allowed. +C The default value is 0. (This lower bound is not +C enforced on the final step before reaching TCRIT +C when ITASK = 4 or 5.) +C +C MAXORD IWORK(5) the maximum order to be allowed. The default +C value is 12 if METH = 1, and 5 if METH = 2. +C If MAXORD exceeds the default value, it will +C be reduced to the default value. +C If MAXORD is changed during the problem, it may +C cause the current order to be reduced. +C +C MXSTEP IWORK(6) maximum number of (internally defined) steps +C allowed during one call to the solver. +C The default value is 500. +C +C MXHNIL IWORK(7) maximum number of messages printed (per problem) +C warning that T + H = T on a step (H = step size). +C This must be positive to result in a non-default +C value. The default value is 10. +C----------------------------------------------------------------------- +C Optional Outputs. +C +C As optional additional output from DLSOIBT, the variables listed +C below are quantities related to the performance of DLSOIBT +C which are available to the user. These are communicated by way of +C the work arrays, but also have internal mnemonic names as shown. +C Except where stated otherwise, all of these outputs are defined +C on any successful return from DLSOIBT, and on any return with +C ISTATE = -1, -2, -4, -5, -6, or -7. On a return with -3 (illegal +C input) or -8, they will be unchanged from their existing values +C (if any), except possibly for TOLSF, LENRW, and LENIW. +C On any error return, outputs relevant to the error will be defined, +C as noted below. +C +C Name Location Meaning +C +C HU RWORK(11) the step size in t last used (successfully). +C +C HCUR RWORK(12) the step size to be attempted on the next step. +C +C TCUR RWORK(13) the current value of the independent variable +C which the solver has actually reached, i.e. the +C current internal mesh point in t. On output, TCUR +C will always be at least as far as the argument +C T, but may be farther (if interpolation was done). +C +C TOLSF RWORK(14) a tolerance scale factor, greater than 1.0, +C computed when a request for too much accuracy was +C detected (ISTATE = -3 if detected at the start of +C the problem, ISTATE = -2 otherwise). If ITOL is +C left unaltered but RTOL and ATOL are uniformly +C scaled up by a factor of TOLSF for the next call, +C then the solver is deemed likely to succeed. +C (The user may also ignore TOLSF and alter the +C tolerance parameters in any other way appropriate.) +C +C NST IWORK(11) the number of steps taken for the problem so far. +C +C NRE IWORK(12) the number of residual evaluations (RES calls) +C for the problem so far. +C +C NJE IWORK(13) the number of Jacobian evaluations (each involving +C an evaluation of a and dr/dy) for the problem so +C far. This equals the number of calls to ADDA and +C (if MITER = 1) to JAC, and the number of matrix +C LU decompositions. +C +C NQU IWORK(14) the method order last used (successfully). +C +C NQCUR IWORK(15) the order to be attempted on the next step. +C +C IMXER IWORK(16) the index of the component of largest magnitude in +C the weighted local error vector ( E(i)/EWT(i) ), +C on an error return with ISTATE = -4 or -5. +C +C LENRW IWORK(17) the length of RWORK actually required. +C This is defined on normal returns and on an illegal +C input return for insufficient storage. +C +C LENIW IWORK(18) the length of IWORK actually required. +C This is defined on normal returns and on an illegal +C input return for insufficient storage. +C +C +C The following two arrays are segments of the RWORK array which +C may also be of interest to the user as optional outputs. +C For each array, the table below gives its internal name, +C its base address in RWORK, and its description. +C +C Name Base Address Description +C +C YH 21 the Nordsieck history array, of size NYH by +C (NQCUR + 1), where NYH is the initial value +C of NEQ. For j = 0,1,...,NQCUR, column j+1 +C of YH contains HCUR**j/factorial(j) times +C the j-th derivative of the interpolating +C polynomial currently representing the solution, +C evaluated at t = TCUR. +C +C ACOR LENRW-NEQ+1 array of size NEQ used for the accumulated +C corrections on each step, scaled on output to +C represent the estimated local error in y on +C the last step. This is the vector E in the +C description of the error control. It is +C defined only on a return from DLSOIBT with +C ISTATE = 2. +C +C----------------------------------------------------------------------- +C Part 2. Other Routines Callable. +C +C The following are optional calls which the user may make to +C gain additional capabilities in conjunction with DLSOIBT. +C (The routines XSETUN and XSETF are designed to conform to the +C SLATEC error handling package.) +C +C Form of Call Function +C CALL XSETUN(LUN) Set the logical unit number, LUN, for +C output of messages from DLSOIBT, if +C the default is not desired. +C The default value of LUN is 6. +C +C CALL XSETF(MFLAG) Set a flag to control the printing of +C messages by DLSOIBT. +C MFLAG = 0 means do not print. (Danger: +C This risks losing valuable information.) +C MFLAG = 1 means print (the default). +C +C Either of the above calls may be made at +C any time and will take effect immediately. +C +C CALL DSRCOM(RSAV,ISAV,JOB) saves and restores the contents of +C the internal Common blocks used by +C DLSOIBT (see Part 3 below). +C RSAV must be a real array of length 218 +C or more, and ISAV must be an integer +C array of length 37 or more. +C JOB=1 means save Common into RSAV/ISAV. +C JOB=2 means restore Common from RSAV/ISAV. +C DSRCOM is useful if one is +C interrupting a run and restarting +C later, or alternating between two or +C more problems solved with DLSOIBT. +C +C CALL DINTDY(,,,,,) Provide derivatives of y, of various +C (see below) orders, at a specified point t, if +C desired. It may be called only after +C a successful return from DLSOIBT. +C +C The detailed instructions for using DINTDY are as follows. +C The form of the call is: +C +C CALL DINTDY (T, K, RWORK(21), NYH, DKY, IFLAG) +C +C The input parameters are: +C +C T = value of independent variable where answers are desired +C (normally the same as the t last returned by DLSOIBT). +C For valid results, T must lie between TCUR - HU and TCUR. +C (See optional outputs for TCUR and HU.) +C K = integer order of the derivative desired. K must satisfy +C 0 .le. K .le. NQCUR, where NQCUR is the current order +C (see optional outputs). The capability corresponding +C to K = 0, i.e. computing y(t), is already provided +C by DLSOIBT directly. Since NQCUR .ge. 1, the first +C derivative dy/dt is always available with DINTDY. +C RWORK(21) = the base address of the history array YH. +C NYH = column length of YH, equal to the initial value of NEQ. +C +C The output parameters are: +C +C DKY = a real array of length NEQ containing the computed value +C of the K-th derivative of y(t). +C IFLAG = integer flag, returned as 0 if K and T were legal, +C -1 if K was illegal, and -2 if T was illegal. +C On an error return, a message is also written. +C----------------------------------------------------------------------- +C Part 3. Common Blocks. +C +C If DLSOIBT is to be used in an overlay situation, the user +C must declare, in the primary overlay, the variables in: +C (1) the call sequence to DLSOIBT, and +C (2) the internal Common block +C /DLS001/ of length 255 (218 double precision words +C followed by 37 integer words), +C +C If DLSOIBT is used on a system in which the contents of internal +C Common blocks are not preserved between calls, the user should +C declare the above Common block in the calling program to insure +C that their contents are preserved. +C +C If the solution of a given problem by DLSOIBT is to be interrupted +C and then later continued, such as when restarting an interrupted run +C or alternating between two or more problems, the user should save, +C following the return from the last DLSOIBT call prior to the +C interruption, the contents of the call sequence variables and the +C internal Common blocks, and later restore these values before the +C next DLSOIBT call for that problem. To save and restore the Common +C blocks, use Subroutine DSRCOM (see Part 2 above). +C +C----------------------------------------------------------------------- +C Part 4. Optionally Replaceable Solver Routines. +C +C Below are descriptions of two routines in the DLSOIBT package which +C relate to the measurement of errors. Either routine can be +C replaced by a user-supplied version, if desired. However, since such +C a replacement may have a major impact on performance, it should be +C done only when absolutely necessary, and only with great caution. +C (Note: The means by which the package version of a routine is +C superseded by the user's version may be system-dependent.) +C +C (a) DEWSET. +C The following subroutine is called just before each internal +C integration step, and sets the array of error weights, EWT, as +C described under ITOL/RTOL/ATOL above: +C SUBROUTINE DEWSET (NEQ, ITOL, RTOL, ATOL, YCUR, EWT) +C where NEQ, ITOL, RTOL, and ATOL are as in the DLSOIBT call sequence, +C YCUR contains the current dependent variable vector, and +C EWT is the array of weights set by DEWSET. +C +C If the user supplies this subroutine, it must return in EWT(i) +C (i = 1,...,NEQ) a positive quantity suitable for comparing errors +C in y(i) to. The EWT array returned by DEWSET is passed to the DVNORM +C routine (see below), and also used by DLSOIBT in the computation +C of the optional output IMXER, the diagonal Jacobian approximation, +C and the increments for difference quotient Jacobians. +C +C In the user-supplied version of DEWSET, it may be desirable to use +C the current values of derivatives of y. Derivatives up to order NQ +C are available from the history array YH, described above under +C optional outputs. In DEWSET, YH is identical to the YCUR array, +C extended to NQ + 1 columns with a column length of NYH and scale +C factors of H**j/factorial(j). On the first call for the problem, +C given by NST = 0, NQ is 1 and H is temporarily set to 1.0. +C NYH is the initial value of NEQ. The quantities NQ, H, and NST +C can be obtained by including in DEWSET the statements: +C DOUBLE PRECISION RLS +C COMMON /DLS001/ RLS(218),ILS(37) +C NQ = ILS(33) +C NST = ILS(34) +C H = RLS(212) +C Thus, for example, the current value of dy/dt can be obtained as +C YCUR(NYH+i)/H (i=1,...,NEQ) (and the division by H is +C unnecessary when NST = 0). +C +C (b) DVNORM. +C The following is a real function routine which computes the weighted +C root-mean-square norm of a vector v: +C D = DVNORM (N, V, W) +C where: +C N = the length of the vector, +C V = real array of length N containing the vector, +C W = real array of length N containing weights, +C D = SQRT( (1/N) * sum(V(i)*W(i))**2 ). +C DVNORM is called with N = NEQ and with W(i) = 1.0/EWT(i), where +C EWT is as set by Subroutine DEWSET. +C +C If the user supplies this function, it should return a non-negative +C value of DVNORM suitable for use in the error control in DLSOIBT. +C None of the arguments should be altered by DVNORM. +C For example, a user-supplied DVNORM routine might: +C -substitute a max-norm of (V(i)*W(i)) for the RMS-norm, or +C -ignore some components of V in the norm, with the effect of +C suppressing the error control on those components of y. +C----------------------------------------------------------------------- +C +C***REVISION HISTORY (YYYYMMDD) +C 19840625 DATE WRITTEN +C 19870330 Major update: corrected comments throughout; +C removed TRET from Common; rewrote EWSET with 4 loops; +C fixed t test in INTDY; added Cray directives in STODI; +C in STODI, fixed DELP init. and logic around PJAC call; +C combined routines to save/restore Common; +C passed LEVEL = 0 in error message calls (except run abort). +C 20010425 Major update: convert source lines to upper case; +C added *DECK lines; changed from 1 to * in dummy dimensions; +C changed names R1MACH/D1MACH to RUMACH/DUMACH; +C renamed routines for uniqueness across single/double prec.; +C converted intrinsic names to generic form; +C removed ILLIN and NTREP (data loaded) from Common; +C removed all 'own' variables from Common; +C changed error messages to quoted strings; +C replaced XERRWV/XERRWD with 1993 revised version; +C converted prologues, comments, error messages to mixed case; +C converted arithmetic IF statements to logical IF statements; +C numerous corrections to prologues and internal comments. +C 20010507 Converted single precision source to double precision. +C 20020502 Corrected declarations in descriptions of user routines. +C 20031105 Restored 'own' variables to Common block, to enable +C interrupt/restart feature. +C 20031112 Added SAVE statements for data-loaded constants. +C 20031117 Changed internal names NRE, LSAVR to NFE, LSAVF resp. +C +C----------------------------------------------------------------------- +C Other routines in the DLSOIBT package. +C +C In addition to Subroutine DLSOIBT, the DLSOIBT package includes the +C following subroutines and function routines: +C DAIGBT computes the initial value of the vector +C dy/dt = A-inverse * g +C DINTDY computes an interpolated value of the y vector at t = TOUT. +C DSTODI is the core integrator, which does one step of the +C integration and the associated error control. +C DCFODE sets all method coefficients and test constants. +C DEWSET sets the error weight vector EWT before each step. +C DVNORM computes the weighted RMS-norm of a vector. +C DSRCOM is a user-callable routine to save and restore +C the contents of the internal Common blocks. +C DPJIBT computes and preprocesses the Jacobian matrix +C and the Newton iteration matrix P. +C DSLSBT manages solution of linear system in chord iteration. +C DDECBT and DSOLBT are routines for solving block-tridiagonal +C systems of linear algebraic equations. +C DGEFA and DGESL are routines from LINPACK for solving full +C systems of linear algebraic equations. +C DDOT is one of the basic linear algebra modules (BLAS). +C DUMACH computes the unit roundoff in a machine-independent manner. +C XERRWD, XSETUN, XSETF, IXSAV, and IUMACH handle the printing of all +C error messages and warnings. XERRWD is machine-dependent. +C Note: DVNORM, DDOT, DUMACH, IXSAV, and IUMACH are function routines. +C All the others are subroutines. +C +C----------------------------------------------------------------------- + EXTERNAL DPJIBT, DSLSBT + DOUBLE PRECISION DUMACH, DVNORM + INTEGER INIT, MXSTEP, MXHNIL, NHNIL, NSLAST, NYH, IOWNS, + 1 ICF, IERPJ, IERSL, JCUR, JSTART, KFLAG, L, + 2 LYH, LEWT, LACOR, LSAVF, LWM, LIWM, METH, MITER, + 3 MAXORD, MAXCOR, MSBP, MXNCF, N, NQ, NST, NFE, NJE, NQU + INTEGER I, I1, I2, IER, IFLAG, IMXER, IRES, KGO, + 1 LENIW, LENRW, LENWM, LP, LYD0, MB, MORD, MXHNL0, MXSTP0, NB + DOUBLE PRECISION ROWNS, + 1 CCMAX, EL0, H, HMIN, HMXI, HU, RC, TN, UROUND + DOUBLE PRECISION ATOLI, AYI, BIG, EWTI, H0, HMAX, HMX, RH, RTOLI, + 1 TCRIT, TDIST, TNEXT, TOL, TOLSF, TP, SIZE, SUM, W0 + DIMENSION MORD(2) + LOGICAL IHIT + CHARACTER*60 MSG + SAVE MORD, MXSTP0, MXHNL0 +C----------------------------------------------------------------------- +C The following internal Common block contains +C (a) variables which are local to any subroutine but whose values must +C be preserved between calls to the routine ("own" variables), and +C (b) variables which are communicated between subroutines. +C The block DLS001 is declared in subroutines DLSOIBT, DINTDY, DSTODI, +C DPJIBT, and DSLSBT. +C Groups of variables are replaced by dummy arrays in the Common +C declarations in routines where those variables are not used. +C----------------------------------------------------------------------- + COMMON /DLS001/ ROWNS(209), + 1 CCMAX, EL0, H, HMIN, HMXI, HU, RC, TN, UROUND, + 2 INIT, MXSTEP, MXHNIL, NHNIL, NSLAST, NYH, IOWNS(6), + 3 ICF, IERPJ, IERSL, JCUR, JSTART, KFLAG, L, + 4 LYH, LEWT, LACOR, LSAVF, LWM, LIWM, METH, MITER, + 5 MAXORD, MAXCOR, MSBP, MXNCF, N, NQ, NST, NFE, NJE, NQU +C + DATA MORD(1),MORD(2)/12,5/, MXSTP0/500/, MXHNL0/10/ +C----------------------------------------------------------------------- +C Block A. +C This code block is executed on every call. +C It tests ISTATE and ITASK for legality and branches appropriately. +C If ISTATE .gt. 1 but the flag INIT shows that initialization has +C not yet been done, an error return occurs. +C If ISTATE = 0 or 1 and TOUT = T, return immediately. +C----------------------------------------------------------------------- + IF (ISTATE .LT. 0 .OR. ISTATE .GT. 3) GO TO 601 + IF (ITASK .LT. 1 .OR. ITASK .GT. 5) GO TO 602 + IF (ISTATE .LE. 1) GO TO 10 + IF (INIT .EQ. 0) GO TO 603 + IF (ISTATE .EQ. 2) GO TO 200 + GO TO 20 + 10 INIT = 0 + IF (TOUT .EQ. T) RETURN +C----------------------------------------------------------------------- +C Block B. +C The next code block is executed for the initial call (ISTATE = 0 or 1) +C or for a continuation call with parameter changes (ISTATE = 3). +C It contains checking of all inputs and various initializations. +C +C First check legality of the non-optional inputs NEQ, ITOL, IOPT, +C MF, MB, and NB. +C----------------------------------------------------------------------- + 20 IF (NEQ(1) .LE. 0) GO TO 604 + IF (ISTATE .LE. 1) GO TO 25 + IF (NEQ(1) .GT. N) GO TO 605 + 25 N = NEQ(1) + IF (ITOL .LT. 1 .OR. ITOL .GT. 4) GO TO 606 + IF (IOPT .LT. 0 .OR. IOPT .GT. 1) GO TO 607 + METH = MF/10 + MITER = MF - 10*METH + IF (METH .LT. 1 .OR. METH .GT. 2) GO TO 608 + IF (MITER .LT. 1 .OR. MITER .GT. 2) GO TO 608 + MB = IWORK(1) + NB = IWORK(2) + IF (MB .LT. 1 .OR. MB .GT. N) GO TO 609 + IF (NB .LT. 4) GO TO 610 + IF (MB*NB .NE. N) GO TO 609 +C Next process and check the optional inputs. -------------------------- + IF (IOPT .EQ. 1) GO TO 40 + MAXORD = MORD(METH) + MXSTEP = MXSTP0 + MXHNIL = MXHNL0 + IF (ISTATE .LE. 1) H0 = 0.0D0 + HMXI = 0.0D0 + HMIN = 0.0D0 + GO TO 60 + 40 MAXORD = IWORK(5) + IF (MAXORD .LT. 0) GO TO 611 + IF (MAXORD .EQ. 0) MAXORD = 100 + MAXORD = MIN(MAXORD,MORD(METH)) + MXSTEP = IWORK(6) + IF (MXSTEP .LT. 0) GO TO 612 + IF (MXSTEP .EQ. 0) MXSTEP = MXSTP0 + MXHNIL = IWORK(7) + IF (MXHNIL .LT. 0) GO TO 613 + IF (MXHNIL .EQ. 0) MXHNIL = MXHNL0 + IF (ISTATE .GT. 1) GO TO 50 + H0 = RWORK(5) + IF ((TOUT - T)*H0 .LT. 0.0D0) GO TO 614 + 50 HMAX = RWORK(6) + IF (HMAX .LT. 0.0D0) GO TO 615 + HMXI = 0.0D0 + IF (HMAX .GT. 0.0D0) HMXI = 1.0D0/HMAX + HMIN = RWORK(7) + IF (HMIN .LT. 0.0D0) GO TO 616 +C----------------------------------------------------------------------- +C Set work array pointers and check lengths LRW and LIW. +C Pointers to segments of RWORK and IWORK are named by prefixing L to +C the name of the segment. E.g., the segment YH starts at RWORK(LYH). +C Segments of RWORK (in order) are denoted YH, WM, EWT, SAVR, ACOR. +C----------------------------------------------------------------------- + 60 LYH = 21 + IF (ISTATE .LE. 1) NYH = N + LWM = LYH + (MAXORD + 1)*NYH + LENWM = 3*MB*MB*NB + 2 + LEWT = LWM + LENWM + LSAVF = LEWT + N + LACOR = LSAVF + N + LENRW = LACOR + N - 1 + IWORK(17) = LENRW + LIWM = 1 + LENIW = 20 + N + IWORK(18) = LENIW + IF (LENRW .GT. LRW) GO TO 617 + IF (LENIW .GT. LIW) GO TO 618 +C Check RTOL and ATOL for legality. ------------------------------------ + RTOLI = RTOL(1) + ATOLI = ATOL(1) + DO 70 I = 1,N + IF (ITOL .GE. 3) RTOLI = RTOL(I) + IF (ITOL .EQ. 2 .OR. ITOL .EQ. 4) ATOLI = ATOL(I) + IF (RTOLI .LT. 0.0D0) GO TO 619 + IF (ATOLI .LT. 0.0D0) GO TO 620 + 70 CONTINUE + IF (ISTATE .LE. 1) GO TO 100 +C If ISTATE = 3, set flag to signal parameter changes to DSTODI. ------- + JSTART = -1 + IF (NQ .LE. MAXORD) GO TO 90 +C MAXORD was reduced below NQ. Copy YH(*,MAXORD+2) into YDOTI.--------- + DO 80 I = 1,N + 80 YDOTI(I) = RWORK(I+LWM-1) +C Reload WM(1) = RWORK(lWM), since lWM may have changed. --------------- + 90 RWORK(LWM) = SQRT(UROUND) + IF (N .EQ. NYH) GO TO 200 +C NEQ was reduced. Zero part of YH to avoid undefined references. ----- + I1 = LYH + L*NYH + I2 = LYH + (MAXORD + 1)*NYH - 1 + IF (I1 .GT. I2) GO TO 200 + DO 95 I = I1,I2 + 95 RWORK(I) = 0.0D0 + GO TO 200 +C----------------------------------------------------------------------- +C Block C. +C The next block is for the initial call only (ISTATE = 0 or 1). +C It contains all remaining initializations, the call to DAIGBT +C (if ISTATE = 1), and the calculation of the initial step size. +C The error weights in EWT are inverted after being loaded. +C----------------------------------------------------------------------- + 100 UROUND = DUMACH() + TN = T + IF (ITASK .NE. 4 .AND. ITASK .NE. 5) GO TO 105 + TCRIT = RWORK(1) + IF ((TCRIT - TOUT)*(TOUT - T) .LT. 0.0D0) GO TO 625 + IF (H0 .NE. 0.0D0 .AND. (T + H0 - TCRIT)*H0 .GT. 0.0D0) + 1 H0 = TCRIT - T + 105 JSTART = 0 + RWORK(LWM) = SQRT(UROUND) + NHNIL = 0 + NST = 0 + NFE = 0 + NJE = 0 + NSLAST = 0 + HU = 0.0D0 + NQU = 0 + CCMAX = 0.3D0 + MAXCOR = 3 + MSBP = 20 + MXNCF = 10 +C Compute initial dy/dt, if necessary, and load it and initial Y into YH + LYD0 = LYH + NYH + LP = LWM + 1 + IF ( ISTATE .EQ. 1 ) GO TO 120 +C DLSOIBT must compute initial dy/dt (LYD0 points to YH(*,2)). --------- + CALL DAIGBT( RES, ADDA, NEQ, T, Y, RWORK(LYD0), + 1 MB, NB, RWORK(LP), IWORK(21), IER ) + NFE = NFE + 1 + IF (IER .LT. 0) GO TO 560 + IF (IER .GT. 0) GO TO 565 + DO 115 I = 1,N + 115 RWORK(I+LYH-1) = Y(I) + GO TO 130 +C Initial dy/dt was supplied. Load into YH (LYD0 points to YH(*,2).). - + 120 DO 125 I = 1,N + RWORK(I+LYH-1) = Y(I) + 125 RWORK(I+LYD0-1) = YDOTI(I) +C Load and invert the EWT array. (H is temporarily set to 1.0.) ------- + 130 CONTINUE + NQ = 1 + H = 1.0D0 + CALL DEWSET (N, ITOL, RTOL, ATOL, RWORK(LYH), RWORK(LEWT)) + DO 135 I = 1,N + IF (RWORK(I+LEWT-1) .LE. 0.0D0) GO TO 621 + 135 RWORK(I+LEWT-1) = 1.0D0/RWORK(I+LEWT-1) +C----------------------------------------------------------------------- +C The coding below computes the step size, H0, to be attempted on the +C first step, unless the user has supplied a value for this. +C First check that TOUT - T differs significantly from zero. +C A scalar tolerance quantity TOL is computed, as MAX(RTOL(i)) +C if this is positive, or MAX(ATOL(i)/ABS(Y(i))) otherwise, adjusted +C so as to be between 100*UROUND and 1.0E-3. +C Then the computed value H0 is given by.. +C NEQ +C H0**2 = TOL / ( w0**-2 + (1/NEQ) * Sum ( YDOT(i)/ywt(i) )**2 ) +C 1 +C where w0 = MAX ( ABS(T), ABS(TOUT) ), +C YDOT(i) = i-th component of initial value of dy/dt, +C ywt(i) = EWT(i)/TOL (a weight for y(i)). +C The sign of H0 is inferred from the initial values of TOUT and T. +C----------------------------------------------------------------------- + IF (H0 .NE. 0.0D0) GO TO 180 + TDIST = ABS(TOUT - T) + W0 = MAX(ABS(T),ABS(TOUT)) + IF (TDIST .LT. 2.0D0*UROUND*W0) GO TO 622 + TOL = RTOL(1) + IF (ITOL .LE. 2) GO TO 145 + DO 140 I = 1,N + 140 TOL = MAX(TOL,RTOL(I)) + 145 IF (TOL .GT. 0.0D0) GO TO 160 + ATOLI = ATOL(1) + DO 150 I = 1,N + IF (ITOL .EQ. 2 .OR. ITOL .EQ. 4) ATOLI = ATOL(I) + AYI = ABS(Y(I)) + IF (AYI .NE. 0.0D0) TOL = MAX(TOL,ATOLI/AYI) + 150 CONTINUE + 160 TOL = MAX(TOL,100.0D0*UROUND) + TOL = MIN(TOL,0.001D0) + SUM = DVNORM (N, RWORK(LYD0), RWORK(LEWT)) + SUM = 1.0D0/(TOL*W0*W0) + TOL*SUM**2 + H0 = 1.0D0/SQRT(SUM) + H0 = MIN(H0,TDIST) + H0 = SIGN(H0,TOUT-T) +C Adjust H0 if necessary to meet HMAX bound. --------------------------- + 180 RH = ABS(H0)*HMXI + IF (RH .GT. 1.0D0) H0 = H0/RH +C Load H with H0 and scale YH(*,2) by H0. ------------------------------ + H = H0 + DO 190 I = 1,N + 190 RWORK(I+LYD0-1) = H0*RWORK(I+LYD0-1) + GO TO 270 +C----------------------------------------------------------------------- +C Block D. +C The next code block is for continuation calls only (ISTATE = 2 or 3) +C and is to check stop conditions before taking a step. +C----------------------------------------------------------------------- + 200 NSLAST = NST + GO TO (210, 250, 220, 230, 240), ITASK + 210 IF ((TN - TOUT)*H .LT. 0.0D0) GO TO 250 + CALL DINTDY (TOUT, 0, RWORK(LYH), NYH, Y, IFLAG) + IF (IFLAG .NE. 0) GO TO 627 + T = TOUT + GO TO 420 + 220 TP = TN - HU*(1.0D0 + 100.0D0*UROUND) + IF ((TP - TOUT)*H .GT. 0.0D0) GO TO 623 + IF ((TN - TOUT)*H .LT. 0.0D0) GO TO 250 + GO TO 400 + 230 TCRIT = RWORK(1) + IF ((TN - TCRIT)*H .GT. 0.0D0) GO TO 624 + IF ((TCRIT - TOUT)*H .LT. 0.0D0) GO TO 625 + IF ((TN - TOUT)*H .LT. 0.0D0) GO TO 245 + CALL DINTDY (TOUT, 0, RWORK(LYH), NYH, Y, IFLAG) + IF (IFLAG .NE. 0) GO TO 627 + T = TOUT + GO TO 420 + 240 TCRIT = RWORK(1) + IF ((TN - TCRIT)*H .GT. 0.0D0) GO TO 624 + 245 HMX = ABS(TN) + ABS(H) + IHIT = ABS(TN - TCRIT) .LE. 100.0D0*UROUND*HMX + IF (IHIT) GO TO 400 + TNEXT = TN + H*(1.0D0 + 4.0D0*UROUND) + IF ((TNEXT - TCRIT)*H .LE. 0.0D0) GO TO 250 + H = (TCRIT - TN)*(1.0D0 - 4.0D0*UROUND) + IF (ISTATE .EQ. 2) JSTART = -2 +C----------------------------------------------------------------------- +C Block E. +C The next block is normally executed for all calls and contains +C the call to the one-step core integrator DSTODI. +C +C This is a looping point for the integration steps. +C +C First check for too many steps being taken, update EWT (if not at +C start of problem), check for too much accuracy being requested, and +C check for H below the roundoff level in T. +C----------------------------------------------------------------------- + 250 CONTINUE + IF ((NST-NSLAST) .GE. MXSTEP) GO TO 500 + CALL DEWSET (N, ITOL, RTOL, ATOL, RWORK(LYH), RWORK(LEWT)) + DO 260 I = 1,N + IF (RWORK(I+LEWT-1) .LE. 0.0D0) GO TO 510 + 260 RWORK(I+LEWT-1) = 1.0D0/RWORK(I+LEWT-1) + 270 TOLSF = UROUND*DVNORM (N, RWORK(LYH), RWORK(LEWT)) + IF (TOLSF .LE. 1.0D0) GO TO 280 + TOLSF = TOLSF*2.0D0 + IF (NST .EQ. 0) GO TO 626 + GO TO 520 + 280 IF ((TN + H) .NE. TN) GO TO 290 + NHNIL = NHNIL + 1 + IF (NHNIL .GT. MXHNIL) GO TO 290 + MSG = 'DLSOIBT- Warning..Internal T (=R1) and H (=R2) are' + CALL XERRWD (MSG, 50, 101, 0, 0, 0, 0, 0, 0.0D0, 0.0D0) + MSG=' such that in the machine, T + H = T on the next step ' + CALL XERRWD (MSG, 60, 101, 0, 0, 0, 0, 0, 0.0D0, 0.0D0) + MSG = ' (H = step size). Solver will continue anyway.' + CALL XERRWD (MSG, 50, 101, 0, 0, 0, 0, 2, TN, H) + IF (NHNIL .LT. MXHNIL) GO TO 290 + MSG = 'DLSOIBT- Above warning has been issued I1 times. ' + CALL XERRWD (MSG, 50, 102, 0, 0, 0, 0, 0, 0.0D0, 0.0D0) + MSG = ' It will not be issued again for this problem.' + CALL XERRWD (MSG, 50, 102, 0, 1, MXHNIL, 0, 0, 0.0D0, 0.0D0) + 290 CONTINUE +C----------------------------------------------------------------------- +C CALL DSTODI(NEQ,Y,YH,NYH,YH1,EWT,SAVF,SAVR,ACOR,WM,IWM,RES, +C ADDA,JAC,DPJIBT,DSLSBT) +C Note: SAVF in DSTODI occupies the same space as YDOTI in DLSOIBT. +C----------------------------------------------------------------------- + CALL DSTODI (NEQ, Y, RWORK(LYH), NYH, RWORK(LYH), RWORK(LEWT), + 1 YDOTI, RWORK(LSAVF), RWORK(LACOR), RWORK(LWM), + 2 IWORK(LIWM), RES, ADDA, JAC, DPJIBT, DSLSBT ) + KGO = 1 - KFLAG + GO TO (300, 530, 540, 400, 550), KGO +C +C KGO = 1:success; 2:error test failure; 3:convergence failure; +C 4:RES ordered return; 5:RES returned error. +C----------------------------------------------------------------------- +C Block F. +C The following block handles the case of a successful return from the +C core integrator (KFLAG = 0). Test for stop conditions. +C----------------------------------------------------------------------- + 300 INIT = 1 + GO TO (310, 400, 330, 340, 350), ITASK +C ITASK = 1. If TOUT has been reached, interpolate. ------------------- + 310 IF ((TN - TOUT)*H .LT. 0.0D0) GO TO 250 + CALL DINTDY (TOUT, 0, RWORK(LYH), NYH, Y, IFLAG) + T = TOUT + GO TO 420 +C ITASK = 3. Jump to exit if TOUT was reached. ------------------------ + 330 IF ((TN - TOUT)*H .GE. 0.0D0) GO TO 400 + GO TO 250 +C ITASK = 4. See if TOUT or TCRIT was reached. Adjust H if necessary. + 340 IF ((TN - TOUT)*H .LT. 0.0D0) GO TO 345 + CALL DINTDY (TOUT, 0, RWORK(LYH), NYH, Y, IFLAG) + T = TOUT + GO TO 420 + 345 HMX = ABS(TN) + ABS(H) + IHIT = ABS(TN - TCRIT) .LE. 100.0D0*UROUND*HMX + IF (IHIT) GO TO 400 + TNEXT = TN + H*(1.0D0 + 4.0D0*UROUND) + IF ((TNEXT - TCRIT)*H .LE. 0.0D0) GO TO 250 + H = (TCRIT - TN)*(1.0D0 - 4.0D0*UROUND) + JSTART = -2 + GO TO 250 +C ITASK = 5. see if TCRIT was reached and jump to exit. --------------- + 350 HMX = ABS(TN) + ABS(H) + IHIT = ABS(TN - TCRIT) .LE. 100.0D0*UROUND*HMX +C----------------------------------------------------------------------- +C Block G. +C The following block handles all successful returns from DLSOIBT. +C If ITASK .ne. 1, Y is loaded from YH and T is set accordingly. +C ISTATE is set to 2, and the optional outputs are loaded into the +C work arrays before returning. +C----------------------------------------------------------------------- + 400 DO 410 I = 1,N + 410 Y(I) = RWORK(I+LYH-1) + T = TN + IF (ITASK .NE. 4 .AND. ITASK .NE. 5) GO TO 420 + IF (IHIT) T = TCRIT + 420 ISTATE = 2 + IF ( KFLAG .EQ. -3 ) ISTATE = 3 + RWORK(11) = HU + RWORK(12) = H + RWORK(13) = TN + IWORK(11) = NST + IWORK(12) = NFE + IWORK(13) = NJE + IWORK(14) = NQU + IWORK(15) = NQ + RETURN +C----------------------------------------------------------------------- +C Block H. +C The following block handles all unsuccessful returns other than +C those for illegal input. First the error message routine is called. +C If there was an error test or convergence test failure, IMXER is set. +C Then Y is loaded from YH and T is set to TN. +C The optional outputs are loaded into the work arrays before returning. +C----------------------------------------------------------------------- +C The maximum number of steps was taken before reaching TOUT. ---------- + 500 MSG = 'DLSOIBT- At current T (=R1), MXSTEP (=I1) steps ' + CALL XERRWD (MSG, 50, 201, 0, 0, 0, 0, 0, 0.0D0, 0.0D0) + MSG = ' taken on this call before reaching TOUT ' + CALL XERRWD (MSG, 50, 201, 0, 1, MXSTEP, 0, 1, TN, 0.0D0) + ISTATE = -1 + GO TO 580 +C EWT(i) .le. 0.0 for some i (not at start of problem). ---------------- + 510 EWTI = RWORK(LEWT+I-1) + MSG = 'DLSOIBT- At T (=R1), EWT(I1) has become R2 .le. 0.' + CALL XERRWD (MSG, 50, 202, 0, 1, I, 0, 2, TN, EWTI) + ISTATE = -6 + GO TO 590 +C Too much accuracy requested for machine precision. ------------------- + 520 MSG = 'DLSOIBT- At T (=R1), too much accuracy requested ' + CALL XERRWD (MSG, 50, 203, 0, 0, 0, 0, 0, 0.0D0, 0.0D0) + MSG = ' for precision of machine.. See TOLSF (=R2) ' + CALL XERRWD (MSG, 50, 203, 0, 0, 0, 0, 2, TN, TOLSF) + RWORK(14) = TOLSF + ISTATE = -2 + GO TO 590 +C KFLAG = -1. Error test failed repeatedly or with ABS(H) = HMIN. ----- + 530 MSG = 'DLSOIBT- At T (=R1) and step size H (=R2), the ' + CALL XERRWD (MSG, 50, 204, 0, 0, 0, 0, 0, 0.0D0, 0.0D0) + MSG = 'error test failed repeatedly or with ABS(H) = HMIN' + CALL XERRWD (MSG, 50, 204, 0, 0, 0, 0, 2, TN, H) + ISTATE = -4 + GO TO 570 +C KFLAG = -2. Convergence failed repeatedly or with ABS(H) = HMIN. ---- + 540 MSG = 'DLSOIBT- At T (=R1) and step size H (=R2), the ' + CALL XERRWD (MSG, 50, 205, 0, 0, 0, 0, 0, 0.0D0, 0.0D0) + MSG = ' corrector convergence failed repeatedly ' + CALL XERRWD (MSG, 50, 205, 0, 0, 0, 0, 0, 0.0D0, 0.0D0) + MSG = ' or with ABS(H) = HMIN ' + CALL XERRWD (MSG, 30, 205, 0, 0, 0, 0, 2, TN, H) + ISTATE = -5 + GO TO 570 +C IRES = 3 returned by RES, despite retries by DSTODI.------------------ + 550 MSG = 'DLSOIBT- At T (=R1) residual routine returned ' + CALL XERRWD (MSG, 50, 206, 0, 0, 0, 0, 0, 0.0D0, 0.0D0) + MSG = ' error IRES = 3 repeatedly. ' + CALL XERRWD (MSG, 40, 206, 0, 0, 0, 0, 1, TN, 0.0D0) + ISTATE = -7 + GO TO 590 +C DAIGBT failed because a diagonal block of A matrix was singular. ----- + 560 IER = -IER + MSG='DLSOIBT- Attempt to initialize dy/dt failed: Matrix A has a' + CALL XERRWD (MSG, 60, 207, 0, 0, 0, 0, 0, 0.0D0, 0.0D0) + MSG = ' singular diagonal block, block no. = (I1) ' + CALL XERRWD (MSG, 50, 207, 0, 1, IER, 0, 0, 0.0D0, 0.0D0) + ISTATE = -8 + RETURN +C DAIGBT failed because RES set IRES to 2 or 3. ------------------------ + 565 MSG = 'DLSOIBT- Attempt to initialize dy/dt failed ' + CALL XERRWD (MSG, 50, 208, 0, 0, 0, 0, 0, 0.0D0, 0.0D0) + MSG = ' because residual routine set its error flag ' + CALL XERRWD (MSG, 50, 208, 0, 0, 0, 0, 0, 0.0D0, 0.0D0) + MSG = ' to IRES = (I1)' + CALL XERRWD (MSG, 20, 208, 0, 1, IER, 0, 0, 0.0D0, 0.0D0) + ISTATE = -8 + RETURN +C Compute IMXER if relevant. ------------------------------------------- + 570 BIG = 0.0D0 + IMXER = 1 + DO 575 I = 1,N + SIZE = ABS(RWORK(I+LACOR-1)*RWORK(I+LEWT-1)) + IF (BIG .GE. SIZE) GO TO 575 + BIG = SIZE + IMXER = I + 575 CONTINUE + IWORK(16) = IMXER +C Compute residual if relevant. ---------------------------------------- + 580 LYD0 = LYH + NYH + DO 585 I = 1,N + RWORK(I+LSAVF-1) = RWORK(I+LYD0-1)/H + 585 Y(I) = RWORK(I+LYH-1) + IRES = 1 + CALL RES (NEQ, TN, Y, RWORK(LSAVF), YDOTI, IRES) + NFE = NFE + 1 + IF (IRES .LE. 1) GO TO 595 + MSG = 'DLSOIBT- Residual routine set its flag IRES ' + CALL XERRWD (MSG, 50, 210, 0, 0, 0, 0, 0, 0.0D0, 0.0D0) + MSG = ' to (I1) when called for final output. ' + CALL XERRWD (MSG, 50, 210, 0, 1, IRES, 0, 0, 0.0D0, 0.0D0) + GO TO 595 +C Set Y vector, T, and optional outputs. ------------------------------- + 590 DO 592 I = 1,N + 592 Y(I) = RWORK(I+LYH-1) + 595 T = TN + RWORK(11) = HU + RWORK(12) = H + RWORK(13) = TN + IWORK(11) = NST + IWORK(12) = NFE + IWORK(13) = NJE + IWORK(14) = NQU + IWORK(15) = NQ + RETURN +C----------------------------------------------------------------------- +C Block I. +C The following block handles all error returns due to illegal input +C (ISTATE = -3), as detected before calling the core integrator. +C First the error message routine is called. If the illegal input +C is a negative ISTATE, the run is aborted (apparent infinite loop). +C----------------------------------------------------------------------- + 601 MSG = 'DLSOIBT- ISTATE (=I1) illegal.' + CALL XERRWD (MSG, 30, 1, 0, 1, ISTATE, 0, 0, 0.0D0, 0.0D0) + IF (ISTATE .LT. 0) GO TO 800 + GO TO 700 + 602 MSG = 'DLSOIBT- ITASK (=I1) illegal. ' + CALL XERRWD (MSG, 30, 2, 0, 1, ITASK, 0, 0, 0.0D0, 0.0D0) + GO TO 700 + 603 MSG = 'DLSOIBT- ISTATE.gt.1 but DLSOIBT not initialized. ' + CALL XERRWD (MSG, 50, 3, 0, 0, 0, 0, 0, 0.0D0, 0.0D0) + GO TO 700 + 604 MSG = 'DLSOIBT- NEQ (=I1) .lt. 1 ' + CALL XERRWD (MSG, 30, 4, 0, 1, NEQ(1), 0, 0, 0.0D0, 0.0D0) + GO TO 700 + 605 MSG = 'DLSOIBT- ISTATE = 3 and NEQ increased (I1 to I2). ' + CALL XERRWD (MSG, 50, 5, 0, 2, N, NEQ(1), 0, 0.0D0, 0.0D0) + GO TO 700 + 606 MSG = 'DLSOIBT- ITOL (=I1) illegal. ' + CALL XERRWD (MSG, 30, 6, 0, 1, ITOL, 0, 0, 0.0D0, 0.0D0) + GO TO 700 + 607 MSG = 'DLSOIBT- IOPT (=I1) illegal. ' + CALL XERRWD (MSG, 30, 7, 0, 1, IOPT, 0, 0, 0.0D0, 0.0D0) + GO TO 700 + 608 MSG = 'DLSOIBT- MF (=I1) illegal. ' + CALL XERRWD (MSG, 30, 8, 0, 1, MF, 0, 0, 0.0D0, 0.0D0) + GO TO 700 + 609 MSG = 'DLSOIBT- MB (=I1) or NB (=I2) illegal. ' + CALL XERRWD (MSG, 40, 9, 0, 2, MB, NB, 0, 0.0D0, 0.0D0) + GO TO 700 + 610 MSG = 'DLSOIBT- NB (=I1) .lt. 4 illegal. ' + CALL XERRWD (MSG, 40, 10, 0, 1, NB, 0, 0, 0.0D0, 0.0D0) + GO TO 700 + 611 MSG = 'DLSOIBT- MAXORD (=I1) .lt. 0 ' + CALL XERRWD (MSG, 30, 11, 0, 1, MAXORD, 0, 0, 0.0D0, 0.0D0) + GO TO 700 + 612 MSG = 'DLSOIBT- MXSTEP (=I1) .lt. 0 ' + CALL XERRWD (MSG, 30, 12, 0, 1, MXSTEP, 0, 0, 0.0D0, 0.0D0) + GO TO 700 + 613 MSG = 'DLSOIBT- MXHNIL (=I1) .lt. 0 ' + CALL XERRWD (MSG, 30, 13, 0, 1, MXHNIL, 0, 0, 0.0D0, 0.0D0) + GO TO 700 + 614 MSG = 'DLSOIBT- TOUT (=R1) behind T (=R2) ' + CALL XERRWD (MSG, 40, 14, 0, 0, 0, 0, 2, TOUT, T) + MSG = ' Integration direction is given by H0 (=R1) ' + CALL XERRWD (MSG, 50, 14, 0, 0, 0, 0, 1, H0, 0.0D0) + GO TO 700 + 615 MSG = 'DLSOIBT- HMAX (=R1) .lt. 0.0 ' + CALL XERRWD (MSG, 30, 15, 0, 0, 0, 0, 1, HMAX, 0.0D0) + GO TO 700 + 616 MSG = 'DLSOIBT- HMIN (=R1) .lt. 0.0 ' + CALL XERRWD (MSG, 30, 16, 0, 0, 0, 0, 1, HMIN, 0.0D0) + GO TO 700 + 617 MSG='DLSOIBT- RWORK length needed, LENRW (=I1), exceeds LRW (=I2)' + CALL XERRWD (MSG, 60, 17, 0, 2, LENRW, LRW, 0, 0.0D0, 0.0D0) + GO TO 700 + 618 MSG='DLSOIBT- IWORK length needed, LENIW (=I1), exceeds LIW (=I2)' + CALL XERRWD (MSG, 60, 18, 0, 2, LENIW, LIW, 0, 0.0D0, 0.0D0) + GO TO 700 + 619 MSG = 'DLSOIBT- RTOL(=I1) is R1 .lt. 0.0 ' + CALL XERRWD (MSG, 40, 19, 0, 1, I, 0, 1, RTOLI, 0.0D0) + GO TO 700 + 620 MSG = 'DLSOIBT- ATOL(=I1) is R1 .lt. 0.0 ' + CALL XERRWD (MSG, 40, 20, 0, 1, I, 0, 1, ATOLI, 0.0D0) + GO TO 700 + 621 EWTI = RWORK(LEWT+I-1) + MSG = 'DLSOIBT- EWT(I1) is R1 .le. 0.0 ' + CALL XERRWD (MSG, 40, 21, 0, 1, I, 0, 1, EWTI, 0.0D0) + GO TO 700 + 622 MSG='DLSOIBT- TOUT(=R1) too close to T(=R2) to start integration.' + CALL XERRWD (MSG, 60, 22, 0, 0, 0, 0, 2, TOUT, T) + GO TO 700 + 623 MSG='DLSOIBT- ITASK = I1 and TOUT (=R1) behind TCUR - HU (= R2) ' + CALL XERRWD (MSG, 60, 23, 0, 1, ITASK, 0, 2, TOUT, TP) + GO TO 700 + 624 MSG='DLSOIBT- ITASK = 4 or 5 and TCRIT (=R1) behind TCUR (=R2) ' + CALL XERRWD (MSG, 60, 24, 0, 0, 0, 0, 2, TCRIT, TN) + GO TO 700 + 625 MSG='DLSOIBT- ITASK = 4 or 5 and TCRIT (=R1) behind TOUT (=R2) ' + CALL XERRWD (MSG, 60, 25, 0, 0, 0, 0, 2, TCRIT, TOUT) + GO TO 700 + 626 MSG = 'DLSOIBT- At start of problem, too much accuracy ' + CALL XERRWD (MSG, 50, 26, 0, 0, 0, 0, 0, 0.0D0, 0.0D0) + MSG=' requested for precision of machine.. See TOLSF (=R1) ' + CALL XERRWD (MSG, 60, 26, 0, 0, 0, 0, 1, TOLSF, 0.0D0) + RWORK(14) = TOLSF + GO TO 700 + 627 MSG = 'DLSOIBT- Trouble in DINTDY. ITASK = I1, TOUT = R1' + CALL XERRWD (MSG, 50, 27, 0, 1, ITASK, 0, 1, TOUT, 0.0D0) +C + 700 ISTATE = -3 + RETURN +C + 800 MSG = 'DLSOIBT- Run aborted.. apparent infinite loop. ' + CALL XERRWD (MSG, 50, 303, 2, 0, 0, 0, 0, 0.0D0, 0.0D0) + RETURN +C----------------------- End of Subroutine DLSOIBT --------------------- + END +*DECK DLSODIS + SUBROUTINE DLSODIS (RES, ADDA, JAC, NEQ, Y, YDOTI, T, TOUT, ITOL, + 1 RTOL, ATOL, ITASK, ISTATE, IOPT, RWORK, LRW, IWORK, LIW, MF ) + EXTERNAL RES, ADDA, JAC + INTEGER NEQ, ITOL, ITASK, ISTATE, IOPT, LRW, IWORK, LIW, MF + DOUBLE PRECISION Y, YDOTI, T, TOUT, RTOL, ATOL, RWORK + DIMENSION NEQ(*), Y(*), YDOTI(*), RTOL(*), ATOL(*), RWORK(LRW), + 1 IWORK(LIW) +C----------------------------------------------------------------------- +C This is the 18 November 2003 version of +C DLSODIS: Livermore Solver for Ordinary Differential equations +C (Implicit form) with general Sparse Jacobian matrices. +C +C This version is in double precision. +C +C DLSODIS solves the initial value problem for linearly implicit +C systems of first order ODEs, +C A(t,y) * dy/dt = g(t,y) , where A(t,y) is a square matrix, +C or, in component form, +C ( a * ( dy / dt )) + ... + ( a * ( dy / dt )) = +C i,1 1 i,NEQ NEQ +C +C = g ( t, y , y ,..., y ) ( i = 1,...,NEQ ) +C i 1 2 NEQ +C +C If A is singular, this is a differential-algebraic system. +C +C DLSODIS is a variant version of the DLSODI package, and is intended +C for stiff problems in which the matrix A and the Jacobian matrix +C d(g - A*s)/dy have arbitrary sparse structures. +C +C Authors: Alan C. Hindmarsh +C Center for Applied Scientific Computing, L-561 +C Lawrence Livermore National Laboratory +C Livermore, CA 94551 +C and +C Sheila Balsdon +C Zycor, Inc. +C Austin, TX 78741 +C----------------------------------------------------------------------- +C References: +C 1. M. K. Seager and S. Balsdon, LSODIS, A Sparse Implicit +C ODE Solver, in Proceedings of the IMACS 10th World Congress, +C Montreal, August 8-13, 1982. +C +C 2. Alan C. Hindmarsh, LSODE and LSODI, Two New Initial Value +C Ordinary Differential Equation Solvers, +C ACM-SIGNUM Newsletter, vol. 15, no. 4 (1980), pp. 10-11. +C +C 3. S. C. Eisenstat, M. C. Gursky, M. H. Schultz, and A. H. Sherman, +C Yale Sparse Matrix Package: I. The Symmetric Codes, +C Int. J. Num. Meth. Eng., vol. 18 (1982), pp. 1145-1151. +C +C 4. S. C. Eisenstat, M. C. Gursky, M. H. Schultz, and A. H. Sherman, +C Yale Sparse Matrix Package: II. The Nonsymmetric Codes, +C Research Report No. 114, Dept. of Computer Sciences, Yale +C University, 1977. +C----------------------------------------------------------------------- +C Summary of Usage. +C +C Communication between the user and the DLSODIS package, for normal +C situations, is summarized here. This summary describes only a subset +C of the full set of options available. See the full description for +C details, including optional communication, nonstandard options, +C and instructions for special situations. See also the example +C problem (with program and output) following this summary. +C +C A. First, provide a subroutine of the form: +C SUBROUTINE RES (NEQ, T, Y, S, R, IRES) +C DOUBLE PRECISION T, Y(*), S(*), R(*) +C which computes the residual function +C r = g(t,y) - A(t,y) * s , +C as a function of t and the vectors y and s. (s is an internally +C generated approximation to dy/dt.) The arrays Y and S are inputs +C to the RES routine and should not be altered. The residual +C vector is to be stored in the array R. The argument IRES should be +C ignored for casual use of DLSODIS. (For uses of IRES, see the +C paragraph on RES in the full description below.) +C +C B. DLSODIS must deal internally with the matrices A and dr/dy, where +C r is the residual function defined above. DLSODIS generates a linear +C combination of these two matrices in sparse form. +C The matrix structure is communicated by a method flag, MF: +C MF = 21 or 22 when the user provides the structures of +C matrix A and dr/dy, +C MF = 121 or 222 when the user does not provide structure +C information, and +C MF = 321 or 422 when the user provides the structure +C of matrix A. +C +C C. You must also provide a subroutine of the form: +C SUBROUTINE ADDA (NEQ, T, Y, J, IAN, JAN, P) +C DOUBLE PRECISION T, Y(*), P(*) +C INTEGER IAN(*), JAN(*) +C which adds the matrix A = A(t,y) to the contents of the array P. +C NEQ, T, Y, and J are input arguments and should not be altered. +C This routine should add the J-th column of matrix A to the array +C P (of length NEQ). I.e. add A(i,J) to P(i) for all relevant +C values of i. The arguments IAN and JAN should be ignored for normal +C situations. DLSODIS will call the ADDA routine with J = 1,2,...,NEQ. +C +C D. For the sake of efficiency, you are encouraged to supply the +C Jacobian matrix dr/dy in closed form, where r = g(t,y) - A(t,y)*s +C (s = a fixed vector) as above. If dr/dy is being supplied, +C use MF = 21, 121, or 321, and provide a subroutine of the form: +C SUBROUTINE JAC (NEQ, T, Y, S, J, IAN, JAN, PDJ) +C DOUBLE PRECISION T, Y(*), S(*), PDJ(*) +C INTEGER IAN(*), JAN(*) +C which computes dr/dy as a function of t, y, and s. Here NEQ, T, Y, S, +C and J are input arguments, and the JAC routine is to load the array +C PDJ (of length NEQ) with the J-th column of dr/dy. I.e. load PDJ(i) +C with dr(i)/dy(J) for all relevant values of i. The arguments IAN and +C JAN should be ignored for normal situations. DLSODIS will call the +C JAC routine with J = 1,2,...,NEQ. +C Only nonzero elements need be loaded. A crude approximation +C to dr/dy, possibly with fewer nonzero elememts, will suffice. +C Note that if A is independent of y (or this dependence +C is weak enough to be ignored) then JAC is to compute dg/dy. +C If it is not feasible to provide a JAC routine, use +C MF = 22, 222, or 422 and DLSODIS will compute an approximate +C Jacobian internally by difference quotients. +C +C E. Next decide whether or not to provide the initial value of the +C derivative vector dy/dt. If the initial value of A(t,y) is +C nonsingular (and not too ill-conditioned), you may let DLSODIS compute +C this vector (ISTATE = 0). (DLSODIS will solve the system A*s = g for +C s, with initial values of A and g.) If A(t,y) is initially +C singular, then the system is a differential-algebraic system, and +C you must make use of the particular form of the system to compute the +C initial values of y and dy/dt. In that case, use ISTATE = 1 and +C load the initial value of dy/dt into the array YDOTI. +C The input array YDOTI and the initial Y array must be consistent with +C the equations A*dy/dt = g. This implies that the initial residual +C r = g(t,y) - A(t,y)*YDOTI must be approximately zero. +C +C F. Write a main program which calls Subroutine DLSODIS once for +C each point at which answers are desired. This should also provide +C for possible use of logical unit 6 for output of error messages by +C DLSODIS. On the first call to DLSODIS, supply arguments as follows: +C RES = name of user subroutine for residual function r. +C ADDA = name of user subroutine for computing and adding A(t,y). +C JAC = name of user subroutine for Jacobian matrix dr/dy +C (MF = 121). If not used, pass a dummy name. +C Note: The names for the RES and ADDA routines and (if used) the +C JAC routine must be declared External in the calling program. +C NEQ = number of scalar equations in the system. +C Y = array of initial values, of length NEQ. +C YDOTI = array of length NEQ (containing initial dy/dt if ISTATE = 1). +C T = the initial value of the independent variable. +C TOUT = first point where output is desired (.ne. T). +C ITOL = 1 or 2 according as ATOL (below) is a scalar or array. +C RTOL = relative tolerance parameter (scalar). +C ATOL = absolute tolerance parameter (scalar or array). +C The estimated local error in y(i) will be controlled so as +C to be roughly less (in magnitude) than +C EWT(i) = RTOL*ABS(Y(i)) + ATOL if ITOL = 1, or +C EWT(i) = RTOL*ABS(Y(i)) + ATOL(i) if ITOL = 2. +C Thus the local error test passes if, in each component, +C either the absolute error is less than ATOL (or ATOL(i)), +C or the relative error is less than RTOL. +C Use RTOL = 0.0 for pure absolute error control, and +C use ATOL = 0.0 (or ATOL(i) = 0.0) for pure relative error +C control. Caution: Actual (global) errors may exceed these +C local tolerances, so choose them conservatively. +C ITASK = 1 for normal computation of output values of y at t = TOUT. +C ISTATE = integer flag (input and output). Set ISTATE = 1 if the +C initial dy/dt is supplied, and 0 otherwise. +C IOPT = 0 to indicate no optional inputs used. +C RWORK = real work array of length at least: +C 20 + (2 + 1./LENRAT)*NNZ + (11 + 9./LENRAT)*NEQ +C where: +C NNZ = the number of nonzero elements in the sparse +C iteration matrix P = A - con*dr/dy (con = scalar) +C (If NNZ is unknown, use an estimate of it.) +C LENRAT = the real to integer wordlength ratio (usually 1 in +C single precision and 2 in double precision). +C In any case, the required size of RWORK cannot generally +C be predicted in advance for any value of MF, and the +C value above is a rough estimate of a crude lower bound. +C Some experimentation with this size may be necessary. +C (When known, the correct required length is an optional +C output, available in IWORK(17).) +C LRW = declared length of RWORK (in user's dimension). +C IWORK = integer work array of length at least 30. +C LIW = declared length of IWORK (in user's dimension). +C MF = method flag. Standard values are: +C 121 for a user-supplied sparse Jacobian. +C 222 for an internally generated sparse Jacobian. +C For other choices of MF, see the paragraph on MF in +C the full description below. +C Note that the main program must declare arrays Y, YDOTI, RWORK, IWORK, +C and possibly ATOL. +C +C G. The output from the first call, or any call, is: +C Y = array of computed values of y(t) vector. +C T = corresponding value of independent variable (normally TOUT). +C ISTATE = 2 if DLSODIS was successful, negative otherwise. +C -1 means excess work done on this call (check all inputs). +C -2 means excess accuracy requested (tolerances too small). +C -3 means illegal input detected (see printed message). +C -4 means repeated error test failures (check all inputs). +C -5 means repeated convergence failures (perhaps bad Jacobian +C supplied or wrong choice of tolerances). +C -6 means error weight became zero during problem. (Solution +C component i vanished, and ATOL or ATOL(i) = 0.) +C -7 cannot occur in casual use. +C -8 means DLSODIS was unable to compute the initial dy/dt. +C in casual use, this means A(t,y) is initially singular. +C Supply YDOTI and use ISTATE = 1 on the first call. +C -9 means a fatal error return flag came from sparse solver +C CDRV by way of DPRJIS or DSOLSS. Should never happen. +C +C A return with ISTATE = -1, -4, or -5, may result from using +C an inappropriate sparsity structure, one that is quite +C different from the initial structure. Consider calling +C DLSODIS again with ISTATE = 3 to force the structure to be +C reevaluated. See the full description of ISTATE below. +C +C If DLSODIS returns ISTATE = -1, -4 or -5, then the output of +C DLSODIS also includes YDOTI = array containing residual vector +C r = g - A * dy/dt evaluated at the current t, y, and dy/dt. +C +C H. To continue the integration after a successful return, simply +C reset TOUT and call DLSODIS again. No other parameters need be reset. +C +C----------------------------------------------------------------------- +C Example Problem. +C +C The following is an example problem, with the coding needed +C for its solution by DLSODIS. The problem comes from the partial +C differential equation (the Burgers equation) +C du/dt = - u * du/dx + eta * d**2 u/dx**2, eta = .05, +C on -1 .le. x .le. 1. The boundary conditions are periodic: +C u(-1,t) = u(1,t) and du/dx(-1,t) = du/dx(1,t) +C The initial profile is a square wave, +C u = 1 in ABS(x) .lt. .5, u = .5 at ABS(x) = .5, u = 0 elsewhere. +C The PDE is discretized in x by a simplified Galerkin method, +C using piecewise linear basis functions, on a grid of 40 intervals. +C The result is a system A * dy/dt = g(y), of size NEQ = 40, +C where y(i) is the approximation to u at x = x(i), with +C x(i) = -1 + (i-1)*delx, delx = 2/NEQ = .05. +C The individual equations in the system are (in order): +C (1/6)dy(NEQ)/dt+(4/6)dy(1)/dt+(1/6)dy(2)/dt +C = r4d*(y(NEQ)**2-y(2)**2)+eodsq*(y(2)-2*y(1)+y(NEQ)) +C for i = 2,3,...,nm1, +C (1/6)dy(i-1)/dt+(4/6)dy(i)/dt+(1/6)dy(i+1)/dt +C = r4d*(y(i-1)**2-y(i+1)**2)+eodsq*(y(i+1)-2*y(i)+y(i-1)) +C and finally +C (1/6)dy(nm1)/dt+(4/6)dy(NEQ)/dt+(1/6)dy(1)/dt +C = r4d*(y(nm1)**2-y(1)**2)+eodsq*(y(1)-2*y(NEQ)+y(nm1)) +C where r4d = 1/(4*delx), eodsq = eta/delx**2 and nm1 = NEQ-1. +C The following coding solves the problem with MF = 121, with output +C of solution statistics at t = .1, .2, .3, and .4, and of the +C solution vector at t = .4. Optional outputs (run statistics) are +C also printed. +C +C EXTERNAL RESID, ADDASP, JACSP +C DOUBLE PRECISION ATOL, RTOL, RW, T, TOUT, Y, YDOTI, R4D, EODSQ, DELX +C DIMENSION Y(40), YDOTI(40), RW(1409), IW(30) +C COMMON /TEST1/ R4D, EODSQ, NM1 +C DATA ITOL/1/, RTOL/1.0D-3/, ATOL/1.0D-3/, ITASK/1/, IOPT/0/ +C DATA NEQ/40/, LRW/1409/, LIW/30/, MF/121/ +C +C DELX = 2.0/NEQ +C R4D = 0.25/DELX +C EODSQ = 0.05/DELX**2 +C NM1 = NEQ - 1 +C DO 10 I = 1,NEQ +C 10 Y(I) = 0.0 +C Y(11) = 0.5 +C DO 15 I = 12,30 +C 15 Y(I) = 1.0 +C Y(31) = 0.5 +C T = 0.0 +C TOUT = 0.1 +C ISTATE = 0 +C DO 30 IO = 1,4 +C CALL DLSODIS (RESID, ADDASP, JACSP, NEQ, Y, YDOTI, T, TOUT, +C 1 ITOL, RTOL, ATOL, ITASK, ISTATE, IOPT, RW, LRW, IW, LIW, MF) +C WRITE(6,20) T,IW(11),RW(11) +C 20 FORMAT(' At t =',F5.2,' No. steps =',I4, +C 1 ' Last step =',D12.4) +C IF (ISTATE .NE. 2) GO TO 90 +C TOUT = TOUT + 0.1 +C 30 CONTINUE +C WRITE (6,40) (Y(I),I=1,NEQ) +C 40 FORMAT(/' Final solution values..'/8(5D12.4/)) +C WRITE(6,50) IW(17),IW(18),IW(11),IW(12),IW(13) +C NNZLU = IW(25) + IW(26) + NEQ +C WRITE(6,60) IW(19),NNZLU +C 50 FORMAT(/' Required RW size =',I5,' IW size =',I4/ +C 1 ' No. steps =',I4,' No. r-s =',I4,' No. J-s =',i4) +C 60 FORMAT(' No. of nonzeros in P matrix =',I4, +C 1 ' No. of nonzeros in LU =',I4) +C STOP +C 90 WRITE (6,95) ISTATE +C 95 FORMAT(///' Error halt.. ISTATE =',I3) +C STOP +C END +C +C SUBROUTINE GFUN (N, T, Y, G) +C DOUBLE PRECISION T, Y, G, R4D, EODSQ +C DIMENSION G(N), Y(N) +C COMMON /TEST1/ R4D, EODSQ, NM1 +C G(1) = R4D*(Y(N)**2-Y(2)**2) + EODSQ*(Y(2)-2.0*Y(1)+Y(N)) +C DO 10 I = 2,NM1 +C G(I) = R4D*(Y(I-1)**2 - Y(I+1)**2) +C 1 + EODSQ*(Y(I+1) - 2.0*Y(I) + Y(I-1)) +C 10 CONTINUE +C G(N) = R4D*(Y(NM1)**2-Y(1)**2) + EODSQ*(Y(1)-2.0*Y(N)+Y(NM1)) +C RETURN +C END +C +C SUBROUTINE RESID (N, T, Y, S, R, IRES) +C DOUBLE PRECISION T, Y, S, R, R4D, EODSQ +C DIMENSION Y(N), S(N), R(N) +C COMMON /TEST1/ R4D, EODSQ, NM1 +C CALL GFUN (N, T, Y, R) +C R(1) = R(1) - (S(N) + 4.0*S(1) + S(2))/6.0 +C DO 10 I = 2,NM1 +C 10 R(I) = R(I) - (S(I-1) + 4.0*S(I) + S(I+1))/6.0 +C R(N) = R(N) - (S(NM1) + 4.0*S(N) + S(1))/6.0 +C RETURN +C END +C +C SUBROUTINE ADDASP (N, T, Y, J, IP, JP, P) +C DOUBLE PRECISION T, Y, P +C DIMENSION Y(N), IP(*), JP(*), P(N) +C JM1 = J - 1 +C JP1 = J + 1 +C IF (J .EQ. N) JP1 = 1 +C IF (J .EQ. 1) JM1 = N +C P(J) = P(J) + (2.0/3.0) +C P(JP1) = P(JP1) + (1.0/6.0) +C P(JM1) = P(JM1) + (1.0/6.0) +C RETURN +C END +C +C SUBROUTINE JACSP (N, T, Y, S, J, IP, JP, PDJ) +C DOUBLE PRECISION T, Y, S, PDJ, R4D, EODSQ +C DIMENSION Y(N), S(N), IP(*), JP(*), PDJ(N) +C COMMON /TEST1/ R4D, EODSQ, NM1 +C JM1 = J - 1 +C JP1 = J + 1 +C IF (J .EQ. 1) JM1 = N +C IF (J .EQ. N) JP1 = 1 +C PDJ(JM1) = -2.0*R4D*Y(J) + EODSQ +C PDJ(J) = -2.0*EODSQ +C PDJ(JP1) = 2.0*R4D*Y(J) + EODSQ +C RETURN +C END +C +C The output of this program (on a CDC-7600 in single precision) +C is as follows: +C +C At t = 0.10 No. steps = 15 Last step = 1.6863e-02 +C At t = 0.20 No. steps = 19 Last step = 2.4101e-02 +C At t = 0.30 No. steps = 22 Last step = 4.3143e-02 +C At t = 0.40 No. steps = 24 Last step = 5.7819e-02 +C +C Final solution values.. +C 1.8371e-02 1.3578e-02 1.5864e-02 2.3805e-02 3.7245e-02 +C 5.6630e-02 8.2538e-02 1.1538e-01 1.5522e-01 2.0172e-01 +C 2.5414e-01 3.1150e-01 3.7259e-01 4.3608e-01 5.0060e-01 +C 5.6482e-01 6.2751e-01 6.8758e-01 7.4415e-01 7.9646e-01 +C 8.4363e-01 8.8462e-01 9.1853e-01 9.4500e-01 9.6433e-01 +C 9.7730e-01 9.8464e-01 9.8645e-01 9.8138e-01 9.6584e-01 +C 9.3336e-01 8.7497e-01 7.8213e-01 6.5315e-01 4.9997e-01 +C 3.4672e-01 2.1758e-01 1.2461e-01 6.6208e-02 3.3784e-02 +C +C Required RW size = 1409 IW size = 30 +C No. steps = 24 No. r-s = 33 No. J-s = 8 +C No. of nonzeros in P matrix = 120 No. of nonzeros in LU = 194 +C +C----------------------------------------------------------------------- +C Full Description of User Interface to DLSODIS. +C +C The user interface to DLSODIS consists of the following parts. +C +C 1. The call sequence to Subroutine DLSODIS, which is a driver +C routine for the solver. This includes descriptions of both +C the call sequence arguments and of user-supplied routines. +C Following these descriptions is a description of +C optional inputs available through the call sequence, and then +C a description of optional outputs (in the work arrays). +C +C 2. Descriptions of other routines in the DLSODIS package that may be +C (optionally) called by the user. These provide the ability to +C alter error message handling, save and restore the internal +C Common, and obtain specified derivatives of the solution y(t). +C +C 3. Descriptions of Common blocks to be declared in overlay +C or similar environments, or to be saved when doing an interrupt +C of the problem and continued solution later. +C +C 4. Description of two routines in the DLSODIS package, either of +C which the user may replace with his/her own version, if desired. +C These relate to the measurement of errors. +C +C----------------------------------------------------------------------- +C Part 1. Call Sequence. +C +C The call sequence parameters used for input only are +C RES, ADDA, JAC, NEQ, TOUT, ITOL, RTOL, ATOL, ITASK, +C IOPT, LRW, LIW, MF, +C and those used for both input and output are +C Y, T, ISTATE, YDOTI. +C The work arrays RWORK and IWORK are also used for conditional and +C optional inputs and optional outputs. (The term output here refers +C to the return from Subroutine DLSODIS to the user's calling program.) +C +C The legality of input parameters will be thoroughly checked on the +C initial call for the problem, but not checked thereafter unless a +C change in input parameters is flagged by ISTATE = 3 on input. +C +C The descriptions of the call arguments are as follows. +C +C RES = the name of the user-supplied subroutine which supplies +C the residual vector for the ODE system, defined by +C r = g(t,y) - A(t,y) * s +C as a function of the scalar t and the vectors +C s and y (s approximates dy/dt). This subroutine +C is to have the form +C SUBROUTINE RES (NEQ, T, Y, S, R, IRES) +C DOUBLE PRECISION T, Y(*), S(*), R(*) +C where NEQ, T, Y, S, and IRES are input, and R and +C IRES are output. Y, S, and R are arrays of length NEQ. +C On input, IRES indicates how DLSODIS will use the +C returned array R, as follows: +C IRES = 1 means that DLSODIS needs the full residual, +C r = g - A*s, exactly. +C IRES = -1 means that DLSODIS is using R only to compute +C the Jacobian dr/dy by difference quotients. +C The RES routine can ignore IRES, or it can omit some terms +C if IRES = -1. If A does not depend on y, then RES can +C just return R = g when IRES = -1. If g - A*s contains other +C additive terms that are independent of y, these can also be +C dropped, if done consistently, when IRES = -1. +C The subroutine should set the flag IRES if it +C encounters a halt condition or illegal input. +C Otherwise, it should not reset IRES. On output, +C IRES = 1 or -1 represents a normal return, and +C DLSODIS continues integrating the ODE. Leave IRES +C unchanged from its input value. +C IRES = 2 tells DLSODIS to immediately return control +C to the calling program, with ISTATE = 3. This lets +C the calling program change parameters of the problem +C if necessary. +C IRES = 3 represents an error condition (for example, an +C illegal value of y). DLSODIS tries to integrate the system +C without getting IRES = 3 from RES. If it cannot, DLSODIS +C returns with ISTATE = -7 or -1. +C On a return with ISTATE = 3, -1, or -7, the values +C of T and Y returned correspond to the last point reached +C successfully without getting the flag IRES = 2 or 3. +C The flag values IRES = 2 and 3 should not be used to +C handle switches or root-stop conditions. This is better +C done by calling DLSODIS in a one-step mode and checking the +C stopping function for a sign change at each step. +C If quantities computed in the RES routine are needed +C externally to DLSODIS, an extra call to RES should be made +C for this purpose, for consistent and accurate results. +C To get the current dy/dt for the S argument, use DINTDY. +C RES must be declared External in the calling +C program. See note below for more about RES. +C +C ADDA = the name of the user-supplied subroutine which adds the +C matrix A = A(t,y) to another matrix stored in sparse form. +C This subroutine is to have the form +C SUBROUTINE ADDA (NEQ, T, Y, J, IAN, JAN, P) +C DOUBLE PRECISION T, Y(*), P(*) +C INTEGER IAN(*), JAN(*) +C where NEQ, T, Y, J, IAN, JAN, and P are input. This routine +C should add the J-th column of matrix A to the array P, of +C length NEQ. Thus a(i,J) is to be added to P(i) for all +C relevant values of i. Here T and Y have the same meaning as +C in Subroutine RES, and J is a column index (1 to NEQ). +C IAN and JAN are undefined in calls to ADDA for structure +C determination (MOSS .ne. 0). Otherwise, IAN and JAN are +C structure descriptors, as defined under optional outputs +C below, and so can be used to determine the relevant row +C indices i, if desired. +C Calls to ADDA are made with J = 1,...,NEQ, in that +C order. ADDA must not alter its input arguments. +C ADDA must be declared External in the calling program. +C See note below for more information about ADDA. +C +C JAC = the name of the user-supplied subroutine which supplies +C the Jacobian matrix, dr/dy, where r = g - A*s. JAC is +C required if MITER = 1, or MOSS = 1 or 3. Otherwise a dummy +C name can be passed. This subroutine is to have the form +C SUBROUTINE JAC (NEQ, T, Y, S, J, IAN, JAN, PDJ) +C DOUBLE PRECISION T, Y(*), S(*), PDJ(*) +C INTEGER IAN(*), JAN(*) +C where NEQ, T, Y, S, J, IAN, and JAN are input. The +C array PDJ, of length NEQ, is to be loaded with column J +C of the Jacobian on output. Thus dr(i)/dy(J) is to be +C loaded into PDJ(i) for all relevant values of i. +C Here T, Y, and S have the same meaning as in Subroutine RES, +C and J is a column index (1 to NEQ). IAN and JAN +C are undefined in calls to JAC for structure determination +C (MOSS .ne. 0). Otherwise, IAN and JAN are structure +C descriptors, as defined under optional outputs below, and +C so can be used to determine the relevant row indices i, if +C desired. +C JAC need not provide dr/dy exactly. A crude +C approximation (possibly with greater sparsity) will do. +C In any case, PDJ is preset to zero by the solver, +C so that only the nonzero elements need be loaded by JAC. +C Calls to JAC are made with J = 1,...,NEQ, in that order, and +C each such set of calls is preceded by a call to RES with the +C same arguments NEQ, T, Y, S, and IRES. Thus to gain some +C efficiency intermediate quantities shared by both calculations +C may be saved in a user Common block by RES and not recomputed +C by JAC, if desired. JAC must not alter its input arguments. +C JAC must be declared External in the calling program. +C See note below for more about JAC. +C +C Note on RES, ADDA, and JAC: +C These subroutines may access user-defined quantities in +C NEQ(2),... and/or in Y(NEQ(1)+1),... if NEQ is an array +C (dimensioned in the subroutines) and/or Y has length +C exceeding NEQ(1). However, these subroutines should not +C alter NEQ(1), Y(1),...,Y(NEQ) or any other input variables. +C See the descriptions of NEQ and Y below. +C +C NEQ = the size of the system (number of first order ordinary +C differential equations or scalar algebraic equations). +C Used only for input. +C NEQ may be decreased, but not increased, during the problem. +C If NEQ is decreased (with ISTATE = 3 on input), the +C remaining components of Y should be left undisturbed, if +C these are to be accessed in RES, ADDA, or JAC. +C +C Normally, NEQ is a scalar, and it is generally referred to +C as a scalar in this user interface description. However, +C NEQ may be an array, with NEQ(1) set to the system size. +C (The DLSODIS package accesses only NEQ(1).) In either case, +C this parameter is passed as the NEQ argument in all calls +C to RES, ADDA, and JAC. Hence, if it is an array, +C locations NEQ(2),... may be used to store other integer data +C and pass it to RES, ADDA, or JAC. Each such subroutine +C must include NEQ in a Dimension statement in that case. +C +C Y = a real array for the vector of dependent variables, of +C length NEQ or more. Used for both input and output on the +C first call (ISTATE = 0 or 1), and only for output on other +C calls. On the first call, Y must contain the vector of +C initial values. On output, Y contains the computed solution +C vector, evaluated at T. If desired, the Y array may be used +C for other purposes between calls to the solver. +C +C This array is passed as the Y argument in all calls to RES, +C ADDA, and JAC. Hence its length may exceed NEQ, +C and locations Y(NEQ+1),... may be used to store other real +C data and pass it to RES, ADDA, or JAC. (The DLSODIS +C package accesses only Y(1),...,Y(NEQ). ) +C +C YDOTI = a real array for the initial value of the vector +C dy/dt and for work space, of dimension at least NEQ. +C +C On input: +C If ISTATE = 0 then DLSODIS will compute the initial value +C of dy/dt, if A is nonsingular. Thus YDOTI will +C serve only as work space and may have any value. +C If ISTATE = 1 then YDOTI must contain the initial value +C of dy/dt. +C If ISTATE = 2 or 3 (continuation calls) then YDOTI +C may have any value. +C Note: If the initial value of A is singular, then +C DLSODIS cannot compute the initial value of dy/dt, so +C it must be provided in YDOTI, with ISTATE = 1. +C +C On output, when DLSODIS terminates abnormally with ISTATE = +C -1, -4, or -5, YDOTI will contain the residual +C r = g(t,y) - A(t,y)*(dy/dt). If r is large, t is near +C its initial value, and YDOTI is supplied with ISTATE = 1, +C there may have been an incorrect input value of +C YDOTI = dy/dt, or the problem (as given to DLSODIS) +C may not have a solution. +C +C If desired, the YDOTI array may be used for other +C purposes between calls to the solver. +C +C T = the independent variable. On input, T is used only on the +C first call, as the initial point of the integration. +C On output, after each call, T is the value at which a +C computed solution y is evaluated (usually the same as TOUT). +C On an error return, T is the farthest point reached. +C +C TOUT = the next value of t at which a computed solution is desired. +C Used only for input. +C +C When starting the problem (ISTATE = 0 or 1), TOUT may be +C equal to T for one call, then should .ne. T for the next +C call. For the initial T, an input value of TOUT .ne. T is +C used in order to determine the direction of the integration +C (i.e. the algebraic sign of the step sizes) and the rough +C scale of the problem. Integration in either direction +C (forward or backward in t) is permitted. +C +C If ITASK = 2 or 5 (one-step modes), TOUT is ignored after +C the first call (i.e. the first call with TOUT .ne. T). +C Otherwise, TOUT is required on every call. +C +C If ITASK = 1, 3, or 4, the values of TOUT need not be +C monotone, but a value of TOUT which backs up is limited +C to the current internal T interval, whose endpoints are +C TCUR - HU and TCUR (see optional outputs, below, for +C TCUR and HU). +C +C ITOL = an indicator for the type of error control. See +C description below under ATOL. Used only for input. +C +C RTOL = a relative error tolerance parameter, either a scalar or +C an array of length NEQ. See description below under ATOL. +C Input only. +C +C ATOL = an absolute error tolerance parameter, either a scalar or +C an array of length NEQ. Input only. +C +C The input parameters ITOL, RTOL, and ATOL determine +C the error control performed by the solver. The solver will +C control the vector E = (E(i)) of estimated local errors +C in y, according to an inequality of the form +C RMS-norm of ( E(i)/EWT(i) ) .le. 1, +C where EWT(i) = RTOL(i)*ABS(Y(i)) + ATOL(i), +C and the RMS-norm (root-mean-square norm) here is +C RMS-norm(v) = SQRT(sum v(i)**2 / NEQ). Here EWT = (EWT(i)) +C is a vector of weights which must always be positive, and +C the values of RTOL and ATOL should all be non-negative. +C The following table gives the types (scalar/array) of +C RTOL and ATOL, and the corresponding form of EWT(i). +C +C ITOL RTOL ATOL EWT(i) +C 1 scalar scalar RTOL*ABS(Y(i)) + ATOL +C 2 scalar array RTOL*ABS(Y(i)) + ATOL(i) +C 3 array scalar RTOL(i)*ABS(Y(i)) + ATOL +C 4 array scalar RTOL(i)*ABS(Y(i)) + ATOL(i) +C +C When either of these parameters is a scalar, it need not +C be dimensioned in the user's calling program. +C +C If none of the above choices (with ITOL, RTOL, and ATOL +C fixed throughout the problem) is suitable, more general +C error controls can be obtained by substituting +C user-supplied routines for the setting of EWT and/or for +C the norm calculation. See Part 4 below. +C +C If global errors are to be estimated by making a repeated +C run on the same problem with smaller tolerances, then all +C components of RTOL and ATOL (i.e. of EWT) should be scaled +C down uniformly. +C +C ITASK = an index specifying the task to be performed. +C Input only. ITASK has the following values and meanings. +C 1 means normal computation of output values of y(t) at +C t = TOUT (by overshooting and interpolating). +C 2 means take one step only and return. +C 3 means stop at the first internal mesh point at or +C beyond t = TOUT and return. +C 4 means normal computation of output values of y(t) at +C t = TOUT but without overshooting t = TCRIT. +C TCRIT must be input as RWORK(1). TCRIT may be equal to +C or beyond TOUT, but not behind it in the direction of +C integration. This option is useful if the problem +C has a singularity at or beyond t = TCRIT. +C 5 means take one step, without passing TCRIT, and return. +C TCRIT must be input as RWORK(1). +C +C Note: If ITASK = 4 or 5 and the solver reaches TCRIT +C (within roundoff), it will return T = TCRIT (exactly) to +C indicate this (unless ITASK = 4 and TOUT comes before TCRIT, +C in which case answers at t = TOUT are returned first). +C +C ISTATE = an index used for input and output to specify the +C state of the calculation. +C +C On input, the values of ISTATE are as follows. +C 0 means this is the first call for the problem, and +C DLSODIS is to compute the initial value of dy/dt +C (while doing other initializations). See note below. +C 1 means this is the first call for the problem, and +C the initial value of dy/dt has been supplied in +C YDOTI (DLSODIS will do other initializations). +C See note below. +C 2 means this is not the first call, and the calculation +C is to continue normally, with no change in any input +C parameters except possibly TOUT and ITASK. +C (If ITOL, RTOL, and/or ATOL are changed between calls +C with ISTATE = 2, the new values will be used but not +C tested for legality.) +C 3 means this is not the first call, and the +C calculation is to continue normally, but with +C a change in input parameters other than +C TOUT and ITASK. Changes are allowed in +C NEQ, ITOL, RTOL, ATOL, IOPT, LRW, LIW, MF, +C the conditional inputs IA, JA, IC, and JC, +C and any of the optional inputs except H0. +C A call with ISTATE = 3 will cause the sparsity +C structure of the problem to be recomputed. +C (Structure information is reread from IA and JA if +C MOSS = 0, 3, or 4 and from IC and JC if MOSS = 0). +C Note: A preliminary call with TOUT = T is not counted +C as a first call here, as no initialization or checking of +C input is done. (Such a call is sometimes useful for the +C purpose of outputting the initial conditions.) +C Thus the first call for which TOUT .ne. T requires +C ISTATE = 0 or 1 on input. +C +C On output, ISTATE has the following values and meanings. +C 0 or 1 means nothing was done; TOUT = T and +C ISTATE = 0 or 1 on input. +C 2 means that the integration was performed successfully. +C 3 means that the user-supplied Subroutine RES signalled +C DLSODIS to halt the integration and return (IRES = 2). +C Integration as far as T was achieved with no occurrence +C of IRES = 2, but this flag was set on attempting the +C next step. +C -1 means an excessive amount of work (more than MXSTEP +C steps) was done on this call, before completing the +C requested task, but the integration was otherwise +C successful as far as T. (MXSTEP is an optional input +C and is normally 500.) To continue, the user may +C simply reset ISTATE to a value .gt. 1 and call again +C (the excess work step counter will be reset to 0). +C In addition, the user may increase MXSTEP to avoid +C this error return (see below on optional inputs). +C -2 means too much accuracy was requested for the precision +C of the machine being used. This was detected before +C completing the requested task, but the integration +C was successful as far as T. To continue, the tolerance +C parameters must be reset, and ISTATE must be set +C to 3. The optional output TOLSF may be used for this +C purpose. (Note: If this condition is detected before +C taking any steps, then an illegal input return +C (ISTATE = -3) occurs instead.) +C -3 means illegal input was detected, before taking any +C integration steps. See written message for details. +C Note: If the solver detects an infinite loop of calls +C to the solver with illegal input, it will cause +C the run to stop. +C -4 means there were repeated error test failures on +C one attempted step, before completing the requested +C task, but the integration was successful as far as T. +C The problem may have a singularity, or the input +C may be inappropriate. +C -5 means there were repeated convergence test failures on +C one attempted step, before completing the requested +C task, but the integration was successful as far as T. +C This may be caused by an inaccurate Jacobian matrix. +C -6 means EWT(i) became zero for some i during the +C integration. Pure relative error control (ATOL(i) = 0.0) +C was requested on a variable which has now vanished. +C the integration was successful as far as T. +C -7 means that the user-supplied Subroutine RES set +C its error flag (IRES = 3) despite repeated tries by +C DLSODIS to avoid that condition. +C -8 means that ISTATE was 0 on input but DLSODIS was unable +C to compute the initial value of dy/dt. See the +C printed message for details. +C -9 means a fatal error return flag came from the sparse +C solver CDRV by way of DPRJIS or DSOLSS (numerical +C factorization or backsolve). This should never happen. +C The integration was successful as far as T. +C +C Note: An error return with ISTATE = -1, -4, or -5 +C may mean that the sparsity structure of the +C problem has changed significantly since it was last +C determined (or input). In that case, one can attempt to +C complete the integration by setting ISTATE = 3 on the next +C call, so that a new structure determination is done. +C +C Note: Since the normal output value of ISTATE is 2, +C it does not need to be reset for normal continuation. +C similarly, ISTATE (= 3) need not be reset if RES told +C DLSODIS to return because the calling program must change +C the parameters of the problem. +C Also, since a negative input value of ISTATE will be +C regarded as illegal, a negative output value requires the +C user to change it, and possibly other inputs, before +C calling the solver again. +C +C IOPT = an integer flag to specify whether or not any optional +C inputs are being used on this call. Input only. +C The optional inputs are listed separately below. +C IOPT = 0 means no optional inputs are being used. +C Default values will be used in all cases. +C IOPT = 1 means one or more optional inputs are being used. +C +C RWORK = a work array used for a mixture of real (double precision) +C and integer work space. +C The length of RWORK (in real words) must be at least +C 20 + NYH*(MAXORD + 1) + 3*NEQ + LWM where +C NYH = the initial value of NEQ, +C MAXORD = 12 (if METH = 1) or 5 (if METH = 2) (unless a +C smaller value is given as an optional input), +C LWM = 2*NNZ + 2*NEQ + (NNZ+9*NEQ)/LENRAT if MITER = 1, +C LWM = 2*NNZ + 2*NEQ + (NNZ+10*NEQ)/LENRAT if MITER = 2. +C in the above formulas, +C NNZ = number of nonzero elements in the iteration matrix +C P = A - con*J (con is a constant and J is the +C Jacobian matrix dr/dy). +C LENRAT = the real to integer wordlength ratio (usually 1 in +C single precision and 2 in double precision). +C (See the MF description for METH and MITER.) +C Thus if MAXORD has its default value and NEQ is constant, +C the minimum length of RWORK is: +C 20 + 16*NEQ + LWM for MF = 11, 111, 311, 12, 212, 412, +C 20 + 9*NEQ + LWM for MF = 21, 121, 321, 22, 222, 422. +C The above formula for LWM is only a crude lower bound. +C The required length of RWORK cannot be readily predicted +C in general, as it depends on the sparsity structure +C of the problem. Some experimentation may be necessary. +C +C The first 20 words of RWORK are reserved for conditional +C and optional inputs and optional outputs. +C +C The following word in RWORK is a conditional input: +C RWORK(1) = TCRIT = critical value of t which the solver +C is not to overshoot. Required if ITASK is +C 4 or 5, and ignored otherwise. (See ITASK.) +C +C LRW = the length of the array RWORK, as declared by the user. +C (This will be checked by the solver.) +C +C IWORK = an integer work array. The length of IWORK must be at least +C 32 + 2*NEQ + NZA + NZC for MOSS = 0, +C 30 for MOSS = 1 or 2, +C 31 + NEQ + NZA for MOSS = 3 or 4. +C (NZA is the number of nonzero elements in matrix A, and +C NZC is the number of nonzero elements in dr/dy.) +C +C In DLSODIS, IWORK is used for conditional and +C optional inputs and optional outputs. +C +C The following two blocks of words in IWORK are conditional +C inputs, required if MOSS = 0, 3, or 4, but not otherwise +C (see the description of MF for MOSS). +C IWORK(30+j) = IA(j) (j=1,...,NEQ+1) +C IWORK(31+NEQ+k) = JA(k) (k=1,...,NZA) +C The two arrays IA and JA describe the sparsity structure +C to be assumed for the matrix A. JA contains the row +C indices where nonzero elements occur, reading in columnwise +C order, and IA contains the starting locations in JA of the +C descriptions of columns 1,...,NEQ, in that order, with +C IA(1) = 1. Thus, for each column index j = 1,...,NEQ, the +C values of the row index i in column j where a nonzero +C element may occur are given by +C i = JA(k), where IA(j) .le. k .lt. IA(j+1). +C If NZA is the total number of nonzero locations assumed, +C then the length of the JA array is NZA, and IA(NEQ+1) must +C be NZA + 1. Duplicate entries are not allowed. +C The following additional blocks of words are required +C if MOSS = 0, but not otherwise. If LC = 31 + NEQ + NZA, then +C IWORK(LC+j) = IC(j) (j=1,...,NEQ+1), and +C IWORK(LC+NEQ+1+k) = JC(k) (k=1,...,NZC) +C The two arrays IC and JC describe the sparsity +C structure to be assumed for the Jacobian matrix dr/dy. +C They are used in the same manner as the above IA and JA +C arrays. If NZC is the number of nonzero locations +C assumed, then the length of the JC array is NZC, and +C IC(NEQ+1) must be NZC + 1. Duplicate entries are not +C allowed. +C +C LIW = the length of the array IWORK, as declared by the user. +C (This will be checked by the solver.) +C +C Note: The work arrays must not be altered between calls to DLSODIS +C for the same problem, except possibly for the conditional and +C optional inputs, and except for the last 3*NEQ words of RWORK. +C The latter space is used for internal scratch space, and so is +C available for use by the user outside DLSODIS between calls, if +C desired (but not for use by RES, ADDA, or JAC). +C +C MF = the method flag. Used only for input. +C MF has three decimal digits-- MOSS, METH, and MITER. +C For standard options: +C MF = 100*MOSS + 10*METH + MITER. +C MOSS indicates the method to be used to obtain the sparsity +C structure of the Jacobian matrix: +C MOSS = 0 means the user has supplied IA, JA, IC, and JC +C (see descriptions under IWORK above). +C MOSS = 1 means the user has supplied JAC (see below) and +C the structure will be obtained from NEQ initial +C calls to JAC and NEQ initial calls to ADDA. +C MOSS = 2 means the structure will be obtained from NEQ+1 +C initial calls to RES and NEQ initial calls to ADDA +C MOSS = 3 like MOSS = 1, except user has supplied IA and JA. +C MOSS = 4 like MOSS = 2, except user has supplied IA and JA. +C METH indicates the basic linear multistep method: +C METH = 1 means the implicit Adams method. +C METH = 2 means the method based on Backward +C Differentiation Formulas (BDFs). +C The BDF method is strongly preferred for stiff problems, +C while the Adams method is preferred when the problem is +C not stiff. If the matrix A(t,y) is nonsingular, +C stiffness here can be taken to mean that of the explicit +C ODE system dy/dt = A-inverse * g. If A is singular, +C the concept of stiffness is not well defined. +C If you do not know whether the problem is stiff, we +C recommend using METH = 2. If it is stiff, the advantage +C of METH = 2 over METH = 1 will be great, while if it is +C not stiff, the advantage of METH = 1 will be slight. +C If maximum efficiency is important, some experimentation +C with METH may be necessary. +C MITER indicates the corrector iteration method: +C MITER = 1 means chord iteration with a user-supplied +C sparse Jacobian, given by Subroutine JAC. +C MITER = 2 means chord iteration with an internally +C generated (difference quotient) sparse +C Jacobian (using NGP extra calls to RES per +C dr/dy value, where NGP is an optional +C output described below.) +C If MITER = 1 or MOSS = 1 or 3 the user must supply a +C Subroutine JAC (the name is arbitrary) as described above +C under JAC. Otherwise, a dummy argument can be used. +C +C The standard choices for MF are: +C MF = 21 or 22 for a stiff problem with IA/JA and IC/JC +C supplied, +C MF = 121 for a stiff problem with JAC supplied, but not +C IA/JA or IC/JC, +C MF = 222 for a stiff problem with neither IA/JA, IC/JC/, +C nor JAC supplied, +C MF = 321 for a stiff problem with IA/JA and JAC supplied, +C but not IC/JC, +C MF = 422 for a stiff problem with IA/JA supplied, but not +C IC/JC or JAC. +C +C The sparseness structure can be changed during the problem +C by making a call to DLSODIS with ISTATE = 3. +C----------------------------------------------------------------------- +C Optional Inputs. +C +C The following is a list of the optional inputs provided for in the +C call sequence. (See also Part 2.) For each such input variable, +C this table lists its name as used in this documentation, its +C location in the call sequence, its meaning, and the default value. +C The use of any of these inputs requires IOPT = 1, and in that +C case all of these inputs are examined. A value of zero for any +C of these optional inputs will cause the default value to be used. +C Thus to use a subset of the optional inputs, simply preload +C locations 5 to 10 in RWORK and IWORK to 0.0 and 0 respectively, and +C then set those of interest to nonzero values. +C +C Name Location Meaning and Default Value +C +C H0 RWORK(5) the step size to be attempted on the first step. +C The default value is determined by the solver. +C +C HMAX RWORK(6) the maximum absolute step size allowed. +C The default value is infinite. +C +C HMIN RWORK(7) the minimum absolute step size allowed. +C The default value is 0. (This lower bound is not +C enforced on the final step before reaching TCRIT +C when ITASK = 4 or 5.) +C +C MAXORD IWORK(5) the maximum order to be allowed. The default +C value is 12 if METH = 1, and 5 if METH = 2. +C If MAXORD exceeds the default value, it will +C be reduced to the default value. +C If MAXORD is changed during the problem, it may +C cause the current order to be reduced. +C +C MXSTEP IWORK(6) maximum number of (internally defined) steps +C allowed during one call to the solver. +C The default value is 500. +C +C MXHNIL IWORK(7) maximum number of messages printed (per problem) +C warning that T + H = T on a step (H = step size). +C This must be positive to result in a non-default +C value. The default value is 10. +C----------------------------------------------------------------------- +C Optional Outputs. +C +C As optional additional output from DLSODIS, the variables listed +C below are quantities related to the performance of DLSODIS +C which are available to the user. These are communicated by way of +C the work arrays, but also have internal mnemonic names as shown. +C Except where stated otherwise, all of these outputs are defined +C on any successful return from DLSODIS, and on any return with +C ISTATE = -1, -2, -4, -5, -6, or -7. On a return with -3 (illegal +C input) or -8, they will be unchanged from their existing values +C (if any), except possibly for TOLSF, LENRW, and LENIW. +C On any error return, outputs relevant to the error will be defined, +C as noted below. +C +C Name Location Meaning +C +C HU RWORK(11) the step size in t last used (successfully). +C +C HCUR RWORK(12) the step size to be attempted on the next step. +C +C TCUR RWORK(13) the current value of the independent variable +C which the solver has actually reached, i.e. the +C current internal mesh point in t. On output, TCUR +C will always be at least as far as the argument +C T, but may be farther (if interpolation was done). +C +C TOLSF RWORK(14) a tolerance scale factor, greater than 1.0, +C computed when a request for too much accuracy was +C detected (ISTATE = -3 if detected at the start of +C the problem, ISTATE = -2 otherwise). If ITOL is +C left unaltered but RTOL and ATOL are uniformly +C scaled up by a factor of TOLSF for the next call, +C then the solver is deemed likely to succeed. +C (The user may also ignore TOLSF and alter the +C tolerance parameters in any other way appropriate.) +C +C NST IWORK(11) the number of steps taken for the problem so far. +C +C NRE IWORK(12) the number of residual evaluations (RES calls) +C for the problem so far, excluding those for +C structure determination (MOSS = 2 or 4). +C +C NJE IWORK(13) the number of Jacobian evaluations (each involving +C an evaluation of A and dr/dy) for the problem so +C far, excluding those for structure determination +C (MOSS = 1 or 3). This equals the number of calls +C to ADDA and (if MITER = 1) JAC. +C +C NQU IWORK(14) the method order last used (successfully). +C +C NQCUR IWORK(15) the order to be attempted on the next step. +C +C IMXER IWORK(16) the index of the component of largest magnitude in +C the weighted local error vector ( E(i)/EWT(i) ), +C on an error return with ISTATE = -4 or -5. +C +C LENRW IWORK(17) the length of RWORK actually required. +C This is defined on normal returns and on an illegal +C input return for insufficient storage. +C +C LENIW IWORK(18) the length of IWORK actually required. +C This is defined on normal returns and on an illegal +C input return for insufficient storage. +C +C NNZ IWORK(19) the number of nonzero elements in the iteration +C matrix P = A - con*J (con is a constant and +C J is the Jacobian matrix dr/dy). +C +C NGP IWORK(20) the number of groups of column indices, used in +C difference quotient Jacobian aproximations if +C MITER = 2. This is also the number of extra RES +C evaluations needed for each Jacobian evaluation. +C +C NLU IWORK(21) the number of sparse LU decompositions for the +C problem so far. (Excludes the LU decomposition +C necessary when ISTATE = 0.) +C +C LYH IWORK(22) the base address in RWORK of the history array YH, +C described below in this list. +C +C IPIAN IWORK(23) the base address of the structure descriptor array +C IAN, described below in this list. +C +C IPJAN IWORK(24) the base address of the structure descriptor array +C JAN, described below in this list. +C +C NZL IWORK(25) the number of nonzero elements in the strict lower +C triangle of the LU factorization used in the chord +C iteration. +C +C NZU IWORK(26) the number of nonzero elements in the strict upper +C triangle of the LU factorization used in the chord +C iteration. The total number of nonzeros in the +C factorization is therefore NZL + NZU + NEQ. +C +C The following four arrays are segments of the RWORK array which +C may also be of interest to the user as optional outputs. +C For each array, the table below gives its internal name, +C its base address, and its description. +C For YH and ACOR, the base addresses are in RWORK (a real array). +C The integer arrays IAN and JAN are to be obtained by declaring an +C integer array IWK and identifying IWK(1) with RWORK(21), using either +C an equivalence statement or a subroutine call. Then the base +C addresses IPIAN (of IAN) and IPJAN (of JAN) in IWK are to be obtained +C as optional outputs IWORK(23) and IWORK(24), respectively. +C Thus IAN(1) is IWK(ipian), etc. +C +C Name Base Address Description +C +C IAN IPIAN (in IWK) structure descriptor array of size NEQ + 1. +C JAN IPJAN (in IWK) structure descriptor array of size NNZ. +C (see above) IAN and JAN together describe the sparsity +C structure of the iteration matrix +C P = A - con*J, as used by DLSODIS. +C JAN contains the row indices of the nonzero +C locations, reading in columnwise order, and +C IAN contains the starting locations in JAN of +C the descriptions of columns 1,...,NEQ, in +C that order, with IAN(1) = 1. Thus for each +C j = 1,...,NEQ, the row indices i of the +C nonzero locations in column j are +C i = JAN(k), IAN(j) .le. k .lt. IAN(j+1). +C Note that IAN(NEQ+1) = NNZ + 1. +C YH LYH the Nordsieck history array, of size NYH by +C (optional (NQCUR + 1), where NYH is the initial value +C output) of NEQ. For j = 0,1,...,NQCUR, column j+1 +C of YH contains HCUR**j/factorial(j) times +C the j-th derivative of the interpolating +C polynomial currently representing the solution, +C evaluated at t = TCUR. The base address LYH +C is another optional output, listed above. +C +C ACOR LENRW-NEQ+1 array of size NEQ used for the accumulated +C corrections on each step, scaled on output to +C represent the estimated local error in y on the +C last step. This is the vector E in the +C description of the error control. It is defined +C only on a return from DLSODIS with ISTATE = 2. +C +C----------------------------------------------------------------------- +C Part 2. Other Routines Callable. +C +C The following are optional calls which the user may make to +C gain additional capabilities in conjunction with DLSODIS. +C (The routines XSETUN and XSETF are designed to conform to the +C SLATEC error handling package.) +C +C Form of Call Function +C CALL XSETUN(LUN) Set the logical unit number, LUN, for +C output of messages from DLSODIS, if +C The default is not desired. +C The default value of LUN is 6. +C +C CALL XSETF(MFLAG) Set a flag to control the printing of +C messages by DLSODIS. +C MFLAG = 0 means do not print. (Danger: +C This risks losing valuable information.) +C MFLAG = 1 means print (the default). +C +C Either of the above calls may be made at +C any time and will take effect immediately. +C +C CALL DSRCMS(RSAV,ISAV,JOB) saves and restores the contents of +C the internal Common blocks used by +C DLSODIS (see Part 3 below). +C RSAV must be a real array of length 224 +C or more, and ISAV must be an integer +C array of length 71 or more. +C JOB=1 means save Common into RSAV/ISAV. +C JOB=2 means restore Common from RSAV/ISAV. +C DSRCMS is useful if one is +C interrupting a run and restarting +C later, or alternating between two or +C more problems solved with DLSODIS. +C +C CALL DINTDY(,,,,,) Provide derivatives of y, of various +C (see below) orders, at a specified point t, if +C desired. It may be called only after +C a successful return from DLSODIS. +C +C The detailed instructions for using DINTDY are as follows. +C The form of the call is: +C +C LYH = IWORK(22) +C CALL DINTDY (T, K, RWORK(LYH), NYH, DKY, IFLAG) +C +C The input parameters are: +C +C T = value of independent variable where answers are desired +C (normally the same as the T last returned by DLSODIS). +C For valid results, T must lie between TCUR - HU and TCUR. +C (See optional outputs for TCUR and HU.) +C K = integer order of the derivative desired. K must satisfy +C 0 .le. K .le. NQCUR, where NQCUR is the current order +C (see optional outputs). The capability corresponding +C to K = 0, i.e. computing y(t), is already provided +C by DLSODIS directly. Since NQCUR .ge. 1, the first +C derivative dy/dt is always available with DINTDY. +C LYH = the base address of the history array YH, obtained +C as an optional output as shown above. +C NYH = column length of YH, equal to the initial value of NEQ. +C +C The output parameters are: +C +C DKY = a real array of length NEQ containing the computed value +C of the K-th derivative of y(t). +C IFLAG = integer flag, returned as 0 if K and T were legal, +C -1 if K was illegal, and -2 if T was illegal. +C On an error return, a message is also written. +C----------------------------------------------------------------------- +C Part 3. Common Blocks. +C +C If DLSODIS is to be used in an overlay situation, the user +C must declare, in the primary overlay, the variables in: +C (1) the call sequence to DLSODIS, and +C (2) the two internal Common blocks +C /DLS001/ of length 255 (218 double precision words +C followed by 37 integer words), +C /DLSS01/ of length 40 (6 double precision words +C followed by 34 integer words). +C +C If DLSODIS is used on a system in which the contents of internal +C Common blocks are not preserved between calls, the user should +C declare the above Common blocks in the calling program to insure +C that their contents are preserved. +C +C If the solution of a given problem by DLSODIS is to be interrupted +C and then later continued, such as when restarting an interrupted run +C or alternating between two or more problems, the user should save, +C following the return from the last DLSODIS call prior to the +C interruption, the contents of the call sequence variables and the +C internal Common blocks, and later restore these values before the +C next DLSODIS call for that problem. To save and restore the Common +C blocks, use Subroutines DSRCMS (see Part 2 above). +C +C----------------------------------------------------------------------- +C Part 4. Optionally Replaceable Solver Routines. +C +C Below are descriptions of two routines in the DLSODIS package which +C relate to the measurement of errors. Either routine can be +C replaced by a user-supplied version, if desired. However, since such +C a replacement may have a major impact on performance, it should be +C done only when absolutely necessary, and only with great caution. +C (Note: The means by which the package version of a routine is +C superseded by the user's version may be system-dependent.) +C +C (a) DEWSET. +C The following subroutine is called just before each internal +C integration step, and sets the array of error weights, EWT, as +C described under ITOL/RTOL/ATOL above: +C SUBROUTINE DEWSET (NEQ, ITOL, RTOL, ATOL, YCUR, EWT) +C where NEQ, ITOL, RTOL, and ATOL are as in the DLSODIS call sequence, +C YCUR contains the current dependent variable vector, and +C EWT is the array of weights set by DEWSET. +C +C If the user supplies this subroutine, it must return in EWT(i) +C (i = 1,...,NEQ) a positive quantity suitable for comparing errors +C in y(i) to. The EWT array returned by DEWSET is passed to the DVNORM +C routine (see below), and also used by DLSODIS in the computation +C of the optional output IMXER, and the increments for difference +C quotient Jacobians. +C +C In the user-supplied version of DEWSET, it may be desirable to use +C the current values of derivatives of y. Derivatives up to order NQ +C are available from the history array YH, described above under +C optional outputs. In DEWSET, YH is identical to the YCUR array, +C extended to NQ + 1 columns with a column length of NYH and scale +C factors of H**j/factorial(j). On the first call for the problem, +C given by NST = 0, NQ is 1 and H is temporarily set to 1.0. +C NYH is the initial value of NEQ. The quantities NQ, H, and NST +C can be obtained by including in DEWSET the statements: +C DOUBLE PRECISION RLS +C COMMON /DLS001/ RLS(218),ILS(37) +C NQ = ILS(33) +C NST = ILS(34) +C H = RLS(212) +C Thus, for example, the current value of dy/dt can be obtained as +C YCUR(NYH+i)/H (i=1,...,NEQ) (and the division by H is +C unnecessary when NST = 0). +C +C (b) DVNORM. +C The following is a real function routine which computes the weighted +C root-mean-square norm of a vector v: +C D = DVNORM (N, V, W) +C where: +C N = the length of the vector, +C V = real array of length N containing the vector, +C W = real array of length N containing weights, +C D = SQRT( (1/N) * sum(V(i)*W(i))**2 ). +C DVNORM is called with N = NEQ and with W(i) = 1.0/EWT(i), where +C EWT is as set by Subroutine DEWSET. +C +C If the user supplies this function, it should return a non-negative +C value of DVNORM suitable for use in the error control in DLSODIS. +C None of the arguments should be altered by DVNORM. +C For example, a user-supplied DVNORM routine might: +C -substitute a max-norm of (V(i)*w(I)) for the RMS-norm, or +C -ignore some components of V in the norm, with the effect of +C suppressing the error control on those components of y. +C----------------------------------------------------------------------- +C +C***REVISION HISTORY (YYYYMMDD) +C 19820714 DATE WRITTEN +C 19830812 Major update, based on recent LSODI and LSODES revisions: +C Upgraded MDI in ODRV package: operates on M + M-transpose. +C Numerous revisions in use of work arrays; +C use wordlength ratio LENRAT; added IPISP & LRAT to Common; +C added optional outputs IPIAN/IPJAN; +C Added routine CNTNZU; added NZL and NZU to /LSS001/; +C changed ADJLR call logic; added optional outputs NZL & NZU; +C revised counter initializations; revised PREPI stmt. nos.; +C revised difference quotient increment; +C eliminated block /LSI001/, using IERPJ flag; +C revised STODI logic after PJAC return; +C revised tuning of H change and step attempts in STODI; +C corrections to main prologue and comments throughout. +C 19870320 Corrected jump on test of umax in CDRV routine. +C 20010125 Numerous revisions: corrected comments throughout; +C removed TRET from Common; rewrote EWSET with 4 loops; +C fixed t test in INTDY; added Cray directives in STODI; +C in STODI, fixed DELP init. and logic around PJAC call; +C combined routines to save/restore Common; +C passed LEVEL = 0 in error message calls (except run abort). +C 20010425 Major update: convert source lines to upper case; +C added *DECK lines; changed from 1 to * in dummy dimensions; +C changed names R1MACH/D1MACH to RUMACH/DUMACH; +C renamed routines for uniqueness across single/double prec.; +C converted intrinsic names to generic form; +C removed ILLIN and NTREP (data loaded) from Common; +C removed all 'own' variables from Common; +C changed error messages to quoted strings; +C replaced XERRWV/XERRWD with 1993 revised version; +C converted prologues, comments, error messages to mixed case; +C converted arithmetic IF statements to logical IF statements; +C numerous corrections to prologues and internal comments. +C 20010507 Converted single precision source to double precision. +C 20020502 Corrected declarations in descriptions of user routines. +C 20031021 Fixed address offset bugs in Subroutine DPREPI. +C 20031027 Changed 0. to 0.0D0 in Subroutine DPREPI. +C 20031105 Restored 'own' variables to Common blocks, to enable +C interrupt/restart feature. +C 20031112 Added SAVE statements for data-loaded constants. +C 20031117 Changed internal names NRE, LSAVR to NFE, LSAVF resp. +C +C----------------------------------------------------------------------- +C Other routines in the DLSODIS package. +C +C In addition to Subroutine DLSODIS, the DLSODIS package includes the +C following subroutines and function routines: +C DIPREPI acts as an interface between DLSODIS and DPREPI, and also +C does adjusting of work space pointers and work arrays. +C DPREPI is called by DIPREPI to compute sparsity and do sparse +C matrix preprocessing. +C DAINVGS computes the initial value of the vector +C dy/dt = A-inverse * g +C ADJLR adjusts the length of required sparse matrix work space. +C It is called by DPREPI. +C CNTNZU is called by DPREPI and counts the nonzero elements in the +C strict upper triangle of P + P-transpose. +C JGROUP is called by DPREPI to compute groups of Jacobian column +C indices for use when MITER = 2. +C DINTDY computes an interpolated value of the y vector at t = TOUT. +C DSTODI is the core integrator, which does one step of the +C integration and the associated error control. +C DCFODE sets all method coefficients and test constants. +C DPRJIS computes and preprocesses the Jacobian matrix J = dr/dy +C and the Newton iteration matrix P = A - h*l0*J. +C DSOLSS manages solution of linear system in chord iteration. +C DEWSET sets the error weight vector EWT before each step. +C DVNORM computes the weighted RMS-norm of a vector. +C DSRCMS is a user-callable routine to save and restore +C the contents of the internal Common blocks. +C ODRV constructs a reordering of the rows and columns of +C a matrix by the minimum degree algorithm. ODRV is a +C driver routine which calls Subroutines MD, MDI, MDM, +C MDP, MDU, and SRO. See Ref. 2 for details. (The ODRV +C module has been modified since Ref. 2, however.) +C CDRV performs reordering, symbolic factorization, numerical +C factorization, or linear system solution operations, +C depending on a path argument IPATH. CDRV is a +C driver routine which calls Subroutines NROC, NSFC, +C NNFC, NNSC, and NNTC. See Ref. 3 for details. +C DLSODIS uses CDRV to solve linear systems in which the +C coefficient matrix is P = A - con*J, where A is the +C matrix for the linear system A(t,y)*dy/dt = g(t,y), +C con is a scalar, and J is an approximation to +C the Jacobian dr/dy. Because CDRV deals with rowwise +C sparsity descriptions, CDRV works with P-transpose, not P. +C DLSODIS also uses CDRV to solve the linear system +C A(t,y)*dy/dt = g(t,y) for dy/dt when ISTATE = 0. +C (For this, CDRV works with A-transpose, not A.) +C DUMACH computes the unit roundoff in a machine-independent manner. +C XERRWD, XSETUN, XSETF, IXSAV, and IUMACH handle the printing of all +C error messages and warnings. XERRWD is machine-dependent. +C Note: DVNORM, DUMACH, IXSAV, and IUMACH are function routines. +C All the others are subroutines. +C +C----------------------------------------------------------------------- + EXTERNAL DPRJIS, DSOLSS + DOUBLE PRECISION DUMACH, DVNORM + INTEGER INIT, MXSTEP, MXHNIL, NHNIL, NSLAST, NYH, IOWNS, + 1 ICF, IERPJ, IERSL, JCUR, JSTART, KFLAG, L, + 2 LYH, LEWT, LACOR, LSAVF, LWM, LIWM, METH, MITER, + 3 MAXORD, MAXCOR, MSBP, MXNCF, N, NQ, NST, NFE, NJE, NQU + INTEGER IPLOST, IESP, ISTATC, IYS, IBA, IBIAN, IBJAN, IBJGP, + 1 IPIAN, IPJAN, IPJGP, IPIGP, IPR, IPC, IPIC, IPISP, IPRSP, IPA, + 2 LENYH, LENYHM, LENWK, LREQ, LRAT, LREST, LWMIN, MOSS, MSBJ, + 3 NSLJ, NGP, NLU, NNZ, NSP, NZL, NZU + INTEGER I, I1, I2, IER, IGO, IFLAG, IMAX, IMUL, IMXER, IPFLAG, + 1 IPGO, IREM, IRES, J, KGO, LENRAT, LENYHT, LENIW, LENRW, + 2 LIA, LIC, LJA, LJC, LRTEM, LWTEM, LYD0, LYHD, LYHN, MF1, + 3 MORD, MXHNL0, MXSTP0, NCOLM + DOUBLE PRECISION ROWNS, + 1 CCMAX, EL0, H, HMIN, HMXI, HU, RC, TN, UROUND + DOUBLE PRECISION CON0, CONMIN, CCMXJ, PSMALL, RBIG, SETH + DOUBLE PRECISION ATOLI, AYI, BIG, EWTI, H0, HMAX, HMX, RH, RTOLI, + 1 TCRIT, TDIST, TNEXT, TOL, TOLSF, TP, SIZE, SUM, W0 + DIMENSION MORD(2) + LOGICAL IHIT + CHARACTER*60 MSG + SAVE LENRAT, MORD, MXSTP0, MXHNL0 +C----------------------------------------------------------------------- +C The following two internal Common blocks contain +C (a) variables which are local to any subroutine but whose values must +C be preserved between calls to the routine ("own" variables), and +C (b) variables which are communicated between subroutines. +C The block DLS001 is declared in subroutines DLSODIS, DIPREPI, DPREPI, +C DINTDY, DSTODI, DPRJIS, and DSOLSS. +C The block DLSS01 is declared in subroutines DLSODIS, DAINVGS, +C DIPREPI, DPREPI, DPRJIS, and DSOLSS. +C Groups of variables are replaced by dummy arrays in the Common +C declarations in routines where those variables are not used. +C----------------------------------------------------------------------- + COMMON /DLS001/ ROWNS(209), + 1 CCMAX, EL0, H, HMIN, HMXI, HU, RC, TN, UROUND, + 2 INIT, MXSTEP, MXHNIL, NHNIL, NSLAST, NYH, IOWNS(6), + 3 ICF, IERPJ, IERSL, JCUR, JSTART, KFLAG, L, + 4 LYH, LEWT, LACOR, LSAVF, LWM, LIWM, METH, MITER, + 5 MAXORD, MAXCOR, MSBP, MXNCF, N, NQ, NST, NFE, NJE, NQU +C + COMMON /DLSS01/ CON0, CONMIN, CCMXJ, PSMALL, RBIG, SETH, + 1 IPLOST, IESP, ISTATC, IYS, IBA, IBIAN, IBJAN, IBJGP, + 2 IPIAN, IPJAN, IPJGP, IPIGP, IPR, IPC, IPIC, IPISP, IPRSP, IPA, + 3 LENYH, LENYHM, LENWK, LREQ, LRAT, LREST, LWMIN, MOSS, MSBJ, + 4 NSLJ, NGP, NLU, NNZ, NSP, NZL, NZU +C + DATA MORD(1),MORD(2)/12,5/, MXSTP0/500/, MXHNL0/10/ +C----------------------------------------------------------------------- +C In the Data statement below, set LENRAT equal to the ratio of +C the wordlength for a real number to that for an integer. Usually, +C LENRAT = 1 for single precision and 2 for double precision. If the +C true ratio is not an integer, use the next smaller integer (.ge. 1), +C----------------------------------------------------------------------- + DATA LENRAT/2/ +C----------------------------------------------------------------------- +C Block A. +C This code block is executed on every call. +C It tests ISTATE and ITASK for legality and branches appropirately. +C If ISTATE .gt. 1 but the flag INIT shows that initialization has +C not yet been done, an error return occurs. +C If ISTATE = 0 or 1 and TOUT = T, return immediately. +C----------------------------------------------------------------------- + IF (ISTATE .LT. 0 .OR. ISTATE .GT. 3) GO TO 601 + IF (ITASK .LT. 1 .OR. ITASK .GT. 5) GO TO 602 + IF (ISTATE .LE. 1) GO TO 10 + IF (INIT .EQ. 0) GO TO 603 + IF (ISTATE .EQ. 2) GO TO 200 + GO TO 20 + 10 INIT = 0 + IF (TOUT .EQ. T) RETURN +C----------------------------------------------------------------------- +C Block B. +C The next code block is executed for the initial call (ISTATE = 0 or 1) +C or for a continuation call with parameter changes (ISTATE = 3). +C It contains checking of all inputs and various initializations. +C If ISTATE = 0 or 1, the final setting of work space pointers, the +C matrix preprocessing, and other initializations are done in Block C. +C +C First check legality of the non-optional inputs NEQ, ITOL, IOPT, and +C MF. +C----------------------------------------------------------------------- + 20 IF (NEQ(1) .LE. 0) GO TO 604 + IF (ISTATE .LE. 1) GO TO 25 + IF (NEQ(1) .GT. N) GO TO 605 + 25 N = NEQ(1) + IF (ITOL .LT. 1 .OR. ITOL .GT. 4) GO TO 606 + IF (IOPT .LT. 0 .OR. IOPT .GT. 1) GO TO 607 + MOSS = MF/100 + MF1 = MF - 100*MOSS + METH = MF1/10 + MITER = MF1 - 10*METH + IF (MOSS .LT. 0 .OR. MOSS .GT. 4) GO TO 608 + IF (MITER .EQ. 2 .AND. MOSS .EQ. 1) MOSS = MOSS + 1 + IF (MITER .EQ. 2 .AND. MOSS .EQ. 3) MOSS = MOSS + 1 + IF (MITER .EQ. 1 .AND. MOSS .EQ. 2) MOSS = MOSS - 1 + IF (MITER .EQ. 1 .AND. MOSS .EQ. 4) MOSS = MOSS - 1 + IF (METH .LT. 1 .OR. METH .GT. 2) GO TO 608 + IF (MITER .LT. 1 .OR. MITER .GT. 2) GO TO 608 +C Next process and check the optional inputs. -------------------------- + IF (IOPT .EQ. 1) GO TO 40 + MAXORD = MORD(METH) + MXSTEP = MXSTP0 + MXHNIL = MXHNL0 + IF (ISTATE .LE. 1) H0 = 0.0D0 + HMXI = 0.0D0 + HMIN = 0.0D0 + GO TO 60 + 40 MAXORD = IWORK(5) + IF (MAXORD .LT. 0) GO TO 611 + IF (MAXORD .EQ. 0) MAXORD = 100 + MAXORD = MIN(MAXORD,MORD(METH)) + MXSTEP = IWORK(6) + IF (MXSTEP .LT. 0) GO TO 612 + IF (MXSTEP .EQ. 0) MXSTEP = MXSTP0 + MXHNIL = IWORK(7) + IF (MXHNIL .LT. 0) GO TO 613 + IF (MXHNIL .EQ. 0) MXHNIL = MXHNL0 + IF (ISTATE .GT. 1) GO TO 50 + H0 = RWORK(5) + IF ((TOUT - T)*H0 .LT. 0.0D0) GO TO 614 + 50 HMAX = RWORK(6) + IF (HMAX .LT. 0.0D0) GO TO 615 + HMXI = 0.0D0 + IF (HMAX .GT. 0.0D0) HMXI = 1.0D0/HMAX + HMIN = RWORK(7) + IF (HMIN .LT. 0.0D0) GO TO 616 +C Check RTOL and ATOL for legality. ------------------------------------ + 60 RTOLI = RTOL(1) + ATOLI = ATOL(1) + DO 65 I = 1,N + IF (ITOL .GE. 3) RTOLI = RTOL(I) + IF (ITOL .EQ. 2 .OR. ITOL .EQ. 4) ATOLI = ATOL(I) + IF (RTOLI .LT. 0.0D0) GO TO 619 + IF (ATOLI .LT. 0.0D0) GO TO 620 + 65 CONTINUE +C----------------------------------------------------------------------- +C Compute required work array lengths, as far as possible, and test +C these against LRW and LIW. Then set tentative pointers for work +C arrays. Pointers to RWORK/IWORK segments are named by prefixing L to +C the name of the segment. E.g., the segment YH starts at RWORK(LYH). +C Segments of RWORK (in order) are denoted WM, YH, SAVR, EWT, ACOR. +C The required length of the matrix work space WM is not yet known, +C and so a crude minimum value is used for the initial tests of LRW +C and LIW, and YH is temporarily stored as far to the right in RWORK +C as possible, to leave the maximum amount of space for WM for matrix +C preprocessing. Thus if MOSS .ne. 2 or 4, some of the segments of +C RWORK are temporarily omitted, as they are not needed in the +C preprocessing. These omitted segments are: ACOR if ISTATE = 1, +C EWT and ACOR if ISTATE = 3 and MOSS = 1, and SAVR, EWT, and ACOR if +C ISTATE = 3 and MOSS = 0. +C----------------------------------------------------------------------- + LRAT = LENRAT + IF (ISTATE .LE. 1) NYH = N + IF (MITER .EQ. 1) LWMIN = 4*N + 10*N/LRAT + IF (MITER .EQ. 2) LWMIN = 4*N + 11*N/LRAT + LENYH = (MAXORD+1)*NYH + LREST = LENYH + 3*N + LENRW = 20 + LWMIN + LREST + IWORK(17) = LENRW + LENIW = 30 + IF (MOSS .NE. 1 .AND. MOSS .NE. 2) LENIW = LENIW + N + 1 + IWORK(18) = LENIW + IF (LENRW .GT. LRW) GO TO 617 + IF (LENIW .GT. LIW) GO TO 618 + LIA = 31 + IF (MOSS .NE. 1 .AND. MOSS .NE. 2) + 1 LENIW = LENIW + IWORK(LIA+N) - 1 + IWORK(18) = LENIW + IF (LENIW .GT. LIW) GO TO 618 + LJA = LIA + N + 1 + LIA = MIN(LIA,LIW) + LJA = MIN(LJA,LIW) + LIC = LENIW + 1 + IF (MOSS .EQ. 0) LENIW = LENIW + N + 1 + IWORK(18) = LENIW + IF (LENIW .GT. LIW) GO TO 618 + IF (MOSS .EQ. 0) LENIW = LENIW + IWORK(LIC+N) - 1 + IWORK(18) = LENIW + IF (LENIW .GT. LIW) GO TO 618 + LJC = LIC + N + 1 + LIC = MIN(LIC,LIW) + LJC = MIN(LJC,LIW) + LWM = 21 + IF (ISTATE .LE. 1) NQ = ISTATE + NCOLM = MIN(NQ+1,MAXORD+2) + LENYHM = NCOLM*NYH + LENYHT = LENYHM + IMUL = 2 + IF (ISTATE .EQ. 3) IMUL = MOSS + IF (ISTATE .EQ. 3 .AND. MOSS .EQ. 3) IMUL = 1 + IF (MOSS .EQ. 2 .OR. MOSS .EQ. 4) IMUL = 3 + LRTEM = LENYHT + IMUL*N + LWTEM = LRW - 20 - LRTEM + LENWK = LWTEM + LYHN = LWM + LWTEM + LSAVF = LYHN + LENYHT + LEWT = LSAVF + N + LACOR = LEWT + N + ISTATC = ISTATE + IF (ISTATE .LE. 1) GO TO 100 +C----------------------------------------------------------------------- +C ISTATE = 3. Move YH to its new location. +C Note that only the part of YH needed for the next step, namely +C MIN(NQ+1,MAXORD+2) columns, is actually moved. +C A temporary error weight array EWT is loaded if MOSS = 2 or 4. +C Sparse matrix processing is done in DIPREPI/DPREPI. +C If MAXORD was reduced below NQ, then the pointers are finally set +C so that SAVR is identical to (YH*,MAXORD+2) +C----------------------------------------------------------------------- + LYHD = LYH - LYHN + IMAX = LYHN - 1 + LENYHM +C Move YH. Move right if LYHD < 0; move left if LYHD > 0. ------------- + IF (LYHD .LT. 0) THEN + DO 72 I = LYHN,IMAX + J = IMAX + LYHN - I + 72 RWORK(J) = RWORK(J+LYHD) + ENDIF + IF (LYHD .GT. 0) THEN + DO 76 I = LYHN,IMAX + 76 RWORK(I) = RWORK(I+LYHD) + ENDIF + 80 LYH = LYHN + IWORK(22) = LYH + IF (MOSS .NE. 2 .AND. MOSS .NE. 4) GO TO 85 +C Temporarily load EWT if MOSS = 2 or 4. + CALL DEWSET (N,ITOL,RTOL,ATOL,RWORK(LYH),RWORK(LEWT)) + DO 82 I = 1,N + IF (RWORK(I+LEWT-1) .LE. 0.0D0) GO TO 621 + 82 RWORK(I+LEWT-1) = 1.0D0/RWORK(I+LEWT-1) + 85 CONTINUE +C DIPREPI and DPREPI do sparse matrix preprocessing. ------------------- + LSAVF = MIN(LSAVF,LRW) + LEWT = MIN(LEWT,LRW) + LACOR = MIN(LACOR,LRW) + CALL DIPREPI (NEQ, Y, YDOTI, RWORK, IWORK(LIA), IWORK(LJA), + 1 IWORK(LIC), IWORK(LJC), IPFLAG, RES, JAC, ADDA) + LENRW = LWM - 1 + LENWK + LREST + IWORK(17) = LENRW + IF (IPFLAG .NE. -1) IWORK(23) = IPIAN + IF (IPFLAG .NE. -1) IWORK(24) = IPJAN + IPGO = -IPFLAG + 1 + GO TO (90, 628, 629, 630, 631, 632, 633, 634, 634), IPGO + 90 IWORK(22) = LYH + LYD0 = LYH + N + IF (LENRW .GT. LRW) GO TO 617 +C Set flag to signal changes to DSTODI.--------------------------------- + JSTART = -1 + IF (NQ .LE. MAXORD) GO TO 94 +C MAXORD was reduced below NQ. Copy YH(*,MAXORD+2) into YDOTI. -------- + DO 92 I = 1,N + 92 YDOTI(I) = RWORK(I+LSAVF-1) + 94 IF (N .EQ. NYH) GO TO 200 +C NEQ was reduced. Zero part of YH to avoid undefined references. ----- + I1 = LYH + L*NYH + I2 = LYH + (MAXORD + 1)*NYH - 1 + IF (I1 .GT. I2) GO TO 200 + DO 95 I = I1,I2 + 95 RWORK(I) = 0.0D0 + GO TO 200 +C----------------------------------------------------------------------- +C Block C. +C The next block is for the initial call only (ISTATE = 0 or 1). +C It contains all remaining initializations, the call to DAINVGS +C (if ISTATE = 0), the sparse matrix preprocessing, and the +C calculation if the initial step size. +C The error weights in EWT are inverted after being loaded. +C----------------------------------------------------------------------- + 100 CONTINUE + LYH = LYHN + IWORK(22) = LYH + TN = T + NST = 0 + NFE = 0 + H = 1.0D0 + NNZ = 0 + NGP = 0 + NZL = 0 + NZU = 0 +C Load the initial value vector in YH.---------------------------------- + DO 105 I = 1,N + 105 RWORK(I+LYH-1) = Y(I) + IF (ISTATE .NE. 1) GO TO 108 +C Initial dy/dt was supplied. Load it into YH (LYD0 points to YH(*,2).) + LYD0 = LYH + NYH + DO 106 I = 1,N + 106 RWORK(I+LYD0-1) = YDOTI(I) + 108 CONTINUE +C Load and invert the EWT array. (H is temporarily set to 1.0.)-------- + CALL DEWSET (N,ITOL,RTOL,ATOL,RWORK(LYH),RWORK(LEWT)) + DO 110 I = 1,N + IF (RWORK(I+LEWT-1) .LE. 0.0D0) GO TO 621 + 110 RWORK(I+LEWT-1) = 1.0D0/RWORK(I+LEWT-1) +C Call DIPREPI and DPREPI to do sparse matrix preprocessing.------------ + LACOR = MIN(LACOR,LRW) + CALL DIPREPI (NEQ, Y, YDOTI, RWORK, IWORK(LIA), IWORK(LJA), + 1 IWORK(LIC), IWORK(LJC), IPFLAG, RES, JAC, ADDA) + LENRW = LWM - 1 + LENWK + LREST + IWORK(17) = LENRW + IF (IPFLAG .NE. -1) IWORK(23) = IPIAN + IF (IPFLAG .NE. -1) IWORK(24) = IPJAN + IPGO = -IPFLAG + 1 + GO TO (115, 628, 629, 630, 631, 632, 633, 634, 634), IPGO + 115 IWORK(22) = LYH + IF (LENRW .GT. LRW) GO TO 617 +C Compute initial dy/dt, if necessary, and load it into YH.------------- + LYD0 = LYH + N + IF (ISTATE .NE. 0) GO TO 120 + CALL DAINVGS (NEQ, T, Y, RWORK(LWM), RWORK(LWM), RWORK(LACOR), + 1 RWORK(LYD0), IER, RES, ADDA) + NFE = NFE + 1 + IGO = IER + 1 + GO TO (120, 565, 560, 560), IGO +C Check TCRIT for legality (ITASK = 4 or 5). --------------------------- + 120 CONTINUE + IF (ITASK .NE. 4 .AND. ITASK .NE. 5) GO TO 125 + TCRIT = RWORK(1) + IF ((TCRIT - TOUT)*(TOUT - T) .LT. 0.0D0) GO TO 625 + IF (H0 .NE. 0.0D0 .AND. (T + H0 - TCRIT)*H0 .GT. 0.0D0) + 1 H0 = TCRIT - T +C Initialize all remaining parameters. --------------------------------- + 125 UROUND = DUMACH() + JSTART = 0 + RWORK(LWM) = SQRT(UROUND) + NHNIL = 0 + NJE = 0 + NLU = 0 + NSLAST = 0 + HU = 0.0D0 + NQU = 0 + CCMAX = 0.3D0 + MAXCOR = 3 + MSBP = 20 + MXNCF = 10 +C----------------------------------------------------------------------- +C The coding below computes the step size, H0, to be attempted on the +C first step, unless the user has supplied a value for this. +C First check that TOUT - T differs significantly from zero. +C A scalar tolerance quantity TOL is computed, as MAX(RTOL(i)) +C if this is positive, or MAX(ATOL(i)/ABS(Y(i))) otherwise, adjusted +C so as to be between 100*UROUND and 1.0E-3. +C Then the computed value H0 is given by.. +C NEQ +C H0**2 = TOL / ( w0**-2 + (1/NEQ) * Sum ( YDOT(i)/ywt(i) )**2 ) +C 1 +C where w0 = MAX ( ABS(T), ABS(TOUT) ), +C YDOT(i) = i-th component of initial value of dy/dt, +C ywt(i) = EWT(i)/TOL (a weight for y(i)). +C The sign of H0 is inferred from the initial values of TOUT and T. +C----------------------------------------------------------------------- + IF (H0 .NE. 0.0D0) GO TO 180 + TDIST = ABS(TOUT - T) + W0 = MAX(ABS(T),ABS(TOUT)) + IF (TDIST .LT. 2.0D0*UROUND*W0) GO TO 622 + TOL = RTOL(1) + IF (ITOL .LE. 2) GO TO 145 + DO 140 I = 1,N + 140 TOL = MAX(TOL,RTOL(I)) + 145 IF (TOL .GT. 0.0D0) GO TO 160 + ATOLI = ATOL(1) + DO 150 I = 1,N + IF (ITOL .EQ. 2 .OR. ITOL .EQ. 4) ATOLI = ATOL(I) + AYI = ABS(Y(I)) + IF (AYI .NE. 0.0D0) TOL = MAX(TOL,ATOLI/AYI) + 150 CONTINUE + 160 TOL = MAX(TOL,100.0D0*UROUND) + TOL = MIN(TOL,0.001D0) + SUM = DVNORM (N, RWORK(LYD0), RWORK(LEWT)) + SUM = 1.0D0/(TOL*W0*W0) + TOL*SUM**2 + H0 = 1.0D0/SQRT(SUM) + H0 = MIN(H0,TDIST) + H0 = SIGN(H0,TOUT-T) +C Adjust H0 if necessary to meet HMAX bound. --------------------------- + 180 RH = ABS(H0)*HMXI + IF (RH .GT. 1.0D0) H0 = H0/RH +C Load H with H0 and scale YH(*,2) by H0. ------------------------------ + H = H0 + DO 190 I = 1,N + 190 RWORK(I+LYD0-1) = H0*RWORK(I+LYD0-1) + GO TO 270 +C----------------------------------------------------------------------- +C Block D. +C The next code block is for continuation calls only (ISTATE = 2 or 3) +C and is to check stop conditions before taking a step. +C----------------------------------------------------------------------- + 200 NSLAST = NST + GO TO (210, 250, 220, 230, 240), ITASK + 210 IF ((TN - TOUT)*H .LT. 0.0D0) GO TO 250 + CALL DINTDY (TOUT, 0, RWORK(LYH), NYH, Y, IFLAG) + IF (IFLAG .NE. 0) GO TO 627 + T = TOUT + GO TO 420 + 220 TP = TN - HU*(1.0D0 + 100.0D0*UROUND) + IF ((TP - TOUT)*H .GT. 0.0D0) GO TO 623 + IF ((TN - TOUT)*H .LT. 0.0D0) GO TO 250 + GO TO 400 + 230 TCRIT = RWORK(1) + IF ((TN - TCRIT)*H .GT. 0.0D0) GO TO 624 + IF ((TCRIT - TOUT)*H .LT. 0.0D0) GO TO 625 + IF ((TN - TOUT)*H .LT. 0.0D0) GO TO 245 + CALL DINTDY (TOUT, 0, RWORK(LYH), NYH, Y, IFLAG) + IF (IFLAG .NE. 0) GO TO 627 + T = TOUT + GO TO 420 + 240 TCRIT = RWORK(1) + IF ((TN - TCRIT)*H .GT. 0.0D0) GO TO 624 + 245 HMX = ABS(TN) + ABS(H) + IHIT = ABS(TN - TCRIT) .LE. 100.0D0*UROUND*HMX + IF (IHIT) GO TO 400 + TNEXT = TN + H*(1.0D0 + 4.0D0*UROUND) + IF ((TNEXT - TCRIT)*H .LE. 0.0D0) GO TO 250 + H = (TCRIT - TN)*(1.0D0 - 4.0D0*UROUND) + IF (ISTATE .EQ. 2) JSTART = -2 +C----------------------------------------------------------------------- +C Block E. +C The next block is normally executed for all calls and contains +C the call to the one-step core integrator DSTODI. +C +C This is a looping point for the integration steps. +C +C First check for too many steps being taken, update EWT (if not at +C start of problem), check for too much accuracy being requested, and +C check for H below the roundoff level in T. +C----------------------------------------------------------------------- + 250 CONTINUE + IF ((NST-NSLAST) .GE. MXSTEP) GO TO 500 + CALL DEWSET (N, ITOL, RTOL, ATOL, RWORK(LYH), RWORK(LEWT)) + DO 260 I = 1,N + IF (RWORK(I+LEWT-1) .LE. 0.0D0) GO TO 510 + 260 RWORK(I+LEWT-1) = 1.0D0/RWORK(I+LEWT-1) + 270 TOLSF = UROUND*DVNORM (N, RWORK(LYH), RWORK(LEWT)) + IF (TOLSF .LE. 1.0D0) GO TO 280 + TOLSF = TOLSF*2.0D0 + IF (NST .EQ. 0) GO TO 626 + GO TO 520 + 280 IF ((TN + H) .NE. TN) GO TO 290 + NHNIL = NHNIL + 1 + IF (NHNIL .GT. MXHNIL) GO TO 290 + MSG = 'DLSODIS- Warning..Internal T (=R1) and H (=R2) are' + CALL XERRWD (MSG, 50, 101, 0, 0, 0, 0, 0, 0.0D0, 0.0D0) + MSG=' such that in the machine, T + H = T on the next step ' + CALL XERRWD (MSG, 60, 101, 0, 0, 0, 0, 0, 0.0D0, 0.0D0) + MSG = ' (H = step size). Solver will continue anyway.' + CALL XERRWD (MSG, 50, 101, 0, 0, 0, 0, 2, TN, H) + IF (NHNIL .LT. MXHNIL) GO TO 290 + MSG = 'DLSODIS- Above warning has been issued I1 times. ' + CALL XERRWD (MSG, 50, 102, 0, 0, 0, 0, 0, 0.0D0, 0.0D0) + MSG = ' It will not be issued again for this problem.' + CALL XERRWD (MSG, 50, 102, 0, 1, MXHNIL, 0, 0, 0.0D0, 0.0D0) + 290 CONTINUE +C----------------------------------------------------------------------- +C CALL DSTODI(NEQ,Y,YH,NYH,YH1,EWT,SAVF,SAVR,ACOR,WM,WM,RES, +C ADDA,JAC,DPRJIS,DSOLSS) +C Note: SAVF in DSTODI occupies the same space as YDOTI in DLSODIS. +C----------------------------------------------------------------------- + CALL DSTODI (NEQ, Y, RWORK(LYH), NYH, RWORK(LYH), RWORK(LEWT), + 1 YDOTI, RWORK(LSAVF), RWORK(LACOR), RWORK(LWM), + 2 RWORK(LWM), RES, ADDA, JAC, DPRJIS, DSOLSS ) + KGO = 1 - KFLAG + GO TO (300, 530, 540, 400, 550, 555), KGO +C +C KGO = 1:success; 2:error test failure; 3:convergence failure; +C 4:RES ordered return; 5:RES returned error; +C 6:fatal error from CDRV via DPRJIS or DSOLSS. +C----------------------------------------------------------------------- +C Block F. +C The following block handles the case of a successful return from the +C core integrator (KFLAG = 0). Test for stop conditions. +C----------------------------------------------------------------------- + 300 INIT = 1 + GO TO (310, 400, 330, 340, 350), ITASK +C ITASK = 1. If TOUT has been reached, interpolate. ------------------- + 310 iF ((TN - TOUT)*H .LT. 0.0D0) GO TO 250 + CALL DINTDY (TOUT, 0, RWORK(LYH), NYH, Y, IFLAG) + T = TOUT + GO TO 420 +C ITASK = 3. Jump to exit if TOUT was reached. ------------------------ + 330 IF ((TN - TOUT)*H .GE. 0.0D0) GO TO 400 + GO TO 250 +C ITASK = 4. See if TOUT or TCRIT was reached. Adjust H if necessary. + 340 IF ((TN - TOUT)*H .LT. 0.0D0) GO TO 345 + CALL DINTDY (TOUT, 0, RWORK(LYH), NYH, Y, IFLAG) + T = TOUT + GO TO 420 + 345 HMX = ABS(TN) + ABS(H) + IHIT = ABS(TN - TCRIT) .LE. 100.0D0*UROUND*HMX + IF (IHIT) GO TO 400 + TNEXT = TN + H*(1.0D0 + 4.0D0*UROUND) + IF ((TNEXT - TCRIT)*H .LE. 0.0D0) GO TO 250 + H = (TCRIT - TN)*(1.0D0 - 4.0D0*UROUND) + JSTART = -2 + GO TO 250 +C ITASK = 5. See if TCRIT was reached and jump to exit. --------------- + 350 HMX = ABS(TN) + ABS(H) + IHIT = ABS(TN - TCRIT) .LE. 100.0D0*UROUND*HMX +C----------------------------------------------------------------------- +C Block G. +C The following block handles all successful returns from DLSODIS. +C if ITASK .ne. 1, Y is loaded from YH and T is set accordingly. +C ISTATE is set to 2, and the optional outputs are loaded into the +C work arrays before returning. +C----------------------------------------------------------------------- + 400 DO 410 I = 1,N + 410 Y(I) = RWORK(I+LYH-1) + T = TN + IF (ITASK .NE. 4 .AND. ITASK .NE. 5) GO TO 420 + IF (IHIT) T = TCRIT + 420 ISTATE = 2 + IF ( KFLAG .EQ. -3 ) ISTATE = 3 + RWORK(11) = HU + RWORK(12) = H + RWORK(13) = TN + IWORK(11) = NST + IWORK(12) = NFE + IWORK(13) = NJE + IWORK(14) = NQU + IWORK(15) = NQ + IWORK(19) = NNZ + IWORK(20) = NGP + IWORK(21) = NLU + IWORK(25) = NZL + IWORK(26) = NZU + RETURN +C----------------------------------------------------------------------- +C Block H. +C The following block handles all unsuccessful returns other than +C those for illegal input. First the error message routine is called. +C If there was an error test or convergence test failure, IMXER is set. +C Then Y is loaded from YH and T is set to TN. +C The optional outputs are loaded into the work arrays before returning. +C----------------------------------------------------------------------- +C The maximum number of steps was taken before reaching TOUT. ---------- + 500 MSG = 'DLSODIS- At current T (=R1), MXSTEP (=I1) steps ' + CALL XERRWD (MSG, 50, 201, 0, 0, 0, 0, 0, 0.0D0, 0.0D0) + MSG = ' taken on this call before reaching TOUT ' + CALL XERRWD (MSG, 50, 201, 0, 1, MXSTEP, 0, 1, TN, 0.0D0) + ISTATE = -1 + GO TO 580 +C EWT(i) .le. 0.0 for some i (not at start of problem). ---------------- + 510 EWTI = RWORK(LEWT+I-1) + MSG = 'DLSODIS- At T (=R1), EWT(I1) has become R2 .le. 0.' + CALL XERRWD (MSG, 50, 202, 0, 1, I, 0, 2, TN, EWTI) + ISTATE = -6 + GO TO 590 +C Too much accuracy requested for machine precision. ------------------- + 520 MSG = 'DLSODIS- At T (=R1), too much accuracy requested ' + CALL XERRWD (MSG, 50, 203, 0, 0, 0, 0, 0, 0.0D0, 0.0D0) + MSG = ' for precision of machine.. See TOLSF (=R2) ' + CALL XERRWD (MSG, 50, 203, 0, 0, 0, 0, 2, TN, TOLSF) + RWORK(14) = TOLSF + ISTATE = -2 + GO TO 590 +C KFLAG = -1. Error test failed repeatedly or with ABS(H) = HMIN. ----- + 530 MSG = 'DLSODIS- At T (=R1) and step size H (=R2), the ' + CALL XERRWD (MSG, 50, 204, 0, 0, 0, 0, 0, 0.0D0, 0.0D0) + MSG=' error test failed repeatedly or with ABS(H) = HMIN ' + CALL XERRWD (MSG, 60, 204, 0, 0, 0, 0, 2, TN, H) + ISTATE = -4 + GO TO 570 +C KFLAG = -2. Convergence failed repeatedly or with ABS(H) = HMIN. ---- + 540 MSG = 'DLSODIS- At T (=R1) and step size H (=R2), the ' + CALL XERRWD (MSG, 50, 205, 0, 0, 0, 0, 0, 0.0D0, 0.0D0) + MSG = ' corrector convergence failed repeatedly ' + CALL XERRWD (MSG, 50, 205, 0, 0, 0, 0, 0, 0.0D0, 0.0D0) + MSG = ' or with ABS(H) = HMIN ' + CALL XERRWD (MSG, 30, 205, 0, 0, 0, 0, 2, TN, H) + ISTATE = -5 + GO TO 570 +C IRES = 3 returned by RES, despite retries by DSTODI. ----------------- + 550 MSG = 'DLSODIS- At T (=R1) residual routine returned ' + CALL XERRWD (MSG, 50, 206, 0, 0, 0, 0, 0, 0.0D0, 0.0D0) + MSG = ' error IRES = 3 repeatedly.' + CALL XERRWD (MSG, 30, 206, 1, 0, 0, 0, 0, TN, 0.0D0) + ISTATE = -7 + GO TO 590 +C KFLAG = -5. Fatal error flag returned by DPRJIS or DSOLSS (CDRV). --- + 555 MSG = 'DLSODIS- At T (=R1) and step size H (=R2), a fatal' + CALL XERRWD (MSG, 50, 207, 0, 0, 0, 0, 0, 0.0D0, 0.0D0) + MSG = ' error flag was returned by CDRV (by way of ' + CALL XERRWD (MSG, 50, 207, 0, 0, 0, 0, 0, 0.0D0, 0.0D0) + MSG = ' Subroutine DPRJIS or DSOLSS) ' + CALL XERRWD (MSG, 40, 207, 0, 0, 0, 0, 2, TN, H) + ISTATE = -9 + GO TO 580 +C DAINVGS failed because matrix A was singular. ------------------------ + 560 MSG='DLSODIS- Attempt to initialize dy/dt failed because matrix A' + CALL XERRWD (MSG, 60, 208, 0, 0, 0, 0, 0, 0.0D0, 0.0D0) + MSG=' was singular. CDRV returned zero pivot error flag. ' + CALL XERRWD (MSG, 60, 208, 0, 0, 0, 0, 0, 0.0D0, 0.0D0) + MSG = 'DAINVGS set its error flag to IER = (I1)' + CALL XERRWD (MSG, 40, 208, 0, 1, IER, 0, 0, 0.0D0, 0.0D0) + ISTATE = -8 + RETURN +C DAINVGS failed because RES set IRES to 2 or 3. ----------------------- + 565 MSG = 'DLSODIS- Attempt to initialize dy/dt failed ' + CALL XERRWD (MSG, 50, 209, 0, 0, 0, 0, 0, 0.0D0, 0.0D0) + MSG = ' because residual routine set its error flag ' + CALL XERRWD (MSG, 50, 209, 0, 0, 0, 0, 0, 0.0D0, 0.0D0) + MSG = ' to IRES = (I1)' + CALL XERRWD (MSG, 20, 209, 0, 1, IER, 0, 0, 0.0D0, 0.0D0) + ISTATE = -8 + RETURN +C Compute IMXER if relevant. ------------------------------------------- + 570 BIG = 0.0D0 + IMXER = 1 + DO 575 I = 1,N + SIZE = ABS(RWORK(I+LACOR-1)*RWORK(I+LEWT-1)) + IF (BIG .GE. SIZE) GO TO 575 + BIG = SIZE + IMXER = I + 575 CONTINUE + IWORK(16) = IMXER +C Compute residual if relevant. ---------------------------------------- + 580 LYD0 = LYH + NYH + DO 585 I = 1, N + RWORK(I+LSAVF-1) = RWORK(I+LYD0-1) / H + 585 Y(I) = RWORK(I+LYH-1) + IRES = 1 + CALL RES (NEQ, TN, Y, RWORK(LSAVF), YDOTI, IRES) + NFE = NFE + 1 + IF ( IRES .LE. 1 ) GO TO 595 + MSG = 'DLSODIS- Residual routine set its flag IRES ' + CALL XERRWD (MSG, 50, 210, 0, 0, 0, 0, 0, 0.0D0, 0.0D0) + MSG = ' to (I1) when called for final output. ' + CALL XERRWD (MSG, 50, 210, 0, 1, IRES, 0, 0, 0.0D0, 0.0D0) + GO TO 595 +C set y vector, t, and optional outputs. ------------------------------- + 590 DO 592 I = 1,N + 592 Y(I) = RWORK(I+LYH-1) + 595 T = TN + RWORK(11) = HU + RWORK(12) = H + RWORK(13) = TN + IWORK(11) = NST + IWORK(12) = NFE + IWORK(13) = NJE + IWORK(14) = NQU + IWORK(15) = NQ + IWORK(19) = NNZ + IWORK(20) = NGP + IWORK(21) = NLU + IWORK(25) = NZL + IWORK(26) = NZU + RETURN +C----------------------------------------------------------------------- +C Block I. +C The following block handles all error returns due to illegal input +C (ISTATE = -3), as detected before calling the core integrator. +C First the error message routine is called. If the illegal input +C is a negative ISTATE, the run is aborted (apparent infinite loop). +C----------------------------------------------------------------------- + 601 MSG = 'DLSODIS- ISTATE (=I1) illegal.' + CALL XERRWD (MSG, 30, 1, 0, 1, ISTATE, 0, 0, 0.0D0, 0.0D0) + IF (ISTATE .LT. 0) GO TO 800 + GO TO 700 + 602 MSG = 'DLSODIS- ITASK (=I1) illegal. ' + CALL XERRWD (MSG, 30, 2, 0, 1, ITASK, 0, 0, 0.0D0, 0.0D0) + GO TO 700 + 603 MSG = 'DLSODIS-ISTATE .gt. 1 but DLSODIS not initialized.' + CALL XERRWD (MSG, 50, 3, 0, 0, 0, 0, 0, 0.0D0, 0.0D0) + GO TO 700 + 604 MSG = 'DLSODIS- NEQ (=I1) .lt. 1 ' + CALL XERRWD (MSG, 30, 4, 0, 1, NEQ(1), 0, 0, 0.0D0, 0.0D0) + GO TO 700 + 605 MSG = 'DLSODIS- ISTATE = 3 and NEQ increased (I1 to I2). ' + CALL XERRWD (MSG, 50, 5, 0, 2, N, NEQ(1), 0, 0.0D0, 0.0D0) + GO TO 700 + 606 MSG = 'DLSODIS- ITOL (=I1) illegal. ' + CALL XERRWD (MSG, 30, 6, 0, 1, ITOL, 0, 0, 0.0D0, 0.0D0) + GO TO 700 + 607 MSG = 'DLSODIS- IOPT (=I1) illegal. ' + CALL XERRWD (MSG, 30, 7, 0, 1, IOPT, 0, 0, 0.0D0, 0.0D0) + GO TO 700 + 608 MSG = 'DLSODIS- MF (=I1) illegal. ' + CALL XERRWD (MSG, 30, 8, 0, 1, MF, 0, 0, 0.0D0, 0.0D0) + GO TO 700 + 611 MSG = 'DLSODIS- MAXORD (=I1) .lt. 0 ' + CALL XERRWD (MSG, 30, 11, 0, 1, MAXORD, 0, 0, 0.0D0, 0.0D0) + GO TO 700 + 612 MSG = 'DLSODIS- MXSTEP (=I1) .lt. 0 ' + CALL XERRWD (MSG, 30, 12, 0, 1, MXSTEP, 0, 0, 0.0D0, 0.0D0) + GO TO 700 + 613 MSG = 'DLSODIS- MXHNIL (=I1) .lt. 0 ' + CALL XERRWD (MSG, 30, 13, 0, 1, MXHNIL, 0, 0, 0.0D0, 0.0D0) + GO TO 700 + 614 MSG = 'DLSODIS- TOUT (=R1) behind T (=R2) ' + CALL XERRWD (MSG, 40, 14, 0, 0, 0, 0, 2, TOUT, T) + MSG = ' Integration direction is given by H0 (=R1) ' + CALL XERRWD (MSG, 50, 14, 0, 0, 0, 0, 1, H0, 0.0D0) + GO TO 700 + 615 MSG = 'DLSODIS- HMAX (=R1) .lt. 0.0 ' + CALL XERRWD (MSG, 30, 15, 0, 0, 0, 0, 1, HMAX, 0.0D0) + GO TO 700 + 616 MSG = 'DLSODIS- HMIN (=R1) .lt. 0.0 ' + CALL XERRWD (MSG, 30, 16, 0, 0, 0, 0, 1, HMIN, 0.0D0) + GO TO 700 + 617 MSG = 'DLSODIS- RWORK length is insufficient to proceed. ' + CALL XERRWD (MSG, 50, 17, 0, 0, 0, 0, 0, 0.0D0, 0.0D0) + MSG=' Length needed is .ge. LENRW (=I1), exceeds LRW (=I2)' + CALL XERRWD (MSG, 60, 17, 0, 2, LENRW, LRW, 0, 0.0D0, 0.0D0) + GO TO 700 + 618 MSG = 'DLSODIS- IWORK length is insufficient to proceed. ' + CALL XERRWD (MSG, 50, 18, 0, 0, 0, 0, 0, 0.0D0, 0.0D0) + MSG=' Length needed is .ge. LENIW (=I1), exceeds LIW (=I2)' + CALL XERRWD (MSG, 60, 18, 0, 2, LENIW, LIW, 0, 0.0D0, 0.0D0) + GO TO 700 + 619 MSG = 'DLSODIS- RTOL(=I1) is R1 .lt. 0.0 ' + CALL XERRWD (MSG, 40, 19, 0, 1, I, 0, 1, RTOLI, 0.0D0) + GO TO 700 + 620 MSG = 'DLSODIS- ATOL(=I1) is R1 .lt. 0.0 ' + CALL XERRWD (MSG, 40, 20, 0, 1, I, 0, 1, ATOLI, 0.0D0) + GO TO 700 + 621 EWTI = RWORK(LEWT+I-1) + MSG = 'DLSODIS- EWT(I1) is R1 .le. 0.0 ' + CALL XERRWD (MSG, 40, 21, 0, 1, I, 0, 1, EWTI, 0.0D0) + GO TO 700 + 622 MSG='DLSODIS- TOUT(=R1) too close to T(=R2) to start integration.' + CALL XERRWD (MSG, 60, 22, 0, 0, 0, 0, 2, TOUT, T) + GO TO 700 + 623 MSG='DLSODIS- ITASK = I1 and TOUT (=R1) behind TCUR - HU (= R2) ' + CALL XERRWD (MSG, 60, 23, 0, 1, ITASK, 0, 2, TOUT, TP) + GO TO 700 + 624 MSG='DLSODIS- ITASK = 4 or 5 and TCRIT (=R1) behind TCUR (=R2) ' + CALL XERRWD (MSG, 60, 24, 0, 0, 0, 0, 2, TCRIT, TN) + GO TO 700 + 625 MSG='DLSODIS- ITASK = 4 or 5 and TCRIT (=R1) behind TOUT (=R2) ' + CALL XERRWD (MSG, 60, 25, 0, 0, 0, 0, 2, TCRIT, TOUT) + GO TO 700 + 626 MSG = 'DLSODIS- At start of problem, too much accuracy ' + CALL XERRWD (MSG, 50, 26, 0, 0, 0, 0, 0, 0.0D0, 0.0D0) + MSG=' requested for precision of machine.. See TOLSF (=R1) ' + CALL XERRWD (MSG, 60, 26, 0, 0, 0, 0, 1, TOLSF, 0.0D0) + RWORK(14) = TOLSF + GO TO 700 + 627 MSG = 'DLSODIS- Trouble in DINTDY. ITASK = I1, TOUT = R1' + CALL XERRWD (MSG, 50, 27, 0, 1, ITASK, 0, 1, TOUT, 0.0D0) + GO TO 700 + 628 MSG='DLSODIS- RWORK length insufficient (for Subroutine DPREPI). ' + CALL XERRWD (MSG, 60, 28, 0, 0, 0, 0, 0, 0.0D0, 0.0D0) + MSG=' Length needed is .ge. LENRW (=I1), exceeds LRW (=I2)' + CALL XERRWD (MSG, 60, 28, 0, 2, LENRW, LRW, 0, 0.0D0, 0.0D0) + GO TO 700 + 629 MSG='DLSODIS- RWORK length insufficient (for Subroutine JGROUP). ' + CALL XERRWD (MSG, 60, 29, 0, 0, 0, 0, 0, 0.0D0, 0.0D0) + MSG=' Length needed is .ge. LENRW (=I1), exceeds LRW (=I2)' + CALL XERRWD (MSG, 60, 29, 0, 2, LENRW, LRW, 0, 0.0D0, 0.0D0) + GO TO 700 + 630 MSG='DLSODIS- RWORK length insufficient (for Subroutine ODRV). ' + CALL XERRWD (MSG, 60, 30, 0, 0, 0, 0, 0, 0.0D0, 0.0D0) + MSG=' Length needed is .ge. LENRW (=I1), exceeds LRW (=I2)' + CALL XERRWD (MSG, 60, 30, 0, 2, LENRW, LRW, 0, 0.0D0, 0.0D0) + GO TO 700 + 631 MSG='DLSODIS- Error from ODRV in Yale Sparse Matrix Package. ' + CALL XERRWD (MSG, 60, 31, 0, 0, 0, 0, 0, 0.0D0, 0.0D0) + IMUL = (IYS - 1)/N + IREM = IYS - IMUL*N + MSG=' At T (=R1), ODRV returned error flag = I1*NEQ + I2. ' + CALL XERRWD (MSG, 60, 31, 0, 2, IMUL, IREM, 1, TN, 0.0D0) + GO TO 700 + 632 MSG='DLSODIS- RWORK length insufficient (for Subroutine CDRV). ' + CALL XERRWD (MSG, 60, 32, 0, 0, 0, 0, 0, 0.0D0, 0.0D0) + MSG=' Length needed is .ge. LENRW (=I1), exceeds LRW (=I2)' + CALL XERRWD (MSG, 60, 32, 0, 2, LENRW, LRW, 0, 0.0D0, 0.0D0) + GO TO 700 + 633 MSG='DLSODIS- Error from CDRV in Yale Sparse Matrix Package. ' + CALL XERRWD (MSG, 60, 33, 0, 0, 0, 0, 0, 0.0D0, 0.0D0) + IMUL = (IYS - 1)/N + IREM = IYS - IMUL*N + MSG=' At T (=R1), CDRV returned error flag = I1*NEQ + I2. ' + CALL XERRWD (MSG, 60, 33, 0, 2, IMUL, IREM, 1, TN, 0.0D0) + IF (IMUL .EQ. 2) THEN + MSG=' Duplicate entry in sparsity structure descriptors. ' + CALL XERRWD (MSG, 60, 33, 0, 0, 0, 0, 0, 0.0D0, 0.0D0) + ENDIF + IF (IMUL .EQ. 3 .OR. IMUL .EQ. 6) THEN + MSG=' Insufficient storage for NSFC (called by CDRV). ' + CALL XERRWD (MSG, 60, 33, 0, 0, 0, 0, 0, 0.0D0, 0.0D0) + ENDIF + GO TO 700 + 634 MSG='DLSODIS- At T (=R1) residual routine (called by DPREPI) ' + CALL XERRWD (MSG, 60, 34, 0, 0, 0, 0, 0, 0.0D0, 0.0D0) + IER = -IPFLAG - 5 + MSG = ' returned error IRES (=I1)' + CALL XERRWD (MSG, 30, 34, 0, 1, IER, 0, 1, TN, 0.0D0) +C + 700 ISTATE = -3 + RETURN +C + 800 MSG = 'DLSODIS- Run aborted.. apparent infinite loop. ' + CALL XERRWD (MSG, 50, 303, 2, 0, 0, 0, 0, 0.0D0, 0.0D0) + RETURN +C----------------------- End of Subroutine DLSODIS --------------------- + END + + diff --git a/applications/PUfoam/MoDeNaModels/bubbleGrowth/src/src/tests.f90 b/applications/PUfoam/MoDeNaModels/bubbleGrowth/src/src/tests.f90 new file mode 100644 index 000000000..37ef38d85 --- /dev/null +++ b/applications/PUfoam/MoDeNaModels/bubbleGrowth/src/src/tests.f90 @@ -0,0 +1,40 @@ +!> @file +!! subroutines for growth of a single bubble and various parametric studies +!! @author Pavel Ferkl +!! @ingroup bblgr +module tests + use model + implicit none + private + public onegrowth +contains +!********************************BEGINNING************************************* +!> simulates one growth of a bubble +subroutine onegrowth + !HORNET windows +! character(len=99) :: fileplacein='C:\Pavel\Dropbox\src\bubblegrowth_src\' + !HORNET linux +! character(len=99) :: fileplacein='/home/me/Dropbox/src/bubblegrowth_src/' + !laptop windows + ! character(len=99) :: fileplacein=& + ! 'C:\Users\pavel\Dropbox\src\bubblegrowth_src\' +! character(len=99) :: fileplacein='./' !current folder + character(len=99) :: fileplacein='../',& !modena + fileplaceout='../results/',& !modena + inputs='inputs.in',outputs_1d='outputs_1d.out',& + outputs_GR='outputs_GR.out',outputs_GR_c='outputs_GR_c.out',& + outputs_GR_p='outputs_GR_p.out',spar='GR_par.dat',concloc + concloc=fileplaceout + inputs=TRIM(ADJUSTL(fileplacein))//TRIM(ADJUSTL(inputs)) + outputs_1d=TRIM(ADJUSTL(fileplaceout))//TRIM(ADJUSTL(outputs_1d)) + outputs_GR=TRIM(ADJUSTL(fileplaceout))//TRIM(ADJUSTL(outputs_GR)) + outputs_GR_c=TRIM(ADJUSTL(fileplaceout))//TRIM(ADJUSTL(outputs_GR_c)) + outputs_GR_p=TRIM(ADJUSTL(fileplaceout))//TRIM(ADJUSTL(outputs_GR_p)) + spar=TRIM(ADJUSTL(fileplaceout))//TRIM(ADJUSTL(spar)) + call read_inputs(inputs) +! call save_surrogate_parameters(spar) + call bblpreproc + call bblinteg(outputs_1d,outputs_GR,outputs_GR_c,outputs_GR_p,concloc) +end subroutine onegrowth +!***********************************END**************************************** +end module tests diff --git a/applications/PUfoam/MoDeNaModels/diffusivity/__init__.py b/applications/PUfoam/MoDeNaModels/diffusivity/__init__.py new file mode 100644 index 000000000..7a64a4452 --- /dev/null +++ b/applications/PUfoam/MoDeNaModels/diffusivity/__init__.py @@ -0,0 +1,40 @@ +''' + + ooo ooooo oooooooooo. ooooo ooo + `88. .888' `888' `Y8b `888b. `8' + 888b d'888 .ooooo. 888 888 .ooooo. 8 `88b. 8 .oooo. + 8 Y88. .P 888 d88' `88b 888 888 d88' `88b 8 `88b. 8 `P )88b + 8 `888' 888 888 888 888 888 888ooo888 8 `88b.8 .oP"888 + 8 Y 888 888 888 888 d88' 888 .o 8 `888 d8( 888 + o8o o888o `Y8bod8P' o888bood8P' `Y8bod8P' o8o `8 `Y888""8o + +Copyright + 2014-2015 MoDeNa Consortium, All rights reserved. + +License + This file is part of Modena. + + Modena is free software; you can redistribute it and/or modify it under + the terms of the GNU General Public License as published by the Free + Software Foundation, either version 3 of the License, or (at your option) + any later version. + + Modena is distributed in the hope that it will be useful, but WITHOUT ANY + WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS + FOR A PARTICULAR PURPOSE. See the GNU General Public License + for more details. + + You should have received a copy of the GNU General Public License along + with Modena. If not, see . + +Description + Python library of FireTasks + +Authors + Henrik Rusche + +Contributors +''' + +import diffusivity + diff --git a/applications/PUfoam/MoDeNaModels/diffusivity/diffusivity.py b/applications/PUfoam/MoDeNaModels/diffusivity/diffusivity.py new file mode 100644 index 000000000..a95ee2827 --- /dev/null +++ b/applications/PUfoam/MoDeNaModels/diffusivity/diffusivity.py @@ -0,0 +1,133 @@ +'''@cond + + ooo ooooo oooooooooo. ooooo ooo + `88. .888' `888' `Y8b `888b. `8' + 888b d'888 .ooooo. 888 888 .ooooo. 8 `88b. 8 .oooo. + 8 Y88. .P 888 d88' `88b 888 888 d88' `88b 8 `88b. 8 `P )88b + 8 `888' 888 888 888 888 888 888ooo888 8 `88b.8 .oP"888 + 8 Y 888 888 888 888 d88' 888 .o 8 `888 d8( 888 + o8o o888o `Y8bod8P' o888bood8P' `Y8bod8P' o8o `8 `Y888""8o + +Copyright + 2014 MoDeNa Consortium, All rights reserved. + +License + This file is part of Modena. + + Modena is free software; you can redistribute it and/or modify it under + the terms of the GNU General Public License as published by the Free + Software Foundation, either version 3 of the License, or (at your option) + any later version. + + Modena is distributed in the hope that it will be useful, but WITHOUT ANY + WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS + FOR A PARTICULAR PURPOSE. See the GNU General Public License + for more details. + + You should have received a copy of the GNU General Public License along + with Modena. If not, see . +@endcond''' + +""" +@file +Surrogate function and model definitions for diffusivity of blowing agents in +polymer. + +@author Erik Laurini +@author Pavel Ferkl +@copyright 2014-2015, MoDeNa Project. GNU Public License. +@ingroup app_aging +""" + +import os +import modena +from modena import CFunction, IndexSet, Workflow2, \ + ForwardMappingModel, BackwardMappingModel, SurrogateModel +import modena.Strategy as Strategy +from fireworks.user_objects.firetasks.script_task import FireTaskBase, ScriptTask +from fireworks import Firework, Workflow, FWAction +from fireworks.utilities.fw_utilities import explicit_serialize +from blessings import Terminal +from jinja2 import Template + +## Create terminal for colour output +term = Terminal() +## List of components, for which surrogate model is provided +species = IndexSet( + name= 'diffusivity_pol_species', + names= [ 'CO2', 'CyP', 'N2', 'O2' ] +) +## Surrogate function for diffusivity of blowing agents in polymer. +# +# Diffusivity is a function of temperature. +f_diffusivity = CFunction( + Ccode=''' +#include "modena.h" +#include "math.h" + +void diffusivityPol +( + const modena_model_t* model, + const double* inputs, + double *outputs +) +{ + {% block variables %}{% endblock %} + + const double a = parameters[0]; + const double b = parameters[1]; + + outputs[0] = a*exp(-(b*(1/T))); +} +''', + # These are global bounds for the function + inputs={ + 'T': {'min': 273, 'max': 450}, + }, + outputs={ + 'diffusivity': {'min': 0, 'max': +9e99, 'argPos': 0}, + }, + parameters={ + 'param0[A]': {'min': 0.0, 'max': +9e99, 'argPos': 0}, + 'param1[A]': {'min': 0.0, 'max': +9e99, 'argPos': 1}, + }, + indices={ + 'A': species, + }, +) +## Surrogate model for diffusivity +# +# Forward mapping model is used. +m_CO2_diffusivity = ForwardMappingModel( + _id='diffusivityPol[A=CO2]', + surrogateFunction=f_diffusivity, + substituteModels=[], + parameters=[0.00123, 6156], +) +## Surrogate model for diffusivity +# +# Forward mapping model is used. +m_CyP_diffusivity = ForwardMappingModel( + _id='diffusivityPol[A=CyP]', + surrogateFunction=f_diffusivity, + substituteModels=[], + parameters=[1.7e-7, 4236], +) +## Surrogate model for diffusivity +# +# Forward mapping model is used. +m_N2_diffusivity = ForwardMappingModel( + _id='diffusivityPol[A=N2]', + surrogateFunction=f_diffusivity, + substituteModels=[], + parameters=[0.003235, 6927], +) +## Surrogate model for diffusivity +# +# Forward mapping model is used. +m_O2_diffusivity = ForwardMappingModel( + _id='diffusivityPol[A=O2]', + surrogateFunction=f_diffusivity, + substituteModels=[], + parameters=[0.00085, 6411], +) diff --git a/applications/PUfoam/MoDeNaModels/foamAging/.gitignore b/applications/PUfoam/MoDeNaModels/foamAging/.gitignore new file mode 100644 index 000000000..9bf557699 --- /dev/null +++ b/applications/PUfoam/MoDeNaModels/foamAging/.gitignore @@ -0,0 +1 @@ +degas diff --git a/applications/PUfoam/MoDeNaModels/foamAging/__init__.py b/applications/PUfoam/MoDeNaModels/foamAging/__init__.py new file mode 100644 index 000000000..c431ca824 --- /dev/null +++ b/applications/PUfoam/MoDeNaModels/foamAging/__init__.py @@ -0,0 +1,40 @@ +''' + + ooo ooooo oooooooooo. ooooo ooo + `88. .888' `888' `Y8b `888b. `8' + 888b d'888 .ooooo. 888 888 .ooooo. 8 `88b. 8 .oooo. + 8 Y88. .P 888 d88' `88b 888 888 d88' `88b 8 `88b. 8 `P )88b + 8 `888' 888 888 888 888 888 888ooo888 8 `88b.8 .oP"888 + 8 Y 888 888 888 888 d88' 888 .o 8 `888 d8( 888 + o8o o888o `Y8bod8P' o888bood8P' `Y8bod8P' o8o `8 `Y888""8o + +Copyright + 2014-2015 MoDeNa Consortium, All rights reserved. + +License + This file is part of Modena. + + Modena is free software; you can redistribute it and/or modify it under + the terms of the GNU General Public License as published by the Free + Software Foundation, either version 3 of the License, or (at your option) + any later version. + + Modena is distributed in the hope that it will be useful, but WITHOUT ANY + WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS + FOR A PARTICULAR PURPOSE. See the GNU General Public License + for more details. + + You should have received a copy of the GNU General Public License along + with Modena. If not, see . + +Description + Python library of FireTasks + +Authors + Henrik Rusche + +Contributors +''' + +from foamAging import m + diff --git a/applications/PUfoam/MoDeNaModels/foamAging/foamAging.py b/applications/PUfoam/MoDeNaModels/foamAging/foamAging.py new file mode 100644 index 000000000..0d7ecdc5c --- /dev/null +++ b/applications/PUfoam/MoDeNaModels/foamAging/foamAging.py @@ -0,0 +1,46 @@ +'''@cond + + ooo ooooo oooooooooo. ooooo ooo + `88. .888' `888' `Y8b `888b. `8' + 888b d'888 .ooooo. 888 888 .ooooo. 8 `88b. 8 .oooo. + 8 Y88. .P 888 d88' `88b 888 888 d88' `88b 8 `88b. 8 `P )88b + 8 `888' 888 888 888 888 888 888ooo888 8 `88b.8 .oP"888 + 8 Y 888 888 888 888 d88' 888 .o 8 `888 d8( 888 + o8o o888o `Y8bod8P' o888bood8P' `Y8bod8P' o8o `8 `Y888""8o + +Copyright + 2014-2015 MoDeNa Consortium, All rights reserved. + +License + This file is part of Modena. + + Modena is free software; you can redistribute it and/or modify it under + the terms of the GNU General Public License as published by the Free + Software Foundation, either version 3 of the License, or (at your option) + any later version. + + Modena is distributed in the hope that it will be useful, but WITHOUT ANY + WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS + FOR A PARTICULAR PURPOSE. See the GNU General Public License + for more details. + + You should have received a copy of the GNU General Public License along + with Modena. If not, see . +@endcond''' + +""" +@file +Backward mapping Firetask for Foam ageing model. +Contains path to the detailed model executable. + +@author Pavel Ferkl +@copyright 2014-2015, MoDeNa Project. GNU Public License. +@ingroup app_aging +""" + +import os +from modena.Strategy import BackwardMappingScriptTask + +m = BackwardMappingScriptTask( + script = os.path.dirname(os.path.abspath(__file__))+'/src/degas' +) diff --git a/applications/PUfoam/MoDeNaModels/foamAging/src/CMakeLists.txt b/applications/PUfoam/MoDeNaModels/foamAging/src/CMakeLists.txt new file mode 100644 index 000000000..491f34c89 --- /dev/null +++ b/applications/PUfoam/MoDeNaModels/foamAging/src/CMakeLists.txt @@ -0,0 +1,18 @@ +cmake_minimum_required (VERSION 2.8) +project (tutorialModels C Fortran) + +if( CMAKE_VERSION VERSION_GREATER "3.0" ) + cmake_policy(SET CMP0042 OLD) + cmake_policy(SET CMP0026 OLD) +endif() + +find_package(MODENA REQUIRED) + +include_directories(${MODENA_INCLUDE_DIRS}) +link_directories(${MODENA_LIBRARY_DIRS}) + +set (CMAKE_Fortran_FLAGS "-ffree-line-length-none -O3") +set (CMAKE_Fortran_MODULE_DIRECTORY mod) +file (GLOB _sources RELATIVE ${CMAKE_CURRENT_SOURCE_DIR} src/*.f*) +add_executable(degas ${_sources}) +target_link_libraries(degas MODENA::modena) diff --git a/applications/PUfoam/MoDeNaModels/foamAging/src/src/InOut.f90 b/applications/PUfoam/MoDeNaModels/foamAging/src/src/InOut.f90 new file mode 100644 index 000000000..f8da2e8fd --- /dev/null +++ b/applications/PUfoam/MoDeNaModels/foamAging/src/src/InOut.f90 @@ -0,0 +1,222 @@ +!> @file +!! subroutines for calculation of equivalent conductivity of the foam +!! @author Michal Vonka +!! @author Pavel Ferkl +!! @ingroup foam_aging + +!> reads input file, packs variables to rpar and ipar variables +subroutine input(rpar, ipar) + implicit none +!c + integer i + integer ipar(*) + integer divwall, ncell + integer nroutputs + integer solModel,diffModel + double precision dcell, dwall, L + double precision pressure ! initial conds + double precision pBCair, pBCCO2, pBCpent ! boundary conds + double precision pICair, pICCO2, pICpent ! initial conds + double precision DO2, DN2, DCO2, Dpent, Dair, Dgas + double precision SO2, SN2, SCO2, Spent, Sair + double precision R, T, temp_cond, rhop + double precision pcA, pcB, pcApcB, TcA, TcB, TcATcB + double precision MA, MB, Mterm ,a, b, aToverTcsb + double precision fstrut,rhof +!c + double precision tend + double precision rpar(*) ! real param + + double precision PI + parameter (PI = 3.1415926d0) + parameter (R = 8.314d0) + +!c Read input params - pak module params :) + open(2, file = '../input.in', status = 'old') + read(2, *) nroutputs + read(2, *) divwall + read(2, *) tend + read(2, *) T + read(2, *) temp_cond + read(2, *) rhop + read(2, *) pressure + + read(2, *) pBCair, pBCCO2, pBCpent ! boundaries + read(2, *) pICair, pICCO2, pICpent ! initial C + + read(2, *) L + read(2, *) dwall + read(2, *) dcell + + read(2, *) fstrut + read(2, *) rhof + read(2, *) solModel + read(2, *) Sair,SCO2,Spent + read(2, *) diffModel + read(2, *) Dair,DCO2,Dpent + + close(2) + continue + + ncell = dint(L/(dcell+dwall)) + continue + ! ! computation of diffusivities and solubilities as a function of T + ! DCO2=12.3d-4*dexp(-51180.0d0/R/T)!/1e0 ! m2/s + ! DO2 =8.5d-4* dexp(-53300.0d0/R/T) + ! DN2=3.24d-3*dexp(-6927.0d0/T) + ! Dpent=1.7d-7*dexp(-4236.0d0/T)!/4e2!/2.5d0 + ! Dair=(0.21d0*DO2+0.79d0*DN2)!/3e1 + ! + ! ! cm3STP/cm3/Pa + ! SCO2 = 7.13d-6*T/343.0d0*dexp(-2587.0d0*(1.0d0/343.0d0-1.0d0/T)) + ! Spent = 4.45d-5*T/353.0d0*dexp(-527.45d0*(1.0d0/353.0d0-1.0d0/T)) + ! Sair = -(5.0d-9 * T**2 - 4.0d-6 * T + 0.0007d0)/10 + ! + ! write(*,*) 'CO2 permeability',SCO2*DCO2 + ! write(*,*) 'pentane permeability',Spent*Dpent + ! write(*,*) 'air permeability',Sair*Dair + + continue + ! gas difusivity accoriding to Bird 1975, p.505, eq. 16.3-1 + pcA = 33.5d0 ! N2 + pcB = 72.9d0 ! CO2 + pcApcB = (pcA*pcB)**(1.0d0/3.0d0) ! CO2, N2, B-1 p. 744 + TcA = 126.2d0 ! N2 + TcB = 304.2d0 ! CO2 + TcATcB = (TcA*TcB)**(5.0d0/12.0d0) + MA = 28.02d0 + MB = 44.01d0 + Mterm = dsqrt(1/MA + 1/MB) + a = 2.7450d-4 ! non-polar pairs + b = 1.823d0 + aToverTcsb = a*(T/dsqrt(TcA*TcB))**b + + ! pressure in atmospheres, cm2/s + Dgas = (aToverTcsb*pcApcB*TcATcB*Mterm)*1.0d5/pressure + continue + Dgas = Dgas * 1.0d-4 ! m2/s + continue + + ipar(1) = nroutputs + ipar(2) = ncell + ipar(4) = divwall+1 ! FV in one cell + ipar(5) = (divwall+1)*ncell ! total number of FV + ipar(6:8) = solModel + ipar(9:11) = diffModel + + rpar(1) = dcell + rpar(2) = dwall + rpar(3) = tend + rpar(4) = Dair ! average air + rpar(5) = DCO2 + rpar(6) = Sair ! average air + rpar(7) = SCO2 + + rpar(8) = pressure + ! rpar(9) = initpressure + rpar(10)= R*T + + rpar(11) = Dpent + rpar(12) = Spent + rpar(13) = Dgas + + rpar(14) = pBCair + rpar(15) = pBCCO2 + rpar(16) = pBCpent + + rpar(17) = pICair*pressure + rpar(18) = pICCO2*pressure + rpar(19) = pICpent*pressure + + rpar(20)=fstrut + rpar(21)=rhof + rpar(22)=temp_cond + rpar(23)=rhop + + continue + + return +end subroutine input +!c +!> saves results to file +subroutine output(iprof, time, ystate, neq) + implicit none + integer i, j, iprof, job + integer nFV, onecell, ncell, neq + integer divwall + + double precision time, test + double precision ystate(*) + double precision dwall, dcell, hwall + + double precision pBCair, pBCCO2, pBCpent, RT ! boundary conds + double precision, allocatable :: length(:) + + character(len=1) :: name_1 ! one character + character(len=2) :: name_2 ! two characters + character(len=3) :: name_3 ! three characters + character(len=4) :: name_f ! final name of file + + continue + ! ipar + dcell = ystate(nEQ + 1) + dwall = ystate(nEQ + 2) + ncell = dint(ystate(nEQ + 11)) + onecell = dint(ystate(nEQ + 12)) != dble(ipar(4)) + divwall = onecell-1 + nFV = ncell*onecell + hwall = dwall/dble(divwall) + + pBCair = ystate(nEQ + 16) != rpar(14) != pBCair + pBCCO2 = ystate(nEQ + 17) != rpar(15) != pBCCO2 + pBCpent= ystate(nEQ + 18) != rpar(16) != pBCpent + RT = ystate(nEQ + 10) + + if (.NOT. allocated(length)) then + allocate (length(0:nFV)) + endif + + ! compute lengths + continue + + length(0:nFV) = 0.0d0 + do i = 0, nFV + if (mod(i,onecell).eq.0) length(i) = length(i-1) + dcell/2.0d0 + if (mod(i,onecell).eq.1) length(i) = length(i-1) + dcell/2.0d0 + if (mod(i,onecell).gt.1) length(i) = length(i-1) + hwall + enddo + +! continue +! write(*,*) length(1:nFV) + continue + + if (iprof < 10) then + write(name_1,'(I1)') iprof + name_f = '000' // name_1 + elseif (iprof >= 10 .and. iprof < 100) then + write(name_2,'(I2)') iprof + name_f = '00' // name_2 + elseif (iprof >= 100 .and. iprof < 1000) then + write(name_3,'(I3)') iprof + name_f = '0' // name_3 + else + write(name_f,'(I4)') iprof + endif + + continue + open(unit=11,file='../results/H2perm_'//trim(name_f)//'.dat') + + ! BC + write (11,100) time/(3600.0d0*24.0d0),length(0), pBCair/RT,pBCCO2/RT,& + pBCpent/RT + ! profiles + do i = 1, nFV + write (11,100) time/(3600.0d0*24.0d0),length(i),ystate(i),& + ystate(nFV+i),ystate(2*nFV+i) + enddo + continue + close (11) + return +100 format (f8.2,F12.8,F12.6,F12.6,F12.6) +end subroutine output +!c diff --git a/applications/PUfoam/MoDeNaModels/foamAging/src/src/conductivity.f90 b/applications/PUfoam/MoDeNaModels/foamAging/src/src/conductivity.f90 new file mode 100644 index 000000000..db041b7a2 --- /dev/null +++ b/applications/PUfoam/MoDeNaModels/foamAging/src/src/conductivity.f90 @@ -0,0 +1,243 @@ +!> @file +!! subroutines for calculation of equivalent conductivity of the foam +!! using Modena calls +!! @author Pavel Ferkl +!! @ingroup foam_aging +module conductivity + use constants + use fmodena + use physicalProperties + implicit none + integer :: gasModel=3 + private + public equcond +contains +!********************************BEGINNING************************************* +!> determine equivalent conductivity of the foam +subroutine equcond(keq,ystate,neq,eps,fstrut,temp) + real(dp), intent(out) :: keq + real(dp), dimension(:), intent(in) :: ystate + integer, intent(in) :: neq + real(dp), intent(in) :: temp,eps,fstrut + real(dp) :: dcell,ccd,cair,ccyp,xcd,xair,xcyp,kgas + real(dp), dimension(4) :: kg,yg,cpg + integer :: i,ncell,onecell,nFV + dcell = ystate(nEQ + 1 ) + ncell = int(ystate(nEQ + 11)) + onecell = int(ystate(nEQ + 12)) != dble(ipar(4)) + nFV = onecell*ncell + !calculate average concentrations + ccd=0 + cair=0 + ccyp=0 + do i=1,ncell + cair=cair+ystate(i*onecell) + ccd=ccd+ystate(nFV+i*onecell) + ccyp=ccyp+ystate(2*nFV+i*onecell) + enddo + cair=cair/ncell + ccd=ccd/ncell + ccyp=ccyp/ncell + xair=cair/(cair+ccd+ccyp) + xcd=ccd/(cair+ccd+ccyp) + xcyp=ccyp/(cair+ccd+ccyp) + kg(1)=cdConductivity(temp) + kg(2)=nitrConductivity(temp) + kg(3)=oxyConductivity(temp) + kg(4)=cypConductivity(temp) + yg=(/xcd,0.79_dp*xair,0.21_dp*xair,xcyp/) + ! yg=(/0.0_dp,0.79_dp*0.5_dp,0.21_dp*0.5_dp,0.5_dp/) + cpg(1)=cdHeatCapacity(temp) + cpg(2)=nitrHeatCapacity(temp) + cpg(3)=oxyHeatCapacity(temp) + cpg(4)=cypHeatCapacity(temp) + select case(gasModel) ! determine conductivity of gas mixture + case (1) + kgas = weightedAverage(kg,yg) + case (2) + kgas = extWassiljewa(kg,yg,Tc,pc,Mg,temp,1._dp) + case (3) + kgas = lindsayBromley(kg,yg,Tb,cpg,Mg,temp) + case (4) + kgas = pandeyPrajapati(kg,yg,Tb,Mg,temp) + case default + stop 'unknown gas conductivity model' + end select + ! write(*,*) yg + ! write(*,*) kg + ! write(*,*) "kgas: ", kgas + ! stop + call modena_inputs_set(kfoamInputs, kfoamEpspos, eps) + call modena_inputs_set(kfoamInputs, kfoamDcellpos, dcell) + call modena_inputs_set(kfoamInputs, kfoamFstrutpos, fstrut) + call modena_inputs_set(kfoamInputs, kfoamKgaspos, kgas) + call modena_inputs_set(kfoamInputs, kfoamTemppos, temp) + ret = modena_model_call (kfoamModena, kfoamInputs, kfoamOutputs) + if (modena_error_occurred()) then + call exit(modena_error()) + endif + keq = modena_outputs_get(kfoamOutputs, 0_c_size_t); !fetch results +end subroutine equcond +!***********************************END**************************************** + + +!********************************BEGINNING************************************* +!> determine thermal conductivity of a mixture +!! simple weighted average +real(dp) function weightedAverage(k,yin) result(kmix) + real(dp), dimension(:), intent(in) :: k !thermal conductivities + real(dp), dimension(:), intent(in) :: yin !molar fractions + integer :: n,i,j + real(dp), dimension(:), allocatable :: y + n=size(k) + allocate(y(n)) + y=yin + if (minval(y)<0) stop 'Input molar fractions to weightedAverage & + cannot be negative.' + y=y/sum(y) + kmix=0 + do i=1,size(k) + kmix=kmix+yin(i)*k(i) + enddo +end function weightedAverage +!***********************************END**************************************** + + +!********************************BEGINNING************************************* +!> determine thermal conductivity of a mixture +!! extended Wassiljewa model, parameters calculated according to Mason and Saxena +!! [link](http://dx.doi.org/10.1016/j.fluid.2007.07.059) +real(dp) function extWassiljewa(k,yin,Tc,pc,M,T,eps) result(kmix) + real(dp), dimension(:), intent(in) :: k !thermal conductivities + real(dp), dimension(:), intent(in) :: yin !molar fractions + real(dp), dimension(:), intent(in) :: Tc !critical temperatures + real(dp), dimension(:), intent(in) :: pc !critical pressures + real(dp), dimension(:), intent(in) :: M !molar masses + real(dp), intent(in) :: T !temperature + real(dp), intent(in) :: eps !parameter close to one + integer :: n,i,j + real(dp) :: x + real(dp), dimension(:), allocatable :: gam,y + real(dp), dimension(:,:), allocatable :: ktr,A + n=size(k) + allocate(y(n),gam(n),ktr(n,n),A(n,n)) + y=yin + if (minval(y)<0) stop 'Input molar fractions to extWassiljewa & + cannot be negative.' + y=y/sum(y) + gam=210*(Tc*M**3/pc**4)**(1/6._dp) + do i=1,n + do j=1,n + ktr(i,j)=gam(j)*(exp(0.0464_dp*T/Tc(i))-exp(-0.2412_dp*T/Tc(i)))/& + gam(i)/(exp(0.0464_dp*T/Tc(j))-exp(-0.2412_dp*T/Tc(j))) + A(i,j)=eps*(1+sqrt(ktr(i,j))*(M(i)/M(j))**0.25_dp)**2/& + sqrt(8*(1+M(i)/M(j))) + enddo + enddo + kmix=0 + do i=1,n + x=0 + do j=1,n + x=x+y(j)*A(i,j) + enddo + kmix=kmix+y(i)*k(i)/x + enddo +end function extWassiljewa +!***********************************END**************************************** + + +!********************************BEGINNING************************************* +!> determine thermal conductivity of a mixture +!! Lindsay-Bromley model +!! see [link](http://dx.doi.org/10.1021/ie50488a017) +real(dp) function lindsayBromley(k,yin,Tb,cp,M,T) result(kmix) + real(dp), dimension(:), intent(in) :: & + k,& !thermal conductivities + yin,& !molar fractions + Tb,& !boiling point temperatures + cp,& !thermal capacities at constant pressure + M !molar masses + real(dp), intent(in) :: & + T !temperature + integer :: n,i,j + real(dp) :: x + real(dp), dimension(:), allocatable :: & + y,& !molar fractions + S,& !Sutherland constants + gam,& !heat capacity ratio + cv !thermal capacities at constant volume + real(dp), dimension(:,:), allocatable :: A + n=size(k) + allocate(y(n),cv(n),S(n),gam(n),A(n,n)) + y=yin + if (minval(y)<0) stop 'Input molar fractions to extWassiljewa & + cannot be negative.' + y=y/sum(y) + do i=1,n + S(i)=1.5_dp*Tb(i) + enddo + cv=cp-Rg !ideal gas assumed + gam=cp/cv + do i=1,n + do j=1,n + x=k(i)/k(j)*cp(j)/cp(i)*(9-5/gam(j))/(9-5/gam(i)) + A(i,j)=0.25_dp*(1+sqrt(x*(M(j)/M(i))**0.75_dp*(T+S(i))/(T+S(j))))**2*& + (T+sqrt(S(i)*S(j)))/(T+S(j)) + enddo + enddo + kmix=0 + do i=1,n + x=0 + do j=1,n + x=x+y(j)*A(i,j) + enddo + kmix=kmix+y(i)*k(i)/x + enddo +end function lindsayBromley +!***********************************END**************************************** + + +!********************************BEGINNING************************************* +!> determine thermal conductivity of a mixture +!! Pandey-Prajapati model +!! see [link](http://www.new1.dli.ernet.in/data1/upload/insa/INSA_1/20005baf_372.pdf) +real(dp) function pandeyPrajapati(k,yin,Tb,M,T) result(kmix) + real(dp), dimension(:), intent(in) :: & + k,& !thermal conductivities + yin,& !molar fractions + Tb,& !boiling point temperatures + M !molar masses + real(dp), intent(in) :: & + T !temperature + integer :: n,i,j + real(dp) :: x + real(dp), dimension(:), allocatable :: & + y,& !molar fractions + S !Sutherland constants + real(dp), dimension(:,:), allocatable :: A + n=size(k) + allocate(y(n),S(n),A(n,n)) + y=yin + if (minval(y)<0) stop 'Input molar fractions to extWassiljewa & + cannot be negative.' + y=y/sum(y) + do i=1,n + S(i)=1.5_dp*Tb(i) + enddo + do i=1,n + do j=1,n + A(i,j)=0.25_dp*(1+sqrt(k(i)/k(j)*(M(i)/M(j))**0.25_dp*& + (T+S(i))/(T+S(j))))**2*(T+sqrt(S(i)*S(j)))/(T+S(j)) + enddo + enddo + kmix=0 + do i=1,n + x=0 + do j=1,n + x=x+y(j)*A(i,j) + enddo + kmix=kmix+y(i)*k(i)/x + enddo +end function pandeyPrajapati +!***********************************END**************************************** +end module conductivity diff --git a/applications/PUfoam/MoDeNaModels/foamAging/src/src/constants.f90 b/applications/PUfoam/MoDeNaModels/foamAging/src/src/constants.f90 new file mode 100644 index 000000000..051ddc8d7 --- /dev/null +++ b/applications/PUfoam/MoDeNaModels/foamAging/src/src/constants.f90 @@ -0,0 +1,26 @@ +!> @file +!! stores parameters and commonly used variables as globals +!! @author Pavel Ferkl +!! @ingroup foam_aging +module constants + use,intrinsic :: iso_fortran_env, only: dp => real64 + implicit none + real(dp), parameter :: & + pi=3.1415926535897932384626433832795028841971693993751058209749445923& + &078164062862089986280348253421170679_dp,& ! @file +!! i/o utilities +!! @author Pavel Ferkl +!! @ingroup foam_cond +module ioutils + implicit none + private + public newunit,str +contains +!********************************BEGINNING************************************* +!> returns lowest i/o unit number not in use +integer function newunit(unit) result(n) + integer, intent(out), optional :: unit + logical inuse + integer, parameter :: & + nmin=123,& ! avoid lower numbers which are sometimes reserved + nmax=999 ! may be system-dependent + do n = nmin, nmax + inquire(unit=n, opened=inuse) + if (.not. inuse) then + if (present(unit)) unit=n + return + end if + end do + write(*,*) "newunit ERROR: available unit not found." + stop +end function newunit +!***********************************END**************************************** + + + +!********************************BEGINNING************************************* +!> converts integer to string +function str(k) + character(len=20) :: str + integer, intent(in) :: k + write (str, *) k + str = adjustl(str) +end function str +!***********************************END**************************************** +end module ioutils diff --git a/applications/PUfoam/MoDeNaModels/foamAging/src/src/main.f90 b/applications/PUfoam/MoDeNaModels/foamAging/src/src/main.f90 new file mode 100644 index 000000000..cbc6592a8 --- /dev/null +++ b/applications/PUfoam/MoDeNaModels/foamAging/src/src/main.f90 @@ -0,0 +1,252 @@ +!> @file +!! Calculate dynamics diffusion in the foam structure. +!! @author Michal Vonka +!! @author Pavel Ferkl +!! @ingroup foam_aging +!c 30.5.2012 - MV (michal.vonka@seznam.cz) +!c 2.7.2012 - MV, remaking to partial pressures of H2 and N2 +!c 6.3.2015 - MV, application to PU foams solved by CO2 penetrating air +! 3.4.2015 PF (pavel.ferkl@vscht.cz), calculation of conductivity +program foam_diffusion + use conductivity + use physicalProperties + use ioutils + use constants + implicit none + integer ipar(20) + + integer nroutputs, multiplicator + + double precision rpar(23) + + integer :: itol, itask, istate, iopt + integer :: MF, ML, MU, LRW, LIW, LENRAT, NNZ, LWM + integer :: nFV, nEQ + integer :: i, counter, fi + integer, allocatable :: IWORK(:) + + double precision :: tin, tout, tend, keq + double precision :: rtol, atol + + double precision, allocatable :: ystate(:), yprime(:) ! vector of state + double precision, allocatable :: RWORK(:) + + real(dp) :: temp,temp_cond + real(dp) :: fstrut + real(dp) :: rhof + real(dp), dimension(3) :: x0 + real(dp) :: eps + real(dp) :: rhop + real(dp) :: ccyp + + external modelPU, jdem +!c +!c --------------------------------------------------------------------- +!c + call createModels + write(*,*) cdConductivity(300._dp) + write(*,*) airConductivity(300._dp) + write(*,*) cypConductivity(300._dp) + write(*,*) gasConductivity(300._dp,1._dp,0._dp,0._dp) + stop + call input(rpar, ipar) + temp=rpar(10)/8.314d0 + nroutputs = ipar(1) + nFV = ipar(5) != (divwall+1)*ncell ! total number of FV + nEQ = 3*nFV + solModel=ipar(6:8) + diffModel = ipar(9:11) +! ----------------------------------- +! find out physical properties +! ----------------------------------- + call createModels + fstrut=rpar(20) + rhof=rpar(21) + rhop=rpar(23) + eps=1-rhof/rhop + temp_cond=rpar(22) + if (ipar(6)==1) then + rpar(6)=airSolubility(temp) + endif + if (ipar(7)==1) then + rpar(7)=cdSolubility(temp) + endif + if (ipar(8)==1) then + rpar(12)=cypSolubility(temp) + endif + if (ipar(9)==1) then + rpar(4)=airDiffusivity(temp) + endif + if (ipar(10)==1) then + rpar(5)=cdDiffusivity(temp) + endif + if (ipar(11)==1) then + rpar(11)=cypDiffusivity(temp) + endif + write(*,*) 'air permeability',rpar(6)*rpar(4) + write(*,*) 'CO2 permeability',rpar(7)*rpar(5) + write(*,*) 'pentane permeability',rpar(12)*rpar(11) +!c ----------------------------------- +!c Allocate memory for working arrays +!c ----------------------------------- + LENRAT = 2 ! usually for double precision + NNZ = 1000*nEQ ! nonzero elements - MV CHECK + LWM = 2*NNZ + 2*NEQ + (NNZ+10*NEQ)/LENRAT ! MITER = 2 + LIW = 31 + NEQ + NNZ +100 + LRW = 20 + (2 + 1./LENRAT)*NNZ + (11 + 9./LENRAT)*NEQ + mf = 222 ! 222 stiff, internally generated jacobi matrix + ! 10 'normal' - chage the allocation to smaller fields + ! 210 structure obtained NEQ+1 calls, implicit Adams, +!c ----------------------------------- +!c Allocate memory for working arrays +!c ----------------------------------- + allocate( ystate(1:nEQ + 20) ) + allocate( yprime(1:nEQ) ) + allocate( rwork (1:LRW) ) + allocate( iwork (1:LIW) ) +!c ---------------------------------- +!c pack ystate +!c ---------------------------------- + ystate(nEQ + 1 ) = rpar(1) != dcell + ystate(nEQ + 2 ) = rpar(2) != dwall + ystate(nEQ + 3 ) = rpar(3) != tend + ystate(nEQ + 4 ) = rpar(4) != 0.21d0*DO2+0.79d0*DN2 ! average air + ystate(nEQ + 5 ) = rpar(5) != DCO2 + ystate(nEQ + 6 ) = rpar(6) != 0.21d0*SO2+0.79d0*SN2 ! average air + ystate(nEQ + 7 ) = rpar(7) != SCO2 + ystate(nEQ + 8 ) = rpar(8) != pressure + ! ystate(nEQ + 9 ) = rpar(9) != initpressure + ystate(nEQ + 10) = rpar(10)!= R*T + ystate(nEQ + 11) = dble(ipar(2))! ncell + ystate(nEQ + 12) = dble(ipar(4)) ! onecell + ystate(nEQ + 13) = rpar(11) != Dpent + ystate(nEQ + 14) = rpar(12) != Spent + ystate(nEQ + 15) = rpar(13) != Dgas + + ystate(nEQ + 16) = rpar(14) != pBCair + ystate(nEQ + 17) = rpar(15) != pBCCO2 + ystate(nEQ + 18) = rpar(16) != pBCpent +!c ---------------------------------- +! initial conditions +!c ---------------------------------- + call initfield(ystate, nFV, nEQ, rpar) + +!c ---------------------------------- +! initialize integration +!c ---------------------------------- + open(10,file='dcmp_progress.out', status='unknown') + tend = rpar(3) + counter = 1 + itol = 1 + rtol = 1.0d-6 + atol = 1.0d-6 + + itask = 1 + istate = 1 + iopt = 0 + + multiplicator = 100 +!c ---------------------------------- +!c Integration loop +!c ---------------------------------- + + continue + open (newunit(fi),file='../results/keq_time.out') + write(fi,'(10A23)') '#time', 'eq.conductivity' +! call output(0, 0.0_dp, ystate, neq) + call equcond(keq,ystate,neq,eps,fstrut,temp_cond) + write(fi,'(10es23.15)') 0.0_dp,keq + do i = 1, nroutputs*multiplicator ! stabilizing multiplicator + + tin = dble(i-1)*(tend )/dble(nroutputs*multiplicator) ! tbeg is 0 + tout = dble(i )*(tend)/dble(nroutputs*multiplicator) + +100 continue ! try to make another run for the initial step simulation + call dlsodes (modelPU, neq, ystate, tin, tout, itol, rtol, atol, itask,& + istate, iopt, rwork, lrw, iwork, liw, jdem, mf) + + ! evaluating the integration + if (istate.lt.0) then + write(*,*) 'Something is wrong, look for ISTATE =', istate + if (istate.eq.-1) then ! not enough steps to reach tout + istate = 1 + iopt = 1 ! start to change something + RWORK(5:8)=0.0d0 + IWORK(5) = 0 + IWORK(6) = counter*1000 + IWORK(7) = 0 + counter = counter + 1 + write(*,*) 'MAXSTEP', IWORK(6) + write(10,*) 'MAXSTEP', IWORK(6) + goto 100 + continue + endif + elseif (counter>3) then + counter=counter-1 + IWORK(6) = counter*1000 + write(*,*) 'MAXSTEP', IWORK(6) + write(10,*) 'MAXSTEP', IWORK(6) + endif + ! some output + if (mod(i,multiplicator).eq.0) then + write(*,*) 'tend', tout/(3600.0d0*24.0d0),'days' + write(10,*) 'tend', tout/(3600.0d0*24.0d0),'days' + call output(i/multiplicator, tout, ystate, neq) + call equcond(keq,ystate,neq,eps,fstrut,temp_cond) + write(fi,'(10es23.15)') tout,keq + endif + continue + enddo +!c ---------------------------------- + close(10) + close(fi) +! +!c ------------------ +!c Deallocate memory +!c ------------------ +!c + deallocate (ystate) + deallocate (yprime) + deallocate (rwork) + deallocate (iwork) +!c + stop + + end + + subroutine initfield(ystate, nFV, nEQ, rpar) + implicit none + + integer i, onecell, nFV, nEQ + double precision pBCair, pBCCO2, pBCpent, RT, pressure + double precision pICair, pICCO2, pICpent + double precision Sair, SCO2, Spent + double precision ystate(*), rpar(*) + + !ncell = dint(ystate(nEQ + 11)) + onecell = dint(ystate(nEQ + 12)) != dble(ipar(4)) + + RT = ystate(nEQ + 10) != rpar(10)!= RT + + Spent = rpar(12) != Spent + Sair = rpar(6) != 0.21d0*SO2+0.79d0*SN2 ! average air + SCO2 = rpar(7) != SCO2 + pressure = rpar(8) != + + pICair = rpar(17) + pICCO2 = rpar(18) + pICpent= rpar(19) + continue + + do i = 1, nFV + if (mod(i,onecell).eq.0) then ! initial concentration in cells + ystate(i ) = pICair /RT + ystate(i+ nFV) = pICCO2 /RT + ystate(i+2*nFV) = pICpent/RT + else ! initial concentration in walls + ystate(i ) = pICair /RT * Sair * pressure + ystate(i+ nFV) = pICCO2 /RT * SCO2 * pressure + ystate(i+2*nFV) = pICpent/RT * Spent* pressure + endif + enddo + end subroutine diff --git a/applications/PUfoam/MoDeNaModels/foamAging/src/src/model.f90 b/applications/PUfoam/MoDeNaModels/foamAging/src/src/model.f90 new file mode 100644 index 000000000..60e5f1e44 --- /dev/null +++ b/applications/PUfoam/MoDeNaModels/foamAging/src/src/model.f90 @@ -0,0 +1,278 @@ +!> @file +!! Main algorithm of for diffusion of gases in the foam. +!! @author Michal Vonka +!! @author Pavel Ferkl +!! @ingroup foam_aging + +!******************************************************************************************* +!0 pointer allocated, +!> model supplied to the integrator +subroutine modelPU(neq, time, ystate, yprime) ! ODEPACK call +! 12/07/23 - change of model to describe diffusion on H2 and N2 throug PS, wall +! is discretized into finite elements, pressure in cell is in equilibrium to the +! pressure on the wall, solubility given by Henry's law cpol = H*cgas +! - not ordinary definition of H but the definition of H fits +! !!!this model is for filling the foam +! 2015/03/12 change in model with respect to ODEPACK calling +! michal.vonka@seznam.cz + implicit none + integer neq ! = 1 (X-direction) + + double precision :: time + double precision :: ystate(*) ! + double precision :: yprime(*) ! + + integer i, j + integer job + integer nFV, onecell, ncell + + double precision Dair, DCO2, Dpent ! difusivities in polymer + double precision Sair, SCO2, Spent ! solubilities + double precision HHair, HHCO2, HHpent ! henry law cPOL = S*p*cGAS = H*cGAS + double precision D ! diffusivity in gas + double precision pBCair, pBCCO2, pBCpent ! boundary conds + + double precision dcell, dwall, hwall + double precision cwg + double precision RT, pressure + + double precision, allocatable :: cAIR(:) , cCO2(:), cPENT(:) !concentrations + double precision, allocatable :: dcAIR(:), dcCO2(:), dcPENT(:) ! changes of partial pressures + double precision, allocatable :: jAIR(:) , jCO2(:),jPENT(:) ! fluxes in x, dir + + !c + dcell = ystate(nEQ + 1 ) + dwall = ystate(nEQ + 2 ) + !tend = ystate(nEQ + 3 ) + Dair = ystate(nEQ + 4 ) != rpar(4) != Dair average air + DCO2 = ystate(nEQ + 5 ) != rpar(5) != DCO2 + Sair = ystate(nEQ + 6 ) != rpar(6) ! Sair + SCO2 = ystate(nEQ + 7 ) != rpar(7) != SCO2 + pressure= ystate(nEQ + 8 ) != rpar(8) != pressure + !ystate(nEQ + 9 ) = rpar(9) != initpressure + RT = ystate(nEQ + 10) != rpar(10)!= R*T + + ncell = dint(ystate(nEQ + 11)) + onecell = dint(ystate(nEQ + 12)) != dble(ipar(4)) + + Dpent = ystate(nEQ + 13) + Spent = ystate(nEQ + 14) + + D = ystate(nEQ + 15) ! = rpar(13) != Dgas = 2.0d-5 ! + nFV = onecell*ncell + + ! boundary conditions + + pBCair = ystate(nEQ + 16) != rpar(14) != pBCair + pBCCO2 = ystate(nEQ + 17) != rpar(15) != pBCCO2 + pBCpent= ystate(nEQ + 18) != rpar(16) != pBCpent + + continue + !c + !c ------------------------------------------------------------ + !c + if (.NOT. allocated(cAIR)) then + allocate ( cAIR(0:nFV)) + allocate (dcAIR(1:nFV)) + allocate (jAIR (0:nFV)) + allocate ( cCO2(0:nFV)) + allocate (dcCO2(1:nFV)) + allocate (jCO2 (0:nFV)) ! fluxes + allocate ( cPENT(0:nFV)) + allocate (dcPENT(1:nFV)) + allocate (jPENT (0:nFV)) + endif + + !c zero fluxes + jAIR(0:nFV) = 0.0d0 + jCO2(0:nFV) = 0.0d0 + jPENT(0:nFV) = 0.0d0 + + dcAIR(1:nFV) = 0.0d0 + dcCO2(1:nFV) = 0.0d0 + dcPENT(1:nFV) = 0.0d0 + !c unpack state vars + job = 1 + + cAIR(1:nFV) = ystate(1:nFV) + cCO2(1:nFV) = ystate(nFV+1:2*nFV) + cPENT(1:nFV) = ystate(2*nFV+1:3*nFV) + !c ************************************************************************ + !c + + hwall = dwall/dfloat(onecell-1) ! size of FV in wall, ocell-1 elements in wall + + !c + !c ************************************************************************ + !c Diffusion of AIR + !c + cAIR(0) = pBCair/RT !pressure/RT ! boudary condition + do j = 0, nFV-1 + if (mod(j,onecell).eq.0) then ! from gas to polymer + HHair = cAIR(j)*RT*Sair ! H = p * S + cwg = (D*hwall*cAIR(j) + Dair*dcell*cAIR(j+1))/(D*hwall+Dair*dcell*HHair) + jAIR(j) = D*(cAIR(j)-cwg)/dcell*2.0d0 + continue + endif + if ((mod(j,onecell).ne.0).and.(mod(j,onecell).ne.(onecell-1))) then ! through polymer + jAIR(j) = Dair*(cAIR(j)-cAIR(j+1))/hwall ! j = D*(Left-Right)/h = - D*(Right-Left)/h + continue + endif + if (mod(j,onecell).eq.(onecell-1)) then ! to gas in cell + HHair = cAIR(j+1)*RT*Sair ! H = p * S, p = c(in next cell)* RT + cwg= (Dair*dcell*cAIR(j)+D*hwall*cAIR(j+1))/(Dair*HHair*dcell+D*hwall) + jAIR(j) = D*(cwg-cAIR(j+1))/dcell*2.0d0 + continue + endif + enddo + jAIR(nFV) = 0.0d0 ! last cell, zero flux + continue + + ! + !c BALANCES AIR + do j = 1, nFV + if (mod(j,onecell).eq.0) then ! balance in cells + dcAIR(j) = (jAIR(j-1) - jAIR(j))/dcell + else ! balance in walls + dcAIR(j) = (jAIR(j-1) - jAIR(j))/hwall + endif + enddo + ! save into the yprime + yprime(1:nFV) = dcAIR(1:nFV) + + !c ************************************************************************ + !!c Diffusion of CO2 + !! + cCO2(0) = pBCCO2/RT ! boudary condition + do j = 0, nFV-1 + if (mod(j,onecell).eq.0) then ! from gas to polymer + HHCO2 = cCO2(j)*RT*SCO2 ! H = p * S + cwg = (D*hwall*cCO2(j) + DCO2*dcell*cCO2(j+1))/(D*hwall+DCO2*dcell*HHCO2) + jCO2(j) = D*(cCO2(j)-cwg)/dcell*2.0d0 + continue + endif + if ((mod(j,onecell).ne.0).and.(mod(j,onecell).ne.(onecell-1))) then ! through polymer + jCO2(j) = DCO2*(cCO2(j)-cCO2(j+1))/hwall ! j = D*(Left-Right)/h = - D*(Right-Left)/h + continue + endif + if (mod(j,onecell).eq.(onecell-1)) then ! to gas in cell + HHCO2 = cCO2(j+1)*RT*SCO2 ! H = p * S, p = c(in next cell)* RT + cwg= (DCO2*dcell*cCO2(j)+D*hwall*cCO2(j+1))/(DCO2*HHCO2*dcell+D*hwall) + jCO2(j) = D*(cwg-cCO2(j+1))/dcell*2.0d0 + continue + endif + enddo + jCO2(nFV) = 0.0d0 ! last cell, zero flux + continue + + ! + !c BALANCES AIR + do j = 1, nFV + if (mod(j,onecell).eq.0) then ! balance in cells + dcCO2(j) = (jCO2(j-1) - jCO2(j))/dcell + else ! balance in walls + dcCO2(j) = (jCO2(j-1) - jCO2(j))/hwall + endif + enddo + ! save into the yprime + yprime(nFV+1:2*nFV) = dcCO2(1:nFV) + + + !c + !c ************************************************************************ + !c Diffusion of PENTANE + !c + cPENT(0) = pBCpent/RT ! boudary condition + do j = 0, nFV-1 + if (mod(j,onecell).eq.0) then ! from gas to polymer + HHpent = cPENT(j)*RT*Spent ! H = p * S + cwg = (D*hwall*cPENT(j) + Dpent*dcell*cPENT(j+1))/(D*hwall+Dpent*dcell*HHpent) + jPENT(j) = D*(cPENT(j)-cwg)/dcell*2.0d0 + continue + endif + if ((mod(j,onecell).ne.0).and.(mod(j,onecell).ne.(onecell-1))) then ! through polymer + jPENT(j) = Dpent*(cPENT(j)-cPENT(j+1))/hwall ! j = D*(Left-Right)/h = - D*(Right-Left)/h + continue + endif + if (mod(j,onecell).eq.(onecell-1)) then ! to gas in cell + HHpent = cPENT(j+1)*RT*Spent ! H = p * S, p = c(in next cell)* RT + cwg= (Dpent*dcell*cPENT(j)+D*hwall*cPENT(j+1))/(Dpent*HHpent*dcell+D*hwall) + jPENT(j) = D*(cwg-cPENT(j+1))/dcell*2.0d0 + continue + endif + enddo + jPENT(nFV) = 0.0d0 ! last cell, zero flux + continue + + ! + !c BALANCES PENTANE + do j = 1, nFV + if (mod(j,onecell).eq.0) then ! balance in cells + dcPENT(j) = (jPENT(j-1) - jPENT(j))/dcell + else ! balance in walls + dcPENT(j) = (jPENT(j-1) - jPENT(j))/hwall + endif + enddo + ! save into the yprime + yprime(2*nFV+1:3*nFV) = dcPENT(1:nFV) + + continue +return +end + + +subroutine jdem (neq, t, y, j, ia, ja, pdj) +!----------------------------------------------------------------------- +! Should introduce own sparcity model, must fill +! be careful about mf for ODE pack +!----------------------------------------------------------------------- +! +integer neq, j, ia, ja +double precision t, y, pdj +dimension y(neq), ia(*), ja(*), pdj(neq) + +return +end + +!do j = 1, ncell ! more complex structure +! !c ! CONTINUITY OF FLUXES on wall gas/polymer - expressed by henry s law on side of gas +! cwg = (Dair*dcell*cAIR((j-1)*(onecell)+1) + D*hwall*cAIR((j-1)*(onecell) ))/(D*hwall+Dair*dcell*HHair) +! !c +! !c ! flux through the gas and wall - constant flux +! !c ! flux_intensity = D * (LEFT-RIGHT) +! jAIR((j-1)*(onecell)) = D*(cAIR((j-1)*(onecell)) - cwg)/(dcell/2.0d0) +! +! !c diffusion through the wall +! do i = 1, onecell-2 ! fluxes through the wall +! jAIR((j-1)*(onecell)+i) = & +! Dair/hwall * (cAIR((j-1)*(onecell) + i) & +! - cAIR((j-1)*(onecell) + i+1)) +!! write(*,*) (j-1)*(onecell) +!! continue +! enddo +! !c ! CONTINUITY OF FLUXES on wall polymer/gas, GAS SIDE +! cwg = (Dair *dcell*cAIR((j-1)*onecell+(onecell-1)) & +! + D* hwall*cAIR((j-1)*onecell+(onecell ))) & +! /(D*hwall+Dair*dcell*HHair) +! !c +! jAIR((j-1)*onecell+(onecell-1))=Dair*(cAIR((j-1)*onecell+(onecell-1)) & +! - cwg*HHair) /(hwall / 2.0d0) +!enddo + +!jAIR(nFV) = 0.0d0 ! last cell, zero flux +!continue + +!c balances in walls +!do j = 1, ncell +! do i = 1, onecell-1 +! dcAIR((j-1)*onecell+i) = (jAIR((j-1)*onecell + i-1) & +! - jAIR((j-1)*onecell + i ))/hwall +! enddo +!enddo +!continue +!!c +!!c ballance of the cells +!do j = 1, ncell +! dcAIR((j-1)*onecell + onecell) = (jAIR((j-1)*onecell + onecell-1) & +! - jAIR((j-1)*onecell+onecell))/dcell +!enddo diff --git a/applications/PUfoam/MoDeNaModels/foamAging/src/src/odepack.f b/applications/PUfoam/MoDeNaModels/foamAging/src/src/odepack.f new file mode 100644 index 000000000..4278052b5 --- /dev/null +++ b/applications/PUfoam/MoDeNaModels/foamAging/src/src/odepack.f @@ -0,0 +1,16587 @@ +*DECK DLSODE + SUBROUTINE DLSODE (F, NEQ, Y, T, TOUT, ITOL, RTOL, ATOL, ITASK, + 1 ISTATE, IOPT, RWORK, LRW, IWORK, LIW, JAC, MF) + EXTERNAL F, JAC + INTEGER NEQ, ITOL, ITASK, ISTATE, IOPT, LRW, IWORK, LIW, MF + DOUBLE PRECISION Y, T, TOUT, RTOL, ATOL, RWORK + DIMENSION NEQ(*), Y(*), RTOL(*), ATOL(*), RWORK(LRW), IWORK(LIW) +C***BEGIN PROLOGUE DLSODE +C***PURPOSE Livermore Solver for Ordinary Differential Equations. +C DLSODE solves the initial-value problem for stiff or +C nonstiff systems of first-order ODE's, +C dy/dt = f(t,y), or, in component form, +C dy(i)/dt = f(i) = f(i,t,y(1),y(2),...,y(N)), i=1,...,N. +C***CATEGORY I1A +C***TYPE DOUBLE PRECISION (SLSODE-S, DLSODE-D) +C***KEYWORDS ORDINARY DIFFERENTIAL EQUATIONS, INITIAL VALUE PROBLEM, +C STIFF, NONSTIFF +C***AUTHOR Hindmarsh, Alan C., (LLNL) +C Center for Applied Scientific Computing, L-561 +C Lawrence Livermore National Laboratory +C Livermore, CA 94551. +C***DESCRIPTION +C +C NOTE: The "Usage" and "Arguments" sections treat only a subset of +C available options, in condensed fashion. The options +C covered and the information supplied will support most +C standard uses of DLSODE. +C +C For more sophisticated uses, full details on all options are +C given in the concluding section, headed "Long Description." +C A synopsis of the DLSODE Long Description is provided at the +C beginning of that section; general topics covered are: +C - Elements of the call sequence; optional input and output +C - Optional supplemental routines in the DLSODE package +C - internal COMMON block +C +C *Usage: +C Communication between the user and the DLSODE package, for normal +C situations, is summarized here. This summary describes a subset +C of the available options. See "Long Description" for complete +C details, including optional communication, nonstandard options, +C and instructions for special situations. +C +C A sample program is given in the "Examples" section. +C +C Refer to the argument descriptions for the definitions of the +C quantities that appear in the following sample declarations. +C +C For MF = 10, +C PARAMETER (LRW = 20 + 16*NEQ, LIW = 20) +C For MF = 21 or 22, +C PARAMETER (LRW = 22 + 9*NEQ + NEQ**2, LIW = 20 + NEQ) +C For MF = 24 or 25, +C PARAMETER (LRW = 22 + 10*NEQ + (2*ML+MU)*NEQ, +C * LIW = 20 + NEQ) +C +C EXTERNAL F, JAC +C INTEGER NEQ, ITOL, ITASK, ISTATE, IOPT, LRW, IWORK(LIW), +C * LIW, MF +C DOUBLE PRECISION Y(NEQ), T, TOUT, RTOL, ATOL(ntol), RWORK(LRW) +C +C CALL DLSODE (F, NEQ, Y, T, TOUT, ITOL, RTOL, ATOL, ITASK, +C * ISTATE, IOPT, RWORK, LRW, IWORK, LIW, JAC, MF) +C +C *Arguments: +C F :EXT Name of subroutine for right-hand-side vector f. +C This name must be declared EXTERNAL in calling +C program. The form of F must be: +C +C SUBROUTINE F (NEQ, T, Y, YDOT) +C INTEGER NEQ +C DOUBLE PRECISION T, Y(*), YDOT(*) +C +C The inputs are NEQ, T, Y. F is to set +C +C YDOT(i) = f(i,T,Y(1),Y(2),...,Y(NEQ)), +C i = 1, ..., NEQ . +C +C NEQ :IN Number of first-order ODE's. +C +C Y :INOUT Array of values of the y(t) vector, of length NEQ. +C Input: For the first call, Y should contain the +C values of y(t) at t = T. (Y is an input +C variable only if ISTATE = 1.) +C Output: On return, Y will contain the values at the +C new t-value. +C +C T :INOUT Value of the independent variable. On return it +C will be the current value of t (normally TOUT). +C +C TOUT :IN Next point where output is desired (.NE. T). +C +C ITOL :IN 1 or 2 according as ATOL (below) is a scalar or +C an array. +C +C RTOL :IN Relative tolerance parameter (scalar). +C +C ATOL :IN Absolute tolerance parameter (scalar or array). +C If ITOL = 1, ATOL need not be dimensioned. +C If ITOL = 2, ATOL must be dimensioned at least NEQ. +C +C The estimated local error in Y(i) will be controlled +C so as to be roughly less (in magnitude) than +C +C EWT(i) = RTOL*ABS(Y(i)) + ATOL if ITOL = 1, or +C EWT(i) = RTOL*ABS(Y(i)) + ATOL(i) if ITOL = 2. +C +C Thus the local error test passes if, in each +C component, either the absolute error is less than +C ATOL (or ATOL(i)), or the relative error is less +C than RTOL. +C +C Use RTOL = 0.0 for pure absolute error control, and +C use ATOL = 0.0 (or ATOL(i) = 0.0) for pure relative +C error control. Caution: Actual (global) errors may +C exceed these local tolerances, so choose them +C conservatively. +C +C ITASK :IN Flag indicating the task DLSODE is to perform. +C Use ITASK = 1 for normal computation of output +C values of y at t = TOUT. +C +C ISTATE:INOUT Index used for input and output to specify the state +C of the calculation. +C Input: +C 1 This is the first call for a problem. +C 2 This is a subsequent call. +C Output: +C 1 Nothing was done, because TOUT was equal to T. +C 2 DLSODE was successful (otherwise, negative). +C Note that ISTATE need not be modified after a +C successful return. +C -1 Excess work done on this call (perhaps wrong +C MF). +C -2 Excess accuracy requested (tolerances too +C small). +C -3 Illegal input detected (see printed message). +C -4 Repeated error test failures (check all +C inputs). +C -5 Repeated convergence failures (perhaps bad +C Jacobian supplied or wrong choice of MF or +C tolerances). +C -6 Error weight became zero during problem +C (solution component i vanished, and ATOL or +C ATOL(i) = 0.). +C +C IOPT :IN Flag indicating whether optional inputs are used: +C 0 No. +C 1 Yes. (See "Optional inputs" under "Long +C Description," Part 1.) +C +C RWORK :WORK Real work array of length at least: +C 20 + 16*NEQ for MF = 10, +C 22 + 9*NEQ + NEQ**2 for MF = 21 or 22, +C 22 + 10*NEQ + (2*ML + MU)*NEQ for MF = 24 or 25. +C +C LRW :IN Declared length of RWORK (in user's DIMENSION +C statement). +C +C IWORK :WORK Integer work array of length at least: +C 20 for MF = 10, +C 20 + NEQ for MF = 21, 22, 24, or 25. +C +C If MF = 24 or 25, input in IWORK(1),IWORK(2) the +C lower and upper Jacobian half-bandwidths ML,MU. +C +C On return, IWORK contains information that may be +C of interest to the user: +C +C Name Location Meaning +C ----- --------- ----------------------------------------- +C NST IWORK(11) Number of steps taken for the problem so +C far. +C NFE IWORK(12) Number of f evaluations for the problem +C so far. +C NJE IWORK(13) Number of Jacobian evaluations (and of +C matrix LU decompositions) for the problem +C so far. +C NQU IWORK(14) Method order last used (successfully). +C LENRW IWORK(17) Length of RWORK actually required. This +C is defined on normal returns and on an +C illegal input return for insufficient +C storage. +C LENIW IWORK(18) Length of IWORK actually required. This +C is defined on normal returns and on an +C illegal input return for insufficient +C storage. +C +C LIW :IN Declared length of IWORK (in user's DIMENSION +C statement). +C +C JAC :EXT Name of subroutine for Jacobian matrix (MF = +C 21 or 24). If used, this name must be declared +C EXTERNAL in calling program. If not used, pass a +C dummy name. The form of JAC must be: +C +C SUBROUTINE JAC (NEQ, T, Y, ML, MU, PD, NROWPD) +C INTEGER NEQ, ML, MU, NROWPD +C DOUBLE PRECISION T, Y(*), PD(NROWPD,*) +C +C See item c, under "Description" below for more +C information about JAC. +C +C MF :IN Method flag. Standard values are: +C 10 Nonstiff (Adams) method, no Jacobian used. +C 21 Stiff (BDF) method, user-supplied full Jacobian. +C 22 Stiff method, internally generated full +C Jacobian. +C 24 Stiff method, user-supplied banded Jacobian. +C 25 Stiff method, internally generated banded +C Jacobian. +C +C *Description: +C DLSODE solves the initial value problem for stiff or nonstiff +C systems of first-order ODE's, +C +C dy/dt = f(t,y) , +C +C or, in component form, +C +C dy(i)/dt = f(i) = f(i,t,y(1),y(2),...,y(NEQ)) +C (i = 1, ..., NEQ) . +C +C DLSODE is a package based on the GEAR and GEARB packages, and on +C the October 23, 1978, version of the tentative ODEPACK user +C interface standard, with minor modifications. +C +C The steps in solving such a problem are as follows. +C +C a. First write a subroutine of the form +C +C SUBROUTINE F (NEQ, T, Y, YDOT) +C INTEGER NEQ +C DOUBLE PRECISION T, Y(*), YDOT(*) +C +C which supplies the vector function f by loading YDOT(i) with +C f(i). +C +C b. Next determine (or guess) whether or not the problem is stiff. +C Stiffness occurs when the Jacobian matrix df/dy has an +C eigenvalue whose real part is negative and large in magnitude +C compared to the reciprocal of the t span of interest. If the +C problem is nonstiff, use method flag MF = 10. If it is stiff, +C there are four standard choices for MF, and DLSODE requires the +C Jacobian matrix in some form. This matrix is regarded either +C as full (MF = 21 or 22), or banded (MF = 24 or 25). In the +C banded case, DLSODE requires two half-bandwidth parameters ML +C and MU. These are, respectively, the widths of the lower and +C upper parts of the band, excluding the main diagonal. Thus the +C band consists of the locations (i,j) with +C +C i - ML <= j <= i + MU , +C +C and the full bandwidth is ML + MU + 1 . +C +C c. If the problem is stiff, you are encouraged to supply the +C Jacobian directly (MF = 21 or 24), but if this is not feasible, +C DLSODE will compute it internally by difference quotients (MF = +C 22 or 25). If you are supplying the Jacobian, write a +C subroutine of the form +C +C SUBROUTINE JAC (NEQ, T, Y, ML, MU, PD, NROWPD) +C INTEGER NEQ, ML, MU, NRWOPD +C DOUBLE PRECISION T, Y(*), PD(NROWPD,*) +C +C which provides df/dy by loading PD as follows: +C - For a full Jacobian (MF = 21), load PD(i,j) with df(i)/dy(j), +C the partial derivative of f(i) with respect to y(j). (Ignore +C the ML and MU arguments in this case.) +C - For a banded Jacobian (MF = 24), load PD(i-j+MU+1,j) with +C df(i)/dy(j); i.e., load the diagonal lines of df/dy into the +C rows of PD from the top down. +C - In either case, only nonzero elements need be loaded. +C +C d. Write a main program that calls subroutine DLSODE once for each +C point at which answers are desired. This should also provide +C for possible use of logical unit 6 for output of error messages +C by DLSODE. +C +C Before the first call to DLSODE, set ISTATE = 1, set Y and T to +C the initial values, and set TOUT to the first output point. To +C continue the integration after a successful return, simply +C reset TOUT and call DLSODE again. No other parameters need be +C reset. +C +C *Examples: +C The following is a simple example problem, with the coding needed +C for its solution by DLSODE. The problem is from chemical kinetics, +C and consists of the following three rate equations: +C +C dy1/dt = -.04*y1 + 1.E4*y2*y3 +C dy2/dt = .04*y1 - 1.E4*y2*y3 - 3.E7*y2**2 +C dy3/dt = 3.E7*y2**2 +C +C on the interval from t = 0.0 to t = 4.E10, with initial conditions +C y1 = 1.0, y2 = y3 = 0. The problem is stiff. +C +C The following coding solves this problem with DLSODE, using +C MF = 21 and printing results at t = .4, 4., ..., 4.E10. It uses +C ITOL = 2 and ATOL much smaller for y2 than for y1 or y3 because y2 +C has much smaller values. At the end of the run, statistical +C quantities of interest are printed. +C +C EXTERNAL FEX, JEX +C INTEGER IOPT, IOUT, ISTATE, ITASK, ITOL, IWORK(23), LIW, LRW, +C * MF, NEQ +C DOUBLE PRECISION ATOL(3), RTOL, RWORK(58), T, TOUT, Y(3) +C NEQ = 3 +C Y(1) = 1.D0 +C Y(2) = 0.D0 +C Y(3) = 0.D0 +C T = 0.D0 +C TOUT = .4D0 +C ITOL = 2 +C RTOL = 1.D-4 +C ATOL(1) = 1.D-6 +C ATOL(2) = 1.D-10 +C ATOL(3) = 1.D-6 +C ITASK = 1 +C ISTATE = 1 +C IOPT = 0 +C LRW = 58 +C LIW = 23 +C MF = 21 +C DO 40 IOUT = 1,12 +C CALL DLSODE (FEX, NEQ, Y, T, TOUT, ITOL, RTOL, ATOL, ITASK, +C * ISTATE, IOPT, RWORK, LRW, IWORK, LIW, JEX, MF) +C WRITE(6,20) T, Y(1), Y(2), Y(3) +C 20 FORMAT(' At t =',D12.4,' y =',3D14.6) +C IF (ISTATE .LT. 0) GO TO 80 +C 40 TOUT = TOUT*10.D0 +C WRITE(6,60) IWORK(11), IWORK(12), IWORK(13) +C 60 FORMAT(/' No. steps =',i4,', No. f-s =',i4,', No. J-s =',i4) +C STOP +C 80 WRITE(6,90) ISTATE +C 90 FORMAT(///' Error halt.. ISTATE =',I3) +C STOP +C END +C +C SUBROUTINE FEX (NEQ, T, Y, YDOT) +C INTEGER NEQ +C DOUBLE PRECISION T, Y(3), YDOT(3) +C YDOT(1) = -.04D0*Y(1) + 1.D4*Y(2)*Y(3) +C YDOT(3) = 3.D7*Y(2)*Y(2) +C YDOT(2) = -YDOT(1) - YDOT(3) +C RETURN +C END +C +C SUBROUTINE JEX (NEQ, T, Y, ML, MU, PD, NRPD) +C INTEGER NEQ, ML, MU, NRPD +C DOUBLE PRECISION T, Y(3), PD(NRPD,3) +C PD(1,1) = -.04D0 +C PD(1,2) = 1.D4*Y(3) +C PD(1,3) = 1.D4*Y(2) +C PD(2,1) = .04D0 +C PD(2,3) = -PD(1,3) +C PD(3,2) = 6.D7*Y(2) +C PD(2,2) = -PD(1,2) - PD(3,2) +C RETURN +C END +C +C The output from this program (on a Cray-1 in single precision) +C is as follows. +C +C At t = 4.0000e-01 y = 9.851726e-01 3.386406e-05 1.479357e-02 +C At t = 4.0000e+00 y = 9.055142e-01 2.240418e-05 9.446344e-02 +C At t = 4.0000e+01 y = 7.158050e-01 9.184616e-06 2.841858e-01 +C At t = 4.0000e+02 y = 4.504846e-01 3.222434e-06 5.495122e-01 +C At t = 4.0000e+03 y = 1.831701e-01 8.940379e-07 8.168290e-01 +C At t = 4.0000e+04 y = 3.897016e-02 1.621193e-07 9.610297e-01 +C At t = 4.0000e+05 y = 4.935213e-03 1.983756e-08 9.950648e-01 +C At t = 4.0000e+06 y = 5.159269e-04 2.064759e-09 9.994841e-01 +C At t = 4.0000e+07 y = 5.306413e-05 2.122677e-10 9.999469e-01 +C At t = 4.0000e+08 y = 5.494530e-06 2.197825e-11 9.999945e-01 +C At t = 4.0000e+09 y = 5.129458e-07 2.051784e-12 9.999995e-01 +C At t = 4.0000e+10 y = -7.170603e-08 -2.868241e-13 1.000000e+00 +C +C No. steps = 330, No. f-s = 405, No. J-s = 69 +C +C *Accuracy: +C The accuracy of the solution depends on the choice of tolerances +C RTOL and ATOL. Actual (global) errors may exceed these local +C tolerances, so choose them conservatively. +C +C *Cautions: +C The work arrays should not be altered between calls to DLSODE for +C the same problem, except possibly for the conditional and optional +C inputs. +C +C *Portability: +C Since NEQ is dimensioned inside DLSODE, some compilers may object +C to a call to DLSODE with NEQ a scalar variable. In this event, +C use DIMENSION NEQ(1). Similar remarks apply to RTOL and ATOL. +C +C Note to Cray users: +C For maximum efficiency, use the CFT77 compiler. Appropriate +C compiler optimization directives have been inserted for CFT77. +C +C *Reference: +C Alan C. Hindmarsh, "ODEPACK, A Systematized Collection of ODE +C Solvers," in Scientific Computing, R. S. Stepleman, et al., Eds. +C (North-Holland, Amsterdam, 1983), pp. 55-64. +C +C *Long Description: +C The following complete description of the user interface to +C DLSODE consists of four parts: +C +C 1. The call sequence to subroutine DLSODE, which is a driver +C routine for the solver. This includes descriptions of both +C the call sequence arguments and user-supplied routines. +C Following these descriptions is a description of optional +C inputs available through the call sequence, and then a +C description of optional outputs in the work arrays. +C +C 2. Descriptions of other routines in the DLSODE package that may +C be (optionally) called by the user. These provide the ability +C to alter error message handling, save and restore the internal +C COMMON, and obtain specified derivatives of the solution y(t). +C +C 3. Descriptions of COMMON block to be declared in overlay or +C similar environments, or to be saved when doing an interrupt +C of the problem and continued solution later. +C +C 4. Description of two routines in the DLSODE package, either of +C which the user may replace with his own version, if desired. +C These relate to the measurement of errors. +C +C +C Part 1. Call Sequence +C ---------------------- +C +C Arguments +C --------- +C The call sequence parameters used for input only are +C +C F, NEQ, TOUT, ITOL, RTOL, ATOL, ITASK, IOPT, LRW, LIW, JAC, MF, +C +C and those used for both input and output are +C +C Y, T, ISTATE. +C +C The work arrays RWORK and IWORK are also used for conditional and +C optional inputs and optional outputs. (The term output here +C refers to the return from subroutine DLSODE to the user's calling +C program.) +C +C The legality of input parameters will be thoroughly checked on the +C initial call for the problem, but not checked thereafter unless a +C change in input parameters is flagged by ISTATE = 3 on input. +C +C The descriptions of the call arguments are as follows. +C +C F The name of the user-supplied subroutine defining the ODE +C system. The system must be put in the first-order form +C dy/dt = f(t,y), where f is a vector-valued function of +C the scalar t and the vector y. Subroutine F is to compute +C the function f. It is to have the form +C +C SUBROUTINE F (NEQ, T, Y, YDOT) +C DOUBLE PRECISION T, Y(*), YDOT(*) +C +C where NEQ, T, and Y are input, and the array YDOT = +C f(T,Y) is output. Y and YDOT are arrays of length NEQ. +C Subroutine F should not alter Y(1),...,Y(NEQ). F must be +C declared EXTERNAL in the calling program. +C +C Subroutine F may access user-defined quantities in +C NEQ(2),... and/or in Y(NEQ(1)+1),..., if NEQ is an array +C (dimensioned in F) and/or Y has length exceeding NEQ(1). +C See the descriptions of NEQ and Y below. +C +C If quantities computed in the F routine are needed +C externally to DLSODE, an extra call to F should be made +C for this purpose, for consistent and accurate results. +C If only the derivative dy/dt is needed, use DINTDY +C instead. +C +C NEQ The size of the ODE system (number of first-order +C ordinary differential equations). Used only for input. +C NEQ may be decreased, but not increased, during the +C problem. If NEQ is decreased (with ISTATE = 3 on input), +C the remaining components of Y should be left undisturbed, +C if these are to be accessed in F and/or JAC. +C +C Normally, NEQ is a scalar, and it is generally referred +C to as a scalar in this user interface description. +C However, NEQ may be an array, with NEQ(1) set to the +C system size. (The DLSODE package accesses only NEQ(1).) +C In either case, this parameter is passed as the NEQ +C argument in all calls to F and JAC. Hence, if it is an +C array, locations NEQ(2),... may be used to store other +C integer data and pass it to F and/or JAC. Subroutines +C F and/or JAC must include NEQ in a DIMENSION statement +C in that case. +C +C Y A real array for the vector of dependent variables, of +C length NEQ or more. Used for both input and output on +C the first call (ISTATE = 1), and only for output on +C other calls. On the first call, Y must contain the +C vector of initial values. On output, Y contains the +C computed solution vector, evaluated at T. If desired, +C the Y array may be used for other purposes between +C calls to the solver. +C +C This array is passed as the Y argument in all calls to F +C and JAC. Hence its length may exceed NEQ, and locations +C Y(NEQ+1),... may be used to store other real data and +C pass it to F and/or JAC. (The DLSODE package accesses +C only Y(1),...,Y(NEQ).) +C +C T The independent variable. On input, T is used only on +C the first call, as the initial point of the integration. +C On output, after each call, T is the value at which a +C computed solution Y is evaluated (usually the same as +C TOUT). On an error return, T is the farthest point +C reached. +C +C TOUT The next value of T at which a computed solution is +C desired. Used only for input. +C +C When starting the problem (ISTATE = 1), TOUT may be equal +C to T for one call, then should not equal T for the next +C call. For the initial T, an input value of TOUT .NE. T +C is used in order to determine the direction of the +C integration (i.e., the algebraic sign of the step sizes) +C and the rough scale of the problem. Integration in +C either direction (forward or backward in T) is permitted. +C +C If ITASK = 2 or 5 (one-step modes), TOUT is ignored +C after the first call (i.e., the first call with +C TOUT .NE. T). Otherwise, TOUT is required on every call. +C +C If ITASK = 1, 3, or 4, the values of TOUT need not be +C monotone, but a value of TOUT which backs up is limited +C to the current internal T interval, whose endpoints are +C TCUR - HU and TCUR. (See "Optional Outputs" below for +C TCUR and HU.) +C +C +C ITOL An indicator for the type of error control. See +C description below under ATOL. Used only for input. +C +C RTOL A relative error tolerance parameter, either a scalar or +C an array of length NEQ. See description below under +C ATOL. Input only. +C +C ATOL An absolute error tolerance parameter, either a scalar or +C an array of length NEQ. Input only. +C +C The input parameters ITOL, RTOL, and ATOL determine the +C error control performed by the solver. The solver will +C control the vector e = (e(i)) of estimated local errors +C in Y, according to an inequality of the form +C +C rms-norm of ( e(i)/EWT(i) ) <= 1, +C +C where +C +C EWT(i) = RTOL(i)*ABS(Y(i)) + ATOL(i), +C +C and the rms-norm (root-mean-square norm) here is +C +C rms-norm(v) = SQRT(sum v(i)**2 / NEQ). +C +C Here EWT = (EWT(i)) is a vector of weights which must +C always be positive, and the values of RTOL and ATOL +C should all be nonnegative. The following table gives the +C types (scalar/array) of RTOL and ATOL, and the +C corresponding form of EWT(i). +C +C ITOL RTOL ATOL EWT(i) +C ---- ------ ------ ----------------------------- +C 1 scalar scalar RTOL*ABS(Y(i)) + ATOL +C 2 scalar array RTOL*ABS(Y(i)) + ATOL(i) +C 3 array scalar RTOL(i)*ABS(Y(i)) + ATOL +C 4 array array RTOL(i)*ABS(Y(i)) + ATOL(i) +C +C When either of these parameters is a scalar, it need not +C be dimensioned in the user's calling program. +C +C If none of the above choices (with ITOL, RTOL, and ATOL +C fixed throughout the problem) is suitable, more general +C error controls can be obtained by substituting +C user-supplied routines for the setting of EWT and/or for +C the norm calculation. See Part 4 below. +C +C If global errors are to be estimated by making a repeated +C run on the same problem with smaller tolerances, then all +C components of RTOL and ATOL (i.e., of EWT) should be +C scaled down uniformly. +C +C ITASK An index specifying the task to be performed. Input +C only. ITASK has the following values and meanings: +C 1 Normal computation of output values of y(t) at +C t = TOUT (by overshooting and interpolating). +C 2 Take one step only and return. +C 3 Stop at the first internal mesh point at or beyond +C t = TOUT and return. +C 4 Normal computation of output values of y(t) at +C t = TOUT but without overshooting t = TCRIT. TCRIT +C must be input as RWORK(1). TCRIT may be equal to or +C beyond TOUT, but not behind it in the direction of +C integration. This option is useful if the problem +C has a singularity at or beyond t = TCRIT. +C 5 Take one step, without passing TCRIT, and return. +C TCRIT must be input as RWORK(1). +C +C Note: If ITASK = 4 or 5 and the solver reaches TCRIT +C (within roundoff), it will return T = TCRIT (exactly) to +C indicate this (unless ITASK = 4 and TOUT comes before +C TCRIT, in which case answers at T = TOUT are returned +C first). +C +C ISTATE An index used for input and output to specify the state +C of the calculation. +C +C On input, the values of ISTATE are as follows: +C 1 This is the first call for the problem +C (initializations will be done). See "Note" below. +C 2 This is not the first call, and the calculation is to +C continue normally, with no change in any input +C parameters except possibly TOUT and ITASK. (If ITOL, +C RTOL, and/or ATOL are changed between calls with +C ISTATE = 2, the new values will be used but not +C tested for legality.) +C 3 This is not the first call, and the calculation is to +C continue normally, but with a change in input +C parameters other than TOUT and ITASK. Changes are +C allowed in NEQ, ITOL, RTOL, ATOL, IOPT, LRW, LIW, MF, +C ML, MU, and any of the optional inputs except H0. +C (See IWORK description for ML and MU.) +C +C Note: A preliminary call with TOUT = T is not counted as +C a first call here, as no initialization or checking of +C input is done. (Such a call is sometimes useful for the +C purpose of outputting the initial conditions.) Thus the +C first call for which TOUT .NE. T requires ISTATE = 1 on +C input. +C +C On output, ISTATE has the following values and meanings: +C 1 Nothing was done, as TOUT was equal to T with +C ISTATE = 1 on input. +C 2 The integration was performed successfully. +C -1 An excessive amount of work (more than MXSTEP steps) +C was done on this call, before completing the +C requested task, but the integration was otherwise +C successful as far as T. (MXSTEP is an optional input +C and is normally 500.) To continue, the user may +C simply reset ISTATE to a value >1 and call again (the +C excess work step counter will be reset to 0). In +C addition, the user may increase MXSTEP to avoid this +C error return; see "Optional Inputs" below. +C -2 Too much accuracy was requested for the precision of +C the machine being used. This was detected before +C completing the requested task, but the integration +C was successful as far as T. To continue, the +C tolerance parameters must be reset, and ISTATE must +C be set to 3. The optional output TOLSF may be used +C for this purpose. (Note: If this condition is +C detected before taking any steps, then an illegal +C input return (ISTATE = -3) occurs instead.) +C -3 Illegal input was detected, before taking any +C integration steps. See written message for details. +C (Note: If the solver detects an infinite loop of +C calls to the solver with illegal input, it will cause +C the run to stop.) +C -4 There were repeated error-test failures on one +C attempted step, before completing the requested task, +C but the integration was successful as far as T. The +C problem may have a singularity, or the input may be +C inappropriate. +C -5 There were repeated convergence-test failures on one +C attempted step, before completing the requested task, +C but the integration was successful as far as T. This +C may be caused by an inaccurate Jacobian matrix, if +C one is being used. +C -6 EWT(i) became zero for some i during the integration. +C Pure relative error control (ATOL(i)=0.0) was +C requested on a variable which has now vanished. The +C integration was successful as far as T. +C +C Note: Since the normal output value of ISTATE is 2, it +C does not need to be reset for normal continuation. Also, +C since a negative input value of ISTATE will be regarded +C as illegal, a negative output value requires the user to +C change it, and possibly other inputs, before calling the +C solver again. +C +C IOPT An integer flag to specify whether any optional inputs +C are being used on this call. Input only. The optional +C inputs are listed under a separate heading below. +C 0 No optional inputs are being used. Default values +C will be used in all cases. +C 1 One or more optional inputs are being used. +C +C RWORK A real working array (double precision). The length of +C RWORK must be at least +C +C 20 + NYH*(MAXORD + 1) + 3*NEQ + LWM +C +C where +C NYH = the initial value of NEQ, +C MAXORD = 12 (if METH = 1) or 5 (if METH = 2) (unless a +C smaller value is given as an optional input), +C LWM = 0 if MITER = 0, +C LWM = NEQ**2 + 2 if MITER = 1 or 2, +C LWM = NEQ + 2 if MITER = 3, and +C LWM = (2*ML + MU + 1)*NEQ + 2 +C if MITER = 4 or 5. +C (See the MF description below for METH and MITER.) +C +C Thus if MAXORD has its default value and NEQ is constant, +C this length is: +C 20 + 16*NEQ for MF = 10, +C 22 + 16*NEQ + NEQ**2 for MF = 11 or 12, +C 22 + 17*NEQ for MF = 13, +C 22 + 17*NEQ + (2*ML + MU)*NEQ for MF = 14 or 15, +C 20 + 9*NEQ for MF = 20, +C 22 + 9*NEQ + NEQ**2 for MF = 21 or 22, +C 22 + 10*NEQ for MF = 23, +C 22 + 10*NEQ + (2*ML + MU)*NEQ for MF = 24 or 25. +C +C The first 20 words of RWORK are reserved for conditional +C and optional inputs and optional outputs. +C +C The following word in RWORK is a conditional input: +C RWORK(1) = TCRIT, the critical value of t which the +C solver is not to overshoot. Required if ITASK +C is 4 or 5, and ignored otherwise. See ITASK. +C +C LRW The length of the array RWORK, as declared by the user. +C (This will be checked by the solver.) +C +C IWORK An integer work array. Its length must be at least +C 20 if MITER = 0 or 3 (MF = 10, 13, 20, 23), or +C 20 + NEQ otherwise (MF = 11, 12, 14, 15, 21, 22, 24, 25). +C (See the MF description below for MITER.) The first few +C words of IWORK are used for conditional and optional +C inputs and optional outputs. +C +C The following two words in IWORK are conditional inputs: +C IWORK(1) = ML These are the lower and upper half- +C IWORK(2) = MU bandwidths, respectively, of the banded +C Jacobian, excluding the main diagonal. +C The band is defined by the matrix locations +C (i,j) with i - ML <= j <= i + MU. ML and MU +C must satisfy 0 <= ML,MU <= NEQ - 1. These are +C required if MITER is 4 or 5, and ignored +C otherwise. ML and MU may in fact be the band +C parameters for a matrix to which df/dy is only +C approximately equal. +C +C LIW The length of the array IWORK, as declared by the user. +C (This will be checked by the solver.) +C +C Note: The work arrays must not be altered between calls to DLSODE +C for the same problem, except possibly for the conditional and +C optional inputs, and except for the last 3*NEQ words of RWORK. +C The latter space is used for internal scratch space, and so is +C available for use by the user outside DLSODE between calls, if +C desired (but not for use by F or JAC). +C +C JAC The name of the user-supplied routine (MITER = 1 or 4) to +C compute the Jacobian matrix, df/dy, as a function of the +C scalar t and the vector y. (See the MF description below +C for MITER.) It is to have the form +C +C SUBROUTINE JAC (NEQ, T, Y, ML, MU, PD, NROWPD) +C DOUBLE PRECISION T, Y(*), PD(NROWPD,*) +C +C where NEQ, T, Y, ML, MU, and NROWPD are input and the +C array PD is to be loaded with partial derivatives +C (elements of the Jacobian matrix) on output. PD must be +C given a first dimension of NROWPD. T and Y have the same +C meaning as in subroutine F. +C +C In the full matrix case (MITER = 1), ML and MU are +C ignored, and the Jacobian is to be loaded into PD in +C columnwise manner, with df(i)/dy(j) loaded into PD(i,j). +C +C In the band matrix case (MITER = 4), the elements within +C the band are to be loaded into PD in columnwise manner, +C with diagonal lines of df/dy loaded into the rows of PD. +C Thus df(i)/dy(j) is to be loaded into PD(i-j+MU+1,j). ML +C and MU are the half-bandwidth parameters (see IWORK). +C The locations in PD in the two triangular areas which +C correspond to nonexistent matrix elements can be ignored +C or loaded arbitrarily, as they are overwritten by DLSODE. +C +C JAC need not provide df/dy exactly. A crude approximation +C (possibly with a smaller bandwidth) will do. +C +C In either case, PD is preset to zero by the solver, so +C that only the nonzero elements need be loaded by JAC. +C Each call to JAC is preceded by a call to F with the same +C arguments NEQ, T, and Y. Thus to gain some efficiency, +C intermediate quantities shared by both calculations may +C be saved in a user COMMON block by F and not recomputed +C by JAC, if desired. Also, JAC may alter the Y array, if +C desired. JAC must be declared EXTERNAL in the calling +C program. +C +C Subroutine JAC may access user-defined quantities in +C NEQ(2),... and/or in Y(NEQ(1)+1),... if NEQ is an array +C (dimensioned in JAC) and/or Y has length exceeding +C NEQ(1). See the descriptions of NEQ and Y above. +C +C MF The method flag. Used only for input. The legal values +C of MF are 10, 11, 12, 13, 14, 15, 20, 21, 22, 23, 24, +C and 25. MF has decimal digits METH and MITER: +C MF = 10*METH + MITER . +C +C METH indicates the basic linear multistep method: +C 1 Implicit Adams method. +C 2 Method based on backward differentiation formulas +C (BDF's). +C +C MITER indicates the corrector iteration method: +C 0 Functional iteration (no Jacobian matrix is +C involved). +C 1 Chord iteration with a user-supplied full (NEQ by +C NEQ) Jacobian. +C 2 Chord iteration with an internally generated +C (difference quotient) full Jacobian (using NEQ +C extra calls to F per df/dy value). +C 3 Chord iteration with an internally generated +C diagonal Jacobian approximation (using one extra call +C to F per df/dy evaluation). +C 4 Chord iteration with a user-supplied banded Jacobian. +C 5 Chord iteration with an internally generated banded +C Jacobian (using ML + MU + 1 extra calls to F per +C df/dy evaluation). +C +C If MITER = 1 or 4, the user must supply a subroutine JAC +C (the name is arbitrary) as described above under JAC. +C For other values of MITER, a dummy argument can be used. +C +C Optional Inputs +C --------------- +C The following is a list of the optional inputs provided for in the +C call sequence. (See also Part 2.) For each such input variable, +C this table lists its name as used in this documentation, its +C location in the call sequence, its meaning, and the default value. +C The use of any of these inputs requires IOPT = 1, and in that case +C all of these inputs are examined. A value of zero for any of +C these optional inputs will cause the default value to be used. +C Thus to use a subset of the optional inputs, simply preload +C locations 5 to 10 in RWORK and IWORK to 0.0 and 0 respectively, +C and then set those of interest to nonzero values. +C +C Name Location Meaning and default value +C ------ --------- ----------------------------------------------- +C H0 RWORK(5) Step size to be attempted on the first step. +C The default value is determined by the solver. +C HMAX RWORK(6) Maximum absolute step size allowed. The +C default value is infinite. +C HMIN RWORK(7) Minimum absolute step size allowed. The +C default value is 0. (This lower bound is not +C enforced on the final step before reaching +C TCRIT when ITASK = 4 or 5.) +C MAXORD IWORK(5) Maximum order to be allowed. The default value +C is 12 if METH = 1, and 5 if METH = 2. (See the +C MF description above for METH.) If MAXORD +C exceeds the default value, it will be reduced +C to the default value. If MAXORD is changed +C during the problem, it may cause the current +C order to be reduced. +C MXSTEP IWORK(6) Maximum number of (internally defined) steps +C allowed during one call to the solver. The +C default value is 500. +C MXHNIL IWORK(7) Maximum number of messages printed (per +C problem) warning that T + H = T on a step +C (H = step size). This must be positive to +C result in a nondefault value. The default +C value is 10. +C +C Optional Outputs +C ---------------- +C As optional additional output from DLSODE, the variables listed +C below are quantities related to the performance of DLSODE which +C are available to the user. These are communicated by way of the +C work arrays, but also have internal mnemonic names as shown. +C Except where stated otherwise, all of these outputs are defined on +C any successful return from DLSODE, and on any return with ISTATE = +C -1, -2, -4, -5, or -6. On an illegal input return (ISTATE = -3), +C they will be unchanged from their existing values (if any), except +C possibly for TOLSF, LENRW, and LENIW. On any error return, +C outputs relevant to the error will be defined, as noted below. +C +C Name Location Meaning +C ----- --------- ------------------------------------------------ +C HU RWORK(11) Step size in t last used (successfully). +C HCUR RWORK(12) Step size to be attempted on the next step. +C TCUR RWORK(13) Current value of the independent variable which +C the solver has actually reached, i.e., the +C current internal mesh point in t. On output, +C TCUR will always be at least as far as the +C argument T, but may be farther (if interpolation +C was done). +C TOLSF RWORK(14) Tolerance scale factor, greater than 1.0, +C computed when a request for too much accuracy +C was detected (ISTATE = -3 if detected at the +C start of the problem, ISTATE = -2 otherwise). +C If ITOL is left unaltered but RTOL and ATOL are +C uniformly scaled up by a factor of TOLSF for the +C next call, then the solver is deemed likely to +C succeed. (The user may also ignore TOLSF and +C alter the tolerance parameters in any other way +C appropriate.) +C NST IWORK(11) Number of steps taken for the problem so far. +C NFE IWORK(12) Number of F evaluations for the problem so far. +C NJE IWORK(13) Number of Jacobian evaluations (and of matrix LU +C decompositions) for the problem so far. +C NQU IWORK(14) Method order last used (successfully). +C NQCUR IWORK(15) Order to be attempted on the next step. +C IMXER IWORK(16) Index of the component of largest magnitude in +C the weighted local error vector ( e(i)/EWT(i) ), +C on an error return with ISTATE = -4 or -5. +C LENRW IWORK(17) Length of RWORK actually required. This is +C defined on normal returns and on an illegal +C input return for insufficient storage. +C LENIW IWORK(18) Length of IWORK actually required. This is +C defined on normal returns and on an illegal +C input return for insufficient storage. +C +C The following two arrays are segments of the RWORK array which may +C also be of interest to the user as optional outputs. For each +C array, the table below gives its internal name, its base address +C in RWORK, and its description. +C +C Name Base address Description +C ---- ------------ ---------------------------------------------- +C YH 21 The Nordsieck history array, of size NYH by +C (NQCUR + 1), where NYH is the initial value of +C NEQ. For j = 0,1,...,NQCUR, column j + 1 of +C YH contains HCUR**j/factorial(j) times the jth +C derivative of the interpolating polynomial +C currently representing the solution, evaluated +C at t = TCUR. +C ACOR LENRW-NEQ+1 Array of size NEQ used for the accumulated +C corrections on each step, scaled on output to +C represent the estimated local error in Y on +C the last step. This is the vector e in the +C description of the error control. It is +C defined only on successful return from DLSODE. +C +C +C Part 2. Other Callable Routines +C -------------------------------- +C +C The following are optional calls which the user may make to gain +C additional capabilities in conjunction with DLSODE. +C +C Form of call Function +C ------------------------ ---------------------------------------- +C CALL XSETUN(LUN) Set the logical unit number, LUN, for +C output of messages from DLSODE, if the +C default is not desired. The default +C value of LUN is 6. This call may be made +C at any time and will take effect +C immediately. +C CALL XSETF(MFLAG) Set a flag to control the printing of +C messages by DLSODE. MFLAG = 0 means do +C not print. (Danger: this risks losing +C valuable information.) MFLAG = 1 means +C print (the default). This call may be +C made at any time and will take effect +C immediately. +C CALL DSRCOM(RSAV,ISAV,JOB) Saves and restores the contents of the +C internal COMMON blocks used by DLSODE +C (see Part 3 below). RSAV must be a +C real array of length 218 or more, and +C ISAV must be an integer array of length +C 37 or more. JOB = 1 means save COMMON +C into RSAV/ISAV. JOB = 2 means restore +C COMMON from same. DSRCOM is useful if +C one is interrupting a run and restarting +C later, or alternating between two or +C more problems solved with DLSODE. +C CALL DINTDY(,,,,,) Provide derivatives of y, of various +C (see below) orders, at a specified point t, if +C desired. It may be called only after a +C successful return from DLSODE. Detailed +C instructions follow. +C +C Detailed instructions for using DINTDY +C -------------------------------------- +C The form of the CALL is: +C +C CALL DINTDY (T, K, RWORK(21), NYH, DKY, IFLAG) +C +C The input parameters are: +C +C T Value of independent variable where answers are +C desired (normally the same as the T last returned by +C DLSODE). For valid results, T must lie between +C TCUR - HU and TCUR. (See "Optional Outputs" above +C for TCUR and HU.) +C K Integer order of the derivative desired. K must +C satisfy 0 <= K <= NQCUR, where NQCUR is the current +C order (see "Optional Outputs"). The capability +C corresponding to K = 0, i.e., computing y(t), is +C already provided by DLSODE directly. Since +C NQCUR >= 1, the first derivative dy/dt is always +C available with DINTDY. +C RWORK(21) The base address of the history array YH. +C NYH Column length of YH, equal to the initial value of NEQ. +C +C The output parameters are: +C +C DKY Real array of length NEQ containing the computed value +C of the Kth derivative of y(t). +C IFLAG Integer flag, returned as 0 if K and T were legal, +C -1 if K was illegal, and -2 if T was illegal. +C On an error return, a message is also written. +C +C +C Part 3. Common Blocks +C ---------------------- +C +C If DLSODE is to be used in an overlay situation, the user must +C declare, in the primary overlay, the variables in: +C (1) the call sequence to DLSODE, +C (2) the internal COMMON block /DLS001/, of length 255 +C (218 double precision words followed by 37 integer words). +C +C If DLSODE is used on a system in which the contents of internal +C COMMON blocks are not preserved between calls, the user should +C declare the above COMMON block in his main program to insure that +C its contents are preserved. +C +C If the solution of a given problem by DLSODE is to be interrupted +C and then later continued, as when restarting an interrupted run or +C alternating between two or more problems, the user should save, +C following the return from the last DLSODE call prior to the +C interruption, the contents of the call sequence variables and the +C internal COMMON block, and later restore these values before the +C next DLSODE call for that problem. In addition, if XSETUN and/or +C XSETF was called for non-default handling of error messages, then +C these calls must be repeated. To save and restore the COMMON +C block, use subroutine DSRCOM (see Part 2 above). +C +C +C Part 4. Optionally Replaceable Solver Routines +C ----------------------------------------------- +C +C Below are descriptions of two routines in the DLSODE package which +C relate to the measurement of errors. Either routine can be +C replaced by a user-supplied version, if desired. However, since +C such a replacement may have a major impact on performance, it +C should be done only when absolutely necessary, and only with great +C caution. (Note: The means by which the package version of a +C routine is superseded by the user's version may be system- +C dependent.) +C +C DEWSET +C ------ +C The following subroutine is called just before each internal +C integration step, and sets the array of error weights, EWT, as +C described under ITOL/RTOL/ATOL above: +C +C SUBROUTINE DEWSET (NEQ, ITOL, RTOL, ATOL, YCUR, EWT) +C +C where NEQ, ITOL, RTOL, and ATOL are as in the DLSODE call +C sequence, YCUR contains the current dependent variable vector, +C and EWT is the array of weights set by DEWSET. +C +C If the user supplies this subroutine, it must return in EWT(i) +C (i = 1,...,NEQ) a positive quantity suitable for comparing errors +C in Y(i) to. The EWT array returned by DEWSET is passed to the +C DVNORM routine (see below), and also used by DLSODE in the +C computation of the optional output IMXER, the diagonal Jacobian +C approximation, and the increments for difference quotient +C Jacobians. +C +C In the user-supplied version of DEWSET, it may be desirable to use +C the current values of derivatives of y. Derivatives up to order NQ +C are available from the history array YH, described above under +C optional outputs. In DEWSET, YH is identical to the YCUR array, +C extended to NQ + 1 columns with a column length of NYH and scale +C factors of H**j/factorial(j). On the first call for the problem, +C given by NST = 0, NQ is 1 and H is temporarily set to 1.0. +C NYH is the initial value of NEQ. The quantities NQ, H, and NST +C can be obtained by including in SEWSET the statements: +C DOUBLE PRECISION RLS +C COMMON /DLS001/ RLS(218),ILS(37) +C NQ = ILS(33) +C NST = ILS(34) +C H = RLS(212) +C Thus, for example, the current value of dy/dt can be obtained as +C YCUR(NYH+i)/H (i=1,...,NEQ) (and the division by H is unnecessary +C when NST = 0). +C +C DVNORM +C ------ +C DVNORM is a real function routine which computes the weighted +C root-mean-square norm of a vector v: +C +C d = DVNORM (n, v, w) +C +C where: +C n = the length of the vector, +C v = real array of length n containing the vector, +C w = real array of length n containing weights, +C d = SQRT( (1/n) * sum(v(i)*w(i))**2 ). +C +C DVNORM is called with n = NEQ and with w(i) = 1.0/EWT(i), where +C EWT is as set by subroutine DEWSET. +C +C If the user supplies this function, it should return a nonnegative +C value of DVNORM suitable for use in the error control in DLSODE. +C None of the arguments should be altered by DVNORM. For example, a +C user-supplied DVNORM routine might: +C - Substitute a max-norm of (v(i)*w(i)) for the rms-norm, or +C - Ignore some components of v in the norm, with the effect of +C suppressing the error control on those components of Y. +C --------------------------------------------------------------------- +C***ROUTINES CALLED DEWSET, DINTDY, DUMACH, DSTODE, DVNORM, XERRWD +C***COMMON BLOCKS DLS001 +C***REVISION HISTORY (YYYYMMDD) +C 19791129 DATE WRITTEN +C 19791213 Minor changes to declarations; DELP init. in STODE. +C 19800118 Treat NEQ as array; integer declarations added throughout; +C minor changes to prologue. +C 19800306 Corrected TESCO(1,NQP1) setting in CFODE. +C 19800519 Corrected access of YH on forced order reduction; +C numerous corrections to prologues and other comments. +C 19800617 In main driver, added loading of SQRT(UROUND) in RWORK; +C minor corrections to main prologue. +C 19800923 Added zero initialization of HU and NQU. +C 19801218 Revised XERRWD routine; minor corrections to main prologue. +C 19810401 Minor changes to comments and an error message. +C 19810814 Numerous revisions: replaced EWT by 1/EWT; used flags +C JCUR, ICF, IERPJ, IERSL between STODE and subordinates; +C added tuning parameters CCMAX, MAXCOR, MSBP, MXNCF; +C reorganized returns from STODE; reorganized type decls.; +C fixed message length in XERRWD; changed default LUNIT to 6; +C changed Common lengths; changed comments throughout. +C 19870330 Major update by ACH: corrected comments throughout; +C removed TRET from Common; rewrote EWSET with 4 loops; +C fixed t test in INTDY; added Cray directives in STODE; +C in STODE, fixed DELP init. and logic around PJAC call; +C combined routines to save/restore Common; +C passed LEVEL = 0 in error message calls (except run abort). +C 19890426 Modified prologue to SLATEC/LDOC format. (FNF) +C 19890501 Many improvements to prologue. (FNF) +C 19890503 A few final corrections to prologue. (FNF) +C 19890504 Minor cosmetic changes. (FNF) +C 19890510 Corrected description of Y in Arguments section. (FNF) +C 19890517 Minor corrections to prologue. (FNF) +C 19920514 Updated with prologue edited 891025 by G. Shaw for manual. +C 19920515 Converted source lines to upper case. (FNF) +C 19920603 Revised XERRWD calls using mixed upper-lower case. (ACH) +C 19920616 Revised prologue comment regarding CFT. (ACH) +C 19921116 Revised prologue comments regarding Common. (ACH). +C 19930326 Added comment about non-reentrancy. (FNF) +C 19930723 Changed D1MACH to DUMACH. (FNF) +C 19930801 Removed ILLIN and NTREP from Common (affects driver logic); +C minor changes to prologue and internal comments; +C changed Hollerith strings to quoted strings; +C changed internal comments to mixed case; +C replaced XERRWD with new version using character type; +C changed dummy dimensions from 1 to *. (ACH) +C 19930809 Changed to generic intrinsic names; changed names of +C subprograms and Common blocks to DLSODE etc. (ACH) +C 19930929 Eliminated use of REAL intrinsic; other minor changes. (ACH) +C 20010412 Removed all 'own' variables from Common block /DLS001/ +C (affects declarations in 6 routines). (ACH) +C 20010509 Minor corrections to prologue. (ACH) +C 20031105 Restored 'own' variables to Common block /DLS001/, to +C enable interrupt/restart feature. (ACH) +C 20031112 Added SAVE statements for data-loaded constants. +C +C***END PROLOGUE DLSODE +C +C*Internal Notes: +C +C Other Routines in the DLSODE Package. +C +C In addition to Subroutine DLSODE, the DLSODE package includes the +C following subroutines and function routines: +C DINTDY computes an interpolated value of the y vector at t = TOUT. +C DSTODE is the core integrator, which does one step of the +C integration and the associated error control. +C DCFODE sets all method coefficients and test constants. +C DPREPJ computes and preprocesses the Jacobian matrix J = df/dy +C and the Newton iteration matrix P = I - h*l0*J. +C DSOLSY manages solution of linear system in chord iteration. +C DEWSET sets the error weight vector EWT before each step. +C DVNORM computes the weighted R.M.S. norm of a vector. +C DSRCOM is a user-callable routine to save and restore +C the contents of the internal Common block. +C DGEFA and DGESL are routines from LINPACK for solving full +C systems of linear algebraic equations. +C DGBFA and DGBSL are routines from LINPACK for solving banded +C linear systems. +C DUMACH computes the unit roundoff in a machine-independent manner. +C XERRWD, XSETUN, XSETF, IXSAV, IUMACH handle the printing of all +C error messages and warnings. XERRWD is machine-dependent. +C Note: DVNORM, DUMACH, IXSAV, and IUMACH are function routines. +C All the others are subroutines. +C +C**End +C +C Declare externals. + EXTERNAL DPRERWORKPJ, DSOLSY + DOUBLE PRECISION DUMACH, DVNORM +C +C Declare all other variables. + INTEGER INIT, MXSTEP, MXHNIL, NHNIL, NSLAST, NYH, IOWNS, + 1 ICF, IERPJ, IERSL, JCUR, JSTART, KFLAG, L, + 2 LYH, LEWT, LACOR, LSAVF, LWM, LIWM, METH, MITER, + 3 MAXORD, MAXCOR, MSBP, MXNCF, N, NQ, NST, NFE, NJE, NQU + INTEGER I, I1, I2, IFLAG, IMXER, KGO, LF0, + 1 LENIW, LENRW, LENWM, ML, MORD, MU, MXHNL0, MXSTP0 + DOUBLE PRECISION ROWNS, + 1 CCMAX, EL0, H, HMIN, HMXI, HU, RC, TN, UROUND + DOUBLE PRECISION ATOLI, AYI, BIG, EWTI, H0, HMAX, HMX, RH, RTOLI, + 1 TCRIT, TDIST, TNEXT, TOL, TOLSF, TP, SIZE, SUM, W0 + DIMENSION MORD(2) + LOGICAL IHIT + CHARACTER*80 MSG + SAVE MORD, MXSTP0, MXHNL0 +C----------------------------------------------------------------------- +C The following internal Common block contains +C (a) variables which are local to any subroutine but whose values must +C be preserved between calls to the routine ("own" variables), and +C (b) variables which are communicated between subroutines. +C The block DLS001 is declared in subroutines DLSODE, DINTDY, DSTODE, +C DPREPJ, and DSOLSY. +C Groups of variables are replaced by dummy arrays in the Common +C declarations in routines where those variables are not used. +C----------------------------------------------------------------------- + COMMON /DLS001/ ROWNS(209), + 1 CCMAX, EL0, H, HMIN, HMXI, HU, RC, TN, UROUND, + 2 INIT, MXSTEP, MXHNIL, NHNIL, NSLAST, NYH, IOWNS(6), + 3 ICF, IERPJ, IERSL, JCUR, JSTART, KFLAG, L, + 4 LYH, LEWT, LACOR, LSAVF, LWM, LIWM, METH, MITER, + 5 MAXORD, MAXCOR, MSBP, MXNCF, N, NQ, NST, NFE, NJE, NQU +C + DATA MORD(1),MORD(2)/12,5/, MXSTP0/500/, MXHNL0/10/ +C----------------------------------------------------------------------- +C Block A. +C This code block is executed on every call. +C It tests ISTATE and ITASK for legality and branches appropriately. +C If ISTATE .GT. 1 but the flag INIT shows that initialization has +C not yet been done, an error return occurs. +C If ISTATE = 1 and TOUT = T, return immediately. +C----------------------------------------------------------------------- +C +C***FIRST EXECUTABLE STATEMENT DLSODE + IF (ISTATE .LT. 1 .OR. ISTATE .GT. 3) GO TO 601 + IF (ITASK .LT. 1 .OR. ITASK .GT. 5) GO TO 602 + IF (ISTATE .EQ. 1) GO TO 10 + IF (INIT .EQ. 0) GO TO 603 + IF (ISTATE .EQ. 2) GO TO 200 + GO TO 20 + 10 INIT = 0 + IF (TOUT .EQ. T) RETURN +C----------------------------------------------------------------------- +C Block B. +C The next code block is executed for the initial call (ISTATE = 1), +C or for a continuation call with parameter changes (ISTATE = 3). +C It contains checking of all inputs and various initializations. +C +C First check legality of the non-optional inputs NEQ, ITOL, IOPT, +C MF, ML, and MU. +C----------------------------------------------------------------------- + 20 IF (NEQ(1) .LE. 0) GO TO 604 + IF (ISTATE .EQ. 1) GO TO 25 + IF (NEQ(1) .GT. N) GO TO 605 + 25 N = NEQ(1) + IF (ITOL .LT. 1 .OR. ITOL .GT. 4) GO TO 606 + IF (IOPT .LT. 0 .OR. IOPT .GT. 1) GO TO 607 + METH = MF/10 + MITER = MF - 10*METH + IF (METH .LT. 1 .OR. METH .GT. 2) GO TO 608 + IF (MITER .LT. 0 .OR. MITER .GT. 5) GO TO 608 + IF (MITER .LE. 3) GO TO 30 + ML = IWORK(1) + MU = IWORK(2) + IF (ML .LT. 0 .OR. ML .GE. N) GO TO 609 + IF (MU .LT. 0 .OR. MU .GE. N) GO TO 610 + 30 CONTINUE +C Next process and check the optional inputs. -------------------------- + IF (IOPT .EQ. 1) GO TO 40 + MAXORD = MORD(METH) + MXSTEP = MXSTP0 + MXHNIL = MXHNL0 + IF (ISTATE .EQ. 1) H0 = 0.0D0 + HMXI = 0.0D0 + HMIN = 0.0D0 + GO TO 60 + 40 MAXORD = IWORK(5) + IF (MAXORD .LT. 0) GO TO 611 + IF (MAXORD .EQ. 0) MAXORD = 100 + MAXORD = MIN(MAXORD,MORD(METH)) + MXSTEP = IWORK(6) + IF (MXSTEP .LT. 0) GO TO 612 + IF (MXSTEP .EQ. 0) MXSTEP = MXSTP0 + MXHNIL = IWORK(7) + IF (MXHNIL .LT. 0) GO TO 613 + IF (MXHNIL .EQ. 0) MXHNIL = MXHNL0 + IF (ISTATE .NE. 1) GO TO 50 + H0 = RWORK(5) + IF ((TOUT - T)*H0 .LT. 0.0D0) GO TO 614 + 50 HMAX = RWORK(6) + IF (HMAX .LT. 0.0D0) GO TO 615 + HMXI = 0.0D0 + IF (HMAX .GT. 0.0D0) HMXI = 1.0D0/HMAX + HMIN = RWORK(7) + IF (HMIN .LT. 0.0D0) GO TO 616 +C----------------------------------------------------------------------- +C Set work array pointers and check lengths LRW and LIW. +C Pointers to segments of RWORK and IWORK are named by prefixing L to +C the name of the segment. E.g., the segment YH starts at RWORK(LYH). +C Segments of RWORK (in order) are denoted YH, WM, EWT, SAVF, ACOR. +C----------------------------------------------------------------------- + 60 LYH = 21 + IF (ISTATE .EQ. 1) NYH = N + LWM = LYH + (MAXORD + 1)*NYH + IF (MITER .EQ. 0) LENWM = 0 + IF (MITER .EQ. 1 .OR. MITER .EQ. 2) LENWM = N*N + 2 + IF (MITER .EQ. 3) LENWM = N + 2 + IF (MITER .GE. 4) LENWM = (2*ML + MU + 1)*N + 2 + LEWT = LWM + LENWM + LSAVF = LEWT + N + LACOR = LSAVF + N + LENRW = LACOR + N - 1 + IWORK(17) = LENRW + LIWM = 1 + LENIW = 20 + N + IF (MITER .EQ. 0 .OR. MITER .EQ. 3) LENIW = 20 + IWORK(18) = LENIW + IF (LENRW .GT. LRW) GO TO 617 + IF (LENIW .GT. LIW) GO TO 618 +C Check RTOL and ATOL for legality. ------------------------------------ + RTOLI = RTOL(1) + ATOLI = ATOL(1) + DO 70 I = 1,N + IF (ITOL .GE. 3) RTOLI = RTOL(I) + IF (ITOL .EQ. 2 .OR. ITOL .EQ. 4) ATOLI = ATOL(I) + IF (RTOLI .LT. 0.0D0) GO TO 619 + IF (ATOLI .LT. 0.0D0) GO TO 620 + 70 CONTINUE + IF (ISTATE .EQ. 1) GO TO 100 +C If ISTATE = 3, set flag to signal parameter changes to DSTODE. ------- + JSTART = -1 + IF (NQ .LE. MAXORD) GO TO 90 +C MAXORD was reduced below NQ. Copy YH(*,MAXORD+2) into SAVF. --------- + DO 80 I = 1,N + 80 RWORK(I+LSAVF-1) = RWORK(I+LWM-1) +C Reload WM(1) = RWORK(LWM), since LWM may have changed. --------------- + 90 IF (MITER .GT. 0) RWORK(LWM) = SQRT(UROUND) + IF (N .EQ. NYH) GO TO 200 +C NEQ was reduced. Zero part of YH to avoid undefined references. ----- + I1 = LYH + L*NYH + I2 = LYH + (MAXORD + 1)*NYH - 1 + IF (I1 .GT. I2) GO TO 200 + DO 95 I = I1,I2 + 95 RWORK(I) = 0.0D0 + GO TO 200 +C----------------------------------------------------------------------- +C Block C. +C The next block is for the initial call only (ISTATE = 1). +C It contains all remaining initializations, the initial call to F, +C and the calculation of the initial step size. +C The error weights in EWT are inverted after being loaded. +C----------------------------------------------------------------------- + 100 UROUND = DUMACH() + TN = T + IF (ITASK .NE. 4 .AND. ITASK .NE. 5) GO TO 110 + TCRIT = RWORK(1) + IF ((TCRIT - TOUT)*(TOUT - T) .LT. 0.0D0) GO TO 625 + IF (H0 .NE. 0.0D0 .AND. (T + H0 - TCRIT)*H0 .GT. 0.0D0) + 1 H0 = TCRIT - T + 110 JSTART = 0 + IF (MITER .GT. 0) RWORK(LWM) = SQRT(UROUND) + NHNIL = 0 + NST = 0 + NJE = 0 + NSLAST = 0 + HU = 0.0D0 + NQU = 0 + CCMAX = 0.3D0 + MAXCOR = 3 + MSBP = 20 + MXNCF = 10 +C Initial call to F. (LF0 points to YH(*,2).) ------------------------- + LF0 = LYH + NYH + CALL F (NEQ, T, Y, RWORK(LF0)) + NFE = 1 +C Load the initial value vector in YH. --------------------------------- + DO 115 I = 1,N + 115 RWORK(I+LYH-1) = Y(I) +C Load and invert the EWT array. (H is temporarily set to 1.0.) ------- + NQ = 1 + H = 1.0D0 + CALL DEWSET (N, ITOL, RTOL, ATOL, RWORK(LYH), RWORK(LEWT)) + DO 120 I = 1,N + IF (RWORK(I+LEWT-1) .LE. 0.0D0) GO TO 621 + 120 RWORK(I+LEWT-1) = 1.0D0/RWORK(I+LEWT-1) +C----------------------------------------------------------------------- +C The coding below computes the step size, H0, to be attempted on the +C first step, unless the user has supplied a value for this. +C First check that TOUT - T differs significantly from zero. +C A scalar tolerance quantity TOL is computed, as MAX(RTOL(I)) +C if this is positive, or MAX(ATOL(I)/ABS(Y(I))) otherwise, adjusted +C so as to be between 100*UROUND and 1.0E-3. +C Then the computed value H0 is given by.. +C NEQ +C H0**2 = TOL / ( w0**-2 + (1/NEQ) * SUM ( f(i)/ywt(i) )**2 ) +C 1 +C where w0 = MAX ( ABS(T), ABS(TOUT) ), +C f(i) = i-th component of initial value of f, +C ywt(i) = EWT(i)/TOL (a weight for y(i)). +C The sign of H0 is inferred from the initial values of TOUT and T. +C----------------------------------------------------------------------- + IF (H0 .NE. 0.0D0) GO TO 180 + TDIST = ABS(TOUT - T) + W0 = MAX(ABS(T),ABS(TOUT)) + IF (TDIST .LT. 2.0D0*UROUND*W0) GO TO 622 + TOL = RTOL(1) + IF (ITOL .LE. 2) GO TO 140 + DO 130 I = 1,N + 130 TOL = MAX(TOL,RTOL(I)) + 140 IF (TOL .GT. 0.0D0) GO TO 160 + ATOLI = ATOL(1) + DO 150 I = 1,N + IF (ITOL .EQ. 2 .OR. ITOL .EQ. 4) ATOLI = ATOL(I) + AYI = ABS(Y(I)) + IF (AYI .NE. 0.0D0) TOL = MAX(TOL,ATOLI/AYI) + 150 CONTINUE + 160 TOL = MAX(TOL,100.0D0*UROUND) + TOL = MIN(TOL,0.001D0) + SUM = DVNORM (N, RWORK(LF0), RWORK(LEWT)) + SUM = 1.0D0/(TOL*W0*W0) + TOL*SUM**2 + H0 = 1.0D0/SQRT(SUM) + H0 = MIN(H0,TDIST) + H0 = SIGN(H0,TOUT-T) +C Adjust H0 if necessary to meet HMAX bound. --------------------------- + 180 RH = ABS(H0)*HMXI + IF (RH .GT. 1.0D0) H0 = H0/RH +C Load H with H0 and scale YH(*,2) by H0. ------------------------------ + H = H0 + DO 190 I = 1,N + 190 RWORK(I+LF0-1) = H0*RWORK(I+LF0-1) + GO TO 270 +C----------------------------------------------------------------------- +C Block D. +C The next code block is for continuation calls only (ISTATE = 2 or 3) +C and is to check stop conditions before taking a step. +C----------------------------------------------------------------------- + 200 NSLAST = NST + GO TO (210, 250, 220, 230, 240), ITASK + 210 IF ((TN - TOUT)*H .LT. 0.0D0) GO TO 250 + CALL DINTDY (TOUT, 0, RWORK(LYH), NYH, Y, IFLAG) + IF (IFLAG .NE. 0) GO TO 627 + T = TOUT + GO TO 420 + 220 TP = TN - HU*(1.0D0 + 100.0D0*UROUND) + IF ((TP - TOUT)*H .GT. 0.0D0) GO TO 623 + IF ((TN - TOUT)*H .LT. 0.0D0) GO TO 250 + GO TO 400 + 230 TCRIT = RWORK(1) + IF ((TN - TCRIT)*H .GT. 0.0D0) GO TO 624 + IF ((TCRIT - TOUT)*H .LT. 0.0D0) GO TO 625 + IF ((TN - TOUT)*H .LT. 0.0D0) GO TO 245 + CALL DINTDY (TOUT, 0, RWORK(LYH), NYH, Y, IFLAG) + IF (IFLAG .NE. 0) GO TO 627 + T = TOUT + GO TO 420 + 240 TCRIT = RWORK(1) + IF ((TN - TCRIT)*H .GT. 0.0D0) GO TO 624 + 245 HMX = ABS(TN) + ABS(H) + IHIT = ABS(TN - TCRIT) .LE. 100.0D0*UROUND*HMX + IF (IHIT) GO TO 400 + TNEXT = TN + H*(1.0D0 + 4.0D0*UROUND) + IF ((TNEXT - TCRIT)*H .LE. 0.0D0) GO TO 250 + H = (TCRIT - TN)*(1.0D0 - 4.0D0*UROUND) + IF (ISTATE .EQ. 2) JSTART = -2 +C----------------------------------------------------------------------- +C Block E. +C The next block is normally executed for all calls and contains +C the call to the one-step core integrator DSTODE. +C +C This is a looping point for the integration steps. +C +C First check for too many steps being taken, update EWT (if not at +C start of problem), check for too much accuracy being requested, and +C check for H below the roundoff level in T. +C----------------------------------------------------------------------- + 250 CONTINUE + IF ((NST-NSLAST) .GE. MXSTEP) GO TO 500 + CALL DEWSET (N, ITOL, RTOL, ATOL, RWORK(LYH), RWORK(LEWT)) + DO 260 I = 1,N + IF (RWORK(I+LEWT-1) .LE. 0.0D0) GO TO 510 + 260 RWORK(I+LEWT-1) = 1.0D0/RWORK(I+LEWT-1) + 270 TOLSF = UROUND*DVNORM (N, RWORK(LYH), RWORK(LEWT)) + IF (TOLSF .LE. 1.0D0) GO TO 280 + TOLSF = TOLSF*2.0D0 + IF (NST .EQ. 0) GO TO 626 + GO TO 520 + 280 IF ((TN + H) .NE. TN) GO TO 290 + NHNIL = NHNIL + 1 + IF (NHNIL .GT. MXHNIL) GO TO 290 + MSG = 'DLSODE- Warning..internal T (=R1) and H (=R2) are' + CALL XERRWD (MSG, 50, 101, 0, 0, 0, 0, 0, 0.0D0, 0.0D0) + MSG=' such that in the machine, T + H = T on the next step ' + CALL XERRWD (MSG, 60, 101, 0, 0, 0, 0, 0, 0.0D0, 0.0D0) + MSG = ' (H = step size). Solver will continue anyway' + CALL XERRWD (MSG, 50, 101, 0, 0, 0, 0, 2, TN, H) + IF (NHNIL .LT. MXHNIL) GO TO 290 + MSG = 'DLSODE- Above warning has been issued I1 times. ' + CALL XERRWD (MSG, 50, 102, 0, 0, 0, 0, 0, 0.0D0, 0.0D0) + MSG = ' It will not be issued again for this problem' + CALL XERRWD (MSG, 50, 102, 0, 1, MXHNIL, 0, 0, 0.0D0, 0.0D0) + 290 CONTINUE +C----------------------------------------------------------------------- +C CALL DSTODE(NEQ,Y,YH,NYH,YH,EWT,SAVF,ACOR,WM,IWM,F,JAC,DPREPJ,DSOLSY) +C----------------------------------------------------------------------- + CALL DSTODE (NEQ, Y, RWORK(LYH), NYH, RWORK(LYH), RWORK(LEWT), + 1 RWORK(LSAVF), RWORK(LACOR), RWORK(LWM), IWORK(LIWM), + 2 F, JAC, DPREPJ, DSOLSY) + KGO = 1 - KFLAG + GO TO (300, 530, 540), KGO +C----------------------------------------------------------------------- +C Block F. +C The following block handles the case of a successful return from the +C core integrator (KFLAG = 0). Test for stop conditions. +C----------------------------------------------------------------------- + 300 INIT = 1 + GO TO (310, 400, 330, 340, 350), ITASK +C ITASK = 1. If TOUT has been reached, interpolate. ------------------- + 310 IF ((TN - TOUT)*H .LT. 0.0D0) GO TO 250 + CALL DINTDY (TOUT, 0, RWORK(LYH), NYH, Y, IFLAG) + T = TOUT + GO TO 420 +C ITASK = 3. Jump to exit if TOUT was reached. ------------------------ + 330 IF ((TN - TOUT)*H .GE. 0.0D0) GO TO 400 + GO TO 250 +C ITASK = 4. See if TOUT or TCRIT was reached. Adjust H if necessary. + 340 IF ((TN - TOUT)*H .LT. 0.0D0) GO TO 345 + CALL DINTDY (TOUT, 0, RWORK(LYH), NYH, Y, IFLAG) + T = TOUT + GO TO 420 + 345 HMX = ABS(TN) + ABS(H) + IHIT = ABS(TN - TCRIT) .LE. 100.0D0*UROUND*HMX + IF (IHIT) GO TO 400 + TNEXT = TN + H*(1.0D0 + 4.0D0*UROUND) + IF ((TNEXT - TCRIT)*H .LE. 0.0D0) GO TO 250 + H = (TCRIT - TN)*(1.0D0 - 4.0D0*UROUND) + JSTART = -2 + GO TO 250 +C ITASK = 5. See if TCRIT was reached and jump to exit. --------------- + 350 HMX = ABS(TN) + ABS(H) + IHIT = ABS(TN - TCRIT) .LE. 100.0D0*UROUND*HMX +C----------------------------------------------------------------------- +C Block G. +C The following block handles all successful returns from DLSODE. +C If ITASK .NE. 1, Y is loaded from YH and T is set accordingly. +C ISTATE is set to 2, and the optional outputs are loaded into the +C work arrays before returning. +C----------------------------------------------------------------------- + 400 DO 410 I = 1,N + 410 Y(I) = RWORK(I+LYH-1) + T = TN + IF (ITASK .NE. 4 .AND. ITASK .NE. 5) GO TO 420 + IF (IHIT) T = TCRIT + 420 ISTATE = 2 + RWORK(11) = HU + RWORK(12) = H + RWORK(13) = TN + IWORK(11) = NST + IWORK(12) = NFE + IWORK(13) = NJE + IWORK(14) = NQU + IWORK(15) = NQ + RETURN +C----------------------------------------------------------------------- +C Block H. +C The following block handles all unsuccessful returns other than +C those for illegal input. First the error message routine is called. +C If there was an error test or convergence test failure, IMXER is set. +C Then Y is loaded from YH and T is set to TN. The optional outputs +C are loaded into the work arrays before returning. +C----------------------------------------------------------------------- +C The maximum number of steps was taken before reaching TOUT. ---------- + 500 MSG = 'DLSODE- At current T (=R1), MXSTEP (=I1) steps ' + CALL XERRWD (MSG, 50, 201, 0, 0, 0, 0, 0, 0.0D0, 0.0D0) + MSG = ' taken on this call before reaching TOUT ' + CALL XERRWD (MSG, 50, 201, 0, 1, MXSTEP, 0, 1, TN, 0.0D0) + ISTATE = -1 + GO TO 580 +C EWT(I) .LE. 0.0 for some I (not at start of problem). ---------------- + 510 EWTI = RWORK(LEWT+I-1) + MSG = 'DLSODE- At T (=R1), EWT(I1) has become R2 .LE. 0.' + CALL XERRWD (MSG, 50, 202, 0, 1, I, 0, 2, TN, EWTI) + ISTATE = -6 + GO TO 580 +C Too much accuracy requested for machine precision. ------------------- + 520 MSG = 'DLSODE- At T (=R1), too much accuracy requested ' + CALL XERRWD (MSG, 50, 203, 0, 0, 0, 0, 0, 0.0D0, 0.0D0) + MSG = ' for precision of machine.. see TOLSF (=R2) ' + CALL XERRWD (MSG, 50, 203, 0, 0, 0, 0, 2, TN, TOLSF) + RWORK(14) = TOLSF + ISTATE = -2 + GO TO 580 +C KFLAG = -1. Error test failed repeatedly or with ABS(H) = HMIN. ----- + 530 MSG = 'DLSODE- At T(=R1) and step size H(=R2), the error' + CALL XERRWD (MSG, 50, 204, 0, 0, 0, 0, 0, 0.0D0, 0.0D0) + MSG = ' test failed repeatedly or with ABS(H) = HMIN' + CALL XERRWD (MSG, 50, 204, 0, 0, 0, 0, 2, TN, H) + ISTATE = -4 + GO TO 560 +C KFLAG = -2. Convergence failed repeatedly or with ABS(H) = HMIN. ---- + 540 MSG = 'DLSODE- At T (=R1) and step size H (=R2), the ' + CALL XERRWD (MSG, 50, 205, 0, 0, 0, 0, 0, 0.0D0, 0.0D0) + MSG = ' corrector convergence failed repeatedly ' + CALL XERRWD (MSG, 50, 205, 0, 0, 0, 0, 0, 0.0D0, 0.0D0) + MSG = ' or with ABS(H) = HMIN ' + CALL XERRWD (MSG, 30, 205, 0, 0, 0, 0, 2, TN, H) + ISTATE = -5 +C Compute IMXER if relevant. ------------------------------------------- + 560 BIG = 0.0D0 + IMXER = 1 + DO 570 I = 1,N + SIZE = ABS(RWORK(I+LACOR-1)*RWORK(I+LEWT-1)) + IF (BIG .GE. SIZE) GO TO 570 + BIG = SIZE + IMXER = I + 570 CONTINUE + IWORK(16) = IMXER +C Set Y vector, T, and optional outputs. ------------------------------- + 580 DO 590 I = 1,N + 590 Y(I) = RWORK(I+LYH-1) + T = TN + RWORK(11) = HU + RWORK(12) = H + RWORK(13) = TN + IWORK(11) = NST + IWORK(12) = NFE + IWORK(13) = NJE + IWORK(14) = NQU + IWORK(15) = NQ + RETURN +C----------------------------------------------------------------------- +C Block I. +C The following block handles all error returns due to illegal input +C (ISTATE = -3), as detected before calling the core integrator. +C First the error message routine is called. If the illegal input +C is a negative ISTATE, the run is aborted (apparent infinite loop). +C----------------------------------------------------------------------- + 601 MSG = 'DLSODE- ISTATE (=I1) illegal ' + CALL XERRWD (MSG, 30, 1, 0, 1, ISTATE, 0, 0, 0.0D0, 0.0D0) + IF (ISTATE .LT. 0) GO TO 800 + GO TO 700 + 602 MSG = 'DLSODE- ITASK (=I1) illegal ' + CALL XERRWD (MSG, 30, 2, 0, 1, ITASK, 0, 0, 0.0D0, 0.0D0) + GO TO 700 + 603 MSG = 'DLSODE- ISTATE .GT. 1 but DLSODE not initialized ' + CALL XERRWD (MSG, 50, 3, 0, 0, 0, 0, 0, 0.0D0, 0.0D0) + GO TO 700 + 604 MSG = 'DLSODE- NEQ (=I1) .LT. 1 ' + CALL XERRWD (MSG, 30, 4, 0, 1, NEQ(1), 0, 0, 0.0D0, 0.0D0) + GO TO 700 + 605 MSG = 'DLSODE- ISTATE = 3 and NEQ increased (I1 to I2) ' + CALL XERRWD (MSG, 50, 5, 0, 2, N, NEQ(1), 0, 0.0D0, 0.0D0) + GO TO 700 + 606 MSG = 'DLSODE- ITOL (=I1) illegal ' + CALL XERRWD (MSG, 30, 6, 0, 1, ITOL, 0, 0, 0.0D0, 0.0D0) + GO TO 700 + 607 MSG = 'DLSODE- IOPT (=I1) illegal ' + CALL XERRWD (MSG, 30, 7, 0, 1, IOPT, 0, 0, 0.0D0, 0.0D0) + GO TO 700 + 608 MSG = 'DLSODE- MF (=I1) illegal ' + CALL XERRWD (MSG, 30, 8, 0, 1, MF, 0, 0, 0.0D0, 0.0D0) + GO TO 700 + 609 MSG = 'DLSODE- ML (=I1) illegal.. .LT.0 or .GE.NEQ (=I2)' + CALL XERRWD (MSG, 50, 9, 0, 2, ML, NEQ(1), 0, 0.0D0, 0.0D0) + GO TO 700 + 610 MSG = 'DLSODE- MU (=I1) illegal.. .LT.0 or .GE.NEQ (=I2)' + CALL XERRWD (MSG, 50, 10, 0, 2, MU, NEQ(1), 0, 0.0D0, 0.0D0) + GO TO 700 + 611 MSG = 'DLSODE- MAXORD (=I1) .LT. 0 ' + CALL XERRWD (MSG, 30, 11, 0, 1, MAXORD, 0, 0, 0.0D0, 0.0D0) + GO TO 700 + 612 MSG = 'DLSODE- MXSTEP (=I1) .LT. 0 ' + CALL XERRWD (MSG, 30, 12, 0, 1, MXSTEP, 0, 0, 0.0D0, 0.0D0) + GO TO 700 + 613 MSG = 'DLSODE- MXHNIL (=I1) .LT. 0 ' + CALL XERRWD (MSG, 30, 13, 0, 1, MXHNIL, 0, 0, 0.0D0, 0.0D0) + GO TO 700 + 614 MSG = 'DLSODE- TOUT (=R1) behind T (=R2) ' + CALL XERRWD (MSG, 40, 14, 0, 0, 0, 0, 2, TOUT, T) + MSG = ' Integration direction is given by H0 (=R1) ' + CALL XERRWD (MSG, 50, 14, 0, 0, 0, 0, 1, H0, 0.0D0) + GO TO 700 + 615 MSG = 'DLSODE- HMAX (=R1) .LT. 0.0 ' + CALL XERRWD (MSG, 30, 15, 0, 0, 0, 0, 1, HMAX, 0.0D0) + GO TO 700 + 616 MSG = 'DLSODE- HMIN (=R1) .LT. 0.0 ' + CALL XERRWD (MSG, 30, 16, 0, 0, 0, 0, 1, HMIN, 0.0D0) + GO TO 700 + 617 CONTINUE + MSG='DLSODE- RWORK length needed, LENRW (=I1), exceeds LRW (=I2)' + CALL XERRWD (MSG, 60, 17, 0, 2, LENRW, LRW, 0, 0.0D0, 0.0D0) + GO TO 700 + 618 CONTINUE + MSG='DLSODE- IWORK length needed, LENIW (=I1), exceeds LIW (=I2)' + CALL XERRWD (MSG, 60, 18, 0, 2, LENIW, LIW, 0, 0.0D0, 0.0D0) + GO TO 700 + 619 MSG = 'DLSODE- RTOL(I1) is R1 .LT. 0.0 ' + CALL XERRWD (MSG, 40, 19, 0, 1, I, 0, 1, RTOLI, 0.0D0) + GO TO 700 + 620 MSG = 'DLSODE- ATOL(I1) is R1 .LT. 0.0 ' + CALL XERRWD (MSG, 40, 20, 0, 1, I, 0, 1, ATOLI, 0.0D0) + GO TO 700 + 621 EWTI = RWORK(LEWT+I-1) + MSG = 'DLSODE- EWT(I1) is R1 .LE. 0.0 ' + CALL XERRWD (MSG, 40, 21, 0, 1, I, 0, 1, EWTI, 0.0D0) + GO TO 700 + 622 CONTINUE + MSG='DLSODE- TOUT (=R1) too close to T(=R2) to start integration' + CALL XERRWD (MSG, 60, 22, 0, 0, 0, 0, 2, TOUT, T) + GO TO 700 + 623 CONTINUE + MSG='DLSODE- ITASK = I1 and TOUT (=R1) behind TCUR - HU (= R2) ' + CALL XERRWD (MSG, 60, 23, 0, 1, ITASK, 0, 2, TOUT, TP) + GO TO 700 + 624 CONTINUE + MSG='DLSODE- ITASK = 4 OR 5 and TCRIT (=R1) behind TCUR (=R2) ' + CALL XERRWD (MSG, 60, 24, 0, 0, 0, 0, 2, TCRIT, TN) + GO TO 700 + 625 CONTINUE + MSG='DLSODE- ITASK = 4 or 5 and TCRIT (=R1) behind TOUT (=R2) ' + CALL XERRWD (MSG, 60, 25, 0, 0, 0, 0, 2, TCRIT, TOUT) + GO TO 700 + 626 MSG = 'DLSODE- At start of problem, too much accuracy ' + CALL XERRWD (MSG, 50, 26, 0, 0, 0, 0, 0, 0.0D0, 0.0D0) + MSG=' requested for precision of machine.. See TOLSF (=R1) ' + CALL XERRWD (MSG, 60, 26, 0, 0, 0, 0, 1, TOLSF, 0.0D0) + RWORK(14) = TOLSF + GO TO 700 + 627 MSG = 'DLSODE- Trouble in DINTDY. ITASK = I1, TOUT = R1' + CALL XERRWD (MSG, 50, 27, 0, 1, ITASK, 0, 1, TOUT, 0.0D0) +C + 700 ISTATE = -3 + RETURN +C + 800 MSG = 'DLSODE- Run aborted.. apparent infinite loop ' + CALL XERRWD (MSG, 50, 303, 2, 0, 0, 0, 0, 0.0D0, 0.0D0) + RETURN +C----------------------- END OF SUBROUTINE DLSODE ---------------------- + END +*DECK DLSODES + SUBROUTINE DLSODES (F, NEQ, Y, T, TOUT, ITOL, RTOL, ATOL, ITASK, + 1 ISTATE, IOPT, RWORK, LRW, IWORK, LIW, JAC, MF) + EXTERNAL F, JAC + INTEGER NEQ, ITOL, ITASK, ISTATE, IOPT, LRW, IWORK, LIW, MF + DOUBLE PRECISION Y, T, TOUT, RTOL, ATOL, RWORK + DIMENSION NEQ(*), Y(*), RTOL(*), ATOL(*), RWORK(LRW), IWORK(LIW) +C----------------------------------------------------------------------- +C This is the 12 November 2003 version of +C DLSODES: Livermore Solver for Ordinary Differential Equations +C with general Sparse Jacobian matrix. +C +C This version is in double precision. +C +C DLSODES solves the initial value problem for stiff or nonstiff +C systems of first order ODEs, +C dy/dt = f(t,y) , or, in component form, +C dy(i)/dt = f(i) = f(i,t,y(1),y(2),...,y(NEQ)) (i = 1,...,NEQ). +C DLSODES is a variant of the DLSODE package, and is intended for +C problems in which the Jacobian matrix df/dy has an arbitrary +C sparse structure (when the problem is stiff). +C +C Authors: Alan C. Hindmarsh +C Center for Applied Scientific Computing, L-561 +C Lawrence Livermore National Laboratory +C Livermore, CA 94551 +C and +C Andrew H. Sherman +C J. S. Nolen and Associates +C Houston, TX 77084 +C----------------------------------------------------------------------- +C References: +C 1. Alan C. Hindmarsh, ODEPACK, A Systematized Collection of ODE +C Solvers, in Scientific Computing, R. S. Stepleman et al. (Eds.), +C North-Holland, Amsterdam, 1983, pp. 55-64. +C +C 2. S. C. Eisenstat, M. C. Gursky, M. H. Schultz, and A. H. Sherman, +C Yale Sparse Matrix Package: I. The Symmetric Codes, +C Int. J. Num. Meth. Eng., 18 (1982), pp. 1145-1151. +C +C 3. S. C. Eisenstat, M. C. Gursky, M. H. Schultz, and A. H. Sherman, +C Yale Sparse Matrix Package: II. The Nonsymmetric Codes, +C Research Report No. 114, Dept. of Computer Sciences, Yale +C University, 1977. +C----------------------------------------------------------------------- +C Summary of Usage. +C +C Communication between the user and the DLSODES package, for normal +C situations, is summarized here. This summary describes only a subset +C of the full set of options available. See the full description for +C details, including optional communication, nonstandard options, +C and instructions for special situations. See also the example +C problem (with program and output) following this summary. +C +C A. First provide a subroutine of the form: +C SUBROUTINE F (NEQ, T, Y, YDOT) +C DOUBLE PRECISION T, Y(*), YDOT(*) +C which supplies the vector function f by loading YDOT(i) with f(i). +C +C B. Next determine (or guess) whether or not the problem is stiff. +C Stiffness occurs when the Jacobian matrix df/dy has an eigenvalue +C whose real part is negative and large in magnitude, compared to the +C reciprocal of the t span of interest. If the problem is nonstiff, +C use a method flag MF = 10. If it is stiff, there are two standard +C choices for the method flag, MF = 121 and MF = 222. In both cases, +C DLSODES requires the Jacobian matrix in some form, and it treats this +C matrix in general sparse form, with sparsity structure determined +C internally. (For options where the user supplies the sparsity +C structure, see the full description of MF below.) +C +C C. If the problem is stiff, you are encouraged to supply the Jacobian +C directly (MF = 121), but if this is not feasible, DLSODES will +C compute it internally by difference quotients (MF = 222). +C If you are supplying the Jacobian, provide a subroutine of the form: +C SUBROUTINE JAC (NEQ, T, Y, J, IAN, JAN, PDJ) +C DOUBLE PRECISION T, Y(*), IAN(*), JAN(*), PDJ(*) +C Here NEQ, T, Y, and J are input arguments, and the JAC routine is to +C load the array PDJ (of length NEQ) with the J-th column of df/dy. +C I.e., load PDJ(i) with df(i)/dy(J) for all relevant values of i. +C The arguments IAN and JAN should be ignored for normal situations. +C DLSODES will call the JAC routine with J = 1,2,...,NEQ. +C Only nonzero elements need be loaded. Usually, a crude approximation +C to df/dy, possibly with fewer nonzero elements, will suffice. +C +C D. Write a main program which calls Subroutine DLSODES once for +C each point at which answers are desired. This should also provide +C for possible use of logical unit 6 for output of error messages by +C DLSODES. On the first call to DLSODES, supply arguments as follows: +C F = name of subroutine for right-hand side vector f. +C This name must be declared External in calling program. +C NEQ = number of first order ODEs. +C Y = array of initial values, of length NEQ. +C T = the initial value of the independent variable t. +C TOUT = first point where output is desired (.ne. T). +C ITOL = 1 or 2 according as ATOL (below) is a scalar or array. +C RTOL = relative tolerance parameter (scalar). +C ATOL = absolute tolerance parameter (scalar or array). +C The estimated local error in Y(i) will be controlled so as +C to be roughly less (in magnitude) than +C EWT(i) = RTOL*ABS(Y(i)) + ATOL if ITOL = 1, or +C EWT(i) = RTOL*ABS(Y(i)) + ATOL(i) if ITOL = 2. +C Thus the local error test passes if, in each component, +C either the absolute error is less than ATOL (or ATOL(i)), +C or the relative error is less than RTOL. +C Use RTOL = 0.0 for pure absolute error control, and +C use ATOL = 0.0 (or ATOL(i) = 0.0) for pure relative error +C control. Caution: actual (global) errors may exceed these +C local tolerances, so choose them conservatively. +C ITASK = 1 for normal computation of output values of Y at t = TOUT. +C ISTATE = integer flag (input and output). Set ISTATE = 1. +C IOPT = 0 to indicate no optional inputs used. +C RWORK = real work array of length at least: +C 20 + 16*NEQ for MF = 10, +C 20 + (2 + 1./LENRAT)*NNZ + (11 + 9./LENRAT)*NEQ +C for MF = 121 or 222, +C where: +C NNZ = the number of nonzero elements in the sparse +C Jacobian (if this is unknown, use an estimate), and +C LENRAT = the real to integer wordlength ratio (usually 1 in +C single precision and 2 in double precision). +C In any case, the required size of RWORK cannot generally +C be predicted in advance if MF = 121 or 222, and the value +C above is a rough estimate of a crude lower bound. Some +C experimentation with this size may be necessary. +C (When known, the correct required length is an optional +C output, available in IWORK(17).) +C LRW = declared length of RWORK (in user dimension). +C IWORK = integer work array of length at least 30. +C LIW = declared length of IWORK (in user dimension). +C JAC = name of subroutine for Jacobian matrix (MF = 121). +C If used, this name must be declared External in calling +C program. If not used, pass a dummy name. +C MF = method flag. Standard values are: +C 10 for nonstiff (Adams) method, no Jacobian used +C 121 for stiff (BDF) method, user-supplied sparse Jacobian +C 222 for stiff method, internally generated sparse Jacobian +C Note that the main program must declare arrays Y, RWORK, IWORK, +C and possibly ATOL. +C +C E. The output from the first call (or any call) is: +C Y = array of computed values of y(t) vector. +C T = corresponding value of independent variable (normally TOUT). +C ISTATE = 2 if DLSODES was successful, negative otherwise. +C -1 means excess work done on this call (perhaps wrong MF). +C -2 means excess accuracy requested (tolerances too small). +C -3 means illegal input detected (see printed message). +C -4 means repeated error test failures (check all inputs). +C -5 means repeated convergence failures (perhaps bad Jacobian +C supplied or wrong choice of MF or tolerances). +C -6 means error weight became zero during problem. (Solution +C component i vanished, and ATOL or ATOL(i) = 0.) +C -7 means a fatal error return flag came from sparse solver +C CDRV by way of DPRJS or DSOLSS. Should never happen. +C A return with ISTATE = -1, -4, or -5 may result from using +C an inappropriate sparsity structure, one that is quite +C different from the initial structure. Consider calling +C DLSODES again with ISTATE = 3 to force the structure to be +C reevaluated. See the full description of ISTATE below. +C +C F. To continue the integration after a successful return, simply +C reset TOUT and call DLSODES again. No other parameters need be reset. +C +C----------------------------------------------------------------------- +C Example Problem. +C +C The following is a simple example problem, with the coding +C needed for its solution by DLSODES. The problem is from chemical +C kinetics, and consists of the following 12 rate equations: +C dy1/dt = -rk1*y1 +C dy2/dt = rk1*y1 + rk11*rk14*y4 + rk19*rk14*y5 +C - rk3*y2*y3 - rk15*y2*y12 - rk2*y2 +C dy3/dt = rk2*y2 - rk5*y3 - rk3*y2*y3 - rk7*y10*y3 +C + rk11*rk14*y4 + rk12*rk14*y6 +C dy4/dt = rk3*y2*y3 - rk11*rk14*y4 - rk4*y4 +C dy5/dt = rk15*y2*y12 - rk19*rk14*y5 - rk16*y5 +C dy6/dt = rk7*y10*y3 - rk12*rk14*y6 - rk8*y6 +C dy7/dt = rk17*y10*y12 - rk20*rk14*y7 - rk18*y7 +C dy8/dt = rk9*y10 - rk13*rk14*y8 - rk10*y8 +C dy9/dt = rk4*y4 + rk16*y5 + rk8*y6 + rk18*y7 +C dy10/dt = rk5*y3 + rk12*rk14*y6 + rk20*rk14*y7 +C + rk13*rk14*y8 - rk7*y10*y3 - rk17*y10*y12 +C - rk6*y10 - rk9*y10 +C dy11/dt = rk10*y8 +C dy12/dt = rk6*y10 + rk19*rk14*y5 + rk20*rk14*y7 +C - rk15*y2*y12 - rk17*y10*y12 +C +C with rk1 = rk5 = 0.1, rk4 = rk8 = rk16 = rk18 = 2.5, +C rk10 = 5.0, rk2 = rk6 = 10.0, rk14 = 30.0, +C rk3 = rk7 = rk9 = rk11 = rk12 = rk13 = rk19 = rk20 = 50.0, +C rk15 = rk17 = 100.0. +C +C The t interval is from 0 to 1000, and the initial conditions +C are y1 = 1, y2 = y3 = ... = y12 = 0. The problem is stiff. +C +C The following coding solves this problem with DLSODES, using MF = 121 +C and printing results at t = .1, 1., 10., 100., 1000. It uses +C ITOL = 1 and mixed relative/absolute tolerance controls. +C During the run and at the end, statistical quantities of interest +C are printed (see optional outputs in the full description below). +C +C EXTERNAL FEX, JEX +C DOUBLE PRECISION ATOL, RTOL, RWORK, T, TOUT, Y +C DIMENSION Y(12), RWORK(500), IWORK(30) +C DATA LRW/500/, LIW/30/ +C NEQ = 12 +C DO 10 I = 1,NEQ +C 10 Y(I) = 0.0D0 +C Y(1) = 1.0D0 +C T = 0.0D0 +C TOUT = 0.1D0 +C ITOL = 1 +C RTOL = 1.0D-4 +C ATOL = 1.0D-6 +C ITASK = 1 +C ISTATE = 1 +C IOPT = 0 +C MF = 121 +C DO 40 IOUT = 1,5 +C CALL DLSODES (FEX, NEQ, Y, T, TOUT, ITOL, RTOL, ATOL, +C 1 ITASK, ISTATE, IOPT, RWORK, LRW, IWORK, LIW, JEX, MF) +C WRITE(6,30)T,IWORK(11),RWORK(11),(Y(I),I=1,NEQ) +C 30 FORMAT(//' At t =',D11.3,4X, +C 1 ' No. steps =',I5,4X,' Last step =',D11.3/ +C 2 ' Y array = ',4D14.5/13X,4D14.5/13X,4D14.5) +C IF (ISTATE .LT. 0) GO TO 80 +C TOUT = TOUT*10.0D0 +C 40 CONTINUE +C LENRW = IWORK(17) +C LENIW = IWORK(18) +C NST = IWORK(11) +C NFE = IWORK(12) +C NJE = IWORK(13) +C NLU = IWORK(21) +C NNZ = IWORK(19) +C NNZLU = IWORK(25) + IWORK(26) + NEQ +C WRITE (6,70) LENRW,LENIW,NST,NFE,NJE,NLU,NNZ,NNZLU +C 70 FORMAT(//' Required RWORK size =',I4,' IWORK size =',I4/ +C 1 ' No. steps =',I4,' No. f-s =',I4,' No. J-s =',I4, +C 2 ' No. LU-s =',I4/' No. of nonzeros in J =',I5, +C 3 ' No. of nonzeros in LU =',I5) +C STOP +C 80 WRITE(6,90)ISTATE +C 90 FORMAT(///' Error halt.. ISTATE =',I3) +C STOP +C END +C +C SUBROUTINE FEX (NEQ, T, Y, YDOT) +C DOUBLE PRECISION T, Y, YDOT +C DOUBLE PRECISION RK1, RK2, RK3, RK4, RK5, RK6, RK7, RK8, RK9, +C 1 RK10, RK11, RK12, RK13, RK14, RK15, RK16, RK17 +C DIMENSION Y(12), YDOT(12) +C DATA RK1/0.1D0/, RK2/10.0D0/, RK3/50.0D0/, RK4/2.5D0/, RK5/0.1D0/, +C 1 RK6/10.0D0/, RK7/50.0D0/, RK8/2.5D0/, RK9/50.0D0/, RK10/5.0D0/, +C 2 RK11/50.0D0/, RK12/50.0D0/, RK13/50.0D0/, RK14/30.0D0/, +C 3 RK15/100.0D0/, RK16/2.5D0/, RK17/100.0D0/, RK18/2.5D0/, +C 4 RK19/50.0D0/, RK20/50.0D0/ +C YDOT(1) = -RK1*Y(1) +C YDOT(2) = RK1*Y(1) + RK11*RK14*Y(4) + RK19*RK14*Y(5) +C 1 - RK3*Y(2)*Y(3) - RK15*Y(2)*Y(12) - RK2*Y(2) +C YDOT(3) = RK2*Y(2) - RK5*Y(3) - RK3*Y(2)*Y(3) - RK7*Y(10)*Y(3) +C 1 + RK11*RK14*Y(4) + RK12*RK14*Y(6) +C YDOT(4) = RK3*Y(2)*Y(3) - RK11*RK14*Y(4) - RK4*Y(4) +C YDOT(5) = RK15*Y(2)*Y(12) - RK19*RK14*Y(5) - RK16*Y(5) +C YDOT(6) = RK7*Y(10)*Y(3) - RK12*RK14*Y(6) - RK8*Y(6) +C YDOT(7) = RK17*Y(10)*Y(12) - RK20*RK14*Y(7) - RK18*Y(7) +C YDOT(8) = RK9*Y(10) - RK13*RK14*Y(8) - RK10*Y(8) +C YDOT(9) = RK4*Y(4) + RK16*Y(5) + RK8*Y(6) + RK18*Y(7) +C YDOT(10) = RK5*Y(3) + RK12*RK14*Y(6) + RK20*RK14*Y(7) +C 1 + RK13*RK14*Y(8) - RK7*Y(10)*Y(3) - RK17*Y(10)*Y(12) +C 2 - RK6*Y(10) - RK9*Y(10) +C YDOT(11) = RK10*Y(8) +C YDOT(12) = RK6*Y(10) + RK19*RK14*Y(5) + RK20*RK14*Y(7) +C 1 - RK15*Y(2)*Y(12) - RK17*Y(10)*Y(12) +C RETURN +C END +C +C SUBROUTINE JEX (NEQ, T, Y, J, IA, JA, PDJ) +C DOUBLE PRECISION T, Y, PDJ +C DOUBLE PRECISION RK1, RK2, RK3, RK4, RK5, RK6, RK7, RK8, RK9, +C 1 RK10, RK11, RK12, RK13, RK14, RK15, RK16, RK17 +C DIMENSION Y(12), IA(*), JA(*), PDJ(12) +C DATA RK1/0.1D0/, RK2/10.0D0/, RK3/50.0D0/, RK4/2.5D0/, RK5/0.1D0/, +C 1 RK6/10.0D0/, RK7/50.0D0/, RK8/2.5D0/, RK9/50.0D0/, RK10/5.0D0/, +C 2 RK11/50.0D0/, RK12/50.0D0/, RK13/50.0D0/, RK14/30.0D0/, +C 3 RK15/100.0D0/, RK16/2.5D0/, RK17/100.0D0/, RK18/2.5D0/, +C 4 RK19/50.0D0/, RK20/50.0D0/ +C GO TO (1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12), J +C 1 PDJ(1) = -RK1 +C PDJ(2) = RK1 +C RETURN +C 2 PDJ(2) = -RK3*Y(3) - RK15*Y(12) - RK2 +C PDJ(3) = RK2 - RK3*Y(3) +C PDJ(4) = RK3*Y(3) +C PDJ(5) = RK15*Y(12) +C PDJ(12) = -RK15*Y(12) +C RETURN +C 3 PDJ(2) = -RK3*Y(2) +C PDJ(3) = -RK5 - RK3*Y(2) - RK7*Y(10) +C PDJ(4) = RK3*Y(2) +C PDJ(6) = RK7*Y(10) +C PDJ(10) = RK5 - RK7*Y(10) +C RETURN +C 4 PDJ(2) = RK11*RK14 +C PDJ(3) = RK11*RK14 +C PDJ(4) = -RK11*RK14 - RK4 +C PDJ(9) = RK4 +C RETURN +C 5 PDJ(2) = RK19*RK14 +C PDJ(5) = -RK19*RK14 - RK16 +C PDJ(9) = RK16 +C PDJ(12) = RK19*RK14 +C RETURN +C 6 PDJ(3) = RK12*RK14 +C PDJ(6) = -RK12*RK14 - RK8 +C PDJ(9) = RK8 +C PDJ(10) = RK12*RK14 +C RETURN +C 7 PDJ(7) = -RK20*RK14 - RK18 +C PDJ(9) = RK18 +C PDJ(10) = RK20*RK14 +C PDJ(12) = RK20*RK14 +C RETURN +C 8 PDJ(8) = -RK13*RK14 - RK10 +C PDJ(10) = RK13*RK14 +C PDJ(11) = RK10 +C 9 RETURN +C 10 PDJ(3) = -RK7*Y(3) +C PDJ(6) = RK7*Y(3) +C PDJ(7) = RK17*Y(12) +C PDJ(8) = RK9 +C PDJ(10) = -RK7*Y(3) - RK17*Y(12) - RK6 - RK9 +C PDJ(12) = RK6 - RK17*Y(12) +C 11 RETURN +C 12 PDJ(2) = -RK15*Y(2) +C PDJ(5) = RK15*Y(2) +C PDJ(7) = RK17*Y(10) +C PDJ(10) = -RK17*Y(10) +C PDJ(12) = -RK15*Y(2) - RK17*Y(10) +C RETURN +C END +C +C The output of this program (on a Cray-1 in single precision) +C is as follows: +C +C +C At t = 1.000e-01 No. steps = 12 Last step = 1.515e-02 +C Y array = 9.90050e-01 6.28228e-03 3.65313e-03 7.51934e-07 +C 1.12167e-09 1.18458e-09 1.77291e-12 3.26476e-07 +C 5.46720e-08 9.99500e-06 4.48483e-08 2.76398e-06 +C +C +C At t = 1.000e+00 No. steps = 33 Last step = 7.880e-02 +C Y array = 9.04837e-01 9.13105e-03 8.20622e-02 2.49177e-05 +C 1.85055e-06 1.96797e-06 1.46157e-07 2.39557e-05 +C 3.26306e-05 7.21621e-04 5.06433e-05 3.05010e-03 +C +C +C At t = 1.000e+01 No. steps = 48 Last step = 1.239e+00 +C Y array = 3.67876e-01 3.68958e-03 3.65133e-01 4.48325e-05 +C 6.10798e-05 4.33148e-05 5.90211e-05 1.18449e-04 +C 3.15235e-03 3.56531e-03 4.15520e-03 2.48741e-01 +C +C +C At t = 1.000e+02 No. steps = 91 Last step = 3.764e+00 +C Y array = 4.44981e-05 4.42666e-07 4.47273e-04 -3.53257e-11 +C 2.81577e-08 -9.67741e-11 2.77615e-07 1.45322e-07 +C 1.56230e-02 4.37394e-06 1.60104e-02 9.52246e-01 +C +C +C At t = 1.000e+03 No. steps = 111 Last step = 4.156e+02 +C Y array = -2.65492e-13 2.60539e-14 -8.59563e-12 6.29355e-14 +C -1.78066e-13 5.71471e-13 -1.47561e-12 4.58078e-15 +C 1.56314e-02 1.37878e-13 1.60184e-02 9.52719e-01 +C +C +C Required RWORK size = 442 IWORK size = 30 +C No. steps = 111 No. f-s = 142 No. J-s = 2 No. LU-s = 20 +C No. of nonzeros in J = 44 No. of nonzeros in LU = 50 +C +C----------------------------------------------------------------------- +C Full Description of User Interface to DLSODES. +C +C The user interface to DLSODES consists of the following parts. +C +C 1. The call sequence to Subroutine DLSODES, which is a driver +C routine for the solver. This includes descriptions of both +C the call sequence arguments and of user-supplied routines. +C Following these descriptions is a description of +C optional inputs available through the call sequence, and then +C a description of optional outputs (in the work arrays). +C +C 2. Descriptions of other routines in the DLSODES package that may be +C (optionally) called by the user. These provide the ability to +C alter error message handling, save and restore the internal +C Common, and obtain specified derivatives of the solution y(t). +C +C 3. Descriptions of Common blocks to be declared in overlay +C or similar environments, or to be saved when doing an interrupt +C of the problem and continued solution later. +C +C 4. Description of two routines in the DLSODES package, either of +C which the user may replace with his/her own version, if desired. +C These relate to the measurement of errors. +C +C----------------------------------------------------------------------- +C Part 1. Call Sequence. +C +C The call sequence parameters used for input only are +C F, NEQ, TOUT, ITOL, RTOL, ATOL, ITASK, IOPT, LRW, LIW, JAC, MF, +C and those used for both input and output are +C Y, T, ISTATE. +C The work arrays RWORK and IWORK are also used for conditional and +C optional inputs and optional outputs. (The term output here refers +C to the return from Subroutine DLSODES to the user's calling program.) +C +C The legality of input parameters will be thoroughly checked on the +C initial call for the problem, but not checked thereafter unless a +C change in input parameters is flagged by ISTATE = 3 on input. +C +C The descriptions of the call arguments are as follows. +C +C F = the name of the user-supplied subroutine defining the +C ODE system. The system must be put in the first-order +C form dy/dt = f(t,y), where f is a vector-valued function +C of the scalar t and the vector y. Subroutine F is to +C compute the function f. It is to have the form +C SUBROUTINE F (NEQ, T, Y, YDOT) +C DOUBLE PRECISION T, Y(*), YDOT(*) +C where NEQ, T, and Y are input, and the array YDOT = f(t,y) +C is output. Y and YDOT are arrays of length NEQ. +C Subroutine F should not alter y(1),...,y(NEQ). +C F must be declared External in the calling program. +C +C Subroutine F may access user-defined quantities in +C NEQ(2),... and/or in Y(NEQ(1)+1),... if NEQ is an array +C (dimensioned in F) and/or Y has length exceeding NEQ(1). +C See the descriptions of NEQ and Y below. +C +C If quantities computed in the F routine are needed +C externally to DLSODES, an extra call to F should be made +C for this purpose, for consistent and accurate results. +C If only the derivative dy/dt is needed, use DINTDY instead. +C +C NEQ = the size of the ODE system (number of first order +C ordinary differential equations). Used only for input. +C NEQ may be decreased, but not increased, during the problem. +C If NEQ is decreased (with ISTATE = 3 on input), the +C remaining components of Y should be left undisturbed, if +C these are to be accessed in F and/or JAC. +C +C Normally, NEQ is a scalar, and it is generally referred to +C as a scalar in this user interface description. However, +C NEQ may be an array, with NEQ(1) set to the system size. +C (The DLSODES package accesses only NEQ(1).) In either case, +C this parameter is passed as the NEQ argument in all calls +C to F and JAC. Hence, if it is an array, locations +C NEQ(2),... may be used to store other integer data and pass +C it to F and/or JAC. Subroutines F and/or JAC must include +C NEQ in a Dimension statement in that case. +C +C Y = a real array for the vector of dependent variables, of +C length NEQ or more. Used for both input and output on the +C first call (ISTATE = 1), and only for output on other calls. +C on the first call, Y must contain the vector of initial +C values. On output, Y contains the computed solution vector, +C evaluated at T. If desired, the Y array may be used +C for other purposes between calls to the solver. +C +C This array is passed as the Y argument in all calls to +C F and JAC. Hence its length may exceed NEQ, and locations +C Y(NEQ+1),... may be used to store other real data and +C pass it to F and/or JAC. (The DLSODES package accesses only +C Y(1),...,Y(NEQ).) +C +C T = the independent variable. On input, T is used only on the +C first call, as the initial point of the integration. +C on output, after each call, T is the value at which a +C computed solution Y is evaluated (usually the same as TOUT). +C On an error return, T is the farthest point reached. +C +C TOUT = the next value of t at which a computed solution is desired. +C Used only for input. +C +C When starting the problem (ISTATE = 1), TOUT may be equal +C to T for one call, then should .ne. T for the next call. +C For the initial T, an input value of TOUT .ne. T is used +C in order to determine the direction of the integration +C (i.e. the algebraic sign of the step sizes) and the rough +C scale of the problem. Integration in either direction +C (forward or backward in t) is permitted. +C +C If ITASK = 2 or 5 (one-step modes), TOUT is ignored after +C the first call (i.e. the first call with TOUT .ne. T). +C Otherwise, TOUT is required on every call. +C +C If ITASK = 1, 3, or 4, the values of TOUT need not be +C monotone, but a value of TOUT which backs up is limited +C to the current internal T interval, whose endpoints are +C TCUR - HU and TCUR (see optional outputs, below, for +C TCUR and HU). +C +C ITOL = an indicator for the type of error control. See +C description below under ATOL. Used only for input. +C +C RTOL = a relative error tolerance parameter, either a scalar or +C an array of length NEQ. See description below under ATOL. +C Input only. +C +C ATOL = an absolute error tolerance parameter, either a scalar or +C an array of length NEQ. Input only. +C +C The input parameters ITOL, RTOL, and ATOL determine +C the error control performed by the solver. The solver will +C control the vector E = (E(i)) of estimated local errors +C in y, according to an inequality of the form +C RMS-norm of ( E(i)/EWT(i) ) .le. 1, +C where EWT(i) = RTOL(i)*ABS(Y(i)) + ATOL(i), +C and the RMS-norm (root-mean-square norm) here is +C RMS-norm(v) = SQRT(sum v(i)**2 / NEQ). Here EWT = (EWT(i)) +C is a vector of weights which must always be positive, and +C the values of RTOL and ATOL should all be non-negative. +C The following table gives the types (scalar/array) of +C RTOL and ATOL, and the corresponding form of EWT(i). +C +C ITOL RTOL ATOL EWT(i) +C 1 scalar scalar RTOL*ABS(Y(i)) + ATOL +C 2 scalar array RTOL*ABS(Y(i)) + ATOL(i) +C 3 array scalar RTOL(i)*ABS(Y(i)) + ATOL +C 4 array array RTOL(i)*ABS(Y(i)) + ATOL(i) +C +C When either of these parameters is a scalar, it need not +C be dimensioned in the user's calling program. +C +C If none of the above choices (with ITOL, RTOL, and ATOL +C fixed throughout the problem) is suitable, more general +C error controls can be obtained by substituting +C user-supplied routines for the setting of EWT and/or for +C the norm calculation. See Part 4 below. +C +C If global errors are to be estimated by making a repeated +C run on the same problem with smaller tolerances, then all +C components of RTOL and ATOL (i.e. of EWT) should be scaled +C down uniformly. +C +C ITASK = an index specifying the task to be performed. +C Input only. ITASK has the following values and meanings. +C 1 means normal computation of output values of y(t) at +C t = TOUT (by overshooting and interpolating). +C 2 means take one step only and return. +C 3 means stop at the first internal mesh point at or +C beyond t = TOUT and return. +C 4 means normal computation of output values of y(t) at +C t = TOUT but without overshooting t = TCRIT. +C TCRIT must be input as RWORK(1). TCRIT may be equal to +C or beyond TOUT, but not behind it in the direction of +C integration. This option is useful if the problem +C has a singularity at or beyond t = TCRIT. +C 5 means take one step, without passing TCRIT, and return. +C TCRIT must be input as RWORK(1). +C +C Note: If ITASK = 4 or 5 and the solver reaches TCRIT +C (within roundoff), it will return T = TCRIT (exactly) to +C indicate this (unless ITASK = 4 and TOUT comes before TCRIT, +C in which case answers at t = TOUT are returned first). +C +C ISTATE = an index used for input and output to specify the +C the state of the calculation. +C +C On input, the values of ISTATE are as follows. +C 1 means this is the first call for the problem +C (initializations will be done). See note below. +C 2 means this is not the first call, and the calculation +C is to continue normally, with no change in any input +C parameters except possibly TOUT and ITASK. +C (If ITOL, RTOL, and/or ATOL are changed between calls +C with ISTATE = 2, the new values will be used but not +C tested for legality.) +C 3 means this is not the first call, and the +C calculation is to continue normally, but with +C a change in input parameters other than +C TOUT and ITASK. Changes are allowed in +C NEQ, ITOL, RTOL, ATOL, IOPT, LRW, LIW, MF, +C the conditional inputs IA and JA, +C and any of the optional inputs except H0. +C In particular, if MITER = 1 or 2, a call with ISTATE = 3 +C will cause the sparsity structure of the problem to be +C recomputed (or reread from IA and JA if MOSS = 0). +C Note: a preliminary call with TOUT = T is not counted +C as a first call here, as no initialization or checking of +C input is done. (Such a call is sometimes useful for the +C purpose of outputting the initial conditions.) +C Thus the first call for which TOUT .ne. T requires +C ISTATE = 1 on input. +C +C On output, ISTATE has the following values and meanings. +C 1 means nothing was done; TOUT = T and ISTATE = 1 on input. +C 2 means the integration was performed successfully. +C -1 means an excessive amount of work (more than MXSTEP +C steps) was done on this call, before completing the +C requested task, but the integration was otherwise +C successful as far as T. (MXSTEP is an optional input +C and is normally 500.) To continue, the user may +C simply reset ISTATE to a value .gt. 1 and call again +C (the excess work step counter will be reset to 0). +C In addition, the user may increase MXSTEP to avoid +C this error return (see below on optional inputs). +C -2 means too much accuracy was requested for the precision +C of the machine being used. This was detected before +C completing the requested task, but the integration +C was successful as far as T. To continue, the tolerance +C parameters must be reset, and ISTATE must be set +C to 3. The optional output TOLSF may be used for this +C purpose. (Note: If this condition is detected before +C taking any steps, then an illegal input return +C (ISTATE = -3) occurs instead.) +C -3 means illegal input was detected, before taking any +C integration steps. See written message for details. +C Note: If the solver detects an infinite loop of calls +C to the solver with illegal input, it will cause +C the run to stop. +C -4 means there were repeated error test failures on +C one attempted step, before completing the requested +C task, but the integration was successful as far as T. +C The problem may have a singularity, or the input +C may be inappropriate. +C -5 means there were repeated convergence test failures on +C one attempted step, before completing the requested +C task, but the integration was successful as far as T. +C This may be caused by an inaccurate Jacobian matrix, +C if one is being used. +C -6 means EWT(i) became zero for some i during the +C integration. Pure relative error control (ATOL(i)=0.0) +C was requested on a variable which has now vanished. +C The integration was successful as far as T. +C -7 means a fatal error return flag came from the sparse +C solver CDRV by way of DPRJS or DSOLSS (numerical +C factorization or backsolve). This should never happen. +C The integration was successful as far as T. +C +C Note: an error return with ISTATE = -1, -4, or -5 and with +C MITER = 1 or 2 may mean that the sparsity structure of the +C problem has changed significantly since it was last +C determined (or input). In that case, one can attempt to +C complete the integration by setting ISTATE = 3 on the next +C call, so that a new structure determination is done. +C +C Note: since the normal output value of ISTATE is 2, +C it does not need to be reset for normal continuation. +C Also, since a negative input value of ISTATE will be +C regarded as illegal, a negative output value requires the +C user to change it, and possibly other inputs, before +C calling the solver again. +C +C IOPT = an integer flag to specify whether or not any optional +C inputs are being used on this call. Input only. +C The optional inputs are listed separately below. +C IOPT = 0 means no optional inputs are being used. +C Default values will be used in all cases. +C IOPT = 1 means one or more optional inputs are being used. +C +C RWORK = a work array used for a mixture of real (double precision) +C and integer work space. +C The length of RWORK (in real words) must be at least +C 20 + NYH*(MAXORD + 1) + 3*NEQ + LWM where +C NYH = the initial value of NEQ, +C MAXORD = 12 (if METH = 1) or 5 (if METH = 2) (unless a +C smaller value is given as an optional input), +C LWM = 0 if MITER = 0, +C LWM = 2*NNZ + 2*NEQ + (NNZ+9*NEQ)/LENRAT if MITER = 1, +C LWM = 2*NNZ + 2*NEQ + (NNZ+10*NEQ)/LENRAT if MITER = 2, +C LWM = NEQ + 2 if MITER = 3. +C In the above formulas, +C NNZ = number of nonzero elements in the Jacobian matrix. +C LENRAT = the real to integer wordlength ratio (usually 1 in +C single precision and 2 in double precision). +C (See the MF description for METH and MITER.) +C Thus if MAXORD has its default value and NEQ is constant, +C the minimum length of RWORK is: +C 20 + 16*NEQ for MF = 10, +C 20 + 16*NEQ + LWM for MF = 11, 111, 211, 12, 112, 212, +C 22 + 17*NEQ for MF = 13, +C 20 + 9*NEQ for MF = 20, +C 20 + 9*NEQ + LWM for MF = 21, 121, 221, 22, 122, 222, +C 22 + 10*NEQ for MF = 23. +C If MITER = 1 or 2, the above formula for LWM is only a +C crude lower bound. The required length of RWORK cannot +C be readily predicted in general, as it depends on the +C sparsity structure of the problem. Some experimentation +C may be necessary. +C +C The first 20 words of RWORK are reserved for conditional +C and optional inputs and optional outputs. +C +C The following word in RWORK is a conditional input: +C RWORK(1) = TCRIT = critical value of t which the solver +C is not to overshoot. Required if ITASK is +C 4 or 5, and ignored otherwise. (See ITASK.) +C +C LRW = the length of the array RWORK, as declared by the user. +C (This will be checked by the solver.) +C +C IWORK = an integer work array. The length of IWORK must be at least +C 31 + NEQ + NNZ if MOSS = 0 and MITER = 1 or 2, or +C 30 otherwise. +C (NNZ is the number of nonzero elements in df/dy.) +C +C In DLSODES, IWORK is used only for conditional and +C optional inputs and optional outputs. +C +C The following two blocks of words in IWORK are conditional +C inputs, required if MOSS = 0 and MITER = 1 or 2, but not +C otherwise (see the description of MF for MOSS). +C IWORK(30+j) = IA(j) (j=1,...,NEQ+1) +C IWORK(31+NEQ+k) = JA(k) (k=1,...,NNZ) +C The two arrays IA and JA describe the sparsity structure +C to be assumed for the Jacobian matrix. JA contains the row +C indices where nonzero elements occur, reading in columnwise +C order, and IA contains the starting locations in JA of the +C descriptions of columns 1,...,NEQ, in that order, with +C IA(1) = 1. Thus, for each column index j = 1,...,NEQ, the +C values of the row index i in column j where a nonzero +C element may occur are given by +C i = JA(k), where IA(j) .le. k .lt. IA(j+1). +C If NNZ is the total number of nonzero locations assumed, +C then the length of the JA array is NNZ, and IA(NEQ+1) must +C be NNZ + 1. Duplicate entries are not allowed. +C +C LIW = the length of the array IWORK, as declared by the user. +C (This will be checked by the solver.) +C +C Note: The work arrays must not be altered between calls to DLSODES +C for the same problem, except possibly for the conditional and +C optional inputs, and except for the last 3*NEQ words of RWORK. +C The latter space is used for internal scratch space, and so is +C available for use by the user outside DLSODES between calls, if +C desired (but not for use by F or JAC). +C +C JAC = name of user-supplied routine (MITER = 1 or MOSS = 1) to +C compute the Jacobian matrix, df/dy, as a function of +C the scalar t and the vector y. It is to have the form +C SUBROUTINE JAC (NEQ, T, Y, J, IAN, JAN, PDJ) +C DOUBLE PRECISION T, Y(*), IAN(*), JAN(*), PDJ(*) +C where NEQ, T, Y, J, IAN, and JAN are input, and the array +C PDJ, of length NEQ, is to be loaded with column J +C of the Jacobian on output. Thus df(i)/dy(J) is to be +C loaded into PDJ(i) for all relevant values of i. +C Here T and Y have the same meaning as in Subroutine F, +C and J is a column index (1 to NEQ). IAN and JAN are +C undefined in calls to JAC for structure determination +C (MOSS = 1). otherwise, IAN and JAN are structure +C descriptors, as defined under optional outputs below, and +C so can be used to determine the relevant row indices i, if +C desired. +C JAC need not provide df/dy exactly. A crude +C approximation (possibly with greater sparsity) will do. +C In any case, PDJ is preset to zero by the solver, +C so that only the nonzero elements need be loaded by JAC. +C Calls to JAC are made with J = 1,...,NEQ, in that order, and +C each such set of calls is preceded by a call to F with the +C same arguments NEQ, T, and Y. Thus to gain some efficiency, +C intermediate quantities shared by both calculations may be +C saved in a user Common block by F and not recomputed by JAC, +C if desired. JAC must not alter its input arguments. +C JAC must be declared External in the calling program. +C Subroutine JAC may access user-defined quantities in +C NEQ(2),... and/or in Y(NEQ(1)+1),... if NEQ is an array +C (dimensioned in JAC) and/or Y has length exceeding NEQ(1). +C See the descriptions of NEQ and Y above. +C +C MF = the method flag. Used only for input. +C MF has three decimal digits-- MOSS, METH, MITER-- +C MF = 100*MOSS + 10*METH + MITER. +C MOSS indicates the method to be used to obtain the sparsity +C structure of the Jacobian matrix if MITER = 1 or 2: +C MOSS = 0 means the user has supplied IA and JA +C (see descriptions under IWORK above). +C MOSS = 1 means the user has supplied JAC (see below) +C and the structure will be obtained from NEQ +C initial calls to JAC. +C MOSS = 2 means the structure will be obtained from NEQ+1 +C initial calls to F. +C METH indicates the basic linear multistep method: +C METH = 1 means the implicit Adams method. +C METH = 2 means the method based on Backward +C Differentiation Formulas (BDFs). +C MITER indicates the corrector iteration method: +C MITER = 0 means functional iteration (no Jacobian matrix +C is involved). +C MITER = 1 means chord iteration with a user-supplied +C sparse Jacobian, given by Subroutine JAC. +C MITER = 2 means chord iteration with an internally +C generated (difference quotient) sparse Jacobian +C (using NGP extra calls to F per df/dy value, +C where NGP is an optional output described below.) +C MITER = 3 means chord iteration with an internally +C generated diagonal Jacobian approximation +C (using 1 extra call to F per df/dy evaluation). +C If MITER = 1 or MOSS = 1, the user must supply a Subroutine +C JAC (the name is arbitrary) as described above under JAC. +C Otherwise, a dummy argument can be used. +C +C The standard choices for MF are: +C MF = 10 for a nonstiff problem, +C MF = 21 or 22 for a stiff problem with IA/JA supplied +C (21 if JAC is supplied, 22 if not), +C MF = 121 for a stiff problem with JAC supplied, +C but not IA/JA, +C MF = 222 for a stiff problem with neither IA/JA nor +C JAC supplied. +C The sparseness structure can be changed during the +C problem by making a call to DLSODES with ISTATE = 3. +C----------------------------------------------------------------------- +C Optional Inputs. +C +C The following is a list of the optional inputs provided for in the +C call sequence. (See also Part 2.) For each such input variable, +C this table lists its name as used in this documentation, its +C location in the call sequence, its meaning, and the default value. +C The use of any of these inputs requires IOPT = 1, and in that +C case all of these inputs are examined. A value of zero for any +C of these optional inputs will cause the default value to be used. +C Thus to use a subset of the optional inputs, simply preload +C locations 5 to 10 in RWORK and IWORK to 0.0 and 0 respectively, and +C then set those of interest to nonzero values. +C +C Name Location Meaning and Default Value +C +C H0 RWORK(5) the step size to be attempted on the first step. +C The default value is determined by the solver. +C +C HMAX RWORK(6) the maximum absolute step size allowed. +C The default value is infinite. +C +C HMIN RWORK(7) the minimum absolute step size allowed. +C The default value is 0. (This lower bound is not +C enforced on the final step before reaching TCRIT +C when ITASK = 4 or 5.) +C +C SETH RWORK(8) the element threshhold for sparsity determination +C when MOSS = 1 or 2. If the absolute value of +C an estimated Jacobian element is .le. SETH, it +C will be assumed to be absent in the structure. +C The default value of SETH is 0. +C +C MAXORD IWORK(5) the maximum order to be allowed. The default +C value is 12 if METH = 1, and 5 if METH = 2. +C If MAXORD exceeds the default value, it will +C be reduced to the default value. +C If MAXORD is changed during the problem, it may +C cause the current order to be reduced. +C +C MXSTEP IWORK(6) maximum number of (internally defined) steps +C allowed during one call to the solver. +C The default value is 500. +C +C MXHNIL IWORK(7) maximum number of messages printed (per problem) +C warning that T + H = T on a step (H = step size). +C This must be positive to result in a non-default +C value. The default value is 10. +C----------------------------------------------------------------------- +C Optional Outputs. +C +C As optional additional output from DLSODES, the variables listed +C below are quantities related to the performance of DLSODES +C which are available to the user. These are communicated by way of +C the work arrays, but also have internal mnemonic names as shown. +C Except where stated otherwise, all of these outputs are defined +C on any successful return from DLSODES, and on any return with +C ISTATE = -1, -2, -4, -5, or -6. On an illegal input return +C (ISTATE = -3), they will be unchanged from their existing values +C (if any), except possibly for TOLSF, LENRW, and LENIW. +C On any error return, outputs relevant to the error will be defined, +C as noted below. +C +C Name Location Meaning +C +C HU RWORK(11) the step size in t last used (successfully). +C +C HCUR RWORK(12) the step size to be attempted on the next step. +C +C TCUR RWORK(13) the current value of the independent variable +C which the solver has actually reached, i.e. the +C current internal mesh point in t. On output, TCUR +C will always be at least as far as the argument +C T, but may be farther (if interpolation was done). +C +C TOLSF RWORK(14) a tolerance scale factor, greater than 1.0, +C computed when a request for too much accuracy was +C detected (ISTATE = -3 if detected at the start of +C the problem, ISTATE = -2 otherwise). If ITOL is +C left unaltered but RTOL and ATOL are uniformly +C scaled up by a factor of TOLSF for the next call, +C then the solver is deemed likely to succeed. +C (The user may also ignore TOLSF and alter the +C tolerance parameters in any other way appropriate.) +C +C NST IWORK(11) the number of steps taken for the problem so far. +C +C NFE IWORK(12) the number of f evaluations for the problem so far, +C excluding those for structure determination +C (MOSS = 2). +C +C NJE IWORK(13) the number of Jacobian evaluations for the problem +C so far, excluding those for structure determination +C (MOSS = 1). +C +C NQU IWORK(14) the method order last used (successfully). +C +C NQCUR IWORK(15) the order to be attempted on the next step. +C +C IMXER IWORK(16) the index of the component of largest magnitude in +C the weighted local error vector ( E(i)/EWT(i) ), +C on an error return with ISTATE = -4 or -5. +C +C LENRW IWORK(17) the length of RWORK actually required. +C This is defined on normal returns and on an illegal +C input return for insufficient storage. +C +C LENIW IWORK(18) the length of IWORK actually required. +C This is defined on normal returns and on an illegal +C input return for insufficient storage. +C +C NNZ IWORK(19) the number of nonzero elements in the Jacobian +C matrix, including the diagonal (MITER = 1 or 2). +C (This may differ from that given by IA(NEQ+1)-1 +C if MOSS = 0, because of added diagonal entries.) +C +C NGP IWORK(20) the number of groups of column indices, used in +C difference quotient Jacobian aproximations if +C MITER = 2. This is also the number of extra f +C evaluations needed for each Jacobian evaluation. +C +C NLU IWORK(21) the number of sparse LU decompositions for the +C problem so far. +C +C LYH IWORK(22) the base address in RWORK of the history array YH, +C described below in this list. +C +C IPIAN IWORK(23) the base address of the structure descriptor array +C IAN, described below in this list. +C +C IPJAN IWORK(24) the base address of the structure descriptor array +C JAN, described below in this list. +C +C NZL IWORK(25) the number of nonzero elements in the strict lower +C triangle of the LU factorization used in the chord +C iteration (MITER = 1 or 2). +C +C NZU IWORK(26) the number of nonzero elements in the strict upper +C triangle of the LU factorization used in the chord +C iteration (MITER = 1 or 2). +C The total number of nonzeros in the factorization +C is therefore NZL + NZU + NEQ. +C +C The following four arrays are segments of the RWORK array which +C may also be of interest to the user as optional outputs. +C For each array, the table below gives its internal name, +C its base address, and its description. +C For YH and ACOR, the base addresses are in RWORK (a real array). +C The integer arrays IAN and JAN are to be obtained by declaring an +C integer array IWK and identifying IWK(1) with RWORK(21), using either +C an equivalence statement or a subroutine call. Then the base +C addresses IPIAN (of IAN) and IPJAN (of JAN) in IWK are to be obtained +C as optional outputs IWORK(23) and IWORK(24), respectively. +C Thus IAN(1) is IWK(IPIAN), etc. +C +C Name Base Address Description +C +C IAN IPIAN (in IWK) structure descriptor array of size NEQ + 1. +C JAN IPJAN (in IWK) structure descriptor array of size NNZ. +C (see above) IAN and JAN together describe the sparsity +C structure of the Jacobian matrix, as used by +C DLSODES when MITER = 1 or 2. +C JAN contains the row indices of the nonzero +C locations, reading in columnwise order, and +C IAN contains the starting locations in JAN of +C the descriptions of columns 1,...,NEQ, in +C that order, with IAN(1) = 1. Thus for each +C j = 1,...,NEQ, the row indices i of the +C nonzero locations in column j are +C i = JAN(k), IAN(j) .le. k .lt. IAN(j+1). +C Note that IAN(NEQ+1) = NNZ + 1. +C (If MOSS = 0, IAN/JAN may differ from the +C input IA/JA because of a different ordering +C in each column, and added diagonal entries.) +C +C YH LYH the Nordsieck history array, of size NYH by +C (optional (NQCUR + 1), where NYH is the initial value +C output) of NEQ. For j = 0,1,...,NQCUR, column j+1 +C of YH contains HCUR**j/factorial(j) times +C the j-th derivative of the interpolating +C polynomial currently representing the solution, +C evaluated at t = TCUR. The base address LYH +C is another optional output, listed above. +C +C ACOR LENRW-NEQ+1 array of size NEQ used for the accumulated +C corrections on each step, scaled on output +C to represent the estimated local error in y +C on the last step. This is the vector E in +C the description of the error control. It is +C defined only on a successful return from +C DLSODES. +C +C----------------------------------------------------------------------- +C Part 2. Other Routines Callable. +C +C The following are optional calls which the user may make to +C gain additional capabilities in conjunction with DLSODES. +C (The rouMETHtines XSETUN and XSETF are designed to conform to the +C SLATEC error handling package.) +C +C Form of Call Function +C CALL XSETUN(LUN) Set the logical unit number, LUN, for +C output of messages from DLSODES, if +C the default is not desired. +C The default value of LUN is 6. +C +C CALL XSETF(MFLAG) Set a flag to control the printing of +C messages by DLSODES. +C MFLAG = 0 means do not print. (Danger: +C This risks losing valuable information.) +C MFLAG = 1 means print (the default). +C +C Either of the above calls may be made at +C any time and will take effect immediately. +C +C CALL DSRCMS(RSAV,ISAV,JOB) saves and restores the contents of +C the internal Common blocks used by +C DLSODES (see Part 3 below). +C RSAV must be a real array of length 224 +C or more, and ISAV must be an integer +C array of length 71 or more. +C JOB=1 means save Common into RSAV/ISAV. +C JOB=2 means restore Common from RSAV/ISAV. +C DSRCMS is useful if one is +C interrupting a run and restarting +C later, or alternating between two or +C more problems solved with DLSODES. +C +C CALL DINTDY(,,,,,) Provide derivatives of y, of various +C (see below) orders, at a specified point t, if +C desired. It may be called only after +C a successful return from DLSODES. +C +C The detailed instructions for using DINTDY are as follows. +C The form of the call is: +C +C LYH = IWORK(22) +C CALL DINTDY (T, K, RWORK(LYH), NYH, DKY, IFLAG) +C +C The input parameters are: +C +C T = value of independent variable where answers are desired +C (normally the same as the T last returned by DLSODES). +C For valid results, T must lie between TCUR - HU and TCUR. +C (See optional outputs for TCUR and HU.) +C K = integer order of the derivative desired. K must satisfy +C 0 .le. K .le. NQCUR, where NQCUR is the current order +C (See optional outputs). The capability corresponding +C to K = 0, i.e. computing y(T), is already provided +C by DLSODES directly. Since NQCUR .ge. 1, the first +C derivative dy/dt is always available with DINTDY. +C LYH = the base address of the history array YH, obtained +C as an optional output as shown above. +C NYH = column length of YH, equal to the initial value of NEQ. +C +C The output parameters are: +C +C DKY = a real array of length NEQ containing the computed value +C of the K-th derivative of y(t). +C IFLAG = integer flag, returned as 0 if K and T were legal, +C -1 if K was illegal, and -2 if T was illegal. +C On an error return, a message is also written. +C----------------------------------------------------------------------- +C Part 3. Common Blocks. +C +C If DLSODES is to be used in an overlay situation, the user +C must declare, in the primary overlay, the variables in: +C (1) the call sequence to DLSODES, and +C (2) the two internal Common blocks +C /DLS001/ of length 255 (218 double precision words +C followed by 37 integer words), +C /DLSS01/ of length 40 (6 double precision words +C followed by 34 integer words), +C +C If DLSODES is used on a system in which the contents of internal +C Common blocks are not preserved between calls, the user should +C declare the above Common blocks in the calling program to insure +C that their contents are preserved. +C +C If the solution of a given problem by DLSODES is to be interrupted +C and then later continued, such as when restarting an interrupted run +C or alternating between two or more problems, the user should save, +C following the return from the last DLSODES call prior to the +C interruption, the contents of the call sequence variables and the +C internal Common blocks, and later restore these values before the +C next DLSODES call for that problem. To save and restore the Common +C blocks, use Subroutine DSRCMS (see Part 2 above). +C +C----------------------------------------------------------------------- +C Part 4. Optionally Replaceable Solver Routines. +C +C Below are descriptions of two routines in the DLSODES package which +C relate to the measurement of errors. Either routine can be +C replaced by a user-supplied version, if desired. However, since such +C a replacement may have a major impact on performance, it should be +C done only when absolutely necessary, and only with great caution. +C (Note: The means by which the package version of a routine is +C superseded by the user's version may be system-dependent.) +C +C (a) DEWSET. +C The following subroutine is called just before each internal +C integration step, and sets the array of error weights, EWT, as +C described under ITOL/RTOL/ATOL above: +C Subroutine DEWSET (NEQ, ITOL, RTOL, ATOL, YCUR, EWT) +C where NEQ, ITOL, RTOL, and ATOL are as in the DLSODES call sequence, +C YCUR contains the current dependent variable vector, and +C EWT is the array of weights set by DEWSET. +C +C If the user supplies this subroutine, it must return in EWT(i) +C (i = 1,...,NEQ) a positive quantity suitable for comparing errors +C in y(i) to. The EWT array returned by DEWSET is passed to the DVNORM +C routine (see below), and also used by DLSODES in the computation +C of the optional output IMXER, the diagonal Jacobian approximation, +C and the increments for difference quotient Jacobians. +C +C In the user-supplied version of DEWSET, it may be desirable to use +C the current values of derivatives of y. Derivatives up to order NQ +C are available from the history array YH, described above under +C optional outputs. In DEWSET, YH is identical to the YCUR array, +C extended to NQ + 1 columns with a column length of NYH and scale +C factors of H**j/factorial(j). On the first call for the problem, +C given by NST = 0, NQ is 1 and H is temporarily set to 1.0. +C NYH is the initial value of NEQ. The quantities NQ, H, and NST +C can be obtained by including in DEWSET the statements: +C DOUBLE PRECISION RLS +C COMMON /DLS001/ RLS(218),ILS(37) +C NQ = ILS(33) +C NST = ILS(34) +C H = RLS(212) +C Thus, for example, the current value of dy/dt can be obtained as +C YCUR(NYH+i)/H (i=1,...,NEQ) (and the division by H is +C unnecessary when NST = 0). +C +C (b) DVNORM. +C The following is a real function routine which computes the weighted +C root-mean-square norm of a vector v: +C D = DVNORM (N, V, W) +C where +C N = the length of the vector, +C V = real array of length N containing the vector, +C W = real array of length N containing weights, +C D = SQRT( (1/N) * sum(V(i)*W(i))**2 ). +C DVNORM is called with N = NEQ and with W(i) = 1.0/EWT(i), where +C EWT is as set by Subroutine DEWSET. +C +C If the user supplies this function, it should return a non-negative +C value of DVNORM suitable for use in the error control in DLSODES. +C None of the arguments should be altered by DVNORM. +C For example, a user-supplied DVNORM routine might: +C -substitute a max-norm of (V(i)*W(i)) for the RMS-norm, or +C -ignore some components of V in the norm, with the effect of +C suppressing the error control on those components of y. +C----------------------------------------------------------------------- +C +C***REVISION HISTORY (YYYYMMDD) +C 19810120 DATE WRITTEN +C 19820315 Upgraded MDI in ODRV package: operates on M + M-transpose. +C 19820426 Numerous revisions in use of work arrays; +C use wordlength ratio LENRAT; added IPISP & LRAT to Common; +C added optional outputs IPIAN/IPJAN; +C numerous corrections to comments. +C 19830503 Added routine CNTNZU; added NZL and NZU to /LSS001/; +C changed ADJLR call logic; added optional outputs NZL & NZU; +C revised counter initializations; revised PREP stmt. numbers; +C corrections to comments throughout. +C 19870320 Corrected jump on test of umax in CDRV routine; +C added ISTATE = -7 return. +C 19870330 Major update: corrected comments throughout; +C removed TRET from Common; rewrote EWSET with 4 loops; +C fixed t test in INTDY; added Cray directives in STODE; +C in STODE, fixed DELP init. and logic around PJAC call; +C combined routines to save/restore Common; +C passed LEVEL = 0 in error message calls (except run abort). +C 20010425 Major update: convert source lines to upper case; +C added *DECK lines; changed from 1 to * in dummy dimensions; +C changed names R1MACH/D1MACH to RUMACH/DUMACH; +C renamed routines for uniqueness across single/double prec.; +C converted intrinsic names to generic form; +C removed ILLIN and NTREP (data loaded) from Common; +C removed all 'own' variables from Common; +C changed error messages to quoted strings; +C replaced XERRWV/XERRWD with 1993 revised version; +C converted prologues, comments, error messages to mixed case; +C converted arithmetic IF statements to logical IF statements; +C numerous corrections to prologues and internal comments. +C 20010507 Converted single precision source to double precision. +C 20020502 Corrected declarations in descriptions of user routines. +C 20031105 Restored 'own' variables to Common blocks, to enable +C interrupt/restart feature. +C 20031112 Added SAVE statements for data-loaded constants. +C +C----------------------------------------------------------------------- +C Other routines in the DLSODES package. +C +C In addition to Subroutine DLSODES, the DLSODES package includes the +C following subroutines and function routines: +C DIPREP acts as an iterface between DLSODES and DPREP, and also does +C adjusting of work space pointers and work arrays. +C DPREP is called by DIPREP to compute sparsity and do sparse matrix +C preprocessing if MITER = 1 or 2. +C JGROUP is called by DPREP to compute groups of Jacobian column +C indices for use when MITER = 2. +C ADJLR adjusts the length of required sparse matrix work space. +C It is called by DPREP. +C CNTNZU is called by DPREP and counts the nonzero elements in the +C strict upper triangle of J + J-transpose, where J = df/dy. +C DINTDY computes an interpolated value of the y vector at t = TOUT. +C DSTODE is the core integrator, which does one step of the +C integration and the associated error control. +C DCFODE sets all method coefficients and test constants. +C DPRJS computes and preprocesses the Jacobian matrix J = df/dy +C and the Newton iteration matrix P = I - h*l0*J. +C DSOLSS manages solution of linear system in chord iteration. +C DEWSET sets the error weight vector EWT before each step. +C DVNORM computes the weighted RMS-norm of a vector. +C DSRCMS is a user-callable routine to save and restore +C the contents of the internal Common blocks. +C ODRV constructs a reordering of the rows and columns of +C a matrix by the minimum degree algorithm. ODRV is a +C driver routine which calls Subroutines MD, MDI, MDM, +C MDP, MDU, and SRO. See Ref. 2 for details. (The ODRV +C module has been modified since Ref. 2, however.) +C CDRV performs reordering, symbolic factorization, numerical +C factorization, or linear system solution operations, +C depending on a path argument ipath. CDRV is a +C driver routine which calls Subroutines NROC, NSFC, +C NNFC, NNSC, and NNTC. See Ref. 3 for details. +C DLSODES uses CDRV to solve linear systems in which the +C coefficient matrix is P = I - con*J, where I is the +C identity, con is a scalar, and J is an approximation to +C the Jacobian df/dy. Because CDRV deals with rowwise +C sparsity descriptions, CDRV works with P-transpose, not P. +C DUMACH computes the unit roundoff in a machine-independent manner. +C XERRWD, XSETUN, XSETF, IXSAV, and IUMACH handle the printing of all +C error messages and warnings. XERRWD is machine-dependent. +C Note: DVNORM, DUMACH, IXSAV, and IUMACH are function routines. +C All the others are subroutines. +C +C----------------------------------------------------------------------- + EXTERNAL DPRJS, DSOLSS + DOUBLE PRECISION DUMACH, DVNORM + INTEGER INIT, MXSTEP, MXHNIL, NHNIL, NSLAST, NYH, IOWNS, + 1 ICF, IERPJ, IERSL, JCUR, JSTART, KFLAG, L, + 2 LYH, LEWT, LACOR, LSAVF, LWM, LIWM, METH, MITER, + 3 MAXORD, MAXCOR, MSBP, MXNCF, N, NQ, NST, NFE, NJE, NQU + INTEGER IPLOST, IESP, ISTATC, IYS, IBA, IBIAN, IBJAN, IBJGP, + 1 IPIAN, IPJAN, IPJGP, IPIGP, IPR, IPC, IPIC, IPISP, IPRSP, IPA, + 2 LENYH, LENYHM, LENWK, LREQ, LRAT, LREST, LWMIN, MOSS, MSBJ, + 3 NSLJ, NGP, NLU, NNZ, NSP, NZL, NZU + INTEGER I, I1, I2, IFLAG, IMAX, IMUL, IMXER, IPFLAG, IPGO, IREM, + 1 J, KGO, LENRAT, LENYHT, LENIW, LENRW, LF0, LIA, LJA, + 2 LRTEM, LWTEM, LYHD, LYHN, MF1, MORD, MXHNL0, MXSTP0, NCOLM + DOUBLE PRECISION ROWNS, + 1 CCMAX, EL0, H, HMIN, HMXI, HU, RC, TN, UROUND + DOUBLE PRECISION CON0, CONMIN, CCMXJ, PSMALL, RBIG, SETH + DOUBLE PRECISION ATOLI, AYI, BIG, EWTI, H0, HMAX, HMX, RH, RTOLI, + 1 TCRIT, TDIST, TNEXT, TOL, TOLSF, TP, SIZE, SUM, W0 + DIMENSION MORD(2) + LOGICAL IHIT + CHARACTER*60 MSG + SAVE LENRAT, MORD, MXSTP0, MXHNL0 +C----------------------------------------------------------------------- +C The following two internal Common blocks contain +C (a) variables which are local to any subroutine but whose values must +C be preserved between calls to the routine ("own" variables), and +C (b) variables which are communicated between subroutines. +C The block DLS001 is declared in subroutines DLSODES, DIPREP, DPREP, +C DINTDY, DSTODE, DPRJS, and DSOLSS. +C The block DLSS01 is declared in subroutines DLSODES, DIPREP, DPREP, +C DPRJS, and DSOLSS. +C Groups of variables are replaced by dummy arrays in the Common +C declarations in routines where those variables are not used. +C----------------------------------------------------------------------- + COMMON /DLS001/ ROWNS(209), + 1 CCMAX, EL0, H, HMIN, HMXI, HU, RC, TN, UROUND, + 2 INIT, MXSTEP, MXHNIL, NHNIL, NSLAST, NYH, IOWNS(6), + 3 ICF, IERPJ, IERSL, JCUR, JSTART, KFLAG, L, + 4 LYH, LEWT, LACOR, LSAVF, LWM, LIWM, METH, MITER, + 5 MAXORD, MAXCOR, MSBP, MXNCF, N, NQ, NST, NFE, NJE, NQU +C + COMMON /DLSS01/ CON0, CONMIN, CCMXJ, PSMALL, RBIG, SETH, + 1 IPLOST, IESP, ISTATC, IYS, IBA, IBIAN, IBJAN, IBJGP, + 2 IPIAN, IPJAN, IPJGP, IPIGP, IPR, IPC, IPIC, IPISP, IPRSP, IPA, + 3 LENYH, LENYHM, LENWK, LREQ, LRAT, LREST, LWMIN, MOSS, MSBJ, + 4 NSLJ, NGP, NLU, NNZ, NSP, NZL, NZU +C + DATA MORD(1),MORD(2)/12,5/, MXSTP0/500/, MXHNL0/10/ +C----------------------------------------------------------------------- +C In the Data statement below, set LENRAT equal to the ratio of +C the wordlength for a real number to that for an integer. Usually, +C LENRAT = 1 for single precision and 2 for double precision. If the +C true ratio is not an integer, use the next smaller integer (.ge. 1). +C----------------------------------------------------------------------- + DATA LENRAT/2/ +C----------------------------------------------------------------------- +C Block A. +C This code block is executed on every call. +C It tests ISTATE and ITASK for legality and branches appropriately. +C If ISTATE .gt. 1 but the flag INIT shows that initialization has +C not yet been done, an error return occurs. +C If ISTATE = 1 and TOUT = T, return immediately. +C----------------------------------------------------------------------- + IF (ISTATE .LT. 1 .OR. ISTATE .GT. 3) GO TO 601 + IF (ITASK .LT. 1 .OR. ITASK .GT. 5) GO TO 602 + IF (ISTATE .EQ. 1) GO TO 10 + IF (INIT .EQ. 0) GO TO 603 + IF (ISTATE .EQ. 2) GO TO 200 + GO TO 20 + 10 INIT = 0 + IF (TOUT .EQ. T) RETURN +C----------------------------------------------------------------------- +C Block B. +C The next code block is executed for the initial call (ISTATE = 1), +C or for a continuation call with parameter changes (ISTATE = 3). +C It contains checking of all inputs and various initializations. +C If ISTATE = 1, the final setting of work space pointers, the matrix +C preprocessing, and other initializations are done in Block C. +C +C First check legality of the non-optional inputs NEQ, ITOL, IOPT, +C MF, ML, and MU. +C----------------------------------------------------------------------- + 20 IF (NEQ(1) .LE. 0) GO TO 604 + IF (ISTATE .EQ. 1) GO TO 25 + IF (NEQ(1) .GT. N) GO TO 605 + 25 N = NEQ(1) + IF (ITOL .LT. 1 .OR. ITOL .GT. 4) GO TO 606 + IF (IOPT .LT. 0 .OR. IOPT .GT. 1) GO TO 607 + MOSS = MF/100 + MF1 = MF - 100*MOSS + METH = MF1/10 + MITER = MF1 - 10*METH + IF (MOSS .LT. 0 .OR. MOSS .GT. 2) GO TO 608 + IF (METH .LT. 1 .OR. METH .GT. 2) GO TO 608 + IF (MITER .LT. 0 .OR. MITER .GT. 3) GO TO 608 + IF (MITER .EQ. 0 .OR. MITER .EQ. 3) MOSS = 0 +C Next process and check the optional inputs. -------------------------- + IF (IOPT .EQ. 1) GO TO 40 + MAXORD = MORD(METH) + MXSTEP = MXSTP0 + MXHNIL = MXHNL0 + IF (ISTATE .EQ. 1) H0 = 0.0D0 + HMXI = 0.0D0 + HMIN = 0.0D0 + SETH = 0.0D0 + GO TO 60 + 40 MAXORD = IWORK(5) + IF (MAXORD .LT. 0) GO TO 611 + IF (MAXORD .EQ. 0) MAXORD = 100 + MAXORD = MIN(MAXORD,MORD(METH)) + MXSTEP = IWORK(6) + IF (MXSTEP .LT. 0) GO TO 612 + IF (MXSTEP .EQ. 0) MXSTEP = MXSTP0 + MXHNIL = IWORK(7) + IF (MXHNIL .LT. 0) GO TO 613 + IF (MXHNIL .EQ. 0) MXHNIL = MXHNL0 + IF (ISTATE .NE. 1) GO TO 50 + H0 = RWORK(5) + IF ((TOUT - T)*H0 .LT. 0.0D0) GO TO 614 + 50 HMAX = RWORK(6) + IF (HMAX .LT. 0.0D0) GO TO 615 + HMXI = 0.0D0 + IF (HMAX .GT. 0.0D0) HMXI = 1.0D0/HMAX + HMIN = RWORK(7) + IF (HMIN .LT. 0.0D0) GO TO 616 + SETH = RWORK(8) + IF (SETH .LT. 0.0D0) GO TO 609 +C Check RTOL and ATOL for legality. ------------------------------------ + 60 RTOLI = RTOL(1) + ATOLI = ATOL(1) + DO 65 I = 1,N + IF (ITOL .GE. 3) RTOLI = RTOL(I) + IF (ITOL .EQ. 2 .OR. ITOL .EQ. 4) ATOLI = ATOL(I) + IF (RTOLI .LT. 0.0D0) GO TO 619 + IF (ATOLI .LT. 0.0D0) GO TO 620 + 65 CONTINUE +C----------------------------------------------------------------------- +C Compute required work array lengths, as far as possible, and test +C these against LRW and LIW. Then set tentative pointers for work +C arrays. Pointers to RWORK/IWORK segments are named by prefixing L to +C the name of the segment. E.g., the segment YH starts at RWORK(LYH). +C Segments of RWORK (in order) are denoted WM, YH, SAVF, EWT, ACOR. +C If MITER = 1 or 2, the required length of the matrix work space WM +C is not yet known, and so a crude minimum value is used for the +C initial tests of LRW and LIW, and YH is temporarily stored as far +C to the right in RWORK as possible, to leave the maximum amount +C of space for WM for matrix preprocessing. Thus if MITER = 1 or 2 +C and MOSS .ne. 2, some of the segments of RWORK are temporarily +C omitted, as they are not needed in the preprocessing. These +C omitted segments are: ACOR if ISTATE = 1, EWT and ACOR if ISTATE = 3 +C and MOSS = 1, and SAVF, EWT, and ACOR if ISTATE = 3 and MOSS = 0. +C----------------------------------------------------------------------- + LRAT = LENRAT + IF (ISTATE .EQ. 1) NYH = N + LWMIN = 0 + IF (MITER .EQ. 1) LWMIN = 4*N + 10*N/LRAT + IF (MITER .EQ. 2) LWMIN = 4*N + 11*N/LRAT + IF (MITER .EQ. 3) LWMIN = N + 2 + LENYH = (MAXORD+1)*NYH + LREST = LENYH + 3*N + LENRW = 20 + LWMIN + LREST + IWORK(17) = LENRW + LENIW = 30 + IF (MOSS .EQ. 0 .AND. MITER .NE. 0 .AND. MITER .NE. 3) + 1 LENIW = LENIW + N + 1 + IWORK(18) = LENIW + IF (LENRW .GT. LRW) GO TO 617 + IF (LENIW .GT. LIW) GO TO 618 + LIA = 31 + IF (MOSS .EQ. 0 .AND. MITER .NE. 0 .AND. MITER .NE. 3) + 1 LENIW = LENIW + IWORK(LIA+N) - 1 + IWORK(18) = LENIW + IF (LENIW .GT. LIW) GO TO 618 + LJA = LIA + N + 1 + LIA = MIN(LIA,LIW) + LJA = MIN(LJA,LIW) + LWM = 21 + IF (ISTATE .EQ. 1) NQ = 1 + NCOLM = MIN(NQ+1,MAXORD+2) + LENYHM = NCOLM*NYH + LENYHT = LENYH + IF (MITER .EQ. 1 .OR. MITER .EQ. 2) LENYHT = LENYHM + IMUL = 2 + IF (ISTATE .EQ. 3) IMUL = MOSS + IF (MOSS .EQ. 2) IMUL = 3 + LRTEM = LENYHT + IMUL*N + LWTEM = LWMIN + IF (MITER .EQ. 1 .OR. MITER .EQ. 2) LWTEM = LRW - 20 - LRTEM + LENWK = LWTEM + LYHN = LWM + LWTEM + LSAVF = LYHN + LENYHT + LEWT = LSAVF + N + LACOR = LEWT + N + ISTATC = ISTATE + IF (ISTATE .EQ. 1) GO TO 100 +C----------------------------------------------------------------------- +C ISTATE = 3. Move YH to its new location. +C Note that only the part of YH needed for the next step, namely +C MIN(NQ+1,MAXORD+2) columns, is actually moved. +C A temporary error weight array EWT is loaded if MOSS = 2. +C Sparse matrix processing is done in DIPREP/DPREP if MITER = 1 or 2. +C If MAXORD was reduced below NQ, then the pointers are finally set +C so that SAVF is identical to YH(*,MAXORD+2). +C----------------------------------------------------------------------- + LYHD = LYH - LYHN + IMAX = LYHN - 1 + LENYHM +C Move YH. Move right if LYHD < 0; move left if LYHD > 0. ------------- + IF (LYHD .LT. 0) THEN + DO 72 I = LYHN,IMAX + J = IMAX + LYHN - I + 72 RWORK(J) = RWORK(J+LYHD) + ENDIF + IF (LYHD .GT. 0) THEN + DO 76 I = LYHN,IMAX + 76 RWORK(I) = RWORK(I+LYHD) + ENDIF + 80 LYH = LYHN + IWORK(22) = LYH + IF (MITER .EQ. 0 .OR. MITER .EQ. 3) GO TO 92 + IF (MOSS .NE. 2) GO TO 85 +C Temporarily load EWT if MITER = 1 or 2 and MOSS = 2. ----------------- + CALL DEWSET (N, ITOL, RTOL, ATOL, RWORK(LYH), RWORK(LEWT)) + DO 82 I = 1,N + IF (RWORK(I+LEWT-1) .LE. 0.0D0) GO TO 621 + 82 RWORK(I+LEWT-1) = 1.0D0/RWORK(I+LEWT-1) + 85 CONTINUE +C DIPREP and DPREP do sparse matrix preprocessing if MITER = 1 or 2. --- + LSAVF = MIN(LSAVF,LRW) + LEWT = MIN(LEWT,LRW) + LACOR = MIN(LACOR,LRW) + CALL DIPREP (NEQ, Y, RWORK, IWORK(LIA),IWORK(LJA), IPFLAG, F, JAC) + LENRW = LWM - 1 + LENWK + LREST + IWORK(17) = LENRW + IF (IPFLAG .NE. -1) IWORK(23) = IPIAN + IF (IPFLAG .NE. -1) IWORK(24) = IPJAN + IPGO = -IPFLAG + 1 + GO TO (90, 628, 629, 630, 631, 632, 633), IPGO + 90 IWORK(22) = LYH + IF (LENRW .GT. LRW) GO TO 617 +C Set flag to signal parameter changes to DSTODE. ---------------------- + 92 JSTART = -1 + IF (N .EQ. NYH) GO TO 200 +C NEQ was reduced. Zero part of YH to avoid undefined references. ----- + I1 = LYH + L*NYH + I2 = LYH + (MAXORD + 1)*NYH - 1 + IF (I1 .GT. I2) GO TO 200 + DO 95 I = I1,I2 + 95 RWORK(I) = 0.0D0 + GO TO 200 +C----------------------------------------------------------------------- +C Block C. +C The next block is for the initial call only (ISTATE = 1). +C It contains all remaining initializations, the initial call to F, +C the sparse matrix preprocessing (MITER = 1 or 2), and the +C calculation of the initial step size. +C The error weights in EWT are inverted after being loaded. +C----------------------------------------------------------------------- + 100 CONTINUE + LYH = LYHN + IWORK(22) = LYH + TN = T + NST = 0 + H = 1.0D0 + NNZ = 0 + NGP = 0 + NZL = 0 + NZU = 0 +C Load the initial value vector in YH. --------------------------------- + DO 105 I = 1,N + 105 RWORK(I+LYH-1) = Y(I) +C Initial call to F. (LF0 points to YH(*,2).) ------------------------- + LF0 = LYH + NYH + CALL F (NEQ, T, Y, RWORK(LF0)) + NFE = 1 +C Load and invert the EWT array. (H is temporarily set to 1.0.) ------- + CALL DEWSET (N, ITOL, RTOL, ATOL, RWORK(LYH), RWORK(LEWT)) + DO 110 I = 1,N + IF (RWORK(I+LEWT-1) .LE. 0.0D0) GO TO 621 + 110 RWORK(I+LEWT-1) = 1.0D0/RWORK(I+LEWT-1) + IF (MITER .EQ. 0 .OR. MITER .EQ. 3) GO TO 120 +C DIPREP and DPREP do sparse matrix preprocessing if MITER = 1 or 2. --- + LACOR = MIN(LACOR,LRW) + CALL DIPREP (NEQ, Y, RWORK, IWORK(LIA),IWORK(LJA), IPFLAG, F, JAC) + LENRW = LWM - 1 + LENWK + LREST + IWORK(17) = LENRW + IF (IPFLAG .NE. -1) IWORK(23) = IPIAN + IF (IPFLAG .NE. -1) IWORK(24) = IPJAN + IPGO = -IPFLAG + 1 + GO TO (115, 628, 629, 630, 631, 632, 633), IPGO + 115 IWORK(22) = LYH + IF (LENRW .GT. LRW) GO TO 617 +C Check TCRIT for legality (ITASK = 4 or 5). --------------------------- + 120 CONTINUE + IF (ITASK .NE. 4 .AND. ITASK .NE. 5) GO TO 125 + TCRIT = RWORK(1) + IF ((TCRIT - TOUT)*(TOUT - T) .LT. 0.0D0) GO TO 625 + IF (H0 .NE. 0.0D0 .AND. (T + H0 - TCRIT)*H0 .GT. 0.0D0) + 1 H0 = TCRIT - T +C Initialize all remaining parameters. --------------------------------- + 125 UROUND = DUMACH() + JSTART = 0 + IF (MITER .NE. 0) RWORK(LWM) = SQRT(UROUND) + MSBJ = 50 + NSLJ = 0 + CCMXJ = 0.2D0 + PSMALL = 1000.0D0*UROUND + RBIG = 0.01D0/PSMALL + NHNIL = 0 + NJE = 0 + NLU = 0 + NSLAST = 0 + HU = 0.0D0 + NQU = 0 + CCMAX = 0.3D0 + MAXCOR = 3 + MSBP = 20 + MXNCF = 10 +C----------------------------------------------------------------------- +C The coding below computes the step size, H0, to be attempted on the +C first step, unless the user has supplied a value for this. +C First check that TOUT - T differs significantly from zero. +C A scalar tolerance quantity TOL is computed, as MAX(RTOL(i)) +C if this is positive, or MAX(ATOL(i)/ABS(Y(i))) otherwise, adjusted +C so as to be between 100*UROUND and 1.0E-3. +C Then the computed value H0 is given by.. +C NEQ +C H0**2 = TOL / ( w0**-2 + (1/NEQ) * Sum ( f(i)/ywt(i) )**2 ) +C 1 +C where w0 = MAX ( ABS(T), ABS(TOUT) ), +C f(i) = i-th component of initial value of f, +C ywt(i) = EWT(i)/TOL (a weight for y(i)). +C The sign of H0 is inferred from the initial values of TOUT and T. +C ABS(H0) is made .le. ABS(TOUT-T) in any case. +C----------------------------------------------------------------------- + LF0 = LYH + NYH + IF (H0 .NE. 0.0D0) GO TO 180 + TDIST = ABS(TOUT - T) + W0 = MAX(ABS(T),ABS(TOUT)) + IF (TDIST .LT. 2.0D0*UROUND*W0) GO TO 622 + TOL = RTOL(1) + IF (ITOL .LE. 2) GO TO 140 + DO 130 I = 1,N + 130 TOL = MAX(TOL,RTOL(I)) + 140 IF (TOL .GT. 0.0D0) GO TO 160 + ATOLI = ATOL(1) + DO 150 I = 1,N + IF (ITOL .EQ. 2 .OR. ITOL .EQ. 4) ATOLI = ATOL(I) + AYI = ABS(Y(I)) + IF (AYI .NE. 0.0D0) TOL = MAX(TOL,ATOLI/AYI) + 150 CONTINUE + 160 TOL = MAX(TOL,100.0D0*UROUND) + TOL = MIN(TOL,0.001D0) + SUM = DVNORM (N, RWORK(LF0), RWORK(LEWT)) + SUM = 1.0D0/(TOL*W0*W0) + TOL*SUM**2 + H0 = 1.0D0/SQRT(SUM) + H0 = MIN(H0,TDIST) + H0 = SIGN(H0,TOUT-T) +C Adjust H0 if necessary to meet HMAX bound. --------------------------- + 180 RH = ABS(H0)*HMXI + IF (RH .GT. 1.0D0) H0 = H0/RH +C Load H with H0 and scale YH(*,2) by H0. ------------------------------ + H = H0 + DO 190 I = 1,N + 190 RWORK(I+LF0-1) = H0*RWORK(I+LF0-1) + GO TO 270 +C----------------------------------------------------------------------- +C Block D. +C The next code block is for continuation calls only (ISTATE = 2 or 3) +C and is to check stop conditions before taking a step. +C----------------------------------------------------------------------- + 200 NSLAST = NST + GO TO (210, 250, 220, 230, 240), ITASK + 210 IF ((TN - TOUT)*H .LT. 0.0D0) GO TO 250 + CALL DINTDY (TOUT, 0, RWORK(LYH), NYH, Y, IFLAG) + IF (IFLAG .NE. 0) GO TO 627 + T = TOUT + GO TO 420 + 220 TP = TN - HU*(1.0D0 + 100.0D0*UROUND) + IF ((TP - TOUT)*H .GT. 0.0D0) GO TO 623 + IF ((TN - TOUT)*H .LT. 0.0D0) GO TO 250 + GO TO 400 + 230 TCRIT = RWORK(1) + IF ((TN - TCRIT)*H .GT. 0.0D0) GO TO 624 + IF ((TCRIT - TOUT)*H .LT. 0.0D0) GO TO 625 + IF ((TN - TOUT)*H .LT. 0.0D0) GO TO 245 + CALL DINTDY (TOUT, 0, RWORK(LYH), NYH, Y, IFLAG) + IF (IFLAG .NE. 0) GO TO 627 + T = TOUT + GO TO 420 + 240 TCRIT = RWORK(1) + IF ((TN - TCRIT)*H .GT. 0.0D0) GO TO 624 + 245 HMX = ABS(TN) + ABS(H) + IHIT = ABS(TN - TCRIT) .LE. 100.0D0*UROUND*HMX + IF (IHIT) GO TO 400 + TNEXT = TN + H*(1.0D0 + 4.0D0*UROUND) + IF ((TNEXT - TCRIT)*H .LE. 0.0D0) GO TO 250 + H = (TCRIT - TN)*(1.0D0 - 4.0D0*UROUND) + IF (ISTATE .EQ. 2) JSTART = -2 +C----------------------------------------------------------------------- +C Block E. +C The next block is normally executed for all calls and contains +C the call to the one-step core integrator DSTODE. +C +C This is a looping point for the integration steps. +C +C First check for too many steps being taken, update EWT (if not at +C start of problem), check for too much accuracy being requested, and +C check for H below the roundoff level in T. +C----------------------------------------------------------------------- + 250 CONTINUE + IF ((NST-NSLAST) .GE. MXSTEP) GO TO 500 + CALL DEWSET (N, ITOL, RTOL, ATOL, RWORK(LYH), RWORK(LEWT)) + DO 260 I = 1,N + IF (RWORK(I+LEWT-1) .LE. 0.0D0) GO TO 510 + 260 RWORK(I+LEWT-1) = 1.0D0/RWORK(I+LEWT-1) + 270 TOLSF = UROUND*DVNORM (N, RWORK(LYH), RWORK(LEWT)) + IF (TOLSF .LE. 1.0D0) GO TO 280 + TOLSF = TOLSF*2.0D0 + IF (NST .EQ. 0) GO TO 626 + GO TO 520 + 280 IF ((TN + H) .NE. TN) GO TO 290 + NHNIL = NHNIL + 1 + IF (NHNIL .GT. MXHNIL) GO TO 290 + MSG = 'DLSODES- Warning..Internal T (=R1) and H (=R2) are' + CALL XERRWD (MSG, 50, 101, 0, 0, 0, 0, 0, 0.0D0, 0.0D0) + MSG=' such that in the machine, T + H = T on the next step ' + CALL XERRWD (MSG, 60, 101, 0, 0, 0, 0, 0, 0.0D0, 0.0D0) + MSG = ' (H = step size). Solver will continue anyway.' + CALL XERRWD (MSG, 50, 101, 0, 0, 0, 0, 2, TN, H) + IF (NHNIL .LT. MXHNIL) GO TO 290 + MSG = 'DLSODES- Above warning has been issued I1 times. ' + CALL XERRWD (MSG, 50, 102, 0, 0, 0, 0, 0, 0.0D0, 0.0D0) + MSG = ' It will not be issued again for this problem.' + CALL XERRWD (MSG, 50, 102, 0, 1, MXHNIL, 0, 0, 0.0D0, 0.0D0) + 290 CONTINUE +C----------------------------------------------------------------------- +C CALL DSTODE(NEQ,Y,YH,NYH,YH,EWT,SAVF,ACOR,WM,WM,F,JAC,DPRJS,DSOLSS) +C----------------------------------------------------------------------- + CALL DSTODE (NEQ, Y, RWORK(LYH), NYH, RWORK(LYH), RWORK(LEWT), + 1 RWORK(LSAVF), RWORK(LACOR), RWORK(LWM), RWORK(LWM), + 2 F, JAC, DPRJS, DSOLSS) + KGO = 1 - KFLAG + GO TO (300, 530, 540, 550), KGO +C----------------------------------------------------------------------- +C Block F. +C The following block handles the case of a successful return from the +C core integrator (KFLAG = 0). Test for stop conditions. +C----------------------------------------------------------------------- + 300 INIT = 1 + GO TO (310, 400, 330, 340, 350), ITASK +C ITASK = 1. if TOUT has been reached, interpolate. ------------------- + 310 IF ((TN - TOUT)*H .LT. 0.0D0) GO TO 250 + CALL DINTDY (TOUT, 0, RWORK(LYH), NYH, Y, IFLAG) + T = TOUT + GO TO 420 +C ITASK = 3. Jump to exit if TOUT was reached. ------------------------ + 330 IF ((TN - TOUT)*H .GE. 0.0D0) GO TO 400 + GO TO 250 +C ITASK = 4. See if TOUT or TCRIT was reached. Adjust H if necessary. + 340 IF ((TN - TOUT)*H .LT. 0.0D0) GO TO 345 + CALL DINTDY (TOUT, 0, RWORK(LYH), NYH, Y, IFLAG) + T = TOUT + GO TO 420 + 345 HMX = ABS(TN) + ABS(H) + IHIT = ABS(TN - TCRIT) .LE. 100.0D0*UROUND*HMX + IF (IHIT) GO TO 400 + TNEXT = TN + H*(1.0D0 + 4.0D0*UROUND) + IF ((TNEXT - TCRIT)*H .LE. 0.0D0) GO TO 250 + H = (TCRIT - TN)*(1.0D0 - 4.0D0*UROUND) + JSTART = -2 + GO TO 250 +C ITASK = 5. See if TCRIT was reached and jump to exit. --------------- + 350 HMX = ABS(TN) + ABS(H) + IHIT = ABS(TN - TCRIT) .LE. 100.0D0*UROUND*HMX +C----------------------------------------------------------------------- +C Block G. +C The following block handles all successful returns from DLSODES. +C If ITASK .ne. 1, Y is loaded from YH and T is set accordingly. +C ISTATE is set to 2, and the optional outputs are loaded into the +C work arrays before returning. +C----------------------------------------------------------------------- + 400 DO 410 I = 1,N + 410 Y(I) = RWORK(I+LYH-1) + T = TN + IF (ITASK .NE. 4 .AND. ITASK .NE. 5) GO TO 420 + IF (IHIT) T = TCRIT + 420 ISTATE = 2 + RWORK(11) = HU + RWORK(12) = H + RWORK(13) = TN + IWORK(11) = NST + IWORK(12) = NFE + IWORK(13) = NJE + IWORK(14) = NQU + IWORK(15) = NQ + IWORK(19) = NNZ + IWORK(20) = NGP + IWORK(21) = NLU + IWORK(25) = NZL + IWORK(26) = NZU + RETURN +C----------------------------------------------------------------------- +C Block H. +C The following block handles all unsuccessful returns other than +C those for illegal input. First the error message routine is called. +C If there was an error test or convergence test failure, IMXER is set. +C Then Y is loaded from YH and T is set to TN. +C The optional outputs are loaded into the work arrays before returning. +C----------------------------------------------------------------------- +C The maximum number of steps was taken before reaching TOUT. ---------- + 500 MSG = 'DLSODES- At current T (=R1), MXSTEP (=I1) steps ' + CALL XERRWD (MSG, 50, 201, 0, 0, 0, 0, 0, 0.0D0, 0.0D0) + MSG = ' taken on this call before reaching TOUT ' + CALL XERRWD (MSG, 50, 201, 0, 1, MXSTEP, 0, 1, TN, 0.0D0) + ISTATE = -1 + GO TO 580 +C EWT(i) .le. 0.0 for some i (not at start of problem). ---------------- + 510 EWTI = RWORK(LEWT+I-1) + MSG = 'DLSODES- At T (=R1), EWT(I1) has become R2 .le. 0.' + CALL XERRWD (MSG, 50, 202, 0, 1, I, 0, 2, TN, EWTI) + ISTATE = -6 + GO TO 580 +C Too much accuracy requested for machine precision. ------------------- + 520 MSG = 'DLSODES- At T (=R1), too much accuracy requested ' + CALL XERRWD (MSG, 50, 203, 0, 0, 0, 0, 0, 0.0D0, 0.0D0) + MSG = ' for precision of machine.. See TOLSF (=R2) ' + CALL XERRWD (MSG, 50, 203, 0, 0, 0, 0, 2, TN, TOLSF) + RWORK(14) = TOLSF + ISTATE = -2 + GO TO 580 +C KFLAG = -1. Error test failed repeatedly or with ABS(H) = HMIN. ----- + 530 MSG = 'DLSODES- At T(=R1) and step size H(=R2), the error' + CALL XERRWD (MSG, 50, 204, 0, 0, 0, 0, 0, 0.0D0, 0.0D0) + MSG = ' test failed repeatedly or with ABS(H) = HMIN' + CALL XERRWD (MSG, 50, 204, 0, 0, 0, 0, 2, TN, H) + ISTATE = -4 + GO TO 560 +C KFLAG = -2. Convergence failed repeatedly or with ABS(H) = HMIN. ---- + 540 MSG = 'DLSODES- At T (=R1) and step size H (=R2), the ' + CALL XERRWD (MSG, 50, 205, 0, 0, 0, 0, 0, 0.0D0, 0.0D0) + MSG = ' corrector convergence failed repeatedly ' + CALL XERRWD (MSG, 50, 205, 0, 0, 0, 0, 0, 0.0D0, 0.0D0) + MSG = ' or with ABS(H) = HMIN ' + CALL XERRWD (MSG, 30, 205, 0, 0, 0, 0, 2, TN, H) + ISTATE = -5 + GO TO 560 +C KFLAG = -3. Fatal error flag returned by DPRJS or DSOLSS (CDRV). ---- + 550 MSG = 'DLSODES- At T (=R1) and step size H (=R2), a fatal' + CALL XERRWD (MSG, 50, 207, 0, 0, 0, 0, 0, 0.0D0, 0.0D0) + MSG = ' error flag was returned by CDRV (by way of ' + CALL XERRWD (MSG, 50, 207, 0, 0, 0, 0, 0, 0.0D0, 0.0D0) + MSG = ' Subroutine DPRJS or DSOLSS) ' + CALL XERRWD (MSG, 40, 207, 0, 0, 0, 0, 2, TN, H) + ISTATE = -7 + GO TO 580 +C Compute IMXER if relevant. ------------------------------------------- + 560 BIG = 0.0D0 + IMXER = 1 + DO 570 I = 1,N + SIZE = ABS(RWORK(I+LACOR-1)*RWORK(I+LEWT-1)) + IF (BIG .GE. SIZE) GO TO 570 + BIG = SIZE + IMXER = I + 570 CONTINUE + IWORK(16) = IMXER +C Set Y vector, T, and optional outputs. ------------------------------- + 580 DO 590 I = 1,N + 590 Y(I) = RWORK(I+LYH-1) + T = TN + RWORK(11) = HU + RWORK(12) = H + RWORK(13) = TN + IWORK(11) = NST + IWORK(12) = NFE + IWORK(13) = NJE + IWORK(14) = NQU + IWORK(15) = NQ + IWORK(19) = NNZ + IWORK(20) = NGP + IWORK(21) = NLU + IWORK(25) = NZL + IWORK(26) = NZU + RETURN +C----------------------------------------------------------------------- +C Block I. +C The following block handles all error returns due to illegal input +C (ISTATE = -3), as detected before calling the core integrator. +C First the error message routine is called. If the illegal input +C is a negative ISTATE, the run is aborted (apparent infinite loop). +C----------------------------------------------------------------------- + 601 MSG = 'DLSODES- ISTATE (=I1) illegal.' + CALL XERRWD (MSG, 30, 1, 0, 1, ISTATE, 0, 0, 0.0D0, 0.0D0) + IF (ISTATE .LT. 0) GO TO 800 + GO TO 700 + 602 MSG = 'DLSODES- ITASK (=I1) illegal. ' + CALL XERRWD (MSG, 30, 2, 0, 1, ITASK, 0, 0, 0.0D0, 0.0D0) + GO TO 700 + 603 MSG = 'DLSODES- ISTATE.gt.1 but DLSODES not initialized. ' + CALL XERRWD (MSG, 50, 3, 0, 0, 0, 0, 0, 0.0D0, 0.0D0) + GO TO 700 + 604 MSG = 'DLSODES- NEQ (=I1) .lt. 1 ' + CALL XERRWD (MSG, 30, 4, 0, 1, NEQ(1), 0, 0, 0.0D0, 0.0D0) + GO TO 700 + 605 MSG = 'DLSODES- ISTATE = 3 and NEQ increased (I1 to I2). ' + CALL XERRWD (MSG, 50, 5, 0, 2, N, NEQ(1), 0, 0.0D0, 0.0D0) + GO TO 700 + 606 MSG = 'DLSODES- ITOL (=I1) illegal. ' + CALL XERRWD (MSG, 30, 6, 0, 1, ITOL, 0, 0, 0.0D0, 0.0D0) + GO TO 700 + 607 MSG = 'DLSODES- IOPT (=I1) illegal. ' + CALL XERRWD (MSG, 30, 7, 0, 1, IOPT, 0, 0, 0.0D0, 0.0D0) + GO TO 700 + 608 MSG = 'DLSODES- MF (=I1) illegal. ' + CALL XERRWD (MSG, 30, 8, 0, 1, MF, 0, 0, 0.0D0, 0.0D0) + GO TO 700 + 609 MSG = 'DLSODES- SETH (=R1) .lt. 0.0 ' + CALL XERRWD (MSG, 30, 9, 0, 0, 0, 0, 1, SETH, 0.0D0) + GO TO 700 + 611 MSG = 'DLSODES- MAXORD (=I1) .lt. 0 ' + CALL XERRWD (MSG, 30, 11, 0, 1, MAXORD, 0, 0, 0.0D0, 0.0D0) + GO TO 700 + 612 MSG = 'DLSODES- MXSTEP (=I1) .lt. 0 ' + CALL XERRWD (MSG, 30, 12, 0, 1, MXSTEP, 0, 0, 0.0D0, 0.0D0) + GO TO 700 + 613 MSG = 'DLSODES- MXHNIL (=I1) .lt. 0 ' + CALL XERRWD (MSG, 30, 13, 0, 1, MXHNIL, 0, 0, 0.0D0, 0.0D0) + GO TO 700 + 614 MSG = 'DLSODES- TOUT (=R1) behind T (=R2) ' + CALL XERRWD (MSG, 40, 14, 0, 0, 0, 0, 2, TOUT, T) + MSG = ' Integration direction is given by H0 (=R1) ' + CALL XERRWD (MSG, 50, 14, 0, 0, 0, 0, 1, H0, 0.0D0) + GO TO 700 + 615 MSG = 'DLSODES- HMAX (=R1) .lt. 0.0 ' + CALL XERRWD (MSG, 30, 15, 0, 0, 0, 0, 1, HMAX, 0.0D0) + GO TO 700 + 616 MSG = 'DLSODES- HMIN (=R1) .lt. 0.0 ' + CALL XERRWD (MSG, 30, 16, 0, 0, 0, 0, 1, HMIN, 0.0D0) + GO TO 700 + 617 MSG = 'DLSODES- RWORK length is insufficient to proceed. ' + CALL XERRWD (MSG, 50, 17, 0, 0, 0, 0, 0, 0.0D0, 0.0D0) + MSG=' Length needed is .ge. LENRW (=I1), exceeds LRW (=I2)' + CALL XERRWD (MSG, 60, 17, 0, 2, LENRW, LRW, 0, 0.0D0, 0.0D0) + GO TO 700 + 618 MSG = 'DLSODES- IWORK length is insufficient to proceed. ' + CALL XERRWD (MSG, 50, 18, 0, 0, 0, 0, 0, 0.0D0, 0.0D0) + MSG=' Length needed is .ge. LENIW (=I1), exceeds LIW (=I2)' + CALL XERRWD (MSG, 60, 18, 0, 2, LENIW, LIW, 0, 0.0D0, 0.0D0) + GO TO 700 + 619 MSG = 'DLSODES- RTOL(I1) is R1 .lt. 0.0 ' + CALL XERRWD (MSG, 40, 19, 0, 1, I, 0, 1, RTOLI, 0.0D0) + GO TO 700 + 620 MSG = 'DLSODES- ATOL(I1) is R1 .lt. 0.0 ' + CALL XERRWD (MSG, 40, 20, 0, 1, I, 0, 1, ATOLI, 0.0D0) + GO TO 700 + 621 EWTI = RWORK(LEWT+I-1) + MSG = 'DLSODES- EWT(I1) is R1 .le. 0.0 ' + CALL XERRWD (MSG, 40, 21, 0, 1, I, 0, 1, EWTI, 0.0D0) + GO TO 700 + 622 MSG='DLSODES- TOUT(=R1) too close to T(=R2) to start integration.' + CALL XERRWD (MSG, 60, 22, 0, 0, 0, 0, 2, TOUT, T) + GO TO 700 + 623 MSG='DLSODES- ITASK = I1 and TOUT (=R1) behind TCUR - HU (= R2) ' + CALL XERRWD (MSG, 60, 23, 0, 1, ITASK, 0, 2, TOUT, TP) + GO TO 700 + 624 MSG='DLSODES- ITASK = 4 or 5 and TCRIT (=R1) behind TCUR (=R2) ' + CALL XERRWD (MSG, 60, 24, 0, 0, 0, 0, 2, TCRIT, TN) + GO TO 700 + 625 MSG='DLSODES- ITASK = 4 or 5 and TCRIT (=R1) behind TOUT (=R2) ' + CALL XERRWD (MSG, 60, 25, 0, 0, 0, 0, 2, TCRIT, TOUT) + GO TO 700 + 626 MSG = 'DLSODES- At start of problem, too much accuracy ' + CALL XERRWD (MSG, 50, 26, 0, 0, 0, 0, 0, 0.0D0, 0.0D0) + MSG=' requested for precision of machine.. See TOLSF (=R1) ' + CALL XERRWD (MSG, 60, 26, 0, 0, 0, 0, 1, TOLSF, 0.0D0) + RWORK(14) = TOLSF + GO TO 700 + 627 MSG = 'DLSODES- Trouble in DINTDY. ITASK = I1, TOUT = R1' + CALL XERRWD (MSG, 50, 27, 0, 1, ITASK, 0, 1, TOUT, 0.0D0) + GO TO 700 + 628 MSG='DLSODES- RWORK length insufficient (for Subroutine DPREP). ' + CALL XERRWD (MSG, 60, 28, 0, 0, 0, 0, 0, 0.0D0, 0.0D0) + MSG=' Length needed is .ge. LENRW (=I1), exceeds LRW (=I2)' + CALL XERRWD (MSG, 60, 28, 0, 2, LENRW, LRW, 0, 0.0D0, 0.0D0) + GO TO 700 + 629 MSG='DLSODES- RWORK length insufficient (for Subroutine JGROUP). ' + CALL XERRWD (MSG, 60, 29, 0, 0, 0, 0, 0, 0.0D0, 0.0D0) + MSG=' Length needed is .ge. LENRW (=I1), exceeds LRW (=I2)' + CALL XERRWD (MSG, 60, 29, 0, 2, LENRW, LRW, 0, 0.0D0, 0.0D0) + GO TO 700 + 630 MSG='DLSODES- RWORK length insufficient (for Subroutine ODRV). ' + CALL XERRWD (MSG, 60, 30, 0, 0, 0, 0, 0, 0.0D0, 0.0D0) + MSG=' Length needed is .ge. LENRW (=I1), exceeds LRW (=I2)' + CALL XERRWD (MSG, 60, 30, 0, 2, LENRW, LRW, 0, 0.0D0, 0.0D0) + GO TO 700 + 631 MSG='DLSODES- Error from ODRV in Yale Sparse Matrix Package. ' + CALL XERRWD (MSG, 60, 31, 0, 0, 0, 0, 0, 0.0D0, 0.0D0) + IMUL = (IYS - 1)/N + IREM = IYS - IMUL*N + MSG=' At T (=R1), ODRV returned error flag = I1*NEQ + I2. ' + CALL XERRWD (MSG, 60, 31, 0, 2, IMUL, IREM, 1, TN, 0.0D0) + GO TO 700 + 632 MSG='DLSODES- RWORK length insufficient (for Subroutine CDRV). ' + CALL XERRWD (MSG, 60, 32, 0, 0, 0, 0, 0, 0.0D0, 0.0D0) + MSG=' Length needed is .ge. LENRW (=I1), exceeds LRW (=I2)' + CALL XERRWD (MSG, 60, 32, 0, 2, LENRW, LRW, 0, 0.0D0, 0.0D0) + GO TO 700 + 633 MSG='DLSODES- Error from CDRV in Yale Sparse Matrix Package. ' + CALL XERRWD (MSG, 60, 33, 0, 0, 0, 0, 0, 0.0D0, 0.0D0) + IMUL = (IYS - 1)/N + IREM = IYS - IMUL*N + MSG=' At T (=R1), CDRV returned error flag = I1*NEQ + I2. ' + CALL XERRWD (MSG, 60, 33, 0, 2, IMUL, IREM, 1, TN, 0.0D0) + IF (IMUL .EQ. 2) THEN + MSG=' Duplicate entry in sparsity structure descriptors. ' + CALL XERRWD (MSG, 60, 33, 0, 0, 0, 0, 0, 0.0D0, 0.0D0) + ENDIF + IF (IMUL .EQ. 3 .OR. IMUL .EQ. 6) THEN + MSG=' Insufficient storage for NSFC (called by CDRV). ' + CALL XERRWD (MSG, 60, 33, 0, 0, 0, 0, 0, 0.0D0, 0.0D0) + ENDIF +C + 700 ISTATE = -3 + RETURN +C + 800 MSG = 'DLSODES- Run aborted.. apparent infinite loop. ' + CALL XERRWD (MSG, 50, 303, 2, 0, 0, 0, 0, 0.0D0, 0.0D0) + RETURN +C----------------------- End of Subroutine DLSODES --------------------- + END +*DECK DLSODA + SUBROUTINE DLSODA (F, NEQ, Y, T, TOUT, ITOL, RTOL, ATOL, ITASK, + 1 ISTATE, IOPT, RWORK, LRW, IWORK, LIW, JAC, JT) + EXTERNAL F, JAC + INTEGER NEQ, ITOL, ITASK, ISTATE, IOPT, LRW, IWORK, LIW, JT + DOUBLE PRECISION Y, T, TOUT, RTOL, ATOL, RWORK + DIMENSION NEQ(*), Y(*), RTOL(*), ATOL(*), RWORK(LRW), IWORK(LIW) +C----------------------------------------------------------------------- +C This is the 12 November 2003 version of +C DLSODA: Livermore Solver for Ordinary Differential Equations, with +C Automatic method switching for stiff and nonstiff problems. +C +C This version is in double precision. +C +C DLSODA solves the initial value problem for stiff or nonstiff +C systems of first order ODEs, +C dy/dt = f(t,y) , or, in component form, +C dy(i)/dt = f(i) = f(i,t,y(1),y(2),...,y(NEQ)) (i = 1,...,NEQ). +C +C This a variant version of the DLSODE package. +C It switches automatically between stiff and nonstiff methods. +C This means that the user does not have to determine whether the +C problem is stiff or not, and the solver will automatically choose the +C appropriate method. It always starts with the nonstiff method. +C +C Authors: Alan C. Hindmarsh +C Center for Applied Scientific Computing, L-561 +C Lawrence Livermore National Laboratory +C Livermore, CA 94551 +C and +C Linda R. Petzold +C Univ. of California at Santa Barbara +C Dept. of Computer Science +C Santa Barbara, CA 93106 +C +C References: +C 1. Alan C. Hindmarsh, ODEPACK, A Systematized Collection of ODE +C Solvers, in Scientific Computing, R. S. Stepleman et al. (Eds.), +C North-Holland, Amsterdam, 1983, pp. 55-64. +C 2. Linda R. Petzold, Automatic Selection of Methods for Solving +C Stiff and Nonstiff Systems of Ordinary Differential Equations, +C Siam J. Sci. Stat. Comput. 4 (1983), pp. 136-148. +C----------------------------------------------------------------------- +C Summary of Usage. +C +C Communication between the user and the DLSODA package, for normal +C situations, is summarized here. This summary describes only a subset +C of the full set of options available. See the full description for +C details, including alternative treatment of the Jacobian matrix, +C optional inputs and outputs, nonstandard options, and +C instructions for special situations. See also the example +C problem (with program and output) following this summary. +C +C A. First provide a subroutine of the form: +C SUBROUTINE F (NEQ, T, Y, YDOT) +C DOUBLE PRECISION T, Y(*), YDOT(*) +C which supplies the vector function f by loading YDOT(i) with f(i). +C +C B. Write a main program which calls Subroutine DLSODA once for +C each point at which answers are desired. This should also provide +C for possible use of logical unit 6 for output of error messages +C by DLSODA. On the first call to DLSODA, supply arguments as follows: +C F = name of subroutine for right-hand side vector f. +C This name must be declared External in calling program. +C NEQ = number of first order ODEs. +C Y = array of initial values, of length NEQ. +C T = the initial value of the independent variable. +C TOUT = first point where output is desired (.ne. T). +C ITOL = 1 or 2 according as ATOL (below) is a scalar or array. +C RTOL = relative tolerance parameter (scalar). +C ATOL = absolute tolerance parameter (scalar or array). +C the estimated local error in y(i) will be controlled so as +C to be less than +C EWT(i) = RTOL*ABS(Y(i)) + ATOL if ITOL = 1, or +C EWT(i) = RTOL*ABS(Y(i)) + ATOL(i) if ITOL = 2. +C Thus the local error test passes if, in each component, +C either the absolute error is less than ATOL (or ATOL(i)), +C or the relative error is less than RTOL. +C Use RTOL = 0.0 for pure absolute error control, and +C use ATOL = 0.0 (or ATOL(i) = 0.0) for pure relative error +C control. Caution: actual (global) errors may exceed these +C local tolerances, so choose them conservatively. +C ITASK = 1 for normal computation of output values of y at t = TOUT. +C ISTATE = integer flag (input and output). Set ISTATE = 1. +C IOPT = 0 to indicate no optional inputs used. +C RWORK = real work array of length at least: +C 22 + NEQ * MAX(16, NEQ + 9). +C See also Paragraph E below. +C LRW = declared length of RWORK (in user's dimension). +C IWORK = integer work array of length at least 20 + NEQ. +C LIW = declared length of IWORK (in user's dimension). +C JAC = name of subroutine for Jacobian matrix. +C Use a dummy name. See also Paragraph E below. +C JT = Jacobian type indicator. Set JT = 2. +C See also Paragraph E below. +C Note that the main program must declare arrays Y, RWORK, IWORK, +C and possibly ATOL. +C +C C. The output from the first call (or any call) is: +C Y = array of computed values of y(t) vector. +C T = corresponding value of independent variable (normally TOUT). +C ISTATE = 2 if DLSODA was successful, negative otherwise. +C -1 means excess work done on this call (perhaps wrong JT). +C -2 means excess accuracy requested (tolerances too small). +C -3 means illegal input detected (see printed message). +C -4 means repeated error test failures (check all inputs). +C -5 means repeated convergence failures (perhaps bad Jacobian +C supplied or wrong choice of JT or tolerances). +C -6 means error weight became zero during problem. (Solution +C component i vanished, and ATOL or ATOL(i) = 0.) +C -7 means work space insufficient to finish (see messages). +C +C D. To continue the integration after a successful return, simply +C reset TOUT and call DLSODA again. No other parameters need be reset. +C +C E. Note: If and when DLSODA regards the problem as stiff, and +C switches methods accordingly, it must make use of the NEQ by NEQ +C Jacobian matrix, J = df/dy. For the sake of simplicity, the +C inputs to DLSODA recommended in Paragraph B above cause DLSODA to +C treat J as a full matrix, and to approximate it internally by +C difference quotients. Alternatively, J can be treated as a band +C matrix (with great potential reduction in the size of the RWORK +C array). Also, in either the full or banded case, the user can supply +C J in closed form, with a routine whose name is passed as the JAC +C argument. These alternatives are described in the paragraphs on +C RWORK, JAC, and JT in the full description of the call sequence below. +C +C----------------------------------------------------------------------- +C Example Problem. +C +C The following is a simple example problem, with the coding +C needed for its solution by DLSODA. The problem is from chemical +C kinetics, and consists of the following three rate equations: +C dy1/dt = -.04*y1 + 1.e4*y2*y3 +C dy2/dt = .04*y1 - 1.e4*y2*y3 - 3.e7*y2**2 +C dy3/dt = 3.e7*y2**2 +C on the interval from t = 0.0 to t = 4.e10, with initial conditions +C y1 = 1.0, y2 = y3 = 0. The problem is stiff. +C +C The following coding solves this problem with DLSODA, +C printing results at t = .4, 4., ..., 4.e10. It uses +C ITOL = 2 and ATOL much smaller for y2 than y1 or y3 because +C y2 has much smaller values. +C At the end of the run, statistical quantities of interest are +C printed (see optional outputs in the full description below). +C +C EXTERNAL FEX +C DOUBLE PRECISION ATOL, RTOL, RWORK, T, TOUT, Y +C DIMENSION Y(3), ATOL(3), RWORK(70), IWORK(23) +C NEQ = 3 +C Y(1) = 1. +C Y(2) = 0. +C Y(3) = 0. +C T = 0. +C TOUT = .4 +C ITOL = 2 +C RTOL = 1.D-4 +C ATOL(1) = 1.D-6 +C ATOL(2) = 1.D-10 +C ATOL(3) = 1.D-6 +C ITASK = 1 +C ISTATE = 1 +C IOPT = 0 +C LRW = 70 +C LIW = 23 +C JT = 2 +C DO 40 IOUT = 1,12 +C CALL DLSODA(FEX,NEQ,Y,T,TOUT,ITOL,RTOL,ATOL,ITASK,ISTATE, +C 1 IOPT,RWORK,LRW,IWORK,LIW,JDUM,JT) +C WRITE(6,20)T,Y(1),Y(2),Y(3) +C 20 FORMAT(' At t =',D12.4,' Y =',3D14.6) +C IF (ISTATE .LT. 0) GO TO 80 +C 40 TOUT = TOUT*10. +C WRITE(6,60)IWORK(11),IWORK(12),IWORK(13),IWORK(19),RWORK(15) +C 60 FORMAT(/' No. steps =',I4,' No. f-s =',I4,' No. J-s =',I4/ +C 1 ' Method last used =',I2,' Last switch was at t =',D12.4) +C STOP +C 80 WRITE(6,90)ISTATE +C 90 FORMAT(///' Error halt.. ISTATE =',I3) +C STOP +C END +C +C SUBROUTINE FEX (NEQ, T, Y, YDOT) +C DOUBLE PRECISION T, Y, YDOT +C DIMENSION Y(3), YDOT(3) +C YDOT(1) = -.04*Y(1) + 1.D4*Y(2)*Y(3) +C YDOT(3) = 3.D7*Y(2)*Y(2) +C YDOT(2) = -YDOT(1) - YDOT(3) +C RETURN +C END +C +C The output of this program (on a CDC-7600 in single precision) +C is as follows: +C +C At t = 4.0000e-01 y = 9.851712e-01 3.386380e-05 1.479493e-02 +C At t = 4.0000e+00 Y = 9.055333e-01 2.240655e-05 9.444430e-02 +C At t = 4.0000e+01 Y = 7.158403e-01 9.186334e-06 2.841505e-01 +C At t = 4.0000e+02 Y = 4.505250e-01 3.222964e-06 5.494717e-01 +C At t = 4.0000e+03 Y = 1.831975e-01 8.941774e-07 8.168016e-01 +C At t = 4.0000e+04 Y = 3.898730e-02 1.621940e-07 9.610125e-01 +C At t = 4.0000e+05 Y = 4.936363e-03 1.984221e-08 9.950636e-01 +C At t = 4.0000e+06 Y = 5.161831e-04 2.065786e-09 9.994838e-01 +C At t = 4.0000e+07 Y = 5.179817e-05 2.072032e-10 9.999482e-01 +C At t = 4.0000e+08 Y = 5.283401e-06 2.113371e-11 9.999947e-01 +C At t = 4.0000e+09 Y = 4.659031e-07 1.863613e-12 9.999995e-01 +C At t = 4.0000e+10 Y = 1.404280e-08 5.617126e-14 1.000000e+00 +C +C No. steps = 361 No. f-s = 693 No. J-s = 64 +C Method last used = 2 Last switch was at t = 6.0092e-03 +C----------------------------------------------------------------------- +C Full description of user interface to DLSODA. +C +C The user interface to DLSODA consists of the following parts. +C +C 1. The call sequence to Subroutine DLSODA, which is a driver +C routine for the solver. This includes descriptions of both +C the call sequence arguments and of user-supplied routines. +C following these descriptions is a description of +C optional inputs available through the call sequence, and then +C a description of optional outputs (in the work arrays). +C +C 2. Descriptions of other routines in the DLSODA package that may be +C (optionally) called by the user. These provide the ability to +C alter error message handling, save and restore the internal +C Common, and obtain specified derivatives of the solution y(t). +C +C 3. Descriptions of Common blocks to be declared in overlay +C or similar environments, or to be saved when doing an interrupt +C of the problem and continued solution later. +C +C 4. Description of a subroutine in the DLSODA package, +C which the user may replace with his/her own version, if desired. +C this relates to the measurement of errors. +C +C----------------------------------------------------------------------- +C Part 1. Call Sequence. +C +C The call sequence parameters used for input only are +C F, NEQ, TOUT, ITOL, RTOL, ATOL, ITASK, IOPT, LRW, LIW, JAC, JT, +C and those used for both input and output are +C Y, T, ISTATE. +C The work arrays RWORK and IWORK are also used for conditional and +C optional inputs and optional outputs. (The term output here refers +C to the return from Subroutine DLSODA to the user's calling program.) +C +C The legality of input parameters will be thoroughly checked on the +C initial call for the problem, but not checked thereafter unless a +C change in input parameters is flagged by ISTATE = 3 on input. +C +C The descriptions of the call arguments are as follows. +C +C F = the name of the user-supplied subroutine defining the +C ODE system. The system must be put in the first-order +C form dy/dt = f(t,y), where f is a vector-valued function +C of the scalar t and the vector y. Subroutine F is to +C compute the function f. It is to have the form +C SUBROUTINE F (NEQ, T, Y, YDOT) +C DOUBLE PRECISION T, Y(*), YDOT(*) +C where NEQ, T, and Y are input, and the array YDOT = f(t,y) +C is output. Y and YDOT are arrays of length NEQ. +C Subroutine F should not alter Y(1),...,Y(NEQ). +C F must be declared External in the calling program. +C +C Subroutine F may access user-defined quantities in +C NEQ(2),... and/or in Y(NEQ(1)+1),... if NEQ is an array +C (dimensioned in F) and/or Y has length exceeding NEQ(1). +C See the descriptions of NEQ and Y below. +C +C If quantities computed in the F routine are needed +C externally to DLSODA, an extra call to F should be made +C for this purpose, for consistent and accurate results. +C If only the derivative dy/dt is needed, use DINTDY instead. +C +C NEQ = the size of the ODE system (number of first order +C ordinary differential equations). Used only for input. +C NEQ may be decreased, but not increased, during the problem. +C If NEQ is decreased (with ISTATE = 3 on input), the +C remaining components of Y should be left undisturbed, if +C these are to be accessed in F and/or JAC. +C +C Normally, NEQ is a scalar, and it is generally referred to +C as a scalar in this user interface description. However, +C NEQ may be an array, with NEQ(1) set to the system size. +C (The DLSODA package accesses only NEQ(1).) In either case, +C this parameter is passed as the NEQ argument in all calls +C to F and JAC. Hence, if it is an array, locations +C NEQ(2),... may be used to store other integer data and pass +C it to F and/or JAC. Subroutines F and/or JAC must include +C NEQ in a Dimension statement in that case. +C +C Y = a real array for the vector of dependent variables, of +C length NEQ or more. Used for both input and output on the +C first call (ISTATE = 1), and only for output on other calls. +C On the first call, Y must contain the vector of initial +C values. On output, Y contains the computed solution vector, +C evaluated at T. If desired, the Y array may be used +C for other purposes between calls to the solver. +C +C This array is passed as the Y argument in all calls to +C F and JAC. Hence its length may exceed NEQ, and locations +C Y(NEQ+1),... may be used to store other real data and +C pass it to F and/or JAC. (The DLSODA package accesses only +C Y(1),...,Y(NEQ).) +C +C T = the independent variable. On input, T is used only on the +C first call, as the initial point of the integration. +C on output, after each call, T is the value at which a +C computed solution Y is evaluated (usually the same as TOUT). +C on an error return, T is the farthest point reached. +C +C TOUT = the next value of t at which a computed solution is desired. +C Used only for input. +C +C When starting the problem (ISTATE = 1), TOUT may be equal +C to T for one call, then should .ne. T for the next call. +C For the initial t, an input value of TOUT .ne. T is used +C in order to determine the direction of the integration +C (i.e. the algebraic sign of the step sizes) and the rough +C scale of the problem. Integration in either direction +C (forward or backward in t) is permitted. +C +C If ITASK = 2 or 5 (one-step modes), TOUT is ignored after +C the first call (i.e. the first call with TOUT .ne. T). +C Otherwise, TOUT is required on every call. +C +C If ITASK = 1, 3, or 4, the values of TOUT need not be +C monotone, but a value of TOUT which backs up is limited +C to the current internal T interval, whose endpoints are +C TCUR - HU and TCUR (see optional outputs, below, for +C TCUR and HU). +C +C ITOL = an indicator for the type of error control. See +C description below under ATOL. Used only for input. +C +C RTOL = a relative error tolerance parameter, either a scalar or +C an array of length NEQ. See description below under ATOL. +C Input only. +C +C ATOL = an absolute error tolerance parameter, either a scalar or +C an array of length NEQ. Input only. +C +C The input parameters ITOL, RTOL, and ATOL determine +C the error control performed by the solver. The solver will +C control the vector E = (E(i)) of estimated local errors +C in y, according to an inequality of the form +C max-norm of ( E(i)/EWT(i) ) .le. 1, +C where EWT = (EWT(i)) is a vector of positive error weights. +C The values of RTOL and ATOL should all be non-negative. +C The following table gives the types (scalar/array) of +C RTOL and ATOL, and the corresponding form of EWT(i). +C +C ITOL RTOL ATOL EWT(i) +C 1 scalar scalar RTOL*ABS(Y(i)) + ATOL +C 2 scalar array RTOL*ABS(Y(i)) + ATOL(i) +C 3 array scalar RTOL(i)*ABS(Y(i)) + ATOL +C 4 array array RTOL(i)*ABS(Y(i)) + ATOL(i) +C +C When either of these parameters is a scalar, it need not +C be dimensioned in the user's calling program. +C +C If none of the above choices (with ITOL, RTOL, and ATOL +C fixed throughout the problem) is suitable, more general +C error controls can be obtained by substituting a +C user-supplied routine for the setting of EWT. +C See Part 4 below. +C +C If global errors are to be estimated by making a repeated +C run on the same problem with smaller tolerances, then all +C components of RTOL and ATOL (i.e. of EWT) should be scaled +C down uniformly. +C +C ITASK = an index specifying the task to be performed. +C Input only. ITASK has the following values and meanings. +C 1 means normal computation of output values of y(t) at +C t = TOUT (by overshooting and interpolating). +C 2 means take one step only and return. +C 3 means stop at the first internal mesh point at or +C beyond t = TOUT and return. +C 4 means normal computation of output values of y(t) at +C t = TOUT but without overshooting t = TCRIT. +C TCRIT must be input as RWORK(1). TCRIT may be equal to +C or beyond TOUT, but not behind it in the direction of +C integration. This option is useful if the problem +C has a singularity at or beyond t = TCRIT. +C 5 means take one step, without passing TCRIT, and return. +C TCRIT must be input as RWORK(1). +C +C Note: If ITASK = 4 or 5 and the solver reaches TCRIT +C (within roundoff), it will return T = TCRIT (exactly) to +C indicate this (unless ITASK = 4 and TOUT comes before TCRIT, +C in which case answers at t = TOUT are returned first). +C +C ISTATE = an index used for input and output to specify the +C the state of the calculation. +C +C On input, the values of ISTATE are as follows. +C 1 means this is the first call for the problem +C (initializations will be done). See note below. +C 2 means this is not the first call, and the calculation +C is to continue normally, with no change in any input +C parameters except possibly TOUT and ITASK. +C (If ITOL, RTOL, and/or ATOL are changed between calls +C with ISTATE = 2, the new values will be used but not +C tested for legality.) +C 3 means this is not the first call, and the +C calculation is to continue normally, but with +C a change in input parameters other than +C TOUT and ITASK. Changes are allowed in +C NEQ, ITOL, RTOL, ATOL, IOPT, LRW, LIW, JT, ML, MU, +C and any optional inputs except H0, MXORDN, and MXORDS. +C (See IWORK description for ML and MU.) +C Note: A preliminary call with TOUT = T is not counted +C as a first call here, as no initialization or checking of +C input is done. (Such a call is sometimes useful for the +C purpose of outputting the initial conditions.) +C Thus the first call for which TOUT .ne. T requires +C ISTATE = 1 on input. +C +C On output, ISTATE has the following values and meanings. +C 1 means nothing was done; TOUT = T and ISTATE = 1 on input. +C 2 means the integration was performed successfully. +C -1 means an excessive amount of work (more than MXSTEP +C steps) was done on this call, before completing the +C requested task, but the integration was otherwise +C successful as far as T. (MXSTEP is an optional input +C and is normally 500.) To continue, the user may +C simply reset ISTATE to a value .gt. 1 and call again +C (the excess work step counter will be reset to 0). +C In addition, the user may increase MXSTEP to avoid +C this error return (see below on optional inputs). +C -2 means too much accuracy was requested for the precision +C of the machine being used. This was detected before +C completing the requested task, but the integration +C was successful as far as T. To continue, the tolerance +C parameters must be reset, and ISTATE must be set +C to 3. The optional output TOLSF may be used for this +C purpose. (Note: If this condition is detected before +C taking any steps, then an illegal input return +C (ISTATE = -3) occurs instead.) +C -3 means illegal input was detected, before taking any +C integration steps. See written message for details. +C Note: If the solver detects an infinite loop of calls +C to the solver with illegal input, it will cause +C the run to stop. +C -4 means there were repeated error test failures on +C one attempted step, before completing the requested +C task, but the integration was successful as far as T. +C The problem may have a singularity, or the input +C may be inappropriate. +C -5 means there were repeated convergence test failures on +C one attempted step, before completing the requested +C task, but the integration was successful as far as T. +C This may be caused by an inaccurate Jacobian matrix, +C if one is being used. +C -6 means EWT(i) became zero for some i during the +C integration. Pure relative error control (ATOL(i)=0.0) +C was requested on a variable which has now vanished. +C The integration was successful as far as T. +C -7 means the length of RWORK and/or IWORK was too small to +C proceed, but the integration was successful as far as T. +C This happens when DLSODA chooses to switch methods +C but LRW and/or LIW is too small for the new method. +C +C Note: Since the normal output value of ISTATE is 2, +C it does not need to be reset for normal continuation. +C Also, since a negative input value of ISTATE will be +C regarded as illegal, a negative output value requires the +C user to change it, and possibly other inputs, before +C calling the solver again. +C +C IOPT = an integer flag to specify whether or not any optional +C inputs are being used on this call. Input only. +C The optional inputs are listed separately below. +C IOPT = 0 means no optional inputs are being used. +C default values will be used in all cases. +C IOPT = 1 means one or more optional inputs are being used. +C +C RWORK = a real array (double precision) for work space, and (in the +C first 20 words) for conditional and optional inputs and +C optional outputs. +C As DLSODA switches automatically between stiff and nonstiff +C methods, the required length of RWORK can change during the +C problem. Thus the RWORK array passed to DLSODA can either +C have a static (fixed) length large enough for both methods, +C or have a dynamic (changing) length altered by the calling +C program in response to output from DLSODA. +C +C --- Fixed Length Case --- +C If the RWORK length is to be fixed, it should be at least +C MAX (LRN, LRS), +C where LRN and LRS are the RWORK lengths required when the +C current method is nonstiff or stiff, respectively. +C +C The separate RWORK length requirements LRN and LRS are +C as follows: +C IF NEQ is constant and the maximum method orders have +C their default values, then +C LRN = 20 + 16*NEQ, +C LRS = 22 + 9*NEQ + NEQ**2 if JT = 1 or 2, +C LRS = 22 + 10*NEQ + (2*ML+MU)*NEQ if JT = 4 or 5. +C Under any other conditions, LRN and LRS are given by: +C LRN = 20 + NYH*(MXORDN+1) + 3*NEQ, +C LRS = 20 + NYH*(MXORDS+1) + 3*NEQ + LMAT, +C where +C NYH = the initial value of NEQ, +C MXORDN = 12, unless a smaller value is given as an +C optional input, +C MXORDS = 5, unless a smaller value is given as an +C optional input, +C LMAT = length of matrix work space: +C LMAT = NEQ**2 + 2 if JT = 1 or 2, +C LMAT = (2*ML + MU + 1)*NEQ + 2 if JT = 4 or 5. +C +C --- Dynamic Length Case --- +C If the length of RWORK is to be dynamic, then it should +C be at least LRN or LRS, as defined above, depending on the +C current method. Initially, it must be at least LRN (since +C DLSODA starts with the nonstiff method). On any return +C from DLSODA, the optional output MCUR indicates the current +C method. If MCUR differs from the value it had on the +C previous return, or if there has only been one call to +C DLSODA and MCUR is now 2, then DLSODA has switched +C methods during the last call, and the length of RWORK +C should be reset (to LRN if MCUR = 1, or to LRS if +C MCUR = 2). (An increase in the RWORK length is required +C if DLSODA returned ISTATE = -7, but not otherwise.) +C After resetting the length, call DLSODA with ISTATE = 3 +C to signal that change. +C +C LRW = the length of the array RWORK, as declared by the user. +C (This will be checked by the solver.) +C +C IWORK = an integer array for work space. +C As DLSODA switches automatically between stiff and nonstiff +C methods, the required length of IWORK can change during +C problem, between +C LIS = 20 + NEQ and LIN = 20, +C respectively. Thus the IWORK array passed to DLSODA can +C either have a fixed length of at least 20 + NEQ, or have a +C dynamic length of at least LIN or LIS, depending on the +C current method. The comments on dynamic length under +C RWORK above apply here. Initially, this length need +C only be at least LIN = 20. +C +C The first few words of IWORK are used for conditional and +C optional inputs and optional outputs. +C +C The following 2 words in IWORK are conditional inputs: +C IWORK(1) = ML these are the lower and upper +C IWORK(2) = MU half-bandwidths, respectively, of the +C banded Jacobian, excluding the main diagonal. +C The band is defined by the matrix locations +C (i,j) with i-ML .le. j .le. i+MU. ML and MU +C must satisfy 0 .le. ML,MU .le. NEQ-1. +C These are required if JT is 4 or 5, and +C ignored otherwise. ML and MU may in fact be +C the band parameters for a matrix to which +C df/dy is only approximately equal. +C +C LIW = the length of the array IWORK, as declared by the user. +C (This will be checked by the solver.) +C +C Note: The base addresses of the work arrays must not be +C altered between calls to DLSODA for the same problem. +C The contents of the work arrays must not be altered +C between calls, except possibly for the conditional and +C optional inputs, and except for the last 3*NEQ words of RWORK. +C The latter space is used for internal scratch space, and so is +C available for use by the user outside DLSODA between calls, if +C desired (but not for use by F or JAC). +C +C JAC = the name of the user-supplied routine to compute the +C Jacobian matrix, df/dy, if JT = 1 or 4. The JAC routine +C is optional, but if the problem is expected to be stiff much +C of the time, you are encouraged to supply JAC, for the sake +C of efficiency. (Alternatively, set JT = 2 or 5 to have +C DLSODA compute df/dy internally by difference quotients.) +C If and when DLSODA uses df/dy, it treats this NEQ by NEQ +C matrix either as full (JT = 1 or 2), or as banded (JT = +C 4 or 5) with half-bandwidths ML and MU (discussed under +C IWORK above). In either case, if JT = 1 or 4, the JAC +C routine must compute df/dy as a function of the scalar t +C and the vector y. It is to have the form +C SUBROUTINE JAC (NEQ, T, Y, ML, MU, PD, NROWPD) +C DOUBLE PRECISION T, Y(*), PD(NROWPD,*) +C where NEQ, T, Y, ML, MU, and NROWPD are input and the array +C PD is to be loaded with partial derivatives (elements of +C the Jacobian matrix) on output. PD must be given a first +C dimension of NROWPD. T and Y have the same meaning as in +C Subroutine F. +C In the full matrix case (JT = 1), ML and MU are +C ignored, and the Jacobian is to be loaded into PD in +C columnwise manner, with df(i)/dy(j) loaded into PD(i,j). +C In the band matrix case (JT = 4), the elements +C within the band are to be loaded into PD in columnwise +C manner, with diagonal lines of df/dy loaded into the rows +C of PD. Thus df(i)/dy(j) is to be loaded into PD(i-j+MU+1,j). +C ML and MU are the half-bandwidth parameters (see IWORK). +C The locations in PD in the two triangular areas which +C correspond to nonexistent matrix elements can be ignored +C or loaded arbitrarily, as they are overwritten by DLSODA. +C JAC need not provide df/dy exactly. A crude +C approximation (possibly with a smaller bandwidth) will do. +C In either case, PD is preset to zero by the solver, +C so that only the nonzero elements need be loaded by JAC. +C Each call to JAC is preceded by a call to F with the same +C arguments NEQ, T, and Y. Thus to gain some efficiency, +C intermediate quantities shared by both calculations may be +C saved in a user Common block by F and not recomputed by JAC, +C if desired. Also, JAC may alter the Y array, if desired. +C JAC must be declared External in the calling program. +C Subroutine JAC may access user-defined quantities in +C NEQ(2),... and/or in Y(NEQ(1)+1),... if NEQ is an array +C (dimensioned in JAC) and/or Y has length exceeding NEQ(1). +C See the descriptions of NEQ and Y above. +C +C JT = Jacobian type indicator. Used only for input. +C JT specifies how the Jacobian matrix df/dy will be +C treated, if and when DLSODA requires this matrix. +C JT has the following values and meanings: +C 1 means a user-supplied full (NEQ by NEQ) Jacobian. +C 2 means an internally generated (difference quotient) full +C Jacobian (using NEQ extra calls to F per df/dy value). +C 4 means a user-supplied banded Jacobian. +C 5 means an internally generated banded Jacobian (using +C ML+MU+1 extra calls to F per df/dy evaluation). +C If JT = 1 or 4, the user must supply a Subroutine JAC +C (the name is arbitrary) as described above under JAC. +C If JT = 2 or 5, a dummy argument can be used. +C----------------------------------------------------------------------- +C Optional Inputs. +C +C The following is a list of the optional inputs provided for in the +C call sequence. (See also Part 2.) For each such input variable, +C this table lists its name as used in this documentation, its +C location in the call sequence, its meaning, and the default value. +C The use of any of these inputs requires IOPT = 1, and in that +C case all of these inputs are examined. A value of zero for any +C of these optional inputs will cause the default value to be used. +C Thus to use a subset of the optional inputs, simply preload +C locations 5 to 10 in RWORK and IWORK to 0.0 and 0 respectively, and +C then set those of interest to nonzero values. +C +C Name Location Meaning and Default Value +C +C H0 RWORK(5) the step size to be attempted on the first step. +C The default value is determined by the solver. +C +C HMAX RWORK(6) the maximum absolute step size allowed. +C The default value is infinite. +C +C HMIN RWORK(7) the minimum absolute step size allowed. +C The default value is 0. (This lower bound is not +C enforced on the final step before reaching TCRIT +C when ITASK = 4 or 5.) +C +C IXPR IWORK(5) flag to generate extra printing at method switches. +C IXPR = 0 means no extra printing (the default). +C IXPR = 1 means print data on each switch. +C T, H, and NST will be printed on the same logical +C unit as used for error messages. +C +C MXSTEP IWORK(6) maximum number of (internally defined) steps +C allowed during one call to the solver. +C The default value is 500. +C +C MXHNIL IWORK(7) maximum number of messages printed (per problem) +C warning that T + H = T on a step (H = step size). +C This must be positive to result in a non-default +C value. The default value is 10. +C +C MXORDN IWORK(8) the maximum order to be allowed for the nonstiff +C (Adams) method. the default value is 12. +C if MXORDN exceeds the default value, it will +C be reduced to the default value. +C MXORDN is held constant during the problem. +C +C MXORDS IWORK(9) the maximum order to be allowed for the stiff +C (BDF) method. The default value is 5. +C If MXORDS exceeds the default value, it will +C be reduced to the default value. +C MXORDS is held constant during the problem. +C----------------------------------------------------------------------- +C Optional Outputs. +C +C As optional additional output from DLSODA, the variables listed +C below are quantities related to the performance of DLSODA +C which are available to the user. These are communicated by way of +C the work arrays, but also have internal mnemonic names as shown. +C except where stated otherwise, all of these outputs are defined +C on any successful return from DLSODA, and on any return with +C ISTATE = -1, -2, -4, -5, or -6. On an illegal input return +C (ISTATE = -3), they will be unchanged from their existing values +C (if any), except possibly for TOLSF, LENRW, and LENIW. +C On any error return, outputs relevant to the error will be defined, +C as noted below. +C +C Name Location Meaning +C +C HU RWORK(11) the step size in t last used (successfully). +C +C HCUR RWORK(12) the step size to be attempted on the next step. +C +C TCUR RWORK(13) the current value of the independent variable +C which the solver has actually reached, i.e. the +C current internal mesh point in t. On output, TCUR +C will always be at least as far as the argument +C T, but may be farther (if interpolation was done). +C +C TOLSF RWORK(14) a tolerance scale factor, greater than 1.0, +C computed when a request for too much accuracy was +C detected (ISTATE = -3 if detected at the start of +C the problem, ISTATE = -2 otherwise). If ITOL is +C left unaltered but RTOL and ATOL are uniformly +C scaled up by a factor of TOLSF for the next call, +C then the solver is deemed likely to succeed. +C (The user may also ignore TOLSF and alter the +C tolerance parameters in any other way appropriate.) +C +C TSW RWORK(15) the value of t at the time of the last method +C switch, if any. +C +C NST IWORK(11) the number of steps taken for the problem so far. +C +C NFE IWORK(12) the number of f evaluations for the problem so far. +C +C NJE IWORK(13) the number of Jacobian evaluations (and of matrix +C LU decompositions) for the problem so far. +C +C NQU IWORK(14) the method order last used (successfully). +C +C NQCUR IWORK(15) the order to be attempted on the next step. +C +C IMXER IWORK(16) the index of the component of largest magnitude in +C the weighted local error vector ( E(i)/EWT(i) ), +C on an error return with ISTATE = -4 or -5. +C +C LENRW IWORK(17) the length of RWORK actually required, assuming +C that the length of RWORK is to be fixed for the +C rest of the problem, and that switching may occur. +C This is defined on normal returns and on an illegal +C input return for insufficient storage. +C +C LENIW IWORK(18) the length of IWORK actually required, assuming +C that the length of IWORK is to be fixed for the +C rest of the problem, and that switching may occur. +C This is defined on normal returns and on an illegal +C input return for insufficient storage. +C +C MUSED IWORK(19) the method indicator for the last successful step: +C 1 means Adams (nonstiff), 2 means BDF (stiff). +C +C MCUR IWORK(20) the current method indicator: +C 1 means Adams (nonstiff), 2 means BDF (stiff). +C This is the method to be attempted +C on the next step. Thus it differs from MUSED +C only if a method switch has just been made. +C +C The following two arrays are segments of the RWORK array which +C may also be of interest to the user as optional outputs. +C For each array, the table below gives its internal name, +C its base address in RWORK, and its description. +C +C Name Base Address Description +C +C YH 21 the Nordsieck history array, of size NYH by +C (NQCUR + 1), where NYH is the initial value +C of NEQ. For j = 0,1,...,NQCUR, column j+1 +C of YH contains HCUR**j/factorial(j) times +C the j-th derivative of the interpolating +C polynomial currently representing the solution, +C evaluated at T = TCUR. +C +C ACOR LACOR array of size NEQ used for the accumulated +C (from Common corrections on each step, scaled on output +C as noted) to represent the estimated local error in y +C on the last step. This is the vector E in +C the description of the error control. It is +C defined only on a successful return from +C DLSODA. The base address LACOR is obtained by +C including in the user's program the +C following 2 lines: +C COMMON /DLS001/ RLS(218), ILS(37) +C LACOR = ILS(22) +C +C----------------------------------------------------------------------- +C Part 2. Other Routines Callable. +C +C The following are optional calls which the user may make to +C gain additional capabilities in conjunction with DLSODA. +C (The routines XSETUN and XSETF are designed to conform to the +C SLATEC error handling package.) +C +C Form of Call Function +C CALL XSETUN(LUN) set the logical unit number, LUN, for +C output of messages from DLSODA, if +C the default is not desired. +C The default value of LUN is 6. +C +C CALL XSETF(MFLAG) set a flag to control the printing of +C messages by DLSODA. +C MFLAG = 0 means do not print. (Danger: +C This risks losing valuable information.) +C MFLAG = 1 means print (the default). +C +C Either of the above calls may be made at +C any time and will take effect immediately. +C +C CALL DSRCMA(RSAV,ISAV,JOB) saves and restores the contents of +C the internal Common blocks used by +C DLSODA (see Part 3 below). +C RSAV must be a real array of length 240 +C or more, and ISAV must be an integer +C array of length 46 or more. +C JOB=1 means save Common into RSAV/ISAV. +C JOB=2 means restore Common from RSAV/ISAV. +C DSRCMA is useful if one is +C interrupting a run and restarting +C later, or alternating between two or +C more problems solved with DLSODA. +C +C CALL DINTDY(,,,,,) provide derivatives of y, of various +C (see below) orders, at a specified point t, if +C desired. It may be called only after +C a successful return from DLSODA. +C +C The detailed instructions for using DINTDY are as follows. +C The form of the call is: +C +C CALL DINTDY (T, K, RWORK(21), NYH, DKY, IFLAG) +C +C The input parameters are: +C +C T = value of independent variable where answers are desired +C (normally the same as the T last returned by DLSODA). +C For valid results, T must lie between TCUR - HU and TCUR. +C (See optional outputs for TCUR and HU.) +C K = integer order of the derivative desired. K must satisfy +C 0 .le. K .le. NQCUR, where NQCUR is the current order +C (see optional outputs). The capability corresponding +C to K = 0, i.e. computing y(T), is already provided +C by DLSODA directly. Since NQCUR .ge. 1, the first +C derivative dy/dt is always available with DINTDY. +C RWORK(21) = the base address of the history array YH. +C NYH = column length of YH, equal to the initial value of NEQ. +C +C The output parameters are: +C +C DKY = a real array of length NEQ containing the computed value +C of the K-th derivative of y(t). +C IFLAG = integer flag, returned as 0 if K and T were legal, +C -1 if K was illegal, and -2 if T was illegal. +C On an error return, a message is also written. +C----------------------------------------------------------------------- +C Part 3. Common Blocks. +C +C If DLSODA is to be used in an overlay situation, the user +C must declare, in the primary overlay, the variables in: +C (1) the call sequence to DLSODA, and +C (2) the two internal Common blocks +C /DLS001/ of length 255 (218 double precision words +C followed by 37 integer words), +C /DLSA01/ of length 31 (22 double precision words +C followed by 9 integer words). +C +C If DLSODA is used on a system in which the contents of internal +C Common blocks are not preserved between calls, the user should +C declare the above Common blocks in the calling program to insure +C that their contents are preserved. +C +C If the solution of a given problem by DLSODA is to be interrupted +C and then later continued, such as when restarting an interrupted run +C or alternating between two or more problems, the user should save, +C following the return from the last DLSODA call prior to the +C interruption, the contents of the call sequence variables and the +C internal Common blocks, and later restore these values before the +C next DLSODA call for that problem. To save and restore the Common +C blocks, use Subroutine DSRCMA (see Part 2 above). +C +C----------------------------------------------------------------------- +C Part 4. Optionally Replaceable Solver Routines. +C +C Below is a description of a routine in the DLSODA package which +C relates to the measurement of errors, and can be +C replaced by a user-supplied version, if desired. However, since such +C a replacement may have a major impact on performance, it should be +C done only when absolutely necessary, and only with great caution. +C (Note: The means by which the package version of a routine is +C superseded by the user's version may be system-dependent.) +C +C (a) DEWSET. +C The following subroutine is called just before each internal +C integration step, and sets the array of error weights, EWT, as +C described under ITOL/RTOL/ATOL above: +C Subroutine DEWSET (NEQ, ITOL, RTOL, ATOL, YCUR, EWT) +C where NEQ, ITOL, RTOL, and ATOL are as in the DLSODA call sequence, +C YCUR contains the current dependent variable vector, and +C EWT is the array of weights set by DEWSET. +C +C If the user supplies this subroutine, it must return in EWT(i) +C (i = 1,...,NEQ) a positive quantity suitable for comparing errors +C in y(i) to. The EWT array returned by DEWSET is passed to the +C DMNORM routine, and also used by DLSODA in the computation +C of the optional output IMXER, and the increments for difference +C quotient Jacobians. +C +C In the user-supplied version of DEWSET, it may be desirable to use +C the current values of derivatives of y. Derivatives up to order NQ +C are available from the history array YH, described above under +C optional outputs. In DEWSET, YH is identical to the YCUR array, +C extended to NQ + 1 columns with a column length of NYH and scale +C factors of H**j/factorial(j). On the first call for the problem, +C given by NST = 0, NQ is 1 and H is temporarily set to 1.0. +C NYH is the initial value of NEQ. The quantities NQ, H, and NST +C can be obtained by including in DEWSET the statements: +C DOUBLE PRECISION RLS +C COMMON /DLS001/ RLS(218),ILS(37) +C NQ = ILS(33) +C NST = ILS(34) +C H = RLS(212) +C Thus, for example, the current value of dy/dt can be obtained as +C YCUR(NYH+i)/H (i=1,...,NEQ) (and the division by H is +C unnecessary when NST = 0). +C----------------------------------------------------------------------- +C +C***REVISION HISTORY (YYYYMMDD) +C 19811102 DATE WRITTEN +C 19820126 Fixed bug in tests of work space lengths; +C minor corrections in main prologue and comments. +C 19870330 Major update: corrected comments throughout; +C removed TRET from Common; rewrote EWSET with 4 loops; +C fixed t test in INTDY; added Cray directives in STODA; +C in STODA, fixed DELP init. and logic around PJAC call; +C combined routines to save/restore Common; +C passed LEVEL = 0 in error message calls (except run abort). +C 19970225 Fixed lines setting JSTART = -2 in Subroutine LSODA. +C 20010425 Major update: convert source lines to upper case; +C added *DECK lines; changed from 1 to * in dummy dimensions; +C changed names R1MACH/D1MACH to RUMACH/DUMACH; +C renamed routines for uniqueness across single/double prec.; +C converted intrinsic names to generic form; +C removed ILLIN and NTREP (data loaded) from Common; +C removed all 'own' variables from Common; +C changed error messages to quoted strings; +C replaced XERRWV/XERRWD with 1993 revised version; +C converted prologues, comments, error messages to mixed case; +C numerous corrections to prologues and internal comments. +C 20010507 Converted single precision source to double precision. +C 20010613 Revised excess accuracy test (to match rest of ODEPACK). +C 20010808 Fixed bug in DPRJA (matrix in DBNORM call). +C 20020502 Corrected declarations in descriptions of user routines. +C 20031105 Restored 'own' variables to Common blocks, to enable +C interrupt/restart feature. +C 20031112 Added SAVE statements for data-loaded constants. +C +C----------------------------------------------------------------------- +C Other routines in the DLSODA package. +C +C In addition to Subroutine DLSODA, the DLSODA package includes the +C following subroutines and function routines: +C DINTDY computes an interpolated value of the y vector at t = TOUT. +C DSTODA is the core integrator, which does one step of the +C integration and the associated error control. +C DCFODE sets all method coefficients and test constants. +C DPRJA computes and preprocesses the Jacobian matrix J = df/dy +C and the Newton iteration matrix P = I - h*l0*J. +C DSOLSY manages solution of linear system in chord iteration. +C DEWSET sets the error weight vector EWT before each step. +C DMNORM computes the weighted max-norm of a vector. +C DFNORM computes the norm of a full matrix consistent with the +C weighted max-norm on vectors. +C DBNORM computes the norm of a band matrix consistent with the +C weighted max-norm on vectors. +C DSRCMA is a user-callable routine to save and restore +C the contents of the internal Common blocks. +C DGEFA and DGESL are routines from LINPACK for solving full +C systems of linear algebraic equations. +C DGBFA and DGBSL are routines from LINPACK for solving banded +C linear systems. +C DUMACH computes the unit roundoff in a machine-independent manner. +C XERRWD, XSETUN, XSETF, IXSAV, and IUMACH handle the printing of all +C error messages and warnings. XERRWD is machine-dependent. +C Note: DMNORM, DFNORM, DBNORM, DUMACH, IXSAV, and IUMACH are +C function routines. All the others are subroutines. +C +C----------------------------------------------------------------------- + EXTERNAL DPRJA, DSOLSY + DOUBLE PRECISION DUMACH, DMNORM + INTEGER INIT, MXSTEP, MXHNIL, NHNIL, NSLAST, NYH, IOWNS, + 1 ICF, IERPJ, IERSL, JCUR, JSTART, KFLAG, L, + 2 LYH, LEWT, LACOR, LSAVF, LWM, LIWM, METH, MITER, + 3 MAXORD, MAXCOR, MSBP, MXNCF, N, NQ, NST, NFE, NJE, NQU + INTEGER INSUFR, INSUFI, IXPR, IOWNS2, JTYP, MUSED, MXORDN, MXORDS + INTEGER I, I1, I2, IFLAG, IMXER, KGO, LF0, + 1 LENIW, LENRW, LENWM, ML, MORD, MU, MXHNL0, MXSTP0 + INTEGER LEN1, LEN1C, LEN1N, LEN1S, LEN2, LENIWC, LENRWC + DOUBLE PRECISION ROWNS, + 1 CCMAX, EL0, H, HMIN, HMXI, HU, RC, TN, UROUND + DOUBLE PRECISION TSW, ROWNS2, PDNORM + DOUBLE PRECISION ATOLI, AYI, BIG, EWTI, H0, HMAX, HMX, RH, RTOLI, + 1 TCRIT, TDIST, TNEXT, TOL, TOLSF, TP, SIZE, SUM, W0 + DIMENSION MORD(2) + LOGICAL IHIT + CHARACTER*60 MSG + SAVE MORD, MXSTP0, MXHNL0 +C----------------------------------------------------------------------- +C The following two internal Common blocks contain +C (a) variables which are local to any subroutine but whose values must +C be preserved between calls to the routine ("own" variables), and +C (b) variables which are communicated between subroutines. +C The block DLS001 is declared in subroutines DLSODA, DINTDY, DSTODA, +C DPRJA, and DSOLSY. +C The block DLSA01 is declared in subroutines DLSODA, DSTODA, and DPRJA. +C Groups of variables are replaced by dummy arrays in the Common +C declarations in routines where those variables are not used. +C----------------------------------------------------------------------- + COMMON /DLS001/ ROWNS(209), + 1 CCMAX, EL0, H, HMIN, HMXI, HU, RC, TN, UROUND, + 2 INIT, MXSTEP, MXHNIL, NHNIL, NSLAST, NYH, IOWNS(6), + 3 ICF, IERPJ, IERSL, JCUR, JSTART, KFLAG, L, + 4 LYH, LEWT, LACOR, LSAVF, LWM, LIWM, METH, MITER, + 5 MAXORD, MAXCOR, MSBP, MXNCF, N, NQ, NST, NFE, NJE, NQU +C + COMMON /DLSA01/ TSW, ROWNS2(20), PDNORM, + 1 INSUFR, INSUFI, IXPR, IOWNS2(2), JTYP, MUSED, MXORDN, MXORDS +C + DATA MORD(1),MORD(2)/12,5/, MXSTP0/500/, MXHNL0/10/ +C----------------------------------------------------------------------- +C Block A. +C This code block is executed on every call. +C It tests ISTATE and ITASK for legality and branches appropriately. +C If ISTATE .gt. 1 but the flag INIT shows that initialization has +C not yet been done, an error return occurs. +C If ISTATE = 1 and TOUT = T, return immediately. +C----------------------------------------------------------------------- + IF (ISTATE .LT. 1 .OR. ISTATE .GT. 3) GO TO 601 + IF (ITASK .LT. 1 .OR. ITASK .GT. 5) GO TO 602 + IF (ISTATE .EQ. 1) GO TO 10 + IF (INIT .EQ. 0) GO TO 603 + IF (ISTATE .EQ. 2) GO TO 200 + GO TO 20 + 10 INIT = 0 + IF (TOUT .EQ. T) RETURN +C----------------------------------------------------------------------- +C Block B. +C The next code block is executed for the initial call (ISTATE = 1), +C or for a continuation call with parameter changes (ISTATE = 3). +C It contains checking of all inputs and various initializations. +C +C First check legality of the non-optional inputs NEQ, ITOL, IOPT, +C JT, ML, and MU. +C----------------------------------------------------------------------- + 20 IF (NEQ(1) .LE. 0) GO TO 604 + IF (ISTATE .EQ. 1) GO TO 25 + IF (NEQ(1) .GT. N) GO TO 605 + 25 N = NEQ(1) + IF (ITOL .LT. 1 .OR. ITOL .GT. 4) GO TO 606 + IF (IOPT .LT. 0 .OR. IOPT .GT. 1) GO TO 607 + IF (JT .EQ. 3 .OR. JT .LT. 1 .OR. JT .GT. 5) GO TO 608 + JTYP = JT + IF (JT .LE. 2) GO TO 30 + ML = IWORK(1) + MU = IWORK(2) + IF (ML .LT. 0 .OR. ML .GE. N) GO TO 609 + IF (MU .LT. 0 .OR. MU .GE. N) GO TO 610 + 30 CONTINUE +C Next process and check the optional inputs. -------------------------- + IF (IOPT .EQ. 1) GO TO 40 + IXPR = 0 + MXSTEP = MXSTP0 + MXHNIL = MXHNL0 + HMXI = 0.0D0 + HMIN = 0.0D0 + IF (ISTATE .NE. 1) GO TO 60 + H0 = 0.0D0 + MXORDN = MORD(1) + MXORDS = MORD(2) + GO TO 60 + 40 IXPR = IWORK(5) + IF (IXPR .LT. 0 .OR. IXPR .GT. 1) GO TO 611 + MXSTEP = IWORK(6) + IF (MXSTEP .LT. 0) GO TO 612 + IF (MXSTEP .EQ. 0) MXSTEP = MXSTP0 + MXHNIL = IWORK(7) + IF (MXHNIL .LT. 0) GO TO 613 + IF (MXHNIL .EQ. 0) MXHNIL = MXHNL0 + IF (ISTATE .NE. 1) GO TO 50 + H0 = RWORK(5) + MXORDN = IWORK(8) + IF (MXORDN .LT. 0) GO TO 628 + IF (MXORDN .EQ. 0) MXORDN = 100 + MXORDN = MIN(MXORDN,MORD(1)) + MXORDS = IWORK(9) + IF (MXORDS .LT. 0) GO TO 629 + IF (MXORDS .EQ. 0) MXORDS = 100 + MXORDS = MIN(MXORDS,MORD(2)) + IF ((TOUT - T)*H0 .LT. 0.0D0) GO TO 614 + 50 HMAX = RWORK(6) + IF (HMAX .LT. 0.0D0) GO TO 615 + HMXI = 0.0D0 + IF (HMAX .GT. 0.0D0) HMXI = 1.0D0/HMAX + HMIN = RWORK(7) + IF (HMIN .LT. 0.0D0) GO TO 616 +C----------------------------------------------------------------------- +C Set work array pointers and check lengths LRW and LIW. +C If ISTATE = 1, METH is initialized to 1 here to facilitate the +C checking of work space lengths. +C Pointers to segments of RWORK and IWORK are named by prefixing L to +C the name of the segment. E.g., the segment YH starts at RWORK(LYH). +C Segments of RWORK (in order) are denoted YH, WM, EWT, SAVF, ACOR. +C If the lengths provided are insufficient for the current method, +C an error return occurs. This is treated as illegal input on the +C first call, but as a problem interruption with ISTATE = -7 on a +C continuation call. If the lengths are sufficient for the current +C method but not for both methods, a warning message is sent. +C----------------------------------------------------------------------- + 60 IF (ISTATE .EQ. 1) METH = 1 + IF (ISTATE .EQ. 1) NYH = N + LYH = 21 + LEN1N = 20 + (MXORDN + 1)*NYH + LEN1S = 20 + (MXORDS + 1)*NYH + LWM = LEN1S + 1 + IF (JT .LE. 2) LENWM = N*N + 2 + IF (JT .GE. 4) LENWM = (2*ML + MU + 1)*N + 2 + LEN1S = LEN1S + LENWM + LEN1C = LEN1N + IF (METH .EQ. 2) LEN1C = LEN1S + LEN1 = MAX(LEN1N,LEN1S) + LEN2 = 3*N + LENRW = LEN1 + LEN2 + LENRWC = LEN1C + LEN2 + IWORK(17) = LENRW + LIWM = 1 + LENIW = 20 + N + LENIWC = 20 + IF (METH .EQ. 2) LENIWC = LENIW + IWORK(18) = LENIW + IF (ISTATE .EQ. 1 .AND. LRW .LT. LENRWC) GO TO 617 + IF (ISTATE .EQ. 1 .AND. LIW .LT. LENIWC) GO TO 618 + IF (ISTATE .EQ. 3 .AND. LRW .LT. LENRWC) GO TO 550 + IF (ISTATE .EQ. 3 .AND. LIW .LT. LENIWC) GO TO 555 + LEWT = LEN1 + 1 + INSUFR = 0 + IF (LRW .GE. LENRW) GO TO 65 + INSUFR = 2 + LEWT = LEN1C + 1 + MSG='DLSODA- Warning.. RWORK length is sufficient for now, but ' + CALL XERRWD (MSG, 60, 103, 0, 0, 0, 0, 0, 0.0D0, 0.0D0) + MSG=' may not be later. Integration will proceed anyway. ' + CALL XERRWD (MSG, 60, 103, 0, 0, 0, 0, 0, 0.0D0, 0.0D0) + MSG = ' Length needed is LENRW = I1, while LRW = I2.' + CALL XERRWD (MSG, 50, 103, 0, 2, LENRW, LRW, 0, 0.0D0, 0.0D0) + 65 LSAVF = LEWT + N + LACOR = LSAVF + N + INSUFI = 0 + IF (LIW .GE. LENIW) GO TO 70 + INSUFI = 2 + MSG='DLSODA- Warning.. IWORK length is sufficient for now, but ' + CALL XERRWD (MSG, 60, 104, 0, 0, 0, 0, 0, 0.0D0, 0.0D0) + MSG=' may not be later. Integration will proceed anyway. ' + CALL XERRWD (MSG, 60, 104, 0, 0, 0, 0, 0, 0.0D0, 0.0D0) + MSG = ' Length needed is LENIW = I1, while LIW = I2.' + CALL XERRWD (MSG, 50, 104, 0, 2, LENIW, LIW, 0, 0.0D0, 0.0D0) + 70 CONTINUE +C Check RTOL and ATOL for legality. ------------------------------------ + RTOLI = RTOL(1) + ATOLI = ATOL(1) + DO 75 I = 1,N + IF (ITOL .GE. 3) RTOLI = RTOL(I) + IF (ITOL .EQ. 2 .OR. ITOL .EQ. 4) ATOLI = ATOL(I) + IF (RTOLI .LT. 0.0D0) GO TO 619 + IF (ATOLI .LT. 0.0D0) GO TO 620 + 75 CONTINUE + IF (ISTATE .EQ. 1) GO TO 100 +C If ISTATE = 3, set flag to signal parameter changes to DSTODA. ------- + JSTART = -1 + IF (N .EQ. NYH) GO TO 200 +C NEQ was reduced. Zero part of YH to avoid undefined references. ----- + I1 = LYH + L*NYH + I2 = LYH + (MAXORD + 1)*NYH - 1 + IF (I1 .GT. I2) GO TO 200 + DO 95 I = I1,I2 + 95 RWORK(I) = 0.0D0 + GO TO 200 +C----------------------------------------------------------------------- +C Block C. +C The next block is for the initial call only (ISTATE = 1). +C It contains all remaining initializations, the initial call to F, +C and the calculation of the initial step size. +C The error weights in EWT are inverted after being loaded. +C----------------------------------------------------------------------- + 100 UROUND = DUMACH() + TN = T + TSW = T + MAXORD = MXORDN + IF (ITASK .NE. 4 .AND. ITASK .NE. 5) GO TO 110 + TCRIT = RWORK(1) + IF ((TCRIT - TOUT)*(TOUT - T) .LT. 0.0D0) GO TO 625 + IF (H0 .NE. 0.0D0 .AND. (T + H0 - TCRIT)*H0 .GT. 0.0D0) + 1 H0 = TCRIT - T + 110 JSTART = 0 + NHNIL = 0 + NST = 0 + NJE = 0 + NSLAST = 0 + HU = 0.0D0 + NQU = 0 + MUSED = 0 + MITER = 0 + CCMAX = 0.3D0 + MAXCOR = 3 + MSBP = 20 + MXNCF = 10 +C Initial call to F. (LF0 points to YH(*,2).) ------------------------- + LF0 = LYH + NYH + CALL F (NEQ, T, Y, RWORK(LF0)) + NFE = 1 +C Load the initial value vector in YH. --------------------------------- + DO 115 I = 1,N + 115 RWORK(I+LYH-1) = Y(I) +C Load and invert the EWT array. (H is temporarily set to 1.0.) ------- + NQ = 1 + H = 1.0D0 + CALL DEWSET (N, ITOL, RTOL, ATOL, RWORK(LYH), RWORK(LEWT)) + DO 120 I = 1,N + IF (RWORK(I+LEWT-1) .LE. 0.0D0) GO TO 621 + 120 RWORK(I+LEWT-1) = 1.0D0/RWORK(I+LEWT-1) +C----------------------------------------------------------------------- +C The coding below computes the step size, H0, to be attempted on the +C first step, unless the user has supplied a value for this. +C First check that TOUT - T differs significantly from zero. +C A scalar tolerance quantity TOL is computed, as MAX(RTOL(i)) +C if this is positive, or MAX(ATOL(i)/ABS(Y(i))) otherwise, adjusted +C so as to be between 100*UROUND and 1.0E-3. +C Then the computed value H0 is given by: +C +C H0**(-2) = 1./(TOL * w0**2) + TOL * (norm(F))**2 +C +C where w0 = MAX ( ABS(T), ABS(TOUT) ), +C F = the initial value of the vector f(t,y), and +C norm() = the weighted vector norm used throughout, given by +C the DMNORM function routine, and weighted by the +C tolerances initially loaded into the EWT array. +C The sign of H0 is inferred from the initial values of TOUT and T. +C ABS(H0) is made .le. ABS(TOUT-T) in any case. +C----------------------------------------------------------------------- + IF (H0 .NE. 0.0D0) GO TO 180 + TDIST = ABS(TOUT - T) + W0 = MAX(ABS(T),ABS(TOUT)) + IF (TDIST .LT. 2.0D0*UROUND*W0) GO TO 622 + TOL = RTOL(1) + IF (ITOL .LE. 2) GO TO 140 + DO 130 I = 1,N + 130 TOL = MAX(TOL,RTOL(I)) + 140 IF (TOL .GT. 0.0D0) GO TO 160 + ATOLI = ATOL(1) + DO 150 I = 1,N + IF (ITOL .EQ. 2 .OR. ITOL .EQ. 4) ATOLI = ATOL(I) + AYI = ABS(Y(I)) + IF (AYI .NE. 0.0D0) TOL = MAX(TOL,ATOLI/AYI) + 150 CONTINUE + 160 TOL = MAX(TOL,100.0D0*UROUND) + TOL = MIN(TOL,0.001D0) + SUM = DMNORM (N, RWORK(LF0), RWORK(LEWT)) + SUM = 1.0D0/(TOL*W0*W0) + TOL*SUM**2 + H0 = 1.0D0/SQRT(SUM) + H0 = MIN(H0,TDIST) + H0 = SIGN(H0,TOUT-T) +C Adjust H0 if necessary to meet HMAX bound. --------------------------- + 180 RH = ABS(H0)*HMXI + IF (RH .GT. 1.0D0) H0 = H0/RH +C Load H with H0 and scale YH(*,2) by H0. ------------------------------ + H = H0 + DO 190 I = 1,N + 190 RWORK(I+LF0-1) = H0*RWORK(I+LF0-1) + GO TO 270 +C----------------------------------------------------------------------- +C Block D. +C The next code block is for continuation calls only (ISTATE = 2 or 3) +C and is to check stop conditions before taking a step. +C----------------------------------------------------------------------- + 200 NSLAST = NST + GO TO (210, 250, 220, 230, 240), ITASK + 210 IF ((TN - TOUT)*H .LT. 0.0D0) GO TO 250 + CALL DINTDY (TOUT, 0, RWORK(LYH), NYH, Y, IFLAG) + IF (IFLAG .NE. 0) GO TO 627 + T = TOUT + GO TO 420 + 220 TP = TN - HU*(1.0D0 + 100.0D0*UROUND) + IF ((TP - TOUT)*H .GT. 0.0D0) GO TO 623 + IF ((TN - TOUT)*H .LT. 0.0D0) GO TO 250 + T = TN + GO TO 400 + 230 TCRIT = RWORK(1) + IF ((TN - TCRIT)*H .GT. 0.0D0) GO TO 624 + IF ((TCRIT - TOUT)*H .LT. 0.0D0) GO TO 625 + IF ((TN - TOUT)*H .LT. 0.0D0) GO TO 245 + CALL DINTDY (TOUT, 0, RWORK(LYH), NYH, Y, IFLAG) + IF (IFLAG .NE. 0) GO TO 627 + T = TOUT + GO TO 420 + 240 TCRIT = RWORK(1) + IF ((TN - TCRIT)*H .GT. 0.0D0) GO TO 624 + 245 HMX = ABS(TN) + ABS(H) + IHIT = ABS(TN - TCRIT) .LE. 100.0D0*UROUND*HMX + IF (IHIT) T = TCRIT + IF (IHIT) GO TO 400 + TNEXT = TN + H*(1.0D0 + 4.0D0*UROUND) + IF ((TNEXT - TCRIT)*H .LE. 0.0D0) GO TO 250 + H = (TCRIT - TN)*(1.0D0 - 4.0D0*UROUND) + IF (ISTATE .EQ. 2 .AND. JSTART .GE. 0) JSTART = -2 +C----------------------------------------------------------------------- +C Block E. +C The next block is normally executed for all calls and contains +C the call to the one-step core integrator DSTODA. +C +C This is a looping point for the integration steps. +C +C First check for too many steps being taken, update EWT (if not at +C start of problem), check for too much accuracy being requested, and +C check for H below the roundoff level in T. +C----------------------------------------------------------------------- + 250 CONTINUE + IF (METH .EQ. MUSED) GO TO 255 + IF (INSUFR .EQ. 1) GO TO 550 + IF (INSUFI .EQ. 1) GO TO 555 + 255 IF ((NST-NSLAST) .GE. MXSTEP) GO TO 500 + CALL DEWSET (N, ITOL, RTOL, ATOL, RWORK(LYH), RWORK(LEWT)) + DO 260 I = 1,N + IF (RWORK(I+LEWT-1) .LE. 0.0D0) GO TO 510 + 260 RWORK(I+LEWT-1) = 1.0D0/RWORK(I+LEWT-1) + 270 TOLSF = UROUND*DMNORM (N, RWORK(LYH), RWORK(LEWT)) + IF (TOLSF .LE. 1.0D0) GO TO 280 + TOLSF = TOLSF*2.0D0 + IF (NST .EQ. 0) GO TO 626 + GO TO 520 + 280 IF ((TN + H) .NE. TN) GO TO 290 + NHNIL = NHNIL + 1 + IF (NHNIL .GT. MXHNIL) GO TO 290 + MSG = 'DLSODA- Warning..Internal T (=R1) and H (=R2) are' + CALL XERRWD (MSG, 50, 101, 0, 0, 0, 0, 0, 0.0D0, 0.0D0) + MSG=' such that in the machine, T + H = T on the next step ' + CALL XERRWD (MSG, 60, 101, 0, 0, 0, 0, 0, 0.0D0, 0.0D0) + MSG = ' (H = step size). Solver will continue anyway.' + CALL XERRWD (MSG, 50, 101, 0, 0, 0, 0, 2, TN, H) + IF (NHNIL .LT. MXHNIL) GO TO 290 + MSG = 'DLSODA- Above warning has been issued I1 times. ' + CALL XERRWD (MSG, 50, 102, 0, 0, 0, 0, 0, 0.0D0, 0.0D0) + MSG = ' It will not be issued again for this problem.' + CALL XERRWD (MSG, 50, 102, 0, 1, MXHNIL, 0, 0, 0.0D0, 0.0D0) + 290 CONTINUE +C----------------------------------------------------------------------- +C CALL DSTODA(NEQ,Y,YH,NYH,YH,EWT,SAVF,ACOR,WM,IWM,F,JAC,DPRJA,DSOLSY) +C----------------------------------------------------------------------- + CALL DSTODA (NEQ, Y, RWORK(LYH), NYH, RWORK(LYH), RWORK(LEWT), + 1 RWORK(LSAVF), RWORK(LACOR), RWORK(LWM), IWORK(LIWM), + 2 F, JAC, DPRJA, DSOLSY) + KGO = 1 - KFLAG + GO TO (300, 530, 540), KGO +C----------------------------------------------------------------------- +C Block F. +C The following block handles the case of a successful return from the +C core integrator (KFLAG = 0). +C If a method switch was just made, record TSW, reset MAXORD, +C set JSTART to -1 to signal DSTODA to complete the switch, +C and do extra printing of data if IXPR = 1. +C Then, in any case, check for stop conditions. +C----------------------------------------------------------------------- + 300 INIT = 1 + IF (METH .EQ. MUSED) GO TO 310 + TSW = TN + MAXORD = MXORDN + IF (METH .EQ. 2) MAXORD = MXORDS + IF (METH .EQ. 2) RWORK(LWM) = SQRT(UROUND) + INSUFR = MIN(INSUFR,1) + INSUFI = MIN(INSUFI,1) + JSTART = -1 + IF (IXPR .EQ. 0) GO TO 310 + IF (METH .EQ. 2) THEN + MSG='DLSODA- A switch to the BDF (stiff) method has occurred ' + CALL XERRWD (MSG, 60, 105, 0, 0, 0, 0, 0, 0.0D0, 0.0D0) + ENDIF + IF (METH .EQ. 1) THEN + MSG='DLSODA- A switch to the Adams (nonstiff) method has occurred' + CALL XERRWD (MSG, 60, 106, 0, 0, 0, 0, 0, 0.0D0, 0.0D0) + ENDIF + MSG=' at T = R1, tentative step size H = R2, step NST = I1 ' + CALL XERRWD (MSG, 60, 107, 0, 1, NST, 0, 2, TN, H) + 310 GO TO (320, 400, 330, 340, 350), ITASK +C ITASK = 1. If TOUT has been reached, interpolate. ------------------- + 320 IF ((TN - TOUT)*H .LT. 0.0D0) GO TO 250 + CALL DINTDY (TOUT, 0, RWORK(LYH), NYH, Y, IFLAG) + T = TOUT + GO TO 420 +C ITASK = 3. Jump to exit if TOUT was reached. ------------------------ + 330 IF ((TN - TOUT)*H .GE. 0.0D0) GO TO 400 + GO TO 250 +C ITASK = 4. See if TOUT or TCRIT was reached. Adjust H if necessary. + 340 IF ((TN - TOUT)*H .LT. 0.0D0) GO TO 345 + CALL DINTDY (TOUT, 0, RWORK(LYH), NYH, Y, IFLAG) + T = TOUT + GO TO 420 + 345 HMX = ABS(TN) + ABS(H) + IHIT = ABS(TN - TCRIT) .LE. 100.0D0*UROUND*HMX + IF (IHIT) GO TO 400 + TNEXT = TN + H*(1.0D0 + 4.0D0*UROUND) + IF ((TNEXT - TCRIT)*H .LE. 0.0D0) GO TO 250 + H = (TCRIT - TN)*(1.0D0 - 4.0D0*UROUND) + IF (JSTART .GE. 0) JSTART = -2 + GO TO 250 +C ITASK = 5. See if TCRIT was reached and jump to exit. --------------- + 350 HMX = ABS(TN) + ABS(H) + IHIT = ABS(TN - TCRIT) .LE. 100.0D0*UROUND*HMX +C----------------------------------------------------------------------- +C Block G. +C The following block handles all successful returns from DLSODA. +C If ITASK .ne. 1, Y is loaded from YH and T is set accordingly. +C ISTATE is set to 2, and the optional outputs are loaded into the +C work arrays before returning. +C----------------------------------------------------------------------- + 400 DO 410 I = 1,N + 410 Y(I) = RWORK(I+LYH-1) + T = TN + IF (ITASK .NE. 4 .AND. ITASK .NE. 5) GO TO 420 + IF (IHIT) T = TCRIT + 420 ISTATE = 2 + RWORK(11) = HU + RWORK(12) = H + RWORK(13) = TN + RWORK(15) = TSW + IWORK(11) = NST + IWORK(12) = NFE + IWORK(13) = NJE + IWORK(14) = NQU + IWORK(15) = NQ + IWORK(19) = MUSED + IWORK(20) = METH + RETURN +C----------------------------------------------------------------------- +C Block H. +C The following block handles all unsuccessful returns other than +C those for illegal input. First the error message routine is called. +C If there was an error test or convergence test failure, IMXER is set. +C Then Y is loaded from YH and T is set to TN. +C The optional outputs are loaded into the work arrays before returning. +C----------------------------------------------------------------------- +C The maximum number of steps was taken before reaching TOUT. ---------- + 500 MSG = 'DLSODA- At current T (=R1), MXSTEP (=I1) steps ' + CALL XERRWD (MSG, 50, 201, 0, 0, 0, 0, 0, 0.0D0, 0.0D0) + MSG = ' taken on this call before reaching TOUT ' + CALL XERRWD (MSG, 50, 201, 0, 1, MXSTEP, 0, 1, TN, 0.0D0) + ISTATE = -1 + GO TO 580 +C EWT(i) .le. 0.0 for some i (not at start of problem). ---------------- + 510 EWTI = RWORK(LEWT+I-1) + MSG = 'DLSODA- At T (=R1), EWT(I1) has become R2 .le. 0.' + CALL XERRWD (MSG, 50, 202, 0, 1, I, 0, 2, TN, EWTI) + ISTATE = -6 + GO TO 580 +C Too much accuracy requested for machine precision. ------------------- + 520 MSG = 'DLSODA- At T (=R1), too much accuracy requested ' + CALL XERRWD (MSG, 50, 203, 0, 0, 0, 0, 0, 0.0D0, 0.0D0) + MSG = ' for precision of machine.. See TOLSF (=R2) ' + CALL XERRWD (MSG, 50, 203, 0, 0, 0, 0, 2, TN, TOLSF) + RWORK(14) = TOLSF + ISTATE = -2 + GO TO 580 +C KFLAG = -1. Error test failed repeatedly or with ABS(H) = HMIN. ----- + 530 MSG = 'DLSODA- At T(=R1) and step size H(=R2), the error' + CALL XERRWD (MSG, 50, 204, 0, 0, 0, 0, 0, 0.0D0, 0.0D0) + MSG = ' test failed repeatedly or with ABS(H) = HMIN' + CALL XERRWD (MSG, 50, 204, 0, 0, 0, 0, 2, TN, H) + ISTATE = -4 + GO TO 560 +C KFLAG = -2. Convergence failed repeatedly or with ABS(H) = HMIN. ---- + 540 MSG = 'DLSODA- At T (=R1) and step size H (=R2), the ' + CALL XERRWD (MSG, 50, 205, 0, 0, 0, 0, 0, 0.0D0, 0.0D0) + MSG = ' corrector convergence failed repeatedly ' + CALL XERRWD (MSG, 50, 205, 0, 0, 0, 0, 0, 0.0D0, 0.0D0) + MSG = ' or with ABS(H) = HMIN ' + CALL XERRWD (MSG, 30, 205, 0, 0, 0, 0, 2, TN, H) + ISTATE = -5 + GO TO 560 +C RWORK length too small to proceed. ----------------------------------- + 550 MSG = 'DLSODA- At current T(=R1), RWORK length too small' + CALL XERRWD (MSG, 50, 206, 0, 0, 0, 0, 0, 0.0D0, 0.0D0) + MSG=' to proceed. The integration was otherwise successful.' + CALL XERRWD (MSG, 60, 206, 0, 0, 0, 0, 1, TN, 0.0D0) + ISTATE = -7 + GO TO 580 +C IWORK length too small to proceed. ----------------------------------- + 555 MSG = 'DLSODA- At current T(=R1), IWORK length too small' + CALL XERRWD (MSG, 50, 207, 0, 0, 0, 0, 0, 0.0D0, 0.0D0) + MSG=' to proceed. The integration was otherwise successful.' + CALL XERRWD (MSG, 60, 207, 0, 0, 0, 0, 1, TN, 0.0D0) + ISTATE = -7 + GO TO 580 +C Compute IMXER if relevant. ------------------------------------------- + 560 BIG = 0.0D0 + IMXER = 1 + DO 570 I = 1,N + SIZE = ABS(RWORK(I+LACOR-1)*RWORK(I+LEWT-1)) + IF (BIG .GE. SIZE) GO TO 570 + BIG = SIZE + IMXER = I + 570 CONTINUE + IWORK(16) = IMXER +C Set Y vector, T, and optional outputs. ------------------------------- + 580 DO 590 I = 1,N + 590 Y(I) = RWORK(I+LYH-1) + T = TN + RWORK(11) = HU + RWORK(12) = H + RWORK(13) = TN + RWORK(15) = TSW + IWORK(11) = NST + IWORK(12) = NFE + IWORK(13) = NJE + IWORK(14) = NQU + IWORK(15) = NQ + IWORK(19) = MUSED + IWORK(20) = METH + RETURN +C----------------------------------------------------------------------- +C Block I. +C The following block handles all error returns due to illegal input +C (ISTATE = -3), as detected before calling the core integrator. +C First the error message routine is called. If the illegal input +C is a negative ISTATE, the run is aborted (apparent infinite loop). +C----------------------------------------------------------------------- + 601 MSG = 'DLSODA- ISTATE (=I1) illegal.' + CALL XERRWD (MSG, 30, 1, 0, 1, ISTATE, 0, 0, 0.0D0, 0.0D0) + IF (ISTATE .LT. 0) GO TO 800 + GO TO 700 + 602 MSG = 'DLSODA- ITASK (=I1) illegal. ' + CALL XERRWD (MSG, 30, 2, 0, 1, ITASK, 0, 0, 0.0D0, 0.0D0) + GO TO 700 + 603 MSG = 'DLSODA- ISTATE .gt. 1 but DLSODA not initialized.' + CALL XERRWD (MSG, 50, 3, 0, 0, 0, 0, 0, 0.0D0, 0.0D0) + GO TO 700 + 604 MSG = 'DLSODA- NEQ (=I1) .lt. 1 ' + CALL XERRWD (MSG, 30, 4, 0, 1, NEQ(1), 0, 0, 0.0D0, 0.0D0) + GO TO 700 + 605 MSG = 'DLSODA- ISTATE = 3 and NEQ increased (I1 to I2). ' + CALL XERRWD (MSG, 50, 5, 0, 2, N, NEQ(1), 0, 0.0D0, 0.0D0) + GO TO 700 + 606 MSG = 'DLSODA- ITOL (=I1) illegal. ' + CALL XERRWD (MSG, 30, 6, 0, 1, ITOL, 0, 0, 0.0D0, 0.0D0) + GO TO 700 + 607 MSG = 'DLSODA- IOPT (=I1) illegal. ' + CALL XERRWD (MSG, 30, 7, 0, 1, IOPT, 0, 0, 0.0D0, 0.0D0) + GO TO 700 + 608 MSG = 'DLSODA- JT (=I1) illegal. ' + CALL XERRWD (MSG, 30, 8, 0, 1, JT, 0, 0, 0.0D0, 0.0D0) + GO TO 700 + 609 MSG = 'DLSODA- ML (=I1) illegal: .lt.0 or .ge.NEQ (=I2) ' + CALL XERRWD (MSG, 50, 9, 0, 2, ML, NEQ(1), 0, 0.0D0, 0.0D0) + GO TO 700 + 610 MSG = 'DLSODA- MU (=I1) illegal: .lt.0 or .ge.NEQ (=I2) ' + CALL XERRWD (MSG, 50, 10, 0, 2, MU, NEQ(1), 0, 0.0D0, 0.0D0) + GO TO 700 + 611 MSG = 'DLSODA- IXPR (=I1) illegal. ' + CALL XERRWD (MSG, 30, 11, 0, 1, IXPR, 0, 0, 0.0D0, 0.0D0) + GO TO 700 + 612 MSG = 'DLSODA- MXSTEP (=I1) .lt. 0 ' + CALL XERRWD (MSG, 30, 12, 0, 1, MXSTEP, 0, 0, 0.0D0, 0.0D0) + GO TO 700 + 613 MSG = 'DLSODA- MXHNIL (=I1) .lt. 0 ' + CALL XERRWD (MSG, 30, 13, 0, 1, MXHNIL, 0, 0, 0.0D0, 0.0D0) + GO TO 700 + 614 MSG = 'DLSODA- TOUT (=R1) behind T (=R2) ' + CALL XERRWD (MSG, 40, 14, 0, 0, 0, 0, 2, TOUT, T) + MSG = ' Integration direction is given by H0 (=R1) ' + CALL XERRWD (MSG, 50, 14, 0, 0, 0, 0, 1, H0, 0.0D0) + GO TO 700 + 615 MSG = 'DLSODA- HMAX (=R1) .lt. 0.0 ' + CALL XERRWD (MSG, 30, 15, 0, 0, 0, 0, 1, HMAX, 0.0D0) + GO TO 700 + 616 MSG = 'DLSODA- HMIN (=R1) .lt. 0.0 ' + CALL XERRWD (MSG, 30, 16, 0, 0, 0, 0, 1, HMIN, 0.0D0) + GO TO 700 + 617 MSG='DLSODA- RWORK length needed, LENRW (=I1), exceeds LRW (=I2)' + CALL XERRWD (MSG, 60, 17, 0, 2, LENRW, LRW, 0, 0.0D0, 0.0D0) + GO TO 700 + 618 MSG='DLSODA- IWORK length needed, LENIW (=I1), exceeds LIW (=I2)' + CALL XERRWD (MSG, 60, 18, 0, 2, LENIW, LIW, 0, 0.0D0, 0.0D0) + GO TO 700 + 619 MSG = 'DLSODA- RTOL(I1) is R1 .lt. 0.0 ' + CALL XERRWD (MSG, 40, 19, 0, 1, I, 0, 1, RTOLI, 0.0D0) + GO TO 700 + 620 MSG = 'DLSODA- ATOL(I1) is R1 .lt. 0.0 ' + CALL XERRWD (MSG, 40, 20, 0, 1, I, 0, 1, ATOLI, 0.0D0) + GO TO 700 + 621 EWTI = RWORK(LEWT+I-1) + MSG = 'DLSODA- EWT(I1) is R1 .le. 0.0 ' + CALL XERRWD (MSG, 40, 21, 0, 1, I, 0, 1, EWTI, 0.0D0) + GO TO 700 + 622 MSG='DLSODA- TOUT(=R1) too close to T(=R2) to start integration.' + CALL XERRWD (MSG, 60, 22, 0, 0, 0, 0, 2, TOUT, T) + GO TO 700 + 623 MSG='DLSODA- ITASK = I1 and TOUT (=R1) behind TCUR - HU (= R2) ' + CALL XERRWD (MSG, 60, 23, 0, 1, ITASK, 0, 2, TOUT, TP) + GO TO 700 + 624 MSG='DLSODA- ITASK = 4 or 5 and TCRIT (=R1) behind TCUR (=R2) ' + CALL XERRWD (MSG, 60, 24, 0, 0, 0, 0, 2, TCRIT, TN) + GO TO 700 + 625 MSG='DLSODA- ITASK = 4 or 5 and TCRIT (=R1) behind TOUT (=R2) ' + CALL XERRWD (MSG, 60, 25, 0, 0, 0, 0, 2, TCRIT, TOUT) + GO TO 700 + 626 MSG = 'DLSODA- At start of problem, too much accuracy ' + CALL XERRWD (MSG, 50, 26, 0, 0, 0, 0, 0, 0.0D0, 0.0D0) + MSG=' requested for precision of machine.. See TOLSF (=R1) ' + CALL XERRWD (MSG, 60, 26, 0, 0, 0, 0, 1, TOLSF, 0.0D0) + RWORK(14) = TOLSF + GO TO 700 + 627 MSG = 'DLSODA- Trouble in DINTDY. ITASK = I1, TOUT = R1' + CALL XERRWD (MSG, 50, 27, 0, 1, ITASK, 0, 1, TOUT, 0.0D0) + GO TO 700 + 628 MSG = 'DLSODA- MXORDN (=I1) .lt. 0 ' + CALL XERRWD (MSG, 30, 28, 0, 1, MXORDN, 0, 0, 0.0D0, 0.0D0) + GO TO 700 + 629 MSG = 'DLSODA- MXORDS (=I1) .lt. 0 ' + CALL XERRWD (MSG, 30, 29, 0, 1, MXORDS, 0, 0, 0.0D0, 0.0D0) +C + 700 ISTATE = -3 + RETURN +C + 800 MSG = 'DLSODA- Run aborted.. apparent infinite loop. ' + CALL XERRWD (MSG, 50, 303, 2, 0, 0, 0, 0, 0.0D0, 0.0D0) + RETURN +C----------------------- End of Subroutine DLSODA ---------------------- + END +*DECK DLSODAR + SUBROUTINE DLSODAR (F, NEQ, Y, T, TOUT, ITOL, RTOL, ATOL, ITASK, + 1 ISTATE, IOPT, RWORK, LRW, IWORK, LIW, JAC, JT, + 2 G, NG, JROOT) + EXTERNAL F, JAC, G + INTEGER NEQ, ITOL, ITASK, ISTATE, IOPT, LRW, IWORK, LIW, JT, + 1 NG, JROOT + DOUBLE PRECISION Y, T, TOUT, RTOL, ATOL, RWORK + DIMENSION NEQ(*), Y(*), RTOL(*), ATOL(*), RWORK(LRW), IWORK(LIW), + 1 JROOT(NG) +C----------------------------------------------------------------------- +C This is the 12 November 2003 version of +C DLSODAR: Livermore Solver for Ordinary Differential Equations, with +C Automatic method switching for stiff and nonstiff problems, +C and with Root-finding. +C +C This version is in double precision. +C +C DLSODAR solves the initial value problem for stiff or nonstiff +C systems of first order ODEs, +C dy/dt = f(t,y) , or, in component form, +C dy(i)/dt = f(i) = f(i,t,y(1),y(2),...,y(NEQ)) (i = 1,...,NEQ). +C At the same time, it locates the roots of any of a set of functions +C g(i) = g(i,t,y(1),...,y(NEQ)) (i = 1,...,ng). +C +C This a variant version of the DLSODE package. It differs from it +C in two ways: +C (a) It switches automatically between stiff and nonstiff methods. +C This means that the user does not have to determine whether the +C problem is stiff or not, and the solver will automatically choose the +C appropriate method. It always starts with the nonstiff method. +C (b) It finds the root of at least one of a set of constraint +C functions g(i) of the independent and dependent variables. +C It finds only those roots for which some g(i), as a function +C of t, changes sign in the interval of integration. +C It then returns the solution at the root, if that occurs +C sooner than the specified stop condition, and otherwise returns +C the solution according the specified stop condition. +C +C Authors: Alan C. Hindmarsh, +C Center for Applied Scientific Computing, L-561 +C Lawrence Livermore National Laboratory +C Livermore, CA 94551 +C and +C Linda R. Petzold +C Univ. of California at Santa Barbara +C Dept. of Computer Science +C Santa Barbara, CA 93106 +C +C References: +C 1. Alan C. Hindmarsh, ODEPACK, A Systematized Collection of ODE +C Solvers, in Scientific Computing, R. S. Stepleman et al. (Eds.), +C North-Holland, Amsterdam, 1983, pp. 55-64. +C 2. Linda R. Petzold, Automatic Selection of Methods for Solving +C Stiff and Nonstiff Systems of Ordinary Differential Equations, +C Siam J. Sci. Stat. Comput. 4 (1983), pp. 136-148. +C 3. Kathie L. Hiebert and Lawrence F. Shampine, Implicitly Defined +C Output Points for Solutions of ODEs, Sandia Report SAND80-0180, +C February 1980. +C----------------------------------------------------------------------- +C Summary of Usage. +C +C Communication between the user and the DLSODAR package, for normal +C situations, is summarized here. This summary describes only a subset +C of the full set of options available. See the full description for +C details, including alternative treatment of the Jacobian matrix, +C optional inputs and outputs, nonstandard options, and +C instructions for special situations. See also the example +C problem (with program and output) following this summary. +C +C A. First provide a subroutine of the form: +C SUBROUTINE F (NEQ, T, Y, YDOT) +C DOUBLE PRECISION T, Y(*), YDOT(*) +C which supplies the vector function f by loading YDOT(i) with f(i). +C +C B. Provide a subroutine of the form: +C SUBROUTINE G (NEQ, T, Y, NG, GOUT) +C DOUBLE PRECISION T, Y(*), GOUT(NG) +C which supplies the vector function g by loading GOUT(i) with +C g(i), the i-th constraint function whose root is sought. +C +C C. Write a main program which calls Subroutine DLSODAR once for +C each point at which answers are desired. This should also provide +C for possible use of logical unit 6 for output of error messages by +C DLSODAR. On the first call to DLSODAR, supply arguments as follows: +C F = name of subroutine for right-hand side vector f. +C This name must be declared External in calling program. +C NEQ = number of first order ODEs. +C Y = array of initial values, of length NEQ. +C T = the initial value of the independent variable. +C TOUT = first point where output is desired (.ne. T). +C ITOL = 1 or 2 according as ATOL (below) is a scalar or array. +C RTOL = relative tolerance parameter (scalar). +C ATOL = absolute tolerance parameter (scalar or array). +C the estimated local error in y(i) will be controlled so as +C to be less than +C EWT(i) = RTOL*ABS(Y(i)) + ATOL if ITOL = 1, or +C EWT(i) = RTOL*ABS(Y(i)) + ATOL(i) if ITOL = 2. +C Thus the local error test passes if, in each component, +C either the absolute error is less than ATOL (or ATOL(i)), +C or the relative error is less than RTOL. +C Use RTOL = 0.0 for pure absolute error control, and +C use ATOL = 0.0 (or ATOL(i) = 0.0) for pure relative error +C control. Caution: actual (global) errors may exceed these +C local tolerances, so choose them conservatively. +C ITASK = 1 for normal computation of output values of y at t = TOUT. +C ISTATE = integer flag (input and output). Set ISTATE = 1. +C IOPT = 0 to indicate no optional inputs used. +C RWORK = real work array of length at least: +C 22 + NEQ * MAX(16, NEQ + 9) + 3*NG. +C See also Paragraph F below. +C LRW = declared length of RWORK (in user's dimension). +C IWORK = integer work array of length at least 20 + NEQ. +C LIW = declared length of IWORK (in user's dimension). +C JAC = name of subroutine for Jacobian matrix. +C Use a dummy name. See also Paragraph F below. +C JT = Jacobian type indicator. Set JT = 2. +C See also Paragraph F below. +C G = name of subroutine for constraint functions, whose +C roots are desired during the integration. +C This name must be declared External in calling program. +C NG = number of constraint functions g(i). If there are none, +C set NG = 0, and pass a dummy name for G. +C JROOT = integer array of length NG for output of root information. +C See next paragraph. +C Note that the main program must declare arrays Y, RWORK, IWORK, +C JROOT, and possibly ATOL. +C +C D. The output from the first call (or any call) is: +C Y = array of computed values of y(t) vector. +C T = corresponding value of independent variable. This is +C TOUT if ISTATE = 2, or the root location if ISTATE = 3, +C or the farthest point reached if DLSODAR was unsuccessful. +C ISTATE = 2 or 3 if DLSODAR was successful, negative otherwise. +C 2 means no root was found, and TOUT was reached as desired. +C 3 means a root was found prior to reaching TOUT. +C -1 means excess work done on this call (perhaps wrong JT). +C -2 means excess accuracy requested (tolerances too small). +C -3 means illegal input detected (see printed message). +C -4 means repeated error test failures (check all inputs). +C -5 means repeated convergence failures (perhaps bad Jacobian +C supplied or wrong choice of JT or tolerances). +C -6 means error weight became zero during problem. (Solution +C component i vanished, and ATOL or ATOL(i) = 0.) +C -7 means work space insufficient to finish (see messages). +C JROOT = array showing roots found if ISTATE = 3 on return. +C JROOT(i) = 1 if g(i) has a root at t, or 0 otherwise. +C +C E. To continue the integration after a successful return, proceed +C as follows: +C (a) If ISTATE = 2 on return, reset TOUT and call DLSODAR again. +C (b) If ISTATE = 3 on return, reset ISTATE to 2, call DLSODAR again. +C In either case, no other parameters need be reset. +C +C F. Note: If and when DLSODAR regards the problem as stiff, and +C switches methods accordingly, it must make use of the NEQ by NEQ +C Jacobian matrix, J = df/dy. For the sake of simplicity, the +C inputs to DLSODAR recommended in Paragraph C above cause DLSODAR to +C treat J as a full matrix, and to approximate it internally by +C difference quotients. Alternatively, J can be treated as a band +C matrix (with great potential reduction in the size of the RWORK +C array). Also, in either the full or banded case, the user can supply +C J in closed form, with a routine whose name is passed as the JAC +C argument. These alternatives are described in the paragraphs on +C RWORK, JAC, and JT in the full description of the call sequence below. +C +C----------------------------------------------------------------------- +C Example Problem. +C +C The following is a simple example problem, with the coding +C needed for its solution by DLSODAR. The problem is from chemical +C kinetics, and consists of the following three rate equations: +C dy1/dt = -.04*y1 + 1.e4*y2*y3 +C dy2/dt = .04*y1 - 1.e4*y2*y3 - 3.e7*y2**2 +C dy3/dt = 3.e7*y2**2 +C on the interval from t = 0.0 to t = 4.e10, with initial conditions +C y1 = 1.0, y2 = y3 = 0. The problem is stiff. +C In addition, we want to find the values of t, y1, y2, and y3 at which +C (1) y1 reaches the value 1.e-4, and +C (2) y3 reaches the value 1.e-2. +C +C The following coding solves this problem with DLSODAR, +C printing results at t = .4, 4., ..., 4.e10, and at the computed +C roots. It uses ITOL = 2 and ATOL much smaller for y2 than y1 or y3 +C because y2 has much smaller values. +C At the end of the run, statistical quantities of interest are +C printed (see optional outputs in the full description below). +C +C EXTERNAL FEX, GEX +C DOUBLE PRECISION ATOL, RTOL, RWORK, T, TOUT, Y +C DIMENSION Y(3), ATOL(3), RWORK(76), IWORK(23), JROOT(2) +C NEQ = 3 +C Y(1) = 1. +C Y(2) = 0. +C Y(3) = 0. +C T = 0. +C TOUT = .4 +C ITOL = 2 +C RTOL = 1.D-4 +C ATOL(1) = 1.D-6 +C ATOL(2) = 1.D-10 +C ATOL(3) = 1.D-6 +C ITASK = 1 +C ISTATE = 1 +C IOPT = 0 +C LRW = 76 +C LIW = 23 +C JT = 2 +C NG = 2 +C DO 40 IOUT = 1,12 +C 10 CALL DLSODAR(FEX,NEQ,Y,T,TOUT,ITOL,RTOL,ATOL,ITASK,ISTATE, +C 1 IOPT,RWORK,LRW,IWORK,LIW,JDUM,JT,GEX,NG,JROOT) +C WRITE(6,20)T,Y(1),Y(2),Y(3) +C 20 FORMAT(' At t =',D12.4,' Y =',3D14.6) +C IF (ISTATE .LT. 0) GO TO 80 +C IF (ISTATE .EQ. 2) GO TO 40 +C WRITE(6,30)JROOT(1),JROOT(2) +C 30 FORMAT(5X,' The above line is a root, JROOT =',2I5) +C ISTATE = 2 +C GO TO 10 +C 40 TOUT = TOUT*10. +C WRITE(6,60)IWORK(11),IWORK(12),IWORK(13),IWORK(10), +C 1 IWORK(19),RWORK(15) +C 60 FORMAT(/' No. steps =',I4,' No. f-s =',I4,' No. J-s =',I4, +C 1 ' No. g-s =',I4/ +C 2 ' Method last used =',I2,' Last switch was at t =',D12.4) +C STOP +C 80 WRITE(6,90)ISTATE +C 90 FORMAT(///' Error halt.. ISTATE =',I3) +C STOP +C END +C +C SUBROUTINE FEX (NEQ, T, Y, YDOT) +C DOUBLE PRECISION T, Y, YDOT +C DIMENSION Y(3), YDOT(3) +C YDOT(1) = -.04*Y(1) + 1.D4*Y(2)*Y(3) +C YDOT(3) = 3.D7*Y(2)*Y(2) +C YDOT(2) = -YDOT(1) - YDOT(3) +C RETURN +C END +C +C SUBROUTINE GEX (NEQ, T, Y, NG, GOUT) +C DOUBLE PRECISION T, Y, GOUT +C DIMENSION Y(3), GOUT(2) +C GOUT(1) = Y(1) - 1.D-4 +C GOUT(2) = Y(3) - 1.D-2 +C RETURN +C END +C +C The output of this program (on a CDC-7600 in single precision) +C is as follows: +C +C At t = 2.6400e-01 y = 9.899653e-01 3.470563e-05 1.000000e-02 +C The above line is a root, JROOT = 0 1 +C At t = 4.0000e-01 Y = 9.851712e-01 3.386380e-05 1.479493e-02 +C At t = 4.0000e+00 Y = 9.055333e-01 2.240655e-05 9.444430e-02 +C At t = 4.0000e+01 Y = 7.158403e-01 9.186334e-06 2.841505e-01 +C At t = 4.0000e+02 Y = 4.505250e-01 3.222964e-06 5.494717e-01 +C At t = 4.0000e+03 Y = 1.831975e-01 8.941774e-07 8.168016e-01 +C At t = 4.0000e+04 Y = 3.898730e-02 1.621940e-07 9.610125e-01 +C At t = 4.0000e+05 Y = 4.936363e-03 1.984221e-08 9.950636e-01 +C At t = 4.0000e+06 Y = 5.161831e-04 2.065786e-09 9.994838e-01 +C At t = 2.0745e+07 Y = 1.000000e-04 4.000395e-10 9.999000e-01 +C The above line is a root, JROOT = 1 0 +C At t = 4.0000e+07 Y = 5.179817e-05 2.072032e-10 9.999482e-01 +C At t = 4.0000e+08 Y = 5.283401e-06 2.113371e-11 9.999947e-01 +C At t = 4.0000e+09 Y = 4.659031e-07 1.863613e-12 9.999995e-01 +C At t = 4.0000e+10 Y = 1.404280e-08 5.617126e-14 1.000000e+00 +C +C No. steps = 361 No. f-s = 693 No. J-s = 64 No. g-s = 390 +C Method last used = 2 Last switch was at t = 6.0092e-03 +C +C----------------------------------------------------------------------- +C Full Description of User Interface to DLSODAR. +C +C The user interface to DLSODAR consists of the following parts. +C +C 1. The call sequence to Subroutine DLSODAR, which is a driver +C routine for the solver. This includes descriptions of both +C the call sequence arguments and of user-supplied routines. +C Following these descriptions is a description of +C optional inputs available through the call sequence, and then +C a description of optional outputs (in the work arrays). +C +C 2. Descriptions of other routines in the DLSODAR package that may be +C (optionally) called by the user. These provide the ability to +C alter error message handling, save and restore the internal +C Common, and obtain specified derivatives of the solution y(t). +C +C 3. Descriptions of Common blocks to be declared in overlay +C or similar environments, or to be saved when doing an interrupt +C of the problem and continued solution later. +C +C 4. Description of a subroutine in the DLSODAR package, +C which the user may replace with his/her own version, if desired. +C this relates to the measurement of errors. +C +C----------------------------------------------------------------------- +C Part 1. Call Sequence. +C +C The call sequence parameters used for input only are +C F, NEQ, TOUT, ITOL, RTOL, ATOL, ITASK, IOPT, LRW, LIW, JAC, +C JT, G, and NG, +C that used only for output is JROOT, +C and those used for both input and output are +C Y, T, ISTATE. +C The work arrays RWORK and IWORK are also used for conditional and +C optional inputs and optional outputs. (The term output here refers +C to the return from Subroutine DLSODAR to the user's calling program.) +C +C The legality of input parameters will be thoroughly checked on the +C initial call for the problem, but not checked thereafter unless a +C change in input parameters is flagged by ISTATE = 3 on input. +C +C The descriptions of the call arguments are as follows. +C +C F = the name of the user-supplied subroutine defining the +C ODE system. The system must be put in the first-order +C form dy/dt = f(t,y), where f is a vector-valued function +C of the scalar t and the vector y. Subroutine F is to +C compute the function f. It is to have the form +C SUBROUTINE F (NEQ, T, Y, YDOT) +C DOUBLE PRECISION T, Y(*), YDOT(*) +C where NEQ, T, and Y are input, and the array YDOT = f(t,y) +C is output. Y and YDOT are arrays of length NEQ. +C Subroutine F should not alter Y(1),...,Y(NEQ). +C F must be declared External in the calling program. +C +C Subroutine F may access user-defined quantities in +C NEQ(2),... and/or in Y(NEQ(1)+1),... if NEQ is an array +C (dimensioned in F) and/or Y has length exceeding NEQ(1). +C See the descriptions of NEQ and Y below. +C +C If quantities computed in the F routine are needed +C externally to DLSODAR, an extra call to F should be made +C for this purpose, for consistent and accurate results. +C If only the derivative dy/dt is needed, use DINTDY instead. +C +C NEQ = the size of the ODE system (number of first order +C ordinary differential equations). Used only for input. +C NEQ may be decreased, but not increased, during the problem. +C If NEQ is decreased (with ISTATE = 3 on input), the +C remaining components of Y should be left undisturbed, if +C these are to be accessed in F and/or JAC. +C +C Normally, NEQ is a scalar, and it is generally referred to +C as a scalar in this user interface description. However, +C NEQ may be an array, with NEQ(1) set to the system size. +C (The DLSODAR package accesses only NEQ(1).) In either case, +C this parameter is passed as the NEQ argument in all calls +C to F, JAC, and G. Hence, if it is an array, locations +C NEQ(2),... may be used to store other integer data and pass +C it to F, JAC, and G. Each such subroutine must include +C NEQ in a Dimension statement in that case. +C +C Y = a real array for the vector of dependent variables, of +C length NEQ or more. Used for both input and output on the +C first call (ISTATE = 1), and only for output on other calls. +C On the first call, Y must contain the vector of initial +C values. On output, Y contains the computed solution vector, +C evaluated at T. If desired, the Y array may be used +C for other purposes between calls to the solver. +C +C This array is passed as the Y argument in all calls to F, +C JAC, and G. Hence its length may exceed NEQ, and locations +C Y(NEQ+1),... may be used to store other real data and +C pass it to F, JAC, and G. (The DLSODAR package accesses only +C Y(1),...,Y(NEQ).) +C +C T = the independent variable. On input, T is used only on the +C first call, as the initial point of the integration. +C On output, after each call, T is the value at which a +C computed solution y is evaluated (usually the same as TOUT). +C If a root was found, T is the computed location of the +C root reached first, on output. +C On an error return, T is the farthest point reached. +C +C TOUT = the next value of t at which a computed solution is desired. +C Used only for input. +C +C When starting the problem (ISTATE = 1), TOUT may be equal +C to T for one call, then should .ne. T for the next call. +C For the initial T, an input value of TOUT .ne. T is used +C in order to determine the direction of the integration +C (i.e. the algebraic sign of the step sizes) and the rough +C scale of the problem. Integration in either direction +C (forward or backward in t) is permitted. +C +C If ITASK = 2 or 5 (one-step modes), TOUT is ignored after +C the first call (i.e. the first call with TOUT .ne. T). +C Otherwise, TOUT is required on every call. +C +C If ITASK = 1, 3, or 4, the values of TOUT need not be +C monotone, but a value of TOUT which backs up is limited +C to the current internal T interval, whose endpoints are +C TCUR - HU and TCUR (see optional outputs, below, for +C TCUR and HU). +C +C ITOL = an indicator for the type of error control. See +C description below under ATOL. Used only for input. +C +C RTOL = a relative error tolerance parameter, either a scalar or +C an array of length NEQ. See description below under ATOL. +C Input only. +C +C ATOL = an absolute error tolerance parameter, either a scalar or +C an array of length NEQ. Input only. +C +C The input parameters ITOL, RTOL, and ATOL determine +C the error control performed by the solver. The solver will +C control the vector E = (E(i)) of estimated local errors +C in y, according to an inequality of the form +C max-norm of ( E(i)/EWT(i) ) .le. 1, +C where EWT = (EWT(i)) is a vector of positive error weights. +C The values of RTOL and ATOL should all be non-negative. +C The following table gives the types (scalar/array) of +C RTOL and ATOL, and the corresponding form of EWT(i). +C +C ITOL RTOL ATOL EWT(i) +C 1 scalar scalar RTOL*ABS(Y(i)) + ATOL +C 2 scalar array RTOL*ABS(Y(i)) + ATOL(i) +C 3 array scalar RTOL(i)*ABS(Y(i)) + ATOL +C 4 array array RTOL(i)*ABS(Y(i)) + ATOL(i) +C +C When either of these parameters is a scalar, it need not +C be dimensioned in the user's calling program. +C +C If none of the above choices (with ITOL, RTOL, and ATOL +C fixed throughout the problem) is suitable, more general +C error controls can be obtained by substituting a +C user-supplied routine for the setting of EWT. +C See Part 4 below. +C +C If global errors are to be estimated by making a repeated +C run on the same problem with smaller tolerances, then all +C components of RTOL and ATOL (i.e. of EWT) should be scaled +C down uniformly. +C +C ITASK = an index specifying the task to be performed. +C input only. ITASK has the following values and meanings. +C 1 means normal computation of output values of y(t) at +C t = TOUT (by overshooting and interpolating). +C 2 means take one step only and return. +C 3 means stop at the first internal mesh point at or +C beyond t = TOUT and return. +C 4 means normal computation of output values of y(t) at +C t = TOUT but without overshooting t = TCRIT. +C TCRIT must be input as RWORK(1). TCRIT may be equal to +C or beyond TOUT, but not behind it in the direction of +C integration. This option is useful if the problem +C has a singularity at or beyond t = TCRIT. +C 5 means take one step, without passing TCRIT, and return. +C TCRIT must be input as RWORK(1). +C +C Note: If ITASK = 4 or 5 and the solver reaches TCRIT +C (within roundoff), it will return T = TCRIT (exactly) to +C indicate this (unless ITASK = 4 and TOUT comes before TCRIT, +C in which case answers at t = TOUT are returned first). +C +C ISTATE = an index used for input and output to specify the +C the state of the calculation. +C +C On input, the values of ISTATE are as follows. +C 1 means this is the first call for the problem +C (initializations will be done). See note below. +C 2 means this is not the first call, and the calculation +C is to continue normally, with no change in any input +C parameters except possibly TOUT and ITASK. +C (If ITOL, RTOL, and/or ATOL are changed between calls +C with ISTATE = 2, the new values will be used but not +C tested for legality.) +C 3 means this is not the first call, and the +C calculation is to continue normally, but with +C a change in input parameters other than +C TOUT and ITASK. Changes are allowed in +C NEQ, ITOL, RTOL, ATOL, IOPT, LRW, LIW, JT, ML, MU, +C and any optional inputs except H0, MXORDN, and MXORDS. +C (See IWORK description for ML and MU.) +C In addition, immediately following a return with +C ISTATE = 3 (root found), NG and G may be changed. +C (But changing NG from 0 to .gt. 0 is not allowed.) +C Note: A preliminary call with TOUT = T is not counted +C as a first call here, as no initialization or checking of +C input is done. (Such a call is sometimes useful for the +C purpose of outputting the initial conditions.) +C Thus the first call for which TOUT .ne. T requires +C ISTATE = 1 on input. +C +C On output, ISTATE has the following values and meanings. +C 1 means nothing was done; TOUT = t and ISTATE = 1 on input. +C 2 means the integration was performed successfully, and +C no roots were found. +C 3 means the integration was successful, and one or more +C roots were found before satisfying the stop condition +C specified by ITASK. See JROOT. +C -1 means an excessive amount of work (more than MXSTEP +C steps) was done on this call, before completing the +C requested task, but the integration was otherwise +C successful as far as T. (MXSTEP is an optional input +C and is normally 500.) To continue, the user may +C simply reset ISTATE to a value .gt. 1 and call again +C (the excess work step counter will be reset to 0). +C In addition, the user may increase MXSTEP to avoid +C this error return (see below on optional inputs). +C -2 means too much accuracy was requested for the precision +C of the machine being used. This was detected before +C completing the requested task, but the integration +C was successful as far as T. To continue, the tolerance +C parameters must be reset, and ISTATE must be set +C to 3. The optional output TOLSF may be used for this +C purpose. (Note: If this condition is detected before +C taking any steps, then an illegal input return +C (ISTATE = -3) occurs instead.) +C -3 means illegal input was detected, before taking any +C integration steps. See written message for details. +C Note: If the solver detects an infinite loop of calls +C to the solver with illegal input, it will cause +C the run to stop. +C -4 means there were repeated error test failures on +C one attempted step, before completing the requested +C task, but the integration was successful as far as T. +C The problem may have a singularity, or the input +C may be inappropriate. +C -5 means there were repeated convergence test failures on +C one attempted step, before completing the requested +C task, but the integration was successful as far as T. +C This may be caused by an inaccurate Jacobian matrix, +C if one is being used. +C -6 means EWT(i) became zero for some i during the +C integration. Pure relative error control (ATOL(i)=0.0) +C was requested on a variable which has now vanished. +C The integration was successful as far as T. +C -7 means the length of RWORK and/or IWORK was too small to +C proceed, but the integration was successful as far as T. +C This happens when DLSODAR chooses to switch methods +C but LRW and/or LIW is too small for the new method. +C +C Note: Since the normal output value of ISTATE is 2, +C it does not need to be reset for normal continuation. +C Also, since a negative input value of ISTATE will be +C regarded as illegal, a negative output value requires the +C user to change it, and possibly other inputs, before +C calling the solver again. +C +C IOPT = an integer flag to specify whether or not any optional +C inputs are being used on this call. Input only. +C The optional inputs are listed separately below. +C IOPT = 0 means no optional inputs are being used. +C Default values will be used in all cases. +C IOPT = 1 means one or more optional inputs are being used. +C +C RWORK = a real array (double precision) for work space, and (in the +C first 20 words) for conditional and optional inputs and +C optional outputs. +C As DLSODAR switches automatically between stiff and nonstiff +C methods, the required length of RWORK can change during the +C problem. Thus the RWORK array passed to DLSODAR can either +C have a static (fixed) length large enough for both methods, +C or have a dynamic (changing) length altered by the calling +C program in response to output from DLSODAR. +C +C --- Fixed Length Case --- +C If the RWORK length is to be fixed, it should be at least +C max (LRN, LRS), +C where LRN and LRS are the RWORK lengths required when the +C current method is nonstiff or stiff, respectively. +C +C The separate RWORK length requirements LRN and LRS are +C as follows: +C If NEQ is constant and the maximum method orders have +C their default values, then +C LRN = 20 + 16*NEQ + 3*NG, +C LRS = 22 + 9*NEQ + NEQ**2 + 3*NG (JT = 1 or 2), +C LRS = 22 + 10*NEQ + (2*ML+MU)*NEQ + 3*NG (JT = 4 or 5). +C Under any other conditions, LRN and LRS are given by: +C LRN = 20 + NYH*(MXORDN+1) + 3*NEQ + 3*NG, +C LRS = 20 + NYH*(MXORDS+1) + 3*NEQ + LMAT + 3*NG, +C where +C NYH = the initial value of NEQ, +C MXORDN = 12, unless a smaller value is given as an +C optional input, +C MXORDS = 5, unless a smaller value is given as an +C optional input, +C LMAT = length of matrix work space: +C LMAT = NEQ**2 + 2 if JT = 1 or 2, +C LMAT = (2*ML + MU + 1)*NEQ + 2 if JT = 4 or 5. +C +C --- Dynamic Length Case --- +C If the length of RWORK is to be dynamic, then it should +C be at least LRN or LRS, as defined above, depending on the +C current method. Initially, it must be at least LRN (since +C DLSODAR starts with the nonstiff method). On any return +C from DLSODAR, the optional output MCUR indicates the current +C method. If MCUR differs from the value it had on the +C previous return, or if there has only been one call to +C DLSODAR and MCUR is now 2, then DLSODAR has switched +C methods during the last call, and the length of RWORK +C should be reset (to LRN if MCUR = 1, or to LRS if +C MCUR = 2). (An increase in the RWORK length is required +C if DLSODAR returned ISTATE = -7, but not otherwise.) +C After resetting the length, call DLSODAR with ISTATE = 3 +C to signal that change. +C +C LRW = the length of the array RWORK, as declared by the user. +C (This will be checked by the solver.) +C +C IWORK = an integer array for work space. +C As DLSODAR switches automatically between stiff and nonstiff +C methods, the required length of IWORK can change during +C problem, between +C LIS = 20 + NEQ and LIN = 20, +C respectively. Thus the IWORK array passed to DLSODAR can +C either have a fixed length of at least 20 + NEQ, or have a +C dynamic length of at least LIN or LIS, depending on the +C current method. The comments on dynamic length under +C RWORK above apply here. Initially, this length need +C only be at least LIN = 20. +C +C The first few words of IWORK are used for conditional and +C optional inputs and optional outputs. +C +C The following 2 words in IWORK are conditional inputs: +C IWORK(1) = ML These are the lower and upper +C IWORK(2) = MU half-bandwidths, respectively, of the +C banded Jacobian, excluding the main diagonal. +C The band is defined by the matrix locations +C (i,j) with i-ML .le. j .le. i+MU. ML and MU +C must satisfy 0 .le. ML,MU .le. NEQ-1. +C These are required if JT is 4 or 5, and +C ignored otherwise. ML and MU may in fact be +C the band parameters for a matrix to which +C df/dy is only approximately equal. +C +C LIW = the length of the array IWORK, as declared by the user. +C (This will be checked by the solver.) +C +C Note: The base addresses of the work arrays must not be +C altered between calls to DLSODAR for the same problem. +C The contents of the work arrays must not be altered +C between calls, except possibly for the conditional and +C optional inputs, and except for the last 3*NEQ words of RWORK. +C The latter space is used for internal scratch space, and so is +C available for use by the user outside DLSODAR between calls, if +C desired (but not for use by F, JAC, or G). +C +C JAC = the name of the user-supplied routine to compute the +C Jacobian matrix, df/dy, if JT = 1 or 4. The JAC routine +C is optional, but if the problem is expected to be stiff much +C of the time, you are encouraged to supply JAC, for the sake +C of efficiency. (Alternatively, set JT = 2 or 5 to have +C DLSODAR compute df/dy internally by difference quotients.) +C If and when DLSODAR uses df/dy, it treats this NEQ by NEQ +C matrix either as full (JT = 1 or 2), or as banded (JT = +C 4 or 5) with half-bandwidths ML and MU (discussed under +C IWORK above). In either case, if JT = 1 or 4, the JAC +C routine must compute df/dy as a function of the scalar t +C and the vector y. It is to have the form +C SUBROUTINE JAC (NEQ, T, Y, ML, MU, PD, NROWPD) +C DOUBLE PRECISION T, Y(*), PD(NROWPD,*) +C where NEQ, T, Y, ML, MU, and NROWPD are input and the array +C PD is to be loaded with partial derivatives (elements of +C the Jacobian matrix) on output. PD must be given a first +C dimension of NROWPD. T and Y have the same meaning as in +C Subroutine F. +C In the full matrix case (JT = 1), ML and MU are +C ignored, and the Jacobian is to be loaded into PD in +C columnwise manner, with df(i)/dy(j) loaded into pd(i,j). +C In the band matrix case (JT = 4), the elements +C within the band are to be loaded into PD in columnwise +C manner, with diagonal lines of df/dy loaded into the rows +C of PD. Thus df(i)/dy(j) is to be loaded into PD(i-j+MU+1,j). +C ML and MU are the half-bandwidth parameters (see IWORK). +C The locations in PD in the two triangular areas which +C correspond to nonexistent matrix elements can be ignored +C or loaded arbitrarily, as they are overwritten by DLSODAR. +C JAC need not provide df/dy exactly. A crude +C approximation (possibly with a smaller bandwidth) will do. +C In either case, PD is preset to zero by the solver, +C so that only the nonzero elements need be loaded by JAC. +C Each call to JAC is preceded by a call to F with the same +C arguments NEQ, T, and Y. Thus to gain some efficiency, +C intermediate quantities shared by both calculations may be +C saved in a user Common block by F and not recomputed by JAC, +C if desired. Also, JAC may alter the Y array, if desired. +C JAC must be declared External in the calling program. +C Subroutine JAC may access user-defined quantities in +C NEQ(2),... and/or in Y(NEQ(1)+1),... if NEQ is an array +C (dimensioned in JAC) and/or Y has length exceeding NEQ(1). +C See the descriptions of NEQ and Y above. +C +C JT = Jacobian type indicator. Used only for input. +C JT specifies how the Jacobian matrix df/dy will be +C treated, if and when DLSODAR requires this matrix. +C JT has the following values and meanings: +C 1 means a user-supplied full (NEQ by NEQ) Jacobian. +C 2 means an internally generated (difference quotient) full +C Jacobian (using NEQ extra calls to F per df/dy value). +C 4 means a user-supplied banded Jacobian. +C 5 means an internally generated banded Jacobian (using +C ML+MU+1 extra calls to F per df/dy evaluation). +C If JT = 1 or 4, the user must supply a Subroutine JAC +C (the name is arbitrary) as described above under JAC. +C If JT = 2 or 5, a dummy argument can be used. +C +C G = the name of subroutine for constraint functions, whose +C roots are desired during the integration. It is to have +C the form +C SUBROUTINE G (NEQ, T, Y, NG, GOUT) +C DOUBLE PRECISION T, Y(*), GOUT(NG) +C where NEQ, T, Y, and NG are input, and the array GOUT +C is output. NEQ, T, and Y have the same meaning as in +C the F routine, and GOUT is an array of length NG. +C For i = 1,...,NG, this routine is to load into GOUT(i) +C the value at (T,Y) of the i-th constraint function g(i). +C DLSODAR will find roots of the g(i) of odd multiplicity +C (i.e. sign changes) as they occur during the integration. +C G must be declared External in the calling program. +C +C Caution: Because of numerical errors in the functions +C g(i) due to roundoff and integration error, DLSODAR may +C return false roots, or return the same root at two or more +C nearly equal values of t. If such false roots are +C suspected, the user should consider smaller error tolerances +C and/or higher precision in the evaluation of the g(i). +C +C If a root of some g(i) defines the end of the problem, +C the input to DLSODAR should nevertheless allow integration +C to a point slightly past that root, so that DLSODAR can +C locate the root by interpolation. +C +C Subroutine G may access user-defined quantities in +C NEQ(2),... and Y(NEQ(1)+1),... if NEQ is an array +C (dimensioned in G) and/or Y has length exceeding NEQ(1). +C See the descriptions of NEQ and Y above. +C +C NG = number of constraint functions g(i). If there are none, +C set NG = 0, and pass a dummy name for G. +C +C JROOT = integer array of length NG. Used only for output. +C On a return with ISTATE = 3 (one or more roots found), +C JROOT(i) = 1 if g(i) has a root at T, or JROOT(i) = 0 if not. +C----------------------------------------------------------------------- +C Optional Inputs. +C +C The following is a list of the optional inputs provided for in the +C call sequence. (See also Part 2.) For each such input variable, +C this table lists its name as used in this documentation, its +C location in the call sequence, its meaning, and the default value. +C The use of any of these inputs requires IOPT = 1, and in that +C case all of these inputs are examined. A value of zero for any +C of these optional inputs will cause the default value to be used. +C Thus to use a subset of the optional inputs, simply preload +C locations 5 to 10 in RWORK and IWORK to 0.0 and 0 respectively, and +C then set those of interest to nonzero values. +C +C Name Location Meaning and Default Value +C +C H0 RWORK(5) the step size to be attempted on the first step. +C The default value is determined by the solver. +C +C HMAX RWORK(6) the maximum absolute step size allowed. +C The default value is infinite. +C +C HMIN RWORK(7) the minimum absolute step size allowed. +C The default value is 0. (This lower bound is not +C enforced on the final step before reaching TCRIT +C when ITASK = 4 or 5.) +C +C IXPR IWORK(5) flag to generate extra printing at method switches. +C IXPR = 0 means no extra printing (the default). +C IXPR = 1 means print data on each switch. +C T, H, and NST will be printed on the same logical +C unit as used for error messages. +C +C MXSTEP IWORK(6) maximum number of (internally defined) steps +C allowed during one call to the solver. +C The default value is 500. +C +C MXHNIL IWORK(7) maximum number of messages printed (per problem) +C warning that T + H = T on a step (H = step size). +C This must be positive to result in a non-default +C value. The default value is 10. +C +C MXORDN IWORK(8) the maximum order to be allowed for the nonstiff +C (Adams) method. The default value is 12. +C If MXORDN exceeds the default value, it will +C be reduced to the default value. +C MXORDN is held constant during the problem. +C +C MXORDS IWORK(9) the maximum order to be allowed for the stiff +C (BDF) method. The default value is 5. +C If MXORDS exceeds the default value, it will +C be reduced to the default value. +C MXORDS is held constant during the problem. +C----------------------------------------------------------------------- +C Optional Outputs. +C +C As optional additional output from DLSODAR, the variables listed +C below are quantities related to the performance of DLSODAR +C which are available to the user. These are communicated by way of +C the work arrays, but also have internal mnemonic names as shown. +C Except where stated otherwise, all of these outputs are defined +C on any successful return from DLSODAR, and on any return with +C ISTATE = -1, -2, -4, -5, or -6. On an illegal input return +C (ISTATE = -3), they will be unchanged from their existing values +C (if any), except possibly for TOLSF, LENRW, and LENIW. +C On any error return, outputs relevant to the error will be defined, +C as noted below. +C +C Name Location Meaning +C +C HU RWORK(11) the step size in t last used (successfully). +C +C HCUR RWORK(12) the step size to be attempted on the next step. +C +C TCUR RWORK(13) the current value of the independent variable +C which the solver has actually reached, i.e. the +C current internal mesh point in t. On output, TCUR +C will always be at least as far as the argument +C T, but may be farther (if interpolation was done). +C +C TOLSF RWORK(14) a tolerance scale factor, greater than 1.0, +C computed when a request for too much accuracy was +C detected (ISTATE = -3 if detected at the start of +C the problem, ISTATE = -2 otherwise). If ITOL is +C left unaltered but RTOL and ATOL are uniformly +C scaled up by a factor of TOLSF for the next call, +C then the solver is deemed likely to succeed. +C (The user may also ignore TOLSF and alter the +C tolerance parameters in any other way appropriate.) +C +C TSW RWORK(15) the value of t at the time of the last method +C switch, if any. +C +C NGE IWORK(10) the number of g evaluations for the problem so far. +C +C NST IWORK(11) the number of steps taken for the problem so far. +C +C NFE IWORK(12) the number of f evaluations for the problem so far. +C +C NJE IWORK(13) the number of Jacobian evaluations (and of matrix +C LU decompositions) for the problem so far. +C +C NQU IWORK(14) the method order last used (successfully). +C +C NQCUR IWORK(15) the order to be attempted on the next step. +C +C IMXER IWORK(16) the index of the component of largest magnitude in +C the weighted local error vector ( E(i)/EWT(i) ), +C on an error return with ISTATE = -4 or -5. +C +C LENRW IWORK(17) the length of RWORK actually required, assuming +C that the length of RWORK is to be fixed for the +C rest of the problem, and that switching may occur. +C This is defined on normal returns and on an illegal +C input return for insufficient storage. +C +C LENIW IWORK(18) the length of IWORK actually required, assuming +C that the length of IWORK is to be fixed for the +C rest of the problem, and that switching may occur. +C This is defined on normal returns and on an illegal +C input return for insufficient storage. +C +C MUSED IWORK(19) the method indicator for the last successful step: +C 1 means Adams (nonstiff), 2 means BDF (stiff). +C +C MCUR IWORK(20) the current method indicator: +C 1 means Adams (nonstiff), 2 means BDF (stiff). +C This is the method to be attempted +C on the next step. Thus it differs from MUSED +C only if a method switch has just been made. +C +C The following two arrays are segments of the RWORK array which +C may also be of interest to the user as optional outputs. +C For each array, the table below gives its internal name, +C its base address in RWORK, and its description. +C +C Name Base Address Description +C +C YH 21 + 3*NG the Nordsieck history array, of size NYH by +C (NQCUR + 1), where NYH is the initial value +C of NEQ. For j = 0,1,...,NQCUR, column j+1 +C of YH contains HCUR**j/factorial(j) times +C the j-th derivative of the interpolating +C polynomial currently representing the solution, +C evaluated at t = TCUR. +C +C ACOR LACOR array of size NEQ used for the accumulated +C (from Common corrections on each step, scaled on output +C as noted) to represent the estimated local error in y +C on the last step. This is the vector E in +C the description of the error control. It is +C defined only on a successful return from +C DLSODAR. The base address LACOR is obtained by +C including in the user's program the +C following 2 lines: +C COMMON /DLS001/ RLS(218), ILS(37) +C LACOR = ILS(22) +C +C----------------------------------------------------------------------- +C Part 2. Other Routines Callable. +C +C The following are optional calls which the user may make to +C gain additional capabilities in conjunction with DLSODAR. +C (The routines XSETUN and XSETF are designed to conform to the +C SLATEC error handling package.) +C +C Form of Call Function +C CALL XSETUN(LUN) Set the logical unit number, LUN, for +C output of messages from DLSODAR, if +C the default is not desired. +C The default value of LUN is 6. +C +C CALL XSETF(MFLAG) Set a flag to control the printing of +C messages by DLSODAR. +C MFLAG = 0 means do not print. (Danger: +C This risks losing valuable information.) +C MFLAG = 1 means print (the default). +C +C Either of the above calls may be made at +C any time and will take effect immediately. +C +C CALL DSRCAR(RSAV,ISAV,JOB) saves and restores the contents of +C the internal Common blocks used by +C DLSODAR (see Part 3 below). +C RSAV must be a real array of length 245 +C or more, and ISAV must be an integer +C array of length 55 or more. +C JOB=1 means save Common into RSAV/ISAV. +C JOB=2 means restore Common from RSAV/ISAV. +C DSRCAR is useful if one is +C interrupting a run and restarting +C later, or alternating between two or +C more problems solved with DLSODAR. +C +C CALL DINTDY(,,,,,) Provide derivatives of y, of various +C (see below) orders, at a specified point t, if +C desired. It may be called only after +C a successful return from DLSODAR. +C +C The detailed instructions for using DINTDY are as follows. +C The form of the call is: +C +C LYH = 21 + 3*NG +C CALL DINTDY (T, K, RWORK(LYH), NYH, DKY, IFLAG) +C +C The input parameters are: +C +C T = value of independent variable where answers are desired +C (normally the same as the T last returned by DLSODAR). +C For valid results, T must lie between TCUR - HU and TCUR. +C (See optional outputs for TCUR and HU.) +C K = integer order of the derivative desired. K must satisfy +C 0 .le. K .le. NQCUR, where NQCUR is the current order +C (see optional outputs). The capability corresponding +C to K = 0, i.e. computing y(t), is already provided +C by DLSODAR directly. Since NQCUR .ge. 1, the first +C derivative dy/dt is always available with DINTDY. +C LYH = 21 + 3*NG = base address in RWORK of the history array YH. +C NYH = column length of YH, equal to the initial value of NEQ. +C +C The output parameters are: +C +C DKY = a real array of length NEQ containing the computed value +C of the K-th derivative of y(t). +C IFLAG = integer flag, returned as 0 if K and T were legal, +C -1 if K was illegal, and -2 if T was illegal. +C On an error return, a message is also written. +C----------------------------------------------------------------------- +C Part 3. Common Blocks. +C +C If DLSODAR is to be used in an overlay situation, the user +C must declare, in the primary overlay, the variables in: +C (1) the call sequence to DLSODAR, and +C (2) the three internal Common blocks +C /DLS001/ of length 255 (218 double precision words +C followed by 37 integer words), +C /DLSA01/ of length 31 (22 double precision words +C followed by 9 integer words). +C /DLSR01/ of length 7 (3 double precision words +C followed by 4 integer words). +C +C If DLSODAR is used on a system in which the contents of internal +C Common blocks are not preserved between calls, the user should +C declare the above Common blocks in the calling program to insure +C that their contents are preserved. +C +C If the solution of a given problem by DLSODAR is to be interrupted +C and then later continued, such as when restarting an interrupted run +C or alternating between two or more problems, the user should save, +C following the return from the last DLSODAR call prior to the +C interruption, the contents of the call sequence variables and the +C internal Common blocks, and later restore these values before the +C next DLSODAR call for that problem. To save and restore the Common +C blocks, use Subroutine DSRCAR (see Part 2 above). +C +C----------------------------------------------------------------------- +C Part 4. Optionally Replaceable Solver Routines. +C +C Below is a description of a routine in the DLSODAR package which +C relates to the measurement of errors, and can be +C replaced by a user-supplied version, if desired. However, since such +C a replacement may have a major impact on performance, it should be +C done only when absolutely necessary, and only with great caution. +C (Note: The means by which the package version of a routine is +C superseded by the user's version may be system-dependent.) +C +C (a) DEWSET. +C The following subroutine is called just before each internal +C integration step, and sets the array of error weights, EWT, as +C described under ITOL/RTOL/ATOL above: +C Subroutine DEWSET (NEQ, ITOL, RTOL, ATOL, YCUR, EWT) +C where NEQ, ITOL, RTOL, and ATOL are as in the DLSODAR call sequence, +C YCUR contains the current dependent variable vector, and +C EWT is the array of weights set by DEWSET. +C +C If the user supplies this subroutine, it must return in EWT(i) +C (i = 1,...,NEQ) a positive quantity suitable for comparing errors +C in y(i) to. The EWT array returned by DEWSET is passed to the +C DMNORM routine, and also used by DLSODAR in the computation +C of the optional output IMXER, and the increments for difference +C quotient Jacobians. +C +C In the user-supplied version of DEWSET, it may be desirable to use +C the current values of derivatives of y. Derivatives up to order NQ +C are available from the history array YH, described above under +C optional outputs. In DEWSET, YH is identical to the YCUR array, +C extended to NQ + 1 columns with a column length of NYH and scale +C factors of H**j/factorial(j). On the first call for the problem, +C given by NST = 0, NQ is 1 and H is temporarily set to 1.0. +C NYH is the initial value of NEQ. The quantities NQ, H, and NST +C can be obtained by including in DEWSET the statements: +C DOUBLE PRECISION RLS +C COMMON /DLS001/ RLS(218),ILS(37) +C NQ = ILS(33) +C NST = ILS(34) +C H = RLS(212) +C Thus, for example, the current value of dy/dt can be obtained as +C YCUR(NYH+i)/H (i=1,...,NEQ) (and the division by H is +C unnecessary when NST = 0). +C----------------------------------------------------------------------- +C +C***REVISION HISTORY (YYYYMMDD) +C 19811102 DATE WRITTEN +C 19820126 Fixed bug in tests of work space lengths; +C minor corrections in main prologue and comments. +C 19820507 Fixed bug in RCHEK in setting HMING. +C 19870330 Major update: corrected comments throughout; +C removed TRET from Common; rewrote EWSET with 4 loops; +C fixed t test in INTDY; added Cray directives in STODA; +C in STODA, fixed DELP init. and logic around PJAC call; +C combined routines to save/restore Common; +C passed LEVEL = 0 in error message calls (except run abort). +C 19970225 Fixed lines setting JSTART = -2 in Subroutine LSODAR. +C 20010425 Major update: convert source lines to upper case; +C added *DECK lines; changed from 1 to * in dummy dimensions; +C changed names R1MACH/D1MACH to RUMACH/DUMACH; +C renamed routines for uniqueness across single/double prec.; +C converted intrinsic names to generic form; +C removed ILLIN and NTREP (data loaded) from Common; +C removed all 'own' variables from Common; +C changed error messages to quoted strings; +C replaced XERRWV/XERRWD with 1993 revised version; +C converted prologues, comments, error messages to mixed case; +C numerous corrections to prologues and internal comments. +C 20010507 Converted single precision source to double precision. +C 20010613 Revised excess accuracy test (to match rest of ODEPACK). +C 20010808 Fixed bug in DPRJA (matrix in DBNORM call). +C 20020502 Corrected declarations in descriptions of user routines. +C 20031105 Restored 'own' variables to Common blocks, to enable +C interrupt/restart feature. +C 20031112 Added SAVE statements for data-loaded constants. +C +C----------------------------------------------------------------------- +C Other routines in the DLSODAR package. +C +C In addition to Subroutine DLSODAR, the DLSODAR package includes the +C following subroutines and function routines: +C DRCHEK does preliminary checking for roots, and serves as an +C interface between Subroutine DLSODAR and Subroutine DROOTS. +C DROOTS finds the leftmost root of a set of functions. +C DINTDY computes an interpolated value of the y vector at t = TOUT. +C DSTODA is the core integrator, which does one step of the +C integration and the associated error control. +C DCFODE sets all method coefficients and test constants. +C DPRJA computes and preprocesses the Jacobian matrix J = df/dy +C and the Newton iteration matrix P = I - h*l0*J. +C DSOLSY manages solution of linear system in chord iteration. +C DEWSET sets the error weight vector EWT before each step. +C DMNORM computes the weighted max-norm of a vector. +C DFNORM computes the norm of a full matrix consistent with the +C weighted max-norm on vectors. +C DBNORM computes the norm of a band matrix consistent with the +C weighted max-norm on vectors. +C DSRCAR is a user-callable routine to save and restore +C the contents of the internal Common blocks. +C DGEFA and DGESL are routines from LINPACK for solving full +C systems of linear algebraic equations. +C DGBFA and DGBSL are routines from LINPACK for solving banded +C linear systems. +C DCOPY is one of the basic linear algebra modules (BLAS). +C DUMACH computes the unit roundoff in a machine-independent manner. +C XERRWD, XSETUN, XSETF, IXSAV, and IUMACH handle the printing of all +C error messages and warnings. XERRWD is machine-dependent. +C Note: DMNORM, DFNORM, DBNORM, DUMACH, IXSAV, and IUMACH are +C function routines. All the others are subroutines. +C +C----------------------------------------------------------------------- + EXTERNAL DPRJA, DSOLSY + DOUBLE PRECISION DUMACH, DMNORM + INTEGER INIT, MXSTEP, MXHNIL, NHNIL, NSLAST, NYH, IOWNS, + 1 ICF, IERPJ, IERSL, JCUR, JSTART, KFLAG, L, + 2 LYH, LEWT, LACOR, LSAVF, LWM, LIWM, METH, MITER, + 3 MAXORD, MAXCOR, MSBP, MXNCF, N, NQ, NST, NFE, NJE, NQU + INTEGER INSUFR, INSUFI, IXPR, IOWNS2, JTYP, MUSED, MXORDN, MXORDS + INTEGER LG0, LG1, LGX, IOWNR3, IRFND, ITASKC, NGC, NGE + INTEGER I, I1, I2, IFLAG, IMXER, KGO, LENIW, + 1 LENRW, LENWM, LF0, ML, MORD, MU, MXHNL0, MXSTP0 + INTEGER LEN1, LEN1C, LEN1N, LEN1S, LEN2, LENIWC, LENRWC + INTEGER IRFP, IRT, LENYH, LYHNEW + DOUBLE PRECISION ROWNS, + 1 CCMAX, EL0, H, HMIN, HMXI, HU, RC, TN, UROUND + DOUBLE PRECISION TSW, ROWNS2, PDNORM + DOUBLE PRECISION ROWNR3, T0, TLAST, TOUTC + DOUBLE PRECISION ATOLI, AYI, BIG, EWTI, H0, HMAX, HMX, RH, RTOLI, + 1 TCRIT, TDIST, TNEXT, TOL, TOLSF, TP, SIZE, SUM, W0 + DIMENSION MORD(2) + LOGICAL IHIT + CHARACTER*60 MSG + SAVE MORD, MXSTP0, MXHNL0 +C----------------------------------------------------------------------- +C The following three internal Common blocks contain +C (a) variables which are local to any subroutine but whose values must +C be preserved between calls to the routine ("own" variables), and +C (b) variables which are communicated between subroutines. +C The block DLS001 is declared in subroutines DLSODAR, DINTDY, DSTODA, +C DPRJA, and DSOLSY. +C The block DLSA01 is declared in subroutines DLSODAR, DSTODA, DPRJA. +C The block DLSR01 is declared in subroutines DLSODAR, DRCHEK, DROOTS. +C Groups of variables are replaced by dummy arrays in the Common +C declarations in routines where those variables are not used. +C----------------------------------------------------------------------- + COMMON /DLS001/ ROWNS(209), + 1 CCMAX, EL0, H, HMIN, HMXI, HU, RC, TN, UROUND, + 2 INIT, MXSTEP, MXHNIL, NHNIL, NSLAST, NYH, IOWNS(6), + 3 ICF, IERPJ, IERSL, JCUR, JSTART, KFLAG, L, + 4 LYH, LEWT, LACOR, LSAVF, LWM, LIWM, METH, MITER, + 5 MAXORD, MAXCOR, MSBP, MXNCF, N, NQ, NST, NFE, NJE, NQU +C + COMMON /DLSA01/ TSW, ROWNS2(20), PDNORM, + 1 INSUFR, INSUFI, IXPR, IOWNS2(2), JTYP, MUSED, MXORDN, MXORDS +C + COMMON /DLSR01/ ROWNR3(2), T0, TLAST, TOUTC, + 1 LG0, LG1, LGX, IOWNR3(2), IRFND, ITASKC, NGC, NGE +C + DATA MORD(1),MORD(2)/12,5/, MXSTP0/500/, MXHNL0/10/ +C----------------------------------------------------------------------- +C Block A. +C This code block is executed on every call. +C It tests ISTATE and ITASK for legality and branches appropriately. +C If ISTATE .gt. 1 but the flag INIT shows that initialization has +C not yet been done, an error return occurs. +C If ISTATE = 1 and TOUT = T, return immediately. +C----------------------------------------------------------------------- + IF (ISTATE .LT. 1 .OR. ISTATE .GT. 3) GO TO 601 + IF (ITASK .LT. 1 .OR. ITASK .GT. 5) GO TO 602 + ITASKC = ITASK + IF (ISTATE .EQ. 1) GO TO 10 + IF (INIT .EQ. 0) GO TO 603 + IF (ISTATE .EQ. 2) GO TO 200 + GO TO 20 + 10 INIT = 0 + IF (TOUT .EQ. T) RETURN +C----------------------------------------------------------------------- +C Block B. +C The next code block is executed for the initial call (ISTATE = 1), +C or for a continuation call with parameter changes (ISTATE = 3). +C It contains checking of all inputs and various initializations. +C +C First check legality of the non-optional inputs NEQ, ITOL, IOPT, +C JT, ML, MU, and NG. +C----------------------------------------------------------------------- + 20 IF (NEQ(1) .LE. 0) GO TO 604 + IF (ISTATE .EQ. 1) GO TO 25 + IF (NEQ(1) .GT. N) GO TO 605 + 25 N = NEQ(1) + IF (ITOL .LT. 1 .OR. ITOL .GT. 4) GO TO 606 + IF (IOPT .LT. 0 .OR. IOPT .GT. 1) GO TO 607 + IF (JT .EQ. 3 .OR. JT .LT. 1 .OR. JT .GT. 5) GO TO 608 + JTYP = JT + IF (JT .LE. 2) GO TO 30 + ML = IWORK(1) + MU = IWORK(2) + IF (ML .LT. 0 .OR. ML .GE. N) GO TO 609 + IF (MU .LT. 0 .OR. MU .GE. N) GO TO 610 + 30 CONTINUE + IF (NG .LT. 0) GO TO 630 + IF (ISTATE .EQ. 1) GO TO 35 + IF (IRFND .EQ. 0 .AND. NG .NE. NGC) GO TO 631 + 35 NGC = NG +C Next process and check the optional inputs. -------------------------- + IF (IOPT .EQ. 1) GO TO 40 + IXPR = 0 + MXSTEP = MXSTP0 + MXHNIL = MXHNL0 + HMXI = 0.0D0 + HMIN = 0.0D0 + IF (ISTATE .NE. 1) GO TO 60 + H0 = 0.0D0 + MXORDN = MORD(1) + MXORDS = MORD(2) + GO TO 60 + 40 IXPR = IWORK(5) + IF (IXPR .LT. 0 .OR. IXPR .GT. 1) GO TO 611 + MXSTEP = IWORK(6) + IF (MXSTEP .LT. 0) GO TO 612 + IF (MXSTEP .EQ. 0) MXSTEP = MXSTP0 + MXHNIL = IWORK(7) + IF (MXHNIL .LT. 0) GO TO 613 + IF (MXHNIL .EQ. 0) MXHNIL = MXHNL0 + IF (ISTATE .NE. 1) GO TO 50 + H0 = RWORK(5) + MXORDN = IWORK(8) + IF (MXORDN .LT. 0) GO TO 628 + IF (MXORDN .EQ. 0) MXORDN = 100 + MXORDN = MIN(MXORDN,MORD(1)) + MXORDS = IWORK(9) + IF (MXORDS .LT. 0) GO TO 629 + IF (MXORDS .EQ. 0) MXORDS = 100 + MXORDS = MIN(MXORDS,MORD(2)) + IF ((TOUT - T)*H0 .LT. 0.0D0) GO TO 614 + 50 HMAX = RWORK(6) + IF (HMAX .LT. 0.0D0) GO TO 615 + HMXI = 0.0D0 + IF (HMAX .GT. 0.0D0) HMXI = 1.0D0/HMAX + HMIN = RWORK(7) + IF (HMIN .LT. 0.0D0) GO TO 616 +C----------------------------------------------------------------------- +C Set work array pointers and check lengths LRW and LIW. +C If ISTATE = 1, METH is initialized to 1 here to facilitate the +C checking of work space lengths. +C Pointers to segments of RWORK and IWORK are named by prefixing L to +C the name of the segment. E.g., the segment YH starts at RWORK(LYH). +C Segments of RWORK (in order) are denoted G0, G1, GX, YH, WM, +C EWT, SAVF, ACOR. +C If the lengths provided are insufficient for the current method, +C an error return occurs. This is treated as illegal input on the +C first call, but as a problem interruption with ISTATE = -7 on a +C continuation call. If the lengths are sufficient for the current +C method but not for both methods, a warning message is sent. +C----------------------------------------------------------------------- + 60 IF (ISTATE .EQ. 1) METH = 1 + IF (ISTATE .EQ. 1) NYH = N + LG0 = 21 + LG1 = LG0 + NG + LGX = LG1 + NG + LYHNEW = LGX + NG + IF (ISTATE .EQ. 1) LYH = LYHNEW + IF (LYHNEW .EQ. LYH) GO TO 62 +C If ISTATE = 3 and NG was changed, shift YH to its new location. ------ + LENYH = L*NYH + IF (LRW .LT. LYHNEW-1+LENYH) GO TO 62 + I1 = 1 + IF (LYHNEW .GT. LYH) I1 = -1 + CALL DCOPY (LENYH, RWORK(LYH), I1, RWORK(LYHNEW), I1) + LYH = LYHNEW + 62 CONTINUE + LEN1N = LYHNEW - 1 + (MXORDN + 1)*NYH + LEN1S = LYHNEW - 1 + (MXORDS + 1)*NYH + LWM = LEN1S + 1 + IF (JT .LE. 2) LENWM = N*N + 2 + IF (JT .GE. 4) LENWM = (2*ML + MU + 1)*N + 2 + LEN1S = LEN1S + LENWM + LEN1C = LEN1N + IF (METH .EQ. 2) LEN1C = LEN1S + LEN1 = MAX(LEN1N,LEN1S) + LEN2 = 3*N + LENRW = LEN1 + LEN2 + LENRWC = LEN1C + LEN2 + IWORK(17) = LENRW + LIWM = 1 + LENIW = 20 + N + LENIWC = 20 + IF (METH .EQ. 2) LENIWC = LENIW + IWORK(18) = LENIW + IF (ISTATE .EQ. 1 .AND. LRW .LT. LENRWC) GO TO 617 + IF (ISTATE .EQ. 1 .AND. LIW .LT. LENIWC) GO TO 618 + IF (ISTATE .EQ. 3 .AND. LRW .LT. LENRWC) GO TO 550 + IF (ISTATE .EQ. 3 .AND. LIW .LT. LENIWC) GO TO 555 + LEWT = LEN1 + 1 + INSUFR = 0 + IF (LRW .GE. LENRW) GO TO 65 + INSUFR = 2 + LEWT = LEN1C + 1 + MSG='DLSODAR- Warning.. RWORK length is sufficient for now, but ' + CALL XERRWD (MSG, 60, 103, 0, 0, 0, 0, 0, 0.0D0, 0.0D0) + MSG=' may not be later. Integration will proceed anyway. ' + CALL XERRWD (MSG, 60, 103, 0, 0, 0, 0, 0, 0.0D0, 0.0D0) + MSG = ' Length needed is LENRW = I1, while LRW = I2.' + CALL XERRWD (MSG, 50, 103, 0, 2, LENRW, LRW, 0, 0.0D0, 0.0D0) + 65 LSAVF = LEWT + N + LACOR = LSAVF + N + INSUFI = 0 + IF (LIW .GE. LENIW) GO TO 70 + INSUFI = 2 + MSG='DLSODAR- Warning.. IWORK length is sufficient for now, but ' + CALL XERRWD (MSG, 60, 104, 0, 0, 0, 0, 0, 0.0D0, 0.0D0) + MSG=' may not be later. Integration will proceed anyway. ' + CALL XERRWD (MSG, 60, 104, 0, 0, 0, 0, 0, 0.0D0, 0.0D0) + MSG = ' Length needed is LENIW = I1, while LIW = I2.' + CALL XERRWD (MSG, 50, 104, 0, 2, LENIW, LIW, 0, 0.0D0, 0.0D0) + 70 CONTINUE +C Check RTOL and ATOL for legality. ------------------------------------ + RTOLI = RTOL(1) + ATOLI = ATOL(1) + DO 75 I = 1,N + IF (ITOL .GE. 3) RTOLI = RTOL(I) + IF (ITOL .EQ. 2 .OR. ITOL .EQ. 4) ATOLI = ATOL(I) + IF (RTOLI .LT. 0.0D0) GO TO 619 + IF (ATOLI .LT. 0.0D0) GO TO 620 + 75 CONTINUE + IF (ISTATE .EQ. 1) GO TO 100 +C if ISTATE = 3, set flag to signal parameter changes to DSTODA. ------- + JSTART = -1 + IF (N .EQ. NYH) GO TO 200 +C NEQ was reduced. zero part of yh to avoid undefined references. ----- + I1 = LYH + L*NYH + I2 = LYH + (MAXORD + 1)*NYH - 1 + IF (I1 .GT. I2) GO TO 200 + DO 95 I = I1,I2 + 95 RWORK(I) = 0.0D0 + GO TO 200 +C----------------------------------------------------------------------- +C Block C. +C The next block is for the initial call only (ISTATE = 1). +C It contains all remaining initializations, the initial call to F, +C and the calculation of the initial step size. +C The error weights in EWT are inverted after being loaded. +C----------------------------------------------------------------------- + 100 UROUND = DUMACH() + TN = T + TSW = T + MAXORD = MXORDN + IF (ITASK .NE. 4 .AND. ITASK .NE. 5) GO TO 110 + TCRIT = RWORK(1) + IF ((TCRIT - TOUT)*(TOUT - T) .LT. 0.0D0) GO TO 625 + IF (H0 .NE. 0.0D0 .AND. (T + H0 - TCRIT)*H0 .GT. 0.0D0) + 1 H0 = TCRIT - T + 110 JSTART = 0 + NHNIL = 0 + NST = 0 + NJE = 0 + NSLAST = 0 + HU = 0.0D0 + NQU = 0 + MUSED = 0 + MITER = 0 + CCMAX = 0.3D0 + MAXCOR = 3 + MSBP = 20 + MXNCF = 10 +C Initial call to F. (LF0 points to YH(*,2).) ------------------------- + LF0 = LYH + NYH + CALL F (NEQ, T, Y, RWORK(LF0)) + NFE = 1 +C Load the initial value vector in YH. --------------------------------- + DO 115 I = 1,N + 115 RWORK(I+LYH-1) = Y(I) +C Load and invert the EWT array. (H is temporarily set to 1.0.) ------- + NQ = 1 + H = 1.0D0 + CALL DEWSET (N, ITOL, RTOL, ATOL, RWORK(LYH), RWORK(LEWT)) + DO 120 I = 1,N + IF (RWORK(I+LEWT-1) .LE. 0.0D0) GO TO 621 + 120 RWORK(I+LEWT-1) = 1.0D0/RWORK(I+LEWT-1) +C----------------------------------------------------------------------- +C The coding below computes the step size, H0, to be attempted on the +C first step, unless the user has supplied a value for this. +C First check that TOUT - T differs significantly from zero. +C A scalar tolerance quantity TOL is computed, as MAX(RTOL(i)) +C if this is positive, or MAX(ATOL(i)/ABS(Y(i))) otherwise, adjusted +C so as to be between 100*UROUND and 1.0E-3. +C Then the computed value H0 is given by: +C +C H0**(-2) = 1./(TOL * w0**2) + TOL * (norm(F))**2 +C +C where w0 = MAX ( ABS(T), ABS(TOUT) ), +C F = the initial value of the vector f(t,y), and +C norm() = the weighted vector norm used throughout, given by +C the DMNORM function routine, and weighted by the +C tolerances initially loaded into the EWT array. +C The sign of H0 is inferred from the initial values of TOUT and T. +C ABS(H0) is made .le. ABS(TOUT-T) in any case. +C----------------------------------------------------------------------- + IF (H0 .NE. 0.0D0) GO TO 180 + TDIST = ABS(TOUT - T) + W0 = MAX(ABS(T),ABS(TOUT)) + IF (TDIST .LT. 2.0D0*UROUND*W0) GO TO 622 + TOL = RTOL(1) + IF (ITOL .LE. 2) GO TO 140 + DO 130 I = 1,N + 130 TOL = MAX(TOL,RTOL(I)) + 140 IF (TOL .GT. 0.0D0) GO TO 160 + ATOLI = ATOL(1) + DO 150 I = 1,N + IF (ITOL .EQ. 2 .OR. ITOL .EQ. 4) ATOLI = ATOL(I) + AYI = ABS(Y(I)) + IF (AYI .NE. 0.0D0) TOL = MAX(TOL,ATOLI/AYI) + 150 CONTINUE + 160 TOL = MAX(TOL,100.0D0*UROUND) + TOL = MIN(TOL,0.001D0) + SUM = DMNORM (N, RWORK(LF0), RWORK(LEWT)) + SUM = 1.0D0/(TOL*W0*W0) + TOL*SUM**2 + H0 = 1.0D0/SQRT(SUM) + H0 = MIN(H0,TDIST) + H0 = SIGN(H0,TOUT-T) +C Adjust H0 if necessary to meet HMAX bound. --------------------------- + 180 RH = ABS(H0)*HMXI + IF (RH .GT. 1.0D0) H0 = H0/RH +C Load H with H0 and scale YH(*,2) by H0. ------------------------------ + H = H0 + DO 190 I = 1,N + 190 RWORK(I+LF0-1) = H0*RWORK(I+LF0-1) +C +C Check for a zero of g at T. ------------------------------------------ + IRFND = 0 + TOUTC = TOUT + IF (NGC .EQ. 0) GO TO 270 + CALL DRCHEK (1, G, NEQ, Y, RWORK(LYH), NYH, + 1 RWORK(LG0), RWORK(LG1), RWORK(LGX), JROOT, IRT) + IF (IRT .EQ. 0) GO TO 270 + GO TO 632 +C----------------------------------------------------------------------- +C Block D. +C The next code block is for continuation calls only (ISTATE = 2 or 3) +C and is to check stop conditions before taking a step. +C First, DRCHEK is called to check for a root within the last step +C taken, other than the last root found there, if any. +C If ITASK = 2 or 5, and y(TN) has not yet been returned to the user +C because of an intervening root, return through Block G. +C----------------------------------------------------------------------- + 200 NSLAST = NST +C + IRFP = IRFND + IF (NGC .EQ. 0) GO TO 205 + IF (ITASK .EQ. 1 .OR. ITASK .EQ. 4) TOUTC = TOUT + CALL DRCHEK (2, G, NEQ, Y, RWORK(LYH), NYH, + 1 RWORK(LG0), RWORK(LG1), RWORK(LGX), JROOT, IRT) + IF (IRT .NE. 1) GO TO 205 + IRFND = 1 + ISTATE = 3 + T = T0 + GO TO 425 + 205 CONTINUE + IRFND = 0 + IF (IRFP .EQ. 1 .AND. TLAST .NE. TN .AND. ITASK .EQ. 2) GO TO 400 +C + GO TO (210, 250, 220, 230, 240), ITASK + 210 IF ((TN - TOUT)*H .LT. 0.0D0) GO TO 250 + CALL DINTDY (TOUT, 0, RWORK(LYH), NYH, Y, IFLAG) + IF (IFLAG .NE. 0) GO TO 627 + T = TOUT + GO TO 420 + 220 TP = TN - HU*(1.0D0 + 100.0D0*UROUND) + IF ((TP - TOUT)*H .GT. 0.0D0) GO TO 623 + IF ((TN - TOUT)*H .LT. 0.0D0) GO TO 250 + T = TN + GO TO 400 + 230 TCRIT = RWORK(1) + IF ((TN - TCRIT)*H .GT. 0.0D0) GO TO 624 + IF ((TCRIT - TOUT)*H .LT. 0.0D0) GO TO 625 + IF ((TN - TOUT)*H .LT. 0.0D0) GO TO 245 + CALL DINTDY (TOUT, 0, RWORK(LYH), NYH, Y, IFLAG) + IF (IFLAG .NE. 0) GO TO 627 + T = TOUT + GO TO 420 + 240 TCRIT = RWORK(1) + IF ((TN - TCRIT)*H .GT. 0.0D0) GO TO 624 + 245 HMX = ABS(TN) + ABS(H) + IHIT = ABS(TN - TCRIT) .LE. 100.0D0*UROUND*HMX + IF (IHIT) T = TCRIT + IF (IRFP .EQ. 1 .AND. TLAST .NE. TN .AND. ITASK .EQ. 5) GO TO 400 + IF (IHIT) GO TO 400 + TNEXT = TN + H*(1.0D0 + 4.0D0*UROUND) + IF ((TNEXT - TCRIT)*H .LE. 0.0D0) GO TO 250 + H = (TCRIT - TN)*(1.0D0 - 4.0D0*UROUND) + IF (ISTATE .EQ. 2 .AND. JSTART .GE. 0) JSTART = -2 +C----------------------------------------------------------------------- +C Block E. +C The next block is normally executed for all calls and contains +C the call to the one-step core integrator DSTODA. +C +C This is a looping point for the integration steps. +C +C First check for too many steps being taken, update EWT (if not at +C start of problem), check for too much accuracy being requested, and +C check for H below the roundoff level in T. +C----------------------------------------------------------------------- + 250 CONTINUE + IF (METH .EQ. MUSED) GO TO 255 + IF (INSUFR .EQ. 1) GO TO 550 + IF (INSUFI .EQ. 1) GO TO 555 + 255 IF ((NST-NSLAST) .GE. MXSTEP) GO TO 500 + CALL DEWSET (N, ITOL, RTOL, ATOL, RWORK(LYH), RWORK(LEWT)) + DO 260 I = 1,N + IF (RWORK(I+LEWT-1) .LE. 0.0D0) GO TO 510 + 260 RWORK(I+LEWT-1) = 1.0D0/RWORK(I+LEWT-1) + 270 TOLSF = UROUND*DMNORM (N, RWORK(LYH), RWORK(LEWT)) + IF (TOLSF .LE. 1.0D0) GO TO 280 + TOLSF = TOLSF*2.0D0 + IF (NST .EQ. 0) GO TO 626 + GO TO 520 + 280 IF ((TN + H) .NE. TN) GO TO 290 + NHNIL = NHNIL + 1 + IF (NHNIL .GT. MXHNIL) GO TO 290 + MSG = 'DLSODAR- Warning..Internal T(=R1) and H(=R2) are ' + CALL XERRWD (MSG, 50, 101, 0, 0, 0, 0, 0, 0.0D0, 0.0D0) + MSG=' such that in the machine, T + H = T on the next step ' + CALL XERRWD (MSG, 60, 101, 0, 0, 0, 0, 0, 0.0D0, 0.0D0) + MSG = ' (H = step size). Solver will continue anyway.' + CALL XERRWD (MSG, 50, 101, 0, 0, 0, 0, 2, TN, H) + IF (NHNIL .LT. MXHNIL) GO TO 290 + MSG = 'DLSODAR- Above warning has been issued I1 times. ' + CALL XERRWD (MSG, 50, 102, 0, 0, 0, 0, 0, 0.0D0, 0.0D0) + MSG = ' It will not be issued again for this problem.' + CALL XERRWD (MSG, 50, 102, 0, 1, MXHNIL, 0, 0, 0.0D0, 0.0D0) + 290 CONTINUE +C----------------------------------------------------------------------- +C CALL DSTODA(NEQ,Y,YH,NYH,YH,EWT,SAVF,ACOR,WM,IWM,F,JAC,DPRJA,DSOLSY) +C----------------------------------------------------------------------- + CALL DSTODA (NEQ, Y, RWORK(LYH), NYH, RWORK(LYH), RWORK(LEWT), + 1 RWORK(LSAVF), RWORK(LACOR), RWORK(LWM), IWORK(LIWM), + 2 F, JAC, DPRJA, DSOLSY) + KGO = 1 - KFLAG + GO TO (300, 530, 540), KGO +C----------------------------------------------------------------------- +C Block F. +C The following block handles the case of a successful return from the +C core integrator (KFLAG = 0). +C If a method switch was just made, record TSW, reset MAXORD, +C set JSTART to -1 to signal DSTODA to complete the switch, +C and do extra printing of data if IXPR = 1. +C Then call DRCHEK to check for a root within the last step. +C Then, if no root was found, check for stop conditions. +C----------------------------------------------------------------------- + 300 INIT = 1 + IF (METH .EQ. MUSED) GO TO 310 + TSW = TN + MAXORD = MXORDN + IF (METH .EQ. 2) MAXORD = MXORDS + IF (METH .EQ. 2) RWORK(LWM) = SQRT(UROUND) + INSUFR = MIN(INSUFR,1) + INSUFI = MIN(INSUFI,1) + JSTART = -1 + IF (IXPR .EQ. 0) GO TO 310 + IF (METH .EQ. 2) THEN + MSG='DLSODAR- A switch to the BDF (stiff) method has occurred ' + CALL XERRWD (MSG, 60, 105, 0, 0, 0, 0, 0, 0.0D0, 0.0D0) + ENDIF + IF (METH .EQ. 1) THEN + MSG='DLSODAR- A switch to the Adams (nonstiff) method occurred ' + CALL XERRWD (MSG, 60, 106, 0, 0, 0, 0, 0, 0.0D0, 0.0D0) + ENDIF + MSG=' at T = R1, tentative step size H = R2, step NST = I1 ' + CALL XERRWD (MSG, 60, 107, 0, 1, NST, 0, 2, TN, H) + 310 CONTINUE +C + IF (NGC .EQ. 0) GO TO 315 + CALL DRCHEK (3, G, NEQ, Y, RWORK(LYH), NYH, + 1 RWORK(LG0), RWORK(LG1), RWORK(LGX), JROOT, IRT) + IF (IRT .NE. 1) GO TO 315 + IRFND = 1 + ISTATE = 3 + T = T0 + GO TO 425 + 315 CONTINUE +C + GO TO (320, 400, 330, 340, 350), ITASK +C ITASK = 1. If TOUT has been reached, interpolate. ------------------- + 320 IF ((TN - TOUT)*H .LT. 0.0D0) GO TO 250 + CALL DINTDY (TOUT, 0, RWORK(LYH), NYH, Y, IFLAG) + T = TOUT + GO TO 420 +C ITASK = 3. Jump to exit if TOUT was reached. ------------------------ + 330 IF ((TN - TOUT)*H .GE. 0.0D0) GO TO 400 + GO TO 250 +C ITASK = 4. See if TOUT or TCRIT was reached. Adjust H if necessary. + 340 IF ((TN - TOUT)*H .LT. 0.0D0) GO TO 345 + CALL DINTDY (TOUT, 0, RWORK(LYH), NYH, Y, IFLAG) + T = TOUT + GO TO 420 + 345 HMX = ABS(TN) + ABS(H) + IHIT = ABS(TN - TCRIT) .LE. 100.0D0*UROUND*HMX + IF (IHIT) GO TO 400 + TNEXT = TN + H*(1.0D0 + 4.0D0*UROUND) + IF ((TNEXT - TCRIT)*H .LE. 0.0D0) GO TO 250 + H = (TCRIT - TN)*(1.0D0 - 4.0D0*UROUND) + IF (JSTART .GE. 0) JSTART = -2 + GO TO 250 +C ITASK = 5. See if TCRIT was reached and jump to exit. --------------- + 350 HMX = ABS(TN) + ABS(H) + IHIT = ABS(TN - TCRIT) .LE. 100.0D0*UROUND*HMX +C----------------------------------------------------------------------- +C Block G. +C The following block handles all successful returns from DLSODAR. +C If ITASK .ne. 1, Y is loaded from YH and T is set accordingly. +C ISTATE is set to 2, and the optional outputs are loaded into the +C work arrays before returning. +C----------------------------------------------------------------------- + 400 DO 410 I = 1,N + 410 Y(I) = RWORK(I+LYH-1) + T = TN + IF (ITASK .NE. 4 .AND. ITASK .NE. 5) GO TO 420 + IF (IHIT) T = TCRIT + 420 ISTATE = 2 + 425 CONTINUE + RWORK(11) = HU + RWORK(12) = H + RWORK(13) = TN + RWORK(15) = TSW + IWORK(11) = NST + IWORK(12) = NFE + IWORK(13) = NJE + IWORK(14) = NQU + IWORK(15) = NQ + IWORK(19) = MUSED + IWORK(20) = METH + IWORK(10) = NGE + TLAST = T + RETURN +C----------------------------------------------------------------------- +C Block H. +C The following block handles all unsuccessful returns other than +C those for illegal input. First the error message routine is called. +C If there was an error test or convergence test failure, IMXER is set. +C Then Y is loaded from YH and T is set to TN. +C The optional outputs are loaded into the work arrays before returning. +C----------------------------------------------------------------------- +C The maximum number of steps was taken before reaching TOUT. ---------- + 500 MSG = 'DLSODAR- At current T (=R1), MXSTEP (=I1) steps ' + CALL XERRWD (MSG, 50, 201, 0, 0, 0, 0, 0, 0.0D0, 0.0D0) + MSG = ' taken on this call before reaching TOUT ' + CALL XERRWD (MSG, 50, 201, 0, 1, MXSTEP, 0, 1, TN, 0.0D0) + ISTATE = -1 + GO TO 580 +C EWT(i) .le. 0.0 for some i (not at start of problem). ---------------- + 510 EWTI = RWORK(LEWT+I-1) + MSG = 'DLSODAR- At T(=R1), EWT(I1) has become R2 .le. 0.' + CALL XERRWD (MSG, 50, 202, 0, 1, I, 0, 2, TN, EWTI) + ISTATE = -6 + GO TO 580 +C Too much accuracy requested for machine precision. ------------------- + 520 MSG = 'DLSODAR- At T (=R1), too much accuracy requested ' + CALL XERRWD (MSG, 50, 203, 0, 0, 0, 0, 0, 0.0D0, 0.0D0) + MSG = ' for precision of machine.. See TOLSF (=R2) ' + CALL XERRWD (MSG, 50, 203, 0, 0, 0, 0, 2, TN, TOLSF) + RWORK(14) = TOLSF + ISTATE = -2 + GO TO 580 +C KFLAG = -1. Error test failed repeatedly or with ABS(H) = HMIN. ----- + 530 MSG = 'DLSODAR- At T(=R1), step size H(=R2), the error ' + CALL XERRWD (MSG, 50, 204, 0, 0, 0, 0, 0, 0.0D0, 0.0D0) + MSG = ' test failed repeatedly or with ABS(H) = HMIN' + CALL XERRWD (MSG, 50, 204, 0, 0, 0, 0, 2, TN, H) + ISTATE = -4 + GO TO 560 +C KFLAG = -2. Convergence failed repeatedly or with ABS(H) = HMIN. ---- + 540 MSG = 'DLSODAR- At T (=R1) and step size H (=R2), the ' + CALL XERRWD (MSG, 50, 205, 0, 0, 0, 0, 0, 0.0D0, 0.0D0) + MSG = ' corrector convergence failed repeatedly ' + CALL XERRWD (MSG, 50, 205, 0, 0, 0, 0, 0, 0.0D0, 0.0D0) + MSG = ' or with ABS(H) = HMIN ' + CALL XERRWD (MSG, 30, 205, 0, 0, 0, 0, 2, TN, H) + ISTATE = -5 + GO TO 560 +C RWORK length too small to proceed. ----------------------------------- + 550 MSG = 'DLSODAR- At current T(=R1), RWORK length too small' + CALL XERRWD (MSG, 50, 206, 0, 0, 0, 0, 0, 0.0D0, 0.0D0) + MSG=' to proceed. The integration was otherwise successful.' + CALL XERRWD (MSG, 60, 206, 0, 0, 0, 0, 1, TN, 0.0D0) + ISTATE = -7 + GO TO 580 +C IWORK length too small to proceed. ----------------------------------- + 555 MSG = 'DLSODAR- At current T(=R1), IWORK length too small' + CALL XERRWD (MSG, 50, 207, 0, 0, 0, 0, 0, 0.0D0, 0.0D0) + MSG=' to proceed. The integration was otherwise successful.' + CALL XERRWD (MSG, 60, 207, 0, 0, 0, 0, 1, TN, 0.0D0) + ISTATE = -7 + GO TO 580 +C Compute IMXER if relevant. ------------------------------------------- + 560 BIG = 0.0D0 + IMXER = 1 + DO 570 I = 1,N + SIZE = ABS(RWORK(I+LACOR-1)*RWORK(I+LEWT-1)) + IF (BIG .GE. SIZE) GO TO 570 + BIG = SIZE + IMXER = I + 570 CONTINUE + IWORK(16) = IMXER +C Set Y vector, T, and optional outputs. ------------------------------- + 580 DO 590 I = 1,N + 590 Y(I) = RWORK(I+LYH-1) + T = TN + RWORK(11) = HU + RWORK(12) = H + RWORK(13) = TN + RWORK(15) = TSW + IWORK(11) = NST + IWORK(12) = NFE + IWORK(13) = NJE + IWORK(14) = NQU + IWORK(15) = NQ + IWORK(19) = MUSED + IWORK(20) = METH + IWORK(10) = NGE + TLAST = T + RETURN +C----------------------------------------------------------------------- +C Block I. +C The following block handles all error returns due to illegal input +C (ISTATE = -3), as detected before calling the core integrator. +C First the error message routine is called. If the illegal input +C is a negative ISTATE, the run is aborted (apparent infinite loop). +C----------------------------------------------------------------------- + 601 MSG = 'DLSODAR- ISTATE(=I1) illegal.' + CALL XERRWD (MSG, 30, 1, 0, 1, ISTATE, 0, 0, 0.0D0, 0.0D0) + IF (ISTATE .LT. 0) GO TO 800 + GO TO 700 + 602 MSG = 'DLSODAR- ITASK (=I1) illegal.' + CALL XERRWD (MSG, 30, 2, 0, 1, ITASK, 0, 0, 0.0D0, 0.0D0) + GO TO 700 + 603 MSG = 'DLSODAR- ISTATE.gt.1 but DLSODAR not initialized.' + CALL XERRWD (MSG, 50, 3, 0, 0, 0, 0, 0, 0.0D0, 0.0D0) + GO TO 700 + 604 MSG = 'DLSODAR- NEQ (=I1) .lt. 1 ' + CALL XERRWD (MSG, 30, 4, 0, 1, NEQ(1), 0, 0, 0.0D0, 0.0D0) + GO TO 700 + 605 MSG = 'DLSODAR- ISTATE = 3 and NEQ increased (I1 to I2).' + CALL XERRWD (MSG, 50, 5, 0, 2, N, NEQ(1), 0, 0.0D0, 0.0D0) + GO TO 700 + 606 MSG = 'DLSODAR- ITOL (=I1) illegal. ' + CALL XERRWD (MSG, 30, 6, 0, 1, ITOL, 0, 0, 0.0D0, 0.0D0) + GO TO 700 + 607 MSG = 'DLSODAR- IOPT (=I1) illegal. ' + CALL XERRWD (MSG, 30, 7, 0, 1, IOPT, 0, 0, 0.0D0, 0.0D0) + GO TO 700 + 608 MSG = 'DLSODAR- JT (=I1) illegal. ' + CALL XERRWD (MSG, 30, 8, 0, 1, JT, 0, 0, 0.0D0, 0.0D0) + GO TO 700 + 609 MSG = 'DLSODAR- ML (=I1) illegal: .lt.0 or .ge.NEQ (=I2)' + CALL XERRWD (MSG, 50, 9, 0, 2, ML, NEQ(1), 0, 0.0D0, 0.0D0) + GO TO 700 + 610 MSG = 'DLSODAR- MU (=I1) illegal: .lt.0 or .ge.NEQ (=I2)' + CALL XERRWD (MSG, 50, 10, 0, 2, MU, NEQ(1), 0, 0.0D0, 0.0D0) + GO TO 700 + 611 MSG = 'DLSODAR- IXPR (=I1) illegal. ' + CALL XERRWD (MSG, 30, 11, 0, 1, IXPR, 0, 0, 0.0D0, 0.0D0) + GO TO 700 + 612 MSG = 'DLSODAR- MXSTEP (=I1) .lt. 0 ' + CALL XERRWD (MSG, 30, 12, 0, 1, MXSTEP, 0, 0, 0.0D0, 0.0D0) + GO TO 700 + 613 MSG = 'DLSODAR- MXHNIL (=I1) .lt. 0 ' + CALL XERRWD (MSG, 30, 13, 0, 1, MXHNIL, 0, 0, 0.0D0, 0.0D0) + GO TO 700 + 614 MSG = 'DLSODAR- TOUT (=R1) behind T (=R2) ' + CALL XERRWD (MSG, 40, 14, 0, 0, 0, 0, 2, TOUT, T) + MSG = ' Integration direction is given by H0 (=R1) ' + CALL XERRWD (MSG, 50, 14, 0, 0, 0, 0, 1, H0, 0.0D0) + GO TO 700 + 615 MSG = 'DLSODAR- HMAX (=R1) .lt. 0.0 ' + CALL XERRWD (MSG, 30, 15, 0, 0, 0, 0, 1, HMAX, 0.0D0) + GO TO 700 + 616 MSG = 'DLSODAR- HMIN (=R1) .lt. 0.0 ' + CALL XERRWD (MSG, 30, 16, 0, 0, 0, 0, 1, HMIN, 0.0D0) + GO TO 700 + 617 MSG='DLSODAR- RWORK length needed, LENRW(=I1), exceeds LRW(=I2) ' + CALL XERRWD (MSG, 60, 17, 0, 2, LENRW, LRW, 0, 0.0D0, 0.0D0) + GO TO 700 + 618 MSG='DLSODAR- IWORK length needed, LENIW(=I1), exceeds LIW(=I2) ' + CALL XERRWD (MSG, 60, 18, 0, 2, LENIW, LIW, 0, 0.0D0, 0.0D0) + GO TO 700 + 619 MSG = 'DLSODAR- RTOL(I1) is R1 .lt. 0.0 ' + CALL XERRWD (MSG, 40, 19, 0, 1, I, 0, 1, RTOLI, 0.0D0) + GO TO 700 + 620 MSG = 'DLSODAR- ATOL(I1) is R1 .lt. 0.0 ' + CALL XERRWD (MSG, 40, 20, 0, 1, I, 0, 1, ATOLI, 0.0D0) + GO TO 700 + 621 EWTI = RWORK(LEWT+I-1) + MSG = 'DLSODAR- EWT(I1) is R1 .le. 0.0 ' + CALL XERRWD (MSG, 40, 21, 0, 1, I, 0, 1, EWTI, 0.0D0) + GO TO 700 + 622 MSG='DLSODAR- TOUT(=R1) too close to T(=R2) to start integration.' + CALL XERRWD (MSG, 60, 22, 0, 0, 0, 0, 2, TOUT, T) + GO TO 700 + 623 MSG='DLSODAR- ITASK = I1 and TOUT (=R1) behind TCUR - HU (= R2) ' + CALL XERRWD (MSG, 60, 23, 0, 1, ITASK, 0, 2, TOUT, TP) + GO TO 700 + 624 MSG='DLSODAR- ITASK = 4 or 5 and TCRIT (=R1) behind TCUR (=R2) ' + CALL XERRWD (MSG, 60, 24, 0, 0, 0, 0, 2, TCRIT, TN) + GO TO 700 + 625 MSG='DLSODAR- ITASK = 4 or 5 and TCRIT (=R1) behind TOUT (=R2) ' + CALL XERRWD (MSG, 60, 25, 0, 0, 0, 0, 2, TCRIT, TOUT) + GO TO 700 + 626 MSG = 'DLSODAR- At start of problem, too much accuracy ' + CALL XERRWD (MSG, 50, 26, 0, 0, 0, 0, 0, 0.0D0, 0.0D0) + MSG=' requested for precision of machine.. See TOLSF (=R1) ' + CALL XERRWD (MSG, 60, 26, 0, 0, 0, 0, 1, TOLSF, 0.0D0) + RWORK(14) = TOLSF + GO TO 700 + 627 MSG = 'DLSODAR- Trouble in DINTDY. ITASK = I1, TOUT = R1' + CALL XERRWD (MSG, 50, 27, 0, 1, ITASK, 0, 1, TOUT, 0.0D0) + GO TO 700 + 628 MSG = 'DLSODAR- MXORDN (=I1) .lt. 0 ' + CALL XERRWD (MSG, 30, 28, 0, 1, MXORDN, 0, 0, 0.0D0, 0.0D0) + GO TO 700 + 629 MSG = 'DLSODAR- MXORDS (=I1) .lt. 0 ' + CALL XERRWD (MSG, 30, 29, 0, 1, MXORDS, 0, 0, 0.0D0, 0.0D0) + GO TO 700 + 630 MSG = 'DLSODAR- NG (=I1) .lt. 0 ' + CALL XERRWD (MSG, 30, 30, 0, 1, NG, 0, 0, 0.0D0, 0.0D0) + GO TO 700 + 631 MSG = 'DLSODAR- NG changed (from I1 to I2) illegally, ' + CALL XERRWD (MSG, 50, 31, 0, 0, 0, 0, 0, 0.0D0, 0.0D0) + MSG = ' i.e. not immediately after a root was found.' + CALL XERRWD (MSG, 50, 31, 0, 2, NGC, NG, 0, 0.0D0, 0.0D0) + GO TO 700 + 632 MSG = 'DLSODAR- One or more components of g has a root ' + CALL XERRWD (MSG, 50, 32, 0, 0, 0, 0, 0, 0.0D0, 0.0D0) + MSG = ' too near to the initial point. ' + CALL XERRWD (MSG, 40, 32, 0, 0, 0, 0, 0, 0.0D0, 0.0D0) +C + 700 ISTATE = -3 + RETURN +C + 800 MSG = 'DLSODAR- Run aborted.. apparent infinite loop. ' + CALL XERRWD (MSG, 50, 303, 2, 0, 0, 0, 0, 0.0D0, 0.0D0) + RETURN +C----------------------- End of Subroutine DLSODAR --------------------- + END +*DECK DLSODPK + SUBROUTINE DLSODPK (F, NEQ, Y, T, TOUT, ITOL, RTOL, ATOL, ITASK, + 1 ISTATE, IOPT, RWORK, LRW, IWORK, LIW, JAC, PSOL, MF) + EXTERNAL F, JAC, PSOL + INTEGER NEQ, ITOL, ITASK, ISTATE, IOPT, LRW, IWORK, LIW, MF + DOUBLE PRECISION Y, T, TOUT, RTOL, ATOL, RWORK + DIMENSION NEQ(*), Y(*), RTOL(*), ATOL(*), RWORK(LRW), IWORK(LIW) +C----------------------------------------------------------------------- +C This is the 18 November 2003 version of +C DLSODPK: Livermore Solver for Ordinary Differential equations, +C with Preconditioned Krylov iteration methods for the +C Newton correction linear systems. +C +C This version is in double precision. +C +C DLSODPK solves the initial value problem for stiff or nonstiff +C systems of first order ODEs, +C dy/dt = f(t,y) , or, in component form, +C dy(i)/dt = f(i) = f(i,t,y(1),y(2),...,y(NEQ)) (i = 1,...,NEQ). +C----------------------------------------------------------------------- +C Introduction. +C +C This is a modification of the DLSODE package which incorporates +C various preconditioned Krylov subspace iteration methods for the +C linear algebraic systems that arise in the case of stiff systems. +C +C The linear systems that must be solved have the form +C A * x = b , where A = identity - hl0 * (df/dy) . +C Here hl0 is a scalar, and df/dy is the Jacobian matrix of partial +C derivatives of f (NEQ by NEQ). +C +C The particular Krylov method is chosen by setting the second digit, +C MITER, in the method flag MF. +C Currently, the values of MITER have the following meanings: +C +C MITER = 1 means the preconditioned Scaled Incomplete +C Orthogonalization Method (SPIOM). +C +C 2 means an incomplete version of the Preconditioned Scaled +C Generalized Minimal Residual method (SPIGMR). +C This is the best choice in general. +C +C 3 means the Preconditioned Conjugate Gradient method (PCG). +C Recommended only when df/dy is symmetric or nearly so. +C +C 4 means the scaled Preconditioned Conjugate Gradient method +C (PCGS). Recommended only when D-inverse * df/dy * D is +C symmetric or nearly so, where D is the diagonal scaling +C matrix with elements 1/EWT(i) (see RTOL/ATOL description). +C +C 9 means that only a user-supplied matrix P (approximating A) +C will be used, with no Krylov iteration done. This option +C allows the user to provide the complete linear system +C solution algorithm, if desired. +C +C The user can apply preconditioning to the linear system A*x = b, +C by means of arbitrary matrices (the preconditioners). +C In the case of SPIOM and SPIGMR, one can apply left and right +C preconditioners P1 and P2, and the basic iterative method is then +C applied to the matrix (P1-inverse)*A*(P2-inverse) instead of to the +C matrix A. The product P1*P2 should be an approximation to matrix A +C such that linear systems with P1 or P2 are easier to solve than with +C A. Preconditioning from the left only or right only means using +C P2 = identity or P1 = identity, respectively. +C In the case of the PCG and PCGS methods, there is only one +C preconditioner matrix P (but it can be the product of more than one). +C It should approximate the matrix A but allow for relatively +C easy solution of linear systems with coefficient matrix P. +C For PCG, P should be positive definite symmetric, or nearly so, +C and for PCGS, the scaled preconditioner D-inverse * P * D +C should be symmetric or nearly so. +C If the Jacobian J = df/dy splits in a natural way into a sum +C J = J1 + J2, then one possible choice of preconditioners is +C P1 = identity - hl0 * J1 and P2 = identity - hl0 * J2 +C provided each of these is easy to solve (or approximately solve). +C +C----------------------------------------------------------------------- +C References: +C 1. Peter N. Brown and Alan C. Hindmarsh, Reduced Storage Matrix +C Methods in Stiff ODE Systems, J. Appl. Math. & Comp., 31 (1989), +C pp. 40-91; also L.L.N.L. Report UCRL-95088, Rev. 1, June 1987. +C 2. Alan C. Hindmarsh, ODEPACK, A Systematized Collection of ODE +C Solvers, in Scientific Computing, R. S. Stepleman et al. (Eds.), +C North-Holland, Amsterdam, 1983, pp. 55-64. +C----------------------------------------------------------------------- +C Authors: Alan C. Hindmarsh and Peter N. Brown +C Center for Applied Scientific Computing, L-561 +C Lawrence Livermore National Laboratory +C Livermore, CA 94551 +C----------------------------------------------------------------------- +C Summary of Usage. +C +C Communication between the user and the DLSODPK package, for normal +C situations, is summarized here. This summary describes only a subset +C of the full set of options available. See the full description for +C details, including optional communication, nonstandard options, +C and instructions for special situations. See also the demonstration +C program distributed with this solver. +C +C A. First provide a subroutine of the form: +C SUBROUTINE F (NEQ, T, Y, YDOT) +C DOUBLE PRECISION T, Y(*), YDOT(*) +C which supplies the vector function f by loading YDOT(i) with f(i). +C +C B. Next determine (or guess) whether or not the problem is stiff. +C Stiffness occurs when the Jacobian matrix df/dy has an eigenvalue +C whose real part is negative and large in magnitude, compared to the +C reciprocal of the t span of interest. If the problem is nonstiff, +C use a method flag MF = 10. If it is stiff, MF should be between 21 +C and 24, or possibly 29. MF = 22 is generally the best choice. +C Use 23 or 24 only if symmetry is present. Use MF = 29 if the +C complete linear system solution is to be provided by the user. +C The following four parameters must also be set. +C IWORK(1) = LWP = length of real array WP for preconditioning. +C IWORK(2) = LIWP = length of integer array IWP for preconditioning. +C IWORK(3) = JPRE = preconditioner type flag: +C = 0 for no preconditioning (P1 = P2 = P = identity) +C = 1 for left-only preconditioning (P2 = identity) +C = 2 for right-only preconditioning (P1 = identity) +C = 3 for two-sided preconditioning (and PCG or PCGS) +C IWORK(4) = JACFLG = flag for whether JAC is called. +C = 0 if JAC is not to be called, +C = 1 if JAC is to be called. +C Use JACFLG = 1 if JAC computes any nonconstant data for use in +C preconditioning, such as Jacobian elements. +C The arrays WP and IWP are work arrays under the user's control, +C for use in the routines that perform preconditioning operations. +C +C C. If the problem is stiff, you must supply two routines that deal +C with the preconditioning of the linear systems to be solved. +C These are as follows: +C +C SUBROUTINE JAC (F, NEQ, T, Y, YSV, REWT, FTY, V, HL0, WP,IWP, IER) +C DOUBLE PRECISION T, Y(*),YSV(*), REWT(*), FTY(*), V(*), HL0, WP(*) +C INTEGER IWP(*) +C This routine must evaluate and preprocess any parts of the +C Jacobian matrix df/dy involved in the preconditioners P1, P2, P. +C The Y and FTY arrays contain the current values of y and f(t,y), +C respectively, and YSV also contains the current value of y. +C The array V is work space of length NEQ. +C JAC must multiply all computed Jacobian elements by the scalar +C -HL0, add the identity matrix, and do any factorization +C operations called for, in preparation for solving linear systems +C with a coefficient matrix of P1, P2, or P. The matrix P1*P2 or P +C should be an approximation to identity - HL0 * (df/dy). +C JAC should return IER = 0 if successful, and IER .ne. 0 if not. +C (If IER .ne. 0, a smaller time step will be tried.) +C +C SUBROUTINE PSOL (NEQ, T, Y, FTY, WK, HL0, WP, IWP, B, LR, IER) +C DOUBLE PRECISION T, Y(*), FTY(*), WK(*), HL0, WP(*), B(*) +C INTEGER IWP(*) +C This routine must solve a linear system with B as right-hand +C side and one of the preconditioning matrices, P1, P2, or P, as +C coefficient matrix, and return the solution vector in B. +C LR is a flag concerning left vs right preconditioning, input +C to PSOL. PSOL is to use P1 if LR = 1 and P2 if LR = 2. +C In the case of the PCG or PCGS method, LR will be 3, and PSOL +C should solve the system P*x = B with the preconditioner matrix P. +C In the case MF = 29 (no Krylov iteration), LR will be 0, +C and PSOL is to return in B the desired approximate solution +C to A * x = B, where A = identity - HL0 * (df/dy). +C PSOL can use data generated in the JAC routine and stored in +C WP and IWP. WK is a work array of length NEQ. +C The argument HL0 is the current value of the scalar appearing +C in the linear system. If the old value, at the time of the last +C JAC call, is needed, it must have been saved by JAC in WP. +C On return, PSOL should set the error flag IER as follows: +C IER = 0 if PSOL was successful, +C IER .gt. 0 if a recoverable error occurred, meaning that the +C time step will be retried, +C IER .lt. 0 if an unrecoverable error occurred, meaning that the +C solver is to stop immediately. +C +C D. Write a main program which calls Subroutine DLSODPK once for +C each point at which answers are desired. This should also provide +C for possible use of logical unit 6 for output of error messages by +C DLSODPK. On the first call to DLSODPK, supply arguments as follows: +C F = name of subroutine for right-hand side vector f. +C This name must be declared External in calling program. +C NEQ = number of first order ODEs. +C Y = array of initial values, of length NEQ. +C T = the initial value of the independent variable. +C TOUT = first point where output is desired (.ne. T). +C ITOL = 1 or 2 according as ATOL (below) is a scalar or array. +C RTOL = relative tolerance parameter (scalar). +C ATOL = absolute tolerance parameter (scalar or array). +C the estimated local error in y(i) will be controlled so as +C to be roughly less (in magnitude) than +C EWT(i) = RTOL*ABS(Y(i)) + ATOL if ITOL = 1, or +C EWT(i) = RTOL*ABS(Y(i)) + ATOL(i) if ITOL = 2. +C Thus the local error test passes if, in each component, +C either the absolute error is less than ATOL (or ATOL(i)), +C or the relative error is less than RTOL. +C Use RTOL = 0.0 for pure absolute error control, and +C use ATOL = 0.0 (or ATOL(i) = 0.0) for pure relative error +C control. Caution: Actual (global) errors may exceed these +C local tolerances, so choose them conservatively. +C ITASK = 1 for normal computation of output values of y at t = TOUT. +C ISTATE = integer flag (input and output). Set ISTATE = 1. +C IOPT = 0 to indicate no optional inputs used. +C RWORK = real work array of length at least: +C 20 + 16*NEQ for MF = 10, +C 45 + 17*NEQ + LWP for MF = 21, +C 61 + 17*NEQ + LWP for MF = 22, +C 20 + 15*NEQ + LWP for MF = 23 or 24, +C 20 + 12*NEQ + LWP for MF = 29. +C LRW = declared length of RWORK (in user's dimension). +C IWORK = integer work array of length at least: +C 30 for MF = 10, +C 35 + LIWP for MF = 21, +C 30 + LIWP for MF = 22, 23, 24, or 29. +C LIW = declared length of IWORK (in user's dimension). +C JAC,PSOL = names of subroutines for preconditioning. +C These names must be declared External in the calling program. +C MF = method flag. Standard values are: +C 10 for nonstiff (Adams) method. +C 21 for stiff (BDF) method, with preconditioned SIOM. +C 22 for stiff method, with preconditioned GMRES method. +C 23 for stiff method, with preconditioned CG method. +C 24 for stiff method, with scaled preconditioned CG method. +C 29 for stiff method, with user's PSOL routine only. +C Note that the main program must declare arrays Y, RWORK, IWORK, +C and possibly ATOL. +C +C E. The output from the first call (or any call) is: +C Y = array of computed values of y(t) vector. +C T = corresponding value of independent variable (normally TOUT). +C ISTATE = 2 if DLSODPK was successful, negative otherwise. +C -1 means excess work done on this call (perhaps wrong MF). +C -2 means excess accuracy requested (tolerances too small). +C -3 means illegal input detected (see printed message). +C -4 means repeated error test failures (check all inputs). +C -5 means repeated convergence failures (perhaps bad JAC +C or PSOL routine supplied or wrong choice of MF or +C tolerances, or this solver is inappropriate). +C -6 means error weight became zero during problem. (Solution +C component i vanished, and ATOL or ATOL(i) = 0.) +C -7 means an unrecoverable error occurred in PSOL. +C +C F. To continue the integration after a successful return, simply +C reset TOUT and call DLSODPK again. No other parameters need be reset. +C +C----------------------------------------------------------------------- +C----------------------------------------------------------------------- +C Full Description of User Interface to DLSODPK. +C +C The user interface to DLSODPK consists of the following parts. +C +C 1. The call sequence to Subroutine DLSODPK, which is a driver +C routine for the solver. This includes descriptions of both +C the call sequence arguments and of user-supplied routines. +C Following these descriptions is a description of +C optional inputs available through the call sequence, and then +C a description of optional outputs (in the work arrays). +C +C 2. Descriptions of other routines in the DLSODPK package that may be +C (optionally) called by the user. These provide the ability to +C alter error message handling, save and restore the internal +C Common, and obtain specified derivatives of the solution y(t). +C +C 3. Descriptions of Common blocks to be declared in overlay +C or similar environments, or to be saved when doing an interrupt +C of the problem and continued solution later. +C +C 4. Description of two routines in the DLSODPK package, either of +C which the user may replace with his/her own version, if desired. +C These relate to the measurement of errors. +C +C----------------------------------------------------------------------- +C Part 1. Call Sequence. +C +C The call sequence parameters used for input only are +C F, NEQ, TOUT, ITOL, RTOL, ATOL, ITASK, IOPT, LRW, LIW, JAC, PSOL, MF, +C and those used for both input and output are +C Y, T, ISTATE. +C The work arrays RWORK and IWORK are also used for conditional and +C optional inputs and optional outputs. (The term output here refers +C to the return from Subroutine DLSODPK to the user's calling program.) +C +C The legality of input parameters will be thoroughly checked on the +C initial call for the problem, but not checked thereafter unless a +C change in input parameters is flagged by ISTATE = 3 on input. +C +C The descriptions of the call arguments are as follows. +C +C F = the name of the user-supplied subroutine defining the +C ODE system. The system must be put in the first-order +C form dy/dt = f(t,y), where f is a vector-valued function +C of the scalar t and the vector y. Subroutine F is to +C compute the function f. It is to have the form +C SUBROUTINE F (NEQ, T, Y, YDOT) +C DOUBLE PRECISION T, Y(*), YDOT(*) +C where NEQ, T, and Y are input, and the array YDOT = f(t,y) +C is output. Y and YDOT are arrays of length NEQ. +C Subroutine F should not alter Y(1),...,Y(NEQ). +C F must be declared External in the calling program. +C +C Subroutine F may access user-defined quantities in +C NEQ(2),... and/or in Y(NEQ(1)+1),... if NEQ is an array +C (dimensioned in F) and/or Y has length exceeding NEQ(1). +C See the descriptions of NEQ and Y below. +C +C If quantities computed in the F routine are needed +C externally to DLSODPK, an extra call to F should be made +C for this purpose, for consistent and accurate results. +C If only the derivative dy/dt is needed, use DINTDY instead. +C +C NEQ = the size of the ODE system (number of first order +C ordinary differential equations). Used only for input. +C NEQ may be decreased, but not increased, during the problem. +C If NEQ is decreased (with ISTATE = 3 on input), the +C remaining components of Y should be left undisturbed, if +C these are to be accessed in the user-supplied subroutines. +C +C Normally, NEQ is a scalar, and it is generally referred to +C as a scalar in this user interface description. However, +C NEQ may be an array, with NEQ(1) set to the system size. +C (The DLSODPK package accesses only NEQ(1).) In either case, +C this parameter is passed as the NEQ argument in all calls +C to F, JAC, and PSOL. Hence, if it is an array, locations +C NEQ(2),... may be used to store other integer data and pass +C it to the user-supplied subroutines. Each such routine must +C include NEQ in a Dimension statement in that case. +C +C Y = a real array for the vector of dependent variables, of +C length NEQ or more. Used for both input and output on the +C first call (ISTATE = 1), and only for output on other calls. +C On the first call, Y must contain the vector of initial +C values. On output, Y contains the computed solution vector, +C evaluated at T. If desired, the Y array may be used +C for other purposes between calls to the solver. +C +C This array is passed as the Y argument in all calls to F, +C JAC, and PSOL. Hence its length may exceed NEQ, and locations +C Y(NEQ+1),... may be used to store other real data and +C pass it to the user-supplied subroutines. (The DLSODPK +C package accesses only Y(1),...,Y(NEQ).) +C +C T = the independent variable. On input, T is used only on the +C first call, as the initial point of the integration. +C On output, after each call, T is the value at which a +C computed solution y is evaluated (usually the same as TOUT). +C On an error return, T is the farthest point reached. +C +C TOUT = the next value of t at which a computed solution is desired. +C Used only for input. +C +C When starting the problem (ISTATE = 1), TOUT may be equal +C to T for one call, then should .ne. T for the next call. +C For the initial T, an input value of TOUT .ne. T is used +C in order to determine the direction of the integration +C (i.e. the algebraic sign of the step sizes) and the rough +C scale of the problem. Integration in either direction +C (forward or backward in t) is permitted. +C +C If ITASK = 2 or 5 (one-step modes), TOUT is ignored after +C the first call (i.e. the first call with TOUT .ne. T). +C Otherwise, TOUT is required on every call. +C +C If ITASK = 1, 3, or 4, the values of TOUT need not be +C monotone, but a value of TOUT which backs up is limited +C to the current internal T interval, whose endpoints are +C TCUR - HU and TCUR (see optional outputs, below, for +C TCUR and HU). +C +C ITOL = an indicator for the type of error control. See +C description below under ATOL. Used only for input. +C +C RTOL = a relative error tolerance parameter, either a scalar or +C an array of length NEQ. See description below under ATOL. +C Input only. +C +C ATOL = an absolute error tolerance parameter, either a scalar or +C an array of length NEQ. Input only. +C +C The input parameters ITOL, RTOL, and ATOL determine +C the error control performed by the solver. The solver will +C control the vector E = (E(i)) of estimated local errors +C in y, according to an inequality of the form +C RMS-norm of ( E(i)/EWT(i) ) .le. 1, +C where EWT(i) = RTOL(i)*ABS(Y(i)) + ATOL(i), +C and the RMS-norm (root-mean-square norm) here is +C RMS-norm(v) = SQRT(sum v(i)**2 / NEQ). Here EWT = (EWT(i)) +C is a vector of weights which must always be positive, and +C the values of RTOL and ATOL should all be non-negative. +C the following table gives the types (scalar/array) of +C RTOL and ATOL, and the corresponding form of EWT(i). +C +C ITOL RTOL ATOL EWT(i) +C 1 scalar scalar RTOL*ABS(Y(i)) + ATOL +C 2 scalar array RTOL*ABS(Y(i)) + ATOL(i) +C 3 array scalar RTOL(i)*ABS(Y(i)) + ATOL +C 4 array array RTOL(i)*ABS(Y(i)) + ATOL(i) +C +C When either of these parameters is a scalar, it need not +C be dimensioned in the user's calling program. +C +C If none of the above choices (with ITOL, RTOL, and ATOL +C fixed throughout the problem) is suitable, more general +C error controls can be obtained by substituting +C user-supplied routines for the setting of EWT and/or for +C the norm calculation. See Part 4 below. +C +C If global errors are to be estimated by making a repeated +C run on the same problem with smaller tolerances, then all +C components of RTOL and ATOL (i.e. of EWT) should be scaled +C down uniformly. +C +C ITASK = an index specifying the task to be performed. +C Input only. ITASK has the following values and meanings. +C 1 means normal computation of output values of y(t) at +C t = TOUT (by overshooting and interpolating). +C 2 means take one step only and return. +C 3 means stop at the first internal mesh point at or +C beyond t = TOUT and return. +C 4 means normal computation of output values of y(t) at +C t = TOUT but without overshooting t = TCRIT. +C TCRIT must be input as RWORK(1). TCRIT may be equal to +C or beyond TOUT, but not behind it in the direction of +C integration. This option is useful if the problem +C has a singularity at or beyond t = TCRIT. +C 5 means take one step, without passing TCRIT, and return. +C TCRIT must be input as RWORK(1). +C +C Note: If ITASK = 4 or 5 and the solver reaches TCRIT +C (within roundoff), it will return T = TCRIT (exactly) to +C indicate this (unless ITASK = 4 and TOUT comes before TCRIT, +C in which case answers at t = TOUT are returned first). +C +C ISTATE = an index used for input and output to specify the +C the state of the calculation. +C +C On input, the values of ISTATE are as follows. +C 1 means this is the first call for the problem +C (initializations will be done). See note below. +C 2 means this is not the first call, and the calculation +C is to continue normally, with no change in any input +C parameters except possibly TOUT and ITASK. +C (If ITOL, RTOL, and/or ATOL are changed between calls +C with ISTATE = 2, the new values will be used but not +C tested for legality.) +C 3 means this is not the first call, and the +C calculation is to continue normally, but with +C a change in input parameters other than +C TOUT and ITASK. Changes are allowed in +C NEQ, ITOL, RTOL, ATOL, IOPT, LRW, LIW, MF, +C and any of the optional inputs except H0. +C Note: A preliminary call with TOUT = T is not counted +C as a first call here, as no initialization or checking of +C input is done. (Such a call is sometimes useful for the +C purpose of outputting the initial conditions.) +C Thus the first call for which TOUT .ne. T requires +C ISTATE = 1 on input. +C +C On output, ISTATE has the following values and meanings. +C 1 means nothing was done; TOUT = T and ISTATE = 1 on input. +C 2 means the integration was performed successfully. +C -1 means an excessive amount of work (more than MXSTEP +C steps) was done on this call, before completing the +C requested task, but the integration was otherwise +C successful as far as T. (MXSTEP is an optional input +C and is normally 500.) To continue, the user may +C simply reset ISTATE to a value .gt. 1 and call again +C (the excess work step counter will be reset to 0). +C In addition, the user may increase MXSTEP to avoid +C this error return (see below on optional inputs). +C -2 means too much accuracy was requested for the precision +C of the machine being used. This was detected before +C completing the requested task, but the integration +C was successful as far as T. To continue, the tolerance +C parameters must be reset, and ISTATE must be set +C to 3. The optional output TOLSF may be used for this +C purpose. (Note: If this condition is detected before +C taking any steps, then an illegal input return +C (ISTATE = -3) occurs instead.) +C -3 means illegal input was detected, before taking any +C integration steps. See written message for details. +C Note: If the solver detects an infinite loop of calls +C to the solver with illegal input, it will cause +C the run to stop. +C -4 means there were repeated error test failures on +C one attempted step, before completing the requested +C task, but the integration was successful as far as T. +C The problem may have a singularity, or the input +C may be inappropriate. +C -5 means there were repeated convergence test failures on +C one attempted step, before completing the requested +C task, but the integration was successful as far as T. +C -6 means EWT(i) became zero for some i during the +C integration. Pure relative error control (ATOL(i)=0.0) +C was requested on a variable which has now vanished. +C The integration was successful as far as T. +C -7 means the PSOL routine returned an unrecoverable error +C flag (IER .lt. 0). The integration was successful as +C far as T. +C +C Note: since the normal output value of ISTATE is 2, +C it does not need to be reset for normal continuation. +C Also, since a negative input value of ISTATE will be +C regarded as illegal, a negative output value requires the +C user to change it, and possibly other inputs, before +C calling the solver again. +C +C IOPT = an integer flag to specify whether or not any optional +C inputs are being used on this call. Input only. +C The optional inputs are listed separately below. +C IOPT = 0 means no optional inputs are being used. +C Default values will be used in all cases. +C IOPT = 1 means one or more optional inputs are being used. +C +C RWORK = a real working array (double precision). +C The length of RWORK must be at least +C 20 + NYH*(MAXORD + 1) + 3*NEQ + LENLS + LWP where +C NYH = the initial value of NEQ, +C MAXORD = 12 (if METH = 1) or 5 (if METH = 2) (unless a +C smaller value is given as an optional input), +C LENLS = length of work space for linear system (Krylov) +C method, excluding preconditioning: +C LENLS = 0 if MITER = 0, +C LENLS = NEQ*(MAXL+3) + MAXL**2 if MITER = 1, +C LENLS = NEQ*(MAXL+3+MIN(1,MAXL-KMP)) +C + (MAXL+3)*MAXL + 1 if MITER = 2, +C LENLS = 6*NEQ if MITER = 3 or 4, +C LENLS = 3*NEQ if MITER = 9. +C (See the MF description for METH and MITER, and the +C list of optional inputs for MAXL and KMP.) +C LWP = length of real user work space for preconditioning +C (see JAC/PSOL). +C Thus if default values are used and NEQ is constant, +C this length is: +C 20 + 16*NEQ for MF = 10, +C 45 + 24*NEQ + LWP FOR MF = 11, +C 61 + 24*NEQ + LWP FOR MF = 12, +C 20 + 22*NEQ + LWP FOR MF = 13 OR 14, +C 20 + 19*NEQ + LWP FOR MF = 19, +C 20 + 9*NEQ FOR MF = 20, +C 45 + 17*NEQ + LWP FOR MF = 21, +C 61 + 17*NEQ + LWP FOR MF = 22, +C 20 + 15*NEQ + LWP FOR MF = 23 OR 24, +C 20 + 12*NEQ + LWP for MF = 29. +C The first 20 words of RWORK are reserved for conditional +C and optional inputs and optional outputs. +C +C The following word in RWORK is a conditional input: +C RWORK(1) = TCRIT = critical value of t which the solver +C is not to overshoot. Required if ITASK is +C 4 or 5, and ignored otherwise. (See ITASK.) +C +C LRW = the length of the array RWORK, as declared by the user. +C (This will be checked by the solver.) +C +C IWORK = an integer work array. The length of IWORK must be at least +C 30 if MITER = 0 (MF = 10 or 20), +C 30 + MAXL + LIWP if MITER = 1 (MF = 11, 21), +C 30 + LIWP if MITER = 2, 3, 4, or 9. +C MAXL = 5 unless a different optional input value is given. +C LIWP = length of integer user work space for preconditioning +C (see conditional input list following). +C The first few words of IWORK are used for conditional and +C optional inputs and optional outputs. +C +C The following 4 words in IWORK are conditional inputs, +C required if MITER .ge. 1: +C IWORK(1) = LWP = length of real array WP for use in +C preconditioning (part of RWORK array). +C IWORK(2) = LIWP = length of integer array IWP for use in +C preconditioning (part of IWORK array). +C The arrays WP and IWP are work arrays under the +C user's control, for use in the routines that +C perform preconditioning operations (JAC and PSOL). +C IWORK(3) = JPRE = preconditioner type flag: +C = 0 for no preconditioning (P1 = P2 = P = identity) +C = 1 for left-only preconditioning (P2 = identity) +C = 2 for right-only preconditioning (P1 = identity) +C = 3 for two-sided preconditioning (and PCG or PCGS) +C IWORK(4) = JACFLG = flag for whether JAC is called. +C = 0 if JAC is not to be called, +C = 1 if JAC is to be called. +C Use JACFLG = 1 if JAC computes any nonconstant +C data needed in preconditioning operations, +C such as some of the Jacobian elements. +C +C LIW = the length of the array IWORK, as declared by the user. +C (This will be checked by the solver.) +C +C Note: The work arrays must not be altered between calls to DLSODPK +C for the same problem, except possibly for the conditional and +C optional inputs, and except for the last 3*NEQ words of RWORK. +C The latter space is used for internal scratch space, and so is +C available for use by the user outside DLSODPK between calls, if +C desired (but not for use by any of the user-supplied subroutines). +C +C JAC = the name of the user-supplied routine to compute any +C Jacobian elements (or approximations) involved in the +C matrix preconditioning operations (MITER .ge. 1). +C It is to have the form +C SUBROUTINE JAC (F, NEQ, T, Y, YSV, REWT, FTY, V, +C 1 HL0, WP, IWP, IER) +C DOUBLE PRECISION T, Y(*),YSV(*), REWT(*), FTY(*), V(*), +C 1 HL0, WP(*) +C INTEGER IWP(*) +C This routine must evaluate and preprocess any parts of the +C Jacobian matrix df/dy used in the preconditioners P1, P2, P. +C the Y and FTY arrays contain the current values of y and +C f(t,y), respectively, and YSV also contains the current +C value of y. The array V is work space of length +C NEQ for use by JAC. REWT is the array of reciprocal error +C weights (1/EWT). JAC must multiply all computed Jacobian +C elements by the scalar -HL0, add the identity matrix, and do +C any factorization operations called for, in preparation +C for solving linear systems with a coefficient matrix of +C P1, P2, or P. The matrix P1*P2 or P should be an +C approximation to identity - HL0 * (df/dy). JAC should +C return IER = 0 if successful, and IER .ne. 0 if not. +C (If IER .ne. 0, a smaller time step will be tried.) +C The arrays WP (of length LWP) and IWP (of length LIWP) +C are for use by JAC and PSOL for work space and for storage +C of data needed for the solution of the preconditioner +C linear systems. Their lengths and contents are under the +C user's control. +C The JAC routine may save relevant Jacobian elements (or +C approximations) used in the preconditioners, along with the +C value of HL0, and use these to reconstruct preconditioner +C matrices later without reevaluationg those elements. +C This may be cost-effective if JAC is called with HL0 +C considerably different from its earlier value, indicating +C that a corrector convergence failure has occurred because +C of the change in HL0, not because of changes in the +C value of the Jacobian. In doing this, use the saved and +C current values of HL0 to decide whether to use saved +C or reevaluated elements. +C JAC may alter V, but may not alter Y, YSV, REWT, FTY, or HL0. +C JAC must be declared External in the calling program. +C Subroutine JAC may access user-defined quantities in +C NEQ(2),... and/or in Y(NEQ(1)+1),... if NEQ is an array +C (dimensioned in JAC) and/or Y has length exceeding NEQ(1). +C See the descriptions of NEQ and Y above. +C +C PSOL = the name of the user-supplied routine for the +C solution of preconditioner linear systems. +C It is to have the form +C SUBROUTINE PSOL (NEQ, T, Y, FTY, WK,HL0, WP,IWP, B, LR,IER) +C DOUBLE PRECISION T, Y(*), FTY(*), WK(*), HL0, WP(*), B(*) +C INTEGER IWP(*) +C This routine must solve a linear system with B as right-hand +C side and one of the preconditioning matrices, P1, P2, or P, +C as coefficient matrix, and return the solution vector in B. +C LR is a flag concerning left vs right preconditioning, input +C to PSOL. PSOL is to use P1 if LR = 1 and P2 if LR = 2. +C In the case of the PCG or PCGS method, LR will be 3, and PSOL +C should solve the system P*x = B with the preconditioner P. +C In the case MITER = 9 (no Krylov iteration), LR will be 0, +C and PSOL is to return in B the desired approximate solution +C to A * x = B, where A = identity - HL0 * (df/dy). +C PSOL can use data generated in the JAC routine and stored in +C WP and IWP. +C The Y and FTY arrays contain the current values of y and +C f(t,y), respectively. The array WK is work space of length +C NEQ for use by PSOL. +C The argument HL0 is the current value of the scalar appearing +C in the linear system. If the old value, as of the last +C JAC call, is needed, it must have been saved by JAC in WP. +C On return, PSOL should set the error flag IER as follows: +C IER = 0 if PSOL was successful, +C IER .gt. 0 on a recoverable error, meaning that the +C time step will be retried, +C IER .lt. 0 on an unrecoverable error, meaning that the +C solver is to stop immediately. +C PSOL may not alter Y, FTY, or HL0. +C PSOL must be declared External in the calling program. +C Subroutine PSOL may access user-defined quantities in +C NEQ(2),... and Y(NEQ(1)+1),... if NEQ is an array +C (dimensioned in PSOL) and/or Y has length exceeding NEQ(1). +C See the descriptions of NEQ and Y above. +C +C MF = the method flag. Used only for input. The legal values of +C MF are 10, 11, 12, 13, 14, 19, 20, 21, 22, 23, 24, and 29. +C MF has decimal digits METH and MITER: MF = 10*METH + MITER. +C METH indicates the basic linear multistep method: +C METH = 1 means the implicit Adams method. +C METH = 2 means the method based on Backward +C Differentiation Formulas (BDFs). +C MITER indicates the corrector iteration method: +C MITER = 0 means functional iteration (no linear system +C is involved). +C MITER = 1 means Newton iteration with Scaled Preconditioned +C Incomplete Orthogonalization Method (SPIOM) +C for the linear systems. +C MITER = 2 means Newton iteration with Scaled Preconditioned +C Generalized Minimal Residual method (SPIGMR) +C for the linear systems. +C MITER = 3 means Newton iteration with Preconditioned +C Conjugate Gradient method (PCG) +C for the linear systems. +C MITER = 4 means Newton iteration with scaled Preconditioned +C Conjugate Gradient method (PCGS) +C for the linear systems. +C MITER = 9 means Newton iteration with only the +C user-supplied PSOL routine called (no Krylov +C iteration) for the linear systems. +C JPRE is ignored, and PSOL is called with LR = 0. +C See comments in the introduction about the choice of MITER. +C If MITER .ge. 1, the user must supply routines JAC and PSOL +C (the names are arbitrary) as described above. +C For MITER = 0, dummy arguments can be used. +C----------------------------------------------------------------------- +C Optional Inputs. +C +C The following is a list of the optional inputs provided for in the +C call sequence. (See also Part 2.) For each such input variable, +C this table lists its name as used in this documentation, its +C location in the call sequence, its meaning, and the default value. +C The use of any of these inputs requires IOPT = 1, and in that +C case all of these inputs are examined. A value of zero for any +C of these optional inputs will cause the default value to be used. +C Thus to use a subset of the optional inputs, simply preload +C locations 5 to 10 in RWORK and IWORK to 0.0 and 0 respectively, and +C then set those of interest to nonzero values. +C +C Name Location Meaning and Default Value +C +C H0 RWORK(5) the step size to be attempted on the first step. +C The default value is determined by the solver. +C +C HMAX RWORK(6) the maximum absolute step size allowed. +C The default value is infinite. +C +C HMIN RWORK(7) the minimum absolute step size allowed. +C The default value is 0. (This lower bound is not +C enforced on the final step before reaching TCRIT +C when ITASK = 4 or 5.) +C +C DELT RWORK(8) convergence test constant in Krylov iteration +C algorithm. The default is .05. +C +C MAXORD IWORK(5) the maximum order to be allowed. The default +C value is 12 if METH = 1, and 5 if METH = 2. +C If MAXORD exceeds the default value, it will +C be reduced to the default value. +C If MAXORD is changed during the problem, it may +C cause the current order to be reduced. +C +C MXSTEP IWORK(6) maximum number of (internally defined) steps +C allowed during one call to the solver. +C The default value is 500. +C +C MXHNIL IWORK(7) maximum number of messages printed (per problem) +C warning that T + H = T on a step (H = step size). +C This must be positive to result in a non-default +C value. The default value is 10. +C +C MAXL IWORK(8) maximum number of iterations in the SPIOM, SPIGMR, +C PCG, or PCGS algorithm (.le. NEQ). +C The default is MAXL = MIN(5,NEQ). +C +C KMP IWORK(9) number of vectors on which orthogonalization +C is done in SPIOM or SPIGMR algorithm (.le. MAXL). +C The default is KMP = MAXL. +C Note: When KMP .lt. MAXL and MF = 22, the length +C of RWORK must be defined accordingly. See +C the definition of RWORK above. +C----------------------------------------------------------------------- +C Optional Outputs. +C +C As optional additional output from DLSODPK, the variables listed +C below are quantities related to the performance of DLSODPK +C which are available to the user. These are communicated by way of +C the work arrays, but also have internal mnemonic names as shown. +C Except where stated otherwise, all of these outputs are defined +C on any successful return from DLSODPK, and on any return with +C ISTATE = -1, -2, -4, -5, -6, or -7. On an illegal input return +C (ISTATE = -3), they will be unchanged from their existing values +C (if any), except possibly for TOLSF, LENRW, and LENIW. +C On any error return, outputs relevant to the error will be defined, +C as noted below. +C +C Name Location Meaning +C +C HU RWORK(11) the step size in t last used (successfully). +C +C HCUR RWORK(12) the step size to be attempted on the next step. +C +C TCUR RWORK(13) the current value of the independent variable +C which the solver has actually reached, i.e. the +C current internal mesh point in t. On output, TCUR +C will always be at least as far as the argument +C T, but may be farther (if interpolation was done). +C +C TOLSF RWORK(14) a tolerance scale factor, greater than 1.0, +C computed when a request for too much accuracy was +C detected (ISTATE = -3 if detected at the start of +C the problem, ISTATE = -2 otherwise). If ITOL is +C left unaltered but RTOL and ATOL are uniformly +C scaled up by a factor of TOLSF for the next call, +C then the solver is deemed likely to succeed. +C (The user may also ignore TOLSF and alter the +C tolerance parameters in any other way appropriate.) +C +C NST IWORK(11) the number of steps taken for the problem so far. +C +C NFE IWORK(12) the number of f evaluations for the problem so far. +C +C NPE IWORK(13) the number of calls to JAC so far (for Jacobian +C evaluation associated with preconditioning). +C +C NQU IWORK(14) the method order last used (successfully). +C +C NQCUR IWORK(15) the order to be attempted on the next step. +C +C IMXER IWORK(16) the index of the component of largest magnitude in +C the weighted local error vector ( E(i)/EWT(i) ), +C on an error return with ISTATE = -4 or -5. +C +C LENRW IWORK(17) the length of RWORK actually required. +C This is defined on normal returns and on an illegal +C input return for insufficient storage. +C +C LENIW IWORK(18) the length of IWORK actually required. +C This is defined on normal returns and on an illegal +C input return for insufficient storage. +C +C NNI IWORK(19) number of nonlinear iterations so far (each of +C which calls an iterative linear solver). +C +C NLI IWORK(20) number of linear iterations so far. +C Note: A measure of the success of algorithm is +C the average number of linear iterations per +C nonlinear iteration, given by NLI/NNI. +C If this is close to MAXL, MAXL may be too small. +C +C NPS IWORK(21) number of preconditioning solve operations +C (PSOL calls) so far. +C +C NCFN IWORK(22) number of convergence failures of the nonlinear +C (Newton) iteration so far. +C Note: A measure of success is the overall +C rate of nonlinear convergence failures, NCFN/NST. +C +C NCFL IWORK(23) number of convergence failures of the linear +C iteration so far. +C Note: A measure of success is the overall +C rate of linear convergence failures, NCFL/NNI. +C +C The following two arrays are segments of the RWORK array which +C may also be of interest to the user as optional outputs. +C For each array, the table below gives its internal name, +C its base address in RWORK, and its description. +C +C Name Base Address Description +C +C YH 21 the Nordsieck history array, of size NYH by +C (NQCUR + 1), where NYH is the initial value +C of NEQ. For j = 0,1,...,NQCUR, column j+1 +C of YH contains HCUR**j/factorial(j) times +C the j-th derivative of the interpolating +C polynomial currently representing the solution, +C evaluated at t = TCUR. +C +C ACOR LENRW-NEQ+1 array of size NEQ used for the accumulated +C corrections on each step, scaled on output +C to represent the estimated local error in y +C on the last step. This is the vector E in +C the description of the error control. It is +C defined only on a successful return from +C DLSODPK. +C +C----------------------------------------------------------------------- +C Part 2. Other Routines Callable. +C +C The following are optional calls which the user may make to +C gain additional capabilities in conjunction with DLSODPK. +C (The routines XSETUN and XSETF are designed to conform to the +C SLATEC error handling package.) +C +C Form of Call Function +C CALL XSETUN(LUN) Set the logical unit number, LUN, for +C output of messages from DLSODPK, if +C the default is not desired. +C The default value of lun is 6. +C +C CALL XSETF(MFLAG) Set a flag to control the printing of +C messages by DLSODPK. +C MFLAG = 0 means do not print. (Danger: +C This risks losing valuable information.) +C MFLAG = 1 means print (the default). +C +C Either of the above calls may be made at +C any time and will take effect immediately. +C +C CALL DSRCPK(RSAV,ISAV,JOB) saves and restores the contents of +C the internal Common blocks used by +C DLSODPK (see Part 3 below). +C RSAV must be a real array of length 222 +C or more, and ISAV must be an integer +C array of length 50 or more. +C JOB=1 means save Common into RSAV/ISAV. +C JOB=2 means restore Common from RSAV/ISAV. +C DSRCPK is useful if one is +C interrupting a run and restarting +C later, or alternating between two or +C more problems solved with DLSODPK. +C +C CALL DINTDY(,,,,,) Provide derivatives of y, of various +C (See below) orders, at a specified point t, if +C desired. It may be called only after +C a successful return from DLSODPK. +C +C The detailed instructions for using DINTDY are as follows. +C The form of the call is: +C +C CALL DINTDY (T, K, RWORK(21), NYH, DKY, IFLAG) +C +C The input parameters are: +C +C T = value of independent variable where answers are desired +C (normally the same as the T last returned by DLSODPK). +C for valid results, T must lie between TCUR - HU and TCUR. +C (See optional outputs for TCUR and HU.) +C K = integer order of the derivative desired. K must satisfy +C 0 .le. K .le. NQCUR, where NQCUR is the current order +C (see optional outputs). The capability corresponding +C to K = 0, i.e. computing y(T), is already provided +C by DLSODPK directly. Since NQCUR .ge. 1, the first +C derivative dy/dt is always available with DINTDY. +C RWORK(21) = the base address of the history array YH. +C NYH = column length of YH, equal to the initial value of NEQ. +C +C The output parameters are: +C +C DKY = a real array of length NEQ containing the computed value +C of the K-th derivative of y(t). +C IFLAG = integer flag, returned as 0 if K and T were legal, +C -1 if K was illegal, and -2 if T was illegal. +C On an error return, a message is also written. +C----------------------------------------------------------------------- +C Part 3. Common Blocks. +C +C If DLSODPK is to be used in an overlay situation, the user +C must declare, in the primary overlay, the variables in: +C (1) the call sequence to DLSODPK, and +C (2) the two internal Common blocks +C /DLS001/ of length 255 (218 double precision words +C followed by 37 integer words), +C /DLPK01/ of length 17 (4 double precision words +C followed by 13 integer words). +C +C If DLSODPK is used on a system in which the contents of internal +C Common blocks are not preserved between calls, the user should +C declare the above Common blocks in the calling program to insure +C that their contents are preserved. +C +C If the solution of a given problem by DLSODPK is to be interrupted +C and then later continued, such as when restarting an interrupted run +C or alternating between two or more problems, the user should save, +C following the return from the last DLSODPK call prior to the +C interruption, the contents of the call sequence variables and the +C internal Common blocks, and later restore these values before the +C next DLSODPK call for that problem. To save and restore the Common +C blocks, use Subroutine DSRCPK (see Part 2 above). +C +C----------------------------------------------------------------------- +C Part 4. Optionally Replaceable Solver Routines. +C +C below are descriptions of two routines in the DLSODPK package which +C relate to the measurement of errors. Either routine can be +C replaced by a user-supplied version, if desired. However, since such +C a replacement may have a major impact on performance, it should be +C done only when absolutely necessary, and only with great caution. +C (Note: The means by which the package version of a routine is +C superseded by the user's version may be system-dependent.) +C +C (a) DEWSET. +C The following subroutine is called just before each internal +C integration step, and sets the array of error weights, EWT, as +C described under ITOL/RTOL/ATOL above: +C SUBROUTINE DEWSET (NEQ, ITOL, RTOL, ATOL, YCUR, EWT) +C where NEQ, ITOL, RTOL, and ATOL are as in the DLSODPK call sequence, +C YCUR contains the current dependent variable vector, and +C EWT is the array of weights set by DEWSET. +C +C If the user supplies this subroutine, it must return in EWT(i) +C (i = 1,...,NEQ) a positive quantity suitable for comparing errors +C in y(i) to. The EWT array returned by DEWSET is passed to the DVNORM +C routine (see below), and also used by DLSODPK in the computation +C of the optional output IMXER, the diagonal Jacobian approximation, +C and the increments for difference quotient Jacobians. +C +C In the user-supplied version of DEWSET, it may be desirable to use +C the current values of derivatives of y. Derivatives up to order NQ +C are available from the history array YH, described above under +C optional outputs. In DEWSET, YH is identical to the YCUR array, +C extended to NQ + 1 columns with a column length of NYH and scale +C factors of H**j/factorial(j). On the first call for the problem, +C given by NST = 0, NQ is 1 and H is temporarily set to 1.0. +C NYH is the initial value of NEQ. The quantities NQ, H, and NST +C can be obtained by including in DEWSET the statements: +C DOUBLE PRECISION RLS +C COMMON /DLS001/ RLS(218),ILS(37) +C NQ = ILS(33) +C NST = ILS(34) +C H = RLS(212) +C Thus, for example, the current value of dy/dt can be obtained as +C YCUR(NYH+i)/H (i=1,...,NEQ) (and the division by H is +C unnecessary when NST = 0). +C +C (b) DVNORM. +C The following is a real function routine which computes the weighted +C root-mean-square norm of a vector v: +C D = DVNORM (N, V, W) +C where: +C N = the length of the vector, +C V = real array of length N containing the vector, +C W = real array of length N containing weights, +C D = SQRT( (1/N) * sum(V(i)*W(i))**2 ). +C DVNORM is called with N = NEQ and with W(i) = 1.0/EWT(i), where +C EWT is as set by Subroutine DEWSET. +C +C If the user supplies this function, it should return a non-negative +C value of DVNORM suitable for use in the error control in DLSODPK. +C None of the arguments should be altered by DVNORM. +C For example, a user-supplied DVNORM routine might: +C -substitute a max-norm of (V(i)*W(i)) for the RMS-norm, or +C -ignore some components of V in the norm, with the effect of +C suppressing the error control on those components of y. +C----------------------------------------------------------------------- +C +C***REVISION HISTORY (YYYYMMDD) +C 19860901 DATE WRITTEN +C 19861010 Numerous minor revisions to SPIOM and SPGMR routines; +C minor corrections to prologues and comments. +C 19870114 Changed name SPGMR to SPIGMR; revised residual norm +C calculation in SPIGMR (for incomplete case); +C revised error return logic in SPIGMR; +C 19870330 Major update: corrected comments throughout; +C removed TRET from Common; rewrote EWSET with 4 loops; +C fixed t test in INTDY; added Cray directives in STODPK; +C in STODPK, fixed DELP init. and logic around PJAC call; +C combined routines to save/restore Common; +C passed LEVEL = 0 in error message calls (except run abort). +C 19871130 Added option MITER = 9; shortened WM array by 2; +C revised early return from SPIOM and SPIGMR; +C replaced copy loops with SCOPY/DCOPY calls; +C minor corrections/revisions to SOLPK, SPIGMR, ATV, ATP; +C corrections to main prologue and internal comments. +C 19880304 Corrections to type declarations in SOLPK, SPIOM, USOL. +C 19891025 Added ISTATE = -7 return; minor revisions to USOL; +C added initialization of JACFLG in main driver; +C removed YH and NYH from PKSET call list; +C minor revisions to SPIOM and SPIGMR; +C corrections to main prologue and internal comments. +C 19900803 Added YSV to JAC call list; minor comment corrections. +C 20010425 Major update: convert source lines to upper case; +C added *DECK lines; changed from 1 to * in dummy dimensions; +C changed names R1MACH/D1MACH to RUMACH/DUMACH; +C renamed routines for uniqueness across single/double prec.; +C converted intrinsic names to generic form; +C removed ILLIN and NTREP (data loaded) from Common; +C removed all 'own' variables from Common; +C changed error messages to quoted strings; +C replaced XERRWV/XERRWD with 1993 revised version; +C converted prologues, comments, error messages to mixed case; +C numerous corrections to prologues and internal comments. +C 20010507 Converted single precision source to double precision. +C 20020502 Corrected declarations in descriptions of user routines. +C 20030603 Corrected duplicate type declaration for DUMACH. +C 20031105 Restored 'own' variables to Common blocks, to enable +C interrupt/restart feature. +C 20031112 Added SAVE statements for data-loaded constants. +C 20031117 Changed internal name NPE to NJE. +C +C----------------------------------------------------------------------- +C Other routines in the DLSODPK package. +C +C In addition to Subroutine DLSODPK, the DLSODPK package includes the +C following subroutines and function routines: +C DINTDY computes an interpolated value of the y vector at t = TOUT. +C DEWSET sets the error weight vector EWT before each step. +C DVNORM computes the weighted RMS-norm of a vector. +C DSTODPK is the core integrator, which does one step of the +C integration and the associated error control. +C DCFODE sets all method coefficients and test constants. +C DPKSET interfaces between DSTODPK and the JAC routine. +C DSOLPK manages solution of linear system in Newton iteration. +C DSPIOM performs the SPIOM algorithm. +C DATV computes a scaled, preconditioned product (I-hl0*J)*v. +C DORTHOG orthogonalizes a vector against previous basis vectors. +C DHEFA generates an LU factorization of a Hessenberg matrix. +C DHESL solves a Hessenberg square linear system. +C DSPIGMR performs the SPIGMR algorithm. +C DHEQR generates a QR factorization of a Hessenberg matrix. +C DHELS finds the least squares solution of a Hessenberg system. +C DPCG performs Preconditioned Conjugate Gradient algorithm (PCG). +C DPCGS performs the PCGS algorithm. +C DATP computes the product A*p, where A = I - hl0*df/dy. +C DUSOL interfaces to the user's PSOL routine (MITER = 9). +C DSRCPK is a user-callable routine to save and restore +C the contents of the internal Common blocks. +C DAXPY, DCOPY, DDOT, DNRM2, and DSCAL are basic linear +C algebra modules (from the BLAS collection). +C DUMACH computes the unit roundoff in a machine-independent manner. +C XERRWD, XSETUN, XSETF, IXSAV, and IUMACH handle the printing of all +C error messages and warnings. XERRWD is machine-dependent. +C Note: DVNORM, DDOT, DNRM2, DUMACH, IXSAV, and IUMACH are function +C routines. All the others are subroutines. +C +C----------------------------------------------------------------------- + DOUBLE PRECISION DUMACH, DVNORM + INTEGER INIT, MXSTEP, MXHNIL, NHNIL, NSLAST, NYH, IOWNS, + 1 ICF, IERPJ, IERSL, JCUR, JSTART, KFLAG, L, + 2 LYH, LEWT, LACOR, LSAVF, LWM, LIWM, METH, MITER, + 3 MAXORD, MAXCOR, MSBP, MXNCF, N, NQ, NST, NFE, NJE, NQU + INTEGER JPRE, JACFLG, LOCWP, LOCIWP, LSAVX, KMP, MAXL, MNEWT, + 1 NNI, NLI, NPS, NCFN, NCFL + INTEGER I, I1, I2, IFLAG, IMXER, KGO, LF0, LENIW, + 1 LENIWK, LENRW, LENWM, LENWK, LIWP, LWP, MORD, MXHNL0, MXSTP0, + 2 NCFN0, NCFL0, NLI0, NNI0, NNID, NSTD, NWARN + DOUBLE PRECISION ROWNS, + 1 CCMAX, EL0, H, HMIN, HMXI, HU, RC, TN, UROUND + DOUBLE PRECISION DELT, EPCON, SQRTN, RSQRTN + DOUBLE PRECISION ATOLI, AVDIM, AYI, BIG, EWTI, H0, HMAX, HMX, + 1 RCFL, RCFN, RH, RTOLI, TCRIT, + 2 TDIST, TNEXT, TOL, TOLSF, TP, SIZE, SUM, W0 + DIMENSION MORD(2) + LOGICAL IHIT, LAVD, LCFN, LCFL, LWARN + CHARACTER*60 MSG + SAVE MORD, MXSTP0, MXHNL0 +C----------------------------------------------------------------------- +C The following two internal Common blocks contain +C (a) variables which are local to any subroutine but whose values must +C be preserved between calls to the routine ("own" variables), and +C (b) variables which are communicated between subroutines. +C The block DLS001 is declared in subroutines DLSODPK, DINTDY, DSTODPK, +C DSOLPK, and DATV. +C The block DLPK01 is declared in subroutines DLSODPK, DSTODPK, DPKSET, +C and DSOLPK. +C Groups of variables are replaced by dummy arrays in the Common +C declarations in routines where those variables are not used. +C----------------------------------------------------------------------- + COMMON /DLS001/ ROWNS(209), + 1 CCMAX, EL0, H, HMIN, HMXI, HU, RC, TN, UROUND, + 2 INIT, MXSTEP, MXHNIL, NHNIL, NSLAST, NYH, IOWNS(6), + 3 ICF, IERPJ, IERSL, JCUR, JSTART, KFLAG, L, + 4 LYH, LEWT, LACOR, LSAVF, LWM, LIWM, METH, MITER, + 5 MAXORD, MAXCOR, MSBP, MXNCF, N, NQ, NST, NFE, NJE, NQU +C + COMMON /DLPK01/ DELT, EPCON, SQRTN, RSQRTN, + 1 JPRE, JACFLG, LOCWP, LOCIWP, LSAVX, KMP, MAXL, MNEWT, + 2 NNI, NLI, NPS, NCFN, NCFL +C + DATA MORD(1),MORD(2)/12,5/, MXSTP0/500/, MXHNL0/10/ +C----------------------------------------------------------------------- +C Block A. +C This code block is executed on every call. +C It tests ISTATE and ITASK for legality and branches appropriately. +C If ISTATE .gt. 1 but the flag INIT shows that initialization has +C not yet been done, an error return occurs. +C If ISTATE = 1 and TOUT = T, return immediately. +C----------------------------------------------------------------------- + IF (ISTATE .LT. 1 .OR. ISTATE .GT. 3) GO TO 601 + IF (ITASK .LT. 1 .OR. ITASK .GT. 5) GO TO 602 + IF (ISTATE .EQ. 1) GO TO 10 + IF (INIT .EQ. 0) GO TO 603 + IF (ISTATE .EQ. 2) GO TO 200 + GO TO 20 + 10 INIT = 0 + IF (TOUT .EQ. T) RETURN +C----------------------------------------------------------------------- +C Block B. +C The next code block is executed for the initial call (ISTATE = 1), +C or for a continuation call with parameter changes (ISTATE = 3). +C It contains checking of all inputs and various initializations. +C +C First check legality of the non-optional inputs NEQ, ITOL, IOPT, MF. +C----------------------------------------------------------------------- + 20 IF (NEQ(1) .LE. 0) GO TO 604 + IF (ISTATE .EQ. 1) GO TO 25 + IF (NEQ(1) .GT. N) GO TO 605 + 25 N = NEQ(1) + IF (ITOL .LT. 1 .OR. ITOL .GT. 4) GO TO 606 + IF (IOPT .LT. 0 .OR. IOPT .GT. 1) GO TO 607 + METH = MF/10 + MITER = MF - 10*METH + IF (METH .LT. 1 .OR. METH .GT. 2) GO TO 608 + IF (MITER .LT. 0) GO TO 608 + IF (MITER .GT. 4 .AND. MITER .LT. 9) GO TO 608 + IF (MITER .GE. 1) JPRE = IWORK(3) + JACFLG = 0 + IF (MITER .GE. 1) JACFLG = IWORK(4) +C Next process and check the optional inputs. -------------------------- + IF (IOPT .EQ. 1) GO TO 40 + MAXORD = MORD(METH) + MXSTEP = MXSTP0 + MXHNIL = MXHNL0 + IF (ISTATE .EQ. 1) H0 = 0.0D0 + HMXI = 0.0D0 + HMIN = 0.0D0 + MAXL = MIN(5,N) + KMP = MAXL + DELT = 0.05D0 + GO TO 60 + 40 MAXORD = IWORK(5) + IF (MAXORD .LT. 0) GO TO 611 + IF (MAXORD .EQ. 0) MAXORD = 100 + MAXORD = MIN(MAXORD,MORD(METH)) + MXSTEP = IWORK(6) + IF (MXSTEP .LT. 0) GO TO 612 + IF (MXSTEP .EQ. 0) MXSTEP = MXSTP0 + MXHNIL = IWORK(7) + IF (MXHNIL .LT. 0) GO TO 613 + IF (MXHNIL .EQ. 0) MXHNIL = MXHNL0 + IF (ISTATE .NE. 1) GO TO 50 + H0 = RWORK(5) + IF ((TOUT - T)*H0 .LT. 0.0D0) GO TO 614 + 50 HMAX = RWORK(6) + IF (HMAX .LT. 0.0D0) GO TO 615 + HMXI = 0.0D0 + IF (HMAX .GT. 0.0D0) HMXI = 1.0D0/HMAX + HMIN = RWORK(7) + IF (HMIN .LT. 0.0D0) GO TO 616 + MAXL = IWORK(8) + IF (MAXL .EQ. 0) MAXL = 5 + MAXL = MIN(MAXL,N) + KMP = IWORK(9) + IF (KMP .EQ. 0 .OR. KMP .GT. MAXL) KMP = MAXL + DELT = RWORK(8) + IF (DELT .EQ. 0.0D0) DELT = 0.05D0 +C----------------------------------------------------------------------- +C Set work array pointers and check lengths LRW and LIW. +C Pointers to segments of RWORK and IWORK are named by prefixing L to +C the name of the segment. E.g., the segment YH starts at RWORK(LYH). +C RWORK segments (in order) are denoted YH, WM, EWT, SAVF, SAVX, ACOR. +C----------------------------------------------------------------------- + 60 LYH = 21 + IF (ISTATE .EQ. 1) NYH = N + LWM = LYH + (MAXORD + 1)*NYH + IF (MITER .EQ. 0) LENWK = 0 + IF (MITER .EQ. 1) LENWK = N*(MAXL+2) + MAXL*MAXL + IF (MITER .EQ. 2) + 1 LENWK = N*(MAXL+2+MIN(1,MAXL-KMP)) + (MAXL+3)*MAXL + 1 + IF (MITER .EQ. 3 .OR. MITER .EQ. 4) LENWK = 5*N + IF (MITER .EQ. 9) LENWK = 2*N + LWP = 0 + IF (MITER .GE. 1) LWP = IWORK(1) + LENWM = LENWK + LWP + LOCWP = LENWK + 1 + LEWT = LWM + LENWM + LSAVF = LEWT + N + LSAVX = LSAVF + N + LACOR = LSAVX + N + IF (MITER .EQ. 0) LACOR = LSAVF + N + LENRW = LACOR + N - 1 + IWORK(17) = LENRW + LIWM = 31 + LENIWK = 0 + IF (MITER .EQ. 1) LENIWK = MAXL + LIWP = 0 + IF (MITER .GE. 1) LIWP = IWORK(2) + LENIW = 30 + LENIWK + LIWP + LOCIWP = LENIWK + 1 + IWORK(18) = LENIW + IF (LENRW .GT. LRW) GO TO 617 + IF (LENIW .GT. LIW) GO TO 618 +C Check RTOL and ATOL for legality. ------------------------------------ + RTOLI = RTOL(1) + ATOLI = ATOL(1) + DO 70 I = 1,N + IF (ITOL .GE. 3) RTOLI = RTOL(I) + IF (ITOL .EQ. 2 .OR. ITOL .EQ. 4) ATOLI = ATOL(I) + IF (RTOLI .LT. 0.0D0) GO TO 619 + IF (ATOLI .LT. 0.0D0) GO TO 620 + 70 CONTINUE +C Load SQRT(N) and its reciprocal in Common. --------------------------- + SQRTN = SQRT(REAL(N)) + RSQRTN = 1.0D0/SQRTN + IF (ISTATE .EQ. 1) GO TO 100 +C If ISTATE = 3, set flag to signal parameter changes to DSTODPK. ------ + JSTART = -1 + IF (NQ .LE. MAXORD) GO TO 90 +C MAXORD was reduced below NQ. Copy YH(*,MAXORD+2) into SAVF. --------- + DO 80 I = 1,N + 80 RWORK(I+LSAVF-1) = RWORK(I+LWM-1) + 90 CONTINUE + IF (N .EQ. NYH) GO TO 200 +C NEQ was reduced. Zero part of YH to avoid undefined references. ----- + I1 = LYH + L*NYH + I2 = LYH + (MAXORD + 1)*NYH - 1 + IF (I1 .GT. I2) GO TO 200 + DO 95 I = I1,I2 + 95 RWORK(I) = 0.0D0 + GO TO 200 +C----------------------------------------------------------------------- +C Block C. +C The next block is for the initial call only (ISTATE = 1). +C It contains all remaining initializations, the initial call to F, +C and the calculation of the initial step size. +C The error weights in EWT are inverted after being loaded. +C----------------------------------------------------------------------- + 100 UROUND = DUMACH() + TN = T + IF (ITASK .NE. 4 .AND. ITASK .NE. 5) GO TO 110 + TCRIT = RWORK(1) + IF ((TCRIT - TOUT)*(TOUT - T) .LT. 0.0D0) GO TO 625 + IF (H0 .NE. 0.0D0 .AND. (T + H0 - TCRIT)*H0 .GT. 0.0D0) + 1 H0 = TCRIT - T + 110 JSTART = 0 + NHNIL = 0 + NST = 0 + NJE = 0 + NSLAST = 0 + NLI0 = 0 + NNI0 = 0 + NCFN0 = 0 + NCFL0 = 0 + NWARN = 0 + HU = 0.0D0 + NQU = 0 + CCMAX = 0.3D0 + MAXCOR = 3 + MSBP = 20 + MXNCF = 10 + NNI = 0 + NLI = 0 + NPS = 0 + NCFN = 0 + NCFL = 0 +C Initial call to F. (LF0 points to YH(*,2).) ------------------------- + LF0 = LYH + NYH + CALL F (NEQ, T, Y, RWORK(LF0)) + NFE = 1 +C Load the initial value vector in YH. --------------------------------- + DO 115 I = 1,N + 115 RWORK(I+LYH-1) = Y(I) +C Load and invert the EWT array. (H is temporarily set to 1.0.) ------- + NQ = 1 + H = 1.0D0 + CALL DEWSET (N, ITOL, RTOL, ATOL, RWORK(LYH), RWORK(LEWT)) + DO 120 I = 1,N + IF (RWORK(I+LEWT-1) .LE. 0.0D0) GO TO 621 + 120 RWORK(I+LEWT-1) = 1.0D0/RWORK(I+LEWT-1) +C----------------------------------------------------------------------- +C The coding below computes the step size, H0, to be attempted on the +C first step, unless the user has supplied a value for this. +C First check that TOUT - T differs significantly from zero. +C A scalar tolerance quantity TOL is computed, as MAX(RTOL(i)) +C if this is positive, or MAX(ATOL(i)/ABS(Y(i))) otherwise, adjusted +C so as to be between 100*UROUND and 1.0E-3. +C Then the computed value H0 is given by.. +C NEQ +C H0**2 = TOL / ( w0**-2 + (1/NEQ) * Sum ( f(i)/ywt(i) )**2 ) +C 1 +C where w0 = MAX ( ABS(T), ABS(TOUT) ), +C f(i) = i-th component of initial value of f, +C ywt(i) = EWT(i)/TOL (a weight for y(i)). +C The sign of H0 is inferred from the initial values of TOUT and T. +C----------------------------------------------------------------------- + IF (H0 .NE. 0.0D0) GO TO 180 + TDIST = ABS(TOUT - T) + W0 = MAX(ABS(T),ABS(TOUT)) + IF (TDIST .LT. 2.0D0*UROUND*W0) GO TO 622 + TOL = RTOL(1) + IF (ITOL .LE. 2) GO TO 140 + DO 130 I = 1,N + 130 TOL = MAX(TOL,RTOL(I)) + 140 IF (TOL .GT. 0.0D0) GO TO 160 + ATOLI = ATOL(1) + DO 150 I = 1,N + IF (ITOL .EQ. 2 .OR. ITOL .EQ. 4) ATOLI = ATOL(I) + AYI = ABS(Y(I)) + IF (AYI .NE. 0.0D0) TOL = MAX(TOL,ATOLI/AYI) + 150 CONTINUE + 160 TOL = MAX(TOL,100.0D0*UROUND) + TOL = MIN(TOL,0.001D0) + SUM = DVNORM (N, RWORK(LF0), RWORK(LEWT)) + SUM = 1.0D0/(TOL*W0*W0) + TOL*SUM**2 + H0 = 1.0D0/SQRT(SUM) + H0 = MIN(H0,TDIST) + H0 = SIGN(H0,TOUT-T) +C Adjust H0 if necessary to meet HMAX bound. --------------------------- + 180 RH = ABS(H0)*HMXI + IF (RH .GT. 1.0D0) H0 = H0/RH +C Load H with H0 and scale YH(*,2) by H0. ------------------------------ + H = H0 + DO 190 I = 1,N + 190 RWORK(I+LF0-1) = H0*RWORK(I+LF0-1) + GO TO 270 +C----------------------------------------------------------------------- +C Block D. +C The next code block is for continuation calls only (ISTATE = 2 or 3) +C and is to check stop conditions before taking a step. +C----------------------------------------------------------------------- + 200 NSLAST = NST + NLI0 = NLI + NNI0 = NNI + NCFN0 = NCFN + NCFL0 = NCFL + NWARN = 0 + GO TO (210, 250, 220, 230, 240), ITASK + 210 IF ((TN - TOUT)*H .LT. 0.0D0) GO TO 250 + CALL DINTDY (TOUT, 0, RWORK(LYH), NYH, Y, IFLAG) + IF (IFLAG .NE. 0) GO TO 627 + T = TOUT + GO TO 420 + 220 TP = TN - HU*(1.0D0 + 100.0D0*UROUND) + IF ((TP - TOUT)*H .GT. 0.0D0) GO TO 623 + IF ((TN - TOUT)*H .LT. 0.0D0) GO TO 250 + GO TO 400 + 230 TCRIT = RWORK(1) + IF ((TN - TCRIT)*H .GT. 0.0D0) GO TO 624 + IF ((TCRIT - TOUT)*H .LT. 0.0D0) GO TO 625 + IF ((TN - TOUT)*H .LT. 0.0D0) GO TO 245 + CALL DINTDY (TOUT, 0, RWORK(LYH), NYH, Y, IFLAG) + IF (IFLAG .NE. 0) GO TO 627 + T = TOUT + GO TO 420 + 240 TCRIT = RWORK(1) + IF ((TN - TCRIT)*H .GT. 0.0D0) GO TO 624 + 245 HMX = ABS(TN) + ABS(H) + IHIT = ABS(TN - TCRIT) .LE. 100.0D0*UROUND*HMX + IF (IHIT) GO TO 400 + TNEXT = TN + H*(1.0D0 + 4.0D0*UROUND) + IF ((TNEXT - TCRIT)*H .LE. 0.0D0) GO TO 250 + H = (TCRIT - TN)*(1.0D0 - 4.0D0*UROUND) + IF (ISTATE .EQ. 2) JSTART = -2 +C----------------------------------------------------------------------- +C Block E. +C The next block is normally executed for all calls and contains +C the call to the one-step core integrator DSTODPK. +C +C This is a looping point for the integration steps. +C +C First check for too many steps being taken, +C Check for poor Newton/Krylov method performance, update EWT (if not +C at start of problem), check for too much accuracy being requested, +C and check for H below the roundoff level in T. +C----------------------------------------------------------------------- + 250 CONTINUE + IF ((NST-NSLAST) .GE. MXSTEP) GO TO 500 + NSTD = NST - NSLAST + NNID = NNI - NNI0 + IF (NSTD .LT. 10 .OR. NNID .EQ. 0) GO TO 255 + AVDIM = REAL(NLI - NLI0)/REAL(NNID) + RCFN = REAL(NCFN - NCFN0)/REAL(NSTD) + RCFL = REAL(NCFL - NCFL0)/REAL(NNID) + LAVD = AVDIM .GT. (MAXL - 0.05D0) + LCFN = RCFN .GT. 0.9D0 + LCFL = RCFL .GT. 0.9D0 + LWARN = LAVD .OR. LCFN .OR. LCFL + IF (.NOT.LWARN) GO TO 255 + NWARN = NWARN + 1 + IF (NWARN .GT. 10) GO TO 255 + IF (LAVD) THEN + MSG='DLSODPK- Warning. Poor iterative algorithm performance seen ' + CALL XERRWD (MSG, 60, 111, 0, 0, 0, 0, 0, 0.0D0, 0.0D0) + ENDIF + IF (LAVD) THEN + MSG=' at T = R1 by average no. of linear iterations = R2 ' + CALL XERRWD (MSG, 60, 111, 0, 0, 0, 0, 2, TN, AVDIM) + ENDIF + IF (LCFN) THEN + MSG='DLSODPK- Warning. Poor iterative algorithm performance seen ' + CALL XERRWD (MSG, 60, 112, 0, 0, 0, 0, 0, 0.0D0, 0.0D0) + ENDIF + IF (LCFN) THEN + MSG=' at T = R1 by nonlinear convergence failure rate = R2 ' + CALL XERRWD (MSG, 60, 112, 0, 0, 0, 0, 2, TN, RCFN) + ENDIF + IF (LCFL) THEN + MSG='DLSODPK- Warning. Poor iterative algorithm performance seen ' + CALL XERRWD (MSG, 60, 113, 0, 0, 0, 0, 0, 0.0D0, 0.0D0) + ENDIF + IF (LCFL) THEN + MSG=' at T = R1 by linear convergence failure rate = R2 ' + CALL XERRWD (MSG, 60, 113, 0, 0, 0, 0, 2, TN, RCFL) + ENDIF + 255 CONTINUE + CALL DEWSET (N, ITOL, RTOL, ATOL, RWORK(LYH), RWORK(LEWT)) + DO 260 I = 1,N + IF (RWORK(I+LEWT-1) .LE. 0.0D0) GO TO 510 + 260 RWORK(I+LEWT-1) = 1.0D0/RWORK(I+LEWT-1) + 270 TOLSF = UROUND*DVNORM (N, RWORK(LYH), RWORK(LEWT)) + IF (TOLSF .LE. 1.0D0) GO TO 280 + TOLSF = TOLSF*2.0D0 + IF (NST .EQ. 0) GO TO 626 + GO TO 520 + 280 IF ((TN + H) .NE. TN) GO TO 290 + NHNIL = NHNIL + 1 + IF (NHNIL .GT. MXHNIL) GO TO 290 + MSG = 'DLSODPK- Warning..Internal T(=R1) and H(=R2) are ' + CALL XERRWD (MSG, 50, 101, 0, 0, 0, 0, 0, 0.0D0, 0.0D0) + MSG=' such that in the machine, T + H = T on the next step ' + CALL XERRWD (MSG, 60, 101, 0, 0, 0, 0, 0, 0.0D0, 0.0D0) + MSG = ' (H = step size). Solver will continue anyway.' + CALL XERRWD (MSG, 50, 101, 0, 0, 0, 0, 2, TN, H) + IF (NHNIL .LT. MXHNIL) GO TO 290 + MSG = 'DLSODPK- Above warning has been issued I1 times. ' + CALL XERRWD (MSG, 50, 102, 0, 0, 0, 0, 0, 0.0D0, 0.0D0) + MSG = ' It will not be issued again for this problem.' + CALL XERRWD (MSG, 50, 102, 0, 1, MXHNIL, 0, 0, 0.0D0, 0.0D0) + 290 CONTINUE +C----------------------------------------------------------------------- +C CALL DSTODPK(NEQ,Y,YH,NYH,YH,EWT,SAVF,SAVX,ACOR,WM,IWM,F,JAC,PSOL) +C----------------------------------------------------------------------- + CALL DSTODPK (NEQ, Y, RWORK(LYH), NYH, RWORK(LYH), RWORK(LEWT), + 1 RWORK(LSAVF), RWORK(LSAVX), RWORK(LACOR), RWORK(LWM), + 2 IWORK(LIWM), F, JAC, PSOL) + KGO = 1 - KFLAG + GO TO (300, 530, 540, 550), KGO +C----------------------------------------------------------------------- +C Block F. +C The following block handles the case of a successful return from the +C core integrator (KFLAG = 0). Test for stop conditions. +C----------------------------------------------------------------------- + 300 INIT = 1 + GO TO (310, 400, 330, 340, 350), ITASK +C ITASK = 1. If TOUT has been reached, interpolate. ------------------- + 310 IF ((TN - TOUT)*H .LT. 0.0D0) GO TO 250 + CALL DINTDY (TOUT, 0, RWORK(LYH), NYH, Y, IFLAG) + T = TOUT + GO TO 420 +C ITASK = 3. Jump to exit if TOUT was reached. ------------------------ + 330 IF ((TN - TOUT)*H .GE. 0.0D0) GO TO 400 + GO TO 250 +C ITASK = 4. See if TOUT or TCRIT was reached. Adjust H if necessary. + 340 IF ((TN - TOUT)*H .LT. 0.0D0) GO TO 345 + CALL DINTDY (TOUT, 0, RWORK(LYH), NYH, Y, IFLAG) + T = TOUT + GO TO 420 + 345 HMX = ABS(TN) + ABS(H) + IHIT = ABS(TN - TCRIT) .LE. 100.0D0*UROUND*HMX + IF (IHIT) GO TO 400 + TNEXT = TN + H*(1.0D0 + 4.0D0*UROUND) + IF ((TNEXT - TCRIT)*H .LE. 0.0D0) GO TO 250 + H = (TCRIT - TN)*(1.0D0 - 4.0D0*UROUND) + JSTART = -2 + GO TO 250 +C ITASK = 5. see if TCRIT was reached and jump to exit. --------------- + 350 HMX = ABS(TN) + ABS(H) + IHIT = ABS(TN - TCRIT) .LE. 100.0D0*UROUND*HMX +C----------------------------------------------------------------------- +C Block G. +C The following block handles all successful returns from DLSODPK. +C If ITASK .ne. 1, Y is loaded from YH and T is set accordingly. +C ISTATE is set to 2, and the optional outputs are loaded into the +C work arrays before returning. +C----------------------------------------------------------------------- + 400 DO 410 I = 1,N + 410 Y(I) = RWORK(I+LYH-1) + T = TN + IF (ITASK .NE. 4 .AND. ITASK .NE. 5) GO TO 420 + IF (IHIT) T = TCRIT + 420 ISTATE = 2 + RWORK(11) = HU + RWORK(12) = H + RWORK(13) = TN + IWORK(11) = NST + IWORK(12) = NFE + IWORK(13) = NJE + IWORK(14) = NQU + IWORK(15) = NQ + IWORK(19) = NNI + IWORK(20) = NLI + IWORK(21) = NPS + IWORK(22) = NCFN + IWORK(23) = NCFL + RETURN +C----------------------------------------------------------------------- +C Block H. +C The following block handles all unsuccessful returns other than +C those for illegal input. First the error message routine is called. +C If there was an error test or convergence test failure, IMXER is set. +C Then Y is loaded from YH and T is set to TN. +C The optional outputs are loaded into the work arrays before returning. +C----------------------------------------------------------------------- +C The maximum number of steps was taken before reaching TOUT. ---------- + 500 MSG = 'DLSODPK- At current T (=R1), MXSTEP (=I1) steps ' + CALL XERRWD (MSG, 50, 201, 0, 0, 0, 0, 0, 0.0D0, 0.0D0) + MSG = ' taken on this call before reaching TOUT ' + CALL XERRWD (MSG, 50, 201, 0, 1, MXSTEP, 0, 1, TN, 0.0D0) + ISTATE = -1 + GO TO 580 +C EWT(i) .le. 0.0 for some i (not at start of problem). ---------------- + 510 EWTI = RWORK(LEWT+I-1) + MSG = 'DLSODPK- At T (=R1), EWT(I1) has become R2.le.0. ' + CALL XERRWD (MSG, 50, 202, 0, 1, I, 0, 2, TN, EWTI) + ISTATE = -6 + GO TO 580 +C Too much accuracy requested for machine precision. ------------------- + 520 MSG = 'DLSODPK- At T (=R1), too much accuracy requested ' + CALL XERRWD (MSG, 50, 203, 0, 0, 0, 0, 0, 0.0D0, 0.0D0) + MSG = ' for precision of machine.. See TOLSF (=R2) ' + CALL XERRWD (MSG, 50, 203, 0, 0, 0, 0, 2, TN, TOLSF) + RWORK(14) = TOLSF + ISTATE = -2 + GO TO 580 +C KFLAG = -1. Error test failed repeatedly or with ABS(H) = HMIN. ----- + 530 MSG = 'DLSODPK- At T(=R1), step size H(=R2), the error ' + CALL XERRWD (MSG, 50, 204, 0, 0, 0, 0, 0, 0.0D0, 0.0D0) + MSG = ' test failed repeatedly or with ABS(H) = HMIN' + CALL XERRWD (MSG, 50, 204, 0, 0, 0, 0, 2, TN, H) + ISTATE = -4 + GO TO 560 +C KFLAG = -2. Convergence failed repeatedly or with ABS(H) = HMIN. ---- + 540 MSG = 'DLSODPK- At T (=R1) and step size H (=R2), the ' + CALL XERRWD (MSG, 50, 205, 0, 0, 0, 0, 0, 0.0D0, 0.0D0) + MSG = ' corrector convergence failed repeatedly ' + CALL XERRWD (MSG, 50, 205, 0, 0, 0, 0, 0, 0.0D0, 0.0D0) + MSG = ' or with ABS(H) = HMIN ' + CALL XERRWD (MSG, 30, 205, 0, 0, 0, 0, 2, TN, H) + ISTATE = -5 + GO TO 560 +C KFLAG = -3. Unrecoverable error from PSOL. -------------------------- + 550 MSG = 'DLSODPK- At T (=R1) an unrecoverable error return' + CALL XERRWD (MSG, 50, 205, 0, 0, 0, 0, 0, 0.0D0, 0.0D0) + MSG = ' was made from Subroutine PSOL ' + CALL XERRWD (MSG, 40, 205, 0, 0, 0, 0, 1, TN, 0.0D0) + ISTATE = -7 + GO TO 580 +C Compute IMXER if relevant. ------------------------------------------- + 560 BIG = 0.0D0 + IMXER = 1 + DO 570 I = 1,N + SIZE = ABS(RWORK(I+LACOR-1)*RWORK(I+LEWT-1)) + IF (BIG .GE. SIZE) GO TO 570 + BIG = SIZE + IMXER = I + 570 CONTINUE + IWORK(16) = IMXER +C Set Y vector, T, and optional outputs. ------------------------------- + 580 DO 590 I = 1,N + 590 Y(I) = RWORK(I+LYH-1) + T = TN + RWORK(11) = HU + RWORK(12) = H + RWORK(13) = TN + IWORK(11) = NST + IWORK(12) = NFE + IWORK(13) = NJE + IWORK(14) = NQU + IWORK(15) = NQ + IWORK(19) = NNI + IWORK(20) = NLI + IWORK(21) = NPS + IWORK(22) = NCFN + IWORK(23) = NCFL + RETURN +C----------------------------------------------------------------------- +C Block I. +C The following block handles all error returns due to illegal input +C (ISTATE = -3), as detected before calling the core integrator. +C First the error message routine is called. If the illegal input +C is a negative ISTATE, the run is aborted (apparent infinite loop). +C----------------------------------------------------------------------- + 601 MSG = 'DLSODPK- ISTATE(=I1) illegal.' + CALL XERRWD (MSG, 30, 1, 0, 1, ISTATE, 0, 0, 0.0D0, 0.0D0) + IF (ISTATE .LT. 0) GO TO 800 + GO TO 700 + 602 MSG = 'DLSODPK- ITASK (=I1) illegal.' + CALL XERRWD (MSG, 30, 2, 0, 1, ITASK, 0, 0, 0.0D0, 0.0D0) + GO TO 700 + 603 MSG = 'DLSODPK- ISTATE.gt.1 but DLSODPK not initialized.' + CALL XERRWD (MSG, 50, 3, 0, 0, 0, 0, 0, 0.0D0, 0.0D0) + GO TO 700 + 604 MSG = 'DLSODPK- NEQ (=I1) .lt. 1 ' + CALL XERRWD (MSG, 30, 4, 0, 1, NEQ(1), 0, 0, 0.0D0, 0.0D0) + GO TO 700 + 605 MSG = 'DLSODPK- ISTATE = 3 and NEQ increased (I1 to I2).' + CALL XERRWD (MSG, 50, 5, 0, 2, N, NEQ(1), 0, 0.0D0, 0.0D0) + GO TO 700 + 606 MSG = 'DLSODPK- ITOL (=I1) illegal. ' + CALL XERRWD (MSG, 30, 6, 0, 1, ITOL, 0, 0, 0.0D0, 0.0D0) + GO TO 700 + 607 MSG = 'DLSODPK- IOPT (=I1) illegal. ' + CALL XERRWD (MSG, 30, 7, 0, 1, IOPT, 0, 0, 0.0D0, 0.0D0) + GO TO 700 + 608 MSG = 'DLSODPK- MF (=I1) illegal. ' + CALL XERRWD (MSG, 30, 8, 0, 1, MF, 0, 0, 0.0D0, 0.0D0) + GO TO 700 + 611 MSG = 'DLSODPK- MAXORD (=I1) .lt. 0 ' + CALL XERRWD (MSG, 30, 11, 0, 1, MAXORD, 0, 0, 0.0D0, 0.0D0) + GO TO 700 + 612 MSG = 'DLSODPK- MXSTEP (=I1) .lt. 0 ' + CALL XERRWD (MSG, 30, 12, 0, 1, MXSTEP, 0, 0, 0.0D0, 0.0D0) + GO TO 700 + 613 MSG = 'DLSODPK- MXHNIL (=I1) .lt. 0 ' + CALL XERRWD (MSG, 30, 13, 0, 1, MXHNIL, 0, 0, 0.0D0, 0.0D0) + GO TO 700 + 614 MSG = 'DLSODPK- TOUT (=R1) behind T (=R2) ' + CALL XERRWD (MSG, 40, 14, 0, 0, 0, 0, 2, TOUT, T) + MSG = ' Integration direction is given by H0 (=R1) ' + CALL XERRWD (MSG, 50, 14, 0, 0, 0, 0, 1, H0, 0.0D0) + GO TO 700 + 615 MSG = 'DLSODPK- HMAX (=R1) .lt. 0.0 ' + CALL XERRWD (MSG, 30, 15, 0, 0, 0, 0, 1, HMAX, 0.0D0) + GO TO 700 + 616 MSG = 'DLSODPK- HMIN (=R1) .lt. 0.0 ' + CALL XERRWD (MSG, 30, 16, 0, 0, 0, 0, 1, HMIN, 0.0D0) + GO TO 700 + 617 MSG='DLSODPK- RWORK length needed, LENRW(=I1), exceeds LRW(=I2) ' + CALL XERRWD (MSG, 60, 17, 0, 2, LENRW, LRW, 0, 0.0D0, 0.0D0) + GO TO 700 + 618 MSG='DLSODPK- IWORK length needed, LENIW(=I1), exceeds LIW(=I2) ' + CALL XERRWD (MSG, 60, 18, 0, 2, LENIW, LIW, 0, 0.0D0, 0.0D0) + GO TO 700 + 619 MSG = 'DLSODPK- RTOL(I1) is R1 .lt. 0.0 ' + CALL XERRWD (MSG, 40, 19, 0, 1, I, 0, 1, RTOLI, 0.0D0) + GO TO 700 + 620 MSG = 'DLSODPK- ATOL(I1) is R1 .lt. 0.0 ' + CALL XERRWD (MSG, 40, 20, 0, 1, I, 0, 1, ATOLI, 0.0D0) + GO TO 700 + 621 EWTI = RWORK(LEWT+I-1) + MSG = 'DLSODPK- EWT(I1) is R1 .le. 0.0 ' + CALL XERRWD (MSG, 40, 21, 0, 1, I, 0, 1, EWTI, 0.0D0) + GO TO 700 + 622 MSG='DLSODPK- TOUT(=R1) too close to T(=R2) to start integration.' + CALL XERRWD (MSG, 60, 22, 0, 0, 0, 0, 2, TOUT, T) + GO TO 700 + 623 MSG='DLSODPK- ITASK = I1 and TOUT (=R1) behind TCUR - HU (= R2) ' + CALL XERRWD (MSG, 60, 23, 0, 1, ITASK, 0, 2, TOUT, TP) + GO TO 700 + 624 MSG='DLSODPK- ITASK = 4 or 5 and TCRIT (=R1) behind TCUR (=R2) ' + CALL XERRWD (MSG, 60, 24, 0, 0, 0, 0, 2, TCRIT, TN) + GO TO 700 + 625 MSG='DLSODPK- ITASK = 4 or 5 and TCRIT (=R1) behind TOUT (=R2) ' + CALL XERRWD (MSG, 60, 25, 0, 0, 0, 0, 2, TCRIT, TOUT) + GO TO 700 + 626 MSG = 'DLSODPK- At start of problem, too much accuracy ' + CALL XERRWD (MSG, 50, 26, 0, 0, 0, 0, 0, 0.0D0, 0.0D0) + MSG=' requested for precision of machine.. See TOLSF (=R1) ' + CALL XERRWD (MSG, 60, 26, 0, 0, 0, 0, 1, TOLSF, 0.0D0) + RWORK(14) = TOLSF + GO TO 700 + 627 MSG = 'DLSODPK- Trouble in DINTDY. ITASK = I1, TOUT = R1' + CALL XERRWD (MSG, 50, 27, 0, 1, ITASK, 0, 1, TOUT, 0.0D0) +C + 700 ISTATE = -3 + RETURN +C + 800 MSG = 'DLSODPK- Run aborted.. apparent infinite loop. ' + CALL XERRWD (MSG, 50, 303, 2, 0, 0, 0, 0, 0.0D0, 0.0D0) + RETURN +C----------------------- End of Subroutine DLSODPK --------------------- + END +*DECK DLSODKR + SUBROUTINE DLSODKR (F, NEQ, Y, T, TOUT, ITOL, RTOL, ATOL, ITASK, + 1 ISTATE, IOPT, RWORK, LRW, IWORK, LIW, JAC, PSOL, + 2 MF, G, NG, JROOT) + EXTERNAL F, JAC, PSOL, G + INTEGER NEQ, ITOL, ITASK, ISTATE, IOPT, LRW, IWORK, LIW, MF, + 1 NG, JROOT + DOUBLE PRECISION Y, T, TOUT, RTOL, ATOL, RWORK + DIMENSION NEQ(*), Y(*), RTOL(*), ATOL(*), RWORK(LRW), IWORK(LIW), + 1 JROOT(*) +C----------------------------------------------------------------------- +C This is the 18 November 2003 version of +C DLSODKR: Livermore Solver for Ordinary Differential equations, +C with preconditioned Krylov iteration methods for the +C Newton correction linear systems, and with Rootfinding. +C +C This version is in double precision. +C +C DLSODKR solves the initial value problem for stiff or nonstiff +C systems of first order ODEs, +C dy/dt = f(t,y) , or, in component form, +C dy(i)/dt = f(i) = f(i,t,y(1),y(2),...,y(NEQ)) (i = 1,...,NEQ). +C At the same time, it locates the roots of any of a set of functions +C g(i) = g(i,t,y(1),...,y(NEQ)) (i = 1,...,ng). +C +C----------------------------------------------------------------------- +C Introduction. +C +C This is a modification of the DLSODE package, and differs from it +C in five ways: +C (a) It uses various preconditioned Krylov subspace iteration methods +C for the linear algebraic systems that arise in the case of stiff +C systems. See the introductory notes below. +C (b) It does automatic switching between functional (fixpoint) +C iteration and Newton iteration in the corrector iteration. +C (c) It finds the root of at least one of a set of constraint +C functions g(i) of the independent and dependent variables. +C It finds only those roots for which some g(i), as a function +C of t, changes sign in the interval of integration. +C It then returns the solution at the root, if that occurs +C sooner than the specified stop condition, and otherwise returns +C the solution according the specified stop condition. +C (d) It supplies to JAC an input flag, JOK, which indicates whether +C JAC may (optionally) bypass the evaluation of Jacobian matrix data +C and instead process saved data (with the current value of scalar hl0). +C (e) It contains a new subroutine that calculates the initial step +C size to be attempted. +C +C +C Introduction to the Krylov methods in DLSODKR: +C +C The linear systems that must be solved have the form +C A * x = b , where A = identity - hl0 * (df/dy) . +C Here hl0 is a scalar, and df/dy is the Jacobian matrix of partial +C derivatives of f (NEQ by NEQ). +C +C The particular Krylov method is chosen by setting the second digit, +C MITER, in the method flag MF. +C Currently, the values of MITER have the following meanings: +C +C MITER = 1 means the Scaled Preconditioned Incomplete +C Orthogonalization Method (SPIOM). +C +C 2 means an incomplete version of the preconditioned scaled +C Generalized Minimal Residual method (SPIGMR). +C This is the best choice in general. +C +C 3 means the Preconditioned Conjugate Gradient method (PCG). +C Recommended only when df/dy is symmetric or nearly so. +C +C 4 means the scaled Preconditioned Conjugate Gradient method +C (PCGS). Recommended only when D-inverse * df/dy * D is +C symmetric or nearly so, where D is the diagonal scaling +C matrix with elements 1/EWT(i) (see RTOL/ATOL description). +C +C 9 means that only a user-supplied matrix P (approximating A) +C will be used, with no Krylov iteration done. This option +C allows the user to provide the complete linear system +C solution algorithm, if desired. +C +C The user can apply preconditioning to the linear system A*x = b, +C by means of arbitrary matrices (the preconditioners). +C In the case of SPIOM and SPIGMR, one can apply left and right +C preconditioners P1 and P2, and the basic iterative method is then +C applied to the matrix (P1-inverse)*A*(P2-inverse) instead of to the +C matrix A. The product P1*P2 should be an approximation to matrix A +C such that linear systems with P1 or P2 are easier to solve than with +C A. Preconditioning from the left only or right only means using +C P2 = identity or P1 = identity, respectively. +C In the case of the PCG and PCGS methods, there is only one +C preconditioner matrix P (but it can be the product of more than one). +C It should approximate the matrix A but allow for relatively +C easy solution of linear systems with coefficient matrix P. +C For PCG, P should be positive definite symmetric, or nearly so, +C and for PCGS, the scaled preconditioner D-inverse * P * D +C should be symmetric or nearly so. +C If the Jacobian J = df/dy splits in a natural way into a sum +C J = J1 + J2, then one possible choice of preconditioners is +C P1 = identity - hl0 * J1 and P2 = identity - hl0 * J2 +C provided each of these is easy to solve (or approximately solve). +C +C----------------------------------------------------------------------- +C References: +C 1. Peter N. Brown and Alan C. Hindmarsh, Reduced Storage Matrix +C Methods in Stiff ODE Systems, J. Appl. Math. & Comp., 31 (1989), +C pp. 40-91; also L.L.N.L. Report UCRL-95088, Rev. 1, June 1987. +C 2. Alan C. Hindmarsh, ODEPACK, A Systematized Collection of ODE +C Solvers, in Scientific Computing, R. S. Stepleman et al. (Eds.), +C North-Holland, Amsterdam, 1983, pp. 55-64. +C----------------------------------------------------------------------- +C Authors: Alan C. Hindmarsh and Peter N. Brown +C Center for Applied Scientific Computing, L-561 +C Lawrence Livermore National Laboratory +C Livermore, CA 94551 +C----------------------------------------------------------------------- +C Summary of Usage. +C +C Communication between the user and the DLSODKR package, for normal +C situations, is summarized here. This summary describes only a subset +C of the full set of options available. See the full description for +C details, including optional communication, nonstandard options, +C and instructions for special situations. See also the demonstration +C program distributed with this solver. +C +C A. First provide a subroutine of the form: +C SUBROUTINE F (NEQ, T, Y, YDOT) +C DOUBLE PRECISION T, Y(*), YDOT(*) +C which supplies the vector function f by loading YDOT(i) with f(i). +C +C B. Provide a subroutine of the form: +C SUBROUTINE G (NEQ, T, Y, NG, GOUT) +C DOUBLE PRECISION T, Y(*), GOUT(NG) +C which supplies the vector function g by loading GOUT(i) with +C g(i), the i-th constraint function whose root is sought. +C +C C. Next determine (or guess) whether or not the problem is stiff. +C Stiffness occurs when the Jacobian matrix df/dy has an eigenvalue +C whose real part is negative and large in magnitude, compared to the +C reciprocal of the t span of interest. If the problem is nonstiff, +C use a method flag MF = 10. If it is stiff, MF should be between 21 +C and 24, or possibly 29. MF = 22 is generally the best choice. +C Use 23 or 24 only if symmetry is present. Use MF = 29 if the +C complete linear system solution is to be provided by the user. +C The following four parameters must also be set. +C IWORK(1) = LWP = length of real array WP for preconditioning. +C IWORK(2) = LIWP = length of integer array IWP for preconditioning. +C IWORK(3) = JPRE = preconditioner type flag: +C = 0 for no preconditioning (P1 = P2 = P = identity) +C = 1 for left-only preconditioning (P2 = identity) +C = 2 for right-only preconditioning (P1 = identity) +C = 3 for two-sided preconditioning (and PCG or PCGS) +C IWORK(4) = JACFLG = flag for whether JAC is called. +C = 0 if JAC is not to be called, +C = 1 if JAC is to be called. +C Use JACFLG = 1 if JAC computes any nonconstant data for use in +C preconditioning, such as Jacobian elements. +C The arrays WP and IWP are work arrays under the user's control, +C for use in the routines that perform preconditioning operations. +C +C D. If the problem is stiff, you must supply two routines that deal +C with the preconditioning of the linear systems to be solved. +C These are as follows: +C +C SUBROUTINE JAC (F, NEQ, T, Y, YSV, REWT, FTY,V,HL0,JOK,WP,IWP,IER) +C DOUBLE PRECISION T, Y(*), YSV(*), REWT(*), FTY(*), V(*), HL0,WP(*) +C INTEGER IWP(*) +C This routine must evaluate and preprocess any parts of the +C Jacobian matrix df/dy involved in the preconditioners P1, P2, P. +C The Y and FTY arrays contain the current values of y and f(t,y), +C respectively, and YSV also contains the current value of y. +C The array V is work space of length NEQ. +C JAC must multiply all computed Jacobian elements by the scalar +C -HL0, add the identity matrix, and do any factorization +C operations called for, in preparation for solving linear systems +C with a coefficient matrix of P1, P2, or P. The matrix P1*P2 or P +C should be an approximation to identity - hl0 * (df/dy). +C JAC should return IER = 0 if successful, and IER .ne. 0 if not. +C (If IER .ne. 0, a smaller time step will be tried.) +C JAC may alter Y and V, but not YSV, REWT, FTY, or HL0. +C The JOK argument can be ignored (or see full description below). +C +C SUBROUTINE PSOL (NEQ, T, Y, FTY, WK, HL0, WP, IWP, B, LR, IER) +C DOUBLE PRECISION T, Y(*), FTY(*), WK(*), HL0, WP(*), B(*) +C INTEGER IWP(*) +C This routine must solve a linear system with B as right-hand +C side and one of the preconditioning matrices, P1, P2, or P, as +C coefficient matrix, and return the solution vector in B. +C LR is a flag concerning left vs right preconditioning, input +C to PSOL. PSOL is to use P1 if LR = 1 and P2 if LR = 2. +C In the case of the PCG or PCGS method, LR will be 3, and PSOL +C should solve the system P*x = B with the preconditioner matrix P. +C In the case MF = 29 (no Krylov iteration), LR will be 0, +C and PSOL is to return in B the desired approximate solution +C to A * x = B, where A = identity - hl0 * (df/dy). +C PSOL can use data generated in the JAC routine and stored in +C WP and IWP. WK is a work array of length NEQ. +C The argument HL0 is the current value of the scalar appearing +C in the linear system. If the old value, at the time of the last +C JAC call, is needed, it must have been saved by JAC in WP. +C on return, PSOL should set the error flag IER as follows: +C IER = 0 if PSOL was successful, +C IER .gt. 0 if a recoverable error occurred, meaning that the +C time step will be retried, +C IER .lt. 0 if an unrecoverable error occurred, meaning that the +C solver is to stop immediately. +C +C E. Write a main program which calls Subroutine DLSODKR once for +C each point at which answers are desired. This should also provide +C for possible use of logical unit 6 for output of error messages +C by DLSODKR. On the first call to DLSODKR, supply arguments as +C follows: +C F = name of subroutine for right-hand side vector f. +C This name must be declared External in calling program. +C NEQ = number of first order ODEs. +C Y = array of initial values, of length NEQ. +C T = the initial value of the independent variable. +C TOUT = first point where output is desired (.ne. T). +C ITOL = 1 or 2 according as ATOL (below) is a scalar or array. +C RTOL = relative tolerance parameter (scalar). +C ATOL = absolute tolerance parameter (scalar or array). +C The estimated local error in y(i) will be controlled so as +C to be roughly less (in magnitude) than +C EWT(i) = RTOL*ABS(Y(i)) + ATOL if ITOL = 1, or +C EWT(i) = RTOL*ABS(Y(i)) + ATOL(i) if ITOL = 2. +C Thus the local error test passes if, in each component, +C either the absolute error is less than ATOL (or ATOL(i)), +C or the relative error is less than RTOL. +C Use RTOL = 0.0 for pure absolute error control, and +C use ATOL = 0.0 (or ATOL(i) = 0.0) for pure relative error +C control. Caution: Actual (global) errors may exceed these +C local tolerances, so choose them conservatively. +C ITASK = 1 for normal computation of output values of y at t = TOUT. +C ISTATE = integer flag (input and output). Set ISTATE = 1. +C IOPT = 0 to indicate no optional inputs used. +C RWORK = real work array of length at least: +C 20 + 16*NEQ + 3*NG for MF = 10, +C 45 + 17*NEQ + 3*NG + LWP for MF = 21, +C 61 + 17*NEQ + 3*NG + LWP for MF = 22, +C 20 + 15*NEQ + 3*NG + LWP for MF = 23 or 24, +C 20 + 12*NEQ + 3*NG + LWP for MF = 29. +C LRW = declared length of RWORK (in user's dimension). +C IWORK = integer work array of length at least: +C 30 for MF = 10, +C 35 + LIWP for MF = 21, +C 30 + LIWP for MF = 22, 23, 24, or 29. +C LIW = declared length of IWORK (in user's dimension). +C JAC,PSOL = names of subroutines for preconditioning. +C These names must be declared External in the calling program. +C MF = method flag. Standard values are: +C 10 for nonstiff (Adams) method. +C 21 for stiff (BDF) method, with preconditioned SIOM. +C 22 for stiff method, with preconditioned GMRES method. +C 23 for stiff method, with preconditioned CG method. +C 24 for stiff method, with scaled preconditioned CG method. +C 29 for stiff method, with user's PSOL routine only. +C G = name of subroutine for constraint functions, whose +C roots are desired during the integration. +C This name must be declared External in calling program. +C NG = number of constraint functions g(i). If there are none, +C set NG = 0, and pass a dummy name for G. +C JROOT = integer array of length NG for output of root information. +C See next paragraph. +C Note that the main program must declare arrays Y, RWORK, IWORK, +C JROOT, and possibly ATOL. +C +C F. The output from the first call (or any call) is: +C Y = array of computed values of y(t) vector. +C T = corresponding value of independent variable (normally TOUT). +C ISTATE = 2 or 3 if DLSODKR was successful, negative otherwise. +C 2 means no root was found, and TOUT was reached as desired. +C 3 means a root was found prior to reaching TOUT. +C -1 means excess work done on this call (perhaps wrong MF). +C -2 means excess accuracy requested (tolerances too small). +C -3 means illegal input detected (see printed message). +C -4 means repeated error test failures (check all inputs). +C -5 means repeated convergence failures (perhaps bad JAC +C or PSOL routine supplied or wrong choice of MF or +C tolerances, or this solver is inappropriate). +C -6 means error weight became zero during problem. (Solution +C component i vanished, and ATOL or ATOL(i) = 0.) +C -7 means an unrecoverable error occurred in PSOL. +C JROOT = array showing roots found if ISTATE = 3 on return. +C JROOT(i) = 1 if g(i) has a root at T, or 0 otherwise. +C +C G. To continue the integration after a successful return, proceed +C as follows: +C (a) If ISTATE = 2 on return, reset TOUT and call DLSODKR again. +C (b) If ISTATE = 3 on return, reset ISTATE to 2 and call DLSODKR again. +C In either case, no other parameters need be reset. +C +C----------------------------------------------------------------------- +C----------------------------------------------------------------------- +C Full Description of User Interface to DLSODKR. +C +C The user interface to DLSODKR consists of the following parts. +C +C 1. The call sequence to Subroutine DLSODKR, which is a driver +C routine for the solver. This includes descriptions of both +C the call sequence arguments and of user-supplied routines. +C Following these descriptions is a description of +C optional inputs available through the call sequence, and then +C a description of optional outputs (in the work arrays). +C +C 2. Descriptions of other routines in the DLSODKR package that may be +C (optionally) called by the user. These provide the ability to +C alter error message handling, save and restore the internal +C Common, and obtain specified derivatives of the solution y(t). +C +C 3. Descriptions of Common blocks to be declared in overlay +C or similar environments, or to be saved when doing an interrupt +C of the problem and continued solution later. +C +C 4. Description of two routines in the DLSODKR package, either of +C which the user may replace with his/her own version, if desired. +C These relate to the measurement of errors. +C +C----------------------------------------------------------------------- +C Part 1. Call Sequence. +C +C The call sequence parameters used for input only are +C F, NEQ, TOUT, ITOL, RTOL, ATOL, ITASK, IOPT, LRW, LIW, JAC, PSOL, MF, +C G, and NG, +C that used only for output is JROOT, +C and those used for both input and output are +C Y, T, ISTATE. +C The work arrays RWORK and IWORK are also used for conditional and +C optional inputs and optional outputs. (The term output here refers +C to the return from Subroutine DLSODKR to the user's calling program.) +C +C The legality of input parameters will be thoroughly checked on the +C initial call for the problem, but not checked thereafter unless a +C change in input parameters is flagged by ISTATE = 3 on input. +C +C The descriptions of the call arguments are as follows. +C +C F = the name of the user-supplied subroutine defining the +C ODE system. The system must be put in the first-order +C form dy/dt = f(t,y), where f is a vector-valued function +C of the scalar t and the vector y. Subroutine F is to +C compute the function f. It is to have the form +C SUBROUTINE F (NEQ, T, Y, YDOT) +C DOUBLE PRECISION T, Y(*), YDOT(*) +C where NEQ, T, and Y are input, and the array YDOT = f(t,y) +C is output. Y and YDOT are arrays of length NEQ. +C Subroutine F should not alter Y(1),...,Y(NEQ). +C F must be declared External in the calling program. +C +C Subroutine F may access user-defined quantities in +C NEQ(2),... and/or in Y(NEQ(1)+1),... if NEQ is an array +C (dimensioned in F) and/or Y has length exceeding NEQ(1). +C See the descriptions of NEQ and Y below. +C +C If quantities computed in the F routine are needed +C externally to DLSODKR, an extra call to F should be made +C for this purpose, for consistent and accurate results. +C If only the derivative dy/dt is needed, use DINTDY instead. +C +C NEQ = the size of the ODE system (number of first order +C ordinary differential equations). Used only for input. +C NEQ may be decreased, but not increased, during the problem. +C If NEQ is decreased (with ISTATE = 3 on input), the +C remaining components of Y should be left undisturbed, if +C these are to be accessed in the user-supplied routines. +C +C Normally, NEQ is a scalar, and it is generally referred to +C as a scalar in this user interface description. However, +C NEQ may be an array, with NEQ(1) set to the system size. +C (The DLSODKR package accesses only NEQ(1).) In either case, +C this parameter is passed as the NEQ argument in all calls +C to the user-supplied routines. Hence, if it is an array, +C locations NEQ(2),... may be used to store other integer data +C and pass it to the user-supplied routines. Each such routine +C must include NEQ in a Dimension statement in that case. +C +C Y = a real array for the vector of dependent variables, of +C length NEQ or more. Used for both input and output on the +C first call (ISTATE = 1), and only for output on other calls. +C On the first call, Y must contain the vector of initial +C values. On output, Y contains the computed solution vector, +C evaluated at T. If desired, the Y array may be used +C for other purposes between calls to the solver. +C +C This array is passed as the Y argument in all calls to F, G, +C JAC, and PSOL. Hence its length may exceed NEQ, and +C locations Y(NEQ+1),... may be used to store other real data +C and pass it to the user-supplied routines. +C (The DLSODKR package accesses only Y(1),...,Y(NEQ).) +C +C T = the independent variable. On input, T is used only on the +C first call, as the initial point of the integration. +C On output, after each call, T is the value at which a +C computed solution y is evaluated (usually the same as TOUT). +C If a root was found, T is the computed location of the +C root reached first, on output. +C On an error return, T is the farthest point reached. +C +C TOUT = the next value of t at which a computed solution is desired. +C Used only for input. +C +C When starting the problem (ISTATE = 1), TOUT may be equal +C to T for one call, then should .ne. T for the next call. +C For the initial T, an input value of TOUT .ne. T is used +C in order to determine the direction of the integration +C (i.e. the algebraic sign of the step sizes) and the rough +C scale of the problem. Integration in either direction +C (forward or backward in t) is permitted. +C +C If ITASK = 2 or 5 (one-step modes), TOUT is ignored after +C the first call (i.e. the first call with TOUT .ne. T). +C Otherwise, TOUT is required on every call. +C +C If ITASK = 1, 3, or 4, the values of TOUT need not be +C monotone, but a value of TOUT which backs up is limited +C to the current internal T interval, whose endpoints are +C TCUR - HU and TCUR (see optional outputs, below, for +C TCUR and HU). +C +C ITOL = an indicator for the type of error control. See +C description below under ATOL. Used only for input. +C +C RTOL = a relative error tolerance parameter, either a scalar or +C an array of length NEQ. See description below under ATOL. +C Input only. +C +C ATOL = an absolute error tolerance parameter, either a scalar or +C an array of length NEQ. Input only. +C +C The input parameters ITOL, RTOL, and ATOL determine +C the error control performed by the solver. The solver will +C control the vector E = (E(i)) of estimated local errors +C in y, according to an inequality of the form +C RMS-norm of ( E(i)/EWT(i) ) .le. 1, +C where EWT(i) = RTOL(i)*ABS(Y(i)) + ATOL(i), +C and the RMS-norm (root-mean-square norm) here is +C RMS-norm(v) = SQRT(sum v(i)**2 / NEQ). Here EWT = (EWT(i)) +C is a vector of weights which must always be positive, and +C the values of RTOL and ATOL should all be non-negative. +C The following table gives the types (scalar/array) of +C RTOL and ATOL, and the corresponding form of EWT(i). +C +C ITOL RTOL ATOL EWT(i) +C 1 scalar scalar RTOL*ABS(Y(i)) + ATOL +C 2 scalar array RTOL*ABS(Y(i)) + ATOL(i) +C 3 array scalar RTOL(i)*ABS(Y(i)) + ATOL +C 4 array array RTOL(i)*ABS(Y(i)) + ATOL(i) +C +C When either of these parameters is a scalar, it need not +C be dimensioned in the user's calling program. +C +C If none of the above choices (with ITOL, RTOL, and ATOL +C fixed throughout the problem) is suitable, more general +C error controls can be obtained by substituting +C user-supplied routines for the setting of EWT and/or for +C the norm calculation. See Part 4 below. +C +C If global errors are to be estimated by making a repeated +C run on the same problem with smaller tolerances, then all +C components of RTOL and ATOL (i.e. of EWT) should be scaled +C down uniformly. +C +C ITASK = an index specifying the task to be performed. +C Input only. ITASK has the following values and meanings. +C 1 means normal computation of output values of y(t) at +C t = TOUT (by overshooting and interpolating). +C 2 means take one step only and return. +C 3 means stop at the first internal mesh point at or +C beyond t = TOUT and return. +C 4 means normal computation of output values of y(t) at +C t = TOUT but without overshooting t = TCRIT. +C TCRIT must be input as RWORK(1). TCRIT may be equal to +C or beyond TOUT, but not behind it in the direction of +C integration. This option is useful if the problem +C has a singularity at or beyond t = TCRIT. +C 5 means take one step, without passing TCRIT, and return. +C TCRIT must be input as RWORK(1). +C +C Note: If ITASK = 4 or 5 and the solver reaches TCRIT +C (within roundoff), it will return T = TCRIT (exactly) to +C indicate this (unless ITASK = 4 and TOUT comes before TCRIT, +C in which case answers at T = TOUT are returned first). +C +C ISTATE = an index used for input and output to specify the +C the state of the calculation. +C +C On input, the values of ISTATE are as follows. +C 1 means this is the first call for the problem +C (initializations will be done). See note below. +C 2 means this is not the first call, and the calculation +C is to continue normally, with no change in any input +C parameters except possibly TOUT and ITASK. +C (If ITOL, RTOL, and/or ATOL are changed between calls +C with ISTATE = 2, the new values will be used but not +C tested for legality.) +C 3 means this is not the first call, and the +C calculation is to continue normally, but with +C a change in input parameters other than +C TOUT and ITASK. Changes are allowed in +C NEQ, ITOL, RTOL, ATOL, IOPT, LRW, LIW, MF, +C and any of the optional inputs except H0. +C In addition, immediately following a return with +C ISTATE = 3 (root found), NG and G may be changed. +C (But changing NG from 0 to .gt. 0 is not allowed.) +C Note: A preliminary call with TOUT = T is not counted +C as a first call here, as no initialization or checking of +C input is done. (Such a call is sometimes useful for the +C purpose of outputting the initial conditions.) +C Thus the first call for which TOUT .ne. T requires +C ISTATE = 1 on input. +C +C On output, ISTATE has the following values and meanings. +C 1 means nothing was done; TOUT = T and ISTATE = 1 on input. +C 2 means the integration was performed successfully. +C 3 means the integration was successful, and one or more +C roots were found before satisfying the stop condition +C specified by ITASK. See JROOT. +C -1 means an excessive amount of work (more than MXSTEP +C steps) was done on this call, before completing the +C requested task, but the integration was otherwise +C successful as far as T. (MXSTEP is an optional input +C and is normally 500.) To continue, the user may +C simply reset ISTATE to a value .gt. 1 and call again +C (the excess work step counter will be reset to 0). +C In addition, the user may increase MXSTEP to avoid +C this error return (see below on optional inputs). +C -2 means too much accuracy was requested for the precision +C of the machine being used. This was detected before +C completing the requested task, but the integration +C was successful as far as T. To continue, the tolerance +C parameters must be reset, and ISTATE must be set +C to 3. The optional output TOLSF may be used for this +C purpose. (Note: If this condition is detected before +C taking any steps, then an illegal input return +C (ISTATE = -3) occurs instead.) +C -3 means illegal input was detected, before taking any +C integration steps. See written message for details. +C Note: If the solver detects an infinite loop of calls +C to the solver with illegal input, it will cause +C the run to stop. +C -4 means there were repeated error test failures on +C one attempted step, before completing the requested +C task, but the integration was successful as far as T. +C The problem may have a singularity, or the input +C may be inappropriate. +C -5 means there were repeated convergence test failures on +C one attempted step, before completing the requested +C task, but the integration was successful as far as T. +C -6 means EWT(i) became zero for some i during the +C integration. Pure relative error control (ATOL(i)=0.0) +C was requested on a variable which has now vanished. +C The integration was successful as far as T. +C -7 means the PSOL routine returned an unrecoverable error +C flag (IER .lt. 0). The integration was successful as +C far as T. +C +C Note: Since the normal output value of ISTATE is 2, +C it does not need to be reset for normal continuation. +C Also, since a negative input value of ISTATE will be +C regarded as illegal, a negative output value requires the +C user to change it, and possibly other inputs, before +C calling the solver again. +C +C IOPT = an integer flag to specify whether or not any optional +C inputs are being used on this call. Input only. +C The optional inputs are listed separately below. +C IOPT = 0 means no optional inputs are being used. +C Default values will be used in all cases. +C IOPT = 1 means one or more optional inputs are being used. +C +C RWORK = a real working array (double precision). +C The length of RWORK must be at least +C 20 + NYH*(MAXORD+1) + 3*NEQ + 3*NG + LENLS + LWP where +C NYH = the initial value of NEQ, +C MAXORD = 12 (if METH = 1) or 5 (if METH = 2) (unless a +C smaller value is given as an optional input), +C LENLS = length of work space for linear system (Krylov) +C method, excluding preconditioning: +C LENLS = 0 if MITER = 0, +C LENLS = NEQ*(MAXL+3) + MAXL**2 if MITER = 1, +C LENLS = NEQ*(MAXL+3+MIN(1,MAXL-KMP)) +C + (MAXL+3)*MAXL + 1 if MITER = 2, +C LENLS = 6*NEQ if MITER = 3 or 4, +C LENLS = 3*NEQ if MITER = 9. +C (See the MF description for METH and MITER, and the +C list of optional inputs for MAXL and KMP.) +C LWP = length of real user work space for preconditioning +C (see JAC/PSOL). +C Thus if default values are used and NEQ is constant, +C this length is: +C 20 + 16*NEQ + 3*NG for MF = 10, +C 45 + 24*NEQ + 3*NG + LWP for MF = 11, +C 61 + 24*NEQ + 3*NG + LWP for MF = 12, +C 20 + 22*NEQ + 3*NG + LWP for MF = 13 or 14, +C 20 + 19*NEQ + 3*NG + LWP for MF = 19, +C 20 + 9*NEQ + 3*NG for MF = 20, +C 45 + 17*NEQ + 3*NG + LWP for MF = 21, +C 61 + 17*NEQ + 3*NG + LWP for MF = 22, +C 20 + 15*NEQ + 3*NG + LWP for MF = 23 or 24, +C 20 + 12*NEQ + 3*NG + LWP for MF = 29. +C The first 20 words of RWORK are reserved for conditional +C and optional inputs and optional outputs. +C +C The following word in RWORK is a conditional input: +C RWORK(1) = TCRIT = critical value of t which the solver +C is not to overshoot. Required if ITASK is +C 4 or 5, and ignored otherwise. (See ITASK.) +C +C LRW = the length of the array RWORK, as declared by the user. +C (This will be checked by the solver.) +C +C IWORK = an integer work array. The length of IWORK must be at least +C 30 if MITER = 0 (MF = 10 or 20), +C 30 + MAXL + LIWP if MITER = 1 (MF = 11, 21), +C 30 + LIWP if MITER = 2, 3, 4, or 9. +C MAXL = 5 unless a different optional input value is given. +C LIWP = length of integer user work space for preconditioning +C (see conditional input list following). +C The first few words of IWORK are used for conditional and +C optional inputs and optional outputs. +C +C The following 4 words in IWORK are conditional inputs, +C required if MITER .ge. 1: +C IWORK(1) = LWP = length of real array WP for use in +C preconditioning (part of RWORK array). +C IWORK(2) = LIWP = length of integer array IWP for use in +C preconditioning (part of IWORK array). +C The arrays WP and IWP are work arrays under the +C user's control, for use in the routines that +C perform preconditioning operations (JAC and PSOL). +C IWORK(3) = JPRE = preconditioner type flag: +C = 0 for no preconditioning (P1 = P2 = P = identity) +C = 1 for left-only preconditioning (P2 = identity) +C = 2 for right-only preconditioning (P1 = identity) +C = 3 for two-sided preconditioning (and PCG or PCGS) +C IWORK(4) = JACFLG = flag for whether JAC is called. +C = 0 if JAC is not to be called, +C = 1 if JAC is to be called. +C Use JACFLG = 1 if JAC computes any nonconstant +C data needed in preconditioning operations, +C such as some of the Jacobian elements. +C +C LIW = the length of the array IWORK, as declared by the user. +C (This will be checked by the solver.) +C +C Note: The work arrays must not be altered between calls to DLSODKR +C for the same problem, except possibly for the conditional and +C optional inputs, and except for the last 3*NEQ words of RWORK. +C The latter space is used for internal scratch space, and so is +C available for use by the user outside DLSODKR between calls, if +C desired (but not for use by any of the user-supplied routines). +C +C JAC = the name of the user-supplied routine to compute any +C Jacobian elements (or approximations) involved in the +C matrix preconditioning operations (MITER .ge. 1). +C It is to have the form +C SUBROUTINE JAC (F, NEQ, T, Y, YSV, REWT, FTY, V, +C 1 HL0, JOK, WP, IWP, IER) +C DOUBLE PRECISION T, Y(*), YSV(*), REWT(*), FTY(*), V(*), +C 1 HL0, WP(*) +C INTEGER IWP(*) +C This routine must evaluate and preprocess any parts of the +C Jacobian matrix df/dy used in the preconditioners P1, P2, P. +C The Y and FTY arrays contain the current values of y and +C f(t,y), respectively, and the YSV array also contains +C the current y vector. The array V is work space of length +C NEQ for use by JAC. REWT is the array of reciprocal error +C weights (1/EWT). JAC must multiply all computed Jacobian +C elements by the scalar -HL0, add the identity matrix, and do +C any factorization operations called for, in preparation +C for solving linear systems with a coefficient matrix of +C P1, P2, or P. The matrix P1*P2 or P should be an +C approximation to identity - hl0 * (df/dy). JAC should +C return IER = 0 if successful, and IER .ne. 0 if not. +C (If IER .ne. 0, a smaller time step will be tried.) +C The arrays WP (of length LWP) and IWP (of length LIWP) +C are for use by JAC and PSOL for work space and for storage +C of data needed for the solution of the preconditioner +C linear systems. Their lengths and contents are under the +C user's control. +C The argument JOK is an input flag for optional use +C by JAC in deciding whether to recompute Jacobian elements +C or use saved values. If JOK = -1, then JAC must compute +C any relevant Jacobian elements (or approximations) used in +C the preconditioners. Optionally, JAC may also save these +C elements for later reuse. If JOK = 1, the integrator has +C made a judgement (based on the convergence history and the +C value of HL0) that JAC need not recompute Jacobian elements, +C but instead use saved values, and the current value of HL0, +C to reconstruct the preconditioner matrices, followed by +C any required factorizations. This may be cost-effective if +C Jacobian elements are costly and storage is available. +C JAC may alter Y and V, but not YSV, REWT, FTY, or HL0. +C JAC must be declared External in the calling program. +C Subroutine JAC may access user-defined quantities in +C NEQ(2),... and/or in Y(NEQ(1)+1),... if NEQ is an array +C (dimensioned in JAC) and/or Y has length exceeding NEQ(1). +C See the descriptions of NEQ and Y above. +C +C PSOL = the name of the user-supplied routine for the +C solution of preconditioner linear systems. +C It is to have the form +C SUBROUTINE PSOL (NEQ, T, Y, FTY, WK,HL0, WP,IWP, B, LR,IER) +C DOUBLE PRECISION T, Y(*), FTY(*), WK(*), HL0, WP(*), B(*) +C INTEGER IWP(*) +C This routine must solve a linear system with B as right-hand +C side and one of the preconditioning matrices, P1, P2, or P, +C as coefficient matrix, and return the solution vector in B. +C LR is a flag concerning left vs right preconditioning, input +C to PSOL. PSOL is to use P1 if LR = 1 and P2 if LR = 2. +C In the case of the PCG or PCGS method, LR will be 3, and PSOL +C should solve the system P*x = B with the preconditioner P. +C In the case MITER = 9 (no Krylov iteration), LR will be 0, +C and PSOL is to return in B the desired approximate solution +C to A * x = B, where A = identity - hl0 * (df/dy). +C PSOL can use data generated in the JAC routine and stored in +C WP and IWP. +C The Y and FTY arrays contain the current values of y and +C f(t,y), respectively. The array WK is work space of length +C NEQ for use by PSOL. +C The argument HL0 is the current value of the scalar appearing +C in the linear system. If the old value, as of the last +C JAC call, is needed, it must have been saved by JAC in WP. +C On return, PSOL should set the error flag IER as follows: +C IER = 0 if PSOL was successful, +C IER .gt. 0 on a recoverable error, meaning that the +C time step will be retried, +C IER .lt. 0 on an unrecoverable error, meaning that the +C solver is to stop immediately. +C PSOL may not alter Y, FTY, or HL0. +C PSOL must be declared External in the calling program. +C Subroutine PSOL may access user-defined quantities in +C NEQ(2),... and Y(NEQ(1)+1),... if NEQ is an array +C (dimensioned in PSOL) and/or Y has length exceeding NEQ(1). +C See the descriptions of NEQ and Y above. +C +C MF = the method flag. Used only for input. The legal values of +C MF are 10, 11, 12, 13, 14, 19, 20, 21, 22, 23, 24, and 29. +C MF has decimal digits METH and MITER: MF = 10*METH + MITER. +C METH indicates the basic linear multistep method: +C METH = 1 means the implicit Adams method. +C METH = 2 means the method based on Backward +C Differentiation Formulas (BDFs). +C MITER indicates the corrector iteration method: +C MITER = 0 means functional iteration (no linear system +C is involved). +C MITER = 1 means Newton iteration with Scaled Preconditioned +C Incomplete Orthogonalization Method (SPIOM) +C for the linear systems. +C MITER = 2 means Newton iteration with Scaled Preconditioned +C Incomplete Generalized Minimal Residual method +C (SPIGMR) for the linear systems. +C MITER = 3 means Newton iteration with Preconditioned +C Conjugate Gradient method (PCG) +C for the linear systems. +C MITER = 4 means Newton iteration with scaled preconditioned +C Conjugate Gradient method (PCGS) +C for the linear systems. +C MITER = 9 means Newton iteration with only the +C user-supplied PSOL routine called (no Krylov +C iteration) for the linear systems. +C JPRE is ignored, and PSOL is called with LR = 0. +C See comments in the introduction about the choice of MITER. +C If MITER .ge. 1, the user must supply routines JAC and PSOL +C (the names are arbitrary) as described above. +C For MITER = 0, a dummy argument can be used. +C +C G = the name of subroutine for constraint functions, whose +C roots are desired during the integration. It is to have +C the form +C SUBROUTINE G (NEQ, T, Y, NG, GOUT) +C DOUBLE PRECISION T, Y(*), GOUT(NG) +C where NEQ, T, Y, and NG are input, and the array GOUT +C is output. NEQ, T, and Y have the same meaning as in +C the F routine, and GOUT is an array of length NG. +C For i = 1,...,NG, this routine is to load into GOUT(i) +C the value at (t,y) of the i-th constraint function g(i). +C DLSODKR will find roots of the g(i) of odd multiplicity +C (i.e. sign changes) as they occur during the integration. +C G must be declared External in the calling program. +C +C Caution: Because of numerical errors in the functions +C g(i) due to roundoff and integration error, DLSODKR may +C return false roots, or return the same root at two or more +C nearly equal values of t. If such false roots are +C suspected, the user should consider smaller error tolerances +C and/or higher precision in the evaluation of the g(i). +C +C If a root of some g(i) defines the end of the problem, +C the input to DLSODKR should nevertheless allow integration +C to a point slightly past that root, so that DLSODKR can +C locate the root by interpolation. +C +C Subroutine G may access user-defined quantities in +C NEQ(2),... and Y(NEQ(1)+1),... if NEQ is an array +C (dimensioned in G) and/or Y has length exceeding NEQ(1). +C See the descriptions of NEQ and Y above. +C +C NG = number of constraint functions g(i). If there are none, +C set NG = 0, and pass a dummy name for G. +C +C JROOT = integer array of length NG. Used only for output. +C On a return with ISTATE = 3 (one or more roots found), +C JROOT(i) = 1 if g(i) has a root at t, or JROOT(i) = 0 if not. +C----------------------------------------------------------------------- +C Optional Inputs. +C +C The following is a list of the optional inputs provided for in the +C call sequence. (See also Part 2.) For each such input variable, +C this table lists its name as used in this documentation, its +C location in the call sequence, its meaning, and the default value. +C The use of any of these inputs requires IOPT = 1, and in that +C case all of these inputs are examined. A value of zero for any +C of these optional inputs will cause the default value to be used. +C Thus to use a subset of the optional inputs, simply preload +C locations 5 to 10 in RWORK and IWORK to 0.0 and 0 respectively, and +C then set those of interest to nonzero values. +C +C Name Location Meaning and Default Value +C +C H0 RWORK(5) the step size to be attempted on the first step. +C The default value is determined by the solver. +C +C HMAX RWORK(6) the maximum absolute step size allowed. +C The default value is infinite. +C +C HMIN RWORK(7) the minimum absolute step size allowed. +C The default value is 0. (This lower bound is not +C enforced on the final step before reaching TCRIT +C when ITASK = 4 or 5.) +C +C DELT RWORK(8) convergence test constant in Krylov iteration +C algorithm. The default is .05. +C +C MAXORD IWORK(5) the maximum order to be allowed. The default +C value is 12 if METH = 1, and 5 if METH = 2. +C If MAXORD exceeds the default value, it will +C be reduced to the default value. +C If MAXORD is changed during the problem, it may +C cause the current order to be reduced. +C +C MXSTEP IWORK(6) maximum number of (internally defined) steps +C allowed during one call to the solver. +C The default value is 500. +C +C MXHNIL IWORK(7) maximum number of messages printed (per problem) +C warning that T + H = T on a step (H = step size). +C This must be positive to result in a non-default +C value. The default value is 10. +C +C MAXL IWORK(8) maximum number of iterations in the SPIOM, SPIGMR, +C PCG, or PCGS algorithm (.le. NEQ). +C The default is MAXL = MIN(5,NEQ). +C +C KMP IWORK(9) number of vectors on which orthogonalization +C is done in SPIOM or SPIGMR algorithm (.le. MAXL). +C The default is KMP = MAXL. +C Note: When KMP .lt. MAXL and MF = 22, the length +C of RWORK must be defined accordingly. See +C the definition of RWORK above. +C----------------------------------------------------------------------- +C Optional Outputs. +C +C As optional additional output from DLSODKR, the variables listed +C below are quantities related to the performance of DLSODKR +C which are available to the user. These are communicated by way of +C the work arrays, but also have internal mnemonic names as shown. +C Except where stated otherwise, all of these outputs are defined +C on any successful return from DLSODKR, and on any return with +C ISTATE = -1, -2, -4, -5, -6, or -7. On an illegal input return +C (ISTATE = -3), they will be unchanged from their existing values +C (if any), except possibly for TOLSF, LENRW, and LENIW. +C On any error return, outputs relevant to the error will be defined, +C as noted below. +C +C Name Location Meaning +C +C HU RWORK(11) the step size in t last used (successfully). +C +C HCUR RWORK(12) the step size to be attempted on the next step. +C +C TCUR RWORK(13) the current value of the independent variable +C which the solver has actually reached, i.e. the +C current internal mesh point in t. On output, TCUR +C will always be at least as far as the argument +C T, but may be farther (if interpolation was done). +C +C TOLSF RWORK(14) a tolerance scale factor, greater than 1.0, +C computed when a request for too much accuracy was +C detected (ISTATE = -3 if detected at the start of +C the problem, ISTATE = -2 otherwise). If ITOL is +C left unaltered but RTOL and ATOL are uniformly +C scaled up by a factor of TOLSF for the next call, +C then the solver is deemed likely to succeed. +C (The user may also ignore TOLSF and alter the +C tolerance parameters in any other way appropriate.) +C +C NGE IWORK(10) the number of g evaluations for the problem so far. +C +C NST IWORK(11) the number of steps taken for the problem so far. +C +C NFE IWORK(12) the number of f evaluations for the problem so far. +C +C NPE IWORK(13) the number of calls to JAC so far (for evaluation +C of preconditioners). +C +C NQU IWORK(14) the method order last used (successfully). +C +C NQCUR IWORK(15) the order to be attempted on the next step. +C +C IMXER IWORK(16) the index of the component of largest magnitude in +C the weighted local error vector ( E(i)/EWT(i) ), +C on an error return with ISTATE = -4 or -5. +C +C LENRW IWORK(17) the length of RWORK actually required. +C This is defined on normal returns and on an illegal +C input return for insufficient storage. +C +C LENIW IWORK(18) the length of IWORK actually required. +C This is defined on normal returns and on an illegal +C input return for insufficient storage. +C +C NNI IWORK(19) number of nonlinear iterations so far (each of +C which calls an iterative linear solver). +C +C NLI IWORK(20) number of linear iterations so far. +C Note: A measure of the success of algorithm is +C the average number of linear iterations per +C nonlinear iteration, given by NLI/NNI. +C If this is close to MAXL, MAXL may be too small. +C +C NPS IWORK(21) number of preconditioning solve operations +C (PSOL calls) so far. +C +C NCFN IWORK(22) number of convergence failures of the nonlinear +C (Newton) iteration so far. +C Note: A measure of success is the overall +C rate of nonlinear convergence failures, NCFN/NST. +C +C NCFL IWORK(23) number of convergence failures of the linear +C iteration so far. +C Note: A measure of success is the overall +C rate of linear convergence failures, NCFL/NNI. +C +C NSFI IWORK(24) number of functional iteration steps so far. +C Note: A measure of the extent to which the +C problem is nonstiff is the ratio NSFI/NST. +C +C NJEV IWORK(25) number of JAC calls with JOK = -1 so far +C (number of evaluations of Jacobian data). +C +C The following two arrays are segments of the RWORK array which +C may also be of interest to the user as optional outputs. +C For each array, the table below gives its internal name, +C its base address in RWORK, and its description. +C +C Name Base Address Description +C +C YH 21 + 3*NG the Nordsieck history array, of size NYH by +C (NQCUR + 1), where NYH is the initial value +C of NEQ. For j = 0,1,...,NQCUR, column j+1 +C of YH contains HCUR**j/factorial(j) times +C the j-th derivative of the interpolating +C polynomial currently representing the solution, +C evaluated at t = TCUR. +C +C ACOR LENRW-NEQ+1 array of size NEQ used for the accumulated +C corrections on each step, scaled on output +C to represent the estimated local error in y +C on the last step. This is the vector E in +C the description of the error control. It is +C defined only on a successful return from +C DLSODKR. +C +C----------------------------------------------------------------------- +C Part 2. Other Routines Callable. +C +C The following are optional calls which the user may make to +C gain additional capabilities in conjunction with DLSODKR. +C (The routines XSETUN and XSETF are designed to conform to the +C SLATEC error handling package.) +C +C Form of Call Function +C CALL XSETUN(LUN) Set the logical unit number, LUN, for +C output of messages from DLSODKR, if +C the default is not desired. +C The default value of LUN is 6. +C +C CALL XSETF(MFLAG) Set a flag to control the printing of +C messages by DLSODKR. +C MFLAG = 0 means do not print. (Danger: +C This risks losing valuable information.) +C MFLAG = 1 means print (the default). +C +C Either of the above calls may be made at +C any time and will take effect immediately. +C +C CALL DSRCKR(RSAV,ISAV,JOB) saves and restores the contents of +C the internal Common blocks used by +C DLSODKR (see Part 3 below). +C RSAV must be a real array of length 228 +C or more, and ISAV must be an integer +C array of length 63 or more. +C JOB=1 means save Common into RSAV/ISAV. +C JOB=2 means restore Common from RSAV/ISAV. +C DSRCKR is useful if one is +C interrupting a run and restarting +C later, or alternating between two or +C more problems solved with DLSODKR. +C +C CALL DINTDY(,,,,,) Provide derivatives of y, of various +C (see below) orders, at a specified point t, if +C desired. It may be called only after +C a successful return from DLSODKR. +C +C The detailed instructions for using DINTDY are as follows. +C The form of the call is: +C +C LYH = 21 + 3*NG +C CALL DINTDY (T, K, RWORK(LYH), NYH, DKY, IFLAG) +C +C The input parameters are: +C +C T = value of independent variable where answers are desired +C (normally the same as the T last returned by DLSODKR). +C For valid results, T must lie between TCUR - HU and TCUR. +C (See optional outputs for TCUR and HU.) +C K = integer order of the derivative desired. K must satisfy +C 0 .le. K .le. NQCUR, where NQCUR is the current order +C (see optional outputs). The capability corresponding +C to K = 0, i.e. computing y(T), is already provided +C by DLSODKR directly. Since NQCUR .ge. 1, the first +C derivative dy/dt is always available with DINTDY. +C LYH = 21 + 3*NG = base address in RWORK of the history array YH. +C NYH = column length of YH, equal to the initial value of NEQ. +C +C The output parameters are: +C +C DKY = a real array of length NEQ containing the computed value +C of the K-th derivative of y(t). +C IFLAG = integer flag, returned as 0 if K and T were legal, +C -1 if K was illegal, and -2 if T was illegal. +C On an error return, a message is also written. +C----------------------------------------------------------------------- +C Part 3. Common Blocks. +C +C If DLSODKR is to be used in an overlay situation, the user +C must declare, in the primary overlay, the variables in: +C (1) the call sequence to DLSODKR, and +C (2) the four internal Common blocks +C /DLS001/ of length 255 (218 double precision words +C followed by 37 integer words), +C /DLS002/ of length 5 (1 double precision word +C followed by 4 integer words), +C /DLPK01/ of length 17 (4 double precision words +C followed by 13 integer words), +C /DLSR01/ of length 14 (5 double precision words +C followed by 9 integer words). +C +C If DLSODKR is used on a system in which the contents of internal +C Common blocks are not preserved between calls, the user should +C declare the above Common blocks in the calling program to insure +C that their contents are preserved. +C +C If the solution of a given problem by DLSODKR is to be interrupted +C and then later continued, such as when restarting an interrupted run +C or alternating between two or more problems, the user should save, +C following the return from the last DLSODKR call prior to the +C interruption, the contents of the call sequence variables and the +C internal Common blocks, and later restore these values before the +C next DLSODKR call for that problem. To save and restore the Common +C blocks, use Subroutine DSRCKR (see Part 2 above). +C +C----------------------------------------------------------------------- +C Part 4. Optionally Replaceable Solver Routines. +C +C Below are descriptions of two routines in the DLSODKR package which +C relate to the measurement of errors. Either routine can be +C replaced by a user-supplied version, if desired. However, since such +C a replacement may have a major impact on performance, it should be +C done only when absolutely necessary, and only with great caution. +C (Note: The means by which the package version of a routine is +C superseded by the user's version may be system-dependent.) +C +C (a) DEWSET. +C The following subroutine is called just before each internal +C integration step, and sets the array of error weights, EWT, as +C described under ITOL/RTOL/ATOL above: +C SUBROUTINE DEWSET (NEQ, ITOL, RTOL, ATOL, YCUR, EWT) +C where NEQ, ITOL, RTOL, and ATOL are as in the DLSODKR call sequence, +C YCUR contains the current dependent variable vector, and +C EWT is the array of weights set by DEWSET. +C +C If the user supplies this subroutine, it must return in EWT(i) +C (i = 1,...,NEQ) a positive quantity suitable for comparing errors +C in y(i) to. The EWT array returned by DEWSET is passed to the DVNORM +C routine (see below), and also used by DLSODKR in the computation +C of the optional output IMXER, the diagonal Jacobian approximation, +C and the increments for difference quotient Jacobians. +C +C In the user-supplied version of DEWSET, it may be desirable to use +C the current values of derivatives of y. Derivatives up to order NQ +C are available from the history array YH, described above under +C optional outputs. In DEWSET, YH is identical to the YCUR array, +C extended to NQ + 1 columns with a column length of NYH and scale +C factors of H**j/factorial(j). On the first call for the problem, +C given by NST = 0, NQ is 1 and H is temporarily set to 1.0. +C NYH is the initial value of NEQ. The quantities NQ, H, and NST +C can be obtained by including in DEWSET the statements: +C DOUBLE PRECISION RLS +C COMMON /DLS001/ RLS(218),ILS(37) +C NQ = ILS(33) +C NST = ILS(34) +C H = RLS(212) +C Thus, for example, the current value of dy/dt can be obtained as +C YCUR(NYH+i)/H (i=1,...,NEQ) (and the division by H is +C unnecessary when NST = 0). +C +C (b) DVNORM. +C The following is a real function routine which computes the weighted +C root-mean-square norm of a vector v: +C D = DVNORM (N, V, W) +C where: +C N = the length of the vector, +C V = real array of length N containing the vector, +C W = real array of length N containing weights, +C D = SQRT( (1/N) * sum(V(i)*W(i))**2 ). +C DVNORM is called with N = NEQ and with W(i) = 1.0/EWT(i), where +C EWT is as set by Subroutine DEWSET. +C +C If the user supplies this function, it should return a non-negative +C value of DVNORM suitable for use in the error control in DLSODKR. +C None of the arguments should be altered by DVNORM. +C For example, a user-supplied DVNORM routine might: +C -substitute a max-norm of (V(i)*W(i)) for the RMS-norm, or +C -ignore some components of V in the norm, with the effect of +C suppressing the error control on those components of y. +C----------------------------------------------------------------------- +C +C***REVISION HISTORY (YYYYMMDD) +C 19900117 DATE WRITTEN +C 19900503 Added iteration switching (functional/Newton). +C 19900802 Added flag for Jacobian-saving in user preconditioner. +C 19900910 Added new initial stepsize routine LHIN. +C 19901019 Corrected LHIN - y array restored. +C 19910909 Changed names STOPK to STOKA, PKSET to SETPK; +C removed unused variables in driver declarations; +C minor corrections to main prologue. +C 20010425 Major update: convert source lines to upper case; +C added *DECK lines; changed from 1 to * in dummy dimensions; +C changed names R1MACH/D1MACH to RUMACH/DUMACH; +C renamed routines for uniqueness across single/double prec.; +C converted intrinsic names to generic form; +C removed ILLIN and NTREP (data loaded) from Common; +C removed all 'own' variables from Common; +C changed error messages to quoted strings; +C replaced XERRWV/XERRWD with 1993 revised version; +C converted prologues, comments, error messages to mixed case; +C numerous corrections to prologues and internal comments. +C 20010507 Converted single precision source to double precision. +C 20020502 Corrected declarations in descriptions of user routines. +C 20030603 Corrected duplicate type declaration for DUMACH. +C 20031105 Restored 'own' variables to Common blocks, to enable +C interrupt/restart feature. +C 20031112 Added SAVE statements for data-loaded constants. +C 20031117 Changed internal name NPE to NJE. +C +C----------------------------------------------------------------------- +C Other routines in the DLSODKR package. +C +C In addition to Subroutine DLSODKR, the DLSODKR package includes the +C following subroutines and function routines: +C DLHIN calculates a step size to be attempted initially. +C DRCHEK does preliminary checking for roots, and serves as an +C interface between Subroutine DLSODKR and Subroutine DROOTS. +C DROOTS finds the leftmost root of a set of functions. +C DINTDY computes an interpolated value of the y vector at t = TOUT. +C DEWSET sets the error weight vector EWT before each step. +C DVNORM computes the weighted RMS-norm of a vector. +C DSTOKA is the core integrator, which does one step of the +C integration and the associated error control. +C DCFODE sets all method coefficients and test constants. +C DSETPK interfaces between DSTOKA and the JAC routine. +C DSOLPK manages solution of linear system in Newton iteration. +C DSPIOM performs the SPIOM algorithm. +C DATV computes a scaled, preconditioned product (I-hl0*J)*v. +C DORTHOG orthogonalizes a vector against previous basis vectors. +C DHEFA generates an LU factorization of a Hessenberg matrix. +C DHESL solves a Hessenberg square linear system. +C DSPIGMR performs the SPIGMR algorithm. +C DHEQR generates a QR factorization of a Hessenberg matrix. +C DHELS finds the least squares solution of a Hessenberg system. +C DPCG performs preconditioned conjugate gradient algorithm (PCG). +C DPCGS performs the PCGS algorithm. +C DATP computes the product A*p, where A = I - hl0*df/dy. +C DUSOL interfaces to the user's PSOL routine (MITER = 9). +C DSRCKR is a user-callable routine to save and restore +C the contents of the internal Common blocks. +C DAXPY, DCOPY, DDOT, DNRM2, and DSCAL are basic linear +C algebra modules (from the BLAS collection). +C DUMACH computes the unit roundoff in a machine-independent manner. +C XERRWD, XSETUN, XSETF, IXSAV, and IUMACH handle the printing of all +C error messages and warnings. XERRWD is machine-dependent. +C Note: DVNORM, DDOT, DNRM2, DUMACH, IXSAV, and IUMACH are function +C routines. All the others are subroutines. +C +C----------------------------------------------------------------------- + DOUBLE PRECISION DUMACH, DVNORM + INTEGER INIT, MXSTEP, MXHNIL, NHNIL, NSLAST, NYH, IOWNS, + 1 ICF, IERPJ, IERSL, JCUR, JSTART, KFLAG, L, + 2 LYH, LEWT, LACOR, LSAVF, LWM, LIWM, METH, MITER, + 3 MAXORD, MAXCOR, MSBP, MXNCF, N, NQ, NST, NFE, NJE, NQU + INTEGER NEWT, NSFI, NSLJ, NJEV + INTEGER LG0, LG1, LGX, IOWNR3, IRFND, ITASKC, NGC, NGE + INTEGER JPRE, JACFLG, LOCWP, LOCIWP, LSAVX, KMP, MAXL, MNEWT, + 1 NNI, NLI, NPS, NCFN, NCFL + INTEGER I, I1, I2, IER, IFLAG, IMXER, KGO, LF0, + 1 LENIW, LENIWK, LENRW, LENWM, LENWK, LIWP, LWP, MORD, MXHNL0, + 2 MXSTP0, NCFN0, NCFL0, NITER, NLI0, NNI0, NNID, NSTD, NWARN + INTEGER IRFP, IRT, LENYH, LYHNEW + DOUBLE PRECISION ROWNS, + 1 CCMAX, EL0, H, HMIN, HMXI, HU, RC, TN, UROUND + DOUBLE PRECISION STIFR + DOUBLE PRECISION ROWNR3, T0, TLAST, TOUTC + DOUBLE PRECISION DELT, EPCON, SQRTN, RSQRTN + DOUBLE PRECISION ATOLI, AVDIM, BIG, EWTI, H0, HMAX, HMX, RCFL, + 1 RCFN, RH, RTOLI, TCRIT, TNEXT, TOLSF, TP, SIZE + DIMENSION MORD(2) + LOGICAL IHIT, LAVD, LCFN, LCFL, LWARN + CHARACTER*60 MSG + SAVE MORD, MXSTP0, MXHNL0 +C----------------------------------------------------------------------- +C The following four internal Common blocks contain +C (a) variables which are local to any subroutine but whose values must +C be preserved between calls to the routine ("own" variables), and +C (b) variables which are communicated between subroutines. +C The block DLS001 is declared in subroutines DLSODKR, DINTDY, +C DSTOKA, DSOLPK, and DATV. +C The block DLS002 is declared in subroutines DLSODKR and DSTOKA. +C The block DLSR01 is declared in subroutines DLSODKR, DRCHEK, DROOTS. +C The block DLPK01 is declared in subroutines DLSODKR, DSTOKA, DSETPK, +C and DSOLPK. +C Groups of variables are replaced by dummy arrays in the Common +C declarations in routines where those variables are not used. +C----------------------------------------------------------------------- + COMMON /DLS001/ ROWNS(209), + 1 CCMAX, EL0, H, HMIN, HMXI, HU, RC, TN, UROUND, + 2 INIT, MXSTEP, MXHNIL, NHNIL, NSLAST, NYH, IOWNS(6), + 3 ICF, IERPJ, IERSL, JCUR, JSTART, KFLAG, L, + 4 LYH, LEWT, LACOR, LSAVF, LWM, LIWM, METH, MITER, + 5 MAXORD, MAXCOR, MSBP, MXNCF, N, NQ, NST, NFE, NJE, NQU +C + COMMON /DLS002/ STIFR, NEWT, NSFI, NSLJ, NJEV +C + COMMON /DLSR01/ ROWNR3(2), T0, TLAST, TOUTC, + 1 LG0, LG1, LGX, IOWNR3(2), IRFND, ITASKC, NGC, NGE +C + COMMON /DLPK01/ DELT, EPCON, SQRTN, RSQRTN, + 1 JPRE, JACFLG, LOCWP, LOCIWP, LSAVX, KMP, MAXL, MNEWT, + 2 NNI, NLI, NPS, NCFN, NCFL +C + DATA MORD(1),MORD(2)/12,5/, MXSTP0/500/, MXHNL0/10/ +C----------------------------------------------------------------------- +C Block A. +C This code block is executed on every call. +C It tests ISTATE and ITASK for legality and branches appropriately. +C If ISTATE .gt. 1 but the flag INIT shows that initialization has +C not yet been done, an error return occurs. +C If ISTATE = 1 and TOUT = T, return immediately. +C----------------------------------------------------------------------- + IF (ISTATE .LT. 1 .OR. ISTATE .GT. 3) GO TO 601 + IF (ITASK .LT. 1 .OR. ITASK .GT. 5) GO TO 602 + ITASKC = ITASK + IF (ISTATE .EQ. 1) GO TO 10 + IF (INIT .EQ. 0) GO TO 603 + IF (ISTATE .EQ. 2) GO TO 200 + GO TO 20 + 10 INIT = 0 + IF (TOUT .EQ. T) RETURN +C----------------------------------------------------------------------- +C Block B. +C The next code block is executed for the initial call (ISTATE = 1), +C or for a continuation call with parameter changes (ISTATE = 3). +C It contains checking of all inputs and various initializations. +C +C First check legality of the non-optional inputs NEQ, ITOL, IOPT, MF, +C and NG. +C----------------------------------------------------------------------- + 20 IF (NEQ(1) .LE. 0) GO TO 604 + IF (ISTATE .EQ. 1) GO TO 25 + IF (NEQ(1) .GT. N) GO TO 605 + 25 N = NEQ(1) + IF (ITOL .LT. 1 .OR. ITOL .GT. 4) GO TO 606 + IF (IOPT .LT. 0 .OR. IOPT .GT. 1) GO TO 607 + METH = MF/10 + MITER = MF - 10*METH + IF (METH .LT. 1 .OR. METH .GT. 2) GO TO 608 + IF (MITER .LT. 0) GO TO 608 + IF (MITER .GT. 4 .AND. MITER .LT. 9) GO TO 608 + IF (MITER .GE. 1) JPRE = IWORK(3) + JACFLG = 0 + IF (MITER .GE. 1) JACFLG = IWORK(4) + IF (NG .LT. 0) GO TO 630 + IF (ISTATE .EQ. 1) GO TO 35 + IF (IRFND .EQ. 0 .AND. NG .NE. NGC) GO TO 631 + 35 NGC = NG +C Next process and check the optional inputs. -------------------------- + IF (IOPT .EQ. 1) GO TO 40 + MAXORD = MORD(METH) + MXSTEP = MXSTP0 + MXHNIL = MXHNL0 + IF (ISTATE .EQ. 1) H0 = 0.0D0 + HMXI = 0.0D0 + HMIN = 0.0D0 + MAXL = MIN(5,N) + KMP = MAXL + DELT = 0.05D0 + GO TO 60 + 40 MAXORD = IWORK(5) + IF (MAXORD .LT. 0) GO TO 611 + IF (MAXORD .EQ. 0) MAXORD = 100 + MAXORD = MIN(MAXORD,MORD(METH)) + MXSTEP = IWORK(6) + IF (MXSTEP .LT. 0) GO TO 612 + IF (MXSTEP .EQ. 0) MXSTEP = MXSTP0 + MXHNIL = IWORK(7) + IF (MXHNIL .LT. 0) GO TO 613 + IF (MXHNIL .EQ. 0) MXHNIL = MXHNL0 + IF (ISTATE .NE. 1) GO TO 50 + H0 = RWORK(5) + IF ((TOUT - T)*H0 .LT. 0.0D0) GO TO 614 + 50 HMAX = RWORK(6) + IF (HMAX .LT. 0.0D0) GO TO 615 + HMXI = 0.0D0 + IF (HMAX .GT. 0.0D0) HMXI = 1.0D0/HMAX + HMIN = RWORK(7) + IF (HMIN .LT. 0.0D0) GO TO 616 + MAXL = IWORK(8) + IF (MAXL .EQ. 0) MAXL = 5 + MAXL = MIN(MAXL,N) + KMP = IWORK(9) + IF (KMP .EQ. 0 .OR. KMP .GT. MAXL) KMP = MAXL + DELT = RWORK(8) + IF (DELT .EQ. 0.0D0) DELT = 0.05D0 +C----------------------------------------------------------------------- +C Set work array pointers and check lengths LRW and LIW. +C Pointers to segments of RWORK and IWORK are named by prefixing L to +C the name of the segment. E.g., the segment YH starts at RWORK(LYH). +C RWORK segments (in order) are denoted G0, G1, GX, YH, WM, +C EWT, SAVF, SAVX, ACOR. +C----------------------------------------------------------------------- + 60 IF (ISTATE .EQ. 1) NYH = N + LG0 = 21 + LG1 = LG0 + NG + LGX = LG1 + NG + LYHNEW = LGX + NG + IF (ISTATE .EQ. 1) LYH = LYHNEW + IF (LYHNEW .EQ. LYH) GO TO 62 +C If ISTATE = 3 and NG was changed, shift YH to its new location. ------ + LENYH = L*NYH + IF (LRW .LT. LYHNEW-1+LENYH) GO TO 62 + I1 = 1 + IF (LYHNEW .GT. LYH) I1 = -1 + CALL DCOPY (LENYH, RWORK(LYH), I1, RWORK(LYHNEW), I1) + LYH = LYHNEW + 62 CONTINUE + LWM = LYH + (MAXORD + 1)*NYH + IF (MITER .EQ. 0) LENWK = 0 + IF (MITER .EQ. 1) LENWK = N*(MAXL+2) + MAXL*MAXL + IF (MITER .EQ. 2) + 1 LENWK = N*(MAXL+2+MIN(1,MAXL-KMP)) + (MAXL+3)*MAXL + 1 + IF (MITER .EQ. 3 .OR. MITER .EQ. 4) LENWK = 5*N + IF (MITER .EQ. 9) LENWK = 2*N + LWP = 0 + IF (MITER .GE. 1) LWP = IWORK(1) + LENWM = LENWK + LWP + LOCWP = LENWK + 1 + LEWT = LWM + LENWM + LSAVF = LEWT + N + LSAVX = LSAVF + N + LACOR = LSAVX + N + IF (MITER .EQ. 0) LACOR = LSAVF + N + LENRW = LACOR + N - 1 + IWORK(17) = LENRW + LIWM = 31 + LENIWK = 0 + IF (MITER .EQ. 1) LENIWK = MAXL + LIWP = 0 + IF (MITER .GE. 1) LIWP = IWORK(2) + LENIW = 30 + LENIWK + LIWP + LOCIWP = LENIWK + 1 + IWORK(18) = LENIW + IF (LENRW .GT. LRW) GO TO 617 + IF (LENIW .GT. LIW) GO TO 618 +C Check RTOL and ATOL for legality. ------------------------------------ + RTOLI = RTOL(1) + ATOLI = ATOL(1) + DO 70 I = 1,N + IF (ITOL .GE. 3) RTOLI = RTOL(I) + IF (ITOL .EQ. 2 .OR. ITOL .EQ. 4) ATOLI = ATOL(I) + IF (RTOLI .LT. 0.0D0) GO TO 619 + IF (ATOLI .LT. 0.0D0) GO TO 620 + 70 CONTINUE +C Load SQRT(N) and its reciprocal in Common. --------------------------- + SQRTN = SQRT(REAL(N)) + RSQRTN = 1.0D0/SQRTN + IF (ISTATE .EQ. 1) GO TO 100 +C If ISTATE = 3, set flag to signal parameter changes to DSTOKA.-------- + JSTART = -1 + IF (NQ .LE. MAXORD) GO TO 90 +C MAXORD was reduced below NQ. Copy YH(*,MAXORD+2) into SAVF. --------- + DO 80 I = 1,N + 80 RWORK(I+LSAVF-1) = RWORK(I+LWM-1) + 90 CONTINUE + IF (N .EQ. NYH) GO TO 200 +C NEQ was reduced. Zero part of YH to avoid undefined references. ----- + I1 = LYH + L*NYH + I2 = LYH + (MAXORD + 1)*NYH - 1 + IF (I1 .GT. I2) GO TO 200 + DO 95 I = I1,I2 + 95 RWORK(I) = 0.0D0 + GO TO 200 +C----------------------------------------------------------------------- +C Block C. +C The next block is for the initial call only (ISTATE = 1). +C It contains all remaining initializations, the initial call to F, +C and the calculation of the initial step size. +C The error weights in EWT are inverted after being loaded. +C----------------------------------------------------------------------- + 100 UROUND = DUMACH() + TN = T + IF (ITASK .NE. 4 .AND. ITASK .NE. 5) GO TO 110 + TCRIT = RWORK(1) + IF ((TCRIT - TOUT)*(TOUT - T) .LT. 0.0D0) GO TO 625 + IF (H0 .NE. 0.0D0 .AND. (T + H0 - TCRIT)*H0 .GT. 0.0D0) + 1 H0 = TCRIT - T + 110 JSTART = 0 + NHNIL = 0 + NST = 0 + NJE = 0 + NSLAST = 0 + NLI0 = 0 + NNI0 = 0 + NCFN0 = 0 + NCFL0 = 0 + NWARN = 0 + HU = 0.0D0 + NQU = 0 + CCMAX = 0.3D0 + MAXCOR = 3 + MSBP = 20 + MXNCF = 10 + NNI = 0 + NLI = 0 + NPS = 0 + NCFN = 0 + NCFL = 0 + NSFI = 0 + NJEV = 0 +C Initial call to F. (LF0 points to YH(*,2).) ------------------------- + LF0 = LYH + NYH + CALL F (NEQ, T, Y, RWORK(LF0)) + NFE = 1 +C Load the initial value vector in YH. --------------------------------- + DO 115 I = 1,N + 115 RWORK(I+LYH-1) = Y(I) +C Load and invert the EWT array. (H is temporarily set to 1.0.) ------- + NQ = 1 + H = 1.0D0 + CALL DEWSET (N, ITOL, RTOL, ATOL, RWORK(LYH), RWORK(LEWT)) + DO 120 I = 1,N + IF (RWORK(I+LEWT-1) .LE. 0.0D0) GO TO 621 + 120 RWORK(I+LEWT-1) = 1.0D0/RWORK(I+LEWT-1) + IF (H0 .NE. 0.0D0) GO TO 180 +C Call DLHIN to set initial step size H0 to be attempted. -------------- + CALL DLHIN (NEQ, N, T, RWORK(LYH), RWORK(LF0), F, TOUT, UROUND, + 1 RWORK(LEWT), ITOL, ATOL, Y, RWORK(LACOR), H0, NITER, IER) + NFE = NFE + NITER + IF (IER .NE. 0) GO TO 622 +C Adjust H0 if necessary to meet HMAX bound. --------------------------- + 180 RH = ABS(H0)*HMXI + IF (RH .GT. 1.0D0) H0 = H0/RH +C Load H with H0 and scale YH(*,2) by H0. ------------------------------ + H = H0 + DO 190 I = 1,N + 190 RWORK(I+LF0-1) = H0*RWORK(I+LF0-1) +C Check for a zero of g at T. ------------------------------------------ + IRFND = 0 + TOUTC = TOUT + IF (NGC .EQ. 0) GO TO 270 + CALL DRCHEK (1, G, NEQ, Y, RWORK(LYH), NYH, + 1 RWORK(LG0), RWORK(LG1), RWORK(LGX), JROOT, IRT) + IF (IRT .EQ. 0) GO TO 270 + GO TO 632 +C----------------------------------------------------------------------- +C Block D. +C The next code block is for continuation calls only (ISTATE = 2 or 3) +C and is to check stop conditions before taking a step. +C First, DRCHEK is called to check for a root within the last step +C taken, other than the last root found there, if any. +C If ITASK = 2 or 5, and y(TN) has not yet been returned to the user +C because of an intervening root, return through Block G. +C----------------------------------------------------------------------- + 200 NSLAST = NST +C + IRFP = IRFND + IF (NGC .EQ. 0) GO TO 205 + IF (ITASK .EQ. 1 .OR. ITASK .EQ. 4) TOUTC = TOUT + CALL DRCHEK (2, G, NEQ, Y, RWORK(LYH), NYH, + 1 RWORK(LG0), RWORK(LG1), RWORK(LGX), JROOT, IRT) + IF (IRT .NE. 1) GO TO 205 + IRFND = 1 + ISTATE = 3 + T = T0 + GO TO 425 + 205 CONTINUE + IRFND = 0 + IF (IRFP .EQ. 1 .AND. TLAST .NE. TN .AND. ITASK .EQ. 2) GO TO 400 +C + NLI0 = NLI + NNI0 = NNI + NCFN0 = NCFN + NCFL0 = NCFL + NWARN = 0 + GO TO (210, 250, 220, 230, 240), ITASK + 210 IF ((TN - TOUT)*H .LT. 0.0D0) GO TO 250 + CALL DINTDY (TOUT, 0, RWORK(LYH), NYH, Y, IFLAG) + IF (IFLAG .NE. 0) GO TO 627 + T = TOUT + GO TO 420 + 220 TP = TN - HU*(1.0D0 + 100.0D0*UROUND) + IF ((TP - TOUT)*H .GT. 0.0D0) GO TO 623 + IF ((TN - TOUT)*H .LT. 0.0D0) GO TO 250 + GO TO 400 + 230 TCRIT = RWORK(1) + IF ((TN - TCRIT)*H .GT. 0.0D0) GO TO 624 + IF ((TCRIT - TOUT)*H .LT. 0.0D0) GO TO 625 + IF ((TN - TOUT)*H .LT. 0.0D0) GO TO 245 + CALL DINTDY (TOUT, 0, RWORK(LYH), NYH, Y, IFLAG) + IF (IFLAG .NE. 0) GO TO 627 + T = TOUT + GO TO 420 + 240 TCRIT = RWORK(1) + IF ((TN - TCRIT)*H .GT. 0.0D0) GO TO 624 + 245 HMX = ABS(TN) + ABS(H) + IHIT = ABS(TN - TCRIT) .LE. 100.0D0*UROUND*HMX + IF (IHIT) T = TCRIT + IF (IRFP .EQ. 1 .AND. TLAST .NE. TN .AND. ITASK .EQ. 5) GO TO 400 + IF (IHIT) GO TO 400 + TNEXT = TN + H*(1.0D0 + 4.0D0*UROUND) + IF ((TNEXT - TCRIT)*H .LE. 0.0D0) GO TO 250 + H = (TCRIT - TN)*(1.0D0 - 4.0D0*UROUND) + IF (ISTATE .EQ. 2) JSTART = -2 +C----------------------------------------------------------------------- +C Block E. +C The next block is normally executed for all calls and contains +C the call to the one-step core integrator DSTOKA. +C +C This is a looping point for the integration steps. +C +C First check for too many steps being taken, +C check for poor Newton/Krylov method performance, update EWT (if not +C at start of problem), check for too much accuracy being requested, +C and check for H below the roundoff level in T. +C----------------------------------------------------------------------- + 250 CONTINUE + IF ((NST-NSLAST) .GE. MXSTEP) GO TO 500 + NSTD = NST - NSLAST + NNID = NNI - NNI0 + IF (NSTD .LT. 10 .OR. NNID .EQ. 0) GO TO 255 + AVDIM = REAL(NLI - NLI0)/REAL(NNID) + RCFN = REAL(NCFN - NCFN0)/REAL(NSTD) + RCFL = REAL(NCFL - NCFL0)/REAL(NNID) + LAVD = AVDIM .GT. (MAXL - 0.05D0) + LCFN = RCFN .GT. 0.9D0 + LCFL = RCFL .GT. 0.9D0 + LWARN = LAVD .OR. LCFN .OR. LCFL + IF (.NOT.LWARN) GO TO 255 + NWARN = NWARN + 1 + IF (NWARN .GT. 10) GO TO 255 + IF (LAVD) THEN + MSG='DLSODKR- Warning. Poor iterative algorithm performance seen ' + CALL XERRWD (MSG, 60, 111, 0, 0, 0, 0, 0, 0.0D0, 0.0D0) + ENDIF + IF (LAVD) THEN + MSG=' at T = R1 by average no. of linear iterations = R2 ' + CALL XERRWD (MSG, 60, 111, 0, 0, 0, 0, 2, TN, AVDIM) + ENDIF + IF (LCFN) THEN + MSG='DLSODKR- Warning. Poor iterative algorithm performance seen ' + CALL XERRWD (MSG, 60, 112, 0, 0, 0, 0, 0, 0.0D0, 0.0D0) + ENDIF + IF (LCFN) THEN + MSG=' at T = R1 by nonlinear convergence failure rate = R2 ' + CALL XERRWD (MSG, 60, 112, 0, 0, 0, 0, 2, TN, RCFN) + ENDIF + IF (LCFL) THEN + MSG='DLSODKR- Warning. Poor iterative algorithm performance seen ' + CALL XERRWD (MSG, 60, 113, 0, 0, 0, 0, 0, 0.0D0, 0.0D0) + ENDIF + IF (LCFL) THEN + MSG=' at T = R1 by linear convergence failure rate = R2 ' + CALL XERRWD (MSG, 60, 113, 0, 0, 0, 0, 2, TN, RCFL) + ENDIF + 255 CONTINUE + CALL DEWSET (N, ITOL, RTOL, ATOL, RWORK(LYH), RWORK(LEWT)) + DO 260 I = 1,N + IF (RWORK(I+LEWT-1) .LE. 0.0D0) GO TO 510 + 260 RWORK(I+LEWT-1) = 1.0D0/RWORK(I+LEWT-1) + 270 TOLSF = UROUND*DVNORM (N, RWORK(LYH), RWORK(LEWT)) + IF (TOLSF .LE. 1.0D0) GO TO 280 + TOLSF = TOLSF*2.0D0 + IF (NST .EQ. 0) GO TO 626 + GO TO 520 + 280 IF ((TN + H) .NE. TN) GO TO 290 + NHNIL = NHNIL + 1 + IF (NHNIL .GT. MXHNIL) GO TO 290 + MSG = 'DLSODKR- Warning.. Internal T(=R1) and H(=R2) are' + CALL XERRWD (MSG, 50, 101, 0, 0, 0, 0, 0, 0.0D0, 0.0D0) + MSG=' such that in the machine, T + H = T on the next step ' + CALL XERRWD (MSG, 60, 101, 0, 0, 0, 0, 0, 0.0D0, 0.0D0) + MSG = ' (H = step size). Solver will continue anyway.' + CALL XERRWD (MSG, 50, 101, 0, 0, 0, 0, 2, TN, H) + IF (NHNIL .LT. MXHNIL) GO TO 290 + MSG = 'DLSODKR- Above warning has been issued I1 times. ' + CALL XERRWD (MSG, 50, 102, 0, 0, 0, 0, 0, 0.0D0, 0.0D0) + MSG = ' It will not be issued again for this problem.' + CALL XERRWD (MSG, 50, 102, 0, 1, MXHNIL, 0, 0, 0.0D0, 0.0D0) + 290 CONTINUE +C----------------------------------------------------------------------- +C CALL DSTOKA(NEQ,Y,YH,NYH,YH,EWT,SAVF,SAVX,ACOR,WM,IWM,F,JAC,PSOL) +C----------------------------------------------------------------------- + CALL DSTOKA (NEQ, Y, RWORK(LYH), NYH, RWORK(LYH), RWORK(LEWT), + 1 RWORK(LSAVF), RWORK(LSAVX), RWORK(LACOR), RWORK(LWM), + 2 IWORK(LIWM), F, JAC, PSOL) + KGO = 1 - KFLAG + GO TO (300, 530, 540, 550), KGO +C----------------------------------------------------------------------- +C Block F. +C The following block handles the case of a successful return from the +C core integrator (KFLAG = 0). +C Call DRCHEK to check for a root within the last step. +C Then, if no root was found, check for stop conditions. +C----------------------------------------------------------------------- + 300 INIT = 1 +C + IF (NGC .EQ. 0) GO TO 315 + CALL DRCHEK (3, G, NEQ, Y, RWORK(LYH), NYH, + 1 RWORK(LG0), RWORK(LG1), RWORK(LGX), JROOT, IRT) + IF (IRT .NE. 1) GO TO 315 + IRFND = 1 + ISTATE = 3 + T = T0 + GO TO 425 + 315 CONTINUE +C + GO TO (310, 400, 330, 340, 350), ITASK +C ITASK = 1. If TOUT has been reached, interpolate. ------------------- + 310 IF ((TN - TOUT)*H .LT. 0.0D0) GO TO 250 + CALL DINTDY (TOUT, 0, RWORK(LYH), NYH, Y, IFLAG) + T = TOUT + GO TO 420 +C ITASK = 3. Jump to exit if TOUT was reached. ------------------------ + 330 IF ((TN - TOUT)*H .GE. 0.0D0) GO TO 400 + GO TO 250 +C ITASK = 4. See if TOUT or TCRIT was reached. Adjust H if necessary. + 340 IF ((TN - TOUT)*H .LT. 0.0D0) GO TO 345 + CALL DINTDY (TOUT, 0, RWORK(LYH), NYH, Y, IFLAG) + T = TOUT + GO TO 420 + 345 HMX = ABS(TN) + ABS(H) + IHIT = ABS(TN - TCRIT) .LE. 100.0D0*UROUND*HMX + IF (IHIT) GO TO 400 + TNEXT = TN + H*(1.0D0 + 4.0D0*UROUND) + IF ((TNEXT - TCRIT)*H .LE. 0.0D0) GO TO 250 + H = (TCRIT - TN)*(1.0D0 - 4.0D0*UROUND) + JSTART = -2 + GO TO 250 +C ITASK = 5. See if TCRIT was reached and jump to exit. --------------- + 350 HMX = ABS(TN) + ABS(H) + IHIT = ABS(TN - TCRIT) .LE. 100.0D0*UROUND*HMX +C----------------------------------------------------------------------- +C Block G. +C The following block handles all successful returns from DLSODKR. +C If ITASK .ne. 1, Y is loaded from YH and T is set accordingly. +C ISTATE is set to 2, and the optional outputs are loaded into the +C work arrays before returning. +C----------------------------------------------------------------------- + 400 DO 410 I = 1,N + 410 Y(I) = RWORK(I+LYH-1) + T = TN + IF (ITASK .NE. 4 .AND. ITASK .NE. 5) GO TO 420 + IF (IHIT) T = TCRIT + 420 ISTATE = 2 + 425 CONTINUE + RWORK(11) = HU + RWORK(12) = H + RWORK(13) = TN + IWORK(11) = NST + IWORK(12) = NFE + IWORK(13) = NJE + IWORK(14) = NQU + IWORK(15) = NQ + IWORK(19) = NNI + IWORK(20) = NLI + IWORK(21) = NPS + IWORK(22) = NCFN + IWORK(23) = NCFL + IWORK(24) = NSFI + IWORK(25) = NJEV + IWORK(10) = NGE + TLAST = T + RETURN +C----------------------------------------------------------------------- +C Block H. +C The following block handles all unsuccessful returns other than +C those for illegal input. First the error message routine is called. +C If there was an error test or convergence test failure, IMXER is set. +C Then Y is loaded from YH and T is set to TN. +C The optional outputs are loaded into the work arrays before returning. +C----------------------------------------------------------------------- +C The maximum number of steps was taken before reaching TOUT. ---------- + 500 MSG = 'DLSODKR- At current T (=R1), MXSTEP (=I1) steps ' + CALL XERRWD (MSG, 50, 201, 0, 0, 0, 0, 0, 0.0D0, 0.0D0) + MSG = ' taken on this call before reaching TOUT ' + CALL XERRWD (MSG, 50, 201, 0, 1, MXSTEP, 0, 1, TN, 0.0D0) + ISTATE = -1 + GO TO 580 +C EWT(i) .le. 0.0 for some i (not at start of problem). ---------------- + 510 EWTI = RWORK(LEWT+I-1) + MSG = 'DLSODKR- At T(=R1), EWT(I1) has become R2 .le. 0.' + CALL XERRWD (MSG, 50, 202, 0, 1, I, 0, 2, TN, EWTI) + ISTATE = -6 + GO TO 580 +C Too much accuracy requested for machine precision. ------------------- + 520 MSG = 'DLSODKR- At T (=R1), too much accuracy requested ' + CALL XERRWD (MSG, 50, 203, 0, 0, 0, 0, 0, 0.0D0, 0.0D0) + MSG = ' for precision of machine.. See TOLSF (=R2) ' + CALL XERRWD (MSG, 50, 203, 0, 0, 0, 0, 2, TN, TOLSF) + RWORK(14) = TOLSF + ISTATE = -2 + GO TO 580 +C KFLAG = -1. Error test failed repeatedly or with ABS(H) = HMIN. ----- + 530 MSG = 'DLSODKR- At T(=R1) and step size H(=R2), the error' + CALL XERRWD (MSG, 50, 204, 0, 0, 0, 0, 0, 0.0D0, 0.0D0) + MSG = ' test failed repeatedly or with ABS(H) = HMIN' + CALL XERRWD (MSG, 50, 204, 0, 0, 0, 0, 2, TN, H) + ISTATE = -4 + GO TO 560 +C KFLAG = -2. Convergence failed repeatedly or with ABS(H) = HMIN. ---- + 540 MSG = 'DLSODKR- At T (=R1) and step size H (=R2), the ' + CALL XERRWD (MSG, 50, 205, 0, 0, 0, 0, 0, 0.0D0, 0.0D0) + MSG = ' corrector convergence failed repeatedly ' + CALL XERRWD (MSG, 50, 205, 0, 0, 0, 0, 0, 0.0D0, 0.0D0) + MSG = ' or with ABS(H) = HMIN ' + CALL XERRWD (MSG, 30, 205, 0, 0, 0, 0, 2, TN, H) + ISTATE = -5 + GO TO 580 +C KFLAG = -3. Unrecoverable error from PSOL. -------------------------- + 550 MSG = 'DLSODKR- At T (=R1) an unrecoverable error return' + CALL XERRWD (MSG, 50, 206, 0, 0, 0, 0, 0, 0.0D0, 0.0D0) + MSG = ' was made from Subroutine PSOL ' + CALL XERRWD (MSG, 40, 206, 0, 0, 0, 0, 1, TN, 0.0D0) + ISTATE = -7 + GO TO 580 +C Compute IMXER if relevant. ------------------------------------------- + 560 BIG = 0.0D0 + IMXER = 1 + DO 570 I = 1,N + SIZE = ABS(RWORK(I+LACOR-1)*RWORK(I+LEWT-1)) + IF (BIG .GE. SIZE) GO TO 570 + BIG = SIZE + IMXER = I + 570 CONTINUE + IWORK(16) = IMXER +C Set Y vector, T, and optional outputs. ------------------------------- + 580 DO 590 I = 1,N + 590 Y(I) = RWORK(I+LYH-1) + T = TN + RWORK(11) = HU + RWORK(12) = H + RWORK(13) = TN + IWORK(11) = NST + IWORK(12) = NFE + IWORK(13) = NJE + IWORK(14) = NQU + IWORK(15) = NQ + IWORK(19) = NNI + IWORK(20) = NLI + IWORK(21) = NPS + IWORK(22) = NCFN + IWORK(23) = NCFL + IWORK(24) = NSFI + IWORK(25) = NJEV + IWORK(10) = NGE + TLAST = T + RETURN +C----------------------------------------------------------------------- +C Block I. +C The following block handles all error returns due to illegal input +C (ISTATE = -3), as detected before calling the core integrator. +C First the error message routine is called. If the illegal input +C is a negative ISTATE, the run is aborted (apparent infinite loop). +C----------------------------------------------------------------------- + 601 MSG = 'DLSODKR- ISTATE(=I1) illegal.' + CALL XERRWD (MSG, 30, 1, 0, 1, ISTATE, 0, 0, 0.0D0, 0.0D0) + IF (ISTATE .LT. 0) GO TO 800 + GO TO 700 + 602 MSG = 'DLSODKR- ITASK (=I1) illegal.' + CALL XERRWD (MSG, 30, 2, 0, 1, ITASK, 0, 0, 0.0D0, 0.0D0) + GO TO 700 + 603 MSG = 'DLSODKR- ISTATE.gt.1 but DLSODKR not initialized. ' + CALL XERRWD (MSG, 50, 3, 0, 0, 0, 0, 0, 0.0D0, 0.0D0) + GO TO 700 + 604 MSG = 'DLSODKR- NEQ (=I1) .lt. 1 ' + CALL XERRWD (MSG, 30, 4, 0, 1, NEQ(1), 0, 0, 0.0D0, 0.0D0) + GO TO 700 + 605 MSG = 'DLSODKR- ISTATE = 3 and NEQ increased (I1 to I2).' + CALL XERRWD (MSG, 50, 5, 0, 2, N, NEQ(1), 0, 0.0D0, 0.0D0) + GO TO 700 + 606 MSG = 'DLSODKR- ITOL (=I1) illegal. ' + CALL XERRWD (MSG, 30, 6, 0, 1, ITOL, 0, 0, 0.0D0, 0.0D0) + GO TO 700 + 607 MSG = 'DLSODKR- IOPT (=I1) illegal. ' + CALL XERRWD (MSG, 30, 7, 0, 1, IOPT, 0, 0, 0.0D0, 0.0D0) + GO TO 700 + 608 MSG = 'DLSODKR- MF (=I1) illegal. ' + CALL XERRWD (MSG, 30, 8, 0, 1, MF, 0, 0, 0.0D0, 0.0D0) + GO TO 700 + 611 MSG = 'DLSODKR- MAXORD (=I1) .lt. 0 ' + CALL XERRWD (MSG, 30, 11, 0, 1, MAXORD, 0, 0, 0.0D0, 0.0D0) + GO TO 700 + 612 MSG = 'DLSODKR- MXSTEP (=I1) .lt. 0 ' + CALL XERRWD (MSG, 30, 12, 0, 1, MXSTEP, 0, 0, 0.0D0, 0.0D0) + GO TO 700 + 613 MSG = 'DLSODKR- MXHNIL (=I1) .lt. 0 ' + CALL XERRWD (MSG, 30, 13, 0, 1, MXHNIL, 0, 0, 0.0D0, 0.0D0) + GO TO 700 + 614 MSG = 'DLSODKR- TOUT (=R1) behind T (=R2) ' + CALL XERRWD (MSG, 40, 14, 0, 0, 0, 0, 2, TOUT, T) + MSG = ' Integration direction is given by H0 (=R1) ' + CALL XERRWD (MSG, 50, 14, 0, 0, 0, 0, 1, H0, 0.0D0) + GO TO 700 + 615 MSG = 'DLSODKR- HMAX (=R1) .lt. 0.0 ' + CALL XERRWD (MSG, 30, 15, 0, 0, 0, 0, 1, HMAX, 0.0D0) + GO TO 700 + 616 MSG = 'DLSODKR- HMIN (=R1) .lt. 0.0 ' + CALL XERRWD (MSG, 30, 16, 0, 0, 0, 0, 1, HMIN, 0.0D0) + GO TO 700 + 617 MSG='DLSODKR- RWORK length needed, LENRW(=I1), exceeds LRW(=I2) ' + CALL XERRWD (MSG, 60, 17, 0, 2, LENRW, LRW, 0, 0.0D0, 0.0D0) + GO TO 700 + 618 MSG='DLSODKR- IWORK length needed, LENIW(=I1), exceeds LIW(=I2) ' + CALL XERRWD (MSG, 60, 18, 0, 2, LENIW, LIW, 0, 0.0D0, 0.0D0) + GO TO 700 + 619 MSG = 'DLSODKR- RTOL(I1) is R1 .lt. 0.0 ' + CALL XERRWD (MSG, 40, 19, 0, 1, I, 0, 1, RTOLI, 0.0D0) + GO TO 700 + 620 MSG = 'DLSODKR- ATOL(I1) is R1 .lt. 0.0 ' + CALL XERRWD (MSG, 40, 20, 0, 1, I, 0, 1, ATOLI, 0.0D0) + GO TO 700 + 621 EWTI = RWORK(LEWT+I-1) + MSG = 'DLSODKR- EWT(I1) is R1 .le. 0.0 ' + CALL XERRWD (MSG, 40, 21, 0, 1, I, 0, 1, EWTI, 0.0D0) + GO TO 700 + 622 MSG='DLSODKR- TOUT(=R1) too close to T(=R2) to start integration.' + CALL XERRWD (MSG, 60, 22, 0, 0, 0, 0, 2, TOUT, T) + GO TO 700 + 623 MSG='DLSODKR- ITASK = I1 and TOUT (=R1) behind TCUR - HU (= R2) ' + CALL XERRWD (MSG, 60, 23, 0, 1, ITASK, 0, 2, TOUT, TP) + GO TO 700 + 624 MSG='DLSODKR- ITASK = 4 or 5 and TCRIT (=R1) behind TCUR (=R2) ' + CALL XERRWD (MSG, 60, 24, 0, 0, 0, 0, 2, TCRIT, TN) + GO TO 700 + 625 MSG='DLSODKR- ITASK = 4 or 5 and TCRIT (=R1) behind TOUT (=R2) ' + CALL XERRWD (MSG, 60, 25, 0, 0, 0, 0, 2, TCRIT, TOUT) + GO TO 700 + 626 MSG = 'DLSODKR- At start of problem, too much accuracy ' + CALL XERRWD (MSG, 50, 26, 0, 0, 0, 0, 0, 0.0D0, 0.0D0) + MSG=' requested for precision of machine.. See TOLSF (=R1) ' + CALL XERRWD (MSG, 60, 26, 0, 0, 0, 0, 1, TOLSF, 0.0D0) + RWORK(14) = TOLSF + GO TO 700 + 627 MSG = 'DLSODKR- Trouble in DINTDY. ITASK = I1, TOUT = R1' + CALL XERRWD (MSG, 50, 27, 0, 1, ITASK, 0, 1, TOUT, 0.0D0) + GO TO 700 + 630 MSG = 'DLSODKR- NG (=I1) .lt. 0 ' + CALL XERRWD (MSG, 30, 30, 0, 1, NG, 0, 0, 0.0D0, 0.0D0) + GO TO 700 + 631 MSG = 'DLSODKR- NG changed (from I1 to I2) illegally, ' + CALL XERRWD (MSG, 50, 31, 0, 0, 0, 0, 0, 0.0D0, 0.0D0) + MSG = ' i.e. not immediately after a root was found.' + CALL XERRWD (MSG, 50, 31, 0, 2, NGC, NG, 0, 0.0D0, 0.0D0) + GO TO 700 + 632 MSG = 'DLSODKR- One or more components of g has a root ' + CALL XERRWD (MSG, 50, 32, 0, 0, 0, 0, 0, 0.0D0, 0.0D0) + MSG = ' too near to the initial point. ' + CALL XERRWD (MSG, 40, 32, 0, 0, 0, 0, 0, 0.0D0, 0.0D0) +C + 700 ISTATE = -3 + RETURN +C + 800 MSG = 'DLSODKR- Run aborted.. apparent infinite loop. ' + CALL XERRWD (MSG, 50, 303, 2, 0, 0, 0, 0, 0.0D0, 0.0D0) + RETURN +C----------------------- End of Subroutine DLSODKR --------------------- + END +*DECK DLSODI + SUBROUTINE DLSODI (RES, ADDA, JAC, NEQ, Y, YDOTI, T, TOUT, ITOL, + 1 RTOL, ATOL, ITASK, ISTATE, IOPT, RWORK, LRW, IWORK, LIW, MF ) + EXTERNAL RES, ADDA, JAC + INTEGER NEQ, ITOL, ITASK, ISTATE, IOPT, LRW, IWORK, LIW, MF + DOUBLE PRECISION Y, YDOTI, T, TOUT, RTOL, ATOL, RWORK + DIMENSION NEQ(*), Y(*), YDOTI(*), RTOL(*), ATOL(*), RWORK(LRW), + 1 IWORK(LIW) +C----------------------------------------------------------------------- +C This is the 18 November 2003 version of +C DLSODI: Livermore Solver for Ordinary Differential Equations +C (Implicit form). +C +C This version is in double precision. +C +C DLSODI solves the initial value problem for linearly implicit +C systems of first order ODEs, +C A(t,y) * dy/dt = g(t,y) , where A(t,y) is a square matrix, +C or, in component form, +C ( a * ( dy / dt )) + ... + ( a * ( dy / dt )) = +C i,1 1 i,NEQ NEQ +C +C = g ( t, y , y ,..., y ) ( i = 1,...,NEQ ) +C i 1 2 NEQ +C +C If A is singular, this is a differential-algebraic system. +C +C DLSODI is a variant version of the DLSODE package. +C----------------------------------------------------------------------- +C Reference: +C Alan C. Hindmarsh, ODEPACK, A Systematized Collection of ODE +C Solvers, in Scientific Computing, R. S. Stepleman et al. (Eds.), +C North-Holland, Amsterdam, 1983, pp. 55-64. +C----------------------------------------------------------------------- +C Authors: Alan C. Hindmarsh and Jeffrey F. Painter +C Center for Applied Scientific Computing, L-561 +C Lawrence Livermore National Laboratory +C Livermore, CA 94551 +C----------------------------------------------------------------------- +C Summary of Usage. +C +C Communication between the user and the DLSODI package, for normal +C situations, is summarized here. This summary describes only a subset +C of the full set of options available. See the full description for +C details, including optional communication, nonstandard options, +C and instructions for special situations. See also the example +C problem (with program and output) following this summary. +C +C A. First, provide a subroutine of the form: +C SUBROUTINE RES (NEQ, T, Y, S, R, IRES) +C DOUBLE PRECISION T, Y(*), S(*), R(*) +C which computes the residual function +C r = g(t,y) - A(t,y) * s , +C as a function of t and the vectors y and s. (s is an internally +C generated approximation to dy/dt.) The arrays Y and S are inputs +C to the RES routine and should not be altered. The residual +C vector is to be stored in the array R. The argument IRES should be +C ignored for casual use of DLSODI. (For uses of IRES, see the +C paragraph on RES in the full description below.) +C +C B. Next, decide whether full or banded form is more economical +C for the storage of matrices. DLSODI must deal internally with the +C matrices A and dr/dy, where r is the residual function defined above. +C DLSODI generates a linear combination of these two matrices, and +C this is treated in either full or banded form. +C The matrix structure is communicated by a method flag MF, +C which is 21 or 22 for the full case, and 24 or 25 in the band case. +C In the banded case, DLSODI requires two half-bandwidth +C parameters ML and MU. These are, respectively, the widths of the +C lower and upper parts of the band, excluding the main diagonal. +C Thus the band consists of the locations (i,j) with +C i-ML .le. j .le. i+MU, and the full bandwidth is ML+MU+1. +C Note that the band must accommodate the nonzero elements of +C A(t,y), dg/dy, and d(A*s)/dy (s fixed). Alternatively, one +C can define a band that encloses only the elements that are relatively +C large in magnitude, and gain some economy in storage and possibly +C also efficiency, although the appropriate threshhold for +C retaining matrix elements is highly problem-dependent. +C +C C. You must also provide a subroutine of the form: +C SUBROUTINE ADDA (NEQ, T, Y, ML, MU, P, NROWP) +C DOUBLE PRECISION T, Y(*), P(NROWP,*) +C which adds the matrix A = A(t,y) to the contents of the array P. +C T and the Y array are input and should not be altered. +C In the full matrix case, this routine should add elements of +C to P in the usual order. I.e., add A(i,j) to P(i,j). (Ignore the +C ML and MU arguments in this case.) +C In the band matrix case, this routine should add element A(i,j) +C to P(i-j+MU+1,j). I.e., add the diagonal lines of A to the rows of +C P from the top down (the top line of A added to the first row of P). +C +C D. For the sake of efficiency, you are encouraged to supply the +C Jacobian matrix dr/dy in closed form, where r = g(t,y) - A(t,y)*s +C (s = a fixed vector) as above. If dr/dy is being supplied, +C use MF = 21 or 24, and provide a subroutine of the form: +C SUBROUTINE JAC (NEQ, T, Y, S, ML, MU, P, NROWP) +C DOUBLE PRECISION T, Y(*), S(*), P(NROWP,*) +C which computes dr/dy as a function of t, y, and s. Here T, Y, and +C S are inputs, and the routine is to load dr/dy into P as follows: +C In the full matrix case (MF = 21), load P(i,j) with dr(i)/dy(j), +C the partial derivative of r(i) with respect to y(j). (Ignore the +C ML and MU arguments in this case.) +C In the band matrix case (MF = 24), load P(i-j+mu+1,j) with +C dr(i)/dy(j), i.e. load the diagonal lines of dr/dy into the rows of +C P from the top down. +C In either case, only nonzero elements need be loaded, and the +C indexing of P is the same as in the ADDA routine. +C Note that if A is independent of y (or this dependence +C is weak enough to be ignored) then JAC is to compute dg/dy. +C If it is not feasible to provide a JAC routine, use +C MF = 22 or 25, and DLSODI will compute an approximate Jacobian +C internally by difference quotients. +C +C E. Next decide whether or not to provide the initial value of the +C derivative vector dy/dt. If the initial value of A(t,y) is +C nonsingular (and not too ill-conditioned), you may let DLSODI compute +C this vector (ISTATE = 0). (DLSODI will solve the system A*s = g for +C s, with initial values of A and g.) If A(t,y) is initially +C singular, then the system is a differential-algebraic system, and +C you must make use of the particular form of the system to compute the +C initial values of y and dy/dt. In that case, use ISTATE = 1 and +C load the initial value of dy/dt into the array YDOTI. +C The input array YDOTI and the initial Y array must be consistent with +C the equations A*dy/dt = g. This implies that the initial residual +C r = g(t,y) - A(t,y)*YDOTI must be approximately zero. +C +C F. Write a main program which calls Subroutine DLSODI once for +C each point at which answers are desired. This should also provide +C for possible use of logical unit 6 for output of error messages +C by DLSODI. On the first call to DLSODI, supply arguments as follows: +C RES = name of user subroutine for residual function r. +C ADDA = name of user subroutine for computing and adding A(t,y). +C JAC = name of user subroutine for Jacobian matrix dr/dy +C (MF = 21 or 24). If not used, pass a dummy name. +C Note: the names for the RES and ADDA routines and (if used) the +C JAC routine must be declared External in the calling program. +C NEQ = number of scalar equations in the system. +C Y = array of initial values, of length NEQ. +C YDOTI = array of length NEQ (containing initial dy/dt if ISTATE = 1). +C T = the initial value of the independent variable. +C TOUT = first point where output is desired (.ne. T). +C ITOL = 1 or 2 according as ATOL (below) is a scalar or array. +C RTOL = relative tolerance parameter (scalar). +C ATOL = absolute tolerance parameter (scalar or array). +C the estimated local error in y(i) will be controlled so as +C to be roughly less (in magnitude) than +C EWT(i) = RTOL*ABS(Y(i)) + ATOL if ITOL = 1, or +C EWT(i) = RTOL*ABS(Y(i)) + ATOL(i) if ITOL = 2. +C Thus the local error test passes if, in each component, +C either the absolute error is less than ATOL (or ATOL(i)), +C or the relative error is less than RTOL. +C Use RTOL = 0.0 for pure absolute error control, and +C use ATOL = 0.0 (or ATOL(i) = 0.0) for pure relative error +C control. Caution: Actual (global) errors may exceed these +C local tolerances, so choose them conservatively. +C ITASK = 1 for normal computation of output values of y at t = TOUT. +C ISTATE = integer flag (input and output). Set ISTATE = 1 if the +C initial dy/dt is supplied, and 0 otherwise. +C IOPT = 0 to indicate no optional inputs used. +C RWORK = real work array of length at least: +C 22 + 9*NEQ + NEQ**2 for MF = 21 or 22, +C 22 + 10*NEQ + (2*ML + MU)*NEQ for MF = 24 or 25. +C LRW = declared length of RWORK (in user's dimension). +C IWORK = integer work array of length at least 20 + NEQ. +C If MF = 24 or 25, input in IWORK(1),IWORK(2) the lower +C and upper half-bandwidths ML,MU. +C LIW = declared length of IWORK (in user's dimension). +C MF = method flag. Standard values are: +C 21 for a user-supplied full Jacobian. +C 22 for an internally generated full Jacobian. +C 24 for a user-supplied banded Jacobian. +C 25 for an internally generated banded Jacobian. +C for other choices of MF, see the paragraph on MF in +C the full description below. +C Note that the main program must declare arrays Y, YDOTI, RWORK, IWORK, +C and possibly ATOL. +C +C G. The output from the first call (or any call) is: +C Y = array of computed values of y(t) vector. +C T = corresponding value of independent variable (normally TOUT). +C ISTATE = 2 if DLSODI was successful, negative otherwise. +C -1 means excess work done on this call (check all inputs). +C -2 means excess accuracy requested (tolerances too small). +C -3 means illegal input detected (see printed message). +C -4 means repeated error test failures (check all inputs). +C -5 means repeated convergence failures (perhaps bad Jacobian +C supplied or wrong choice of tolerances). +C -6 means error weight became zero during problem. (Solution +C component i vanished, and ATOL or ATOL(i) = 0.) +C -7 cannot occur in casual use. +C -8 means DLSODI was unable to compute the initial dy/dt. +C In casual use, this means A(t,y) is initially singular. +C Supply YDOTI and use ISTATE = 1 on the first call. +C +C If DLSODI returns ISTATE = -1, -4, or -5, then the output of +C DLSODI also includes YDOTI = array containing residual vector +C r = g - A * dy/dt evaluated at the current t, y, and dy/dt. +C +C H. To continue the integration after a successful return, simply +C reset TOUT and call DLSODI again. No other parameters need be reset. +C +C----------------------------------------------------------------------- +C Example Problem. +C +C The following is a simple example problem, with the coding +C needed for its solution by DLSODI. The problem is from chemical +C kinetics, and consists of the following three equations: +C dy1/dt = -.04*y1 + 1.e4*y2*y3 +C dy2/dt = .04*y1 - 1.e4*y2*y3 - 3.e7*y2**2 +C 0. = y1 + y2 + y3 - 1. +C on the interval from t = 0.0 to t = 4.e10, with initial conditions +C y1 = 1.0, y2 = y3 = 0. +C +C The following coding solves this problem with DLSODI, using MF = 21 +C and printing results at t = .4, 4., ..., 4.e10. It uses +C ITOL = 2 and ATOL much smaller for y2 than y1 or y3 because +C y2 has much smaller values. dy/dt is supplied in YDOTI. We had +C obtained the initial value of dy3/dt by differentiating the +C third equation and evaluating the first two at t = 0. +C At the end of the run, statistical quantities of interest are +C printed (see optional outputs in the full description below). +C +C EXTERNAL RESID, APLUSP, DGBYDY +C DOUBLE PRECISION ATOL, RTOL, RWORK, T, TOUT, Y, YDOTI +C DIMENSION Y(3), YDOTI(3), ATOL(3), RWORK(58), IWORK(23) +C NEQ = 3 +C Y(1) = 1. +C Y(2) = 0. +C Y(3) = 0. +C YDOTI(1) = -.04 +C YDOTI(2) = .04 +C YDOTI(3) = 0. +C T = 0. +C TOUT = .4 +C ITOL = 2 +C RTOL = 1.D-4 +C ATOL(1) = 1.D-6 +C ATOL(2) = 1.D-10 +C ATOL(3) = 1.D-6 +C ITASK = 1 +C ISTATE = 1 +C IOPT = 0 +C LRW = 58 +C LIW = 23 +C MF = 21 +C DO 40 IOUT = 1,12 +C CALL DLSODI(RESID, APLUSP, DGBYDY, NEQ, Y, YDOTI, T, TOUT, ITOL, +C 1 RTOL, ATOL, ITASK, ISTATE, IOPT, RWORK, LRW, IWORK, LIW, MF) +C WRITE (6,20) T, Y(1), Y(2), Y(3) +C 20 FORMAT(' At t =',D12.4,' Y =',3D14.6) +C IF (ISTATE .LT. 0 ) GO TO 80 +C 40 TOUT = TOUT*10. +C WRITE (6,60) IWORK(11), IWORK(12), IWORK(13) +C 60 FORMAT(/' No. steps =',I4,' No. r-s =',I4,' No. J-s =',I4) +C STOP +C 80 WRITE (6,90) ISTATE +C 90 FORMAT(///' Error halt.. ISTATE =',I3) +C STOP +C END +C +C SUBROUTINE RESID(NEQ, T, Y, S, R, IRES) +C DOUBLE PRECISION T, Y, S, R +C DIMENSION Y(3), S(3), R(3) +C R(1) = -.04*Y(1) + 1.D4*Y(2)*Y(3) - S(1) +C R(2) = .04*Y(1) - 1.D4*Y(2)*Y(3) - 3.D7*Y(2)*Y(2) - S(2) +C R(3) = Y(1) + Y(2) + Y(3) - 1. +C RETURN +C END +C +C SUBROUTINE APLUSP(NEQ, T, Y, ML, MU, P, NROWP) +C DOUBLE PRECISION T, Y, P +C DIMENSION Y(3), P(NROWP,3) +C P(1,1) = P(1,1) + 1. +C P(2,2) = P(2,2) + 1. +C RETURN +C END +C +C SUBROUTINE DGBYDY(NEQ, T, Y, S, ML, MU, P, NROWP) +C DOUBLE PRECISION T, Y, S, P +C DIMENSION Y(3), S(3), P(NROWP,3) +C P(1,1) = -.04 +C P(1,2) = 1.D4*Y(3) +C P(1,3) = 1.D4*Y(2) +C P(2,1) = .04 +C P(2,2) = -1.D4*Y(3) - 6.D7*Y(2) +C P(2,3) = -1.D4*Y(2) +C P(3,1) = 1. +C P(3,2) = 1. +C P(3,3) = 1. +C RETURN +C END +C +C The output of this program (on a CDC-7600 in single precision) +C is as follows: +C +C At t = 4.0000e-01 Y = 9.851726e-01 3.386406e-05 1.479357e-02 +C At t = 4.0000e+00 Y = 9.055142e-01 2.240418e-05 9.446344e-02 +C At t = 4.0000e+01 Y = 7.158050e-01 9.184616e-06 2.841858e-01 +C At t = 4.0000e+02 Y = 4.504846e-01 3.222434e-06 5.495122e-01 +C At t = 4.0000e+03 Y = 1.831701e-01 8.940379e-07 8.168290e-01 +C At t = 4.0000e+04 Y = 3.897016e-02 1.621193e-07 9.610297e-01 +C At t = 4.0000e+05 Y = 4.935213e-03 1.983756e-08 9.950648e-01 +C At t = 4.0000e+06 Y = 5.159269e-04 2.064759e-09 9.994841e-01 +C At t = 4.0000e+07 Y = 5.306413e-05 2.122677e-10 9.999469e-01 +C At t = 4.0000e+08 Y = 5.494532e-06 2.197826e-11 9.999945e-01 +C At t = 4.0000e+09 Y = 5.129457e-07 2.051784e-12 9.999995e-01 +C At t = 4.0000e+10 Y = -7.170472e-08 -2.868188e-13 1.000000e+00 +C +C No. steps = 330 No. r-s = 404 No. J-s = 69 +C +C----------------------------------------------------------------------- +C Full Description of User Interface to DLSODI. +C +C The user interface to DLSODI consists of the following parts. +C +C 1. The call sequence to Subroutine DLSODI, which is a driver +C routine for the solver. This includes descriptions of both +C the call sequence arguments and of user-supplied routines. +C Following these descriptions is a description of +C optional inputs available through the call sequence, and then +C a description of optional outputs (in the work arrays). +C +C 2. Descriptions of other routines in the DLSODI package that may be +C (optionally) called by the user. These provide the ability to +C alter error message handling, save and restore the internal +C Common, and obtain specified derivatives of the solution y(t). +C +C 3. Descriptions of Common blocks to be declared in overlay +C or similar environments, or to be saved when doing an interrupt +C of the problem and continued solution later. +C +C 4. Description of two routines in the DLSODI package, either of +C which the user may replace with his/her own version, if desired. +C These relate to the measurement of errors. +C +C----------------------------------------------------------------------- +C Part 1. Call Sequence. +C +C The call sequence parameters used for input only are +C RES, ADDA, JAC, NEQ, TOUT, ITOL, RTOL, ATOL, ITASK, +C IOPT, LRW, LIW, MF, +C and those used for both input and output are +C Y, T, ISTATE, YDOTI. +C The work arrays RWORK and IWORK are also used for conditional and +C optional inputs and optional outputs. (The term output here refers +C to the return from Subroutine DLSODI to the user's calling program.) +C +C The legality of input parameters will be thoroughly checked on the +C initial call for the problem, but not checked thereafter unless a +C change in input parameters is flagged by ISTATE = 3 on input. +C +C The descriptions of the call arguments are as follows. +C +C RES = the name of the user-supplied subroutine which supplies +C the residual vector for the ODE system, defined by +C r = g(t,y) - A(t,y) * s +C as a function of the scalar t and the vectors +C s and y (s approximates dy/dt). This subroutine +C is to have the form +C SUBROUTINE RES (NEQ, T, Y, S, R, IRES) +C DOUBLE PRECISION T, Y(*), S(*), R(*) +C where NEQ, T, Y, S, and IRES are input, and R and +C IRES are output. Y, S, and R are arrays of length NEQ. +C On input, IRES indicates how DLSODI will use the +C returned array R, as follows: +C IRES = 1 means that DLSODI needs the full residual, +C r = g - A*s, exactly. +C IRES = -1 means that DLSODI is using R only to compute +C the Jacobian dr/dy by difference quotients. +C The RES routine can ignore IRES, or it can omit some terms +C if IRES = -1. If A does not depend on y, then RES can +C just return R = g when IRES = -1. If g - A*s contains other +C additive terms that are independent of y, these can also be +C dropped, if done consistently, when IRES = -1. +C The subroutine should set the flag IRES if it +C encounters a halt condition or illegal input. +C Otherwise, it should not reset IRES. On output, +C IRES = 1 or -1 represents a normal return, and +C DLSODI continues integrating the ODE. Leave IRES +C unchanged from its input value. +C IRES = 2 tells DLSODI to immediately return control +C to the calling program, with ISTATE = 3. This lets +C the calling program change parameters of the problem, +C if necessary. +C IRES = 3 represents an error condition (for example, an +C illegal value of y). DLSODI tries to integrate the system +C without getting IRES = 3 from RES. If it cannot, DLSODI +C returns with ISTATE = -7 or -1. +C On an DLSODI return with ISTATE = 3, -1, or -7, the values +C of T and Y returned correspond to the last point reached +C successfully without getting the flag IRES = 2 or 3. +C The flag values IRES = 2 and 3 should not be used to +C handle switches or root-stop conditions. This is better +C done by calling DLSODI in a one-step mode and checking the +C stopping function for a sign change at each step. +C If quantities computed in the RES routine are needed +C externally to DLSODI, an extra call to RES should be made +C for this purpose, for consistent and accurate results. +C To get the current dy/dt for the S argument, use DINTDY. +C RES must be declared External in the calling +C program. See note below for more about RES. +C +C ADDA = the name of the user-supplied subroutine which adds the +C matrix A = A(t,y) to another matrix stored in the same form +C as A. The storage form is determined by MITER (see MF). +C This subroutine is to have the form +C SUBROUTINE ADDA (NEQ, T, Y, ML, MU, P, NROWP) +C DOUBLE PRECISION T, Y(*), P(NROWP,*) +C where NEQ, T, Y, ML, MU, and NROWP are input and P is +C output. Y is an array of length NEQ, and the matrix P is +C stored in an NROWP by NEQ array. +C In the full matrix case ( MITER = 1 or 2) ADDA should +C add A to P(i,j). ML and MU are ignored. +C i,j +C In the band matrix case ( MITER = 4 or 5) ADDA should +C add A to P(i-j+MU+1,j). +C i,j +C See JAC for details on this band storage form. +C ADDA must be declared External in the calling program. +C See note below for more information about ADDA. +C +C JAC = the name of the user-supplied subroutine which supplies the +C Jacobian matrix, dr/dy, where r = g - A*s. The form of the +C Jacobian matrix is determined by MITER. JAC is required +C if MITER = 1 or 4 -- otherwise a dummy name can be +C passed. This subroutine is to have the form +C SUBROUTINE JAC ( NEQ, T, Y, S, ML, MU, P, NROWP ) +C DOUBLE PRECISION T, Y(*), S(*), P(NROWP,*) +C where NEQ, T, Y, S, ML, MU, and NROWP are input and P +C is output. Y and S are arrays of length NEQ, and the +C matrix P is stored in an NROWP by NEQ array. +C P is to be loaded with partial derivatives (elements +C of the Jacobian matrix) on output. +C In the full matrix case (MITER = 1), ML and MU +C are ignored and the Jacobian is to be loaded into P +C by columns-- i.e., dr(i)/dy(j) is loaded into P(i,j). +C In the band matrix case (MITER = 4), the elements +C within the band are to be loaded into P by columns, +C with diagonal lines of dr/dy loaded into the +C rows of P. Thus dr(i)/dy(j) is to be loaded +C into P(i-j+MU+1,j). The locations in P in the two +C triangular areas which correspond to nonexistent matrix +C elements can be ignored or loaded arbitrarily, as they +C they are overwritten by DLSODI. ML and MU are the +C half-bandwidth parameters (see IWORK). +C In either case, P is preset to zero by the solver, +C so that only the nonzero elements need be loaded by JAC. +C Each call to JAC is preceded by a call to RES with the same +C arguments NEQ, T, Y, and S. Thus to gain some efficiency, +C intermediate quantities shared by both calculations may be +C saved in a user Common block by RES and not recomputed by JAC +C if desired. Also, JAC may alter the Y array, if desired. +C JAC need not provide dr/dy exactly. A crude +C approximation (possibly with a smaller bandwidth) will do. +C JAC must be declared External in the calling program. +C See note below for more about JAC. +C +C Note on RES, ADDA, and JAC: +C These subroutines may access user-defined quantities in +C NEQ(2),... and/or in Y(NEQ(1)+1),... if NEQ is an array +C (dimensioned in the subroutines) and/or Y has length +C exceeding NEQ(1). However, these routines should not alter +C NEQ(1), Y(1),...,Y(NEQ) or any other input variables. +C See the descriptions of NEQ and Y below. +C +C NEQ = the size of the system (number of first order ordinary +C differential equations or scalar algebraic equations). +C Used only for input. +C NEQ may be decreased, but not increased, during the problem. +C If NEQ is decreased (with ISTATE = 3 on input), the +C remaining components of Y should be left undisturbed, if +C these are to be accessed in RES, ADDA, or JAC. +C +C Normally, NEQ is a scalar, and it is generally referred to +C as a scalar in this user interface description. However, +C NEQ may be an array, with NEQ(1) set to the system size. +C (The DLSODI package accesses only NEQ(1).) In either case, +C this parameter is passed as the NEQ argument in all calls +C to RES, ADDA, and JAC. Hence, if it is an array, +C locations NEQ(2),... may be used to store other integer data +C and pass it to RES, ADDA, or JAC. Each such subroutine +C must include NEQ in a Dimension statement in that case. +C +C Y = a real array for the vector of dependent variables, of +C length NEQ or more. Used for both input and output on the +C first call (ISTATE = 0 or 1), and only for output on other +C calls. On the first call, Y must contain the vector of +C initial values. On output, Y contains the computed solution +C vector, evaluated at T. If desired, the Y array may be used +C for other purposes between calls to the solver. +C +C This array is passed as the Y argument in all calls to RES, +C ADDA, and JAC. Hence its length may exceed NEQ, +C and locations Y(NEQ+1),... may be used to store other real +C data and pass it to RES, ADDA, or JAC. (The DLSODI +C package accesses only Y(1),...,Y(NEQ). ) +C +C YDOTI = a real array for the initial value of the vector +C dy/dt and for work space, of dimension at least NEQ. +C +C On input: +C If ISTATE = 0, then DLSODI will compute the initial value +C of dy/dt, if A is nonsingular. Thus YDOTI will +C serve only as work space and may have any value. +C If ISTATE = 1, then YDOTI must contain the initial value +C of dy/dt. +C If ISTATE = 2 or 3 (continuation calls), then YDOTI +C may have any value. +C Note: If the initial value of A is singular, then +C DLSODI cannot compute the initial value of dy/dt, so +C it must be provided in YDOTI, with ISTATE = 1. +C +C On output, when DLSODI terminates abnormally with ISTATE = +C -1, -4, or -5, YDOTI will contain the residual +C r = g(t,y) - A(t,y)*(dy/dt). If r is large, t is near +C its initial value, and YDOTI is supplied with ISTATE = 1, +C then there may have been an incorrect input value of +C YDOTI = dy/dt, or the problem (as given to DLSODI) +C may not have a solution. +C +C If desired, the YDOTI array may be used for other +C purposes between calls to the solver. +C +C T = the independent variable. On input, T is used only on the +C first call, as the initial point of the integration. +C On output, after each call, T is the value at which a +C computed solution Y is evaluated (usually the same as TOUT). +C on an error return, T is the farthest point reached. +C +C TOUT = the next value of t at which a computed solution is desired. +C Used only for input. +C +C When starting the problem (ISTATE = 0 or 1), TOUT may be +C equal to T for one call, then should .ne. T for the next +C call. For the initial T, an input value of TOUT .ne. T is +C used in order to determine the direction of the integration +C (i.e. the algebraic sign of the step sizes) and the rough +C scale of the problem. Integration in either direction +C (forward or backward in t) is permitted. +C +C If ITASK = 2 or 5 (one-step modes), TOUT is ignored after +C the first call (i.e. the first call with TOUT .ne. T). +C Otherwise, TOUT is required on every call. +C +C If ITASK = 1, 3, or 4, the values of TOUT need not be +C monotone, but a value of TOUT which backs up is limited +C to the current internal T interval, whose endpoints are +C TCUR - HU and TCUR (see optional outputs, below, for +C TCUR and HU). +C +C ITOL = an indicator for the type of error control. See +C description below under ATOL. Used only for input. +C +C RTOL = a relative error tolerance parameter, either a scalar or +C an array of length NEQ. See description below under ATOL. +C Input only. +C +C ATOL = an absolute error tolerance parameter, either a scalar or +C an array of length NEQ. Input only. +C +C The input parameters ITOL, RTOL, and ATOL determine +C the error control performed by the solver. The solver will +C control the vector E = (E(i)) of estimated local errors +C in y, according to an inequality of the form +C RMS-norm of ( E(i)/EWT(i) ) .le. 1, +C where EWT(i) = RTOL(i)*ABS(Y(i)) + ATOL(i), +C and the RMS-norm (root-mean-square norm) here is +C RMS-norm(v) = SQRT(sum v(i)**2 / NEQ). Here EWT = (EWT(i)) +C is a vector of weights which must always be positive, and +C the values of RTOL and ATOL should all be non-negative. +C The following table gives the types (scalar/array) of +C RTOL and ATOL, and the corresponding form of EWT(i). +C +C ITOL RTOL ATOL EWT(i) +C 1 scalar scalar RTOL*ABS(Y(i)) + ATOL +C 2 scalar array RTOL*ABS(Y(i)) + ATOL(i) +C 3 array scalar RTOL(i)*ABS(Y(i)) + ATOL +C 4 array scalar RTOL(i)*ABS(Y(i)) + ATOL(i) +C +C When either of these parameters is a scalar, it need not +C be dimensioned in the user's calling program. +C +C If none of the above choices (with ITOL, RTOL, and ATOL +C fixed throughout the problem) is suitable, more general +C error controls can be obtained by substituting +C user-supplied routines for the setting of EWT and/or for +C the norm calculation. See Part 4 below. +C +C If global errors are to be estimated by making a repeated +C run on the same problem with smaller tolerances, then all +C components of RTOL and ATOL (i.e. of EWT) should be scaled +C down uniformly. +C +C ITASK = an index specifying the task to be performed. +C Input only. ITASK has the following values and meanings. +C 1 means normal computation of output values of y(t) at +C t = TOUT (by overshooting and interpolating). +C 2 means take one step only and return. +C 3 means stop at the first internal mesh point at or +C beyond t = TOUT and return. +C 4 means normal computation of output values of y(t) at +C t = TOUT but without overshooting t = TCRIT. +C TCRIT must be input as RWORK(1). TCRIT may be equal to +C or beyond TOUT, but not behind it in the direction of +C integration. This option is useful if the problem +C has a singularity at or beyond t = TCRIT. +C 5 means take one step, without passing TCRIT, and return. +C TCRIT must be input as RWORK(1). +C +C Note: If ITASK = 4 or 5 and the solver reaches TCRIT +C (within roundoff), it will return T = TCRIT (exactly) to +C indicate this (unless ITASK = 4 and TOUT comes before TCRIT, +C in which case answers at t = TOUT are returned first). +C +C ISTATE = an index used for input and output to specify the +C state of the calculation. +C +C On input, the values of ISTATE are as follows. +C 0 means this is the first call for the problem, and +C DLSODI is to compute the initial value of dy/dt +C (while doing other initializations). See note below. +C 1 means this is the first call for the problem, and +C the initial value of dy/dt has been supplied in +C YDOTI (DLSODI will do other initializations). See note +C below. +C 2 means this is not the first call, and the calculation +C is to continue normally, with no change in any input +C parameters except possibly TOUT and ITASK. +C (If ITOL, RTOL, and/or ATOL are changed between calls +C with ISTATE = 2, the new values will be used but not +C tested for legality.) +C 3 means this is not the first call, and the +C calculation is to continue normally, but with +C a change in input parameters other than +C TOUT and ITASK. Changes are allowed in +C NEQ, ITOL, RTOL, ATOL, IOPT, LRW, LIW, MF, ML, MU, +C and any of the optional inputs except H0. +C (See IWORK description for ML and MU.) +C Note: A preliminary call with TOUT = T is not counted +C as a first call here, as no initialization or checking of +C input is done. (Such a call is sometimes useful for the +C purpose of outputting the initial conditions.) +C Thus the first call for which TOUT .ne. T requires +C ISTATE = 0 or 1 on input. +C +C On output, ISTATE has the following values and meanings. +C 0 or 1 means nothing was done; TOUT = t and +C ISTATE = 0 or 1 on input. +C 2 means that the integration was performed successfully. +C 3 means that the user-supplied Subroutine RES signalled +C DLSODI to halt the integration and return (IRES = 2). +C Integration as far as T was achieved with no occurrence +C of IRES = 2, but this flag was set on attempting the +C next step. +C -1 means an excessive amount of work (more than MXSTEP +C steps) was done on this call, before completing the +C requested task, but the integration was otherwise +C successful as far as T. (MXSTEP is an optional input +C and is normally 500.) To continue, the user may +C simply reset ISTATE to a value .gt. 1 and call again +C (the excess work step counter will be reset to 0). +C In addition, the user may increase MXSTEP to avoid +C this error return (see below on optional inputs). +C -2 means too much accuracy was requested for the precision +C of the machine being used. This was detected before +C completing the requested task, but the integration +C was successful as far as T. To continue, the tolerance +C parameters must be reset, and ISTATE must be set +C to 3. The optional output TOLSF may be used for this +C purpose. (Note: If this condition is detected before +C taking any steps, then an illegal input return +C (ISTATE = -3) occurs instead.) +C -3 means illegal input was detected, before taking any +C integration steps. See written message for details. +C Note: If the solver detects an infinite loop of calls +C to the solver with illegal input, it will cause +C the run to stop. +C -4 means there were repeated error test failures on +C one attempted step, before completing the requested +C task, but the integration was successful as far as T. +C The problem may have a singularity, or the input +C may be inappropriate. +C -5 means there were repeated convergence test failures on +C one attempted step, before completing the requested +C task, but the integration was successful as far as T. +C This may be caused by an inaccurate Jacobian matrix. +C -6 means EWT(i) became zero for some i during the +C integration. pure relative error control (ATOL(i)=0.0) +C was requested on a variable which has now vanished. +C the integration was successful as far as T. +C -7 means that the user-supplied Subroutine RES set +C its error flag (IRES = 3) despite repeated tries by +C DLSODI to avoid that condition. +C -8 means that ISTATE was 0 on input but DLSODI was unable +C to compute the initial value of dy/dt. See the +C printed message for details. +C +C Note: Since the normal output value of ISTATE is 2, +C it does not need to be reset for normal continuation. +C Similarly, ISTATE (= 3) need not be reset if RES told +C DLSODI to return because the calling program must change +C the parameters of the problem. +C Also, since a negative input value of ISTATE will be +C regarded as illegal, a negative output value requires the +C user to change it, and possibly other inputs, before +C calling the solver again. +C +C IOPT = an integer flag to specify whether or not any optional +C inputs are being used on this call. Input only. +C The optional inputs are listed separately below. +C IOPT = 0 means no optional inputs are being used. +C Default values will be used in all cases. +C IOPT = 1 means one or more optional inputs are being used. +C +C RWORK = a real working array (double precision). +C The length of RWORK must be at least +C 20 + NYH*(MAXORD + 1) + 3*NEQ + LENWM where +C NYH = the initial value of NEQ, +C MAXORD = 12 (if METH = 1) or 5 (if METH = 2) (unless a +C smaller value is given as an optional input), +C LENWM = NEQ**2 + 2 if MITER is 1 or 2, and +C LENWM = (2*ML+MU+1)*NEQ + 2 if MITER is 4 or 5. +C (See MF description for the definition of METH and MITER.) +C Thus if MAXORD has its default value and NEQ is constant, +C this length is +C 22 + 16*NEQ + NEQ**2 for MF = 11 or 12, +C 22 + 17*NEQ + (2*ML+MU)*NEQ for MF = 14 or 15, +C 22 + 9*NEQ + NEQ**2 for MF = 21 or 22, +C 22 + 10*NEQ + (2*ML+MU)*NEQ for MF = 24 or 25. +C The first 20 words of RWORK are reserved for conditional +C and optional inputs and optional outputs. +C +C The following word in RWORK is a conditional input: +C RWORK(1) = TCRIT = critical value of t which the solver +C is not to overshoot. Required if ITASK is +C 4 or 5, and ignored otherwise. (See ITASK.) +C +C LRW = the length of the array RWORK, as declared by the user. +C (This will be checked by the solver.) +C +C IWORK = an integer work array. The length of IWORK must be at least +C 20 + NEQ . The first few words of IWORK are used for +C conditional and optional inputs and optional outputs. +C +C The following 2 words in IWORK are conditional inputs: +C IWORK(1) = ML These are the lower and upper +C IWORK(2) = MU half-bandwidths, respectively, of the +C matrices in the problem-- the Jacobian dr/dy +C and the left-hand side matrix A. These +C half-bandwidths exclude the main diagonal, +C so the total bandwidth is ML + MU + 1 . +C The band is defined by the matrix locations +C (i,j) with i-ML .le. j .le. i+MU. ML and MU +C must satisfy 0 .le. ML,MU .le. NEQ-1. +C These are required if MITER is 4 or 5, and +C ignored otherwise. +C ML and MU may in fact be the band parameters +C for matrices to which dr/dy and A are only +C approximately equal. +C +C LIW = the length of the array IWORK, as declared by the user. +C (This will be checked by the solver.) +C +C Note: The work arrays must not be altered between calls to DLSODI +C for the same problem, except possibly for the conditional and +C optional inputs, and except for the last 3*NEQ words of RWORK. +C The latter space is used for internal scratch space, and so is +C available for use by the user outside DLSODI between calls, if +C desired (but not for use by RES, ADDA, or JAC). +C +C MF = the method flag. Used only for input. The legal values of +C MF are 11, 12, 14, 15, 21, 22, 24, and 25. +C MF has decimal digits METH and MITER: MF = 10*METH + MITER. +C METH indicates the basic linear multistep method: +C METH = 1 means the implicit Adams method. +C METH = 2 means the method based on Backward +C Differentiation Formulas (BDFs). +C The BDF method is strongly preferred for stiff +C problems, while the Adams method is preferred when +C the problem is not stiff. If the matrix A(t,y) is +C nonsingular, stiffness here can be taken to mean that of +C the explicit ODE system dy/dt = A-inverse * g. If A is +C singular, the concept of stiffness is not well defined. +C If you do not know whether the problem is stiff, we +C recommend using METH = 2. If it is stiff, the advantage +C of METH = 2 over METH = 1 will be great, while if it is +C not stiff, the advantage of METH = 1 will be slight. +C If maximum efficiency is important, some experimentation +C with METH may be necessary. +C MITER indicates the corrector iteration method: +C MITER = 1 means chord iteration with a user-supplied +C full (NEQ by NEQ) Jacobian. +C MITER = 2 means chord iteration with an internally +C generated (difference quotient) full Jacobian. +C This uses NEQ+1 extra calls to RES per dr/dy +C evaluation. +C MITER = 4 means chord iteration with a user-supplied +C banded Jacobian. +C MITER = 5 means chord iteration with an internally +C generated banded Jacobian (using ML+MU+2 +C extra calls to RES per dr/dy evaluation). +C If MITER = 1 or 4, the user must supply a Subroutine JAC +C (the name is arbitrary) as described above under JAC. +C For other values of MITER, a dummy argument can be used. +C----------------------------------------------------------------------- +C Optional Inputs. +C +C The following is a list of the optional inputs provided for in the +C call sequence. (See also Part 2.) For each such input variable, +C this table lists its name as used in this documentation, its +C location in the call sequence, its meaning, and the default value. +C the use of any of these inputs requires IOPT = 1, and in that +C case all of these inputs are examined. A value of zero for any +C of these optional inputs will cause the default value to be used. +C Thus to use a subset of the optional inputs, simply preload +C locations 5 to 10 in RWORK and IWORK to 0.0 and 0 respectively, and +C then set those of interest to nonzero values. +C +C Name Location Meaning and Default Value +C +C H0 RWORK(5) the step size to be attempted on the first step. +C The default value is determined by the solver. +C +C HMAX RWORK(6) the maximum absolute step size allowed. +C The default value is infinite. +C +C HMIN RWORK(7) the minimum absolute step size allowed. +C The default value is 0. (This lower bound is not +C enforced on the final step before reaching TCRIT +C when ITASK = 4 or 5.) +C +C MAXORD IWORK(5) the maximum order to be allowed. The default +C value is 12 if METH = 1, and 5 if METH = 2. +C If MAXORD exceeds the default value, it will +C be reduced to the default value. +C If MAXORD is changed during the problem, it may +C cause the current order to be reduced. +C +C MXSTEP IWORK(6) maximum number of (internally defined) steps +C allowed during one call to the solver. +C The default value is 500. +C +C MXHNIL IWORK(7) maximum number of messages printed (per problem) +C warning that T + H = T on a step (H = step size). +C This must be positive to result in a non-default +C value. The default value is 10. +C----------------------------------------------------------------------- +C Optional Outputs. +C +C As optional additional output from DLSODI, the variables listed +C below are quantities related to the performance of DLSODI +C which are available to the user. These are communicated by way of +C the work arrays, but also have internal mnemonic names as shown. +C Except where stated otherwise, all of these outputs are defined +C on any successful return from DLSODI, and on any return with +C ISTATE = -1, -2, -4, -5, -6, or -7. On a return with -3 (illegal +C input) or -8, they will be unchanged from their existing values +C (if any), except possibly for TOLSF, LENRW, and LENIW. +C On any error return, outputs relevant to the error will be defined, +C as noted below. +C +C Name Location Meaning +C +C HU RWORK(11) the step size in t last used (successfully). +C +C HCUR RWORK(12) the step size to be attempted on the next step. +C +C TCUR RWORK(13) the current value of the independent variable +C which the solver has actually reached, i.e. the +C current internal mesh point in t. On output, TCUR +C will always be at least as far as the argument +C T, but may be farther (if interpolation was done). +C +C TOLSF RWORK(14) a tolerance scale factor, greater than 1.0, +C computed when a request for too much accuracy was +C detected (ISTATE = -3 if detected at the start of +C the problem, ISTATE = -2 otherwise). If ITOL is +C left unaltered but RTOL and ATOL are uniformly +C scaled up by a factor of TOLSF for the next call, +C then the solver is deemed likely to succeed. +C (The user may also ignore TOLSF and alter the +C tolerance parameters in any other way appropriate.) +C +C NST IWORK(11) the number of steps taken for the problem so far. +C +C NRE IWORK(12) the number of residual evaluations (RES calls) +C for the problem so far. +C +C NJE IWORK(13) the number of Jacobian evaluations (each involving +C an evaluation of A and dr/dy) for the problem so +C far. This equals the number of calls to ADDA and +C (if MITER = 1 or 4) JAC, and the number of matrix +C LU decompositions. +C +C NQU IWORK(14) the method order last used (successfully). +C +C NQCUR IWORK(15) the order to be attempted on the next step. +C +C IMXER IWORK(16) the index of the component of largest magnitude in +C the weighted local error vector ( E(i)/EWT(i) ), +C on an error return with ISTATE = -4 or -5. +C +C LENRW IWORK(17) the length of RWORK actually required. +C This is defined on normal returns and on an illegal +C input return for insufficient storage. +C +C LENIW IWORK(18) the length of IWORK actually required. +C This is defined on normal returns and on an illegal +C input return for insufficient storage. +C +C +C The following two arrays are segments of the RWORK array which +C may also be of interest to the user as optional outputs. +C For each array, the table below gives its internal name, +C its base address in RWORK, and its description. +C +C Name Base Address Description +C +C YH 21 the Nordsieck history array, of size NYH by +C (NQCUR + 1), where NYH is the initial value +C of NEQ. For j = 0,1,...,NQCUR, column j+1 +C of YH contains HCUR**j/factorial(j) times +C the j-th derivative of the interpolating +C polynomial currently representing the solution, +C evaluated at t = TCUR. +C +C ACOR LENRW-NEQ+1 array of size NEQ used for the accumulated +C corrections on each step, scaled on output to +C represent the estimated local error in y on the +C last step. This is the vector E in the descrip- +C tion of the error control. It is defined only +C on a return from DLSODI with ISTATE = 2. +C +C----------------------------------------------------------------------- +C Part 2. Other Routines Callable. +C +C The following are optional calls which the user may make to +C gain additional capabilities in conjunction with DLSODI. +C (The routines XSETUN and XSETF are designed to conform to the +C SLATEC error handling package.) +C +C Form of Call Function +C CALL XSETUN(LUN) Set the logical unit number, LUN, for +C output of messages from DLSODI, if +C the default is not desired. +C The default value of LUN is 6. +C +C CALL XSETF(MFLAG) Set a flag to control the printing of +C messages by DLSODI. +C MFLAG = 0 means do not print. (Danger: +C This risks losing valuable information.) +C MFLAG = 1 means print (the default). +C +C Either of the above calls may be made at +C any time and will take effect immediately. +C +C CALL DSRCOM(RSAV,ISAV,JOB) saves and restores the contents of +C the internal Common blocks used by +C DLSODI (see Part 3 below). +C RSAV must be a real array of length 218 +C or more, and ISAV must be an integer +C array of length 37 or more. +C JOB=1 means save Common into RSAV/ISAV. +C JOB=2 means restore Common from RSAV/ISAV. +C DSRCOM is useful if one is +C interrupting a run and restarting +C later, or alternating between two or +C more problems solved with DLSODI. +C +C CALL DINTDY(,,,,,) Provide derivatives of y, of various +C (see below) orders, at a specified point t, if +C desired. It may be called only after +C a successful return from DLSODI. +C +C The detailed instructions for using DINTDY are as follows. +C The form of the call is: +C +C CALL DINTDY (T, K, RWORK(21), NYH, DKY, IFLAG) +C +C The input parameters are: +C +C T = value of independent variable where answers are desired +C (normally the same as the T last returned by DLSODI). +C For valid results, T must lie between TCUR - HU and TCUR. +C (See optional outputs for TCUR and HU.) +C K = integer order of the derivative desired. K must satisfy +C 0 .le. K .le. NQCUR, where NQCUR is the current order +C (see optional outputs). The capability corresponding +C to K = 0, i.e. computing y(T), is already provided +C by DLSODI directly. Since NQCUR .ge. 1, the first +C derivative dy/dt is always available with DINTDY. +C RWORK(21) = the base address of the history array YH. +C NYH = column length of YH, equal to the initial value of NEQ. +C +C The output parameters are: +C +C DKY = a real array of length NEQ containing the computed value +C of the K-th derivative of y(t). +C IFLAG = integer flag, returned as 0 if K and T were legal, +C -1 if K was illegal, and -2 if T was illegal. +C On an error return, a message is also written. +C----------------------------------------------------------------------- +C Part 3. Common Blocks. +C +C If DLSODI is to be used in an overlay situation, the user +C must declare, in the primary overlay, the variables in: +C (1) the call sequence to DLSODI, and +C (2) the internal Common block +C /DLS001/ of length 255 (218 double precision words +C followed by 37 integer words), +C +C If DLSODI is used on a system in which the contents of internal +C Common blocks are not preserved between calls, the user should +C declare the above Common block in the calling program to insure +C that their contents are preserved. +C +C If the solution of a given problem by DLSODI is to be interrupted +C and then later continued, such as when restarting an interrupted run +C or alternating between two or more problems, the user should save, +C following the return from the last DLSODI call prior to the +C interruption, the contents of the call sequence variables and the +C internal Common blocks, and later restore these values before the +C next DLSODI call for that problem. To save and restore the Common +C blocks, use Subroutine DSRCOM (see Part 2 above). +C +C----------------------------------------------------------------------- +C Part 4. Optionally Replaceable Solver Routines. +C +C Below are descriptions of two routines in the DLSODI package which +C relate to the measurement of errors. Either routine can be +C replaced by a user-supplied version, if desired. However, since such +C a replacement may have a major impact on performance, it should be +C done only when absolutely necessary, and only with great caution. +C (Note: The means by which the package version of a routine is +C superseded by the user's version may be system-dependent.) +C +C (a) DEWSET. +C The following subroutine is called just before each internal +C integration step, and sets the array of error weights, EWT, as +C described under ITOL/RTOL/ATOL above: +C SUBROUTINE DEWSET (NEQ, ITOL, RTOL, ATOL, YCUR, EWT) +C where NEQ, ITOL, RTOL, and ATOL are as in the DLSODI call sequence, +C YCUR contains the current dependent variable vector, and +C EWT is the array of weights set by DEWSET. +C +C If the user supplies this subroutine, it must return in EWT(i) +C (i = 1,...,NEQ) a positive quantity suitable for comparing errors +C in y(i) to. The EWT array returned by DEWSET is passed to the DVNORM +C routine (see below), and also used by DLSODI in the computation +C of the optional output IMXER, the diagonal Jacobian approximation, +C and the increments for difference quotient Jacobians. +C +C In the user-supplied version of DEWSET, it may be desirable to use +C the current values of derivatives of y. Derivatives up to order NQ +C are available from the history array YH, described above under +C optional outputs. In DEWSET, YH is identical to the YCUR array, +C extended to NQ + 1 columns with a column length of NYH and scale +C factors of H**j/factorial(j). On the first call for the problem, +C given by NST = 0, NQ is 1 and H is temporarily set to 1.0. +C NYH is the initial value of NEQ. The quantities NQ, H, and NST +C can be obtained by including in DEWSET the statements: +C DOUBLE PRECISION RLS +C COMMON /DLS001/ RLS(218),ILS(37) +C NQ = ILS(33) +C NST = ILS(34) +C H = RLS(212) +C Thus, for example, the current value of dy/dt can be obtained as +C YCUR(NYH+i)/H (i=1,...,NEQ) (and the division by H is +C unnecessary when NST = 0). +C +C (b) DVNORM. +C The following is a real function routine which computes the weighted +C root-mean-square norm of a vector v: +C D = DVNORM (N, V, W) +C where: +C N = the length of the vector, +C V = real array of length N containing the vector, +C W = real array of length N containing weights, +C D = SQRT( (1/N) * sum(V(i)*W(i))**2 ). +C DVNORM is called with N = NEQ and with W(i) = 1.0/EWT(i), where +C EWT is as set by Subroutine DEWSET. +C +C If the user supplies this function, it should return a non-negative +C value of DVNORM suitable for use in the error control in DLSODI. +C None of the arguments should be altered by DVNORM. +C For example, a user-supplied DVNORM routine might: +C -substitute a max-norm of (V(i)*W(i)) for the RMS-norm, or +C -ignore some components of V in the norm, with the effect of +C suppressing the error control on those components of y. +C----------------------------------------------------------------------- +C +C***REVISION HISTORY (YYYYMMDD) +C 19800424 DATE WRITTEN +C 19800519 Corrected access of YH on forced order reduction; +C numerous corrections to prologues and other comments. +C 19800617 In main driver, added loading of SQRT(UROUND) in RWORK; +C minor corrections to main prologue. +C 19800903 Corrected ISTATE logic; minor changes in prologue. +C 19800923 Added zero initialization of HU and NQU. +C 19801028 Reorganized RES calls in AINVG, STODI, and PREPJI; +C in LSODI, corrected NRE increment and reset LDY0 at 580; +C numerous corrections to main prologue. +C 19801218 Revised XERRWD routine; minor corrections to main prologue. +C 19810330 Added Common block /LSI001/; use LSODE's INTDY and SOLSY; +C minor corrections to XERRWD and error message at 604; +C minor corrections to declarations; corrections to prologues. +C 19810818 Numerous revisions: replaced EWT by 1/EWT; used flags +C JCUR, ICF, IERPJ, IERSL between STODI and subordinates; +C added tuning parameters CCMAX, MAXCOR, MSBP, MXNCF; +C reorganized returns from STODI; reorganized type decls.; +C fixed message length in XERRWD; changed default LUNIT to 6; +C changed Common lengths; changed comments throughout. +C 19820906 Corrected use of ABS(H) in STODI; minor comment fixes. +C 19830510 Numerous revisions: revised diff. quotient increment; +C eliminated block /LSI001/, using IERPJ flag; +C revised STODI logic after PJAC return; +C revised tuning of H change and step attempts in STODI; +C corrections to main prologue and internal comments. +C 19870330 Major update: corrected comments throughout; +C removed TRET from Common; rewrote EWSET with 4 loops; +C fixed t test in INTDY; added Cray directives in STODI; +C in STODI, fixed DELP init. and logic around PJAC call; +C combined routines to save/restore Common; +C passed LEVEL = 0 in error message calls (except run abort). +C 20010425 Major update: convert source lines to upper case; +C added *DECK lines; changed from 1 to * in dummy dimensions; +C changed names R1MACH/D1MACH to RUMACH/DUMACH; +C renamed routines for uniqueness across single/double prec.; +C converted intrinsic names to generic form; +C removed ILLIN and NTREP (data loaded) from Common; +C removed all 'own' variables from Common; +C changed error messages to quoted strings; +C replaced XERRWV/XERRWD with 1993 revised version; +C converted prologues, comments, error messages to mixed case; +C converted arithmetic IF statements to logical IF statements; +C numerous corrections to prologues and internal comments. +C 20010507 Converted single precision source to double precision. +C 20020502 Corrected declarations in descriptions of user routines. +C 20031105 Restored 'own' variables to Common block, to enable +C interrupt/restart feature. +C 20031112 Added SAVE statements for data-loaded constants. +C 20031117 Changed internal names NRE, LSAVR to NFE, LSAVF resp. +C +C----------------------------------------------------------------------- +C Other routines in the DLSODI package. +C +C In addition to Subroutine DLSODI, the DLSODI package includes the +C following subroutines and function routines: +C DAINVG computes the initial value of the vector +C dy/dt = A-inverse * g +C DINTDY computes an interpolated value of the y vector at t = TOUT. +C DSTODI is the core integrator, which does one step of the +C integration and the associated error control. +C DCFODE sets all method coefficients and test constants. +C DPREPJI computes and preprocesses the Jacobian matrix +C and the Newton iteration matrix P. +C DSOLSY manages solution of linear system in chord iteration. +C DEWSET sets the error weight vector EWT before each step. +C DVNORM computes the weighted RMS-norm of a vector. +C DSRCOM is a user-callable routine to save and restore +C the contents of the internal Common blocks. +C DGEFA and DGESL are routines from LINPACK for solving full +C systems of linear algebraic equations. +C DGBFA and DGBSL are routines from LINPACK for solving banded +C linear systems. +C DUMACH computes the unit roundoff in a machine-independent manner. +C XERRWD, XSETUN, XSETF, IXSAV, and IUMACH handle the printing of all +C error messages and warnings. XERRWD is machine-dependent. +C Note: DVNORM, DUMACH, IXSAV, and IUMACH are function routines. +C All the others are subroutines. +C +C----------------------------------------------------------------------- + EXTERNAL DPREPJI, DSOLSY + DOUBLE PRECISION DUMACH, DVNORM + INTEGER INIT, MXSTEP, MXHNIL, NHNIL, NSLAST, NYH, IOWNS, + 1 ICF, IERPJ, IERSL, JCUR, JSTART, KFLAG, L, + 2 LYH, LEWT, LACOR, LSAVF, LWM, LIWM, METH, MITER, + 3 MAXORD, MAXCOR, MSBP, MXNCF, N, NQ, NST, NFE, NJE, NQU + INTEGER I, I1, I2, IER, IFLAG, IMXER, IRES, KGO, + 1 LENIW, LENRW, LENWM, LP, LYD0, ML, MORD, MU, MXHNL0, MXSTP0 + DOUBLE PRECISION ROWNS, + 1 CCMAX, EL0, H, HMIN, HMXI, HU, RC, TN, UROUND + DOUBLE PRECISION ATOLI, AYI, BIG, EWTI, H0, HMAX, HMX, RH, RTOLI, + 1 TCRIT, TDIST, TNEXT, TOL, TOLSF, TP, SIZE, SUM, W0 + DIMENSION MORD(2) + LOGICAL IHIT + CHARACTER*60 MSG + SAVE MORD, MXSTP0, MXHNL0 +C----------------------------------------------------------------------- +C The following internal Common block contains +C (a) variables which are local to any subroutine but whose values must +C be preserved between calls to the routine ("own" variables), and +C (b) variables which are communicated between subroutines. +C The block DLS001 is declared in subroutines DLSODI, DINTDY, DSTODI, +C DPREPJI, and DSOLSY. +C Groups of variables are replaced by dummy arrays in the Common +C declarations in routines where those variables are not used. +C----------------------------------------------------------------------- + COMMON /DLS001/ ROWNS(209), + 1 CCMAX, EL0, H, HMIN, HMXI, HU, RC, TN, UROUND, + 2 INIT, MXSTEP, MXHNIL, NHNIL, NSLAST, NYH, IOWNS(6), + 3 ICF, IERPJ, IERSL, JCUR, JSTART, KFLAG, L, + 4 LYH, LEWT, LACOR, LSAVF, LWM, LIWM, METH, MITER, + 5 MAXORD, MAXCOR, MSBP, MXNCF, N, NQ, NST, NFE, NJE, NQU +C + DATA MORD(1),MORD(2)/12,5/, MXSTP0/500/, MXHNL0/10/ +C----------------------------------------------------------------------- +C Block A. +C This code block is executed on every call. +C It tests ISTATE and ITASK for legality and branches appropriately. +C If ISTATE .gt. 1 but the flag INIT shows that initialization has +C not yet been done, an error return occurs. +C If ISTATE = 0 or 1 and TOUT = T, return immediately. +C----------------------------------------------------------------------- + IF (ISTATE .LT. 0 .OR. ISTATE .GT. 3) GO TO 601 + IF (ITASK .LT. 1 .OR. ITASK .GT. 5) GO TO 602 + IF (ISTATE .LE. 1) GO TO 10 + IF (INIT .EQ. 0) GO TO 603 + IF (ISTATE .EQ. 2) GO TO 200 + GO TO 20 + 10 INIT = 0 + IF (TOUT .EQ. T) RETURN +C----------------------------------------------------------------------- +C Block B. +C The next code block is executed for the initial call (ISTATE = 0 or 1) +C or for a continuation call with parameter changes (ISTATE = 3). +C It contains checking of all inputs and various initializations. +C +C First check legality of the non-optional inputs NEQ, ITOL, IOPT, +C MF, ML, and MU. +C----------------------------------------------------------------------- + 20 IF (NEQ(1) .LE. 0) GO TO 604 + IF (ISTATE .LE. 1) GO TO 25 + IF (NEQ(1) .GT. N) GO TO 605 + 25 N = NEQ(1) + IF (ITOL .LT. 1 .OR. ITOL .GT. 4) GO TO 606 + IF (IOPT .LT. 0 .OR. IOPT .GT. 1) GO TO 607 + METH = MF/10 + MITER = MF - 10*METH + IF (METH .LT. 1 .OR. METH .GT. 2) GO TO 608 + IF (MITER .LE. 0 .OR. MITER .GT. 5) GO TO 608 + IF (MITER .EQ. 3) GO TO 608 + IF (MITER .LT. 3) GO TO 30 + ML = IWORK(1) + MU = IWORK(2) + IF (ML .LT. 0 .OR. ML .GE. N) GO TO 609 + IF (MU .LT. 0 .OR. MU .GE. N) GO TO 610 + 30 CONTINUE +C Next process and check the optional inputs. -------------------------- + IF (IOPT .EQ. 1) GO TO 40 + MAXORD = MORD(METH) + MXSTEP = MXSTP0 + MXHNIL = MXHNL0 + IF (ISTATE .LE. 1) H0 = 0.0D0 + HMXI = 0.0D0 + HMIN = 0.0D0 + GO TO 60 + 40 MAXORD = IWORK(5) + IF (MAXORD .LT. 0) GO TO 611 + IF (MAXORD .EQ. 0) MAXORD = 100 + MAXORD = MIN(MAXORD,MORD(METH)) + MXSTEP = IWORK(6) + IF (MXSTEP .LT. 0) GO TO 612 + IF (MXSTEP .EQ. 0) MXSTEP = MXSTP0 + MXHNIL = IWORK(7) + IF (MXHNIL .LT. 0) GO TO 613 + IF (MXHNIL .EQ. 0) MXHNIL = MXHNL0 + IF (ISTATE .GT. 1) GO TO 50 + H0 = RWORK(5) + IF ((TOUT - T)*H0 .LT. 0.0D0) GO TO 614 + 50 HMAX = RWORK(6) + IF (HMAX .LT. 0.0D0) GO TO 615 + HMXI = 0.0D0 + IF (HMAX .GT. 0.0D0) HMXI = 1.0D0/HMAX + HMIN = RWORK(7) + IF (HMIN .LT. 0.0D0) GO TO 616 +C----------------------------------------------------------------------- +C Set work array pointers and check lengths LRW and LIW. +C Pointers to segments of RWORK and IWORK are named by prefixing L to +C the name of the segment. E.g., the segment YH starts at RWORK(LYH). +C Segments of RWORK (in order) are denoted YH, WM, EWT, SAVR, ACOR. +C----------------------------------------------------------------------- + 60 LYH = 21 + IF (ISTATE .LE. 1) NYH = N + LWM = LYH + (MAXORD + 1)*NYH + IF (MITER .LE. 2) LENWM = N*N + 2 + IF (MITER .GE. 4) LENWM = (2*ML + MU + 1)*N + 2 + LEWT = LWM + LENWM + LSAVF = LEWT + N + LACOR = LSAVF + N + LENRW = LACOR + N - 1 + IWORK(17) = LENRW + LIWM = 1 + LENIW = 20 + N + IWORK(18) = LENIW + IF (LENRW .GT. LRW) GO TO 617 + IF (LENIW .GT. LIW) GO TO 618 +C Check RTOL and ATOL for legality. ------------------------------------ + RTOLI = RTOL(1) + ATOLI = ATOL(1) + DO 70 I = 1,N + IF (ITOL .GE. 3) RTOLI = RTOL(I) + IF (ITOL .EQ. 2 .OR. ITOL .EQ. 4) ATOLI = ATOL(I) + IF (RTOLI .LT. 0.0D0) GO TO 619 + IF (ATOLI .LT. 0.0D0) GO TO 620 + 70 CONTINUE + IF (ISTATE .LE. 1) GO TO 100 +C If ISTATE = 3, set flag to signal parameter changes to DSTODI. ------- + JSTART = -1 + IF (NQ .LE. MAXORD) GO TO 90 +C MAXORD was reduced below NQ. Copy YH(*,MAXORD+2) into YDOTI.--------- + DO 80 I = 1,N + 80 YDOTI(I) = RWORK(I+LWM-1) +C Reload WM(1) = RWORK(lWM), since lWM may have changed. --------------- + 90 RWORK(LWM) = SQRT(UROUND) + IF (N .EQ. NYH) GO TO 200 +C NEQ was reduced. Zero part of YH to avoid undefined references. ----- + I1 = LYH + L*NYH + I2 = LYH + (MAXORD + 1)*NYH - 1 + IF (I1 .GT. I2) GO TO 200 + DO 95 I = I1,I2 + 95 RWORK(I) = 0.0D0 + GO TO 200 +C----------------------------------------------------------------------- +C Block C. +C The next block is for the initial call only (ISTATE = 0 or 1). +C It contains all remaining initializations, the call to DAINVG +C (if ISTATE = 1), and the calculation of the initial step size. +C The error weights in EWT are inverted after being loaded. +C----------------------------------------------------------------------- + 100 UROUND = DUMACH() + TN = T + IF (ITASK .NE. 4 .AND. ITASK .NE. 5) GO TO 105 + TCRIT = RWORK(1) + IF ((TCRIT - TOUT)*(TOUT - T) .LT. 0.0D0) GO TO 625 + IF (H0 .NE. 0.0D0 .AND. (T + H0 - TCRIT)*H0 .GT. 0.0D0) + 1 H0 = TCRIT - T + 105 JSTART = 0 + RWORK(LWM) = SQRT(UROUND) + NHNIL = 0 + NST = 0 + NFE = 0 + NJE = 0 + NSLAST = 0 + HU = 0.0D0 + NQU = 0 + CCMAX = 0.3D0 + MAXCOR = 3 + MSBP = 20 + MXNCF = 10 +C Compute initial dy/dt, if necessary, and load it and initial Y into YH + LYD0 = LYH + NYH + LP = LWM + 1 + IF (ISTATE .EQ. 1) GO TO 120 +C DLSODI must compute initial dy/dt (LYD0 points to YH(*,2)). ---------- + CALL DAINVG( RES, ADDA, NEQ, T, Y, RWORK(LYD0), MITER, + 1 ML, MU, RWORK(LP), IWORK(21), IER ) + NFE = NFE + 1 + IF (IER .LT. 0) GO TO 560 + IF (IER .GT. 0) GO TO 565 + DO 115 I = 1,N + 115 RWORK(I+LYH-1) = Y(I) + GO TO 130 +C Initial dy/dt was supplied. Load into YH (LYD0 points to YH(*,2).). - + 120 DO 125 I = 1,N + RWORK(I+LYH-1) = Y(I) + 125 RWORK(I+LYD0-1) = YDOTI(I) +C Load and invert the EWT array. (H is temporarily set to 1.0.) ------- + 130 CONTINUE + NQ = 1 + H = 1.0D0 + CALL DEWSET (N, ITOL, RTOL, ATOL, RWORK(LYH), RWORK(LEWT)) + DO 135 I = 1,N + IF (RWORK(I+LEWT-1) .LE. 0.0D0) GO TO 621 + 135 RWORK(I+LEWT-1) = 1.0D0/RWORK(I+LEWT-1) +C----------------------------------------------------------------------- +C The coding below computes the step size, H0, to be attempted on the +C first step, unless the user has supplied a value for this. +C First check that TOUT - T differs significantly from zero. +C A scalar tolerance quantity TOL is computed, as MAX(RTOL(i)) +C if this is positive, or MAX(ATOL(i)/ABS(Y(i))) otherwise, adjusted +C so as to be between 100*UROUND and 1.0E-3. +C Then the computed value H0 is given by.. +C NEQ +C H0**2 = TOL / ( w0**-2 + (1/NEQ) * Sum ( YDOT(i)/ywt(i) )**2 ) +C 1 +C where w0 = MAX ( ABS(T), ABS(TOUT) ), +C YDOT(i) = i-th component of initial value of dy/dt, +C ywt(i) = EWT(i)/TOL (a weight for y(i)). +C The sign of H0 is inferred from the initial values of TOUT and T. +C----------------------------------------------------------------------- + IF (H0 .NE. 0.0D0) GO TO 180 + TDIST = ABS(TOUT - T) + W0 = MAX(ABS(T),ABS(TOUT)) + IF (TDIST .LT. 2.0D0*UROUND*W0) GO TO 622 + TOL = RTOL(1) + IF (ITOL .LE. 2) GO TO 145 + DO 140 I = 1,N + 140 TOL = MAX(TOL,RTOL(I)) + 145 IF (TOL .GT. 0.0D0) GO TO 160 + ATOLI = ATOL(1) + DO 150 I = 1,N + IF (ITOL .EQ. 2 .OR. ITOL .EQ. 4) ATOLI = ATOL(I) + AYI = ABS(Y(I)) + IF (AYI .NE. 0.0D0) TOL = MAX(TOL,ATOLI/AYI) + 150 CONTINUE + 160 TOL = MAX(TOL,100.0D0*UROUND) + TOL = MIN(TOL,0.001D0) + SUM = DVNORM (N, RWORK(LYD0), RWORK(LEWT)) + SUM = 1.0D0/(TOL*W0*W0) + TOL*SUM**2 + H0 = 1.0D0/SQRT(SUM) + H0 = MIN(H0,TDIST) + H0 = SIGN(H0,TOUT-T) +C Adjust H0 if necessary to meet HMAX bound. --------------------------- + 180 RH = ABS(H0)*HMXI + IF (RH .GT. 1.0D0) H0 = H0/RH +C Load H with H0 and scale YH(*,2) by H0. ------------------------------ + H = H0 + DO 190 I = 1,N + 190 RWORK(I+LYD0-1) = H0*RWORK(I+LYD0-1) + GO TO 270 +C----------------------------------------------------------------------- +C Block D. +C The next code block is for continuation calls only (ISTATE = 2 or 3) +C and is to check stop conditions before taking a step. +C----------------------------------------------------------------------- + 200 NSLAST = NST + GO TO (210, 250, 220, 230, 240), ITASK + 210 IF ((TN - TOUT)*H .LT. 0.0D0) GO TO 250 + CALL DINTDY (TOUT, 0, RWORK(LYH), NYH, Y, IFLAG) + IF (IFLAG .NE. 0) GO TO 627 + T = TOUT + GO TO 420 + 220 TP = TN - HU*(1.0D0 + 100.0D0*UROUND) + IF ((TP - TOUT)*H .GT. 0.0D0) GO TO 623 + IF ((TN - TOUT)*H .LT. 0.0D0) GO TO 250 + GO TO 400 + 230 TCRIT = RWORK(1) + IF ((TN - TCRIT)*H .GT. 0.0D0) GO TO 624 + IF ((TCRIT - TOUT)*H .LT. 0.0D0) GO TO 625 + IF ((TN - TOUT)*H .LT. 0.0D0) GO TO 245 + CALL DINTDY (TOUT, 0, RWORK(LYH), NYH, Y, IFLAG) + IF (IFLAG .NE. 0) GO TO 627 + T = TOUT + GO TO 420 + 240 TCRIT = RWORK(1) + IF ((TN - TCRIT)*H .GT. 0.0D0) GO TO 624 + 245 HMX = ABS(TN) + ABS(H) + IHIT = ABS(TN - TCRIT) .LE. 100.0D0*UROUND*HMX + IF (IHIT) GO TO 400 + TNEXT = TN + H*(1.0D0 + 4.0D0*UROUND) + IF ((TNEXT - TCRIT)*H .LE. 0.0D0) GO TO 250 + H = (TCRIT - TN)*(1.0D0 - 4.0D0*UROUND) + IF (ISTATE .EQ. 2) JSTART = -2 +C----------------------------------------------------------------------- +C Block E. +C The next block is normally executed for all calls and contains +C the call to the one-step core integrator DSTODI. +C +C This is a looping point for the integration steps. +C +C First check for too many steps being taken, update EWT (if not at +C start of problem), check for too much accuracy being requested, and +C check for H below the roundoff level in T. +C----------------------------------------------------------------------- + 250 CONTINUE + IF ((NST-NSLAST) .GE. MXSTEP) GO TO 500 + CALL DEWSET (N, ITOL, RTOL, ATOL, RWORK(LYH), RWORK(LEWT)) + DO 260 I = 1,N + IF (RWORK(I+LEWT-1) .LE. 0.0D0) GO TO 510 + 260 RWORK(I+LEWT-1) = 1.0D0/RWORK(I+LEWT-1) + 270 TOLSF = UROUND*DVNORM (N, RWORK(LYH), RWORK(LEWT)) + IF (TOLSF .LE. 1.0D0) GO TO 280 + TOLSF = TOLSF*2.0D0 + IF (NST .EQ. 0) GO TO 626 + GO TO 520 + 280 IF ((TN + H) .NE. TN) GO TO 290 + NHNIL = NHNIL + 1 + IF (NHNIL .GT. MXHNIL) GO TO 290 + MSG = 'DLSODI- Warning..Internal T (=R1) and H (=R2) are' + CALL XERRWD (MSG, 50, 101, 0, 0, 0, 0, 0, 0.0D0, 0.0D0) + MSG=' such that in the machine, T + H = T on the next step ' + CALL XERRWD (MSG, 60, 101, 0, 0, 0, 0, 0, 0.0D0, 0.0D0) + MSG = ' (H = step size). Solver will continue anyway.' + CALL XERRWD (MSG, 50, 101, 0, 0, 0, 0, 2, TN, H) + IF (NHNIL .LT. MXHNIL) GO TO 290 + MSG = 'DLSODI- Above warning has been issued I1 times. ' + CALL XERRWD (MSG, 50, 102, 0, 0, 0, 0, 0, 0.0D0, 0.0D0) + MSG = ' It will not be issued again for this problem.' + CALL XERRWD (MSG, 50, 102, 0, 1, MXHNIL, 0, 0, 0.0D0, 0.0D0) + 290 CONTINUE +C----------------------------------------------------------------------- +C CALL DSTODI(NEQ,Y,YH,NYH,YH1,EWT,SAVF,SAVR,ACOR,WM,IWM,RES, +C ADDA,JAC,DPREPJI,DSOLSY) +C Note: SAVF in DSTODI occupies the same space as YDOTI in DLSODI. +C----------------------------------------------------------------------- + CALL DSTODI (NEQ, Y, RWORK(LYH), NYH, RWORK(LYH), RWORK(LEWT), + 1 YDOTI, RWORK(LSAVF), RWORK(LACOR), RWORK(LWM), + 2 IWORK(LIWM), RES, ADDA, JAC, DPREPJI, DSOLSY ) + KGO = 1 - KFLAG + GO TO (300, 530, 540, 400, 550), KGO +C +C KGO = 1:success; 2:error test failure; 3:convergence failure; +C 4:RES ordered return. 5:RES returned error. +C----------------------------------------------------------------------- +C Block F. +C The following block handles the case of a successful return from the +C core integrator (KFLAG = 0). Test for stop conditions. +C----------------------------------------------------------------------- + 300 INIT = 1 + GO TO (310, 400, 330, 340, 350), ITASK +C ITASK = 1. If TOUT has been reached, interpolate. ------------------- + 310 IF ((TN - TOUT)*H .LT. 0.0D0) GO TO 250 + CALL DINTDY (TOUT, 0, RWORK(LYH), NYH, Y, IFLAG) + T = TOUT + GO TO 420 +C ITASK = 3. Jump to exit if TOUT was reached. ------------------------ + 330 IF ((TN - TOUT)*H .GE. 0.0D0) GO TO 400 + GO TO 250 +C ITASK = 4. see if TOUT or TCRIT was reached. adjust h if necessary. + 340 IF ((TN - TOUT)*H .LT. 0.0D0) GO TO 345 + CALL DINTDY (TOUT, 0, RWORK(LYH), NYH, Y, IFLAG) + T = TOUT + GO TO 420 + 345 HMX = ABS(TN) + ABS(H) + IHIT = ABS(TN - TCRIT) .LE. 100.0D0*UROUND*HMX + IF (IHIT) GO TO 400 + TNEXT = TN + H*(1.0D0 + 4.0D0*UROUND) + IF ((TNEXT - TCRIT)*H .LE. 0.0D0) GO TO 250 + H = (TCRIT - TN)*(1.0D0 - 4.0D0*UROUND) + JSTART = -2 + GO TO 250 +C ITASK = 5. See if TCRIT was reached and jump to exit. --------------- + 350 HMX = ABS(TN) + ABS(H) + IHIT = ABS(TN - TCRIT) .LE. 100.0D0*UROUND*HMX +C----------------------------------------------------------------------- +C Block G. +C The following block handles all successful returns from DLSODI. +C if ITASK .ne. 1, Y is loaded from YH and T is set accordingly. +C ISTATE is set to 2, and the optional outputs are loaded into the +C work arrays before returning. +C----------------------------------------------------------------------- + 400 DO 410 I = 1,N + 410 Y(I) = RWORK(I+LYH-1) + T = TN + IF (ITASK .NE. 4 .AND. ITASK .NE. 5) GO TO 420 + IF (IHIT) T = TCRIT + 420 ISTATE = 2 + IF (KFLAG .EQ. -3) ISTATE = 3 + RWORK(11) = HU + RWORK(12) = H + RWORK(13) = TN + IWORK(11) = NST + IWORK(12) = NFE + IWORK(13) = NJE + IWORK(14) = NQU + IWORK(15) = NQ + RETURN +C----------------------------------------------------------------------- +C Block H. +C The following block handles all unsuccessful returns other than +C those for illegal input. First the error message routine is called. +C If there was an error test or convergence test failure, IMXER is set. +C Then Y is loaded from YH and T is set to TN. +C The optional outputs are loaded into the work arrays before returning. +C----------------------------------------------------------------------- +C The maximum number of steps was taken before reaching TOUT. ---------- + 500 MSG = 'DLSODI- At current T (=R1), MXSTEP (=I1) steps ' + CALL XERRWD (MSG, 50, 201, 0, 0, 0, 0, 0, 0.0D0, 0.0D0) + MSG = ' taken on this call before reaching TOUT ' + CALL XERRWD (MSG, 50, 201, 0, 1, MXSTEP, 0, 1, TN, 0.0D0) + ISTATE = -1 + GO TO 580 +C EWT(i) .le. 0.0 for some i (not at start of problem). ---------------- + 510 EWTI = RWORK(LEWT+I-1) + MSG = 'DLSODI- At T (=R1), EWT(I1) has become R2 .le. 0.' + CALL XERRWD (MSG, 50, 202, 0, 1, I, 0, 2, TN, EWTI) + ISTATE = -6 + GO TO 590 +C Too much accuracy requested for machine precision. ------------------- + 520 MSG = 'DLSODI- At T (=R1), too much accuracy requested ' + CALL XERRWD (MSG, 50, 203, 0, 0, 0, 0, 0, 0.0D0, 0.0D0) + MSG = ' for precision of machine.. See TOLSF (=R2) ' + CALL XERRWD (MSG, 50, 203, 0, 0, 0, 0, 2, TN, TOLSF) + RWORK(14) = TOLSF + ISTATE = -2 + GO TO 590 +C KFLAG = -1. Error test failed repeatedly or with ABS(H) = HMIN. ----- + 530 MSG = 'DLSODI- At T(=R1) and step size H(=R2), the error' + CALL XERRWD (MSG, 50, 204, 0, 0, 0, 0, 0, 0.0D0, 0.0D0) + MSG = ' test failed repeatedly or with ABS(H) = HMIN' + CALL XERRWD (MSG, 50, 204, 0, 0, 0, 0, 2, TN, H) + ISTATE = -4 + GO TO 570 +C KFLAG = -2. Convergence failed repeatedly or with ABS(H) = HMIN. ---- + 540 MSG = 'DLSODI- At T (=R1) and step size H (=R2), the ' + CALL XERRWD (MSG, 50, 205, 0, 0, 0, 0, 0, 0.0D0, 0.0D0) + MSG = ' corrector convergence failed repeatedly ' + CALL XERRWD (MSG, 50, 205, 0, 0, 0, 0, 0, 0.0D0, 0.0D0) + MSG = ' or with ABS(H) = HMIN ' + CALL XERRWD (MSG, 30, 205, 0, 0, 0, 0, 2, TN, H) + ISTATE = -5 + GO TO 570 +C IRES = 3 returned by RES, despite retries by DSTODI. ----------------- + 550 MSG = 'DLSODI- At T (=R1) residual routine returned ' + CALL XERRWD (MSG, 50, 206, 0, 0, 0, 0, 0, 0.0D0, 0.0D0) + MSG = ' error IRES = 3 repeatedly. ' + CALL XERRWD (MSG, 40, 206, 0, 0, 0, 0, 1, TN, 0.0D0) + ISTATE = -7 + GO TO 590 +C DAINVG failed because matrix A was singular. ------------------------- + 560 IER = -IER + MSG='DLSODI- Attempt to initialize dy/dt failed: Matrix A is ' + CALL XERRWD (MSG, 60, 207, 0, 0, 0, 0, 0, 0.0D0, 0.0D0) + MSG = ' singular. DGEFA or DGBFA returned INFO = I1' + CALL XERRWD (MSG, 50, 207, 0, 1, IER, 0, 0, 0.0D0, 0.0D0) + ISTATE = -8 + RETURN +C DAINVG failed because RES set IRES to 2 or 3. ------------------------ + 565 MSG = 'DLSODI- Attempt to initialize dy/dt failed ' + CALL XERRWD (MSG, 50, 208, 0, 0, 0, 0, 0, 0.0D0, 0.0D0) + MSG = ' because residual routine set its error flag ' + CALL XERRWD (MSG, 50, 208, 0, 0, 0, 0, 0, 0.0D0, 0.0D0) + MSG = ' to IRES = (I1)' + CALL XERRWD (MSG, 20, 208, 0, 1, IER, 0, 0, 0.0D0, 0.0D0) + ISTATE = -8 + RETURN +C Compute IMXER if relevant. ------------------------------------------- + 570 BIG = 0.0D0 + IMXER = 1 + DO 575 I = 1,N + SIZE = ABS(RWORK(I+LACOR-1)*RWORK(I+LEWT-1)) + IF (BIG .GE. SIZE) GO TO 575 + BIG = SIZE + IMXER = I + 575 CONTINUE + IWORK(16) = IMXER +C Compute residual if relevant. ---------------------------------------- + 580 LYD0 = LYH + NYH + DO 585 I = 1,N + RWORK(I+LSAVF-1) = RWORK(I+LYD0-1)/H + 585 Y(I) = RWORK(I+LYH-1) + IRES = 1 + CALL RES (NEQ, TN, Y, RWORK(LSAVF), YDOTI, IRES ) + NFE = NFE + 1 + IF (IRES .LE. 1) GO TO 595 + MSG = 'DLSODI- Residual routine set its flag IRES ' + CALL XERRWD (MSG, 50, 210, 0, 0, 0, 0, 0, 0.0D0, 0.0D0) + MSG = ' to (I1) when called for final output. ' + CALL XERRWD (MSG, 50, 210, 0, 1, IRES, 0, 0, 0.0D0, 0.0D0) + GO TO 595 +C Set Y vector, T, and optional outputs. ------------------------------- + 590 DO 592 I = 1,N + 592 Y(I) = RWORK(I+LYH-1) + 595 T = TN + RWORK(11) = HU + RWORK(12) = H + RWORK(13) = TN + IWORK(11) = NST + IWORK(12) = NFE + IWORK(13) = NJE + IWORK(14) = NQU + IWORK(15) = NQ + RETURN +C----------------------------------------------------------------------- +C Block I. +C The following block handles all error returns due to illegal input +C (ISTATE = -3), as detected before calling the core integrator. +C First the error message routine is called. If the illegal input +C is a negative ISTATE, the run is aborted (apparent infinite loop). +C----------------------------------------------------------------------- + 601 MSG = 'DLSODI- ISTATE (=I1) illegal.' + CALL XERRWD (MSG, 30, 1, 0, 1, ISTATE, 0, 0, 0.0D0, 0.0D0) + IF (ISTATE .LT. 0) GO TO 800 + GO TO 700 + 602 MSG = 'DLSODI- ITASK (=I1) illegal. ' + CALL XERRWD (MSG, 30, 2, 0, 1, ITASK, 0, 0, 0.0D0, 0.0D0) + GO TO 700 + 603 MSG = 'DLSODI- ISTATE .gt. 1 but DLSODI not initialized.' + CALL XERRWD (MSG, 50, 3, 0, 0, 0, 0, 0, 0.0D0, 0.0D0) + GO TO 700 + 604 MSG = 'DLSODI- NEQ (=I1) .lt. 1 ' + CALL XERRWD (MSG, 30, 4, 0, 1, NEQ(1), 0, 0, 0.0D0, 0.0D0) + GO TO 700 + 605 MSG = 'DLSODI- ISTATE = 3 and NEQ increased (I1 to I2). ' + CALL XERRWD (MSG, 50, 5, 0, 2, N, NEQ(1), 0, 0.0D0, 0.0D0) + GO TO 700 + 606 MSG = 'DLSODI- ITOL (=I1) illegal. ' + CALL XERRWD (MSG, 30, 6, 0, 1, ITOL, 0, 0, 0.0D0, 0.0D0) + GO TO 700 + 607 MSG = 'DLSODI- IOPT (=I1) illegal. ' + CALL XERRWD (MSG, 30, 7, 0, 1, IOPT, 0, 0, 0.0D0, 0.0D0) + GO TO 700 + 608 MSG = 'DLSODI- MF (=I1) illegal. ' + CALL XERRWD (MSG, 30, 8, 0, 1, MF, 0, 0, 0.0D0, 0.0D0) + GO TO 700 + 609 MSG = 'DLSODI- ML(=I1) illegal: .lt. 0 or .ge. NEQ(=I2) ' + CALL XERRWD (MSG, 50, 9, 0, 2, ML, NEQ(1), 0, 0.0D0, 0.0D0) + GO TO 700 + 610 MSG = 'DLSODI- MU(=I1) illegal: .lt. 0 or .ge. NEQ(=I2) ' + CALL XERRWD (MSG, 50, 10, 0, 2, MU, NEQ(1), 0, 0.0D0, 0.0D0) + GO TO 700 + 611 MSG = 'DLSODI- MAXORD (=I1) .lt. 0 ' + CALL XERRWD (MSG, 30, 11, 0, 1, MAXORD, 0, 0, 0.0D0, 0.0D0) + GO TO 700 + 612 MSG = 'DLSODI- MXSTEP (=I1) .lt. 0 ' + CALL XERRWD (MSG, 30, 12, 0, 1, MXSTEP, 0, 0, 0.0D0, 0.0D0) + GO TO 700 + 613 MSG = 'DLSODI- MXHNIL (=I1) .lt. 0 ' + CALL XERRWD (MSG, 30, 13, 0, 1, MXHNIL, 0, 0, 0.0D0, 0.0D0) + GO TO 700 + 614 MSG = 'DLSODI- TOUT (=R1) behind T (=R2) ' + CALL XERRWD (MSG, 40, 14, 0, 0, 0, 0, 2, TOUT, T) + MSG = ' Integration direction is given by H0 (=R1) ' + CALL XERRWD (MSG, 50, 14, 0, 0, 0, 0, 1, H0, 0.0D0) + GO TO 700 + 615 MSG = 'DLSODI- HMAX (=R1) .lt. 0.0 ' + CALL XERRWD (MSG, 30, 15, 0, 0, 0, 0, 1, HMAX, 0.0D0) + GO TO 700 + 616 MSG = 'DLSODI- HMIN (=R1) .lt. 0.0 ' + CALL XERRWD (MSG, 30, 16, 0, 0, 0, 0, 1, HMIN, 0.0D0) + GO TO 700 + 617 MSG='DLSODI- RWORK length needed, LENRW (=I1), exceeds LRW (=I2)' + CALL XERRWD (MSG, 60, 17, 0, 2, LENRW, LRW, 0, 0.0D0, 0.0D0) + GO TO 700 + 618 MSG='DLSODI- IWORK length needed, LENIW (=I1), exceeds LIW (=I2)' + CALL XERRWD (MSG, 60, 18, 0, 2, LENIW, LIW, 0, 0.0D0, 0.0D0) + GO TO 700 + 619 MSG = 'DLSODI- RTOL(=I1) is R1 .lt. 0.0 ' + CALL XERRWD (MSG, 40, 19, 0, 1, I, 0, 1, RTOLI, 0.0D0) + GO TO 700 + 620 MSG = 'DLSODI- ATOL(=I1) is R1 .lt. 0.0 ' + CALL XERRWD (MSG, 40, 20, 0, 1, I, 0, 1, ATOLI, 0.0D0) + GO TO 700 + 621 EWTI = RWORK(LEWT+I-1) + MSG = 'DLSODI- EWT(I1) is R1 .le. 0.0 ' + CALL XERRWD (MSG, 40, 21, 0, 1, I, 0, 1, EWTI, 0.0D0) + GO TO 700 + 622 MSG='DLSODI- TOUT(=R1) too close to T(=R2) to start integration.' + CALL XERRWD (MSG, 60, 22, 0, 0, 0, 0, 2, TOUT, T) + GO TO 700 + 623 MSG='DLSODI- ITASK = I1 and TOUT (=R1) behind TCUR - HU (= R2) ' + CALL XERRWD (MSG, 60, 23, 0, 1, ITASK, 0, 2, TOUT, TP) + GO TO 700 + 624 MSG='DLSODI- ITASK = 4 or 5 and TCRIT (=R1) behind TCUR (=R2) ' + CALL XERRWD (MSG, 60, 24, 0, 0, 0, 0, 2, TCRIT, TN) + GO TO 700 + 625 MSG='DLSODI- ITASK = 4 or 5 and TCRIT (=R1) behind TOUT (=R2) ' + CALL XERRWD (MSG, 60, 25, 0, 0, 0, 0, 2, TCRIT, TOUT) + GO TO 700 + 626 MSG = 'DLSODI- At start of problem, too much accuracy ' + CALL XERRWD (MSG, 50, 26, 0, 0, 0, 0, 0, 0.0D0, 0.0D0) + MSG=' requested for precision of machine.. See TOLSF (=R1) ' + CALL XERRWD (MSG, 60, 26, 0, 0, 0, 0, 1, TOLSF, 0.0D0) + RWORK(14) = TOLSF + GO TO 700 + 627 MSG = 'DLSODI- Trouble in DINTDY. ITASK = I1, TOUT = R1' + CALL XERRWD (MSG, 50, 27, 0, 1, ITASK, 0, 1, TOUT, 0.0D0) +C + 700 ISTATE = -3 + RETURN +C + 800 MSG = 'DLSODI- Run aborted.. apparent infinite loop. ' + CALL XERRWD (MSG, 50, 303, 2, 0, 0, 0, 0, 0.0D0, 0.0D0) + RETURN +C----------------------- End of Subroutine DLSODI ---------------------- + END +*DECK DLSOIBT + SUBROUTINE DLSOIBT (RES, ADDA, JAC, NEQ, Y, YDOTI, T, TOUT, ITOL, + 1 RTOL, ATOL, ITASK, ISTATE, IOPT, RWORK, LRW, IWORK, LIW, MF ) + EXTERNAL RES, ADDA, JAC + INTEGER NEQ, ITOL, ITASK, ISTATE, IOPT, LRW, IWORK, LIW, MF + DOUBLE PRECISION Y, YDOTI, T, TOUT, RTOL, ATOL, RWORK + DIMENSION NEQ(*), Y(*), YDOTI(*), RTOL(*), ATOL(*), RWORK(LRW), + 1 IWORK(LIW) +C----------------------------------------------------------------------- +C This is the 18 November 2003 version of +C DLSOIBT: Livermore Solver for Ordinary differential equations given +C in Implicit form, with Block-Tridiagonal Jacobian treatment. +C +C This version is in double precision. +C +C DLSOIBT solves the initial value problem for linearly implicit +C systems of first order ODEs, +C A(t,y) * dy/dt = g(t,y) , where A(t,y) is a square matrix, +C or, in component form, +C ( a * ( dy / dt )) + ... + ( a * ( dy / dt )) = +C i,1 1 i,NEQ NEQ +C +C = g ( t, y , y ,..., y ) ( i = 1,...,NEQ ) +C i 1 2 NEQ +C +C If A is singular, this is a differential-algebraic system. +C +C DLSOIBT is a variant version of the DLSODI package, for the case where +C the matrices A, dg/dy, and d(A*s)/dy are all block-tridiagonal. +C----------------------------------------------------------------------- +C Reference: +C Alan C. Hindmarsh, ODEPACK, A Systematized Collection of ODE +C Solvers, in Scientific Computing, R. S. Stepleman et al. (Eds.), +C North-Holland, Amsterdam, 1983, pp. 55-64. +C----------------------------------------------------------------------- +C Authors: Alan C. Hindmarsh and Jeffrey F. Painter +C Center for Applied Scientific Computing, L-561 +C Lawrence Livermore National Laboratory +C Livermore, CA 94551 +C and +C Charles S. Kenney +C formerly at: Naval Weapons Center +C China Lake, CA 93555 +C----------------------------------------------------------------------- +C Summary of Usage. +C +C Communication between the user and the DLSOIBT package, for normal +C situations, is summarized here. This summary describes only a subset +C of the full set of options available. See the full description for +C details, including optional communication, nonstandard options, +C and instructions for special situations. See also the example +C problem (with program and output) following this summary. +C +C A. First, provide a subroutine of the form: +C SUBROUTINE RES (NEQ, T, Y, S, R, IRES) +C DOUBLE PRECISION T, Y(*), S(*), R(*) +C which computes the residual function +C r = g(t,y) - A(t,y) * s , +C as a function of t and the vectors y and s. (s is an internally +C generated approximation to dy/dt.) The arrays Y and S are inputs +C to the RES routine and should not be altered. The residual +C vector is to be stored in the array R. The argument IRES should be +C ignored for casual use of DLSOIBT. (For uses of IRES, see the +C paragraph on RES in the full description below.) +C +C B. Next, identify the block structure of the matrices A = A(t,y) and +C dr/dy. DLSOIBT must deal internally with a linear combination, P, of +C these two matrices. The matrix P (hence both A and dr/dy) must have +C a block-tridiagonal form with fixed structure parameters +C MB = block size, MB .ge. 1, and +C NB = number of blocks in each direction, NB .ge. 4, +C with MB*NB = NEQ. In each of the NB block-rows of the matrix P +C (each consisting of MB consecutive rows), the nonzero elements are +C to lie in three consecutive MB by MB blocks. In block-rows +C 2 through NB - 1, these are centered about the main diagonal. +C in block-rows 1 and NB, they are the diagonal blocks and the two +C blocks adjacent to the diagonal block. (Thus block positions (1,3) +C and (NB,NB-2) can be nonzero.) +C Alternatively, P (hence A and dr/dy) may be only approximately +C equal to matrices with this form, and DLSOIBT should still succeed. +C The block-tridiagonal matrix P is described by three arrays, +C each of size MB by MB by NB: +C PA = array of diagonal blocks, +C PB = array of superdiagonal (and one subdiagonal) blocks, and +C PC = array of subdiagonal (and one superdiagonal) blocks. +C Specifically, the three MB by MB blocks in the k-th block-row of P +C are stored in (reading across): +C PC(*,*,k) = block to the left of the diagonal block, +C PA(*,*,k) = diagonal block, and +C PB(*,*,k) = block to the right of the diagonal block, +C except for k = 1, where the three blocks (reading across) are +C PA(*,*,1) (= diagonal block), PB(*,*,1), and PC(*,*,1), +C and k = NB, where they are +C PB(*,*,NB), PC(*,*,NB), and PA(*,*,NB) (= diagonal block). +C (Each asterisk * stands for an index that ranges from 1 to MB.) +C +C C. You must also provide a subroutine of the form: +C SUBROUTINE ADDA (NEQ, T, Y, MB, NB, PA, PB, PC) +C DOUBLE PRECISION T, Y(*), PA(MB,MB,NB), PB(MB,MB,NB), PC(MB,MB,NB) +C which adds the nonzero blocks of the matrix A = A(t,y) to the +C contents of the arrays PA, PB, and PC, following the structure +C description in Paragraph B above. +C T and the Y array are input and should not be altered. +C Thus the affect of ADDA should be the following: +C DO 30 K = 1,NB +C DO 20 J = 1,MB +C DO 10 I = 1,MB +C PA(I,J,K) = PA(I,J,K) + +C ( (I,J) element of K-th diagonal block of A) +C PB(I,J,K) = PB(I,J,K) + +C ( (I,J) element of block in block position (K,K+1) of A, +C or in block position (NB,NB-2) if K = NB) +C PC(I,J,K) = PC(I,J,K) + +C ( (I,J) element of block in block position (K,K-1) of A, +C or in block position (1,3) if K = 1) +C 10 CONTINUE +C 20 CONTINUE +C 30 CONTINUE +C +C D. For the sake of efficiency, you are encouraged to supply the +C Jacobian matrix dr/dy in closed form, where r = g(t,y) - A(t,y)*s +C (s = a fixed vector) as above. If dr/dy is being supplied, +C use MF = 21, and provide a subroutine of the form: +C SUBROUTINE JAC (NEQ, T, Y, S, MB, NB, PA, PB, PC) +C DOUBLE PRECISION T, Y(*), S(*), PA(MB,MB,NB), PB(MB,MB,NB), +C 1 PC(MB,MB,NB) +C which computes dr/dy as a function of t, y, and s. Here T, Y, and +C S are inputs, and the routine is to load dr/dy into PA, PB, PC, +C according to the structure description in Paragraph B above. +C That is, load the diagonal blocks into PA, the superdiagonal blocks +C (and block (NB,NB-2) ) into PB, and the subdiagonal blocks (and +C block (1,3) ) into PC. The blocks in block-row k of dr/dy are to +C be loaded into PA(*,*,k), PB(*,*,k), and PC(*,*,k). +C Only nonzero elements need be loaded, and the indexing +C of PA, PB, and PC is the same as in the ADDA routine. +C Note that if A is independent of Y (or this dependence +C is weak enough to be ignored) then JAC is to compute dg/dy. +C If it is not feasible to provide a JAC routine, use +C MF = 22, and DLSOIBT will compute an approximate Jacobian +C internally by difference quotients. +C +C E. Next decide whether or not to provide the initial value of the +C derivative vector dy/dt. If the initial value of A(t,y) is +C nonsingular (and not too ill-conditioned), you may let DLSOIBT compute +C this vector (ISTATE = 0). (DLSOIBT will solve the system A*s = g for +C s, with initial values of A and g.) If A(t,y) is initially +C singular, then the system is a differential-algebraic system, and +C you must make use of the particular form of the system to compute the +C initial values of y and dy/dt. In that case, use ISTATE = 1 and +C load the initial value of dy/dt into the array YDOTI. +C The input array YDOTI and the initial Y array must be consistent with +C the equations A*dy/dt = g. This implies that the initial residual +C r = g(t,y) - A(t,y)*YDOTI must be approximately zero. +C +C F. Write a main program which calls Subroutine DLSOIBT once for +C each point at which answers are desired. This should also provide +C for possible use of logical unit 6 for output of error messages by +C DLSOIBT. on the first call to DLSOIBT, supply arguments as follows: +C RES = name of user subroutine for residual function r. +C ADDA = name of user subroutine for computing and adding A(t,y). +C JAC = name of user subroutine for Jacobian matrix dr/dy +C (MF = 21). If not used, pass a dummy name. +C Note: the names for the RES and ADDA routines and (if used) the +C JAC routine must be declared External in the calling program. +C NEQ = number of scalar equations in the system. +C Y = array of initial values, of length NEQ. +C YDOTI = array of length NEQ (containing initial dy/dt if ISTATE = 1). +C T = the initial value of the independent variable. +C TOUT = first point where output is desired (.ne. T). +C ITOL = 1 or 2 according as ATOL (below) is a scalar or array. +C RTOL = relative tolerance parameter (scalar). +C ATOL = absolute tolerance parameter (scalar or array). +C the estimated local error in y(i) will be controlled so as +C to be roughly less (in magnitude) than +C EWT(i) = RTOL*ABS(Y(i)) + ATOL if ITOL = 1, or +C EWT(i) = RTOL*ABS(Y(i)) + ATOL(i) if ITOL = 2. +C Thus the local error test passes if, in each component, +C either the absolute error is less than ATOL (or ATOL(i)), +C or the relative error is less than RTOL. +C Use RTOL = 0.0 for pure absolute error control, and +C use ATOL = 0.0 (or ATOL(i) = 0.0) for pure relative error +C control. Caution: Actual (global) errors may exceed these +C local tolerances, so choose them conservatively. +C ITASK = 1 for normal computation of output values of y at t = TOUT. +C ISTATE = integer flag (input and output). Set ISTATE = 1 if the +C initial dy/dt is supplied, and 0 otherwise. +C IOPT = 0 to indicate no optional inputs used. +C RWORK = real work array of length at least: +C 22 + 9*NEQ + 3*MB*MB*NB for MF = 21 or 22. +C LRW = declared length of RWORK (in user's dimension). +C IWORK = integer work array of length at least 20 + NEQ. +C Input in IWORK(1) the block size MB and in IWORK(2) the +C number NB of blocks in each direction along the matrix A. +C These must satisfy MB .ge. 1, NB .ge. 4, and MB*NB = NEQ. +C LIW = declared length of IWORK (in user's dimension). +C MF = method flag. Standard values are: +C 21 for a user-supplied Jacobian. +C 22 for an internally generated Jacobian. +C For other choices of MF, see the paragraph on MF in +C the full description below. +C Note that the main program must declare arrays Y, YDOTI, RWORK, IWORK, +C and possibly ATOL. +C +C G. The output from the first call (or any call) is: +C Y = array of computed values of y(t) vector. +C T = corresponding value of independent variable (normally TOUT). +C ISTATE = 2 if DLSOIBT was successful, negative otherwise. +C -1 means excess work done on this call (check all inputs). +C -2 means excess accuracy requested (tolerances too small). +C -3 means illegal input detected (see printed message). +C -4 means repeated error test failures (check all inputs). +C -5 means repeated convergence failures (perhaps bad Jacobian +C supplied or wrong choice of tolerances). +C -6 means error weight became zero during problem. (Solution +C component i vanished, and ATOL or ATOL(i) = 0.) +C -7 cannot occur in casual use. +C -8 means DLSOIBT was unable to compute the initial dy/dt. +C In casual use, this means A(t,y) is initially singular. +C Supply YDOTI and use ISTATE = 1 on the first call. +C +C If DLSOIBT returns ISTATE = -1, -4, or -5, then the output of +C DLSOIBT also includes YDOTI = array containing residual vector +C r = g - A * dy/dt evaluated at the current t, y, and dy/dt. +C +C H. To continue the integration after a successful return, simply +C reset TOUT and call DLSOIBT again. No other parameters need be reset. +C +C----------------------------------------------------------------------- +C Example Problem. +C +C The following is an example problem, with the coding needed +C for its solution by DLSOIBT. The problem comes from the partial +C differential equation (the Burgers equation) +C du/dt = - u * du/dx + eta * d**2 u/dx**2, eta = .05, +C on -1 .le. x .le. 1. The boundary conditions are +C du/dx = 0 at x = -1 and at x = 1. +C The initial profile is a square wave, +C u = 1 in ABS(x) .lt. .5, u = .5 at ABS(x) = .5, u = 0 elsewhere. +C The PDE is discretized in x by a simplified Galerkin method, +C using piecewise linear basis functions, on a grid of 40 intervals. +C The equations at x = -1 and 1 use a 3-point difference approximation +C for the right-hand side. The result is a system A * dy/dt = g(y), +C of size NEQ = 41, where y(i) is the approximation to u at x = x(i), +C with x(i) = -1 + (i-1)*delx, delx = 2/(NEQ-1) = .05. The individual +C equations in the system are +C dy(1)/dt = ( y(3) - 2*y(2) + y(1) ) * eta / delx**2, +C dy(NEQ)/dt = ( y(NEQ-2) - 2*y(NEQ-1) + y(NEQ) ) * eta / delx**2, +C and for i = 2, 3, ..., NEQ-1, +C (1/6) dy(i-1)/dt + (4/6) dy(i)/dt + (1/6) dy(i+1)/dt +C = ( y(i-1)**2 - y(i+1)**2 ) / (4*delx) +C + ( y(i+1) - 2*y(i) + y(i-1) ) * eta / delx**2. +C The following coding solves the problem with MF = 21, with output +C of solution statistics at t = .1, .2, .3, and .4, and of the +C solution vector at t = .4. Here the block size is just MB = 1. +C +C EXTERNAL RESID, ADDABT, JACBT +C DOUBLE PRECISION ATOL, RTOL, RWORK, T, TOUT, Y, YDOTI +C DIMENSION Y(41), YDOTI(41), RWORK(514), IWORK(61) +C NEQ = 41 +C DO 10 I = 1,NEQ +C 10 Y(I) = 0.0 +C Y(11) = 0.5 +C DO 20 I = 12,30 +C 20 Y(I) = 1.0 +C Y(31) = 0.5 +C T = 0.0 +C TOUT = 0.1 +C ITOL = 1 +C RTOL = 1.0D-4 +C ATOL = 1.0D-5 +C ITASK = 1 +C ISTATE = 0 +C IOPT = 0 +C LRW = 514 +C LIW = 61 +C IWORK(1) = 1 +C IWORK(2) = NEQ +C MF = 21 +C DO 40 IO = 1,4 +C CALL DLSOIBT (RESID, ADDABT, JACBT, NEQ, Y, YDOTI, T, TOUT, +C 1 ITOL,RTOL,ATOL, ITASK, ISTATE, IOPT, RWORK,LRW,IWORK,LIW, MF) +C WRITE (6,30) T, IWORK(11), IWORK(12), IWORK(13) +C 30 FORMAT(' At t =',F5.2,' No. steps =',I4,' No. r-s =',I4, +C 1 ' No. J-s =',I3) +C IF (ISTATE .NE. 2) GO TO 90 +C TOUT = TOUT + 0.1 +C 40 CONTINUE +C WRITE(6,50) (Y(I),I=1,NEQ) +C 50 FORMAT(/' Final solution values..'/9(5D12.4/)) +C STOP +C 90 WRITE(6,95) ISTATE +C 95 FORMAT(///' Error halt.. ISTATE =',I3) +C STOP +C END +C +C SUBROUTINE RESID (N, T, Y, S, R, IRES) +C DOUBLE PRECISION T, Y, S, R, ETA, DELX, EODSQ +C DIMENSION Y(N), S(N), R(N) +C DATA ETA/0.05/, DELX/0.05/ +C EODSQ = ETA/DELX**2 +C R(1) = EODSQ*(Y(3) - 2.0*Y(2) + Y(1)) - S(1) +C NM1 = N - 1 +C DO 10 I = 2,NM1 +C R(I) = (Y(I-1)**2 - Y(I+1)**2)/(4.0*DELX) +C 1 + EODSQ*(Y(I+1) - 2.0*Y(I) + Y(I-1)) +C 2 - (S(I-1) + 4.0*S(I) + S(I+1))/6.0 +C 10 CONTINUE +C R(N) = EODSQ*(Y(N-2) - 2.0*Y(NM1) + Y(N)) - S(N) +C RETURN +C END +C +C SUBROUTINE ADDABT (N, T, Y, MB, NB, PA, PB, PC) +C DOUBLE PRECISION T, Y, PA, PB, PC +C DIMENSION Y(N), PA(MB,MB,NB), PB(MB,MB,NB), PC(MB,MB,NB) +C PA(1,1,1) = PA(1,1,1) + 1.0 +C NM1 = N - 1 +C DO 10 K = 2,NM1 +C PA(1,1,K) = PA(1,1,K) + (4.0/6.0) +C PB(1,1,K) = PB(1,1,K) + (1.0/6.0) +C PC(1,1,K) = PC(1,1,K) + (1.0/6.0) +C 10 CONTINUE +C PA(1,1,N) = PA(1,1,N) + 1.0 +C RETURN +C END +C +C SUBROUTINE JACBT (N, T, Y, S, MB, NB, PA, PB, PC) +C DOUBLE PRECISION T, Y, S, PA, PB, PC, ETA, DELX, EODSQ +C DIMENSION Y(N), S(N), PA(MB,MB,NB),PB(MB,MB,NB),PC(MB,MB,NB) +C DATA ETA/0.05/, DELX/0.05/ +C EODSQ = ETA/DELX**2 +C PA(1,1,1) = EODSQ +C PB(1,1,1) = -2.0*EODSQ +C PC(1,1,1) = EODSQ +C DO 10 K = 2,N +C PA(1,1,K) = -2.0*EODSQ +C PB(1,1,K) = -Y(K+1)*(0.5/DELX) + EODSQ +C PC(1,1,K) = Y(K-1)*(0.5/DELX) + EODSQ +C 10 CONTINUE +C PB(1,1,N) = EODSQ +C PC(1,1,N) = -2.0*EODSQ +C PA(1,1,N) = EODSQ +C RETURN +C END +C +C The output of this program (on a CDC-7600 in single precision) +C is as follows: +C +C At t = 0.10 No. steps = 35 No. r-s = 45 No. J-s = 9 +C At t = 0.20 No. steps = 43 No. r-s = 54 No. J-s = 10 +C At t = 0.30 No. steps = 48 No. r-s = 60 No. J-s = 11 +C At t = 0.40 No. steps = 51 No. r-s = 64 No. J-s = 12 +C +C Final solution values.. +C 1.2747e-02 1.1997e-02 1.5560e-02 2.3767e-02 3.7224e-02 +C 5.6646e-02 8.2645e-02 1.1557e-01 1.5541e-01 2.0177e-01 +C 2.5397e-01 3.1104e-01 3.7189e-01 4.3530e-01 5.0000e-01 +C 5.6472e-01 6.2816e-01 6.8903e-01 7.4612e-01 7.9829e-01 +C 8.4460e-01 8.8438e-01 9.1727e-01 9.4330e-01 9.6281e-01 +C 9.7632e-01 9.8426e-01 9.8648e-01 9.8162e-01 9.6617e-01 +C 9.3374e-01 8.7535e-01 7.8236e-01 6.5321e-01 5.0003e-01 +C 3.4709e-01 2.1876e-01 1.2771e-01 7.3671e-02 5.0642e-02 +C 5.4496e-02 +C +C----------------------------------------------------------------------- +C Full Description of User Interface to DLSOIBT. +C +C The user interface to DLSOIBT consists of the following parts. +C +C 1. The call sequence to Subroutine DLSOIBT, which is a driver +C routine for the solver. This includes descriptions of both +C the call sequence arguments and of user-supplied routines. +C Following these descriptions is a description of +C optional inputs available through the call sequence, and then +C a description of optional outputs (in the work arrays). +C +C 2. Descriptions of other routines in the DLSOIBT package that may be +C (optionally) called by the user. These provide the ability to +C alter error message handling, save and restore the internal +C Common, and obtain specified derivatives of the solution y(t). +C +C 3. Descriptions of Common blocks to be declared in overlay +C or similar environments, or to be saved when doing an interrupt +C of the problem and continued solution later. +C +C 4. Description of two routines in the DLSOIBT package, either of +C which the user may replace with his/her own version, if desired. +C These relate to the measurement of errors. +C +C----------------------------------------------------------------------- +C Part 1. Call Sequence. +C +C The call sequence parameters used for input only are +C RES, ADDA, JAC, NEQ, TOUT, ITOL, RTOL, ATOL, ITASK, +C IOPT, LRW, LIW, MF, +C and those used for both input and output are +C Y, T, ISTATE, YDOTI. +C The work arrays RWORK and IWORK are also used for additional and +C optional inputs and optional outputs. (The term output here refers +C to the return from Subroutine DLSOIBT to the user's calling program.) +C +C The legality of input parameters will be thoroughly checked on the +C initial call for the problem, but not checked thereafter unless a +C change in input parameters is flagged by ISTATE = 3 on input. +C +C The descriptions of the call arguments are as follows. +C +C RES = the name of the user-supplied subroutine which supplies +C the residual vector for the ODE system, defined by +C r = g(t,y) - A(t,y) * s +C as a function of the scalar t and the vectors +C s and y (s approximates dy/dt). This subroutine +C is to have the form +C SUBROUTINE RES (NEQ, T, Y, S, R, IRES) +C DOUBLE PRECISION T, Y(*), S(*), R(*) +C where NEQ, T, Y, S, and IRES are input, and R and +C IRES are output. Y, S, and R are arrays of length NEQ. +C On input, IRES indicates how DLSOIBT will use the +C returned array R, as follows: +C IRES = 1 means that DLSOIBT needs the full residual, +C r = g - A*s, exactly. +C IRES = -1 means that DLSOIBT is using R only to compute +C the Jacobian dr/dy by difference quotients. +C The RES routine can ignore IRES, or it can omit some terms +C if IRES = -1. If A does not depend on y, then RES can +C just return R = g when IRES = -1. If g - A*s contains other +C additive terms that are independent of y, these can also be +C dropped, if done consistently, when IRES = -1. +C The subroutine should set the flag IRES if it +C encounters a halt condition or illegal input. +C Otherwise, it should not reset IRES. On output, +C IRES = 1 or -1 represents a normal return, and +C DLSOIBT continues integrating the ODE. Leave IRES +C unchanged from its input value. +C IRES = 2 tells DLSOIBT to immediately return control +C to the calling program, with ISTATE = 3. This lets +C the calling program change parameters of the problem +C if necessary. +C IRES = 3 represents an error condition (for example, an +C illegal value of y). DLSOIBT tries to integrate the system +C without getting IRES = 3 from RES. If it cannot, DLSOIBT +C returns with ISTATE = -7 or -1. +C On an DLSOIBT return with ISTATE = 3, -1, or -7, the +C values of T and Y returned correspond to the last point +C reached successfully without getting the flag IRES = 2 or 3. +C The flag values IRES = 2 and 3 should not be used to +C handle switches or root-stop conditions. This is better +C done by calling DLSOIBT in a one-step mode and checking the +C stopping function for a sign change at each step. +C If quantities computed in the RES routine are needed +C externally to DLSOIBT, an extra call to RES should be made +C for this purpose, for consistent and accurate results. +C To get the current dy/dt for the S argument, use DINTDY. +C RES must be declared External in the calling +C program. See note below for more about RES. +C +C ADDA = the name of the user-supplied subroutine which adds the +C matrix A = A(t,y) to another matrix, P, stored in +C block-tridiagonal form. This routine is to have the form +C SUBROUTINE ADDA (NEQ, T, Y, MB, NB, PA, PB, PC) +C DOUBLE PRECISION T, Y(*), PA(MB,MB,NB), PB(MB,MB,NB), +C 1 PC(MB,MB,NB) +C where NEQ, T, Y, MB, NB, and the arrays PA, PB, and PC +C are input, and the arrays PA, PB, and PC are output. +C Y is an array of length NEQ, and the arrays PA, PB, PC +C are all MB by MB by NB. +C Here a block-tridiagonal structure is assumed for A(t,y), +C and also for the matrix P to which A is added here, +C as described in Paragraph B of the Summary of Usage above. +C Thus the affect of ADDA should be the following: +C DO 30 K = 1,NB +C DO 20 J = 1,MB +C DO 10 I = 1,MB +C PA(I,J,K) = PA(I,J,K) + +C ( (I,J) element of K-th diagonal block of A) +C PB(I,J,K) = PB(I,J,K) + +C ( (I,J) element of block (K,K+1) of A, +C or block (NB,NB-2) if K = NB) +C PC(I,J,K) = PC(I,J,K) + +C ( (I,J) element of block (K,K-1) of A, +C or block (1,3) if K = 1) +C 10 CONTINUE +C 20 CONTINUE +C 30 CONTINUE +C ADDA must be declared External in the calling program. +C See note below for more information about ADDA. +C +C JAC = the name of the user-supplied subroutine which supplies +C the Jacobian matrix, dr/dy, where r = g - A*s. JAC is +C required if MITER = 1. Otherwise a dummy name can be +C passed. This subroutine is to have the form +C SUBROUTINE JAC (NEQ, T, Y, S, MB, NB, PA, PB, PC) +C DOUBLE PRECISION T, Y(*), S(*), PA(MB,MB,NB), +C 1 PB(MB,MB,NB), PC(MB,MB,NB) +C where NEQ, T, Y, S, MB, NB, and the arrays PA, PB, and PC +C are input, and the arrays PA, PB, and PC are output. +C Y and S are arrays of length NEQ, and the arrays PA, PB, PC +C are all MB by MB by NB. +C PA, PB, and PC are to be loaded with partial derivatives +C (elements of the Jacobian matrix) on output, in terms of the +C block-tridiagonal structure assumed, as described +C in Paragraph B of the Summary of Usage above. +C That is, load the diagonal blocks into PA, the +C superdiagonal blocks (and block (NB,NB-2) ) into PB, and +C the subdiagonal blocks (and block (1,3) ) into PC. +C The blocks in block-row k of dr/dy are to be loaded into +C PA(*,*,k), PB(*,*,k), and PC(*,*,k). +C Thus the affect of JAC should be the following: +C DO 30 K = 1,NB +C DO 20 J = 1,MB +C DO 10 I = 1,MB +C PA(I,J,K) = ( (I,J) element of +C K-th diagonal block of dr/dy) +C PB(I,J,K) = ( (I,J) element of block (K,K+1) +C of dr/dy, or block (NB,NB-2) if K = NB) +C PC(I,J,K) = ( (I,J) element of block (K,K-1) +C of dr/dy, or block (1,3) if K = 1) +C 10 CONTINUE +C 20 CONTINUE +C 30 CONTINUE +C PA, PB, and PC are preset to zero by the solver, +C so that only the nonzero elements need be loaded by JAC. +C Each call to JAC is preceded by a call to RES with the same +C arguments NEQ, T, Y, and S. Thus to gain some efficiency, +C intermediate quantities shared by both calculations may be +C saved in a user Common block by RES and not recomputed by JAC +C if desired. Also, JAC may alter the Y array, if desired. +C JAC need not provide dr/dy exactly. A crude +C approximation will do, so that DLSOIBT may be used when +C A and dr/dy are not really block-tridiagonal, but are close +C to matrices that are. +C JAC must be declared External in the calling program. +C See note below for more about JAC. +C +C Note on RES, ADDA, and JAC: +C These subroutines may access user-defined quantities in +C NEQ(2),... and/or in Y(NEQ(1)+1),... if NEQ is an array +C (dimensioned in the subroutines) and/or Y has length +C exceeding NEQ(1). However, these routines should not alter +C NEQ(1), Y(1),...,Y(NEQ) or any other input variables. +C See the descriptions of NEQ and Y below. +C +C NEQ = the size of the system (number of first order ordinary +C differential equations or scalar algebraic equations). +C Used only for input. +C NEQ may be decreased, but not increased, during the problem. +C If NEQ is decreased (with ISTATE = 3 on input), the +C remaining components of Y should be left undisturbed, if +C these are to be accessed in RES, ADDA, or JAC. +C +C Normally, NEQ is a scalar, and it is generally referred to +C as a scalar in this user interface description. However, +C NEQ may be an array, with NEQ(1) set to the system size. +C (The DLSOIBT package accesses only NEQ(1).) In either case, +C this parameter is passed as the NEQ argument in all calls +C to RES, ADDA, and JAC. Hence, if it is an array, +C locations NEQ(2),... may be used to store other integer data +C and pass it to RES, ADDA, or JAC. Each such subroutine +C must include NEQ in a Dimension statement in that case. +C +C Y = a real array for the vector of dependent variables, of +C length NEQ or more. Used for both input and output on the +C first call (ISTATE = 0 or 1), and only for output on other +C calls. On the first call, Y must contain the vector of +C initial values. On output, Y contains the computed solution +C vector, evaluated at t. If desired, the Y array may be used +C for other purposes between calls to the solver. +C +C This array is passed as the Y argument in all calls to RES, +C ADDA, and JAC. Hence its length may exceed NEQ, +C and locations Y(NEQ+1),... may be used to store other real +C data and pass it to RES, ADDA, or JAC. (The DLSOIBT +C package accesses only Y(1),...,Y(NEQ). ) +C +C YDOTI = a real array for the initial value of the vector +C dy/dt and for work space, of dimension at least NEQ. +C +C On input: +C If ISTATE = 0 then DLSOIBT will compute the initial value +C of dy/dt, if A is nonsingular. Thus YDOTI will +C serve only as work space and may have any value. +C If ISTATE = 1 then YDOTI must contain the initial value +C of dy/dt. +C If ISTATE = 2 or 3 (continuation calls) then YDOTI +C may have any value. +C Note: If the initial value of A is singular, then +C DLSOIBT cannot compute the initial value of dy/dt, so +C it must be provided in YDOTI, with ISTATE = 1. +C +C On output, when DLSOIBT terminates abnormally with ISTATE = +C -1, -4, or -5, YDOTI will contain the residual +C r = g(t,y) - A(t,y)*(dy/dt). If r is large, t is near +C its initial value, and YDOTI is supplied with ISTATE = 1, +C there may have been an incorrect input value of +C YDOTI = dy/dt, or the problem (as given to DLSOIBT) +C may not have a solution. +C +C If desired, the YDOTI array may be used for other +C purposes between calls to the solver. +C +C T = the independent variable. On input, T is used only on the +C first call, as the initial point of the integration. +C On output, after each call, T is the value at which a +C computed solution y is evaluated (usually the same as TOUT). +C On an error return, T is the farthest point reached. +C +C TOUT = the next value of t at which a computed solution is desired. +C Used only for input. +C +C When starting the problem (ISTATE = 0 or 1), TOUT may be +C equal to T for one call, then should .ne. T for the next +C call. For the initial T, an input value of TOUT .ne. T is +C used in order to determine the direction of the integration +C (i.e. the algebraic sign of the step sizes) and the rough +C scale of the problem. Integration in either direction +C (forward or backward in t) is permitted. +C +C If ITASK = 2 or 5 (one-step modes), TOUT is ignored after +C the first call (i.e. the first call with TOUT .ne. T). +C Otherwise, TOUT is required on every call. +C +C If ITASK = 1, 3, or 4, the values of TOUT need not be +C monotone, but a value of TOUT which backs up is limited +C to the current internal T interval, whose endpoints are +C TCUR - HU and TCUR (see optional outputs, below, for +C TCUR and HU). +C +C ITOL = an indicator for the type of error control. See +C description below under ATOL. Used only for input. +C +C RTOL = a relative error tolerance parameter, either a scalar or +C an array of length NEQ. See description below under ATOL. +C Input only. +C +C ATOL = an absolute error tolerance parameter, either a scalar or +C an array of length NEQ. Input only. +C +C The input parameters ITOL, RTOL, and ATOL determine +C the error control performed by the solver. The solver will +C control the vector E = (E(i)) of estimated local errors +C in y, according to an inequality of the form +C RMS-norm of ( E(i)/EWT(i) ) .le. 1, +C where EWT(i) = RTOL(i)*ABS(Y(i)) + ATOL(i), +C and the RMS-norm (root-mean-square norm) here is +C RMS-norm(v) = SQRT(sum v(i)**2 / NEQ). Here EWT = (EWT(i)) +C is a vector of weights which must always be positive, and +C the values of RTOL and ATOL should all be non-negative. +C The following table gives the types (scalar/array) of +C RTOL and ATOL, and the corresponding form of EWT(i). +C +C ITOL RTOL ATOL EWT(i) +C 1 scalar scalar RTOL*ABS(Y(i)) + ATOL +C 2 scalar array RTOL*ABS(Y(i)) + ATOL(i) +C 3 array scalar RTOL(i)*ABS(Y(i)) + ATOL +C 4 array scalar RTOL(i)*ABS(Y(i)) + ATOL(i) +C +C When either of these parameters is a scalar, it need not +C be dimensioned in the user's calling program. +C +C If none of the above choices (with ITOL, RTOL, and ATOL +C fixed throughout the problem) is suitable, more general +C error controls can be obtained by substituting +C user-supplied routines for the setting of EWT and/or for +C the norm calculation. See Part 4 below. +C +C If global errors are to be estimated by making a repeated +C run on the same problem with smaller tolerances, then all +C components of RTOL and ATOL (i.e. of EWT) should be scaled +C down uniformly. +C +C ITASK = an index specifying the task to be performed. +C Input only. ITASK has the following values and meanings. +C 1 means normal computation of output values of y(t) at +C t = TOUT (by overshooting and interpolating). +C 2 means take one step only and return. +C 3 means stop at the first internal mesh point at or +C beyond t = TOUT and return. +C 4 means normal computation of output values of y(t) at +C t = TOUT but without overshooting t = TCRIT. +C TCRIT must be input as RWORK(1). TCRIT may be equal to +C or beyond TOUT, but not behind it in the direction of +C integration. This option is useful if the problem +C has a singularity at or beyond t = TCRIT. +C 5 means take one step, without passing TCRIT, and return. +C TCRIT must be input as RWORK(1). +C +C Note: If ITASK = 4 or 5 and the solver reaches TCRIT +C (within roundoff), it will return T = TCRIT (exactly) to +C indicate this (unless ITASK = 4 and TOUT comes before TCRIT, +C in which case answers at t = TOUT are returned first). +C +C ISTATE = an index used for input and output to specify the +C state of the calculation. +C +C On input, the values of ISTATE are as follows. +C 0 means this is the first call for the problem, and +C DLSOIBT is to compute the initial value of dy/dt +C (while doing other initializations). See note below. +C 1 means this is the first call for the problem, and +C the initial value of dy/dt has been supplied in +C YDOTI (DLSOIBT will do other initializations). +C See note below. +C 2 means this is not the first call, and the calculation +C is to continue normally, with no change in any input +C parameters except possibly TOUT and ITASK. +C (If ITOL, RTOL, and/or ATOL are changed between calls +C with ISTATE = 2, the new values will be used but not +C tested for legality.) +C 3 means this is not the first call, and the +C calculation is to continue normally, but with +C a change in input parameters other than +C TOUT and ITASK. Changes are allowed in +C NEQ, ITOL, RTOL, ATOL, IOPT, LRW, LIW, MF, MB, NB, +C and any of the optional inputs except H0. +C (See IWORK description for MB and NB.) +C Note: A preliminary call with TOUT = T is not counted +C as a first call here, as no initialization or checking of +C input is done. (Such a call is sometimes useful for the +C purpose of outputting the initial conditions.) +C Thus the first call for which TOUT .ne. T requires +C ISTATE = 0 or 1 on input. +C +C On output, ISTATE has the following values and meanings. +C 0 or 1 means nothing was done; TOUT = t and +C ISTATE = 0 or 1 on input. +C 2 means that the integration was performed successfully. +C 3 means that the user-supplied Subroutine RES signalled +C DLSOIBT to halt the integration and return (IRES = 2). +C Integration as far as T was achieved with no occurrence +C of IRES = 2, but this flag was set on attempting the +C next step. +C -1 means an excessive amount of work (more than MXSTEP +C steps) was done on this call, before completing the +C requested task, but the integration was otherwise +C successful as far as T. (MXSTEP is an optional input +C and is normally 500.) To continue, the user may +C simply reset ISTATE to a value .gt. 1 and call again +C (the excess work step counter will be reset to 0). +C In addition, the user may increase MXSTEP to avoid +C this error return (see below on optional inputs). +C -2 means too much accuracy was requested for the precision +C of the machine being used. This was detected before +C completing the requested task, but the integration +C was successful as far as T. To continue, the tolerance +C parameters must be reset, and ISTATE must be set +C to 3. The optional output TOLSF may be used for this +C purpose. (Note: If this condition is detected before +C taking any steps, then an illegal input return +C (ISTATE = -3) occurs instead.) +C -3 means illegal input was detected, before taking any +C integration steps. See written message for details. +C Note: If the solver detects an infinite loop of calls +C to the solver with illegal input, it will cause +C the run to stop. +C -4 means there were repeated error test failures on +C one attempted step, before completing the requested +C task, but the integration was successful as far as T. +C The problem may have a singularity, or the input +C may be inappropriate. +C -5 means there were repeated convergence test failures on +C one attempted step, before completing the requested +C task, but the integration was successful as far as T. +C This may be caused by an inaccurate Jacobian matrix. +C -6 means EWT(i) became zero for some i during the +C integration. Pure relative error control (ATOL(i) = 0.0) +C was requested on a variable which has now vanished. +C The integration was successful as far as T. +C -7 means that the user-supplied Subroutine RES set +C its error flag (IRES = 3) despite repeated tries by +C DLSOIBT to avoid that condition. +C -8 means that ISTATE was 0 on input but DLSOIBT was unable +C to compute the initial value of dy/dt. See the +C printed message for details. +C +C Note: Since the normal output value of ISTATE is 2, +C it does not need to be reset for normal continuation. +C Similarly, ISTATE (= 3) need not be reset if RES told +C DLSOIBT to return because the calling program must change +C the parameters of the problem. +C Also, since a negative input value of ISTATE will be +C regarded as illegal, a negative output value requires the +C user to change it, and possibly other inputs, before +C calling the solver again. +C +C IOPT = an integer flag to specify whether or not any optional +C inputs are being used on this call. Input only. +C The optional inputs are listed separately below. +C IOPT = 0 means no optional inputs are being used. +C Default values will be used in all cases. +C IOPT = 1 means one or more optional inputs are being used. +C +C RWORK = a real working array (double precision). +C The length of RWORK must be at least +C 20 + NYH*(MAXORD + 1) + 3*NEQ + LENWM where +C NYH = the initial value of NEQ, +C MAXORD = 12 (if METH = 1) or 5 (if METH = 2) (unless a +C smaller value is given as an optional input), +C LENWM = 3*MB*MB*NB + 2. +C (See MF description for the definition of METH.) +C Thus if MAXORD has its default value and NEQ is constant, +C this length is +C 22 + 16*NEQ + 3*MB*MB*NB for MF = 11 or 12, +C 22 + 9*NEQ + 3*MB*MB*NB for MF = 21 or 22. +C The first 20 words of RWORK are reserved for conditional +C and optional inputs and optional outputs. +C +C The following word in RWORK is a conditional input: +C RWORK(1) = TCRIT = critical value of t which the solver +C is not to overshoot. Required if ITASK is +C 4 or 5, and ignored otherwise. (See ITASK.) +C +C LRW = the length of the array RWORK, as declared by the user. +C (This will be checked by the solver.) +C +C IWORK = an integer work array. The length of IWORK must be at least +C 20 + NEQ . The first few words of IWORK are used for +C additional and optional inputs and optional outputs. +C +C The following 2 words in IWORK are additional required +C inputs to DLSOIBT: +C IWORK(1) = MB = block size +C IWORK(2) = NB = number of blocks in the main diagonal +C These must satisfy MB .ge. 1, NB .ge. 4, and MB*NB = NEQ. +C +C LIW = the length of the array IWORK, as declared by the user. +C (This will be checked by the solver.) +C +C Note: The work arrays must not be altered between calls to DLSOIBT +C for the same problem, except possibly for the additional and +C optional inputs, and except for the last 3*NEQ words of RWORK. +C The latter space is used for internal scratch space, and so is +C available for use by the user outside DLSOIBT between calls, if +C desired (but not for use by RES, ADDA, or JAC). +C +C MF = the method flag. used only for input. The legal values of +C MF are 11, 12, 21, and 22. +C MF has decimal digits METH and MITER: MF = 10*METH + MITER. +C METH indicates the basic linear multistep method: +C METH = 1 means the implicit Adams method. +C METH = 2 means the method based on Backward +C Differentiation Formulas (BDFS). +C The BDF method is strongly preferred for stiff +C problems, while the Adams method is preferred when the +C problem is not stiff. If the matrix A(t,y) is +C nonsingular, stiffness here can be taken to mean that of +C the explicit ODE system dy/dt = A-inverse * g. If A is +C singular, the concept of stiffness is not well defined. +C If you do not know whether the problem is stiff, we +C recommend using METH = 2. If it is stiff, the advantage +C of METH = 2 over METH = 1 will be great, while if it is +C not stiff, the advantage of METH = 1 will be slight. +C If maximum efficiency is important, some experimentation +C with METH may be necessary. +C MITER indicates the corrector iteration method: +C MITER = 1 means chord iteration with a user-supplied +C block-tridiagonal Jacobian. +C MITER = 2 means chord iteration with an internally +C generated (difference quotient) block- +C tridiagonal Jacobian approximation, using +C 3*MB+1 extra calls to RES per dr/dy evaluation. +C If MITER = 1, the user must supply a Subroutine JAC +C (the name is arbitrary) as described above under JAC. +C For MITER = 2, a dummy argument can be used. +C----------------------------------------------------------------------- +C Optional Inputs. +C +C The following is a list of the optional inputs provided for in the +C call sequence. (See also Part 2.) For each such input variable, +C this table lists its name as used in this documentation, its +C location in the call sequence, its meaning, and the default value. +C The use of any of these inputs requires IOPT = 1, and in that +C case all of these inputs are examined. A value of zero for any +C of these optional inputs will cause the default value to be used. +C Thus to use a subset of the optional inputs, simply preload +C locations 5 to 10 in RWORK and IWORK to 0.0 and 0 respectively, and +C then set those of interest to nonzero values. +C +C Name Location Meaning and Default Value +C +C H0 RWORK(5) the step size to be attempted on the first step. +C The default value is determined by the solver. +C +C HMAX RWORK(6) the maximum absolute step size allowed. +C The default value is infinite. +C +C HMIN RWORK(7) the minimum absolute step size allowed. +C The default value is 0. (This lower bound is not +C enforced on the final step before reaching TCRIT +C when ITASK = 4 or 5.) +C +C MAXORD IWORK(5) the maximum order to be allowed. The default +C value is 12 if METH = 1, and 5 if METH = 2. +C If MAXORD exceeds the default value, it will +C be reduced to the default value. +C If MAXORD is changed during the problem, it may +C cause the current order to be reduced. +C +C MXSTEP IWORK(6) maximum number of (internally defined) steps +C allowed during one call to the solver. +C The default value is 500. +C +C MXHNIL IWORK(7) maximum number of messages printed (per problem) +C warning that T + H = T on a step (H = step size). +C This must be positive to result in a non-default +C value. The default value is 10. +C----------------------------------------------------------------------- +C Optional Outputs. +C +C As optional additional output from DLSOIBT, the variables listed +C below are quantities related to the performance of DLSOIBT +C which are available to the user. These are communicated by way of +C the work arrays, but also have internal mnemonic names as shown. +C Except where stated otherwise, all of these outputs are defined +C on any successful return from DLSOIBT, and on any return with +C ISTATE = -1, -2, -4, -5, -6, or -7. On a return with -3 (illegal +C input) or -8, they will be unchanged from their existing values +C (if any), except possibly for TOLSF, LENRW, and LENIW. +C On any error return, outputs relevant to the error will be defined, +C as noted below. +C +C Name Location Meaning +C +C HU RWORK(11) the step size in t last used (successfully). +C +C HCUR RWORK(12) the step size to be attempted on the next step. +C +C TCUR RWORK(13) the current value of the independent variable +C which the solver has actually reached, i.e. the +C current internal mesh point in t. On output, TCUR +C will always be at least as far as the argument +C T, but may be farther (if interpolation was done). +C +C TOLSF RWORK(14) a tolerance scale factor, greater than 1.0, +C computed when a request for too much accuracy was +C detected (ISTATE = -3 if detected at the start of +C the problem, ISTATE = -2 otherwise). If ITOL is +C left unaltered but RTOL and ATOL are uniformly +C scaled up by a factor of TOLSF for the next call, +C then the solver is deemed likely to succeed. +C (The user may also ignore TOLSF and alter the +C tolerance parameters in any other way appropriate.) +C +C NST IWORK(11) the number of steps taken for the problem so far. +C +C NRE IWORK(12) the number of residual evaluations (RES calls) +C for the problem so far. +C +C NJE IWORK(13) the number of Jacobian evaluations (each involving +C an evaluation of a and dr/dy) for the problem so +C far. This equals the number of calls to ADDA and +C (if MITER = 1) to JAC, and the number of matrix +C LU decompositions. +C +C NQU IWORK(14) the method order last used (successfully). +C +C NQCUR IWORK(15) the order to be attempted on the next step. +C +C IMXER IWORK(16) the index of the component of largest magnitude in +C the weighted local error vector ( E(i)/EWT(i) ), +C on an error return with ISTATE = -4 or -5. +C +C LENRW IWORK(17) the length of RWORK actually required. +C This is defined on normal returns and on an illegal +C input return for insufficient storage. +C +C LENIW IWORK(18) the length of IWORK actually required. +C This is defined on normal returns and on an illegal +C input return for insufficient storage. +C +C +C The following two arrays are segments of the RWORK array which +C may also be of interest to the user as optional outputs. +C For each array, the table below gives its internal name, +C its base address in RWORK, and its description. +C +C Name Base Address Description +C +C YH 21 the Nordsieck history array, of size NYH by +C (NQCUR + 1), where NYH is the initial value +C of NEQ. For j = 0,1,...,NQCUR, column j+1 +C of YH contains HCUR**j/factorial(j) times +C the j-th derivative of the interpolating +C polynomial currently representing the solution, +C evaluated at t = TCUR. +C +C ACOR LENRW-NEQ+1 array of size NEQ used for the accumulated +C corrections on each step, scaled on output to +C represent the estimated local error in y on +C the last step. This is the vector E in the +C description of the error control. It is +C defined only on a return from DLSOIBT with +C ISTATE = 2. +C +C----------------------------------------------------------------------- +C Part 2. Other Routines Callable. +C +C The following are optional calls which the user may make to +C gain additional capabilities in conjunction with DLSOIBT. +C (The routines XSETUN and XSETF are designed to conform to the +C SLATEC error handling package.) +C +C Form of Call Function +C CALL XSETUN(LUN) Set the logical unit number, LUN, for +C output of messages from DLSOIBT, if +C the default is not desired. +C The default value of LUN is 6. +C +C CALL XSETF(MFLAG) Set a flag to control the printing of +C messages by DLSOIBT. +C MFLAG = 0 means do not print. (Danger: +C This risks losing valuable information.) +C MFLAG = 1 means print (the default). +C +C Either of the above calls may be made at +C any time and will take effect immediately. +C +C CALL DSRCOM(RSAV,ISAV,JOB) saves and restores the contents of +C the internal Common blocks used by +C DLSOIBT (see Part 3 below). +C RSAV must be a real array of length 218 +C or more, and ISAV must be an integer +C array of length 37 or more. +C JOB=1 means save Common into RSAV/ISAV. +C JOB=2 means restore Common from RSAV/ISAV. +C DSRCOM is useful if one is +C interrupting a run and restarting +C later, or alternating between two or +C more problems solved with DLSOIBT. +C +C CALL DINTDY(,,,,,) Provide derivatives of y, of various +C (see below) orders, at a specified point t, if +C desired. It may be called only after +C a successful return from DLSOIBT. +C +C The detailed instructions for using DINTDY are as follows. +C The form of the call is: +C +C CALL DINTDY (T, K, RWORK(21), NYH, DKY, IFLAG) +C +C The input parameters are: +C +C T = value of independent variable where answers are desired +C (normally the same as the t last returned by DLSOIBT). +C For valid results, T must lie between TCUR - HU and TCUR. +C (See optional outputs for TCUR and HU.) +C K = integer order of the derivative desired. K must satisfy +C 0 .le. K .le. NQCUR, where NQCUR is the current order +C (see optional outputs). The capability corresponding +C to K = 0, i.e. computing y(t), is already provided +C by DLSOIBT directly. Since NQCUR .ge. 1, the first +C derivative dy/dt is always available with DINTDY. +C RWORK(21) = the base address of the history array YH. +C NYH = column length of YH, equal to the initial value of NEQ. +C +C The output parameters are: +C +C DKY = a real array of length NEQ containing the computed value +C of the K-th derivative of y(t). +C IFLAG = integer flag, returned as 0 if K and T were legal, +C -1 if K was illegal, and -2 if T was illegal. +C On an error return, a message is also written. +C----------------------------------------------------------------------- +C Part 3. Common Blocks. +C +C If DLSOIBT is to be used in an overlay situation, the user +C must declare, in the primary overlay, the variables in: +C (1) the call sequence to DLSOIBT, and +C (2) the internal Common block +C /DLS001/ of length 255 (218 double precision words +C followed by 37 integer words), +C +C If DLSOIBT is used on a system in which the contents of internal +C Common blocks are not preserved between calls, the user should +C declare the above Common block in the calling program to insure +C that their contents are preserved. +C +C If the solution of a given problem by DLSOIBT is to be interrupted +C and then later continued, such as when restarting an interrupted run +C or alternating between two or more problems, the user should save, +C following the return from the last DLSOIBT call prior to the +C interruption, the contents of the call sequence variables and the +C internal Common blocks, and later restore these values before the +C next DLSOIBT call for that problem. To save and restore the Common +C blocks, use Subroutine DSRCOM (see Part 2 above). +C +C----------------------------------------------------------------------- +C Part 4. Optionally Replaceable Solver Routines. +C +C Below are descriptions of two routines in the DLSOIBT package which +C relate to the measurement of errors. Either routine can be +C replaced by a user-supplied version, if desired. However, since such +C a replacement may have a major impact on performance, it should be +C done only when absolutely necessary, and only with great caution. +C (Note: The means by which the package version of a routine is +C superseded by the user's version may be system-dependent.) +C +C (a) DEWSET. +C The following subroutine is called just before each internal +C integration step, and sets the array of error weights, EWT, as +C described under ITOL/RTOL/ATOL above: +C SUBROUTINE DEWSET (NEQ, ITOL, RTOL, ATOL, YCUR, EWT) +C where NEQ, ITOL, RTOL, and ATOL are as in the DLSOIBT call sequence, +C YCUR contains the current dependent variable vector, and +C EWT is the array of weights set by DEWSET. +C +C If the user supplies this subroutine, it must return in EWT(i) +C (i = 1,...,NEQ) a positive quantity suitable for comparing errors +C in y(i) to. The EWT array returned by DEWSET is passed to the DVNORM +C routine (see below), and also used by DLSOIBT in the computation +C of the optional output IMXER, the diagonal Jacobian approximation, +C and the increments for difference quotient Jacobians. +C +C In the user-supplied version of DEWSET, it may be desirable to use +C the current values of derivatives of y. Derivatives up to order NQ +C are available from the history array YH, described above under +C optional outputs. In DEWSET, YH is identical to the YCUR array, +C extended to NQ + 1 columns with a column length of NYH and scale +C factors of H**j/factorial(j). On the first call for the problem, +C given by NST = 0, NQ is 1 and H is temporarily set to 1.0. +C NYH is the initial value of NEQ. The quantities NQ, H, and NST +C can be obtained by including in DEWSET the statements: +C DOUBLE PRECISION RLS +C COMMON /DLS001/ RLS(218),ILS(37) +C NQ = ILS(33) +C NST = ILS(34) +C H = RLS(212) +C Thus, for example, the current value of dy/dt can be obtained as +C YCUR(NYH+i)/H (i=1,...,NEQ) (and the division by H is +C unnecessary when NST = 0). +C +C (b) DVNORM. +C The following is a real function routine which computes the weighted +C root-mean-square norm of a vector v: +C D = DVNORM (N, V, W) +C where: +C N = the length of the vector, +C V = real array of length N containing the vector, +C W = real array of length N containing weights, +C D = SQRT( (1/N) * sum(V(i)*W(i))**2 ). +C DVNORM is called with N = NEQ and with W(i) = 1.0/EWT(i), where +C EWT is as set by Subroutine DEWSET. +C +C If the user supplies this function, it should return a non-negative +C value of DVNORM suitable for use in the error control in DLSOIBT. +C None of the arguments should be altered by DVNORM. +C For example, a user-supplied DVNORM routine might: +C -substitute a max-norm of (V(i)*W(i)) for the RMS-norm, or +C -ignore some components of V in the norm, with the effect of +C suppressing the error control on those components of y. +C----------------------------------------------------------------------- +C +C***REVISION HISTORY (YYYYMMDD) +C 19840625 DATE WRITTEN +C 19870330 Major update: corrected comments throughout; +C removed TRET from Common; rewrote EWSET with 4 loops; +C fixed t test in INTDY; added Cray directives in STODI; +C in STODI, fixed DELP init. and logic around PJAC call; +C combined routines to save/restore Common; +C passed LEVEL = 0 in error message calls (except run abort). +C 20010425 Major update: convert source lines to upper case; +C added *DECK lines; changed from 1 to * in dummy dimensions; +C changed names R1MACH/D1MACH to RUMACH/DUMACH; +C renamed routines for uniqueness across single/double prec.; +C converted intrinsic names to generic form; +C removed ILLIN and NTREP (data loaded) from Common; +C removed all 'own' variables from Common; +C changed error messages to quoted strings; +C replaced XERRWV/XERRWD with 1993 revised version; +C converted prologues, comments, error messages to mixed case; +C converted arithmetic IF statements to logical IF statements; +C numerous corrections to prologues and internal comments. +C 20010507 Converted single precision source to double precision. +C 20020502 Corrected declarations in descriptions of user routines. +C 20031105 Restored 'own' variables to Common block, to enable +C interrupt/restart feature. +C 20031112 Added SAVE statements for data-loaded constants. +C 20031117 Changed internal names NRE, LSAVR to NFE, LSAVF resp. +C +C----------------------------------------------------------------------- +C Other routines in the DLSOIBT package. +C +C In addition to Subroutine DLSOIBT, the DLSOIBT package includes the +C following subroutines and function routines: +C DAIGBT computes the initial value of the vector +C dy/dt = A-inverse * g +C DINTDY computes an interpolated value of the y vector at t = TOUT. +C DSTODI is the core integrator, which does one step of the +C integration and the associated error control. +C DCFODE sets all method coefficients and test constants. +C DEWSET sets the error weight vector EWT before each step. +C DVNORM computes the weighted RMS-norm of a vector. +C DSRCOM is a user-callable routine to save and restore +C the contents of the internal Common blocks. +C DPJIBT computes and preprocesses the Jacobian matrix +C and the Newton iteration matrix P. +C DSLSBT manages solution of linear system in chord iteration. +C DDECBT and DSOLBT are routines for solving block-tridiagonal +C systems of linear algebraic equations. +C DGEFA and DGESL are routines from LINPACK for solving full +C systems of linear algebraic equations. +C DDOT is one of the basic linear algebra modules (BLAS). +C DUMACH computes the unit roundoff in a machine-independent manner. +C XERRWD, XSETUN, XSETF, IXSAV, and IUMACH handle the printing of all +C error messages and warnings. XERRWD is machine-dependent. +C Note: DVNORM, DDOT, DUMACH, IXSAV, and IUMACH are function routines. +C All the others are subroutines. +C +C----------------------------------------------------------------------- + EXTERNAL DPJIBT, DSLSBT + DOUBLE PRECISION DUMACH, DVNORM + INTEGER INIT, MXSTEP, MXHNIL, NHNIL, NSLAST, NYH, IOWNS, + 1 ICF, IERPJ, IERSL, JCUR, JSTART, KFLAG, L, + 2 LYH, LEWT, LACOR, LSAVF, LWM, LIWM, METH, MITER, + 3 MAXORD, MAXCOR, MSBP, MXNCF, N, NQ, NST, NFE, NJE, NQU + INTEGER I, I1, I2, IER, IFLAG, IMXER, IRES, KGO, + 1 LENIW, LENRW, LENWM, LP, LYD0, MB, MORD, MXHNL0, MXSTP0, NB + DOUBLE PRECISION ROWNS, + 1 CCMAX, EL0, H, HMIN, HMXI, HU, RC, TN, UROUND + DOUBLE PRECISION ATOLI, AYI, BIG, EWTI, H0, HMAX, HMX, RH, RTOLI, + 1 TCRIT, TDIST, TNEXT, TOL, TOLSF, TP, SIZE, SUM, W0 + DIMENSION MORD(2) + LOGICAL IHIT + CHARACTER*60 MSG + SAVE MORD, MXSTP0, MXHNL0 +C----------------------------------------------------------------------- +C The following internal Common block contains +C (a) variables which are local to any subroutine but whose values must +C be preserved between calls to the routine ("own" variables), and +C (b) variables which are communicated between subroutines. +C The block DLS001 is declared in subroutines DLSOIBT, DINTDY, DSTODI, +C DPJIBT, and DSLSBT. +C Groups of variables are replaced by dummy arrays in the Common +C declarations in routines where those variables are not used. +C----------------------------------------------------------------------- + COMMON /DLS001/ ROWNS(209), + 1 CCMAX, EL0, H, HMIN, HMXI, HU, RC, TN, UROUND, + 2 INIT, MXSTEP, MXHNIL, NHNIL, NSLAST, NYH, IOWNS(6), + 3 ICF, IERPJ, IERSL, JCUR, JSTART, KFLAG, L, + 4 LYH, LEWT, LACOR, LSAVF, LWM, LIWM, METH, MITER, + 5 MAXORD, MAXCOR, MSBP, MXNCF, N, NQ, NST, NFE, NJE, NQU +C + DATA MORD(1),MORD(2)/12,5/, MXSTP0/500/, MXHNL0/10/ +C----------------------------------------------------------------------- +C Block A. +C This code block is executed on every call. +C It tests ISTATE and ITASK for legality and branches appropriately. +C If ISTATE .gt. 1 but the flag INIT shows that initialization has +C not yet been done, an error return occurs. +C If ISTATE = 0 or 1 and TOUT = T, return immediately. +C----------------------------------------------------------------------- + IF (ISTATE .LT. 0 .OR. ISTATE .GT. 3) GO TO 601 + IF (ITASK .LT. 1 .OR. ITASK .GT. 5) GO TO 602 + IF (ISTATE .LE. 1) GO TO 10 + IF (INIT .EQ. 0) GO TO 603 + IF (ISTATE .EQ. 2) GO TO 200 + GO TO 20 + 10 INIT = 0 + IF (TOUT .EQ. T) RETURN +C----------------------------------------------------------------------- +C Block B. +C The next code block is executed for the initial call (ISTATE = 0 or 1) +C or for a continuation call with parameter changes (ISTATE = 3). +C It contains checking of all inputs and various initializations. +C +C First check legality of the non-optional inputs NEQ, ITOL, IOPT, +C MF, MB, and NB. +C----------------------------------------------------------------------- + 20 IF (NEQ(1) .LE. 0) GO TO 604 + IF (ISTATE .LE. 1) GO TO 25 + IF (NEQ(1) .GT. N) GO TO 605 + 25 N = NEQ(1) + IF (ITOL .LT. 1 .OR. ITOL .GT. 4) GO TO 606 + IF (IOPT .LT. 0 .OR. IOPT .GT. 1) GO TO 607 + METH = MF/10 + MITER = MF - 10*METH + IF (METH .LT. 1 .OR. METH .GT. 2) GO TO 608 + IF (MITER .LT. 1 .OR. MITER .GT. 2) GO TO 608 + MB = IWORK(1) + NB = IWORK(2) + IF (MB .LT. 1 .OR. MB .GT. N) GO TO 609 + IF (NB .LT. 4) GO TO 610 + IF (MB*NB .NE. N) GO TO 609 +C Next process and check the optional inputs. -------------------------- + IF (IOPT .EQ. 1) GO TO 40 + MAXORD = MORD(METH) + MXSTEP = MXSTP0 + MXHNIL = MXHNL0 + IF (ISTATE .LE. 1) H0 = 0.0D0 + HMXI = 0.0D0 + HMIN = 0.0D0 + GO TO 60 + 40 MAXORD = IWORK(5) + IF (MAXORD .LT. 0) GO TO 611 + IF (MAXORD .EQ. 0) MAXORD = 100 + MAXORD = MIN(MAXORD,MORD(METH)) + MXSTEP = IWORK(6) + IF (MXSTEP .LT. 0) GO TO 612 + IF (MXSTEP .EQ. 0) MXSTEP = MXSTP0 + MXHNIL = IWORK(7) + IF (MXHNIL .LT. 0) GO TO 613 + IF (MXHNIL .EQ. 0) MXHNIL = MXHNL0 + IF (ISTATE .GT. 1) GO TO 50 + H0 = RWORK(5) + IF ((TOUT - T)*H0 .LT. 0.0D0) GO TO 614 + 50 HMAX = RWORK(6) + IF (HMAX .LT. 0.0D0) GO TO 615 + HMXI = 0.0D0 + IF (HMAX .GT. 0.0D0) HMXI = 1.0D0/HMAX + HMIN = RWORK(7) + IF (HMIN .LT. 0.0D0) GO TO 616 +C----------------------------------------------------------------------- +C Set work array pointers and check lengths LRW and LIW. +C Pointers to segments of RWORK and IWORK are named by prefixing L to +C the name of the segment. E.g., the segment YH starts at RWORK(LYH). +C Segments of RWORK (in order) are denoted YH, WM, EWT, SAVR, ACOR. +C----------------------------------------------------------------------- + 60 LYH = 21 + IF (ISTATE .LE. 1) NYH = N + LWM = LYH + (MAXORD + 1)*NYH + LENWM = 3*MB*MB*NB + 2 + LEWT = LWM + LENWM + LSAVF = LEWT + N + LACOR = LSAVF + N + LENRW = LACOR + N - 1 + IWORK(17) = LENRW + LIWM = 1 + LENIW = 20 + N + IWORK(18) = LENIW + IF (LENRW .GT. LRW) GO TO 617 + IF (LENIW .GT. LIW) GO TO 618 +C Check RTOL and ATOL for legality. ------------------------------------ + RTOLI = RTOL(1) + ATOLI = ATOL(1) + DO 70 I = 1,N + IF (ITOL .GE. 3) RTOLI = RTOL(I) + IF (ITOL .EQ. 2 .OR. ITOL .EQ. 4) ATOLI = ATOL(I) + IF (RTOLI .LT. 0.0D0) GO TO 619 + IF (ATOLI .LT. 0.0D0) GO TO 620 + 70 CONTINUE + IF (ISTATE .LE. 1) GO TO 100 +C If ISTATE = 3, set flag to signal parameter changes to DSTODI. ------- + JSTART = -1 + IF (NQ .LE. MAXORD) GO TO 90 +C MAXORD was reduced below NQ. Copy YH(*,MAXORD+2) into YDOTI.--------- + DO 80 I = 1,N + 80 YDOTI(I) = RWORK(I+LWM-1) +C Reload WM(1) = RWORK(lWM), since lWM may have changed. --------------- + 90 RWORK(LWM) = SQRT(UROUND) + IF (N .EQ. NYH) GO TO 200 +C NEQ was reduced. Zero part of YH to avoid undefined references. ----- + I1 = LYH + L*NYH + I2 = LYH + (MAXORD + 1)*NYH - 1 + IF (I1 .GT. I2) GO TO 200 + DO 95 I = I1,I2 + 95 RWORK(I) = 0.0D0 + GO TO 200 +C----------------------------------------------------------------------- +C Block C. +C The next block is for the initial call only (ISTATE = 0 or 1). +C It contains all remaining initializations, the call to DAIGBT +C (if ISTATE = 1), and the calculation of the initial step size. +C The error weights in EWT are inverted after being loaded. +C----------------------------------------------------------------------- + 100 UROUND = DUMACH() + TN = T + IF (ITASK .NE. 4 .AND. ITASK .NE. 5) GO TO 105 + TCRIT = RWORK(1) + IF ((TCRIT - TOUT)*(TOUT - T) .LT. 0.0D0) GO TO 625 + IF (H0 .NE. 0.0D0 .AND. (T + H0 - TCRIT)*H0 .GT. 0.0D0) + 1 H0 = TCRIT - T + 105 JSTART = 0 + RWORK(LWM) = SQRT(UROUND) + NHNIL = 0 + NST = 0 + NFE = 0 + NJE = 0 + NSLAST = 0 + HU = 0.0D0 + NQU = 0 + CCMAX = 0.3D0 + MAXCOR = 3 + MSBP = 20 + MXNCF = 10 +C Compute initial dy/dt, if necessary, and load it and initial Y into YH + LYD0 = LYH + NYH + LP = LWM + 1 + IF ( ISTATE .EQ. 1 ) GO TO 120 +C DLSOIBT must compute initial dy/dt (LYD0 points to YH(*,2)). --------- + CALL DAIGBT( RES, ADDA, NEQ, T, Y, RWORK(LYD0), + 1 MB, NB, RWORK(LP), IWORK(21), IER ) + NFE = NFE + 1 + IF (IER .LT. 0) GO TO 560 + IF (IER .GT. 0) GO TO 565 + DO 115 I = 1,N + 115 RWORK(I+LYH-1) = Y(I) + GO TO 130 +C Initial dy/dt was supplied. Load into YH (LYD0 points to YH(*,2).). - + 120 DO 125 I = 1,N + RWORK(I+LYH-1) = Y(I) + 125 RWORK(I+LYD0-1) = YDOTI(I) +C Load and invert the EWT array. (H is temporarily set to 1.0.) ------- + 130 CONTINUE + NQ = 1 + H = 1.0D0 + CALL DEWSET (N, ITOL, RTOL, ATOL, RWORK(LYH), RWORK(LEWT)) + DO 135 I = 1,N + IF (RWORK(I+LEWT-1) .LE. 0.0D0) GO TO 621 + 135 RWORK(I+LEWT-1) = 1.0D0/RWORK(I+LEWT-1) +C----------------------------------------------------------------------- +C The coding below computes the step size, H0, to be attempted on the +C first step, unless the user has supplied a value for this. +C First check that TOUT - T differs significantly from zero. +C A scalar tolerance quantity TOL is computed, as MAX(RTOL(i)) +C if this is positive, or MAX(ATOL(i)/ABS(Y(i))) otherwise, adjusted +C so as to be between 100*UROUND and 1.0E-3. +C Then the computed value H0 is given by.. +C NEQ +C H0**2 = TOL / ( w0**-2 + (1/NEQ) * Sum ( YDOT(i)/ywt(i) )**2 ) +C 1 +C where w0 = MAX ( ABS(T), ABS(TOUT) ), +C YDOT(i) = i-th component of initial value of dy/dt, +C ywt(i) = EWT(i)/TOL (a weight for y(i)). +C The sign of H0 is inferred from the initial values of TOUT and T. +C----------------------------------------------------------------------- + IF (H0 .NE. 0.0D0) GO TO 180 + TDIST = ABS(TOUT - T) + W0 = MAX(ABS(T),ABS(TOUT)) + IF (TDIST .LT. 2.0D0*UROUND*W0) GO TO 622 + TOL = RTOL(1) + IF (ITOL .LE. 2) GO TO 145 + DO 140 I = 1,N + 140 TOL = MAX(TOL,RTOL(I)) + 145 IF (TOL .GT. 0.0D0) GO TO 160 + ATOLI = ATOL(1) + DO 150 I = 1,N + IF (ITOL .EQ. 2 .OR. ITOL .EQ. 4) ATOLI = ATOL(I) + AYI = ABS(Y(I)) + IF (AYI .NE. 0.0D0) TOL = MAX(TOL,ATOLI/AYI) + 150 CONTINUE + 160 TOL = MAX(TOL,100.0D0*UROUND) + TOL = MIN(TOL,0.001D0) + SUM = DVNORM (N, RWORK(LYD0), RWORK(LEWT)) + SUM = 1.0D0/(TOL*W0*W0) + TOL*SUM**2 + H0 = 1.0D0/SQRT(SUM) + H0 = MIN(H0,TDIST) + H0 = SIGN(H0,TOUT-T) +C Adjust H0 if necessary to meet HMAX bound. --------------------------- + 180 RH = ABS(H0)*HMXI + IF (RH .GT. 1.0D0) H0 = H0/RH +C Load H with H0 and scale YH(*,2) by H0. ------------------------------ + H = H0 + DO 190 I = 1,N + 190 RWORK(I+LYD0-1) = H0*RWORK(I+LYD0-1) + GO TO 270 +C----------------------------------------------------------------------- +C Block D. +C The next code block is for continuation calls only (ISTATE = 2 or 3) +C and is to check stop conditions before taking a step. +C----------------------------------------------------------------------- + 200 NSLAST = NST + GO TO (210, 250, 220, 230, 240), ITASK + 210 IF ((TN - TOUT)*H .LT. 0.0D0) GO TO 250 + CALL DINTDY (TOUT, 0, RWORK(LYH), NYH, Y, IFLAG) + IF (IFLAG .NE. 0) GO TO 627 + T = TOUT + GO TO 420 + 220 TP = TN - HU*(1.0D0 + 100.0D0*UROUND) + IF ((TP - TOUT)*H .GT. 0.0D0) GO TO 623 + IF ((TN - TOUT)*H .LT. 0.0D0) GO TO 250 + GO TO 400 + 230 TCRIT = RWORK(1) + IF ((TN - TCRIT)*H .GT. 0.0D0) GO TO 624 + IF ((TCRIT - TOUT)*H .LT. 0.0D0) GO TO 625 + IF ((TN - TOUT)*H .LT. 0.0D0) GO TO 245 + CALL DINTDY (TOUT, 0, RWORK(LYH), NYH, Y, IFLAG) + IF (IFLAG .NE. 0) GO TO 627 + T = TOUT + GO TO 420 + 240 TCRIT = RWORK(1) + IF ((TN - TCRIT)*H .GT. 0.0D0) GO TO 624 + 245 HMX = ABS(TN) + ABS(H) + IHIT = ABS(TN - TCRIT) .LE. 100.0D0*UROUND*HMX + IF (IHIT) GO TO 400 + TNEXT = TN + H*(1.0D0 + 4.0D0*UROUND) + IF ((TNEXT - TCRIT)*H .LE. 0.0D0) GO TO 250 + H = (TCRIT - TN)*(1.0D0 - 4.0D0*UROUND) + IF (ISTATE .EQ. 2) JSTART = -2 +C----------------------------------------------------------------------- +C Block E. +C The next block is normally executed for all calls and contains +C the call to the one-step core integrator DSTODI. +C +C This is a looping point for the integration steps. +C +C First check for too many steps being taken, update EWT (if not at +C start of problem), check for too much accuracy being requested, and +C check for H below the roundoff level in T. +C----------------------------------------------------------------------- + 250 CONTINUE + IF ((NST-NSLAST) .GE. MXSTEP) GO TO 500 + CALL DEWSET (N, ITOL, RTOL, ATOL, RWORK(LYH), RWORK(LEWT)) + DO 260 I = 1,N + IF (RWORK(I+LEWT-1) .LE. 0.0D0) GO TO 510 + 260 RWORK(I+LEWT-1) = 1.0D0/RWORK(I+LEWT-1) + 270 TOLSF = UROUND*DVNORM (N, RWORK(LYH), RWORK(LEWT)) + IF (TOLSF .LE. 1.0D0) GO TO 280 + TOLSF = TOLSF*2.0D0 + IF (NST .EQ. 0) GO TO 626 + GO TO 520 + 280 IF ((TN + H) .NE. TN) GO TO 290 + NHNIL = NHNIL + 1 + IF (NHNIL .GT. MXHNIL) GO TO 290 + MSG = 'DLSOIBT- Warning..Internal T (=R1) and H (=R2) are' + CALL XERRWD (MSG, 50, 101, 0, 0, 0, 0, 0, 0.0D0, 0.0D0) + MSG=' such that in the machine, T + H = T on the next step ' + CALL XERRWD (MSG, 60, 101, 0, 0, 0, 0, 0, 0.0D0, 0.0D0) + MSG = ' (H = step size). Solver will continue anyway.' + CALL XERRWD (MSG, 50, 101, 0, 0, 0, 0, 2, TN, H) + IF (NHNIL .LT. MXHNIL) GO TO 290 + MSG = 'DLSOIBT- Above warning has been issued I1 times. ' + CALL XERRWD (MSG, 50, 102, 0, 0, 0, 0, 0, 0.0D0, 0.0D0) + MSG = ' It will not be issued again for this problem.' + CALL XERRWD (MSG, 50, 102, 0, 1, MXHNIL, 0, 0, 0.0D0, 0.0D0) + 290 CONTINUE +C----------------------------------------------------------------------- +C CALL DSTODI(NEQ,Y,YH,NYH,YH1,EWT,SAVF,SAVR,ACOR,WM,IWM,RES, +C ADDA,JAC,DPJIBT,DSLSBT) +C Note: SAVF in DSTODI occupies the same space as YDOTI in DLSOIBT. +C----------------------------------------------------------------------- + CALL DSTODI (NEQ, Y, RWORK(LYH), NYH, RWORK(LYH), RWORK(LEWT), + 1 YDOTI, RWORK(LSAVF), RWORK(LACOR), RWORK(LWM), + 2 IWORK(LIWM), RES, ADDA, JAC, DPJIBT, DSLSBT ) + KGO = 1 - KFLAG + GO TO (300, 530, 540, 400, 550), KGO +C +C KGO = 1:success; 2:error test failure; 3:convergence failure; +C 4:RES ordered return; 5:RES returned error. +C----------------------------------------------------------------------- +C Block F. +C The following block handles the case of a successful return from the +C core integrator (KFLAG = 0). Test for stop conditions. +C----------------------------------------------------------------------- + 300 INIT = 1 + GO TO (310, 400, 330, 340, 350), ITASK +C ITASK = 1. If TOUT has been reached, interpolate. ------------------- + 310 IF ((TN - TOUT)*H .LT. 0.0D0) GO TO 250 + CALL DINTDY (TOUT, 0, RWORK(LYH), NYH, Y, IFLAG) + T = TOUT + GO TO 420 +C ITASK = 3. Jump to exit if TOUT was reached. ------------------------ + 330 IF ((TN - TOUT)*H .GE. 0.0D0) GO TO 400 + GO TO 250 +C ITASK = 4. See if TOUT or TCRIT was reached. Adjust H if necessary. + 340 IF ((TN - TOUT)*H .LT. 0.0D0) GO TO 345 + CALL DINTDY (TOUT, 0, RWORK(LYH), NYH, Y, IFLAG) + T = TOUT + GO TO 420 + 345 HMX = ABS(TN) + ABS(H) + IHIT = ABS(TN - TCRIT) .LE. 100.0D0*UROUND*HMX + IF (IHIT) GO TO 400 + TNEXT = TN + H*(1.0D0 + 4.0D0*UROUND) + IF ((TNEXT - TCRIT)*H .LE. 0.0D0) GO TO 250 + H = (TCRIT - TN)*(1.0D0 - 4.0D0*UROUND) + JSTART = -2 + GO TO 250 +C ITASK = 5. see if TCRIT was reached and jump to exit. --------------- + 350 HMX = ABS(TN) + ABS(H) + IHIT = ABS(TN - TCRIT) .LE. 100.0D0*UROUND*HMX +C----------------------------------------------------------------------- +C Block G. +C The following block handles all successful returns from DLSOIBT. +C If ITASK .ne. 1, Y is loaded from YH and T is set accordingly. +C ISTATE is set to 2, and the optional outputs are loaded into the +C work arrays before returning. +C----------------------------------------------------------------------- + 400 DO 410 I = 1,N + 410 Y(I) = RWORK(I+LYH-1) + T = TN + IF (ITASK .NE. 4 .AND. ITASK .NE. 5) GO TO 420 + IF (IHIT) T = TCRIT + 420 ISTATE = 2 + IF ( KFLAG .EQ. -3 ) ISTATE = 3 + RWORK(11) = HU + RWORK(12) = H + RWORK(13) = TN + IWORK(11) = NST + IWORK(12) = NFE + IWORK(13) = NJE + IWORK(14) = NQU + IWORK(15) = NQ + RETURN +C----------------------------------------------------------------------- +C Block H. +C The following block handles all unsuccessful returns other than +C those for illegal input. First the error message routine is called. +C If there was an error test or convergence test failure, IMXER is set. +C Then Y is loaded from YH and T is set to TN. +C The optional outputs are loaded into the work arrays before returning. +C----------------------------------------------------------------------- +C The maximum number of steps was taken before reaching TOUT. ---------- + 500 MSG = 'DLSOIBT- At current T (=R1), MXSTEP (=I1) steps ' + CALL XERRWD (MSG, 50, 201, 0, 0, 0, 0, 0, 0.0D0, 0.0D0) + MSG = ' taken on this call before reaching TOUT ' + CALL XERRWD (MSG, 50, 201, 0, 1, MXSTEP, 0, 1, TN, 0.0D0) + ISTATE = -1 + GO TO 580 +C EWT(i) .le. 0.0 for some i (not at start of problem). ---------------- + 510 EWTI = RWORK(LEWT+I-1) + MSG = 'DLSOIBT- At T (=R1), EWT(I1) has become R2 .le. 0.' + CALL XERRWD (MSG, 50, 202, 0, 1, I, 0, 2, TN, EWTI) + ISTATE = -6 + GO TO 590 +C Too much accuracy requested for machine precision. ------------------- + 520 MSG = 'DLSOIBT- At T (=R1), too much accuracy requested ' + CALL XERRWD (MSG, 50, 203, 0, 0, 0, 0, 0, 0.0D0, 0.0D0) + MSG = ' for precision of machine.. See TOLSF (=R2) ' + CALL XERRWD (MSG, 50, 203, 0, 0, 0, 0, 2, TN, TOLSF) + RWORK(14) = TOLSF + ISTATE = -2 + GO TO 590 +C KFLAG = -1. Error test failed repeatedly or with ABS(H) = HMIN. ----- + 530 MSG = 'DLSOIBT- At T (=R1) and step size H (=R2), the ' + CALL XERRWD (MSG, 50, 204, 0, 0, 0, 0, 0, 0.0D0, 0.0D0) + MSG = 'error test failed repeatedly or with ABS(H) = HMIN' + CALL XERRWD (MSG, 50, 204, 0, 0, 0, 0, 2, TN, H) + ISTATE = -4 + GO TO 570 +C KFLAG = -2. Convergence failed repeatedly or with ABS(H) = HMIN. ---- + 540 MSG = 'DLSOIBT- At T (=R1) and step size H (=R2), the ' + CALL XERRWD (MSG, 50, 205, 0, 0, 0, 0, 0, 0.0D0, 0.0D0) + MSG = ' corrector convergence failed repeatedly ' + CALL XERRWD (MSG, 50, 205, 0, 0, 0, 0, 0, 0.0D0, 0.0D0) + MSG = ' or with ABS(H) = HMIN ' + CALL XERRWD (MSG, 30, 205, 0, 0, 0, 0, 2, TN, H) + ISTATE = -5 + GO TO 570 +C IRES = 3 returned by RES, despite retries by DSTODI.------------------ + 550 MSG = 'DLSOIBT- At T (=R1) residual routine returned ' + CALL XERRWD (MSG, 50, 206, 0, 0, 0, 0, 0, 0.0D0, 0.0D0) + MSG = ' error IRES = 3 repeatedly. ' + CALL XERRWD (MSG, 40, 206, 0, 0, 0, 0, 1, TN, 0.0D0) + ISTATE = -7 + GO TO 590 +C DAIGBT failed because a diagonal block of A matrix was singular. ----- + 560 IER = -IER + MSG='DLSOIBT- Attempt to initialize dy/dt failed: Matrix A has a' + CALL XERRWD (MSG, 60, 207, 0, 0, 0, 0, 0, 0.0D0, 0.0D0) + MSG = ' singular diagonal block, block no. = (I1) ' + CALL XERRWD (MSG, 50, 207, 0, 1, IER, 0, 0, 0.0D0, 0.0D0) + ISTATE = -8 + RETURN +C DAIGBT failed because RES set IRES to 2 or 3. ------------------------ + 565 MSG = 'DLSOIBT- Attempt to initialize dy/dt failed ' + CALL XERRWD (MSG, 50, 208, 0, 0, 0, 0, 0, 0.0D0, 0.0D0) + MSG = ' because residual routine set its error flag ' + CALL XERRWD (MSG, 50, 208, 0, 0, 0, 0, 0, 0.0D0, 0.0D0) + MSG = ' to IRES = (I1)' + CALL XERRWD (MSG, 20, 208, 0, 1, IER, 0, 0, 0.0D0, 0.0D0) + ISTATE = -8 + RETURN +C Compute IMXER if relevant. ------------------------------------------- + 570 BIG = 0.0D0 + IMXER = 1 + DO 575 I = 1,N + SIZE = ABS(RWORK(I+LACOR-1)*RWORK(I+LEWT-1)) + IF (BIG .GE. SIZE) GO TO 575 + BIG = SIZE + IMXER = I + 575 CONTINUE + IWORK(16) = IMXER +C Compute residual if relevant. ---------------------------------------- + 580 LYD0 = LYH + NYH + DO 585 I = 1,N + RWORK(I+LSAVF-1) = RWORK(I+LYD0-1)/H + 585 Y(I) = RWORK(I+LYH-1) + IRES = 1 + CALL RES (NEQ, TN, Y, RWORK(LSAVF), YDOTI, IRES) + NFE = NFE + 1 + IF (IRES .LE. 1) GO TO 595 + MSG = 'DLSOIBT- Residual routine set its flag IRES ' + CALL XERRWD (MSG, 50, 210, 0, 0, 0, 0, 0, 0.0D0, 0.0D0) + MSG = ' to (I1) when called for final output. ' + CALL XERRWD (MSG, 50, 210, 0, 1, IRES, 0, 0, 0.0D0, 0.0D0) + GO TO 595 +C Set Y vector, T, and optional outputs. ------------------------------- + 590 DO 592 I = 1,N + 592 Y(I) = RWORK(I+LYH-1) + 595 T = TN + RWORK(11) = HU + RWORK(12) = H + RWORK(13) = TN + IWORK(11) = NST + IWORK(12) = NFE + IWORK(13) = NJE + IWORK(14) = NQU + IWORK(15) = NQ + RETURN +C----------------------------------------------------------------------- +C Block I. +C The following block handles all error returns due to illegal input +C (ISTATE = -3), as detected before calling the core integrator. +C First the error message routine is called. If the illegal input +C is a negative ISTATE, the run is aborted (apparent infinite loop). +C----------------------------------------------------------------------- + 601 MSG = 'DLSOIBT- ISTATE (=I1) illegal.' + CALL XERRWD (MSG, 30, 1, 0, 1, ISTATE, 0, 0, 0.0D0, 0.0D0) + IF (ISTATE .LT. 0) GO TO 800 + GO TO 700 + 602 MSG = 'DLSOIBT- ITASK (=I1) illegal. ' + CALL XERRWD (MSG, 30, 2, 0, 1, ITASK, 0, 0, 0.0D0, 0.0D0) + GO TO 700 + 603 MSG = 'DLSOIBT- ISTATE.gt.1 but DLSOIBT not initialized. ' + CALL XERRWD (MSG, 50, 3, 0, 0, 0, 0, 0, 0.0D0, 0.0D0) + GO TO 700 + 604 MSG = 'DLSOIBT- NEQ (=I1) .lt. 1 ' + CALL XERRWD (MSG, 30, 4, 0, 1, NEQ(1), 0, 0, 0.0D0, 0.0D0) + GO TO 700 + 605 MSG = 'DLSOIBT- ISTATE = 3 and NEQ increased (I1 to I2). ' + CALL XERRWD (MSG, 50, 5, 0, 2, N, NEQ(1), 0, 0.0D0, 0.0D0) + GO TO 700 + 606 MSG = 'DLSOIBT- ITOL (=I1) illegal. ' + CALL XERRWD (MSG, 30, 6, 0, 1, ITOL, 0, 0, 0.0D0, 0.0D0) + GO TO 700 + 607 MSG = 'DLSOIBT- IOPT (=I1) illegal. ' + CALL XERRWD (MSG, 30, 7, 0, 1, IOPT, 0, 0, 0.0D0, 0.0D0) + GO TO 700 + 608 MSG = 'DLSOIBT- MF (=I1) illegal. ' + CALL XERRWD (MSG, 30, 8, 0, 1, MF, 0, 0, 0.0D0, 0.0D0) + GO TO 700 + 609 MSG = 'DLSOIBT- MB (=I1) or NB (=I2) illegal. ' + CALL XERRWD (MSG, 40, 9, 0, 2, MB, NB, 0, 0.0D0, 0.0D0) + GO TO 700 + 610 MSG = 'DLSOIBT- NB (=I1) .lt. 4 illegal. ' + CALL XERRWD (MSG, 40, 10, 0, 1, NB, 0, 0, 0.0D0, 0.0D0) + GO TO 700 + 611 MSG = 'DLSOIBT- MAXORD (=I1) .lt. 0 ' + CALL XERRWD (MSG, 30, 11, 0, 1, MAXORD, 0, 0, 0.0D0, 0.0D0) + GO TO 700 + 612 MSG = 'DLSOIBT- MXSTEP (=I1) .lt. 0 ' + CALL XERRWD (MSG, 30, 12, 0, 1, MXSTEP, 0, 0, 0.0D0, 0.0D0) + GO TO 700 + 613 MSG = 'DLSOIBT- MXHNIL (=I1) .lt. 0 ' + CALL XERRWD (MSG, 30, 13, 0, 1, MXHNIL, 0, 0, 0.0D0, 0.0D0) + GO TO 700 + 614 MSG = 'DLSOIBT- TOUT (=R1) behind T (=R2) ' + CALL XERRWD (MSG, 40, 14, 0, 0, 0, 0, 2, TOUT, T) + MSG = ' Integration direction is given by H0 (=R1) ' + CALL XERRWD (MSG, 50, 14, 0, 0, 0, 0, 1, H0, 0.0D0) + GO TO 700 + 615 MSG = 'DLSOIBT- HMAX (=R1) .lt. 0.0 ' + CALL XERRWD (MSG, 30, 15, 0, 0, 0, 0, 1, HMAX, 0.0D0) + GO TO 700 + 616 MSG = 'DLSOIBT- HMIN (=R1) .lt. 0.0 ' + CALL XERRWD (MSG, 30, 16, 0, 0, 0, 0, 1, HMIN, 0.0D0) + GO TO 700 + 617 MSG='DLSOIBT- RWORK length needed, LENRW (=I1), exceeds LRW (=I2)' + CALL XERRWD (MSG, 60, 17, 0, 2, LENRW, LRW, 0, 0.0D0, 0.0D0) + GO TO 700 + 618 MSG='DLSOIBT- IWORK length needed, LENIW (=I1), exceeds LIW (=I2)' + CALL XERRWD (MSG, 60, 18, 0, 2, LENIW, LIW, 0, 0.0D0, 0.0D0) + GO TO 700 + 619 MSG = 'DLSOIBT- RTOL(=I1) is R1 .lt. 0.0 ' + CALL XERRWD (MSG, 40, 19, 0, 1, I, 0, 1, RTOLI, 0.0D0) + GO TO 700 + 620 MSG = 'DLSOIBT- ATOL(=I1) is R1 .lt. 0.0 ' + CALL XERRWD (MSG, 40, 20, 0, 1, I, 0, 1, ATOLI, 0.0D0) + GO TO 700 + 621 EWTI = RWORK(LEWT+I-1) + MSG = 'DLSOIBT- EWT(I1) is R1 .le. 0.0 ' + CALL XERRWD (MSG, 40, 21, 0, 1, I, 0, 1, EWTI, 0.0D0) + GO TO 700 + 622 MSG='DLSOIBT- TOUT(=R1) too close to T(=R2) to start integration.' + CALL XERRWD (MSG, 60, 22, 0, 0, 0, 0, 2, TOUT, T) + GO TO 700 + 623 MSG='DLSOIBT- ITASK = I1 and TOUT (=R1) behind TCUR - HU (= R2) ' + CALL XERRWD (MSG, 60, 23, 0, 1, ITASK, 0, 2, TOUT, TP) + GO TO 700 + 624 MSG='DLSOIBT- ITASK = 4 or 5 and TCRIT (=R1) behind TCUR (=R2) ' + CALL XERRWD (MSG, 60, 24, 0, 0, 0, 0, 2, TCRIT, TN) + GO TO 700 + 625 MSG='DLSOIBT- ITASK = 4 or 5 and TCRIT (=R1) behind TOUT (=R2) ' + CALL XERRWD (MSG, 60, 25, 0, 0, 0, 0, 2, TCRIT, TOUT) + GO TO 700 + 626 MSG = 'DLSOIBT- At start of problem, too much accuracy ' + CALL XERRWD (MSG, 50, 26, 0, 0, 0, 0, 0, 0.0D0, 0.0D0) + MSG=' requested for precision of machine.. See TOLSF (=R1) ' + CALL XERRWD (MSG, 60, 26, 0, 0, 0, 0, 1, TOLSF, 0.0D0) + RWORK(14) = TOLSF + GO TO 700 + 627 MSG = 'DLSOIBT- Trouble in DINTDY. ITASK = I1, TOUT = R1' + CALL XERRWD (MSG, 50, 27, 0, 1, ITASK, 0, 1, TOUT, 0.0D0) +C + 700 ISTATE = -3 + RETURN +C + 800 MSG = 'DLSOIBT- Run aborted.. apparent infinite loop. ' + CALL XERRWD (MSG, 50, 303, 2, 0, 0, 0, 0, 0.0D0, 0.0D0) + RETURN +C----------------------- End of Subroutine DLSOIBT --------------------- + END +*DECK DLSODIS + SUBROUTINE DLSODIS (RES, ADDA, JAC, NEQ, Y, YDOTI, T, TOUT, ITOL, + 1 RTOL, ATOL, ITASK, ISTATE, IOPT, RWORK, LRW, IWORK, LIW, MF ) + EXTERNAL RES, ADDA, JAC + INTEGER NEQ, ITOL, ITASK, ISTATE, IOPT, LRW, IWORK, LIW, MF + DOUBLE PRECISION Y, YDOTI, T, TOUT, RTOL, ATOL, RWORK + DIMENSION NEQ(*), Y(*), YDOTI(*), RTOL(*), ATOL(*), RWORK(LRW), + 1 IWORK(LIW) +C----------------------------------------------------------------------- +C This is the 18 November 2003 version of +C DLSODIS: Livermore Solver for Ordinary Differential equations +C (Implicit form) with general Sparse Jacobian matrices. +C +C This version is in double precision. +C +C DLSODIS solves the initial value problem for linearly implicit +C systems of first order ODEs, +C A(t,y) * dy/dt = g(t,y) , where A(t,y) is a square matrix, +C or, in component form, +C ( a * ( dy / dt )) + ... + ( a * ( dy / dt )) = +C i,1 1 i,NEQ NEQ +C +C = g ( t, y , y ,..., y ) ( i = 1,...,NEQ ) +C i 1 2 NEQ +C +C If A is singular, this is a differential-algebraic system. +C +C DLSODIS is a variant version of the DLSODI package, and is intended +C for stiff problems in which the matrix A and the Jacobian matrix +C d(g - A*s)/dy have arbitrary sparse structures. +C +C Authors: Alan C. Hindmarsh +C Center for Applied Scientific Computing, L-561 +C Lawrence Livermore National Laboratory +C Livermore, CA 94551 +C and +C Sheila Balsdon +C Zycor, Inc. +C Austin, TX 78741 +C----------------------------------------------------------------------- +C References: +C 1. M. K. Seager and S. Balsdon, LSODIS, A Sparse Implicit +C ODE Solver, in Proceedings of the IMACS 10th World Congress, +C Montreal, August 8-13, 1982. +C +C 2. Alan C. Hindmarsh, LSODE and LSODI, Two New Initial Value +C Ordinary Differential Equation Solvers, +C ACM-SIGNUM Newsletter, vol. 15, no. 4 (1980), pp. 10-11. +C +C 3. S. C. Eisenstat, M. C. Gursky, M. H. Schultz, and A. H. Sherman, +C Yale Sparse Matrix Package: I. The Symmetric Codes, +C Int. J. Num. Meth. Eng., vol. 18 (1982), pp. 1145-1151. +C +C 4. S. C. Eisenstat, M. C. Gursky, M. H. Schultz, and A. H. Sherman, +C Yale Sparse Matrix Package: II. The Nonsymmetric Codes, +C Research Report No. 114, Dept. of Computer Sciences, Yale +C University, 1977. +C----------------------------------------------------------------------- +C Summary of Usage. +C +C Communication between the user and the DLSODIS package, for normal +C situations, is summarized here. This summary describes only a subset +C of the full set of options available. See the full description for +C details, including optional communication, nonstandard options, +C and instructions for special situations. See also the example +C problem (with program and output) following this summary. +C +C A. First, provide a subroutine of the form: +C SUBROUTINE RES (NEQ, T, Y, S, R, IRES) +C DOUBLE PRECISION T, Y(*), S(*), R(*) +C which computes the residual function +C r = g(t,y) - A(t,y) * s , +C as a function of t and the vectors y and s. (s is an internally +C generated approximation to dy/dt.) The arrays Y and S are inputs +C to the RES routine and should not be altered. The residual +C vector is to be stored in the array R. The argument IRES should be +C ignored for casual use of DLSODIS. (For uses of IRES, see the +C paragraph on RES in the full description below.) +C +C B. DLSODIS must deal internally with the matrices A and dr/dy, where +C r is the residual function defined above. DLSODIS generates a linear +C combination of these two matrices in sparse form. +C The matrix structure is communicated by a method flag, MF: +C MF = 21 or 22 when the user provides the structures of +C matrix A and dr/dy, +C MF = 121 or 222 when the user does not provide structure +C information, and +C MF = 321 or 422 when the user provides the structure +C of matrix A. +C +C C. You must also provide a subroutine of the form: +C SUBROUTINE ADDA (NEQ, T, Y, J, IAN, JAN, P) +C DOUBLE PRECISION T, Y(*), P(*) +C INTEGER IAN(*), JAN(*) +C which adds the matrix A = A(t,y) to the contents of the array P. +C NEQ, T, Y, and J are input arguments and should not be altered. +C This routine should add the J-th column of matrix A to the array +C P (of length NEQ). I.e. add A(i,J) to P(i) for all relevant +C values of i. The arguments IAN and JAN should be ignored for normal +C situations. DLSODIS will call the ADDA routine with J = 1,2,...,NEQ. +C +C D. For the sake of efficiency, you are encouraged to supply the +C Jacobian matrix dr/dy in closed form, where r = g(t,y) - A(t,y)*s +C (s = a fixed vector) as above. If dr/dy is being supplied, +C use MF = 21, 121, or 321, and provide a subroutine of the form: +C SUBROUTINE JAC (NEQ, T, Y, S, J, IAN, JAN, PDJ) +C DOUBLE PRECISION T, Y(*), S(*), PDJ(*) +C INTEGER IAN(*), JAN(*) +C which computes dr/dy as a function of t, y, and s. Here NEQ, T, Y, S, +C and J are input arguments, and the JAC routine is to load the array +C PDJ (of length NEQ) with the J-th column of dr/dy. I.e. load PDJ(i) +C with dr(i)/dy(J) for all relevant values of i. The arguments IAN and +C JAN should be ignored for normal situations. DLSODIS will call the +C JAC routine with J = 1,2,...,NEQ. +C Only nonzero elements need be loaded. A crude approximation +C to dr/dy, possibly with fewer nonzero elememts, will suffice. +C Note that if A is independent of y (or this dependence +C is weak enough to be ignored) then JAC is to compute dg/dy. +C If it is not feasible to provide a JAC routine, use +C MF = 22, 222, or 422 and DLSODIS will compute an approximate +C Jacobian internally by difference quotients. +C +C E. Next decide whether or not to provide the initial value of the +C derivative vector dy/dt. If the initial value of A(t,y) is +C nonsingular (and not too ill-conditioned), you may let DLSODIS compute +C this vector (ISTATE = 0). (DLSODIS will solve the system A*s = g for +C s, with initial values of A and g.) If A(t,y) is initially +C singular, then the system is a differential-algebraic system, and +C you must make use of the particular form of the system to compute the +C initial values of y and dy/dt. In that case, use ISTATE = 1 and +C load the initial value of dy/dt into the array YDOTI. +C The input array YDOTI and the initial Y array must be consistent with +C the equations A*dy/dt = g. This implies that the initial residual +C r = g(t,y) - A(t,y)*YDOTI must be approximately zero. +C +C F. Write a main program which calls Subroutine DLSODIS once for +C each point at which answers are desired. This should also provide +C for possible use of logical unit 6 for output of error messages by +C DLSODIS. On the first call to DLSODIS, supply arguments as follows: +C RES = name of user subroutine for residual function r. +C ADDA = name of user subroutine for computing and adding A(t,y). +C JAC = name of user subroutine for Jacobian matrix dr/dy +C (MF = 121). If not used, pass a dummy name. +C Note: The names for the RES and ADDA routines and (if used) the +C JAC routine must be declared External in the calling program. +C NEQ = number of scalar equations in the system. +C Y = array of initial values, of length NEQ. +C YDOTI = array of length NEQ (containing initial dy/dt if ISTATE = 1). +C T = the initial value of the independent variable. +C TOUT = first point where output is desired (.ne. T). +C ITOL = 1 or 2 according as ATOL (below) is a scalar or array. +C RTOL = relative tolerance parameter (scalar). +C ATOL = absolute tolerance parameter (scalar or array). +C The estimated local error in y(i) will be controlled so as +C to be roughly less (in magnitude) than +C EWT(i) = RTOL*ABS(Y(i)) + ATOL if ITOL = 1, or +C EWT(i) = RTOL*ABS(Y(i)) + ATOL(i) if ITOL = 2. +C Thus the local error test passes if, in each component, +C either the absolute error is less than ATOL (or ATOL(i)), +C or the relative error is less than RTOL. +C Use RTOL = 0.0 for pure absolute error control, and +C use ATOL = 0.0 (or ATOL(i) = 0.0) for pure relative error +C control. Caution: Actual (global) errors may exceed these +C local tolerances, so choose them conservatively. +C ITASK = 1 for normal computation of output values of y at t = TOUT. +C ISTATE = integer flag (input and output). Set ISTATE = 1 if the +C initial dy/dt is supplied, and 0 otherwise. +C IOPT = 0 to indicate no optional inputs used. +C RWORK = real work array of length at least: +C 20 + (2 + 1./LENRAT)*NNZ + (11 + 9./LENRAT)*NEQ +C where: +C NNZ = the number of nonzero elements in the sparse +C iteration matrix P = A - con*dr/dy (con = scalar) +C (If NNZ is unknown, use an estimate of it.) +C LENRAT = the real to integer wordlength ratio (usually 1 in +C single precision and 2 in double precision). +C In any case, the required size of RWORK cannot generally +C be predicted in advance for any value of MF, and the +C value above is a rough estimate of a crude lower bound. +C Some experimentation with this size may be necessary. +C (When known, the correct required length is an optional +C output, available in IWORK(17).) +C LRW = declared length of RWORK (in user's dimension). +C IWORK = integer work array of length at least 30. +C LIW = declared length of IWORK (in user's dimension). +C MF = method flag. Standard values are: +C 121 for a user-supplied sparse Jacobian. +C 222 for an internally generated sparse Jacobian. +C For other choices of MF, see the paragraph on MF in +C the full description below. +C Note that the main program must declare arrays Y, YDOTI, RWORK, IWORK, +C and possibly ATOL. +C +C G. The output from the first call, or any call, is: +C Y = array of computed values of y(t) vector. +C T = corresponding value of independent variable (normally TOUT). +C ISTATE = 2 if DLSODIS was successful, negative otherwise. +C -1 means excess work done on this call (check all inputs). +C -2 means excess accuracy requested (tolerances too small). +C -3 means illegal input detected (see printed message). +C -4 means repeated error test failures (check all inputs). +C -5 means repeated convergence failures (perhaps bad Jacobian +C supplied or wrong choice of tolerances). +C -6 means error weight became zero during problem. (Solution +C component i vanished, and ATOL or ATOL(i) = 0.) +C -7 cannot occur in casual use. +C -8 means DLSODIS was unable to compute the initial dy/dt. +C in casual use, this means A(t,y) is initially singular. +C Supply YDOTI and use ISTATE = 1 on the first call. +C -9 means a fatal error return flag came from sparse solver +C CDRV by way of DPRJIS or DSOLSS. Should never happen. +C +C A return with ISTATE = -1, -4, or -5, may result from using +C an inappropriate sparsity structure, one that is quite +C different from the initial structure. Consider calling +C DLSODIS again with ISTATE = 3 to force the structure to be +C reevaluated. See the full description of ISTATE below. +C +C If DLSODIS returns ISTATE = -1, -4 or -5, then the output of +C DLSODIS also includes YDOTI = array containing residual vector +C r = g - A * dy/dt evaluated at the current t, y, and dy/dt. +C +C H. To continue the integration after a successful return, simply +C reset TOUT and call DLSODIS again. No other parameters need be reset. +C +C----------------------------------------------------------------------- +C Example Problem. +C +C The following is an example problem, with the coding needed +C for its solution by DLSODIS. The problem comes from the partial +C differential equation (the Burgers equation) +C du/dt = - u * du/dx + eta * d**2 u/dx**2, eta = .05, +C on -1 .le. x .le. 1. The boundary conditions are periodic: +C u(-1,t) = u(1,t) and du/dx(-1,t) = du/dx(1,t) +C The initial profile is a square wave, +C u = 1 in ABS(x) .lt. .5, u = .5 at ABS(x) = .5, u = 0 elsewhere. +C The PDE is discretized in x by a simplified Galerkin method, +C using piecewise linear basis functions, on a grid of 40 intervals. +C The result is a system A * dy/dt = g(y), of size NEQ = 40, +C where y(i) is the approximation to u at x = x(i), with +C x(i) = -1 + (i-1)*delx, delx = 2/NEQ = .05. +C The individual equations in the system are (in order): +C (1/6)dy(NEQ)/dt+(4/6)dy(1)/dt+(1/6)dy(2)/dt +C = r4d*(y(NEQ)**2-y(2)**2)+eodsq*(y(2)-2*y(1)+y(NEQ)) +C for i = 2,3,...,nm1, +C (1/6)dy(i-1)/dt+(4/6)dy(i)/dt+(1/6)dy(i+1)/dt +C = r4d*(y(i-1)**2-y(i+1)**2)+eodsq*(y(i+1)-2*y(i)+y(i-1)) +C and finally +C (1/6)dy(nm1)/dt+(4/6)dy(NEQ)/dt+(1/6)dy(1)/dt +C = r4d*(y(nm1)**2-y(1)**2)+eodsq*(y(1)-2*y(NEQ)+y(nm1)) +C where r4d = 1/(4*delx), eodsq = eta/delx**2 and nm1 = NEQ-1. +C The following coding solves the problem with MF = 121, with output +C of solution statistics at t = .1, .2, .3, and .4, and of the +C solution vector at t = .4. Optional outputs (run statistics) are +C also printed. +C +C EXTERNAL RESID, ADDASP, JACSP +C DOUBLE PRECISION ATOL, RTOL, RW, T, TOUT, Y, YDOTI, R4D, EODSQ, DELX +C DIMENSION Y(40), YDOTI(40), RW(1409), IW(30) +C COMMON /TEST1/ R4D, EODSQ, NM1 +C DATA ITOL/1/, RTOL/1.0D-3/, ATOL/1.0D-3/, ITASK/1/, IOPT/0/ +C DATA NEQ/40/, LRW/1409/, LIW/30/, MF/121/ +C +C DELX = 2.0/NEQ +C R4D = 0.25/DELX +C EODSQ = 0.05/DELX**2 +C NM1 = NEQ - 1 +C DO 10 I = 1,NEQ +C 10 Y(I) = 0.0 +C Y(11) = 0.5 +C DO 15 I = 12,30 +C 15 Y(I) = 1.0 +C Y(31) = 0.5 +C T = 0.0 +C TOUT = 0.1 +C ISTATE = 0 +C DO 30 IO = 1,4 +C CALL DLSODIS (RESID, ADDASP, JACSP, NEQ, Y, YDOTI, T, TOUT, +C 1 ITOL, RTOL, ATOL, ITASK, ISTATE, IOPT, RW, LRW, IW, LIW, MF) +C WRITE(6,20) T,IW(11),RW(11) +C 20 FORMAT(' At t =',F5.2,' No. steps =',I4, +C 1 ' Last step =',D12.4) +C IF (ISTATE .NE. 2) GO TO 90 +C TOUT = TOUT + 0.1 +C 30 CONTINUE +C WRITE (6,40) (Y(I),I=1,NEQ) +C 40 FORMAT(/' Final solution values..'/8(5D12.4/)) +C WRITE(6,50) IW(17),IW(18),IW(11),IW(12),IW(13) +C NNZLU = IW(25) + IW(26) + NEQ +C WRITE(6,60) IW(19),NNZLU +C 50 FORMAT(/' Required RW size =',I5,' IW size =',I4/ +C 1 ' No. steps =',I4,' No. r-s =',I4,' No. J-s =',i4) +C 60 FORMAT(' No. of nonzeros in P matrix =',I4, +C 1 ' No. of nonzeros in LU =',I4) +C STOP +C 90 WRITE (6,95) ISTATE +C 95 FORMAT(///' Error halt.. ISTATE =',I3) +C STOP +C END +C +C SUBROUTINE GFUN (N, T, Y, G) +C DOUBLE PRECISION T, Y, G, R4D, EODSQ +C DIMENSION G(N), Y(N) +C COMMON /TEST1/ R4D, EODSQ, NM1 +C G(1) = R4D*(Y(N)**2-Y(2)**2) + EODSQ*(Y(2)-2.0*Y(1)+Y(N)) +C DO 10 I = 2,NM1 +C G(I) = R4D*(Y(I-1)**2 - Y(I+1)**2) +C 1 + EODSQ*(Y(I+1) - 2.0*Y(I) + Y(I-1)) +C 10 CONTINUE +C G(N) = R4D*(Y(NM1)**2-Y(1)**2) + EODSQ*(Y(1)-2.0*Y(N)+Y(NM1)) +C RETURN +C END +C +C SUBROUTINE RESID (N, T, Y, S, R, IRES) +C DOUBLE PRECISION T, Y, S, R, R4D, EODSQ +C DIMENSION Y(N), S(N), R(N) +C COMMON /TEST1/ R4D, EODSQ, NM1 +C CALL GFUN (N, T, Y, R) +C R(1) = R(1) - (S(N) + 4.0*S(1) + S(2))/6.0 +C DO 10 I = 2,NM1 +C 10 R(I) = R(I) - (S(I-1) + 4.0*S(I) + S(I+1))/6.0 +C R(N) = R(N) - (S(NM1) + 4.0*S(N) + S(1))/6.0 +C RETURN +C END +C +C SUBROUTINE ADDASP (N, T, Y, J, IP, JP, P) +C DOUBLE PRECISION T, Y, P +C DIMENSION Y(N), IP(*), JP(*), P(N) +C JM1 = J - 1 +C JP1 = J + 1 +C IF (J .EQ. N) JP1 = 1 +C IF (J .EQ. 1) JM1 = N +C P(J) = P(J) + (2.0/3.0) +C P(JP1) = P(JP1) + (1.0/6.0) +C P(JM1) = P(JM1) + (1.0/6.0) +C RETURN +C END +C +C SUBROUTINE JACSP (N, T, Y, S, J, IP, JP, PDJ) +C DOUBLE PRECISION T, Y, S, PDJ, R4D, EODSQ +C DIMENSION Y(N), S(N), IP(*), JP(*), PDJ(N) +C COMMON /TEST1/ R4D, EODSQ, NM1 +C JM1 = J - 1 +C JP1 = J + 1 +C IF (J .EQ. 1) JM1 = N +C IF (J .EQ. N) JP1 = 1 +C PDJ(JM1) = -2.0*R4D*Y(J) + EODSQ +C PDJ(J) = -2.0*EODSQ +C PDJ(JP1) = 2.0*R4D*Y(J) + EODSQ +C RETURN +C END +C +C The output of this program (on a CDC-7600 in single precision) +C is as follows: +C +C At t = 0.10 No. steps = 15 Last step = 1.6863e-02 +C At t = 0.20 No. steps = 19 Last step = 2.4101e-02 +C At t = 0.30 No. steps = 22 Last step = 4.3143e-02 +C At t = 0.40 No. steps = 24 Last step = 5.7819e-02 +C +C Final solution values.. +C 1.8371e-02 1.3578e-02 1.5864e-02 2.3805e-02 3.7245e-02 +C 5.6630e-02 8.2538e-02 1.1538e-01 1.5522e-01 2.0172e-01 +C 2.5414e-01 3.1150e-01 3.7259e-01 4.3608e-01 5.0060e-01 +C 5.6482e-01 6.2751e-01 6.8758e-01 7.4415e-01 7.9646e-01 +C 8.4363e-01 8.8462e-01 9.1853e-01 9.4500e-01 9.6433e-01 +C 9.7730e-01 9.8464e-01 9.8645e-01 9.8138e-01 9.6584e-01 +C 9.3336e-01 8.7497e-01 7.8213e-01 6.5315e-01 4.9997e-01 +C 3.4672e-01 2.1758e-01 1.2461e-01 6.6208e-02 3.3784e-02 +C +C Required RW size = 1409 IW size = 30 +C No. steps = 24 No. r-s = 33 No. J-s = 8 +C No. of nonzeros in P matrix = 120 No. of nonzeros in LU = 194 +C +C----------------------------------------------------------------------- +C Full Description of User Interface to DLSODIS. +C +C The user interface to DLSODIS consists of the following parts. +C +C 1. The call sequence to Subroutine DLSODIS, which is a driver +C routine for the solver. This includes descriptions of both +C the call sequence arguments and of user-supplied routines. +C Following these descriptions is a description of +C optional inputs available through the call sequence, and then +C a description of optional outputs (in the work arrays). +C +C 2. Descriptions of other routines in the DLSODIS package that may be +C (optionally) called by the user. These provide the ability to +C alter error message handling, save and restore the internal +C Common, and obtain specified derivatives of the solution y(t). +C +C 3. Descriptions of Common blocks to be declared in overlay +C or similar environments, or to be saved when doing an interrupt +C of the problem and continued solution later. +C +C 4. Description of two routines in the DLSODIS package, either of +C which the user may replace with his/her own version, if desired. +C These relate to the measurement of errors. +C +C----------------------------------------------------------------------- +C Part 1. Call Sequence. +C +C The call sequence parameters used for input only are +C RES, ADDA, JAC, NEQ, TOUT, ITOL, RTOL, ATOL, ITASK, +C IOPT, LRW, LIW, MF, +C and those used for both input and output are +C Y, T, ISTATE, YDOTI. +C The work arrays RWORK and IWORK are also used for conditional and +C optional inputs and optional outputs. (The term output here refers +C to the return from Subroutine DLSODIS to the user's calling program.) +C +C The legality of input parameters will be thoroughly checked on the +C initial call for the problem, but not checked thereafter unless a +C change in input parameters is flagged by ISTATE = 3 on input. +C +C The descriptions of the call arguments are as follows. +C +C RES = the name of the user-supplied subroutine which supplies +C the residual vector for the ODE system, defined by +C r = g(t,y) - A(t,y) * s +C as a function of the scalar t and the vectors +C s and y (s approximates dy/dt). This subroutine +C is to have the form +C SUBROUTINE RES (NEQ, T, Y, S, R, IRES) +C DOUBLE PRECISION T, Y(*), S(*), R(*) +C where NEQ, T, Y, S, and IRES are input, and R and +C IRES are output. Y, S, and R are arrays of length NEQ. +C On input, IRES indicates how DLSODIS will use the +C returned array R, as follows: +C IRES = 1 means that DLSODIS needs the full residual, +C r = g - A*s, exactly. +C IRES = -1 means that DLSODIS is using R only to compute +C the Jacobian dr/dy by difference quotients. +C The RES routine can ignore IRES, or it can omit some terms +C if IRES = -1. If A does not depend on y, then RES can +C just return R = g when IRES = -1. If g - A*s contains other +C additive terms that are independent of y, these can also be +C dropped, if done consistently, when IRES = -1. +C The subroutine should set the flag IRES if it +C encounters a halt condition or illegal input. +C Otherwise, it should not reset IRES. On output, +C IRES = 1 or -1 represents a normal return, and +C DLSODIS continues integrating the ODE. Leave IRES +C unchanged from its input value. +C IRES = 2 tells DLSODIS to immediately return control +C to the calling program, with ISTATE = 3. This lets +C the calling program change parameters of the problem +C if necessary. +C IRES = 3 represents an error condition (for example, an +C illegal value of y). DLSODIS tries to integrate the system +C without getting IRES = 3 from RES. If it cannot, DLSODIS +C returns with ISTATE = -7 or -1. +C On a return with ISTATE = 3, -1, or -7, the values +C of T and Y returned correspond to the last point reached +C successfully without getting the flag IRES = 2 or 3. +C The flag values IRES = 2 and 3 should not be used to +C handle switches or root-stop conditions. This is better +C done by calling DLSODIS in a one-step mode and checking the +C stopping function for a sign change at each step. +C If quantities computed in the RES routine are needed +C externally to DLSODIS, an extra call to RES should be made +C for this purpose, for consistent and accurate results. +C To get the current dy/dt for the S argument, use DINTDY. +C RES must be declared External in the calling +C program. See note below for more about RES. +C +C ADDA = the name of the user-supplied subroutine which adds the +C matrix A = A(t,y) to another matrix stored in sparse form. +C This subroutine is to have the form +C SUBROUTINE ADDA (NEQ, T, Y, J, IAN, JAN, P) +C DOUBLE PRECISION T, Y(*), P(*) +C INTEGER IAN(*), JAN(*) +C where NEQ, T, Y, J, IAN, JAN, and P are input. This routine +C should add the J-th column of matrix A to the array P, of +C length NEQ. Thus a(i,J) is to be added to P(i) for all +C relevant values of i. Here T and Y have the same meaning as +C in Subroutine RES, and J is a column index (1 to NEQ). +C IAN and JAN are undefined in calls to ADDA for structure +C determination (MOSS .ne. 0). Otherwise, IAN and JAN are +C structure descriptors, as defined under optional outputs +C below, and so can be used to determine the relevant row +C indices i, if desired. +C Calls to ADDA are made with J = 1,...,NEQ, in that +C order. ADDA must not alter its input arguments. +C ADDA must be declared External in the calling program. +C See note below for more information about ADDA. +C +C JAC = the name of the user-supplied subroutine which supplies +C the Jacobian matrix, dr/dy, where r = g - A*s. JAC is +C required if MITER = 1, or MOSS = 1 or 3. Otherwise a dummy +C name can be passed. This subroutine is to have the form +C SUBROUTINE JAC (NEQ, T, Y, S, J, IAN, JAN, PDJ) +C DOUBLE PRECISION T, Y(*), S(*), PDJ(*) +C INTEGER IAN(*), JAN(*) +C where NEQ, T, Y, S, J, IAN, and JAN are input. The +C array PDJ, of length NEQ, is to be loaded with column J +C of the Jacobian on output. Thus dr(i)/dy(J) is to be +C loaded into PDJ(i) for all relevant values of i. +C Here T, Y, and S have the same meaning as in Subroutine RES, +C and J is a column index (1 to NEQ). IAN and JAN +C are undefined in calls to JAC for structure determination +C (MOSS .ne. 0). Otherwise, IAN and JAN are structure +C descriptors, as defined under optional outputs below, and +C so can be used to determine the relevant row indices i, if +C desired. +C JAC need not provide dr/dy exactly. A crude +C approximation (possibly with greater sparsity) will do. +C In any case, PDJ is preset to zero by the solver, +C so that only the nonzero elements need be loaded by JAC. +C Calls to JAC are made with J = 1,...,NEQ, in that order, and +C each such set of calls is preceded by a call to RES with the +C same arguments NEQ, T, Y, S, and IRES. Thus to gain some +C efficiency intermediate quantities shared by both calculations +C may be saved in a user Common block by RES and not recomputed +C by JAC, if desired. JAC must not alter its input arguments. +C JAC must be declared External in the calling program. +C See note below for more about JAC. +C +C Note on RES, ADDA, and JAC: +C These subroutines may access user-defined quantities in +C NEQ(2),... and/or in Y(NEQ(1)+1),... if NEQ is an array +C (dimensioned in the subroutines) and/or Y has length +C exceeding NEQ(1). However, these subroutines should not +C alter NEQ(1), Y(1),...,Y(NEQ) or any other input variables. +C See the descriptions of NEQ and Y below. +C +C NEQ = the size of the system (number of first order ordinary +C differential equations or scalar algebraic equations). +C Used only for input. +C NEQ may be decreased, but not increased, during the problem. +C If NEQ is decreased (with ISTATE = 3 on input), the +C remaining components of Y should be left undisturbed, if +C these are to be accessed in RES, ADDA, or JAC. +C +C Normally, NEQ is a scalar, and it is generally referred to +C as a scalar in this user interface description. However, +C NEQ may be an array, with NEQ(1) set to the system size. +C (The DLSODIS package accesses only NEQ(1).) In either case, +C this parameter is passed as the NEQ argument in all calls +C to RES, ADDA, and JAC. Hence, if it is an array, +C locations NEQ(2),... may be used to store other integer data +C and pass it to RES, ADDA, or JAC. Each such subroutine +C must include NEQ in a Dimension statement in that case. +C +C Y = a real array for the vector of dependent variables, of +C length NEQ or more. Used for both input and output on the +C first call (ISTATE = 0 or 1), and only for output on other +C calls. On the first call, Y must contain the vector of +C initial values. On output, Y contains the computed solution +C vector, evaluated at T. If desired, the Y array may be used +C for other purposes between calls to the solver. +C +C This array is passed as the Y argument in all calls to RES, +C ADDA, and JAC. Hence its length may exceed NEQ, +C and locations Y(NEQ+1),... may be used to store other real +C data and pass it to RES, ADDA, or JAC. (The DLSODIS +C package accesses only Y(1),...,Y(NEQ). ) +C +C YDOTI = a real array for the initial value of the vector +C dy/dt and for work space, of dimension at least NEQ. +C +C On input: +C If ISTATE = 0 then DLSODIS will compute the initial value +C of dy/dt, if A is nonsingular. Thus YDOTI will +C serve only as work space and may have any value. +C If ISTATE = 1 then YDOTI must contain the initial value +C of dy/dt. +C If ISTATE = 2 or 3 (continuation calls) then YDOTI +C may have any value. +C Note: If the initial value of A is singular, then +C DLSODIS cannot compute the initial value of dy/dt, so +C it must be provided in YDOTI, with ISTATE = 1. +C +C On output, when DLSODIS terminates abnormally with ISTATE = +C -1, -4, or -5, YDOTI will contain the residual +C r = g(t,y) - A(t,y)*(dy/dt). If r is large, t is near +C its initial value, and YDOTI is supplied with ISTATE = 1, +C there may have been an incorrect input value of +C YDOTI = dy/dt, or the problem (as given to DLSODIS) +C may not have a solution. +C +C If desired, the YDOTI array may be used for other +C purposes between calls to the solver. +C +C T = the independent variable. On input, T is used only on the +C first call, as the initial point of the integration. +C On output, after each call, T is the value at which a +C computed solution y is evaluated (usually the same as TOUT). +C On an error return, T is the farthest point reached. +C +C TOUT = the next value of t at which a computed solution is desired. +C Used only for input. +C +C When starting the problem (ISTATE = 0 or 1), TOUT may be +C equal to T for one call, then should .ne. T for the next +C call. For the initial T, an input value of TOUT .ne. T is +C used in order to determine the direction of the integration +C (i.e. the algebraic sign of the step sizes) and the rough +C scale of the problem. Integration in either direction +C (forward or backward in t) is permitted. +C +C If ITASK = 2 or 5 (one-step modes), TOUT is ignored after +C the first call (i.e. the first call with TOUT .ne. T). +C Otherwise, TOUT is required on every call. +C +C If ITASK = 1, 3, or 4, the values of TOUT need not be +C monotone, but a value of TOUT which backs up is limited +C to the current internal T interval, whose endpoints are +C TCUR - HU and TCUR (see optional outputs, below, for +C TCUR and HU). +C +C ITOL = an indicator for the type of error control. See +C description below under ATOL. Used only for input. +C +C RTOL = a relative error tolerance parameter, either a scalar or +C an array of length NEQ. See description below under ATOL. +C Input only. +C +C ATOL = an absolute error tolerance parameter, either a scalar or +C an array of length NEQ. Input only. +C +C The input parameters ITOL, RTOL, and ATOL determine +C the error control performed by the solver. The solver will +C control the vector E = (E(i)) of estimated local errors +C in y, according to an inequality of the form +C RMS-norm of ( E(i)/EWT(i) ) .le. 1, +C where EWT(i) = RTOL(i)*ABS(Y(i)) + ATOL(i), +C and the RMS-norm (root-mean-square norm) here is +C RMS-norm(v) = SQRT(sum v(i)**2 / NEQ). Here EWT = (EWT(i)) +C is a vector of weights which must always be positive, and +C the values of RTOL and ATOL should all be non-negative. +C The following table gives the types (scalar/array) of +C RTOL and ATOL, and the corresponding form of EWT(i). +C +C ITOL RTOL ATOL EWT(i) +C 1 scalar scalar RTOL*ABS(Y(i)) + ATOL +C 2 scalar array RTOL*ABS(Y(i)) + ATOL(i) +C 3 array scalar RTOL(i)*ABS(Y(i)) + ATOL +C 4 array scalar RTOL(i)*ABS(Y(i)) + ATOL(i) +C +C When either of these parameters is a scalar, it need not +C be dimensioned in the user's calling program. +C +C If none of the above choices (with ITOL, RTOL, and ATOL +C fixed throughout the problem) is suitable, more general +C error controls can be obtained by substituting +C user-supplied routines for the setting of EWT and/or for +C the norm calculation. See Part 4 below. +C +C If global errors are to be estimated by making a repeated +C run on the same problem with smaller tolerances, then all +C components of RTOL and ATOL (i.e. of EWT) should be scaled +C down uniformly. +C +C ITASK = an index specifying the task to be performed. +C Input only. ITASK has the following values and meanings. +C 1 means normal computation of output values of y(t) at +C t = TOUT (by overshooting and interpolating). +C 2 means take one step only and return. +C 3 means stop at the first internal mesh point at or +C beyond t = TOUT and return. +C 4 means normal computation of output values of y(t) at +C t = TOUT but without overshooting t = TCRIT. +C TCRIT must be input as RWORK(1). TCRIT may be equal to +C or beyond TOUT, but not behind it in the direction of +C integration. This option is useful if the problem +C has a singularity at or beyond t = TCRIT. +C 5 means take one step, without passing TCRIT, and return. +C TCRIT must be input as RWORK(1). +C +C Note: If ITASK = 4 or 5 and the solver reaches TCRIT +C (within roundoff), it will return T = TCRIT (exactly) to +C indicate this (unless ITASK = 4 and TOUT comes before TCRIT, +C in which case answers at t = TOUT are returned first). +C +C ISTATE = an index used for input and output to specify the +C state of the calculation. +C +C On input, the values of ISTATE are as follows. +C 0 means this is the first call for the problem, and +C DLSODIS is to compute the initial value of dy/dt +C (while doing other initializations). See note below. +C 1 means this is the first call for the problem, and +C the initial value of dy/dt has been supplied in +C YDOTI (DLSODIS will do other initializations). +C See note below. +C 2 means this is not the first call, and the calculation +C is to continue normally, with no change in any input +C parameters except possibly TOUT and ITASK. +C (If ITOL, RTOL, and/or ATOL are changed between calls +C with ISTATE = 2, the new values will be used but not +C tested for legality.) +C 3 means this is not the first call, and the +C calculation is to continue normally, but with +C a change in input parameters other than +C TOUT and ITASK. Changes are allowed in +C NEQ, ITOL, RTOL, ATOL, IOPT, LRW, LIW, MF, +C the conditional inputs IA, JA, IC, and JC, +C and any of the optional inputs except H0. +C A call with ISTATE = 3 will cause the sparsity +C structure of the problem to be recomputed. +C (Structure information is reread from IA and JA if +C MOSS = 0, 3, or 4 and from IC and JC if MOSS = 0). +C Note: A preliminary call with TOUT = T is not counted +C as a first call here, as no initialization or checking of +C input is done. (Such a call is sometimes useful for the +C purpose of outputting the initial conditions.) +C Thus the first call for which TOUT .ne. T requires +C ISTATE = 0 or 1 on input. +C +C On output, ISTATE has the following values and meanings. +C 0 or 1 means nothing was done; TOUT = T and +C ISTATE = 0 or 1 on input. +C 2 means that the integration was performed successfully. +C 3 means that the user-supplied Subroutine RES signalled +C DLSODIS to halt the integration and return (IRES = 2). +C Integration as far as T was achieved with no occurrence +C of IRES = 2, but this flag was set on attempting the +C next step. +C -1 means an excessive amount of work (more than MXSTEP +C steps) was done on this call, before completing the +C requested task, but the integration was otherwise +C successful as far as T. (MXSTEP is an optional input +C and is normally 500.) To continue, the user may +C simply reset ISTATE to a value .gt. 1 and call again +C (the excess work step counter will be reset to 0). +C In addition, the user may increase MXSTEP to avoid +C this error return (see below on optional inputs). +C -2 means too much accuracy was requested for the precision +C of the machine being used. This was detected before +C completing the requested task, but the integration +C was successful as far as T. To continue, the tolerance +C parameters must be reset, and ISTATE must be set +C to 3. The optional output TOLSF may be used for this +C purpose. (Note: If this condition is detected before +C taking any steps, then an illegal input return +C (ISTATE = -3) occurs instead.) +C -3 means illegal input was detected, before taking any +C integration steps. See written message for details. +C Note: If the solver detects an infinite loop of calls +C to the solver with illegal input, it will cause +C the run to stop. +C -4 means there were repeated error test failures on +C one attempted step, before completing the requested +C task, but the integration was successful as far as T. +C The problem may have a singularity, or the input +C may be inappropriate. +C -5 means there were repeated convergence test failures on +C one attempted step, before completing the requested +C task, but the integration was successful as far as T. +C This may be caused by an inaccurate Jacobian matrix. +C -6 means EWT(i) became zero for some i during the +C integration. Pure relative error control (ATOL(i) = 0.0) +C was requested on a variable which has now vanished. +C the integration was successful as far as T. +C -7 means that the user-supplied Subroutine RES set +C its error flag (IRES = 3) despite repeated tries by +C DLSODIS to avoid that condition. +C -8 means that ISTATE was 0 on input but DLSODIS was unable +C to compute the initial value of dy/dt. See the +C printed message for details. +C -9 means a fatal error return flag came from the sparse +C solver CDRV by way of DPRJIS or DSOLSS (numerical +C factorization or backsolve). This should never happen. +C The integration was successful as far as T. +C +C Note: An error return with ISTATE = -1, -4, or -5 +C may mean that the sparsity structure of the +C problem has changed significantly since it was last +C determined (or input). In that case, one can attempt to +C complete the integration by setting ISTATE = 3 on the next +C call, so that a new structure determination is done. +C +C Note: Since the normal output value of ISTATE is 2, +C it does not need to be reset for normal continuation. +C similarly, ISTATE (= 3) need not be reset if RES told +C DLSODIS to return because the calling program must change +C the parameters of the problem. +C Also, since a negative input value of ISTATE will be +C regarded as illegal, a negative output value requires the +C user to change it, and possibly other inputs, before +C calling the solver again. +C +C IOPT = an integer flag to specify whether or not any optional +C inputs are being used on this call. Input only. +C The optional inputs are listed separately below. +C IOPT = 0 means no optional inputs are being used. +C Default values will be used in all cases. +C IOPT = 1 means one or more optional inputs are being used. +C +C RWORK = a work array used for a mixture of real (double precision) +C and integer work space. +C The length of RWORK (in real words) must be at least +C 20 + NYH*(MAXORD + 1) + 3*NEQ + LWM where +C NYH = the initial value of NEQ, +C MAXORD = 12 (if METH = 1) or 5 (if METH = 2) (unless a +C smaller value is given as an optional input), +C LWM = 2*NNZ + 2*NEQ + (NNZ+9*NEQ)/LENRAT if MITER = 1, +C LWM = 2*NNZ + 2*NEQ + (NNZ+10*NEQ)/LENRAT if MITER = 2. +C in the above formulas, +C NNZ = number of nonzero elements in the iteration matrix +C P = A - con*J (con is a constant and J is the +C Jacobian matrix dr/dy). +C LENRAT = the real to integer wordlength ratio (usually 1 in +C single precision and 2 in double precision). +C (See the MF description for METH and MITER.) +C Thus if MAXORD has its default value and NEQ is constant, +C the minimum length of RWORK is: +C 20 + 16*NEQ + LWM for MF = 11, 111, 311, 12, 212, 412, +C 20 + 9*NEQ + LWM for MF = 21, 121, 321, 22, 222, 422. +C The above formula for LWM is only a crude lower bound. +C The required length of RWORK cannot be readily predicted +C in general, as it depends on the sparsity structure +C of the problem. Some experimentation may be necessary. +C +C The first 20 words of RWORK are reserved for conditional +C and optional inputs and optional outputs. +C +C The following word in RWORK is a conditional input: +C RWORK(1) = TCRIT = critical value of t which the solver +C is not to overshoot. Required if ITASK is +C 4 or 5, and ignored otherwise. (See ITASK.) +C +C LRW = the length of the array RWORK, as declared by the user. +C (This will be checked by the solver.) +C +C IWORK = an integer work array. The length of IWORK must be at least +C 32 + 2*NEQ + NZA + NZC for MOSS = 0, +C 30 for MOSS = 1 or 2, +C 31 + NEQ + NZA for MOSS = 3 or 4. +C (NZA is the number of nonzero elements in matrix A, and +C NZC is the number of nonzero elements in dr/dy.) +C +C In DLSODIS, IWORK is used for conditional and +C optional inputs and optional outputs. +C +C The following two blocks of words in IWORK are conditional +C inputs, required if MOSS = 0, 3, or 4, but not otherwise +C (see the description of MF for MOSS). +C IWORK(30+j) = IA(j) (j=1,...,NEQ+1) +C IWORK(31+NEQ+k) = JA(k) (k=1,...,NZA) +C The two arrays IA and JA describe the sparsity structure +C to be assumed for the matrix A. JA contains the row +C indices where nonzero elements occur, reading in columnwise +C order, and IA contains the starting locations in JA of the +C descriptions of columns 1,...,NEQ, in that order, with +C IA(1) = 1. Thus, for each column index j = 1,...,NEQ, the +C values of the row index i in column j where a nonzero +C element may occur are given by +C i = JA(k), where IA(j) .le. k .lt. IA(j+1). +C If NZA is the total number of nonzero locations assumed, +C then the length of the JA array is NZA, and IA(NEQ+1) must +C be NZA + 1. Duplicate entries are not allowed. +C The following additional blocks of words are required +C if MOSS = 0, but not otherwise. If LC = 31 + NEQ + NZA, then +C IWORK(LC+j) = IC(j) (j=1,...,NEQ+1), and +C IWORK(LC+NEQ+1+k) = JC(k) (k=1,...,NZC) +C The two arrays IC and JC describe the sparsity +C structure to be assumed for the Jacobian matrix dr/dy. +C They are used in the same manner as the above IA and JA +C arrays. If NZC is the number of nonzero locations +C assumed, then the length of the JC array is NZC, and +C IC(NEQ+1) must be NZC + 1. Duplicate entries are not +C allowed. +C +C LIW = the length of the array IWORK, as declared by the user. +C (This will be checked by the solver.) +C +C Note: The work arrays must not be altered between calls to DLSODIS +C for the same problem, except possibly for the conditional and +C optional inputs, and except for the last 3*NEQ words of RWORK. +C The latter space is used for internal scratch space, and so is +C available for use by the user outside DLSODIS between calls, if +C desired (but not for use by RES, ADDA, or JAC). +C +C MF = the method flag. Used only for input. +C MF has three decimal digits-- MOSS, METH, and MITER. +C For standard options: +C MF = 100*MOSS + 10*METH + MITER. +C MOSS indicates the method to be used to obtain the sparsity +C structure of the Jacobian matrix: +C MOSS = 0 means the user has supplied IA, JA, IC, and JC +C (see descriptions under IWORK above). +C MOSS = 1 means the user has supplied JAC (see below) and +C the structure will be obtained from NEQ initial +C calls to JAC and NEQ initial calls to ADDA. +C MOSS = 2 means the structure will be obtained from NEQ+1 +C initial calls to RES and NEQ initial calls to ADDA +C MOSS = 3 like MOSS = 1, except user has supplied IA and JA. +C MOSS = 4 like MOSS = 2, except user has supplied IA and JA. +C METH indicates the basic linear multistep method: +C METH = 1 means the implicit Adams method. +C METH = 2 means the method based on Backward +C Differentiation Formulas (BDFs). +C The BDF method is strongly preferred for stiff problems, +C while the Adams method is preferred when the problem is +C not stiff. If the matrix A(t,y) is nonsingular, +C stiffness here can be taken to mean that of the explicit +C ODE system dy/dt = A-inverse * g. If A is singular, +C the concept of stiffness is not well defined. +C If you do not know whether the problem is stiff, we +C recommend using METH = 2. If it is stiff, the advantage +C of METH = 2 over METH = 1 will be great, while if it is +C not stiff, the advantage of METH = 1 will be slight. +C If maximum efficiency is important, some experimentation +C with METH may be necessary. +C MITER indicates the corrector iteration method: +C MITER = 1 means chord iteration with a user-supplied +C sparse Jacobian, given by Subroutine JAC. +C MITER = 2 means chord iteration with an internally +C generated (difference quotient) sparse +C Jacobian (using NGP extra calls to RES per +C dr/dy value, where NGP is an optional +C output described below.) +C If MITER = 1 or MOSS = 1 or 3 the user must supply a +C Subroutine JAC (the name is arbitrary) as described above +C under JAC. Otherwise, a dummy argument can be used. +C +C The standard choices for MF are: +C MF = 21 or 22 for a stiff problem with IA/JA and IC/JC +C supplied, +C MF = 121 for a stiff problem with JAC supplied, but not +C IA/JA or IC/JC, +C MF = 222 for a stiff problem with neither IA/JA, IC/JC/, +C nor JAC supplied, +C MF = 321 for a stiff problem with IA/JA and JAC supplied, +C but not IC/JC, +C MF = 422 for a stiff problem with IA/JA supplied, but not +C IC/JC or JAC. +C +C The sparseness structure can be changed during the problem +C by making a call to DLSODIS with ISTATE = 3. +C----------------------------------------------------------------------- +C Optional Inputs. +C +C The following is a list of the optional inputs provided for in the +C call sequence. (See also Part 2.) For each such input variable, +C this table lists its name as used in this documentation, its +C location in the call sequence, its meaning, and the default value. +C The use of any of these inputs requires IOPT = 1, and in that +C case all of these inputs are examined. A value of zero for any +C of these optional inputs will cause the default value to be used. +C Thus to use a subset of the optional inputs, simply preload +C locations 5 to 10 in RWORK and IWORK to 0.0 and 0 respectively, and +C then set those of interest to nonzero values. +C +C Name Location Meaning and Default Value +C +C H0 RWORK(5) the step size to be attempted on the first step. +C The default value is determined by the solver. +C +C HMAX RWORK(6) the maximum absolute step size allowed. +C The default value is infinite. +C +C HMIN RWORK(7) the minimum absolute step size allowed. +C The default value is 0. (This lower bound is not +C enforced on the final step before reaching TCRIT +C when ITASK = 4 or 5.) +C +C MAXORD IWORK(5) the maximum order to be allowed. The default +C value is 12 if METH = 1, and 5 if METH = 2. +C If MAXORD exceeds the default value, it will +C be reduced to the default value. +C If MAXORD is changed during the problem, it may +C cause the current order to be reduced. +C +C MXSTEP IWORK(6) maximum number of (internally defined) steps +C allowed during one call to the solver. +C The default value is 500. +C +C MXHNIL IWORK(7) maximum number of messages printed (per problem) +C warning that T + H = T on a step (H = step size). +C This must be positive to result in a non-default +C value. The default value is 10. +C----------------------------------------------------------------------- +C Optional Outputs. +C +C As optional additional output from DLSODIS, the variables listed +C below are quantities related to the performance of DLSODIS +C which are available to the user. These are communicated by way of +C the work arrays, but also have internal mnemonic names as shown. +C Except where stated otherwise, all of these outputs are defined +C on any successful return from DLSODIS, and on any return with +C ISTATE = -1, -2, -4, -5, -6, or -7. On a return with -3 (illegal +C input) or -8, they will be unchanged from their existing values +C (if any), except possibly for TOLSF, LENRW, and LENIW. +C On any error return, outputs relevant to the error will be defined, +C as noted below. +C +C Name Location Meaning +C +C HU RWORK(11) the step size in t last used (successfully). +C +C HCUR RWORK(12) the step size to be attempted on the next step. +C +C TCUR RWORK(13) the current value of the independent variable +C which the solver has actually reached, i.e. the +C current internal mesh point in t. On output, TCUR +C will always be at least as far as the argument +C T, but may be farther (if interpolation was done). +C +C TOLSF RWORK(14) a tolerance scale factor, greater than 1.0, +C computed when a request for too much accuracy was +C detected (ISTATE = -3 if detected at the start of +C the problem, ISTATE = -2 otherwise). If ITOL is +C left unaltered but RTOL and ATOL are uniformly +C scaled up by a factor of TOLSF for the next call, +C then the solver is deemed likely to succeed. +C (The user may also ignore TOLSF and alter the +C tolerance parameters in any other way appropriate.) +C +C NST IWORK(11) the number of steps taken for the problem so far. +C +C NRE IWORK(12) the number of residual evaluations (RES calls) +C for the problem so far, excluding those for +C structure determination (MOSS = 2 or 4). +C +C NJE IWORK(13) the number of Jacobian evaluations (each involving +C an evaluation of A and dr/dy) for the problem so +C far, excluding those for structure determination +C (MOSS = 1 or 3). This equals the number of calls +C to ADDA and (if MITER = 1) JAC. +C +C NQU IWORK(14) the method order last used (successfully). +C +C NQCUR IWORK(15) the order to be attempted on the next step. +C +C IMXER IWORK(16) the index of the component of largest magnitude in +C the weighted local error vector ( E(i)/EWT(i) ), +C on an error return with ISTATE = -4 or -5. +C +C LENRW IWORK(17) the length of RWORK actually required. +C This is defined on normal returns and on an illegal +C input return for insufficient storage. +C +C LENIW IWORK(18) the length of IWORK actually required. +C This is defined on normal returns and on an illegal +C input return for insufficient storage. +C +C NNZ IWORK(19) the number of nonzero elements in the iteration +C matrix P = A - con*J (con is a constant and +C J is the Jacobian matrix dr/dy). +C +C NGP IWORK(20) the number of groups of column indices, used in +C difference quotient Jacobian aproximations if +C MITER = 2. This is also the number of extra RES +C evaluations needed for each Jacobian evaluation. +C +C NLU IWORK(21) the number of sparse LU decompositions for the +C problem so far. (Excludes the LU decomposition +C necessary when ISTATE = 0.) +C +C LYH IWORK(22) the base address in RWORK of the history array YH, +C described below in this list. +C +C IPIAN IWORK(23) the base address of the structure descriptor array +C IAN, described below in this list. +C +C IPJAN IWORK(24) the base address of the structure descriptor array +C JAN, described below in this list. +C +C NZL IWORK(25) the number of nonzero elements in the strict lower +C triangle of the LU factorization used in the chord +C iteration. +C +C NZU IWORK(26) the number of nonzero elements in the strict upper +C triangle of the LU factorization used in the chord +C iteration. The total number of nonzeros in the +C factorization is therefore NZL + NZU + NEQ. +C +C The following four arrays are segments of the RWORK array which +C may also be of interest to the user as optional outputs. +C For each array, the table below gives its internal name, +C its base address, and its description. +C For YH and ACOR, the base addresses are in RWORK (a real array). +C The integer arrays IAN and JAN are to be obtained by declaring an +C integer array IWK and identifying IWK(1) with RWORK(21), using either +C an equivalence statement or a subroutine call. Then the base +C addresses IPIAN (of IAN) and IPJAN (of JAN) in IWK are to be obtained +C as optional outputs IWORK(23) and IWORK(24), respectively. +C Thus IAN(1) is IWK(ipian), etc. +C +C Name Base Address Description +C +C IAN IPIAN (in IWK) structure descriptor array of size NEQ + 1. +C JAN IPJAN (in IWK) structure descriptor array of size NNZ. +C (see above) IAN and JAN together describe the sparsity +C structure of the iteration matrix +C P = A - con*J, as used by DLSODIS. +C JAN contains the row indices of the nonzero +C locations, reading in columnwise order, and +C IAN contains the starting locations in JAN of +C the descriptions of columns 1,...,NEQ, in +C that order, with IAN(1) = 1. Thus for each +C j = 1,...,NEQ, the row indices i of the +C nonzero locations in column j are +C i = JAN(k), IAN(j) .le. k .lt. IAN(j+1). +C Note that IAN(NEQ+1) = NNZ + 1. +C YH LYH the Nordsieck history array, of size NYH by +C (optional (NQCUR + 1), where NYH is the initial value +C output) of NEQ. For j = 0,1,...,NQCUR, column j+1 +C of YH contains HCUR**j/factorial(j) times +C the j-th derivative of the interpolating +C polynomial currently representing the solution, +C evaluated at t = TCUR. The base address LYH +C is another optional output, listed above. +C +C ACOR LENRW-NEQ+1 array of size NEQ used for the accumulated +C corrections on each step, scaled on output to +C represent the estimated local error in y on the +C last step. This is the vector E in the +C description of the error control. It is defined +C only on a return from DLSODIS with ISTATE = 2. +C +C----------------------------------------------------------------------- +C Part 2. Other Routines Callable. +C +C The following are optional calls which the user may make to +C gain additional capabilities in conjunction with DLSODIS. +C (The routines XSETUN and XSETF are designed to conform to the +C SLATEC error handling package.) +C +C Form of Call Function +C CALL XSETUN(LUN) Set the logical unit number, LUN, for +C output of messages from DLSODIS, if +C The default is not desired. +C The default value of LUN is 6. +C +C CALL XSETF(MFLAG) Set a flag to control the printing of +C messages by DLSODIS. +C MFLAG = 0 means do not print. (Danger: +C This risks losing valuable information.) +C MFLAG = 1 means print (the default). +C +C Either of the above calls may be made at +C any time and will take effect immediately. +C +C CALL DSRCMS(RSAV,ISAV,JOB) saves and restores the contents of +C the internal Common blocks used by +C DLSODIS (see Part 3 below). +C RSAV must be a real array of length 224 +C or more, and ISAV must be an integer +C array of length 71 or more. +C JOB=1 means save Common into RSAV/ISAV. +C JOB=2 means restore Common from RSAV/ISAV. +C DSRCMS is useful if one is +C interrupting a run and restarting +C later, or alternating between two or +C more problems solved with DLSODIS. +C +C CALL DINTDY(,,,,,) Provide derivatives of y, of various +C (see below) orders, at a specified point t, if +C desired. It may be called only after +C a successful return from DLSODIS. +C +C The detailed instructions for using DINTDY are as follows. +C The form of the call is: +C +C LYH = IWORK(22) +C CALL DINTDY (T, K, RWORK(LYH), NYH, DKY, IFLAG) +C +C The input parameters are: +C +C T = value of independent variable where answers are desired +C (normally the same as the T last returned by DLSODIS). +C For valid results, T must lie between TCUR - HU and TCUR. +C (See optional outputs for TCUR and HU.) +C K = integer order of the derivative desired. K must satisfy +C 0 .le. K .le. NQCUR, where NQCUR is the current order +C (see optional outputs). The capability corresponding +C to K = 0, i.e. computing y(t), is already provided +C by DLSODIS directly. Since NQCUR .ge. 1, the first +C derivative dy/dt is always available with DINTDY. +C LYH = the base address of the history array YH, obtained +C as an optional output as shown above. +C NYH = column length of YH, equal to the initial value of NEQ. +C +C The output parameters are: +C +C DKY = a real array of length NEQ containing the computed value +C of the K-th derivative of y(t). +C IFLAG = integer flag, returned as 0 if K and T were legal, +C -1 if K was illegal, and -2 if T was illegal. +C On an error return, a message is also written. +C----------------------------------------------------------------------- +C Part 3. Common Blocks. +C +C If DLSODIS is to be used in an overlay situation, the user +C must declare, in the primary overlay, the variables in: +C (1) the call sequence to DLSODIS, and +C (2) the two internal Common blocks +C /DLS001/ of length 255 (218 double precision words +C followed by 37 integer words), +C /DLSS01/ of length 40 (6 double precision words +C followed by 34 integer words). +C +C If DLSODIS is used on a system in which the contents of internal +C Common blocks are not preserved between calls, the user should +C declare the above Common blocks in the calling program to insure +C that their contents are preserved. +C +C If the solution of a given problem by DLSODIS is to be interrupted +C and then later continued, such as when restarting an interrupted run +C or alternating between two or more problems, the user should save, +C following the return from the last DLSODIS call prior to the +C interruption, the contents of the call sequence variables and the +C internal Common blocks, and later restore these values before the +C next DLSODIS call for that problem. To save and restore the Common +C blocks, use Subroutines DSRCMS (see Part 2 above). +C +C----------------------------------------------------------------------- +C Part 4. Optionally Replaceable Solver Routines. +C +C Below are descriptions of two routines in the DLSODIS package which +C relate to the measurement of errors. Either routine can be +C replaced by a user-supplied version, if desired. However, since such +C a replacement may have a major impact on performance, it should be +C done only when absolutely necessary, and only with great caution. +C (Note: The means by which the package version of a routine is +C superseded by the user's version may be system-dependent.) +C +C (a) DEWSET. +C The following subroutine is called just before each internal +C integration step, and sets the array of error weights, EWT, as +C described under ITOL/RTOL/ATOL above: +C SUBROUTINE DEWSET (NEQ, ITOL, RTOL, ATOL, YCUR, EWT) +C where NEQ, ITOL, RTOL, and ATOL are as in the DLSODIS call sequence, +C YCUR contains the current dependent variable vector, and +C EWT is the array of weights set by DEWSET. +C +C If the user supplies this subroutine, it must return in EWT(i) +C (i = 1,...,NEQ) a positive quantity suitable for comparing errors +C in y(i) to. The EWT array returned by DEWSET is passed to the DVNORM +C routine (see below), and also used by DLSODIS in the computation +C of the optional output IMXER, and the increments for difference +C quotient Jacobians. +C +C In the user-supplied version of DEWSET, it may be desirable to use +C the current values of derivatives of y. Derivatives up to order NQ +C are available from the history array YH, described above under +C optional outputs. In DEWSET, YH is identical to the YCUR array, +C extended to NQ + 1 columns with a column length of NYH and scale +C factors of H**j/factorial(j). On the first call for the problem, +C given by NST = 0, NQ is 1 and H is temporarily set to 1.0. +C NYH is the initial value of NEQ. The quantities NQ, H, and NST +C can be obtained by including in DEWSET the statements: +C DOUBLE PRECISION RLS +C COMMON /DLS001/ RLS(218),ILS(37) +C NQ = ILS(33) +C NST = ILS(34) +C H = RLS(212) +C Thus, for example, the current value of dy/dt can be obtained as +C YCUR(NYH+i)/H (i=1,...,NEQ) (and the division by H is +C unnecessary when NST = 0). +C +C (b) DVNORM. +C The following is a real function routine which computes the weighted +C root-mean-square norm of a vector v: +C D = DVNORM (N, V, W) +C where: +C N = the length of the vector, +C V = real array of length N containing the vector, +C W = real array of length N containing weights, +C D = SQRT( (1/N) * sum(V(i)*W(i))**2 ). +C DVNORM is called with N = NEQ and with W(i) = 1.0/EWT(i), where +C EWT is as set by Subroutine DEWSET. +C +C If the user supplies this function, it should return a non-negative +C value of DVNORM suitable for use in the error control in DLSODIS. +C None of the arguments should be altered by DVNORM. +C For example, a user-supplied DVNORM routine might: +C -substitute a max-norm of (V(i)*w(I)) for the RMS-norm, or +C -ignore some components of V in the norm, with the effect of +C suppressing the error control on those components of y. +C----------------------------------------------------------------------- +C +C***REVISION HISTORY (YYYYMMDD) +C 19820714 DATE WRITTEN +C 19830812 Major update, based on recent LSODI and LSODES revisions: +C Upgraded MDI in ODRV package: operates on M + M-transpose. +C Numerous revisions in use of work arrays; +C use wordlength ratio LENRAT; added IPISP & LRAT to Common; +C added optional outputs IPIAN/IPJAN; +C Added routine CNTNZU; added NZL and NZU to /LSS001/; +C changed ADJLR call logic; added optional outputs NZL & NZU; +C revised counter initializations; revised PREPI stmt. nos.; +C revised difference quotient increment; +C eliminated block /LSI001/, using IERPJ flag; +C revised STODI logic after PJAC return; +C revised tuning of H change and step attempts in STODI; +C corrections to main prologue and comments throughout. +C 19870320 Corrected jump on test of umax in CDRV routine. +C 20010125 Numerous revisions: corrected comments throughout; +C removed TRET from Common; rewrote EWSET with 4 loops; +C fixed t test in INTDY; added Cray directives in STODI; +C in STODI, fixed DELP init. and logic around PJAC call; +C combined routines to save/restore Common; +C passed LEVEL = 0 in error message calls (except run abort). +C 20010425 Major update: convert source lines to upper case; +C added *DECK lines; changed from 1 to * in dummy dimensions; +C changed names R1MACH/D1MACH to RUMACH/DUMACH; +C renamed routines for uniqueness across single/double prec.; +C converted intrinsic names to generic form; +C removed ILLIN and NTREP (data loaded) from Common; +C removed all 'own' variables from Common; +C changed error messages to quoted strings; +C replaced XERRWV/XERRWD with 1993 revised version; +C converted prologues, comments, error messages to mixed case; +C converted arithmetic IF statements to logical IF statements; +C numerous corrections to prologues and internal comments. +C 20010507 Converted single precision source to double precision. +C 20020502 Corrected declarations in descriptions of user routines. +C 20031021 Fixed address offset bugs in Subroutine DPREPI. +C 20031027 Changed 0. to 0.0D0 in Subroutine DPREPI. +C 20031105 Restored 'own' variables to Common blocks, to enable +C interrupt/restart feature. +C 20031112 Added SAVE statements for data-loaded constants. +C 20031117 Changed internal names NRE, LSAVR to NFE, LSAVF resp. +C +C----------------------------------------------------------------------- +C Other routines in the DLSODIS package. +C +C In addition to Subroutine DLSODIS, the DLSODIS package includes the +C following subroutines and function routines: +C DIPREPI acts as an interface between DLSODIS and DPREPI, and also +C does adjusting of work space pointers and work arrays. +C DPREPI is called by DIPREPI to compute sparsity and do sparse +C matrix preprocessing. +C DAINVGS computes the initial value of the vector +C dy/dt = A-inverse * g +C ADJLR adjusts the length of required sparse matrix work space. +C It is called by DPREPI. +C CNTNZU is called by DPREPI and counts the nonzero elements in the +C strict upper triangle of P + P-transpose. +C JGROUP is called by DPREPI to compute groups of Jacobian column +C indices for use when MITER = 2. +C DINTDY computes an interpolated value of the y vector at t = TOUT. +C DSTODI is the core integrator, which does one step of the +C integration and the associated error control. +C DCFODE sets all method coefficients and test constants. +C DPRJIS computes and preprocesses the Jacobian matrix J = dr/dy +C and the Newton iteration matrix P = A - h*l0*J. +C DSOLSS manages solution of linear system in chord iteration. +C DEWSET sets the error weight vector EWT before each step. +C DVNORM computes the weighted RMS-norm of a vector. +C DSRCMS is a user-callable routine to save and restore +C the contents of the internal Common blocks. +C ODRV constructs a reordering of the rows and columns of +C a matrix by the minimum degree algorithm. ODRV is a +C driver routine which calls Subroutines MD, MDI, MDM, +C MDP, MDU, and SRO. See Ref. 2 for details. (The ODRV +C module has been modified since Ref. 2, however.) +C CDRV performs reordering, symbolic factorization, numerical +C factorization, or linear system solution operations, +C depending on a path argument IPATH. CDRV is a +C driver routine which calls Subroutines NROC, NSFC, +C NNFC, NNSC, and NNTC. See Ref. 3 for details. +C DLSODIS uses CDRV to solve linear systems in which the +C coefficient matrix is P = A - con*J, where A is the +C matrix for the linear system A(t,y)*dy/dt = g(t,y), +C con is a scalar, and J is an approximation to +C the Jacobian dr/dy. Because CDRV deals with rowwise +C sparsity descriptions, CDRV works with P-transpose, not P. +C DLSODIS also uses CDRV to solve the linear system +C A(t,y)*dy/dt = g(t,y) for dy/dt when ISTATE = 0. +C (For this, CDRV works with A-transpose, not A.) +C DUMACH computes the unit roundoff in a machine-independent manner. +C XERRWD, XSETUN, XSETF, IXSAV, and IUMACH handle the printing of all +C error messages and warnings. XERRWD is machine-dependent. +C Note: DVNORM, DUMACH, IXSAV, and IUMACH are function routines. +C All the others are subroutines. +C +C----------------------------------------------------------------------- + EXTERNAL DPRJIS, DSOLSS + DOUBLE PRECISION DUMACH, DVNORM + INTEGER INIT, MXSTEP, MXHNIL, NHNIL, NSLAST, NYH, IOWNS, + 1 ICF, IERPJ, IERSL, JCUR, JSTART, KFLAG, L, + 2 LYH, LEWT, LACOR, LSAVF, LWM, LIWM, METH, MITER, + 3 MAXORD, MAXCOR, MSBP, MXNCF, N, NQ, NST, NFE, NJE, NQU + INTEGER IPLOST, IESP, ISTATC, IYS, IBA, IBIAN, IBJAN, IBJGP, + 1 IPIAN, IPJAN, IPJGP, IPIGP, IPR, IPC, IPIC, IPISP, IPRSP, IPA, + 2 LENYH, LENYHM, LENWK, LREQ, LRAT, LREST, LWMIN, MOSS, MSBJ, + 3 NSLJ, NGP, NLU, NNZ, NSP, NZL, NZU + INTEGER I, I1, I2, IER, IGO, IFLAG, IMAX, IMUL, IMXER, IPFLAG, + 1 IPGO, IREM, IRES, J, KGO, LENRAT, LENYHT, LENIW, LENRW, + 2 LIA, LIC, LJA, LJC, LRTEM, LWTEM, LYD0, LYHD, LYHN, MF1, + 3 MORD, MXHNL0, MXSTP0, NCOLM + DOUBLE PRECISION ROWNS, + 1 CCMAX, EL0, H, HMIN, HMXI, HU, RC, TN, UROUND + DOUBLE PRECISION CON0, CONMIN, CCMXJ, PSMALL, RBIG, SETH + DOUBLE PRECISION ATOLI, AYI, BIG, EWTI, H0, HMAX, HMX, RH, RTOLI, + 1 TCRIT, TDIST, TNEXT, TOL, TOLSF, TP, SIZE, SUM, W0 + DIMENSION MORD(2) + LOGICAL IHIT + CHARACTER*60 MSG + SAVE LENRAT, MORD, MXSTP0, MXHNL0 +C----------------------------------------------------------------------- +C The following two internal Common blocks contain +C (a) variables which are local to any subroutine but whose values must +C be preserved between calls to the routine ("own" variables), and +C (b) variables which are communicated between subroutines. +C The block DLS001 is declared in subroutines DLSODIS, DIPREPI, DPREPI, +C DINTDY, DSTODI, DPRJIS, and DSOLSS. +C The block DLSS01 is declared in subroutines DLSODIS, DAINVGS, +C DIPREPI, DPREPI, DPRJIS, and DSOLSS. +C Groups of variables are replaced by dummy arrays in the Common +C declarations in routines where those variables are not used. +C----------------------------------------------------------------------- + COMMON /DLS001/ ROWNS(209), + 1 CCMAX, EL0, H, HMIN, HMXI, HU, RC, TN, UROUND, + 2 INIT, MXSTEP, MXHNIL, NHNIL, NSLAST, NYH, IOWNS(6), + 3 ICF, IERPJ, IERSL, JCUR, JSTART, KFLAG, L, + 4 LYH, LEWT, LACOR, LSAVF, LWM, LIWM, METH, MITER, + 5 MAXORD, MAXCOR, MSBP, MXNCF, N, NQ, NST, NFE, NJE, NQU +C + COMMON /DLSS01/ CON0, CONMIN, CCMXJ, PSMALL, RBIG, SETH, + 1 IPLOST, IESP, ISTATC, IYS, IBA, IBIAN, IBJAN, IBJGP, + 2 IPIAN, IPJAN, IPJGP, IPIGP, IPR, IPC, IPIC, IPISP, IPRSP, IPA, + 3 LENYH, LENYHM, LENWK, LREQ, LRAT, LREST, LWMIN, MOSS, MSBJ, + 4 NSLJ, NGP, NLU, NNZ, NSP, NZL, NZU +C + DATA MORD(1),MORD(2)/12,5/, MXSTP0/500/, MXHNL0/10/ +C----------------------------------------------------------------------- +C In the Data statement below, set LENRAT equal to the ratio of +C the wordlength for a real number to that for an integer. Usually, +C LENRAT = 1 for single precision and 2 for double precision. If the +C true ratio is not an integer, use the next smaller integer (.ge. 1), +C----------------------------------------------------------------------- + DATA LENRAT/2/ +C----------------------------------------------------------------------- +C Block A. +C This code block is executed on every call. +C It tests ISTATE and ITASK for legality and branches appropirately. +C If ISTATE .gt. 1 but the flag INIT shows that initialization has +C not yet been done, an error return occurs. +C If ISTATE = 0 or 1 and TOUT = T, return immediately. +C----------------------------------------------------------------------- + IF (ISTATE .LT. 0 .OR. ISTATE .GT. 3) GO TO 601 + IF (ITASK .LT. 1 .OR. ITASK .GT. 5) GO TO 602 + IF (ISTATE .LE. 1) GO TO 10 + IF (INIT .EQ. 0) GO TO 603 + IF (ISTATE .EQ. 2) GO TO 200 + GO TO 20 + 10 INIT = 0 + IF (TOUT .EQ. T) RETURN +C----------------------------------------------------------------------- +C Block B. +C The next code block is executed for the initial call (ISTATE = 0 or 1) +C or for a continuation call with parameter changes (ISTATE = 3). +C It contains checking of all inputs and various initializations. +C If ISTATE = 0 or 1, the final setting of work space pointers, the +C matrix preprocessing, and other initializations are done in Block C. +C +C First check legality of the non-optional inputs NEQ, ITOL, IOPT, and +C MF. +C----------------------------------------------------------------------- + 20 IF (NEQ(1) .LE. 0) GO TO 604 + IF (ISTATE .LE. 1) GO TO 25 + IF (NEQ(1) .GT. N) GO TO 605 + 25 N = NEQ(1) + IF (ITOL .LT. 1 .OR. ITOL .GT. 4) GO TO 606 + IF (IOPT .LT. 0 .OR. IOPT .GT. 1) GO TO 607 + MOSS = MF/100 + MF1 = MF - 100*MOSS + METH = MF1/10 + MITER = MF1 - 10*METH + IF (MOSS .LT. 0 .OR. MOSS .GT. 4) GO TO 608 + IF (MITER .EQ. 2 .AND. MOSS .EQ. 1) MOSS = MOSS + 1 + IF (MITER .EQ. 2 .AND. MOSS .EQ. 3) MOSS = MOSS + 1 + IF (MITER .EQ. 1 .AND. MOSS .EQ. 2) MOSS = MOSS - 1 + IF (MITER .EQ. 1 .AND. MOSS .EQ. 4) MOSS = MOSS - 1 + IF (METH .LT. 1 .OR. METH .GT. 2) GO TO 608 + IF (MITER .LT. 1 .OR. MITER .GT. 2) GO TO 608 +C Next process and check the optional inputs. -------------------------- + IF (IOPT .EQ. 1) GO TO 40 + MAXORD = MORD(METH) + MXSTEP = MXSTP0 + MXHNIL = MXHNL0 + IF (ISTATE .LE. 1) H0 = 0.0D0 + HMXI = 0.0D0 + HMIN = 0.0D0 + GO TO 60 + 40 MAXORD = IWORK(5) + IF (MAXORD .LT. 0) GO TO 611 + IF (MAXORD .EQ. 0) MAXORD = 100 + MAXORD = MIN(MAXORD,MORD(METH)) + MXSTEP = IWORK(6) + IF (MXSTEP .LT. 0) GO TO 612 + IF (MXSTEP .EQ. 0) MXSTEP = MXSTP0 + MXHNIL = IWORK(7) + IF (MXHNIL .LT. 0) GO TO 613 + IF (MXHNIL .EQ. 0) MXHNIL = MXHNL0 + IF (ISTATE .GT. 1) GO TO 50 + H0 = RWORK(5) + IF ((TOUT - T)*H0 .LT. 0.0D0) GO TO 614 + 50 HMAX = RWORK(6) + IF (HMAX .LT. 0.0D0) GO TO 615 + HMXI = 0.0D0 + IF (HMAX .GT. 0.0D0) HMXI = 1.0D0/HMAX + HMIN = RWORK(7) + IF (HMIN .LT. 0.0D0) GO TO 616 +C Check RTOL and ATOL for legality. ------------------------------------ + 60 RTOLI = RTOL(1) + ATOLI = ATOL(1) + DO 65 I = 1,N + IF (ITOL .GE. 3) RTOLI = RTOL(I) + IF (ITOL .EQ. 2 .OR. ITOL .EQ. 4) ATOLI = ATOL(I) + IF (RTOLI .LT. 0.0D0) GO TO 619 + IF (ATOLI .LT. 0.0D0) GO TO 620 + 65 CONTINUE +C----------------------------------------------------------------------- +C Compute required work array lengths, as far as possible, and test +C these against LRW and LIW. Then set tentative pointers for work +C arrays. Pointers to RWORK/IWORK segments are named by prefixing L to +C the name of the segment. E.g., the segment YH starts at RWORK(LYH). +C Segments of RWORK (in order) are denoted WM, YH, SAVR, EWT, ACOR. +C The required length of the matrix work space WM is not yet known, +C and so a crude minimum value is used for the initial tests of LRW +C and LIW, and YH is temporarily stored as far to the right in RWORK +C as possible, to leave the maximum amount of space for WM for matrix +C preprocessing. Thus if MOSS .ne. 2 or 4, some of the segments of +C RWORK are temporarily omitted, as they are not needed in the +C preprocessing. These omitted segments are: ACOR if ISTATE = 1, +C EWT and ACOR if ISTATE = 3 and MOSS = 1, and SAVR, EWT, and ACOR if +C ISTATE = 3 and MOSS = 0. +C----------------------------------------------------------------------- + LRAT = LENRAT + IF (ISTATE .LE. 1) NYH = N + IF (MITER .EQ. 1) LWMIN = 4*N + 10*N/LRAT + IF (MITER .EQ. 2) LWMIN = 4*N + 11*N/LRAT + LENYH = (MAXORD+1)*NYH + LREST = LENYH + 3*N + LENRW = 20 + LWMIN + LREST + IWORK(17) = LENRW + LENIW = 30 + IF (MOSS .NE. 1 .AND. MOSS .NE. 2) LENIW = LENIW + N + 1 + IWORK(18) = LENIW + IF (LENRW .GT. LRW) GO TO 617 + IF (LENIW .GT. LIW) GO TO 618 + LIA = 31 + IF (MOSS .NE. 1 .AND. MOSS .NE. 2) + 1 LENIW = LENIW + IWORK(LIA+N) - 1 + IWORK(18) = LENIW + IF (LENIW .GT. LIW) GO TO 618 + LJA = LIA + N + 1 + LIA = MIN(LIA,LIW) + LJA = MIN(LJA,LIW) + LIC = LENIW + 1 + IF (MOSS .EQ. 0) LENIW = LENIW + N + 1 + IWORK(18) = LENIW + IF (LENIW .GT. LIW) GO TO 618 + IF (MOSS .EQ. 0) LENIW = LENIW + IWORK(LIC+N) - 1 + IWORK(18) = LENIW + IF (LENIW .GT. LIW) GO TO 618 + LJC = LIC + N + 1 + LIC = MIN(LIC,LIW) + LJC = MIN(LJC,LIW) + LWM = 21 + IF (ISTATE .LE. 1) NQ = ISTATE + NCOLM = MIN(NQ+1,MAXORD+2) + LENYHM = NCOLM*NYH + LENYHT = LENYHM + IMUL = 2 + IF (ISTATE .EQ. 3) IMUL = MOSS + IF (ISTATE .EQ. 3 .AND. MOSS .EQ. 3) IMUL = 1 + IF (MOSS .EQ. 2 .OR. MOSS .EQ. 4) IMUL = 3 + LRTEM = LENYHT + IMUL*N + LWTEM = LRW - 20 - LRTEM + LENWK = LWTEM + LYHN = LWM + LWTEM + LSAVF = LYHN + LENYHT + LEWT = LSAVF + N + LACOR = LEWT + N + ISTATC = ISTATE + IF (ISTATE .LE. 1) GO TO 100 +C----------------------------------------------------------------------- +C ISTATE = 3. Move YH to its new location. +C Note that only the part of YH needed for the next step, namely +C MIN(NQ+1,MAXORD+2) columns, is actually moved. +C A temporary error weight array EWT is loaded if MOSS = 2 or 4. +C Sparse matrix processing is done in DIPREPI/DPREPI. +C If MAXORD was reduced below NQ, then the pointers are finally set +C so that SAVR is identical to (YH*,MAXORD+2) +C----------------------------------------------------------------------- + LYHD = LYH - LYHN + IMAX = LYHN - 1 + LENYHM +C Move YH. Move right if LYHD < 0; move left if LYHD > 0. ------------- + IF (LYHD .LT. 0) THEN + DO 72 I = LYHN,IMAX + J = IMAX + LYHN - I + 72 RWORK(J) = RWORK(J+LYHD) + ENDIF + IF (LYHD .GT. 0) THEN + DO 76 I = LYHN,IMAX + 76 RWORK(I) = RWORK(I+LYHD) + ENDIF + 80 LYH = LYHN + IWORK(22) = LYH + IF (MOSS .NE. 2 .AND. MOSS .NE. 4) GO TO 85 +C Temporarily load EWT if MOSS = 2 or 4. + CALL DEWSET (N,ITOL,RTOL,ATOL,RWORK(LYH),RWORK(LEWT)) + DO 82 I = 1,N + IF (RWORK(I+LEWT-1) .LE. 0.0D0) GO TO 621 + 82 RWORK(I+LEWT-1) = 1.0D0/RWORK(I+LEWT-1) + 85 CONTINUE +C DIPREPI and DPREPI do sparse matrix preprocessing. ------------------- + LSAVF = MIN(LSAVF,LRW) + LEWT = MIN(LEWT,LRW) + LACOR = MIN(LACOR,LRW) + CALL DIPREPI (NEQ, Y, YDOTI, RWORK, IWORK(LIA), IWORK(LJA), + 1 IWORK(LIC), IWORK(LJC), IPFLAG, RES, JAC, ADDA) + LENRW = LWM - 1 + LENWK + LREST + IWORK(17) = LENRW + IF (IPFLAG .NE. -1) IWORK(23) = IPIAN + IF (IPFLAG .NE. -1) IWORK(24) = IPJAN + IPGO = -IPFLAG + 1 + GO TO (90, 628, 629, 630, 631, 632, 633, 634, 634), IPGO + 90 IWORK(22) = LYH + LYD0 = LYH + N + IF (LENRW .GT. LRW) GO TO 617 +C Set flag to signal changes to DSTODI.--------------------------------- + JSTART = -1 + IF (NQ .LE. MAXORD) GO TO 94 +C MAXORD was reduced below NQ. Copy YH(*,MAXORD+2) into YDOTI. -------- + DO 92 I = 1,N + 92 YDOTI(I) = RWORK(I+LSAVF-1) + 94 IF (N .EQ. NYH) GO TO 200 +C NEQ was reduced. Zero part of YH to avoid undefined references. ----- + I1 = LYH + L*NYH + I2 = LYH + (MAXORD + 1)*NYH - 1 + IF (I1 .GT. I2) GO TO 200 + DO 95 I = I1,I2 + 95 RWORK(I) = 0.0D0 + GO TO 200 +C----------------------------------------------------------------------- +C Block C. +C The next block is for the initial call only (ISTATE = 0 or 1). +C It contains all remaining initializations, the call to DAINVGS +C (if ISTATE = 0), the sparse matrix preprocessing, and the +C calculation if the initial step size. +C The error weights in EWT are inverted after being loaded. +C----------------------------------------------------------------------- + 100 CONTINUE + LYH = LYHN + IWORK(22) = LYH + TN = T + NST = 0 + NFE = 0 + H = 1.0D0 + NNZ = 0 + NGP = 0 + NZL = 0 + NZU = 0 +C Load the initial value vector in YH.---------------------------------- + DO 105 I = 1,N + 105 RWORK(I+LYH-1) = Y(I) + IF (ISTATE .NE. 1) GO TO 108 +C Initial dy/dt was supplied. Load it into YH (LYD0 points to YH(*,2).) + LYD0 = LYH + NYH + DO 106 I = 1,N + 106 RWORK(I+LYD0-1) = YDOTI(I) + 108 CONTINUE +C Load and invert the EWT array. (H is temporarily set to 1.0.)-------- + CALL DEWSET (N,ITOL,RTOL,ATOL,RWORK(LYH),RWORK(LEWT)) + DO 110 I = 1,N + IF (RWORK(I+LEWT-1) .LE. 0.0D0) GO TO 621 + 110 RWORK(I+LEWT-1) = 1.0D0/RWORK(I+LEWT-1) +C Call DIPREPI and DPREPI to do sparse matrix preprocessing.------------ + LACOR = MIN(LACOR,LRW) + CALL DIPREPI (NEQ, Y, YDOTI, RWORK, IWORK(LIA), IWORK(LJA), + 1 IWORK(LIC), IWORK(LJC), IPFLAG, RES, JAC, ADDA) + LENRW = LWM - 1 + LENWK + LREST + IWORK(17) = LENRW + IF (IPFLAG .NE. -1) IWORK(23) = IPIAN + IF (IPFLAG .NE. -1) IWORK(24) = IPJAN + IPGO = -IPFLAG + 1 + GO TO (115, 628, 629, 630, 631, 632, 633, 634, 634), IPGO + 115 IWORK(22) = LYH + IF (LENRW .GT. LRW) GO TO 617 +C Compute initial dy/dt, if necessary, and load it into YH.------------- + LYD0 = LYH + N + IF (ISTATE .NE. 0) GO TO 120 + CALL DAINVGS (NEQ, T, Y, RWORK(LWM), RWORK(LWM), RWORK(LACOR), + 1 RWORK(LYD0), IER, RES, ADDA) + NFE = NFE + 1 + IGO = IER + 1 + GO TO (120, 565, 560, 560), IGO +C Check TCRIT for legality (ITASK = 4 or 5). --------------------------- + 120 CONTINUE + IF (ITASK .NE. 4 .AND. ITASK .NE. 5) GO TO 125 + TCRIT = RWORK(1) + IF ((TCRIT - TOUT)*(TOUT - T) .LT. 0.0D0) GO TO 625 + IF (H0 .NE. 0.0D0 .AND. (T + H0 - TCRIT)*H0 .GT. 0.0D0) + 1 H0 = TCRIT - T +C Initialize all remaining parameters. --------------------------------- + 125 UROUND = DUMACH() + JSTART = 0 + RWORK(LWM) = SQRT(UROUND) + NHNIL = 0 + NJE = 0 + NLU = 0 + NSLAST = 0 + HU = 0.0D0 + NQU = 0 + CCMAX = 0.3D0 + MAXCOR = 3 + MSBP = 20 + MXNCF = 10 +C----------------------------------------------------------------------- +C The coding below computes the step size, H0, to be attempted on the +C first step, unless the user has supplied a value for this. +C First check that TOUT - T differs significantly from zero. +C A scalar tolerance quantity TOL is computed, as MAX(RTOL(i)) +C if this is positive, or MAX(ATOL(i)/ABS(Y(i))) otherwise, adjusted +C so as to be between 100*UROUND and 1.0E-3. +C Then the computed value H0 is given by.. +C NEQ +C H0**2 = TOL / ( w0**-2 + (1/NEQ) * Sum ( YDOT(i)/ywt(i) )**2 ) +C 1 +C where w0 = MAX ( ABS(T), ABS(TOUT) ), +C YDOT(i) = i-th component of initial value of dy/dt, +C ywt(i) = EWT(i)/TOL (a weight for y(i)). +C The sign of H0 is inferred from the initial values of TOUT and T. +C----------------------------------------------------------------------- + IF (H0 .NE. 0.0D0) GO TO 180 + TDIST = ABS(TOUT - T) + W0 = MAX(ABS(T),ABS(TOUT)) + IF (TDIST .LT. 2.0D0*UROUND*W0) GO TO 622 + TOL = RTOL(1) + IF (ITOL .LE. 2) GO TO 145 + DO 140 I = 1,N + 140 TOL = MAX(TOL,RTOL(I)) + 145 IF (TOL .GT. 0.0D0) GO TO 160 + ATOLI = ATOL(1) + DO 150 I = 1,N + IF (ITOL .EQ. 2 .OR. ITOL .EQ. 4) ATOLI = ATOL(I) + AYI = ABS(Y(I)) + IF (AYI .NE. 0.0D0) TOL = MAX(TOL,ATOLI/AYI) + 150 CONTINUE + 160 TOL = MAX(TOL,100.0D0*UROUND) + TOL = MIN(TOL,0.001D0) + SUM = DVNORM (N, RWORK(LYD0), RWORK(LEWT)) + SUM = 1.0D0/(TOL*W0*W0) + TOL*SUM**2 + H0 = 1.0D0/SQRT(SUM) + H0 = MIN(H0,TDIST) + H0 = SIGN(H0,TOUT-T) +C Adjust H0 if necessary to meet HMAX bound. --------------------------- + 180 RH = ABS(H0)*HMXI + IF (RH .GT. 1.0D0) H0 = H0/RH +C Load H with H0 and scale YH(*,2) by H0. ------------------------------ + H = H0 + DO 190 I = 1,N + 190 RWORK(I+LYD0-1) = H0*RWORK(I+LYD0-1) + GO TO 270 +C----------------------------------------------------------------------- +C Block D. +C The next code block is for continuation calls only (ISTATE = 2 or 3) +C and is to check stop conditions before taking a step. +C----------------------------------------------------------------------- + 200 NSLAST = NST + GO TO (210, 250, 220, 230, 240), ITASK + 210 IF ((TN - TOUT)*H .LT. 0.0D0) GO TO 250 + CALL DINTDY (TOUT, 0, RWORK(LYH), NYH, Y, IFLAG) + IF (IFLAG .NE. 0) GO TO 627 + T = TOUT + GO TO 420 + 220 TP = TN - HU*(1.0D0 + 100.0D0*UROUND) + IF ((TP - TOUT)*H .GT. 0.0D0) GO TO 623 + IF ((TN - TOUT)*H .LT. 0.0D0) GO TO 250 + GO TO 400 + 230 TCRIT = RWORK(1) + IF ((TN - TCRIT)*H .GT. 0.0D0) GO TO 624 + IF ((TCRIT - TOUT)*H .LT. 0.0D0) GO TO 625 + IF ((TN - TOUT)*H .LT. 0.0D0) GO TO 245 + CALL DINTDY (TOUT, 0, RWORK(LYH), NYH, Y, IFLAG) + IF (IFLAG .NE. 0) GO TO 627 + T = TOUT + GO TO 420 + 240 TCRIT = RWORK(1) + IF ((TN - TCRIT)*H .GT. 0.0D0) GO TO 624 + 245 HMX = ABS(TN) + ABS(H) + IHIT = ABS(TN - TCRIT) .LE. 100.0D0*UROUND*HMX + IF (IHIT) GO TO 400 + TNEXT = TN + H*(1.0D0 + 4.0D0*UROUND) + IF ((TNEXT - TCRIT)*H .LE. 0.0D0) GO TO 250 + H = (TCRIT - TN)*(1.0D0 - 4.0D0*UROUND) + IF (ISTATE .EQ. 2) JSTART = -2 +C----------------------------------------------------------------------- +C Block E. +C The next block is normally executed for all calls and contains +C the call to the one-step core integrator DSTODI. +C +C This is a looping point for the integration steps. +C +C First check for too many steps being taken, update EWT (if not at +C start of problem), check for too much accuracy being requested, and +C check for H below the roundoff level in T. +C----------------------------------------------------------------------- + 250 CONTINUE + IF ((NST-NSLAST) .GE. MXSTEP) GO TO 500 + CALL DEWSET (N, ITOL, RTOL, ATOL, RWORK(LYH), RWORK(LEWT)) + DO 260 I = 1,N + IF (RWORK(I+LEWT-1) .LE. 0.0D0) GO TO 510 + 260 RWORK(I+LEWT-1) = 1.0D0/RWORK(I+LEWT-1) + 270 TOLSF = UROUND*DVNORM (N, RWORK(LYH), RWORK(LEWT)) + IF (TOLSF .LE. 1.0D0) GO TO 280 + TOLSF = TOLSF*2.0D0 + IF (NST .EQ. 0) GO TO 626 + GO TO 520 + 280 IF ((TN + H) .NE. TN) GO TO 290 + NHNIL = NHNIL + 1 + IF (NHNIL .GT. MXHNIL) GO TO 290 + MSG = 'DLSODIS- Warning..Internal T (=R1) and H (=R2) are' + CALL XERRWD (MSG, 50, 101, 0, 0, 0, 0, 0, 0.0D0, 0.0D0) + MSG=' such that in the machine, T + H = T on the next step ' + CALL XERRWD (MSG, 60, 101, 0, 0, 0, 0, 0, 0.0D0, 0.0D0) + MSG = ' (H = step size). Solver will continue anyway.' + CALL XERRWD (MSG, 50, 101, 0, 0, 0, 0, 2, TN, H) + IF (NHNIL .LT. MXHNIL) GO TO 290 + MSG = 'DLSODIS- Above warning has been issued I1 times. ' + CALL XERRWD (MSG, 50, 102, 0, 0, 0, 0, 0, 0.0D0, 0.0D0) + MSG = ' It will not be issued again for this problem.' + CALL XERRWD (MSG, 50, 102, 0, 1, MXHNIL, 0, 0, 0.0D0, 0.0D0) + 290 CONTINUE +C----------------------------------------------------------------------- +C CALL DSTODI(NEQ,Y,YH,NYH,YH1,EWT,SAVF,SAVR,ACOR,WM,WM,RES, +C ADDA,JAC,DPRJIS,DSOLSS) +C Note: SAVF in DSTODI occupies the same space as YDOTI in DLSODIS. +C----------------------------------------------------------------------- + CALL DSTODI (NEQ, Y, RWORK(LYH), NYH, RWORK(LYH), RWORK(LEWT), + 1 YDOTI, RWORK(LSAVF), RWORK(LACOR), RWORK(LWM), + 2 RWORK(LWM), RES, ADDA, JAC, DPRJIS, DSOLSS ) + KGO = 1 - KFLAG + GO TO (300, 530, 540, 400, 550, 555), KGO +C +C KGO = 1:success; 2:error test failure; 3:convergence failure; +C 4:RES ordered return; 5:RES returned error; +C 6:fatal error from CDRV via DPRJIS or DSOLSS. +C----------------------------------------------------------------------- +C Block F. +C The following block handles the case of a successful return from the +C core integrator (KFLAG = 0). Test for stop conditions. +C----------------------------------------------------------------------- + 300 INIT = 1 + GO TO (310, 400, 330, 340, 350), ITASK +C ITASK = 1. If TOUT has been reached, interpolate. ------------------- + 310 iF ((TN - TOUT)*H .LT. 0.0D0) GO TO 250 + CALL DINTDY (TOUT, 0, RWORK(LYH), NYH, Y, IFLAG) + T = TOUT + GO TO 420 +C ITASK = 3. Jump to exit if TOUT was reached. ------------------------ + 330 IF ((TN - TOUT)*H .GE. 0.0D0) GO TO 400 + GO TO 250 +C ITASK = 4. See if TOUT or TCRIT was reached. Adjust H if necessary. + 340 IF ((TN - TOUT)*H .LT. 0.0D0) GO TO 345 + CALL DINTDY (TOUT, 0, RWORK(LYH), NYH, Y, IFLAG) + T = TOUT + GO TO 420 + 345 HMX = ABS(TN) + ABS(H) + IHIT = ABS(TN - TCRIT) .LE. 100.0D0*UROUND*HMX + IF (IHIT) GO TO 400 + TNEXT = TN + H*(1.0D0 + 4.0D0*UROUND) + IF ((TNEXT - TCRIT)*H .LE. 0.0D0) GO TO 250 + H = (TCRIT - TN)*(1.0D0 - 4.0D0*UROUND) + JSTART = -2 + GO TO 250 +C ITASK = 5. See if TCRIT was reached and jump to exit. --------------- + 350 HMX = ABS(TN) + ABS(H) + IHIT = ABS(TN - TCRIT) .LE. 100.0D0*UROUND*HMX +C----------------------------------------------------------------------- +C Block G. +C The following block handles all successful returns from DLSODIS. +C if ITASK .ne. 1, Y is loaded from YH and T is set accordingly. +C ISTATE is set to 2, and the optional outputs are loaded into the +C work arrays before returning. +C----------------------------------------------------------------------- + 400 DO 410 I = 1,N + 410 Y(I) = RWORK(I+LYH-1) + T = TN + IF (ITASK .NE. 4 .AND. ITASK .NE. 5) GO TO 420 + IF (IHIT) T = TCRIT + 420 ISTATE = 2 + IF ( KFLAG .EQ. -3 ) ISTATE = 3 + RWORK(11) = HU + RWORK(12) = H + RWORK(13) = TN + IWORK(11) = NST + IWORK(12) = NFE + IWORK(13) = NJE + IWORK(14) = NQU + IWORK(15) = NQ + IWORK(19) = NNZ + IWORK(20) = NGP + IWORK(21) = NLU + IWORK(25) = NZL + IWORK(26) = NZU + RETURN +C----------------------------------------------------------------------- +C Block H. +C The following block handles all unsuccessful returns other than +C those for illegal input. First the error message routine is called. +C If there was an error test or convergence test failure, IMXER is set. +C Then Y is loaded from YH and T is set to TN. +C The optional outputs are loaded into the work arrays before returning. +C----------------------------------------------------------------------- +C The maximum number of steps was taken before reaching TOUT. ---------- + 500 MSG = 'DLSODIS- At current T (=R1), MXSTEP (=I1) steps ' + CALL XERRWD (MSG, 50, 201, 0, 0, 0, 0, 0, 0.0D0, 0.0D0) + MSG = ' taken on this call before reaching TOUT ' + CALL XERRWD (MSG, 50, 201, 0, 1, MXSTEP, 0, 1, TN, 0.0D0) + ISTATE = -1 + GO TO 580 +C EWT(i) .le. 0.0 for some i (not at start of problem). ---------------- + 510 EWTI = RWORK(LEWT+I-1) + MSG = 'DLSODIS- At T (=R1), EWT(I1) has become R2 .le. 0.' + CALL XERRWD (MSG, 50, 202, 0, 1, I, 0, 2, TN, EWTI) + ISTATE = -6 + GO TO 590 +C Too much accuracy requested for machine precision. ------------------- + 520 MSG = 'DLSODIS- At T (=R1), too much accuracy requested ' + CALL XERRWD (MSG, 50, 203, 0, 0, 0, 0, 0, 0.0D0, 0.0D0) + MSG = ' for precision of machine.. See TOLSF (=R2) ' + CALL XERRWD (MSG, 50, 203, 0, 0, 0, 0, 2, TN, TOLSF) + RWORK(14) = TOLSF + ISTATE = -2 + GO TO 590 +C KFLAG = -1. Error test failed repeatedly or with ABS(H) = HMIN. ----- + 530 MSG = 'DLSODIS- At T (=R1) and step size H (=R2), the ' + CALL XERRWD (MSG, 50, 204, 0, 0, 0, 0, 0, 0.0D0, 0.0D0) + MSG=' error test failed repeatedly or with ABS(H) = HMIN ' + CALL XERRWD (MSG, 60, 204, 0, 0, 0, 0, 2, TN, H) + ISTATE = -4 + GO TO 570 +C KFLAG = -2. Convergence failed repeatedly or with ABS(H) = HMIN. ---- + 540 MSG = 'DLSODIS- At T (=R1) and step size H (=R2), the ' + CALL XERRWD (MSG, 50, 205, 0, 0, 0, 0, 0, 0.0D0, 0.0D0) + MSG = ' corrector convergence failed repeatedly ' + CALL XERRWD (MSG, 50, 205, 0, 0, 0, 0, 0, 0.0D0, 0.0D0) + MSG = ' or with ABS(H) = HMIN ' + CALL XERRWD (MSG, 30, 205, 0, 0, 0, 0, 2, TN, H) + ISTATE = -5 + GO TO 570 +C IRES = 3 returned by RES, despite retries by DSTODI. ----------------- + 550 MSG = 'DLSODIS- At T (=R1) residual routine returned ' + CALL XERRWD (MSG, 50, 206, 0, 0, 0, 0, 0, 0.0D0, 0.0D0) + MSG = ' error IRES = 3 repeatedly.' + CALL XERRWD (MSG, 30, 206, 1, 0, 0, 0, 0, TN, 0.0D0) + ISTATE = -7 + GO TO 590 +C KFLAG = -5. Fatal error flag returned by DPRJIS or DSOLSS (CDRV). --- + 555 MSG = 'DLSODIS- At T (=R1) and step size H (=R2), a fatal' + CALL XERRWD (MSG, 50, 207, 0, 0, 0, 0, 0, 0.0D0, 0.0D0) + MSG = ' error flag was returned by CDRV (by way of ' + CALL XERRWD (MSG, 50, 207, 0, 0, 0, 0, 0, 0.0D0, 0.0D0) + MSG = ' Subroutine DPRJIS or DSOLSS) ' + CALL XERRWD (MSG, 40, 207, 0, 0, 0, 0, 2, TN, H) + ISTATE = -9 + GO TO 580 +C DAINVGS failed because matrix A was singular. ------------------------ + 560 MSG='DLSODIS- Attempt to initialize dy/dt failed because matrix A' + CALL XERRWD (MSG, 60, 208, 0, 0, 0, 0, 0, 0.0D0, 0.0D0) + MSG=' was singular. CDRV returned zero pivot error flag. ' + CALL XERRWD (MSG, 60, 208, 0, 0, 0, 0, 0, 0.0D0, 0.0D0) + MSG = 'DAINVGS set its error flag to IER = (I1)' + CALL XERRWD (MSG, 40, 208, 0, 1, IER, 0, 0, 0.0D0, 0.0D0) + ISTATE = -8 + RETURN +C DAINVGS failed because RES set IRES to 2 or 3. ----------------------- + 565 MSG = 'DLSODIS- Attempt to initialize dy/dt failed ' + CALL XERRWD (MSG, 50, 209, 0, 0, 0, 0, 0, 0.0D0, 0.0D0) + MSG = ' because residual routine set its error flag ' + CALL XERRWD (MSG, 50, 209, 0, 0, 0, 0, 0, 0.0D0, 0.0D0) + MSG = ' to IRES = (I1)' + CALL XERRWD (MSG, 20, 209, 0, 1, IER, 0, 0, 0.0D0, 0.0D0) + ISTATE = -8 + RETURN +C Compute IMXER if relevant. ------------------------------------------- + 570 BIG = 0.0D0 + IMXER = 1 + DO 575 I = 1,N + SIZE = ABS(RWORK(I+LACOR-1)*RWORK(I+LEWT-1)) + IF (BIG .GE. SIZE) GO TO 575 + BIG = SIZE + IMXER = I + 575 CONTINUE + IWORK(16) = IMXER +C Compute residual if relevant. ---------------------------------------- + 580 LYD0 = LYH + NYH + DO 585 I = 1, N + RWORK(I+LSAVF-1) = RWORK(I+LYD0-1) / H + 585 Y(I) = RWORK(I+LYH-1) + IRES = 1 + CALL RES (NEQ, TN, Y, RWORK(LSAVF), YDOTI, IRES) + NFE = NFE + 1 + IF ( IRES .LE. 1 ) GO TO 595 + MSG = 'DLSODIS- Residual routine set its flag IRES ' + CALL XERRWD (MSG, 50, 210, 0, 0, 0, 0, 0, 0.0D0, 0.0D0) + MSG = ' to (I1) when called for final output. ' + CALL XERRWD (MSG, 50, 210, 0, 1, IRES, 0, 0, 0.0D0, 0.0D0) + GO TO 595 +C set y vector, t, and optional outputs. ------------------------------- + 590 DO 592 I = 1,N + 592 Y(I) = RWORK(I+LYH-1) + 595 T = TN + RWORK(11) = HU + RWORK(12) = H + RWORK(13) = TN + IWORK(11) = NST + IWORK(12) = NFE + IWORK(13) = NJE + IWORK(14) = NQU + IWORK(15) = NQ + IWORK(19) = NNZ + IWORK(20) = NGP + IWORK(21) = NLU + IWORK(25) = NZL + IWORK(26) = NZU + RETURN +C----------------------------------------------------------------------- +C Block I. +C The following block handles all error returns due to illegal input +C (ISTATE = -3), as detected before calling the core integrator. +C First the error message routine is called. If the illegal input +C is a negative ISTATE, the run is aborted (apparent infinite loop). +C----------------------------------------------------------------------- + 601 MSG = 'DLSODIS- ISTATE (=I1) illegal.' + CALL XERRWD (MSG, 30, 1, 0, 1, ISTATE, 0, 0, 0.0D0, 0.0D0) + IF (ISTATE .LT. 0) GO TO 800 + GO TO 700 + 602 MSG = 'DLSODIS- ITASK (=I1) illegal. ' + CALL XERRWD (MSG, 30, 2, 0, 1, ITASK, 0, 0, 0.0D0, 0.0D0) + GO TO 700 + 603 MSG = 'DLSODIS-ISTATE .gt. 1 but DLSODIS not initialized.' + CALL XERRWD (MSG, 50, 3, 0, 0, 0, 0, 0, 0.0D0, 0.0D0) + GO TO 700 + 604 MSG = 'DLSODIS- NEQ (=I1) .lt. 1 ' + CALL XERRWD (MSG, 30, 4, 0, 1, NEQ(1), 0, 0, 0.0D0, 0.0D0) + GO TO 700 + 605 MSG = 'DLSODIS- ISTATE = 3 and NEQ increased (I1 to I2). ' + CALL XERRWD (MSG, 50, 5, 0, 2, N, NEQ(1), 0, 0.0D0, 0.0D0) + GO TO 700 + 606 MSG = 'DLSODIS- ITOL (=I1) illegal. ' + CALL XERRWD (MSG, 30, 6, 0, 1, ITOL, 0, 0, 0.0D0, 0.0D0) + GO TO 700 + 607 MSG = 'DLSODIS- IOPT (=I1) illegal. ' + CALL XERRWD (MSG, 30, 7, 0, 1, IOPT, 0, 0, 0.0D0, 0.0D0) + GO TO 700 + 608 MSG = 'DLSODIS- MF (=I1) illegal. ' + CALL XERRWD (MSG, 30, 8, 0, 1, MF, 0, 0, 0.0D0, 0.0D0) + GO TO 700 + 611 MSG = 'DLSODIS- MAXORD (=I1) .lt. 0 ' + CALL XERRWD (MSG, 30, 11, 0, 1, MAXORD, 0, 0, 0.0D0, 0.0D0) + GO TO 700 + 612 MSG = 'DLSODIS- MXSTEP (=I1) .lt. 0 ' + CALL XERRWD (MSG, 30, 12, 0, 1, MXSTEP, 0, 0, 0.0D0, 0.0D0) + GO TO 700 + 613 MSG = 'DLSODIS- MXHNIL (=I1) .lt. 0 ' + CALL XERRWD (MSG, 30, 13, 0, 1, MXHNIL, 0, 0, 0.0D0, 0.0D0) + GO TO 700 + 614 MSG = 'DLSODIS- TOUT (=R1) behind T (=R2) ' + CALL XERRWD (MSG, 40, 14, 0, 0, 0, 0, 2, TOUT, T) + MSG = ' Integration direction is given by H0 (=R1) ' + CALL XERRWD (MSG, 50, 14, 0, 0, 0, 0, 1, H0, 0.0D0) + GO TO 700 + 615 MSG = 'DLSODIS- HMAX (=R1) .lt. 0.0 ' + CALL XERRWD (MSG, 30, 15, 0, 0, 0, 0, 1, HMAX, 0.0D0) + GO TO 700 + 616 MSG = 'DLSODIS- HMIN (=R1) .lt. 0.0 ' + CALL XERRWD (MSG, 30, 16, 0, 0, 0, 0, 1, HMIN, 0.0D0) + GO TO 700 + 617 MSG = 'DLSODIS- RWORK length is insufficient to proceed. ' + CALL XERRWD (MSG, 50, 17, 0, 0, 0, 0, 0, 0.0D0, 0.0D0) + MSG=' Length needed is .ge. LENRW (=I1), exceeds LRW (=I2)' + CALL XERRWD (MSG, 60, 17, 0, 2, LENRW, LRW, 0, 0.0D0, 0.0D0) + GO TO 700 + 618 MSG = 'DLSODIS- IWORK length is insufficient to proceed. ' + CALL XERRWD (MSG, 50, 18, 0, 0, 0, 0, 0, 0.0D0, 0.0D0) + MSG=' Length needed is .ge. LENIW (=I1), exceeds LIW (=I2)' + CALL XERRWD (MSG, 60, 18, 0, 2, LENIW, LIW, 0, 0.0D0, 0.0D0) + GO TO 700 + 619 MSG = 'DLSODIS- RTOL(=I1) is R1 .lt. 0.0 ' + CALL XERRWD (MSG, 40, 19, 0, 1, I, 0, 1, RTOLI, 0.0D0) + GO TO 700 + 620 MSG = 'DLSODIS- ATOL(=I1) is R1 .lt. 0.0 ' + CALL XERRWD (MSG, 40, 20, 0, 1, I, 0, 1, ATOLI, 0.0D0) + GO TO 700 + 621 EWTI = RWORK(LEWT+I-1) + MSG = 'DLSODIS- EWT(I1) is R1 .le. 0.0 ' + CALL XERRWD (MSG, 40, 21, 0, 1, I, 0, 1, EWTI, 0.0D0) + GO TO 700 + 622 MSG='DLSODIS- TOUT(=R1) too close to T(=R2) to start integration.' + CALL XERRWD (MSG, 60, 22, 0, 0, 0, 0, 2, TOUT, T) + GO TO 700 + 623 MSG='DLSODIS- ITASK = I1 and TOUT (=R1) behind TCUR - HU (= R2) ' + CALL XERRWD (MSG, 60, 23, 0, 1, ITASK, 0, 2, TOUT, TP) + GO TO 700 + 624 MSG='DLSODIS- ITASK = 4 or 5 and TCRIT (=R1) behind TCUR (=R2) ' + CALL XERRWD (MSG, 60, 24, 0, 0, 0, 0, 2, TCRIT, TN) + GO TO 700 + 625 MSG='DLSODIS- ITASK = 4 or 5 and TCRIT (=R1) behind TOUT (=R2) ' + CALL XERRWD (MSG, 60, 25, 0, 0, 0, 0, 2, TCRIT, TOUT) + GO TO 700 + 626 MSG = 'DLSODIS- At start of problem, too much accuracy ' + CALL XERRWD (MSG, 50, 26, 0, 0, 0, 0, 0, 0.0D0, 0.0D0) + MSG=' requested for precision of machine.. See TOLSF (=R1) ' + CALL XERRWD (MSG, 60, 26, 0, 0, 0, 0, 1, TOLSF, 0.0D0) + RWORK(14) = TOLSF + GO TO 700 + 627 MSG = 'DLSODIS- Trouble in DINTDY. ITASK = I1, TOUT = R1' + CALL XERRWD (MSG, 50, 27, 0, 1, ITASK, 0, 1, TOUT, 0.0D0) + GO TO 700 + 628 MSG='DLSODIS- RWORK length insufficient (for Subroutine DPREPI). ' + CALL XERRWD (MSG, 60, 28, 0, 0, 0, 0, 0, 0.0D0, 0.0D0) + MSG=' Length needed is .ge. LENRW (=I1), exceeds LRW (=I2)' + CALL XERRWD (MSG, 60, 28, 0, 2, LENRW, LRW, 0, 0.0D0, 0.0D0) + GO TO 700 + 629 MSG='DLSODIS- RWORK length insufficient (for Subroutine JGROUP). ' + CALL XERRWD (MSG, 60, 29, 0, 0, 0, 0, 0, 0.0D0, 0.0D0) + MSG=' Length needed is .ge. LENRW (=I1), exceeds LRW (=I2)' + CALL XERRWD (MSG, 60, 29, 0, 2, LENRW, LRW, 0, 0.0D0, 0.0D0) + GO TO 700 + 630 MSG='DLSODIS- RWORK length insufficient (for Subroutine ODRV). ' + CALL XERRWD (MSG, 60, 30, 0, 0, 0, 0, 0, 0.0D0, 0.0D0) + MSG=' Length needed is .ge. LENRW (=I1), exceeds LRW (=I2)' + CALL XERRWD (MSG, 60, 30, 0, 2, LENRW, LRW, 0, 0.0D0, 0.0D0) + GO TO 700 + 631 MSG='DLSODIS- Error from ODRV in Yale Sparse Matrix Package. ' + CALL XERRWD (MSG, 60, 31, 0, 0, 0, 0, 0, 0.0D0, 0.0D0) + IMUL = (IYS - 1)/N + IREM = IYS - IMUL*N + MSG=' At T (=R1), ODRV returned error flag = I1*NEQ + I2. ' + CALL XERRWD (MSG, 60, 31, 0, 2, IMUL, IREM, 1, TN, 0.0D0) + GO TO 700 + 632 MSG='DLSODIS- RWORK length insufficient (for Subroutine CDRV). ' + CALL XERRWD (MSG, 60, 32, 0, 0, 0, 0, 0, 0.0D0, 0.0D0) + MSG=' Length needed is .ge. LENRW (=I1), exceeds LRW (=I2)' + CALL XERRWD (MSG, 60, 32, 0, 2, LENRW, LRW, 0, 0.0D0, 0.0D0) + GO TO 700 + 633 MSG='DLSODIS- Error from CDRV in Yale Sparse Matrix Package. ' + CALL XERRWD (MSG, 60, 33, 0, 0, 0, 0, 0, 0.0D0, 0.0D0) + IMUL = (IYS - 1)/N + IREM = IYS - IMUL*N + MSG=' At T (=R1), CDRV returned error flag = I1*NEQ + I2. ' + CALL XERRWD (MSG, 60, 33, 0, 2, IMUL, IREM, 1, TN, 0.0D0) + IF (IMUL .EQ. 2) THEN + MSG=' Duplicate entry in sparsity structure descriptors. ' + CALL XERRWD (MSG, 60, 33, 0, 0, 0, 0, 0, 0.0D0, 0.0D0) + ENDIF + IF (IMUL .EQ. 3 .OR. IMUL .EQ. 6) THEN + MSG=' Insufficient storage for NSFC (called by CDRV). ' + CALL XERRWD (MSG, 60, 33, 0, 0, 0, 0, 0, 0.0D0, 0.0D0) + ENDIF + GO TO 700 + 634 MSG='DLSODIS- At T (=R1) residual routine (called by DPREPI) ' + CALL XERRWD (MSG, 60, 34, 0, 0, 0, 0, 0, 0.0D0, 0.0D0) + IER = -IPFLAG - 5 + MSG = ' returned error IRES (=I1)' + CALL XERRWD (MSG, 30, 34, 0, 1, IER, 0, 1, TN, 0.0D0) +C + 700 ISTATE = -3 + RETURN +C + 800 MSG = 'DLSODIS- Run aborted.. apparent infinite loop. ' + CALL XERRWD (MSG, 50, 303, 2, 0, 0, 0, 0, 0.0D0, 0.0D0) + RETURN +C----------------------- End of Subroutine DLSODIS --------------------- + END + + diff --git a/applications/PUfoam/MoDeNaModels/foamAging/src/src/odepack_sub1.f b/applications/PUfoam/MoDeNaModels/foamAging/src/src/odepack_sub1.f new file mode 100644 index 000000000..5fe02d207 --- /dev/null +++ b/applications/PUfoam/MoDeNaModels/foamAging/src/src/odepack_sub1.f @@ -0,0 +1,10136 @@ +*DECK DUMACH + DOUBLE PRECISION FUNCTION DUMACH () +C***BEGIN PROLOGUE DUMACH +C***PURPOSE Compute the unit roundoff of the machine. +C***CATEGORY R1 +C***TYPE DOUBLE PRECISION (RUMACH-S, DUMACH-D) +C***KEYWORDS MACHINE CONSTANTS +C***AUTHOR Hindmarsh, Alan C., (LLNL) +C***DESCRIPTION +C *Usage: +C DOUBLE PRECISION A, DUMACH +C A = DUMACH() +C +C *Function Return Values: +C A : the unit roundoff of the machine. +C +C *Description: +C The unit roundoff is defined as the smallest positive machine +C number u such that 1.0 + u .ne. 1.0. This is computed by DUMACH +C in a machine-independent manner. +C +C***REFERENCES (NONE) +C***ROUTINES CALLED DUMSUM +C***REVISION HISTORY (YYYYMMDD) +C 19930216 DATE WRITTEN +C 19930818 Added SLATEC-format prologue. (FNF) +C 20030707 Added DUMSUM to force normal storage of COMP. (ACH) +C***END PROLOGUE DUMACH +C + DOUBLE PRECISION U, COMP +C***FIRST EXECUTABLE STATEMENT DUMACH + U = 1.0D0 + 10 U = U*0.5D0 + CALL DUMSUM(1.0D0, U, COMP) + IF (COMP .NE. 1.0D0) GO TO 10 + DUMACH = U*2.0D0 + RETURN +C----------------------- End of Function DUMACH ------------------------ + END + SUBROUTINE DUMSUM(A,B,C) +C Routine to force normal storing of A + B, for DUMACH. + DOUBLE PRECISION A, B, C + C = A + B + RETURN + END +*DECK DCFODE + SUBROUTINE DCFODE (METH, ELCO, TESCO) +C***BEGIN PROLOGUE DCFODE +C***SUBSIDIARY +C***PURPOSE Set ODE integrator coefficients. +C***TYPE DOUBLE PRECISION (SCFODE-S, DCFODE-D) +C***AUTHOR Hindmarsh, Alan C., (LLNL) +C***DESCRIPTION +C +C DCFODE is called by the integrator routine to set coefficients +C needed there. The coefficients for the current method, as +C given by the value of METH, are set for all orders and saved. +C The maximum order assumed here is 12 if METH = 1 and 5 if METH = 2. +C (A smaller value of the maximum order is also allowed.) +C DCFODE is called once at the beginning of the problem, +C and is not called again unless and until METH is changed. +C +C The ELCO array contains the basic method coefficients. +C The coefficients el(i), 1 .le. i .le. nq+1, for the method of +C order nq are stored in ELCO(i,nq). They are given by a genetrating +C polynomial, i.e., +C l(x) = el(1) + el(2)*x + ... + el(nq+1)*x**nq. +C For the implicit Adams methods, l(x) is given by +C dl/dx = (x+1)*(x+2)*...*(x+nq-1)/factorial(nq-1), l(-1) = 0. +C For the BDF methods, l(x) is given by +C l(x) = (x+1)*(x+2)* ... *(x+nq)/K, +C where K = factorial(nq)*(1 + 1/2 + ... + 1/nq). +C +C The TESCO array contains test constants used for the +C local error test and the selection of step size and/or order. +C At order nq, TESCO(k,nq) is used for the selection of step +C size at order nq - 1 if k = 1, at order nq if k = 2, and at order +C nq + 1 if k = 3. +C +C***SEE ALSO DLSODE +C***ROUTINES CALLED (NONE) +C***REVISION HISTORY (YYMMDD) +C 791129 DATE WRITTEN +C 890501 Modified prologue to SLATEC/LDOC format. (FNF) +C 890503 Minor cosmetic changes. (FNF) +C 930809 Renamed to allow single/double precision versions. (ACH) +C***END PROLOGUE DCFODE +C**End + INTEGER METH + INTEGER I, IB, NQ, NQM1, NQP1 + DOUBLE PRECISION ELCO, TESCO + DOUBLE PRECISION AGAMQ, FNQ, FNQM1, PC, PINT, RAGQ, + 1 RQFAC, RQ1FAC, TSIGN, XPIN + DIMENSION ELCO(13,12), TESCO(3,12) + DIMENSION PC(12) +C +C***FIRST EXECUTABLE STATEMENT DCFODE + GO TO (100, 200), METH +C + 100 ELCO(1,1) = 1.0D0 + ELCO(2,1) = 1.0D0 + TESCO(1,1) = 0.0D0 + TESCO(2,1) = 2.0D0 + TESCO(1,2) = 1.0D0 + TESCO(3,12) = 0.0D0 + PC(1) = 1.0D0 + RQFAC = 1.0D0 + DO 140 NQ = 2,12 +C----------------------------------------------------------------------- +C The PC array will contain the coefficients of the polynomial +C p(x) = (x+1)*(x+2)*...*(x+nq-1). +C Initially, p(x) = 1. +C----------------------------------------------------------------------- + RQ1FAC = RQFAC + RQFAC = RQFAC/NQ + NQM1 = NQ - 1 + FNQM1 = NQM1 + NQP1 = NQ + 1 +C Form coefficients of p(x)*(x+nq-1). ---------------------------------- + PC(NQ) = 0.0D0 + DO 110 IB = 1,NQM1 + I = NQP1 - IB + 110 PC(I) = PC(I-1) + FNQM1*PC(I) + PC(1) = FNQM1*PC(1) +C Compute integral, -1 to 0, of p(x) and x*p(x). ----------------------- + PINT = PC(1) + XPIN = PC(1)/2.0D0 + TSIGN = 1.0D0 + DO 120 I = 2,NQ + TSIGN = -TSIGN + PINT = PINT + TSIGN*PC(I)/I + 120 XPIN = XPIN + TSIGN*PC(I)/(I+1) +C Store coefficients in ELCO and TESCO. -------------------------------- + ELCO(1,NQ) = PINT*RQ1FAC + ELCO(2,NQ) = 1.0D0 + DO 130 I = 2,NQ + 130 ELCO(I+1,NQ) = RQ1FAC*PC(I)/I + AGAMQ = RQFAC*XPIN + RAGQ = 1.0D0/AGAMQ + TESCO(2,NQ) = RAGQ + IF (NQ .LT. 12) TESCO(1,NQP1) = RAGQ*RQFAC/NQP1 + TESCO(3,NQM1) = RAGQ + 140 CONTINUE + RETURN +C + 200 PC(1) = 1.0D0 + RQ1FAC = 1.0D0 + DO 230 NQ = 1,5 +C----------------------------------------------------------------------- +C The PC array will contain the coefficients of the polynomial +C p(x) = (x+1)*(x+2)*...*(x+nq). +C Initially, p(x) = 1. +C----------------------------------------------------------------------- + FNQ = NQ + NQP1 = NQ + 1 +C Form coefficients of p(x)*(x+nq). ------------------------------------ + PC(NQP1) = 0.0D0 + DO 210 IB = 1,NQ + I = NQ + 2 - IB + 210 PC(I) = PC(I-1) + FNQ*PC(I) + PC(1) = FNQ*PC(1) +C Store coefficients in ELCO and TESCO. -------------------------------- + DO 220 I = 1,NQP1 + 220 ELCO(I,NQ) = PC(I)/PC(2) + ELCO(2,NQ) = 1.0D0 + TESCO(1,NQ) = RQ1FAC + TESCO(2,NQ) = NQP1/ELCO(1,NQ) + TESCO(3,NQ) = (NQ+2)/ELCO(1,NQ) + RQ1FAC = RQ1FAC/FNQ + 230 CONTINUE + RETURN +C----------------------- END OF SUBROUTINE DCFODE ---------------------- + END +*DECK DINTDY + SUBROUTINE DINTDY (T, K, YH, NYH, DKY, IFLAG) +C***BEGIN PROLOGUE DINTDY +C***SUBSIDIARY +C***PURPOSE Interpolate solution derivatives. +C***TYPE DOUBLE PRECISION (SINTDY-S, DINTDY-D) +C***AUTHOR Hindmarsh, Alan C., (LLNL) +C***DESCRIPTION +C +C DINTDY computes interpolated values of the K-th derivative of the +C dependent variable vector y, and stores it in DKY. This routine +C is called within the package with K = 0 and T = TOUT, but may +C also be called by the user for any K up to the current order. +C (See detailed instructions in the usage documentation.) +C +C The computed values in DKY are gotten by interpolation using the +C Nordsieck history array YH. This array corresponds uniquely to a +C vector-valued polynomial of degree NQCUR or less, and DKY is set +C to the K-th derivative of this polynomial at T. +C The formula for DKY is: +C q +C DKY(i) = sum c(j,K) * (T - tn)**(j-K) * h**(-j) * YH(i,j+1) +C j=K +C where c(j,K) = j*(j-1)*...*(j-K+1), q = NQCUR, tn = TCUR, h = HCUR. +C The quantities nq = NQCUR, l = nq+1, N = NEQ, tn, and h are +C communicated by COMMON. The above sum is done in reverse order. +C IFLAG is returned negative if either K or T is out of bounds. +C +C***SEE ALSO DLSODE +C***ROUTINES CALLED XERRWD +C***COMMON BLOCKS DLS001 +C***REVISION HISTORY (YYMMDD) +C 791129 DATE WRITTEN +C 890501 Modified prologue to SLATEC/LDOC format. (FNF) +C 890503 Minor cosmetic changes. (FNF) +C 930809 Renamed to allow single/double precision versions. (ACH) +C 010418 Reduced size of Common block /DLS001/. (ACH) +C 031105 Restored 'own' variables to Common block /DLS001/, to +C enable interrupt/restart feature. (ACH) +C 050427 Corrected roundoff decrement in TP. (ACH) +C***END PROLOGUE DINTDY +C**End + INTEGER K, NYH, IFLAG + DOUBLE PRECISION T, YH, DKY + DIMENSION YH(NYH,*), DKY(*) + INTEGER IOWND, IOWNS, + 1 ICF, IERPJ, IERSL, JCUR, JSTART, KFLAG, L, + 2 LYH, LEWT, LACOR, LSAVF, LWM, LIWM, METH, MITER, + 3 MAXORD, MAXCOR, MSBP, MXNCF, N, NQ, NST, NFE, NJE, NQU + DOUBLE PRECISION ROWNS, + 1 CCMAX, EL0, H, HMIN, HMXI, HU, RC, TN, UROUND + COMMON /DLS001/ ROWNS(209), + 1 CCMAX, EL0, H, HMIN, HMXI, HU, RC, TN, UROUND, + 2 IOWND(6), IOWNS(6), + 3 ICF, IERPJ, IERSL, JCUR, JSTART, KFLAG, L, + 4 LYH, LEWT, LACOR, LSAVF, LWM, LIWM, METH, MITER, + 5 MAXORD, MAXCOR, MSBP, MXNCF, N, NQ, NST, NFE, NJE, NQU + INTEGER I, IC, J, JB, JB2, JJ, JJ1, JP1 + DOUBLE PRECISION C, R, S, TP + CHARACTER*80 MSG +C +C***FIRST EXECUTABLE STATEMENT DINTDY + IFLAG = 0 + IF (K .LT. 0 .OR. K .GT. NQ) GO TO 80 + TP = TN - HU - 100.0D0*UROUND*SIGN(ABS(TN) + ABS(HU), HU) + IF ((T-TP)*(T-TN) .GT. 0.0D0) GO TO 90 +C + S = (T - TN)/H + IC = 1 + IF (K .EQ. 0) GO TO 15 + JJ1 = L - K + DO 10 JJ = JJ1,NQ + 10 IC = IC*JJ + 15 C = IC + DO 20 I = 1,N + 20 DKY(I) = C*YH(I,L) + IF (K .EQ. NQ) GO TO 55 + JB2 = NQ - K + DO 50 JB = 1,JB2 + J = NQ - JB + JP1 = J + 1 + IC = 1 + IF (K .EQ. 0) GO TO 35 + JJ1 = JP1 - K + DO 30 JJ = JJ1,J + 30 IC = IC*JJ + 35 C = IC + DO 40 I = 1,N + 40 DKY(I) = C*YH(I,JP1) + S*DKY(I) + 50 CONTINUE + IF (K .EQ. 0) RETURN + 55 R = H**(-K) + DO 60 I = 1,N + 60 DKY(I) = R*DKY(I) + RETURN +C + 80 MSG = 'DINTDY- K (=I1) illegal ' + CALL XERRWD (MSG, 30, 51, 0, 1, K, 0, 0, 0.0D0, 0.0D0) + IFLAG = -1 + RETURN + 90 MSG = 'DINTDY- T (=R1) illegal ' + CALL XERRWD (MSG, 30, 52, 0, 0, 0, 0, 1, T, 0.0D0) + MSG=' T not in interval TCUR - HU (= R1) to TCUR (=R2) ' + CALL XERRWD (MSG, 60, 52, 0, 0, 0, 0, 2, TP, TN) + IFLAG = -2 + RETURN +C----------------------- END OF SUBROUTINE DINTDY ---------------------- + END +*DECK DPREPJ + SUBROUTINE DPREPJ (NEQ, Y, YH, NYH, EWT, FTEM, SAVF, WM, IWM, + 1 F, JAC) +C***BEGIN PROLOGUE DPREPJ +C***SUBSIDIARY +C***PURPOSE Compute and process Newton iteration matrix. +C***TYPE DOUBLE PRECISION (SPREPJ-S, DPREPJ-D) +C***AUTHOR Hindmarsh, Alan C., (LLNL) +C***DESCRIPTION +C +C DPREPJ is called by DSTODE to compute and process the matrix +C P = I - h*el(1)*J , where J is an approximation to the Jacobian. +C Here J is computed by the user-supplied routine JAC if +C MITER = 1 or 4, or by finite differencing if MITER = 2, 3, or 5. +C If MITER = 3, a diagonal approximation to J is used. +C J is stored in WM and replaced by P. If MITER .ne. 3, P is then +C subjected to LU decomposition in preparation for later solution +C of linear systems with P as coefficient matrix. This is done +C by DGEFA if MITER = 1 or 2, and by DGBFA if MITER = 4 or 5. +C +C In addition to variables described in DSTODE and DLSODE prologues, +C communication with DPREPJ uses the following: +C Y = array containing predicted values on entry. +C FTEM = work array of length N (ACOR in DSTODE). +C SAVF = array containing f evaluated at predicted y. +C WM = real work space for matrices. On output it contains the +C inverse diagonal matrix if MITER = 3 and the LU decomposition +C of P if MITER is 1, 2 , 4, or 5. +C Storage of matrix elements starts at WM(3). +C WM also contains the following matrix-related data: +C WM(1) = SQRT(UROUND), used in numerical Jacobian increments. +C WM(2) = H*EL0, saved for later use if MITER = 3. +C IWM = integer work space containing pivot information, starting at +C IWM(21), if MITER is 1, 2, 4, or 5. IWM also contains band +C parameters ML = IWM(1) and MU = IWM(2) if MITER is 4 or 5. +C EL0 = EL(1) (input). +C IERPJ = output error flag, = 0 if no trouble, .gt. 0 if +C P matrix found to be singular. +C JCUR = output flag = 1 to indicate that the Jacobian matrix +C (or approximation) is now current. +C This routine also uses the COMMON variables EL0, H, TN, UROUND, +C MITER, N, NFE, and NJE. +C +C***SEE ALSO DLSODE +C***ROUTINES CALLED DGBFA, DGEFA, DVNORM +C***COMMON BLOCKS DLS001 +C***REVISION HISTORY (YYMMDD) +C 791129 DATE WRITTEN +C 890501 Modified prologue to SLATEC/LDOC format. (FNF) +C 890504 Minor cosmetic changes. (FNF) +C 930809 Renamed to allow single/double precision versions. (ACH) +C 010418 Reduced size of Common block /DLS001/. (ACH) +C 031105 Restored 'own' variables to Common block /DLS001/, to +C enable interrupt/restart feature. (ACH) +C***END PROLOGUE DPREPJ +C**End + EXTERNAL F, JAC + INTEGER NEQ, NYH, IWM + DOUBLE PRECISION Y, YH, EWT, FTEM, SAVF, WM + DIMENSION NEQ(*), Y(*), YH(NYH,*), EWT(*), FTEM(*), SAVF(*), + 1 WM(*), IWM(*) + INTEGER IOWND, IOWNS, + 1 ICF, IERPJ, IERSL, JCUR, JSTART, KFLAG, L, + 2 LYH, LEWT, LACOR, LSAVF, LWM, LIWM, METH, MITER, + 3 MAXORD, MAXCOR, MSBP, MXNCF, N, NQ, NST, NFE, NJE, NQU + DOUBLE PRECISION ROWNS, + 1 CCMAX, EL0, H, HMIN, HMXI, HU, RC, TN, UROUND + COMMON /DLS001/ ROWNS(209), + 1 CCMAX, EL0, H, HMIN, HMXI, HU, RC, TN, UROUND, + 2 IOWND(6), IOWNS(6), + 3 ICF, IERPJ, IERSL, JCUR, JSTART, KFLAG, L, + 4 LYH, LEWT, LACOR, LSAVF, LWM, LIWM, METH, MITER, + 5 MAXORD, MAXCOR, MSBP, MXNCF, N, NQ, NST, NFE, NJE, NQU + INTEGER I, I1, I2, IER, II, J, J1, JJ, LENP, + 1 MBA, MBAND, MEB1, MEBAND, ML, ML3, MU, NP1 + DOUBLE PRECISION CON, DI, FAC, HL0, R, R0, SRUR, YI, YJ, YJJ, + 1 DVNORM +C +C***FIRST EXECUTABLE STATEMENT DPREPJ + NJE = NJE + 1 + IERPJ = 0 + JCUR = 1 + HL0 = H*EL0 + GO TO (100, 200, 300, 400, 500), MITER +C If MITER = 1, call JAC and multiply by scalar. ----------------------- + 100 LENP = N*N + DO 110 I = 1,LENP + 110 WM(I+2) = 0.0D0 + CALL JAC (NEQ, TN, Y, 0, 0, WM(3), N) + CON = -HL0 + DO 120 I = 1,LENP + 120 WM(I+2) = WM(I+2)*CON + GO TO 240 +C If MITER = 2, make N calls to F to approximate J. -------------------- + 200 FAC = DVNORM (N, SAVF, EWT) + R0 = 1000.0D0*ABS(H)*UROUND*N*FAC + IF (R0 .EQ. 0.0D0) R0 = 1.0D0 + SRUR = WM(1) + J1 = 2 + DO 230 J = 1,N + YJ = Y(J) + R = MAX(SRUR*ABS(YJ),R0/EWT(J)) + Y(J) = Y(J) + R + FAC = -HL0/R + CALL F (NEQ, TN, Y, FTEM) + DO 220 I = 1,N + 220 WM(I+J1) = (FTEM(I) - SAVF(I))*FAC + Y(J) = YJ + J1 = J1 + N + 230 CONTINUE + NFE = NFE + N +C Add identity matrix. ------------------------------------------------- + 240 J = 3 + NP1 = N + 1 + DO 250 I = 1,N + WM(J) = WM(J) + 1.0D0 + 250 J = J + NP1 +C Do LU decomposition on P. -------------------------------------------- + CALL DGEFA (WM(3), N, N, IWM(21), IER) + IF (IER .NE. 0) IERPJ = 1 + RETURN +C If MITER = 3, construct a diagonal approximation to J and P. --------- + 300 WM(2) = HL0 + R = EL0*0.1D0 + DO 310 I = 1,N + 310 Y(I) = Y(I) + R*(H*SAVF(I) - YH(I,2)) + CALL F (NEQ, TN, Y, WM(3)) + NFE = NFE + 1 + DO 320 I = 1,N + R0 = H*SAVF(I) - YH(I,2) + DI = 0.1D0*R0 - H*(WM(I+2) - SAVF(I)) + WM(I+2) = 1.0D0 + IF (ABS(R0) .LT. UROUND/EWT(I)) GO TO 320 + IF (ABS(DI) .EQ. 0.0D0) GO TO 330 + WM(I+2) = 0.1D0*R0/DI + 320 CONTINUE + RETURN + 330 IERPJ = 1 + RETURN +C If MITER = 4, call JAC and multiply by scalar. ----------------------- + 400 ML = IWM(1) + MU = IWM(2) + ML3 = ML + 3 + MBAND = ML + MU + 1 + MEBAND = MBAND + ML + LENP = MEBAND*N + DO 410 I = 1,LENP + 410 WM(I+2) = 0.0D0 + CALL JAC (NEQ, TN, Y, ML, MU, WM(ML3), MEBAND) + CON = -HL0 + DO 420 I = 1,LENP + 420 WM(I+2) = WM(I+2)*CON + GO TO 570 +C If MITER = 5, make MBAND calls to F to approximate J. ---------------- + 500 ML = IWM(1) + MU = IWM(2) + MBAND = ML + MU + 1 + MBA = MIN(MBAND,N) + MEBAND = MBAND + ML + MEB1 = MEBAND - 1 + SRUR = WM(1) + FAC = DVNORM (N, SAVF, EWT) + R0 = 1000.0D0*ABS(H)*UROUND*N*FAC + IF (R0 .EQ. 0.0D0) R0 = 1.0D0 + DO 560 J = 1,MBA + DO 530 I = J,N,MBAND + YI = Y(I) + R = MAX(SRUR*ABS(YI),R0/EWT(I)) + 530 Y(I) = Y(I) + R + CALL F (NEQ, TN, Y, FTEM) + DO 550 JJ = J,N,MBAND + Y(JJ) = YH(JJ,1) + YJJ = Y(JJ) + R = MAX(SRUR*ABS(YJJ),R0/EWT(JJ)) + FAC = -HL0/R + I1 = MAX(JJ-MU,1) + I2 = MIN(JJ+ML,N) + II = JJ*MEB1 - ML + 2 + DO 540 I = I1,I2 + 540 WM(II+I) = (FTEM(I) - SAVF(I))*FAC + 550 CONTINUE + 560 CONTINUE + NFE = NFE + MBA +C Add identity matrix. ------------------------------------------------- + 570 II = MBAND + 2 + DO 580 I = 1,N + WM(II) = WM(II) + 1.0D0 + 580 II = II + MEBAND +C Do LU decomposition of P. -------------------------------------------- + CALL DGBFA (WM(3), MEBAND, N, ML, MU, IWM(21), IER) + IF (IER .NE. 0) IERPJ = 1 + RETURN +C----------------------- END OF SUBROUTINE DPREPJ ---------------------- + END +*DECK DSOLSY + SUBROUTINE DSOLSY (WM, IWM, X, TEM) +C***BEGIN PROLOGUE DSOLSY +C***SUBSIDIARY +C***PURPOSE ODEPACK linear system solver. +C***TYPE DOUBLE PRECISION (SSOLSY-S, DSOLSY-D) +C***AUTHOR Hindmarsh, Alan C., (LLNL) +C***DESCRIPTION +C +C This routine manages the solution of the linear system arising from +C a chord iteration. It is called if MITER .ne. 0. +C If MITER is 1 or 2, it calls DGESL to accomplish this. +C If MITER = 3 it updates the coefficient h*EL0 in the diagonal +C matrix, and then computes the solution. +C If MITER is 4 or 5, it calls DGBSL. +C Communication with DSOLSY uses the following variables: +C WM = real work space containing the inverse diagonal matrix if +C MITER = 3 and the LU decomposition of the matrix otherwise. +C Storage of matrix elements starts at WM(3). +C WM also contains the following matrix-related data: +C WM(1) = SQRT(UROUND) (not used here), +C WM(2) = HL0, the previous value of h*EL0, used if MITER = 3. +C IWM = integer work space containing pivot information, starting at +C IWM(21), if MITER is 1, 2, 4, or 5. IWM also contains band +C parameters ML = IWM(1) and MU = IWM(2) if MITER is 4 or 5. +C X = the right-hand side vector on input, and the solution vector +C on output, of length N. +C TEM = vector of work space of length N, not used in this version. +C IERSL = output flag (in COMMON). IERSL = 0 if no trouble occurred. +C IERSL = 1 if a singular matrix arose with MITER = 3. +C This routine also uses the COMMON variables EL0, H, MITER, and N. +C +C***SEE ALSO DLSODE +C***ROUTINES CALLED DGBSL, DGESL +C***COMMON BLOCKS DLS001 +C***REVISION HISTORY (YYMMDD) +C 791129 DATE WRITTEN +C 890501 Modified prologue to SLATEC/LDOC format. (FNF) +C 890503 Minor cosmetic changes. (FNF) +C 930809 Renamed to allow single/double precision versions. (ACH) +C 010418 Reduced size of Common block /DLS001/. (ACH) +C 031105 Restored 'own' variables to Common block /DLS001/, to +C enable interrupt/restart feature. (ACH) +C***END PROLOGUE DSOLSY +C**End + INTEGER IWM + DOUBLE PRECISION WM, X, TEM + DIMENSION WM(*), IWM(*), X(*), TEM(*) + INTEGER IOWND, IOWNS, + 1 ICF, IERPJ, IERSL, JCUR, JSTART, KFLAG, L, + 2 LYH, LEWT, LACOR, LSAVF, LWM, LIWM, METH, MITER, + 3 MAXORD, MAXCOR, MSBP, MXNCF, N, NQ, NST, NFE, NJE, NQU + DOUBLE PRECISION ROWNS, + 1 CCMAX, EL0, H, HMIN, HMXI, HU, RC, TN, UROUND + COMMON /DLS001/ ROWNS(209), + 1 CCMAX, EL0, H, HMIN, HMXI, HU, RC, TN, UROUND, + 2 IOWND(6), IOWNS(6), + 3 ICF, IERPJ, IERSL, JCUR, JSTART, KFLAG, L, + 4 LYH, LEWT, LACOR, LSAVF, LWM, LIWM, METH, MITER, + 5 MAXORD, MAXCOR, MSBP, MXNCF, N, NQ, NST, NFE, NJE, NQU + INTEGER I, MEBAND, ML, MU + DOUBLE PRECISION DI, HL0, PHL0, R +C +C***FIRST EXECUTABLE STATEMENT DSOLSY + IERSL = 0 + GO TO (100, 100, 300, 400, 400), MITER + 100 CALL DGESL (WM(3), N, N, IWM(21), X, 0) + RETURN +C + 300 PHL0 = WM(2) + HL0 = H*EL0 + WM(2) = HL0 + IF (HL0 .EQ. PHL0) GO TO 330 + R = HL0/PHL0 + DO 320 I = 1,N + DI = 1.0D0 - R*(1.0D0 - 1.0D0/WM(I+2)) + IF (ABS(DI) .EQ. 0.0D0) GO TO 390 + 320 WM(I+2) = 1.0D0/DI + 330 DO 340 I = 1,N + 340 X(I) = WM(I+2)*X(I) + RETURN + 390 IERSL = 1 + RETURN +C + 400 ML = IWM(1) + MU = IWM(2) + MEBAND = 2*ML + MU + 1 + CALL DGBSL (WM(3), MEBAND, N, ML, MU, IWM(21), X, 0) + RETURN +C----------------------- END OF SUBROUTINE DSOLSY ---------------------- + END +*DECK DSRCOM + SUBROUTINE DSRCOM (RSAV, ISAV, JOB) +C***BEGIN PROLOGUE DSRCOM +C***SUBSIDIARY +C***PURPOSE Save/restore ODEPACK COMMON blocks. +C***TYPE DOUBLE PRECISION (SSRCOM-S, DSRCOM-D) +C***AUTHOR Hindmarsh, Alan C., (LLNL) +C***DESCRIPTION +C +C This routine saves or restores (depending on JOB) the contents of +C the COMMON block DLS001, which is used internally +C by one or more ODEPACK solvers. +C +C RSAV = real array of length 218 or more. +C ISAV = integer array of length 37 or more. +C JOB = flag indicating to save or restore the COMMON blocks: +C JOB = 1 if COMMON is to be saved (written to RSAV/ISAV) +C JOB = 2 if COMMON is to be restored (read from RSAV/ISAV) +C A call with JOB = 2 presumes a prior call with JOB = 1. +C +C***SEE ALSO DLSODE +C***ROUTINES CALLED (NONE) +C***COMMON BLOCKS DLS001 +C***REVISION HISTORY (YYMMDD) +C 791129 DATE WRITTEN +C 890501 Modified prologue to SLATEC/LDOC format. (FNF) +C 890503 Minor cosmetic changes. (FNF) +C 921116 Deleted treatment of block /EH0001/. (ACH) +C 930801 Reduced Common block length by 2. (ACH) +C 930809 Renamed to allow single/double precision versions. (ACH) +C 010418 Reduced Common block length by 209+12. (ACH) +C 031105 Restored 'own' variables to Common block /DLS001/, to +C enable interrupt/restart feature. (ACH) +C 031112 Added SAVE statement for data-loaded constants. +C***END PROLOGUE DSRCOM +C**End + INTEGER ISAV, JOB + INTEGER ILS + INTEGER I, LENILS, LENRLS + DOUBLE PRECISION RSAV, RLS + DIMENSION RSAV(*), ISAV(*) + SAVE LENRLS, LENILS + COMMON /DLS001/ RLS(218), ILS(37) + DATA LENRLS/218/, LENILS/37/ +C +C***FIRST EXECUTABLE STATEMENT DSRCOM + IF (JOB .EQ. 2) GO TO 100 +C + DO 10 I = 1,LENRLS + 10 RSAV(I) = RLS(I) + DO 20 I = 1,LENILS + 20 ISAV(I) = ILS(I) + RETURN +C + 100 CONTINUE + DO 110 I = 1,LENRLS + 110 RLS(I) = RSAV(I) + DO 120 I = 1,LENILS + 120 ILS(I) = ISAV(I) + RETURN +C----------------------- END OF SUBROUTINE DSRCOM ---------------------- + END +*DECK DSTODE + SUBROUTINE DSTODE (NEQ, Y, YH, NYH, YH1, EWT, SAVF, ACOR, + 1 WM, IWM, F, JAC, PJAC, SLVS) +C***BEGIN PROLOGUE DSTODE +C***SUBSIDIARY +C***PURPOSE Performs one step of an ODEPACK integration. +C***TYPE DOUBLE PRECISION (SSTODE-S, DSTODE-D) +C***AUTHOR Hindmarsh, Alan C., (LLNL) +C***DESCRIPTION +C +C DSTODE performs one step of the integration of an initial value +C problem for a system of ordinary differential equations. +C Note: DSTODE is independent of the value of the iteration method +C indicator MITER, when this is .ne. 0, and hence is independent +C of the type of chord method used, or the Jacobian structure. +C Communication with DSTODE is done with the following variables: +C +C NEQ = integer array containing problem size in NEQ(1), and +C passed as the NEQ argument in all calls to F and JAC. +C Y = an array of length .ge. N used as the Y argument in +C all calls to F and JAC. +C YH = an NYH by LMAX array containing the dependent variables +C and their approximate scaled derivatives, where +C LMAX = MAXORD + 1. YH(i,j+1) contains the approximate +C j-th derivative of y(i), scaled by h**j/factorial(j) +C (j = 0,1,...,NQ). on entry for the first step, the first +C two columns of YH must be set from the initial values. +C NYH = a constant integer .ge. N, the first dimension of YH. +C YH1 = a one-dimensional array occupying the same space as YH. +C EWT = an array of length N containing multiplicative weights +C for local error measurements. Local errors in Y(i) are +C compared to 1.0/EWT(i) in various error tests. +C SAVF = an array of working storage, of length N. +C Also used for input of YH(*,MAXORD+2) when JSTART = -1 +C and MAXORD .lt. the current order NQ. +C ACOR = a work array of length N, used for the accumulated +C corrections. On a successful return, ACOR(i) contains +C the estimated one-step local error in Y(i). +C WM,IWM = real and integer work arrays associated with matrix +C operations in chord iteration (MITER .ne. 0). +C PJAC = name of routine to evaluate and preprocess Jacobian matrix +C and P = I - h*el0*JAC, if a chord method is being used. +C SLVS = name of routine to solve linear system in chord iteration. +C CCMAX = maximum relative change in h*el0 before PJAC is called. +C H = the step size to be attempted on the next step. +C H is altered by the error control algorithm during the +C problem. H can be either positive or negative, but its +C sign must remain constant throughout the problem. +C HMIN = the minimum absolute value of the step size h to be used. +C HMXI = inverse of the maximum absolute value of h to be used. +C HMXI = 0.0 is allowed and corresponds to an infinite hmax. +C HMIN and HMXI may be changed at any time, but will not +C take effect until the next change of h is considered. +C TN = the independent variable. TN is updated on each step taken. +C JSTART = an integer used for input only, with the following +C values and meanings: +C 0 perform the first step. +C .gt.0 take a new step continuing from the last. +C -1 take the next step with a new value of H, MAXORD, +C N, METH, MITER, and/or matrix parameters. +C -2 take the next step with a new value of H, +C but with other inputs unchanged. +C On return, JSTART is set to 1 to facilitate continuation. +C KFLAG = a completion code with the following meanings: +C 0 the step was succesful. +C -1 the requested error could not be achieved. +C -2 corrector convergence could not be achieved. +C -3 fatal error in PJAC or SLVS. +C A return with KFLAG = -1 or -2 means either +C abs(H) = HMIN or 10 consecutive failures occurred. +C On a return with KFLAG negative, the values of TN and +C the YH array are as of the beginning of the last +C step, and H is the last step size attempted. +C MAXORD = the maximum order of integration method to be allowed. +C MAXCOR = the maximum number of corrector iterations allowed. +C MSBP = maximum number of steps between PJAC calls (MITER .gt. 0). +C MXNCF = maximum number of convergence failures allowed. +C METH/MITER = the method flags. See description in driver. +C N = the number of first-order differential equations. +C The values of CCMAX, H, HMIN, HMXI, TN, JSTART, KFLAG, MAXORD, +C MAXCOR, MSBP, MXNCF, METH, MITER, and N are communicated via COMMON. +C +C***SEE ALSO DLSODE +C***ROUTINES CALLED DCFODE, DVNORM +C***COMMON BLOCKS DLS001 +C***REVISION HISTORY (YYMMDD) +C 791129 DATE WRITTEN +C 890501 Modified prologue to SLATEC/LDOC format. (FNF) +C 890503 Minor cosmetic changes. (FNF) +C 930809 Renamed to allow single/double precision versions. (ACH) +C 010418 Reduced size of Common block /DLS001/. (ACH) +C 031105 Restored 'own' variables to Common block /DLS001/, to +C enable interrupt/restart feature. (ACH) +C***END PROLOGUE DSTODE +C**End + EXTERNAL F, JAC, PJAC, SLVS + INTEGER NEQ, NYH, IWM + DOUBLE PRECISION Y, YH, YH1, EWT, SAVF, ACOR, WM + DIMENSION NEQ(*), Y(*), YH(NYH,*), YH1(*), EWT(*), SAVF(*), + 1 ACOR(*), WM(*), IWM(*) + INTEGER IOWND, IALTH, IPUP, LMAX, MEO, NQNYH, NSLP, + 1 ICF, IERPJ, IERSL, JCUR, JSTART, KFLAG, L, + 2 LYH, LEWT, LACOR, LSAVF, LWM, LIWM, METH, MITER, + 3 MAXORD, MAXCOR, MSBP, MXNCF, N, NQ, NST, NFE, NJE, NQU + INTEGER I, I1, IREDO, IRET, J, JB, M, NCF, NEWQ + DOUBLE PRECISION CONIT, CRATE, EL, ELCO, HOLD, RMAX, TESCO, + 2 CCMAX, EL0, H, HMIN, HMXI, HU, RC, TN, UROUND + DOUBLE PRECISION DCON, DDN, DEL, DELP, DSM, DUP, EXDN, EXSM, EXUP, + 1 R, RH, RHDN, RHSM, RHUP, TOLD, DVNORM + COMMON /DLS001/ CONIT, CRATE, EL(13), ELCO(13,12), + 1 HOLD, RMAX, TESCO(3,12), + 2 CCMAX, EL0, H, HMIN, HMXI, HU, RC, TN, UROUND, + 3 IOWND(6), IALTH, IPUP, LMAX, MEO, NQNYH, NSLP, + 3 ICF, IERPJ, IERSL, JCUR, JSTART, KFLAG, L, + 4 LYH, LEWT, LACOR, LSAVF, LWM, LIWM, METH, MITER, + 5 MAXORD, MAXCOR, MSBP, MXNCF, N, NQ, NST, NFE, NJE, NQU +C +C***FIRST EXECUTABLE STATEMENT DSTODE + KFLAG = 0 + TOLD = TN + NCF = 0 + IERPJ = 0 + IERSL = 0 + JCUR = 0 + ICF = 0 + DELP = 0.0D0 + IF (JSTART .GT. 0) GO TO 200 + IF (JSTART .EQ. -1) GO TO 100 + IF (JSTART .EQ. -2) GO TO 160 +C----------------------------------------------------------------------- +C On the first call, the order is set to 1, and other variables are +C initialized. RMAX is the maximum ratio by which H can be increased +C in a single step. It is initially 1.E4 to compensate for the small +C initial H, but then is normally equal to 10. If a failure +C occurs (in corrector convergence or error test), RMAX is set to 2 +C for the next increase. +C----------------------------------------------------------------------- + LMAX = MAXORD + 1 + NQ = 1 + L = 2 + IALTH = 2 + RMAX = 10000.0D0 + RC = 0.0D0 + EL0 = 1.0D0 + CRATE = 0.7D0 + HOLD = H + MEO = METH + NSLP = 0 + IPUP = MITER + IRET = 3 + GO TO 140 +C----------------------------------------------------------------------- +C The following block handles preliminaries needed when JSTART = -1. +C IPUP is set to MITER to force a matrix update. +C If an order increase is about to be considered (IALTH = 1), +C IALTH is reset to 2 to postpone consideration one more step. +C If the caller has changed METH, DCFODE is called to reset +C the coefficients of the method. +C If the caller has changed MAXORD to a value less than the current +C order NQ, NQ is reduced to MAXORD, and a new H chosen accordingly. +C If H is to be changed, YH must be rescaled. +C If H or METH is being changed, IALTH is reset to L = NQ + 1 +C to prevent further changes in H for that many steps. +C----------------------------------------------------------------------- + 100 IPUP = MITER + LMAX = MAXORD + 1 + IF (IALTH .EQ. 1) IALTH = 2 + IF (METH .EQ. MEO) GO TO 110 + CALL DCFODE (METH, ELCO, TESCO) + MEO = METH + IF (NQ .GT. MAXORD) GO TO 120 + IALTH = L + IRET = 1 + GO TO 150 + 110 IF (NQ .LE. MAXORD) GO TO 160 + 120 NQ = MAXORD + L = LMAX + DO 125 I = 1,L + 125 EL(I) = ELCO(I,NQ) + NQNYH = NQ*NYH + RC = RC*EL(1)/EL0 + EL0 = EL(1) + CONIT = 0.5D0/(NQ+2) + DDN = DVNORM (N, SAVF, EWT)/TESCO(1,L) + EXDN = 1.0D0/L + RHDN = 1.0D0/(1.3D0*DDN**EXDN + 0.0000013D0) + RH = MIN(RHDN,1.0D0) + IREDO = 3 + IF (H .EQ. HOLD) GO TO 170 + RH = MIN(RH,ABS(H/HOLD)) + H = HOLD + GO TO 175 +C----------------------------------------------------------------------- +C DCFODE is called to get all the integration coefficients for the +C current METH. Then the EL vector and related constants are reset +C whenever the order NQ is changed, or at the start of the problem. +C----------------------------------------------------------------------- + 140 CALL DCFODE (METH, ELCO, TESCO) + 150 DO 155 I = 1,L + 155 EL(I) = ELCO(I,NQ) + NQNYH = NQ*NYH + RC = RC*EL(1)/EL0 + EL0 = EL(1) + CONIT = 0.5D0/(NQ+2) + GO TO (160, 170, 200), IRET +C----------------------------------------------------------------------- +C If H is being changed, the H ratio RH is checked against +C RMAX, HMIN, and HMXI, and the YH array rescaled. IALTH is set to +C L = NQ + 1 to prevent a change of H for that many steps, unless +C forced by a convergence or error test failure. +C----------------------------------------------------------------------- + 160 IF (H .EQ. HOLD) GO TO 200 + RH = H/HOLD + H = HOLD + IREDO = 3 + GO TO 175 + 170 RH = MAX(RH,HMIN/ABS(H)) + 175 RH = MIN(RH,RMAX) + RH = RH/MAX(1.0D0,ABS(H)*HMXI*RH) + R = 1.0D0 + DO 180 J = 2,L + R = R*RH + DO 180 I = 1,N + 180 YH(I,J) = YH(I,J)*R + H = H*RH + RC = RC*RH + IALTH = L + IF (IREDO .EQ. 0) GO TO 690 +C----------------------------------------------------------------------- +C This section computes the predicted values by effectively +C multiplying the YH array by the Pascal Triangle matrix. +C RC is the ratio of new to old values of the coefficient H*EL(1). +C When RC differs from 1 by more than CCMAX, IPUP is set to MITER +C to force PJAC to be called, if a Jacobian is involved. +C In any case, PJAC is called at least every MSBP steps. +C----------------------------------------------------------------------- + 200 IF (ABS(RC-1.0D0) .GT. CCMAX) IPUP = MITER + IF (NST .GE. NSLP+MSBP) IPUP = MITER + TN = TN + H + I1 = NQNYH + 1 + DO 215 JB = 1,NQ + I1 = I1 - NYH +Cdir$ ivdep + DO 210 I = I1,NQNYH + 210 YH1(I) = YH1(I) + YH1(I+NYH) + 215 CONTINUE +C----------------------------------------------------------------------- +C Up to MAXCOR corrector iterations are taken. A convergence test is +C made on the R.M.S. norm of each correction, weighted by the error +C weight vector EWT. The sum of the corrections is accumulated in the +C vector ACOR(i). The YH array is not altered in the corrector loop. +C----------------------------------------------------------------------- + 220 M = 0 + DO 230 I = 1,N + 230 Y(I) = YH(I,1) + CALL F (NEQ, TN, Y, SAVF) + NFE = NFE + 1 + IF (IPUP .LE. 0) GO TO 250 +C----------------------------------------------------------------------- +C If indicated, the matrix P = I - h*el(1)*J is reevaluated and +C preprocessed before starting the corrector iteration. IPUP is set +C to 0 as an indicator that this has been done. +C----------------------------------------------------------------------- + CALL PJAC (NEQ, Y, YH, NYH, EWT, ACOR, SAVF, WM, IWM, F, JAC) + IPUP = 0 + RC = 1.0D0 + NSLP = NST + CRATE = 0.7D0 + IF (IERPJ .NE. 0) GO TO 430 + 250 DO 260 I = 1,N + 260 ACOR(I) = 0.0D0 + 270 IF (MITER .NE. 0) GO TO 350 +C----------------------------------------------------------------------- +C In the case of functional iteration, update Y directly from +C the result of the last function evaluation. +C----------------------------------------------------------------------- + DO 290 I = 1,N + SAVF(I) = H*SAVF(I) - YH(I,2) + 290 Y(I) = SAVF(I) - ACOR(I) + DEL = DVNORM (N, Y, EWT) + DO 300 I = 1,N + Y(I) = YH(I,1) + EL(1)*SAVF(I) + 300 ACOR(I) = SAVF(I) + GO TO 400 +C----------------------------------------------------------------------- +C In the case of the chord method, compute the corrector error, +C and solve the linear system with that as right-hand side and +C P as coefficient matrix. +C----------------------------------------------------------------------- + 350 DO 360 I = 1,N + 360 Y(I) = H*SAVF(I) - (YH(I,2) + ACOR(I)) + CALL SLVS (WM, IWM, Y, SAVF) + IF (IERSL .LT. 0) GO TO 430 + IF (IERSL .GT. 0) GO TO 410 + DEL = DVNORM (N, Y, EWT) + DO 380 I = 1,N + ACOR(I) = ACOR(I) + Y(I) + 380 Y(I) = YH(I,1) + EL(1)*ACOR(I) +C----------------------------------------------------------------------- +C Test for convergence. If M.gt.0, an estimate of the convergence +C rate constant is stored in CRATE, and this is used in the test. +C----------------------------------------------------------------------- + 400 IF (M .NE. 0) CRATE = MAX(0.2D0*CRATE,DEL/DELP) + DCON = DEL*MIN(1.0D0,1.5D0*CRATE)/(TESCO(2,NQ)*CONIT) + IF (DCON .LE. 1.0D0) GO TO 450 + M = M + 1 + IF (M .EQ. MAXCOR) GO TO 410 + IF (M .GE. 2 .AND. DEL .GT. 2.0D0*DELP) GO TO 410 + DELP = DEL + CALL F (NEQ, TN, Y, SAVF) + NFE = NFE + 1 + GO TO 270 +C----------------------------------------------------------------------- +C The corrector iteration failed to converge. +C If MITER .ne. 0 and the Jacobian is out of date, PJAC is called for +C the next try. Otherwise the YH array is retracted to its values +C before prediction, and H is reduced, if possible. If H cannot be +C reduced or MXNCF failures have occurred, exit with KFLAG = -2. +C----------------------------------------------------------------------- + 410 IF (MITER .EQ. 0 .OR. JCUR .EQ. 1) GO TO 430 + ICF = 1 + IPUP = MITER + GO TO 220 + 430 ICF = 2 + NCF = NCF + 1 + RMAX = 2.0D0 + TN = TOLD + I1 = NQNYH + 1 + DO 445 JB = 1,NQ + I1 = I1 - NYH +Cdir$ ivdep + DO 440 I = I1,NQNYH + 440 YH1(I) = YH1(I) - YH1(I+NYH) + 445 CONTINUE + IF (IERPJ .LT. 0 .OR. IERSL .LT. 0) GO TO 680 + IF (ABS(H) .LE. HMIN*1.00001D0) GO TO 670 + IF (NCF .EQ. MXNCF) GO TO 670 + RH = 0.25D0 + IPUP = MITER + IREDO = 1 + GO TO 170 +C----------------------------------------------------------------------- +C The corrector has converged. JCUR is set to 0 +C to signal that the Jacobian involved may need updating later. +C The local error test is made and control passes to statement 500 +C if it fails. +C----------------------------------------------------------------------- + 450 JCUR = 0 + IF (M .EQ. 0) DSM = DEL/TESCO(2,NQ) + IF (M .GT. 0) DSM = DVNORM (N, ACOR, EWT)/TESCO(2,NQ) + IF (DSM .GT. 1.0D0) GO TO 500 +C----------------------------------------------------------------------- +C After a successful step, update the YH array. +C Consider changing H if IALTH = 1. Otherwise decrease IALTH by 1. +C If IALTH is then 1 and NQ .lt. MAXORD, then ACOR is saved for +C use in a possible order increase on the next step. +C If a change in H is considered, an increase or decrease in order +C by one is considered also. A change in H is made only if it is by a +C factor of at least 1.1. If not, IALTH is set to 3 to prevent +C testing for that many steps. +C----------------------------------------------------------------------- + KFLAG = 0 + IREDO = 0 + NST = NST + 1 + HU = H + NQU = NQ + DO 470 J = 1,L + DO 470 I = 1,N + 470 YH(I,J) = YH(I,J) + EL(J)*ACOR(I) + IALTH = IALTH - 1 + IF (IALTH .EQ. 0) GO TO 520 + IF (IALTH .GT. 1) GO TO 700 + IF (L .EQ. LMAX) GO TO 700 + DO 490 I = 1,N + 490 YH(I,LMAX) = ACOR(I) + GO TO 700 +C----------------------------------------------------------------------- +C The error test failed. KFLAG keeps track of multiple failures. +C Restore TN and the YH array to their previous values, and prepare +C to try the step again. Compute the optimum step size for this or +C one lower order. After 2 or more failures, H is forced to decrease +C by a factor of 0.2 or less. +C----------------------------------------------------------------------- + 500 KFLAG = KFLAG - 1 + TN = TOLD + I1 = NQNYH + 1 + DO 515 JB = 1,NQ + I1 = I1 - NYH +Cdir$ ivdep + DO 510 I = I1,NQNYH + 510 YH1(I) = YH1(I) - YH1(I+NYH) + 515 CONTINUE + RMAX = 2.0D0 + IF (ABS(H) .LE. HMIN*1.00001D0) GO TO 660 + IF (KFLAG .LE. -3) GO TO 640 + IREDO = 2 + RHUP = 0.0D0 + GO TO 540 +C----------------------------------------------------------------------- +C Regardless of the success or failure of the step, factors +C RHDN, RHSM, and RHUP are computed, by which H could be multiplied +C at order NQ - 1, order NQ, or order NQ + 1, respectively. +C In the case of failure, RHUP = 0.0 to avoid an order increase. +C The largest of these is determined and the new order chosen +C accordingly. If the order is to be increased, we compute one +C additional scaled derivative. +C----------------------------------------------------------------------- + 520 RHUP = 0.0D0 + IF (L .EQ. LMAX) GO TO 540 + DO 530 I = 1,N + 530 SAVF(I) = ACOR(I) - YH(I,LMAX) + DUP = DVNORM (N, SAVF, EWT)/TESCO(3,NQ) + EXUP = 1.0D0/(L+1) + RHUP = 1.0D0/(1.4D0*DUP**EXUP + 0.0000014D0) + 540 EXSM = 1.0D0/L + RHSM = 1.0D0/(1.2D0*DSM**EXSM + 0.0000012D0) + RHDN = 0.0D0 + IF (NQ .EQ. 1) GO TO 560 + DDN = DVNORM (N, YH(1,L), EWT)/TESCO(1,NQ) + EXDN = 1.0D0/NQ + RHDN = 1.0D0/(1.3D0*DDN**EXDN + 0.0000013D0) + 560 IF (RHSM .GE. RHUP) GO TO 570 + IF (RHUP .GT. RHDN) GO TO 590 + GO TO 580 + 570 IF (RHSM .LT. RHDN) GO TO 580 + NEWQ = NQ + RH = RHSM + GO TO 620 + 580 NEWQ = NQ - 1 + RH = RHDN + IF (KFLAG .LT. 0 .AND. RH .GT. 1.0D0) RH = 1.0D0 + GO TO 620 + 590 NEWQ = L + RH = RHUP + IF (RH .LT. 1.1D0) GO TO 610 + R = EL(L)/L + DO 600 I = 1,N + 600 YH(I,NEWQ+1) = ACOR(I)*R + GO TO 630 + 610 IALTH = 3 + GO TO 700 + 620 IF ((KFLAG .EQ. 0) .AND. (RH .LT. 1.1D0)) GO TO 610 + IF (KFLAG .LE. -2) RH = MIN(RH,0.2D0) +C----------------------------------------------------------------------- +C If there is a change of order, reset NQ, l, and the coefficients. +C In any case H is reset according to RH and the YH array is rescaled. +C Then exit from 690 if the step was OK, or redo the step otherwise. +C----------------------------------------------------------------------- + IF (NEWQ .EQ. NQ) GO TO 170 + 630 NQ = NEWQ + L = NQ + 1 + IRET = 2 + GO TO 150 +C----------------------------------------------------------------------- +C Control reaches this section if 3 or more failures have occured. +C If 10 failures have occurred, exit with KFLAG = -1. +C It is assumed that the derivatives that have accumulated in the +C YH array have errors of the wrong order. Hence the first +C derivative is recomputed, and the order is set to 1. Then +C H is reduced by a factor of 10, and the step is retried, +C until it succeeds or H reaches HMIN. +C----------------------------------------------------------------------- + 640 IF (KFLAG .EQ. -10) GO TO 660 + RH = 0.1D0 + RH = MAX(HMIN/ABS(H),RH) + H = H*RH + DO 645 I = 1,N + 645 Y(I) = YH(I,1) + CALL F (NEQ, TN, Y, SAVF) + NFE = NFE + 1 + DO 650 I = 1,N + 650 YH(I,2) = H*SAVF(I) + IPUP = MITER + IALTH = 5 + IF (NQ .EQ. 1) GO TO 200 + NQ = 1 + L = 2 + IRET = 3 + GO TO 150 +C----------------------------------------------------------------------- +C All returns are made through this section. H is saved in HOLD +C to allow the caller to change H on the next step. +C----------------------------------------------------------------------- + 660 KFLAG = -1 + GO TO 720 + 670 KFLAG = -2 + GO TO 720 + 680 KFLAG = -3 + GO TO 720 + 690 RMAX = 10.0D0 + 700 R = 1.0D0/TESCO(2,NQU) + DO 710 I = 1,N + 710 ACOR(I) = ACOR(I)*R + 720 HOLD = H + JSTART = 1 + RETURN +C----------------------- END OF SUBROUTINE DSTODE ---------------------- + END +*DECK DEWSET + SUBROUTINE DEWSET (N, ITOL, RTOL, ATOL, YCUR, EWT) +C***BEGIN PROLOGUE DEWSET +C***SUBSIDIARY +C***PURPOSE Set error weight vector. +C***TYPE DOUBLE PRECISION (SEWSET-S, DEWSET-D) +C***AUTHOR Hindmarsh, Alan C., (LLNL) +C***DESCRIPTION +C +C This subroutine sets the error weight vector EWT according to +C EWT(i) = RTOL(i)*ABS(YCUR(i)) + ATOL(i), i = 1,...,N, +C with the subscript on RTOL and/or ATOL possibly replaced by 1 above, +C depending on the value of ITOL. +C +C***SEE ALSO DLSODE +C***ROUTINES CALLED (NONE) +C***REVISION HISTORY (YYMMDD) +C 791129 DATE WRITTEN +C 890501 Modified prologue to SLATEC/LDOC format. (FNF) +C 890503 Minor cosmetic changes. (FNF) +C 930809 Renamed to allow single/double precision versions. (ACH) +C***END PROLOGUE DEWSET +C**End + INTEGER N, ITOL + INTEGER I + DOUBLE PRECISION RTOL, ATOL, YCUR, EWT + DIMENSION RTOL(*), ATOL(*), YCUR(N), EWT(N) +C +C***FIRST EXECUTABLE STATEMENT DEWSET + GO TO (10, 20, 30, 40), ITOL + 10 CONTINUE + DO 15 I = 1,N + 15 EWT(I) = RTOL(1)*ABS(YCUR(I)) + ATOL(1) + RETURN + 20 CONTINUE + DO 25 I = 1,N + 25 EWT(I) = RTOL(1)*ABS(YCUR(I)) + ATOL(I) + RETURN + 30 CONTINUE + DO 35 I = 1,N + 35 EWT(I) = RTOL(I)*ABS(YCUR(I)) + ATOL(1) + RETURN + 40 CONTINUE + DO 45 I = 1,N + 45 EWT(I) = RTOL(I)*ABS(YCUR(I)) + ATOL(I) + RETURN +C----------------------- END OF SUBROUTINE DEWSET ---------------------- + END +*DECK DVNORM + DOUBLE PRECISION FUNCTION DVNORM (N, V, W) +C***BEGIN PROLOGUE DVNORM +C***SUBSIDIARY +C***PURPOSE Weighted root-mean-square vector norm. +C***TYPE DOUBLE PRECISION (SVNORM-S, DVNORM-D) +C***AUTHOR Hindmarsh, Alan C., (LLNL) +C***DESCRIPTION +C +C This function routine computes the weighted root-mean-square norm +C of the vector of length N contained in the array V, with weights +C contained in the array W of length N: +C DVNORM = SQRT( (1/N) * SUM( V(i)*W(i) )**2 ) +C +C***SEE ALSO DLSODE +C***ROUTINES CALLED (NONE) +C***REVISION HISTORY (YYMMDD) +C 791129 DATE WRITTEN +C 890501 Modified prologue to SLATEC/LDOC format. (FNF) +C 890503 Minor cosmetic changes. (FNF) +C 930809 Renamed to allow single/double precision versions. (ACH) +C***END PROLOGUE DVNORM +C**End + INTEGER N, I + DOUBLE PRECISION V, W, SUM + DIMENSION V(N), W(N) +C +C***FIRST EXECUTABLE STATEMENT DVNORM + SUM = 0.0D0 + DO 10 I = 1,N + 10 SUM = SUM + (V(I)*W(I))**2 + DVNORM = SQRT(SUM/N) + RETURN +C----------------------- END OF FUNCTION DVNORM ------------------------ + END +*DECK DIPREP + SUBROUTINE DIPREP (NEQ, Y, RWORK, IA, JA, IPFLAG, F, JAC) + EXTERNAL F, JAC + INTEGER NEQ, IA, JA, IPFLAG + DOUBLE PRECISION Y, RWORK + DIMENSION NEQ(*), Y(*), RWORK(*), IA(*), JA(*) + INTEGER IOWND, IOWNS, + 1 ICF, IERPJ, IERSL, JCUR, JSTART, KFLAG, L, + 2 LYH, LEWT, LACOR, LSAVF, LWM, LIWM, METH, MITER, + 3 MAXORD, MAXCOR, MSBP, MXNCF, N, NQ, NST, NFE, NJE, NQU + INTEGER IPLOST, IESP, ISTATC, IYS, IBA, IBIAN, IBJAN, IBJGP, + 1 IPIAN, IPJAN, IPJGP, IPIGP, IPR, IPC, IPIC, IPISP, IPRSP, IPA, + 2 LENYH, LENYHM, LENWK, LREQ, LRAT, LREST, LWMIN, MOSS, MSBJ, + 3 NSLJ, NGP, NLU, NNZ, NSP, NZL, NZU + DOUBLE PRECISION ROWNS, + 1 CCMAX, EL0, H, HMIN, HMXI, HU, RC, TN, UROUND + DOUBLE PRECISION RLSS + COMMON /DLS001/ ROWNS(209), + 1 CCMAX, EL0, H, HMIN, HMXI, HU, RC, TN, UROUND, + 2 IOWND(6), IOWNS(6), + 3 ICF, IERPJ, IERSL, JCUR, JSTART, KFLAG, L, + 4 LYH, LEWT, LACOR, LSAVF, LWM, LIWM, METH, MITER, + 5 MAXORD, MAXCOR, MSBP, MXNCF, N, NQ, NST, NFE, NJE, NQU + COMMON /DLSS01/ RLSS(6), + 1 IPLOST, IESP, ISTATC, IYS, IBA, IBIAN, IBJAN, IBJGP, + 2 IPIAN, IPJAN, IPJGP, IPIGP, IPR, IPC, IPIC, IPISP, IPRSP, IPA, + 3 LENYH, LENYHM, LENWK, LREQ, LRAT, LREST, LWMIN, MOSS, MSBJ, + 4 NSLJ, NGP, NLU, NNZ, NSP, NZL, NZU + INTEGER I, IMAX, LEWTN, LYHD, LYHN +C----------------------------------------------------------------------- +C This routine serves as an interface between the driver and +C Subroutine DPREP. It is called only if MITER is 1 or 2. +C Tasks performed here are: +C * call DPREP, +C * reset the required WM segment length LENWK, +C * move YH back to its final location (following WM in RWORK), +C * reset pointers for YH, SAVF, EWT, and ACOR, and +C * move EWT to its new position if ISTATE = 1. +C IPFLAG is an output error indication flag. IPFLAG = 0 if there was +C no trouble, and IPFLAG is the value of the DPREP error flag IPPER +C if there was trouble in Subroutine DPREP. +C----------------------------------------------------------------------- + IPFLAG = 0 +C Call DPREP to do matrix preprocessing operations. -------------------- + CALL DPREP (NEQ, Y, RWORK(LYH), RWORK(LSAVF), RWORK(LEWT), + 1 RWORK(LACOR), IA, JA, RWORK(LWM), RWORK(LWM), IPFLAG, F, JAC) + LENWK = MAX(LREQ,LWMIN) + IF (IPFLAG .LT. 0) RETURN +C If DPREP was successful, move YH to end of required space for WM. ---- + LYHN = LWM + LENWK + IF (LYHN .GT. LYH) RETURN + LYHD = LYH - LYHN + IF (LYHD .EQ. 0) GO TO 20 + IMAX = LYHN - 1 + LENYHM + DO 10 I = LYHN,IMAX + 10 RWORK(I) = RWORK(I+LYHD) + LYH = LYHN +C Reset pointers for SAVF, EWT, and ACOR. ------------------------------ + 20 LSAVF = LYH + LENYH + LEWTN = LSAVF + N + LACOR = LEWTN + N + IF (ISTATC .EQ. 3) GO TO 40 +C If ISTATE = 1, move EWT (left) to its new position. ------------------ + IF (LEWTN .GT. LEWT) RETURN + DO 30 I = 1,N + 30 RWORK(I+LEWTN-1) = RWORK(I+LEWT-1) + 40 LEWT = LEWTN + RETURN +C----------------------- End of Subroutine DIPREP ---------------------- + END +*DECK DPREP + SUBROUTINE DPREP (NEQ, Y, YH, SAVF, EWT, FTEM, IA, JA, + 1 WK, IWK, IPPER, F, JAC) + EXTERNAL F,JAC + INTEGER NEQ, IA, JA, IWK, IPPER + DOUBLE PRECISION Y, YH, SAVF, EWT, FTEM, WK + DIMENSION NEQ(*), Y(*), YH(*), SAVF(*), EWT(*), FTEM(*), + 1 IA(*), JA(*), WK(*), IWK(*) + INTEGER IOWND, IOWNS, + 1 ICF, IERPJ, IERSL, JCUR, JSTART, KFLAG, L, + 2 LYH, LEWT, LACOR, LSAVF, LWM, LIWM, METH, MITER, + 3 MAXORD, MAXCOR, MSBP, MXNCF, N, NQ, NST, NFE, NJE, NQU + INTEGER IPLOST, IESP, ISTATC, IYS, IBA, IBIAN, IBJAN, IBJGP, + 1 IPIAN, IPJAN, IPJGP, IPIGP, IPR, IPC, IPIC, IPISP, IPRSP, IPA, + 2 LENYH, LENYHM, LENWK, LREQ, LRAT, LREST, LWMIN, MOSS, MSBJ, + 3 NSLJ, NGP, NLU, NNZ, NSP, NZL, NZU + DOUBLE PRECISION ROWNS, + 1 CCMAX, EL0, H, HMIN, HMXI, HU, RC, TN, UROUND + DOUBLE PRECISION CON0, CONMIN, CCMXJ, PSMALL, RBIG, SETH + COMMON /DLS001/ ROWNS(209), + 1 CCMAX, EL0, H, HMIN, HMXI, HU, RC, TN, UROUND, + 2 IOWND(6), IOWNS(6), + 3 ICF, IERPJ, IERSL, JCUR, JSTART, KFLAG, L, + 4 LYH, LEWT, LACOR, LSAVF, LWM, LIWM, METH, MITER, + 5 MAXORD, MAXCOR, MSBP, MXNCF, N, NQ, NST, NFE, NJE, NQU + COMMON /DLSS01/ CON0, CONMIN, CCMXJ, PSMALL, RBIG, SETH, + 1 IPLOST, IESP, ISTATC, IYS, IBA, IBIAN, IBJAN, IBJGP, + 2 IPIAN, IPJAN, IPJGP, IPIGP, IPR, IPC, IPIC, IPISP, IPRSP, IPA, + 3 LENYH, LENYHM, LENWK, LREQ, LRAT, LREST, LWMIN, MOSS, MSBJ, + 4 NSLJ, NGP, NLU, NNZ, NSP, NZL, NZU + INTEGER I, IBR, IER, IPIL, IPIU, IPTT1, IPTT2, J, JFOUND, K, + 1 KNEW, KMAX, KMIN, LDIF, LENIGP, LIWK, MAXG, NP1, NZSUT + DOUBLE PRECISION DQ, DYJ, ERWT, FAC, YJ +C----------------------------------------------------------------------- +C This routine performs preprocessing related to the sparse linear +C systems that must be solved if MITER = 1 or 2. +C The operations that are performed here are: +C * compute sparseness structure of Jacobian according to MOSS, +C * compute grouping of column indices (MITER = 2), +C * compute a new ordering of rows and columns of the matrix, +C * reorder JA corresponding to the new ordering, +C * perform a symbolic LU factorization of the matrix, and +C * set pointers for segments of the IWK/WK array. +C In addition to variables described previously, DPREP uses the +C following for communication: +C YH = the history array. Only the first column, containing the +C current Y vector, is used. Used only if MOSS .ne. 0. +C SAVF = a work array of length NEQ, used only if MOSS .ne. 0. +C EWT = array of length NEQ containing (inverted) error weights. +C Used only if MOSS = 2 or if ISTATE = MOSS = 1. +C FTEM = a work array of length NEQ, identical to ACOR in the driver, +C used only if MOSS = 2. +C WK = a real work array of length LENWK, identical to WM in +C the driver. +C IWK = integer work array, assumed to occupy the same space as WK. +C LENWK = the length of the work arrays WK and IWK. +C ISTATC = a copy of the driver input argument ISTATE (= 1 on the +C first call, = 3 on a continuation call). +C IYS = flag value from ODRV or CDRV. +C IPPER = output error flag with the following values and meanings: +C 0 no error. +C -1 insufficient storage for internal structure pointers. +C -2 insufficient storage for JGROUP. +C -3 insufficient storage for ODRV. +C -4 other error flag from ODRV (should never occur). +C -5 insufficient storage for CDRV. +C -6 other error flag from CDRV. +C----------------------------------------------------------------------- + IBIAN = LRAT*2 + IPIAN = IBIAN + 1 + NP1 = N + 1 + IPJAN = IPIAN + NP1 + IBJAN = IPJAN - 1 + LIWK = LENWK*LRAT + IF (IPJAN+N-1 .GT. LIWK) GO TO 210 + IF (MOSS .EQ. 0) GO TO 30 +C + IF (ISTATC .EQ. 3) GO TO 20 +C ISTATE = 1 and MOSS .ne. 0. Perturb Y for structure determination. -- + DO 10 I = 1,N + ERWT = 1.0D0/EWT(I) + FAC = 1.0D0 + 1.0D0/(I + 1.0D0) + Y(I) = Y(I) + FAC*SIGN(ERWT,Y(I)) + 10 CONTINUE + GO TO (70, 100), MOSS +C + 20 CONTINUE +C ISTATE = 3 and MOSS .ne. 0. Load Y from YH(*,1). -------------------- + DO 25 I = 1,N + 25 Y(I) = YH(I) + GO TO (70, 100), MOSS +C +C MOSS = 0. Process user's IA,JA. Add diagonal entries if necessary. - + 30 KNEW = IPJAN + KMIN = IA(1) + IWK(IPIAN) = 1 + DO 60 J = 1,N + JFOUND = 0 + KMAX = IA(J+1) - 1 + IF (KMIN .GT. KMAX) GO TO 45 + DO 40 K = KMIN,KMAX + I = JA(K) + IF (I .EQ. J) JFOUND = 1 + IF (KNEW .GT. LIWK) GO TO 210 + IWK(KNEW) = I + KNEW = KNEW + 1 + 40 CONTINUE + IF (JFOUND .EQ. 1) GO TO 50 + 45 IF (KNEW .GT. LIWK) GO TO 210 + IWK(KNEW) = J + KNEW = KNEW + 1 + 50 IWK(IPIAN+J) = KNEW + 1 - IPJAN + KMIN = KMAX + 1 + 60 CONTINUE + GO TO 140 +C +C MOSS = 1. Compute structure from user-supplied Jacobian routine JAC. + 70 CONTINUE +C A dummy call to F allows user to create temporaries for use in JAC. -- + CALL F (NEQ, TN, Y, SAVF) + K = IPJAN + IWK(IPIAN) = 1 + DO 90 J = 1,N + IF (K .GT. LIWK) GO TO 210 + IWK(K) = J + K = K + 1 + DO 75 I = 1,N + 75 SAVF(I) = 0.0D0 + CALL JAC (NEQ, TN, Y, J, IWK(IPIAN), IWK(IPJAN), SAVF) + DO 80 I = 1,N + IF (ABS(SAVF(I)) .LE. SETH) GO TO 80 + IF (I .EQ. J) GO TO 80 + IF (K .GT. LIWK) GO TO 210 + IWK(K) = I + K = K + 1 + 80 CONTINUE + IWK(IPIAN+J) = K + 1 - IPJAN + 90 CONTINUE + GO TO 140 +C +C MOSS = 2. Compute structure from results of N + 1 calls to F. ------- + 100 K = IPJAN + IWK(IPIAN) = 1 + CALL F (NEQ, TN, Y, SAVF) + DO 120 J = 1,N + IF (K .GT. LIWK) GO TO 210 + IWK(K) = J + K = K + 1 + YJ = Y(J) + ERWT = 1.0D0/EWT(J) + DYJ = SIGN(ERWT,YJ) + Y(J) = YJ + DYJ + CALL F (NEQ, TN, Y, FTEM) + Y(J) = YJ + DO 110 I = 1,N + DQ = (FTEM(I) - SAVF(I))/DYJ + IF (ABS(DQ) .LE. SETH) GO TO 110 + IF (I .EQ. J) GO TO 110 + IF (K .GT. LIWK) GO TO 210 + IWK(K) = I + K = K + 1 + 110 CONTINUE + IWK(IPIAN+J) = K + 1 - IPJAN + 120 CONTINUE +C + 140 CONTINUE + IF (MOSS .EQ. 0 .OR. ISTATC .NE. 1) GO TO 150 +C If ISTATE = 1 and MOSS .ne. 0, restore Y from YH. -------------------- + DO 145 I = 1,N + 145 Y(I) = YH(I) + 150 NNZ = IWK(IPIAN+N) - 1 + LENIGP = 0 + IPIGP = IPJAN + NNZ + IF (MITER .NE. 2) GO TO 160 +C +C Compute grouping of column indices (MITER = 2). ---------------------- + MAXG = NP1 + IPJGP = IPJAN + NNZ + IBJGP = IPJGP - 1 + IPIGP = IPJGP + N + IPTT1 = IPIGP + NP1 + IPTT2 = IPTT1 + N + LREQ = IPTT2 + N - 1 + IF (LREQ .GT. LIWK) GO TO 220 + CALL JGROUP (N, IWK(IPIAN), IWK(IPJAN), MAXG, NGP, IWK(IPIGP), + 1 IWK(IPJGP), IWK(IPTT1), IWK(IPTT2), IER) + IF (IER .NE. 0) GO TO 220 + LENIGP = NGP + 1 +C +C Compute new ordering of rows/columns of Jacobian. -------------------- + 160 IPR = IPIGP + LENIGP + IPC = IPR + IPIC = IPC + N + IPISP = IPIC + N + IPRSP = (IPISP - 2)/LRAT + 2 + IESP = LENWK + 1 - IPRSP + IF (IESP .LT. 0) GO TO 230 + IBR = IPR - 1 + DO 170 I = 1,N + 170 IWK(IBR+I) = I + NSP = LIWK + 1 - IPISP + CALL ODRV (N, IWK(IPIAN), IWK(IPJAN), WK, IWK(IPR), IWK(IPIC), + 1 NSP, IWK(IPISP), 1, IYS) + IF (IYS .EQ. 11*N+1) GO TO 240 + IF (IYS .NE. 0) GO TO 230 +C +C Reorder JAN and do symbolic LU factorization of matrix. -------------- + IPA = LENWK + 1 - NNZ + NSP = IPA - IPRSP + LREQ = MAX(12*N/LRAT, 6*N/LRAT+2*N+NNZ) + 3 + LREQ = LREQ + IPRSP - 1 + NNZ + IF (LREQ .GT. LENWK) GO TO 250 + IBA = IPA - 1 + DO 180 I = 1,NNZ + 180 WK(IBA+I) = 0.0D0 + IPISP = LRAT*(IPRSP - 1) + 1 + CALL CDRV (N,IWK(IPR),IWK(IPC),IWK(IPIC),IWK(IPIAN),IWK(IPJAN), + 1 WK(IPA),WK(IPA),WK(IPA),NSP,IWK(IPISP),WK(IPRSP),IESP,5,IYS) + LREQ = LENWK - IESP + IF (IYS .EQ. 10*N+1) GO TO 250 + IF (IYS .NE. 0) GO TO 260 + IPIL = IPISP + IPIU = IPIL + 2*N + 1 + NZU = IWK(IPIL+N) - IWK(IPIL) + NZL = IWK(IPIU+N) - IWK(IPIU) + IF (LRAT .GT. 1) GO TO 190 + CALL ADJLR (N, IWK(IPISP), LDIF) + LREQ = LREQ + LDIF + 190 CONTINUE + IF (LRAT .EQ. 2 .AND. NNZ .EQ. N) LREQ = LREQ + 1 + NSP = NSP + LREQ - LENWK + IPA = LREQ + 1 - NNZ + IBA = IPA - 1 + IPPER = 0 + RETURN +C + 210 IPPER = -1 + LREQ = 2 + (2*N + 1)/LRAT + LREQ = MAX(LENWK+1,LREQ) + RETURN +C + 220 IPPER = -2 + LREQ = (LREQ - 1)/LRAT + 1 + RETURN +C + 230 IPPER = -3 + CALL CNTNZU (N, IWK(IPIAN), IWK(IPJAN), NZSUT) + LREQ = LENWK - IESP + (3*N + 4*NZSUT - 1)/LRAT + 1 + RETURN +C + 240 IPPER = -4 + RETURN +C + 250 IPPER = -5 + RETURN +C + 260 IPPER = -6 + LREQ = LENWK + RETURN +C----------------------- End of Subroutine DPREP ----------------------- + END +*DECK JGROUP + SUBROUTINE JGROUP (N,IA,JA,MAXG,NGRP,IGP,JGP,INCL,JDONE,IER) + INTEGER N, IA, JA, MAXG, NGRP, IGP, JGP, INCL, JDONE, IER + DIMENSION IA(*), JA(*), IGP(*), JGP(*), INCL(*), JDONE(*) +C----------------------------------------------------------------------- +C This subroutine constructs groupings of the column indices of +C the Jacobian matrix, used in the numerical evaluation of the +C Jacobian by finite differences. +C +C Input: +C N = the order of the matrix. +C IA,JA = sparse structure descriptors of the matrix by rows. +C MAXG = length of available storage in the IGP array. +C +C Output: +C NGRP = number of groups. +C JGP = array of length N containing the column indices by groups. +C IGP = pointer array of length NGRP + 1 to the locations in JGP +C of the beginning of each group. +C IER = error indicator. IER = 0 if no error occurred, or 1 if +C MAXG was insufficient. +C +C INCL and JDONE are working arrays of length N. +C----------------------------------------------------------------------- + INTEGER I, J, K, KMIN, KMAX, NCOL, NG +C + IER = 0 + DO 10 J = 1,N + 10 JDONE(J) = 0 + NCOL = 1 + DO 60 NG = 1,MAXG + IGP(NG) = NCOL + DO 20 I = 1,N + 20 INCL(I) = 0 + DO 50 J = 1,N +C Reject column J if it is already in a group.-------------------------- + IF (JDONE(J) .EQ. 1) GO TO 50 + KMIN = IA(J) + KMAX = IA(J+1) - 1 + DO 30 K = KMIN,KMAX +C Reject column J if it overlaps any column already in this group.------ + I = JA(K) + IF (INCL(I) .EQ. 1) GO TO 50 + 30 CONTINUE +C Accept column J into group NG.---------------------------------------- + JGP(NCOL) = J + NCOL = NCOL + 1 + JDONE(J) = 1 + DO 40 K = KMIN,KMAX + I = JA(K) + 40 INCL(I) = 1 + 50 CONTINUE +C Stop if this group is empty (grouping is complete).------------------- + IF (NCOL .EQ. IGP(NG)) GO TO 70 + 60 CONTINUE +C Error return if not all columns were chosen (MAXG too small).--------- + IF (NCOL .LE. N) GO TO 80 + NG = MAXG + 70 NGRP = NG - 1 + RETURN + 80 IER = 1 + RETURN +C----------------------- End of Subroutine JGROUP ---------------------- + END +*DECK ADJLR + SUBROUTINE ADJLR (N, ISP, LDIF) + INTEGER N, ISP, LDIF + DIMENSION ISP(*) +C----------------------------------------------------------------------- +C This routine computes an adjustment, LDIF, to the required +C integer storage space in IWK (sparse matrix work space). +C It is called only if the word length ratio is LRAT = 1. +C This is to account for the possibility that the symbolic LU phase +C may require more storage than the numerical LU and solution phases. +C----------------------------------------------------------------------- + INTEGER IP, JLMAX, JUMAX, LNFC, LSFC, NZLU +C + IP = 2*N + 1 +C Get JLMAX = IJL(N) and JUMAX = IJU(N) (sizes of JL and JU). ---------- + JLMAX = ISP(IP) + JUMAX = ISP(IP+IP) +C NZLU = (size of L) + (size of U) = (IL(N+1)-IL(1)) + (IU(N+1)-IU(1)). + NZLU = ISP(N+1) - ISP(1) + ISP(IP+N+1) - ISP(IP+1) + LSFC = 12*N + 3 + 2*MAX(JLMAX,JUMAX) + LNFC = 9*N + 2 + JLMAX + JUMAX + NZLU + LDIF = MAX(0, LSFC - LNFC) + RETURN +C----------------------- End of Subroutine ADJLR ----------------------- + END +*DECK CNTNZU + SUBROUTINE CNTNZU (N, IA, JA, NZSUT) + INTEGER N, IA, JA, NZSUT + DIMENSION IA(*), JA(*) +C----------------------------------------------------------------------- +C This routine counts the number of nonzero elements in the strict +C upper triangle of the matrix M + M(transpose), where the sparsity +C structure of M is given by pointer arrays IA and JA. +C This is needed to compute the storage requirements for the +C sparse matrix reordering operation in ODRV. +C----------------------------------------------------------------------- + INTEGER II, JJ, J, JMIN, JMAX, K, KMIN, KMAX, NUM +C + NUM = 0 + DO 50 II = 1,N + JMIN = IA(II) + JMAX = IA(II+1) - 1 + IF (JMIN .GT. JMAX) GO TO 50 + DO 40 J = JMIN,JMAX + IF (JA(J) - II) 10, 40, 30 + 10 JJ =JA(J) + KMIN = IA(JJ) + KMAX = IA(JJ+1) - 1 + IF (KMIN .GT. KMAX) GO TO 30 + DO 20 K = KMIN,KMAX + IF (JA(K) .EQ. II) GO TO 40 + 20 CONTINUE + 30 NUM = NUM + 1 + 40 CONTINUE + 50 CONTINUE + NZSUT = NUM + RETURN +C----------------------- End of Subroutine CNTNZU ---------------------- + END +*DECK DPRJS + SUBROUTINE DPRJS (NEQ,Y,YH,NYH,EWT,FTEM,SAVF,WK,IWK,F,JAC) + EXTERNAL F,JAC + INTEGER NEQ, NYH, IWK + DOUBLE PRECISION Y, YH, EWT, FTEM, SAVF, WK + DIMENSION NEQ(*), Y(*), YH(NYH,*), EWT(*), FTEM(*), SAVF(*), + 1 WK(*), IWK(*) + INTEGER IOWND, IOWNS, + 1 ICF, IERPJ, IERSL, JCUR, JSTART, KFLAG, L, + 2 LYH, LEWT, LACOR, LSAVF, LWM, LIWM, METH, MITER, + 3 MAXORD, MAXCOR, MSBP, MXNCF, N, NQ, NST, NFE, NJE, NQU + INTEGER IPLOST, IESP, ISTATC, IYS, IBA, IBIAN, IBJAN, IBJGP, + 1 IPIAN, IPJAN, IPJGP, IPIGP, IPR, IPC, IPIC, IPISP, IPRSP, IPA, + 2 LENYH, LENYHM, LENWK, LREQ, LRAT, LREST, LWMIN, MOSS, MSBJ, + 3 NSLJ, NGP, NLU, NNZ, NSP, NZL, NZU + DOUBLE PRECISION ROWNS, + 1 CCMAX, EL0, H, HMIN, HMXI, HU, RC, TN, UROUND + DOUBLE PRECISION CON0, CONMIN, CCMXJ, PSMALL, RBIG, SETH + COMMON /DLS001/ ROWNS(209), + 1 CCMAX, EL0, H, HMIN, HMXI, HU, RC, TN, UROUND, + 2 IOWND(6), IOWNS(6), + 3 ICF, IERPJ, IERSL, JCUR, JSTART, KFLAG, L, + 4 LYH, LEWT, LACOR, LSAVF, LWM, LIWM, METH, MITER, + 5 MAXORD, MAXCOR, MSBP, MXNCF, N, NQ, NST, NFE, NJE, NQU + COMMON /DLSS01/ CON0, CONMIN, CCMXJ, PSMALL, RBIG, SETH, + 1 IPLOST, IESP, ISTATC, IYS, IBA, IBIAN, IBJAN, IBJGP, + 2 IPIAN, IPJAN, IPJGP, IPIGP, IPR, IPC, IPIC, IPISP, IPRSP, IPA, + 3 LENYH, LENYHM, LENWK, LREQ, LRAT, LREST, LWMIN, MOSS, MSBJ, + 4 NSLJ, NGP, NLU, NNZ, NSP, NZL, NZU + INTEGER I, IMUL, J, JJ, JOK, JMAX, JMIN, K, KMAX, KMIN, NG + DOUBLE PRECISION CON, DI, FAC, HL0, PIJ, R, R0, RCON, RCONT, + 1 SRUR, DVNORM +C----------------------------------------------------------------------- +C DPRJS is called to compute and process the matrix +C P = I - H*EL(1)*J , where J is an approximation to the Jacobian. +C J is computed by columns, either by the user-supplied routine JAC +C if MITER = 1, or by finite differencing if MITER = 2. +C if MITER = 3, a diagonal approximation to J is used. +C if MITER = 1 or 2, and if the existing value of the Jacobian +C (as contained in P) is considered acceptable, then a new value of +C P is reconstructed from the old value. In any case, when MITER +C is 1 or 2, the P matrix is subjected to LU decomposition in CDRV. +C P and its LU decomposition are stored (separately) in WK. +C +C In addition to variables described previously, communication +C with DPRJS uses the following: +C Y = array containing predicted values on entry. +C FTEM = work array of length N (ACOR in DSTODE). +C SAVF = array containing f evaluated at predicted y. +C WK = real work space for matrices. On output it contains the +C inverse diagonal matrix if MITER = 3, and P and its sparse +C LU decomposition if MITER is 1 or 2. +C Storage of matrix elements starts at WK(3). +C WK also contains the following matrix-related data: +C WK(1) = SQRT(UROUND), used in numerical Jacobian increments. +C WK(2) = H*EL0, saved for later use if MITER = 3. +C IWK = integer work space for matrix-related data, assumed to +C be equivalenced to WK. In addition, WK(IPRSP) and IWK(IPISP) +C are assumed to have identical locations. +C EL0 = EL(1) (input). +C IERPJ = output error flag (in Common). +C = 0 if no error. +C = 1 if zero pivot found in CDRV. +C = 2 if a singular matrix arose with MITER = 3. +C = -1 if insufficient storage for CDRV (should not occur here). +C = -2 if other error found in CDRV (should not occur here). +C JCUR = output flag showing status of (approximate) Jacobian matrix: +C = 1 to indicate that the Jacobian is now current, or +C = 0 to indicate that a saved value was used. +C This routine also uses other variables in Common. +C----------------------------------------------------------------------- + HL0 = H*EL0 + CON = -HL0 + IF (MITER .EQ. 3) GO TO 300 +C See whether J should be reevaluated (JOK = 0) or not (JOK = 1). ------ + JOK = 1 + IF (NST .EQ. 0 .OR. NST .GE. NSLJ+MSBJ) JOK = 0 + IF (ICF .EQ. 1 .AND. ABS(RC - 1.0D0) .LT. CCMXJ) JOK = 0 + IF (ICF .EQ. 2) JOK = 0 + IF (JOK .EQ. 1) GO TO 250 +C +C MITER = 1 or 2, and the Jacobian is to be reevaluated. --------------- + 20 JCUR = 1 + NJE = NJE + 1 + NSLJ = NST + IPLOST = 0 + CONMIN = ABS(CON) + GO TO (100, 200), MITER +C +C If MITER = 1, call JAC, multiply by scalar, and add identity. -------- + 100 CONTINUE + KMIN = IWK(IPIAN) + DO 130 J = 1, N + KMAX = IWK(IPIAN+J) - 1 + DO 110 I = 1,N + 110 FTEM(I) = 0.0D0 + CALL JAC (NEQ, TN, Y, J, IWK(IPIAN), IWK(IPJAN), FTEM) + DO 120 K = KMIN, KMAX + I = IWK(IBJAN+K) + WK(IBA+K) = FTEM(I)*CON + IF (I .EQ. J) WK(IBA+K) = WK(IBA+K) + 1.0D0 + 120 CONTINUE + KMIN = KMAX + 1 + 130 CONTINUE + GO TO 290 +C +C If MITER = 2, make NGP calls to F to approximate J and P. ------------ + 200 CONTINUE + FAC = DVNORM(N, SAVF, EWT) + R0 = 1000.0D0 * ABS(H) * UROUND * N * FAC + IF (R0 .EQ. 0.0D0) R0 = 1.0D0 + SRUR = WK(1) + JMIN = IWK(IPIGP) + DO 240 NG = 1,NGP + JMAX = IWK(IPIGP+NG) - 1 + DO 210 J = JMIN,JMAX + JJ = IWK(IBJGP+J) + R = MAX(SRUR*ABS(Y(JJ)),R0/EWT(JJ)) + 210 Y(JJ) = Y(JJ) + R + CALL F (NEQ, TN, Y, FTEM) + DO 230 J = JMIN,JMAX + JJ = IWK(IBJGP+J) + Y(JJ) = YH(JJ,1) + R = MAX(SRUR*ABS(Y(JJ)),R0/EWT(JJ)) + FAC = -HL0/R + KMIN =IWK(IBIAN+JJ) + KMAX =IWK(IBIAN+JJ+1) - 1 + DO 220 K = KMIN,KMAX + I = IWK(IBJAN+K) + WK(IBA+K) = (FTEM(I) - SAVF(I))*FAC + IF (I .EQ. JJ) WK(IBA+K) = WK(IBA+K) + 1.0D0 + 220 CONTINUE + 230 CONTINUE + JMIN = JMAX + 1 + 240 CONTINUE + NFE = NFE + NGP + GO TO 290 +C +C If JOK = 1, reconstruct new P from old P. ---------------------------- + 250 JCUR = 0 + RCON = CON/CON0 + RCONT = ABS(CON)/CONMIN + IF (RCONT .GT. RBIG .AND. IPLOST .EQ. 1) GO TO 20 + KMIN = IWK(IPIAN) + DO 275 J = 1,N + KMAX = IWK(IPIAN+J) - 1 + DO 270 K = KMIN,KMAX + I = IWK(IBJAN+K) + PIJ = WK(IBA+K) + IF (I .NE. J) GO TO 260 + PIJ = PIJ - 1.0D0 + IF (ABS(PIJ) .GE. PSMALL) GO TO 260 + IPLOST = 1 + CONMIN = MIN(ABS(CON0),CONMIN) + 260 PIJ = PIJ*RCON + IF (I .EQ. J) PIJ = PIJ + 1.0D0 + WK(IBA+K) = PIJ + 270 CONTINUE + KMIN = KMAX + 1 + 275 CONTINUE +C +C Do numerical factorization of P matrix. ------------------------------ + 290 NLU = NLU + 1 + CON0 = CON + IERPJ = 0 + DO 295 I = 1,N + 295 FTEM(I) = 0.0D0 + CALL CDRV (N,IWK(IPR),IWK(IPC),IWK(IPIC),IWK(IPIAN),IWK(IPJAN), + 1 WK(IPA),FTEM,FTEM,NSP,IWK(IPISP),WK(IPRSP),IESP,2,IYS) + IF (IYS .EQ. 0) RETURN + IMUL = (IYS - 1)/N + IERPJ = -2 + IF (IMUL .EQ. 8) IERPJ = 1 + IF (IMUL .EQ. 10) IERPJ = -1 + RETURN +C +C If MITER = 3, construct a diagonal approximation to J and P. --------- + 300 CONTINUE + JCUR = 1 + NJE = NJE + 1 + WK(2) = HL0 + IERPJ = 0 + R = EL0*0.1D0 + DO 310 I = 1,N + 310 Y(I) = Y(I) + R*(H*SAVF(I) - YH(I,2)) + CALL F (NEQ, TN, Y, WK(3)) + NFE = NFE + 1 + DO 320 I = 1,N + R0 = H*SAVF(I) - YH(I,2) + DI = 0.1D0*R0 - H*(WK(I+2) - SAVF(I)) + WK(I+2) = 1.0D0 + IF (ABS(R0) .LT. UROUND/EWT(I)) GO TO 320 + IF (ABS(DI) .EQ. 0.0D0) GO TO 330 + WK(I+2) = 0.1D0*R0/DI + 320 CONTINUE + RETURN + 330 IERPJ = 2 + RETURN +C----------------------- End of Subroutine DPRJS ----------------------- + END +*DECK DSOLSS + SUBROUTINE DSOLSS (WK, IWK, X, TEM) + INTEGER IWK + DOUBLE PRECISION WK, X, TEM + DIMENSION WK(*), IWK(*), X(*), TEM(*) + INTEGER IOWND, IOWNS, + 1 ICF, IERPJ, IERSL, JCUR, JSTART, KFLAG, L, + 2 LYH, LEWT, LACOR, LSAVF, LWM, LIWM, METH, MITER, + 3 MAXORD, MAXCOR, MSBP, MXNCF, N, NQ, NST, NFE, NJE, NQU + INTEGER IPLOST, IESP, ISTATC, IYS, IBA, IBIAN, IBJAN, IBJGP, + 1 IPIAN, IPJAN, IPJGP, IPIGP, IPR, IPC, IPIC, IPISP, IPRSP, IPA, + 2 LENYH, LENYHM, LENWK, LREQ, LRAT, LREST, LWMIN, MOSS, MSBJ, + 3 NSLJ, NGP, NLU, NNZ, NSP, NZL, NZU + DOUBLE PRECISION ROWNS, + 1 CCMAX, EL0, H, HMIN, HMXI, HU, RC, TN, UROUND + DOUBLE PRECISION RLSS + COMMON /DLS001/ ROWNS(209), + 1 CCMAX, EL0, H, HMIN, HMXI, HU, RC, TN, UROUND, + 2 IOWND(6), IOWNS(6), + 3 ICF, IERPJ, IERSL, JCUR, JSTART, KFLAG, L, + 4 LYH, LEWT, LACOR, LSAVF, LWM, LIWM, METH, MITER, + 5 MAXORD, MAXCOR, MSBP, MXNCF, N, NQ, NST, NFE, NJE, NQU + COMMON /DLSS01/ RLSS(6), + 1 IPLOST, IESP, ISTATC, IYS, IBA, IBIAN, IBJAN, IBJGP, + 2 IPIAN, IPJAN, IPJGP, IPIGP, IPR, IPC, IPIC, IPISP, IPRSP, IPA, + 3 LENYH, LENYHM, LENWK, LREQ, LRAT, LREST, LWMIN, MOSS, MSBJ, + 4 NSLJ, NGP, NLU, NNZ, NSP, NZL, NZU + INTEGER I + DOUBLE PRECISION DI, HL0, PHL0, R +C----------------------------------------------------------------------- +C This routine manages the solution of the linear system arising from +C a chord iteration. It is called if MITER .ne. 0. +C If MITER is 1 or 2, it calls CDRV to accomplish this. +C If MITER = 3 it updates the coefficient H*EL0 in the diagonal +C matrix, and then computes the solution. +C communication with DSOLSS uses the following variables: +C WK = real work space containing the inverse diagonal matrix if +C MITER = 3 and the LU decomposition of the matrix otherwise. +C Storage of matrix elements starts at WK(3). +C WK also contains the following matrix-related data: +C WK(1) = SQRT(UROUND) (not used here), +C WK(2) = HL0, the previous value of H*EL0, used if MITER = 3. +C IWK = integer work space for matrix-related data, assumed to +C be equivalenced to WK. In addition, WK(IPRSP) and IWK(IPISP) +C are assumed to have identical locations. +C X = the right-hand side vector on input, and the solution vector +C on output, of length N. +C TEM = vector of work space of length N, not used in this version. +C IERSL = output flag (in Common). +C IERSL = 0 if no trouble occurred. +C IERSL = -1 if CDRV returned an error flag (MITER = 1 or 2). +C This should never occur and is considered fatal. +C IERSL = 1 if a singular matrix arose with MITER = 3. +C This routine also uses other variables in Common. +C----------------------------------------------------------------------- + IERSL = 0 + GO TO (100, 100, 300), MITER + 100 CALL CDRV (N,IWK(IPR),IWK(IPC),IWK(IPIC),IWK(IPIAN),IWK(IPJAN), + 1 WK(IPA),X,X,NSP,IWK(IPISP),WK(IPRSP),IESP,4,IERSL) + IF (IERSL .NE. 0) IERSL = -1 + RETURN +C + 300 PHL0 = WK(2) + HL0 = H*EL0 + WK(2) = HL0 + IF (HL0 .EQ. PHL0) GO TO 330 + R = HL0/PHL0 + DO 320 I = 1,N + DI = 1.0D0 - R*(1.0D0 - 1.0D0/WK(I+2)) + IF (ABS(DI) .EQ. 0.0D0) GO TO 390 + 320 WK(I+2) = 1.0D0/DI + 330 DO 340 I = 1,N + 340 X(I) = WK(I+2)*X(I) + RETURN + 390 IERSL = 1 + RETURN +C +C----------------------- End of Subroutine DSOLSS ---------------------- + END +*DECK DSRCMS + SUBROUTINE DSRCMS (RSAV, ISAV, JOB) +C----------------------------------------------------------------------- +C This routine saves or restores (depending on JOB) the contents of +C the Common blocks DLS001, DLSS01, which are used +C internally by one or more ODEPACK solvers. +C +C RSAV = real array of length 224 or more. +C ISAV = integer array of length 71 or more. +C JOB = flag indicating to save or restore the Common blocks: +C JOB = 1 if Common is to be saved (written to RSAV/ISAV) +C JOB = 2 if Common is to be restored (read from RSAV/ISAV) +C A call with JOB = 2 presumes a prior call with JOB = 1. +C----------------------------------------------------------------------- + INTEGER ISAV, JOB + INTEGER ILS, ILSS + INTEGER I, LENILS, LENISS, LENRLS, LENRSS + DOUBLE PRECISION RSAV, RLS, RLSS + DIMENSION RSAV(*), ISAV(*) + SAVE LENRLS, LENILS, LENRSS, LENISS + COMMON /DLS001/ RLS(218), ILS(37) + COMMON /DLSS01/ RLSS(6), ILSS(34) + DATA LENRLS/218/, LENILS/37/, LENRSS/6/, LENISS/34/ +C + IF (JOB .EQ. 2) GO TO 100 + DO 10 I = 1,LENRLS + 10 RSAV(I) = RLS(I) + DO 15 I = 1,LENRSS + 15 RSAV(LENRLS+I) = RLSS(I) +C + DO 20 I = 1,LENILS + 20 ISAV(I) = ILS(I) + DO 25 I = 1,LENISS + 25 ISAV(LENILS+I) = ILSS(I) +C + RETURN +C + 100 CONTINUE + DO 110 I = 1,LENRLS + 110 RLS(I) = RSAV(I) + DO 115 I = 1,LENRSS + 115 RLSS(I) = RSAV(LENRLS+I) +C + DO 120 I = 1,LENILS + 120 ILS(I) = ISAV(I) + DO 125 I = 1,LENISS + 125 ILSS(I) = ISAV(LENILS+I) +C + RETURN +C----------------------- End of Subroutine DSRCMS ---------------------- + END +*DECK ODRV + subroutine odrv + * (n, ia,ja,a, p,ip, nsp,isp, path, flag) +c 5/2/83 +c*********************************************************************** +c odrv -- driver for sparse matrix reordering routines +c*********************************************************************** +c +c description +c +c odrv finds a minimum degree ordering of the rows and columns +c of a matrix m stored in (ia,ja,a) format (see below). for the +c reordered matrix, the work and storage required to perform +c gaussian elimination is (usually) significantly less. +c +c note.. odrv and its subordinate routines have been modified to +c compute orderings for general matrices, not necessarily having any +c symmetry. the miminum degree ordering is computed for the +c structure of the symmetric matrix m + m-transpose. +c modifications to the original odrv module have been made in +c the coding in subroutine mdi, and in the initial comments in +c subroutines odrv and md. +c +c if only the nonzero entries in the upper triangle of m are being +c stored, then odrv symmetrically reorders (ia,ja,a), (optionally) +c with the diagonal entries placed first in each row. this is to +c ensure that if m(i,j) will be in the upper triangle of m with +c respect to the new ordering, then m(i,j) is stored in row i (and +c thus m(j,i) is not stored), whereas if m(i,j) will be in the +c strict lower triangle of m, then m(j,i) is stored in row j (and +c thus m(i,j) is not stored). +c +c +c storage of sparse matrices +c +c the nonzero entries of the matrix m are stored row-by-row in the +c array a. to identify the individual nonzero entries in each row, +c we need to know in which column each entry lies. these column +c indices are stored in the array ja. i.e., if a(k) = m(i,j), then +c ja(k) = j. to identify the individual rows, we need to know where +c each row starts. these row pointers are stored in the array ia. +c i.e., if m(i,j) is the first nonzero entry (stored) in the i-th row +c and a(k) = m(i,j), then ia(i) = k. moreover, ia(n+1) points to +c the first location following the last element in the last row. +c thus, the number of entries in the i-th row is ia(i+1) - ia(i), +c the nonzero entries in the i-th row are stored consecutively in +c +c a(ia(i)), a(ia(i)+1), ..., a(ia(i+1)-1), +c +c and the corresponding column indices are stored consecutively in +c +c ja(ia(i)), ja(ia(i)+1), ..., ja(ia(i+1)-1). +c +c when the coefficient matrix is symmetric, only the nonzero entries +c in the upper triangle need be stored. for example, the matrix +c +c ( 1 0 2 3 0 ) +c ( 0 4 0 0 0 ) +c m = ( 2 0 5 6 0 ) +c ( 3 0 6 7 8 ) +c ( 0 0 0 8 9 ) +c +c could be stored as +c +c - 1 2 3 4 5 6 7 8 9 10 11 12 13 +c ---+-------------------------------------- +c ia - 1 4 5 8 12 14 +c ja - 1 3 4 2 1 3 4 1 3 4 5 4 5 +c a - 1 2 3 4 2 5 6 3 6 7 8 8 9 +c +c or (symmetrically) as +c +c - 1 2 3 4 5 6 7 8 9 +c ---+-------------------------- +c ia - 1 4 5 7 9 10 +c ja - 1 3 4 2 3 4 4 5 5 +c a - 1 2 3 4 5 6 7 8 9 . +c +c +c parameters +c +c n - order of the matrix +c +c ia - integer one-dimensional array containing pointers to delimit +c rows in ja and a. dimension = n+1 +c +c ja - integer one-dimensional array containing the column indices +c corresponding to the elements of a. dimension = number of +c nonzero entries in (the upper triangle of) m +c +c a - real one-dimensional array containing the nonzero entries in +c (the upper triangle of) m, stored by rows. dimension = +c number of nonzero entries in (the upper triangle of) m +c +c p - integer one-dimensional array used to return the permutation +c of the rows and columns of m corresponding to the minimum +c degree ordering. dimension = n +c +c ip - integer one-dimensional array used to return the inverse of +c the permutation returned in p. dimension = n +c +c nsp - declared dimension of the one-dimensional array isp. nsp +c must be at least 3n+4k, where k is the number of nonzeroes +c in the strict upper triangle of m +c +c isp - integer one-dimensional array used for working storage. +c dimension = nsp +c +c path - integer path specification. values and their meanings are - +c 1 find minimum degree ordering only +c 2 find minimum degree ordering and reorder symmetrically +c stored matrix (used when only the nonzero entries in +c the upper triangle of m are being stored) +c 3 reorder symmetrically stored matrix as specified by +c input permutation (used when an ordering has already +c been determined and only the nonzero entries in the +c upper triangle of m are being stored) +c 4 same as 2 but put diagonal entries at start of each row +c 5 same as 3 but put diagonal entries at start of each row +c +c flag - integer error flag. values and their meanings are - +c 0 no errors detected +c 9n+k insufficient storage in md +c 10n+1 insufficient storage in odrv +c 11n+1 illegal path specification +c +c +c conversion from real to double precision +c +c change the real declarations in odrv and sro to double precision +c declarations. +c +c----------------------------------------------------------------------- +c + integer ia(*), ja(*), p(*), ip(*), isp(*), path, flag, + * v, l, head, tmp, q +c... real a(*) + double precision a(*) + logical dflag +c +c----initialize error flag and validate path specification + flag = 0 + if (path.lt.1 .or. 5.lt.path) go to 111 +c +c----allocate storage and find minimum degree ordering + if ((path-1) * (path-2) * (path-4) .ne. 0) go to 1 + max = (nsp-n)/2 + v = 1 + l = v + max + head = l + max + next = head + n + if (max.lt.n) go to 110 +c + call md + * (n, ia,ja, max,isp(v),isp(l), isp(head),p,ip, isp(v), flag) + if (flag.ne.0) go to 100 +c +c----allocate storage and symmetrically reorder matrix + 1 if ((path-2) * (path-3) * (path-4) * (path-5) .ne. 0) go to 2 + tmp = (nsp+1) - n + q = tmp - (ia(n+1)-1) + if (q.lt.1) go to 110 +c + dflag = path.eq.4 .or. path.eq.5 + call sro + * (n, ip, ia, ja, a, isp(tmp), isp(q), dflag) +c + 2 return +c +c ** error -- error detected in md + 100 return +c ** error -- insufficient storage + 110 flag = 10*n + 1 + return +c ** error -- illegal path specified + 111 flag = 11*n + 1 + return + end + subroutine md + * (n, ia,ja, max, v,l, head,last,next, mark, flag) +c*********************************************************************** +c md -- minimum degree algorithm (based on element model) +c*********************************************************************** +c +c description +c +c md finds a minimum degree ordering of the rows and columns of a +c general sparse matrix m stored in (ia,ja,a) format. +c when the structure of m is nonsymmetric, the ordering is that +c obtained for the symmetric matrix m + m-transpose. +c +c +c additional parameters +c +c max - declared dimension of the one-dimensional arrays v and l. +c max must be at least n+2k, where k is the number of +c nonzeroes in the strict upper triangle of m + m-transpose +c +c v - integer one-dimensional work array. dimension = max +c +c l - integer one-dimensional work array. dimension = max +c +c head - integer one-dimensional work array. dimension = n +c +c last - integer one-dimensional array used to return the permutation +c of the rows and columns of m corresponding to the minimum +c degree ordering. dimension = n +c +c next - integer one-dimensional array used to return the inverse of +c the permutation returned in last. dimension = n +c +c mark - integer one-dimensional work array (may be the same as v). +c dimension = n +c +c flag - integer error flag. values and their meanings are - +c 0 no errors detected +c 9n+k insufficient storage in md +c +c +c definitions of internal parameters +c +c ---------+--------------------------------------------------------- +c v(s) - value field of list entry +c ---------+--------------------------------------------------------- +c l(s) - link field of list entry (0 =) end of list) +c ---------+--------------------------------------------------------- +c l(vi) - pointer to element list of uneliminated vertex vi +c ---------+--------------------------------------------------------- +c l(ej) - pointer to boundary list of active element ej +c ---------+--------------------------------------------------------- +c head(d) - vj =) vj head of d-list d +c - 0 =) no vertex in d-list d +c +c +c - vi uneliminated vertex +c - vi in ek - vi not in ek +c ---------+-----------------------------+--------------------------- +c next(vi) - undefined but nonnegative - vj =) vj next in d-list +c - - 0 =) vi tail of d-list +c ---------+-----------------------------+--------------------------- +c last(vi) - (not set until mdp) - -d =) vi head of d-list d +c --vk =) compute degree - vj =) vj last in d-list +c - ej =) vi prototype of ej - 0 =) vi not in any d-list +c - 0 =) do not compute degree - +c ---------+-----------------------------+--------------------------- +c mark(vi) - mark(vk) - nonneg. tag .lt. mark(vk) +c +c +c - vi eliminated vertex +c - ei active element - otherwise +c ---------+-----------------------------+--------------------------- +c next(vi) - -j =) vi was j-th vertex - -j =) vi was j-th vertex +c - to be eliminated - to be eliminated +c ---------+-----------------------------+--------------------------- +c last(vi) - m =) size of ei = m - undefined +c ---------+-----------------------------+--------------------------- +c mark(vi) - -m =) overlap count of ei - undefined +c - with ek = m - +c - otherwise nonnegative tag - +c - .lt. mark(vk) - +c +c----------------------------------------------------------------------- +c + integer ia(*), ja(*), v(*), l(*), head(*), last(*), next(*), + * mark(*), flag, tag, dmin, vk,ek, tail + equivalence (vk,ek) +c +c----initialization + tag = 0 + call mdi + * (n, ia,ja, max,v,l, head,last,next, mark,tag, flag) + if (flag.ne.0) return +c + k = 0 + dmin = 1 +c +c----while k .lt. n do + 1 if (k.ge.n) go to 4 +c +c------search for vertex of minimum degree + 2 if (head(dmin).gt.0) go to 3 + dmin = dmin + 1 + go to 2 +c +c------remove vertex vk of minimum degree from degree list + 3 vk = head(dmin) + head(dmin) = next(vk) + if (head(dmin).gt.0) last(head(dmin)) = -dmin +c +c------number vertex vk, adjust tag, and tag vk + k = k+1 + next(vk) = -k + last(ek) = dmin - 1 + tag = tag + last(ek) + mark(vk) = tag +c +c------form element ek from uneliminated neighbors of vk + call mdm + * (vk,tail, v,l, last,next, mark) +c +c------purge inactive elements and do mass elimination + call mdp + * (k,ek,tail, v,l, head,last,next, mark) +c +c------update degrees of uneliminated vertices in ek + call mdu + * (ek,dmin, v,l, head,last,next, mark) +c + go to 1 +c +c----generate inverse permutation from permutation + 4 do 5 k=1,n + next(k) = -next(k) + 5 last(next(k)) = k +c + return + end + subroutine mdi + * (n, ia,ja, max,v,l, head,last,next, mark,tag, flag) +c*********************************************************************** +c mdi -- initialization +c*********************************************************************** + integer ia(*), ja(*), v(*), l(*), head(*), last(*), next(*), + * mark(*), tag, flag, sfs, vi,dvi, vj +c +c----initialize degrees, element lists, and degree lists + do 1 vi=1,n + mark(vi) = 1 + l(vi) = 0 + 1 head(vi) = 0 + sfs = n+1 +c +c----create nonzero structure +c----for each nonzero entry a(vi,vj) + do 6 vi=1,n + jmin = ia(vi) + jmax = ia(vi+1) - 1 + if (jmin.gt.jmax) go to 6 + do 5 j=jmin,jmax + vj = ja(j) + if (vj-vi) 2, 5, 4 +c +c------if a(vi,vj) is in strict lower triangle +c------check for previous occurrence of a(vj,vi) + 2 lvk = vi + kmax = mark(vi) - 1 + if (kmax .eq. 0) go to 4 + do 3 k=1,kmax + lvk = l(lvk) + if (v(lvk).eq.vj) go to 5 + 3 continue +c----for unentered entries a(vi,vj) + 4 if (sfs.ge.max) go to 101 +c +c------enter vj in element list for vi + mark(vi) = mark(vi) + 1 + v(sfs) = vj + l(sfs) = l(vi) + l(vi) = sfs + sfs = sfs+1 +c +c------enter vi in element list for vj + mark(vj) = mark(vj) + 1 + v(sfs) = vi + l(sfs) = l(vj) + l(vj) = sfs + sfs = sfs+1 + 5 continue + 6 continue +c +c----create degree lists and initialize mark vector + do 7 vi=1,n + dvi = mark(vi) + next(vi) = head(dvi) + head(dvi) = vi + last(vi) = -dvi + nextvi = next(vi) + if (nextvi.gt.0) last(nextvi) = vi + 7 mark(vi) = tag +c + return +c +c ** error- insufficient storage + 101 flag = 9*n + vi + return + end + subroutine mdm + * (vk,tail, v,l, last,next, mark) +c*********************************************************************** +c mdm -- form element from uneliminated neighbors of vk +c*********************************************************************** + integer vk, tail, v(*), l(*), last(*), next(*), mark(*), + * tag, s,ls,vs,es, b,lb,vb, blp,blpmax + equivalence (vs, es) +c +c----initialize tag and list of uneliminated neighbors + tag = mark(vk) + tail = vk +c +c----for each vertex/element vs/es in element list of vk + ls = l(vk) + 1 s = ls + if (s.eq.0) go to 5 + ls = l(s) + vs = v(s) + if (next(vs).lt.0) go to 2 +c +c------if vs is uneliminated vertex, then tag and append to list of +c------uneliminated neighbors + mark(vs) = tag + l(tail) = s + tail = s + go to 4 +c +c------if es is active element, then ... +c--------for each vertex vb in boundary list of element es + 2 lb = l(es) + blpmax = last(es) + do 3 blp=1,blpmax + b = lb + lb = l(b) + vb = v(b) +c +c----------if vb is untagged vertex, then tag and append to list of +c----------uneliminated neighbors + if (mark(vb).ge.tag) go to 3 + mark(vb) = tag + l(tail) = b + tail = b + 3 continue +c +c--------mark es inactive + mark(es) = tag +c + 4 go to 1 +c +c----terminate list of uneliminated neighbors + 5 l(tail) = 0 +c + return + end + subroutine mdp + * (k,ek,tail, v,l, head,last,next, mark) +c*********************************************************************** +c mdp -- purge inactive elements and do mass elimination +c*********************************************************************** + integer ek, tail, v(*), l(*), head(*), last(*), next(*), + * mark(*), tag, free, li,vi,lvi,evi, s,ls,es, ilp,ilpmax +c +c----initialize tag + tag = mark(ek) +c +c----for each vertex vi in ek + li = ek + ilpmax = last(ek) + if (ilpmax.le.0) go to 12 + do 11 ilp=1,ilpmax + i = li + li = l(i) + vi = v(li) +c +c------remove vi from degree list + if (last(vi).eq.0) go to 3 + if (last(vi).gt.0) go to 1 + head(-last(vi)) = next(vi) + go to 2 + 1 next(last(vi)) = next(vi) + 2 if (next(vi).gt.0) last(next(vi)) = last(vi) +c +c------remove inactive items from element list of vi + 3 ls = vi + 4 s = ls + ls = l(s) + if (ls.eq.0) go to 6 + es = v(ls) + if (mark(es).lt.tag) go to 5 + free = ls + l(s) = l(ls) + ls = s + 5 go to 4 +c +c------if vi is interior vertex, then remove from list and eliminate + 6 lvi = l(vi) + if (lvi.ne.0) go to 7 + l(i) = l(li) + li = i +c + k = k+1 + next(vi) = -k + last(ek) = last(ek) - 1 + go to 11 +c +c------else ... +c--------classify vertex vi + 7 if (l(lvi).ne.0) go to 9 + evi = v(lvi) + if (next(evi).ge.0) go to 9 + if (mark(evi).lt.0) go to 8 +c +c----------if vi is prototype vertex, then mark as such, initialize +c----------overlap count for corresponding element, and move vi to end +c----------of boundary list + last(vi) = evi + mark(evi) = -1 + l(tail) = li + tail = li + l(i) = l(li) + li = i + go to 10 +c +c----------else if vi is duplicate vertex, then mark as such and adjust +c----------overlap count for corresponding element + 8 last(vi) = 0 + mark(evi) = mark(evi) - 1 + go to 10 +c +c----------else mark vi to compute degree + 9 last(vi) = -ek +c +c--------insert ek in element list of vi + 10 v(free) = ek + l(free) = l(vi) + l(vi) = free + 11 continue +c +c----terminate boundary list + 12 l(tail) = 0 +c + return + end + subroutine mdu + * (ek,dmin, v,l, head,last,next, mark) +c*********************************************************************** +c mdu -- update degrees of uneliminated vertices in ek +c*********************************************************************** + integer ek, dmin, v(*), l(*), head(*), last(*), next(*), + * mark(*), tag, vi,evi,dvi, s,vs,es, b,vb, ilp,ilpmax, + * blp,blpmax + equivalence (vs, es) +c +c----initialize tag + tag = mark(ek) - last(ek) +c +c----for each vertex vi in ek + i = ek + ilpmax = last(ek) + if (ilpmax.le.0) go to 11 + do 10 ilp=1,ilpmax + i = l(i) + vi = v(i) + if (last(vi)) 1, 10, 8 +c +c------if vi neither prototype nor duplicate vertex, then merge elements +c------to compute degree + 1 tag = tag + 1 + dvi = last(ek) +c +c--------for each vertex/element vs/es in element list of vi + s = l(vi) + 2 s = l(s) + if (s.eq.0) go to 9 + vs = v(s) + if (next(vs).lt.0) go to 3 +c +c----------if vs is uneliminated vertex, then tag and adjust degree + mark(vs) = tag + dvi = dvi + 1 + go to 5 +c +c----------if es is active element, then expand +c------------check for outmatched vertex + 3 if (mark(es).lt.0) go to 6 +c +c------------for each vertex vb in es + b = es + blpmax = last(es) + do 4 blp=1,blpmax + b = l(b) + vb = v(b) +c +c--------------if vb is untagged, then tag and adjust degree + if (mark(vb).ge.tag) go to 4 + mark(vb) = tag + dvi = dvi + 1 + 4 continue +c + 5 go to 2 +c +c------else if vi is outmatched vertex, then adjust overlaps but do not +c------compute degree + 6 last(vi) = 0 + mark(es) = mark(es) - 1 + 7 s = l(s) + if (s.eq.0) go to 10 + es = v(s) + if (mark(es).lt.0) mark(es) = mark(es) - 1 + go to 7 +c +c------else if vi is prototype vertex, then calculate degree by +c------inclusion/exclusion and reset overlap count + 8 evi = last(vi) + dvi = last(ek) + last(evi) + mark(evi) + mark(evi) = 0 +c +c------insert vi in appropriate degree list + 9 next(vi) = head(dvi) + head(dvi) = vi + last(vi) = -dvi + if (next(vi).gt.0) last(next(vi)) = vi + if (dvi.lt.dmin) dmin = dvi +c + 10 continue +c + 11 return + end + subroutine sro + * (n, ip, ia,ja,a, q, r, dflag) +c*********************************************************************** +c sro -- symmetric reordering of sparse symmetric matrix +c*********************************************************************** +c +c description +c +c the nonzero entries of the matrix m are assumed to be stored +c symmetrically in (ia,ja,a) format (i.e., not both m(i,j) and m(j,i) +c are stored if i ne j). +c +c sro does not rearrange the order of the rows, but does move +c nonzeroes from one row to another to ensure that if m(i,j) will be +c in the upper triangle of m with respect to the new ordering, then +c m(i,j) is stored in row i (and thus m(j,i) is not stored), whereas +c if m(i,j) will be in the strict lower triangle of m, then m(j,i) is +c stored in row j (and thus m(i,j) is not stored). +c +c +c additional parameters +c +c q - integer one-dimensional work array. dimension = n +c +c r - integer one-dimensional work array. dimension = number of +c nonzero entries in the upper triangle of m +c +c dflag - logical variable. if dflag = .true., then store nonzero +c diagonal elements at the beginning of the row +c +c----------------------------------------------------------------------- +c + integer ip(*), ia(*), ja(*), q(*), r(*) +c... real a(*), ak + double precision a(*), ak + logical dflag +c +c +c--phase 1 -- find row in which to store each nonzero +c----initialize count of nonzeroes to be stored in each row + do 1 i=1,n + 1 q(i) = 0 +c +c----for each nonzero element a(j) + do 3 i=1,n + jmin = ia(i) + jmax = ia(i+1) - 1 + if (jmin.gt.jmax) go to 3 + do 2 j=jmin,jmax +c +c--------find row (=r(j)) and column (=ja(j)) in which to store a(j) ... + k = ja(j) + if (ip(k).lt.ip(i)) ja(j) = i + if (ip(k).ge.ip(i)) k = i + r(j) = k +c +c--------... and increment count of nonzeroes (=q(r(j)) in that row + 2 q(k) = q(k) + 1 + 3 continue +c +c +c--phase 2 -- find new ia and permutation to apply to (ja,a) +c----determine pointers to delimit rows in permuted (ja,a) + do 4 i=1,n + ia(i+1) = ia(i) + q(i) + 4 q(i) = ia(i+1) +c +c----determine where each (ja(j),a(j)) is stored in permuted (ja,a) +c----for each nonzero element (in reverse order) + ilast = 0 + jmin = ia(1) + jmax = ia(n+1) - 1 + j = jmax + do 6 jdummy=jmin,jmax + i = r(j) + if (.not.dflag .or. ja(j).ne.i .or. i.eq.ilast) go to 5 +c +c------if dflag, then put diagonal nonzero at beginning of row + r(j) = ia(i) + ilast = i + go to 6 +c +c------put (off-diagonal) nonzero in last unused location in row + 5 q(i) = q(i) - 1 + r(j) = q(i) +c + 6 j = j-1 +c +c +c--phase 3 -- permute (ja,a) to upper triangular form (wrt new ordering) + do 8 j=jmin,jmax + 7 if (r(j).eq.j) go to 8 + k = r(j) + r(j) = r(k) + r(k) = k + jak = ja(k) + ja(k) = ja(j) + ja(j) = jak + ak = a(k) + a(k) = a(j) + a(j) = ak + go to 7 + 8 continue +c + return + end +*DECK CDRV + subroutine cdrv + * (n, r,c,ic, ia,ja,a, b, z, nsp,isp,rsp,esp, path, flag) +c*** subroutine cdrv +c*** driver for subroutines for solving sparse nonsymmetric systems of +c linear equations (compressed pointer storage) +c +c +c parameters +c class abbreviations are-- +c n - integer variable +c f - real variable +c v - supplies a value to the driver +c r - returns a result from the driver +c i - used internally by the driver +c a - array +c +c class - parameter +c ------+---------- +c - +c the nonzero entries of the coefficient matrix m are stored +c row-by-row in the array a. to identify the individual nonzero +c entries in each row, we need to know in which column each entry +c lies. the column indices which correspond to the nonzero entries +c of m are stored in the array ja. i.e., if a(k) = m(i,j), then +c ja(k) = j. in addition, we need to know where each row starts and +c how long it is. the index positions in ja and a where the rows of +c m begin are stored in the array ia. i.e., if m(i,j) is the first +c nonzero entry (stored) in the i-th row and a(k) = m(i,j), then +c ia(i) = k. moreover, the index in ja and a of the first location +c following the last element in the last row is stored in ia(n+1). +c thus, the number of entries in the i-th row is given by +c ia(i+1) - ia(i), the nonzero entries of the i-th row are stored +c consecutively in +c a(ia(i)), a(ia(i)+1), ..., a(ia(i+1)-1), +c and the corresponding column indices are stored consecutively in +c ja(ia(i)), ja(ia(i)+1), ..., ja(ia(i+1)-1). +c for example, the 5 by 5 matrix +c ( 1. 0. 2. 0. 0.) +c ( 0. 3. 0. 0. 0.) +c m = ( 0. 4. 5. 6. 0.) +c ( 0. 0. 0. 7. 0.) +c ( 0. 0. 0. 8. 9.) +c would be stored as +c - 1 2 3 4 5 6 7 8 9 +c ---+-------------------------- +c ia - 1 3 4 7 8 10 +c ja - 1 3 2 2 3 4 4 4 5 +c a - 1. 2. 3. 4. 5. 6. 7. 8. 9. . +c +c nv - n - number of variables/equations. +c fva - a - nonzero entries of the coefficient matrix m, stored +c - by rows. +c - size = number of nonzero entries in m. +c nva - ia - pointers to delimit the rows in a. +c - size = n+1. +c nva - ja - column numbers corresponding to the elements of a. +c - size = size of a. +c fva - b - right-hand side b. b and z can the same array. +c - size = n. +c fra - z - solution x. b and z can be the same array. +c - size = n. +c +c the rows and columns of the original matrix m can be +c reordered (e.g., to reduce fillin or ensure numerical stability) +c before calling the driver. if no reordering is done, then set +c r(i) = c(i) = ic(i) = i for i=1,...,n. the solution z is returned +c in the original order. +c if the columns have been reordered (i.e., c(i).ne.i for some +c i), then the driver will call a subroutine (nroc) which rearranges +c each row of ja and a, leaving the rows in the original order, but +c placing the elements of each row in increasing order with respect +c to the new ordering. if path.ne.1, then nroc is assumed to have +c been called already. +c +c nva - r - ordering of the rows of m. +c - size = n. +c nva - c - ordering of the columns of m. +c - size = n. +c nva - ic - inverse of the ordering of the columns of m. i.e., +c - ic(c(i)) = i for i=1,...,n. +c - size = n. +c +c the solution of the system of linear equations is divided into +c three stages -- +c nsfc -- the matrix m is processed symbolically to determine where +c fillin will occur during the numeric factorization. +c nnfc -- the matrix m is factored numerically into the product ldu +c of a unit lower triangular matrix l, a diagonal matrix +c d, and a unit upper triangular matrix u, and the system +c mx = b is solved. +c nnsc -- the linear system mx = b is solved using the ldu +c or factorization from nnfc. +c nntc -- the transposed linear system mt x = b is solved using +c the ldu factorization from nnf. +c for several systems whose coefficient matrices have the same +c nonzero structure, nsfc need be done only once (for the first +c system). then nnfc is done once for each additional system. for +c several systems with the same coefficient matrix, nsfc and nnfc +c need be done only once (for the first system). then nnsc or nntc +c is done once for each additional right-hand side. +c +c nv - path - path specification. values and their meanings are -- +c - 1 perform nroc, nsfc, and nnfc. +c - 2 perform nnfc only (nsfc is assumed to have been +c - done in a manner compatible with the storage +c - allocation used in the driver). +c - 3 perform nnsc only (nsfc and nnfc are assumed to +c - have been done in a manner compatible with the +c - storage allocation used in the driver). +c - 4 perform nntc only (nsfc and nnfc are assumed to +c - have been done in a manner compatible with the +c - storage allocation used in the driver). +c - 5 perform nroc and nsfc. +c +c various errors are detected by the driver and the individual +c subroutines. +c +c nr - flag - error flag. values and their meanings are -- +c - 0 no errors detected +c - n+k null row in a -- row = k +c - 2n+k duplicate entry in a -- row = k +c - 3n+k insufficient storage in nsfc -- row = k +c - 4n+1 insufficient storage in nnfc +c - 5n+k null pivot -- row = k +c - 6n+k insufficient storage in nsfc -- row = k +c - 7n+1 insufficient storage in nnfc +c - 8n+k zero pivot -- row = k +c - 10n+1 insufficient storage in cdrv +c - 11n+1 illegal path specification +c +c working storage is needed for the factored form of the matrix +c m plus various temporary vectors. the arrays isp and rsp should be +c equivalenced. integer storage is allocated from the beginning of +c isp and real storage from the end of rsp. +c +c nv - nsp - declared dimension of rsp. nsp generally must +c - be larger than 8n+2 + 2k (where k = (number of +c - nonzero entries in m)). +c nvira - isp - integer working storage divided up into various arrays +c - needed by the subroutines. isp and rsp should be +c - equivalenced. +c - size = lratio*nsp. +c fvira - rsp - real working storage divided up into various arrays +c - needed by the subroutines. isp and rsp should be +c - equivalenced. +c - size = nsp. +c nr - esp - if sufficient storage was available to perform the +c - symbolic factorization (nsfc), then esp is set to +c - the amount of excess storage provided (negative if +c - insufficient storage was available to perform the +c - numeric factorization (nnfc)). +c +c +c conversion to double precision +c +c to convert these routines for double precision arrays.. +c (1) use the double precision declarations in place of the real +c declarations in each subprogram, as given in comment cards. +c (2) change the data-loaded value of the integer lratio +c in subroutine cdrv, as indicated below. +c (3) change e0 to d0 in the constants in statement number 10 +c in subroutine nnfc and the line following that. +c + integer r(*), c(*), ic(*), ia(*), ja(*), isp(*), esp, path, + * flag, d, u, q, row, tmp, ar, umax +c real a(*), b(*), z(*), rsp(*) + double precision a(*), b(*), z(*), rsp(*) +c +c set lratio equal to the ratio between the length of floating point +c and integer array data. e. g., lratio = 1 for (real, integer), +c lratio = 2 for (double precision, integer) +c + data lratio/2/ +c + if (path.lt.1 .or. 5.lt.path) go to 111 +c******initialize and divide up temporary storage ******************* + il = 1 + ijl = il + (n+1) + iu = ijl + n + iju = iu + (n+1) + irl = iju + n + jrl = irl + n + jl = jrl + n +c +c ****** reorder a if necessary, call nsfc if flag is set *********** + if ((path-1) * (path-5) .ne. 0) go to 5 + max = (lratio*nsp + 1 - jl) - (n+1) - 5*n + jlmax = max/2 + q = jl + jlmax + ira = q + (n+1) + jra = ira + n + irac = jra + n + iru = irac + n + jru = iru + n + jutmp = jru + n + jumax = lratio*nsp + 1 - jutmp + esp = max/lratio + if (jlmax.le.0 .or. jumax.le.0) go to 110 +c + do 1 i=1,n + if (c(i).ne.i) go to 2 + 1 continue + go to 3 + 2 ar = nsp + 1 - n + call nroc + * (n, ic, ia,ja,a, isp(il), rsp(ar), isp(iu), flag) + if (flag.ne.0) go to 100 +c + 3 call nsfc + * (n, r, ic, ia,ja, + * jlmax, isp(il), isp(jl), isp(ijl), + * jumax, isp(iu), isp(jutmp), isp(iju), + * isp(q), isp(ira), isp(jra), isp(irac), + * isp(irl), isp(jrl), isp(iru), isp(jru), flag) + if(flag .ne. 0) go to 100 +c ****** move ju next to jl ***************************************** + jlmax = isp(ijl+n-1) + ju = jl + jlmax + jumax = isp(iju+n-1) + if (jumax.le.0) go to 5 + do 4 j=1,jumax + 4 isp(ju+j-1) = isp(jutmp+j-1) +c +c ****** call remaining subroutines ********************************* + 5 jlmax = isp(ijl+n-1) + ju = jl + jlmax + jumax = isp(iju+n-1) + l = (ju + jumax - 2 + lratio) / lratio + 1 + lmax = isp(il+n) - 1 + d = l + lmax + u = d + n + row = nsp + 1 - n + tmp = row - n + umax = tmp - u + esp = umax - (isp(iu+n) - 1) +c + if ((path-1) * (path-2) .ne. 0) go to 6 + if (umax.lt.0) go to 110 + call nnfc + * (n, r, c, ic, ia, ja, a, z, b, + * lmax, isp(il), isp(jl), isp(ijl), rsp(l), rsp(d), + * umax, isp(iu), isp(ju), isp(iju), rsp(u), + * rsp(row), rsp(tmp), isp(irl), isp(jrl), flag) + if(flag .ne. 0) go to 100 +c + 6 if ((path-3) .ne. 0) go to 7 + call nnsc + * (n, r, c, isp(il), isp(jl), isp(ijl), rsp(l), + * rsp(d), isp(iu), isp(ju), isp(iju), rsp(u), + * z, b, rsp(tmp)) +c + 7 if ((path-4) .ne. 0) go to 8 + call nntc + * (n, r, c, isp(il), isp(jl), isp(ijl), rsp(l), + * rsp(d), isp(iu), isp(ju), isp(iju), rsp(u), + * z, b, rsp(tmp)) + 8 return +c +c ** error.. error detected in nroc, nsfc, nnfc, or nnsc + 100 return +c ** error.. insufficient storage + 110 flag = 10*n + 1 + return +c ** error.. illegal path specification + 111 flag = 11*n + 1 + return + end + subroutine nroc (n, ic, ia, ja, a, jar, ar, p, flag) +c +c ---------------------------------------------------------------- +c +c yale sparse matrix package - nonsymmetric codes +c solving the system of equations mx = b +c +c i. calling sequences +c the coefficient matrix can be processed by an ordering routine +c (e.g., to reduce fillin or ensure numerical stability) before using +c the remaining subroutines. if no reordering is done, then set +c r(i) = c(i) = ic(i) = i for i=1,...,n. if an ordering subroutine +c is used, then nroc should be used to reorder the coefficient matrix +c the calling sequence is -- +c ( (matrix ordering)) +c (nroc (matrix reordering)) +c nsfc (symbolic factorization to determine where fillin will +c occur during numeric factorization) +c nnfc (numeric factorization into product ldu of unit lower +c triangular matrix l, diagonal matrix d, and unit +c upper triangular matrix u, and solution of linear +c system) +c nnsc (solution of linear system for additional right-hand +c side using ldu factorization from nnfc) +c (if only one system of equations is to be solved, then the +c subroutine trk should be used.) +c +c ii. storage of sparse matrices +c the nonzero entries of the coefficient matrix m are stored +c row-by-row in the array a. to identify the individual nonzero +c entries in each row, we need to know in which column each entry +c lies. the column indices which correspond to the nonzero entries +c of m are stored in the array ja. i.e., if a(k) = m(i,j), then +c ja(k) = j. in addition, we need to know where each row starts and +c how long it is. the index positions in ja and a where the rows of +c m begin are stored in the array ia. i.e., if m(i,j) is the first +c (leftmost) entry in the i-th row and a(k) = m(i,j), then +c ia(i) = k. moreover, the index in ja and a of the first location +c following the last element in the last row is stored in ia(n+1). +c thus, the number of entries in the i-th row is given by +c ia(i+1) - ia(i), the nonzero entries of the i-th row are stored +c consecutively in +c a(ia(i)), a(ia(i)+1), ..., a(ia(i+1)-1), +c and the corresponding column indices are stored consecutively in +c ja(ia(i)), ja(ia(i)+1), ..., ja(ia(i+1)-1). +c for example, the 5 by 5 matrix +c ( 1. 0. 2. 0. 0.) +c ( 0. 3. 0. 0. 0.) +c m = ( 0. 4. 5. 6. 0.) +c ( 0. 0. 0. 7. 0.) +c ( 0. 0. 0. 8. 9.) +c would be stored as +c - 1 2 3 4 5 6 7 8 9 +c ---+-------------------------- +c ia - 1 3 4 7 8 10 +c ja - 1 3 2 2 3 4 4 4 5 +c a - 1. 2. 3. 4. 5. 6. 7. 8. 9. . +c +c the strict upper (lower) triangular portion of the matrix +c u (l) is stored in a similar fashion using the arrays iu, ju, u +c (il, jl, l) except that an additional array iju (ijl) is used to +c compress storage of ju (jl) by allowing some sequences of column +c (row) indices to used for more than one row (column) (n.b., l is +c stored by columns). iju(k) (ijl(k)) points to the starting +c location in ju (jl) of entries for the kth row (column). +c compression in ju (jl) occurs in two ways. first, if a row +c (column) i was merged into the current row (column) k, and the +c number of elements merged in from (the tail portion of) row +c (column) i is the same as the final length of row (column) k, then +c the kth row (column) and the tail of row (column) i are identical +c and iju(k) (ijl(k)) points to the start of the tail. second, if +c some tail portion of the (k-1)st row (column) is identical to the +c head of the kth row (column), then iju(k) (ijl(k)) points to the +c start of that tail portion. for example, the nonzero structure of +c the strict upper triangular part of the matrix +c d 0 x x x +c 0 d 0 x x +c 0 0 d x 0 +c 0 0 0 d x +c 0 0 0 0 d +c would be represented as +c - 1 2 3 4 5 6 +c ----+------------ +c iu - 1 4 6 7 8 8 +c ju - 3 4 5 4 +c iju - 1 2 4 3 . +c the diagonal entries of l and u are assumed to be equal to one and +c are not stored. the array d contains the reciprocals of the +c diagonal entries of the matrix d. +c +c iii. additional storage savings +c in nsfc, r and ic can be the same array in the calling +c sequence if no reordering of the coefficient matrix has been done. +c in nnfc, r, c, and ic can all be the same array if no +c reordering has been done. if only the rows have been reordered, +c then c and ic can be the same array. if the row and column +c orderings are the same, then r and c can be the same array. z and +c row can be the same array. +c in nnsc or nntc, r and c can be the same array if no +c reordering has been done or if the row and column orderings are the +c same. z and b can be the same array. however, then b will be +c destroyed. +c +c iv. parameters +c following is a list of parameters to the programs. names are +c uniform among the various subroutines. class abbreviations are -- +c n - integer variable +c f - real variable +c v - supplies a value to a subroutine +c r - returns a result from a subroutine +c i - used internally by a subroutine +c a - array +c +c class - parameter +c ------+---------- +c fva - a - nonzero entries of the coefficient matrix m, stored +c - by rows. +c - size = number of nonzero entries in m. +c fva - b - right-hand side b. +c - size = n. +c nva - c - ordering of the columns of m. +c - size = n. +c fvra - d - reciprocals of the diagonal entries of the matrix d. +c - size = n. +c nr - flag - error flag. values and their meanings are -- +c - 0 no errors detected +c - n+k null row in a -- row = k +c - 2n+k duplicate entry in a -- row = k +c - 3n+k insufficient storage for jl -- row = k +c - 4n+1 insufficient storage for l +c - 5n+k null pivot -- row = k +c - 6n+k insufficient storage for ju -- row = k +c - 7n+1 insufficient storage for u +c - 8n+k zero pivot -- row = k +c nva - ia - pointers to delimit the rows of a. +c - size = n+1. +c nvra - ijl - pointers to the first element in each column in jl, +c - used to compress storage in jl. +c - size = n. +c nvra - iju - pointers to the first element in each row in ju, used +c - to compress storage in ju. +c - size = n. +c nvra - il - pointers to delimit the columns of l. +c - size = n+1. +c nvra - iu - pointers to delimit the rows of u. +c - size = n+1. +c nva - ja - column numbers corresponding to the elements of a. +c - size = size of a. +c nvra - jl - row numbers corresponding to the elements of l. +c - size = jlmax. +c nv - jlmax - declared dimension of jl. jlmax must be larger than +c - the number of nonzeros in the strict lower triangle +c - of m plus fillin minus compression. +c nvra - ju - column numbers corresponding to the elements of u. +c - size = jumax. +c nv - jumax - declared dimension of ju. jumax must be larger than +c - the number of nonzeros in the strict upper triangle +c - of m plus fillin minus compression. +c fvra - l - nonzero entries in the strict lower triangular portion +c - of the matrix l, stored by columns. +c - size = lmax. +c nv - lmax - declared dimension of l. lmax must be larger than +c - the number of nonzeros in the strict lower triangle +c - of m plus fillin (il(n+1)-1 after nsfc). +c nv - n - number of variables/equations. +c nva - r - ordering of the rows of m. +c - size = n. +c fvra - u - nonzero entries in the strict upper triangular portion +c - of the matrix u, stored by rows. +c - size = umax. +c nv - umax - declared dimension of u. umax must be larger than +c - the number of nonzeros in the strict upper triangle +c - of m plus fillin (iu(n+1)-1 after nsfc). +c fra - z - solution x. +c - size = n. +c +c ---------------------------------------------------------------- +c +c*** subroutine nroc +c*** reorders rows of a, leaving row order unchanged +c +c +c input parameters.. n, ic, ia, ja, a +c output parameters.. ja, a, flag +c +c parameters used internally.. +c nia - p - at the kth step, p is a linked list of the reordered +c - column indices of the kth row of a. p(n+1) points +c - to the first entry in the list. +c - size = n+1. +c nia - jar - at the kth step,jar contains the elements of the +c - reordered column indices of a. +c - size = n. +c fia - ar - at the kth step, ar contains the elements of the +c - reordered row of a. +c - size = n. +c + integer ic(*), ia(*), ja(*), jar(*), p(*), flag +c real a(*), ar(*) + double precision a(*), ar(*) +c +c ****** for each nonempty row ******************************* + do 5 k=1,n + jmin = ia(k) + jmax = ia(k+1) - 1 + if(jmin .gt. jmax) go to 5 + p(n+1) = n + 1 +c ****** insert each element in the list ********************* + do 3 j=jmin,jmax + newj = ic(ja(j)) + i = n + 1 + 1 if(p(i) .ge. newj) go to 2 + i = p(i) + go to 1 + 2 if(p(i) .eq. newj) go to 102 + p(newj) = p(i) + p(i) = newj + jar(newj) = ja(j) + ar(newj) = a(j) + 3 continue +c ****** replace old row in ja and a ************************* + i = n + 1 + do 4 j=jmin,jmax + i = p(i) + ja(j) = jar(i) + 4 a(j) = ar(i) + 5 continue + flag = 0 + return +c +c ** error.. duplicate entry in a + 102 flag = n + k + return + end + subroutine nsfc + * (n, r, ic, ia,ja, jlmax,il,jl,ijl, jumax,iu,ju,iju, + * q, ira,jra, irac, irl,jrl, iru,jru, flag) +c*** subroutine nsfc +c*** symbolic ldu-factorization of nonsymmetric sparse matrix +c (compressed pointer storage) +c +c +c input variables.. n, r, ic, ia, ja, jlmax, jumax. +c output variables.. il, jl, ijl, iu, ju, iju, flag. +c +c parameters used internally.. +c nia - q - suppose m* is the result of reordering m. if +c - processing of the ith row of m* (hence the ith +c - row of u) is being done, q(j) is initially +c - nonzero if m*(i,j) is nonzero (j.ge.i). since +c - values need not be stored, each entry points to the +c - next nonzero and q(n+1) points to the first. n+1 +c - indicates the end of the list. for example, if n=9 +c - and the 5th row of m* is +c - 0 x x 0 x 0 0 x 0 +c - then q will initially be +c - a a a a 8 a a 10 5 (a - arbitrary). +c - as the algorithm proceeds, other elements of q +c - are inserted in the list because of fillin. +c - q is used in an analogous manner to compute the +c - ith column of l. +c - size = n+1. +c nia - ira, - vectors used to find the columns of m. at the kth +c nia - jra, step of the factorization, irac(k) points to the +c nia - irac head of a linked list in jra of row indices i +c - such that i .ge. k and m(i,k) is nonzero. zero +c - indicates the end of the list. ira(i) (i.ge.k) +c - points to the smallest j such that j .ge. k and +c - m(i,j) is nonzero. +c - size of each = n. +c nia - irl, - vectors used to find the rows of l. at the kth step +c nia - jrl of the factorization, jrl(k) points to the head +c - of a linked list in jrl of column indices j +c - such j .lt. k and l(k,j) is nonzero. zero +c - indicates the end of the list. irl(j) (j.lt.k) +c - points to the smallest i such that i .ge. k and +c - l(i,j) is nonzero. +c - size of each = n. +c nia - iru, - vectors used in a manner analogous to irl and jrl +c nia - jru to find the columns of u. +c - size of each = n. +c +c internal variables.. +c jlptr - points to the last position used in jl. +c juptr - points to the last position used in ju. +c jmin,jmax - are the indices in a or u of the first and last +c elements to be examined in a given row. +c for example, jmin=ia(k), jmax=ia(k+1)-1. +c + integer cend, qm, rend, rk, vj + integer ia(*), ja(*), ira(*), jra(*), il(*), jl(*), ijl(*) + integer iu(*), ju(*), iju(*), irl(*), jrl(*), iru(*), jru(*) + integer r(*), ic(*), q(*), irac(*), flag +c +c ****** initialize pointers **************************************** + np1 = n + 1 + jlmin = 1 + jlptr = 0 + il(1) = 1 + jumin = 1 + juptr = 0 + iu(1) = 1 + do 1 k=1,n + irac(k) = 0 + jra(k) = 0 + jrl(k) = 0 + 1 jru(k) = 0 +c ****** initialize column pointers for a *************************** + do 2 k=1,n + rk = r(k) + iak = ia(rk) + if (iak .ge. ia(rk+1)) go to 101 + jaiak = ic(ja(iak)) + if (jaiak .gt. k) go to 105 + jra(k) = irac(jaiak) + irac(jaiak) = k + 2 ira(k) = iak +c +c ****** for each column of l and row of u ************************** + do 41 k=1,n +c +c ****** initialize q for computing kth column of l ***************** + q(np1) = np1 + luk = -1 +c ****** by filling in kth column of a ****************************** + vj = irac(k) + if (vj .eq. 0) go to 5 + 3 qm = np1 + 4 m = qm + qm = q(m) + if (qm .lt. vj) go to 4 + if (qm .eq. vj) go to 102 + luk = luk + 1 + q(m) = vj + q(vj) = qm + vj = jra(vj) + if (vj .ne. 0) go to 3 +c ****** link through jru ******************************************* + 5 lastid = 0 + lasti = 0 + ijl(k) = jlptr + i = k + 6 i = jru(i) + if (i .eq. 0) go to 10 + qm = np1 + jmin = irl(i) + jmax = ijl(i) + il(i+1) - il(i) - 1 + long = jmax - jmin + if (long .lt. 0) go to 6 + jtmp = jl(jmin) + if (jtmp .ne. k) long = long + 1 + if (jtmp .eq. k) r(i) = -r(i) + if (lastid .ge. long) go to 7 + lasti = i + lastid = long +c ****** and merge the corresponding columns into the kth column **** + 7 do 9 j=jmin,jmax + vj = jl(j) + 8 m = qm + qm = q(m) + if (qm .lt. vj) go to 8 + if (qm .eq. vj) go to 9 + luk = luk + 1 + q(m) = vj + q(vj) = qm + qm = vj + 9 continue + go to 6 +c ****** lasti is the longest column merged into the kth ************ +c ****** see if it equals the entire kth column ********************* + 10 qm = q(np1) + if (qm .ne. k) go to 105 + if (luk .eq. 0) go to 17 + if (lastid .ne. luk) go to 11 +c ****** if so, jl can be compressed ******************************** + irll = irl(lasti) + ijl(k) = irll + 1 + if (jl(irll) .ne. k) ijl(k) = ijl(k) - 1 + go to 17 +c ****** if not, see if kth column can overlap the previous one ***** + 11 if (jlmin .gt. jlptr) go to 15 + qm = q(qm) + do 12 j=jlmin,jlptr + if (jl(j) - qm) 12, 13, 15 + 12 continue + go to 15 + 13 ijl(k) = j + do 14 i=j,jlptr + if (jl(i) .ne. qm) go to 15 + qm = q(qm) + if (qm .gt. n) go to 17 + 14 continue + jlptr = j - 1 +c ****** move column indices from q to jl, update vectors *********** + 15 jlmin = jlptr + 1 + ijl(k) = jlmin + if (luk .eq. 0) go to 17 + jlptr = jlptr + luk + if (jlptr .gt. jlmax) go to 103 + qm = q(np1) + do 16 j=jlmin,jlptr + qm = q(qm) + 16 jl(j) = qm + 17 irl(k) = ijl(k) + il(k+1) = il(k) + luk +c +c ****** initialize q for computing kth row of u ******************** + q(np1) = np1 + luk = -1 +c ****** by filling in kth row of reordered a *********************** + rk = r(k) + jmin = ira(k) + jmax = ia(rk+1) - 1 + if (jmin .gt. jmax) go to 20 + do 19 j=jmin,jmax + vj = ic(ja(j)) + qm = np1 + 18 m = qm + qm = q(m) + if (qm .lt. vj) go to 18 + if (qm .eq. vj) go to 102 + luk = luk + 1 + q(m) = vj + q(vj) = qm + 19 continue +c ****** link through jrl, ****************************************** + 20 lastid = 0 + lasti = 0 + iju(k) = juptr + i = k + i1 = jrl(k) + 21 i = i1 + if (i .eq. 0) go to 26 + i1 = jrl(i) + qm = np1 + jmin = iru(i) + jmax = iju(i) + iu(i+1) - iu(i) - 1 + long = jmax - jmin + if (long .lt. 0) go to 21 + jtmp = ju(jmin) + if (jtmp .eq. k) go to 22 +c ****** update irl and jrl, ***************************************** + long = long + 1 + cend = ijl(i) + il(i+1) - il(i) + irl(i) = irl(i) + 1 + if (irl(i) .ge. cend) go to 22 + j = jl(irl(i)) + jrl(i) = jrl(j) + jrl(j) = i + 22 if (lastid .ge. long) go to 23 + lasti = i + lastid = long +c ****** and merge the corresponding rows into the kth row ********** + 23 do 25 j=jmin,jmax + vj = ju(j) + 24 m = qm + qm = q(m) + if (qm .lt. vj) go to 24 + if (qm .eq. vj) go to 25 + luk = luk + 1 + q(m) = vj + q(vj) = qm + qm = vj + 25 continue + go to 21 +c ****** update jrl(k) and irl(k) *********************************** + 26 if (il(k+1) .le. il(k)) go to 27 + j = jl(irl(k)) + jrl(k) = jrl(j) + jrl(j) = k +c ****** lasti is the longest row merged into the kth *************** +c ****** see if it equals the entire kth row ************************ + 27 qm = q(np1) + if (qm .ne. k) go to 105 + if (luk .eq. 0) go to 34 + if (lastid .ne. luk) go to 28 +c ****** if so, ju can be compressed ******************************** + irul = iru(lasti) + iju(k) = irul + 1 + if (ju(irul) .ne. k) iju(k) = iju(k) - 1 + go to 34 +c ****** if not, see if kth row can overlap the previous one ******** + 28 if (jumin .gt. juptr) go to 32 + qm = q(qm) + do 29 j=jumin,juptr + if (ju(j) - qm) 29, 30, 32 + 29 continue + go to 32 + 30 iju(k) = j + do 31 i=j,juptr + if (ju(i) .ne. qm) go to 32 + qm = q(qm) + if (qm .gt. n) go to 34 + 31 continue + juptr = j - 1 +c ****** move row indices from q to ju, update vectors ************** + 32 jumin = juptr + 1 + iju(k) = jumin + if (luk .eq. 0) go to 34 + juptr = juptr + luk + if (juptr .gt. jumax) go to 106 + qm = q(np1) + do 33 j=jumin,juptr + qm = q(qm) + 33 ju(j) = qm + 34 iru(k) = iju(k) + iu(k+1) = iu(k) + luk +c +c ****** update iru, jru ******************************************** + i = k + 35 i1 = jru(i) + if (r(i) .lt. 0) go to 36 + rend = iju(i) + iu(i+1) - iu(i) + if (iru(i) .ge. rend) go to 37 + j = ju(iru(i)) + jru(i) = jru(j) + jru(j) = i + go to 37 + 36 r(i) = -r(i) + 37 i = i1 + if (i .eq. 0) go to 38 + iru(i) = iru(i) + 1 + go to 35 +c +c ****** update ira, jra, irac ************************************** + 38 i = irac(k) + if (i .eq. 0) go to 41 + 39 i1 = jra(i) + ira(i) = ira(i) + 1 + if (ira(i) .ge. ia(r(i)+1)) go to 40 + irai = ira(i) + jairai = ic(ja(irai)) + if (jairai .gt. i) go to 40 + jra(i) = irac(jairai) + irac(jairai) = i + 40 i = i1 + if (i .ne. 0) go to 39 + 41 continue +c + ijl(n) = jlptr + iju(n) = juptr + flag = 0 + return +c +c ** error.. null row in a + 101 flag = n + rk + return +c ** error.. duplicate entry in a + 102 flag = 2*n + rk + return +c ** error.. insufficient storage for jl + 103 flag = 3*n + k + return +c ** error.. null pivot + 105 flag = 5*n + k + return +c ** error.. insufficient storage for ju + 106 flag = 6*n + k + return + end + subroutine nnfc + * (n, r,c,ic, ia,ja,a, z, b, + * lmax,il,jl,ijl,l, d, umax,iu,ju,iju,u, + * row, tmp, irl,jrl, flag) +c*** subroutine nnfc +c*** numerical ldu-factorization of sparse nonsymmetric matrix and +c solution of system of linear equations (compressed pointer +c storage) +c +c +c input variables.. n, r, c, ic, ia, ja, a, b, +c il, jl, ijl, lmax, iu, ju, iju, umax +c output variables.. z, l, d, u, flag +c +c parameters used internally.. +c nia - irl, - vectors used to find the rows of l. at the kth step +c nia - jrl of the factorization, jrl(k) points to the head +c - of a linked list in jrl of column indices j +c - such j .lt. k and l(k,j) is nonzero. zero +c - indicates the end of the list. irl(j) (j.lt.k) +c - points to the smallest i such that i .ge. k and +c - l(i,j) is nonzero. +c - size of each = n. +c fia - row - holds intermediate values in calculation of u and l. +c - size = n. +c fia - tmp - holds new right-hand side b* for solution of the +c - equation ux = b*. +c - size = n. +c +c internal variables.. +c jmin, jmax - indices of the first and last positions in a row to +c be examined. +c sum - used in calculating tmp. +c + integer rk,umax + integer r(*), c(*), ic(*), ia(*), ja(*), il(*), jl(*), ijl(*) + integer iu(*), ju(*), iju(*), irl(*), jrl(*), flag +c real a(*), l(*), d(*), u(*), z(*), b(*), row(*) +c real tmp(*), lki, sum, dk + double precision a(*), l(*), d(*), u(*), z(*), b(*), row(*) + double precision tmp(*), lki, sum, dk +c +c ****** initialize pointers and test storage *********************** + if(il(n+1)-1 .gt. lmax) go to 104 + if(iu(n+1)-1 .gt. umax) go to 107 + do 1 k=1,n + irl(k) = il(k) + jrl(k) = 0 + 1 continue +c +c ****** for each row *********************************************** + do 19 k=1,n +c ****** reverse jrl and zero row where kth row of l will fill in *** + row(k) = 0 + i1 = 0 + if (jrl(k) .eq. 0) go to 3 + i = jrl(k) + 2 i2 = jrl(i) + jrl(i) = i1 + i1 = i + row(i) = 0 + i = i2 + if (i .ne. 0) go to 2 +c ****** set row to zero where u will fill in *********************** + 3 jmin = iju(k) + jmax = jmin + iu(k+1) - iu(k) - 1 + if (jmin .gt. jmax) go to 5 + do 4 j=jmin,jmax + 4 row(ju(j)) = 0 +c ****** place kth row of a in row ********************************** + 5 rk = r(k) + jmin = ia(rk) + jmax = ia(rk+1) - 1 + do 6 j=jmin,jmax + row(ic(ja(j))) = a(j) + 6 continue +c ****** initialize sum, and link through jrl *********************** + sum = b(rk) + i = i1 + if (i .eq. 0) go to 10 +c ****** assign the kth row of l and adjust row, sum **************** + 7 lki = -row(i) +c ****** if l is not required, then comment out the following line ** + l(irl(i)) = -lki + sum = sum + lki * tmp(i) + jmin = iu(i) + jmax = iu(i+1) - 1 + if (jmin .gt. jmax) go to 9 + mu = iju(i) - jmin + do 8 j=jmin,jmax + 8 row(ju(mu+j)) = row(ju(mu+j)) + lki * u(j) + 9 i = jrl(i) + if (i .ne. 0) go to 7 +c +c ****** assign kth row of u and diagonal d, set tmp(k) ************* + 10 if (row(k) .eq. 0.0d0) go to 108 + dk = 1.0d0 / row(k) + d(k) = dk + tmp(k) = sum * dk + if (k .eq. n) go to 19 + jmin = iu(k) + jmax = iu(k+1) - 1 + if (jmin .gt. jmax) go to 12 + mu = iju(k) - jmin + do 11 j=jmin,jmax + 11 u(j) = row(ju(mu+j)) * dk + 12 continue +c +c ****** update irl and jrl, keeping jrl in decreasing order ******** + i = i1 + if (i .eq. 0) go to 18 + 14 irl(i) = irl(i) + 1 + i1 = jrl(i) + if (irl(i) .ge. il(i+1)) go to 17 + ijlb = irl(i) - il(i) + ijl(i) + j = jl(ijlb) + 15 if (i .gt. jrl(j)) go to 16 + j = jrl(j) + go to 15 + 16 jrl(i) = jrl(j) + jrl(j) = i + 17 i = i1 + if (i .ne. 0) go to 14 + 18 if (irl(k) .ge. il(k+1)) go to 19 + j = jl(ijl(k)) + jrl(k) = jrl(j) + jrl(j) = k + 19 continue +c +c ****** solve ux = tmp by back substitution ********************** + k = n + do 22 i=1,n + sum = tmp(k) + jmin = iu(k) + jmax = iu(k+1) - 1 + if (jmin .gt. jmax) go to 21 + mu = iju(k) - jmin + do 20 j=jmin,jmax + 20 sum = sum - u(j) * tmp(ju(mu+j)) + 21 tmp(k) = sum + z(c(k)) = sum + 22 k = k-1 + flag = 0 + return +c +c ** error.. insufficient storage for l + 104 flag = 4*n + 1 + return +c ** error.. insufficient storage for u + 107 flag = 7*n + 1 + return +c ** error.. zero pivot + 108 flag = 8*n + k + return + end + subroutine nnsc + * (n, r, c, il, jl, ijl, l, d, iu, ju, iju, u, z, b, tmp) +c*** subroutine nnsc +c*** numerical solution of sparse nonsymmetric system of linear +c equations given ldu-factorization (compressed pointer storage) +c +c +c input variables.. n, r, c, il, jl, ijl, l, d, iu, ju, iju, u, b +c output variables.. z +c +c parameters used internally.. +c fia - tmp - temporary vector which gets result of solving ly = b. +c - size = n. +c +c internal variables.. +c jmin, jmax - indices of the first and last positions in a row of +c u or l to be used. +c + integer r(*), c(*), il(*), jl(*), ijl(*), iu(*), ju(*), iju(*) +c real l(*), d(*), u(*), b(*), z(*), tmp(*), tmpk, sum + double precision l(*), d(*), u(*), b(*), z(*), tmp(*), tmpk,sum +c +c ****** set tmp to reordered b ************************************* + do 1 k=1,n + 1 tmp(k) = b(r(k)) +c ****** solve ly = b by forward substitution ********************* + do 3 k=1,n + jmin = il(k) + jmax = il(k+1) - 1 + tmpk = -d(k) * tmp(k) + tmp(k) = -tmpk + if (jmin .gt. jmax) go to 3 + ml = ijl(k) - jmin + do 2 j=jmin,jmax + 2 tmp(jl(ml+j)) = tmp(jl(ml+j)) + tmpk * l(j) + 3 continue +c ****** solve ux = y by back substitution ************************ + k = n + do 6 i=1,n + sum = -tmp(k) + jmin = iu(k) + jmax = iu(k+1) - 1 + if (jmin .gt. jmax) go to 5 + mu = iju(k) - jmin + do 4 j=jmin,jmax + 4 sum = sum + u(j) * tmp(ju(mu+j)) + 5 tmp(k) = -sum + z(c(k)) = -sum + k = k - 1 + 6 continue + return + end + subroutine nntc + * (n, r, c, il, jl, ijl, l, d, iu, ju, iju, u, z, b, tmp) +c*** subroutine nntc +c*** numeric solution of the transpose of a sparse nonsymmetric system +c of linear equations given lu-factorization (compressed pointer +c storage) +c +c +c input variables.. n, r, c, il, jl, ijl, l, d, iu, ju, iju, u, b +c output variables.. z +c +c parameters used internally.. +c fia - tmp - temporary vector which gets result of solving ut y = b +c - size = n. +c +c internal variables.. +c jmin, jmax - indices of the first and last positions in a row of +c u or l to be used. +c + integer r(*), c(*), il(*), jl(*), ijl(*), iu(*), ju(*), iju(*) +c real l(*), d(*), u(*), b(*), z(*), tmp(*), tmpk,sum + double precision l(*), d(*), u(*), b(*), z(*), tmp(*), tmpk,sum +c +c ****** set tmp to reordered b ************************************* + do 1 k=1,n + 1 tmp(k) = b(c(k)) +c ****** solve ut y = b by forward substitution ******************* + do 3 k=1,n + jmin = iu(k) + jmax = iu(k+1) - 1 + tmpk = -tmp(k) + if (jmin .gt. jmax) go to 3 + mu = iju(k) - jmin + do 2 j=jmin,jmax + 2 tmp(ju(mu+j)) = tmp(ju(mu+j)) + tmpk * u(j) + 3 continue +c ****** solve lt x = y by back substitution ********************** + k = n + do 6 i=1,n + sum = -tmp(k) + jmin = il(k) + jmax = il(k+1) - 1 + if (jmin .gt. jmax) go to 5 + ml = ijl(k) - jmin + do 4 j=jmin,jmax + 4 sum = sum + l(j) * tmp(jl(ml+j)) + 5 tmp(k) = -sum * d(k) + z(r(k)) = tmp(k) + k = k - 1 + 6 continue + return + end +*DECK DSTODA + SUBROUTINE DSTODA (NEQ, Y, YH, NYH, YH1, EWT, SAVF, ACOR, + 1 WM, IWM, F, JAC, PJAC, SLVS) + EXTERNAL F, JAC, PJAC, SLVS + INTEGER NEQ, NYH, IWM + DOUBLE PRECISION Y, YH, YH1, EWT, SAVF, ACOR, WM + DIMENSION NEQ(*), Y(*), YH(NYH,*), YH1(*), EWT(*), SAVF(*), + 1 ACOR(*), WM(*), IWM(*) + INTEGER IOWND, IALTH, IPUP, LMAX, MEO, NQNYH, NSLP, + 1 ICF, IERPJ, IERSL, JCUR, JSTART, KFLAG, L, + 2 LYH, LEWT, LACOR, LSAVF, LWM, LIWM, METH, MITER, + 3 MAXORD, MAXCOR, MSBP, MXNCF, N, NQ, NST, NFE, NJE, NQU + INTEGER IOWND2, ICOUNT, IRFLAG, JTYP, MUSED, MXORDN, MXORDS + DOUBLE PRECISION CONIT, CRATE, EL, ELCO, HOLD, RMAX, TESCO, + 2 CCMAX, EL0, H, HMIN, HMXI, HU, RC, TN, UROUND + DOUBLE PRECISION ROWND2, CM1, CM2, PDEST, PDLAST, RATIO, + 1 PDNORM + COMMON /DLS001/ CONIT, CRATE, EL(13), ELCO(13,12), + 1 HOLD, RMAX, TESCO(3,12), + 2 CCMAX, EL0, H, HMIN, HMXI, HU, RC, TN, UROUND, + 3 IOWND(6), IALTH, IPUP, LMAX, MEO, NQNYH, NSLP, + 4 ICF, IERPJ, IERSL, JCUR, JSTART, KFLAG, L, + 5 LYH, LEWT, LACOR, LSAVF, LWM, LIWM, METH, MITER, + 6 MAXORD, MAXCOR, MSBP, MXNCF, N, NQ, NST, NFE, NJE, NQU + COMMON /DLSA01/ ROWND2, CM1(12), CM2(5), PDEST, PDLAST, RATIO, + 1 PDNORM, + 2 IOWND2(3), ICOUNT, IRFLAG, JTYP, MUSED, MXORDN, MXORDS + INTEGER I, I1, IREDO, IRET, J, JB, M, NCF, NEWQ + INTEGER LM1, LM1P1, LM2, LM2P1, NQM1, NQM2 + DOUBLE PRECISION DCON, DDN, DEL, DELP, DSM, DUP, EXDN, EXSM, EXUP, + 1 R, RH, RHDN, RHSM, RHUP, TOLD, DMNORM + DOUBLE PRECISION ALPHA, DM1,DM2, EXM1,EXM2, + 1 PDH, PNORM, RATE, RH1, RH1IT, RH2, RM, SM1(12) + SAVE SM1 + DATA SM1/0.5D0, 0.575D0, 0.55D0, 0.45D0, 0.35D0, 0.25D0, + 1 0.20D0, 0.15D0, 0.10D0, 0.075D0, 0.050D0, 0.025D0/ +C----------------------------------------------------------------------- +C DSTODA performs one step of the integration of an initial value +C problem for a system of ordinary differential equations. +C Note: DSTODA is independent of the value of the iteration method +C indicator MITER, when this is .ne. 0, and hence is independent +C of the type of chord method used, or the Jacobian structure. +C Communication with DSTODA is done with the following variables: +C +C Y = an array of length .ge. N used as the Y argument in +C all calls to F and JAC. +C NEQ = integer array containing problem size in NEQ(1), and +C passed as the NEQ argument in all calls to F and JAC. +C YH = an NYH by LMAX array containing the dependent variables +C and their approximate scaled derivatives, where +C LMAX = MAXORD + 1. YH(i,j+1) contains the approximate +C j-th derivative of y(i), scaled by H**j/factorial(j) +C (j = 0,1,...,NQ). On entry for the first step, the first +C two columns of YH must be set from the initial values. +C NYH = a constant integer .ge. N, the first dimension of YH. +C YH1 = a one-dimensional array occupying the same space as YH. +C EWT = an array of length N containing multiplicative weights +C for local error measurements. Local errors in y(i) are +C compared to 1.0/EWT(i) in various error tests. +C SAVF = an array of working storage, of length N. +C ACOR = a work array of length N, used for the accumulated +C corrections. On a successful return, ACOR(i) contains +C the estimated one-step local error in y(i). +C WM,IWM = real and integer work arrays associated with matrix +C operations in chord iteration (MITER .ne. 0). +C PJAC = name of routine to evaluate and preprocess Jacobian matrix +C and P = I - H*EL0*Jac, if a chord method is being used. +C It also returns an estimate of norm(Jac) in PDNORM. +C SLVS = name of routine to solve linear system in chord iteration. +C CCMAX = maximum relative change in H*EL0 before PJAC is called. +C H = the step size to be attempted on the next step. +C H is altered by the error control algorithm during the +C problem. H can be either positive or negative, but its +C sign must remain constant throughout the problem. +C HMIN = the minimum absolute value of the step size H to be used. +C HMXI = inverse of the maximum absolute value of H to be used. +C HMXI = 0.0 is allowed and corresponds to an infinite HMAX. +C HMIN and HMXI may be changed at any time, but will not +C take effect until the next change of H is considered. +C TN = the independent variable. TN is updated on each step taken. +C JSTART = an integer used for input only, with the following +C values and meanings: +C 0 perform the first step. +C .gt.0 take a new step continuing from the last. +C -1 take the next step with a new value of H, +C N, METH, MITER, and/or matrix parameters. +C -2 take the next step with a new value of H, +C but with other inputs unchanged. +C On return, JSTART is set to 1 to facilitate continuation. +C KFLAG = a completion code with the following meanings: +C 0 the step was succesful. +C -1 the requested error could not be achieved. +C -2 corrector convergence could not be achieved. +C -3 fatal error in PJAC or SLVS. +C A return with KFLAG = -1 or -2 means either +C ABS(H) = HMIN or 10 consecutive failures occurred. +C On a return with KFLAG negative, the values of TN and +C the YH array are as of the beginning of the last +C step, and H is the last step size attempted. +C MAXORD = the maximum order of integration method to be allowed. +C MAXCOR = the maximum number of corrector iterations allowed. +C MSBP = maximum number of steps between PJAC calls (MITER .gt. 0). +C MXNCF = maximum number of convergence failures allowed. +C METH = current method. +C METH = 1 means Adams method (nonstiff) +C METH = 2 means BDF method (stiff) +C METH may be reset by DSTODA. +C MITER = corrector iteration method. +C MITER = 0 means functional iteration. +C MITER = JT .gt. 0 means a chord iteration corresponding +C to Jacobian type JT. (The DLSODA/DLSODAR argument JT is +C communicated here as JTYP, but is not used in DSTODA +C except to load MITER following a method switch.) +C MITER may be reset by DSTODA. +C N = the number of first-order differential equations. +C----------------------------------------------------------------------- + KFLAG = 0 + TOLD = TN + NCF = 0 + IERPJ = 0 + IERSL = 0 + JCUR = 0 + ICF = 0 + DELP = 0.0D0 + IF (JSTART .GT. 0) GO TO 200 + IF (JSTART .EQ. -1) GO TO 100 + IF (JSTART .EQ. -2) GO TO 160 +C----------------------------------------------------------------------- +C On the first call, the order is set to 1, and other variables are +C initialized. RMAX is the maximum ratio by which H can be increased +C in a single step. It is initially 1.E4 to compensate for the small +C initial H, but then is normally equal to 10. If a failure +C occurs (in corrector convergence or error test), RMAX is set at 2 +C for the next increase. +C DCFODE is called to get the needed coefficients for both methods. +C----------------------------------------------------------------------- + LMAX = MAXORD + 1 + NQ = 1 + L = 2 + IALTH = 2 + RMAX = 10000.0D0 + RC = 0.0D0 + EL0 = 1.0D0 + CRATE = 0.7D0 + HOLD = H + NSLP = 0 + IPUP = MITER + IRET = 3 +C Initialize switching parameters. METH = 1 is assumed initially. ----- + ICOUNT = 20 + IRFLAG = 0 + PDEST = 0.0D0 + PDLAST = 0.0D0 + RATIO = 5.0D0 + CALL DCFODE (2, ELCO, TESCO) + DO 10 I = 1,5 + 10 CM2(I) = TESCO(2,I)*ELCO(I+1,I) + CALL DCFODE (1, ELCO, TESCO) + DO 20 I = 1,12 + 20 CM1(I) = TESCO(2,I)*ELCO(I+1,I) + GO TO 150 +C----------------------------------------------------------------------- +C The following block handles preliminaries needed when JSTART = -1. +C IPUP is set to MITER to force a matrix update. +C If an order increase is about to be considered (IALTH = 1), +C IALTH is reset to 2 to postpone consideration one more step. +C If the caller has changed METH, DCFODE is called to reset +C the coefficients of the method. +C If H is to be changed, YH must be rescaled. +C If H or METH is being changed, IALTH is reset to L = NQ + 1 +C to prevent further changes in H for that many steps. +C----------------------------------------------------------------------- + 100 IPUP = MITER + LMAX = MAXORD + 1 + IF (IALTH .EQ. 1) IALTH = 2 + IF (METH .EQ. MUSED) GO TO 160 + CALL DCFODE (METH, ELCO, TESCO) + IALTH = L + IRET = 1 +C----------------------------------------------------------------------- +C The el vector and related constants are reset +C whenever the order NQ is changed, or at the start of the problem. +C----------------------------------------------------------------------- + 150 DO 155 I = 1,L + 155 EL(I) = ELCO(I,NQ) + NQNYH = NQ*NYH + RC = RC*EL(1)/EL0 + EL0 = EL(1) + CONIT = 0.5D0/(NQ+2) + GO TO (160, 170, 200), IRET +C----------------------------------------------------------------------- +C If H is being changed, the H ratio RH is checked against +C RMAX, HMIN, and HMXI, and the YH array rescaled. IALTH is set to +C L = NQ + 1 to prevent a change of H for that many steps, unless +C forced by a convergence or error test failure. +C----------------------------------------------------------------------- + 160 IF (H .EQ. HOLD) GO TO 200 + RH = H/HOLD + H = HOLD + IREDO = 3 + GO TO 175 + 170 RH = MAX(RH,HMIN/ABS(H)) + 175 RH = MIN(RH,RMAX) + RH = RH/MAX(1.0D0,ABS(H)*HMXI*RH) +C----------------------------------------------------------------------- +C If METH = 1, also restrict the new step size by the stability region. +C If this reduces H, set IRFLAG to 1 so that if there are roundoff +C problems later, we can assume that is the cause of the trouble. +C----------------------------------------------------------------------- + IF (METH .EQ. 2) GO TO 178 + IRFLAG = 0 + PDH = MAX(ABS(H)*PDLAST,0.000001D0) + IF (RH*PDH*1.00001D0 .LT. SM1(NQ)) GO TO 178 + RH = SM1(NQ)/PDH + IRFLAG = 1 + 178 CONTINUE + R = 1.0D0 + DO 180 J = 2,L + R = R*RH + DO 180 I = 1,N + 180 YH(I,J) = YH(I,J)*R + H = H*RH + RC = RC*RH + IALTH = L + IF (IREDO .EQ. 0) GO TO 690 +C----------------------------------------------------------------------- +C This section computes the predicted values by effectively +C multiplying the YH array by the Pascal triangle matrix. +C RC is the ratio of new to old values of the coefficient H*EL(1). +C When RC differs from 1 by more than CCMAX, IPUP is set to MITER +C to force PJAC to be called, if a Jacobian is involved. +C In any case, PJAC is called at least every MSBP steps. +C----------------------------------------------------------------------- + 200 IF (ABS(RC-1.0D0) .GT. CCMAX) IPUP = MITER + IF (NST .GE. NSLP+MSBP) IPUP = MITER + TN = TN + H + I1 = NQNYH + 1 + DO 215 JB = 1,NQ + I1 = I1 - NYH +CDIR$ IVDEP + DO 210 I = I1,NQNYH + 210 YH1(I) = YH1(I) + YH1(I+NYH) + 215 CONTINUE + PNORM = DMNORM (N, YH1, EWT) +C----------------------------------------------------------------------- +C Up to MAXCOR corrector iterations are taken. A convergence test is +C made on the RMS-norm of each correction, weighted by the error +C weight vector EWT. The sum of the corrections is accumulated in the +C vector ACOR(i). The YH array is not altered in the corrector loop. +C----------------------------------------------------------------------- + 220 M = 0 + RATE = 0.0D0 + DEL = 0.0D0 + DO 230 I = 1,N + 230 Y(I) = YH(I,1) + CALL F (NEQ, TN, Y, SAVF) + NFE = NFE + 1 + IF (IPUP .LE. 0) GO TO 250 +C----------------------------------------------------------------------- +C If indicated, the matrix P = I - H*EL(1)*J is reevaluated and +C preprocessed before starting the corrector iteration. IPUP is set +C to 0 as an indicator that this has been done. +C----------------------------------------------------------------------- + CALL PJAC (NEQ, Y, YH, NYH, EWT, ACOR, SAVF, WM, IWM, F, JAC) + IPUP = 0 + RC = 1.0D0 + NSLP = NST + CRATE = 0.7D0 + IF (IERPJ .NE. 0) GO TO 430 + 250 DO 260 I = 1,N + 260 ACOR(I) = 0.0D0 + 270 IF (MITER .NE. 0) GO TO 350 +C----------------------------------------------------------------------- +C In the case of functional iteration, update Y directly from +C the result of the last function evaluation. +C----------------------------------------------------------------------- + DO 290 I = 1,N + SAVF(I) = H*SAVF(I) - YH(I,2) + 290 Y(I) = SAVF(I) - ACOR(I) + DEL = DMNORM (N, Y, EWT) + DO 300 I = 1,N + Y(I) = YH(I,1) + EL(1)*SAVF(I) + 300 ACOR(I) = SAVF(I) + GO TO 400 +C----------------------------------------------------------------------- +C In the case of the chord method, compute the corrector error, +C and solve the linear system with that as right-hand side and +C P as coefficient matrix. +C----------------------------------------------------------------------- + 350 DO 360 I = 1,N + 360 Y(I) = H*SAVF(I) - (YH(I,2) + ACOR(I)) + CALL SLVS (WM, IWM, Y, SAVF) + IF (IERSL .LT. 0) GO TO 430 + IF (IERSL .GT. 0) GO TO 410 + DEL = DMNORM (N, Y, EWT) + DO 380 I = 1,N + ACOR(I) = ACOR(I) + Y(I) + 380 Y(I) = YH(I,1) + EL(1)*ACOR(I) +C----------------------------------------------------------------------- +C Test for convergence. If M .gt. 0, an estimate of the convergence +C rate constant is stored in CRATE, and this is used in the test. +C +C We first check for a change of iterates that is the size of +C roundoff error. If this occurs, the iteration has converged, and a +C new rate estimate is not formed. +C In all other cases, force at least two iterations to estimate a +C local Lipschitz constant estimate for Adams methods. +C On convergence, form PDEST = local maximum Lipschitz constant +C estimate. PDLAST is the most recent nonzero estimate. +C----------------------------------------------------------------------- + 400 CONTINUE + IF (DEL .LE. 100.0D0*PNORM*UROUND) GO TO 450 + IF (M .EQ. 0 .AND. METH .EQ. 1) GO TO 405 + IF (M .EQ. 0) GO TO 402 + RM = 1024.0D0 + IF (DEL .LE. 1024.0D0*DELP) RM = DEL/DELP + RATE = MAX(RATE,RM) + CRATE = MAX(0.2D0*CRATE,RM) + 402 DCON = DEL*MIN(1.0D0,1.5D0*CRATE)/(TESCO(2,NQ)*CONIT) + IF (DCON .GT. 1.0D0) GO TO 405 + PDEST = MAX(PDEST,RATE/ABS(H*EL(1))) + IF (PDEST .NE. 0.0D0) PDLAST = PDEST + GO TO 450 + 405 CONTINUE + M = M + 1 + IF (M .EQ. MAXCOR) GO TO 410 + IF (M .GE. 2 .AND. DEL .GT. 2.0D0*DELP) GO TO 410 + DELP = DEL + CALL F (NEQ, TN, Y, SAVF) + NFE = NFE + 1 + GO TO 270 +C----------------------------------------------------------------------- +C The corrector iteration failed to converge. +C If MITER .ne. 0 and the Jacobian is out of date, PJAC is called for +C the next try. Otherwise the YH array is retracted to its values +C before prediction, and H is reduced, if possible. If H cannot be +C reduced or MXNCF failures have occurred, exit with KFLAG = -2. +C----------------------------------------------------------------------- + 410 IF (MITER .EQ. 0 .OR. JCUR .EQ. 1) GO TO 430 + ICF = 1 + IPUP = MITER + GO TO 220 + 430 ICF = 2 + NCF = NCF + 1 + RMAX = 2.0D0 + TN = TOLD + I1 = NQNYH + 1 + DO 445 JB = 1,NQ + I1 = I1 - NYH +CDIR$ IVDEP + DO 440 I = I1,NQNYH + 440 YH1(I) = YH1(I) - YH1(I+NYH) + 445 CONTINUE + IF (IERPJ .LT. 0 .OR. IERSL .LT. 0) GO TO 680 + IF (ABS(H) .LE. HMIN*1.00001D0) GO TO 670 + IF (NCF .EQ. MXNCF) GO TO 670 + RH = 0.25D0 + IPUP = MITER + IREDO = 1 + GO TO 170 +C----------------------------------------------------------------------- +C The corrector has converged. JCUR is set to 0 +C to signal that the Jacobian involved may need updating later. +C The local error test is made and control passes to statement 500 +C if it fails. +C----------------------------------------------------------------------- + 450 JCUR = 0 + IF (M .EQ. 0) DSM = DEL/TESCO(2,NQ) + IF (M .GT. 0) DSM = DMNORM (N, ACOR, EWT)/TESCO(2,NQ) + IF (DSM .GT. 1.0D0) GO TO 500 +C----------------------------------------------------------------------- +C After a successful step, update the YH array. +C Decrease ICOUNT by 1, and if it is -1, consider switching methods. +C If a method switch is made, reset various parameters, +C rescale the YH array, and exit. If there is no switch, +C consider changing H if IALTH = 1. Otherwise decrease IALTH by 1. +C If IALTH is then 1 and NQ .lt. MAXORD, then ACOR is saved for +C use in a possible order increase on the next step. +C If a change in H is considered, an increase or decrease in order +C by one is considered also. A change in H is made only if it is by a +C factor of at least 1.1. If not, IALTH is set to 3 to prevent +C testing for that many steps. +C----------------------------------------------------------------------- + KFLAG = 0 + IREDO = 0 + NST = NST + 1 + HU = H + NQU = NQ + MUSED = METH + DO 460 J = 1,L + DO 460 I = 1,N + 460 YH(I,J) = YH(I,J) + EL(J)*ACOR(I) + ICOUNT = ICOUNT - 1 + IF (ICOUNT .GE. 0) GO TO 488 + IF (METH .EQ. 2) GO TO 480 +C----------------------------------------------------------------------- +C We are currently using an Adams method. Consider switching to BDF. +C If the current order is greater than 5, assume the problem is +C not stiff, and skip this section. +C If the Lipschitz constant and error estimate are not polluted +C by roundoff, go to 470 and perform the usual test. +C Otherwise, switch to the BDF methods if the last step was +C restricted to insure stability (irflag = 1), and stay with Adams +C method if not. When switching to BDF with polluted error estimates, +C in the absence of other information, double the step size. +C +C When the estimates are OK, we make the usual test by computing +C the step size we could have (ideally) used on this step, +C with the current (Adams) method, and also that for the BDF. +C If NQ .gt. MXORDS, we consider changing to order MXORDS on switching. +C Compare the two step sizes to decide whether to switch. +C The step size advantage must be at least RATIO = 5 to switch. +C----------------------------------------------------------------------- + IF (NQ .GT. 5) GO TO 488 + IF (DSM .GT. 100.0D0*PNORM*UROUND .AND. PDEST .NE. 0.0D0) + 1 GO TO 470 + IF (IRFLAG .EQ. 0) GO TO 488 + RH2 = 2.0D0 + NQM2 = MIN(NQ,MXORDS) + GO TO 478 + 470 CONTINUE + EXSM = 1.0D0/L + RH1 = 1.0D0/(1.2D0*DSM**EXSM + 0.0000012D0) + RH1IT = 2.0D0*RH1 + PDH = PDLAST*ABS(H) + IF (PDH*RH1 .GT. 0.00001D0) RH1IT = SM1(NQ)/PDH + RH1 = MIN(RH1,RH1IT) + IF (NQ .LE. MXORDS) GO TO 474 + NQM2 = MXORDS + LM2 = MXORDS + 1 + EXM2 = 1.0D0/LM2 + LM2P1 = LM2 + 1 + DM2 = DMNORM (N, YH(1,LM2P1), EWT)/CM2(MXORDS) + RH2 = 1.0D0/(1.2D0*DM2**EXM2 + 0.0000012D0) + GO TO 476 + 474 DM2 = DSM*(CM1(NQ)/CM2(NQ)) + RH2 = 1.0D0/(1.2D0*DM2**EXSM + 0.0000012D0) + NQM2 = NQ + 476 CONTINUE + IF (RH2 .LT. RATIO*RH1) GO TO 488 +C THE SWITCH TEST PASSED. RESET RELEVANT QUANTITIES FOR BDF. ---------- + 478 RH = RH2 + ICOUNT = 20 + METH = 2 + MITER = JTYP + PDLAST = 0.0D0 + NQ = NQM2 + L = NQ + 1 + GO TO 170 +C----------------------------------------------------------------------- +C We are currently using a BDF method. Consider switching to Adams. +C Compute the step size we could have (ideally) used on this step, +C with the current (BDF) method, and also that for the Adams. +C If NQ .gt. MXORDN, we consider changing to order MXORDN on switching. +C Compare the two step sizes to decide whether to switch. +C The step size advantage must be at least 5/RATIO = 1 to switch. +C If the step size for Adams would be so small as to cause +C roundoff pollution, we stay with BDF. +C----------------------------------------------------------------------- + 480 CONTINUE + EXSM = 1.0D0/L + IF (MXORDN .GE. NQ) GO TO 484 + NQM1 = MXORDN + LM1 = MXORDN + 1 + EXM1 = 1.0D0/LM1 + LM1P1 = LM1 + 1 + DM1 = DMNORM (N, YH(1,LM1P1), EWT)/CM1(MXORDN) + RH1 = 1.0D0/(1.2D0*DM1**EXM1 + 0.0000012D0) + GO TO 486 + 484 DM1 = DSM*(CM2(NQ)/CM1(NQ)) + RH1 = 1.0D0/(1.2D0*DM1**EXSM + 0.0000012D0) + NQM1 = NQ + EXM1 = EXSM + 486 RH1IT = 2.0D0*RH1 + PDH = PDNORM*ABS(H) + IF (PDH*RH1 .GT. 0.00001D0) RH1IT = SM1(NQM1)/PDH + RH1 = MIN(RH1,RH1IT) + RH2 = 1.0D0/(1.2D0*DSM**EXSM + 0.0000012D0) + IF (RH1*RATIO .LT. 5.0D0*RH2) GO TO 488 + ALPHA = MAX(0.001D0,RH1) + DM1 = (ALPHA**EXM1)*DM1 + IF (DM1 .LE. 1000.0D0*UROUND*PNORM) GO TO 488 +C The switch test passed. Reset relevant quantities for Adams. -------- + RH = RH1 + ICOUNT = 20 + METH = 1 + MITER = 0 + PDLAST = 0.0D0 + NQ = NQM1 + L = NQ + 1 + GO TO 170 +C +C No method switch is being made. Do the usual step/order selection. -- + 488 CONTINUE + IALTH = IALTH - 1 + IF (IALTH .EQ. 0) GO TO 520 + IF (IALTH .GT. 1) GO TO 700 + IF (L .EQ. LMAX) GO TO 700 + DO 490 I = 1,N + 490 YH(I,LMAX) = ACOR(I) + GO TO 700 +C----------------------------------------------------------------------- +C The error test failed. KFLAG keeps track of multiple failures. +C Restore TN and the YH array to their previous values, and prepare +C to try the step again. Compute the optimum step size for this or +C one lower order. After 2 or more failures, H is forced to decrease +C by a factor of 0.2 or less. +C----------------------------------------------------------------------- + 500 KFLAG = KFLAG - 1 + TN = TOLD + I1 = NQNYH + 1 + DO 515 JB = 1,NQ + I1 = I1 - NYH +CDIR$ IVDEP + DO 510 I = I1,NQNYH + 510 YH1(I) = YH1(I) - YH1(I+NYH) + 515 CONTINUE + RMAX = 2.0D0 + IF (ABS(H) .LE. HMIN*1.00001D0) GO TO 660 + IF (KFLAG .LE. -3) GO TO 640 + IREDO = 2 + RHUP = 0.0D0 + GO TO 540 +C----------------------------------------------------------------------- +C Regardless of the success or failure of the step, factors +C RHDN, RHSM, and RHUP are computed, by which H could be multiplied +C at order NQ - 1, order NQ, or order NQ + 1, respectively. +C In the case of failure, RHUP = 0.0 to avoid an order increase. +C The largest of these is determined and the new order chosen +C accordingly. If the order is to be increased, we compute one +C additional scaled derivative. +C----------------------------------------------------------------------- + 520 RHUP = 0.0D0 + IF (L .EQ. LMAX) GO TO 540 + DO 530 I = 1,N + 530 SAVF(I) = ACOR(I) - YH(I,LMAX) + DUP = DMNORM (N, SAVF, EWT)/TESCO(3,NQ) + EXUP = 1.0D0/(L+1) + RHUP = 1.0D0/(1.4D0*DUP**EXUP + 0.0000014D0) + 540 EXSM = 1.0D0/L + RHSM = 1.0D0/(1.2D0*DSM**EXSM + 0.0000012D0) + RHDN = 0.0D0 + IF (NQ .EQ. 1) GO TO 550 + DDN = DMNORM (N, YH(1,L), EWT)/TESCO(1,NQ) + EXDN = 1.0D0/NQ + RHDN = 1.0D0/(1.3D0*DDN**EXDN + 0.0000013D0) +C If METH = 1, limit RH according to the stability region also. -------- + 550 IF (METH .EQ. 2) GO TO 560 + PDH = MAX(ABS(H)*PDLAST,0.000001D0) + IF (L .LT. LMAX) RHUP = MIN(RHUP,SM1(L)/PDH) + RHSM = MIN(RHSM,SM1(NQ)/PDH) + IF (NQ .GT. 1) RHDN = MIN(RHDN,SM1(NQ-1)/PDH) + PDEST = 0.0D0 + 560 IF (RHSM .GE. RHUP) GO TO 570 + IF (RHUP .GT. RHDN) GO TO 590 + GO TO 580 + 570 IF (RHSM .LT. RHDN) GO TO 580 + NEWQ = NQ + RH = RHSM + GO TO 620 + 580 NEWQ = NQ - 1 + RH = RHDN + IF (KFLAG .LT. 0 .AND. RH .GT. 1.0D0) RH = 1.0D0 + GO TO 620 + 590 NEWQ = L + RH = RHUP + IF (RH .LT. 1.1D0) GO TO 610 + R = EL(L)/L + DO 600 I = 1,N + 600 YH(I,NEWQ+1) = ACOR(I)*R + GO TO 630 + 610 IALTH = 3 + GO TO 700 +C If METH = 1 and H is restricted by stability, bypass 10 percent test. + 620 IF (METH .EQ. 2) GO TO 622 + IF (RH*PDH*1.00001D0 .GE. SM1(NEWQ)) GO TO 625 + 622 IF (KFLAG .EQ. 0 .AND. RH .LT. 1.1D0) GO TO 610 + 625 IF (KFLAG .LE. -2) RH = MIN(RH,0.2D0) +C----------------------------------------------------------------------- +C If there is a change of order, reset NQ, L, and the coefficients. +C In any case H is reset according to RH and the YH array is rescaled. +C Then exit from 690 if the step was OK, or redo the step otherwise. +C----------------------------------------------------------------------- + IF (NEWQ .EQ. NQ) GO TO 170 + 630 NQ = NEWQ + L = NQ + 1 + IRET = 2 + GO TO 150 +C----------------------------------------------------------------------- +C Control reaches this section if 3 or more failures have occured. +C If 10 failures have occurred, exit with KFLAG = -1. +C It is assumed that the derivatives that have accumulated in the +C YH array have errors of the wrong order. Hence the first +C derivative is recomputed, and the order is set to 1. Then +C H is reduced by a factor of 10, and the step is retried, +C until it succeeds or H reaches HMIN. +C----------------------------------------------------------------------- + 640 IF (KFLAG .EQ. -10) GO TO 660 + RH = 0.1D0 + RH = MAX(HMIN/ABS(H),RH) + H = H*RH + DO 645 I = 1,N + 645 Y(I) = YH(I,1) + CALL F (NEQ, TN, Y, SAVF) + NFE = NFE + 1 + DO 650 I = 1,N + 650 YH(I,2) = H*SAVF(I) + IPUP = MITER + IALTH = 5 + IF (NQ .EQ. 1) GO TO 200 + NQ = 1 + L = 2 + IRET = 3 + GO TO 150 +C----------------------------------------------------------------------- +C All returns are made through this section. H is saved in HOLD +C to allow the caller to change H on the next step. +C----------------------------------------------------------------------- + 660 KFLAG = -1 + GO TO 720 + 670 KFLAG = -2 + GO TO 720 + 680 KFLAG = -3 + GO TO 720 + 690 RMAX = 10.0D0 + 700 R = 1.0D0/TESCO(2,NQU) + DO 710 I = 1,N + 710 ACOR(I) = ACOR(I)*R + 720 HOLD = H + JSTART = 1 + RETURN +C----------------------- End of Subroutine DSTODA ---------------------- + END +*DECK DPRJA + SUBROUTINE DPRJA (NEQ, Y, YH, NYH, EWT, FTEM, SAVF, WM, IWM, + 1 F, JAC) + EXTERNAL F, JAC + INTEGER NEQ, NYH, IWM + DOUBLE PRECISION Y, YH, EWT, FTEM, SAVF, WM + DIMENSION NEQ(*), Y(*), YH(NYH,*), EWT(*), FTEM(*), SAVF(*), + 1 WM(*), IWM(*) + INTEGER IOWND, IOWNS, + 1 ICF, IERPJ, IERSL, JCUR, JSTART, KFLAG, L, + 2 LYH, LEWT, LACOR, LSAVF, LWM, LIWM, METH, MITER, + 3 MAXORD, MAXCOR, MSBP, MXNCF, N, NQ, NST, NFE, NJE, NQU + INTEGER IOWND2, IOWNS2, JTYP, MUSED, MXORDN, MXORDS + DOUBLE PRECISION ROWNS, + 1 CCMAX, EL0, H, HMIN, HMXI, HU, RC, TN, UROUND + DOUBLE PRECISION ROWND2, ROWNS2, PDNORM + COMMON /DLS001/ ROWNS(209), + 1 CCMAX, EL0, H, HMIN, HMXI, HU, RC, TN, UROUND, + 2 IOWND(6), IOWNS(6), + 3 ICF, IERPJ, IERSL, JCUR, JSTART, KFLAG, L, + 4 LYH, LEWT, LACOR, LSAVF, LWM, LIWM, METH, MITER, + 5 MAXORD, MAXCOR, MSBP, MXNCF, N, NQ, NST, NFE, NJE, NQU + COMMON /DLSA01/ ROWND2, ROWNS2(20), PDNORM, + 1 IOWND2(3), IOWNS2(2), JTYP, MUSED, MXORDN, MXORDS + INTEGER I, I1, I2, IER, II, J, J1, JJ, LENP, + 1 MBA, MBAND, MEB1, MEBAND, ML, ML3, MU, NP1 + DOUBLE PRECISION CON, FAC, HL0, R, R0, SRUR, YI, YJ, YJJ, + 1 DMNORM, DFNORM, DBNORM +C----------------------------------------------------------------------- +C DPRJA is called by DSTODA to compute and process the matrix +C P = I - H*EL(1)*J , where J is an approximation to the Jacobian. +C Here J is computed by the user-supplied routine JAC if +C MITER = 1 or 4 or by finite differencing if MITER = 2 or 5. +C J, scaled by -H*EL(1), is stored in WM. Then the norm of J (the +C matrix norm consistent with the weighted max-norm on vectors given +C by DMNORM) is computed, and J is overwritten by P. P is then +C subjected to LU decomposition in preparation for later solution +C of linear systems with P as coefficient matrix. This is done +C by DGEFA if MITER = 1 or 2, and by DGBFA if MITER = 4 or 5. +C +C In addition to variables described previously, communication +C with DPRJA uses the following: +C Y = array containing predicted values on entry. +C FTEM = work array of length N (ACOR in DSTODA). +C SAVF = array containing f evaluated at predicted y. +C WM = real work space for matrices. On output it contains the +C LU decomposition of P. +C Storage of matrix elements starts at WM(3). +C WM also contains the following matrix-related data: +C WM(1) = SQRT(UROUND), used in numerical Jacobian increments. +C IWM = integer work space containing pivot information, starting at +C IWM(21). IWM also contains the band parameters +C ML = IWM(1) and MU = IWM(2) if MITER is 4 or 5. +C EL0 = EL(1) (input). +C PDNORM= norm of Jacobian matrix. (Output). +C IERPJ = output error flag, = 0 if no trouble, .gt. 0 if +C P matrix found to be singular. +C JCUR = output flag = 1 to indicate that the Jacobian matrix +C (or approximation) is now current. +C This routine also uses the Common variables EL0, H, TN, UROUND, +C MITER, N, NFE, and NJE. +C----------------------------------------------------------------------- + NJE = NJE + 1 + IERPJ = 0 + JCUR = 1 + HL0 = H*EL0 + GO TO (100, 200, 300, 400, 500), MITER +C If MITER = 1, call JAC and multiply by scalar. ----------------------- + 100 LENP = N*N + DO 110 I = 1,LENP + 110 WM(I+2) = 0.0D0 + CALL JAC (NEQ, TN, Y, 0, 0, WM(3), N) + CON = -HL0 + DO 120 I = 1,LENP + 120 WM(I+2) = WM(I+2)*CON + GO TO 240 +C If MITER = 2, make N calls to F to approximate J. -------------------- + 200 FAC = DMNORM (N, SAVF, EWT) + R0 = 1000.0D0*ABS(H)*UROUND*N*FAC + IF (R0 .EQ. 0.0D0) R0 = 1.0D0 + SRUR = WM(1) + J1 = 2 + DO 230 J = 1,N + YJ = Y(J) + R = MAX(SRUR*ABS(YJ),R0/EWT(J)) + Y(J) = Y(J) + R + FAC = -HL0/R + CALL F (NEQ, TN, Y, FTEM) + DO 220 I = 1,N + 220 WM(I+J1) = (FTEM(I) - SAVF(I))*FAC + Y(J) = YJ + J1 = J1 + N + 230 CONTINUE + NFE = NFE + N + 240 CONTINUE +C Compute norm of Jacobian. -------------------------------------------- + PDNORM = DFNORM (N, WM(3), EWT)/ABS(HL0) +C Add identity matrix. ------------------------------------------------- + J = 3 + NP1 = N + 1 + DO 250 I = 1,N + WM(J) = WM(J) + 1.0D0 + 250 J = J + NP1 +C Do LU decomposition on P. -------------------------------------------- + CALL DGEFA (WM(3), N, N, IWM(21), IER) + IF (IER .NE. 0) IERPJ = 1 + RETURN +C Dummy block only, since MITER is never 3 in this routine. ------------ + 300 RETURN +C If MITER = 4, call JAC and multiply by scalar. ----------------------- + 400 ML = IWM(1) + MU = IWM(2) + ML3 = ML + 3 + MBAND = ML + MU + 1 + MEBAND = MBAND + ML + LENP = MEBAND*N + DO 410 I = 1,LENP + 410 WM(I+2) = 0.0D0 + CALL JAC (NEQ, TN, Y, ML, MU, WM(ML3), MEBAND) + CON = -HL0 + DO 420 I = 1,LENP + 420 WM(I+2) = WM(I+2)*CON + GO TO 570 +C If MITER = 5, make MBAND calls to F to approximate J. ---------------- + 500 ML = IWM(1) + MU = IWM(2) + MBAND = ML + MU + 1 + MBA = MIN(MBAND,N) + MEBAND = MBAND + ML + MEB1 = MEBAND - 1 + SRUR = WM(1) + FAC = DMNORM (N, SAVF, EWT) + R0 = 1000.0D0*ABS(H)*UROUND*N*FAC + IF (R0 .EQ. 0.0D0) R0 = 1.0D0 + DO 560 J = 1,MBA + DO 530 I = J,N,MBAND + YI = Y(I) + R = MAX(SRUR*ABS(YI),R0/EWT(I)) + 530 Y(I) = Y(I) + R + CALL F (NEQ, TN, Y, FTEM) + DO 550 JJ = J,N,MBAND + Y(JJ) = YH(JJ,1) + YJJ = Y(JJ) + R = MAX(SRUR*ABS(YJJ),R0/EWT(JJ)) + FAC = -HL0/R + I1 = MAX(JJ-MU,1) + I2 = MIN(JJ+ML,N) + II = JJ*MEB1 - ML + 2 + DO 540 I = I1,I2 + 540 WM(II+I) = (FTEM(I) - SAVF(I))*FAC + 550 CONTINUE + 560 CONTINUE + NFE = NFE + MBA + 570 CONTINUE +C Compute norm of Jacobian. -------------------------------------------- + PDNORM = DBNORM (N, WM(ML+3), MEBAND, ML, MU, EWT)/ABS(HL0) +C Add identity matrix. ------------------------------------------------- + II = MBAND + 2 + DO 580 I = 1,N + WM(II) = WM(II) + 1.0D0 + 580 II = II + MEBAND +C Do LU decomposition of P. -------------------------------------------- + CALL DGBFA (WM(3), MEBAND, N, ML, MU, IWM(21), IER) + IF (IER .NE. 0) IERPJ = 1 + RETURN +C----------------------- End of Subroutine DPRJA ----------------------- + END +*DECK DMNORM + DOUBLE PRECISION FUNCTION DMNORM (N, V, W) +C----------------------------------------------------------------------- +C This function routine computes the weighted max-norm +C of the vector of length N contained in the array V, with weights +C contained in the array w of length N: +C DMNORM = MAX(i=1,...,N) ABS(V(i))*W(i) +C----------------------------------------------------------------------- + INTEGER N, I + DOUBLE PRECISION V, W, VM + DIMENSION V(N), W(N) + VM = 0.0D0 + DO 10 I = 1,N + 10 VM = MAX(VM,ABS(V(I))*W(I)) + DMNORM = VM + RETURN +C----------------------- End of Function DMNORM ------------------------ + END +*DECK DFNORM + DOUBLE PRECISION FUNCTION DFNORM (N, A, W) +C----------------------------------------------------------------------- +C This function computes the norm of a full N by N matrix, +C stored in the array A, that is consistent with the weighted max-norm +C on vectors, with weights stored in the array W: +C DFNORM = MAX(i=1,...,N) ( W(i) * Sum(j=1,...,N) ABS(a(i,j))/W(j) ) +C----------------------------------------------------------------------- + INTEGER N, I, J + DOUBLE PRECISION A, W, AN, SUM + DIMENSION A(N,N), W(N) + AN = 0.0D0 + DO 20 I = 1,N + SUM = 0.0D0 + DO 10 J = 1,N + 10 SUM = SUM + ABS(A(I,J))/W(J) + AN = MAX(AN,SUM*W(I)) + 20 CONTINUE + DFNORM = AN + RETURN +C----------------------- End of Function DFNORM ------------------------ + END +*DECK DBNORM + DOUBLE PRECISION FUNCTION DBNORM (N, A, NRA, ML, MU, W) +C----------------------------------------------------------------------- +C This function computes the norm of a banded N by N matrix, +C stored in the array A, that is consistent with the weighted max-norm +C on vectors, with weights stored in the array W. +C ML and MU are the lower and upper half-bandwidths of the matrix. +C NRA is the first dimension of the A array, NRA .ge. ML+MU+1. +C In terms of the matrix elements a(i,j), the norm is given by: +C DBNORM = MAX(i=1,...,N) ( W(i) * Sum(j=1,...,N) ABS(a(i,j))/W(j) ) +C----------------------------------------------------------------------- + INTEGER N, NRA, ML, MU + INTEGER I, I1, JLO, JHI, J + DOUBLE PRECISION A, W + DOUBLE PRECISION AN, SUM + DIMENSION A(NRA,N), W(N) + AN = 0.0D0 + DO 20 I = 1,N + SUM = 0.0D0 + I1 = I + MU + 1 + JLO = MAX(I-ML,1) + JHI = MIN(I+MU,N) + DO 10 J = JLO,JHI + 10 SUM = SUM + ABS(A(I1-J,J))/W(J) + AN = MAX(AN,SUM*W(I)) + 20 CONTINUE + DBNORM = AN + RETURN +C----------------------- End of Function DBNORM ------------------------ + END +*DECK DSRCMA + SUBROUTINE DSRCMA (RSAV, ISAV, JOB) +C----------------------------------------------------------------------- +C This routine saves or restores (depending on JOB) the contents of +C the Common blocks DLS001, DLSA01, which are used +C internally by one or more ODEPACK solvers. +C +C RSAV = real array of length 240 or more. +C ISAV = integer array of length 46 or more. +C JOB = flag indicating to save or restore the Common blocks: +C JOB = 1 if Common is to be saved (written to RSAV/ISAV) +C JOB = 2 if Common is to be restored (read from RSAV/ISAV) +C A call with JOB = 2 presumes a prior call with JOB = 1. +C----------------------------------------------------------------------- + INTEGER ISAV, JOB + INTEGER ILS, ILSA + INTEGER I, LENRLS, LENILS, LENRLA, LENILA + DOUBLE PRECISION RSAV + DOUBLE PRECISION RLS, RLSA + DIMENSION RSAV(*), ISAV(*) + SAVE LENRLS, LENILS, LENRLA, LENILA + COMMON /DLS001/ RLS(218), ILS(37) + COMMON /DLSA01/ RLSA(22), ILSA(9) + DATA LENRLS/218/, LENILS/37/, LENRLA/22/, LENILA/9/ +C + IF (JOB .EQ. 2) GO TO 100 + DO 10 I = 1,LENRLS + 10 RSAV(I) = RLS(I) + DO 15 I = 1,LENRLA + 15 RSAV(LENRLS+I) = RLSA(I) +C + DO 20 I = 1,LENILS + 20 ISAV(I) = ILS(I) + DO 25 I = 1,LENILA + 25 ISAV(LENILS+I) = ILSA(I) +C + RETURN +C + 100 CONTINUE + DO 110 I = 1,LENRLS + 110 RLS(I) = RSAV(I) + DO 115 I = 1,LENRLA + 115 RLSA(I) = RSAV(LENRLS+I) +C + DO 120 I = 1,LENILS + 120 ILS(I) = ISAV(I) + DO 125 I = 1,LENILA + 125 ILSA(I) = ISAV(LENILS+I) +C + RETURN +C----------------------- End of Subroutine DSRCMA ---------------------- + END +*DECK DRCHEK + SUBROUTINE DRCHEK (JOB, G, NEQ, Y, YH,NYH, G0, G1, GX, JROOT, IRT) + EXTERNAL G + INTEGER JOB, NEQ, NYH, JROOT, IRT + DOUBLE PRECISION Y, YH, G0, G1, GX + DIMENSION NEQ(*), Y(*), YH(NYH,*), G0(*), G1(*), GX(*), JROOT(*) + INTEGER IOWND, IOWNS, + 1 ICF, IERPJ, IERSL, JCUR, JSTART, KFLAG, L, + 2 LYH, LEWT, LACOR, LSAVF, LWM, LIWM, METH, MITER, + 3 MAXORD, MAXCOR, MSBP, MXNCF, N, NQ, NST, NFE, NJE, NQU + INTEGER IOWND3, IOWNR3, IRFND, ITASKC, NGC, NGE + DOUBLE PRECISION ROWNS, + 1 CCMAX, EL0, H, HMIN, HMXI, HU, RC, TN, UROUND + DOUBLE PRECISION ROWNR3, T0, TLAST, TOUTC + COMMON /DLS001/ ROWNS(209), + 1 CCMAX, EL0, H, HMIN, HMXI, HU, RC, TN, UROUND, + 2 IOWND(6), IOWNS(6), + 3 ICF, IERPJ, IERSL, JCUR, JSTART, KFLAG, L, + 4 LYH, LEWT, LACOR, LSAVF, LWM, LIWM, METH, MITER, + 5 MAXORD, MAXCOR, MSBP, MXNCF, N, NQ, NST, NFE, NJE, NQU + COMMON /DLSR01/ ROWNR3(2), T0, TLAST, TOUTC, + 1 IOWND3(3), IOWNR3(2), IRFND, ITASKC, NGC, NGE + INTEGER I, IFLAG, JFLAG + DOUBLE PRECISION HMING, T1, TEMP1, TEMP2, X + LOGICAL ZROOT +C----------------------------------------------------------------------- +C This routine checks for the presence of a root in the vicinity of +C the current T, in a manner depending on the input flag JOB. It calls +C Subroutine DROOTS to locate the root as precisely as possible. +C +C In addition to variables described previously, DRCHEK +C uses the following for communication: +C JOB = integer flag indicating type of call: +C JOB = 1 means the problem is being initialized, and DRCHEK +C is to look for a root at or very near the initial T. +C JOB = 2 means a continuation call to the solver was just +C made, and DRCHEK is to check for a root in the +C relevant part of the step last taken. +C JOB = 3 means a successful step was just taken, and DRCHEK +C is to look for a root in the interval of the step. +C G0 = array of length NG, containing the value of g at T = T0. +C G0 is input for JOB .ge. 2, and output in all cases. +C G1,GX = arrays of length NG for work space. +C IRT = completion flag: +C IRT = 0 means no root was found. +C IRT = -1 means JOB = 1 and a root was found too near to T. +C IRT = 1 means a legitimate root was found (JOB = 2 or 3). +C On return, T0 is the root location, and Y is the +C corresponding solution vector. +C T0 = value of T at one endpoint of interval of interest. Only +C roots beyond T0 in the direction of integration are sought. +C T0 is input if JOB .ge. 2, and output in all cases. +C T0 is updated by DRCHEK, whether a root is found or not. +C TLAST = last value of T returned by the solver (input only). +C TOUTC = copy of TOUT (input only). +C IRFND = input flag showing whether the last step taken had a root. +C IRFND = 1 if it did, = 0 if not. +C ITASKC = copy of ITASK (input only). +C NGC = copy of NG (input only). +C----------------------------------------------------------------------- + IRT = 0 + DO 10 I = 1,NGC + 10 JROOT(I) = 0 + HMING = (ABS(TN) + ABS(H))*UROUND*100.0D0 +C + GO TO (100, 200, 300), JOB +C +C Evaluate g at initial T, and check for zero values. ------------------ + 100 CONTINUE + T0 = TN + CALL G (NEQ, T0, Y, NGC, G0) + NGE = 1 + ZROOT = .FALSE. + DO 110 I = 1,NGC + 110 IF (ABS(G0(I)) .LE. 0.0D0) ZROOT = .TRUE. + IF (.NOT. ZROOT) GO TO 190 +C g has a zero at T. Look at g at T + (small increment). -------------- + TEMP2 = MAX(HMING/ABS(H), 0.1D0) + TEMP1 = TEMP2*H + T0 = T0 + TEMP1 + DO 120 I = 1,N + 120 Y(I) = Y(I) + TEMP2*YH(I,2) + CALL G (NEQ, T0, Y, NGC, G0) + NGE = NGE + 1 + ZROOT = .FALSE. + DO 130 I = 1,NGC + 130 IF (ABS(G0(I)) .LE. 0.0D0) ZROOT = .TRUE. + IF (.NOT. ZROOT) GO TO 190 +C g has a zero at T and also close to T. Take error return. ----------- + IRT = -1 + RETURN +C + 190 CONTINUE + RETURN +C +C + 200 CONTINUE + IF (IRFND .EQ. 0) GO TO 260 +C If a root was found on the previous step, evaluate G0 = g(T0). ------- + CALL DINTDY (T0, 0, YH, NYH, Y, IFLAG) + CALL G (NEQ, T0, Y, NGC, G0) + NGE = NGE + 1 + ZROOT = .FALSE. + DO 210 I = 1,NGC + 210 IF (ABS(G0(I)) .LE. 0.0D0) ZROOT = .TRUE. + IF (.NOT. ZROOT) GO TO 260 +C g has a zero at T0. Look at g at T + (small increment). ------------- + TEMP1 = SIGN(HMING,H) + T0 = T0 + TEMP1 + IF ((T0 - TN)*H .LT. 0.0D0) GO TO 230 + TEMP2 = TEMP1/H + DO 220 I = 1,N + 220 Y(I) = Y(I) + TEMP2*YH(I,2) + GO TO 240 + 230 CALL DINTDY (T0, 0, YH, NYH, Y, IFLAG) + 240 CALL G (NEQ, T0, Y, NGC, G0) + NGE = NGE + 1 + ZROOT = .FALSE. + DO 250 I = 1,NGC + IF (ABS(G0(I)) .GT. 0.0D0) GO TO 250 + JROOT(I) = 1 + ZROOT = .TRUE. + 250 CONTINUE + IF (.NOT. ZROOT) GO TO 260 +C g has a zero at T0 and also close to T0. Return root. --------------- + IRT = 1 + RETURN +C G0 has no zero components. Proceed to check relevant interval. ------ + 260 IF (TN .EQ. TLAST) GO TO 390 +C + 300 CONTINUE +C Set T1 to TN or TOUTC, whichever comes first, and get g at T1. ------- + IF (ITASKC.EQ.2 .OR. ITASKC.EQ.3 .OR. ITASKC.EQ.5) GO TO 310 + IF ((TOUTC - TN)*H .GE. 0.0D0) GO TO 310 + T1 = TOUTC + IF ((T1 - T0)*H .LE. 0.0D0) GO TO 390 + CALL DINTDY (T1, 0, YH, NYH, Y, IFLAG) + GO TO 330 + 310 T1 = TN + DO 320 I = 1,N + 320 Y(I) = YH(I,1) + 330 CALL G (NEQ, T1, Y, NGC, G1) + NGE = NGE + 1 +C Call DROOTS to search for root in interval from T0 to T1. ------------ + JFLAG = 0 + 350 CONTINUE + CALL DROOTS (NGC, HMING, JFLAG, T0, T1, G0, G1, GX, X, JROOT) + IF (JFLAG .GT. 1) GO TO 360 + CALL DINTDY (X, 0, YH, NYH, Y, IFLAG) + CALL G (NEQ, X, Y, NGC, GX) + NGE = NGE + 1 + GO TO 350 + 360 T0 = X + CALL DCOPY (NGC, GX, 1, G0, 1) + IF (JFLAG .EQ. 4) GO TO 390 +C Found a root. Interpolate to X and return. -------------------------- + CALL DINTDY (X, 0, YH, NYH, Y, IFLAG) + IRT = 1 + RETURN +C + 390 CONTINUE + RETURN +C----------------------- End of Subroutine DRCHEK ---------------------- + END +*DECK DROOTS + SUBROUTINE DROOTS (NG, HMIN, JFLAG, X0, X1, G0, G1, GX, X, JROOT) + INTEGER NG, JFLAG, JROOT + DOUBLE PRECISION HMIN, X0, X1, G0, G1, GX, X + DIMENSION G0(NG), G1(NG), GX(NG), JROOT(NG) + INTEGER IOWND3, IMAX, LAST, IDUM3 + DOUBLE PRECISION ALPHA, X2, RDUM3 + COMMON /DLSR01/ ALPHA, X2, RDUM3(3), + 1 IOWND3(3), IMAX, LAST, IDUM3(4) +C----------------------------------------------------------------------- +C This subroutine finds the leftmost root of a set of arbitrary +C functions gi(x) (i = 1,...,NG) in an interval (X0,X1). Only roots +C of odd multiplicity (i.e. changes of sign of the gi) are found. +C Here the sign of X1 - X0 is arbitrary, but is constant for a given +C problem, and -leftmost- means nearest to X0. +C The values of the vector-valued function g(x) = (gi, i=1...NG) +C are communicated through the call sequence of DROOTS. +C The method used is the Illinois algorithm. +C +C Reference: +C Kathie L. Hiebert and Lawrence F. Shampine, Implicitly Defined +C Output Points for Solutions of ODEs, Sandia Report SAND80-0180, +C February 1980. +C +C Description of parameters. +C +C NG = number of functions gi, or the number of components of +C the vector valued function g(x). Input only. +C +C HMIN = resolution parameter in X. Input only. When a root is +C found, it is located only to within an error of HMIN in X. +C Typically, HMIN should be set to something on the order of +C 100 * UROUND * MAX(ABS(X0),ABS(X1)), +C where UROUND is the unit roundoff of the machine. +C +C JFLAG = integer flag for input and output communication. +C +C On input, set JFLAG = 0 on the first call for the problem, +C and leave it unchanged until the problem is completed. +C (The problem is completed when JFLAG .ge. 2 on return.) +C +C On output, JFLAG has the following values and meanings: +C JFLAG = 1 means DROOTS needs a value of g(x). Set GX = g(X) +C and call DROOTS again. +C JFLAG = 2 means a root has been found. The root is +C at X, and GX contains g(X). (Actually, X is the +C rightmost approximation to the root on an interval +C (X0,X1) of size HMIN or less.) +C JFLAG = 3 means X = X1 is a root, with one or more of the gi +C being zero at X1 and no sign changes in (X0,X1). +C GX contains g(X) on output. +C JFLAG = 4 means no roots (of odd multiplicity) were +C found in (X0,X1) (no sign changes). +C +C X0,X1 = endpoints of the interval where roots are sought. +C X1 and X0 are input when JFLAG = 0 (first call), and +C must be left unchanged between calls until the problem is +C completed. X0 and X1 must be distinct, but X1 - X0 may be +C of either sign. However, the notion of -left- and -right- +C will be used to mean nearer to X0 or X1, respectively. +C When JFLAG .ge. 2 on return, X0 and X1 are output, and +C are the endpoints of the relevant interval. +C +C G0,G1 = arrays of length NG containing the vectors g(X0) and g(X1), +C respectively. When JFLAG = 0, G0 and G1 are input and +C none of the G0(i) should be zero. +C When JFLAG .ge. 2 on return, G0 and G1 are output. +C +C GX = array of length NG containing g(X). GX is input +C when JFLAG = 1, and output when JFLAG .ge. 2. +C +C X = independent variable value. Output only. +C When JFLAG = 1 on output, X is the point at which g(x) +C is to be evaluated and loaded into GX. +C When JFLAG = 2 or 3, X is the root. +C When JFLAG = 4, X is the right endpoint of the interval, X1. +C +C JROOT = integer array of length NG. Output only. +C When JFLAG = 2 or 3, JROOT indicates which components +C of g(x) have a root at X. JROOT(i) is 1 if the i-th +C component has a root, and JROOT(i) = 0 otherwise. +C----------------------------------------------------------------------- + INTEGER I, IMXOLD, NXLAST + DOUBLE PRECISION T2, TMAX, FRACINT, FRACSUB, ZERO,HALF,TENTH,FIVE + LOGICAL ZROOT, SGNCHG, XROOT + SAVE ZERO, HALF, TENTH, FIVE + DATA ZERO/0.0D0/, HALF/0.5D0/, TENTH/0.1D0/, FIVE/5.0D0/ +C + IF (JFLAG .EQ. 1) GO TO 200 +C JFLAG .ne. 1. Check for change in sign of g or zero at X1. ---------- + IMAX = 0 + TMAX = ZERO + ZROOT = .FALSE. + DO 120 I = 1,NG + IF (ABS(G1(I)) .GT. ZERO) GO TO 110 + ZROOT = .TRUE. + GO TO 120 +C At this point, G0(i) has been checked and cannot be zero. ------------ + 110 IF (SIGN(1.0D0,G0(I)) .EQ. SIGN(1.0D0,G1(I))) GO TO 120 + T2 = ABS(G1(I)/(G1(I)-G0(I))) + IF (T2 .LE. TMAX) GO TO 120 + TMAX = T2 + IMAX = I + 120 CONTINUE + IF (IMAX .GT. 0) GO TO 130 + SGNCHG = .FALSE. + GO TO 140 + 130 SGNCHG = .TRUE. + 140 IF (.NOT. SGNCHG) GO TO 400 +C There is a sign change. Find the first root in the interval. -------- + XROOT = .FALSE. + NXLAST = 0 + LAST = 1 +C +C Repeat until the first root in the interval is found. Loop point. --- + 150 CONTINUE + IF (XROOT) GO TO 300 + IF (NXLAST .EQ. LAST) GO TO 160 + ALPHA = 1.0D0 + GO TO 180 + 160 IF (LAST .EQ. 0) GO TO 170 + ALPHA = 0.5D0*ALPHA + GO TO 180 + 170 ALPHA = 2.0D0*ALPHA + 180 X2 = X1 - (X1 - X0)*G1(IMAX) / (G1(IMAX) - ALPHA*G0(IMAX)) +C If X2 is too close to X0 or X1, adjust it inward, by a fractional ---- +C distance that is between 0.1 and 0.5. -------------------------------- + IF (ABS(X2 - X0) < HALF*HMIN) THEN + FRACINT = ABS(X1 - X0)/HMIN + FRACSUB = TENTH + IF (FRACINT .LE. FIVE) FRACSUB = HALF/FRACINT + X2 = X0 + FRACSUB*(X1 - X0) + ENDIF + IF (ABS(X1 - X2) < HALF*HMIN) THEN + FRACINT = ABS(X1 - X0)/HMIN + FRACSUB = TENTH + IF (FRACINT .LE. FIVE) FRACSUB = HALF/FRACINT + X2 = X1 - FRACSUB*(X1 - X0) + ENDIF + JFLAG = 1 + X = X2 +C Return to the calling routine to get a value of GX = g(X). ----------- + RETURN +C Check to see in which interval g changes sign. ----------------------- + 200 IMXOLD = IMAX + IMAX = 0 + TMAX = ZERO + ZROOT = .FALSE. + DO 220 I = 1,NG + IF (ABS(GX(I)) .GT. ZERO) GO TO 210 + ZROOT = .TRUE. + GO TO 220 +C Neither G0(i) nor GX(i) can be zero at this point. ------------------- + 210 IF (SIGN(1.0D0,G0(I)) .EQ. SIGN(1.0D0,GX(I))) GO TO 220 + T2 = ABS(GX(I)/(GX(I) - G0(I))) + IF (T2 .LE. TMAX) GO TO 220 + TMAX = T2 + IMAX = I + 220 CONTINUE + IF (IMAX .GT. 0) GO TO 230 + SGNCHG = .FALSE. + IMAX = IMXOLD + GO TO 240 + 230 SGNCHG = .TRUE. + 240 NXLAST = LAST + IF (.NOT. SGNCHG) GO TO 250 +C Sign change between X0 and X2, so replace X1 with X2. ---------------- + X1 = X2 + CALL DCOPY (NG, GX, 1, G1, 1) + LAST = 1 + XROOT = .FALSE. + GO TO 270 + 250 IF (.NOT. ZROOT) GO TO 260 +C Zero value at X2 and no sign change in (X0,X2), so X2 is a root. ----- + X1 = X2 + CALL DCOPY (NG, GX, 1, G1, 1) + XROOT = .TRUE. + GO TO 270 +C No sign change between X0 and X2. Replace X0 with X2. --------------- + 260 CONTINUE + CALL DCOPY (NG, GX, 1, G0, 1) + X0 = X2 + LAST = 0 + XROOT = .FALSE. + 270 IF (ABS(X1-X0) .LE. HMIN) XROOT = .TRUE. + GO TO 150 +C +C Return with X1 as the root. Set JROOT. Set X = X1 and GX = G1. ----- + 300 JFLAG = 2 + X = X1 + CALL DCOPY (NG, G1, 1, GX, 1) + DO 320 I = 1,NG + JROOT(I) = 0 + IF (ABS(G1(I)) .GT. ZERO) GO TO 310 + JROOT(I) = 1 + GO TO 320 + 310 IF (SIGN(1.0D0,G0(I)) .NE. SIGN(1.0D0,G1(I))) JROOT(I) = 1 + 320 CONTINUE + RETURN +C +C No sign change in the interval. Check for zero at right endpoint. --- + 400 IF (.NOT. ZROOT) GO TO 420 +C +C Zero value at X1 and no sign change in (X0,X1). Return JFLAG = 3. --- + X = X1 + CALL DCOPY (NG, G1, 1, GX, 1) + DO 410 I = 1,NG + JROOT(I) = 0 + IF (ABS(G1(I)) .LE. ZERO) JROOT (I) = 1 + 410 CONTINUE + JFLAG = 3 + RETURN +C +C No sign changes in this interval. Set X = X1, return JFLAG = 4. ----- + 420 CALL DCOPY (NG, G1, 1, GX, 1) + X = X1 + JFLAG = 4 + RETURN +C----------------------- End of Subroutine DROOTS ---------------------- + END +*DECK DSRCAR + SUBROUTINE DSRCAR (RSAV, ISAV, JOB) +C----------------------------------------------------------------------- +C This routine saves or restores (depending on JOB) the contents of +C the Common blocks DLS001, DLSA01, DLSR01, which are used +C internally by one or more ODEPACK solvers. +C +C RSAV = real array of length 245 or more. +C ISAV = integer array of length 55 or more. +C JOB = flag indicating to save or restore the Common blocks: +C JOB = 1 if Common is to be saved (written to RSAV/ISAV) +C JOB = 2 if Common is to be restored (read from RSAV/ISAV) +C A call with JOB = 2 presumes a prior call with JOB = 1. +C----------------------------------------------------------------------- + INTEGER ISAV, JOB + INTEGER ILS, ILSA, ILSR + INTEGER I, IOFF, LENRLS, LENILS, LENRLA, LENILA, LENRLR, LENILR + DOUBLE PRECISION RSAV + DOUBLE PRECISION RLS, RLSA, RLSR + DIMENSION RSAV(*), ISAV(*) + SAVE LENRLS, LENILS, LENRLA, LENILA, LENRLR, LENILR + COMMON /DLS001/ RLS(218), ILS(37) + COMMON /DLSA01/ RLSA(22), ILSA(9) + COMMON /DLSR01/ RLSR(5), ILSR(9) + DATA LENRLS/218/, LENILS/37/, LENRLA/22/, LENILA/9/ + DATA LENRLR/5/, LENILR/9/ +C + IF (JOB .EQ. 2) GO TO 100 + DO 10 I = 1,LENRLS + 10 RSAV(I) = RLS(I) + DO 15 I = 1,LENRLA + 15 RSAV(LENRLS+I) = RLSA(I) + IOFF = LENRLS + LENRLA + DO 20 I = 1,LENRLR + 20 RSAV(IOFF+I) = RLSR(I) +C + DO 30 I = 1,LENILS + 30 ISAV(I) = ILS(I) + DO 35 I = 1,LENILA + 35 ISAV(LENILS+I) = ILSA(I) + IOFF = LENILS + LENILA + DO 40 I = 1,LENILR + 40 ISAV(IOFF+I) = ILSR(I) +C + RETURN +C + 100 CONTINUE + DO 110 I = 1,LENRLS + 110 RLS(I) = RSAV(I) + DO 115 I = 1,LENRLA + 115 RLSA(I) = RSAV(LENRLS+I) + IOFF = LENRLS + LENRLA + DO 120 I = 1,LENRLR + 120 RLSR(I) = RSAV(IOFF+I) +C + DO 130 I = 1,LENILS + 130 ILS(I) = ISAV(I) + DO 135 I = 1,LENILA + 135 ILSA(I) = ISAV(LENILS+I) + IOFF = LENILS + LENILA + DO 140 I = 1,LENILR + 140 ILSR(I) = ISAV(IOFF+I) +C + RETURN +C----------------------- End of Subroutine DSRCAR ---------------------- + END +*DECK DSTODPK + SUBROUTINE DSTODPK (NEQ, Y, YH, NYH, YH1, EWT, SAVF, SAVX, ACOR, + 1 WM, IWM, F, JAC, PSOL) + EXTERNAL F, JAC, PSOL + INTEGER NEQ, NYH, IWM + DOUBLE PRECISION Y, YH, YH1, EWT, SAVF, SAVX, ACOR, WM + DIMENSION NEQ(*), Y(*), YH(NYH,*), YH1(*), EWT(*), SAVF(*), + 1 SAVX(*), ACOR(*), WM(*), IWM(*) + INTEGER IOWND, IALTH, IPUP, LMAX, MEO, NQNYH, NSLP, + 1 ICF, IERPJ, IERSL, JCUR, JSTART, KFLAG, L, + 2 LYH, LEWT, LACOR, LSAVF, LWM, LIWM, METH, MITER, + 3 MAXORD, MAXCOR, MSBP, MXNCF, N, NQ, NST, NFE, NJE, NQU + INTEGER JPRE, JACFLG, LOCWP, LOCIWP, LSAVX, KMP, MAXL, MNEWT, + 1 NNI, NLI, NPS, NCFN, NCFL + DOUBLE PRECISION CONIT, CRATE, EL, ELCO, HOLD, RMAX, TESCO, + 2 CCMAX, EL0, H, HMIN, HMXI, HU, RC, TN, UROUND + DOUBLE PRECISION DELT, EPCON, SQRTN, RSQRTN + COMMON /DLS001/ CONIT, CRATE, EL(13), ELCO(13,12), + 1 HOLD, RMAX, TESCO(3,12), + 2 CCMAX, EL0, H, HMIN, HMXI, HU, RC, TN, UROUND, + 3 IOWND(6), IALTH, IPUP, LMAX, MEO, NQNYH, NSLP, + 3 ICF, IERPJ, IERSL, JCUR, JSTART, KFLAG, L, + 4 LYH, LEWT, LACOR, LSAVF, LWM, LIWM, METH, MITER, + 5 MAXORD, MAXCOR, MSBP, MXNCF, N, NQ, NST, NFE, NJE, NQU + COMMON /DLPK01/ DELT, EPCON, SQRTN, RSQRTN, + 1 JPRE, JACFLG, LOCWP, LOCIWP, LSAVX, KMP, MAXL, MNEWT, + 2 NNI, NLI, NPS, NCFN, NCFL +C----------------------------------------------------------------------- +C DSTODPK performs one step of the integration of an initial value +C problem for a system of Ordinary Differential Equations. +C----------------------------------------------------------------------- +C The following changes were made to generate Subroutine DSTODPK +C from Subroutine DSTODE: +C 1. The array SAVX was added to the call sequence. +C 2. PJAC and SLVS were replaced by PSOL in the call sequence. +C 3. The Common block /DLPK01/ was added for communication. +C 4. The test constant EPCON is loaded into Common below statement +C numbers 125 and 155, and used below statement 400. +C 5. The Newton iteration counter MNEWT is set below 220 and 400. +C 6. The call to PJAC was replaced with a call to DPKSET (fixed name), +C with a longer call sequence, called depending on JACFLG. +C 7. The corrector residual is stored in SAVX (not Y) at 360, +C and the solution vector is in SAVX in the 380 loop. +C 8. SLVS was renamed DSOLPK and includes NEQ, SAVX, EWT, F, and JAC. +C SAVX was added because DSOLPK now needs Y and SAVF undisturbed. +C 9. The nonlinear convergence failure count NCFN is set at 430. +C----------------------------------------------------------------------- +C Note: DSTODPK is independent of the value of the iteration method +C indicator MITER, when this is .ne. 0, and hence is independent +C of the type of chord method used, or the Jacobian structure. +C Communication with DSTODPK is done with the following variables: +C +C NEQ = integer array containing problem size in NEQ(1), and +C passed as the NEQ argument in all calls to F and JAC. +C Y = an array of length .ge. N used as the Y argument in +C all calls to F and JAC. +C YH = an NYH by LMAX array containing the dependent variables +C and their approximate scaled derivatives, where +C LMAX = MAXORD + 1. YH(i,j+1) contains the approximate +C j-th derivative of y(i), scaled by H**j/factorial(j) +C (j = 0,1,...,NQ). On entry for the first step, the first +C two columns of YH must be set from the initial values. +C NYH = a constant integer .ge. N, the first dimension of YH. +C YH1 = a one-dimensional array occupying the same space as YH. +C EWT = an array of length N containing multiplicative weights +C for local error measurements. Local errors in y(i) are +C compared to 1.0/EWT(i) in various error tests. +C SAVF = an array of working storage, of length N. +C Also used for input of YH(*,MAXORD+2) when JSTART = -1 +C and MAXORD .lt. the current order NQ. +C SAVX = an array of working storage, of length N. +C ACOR = a work array of length N, used for the accumulated +C corrections. On a successful return, ACOR(i) contains +C the estimated one-step local error in y(i). +C WM,IWM = real and integer work arrays associated with matrix +C operations in chord iteration (MITER .ne. 0). +C CCMAX = maximum relative change in H*EL0 before DPKSET is called. +C H = the step size to be attempted on the next step. +C H is altered by the error control algorithm during the +C problem. H can be either positive or negative, but its +C sign must remain constant throughout the problem. +C HMIN = the minimum absolute value of the step size H to be used. +C HMXI = inverse of the maximum absolute value of H to be used. +C HMXI = 0.0 is allowed and corresponds to an infinite HMAX. +C HMIN and HMXI may be changed at any time, but will not +C take effect until the next change of H is considered. +C TN = the independent variable. TN is updated on each step taken. +C JSTART = an integer used for input only, with the following +C values and meanings: +C 0 perform the first step. +C .gt.0 take a new step continuing from the last. +C -1 take the next step with a new value of H, MAXORD, +C N, METH, MITER, and/or matrix parameters. +C -2 take the next step with a new value of H, +C but with other inputs unchanged. +C On return, JSTART is set to 1 to facilitate continuation. +C KFLAG = a completion code with the following meanings: +C 0 the step was succesful. +C -1 the requested error could not be achieved. +C -2 corrector convergence could not be achieved. +C -3 fatal error in DPKSET or DSOLPK. +C A return with KFLAG = -1 or -2 means either +C ABS(H) = HMIN or 10 consecutive failures occurred. +C On a return with KFLAG negative, the values of TN and +C the YH array are as of the beginning of the last +C step, and H is the last step size attempted. +C MAXORD = the maximum order of integration method to be allowed. +C MAXCOR = the maximum number of corrector iterations allowed. +C MSBP = maximum number of steps between DPKSET calls (MITER .gt. 0). +C MXNCF = maximum number of convergence failures allowed. +C METH/MITER = the method flags. See description in driver. +C N = the number of first-order differential equations. +C----------------------------------------------------------------------- + INTEGER I, I1, IREDO, IRET, J, JB, M, NCF, NEWQ + DOUBLE PRECISION DCON, DDN, DEL, DELP, DSM, DUP, EXDN, EXSM, EXUP, + 1 R, RH, RHDN, RHSM, RHUP, TOLD, DVNORM +C + KFLAG = 0 + TOLD = TN + NCF = 0 + IERPJ = 0 + IERSL = 0 + JCUR = 0 + ICF = 0 + DELP = 0.0D0 + IF (JSTART .GT. 0) GO TO 200 + IF (JSTART .EQ. -1) GO TO 100 + IF (JSTART .EQ. -2) GO TO 160 +C----------------------------------------------------------------------- +C On the first call, the order is set to 1, and other variables are +C initialized. RMAX is the maximum ratio by which H can be increased +C in a single step. It is initially 1.E4 to compensate for the small +C initial H, but then is normally equal to 10. If a failure +C occurs (in corrector convergence or error test), RMAX is set at 2 +C for the next increase. +C----------------------------------------------------------------------- + LMAX = MAXORD + 1 + NQ = 1 + L = 2 + IALTH = 2 + RMAX = 10000.0D0 + RC = 0.0D0 + EL0 = 1.0D0 + CRATE = 0.7D0 + HOLD = H + MEO = METH + NSLP = 0 + IPUP = MITER + IRET = 3 + GO TO 140 +C----------------------------------------------------------------------- +C The following block handles preliminaries needed when JSTART = -1. +C IPUP is set to MITER to force a matrix update. +C If an order increase is about to be considered (IALTH = 1), +C IALTH is reset to 2 to postpone consideration one more step. +C If the caller has changed METH, DCFODE is called to reset +C the coefficients of the method. +C If the caller has changed MAXORD to a value less than the current +C order NQ, NQ is reduced to MAXORD, and a new H chosen accordingly. +C If H is to be changed, YH must be rescaled. +C If H or METH is being changed, IALTH is reset to L = NQ + 1 +C to prevent further changes in H for that many steps. +C----------------------------------------------------------------------- + 100 IPUP = MITER + LMAX = MAXORD + 1 + IF (IALTH .EQ. 1) IALTH = 2 + IF (METH .EQ. MEO) GO TO 110 + CALL DCFODE (METH, ELCO, TESCO) + MEO = METH + IF (NQ .GT. MAXORD) GO TO 120 + IALTH = L + IRET = 1 + GO TO 150 + 110 IF (NQ .LE. MAXORD) GO TO 160 + 120 NQ = MAXORD + L = LMAX + DO 125 I = 1,L + 125 EL(I) = ELCO(I,NQ) + NQNYH = NQ*NYH + RC = RC*EL(1)/EL0 + EL0 = EL(1) + CONIT = 0.5D0/(NQ+2) + EPCON = CONIT*TESCO(2,NQ) + DDN = DVNORM (N, SAVF, EWT)/TESCO(1,L) + EXDN = 1.0D0/L + RHDN = 1.0D0/(1.3D0*DDN**EXDN + 0.0000013D0) + RH = MIN(RHDN,1.0D0) + IREDO = 3 + IF (H .EQ. HOLD) GO TO 170 + RH = MIN(RH,ABS(H/HOLD)) + H = HOLD + GO TO 175 +C----------------------------------------------------------------------- +C DCFODE is called to get all the integration coefficients for the +C current METH. Then the EL vector and related constants are reset +C whenever the order NQ is changed, or at the start of the problem. +C----------------------------------------------------------------------- + 140 CALL DCFODE (METH, ELCO, TESCO) + 150 DO 155 I = 1,L + 155 EL(I) = ELCO(I,NQ) + NQNYH = NQ*NYH + RC = RC*EL(1)/EL0 + EL0 = EL(1) + CONIT = 0.5D0/(NQ+2) + EPCON = CONIT*TESCO(2,NQ) + GO TO (160, 170, 200), IRET +C----------------------------------------------------------------------- +C If H is being changed, the H ratio RH is checked against +C RMAX, HMIN, and HMXI, and the YH array rescaled. IALTH is set to +C L = NQ + 1 to prevent a change of H for that many steps, unless +C forced by a convergence or error test failure. +C----------------------------------------------------------------------- + 160 IF (H .EQ. HOLD) GO TO 200 + RH = H/HOLD + H = HOLD + IREDO = 3 + GO TO 175 + 170 RH = MAX(RH,HMIN/ABS(H)) + 175 RH = MIN(RH,RMAX) + RH = RH/MAX(1.0D0,ABS(H)*HMXI*RH) + R = 1.0D0 + DO 180 J = 2,L + R = R*RH + DO 180 I = 1,N + 180 YH(I,J) = YH(I,J)*R + H = H*RH + RC = RC*RH + IALTH = L + IF (IREDO .EQ. 0) GO TO 690 +C----------------------------------------------------------------------- +C This section computes the predicted values by effectively +C multiplying the YH array by the Pascal triangle matrix. +C The flag IPUP is set according to whether matrix data is involved +C (JACFLG .ne. 0) or not (JACFLG = 0), to trigger a call to DPKSET. +C IPUP is set to MITER when RC differs from 1 by more than CCMAX, +C and at least every MSBP steps, when JACFLG = 1. +C RC is the ratio of new to old values of the coefficient H*EL(1). +C----------------------------------------------------------------------- + 200 IF (JACFLG .NE. 0) GO TO 202 + IPUP = 0 + CRATE = 0.7D0 + GO TO 205 + 202 IF (ABS(RC-1.0D0) .GT. CCMAX) IPUP = MITER + IF (NST .GE. NSLP+MSBP) IPUP = MITER + 205 TN = TN + H + I1 = NQNYH + 1 + DO 215 JB = 1,NQ + I1 = I1 - NYH +CDIR$ IVDEP + DO 210 I = I1,NQNYH + 210 YH1(I) = YH1(I) + YH1(I+NYH) + 215 CONTINUE +C----------------------------------------------------------------------- +C Up to MAXCOR corrector iterations are taken. A convergence test is +C made on the RMS-norm of each correction, weighted by the error +C weight vector EWT. The sum of the corrections is accumulated in the +C vector ACOR(i). The YH array is not altered in the corrector loop. +C----------------------------------------------------------------------- + 220 M = 0 + MNEWT = 0 + DO 230 I = 1,N + 230 Y(I) = YH(I,1) + CALL F (NEQ, TN, Y, SAVF) + NFE = NFE + 1 + IF (IPUP .LE. 0) GO TO 250 +C----------------------------------------------------------------------- +C If indicated, DPKSET is called to update any matrix data needed, +C before starting the corrector iteration. +C IPUP is set to 0 as an indicator that this has been done. +C----------------------------------------------------------------------- + CALL DPKSET (NEQ, Y, YH1, EWT, ACOR, SAVF, WM, IWM, F, JAC) + IPUP = 0 + RC = 1.0D0 + NSLP = NST + CRATE = 0.7D0 + IF (IERPJ .NE. 0) GO TO 430 + 250 DO 260 I = 1,N + 260 ACOR(I) = 0.0D0 + 270 IF (MITER .NE. 0) GO TO 350 +C----------------------------------------------------------------------- +C In the case of functional iteration, update Y directly from +C the result of the last function evaluation. +C----------------------------------------------------------------------- + DO 290 I = 1,N + SAVF(I) = H*SAVF(I) - YH(I,2) + 290 Y(I) = SAVF(I) - ACOR(I) + DEL = DVNORM (N, Y, EWT) + DO 300 I = 1,N + Y(I) = YH(I,1) + EL(1)*SAVF(I) + 300 ACOR(I) = SAVF(I) + GO TO 400 +C----------------------------------------------------------------------- +C In the case of the chord method, compute the corrector error, +C and solve the linear system with that as right-hand side and +C P as coefficient matrix. +C----------------------------------------------------------------------- + 350 DO 360 I = 1,N + 360 SAVX(I) = H*SAVF(I) - (YH(I,2) + ACOR(I)) + CALL DSOLPK (NEQ, Y, SAVF, SAVX, EWT, WM, IWM, F, PSOL) + IF (IERSL .LT. 0) GO TO 430 + IF (IERSL .GT. 0) GO TO 410 + DEL = DVNORM (N, SAVX, EWT) + DO 380 I = 1,N + ACOR(I) = ACOR(I) + SAVX(I) + 380 Y(I) = YH(I,1) + EL(1)*ACOR(I) +C----------------------------------------------------------------------- +C Test for convergence. If M .gt. 0, an estimate of the convergence +C rate constant is stored in CRATE, and this is used in the test. +C----------------------------------------------------------------------- + 400 IF (M .NE. 0) CRATE = MAX(0.2D0*CRATE,DEL/DELP) + DCON = DEL*MIN(1.0D0,1.5D0*CRATE)/EPCON + IF (DCON .LE. 1.0D0) GO TO 450 + M = M + 1 + IF (M .EQ. MAXCOR) GO TO 410 + IF (M .GE. 2 .AND. DEL .GT. 2.0D0*DELP) GO TO 410 + MNEWT = M + DELP = DEL + CALL F (NEQ, TN, Y, SAVF) + NFE = NFE + 1 + GO TO 270 +C----------------------------------------------------------------------- +C The corrector iteration failed to converge. +C If MITER .ne. 0 and the Jacobian is out of date, DPKSET is called for +C the next try. Otherwise the YH array is retracted to its values +C before prediction, and H is reduced, if possible. If H cannot be +C reduced or MXNCF failures have occurred, exit with KFLAG = -2. +C----------------------------------------------------------------------- + 410 IF (MITER.EQ.0 .OR. JCUR.EQ.1 .OR. JACFLG.EQ.0) GO TO 430 + ICF = 1 + IPUP = MITER + GO TO 220 + 430 ICF = 2 + NCF = NCF + 1 + NCFN = NCFN + 1 + RMAX = 2.0D0 + TN = TOLD + I1 = NQNYH + 1 + DO 445 JB = 1,NQ + I1 = I1 - NYH +CDIR$ IVDEP + DO 440 I = I1,NQNYH + 440 YH1(I) = YH1(I) - YH1(I+NYH) + 445 CONTINUE + IF (IERPJ .LT. 0 .OR. IERSL .LT. 0) GO TO 680 + IF (ABS(H) .LE. HMIN*1.00001D0) GO TO 670 + IF (NCF .EQ. MXNCF) GO TO 670 + RH = 0.5D0 + IPUP = MITER + IREDO = 1 + GO TO 170 +C----------------------------------------------------------------------- +C The corrector has converged. JCUR is set to 0 +C to signal that the Jacobian involved may need updating later. +C The local error test is made and control passes to statement 500 +C if it fails. +C----------------------------------------------------------------------- + 450 JCUR = 0 + IF (M .EQ. 0) DSM = DEL/TESCO(2,NQ) + IF (M .GT. 0) DSM = DVNORM (N, ACOR, EWT)/TESCO(2,NQ) + IF (DSM .GT. 1.0D0) GO TO 500 +C----------------------------------------------------------------------- +C After a successful step, update the YH array. +C Consider changing H if IALTH = 1. Otherwise decrease IALTH by 1. +C If IALTH is then 1 and NQ .lt. MAXORD, then ACOR is saved for +C use in a possible order increase on the next step. +C If a change in H is considered, an increase or decrease in order +C by one is considered also. A change in H is made only if it is by a +C factor of at least 1.1. If not, IALTH is set to 3 to prevent +C testing for that many steps. +C----------------------------------------------------------------------- + KFLAG = 0 + IREDO = 0 + NST = NST + 1 + HU = H + NQU = NQ + DO 470 J = 1,L + DO 470 I = 1,N + 470 YH(I,J) = YH(I,J) + EL(J)*ACOR(I) + IALTH = IALTH - 1 + IF (IALTH .EQ. 0) GO TO 520 + IF (IALTH .GT. 1) GO TO 700 + IF (L .EQ. LMAX) GO TO 700 + DO 490 I = 1,N + 490 YH(I,LMAX) = ACOR(I) + GO TO 700 +C----------------------------------------------------------------------- +C The error test failed. KFLAG keeps track of multiple failures. +C Restore TN and the YH array to their previous values, and prepare +C to try the step again. Compute the optimum step size for this or +C one lower order. After 2 or more failures, H is forced to decrease +C by a factor of 0.2 or less. +C----------------------------------------------------------------------- + 500 KFLAG = KFLAG - 1 + TN = TOLD + I1 = NQNYH + 1 + DO 515 JB = 1,NQ + I1 = I1 - NYH +CDIR$ IVDEP + DO 510 I = I1,NQNYH + 510 YH1(I) = YH1(I) - YH1(I+NYH) + 515 CONTINUE + RMAX = 2.0D0 + IF (ABS(H) .LE. HMIN*1.00001D0) GO TO 660 + IF (KFLAG .LE. -3) GO TO 640 + IREDO = 2 + RHUP = 0.0D0 + GO TO 540 +C----------------------------------------------------------------------- +C Regardless of the success or failure of the step, factors +C RHDN, RHSM, and RHUP are computed, by which H could be multiplied +C at order NQ - 1, order NQ, or order NQ + 1, respectively. +C In the case of failure, RHUP = 0.0 to avoid an order increase. +C the largest of these is determined and the new order chosen +C accordingly. If the order is to be increased, we compute one +C additional scaled derivative. +C----------------------------------------------------------------------- + 520 RHUP = 0.0D0 + IF (L .EQ. LMAX) GO TO 540 + DO 530 I = 1,N + 530 SAVF(I) = ACOR(I) - YH(I,LMAX) + DUP = DVNORM (N, SAVF, EWT)/TESCO(3,NQ) + EXUP = 1.0D0/(L+1) + RHUP = 1.0D0/(1.4D0*DUP**EXUP + 0.0000014D0) + 540 EXSM = 1.0D0/L + RHSM = 1.0D0/(1.2D0*DSM**EXSM + 0.0000012D0) + RHDN = 0.0D0 + IF (NQ .EQ. 1) GO TO 560 + DDN = DVNORM (N, YH(1,L), EWT)/TESCO(1,NQ) + EXDN = 1.0D0/NQ + RHDN = 1.0D0/(1.3D0*DDN**EXDN + 0.0000013D0) + 560 IF (RHSM .GE. RHUP) GO TO 570 + IF (RHUP .GT. RHDN) GO TO 590 + GO TO 580 + 570 IF (RHSM .LT. RHDN) GO TO 580 + NEWQ = NQ + RH = RHSM + GO TO 620 + 580 NEWQ = NQ - 1 + RH = RHDN + IF (KFLAG .LT. 0 .AND. RH .GT. 1.0D0) RH = 1.0D0 + GO TO 620 + 590 NEWQ = L + RH = RHUP + IF (RH .LT. 1.1D0) GO TO 610 + R = EL(L)/L + DO 600 I = 1,N + 600 YH(I,NEWQ+1) = ACOR(I)*R + GO TO 630 + 610 IALTH = 3 + GO TO 700 + 620 IF ((KFLAG .EQ. 0) .AND. (RH .LT. 1.1D0)) GO TO 610 + IF (KFLAG .LE. -2) RH = MIN(RH,0.2D0) +C----------------------------------------------------------------------- +C If there is a change of order, reset NQ, L, and the coefficients. +C In any case H is reset according to RH and the YH array is rescaled. +C Then exit from 690 if the step was OK, or redo the step otherwise. +C----------------------------------------------------------------------- + IF (NEWQ .EQ. NQ) GO TO 170 + 630 NQ = NEWQ + L = NQ + 1 + IRET = 2 + GO TO 150 +C----------------------------------------------------------------------- +C Control reaches this section if 3 or more failures have occured. +C If 10 failures have occurred, exit with KFLAG = -1. +C It is assumed that the derivatives that have accumulated in the +C YH array have errors of the wrong order. Hence the first +C derivative is recomputed, and the order is set to 1. Then +C H is reduced by a factor of 10, and the step is retried, +C until it succeeds or H reaches HMIN. +C----------------------------------------------------------------------- + 640 IF (KFLAG .EQ. -10) GO TO 660 + RH = 0.1D0 + RH = MAX(HMIN/ABS(H),RH) + H = H*RH + DO 645 I = 1,N + 645 Y(I) = YH(I,1) + CALL F (NEQ, TN, Y, SAVF) + NFE = NFE + 1 + DO 650 I = 1,N + 650 YH(I,2) = H*SAVF(I) + IPUP = MITER + IALTH = 5 + IF (NQ .EQ. 1) GO TO 200 + NQ = 1 + L = 2 + IRET = 3 + GO TO 150 +C----------------------------------------------------------------------- +C All returns are made through this section. H is saved in HOLD +C to allow the caller to change H on the next step. +C----------------------------------------------------------------------- + 660 KFLAG = -1 + GO TO 720 + 670 KFLAG = -2 + GO TO 720 + 680 KFLAG = -3 + GO TO 720 + 690 RMAX = 10.0D0 + 700 R = 1.0D0/TESCO(2,NQU) + DO 710 I = 1,N + 710 ACOR(I) = ACOR(I)*R + 720 HOLD = H + JSTART = 1 + RETURN +C----------------------- End of Subroutine DSTODPK --------------------- + END +*DECK DPKSET + SUBROUTINE DPKSET (NEQ, Y, YSV, EWT, FTEM, SAVF, WM, IWM, F, JAC) + EXTERNAL F, JAC + INTEGER NEQ, IWM + DOUBLE PRECISION Y, YSV, EWT, FTEM, SAVF, WM + DIMENSION NEQ(*), Y(*), YSV(*), EWT(*), FTEM(*), SAVF(*), + 1 WM(*), IWM(*) + INTEGER IOWND, IOWNS, + 1 ICF, IERPJ, IERSL, JCUR, JSTART, KFLAG, L, + 2 LYH, LEWT, LACOR, LSAVF, LWM, LIWM, METH, MITER, + 3 MAXORD, MAXCOR, MSBP, MXNCF, N, NQ, NST, NFE, NJE, NQU + INTEGER JPRE, JACFLG, LOCWP, LOCIWP, LSAVX, KMP, MAXL, MNEWT, + 1 NNI, NLI, NPS, NCFN, NCFL + DOUBLE PRECISION ROWNS, + 1 CCMAX, EL0, H, HMIN, HMXI, HU, RC, TN, UROUND + DOUBLE PRECISION DELT, EPCON, SQRTN, RSQRTN + COMMON /DLS001/ ROWNS(209), + 1 CCMAX, EL0, H, HMIN, HMXI, HU, RC, TN, UROUND, + 2 IOWND(6), IOWNS(6), + 3 ICF, IERPJ, IERSL, JCUR, JSTART, KFLAG, L, + 4 LYH, LEWT, LACOR, LSAVF, LWM, LIWM, METH, MITER, + 5 MAXORD, MAXCOR, MSBP, MXNCF, N, NQ, NST, NFE, NJE, NQU + COMMON /DLPK01/ DELT, EPCON, SQRTN, RSQRTN, + 1 JPRE, JACFLG, LOCWP, LOCIWP, LSAVX, KMP, MAXL, MNEWT, + 2 NNI, NLI, NPS, NCFN, NCFL +C----------------------------------------------------------------------- +C DPKSET is called by DSTODPK to interface with the user-supplied +C routine JAC, to compute and process relevant parts of +C the matrix P = I - H*EL(1)*J , where J is the Jacobian df/dy, +C as need for preconditioning matrix operations later. +C +C In addition to variables described previously, communication +C with DPKSET uses the following: +C Y = array containing predicted values on entry. +C YSV = array containing predicted y, to be saved (YH1 in DSTODPK). +C FTEM = work array of length N (ACOR in DSTODPK). +C SAVF = array containing f evaluated at predicted y. +C WM = real work space for matrices. +C Space for preconditioning data starts at WM(LOCWP). +C IWM = integer work space. +C Space for preconditioning data starts at IWM(LOCIWP). +C IERPJ = output error flag, = 0 if no trouble, .gt. 0 if +C JAC returned an error flag. +C JCUR = output flag = 1 to indicate that the Jacobian matrix +C (or approximation) is now current. +C This routine also uses Common variables EL0, H, TN, IERPJ, JCUR, NJE. +C----------------------------------------------------------------------- + INTEGER IER + DOUBLE PRECISION HL0 +C + IERPJ = 0 + JCUR = 1 + HL0 = EL0*H + CALL JAC (F, NEQ, TN, Y, YSV, EWT, SAVF, FTEM, HL0, + 1 WM(LOCWP), IWM(LOCIWP), IER) + NJE = NJE + 1 + IF (IER .EQ. 0) RETURN + IERPJ = 1 + RETURN +C----------------------- End of Subroutine DPKSET ---------------------- + END +*DECK DSOLPK + SUBROUTINE DSOLPK (NEQ, Y, SAVF, X, EWT, WM, IWM, F, PSOL) + EXTERNAL F, PSOL + INTEGER NEQ, IWM + DOUBLE PRECISION Y, SAVF, X, EWT, WM + DIMENSION NEQ(*), Y(*), SAVF(*), X(*), EWT(*), WM(*), IWM(*) + INTEGER IOWND, IOWNS, + 1 ICF, IERPJ, IERSL, JCUR, JSTART, KFLAG, L, + 2 LYH, LEWT, LACOR, LSAVF, LWM, LIWM, METH, MITER, + 3 MAXORD, MAXCOR, MSBP, MXNCF, N, NQ, NST, NFE, NJE, NQU + INTEGER JPRE, JACFLG, LOCWP, LOCIWP, LSAVX, KMP, MAXL, MNEWT, + 1 NNI, NLI, NPS, NCFN, NCFL + DOUBLE PRECISION ROWNS, + 1 CCMAX, EL0, H, HMIN, HMXI, HU, RC, TN, UROUND + DOUBLE PRECISION DELT, EPCON, SQRTN, RSQRTN + COMMON /DLS001/ ROWNS(209), + 1 CCMAX, EL0, H, HMIN, HMXI, HU, RC, TN, UROUND, + 2 IOWND(6), IOWNS(6), + 3 ICF, IERPJ, IERSL, JCUR, JSTART, KFLAG, L, + 4 LYH, LEWT, LACOR, LSAVF, LWM, LIWM, METH, MITER, + 5 MAXORD, MAXCOR, MSBP, MXNCF, N, NQ, NST, NFE, NJE, NQU + COMMON /DLPK01/ DELT, EPCON, SQRTN, RSQRTN, + 1 JPRE, JACFLG, LOCWP, LOCIWP, LSAVX, KMP, MAXL, MNEWT, + 2 NNI, NLI, NPS, NCFN, NCFL +C----------------------------------------------------------------------- +C This routine interfaces to one of DSPIOM, DSPIGMR, DPCG, DPCGS, or +C DUSOL, for the solution of the linear system arising from a Newton +C iteration. It is called if MITER .ne. 0. +C In addition to variables described elsewhere, +C communication with DSOLPK uses the following variables: +C WM = real work space containing data for the algorithm +C (Krylov basis vectors, Hessenberg matrix, etc.) +C IWM = integer work space containing data for the algorithm +C X = the right-hand side vector on input, and the solution vector +C on output, of length N. +C IERSL = output flag (in Common): +C IERSL = 0 means no trouble occurred. +C IERSL = 1 means the iterative method failed to converge. +C If the preconditioner is out of date, the step +C is repeated with a new preconditioner. +C Otherwise, the stepsize is reduced (forcing a +C new evaluation of the preconditioner) and the +C step is repeated. +C IERSL = -1 means there was a nonrecoverable error in the +C iterative solver, and an error exit occurs. +C This routine also uses the Common variables TN, EL0, H, N, MITER, +C DELT, EPCON, SQRTN, RSQRTN, MAXL, KMP, MNEWT, NNI, NLI, NPS, NCFL, +C LOCWP, LOCIWP. +C----------------------------------------------------------------------- + INTEGER IFLAG, LB, LDL, LHES, LIOM, LGMR, LPCG, LP, LQ, LR, + 1 LV, LW, LWK, LZ, MAXLP1, NPSL + DOUBLE PRECISION DELTA, HL0 +C + IERSL = 0 + HL0 = H*EL0 + DELTA = DELT*EPCON + GO TO (100, 200, 300, 400, 900, 900, 900, 900, 900), MITER +C----------------------------------------------------------------------- +C Use the SPIOM algorithm to solve the linear system P*x = -f. +C----------------------------------------------------------------------- + 100 CONTINUE + LV = 1 + LB = LV + N*MAXL + LHES = LB + N + LWK = LHES + MAXL*MAXL + CALL DCOPY (N, X, 1, WM(LB), 1) + CALL DSCAL (N, RSQRTN, EWT, 1) + CALL DSPIOM (NEQ, TN, Y, SAVF, WM(LB), EWT, N, MAXL, KMP, DELTA, + 1 HL0, JPRE, MNEWT, F, PSOL, NPSL, X, WM(LV), WM(LHES), IWM, + 2 LIOM, WM(LOCWP), IWM(LOCIWP), WM(LWK), IFLAG) + NNI = NNI + 1 + NLI = NLI + LIOM + NPS = NPS + NPSL + CALL DSCAL (N, SQRTN, EWT, 1) + IF (IFLAG .NE. 0) NCFL = NCFL + 1 + IF (IFLAG .GE. 2) IERSL = 1 + IF (IFLAG .LT. 0) IERSL = -1 + RETURN +C----------------------------------------------------------------------- +C Use the SPIGMR algorithm to solve the linear system P*x = -f. +C----------------------------------------------------------------------- + 200 CONTINUE + MAXLP1 = MAXL + 1 + LV = 1 + LB = LV + N*MAXL + LHES = LB + N + 1 + LQ = LHES + MAXL*MAXLP1 + LWK = LQ + 2*MAXL + LDL = LWK + MIN(1,MAXL-KMP)*N + CALL DCOPY (N, X, 1, WM(LB), 1) + CALL DSCAL (N, RSQRTN, EWT, 1) + CALL DSPIGMR (NEQ, TN, Y, SAVF, WM(LB), EWT, N, MAXL, MAXLP1, KMP, + 1 DELTA, HL0, JPRE, MNEWT, F, PSOL, NPSL, X, WM(LV), WM(LHES), + 2 WM(LQ), LGMR, WM(LOCWP), IWM(LOCIWP), WM(LWK), WM(LDL), IFLAG) + NNI = NNI + 1 + NLI = NLI + LGMR + NPS = NPS + NPSL + CALL DSCAL (N, SQRTN, EWT, 1) + IF (IFLAG .NE. 0) NCFL = NCFL + 1 + IF (IFLAG .GE. 2) IERSL = 1 + IF (IFLAG .LT. 0) IERSL = -1 + RETURN +C----------------------------------------------------------------------- +C Use DPCG to solve the linear system P*x = -f +C----------------------------------------------------------------------- + 300 CONTINUE + LR = 1 + LP = LR + N + LW = LP + N + LZ = LW + N + LWK = LZ + N + CALL DCOPY (N, X, 1, WM(LR), 1) + CALL DPCG (NEQ, TN, Y, SAVF, WM(LR), EWT, N, MAXL, DELTA, HL0, + 1 JPRE, MNEWT, F, PSOL, NPSL, X, WM(LP), WM(LW), WM(LZ), + 2 LPCG, WM(LOCWP), IWM(LOCIWP), WM(LWK), IFLAG) + NNI = NNI + 1 + NLI = NLI + LPCG + NPS = NPS + NPSL + IF (IFLAG .NE. 0) NCFL = NCFL + 1 + IF (IFLAG .GE. 2) IERSL = 1 + IF (IFLAG .LT. 0) IERSL = -1 + RETURN +C----------------------------------------------------------------------- +C Use DPCGS to solve the linear system P*x = -f +C----------------------------------------------------------------------- + 400 CONTINUE + LR = 1 + LP = LR + N + LW = LP + N + LZ = LW + N + LWK = LZ + N + CALL DCOPY (N, X, 1, WM(LR), 1) + CALL DPCGS (NEQ, TN, Y, SAVF, WM(LR), EWT, N, MAXL, DELTA, HL0, + 1 JPRE, MNEWT, F, PSOL, NPSL, X, WM(LP), WM(LW), WM(LZ), + 2 LPCG, WM(LOCWP), IWM(LOCIWP), WM(LWK), IFLAG) + NNI = NNI + 1 + NLI = NLI + LPCG + NPS = NPS + NPSL + IF (IFLAG .NE. 0) NCFL = NCFL + 1 + IF (IFLAG .GE. 2) IERSL = 1 + IF (IFLAG .LT. 0) IERSL = -1 + RETURN +C----------------------------------------------------------------------- +C Use DUSOL, which interfaces to PSOL, to solve the linear system +C (no Krylov iteration). +C----------------------------------------------------------------------- + 900 CONTINUE + LB = 1 + LWK = LB + N + CALL DCOPY (N, X, 1, WM(LB), 1) + CALL DUSOL (NEQ, TN, Y, SAVF, WM(LB), EWT, N, DELTA, HL0, MNEWT, + 1 PSOL, NPSL, X, WM(LOCWP), IWM(LOCIWP), WM(LWK), IFLAG) + NNI = NNI + 1 + NPS = NPS + NPSL + IF (IFLAG .NE. 0) NCFL = NCFL + 1 + IF (IFLAG .EQ. 3) IERSL = 1 + IF (IFLAG .LT. 0) IERSL = -1 + RETURN +C----------------------- End of Subroutine DSOLPK ---------------------- + END +*DECK DSPIOM + SUBROUTINE DSPIOM (NEQ, TN, Y, SAVF, B, WGHT, N, MAXL, KMP, DELTA, + 1 HL0, JPRE, MNEWT, F, PSOL, NPSL, X, V, HES, IPVT, + 2 LIOM, WP, IWP, WK, IFLAG) + EXTERNAL F, PSOL + INTEGER NEQ,N,MAXL,KMP,JPRE,MNEWT,NPSL,IPVT,LIOM,IWP,IFLAG + DOUBLE PRECISION TN,Y,SAVF,B,WGHT,DELTA,HL0,X,V,HES,WP,WK + DIMENSION NEQ(*), Y(*), SAVF(*), B(*), WGHT(*), X(*), V(N,*), + 1 HES(MAXL,MAXL), IPVT(*), WP(*), IWP(*), WK(*) +C----------------------------------------------------------------------- +C This routine solves the linear system A * x = b using a scaled +C preconditioned version of the Incomplete Orthogonalization Method. +C An initial guess of x = 0 is assumed. +C----------------------------------------------------------------------- +C +C On entry +C +C NEQ = problem size, passed to F and PSOL (NEQ(1) = N). +C +C TN = current value of t. +C +C Y = array containing current dependent variable vector. +C +C SAVF = array containing current value of f(t,y). +C +C B = the right hand side of the system A*x = b. +C B is also used as work space when computing the +C final approximation. +C (B is the same as V(*,MAXL+1) in the call to DSPIOM.) +C +C WGHT = array of length N containing scale factors. +C 1/WGHT(i) are the diagonal elements of the diagonal +C scaling matrix D. +C +C N = the order of the matrix A, and the lengths +C of the vectors Y, SAVF, B, WGHT, and X. +C +C MAXL = the maximum allowable order of the matrix HES. +C +C KMP = the number of previous vectors the new vector VNEW +C must be made orthogonal to. KMP .le. MAXL. +C +C DELTA = tolerance on residuals b - A*x in weighted RMS-norm. +C +C HL0 = current value of (step size h) * (coefficient l0). +C +C JPRE = preconditioner type flag. +C +C MNEWT = Newton iteration counter (.ge. 0). +C +C WK = real work array of length N used by DATV and PSOL. +C +C WP = real work array used by preconditioner PSOL. +C +C IWP = integer work array used by preconditioner PSOL. +C +C On return +C +C X = the final computed approximation to the solution +C of the system A*x = b. +C +C V = the N by (LIOM+1) array containing the LIOM +C orthogonal vectors V(*,1) to V(*,LIOM). +C +C HES = the LU factorization of the LIOM by LIOM upper +C Hessenberg matrix whose entries are the +C scaled inner products of A*V(*,k) and V(*,i). +C +C IPVT = an integer array containg pivoting information. +C It is loaded in DHEFA and used in DHESL. +C +C LIOM = the number of iterations performed, and current +C order of the upper Hessenberg matrix HES. +C +C NPSL = the number of calls to PSOL. +C +C IFLAG = integer error flag: +C 0 means convergence in LIOM iterations, LIOM.le.MAXL. +C 1 means the convergence test did not pass in MAXL +C iterations, but the residual norm is .lt. 1, +C or .lt. norm(b) if MNEWT = 0, and so X is computed. +C 2 means the convergence test did not pass in MAXL +C iterations, residual .gt. 1, and X is undefined. +C 3 means there was a recoverable error in PSOL +C caused by the preconditioner being out of date. +C -1 means there was a nonrecoverable error in PSOL. +C +C----------------------------------------------------------------------- + INTEGER I, IER, INFO, J, K, LL, LM1 + DOUBLE PRECISION BNRM, BNRM0, PROD, RHO, SNORMW, DNRM2, TEM +C + IFLAG = 0 + LIOM = 0 + NPSL = 0 +C----------------------------------------------------------------------- +C The initial residual is the vector b. Apply scaling to b, and test +C for an immediate return with X = 0 or X = b. +C----------------------------------------------------------------------- + DO 10 I = 1,N + 10 V(I,1) = B(I)*WGHT(I) + BNRM0 = DNRM2 (N, V, 1) + BNRM = BNRM0 + IF (BNRM0 .GT. DELTA) GO TO 30 + IF (MNEWT .GT. 0) GO TO 20 + CALL DCOPY (N, B, 1, X, 1) + RETURN + 20 DO 25 I = 1,N + 25 X(I) = 0.0D0 + RETURN + 30 CONTINUE +C Apply inverse of left preconditioner to vector b. -------------------- + IER = 0 + IF (JPRE .EQ. 0 .OR. JPRE .EQ. 2) GO TO 55 + CALL PSOL (NEQ, TN, Y, SAVF, WK, HL0, WP, IWP, B, 1, IER) + NPSL = 1 + IF (IER .NE. 0) GO TO 300 +C Calculate norm of scaled vector V(*,1) and normalize it. ------------- + DO 50 I = 1,N + 50 V(I,1) = B(I)*WGHT(I) + BNRM = DNRM2(N, V, 1) + DELTA = DELTA*(BNRM/BNRM0) + 55 TEM = 1.0D0/BNRM + CALL DSCAL (N, TEM, V(1,1), 1) +C Zero out the HES array. ---------------------------------------------- + DO 65 J = 1,MAXL + DO 60 I = 1,MAXL + 60 HES(I,J) = 0.0D0 + 65 CONTINUE +C----------------------------------------------------------------------- +C Main loop on LL = l to compute the vectors V(*,2) to V(*,MAXL). +C The running product PROD is needed for the convergence test. +C----------------------------------------------------------------------- + PROD = 1.0D0 + DO 90 LL = 1,MAXL + LIOM = LL +C----------------------------------------------------------------------- +C Call routine DATV to compute VNEW = Abar*v(l), where Abar is +C the matrix A with scaling and inverse preconditioner factors applied. +C Call routine DORTHOG to orthogonalize the new vector vnew = V(*,l+1). +C Call routine DHEFA to update the factors of HES. +C----------------------------------------------------------------------- + CALL DATV (NEQ, Y, SAVF, V(1,LL), WGHT, X, F, PSOL, V(1,LL+1), + 1 WK, WP, IWP, HL0, JPRE, IER, NPSL) + IF (IER .NE. 0) GO TO 300 + CALL DORTHOG (V(1,LL+1), V, HES, N, LL, MAXL, KMP, SNORMW) + CALL DHEFA (HES, MAXL, LL, IPVT, INFO, LL) + LM1 = LL - 1 + IF (LL .GT. 1 .AND. IPVT(LM1) .EQ. LM1) PROD = PROD*HES(LL,LM1) + IF (INFO .NE. LL) GO TO 70 +C----------------------------------------------------------------------- +C The last pivot in HES was found to be zero. +C If vnew = 0 or l = MAXL, take an error return with IFLAG = 2. +C otherwise, continue the iteration without a convergence test. +C----------------------------------------------------------------------- + IF (SNORMW .EQ. 0.0D0) GO TO 120 + IF (LL .EQ. MAXL) GO TO 120 + GO TO 80 +C----------------------------------------------------------------------- +C Update RHO, the estimate of the norm of the residual b - A*x(l). +C test for convergence. If passed, compute approximation x(l). +C If failed and l .lt. MAXL, then continue iterating. +C----------------------------------------------------------------------- + 70 CONTINUE + RHO = BNRM*SNORMW*ABS(PROD/HES(LL,LL)) + IF (RHO .LE. DELTA) GO TO 200 + IF (LL .EQ. MAXL) GO TO 100 +C If l .lt. MAXL, store HES(l+1,l) and normalize the vector v(*,l+1). + 80 CONTINUE + HES(LL+1,LL) = SNORMW + TEM = 1.0D0/SNORMW + CALL DSCAL (N, TEM, V(1,LL+1), 1) + 90 CONTINUE +C----------------------------------------------------------------------- +C l has reached MAXL without passing the convergence test: +C If RHO is not too large, compute a solution anyway and return with +C IFLAG = 1. Otherwise return with IFLAG = 2. +C----------------------------------------------------------------------- + 100 CONTINUE + IF (RHO .LE. 1.0D0) GO TO 150 + IF (RHO .LE. BNRM .AND. MNEWT .EQ. 0) GO TO 150 + 120 CONTINUE + IFLAG = 2 + RETURN + 150 IFLAG = 1 +C----------------------------------------------------------------------- +C Compute the approximation x(l) to the solution. +C Since the vector X was used as work space, and the initial guess +C of the Newton correction is zero, X must be reset to zero. +C----------------------------------------------------------------------- + 200 CONTINUE + LL = LIOM + DO 210 K = 1,LL + 210 B(K) = 0.0D0 + B(1) = BNRM + CALL DHESL (HES, MAXL, LL, IPVT, B) + DO 220 K = 1,N + 220 X(K) = 0.0D0 + DO 230 I = 1,LL + CALL DAXPY (N, B(I), V(1,I), 1, X, 1) + 230 CONTINUE + DO 240 I = 1,N + 240 X(I) = X(I)/WGHT(I) + IF (JPRE .LE. 1) RETURN + CALL PSOL (NEQ, TN, Y, SAVF, WK, HL0, WP, IWP, X, 2, IER) + NPSL = NPSL + 1 + IF (IER .NE. 0) GO TO 300 + RETURN +C----------------------------------------------------------------------- +C This block handles error returns forced by routine PSOL. +C----------------------------------------------------------------------- + 300 CONTINUE + IF (IER .LT. 0) IFLAG = -1 + IF (IER .GT. 0) IFLAG = 3 + RETURN +C----------------------- End of Subroutine DSPIOM ---------------------- + END +*DECK DATV + SUBROUTINE DATV (NEQ, Y, SAVF, V, WGHT, FTEM, F, PSOL, Z, VTEM, + 1 WP, IWP, HL0, JPRE, IER, NPSL) + EXTERNAL F, PSOL + INTEGER NEQ, IWP, JPRE, IER, NPSL + DOUBLE PRECISION Y, SAVF, V, WGHT, FTEM, Z, VTEM, WP, HL0 + DIMENSION NEQ(*), Y(*), SAVF(*), V(*), WGHT(*), FTEM(*), Z(*), + 1 VTEM(*), WP(*), IWP(*) + INTEGER IOWND, IOWNS, + 1 ICF, IERPJ, IERSL, JCUR, JSTART, KFLAG, L, + 2 LYH, LEWT, LACOR, LSAVF, LWM, LIWM, METH, MITER, + 3 MAXORD, MAXCOR, MSBP, MXNCF, N, NQ, NST, NFE, NJE, NQU + DOUBLE PRECISION ROWNS, + 1 CCMAX, EL0, H, HMIN, HMXI, HU, RC, TN, UROUND + COMMON /DLS001/ ROWNS(209), + 1 CCMAX, EL0, H, HMIN, HMXI, HU, RC, TN, UROUND, + 2 IOWND(6), IOWNS(6), + 3 ICF, IERPJ, IERSL, JCUR, JSTART, KFLAG, L, + 4 LYH, LEWT, LACOR, LSAVF, LWM, LIWM, METH, MITER, + 5 MAXORD, MAXCOR, MSBP, MXNCF, N, NQ, NST, NFE, NJE, NQU +C----------------------------------------------------------------------- +C This routine computes the product +C +C (D-inverse)*(P1-inverse)*(I - hl0*df/dy)*(P2-inverse)*(D*v), +C +C where D is a diagonal scaling matrix, and P1 and P2 are the +C left and right preconditioning matrices, respectively. +C v is assumed to have WRMS norm equal to 1. +C The product is stored in z. This is computed by a +C difference quotient, a call to F, and two calls to PSOL. +C----------------------------------------------------------------------- +C +C On entry +C +C NEQ = problem size, passed to F and PSOL (NEQ(1) = N). +C +C Y = array containing current dependent variable vector. +C +C SAVF = array containing current value of f(t,y). +C +C V = real array of length N (can be the same array as Z). +C +C WGHT = array of length N containing scale factors. +C 1/WGHT(i) are the diagonal elements of the matrix D. +C +C FTEM = work array of length N. +C +C VTEM = work array of length N used to store the +C unscaled version of V. +C +C WP = real work array used by preconditioner PSOL. +C +C IWP = integer work array used by preconditioner PSOL. +C +C HL0 = current value of (step size h) * (coefficient l0). +C +C JPRE = preconditioner type flag. +C +C +C On return +C +C Z = array of length N containing desired scaled +C matrix-vector product. +C +C IER = error flag from PSOL. +C +C NPSL = the number of calls to PSOL. +C +C In addition, this routine uses the Common variables TN, N, NFE. +C----------------------------------------------------------------------- + INTEGER I + DOUBLE PRECISION FAC, RNORM, DNRM2, TEMPN +C +C Set VTEM = D * V. + DO 10 I = 1,N + 10 VTEM(I) = V(I)/WGHT(I) + IER = 0 + IF (JPRE .GE. 2) GO TO 30 +C +C JPRE = 0 or 1. Save Y in Z and increment Y by VTEM. + CALL DCOPY (N, Y, 1, Z, 1) + DO 20 I = 1,N + 20 Y(I) = Z(I) + VTEM(I) + FAC = HL0 + GO TO 60 +C +C JPRE = 2 or 3. Apply inverse of right preconditioner to VTEM. + 30 CONTINUE + CALL PSOL (NEQ, TN, Y, SAVF, FTEM, HL0, WP, IWP, VTEM, 2, IER) + NPSL = NPSL + 1 + IF (IER .NE. 0) RETURN +C Calculate L-2 norm of (D-inverse) * VTEM. + DO 40 I = 1,N + 40 Z(I) = VTEM(I)*WGHT(I) + TEMPN = DNRM2 (N, Z, 1) + RNORM = 1.0D0/TEMPN +C Save Y in Z and increment Y by VTEM/norm. + CALL DCOPY (N, Y, 1, Z, 1) + DO 50 I = 1,N + 50 Y(I) = Z(I) + VTEM(I)*RNORM + FAC = HL0*TEMPN +C +C For all JPRE, call F with incremented Y argument, and restore Y. + 60 CONTINUE + CALL F (NEQ, TN, Y, FTEM) + NFE = NFE + 1 + CALL DCOPY (N, Z, 1, Y, 1) +C Set Z = (identity - hl0*Jacobian) * VTEM, using difference quotient. + DO 70 I = 1,N + 70 Z(I) = FTEM(I) - SAVF(I) + DO 80 I = 1,N + 80 Z(I) = VTEM(I) - FAC*Z(I) +C Apply inverse of left preconditioner to Z, if nontrivial. + IF (JPRE .EQ. 0 .OR. JPRE .EQ. 2) GO TO 85 + CALL PSOL (NEQ, TN, Y, SAVF, FTEM, HL0, WP, IWP, Z, 1, IER) + NPSL = NPSL + 1 + IF (IER .NE. 0) RETURN + 85 CONTINUE +C Apply D-inverse to Z and return. + DO 90 I = 1,N + 90 Z(I) = Z(I)*WGHT(I) + RETURN +C----------------------- End of Subroutine DATV ------------------------ + END +*DECK DORTHOG + SUBROUTINE DORTHOG (VNEW, V, HES, N, LL, LDHES, KMP, SNORMW) + INTEGER N, LL, LDHES, KMP + DOUBLE PRECISION VNEW, V, HES, SNORMW + DIMENSION VNEW(*), V(N,*), HES(LDHES,*) +C----------------------------------------------------------------------- +C This routine orthogonalizes the vector VNEW against the previous +C KMP vectors in the V array. It uses a modified Gram-Schmidt +C orthogonalization procedure with conditional reorthogonalization. +C This is the version of 28 may 1986. +C----------------------------------------------------------------------- +C +C On entry +C +C VNEW = the vector of length N containing a scaled product +C of the Jacobian and the vector V(*,LL). +C +C V = the N x l array containing the previous LL +C orthogonal vectors v(*,1) to v(*,LL). +C +C HES = an LL x LL upper Hessenberg matrix containing, +C in HES(i,k), k.lt.LL, scaled inner products of +C A*V(*,k) and V(*,i). +C +C LDHES = the leading dimension of the HES array. +C +C N = the order of the matrix A, and the length of VNEW. +C +C LL = the current order of the matrix HES. +C +C KMP = the number of previous vectors the new vector VNEW +C must be made orthogonal to (KMP .le. MAXL). +C +C +C On return +C +C VNEW = the new vector orthogonal to V(*,i0) to V(*,LL), +C where i0 = MAX(1, LL-KMP+1). +C +C HES = upper Hessenberg matrix with column LL filled in with +C scaled inner products of A*V(*,LL) and V(*,i). +C +C SNORMW = L-2 norm of VNEW. +C +C----------------------------------------------------------------------- + INTEGER I, I0 + DOUBLE PRECISION ARG, DDOT, DNRM2, SUMDSQ, TEM, VNRM +C +C Get norm of unaltered VNEW for later use. ---------------------------- + VNRM = DNRM2 (N, VNEW, 1) +C----------------------------------------------------------------------- +C Do modified Gram-Schmidt on VNEW = A*v(LL). +C Scaled inner products give new column of HES. +C Projections of earlier vectors are subtracted from VNEW. +C----------------------------------------------------------------------- + I0 = MAX(1,LL-KMP+1) + DO 10 I = I0,LL + HES(I,LL) = DDOT (N, V(1,I), 1, VNEW, 1) + TEM = -HES(I,LL) + CALL DAXPY (N, TEM, V(1,I), 1, VNEW, 1) + 10 CONTINUE +C----------------------------------------------------------------------- +C Compute SNORMW = norm of VNEW. +C If VNEW is small compared to its input value (in norm), then +C reorthogonalize VNEW to V(*,1) through V(*,LL). +C Correct if relative correction exceeds 1000*(unit roundoff). +C finally, correct SNORMW using the dot products involved. +C----------------------------------------------------------------------- + SNORMW = DNRM2 (N, VNEW, 1) + IF (VNRM + 0.001D0*SNORMW .NE. VNRM) RETURN + SUMDSQ = 0.0D0 + DO 30 I = I0,LL + TEM = -DDOT (N, V(1,I), 1, VNEW, 1) + IF (HES(I,LL) + 0.001D0*TEM .EQ. HES(I,LL)) GO TO 30 + HES(I,LL) = HES(I,LL) - TEM + CALL DAXPY (N, TEM, V(1,I), 1, VNEW, 1) + SUMDSQ = SUMDSQ + TEM**2 + 30 CONTINUE + IF (SUMDSQ .EQ. 0.0D0) RETURN + ARG = MAX(0.0D0,SNORMW**2 - SUMDSQ) + SNORMW = SQRT(ARG) +C + RETURN +C----------------------- End of Subroutine DORTHOG --------------------- + END +*DECK DSPIGMR + SUBROUTINE DSPIGMR (NEQ, TN, Y, SAVF, B, WGHT, N, MAXL, MAXLP1, + 1 KMP, DELTA, HL0, JPRE, MNEWT, F, PSOL, NPSL, X, V, HES, Q, + 2 LGMR, WP, IWP, WK, DL, IFLAG) + EXTERNAL F, PSOL + INTEGER NEQ,N,MAXL,MAXLP1,KMP,JPRE,MNEWT,NPSL,LGMR,IWP,IFLAG + DOUBLE PRECISION TN,Y,SAVF,B,WGHT,DELTA,HL0,X,V,HES,Q,WP,WK,DL + DIMENSION NEQ(*), Y(*), SAVF(*), B(*), WGHT(*), X(*), V(N,*), + 1 HES(MAXLP1,*), Q(*), WP(*), IWP(*), WK(*), DL(*) +C----------------------------------------------------------------------- +C This routine solves the linear system A * x = b using a scaled +C preconditioned version of the Generalized Minimal Residual method. +C An initial guess of x = 0 is assumed. +C----------------------------------------------------------------------- +C +C On entry +C +C NEQ = problem size, passed to F and PSOL (NEQ(1) = N). +C +C TN = current value of t. +C +C Y = array containing current dependent variable vector. +C +C SAVF = array containing current value of f(t,y). +C +C B = the right hand side of the system A*x = b. +C B is also used as work space when computing +C the final approximation. +C (B is the same as V(*,MAXL+1) in the call to DSPIGMR.) +C +C WGHT = the vector of length N containing the nonzero +C elements of the diagonal scaling matrix. +C +C N = the order of the matrix A, and the lengths +C of the vectors WGHT, B and X. +C +C MAXL = the maximum allowable order of the matrix HES. +C +C MAXLP1 = MAXL + 1, used for dynamic dimensioning of HES. +C +C KMP = the number of previous vectors the new vector VNEW +C must be made orthogonal to. KMP .le. MAXL. +C +C DELTA = tolerance on residuals b - A*x in weighted RMS-norm. +C +C HL0 = current value of (step size h) * (coefficient l0). +C +C JPRE = preconditioner type flag. +C +C MNEWT = Newton iteration counter (.ge. 0). +C +C WK = real work array used by routine DATV and PSOL. +C +C DL = real work array used for calculation of the residual +C norm RHO when the method is incomplete (KMP .lt. MAXL). +C Not needed or referenced in complete case (KMP = MAXL). +C +C WP = real work array used by preconditioner PSOL. +C +C IWP = integer work array used by preconditioner PSOL. +C +C On return +C +C X = the final computed approximation to the solution +C of the system A*x = b. +C +C LGMR = the number of iterations performed and +C the current order of the upper Hessenberg +C matrix HES. +C +C NPSL = the number of calls to PSOL. +C +C V = the N by (LGMR+1) array containing the LGMR +C orthogonal vectors V(*,1) to V(*,LGMR). +C +C HES = the upper triangular factor of the QR decomposition +C of the (LGMR+1) by lgmr upper Hessenberg matrix whose +C entries are the scaled inner-products of A*V(*,i) +C and V(*,k). +C +C Q = real array of length 2*MAXL containing the components +C of the Givens rotations used in the QR decomposition +C of HES. It is loaded in DHEQR and used in DHELS. +C +C IFLAG = integer error flag: +C 0 means convergence in LGMR iterations, LGMR .le. MAXL. +C 1 means the convergence test did not pass in MAXL +C iterations, but the residual norm is .lt. 1, +C or .lt. norm(b) if MNEWT = 0, and so x is computed. +C 2 means the convergence test did not pass in MAXL +C iterations, residual .gt. 1, and X is undefined. +C 3 means there was a recoverable error in PSOL +C caused by the preconditioner being out of date. +C -1 means there was a nonrecoverable error in PSOL. +C +C----------------------------------------------------------------------- + INTEGER I, IER, INFO, IP1, I2, J, K, LL, LLP1 + DOUBLE PRECISION BNRM,BNRM0,C,DLNRM,PROD,RHO,S,SNORMW,DNRM2,TEM +C + IFLAG = 0 + LGMR = 0 + NPSL = 0 +C----------------------------------------------------------------------- +C The initial residual is the vector b. Apply scaling to b, and test +C for an immediate return with X = 0 or X = b. +C----------------------------------------------------------------------- + DO 10 I = 1,N + 10 V(I,1) = B(I)*WGHT(I) + BNRM0 = DNRM2 (N, V, 1) + BNRM = BNRM0 + IF (BNRM0 .GT. DELTA) GO TO 30 + IF (MNEWT .GT. 0) GO TO 20 + CALL DCOPY (N, B, 1, X, 1) + RETURN + 20 DO 25 I = 1,N + 25 X(I) = 0.0D0 + RETURN + 30 CONTINUE +C Apply inverse of left preconditioner to vector b. -------------------- + IER = 0 + IF (JPRE .EQ. 0 .OR. JPRE .EQ. 2) GO TO 55 + CALL PSOL (NEQ, TN, Y, SAVF, WK, HL0, WP, IWP, B, 1, IER) + NPSL = 1 + IF (IER .NE. 0) GO TO 300 +C Calculate norm of scaled vector V(*,1) and normalize it. ------------- + DO 50 I = 1,N + 50 V(I,1) = B(I)*WGHT(I) + BNRM = DNRM2 (N, V, 1) + DELTA = DELTA*(BNRM/BNRM0) + 55 TEM = 1.0D0/BNRM + CALL DSCAL (N, TEM, V(1,1), 1) +C Zero out the HES array. ---------------------------------------------- + DO 65 J = 1,MAXL + DO 60 I = 1,MAXLP1 + 60 HES(I,J) = 0.0D0 + 65 CONTINUE +C----------------------------------------------------------------------- +C Main loop to compute the vectors V(*,2) to V(*,MAXL). +C The running product PROD is needed for the convergence test. +C----------------------------------------------------------------------- + PROD = 1.0D0 + DO 90 LL = 1,MAXL + LGMR = LL +C----------------------------------------------------------------------- +C Call routine DATV to compute VNEW = Abar*v(ll), where Abar is +C the matrix A with scaling and inverse preconditioner factors applied. +C Call routine DORTHOG to orthogonalize the new vector VNEW = V(*,LL+1). +C Call routine DHEQR to update the factors of HES. +C----------------------------------------------------------------------- + CALL DATV (NEQ, Y, SAVF, V(1,LL), WGHT, X, F, PSOL, V(1,LL+1), + 1 WK, WP, IWP, HL0, JPRE, IER, NPSL) + IF (IER .NE. 0) GO TO 300 + CALL DORTHOG (V(1,LL+1), V, HES, N, LL, MAXLP1, KMP, SNORMW) + HES(LL+1,LL) = SNORMW + CALL DHEQR (HES, MAXLP1, LL, Q, INFO, LL) + IF (INFO .EQ. LL) GO TO 120 +C----------------------------------------------------------------------- +C Update RHO, the estimate of the norm of the residual b - A*xl. +C If KMP .lt. MAXL, then the vectors V(*,1),...,V(*,LL+1) are not +C necessarily orthogonal for LL .gt. KMP. The vector DL must then +C be computed, and its norm used in the calculation of RHO. +C----------------------------------------------------------------------- + PROD = PROD*Q(2*LL) + RHO = ABS(PROD*BNRM) + IF ((LL.GT.KMP) .AND. (KMP.LT.MAXL)) THEN + IF (LL .EQ. KMP+1) THEN + CALL DCOPY (N, V(1,1), 1, DL, 1) + DO 75 I = 1,KMP + IP1 = I + 1 + I2 = I*2 + S = Q(I2) + C = Q(I2-1) + DO 70 K = 1,N + 70 DL(K) = S*DL(K) + C*V(K,IP1) + 75 CONTINUE + ENDIF + S = Q(2*LL) + C = Q(2*LL-1)/SNORMW + LLP1 = LL + 1 + DO 80 K = 1,N + 80 DL(K) = S*DL(K) + C*V(K,LLP1) + DLNRM = DNRM2 (N, DL, 1) + RHO = RHO*DLNRM + ENDIF +C----------------------------------------------------------------------- +C Test for convergence. If passed, compute approximation xl. +C if failed and LL .lt. MAXL, then continue iterating. +C----------------------------------------------------------------------- + IF (RHO .LE. DELTA) GO TO 200 + IF (LL .EQ. MAXL) GO TO 100 +C----------------------------------------------------------------------- +C Rescale so that the norm of V(1,LL+1) is one. +C----------------------------------------------------------------------- + TEM = 1.0D0/SNORMW + CALL DSCAL (N, TEM, V(1,LL+1), 1) + 90 CONTINUE + 100 CONTINUE + IF (RHO .LE. 1.0D0) GO TO 150 + IF (RHO .LE. BNRM .AND. MNEWT .EQ. 0) GO TO 150 + 120 CONTINUE + IFLAG = 2 + RETURN + 150 IFLAG = 1 +C----------------------------------------------------------------------- +C Compute the approximation xl to the solution. +C Since the vector X was used as work space, and the initial guess +C of the Newton correction is zero, X must be reset to zero. +C----------------------------------------------------------------------- + 200 CONTINUE + LL = LGMR + LLP1 = LL + 1 + DO 210 K = 1,LLP1 + 210 B(K) = 0.0D0 + B(1) = BNRM + CALL DHELS (HES, MAXLP1, LL, Q, B) + DO 220 K = 1,N + 220 X(K) = 0.0D0 + DO 230 I = 1,LL + CALL DAXPY (N, B(I), V(1,I), 1, X, 1) + 230 CONTINUE + DO 240 I = 1,N + 240 X(I) = X(I)/WGHT(I) + IF (JPRE .LE. 1) RETURN + CALL PSOL (NEQ, TN, Y, SAVF, WK, HL0, WP, IWP, X, 2, IER) + NPSL = NPSL + 1 + IF (IER .NE. 0) GO TO 300 + RETURN +C----------------------------------------------------------------------- +C This block handles error returns forced by routine PSOL. +C----------------------------------------------------------------------- + 300 CONTINUE + IF (IER .LT. 0) IFLAG = -1 + IF (IER .GT. 0) IFLAG = 3 +C + RETURN +C----------------------- End of Subroutine DSPIGMR --------------------- + END +*DECK DPCG + SUBROUTINE DPCG (NEQ, TN, Y, SAVF, R, WGHT, N, MAXL, DELTA, HL0, + 1 JPRE, MNEWT, F, PSOL, NPSL, X, P, W, Z, LPCG, WP, IWP, WK, IFLAG) + EXTERNAL F, PSOL + INTEGER NEQ, N, MAXL, JPRE, MNEWT, NPSL, LPCG, IWP, IFLAG + DOUBLE PRECISION TN,Y,SAVF,R,WGHT,DELTA,HL0,X,P,W,Z,WP,WK + DIMENSION NEQ(*), Y(*), SAVF(*), R(*), WGHT(*), X(*), P(*), W(*), + 1 Z(*), WP(*), IWP(*), WK(*) +C----------------------------------------------------------------------- +C This routine computes the solution to the system A*x = b using a +C preconditioned version of the Conjugate Gradient algorithm. +C It is assumed here that the matrix A and the preconditioner +C matrix M are symmetric positive definite or nearly so. +C----------------------------------------------------------------------- +C +C On entry +C +C NEQ = problem size, passed to F and PSOL (NEQ(1) = N). +C +C TN = current value of t. +C +C Y = array containing current dependent variable vector. +C +C SAVF = array containing current value of f(t,y). +C +C R = the right hand side of the system A*x = b. +C +C WGHT = array of length N containing scale factors. +C 1/WGHT(i) are the diagonal elements of the diagonal +C scaling matrix D. +C +C N = the order of the matrix A, and the lengths +C of the vectors Y, SAVF, R, WGHT, P, W, Z, WK, and X. +C +C MAXL = the maximum allowable number of iterates. +C +C DELTA = tolerance on residuals b - A*x in weighted RMS-norm. +C +C HL0 = current value of (step size h) * (coefficient l0). +C +C JPRE = preconditioner type flag. +C +C MNEWT = Newton iteration counter (.ge. 0). +C +C WK = real work array used by routine DATP. +C +C WP = real work array used by preconditioner PSOL. +C +C IWP = integer work array used by preconditioner PSOL. +C +C On return +C +C X = the final computed approximation to the solution +C of the system A*x = b. +C +C LPCG = the number of iterations performed, and current +C order of the upper Hessenberg matrix HES. +C +C NPSL = the number of calls to PSOL. +C +C IFLAG = integer error flag: +C 0 means convergence in LPCG iterations, LPCG .le. MAXL. +C 1 means the convergence test did not pass in MAXL +C iterations, but the residual norm is .lt. 1, +C or .lt. norm(b) if MNEWT = 0, and so X is computed. +C 2 means the convergence test did not pass in MAXL +C iterations, residual .gt. 1, and X is undefined. +C 3 means there was a recoverable error in PSOL +C caused by the preconditioner being out of date. +C 4 means there was a zero denominator in the algorithm. +C The system matrix or preconditioner matrix is not +C sufficiently close to being symmetric pos. definite. +C -1 means there was a nonrecoverable error in PSOL. +C +C----------------------------------------------------------------------- + INTEGER I, IER + DOUBLE PRECISION ALPHA,BETA,BNRM,PTW,RNRM,DDOT,DVNORM,ZTR,ZTR0 +C + IFLAG = 0 + NPSL = 0 + LPCG = 0 + DO 10 I = 1,N + 10 X(I) = 0.0D0 + BNRM = DVNORM (N, R, WGHT) +C Test for immediate return with X = 0 or X = b. ----------------------- + IF (BNRM .GT. DELTA) GO TO 20 + IF (MNEWT .GT. 0) RETURN + CALL DCOPY (N, R, 1, X, 1) + RETURN +C + 20 ZTR = 0.0D0 +C Loop point for PCG iterations. --------------------------------------- + 30 CONTINUE + LPCG = LPCG + 1 + CALL DCOPY (N, R, 1, Z, 1) + IER = 0 + IF (JPRE .EQ. 0) GO TO 40 + CALL PSOL (NEQ, TN, Y, SAVF, WK, HL0, WP, IWP, Z, 3, IER) + NPSL = NPSL + 1 + IF (IER .NE. 0) GO TO 100 + 40 CONTINUE + ZTR0 = ZTR + ZTR = DDOT (N, Z, 1, R, 1) + IF (LPCG .NE. 1) GO TO 50 + CALL DCOPY (N, Z, 1, P, 1) + GO TO 70 + 50 CONTINUE + IF (ZTR0 .EQ. 0.0D0) GO TO 200 + BETA = ZTR/ZTR0 + DO 60 I = 1,N + 60 P(I) = Z(I) + BETA*P(I) + 70 CONTINUE +C----------------------------------------------------------------------- +C Call DATP to compute A*p and return the answer in W. +C----------------------------------------------------------------------- + CALL DATP (NEQ, Y, SAVF, P, WGHT, HL0, WK, F, W) +C + PTW = DDOT (N, P, 1, W, 1) + IF (PTW .EQ. 0.0D0) GO TO 200 + ALPHA = ZTR/PTW + CALL DAXPY (N, ALPHA, P, 1, X, 1) + ALPHA = -ALPHA + CALL DAXPY (N, ALPHA, W, 1, R, 1) + RNRM = DVNORM (N, R, WGHT) + IF (RNRM .LE. DELTA) RETURN + IF (LPCG .LT. MAXL) GO TO 30 + IFLAG = 2 + IF (RNRM .LE. 1.0D0) IFLAG = 1 + IF (RNRM .LE. BNRM .AND. MNEWT .EQ. 0) IFLAG = 1 + RETURN +C----------------------------------------------------------------------- +C This block handles error returns from PSOL. +C----------------------------------------------------------------------- + 100 CONTINUE + IF (IER .LT. 0) IFLAG = -1 + IF (IER .GT. 0) IFLAG = 3 + RETURN +C----------------------------------------------------------------------- +C This block handles division by zero errors. +C----------------------------------------------------------------------- + 200 CONTINUE + IFLAG = 4 + RETURN +C----------------------- End of Subroutine DPCG ------------------------ + END +*DECK DPCGS + SUBROUTINE DPCGS (NEQ, TN, Y, SAVF, R, WGHT, N, MAXL, DELTA, HL0, + 1 JPRE, MNEWT, F, PSOL, NPSL, X, P, W, Z, LPCG, WP, IWP, WK, IFLAG) + EXTERNAL F, PSOL + INTEGER NEQ, N, MAXL, JPRE, MNEWT, NPSL, LPCG, IWP, IFLAG + DOUBLE PRECISION TN,Y,SAVF,R,WGHT,DELTA,HL0,X,P,W,Z,WP,WK + DIMENSION NEQ(*), Y(*), SAVF(*), R(*), WGHT(*), X(*), P(*), W(*), + 1 Z(*), WP(*), IWP(*), WK(*) +C----------------------------------------------------------------------- +C This routine computes the solution to the system A*x = b using a +C scaled preconditioned version of the Conjugate Gradient algorithm. +C It is assumed here that the scaled matrix D**-1 * A * D and the +C scaled preconditioner D**-1 * M * D are close to being +C symmetric positive definite. +C----------------------------------------------------------------------- +C +C On entry +C +C NEQ = problem size, passed to F and PSOL (NEQ(1) = N). +C +C TN = current value of t. +C +C Y = array containing current dependent variable vector. +C +C SAVF = array containing current value of f(t,y). +C +C R = the right hand side of the system A*x = b. +C +C WGHT = array of length N containing scale factors. +C 1/WGHT(i) are the diagonal elements of the diagonal +C scaling matrix D. +C +C N = the order of the matrix A, and the lengths +C of the vectors Y, SAVF, R, WGHT, P, W, Z, WK, and X. +C +C MAXL = the maximum allowable number of iterates. +C +C DELTA = tolerance on residuals b - A*x in weighted RMS-norm. +C +C HL0 = current value of (step size h) * (coefficient l0). +C +C JPRE = preconditioner type flag. +C +C MNEWT = Newton iteration counter (.ge. 0). +C +C WK = real work array used by routine DATP. +C +C WP = real work array used by preconditioner PSOL. +C +C IWP = integer work array used by preconditioner PSOL. +C +C On return +C +C X = the final computed approximation to the solution +C of the system A*x = b. +C +C LPCG = the number of iterations performed, and current +C order of the upper Hessenberg matrix HES. +C +C NPSL = the number of calls to PSOL. +C +C IFLAG = integer error flag: +C 0 means convergence in LPCG iterations, LPCG .le. MAXL. +C 1 means the convergence test did not pass in MAXL +C iterations, but the residual norm is .lt. 1, +C or .lt. norm(b) if MNEWT = 0, and so X is computed. +C 2 means the convergence test did not pass in MAXL +C iterations, residual .gt. 1, and X is undefined. +C 3 means there was a recoverable error in PSOL +C caused by the preconditioner being out of date. +C 4 means there was a zero denominator in the algorithm. +C the scaled matrix or scaled preconditioner is not +C sufficiently close to being symmetric pos. definite. +C -1 means there was a nonrecoverable error in PSOL. +C +C----------------------------------------------------------------------- + INTEGER I, IER + DOUBLE PRECISION ALPHA, BETA, BNRM, PTW, RNRM, DVNORM, ZTR, ZTR0 +C + IFLAG = 0 + NPSL = 0 + LPCG = 0 + DO 10 I = 1,N + 10 X(I) = 0.0D0 + BNRM = DVNORM (N, R, WGHT) +C Test for immediate return with X = 0 or X = b. ----------------------- + IF (BNRM .GT. DELTA) GO TO 20 + IF (MNEWT .GT. 0) RETURN + CALL DCOPY (N, R, 1, X, 1) + RETURN +C + 20 ZTR = 0.0D0 +C Loop point for PCG iterations. --------------------------------------- + 30 CONTINUE + LPCG = LPCG + 1 + CALL DCOPY (N, R, 1, Z, 1) + IER = 0 + IF (JPRE .EQ. 0) GO TO 40 + CALL PSOL (NEQ, TN, Y, SAVF, WK, HL0, WP, IWP, Z, 3, IER) + NPSL = NPSL + 1 + IF (IER .NE. 0) GO TO 100 + 40 CONTINUE + ZTR0 = ZTR + ZTR = 0.0D0 + DO 45 I = 1,N + 45 ZTR = ZTR + Z(I)*R(I)*WGHT(I)**2 + IF (LPCG .NE. 1) GO TO 50 + CALL DCOPY (N, Z, 1, P, 1) + GO TO 70 + 50 CONTINUE + IF (ZTR0 .EQ. 0.0D0) GO TO 200 + BETA = ZTR/ZTR0 + DO 60 I = 1,N + 60 P(I) = Z(I) + BETA*P(I) + 70 CONTINUE +C----------------------------------------------------------------------- +C Call DATP to compute A*p and return the answer in W. +C----------------------------------------------------------------------- + CALL DATP (NEQ, Y, SAVF, P, WGHT, HL0, WK, F, W) +C + PTW = 0.0D0 + DO 80 I = 1,N + 80 PTW = PTW + P(I)*W(I)*WGHT(I)**2 + IF (PTW .EQ. 0.0D0) GO TO 200 + ALPHA = ZTR/PTW + CALL DAXPY (N, ALPHA, P, 1, X, 1) + ALPHA = -ALPHA + CALL DAXPY (N, ALPHA, W, 1, R, 1) + RNRM = DVNORM (N, R, WGHT) + IF (RNRM .LE. DELTA) RETURN + IF (LPCG .LT. MAXL) GO TO 30 + IFLAG = 2 + IF (RNRM .LE. 1.0D0) IFLAG = 1 + IF (RNRM .LE. BNRM .AND. MNEWT .EQ. 0) IFLAG = 1 + RETURN +C----------------------------------------------------------------------- +C This block handles error returns from PSOL. +C----------------------------------------------------------------------- + 100 CONTINUE + IF (IER .LT. 0) IFLAG = -1 + IF (IER .GT. 0) IFLAG = 3 + RETURN +C----------------------------------------------------------------------- +C This block handles division by zero errors. +C----------------------------------------------------------------------- + 200 CONTINUE + IFLAG = 4 + RETURN +C----------------------- End of Subroutine DPCGS ----------------------- + END +*DECK DATP + SUBROUTINE DATP (NEQ, Y, SAVF, P, WGHT, HL0, WK, F, W) + EXTERNAL F + INTEGER NEQ + DOUBLE PRECISION Y, SAVF, P, WGHT, HL0, WK, W + DIMENSION NEQ(*), Y(*), SAVF(*), P(*), WGHT(*), WK(*), W(*) + INTEGER IOWND, IOWNS, + 1 ICF, IERPJ, IERSL, JCUR, JSTART, KFLAG, L, + 2 LYH, LEWT, LACOR, LSAVF, LWM, LIWM, METH, MITER, + 3 MAXORD, MAXCOR, MSBP, MXNCF, N, NQ, NST, NFE, NJE, NQU + DOUBLE PRECISION ROWNS, + 1 CCMAX, EL0, H, HMIN, HMXI, HU, RC, TN, UROUND + COMMON /DLS001/ ROWNS(209), + 1 CCMAX, EL0, H, HMIN, HMXI, HU, RC, TN, UROUND, + 2 IOWND(6), IOWNS(6), + 3 ICF, IERPJ, IERSL, JCUR, JSTART, KFLAG, L, + 4 LYH, LEWT, LACOR, LSAVF, LWM, LIWM, METH, MITER, + 5 MAXORD, MAXCOR, MSBP, MXNCF, N, NQ, NST, NFE, NJE, NQU +C----------------------------------------------------------------------- +C This routine computes the product +C +C w = (I - hl0*df/dy)*p +C +C This is computed by a call to F and a difference quotient. +C----------------------------------------------------------------------- +C +C On entry +C +C NEQ = problem size, passed to F and PSOL (NEQ(1) = N). +C +C Y = array containing current dependent variable vector. +C +C SAVF = array containing current value of f(t,y). +C +C P = real array of length N. +C +C WGHT = array of length N containing scale factors. +C 1/WGHT(i) are the diagonal elements of the matrix D. +C +C WK = work array of length N. +C +C On return +C +C +C W = array of length N containing desired +C matrix-vector product. +C +C In addition, this routine uses the Common variables TN, N, NFE. +C----------------------------------------------------------------------- + INTEGER I + DOUBLE PRECISION FAC, PNRM, RPNRM, DVNORM +C + PNRM = DVNORM (N, P, WGHT) + RPNRM = 1.0D0/PNRM + CALL DCOPY (N, Y, 1, W, 1) + DO 20 I = 1,N + 20 Y(I) = W(I) + P(I)*RPNRM + CALL F (NEQ, TN, Y, WK) + NFE = NFE + 1 + CALL DCOPY (N, W, 1, Y, 1) + FAC = HL0*PNRM + DO 40 I = 1,N + 40 W(I) = P(I) - FAC*(WK(I) - SAVF(I)) + RETURN +C----------------------- End of Subroutine DATP ------------------------ + END +*DECK DUSOL + SUBROUTINE DUSOL (NEQ, TN, Y, SAVF, B, WGHT, N, DELTA, HL0, MNEWT, + 1 PSOL, NPSL, X, WP, IWP, WK, IFLAG) + EXTERNAL PSOL + INTEGER NEQ, N, MNEWT, NPSL, IWP, IFLAG + DOUBLE PRECISION TN, Y, SAVF, B, WGHT, DELTA, HL0, X, WP, WK + DIMENSION NEQ(*), Y(*), SAVF(*), B(*), WGHT(*), X(*), + 1 WP(*), IWP(*), WK(*) +C----------------------------------------------------------------------- +C This routine solves the linear system A * x = b using only a call +C to the user-supplied routine PSOL (no Krylov iteration). +C If the norm of the right-hand side vector b is smaller than DELTA, +C the vector X returned is X = b (if MNEWT = 0) or X = 0 otherwise. +C PSOL is called with an LR argument of 0. +C----------------------------------------------------------------------- +C +C On entry +C +C NEQ = problem size, passed to F and PSOL (NEQ(1) = N). +C +C TN = current value of t. +C +C Y = array containing current dependent variable vector. +C +C SAVF = array containing current value of f(t,y). +C +C B = the right hand side of the system A*x = b. +C +C WGHT = the vector of length N containing the nonzero +C elements of the diagonal scaling matrix. +C +C N = the order of the matrix A, and the lengths +C of the vectors WGHT, B and X. +C +C DELTA = tolerance on residuals b - A*x in weighted RMS-norm. +C +C HL0 = current value of (step size h) * (coefficient l0). +C +C MNEWT = Newton iteration counter (.ge. 0). +C +C WK = real work array used by PSOL. +C +C WP = real work array used by preconditioner PSOL. +C +C IWP = integer work array used by preconditioner PSOL. +C +C On return +C +C X = the final computed approximation to the solution +C of the system A*x = b. +C +C NPSL = the number of calls to PSOL. +C +C IFLAG = integer error flag: +C 0 means no trouble occurred. +C 3 means there was a recoverable error in PSOL +C caused by the preconditioner being out of date. +C -1 means there was a nonrecoverable error in PSOL. +C +C----------------------------------------------------------------------- + INTEGER I, IER + DOUBLE PRECISION BNRM, DVNORM +C + IFLAG = 0 + NPSL = 0 +C----------------------------------------------------------------------- +C Test for an immediate return with X = 0 or X = b. +C----------------------------------------------------------------------- + BNRM = DVNORM (N, B, WGHT) + IF (BNRM .GT. DELTA) GO TO 30 + IF (MNEWT .GT. 0) GO TO 10 + CALL DCOPY (N, B, 1, X, 1) + RETURN + 10 DO 20 I = 1,N + 20 X(I) = 0.0D0 + RETURN +C Make call to PSOL and copy result from B to X. ----------------------- + 30 IER = 0 + CALL PSOL (NEQ, TN, Y, SAVF, WK, HL0, WP, IWP, B, 0, IER) + NPSL = 1 + IF (IER .NE. 0) GO TO 100 + CALL DCOPY (N, B, 1, X, 1) + RETURN +C----------------------------------------------------------------------- +C This block handles error returns forced by routine PSOL. +C----------------------------------------------------------------------- + 100 CONTINUE + IF (IER .LT. 0) IFLAG = -1 + IF (IER .GT. 0) IFLAG = 3 + RETURN +C----------------------- End of Subroutine DUSOL ----------------------- + END +*DECK DSRCPK + SUBROUTINE DSRCPK (RSAV, ISAV, JOB) +C----------------------------------------------------------------------- +C This routine saves or restores (depending on JOB) the contents of +C the Common blocks DLS001, DLPK01, which are used +C internally by the DLSODPK solver. +C +C RSAV = real array of length 222 or more. +C ISAV = integer array of length 50 or more. +C JOB = flag indicating to save or restore the Common blocks: +C JOB = 1 if Common is to be saved (written to RSAV/ISAV) +C JOB = 2 if Common is to be restored (read from RSAV/ISAV) +C A call with JOB = 2 presumes a prior call with JOB = 1. +C----------------------------------------------------------------------- + INTEGER ISAV, JOB + INTEGER ILS, ILSP + INTEGER I, LENILP, LENRLP, LENILS, LENRLS + DOUBLE PRECISION RSAV, RLS, RLSP + DIMENSION RSAV(*), ISAV(*) + SAVE LENRLS, LENILS, LENRLP, LENILP + COMMON /DLS001/ RLS(218), ILS(37) + COMMON /DLPK01/ RLSP(4), ILSP(13) + DATA LENRLS/218/, LENILS/37/, LENRLP/4/, LENILP/13/ +C + IF (JOB .EQ. 2) GO TO 100 + CALL DCOPY (LENRLS, RLS, 1, RSAV, 1) + CALL DCOPY (LENRLP, RLSP, 1, RSAV(LENRLS+1), 1) + DO 20 I = 1,LENILS + 20 ISAV(I) = ILS(I) + DO 40 I = 1,LENILP + 40 ISAV(LENILS+I) = ILSP(I) + RETURN +C + 100 CONTINUE + CALL DCOPY (LENRLS, RSAV, 1, RLS, 1) + CALL DCOPY (LENRLP, RSAV(LENRLS+1), 1, RLSP, 1) + DO 120 I = 1,LENILS + 120 ILS(I) = ISAV(I) + DO 140 I = 1,LENILP + 140 ILSP(I) = ISAV(LENILS+I) + RETURN +C----------------------- End of Subroutine DSRCPK ---------------------- + END +*DECK DHEFA + SUBROUTINE DHEFA (A, LDA, N, IPVT, INFO, JOB) + INTEGER LDA, N, IPVT(*), INFO, JOB + DOUBLE PRECISION A(LDA,*) +C----------------------------------------------------------------------- +C This routine is a modification of the LINPACK routine DGEFA and +C performs an LU decomposition of an upper Hessenberg matrix A. +C There are two options available: +C +C (1) performing a fresh factorization +C (2) updating the LU factors by adding a row and a +C column to the matrix A. +C----------------------------------------------------------------------- +C DHEFA factors an upper Hessenberg matrix by elimination. +C +C On entry +C +C A DOUBLE PRECISION(LDA, N) +C the matrix to be factored. +C +C LDA INTEGER +C the leading dimension of the array A . +C +C N INTEGER +C the order of the matrix A . +C +C JOB INTEGER +C JOB = 1 means that a fresh factorization of the +C matrix A is desired. +C JOB .ge. 2 means that the current factorization of A +C will be updated by the addition of a row +C and a column. +C +C On return +C +C A an upper triangular matrix and the multipliers +C which were used to obtain it. +C The factorization can be written A = L*U where +C L is a product of permutation and unit lower +C triangular matrices and U is upper triangular. +C +C IPVT INTEGER(N) +C an integer vector of pivot indices. +C +C INFO INTEGER +C = 0 normal value. +C = k if U(k,k) .eq. 0.0 . This is not an error +C condition for this subroutine, but it does +C indicate that DHESL will divide by zero if called. +C +C Modification of LINPACK, by Peter Brown, LLNL. +C Written 7/20/83. This version dated 6/20/01. +C +C BLAS called: DAXPY, IDAMAX +C----------------------------------------------------------------------- + INTEGER IDAMAX, J, K, KM1, KP1, L, NM1 + DOUBLE PRECISION T +C + IF (JOB .GT. 1) GO TO 80 +C +C A new facorization is desired. This is essentially the LINPACK +C code with the exception that we know there is only one nonzero +C element below the main diagonal. +C +C Gaussian elimination with partial pivoting +C + INFO = 0 + NM1 = N - 1 + IF (NM1 .LT. 1) GO TO 70 + DO 60 K = 1, NM1 + KP1 = K + 1 +C +C Find L = pivot index +C + L = IDAMAX (2, A(K,K), 1) + K - 1 + IPVT(K) = L +C +C Zero pivot implies this column already triangularized +C + IF (A(L,K) .EQ. 0.0D0) GO TO 40 +C +C Interchange if necessary +C + IF (L .EQ. K) GO TO 10 + T = A(L,K) + A(L,K) = A(K,K) + A(K,K) = T + 10 CONTINUE +C +C Compute multipliers +C + T = -1.0D0/A(K,K) + A(K+1,K) = A(K+1,K)*T +C +C Row elimination with column indexing +C + DO 30 J = KP1, N + T = A(L,J) + IF (L .EQ. K) GO TO 20 + A(L,J) = A(K,J) + A(K,J) = T + 20 CONTINUE + CALL DAXPY (N-K, T, A(K+1,K), 1, A(K+1,J), 1) + 30 CONTINUE + GO TO 50 + 40 CONTINUE + INFO = K + 50 CONTINUE + 60 CONTINUE + 70 CONTINUE + IPVT(N) = N + IF (A(N,N) .EQ. 0.0D0) INFO = N + RETURN +C +C The old factorization of A will be updated. A row and a column +C has been added to the matrix A. +C N-1 is now the old order of the matrix. +C + 80 CONTINUE + NM1 = N - 1 +C +C Perform row interchanges on the elements of the new column, and +C perform elimination operations on the elements using the multipliers. +C + IF (NM1 .LE. 1) GO TO 105 + DO 100 K = 2,NM1 + KM1 = K - 1 + L = IPVT(KM1) + T = A(L,N) + IF (L .EQ. KM1) GO TO 90 + A(L,N) = A(KM1,N) + A(KM1,N) = T + 90 CONTINUE + A(K,N) = A(K,N) + A(K,KM1)*T + 100 CONTINUE + 105 CONTINUE +C +C Complete update of factorization by decomposing last 2x2 block. +C + INFO = 0 +C +C Find L = pivot index +C + L = IDAMAX (2, A(NM1,NM1), 1) + NM1 - 1 + IPVT(NM1) = L +C +C Zero pivot implies this column already triangularized +C + IF (A(L,NM1) .EQ. 0.0D0) GO TO 140 +C +C Interchange if necessary +C + IF (L .EQ. NM1) GO TO 110 + T = A(L,NM1) + A(L,NM1) = A(NM1,NM1) + A(NM1,NM1) = T + 110 CONTINUE +C +C Compute multipliers +C + T = -1.0D0/A(NM1,NM1) + A(N,NM1) = A(N,NM1)*T +C +C Row elimination with column indexing +C + T = A(L,N) + IF (L .EQ. NM1) GO TO 120 + A(L,N) = A(NM1,N) + A(NM1,N) = T + 120 CONTINUE + A(N,N) = A(N,N) + T*A(N,NM1) + GO TO 150 + 140 CONTINUE + INFO = NM1 + 150 CONTINUE + IPVT(N) = N + IF (A(N,N) .EQ. 0.0D0) INFO = N + RETURN +C----------------------- End of Subroutine DHEFA ----------------------- + END +*DECK DHESL + SUBROUTINE DHESL (A, LDA, N, IPVT, B) + INTEGER LDA, N, IPVT(*) + DOUBLE PRECISION A(LDA,*), B(*) +C----------------------------------------------------------------------- +C This is essentially the LINPACK routine DGESL except for changes +C due to the fact that A is an upper Hessenberg matrix. +C----------------------------------------------------------------------- +C DHESL solves the real system A * x = b +C using the factors computed by DHEFA. +C +C On entry +C +C A DOUBLE PRECISION(LDA, N) +C the output from DHEFA. +C +C LDA INTEGER +C the leading dimension of the array A . +C +C N INTEGER +C the order of the matrix A . +C +C IPVT INTEGER(N) +C the pivot vector from DHEFA. +C +C B DOUBLE PRECISION(N) +C the right hand side vector. +C +C On return +C +C B the solution vector x . +C +C Modification of LINPACK, by Peter Brown, LLNL. +C Written 7/20/83. This version dated 6/20/01. +C +C BLAS called: DAXPY +C----------------------------------------------------------------------- + INTEGER K, KB, L, NM1 + DOUBLE PRECISION T +C + NM1 = N - 1 +C +C Solve A * x = b +C First solve L*y = b +C + IF (NM1 .LT. 1) GO TO 30 + DO 20 K = 1, NM1 + L = IPVT(K) + T = B(L) + IF (L .EQ. K) GO TO 10 + B(L) = B(K) + B(K) = T + 10 CONTINUE + B(K+1) = B(K+1) + T*A(K+1,K) + 20 CONTINUE + 30 CONTINUE +C +C Now solve U*x = y +C + DO 40 KB = 1, N + K = N + 1 - KB + B(K) = B(K)/A(K,K) + T = -B(K) + CALL DAXPY (K-1, T, A(1,K), 1, B(1), 1) + 40 CONTINUE + RETURN +C----------------------- End of Subroutine DHESL ----------------------- + END +*DECK DHEQR + SUBROUTINE DHEQR (A, LDA, N, Q, INFO, IJOB) + INTEGER LDA, N, INFO, IJOB + DOUBLE PRECISION A(LDA,*), Q(*) +C----------------------------------------------------------------------- +C This routine performs a QR decomposition of an upper +C Hessenberg matrix A. There are two options available: +C +C (1) performing a fresh decomposition +C (2) updating the QR factors by adding a row and a +C column to the matrix A. +C----------------------------------------------------------------------- +C DHEQR decomposes an upper Hessenberg matrix by using Givens +C rotations. +C +C On entry +C +C A DOUBLE PRECISION(LDA, N) +C the matrix to be decomposed. +C +C LDA INTEGER +C the leading dimension of the array A . +C +C N INTEGER +C A is an (N+1) by N Hessenberg matrix. +C +C IJOB INTEGER +C = 1 means that a fresh decomposition of the +C matrix A is desired. +C .ge. 2 means that the current decomposition of A +C will be updated by the addition of a row +C and a column. +C On return +C +C A the upper triangular matrix R. +C The factorization can be written Q*A = R, where +C Q is a product of Givens rotations and R is upper +C triangular. +C +C Q DOUBLE PRECISION(2*N) +C the factors c and s of each Givens rotation used +C in decomposing A. +C +C INFO INTEGER +C = 0 normal value. +C = k if A(k,k) .eq. 0.0 . This is not an error +C condition for this subroutine, but it does +C indicate that DHELS will divide by zero +C if called. +C +C Modification of LINPACK, by Peter Brown, LLNL. +C Written 1/13/86. This version dated 6/20/01. +C----------------------------------------------------------------------- + INTEGER I, IQ, J, K, KM1, KP1, NM1 + DOUBLE PRECISION C, S, T, T1, T2 +C + IF (IJOB .GT. 1) GO TO 70 +C +C A new facorization is desired. +C +C QR decomposition without pivoting +C + INFO = 0 + DO 60 K = 1, N + KM1 = K - 1 + KP1 = K + 1 +C +C Compute kth column of R. +C First, multiply the kth column of A by the previous +C k-1 Givens rotations. +C + IF (KM1 .LT. 1) GO TO 20 + DO 10 J = 1, KM1 + I = 2*(J-1) + 1 + T1 = A(J,K) + T2 = A(J+1,K) + C = Q(I) + S = Q(I+1) + A(J,K) = C*T1 - S*T2 + A(J+1,K) = S*T1 + C*T2 + 10 CONTINUE +C +C Compute Givens components c and s +C + 20 CONTINUE + IQ = 2*KM1 + 1 + T1 = A(K,K) + T2 = A(KP1,K) + IF (T2 .NE. 0.0D0) GO TO 30 + C = 1.0D0 + S = 0.0D0 + GO TO 50 + 30 CONTINUE + IF (ABS(T2) .LT. ABS(T1)) GO TO 40 + T = T1/T2 + S = -1.0D0/SQRT(1.0D0+T*T) + C = -S*T + GO TO 50 + 40 CONTINUE + T = T2/T1 + C = 1.0D0/SQRT(1.0D0+T*T) + S = -C*T + 50 CONTINUE + Q(IQ) = C + Q(IQ+1) = S + A(K,K) = C*T1 - S*T2 + IF (A(K,K) .EQ. 0.0D0) INFO = K + 60 CONTINUE + RETURN +C +C The old factorization of A will be updated. A row and a column +C has been added to the matrix A. +C N by N-1 is now the old size of the matrix. +C + 70 CONTINUE + NM1 = N - 1 +C +C Multiply the new column by the N previous Givens rotations. +C + DO 100 K = 1,NM1 + I = 2*(K-1) + 1 + T1 = A(K,N) + T2 = A(K+1,N) + C = Q(I) + S = Q(I+1) + A(K,N) = C*T1 - S*T2 + A(K+1,N) = S*T1 + C*T2 + 100 CONTINUE +C +C Complete update of decomposition by forming last Givens rotation, +C and multiplying it times the column vector (A(N,N), A(N+1,N)). +C + INFO = 0 + T1 = A(N,N) + T2 = A(N+1,N) + IF (T2 .NE. 0.0D0) GO TO 110 + C = 1.0D0 + S = 0.0D0 + GO TO 130 + 110 CONTINUE + IF (ABS(T2) .LT. ABS(T1)) GO TO 120 + T = T1/T2 + S = -1.0D0/SQRT(1.0D0+T*T) + C = -S*T + GO TO 130 + 120 CONTINUE + T = T2/T1 + C = 1.0D0/SQRT(1.0D0+T*T) + S = -C*T + 130 CONTINUE + IQ = 2*N - 1 + Q(IQ) = C + Q(IQ+1) = S + A(N,N) = C*T1 - S*T2 + IF (A(N,N) .EQ. 0.0D0) INFO = N + RETURN +C----------------------- End of Subroutine DHEQR ----------------------- + END +*DECK DHELS + SUBROUTINE DHELS (A, LDA, N, Q, B) + INTEGER LDA, N + DOUBLE PRECISION A(LDA,*), B(*), Q(*) +C----------------------------------------------------------------------- +C This is part of the LINPACK routine DGESL with changes +C due to the fact that A is an upper Hessenberg matrix. +C----------------------------------------------------------------------- +C DHELS solves the least squares problem +C +C min (b-A*x, b-A*x) +C +C using the factors computed by DHEQR. +C +C On entry +C +C A DOUBLE PRECISION(LDA, N) +C the output from DHEQR which contains the upper +C triangular factor R in the QR decomposition of A. +C +C LDA INTEGER +C the leading dimension of the array A . +C +C N INTEGER +C A is originally an (N+1) by N matrix. +C +C Q DOUBLE PRECISION(2*N) +C The coefficients of the N givens rotations +C used in the QR factorization of A. +C +C B DOUBLE PRECISION(N+1) +C the right hand side vector. +C +C On return +C +C B the solution vector x . +C +C Modification of LINPACK, by Peter Brown, LLNL. +C Written 1/13/86. This version dated 6/20/01. +C +C BLAS called: DAXPY +C----------------------------------------------------------------------- + INTEGER IQ, K, KB, KP1 + DOUBLE PRECISION C, S, T, T1, T2 +C +C Minimize (b-A*x, b-A*x) +C First form Q*b. +C + DO 20 K = 1, N + KP1 = K + 1 + IQ = 2*(K-1) + 1 + C = Q(IQ) + S = Q(IQ+1) + T1 = B(K) + T2 = B(KP1) + B(K) = C*T1 - S*T2 + B(KP1) = S*T1 + C*T2 + 20 CONTINUE +C +C Now solve R*x = Q*b. +C + DO 40 KB = 1, N + K = N + 1 - KB + B(K) = B(K)/A(K,K) + T = -B(K) + CALL DAXPY (K-1, T, A(1,K), 1, B(1), 1) + 40 CONTINUE + RETURN +C----------------------- End of Subroutine DHELS ----------------------- + END +*DECK DLHIN + SUBROUTINE DLHIN (NEQ, N, T0, Y0, YDOT, F, TOUT, UROUND, + 1 EWT, ITOL, ATOL, Y, TEMP, H0, NITER, IER) + EXTERNAL F + DOUBLE PRECISION T0, Y0, YDOT, TOUT, UROUND, EWT, ATOL, Y, + 1 TEMP, H0 + INTEGER NEQ, N, ITOL, NITER, IER + DIMENSION NEQ(*), Y0(*), YDOT(*), EWT(*), ATOL(*), Y(*), TEMP(*) +C----------------------------------------------------------------------- +C Call sequence input -- NEQ, N, T0, Y0, YDOT, F, TOUT, UROUND, +C EWT, ITOL, ATOL, Y, TEMP +C Call sequence output -- H0, NITER, IER +C Common block variables accessed -- None +C +C Subroutines called by DLHIN: F, DCOPY +C Function routines called by DLHIN: DVNORM +C----------------------------------------------------------------------- +C This routine computes the step size, H0, to be attempted on the +C first step, when the user has not supplied a value for this. +C +C First we check that TOUT - T0 differs significantly from zero. Then +C an iteration is done to approximate the initial second derivative +C and this is used to define H from WRMS-norm(H**2 * yddot / 2) = 1. +C A bias factor of 1/2 is applied to the resulting h. +C The sign of H0 is inferred from the initial values of TOUT and T0. +C +C Communication with DLHIN is done with the following variables: +C +C NEQ = NEQ array of solver, passed to F. +C N = size of ODE system, input. +C T0 = initial value of independent variable, input. +C Y0 = vector of initial conditions, input. +C YDOT = vector of initial first derivatives, input. +C F = name of subroutine for right-hand side f(t,y), input. +C TOUT = first output value of independent variable +C UROUND = machine unit roundoff +C EWT, ITOL, ATOL = error weights and tolerance parameters +C as described in the driver routine, input. +C Y, TEMP = work arrays of length N. +C H0 = step size to be attempted, output. +C NITER = number of iterations (and of f evaluations) to compute H0, +C output. +C IER = the error flag, returned with the value +C IER = 0 if no trouble occurred, or +C IER = -1 if TOUT and t0 are considered too close to proceed. +C----------------------------------------------------------------------- +C +C Type declarations for local variables -------------------------------- +C + DOUBLE PRECISION AFI, ATOLI, DELYI, HALF, HG, HLB, HNEW, HRAT, + 1 HUB, HUN, PT1, T1, TDIST, TROUND, TWO, DVNORM, YDDNRM + INTEGER I, ITER +C----------------------------------------------------------------------- +C The following Fortran-77 declaration is to cause the values of the +C listed (local) variables to be saved between calls to this integrator. +C----------------------------------------------------------------------- + SAVE HALF, HUN, PT1, TWO + DATA HALF /0.5D0/, HUN /100.0D0/, PT1 /0.1D0/, TWO /2.0D0/ +C + NITER = 0 + TDIST = ABS(TOUT - T0) + TROUND = UROUND*MAX(ABS(T0),ABS(TOUT)) + IF (TDIST .LT. TWO*TROUND) GO TO 100 +C +C Set a lower bound on H based on the roundoff level in T0 and TOUT. --- + HLB = HUN*TROUND +C Set an upper bound on H based on TOUT-T0 and the initial Y and YDOT. - + HUB = PT1*TDIST + ATOLI = ATOL(1) + DO 10 I = 1,N + IF (ITOL .EQ. 2 .OR. ITOL .EQ. 4) ATOLI = ATOL(I) + DELYI = PT1*ABS(Y0(I)) + ATOLI + AFI = ABS(YDOT(I)) + IF (AFI*HUB .GT. DELYI) HUB = DELYI/AFI + 10 CONTINUE +C +C Set initial guess for H as geometric mean of upper and lower bounds. - + ITER = 0 + HG = SQRT(HLB*HUB) +C If the bounds have crossed, exit with the mean value. ---------------- + IF (HUB .LT. HLB) THEN + H0 = HG + GO TO 90 + ENDIF +C +C Looping point for iteration. ----------------------------------------- + 50 CONTINUE +C Estimate the second derivative as a difference quotient in f. -------- + T1 = T0 + HG + DO 60 I = 1,N + 60 Y(I) = Y0(I) + HG*YDOT(I) + CALL F (NEQ, T1, Y, TEMP) + DO 70 I = 1,N + 70 TEMP(I) = (TEMP(I) - YDOT(I))/HG + YDDNRM = DVNORM (N, TEMP, EWT) +C Get the corresponding new value of H. -------------------------------- + IF (YDDNRM*HUB*HUB .GT. TWO) THEN + HNEW = SQRT(TWO/YDDNRM) + ELSE + HNEW = SQRT(HG*HUB) + ENDIF + ITER = ITER + 1 +C----------------------------------------------------------------------- +C Test the stopping conditions. +C Stop if the new and previous H values differ by a factor of .lt. 2. +C Stop if four iterations have been done. Also, stop with previous H +C if hnew/hg .gt. 2 after first iteration, as this probably means that +C the second derivative value is bad because of cancellation error. +C----------------------------------------------------------------------- + IF (ITER .GE. 4) GO TO 80 + HRAT = HNEW/HG + IF ( (HRAT .GT. HALF) .AND. (HRAT .LT. TWO) ) GO TO 80 + IF ( (ITER .GE. 2) .AND. (HNEW .GT. TWO*HG) ) THEN + HNEW = HG + GO TO 80 + ENDIF + HG = HNEW + GO TO 50 +C +C Iteration done. Apply bounds, bias factor, and sign. ---------------- + 80 H0 = HNEW*HALF + IF (H0 .LT. HLB) H0 = HLB + IF (H0 .GT. HUB) H0 = HUB + 90 H0 = SIGN(H0, TOUT - T0) +C Restore Y array from Y0, then exit. ---------------------------------- + CALL DCOPY (N, Y0, 1, Y, 1) + NITER = ITER + IER = 0 + RETURN +C Error return for TOUT - T0 too small. -------------------------------- + 100 IER = -1 + RETURN +C----------------------- End of Subroutine DLHIN ----------------------- + END +*DECK DSTOKA + SUBROUTINE DSTOKA (NEQ, Y, YH, NYH, YH1, EWT, SAVF, SAVX, ACOR, + 1 WM, IWM, F, JAC, PSOL) + EXTERNAL F, JAC, PSOL + INTEGER NEQ, NYH, IWM + DOUBLE PRECISION Y, YH, YH1, EWT, SAVF, SAVX, ACOR, WM + DIMENSION NEQ(*), Y(*), YH(NYH,*), YH1(*), EWT(*), SAVF(*), + 1 SAVX(*), ACOR(*), WM(*), IWM(*) + INTEGER IOWND, IALTH, IPUP, LMAX, MEO, NQNYH, NSLP, + 1 ICF, IERPJ, IERSL, JCUR, JSTART, KFLAG, L, + 2 LYH, LEWT, LACOR, LSAVF, LWM, LIWM, METH, MITER, + 3 MAXORD, MAXCOR, MSBP, MXNCF, N, NQ, NST, NFE, NJE, NQU + INTEGER NEWT, NSFI, NSLJ, NJEV + INTEGER JPRE, JACFLG, LOCWP, LOCIWP, LSAVX, KMP, MAXL, MNEWT, + 1 NNI, NLI, NPS, NCFN, NCFL + DOUBLE PRECISION CONIT, CRATE, EL, ELCO, HOLD, RMAX, TESCO, + 2 CCMAX, EL0, H, HMIN, HMXI, HU, RC, TN, UROUND + DOUBLE PRECISION STIFR + DOUBLE PRECISION DELT, EPCON, SQRTN, RSQRTN + COMMON /DLS001/ CONIT, CRATE, EL(13), ELCO(13,12), + 1 HOLD, RMAX, TESCO(3,12), + 2 CCMAX, EL0, H, HMIN, HMXI, HU, RC, TN, UROUND, + 3 IOWND(6), IALTH, IPUP, LMAX, MEO, NQNYH, NSLP, + 3 ICF, IERPJ, IERSL, JCUR, JSTART, KFLAG, L, + 4 LYH, LEWT, LACOR, LSAVF, LWM, LIWM, METH, MITER, + 5 MAXORD, MAXCOR, MSBP, MXNCF, N, NQ, NST, NFE, NJE, NQU + COMMON /DLS002/ STIFR, NEWT, NSFI, NSLJ, NJEV + COMMON /DLPK01/ DELT, EPCON, SQRTN, RSQRTN, + 1 JPRE, JACFLG, LOCWP, LOCIWP, LSAVX, KMP, MAXL, MNEWT, + 2 NNI, NLI, NPS, NCFN, NCFL +C----------------------------------------------------------------------- +C DSTOKA performs one step of the integration of an initial value +C problem for a system of Ordinary Differential Equations. +C +C This routine was derived from Subroutine DSTODPK in the DLSODPK +C package by the addition of automatic functional/Newton iteration +C switching and logic for re-use of Jacobian data. +C----------------------------------------------------------------------- +C Note: DSTOKA is independent of the value of the iteration method +C indicator MITER, when this is .ne. 0, and hence is independent +C of the type of chord method used, or the Jacobian structure. +C Communication with DSTOKA is done with the following variables: +C +C NEQ = integer array containing problem size in NEQ(1), and +C passed as the NEQ argument in all calls to F and JAC. +C Y = an array of length .ge. N used as the Y argument in +C all calls to F and JAC. +C YH = an NYH by LMAX array containing the dependent variables +C and their approximate scaled derivatives, where +C LMAX = MAXORD + 1. YH(i,j+1) contains the approximate +C j-th derivative of y(i), scaled by H**j/factorial(j) +C (j = 0,1,...,NQ). On entry for the first step, the first +C two columns of YH must be set from the initial values. +C NYH = a constant integer .ge. N, the first dimension of YH. +C YH1 = a one-dimensional array occupying the same space as YH. +C EWT = an array of length N containing multiplicative weights +C for local error measurements. Local errors in y(i) are +C compared to 1.0/EWT(i) in various error tests. +C SAVF = an array of working storage, of length N. +C Also used for input of YH(*,MAXORD+2) when JSTART = -1 +C and MAXORD .lt. the current order NQ. +C SAVX = an array of working storage, of length N. +C ACOR = a work array of length N, used for the accumulated +C corrections. On a successful return, ACOR(i) contains +C the estimated one-step local error in y(i). +C WM,IWM = real and integer work arrays associated with matrix +C operations in chord iteration (MITER .ne. 0). +C CCMAX = maximum relative change in H*EL0 before DSETPK is called. +C H = the step size to be attempted on the next step. +C H is altered by the error control algorithm during the +C problem. H can be either positive or negative, but its +C sign must remain constant throughout the problem. +C HMIN = the minimum absolute value of the step size H to be used. +C HMXI = inverse of the maximum absolute value of H to be used. +C HMXI = 0.0 is allowed and corresponds to an infinite HMAX. +C HMIN and HMXI may be changed at any time, but will not +C take effect until the next change of H is considered. +C TN = the independent variable. TN is updated on each step taken. +C JSTART = an integer used for input only, with the following +C values and meanings: +C 0 perform the first step. +C .gt.0 take a new step continuing from the last. +C -1 take the next step with a new value of H, MAXORD, +C N, METH, MITER, and/or matrix parameters. +C -2 take the next step with a new value of H, +C but with other inputs unchanged. +C On return, JSTART is set to 1 to facilitate continuation. +C KFLAG = a completion code with the following meanings: +C 0 the step was succesful. +C -1 the requested error could not be achieved. +C -2 corrector convergence could not be achieved. +C -3 fatal error in DSETPK or DSOLPK. +C A return with KFLAG = -1 or -2 means either +C ABS(H) = HMIN or 10 consecutive failures occurred. +C On a return with KFLAG negative, the values of TN and +C the YH array are as of the beginning of the last +C step, and H is the last step size attempted. +C MAXORD = the maximum order of integration method to be allowed. +C MAXCOR = the maximum number of corrector iterations allowed. +C MSBP = maximum number of steps between DSETPK calls (MITER .gt. 0). +C MXNCF = maximum number of convergence failures allowed. +C METH/MITER = the method flags. See description in driver. +C N = the number of first-order differential equations. +C----------------------------------------------------------------------- + INTEGER I, I1, IREDO, IRET, J, JB, JOK, M, NCF, NEWQ, NSLOW + DOUBLE PRECISION DCON, DDN, DEL, DELP, DRC, DSM, DUP, EXDN, EXSM, + 1 EXUP, DFNORM, R, RH, RHDN, RHSM, RHUP, ROC, STIFF, TOLD, DVNORM +C + KFLAG = 0 + TOLD = TN + NCF = 0 + IERPJ = 0 + IERSL = 0 + JCUR = 0 + ICF = 0 + DELP = 0.0D0 + IF (JSTART .GT. 0) GO TO 200 + IF (JSTART .EQ. -1) GO TO 100 + IF (JSTART .EQ. -2) GO TO 160 +C----------------------------------------------------------------------- +C On the first call, the order is set to 1, and other variables are +C initialized. RMAX is the maximum ratio by which H can be increased +C in a single step. It is initially 1.E4 to compensate for the small +C initial H, but then is normally equal to 10. If a failure +C occurs (in corrector convergence or error test), RMAX is set at 2 +C for the next increase. +C----------------------------------------------------------------------- + LMAX = MAXORD + 1 + NQ = 1 + L = 2 + IALTH = 2 + RMAX = 10000.0D0 + RC = 0.0D0 + EL0 = 1.0D0 + CRATE = 0.7D0 + HOLD = H + MEO = METH + NSLP = 0 + NSLJ = 0 + IPUP = 0 + IRET = 3 + NEWT = 0 + STIFR = 0.0D0 + GO TO 140 +C----------------------------------------------------------------------- +C The following block handles preliminaries needed when JSTART = -1. +C IPUP is set to MITER to force a matrix update. +C If an order increase is about to be considered (IALTH = 1), +C IALTH is reset to 2 to postpone consideration one more step. +C If the caller has changed METH, DCFODE is called to reset +C the coefficients of the method. +C If the caller has changed MAXORD to a value less than the current +C order NQ, NQ is reduced to MAXORD, and a new H chosen accordingly. +C If H is to be changed, YH must be rescaled. +C If H or METH is being changed, IALTH is reset to L = NQ + 1 +C to prevent further changes in H for that many steps. +C----------------------------------------------------------------------- + 100 IPUP = MITER + LMAX = MAXORD + 1 + IF (IALTH .EQ. 1) IALTH = 2 + IF (METH .EQ. MEO) GO TO 110 + CALL DCFODE (METH, ELCO, TESCO) + MEO = METH + IF (NQ .GT. MAXORD) GO TO 120 + IALTH = L + IRET = 1 + GO TO 150 + 110 IF (NQ .LE. MAXORD) GO TO 160 + 120 NQ = MAXORD + L = LMAX + DO 125 I = 1,L + 125 EL(I) = ELCO(I,NQ) + NQNYH = NQ*NYH + RC = RC*EL(1)/EL0 + EL0 = EL(1) + CONIT = 0.5D0/(NQ+2) + EPCON = CONIT*TESCO(2,NQ) + DDN = DVNORM (N, SAVF, EWT)/TESCO(1,L) + EXDN = 1.0D0/L + RHDN = 1.0D0/(1.3D0*DDN**EXDN + 0.0000013D0) + RH = MIN(RHDN,1.0D0) + IREDO = 3 + IF (H .EQ. HOLD) GO TO 170 + RH = MIN(RH,ABS(H/HOLD)) + H = HOLD + GO TO 175 +C----------------------------------------------------------------------- +C DCFODE is called to get all the integration coefficients for the +C current METH. Then the EL vector and related constants are reset +C whenever the order NQ is changed, or at the start of the problem. +C----------------------------------------------------------------------- + 140 CALL DCFODE (METH, ELCO, TESCO) + 150 DO 155 I = 1,L + 155 EL(I) = ELCO(I,NQ) + NQNYH = NQ*NYH + RC = RC*EL(1)/EL0 + EL0 = EL(1) + CONIT = 0.5D0/(NQ+2) + EPCON = CONIT*TESCO(2,NQ) + GO TO (160, 170, 200), IRET +C----------------------------------------------------------------------- +C If H is being changed, the H ratio RH is checked against +C RMAX, HMIN, and HMXI, and the YH array rescaled. IALTH is set to +C L = NQ + 1 to prevent a change of H for that many steps, unless +C forced by a convergence or error test failure. +C----------------------------------------------------------------------- + 160 IF (H .EQ. HOLD) GO TO 200 + RH = H/HOLD + H = HOLD + IREDO = 3 + GO TO 175 + 170 RH = MAX(RH,HMIN/ABS(H)) + 175 RH = MIN(RH,RMAX) + RH = RH/MAX(1.0D0,ABS(H)*HMXI*RH) + R = 1.0D0 + DO 180 J = 2,L + R = R*RH + DO 180 I = 1,N + 180 YH(I,J) = YH(I,J)*R + H = H*RH + RC = RC*RH + IALTH = L + IF (IREDO .EQ. 0) GO TO 690 +C----------------------------------------------------------------------- +C This section computes the predicted values by effectively +C multiplying the YH array by the Pascal triangle matrix. +C The flag IPUP is set according to whether matrix data is involved +C (NEWT .gt. 0 .and. JACFLG .ne. 0) or not, to trigger a call to DSETPK. +C IPUP is set to MITER when RC differs from 1 by more than CCMAX, +C and at least every MSBP steps, when JACFLG = 1. +C RC is the ratio of new to old values of the coefficient H*EL(1). +C----------------------------------------------------------------------- + 200 IF (NEWT .EQ. 0 .OR. JACFLG .EQ. 0) THEN + DRC = 0.0D0 + IPUP = 0 + CRATE = 0.7D0 + ELSE + DRC = ABS(RC - 1.0D0) + IF (DRC .GT. CCMAX) IPUP = MITER + IF (NST .GE. NSLP+MSBP) IPUP = MITER + ENDIF + TN = TN + H + I1 = NQNYH + 1 + DO 215 JB = 1,NQ + I1 = I1 - NYH +CDIR$ IVDEP + DO 210 I = I1,NQNYH + 210 YH1(I) = YH1(I) + YH1(I+NYH) + 215 CONTINUE +C----------------------------------------------------------------------- +C Up to MAXCOR corrector iterations are taken. A convergence test is +C made on the RMS-norm of each correction, weighted by the error +C weight vector EWT. The sum of the corrections is accumulated in the +C vector ACOR(i). The YH array is not altered in the corrector loop. +C Within the corrector loop, an estimated rate of convergence (ROC) +C and a stiffness ratio estimate (STIFF) are kept. Corresponding +C global estimates are kept as CRATE and stifr. +C----------------------------------------------------------------------- + 220 M = 0 + MNEWT = 0 + STIFF = 0.0D0 + ROC = 0.05D0 + NSLOW = 0 + DO 230 I = 1,N + 230 Y(I) = YH(I,1) + CALL F (NEQ, TN, Y, SAVF) + NFE = NFE + 1 + IF (NEWT .EQ. 0 .OR. IPUP .LE. 0) GO TO 250 +C----------------------------------------------------------------------- +C If indicated, DSETPK is called to update any matrix data needed, +C before starting the corrector iteration. +C JOK is set to indicate if the matrix data need not be recomputed. +C IPUP is set to 0 as an indicator that the matrix data is up to date. +C----------------------------------------------------------------------- + JOK = 1 + IF (NST .EQ. 0 .OR. NST .GT. NSLJ+50) JOK = -1 + IF (ICF .EQ. 1 .AND. DRC .LT. 0.2D0) JOK = -1 + IF (ICF .EQ. 2) JOK = -1 + IF (JOK .EQ. -1) THEN + NSLJ = NST + NJEV = NJEV + 1 + ENDIF + CALL DSETPK (NEQ, Y, YH1, EWT, ACOR, SAVF, JOK, WM, IWM, F, JAC) + IPUP = 0 + RC = 1.0D0 + DRC = 0.0D0 + NSLP = NST + CRATE = 0.7D0 + IF (IERPJ .NE. 0) GO TO 430 + 250 DO 260 I = 1,N + 260 ACOR(I) = 0.0D0 + 270 IF (NEWT .NE. 0) GO TO 350 +C----------------------------------------------------------------------- +C In the case of functional iteration, update Y directly from +C the result of the last function evaluation, and STIFF is set to 1.0. +C----------------------------------------------------------------------- + DO 290 I = 1,N + SAVF(I) = H*SAVF(I) - YH(I,2) + 290 Y(I) = SAVF(I) - ACOR(I) + DEL = DVNORM (N, Y, EWT) + DO 300 I = 1,N + Y(I) = YH(I,1) + EL(1)*SAVF(I) + 300 ACOR(I) = SAVF(I) + STIFF = 1.0D0 + GO TO 400 +C----------------------------------------------------------------------- +C In the case of the chord method, compute the corrector error, +C and solve the linear system with that as right-hand side and +C P as coefficient matrix. STIFF is set to the ratio of the norms +C of the residual and the correction vector. +C----------------------------------------------------------------------- + 350 DO 360 I = 1,N + 360 SAVX(I) = H*SAVF(I) - (YH(I,2) + ACOR(I)) + DFNORM = DVNORM (N, SAVX, EWT) + CALL DSOLPK (NEQ, Y, SAVF, SAVX, EWT, WM, IWM, F, PSOL) + IF (IERSL .LT. 0) GO TO 430 + IF (IERSL .GT. 0) GO TO 410 + DEL = DVNORM (N, SAVX, EWT) + IF (DEL .GT. 1.0D-8) STIFF = MAX(STIFF, DFNORM/DEL) + DO 380 I = 1,N + ACOR(I) = ACOR(I) + SAVX(I) + 380 Y(I) = YH(I,1) + EL(1)*ACOR(I) +C----------------------------------------------------------------------- +C Test for convergence. If M .gt. 0, an estimate of the convergence +C rate constant is made for the iteration switch, and is also used +C in the convergence test. If the iteration seems to be diverging or +C converging at a slow rate (.gt. 0.8 more than once), it is stopped. +C----------------------------------------------------------------------- + 400 IF (M .NE. 0) THEN + ROC = MAX(0.05D0, DEL/DELP) + CRATE = MAX(0.2D0*CRATE,ROC) + ENDIF + DCON = DEL*MIN(1.0D0,1.5D0*CRATE)/EPCON + IF (DCON .LE. 1.0D0) GO TO 450 + M = M + 1 + IF (M .EQ. MAXCOR) GO TO 410 + IF (M .GE. 2 .AND. DEL .GT. 2.0D0*DELP) GO TO 410 + IF (ROC .GT. 10.0D0) GO TO 410 + IF (ROC .GT. 0.8D0) NSLOW = NSLOW + 1 + IF (NSLOW .GE. 2) GO TO 410 + MNEWT = M + DELP = DEL + CALL F (NEQ, TN, Y, SAVF) + NFE = NFE + 1 + GO TO 270 +C----------------------------------------------------------------------- +C The corrector iteration failed to converge. +C If functional iteration is being done (NEWT = 0) and MITER .gt. 0 +C (and this is not the first step), then switch to Newton +C (NEWT = MITER), and retry the step. (Setting STIFR = 1023 insures +C that a switch back will not occur for 10 step attempts.) +C If Newton iteration is being done, but using a preconditioner that +C is out of date (JACFLG .ne. 0 .and. JCUR = 0), then signal for a +C re-evalutation of the preconditioner, and retry the step. +C In all other cases, the YH array is retracted to its values +C before prediction, and H is reduced, if possible. If H cannot be +C reduced or MXNCF failures have occurred, exit with KFLAG = -2. +C----------------------------------------------------------------------- + 410 ICF = 1 + IF (NEWT .EQ. 0) THEN + IF (NST .EQ. 0) GO TO 430 + IF (MITER .EQ. 0) GO TO 430 + NEWT = MITER + STIFR = 1023.0D0 + IPUP = MITER + GO TO 220 + ENDIF + IF (JCUR.EQ.1 .OR. JACFLG.EQ.0) GO TO 430 + IPUP = MITER + GO TO 220 + 430 ICF = 2 + NCF = NCF + 1 + NCFN = NCFN + 1 + RMAX = 2.0D0 + TN = TOLD + I1 = NQNYH + 1 + DO 445 JB = 1,NQ + I1 = I1 - NYH +CDIR$ IVDEP + DO 440 I = I1,NQNYH + 440 YH1(I) = YH1(I) - YH1(I+NYH) + 445 CONTINUE + IF (IERPJ .LT. 0 .OR. IERSL .LT. 0) GO TO 680 + IF (ABS(H) .LE. HMIN*1.00001D0) GO TO 670 + IF (NCF .EQ. MXNCF) GO TO 670 + RH = 0.5D0 + IPUP = MITER + IREDO = 1 + GO TO 170 +C----------------------------------------------------------------------- +C The corrector has converged. JCUR is set to 0 to signal that the +C preconditioner involved may need updating later. +C The stiffness ratio STIFR is updated using the latest STIFF value. +C The local error test is made and control passes to statement 500 +C if it fails. +C----------------------------------------------------------------------- + 450 JCUR = 0 + IF (NEWT .GT. 0) STIFR = 0.5D0*(STIFR + STIFF) + IF (M .EQ. 0) DSM = DEL/TESCO(2,NQ) + IF (M .GT. 0) DSM = DVNORM (N, ACOR, EWT)/TESCO(2,NQ) + IF (DSM .GT. 1.0D0) GO TO 500 +C----------------------------------------------------------------------- +C After a successful step, update the YH array. +C If Newton iteration is being done and STIFR is less than 1.5, +C then switch to functional iteration. +C Consider changing H if IALTH = 1. Otherwise decrease IALTH by 1. +C If IALTH is then 1 and NQ .lt. MAXORD, then ACOR is saved for +C use in a possible order increase on the next step. +C If a change in H is considered, an increase or decrease in order +C by one is considered also. A change in H is made only if it is by a +C factor of at least 1.1. If not, IALTH is set to 3 to prevent +C testing for that many steps. +C----------------------------------------------------------------------- + KFLAG = 0 + IREDO = 0 + NST = NST + 1 + IF (NEWT .EQ. 0) NSFI = NSFI + 1 + IF (NEWT .GT. 0 .AND. STIFR .LT. 1.5D0) NEWT = 0 + HU = H + NQU = NQ + DO 470 J = 1,L + DO 470 I = 1,N + 470 YH(I,J) = YH(I,J) + EL(J)*ACOR(I) + IALTH = IALTH - 1 + IF (IALTH .EQ. 0) GO TO 520 + IF (IALTH .GT. 1) GO TO 700 + IF (L .EQ. LMAX) GO TO 700 + DO 490 I = 1,N + 490 YH(I,LMAX) = ACOR(I) + GO TO 700 +C----------------------------------------------------------------------- +C The error test failed. KFLAG keeps track of multiple failures. +C Restore TN and the YH array to their previous values, and prepare +C to try the step again. Compute the optimum step size for this or +C one lower order. After 2 or more failures, H is forced to decrease +C by a factor of 0.2 or less. +C----------------------------------------------------------------------- + 500 KFLAG = KFLAG - 1 + TN = TOLD + I1 = NQNYH + 1 + DO 515 JB = 1,NQ + I1 = I1 - NYH +CDIR$ IVDEP + DO 510 I = I1,NQNYH + 510 YH1(I) = YH1(I) - YH1(I+NYH) + 515 CONTINUE + RMAX = 2.0D0 + IF (ABS(H) .LE. HMIN*1.00001D0) GO TO 660 + IF (KFLAG .LE. -3) GO TO 640 + IREDO = 2 + RHUP = 0.0D0 + GO TO 540 +C----------------------------------------------------------------------- +C Regardless of the success or failure of the step, factors +C RHDN, RHSM, and RHUP are computed, by which H could be multiplied +C at order NQ - 1, order NQ, or order NQ + 1, respectively. +C in the case of failure, RHUP = 0.0 to avoid an order increase. +C the largest of these is determined and the new order chosen +C accordingly. If the order is to be increased, we compute one +C additional scaled derivative. +C----------------------------------------------------------------------- + 520 RHUP = 0.0D0 + IF (L .EQ. LMAX) GO TO 540 + DO 530 I = 1,N + 530 SAVF(I) = ACOR(I) - YH(I,LMAX) + DUP = DVNORM (N, SAVF, EWT)/TESCO(3,NQ) + EXUP = 1.0D0/(L+1) + RHUP = 1.0D0/(1.4D0*DUP**EXUP + 0.0000014D0) + 540 EXSM = 1.0D0/L + RHSM = 1.0D0/(1.2D0*DSM**EXSM + 0.0000012D0) + RHDN = 0.0D0 + IF (NQ .EQ. 1) GO TO 560 + DDN = DVNORM (N, YH(1,L), EWT)/TESCO(1,NQ) + EXDN = 1.0D0/NQ + RHDN = 1.0D0/(1.3D0*DDN**EXDN + 0.0000013D0) + 560 IF (RHSM .GE. RHUP) GO TO 570 + IF (RHUP .GT. RHDN) GO TO 590 + GO TO 580 + 570 IF (RHSM .LT. RHDN) GO TO 580 + NEWQ = NQ + RH = RHSM + GO TO 620 + 580 NEWQ = NQ - 1 + RH = RHDN + IF (KFLAG .LT. 0 .AND. RH .GT. 1.0D0) RH = 1.0D0 + GO TO 620 + 590 NEWQ = L + RH = RHUP + IF (RH .LT. 1.1D0) GO TO 610 + R = EL(L)/L + DO 600 I = 1,N + 600 YH(I,NEWQ+1) = ACOR(I)*R + GO TO 630 + 610 IALTH = 3 + GO TO 700 + 620 IF ((KFLAG .EQ. 0) .AND. (RH .LT. 1.1D0)) GO TO 610 + IF (KFLAG .LE. -2) RH = MIN(RH,0.2D0) +C----------------------------------------------------------------------- +C If there is a change of order, reset NQ, L, and the coefficients. +C In any case H is reset according to RH and the YH array is rescaled. +C Then exit from 690 if the step was OK, or redo the step otherwise. +C----------------------------------------------------------------------- + IF (NEWQ .EQ. NQ) GO TO 170 + 630 NQ = NEWQ + L = NQ + 1 + IRET = 2 + GO TO 150 +C----------------------------------------------------------------------- +C Control reaches this section if 3 or more failures have occured. +C If 10 failures have occurred, exit with KFLAG = -1. +C It is assumed that the derivatives that have accumulated in the +C YH array have errors of the wrong order. Hence the first +C derivative is recomputed, and the order is set to 1. Then +C H is reduced by a factor of 10, and the step is retried, +C until it succeeds or H reaches HMIN. +C----------------------------------------------------------------------- + 640 IF (KFLAG .EQ. -10) GO TO 660 + RH = 0.1D0 + RH = MAX(HMIN/ABS(H),RH) + H = H*RH + DO 645 I = 1,N + 645 Y(I) = YH(I,1) + CALL F (NEQ, TN, Y, SAVF) + NFE = NFE + 1 + DO 650 I = 1,N + 650 YH(I,2) = H*SAVF(I) + IPUP = MITER + IALTH = 5 + IF (NQ .EQ. 1) GO TO 200 + NQ = 1 + L = 2 + IRET = 3 + GO TO 150 +C----------------------------------------------------------------------- +C All returns are made through this section. H is saved in HOLD +C to allow the caller to change H on the next step. +C----------------------------------------------------------------------- + 660 KFLAG = -1 + GO TO 720 + 670 KFLAG = -2 + GO TO 720 + 680 KFLAG = -3 + GO TO 720 + 690 RMAX = 10.0D0 + 700 R = 1.0D0/TESCO(2,NQU) + DO 710 I = 1,N + 710 ACOR(I) = ACOR(I)*R + 720 HOLD = H + JSTART = 1 + RETURN +C----------------------- End of Subroutine DSTOKA ---------------------- + END +*DECK DSETPK + SUBROUTINE DSETPK (NEQ, Y, YSV, EWT, FTEM, SAVF, JOK, WM, IWM, + 1 F, JAC) + EXTERNAL F, JAC + INTEGER NEQ, JOK, IWM + DOUBLE PRECISION Y, YSV, EWT, FTEM, SAVF, WM + DIMENSION NEQ(*), Y(*), YSV(*), EWT(*), FTEM(*), SAVF(*), + 1 WM(*), IWM(*) + INTEGER IOWND, IOWNS, + 1 ICF, IERPJ, IERSL, JCUR, JSTART, KFLAG, L, + 2 LYH, LEWT, LACOR, LSAVF, LWM, LIWM, METH, MITER, + 3 MAXORD, MAXCOR, MSBP, MXNCF, N, NQ, NST, NFE, NJE, NQU + INTEGER JPRE, JACFLG, LOCWP, LOCIWP, LSAVX, KMP, MAXL, MNEWT, + 1 NNI, NLI, NPS, NCFN, NCFL + DOUBLE PRECISION ROWNS, + 1 CCMAX, EL0, H, HMIN, HMXI, HU, RC, TN, UROUND + DOUBLE PRECISION DELT, EPCON, SQRTN, RSQRTN + COMMON /DLS001/ ROWNS(209), + 1 CCMAX, EL0, H, HMIN, HMXI, HU, RC, TN, UROUND, + 2 IOWND(6), IOWNS(6), + 3 ICF, IERPJ, IERSL, JCUR, JSTART, KFLAG, L, + 4 LYH, LEWT, LACOR, LSAVF, LWM, LIWM, METH, MITER, + 5 MAXORD, MAXCOR, MSBP, MXNCF, N, NQ, NST, NFE, NJE, NQU + COMMON /DLPK01/ DELT, EPCON, SQRTN, RSQRTN, + 1 JPRE, JACFLG, LOCWP, LOCIWP, LSAVX, KMP, MAXL, MNEWT, + 2 NNI, NLI, NPS, NCFN, NCFL +C----------------------------------------------------------------------- +C DSETPK is called by DSTOKA to interface with the user-supplied +C routine JAC, to compute and process relevant parts of +C the matrix P = I - H*EL(1)*J , where J is the Jacobian df/dy, +C as need for preconditioning matrix operations later. +C +C In addition to variables described previously, communication +C with DSETPK uses the following: +C Y = array containing predicted values on entry. +C YSV = array containing predicted y, to be saved (YH1 in DSTOKA). +C FTEM = work array of length N (ACOR in DSTOKA). +C SAVF = array containing f evaluated at predicted y. +C JOK = input flag showing whether it was judged that Jacobian matrix +C data need not be recomputed (JOK = 1) or needs to be +C (JOK = -1). +C WM = real work space for matrices. +C Space for preconditioning data starts at WM(LOCWP). +C IWM = integer work space. +C Space for preconditioning data starts at IWM(LOCIWP). +C IERPJ = output error flag, = 0 if no trouble, .gt. 0 if +C JAC returned an error flag. +C JCUR = output flag to indicate whether the matrix data involved +C is now current (JCUR = 1) or not (JCUR = 0). +C This routine also uses Common variables EL0, H, TN, IERPJ, JCUR, NJE. +C----------------------------------------------------------------------- + INTEGER IER + DOUBLE PRECISION HL0 +C + IERPJ = 0 + JCUR = 0 + IF (JOK .EQ. -1) JCUR = 1 + HL0 = EL0*H + CALL JAC (F, NEQ, TN, Y, YSV, EWT, SAVF, FTEM, HL0, JOK, + 1 WM(LOCWP), IWM(LOCIWP), IER) + NJE = NJE + 1 + IF (IER .EQ. 0) RETURN + IERPJ = 1 + RETURN +C----------------------- End of Subroutine DSETPK ---------------------- + END +*DECK DSRCKR + SUBROUTINE DSRCKR (RSAV, ISAV, JOB) +C----------------------------------------------------------------------- +C This routine saves or restores (depending on JOB) the contents of +C the Common blocks DLS001, DLS002, DLSR01, DLPK01, which +C are used internally by the DLSODKR solver. +C +C RSAV = real array of length 228 or more. +C ISAV = integer array of length 63 or more. +C JOB = flag indicating to save or restore the Common blocks: +C JOB = 1 if Common is to be saved (written to RSAV/ISAV) +C JOB = 2 if Common is to be restored (read from RSAV/ISAV) +C A call with JOB = 2 presumes a prior call with JOB = 1. +C----------------------------------------------------------------------- + INTEGER ISAV, JOB + INTEGER ILS, ILS2, ILSR, ILSP + INTEGER I, IOFF, LENILP, LENRLP, LENILS, LENRLS, LENILR, LENRLR + DOUBLE PRECISION RSAV, RLS, RLS2, RLSR, RLSP + DIMENSION RSAV(*), ISAV(*) + SAVE LENRLS, LENILS, LENRLP, LENILP, LENRLR, LENILR + COMMON /DLS001/ RLS(218), ILS(37) + COMMON /DLS002/ RLS2, ILS2(4) + COMMON /DLSR01/ RLSR(5), ILSR(9) + COMMON /DLPK01/ RLSP(4), ILSP(13) + DATA LENRLS/218/, LENILS/37/, LENRLP/4/, LENILP/13/ + DATA LENRLR/5/, LENILR/9/ +C + IF (JOB .EQ. 2) GO TO 100 + CALL DCOPY (LENRLS, RLS, 1, RSAV, 1) + RSAV(LENRLS+1) = RLS2 + CALL DCOPY (LENRLR, RLSR, 1, RSAV(LENRLS+2), 1) + CALL DCOPY (LENRLP, RLSP, 1, RSAV(LENRLS+LENRLR+2), 1) + DO 20 I = 1,LENILS + 20 ISAV(I) = ILS(I) + ISAV(LENILS+1) = ILS2(1) + ISAV(LENILS+2) = ILS2(2) + ISAV(LENILS+3) = ILS2(3) + ISAV(LENILS+4) = ILS2(4) + IOFF = LENILS + 2 + DO 30 I = 1,LENILR + 30 ISAV(IOFF+I) = ILSR(I) + IOFF = IOFF + LENILR + DO 40 I = 1,LENILP + 40 ISAV(IOFF+I) = ILSP(I) + RETURN +C + 100 CONTINUE + CALL DCOPY (LENRLS, RSAV, 1, RLS, 1) + RLS2 = RSAV(LENRLS+1) + CALL DCOPY (LENRLR, RSAV(LENRLS+2), 1, RLSR, 1) + CALL DCOPY (LENRLP, RSAV(LENRLS+LENRLR+2), 1, RLSP, 1) + DO 120 I = 1,LENILS + 120 ILS(I) = ISAV(I) + ILS2(1) = ISAV(LENILS+1) + ILS2(2) = ISAV(LENILS+2) + ILS2(3) = ISAV(LENILS+3) + ILS2(4) = ISAV(LENILS+4) + IOFF = LENILS + 2 + DO 130 I = 1,LENILR + 130 ILSR(I) = ISAV(IOFF+I) + IOFF = IOFF + LENILR + DO 140 I = 1,LENILP + 140 ILSP(I) = ISAV(IOFF+I) + RETURN +C----------------------- End of Subroutine DSRCKR ---------------------- + END +*DECK DAINVG + SUBROUTINE DAINVG (RES, ADDA, NEQ, T, Y, YDOT, MITER, + 1 ML, MU, PW, IPVT, IER ) + EXTERNAL RES, ADDA + INTEGER NEQ, MITER, ML, MU, IPVT, IER + INTEGER I, LENPW, MLP1, NROWPW + DOUBLE PRECISION T, Y, YDOT, PW + DIMENSION Y(*), YDOT(*), PW(*), IPVT(*) +C----------------------------------------------------------------------- +C This subroutine computes the initial value +C of the vector YDOT satisfying +C A * YDOT = g(t,y) +C when A is nonsingular. It is called by DLSODI for +C initialization only, when ISTATE = 0 . +C DAINVG returns an error flag IER: +C IER = 0 means DAINVG was successful. +C IER .ge. 2 means RES returned an error flag IRES = IER. +C IER .lt. 0 means the a-matrix was found to be singular. +C----------------------------------------------------------------------- +C + IF (MITER .GE. 4) GO TO 100 +C +C Full matrix case ----------------------------------------------------- +C + LENPW = NEQ*NEQ + DO 10 I = 1, LENPW + 10 PW(I) = 0.0D0 +C + IER = 1 + CALL RES ( NEQ, T, Y, PW, YDOT, IER ) + IF (IER .GT. 1) RETURN +C + CALL ADDA ( NEQ, T, Y, 0, 0, PW, NEQ ) + CALL DGEFA ( PW, NEQ, NEQ, IPVT, IER ) + IF (IER .EQ. 0) GO TO 20 + IER = -IER + RETURN + 20 CALL DGESL ( PW, NEQ, NEQ, IPVT, YDOT, 0 ) + RETURN +C +C Band matrix case ----------------------------------------------------- +C + 100 CONTINUE + NROWPW = 2*ML + MU + 1 + LENPW = NEQ * NROWPW + DO 110 I = 1, LENPW + 110 PW(I) = 0.0D0 +C + IER = 1 + CALL RES ( NEQ, T, Y, PW, YDOT, IER ) + IF (IER .GT. 1) RETURN +C + MLP1 = ML + 1 + CALL ADDA ( NEQ, T, Y, ML, MU, PW(MLP1), NROWPW ) + CALL DGBFA ( PW, NROWPW, NEQ, ML, MU, IPVT, IER ) + IF (IER .EQ. 0) GO TO 120 + IER = -IER + RETURN + 120 CALL DGBSL ( PW, NROWPW, NEQ, ML, MU, IPVT, YDOT, 0 ) + RETURN +C----------------------- End of Subroutine DAINVG ---------------------- + END +*DECK DSTODI + SUBROUTINE DSTODI (NEQ, Y, YH, NYH, YH1, EWT, SAVF, SAVR, + 1 ACOR, WM, IWM, RES, ADDA, JAC, PJAC, SLVS ) + EXTERNAL RES, ADDA, JAC, PJAC, SLVS + INTEGER NEQ, NYH, IWM + DOUBLE PRECISION Y, YH, YH1, EWT, SAVF, SAVR, ACOR, WM + DIMENSION NEQ(*), Y(*), YH(NYH,*), YH1(*), EWT(*), SAVF(*), + 1 SAVR(*), ACOR(*), WM(*), IWM(*) + INTEGER IOWND, IALTH, IPUP, LMAX, MEO, NQNYH, NSLP, + 1 ICF, IERPJ, IERSL, JCUR, JSTART, KFLAG, L, + 2 LYH, LEWT, LACOR, LSAVF, LWM, LIWM, METH, MITER, + 3 MAXORD, MAXCOR, MSBP, MXNCF, N, NQ, NST, NFE, NJE, NQU + DOUBLE PRECISION CONIT, CRATE, EL, ELCO, HOLD, RMAX, TESCO, + 2 CCMAX, EL0, H, HMIN, HMXI, HU, RC, TN, UROUND + COMMON /DLS001/ CONIT, CRATE, EL(13), ELCO(13,12), + 1 HOLD, RMAX, TESCO(3,12), + 2 CCMAX, EL0, H, HMIN, HMXI, HU, RC, TN, UROUND, + 3 IOWND(6), IALTH, IPUP, LMAX, MEO, NQNYH, NSLP, + 3 ICF, IERPJ, IERSL, JCUR, JSTART, KFLAG, L, + 4 LYH, LEWT, LACOR, LSAVF, LWM, LIWM, METH, MITER, + 5 MAXORD, MAXCOR, MSBP, MXNCF, N, NQ, NST, NFE, NJE, NQU + INTEGER I, I1, IREDO, IRES, IRET, J, JB, KGO, M, NCF, NEWQ + DOUBLE PRECISION DCON, DDN, DEL, DELP, DSM, DUP, + 1 ELJH, EL1H, EXDN, EXSM, EXUP, + 2 R, RH, RHDN, RHSM, RHUP, TOLD, DVNORM +C----------------------------------------------------------------------- +C DSTODI performs one step of the integration of an initial value +C problem for a system of Ordinary Differential Equations. +C Note: DSTODI is independent of the value of the iteration method +C indicator MITER, and hence is independent +C of the type of chord method used, or the Jacobian structure. +C Communication with DSTODI is done with the following variables: +C +C NEQ = integer array containing problem size in NEQ(1), and +C passed as the NEQ argument in all calls to RES, ADDA, +C and JAC. +C Y = an array of length .ge. N used as the Y argument in +C all calls to RES, JAC, and ADDA. +C NEQ = integer array containing problem size in NEQ(1), and +C passed as the NEQ argument in all calls tO RES, G, ADDA, +C and JAC. +C YH = an NYH by LMAX array containing the dependent variables +C and their approximate scaled derivatives, where +C LMAX = MAXORD + 1. YH(i,j+1) contains the approximate +C j-th derivative of y(i), scaled by H**j/factorial(j) +C (j = 0,1,...,NQ). On entry for the first step, the first +C two columns of YH must be set from the initial values. +C NYH = a constant integer .ge. N, the first dimension of YH. +C YH1 = a one-dimensional array occupying the same space as YH. +C EWT = an array of length N containing multiplicative weights +C for local error measurements. Local errors in y(i) are +C compared to 1.0/EWT(i) in various error tests. +C SAVF = an array of working storage, of length N. also used for +C input of YH(*,MAXORD+2) when JSTART = -1 and MAXORD is less +C than the current order NQ. +C Same as YDOTI in the driver. +C SAVR = an array of working storage, of length N. +C ACOR = a work array of length N used for the accumulated +C corrections. On a succesful return, ACOR(i) contains +C the estimated one-step local error in y(i). +C WM,IWM = real and integer work arrays associated with matrix +C operations in chord iteration. +C PJAC = name of routine to evaluate and preprocess Jacobian matrix. +C SLVS = name of routine to solve linear system in chord iteration. +C CCMAX = maximum relative change in H*EL0 before PJAC is called. +C H = the step size to be attempted on the next step. +C H is altered by the error control algorithm during the +C problem. H can be either positive or negative, but its +C sign must remain constant throughout the problem. +C HMIN = the minimum absolute value of the step size H to be used. +C HMXI = inverse of the maximum absolute value of H to be used. +C HMXI = 0.0 is allowed and corresponds to an infinite HMAX. +C HMIN and HMXI may be changed at any time, but will not +C take effect until the next change of H is considered. +C TN = the independent variable. TN is updated on each step taken. +C JSTART = an integer used for input only, with the following +C values and meanings: +C 0 perform the first step. +C .gt.0 take a new step continuing from the last. +C -1 take the next step with a new value of H, MAXORD, +C N, METH, MITER, and/or matrix parameters. +C -2 take the next step with a new value of H, +C but with other inputs unchanged. +C On return, JSTART is set to 1 to facilitate continuation. +C KFLAG = a completion code with the following meanings: +C 0 the step was succesful. +C -1 the requested error could not be achieved. +C -2 corrector convergence could not be achieved. +C -3 RES ordered immediate return. +C -4 error condition from RES could not be avoided. +C -5 fatal error in PJAC or SLVS. +C A return with KFLAG = -1, -2, or -4 means either +C ABS(H) = HMIN or 10 consecutive failures occurred. +C On a return with KFLAG negative, the values of TN and +C the YH array are as of the beginning of the last +C step, and H is the last step size attempted. +C MAXORD = the maximum order of integration method to be allowed. +C MAXCOR = the maximum number of corrector iterations allowed. +C MSBP = maximum number of steps between PJAC calls. +C MXNCF = maximum number of convergence failures allowed. +C METH/MITER = the method flags. See description in driver. +C N = the number of first-order differential equations. +C----------------------------------------------------------------------- + KFLAG = 0 + TOLD = TN + NCF = 0 + IERPJ = 0 + IERSL = 0 + JCUR = 0 + ICF = 0 + DELP = 0.0D0 + IF (JSTART .GT. 0) GO TO 200 + IF (JSTART .EQ. -1) GO TO 100 + IF (JSTART .EQ. -2) GO TO 160 +C----------------------------------------------------------------------- +C On the first call, the order is set to 1, and other variables are +C initialized. RMAX is the maximum ratio by which H can be increased +C in a single step. It is initially 1.E4 to compensate for the small +C initial H, but then is normally equal to 10. If a failure +C occurs (in corrector convergence or error test), RMAX is set at 2 +C for the next increase. +C----------------------------------------------------------------------- + LMAX = MAXORD + 1 + NQ = 1 + L = 2 + IALTH = 2 + RMAX = 10000.0D0 + RC = 0.0D0 + EL0 = 1.0D0 + CRATE = 0.7D0 + HOLD = H + MEO = METH + NSLP = 0 + IPUP = MITER + IRET = 3 + GO TO 140 +C----------------------------------------------------------------------- +C The following block handles preliminaries needed when JSTART = -1. +C IPUP is set to MITER to force a matrix update. +C If an order increase is about to be considered (IALTH = 1), +C IALTH is reset to 2 to postpone consideration one more step. +C If the caller has changed METH, DCFODE is called to reset +C the coefficients of the method. +C If the caller has changed MAXORD to a value less than the current +C order NQ, NQ is reduced to MAXORD, and a new H chosen accordingly. +C If H is to be changed, YH must be rescaled. +C If H or METH is being changed, IALTH is reset to L = NQ + 1 +C to prevent further changes in H for that many steps. +C----------------------------------------------------------------------- + 100 IPUP = MITER + LMAX = MAXORD + 1 + IF (IALTH .EQ. 1) IALTH = 2 + IF (METH .EQ. MEO) GO TO 110 + CALL DCFODE (METH, ELCO, TESCO) + MEO = METH + IF (NQ .GT. MAXORD) GO TO 120 + IALTH = L + IRET = 1 + GO TO 150 + 110 IF (NQ .LE. MAXORD) GO TO 160 + 120 NQ = MAXORD + L = LMAX + DO 125 I = 1,L + 125 EL(I) = ELCO(I,NQ) + NQNYH = NQ*NYH + RC = RC*EL(1)/EL0 + EL0 = EL(1) + CONIT = 0.5D0/(NQ+2) + DDN = DVNORM (N, SAVF, EWT)/TESCO(1,L) + EXDN = 1.0D0/L + RHDN = 1.0D0/(1.3D0*DDN**EXDN + 0.0000013D0) + RH = MIN(RHDN,1.0D0) + IREDO = 3 + IF (H .EQ. HOLD) GO TO 170 + RH = MIN(RH,ABS(H/HOLD)) + H = HOLD + GO TO 175 +C----------------------------------------------------------------------- +C DCFODE is called to get all the integration coefficients for the +C current METH. Then the EL vector and related constants are reset +C whenever the order NQ is changed, or at the start of the problem. +C----------------------------------------------------------------------- + 140 CALL DCFODE (METH, ELCO, TESCO) + 150 DO 155 I = 1,L + 155 EL(I) = ELCO(I,NQ) + NQNYH = NQ*NYH + RC = RC*EL(1)/EL0 + EL0 = EL(1) + CONIT = 0.5D0/(NQ+2) + GO TO (160, 170, 200), IRET +C----------------------------------------------------------------------- +C If H is being changed, the H ratio RH is checked against +C RMAX, HMIN, and HMXI, and the YH array rescaled. IALTH is set to +C L = NQ + 1 to prevent a change of H for that many steps, unless +C forced by a convergence or error test failure. +C----------------------------------------------------------------------- + 160 IF (H .EQ. HOLD) GO TO 200 + RH = H/HOLD + H = HOLD + IREDO = 3 + GO TO 175 + 170 RH = MAX(RH,HMIN/ABS(H)) + 175 RH = MIN(RH,RMAX) + RH = RH/MAX(1.0D0,ABS(H)*HMXI*RH) + R = 1.0D0 + DO 180 J = 2,L + R = R*RH + DO 180 I = 1,N + 180 YH(I,J) = YH(I,J)*R + H = H*RH + RC = RC*RH + IALTH = L + IF (IREDO .EQ. 0) GO TO 690 +C----------------------------------------------------------------------- +C This section computes the predicted values by effectively +C multiplying the YH array by the Pascal triangle matrix. +C RC is the ratio of new to old values of the coefficient H*EL(1). +C When RC differs from 1 by more than CCMAX, IPUP is set to MITER +C to force PJAC to be called. +C In any case, PJAC is called at least every MSBP steps. +C----------------------------------------------------------------------- + 200 IF (ABS(RC-1.0D0) .GT. CCMAX) IPUP = MITER + IF (NST .GE. NSLP+MSBP) IPUP = MITER + TN = TN + H + I1 = NQNYH + 1 + DO 215 JB = 1,NQ + I1 = I1 - NYH +CDIR$ IVDEP + DO 210 I = I1,NQNYH + 210 YH1(I) = YH1(I) + YH1(I+NYH) + 215 CONTINUE +C----------------------------------------------------------------------- +C Up to MAXCOR corrector iterations are taken. A convergence test is +C made on the RMS-norm of each correction, weighted by H and the +C error weight vector EWT. The sum of the corrections is accumulated +C in ACOR(i). The YH array is not altered in the corrector loop. +C----------------------------------------------------------------------- + 220 M = 0 + DO 230 I = 1,N + SAVF(I) = YH(I,2) / H + 230 Y(I) = YH(I,1) + IF (IPUP .LE. 0) GO TO 240 +C----------------------------------------------------------------------- +C If indicated, the matrix P = A - H*EL(1)*dr/dy is reevaluated and +C preprocessed before starting the corrector iteration. IPUP is set +C to 0 as an indicator that this has been done. +C----------------------------------------------------------------------- + CALL PJAC (NEQ, Y, YH, NYH, EWT, ACOR, SAVR, SAVF, WM, IWM, + 1 RES, JAC, ADDA ) + IPUP = 0 + RC = 1.0D0 + NSLP = NST + CRATE = 0.7D0 + IF (IERPJ .EQ. 0) GO TO 250 + IF (IERPJ .LT. 0) GO TO 435 + IRES = IERPJ + GO TO (430, 435, 430), IRES +C Get residual at predicted values, if not already done in PJAC. ------- + 240 IRES = 1 + CALL RES ( NEQ, TN, Y, SAVF, SAVR, IRES ) + NFE = NFE + 1 + KGO = ABS(IRES) + GO TO ( 250, 435, 430 ) , KGO + 250 DO 260 I = 1,N + 260 ACOR(I) = 0.0D0 +C----------------------------------------------------------------------- +C Solve the linear system with the current residual as +C right-hand side and P as coefficient matrix. +C----------------------------------------------------------------------- + 270 CONTINUE + CALL SLVS (WM, IWM, SAVR, SAVF) + IF (IERSL .LT. 0) GO TO 430 + IF (IERSL .GT. 0) GO TO 410 + EL1H = EL(1) * H + DEL = DVNORM (N, SAVR, EWT) * ABS(H) + DO 380 I = 1,N + ACOR(I) = ACOR(I) + SAVR(I) + SAVF(I) = ACOR(I) + YH(I,2)/H + 380 Y(I) = YH(I,1) + EL1H*ACOR(I) +C----------------------------------------------------------------------- +C Test for convergence. If M .gt. 0, an estimate of the convergence +C rate constant is stored in CRATE, and this is used in the test. +C----------------------------------------------------------------------- + IF (M .NE. 0) CRATE = MAX(0.2D0*CRATE,DEL/DELP) + DCON = DEL*MIN(1.0D0,1.5D0*CRATE)/(TESCO(2,NQ)*CONIT) + IF (DCON .LE. 1.0D0) GO TO 460 + M = M + 1 + IF (M .EQ. MAXCOR) GO TO 410 + IF (M .GE. 2 .AND. DEL .GT. 2.0D0*DELP) GO TO 410 + DELP = DEL + IRES = 1 + CALL RES ( NEQ, TN, Y, SAVF, SAVR, IRES ) + NFE = NFE + 1 + KGO = ABS(IRES) + GO TO ( 270, 435, 410 ) , KGO +C----------------------------------------------------------------------- +C The correctors failed to converge, or RES has returned abnormally. +C on a convergence failure, if the Jacobian is out of date, PJAC is +C called for the next try. Otherwise the YH array is retracted to its +C values before prediction, and H is reduced, if possible. +C take an error exit if IRES = 2, or H cannot be reduced, or MXNCF +C failures have occurred, or a fatal error occurred in PJAC or SLVS. +C----------------------------------------------------------------------- + 410 ICF = 1 + IF (JCUR .EQ. 1) GO TO 430 + IPUP = MITER + GO TO 220 + 430 ICF = 2 + NCF = NCF + 1 + RMAX = 2.0D0 + 435 TN = TOLD + I1 = NQNYH + 1 + DO 445 JB = 1,NQ + I1 = I1 - NYH +CDIR$ IVDEP + DO 440 I = I1,NQNYH + 440 YH1(I) = YH1(I) - YH1(I+NYH) + 445 CONTINUE + IF (IRES .EQ. 2) GO TO 680 + IF (IERPJ .LT. 0 .OR. IERSL .LT. 0) GO TO 685 + IF (ABS(H) .LE. HMIN*1.00001D0) GO TO 450 + IF (NCF .EQ. MXNCF) GO TO 450 + RH = 0.25D0 + IPUP = MITER + IREDO = 1 + GO TO 170 + 450 IF (IRES .EQ. 3) GO TO 680 + GO TO 670 +C----------------------------------------------------------------------- +C The corrector has converged. JCUR is set to 0 +C to signal that the Jacobian involved may need updating later. +C The local error test is made and control passes to statement 500 +C if it fails. +C----------------------------------------------------------------------- + 460 JCUR = 0 + IF (M .EQ. 0) DSM = DEL/TESCO(2,NQ) + IF (M .GT. 0) DSM = ABS(H) * DVNORM (N, ACOR, EWT)/TESCO(2,NQ) + IF (DSM .GT. 1.0D0) GO TO 500 +C----------------------------------------------------------------------- +C After a successful step, update the YH array. +C Consider changing H if IALTH = 1. Otherwise decrease IALTH by 1. +C If IALTH is then 1 and NQ .lt. MAXORD, then ACOR is saved for +C use in a possible order increase on the next step. +C If a change in H is considered, an increase or decrease in order +C by one is considered also. A change in H is made only if it is by a +C factor of at least 1.1. If not, IALTH is set to 3 to prevent +C testing for that many steps. +C----------------------------------------------------------------------- + KFLAG = 0 + IREDO = 0 + NST = NST + 1 + HU = H + NQU = NQ + DO 470 J = 1,L + ELJH = EL(J)*H + DO 470 I = 1,N + 470 YH(I,J) = YH(I,J) + ELJH*ACOR(I) + IALTH = IALTH - 1 + IF (IALTH .EQ. 0) GO TO 520 + IF (IALTH .GT. 1) GO TO 700 + IF (L .EQ. LMAX) GO TO 700 + DO 490 I = 1,N + 490 YH(I,LMAX) = ACOR(I) + GO TO 700 +C----------------------------------------------------------------------- +C The error test failed. KFLAG keeps track of multiple failures. +C restore TN and the YH array to their previous values, and prepare +C to try the step again. Compute the optimum step size for this or +C one lower order. After 2 or more failures, H is forced to decrease +C by a factor of 0.1 or less. +C----------------------------------------------------------------------- + 500 KFLAG = KFLAG - 1 + TN = TOLD + I1 = NQNYH + 1 + DO 515 JB = 1,NQ + I1 = I1 - NYH +CDIR$ IVDEP + DO 510 I = I1,NQNYH + 510 YH1(I) = YH1(I) - YH1(I+NYH) + 515 CONTINUE + RMAX = 2.0D0 + IF (ABS(H) .LE. HMIN*1.00001D0) GO TO 660 + IF (KFLAG .LE. -7) GO TO 660 + IREDO = 2 + RHUP = 0.0D0 + GO TO 540 +C----------------------------------------------------------------------- +C Regardless of the success or failure of the step, factors +C RHDN, RHSM, and RHUP are computed, by which H could be multiplied +C at order NQ - 1, order NQ, or order NQ + 1, respectively. +C In the case of failure, RHUP = 0.0 to avoid an order increase. +C The largest of these is determined and the new order chosen +C accordingly. If the order is to be increased, we compute one +C additional scaled derivative. +C----------------------------------------------------------------------- + 520 RHUP = 0.0D0 + IF (L .EQ. LMAX) GO TO 540 + DO 530 I = 1,N + 530 SAVF(I) = ACOR(I) - YH(I,LMAX) + DUP = ABS(H) * DVNORM (N, SAVF, EWT)/TESCO(3,NQ) + EXUP = 1.0D0/(L+1) + RHUP = 1.0D0/(1.4D0*DUP**EXUP + 0.0000014D0) + 540 EXSM = 1.0D0/L + RHSM = 1.0D0/(1.2D0*DSM**EXSM + 0.0000012D0) + RHDN = 0.0D0 + IF (NQ .EQ. 1) GO TO 560 + DDN = DVNORM (N, YH(1,L), EWT)/TESCO(1,NQ) + EXDN = 1.0D0/NQ + RHDN = 1.0D0/(1.3D0*DDN**EXDN + 0.0000013D0) + 560 IF (RHSM .GE. RHUP) GO TO 570 + IF (RHUP .GT. RHDN) GO TO 590 + GO TO 580 + 570 IF (RHSM .LT. RHDN) GO TO 580 + NEWQ = NQ + RH = RHSM + GO TO 620 + 580 NEWQ = NQ - 1 + RH = RHDN + IF (KFLAG .LT. 0 .AND. RH .GT. 1.0D0) RH = 1.0D0 + GO TO 620 + 590 NEWQ = L + RH = RHUP + IF (RH .LT. 1.1D0) GO TO 610 + R = H*EL(L)/L + DO 600 I = 1,N + 600 YH(I,NEWQ+1) = ACOR(I)*R + GO TO 630 + 610 IALTH = 3 + GO TO 700 + 620 IF ((KFLAG .EQ. 0) .AND. (RH .LT. 1.1D0)) GO TO 610 + IF (KFLAG .LE. -2) RH = MIN(RH,0.1D0) +C----------------------------------------------------------------------- +C If there is a change of order, reset NQ, L, and the coefficients. +C In any case H is reset according to RH and the YH array is rescaled. +C Then exit from 690 if the step was OK, or redo the step otherwise. +C----------------------------------------------------------------------- + IF (NEWQ .EQ. NQ) GO TO 170 + 630 NQ = NEWQ + L = NQ + 1 + IRET = 2 + GO TO 150 +C----------------------------------------------------------------------- +C All returns are made through this section. H is saved in HOLD +C to allow the caller to change H on the next step. +C----------------------------------------------------------------------- + 660 KFLAG = -1 + GO TO 720 + 670 KFLAG = -2 + GO TO 720 + 680 KFLAG = -1 - IRES + GO TO 720 + 685 KFLAG = -5 + GO TO 720 + 690 RMAX = 10.0D0 + 700 R = H/TESCO(2,NQU) + DO 710 I = 1,N + 710 ACOR(I) = ACOR(I)*R + 720 HOLD = H + JSTART = 1 + RETURN +C----------------------- End of Subroutine DSTODI ---------------------- + END +*DECK DPREPJI + SUBROUTINE DPREPJI (NEQ, Y, YH, NYH, EWT, RTEM, SAVR, S, WM, IWM, + 1 RES, JAC, ADDA) + EXTERNAL RES, JAC, ADDA + INTEGER NEQ, NYH, IWM + DOUBLE PRECISION Y, YH, EWT, RTEM, SAVR, S, WM + DIMENSION NEQ(*), Y(*), YH(NYH,*), EWT(*), RTEM(*), + 1 S(*), SAVR(*), WM(*), IWM(*) + INTEGER IOWND, IOWNS, + 1 ICF, IERPJ, IERSL, JCUR, JSTART, KFLAG, L, + 2 LYH, LEWT, LACOR, LSAVF, LWM, LIWM, METH, MITER, + 3 MAXORD, MAXCOR, MSBP, MXNCF, N, NQ, NST, NFE, NJE, NQU + DOUBLE PRECISION ROWNS, + 1 CCMAX, EL0, H, HMIN, HMXI, HU, RC, TN, UROUND + COMMON /DLS001/ ROWNS(209), + 1 CCMAX, EL0, H, HMIN, HMXI, HU, RC, TN, UROUND, + 2 IOWND(6), IOWNS(6), + 3 ICF, IERPJ, IERSL, JCUR, JSTART, KFLAG, L, + 4 LYH, LEWT, LACOR, LSAVF, LWM, LIWM, METH, MITER, + 5 MAXORD, MAXCOR, MSBP, MXNCF, N, NQ, NST, NFE, NJE, NQU + INTEGER I, I1, I2, IER, II, IRES, J, J1, JJ, LENP, + 1 MBA, MBAND, MEB1, MEBAND, ML, ML3, MU + DOUBLE PRECISION CON, FAC, HL0, R, SRUR, YI, YJ, YJJ +C----------------------------------------------------------------------- +C DPREPJI is called by DSTODI to compute and process the matrix +C P = A - H*EL(1)*J , where J is an approximation to the Jacobian dr/dy, +C where r = g(t,y) - A(t,y)*s. Here J is computed by the user-supplied +C routine JAC if MITER = 1 or 4, or by finite differencing if MITER = +C 2 or 5. J is stored in WM, rescaled, and ADDA is called to generate +C P. P is then subjected to LU decomposition in preparation +C for later solution of linear systems with P as coefficient +C matrix. This is done by DGEFA if MITER = 1 or 2, and by +C DGBFA if MITER = 4 or 5. +C +C In addition to variables described previously, communication +C with DPREPJI uses the following: +C Y = array containing predicted values on entry. +C RTEM = work array of length N (ACOR in DSTODI). +C SAVR = array used for output only. On output it contains the +C residual evaluated at current values of t and y. +C S = array containing predicted values of dy/dt (SAVF in DSTODI). +C WM = real work space for matrices. On output it contains the +C LU decomposition of P. +C Storage of matrix elements starts at WM(3). +C WM also contains the following matrix-related data: +C WM(1) = SQRT(UROUND), used in numerical Jacobian increments. +C IWM = integer work space containing pivot information, starting at +C IWM(21). IWM also contains the band parameters +C ML = IWM(1) and MU = IWM(2) if MITER is 4 or 5. +C EL0 = el(1) (input). +C IERPJ = output error flag. +C = 0 if no trouble occurred, +C = 1 if the P matrix was found to be singular, +C = IRES (= 2 or 3) if RES returned IRES = 2 or 3. +C JCUR = output flag = 1 to indicate that the Jacobian matrix +C (or approximation) is now current. +C This routine also uses the Common variables EL0, H, TN, UROUND, +C MITER, N, NFE, and NJE. +C----------------------------------------------------------------------- + NJE = NJE + 1 + HL0 = H*EL0 + IERPJ = 0 + JCUR = 1 + GO TO (100, 200, 300, 400, 500), MITER +C If MITER = 1, call RES, then JAC, and multiply by scalar. ------------ + 100 IRES = 1 + CALL RES (NEQ, TN, Y, S, SAVR, IRES) + NFE = NFE + 1 + IF (IRES .GT. 1) GO TO 600 + LENP = N*N + DO 110 I = 1,LENP + 110 WM(I+2) = 0.0D0 + CALL JAC ( NEQ, TN, Y, S, 0, 0, WM(3), N ) + CON = -HL0 + DO 120 I = 1,LENP + 120 WM(I+2) = WM(I+2)*CON + GO TO 240 +C If MITER = 2, make N + 1 calls to RES to approximate J. -------------- + 200 CONTINUE + IRES = -1 + CALL RES (NEQ, TN, Y, S, SAVR, IRES) + NFE = NFE + 1 + IF (IRES .GT. 1) GO TO 600 + SRUR = WM(1) + J1 = 2 + DO 230 J = 1,N + YJ = Y(J) + R = MAX(SRUR*ABS(YJ),0.01D0/EWT(J)) + Y(J) = Y(J) + R + FAC = -HL0/R + CALL RES ( NEQ, TN, Y, S, RTEM, IRES ) + NFE = NFE + 1 + IF (IRES .GT. 1) GO TO 600 + DO 220 I = 1,N + 220 WM(I+J1) = (RTEM(I) - SAVR(I))*FAC + Y(J) = YJ + J1 = J1 + N + 230 CONTINUE + IRES = 1 + CALL RES (NEQ, TN, Y, S, SAVR, IRES) + NFE = NFE + 1 + IF (IRES .GT. 1) GO TO 600 +C Add matrix A. -------------------------------------------------------- + 240 CONTINUE + CALL ADDA(NEQ, TN, Y, 0, 0, WM(3), N) +C Do LU decomposition on P. -------------------------------------------- + CALL DGEFA (WM(3), N, N, IWM(21), IER) + IF (IER .NE. 0) IERPJ = 1 + RETURN +C Dummy section for MITER = 3 + 300 RETURN +C If MITER = 4, call RES, then JAC, and multiply by scalar. ------------ + 400 IRES = 1 + CALL RES (NEQ, TN, Y, S, SAVR, IRES) + NFE = NFE + 1 + IF (IRES .GT. 1) GO TO 600 + ML = IWM(1) + MU = IWM(2) + ML3 = ML + 3 + MBAND = ML + MU + 1 + MEBAND = MBAND + ML + LENP = MEBAND*N + DO 410 I = 1,LENP + 410 WM(I+2) = 0.0D0 + CALL JAC ( NEQ, TN, Y, S, ML, MU, WM(ML3), MEBAND) + CON = -HL0 + DO 420 I = 1,LENP + 420 WM(I+2) = WM(I+2)*CON + GO TO 570 +C If MITER = 5, make ML + MU + 2 calls to RES to approximate J. -------- + 500 CONTINUE + IRES = -1 + CALL RES (NEQ, TN, Y, S, SAVR, IRES) + NFE = NFE + 1 + IF (IRES .GT. 1) GO TO 600 + ML = IWM(1) + MU = IWM(2) + ML3 = ML + 3 + MBAND = ML + MU + 1 + MBA = MIN(MBAND,N) + MEBAND = MBAND + ML + MEB1 = MEBAND - 1 + SRUR = WM(1) + DO 560 J = 1,MBA + DO 530 I = J,N,MBAND + YI = Y(I) + R = MAX(SRUR*ABS(YI),0.01D0/EWT(I)) + 530 Y(I) = Y(I) + R + CALL RES ( NEQ, TN, Y, S, RTEM, IRES) + NFE = NFE + 1 + IF (IRES .GT. 1) GO TO 600 + DO 550 JJ = J,N,MBAND + Y(JJ) = YH(JJ,1) + YJJ = Y(JJ) + R = MAX(SRUR*ABS(YJJ),0.01D0/EWT(JJ)) + FAC = -HL0/R + I1 = MAX(JJ-MU,1) + I2 = MIN(JJ+ML,N) + II = JJ*MEB1 - ML + 2 + DO 540 I = I1,I2 + 540 WM(II+I) = (RTEM(I) - SAVR(I))*FAC + 550 CONTINUE + 560 CONTINUE + IRES = 1 + CALL RES (NEQ, TN, Y, S, SAVR, IRES) + NFE = NFE + 1 + IF (IRES .GT. 1) GO TO 600 +C Add matrix A. -------------------------------------------------------- + 570 CONTINUE + CALL ADDA(NEQ, TN, Y, ML, MU, WM(ML3), MEBAND) +C Do LU decomposition of P. -------------------------------------------- + CALL DGBFA (WM(3), MEBAND, N, ML, MU, IWM(21), IER) + IF (IER .NE. 0) IERPJ = 1 + RETURN +C Error return for IRES = 2 or IRES = 3 return from RES. --------------- + 600 IERPJ = IRES + RETURN +C----------------------- End of Subroutine DPREPJI --------------------- + END +*DECK DAIGBT + SUBROUTINE DAIGBT (RES, ADDA, NEQ, T, Y, YDOT, + 1 MB, NB, PW, IPVT, IER ) + EXTERNAL RES, ADDA + INTEGER NEQ, MB, NB, IPVT, IER + INTEGER I, LENPW, LBLOX, LPB, LPC + DOUBLE PRECISION T, Y, YDOT, PW + DIMENSION Y(*), YDOT(*), PW(*), IPVT(*), NEQ(*) +C----------------------------------------------------------------------- +C This subroutine computes the initial value +C of the vector YDOT satisfying +C A * YDOT = g(t,y) +C when A is nonsingular. It is called by DLSOIBT for +C initialization only, when ISTATE = 0 . +C DAIGBT returns an error flag IER: +C IER = 0 means DAIGBT was successful. +C IER .ge. 2 means RES returned an error flag IRES = IER. +C IER .lt. 0 means the A matrix was found to have a singular +C diagonal block (hence YDOT could not be solved for). +C----------------------------------------------------------------------- + LBLOX = MB*MB*NB + LPB = 1 + LBLOX + LPC = LPB + LBLOX + LENPW = 3*LBLOX + DO 10 I = 1,LENPW + 10 PW(I) = 0.0D0 + IER = 1 + CALL RES (NEQ, T, Y, PW, YDOT, IER) + IF (IER .GT. 1) RETURN + CALL ADDA (NEQ, T, Y, MB, NB, PW(1), PW(LPB), PW(LPC) ) + CALL DDECBT (MB, NB, PW, PW(LPB), PW(LPC), IPVT, IER) + IF (IER .EQ. 0) GO TO 20 + IER = -IER + RETURN + 20 CALL DSOLBT (MB, NB, PW, PW(LPB), PW(LPC), YDOT, IPVT) + RETURN +C----------------------- End of Subroutine DAIGBT ---------------------- + END +*DECK DPJIBT + SUBROUTINE DPJIBT (NEQ, Y, YH, NYH, EWT, RTEM, SAVR, S, WM, IWM, + 1 RES, JAC, ADDA) + EXTERNAL RES, JAC, ADDA + INTEGER NEQ, NYH, IWM + DOUBLE PRECISION Y, YH, EWT, RTEM, SAVR, S, WM + DIMENSION NEQ(*), Y(*), YH(NYH,*), EWT(*), RTEM(*), + 1 S(*), SAVR(*), WM(*), IWM(*) + INTEGER IOWND, IOWNS, + 1 ICF, IERPJ, IERSL, JCUR, JSTART, KFLAG, L, + 2 LYH, LEWT, LACOR, LSAVF, LWM, LIWM, METH, MITER, + 3 MAXORD, MAXCOR, MSBP, MXNCF, N, NQ, NST, NFE, NJE, NQU + DOUBLE PRECISION ROWNS, + 1 CCMAX, EL0, H, HMIN, HMXI, HU, RC, TN, UROUND + COMMON /DLS001/ ROWNS(209), + 1 CCMAX, EL0, H, HMIN, HMXI, HU, RC, TN, UROUND, + 2 IOWND(6), IOWNS(6), + 3 ICF, IERPJ, IERSL, JCUR, JSTART, KFLAG, L, + 4 LYH, LEWT, LACOR, LSAVF, LWM, LIWM, METH, MITER, + 5 MAXORD, MAXCOR, MSBP, MXNCF, N, NQ, NST, NFE, NJE, NQU + INTEGER I, IER, IIA, IIB, IIC, IPA, IPB, IPC, IRES, J, J1, J2, + 1 K, K1, LENP, LBLOX, LPB, LPC, MB, MBSQ, MWID, NB + DOUBLE PRECISION CON, FAC, HL0, R, SRUR +C----------------------------------------------------------------------- +C DPJIBT is called by DSTODI to compute and process the matrix +C P = A - H*EL(1)*J , where J is an approximation to the Jacobian dr/dy, +C and r = g(t,y) - A(t,y)*s. Here J is computed by the user-supplied +C routine JAC if MITER = 1, or by finite differencing if MITER = 2. +C J is stored in WM, rescaled, and ADDA is called to generate P. +C P is then subjected to LU decomposition by DDECBT in preparation +C for later solution of linear systems with P as coefficient matrix. +C +C In addition to variables described previously, communication +C with DPJIBT uses the following: +C Y = array containing predicted values on entry. +C RTEM = work array of length N (ACOR in DSTODI). +C SAVR = array used for output only. On output it contains the +C residual evaluated at current values of t and y. +C S = array containing predicted values of dy/dt (SAVF in DSTODI). +C WM = real work space for matrices. On output it contains the +C LU decomposition of P. +C Storage of matrix elements starts at WM(3). +C WM also contains the following matrix-related data: +C WM(1) = SQRT(UROUND), used in numerical Jacobian increments. +C IWM = integer work space containing pivot information, starting at +C IWM(21). IWM also contains block structure parameters +C MB = IWM(1) and NB = IWM(2). +C EL0 = EL(1) (input). +C IERPJ = output error flag. +C = 0 if no trouble occurred, +C = 1 if the P matrix was found to be unfactorable, +C = IRES (= 2 or 3) if RES returned IRES = 2 or 3. +C JCUR = output flag = 1 to indicate that the Jacobian matrix +C (or approximation) is now current. +C This routine also uses the Common variables EL0, H, TN, UROUND, +C MITER, N, NFE, and NJE. +C----------------------------------------------------------------------- + NJE = NJE + 1 + HL0 = H*EL0 + IERPJ = 0 + JCUR = 1 + MB = IWM(1) + NB = IWM(2) + MBSQ = MB*MB + LBLOX = MBSQ*NB + LPB = 3 + LBLOX + LPC = LPB + LBLOX + LENP = 3*LBLOX + GO TO (100, 200), MITER +C If MITER = 1, call RES, then JAC, and multiply by scalar. ------------ + 100 IRES = 1 + CALL RES (NEQ, TN, Y, S, SAVR, IRES) + NFE = NFE + 1 + IF (IRES .GT. 1) GO TO 600 + DO 110 I = 1,LENP + 110 WM(I+2) = 0.0D0 + CALL JAC (NEQ, TN, Y, S, MB, NB, WM(3), WM(LPB), WM(LPC)) + CON = -HL0 + DO 120 I = 1,LENP + 120 WM(I+2) = WM(I+2)*CON + GO TO 260 +C +C If MITER = 2, make 3*MB + 1 calls to RES to approximate J. ----------- + 200 CONTINUE + IRES = -1 + CALL RES (NEQ, TN, Y, S, SAVR, IRES) + NFE = NFE + 1 + IF (IRES .GT. 1) GO TO 600 + MWID = 3*MB + SRUR = WM(1) + DO 205 I = 1,LENP + 205 WM(2+I) = 0.0D0 + DO 250 K = 1,3 + DO 240 J = 1,MB +C Increment Y(I) for group of column indices, and call RES. ---- + J1 = J+(K-1)*MB + DO 210 I = J1,N,MWID + R = MAX(SRUR*ABS(Y(I)),0.01D0/EWT(I)) + Y(I) = Y(I) + R + 210 CONTINUE + CALL RES (NEQ, TN, Y, S, RTEM, IRES) + NFE = NFE + 1 + IF (IRES .GT. 1) GO TO 600 + DO 215 I = 1,N + 215 RTEM(I) = RTEM(I) - SAVR(I) + K1 = K + DO 230 I = J1,N,MWID +C Get Jacobian elements in column I (block-column K1). ------- + Y(I) = YH(I,1) + R = MAX(SRUR*ABS(Y(I)),0.01D0/EWT(I)) + FAC = -HL0/R +C Compute and load elements PA(*,J,K1). ---------------------- + IIA = I - J + IPA = 2 + (J-1)*MB + (K1-1)*MBSQ + DO 221 J2 = 1,MB + 221 WM(IPA+J2) = RTEM(IIA+J2)*FAC + IF (K1 .LE. 1) GO TO 223 +C Compute and load elements PB(*,J,K1-1). -------------------- + IIB = IIA - MB + IPB = IPA + LBLOX - MBSQ + DO 222 J2 = 1,MB + 222 WM(IPB+J2) = RTEM(IIB+J2)*FAC + 223 CONTINUE + IF (K1 .GE. NB) GO TO 225 +C Compute and load elements PC(*,J,K1+1). -------------------- + IIC = IIA + MB + IPC = IPA + 2*LBLOX + MBSQ + DO 224 J2 = 1,MB + 224 WM(IPC+J2) = RTEM(IIC+J2)*FAC + 225 CONTINUE + IF (K1 .NE. 3) GO TO 227 +C Compute and load elements PC(*,J,1). ----------------------- + IPC = IPA - 2*MBSQ + 2*LBLOX + DO 226 J2 = 1,MB + 226 WM(IPC+J2) = RTEM(J2)*FAC + 227 CONTINUE + IF (K1 .NE. NB-2) GO TO 229 +C Compute and load elements PB(*,J,NB). ---------------------- + IIB = N - MB + IPB = IPA + 2*MBSQ + LBLOX + DO 228 J2 = 1,MB + 228 WM(IPB+J2) = RTEM(IIB+J2)*FAC + 229 K1 = K1 + 3 + 230 CONTINUE + 240 CONTINUE + 250 CONTINUE +C RES call for first corrector iteration. ------------------------------ + IRES = 1 + CALL RES (NEQ, TN, Y, S, SAVR, IRES) + NFE = NFE + 1 + IF (IRES .GT. 1) GO TO 600 +C Add matrix A. -------------------------------------------------------- + 260 CONTINUE + CALL ADDA (NEQ, TN, Y, MB, NB, WM(3), WM(LPB), WM(LPC)) +C Do LU decomposition on P. -------------------------------------------- + CALL DDECBT (MB, NB, WM(3), WM(LPB), WM(LPC), IWM(21), IER) + IF (IER .NE. 0) IERPJ = 1 + RETURN +C Error return for IRES = 2 or IRES = 3 return from RES. --------------- + 600 IERPJ = IRES + RETURN +C----------------------- End of Subroutine DPJIBT ---------------------- + END +*DECK DSLSBT + SUBROUTINE DSLSBT (WM, IWM, X, TEM) + INTEGER IWM + INTEGER LBLOX, LPB, LPC, MB, NB + DOUBLE PRECISION WM, X, TEM + DIMENSION WM(*), IWM(*), X(*), TEM(*) +C----------------------------------------------------------------------- +C This routine acts as an interface between the core integrator +C routine and the DSOLBT routine for the solution of the linear system +C arising from chord iteration. +C Communication with DSLSBT uses the following variables: +C WM = real work space containing the LU decomposition, +C starting at WM(3). +C IWM = integer work space containing pivot information, starting at +C IWM(21). IWM also contains block structure parameters +C MB = IWM(1) and NB = IWM(2). +C X = the right-hand side vector on input, and the solution vector +C on output, of length N. +C TEM = vector of work space of length N, not used in this version. +C----------------------------------------------------------------------- + MB = IWM(1) + NB = IWM(2) + LBLOX = MB*MB*NB + LPB = 3 + LBLOX + LPC = LPB + LBLOX + CALL DSOLBT (MB, NB, WM(3), WM(LPB), WM(LPC), X, IWM(21)) + RETURN +C----------------------- End of Subroutine DSLSBT ---------------------- + END +*DECK DDECBT + SUBROUTINE DDECBT (M, N, A, B, C, IP, IER) + INTEGER M, N, IP(M,N), IER + DOUBLE PRECISION A(M,M,N), B(M,M,N), C(M,M,N) +C----------------------------------------------------------------------- +C Block-tridiagonal matrix decomposition routine. +C Written by A. C. Hindmarsh. +C Latest revision: November 10, 1983 (ACH) +C Reference: UCID-30150 +C Solution of Block-Tridiagonal Systems of Linear +C Algebraic Equations +C A.C. Hindmarsh +C February 1977 +C The input matrix contains three blocks of elements in each block-row, +C including blocks in the (1,3) and (N,N-2) block positions. +C DDECBT uses block Gauss elimination and Subroutines DGEFA and DGESL +C for solution of blocks. Partial pivoting is done within +C block-rows only. +C +C Note: this version uses LINPACK routines DGEFA/DGESL instead of +C of dec/sol for solution of blocks, and it uses the BLAS routine DDOT +C for dot product calculations. +C +C Input: +C M = order of each block. +C N = number of blocks in each direction of the matrix. +C N must be 4 or more. The complete matrix has order M*N. +C A = M by M by N array containing diagonal blocks. +C A(i,j,k) contains the (i,j) element of the k-th block. +C B = M by M by N array containing the super-diagonal blocks +C (in B(*,*,k) for k = 1,...,N-1) and the block in the (N,N-2) +C block position (in B(*,*,N)). +C C = M by M by N array containing the subdiagonal blocks +C (in C(*,*,k) for k = 2,3,...,N) and the block in the +C (1,3) block position (in C(*,*,1)). +C IP = integer array of length M*N for working storage. +C Output: +C A,B,C = M by M by N arrays containing the block-LU decomposition +C of the input matrix. +C IP = M by N array of pivot information. IP(*,k) contains +C information for the k-th digonal block. +C IER = 0 if no trouble occurred, or +C = -1 if the input value of M or N was illegal, or +C = k if a singular matrix was found in the k-th diagonal block. +C Use DSOLBT to solve the associated linear system. +C +C External routines required: DGEFA and DGESL (from LINPACK) and +C DDOT (from the BLAS, or Basic Linear Algebra package). +C----------------------------------------------------------------------- + INTEGER NM1, NM2, KM1, I, J, K + DOUBLE PRECISION DP, DDOT + IF (M .LT. 1 .OR. N .LT. 4) GO TO 210 + NM1 = N - 1 + NM2 = N - 2 +C Process the first block-row. ----------------------------------------- + CALL DGEFA (A, M, M, IP, IER) + K = 1 + IF (IER .NE. 0) GO TO 200 + DO 10 J = 1,M + CALL DGESL (A, M, M, IP, B(1,J,1), 0) + CALL DGESL (A, M, M, IP, C(1,J,1), 0) + 10 CONTINUE +C Adjust B(*,*,2). ----------------------------------------------------- + DO 40 J = 1,M + DO 30 I = 1,M + DP = DDOT (M, C(I,1,2), M, C(1,J,1), 1) + B(I,J,2) = B(I,J,2) - DP + 30 CONTINUE + 40 CONTINUE +C Main loop. Process block-rows 2 to N-1. ----------------------------- + DO 100 K = 2,NM1 + KM1 = K - 1 + DO 70 J = 1,M + DO 60 I = 1,M + DP = DDOT (M, C(I,1,K), M, B(1,J,KM1), 1) + A(I,J,K) = A(I,J,K) - DP + 60 CONTINUE + 70 CONTINUE + CALL DGEFA (A(1,1,K), M, M, IP(1,K), IER) + IF (IER .NE. 0) GO TO 200 + DO 80 J = 1,M + 80 CALL DGESL (A(1,1,K), M, M, IP(1,K), B(1,J,K), 0) + 100 CONTINUE +C Process last block-row and return. ----------------------------------- + DO 130 J = 1,M + DO 120 I = 1,M + DP = DDOT (M, B(I,1,N), M, B(1,J,NM2), 1) + C(I,J,N) = C(I,J,N) - DP + 120 CONTINUE + 130 CONTINUE + DO 160 J = 1,M + DO 150 I = 1,M + DP = DDOT (M, C(I,1,N), M, B(1,J,NM1), 1) + A(I,J,N) = A(I,J,N) - DP + 150 CONTINUE + 160 CONTINUE + CALL DGEFA (A(1,1,N), M, M, IP(1,N), IER) + K = N + IF (IER .NE. 0) GO TO 200 + RETURN +C Error returns. ------------------------------------------------------- + 200 IER = K + RETURN + 210 IER = -1 + RETURN +C----------------------- End of Subroutine DDECBT ---------------------- + END +*DECK DSOLBT + SUBROUTINE DSOLBT (M, N, A, B, C, Y, IP) + INTEGER M, N, IP(M,N) + DOUBLE PRECISION A(M,M,N), B(M,M,N), C(M,M,N), Y(M,N) +C----------------------------------------------------------------------- +C Solution of block-tridiagonal linear system. +C Coefficient matrix must have been previously processed by DDECBT. +C M, N, A,B,C, and IP must not have been changed since call to DDECBT. +C Written by A. C. Hindmarsh. +C Input: +C M = order of each block. +C N = number of blocks in each direction of matrix. +C A,B,C = M by M by N arrays containing block LU decomposition +C of coefficient matrix from DDECBT. +C IP = M by N integer array of pivot information from DDECBT. +C Y = array of length M*N containg the right-hand side vector +C (treated as an M by N array here). +C Output: +C Y = solution vector, of length M*N. +C +C External routines required: DGESL (LINPACK) and DDOT (BLAS). +C----------------------------------------------------------------------- +C + INTEGER NM1, NM2, I, K, KB, KM1, KP1 + DOUBLE PRECISION DP, DDOT + NM1 = N - 1 + NM2 = N - 2 +C Forward solution sweep. ---------------------------------------------- + CALL DGESL (A, M, M, IP, Y, 0) + DO 30 K = 2,NM1 + KM1 = K - 1 + DO 20 I = 1,M + DP = DDOT (M, C(I,1,K), M, Y(1,KM1), 1) + Y(I,K) = Y(I,K) - DP + 20 CONTINUE + CALL DGESL (A(1,1,K), M, M, IP(1,K), Y(1,K), 0) + 30 CONTINUE + DO 50 I = 1,M + DP = DDOT (M, C(I,1,N), M, Y(1,NM1), 1) + 1 + DDOT (M, B(I,1,N), M, Y(1,NM2), 1) + Y(I,N) = Y(I,N) - DP + 50 CONTINUE + CALL DGESL (A(1,1,N), M, M, IP(1,N), Y(1,N), 0) +C Backward solution sweep. --------------------------------------------- + DO 80 KB = 1,NM1 + K = N - KB + KP1 = K + 1 + DO 70 I = 1,M + DP = DDOT (M, B(I,1,K), M, Y(1,KP1), 1) + Y(I,K) = Y(I,K) - DP + 70 CONTINUE + 80 CONTINUE + DO 100 I = 1,M + DP = DDOT (M, C(I,1,1), M, Y(1,3), 1) + Y(I,1) = Y(I,1) - DP + 100 CONTINUE + RETURN +C----------------------- End of Subroutine DSOLBT ---------------------- + END +*DECK DIPREPI + SUBROUTINE DIPREPI (NEQ, Y, S, RWORK, IA, JA, IC, JC, IPFLAG, + 1 RES, JAC, ADDA) + EXTERNAL RES, JAC, ADDA + INTEGER NEQ, IA, JA, IC, JC, IPFLAG + DOUBLE PRECISION Y, S, RWORK + DIMENSION NEQ(*), Y(*), S(*), RWORK(*), IA(*), JA(*), IC(*), JC(*) + INTEGER IOWND, IOWNS, + 1 ICF, IERPJ, IERSL, JCUR, JSTART, KFLAG, L, + 2 LYH, LEWT, LACOR, LSAVF, LWM, LIWM, METH, MITER, + 3 MAXORD, MAXCOR, MSBP, MXNCF, N, NQ, NST, NFE, NJE, NQU + INTEGER IPLOST, IESP, ISTATC, IYS, IBA, IBIAN, IBJAN, IBJGP, + 1 IPIAN, IPJAN, IPJGP, IPIGP, IPR, IPC, IPIC, IPISP, IPRSP, IPA, + 2 LENYH, LENYHM, LENWK, LREQ, LRAT, LREST, LWMIN, MOSS, MSBJ, + 3 NSLJ, NGP, NLU, NNZ, NSP, NZL, NZU + DOUBLE PRECISION ROWNS, + 1 CCMAX, EL0, H, HMIN, HMXI, HU, RC, TN, UROUND + DOUBLE PRECISION RLSS + COMMON /DLS001/ ROWNS(209), + 1 CCMAX, EL0, H, HMIN, HMXI, HU, RC, TN, UROUND, + 2 IOWND(6), IOWNS(6), + 3 ICF, IERPJ, IERSL, JCUR, JSTART, KFLAG, L, + 4 LYH, LEWT, LACOR, LSAVF, LWM, LIWM, METH, MITER, + 5 MAXORD, MAXCOR, MSBP, MXNCF, N, NQ, NST, NFE, NJE, NQU + COMMON /DLSS01/ RLSS(6), + 1 IPLOST, IESP, ISTATC, IYS, IBA, IBIAN, IBJAN, IBJGP, + 2 IPIAN, IPJAN, IPJGP, IPIGP, IPR, IPC, IPIC, IPISP, IPRSP, IPA, + 3 LENYH, LENYHM, LENWK, LREQ, LRAT, LREST, LWMIN, MOSS, MSBJ, + 4 NSLJ, NGP, NLU, NNZ, NSP, NZL, NZU + INTEGER I, IMAX, LEWTN, LYHD, LYHN +C----------------------------------------------------------------------- +C This routine serves as an interface between the driver and +C Subroutine DPREPI. Tasks performed here are: +C * call DPREPI, +C * reset the required WM segment length LENWK, +C * move YH back to its final location (following WM in RWORK), +C * reset pointers for YH, SAVR, EWT, and ACOR, and +C * move EWT to its new position if ISTATE = 0 or 1. +C IPFLAG is an output error indication flag. IPFLAG = 0 if there was +C no trouble, and IPFLAG is the value of the DPREPI error flag IPPER +C if there was trouble in Subroutine DPREPI. +C----------------------------------------------------------------------- + IPFLAG = 0 +C Call DPREPI to do matrix preprocessing operations. ------------------- + CALL DPREPI (NEQ, Y, S, RWORK(LYH), RWORK(LSAVF), RWORK(LEWT), + 1 RWORK(LACOR), IA, JA, IC, JC, RWORK(LWM), RWORK(LWM), IPFLAG, + 2 RES, JAC, ADDA) + LENWK = MAX(LREQ,LWMIN) + IF (IPFLAG .LT. 0) RETURN +C If DPREPI was successful, move YH to end of required space for WM. --- + LYHN = LWM + LENWK + IF (LYHN .GT. LYH) RETURN + LYHD = LYH - LYHN + IF (LYHD .EQ. 0) GO TO 20 + IMAX = LYHN - 1 + LENYHM + DO 10 I=LYHN,IMAX + 10 RWORK(I) = RWORK(I+LYHD) + LYH = LYHN +C Reset pointers for SAVR, EWT, and ACOR. ------------------------------ + 20 LSAVF = LYH + LENYH + LEWTN = LSAVF + N + LACOR = LEWTN + N + IF (ISTATC .EQ. 3) GO TO 40 +C If ISTATE = 1, move EWT (left) to its new position. ------------------ + IF (LEWTN .GT. LEWT) RETURN + DO 30 I=1,N + 30 RWORK(I+LEWTN-1) = RWORK(I+LEWT-1) + 40 LEWT = LEWTN + RETURN +C----------------------- End of Subroutine DIPREPI --------------------- + END +*DECK DPREPI + SUBROUTINE DPREPI (NEQ, Y, S, YH, SAVR, EWT, RTEM, IA, JA, IC, JC, + 1 WK, IWK, IPPER, RES, JAC, ADDA) + EXTERNAL RES, JAC, ADDA + INTEGER NEQ, IA, JA, IC, JC, IWK, IPPER + DOUBLE PRECISION Y, S, YH, SAVR, EWT, RTEM, WK + DIMENSION NEQ(*), Y(*), S(*), YH(*), SAVR(*), EWT(*), RTEM(*), + 1 IA(*), JA(*), IC(*), JC(*), WK(*), IWK(*) + INTEGER IOWND, IOWNS, + 1 ICF, IERPJ, IERSL, JCUR, JSTART, KFLAG, L, + 2 LYH, LEWT, LACOR, LSAVF, LWM, LIWM, METH, MITER, + 3 MAXORD, MAXCOR, MSBP, MXNCF, N, NQ, NST, NFE, NJE, NQU + INTEGER IPLOST, IESP, ISTATC, IYS, IBA, IBIAN, IBJAN, IBJGP, + 1 IPIAN, IPJAN, IPJGP, IPIGP, IPR, IPC, IPIC, IPISP, IPRSP, IPA, + 2 LENYH, LENYHM, LENWK, LREQ, LRAT, LREST, LWMIN, MOSS, MSBJ, + 3 NSLJ, NGP, NLU, NNZ, NSP, NZL, NZU + DOUBLE PRECISION ROWNS, + 1 CCMAX, EL0, H, HMIN, HMXI, HU, RC, TN, UROUND + DOUBLE PRECISION RLSS + COMMON /DLS001/ ROWNS(209), + 1 CCMAX, EL0, H, HMIN, HMXI, HU, RC, TN, UROUND, + 2 IOWND(6), IOWNS(6), + 3 ICF, IERPJ, IERSL, JCUR, JSTART, KFLAG, L, + 4 LYH, LEWT, LACOR, LSAVF, LWM, LIWM, METH, MITER, + 5 MAXORD, MAXCOR, MSBP, MXNCF, N, NQ, NST, NFE, NJE, NQU + COMMON /DLSS01/ RLSS(6), + 1 IPLOST, IESP, ISTATC, IYS, IBA, IBIAN, IBJAN, IBJGP, + 2 IPIAN, IPJAN, IPJGP, IPIGP, IPR, IPC, IPIC, IPISP, IPRSP, IPA, + 3 LENYH, LENYHM, LENWK, LREQ, LRAT, LREST, LWMIN, MOSS, MSBJ, + 4 NSLJ, NGP, NLU, NNZ, NSP, NZL, NZU + INTEGER I, IBR, IER, IPIL, IPIU, IPTT1, IPTT2, J, K, KNEW, KAMAX, + 1 KAMIN, KCMAX, KCMIN, LDIF, LENIGP, LENWK1, LIWK, LJFO, MAXG, + 2 NP1, NZSUT + DOUBLE PRECISION ERWT, FAC, YJ +C----------------------------------------------------------------------- +C This routine performs preprocessing related to the sparse linear +C systems that must be solved. +C The operations that are performed here are: +C * compute sparseness structure of the iteration matrix +C P = A - con*J according to MOSS, +C * compute grouping of column indices (MITER = 2), +C * compute a new ordering of rows and columns of the matrix, +C * reorder JA corresponding to the new ordering, +C * perform a symbolic LU factorization of the matrix, and +C * set pointers for segments of the IWK/WK array. +C In addition to variables described previously, DPREPI uses the +C following for communication: +C YH = the history array. Only the first column, containing the +C current Y vector, is used. Used only if MOSS .ne. 0. +C S = array of length NEQ, identical to YDOTI in the driver, used +C only if MOSS .ne. 0. +C SAVR = a work array of length NEQ, used only if MOSS .ne. 0. +C EWT = array of length NEQ containing (inverted) error weights. +C Used only if MOSS = 2 or 4 or if ISTATE = MOSS = 1. +C RTEM = a work array of length NEQ, identical to ACOR in the driver, +C used only if MOSS = 2 or 4. +C WK = a real work array of length LENWK, identical to WM in +C the driver. +C IWK = integer work array, assumed to occupy the same space as WK. +C LENWK = the length of the work arrays WK and IWK. +C ISTATC = a copy of the driver input argument ISTATE (= 1 on the +C first call, = 3 on a continuation call). +C IYS = flag value from ODRV or CDRV. +C IPPER = output error flag , with the following values and meanings: +C = 0 no error. +C = -1 insufficient storage for internal structure pointers. +C = -2 insufficient storage for JGROUP. +C = -3 insufficient storage for ODRV. +C = -4 other error flag from ODRV (should never occur). +C = -5 insufficient storage for CDRV. +C = -6 other error flag from CDRV. +C = -7 if the RES routine returned error flag IRES = IER = 2. +C = -8 if the RES routine returned error flag IRES = IER = 3. +C----------------------------------------------------------------------- + IBIAN = LRAT*2 + IPIAN = IBIAN + 1 + NP1 = N + 1 + IPJAN = IPIAN + NP1 + IBJAN = IPJAN - 1 + LENWK1 = LENWK - N + LIWK = LENWK*LRAT + IF (MOSS .EQ. 0) LIWK = LIWK - N + IF (MOSS .EQ. 1 .OR. MOSS .EQ. 2) LIWK = LENWK1*LRAT + IF (IPJAN+N-1 .GT. LIWK) GO TO 310 + IF (MOSS .EQ. 0) GO TO 30 +C + IF (ISTATC .EQ. 3) GO TO 20 +C ISTATE = 1 and MOSS .ne. 0. Perturb Y for structure determination. +C Initialize S with random nonzero elements for structure determination. + DO 10 I=1,N + ERWT = 1.0D0/EWT(I) + FAC = 1.0D0 + 1.0D0/(I + 1.0D0) + Y(I) = Y(I) + FAC*SIGN(ERWT,Y(I)) + S(I) = 1.0D0 + FAC*ERWT + 10 CONTINUE + GO TO (70, 100, 150, 200), MOSS +C + 20 CONTINUE +C ISTATE = 3 and MOSS .ne. 0. Load Y from YH(*,1) and S from YH(*,2). -- + DO 25 I = 1,N + Y(I) = YH(I) + 25 S(I) = YH(N+I) + GO TO (70, 100, 150, 200), MOSS +C +C MOSS = 0. Process user's IA,JA and IC,JC. ---------------------------- + 30 KNEW = IPJAN + KAMIN = IA(1) + KCMIN = IC(1) + IWK(IPIAN) = 1 + DO 60 J = 1,N + DO 35 I = 1,N + 35 IWK(LIWK+I) = 0 + KAMAX = IA(J+1) - 1 + IF (KAMIN .GT. KAMAX) GO TO 45 + DO 40 K = KAMIN,KAMAX + I = JA(K) + IWK(LIWK+I) = 1 + IF (KNEW .GT. LIWK) GO TO 310 + IWK(KNEW) = I + KNEW = KNEW + 1 + 40 CONTINUE + 45 KAMIN = KAMAX + 1 + KCMAX = IC(J+1) - 1 + IF (KCMIN .GT. KCMAX) GO TO 55 + DO 50 K = KCMIN,KCMAX + I = JC(K) + IF (IWK(LIWK+I) .NE. 0) GO TO 50 + IF (KNEW .GT. LIWK) GO TO 310 + IWK(KNEW) = I + KNEW = KNEW + 1 + 50 CONTINUE + 55 IWK(IPIAN+J) = KNEW + 1 - IPJAN + KCMIN = KCMAX + 1 + 60 CONTINUE + GO TO 240 +C +C MOSS = 1. Compute structure from user-supplied Jacobian routine JAC. - + 70 CONTINUE +C A dummy call to RES allows user to create temporaries for use in JAC. + IER = 1 + CALL RES (NEQ, TN, Y, S, SAVR, IER) + IF (IER .GT. 1) GO TO 370 + DO 75 I = 1,N + SAVR(I) = 0.0D0 + 75 WK(LENWK1+I) = 0.0D0 + K = IPJAN + IWK(IPIAN) = 1 + DO 95 J = 1,N + CALL ADDA (NEQ, TN, Y, J, IWK(IPIAN), IWK(IPJAN), WK(LENWK1+1)) + CALL JAC (NEQ, TN, Y, S, J, IWK(IPIAN), IWK(IPJAN), SAVR) + DO 90 I = 1,N + LJFO = LENWK1 + I + IF (WK(LJFO) .EQ. 0.0D0) GO TO 80 + WK(LJFO) = 0.0D0 + SAVR(I) = 0.0D0 + GO TO 85 + 80 IF (SAVR(I) .EQ. 0.0D0) GO TO 90 + SAVR(I) = 0.0D0 + 85 IF (K .GT. LIWK) GO TO 310 + IWK(K) = I + K = K+1 + 90 CONTINUE + IWK(IPIAN+J) = K + 1 - IPJAN + 95 CONTINUE + GO TO 240 +C +C MOSS = 2. Compute structure from results of N + 1 calls to RES. ------ + 100 DO 105 I = 1,N + 105 WK(LENWK1+I) = 0.0D0 + K = IPJAN + IWK(IPIAN) = 1 + IER = -1 + IF (MITER .EQ. 1) IER = 1 + CALL RES (NEQ, TN, Y, S, SAVR, IER) + IF (IER .GT. 1) GO TO 370 + DO 130 J = 1,N + CALL ADDA (NEQ, TN, Y, J, IWK(IPIAN), IWK(IPJAN), WK(LENWK1+1)) + YJ = Y(J) + ERWT = 1.0D0/EWT(J) + Y(J) = YJ + SIGN(ERWT,YJ) + CALL RES (NEQ, TN, Y, S, RTEM, IER) + IF (IER .GT. 1) RETURN + Y(J) = YJ + DO 120 I = 1,N + LJFO = LENWK1 + I + IF (WK(LJFO) .EQ. 0.0D0) GO TO 110 + WK(LJFO) = 0.0D0 + GO TO 115 + 110 IF (RTEM(I) .EQ. SAVR(I)) GO TO 120 + 115 IF (K .GT. LIWK) GO TO 310 + IWK(K) = I + K = K + 1 + 120 CONTINUE + IWK(IPIAN+J) = K + 1 - IPJAN + 130 CONTINUE + GO TO 240 +C +C MOSS = 3. Compute structure from the user's IA/JA and JAC routine. --- + 150 CONTINUE +C A dummy call to RES allows user to create temporaries for use in JAC. + IER = 1 + CALL RES (NEQ, TN, Y, S, SAVR, IER) + IF (IER .GT. 1) GO TO 370 + DO 155 I = 1,N + 155 SAVR(I) = 0.0D0 + KNEW = IPJAN + KAMIN = IA(1) + IWK(IPIAN) = 1 + DO 190 J = 1,N + CALL JAC (NEQ, TN, Y, S, J, IWK(IPIAN), IWK(IPJAN), SAVR) + KAMAX = IA(J+1) - 1 + IF (KAMIN .GT. KAMAX) GO TO 170 + DO 160 K = KAMIN,KAMAX + I = JA(K) + SAVR(I) = 0.0D0 + IF (KNEW .GT. LIWK) GO TO 310 + IWK(KNEW) = I + KNEW = KNEW + 1 + 160 CONTINUE + 170 KAMIN = KAMAX + 1 + DO 180 I = 1,N + IF (SAVR(I) .EQ. 0.0D0) GO TO 180 + SAVR(I) = 0.0D0 + IF (KNEW .GT. LIWK) GO TO 310 + IWK(KNEW) = I + KNEW = KNEW + 1 + 180 CONTINUE + IWK(IPIAN+J) = KNEW + 1 - IPJAN + 190 CONTINUE + GO TO 240 +C +C MOSS = 4. Compute structure from user's IA/JA and N + 1 RES calls. --- + 200 KNEW = IPJAN + KAMIN = IA(1) + IWK(IPIAN) = 1 + IER = -1 + IF (MITER .EQ. 1) IER = 1 + CALL RES (NEQ, TN, Y, S, SAVR, IER) + IF (IER .GT. 1) GO TO 370 + DO 235 J = 1,N + YJ = Y(J) + ERWT = 1.0D0/EWT(J) + Y(J) = YJ + SIGN(ERWT,YJ) + CALL RES (NEQ, TN, Y, S, RTEM, IER) + IF (IER .GT. 1) RETURN + Y(J) = YJ + KAMAX = IA(J+1) - 1 + IF (KAMIN .GT. KAMAX) GO TO 225 + DO 220 K = KAMIN,KAMAX + I = JA(K) + RTEM(I) = SAVR(I) + IF (KNEW .GT. LIWK) GO TO 310 + IWK(KNEW) = I + KNEW = KNEW + 1 + 220 CONTINUE + 225 KAMIN = KAMAX + 1 + DO 230 I = 1,N + IF (RTEM(I) .EQ. SAVR(I)) GO TO 230 + IF (KNEW .GT. LIWK) GO TO 310 + IWK(KNEW) = I + KNEW = KNEW + 1 + 230 CONTINUE + IWK(IPIAN+J) = KNEW + 1 - IPJAN + 235 CONTINUE +C + 240 CONTINUE + IF (MOSS .EQ. 0 .OR. ISTATC .EQ. 3) GO TO 250 +C If ISTATE = 0 or 1 and MOSS .ne. 0, restore Y from YH. --------------- + DO 245 I = 1,N + 245 Y(I) = YH(I) + 250 NNZ = IWK(IPIAN+N) - 1 + IPPER = 0 + NGP = 0 + LENIGP = 0 + IPIGP = IPJAN + NNZ + IF (MITER .NE. 2) GO TO 260 +C +C Compute grouping of column indices (MITER = 2). ---------------------- +C + MAXG = NP1 + IPJGP = IPJAN + NNZ + IBJGP = IPJGP - 1 + IPIGP = IPJGP + N + IPTT1 = IPIGP + NP1 + IPTT2 = IPTT1 + N + LREQ = IPTT2 + N - 1 + IF (LREQ .GT. LIWK) GO TO 320 + CALL JGROUP (N, IWK(IPIAN), IWK(IPJAN), MAXG, NGP, IWK(IPIGP), + 1 IWK(IPJGP), IWK(IPTT1), IWK(IPTT2), IER) + IF (IER .NE. 0) GO TO 320 + LENIGP = NGP + 1 +C +C Compute new ordering of rows/columns of Jacobian. -------------------- + 260 IPR = IPIGP + LENIGP + IPC = IPR + IPIC = IPC + N + IPISP = IPIC + N + IPRSP = (IPISP-2)/LRAT + 2 + IESP = LENWK + 1 - IPRSP + IF (IESP .LT. 0) GO TO 330 + IBR = IPR - 1 + DO 270 I = 1,N + 270 IWK(IBR+I) = I + NSP = LIWK + 1 - IPISP + CALL ODRV(N, IWK(IPIAN), IWK(IPJAN), WK, IWK(IPR), IWK(IPIC), NSP, + 1 IWK(IPISP), 1, IYS) + IF (IYS .EQ. 11*N+1) GO TO 340 + IF (IYS .NE. 0) GO TO 330 +C +C Reorder JAN and do symbolic LU factorization of matrix. -------------- + IPA = LENWK + 1 - NNZ + NSP = IPA - IPRSP + LREQ = MAX(12*N/LRAT, 6*N/LRAT+2*N+NNZ) + 3 + LREQ = LREQ + IPRSP - 1 + NNZ + IF (LREQ .GT. LENWK) GO TO 350 + IBA = IPA - 1 + DO 280 I = 1,NNZ + 280 WK(IBA+I) = 0.0D0 + IPISP = LRAT*(IPRSP - 1) + 1 + CALL CDRV(N,IWK(IPR),IWK(IPC),IWK(IPIC),IWK(IPIAN),IWK(IPJAN), + 1 WK(IPA),WK(IPA),WK(IPA),NSP,IWK(IPISP),WK(IPRSP),IESP,5,IYS) + LREQ = LENWK - IESP + IF (IYS .EQ. 10*N+1) GO TO 350 + IF (IYS .NE. 0) GO TO 360 + IPIL = IPISP + IPIU = IPIL + 2*N + 1 + NZU = IWK(IPIL+N) - IWK(IPIL) + NZL = IWK(IPIU+N) - IWK(IPIU) + IF (LRAT .GT. 1) GO TO 290 + CALL ADJLR (N, IWK(IPISP), LDIF) + LREQ = LREQ + LDIF + 290 CONTINUE + IF (LRAT .EQ. 2 .AND. NNZ .EQ. N) LREQ = LREQ + 1 + NSP = NSP + LREQ - LENWK + IPA = LREQ + 1 - NNZ + IBA = IPA - 1 + IPPER = 0 + RETURN +C + 310 IPPER = -1 + LREQ = 2 + (2*N + 1)/LRAT + LREQ = MAX(LENWK+1,LREQ) + RETURN +C + 320 IPPER = -2 + LREQ = (LREQ - 1)/LRAT + 1 + RETURN +C + 330 IPPER = -3 + CALL CNTNZU (N, IWK(IPIAN), IWK(IPJAN), NZSUT) + LREQ = LENWK - IESP + (3*N + 4*NZSUT - 1)/LRAT + 1 + RETURN +C + 340 IPPER = -4 + RETURN +C + 350 IPPER = -5 + RETURN +C + 360 IPPER = -6 + LREQ = LENWK + RETURN +C + 370 IPPER = -IER - 5 + LREQ = 2 + (2*N + 1)/LRAT + RETURN +C----------------------- End of Subroutine DPREPI ---------------------- + END +*DECK DAINVGS + SUBROUTINE DAINVGS (NEQ, T, Y, WK, IWK, TEM, YDOT, IER, RES, ADDA) + EXTERNAL RES, ADDA + INTEGER NEQ, IWK, IER + INTEGER IPLOST, IESP, ISTATC, IYS, IBA, IBIAN, IBJAN, IBJGP, + 1 IPIAN, IPJAN, IPJGP, IPIGP, IPR, IPC, IPIC, IPISP, IPRSP, IPA, + 2 LENYH, LENYHM, LENWK, LREQ, LRAT, LREST, LWMIN, MOSS, MSBJ, + 3 NSLJ, NGP, NLU, NNZ, NSP, NZL, NZU + INTEGER I, IMUL, J, K, KMIN, KMAX + DOUBLE PRECISION T, Y, WK, TEM, YDOT + DOUBLE PRECISION RLSS + DIMENSION Y(*), WK(*), IWK(*), TEM(*), YDOT(*) + COMMON /DLSS01/ RLSS(6), + 1 IPLOST, IESP, ISTATC, IYS, IBA, IBIAN, IBJAN, IBJGP, + 2 IPIAN, IPJAN, IPJGP, IPIGP, IPR, IPC, IPIC, IPISP, IPRSP, IPA, + 3 LENYH, LENYHM, LENWK, LREQ, LRAT, LREST, LWMIN, MOSS, MSBJ, + 4 NSLJ, NGP, NLU, NNZ, NSP, NZL, NZU +C----------------------------------------------------------------------- +C This subroutine computes the initial value of the vector YDOT +C satisfying +C A * YDOT = g(t,y) +C when A is nonsingular. It is called by DLSODIS for initialization +C only, when ISTATE = 0. The matrix A is subjected to LU +C decomposition in CDRV. Then the system A*YDOT = g(t,y) is solved +C in CDRV. +C In addition to variables described previously, communication +C with DAINVGS uses the following: +C Y = array of initial values. +C WK = real work space for matrices. On output it contains A and +C its LU decomposition. The LU decomposition is not entirely +C sparse unless the structure of the matrix A is identical to +C the structure of the Jacobian matrix dr/dy. +C Storage of matrix elements starts at WK(3). +C WK(1) = SQRT(UROUND), not used here. +C IWK = integer work space for matrix-related data, assumed to +C be equivalenced to WK. In addition, WK(IPRSP) and WK(IPISP) +C are assumed to have identical locations. +C TEM = vector of work space of length N (ACOR in DSTODI). +C YDOT = output vector containing the initial dy/dt. YDOT(i) contains +C dy(i)/dt when the matrix A is non-singular. +C IER = output error flag with the following values and meanings: +C = 0 if DAINVGS was successful. +C = 1 if the A-matrix was found to be singular. +C = 2 if RES returned an error flag IRES = IER = 2. +C = 3 if RES returned an error flag IRES = IER = 3. +C = 4 if insufficient storage for CDRV (should not occur here). +C = 5 if other error found in CDRV (should not occur here). +C----------------------------------------------------------------------- +C + DO 10 I = 1,NNZ + 10 WK(IBA+I) = 0.0D0 +C + IER = 1 + CALL RES (NEQ, T, Y, WK(IPA), YDOT, IER) + IF (IER .GT. 1) RETURN +C + KMIN = IWK(IPIAN) + DO 30 J = 1,NEQ + KMAX = IWK(IPIAN+J) - 1 + DO 15 K = KMIN,KMAX + I = IWK(IBJAN+K) + 15 TEM(I) = 0.0D0 + CALL ADDA (NEQ, T, Y, J, IWK(IPIAN), IWK(IPJAN), TEM) + DO 20 K = KMIN,KMAX + I = IWK(IBJAN+K) + 20 WK(IBA+K) = TEM(I) + KMIN = KMAX + 1 + 30 CONTINUE + NLU = NLU + 1 + IER = 0 + DO 40 I = 1,NEQ + 40 TEM(I) = 0.0D0 +C +C Numerical factorization of matrix A. --------------------------------- + CALL CDRV (NEQ,IWK(IPR),IWK(IPC),IWK(IPIC),IWK(IPIAN),IWK(IPJAN), + 1 WK(IPA),TEM,TEM,NSP,IWK(IPISP),WK(IPRSP),IESP,2,IYS) + IF (IYS .EQ. 0) GO TO 50 + IMUL = (IYS - 1)/NEQ + IER = 5 + IF (IMUL .EQ. 8) IER = 1 + IF (IMUL .EQ. 10) IER = 4 + RETURN +C +C Solution of the linear system. --------------------------------------- + 50 CALL CDRV (NEQ,IWK(IPR),IWK(IPC),IWK(IPIC),IWK(IPIAN),IWK(IPJAN), + 1 WK(IPA),YDOT,YDOT,NSP,IWK(IPISP),WK(IPRSP),IESP,4,IYS) + IF (IYS .NE. 0) IER = 5 + RETURN +C----------------------- End of Subroutine DAINVGS --------------------- + END +*DECK DPRJIS + SUBROUTINE DPRJIS (NEQ, Y, YH, NYH, EWT, RTEM, SAVR, S, WK, IWK, + 1 RES, JAC, ADDA) + EXTERNAL RES, JAC, ADDA + INTEGER NEQ, NYH, IWK + DOUBLE PRECISION Y, YH, EWT, RTEM, SAVR, S, WK + DIMENSION NEQ(*), Y(*), YH(NYH,*), EWT(*), RTEM(*), + 1 S(*), SAVR(*), WK(*), IWK(*) + INTEGER IOWND, IOWNS, + 1 ICF, IERPJ, IERSL, JCUR, JSTART, KFLAG, L, + 2 LYH, LEWT, LACOR, LSAVF, LWM, LIWM, METH, MITER, + 3 MAXORD, MAXCOR, MSBP, MXNCF, N, NQ, NST, NFE, NJE, NQU + INTEGER IPLOST, IESP, ISTATC, IYS, IBA, IBIAN, IBJAN, IBJGP, + 1 IPIAN, IPJAN, IPJGP, IPIGP, IPR, IPC, IPIC, IPISP, IPRSP, IPA, + 2 LENYH, LENYHM, LENWK, LREQ, LRAT, LREST, LWMIN, MOSS, MSBJ, + 3 NSLJ, NGP, NLU, NNZ, NSP, NZL, NZU + DOUBLE PRECISION ROWNS, + 1 CCMAX, EL0, H, HMIN, HMXI, HU, RC, TN, UROUND + DOUBLE PRECISION RLSS + COMMON /DLS001/ ROWNS(209), + 1 CCMAX, EL0, H, HMIN, HMXI, HU, RC, TN, UROUND, + 2 IOWND(6), IOWNS(6), + 3 ICF, IERPJ, IERSL, JCUR, JSTART, KFLAG, L, + 4 LYH, LEWT, LACOR, LSAVF, LWM, LIWM, METH, MITER, + 5 MAXORD, MAXCOR, MSBP, MXNCF, N, NQ, NST, NFE, NJE, NQU + COMMON /DLSS01/ RLSS(6), + 1 IPLOST, IESP, ISTATC, IYS, IBA, IBIAN, IBJAN, IBJGP, + 2 IPIAN, IPJAN, IPJGP, IPIGP, IPR, IPC, IPIC, IPISP, IPRSP, IPA, + 3 LENYH, LENYHM, LENWK, LREQ, LRAT, LREST, LWMIN, MOSS, MSBJ, + 4 NSLJ, NGP, NLU, NNZ, NSP, NZL, NZU + INTEGER I, IMUL, IRES, J, JJ, JMAX, JMIN, K, KMAX, KMIN, NG + DOUBLE PRECISION CON, FAC, HL0, R, SRUR +C----------------------------------------------------------------------- +C DPRJIS is called to compute and process the matrix +C P = A - H*EL(1)*J, where J is an approximation to the Jacobian dr/dy, +C where r = g(t,y) - A(t,y)*s. J is computed by columns, either by +C the user-supplied routine JAC if MITER = 1, or by finite differencing +C if MITER = 2. J is stored in WK, rescaled, and ADDA is called to +C generate P. The matrix P is subjected to LU decomposition in CDRV. +C P and its LU decomposition are stored separately in WK. +C +C In addition to variables described previously, communication +C with DPRJIS uses the following: +C Y = array containing predicted values on entry. +C RTEM = work array of length N (ACOR in DSTODI). +C SAVR = array containing r evaluated at predicted y. On output it +C contains the residual evaluated at current values of t and y. +C S = array containing predicted values of dy/dt (SAVF in DSTODI). +C WK = real work space for matrices. On output it contains P and +C its sparse LU decomposition. Storage of matrix elements +C starts at WK(3). +C WK also contains the following matrix-related data. +C WK(1) = SQRT(UROUND), used in numerical Jacobian increments. +C IWK = integer work space for matrix-related data, assumed to be +C equivalenced to WK. In addition, WK(IPRSP) and IWK(IPISP) +C are assumed to have identical locations. +C EL0 = EL(1) (input). +C IERPJ = output error flag (in COMMON). +C = 0 if no error. +C = 1 if zero pivot found in CDRV. +C = IRES (= 2 or 3) if RES returned IRES = 2 or 3. +C = -1 if insufficient storage for CDRV (should not occur). +C = -2 if other error found in CDRV (should not occur here). +C JCUR = output flag = 1 to indicate that the Jacobian matrix +C (or approximation) is now current. +C This routine also uses other variables in Common. +C----------------------------------------------------------------------- + HL0 = H*EL0 + CON = -HL0 + JCUR = 1 + NJE = NJE + 1 + GO TO (100, 200), MITER +C +C If MITER = 1, call RES, then call JAC and ADDA for each column. ------ + 100 IRES = 1 + CALL RES (NEQ, TN, Y, S, SAVR, IRES) + NFE = NFE + 1 + IF (IRES .GT. 1) GO TO 600 + KMIN = IWK(IPIAN) + DO 130 J = 1,N + KMAX = IWK(IPIAN+J)-1 + DO 110 I = 1,N + 110 RTEM(I) = 0.0D0 + CALL JAC (NEQ, TN, Y, S, J, IWK(IPIAN), IWK(IPJAN), RTEM) + DO 120 I = 1,N + 120 RTEM(I) = RTEM(I)*CON + CALL ADDA (NEQ, TN, Y, J, IWK(IPIAN), IWK(IPJAN), RTEM) + DO 125 K = KMIN,KMAX + I = IWK(IBJAN+K) + WK(IBA+K) = RTEM(I) + 125 CONTINUE + KMIN = KMAX + 1 + 130 CONTINUE + GO TO 290 +C +C If MITER = 2, make NGP + 1 calls to RES to approximate J and P. ------ + 200 CONTINUE + IRES = -1 + CALL RES (NEQ, TN, Y, S, SAVR, IRES) + NFE = NFE + 1 + IF (IRES .GT. 1) GO TO 600 + SRUR = WK(1) + JMIN = IWK(IPIGP) + DO 240 NG = 1,NGP + JMAX = IWK(IPIGP+NG) - 1 + DO 210 J = JMIN,JMAX + JJ = IWK(IBJGP+J) + R = MAX(SRUR*ABS(Y(JJ)),0.01D0/EWT(JJ)) + 210 Y(JJ) = Y(JJ) + R + CALL RES (NEQ,TN,Y,S,RTEM,IRES) + NFE = NFE + 1 + IF (IRES .GT. 1) GO TO 600 + DO 230 J = JMIN,JMAX + JJ = IWK(IBJGP+J) + Y(JJ) = YH(JJ,1) + R = MAX(SRUR*ABS(Y(JJ)),0.01D0/EWT(JJ)) + FAC = -HL0/R + KMIN = IWK(IBIAN+JJ) + KMAX = IWK(IBIAN+JJ+1) - 1 + DO 220 K = KMIN,KMAX + I = IWK(IBJAN+K) + RTEM(I) = (RTEM(I) - SAVR(I))*FAC + 220 CONTINUE + CALL ADDA (NEQ, TN, Y, JJ, IWK(IPIAN), IWK(IPJAN), RTEM) + DO 225 K = KMIN,KMAX + I = IWK(IBJAN+K) + WK(IBA+K) = RTEM(I) + 225 CONTINUE + 230 CONTINUE + JMIN = JMAX + 1 + 240 CONTINUE + IRES = 1 + CALL RES (NEQ, TN, Y, S, SAVR, IRES) + NFE = NFE + 1 + IF (IRES .GT. 1) GO TO 600 +C +C Do numerical factorization of P matrix. ------------------------------ + 290 NLU = NLU + 1 + IERPJ = 0 + DO 295 I = 1,N + 295 RTEM(I) = 0.0D0 + CALL CDRV (N,IWK(IPR),IWK(IPC),IWK(IPIC),IWK(IPIAN),IWK(IPJAN), + 1 WK(IPA),RTEM,RTEM,NSP,IWK(IPISP),WK(IPRSP),IESP,2,IYS) + IF (IYS .EQ. 0) RETURN + IMUL = (IYS - 1)/N + IERPJ = -2 + IF (IMUL .EQ. 8) IERPJ = 1 + IF (IMUL .EQ. 10) IERPJ = -1 + RETURN +C Error return for IRES = 2 or IRES = 3 return from RES. --------------- + 600 IERPJ = IRES + RETURN +C----------------------- End of Subroutine DPRJIS ---------------------- + END + diff --git a/applications/PUfoam/MoDeNaModels/foamAging/src/src/odepack_sub2.f b/applications/PUfoam/MoDeNaModels/foamAging/src/src/odepack_sub2.f new file mode 100644 index 000000000..c4b4ff0d0 --- /dev/null +++ b/applications/PUfoam/MoDeNaModels/foamAging/src/src/odepack_sub2.f @@ -0,0 +1,1441 @@ +*DECK DGEFA + SUBROUTINE DGEFA (A, LDA, N, IPVT, INFO) +C***BEGIN PROLOGUE DGEFA +C***PURPOSE Factor a matrix using Gaussian elimination. +C***CATEGORY D2A1 +C***TYPE DOUBLE PRECISION (SGEFA-S, DGEFA-D, CGEFA-C) +C***KEYWORDS GENERAL MATRIX, LINEAR ALGEBRA, LINPACK, +C MATRIX FACTORIZATION +C***AUTHOR Moler, C. B., (U. of New Mexico) +C***DESCRIPTION +C +C DGEFA factors a double precision matrix by Gaussian elimination. +C +C DGEFA is usually called by DGECO, but it can be called +C directly with a saving in time if RCOND is not needed. +C (Time for DGECO) = (1 + 9/N)*(Time for DGEFA) . +C +C On Entry +C +C A DOUBLE PRECISION(LDA, N) +C the matrix to be factored. +C +C LDA INTEGER +C the leading dimension of the array A . +C +C N INTEGER +C the order of the matrix A . +C +C On Return +C +C A an upper triangular matrix and the multipliers +C which were used to obtain it. +C The factorization can be written A = L*U where +C L is a product of permutation and unit lower +C triangular matrices and U is upper triangular. +C +C IPVT INTEGER(N) +C an integer vector of pivot indices. +C +C INFO INTEGER +C = 0 normal value. +C = K if U(K,K) .EQ. 0.0 . This is not an error +C condition for this subroutine, but it does +C indicate that DGESL or DGEDI will divide by zero +C if called. Use RCOND in DGECO for a reliable +C indication of singularity. +C +C***REFERENCES J. J. Dongarra, J. R. Bunch, C. B. Moler, and G. W. +C Stewart, LINPACK Users' Guide, SIAM, 1979. +C***ROUTINES CALLED DAXPY, DSCAL, IDAMAX +C***REVISION HISTORY (YYMMDD) +C 780814 DATE WRITTEN +C 890831 Modified array declarations. (WRB) +C 890831 REVISION DATE from Version 3.2 +C 891214 Prologue converted to Version 4.0 format. (BAB) +C 900326 Removed duplicate information from DESCRIPTION section. +C (WRB) +C 920501 Reformatted the REFERENCES section. (WRB) +C***END PROLOGUE DGEFA + INTEGER LDA,N,IPVT(*),INFO + DOUBLE PRECISION A(LDA,*) +C + DOUBLE PRECISION T + INTEGER IDAMAX,J,K,KP1,L,NM1 +C +C GAUSSIAN ELIMINATION WITH PARTIAL PIVOTING +C +C***FIRST EXECUTABLE STATEMENT DGEFA + INFO = 0 + NM1 = N - 1 + IF (NM1 .LT. 1) GO TO 70 + DO 60 K = 1, NM1 + KP1 = K + 1 +C +C FIND L = PIVOT INDEX +C + L = IDAMAX(N-K+1,A(K,K),1) + K - 1 + IPVT(K) = L +C +C ZERO PIVOT IMPLIES THIS COLUMN ALREADY TRIANGULARIZED +C + IF (A(L,K) .EQ. 0.0D0) GO TO 40 +C +C INTERCHANGE IF NECESSARY +C + IF (L .EQ. K) GO TO 10 + T = A(L,K) + A(L,K) = A(K,K) + A(K,K) = T + 10 CONTINUE +C +C COMPUTE MULTIPLIERS +C + T = -1.0D0/A(K,K) + CALL DSCAL(N-K,T,A(K+1,K),1) +C +C ROW ELIMINATION WITH COLUMN INDEXING +C + DO 30 J = KP1, N + T = A(L,J) + IF (L .EQ. K) GO TO 20 + A(L,J) = A(K,J) + A(K,J) = T + 20 CONTINUE + CALL DAXPY(N-K,T,A(K+1,K),1,A(K+1,J),1) + 30 CONTINUE + GO TO 50 + 40 CONTINUE + INFO = K + 50 CONTINUE + 60 CONTINUE + 70 CONTINUE + IPVT(N) = N + IF (A(N,N) .EQ. 0.0D0) INFO = N + RETURN + END +*DECK DGESL + SUBROUTINE DGESL (A, LDA, N, IPVT, B, JOB) +C***BEGIN PROLOGUE DGESL +C***PURPOSE Solve the real system A*X=B or TRANS(A)*X=B using the +C factors computed by DGECO or DGEFA. +C***CATEGORY D2A1 +C***TYPE DOUBLE PRECISION (SGESL-S, DGESL-D, CGESL-C) +C***KEYWORDS LINEAR ALGEBRA, LINPACK, MATRIX, SOLVE +C***AUTHOR Moler, C. B., (U. of New Mexico) +C***DESCRIPTION +C +C DGESL solves the double precision system +C A * X = B or TRANS(A) * X = B +C using the factors computed by DGECO or DGEFA. +C +C On Entry +C +C A DOUBLE PRECISION(LDA, N) +C the output from DGECO or DGEFA. +C +C LDA INTEGER +C the leading dimension of the array A . +C +C N INTEGER +C the order of the matrix A . +C +C IPVT INTEGER(N) +C the pivot vector from DGECO or DGEFA. +C +C B DOUBLE PRECISION(N) +C the right hand side vector. +C +C JOB INTEGER +C = 0 to solve A*X = B , +C = nonzero to solve TRANS(A)*X = B where +C TRANS(A) is the transpose. +C +C On Return +C +C B the solution vector X . +C +C Error Condition +C +C A division by zero will occur if the input factor contains a +C zero on the diagonal. Technically this indicates singularity +C but it is often caused by improper arguments or improper +C setting of LDA . It will not occur if the subroutines are +C called correctly and if DGECO has set RCOND .GT. 0.0 +C or DGEFA has set INFO .EQ. 0 . +C +C To compute INVERSE(A) * C where C is a matrix +C with P columns +C CALL DGECO(A,LDA,N,IPVT,RCOND,Z) +C IF (RCOND is too small) GO TO ... +C DO 10 J = 1, P +C CALL DGESL(A,LDA,N,IPVT,C(1,J),0) +C 10 CONTINUE +C +C***REFERENCES J. J. Dongarra, J. R. Bunch, C. B. Moler, and G. W. +C Stewart, LINPACK Users' Guide, SIAM, 1979. +C***ROUTINES CALLED DAXPY, DDOT +C***REVISION HISTORY (YYMMDD) +C 780814 DATE WRITTEN +C 890831 Modified array declarations. (WRB) +C 890831 REVISION DATE from Version 3.2 +C 891214 Prologue converted to Version 4.0 format. (BAB) +C 900326 Removed duplicate information from DESCRIPTION section. +C (WRB) +C 920501 Reformatted the REFERENCES section. (WRB) +C***END PROLOGUE DGESL + INTEGER LDA,N,IPVT(*),JOB + DOUBLE PRECISION A(LDA,*),B(*) +C + DOUBLE PRECISION DDOT,T + INTEGER K,KB,L,NM1 +C***FIRST EXECUTABLE STATEMENT DGESL + NM1 = N - 1 + IF (JOB .NE. 0) GO TO 50 +C +C JOB = 0 , SOLVE A * X = B +C FIRST SOLVE L*Y = B +C + IF (NM1 .LT. 1) GO TO 30 + DO 20 K = 1, NM1 + L = IPVT(K) + T = B(L) + IF (L .EQ. K) GO TO 10 + B(L) = B(K) + B(K) = T + 10 CONTINUE + CALL DAXPY(N-K,T,A(K+1,K),1,B(K+1),1) + 20 CONTINUE + 30 CONTINUE +C +C NOW SOLVE U*X = Y +C + DO 40 KB = 1, N + K = N + 1 - KB + B(K) = B(K)/A(K,K) + T = -B(K) + CALL DAXPY(K-1,T,A(1,K),1,B(1),1) + 40 CONTINUE + GO TO 100 + 50 CONTINUE +C +C JOB = NONZERO, SOLVE TRANS(A) * X = B +C FIRST SOLVE TRANS(U)*Y = B +C + DO 60 K = 1, N + T = DDOT(K-1,A(1,K),1,B(1),1) + B(K) = (B(K) - T)/A(K,K) + 60 CONTINUE +C +C NOW SOLVE TRANS(L)*X = Y +C + IF (NM1 .LT. 1) GO TO 90 + DO 80 KB = 1, NM1 + K = N - KB + B(K) = B(K) + DDOT(N-K,A(K+1,K),1,B(K+1),1) + L = IPVT(K) + IF (L .EQ. K) GO TO 70 + T = B(L) + B(L) = B(K) + B(K) = T + 70 CONTINUE + 80 CONTINUE + 90 CONTINUE + 100 CONTINUE + RETURN + END +*DECK DGBFA + SUBROUTINE DGBFA (ABD, LDA, N, ML, MU, IPVT, INFO) +C***BEGIN PROLOGUE DGBFA +C***PURPOSE Factor a band matrix using Gaussian elimination. +C***CATEGORY D2A2 +C***TYPE DOUBLE PRECISION (SGBFA-S, DGBFA-D, CGBFA-C) +C***KEYWORDS BANDED, LINEAR ALGEBRA, LINPACK, MATRIX FACTORIZATION +C***AUTHOR Moler, C. B., (U. of New Mexico) +C***DESCRIPTION +C +C DGBFA factors a double precision band matrix by elimination. +C +C DGBFA is usually called by DGBCO, but it can be called +C directly with a saving in time if RCOND is not needed. +C +C On Entry +C +C ABD DOUBLE PRECISION(LDA, N) +C contains the matrix in band storage. The columns +C of the matrix are stored in the columns of ABD and +C the diagonals of the matrix are stored in rows +C ML+1 through 2*ML+MU+1 of ABD . +C See the comments below for details. +C +C LDA INTEGER +C the leading dimension of the array ABD . +C LDA must be .GE. 2*ML + MU + 1 . +C +C N INTEGER +C the order of the original matrix. +C +C ML INTEGER +C number of diagonals below the main diagonal. +C 0 .LE. ML .LT. N . +C +C MU INTEGER +C number of diagonals above the main diagonal. +C 0 .LE. MU .LT. N . +C More efficient if ML .LE. MU . +C On Return +C +C ABD an upper triangular matrix in band storage and +C the multipliers which were used to obtain it. +C The factorization can be written A = L*U where +C L is a product of permutation and unit lower +C triangular matrices and U is upper triangular. +C +C IPVT INTEGER(N) +C an integer vector of pivot indices. +C +C INFO INTEGER +C = 0 normal value. +C = K if U(K,K) .EQ. 0.0 . This is not an error +C condition for this subroutine, but it does +C indicate that DGBSL will divide by zero if +C called. Use RCOND in DGBCO for a reliable +C indication of singularity. +C +C Band Storage +C +C If A is a band matrix, the following program segment +C will set up the input. +C +C ML = (band width below the diagonal) +C MU = (band width above the diagonal) +C M = ML + MU + 1 +C DO 20 J = 1, N +C I1 = MAX(1, J-MU) +C I2 = MIN(N, J+ML) +C DO 10 I = I1, I2 +C K = I - J + M +C ABD(K,J) = A(I,J) +C 10 CONTINUE +C 20 CONTINUE +C +C This uses rows ML+1 through 2*ML+MU+1 of ABD . +C In addition, the first ML rows in ABD are used for +C elements generated during the triangularization. +C The total number of rows needed in ABD is 2*ML+MU+1 . +C The ML+MU by ML+MU upper left triangle and the +C ML by ML lower right triangle are not referenced. +C +C***REFERENCES J. J. Dongarra, J. R. Bunch, C. B. Moler, and G. W. +C Stewart, LINPACK Users' Guide, SIAM, 1979. +C***ROUTINES CALLED DAXPY, DSCAL, IDAMAX +C***REVISION HISTORY (YYMMDD) +C 780814 DATE WRITTEN +C 890531 Changed all specific intrinsics to generic. (WRB) +C 890831 Modified array declarations. (WRB) +C 890831 REVISION DATE from Version 3.2 +C 891214 Prologue converted to Version 4.0 format. (BAB) +C 900326 Removed duplicate information from DESCRIPTION section. +C (WRB) +C 920501 Reformatted the REFERENCES section. (WRB) +C***END PROLOGUE DGBFA + INTEGER LDA,N,ML,MU,IPVT(*),INFO + DOUBLE PRECISION ABD(LDA,*) +C + DOUBLE PRECISION T + INTEGER I,IDAMAX,I0,J,JU,JZ,J0,J1,K,KP1,L,LM,M,MM,NM1 +C +C***FIRST EXECUTABLE STATEMENT DGBFA + M = ML + MU + 1 + INFO = 0 +C +C ZERO INITIAL FILL-IN COLUMNS +C + J0 = MU + 2 + J1 = MIN(N,M) - 1 + IF (J1 .LT. J0) GO TO 30 + DO 20 JZ = J0, J1 + I0 = M + 1 - JZ + DO 10 I = I0, ML + ABD(I,JZ) = 0.0D0 + 10 CONTINUE + 20 CONTINUE + 30 CONTINUE + JZ = J1 + JU = 0 +C +C GAUSSIAN ELIMINATION WITH PARTIAL PIVOTING +C + NM1 = N - 1 + IF (NM1 .LT. 1) GO TO 130 + DO 120 K = 1, NM1 + KP1 = K + 1 +C +C ZERO NEXT FILL-IN COLUMN +C + JZ = JZ + 1 + IF (JZ .GT. N) GO TO 50 + IF (ML .LT. 1) GO TO 50 + DO 40 I = 1, ML + ABD(I,JZ) = 0.0D0 + 40 CONTINUE + 50 CONTINUE +C +C FIND L = PIVOT INDEX +C + LM = MIN(ML,N-K) + L = IDAMAX(LM+1,ABD(M,K),1) + M - 1 + IPVT(K) = L + K - M +C +C ZERO PIVOT IMPLIES THIS COLUMN ALREADY TRIANGULARIZED +C + IF (ABD(L,K) .EQ. 0.0D0) GO TO 100 +C +C INTERCHANGE IF NECESSARY +C + IF (L .EQ. M) GO TO 60 + T = ABD(L,K) + ABD(L,K) = ABD(M,K) + ABD(M,K) = T + 60 CONTINUE +C +C COMPUTE MULTIPLIERS +C + T = -1.0D0/ABD(M,K) + CALL DSCAL(LM,T,ABD(M+1,K),1) +C +C ROW ELIMINATION WITH COLUMN INDEXING +C + JU = MIN(MAX(JU,MU+IPVT(K)),N) + MM = M + IF (JU .LT. KP1) GO TO 90 + DO 80 J = KP1, JU + L = L - 1 + MM = MM - 1 + T = ABD(L,J) + IF (L .EQ. MM) GO TO 70 + ABD(L,J) = ABD(MM,J) + ABD(MM,J) = T + 70 CONTINUE + CALL DAXPY(LM,T,ABD(M+1,K),1,ABD(MM+1,J),1) + 80 CONTINUE + 90 CONTINUE + GO TO 110 + 100 CONTINUE + INFO = K + 110 CONTINUE + 120 CONTINUE + 130 CONTINUE + IPVT(N) = N + IF (ABD(M,N) .EQ. 0.0D0) INFO = N + RETURN + END +*DECK DGBSL + SUBROUTINE DGBSL (ABD, LDA, N, ML, MU, IPVT, B, JOB) +C***BEGIN PROLOGUE DGBSL +C***PURPOSE Solve the real band system A*X=B or TRANS(A)*X=B using +C the factors computed by DGBCO or DGBFA. +C***CATEGORY D2A2 +C***TYPE DOUBLE PRECISION (SGBSL-S, DGBSL-D, CGBSL-C) +C***KEYWORDS BANDED, LINEAR ALGEBRA, LINPACK, MATRIX, SOLVE +C***AUTHOR Moler, C. B., (U. of New Mexico) +C***DESCRIPTION +C +C DGBSL solves the double precision band system +C A * X = B or TRANS(A) * X = B +C using the factors computed by DGBCO or DGBFA. +C +C On Entry +C +C ABD DOUBLE PRECISION(LDA, N) +C the output from DGBCO or DGBFA. +C +C LDA INTEGER +C the leading dimension of the array ABD . +C +C N INTEGER +C the order of the original matrix. +C +C ML INTEGER +C number of diagonals below the main diagonal. +C +C MU INTEGER +C number of diagonals above the main diagonal. +C +C IPVT INTEGER(N) +C the pivot vector from DGBCO or DGBFA. +C +C B DOUBLE PRECISION(N) +C the right hand side vector. +C +C JOB INTEGER +C = 0 to solve A*X = B , +C = nonzero to solve TRANS(A)*X = B , where +C TRANS(A) is the transpose. +C +C On Return +C +C B the solution vector X . +C +C Error Condition +C +C A division by zero will occur if the input factor contains a +C zero on the diagonal. Technically this indicates singularity +C but it is often caused by improper arguments or improper +C setting of LDA . It will not occur if the subroutines are +C called correctly and if DGBCO has set RCOND .GT. 0.0 +C or DGBFA has set INFO .EQ. 0 . +C +C To compute INVERSE(A) * C where C is a matrix +C with P columns +C CALL DGBCO(ABD,LDA,N,ML,MU,IPVT,RCOND,Z) +C IF (RCOND is too small) GO TO ... +C DO 10 J = 1, P +C CALL DGBSL(ABD,LDA,N,ML,MU,IPVT,C(1,J),0) +C 10 CONTINUE +C +C***REFERENCES J. J. Dongarra, J. R. Bunch, C. B. Moler, and G. W. +C Stewart, LINPACK Users' Guide, SIAM, 1979. +C***ROUTINES CALLED DAXPY, DDOT +C***REVISION HISTORY (YYMMDD) +C 780814 DATE WRITTEN +C 890531 Changed all specific intrinsics to generic. (WRB) +C 890831 Modified array declarations. (WRB) +C 890831 REVISION DATE from Version 3.2 +C 891214 Prologue converted to Version 4.0 format. (BAB) +C 900326 Removed duplicate information from DESCRIPTION section. +C (WRB) +C 920501 Reformatted the REFERENCES section. (WRB) +C***END PROLOGUE DGBSL + INTEGER LDA,N,ML,MU,IPVT(*),JOB + DOUBLE PRECISION ABD(LDA,*),B(*) +C + DOUBLE PRECISION DDOT,T + INTEGER K,KB,L,LA,LB,LM,M,NM1 +C***FIRST EXECUTABLE STATEMENT DGBSL + M = MU + ML + 1 + NM1 = N - 1 + IF (JOB .NE. 0) GO TO 50 +C +C JOB = 0 , SOLVE A * X = B +C FIRST SOLVE L*Y = B +C + IF (ML .EQ. 0) GO TO 30 + IF (NM1 .LT. 1) GO TO 30 + DO 20 K = 1, NM1 + LM = MIN(ML,N-K) + L = IPVT(K) + T = B(L) + IF (L .EQ. K) GO TO 10 + B(L) = B(K) + B(K) = T + 10 CONTINUE + CALL DAXPY(LM,T,ABD(M+1,K),1,B(K+1),1) + 20 CONTINUE + 30 CONTINUE +C +C NOW SOLVE U*X = Y +C + DO 40 KB = 1, N + K = N + 1 - KB + B(K) = B(K)/ABD(M,K) + LM = MIN(K,M) - 1 + LA = M - LM + LB = K - LM + T = -B(K) + CALL DAXPY(LM,T,ABD(LA,K),1,B(LB),1) + 40 CONTINUE + GO TO 100 + 50 CONTINUE +C +C JOB = NONZERO, SOLVE TRANS(A) * X = B +C FIRST SOLVE TRANS(U)*Y = B +C + DO 60 K = 1, N + LM = MIN(K,M) - 1 + LA = M - LM + LB = K - LM + T = DDOT(LM,ABD(LA,K),1,B(LB),1) + B(K) = (B(K) - T)/ABD(M,K) + 60 CONTINUE +C +C NOW SOLVE TRANS(L)*X = Y +C + IF (ML .EQ. 0) GO TO 90 + IF (NM1 .LT. 1) GO TO 90 + DO 80 KB = 1, NM1 + K = N - KB + LM = MIN(ML,N-K) + B(K) = B(K) + DDOT(LM,ABD(M+1,K),1,B(K+1),1) + L = IPVT(K) + IF (L .EQ. K) GO TO 70 + T = B(L) + B(L) = B(K) + B(K) = T + 70 CONTINUE + 80 CONTINUE + 90 CONTINUE + 100 CONTINUE + RETURN + END +*DECK DAXPY + SUBROUTINE DAXPY (N, DA, DX, INCX, DY, INCY) +C***BEGIN PROLOGUE DAXPY +C***PURPOSE Compute a constant times a vector plus a vector. +C***CATEGORY D1A7 +C***TYPE DOUBLE PRECISION (SAXPY-S, DAXPY-D, CAXPY-C) +C***KEYWORDS BLAS, LINEAR ALGEBRA, TRIAD, VECTOR +C***AUTHOR Lawson, C. L., (JPL) +C Hanson, R. J., (SNLA) +C Kincaid, D. R., (U. of Texas) +C Krogh, F. T., (JPL) +C***DESCRIPTION +C +C B L A S Subprogram +C Description of Parameters +C +C --Input-- +C N number of elements in input vector(s) +C DA double precision scalar multiplier +C DX double precision vector with N elements +C INCX storage spacing between elements of DX +C DY double precision vector with N elements +C INCY storage spacing between elements of DY +C +C --Output-- +C DY double precision result (unchanged if N .LE. 0) +C +C Overwrite double precision DY with double precision DA*DX + DY. +C For I = 0 to N-1, replace DY(LY+I*INCY) with DA*DX(LX+I*INCX) + +C DY(LY+I*INCY), +C where LX = 1 if INCX .GE. 0, else LX = 1+(1-N)*INCX, and LY is +C defined in a similar way using INCY. +C +C***REFERENCES C. L. Lawson, R. J. Hanson, D. R. Kincaid and F. T. +C Krogh, Basic linear algebra subprograms for Fortran +C usage, Algorithm No. 539, Transactions on Mathematical +C Software 5, 3 (September 1979), pp. 308-323. +C***ROUTINES CALLED (NONE) +C***REVISION HISTORY (YYMMDD) +C 791001 DATE WRITTEN +C 890831 Modified array declarations. (WRB) +C 890831 REVISION DATE from Version 3.2 +C 891214 Prologue converted to Version 4.0 format. (BAB) +C 920310 Corrected definition of LX in DESCRIPTION. (WRB) +C 920501 Reformatted the REFERENCES section. (WRB) +C***END PROLOGUE DAXPY + DOUBLE PRECISION DX(*), DY(*), DA +C***FIRST EXECUTABLE STATEMENT DAXPY + IF (N.LE.0 .OR. DA.EQ.0.0D0) RETURN + IF (INCX .EQ. INCY) IF (INCX-1) 5,20,60 +C +C Code for unequal or nonpositive increments. +C + 5 IX = 1 + IY = 1 + IF (INCX .LT. 0) IX = (-N+1)*INCX + 1 + IF (INCY .LT. 0) IY = (-N+1)*INCY + 1 + DO 10 I = 1,N + DY(IY) = DY(IY) + DA*DX(IX) + IX = IX + INCX + IY = IY + INCY + 10 CONTINUE + RETURN +C +C Code for both increments equal to 1. +C +C Clean-up loop so remaining vector length is a multiple of 4. +C + 20 M = MOD(N,4) + IF (M .EQ. 0) GO TO 40 + DO 30 I = 1,M + DY(I) = DY(I) + DA*DX(I) + 30 CONTINUE + IF (N .LT. 4) RETURN + 40 MP1 = M + 1 + DO 50 I = MP1,N,4 + DY(I) = DY(I) + DA*DX(I) + DY(I+1) = DY(I+1) + DA*DX(I+1) + DY(I+2) = DY(I+2) + DA*DX(I+2) + DY(I+3) = DY(I+3) + DA*DX(I+3) + 50 CONTINUE + RETURN +C +C Code for equal, positive, non-unit increments. +C + 60 NS = N*INCX + DO 70 I = 1,NS,INCX + DY(I) = DA*DX(I) + DY(I) + 70 CONTINUE + RETURN + END +*DECK DCOPY + SUBROUTINE DCOPY (N, DX, INCX, DY, INCY) +C***BEGIN PROLOGUE DCOPY +C***PURPOSE Copy a vector. +C***CATEGORY D1A5 +C***TYPE DOUBLE PRECISION (SCOPY-S, DCOPY-D, CCOPY-C, ICOPY-I) +C***KEYWORDS BLAS, COPY, LINEAR ALGEBRA, VECTOR +C***AUTHOR Lawson, C. L., (JPL) +C Hanson, R. J., (SNLA) +C Kincaid, D. R., (U. of Texas) +C Krogh, F. T., (JPL) +C***DESCRIPTION +C +C B L A S Subprogram +C Description of Parameters +C +C --Input-- +C N number of elements in input vector(s) +C DX double precision vector with N elements +C INCX storage spacing between elements of DX +C DY double precision vector with N elements +C INCY storage spacing between elements of DY +C +C --Output-- +C DY copy of vector DX (unchanged if N .LE. 0) +C +C Copy double precision DX to double precision DY. +C For I = 0 to N-1, copy DX(LX+I*INCX) to DY(LY+I*INCY), +C where LX = 1 if INCX .GE. 0, else LX = 1+(1-N)*INCX, and LY is +C defined in a similar way using INCY. +C +C***REFERENCES C. L. Lawson, R. J. Hanson, D. R. Kincaid and F. T. +C Krogh, Basic linear algebra subprograms for Fortran +C usage, Algorithm No. 539, Transactions on Mathematical +C Software 5, 3 (September 1979), pp. 308-323. +C***ROUTINES CALLED (NONE) +C***REVISION HISTORY (YYMMDD) +C 791001 DATE WRITTEN +C 890831 Modified array declarations. (WRB) +C 890831 REVISION DATE from Version 3.2 +C 891214 Prologue converted to Version 4.0 format. (BAB) +C 920310 Corrected definition of LX in DESCRIPTION. (WRB) +C 920501 Reformatted the REFERENCES section. (WRB) +C***END PROLOGUE DCOPY + DOUBLE PRECISION DX(*), DY(*) +C***FIRST EXECUTABLE STATEMENT DCOPY + IF (N .LE. 0) RETURN + IF (INCX .EQ. INCY) IF (INCX-1) 5,20,60 +C +C Code for unequal or nonpositive increments. +C + 5 IX = 1 + IY = 1 + IF (INCX .LT. 0) IX = (-N+1)*INCX + 1 + IF (INCY .LT. 0) IY = (-N+1)*INCY + 1 + DO 10 I = 1,N + DY(IY) = DX(IX) + IX = IX + INCX + IY = IY + INCY + 10 CONTINUE + RETURN +C +C Code for both increments equal to 1. +C +C Clean-up loop so remaining vector length is a multiple of 7. +C + 20 M = MOD(N,7) + IF (M .EQ. 0) GO TO 40 + DO 30 I = 1,M + DY(I) = DX(I) + 30 CONTINUE + IF (N .LT. 7) RETURN + 40 MP1 = M + 1 + DO 50 I = MP1,N,7 + DY(I) = DX(I) + DY(I+1) = DX(I+1) + DY(I+2) = DX(I+2) + DY(I+3) = DX(I+3) + DY(I+4) = DX(I+4) + DY(I+5) = DX(I+5) + DY(I+6) = DX(I+6) + 50 CONTINUE + RETURN +C +C Code for equal, positive, non-unit increments. +C + 60 NS = N*INCX + DO 70 I = 1,NS,INCX + DY(I) = DX(I) + 70 CONTINUE + RETURN + END +*DECK DDOT + DOUBLE PRECISION FUNCTION DDOT (N, DX, INCX, DY, INCY) +C***BEGIN PROLOGUE DDOT +C***PURPOSE Compute the inner product of two vectors. +C***CATEGORY D1A4 +C***TYPE DOUBLE PRECISION (SDOT-S, DDOT-D, CDOTU-C) +C***KEYWORDS BLAS, INNER PRODUCT, LINEAR ALGEBRA, VECTOR +C***AUTHOR Lawson, C. L., (JPL) +C Hanson, R. J., (SNLA) +C Kincaid, D. R., (U. of Texas) +C Krogh, F. T., (JPL) +C***DESCRIPTION +C +C B L A S Subprogram +C Description of Parameters +C +C --Input-- +C N number of elements in input vector(s) +C DX double precision vector with N elements +C INCX storage spacing between elements of DX +C DY double precision vector with N elements +C INCY storage spacing between elements of DY +C +C --Output-- +C DDOT double precision dot product (zero if N .LE. 0) +C +C Returns the dot product of double precision DX and DY. +C DDOT = sum for I = 0 to N-1 of DX(LX+I*INCX) * DY(LY+I*INCY), +C where LX = 1 if INCX .GE. 0, else LX = 1+(1-N)*INCX, and LY is +C defined in a similar way using INCY. +C +C***REFERENCES C. L. Lawson, R. J. Hanson, D. R. Kincaid and F. T. +C Krogh, Basic linear algebra subprograms for Fortran +C usage, Algorithm No. 539, Transactions on Mathematical +C Software 5, 3 (September 1979), pp. 308-323. +C***ROUTINES CALLED (NONE) +C***REVISION HISTORY (YYMMDD) +C 791001 DATE WRITTEN +C 890831 Modified array declarations. (WRB) +C 890831 REVISION DATE from Version 3.2 +C 891214 Prologue converted to Version 4.0 format. (BAB) +C 920310 Corrected definition of LX in DESCRIPTION. (WRB) +C 920501 Reformatted the REFERENCES section. (WRB) +C***END PROLOGUE DDOT + DOUBLE PRECISION DX(*), DY(*) +C***FIRST EXECUTABLE STATEMENT DDOT + DDOT = 0.0D0 + IF (N .LE. 0) RETURN + IF (INCX .EQ. INCY) IF (INCX-1) 5,20,60 +C +C Code for unequal or nonpositive increments. +C + 5 IX = 1 + IY = 1 + IF (INCX .LT. 0) IX = (-N+1)*INCX + 1 + IF (INCY .LT. 0) IY = (-N+1)*INCY + 1 + DO 10 I = 1,N + DDOT = DDOT + DX(IX)*DY(IY) + IX = IX + INCX + IY = IY + INCY + 10 CONTINUE + RETURN +C +C Code for both increments equal to 1. +C +C Clean-up loop so remaining vector length is a multiple of 5. +C + 20 M = MOD(N,5) + IF (M .EQ. 0) GO TO 40 + DO 30 I = 1,M + DDOT = DDOT + DX(I)*DY(I) + 30 CONTINUE + IF (N .LT. 5) RETURN + 40 MP1 = M + 1 + DO 50 I = MP1,N,5 + DDOT = DDOT + DX(I)*DY(I) + DX(I+1)*DY(I+1) + DX(I+2)*DY(I+2) + + 1 DX(I+3)*DY(I+3) + DX(I+4)*DY(I+4) + 50 CONTINUE + RETURN +C +C Code for equal, positive, non-unit increments. +C + 60 NS = N*INCX + DO 70 I = 1,NS,INCX + DDOT = DDOT + DX(I)*DY(I) + 70 CONTINUE + RETURN + END +*DECK DNRM2 + DOUBLE PRECISION FUNCTION DNRM2 (N, DX, INCX) +C***BEGIN PROLOGUE DNRM2 +C***PURPOSE Compute the Euclidean length (L2 norm) of a vector. +C***CATEGORY D1A3B +C***TYPE DOUBLE PRECISION (SNRM2-S, DNRM2-D, SCNRM2-C) +C***KEYWORDS BLAS, EUCLIDEAN LENGTH, EUCLIDEAN NORM, L2, +C LINEAR ALGEBRA, UNITARY, VECTOR +C***AUTHOR Lawson, C. L., (JPL) +C Hanson, R. J., (SNLA) +C Kincaid, D. R., (U. of Texas) +C Krogh, F. T., (JPL) +C***DESCRIPTION +C +C B L A S Subprogram +C Description of parameters +C +C --Input-- +C N number of elements in input vector(s) +C DX double precision vector with N elements +C INCX storage spacing between elements of DX +C +C --Output-- +C DNRM2 double precision result (zero if N .LE. 0) +C +C Euclidean norm of the N-vector stored in DX with storage +C increment INCX. +C If N .LE. 0, return with result = 0. +C If N .GE. 1, then INCX must be .GE. 1 +C +C Four phase method using two built-in constants that are +C hopefully applicable to all machines. +C CUTLO = maximum of SQRT(U/EPS) over all known machines. +C CUTHI = minimum of SQRT(V) over all known machines. +C where +C EPS = smallest no. such that EPS + 1. .GT. 1. +C U = smallest positive no. (underflow limit) +C V = largest no. (overflow limit) +C +C Brief outline of algorithm. +C +C Phase 1 scans zero components. +C move to phase 2 when a component is nonzero and .LE. CUTLO +C move to phase 3 when a component is .GT. CUTLO +C move to phase 4 when a component is .GE. CUTHI/M +C where M = N for X() real and M = 2*N for complex. +C +C Values for CUTLO and CUTHI. +C From the environmental parameters listed in the IMSL converter +C document the limiting values are as follows: +C CUTLO, S.P. U/EPS = 2**(-102) for Honeywell. Close seconds are +C Univac and DEC at 2**(-103) +C Thus CUTLO = 2**(-51) = 4.44089E-16 +C CUTHI, S.P. V = 2**127 for Univac, Honeywell, and DEC. +C Thus CUTHI = 2**(63.5) = 1.30438E19 +C CUTLO, D.P. U/EPS = 2**(-67) for Honeywell and DEC. +C Thus CUTLO = 2**(-33.5) = 8.23181D-11 +C CUTHI, D.P. same as S.P. CUTHI = 1.30438D19 +C DATA CUTLO, CUTHI /8.232D-11, 1.304D19/ +C DATA CUTLO, CUTHI /4.441E-16, 1.304E19/ +C +C***REFERENCES C. L. Lawson, R. J. Hanson, D. R. Kincaid and F. T. +C Krogh, Basic linear algebra subprograms for Fortran +C usage, Algorithm No. 539, Transactions on Mathematical +C Software 5, 3 (September 1979), pp. 308-323. +C***ROUTINES CALLED (NONE) +C***REVISION HISTORY (YYMMDD) +C 791001 DATE WRITTEN +C 890531 Changed all specific intrinsics to generic. (WRB) +C 890831 Modified array declarations. (WRB) +C 890831 REVISION DATE from Version 3.2 +C 891214 Prologue converted to Version 4.0 format. (BAB) +C 920501 Reformatted the REFERENCES section. (WRB) +C***END PROLOGUE DNRM2 + INTEGER NEXT + DOUBLE PRECISION DX(*), CUTLO, CUTHI, HITEST, SUM, XMAX, ZERO, + + ONE + SAVE CUTLO, CUTHI, ZERO, ONE + DATA ZERO, ONE /0.0D0, 1.0D0/ +C + DATA CUTLO, CUTHI /8.232D-11, 1.304D19/ +C***FIRST EXECUTABLE STATEMENT DNRM2 + IF (N .GT. 0) GO TO 10 + DNRM2 = ZERO + GO TO 300 +C + 10 ASSIGN 30 TO NEXT + SUM = ZERO + NN = N * INCX +C +C BEGIN MAIN LOOP +C + I = 1 + 20 GO TO NEXT,(30, 50, 70, 110) + 30 IF (ABS(DX(I)) .GT. CUTLO) GO TO 85 + ASSIGN 50 TO NEXT + XMAX = ZERO +C +C PHASE 1. SUM IS ZERO +C + 50 IF (DX(I) .EQ. ZERO) GO TO 200 + IF (ABS(DX(I)) .GT. CUTLO) GO TO 85 +C +C PREPARE FOR PHASE 2. +C + ASSIGN 70 TO NEXT + GO TO 105 +C +C PREPARE FOR PHASE 4. +C + 100 I = J + ASSIGN 110 TO NEXT + SUM = (SUM / DX(I)) / DX(I) + 105 XMAX = ABS(DX(I)) + GO TO 115 +C +C PHASE 2. SUM IS SMALL. +C SCALE TO AVOID DESTRUCTIVE UNDERFLOW. +C + 70 IF (ABS(DX(I)) .GT. CUTLO) GO TO 75 +C +C COMMON CODE FOR PHASES 2 AND 4. +C IN PHASE 4 SUM IS LARGE. SCALE TO AVOID OVERFLOW. +C + 110 IF (ABS(DX(I)) .LE. XMAX) GO TO 115 + SUM = ONE + SUM * (XMAX / DX(I))**2 + XMAX = ABS(DX(I)) + GO TO 200 +C + 115 SUM = SUM + (DX(I)/XMAX)**2 + GO TO 200 +C +C PREPARE FOR PHASE 3. +C + 75 SUM = (SUM * XMAX) * XMAX +C +C FOR REAL OR D.P. SET HITEST = CUTHI/N +C FOR COMPLEX SET HITEST = CUTHI/(2*N) +C + 85 HITEST = CUTHI / N +C +C PHASE 3. SUM IS MID-RANGE. NO SCALING. +C + DO 95 J = I,NN,INCX + IF (ABS(DX(J)) .GE. HITEST) GO TO 100 + 95 SUM = SUM + DX(J)**2 + DNRM2 = SQRT(SUM) + GO TO 300 +C + 200 CONTINUE + I = I + INCX + IF (I .LE. NN) GO TO 20 +C +C END OF MAIN LOOP. +C +C COMPUTE SQUARE ROOT AND ADJUST FOR SCALING. +C + DNRM2 = XMAX * SQRT(SUM) + 300 CONTINUE + RETURN + END +*DECK DSCAL + SUBROUTINE DSCAL (N, DA, DX, INCX) +C***BEGIN PROLOGUE DSCAL +C***PURPOSE Multiply a vector by a constant. +C***CATEGORY D1A6 +C***TYPE DOUBLE PRECISION (SSCAL-S, DSCAL-D, CSCAL-C) +C***KEYWORDS BLAS, LINEAR ALGEBRA, SCALE, VECTOR +C***AUTHOR Lawson, C. L., (JPL) +C Hanson, R. J., (SNLA) +C Kincaid, D. R., (U. of Texas) +C Krogh, F. T., (JPL) +C***DESCRIPTION +C +C B L A S Subprogram +C Description of Parameters +C +C --Input-- +C N number of elements in input vector(s) +C DA double precision scale factor +C DX double precision vector with N elements +C INCX storage spacing between elements of DX +C +C --Output-- +C DX double precision result (unchanged if N.LE.0) +C +C Replace double precision DX by double precision DA*DX. +C For I = 0 to N-1, replace DX(IX+I*INCX) with DA * DX(IX+I*INCX), +C where IX = 1 if INCX .GE. 0, else IX = 1+(1-N)*INCX. +C +C***REFERENCES C. L. Lawson, R. J. Hanson, D. R. Kincaid and F. T. +C Krogh, Basic linear algebra subprograms for Fortran +C usage, Algorithm No. 539, Transactions on Mathematical +C Software 5, 3 (September 1979), pp. 308-323. +C***ROUTINES CALLED (NONE) +C***REVISION HISTORY (YYMMDD) +C 791001 DATE WRITTEN +C 890831 Modified array declarations. (WRB) +C 890831 REVISION DATE from Version 3.2 +C 891214 Prologue converted to Version 4.0 format. (BAB) +C 900821 Modified to correct problem with a negative increment. +C (WRB) +C 920501 Reformatted the REFERENCES section. (WRB) +C***END PROLOGUE DSCAL + DOUBLE PRECISION DA, DX(*) + INTEGER I, INCX, IX, M, MP1, N +C***FIRST EXECUTABLE STATEMENT DSCAL + IF (N .LE. 0) RETURN + IF (INCX .EQ. 1) GOTO 20 +C +C Code for increment not equal to 1. +C + IX = 1 + IF (INCX .LT. 0) IX = (-N+1)*INCX + 1 + DO 10 I = 1,N + DX(IX) = DA*DX(IX) + IX = IX + INCX + 10 CONTINUE + RETURN +C +C Code for increment equal to 1. +C +C Clean-up loop so remaining vector length is a multiple of 5. +C + 20 M = MOD(N,5) + IF (M .EQ. 0) GOTO 40 + DO 30 I = 1,M + DX(I) = DA*DX(I) + 30 CONTINUE + IF (N .LT. 5) RETURN + 40 MP1 = M + 1 + DO 50 I = MP1,N,5 + DX(I) = DA*DX(I) + DX(I+1) = DA*DX(I+1) + DX(I+2) = DA*DX(I+2) + DX(I+3) = DA*DX(I+3) + DX(I+4) = DA*DX(I+4) + 50 CONTINUE + RETURN + END +*DECK IDAMAX + INTEGER FUNCTION IDAMAX (N, DX, INCX) +C***BEGIN PROLOGUE IDAMAX +C***PURPOSE Find the smallest index of that component of a vector +C having the maximum magnitude. +C***CATEGORY D1A2 +C***TYPE DOUBLE PRECISION (ISAMAX-S, IDAMAX-D, ICAMAX-C) +C***KEYWORDS BLAS, LINEAR ALGEBRA, MAXIMUM COMPONENT, VECTOR +C***AUTHOR Lawson, C. L., (JPL) +C Hanson, R. J., (SNLA) +C Kincaid, D. R., (U. of Texas) +C Krogh, F. T., (JPL) +C***DESCRIPTION +C +C B L A S Subprogram +C Description of Parameters +C +C --Input-- +C N number of elements in input vector(s) +C DX double precision vector with N elements +C INCX storage spacing between elements of DX +C +C --Output-- +C IDAMAX smallest index (zero if N .LE. 0) +C +C Find smallest index of maximum magnitude of double precision DX. +C IDAMAX = first I, I = 1 to N, to maximize ABS(DX(IX+(I-1)*INCX)), +C where IX = 1 if INCX .GE. 0, else IX = 1+(1-N)*INCX. +C +C***REFERENCES C. L. Lawson, R. J. Hanson, D. R. Kincaid and F. T. +C Krogh, Basic linear algebra subprograms for Fortran +C usage, Algorithm No. 539, Transactions on Mathematical +C Software 5, 3 (September 1979), pp. 308-323. +C***ROUTINES CALLED (NONE) +C***REVISION HISTORY (YYMMDD) +C 791001 DATE WRITTEN +C 890531 Changed all specific intrinsics to generic. (WRB) +C 890531 REVISION DATE from Version 3.2 +C 891214 Prologue converted to Version 4.0 format. (BAB) +C 900821 Modified to correct problem with a negative increment. +C (WRB) +C 920501 Reformatted the REFERENCES section. (WRB) +C***END PROLOGUE IDAMAX + DOUBLE PRECISION DX(*), DMAX, XMAG + INTEGER I, INCX, IX, N +C***FIRST EXECUTABLE STATEMENT IDAMAX + IDAMAX = 0 + IF (N .LE. 0) RETURN + IDAMAX = 1 + IF (N .EQ. 1) RETURN +C + IF (INCX .EQ. 1) GOTO 20 +C +C Code for increments not equal to 1. +C + IX = 1 + IF (INCX .LT. 0) IX = (-N+1)*INCX + 1 + DMAX = ABS(DX(IX)) + IX = IX + INCX + DO 10 I = 2,N + XMAG = ABS(DX(IX)) + IF (XMAG .GT. DMAX) THEN + IDAMAX = I + DMAX = XMAG + ENDIF + IX = IX + INCX + 10 CONTINUE + RETURN +C +C Code for increments equal to 1. +C + 20 DMAX = ABS(DX(1)) + DO 30 I = 2,N + XMAG = ABS(DX(I)) + IF (XMAG .GT. DMAX) THEN + IDAMAX = I + DMAX = XMAG + ENDIF + 30 CONTINUE + RETURN + END +*DECK XERRWD + SUBROUTINE XERRWD (MSG, NMES, NERR, LEVEL, NI, I1, I2, NR, R1, R2) +C***BEGIN PROLOGUE XERRWD +C***SUBSIDIARY +C***PURPOSE Write error message with values. +C***CATEGORY R3C +C***TYPE DOUBLE PRECISION (XERRWV-S, XERRWD-D) +C***AUTHOR Hindmarsh, Alan C., (LLNL) +C***DESCRIPTION +C +C Subroutines XERRWD, XSETF, XSETUN, and the function routine IXSAV, +C as given here, constitute a simplified version of the SLATEC error +C handling package. +C +C All arguments are input arguments. +C +C MSG = The message (character array). +C NMES = The length of MSG (number of characters). +C NERR = The error number (not used). +C LEVEL = The error level.. +C 0 or 1 means recoverable (control returns to caller). +C 2 means fatal (run is aborted--see note below). +C NI = Number of integers (0, 1, or 2) to be printed with message. +C I1,I2 = Integers to be printed, depending on NI. +C NR = Number of reals (0, 1, or 2) to be printed with message. +C R1,R2 = Reals to be printed, depending on NR. +C +C Note.. this routine is machine-dependent and specialized for use +C in limited context, in the following ways.. +C 1. The argument MSG is assumed to be of type CHARACTER, and +C the message is printed with a format of (1X,A). +C 2. The message is assumed to take only one line. +C Multi-line messages are generated by repeated calls. +C 3. If LEVEL = 2, control passes to the statement STOP +C to abort the run. This statement may be machine-dependent. +C 4. R1 and R2 are assumed to be in double precision and are printed +C in D21.13 format. +C +C***ROUTINES CALLED IXSAV +C***REVISION HISTORY (YYMMDD) +C 920831 DATE WRITTEN +C 921118 Replaced MFLGSV/LUNSAV by IXSAV. (ACH) +C 930329 Modified prologue to SLATEC format. (FNF) +C 930407 Changed MSG from CHARACTER*1 array to variable. (FNF) +C 930922 Minor cosmetic change. (FNF) +C***END PROLOGUE XERRWD +C +C*Internal Notes: +C +C For a different default logical unit number, IXSAV (or a subsidiary +C routine that it calls) will need to be modified. +C For a different run-abort command, change the statement following +C statement 100 at the end. +C----------------------------------------------------------------------- +C Subroutines called by XERRWD.. None +C Function routine called by XERRWD.. IXSAV +C----------------------------------------------------------------------- +C**End +C +C Declare arguments. +C + DOUBLE PRECISION R1, R2 + INTEGER NMES, NERR, LEVEL, NI, I1, I2, NR + CHARACTER*(*) MSG +C +C Declare local variables. +C + INTEGER LUNIT, IXSAV, MESFLG +C +C Get logical unit number and message print flag. +C +C***FIRST EXECUTABLE STATEMENT XERRWD + LUNIT = IXSAV (1, 0, .FALSE.) + MESFLG = IXSAV (2, 0, .FALSE.) + IF (MESFLG .EQ. 0) GO TO 100 +C +C Write the message. +C + WRITE (LUNIT,10) MSG + 10 FORMAT(1X,A) + IF (NI .EQ. 1) WRITE (LUNIT, 20) I1 + 20 FORMAT(6X,'In above message, I1 =',I10) + IF (NI .EQ. 2) WRITE (LUNIT, 30) I1,I2 + 30 FORMAT(6X,'In above message, I1 =',I10,3X,'I2 =',I10) + IF (NR .EQ. 1) WRITE (LUNIT, 40) R1 + 40 FORMAT(6X,'In above message, R1 =',D21.13) + IF (NR .EQ. 2) WRITE (LUNIT, 50) R1,R2 + 50 FORMAT(6X,'In above, R1 =',D21.13,3X,'R2 =',D21.13) +C +C Abort the run if LEVEL = 2. +C + 100 IF (LEVEL .NE. 2) RETURN + STOP +C----------------------- End of Subroutine XERRWD ---------------------- + END +*DECK XSETF + SUBROUTINE XSETF (MFLAG) +C***BEGIN PROLOGUE XSETF +C***PURPOSE Reset the error print control flag. +C***CATEGORY R3A +C***TYPE ALL (XSETF-A) +C***KEYWORDS ERROR CONTROL +C***AUTHOR Hindmarsh, Alan C., (LLNL) +C***DESCRIPTION +C +C XSETF sets the error print control flag to MFLAG: +C MFLAG=1 means print all messages (the default). +C MFLAG=0 means no printing. +C +C***SEE ALSO XERRWD, XERRWV +C***REFERENCES (NONE) +C***ROUTINES CALLED IXSAV +C***REVISION HISTORY (YYMMDD) +C 921118 DATE WRITTEN +C 930329 Added SLATEC format prologue. (FNF) +C 930407 Corrected SEE ALSO section. (FNF) +C 930922 Made user-callable, and other cosmetic changes. (FNF) +C***END PROLOGUE XSETF +C +C Subroutines called by XSETF.. None +C Function routine called by XSETF.. IXSAV +C----------------------------------------------------------------------- +C**End + INTEGER MFLAG, JUNK, IXSAV +C +C***FIRST EXECUTABLE STATEMENT XSETF + IF (MFLAG .EQ. 0 .OR. MFLAG .EQ. 1) JUNK = IXSAV (2,MFLAG,.TRUE.) + RETURN +C----------------------- End of Subroutine XSETF ----------------------- + END +*DECK XSETUN + SUBROUTINE XSETUN (LUN) +C***BEGIN PROLOGUE XSETUN +C***PURPOSE Reset the logical unit number for error messages. +C***CATEGORY R3B +C***TYPE ALL (XSETUN-A) +C***KEYWORDS ERROR CONTROL +C***DESCRIPTION +C +C XSETUN sets the logical unit number for error messages to LUN. +C +C***AUTHOR Hindmarsh, Alan C., (LLNL) +C***SEE ALSO XERRWD, XERRWV +C***REFERENCES (NONE) +C***ROUTINES CALLED IXSAV +C***REVISION HISTORY (YYMMDD) +C 921118 DATE WRITTEN +C 930329 Added SLATEC format prologue. (FNF) +C 930407 Corrected SEE ALSO section. (FNF) +C 930922 Made user-callable, and other cosmetic changes. (FNF) +C***END PROLOGUE XSETUN +C +C Subroutines called by XSETUN.. None +C Function routine called by XSETUN.. IXSAV +C----------------------------------------------------------------------- +C**End + INTEGER LUN, JUNK, IXSAV +C +C***FIRST EXECUTABLE STATEMENT XSETUN + IF (LUN .GT. 0) JUNK = IXSAV (1,LUN,.TRUE.) + RETURN +C----------------------- End of Subroutine XSETUN ---------------------- + END +*DECK IXSAV + INTEGER FUNCTION IXSAV (IPAR, IVALUE, ISET) +C***BEGIN PROLOGUE IXSAV +C***SUBSIDIARY +C***PURPOSE Save and recall error message control parameters. +C***CATEGORY R3C +C***TYPE ALL (IXSAV-A) +C***AUTHOR Hindmarsh, Alan C., (LLNL) +C***DESCRIPTION +C +C IXSAV saves and recalls one of two error message parameters: +C LUNIT, the logical unit number to which messages are printed, and +C MESFLG, the message print flag. +C This is a modification of the SLATEC library routine J4SAVE. +C +C Saved local variables.. +C LUNIT = Logical unit number for messages. The default is obtained +C by a call to IUMACH (may be machine-dependent). +C MESFLG = Print control flag.. +C 1 means print all messages (the default). +C 0 means no printing. +C +C On input.. +C IPAR = Parameter indicator (1 for LUNIT, 2 for MESFLG). +C IVALUE = The value to be set for the parameter, if ISET = .TRUE. +C ISET = Logical flag to indicate whether to read or write. +C If ISET = .TRUE., the parameter will be given +C the value IVALUE. If ISET = .FALSE., the parameter +C will be unchanged, and IVALUE is a dummy argument. +C +C On return.. +C IXSAV = The (old) value of the parameter. +C +C***SEE ALSO XERRWD, XERRWV +C***ROUTINES CALLED IUMACH +C***REVISION HISTORY (YYMMDD) +C 921118 DATE WRITTEN +C 930329 Modified prologue to SLATEC format. (FNF) +C 930915 Added IUMACH call to get default output unit. (ACH) +C 930922 Minor cosmetic changes. (FNF) +C 010425 Type declaration for IUMACH added. (ACH) +C***END PROLOGUE IXSAV +C +C Subroutines called by IXSAV.. None +C Function routine called by IXSAV.. IUMACH +C----------------------------------------------------------------------- +C**End + LOGICAL ISET + INTEGER IPAR, IVALUE +C----------------------------------------------------------------------- + INTEGER IUMACH, LUNIT, MESFLG +C----------------------------------------------------------------------- +C The following Fortran-77 declaration is to cause the values of the +C listed (local) variables to be saved between calls to this routine. +C----------------------------------------------------------------------- + SAVE LUNIT, MESFLG + DATA LUNIT/-1/, MESFLG/1/ +C +C***FIRST EXECUTABLE STATEMENT IXSAV + IF (IPAR .EQ. 1) THEN + IF (LUNIT .EQ. -1) LUNIT = IUMACH() + IXSAV = LUNIT + IF (ISET) LUNIT = IVALUE + ENDIF +C + IF (IPAR .EQ. 2) THEN + IXSAV = MESFLG + IF (ISET) MESFLG = IVALUE + ENDIF +C + RETURN +C----------------------- End of Function IXSAV ------------------------- + END +*DECK IUMACH + INTEGER FUNCTION IUMACH() +C***BEGIN PROLOGUE IUMACH +C***PURPOSE Provide standard output unit number. +C***CATEGORY R1 +C***TYPE INTEGER (IUMACH-I) +C***KEYWORDS MACHINE CONSTANTS +C***AUTHOR Hindmarsh, Alan C., (LLNL) +C***DESCRIPTION +C *Usage: +C INTEGER LOUT, IUMACH +C LOUT = IUMACH() +C +C *Function Return Values: +C LOUT : the standard logical unit for Fortran output. +C +C***REFERENCES (NONE) +C***ROUTINES CALLED (NONE) +C***REVISION HISTORY (YYMMDD) +C 930915 DATE WRITTEN +C 930922 Made user-callable, and other cosmetic changes. (FNF) +C***END PROLOGUE IUMACH +C +C*Internal Notes: +C The built-in value of 6 is standard on a wide range of Fortran +C systems. This may be machine-dependent. +C**End +C***FIRST EXECUTABLE STATEMENT IUMACH + IUMACH = 6 +C + RETURN +C----------------------- End of Function IUMACH ------------------------ + END diff --git a/applications/PUfoam/MoDeNaModels/foamAging/src/src/physicalProperties.f90 b/applications/PUfoam/MoDeNaModels/foamAging/src/src/physicalProperties.f90 new file mode 100644 index 000000000..190dd51df --- /dev/null +++ b/applications/PUfoam/MoDeNaModels/foamAging/src/src/physicalProperties.f90 @@ -0,0 +1,501 @@ +!> @file +!! subroutines for calculation of physical properties of polymer and blowing +!! agents using Modena calls +!! @author Michal Vonka +!! @author Pavel Ferkl +!! @ingroup foam_aging +module physicalProperties + use constants + use fmodena + implicit none + integer :: solModel(3),diffModel(3) + !modena variables + integer(c_int) :: ret + type(c_ptr) :: rhopModena = c_null_ptr + type(c_ptr) :: rhopInputs = c_null_ptr + type(c_ptr) :: rhopOutputs = c_null_ptr + integer(c_size_t) :: rhopTemppos + type(c_ptr) :: kfoamModena = c_null_ptr + type(c_ptr) :: kfoamInputs = c_null_ptr + type(c_ptr) :: kfoamOutputs = c_null_ptr + integer(c_size_t) :: kfoamEpspos + integer(c_size_t) :: kfoamDcellpos + integer(c_size_t) :: kfoamFstrutpos + integer(c_size_t) :: kfoamKgaspos + integer(c_size_t) :: kfoamTemppos + type(c_ptr) :: kgasModena = c_null_ptr + type(c_ptr) :: kgasInputs = c_null_ptr + type(c_ptr) :: kgasOutputs = c_null_ptr + integer(c_size_t) :: kgasTemppos + integer(c_size_t) :: kgasXco2pos + integer(c_size_t) :: kgasXairpos + integer(c_size_t) :: kgasXcyppos + type(c_ptr) :: kcdModena = c_null_ptr + type(c_ptr) :: kcdInputs = c_null_ptr + type(c_ptr) :: kcdOutputs = c_null_ptr + integer(c_size_t) :: kcdTemppos + type(c_ptr) :: kairModena = c_null_ptr + type(c_ptr) :: kairInputs = c_null_ptr + type(c_ptr) :: kairOutputs = c_null_ptr + integer(c_size_t) :: kairTemppos + type(c_ptr) :: kcypModena = c_null_ptr + type(c_ptr) :: kcypInputs = c_null_ptr + type(c_ptr) :: kcypOutputs = c_null_ptr + integer(c_size_t) :: kcypTemppos + type(c_ptr) :: scdModena = c_null_ptr + type(c_ptr) :: scdInputs = c_null_ptr + type(c_ptr) :: scdOutputs = c_null_ptr + integer(c_size_t) :: scdTemppos + type(c_ptr) :: sairModena = c_null_ptr + type(c_ptr) :: sairInputs = c_null_ptr + type(c_ptr) :: sairOutputs = c_null_ptr + integer(c_size_t) :: sairTemppos + type(c_ptr) :: scypModena = c_null_ptr + type(c_ptr) :: scypInputs = c_null_ptr + type(c_ptr) :: scypOutputs = c_null_ptr + integer(c_size_t) :: scypTemppos + type(c_ptr) :: dcdModena = c_null_ptr + type(c_ptr) :: dcdInputs = c_null_ptr + type(c_ptr) :: dcdOutputs = c_null_ptr + integer(c_size_t) :: dcdTemppos + type(c_ptr) :: dcypModena = c_null_ptr + type(c_ptr) :: dcypInputs = c_null_ptr + type(c_ptr) :: dcypOutputs = c_null_ptr + integer(c_size_t) :: dcypTemppos + type(c_ptr) :: do2Modena = c_null_ptr + type(c_ptr) :: do2Inputs = c_null_ptr + type(c_ptr) :: do2Outputs = c_null_ptr + integer(c_size_t) :: do2Temppos + type(c_ptr) :: dn2Modena = c_null_ptr + type(c_ptr) :: dn2Inputs = c_null_ptr + type(c_ptr) :: dn2Outputs = c_null_ptr + integer(c_size_t) :: dn2Temppos +contains +!********************************BEGINNING************************************* +!> creates Modena models +subroutine createModels +! rhopModena = modena_model_new (client, c_char_"polymerDensity"//c_null_char); +! rhopInputs = modena_inputs_new (rhopModena); +! rhopOutputs = modena_outputs_new (rhopModena); +! rhopTemppos = modena_model_inputs_argPos(rhopModena, c_char_"T"//c_null_char); +! call modena_model_argPos_check(rhopModena) + kfoamModena = modena_model_new (c_char_"foamConductivity"//c_null_char); + kfoamInputs = modena_inputs_new (kfoamModena); + kfoamOutputs = modena_outputs_new (kfoamModena); + kfoamEpspos = modena_model_inputs_argPos(& + kfoamModena, c_char_"eps"//c_null_char); + kfoamDcellpos = modena_model_inputs_argPos(& + kfoamModena, c_char_"dcell"//c_null_char); + kfoamFstrutpos = modena_model_inputs_argPos(& + kfoamModena, c_char_"fstrut"//c_null_char); + kfoamKgaspos = modena_model_inputs_argPos(& + kfoamModena, c_char_"kgas"//c_null_char); + kfoamTemppos = modena_model_inputs_argPos(& + kfoamModena, c_char_"T"//c_null_char); + call modena_model_argPos_check(kfoamModena) + write(*,*) 'loading gasMixtureConductivity model' + kgasModena = modena_model_new (& + c_char_"gasMixtureConductivity"//c_null_char); + write(*,*) 'loading gasMixtureConductivity model OK' + kgasInputs = modena_inputs_new (kgasModena); + kgasOutputs = modena_outputs_new (kgasModena); + write(*,*) 'setting inputs' + kgasTemppos = modena_model_inputs_argPos(kgasModena, c_char_"T"//c_null_char); + kgasXco2pos = modena_model_inputs_argPos(kgasModena, c_char_"x[A=CO2]"//c_null_char); + write(*,*) 'setting inputs OK' + kgasXairpos = modena_model_inputs_argPos(kgasModena, c_char_"x[A=Air]"//c_null_char); + kgasXcyppos = modena_model_inputs_argPos(kgasModena, c_char_"x[A=CyP]"//c_null_char); + call modena_model_argPos_check(kgasModena) + kcdModena = modena_model_new (& + c_char_"gas_thermal_conductivity[A=CO2]"//c_null_char); + kcdInputs = modena_inputs_new (kcdModena); + kcdOutputs = modena_outputs_new (kcdModena); + kcdTemppos = modena_model_inputs_argPos(kcdModena, c_char_"T"//c_null_char); + call modena_model_argPos_check(kcdModena) + kairModena = modena_model_new (& + c_char_"gas_thermal_conductivity[A=Air]"//c_null_char); + kairInputs = modena_inputs_new (kairModena); + kairOutputs = modena_outputs_new (kairModena); + kairTemppos = modena_model_inputs_argPos(kairModena, c_char_"T"//c_null_char); + call modena_model_argPos_check(kairModena) + kcypModena = modena_model_new (& + c_char_"gas_thermal_conductivity[A=CyP]"//c_null_char); + kcypInputs = modena_inputs_new (kcypModena); + kcypOutputs = modena_outputs_new (kcypModena); + kcypTemppos = modena_model_inputs_argPos(kcypModena, c_char_"T"//c_null_char); + call modena_model_argPos_check(kcypModena) + if (solModel(1)==1) then + sairModena = modena_model_new (& + c_char_"solubilityPol[A=Air]"//c_null_char); + sairInputs = modena_inputs_new (sairModena); + sairOutputs = modena_outputs_new (sairModena); + sairTemppos = modena_model_inputs_argPos(& + sairModena, c_char_"T"//c_null_char); + call modena_model_argPos_check(sairModena) + endif + if (solModel(2)==1) then + scdModena = modena_model_new (& + c_char_"solubilityPol[A=CO2]"//c_null_char); + scdInputs = modena_inputs_new (scdModena); + scdOutputs = modena_outputs_new (scdModena); + scdTemppos = modena_model_inputs_argPos(& + scdModena, c_char_"T"//c_null_char); + call modena_model_argPos_check(scdModena) + endif + if (solModel(3)==1) then + scypModena = modena_model_new (& + c_char_"solubilityPol[A=CyP]"//c_null_char); + scypInputs = modena_inputs_new (scypModena); + scypOutputs = modena_outputs_new (scypModena); + scypTemppos = modena_model_inputs_argPos(& + scypModena, c_char_"T"//c_null_char); + call modena_model_argPos_check(scypModena) + endif + if (diffModel(1)==1) then + do2Modena = modena_model_new (& + c_char_"diffusivityPol[A=O2]"//c_null_char); + do2Inputs = modena_inputs_new (do2Modena); + do2Outputs = modena_outputs_new (do2Modena); + do2Temppos = modena_model_inputs_argPos(& + do2Modena, c_char_"T"//c_null_char); + call modena_model_argPos_check(do2Modena) + dn2Modena = modena_model_new (& + c_char_"diffusivityPol[A=N2]"//c_null_char); + dn2Inputs = modena_inputs_new (dn2Modena); + dn2Outputs = modena_outputs_new (dn2Modena); + dn2Temppos = modena_model_inputs_argPos(& + dn2Modena, c_char_"T"//c_null_char); + call modena_model_argPos_check(dn2Modena) + endif + if (diffModel(2)==1) then + dcdModena = modena_model_new (& + c_char_"diffusivityPol[A=CO2]"//c_null_char); + dcdInputs = modena_inputs_new (dcdModena); + dcdOutputs = modena_outputs_new (dcdModena); + dcdTemppos = modena_model_inputs_argPos(& + dcdModena, c_char_"T"//c_null_char); + call modena_model_argPos_check(dcdModena) + endif + if (diffModel(3)==1) then + dcypModena = modena_model_new (& + c_char_"diffusivityPol[A=CyP]"//c_null_char); + dcypInputs = modena_inputs_new (dcypModena); + dcypOutputs = modena_outputs_new (dcypModena); + dcypTemppos = modena_model_inputs_argPos(& + dcypModena, c_char_"T"//c_null_char); + call modena_model_argPos_check(dcypModena) + endif +end subroutine createModels +!***********************************END**************************************** + + +!********************************BEGINNING************************************* +!> destroys Modena models +subroutine destroyModels +! call modena_inputs_destroy (rhopInputs); +! call modena_outputs_destroy (rhopOutputs); +! call modena_model_destroy (rhopModena); + call modena_inputs_destroy (kfoamInputs); + call modena_outputs_destroy (kfoamOutputs); + call modena_model_destroy (kfoamModena); + call modena_inputs_destroy (kgasInputs); + call modena_outputs_destroy (kgasOutputs); + call modena_model_destroy (kgasModena); + call modena_inputs_destroy (kcdInputs); + call modena_outputs_destroy (kcdOutputs); + call modena_model_destroy (kcdModena); + call modena_inputs_destroy (kairInputs); + call modena_outputs_destroy (kairOutputs); + call modena_model_destroy (kairModena); + call modena_inputs_destroy (kcypInputs); + call modena_outputs_destroy (kcypOutputs); + call modena_model_destroy (kcypModena); + call modena_inputs_destroy (scdInputs); + call modena_outputs_destroy (scdOutputs); + call modena_model_destroy (scdModena); + call modena_inputs_destroy (sairInputs); + call modena_outputs_destroy (sairOutputs); + call modena_model_destroy (sairModena); + call modena_inputs_destroy (scypInputs); + call modena_outputs_destroy (scypOutputs); + call modena_model_destroy (scypModena); + call modena_inputs_destroy (dcdInputs); + call modena_outputs_destroy (dcdOutputs); + call modena_model_destroy (dcdModena); + call modena_inputs_destroy (dcypInputs); + call modena_outputs_destroy (dcypOutputs); + call modena_model_destroy (dcypModena); + call modena_inputs_destroy (do2Inputs); + call modena_outputs_destroy (do2Outputs); + call modena_model_destroy (do2Modena); + call modena_inputs_destroy (dn2Inputs); + call modena_outputs_destroy (dn2Outputs); + call modena_model_destroy (dn2Modena); +end subroutine destroyModels +!***********************************END**************************************** + + +!********************************BEGINNING************************************* +!> calculation of density of polymer +real(dp) function polymerDensity(temp) + real(dp), intent(in) :: temp + call modena_inputs_set(rhopInputs, rhopTemppos, temp) + ret = modena_model_call (rhopModena, rhopInputs, rhopOutputs) + if(ret /= 0) then + call exit(ret) + endif + polymerDensity=modena_outputs_get(rhopOutputs, 0_c_size_t) +end function polymerDensity +!***********************************END**************************************** + + +!********************************BEGINNING************************************* +!> thermal conductivity of mixture of blowing agents +real(dp) function gasConductivity(temp,xco2,xair,xcyp) + real(dp), intent(in) :: temp,xco2,xair,xcyp + call modena_inputs_set(kgasInputs, kgasTemppos, temp) + call modena_inputs_set(kgasInputs, kgasXco2pos, xco2) + call modena_inputs_set(kgasInputs, kgasXairpos, xair) + call modena_inputs_set(kgasInputs, kgasXcyppos, xcyp) + ret = modena_model_call (kgasModena, kgasInputs, kgasOutputs) + if(ret /= 0) then + call exit(ret) + endif + gasConductivity=modena_outputs_get(kgasOutputs, 0_c_size_t) +end function gasConductivity +!***********************************END**************************************** + + +!********************************BEGINNING************************************* +!> thermal conductivity of carbon dioxide +real(dp) function cdConductivity(temp) + real(dp), intent(in) :: temp + call modena_inputs_set(kcdInputs, kcdTemppos, temp) + ret = modena_model_call (kcdModena, kcdInputs, kcdOutputs) + if(ret /= 0) then + call exit(ret) + endif + cdConductivity=modena_outputs_get(kcdOutputs, 0_c_size_t) +end function cdConductivity +!***********************************END**************************************** + + +!********************************BEGINNING************************************* +!> thermal conductivity of air +real(dp) function airConductivity(temp) + real(dp), intent(in) :: temp + call modena_inputs_set(kairInputs, kairTemppos, temp) + ret = modena_model_call (kairModena, kairInputs, kairOutputs) + if(ret /= 0) then + call exit(ret) + endif + airConductivity=modena_outputs_get(kairOutputs, 0_c_size_t) +end function airConductivity +!***********************************END**************************************** + + +!********************************BEGINNING************************************* +!> thermal conductivity of cyclo pentane +real(dp) function cypConductivity(temp) + real(dp), intent(in) :: temp + call modena_inputs_set(kcypInputs, kcypTemppos, temp) + ret = modena_model_call (kcypModena, kcypInputs, kcypOutputs) + if(ret /= 0) then + call exit(ret) + endif + cypConductivity=modena_outputs_get(kcypOutputs, 0_c_size_t) +end function cypConductivity +!***********************************END**************************************** + + +!********************************BEGINNING************************************* +!> thermal conductivity of nitrogen +real(dp) function nitrConductivity(temp) + real(dp), intent(in) :: temp + nitrConductivity=(0.3918e-3_dp)+(0.9814e-4_dp)*temp+& + (-5.0660e-8_dp)*temp**2+(1.503479e-11_dp)*temp**3 +end function nitrConductivity +!***********************************END**************************************** + + +!********************************BEGINNING************************************* +!> thermal conductivity of oxygen +real(dp) function oxyConductivity(temp) + real(dp), intent(in) :: temp + oxyConductivity=(-0.3272e-3_dp)+(0.9965e-4_dp)*temp+& + (-3.7426e-8_dp)*temp**2+(0.973012e-11_dp)*temp**3 +end function oxyConductivity +!***********************************END**************************************** + + +!********************************BEGINNING************************************* +!> solubility of carbon dioxide +real(dp) function cdSolubility(temp) + real(dp), intent(in) :: temp + call modena_inputs_set(scdInputs, scdTemppos, temp) + ret = modena_model_call (scdModena, scdInputs, scdOutputs) + if(ret /= 0) then + call exit(ret) + endif + cdSolubility=modena_outputs_get(scdOutputs, 0_c_size_t) +end function cdSolubility +!***********************************END**************************************** + + +!********************************BEGINNING************************************* +!> solubility of air +real(dp) function airSolubility(temp) + real(dp), intent(in) :: temp + call modena_inputs_set(sairInputs, sairTemppos, temp) + ret = modena_model_call (sairModena, sairInputs, sairOutputs) + if(ret /= 0) then + call exit(ret) + endif + airSolubility=modena_outputs_get(sairOutputs, 0_c_size_t) +end function airSolubility +!***********************************END**************************************** + + +!********************************BEGINNING************************************* +!> solubility of cyclo pentane +real(dp) function cypSolubility(temp) + real(dp), intent(in) :: temp + call modena_inputs_set(scypInputs, scypTemppos, temp) + ret = modena_model_call (scypModena, scypInputs, scypOutputs) + if(ret /= 0) then + call exit(ret) + endif + cypSolubility=modena_outputs_get(scypOutputs, 0_c_size_t) +end function cypSolubility +!***********************************END**************************************** + + +!********************************BEGINNING************************************* +!> diffusivity of carbon dioxide +real(dp) function cdDiffusivity(temp) + real(dp), intent(in) :: temp + call modena_inputs_set(dcdInputs, dcdTemppos, temp) + ret = modena_model_call (dcdModena, dcdInputs, dcdOutputs) + if(ret /= 0) then + call exit(ret) + endif + cdDiffusivity=modena_outputs_get(dcdOutputs, 0_c_size_t) +end function cdDiffusivity +!***********************************END**************************************** + + +!********************************BEGINNING************************************* +!> diffusivity of cyclo pentane +real(dp) function cypDiffusivity(temp) + real(dp), intent(in) :: temp + call modena_inputs_set(dcypInputs, dcypTemppos, temp) + ret = modena_model_call (dcypModena, dcypInputs, dcypOutputs) + if(ret /= 0) then + call exit(ret) + endif + cypDiffusivity=modena_outputs_get(dcypOutputs, 0_c_size_t) +end function cypDiffusivity +!***********************************END**************************************** + + +!********************************BEGINNING************************************* +!> diffusivity of air +real(dp) function airDiffusivity(temp) + real(dp), intent(in) :: temp + call modena_inputs_set(do2Inputs, do2Temppos, temp) + ret = modena_model_call (do2Modena, do2Inputs, do2Outputs) + if(ret /= 0) then + call exit(ret) + endif + airDiffusivity=0.21_dp*modena_outputs_get(do2Outputs, 0_c_size_t) + call modena_inputs_set(dn2Inputs, dn2Temppos, temp) + ret = modena_model_call (dn2Modena, dn2Inputs, dn2Outputs) + if(ret /= 0) then + call exit(ret) + endif + airDiffusivity=& + airDiffusivity+0.79_dp*modena_outputs_get(dn2Outputs, 0_c_size_t) +end function airDiffusivity +!***********************************END**************************************** + + +!********************************BEGINNING************************************* +!> heat capacity of carbon dioxide at constant pressure (J/mol/K) +!! [link](http://webbook.nist.gov/cgi/cbook.cgi?ID=C124389&Units=SI&Mask=1#Thermo-Gas) +real(dp) function cdHeatCapacity(temp) + real(dp), intent(in) :: temp + real(dp) :: & + t,& + a=24.99735_dp,& + b=55.18696_dp,& + c=-33.69137_dp,& + d=7.948387_dp,& + e=-0.136638_dp + t=temp/1e3 + cdHeatCapacity=a+b*t+c*t**2+d*t**3+e/t**2 +end function cdHeatCapacity +!***********************************END**************************************** + + +!********************************BEGINNING************************************* +!> heat capacity of cyclo-pentane at constant pressure (J/mol/K) +!! fitted to data from [link](http://webbook.nist.gov/cgi/cbook.cgi?ID=C287923&Units=SI&Mask=1#Thermo-Gas) +real(dp) function cypHeatCapacity(temp) + real(dp), intent(in) :: temp + real(dp) :: & + t,& + a=-25.6132057_dp,& + b=226.4176882_dp,& + c=574.2688767_dp,& + d=-670.5517907_dp,& + e=0.6765321_dp + t=temp/1e3 + cypHeatCapacity=a+b*t+c*t**2+d*t**3+e/t**2 +end function cypHeatCapacity +!***********************************END**************************************** + + +!********************************BEGINNING************************************* +!> heat capacity of air at constant pressure (J/mol/K) +real(dp) function airHeatCapacity(temp) + real(dp), intent(in) :: temp + airHeatCapacity=0.21_dp*oxyHeatCapacity(temp)+0.79_dp*nitrHeatCapacity(temp) +end function airHeatCapacity +!***********************************END**************************************** + + +!********************************BEGINNING************************************* +!> heat capacity of nitrogen at constant pressure (J/mol/K) +!! [link](http://webbook.nist.gov/cgi/cbook.cgi?ID=C7727379&Units=SI&Mask=1#Thermo-Gas) +real(dp) function nitrHeatCapacity(temp) + real(dp), intent(in) :: temp + real(dp) :: & + t,& + a=28.98641_dp,& + b=1.853978_dp,& + c=-9.647459_dp,& + d=16.63537_dp,& + e=0.000117_dp + t=temp/1e3 + nitrHeatCapacity=a+b*t+c*t**2+d*t**3+e/t**2 +end function nitrHeatCapacity +!***********************************END**************************************** + + +!********************************BEGINNING************************************* +!> heat capacity of oxygen at constant pressure (J/mol/K) +!! [link](http://webbook.nist.gov/cgi/cbook.cgi?ID=C7782447&Units=SI&Mask=1#Thermo-Gas) +real(dp) function oxyHeatCapacity(temp) + real(dp), intent(in) :: temp + real(dp) :: & + t,& + a=31.32234_dp,& + b=-20.23531_dp,& + c=57.86644_dp,& + d=-36.50624_dp,& + e=-0.007374_dp + t=temp/1e3 + oxyHeatCapacity=a+b*t+c*t**2+d*t**3+e/t**2 +end function oxyHeatCapacity +!***********************************END**************************************** +end module physicalProperties diff --git a/applications/PUfoam/MoDeNaModels/foamConductivity/.gitignore b/applications/PUfoam/MoDeNaModels/foamConductivity/.gitignore new file mode 100644 index 000000000..e65a6a0c4 --- /dev/null +++ b/applications/PUfoam/MoDeNaModels/foamConductivity/.gitignore @@ -0,0 +1 @@ +kfoam diff --git a/applications/PUfoam/MoDeNaModels/foamConductivity/__init__.py b/applications/PUfoam/MoDeNaModels/foamConductivity/__init__.py new file mode 100644 index 000000000..5c890545b --- /dev/null +++ b/applications/PUfoam/MoDeNaModels/foamConductivity/__init__.py @@ -0,0 +1,41 @@ +''' + + ooo ooooo oooooooooo. ooooo ooo + `88. .888' `888' `Y8b `888b. `8' + 888b d'888 .ooooo. 888 888 .ooooo. 8 `88b. 8 .oooo. + 8 Y88. .P 888 d88' `88b 888 888 d88' `88b 8 `88b. 8 `P )88b + 8 `888' 888 888 888 888 888 888ooo888 8 `88b.8 .oP"888 + 8 Y 888 888 888 888 d88' 888 .o 8 `888 d8( 888 + o8o o888o `Y8bod8P' o888bood8P' `Y8bod8P' o8o `8 `Y888""8o + +Copyright + 2014-2015 MoDeNa Consortium, All rights reserved. + +License + This file is part of Modena. + + Modena is free software; you can redistribute it and/or modify it under + the terms of the GNU General Public License as published by the Free + Software Foundation, either version 3 of the License, or (at your option) + any later version. + + Modena is distributed in the hope that it will be useful, but WITHOUT ANY + WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS + FOR A PARTICULAR PURPOSE. See the GNU General Public License + for more details. + + You should have received a copy of the GNU General Public License along + with Modena. If not, see . + +Description + Python library of FireTasks + +Authors + Henrik Rusche + +Contributors +''' + + +from foamConductivity import m_foamConductivity +from foamConductivity import m_simulation diff --git a/applications/PUfoam/MoDeNaModels/foamConductivity/foamConductivity.py b/applications/PUfoam/MoDeNaModels/foamConductivity/foamConductivity.py new file mode 100644 index 000000000..d6bd9403f --- /dev/null +++ b/applications/PUfoam/MoDeNaModels/foamConductivity/foamConductivity.py @@ -0,0 +1,244 @@ +'''@cond + + ooo ooooo oooooooooo. ooooo ooo + `88. .888' `888' `Y8b `888b. `8' + 888b d'888 .ooooo. 888 888 .ooooo. 8 `88b. 8 .oooo. + 8 Y88. .P 888 d88' `88b 888 888 d88' `88b 8 `88b. 8 `P )88b + 8 `888' 888 888 888 888 888 888ooo888 8 `88b.8 .oP"888 + 8 Y 888 888 888 888 d88' 888 .o 8 `888 d8( 888 + o8o o888o `Y8bod8P' o888bood8P' `Y8bod8P' o8o `8 `Y888""8o + +Copyright + 2014-2015 MoDeNa Consortium, All rights reserved. + +License + This file is part of Modena. + + Modena is free software; you can redistribute it and/or modify it under + the terms of the GNU General Public License as published by the Free + Software Foundation, either version 3 of the License, or (at your option) + any later version. + + Modena is distributed in the hope that it will be useful, but WITHOUT ANY + WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS + FOR A PARTICULAR PURPOSE. See the GNU General Public License + for more details. + + You should have received a copy of the GNU General Public License along + with Modena. If not, see . +@endcond''' + +""" +@file +Surrogate function, model definition and backward mapping FireTask for +Foam conductivity model. + +@author Pavel Ferkl +@copyright 2014-2015, MoDeNa Project. GNU Public License. +@ingroup app_aging +""" + +import os +from modena import * +import modena.Strategy as Strategy +from fireworks.utilities.fw_utilities import explicit_serialize +from jinja2 import Template +import polymerConductivity + + +@explicit_serialize +class FoamConductivityExactTask(ModenaFireTask): + """ + A FireTask that starts a microscopic code and updates the database. + """ + def task(self, fw_spec): + + eps = self['point']['eps'] + dcell = self['point']['dcell'] + fstrut = self['point']['fstrut'] + kgas = self['point']['kgas'] + temp = self['point']['T'] + + # Write input + f = open('inputs.in', 'w') + f.write('{0:.6e}\n'.format(temp+1)) + f.write('{0:.6e}\n'.format(temp-1)) + f.write('{0:.6e}\n'.format(kgas)) + f.write('0.9\n') + f.write('0.9\n') + f.write('1.2\n') + f.write('1.1e3\n') + f.write('{0:.6e}\n'.format(eps)) + f.write('{0:.6e}\n'.format(dcell)) + f.write('2\n') + f.write('0.5e-6\n') + f.write('{0:.6e}\n'.format(fstrut)) + f.write('1e-6\n') + f.write('3e-2\n') + f.write('200\n') + f.write('10000\n') + f.write('t\n') + f.write('0.2\n') + f.write('10\n') + f.close() + + # Execute the detailed model + # path to **this** file + /src/... + # will break if distributed computing + os.system(os.path.dirname(os.path.abspath(__file__))+'/src/kfoam') + + # Analyse output + # os.getcwd() returns the path to the "launcher" directory + try: + FILE = open(os.getcwd()+'/outputs.out','r') + except IOError: + raise IOError("File not found") + + self['point']['kfoam'] = float(FILE.readline()) + + os.remove('inputs.in') + os.remove('outputs.out') + +## Surrogate function for thermal conductivity of the foam. +# +# Foam conductivity is a function of porosity, cell size, strut content, +# conductivity of gas and solid phase and temperature. +f_foamConductivity = CFunction( + Ccode=''' +#include "modena.h" +#include "math.h" + +void tcfoam_SM +( + const modena_model_t* model, + const double* inputs, + double *outputs +) +{ + {% block variables %}{% endblock %} + + const double alpha = parameters[1]; + const double beta = parameters[0]; + + const double sigma=5.67e-8; + + double fs,Xs,Xw,X,kappa,kr; + double kfoam; + + fs=alpha*fstrut; + Xs=(1+4*kgas/(kgas+polymer_thermal_conductivity))/3.0; + Xw=2*(1+kgas/(2*polymer_thermal_conductivity))/3.0; + X=(1-fs)*Xw+fs*Xs; + kappa=4.09*sqrt(1-eps)/dcell; + kr=16*sigma*pow(T,3)/(3*kappa); + kfoam = (kgas*eps+polymer_thermal_conductivity*X*(1-eps))/(eps+(1-eps)*X)+beta*kr; + + outputs[0] = kfoam; +} +''', + # These are global bounds for the function + inputs={ + 'eps': {'min': 0, 'max': 1}, + 'dcell': {'min': 0, 'max': 1e-1}, + 'fstrut': {'min': 0, 'max': 1}, + 'kgas': {'min': 0, 'max': 1e-1}, + 'polymer_thermal_conductivity': {'min': 0, 'max': 1e0}, + 'T': {'min': 273, 'max': 450}, + }, + outputs={ + 'kfoam': {'min': 0, 'max': 1e0, 'argPos': 0}, + }, + parameters={ + 'param1': {'min': -1e9, 'max': 1e9 + 2, 'argPos': 0}, + 'param2': {'min': -1e9, 'max': 1e9 + 2, 'argPos': 1}, + }, +) + +# use input file to Foam aging application to initialize with reasonable data. +fname='input.in' +try: + f = open(fname,'r') +except IOError: + f = open(os.getcwd()+'/../'+fname,'r') + +a=f.readline() +a=f.readline() +a=f.readline() +a=f.readline() +a=f.readline() +T0=float(a.split()[0]) +a=f.readline() +rhop=float(a.split()[0]) +a=f.readline() +a=f.readline() +a=f.readline() +a=f.readline() +a=f.readline() +a=f.readline() +dcell0=float(a.split()[0]) +a=f.readline() +fstrut0=float(a.split()[0]) +a=f.readline() +rho0=float(a.split()[0]) +f.close() +eps0=1-rho0/rhop +kgas0=0.012 +eps=[] +dcell=[] +fstrut=[] +kgas=[] +T=[] + +for i in xrange(4): + eps.append(eps0) + dcell.append(dcell0) + fstrut.append(fstrut0) + kgas.append(kgas0*(1+0.01*i)) + T.append(T0) + +initialPoints_foamConductivity_auto = { + 'eps': eps, + 'dcell': dcell, + 'fstrut': fstrut, + 'kgas': kgas, + 'T': T, +} + +initialPoints_foamConductivity_test = { + 'eps': [0.95], + 'dcell': [300e-6], + 'fstrut': [0.8], + 'kgas': [0.12], + 'T': [300], +} + +## Surrogate model for foam conductivity +# +# Backward mapping model is used. +m_foamConductivity = BackwardMappingModel( + _id='foamConductivity', + surrogateFunction=f_foamConductivity, + exactTask=FoamConductivityExactTask(), + substituteModels=[polymerConductivity.m_polymer_thermal_conductivity], + initialisationStrategy=Strategy.InitialPoints( + initialPoints=initialPoints_foamConductivity_auto, + ), + outOfBoundsStrategy=Strategy.ExtendSpaceStochasticSampling( + nNewPoints=4 + ), + parameterFittingStrategy=Strategy.NonLinFitWithErrorContol( + testDataPercentage=0.2, + maxError=0.01, + improveErrorStrategy=Strategy.StochasticSampling( + nNewPoints=2 + ), + maxIterations=5 # Currently not used + ), +) + +## Foam conductivity simulation +# +# For the case, when only foam conductivity and no aging is needed. +m_simulation = Strategy.BackwardMappingScriptTask( + script=os.path.dirname(os.path.abspath(__file__))+'/src/kfoam' +) diff --git a/applications/PUfoam/MoDeNaModels/foamConductivity/src/CMakeLists.txt b/applications/PUfoam/MoDeNaModels/foamConductivity/src/CMakeLists.txt new file mode 100644 index 000000000..a212cb10c --- /dev/null +++ b/applications/PUfoam/MoDeNaModels/foamConductivity/src/CMakeLists.txt @@ -0,0 +1,21 @@ +cmake_minimum_required (VERSION 2.8) +project (tutorialModels C Fortran) + +if( CMAKE_VERSION VERSION_GREATER "3.0" ) + cmake_policy(SET CMP0042 OLD) + cmake_policy(SET CMP0026 OLD) +endif() + +find_package(MODENA REQUIRED) + +include_directories(${MODENA_INCLUDE_DIRS}) +link_directories(${MODENA_LIBRARY_DIRS}) + +find_package(LAPACK REQUIRED) +find_package(BLAS REQUIRED) + +set (CMAKE_Fortran_FLAGS "-ffree-line-length-none -O3") +set (CMAKE_Fortran_MODULE_DIRECTORY mod) +file (GLOB _sources RELATIVE ${CMAKE_CURRENT_SOURCE_DIR} src/*.f*) +add_executable(kfoam ${_sources}) +target_link_libraries(kfoam ${LAPACK_LIBRARIES} ${BLAS_LIBRARIES} MODENA::modena) diff --git a/applications/PUfoam/MoDeNaModels/foamConductivity/src/src/besselj.f90 b/applications/PUfoam/MoDeNaModels/foamConductivity/src/src/besselj.f90 new file mode 100644 index 000000000..9a0ebff34 --- /dev/null +++ b/applications/PUfoam/MoDeNaModels/foamConductivity/src/src/besselj.f90 @@ -0,0 +1,4423 @@ +module besselj + implicit none + private + public ZBESJ +contains +!***************************************************************** +!* EVALUATE A J-BESSEL FUNCTION OF COMPLEX ARGUMENT (FIRST KIND) * +!* ------------------------------------------------------------- * +!* SAMPLE RUN: * +!* (Evaluate J0 to J4 for argument Z=(1.0,2.0) ). * +!* * +!* zr(0) = 1.586259 * +!* zi(0) = -1.391602 * +!* zr(1) = 1.291848 * +!* zi(1) = 1.010488 * +!* zr(2) = -0.261130 * +!* zi(2) = 0.762320 * +!* zr(3) = -0.281040 * +!* zi(3) = 0.017175 * +!* zr(4) = -0.034898 * +!* zi(4) = -0.067215 * +!* NZ = 0 * +!* Error code: 0 * +!* * +!* ------------------------------------------------------------- * +!* Ref.: From Numath Library By Tuan Dang Trong in Fortran 77 * +!* [BIBLI 18]. * +!* * +!* F90 Release 1.0 By J-P Moreau, Paris * +!* (www.jpmoreau.fr) * +!***************************************************************** +!Note: to link with Complex.f90 and Utilit.f90. +!--------------------------------------------- +!PROGRAM TEST_ZBESJ +!real*8 zr,zi, cyr(10), cyi(10) + +! n=5 +! zr=1.d0; zi=2.d0 +! call ZBESJ(zr,zi,0,1,n,cyr,cyi,nz,ierr) + +! print *,' ' +! do i=1, n +! write(*,10) i-1, cyr(i) +! write(*,11) i-1, cyi(i) +! end do +! print *,' NZ=', NZ +! print *,' Error code:', ierr +! print *,' ' + +!10 format(' zr(',I1,') = ',F10.6) +!11 format(' zi(',I1,') = ',F10.6) +! +!END + +SUBROUTINE ZBESJ(ZR, ZI, FNU, KODE, N, CYR, CYI, NZ, IERR) +USE UTILIT !For I1MACH,D1MACH. +USE COMPLEX !For ZABS +!***BEGIN PROLOGUE ZBESJ +!***DATE WRITTEN 830501 (YYMMDD) +!***REVISION DATE 830501 (YYMMDD) +!***CATEGORY NO. B5K +!***KEYWORDS J-BESSEL FUNCTION,BESSEL FUNCTION OF COMPLEX ARGUMENT, +! BESSEL FUNCTION OF FIRST KIND +!***AUTHOR AMOS, DONALD E., SANDIA NATIONAL LABORATORIES +!***PURPOSE TO COMPUTE THE J-BESSEL FUNCTION OF A COMPLEX ARGUMENT +!***DESCRIPTION +! +! ***A DOUBLE PRECISION ROUTINE*** +! ON KODE=1, CBESJ COMPUTES AN N MEMBER SEQUENCE OF COMPLEX +! BESSEL FUNCTIONS CY(I)=J(FNU+I-1,Z) FOR REAL, NONNEGATIVE +! ORDERS FNU+I-1, I=1,...,N AND COMPLEX Z IN THE CUT PLANE +! -PI.LT.ARG(Z).LE.PI. ON KODE=2, CBESJ RETURNS THE SCALED +! FUNCTIONS +! +! CY(I)=EXP(-ABS(Y))*J(FNU+I-1,Z) I = 1,...,N , Y=AIMAG(Z) +! +! WHICH REMOVE THE EXPONENTIAL GROWTH IN BOTH THE UPPER AND +! LOWER HALF PLANES FOR Z TO INFINITY. DEFINITIONS AND NOTATION +! ARE FOUND IN THE NBS HANDBOOK OF MATHEMATICAL FUNCTIONS +! (REF. 1). +! +! INPUT ZR,ZI,FNU ARE DOUBLE PRECISION +! ZR,ZI - Z=CMPLX(ZR,ZI), -PI.LT.ARG(Z).LE.PI +! FNU - ORDER OF INITIAL J FUNCTION, FNU.GE.0.0D0 +! KODE - A PARAMETER TO INDICATE THE SCALING OPTION +! KODE= 1 RETURNS +! CY(I)=J(FNU+I-1,Z), I=1,...,N +! = 2 RETURNS +! CY(I)=J(FNU+I-1,Z)EXP(-ABS(Y)), I=1,...,N +! N - NUMBER OF MEMBERS OF THE SEQUENCE, N.GE.1 +! +! OUTPUT CYR,CYI ARE DOUBLE PRECISION +! CYR,CYI- DOUBLE PRECISION VECTORS WHOSE FIRST N COMPONENTS +! CONTAIN REAL AND IMAGINARY PARTS FOR THE SEQUENCE +! CY(I)=J(FNU+I-1,Z) OR +! CY(I)=J(FNU+I-1,Z)EXP(-ABS(Y)) I=1,...,N +! DEPENDING ON KODE, Y=AIMAG(Z). +! NZ - NUMBER OF COMPONENTS SET TO ZERO DUE TO UNDERFLOW, +! NZ= 0 , NORMAL RETURN +! NZ.GT.0 , LAST NZ COMPONENTS OF CY SET ZERO DUE +! TO UNDERFLOW, CY(I)=CMPLX(0.0D0,0.0D0), +! I = N-NZ+1,...,N +! IERR - ERROR FLAG +! IERR=0, NORMAL RETURN - COMPUTATION COMPLETED +! IERR=1, INPUT ERROR - NO COMPUTATION +! IERR=2, OVERFLOW - NO COMPUTATION, AIMAG(Z) +! TOO LARGE ON KODE=1 +! IERR=3, CABS(Z) OR FNU+N-1 LARGE - COMPUTATION DONE +! BUT LOSSES OF SIGNIFCANCE BY ARGUMENT +! REDUCTION PRODUCE LESS THAN HALF OF MACHINE +! ACCURACY +! IERR=4, CABS(Z) OR FNU+N-1 TOO LARGE - NO COMPUTA- +! TION BECAUSE OF COMPLETE LOSSES OF SIGNIFI- +! CANCE BY ARGUMENT REDUCTION +! IERR=5, ERROR - NO COMPUTATION, +! ALGORITHM TERMINATION CONDITION NOT MET +! +!***LONG DESCRIPTION +! +! THE COMPUTATION IS CARRIED OUT BY THE FORMULA +! +! J(FNU,Z)=EXP( FNU*PI*I/2)*I(FNU,-I*Z) AIMAG(Z).GE.0.0 +! +! J(FNU,Z)=EXP(-FNU*PI*I/2)*I(FNU, I*Z) AIMAG(Z).LT.0.0 +! +! WHERE I**2 = -1 AND I(FNU,Z) IS THE I BESSEL FUNCTION. +! +! FOR NEGATIVE ORDERS,THE FORMULA +! +! J(-FNU,Z) = J(FNU,Z)*COS(PI*FNU) - Y(FNU,Z)*SIN(PI*FNU) +! +! CAN BE USED. HOWEVER,FOR LARGE ORDERS CLOSE TO INTEGERS, THE +! THE FUNCTION CHANGES RADICALLY. WHEN FNU IS A LARGE POSITIVE +! INTEGER,THE MAGNITUDE OF J(-FNU,Z)=J(FNU,Z)*COS(PI*FNU) IS A +! LARGE NEGATIVE POWER OF TEN. BUT WHEN FNU IS NOT AN INTEGER, +! Y(FNU,Z) DOMINATES IN MAGNITUDE WITH A LARGE POSITIVE POWER OF +! TEN AND THE MOST THAT THE SECOND TERM CAN BE REDUCED IS BY +! UNIT ROUNDOFF FROM THE COEFFICIENT. THUS, WIDE CHANGES CAN +! OCCUR WITHIN UNIT ROUNDOFF OF A LARGE INTEGER FOR FNU. HERE, +! LARGE MEANS FNU.GT.CABS(Z). +! +! IN MOST COMPLEX VARIABLE COMPUTATION, ONE MUST EVALUATE ELE- +! MENTARY FUNCTIONS. WHEN THE MAGNITUDE OF Z OR FNU+N-1 IS +! LARGE, LOSSES OF SIGNIFICANCE BY ARGUMENT REDUCTION OCCUR. +! CONSEQUENTLY, IF EITHER ONE EXCEEDS U1=SQRT(0.5/UR), THEN +! LOSSES EXCEEDING HALF PRECISION ARE LIKELY AND AN ERROR FLAG +! IERR=3 IS TRIGGERED WHERE UR=DMAX1(D1MACH(4),1.0D-18) IS +! DOUBLE PRECISION UNIT ROUNDOFF LIMITED TO 18 DIGITS PRECISION. +! IF EITHER IS LARGER THAN U2=0.5/UR, THEN ALL SIGNIFICANCE IS +! LOST AND IERR=4. IN ORDER TO USE THE INT FUNCTION, ARGUMENTS +! MUST BE FURTHER RESTRICTED NOT TO EXCEED THE LARGEST MACHINE +! INTEGER, U3=I1MACH(9). THUS, THE MAGNITUDE OF Z AND FNU+N-1 IS +! RESTRICTED BY MIN(U2,U3). ON 32 BIT MACHINES, U1,U2, AND U3 +! ARE APPROXIMATELY 2.0E+3, 4.2E+6, 2.1E+9 IN SINGLE PRECISION +! ARITHMETIC AND 1.3E+8, 1.8E+16, 2.1E+9 IN DOUBLE PRECISION +! ARITHMETIC RESPECTIVELY. THIS MAKES U2 AND U3 LIMITING IN +! THEIR RESPECTIVE ARITHMETICS. THIS MEANS THAT ONE CAN EXPECT +! TO RETAIN, IN THE WORST CASES ON 32 BIT MACHINES, NO DIGITS +! IN SINGLE AND ONLY 7 DIGITS IN DOUBLE PRECISION ARITHMETIC. +! SIMILAR CONSIDERATIONS HOLD FOR OTHER MACHINES. +! +! THE APPROXIMATE RELATIVE ERROR IN THE MAGNITUDE OF A COMPLEX +! BESSEL FUNCTION CAN BE EXPRESSED BY P*10**S WHERE P=MAX(UNIT +! ROUNDOFF,1.0E-18) IS THE NOMINAL PRECISION AND 10**S REPRE- +! SENTS THE INCREASE IN ERROR DUE TO ARGUMENT REDUCTION IN THE +! ELEMENTARY FUNCTIONS. HERE, S=MAX(1,ABS(LOG10(CABS(Z))), +! ABS(LOG10(FNU))) APPROXIMATELY (I.E. S=MAX(1,ABS(EXPONENT OF +! CABS(Z),ABS(EXPONENT OF FNU)) ). HOWEVER, THE PHASE ANGLE MAY +! HAVE ONLY ABSOLUTE ACCURACY. THIS IS MOST LIKELY TO OCCUR WHEN +! ONE COMPONENT (IN ABSOLUTE VALUE) IS LARGER THAN THE OTHER BY +! SEVERAL ORDERS OF MAGNITUDE. IF ONE COMPONENT IS 10**K LARGER +! THAN THE OTHER, THEN ONE CAN EXPECT ONLY MAX(ABS(LOG10(P))-K, +! 0) SIGNIFICANT DIGITS; OR, STATED ANOTHER WAY, WHEN K EXCEEDS +! THE EXPONENT OF P, NO SIGNIFICANT DIGITS REMAIN IN THE SMALLER +! COMPONENT. HOWEVER, THE PHASE ANGLE RETAINS ABSOLUTE ACCURACY +! BECAUSE, IN COMPLEX ARITHMETIC WITH PRECISION P, THE SMALLER +! COMPONENT WILL NOT (AS A RULE) DECREASE BELOW P TIMES THE +! MAGNITUDE OF THE LARGER COMPONENT. IN THESE EXTREME CASES, +! THE PRINCIPAL PHASE ANGLE IS ON THE ORDER OF +P, -P, PI/2-P, +! OR -PI/2+P. +! +!***REFERENCES HANDBOOK OF MATHEMATICAL FUNCTIONS BY M. ABRAMOWITZ +! AND I. A. STEGUN, NBS AMS SERIES 55, U.S. DEPT. OF +! COMMERCE, 1955. +! +! COMPUTATION OF BESSEL FUNCTIONS OF COMPLEX ARGUMENT +! BY D. E. AMOS, SAND83-0083, MAY, 1983. +! +! COMPUTATION OF BESSEL FUNCTIONS OF COMPLEX ARGUMENT +! AND LARGE ORDER BY D. E. AMOS, SAND83-0643, MAY, 1983 +! +! A SUBROUTINE PACKAGE FOR BESSEL FUNCTIONS OF A COMPLEX +! ARGUMENT AND NONNEGATIVE ORDER BY D. E. AMOS, SAND85- +! 1018, MAY, 1985 +! +! A PORTABLE PACKAGE FOR BESSEL FUNCTIONS OF A COMPLEX +! ARGUMENT AND NONNEGATIVE ORDER BY D. E. AMOS, TRANS. +! MATH. SOFTWARE, 1986 +! +!***ROUTINES CALLED ZABS,ZBINU,I1MACH,D1MACH +!***END PROLOGUE ZBESJ +! +! COMPLEX CI,CSGN,CY,Z,ZN + DOUBLE PRECISION AA, ALIM, ARG, CII, CSGNI, CSGNR, CYI, CYR, DIG, & + ELIM, FNU, FNUL, HPI, RL, R1M5, STR, TOL, ZI, ZNI, ZNR, ZR, & + BB, FN, AZ + INTEGER I, IERR, INU, INUH, IR, K, KODE, K1, K2, N, NL, NZ + DIMENSION CYR(1), CYI(1) + DATA HPI /1.57079632679489662D0/ + +!***FIRST EXECUTABLE STATEMENT ZBESJ + IERR = 0 + NZ=0 + IF (FNU.LT.0.0D0) IERR=1 + IF (KODE.LT.1 .OR. KODE.GT.2) IERR=1 + IF (N.LT.1) IERR=1 + IF (IERR.NE.0) RETURN +!----------------------------------------------------------------------- +! SET PARAMETERS RELATED TO MACHINE CONSTANTS. +! TOL IS THE APPROXIMATE UNIT ROUNDOFF LIMITED TO 1.0E-18. +! ELIM IS THE APPROXIMATE EXPONENTIAL OVER- AND UNDERFLOW LIMIT. +! EXP(-ELIM).LT.EXP(-ALIM)=EXP(-ELIM)/TOL AND +! EXP(ELIM).GT.EXP(ALIM)=EXP(ELIM)*TOL ARE INTERVALS NEAR +! UNDERFLOW AND OVERFLOW LIMITS WHERE SCALED ARITHMETIC IS DONE. +! RL IS THE LOWER BOUNDARY OF THE ASYMPTOTIC EXPANSION FOR LARGE Z. +! DIG = NUMBER OF BASE 10 DIGITS IN TOL = 10**(-DIG). +! FNUL IS THE LOWER BOUNDARY OF THE ASYMPTOTIC SERIES FOR LARGE FNU. +!----------------------------------------------------------------------- + TOL = DMAX1(D1MACH(4),1.0D-18) + K1 = I1MACH(15) + K2 = I1MACH(16) + R1M5 = D1MACH(5) + K = MIN0(IABS(K1),IABS(K2)) + ELIM = 2.303D0*(DBLE(FLOAT(K))*R1M5-3.0D0) + K1 = I1MACH(14) - 1 + AA = R1M5*DBLE(FLOAT(K1)) + DIG = DMIN1(AA,18.0D0) + AA = AA*2.303D0 + ALIM = ELIM + DMAX1(-AA,-41.45D0) + RL = 1.2D0*DIG + 3.0D0 + FNUL = 10.0D0 + 6.0D0*(DIG-3.0D0) +!----------------------------------------------------------------------- +! TEST FOR PROPER RANGE +!----------------------------------------------------------------------- + AZ = ZABS(ZR,ZI) + FN = FNU+DBLE(FLOAT(N-1)) + AA = 0.5D0/TOL + BB=DBLE(FLOAT(I1MACH(9)))*0.5D0 + AA = DMIN1(AA,BB) + IF (AZ.GT.AA) GO TO 260 + IF (FN.GT.AA) GO TO 260 + AA = DSQRT(AA) + IF (AZ.GT.AA) IERR=3 + IF (FN.GT.AA) IERR=3 +!----------------------------------------------------------------------- +! CALCULATE CSGN=EXP(FNU*HPI*I) TO MINIMIZE LOSSES OF SIGNIFICANCE +! WHEN FNU IS LARGE +!----------------------------------------------------------------------- + CII = 1.0D0 + INU = INT(SNGL(FNU)) + INUH = INU/2 + IR = INU - 2*INUH + ARG = (FNU-DBLE(FLOAT(INU-IR)))*HPI + CSGNR = DCOS(ARG) + CSGNI = DSIN(ARG) + IF (MOD(INUH,2).EQ.0) GO TO 40 + CSGNR = -CSGNR + CSGNI = -CSGNI + 40 CONTINUE +!----------------------------------------------------------------------- +! ZN IS IN THE RIGHT HALF PLANE +!----------------------------------------------------------------------- + ZNR = ZI + ZNI = -ZR + IF (ZI.GE.0.0D0) GO TO 50 + ZNR = -ZNR + ZNI = -ZNI + CSGNI = -CSGNI + CII = -CII + 50 CONTINUE + CALL ZBINU(ZNR, ZNI, FNU, KODE, N, CYR, CYI, NZ, RL, FNUL, TOL, & + ELIM, ALIM) + IF (NZ.LT.0) GO TO 130 + NL = N - NZ + IF (NL.EQ.0) RETURN + DO 60 I=1,NL + STR = CYR(I)*CSGNR - CYI(I)*CSGNI + CYI(I) = CYR(I)*CSGNI + CYI(I)*CSGNR + CYR(I) = STR + STR = -CSGNI*CII + CSGNI = CSGNR*CII + CSGNR = STR + 60 CONTINUE + RETURN + 130 CONTINUE + IF(NZ.EQ.(-2)) GO TO 140 + NZ = 0 + IERR = 2 + RETURN + 140 CONTINUE + NZ=0 + IERR=5 + RETURN + 260 CONTINUE + NZ=0 + IERR=4 + RETURN + END + + + +SUBROUTINE ZUCHK(YR, YI, NZ, ASCLE, TOL) +!***BEGIN PROLOGUE ZUCHK +!***REFER TO ZSERI,ZUOIK,ZUNK1,ZUNK2,ZUNI1,ZUNI2,ZKSCL +! +! Y ENTERS AS A SCALED QUANTITY WHOSE MAGNITUDE IS GREATER THAN +! EXP(-ALIM)=ASCLE=1.0E+3*D1MACH(1)/TOL. THE TEST IS MADE TO SEE +! IF THE MAGNITUDE OF THE REAL OR IMAGINARY PART WOULD UNDERFLOW +! WHEN Y IS SCALED (BY TOL) TO ITS PROPER VALUE. Y IS ACCEPTED +! IF THE UNDERFLOW IS AT LEAST ONE PRECISION BELOW THE MAGNITUDE +! OF THE LARGEST COMPONENT; OTHERWISE THE PHASE ANGLE DOES NOT HAVE +! ABSOLUTE ACCURACY AND AN UNDERFLOW IS ASSUMED. +! +!***ROUTINES CALLED (NONE) +!***END PROLOGUE ZUCHK +! +! COMPLEX Y + DOUBLE PRECISION ASCLE, SS, ST, TOL, WR, WI, YR, YI + INTEGER NZ + NZ = 0 + WR = DABS(YR) + WI = DABS(YI) + ST = DMIN1(WR,WI) + IF (ST.GT.ASCLE) RETURN + SS = DMAX1(WR,WI) + ST = ST/TOL + IF (SS.LT.ST) NZ = 1 + RETURN +END + +SUBROUTINE ZBINU(ZR, ZI, FNU, KODE, N, CYR, CYI, NZ, RL, FNUL, TOL, ELIM, ALIM) +USE COMPLEX +!***BEGIN PROLOGUE ZBINU +!***REFER TO ZBESH,ZBESI,ZBESJ,ZBESK,ZAIRY,ZBIRY + +! ZBINU COMPUTES THE I FUNCTION IN THE RIGHT HALF Z PLANE + +!***ROUTINES CALLED ZABS,ZASYI,ZBUNI,ZMLRI,ZSERI,ZUOIK,ZWRSK +!***END PROLOGUE ZBINU + DOUBLE PRECISION ALIM, AZ, CWI, CWR, CYI, CYR, DFNU, ELIM, FNU, & + FNUL, RL, TOL, ZEROI, ZEROR, ZI, ZR + INTEGER I, INW, KODE, N, NLAST, NN, NUI, NW, NZ + DIMENSION CYR(1), CYI(1), CWR(2), CWI(2) + DATA ZEROR,ZEROI / 0.0D0, 0.0D0 / + + NZ = 0 + AZ = ZABS(ZR,ZI) + NN = N + DFNU = FNU + DBLE(FLOAT(N-1)) + IF (AZ.LE.2.0D0) GO TO 10 + IF (AZ*AZ*0.25D0.GT.DFNU+1.0D0) GO TO 20 + 10 CONTINUE +!----------------------------------------------------------------------- +! POWER SERIES +!----------------------------------------------------------------------- + CALL ZSERI(ZR, ZI, FNU, KODE, NN, CYR, CYI, NW, TOL, ELIM, ALIM) + INW = IABS(NW) + NZ = NZ + INW + NN = NN - INW + IF (NN.EQ.0) RETURN + IF (NW.GE.0) GO TO 120 + DFNU = FNU + DBLE(FLOAT(NN-1)) + 20 CONTINUE + IF (AZ.LT.RL) GO TO 40 + IF (DFNU.LE.1.0D0) GO TO 30 + IF (AZ+AZ.LT.DFNU*DFNU) GO TO 50 +!----------------------------------------------------------------------- +! ASYMPTOTIC EXPANSION FOR LARGE Z +!----------------------------------------------------------------------- + 30 CONTINUE + CALL ZASYI(ZR, ZI, FNU, KODE, NN, CYR, CYI, NW, RL, TOL, ELIM, ALIM) + IF (NW.LT.0) GO TO 130 + GO TO 120 + 40 CONTINUE + IF (DFNU.LE.1.0D0) GO TO 70 + 50 CONTINUE +!----------------------------------------------------------------------- +! OVERFLOW AND UNDERFLOW TEST ON I SEQUENCE FOR MILLER ALGORITHM +!----------------------------------------------------------------------- + CALL ZUOIK(ZR, ZI, FNU, KODE, 1, NN, CYR, CYI, NW, TOL, ELIM, ALIM) + IF (NW.LT.0) GO TO 130 + NZ = NZ + NW + NN = NN - NW + IF (NN.EQ.0) RETURN + DFNU = FNU+DBLE(FLOAT(NN-1)) + IF (DFNU.GT.FNUL) GO TO 110 + IF (AZ.GT.FNUL) GO TO 110 + 60 CONTINUE + IF (AZ.GT.RL) GO TO 80 + 70 CONTINUE +!----------------------------------------------------------------------- +! MILLER ALGORITHM NORMALIZED BY THE SERIES +!----------------------------------------------------------------------- + CALL ZMLRI(ZR, ZI, FNU, KODE, NN, CYR, CYI, NW, TOL) + IF(NW.LT.0) GO TO 130 + GO TO 120 + 80 CONTINUE +!----------------------------------------------------------------------- +! MILLER ALGORITHM NORMALIZED BY THE WRONSKIAN +!----------------------------------------------------------------------- +!----------------------------------------------------------------------- +! OVERFLOW TEST ON K FUNCTIONS USED IN WRONSKIAN +!----------------------------------------------------------------------- + CALL ZUOIK(ZR, ZI, FNU, KODE, 2, 2, CWR, CWI, NW, TOL, ELIM, ALIM) + IF (NW.GE.0) GO TO 100 + NZ = NN + DO 90 I=1,NN + CYR(I) = ZEROR + CYI(I) = ZEROI + 90 CONTINUE + RETURN + 100 CONTINUE + IF (NW.GT.0) GO TO 130 + CALL ZWRSK(ZR, ZI, FNU, KODE, NN, CYR, CYI, NW, CWR, CWI, TOL, ELIM, ALIM) + IF (NW.LT.0) GO TO 130 + GO TO 120 + 110 CONTINUE +!----------------------------------------------------------------------- +! INCREMENT FNU+NN-1 UP TO FNUL, COMPUTE AND RECUR BACKWARD +!----------------------------------------------------------------------- + NUI = INT(SNGL(FNUL-DFNU)) + 1 + NUI = MAX0(NUI,0) + CALL ZBUNI(ZR, ZI, FNU, KODE, NN, CYR, CYI, NW, NUI, NLAST, FNUL, & + TOL, ELIM, ALIM) + IF (NW.LT.0) GO TO 130 + NZ = NZ + NW + IF (NLAST.EQ.0) GO TO 120 + NN = NLAST + GO TO 60 + 120 CONTINUE + RETURN + 130 CONTINUE + NZ = -1 + IF(NW.EQ.(-2)) NZ=-2 + RETURN + END + +SUBROUTINE ZSERI(ZR, ZI, FNU, KODE, N, YR, YI, NZ, TOL, ELIM, ALIM) +USE UTILIT +USE COMPLEX +!***BEGIN PROLOGUE ZSERI +!***REFER TO ZBESI,ZBESK +! +! ZSERI COMPUTES THE I BESSEL FUNCTION FOR REAL(Z).GE.0.0 BY +! MEANS OF THE POWER SERIES FOR LARGE CABS(Z) IN THE +! REGION CABS(Z).LE.2*SQRT(FNU+1). NZ=0 IS A NORMAL RETURN. +! NZ.GT.0 MEANS THAT THE LAST NZ COMPONENTS WERE SET TO ZERO +! DUE TO UNDERFLOW. NZ.LT.0 MEANS UNDERFLOW OCCURRED, BUT THE +! CONDITION CABS(Z).LE.2*SQRT(FNU+1) WAS VIOLATED AND THE +! COMPUTATION MUST BE COMPLETED IN ANOTHER ROUTINE WITH N=N-ABS(NZ). +! +!***ROUTINES CALLED DGAMLN,D1MACH,ZUCHK,ZABS,ZDIV,ZLOG,ZMLT +!***END PROLOGUE ZSERI +! COMPLEX AK1,CK,COEF,CONE,CRSC,CSCL,CZ,CZERO,HZ,RZ,S1,S2,Y,Z + DOUBLE PRECISION AA, ACZ, AK, AK1I, AK1R, ALIM, ARM, ASCLE, ATOL, & + AZ, CKI, CKR, COEFI, COEFR, CONEI, CONER, CRSCR, CZI, CZR, DFNU, & + ELIM, FNU, FNUP, HZI, HZR, RAZ, RS, RTR1, RZI, RZR, S, SS, STI, & + STR, S1I, S1R, S2I, S2R, TOL, YI, YR, WI, WR, ZEROI, ZEROR, ZI, & + ZR!, DGAMLN + INTEGER I, IB, IDUM, IFLAG, IL, K, KODE, L, M, N, NN, NZ, NW + DIMENSION YR(1), YI(1), WR(2), WI(2) + DATA ZEROR,ZEROI,CONER,CONEI / 0.0D0, 0.0D0, 1.0D0, 0.0D0 / + + NZ = 0 + AZ = ZABS(ZR,ZI) + IF (AZ.EQ.0.0D0) GO TO 160 + ARM = 1.0D+3*D1MACH(1) + RTR1 = DSQRT(ARM) + CRSCR = 1.0D0 + IFLAG = 0 + IF (AZ.LT.ARM) GO TO 150 + HZR = 0.5D0*ZR + HZI = 0.5D0*ZI + CZR = ZEROR + CZI = ZEROI + IF (AZ.LE.RTR1) GO TO 10 + CALL ZMLT(HZR, HZI, HZR, HZI, CZR, CZI) + 10 CONTINUE + ACZ = ZABS(CZR,CZI) + NN = N + CALL ZLOG(HZR, HZI, CKR, CKI, IDUM) + 20 CONTINUE + DFNU = FNU + DBLE(FLOAT(NN-1)) + FNUP = DFNU + 1.0D0 +!----------------------------------------------------------------------- +! UNDERFLOW TEST +!----------------------------------------------------------------------- + AK1R = CKR*DFNU + AK1I = CKI*DFNU + AK = DGAMLN(FNUP,IDUM) + AK1R = AK1R - AK + IF (KODE.EQ.2) AK1R = AK1R - ZR + IF (AK1R.GT.(-ELIM)) GO TO 40 + 30 CONTINUE + NZ = NZ + 1 + YR(NN) = ZEROR + YI(NN) = ZEROI + IF (ACZ.GT.DFNU) GO TO 190 + NN = NN - 1 + IF (NN.EQ.0) RETURN + GO TO 20 + 40 CONTINUE + IF (AK1R.GT.(-ALIM)) GO TO 50 + IFLAG = 1 + SS = 1.0D0/TOL + CRSCR = TOL + ASCLE = ARM*SS + 50 CONTINUE + AA = DEXP(AK1R) + IF (IFLAG.EQ.1) AA = AA*SS + COEFR = AA*DCOS(AK1I) + COEFI = AA*DSIN(AK1I) + ATOL = TOL*ACZ/FNUP + IL = MIN0(2,NN) + DO 90 I=1,IL + DFNU = FNU + DBLE(FLOAT(NN-I)) + FNUP = DFNU + 1.0D0 + S1R = CONER + S1I = CONEI + IF (ACZ.LT.TOL*FNUP) GO TO 70 + AK1R = CONER + AK1I = CONEI + AK = FNUP + 2.0D0 + S = FNUP + AA = 2.0D0 + 60 CONTINUE + RS = 1.0D0/S + STR = AK1R*CZR - AK1I*CZI + STI = AK1R*CZI + AK1I*CZR + AK1R = STR*RS + AK1I = STI*RS + S1R = S1R + AK1R + S1I = S1I + AK1I + S = S + AK + AK = AK + 2.0D0 + AA = AA*ACZ*RS + IF (AA.GT.ATOL) GO TO 60 + 70 CONTINUE + S2R = S1R*COEFR - S1I*COEFI + S2I = S1R*COEFI + S1I*COEFR + WR(I) = S2R + WI(I) = S2I + IF (IFLAG.EQ.0) GO TO 80 + CALL ZUCHK(S2R, S2I, NW, ASCLE, TOL) + IF (NW.NE.0) GO TO 30 + 80 CONTINUE + M = NN - I + 1 + YR(M) = S2R*CRSCR + YI(M) = S2I*CRSCR + IF (I.EQ.IL) GO TO 90 + CALL ZDIV(COEFR, COEFI, HZR, HZI, STR, STI) + COEFR = STR*DFNU + COEFI = STI*DFNU + 90 CONTINUE + IF (NN.LE.2) RETURN + K = NN - 2 + AK = DBLE(FLOAT(K)) + RAZ = 1.0D0/AZ + STR = ZR*RAZ + STI = -ZI*RAZ + RZR = (STR+STR)*RAZ + RZI = (STI+STI)*RAZ + IF (IFLAG.EQ.1) GO TO 120 + IB = 3 + 100 CONTINUE + DO 110 I=IB,NN + YR(K) = (AK+FNU)*(RZR*YR(K+1)-RZI*YI(K+1)) + YR(K+2) + YI(K) = (AK+FNU)*(RZR*YI(K+1)+RZI*YR(K+1)) + YI(K+2) + AK = AK - 1.0D0 + K = K - 1 + 110 CONTINUE + RETURN +!----------------------------------------------------------------------- +! RECUR BACKWARD WITH SCALED VALUES +!----------------------------------------------------------------------- + 120 CONTINUE +!----------------------------------------------------------------------- +! EXP(-ALIM)=EXP(-ELIM)/TOL=APPROX. ONE PRECISION ABOVE THE +! UNDERFLOW LIMIT = ASCLE = D1MACH(1)*SS*1.0D+3 +!----------------------------------------------------------------------- + S1R = WR(1) + S1I = WI(1) + S2R = WR(2) + S2I = WI(2) + DO 130 L=3,NN + CKR = S2R + CKI = S2I + S2R = S1R + (AK+FNU)*(RZR*CKR-RZI*CKI) + S2I = S1I + (AK+FNU)*(RZR*CKI+RZI*CKR) + S1R = CKR + S1I = CKI + CKR = S2R*CRSCR + CKI = S2I*CRSCR + YR(K) = CKR + YI(K) = CKI + AK = AK - 1.0D0 + K = K - 1 + IF (ZABS(CKR,CKI).GT.ASCLE) GO TO 140 + 130 CONTINUE + RETURN + 140 CONTINUE + IB = L + 1 + IF (IB.GT.NN) RETURN + GO TO 100 + 150 CONTINUE + NZ = N + IF (FNU.EQ.0.0D0) NZ = NZ - 1 + 160 CONTINUE + YR(1) = ZEROR + YI(1) = ZEROI + IF (FNU.NE.0.0D0) GO TO 170 + YR(1) = CONER + YI(1) = CONEI + 170 CONTINUE + IF (N.EQ.1) RETURN + DO 180 I=2,N + YR(I) = ZEROR + YI(I) = ZEROI + 180 CONTINUE + RETURN +!----------------------------------------------------------------------- +! RETURN WITH NZ.LT.0 IF CABS(Z*Z/4).GT.FNU+N-NZ-1 COMPLETE +! THE CALCULATION IN CBINU WITH N=N-IABS(NZ) +!----------------------------------------------------------------------- + 190 CONTINUE + NZ = -NZ + RETURN + END + +SUBROUTINE ZASYI(ZR, ZI, FNU, KODE, N, YR, YI, NZ, RL, TOL, ELIM, ALIM) +USE UTILIT +USE COMPLEX +!***BEGIN PROLOGUE ZASYI +!***REFER TO ZBESI,ZBESK + +! ZASYI COMPUTES THE I BESSEL FUNCTION FOR REAL(Z).GE.0.0 BY +! MEANS OF THE ASYMPTOTIC EXPANSION FOR LARGE CABS(Z) IN THE +! REGION CABS(Z).GT.MAX(RL,FNU*FNU/2). NZ=0 IS A NORMAL RETURN. +! NZ.LT.0 INDICATES AN OVERFLOW ON KODE=1. +! +!***ROUTINES CALLED D1MACH,ZABS,ZDIV,ZEXP,ZMLT,ZSQRT +!***END PROLOGUE ZASYI +! COMPLEX AK1,CK,CONE,CS1,CS2,CZ,CZERO,DK,EZ,P1,RZ,S2,Y,Z + DOUBLE PRECISION AA, AEZ, AK, AK1I, AK1R, ALIM, ARG, ARM, ATOL, & + AZ, BB, BK, CKI, CKR, CONEI, CONER, CS1I, CS1R, CS2I, CS2R, CZI, & + CZR, DFNU, DKI, DKR, DNU2, ELIM, EZI, EZR, FDN, FNU, PI, P1I, & + P1R, RAZ, RL, RTPI, RTR1, RZI, RZR, S, SGN, SQK, STI, STR, S2I, & + S2R, TOL, TZI, TZR, YI, YR, ZEROI, ZEROR, ZI, ZR + INTEGER I, IB, IL, INU, J, JL, K, KODE, KODED, M, N, NN, NZ + DIMENSION YR(1), YI(1) + DATA PI, RTPI /3.14159265358979324D0 , 0.159154943091895336D0 / + DATA ZEROR,ZEROI,CONER,CONEI / 0.0D0, 0.0D0, 1.0D0, 0.0D0 / + + NZ = 0 + AZ = ZABS(ZR,ZI) + ARM = 1.0D+3*D1MACH(1) + RTR1 = DSQRT(ARM) + IL = MIN0(2,N) + DFNU = FNU + DBLE(FLOAT(N-IL)) +!----------------------------------------------------------------------- +! OVERFLOW TEST +!----------------------------------------------------------------------- + RAZ = 1.0D0/AZ + STR = ZR*RAZ + STI = -ZI*RAZ + AK1R = RTPI*STR*RAZ + AK1I = RTPI*STI*RAZ + CALL ZSQRT(AK1R, AK1I, AK1R, AK1I) + CZR = ZR + CZI = ZI + IF (KODE.NE.2) GO TO 10 + CZR = ZEROR + CZI = ZI + 10 CONTINUE + IF (DABS(CZR).GT.ELIM) GO TO 100 + DNU2 = DFNU + DFNU + KODED = 1 + IF ((DABS(CZR).GT.ALIM) .AND. (N.GT.2)) GO TO 20 + KODED = 0 + CALL ZEXP(CZR, CZI, STR, STI) + CALL ZMLT(AK1R, AK1I, STR, STI, AK1R, AK1I) + 20 CONTINUE + FDN = 0.0D0 + IF (DNU2.GT.RTR1) FDN = DNU2*DNU2 + EZR = ZR*8.0D0 + EZI = ZI*8.0D0 +!----------------------------------------------------------------------- +! WHEN Z IS IMAGINARY, THE ERROR TEST MUST BE MADE RELATIVE TO THE +! FIRST RECIPROCAL POWER SINCE THIS IS THE LEADING TERM OF THE +! EXPANSION FOR THE IMAGINARY PART. +!----------------------------------------------------------------------- + AEZ = 8.0D0*AZ + S = TOL/AEZ + JL = INT(SNGL(RL+RL)) + 2 + P1R = ZEROR + P1I = ZEROI + IF (ZI.EQ.0.0D0) GO TO 30 +!----------------------------------------------------------------------- +! CALCULATE EXP(PI*(0.5+FNU+N-IL)*I) TO MINIMIZE LOSSES OF +! SIGNIFICANCE WHEN FNU OR N IS LARGE +!----------------------------------------------------------------------- + INU = INT(SNGL(FNU)) + ARG = (FNU-DBLE(FLOAT(INU)))*PI + INU = INU + N - IL + AK = -DSIN(ARG) + BK = DCOS(ARG) + IF (ZI.LT.0.0D0) BK = -BK + P1R = AK + P1I = BK + IF (MOD(INU,2).EQ.0) GO TO 30 + P1R = -P1R + P1I = -P1I + 30 CONTINUE + DO 70 K=1,IL + SQK = FDN - 1.0D0 + ATOL = S*DABS(SQK) + SGN = 1.0D0 + CS1R = CONER + CS1I = CONEI + CS2R = CONER + CS2I = CONEI + CKR = CONER + CKI = CONEI + AK = 0.0D0 + AA = 1.0D0 + BB = AEZ + DKR = EZR + DKI = EZI + DO 40 J=1,JL + CALL ZDIV(CKR, CKI, DKR, DKI, STR, STI) + CKR = STR*SQK + CKI = STI*SQK + CS2R = CS2R + CKR + CS2I = CS2I + CKI + SGN = -SGN + CS1R = CS1R + CKR*SGN + CS1I = CS1I + CKI*SGN + DKR = DKR + EZR + DKI = DKI + EZI + AA = AA*DABS(SQK)/BB + BB = BB + AEZ + AK = AK + 8.0D0 + SQK = SQK - AK + IF (AA.LE.ATOL) GO TO 50 + 40 CONTINUE + GO TO 110 + 50 CONTINUE + S2R = CS1R + S2I = CS1I + IF (ZR+ZR.GE.ELIM) GO TO 60 + TZR = ZR + ZR + TZI = ZI + ZI + CALL ZEXP(-TZR, -TZI, STR, STI) + CALL ZMLT(STR, STI, P1R, P1I, STR, STI) + CALL ZMLT(STR, STI, CS2R, CS2I, STR, STI) + S2R = S2R + STR + S2I = S2I + STI + 60 CONTINUE + FDN = FDN + 8.0D0*DFNU + 4.0D0 + P1R = -P1R + P1I = -P1I + M = N - IL + K + YR(M) = S2R*AK1R - S2I*AK1I + YI(M) = S2R*AK1I + S2I*AK1R + 70 CONTINUE + IF (N.LE.2) RETURN + NN = N + K = NN - 2 + AK = DBLE(FLOAT(K)) + STR = ZR*RAZ + STI = -ZI*RAZ + RZR = (STR+STR)*RAZ + RZI = (STI+STI)*RAZ + IB = 3 + DO 80 I=IB,NN + YR(K) = (AK+FNU)*(RZR*YR(K+1)-RZI*YI(K+1)) + YR(K+2) + YI(K) = (AK+FNU)*(RZR*YI(K+1)+RZI*YR(K+1)) + YI(K+2) + AK = AK - 1.0D0 + K = K - 1 + 80 CONTINUE + IF (KODED.EQ.0) RETURN + CALL ZEXP(CZR, CZI, CKR, CKI) + DO 90 I=1,NN + STR = YR(I)*CKR - YI(I)*CKI + YI(I) = YR(I)*CKI + YI(I)*CKR + YR(I) = STR + 90 CONTINUE + RETURN + 100 CONTINUE + NZ = -1 + RETURN + 110 CONTINUE + NZ=-2 + RETURN + END + +SUBROUTINE ZUOIK(ZR, ZI, FNU, KODE, IKFLG, N, YR, YI, NUF, TOL, ELIM, ALIM) +USE UTILIT +USE COMPLEX +!***BEGIN PROLOGUE ZUOIK +!***REFER TO ZBESI,ZBESK,ZBESH +! +! ZUOIK COMPUTES THE LEADING TERMS OF THE UNIFORM ASYMPTOTIC +! EXPANSIONS FOR THE I AND K FUNCTIONS AND COMPARES THEM +! (IN LOGARITHMI! FORM) TO ALIM AND ELIM FOR OVER AND UNDERFLOW +! WHERE ALIM.LT.ELIM. IF THE MAGNITUDE, BASED ON THE LEADING +! EXPONENTIAL, IS LESS THAN ALIM OR GREATER THAN -ALIM, THEN +! THE RESULT IS ON SCALE. IF NOT, THEN A REFINED TEST USING OTHER +! MULTIPLIERS (IN LOGARITHMI! FORM) IS MADE BASED ON ELIM. HERE +! EXP(-ELIM)=SMALLEST MACHINE NUMBER*1.0E+3 AND EXP(-ALIM)= +! EXP(-ELIM)/TOL +! +! IKFLG=1 MEANS THE I SEQUENCE IS TESTED +! =2 MEANS THE K SEQUENCE IS TESTED +! NUF = 0 MEANS THE LAST MEMBER OF THE SEQUENCE IS ON SCALE +! =-1 MEANS AN OVERFLOW WOULD OCCUR +! IKFLG=1 AND NUF.GT.0 MEANS THE LAST NUF Y VALUES WERE SET TO ZERO +! THE FIRST N-NUF VALUES MUST BE SET BY ANOTHER ROUTINE +! IKFLG=2 AND NUF.EQ.N MEANS ALL Y VALUES WERE SET TO ZERO +! IKFLG=2 AND 0.LT.NUF.LT.N NOT CONSIDERED. Y MUST BE SET BY +! ANOTHER ROUTINE +! +!***ROUTINES CALLED ZUCHK,ZUNHJ,ZUNIK,D1MACH,ZABS,ZLOG +!***END PROLOGUE ZUOIK +! COMPLEX ARG,ASUM,BSUM,CWRK,CZ,CZERO,PHI,SUM,Y,Z,ZB,ZETA1,ZETA2,ZN, +! *ZR + DOUBLE PRECISION AARG, AIC, ALIM, APHI, ARGI, ARGR, ASUMI, ASUMR, & + ASCLE, AX, AY, BSUMI, BSUMR, CWRKI, CWRKR, CZI, CZR, ELIM, FNN, & + FNU, GNN, GNU, PHII, PHIR, RCZ, STR, STI, SUMI, SUMR, TOL, YI, & + YR, ZBI, ZBR, ZEROI, ZEROR, ZETA1I, ZETA1R, ZETA2I, ZETA2R, ZI, & + ZNI, ZNR, ZR, ZRI, ZRR + INTEGER I, IDUM, IFORM, IKFLG, INIT, KODE, N, NN, NUF, NW + DIMENSION YR(1), YI(1), CWRKR(16), CWRKI(16) + DATA ZEROR,ZEROI / 0.0D0, 0.0D0 / + DATA AIC / 1.265512123484645396D+00 / + NUF = 0 + NN = N + ZRR = ZR + ZRI = ZI + IF (ZR.GE.0.0D0) GO TO 10 + ZRR = -ZR + ZRI = -ZI + 10 CONTINUE + ZBR = ZRR + ZBI = ZRI + AX = DABS(ZR)*1.7321D0 + AY = DABS(ZI) + IFORM = 1 + IF (AY.GT.AX) IFORM = 2 + GNU = DMAX1(FNU,1.0D0) + IF (IKFLG.EQ.1) GO TO 20 + FNN = DBLE(FLOAT(NN)) + GNN = FNU + FNN - 1.0D0 + GNU = DMAX1(GNN,FNN) + 20 CONTINUE +!----------------------------------------------------------------------- +! ONLY THE MAGNITUDE OF ARG AND PHI ARE NEEDED ALONG WITH THE +! REAL PARTS OF ZETA1, ZETA2 AND ZB. NO ATTEMPT IS MADE TO GET +! THE SIGN OF THE IMAGINARY PART CORRECT. +!----------------------------------------------------------------------- + IF (IFORM.EQ.2) GO TO 30 + INIT = 0 + CALL ZUNIK(ZRR, ZRI, GNU, IKFLG, 1, TOL, INIT, PHIR, PHII, & + ZETA1R, ZETA1I, ZETA2R, ZETA2I, SUMR, SUMI, CWRKR, CWRKI) + CZR = -ZETA1R + ZETA2R + CZI = -ZETA1I + ZETA2I + GO TO 50 + 30 CONTINUE + ZNR = ZRI + ZNI = -ZRR + IF (ZI.GT.0.0D0) GO TO 40 + ZNR = -ZNR + 40 CONTINUE + CALL ZUNHJ(ZNR, ZNI, GNU, 1, TOL, PHIR, PHII, ARGR, ARGI, ZETA1R, & + ZETA1I, ZETA2R, ZETA2I, ASUMR, ASUMI, BSUMR, BSUMI) + CZR = -ZETA1R + ZETA2R + CZI = -ZETA1I + ZETA2I + AARG = ZABS(ARGR,ARGI) + 50 CONTINUE + IF (KODE.EQ.1) GO TO 60 + CZR = CZR - ZBR + CZI = CZI - ZBI + 60 CONTINUE + IF (IKFLG.EQ.1) GO TO 70 + CZR = -CZR + CZI = -CZI + 70 CONTINUE + APHI = ZABS(PHIR,PHII) + RCZ = CZR +!----------------------------------------------------------------------- +! OVERFLOW TEST +!----------------------------------------------------------------------- + IF (RCZ.GT.ELIM) GO TO 210 + IF (RCZ.LT.ALIM) GO TO 80 + RCZ = RCZ + DLOG(APHI) + IF (IFORM.EQ.2) RCZ = RCZ - 0.25D0*DLOG(AARG) - AIC + IF (RCZ.GT.ELIM) GO TO 210 + GO TO 130 + 80 CONTINUE +!----------------------------------------------------------------------- +! UNDERFLOW TEST +!----------------------------------------------------------------------- + IF (RCZ.LT.(-ELIM)) GO TO 90 + IF (RCZ.GT.(-ALIM)) GO TO 130 + RCZ = RCZ + DLOG(APHI) + IF (IFORM.EQ.2) RCZ = RCZ - 0.25D0*DLOG(AARG) - AIC + IF (RCZ.GT.(-ELIM)) GO TO 110 + 90 CONTINUE + DO 100 I=1,NN + YR(I) = ZEROR + YI(I) = ZEROI + 100 CONTINUE + NUF = NN + RETURN + 110 CONTINUE + ASCLE = 1.0D+3*D1MACH(1)/TOL + CALL ZLOG(PHIR, PHII, STR, STI, IDUM) + CZR = CZR + STR + CZI = CZI + STI + IF (IFORM.EQ.1) GO TO 120 + CALL ZLOG(ARGR, ARGI, STR, STI, IDUM) + CZR = CZR - 0.25D0*STR - AIC + CZI = CZI - 0.25D0*STI + 120 CONTINUE + AX = DEXP(RCZ)/TOL + AY = CZI + CZR = AX*DCOS(AY) + CZI = AX*DSIN(AY) + CALL ZUCHK(CZR, CZI, NW, ASCLE, TOL) + IF (NW.NE.0) GO TO 90 + 130 CONTINUE + IF (IKFLG.EQ.2) RETURN + IF (N.EQ.1) RETURN +!----------------------------------------------------------------------- +! SET UNDERFLOWS ON I SEQUENCE +!----------------------------------------------------------------------- + 140 CONTINUE + GNU = FNU + DBLE(FLOAT(NN-1)) + IF (IFORM.EQ.2) GO TO 150 + INIT = 0 + CALL ZUNIK(ZRR, ZRI, GNU, IKFLG, 1, TOL, INIT, PHIR, PHII, & + ZETA1R, ZETA1I, ZETA2R, ZETA2I, SUMR, SUMI, CWRKR, CWRKI) + CZR = -ZETA1R + ZETA2R + CZI = -ZETA1I + ZETA2I + GO TO 160 + 150 CONTINUE + CALL ZUNHJ(ZNR, ZNI, GNU, 1, TOL, PHIR, PHII, ARGR, ARGI, ZETA1R, & + ZETA1I, ZETA2R, ZETA2I, ASUMR, ASUMI, BSUMR, BSUMI) + CZR = -ZETA1R + ZETA2R + CZI = -ZETA1I + ZETA2I + AARG = ZABS(ARGR,ARGI) + 160 CONTINUE + IF (KODE.EQ.1) GO TO 170 + CZR = CZR - ZBR + CZI = CZI - ZBI + 170 CONTINUE + APHI = ZABS(PHIR,PHII) + RCZ = CZR + IF (RCZ.LT.(-ELIM)) GO TO 180 + IF (RCZ.GT.(-ALIM)) RETURN + RCZ = RCZ + DLOG(APHI) + IF (IFORM.EQ.2) RCZ = RCZ - 0.25D0*DLOG(AARG) - AIC + IF (RCZ.GT.(-ELIM)) GO TO 190 + 180 CONTINUE + YR(NN) = ZEROR + YI(NN) = ZEROI + NN = NN - 1 + NUF = NUF + 1 + IF (NN.EQ.0) RETURN + GO TO 140 + 190 CONTINUE + ASCLE = 1.0D+3*D1MACH(1)/TOL + CALL ZLOG(PHIR, PHII, STR, STI, IDUM) + CZR = CZR + STR + CZI = CZI + STI + IF (IFORM.EQ.1) GO TO 200 + CALL ZLOG(ARGR, ARGI, STR, STI, IDUM) + CZR = CZR - 0.25D0*STR - AIC + CZI = CZI - 0.25D0*STI + 200 CONTINUE + AX = DEXP(RCZ)/TOL + AY = CZI + CZR = AX*DCOS(AY) + CZI = AX*DSIN(AY) + CALL ZUCHK(CZR, CZI, NW, ASCLE, TOL) + IF (NW.NE.0) GO TO 180 + RETURN + 210 CONTINUE + NUF = -1 + RETURN + END + +SUBROUTINE ZBUNI(ZR, ZI, FNU, KODE, N, YR, YI, NZ, NUI, NLAST, FNUL, TOL, ELIM, ALIM) +USE UTILIT +USE COMPLEX +!***BEGIN PROLOGUE ZBUNI +!***REFER TO ZBESI,ZBESK +! +! ZBUNI COMPUTES THE I BESSEL FUNCTION FOR LARGE CABS(Z).GT. +! FNUL AND FNU+N-1.LT.FNUL. THE ORDER IS INCREASED FROM +! FNU+N-1 GREATER THAN FNUL BY ADDING NUI AND COMPUTING +! ACCORDING TO THE UNIFORM ASYMPTOTIC EXPANSION FOR I(FNU,Z) +! ON IFORM=1 AND THE EXPANSION FOR J(FNU,Z) ON IFORM=2 +! +!***ROUTINES CALLED ZUNI1,ZUNI2,ZABS,D1MACH +!***END PROLOGUE ZBUNI +! COMPLEX CSCL,CSCR,CY,RZ,ST,S1,S2,Y,Z + DOUBLE PRECISION ALIM, AX, AY, CSCLR, CSCRR, CYI, CYR, DFNU, & + ELIM, FNU, FNUI, FNUL, GNU, RAZ, RZI, RZR, STI, STR, S1I, S1R, & + S2I, S2R, TOL, YI, YR, ZI, ZR, ASCLE, BRY, C1R, C1I, C1M + INTEGER I, IFLAG, IFORM, K, KODE, N, NL, NLAST, NUI, NW, NZ + DIMENSION YR(1), YI(1), CYR(2), CYI(2), BRY(3) + NZ = 0 + AX = DABS(ZR)*1.7321D0 + AY = DABS(ZI) + IFORM = 1 + IF (AY.GT.AX) IFORM = 2 + IF (NUI.EQ.0) GO TO 60 + FNUI = DBLE(FLOAT(NUI)) + DFNU = FNU + DBLE(FLOAT(N-1)) + GNU = DFNU + FNUI + IF (IFORM.EQ.2) GO TO 10 +!----------------------------------------------------------------------- +! ASYMPTOTIC EXPANSION FOR I(FNU,Z) FOR LARGE FNU APPLIED IN +! -PI/3.LE.ARG(Z).LE.PI/3 +!----------------------------------------------------------------------- + CALL ZUNI1(ZR, ZI, GNU, KODE, 2, CYR, CYI, NW, NLAST, FNUL, TOL, ELIM, ALIM) + GO TO 20 + 10 CONTINUE +!----------------------------------------------------------------------- +! ASYMPTOTIC EXPANSION FOR J(FNU,Z*EXP(M*HPI)) FOR LARGE FNU +! APPLIED IN PI/3.LT.ABS(ARG(Z)).LE.PI/2 WHERE M=+I OR -I +! AND HPI=PI/2 +!----------------------------------------------------------------------- + CALL ZUNI2(ZR, ZI, GNU, KODE, 2, CYR, CYI, NW, NLAST, FNUL, TOL, ELIM, ALIM) + 20 CONTINUE + IF (NW.LT.0) GO TO 50 + IF (NW.NE.0) GO TO 90 + STR = ZABS(CYR(1),CYI(1)) +!---------------------------------------------------------------------- +! SCALE BACKWARD RECURRENCE, BRY(3) IS DEFINED BUT NEVER USED +!---------------------------------------------------------------------- + BRY(1)=1.0D+3*D1MACH(1)/TOL + BRY(2) = 1.0D0/BRY(1) + BRY(3) = BRY(2) + IFLAG = 2 + ASCLE = BRY(2) + CSCLR = 1.0D0 + IF (STR.GT.BRY(1)) GO TO 21 + IFLAG = 1 + ASCLE = BRY(1) + CSCLR = 1.0D0/TOL + GO TO 25 + 21 CONTINUE + IF (STR.LT.BRY(2)) GO TO 25 + IFLAG = 3 + ASCLE=BRY(3) + CSCLR = TOL + 25 CONTINUE + CSCRR = 1.0D0/CSCLR + S1R = CYR(2)*CSCLR + S1I = CYI(2)*CSCLR + S2R = CYR(1)*CSCLR + S2I = CYI(1)*CSCLR + RAZ = 1.0D0/ZABS(ZR,ZI) + STR = ZR*RAZ + STI = -ZI*RAZ + RZR = (STR+STR)*RAZ + RZI = (STI+STI)*RAZ + DO 30 I=1,NUI + STR = S2R + STI = S2I + S2R = (DFNU+FNUI)*(RZR*STR-RZI*STI) + S1R + S2I = (DFNU+FNUI)*(RZR*STI+RZI*STR) + S1I + S1R = STR + S1I = STI + FNUI = FNUI - 1.0D0 + IF (IFLAG.GE.3) GO TO 30 + STR = S2R*CSCRR + STI = S2I*CSCRR + C1R = DABS(STR) + C1I = DABS(STI) + C1M = DMAX1(C1R,C1I) + IF (C1M.LE.ASCLE) GO TO 30 + IFLAG = IFLAG+1 + ASCLE = BRY(IFLAG) + S1R = S1R*CSCRR + S1I = S1I*CSCRR + S2R = STR + S2I = STI + CSCLR = CSCLR*TOL + CSCRR = 1.0D0/CSCLR + S1R = S1R*CSCLR + S1I = S1I*CSCLR + S2R = S2R*CSCLR + S2I = S2I*CSCLR + 30 CONTINUE + YR(N) = S2R*CSCRR + YI(N) = S2I*CSCRR + IF (N.EQ.1) RETURN + NL = N - 1 + FNUI = DBLE(FLOAT(NL)) + K = NL + DO 40 I=1,NL + STR = S2R + STI = S2I + S2R = (FNU+FNUI)*(RZR*STR-RZI*STI) + S1R + S2I = (FNU+FNUI)*(RZR*STI+RZI*STR) + S1I + S1R = STR + S1I = STI + STR = S2R*CSCRR + STI = S2I*CSCRR + YR(K) = STR + YI(K) = STI + FNUI = FNUI - 1.0D0 + K = K - 1 + IF (IFLAG.GE.3) GO TO 40 + C1R = DABS(STR) + C1I = DABS(STI) + C1M = DMAX1(C1R,C1I) + IF (C1M.LE.ASCLE) GO TO 40 + IFLAG = IFLAG+1 + ASCLE = BRY(IFLAG) + S1R = S1R*CSCRR + S1I = S1I*CSCRR + S2R = STR + S2I = STI + CSCLR = CSCLR*TOL + CSCRR = 1.0D0/CSCLR + S1R = S1R*CSCLR + S1I = S1I*CSCLR + S2R = S2R*CSCLR + S2I = S2I*CSCLR + 40 CONTINUE + RETURN + 50 CONTINUE + NZ = -1 + IF(NW.EQ.(-2)) NZ=-2 + RETURN + 60 CONTINUE + IF (IFORM.EQ.2) GO TO 70 +!----------------------------------------------------------------------- +! ASYMPTOTIC EXPANSION FOR I(FNU,Z) FOR LARGE FNU APPLIED IN +! -PI/3.LE.ARG(Z).LE.PI/3 +!----------------------------------------------------------------------- + CALL ZUNI1(ZR, ZI, FNU, KODE, N, YR, YI, NW, NLAST, FNUL, TOL, ELIM, ALIM) + GO TO 80 + 70 CONTINUE +!----------------------------------------------------------------------- +! ASYMPTOTIC EXPANSION FOR J(FNU,Z*EXP(M*HPI)) FOR LARGE FNU +! APPLIED IN PI/3.LT.ABS(ARG(Z)).LE.PI/2 WHERE M=+I OR -I +! AND HPI=PI/2 +!----------------------------------------------------------------------- + CALL ZUNI2(ZR, ZI, FNU, KODE, N, YR, YI, NW, NLAST, FNUL, TOL, ELIM, ALIM) + 80 CONTINUE + IF (NW.LT.0) GO TO 50 + NZ = NW + RETURN + 90 CONTINUE + NLAST = N + RETURN + END + +SUBROUTINE ZUNI1(ZR, ZI, FNU, KODE, N, YR, YI, NZ, NLAST, FNUL, TOL, ELIM, ALIM) +USE UTILIT +USE COMPLEX +!***BEGIN PROLOGUE ZUNI1 +!***REFER TO ZBESI,ZBESK +! +! ZUNI1 COMPUTES I(FNU,Z) BY MEANS OF THE UNIFORM ASYMPTOTIC +! EXPANSION FOR I(FNU,Z) IN -PI/3.LE.ARG Z.LE.PI/3. +! +! FNUL IS THE SMALLEST ORDER PERMITTED FOR THE ASYMPTOTIC +! EXPANSION. NLAST=0 MEANS ALL OF THE Y VALUES WERE SET. +! NLAST.NE.0 IS THE NUMBER LEFT TO BE COMPUTED BY ANOTHER +! FORMULA FOR ORDERS FNU TO FNU+NLAST-1 BECAUSE FNU+NLAST-1.LT.FNUL. +! Y(I)=CZERO FOR I=NLAST+1,N +! +!***ROUTINES CALLED ZUCHK,ZUNIK,ZUOIK,D1MACH,ZABS +!***END PROLOGUE ZUNI1 +! COMPLEX CFN,CONE,CRSC,CSCL,CSR,CSS,CWRK,CZERO,C1,C2,PHI,RZ,SUM,S1, +! *S2,Y,Z,ZETA1,ZETA2 + DOUBLE PRECISION ALIM, APHI, ASCLE, BRY, CONEI, CONER, CRSC, & + CSCL, CSRR, CSSR, CWRKI, CWRKR, C1R, C2I, C2M, C2R, ELIM, FN, & + FNU, FNUL, PHII, PHIR, RAST, RS1, RZI, RZR, STI, STR, SUMI, & + SUMR, S1I, S1R, S2I, S2R, TOL, YI, YR, ZEROI, ZEROR, ZETA1I, & + ZETA1R, ZETA2I, ZETA2R, ZI, ZR, CYR, CYI + INTEGER I, IFLAG, INIT, K, KODE, M, N, ND, NLAST, NN, NUF, NW, NZ + DIMENSION BRY(3), YR(1), YI(1), CWRKR(16), CWRKI(16), CSSR(3), & + CSRR(3), CYR(2), CYI(2) + DATA ZEROR,ZEROI,CONER,CONEI / 0.0D0, 0.0D0, 1.0D0, 0.0D0 / + + NZ = 0 + ND = N + NLAST = 0 +!----------------------------------------------------------------------- +! COMPUTED VALUES WITH EXPONENTS BETWEEN ALIM AND ELIM IN MAG- +! NITUDE ARE SCALED TO KEEP INTERMEDIATE ARITHMETIC ON SCALE, +! EXP(ALIM)=EXP(ELIM)*TOL +!----------------------------------------------------------------------- + CSCL = 1.0D0/TOL + CRSC = TOL + CSSR(1) = CSCL + CSSR(2) = CONER + CSSR(3) = CRSC + CSRR(1) = CRSC + CSRR(2) = CONER + CSRR(3) = CSCL + BRY(1) = 1.0D+3*D1MACH(1)/TOL +!----------------------------------------------------------------------- +! CHECK FOR UNDERFLOW AND OVERFLOW ON FIRST MEMBER +!----------------------------------------------------------------------- + FN = DMAX1(FNU,1.0D0) + INIT = 0 + CALL ZUNIK(ZR, ZI, FN, 1, 1, TOL, INIT, PHIR, PHII, ZETA1R, & + ZETA1I, ZETA2R, ZETA2I, SUMR, SUMI, CWRKR, CWRKI) + IF (KODE.EQ.1) GO TO 10 + STR = ZR + ZETA2R + STI = ZI + ZETA2I + RAST = FN/ZABS(STR,STI) + STR = STR*RAST*RAST + STI = -STI*RAST*RAST + S1R = -ZETA1R + STR + S1I = -ZETA1I + STI + GO TO 20 + 10 CONTINUE + S1R = -ZETA1R + ZETA2R + S1I = -ZETA1I + ZETA2I + 20 CONTINUE + RS1 = S1R + IF (DABS(RS1).GT.ELIM) GO TO 130 + 30 CONTINUE + NN = MIN0(2,ND) + DO 80 I=1,NN + FN = FNU + DBLE(FLOAT(ND-I)) + INIT = 0 + CALL ZUNIK(ZR, ZI, FN, 1, 0, TOL, INIT, PHIR, PHII, ZETA1R, & + ZETA1I, ZETA2R, ZETA2I, SUMR, SUMI, CWRKR, CWRKI) + IF (KODE.EQ.1) GO TO 40 + STR = ZR + ZETA2R + STI = ZI + ZETA2I + RAST = FN/ZABS(STR,STI) + STR = STR*RAST*RAST + STI = -STI*RAST*RAST + S1R = -ZETA1R + STR + S1I = -ZETA1I + STI + ZI + GO TO 50 + 40 CONTINUE + S1R = -ZETA1R + ZETA2R + S1I = -ZETA1I + ZETA2I + 50 CONTINUE +!----------------------------------------------------------------------- +! TEST FOR UNDERFLOW AND OVERFLOW +!----------------------------------------------------------------------- + RS1 = S1R + IF (DABS(RS1).GT.ELIM) GO TO 110 + IF (I.EQ.1) IFLAG = 2 + IF (DABS(RS1).LT.ALIM) GO TO 60 +!----------------------------------------------------------------------- +! REFINE TEST AND SCALE +!----------------------------------------------------------------------- + APHI = ZABS(PHIR,PHII) + RS1 = RS1 + DLOG(APHI) + IF (DABS(RS1).GT.ELIM) GO TO 110 + IF (I.EQ.1) IFLAG = 1 + IF (RS1.LT.0.0D0) GO TO 60 + IF (I.EQ.1) IFLAG = 3 + 60 CONTINUE +!----------------------------------------------------------------------- +! SCALE S1 IF CABS(S1).LT.ASCLE +!----------------------------------------------------------------------- + S2R = PHIR*SUMR - PHII*SUMI + S2I = PHIR*SUMI + PHII*SUMR + STR = DEXP(S1R)*CSSR(IFLAG) + S1R = STR*DCOS(S1I) + S1I = STR*DSIN(S1I) + STR = S2R*S1R - S2I*S1I + S2I = S2R*S1I + S2I*S1R + S2R = STR + IF (IFLAG.NE.1) GO TO 70 + CALL ZUCHK(S2R, S2I, NW, BRY(1), TOL) + IF (NW.NE.0) GO TO 110 + 70 CONTINUE + CYR(I) = S2R + CYI(I) = S2I + M = ND - I + 1 + YR(M) = S2R*CSRR(IFLAG) + YI(M) = S2I*CSRR(IFLAG) + 80 CONTINUE + IF (ND.LE.2) GO TO 100 + RAST = 1.0D0/ZABS(ZR,ZI) + STR = ZR*RAST + STI = -ZI*RAST + RZR = (STR+STR)*RAST + RZI = (STI+STI)*RAST + BRY(2) = 1.0D0/BRY(1) + BRY(3) = D1MACH(2) + S1R = CYR(1) + S1I = CYI(1) + S2R = CYR(2) + S2I = CYI(2) + C1R = CSRR(IFLAG) + ASCLE = BRY(IFLAG) + K = ND - 2 + FN = DBLE(FLOAT(K)) + DO 90 I=3,ND + C2R = S2R + C2I = S2I + S2R = S1R + (FNU+FN)*(RZR*C2R-RZI*C2I) + S2I = S1I + (FNU+FN)*(RZR*C2I+RZI*C2R) + S1R = C2R + S1I = C2I + C2R = S2R*C1R + C2I = S2I*C1R + YR(K) = C2R + YI(K) = C2I + K = K - 1 + FN = FN - 1.0D0 + IF (IFLAG.GE.3) GO TO 90 + STR = DABS(C2R) + STI = DABS(C2I) + C2M = DMAX1(STR,STI) + IF (C2M.LE.ASCLE) GO TO 90 + IFLAG = IFLAG + 1 + ASCLE = BRY(IFLAG) + S1R = S1R*C1R + S1I = S1I*C1R + S2R = C2R + S2I = C2I + S1R = S1R*CSSR(IFLAG) + S1I = S1I*CSSR(IFLAG) + S2R = S2R*CSSR(IFLAG) + S2I = S2I*CSSR(IFLAG) + C1R = CSRR(IFLAG) + 90 CONTINUE + 100 CONTINUE + RETURN +!----------------------------------------------------------------------- +! SET UNDERFLOW AND UPDATE PARAMETERS +!----------------------------------------------------------------------- + 110 CONTINUE + IF (RS1.GT.0.0D0) GO TO 120 + YR(ND) = ZEROR + YI(ND) = ZEROI + NZ = NZ + 1 + ND = ND - 1 + IF (ND.EQ.0) GO TO 100 + CALL ZUOIK(ZR, ZI, FNU, KODE, 1, ND, YR, YI, NUF, TOL, ELIM, ALIM) + IF (NUF.LT.0) GO TO 120 + ND = ND - NUF + NZ = NZ + NUF + IF (ND.EQ.0) GO TO 100 + FN = FNU + DBLE(FLOAT(ND-1)) + IF (FN.GE.FNUL) GO TO 30 + NLAST = ND + RETURN + 120 CONTINUE + NZ = -1 + RETURN + 130 CONTINUE + IF (RS1.GT.0.0D0) GO TO 120 + NZ = N + DO 140 I=1,N + YR(I) = ZEROR + YI(I) = ZEROI + 140 CONTINUE + RETURN + END + +SUBROUTINE ZUNI2(ZR, ZI, FNU, KODE, N, YR, YI, NZ, NLAST, FNUL, TOL, ELIM, ALIM) +USE UTILIT +USE COMPLEX +!***BEGIN PROLOGUE ZUNI2 +!***REFER TO ZBESI,ZBESK +! +! ZUNI2 COMPUTES I(FNU,Z) IN THE RIGHT HALF PLANE BY MEANS OF +! UNIFORM ASYMPTOTIC EXPANSION FOR J(FNU,ZN) WHERE ZN IS Z*I +! OR -Z*I AND ZN IS IN THE RIGHT HALF PLANE ALSO. +! +! FNUL IS THE SMALLEST ORDER PERMITTED FOR THE ASYMPTOTIC +! EXPANSION. NLAST=0 MEANS ALL OF THE Y VALUES WERE SET. +! NLAST.NE.0 IS THE NUMBER LEFT TO BE COMPUTED BY ANOTHER +! FORMULA FOR ORDERS FNU TO FNU+NLAST-1 BECAUSE FNU+NLAST-1.LT.FNUL. +! Y(I)=CZERO FOR I=NLAST+1,N +! +!***ROUTINES CALLED ZAIRY,ZUCHK,ZUNHJ,ZUOIK,D1MACH,ZABS +!***END PROLOGUE ZUNI2 +! COMPLEX AI,ARG,ASUM,BSUM,CFN,CI,CID,CIP,CONE,CRSC,CSCL,CSR,CSS, +! *CZERO,C1,C2,DAI,PHI,RZ,S1,S2,Y,Z,ZB,ZETA1,ZETA2,ZN + DOUBLE PRECISION AARG, AIC, AII, AIR, ALIM, ANG, APHI, ARGI, & + ARGR, ASCLE, ASUMI, ASUMR, BRY, BSUMI, BSUMR, CIDI, CIPI, CIPR, & + CONEI, CONER, CRSC, CSCL, CSRR, CSSR, C1R, C2I, C2M, C2R, DAII, & + DAIR, ELIM, FN, FNU, FNUL, HPI, PHII, PHIR, RAST, RAZ, RS1, RZI, & + RZR, STI, STR, S1I, S1R, S2I, S2R, TOL, YI, YR, ZBI, ZBR, ZEROI, & + ZEROR, ZETA1I, ZETA1R, ZETA2I, ZETA2R, ZI, ZNI, ZNR, ZR, CYR, CYI + INTEGER I, IFLAG, IN, INU, J, K, KODE, N, NAI, ND, NDAI, NLAST, & + NN, NUF, NW, NZ, IDUM + DIMENSION BRY(3), YR(1), YI(1), CIPR(4), CIPI(4), CSSR(3), & + CSRR(3), CYR(2), CYI(2) + DATA ZEROR,ZEROI,CONER,CONEI / 0.0D0, 0.0D0, 1.0D0, 0.0D0 / + DATA CIPR(1),CIPI(1),CIPR(2),CIPI(2),CIPR(3),CIPI(3),CIPR(4), & + CIPI(4)/ 1.0D0,0.0D0, 0.0D0,1.0D0, -1.0D0,0.0D0, 0.0D0,-1.0D0/ + DATA HPI, AIC /1.57079632679489662D+00, 1.265512123484645396D+00/ + + NZ = 0 + ND = N + NLAST = 0 +!----------------------------------------------------------------------- +! COMPUTED VALUES WITH EXPONENTS BETWEEN ALIM AND ELIM IN MAG- +! NITUDE ARE SCALED TO KEEP INTERMEDIATE ARITHMETIC ON SCALE, +! EXP(ALIM)=EXP(ELIM)*TOL +!----------------------------------------------------------------------- + CSCL = 1.0D0/TOL + CRSC = TOL + CSSR(1) = CSCL + CSSR(2) = CONER + CSSR(3) = CRSC + CSRR(1) = CRSC + CSRR(2) = CONER + CSRR(3) = CSCL + BRY(1) = 1.0D+3*D1MACH(1)/TOL +!----------------------------------------------------------------------- +! ZN IS IN THE RIGHT HALF PLANE AFTER ROTATION BY CI OR -CI +!----------------------------------------------------------------------- + ZNR = ZI + ZNI = -ZR + ZBR = ZR + ZBI = ZI + CIDI = -CONER + INU = INT(SNGL(FNU)) + ANG = HPI*(FNU-DBLE(FLOAT(INU))) + C2R = DCOS(ANG) + C2I = DSIN(ANG) + IN = INU + N - 1 + IN = MOD(IN,4) + 1 + STR = C2R*CIPR(IN) - C2I*CIPI(IN) + C2I = C2R*CIPI(IN) + C2I*CIPR(IN) + C2R = STR + IF (ZI.GT.0.0D0) GO TO 10 + ZNR = -ZNR + ZBI = -ZBI + CIDI = -CIDI + C2I = -C2I + 10 CONTINUE +!----------------------------------------------------------------------- +! CHECK FOR UNDERFLOW AND OVERFLOW ON FIRST MEMBER +!----------------------------------------------------------------------- + FN = DMAX1(FNU,1.0D0) + CALL ZUNHJ(ZNR, ZNI, FN, 1, TOL, PHIR, PHII, ARGR, ARGI, ZETA1R, & + ZETA1I, ZETA2R, ZETA2I, ASUMR, ASUMI, BSUMR, BSUMI) + IF (KODE.EQ.1) GO TO 20 + STR = ZBR + ZETA2R + STI = ZBI + ZETA2I + RAST = FN/ZABS(STR,STI) + STR = STR*RAST*RAST + STI = -STI*RAST*RAST + S1R = -ZETA1R + STR + S1I = -ZETA1I + STI + GO TO 30 + 20 CONTINUE + S1R = -ZETA1R + ZETA2R + S1I = -ZETA1I + ZETA2I + 30 CONTINUE + RS1 = S1R + IF (DABS(RS1).GT.ELIM) GO TO 150 + 40 CONTINUE + NN = MIN0(2,ND) + DO 90 I=1,NN + FN = FNU + DBLE(FLOAT(ND-I)) + CALL ZUNHJ(ZNR, ZNI, FN, 0, TOL, PHIR, PHII, ARGR, ARGI, & + ZETA1R, ZETA1I, ZETA2R, ZETA2I, ASUMR, ASUMI, BSUMR, BSUMI) + IF (KODE.EQ.1) GO TO 50 + STR = ZBR + ZETA2R + STI = ZBI + ZETA2I + RAST = FN/ZABS(STR,STI) + STR = STR*RAST*RAST + STI = -STI*RAST*RAST + S1R = -ZETA1R + STR + S1I = -ZETA1I + STI + DABS(ZI) + GO TO 60 + 50 CONTINUE + S1R = -ZETA1R + ZETA2R + S1I = -ZETA1I + ZETA2I + 60 CONTINUE +!----------------------------------------------------------------------- +! TEST FOR UNDERFLOW AND OVERFLOW +!----------------------------------------------------------------------- + RS1 = S1R + IF (DABS(RS1).GT.ELIM) GO TO 120 + IF (I.EQ.1) IFLAG = 2 + IF (DABS(RS1).LT.ALIM) GO TO 70 +!----------------------------------------------------------------------- +! REFINE TEST AND SCALE +!----------------------------------------------------------------------- + APHI = ZABS(PHIR,PHII) + AARG = ZABS(ARGR,ARGI) + RS1 = RS1 + DLOG(APHI) - 0.25D0*DLOG(AARG) - AIC + IF (DABS(RS1).GT.ELIM) GO TO 120 + IF (I.EQ.1) IFLAG = 1 + IF (RS1.LT.0.0D0) GO TO 70 + IF (I.EQ.1) IFLAG = 3 + 70 CONTINUE +!----------------------------------------------------------------------- +! SCALE S1 TO KEEP INTERMEDIATE ARITHMETIC ON SCALE NEAR +! EXPONENT EXTREMES +!----------------------------------------------------------------------- + CALL ZAIRY(ARGR, ARGI, 0, 2, AIR, AII, NAI, IDUM) + CALL ZAIRY(ARGR, ARGI, 1, 2, DAIR, DAII, NDAI, IDUM) + STR = DAIR*BSUMR - DAII*BSUMI + STI = DAIR*BSUMI + DAII*BSUMR + STR = STR + (AIR*ASUMR-AII*ASUMI) + STI = STI + (AIR*ASUMI+AII*ASUMR) + S2R = PHIR*STR - PHII*STI + S2I = PHIR*STI + PHII*STR + STR = DEXP(S1R)*CSSR(IFLAG) + S1R = STR*DCOS(S1I) + S1I = STR*DSIN(S1I) + STR = S2R*S1R - S2I*S1I + S2I = S2R*S1I + S2I*S1R + S2R = STR + IF (IFLAG.NE.1) GO TO 80 + CALL ZUCHK(S2R, S2I, NW, BRY(1), TOL) + IF (NW.NE.0) GO TO 120 + 80 CONTINUE + IF (ZI.LE.0.0D0) S2I = -S2I + STR = S2R*C2R - S2I*C2I + S2I = S2R*C2I + S2I*C2R + S2R = STR + CYR(I) = S2R + CYI(I) = S2I + J = ND - I + 1 + YR(J) = S2R*CSRR(IFLAG) + YI(J) = S2I*CSRR(IFLAG) + STR = -C2I*CIDI + C2I = C2R*CIDI + C2R = STR + 90 CONTINUE + IF (ND.LE.2) GO TO 110 + RAZ = 1.0D0/ZABS(ZR,ZI) + STR = ZR*RAZ + STI = -ZI*RAZ + RZR = (STR+STR)*RAZ + RZI = (STI+STI)*RAZ + BRY(2) = 1.0D0/BRY(1) + BRY(3) = D1MACH(2) + S1R = CYR(1) + S1I = CYI(1) + S2R = CYR(2) + S2I = CYI(2) + C1R = CSRR(IFLAG) + ASCLE = BRY(IFLAG) + K = ND - 2 + FN = DBLE(FLOAT(K)) + DO 100 I=3,ND + C2R = S2R + C2I = S2I + S2R = S1R + (FNU+FN)*(RZR*C2R-RZI*C2I) + S2I = S1I + (FNU+FN)*(RZR*C2I+RZI*C2R) + S1R = C2R + S1I = C2I + C2R = S2R*C1R + C2I = S2I*C1R + YR(K) = C2R + YI(K) = C2I + K = K - 1 + FN = FN - 1.0D0 + IF (IFLAG.GE.3) GO TO 100 + STR = DABS(C2R) + STI = DABS(C2I) + C2M = DMAX1(STR,STI) + IF (C2M.LE.ASCLE) GO TO 100 + IFLAG = IFLAG + 1 + ASCLE = BRY(IFLAG) + S1R = S1R*C1R + S1I = S1I*C1R + S2R = C2R + S2I = C2I + S1R = S1R*CSSR(IFLAG) + S1I = S1I*CSSR(IFLAG) + S2R = S2R*CSSR(IFLAG) + S2I = S2I*CSSR(IFLAG) + C1R = CSRR(IFLAG) + 100 CONTINUE + 110 CONTINUE + RETURN + 120 CONTINUE + IF (RS1.GT.0.0D0) GO TO 140 +!----------------------------------------------------------------------- +! SET UNDERFLOW AND UPDATE PARAMETERS +!----------------------------------------------------------------------- + YR(ND) = ZEROR + YI(ND) = ZEROI + NZ = NZ + 1 + ND = ND - 1 + IF (ND.EQ.0) GO TO 110 + CALL ZUOIK(ZR, ZI, FNU, KODE, 1, ND, YR, YI, NUF, TOL, ELIM, ALIM) + IF (NUF.LT.0) GO TO 140 + ND = ND - NUF + NZ = NZ + NUF + IF (ND.EQ.0) GO TO 110 + FN = FNU + DBLE(FLOAT(ND-1)) + IF (FN.LT.FNUL) GO TO 130 + FN = CIDI + J = NUF + 1 + K = MOD(J,4) + 1 + S1R = CIPR(K) + S1I = CIPI(K) + IF (FN.LT.0.0D0) S1I = -S1I + STR = C2R*S1R - C2I*S1I + C2I = C2R*S1I + C2I*S1R + C2R = STR + GO TO 40 + 130 CONTINUE + NLAST = ND + RETURN + 140 CONTINUE + NZ = -1 + RETURN + 150 CONTINUE + IF (RS1.GT.0.0D0) GO TO 140 + NZ = N + DO 160 I=1,N + YR(I) = ZEROR + YI(I) = ZEROI + 160 CONTINUE + RETURN + END + +SUBROUTINE ZWRSK(ZRR, ZRI, FNU, KODE, N, YR, YI, NZ, CWR, CWI, TOL, ELIM, ALIM) +USE UTILIT +USE COMPLEX +!***BEGIN PROLOGUE ZWRSK +!***REFER TO ZBESI,ZBESK +! +! ZWRSK COMPUTES THE I BESSEL FUNCTION FOR RE(Z).GE.0.0 BY +! NORMALIZING THE I FUNCTION RATIOS FROM ZRATI BY THE WRONSKIAN +! +!***ROUTINES CALLED D1MACH,ZBKNU,ZRATI,ZABS +!***END PROLOGUE ZWRSK +! COMPLEX CINU,CSCL,CT,CW,C1,C2,RCT,ST,Y,ZR + DOUBLE PRECISION ACT, ACW, ALIM, ASCLE, CINUI, CINUR, CSCLR, CTI, & + CTR, CWI, CWR, C1I, C1R, C2I, C2R, ELIM, FNU, PTI, PTR, RACT, & + STI, STR, TOL, YI, YR, ZRI, ZRR + INTEGER I, KODE, N, NW, NZ + DIMENSION YR(1), YI(1), CWR(2), CWI(2) +!----------------------------------------------------------------------- +! I(FNU+I-1,Z) BY BACKWARD RECURRENCE FOR RATIOS +! Y(I)=I(FNU+I,Z)/I(FNU+I-1,Z) FROM CRATI NORMALIZED BY THE +! WRONSKIAN WITH K(FNU,Z) AND K(FNU+1,Z) FROM CBKNU. +!----------------------------------------------------------------------- + NZ = 0 + CALL ZBKNU(ZRR, ZRI, FNU, KODE, 2, CWR, CWI, NW, TOL, ELIM, ALIM) + IF (NW.NE.0) GO TO 50 + CALL ZRATI(ZRR, ZRI, FNU, N, YR, YI, TOL) +!----------------------------------------------------------------------- +! RECUR FORWARD ON I(FNU+1,Z) = R(FNU,Z)*I(FNU,Z), +! R(FNU+J-1,Z)=Y(J), J=1,...,N +!----------------------------------------------------------------------- + CINUR = 1.0D0 + CINUI = 0.0D0 + IF (KODE.EQ.1) GO TO 10 + CINUR = DCOS(ZRI) + CINUI = DSIN(ZRI) + 10 CONTINUE +!----------------------------------------------------------------------- +! ON LOW EXPONENT MACHINES THE K FUNCTIONS CAN BE CLOSE TO BOTH +! THE UNDER AND OVERFLOW LIMITS AND THE NORMALIZATION MUST BE +! SCALED TO PREVENT OVER OR UNDERFLOW. CUOIK HAS DETERMINED THAT +! THE RESULT IS ON SCALE. +!----------------------------------------------------------------------- + ACW = ZABS(CWR(2),CWI(2)) + ASCLE = 1.0D+3*D1MACH(1)/TOL + CSCLR = 1.0D0 + IF (ACW.GT.ASCLE) GO TO 20 + CSCLR = 1.0D0/TOL + GO TO 30 + 20 CONTINUE + ASCLE = 1.0D0/ASCLE + IF (ACW.LT.ASCLE) GO TO 30 + CSCLR = TOL + 30 CONTINUE + C1R = CWR(1)*CSCLR + C1I = CWI(1)*CSCLR + C2R = CWR(2)*CSCLR + C2I = CWI(2)*CSCLR + STR = YR(1) + STI = YI(1) +!----------------------------------------------------------------------- +! CINU=CINU*(CONJG(CT)/CABS(CT))*(1.0D0/CABS(CT) PREVENTS +! UNDER- OR OVERFLOW PREMATURELY BY SQUARING CABS(CT) +!----------------------------------------------------------------------- + PTR = STR*C1R - STI*C1I + PTI = STR*C1I + STI*C1R + PTR = PTR + C2R + PTI = PTI + C2I + CTR = ZRR*PTR - ZRI*PTI + CTI = ZRR*PTI + ZRI*PTR + ACT = ZABS(CTR,CTI) + RACT = 1.0D0/ACT + CTR = CTR*RACT + CTI = -CTI*RACT + PTR = CINUR*RACT + PTI = CINUI*RACT + CINUR = PTR*CTR - PTI*CTI + CINUI = PTR*CTI + PTI*CTR + YR(1) = CINUR*CSCLR + YI(1) = CINUI*CSCLR + IF (N.EQ.1) RETURN + DO 40 I=2,N + PTR = STR*CINUR - STI*CINUI + CINUI = STR*CINUI + STI*CINUR + CINUR = PTR + STR = YR(I) + STI = YI(I) + YR(I) = CINUR*CSCLR + YI(I) = CINUI*CSCLR + 40 CONTINUE + RETURN + 50 CONTINUE + NZ = -1 + IF(NW.EQ.(-2)) NZ=-2 + RETURN +END + +SUBROUTINE ZBKNU(ZR, ZI, FNU, KODE, N, YR, YI, NZ, TOL, ELIM, ALIM) +USE UTILIT +USE COMPLEX +!***BEGIN PROLOGUE ZBKNU +!***REFER TO ZBESI,ZBESK,ZAIRY,ZBESH +! +! ZBKNU COMPUTES THE K BESSEL FUNCTION IN THE RIGHT HALF Z PLANE. +! +!***ROUTINES CALLED DGAMLN,I1MACH,D1MACH,ZKSCL,ZSHCH,ZUCHK,ZABS,ZDIV, +! ZEXP,ZLOG,ZMLT,ZSQRT +!***END PROLOGUE ZBKNU +! + DOUBLE PRECISION AA, AK, ALIM, ASCLE, A1, A2, BB, BK, BRY, CAZ, & + CBI, CBR, CC, CCHI, CCHR, CKI, CKR, COEFI, COEFR, CONEI, CONER, & + CRSCR, CSCLR, CSHI, CSHR, CSI, CSR, CSRR, CSSR, CTWOI, CTWOR, & + CZEROI, CZEROR, CZI, CZR, DNU, DNU2, DPI, ELIM, ETEST, FC, FHS, & + FI, FK, FKS, FMUI, FMUR, FNU, FPI, FR, G1, G2, HPI, PI, PR, PTI,& + PTR, P1I, P1R, P2I, P2M, P2R, QI, QR, RAK, RCAZ, RTHPI, RZI, & + RZR, R1, S, SMUI, SMUR, SPI, STI, STR, S1I, S1R, S2I, S2R, TM, & + TOL, TTH, T1, T2, YI, YR, ZI, ZR, ELM, CELMR, ZDR, ZDI, & + AS, ALAS, HELIM, CYR, CYI!, DGAMLN + INTEGER I, IFLAG, INU, K, KFLAG, KK, KMAX, KODE, KODED, N, NZ, & + IDUM, J, IC, INUB, NW + DIMENSION YR(N), YI(N), CC(8), CSSR(3), CSRR(3), BRY(3), CYR(2),& + CYI(2) +! COMPLEX Z,Y,A,B,RZ,SMU,FU,FMU,F,FLRZ,CZ,S1,S2,CSH,CCH +! COMPLEX CK,P,Q,COEF,P1,P2,CBK,PT,CZERO,CONE,CTWO,ST,EZ,CS,DK + + DATA KMAX / 30 / + DATA CZEROR,CZEROI,CONER,CONEI,CTWOR,CTWOI,R1/ & + 0.0D0 , 0.0D0 , 1.0D0 , 0.0D0 , 2.0D0 , 0.0D0 , 2.0D0 / + DATA DPI, RTHPI, SPI ,HPI, FPI, TTH / & + 3.14159265358979324D0, 1.25331413731550025D0, & + 1.90985931710274403D0, 1.57079632679489662D0, & + 1.89769999331517738D0, 6.66666666666666666D-01/ + DATA CC(1), CC(2), CC(3), CC(4), CC(5), CC(6), CC(7), CC(8)/ & + 5.77215664901532861D-01, -4.20026350340952355D-02, & + -4.21977345555443367D-02, 7.21894324666309954D-03, & + -2.15241674114950973D-04, -2.01348547807882387D-05, & + 1.13302723198169588D-06, 6.11609510448141582D-09/ + + CAZ = ZABS(ZR,ZI) + CSCLR = 1.0D0/TOL + CRSCR = TOL + CSSR(1) = CSCLR + CSSR(2) = 1.0D0 + CSSR(3) = CRSCR + CSRR(1) = CRSCR + CSRR(2) = 1.0D0 + CSRR(3) = CSCLR + BRY(1) = 1.0D+3*D1MACH(1)/TOL + BRY(2) = 1.0D0/BRY(1) + BRY(3) = D1MACH(2) + NZ = 0 + IFLAG = 0 + KODED = KODE + RCAZ = 1.0D0/CAZ + STR = ZR*RCAZ + STI = -ZI*RCAZ + RZR = (STR+STR)*RCAZ + RZI = (STI+STI)*RCAZ + INU = INT(SNGL(FNU+0.5D0)) + DNU = FNU - DBLE(FLOAT(INU)) + IF (DABS(DNU).EQ.0.5D0) GO TO 110 + DNU2 = 0.0D0 + IF (DABS(DNU).GT.TOL) DNU2 = DNU*DNU + IF (CAZ.GT.R1) GO TO 110 +!----------------------------------------------------------------------- +! SERIES FOR CABS(Z).LE.R1 +!----------------------------------------------------------------------- + FC = 1.0D0 + CALL ZLOG(RZR, RZI, SMUR, SMUI, IDUM) + FMUR = SMUR*DNU + FMUI = SMUI*DNU + CALL ZSHCH(FMUR, FMUI, CSHR, CSHI, CCHR, CCHI) + IF (DNU.EQ.0.0D0) GO TO 10 + FC = DNU*DPI + FC = FC/DSIN(FC) + SMUR = CSHR/DNU + SMUI = CSHI/DNU + 10 CONTINUE + A2 = 1.0D0 + DNU +!----------------------------------------------------------------------- +! GAM(1-Z)*GAM(1+Z)=PI*Z/SIN(PI*Z), T1=1/GAM(1-DNU), T2=1/GAM(1+DNU) +!----------------------------------------------------------------------- + T2 = DEXP(-DGAMLN(A2,IDUM)) + T1 = 1.0D0/(T2*FC) + IF (DABS(DNU).GT.0.1D0) GO TO 40 +!----------------------------------------------------------------------- +! SERIES FOR F0 TO RESOLVE INDETERMINACY FOR SMALL ABS(DNU) +!----------------------------------------------------------------------- + AK = 1.0D0 + S = CC(1) + DO 20 K=2,8 + AK = AK*DNU2 + TM = CC(K)*AK + S = S + TM + IF (DABS(TM).LT.TOL) GO TO 30 + 20 CONTINUE + 30 G1 = -S + GO TO 50 + 40 CONTINUE + G1 = (T1-T2)/(DNU+DNU) + 50 CONTINUE + G2 = (T1+T2)*0.5D0 + FR = FC*(CCHR*G1+SMUR*G2) + FI = FC*(CCHI*G1+SMUI*G2) + CALL ZEXP(FMUR, FMUI, STR, STI) + PR = 0.5D0*STR/T2 + PI = 0.5D0*STI/T2 + CALL ZDIV(0.5D0, 0.0D0, STR, STI, PTR, PTI) + QR = PTR/T1 + QI = PTI/T1 + S1R = FR + S1I = FI + S2R = PR + S2I = PI + AK = 1.0D0 + A1 = 1.0D0 + CKR = CONER + CKI = CONEI + BK = 1.0D0 - DNU2 + IF (INU.GT.0 .OR. N.GT.1) GO TO 80 +!----------------------------------------------------------------------- +! GENERATE K(FNU,Z), 0.0D0 .LE. FNU .LT. 0.5D0 AND N=1 +!----------------------------------------------------------------------- + IF (CAZ.LT.TOL) GO TO 70 + CALL ZMLT(ZR, ZI, ZR, ZI, CZR, CZI) + CZR = 0.25D0*CZR + CZI = 0.25D0*CZI + T1 = 0.25D0*CAZ*CAZ + 60 CONTINUE + FR = (FR*AK+PR+QR)/BK + FI = (FI*AK+PI+QI)/BK + STR = 1.0D0/(AK-DNU) + PR = PR*STR + PI = PI*STR + STR = 1.0D0/(AK+DNU) + QR = QR*STR + QI = QI*STR + STR = CKR*CZR - CKI*CZI + RAK = 1.0D0/AK + CKI = (CKR*CZI+CKI*CZR)*RAK + CKR = STR*RAK + S1R = CKR*FR - CKI*FI + S1R + S1I = CKR*FI + CKI*FR + S1I + A1 = A1*T1*RAK + BK = BK + AK + AK + 1.0D0 + AK = AK + 1.0D0 + IF (A1.GT.TOL) GO TO 60 + 70 CONTINUE + YR(1) = S1R + YI(1) = S1I + IF (KODED.EQ.1) RETURN + CALL ZEXP(ZR, ZI, STR, STI) + CALL ZMLT(S1R, S1I, STR, STI, YR(1), YI(1)) + RETURN +!----------------------------------------------------------------------- +! GENERATE K(DNU,Z) AND K(DNU+1,Z) FOR FORWARD RECURRENCE +!----------------------------------------------------------------------- + 80 CONTINUE + IF (CAZ.LT.TOL) GO TO 100 + CALL ZMLT(ZR, ZI, ZR, ZI, CZR, CZI) + CZR = 0.25D0*CZR + CZI = 0.25D0*CZI + T1 = 0.25D0*CAZ*CAZ + 90 CONTINUE + FR = (FR*AK+PR+QR)/BK + FI = (FI*AK+PI+QI)/BK + STR = 1.0D0/(AK-DNU) + PR = PR*STR + PI = PI*STR + STR = 1.0D0/(AK+DNU) + QR = QR*STR + QI = QI*STR + STR = CKR*CZR - CKI*CZI + RAK = 1.0D0/AK + CKI = (CKR*CZI+CKI*CZR)*RAK + CKR = STR*RAK + S1R = CKR*FR - CKI*FI + S1R + S1I = CKR*FI + CKI*FR + S1I + STR = PR - FR*AK + STI = PI - FI*AK + S2R = CKR*STR - CKI*STI + S2R + S2I = CKR*STI + CKI*STR + S2I + A1 = A1*T1*RAK + BK = BK + AK + AK + 1.0D0 + AK = AK + 1.0D0 + IF (A1.GT.TOL) GO TO 90 + 100 CONTINUE + KFLAG = 2 + A1 = FNU + 1.0D0 + AK = A1*DABS(SMUR) + IF (AK.GT.ALIM) KFLAG = 3 + STR = CSSR(KFLAG) + P2R = S2R*STR + P2I = S2I*STR + CALL ZMLT(P2R, P2I, RZR, RZI, S2R, S2I) + S1R = S1R*STR + S1I = S1I*STR + IF (KODED.EQ.1) GO TO 210 + CALL ZEXP(ZR, ZI, FR, FI) + CALL ZMLT(S1R, S1I, FR, FI, S1R, S1I) + CALL ZMLT(S2R, S2I, FR, FI, S2R, S2I) + GO TO 210 +!----------------------------------------------------------------------- +! IFLAG=0 MEANS NO UNDERFLOW OCCURRED +! IFLAG=1 MEANS AN UNDERFLOW OCCURRED- COMPUTATION PROCEEDS WITH +! KODED=2 AND A TEST FOR ON SCALE VALUES IS MADE DURING FORWARD +! RECURSION +!----------------------------------------------------------------------- + 110 CONTINUE + CALL ZSQRT(ZR, ZI, STR, STI) + CALL ZDIV(RTHPI, CZEROI, STR, STI, COEFR, COEFI) + KFLAG = 2 + IF (KODED.EQ.2) GO TO 120 + IF (ZR.GT.ALIM) GO TO 290 +! BLANK LINE + STR = DEXP(-ZR)*CSSR(KFLAG) + STI = -STR*DSIN(ZI) + STR = STR*DCOS(ZI) + CALL ZMLT(COEFR, COEFI, STR, STI, COEFR, COEFI) + 120 CONTINUE + IF (DABS(DNU).EQ.0.5D0) GO TO 300 +!----------------------------------------------------------------------- +! MILLER ALGORITHM FOR CABS(Z).GT.R1 +!----------------------------------------------------------------------- + AK = DCOS(DPI*DNU) + AK = DABS(AK) + IF (AK.EQ.CZEROR) GO TO 300 + FHS = DABS(0.25D0-DNU2) + IF (FHS.EQ.CZEROR) GO TO 300 +!----------------------------------------------------------------------- +! COMPUTE R2=F(E). IF CABS(Z).GE.R2, USE FORWARD RECURRENCE TO +! DETERMINE THE BACKWARD INDEX K. R2=F(E) IS A STRAIGHT LINE ON +! 12.LE.E.LE.60. E IS COMPUTED FROM 2**(-E)=B**(1-I1MACH(14))= +! TOL WHERE B IS THE BASE OF THE ARITHMETIC. +!----------------------------------------------------------------------- + T1 = DBLE(FLOAT(I1MACH(14)-1)) + T1 = T1*D1MACH(5)*3.321928094D0 + T1 = DMAX1(T1,12.0D0) + T1 = DMIN1(T1,60.0D0) + T2 = TTH*T1 - 6.0D0 + IF (ZR.NE.0.0D0) GO TO 130 + T1 = HPI + GO TO 140 + 130 CONTINUE + T1 = DATAN(ZI/ZR) + T1 = DABS(T1) + 140 CONTINUE + IF (T2.GT.CAZ) GO TO 170 +!----------------------------------------------------------------------- +! FORWARD RECURRENCE LOOP WHEN CABS(Z).GE.R2 +!----------------------------------------------------------------------- + ETEST = AK/(DPI*CAZ*TOL) + FK = CONER + IF (ETEST.LT.CONER) GO TO 180 + FKS = CTWOR + CKR = CAZ + CAZ + CTWOR + P1R = CZEROR + P2R = CONER + DO 150 I=1,KMAX + AK = FHS/FKS + CBR = CKR/(FK+CONER) + PTR = P2R + P2R = CBR*P2R - P1R*AK + P1R = PTR + CKR = CKR + CTWOR + FKS = FKS + FK + FK + CTWOR + FHS = FHS + FK + FK + FK = FK + CONER + STR = DABS(P2R)*FK + IF (ETEST.LT.STR) GO TO 160 + 150 CONTINUE + GO TO 310 + 160 CONTINUE + FK = FK + SPI*T1*DSQRT(T2/CAZ) + FHS = DABS(0.25D0-DNU2) + GO TO 180 + 170 CONTINUE +!----------------------------------------------------------------------- +! COMPUTE BACKWARD INDEX K FOR CABS(Z).LT.R2 +!----------------------------------------------------------------------- + A2 = DSQRT(CAZ) + AK = FPI*AK/(TOL*DSQRT(A2)) + AA = 3.0D0*T1/(1.0D0+CAZ) + BB = 14.7D0*T1/(28.0D0+CAZ) + AK = (DLOG(AK)+CAZ*DCOS(AA)/(1.0D0+0.008D0*CAZ))/DCOS(BB) + FK = 0.12125D0*AK*AK/CAZ + 1.5D0 + 180 CONTINUE +!----------------------------------------------------------------------- +! BACKWARD RECURRENCE LOOP FOR MILLER ALGORITHM +!----------------------------------------------------------------------- + K = INT(SNGL(FK)) + FK = DBLE(FLOAT(K)) + FKS = FK*FK + P1R = CZEROR + P1I = CZEROI + P2R = TOL + P2I = CZEROI + CSR = P2R + CSI = P2I + DO 190 I=1,K + A1 = FKS - FK + AK = (FKS+FK)/(A1+FHS) + RAK = 2.0D0/(FK+CONER) + CBR = (FK+ZR)*RAK + CBI = ZI*RAK + PTR = P2R + PTI = P2I + P2R = (PTR*CBR-PTI*CBI-P1R)*AK + P2I = (PTI*CBR+PTR*CBI-P1I)*AK + P1R = PTR + P1I = PTI + CSR = CSR + P2R + CSI = CSI + P2I + FKS = A1 - FK + CONER + FK = FK - CONER + 190 CONTINUE +!----------------------------------------------------------------------- +! COMPUTE (P2/CS)=(P2/CABS(CS))*(CONJG(CS)/CABS(CS)) FOR BETTER +! SCALING +!----------------------------------------------------------------------- + TM = ZABS(CSR,CSI) + PTR = 1.0D0/TM + S1R = P2R*PTR + S1I = P2I*PTR + CSR = CSR*PTR + CSI = -CSI*PTR + CALL ZMLT(COEFR, COEFI, S1R, S1I, STR, STI) + CALL ZMLT(STR, STI, CSR, CSI, S1R, S1I) + IF (INU.GT.0 .OR. N.GT.1) GO TO 200 + ZDR = ZR + ZDI = ZI + IF(IFLAG.EQ.1) GO TO 270 + GO TO 240 + 200 CONTINUE +!----------------------------------------------------------------------- +! COMPUTE P1/P2=(P1/CABS(P2)*CONJG(P2)/CABS(P2) FOR SCALING +!----------------------------------------------------------------------- + TM = ZABS(P2R,P2I) + PTR = 1.0D0/TM + P1R = P1R*PTR + P1I = P1I*PTR + P2R = P2R*PTR + P2I = -P2I*PTR + CALL ZMLT(P1R, P1I, P2R, P2I, PTR, PTI) + STR = DNU + 0.5D0 - PTR + STI = -PTI + CALL ZDIV(STR, STI, ZR, ZI, STR, STI) + STR = STR + 1.0D0 + CALL ZMLT(STR, STI, S1R, S1I, S2R, S2I) +!----------------------------------------------------------------------- +! FORWARD RECURSION ON THE THREE TERM RECURSION WITH RELATION WITH +! SCALING NEAR EXPONENT EXTREMES ON KFLAG=1 OR KFLAG=3 +!----------------------------------------------------------------------- + 210 CONTINUE + STR = DNU + 1.0D0 + CKR = STR*RZR + CKI = STR*RZI + IF (N.EQ.1) INU = INU - 1 + IF (INU.GT.0) GO TO 220 + IF (N.GT.1) GO TO 215 + S1R = S2R + S1I = S2I + 215 CONTINUE + ZDR = ZR + ZDI = ZI + IF(IFLAG.EQ.1) GO TO 270 + GO TO 240 + 220 CONTINUE + INUB = 1 + IF(IFLAG.EQ.1) GO TO 261 + 225 CONTINUE + P1R = CSRR(KFLAG) + ASCLE = BRY(KFLAG) + DO 230 I=INUB,INU + STR = S2R + STI = S2I + S2R = CKR*STR - CKI*STI + S1R + S2I = CKR*STI + CKI*STR + S1I + S1R = STR + S1I = STI + CKR = CKR + RZR + CKI = CKI + RZI + IF (KFLAG.GE.3) GO TO 230 + P2R = S2R*P1R + P2I = S2I*P1R + STR = DABS(P2R) + STI = DABS(P2I) + P2M = DMAX1(STR,STI) + IF (P2M.LE.ASCLE) GO TO 230 + KFLAG = KFLAG + 1 + ASCLE = BRY(KFLAG) + S1R = S1R*P1R + S1I = S1I*P1R + S2R = P2R + S2I = P2I + STR = CSSR(KFLAG) + S1R = S1R*STR + S1I = S1I*STR + S2R = S2R*STR + S2I = S2I*STR + P1R = CSRR(KFLAG) + 230 CONTINUE + IF (N.NE.1) GO TO 240 + S1R = S2R + S1I = S2I + 240 CONTINUE + STR = CSRR(KFLAG) + YR(1) = S1R*STR + YI(1) = S1I*STR + IF (N.EQ.1) RETURN + YR(2) = S2R*STR + YI(2) = S2I*STR + IF (N.EQ.2) RETURN + KK = 2 + 250 CONTINUE + KK = KK + 1 + IF (KK.GT.N) RETURN + P1R = CSRR(KFLAG) + ASCLE = BRY(KFLAG) + DO 260 I=KK,N + P2R = S2R + P2I = S2I + S2R = CKR*P2R - CKI*P2I + S1R + S2I = CKI*P2R + CKR*P2I + S1I + S1R = P2R + S1I = P2I + CKR = CKR + RZR + CKI = CKI + RZI + P2R = S2R*P1R + P2I = S2I*P1R + YR(I) = P2R + YI(I) = P2I + IF (KFLAG.GE.3) GO TO 260 + STR = DABS(P2R) + STI = DABS(P2I) + P2M = DMAX1(STR,STI) + IF (P2M.LE.ASCLE) GO TO 260 + KFLAG = KFLAG + 1 + ASCLE = BRY(KFLAG) + S1R = S1R*P1R + S1I = S1I*P1R + S2R = P2R + S2I = P2I + STR = CSSR(KFLAG) + S1R = S1R*STR + S1I = S1I*STR + S2R = S2R*STR + S2I = S2I*STR + P1R = CSRR(KFLAG) + 260 CONTINUE + RETURN +!----------------------------------------------------------------------- +! IFLAG=1 CASES, FORWARD RECURRENCE ON SCALED VALUES ON UNDERFLOW +!----------------------------------------------------------------------- + 261 CONTINUE + HELIM = 0.5D0*ELIM + ELM = DEXP(-ELIM) + CELMR = ELM + ASCLE = BRY(1) + ZDR = ZR + ZDI = ZI + IC = -1 + J = 2 + DO 262 I=1,INU + STR = S2R + STI = S2I + S2R = STR*CKR-STI*CKI+S1R + S2I = STI*CKR+STR*CKI+S1I + S1R = STR + S1I = STI + CKR = CKR+RZR + CKI = CKI+RZI + AS = ZABS(S2R,S2I) + ALAS = DLOG(AS) + P2R = -ZDR+ALAS + IF(P2R.LT.(-ELIM)) GO TO 263 + CALL ZLOG(S2R,S2I,STR,STI,IDUM) + P2R = -ZDR+STR + P2I = -ZDI+STI + P2M = DEXP(P2R)/TOL + P1R = P2M*DCOS(P2I) + P1I = P2M*DSIN(P2I) + CALL ZUCHK(P1R,P1I,NW,ASCLE,TOL) + IF(NW.NE.0) GO TO 263 + J = 3 - J + CYR(J) = P1R + CYI(J) = P1I + IF(IC.EQ.(I-1)) GO TO 264 + IC = I + GO TO 262 + 263 CONTINUE + IF(ALAS.LT.HELIM) GO TO 262 + ZDR = ZDR-ELIM + S1R = S1R*CELMR + S1I = S1I*CELMR + S2R = S2R*CELMR + S2I = S2I*CELMR + 262 CONTINUE + IF(N.NE.1) GO TO 270 + S1R = S2R + S1I = S2I + GO TO 270 + 264 CONTINUE + KFLAG = 1 + INUB = I+1 + S2R = CYR(J) + S2I = CYI(J) + J = 3 - J + S1R = CYR(J) + S1I = CYI(J) + IF(INUB.LE.INU) GO TO 225 + IF(N.NE.1) GO TO 240 + S1R = S2R + S1I = S2I + GO TO 240 + 270 CONTINUE + YR(1) = S1R + YI(1) = S1I + IF(N.EQ.1) GO TO 280 + YR(2) = S2R + YI(2) = S2I + 280 CONTINUE + ASCLE = BRY(1) + CALL ZKSCL(ZDR,ZDI,FNU,N,YR,YI,NZ,RZR,RZI,ASCLE,TOL,ELIM) + INU = N - NZ + IF (INU.LE.0) RETURN + KK = NZ + 1 + S1R = YR(KK) + S1I = YI(KK) + YR(KK) = S1R*CSRR(1) + YI(KK) = S1I*CSRR(1) + IF (INU.EQ.1) RETURN + KK = NZ + 2 + S2R = YR(KK) + S2I = YI(KK) + YR(KK) = S2R*CSRR(1) + YI(KK) = S2I*CSRR(1) + IF (INU.EQ.2) RETURN + T2 = FNU + DBLE(FLOAT(KK-1)) + CKR = T2*RZR + CKI = T2*RZI + KFLAG = 1 + GO TO 250 + 290 CONTINUE +!----------------------------------------------------------------------- +! SCALE BY DEXP(Z), IFLAG = 1 CASES +!----------------------------------------------------------------------- + KODED = 2 + IFLAG = 1 + KFLAG = 2 + GO TO 120 +!----------------------------------------------------------------------- +! FNU=HALF ODD INTEGER CASE, DNU=-0.5 +!----------------------------------------------------------------------- + 300 CONTINUE + S1R = COEFR + S1I = COEFI + S2R = COEFR + S2I = COEFI + GO TO 210 + + 310 CONTINUE + NZ=-2 + RETURN +END + +SUBROUTINE ZKSCL(ZRR,ZRI,FNU,N,YR,YI,NZ,RZR,RZI,ASCLE,TOL,ELIM) +USE COMPLEX +!***BEGIN PROLOGUE ZKSCL +!***REFER TO ZBESK +! +! SET K FUNCTIONS TO ZERO ON UNDERFLOW, CONTINUE RECURRENCE +! ON SCALED FUNCTIONS UNTIL TWO MEMBERS COME ON SCALE, THEN +! RETURN WITH MIN(NZ+2,N) VALUES SCALED BY 1/TOL. +! +!***ROUTINES CALLED ZUCHK,ZABS,ZLOG +!***END PROLOGUE ZKSCL +! COMPLEX CK,CS,CY,CZERO,RZ,S1,S2,Y,ZR,ZD,CELM + DOUBLE PRECISION ACS, AS, ASCLE, CKI, CKR, CSI, CSR, CYI, & + CYR, ELIM, FN, FNU, RZI, RZR, STR, S1I, S1R, S2I, S2R, & + TOL, YI, YR, ZEROI, ZEROR, ZRI, ZRR, ZDR, ZDI, CELMR, & + ELM, HELIM, ALAS + INTEGER I, IC, IDUM, KK, N, NN, NW, NZ + DIMENSION YR(1), YI(1), CYR(2), CYI(2) + DATA ZEROR,ZEROI / 0.0D0 , 0.0D0 / + + NZ = 0 + IC = 0 + NN = MIN0(2,N) + DO 10 I=1,NN + S1R = YR(I) + S1I = YI(I) + CYR(I) = S1R + CYI(I) = S1I + AS = ZABS(S1R,S1I) + ACS = -ZRR + DLOG(AS) + NZ = NZ + 1 + YR(I) = ZEROR + YI(I) = ZEROI + IF (ACS.LT.(-ELIM)) GO TO 10 + CALL ZLOG(S1R, S1I, CSR, CSI, IDUM) + CSR = CSR - ZRR + CSI = CSI - ZRI + STR = DEXP(CSR)/TOL + CSR = STR*DCOS(CSI) + CSI = STR*DSIN(CSI) + CALL ZUCHK(CSR, CSI, NW, ASCLE, TOL) + IF (NW.NE.0) GO TO 10 + YR(I) = CSR + YI(I) = CSI + IC = I + NZ = NZ - 1 + 10 CONTINUE + IF (N.EQ.1) RETURN + IF (IC.GT.1) GO TO 20 + YR(1) = ZEROR + YI(1) = ZEROI + NZ = 2 + 20 CONTINUE + IF (N.EQ.2) RETURN + IF (NZ.EQ.0) RETURN + FN = FNU + 1.0D0 + CKR = FN*RZR + CKI = FN*RZI + S1R = CYR(1) + S1I = CYI(1) + S2R = CYR(2) + S2I = CYI(2) + HELIM = 0.5D0*ELIM + ELM = DEXP(-ELIM) + CELMR = ELM + ZDR = ZRR + ZDI = ZRI + +! FIND TWO CONSECUTIVE Y VALUES ON SCALE. SCALE RECURRENCE IF +! S2 GETS LARGER THAN EXP(ELIM/2) + + DO 30 I=3,N + KK = I + CSR = S2R + CSI = S2I + S2R = CKR*CSR - CKI*CSI + S1R + S2I = CKI*CSR + CKR*CSI + S1I + S1R = CSR + S1I = CSI + CKR = CKR + RZR + CKI = CKI + RZI + AS = ZABS(S2R,S2I) + ALAS = DLOG(AS) + ACS = -ZDR + ALAS + NZ = NZ + 1 + YR(I) = ZEROR + YI(I) = ZEROI + IF (ACS.LT.(-ELIM)) GO TO 25 + CALL ZLOG(S2R, S2I, CSR, CSI, IDUM) + CSR = CSR - ZDR + CSI = CSI - ZDI + STR = DEXP(CSR)/TOL + CSR = STR*DCOS(CSI) + CSI = STR*DSIN(CSI) + CALL ZUCHK(CSR, CSI, NW, ASCLE, TOL) + IF (NW.NE.0) GO TO 25 + YR(I) = CSR + YI(I) = CSI + NZ = NZ - 1 + IF (IC.EQ.KK-1) GO TO 40 + IC = KK + GO TO 30 + 25 CONTINUE + IF(ALAS.LT.HELIM) GO TO 30 + ZDR = ZDR - ELIM + S1R = S1R*CELMR + S1I = S1I*CELMR + S2R = S2R*CELMR + S2I = S2I*CELMR + 30 CONTINUE + NZ = N + IF(IC.EQ.N) NZ=N-1 + GO TO 45 + 40 CONTINUE + NZ = KK - 2 + 45 CONTINUE + DO 50 I=1,NZ + YR(I) = ZEROR + YI(I) = ZEROI + 50 CONTINUE + RETURN +END + +SUBROUTINE ZSHCH(ZR, ZI, CSHR, CSHI, CCHR, CCHI) +!***BEGIN PROLOGUE ZSHCH +!***REFER TO ZBESK,ZBESH +! +! ZSHCH COMPUTES THE COMPLEX HYPERBOLI! FUNCTIONS CSH=SINH(X+I*Y) +! AND CCH=COSH(X+I*Y), WHERE I**2=-1. +! +!***ROUTINES CALLED (NONE) +!***END PROLOGUE ZSHCH +! + DOUBLE PRECISION CCHI, CCHR, CH, CN, CSHI, CSHR, SH, SN, ZI, ZR, DCOSH, DSINH + SH = DSINH(ZR) + CH = DCOSH(ZR) + SN = DSIN(ZI) + CN = DCOS(ZI) + CSHR = SH*CN + CSHI = CH*SN + CCHR = CH*CN + CCHI = SH*SN + RETURN +END + +SUBROUTINE ZMLRI(ZR, ZI, FNU, KODE, N, YR, YI, NZ, TOL) +USE UTILIT +USE COMPLEX +!***BEGIN PROLOGUE ZMLRI +!***REFER TO ZBESI,ZBESK +! +! ZMLRI COMPUTES THE I BESSEL FUNCTION FOR RE(Z).GE.0.0 BY THE +! MILLER ALGORITHM NORMALIZED BY A NEUMANN SERIES. +! +!***ROUTINES CALLED DGAMLN,D1MACH,ZABS,ZEXP,ZLOG,ZMLT +!***END PROLOGUE ZMLRI +! COMPLEX CK,CNORM,CONE,CTWO,CZERO,PT,P1,P2,RZ,SUM,Y,Z + DOUBLE PRECISION ACK, AK, AP, AT, AZ, BK, CKI, CKR, CNORMI, & + CNORMR, CONEI, CONER, FKAP, FKK, FLAM, FNF, FNU, PTI, PTR, P1I, & + P1R, P2I, P2R, RAZ, RHO, RHO2, RZI, RZR, SCLE, STI, STR, SUMI, & + SUMR, TFNF, TOL, TST, YI, YR, ZEROI, ZEROR, ZI, ZR!, DGAMLN + INTEGER I, IAZ, IDUM, IFNU, INU, ITIME, K, KK, KM, KODE, M, N, NZ + DIMENSION YR(1), YI(1) + DATA ZEROR,ZEROI,CONER,CONEI / 0.0D0, 0.0D0, 1.0D0, 0.0D0 / + SCLE = D1MACH(1)/TOL + NZ=0 + AZ = ZABS(ZR,ZI) + IAZ = INT(SNGL(AZ)) + IFNU = INT(SNGL(FNU)) + INU = IFNU + N - 1 + AT = DBLE(FLOAT(IAZ)) + 1.0D0 + RAZ = 1.0D0/AZ + STR = ZR*RAZ + STI = -ZI*RAZ + CKR = STR*AT*RAZ + CKI = STI*AT*RAZ + RZR = (STR+STR)*RAZ + RZI = (STI+STI)*RAZ + P1R = ZEROR + P1I = ZEROI + P2R = CONER + P2I = CONEI + ACK = (AT+1.0D0)*RAZ + RHO = ACK + DSQRT(ACK*ACK-1.0D0) + RHO2 = RHO*RHO + TST = (RHO2+RHO2)/((RHO2-1.0D0)*(RHO-1.0D0)) + TST = TST/TOL +!----------------------------------------------------------------------- +! COMPUTE RELATIVE TRUNCATION ERROR INDEX FOR SERIES +!----------------------------------------------------------------------- + AK = AT + DO 10 I=1,80 + PTR = P2R + PTI = P2I + P2R = P1R - (CKR*PTR-CKI*PTI) + P2I = P1I - (CKI*PTR+CKR*PTI) + P1R = PTR + P1I = PTI + CKR = CKR + RZR + CKI = CKI + RZI + AP = ZABS(P2R,P2I) + IF (AP.GT.TST*AK*AK) GO TO 20 + AK = AK + 1.0D0 + 10 CONTINUE + GO TO 110 + 20 CONTINUE + I = I + 1 + K = 0 + IF (INU.LT.IAZ) GO TO 40 +!----------------------------------------------------------------------- +! COMPUTE RELATIVE TRUNCATION ERROR FOR RATIOS +!----------------------------------------------------------------------- + P1R = ZEROR + P1I = ZEROI + P2R = CONER + P2I = CONEI + AT = DBLE(FLOAT(INU)) + 1.0D0 + STR = ZR*RAZ + STI = -ZI*RAZ + CKR = STR*AT*RAZ + CKI = STI*AT*RAZ + ACK = AT*RAZ + TST = DSQRT(ACK/TOL) + ITIME = 1 + DO 30 K=1,80 + PTR = P2R + PTI = P2I + P2R = P1R - (CKR*PTR-CKI*PTI) + P2I = P1I - (CKR*PTI+CKI*PTR) + P1R = PTR + P1I = PTI + CKR = CKR + RZR + CKI = CKI + RZI + AP = ZABS(P2R,P2I) + IF (AP.LT.TST) GO TO 30 + IF (ITIME.EQ.2) GO TO 40 + ACK = ZABS(CKR,CKI) + FLAM = ACK + DSQRT(ACK*ACK-1.0D0) + FKAP = AP/ZABS(P1R,P1I) + RHO = DMIN1(FLAM,FKAP) + TST = TST*DSQRT(RHO/(RHO*RHO-1.0D0)) + ITIME = 2 + 30 CONTINUE + GO TO 110 + 40 CONTINUE +!----------------------------------------------------------------------- +! BACKWARD RECURRENCE AND SUM NORMALIZING RELATION +!----------------------------------------------------------------------- + K = K + 1 + KK = MAX0(I+IAZ,K+INU) + FKK = DBLE(FLOAT(KK)) + P1R = ZEROR + P1I = ZEROI +!----------------------------------------------------------------------- +! SCALE P2 AND SUM BY SCLE +!----------------------------------------------------------------------- + P2R = SCLE + P2I = ZEROI + FNF = FNU - DBLE(FLOAT(IFNU)) + TFNF = FNF + FNF + BK = DGAMLN(FKK+TFNF+1.0D0,IDUM) - DGAMLN(FKK+1.0D0,IDUM) - & + DGAMLN(TFNF+1.0D0,IDUM) + BK = DEXP(BK) + SUMR = ZEROR + SUMI = ZEROI + KM = KK - INU + DO 50 I=1,KM + PTR = P2R + PTI = P2I + P2R = P1R + (FKK+FNF)*(RZR*PTR-RZI*PTI) + P2I = P1I + (FKK+FNF)*(RZI*PTR+RZR*PTI) + P1R = PTR + P1I = PTI + AK = 1.0D0 - TFNF/(FKK+TFNF) + ACK = BK*AK + SUMR = SUMR + (ACK+BK)*P1R + SUMI = SUMI + (ACK+BK)*P1I + BK = ACK + FKK = FKK - 1.0D0 + 50 CONTINUE + YR(N) = P2R + YI(N) = P2I + IF (N.EQ.1) GO TO 70 + DO 60 I=2,N + PTR = P2R + PTI = P2I + P2R = P1R + (FKK+FNF)*(RZR*PTR-RZI*PTI) + P2I = P1I + (FKK+FNF)*(RZI*PTR+RZR*PTI) + P1R = PTR + P1I = PTI + AK = 1.0D0 - TFNF/(FKK+TFNF) + ACK = BK*AK + SUMR = SUMR + (ACK+BK)*P1R + SUMI = SUMI + (ACK+BK)*P1I + BK = ACK + FKK = FKK - 1.0D0 + M = N - I + 1 + YR(M) = P2R + YI(M) = P2I + 60 CONTINUE + 70 CONTINUE + IF (IFNU.LE.0) GO TO 90 + DO 80 I=1,IFNU + PTR = P2R + PTI = P2I + P2R = P1R + (FKK+FNF)*(RZR*PTR-RZI*PTI) + P2I = P1I + (FKK+FNF)*(RZR*PTI+RZI*PTR) + P1R = PTR + P1I = PTI + AK = 1.0D0 - TFNF/(FKK+TFNF) + ACK = BK*AK + SUMR = SUMR + (ACK+BK)*P1R + SUMI = SUMI + (ACK+BK)*P1I + BK = ACK + FKK = FKK - 1.0D0 + 80 CONTINUE + 90 CONTINUE + PTR = ZR + PTI = ZI + IF (KODE.EQ.2) PTR = ZEROR + CALL ZLOG(RZR, RZI, STR, STI, IDUM) + P1R = -FNF*STR + PTR + P1I = -FNF*STI + PTI + AP = DGAMLN(1.0D0+FNF,IDUM) + PTR = P1R - AP + PTI = P1I +!----------------------------------------------------------------------- +! THE DIVISION CEXP(PT)/(SUM+P2) IS ALTERED TO AVOID OVERFLOW +! IN THE DENOMINATOR BY SQUARING LARGE QUANTITIES +!----------------------------------------------------------------------- + P2R = P2R + SUMR + P2I = P2I + SUMI + AP = ZABS(P2R,P2I) + P1R = 1.0D0/AP + CALL ZEXP(PTR, PTI, STR, STI) + CKR = STR*P1R + CKI = STI*P1R + PTR = P2R*P1R + PTI = -P2I*P1R + CALL ZMLT(CKR, CKI, PTR, PTI, CNORMR, CNORMI) + DO 100 I=1,N + STR = YR(I)*CNORMR - YI(I)*CNORMI + YI(I) = YR(I)*CNORMI + YI(I)*CNORMR + YR(I) = STR + 100 CONTINUE + RETURN + 110 CONTINUE + NZ=-2 + RETURN +END + +DOUBLE PRECISION FUNCTION DGAMLN(Z,IERR) +USE UTILIT +!***BEGIN PROLOGUE DGAMLN +!***DATE WRITTEN 830501 (YYMMDD) +!***REVISION DATE 830501 (YYMMDD) +!***CATEGORY NO. B5F +!***KEYWORDS GAMMA FUNCTION,LOGARITHM OF GAMMA FUNCTION +!***AUTHOR AMOS, DONALD E., SANDIA NATIONAL LABORATORIES +!***PURPOSE TO COMPUTE THE LOGARITHM OF THE GAMMA FUNCTION +!***DESCRIPTION +! +! **** A DOUBLE PRECISION ROUTINE **** +! DGAMLN COMPUTES THE NATURAL LOG OF THE GAMMA FUNCTION FOR +! Z.GT.0. THE ASYMPTOTIC EXPANSION IS USED TO GENERATE VALUES +! GREATER THAN ZMIN WHICH ARE ADJUSTED BY THE RECURSION +! G(Z+1)=Z*G(Z) FOR Z.LE.ZMIN. THE FUNCTION WAS MADE AS +! PORTABLE AS POSSIBLE BY COMPUTIMG ZMIN FROM THE NUMBER OF BASE +! 10 DIGITS IN A WORD, RLN=AMAX1(-ALOG10(R1MACH(4)),0.5E-18) +! LIMITED TO 18 DIGITS OF (RELATIVE) ACCURACY. +! +! SINCE INTEGER ARGUMENTS ARE COMMON, A TABLE LOOK UP ON 100 +! VALUES IS USED FOR SPEED OF EXECUTION. +! +! DESCRIPTION OF ARGUMENTS +! +! INPUT Z IS D0UBLE PRECISION +! Z - ARGUMENT, Z.GT.0.0D0 +! +! OUTPUT DGAMLN IS DOUBLE PRECISION +! DGAMLN - NATURAL LOG OF THE GAMMA FUNCTION AT Z.NE.0.0D0 +! IERR - ERROR FLAG +! IERR=0, NORMAL RETURN, COMPUTATION COMPLETED +! IERR=1, Z.LE.0.0D0, NO COMPUTATION +! +! +!***REFERENCES COMPUTATION OF BESSEL FUNCTIONS OF COMPLEX ARGUMENT +! BY D. E. AMOS, SAND83-0083, MAY, 1983. +!***ROUTINES CALLED I1MACH,D1MACH +!***END PROLOGUE DGAMLN + DOUBLE PRECISION CF, CON, FLN, FZ, GLN, RLN, S, TLG, TRM, TST, & + T1, WDTOL, Z, ZDMY, ZINC, ZM, ZMIN, ZP, ZSQ + INTEGER I, IERR, I1M, K, MZ, NZ + DIMENSION CF(22), GLN(100) +! LNGAMMA(N), N=1,100 + DATA GLN(1), GLN(2), GLN(3), GLN(4), GLN(5), GLN(6), GLN(7), & + GLN(8), GLN(9), GLN(10), GLN(11), GLN(12), GLN(13), GLN(14), & + GLN(15), GLN(16), GLN(17), GLN(18), GLN(19), GLN(20), & + GLN(21), GLN(22)/ & + 0.00000000000000000D+00, 0.00000000000000000D+00, & + 6.93147180559945309D-01, 1.79175946922805500D+00, & + 3.17805383034794562D+00, 4.78749174278204599D+00, & + 6.57925121201010100D+00, 8.52516136106541430D+00, & + 1.06046029027452502D+01, 1.28018274800814696D+01, & + 1.51044125730755153D+01, 1.75023078458738858D+01, & + 1.99872144956618861D+01, 2.25521638531234229D+01, & + 2.51912211827386815D+01, 2.78992713838408916D+01, & + 3.06718601060806728D+01, 3.35050734501368889D+01, & + 3.63954452080330536D+01, 3.93398841871994940D+01, & + 4.23356164607534850D+01, 4.53801388984769080D+01/ + DATA GLN(23), GLN(24), GLN(25), GLN(26), GLN(27), GLN(28), & + GLN(29), GLN(30), GLN(31), GLN(32), GLN(33), GLN(34), & + GLN(35), GLN(36), GLN(37), GLN(38), GLN(39), GLN(40), & + GLN(41), GLN(42), GLN(43), GLN(44)/ & + 4.84711813518352239D+01, 5.16066755677643736D+01, & + 5.47847293981123192D+01, 5.80036052229805199D+01, & + 6.12617017610020020D+01, 6.45575386270063311D+01, & + 6.78897431371815350D+01, 7.12570389671680090D+01, & + 7.46582363488301644D+01, 7.80922235533153106D+01, & + 8.15579594561150372D+01, 8.50544670175815174D+01, & + 8.85808275421976788D+01, 9.21361756036870925D+01, & + 9.57196945421432025D+01, 9.93306124547874269D+01, & + 1.02968198614513813D+02, 1.06631760260643459D+02, & + 1.10320639714757395D+02, 1.14034211781461703D+02, & + 1.17771881399745072D+02, 1.21533081515438634D+02/ + DATA GLN(45), GLN(46), GLN(47), GLN(48), GLN(49), GLN(50), & + GLN(51), GLN(52), GLN(53), GLN(54), GLN(55), GLN(56), & + GLN(57), GLN(58), GLN(59), GLN(60), GLN(61), GLN(62), & + GLN(63), GLN(64), GLN(65), GLN(66)/ & + 1.25317271149356895D+02, 1.29123933639127215D+02, & + 1.32952575035616310D+02, 1.36802722637326368D+02, & + 1.40673923648234259D+02, 1.44565743946344886D+02, & + 1.48477766951773032D+02, 1.52409592584497358D+02, & + 1.56360836303078785D+02, 1.60331128216630907D+02, & + 1.64320112263195181D+02, 1.68327445448427652D+02, & + 1.72352797139162802D+02, 1.76395848406997352D+02, & + 1.80456291417543771D+02, 1.84533828861449491D+02, & + 1.88628173423671591D+02, 1.92739047287844902D+02, & + 1.96866181672889994D+02, 2.01009316399281527D+02, & + 2.05168199482641199D+02, 2.09342586752536836D+02/ + DATA GLN(67), GLN(68), GLN(69), GLN(70), GLN(71), GLN(72), & + GLN(73), GLN(74), GLN(75), GLN(76), GLN(77), GLN(78), & + GLN(79), GLN(80), GLN(81), GLN(82), GLN(83), GLN(84), & + GLN(85), GLN(86), GLN(87), GLN(88)/ & + 2.13532241494563261D+02, 2.17736934113954227D+02, & + 2.21956441819130334D+02, 2.26190548323727593D+02, & + 2.30439043565776952D+02, 2.34701723442818268D+02, & + 2.38978389561834323D+02, 2.43268849002982714D+02, & + 2.47572914096186884D+02, 2.51890402209723194D+02, & + 2.56221135550009525D+02, 2.60564940971863209D+02, & + 2.64921649798552801D+02, 2.69291097651019823D+02, & + 2.73673124285693704D+02, 2.78067573440366143D+02, & + 2.82474292687630396D+02, 2.86893133295426994D+02, & + 2.91323950094270308D+02, 2.95766601350760624D+02, & + 3.00220948647014132D+02, 3.04686856765668715D+02/ + DATA GLN(89), GLN(90), GLN(91), GLN(92), GLN(93), GLN(94), & + GLN(95), GLN(96), GLN(97), GLN(98), GLN(99), GLN(100)/ & + 3.09164193580146922D+02, 3.13652829949879062D+02, & + 3.18152639620209327D+02, 3.22663499126726177D+02, & + 3.27185287703775217D+02, 3.31717887196928473D+02, & + 3.36261181979198477D+02, 3.40815058870799018D+02, & + 3.45379407062266854D+02, 3.49954118040770237D+02, & + 3.54539085519440809D+02, 3.59134205369575399D+02/ +! COEFFICIENTS OF ASYMPTOTIC EXPANSION + DATA CF(1), CF(2), CF(3), CF(4), CF(5), CF(6), CF(7), CF(8), & + CF(9), CF(10), CF(11), CF(12), CF(13), CF(14), CF(15), & + CF(16), CF(17), CF(18), CF(19), CF(20), CF(21), CF(22)/ & + 8.33333333333333333D-02, -2.77777777777777778D-03, & + 7.93650793650793651D-04, -5.95238095238095238D-04, & + 8.41750841750841751D-04, -1.91752691752691753D-03, & + 6.41025641025641026D-03, -2.95506535947712418D-02, & + 1.79644372368830573D-01, -1.39243221690590112D+00, & + 1.34028640441683920D+01, -1.56848284626002017D+02, & + 2.19310333333333333D+03, -3.61087712537249894D+04, & + 6.91472268851313067D+05, -1.52382215394074162D+07, & + 3.82900751391414141D+08, -1.08822660357843911D+10, & + 3.47320283765002252D+11, -1.23696021422692745D+13, & + 4.88788064793079335D+14, -2.13203339609193739D+16/ + +! LN(2*PI) + DATA CON / 1.83787706640934548D+00/ + +!***FIRST EXECUTABLE STATEMENT DGAMLN + IERR=0 + IF (Z.LE.0.0D0) GO TO 70 + IF (Z.GT.101.0D0) GO TO 10 + NZ = INT(SNGL(Z)) + FZ = Z - FLOAT(NZ) + IF (FZ.GT.0.0D0) GO TO 10 + IF (NZ.GT.100) GO TO 10 + DGAMLN = GLN(NZ) + RETURN + 10 CONTINUE + WDTOL = D1MACH(4) + WDTOL = DMAX1(WDTOL,0.5D-18) + I1M = I1MACH(14) + RLN = D1MACH(5)*FLOAT(I1M) + FLN = DMIN1(RLN,20.0D0) + FLN = DMAX1(FLN,3.0D0) + FLN = FLN - 3.0D0 + ZM = 1.8000D0 + 0.3875D0*FLN + MZ = INT(SNGL(ZM)) + 1 + ZMIN = FLOAT(MZ) + ZDMY = Z + ZINC = 0.0D0 + IF (Z.GE.ZMIN) GO TO 20 + ZINC = ZMIN - FLOAT(NZ) + ZDMY = Z + ZINC + 20 CONTINUE + ZP = 1.0D0/ZDMY + T1 = CF(1)*ZP + S = T1 + IF (ZP.LT.WDTOL) GO TO 40 + ZSQ = ZP*ZP + TST = T1*WDTOL + DO 30 K=2,22 + ZP = ZP*ZSQ + TRM = CF(K)*ZP + IF (DABS(TRM).LT.TST) GO TO 40 + S = S + TRM + 30 CONTINUE + 40 CONTINUE + IF (ZINC.NE.0.0D0) GO TO 50 + TLG = DLOG(Z) + DGAMLN = Z*(TLG-1.0D0) + 0.5D0*(CON-TLG) + S + RETURN + 50 CONTINUE + ZP = 1.0D0 + NZ = INT(SNGL(ZINC)) + DO 60 I=1,NZ + ZP = ZP*(Z+FLOAT(I-1)) + 60 CONTINUE + TLG = DLOG(ZDMY) + DGAMLN = ZDMY*(TLG-1.0D0) - DLOG(ZP) + 0.5D0*(CON-TLG) + S + RETURN + + 70 CONTINUE + IERR=1 + RETURN +END + +SUBROUTINE ZUNIK(ZRR, ZRI, FNU, IKFLG, IPMTR, TOL, INIT, PHIR, & + PHII, ZETA1R, ZETA1I, ZETA2R, ZETA2I, SUMR, SUMI, CWRKR, CWRKI) +USE COMPLEX +!***BEGIN PROLOGUE ZUNIK +!***REFER TO ZBESI,ZBESK +! +! ZUNIK COMPUTES PARAMETERS FOR THE UNIFORM ASYMPTOTIC +! EXPANSIONS OF THE I AND K FUNCTIONS ON IKFLG= 1 OR 2 +! RESPECTIVELY BY +! +! W(FNU,ZR) = PHI*EXP(ZETA)*SUM +! +! WHERE ZETA=-ZETA1 + ZETA2 OR +! ZETA1 - ZETA2 +! +! THE FIRST CALL MUST HAVE INIT=0. SUBSEQUENT CALLS WITH THE +! SAME ZR AND FNU WILL RETURN THE I OR K FUNCTION ON IKFLG= +! 1 OR 2 WITH NO CHANGE IN INIT. CWRK IS A COMPLEX WORK +! ARRAY. IPMTR=0 COMPUTES ALL PARAMETERS. IPMTR=1 COMPUTES PHI, +! ZETA1,ZETA2. +! +!***ROUTINES CALLED ZDIV,ZLOG,ZSQRT +!***END PROLOGUE ZUNIK +! COMPLEX CFN,CON,CONE,CRFN,CWRK,CZERO,PHI,S,SR,SUM,T,T2,ZETA1, +! *ZETA2,ZN,ZR + DOUBLE PRECISION AC, C, CON, CONEI, CONER, CRFNI, CRFNR, CWRKI, & + CWRKR, FNU, PHII, PHIR, RFN, SI, SR, SRI, SRR, STI, STR, SUMI, & + SUMR, TEST, TI, TOL, TR, T2I, T2R, ZEROI, ZEROR, ZETA1I, ZETA1R, & + ZETA2I, ZETA2R, ZNI, ZNR, ZRI, ZRR + INTEGER I, IDUM, IKFLG, INIT, IPMTR, J, K, L + DIMENSION C(120), CWRKR(16), CWRKI(16), CON(2) + DATA ZEROR,ZEROI,CONER,CONEI / 0.0D0, 0.0D0, 1.0D0, 0.0D0 / + DATA CON(1), CON(2) / & + 3.98942280401432678D-01, 1.25331413731550025D+00 / + DATA C(1), C(2), C(3), C(4), C(5), C(6), C(7), C(8), C(9), C(10), & + C(11), C(12), C(13), C(14), C(15), C(16), C(17), C(18), & + C(19), C(20), C(21), C(22), C(23), C(24)/ & + 1.00000000000000000D+00, -2.08333333333333333D-01, & + 1.25000000000000000D-01, 3.34201388888888889D-01, & + -4.01041666666666667D-01, 7.03125000000000000D-02, & + -1.02581259645061728D+00, 1.84646267361111111D+00, & + -8.91210937500000000D-01, 7.32421875000000000D-02, & + 4.66958442342624743D+00, -1.12070026162229938D+01, & + 8.78912353515625000D+00, -2.36408691406250000D+00, & + 1.12152099609375000D-01, -2.82120725582002449D+01, & + 8.46362176746007346D+01, -9.18182415432400174D+01, & + 4.25349987453884549D+01, -7.36879435947963170D+00, & + 2.27108001708984375D-01, 2.12570130039217123D+02, & + -7.65252468141181642D+02, 1.05999045252799988D+03/ + DATA C(25), C(26), C(27), C(28), C(29), C(30), C(31), C(32), & + C(33), C(34), C(35), C(36), C(37), C(38), C(39), C(40), & + C(41), C(42), C(43), C(44), C(45), C(46), C(47), C(48)/ & + -6.99579627376132541D+02, 2.18190511744211590D+02, & + -2.64914304869515555D+01, 5.72501420974731445D-01, & + -1.91945766231840700D+03, 8.06172218173730938D+03, & + -1.35865500064341374D+04, 1.16553933368645332D+04, & + -5.30564697861340311D+03, 1.20090291321635246D+03, & + -1.08090919788394656D+02, 1.72772750258445740D+00, & + 2.02042913309661486D+04, -9.69805983886375135D+04, & + 1.92547001232531532D+05, -2.03400177280415534D+05, & + 1.22200464983017460D+05, -4.11926549688975513D+04, & + 7.10951430248936372D+03, -4.93915304773088012D+02, & + 6.07404200127348304D+00, -2.42919187900551333D+05, & + 1.31176361466297720D+06, -2.99801591853810675D+06/ + DATA C(49), C(50), C(51), C(52), C(53), C(54), C(55), C(56), & + C(57), C(58), C(59), C(60), C(61), C(62), C(63), C(64), & + C(65), C(66), C(67), C(68), C(69), C(70), C(71), C(72)/ & + 3.76327129765640400D+06, -2.81356322658653411D+06, & + 1.26836527332162478D+06, -3.31645172484563578D+05, & + 4.52187689813627263D+04, -2.49983048181120962D+03, & + 2.43805296995560639D+01, 3.28446985307203782D+06, & + -1.97068191184322269D+07, 5.09526024926646422D+07, & + -7.41051482115326577D+07, 6.63445122747290267D+07, & + -3.75671766607633513D+07, 1.32887671664218183D+07, & + -2.78561812808645469D+06, 3.08186404612662398D+05, & + -1.38860897537170405D+04, 1.10017140269246738D+02, & + -4.93292536645099620D+07, 3.25573074185765749D+08, & + -9.39462359681578403D+08, 1.55359689957058006D+09, & + -1.62108055210833708D+09, 1.10684281682301447D+09/ + DATA C(73), C(74), C(75), C(76), C(77), C(78), C(79), C(80), & + C(81), C(82), C(83), C(84), C(85), C(86), C(87), C(88), & + C(89), C(90), C(91), C(92), C(93), C(94), C(95), C(96)/ & + -4.95889784275030309D+08, 1.42062907797533095D+08, & + -2.44740627257387285D+07, 2.24376817792244943D+06, & + -8.40054336030240853D+04, 5.51335896122020586D+02, & + 8.14789096118312115D+08, -5.86648149205184723D+09, & + 1.86882075092958249D+10, -3.46320433881587779D+10, & + 4.12801855797539740D+10, -3.30265997498007231D+10, & + 1.79542137311556001D+10, -6.56329379261928433D+09, & + 1.55927986487925751D+09, -2.25105661889415278D+08, & + 1.73951075539781645D+07, -5.49842327572288687D+05, & + 3.03809051092238427D+03, -1.46792612476956167D+10, & + 1.14498237732025810D+11, -3.99096175224466498D+11, & + 8.19218669548577329D+11, -1.09837515608122331D+12/ + DATA C(97), C(98), C(99), C(100), C(101), C(102), C(103), C(104), & + C(105), C(106), C(107), C(108), C(109), C(110), C(111), & + C(112), C(113), C(114), C(115), C(116), C(117), C(118)/ & + 1.00815810686538209D+12, -6.45364869245376503D+11, & + 2.87900649906150589D+11, -8.78670721780232657D+10, & + 1.76347306068349694D+10, -2.16716498322379509D+09, & + 1.43157876718888981D+08, -3.87183344257261262D+06, & + 1.82577554742931747D+04, 2.86464035717679043D+11, & + -2.40629790002850396D+12, 9.10934118523989896D+12, & + -2.05168994109344374D+13, 3.05651255199353206D+13, & + -3.16670885847851584D+13, 2.33483640445818409D+13, & + -1.23204913055982872D+13, 4.61272578084913197D+12, & + -1.19655288019618160D+12, 2.05914503232410016D+11, & + -2.18229277575292237D+10, 1.24700929351271032D+09/ + DATA C(119), C(120)/ & + -2.91883881222208134D+07, 1.18838426256783253D+05/ + + IF (INIT.NE.0) GO TO 40 +!----------------------------------------------------------------------- +! INITIALIZE ALL VARIABLES +!----------------------------------------------------------------------- + RFN = 1.0D0/FNU + TR = ZRR*RFN + TI = ZRI*RFN + SR = CONER + (TR*TR-TI*TI) + SI = CONEI + (TR*TI+TI*TR) + CALL ZSQRT(SR, SI, SRR, SRI) + STR = CONER + SRR + STI = CONEI + SRI + CALL ZDIV(STR, STI, TR, TI, ZNR, ZNI) + CALL ZLOG(ZNR, ZNI, STR, STI, IDUM) + ZETA1R = FNU*STR + ZETA1I = FNU*STI + ZETA2R = FNU*SRR + ZETA2I = FNU*SRI + CALL ZDIV(CONER, CONEI, SRR, SRI, TR, TI) + SRR = TR*RFN + SRI = TI*RFN + CALL ZSQRT(SRR, SRI, CWRKR(16), CWRKI(16)) + PHIR = CWRKR(16)*CON(IKFLG) + PHII = CWRKI(16)*CON(IKFLG) + IF (IPMTR.NE.0) RETURN + CALL ZDIV(CONER, CONEI, SR, SI, T2R, T2I) + CWRKR(1) = CONER + CWRKI(1) = CONEI + CRFNR = CONER + CRFNI = CONEI + AC = 1.0D0 + L = 1 + DO 20 K=2,15 + SR = ZEROR + SI = ZEROI + DO 10 J=1,K + L = L + 1 + STR = SR*T2R - SI*T2I + C(L) + SI = SR*T2I + SI*T2R + SR = STR + 10 CONTINUE + STR = CRFNR*SRR - CRFNI*SRI + CRFNI = CRFNR*SRI + CRFNI*SRR + CRFNR = STR + CWRKR(K) = CRFNR*SR - CRFNI*SI + CWRKI(K) = CRFNR*SI + CRFNI*SR + AC = AC*RFN + TEST = DABS(CWRKR(K)) + DABS(CWRKI(K)) + IF (AC.LT.TOL .AND. TEST.LT.TOL) GO TO 30 + 20 CONTINUE + K = 15 + 30 CONTINUE + INIT = K + 40 CONTINUE + IF (IKFLG.EQ.2) GO TO 60 +!----------------------------------------------------------------------- +! COMPUTE SUM FOR THE I FUNCTION +!----------------------------------------------------------------------- + SR = ZEROR + SI = ZEROI + DO 50 I=1,INIT + SR = SR + CWRKR(I) + SI = SI + CWRKI(I) + 50 CONTINUE + SUMR = SR + SUMI = SI + PHIR = CWRKR(16)*CON(1) + PHII = CWRKI(16)*CON(1) + RETURN + 60 CONTINUE +!----------------------------------------------------------------------- +! COMPUTE SUM FOR THE K FUNCTION +!----------------------------------------------------------------------- + SR = ZEROR + SI = ZEROI + TR = CONER + DO 70 I=1,INIT + SR = SR + TR*CWRKR(I) + SI = SI + TR*CWRKI(I) + TR = -TR + 70 CONTINUE + SUMR = SR + SUMI = SI + PHIR = CWRKR(16)*CON(2) + PHII = CWRKI(16)*CON(2) + RETURN +END + +SUBROUTINE ZUNHJ(ZR, ZI, FNU, IPMTR, TOL, PHIR, PHII, ARGR, ARGI, & + ZETA1R, ZETA1I, ZETA2R, ZETA2I, ASUMR, ASUMI, BSUMR, BSUMI) +USE COMPLEX +!***BEGIN PROLOGUE ZUNHJ +!***REFER TO ZBESI,ZBESK +! +! REFERENCES +! HANDBOOK OF MATHEMATICAL FUNCTIONS BY M. ABRAMOWITZ AND I.A. +! STEGUN, AMS55, NATIONAL BUREAU OF STANDARDS, 1965, CHAPTER 9. +! +! ASYMPTOTICS AND SPECIAL FUNCTIONS BY F.W.J. OLVER, ACADEMIC +! PRESS, N.Y., 1974, PAGE 420 +! +! ABSTRACT +! ZUNHJ COMPUTES PARAMETERS FOR BESSEL FUNCTIONS C(FNU,Z) = +! J(FNU,Z), Y(FNU,Z) OR H(I,FNU,Z) I=1,2 FOR LARGE ORDERS FNU +! BY MEANS OF THE UNIFORM ASYMPTOTIC EXPANSION +! +! C(FNU,Z)=C1*PHI*( ASUM*AIRY(ARG) + C2*BSUM*DAIRY(ARG) ) +! +! FOR PROPER CHOICES OF C1, C2, AIRY AND DAIRY WHERE AIRY IS +! AN AIRY FUNCTION AND DAIRY IS ITS DERIVATIVE. +! +! (2/3)*FNU*ZETA**1.5 = ZETA1-ZETA2, +! +! ZETA1=0.5*FNU*CLOG((1+W)/(1-W)), ZETA2=FNU*W FOR SCALING +! PURPOSES IN AIRY FUNCTIONS FROM CAIRY OR CBIRY. +! +! MCONJ=SIGN OF AIMAG(Z), BUT IS AMBIGUOUS WHEN Z IS REAL AND +! MUST BE SPECIFIED. IPMTR=0 RETURNS ALL PARAMETERS. IPMTR= +! 1 COMPUTES ALL EXCEPT ASUM AND BSUM. +! +!***ROUTINES CALLED ZABS,ZDIV,ZLOG,ZSQRT +!***END PROLOGUE ZUNHJ +! COMPLEX ARG,ASUM,BSUM,CFNU,CONE,CR,CZERO,DR,P,PHI,PRZTH,PTFN, +! *RFN13,RTZTA,RZTH,SUMA,SUMB,TFN,T2,UP,W,W2,Z,ZA,ZB,ZC,ZETA,ZETA1, +! *ZETA2,ZTH + DOUBLE PRECISION ALFA, ANG, AP, AR, ARGI, ARGR, ASUMI, ASUMR, & + ATOL, AW2, AZTH, BETA, BR, BSUMI, BSUMR, BTOL, C, CONEI, CONER, & + CRI, CRR, DRI, DRR, EX1, EX2, FNU, FN13, FN23, GAMA, GPI, HPI, & + PHII, PHIR, PI, PP, PR, PRZTHI, PRZTHR, PTFNI, PTFNR, RAW, RAW2, & + RAZTH, RFNU, RFNU2, RFN13, RTZTI, RTZTR, RZTHI, RZTHR, STI, STR, & + SUMAI, SUMAR, SUMBI, SUMBR, TEST, TFNI, TFNR, THPI, TOL, TZAI, & + TZAR, T2I, T2R, UPI, UPR, WI, WR, W2I, W2R, ZAI, ZAR, ZBI, ZBR, & + ZCI, ZCR, ZEROI, ZEROR, ZETAI, ZETAR, ZETA1I, ZETA1R, ZETA2I, & + ZETA2R, ZI, ZR, ZTHI, ZTHR + INTEGER IAS, IBS, IPMTR, IS, J, JR, JU, K, KMAX, KP1, KS, L, LR, & + LRP1, L1, L2, M, IDUM + DIMENSION AR(14), BR(14), C(105), ALFA(180), BETA(210), GAMA(30), & + AP(30), PR(30), PI(30), UPR(14), UPI(14), CRR(14), CRI(14), & + DRR(14), DRI(14) + DATA AR(1), AR(2), AR(3), AR(4), AR(5), AR(6), AR(7), AR(8), & + AR(9), AR(10), AR(11), AR(12), AR(13), AR(14)/ & + 1.00000000000000000D+00, 1.04166666666666667D-01, & + 8.35503472222222222D-02, 1.28226574556327160D-01, & + 2.91849026464140464D-01, 8.81627267443757652D-01, & + 3.32140828186276754D+00, 1.49957629868625547D+01, & + 7.89230130115865181D+01, 4.74451538868264323D+02, & + 3.20749009089066193D+03, 2.40865496408740049D+04, & + 1.98923119169509794D+05, 1.79190200777534383D+06/ + DATA BR(1), BR(2), BR(3), BR(4), BR(5), BR(6), BR(7), BR(8), & + BR(9), BR(10), BR(11), BR(12), BR(13), BR(14)/ & + 1.00000000000000000D+00, -1.45833333333333333D-01, & + -9.87413194444444444D-02, -1.43312053915895062D-01, & + -3.17227202678413548D-01, -9.42429147957120249D-01, & + -3.51120304082635426D+00, -1.57272636203680451D+01, & + -8.22814390971859444D+01, -4.92355370523670524D+02, & + -3.31621856854797251D+03, -2.48276742452085896D+04, & + -2.04526587315129788D+05, -1.83844491706820990D+06/ + DATA C(1), C(2), C(3), C(4), C(5), C(6), C(7), C(8), C(9), C(10), & + C(11), C(12), C(13), C(14), C(15), C(16), C(17), C(18), & + C(19), C(20), C(21), C(22), C(23), C(24)/ & + 1.00000000000000000D+00, -2.08333333333333333D-01, & + 1.25000000000000000D-01, 3.34201388888888889D-01, & + -4.01041666666666667D-01, 7.03125000000000000D-02, & + -1.02581259645061728D+00, 1.84646267361111111D+00, & + -8.91210937500000000D-01, 7.32421875000000000D-02, & + 4.66958442342624743D+00, -1.12070026162229938D+01, & + 8.78912353515625000D+00, -2.36408691406250000D+00, & + 1.12152099609375000D-01, -2.82120725582002449D+01, & + 8.46362176746007346D+01, -9.18182415432400174D+01, & + 4.25349987453884549D+01, -7.36879435947963170D+00, & + 2.27108001708984375D-01, 2.12570130039217123D+02, & + -7.65252468141181642D+02, 1.05999045252799988D+03/ + DATA C(25), C(26), C(27), C(28), C(29), C(30), C(31), C(32), & + C(33), C(34), C(35), C(36), C(37), C(38), C(39), C(40), & + C(41), C(42), C(43), C(44), C(45), C(46), C(47), C(48)/ & + -6.99579627376132541D+02, 2.18190511744211590D+02, & + -2.64914304869515555D+01, 5.72501420974731445D-01, & + -1.91945766231840700D+03, 8.06172218173730938D+03, & + -1.35865500064341374D+04, 1.16553933368645332D+04, & + -5.30564697861340311D+03, 1.20090291321635246D+03, & + -1.08090919788394656D+02, 1.72772750258445740D+00, & + 2.02042913309661486D+04, -9.69805983886375135D+04, & + 1.92547001232531532D+05, -2.03400177280415534D+05, & + 1.22200464983017460D+05, -4.11926549688975513D+04, & + 7.10951430248936372D+03, -4.93915304773088012D+02, & + 6.07404200127348304D+00, -2.42919187900551333D+05, & + 1.31176361466297720D+06, -2.99801591853810675D+06/ + DATA C(49), C(50), C(51), C(52), C(53), C(54), C(55), C(56), & + C(57), C(58), C(59), C(60), C(61), C(62), C(63), C(64), & + C(65), C(66), C(67), C(68), C(69), C(70), C(71), C(72)/ & + 3.76327129765640400D+06, -2.81356322658653411D+06, & + 1.26836527332162478D+06, -3.31645172484563578D+05, & + 4.52187689813627263D+04, -2.49983048181120962D+03, & + 2.43805296995560639D+01, 3.28446985307203782D+06, & + -1.97068191184322269D+07, 5.09526024926646422D+07, & + -7.41051482115326577D+07, 6.63445122747290267D+07, & + -3.75671766607633513D+07, 1.32887671664218183D+07, & + -2.78561812808645469D+06, 3.08186404612662398D+05, & + -1.38860897537170405D+04, 1.10017140269246738D+02, & + -4.93292536645099620D+07, 3.25573074185765749D+08, & + -9.39462359681578403D+08, 1.55359689957058006D+09, & + -1.62108055210833708D+09, 1.10684281682301447D+09/ + DATA C(73), C(74), C(75), C(76), C(77), C(78), C(79), C(80), & + C(81), C(82), C(83), C(84), C(85), C(86), C(87), C(88), & + C(89), C(90), C(91), C(92), C(93), C(94), C(95), C(96)/ & + -4.95889784275030309D+08, 1.42062907797533095D+08, & + -2.44740627257387285D+07, 2.24376817792244943D+06, & + -8.40054336030240853D+04, 5.51335896122020586D+02, & + 8.14789096118312115D+08, -5.86648149205184723D+09, & + 1.86882075092958249D+10, -3.46320433881587779D+10, & + 4.12801855797539740D+10, -3.30265997498007231D+10, & + 1.79542137311556001D+10, -6.56329379261928433D+09, & + 1.55927986487925751D+09, -2.25105661889415278D+08, & + 1.73951075539781645D+07, -5.49842327572288687D+05, & + 3.03809051092238427D+03, -1.46792612476956167D+10, & + 1.14498237732025810D+11, -3.99096175224466498D+11, & + 8.19218669548577329D+11, -1.09837515608122331D+12/ + DATA C(97), C(98), C(99), C(100), C(101), C(102), C(103), C(104), & + C(105)/ & + 1.00815810686538209D+12, -6.45364869245376503D+11, & + 2.87900649906150589D+11, -8.78670721780232657D+10, & + 1.76347306068349694D+10, -2.16716498322379509D+09, & + 1.43157876718888981D+08, -3.87183344257261262D+06, & + 1.82577554742931747D+04/ + DATA ALFA(1), ALFA(2), ALFA(3), ALFA(4), ALFA(5), ALFA(6), & + ALFA(7), ALFA(8), ALFA(9), ALFA(10), ALFA(11), ALFA(12), & + ALFA(13), ALFA(14), ALFA(15), ALFA(16), ALFA(17), ALFA(18), & + ALFA(19), ALFA(20), ALFA(21), ALFA(22)/ & + -4.44444444444444444D-03, -9.22077922077922078D-04, & + -8.84892884892884893D-05, 1.65927687832449737D-04, & + 2.46691372741792910D-04, 2.65995589346254780D-04, & + 2.61824297061500945D-04, 2.48730437344655609D-04, & + 2.32721040083232098D-04, 2.16362485712365082D-04, & + 2.00738858762752355D-04, 1.86267636637545172D-04, & + 1.73060775917876493D-04, 1.61091705929015752D-04, & + 1.50274774160908134D-04, 1.40503497391269794D-04, & + 1.31668816545922806D-04, 1.23667445598253261D-04, & + 1.16405271474737902D-04, 1.09798298372713369D-04, & + 1.03772410422992823D-04, 9.82626078369363448D-05/ + DATA ALFA(23), ALFA(24), ALFA(25), ALFA(26), ALFA(27), ALFA(28), & + ALFA(29), ALFA(30), ALFA(31), ALFA(32), ALFA(33), ALFA(34), & + ALFA(35), ALFA(36), ALFA(37), ALFA(38), ALFA(39), ALFA(40), & + ALFA(41), ALFA(42), ALFA(43), ALFA(44)/ & + 9.32120517249503256D-05, 8.85710852478711718D-05, & + 8.42963105715700223D-05, 8.03497548407791151D-05, & + 7.66981345359207388D-05, 7.33122157481777809D-05, & + 7.01662625163141333D-05, 6.72375633790160292D-05, & + 6.93735541354588974D-04, 2.32241745182921654D-04, & + -1.41986273556691197D-05, -1.16444931672048640D-04, & + -1.50803558053048762D-04, -1.55121924918096223D-04, & + -1.46809756646465549D-04, -1.33815503867491367D-04, & + -1.19744975684254051D-04, -1.06184319207974020D-04, & + -9.37699549891194492D-05, -8.26923045588193274D-05, & + -7.29374348155221211D-05, -6.44042357721016283D-05/ + DATA ALFA(45), ALFA(46), ALFA(47), ALFA(48), ALFA(49), ALFA(50), & + ALFA(51), ALFA(52), ALFA(53), ALFA(54), ALFA(55), ALFA(56), & + ALFA(57), ALFA(58), ALFA(59), ALFA(60), ALFA(61), ALFA(62), & + ALFA(63), ALFA(64), ALFA(65), ALFA(66)/ & + -5.69611566009369048D-05, -5.04731044303561628D-05, & + -4.48134868008882786D-05, -3.98688727717598864D-05, & + -3.55400532972042498D-05, -3.17414256609022480D-05, & + -2.83996793904174811D-05, -2.54522720634870566D-05, & + -2.28459297164724555D-05, -2.05352753106480604D-05, & + -1.84816217627666085D-05, -1.66519330021393806D-05, & + -1.50179412980119482D-05, -1.35554031379040526D-05, & + -1.22434746473858131D-05, -1.10641884811308169D-05, & + -3.54211971457743841D-04, -1.56161263945159416D-04, & + 3.04465503594936410D-05, 1.30198655773242693D-04, & + 1.67471106699712269D-04, 1.70222587683592569D-04/ + DATA ALFA(67), ALFA(68), ALFA(69), ALFA(70), ALFA(71), ALFA(72), & + ALFA(73), ALFA(74), ALFA(75), ALFA(76), ALFA(77), ALFA(78), & + ALFA(79), ALFA(80), ALFA(81), ALFA(82), ALFA(83), ALFA(84), & + ALFA(85), ALFA(86), ALFA(87), ALFA(88)/ & + 1.56501427608594704D-04, 1.36339170977445120D-04, & + 1.14886692029825128D-04, 9.45869093034688111D-05, & + 7.64498419250898258D-05, 6.07570334965197354D-05, & + 4.74394299290508799D-05, 3.62757512005344297D-05, & + 2.69939714979224901D-05, 1.93210938247939253D-05, & + 1.30056674793963203D-05, 7.82620866744496661D-06, & + 3.59257485819351583D-06, 1.44040049814251817D-07, & + -2.65396769697939116D-06, -4.91346867098485910D-06, & + -6.72739296091248287D-06, -8.17269379678657923D-06, & + -9.31304715093561232D-06, -1.02011418798016441D-05, & + -1.08805962510592880D-05, -1.13875481509603555D-05/ + DATA ALFA(89), ALFA(90), ALFA(91), ALFA(92), ALFA(93), ALFA(94), & + ALFA(95), ALFA(96), ALFA(97), ALFA(98), ALFA(99), ALFA(100), & + ALFA(101), ALFA(102), ALFA(103), ALFA(104), ALFA(105), & + ALFA(106), ALFA(107), ALFA(108), ALFA(109), ALFA(110)/ & + -1.17519675674556414D-05, -1.19987364870944141D-05, & + 3.78194199201772914D-04, 2.02471952761816167D-04, & + -6.37938506318862408D-05, -2.38598230603005903D-04, & + -3.10916256027361568D-04, -3.13680115247576316D-04, & + -2.78950273791323387D-04, -2.28564082619141374D-04, & + -1.75245280340846749D-04, -1.25544063060690348D-04, & + -8.22982872820208365D-05, -4.62860730588116458D-05, & + -1.72334302366962267D-05, 5.60690482304602267D-06, & + 2.31395443148286800D-05, 3.62642745856793957D-05, & + 4.58006124490188752D-05, 5.24595294959114050D-05, & + 5.68396208545815266D-05, 5.94349820393104052D-05/ + DATA ALFA(111), ALFA(112), ALFA(113), ALFA(114), ALFA(115), & + ALFA(116), ALFA(117), ALFA(118), ALFA(119), ALFA(120), & + ALFA(121), ALFA(122), ALFA(123), ALFA(124), ALFA(125), & + ALFA(126), ALFA(127), ALFA(128), ALFA(129), ALFA(130)/ & + 6.06478527578421742D-05, 6.08023907788436497D-05, & + 6.01577894539460388D-05, 5.89199657344698500D-05, & + 5.72515823777593053D-05, 5.52804375585852577D-05, & + 5.31063773802880170D-05, 5.08069302012325706D-05, & + 4.84418647620094842D-05, 4.60568581607475370D-05, & + -6.91141397288294174D-04, -4.29976633058871912D-04, & + 1.83067735980039018D-04, 6.60088147542014144D-04, & + 8.75964969951185931D-04, 8.77335235958235514D-04, & + 7.49369585378990637D-04, 5.63832329756980918D-04, & + 3.68059319971443156D-04, 1.88464535514455599D-04/ + DATA ALFA(131), ALFA(132), ALFA(133), ALFA(134), ALFA(135), & + ALFA(136), ALFA(137), ALFA(138), ALFA(139), ALFA(140), & + ALFA(141), ALFA(142), ALFA(143), ALFA(144), ALFA(145), & + ALFA(146), ALFA(147), ALFA(148), ALFA(149), ALFA(150)/ & + 3.70663057664904149D-05, -8.28520220232137023D-05, & + -1.72751952869172998D-04, -2.36314873605872983D-04, & + -2.77966150694906658D-04, -3.02079514155456919D-04, & + -3.12594712643820127D-04, -3.12872558758067163D-04, & + -3.05678038466324377D-04, -2.93226470614557331D-04, & + -2.77255655582934777D-04, -2.59103928467031709D-04, & + -2.39784014396480342D-04, -2.20048260045422848D-04, & + -2.00443911094971498D-04, -1.81358692210970687D-04, & + -1.63057674478657464D-04, -1.45712672175205844D-04, & + -1.29425421983924587D-04, -1.14245691942445952D-04/ + DATA ALFA(151), ALFA(152), ALFA(153), ALFA(154), ALFA(155), & + ALFA(156), ALFA(157), ALFA(158), ALFA(159), ALFA(160), & + ALFA(161), ALFA(162), ALFA(163), ALFA(164), ALFA(165), & + ALFA(166), ALFA(167), ALFA(168), ALFA(169), ALFA(170)/ & + 1.92821964248775885D-03, 1.35592576302022234D-03, & + -7.17858090421302995D-04, -2.58084802575270346D-03, & + -3.49271130826168475D-03, -3.46986299340960628D-03, & + -2.82285233351310182D-03, -1.88103076404891354D-03, & + -8.89531718383947600D-04, 3.87912102631035228D-06, & + 7.28688540119691412D-04, 1.26566373053457758D-03, & + 1.62518158372674427D-03, 1.83203153216373172D-03, & + 1.91588388990527909D-03, 1.90588846755546138D-03, & + 1.82798982421825727D-03, 1.70389506421121530D-03, & + 1.55097127171097686D-03, 1.38261421852276159D-03/ + DATA ALFA(171), ALFA(172), ALFA(173), ALFA(174), ALFA(175), & + ALFA(176), ALFA(177), ALFA(178), ALFA(179), ALFA(180)/ & + 1.20881424230064774D-03, 1.03676532638344962D-03, & + 8.71437918068619115D-04, 7.16080155297701002D-04, & + 5.72637002558129372D-04, 4.42089819465802277D-04, & + 3.24724948503090564D-04, 2.20342042730246599D-04, & + 1.28412898401353882D-04, 4.82005924552095464D-05/ + DATA BETA(1), BETA(2), BETA(3), BETA(4), BETA(5), BETA(6), & + BETA(7), BETA(8), BETA(9), BETA(10), BETA(11), BETA(12), & + BETA(13), BETA(14), BETA(15), BETA(16), BETA(17), BETA(18), & + BETA(19), BETA(20), BETA(21), BETA(22)/ & + 1.79988721413553309D-02, 5.59964911064388073D-03, & + 2.88501402231132779D-03, 1.80096606761053941D-03, & + 1.24753110589199202D-03, 9.22878876572938311D-04, & + 7.14430421727287357D-04, 5.71787281789704872D-04, & + 4.69431007606481533D-04, 3.93232835462916638D-04, & + 3.34818889318297664D-04, 2.88952148495751517D-04, & + 2.52211615549573284D-04, 2.22280580798883327D-04, & + 1.97541838033062524D-04, 1.76836855019718004D-04, & + 1.59316899661821081D-04, 1.44347930197333986D-04, & + 1.31448068119965379D-04, 1.20245444949302884D-04, & + 1.10449144504599392D-04, 1.01828770740567258D-04/ + DATA BETA(23), BETA(24), BETA(25), BETA(26), BETA(27), BETA(28), & + BETA(29), BETA(30), BETA(31), BETA(32), BETA(33), BETA(34), & + BETA(35), BETA(36), BETA(37), BETA(38), BETA(39), BETA(40), & + BETA(41), BETA(42), BETA(43), BETA(44)/ & + 9.41998224204237509D-05, 8.74130545753834437D-05, & + 8.13466262162801467D-05, 7.59002269646219339D-05, & + 7.09906300634153481D-05, 6.65482874842468183D-05, & + 6.25146958969275078D-05, 5.88403394426251749D-05, & + -1.49282953213429172D-03, -8.78204709546389328D-04, & + -5.02916549572034614D-04, -2.94822138512746025D-04, & + -1.75463996970782828D-04, -1.04008550460816434D-04, & + -5.96141953046457895D-05, -3.12038929076098340D-05, & + -1.26089735980230047D-05, -2.42892608575730389D-07, & + 8.05996165414273571D-06, 1.36507009262147391D-05, & + 1.73964125472926261D-05, 1.98672978842133780D-05/ + DATA BETA(45), BETA(46), BETA(47), BETA(48), BETA(49), BETA(50), & + BETA(51), BETA(52), BETA(53), BETA(54), BETA(55), BETA(56), & + BETA(57), BETA(58), BETA(59), BETA(60), BETA(61), BETA(62), & + BETA(63), BETA(64), BETA(65), BETA(66)/ & + 2.14463263790822639D-05, 2.23954659232456514D-05, & + 2.28967783814712629D-05, 2.30785389811177817D-05, & + 2.30321976080909144D-05, 2.28236073720348722D-05, & + 2.25005881105292418D-05, 2.20981015361991429D-05, & + 2.16418427448103905D-05, 2.11507649256220843D-05, & + 2.06388749782170737D-05, 2.01165241997081666D-05, & + 1.95913450141179244D-05, 1.90689367910436740D-05, & + 1.85533719641636667D-05, 1.80475722259674218D-05, & + 5.52213076721292790D-04, 4.47932581552384646D-04, & + 2.79520653992020589D-04, 1.52468156198446602D-04, & + 6.93271105657043598D-05, 1.76258683069991397D-05/ + DATA BETA(67), BETA(68), BETA(69), BETA(70), BETA(71), BETA(72), & + BETA(73), BETA(74), BETA(75), BETA(76), BETA(77), BETA(78), & + BETA(79), BETA(80), BETA(81), BETA(82), BETA(83), BETA(84), & + BETA(85), BETA(86), BETA(87), BETA(88)/ & + -1.35744996343269136D-05, -3.17972413350427135D-05, & + -4.18861861696693365D-05, -4.69004889379141029D-05, & + -4.87665447413787352D-05, -4.87010031186735069D-05, & + -4.74755620890086638D-05, -4.55813058138628452D-05, & + -4.33309644511266036D-05, -4.09230193157750364D-05, & + -3.84822638603221274D-05, -3.60857167535410501D-05, & + -3.37793306123367417D-05, -3.15888560772109621D-05, & + -2.95269561750807315D-05, -2.75978914828335759D-05, & + -2.58006174666883713D-05, -2.41308356761280200D-05, & + -2.25823509518346033D-05, -2.11479656768912971D-05, & + -1.98200638885294927D-05, -1.85909870801065077D-05/ + DATA BETA(89), BETA(90), BETA(91), BETA(92), BETA(93), BETA(94), & + BETA(95), BETA(96), BETA(97), BETA(98), BETA(99), BETA(100), & + BETA(101), BETA(102), BETA(103), BETA(104), BETA(105), & + BETA(106), BETA(107), BETA(108), BETA(109), BETA(110)/ & + -1.74532699844210224D-05, -1.63997823854497997D-05, & + -4.74617796559959808D-04, -4.77864567147321487D-04, & + -3.20390228067037603D-04, -1.61105016119962282D-04, & + -4.25778101285435204D-05, 3.44571294294967503D-05, & + 7.97092684075674924D-05, 1.03138236708272200D-04, & + 1.12466775262204158D-04, 1.13103642108481389D-04, & + 1.08651634848774268D-04, 1.01437951597661973D-04, & + 9.29298396593363896D-05, 8.40293133016089978D-05, & + 7.52727991349134062D-05, 6.69632521975730872D-05, & + 5.92564547323194704D-05, 5.22169308826975567D-05, & + 4.58539485165360646D-05, 4.01445513891486808D-05/ + DATA BETA(111), BETA(112), BETA(113), BETA(114), BETA(115), & + BETA(116), BETA(117), BETA(118), BETA(119), BETA(120), & + BETA(121), BETA(122), BETA(123), BETA(124), BETA(125), & + BETA(126), BETA(127), BETA(128), BETA(129), BETA(130)/ & + 3.50481730031328081D-05, 3.05157995034346659D-05, & + 2.64956119950516039D-05, 2.29363633690998152D-05, & + 1.97893056664021636D-05, 1.70091984636412623D-05, & + 1.45547428261524004D-05, 1.23886640995878413D-05, & + 1.04775876076583236D-05, 8.79179954978479373D-06, & + 7.36465810572578444D-04, 8.72790805146193976D-04, & + 6.22614862573135066D-04, 2.85998154194304147D-04, & + 3.84737672879366102D-06, -1.87906003636971558D-04, & + -2.97603646594554535D-04, -3.45998126832656348D-04, & + -3.53382470916037712D-04, -3.35715635775048757D-04/ + DATA BETA(131), BETA(132), BETA(133), BETA(134), BETA(135), & + BETA(136), BETA(137), BETA(138), BETA(139), BETA(140), & + BETA(141), BETA(142), BETA(143), BETA(144), BETA(145), & + BETA(146), BETA(147), BETA(148), BETA(149), BETA(150)/ & + -3.04321124789039809D-04, -2.66722723047612821D-04, & + -2.27654214122819527D-04, -1.89922611854562356D-04, & + -1.55058918599093870D-04, -1.23778240761873630D-04, & + -9.62926147717644187D-05, -7.25178327714425337D-05, & + -5.22070028895633801D-05, -3.50347750511900522D-05, & + -2.06489761035551757D-05, -8.70106096849767054D-06, & + 1.13698686675100290D-06, 9.16426474122778849D-06, & + 1.56477785428872620D-05, 2.08223629482466847D-05, & + 2.48923381004595156D-05, 2.80340509574146325D-05, & + 3.03987774629861915D-05, 3.21156731406700616D-05/ + DATA BETA(151), BETA(152), BETA(153), BETA(154), BETA(155), & + BETA(156), BETA(157), BETA(158), BETA(159), BETA(160), & + BETA(161), BETA(162), BETA(163), BETA(164), BETA(165), & + BETA(166), BETA(167), BETA(168), BETA(169), BETA(170)/ & + -1.80182191963885708D-03, -2.43402962938042533D-03, & + -1.83422663549856802D-03, -7.62204596354009765D-04, & + 2.39079475256927218D-04, 9.49266117176881141D-04, & + 1.34467449701540359D-03, 1.48457495259449178D-03, & + 1.44732339830617591D-03, 1.30268261285657186D-03, & + 1.10351597375642682D-03, 8.86047440419791759D-04, & + 6.73073208165665473D-04, 4.77603872856582378D-04, & + 3.05991926358789362D-04, 1.60315694594721630D-04, & + 4.00749555270613286D-05, -5.66607461635251611D-05, & + -1.32506186772982638D-04, -1.90296187989614057D-04/ + DATA BETA(171), BETA(172), BETA(173), BETA(174), BETA(175), & + BETA(176), BETA(177), BETA(178), BETA(179), BETA(180), & + BETA(181), BETA(182), BETA(183), BETA(184), BETA(185), & + BETA(186), BETA(187), BETA(188), BETA(189), BETA(190)/ & + -2.32811450376937408D-04, -2.62628811464668841D-04, & + -2.82050469867598672D-04, -2.93081563192861167D-04, & + -2.97435962176316616D-04, -2.96557334239348078D-04, & + -2.91647363312090861D-04, -2.83696203837734166D-04, & + -2.73512317095673346D-04, -2.61750155806768580D-04, & + 6.38585891212050914D-03, 9.62374215806377941D-03, & + 7.61878061207001043D-03, 2.83219055545628054D-03, & + -2.09841352012720090D-03, -5.73826764216626498D-03, & + -7.70804244495414620D-03, -8.21011692264844401D-03, & + -7.65824520346905413D-03, -6.47209729391045177D-03/ + DATA BETA(191), BETA(192), BETA(193), BETA(194), BETA(195), & + BETA(196), BETA(197), BETA(198), BETA(199), BETA(200), & + BETA(201), BETA(202), BETA(203), BETA(204), BETA(205), & + BETA(206), BETA(207), BETA(208), BETA(209), BETA(210)/ & + -4.99132412004966473D-03, -3.45612289713133280D-03, & + -2.01785580014170775D-03, -7.59430686781961401D-04, & + 2.84173631523859138D-04, 1.10891667586337403D-03, & + 1.72901493872728771D-03, 2.16812590802684701D-03, & + 2.45357710494539735D-03, 2.61281821058334862D-03, & + 2.67141039656276912D-03, 2.65203073395980430D-03, & + 2.57411652877287315D-03, 2.45389126236094427D-03, & + 2.30460058071795494D-03, 2.13684837686712662D-03, & + 1.95896528478870911D-03, 1.77737008679454412D-03, & + 1.59690280765839059D-03, 1.42111975664438546D-03/ + DATA GAMA(1), GAMA(2), GAMA(3), GAMA(4), GAMA(5), GAMA(6), & + GAMA(7), GAMA(8), GAMA(9), GAMA(10), GAMA(11), GAMA(12), & + GAMA(13), GAMA(14), GAMA(15), GAMA(16), GAMA(17), GAMA(18), & + GAMA(19), GAMA(20), GAMA(21), GAMA(22)/ & + 6.29960524947436582D-01, 2.51984209978974633D-01, & + 1.54790300415655846D-01, 1.10713062416159013D-01, & + 8.57309395527394825D-02, 6.97161316958684292D-02, & + 5.86085671893713576D-02, 5.04698873536310685D-02, & + 4.42600580689154809D-02, 3.93720661543509966D-02, & + 3.54283195924455368D-02, 3.21818857502098231D-02, & + 2.94646240791157679D-02, 2.71581677112934479D-02, & + 2.51768272973861779D-02, 2.34570755306078891D-02, & + 2.19508390134907203D-02, 2.06210828235646240D-02, & + 1.94388240897880846D-02, 1.83810633800683158D-02, & + 1.74293213231963172D-02, 1.65685837786612353D-02/ + DATA GAMA(23), GAMA(24), GAMA(25), GAMA(26), GAMA(27), GAMA(28), & + GAMA(29), GAMA(30)/ & + 1.57865285987918445D-02, 1.50729501494095594D-02, & + 1.44193250839954639D-02, 1.38184805735341786D-02, & + 1.32643378994276568D-02, 1.27517121970498651D-02, & + 1.22761545318762767D-02, 1.18338262398482403D-02/ + DATA EX1, EX2, HPI, GPI, THPI / & + 3.33333333333333333D-01, 6.66666666666666667D-01, & + 1.57079632679489662D+00, 3.14159265358979324D+00, & + 4.71238898038468986D+00/ + DATA ZEROR,ZEROI,CONER,CONEI / 0.0D0, 0.0D0, 1.0D0, 0.0D0 / + + RFNU = 1.0D0/FNU + ZBR = ZR*RFNU + ZBI = ZI*RFNU + RFNU2 = RFNU*RFNU +!----------------------------------------------------------------------- +! COMPUTE IN THE FOURTH QUADRANT +!----------------------------------------------------------------------- + FN13 = FNU**EX1 + FN23 = FN13*FN13 + RFN13 = 1.0D0/FN13 + W2R = CONER - ZBR*ZBR + ZBI*ZBI + W2I = CONEI - ZBR*ZBI - ZBR*ZBI + AW2 = ZABS(W2R,W2I) + IF (AW2.GT.0.25D0) GO TO 130 +!----------------------------------------------------------------------- +! POWER SERIES FOR CABS(W2).LE.0.25D0 +!----------------------------------------------------------------------- + K = 1 + PR(1) = CONER + PI(1) = CONEI + SUMAR = GAMA(1) + SUMAI = ZEROI + AP(1) = 1.0D0 + IF (AW2.LT.TOL) GO TO 20 + DO 10 K=2,30 + PR(K) = PR(K-1)*W2R - PI(K-1)*W2I + PI(K) = PR(K-1)*W2I + PI(K-1)*W2R + SUMAR = SUMAR + PR(K)*GAMA(K) + SUMAI = SUMAI + PI(K)*GAMA(K) + AP(K) = AP(K-1)*AW2 + IF (AP(K).LT.TOL) GO TO 20 + 10 CONTINUE + K = 30 + 20 CONTINUE + KMAX = K + ZETAR = W2R*SUMAR - W2I*SUMAI + ZETAI = W2R*SUMAI + W2I*SUMAR + ARGR = ZETAR*FN23 + ARGI = ZETAI*FN23 + CALL ZSQRT(SUMAR, SUMAI, ZAR, ZAI) + CALL ZSQRT(W2R, W2I, STR, STI) + ZETA2R = STR*FNU + ZETA2I = STI*FNU + STR = CONER + EX2*(ZETAR*ZAR-ZETAI*ZAI) + STI = CONEI + EX2*(ZETAR*ZAI+ZETAI*ZAR) + ZETA1R = STR*ZETA2R - STI*ZETA2I + ZETA1I = STR*ZETA2I + STI*ZETA2R + ZAR = ZAR + ZAR + ZAI = ZAI + ZAI + CALL ZSQRT(ZAR, ZAI, STR, STI) + PHIR = STR*RFN13 + PHII = STI*RFN13 + IF (IPMTR.EQ.1) GO TO 120 +!----------------------------------------------------------------------- +! SUM SERIES FOR ASUM AND BSUM +!----------------------------------------------------------------------- + SUMBR = ZEROR + SUMBI = ZEROI + DO 30 K=1,KMAX + SUMBR = SUMBR + PR(K)*BETA(K) + SUMBI = SUMBI + PI(K)*BETA(K) + 30 CONTINUE + ASUMR = ZEROR + ASUMI = ZEROI + BSUMR = SUMBR + BSUMI = SUMBI + L1 = 0 + L2 = 30 + BTOL = TOL*(DABS(BSUMR)+DABS(BSUMI)) + ATOL = TOL + PP = 1.0D0 + IAS = 0 + IBS = 0 + IF (RFNU2.LT.TOL) GO TO 110 + DO 100 IS=2,7 + ATOL = ATOL/RFNU2 + PP = PP*RFNU2 + IF (IAS.EQ.1) GO TO 60 + SUMAR = ZEROR + SUMAI = ZEROI + DO 40 K=1,KMAX + M = L1 + K + SUMAR = SUMAR + PR(K)*ALFA(M) + SUMAI = SUMAI + PI(K)*ALFA(M) + IF (AP(K).LT.ATOL) GO TO 50 + 40 CONTINUE + 50 CONTINUE + ASUMR = ASUMR + SUMAR*PP + ASUMI = ASUMI + SUMAI*PP + IF (PP.LT.TOL) IAS = 1 + 60 CONTINUE + IF (IBS.EQ.1) GO TO 90 + SUMBR = ZEROR + SUMBI = ZEROI + DO 70 K=1,KMAX + M = L2 + K + SUMBR = SUMBR + PR(K)*BETA(M) + SUMBI = SUMBI + PI(K)*BETA(M) + IF (AP(K).LT.ATOL) GO TO 80 + 70 CONTINUE + 80 CONTINUE + BSUMR = BSUMR + SUMBR*PP + BSUMI = BSUMI + SUMBI*PP + IF (PP.LT.BTOL) IBS = 1 + 90 CONTINUE + IF (IAS.EQ.1 .AND. IBS.EQ.1) GO TO 110 + L1 = L1 + 30 + L2 = L2 + 30 + 100 CONTINUE + 110 CONTINUE + ASUMR = ASUMR + CONER + PP = RFNU*RFN13 + BSUMR = BSUMR*PP + BSUMI = BSUMI*PP + 120 CONTINUE + RETURN +!----------------------------------------------------------------------- +! CABS(W2).GT.0.25D0 +!----------------------------------------------------------------------- + 130 CONTINUE + CALL ZSQRT(W2R, W2I, WR, WI) + IF (WR.LT.0.0D0) WR = 0.0D0 + IF (WI.LT.0.0D0) WI = 0.0D0 + STR = CONER + WR + STI = WI + CALL ZDIV(STR, STI, ZBR, ZBI, ZAR, ZAI) + CALL ZLOG(ZAR, ZAI, ZCR, ZCI, IDUM) + IF (ZCI.LT.0.0D0) ZCI = 0.0D0 + IF (ZCI.GT.HPI) ZCI = HPI + IF (ZCR.LT.0.0D0) ZCR = 0.0D0 + ZTHR = (ZCR-WR)*1.5D0 + ZTHI = (ZCI-WI)*1.5D0 + ZETA1R = ZCR*FNU + ZETA1I = ZCI*FNU + ZETA2R = WR*FNU + ZETA2I = WI*FNU + AZTH = ZABS(ZTHR,ZTHI) + ANG = THPI + IF (ZTHR.GE.0.0D0 .AND. ZTHI.LT.0.0D0) GO TO 140 + ANG = HPI + IF (ZTHR.EQ.0.0D0) GO TO 140 + ANG = DATAN(ZTHI/ZTHR) + IF (ZTHR.LT.0.0D0) ANG = ANG + GPI + 140 CONTINUE + PP = AZTH**EX2 + ANG = ANG*EX2 + ZETAR = PP*DCOS(ANG) + ZETAI = PP*DSIN(ANG) + IF (ZETAI.LT.0.0D0) ZETAI = 0.0D0 + ARGR = ZETAR*FN23 + ARGI = ZETAI*FN23 + CALL ZDIV(ZTHR, ZTHI, ZETAR, ZETAI, RTZTR, RTZTI) + CALL ZDIV(RTZTR, RTZTI, WR, WI, ZAR, ZAI) + TZAR = ZAR + ZAR + TZAI = ZAI + ZAI + CALL ZSQRT(TZAR, TZAI, STR, STI) + PHIR = STR*RFN13 + PHII = STI*RFN13 + IF (IPMTR.EQ.1) GO TO 120 + RAW = 1.0D0/DSQRT(AW2) + STR = WR*RAW + STI = -WI*RAW + TFNR = STR*RFNU*RAW + TFNI = STI*RFNU*RAW + RAZTH = 1.0D0/AZTH + STR = ZTHR*RAZTH + STI = -ZTHI*RAZTH + RZTHR = STR*RAZTH*RFNU + RZTHI = STI*RAZTH*RFNU + ZCR = RZTHR*AR(2) + ZCI = RZTHI*AR(2) + RAW2 = 1.0D0/AW2 + STR = W2R*RAW2 + STI = -W2I*RAW2 + T2R = STR*RAW2 + T2I = STI*RAW2 + STR = T2R*C(2) + C(3) + STI = T2I*C(2) + UPR(2) = STR*TFNR - STI*TFNI + UPI(2) = STR*TFNI + STI*TFNR + BSUMR = UPR(2) + ZCR + BSUMI = UPI(2) + ZCI + ASUMR = ZEROR + ASUMI = ZEROI + IF (RFNU.LT.TOL) GO TO 220 + PRZTHR = RZTHR + PRZTHI = RZTHI + PTFNR = TFNR + PTFNI = TFNI + UPR(1) = CONER + UPI(1) = CONEI + PP = 1.0D0 + BTOL = TOL*(DABS(BSUMR)+DABS(BSUMI)) + KS = 0 + KP1 = 2 + L = 3 + IAS = 0 + IBS = 0 + DO 210 LR=2,12,2 + LRP1 = LR + 1 +!----------------------------------------------------------------------- +! COMPUTE TWO ADDITIONAL CR, DR, AND UP FOR TWO MORE TERMS IN +! NEXT SUMA AND SUMB +!----------------------------------------------------------------------- + DO 160 K=LR,LRP1 + KS = KS + 1 + KP1 = KP1 + 1 + L = L + 1 + ZAR = C(L) + ZAI = ZEROI + DO 150 J=2,KP1 + L = L + 1 + STR = ZAR*T2R - T2I*ZAI + C(L) + ZAI = ZAR*T2I + ZAI*T2R + ZAR = STR + 150 CONTINUE + STR = PTFNR*TFNR - PTFNI*TFNI + PTFNI = PTFNR*TFNI + PTFNI*TFNR + PTFNR = STR + UPR(KP1) = PTFNR*ZAR - PTFNI*ZAI + UPI(KP1) = PTFNI*ZAR + PTFNR*ZAI + CRR(KS) = PRZTHR*BR(KS+1) + CRI(KS) = PRZTHI*BR(KS+1) + STR = PRZTHR*RZTHR - PRZTHI*RZTHI + PRZTHI = PRZTHR*RZTHI + PRZTHI*RZTHR + PRZTHR = STR + DRR(KS) = PRZTHR*AR(KS+2) + DRI(KS) = PRZTHI*AR(KS+2) + 160 CONTINUE + PP = PP*RFNU2 + IF (IAS.EQ.1) GO TO 180 + SUMAR = UPR(LRP1) + SUMAI = UPI(LRP1) + JU = LRP1 + DO 170 JR=1,LR + JU = JU - 1 + SUMAR = SUMAR + CRR(JR)*UPR(JU) - CRI(JR)*UPI(JU) + SUMAI = SUMAI + CRR(JR)*UPI(JU) + CRI(JR)*UPR(JU) + 170 CONTINUE + ASUMR = ASUMR + SUMAR + ASUMI = ASUMI + SUMAI + TEST = DABS(SUMAR) + DABS(SUMAI) + IF (PP.LT.TOL .AND. TEST.LT.TOL) IAS = 1 + 180 CONTINUE + IF (IBS.EQ.1) GO TO 200 + SUMBR = UPR(LR+2) + UPR(LRP1)*ZCR - UPI(LRP1)*ZCI + SUMBI = UPI(LR+2) + UPR(LRP1)*ZCI + UPI(LRP1)*ZCR + JU = LRP1 + DO 190 JR=1,LR + JU = JU - 1 + SUMBR = SUMBR + DRR(JR)*UPR(JU) - DRI(JR)*UPI(JU) + SUMBI = SUMBI + DRR(JR)*UPI(JU) + DRI(JR)*UPR(JU) + 190 CONTINUE + BSUMR = BSUMR + SUMBR + BSUMI = BSUMI + SUMBI + TEST = DABS(SUMBR) + DABS(SUMBI) + IF (PP.LT.BTOL .AND. TEST.LT.BTOL) IBS = 1 + 200 CONTINUE + IF (IAS.EQ.1 .AND. IBS.EQ.1) GO TO 220 + 210 CONTINUE + 220 CONTINUE + ASUMR = ASUMR + CONER + STR = -BSUMR*RFN13 + STI = -BSUMI*RFN13 + CALL ZDIV(STR, STI, RTZTR, RTZTI, BSUMR, BSUMI) + GO TO 120 +END + +SUBROUTINE ZRATI(ZR, ZI, FNU, N, CYR, CYI, TOL) +USE COMPLEX +!***BEGIN PROLOGUE ZRATI +!***REFER TO ZBESI,ZBESK,ZBESH +! +! ZRATI COMPUTES RATIOS OF I BESSEL FUNCTIONS BY BACKWARD +! RECURRENCE. THE STARTING INDEX IS DETERMINED BY FORWARD +! RECURRENCE AS DESCRIBED IN J. RES. OF NAT. BUR. OF STANDARDS-B, +! MATHEMATICAL SCIENCES, VOL 77B, P111-114, SEPTEMBER, 1973, +! BESSEL FUNCTIONS I AND J OF COMPLEX ARGUMENT AND INTEGER ORDER, +! BY D. J. SOOKNE. +! +!***ROUTINES CALLED ZABS,ZDIV +!***END PROLOGUE ZRATI +! COMPLEX Z,CY(1),CONE,CZERO,P1,P2,T1,RZ,PT,CDFNU + DOUBLE PRECISION AK, AMAGZ, AP1, AP2, ARG, AZ, CDFNUI, CDFNUR, & + CONEI, CONER, CYI, CYR, CZEROI, CZEROR, DFNU, FDNU, FLAM, FNU, & + FNUP, PTI, PTR, P1I, P1R, P2I, P2R, RAK, RAP1, RHO, RT2, RZI, & + RZR, TEST, TEST1, TOL, TTI, TTR, T1I, T1R, ZI, ZR + INTEGER I, ID, IDNU, INU, ITIME, K, KK, MAGZ, N + DIMENSION CYR(1), CYI(1) + DATA CZEROR,CZEROI,CONER,CONEI,RT2 & + /0.0D0, 0.0D0, 1.0D0, 0.0D0, 1.41421356237309505D0/ + AZ = ZABS(ZR,ZI) + INU = INT(SNGL(FNU)) + IDNU = INU + N - 1 + MAGZ = INT(SNGL(AZ)) + AMAGZ = DBLE(FLOAT(MAGZ+1)) + FDNU = DBLE(FLOAT(IDNU)) + FNUP = DMAX1(AMAGZ,FDNU) + ID = IDNU - MAGZ - 1 + ITIME = 1 + K = 1 + PTR = 1.0D0/AZ + RZR = PTR*(ZR+ZR)*PTR + RZI = -PTR*(ZI+ZI)*PTR + T1R = RZR*FNUP + T1I = RZI*FNUP + P2R = -T1R + P2I = -T1I + P1R = CONER + P1I = CONEI + T1R = T1R + RZR + T1I = T1I + RZI + IF (ID.GT.0) ID = 0 + AP2 = ZABS(P2R,P2I) + AP1 = ZABS(P1R,P1I) +!----------------------------------------------------------------------- +! THE OVERFLOW TEST ON K(FNU+I-1,Z) BEFORE THE CALL TO CBKNU +! GUARANTEES THAT P2 IS ON SCALE. SCALE TEST1 AND ALL SUBSEQUENT +! P2 VALUES BY AP1 TO ENSURE THAT AN OVERFLOW DOES NOT OCCUR +! PREMATURELY. +!----------------------------------------------------------------------- + ARG = (AP2+AP2)/(AP1*TOL) + TEST1 = DSQRT(ARG) + TEST = TEST1 + RAP1 = 1.0D0/AP1 + P1R = P1R*RAP1 + P1I = P1I*RAP1 + P2R = P2R*RAP1 + P2I = P2I*RAP1 + AP2 = AP2*RAP1 + 10 CONTINUE + K = K + 1 + AP1 = AP2 + PTR = P2R + PTI = P2I + P2R = P1R - (T1R*PTR-T1I*PTI) + P2I = P1I - (T1R*PTI+T1I*PTR) + P1R = PTR + P1I = PTI + T1R = T1R + RZR + T1I = T1I + RZI + AP2 = ZABS(P2R,P2I) + IF (AP1.LE.TEST) GO TO 10 + IF (ITIME.EQ.2) GO TO 20 + AK = ZABS(T1R,T1I)*0.5D0 + FLAM = AK + DSQRT(AK*AK-1.0D0) + RHO = DMIN1(AP2/AP1,FLAM) + TEST = TEST1*DSQRT(RHO/(RHO*RHO-1.0D0)) + ITIME = 2 + GO TO 10 + 20 CONTINUE + KK = K + 1 - ID + AK = DBLE(FLOAT(KK)) + T1R = AK + T1I = CZEROI + DFNU = FNU + DBLE(FLOAT(N-1)) + P1R = 1.0D0/AP2 + P1I = CZEROI + P2R = CZEROR + P2I = CZEROI + DO 30 I=1,KK + PTR = P1R + PTI = P1I + RAP1 = DFNU + T1R + TTR = RZR*RAP1 + TTI = RZI*RAP1 + P1R = (PTR*TTR-PTI*TTI) + P2R + P1I = (PTR*TTI+PTI*TTR) + P2I + P2R = PTR + P2I = PTI + T1R = T1R - CONER + 30 CONTINUE + IF (P1R.NE.CZEROR .OR. P1I.NE.CZEROI) GO TO 40 + P1R = TOL + P1I = TOL + 40 CONTINUE + CALL ZDIV(P2R, P2I, P1R, P1I, CYR(N), CYI(N)) + IF (N.EQ.1) RETURN + K = N - 1 + AK = DBLE(FLOAT(K)) + T1R = AK + T1I = CZEROI + CDFNUR = FNU*RZR + CDFNUI = FNU*RZI + DO 60 I=2,N + PTR = CDFNUR + (T1R*RZR-T1I*RZI) + CYR(K+1) + PTI = CDFNUI + (T1R*RZI+T1I*RZR) + CYI(K+1) + AK = ZABS(PTR,PTI) + IF (AK.NE.CZEROR) GO TO 50 + PTR = TOL + PTI = TOL + AK = TOL*RT2 + 50 CONTINUE + RAK = CONER/AK + CYR(K) = RAK*PTR*RAK + CYI(K) = -RAK*PTI*RAK + T1R = T1R - CONER + K = K - 1 + 60 CONTINUE + RETURN +END + +SUBROUTINE ZAIRY(ZR, ZI, ID, KODE, AIR, AII, NZ, IERR) +USE UTILIT +USE COMPLEX +!***BEGIN PROLOGUE ZAIRY +!***DATE WRITTEN 830501 (YYMMDD) +!***REVISION DATE 830501 (YYMMDD) +!***CATEGORY NO. B5K +!***KEYWORDS AIRY FUNCTION,BESSEL FUNCTIONS OF ORDER ONE THIRD +!***AUTHOR AMOS, DONALD E., SANDIA NATIONAL LABORATORIES +!***PURPOSE TO COMPUTE AIRY FUNCTIONS AI(Z) AND DAI(Z) FOR COMPLEX Z +!***DESCRIPTION +! +! ***A DOUBLE PRECISION ROUTINE*** +! ON KODE=1, ZAIRY COMPUTES THE COMPLEX AIRY FUNCTION AI(Z) OR +! ITS DERIVATIVE DAI(Z)/DZ ON ID=0 OR ID=1 RESPECTIVELY. ON +! KODE=2, A SCALING OPTION CEXP(ZTA)*AI(Z) OR CEXP(ZTA)* +! DAI(Z)/DZ IS PROVIDED TO REMOVE THE EXPONENTIAL DECAY IN +! -PI/3.LT.ARG(Z).LT.PI/3 AND THE EXPONENTIAL GROWTH IN +! PI/3.LT.ABS(ARG(Z)).LT.PI WHERE ZTA=(2/3)*Z*CSQRT(Z). +! +! WHILE THE AIRY FUNCTIONS AI(Z) AND DAI(Z)/DZ ARE ANALYTI! IN +! THE WHOLE Z PLANE, THE CORRESPONDING SCALED FUNCTIONS DEFINED +! FOR KODE=2 HAVE A CUT ALONG THE NEGATIVE REAL AXIS. +! DEFINTIONS AND NOTATION ARE FOUND IN THE NBS HANDBOOK OF +! MATHEMATICAL FUNCTIONS (REF. 1). +! +! INPUT ZR,ZI ARE DOUBLE PRECISION +! ZR,ZI - Z=CMPLX(ZR,ZI) +! ID - ORDER OF DERIVATIVE, ID=0 OR ID=1 +! KODE - A PARAMETER TO INDICATE THE SCALING OPTION +! KODE= 1 RETURNS +! AI=AI(Z) ON ID=0 OR +! AI=DAI(Z)/DZ ON ID=1 +! = 2 RETURNS +! AI=CEXP(ZTA)*AI(Z) ON ID=0 OR +! AI=CEXP(ZTA)*DAI(Z)/DZ ON ID=1 WHERE +! ZTA=(2/3)*Z*CSQRT(Z) +! +! OUTPUT AIR,AII ARE DOUBLE PRECISION +! AIR,AII- COMPLEX ANSWER DEPENDING ON THE CHOICES FOR ID AND +! KODE +! NZ - UNDERFLOW INDICATOR +! NZ= 0 , NORMAL RETURN +! NZ= 1 , AI=CMPLX(0.0D0,0.0D0) DUE TO UNDERFLOW IN +! -PI/3.LT.ARG(Z).LT.PI/3 ON KODE=1 +! IERR - ERROR FLAG +! IERR=0, NORMAL RETURN - COMPUTATION COMPLETED +! IERR=1, INPUT ERROR - NO COMPUTATION +! IERR=2, OVERFLOW - NO COMPUTATION, REAL(ZTA) +! TOO LARGE ON KODE=1 +! IERR=3, CABS(Z) LARGE - COMPUTATION COMPLETED +! LOSSES OF SIGNIFCANCE BY ARGUMENT REDUCTION +! PRODUCE LESS THAN HALF OF MACHINE ACCURACY +! IERR=4, CABS(Z) TOO LARGE - NO COMPUTATION +! COMPLETE LOSS OF ACCURACY BY ARGUMENT +! REDUCTION +! IERR=5, ERROR - NO COMPUTATION, +! ALGORITHM TERMINATION CONDITION NOT MET +! +!***LONG DESCRIPTION +! +! AI AND DAI ARE COMPUTED FOR CABS(Z).GT.1.0 FROM THE K BESSEL +! FUNCTIONS BY +! +! AI(Z)=C*SQRT(Z)*K(1/3,ZTA) , DAI(Z)=-C*Z*K(2/3,ZTA) +! C=1.0/(PI*SQRT(3.0)) +! ZTA=(2/3)*Z**(3/2) +! +! WITH THE POWER SERIES FOR CABS(Z).LE.1.0. +! +! IN MOST COMPLEX VARIABLE COMPUTATION, ONE MUST EVALUATE ELE- +! MENTARY FUNCTIONS. WHEN THE MAGNITUDE OF Z IS LARGE, LOSSES +! OF SIGNIFICANCE BY ARGUMENT REDUCTION OCCUR. CONSEQUENTLY, IF +! THE MAGNITUDE OF ZETA=(2/3)*Z**1.5 EXCEEDS U1=SQRT(0.5/UR), +! THEN LOSSES EXCEEDING HALF PRECISION ARE LIKELY AND AN ERROR +! FLAG IERR=3 IS TRIGGERED WHERE UR=DMAX1(D1MACH(4),1.0D-18) IS +! DOUBLE PRECISION UNIT ROUNDOFF LIMITED TO 18 DIGITS PRECISION. +! ALSO, IF THE MAGNITUDE OF ZETA IS LARGER THAN U2=0.5/UR, THEN +! ALL SIGNIFICANCE IS LOST AND IERR=4. IN ORDER TO USE THE INT +! FUNCTION, ZETA MUST BE FURTHER RESTRICTED NOT TO EXCEED THE +! LARGEST INTEGER, U3=I1MACH(9). THUS, THE MAGNITUDE OF ZETA +! MUST BE RESTRICTED BY MIN(U2,U3). ON 32 BIT MACHINES, U1,U2, +! AND U3 ARE APPROXIMATELY 2.0E+3, 4.2E+6, 2.1E+9 IN SINGLE +! PRECISION ARITHMETIC AND 1.3E+8, 1.8E+16, 2.1E+9 IN DOUBLE +! PRECISION ARITHMETIC RESPECTIVELY. THIS MAKES U2 AND U3 LIMIT- +! ING IN THEIR RESPECTIVE ARITHMETICS. THIS MEANS THAT THE MAG- +! NITUDE OF Z CANNOT EXCEED 3.1E+4 IN SINGLE AND 2.1E+6 IN +! DOUBLE PRECISION ARITHMETIC. THIS ALSO MEANS THAT ONE CAN +! EXPECT TO RETAIN, IN THE WORST CASES ON 32 BIT MACHINES, +! NO DIGITS IN SINGLE PRECISION AND ONLY 7 DIGITS IN DOUBLE +! PRECISION ARITHMETIC. SIMILAR CONSIDERATIONS HOLD FOR OTHER +! MACHINES. +! +! THE APPROXIMATE RELATIVE ERROR IN THE MAGNITUDE OF A COMPLEX +! BESSEL FUNCTION CAN BE EXPRESSED BY P*10**S WHERE P=MAX(UNIT +! ROUNDOFF,1.0E-18) IS THE NOMINAL PRECISION AND 10**S REPRE- +! SENTS THE INCREASE IN ERROR DUE TO ARGUMENT REDUCTION IN THE +! ELEMENTARY FUNCTIONS. HERE, S=MAX(1,ABS(LOG10(CABS(Z))), +! ABS(LOG10(FNU))) APPROXIMATELY (I.E. S=MAX(1,ABS(EXPONENT OF +! CABS(Z),ABS(EXPONENT OF FNU)) ). HOWEVER, THE PHASE ANGLE MAY +! HAVE ONLY ABSOLUTE ACCURACY. THIS IS MOST LIKELY TO OCCUR WHEN +! ONE COMPONENT (IN ABSOLUTE VALUE) IS LARGER THAN THE OTHER BY +! SEVERAL ORDERS OF MAGNITUDE. IF ONE COMPONENT IS 10**K LARGER +! THAN THE OTHER, THEN ONE CAN EXPECT ONLY MAX(ABS(LOG10(P))-K, +! 0) SIGNIFICANT DIGITS; OR, STATED ANOTHER WAY, WHEN K EXCEEDS +! THE EXPONENT OF P, NO SIGNIFICANT DIGITS REMAIN IN THE SMALLER +! COMPONENT. HOWEVER, THE PHASE ANGLE RETAINS ABSOLUTE ACCURACY +! BECAUSE, IN COMPLEX ARITHMETIC WITH PRECISION P, THE SMALLER +! COMPONENT WILL NOT (AS A RULE) DECREASE BELOW P TIMES THE +! MAGNITUDE OF THE LARGER COMPONENT. IN THESE EXTREME CASES, +! THE PRINCIPAL PHASE ANGLE IS ON THE ORDER OF +P, -P, PI/2-P, +! OR -PI/2+P. +! +!***REFERENCES HANDBOOK OF MATHEMATICAL FUNCTIONS BY M. ABRAMOWITZ +! AND I. A. STEGUN, NBS AMS SERIES 55, U.S. DEPT. OF +! COMMERCE, 1955. +! +! COMPUTATION OF BESSEL FUNCTIONS OF COMPLEX ARGUMENT +! AND LARGE ORDER BY D. E. AMOS, SAND83-0643, MAY, 1983 +! +! A SUBROUTINE PACKAGE FOR BESSEL FUNCTIONS OF A COMPLEX +! ARGUMENT AND NONNEGATIVE ORDER BY D. E. AMOS, SAND85- +! 1018, MAY, 1985 +! +! A PORTABLE PACKAGE FOR BESSEL FUNCTIONS OF A COMPLEX +! ARGUMENT AND NONNEGATIVE ORDER BY D. E. AMOS, TRANS. +! MATH. SOFTWARE, 1986 +! +!***ROUTINES CALLED ZACAI,ZBKNU,ZEXP,ZSQRT,I1MACH,D1MACH +!***END PROLOGUE ZAIRY +! COMPLEX AI,CONE,CSQ,CY,S1,S2,TRM1,TRM2,Z,ZTA,Z3 + DOUBLE PRECISION AA, AD, AII, AIR, AK, ALIM, ATRM, AZ, AZ3, BK, & + CC, CK, COEF, CONEI, CONER, CSQI, CSQR, CYI, CYR, C1, C2, DIG, & + DK, D1, D2, ELIM, FID, FNU, PTR, RL, R1M5, SFAC, STI, STR, & + S1I, S1R, S2I, S2R, TOL, TRM1I, TRM1R, TRM2I, TRM2R, TTH, ZEROI, & + ZEROR, ZI, ZR, ZTAI, ZTAR, Z3I, Z3R, ALAZ, BB + INTEGER ID, IERR, IFLAG, K, KODE, K1, K2, MR, NN, NZ + DIMENSION CYR(1), CYI(1) + DATA TTH, C1, C2, COEF /6.66666666666666667D-01, & + 3.55028053887817240D-01,2.58819403792806799D-01, & + 1.83776298473930683D-01/ + DATA ZEROR, ZEROI, CONER, CONEI /0.0D0,0.0D0,1.0D0,0.0D0/ +!***FIRST EXECUTABLE STATEMENT ZAIRY + IERR = 0 + NZ=0 + IF (ID.LT.0 .OR. ID.GT.1) IERR=1 + IF (KODE.LT.1 .OR. KODE.GT.2) IERR=1 + IF (IERR.NE.0) RETURN + AZ = ZABS(ZR,ZI) + TOL = DMAX1(D1MACH(4),1.0D-18) + FID = DBLE(FLOAT(ID)) + IF (AZ.GT.1.0D0) GO TO 70 +!----------------------------------------------------------------------- +! POWER SERIES FOR CABS(Z).LE.1. +!----------------------------------------------------------------------- + S1R = CONER + S1I = CONEI + S2R = CONER + S2I = CONEI + IF (AZ.LT.TOL) GO TO 170 + AA = AZ*AZ + IF (AA.LT.TOL/AZ) GO TO 40 + TRM1R = CONER + TRM1I = CONEI + TRM2R = CONER + TRM2I = CONEI + ATRM = 1.0D0 + STR = ZR*ZR - ZI*ZI + STI = ZR*ZI + ZI*ZR + Z3R = STR*ZR - STI*ZI + Z3I = STR*ZI + STI*ZR + AZ3 = AZ*AA + AK = 2.0D0 + FID + BK = 3.0D0 - FID - FID + CK = 4.0D0 - FID + DK = 3.0D0 + FID + FID + D1 = AK*DK + D2 = BK*CK + AD = DMIN1(D1,D2) + AK = 24.0D0 + 9.0D0*FID + BK = 30.0D0 - 9.0D0*FID + DO 30 K=1,25 + STR = (TRM1R*Z3R-TRM1I*Z3I)/D1 + TRM1I = (TRM1R*Z3I+TRM1I*Z3R)/D1 + TRM1R = STR + S1R = S1R + TRM1R + S1I = S1I + TRM1I + STR = (TRM2R*Z3R-TRM2I*Z3I)/D2 + TRM2I = (TRM2R*Z3I+TRM2I*Z3R)/D2 + TRM2R = STR + S2R = S2R + TRM2R + S2I = S2I + TRM2I + ATRM = ATRM*AZ3/AD + D1 = D1 + AK + D2 = D2 + BK + AD = DMIN1(D1,D2) + IF (ATRM.LT.TOL*AD) GO TO 40 + AK = AK + 18.0D0 + BK = BK + 18.0D0 + 30 CONTINUE + 40 CONTINUE + IF (ID.EQ.1) GO TO 50 + AIR = S1R*C1 - C2*(ZR*S2R-ZI*S2I) + AII = S1I*C1 - C2*(ZR*S2I+ZI*S2R) + IF (KODE.EQ.1) RETURN + CALL ZSQRT(ZR, ZI, STR, STI) + ZTAR = TTH*(ZR*STR-ZI*STI) + ZTAI = TTH*(ZR*STI+ZI*STR) + CALL ZEXP(ZTAR, ZTAI, STR, STI) + PTR = AIR*STR - AII*STI + AII = AIR*STI + AII*STR + AIR = PTR + RETURN + 50 CONTINUE + AIR = -S2R*C2 + AII = -S2I*C2 + IF (AZ.LE.TOL) GO TO 60 + STR = ZR*S1R - ZI*S1I + STI = ZR*S1I + ZI*S1R + CC = C1/(1.0D0+FID) + AIR = AIR + CC*(STR*ZR-STI*ZI) + AII = AII + CC*(STR*ZI+STI*ZR) + 60 CONTINUE + IF (KODE.EQ.1) RETURN + CALL ZSQRT(ZR, ZI, STR, STI) + ZTAR = TTH*(ZR*STR-ZI*STI) + ZTAI = TTH*(ZR*STI+ZI*STR) + CALL ZEXP(ZTAR, ZTAI, STR, STI) + PTR = STR*AIR - STI*AII + AII = STR*AII + STI*AIR + AIR = PTR + RETURN +!----------------------------------------------------------------------- +! CASE FOR CABS(Z).GT.1.0 +!----------------------------------------------------------------------- + 70 CONTINUE + FNU = (1.0D0+FID)/3.0D0 +!----------------------------------------------------------------------- +! SET PARAMETERS RELATED TO MACHINE CONSTANTS. +! TOL IS THE APPROXIMATE UNIT ROUNDOFF LIMITED TO 1.0D-18. +! ELIM IS THE APPROXIMATE EXPONENTIAL OVER- AND UNDERFLOW LIMIT. +! EXP(-ELIM).LT.EXP(-ALIM)=EXP(-ELIM)/TOL AND +! EXP(ELIM).GT.EXP(ALIM)=EXP(ELIM)*TOL ARE INTERVALS NEAR +! UNDERFLOW AND OVERFLOW LIMITS WHERE SCALED ARITHMETIC IS DONE. +! RL IS THE LOWER BOUNDARY OF THE ASYMPTOTIC EXPANSION FOR LARGE Z. +! DIG = NUMBER OF BASE 10 DIGITS IN TOL = 10**(-DIG). +!----------------------------------------------------------------------- + K1 = I1MACH(15) + K2 = I1MACH(16) + R1M5 = D1MACH(5) + K = MIN0(IABS(K1),IABS(K2)) + ELIM = 2.303D0*(DBLE(FLOAT(K))*R1M5-3.0D0) + K1 = I1MACH(14) - 1 + AA = R1M5*DBLE(FLOAT(K1)) + DIG = DMIN1(AA,18.0D0) + AA = AA*2.303D0 + ALIM = ELIM + DMAX1(-AA,-41.45D0) + RL = 1.2D0*DIG + 3.0D0 + ALAZ = DLOG(AZ) +!----------------------------------------------------------------------- +! TEST FOR PROPER RANGE +!----------------------------------------------------------------------- + AA=0.5D0/TOL + BB=DBLE(FLOAT(I1MACH(9)))*0.5D0 + AA=DMIN1(AA,BB) + AA=AA**TTH + IF (AZ.GT.AA) GO TO 260 + AA=DSQRT(AA) + IF (AZ.GT.AA) IERR=3 + CALL ZSQRT(ZR, ZI, CSQR, CSQI) + ZTAR = TTH*(ZR*CSQR-ZI*CSQI) + ZTAI = TTH*(ZR*CSQI+ZI*CSQR) +!----------------------------------------------------------------------- +! RE(ZTA).LE.0 WHEN RE(Z).LT.0, ESPECIALLY WHEN IM(Z) IS SMALL +!----------------------------------------------------------------------- + IFLAG = 0 + SFAC = 1.0D0 + AK = ZTAI + IF (ZR.GE.0.0D0) GO TO 80 + BK = ZTAR + CK = -DABS(BK) + ZTAR = CK + ZTAI = AK + 80 CONTINUE + IF (ZI.NE.0.0D0) GO TO 90 + IF (ZR.GT.0.0D0) GO TO 90 + ZTAR = 0.0D0 + ZTAI = AK + 90 CONTINUE + AA = ZTAR + IF (AA.GE.0.0D0 .AND. ZR.GT.0.0D0) GO TO 110 + IF (KODE.EQ.2) GO TO 100 +!----------------------------------------------------------------------- +! OVERFLOW TEST +!----------------------------------------------------------------------- + IF (AA.GT.(-ALIM)) GO TO 100 + AA = -AA + 0.25D0*ALAZ + IFLAG = 1 + SFAC = TOL + IF (AA.GT.ELIM) GO TO 270 + 100 CONTINUE +!----------------------------------------------------------------------- +! CBKNU AND CACON RETURN EXP(ZTA)*K(FNU,ZTA) ON KODE=2 +!----------------------------------------------------------------------- + MR = 1 + IF (ZI.LT.0.0D0) MR = -1 + CALL ZACAI(ZTAR, ZTAI, FNU, KODE, MR, 1, CYR, CYI, NN, RL, TOL, & + ELIM, ALIM) + IF (NN.LT.0) GO TO 280 + NZ = NZ + NN + GO TO 130 + 110 CONTINUE + IF (KODE.EQ.2) GO TO 120 +!----------------------------------------------------------------------- +! UNDERFLOW TEST +!----------------------------------------------------------------------- + IF (AA.LT.ALIM) GO TO 120 + AA = -AA - 0.25D0*ALAZ + IFLAG = 2 + SFAC = 1.0D0/TOL + IF (AA.LT.(-ELIM)) GO TO 210 + 120 CONTINUE + CALL ZBKNU(ZTAR, ZTAI, FNU, KODE, 1, CYR, CYI, NZ, TOL, ELIM, ALIM) + 130 CONTINUE + S1R = CYR(1)*COEF + S1I = CYI(1)*COEF + IF (IFLAG.NE.0) GO TO 150 + IF (ID.EQ.1) GO TO 140 + AIR = CSQR*S1R - CSQI*S1I + AII = CSQR*S1I + CSQI*S1R + RETURN + 140 CONTINUE + AIR = -(ZR*S1R-ZI*S1I) + AII = -(ZR*S1I+ZI*S1R) + RETURN + 150 CONTINUE + S1R = S1R*SFAC + S1I = S1I*SFAC + IF (ID.EQ.1) GO TO 160 + STR = S1R*CSQR - S1I*CSQI + S1I = S1R*CSQI + S1I*CSQR + S1R = STR + AIR = S1R/SFAC + AII = S1I/SFAC + RETURN + 160 CONTINUE + STR = -(S1R*ZR-S1I*ZI) + S1I = -(S1R*ZI+S1I*ZR) + S1R = STR + AIR = S1R/SFAC + AII = S1I/SFAC + RETURN + 170 CONTINUE + AA = 1.0D+3*D1MACH(1) + S1R = ZEROR + S1I = ZEROI + IF (ID.EQ.1) GO TO 190 + IF (AZ.LE.AA) GO TO 180 + S1R = C2*ZR + S1I = C2*ZI + 180 CONTINUE + AIR = C1 - S1R + AII = -S1I + RETURN + 190 CONTINUE + AIR = -C2 + AII = 0.0D0 + AA = DSQRT(AA) + IF (AZ.LE.AA) GO TO 200 + S1R = 0.5D0*(ZR*ZR-ZI*ZI) + S1I = ZR*ZI + 200 CONTINUE + AIR = AIR + C1*S1R + AII = AII + C1*S1I + RETURN + 210 CONTINUE + NZ = 1 + AIR = ZEROR + AII = ZEROI + RETURN + 270 CONTINUE + NZ = 0 + IERR=2 + RETURN + 280 CONTINUE + IF(NN.EQ.(-1)) GO TO 270 + NZ=0 + IERR=5 + RETURN + 260 CONTINUE + IERR=4 + NZ=0 + RETURN +END + +SUBROUTINE ZACAI(ZR, ZI, FNU, KODE, MR, N, YR, YI, NZ, RL, TOL, ELIM, ALIM) +USE UTILIT +USE COMPLEX +!***BEGIN PROLOGUE ZACAI +!***REFER TO ZAIRY +! +! ZACAI APPLIES THE ANALYTIC CONTINUATION FORMULA +! +! K(FNU,ZN*EXP(MP))=K(FNU,ZN)*EXP(-MP*FNU) - MP*I(FNU,ZN) +! MP=PI*MR*CMPLX(0.0,1.0) +! +! TO CONTINUE THE K FUNCTION FROM THE RIGHT HALF TO THE LEFT +! HALF Z PLANE FOR USE WITH ZAIRY WHERE FNU=1/3 OR 2/3 AND N=1. +! ZACAI IS THE SAME AS ZACON WITH THE PARTS FOR LARGER ORDERS AND +! RECURRENCE REMOVED. A RECURSIVE CALL TO ZACON CAN RESULT IF ZACON +! IS CALLED FROM ZAIRY. +! +!***ROUTINES CALLED ZASYI,ZBKNU,ZMLRI,ZSERI,ZS1S2,D1MACH,ZABS +!***END PROLOGUE ZACAI +! COMPLEX CSGN,CSPN,C1,C2,Y,Z,ZN,CY + DOUBLE PRECISION ALIM, ARG, ASCLE, AZ, CSGNR, CSGNI, CSPNR, & + CSPNI, C1R, C1I, C2R, C2I, CYR, CYI, DFNU, ELIM, FMR, FNU, PI, & + RL, SGN, TOL, YY, YR, YI, ZR, ZI, ZNR, ZNI + INTEGER INU, IUF, KODE, MR, N, NN, NW, NZ + DIMENSION YR(1), YI(1), CYR(2), CYI(2) + DATA PI / 3.14159265358979324D0 / + NZ = 0 + ZNR = -ZR + ZNI = -ZI + AZ = ZABS(ZR,ZI) + NN = N + DFNU = FNU + DBLE(FLOAT(N-1)) + IF (AZ.LE.2.0D0) GO TO 10 + IF (AZ*AZ*0.25D0.GT.DFNU+1.0D0) GO TO 20 + 10 CONTINUE +!----------------------------------------------------------------------- +! POWER SERIES FOR THE I FUNCTION +!----------------------------------------------------------------------- + CALL ZSERI(ZNR, ZNI, FNU, KODE, NN, YR, YI, NW, TOL, ELIM, ALIM) + GO TO 40 + 20 CONTINUE + IF (AZ.LT.RL) GO TO 30 +!----------------------------------------------------------------------- +! ASYMPTOTIC EXPANSION FOR LARGE Z FOR THE I FUNCTION +!----------------------------------------------------------------------- + CALL ZASYI(ZNR, ZNI, FNU, KODE, NN, YR, YI, NW, RL, TOL, ELIM, ALIM) + IF (NW.LT.0) GO TO 80 + GO TO 40 + 30 CONTINUE +!----------------------------------------------------------------------- +! MILLER ALGORITHM NORMALIZED BY THE SERIES FOR THE I FUNCTION +!----------------------------------------------------------------------- + CALL ZMLRI(ZNR, ZNI, FNU, KODE, NN, YR, YI, NW, TOL) + IF(NW.LT.0) GO TO 80 + 40 CONTINUE +!----------------------------------------------------------------------- +! ANALYTIC CONTINUATION TO THE LEFT HALF PLANE FOR THE K FUNCTION +!----------------------------------------------------------------------- + CALL ZBKNU(ZNR, ZNI, FNU, KODE, 1, CYR, CYI, NW, TOL, ELIM, ALIM) + IF (NW.NE.0) GO TO 80 + FMR = DBLE(FLOAT(MR)) + SGN = -DSIGN(PI,FMR) + CSGNR = 0.0D0 + CSGNI = SGN + IF (KODE.EQ.1) GO TO 50 + YY = -ZNI + CSGNR = -CSGNI*DSIN(YY) + CSGNI = CSGNI*DCOS(YY) + 50 CONTINUE +!----------------------------------------------------------------------- +! CALCULATE CSPN=EXP(FNU*PI*I) TO MINIMIZE LOSSES OF SIGNIFICANCE +! WHEN FNU IS LARGE +!----------------------------------------------------------------------- + INU = INT(SNGL(FNU)) + ARG = (FNU-DBLE(FLOAT(INU)))*SGN + CSPNR = DCOS(ARG) + CSPNI = DSIN(ARG) + IF (MOD(INU,2).EQ.0) GO TO 60 + CSPNR = -CSPNR + CSPNI = -CSPNI + 60 CONTINUE + C1R = CYR(1) + C1I = CYI(1) + C2R = YR(1) + C2I = YI(1) + IF (KODE.EQ.1) GO TO 70 + IUF = 0 + ASCLE = 1.0D+3*D1MACH(1)/TOL + CALL ZS1S2(ZNR, ZNI, C1R, C1I, C2R, C2I, NW, ASCLE, ALIM, IUF) + NZ = NZ + NW + 70 CONTINUE + YR(1) = CSPNR*C1R - CSPNI*C1I + CSGNR*C2R - CSGNI*C2I + YI(1) = CSPNR*C1I + CSPNI*C1R + CSGNR*C2I + CSGNI*C2R + RETURN + 80 CONTINUE + NZ = -1 + IF(NW.EQ.(-2)) NZ=-2 + RETURN +END + +SUBROUTINE ZS1S2(ZRR, ZRI, S1R, S1I, S2R, S2I, NZ, ASCLE, ALIM, IUF) +USE COMPLEX +!***BEGIN PROLOGUE ZS1S2 +!***REFER TO ZBESK,ZAIRY +! +! ZS1S2 TESTS FOR A POSSIBLE UNDERFLOW RESULTING FROM THE +! ADDITION OF THE I AND K FUNCTIONS IN THE ANALYTIC CON- +! TINUATION FORMULA WHERE S1=K FUNCTION AND S2=I FUNCTION. +! ON KODE=1 THE I AND K FUNCTIONS ARE DIFFERENT ORDERS OF +! MAGNITUDE, BUT FOR KODE=2 THEY CAN BE OF THE SAME ORDER +! OF MAGNITUDE AND THE MAXIMUM MUST BE AT LEAST ONE +! PRECISION ABOVE THE UNDERFLOW LIMIT. +! +!***ROUTINES CALLED ZABS,ZEXP,ZLOG +!***END PROLOGUE ZS1S2 +! COMPLEX CZERO,C1,S1,S1D,S2,ZR + DOUBLE PRECISION AA, ALIM, ALN, ASCLE, AS1, AS2, C1I, C1R, S1DI, & + S1DR, S1I, S1R, S2I, S2R, ZEROI, ZEROR, ZRI, ZRR + INTEGER IUF, IDUM, NZ + DATA ZEROR,ZEROI / 0.0D0 , 0.0D0 / + NZ = 0 + AS1 = ZABS(S1R,S1I) + AS2 = ZABS(S2R,S2I) + IF (S1R.EQ.0.0D0 .AND. S1I.EQ.0.0D0) GO TO 10 + IF (AS1.EQ.0.0D0) GO TO 10 + ALN = -ZRR - ZRR + DLOG(AS1) + S1DR = S1R + S1DI = S1I + S1R = ZEROR + S1I = ZEROI + AS1 = ZEROR + IF (ALN.LT.(-ALIM)) GO TO 10 + CALL ZLOG(S1DR, S1DI, C1R, C1I, IDUM) + C1R = C1R - ZRR - ZRR + C1I = C1I - ZRI - ZRI + CALL ZEXP(C1R, C1I, S1R, S1I) + AS1 = ZABS(S1R,S1I) + IUF = IUF + 1 + 10 CONTINUE + AA = DMAX1(AS1,AS2) + IF (AA.GT.ASCLE) RETURN + S1R = ZEROR + S1I = ZEROI + S2R = ZEROR + S2I = ZEROI + NZ = 1 + IUF = 0 + RETURN +END +end module besselj +!end of file tzbesj.f90 diff --git a/applications/PUfoam/MoDeNaModels/foamConductivity/src/src/bessely.f90 b/applications/PUfoam/MoDeNaModels/foamConductivity/src/src/bessely.f90 new file mode 100644 index 000000000..afe7a7e5b --- /dev/null +++ b/applications/PUfoam/MoDeNaModels/foamConductivity/src/src/bessely.f90 @@ -0,0 +1,5888 @@ +module bessely + implicit none + private + public ZBESY +contains +!***************************************************************** +!* EVALUATE A Y-BESSEL FUNCTION OF COMPLEX ARGUMENT (SECOND KIND)* +!* ------------------------------------------------------------- * +!* SAMPLE RUN: * +!* (Evaluate Y0 to Y4 for argument Z=(1.0,2.0) ). * +!* * +!* zr(0) = 1.367419 * +!* zi(0) = 1.521507 * +!* zr(1) = -1.089470 * +!* zi(1) = 1.314951 * +!* zr(2) = -0.751245 * +!* zi(2) = -0.123950 * +!* zr(3) = 0.290153 * +!* zi(3) = -0.212119 * +!* zr(4) = 0.590344 * +!* zi(4) = -0.826960 * +!* NZ = 0 * +!* Error code: 0 * +!* * +!* ------------------------------------------------------------- * +!* Ref.: From Numath Library By Tuan Dang Trong in Fortran 77 * +!* [BIBLI 18]. * +!* * +!* F90 Release 1.0 By J-P Moreau, Paris * +!* (www.jpmoreau.fr) * +!***************************************************************** +!PROGRAM TEST_ZBESY + +! real*8 zr, zi +! real*8 cyr(10), cyi(10), cwr(10), cwi(10) + +! n=5 +! zr=1.d0; zi=2.d0 + +! call ZBESY(zr,zi,0.d0,1,n,cyr,cyi,nz,cwr,cwi,ierr) + +! print *,' ' +! do i=1, n +! write(*,10) i-1, cyr(i) +! write(*,11) i-1, cyi(i) +! end do +! print *,' NZ=', NZ +! print *,' Error code:', ierr +! print *,' ' +! stop + +!10 format(' zr(',I1,') = ',F10.6) +!11 format(' zi(',I1,') = ',F10.6) + +!END + + +SUBROUTINE ZBESY(ZR, ZI, FNU, KODE, N, CYR, CYI, NZ, CWRKR, CWRKI, IERR) +USE UTILIT +!***BEGIN PROLOGUE ZBESY +!***DATE WRITTEN 830501 (YYMMDD) +!***REVISION DATE 830501 (YYMMDD) +!***CATEGORY NO. B5K +!***KEYWORDS Y-BESSEL FUNCTION,BESSEL FUNCTION OF COMPLEX ARGUMENT, +! BESSEL FUNCTION OF SECOND KIND +!***AUTHOR AMOS, DONALD E., SANDIA NATIONAL LABORATORIES +!***PURPOSE TO COMPUTE THE Y-BESSEL FUNCTION OF A COMPLEX ARGUMENT +!***DESCRIPTION +! +! ***A DOUBLE PRECISION ROUTINE*** +! +! ON KODE=1, CBESY COMPUTES AN N MEMBER SEQUENCE OF COMPLEX +! BESSEL FUNCTIONS CY(I)=Y(FNU+I-1,Z) FOR REAL, NONNEGATIVE +! ORDERS FNU+I-1, I=1,...,N AND COMPLEX Z IN THE CUT PLANE +! -PI.LT.ARG(Z).LE.PI. ON KODE=2, CBESY RETURNS THE SCALED +! FUNCTIONS +! +! CY(I)=EXP(-ABS(Y))*Y(FNU+I-1,Z) I = 1,...,N , Y=AIMAG(Z) +! +! WHICH REMOVE THE EXPONENTIAL GROWTH IN BOTH THE UPPER AND +! LOWER HALF PLANES FOR Z TO INFINITY. DEFINITIONS AND NOTATION +! ARE FOUND IN THE NBS HANDBOOK OF MATHEMATICAL FUNCTIONS +! (REF. 1). +! +! INPUT ZR,ZI,FNU ARE DOUBLE PRECISION +! ZR,ZI - Z=CMPLX(ZR,ZI), Z.NE.CMPLX(0.0D0,0.0D0), +! -PI.LT.ARG(Z).LE.PI +! FNU - ORDER OF INITIAL Y FUNCTION, FNU.GE.0.0D0 +! KODE - A PARAMETER TO INDICATE THE SCALING OPTION +! KODE= 1 RETURNS +! CY(I)=Y(FNU+I-1,Z), I=1,...,N +! = 2 RETURNS +! CY(I)=Y(FNU+I-1,Z)*EXP(-ABS(Y)), I=1,...,N +! WHERE Y=AIMAG(Z) +! N - NUMBER OF MEMBERS OF THE SEQUENCE, N.GE.1 +! CWRKR, - DOUBLE PRECISION WORK VECTORS OF DIMENSION AT +! CWRKI AT LEAST N +! +! OUTPUT CYR,CYI ARE DOUBLE PRECISION +! CYR,CYI- DOUBLE PRECISION VECTORS WHOSE FIRST N COMPONENTS +! CONTAIN REAL AND IMAGINARY PARTS FOR THE SEQUENCE +! CY(I)=Y(FNU+I-1,Z) OR +! CY(I)=Y(FNU+I-1,Z)*EXP(-ABS(Y)) I=1,...,N +! DEPENDING ON KODE. +! NZ - NZ=0 , A NORMAL RETURN +! NZ.GT.0 , NZ COMPONENTS OF CY SET TO ZERO DUE TO +! UNDERFLOW (GENERALLY ON KODE=2) +! IERR - ERROR FLAG +! IERR=0, NORMAL RETURN - COMPUTATION COMPLETED +! IERR=1, INPUT ERROR - NO COMPUTATION +! IERR=2, OVERFLOW - NO COMPUTATION, FNU IS +! TOO LARGE OR CABS(Z) IS TOO SMALL OR BOTH +! IERR=3, CABS(Z) OR FNU+N-1 LARGE - COMPUTATION DONE +! BUT LOSSES OF SIGNIFCANCE BY ARGUMENT +! REDUCTION PRODUCE LESS THAN HALF OF MACHINE +! ACCURACY +! IERR=4, CABS(Z) OR FNU+N-1 TOO LARGE - NO COMPUTA- +! TION BECAUSE OF COMPLETE LOSSES OF SIGNIFI- +! CANCE BY ARGUMENT REDUCTION +! IERR=5, ERROR - NO COMPUTATION, +! ALGORITHM TERMINATION CONDITION NOT MET +! +!***LONG DESCRIPTION +! +! THE COMPUTATION IS CARRIED OUT BY THE FORMULA +! +! Y(FNU,Z)=0.5*(H(1,FNU,Z)-H(2,FNU,Z))/I +! +! WHERE I**2 = -1 AND THE HANKEL BESSEL FUNCTIONS H(1,FNU,Z) +! AND H(2,FNU,Z) ARE CALCULATED IN CBESH. +! +! FOR NEGATIVE ORDERS,THE FORMULA +! +! Y(-FNU,Z) = Y(FNU,Z)*COS(PI*FNU) + J(FNU,Z)*SIN(PI*FNU) +! +! CAN BE USED. HOWEVER,FOR LARGE ORDERS CLOSE TO HALF ODD +! INTEGERS THE FUNCTION CHANGES RADICALLY. WHEN FNU IS A LARGE +! POSITIVE HALF ODD INTEGER,THE MAGNITUDE OF Y(-FNU,Z)=J(FNU,Z)* +! SIN(PI*FNU) IS A LARGE NEGATIVE POWER OF TEN. BUT WHEN FNU IS +! NOT A HALF ODD INTEGER, Y(FNU,Z) DOMINATES IN MAGNITUDE WITH A +! LARGE POSITIVE POWER OF TEN AND THE MOST THAT THE SECOND TERM +! CAN BE REDUCED IS BY UNIT ROUNDOFF FROM THE COEFFICIENT. THUS, +! WIDE CHANGES CAN OCCUR WITHIN UNIT ROUNDOFF OF A LARGE HALF +! ODD INTEGER. HERE, LARGE MEANS FNU.GT.CABS(Z). +! +! IN MOST COMPLEX VARIABLE COMPUTATION, ONE MUST EVALUATE ELE- +! MENTARY FUNCTIONS. WHEN THE MAGNITUDE OF Z OR FNU+N-1 IS +! LARGE, LOSSES OF SIGNIFICANCE BY ARGUMENT REDUCTION OCCUR. +! CONSEQUENTLY, IF EITHER ONE EXCEEDS U1=SQRT(0.5/UR), THEN +! LOSSES EXCEEDING HALF PRECISION ARE LIKELY AND AN ERROR FLAG +! IERR=3 IS TRIGGERED WHERE UR=DMAX1(D1MACH(4),1.0D-18) IS +! DOUBLE PRECISION UNIT ROUNDOFF LIMITED TO 18 DIGITS PRECISION. +! IF EITHER IS LARGER THAN U2=0.5/UR, THEN ALL SIGNIFICANCE IS +! LOST AND IERR=4. IN ORDER TO USE THE INT FUNCTION, ARGUMENTS +! MUST BE FURTHER RESTRICTED NOT TO EXCEED THE LARGEST MACHINE +! INTEGER, U3=I1MACH(9). THUS, THE MAGNITUDE OF Z AND FNU+N-1 IS +! RESTRICTED BY MIN(U2,U3). ON 32 BIT MACHINES, U1,U2, AND U3 +! ARE APPROXIMATELY 2.0E+3, 4.2E+6, 2.1E+9 IN SINGLE PRECISION +! ARITHMETIC AND 1.3E+8, 1.8E+16, 2.1E+9 IN DOUBLE PRECISION +! ARITHMETIC RESPECTIVELY. THIS MAKES U2 AND U3 LIMITING IN +! THEIR RESPECTIVE ARITHMETICS. THIS MEANS THAT ONE CAN EXPECT +! TO RETAIN, IN THE WORST CASES ON 32 BIT MACHINES, NO DIGITS +! IN SINGLE AND ONLY 7 DIGITS IN DOUBLE PRECISION ARITHMETIC. +! SIMILAR CONSIDERATIONS HOLD FOR OTHER MACHINES. +! +! THE APPROXIMATE RELATIVE ERROR IN THE MAGNITUDE OF A COMPLEX +! BESSEL FUNCTION CAN BE EXPRESSED BY P*10**S WHERE P=MAX(UNIT +! ROUNDOFF,1.0E-18) IS THE NOMINAL PRECISION AND 10**S REPRE- +! SENTS THE INCREASE IN ERROR DUE TO ARGUMENT REDUCTION IN THE +! ELEMENTARY FUNCTIONS. HERE, S=MAX(1,ABS(LOG10(CABS(Z))), +! ABS(LOG10(FNU))) APPROXIMATELY (I.E. S=MAX(1,ABS(EXPONENT OF +! CABS(Z),ABS(EXPONENT OF FNU)) ). HOWEVER, THE PHASE ANGLE MAY +! HAVE ONLY ABSOLUTE ACCURACY. THIS IS MOST LIKELY TO OCCUR WHEN +! ONE COMPONENT (IN ABSOLUTE VALUE) IS LARGER THAN THE OTHER BY +! SEVERAL ORDERS OF MAGNITUDE. IF ONE COMPONENT IS 10**K LARGER +! THAN THE OTHER, THEN ONE CAN EXPECT ONLY MAX(ABS(LOG10(P))-K, +! 0) SIGNIFICANT DIGITS; OR, STATED ANOTHER WAY, WHEN K EXCEEDS +! THE EXPONENT OF P, NO SIGNIFICANT DIGITS REMAIN IN THE SMALLER +! COMPONENT. HOWEVER, THE PHASE ANGLE RETAINS ABSOLUTE ACCURACY +! BECAUSE, IN COMPLEX ARITHMETIC WITH PRECISION P, THE SMALLER +! COMPONENT WILL NOT (AS A RULE) DECREASE BELOW P TIMES THE +! MAGNITUDE OF THE LARGER COMPONENT. IN THESE EXTREME CASES, +! THE PRINCIPAL PHASE ANGLE IS ON THE ORDER OF +P, -P, PI/2-P, +! OR -PI/2+P. +! +!***REFERENCES HANDBOOK OF MATHEMATICAL FUNCTIONS BY M. ABRAMOWITZ +! AND I. A. STEGUN, NBS AMS SERIES 55, U.S. DEPT. OF +! COMMERCE, 1955. +! +! COMPUTATION OF BESSEL FUNCTIONS OF COMPLEX ARGUMENT +! BY D. E. AMOS, SAND83-0083, MAY, 1983. +! +! COMPUTATION OF BESSEL FUNCTIONS OF COMPLEX ARGUMENT +! AND LARGE ORDER BY D. E. AMOS, SAND83-0643, MAY, 1983 +! +! A SUBROUTINE PACKAGE FOR BESSEL FUNCTIONS OF A COMPLEX +! ARGUMENT AND NONNEGATIVE ORDER BY D. E. AMOS, SAND85- +! 1018, MAY, 1985 +! +! A PORTABLE PACKAGE FOR BESSEL FUNCTIONS OF A COMPLEX +! ARGUMENT AND NONNEGATIVE ORDER BY D. E. AMOS, TRANS. +! MATH. SOFTWARE, 1986 +! +!***ROUTINES CALLED ZBESH,I1MACH,D1MACH +!***END PROLOGUE ZBESY +! +! COMPLEX CWRK,CY,C1,C2,EX,HCI,Z + DOUBLE PRECISION CWRKI, CWRKR, CYI, CYR, C1I, C1R, C2I, C2R, & + ELIM, EXI, EXR, EY, FNU, HCII, STI, STR, TAY, ZI, ZR, DEXP + INTEGER I, IERR, K, KODE, K1, K2, N, NZ, NZ1, NZ2 + DIMENSION CYR(1), CYI(1), CWRKR(1), CWRKI(1) +!***FIRST EXECUTABLE STATEMENT ZBESY + IERR = 0 + NZ=0 + IF (ZR.EQ.0.0D0 .AND. ZI.EQ.0.0D0) IERR=1 + IF (FNU.LT.0.0D0) IERR=1 + IF (KODE.LT.1 .OR. KODE.GT.2) IERR=1 + IF (N.LT.1) IERR=1 + IF (IERR.NE.0) RETURN + HCII = 0.5D0 + CALL ZBESH(ZR, ZI, FNU, KODE, 1, N, CYR, CYI, NZ1, IERR) + IF (IERR.NE.0.AND.IERR.NE.3) GO TO 170 + CALL ZBESH(ZR, ZI, FNU, KODE, 2, N, CWRKR, CWRKI, NZ2, IERR) + IF (IERR.NE.0.AND.IERR.NE.3) GO TO 170 + NZ = MIN0(NZ1,NZ2) + IF (KODE.EQ.2) GO TO 60 + DO 50 I=1,N + STR = CWRKR(I) - CYR(I) + STI = CWRKI(I) - CYI(I) + CYR(I) = -STI*HCII + CYI(I) = STR*HCII + 50 CONTINUE + RETURN + 60 CONTINUE + K1 = I1MACH(15) + K2 = I1MACH(16) + K = MIN0(IABS(K1),IABS(K2)) +!----------------------------------------------------------------------- +! ELIM IS THE APPROXIMATE EXPONENTIAL UNDER- AND OVERFLOW LIMIT +!----------------------------------------------------------------------- + ELIM = 2.303D0*(DBLE(FLOAT(K))*D1MACH(5)-3.0D0) + EXR = DCOS(ZR) + EXI = DSIN(ZR) + EY = 0.0D0 + TAY = DABS(ZI+ZI) + IF (TAY.LT.ELIM) EY = DEXP(-TAY) + IF (ZI.LT.0.0D0) GO TO 90 + C1R = EXR*EY + C1I = EXI*EY + C2R = EXR + C2I = -EXI + 70 CONTINUE + NZ = 0 + DO 80 I=1,N + STR = C1R*CYR(I) - C1I*CYI(I) + STI = C1R*CYI(I) + C1I*CYR(I) + STR = -STR + C2R*CWRKR(I) - C2I*CWRKI(I) + STI = -STI + C2R*CWRKI(I) + C2I*CWRKR(I) + CYR(I) = -STI*HCII + CYI(I) = STR*HCII + IF (STR.EQ.0.0D0 .AND. STI.EQ.0.0D0 .AND. EY.EQ.0.0D0) NZ = NZ + 1 + 80 CONTINUE + RETURN + 90 CONTINUE + C1R = EXR + C1I = EXI + C2R = EXR*EY + C2I = -EXI*EY + GO TO 70 + 170 CONTINUE + NZ = 0 + RETURN +END + + +SUBROUTINE ZBESH(ZR, ZI, FNU, KODE, M, N, CYR, CYI, NZ, IERR) +USE UTILIT +USE COMPLEX +!***BEGIN PROLOGUE ZBESH +!***DATE WRITTEN 830501 (YYMMDD) +!***REVISION DATE 830501 (YYMMDD) +!***CATEGORY NO. B5K +!***KEYWORDS H-BESSEL FUNCTIONS,BESSEL FUNCTIONS OF COMPLEX ARGUMENT, +! BESSEL FUNCTIONS OF THIRD KIND,HANKEL FUNCTIONS +!***AUTHOR AMOS, DONALD E., SANDIA NATIONAL LABORATORIES +!***PURPOSE TO COMPUTE THE H-BESSEL FUNCTIONS OF A COMPLEX ARGUMENT +!***DESCRIPTION +! +! ***A DOUBLE PRECISION ROUTINE*** +! ON KODE=1, ZBESH COMPUTES AN N MEMBER SEQUENCE OF COMPLEX +! HANKEL (BESSEL) FUNCTIONS CY(J)=H(M,FNU+J-1,Z) FOR KINDS M=1 +! OR 2, REAL, NONNEGATIVE ORDERS FNU+J-1, J=1,...,N, AND COMPLEX +! Z.NE.CMPLX(0.0,0.0) IN THE CUT PLANE -PI.LT.ARG(Z).LE.PI. +! ON KODE=2, ZBESH RETURNS THE SCALED HANKEL FUNCTIONS +! +! CY(I)=EXP(-MM*Z*I)*H(M,FNU+J-1,Z) MM=3-2*M, I**2=-1. +! +! WHICH REMOVES THE EXPONENTIAL BEHAVIOR IN BOTH THE UPPER AND +! LOWER HALF PLANES. DEFINITIONS AND NOTATION ARE FOUND IN THE +! NBS HANDBOOK OF MATHEMATICAL FUNCTIONS (REF. 1). +! +! INPUT ZR,ZI,FNU ARE DOUBLE PRECISION +! ZR,ZI - Z=CMPLX(ZR,ZI), Z.NE.CMPLX(0.0D0,0.0D0), +! -PT.LT.ARG(Z).LE.PI +! FNU - ORDER OF INITIAL H FUNCTION, FNU.GE.0.0D0 +! KODE - A PARAMETER TO INDICATE THE SCALING OPTION +! KODE= 1 RETURNS +! CY(J)=H(M,FNU+J-1,Z), J=1,...,N +! = 2 RETURNS +! CY(J)=H(M,FNU+J-1,Z)*EXP(-I*Z*(3-2M)) +! J=1,...,N , I**2=-1 +! M - KIND OF HANKEL FUNCTION, M=1 OR 2 +! N - NUMBER OF MEMBERS IN THE SEQUENCE, N.GE.1 +! +! OUTPUT CYR,CYI ARE DOUBLE PRECISION +! CYR,CYI- DOUBLE PRECISION VECTORS WHOSE FIRST N COMPONENTS +! CONTAIN REAL AND IMAGINARY PARTS FOR THE SEQUENCE +! CY(J)=H(M,FNU+J-1,Z) OR +! CY(J)=H(M,FNU+J-1,Z)*EXP(-I*Z*(3-2M)) J=1,...,N +! DEPENDING ON KODE, I**2=-1. +! NZ - NUMBER OF COMPONENTS SET TO ZERO DUE TO UNDERFLOW, +! NZ= 0 , NORMAL RETURN +! NZ.GT.0 , FIRST NZ COMPONENTS OF CY SET TO ZERO DUE +! TO UNDERFLOW, CY(J)=CMPLX(0.0D0,0.0D0) +! J=1,...,NZ WHEN Y.GT.0.0 AND M=1 OR +! Y.LT.0.0 AND M=2. FOR THE COMPLMENTARY +! HALF PLANES, NZ STATES ONLY THE NUMBER +! OF UNDERFLOWS. +! IERR - ERROR FLAG +! IERR=0, NORMAL RETURN - COMPUTATION COMPLETED +! IERR=1, INPUT ERROR - NO COMPUTATION +! IERR=2, OVERFLOW - NO COMPUTATION, FNU TOO +! LARGE OR CABS(Z) TOO SMALL OR BOTH +! IERR=3, CABS(Z) OR FNU+N-1 LARGE - COMPUTATION DONE +! BUT LOSSES OF SIGNIFCANCE BY ARGUMENT +! REDUCTION PRODUCE LESS THAN HALF OF MACHINE +! ACCURACY +! IERR=4, CABS(Z) OR FNU+N-1 TOO LARGE - NO COMPUTA- +! TION BECAUSE OF COMPLETE LOSSES OF SIGNIFI- +! CANCE BY ARGUMENT REDUCTION +! IERR=5, ERROR - NO COMPUTATION, +! ALGORITHM TERMINATION CONDITION NOT MET +! +!***LONG DESCRIPTION +! +! THE COMPUTATION IS CARRIED OUT BY THE RELATION +! +! H(M,FNU,Z)=(1/MP)*EXP(-MP*FNU)*K(FNU,Z*EXP(-MP)) +! MP=MM*HPI*I, MM=3-2*M, HPI=PI/2, I**2=-1 +! +! FOR M=1 OR 2 WHERE THE K BESSEL FUNCTION IS COMPUTED FOR THE +! RIGHT HALF PLANE RE(Z).GE.0.0. THE K FUNCTION IS CONTINUED +! TO THE LEFT HALF PLANE BY THE RELATION +! +! K(FNU,Z*EXP(MP)) = EXP(-MP*FNU)*K(FNU,Z)-MP*I(FNU,Z) +! MP=MR*PI*I, MR=+1 OR -1, RE(Z).GT.0, I**2=-1 +! +! WHERE I(FNU,Z) IS THE I BESSEL FUNCTION. +! +! EXPONENTIAL DECAY OF H(M,FNU,Z) OCCURS IN THE UPPER HALF Z +! PLANE FOR M=1 AND THE LOWER HALF Z PLANE FOR M=2. EXPONENTIAL +! GROWTH OCCURS IN THE COMPLEMENTARY HALF PLANES. SCALING +! BY EXP(-MM*Z*I) REMOVES THE EXPONENTIAL BEHAVIOR IN THE +! WHOLE Z PLANE FOR Z TO INFINITY. +! +! FOR NEGATIVE ORDERS,THE FORMULAE +! +! H(1,-FNU,Z) = H(1,FNU,Z)*CEXP( PI*FNU*I) +! H(2,-FNU,Z) = H(2,FNU,Z)*CEXP(-PI*FNU*I) +! I**2=-1 +! +! CAN BE USED. +! +! IN MOST COMPLEX VARIABLE COMPUTATION, ONE MUST EVALUATE ELE- +! MENTARY FUNCTIONS. WHEN THE MAGNITUDE OF Z OR FNU+N-1 IS +! LARGE, LOSSES OF SIGNIFICANCE BY ARGUMENT REDUCTION OCCUR. +! CONSEQUENTLY, IF EITHER ONE EXCEEDS U1=SQRT(0.5/UR), THEN +! LOSSES EXCEEDING HALF PRECISION ARE LIKELY AND AN ERROR FLAG +! IERR=3 IS TRIGGERED WHERE UR=DMAX1(D1MACH(4),1.0D-18) IS +! DOUBLE PRECISION UNIT ROUNDOFF LIMITED TO 18 DIGITS PRECISION. +! IF EITHER IS LARGER THAN U2=0.5/UR, THEN ALL SIGNIFICANCE IS +! LOST AND IERR=4. IN ORDER TO USE THE INT FUNCTION, ARGUMENTS +! MUST BE FURTHER RESTRICTED NOT TO EXCEED THE LARGEST MACHINE +! INTEGER, U3=I1MACH(9). THUS, THE MAGNITUDE OF Z AND FNU+N-1 IS +! RESTRICTED BY MIN(U2,U3). ON 32 BIT MACHINES, U1,U2, AND U3 +! ARE APPROXIMATELY 2.0E+3, 4.2E+6, 2.1E+9 IN SINGLE PRECISION +! ARITHMETI! AND 1.3E+8, 1.8E+16, 2.1E+9 IN DOUBLE PRECISION +! ARITHMETI! RESPECTIVELY. THIS MAKES U2 AND U3 LIMITING IN +! THEIR RESPECTIVE ARITHMETICS. THIS MEANS THAT ONE CAN EXPECT +! TO RETAIN, IN THE WORST CASES ON 32 BIT MACHINES, NO DIGITS +! IN SINGLE AND ONLY 7 DIGITS IN DOUBLE PRECISION ARITHMETIC. +! SIMILAR CONSIDERATIONS HOLD FOR OTHER MACHINES. +! +! THE APPROXIMATE RELATIVE ERROR IN THE MAGNITUDE OF A COMPLEX +! BESSEL FUNCTION CAN BE EXPRESSED BY P*10**S WHERE P=MAX(UNIT +! ROUNDOFF,1.0D-18) IS THE NOMINAL PRECISION AND 10**S REPRE- +! SENTS THE INCREASE IN ERROR DUE TO ARGUMENT REDUCTION IN THE +! ELEMENTARY FUNCTIONS. HERE, S=MAX(1,ABS(LOG10(CABS(Z))), +! ABS(LOG10(FNU))) APPROXIMATELY (I.E. S=MAX(1,ABS(EXPONENT OF +! CABS(Z),ABS(EXPONENT OF FNU)) ). HOWEVER, THE PHASE ANGLE MAY +! HAVE ONLY ABSOLUTE ACCURACY. THIS IS MOST LIKELY TO OCCUR WHEN +! ONE COMPONENT (IN ABSOLUTE VALUE) IS LARGER THAN THE OTHER BY +! SEVERAL ORDERS OF MAGNITUDE. IF ONE COMPONENT IS 10**K LARGER +! THAN THE OTHER, THEN ONE CAN EXPECT ONLY MAX(ABS(LOG10(P))-K, +! 0) SIGNIFICANT DIGITS; OR, STATED ANOTHER WAY, WHEN K EXCEEDS +! THE EXPONENT OF P, NO SIGNIFICANT DIGITS REMAIN IN THE SMALLER +! COMPONENT. HOWEVER, THE PHASE ANGLE RETAINS ABSOLUTE ACCURACY +! BECAUSE, IN COMPLEX ARITHMETI! WITH PRECISION P, THE SMALLER +! COMPONENT WILL NOT (AS A RULE) DECREASE BELOW P TIMES THE +! MAGNITUDE OF THE LARGER COMPONENT. IN THESE EXTREME CASES, +! THE PRINCIPAL PHASE ANGLE IS ON THE ORDER OF +P, -P, PI/2-P, +! OR -PI/2+P. +! +!***REFERENCES HANDBOOK OF MATHEMATICAL FUNCTIONS BY M. ABRAMOWITZ +! AND I. A. STEGUN, NBS AMS SERIES 55, U.S. DEPT. OF +! COMMERCE, 1955. +! +! COMPUTATION OF BESSEL FUNCTIONS OF COMPLEX ARGUMENT +! BY D. E. AMOS, SAND83-0083, MAY, 1983. +! +! COMPUTATION OF BESSEL FUNCTIONS OF COMPLEX ARGUMENT +! AND LARGE ORDER BY D. E. AMOS, SAND83-0643, MAY, 1983 +! +! A SUBROUTINE PACKAGE FOR BESSEL FUNCTIONS OF A COMPLEX +! ARGUMENT AND NONNEGATIVE ORDER BY D. E. AMOS, SAND85- +! 1018, MAY, 1985 +! +! A PORTABLE PACKAGE FOR BESSEL FUNCTIONS OF A COMPLEX +! ARGUMENT AND NONNEGATIVE ORDER BY D. E. AMOS, TRANS. +! MATH. SOFTWARE, 1986 +! +!***ROUTINES CALLED ZACON,ZBKNU,ZBUNK,ZUOIK,ZABS,I1MACH,D1MACH +!***END PROLOGUE ZBESH +! +! COMPLEX CY,Z,ZN,ZT + DOUBLE PRECISION AA, ALIM, ALN, ARG, AZ, CYI, CYR, DIG, ELIM, & + FMM, FN, FNU, FNUL, HPI, RHPI, RL, R1M5, SGN, STR, TOL, UFL, ZI, & + ZNI, ZNR, ZR, ZTI, BB + INTEGER I, IERR, INU, INUH, IR, K, KODE, K1, K2, M, & + MM, MR, N, NN, NUF, NW, NZ + DIMENSION CYR(N), CYI(N) + + DATA HPI /1.57079632679489662D0/ + +!***FIRST EXECUTABLE STATEMENT ZBESH + IERR = 0 + NZ=0 + IF (ZR.EQ.0.0D0 .AND. ZI.EQ.0.0D0) IERR=1 + IF (FNU.LT.0.0D0) IERR=1 + IF (M.LT.1 .OR. M.GT.2) IERR=1 + IF (KODE.LT.1 .OR. KODE.GT.2) IERR=1 + IF (N.LT.1) IERR=1 + IF (IERR.NE.0) RETURN + NN = N +!----------------------------------------------------------------------- +! SET PARAMETERS RELATED TO MACHINE CONSTANTS. +! TOL IS THE APPROXIMATE UNIT ROUNDOFF LIMITED TO 1.0E-18. +! ELIM IS THE APPROXIMATE EXPONENTIAL OVER- AND UNDERFLOW LIMIT. +! EXP(-ELIM).LT.EXP(-ALIM)=EXP(-ELIM)/TOL AND +! EXP(ELIM).GT.EXP(ALIM)=EXP(ELIM)*TOL ARE INTERVALS NEAR +! UNDERFLOW AND OVERFLOW LIMITS WHERE SCALED ARITHMETIC IS DONE. +! RL IS THE LOWER BOUNDARY OF THE ASYMPTOTIC EXPANSION FOR LARGE Z. +! DIG = NUMBER OF BASE 10 DIGITS IN TOL = 10**(-DIG). +! FNUL IS THE LOWER BOUNDARY OF THE ASYMPTOTIC SERIES FOR LARGE FNU +!----------------------------------------------------------------------- + TOL = DMAX1(D1MACH(4),1.0D-18) + K1 = I1MACH(15) + K2 = I1MACH(16) + R1M5 = D1MACH(5) + K = MIN0(IABS(K1),IABS(K2)) + ELIM = 2.303D0*(DBLE(FLOAT(K))*R1M5-3.0D0) + K1 = I1MACH(14) - 1 + AA = R1M5*DBLE(FLOAT(K1)) + DIG = DMIN1(AA,18.0D0) + AA = AA*2.303D0 + ALIM = ELIM + DMAX1(-AA,-41.45D0) + FNUL = 10.0D0 + 6.0D0*(DIG-3.0D0) + RL = 1.2D0*DIG + 3.0D0 + FN = FNU + DBLE(FLOAT(NN-1)) + MM = 3 - M - M + FMM = DBLE(FLOAT(MM)) + ZNR = FMM*ZI + ZNI = -FMM*ZR +!----------------------------------------------------------------------- +! TEST FOR PROPER RANGE +!----------------------------------------------------------------------- + AZ = ZABS(ZR,ZI) + AA = 0.5D0/TOL + BB=DBLE(FLOAT(I1MACH(9)))*0.5D0 + AA = DMIN1(AA,BB) + IF (AZ.GT.AA) GO TO 260 + IF (FN.GT.AA) GO TO 260 + AA = DSQRT(AA) + IF (AZ.GT.AA) IERR=3 + IF (FN.GT.AA) IERR=3 +!----------------------------------------------------------------------- +! OVERFLOW TEST ON THE LAST MEMBER OF THE SEQUENCE +!----------------------------------------------------------------------- + UFL = DEXP(-ELIM) + IF (AZ.LT.UFL) GO TO 230 + IF (FNU.GT.FNUL) GO TO 90 + IF (FN.LE.1.0D0) GO TO 70 + IF (FN.GT.2.0D0) GO TO 60 + IF (AZ.GT.TOL) GO TO 70 + ARG = 0.5D0*AZ + ALN = -FN*DLOG(ARG) + IF (ALN.GT.ELIM) GO TO 230 + GO TO 70 + 60 CONTINUE + CALL ZUOIK(ZNR, ZNI, FNU, KODE, 2, NN, CYR, CYI, NUF, TOL, ELIM, ALIM) + IF (NUF.LT.0) GO TO 230 + NZ = NZ + NUF + NN = NN - NUF +!----------------------------------------------------------------------- +! HERE NN=N OR NN=0 SINCE NUF=0,NN, OR -1 ON RETURN FROM CUOIK +! IF NUF=NN, THEN CY(I)=CZERO FOR ALL I +!----------------------------------------------------------------------- + IF (NN.EQ.0) GO TO 140 + 70 CONTINUE + IF ((ZNR.LT.0.0D0) .OR. (ZNR.EQ.0.0D0 .AND. ZNI.LT.0.0D0 .AND. & + M.EQ.2)) GO TO 80 +!----------------------------------------------------------------------- +! RIGHT HALF PLANE COMPUTATION, XN.GE.0. .AND. (XN.NE.0. .OR. +! YN.GE.0. .OR. M=1) +!----------------------------------------------------------------------- + CALL ZBKNU(ZNR, ZNI, FNU, KODE, NN, CYR, CYI, NZ, TOL, ELIM, ALIM) + GO TO 110 +!----------------------------------------------------------------------- +! LEFT HALF PLANE COMPUTATION +!----------------------------------------------------------------------- + 80 CONTINUE + MR = -MM + CALL ZACON(ZNR, ZNI, FNU, KODE, MR, NN, CYR, CYI, NW, RL, FNUL, & + TOL, ELIM, ALIM) + IF (NW.LT.0) GO TO 240 + NZ=NW + GO TO 110 + 90 CONTINUE +!----------------------------------------------------------------------- +! UNIFORM ASYMPTOTIC EXPANSIONS FOR FNU.GT.FNUL +!----------------------------------------------------------------------- + MR = 0 + IF ((ZNR.GE.0.0D0) .AND. (ZNR.NE.0.0D0 .OR. ZNI.GE.0.0D0 .OR. & + M.NE.2)) GO TO 100 + MR = -MM + IF (ZNR.NE.0.0D0 .OR. ZNI.GE.0.0D0) GO TO 100 + ZNR = -ZNR + ZNI = -ZNI + 100 CONTINUE + CALL ZBUNK(ZNR, ZNI, FNU, KODE, MR, NN, CYR, CYI, NW, TOL, ELIM, ALIM) + IF (NW.LT.0) GO TO 240 + NZ = NZ + NW + 110 CONTINUE +!----------------------------------------------------------------------- +! H(M,FNU,Z) = -FMM*(I/HPI)*(ZT**FNU)*K(FNU,-Z*ZT) +! +! ZT=EXP(-FMM*HPI*I) = CMPLX(0.0,-FMM), FMM=3-2*M, M=1,2 +!----------------------------------------------------------------------- + SGN = DSIGN(HPI,-FMM) +!----------------------------------------------------------------------- +! CALCULATE EXP(FNU*HPI*I) TO MINIMIZE LOSSES OF SIGNIFICANCE +! WHEN FNU IS LARGE +!----------------------------------------------------------------------- + INU = INT(SNGL(FNU)) + INUH = INU/2 + IR = INU - 2*INUH + ARG = (FNU-DBLE(FLOAT(INU-IR)))*SGN + RHPI = 1.0D0/SGN + ZNI = RHPI*DCOS(ARG) + ZNR = -RHPI*DSIN(ARG) + IF (MOD(INUH,2).EQ.0) GO TO 120 + ZNR = -ZNR + ZNI = -ZNI + 120 CONTINUE + ZTI = -FMM + DO 130 I=1,NN + STR = CYR(I)*ZNR - CYI(I)*ZNI + CYI(I) = CYR(I)*ZNI + CYI(I)*ZNR + CYR(I) = STR + STR = -ZNI*ZTI + ZNI = ZNR*ZTI + ZNR = STR + 130 CONTINUE + RETURN + 140 CONTINUE + IF (ZNR.LT.0.0D0) GO TO 230 + RETURN + 230 CONTINUE + NZ=0 + IERR=2 + RETURN + 240 CONTINUE + IF(NW.EQ.(-1)) GO TO 230 + NZ=0 + IERR=5 + RETURN + 260 CONTINUE + NZ=0 + IERR=4 + RETURN +END + +SUBROUTINE ZUOIK(ZR, ZI, FNU, KODE, IKFLG, N, YR, YI, NUF, TOL, ELIM, ALIM) +USE UTILIT +USE COMPLEX +!***BEGIN PROLOGUE ZUOIK +!***REFER TO ZBESI,ZBESK,ZBESH +! +! ZUOIK COMPUTES THE LEADING TERMS OF THE UNIFORM ASYMPTOTIC +! EXPANSIONS FOR THE I AND K FUNCTIONS AND COMPARES THEM +! (IN LOGARITHMI! FORM) TO ALIM AND ELIM FOR OVER AND UNDERFLOW +! WHERE ALIM.LT.ELIM. IF THE MAGNITUDE, BASED ON THE LEADING +! EXPONENTIAL, IS LESS THAN ALIM OR GREATER THAN -ALIM, THEN +! THE RESULT IS ON SCALE. IF NOT, THEN A REFINED TEST USING OTHER +! MULTIPLIERS (IN LOGARITHMI! FORM) IS MADE BASED ON ELIM. HERE +! EXP(-ELIM)=SMALLEST MACHINE NUMBER*1.0E+3 AND EXP(-ALIM)= +! EXP(-ELIM)/TOL +! +! IKFLG=1 MEANS THE I SEQUENCE IS TESTED +! =2 MEANS THE K SEQUENCE IS TESTED +! NUF = 0 MEANS THE LAST MEMBER OF THE SEQUENCE IS ON SCALE +! =-1 MEANS AN OVERFLOW WOULD OCCUR +! IKFLG=1 AND NUF.GT.0 MEANS THE LAST NUF Y VALUES WERE SET TO ZERO +! THE FIRST N-NUF VALUES MUST BE SET BY ANOTHER ROUTINE +! IKFLG=2 AND NUF.EQ.N MEANS ALL Y VALUES WERE SET TO ZERO +! IKFLG=2 AND 0.LT.NUF.LT.N NOT CONSIDERED. Y MUST BE SET BY +! ANOTHER ROUTINE +! +!***ROUTINES CALLED ZUCHK,ZUNHJ,ZUNIK,D1MACH,ZABS,ZLOG +!***END PROLOGUE ZUOIK +! COMPLEX ARG,ASUM,BSUM,CWRK,CZ,CZERO,PHI,SUM,Y,Z,ZB,ZETA1,ZETA2,ZN, +! *ZR + DOUBLE PRECISION AARG, AIC, ALIM, APHI, ARGI, ARGR, ASUMI, ASUMR, & + ASCLE, AX, AY, BSUMI, BSUMR, CWRKI, CWRKR, CZI, CZR, ELIM, FNN, & + FNU, GNN, GNU, PHII, PHIR, RCZ, STR, STI, SUMI, SUMR, TOL, YI, & + YR, ZBI, ZBR, ZEROI, ZEROR, ZETA1I, ZETA1R, ZETA2I, ZETA2R, ZI, & + ZNI, ZNR, ZR, ZRI, ZRR + INTEGER I, IDUM, IFORM, IKFLG, INIT, KODE, N, NN, NUF, NW + DIMENSION YR(1), YI(1), CWRKR(16), CWRKI(16) + DATA ZEROR,ZEROI / 0.0D0, 0.0D0 / + DATA AIC / 1.265512123484645396D+00 / + NUF = 0 + NN = N + ZRR = ZR + ZRI = ZI + IF (ZR.GE.0.0D0) GO TO 10 + ZRR = -ZR + ZRI = -ZI + 10 CONTINUE + ZBR = ZRR + ZBI = ZRI + AX = DABS(ZR)*1.7321D0 + AY = DABS(ZI) + IFORM = 1 + IF (AY.GT.AX) IFORM = 2 + GNU = DMAX1(FNU,1.0D0) + IF (IKFLG.EQ.1) GO TO 20 + FNN = DBLE(FLOAT(NN)) + GNN = FNU + FNN - 1.0D0 + GNU = DMAX1(GNN,FNN) + 20 CONTINUE +!----------------------------------------------------------------------- +! ONLY THE MAGNITUDE OF ARG AND PHI ARE NEEDED ALONG WITH THE +! REAL PARTS OF ZETA1, ZETA2 AND ZB. NO ATTEMPT IS MADE TO GET +! THE SIGN OF THE IMAGINARY PART CORRECT. +!----------------------------------------------------------------------- + IF (IFORM.EQ.2) GO TO 30 + INIT = 0 + CALL ZUNIK(ZRR, ZRI, GNU, IKFLG, 1, TOL, INIT, PHIR, PHII, & + ZETA1R, ZETA1I, ZETA2R, ZETA2I, SUMR, SUMI, CWRKR, CWRKI) + CZR = -ZETA1R + ZETA2R + CZI = -ZETA1I + ZETA2I + GO TO 50 + 30 CONTINUE + ZNR = ZRI + ZNI = -ZRR + IF (ZI.GT.0.0D0) GO TO 40 + ZNR = -ZNR + 40 CONTINUE + CALL ZUNHJ(ZNR, ZNI, GNU, 1, TOL, PHIR, PHII, ARGR, ARGI, ZETA1R, & + ZETA1I, ZETA2R, ZETA2I, ASUMR, ASUMI, BSUMR, BSUMI) + CZR = -ZETA1R + ZETA2R + CZI = -ZETA1I + ZETA2I + AARG = ZABS(ARGR,ARGI) + 50 CONTINUE + IF (KODE.EQ.1) GO TO 60 + CZR = CZR - ZBR + CZI = CZI - ZBI + 60 CONTINUE + IF (IKFLG.EQ.1) GO TO 70 + CZR = -CZR + CZI = -CZI + 70 CONTINUE + APHI = ZABS(PHIR,PHII) + RCZ = CZR +!----------------------------------------------------------------------- +! OVERFLOW TEST +!----------------------------------------------------------------------- + IF (RCZ.GT.ELIM) GO TO 210 + IF (RCZ.LT.ALIM) GO TO 80 + RCZ = RCZ + DLOG(APHI) + IF (IFORM.EQ.2) RCZ = RCZ - 0.25D0*DLOG(AARG) - AIC + IF (RCZ.GT.ELIM) GO TO 210 + GO TO 130 + 80 CONTINUE +!----------------------------------------------------------------------- +! UNDERFLOW TEST +!----------------------------------------------------------------------- + IF (RCZ.LT.(-ELIM)) GO TO 90 + IF (RCZ.GT.(-ALIM)) GO TO 130 + RCZ = RCZ + DLOG(APHI) + IF (IFORM.EQ.2) RCZ = RCZ - 0.25D0*DLOG(AARG) - AIC + IF (RCZ.GT.(-ELIM)) GO TO 110 + 90 CONTINUE + DO 100 I=1,NN + YR(I) = ZEROR + YI(I) = ZEROI + 100 CONTINUE + NUF = NN + RETURN + 110 CONTINUE + ASCLE = 1.0D+3*D1MACH(1)/TOL + CALL ZLOG(PHIR, PHII, STR, STI, IDUM) + CZR = CZR + STR + CZI = CZI + STI + IF (IFORM.EQ.1) GO TO 120 + CALL ZLOG(ARGR, ARGI, STR, STI, IDUM) + CZR = CZR - 0.25D0*STR - AIC + CZI = CZI - 0.25D0*STI + 120 CONTINUE + AX = DEXP(RCZ)/TOL + AY = CZI + CZR = AX*DCOS(AY) + CZI = AX*DSIN(AY) + CALL ZUCHK(CZR, CZI, NW, ASCLE, TOL) + IF (NW.NE.0) GO TO 90 + 130 CONTINUE + IF (IKFLG.EQ.2) RETURN + IF (N.EQ.1) RETURN +!----------------------------------------------------------------------- +! SET UNDERFLOWS ON I SEQUENCE +!----------------------------------------------------------------------- + 140 CONTINUE + GNU = FNU + DBLE(FLOAT(NN-1)) + IF (IFORM.EQ.2) GO TO 150 + INIT = 0 + CALL ZUNIK(ZRR, ZRI, GNU, IKFLG, 1, TOL, INIT, PHIR, PHII, & + ZETA1R, ZETA1I, ZETA2R, ZETA2I, SUMR, SUMI, CWRKR, CWRKI) + CZR = -ZETA1R + ZETA2R + CZI = -ZETA1I + ZETA2I + GO TO 160 + 150 CONTINUE + CALL ZUNHJ(ZNR, ZNI, GNU, 1, TOL, PHIR, PHII, ARGR, ARGI, ZETA1R, & + ZETA1I, ZETA2R, ZETA2I, ASUMR, ASUMI, BSUMR, BSUMI) + CZR = -ZETA1R + ZETA2R + CZI = -ZETA1I + ZETA2I + AARG = ZABS(ARGR,ARGI) + 160 CONTINUE + IF (KODE.EQ.1) GO TO 170 + CZR = CZR - ZBR + CZI = CZI - ZBI + 170 CONTINUE + APHI = ZABS(PHIR,PHII) + RCZ = CZR + IF (RCZ.LT.(-ELIM)) GO TO 180 + IF (RCZ.GT.(-ALIM)) RETURN + RCZ = RCZ + DLOG(APHI) + IF (IFORM.EQ.2) RCZ = RCZ - 0.25D0*DLOG(AARG) - AIC + IF (RCZ.GT.(-ELIM)) GO TO 190 + 180 CONTINUE + YR(NN) = ZEROR + YI(NN) = ZEROI + NN = NN - 1 + NUF = NUF + 1 + IF (NN.EQ.0) RETURN + GO TO 140 + 190 CONTINUE + ASCLE = 1.0D+3*D1MACH(1)/TOL + CALL ZLOG(PHIR, PHII, STR, STI, IDUM) + CZR = CZR + STR + CZI = CZI + STI + IF (IFORM.EQ.1) GO TO 200 + CALL ZLOG(ARGR, ARGI, STR, STI, IDUM) + CZR = CZR - 0.25D0*STR - AIC + CZI = CZI - 0.25D0*STI + 200 CONTINUE + AX = DEXP(RCZ)/TOL + AY = CZI + CZR = AX*DCOS(AY) + CZI = AX*DSIN(AY) + CALL ZUCHK(CZR, CZI, NW, ASCLE, TOL) + IF (NW.NE.0) GO TO 180 + RETURN + 210 CONTINUE + NUF = -1 + RETURN + END + +SUBROUTINE ZBKNU(ZR, ZI, FNU, KODE, N, YR, YI, NZ, TOL, ELIM, ALIM) +USE UTILIT +USE COMPLEX +!***BEGIN PROLOGUE ZBKNU +!***REFER TO ZBESI,ZBESK,ZAIRY,ZBESH +! +! ZBKNU COMPUTES THE K BESSEL FUNCTION IN THE RIGHT HALF Z PLANE. +! +!***ROUTINES CALLED DGAMLN,I1MACH,D1MACH,ZKSCL,ZSHCH,ZUCHK,ZABS,ZDIV, +! ZEXP,ZLOG,ZMLT,ZSQRT +!***END PROLOGUE ZBKNU +! + DOUBLE PRECISION AA, AK, ALIM, ASCLE, A1, A2, BB, BK, BRY, CAZ, & + CBI, CBR, CC, CCHI, CCHR, CKI, CKR, COEFI, COEFR, CONEI, CONER, & + CRSCR, CSCLR, CSHI, CSHR, CSI, CSR, CSRR, CSSR, CTWOI, CTWOR, & + CZEROI, CZEROR, CZI, CZR, DNU, DNU2, DPI, ELIM, ETEST, FC, FHS, & + FI, FK, FKS, FMUI, FMUR, FNU, FPI, FR, G1, G2, HPI, PI, PR, PTI,& + PTR, P1I, P1R, P2I, P2M, P2R, QI, QR, RAK, RCAZ, RTHPI, RZI, & + RZR, R1, S, SMUI, SMUR, SPI, STI, STR, S1I, S1R, S2I, S2R, TM, & + TOL, TTH, T1, T2, YI, YR, ZI, ZR, ELM, CELMR, ZDR, ZDI, & + AS, ALAS, HELIM, CYR, CYI!, DGAMLN + INTEGER I, IFLAG, INU, K, KFLAG, KK, KMAX, KODE, KODED, N, NZ, & + IDUM, J, IC, INUB, NW + DIMENSION YR(N), YI(N), CC(8), CSSR(3), CSRR(3), BRY(3), CYR(2),& + CYI(2) +! COMPLEX Z,Y,A,B,RZ,SMU,FU,FMU,F,FLRZ,CZ,S1,S2,CSH,CCH +! COMPLEX CK,P,Q,COEF,P1,P2,CBK,PT,CZERO,CONE,CTWO,ST,EZ,CS,DK + + DATA KMAX / 30 / + DATA CZEROR,CZEROI,CONER,CONEI,CTWOR,CTWOI,R1/ & + 0.0D0 , 0.0D0 , 1.0D0 , 0.0D0 , 2.0D0 , 0.0D0 , 2.0D0 / + DATA DPI, RTHPI, SPI ,HPI, FPI, TTH / & + 3.14159265358979324D0, 1.25331413731550025D0, & + 1.90985931710274403D0, 1.57079632679489662D0, & + 1.89769999331517738D0, 6.66666666666666666D-01/ + DATA CC(1), CC(2), CC(3), CC(4), CC(5), CC(6), CC(7), CC(8)/ & + 5.77215664901532861D-01, -4.20026350340952355D-02, & + -4.21977345555443367D-02, 7.21894324666309954D-03, & + -2.15241674114950973D-04, -2.01348547807882387D-05, & + 1.13302723198169588D-06, 6.11609510448141582D-09/ + + CAZ = ZABS(ZR,ZI) + CSCLR = 1.0D0/TOL + CRSCR = TOL + CSSR(1) = CSCLR + CSSR(2) = 1.0D0 + CSSR(3) = CRSCR + CSRR(1) = CRSCR + CSRR(2) = 1.0D0 + CSRR(3) = CSCLR + BRY(1) = 1.0D+3*D1MACH(1)/TOL + BRY(2) = 1.0D0/BRY(1) + BRY(3) = D1MACH(2) + NZ = 0 + IFLAG = 0 + KODED = KODE + RCAZ = 1.0D0/CAZ + STR = ZR*RCAZ + STI = -ZI*RCAZ + RZR = (STR+STR)*RCAZ + RZI = (STI+STI)*RCAZ + INU = INT(SNGL(FNU+0.5D0)) + DNU = FNU - DBLE(FLOAT(INU)) + IF (DABS(DNU).EQ.0.5D0) GO TO 110 + DNU2 = 0.0D0 + IF (DABS(DNU).GT.TOL) DNU2 = DNU*DNU + IF (CAZ.GT.R1) GO TO 110 +!----------------------------------------------------------------------- +! SERIES FOR CABS(Z).LE.R1 +!----------------------------------------------------------------------- + FC = 1.0D0 + CALL ZLOG(RZR, RZI, SMUR, SMUI, IDUM) + FMUR = SMUR*DNU + FMUI = SMUI*DNU + CALL ZSHCH(FMUR, FMUI, CSHR, CSHI, CCHR, CCHI) + IF (DNU.EQ.0.0D0) GO TO 10 + FC = DNU*DPI + FC = FC/DSIN(FC) + SMUR = CSHR/DNU + SMUI = CSHI/DNU + 10 CONTINUE + A2 = 1.0D0 + DNU +!----------------------------------------------------------------------- +! GAM(1-Z)*GAM(1+Z)=PI*Z/SIN(PI*Z), T1=1/GAM(1-DNU), T2=1/GAM(1+DNU) +!----------------------------------------------------------------------- + T2 = DEXP(-DGAMLN(A2,IDUM)) + T1 = 1.0D0/(T2*FC) + IF (DABS(DNU).GT.0.1D0) GO TO 40 +!----------------------------------------------------------------------- +! SERIES FOR F0 TO RESOLVE INDETERMINACY FOR SMALL ABS(DNU) +!----------------------------------------------------------------------- + AK = 1.0D0 + S = CC(1) + DO 20 K=2,8 + AK = AK*DNU2 + TM = CC(K)*AK + S = S + TM + IF (DABS(TM).LT.TOL) GO TO 30 + 20 CONTINUE + 30 G1 = -S + GO TO 50 + 40 CONTINUE + G1 = (T1-T2)/(DNU+DNU) + 50 CONTINUE + G2 = (T1+T2)*0.5D0 + FR = FC*(CCHR*G1+SMUR*G2) + FI = FC*(CCHI*G1+SMUI*G2) + CALL ZEXP(FMUR, FMUI, STR, STI) + PR = 0.5D0*STR/T2 + PI = 0.5D0*STI/T2 + CALL ZDIV(0.5D0, 0.0D0, STR, STI, PTR, PTI) + QR = PTR/T1 + QI = PTI/T1 + S1R = FR + S1I = FI + S2R = PR + S2I = PI + AK = 1.0D0 + A1 = 1.0D0 + CKR = CONER + CKI = CONEI + BK = 1.0D0 - DNU2 + IF (INU.GT.0 .OR. N.GT.1) GO TO 80 +!----------------------------------------------------------------------- +! GENERATE K(FNU,Z), 0.0D0 .LE. FNU .LT. 0.5D0 AND N=1 +!----------------------------------------------------------------------- + IF (CAZ.LT.TOL) GO TO 70 + CALL ZMLT(ZR, ZI, ZR, ZI, CZR, CZI) + CZR = 0.25D0*CZR + CZI = 0.25D0*CZI + T1 = 0.25D0*CAZ*CAZ + 60 CONTINUE + FR = (FR*AK+PR+QR)/BK + FI = (FI*AK+PI+QI)/BK + STR = 1.0D0/(AK-DNU) + PR = PR*STR + PI = PI*STR + STR = 1.0D0/(AK+DNU) + QR = QR*STR + QI = QI*STR + STR = CKR*CZR - CKI*CZI + RAK = 1.0D0/AK + CKI = (CKR*CZI+CKI*CZR)*RAK + CKR = STR*RAK + S1R = CKR*FR - CKI*FI + S1R + S1I = CKR*FI + CKI*FR + S1I + A1 = A1*T1*RAK + BK = BK + AK + AK + 1.0D0 + AK = AK + 1.0D0 + IF (A1.GT.TOL) GO TO 60 + 70 CONTINUE + YR(1) = S1R + YI(1) = S1I + IF (KODED.EQ.1) RETURN + CALL ZEXP(ZR, ZI, STR, STI) + CALL ZMLT(S1R, S1I, STR, STI, YR(1), YI(1)) + RETURN +!----------------------------------------------------------------------- +! GENERATE K(DNU,Z) AND K(DNU+1,Z) FOR FORWARD RECURRENCE +!----------------------------------------------------------------------- + 80 CONTINUE + IF (CAZ.LT.TOL) GO TO 100 + CALL ZMLT(ZR, ZI, ZR, ZI, CZR, CZI) + CZR = 0.25D0*CZR + CZI = 0.25D0*CZI + T1 = 0.25D0*CAZ*CAZ + 90 CONTINUE + FR = (FR*AK+PR+QR)/BK + FI = (FI*AK+PI+QI)/BK + STR = 1.0D0/(AK-DNU) + PR = PR*STR + PI = PI*STR + STR = 1.0D0/(AK+DNU) + QR = QR*STR + QI = QI*STR + STR = CKR*CZR - CKI*CZI + RAK = 1.0D0/AK + CKI = (CKR*CZI+CKI*CZR)*RAK + CKR = STR*RAK + S1R = CKR*FR - CKI*FI + S1R + S1I = CKR*FI + CKI*FR + S1I + STR = PR - FR*AK + STI = PI - FI*AK + S2R = CKR*STR - CKI*STI + S2R + S2I = CKR*STI + CKI*STR + S2I + A1 = A1*T1*RAK + BK = BK + AK + AK + 1.0D0 + AK = AK + 1.0D0 + IF (A1.GT.TOL) GO TO 90 + 100 CONTINUE + KFLAG = 2 + A1 = FNU + 1.0D0 + AK = A1*DABS(SMUR) + IF (AK.GT.ALIM) KFLAG = 3 + STR = CSSR(KFLAG) + P2R = S2R*STR + P2I = S2I*STR + CALL ZMLT(P2R, P2I, RZR, RZI, S2R, S2I) + S1R = S1R*STR + S1I = S1I*STR + IF (KODED.EQ.1) GO TO 210 + CALL ZEXP(ZR, ZI, FR, FI) + CALL ZMLT(S1R, S1I, FR, FI, S1R, S1I) + CALL ZMLT(S2R, S2I, FR, FI, S2R, S2I) + GO TO 210 +!----------------------------------------------------------------------- +! IFLAG=0 MEANS NO UNDERFLOW OCCURRED +! IFLAG=1 MEANS AN UNDERFLOW OCCURRED- COMPUTATION PROCEEDS WITH +! KODED=2 AND A TEST FOR ON SCALE VALUES IS MADE DURING FORWARD +! RECURSION +!----------------------------------------------------------------------- + 110 CONTINUE + CALL ZSQRT(ZR, ZI, STR, STI) + CALL ZDIV(RTHPI, CZEROI, STR, STI, COEFR, COEFI) + KFLAG = 2 + IF (KODED.EQ.2) GO TO 120 + IF (ZR.GT.ALIM) GO TO 290 +! BLANK LINE + STR = DEXP(-ZR)*CSSR(KFLAG) + STI = -STR*DSIN(ZI) + STR = STR*DCOS(ZI) + CALL ZMLT(COEFR, COEFI, STR, STI, COEFR, COEFI) + 120 CONTINUE + IF (DABS(DNU).EQ.0.5D0) GO TO 300 +!----------------------------------------------------------------------- +! MILLER ALGORITHM FOR CABS(Z).GT.R1 +!----------------------------------------------------------------------- + AK = DCOS(DPI*DNU) + AK = DABS(AK) + IF (AK.EQ.CZEROR) GO TO 300 + FHS = DABS(0.25D0-DNU2) + IF (FHS.EQ.CZEROR) GO TO 300 +!----------------------------------------------------------------------- +! COMPUTE R2=F(E). IF CABS(Z).GE.R2, USE FORWARD RECURRENCE TO +! DETERMINE THE BACKWARD INDEX K. R2=F(E) IS A STRAIGHT LINE ON +! 12.LE.E.LE.60. E IS COMPUTED FROM 2**(-E)=B**(1-I1MACH(14))= +! TOL WHERE B IS THE BASE OF THE ARITHMETIC. +!----------------------------------------------------------------------- + T1 = DBLE(FLOAT(I1MACH(14)-1)) + T1 = T1*D1MACH(5)*3.321928094D0 + T1 = DMAX1(T1,12.0D0) + T1 = DMIN1(T1,60.0D0) + T2 = TTH*T1 - 6.0D0 + IF (ZR.NE.0.0D0) GO TO 130 + T1 = HPI + GO TO 140 + 130 CONTINUE + T1 = DATAN(ZI/ZR) + T1 = DABS(T1) + 140 CONTINUE + IF (T2.GT.CAZ) GO TO 170 +!----------------------------------------------------------------------- +! FORWARD RECURRENCE LOOP WHEN CABS(Z).GE.R2 +!----------------------------------------------------------------------- + ETEST = AK/(DPI*CAZ*TOL) + FK = CONER + IF (ETEST.LT.CONER) GO TO 180 + FKS = CTWOR + CKR = CAZ + CAZ + CTWOR + P1R = CZEROR + P2R = CONER + DO 150 I=1,KMAX + AK = FHS/FKS + CBR = CKR/(FK+CONER) + PTR = P2R + P2R = CBR*P2R - P1R*AK + P1R = PTR + CKR = CKR + CTWOR + FKS = FKS + FK + FK + CTWOR + FHS = FHS + FK + FK + FK = FK + CONER + STR = DABS(P2R)*FK + IF (ETEST.LT.STR) GO TO 160 + 150 CONTINUE + GO TO 310 + 160 CONTINUE + FK = FK + SPI*T1*DSQRT(T2/CAZ) + FHS = DABS(0.25D0-DNU2) + GO TO 180 + 170 CONTINUE +!----------------------------------------------------------------------- +! COMPUTE BACKWARD INDEX K FOR CABS(Z).LT.R2 +!----------------------------------------------------------------------- + A2 = DSQRT(CAZ) + AK = FPI*AK/(TOL*DSQRT(A2)) + AA = 3.0D0*T1/(1.0D0+CAZ) + BB = 14.7D0*T1/(28.0D0+CAZ) + AK = (DLOG(AK)+CAZ*DCOS(AA)/(1.0D0+0.008D0*CAZ))/DCOS(BB) + FK = 0.12125D0*AK*AK/CAZ + 1.5D0 + 180 CONTINUE +!----------------------------------------------------------------------- +! BACKWARD RECURRENCE LOOP FOR MILLER ALGORITHM +!----------------------------------------------------------------------- + K = INT(SNGL(FK)) + FK = DBLE(FLOAT(K)) + FKS = FK*FK + P1R = CZEROR + P1I = CZEROI + P2R = TOL + P2I = CZEROI + CSR = P2R + CSI = P2I + DO 190 I=1,K + A1 = FKS - FK + AK = (FKS+FK)/(A1+FHS) + RAK = 2.0D0/(FK+CONER) + CBR = (FK+ZR)*RAK + CBI = ZI*RAK + PTR = P2R + PTI = P2I + P2R = (PTR*CBR-PTI*CBI-P1R)*AK + P2I = (PTI*CBR+PTR*CBI-P1I)*AK + P1R = PTR + P1I = PTI + CSR = CSR + P2R + CSI = CSI + P2I + FKS = A1 - FK + CONER + FK = FK - CONER + 190 CONTINUE +!----------------------------------------------------------------------- +! COMPUTE (P2/CS)=(P2/CABS(CS))*(CONJG(CS)/CABS(CS)) FOR BETTER +! SCALING +!----------------------------------------------------------------------- + TM = ZABS(CSR,CSI) + PTR = 1.0D0/TM + S1R = P2R*PTR + S1I = P2I*PTR + CSR = CSR*PTR + CSI = -CSI*PTR + CALL ZMLT(COEFR, COEFI, S1R, S1I, STR, STI) + CALL ZMLT(STR, STI, CSR, CSI, S1R, S1I) + IF (INU.GT.0 .OR. N.GT.1) GO TO 200 + ZDR = ZR + ZDI = ZI + IF(IFLAG.EQ.1) GO TO 270 + GO TO 240 + 200 CONTINUE +!----------------------------------------------------------------------- +! COMPUTE P1/P2=(P1/CABS(P2)*CONJG(P2)/CABS(P2) FOR SCALING +!----------------------------------------------------------------------- + TM = ZABS(P2R,P2I) + PTR = 1.0D0/TM + P1R = P1R*PTR + P1I = P1I*PTR + P2R = P2R*PTR + P2I = -P2I*PTR + CALL ZMLT(P1R, P1I, P2R, P2I, PTR, PTI) + STR = DNU + 0.5D0 - PTR + STI = -PTI + CALL ZDIV(STR, STI, ZR, ZI, STR, STI) + STR = STR + 1.0D0 + CALL ZMLT(STR, STI, S1R, S1I, S2R, S2I) +!----------------------------------------------------------------------- +! FORWARD RECURSION ON THE THREE TERM RECURSION WITH RELATION WITH +! SCALING NEAR EXPONENT EXTREMES ON KFLAG=1 OR KFLAG=3 +!----------------------------------------------------------------------- + 210 CONTINUE + STR = DNU + 1.0D0 + CKR = STR*RZR + CKI = STR*RZI + IF (N.EQ.1) INU = INU - 1 + IF (INU.GT.0) GO TO 220 + IF (N.GT.1) GO TO 215 + S1R = S2R + S1I = S2I + 215 CONTINUE + ZDR = ZR + ZDI = ZI + IF(IFLAG.EQ.1) GO TO 270 + GO TO 240 + 220 CONTINUE + INUB = 1 + IF(IFLAG.EQ.1) GO TO 261 + 225 CONTINUE + P1R = CSRR(KFLAG) + ASCLE = BRY(KFLAG) + DO 230 I=INUB,INU + STR = S2R + STI = S2I + S2R = CKR*STR - CKI*STI + S1R + S2I = CKR*STI + CKI*STR + S1I + S1R = STR + S1I = STI + CKR = CKR + RZR + CKI = CKI + RZI + IF (KFLAG.GE.3) GO TO 230 + P2R = S2R*P1R + P2I = S2I*P1R + STR = DABS(P2R) + STI = DABS(P2I) + P2M = DMAX1(STR,STI) + IF (P2M.LE.ASCLE) GO TO 230 + KFLAG = KFLAG + 1 + ASCLE = BRY(KFLAG) + S1R = S1R*P1R + S1I = S1I*P1R + S2R = P2R + S2I = P2I + STR = CSSR(KFLAG) + S1R = S1R*STR + S1I = S1I*STR + S2R = S2R*STR + S2I = S2I*STR + P1R = CSRR(KFLAG) + 230 CONTINUE + IF (N.NE.1) GO TO 240 + S1R = S2R + S1I = S2I + 240 CONTINUE + STR = CSRR(KFLAG) + YR(1) = S1R*STR + YI(1) = S1I*STR + IF (N.EQ.1) RETURN + YR(2) = S2R*STR + YI(2) = S2I*STR + IF (N.EQ.2) RETURN + KK = 2 + 250 CONTINUE + KK = KK + 1 + IF (KK.GT.N) RETURN + P1R = CSRR(KFLAG) + ASCLE = BRY(KFLAG) + DO 260 I=KK,N + P2R = S2R + P2I = S2I + S2R = CKR*P2R - CKI*P2I + S1R + S2I = CKI*P2R + CKR*P2I + S1I + S1R = P2R + S1I = P2I + CKR = CKR + RZR + CKI = CKI + RZI + P2R = S2R*P1R + P2I = S2I*P1R + YR(I) = P2R + YI(I) = P2I + IF (KFLAG.GE.3) GO TO 260 + STR = DABS(P2R) + STI = DABS(P2I) + P2M = DMAX1(STR,STI) + IF (P2M.LE.ASCLE) GO TO 260 + KFLAG = KFLAG + 1 + ASCLE = BRY(KFLAG) + S1R = S1R*P1R + S1I = S1I*P1R + S2R = P2R + S2I = P2I + STR = CSSR(KFLAG) + S1R = S1R*STR + S1I = S1I*STR + S2R = S2R*STR + S2I = S2I*STR + P1R = CSRR(KFLAG) + 260 CONTINUE + RETURN +!----------------------------------------------------------------------- +! IFLAG=1 CASES, FORWARD RECURRENCE ON SCALED VALUES ON UNDERFLOW +!----------------------------------------------------------------------- + 261 CONTINUE + HELIM = 0.5D0*ELIM + ELM = DEXP(-ELIM) + CELMR = ELM + ASCLE = BRY(1) + ZDR = ZR + ZDI = ZI + IC = -1 + J = 2 + DO 262 I=1,INU + STR = S2R + STI = S2I + S2R = STR*CKR-STI*CKI+S1R + S2I = STI*CKR+STR*CKI+S1I + S1R = STR + S1I = STI + CKR = CKR+RZR + CKI = CKI+RZI + AS = ZABS(S2R,S2I) + ALAS = DLOG(AS) + P2R = -ZDR+ALAS + IF(P2R.LT.(-ELIM)) GO TO 263 + CALL ZLOG(S2R,S2I,STR,STI,IDUM) + P2R = -ZDR+STR + P2I = -ZDI+STI + P2M = DEXP(P2R)/TOL + P1R = P2M*DCOS(P2I) + P1I = P2M*DSIN(P2I) + CALL ZUCHK(P1R,P1I,NW,ASCLE,TOL) + IF(NW.NE.0) GO TO 263 + J = 3 - J + CYR(J) = P1R + CYI(J) = P1I + IF(IC.EQ.(I-1)) GO TO 264 + IC = I + GO TO 262 + 263 CONTINUE + IF(ALAS.LT.HELIM) GO TO 262 + ZDR = ZDR-ELIM + S1R = S1R*CELMR + S1I = S1I*CELMR + S2R = S2R*CELMR + S2I = S2I*CELMR + 262 CONTINUE + IF(N.NE.1) GO TO 270 + S1R = S2R + S1I = S2I + GO TO 270 + 264 CONTINUE + KFLAG = 1 + INUB = I+1 + S2R = CYR(J) + S2I = CYI(J) + J = 3 - J + S1R = CYR(J) + S1I = CYI(J) + IF(INUB.LE.INU) GO TO 225 + IF(N.NE.1) GO TO 240 + S1R = S2R + S1I = S2I + GO TO 240 + 270 CONTINUE + YR(1) = S1R + YI(1) = S1I + IF(N.EQ.1) GO TO 280 + YR(2) = S2R + YI(2) = S2I + 280 CONTINUE + ASCLE = BRY(1) + CALL ZKSCL(ZDR,ZDI,FNU,N,YR,YI,NZ,RZR,RZI,ASCLE,TOL,ELIM) + INU = N - NZ + IF (INU.LE.0) RETURN + KK = NZ + 1 + S1R = YR(KK) + S1I = YI(KK) + YR(KK) = S1R*CSRR(1) + YI(KK) = S1I*CSRR(1) + IF (INU.EQ.1) RETURN + KK = NZ + 2 + S2R = YR(KK) + S2I = YI(KK) + YR(KK) = S2R*CSRR(1) + YI(KK) = S2I*CSRR(1) + IF (INU.EQ.2) RETURN + T2 = FNU + DBLE(FLOAT(KK-1)) + CKR = T2*RZR + CKI = T2*RZI + KFLAG = 1 + GO TO 250 + 290 CONTINUE +!----------------------------------------------------------------------- +! SCALE BY DEXP(Z), IFLAG = 1 CASES +!----------------------------------------------------------------------- + KODED = 2 + IFLAG = 1 + KFLAG = 2 + GO TO 120 +!----------------------------------------------------------------------- +! FNU=HALF ODD INTEGER CASE, DNU=-0.5 +!----------------------------------------------------------------------- + 300 CONTINUE + S1R = COEFR + S1I = COEFI + S2R = COEFR + S2I = COEFI + GO TO 210 + + 310 CONTINUE + NZ=-2 + RETURN +END + +SUBROUTINE ZACON(ZR, ZI, FNU, KODE, MR, N, YR, YI, NZ, RL, FNUL, TOL, ELIM, ALIM) +USE UTILIT +USE COMPLEX +!***BEGIN PROLOGUE ZACON +!***REFER TO ZBESK,ZBESH +! +! ZACON APPLIES THE ANALYTIC CONTINUATION FORMULA +! +! K(FNU,ZN*EXP(MP))=K(FNU,ZN)*EXP(-MP*FNU) - MP*I(FNU,ZN) +! MP=PI*MR*CMPLX(0.0,1.0) +! +! TO CONTINUE THE K FUNCTION FROM THE RIGHT HALF TO THE LEFT +! HALF Z PLANE +! +!***ROUTINES CALLED ZBINU,ZBKNU,ZS1S2,D1MACH,ZABS,ZMLT +!***END PROLOGUE ZACON +! COMPLEX CK,CONE,CSCL,CSCR,CSGN,CSPN,CY,CZERO,C1,C2,RZ,SC1,SC2,ST, +! *S1,S2,Y,Z,ZN + DOUBLE PRECISION ALIM, ARG, ASCLE, AS2, AZN, BRY, BSCLE, CKI, & + CKR, CONEI, CONER, CPN, CSCL, CSCR, CSGNI, CSGNR, CSPNI, CSPNR, & + CSR, CSRR, CSSR, CYI, CYR, C1I, C1M, C1R, C2I, C2R, ELIM, FMR, & + FN, FNU, FNUL, PI, PTI, PTR, RAZN, RL, RZI, RZR, SC1I, SC1R, & + SC2I, SC2R, SGN, SPN, STI, STR, S1I, S1R, S2I, S2R, TOL, YI, YR, & + YY, ZEROI, ZEROR, ZI, ZNI, ZNR, ZR + INTEGER I, INU, IUF, KFLAG, KODE, MR, N, NN, NW, NZ + DIMENSION YR(N), YI(N), CYR(2), CYI(2), CSSR(3), CSRR(3), BRY(3) + DATA PI / 3.14159265358979324D0 / + DATA ZEROR,ZEROI,CONER,CONEI / 0.0D0,0.0D0,1.0D0,0.0D0 / + NZ = 0 + ZNR = -ZR + ZNI = -ZI + NN = N + CALL ZBINU(ZNR, ZNI, FNU, KODE, NN, YR, YI, NW, RL, FNUL, TOL, ELIM, ALIM) + IF (NW.LT.0) GO TO 90 +!----------------------------------------------------------------------- +! ANALYTIC CONTINUATION TO THE LEFT HALF PLANE FOR THE K FUNCTION +!----------------------------------------------------------------------- + NN = MIN0(2,N) + CALL ZBKNU(ZNR, ZNI, FNU, KODE, NN, CYR, CYI, NW, TOL, ELIM, ALIM) + IF (NW.NE.0) GO TO 90 + S1R = CYR(1) + S1I = CYI(1) + FMR = DBLE(FLOAT(MR)) + SGN = -DSIGN(PI,FMR) + CSGNR = ZEROR + CSGNI = SGN + IF (KODE.EQ.1) GO TO 10 + YY = -ZNI + CPN = DCOS(YY) + SPN = DSIN(YY) + CALL ZMLT(CSGNR, CSGNI, CPN, SPN, CSGNR, CSGNI) + 10 CONTINUE +!----------------------------------------------------------------------- +! CALCULATE CSPN=EXP(FNU*PI*I) TO MINIMIZE LOSSES OF SIGNIFICANCE +! WHEN FNU IS LARGE +!----------------------------------------------------------------------- + INU = INT(SNGL(FNU)) + ARG = (FNU-DBLE(FLOAT(INU)))*SGN + CPN = DCOS(ARG) + SPN = DSIN(ARG) + CSPNR = CPN + CSPNI = SPN + IF (MOD(INU,2).EQ.0) GO TO 20 + CSPNR = -CSPNR + CSPNI = -CSPNI + 20 CONTINUE + IUF = 0 + C1R = S1R + C1I = S1I + C2R = YR(1) + C2I = YI(1) + ASCLE = 1.0D+3*D1MACH(1)/TOL + IF (KODE.EQ.1) GO TO 30 + CALL ZS1S2(ZNR, ZNI, C1R, C1I, C2R, C2I, NW, ASCLE, ALIM, IUF) + NZ = NZ + NW + SC1R = C1R + SC1I = C1I + 30 CONTINUE + CALL ZMLT(CSPNR, CSPNI, C1R, C1I, STR, STI) + CALL ZMLT(CSGNR, CSGNI, C2R, C2I, PTR, PTI) + YR(1) = STR + PTR + YI(1) = STI + PTI + IF (N.EQ.1) RETURN + CSPNR = -CSPNR + CSPNI = -CSPNI + S2R = CYR(2) + S2I = CYI(2) + C1R = S2R + C1I = S2I + C2R = YR(2) + C2I = YI(2) + IF (KODE.EQ.1) GO TO 40 + CALL ZS1S2(ZNR, ZNI, C1R, C1I, C2R, C2I, NW, ASCLE, ALIM, IUF) + NZ = NZ + NW + SC2R = C1R + SC2I = C1I + 40 CONTINUE + CALL ZMLT(CSPNR, CSPNI, C1R, C1I, STR, STI) + CALL ZMLT(CSGNR, CSGNI, C2R, C2I, PTR, PTI) + YR(2) = STR + PTR + YI(2) = STI + PTI + IF (N.EQ.2) RETURN + CSPNR = -CSPNR + CSPNI = -CSPNI + AZN = ZABS(ZNR,ZNI) + RAZN = 1.0D0/AZN + STR = ZNR*RAZN + STI = -ZNI*RAZN + RZR = (STR+STR)*RAZN + RZI = (STI+STI)*RAZN + FN = FNU + 1.0D0 + CKR = FN*RZR + CKI = FN*RZI +!----------------------------------------------------------------------- +! SCALE NEAR EXPONENT EXTREMES DURING RECURRENCE ON K FUNCTIONS +!----------------------------------------------------------------------- + CSCL = 1.0D0/TOL + CSCR = TOL + CSSR(1) = CSCL + CSSR(2) = CONER + CSSR(3) = CSCR + CSRR(1) = CSCR + CSRR(2) = CONER + CSRR(3) = CSCL + BRY(1) = ASCLE + BRY(2) = 1.0D0/ASCLE + BRY(3) = D1MACH(2) + AS2 = ZABS(S2R,S2I) + KFLAG = 2 + IF (AS2.GT.BRY(1)) GO TO 50 + KFLAG = 1 + GO TO 60 + 50 CONTINUE + IF (AS2.LT.BRY(2)) GO TO 60 + KFLAG = 3 + 60 CONTINUE + BSCLE = BRY(KFLAG) + S1R = S1R*CSSR(KFLAG) + S1I = S1I*CSSR(KFLAG) + S2R = S2R*CSSR(KFLAG) + S2I = S2I*CSSR(KFLAG) + CSR = CSRR(KFLAG) + DO 80 I=3,N + STR = S2R + STI = S2I + S2R = CKR*STR - CKI*STI + S1R + S2I = CKR*STI + CKI*STR + S1I + S1R = STR + S1I = STI + C1R = S2R*CSR + C1I = S2I*CSR + STR = C1R + STI = C1I + C2R = YR(I) + C2I = YI(I) + IF (KODE.EQ.1) GO TO 70 + IF (IUF.LT.0) GO TO 70 + CALL ZS1S2(ZNR, ZNI, C1R, C1I, C2R, C2I, NW, ASCLE, ALIM, IUF) + NZ = NZ + NW + SC1R = SC2R + SC1I = SC2I + SC2R = C1R + SC2I = C1I + IF (IUF.NE.3) GO TO 70 + IUF = -4 + S1R = SC1R*CSSR(KFLAG) + S1I = SC1I*CSSR(KFLAG) + S2R = SC2R*CSSR(KFLAG) + S2I = SC2I*CSSR(KFLAG) + STR = SC2R + STI = SC2I + 70 CONTINUE + PTR = CSPNR*C1R - CSPNI*C1I + PTI = CSPNR*C1I + CSPNI*C1R + YR(I) = PTR + CSGNR*C2R - CSGNI*C2I + YI(I) = PTI + CSGNR*C2I + CSGNI*C2R + CKR = CKR + RZR + CKI = CKI + RZI + CSPNR = -CSPNR + CSPNI = -CSPNI + IF (KFLAG.GE.3) GO TO 80 + PTR = DABS(C1R) + PTI = DABS(C1I) + C1M = DMAX1(PTR,PTI) + IF (C1M.LE.BSCLE) GO TO 80 + KFLAG = KFLAG + 1 + BSCLE = BRY(KFLAG) + S1R = S1R*CSR + S1I = S1I*CSR + S2R = STR + S2I = STI + S1R = S1R*CSSR(KFLAG) + S1I = S1I*CSSR(KFLAG) + S2R = S2R*CSSR(KFLAG) + S2I = S2I*CSSR(KFLAG) + CSR = CSRR(KFLAG) + 80 CONTINUE + RETURN + 90 CONTINUE + NZ = -1 + IF(NW.EQ.(-2)) NZ=-2 + RETURN +END + +SUBROUTINE ZBUNK(ZR, ZI, FNU, KODE, MR, N, YR, YI, NZ, TOL, ELIM, ALIM) +!***BEGIN PROLOGUE ZBUNK +!***REFER TO ZBESK,ZBESH +! +! ZBUNK COMPUTES THE K BESSEL FUNCTION FOR FNU.GT.FNUL. +! ACCORDING TO THE UNIFORM ASYMPTOTIC EXPANSION FOR K(FNU,Z) +! IN ZUNK1 AND THE EXPANSION FOR H(2,FNU,Z) IN ZUNK2 +! +!***ROUTINES CALLED ZUNK1,ZUNK2 +!***END PROLOGUE ZBUNK +! COMPLEX Y,Z + DOUBLE PRECISION ALIM, AX, AY, ELIM, FNU, TOL, YI, YR, ZI, ZR + INTEGER KODE, MR, N, NZ + DIMENSION YR(1), YI(1) + NZ = 0 + AX = DABS(ZR)*1.7321D0 + AY = DABS(ZI) + IF (AY.GT.AX) GO TO 10 +!----------------------------------------------------------------------- +! ASYMPTOTIC EXPANSION FOR K(FNU,Z) FOR LARGE FNU APPLIED IN +! -PI/3.LE.ARG(Z).LE.PI/3 +!----------------------------------------------------------------------- + CALL ZUNK1(ZR, ZI, FNU, KODE, MR, N, YR, YI, NZ, TOL, ELIM, ALIM) + GO TO 20 + 10 CONTINUE +!----------------------------------------------------------------------- +! ASYMPTOTIC EXPANSION FOR H(2,FNU,Z*EXP(M*HPI)) FOR LARGE FNU +! APPLIED IN PI/3.LT.ABS(ARG(Z)).LE.PI/2 WHERE M=+I OR -I +! AND HPI=PI/2 +!----------------------------------------------------------------------- + CALL ZUNK2(ZR, ZI, FNU, KODE, MR, N, YR, YI, NZ, TOL, ELIM, ALIM) + 20 CONTINUE + RETURN +END + +SUBROUTINE ZUNIK(ZRR, ZRI, FNU, IKFLG, IPMTR, TOL, INIT, PHIR, & + PHII, ZETA1R, ZETA1I, ZETA2R, ZETA2I, SUMR, SUMI, CWRKR, CWRKI) +USE COMPLEX +!***BEGIN PROLOGUE ZUNIK +!***REFER TO ZBESI,ZBESK +! +! ZUNIK COMPUTES PARAMETERS FOR THE UNIFORM ASYMPTOTIC +! EXPANSIONS OF THE I AND K FUNCTIONS ON IKFLG= 1 OR 2 +! RESPECTIVELY BY +! +! W(FNU,ZR) = PHI*EXP(ZETA)*SUM +! +! WHERE ZETA=-ZETA1 + ZETA2 OR +! ZETA1 - ZETA2 +! +! THE FIRST CALL MUST HAVE INIT=0. SUBSEQUENT CALLS WITH THE +! SAME ZR AND FNU WILL RETURN THE I OR K FUNCTION ON IKFLG= +! 1 OR 2 WITH NO CHANGE IN INIT. CWRK IS A COMPLEX WORK +! ARRAY. IPMTR=0 COMPUTES ALL PARAMETERS. IPMTR=1 COMPUTES PHI, +! ZETA1,ZETA2. +! +!***ROUTINES CALLED ZDIV,ZLOG,ZSQRT +!***END PROLOGUE ZUNIK +! COMPLEX CFN,CON,CONE,CRFN,CWRK,CZERO,PHI,S,SR,SUM,T,T2,ZETA1, +! *ZETA2,ZN,ZR + DOUBLE PRECISION AC, C, CON, CONEI, CONER, CRFNI, CRFNR, CWRKI, & + CWRKR, FNU, PHII, PHIR, RFN, SI, SR, SRI, SRR, STI, STR, SUMI, & + SUMR, TEST, TI, TOL, TR, T2I, T2R, ZEROI, ZEROR, ZETA1I, ZETA1R, & + ZETA2I, ZETA2R, ZNI, ZNR, ZRI, ZRR + INTEGER I, IDUM, IKFLG, INIT, IPMTR, J, K, L + DIMENSION C(120), CWRKR(16), CWRKI(16), CON(2) + DATA ZEROR,ZEROI,CONER,CONEI / 0.0D0, 0.0D0, 1.0D0, 0.0D0 / + DATA CON(1), CON(2) / & + 3.98942280401432678D-01, 1.25331413731550025D+00 / + DATA C(1), C(2), C(3), C(4), C(5), C(6), C(7), C(8), C(9), C(10), & + C(11), C(12), C(13), C(14), C(15), C(16), C(17), C(18), & + C(19), C(20), C(21), C(22), C(23), C(24)/ & + 1.00000000000000000D+00, -2.08333333333333333D-01, & + 1.25000000000000000D-01, 3.34201388888888889D-01, & + -4.01041666666666667D-01, 7.03125000000000000D-02, & + -1.02581259645061728D+00, 1.84646267361111111D+00, & + -8.91210937500000000D-01, 7.32421875000000000D-02, & + 4.66958442342624743D+00, -1.12070026162229938D+01, & + 8.78912353515625000D+00, -2.36408691406250000D+00, & + 1.12152099609375000D-01, -2.82120725582002449D+01, & + 8.46362176746007346D+01, -9.18182415432400174D+01, & + 4.25349987453884549D+01, -7.36879435947963170D+00, & + 2.27108001708984375D-01, 2.12570130039217123D+02, & + -7.65252468141181642D+02, 1.05999045252799988D+03/ + DATA C(25), C(26), C(27), C(28), C(29), C(30), C(31), C(32), & + C(33), C(34), C(35), C(36), C(37), C(38), C(39), C(40), & + C(41), C(42), C(43), C(44), C(45), C(46), C(47), C(48)/ & + -6.99579627376132541D+02, 2.18190511744211590D+02, & + -2.64914304869515555D+01, 5.72501420974731445D-01, & + -1.91945766231840700D+03, 8.06172218173730938D+03, & + -1.35865500064341374D+04, 1.16553933368645332D+04, & + -5.30564697861340311D+03, 1.20090291321635246D+03, & + -1.08090919788394656D+02, 1.72772750258445740D+00, & + 2.02042913309661486D+04, -9.69805983886375135D+04, & + 1.92547001232531532D+05, -2.03400177280415534D+05, & + 1.22200464983017460D+05, -4.11926549688975513D+04, & + 7.10951430248936372D+03, -4.93915304773088012D+02, & + 6.07404200127348304D+00, -2.42919187900551333D+05, & + 1.31176361466297720D+06, -2.99801591853810675D+06/ + DATA C(49), C(50), C(51), C(52), C(53), C(54), C(55), C(56), & + C(57), C(58), C(59), C(60), C(61), C(62), C(63), C(64), & + C(65), C(66), C(67), C(68), C(69), C(70), C(71), C(72)/ & + 3.76327129765640400D+06, -2.81356322658653411D+06, & + 1.26836527332162478D+06, -3.31645172484563578D+05, & + 4.52187689813627263D+04, -2.49983048181120962D+03, & + 2.43805296995560639D+01, 3.28446985307203782D+06, & + -1.97068191184322269D+07, 5.09526024926646422D+07, & + -7.41051482115326577D+07, 6.63445122747290267D+07, & + -3.75671766607633513D+07, 1.32887671664218183D+07, & + -2.78561812808645469D+06, 3.08186404612662398D+05, & + -1.38860897537170405D+04, 1.10017140269246738D+02, & + -4.93292536645099620D+07, 3.25573074185765749D+08, & + -9.39462359681578403D+08, 1.55359689957058006D+09, & + -1.62108055210833708D+09, 1.10684281682301447D+09/ + DATA C(73), C(74), C(75), C(76), C(77), C(78), C(79), C(80), & + C(81), C(82), C(83), C(84), C(85), C(86), C(87), C(88), & + C(89), C(90), C(91), C(92), C(93), C(94), C(95), C(96)/ & + -4.95889784275030309D+08, 1.42062907797533095D+08, & + -2.44740627257387285D+07, 2.24376817792244943D+06, & + -8.40054336030240853D+04, 5.51335896122020586D+02, & + 8.14789096118312115D+08, -5.86648149205184723D+09, & + 1.86882075092958249D+10, -3.46320433881587779D+10, & + 4.12801855797539740D+10, -3.30265997498007231D+10, & + 1.79542137311556001D+10, -6.56329379261928433D+09, & + 1.55927986487925751D+09, -2.25105661889415278D+08, & + 1.73951075539781645D+07, -5.49842327572288687D+05, & + 3.03809051092238427D+03, -1.46792612476956167D+10, & + 1.14498237732025810D+11, -3.99096175224466498D+11, & + 8.19218669548577329D+11, -1.09837515608122331D+12/ + DATA C(97), C(98), C(99), C(100), C(101), C(102), C(103), C(104), & + C(105), C(106), C(107), C(108), C(109), C(110), C(111), & + C(112), C(113), C(114), C(115), C(116), C(117), C(118)/ & + 1.00815810686538209D+12, -6.45364869245376503D+11, & + 2.87900649906150589D+11, -8.78670721780232657D+10, & + 1.76347306068349694D+10, -2.16716498322379509D+09, & + 1.43157876718888981D+08, -3.87183344257261262D+06, & + 1.82577554742931747D+04, 2.86464035717679043D+11, & + -2.40629790002850396D+12, 9.10934118523989896D+12, & + -2.05168994109344374D+13, 3.05651255199353206D+13, & + -3.16670885847851584D+13, 2.33483640445818409D+13, & + -1.23204913055982872D+13, 4.61272578084913197D+12, & + -1.19655288019618160D+12, 2.05914503232410016D+11, & + -2.18229277575292237D+10, 1.24700929351271032D+09/ + DATA C(119), C(120)/ & + -2.91883881222208134D+07, 1.18838426256783253D+05/ + + IF (INIT.NE.0) GO TO 40 +!----------------------------------------------------------------------- +! INITIALIZE ALL VARIABLES +!----------------------------------------------------------------------- + RFN = 1.0D0/FNU + TR = ZRR*RFN + TI = ZRI*RFN + SR = CONER + (TR*TR-TI*TI) + SI = CONEI + (TR*TI+TI*TR) + CALL ZSQRT(SR, SI, SRR, SRI) + STR = CONER + SRR + STI = CONEI + SRI + CALL ZDIV(STR, STI, TR, TI, ZNR, ZNI) + CALL ZLOG(ZNR, ZNI, STR, STI, IDUM) + ZETA1R = FNU*STR + ZETA1I = FNU*STI + ZETA2R = FNU*SRR + ZETA2I = FNU*SRI + CALL ZDIV(CONER, CONEI, SRR, SRI, TR, TI) + SRR = TR*RFN + SRI = TI*RFN + CALL ZSQRT(SRR, SRI, CWRKR(16), CWRKI(16)) + PHIR = CWRKR(16)*CON(IKFLG) + PHII = CWRKI(16)*CON(IKFLG) + IF (IPMTR.NE.0) RETURN + CALL ZDIV(CONER, CONEI, SR, SI, T2R, T2I) + CWRKR(1) = CONER + CWRKI(1) = CONEI + CRFNR = CONER + CRFNI = CONEI + AC = 1.0D0 + L = 1 + DO 20 K=2,15 + SR = ZEROR + SI = ZEROI + DO 10 J=1,K + L = L + 1 + STR = SR*T2R - SI*T2I + C(L) + SI = SR*T2I + SI*T2R + SR = STR + 10 CONTINUE + STR = CRFNR*SRR - CRFNI*SRI + CRFNI = CRFNR*SRI + CRFNI*SRR + CRFNR = STR + CWRKR(K) = CRFNR*SR - CRFNI*SI + CWRKI(K) = CRFNR*SI + CRFNI*SR + AC = AC*RFN + TEST = DABS(CWRKR(K)) + DABS(CWRKI(K)) + IF (AC.LT.TOL .AND. TEST.LT.TOL) GO TO 30 + 20 CONTINUE + K = 15 + 30 CONTINUE + INIT = K + 40 CONTINUE + IF (IKFLG.EQ.2) GO TO 60 +!----------------------------------------------------------------------- +! COMPUTE SUM FOR THE I FUNCTION +!----------------------------------------------------------------------- + SR = ZEROR + SI = ZEROI + DO 50 I=1,INIT + SR = SR + CWRKR(I) + SI = SI + CWRKI(I) + 50 CONTINUE + SUMR = SR + SUMI = SI + PHIR = CWRKR(16)*CON(1) + PHII = CWRKI(16)*CON(1) + RETURN + 60 CONTINUE +!----------------------------------------------------------------------- +! COMPUTE SUM FOR THE K FUNCTION +!----------------------------------------------------------------------- + SR = ZEROR + SI = ZEROI + TR = CONER + DO 70 I=1,INIT + SR = SR + TR*CWRKR(I) + SI = SI + TR*CWRKI(I) + TR = -TR + 70 CONTINUE + SUMR = SR + SUMI = SI + PHIR = CWRKR(16)*CON(2) + PHII = CWRKI(16)*CON(2) + RETURN +END + +SUBROUTINE ZUNK1(ZR, ZI, FNU, KODE, MR, N, YR, YI, NZ, TOL, ELIM, ALIM) +USE UTILIT +USE COMPLEX +!***BEGIN PROLOGUE ZUNK1 +!***REFER TO ZBESK +! +! ZUNK1 COMPUTES K(FNU,Z) AND ITS ANALYTIC CONTINUATION FROM THE +! RIGHT HALF PLANE TO THE LEFT HALF PLANE BY MEANS OF THE +! UNIFORM ASYMPTOTIC EXPANSION. +! MR INDICATES THE DIRECTION OF ROTATION FOR ANALYTIC CONTINUATION. +! NZ=-1 MEANS AN OVERFLOW WILL OCCUR +! +!***ROUTINES CALLED ZKSCL,ZS1S2,ZUCHK,ZUNIK,D1MACH,ZABS +!***END PROLOGUE ZUNK1 +! COMPLEX CFN,CK,CONE,CRSC,CS,CSCL,CSGN,CSPN,CSR,CSS,CWRK,CY,CZERO, +! *C1,C2,PHI,PHID,RZ,SUM,SUMD,S1,S2,Y,Z,ZETA1,ZETA1D,ZETA2,ZETA2D,ZR + DOUBLE PRECISION ALIM, ANG, APHI, ASC, ASCLE, BRY, CKI, CKR, & + CONEI, CONER, CRSC, CSCL, CSGNI, CSPNI, CSPNR, CSR, CSRR, CSSR, & + CWRKI, CWRKR, CYI, CYR, C1I, C1R, C2I, C2M, C2R, ELIM, FMR, FN, & + FNF, FNU, PHIDI, PHIDR, PHII, PHIR, PI, RAST, RAZR, RS1, RZI, & + RZR, SGN, STI, STR, SUMDI, SUMDR, SUMI, SUMR, S1I, S1R, S2I, & + S2R, TOL, YI, YR, ZEROI, ZEROR, ZETA1I, ZETA1R, ZETA2I, ZETA2R, & + ZET1DI, ZET1DR, ZET2DI, ZET2DR, ZI, ZR, ZRI, ZRR + INTEGER I, IB, IFLAG, IFN, IL, INIT, INU, IUF, K, KDFLG, KFLAG, & + KK, KODE, MR, N, NW, NZ, INITD, IC, IPARD, J, M + DIMENSION BRY(3), INIT(2), YR(1), YI(1), SUMR(2), SUMI(2), & + ZETA1R(2), ZETA1I(2), ZETA2R(2), ZETA2I(2), CYR(2), CYI(2), & + CWRKR(16,3), CWRKI(16,3), CSSR(3), CSRR(3), PHIR(2), PHII(2) + DATA ZEROR,ZEROI,CONER,CONEI / 0.0D0, 0.0D0, 1.0D0, 0.0D0 / + DATA PI / 3.14159265358979324D0 / + + KDFLG = 1 + NZ = 0 +!----------------------------------------------------------------------- +! EXP(-ALIM)=EXP(-ELIM)/TOL=APPROX. ONE PRECISION GREATER THAN +! THE UNDERFLOW LIMIT +!----------------------------------------------------------------------- + CSCL = 1.0D0/TOL + CRSC = TOL + CSSR(1) = CSCL + CSSR(2) = CONER + CSSR(3) = CRSC + CSRR(1) = CRSC + CSRR(2) = CONER + CSRR(3) = CSCL + BRY(1) = 1.0D+3*D1MACH(1)/TOL + BRY(2) = 1.0D0/BRY(1) + BRY(3) = D1MACH(2) + ZRR = ZR + ZRI = ZI + IF (ZR.GE.0.0D0) GO TO 10 + ZRR = -ZR + ZRI = -ZI + 10 CONTINUE + J = 2 + DO 70 I=1,N +!----------------------------------------------------------------------- +! J FLIP FLOPS BETWEEN 1 AND 2 IN J = 3 - J +!----------------------------------------------------------------------- + J = 3 - J + FN = FNU + DBLE(FLOAT(I-1)) + INIT(J) = 0 + CALL ZUNIK(ZRR, ZRI, FN, 2, 0, TOL, INIT(J), PHIR(J), PHII(J), & + ZETA1R(J), ZETA1I(J), ZETA2R(J), ZETA2I(J), SUMR(J), SUMI(J), & + CWRKR(1,J), CWRKI(1,J)) + IF (KODE.EQ.1) GO TO 20 + STR = ZRR + ZETA2R(J) + STI = ZRI + ZETA2I(J) + RAST = FN/ZABS(STR,STI) + STR = STR*RAST*RAST + STI = -STI*RAST*RAST + S1R = ZETA1R(J) - STR + S1I = ZETA1I(J) - STI + GO TO 30 + 20 CONTINUE + S1R = ZETA1R(J) - ZETA2R(J) + S1I = ZETA1I(J) - ZETA2I(J) + 30 CONTINUE + RS1 = S1R +!----------------------------------------------------------------------- +! TEST FOR UNDERFLOW AND OVERFLOW +!----------------------------------------------------------------------- + IF (DABS(RS1).GT.ELIM) GO TO 60 + IF (KDFLG.EQ.1) KFLAG = 2 + IF (DABS(RS1).LT.ALIM) GO TO 40 +!----------------------------------------------------------------------- +! REFINE TEST AND SCALE +!----------------------------------------------------------------------- + APHI = ZABS(PHIR(J),PHII(J)) + RS1 = RS1 + DLOG(APHI) + IF (DABS(RS1).GT.ELIM) GO TO 60 + IF (KDFLG.EQ.1) KFLAG = 1 + IF (RS1.LT.0.0D0) GO TO 40 + IF (KDFLG.EQ.1) KFLAG = 3 + 40 CONTINUE +!----------------------------------------------------------------------- +! SCALE S1 TO KEEP INTERMEDIATE ARITHMETIC ON SCALE NEAR +! EXPONENT EXTREMES +!----------------------------------------------------------------------- + S2R = PHIR(J)*SUMR(J) - PHII(J)*SUMI(J) + S2I = PHIR(J)*SUMI(J) + PHII(J)*SUMR(J) + STR = DEXP(S1R)*CSSR(KFLAG) + S1R = STR*DCOS(S1I) + S1I = STR*DSIN(S1I) + STR = S2R*S1R - S2I*S1I + S2I = S1R*S2I + S2R*S1I + S2R = STR + IF (KFLAG.NE.1) GO TO 50 + CALL ZUCHK(S2R, S2I, NW, BRY(1), TOL) + IF (NW.NE.0) GO TO 60 + 50 CONTINUE + CYR(KDFLG) = S2R + CYI(KDFLG) = S2I + YR(I) = S2R*CSRR(KFLAG) + YI(I) = S2I*CSRR(KFLAG) + IF (KDFLG.EQ.2) GO TO 75 + KDFLG = 2 + GO TO 70 + 60 CONTINUE + IF (RS1.GT.0.0D0) GO TO 300 +!----------------------------------------------------------------------- +! FOR ZR.LT.0.0, THE I FUNCTION TO BE ADDED WILL OVERFLOW +!----------------------------------------------------------------------- + IF (ZR.LT.0.0D0) GO TO 300 + KDFLG = 1 + YR(I)=ZEROR + YI(I)=ZEROI + NZ=NZ+1 + IF (I.EQ.1) GO TO 70 + IF ((YR(I-1).EQ.ZEROR).AND.(YI(I-1).EQ.ZEROI)) GO TO 70 + YR(I-1)=ZEROR + YI(I-1)=ZEROI + NZ=NZ+1 + 70 CONTINUE + I = N + 75 CONTINUE + RAZR = 1.0D0/ZABS(ZRR,ZRI) + STR = ZRR*RAZR + STI = -ZRI*RAZR + RZR = (STR+STR)*RAZR + RZI = (STI+STI)*RAZR + CKR = FN*RZR + CKI = FN*RZI + IB = I + 1 + IF (N.LT.IB) GO TO 160 +!----------------------------------------------------------------------- +! TEST LAST MEMBER FOR UNDERFLOW AND OVERFLOW. SET SEQUENCE TO ZERO +! ON UNDERFLOW. +!----------------------------------------------------------------------- + FN = FNU + DBLE(FLOAT(N-1)) + IPARD = 1 + IF (MR.NE.0) IPARD = 0 + INITD = 0 + CALL ZUNIK(ZRR, ZRI, FN, 2, IPARD, TOL, INITD, PHIDR, PHIDI, & + ZET1DR, ZET1DI, ZET2DR, ZET2DI, SUMDR, SUMDI, CWRKR(1,3), & + CWRKI(1,3)) + IF (KODE.EQ.1) GO TO 80 + STR = ZRR + ZET2DR + STI = ZRI + ZET2DI + RAST = FN/ZABS(STR,STI) + STR = STR*RAST*RAST + STI = -STI*RAST*RAST + S1R = ZET1DR - STR + S1I = ZET1DI - STI + GO TO 90 + 80 CONTINUE + S1R = ZET1DR - ZET2DR + S1I = ZET1DI - ZET2DI + 90 CONTINUE + RS1 = S1R + IF (DABS(RS1).GT.ELIM) GO TO 95 + IF (DABS(RS1).LT.ALIM) GO TO 100 +!----------------------------------------------------------------------- +! REFINE ESTIMATE AND TEST +!----------------------------------------------------------------------- + APHI = ZABS(PHIDR,PHIDI) + RS1 = RS1+DLOG(APHI) + IF (DABS(RS1).LT.ELIM) GO TO 100 + 95 CONTINUE + IF (DABS(RS1).GT.0.0D0) GO TO 300 +!----------------------------------------------------------------------- +! FOR ZR.LT.0.0, THE I FUNCTION TO BE ADDED WILL OVERFLOW +!----------------------------------------------------------------------- + IF (ZR.LT.0.0D0) GO TO 300 + NZ = N + DO 96 I=1,N + YR(I) = ZEROR + YI(I) = ZEROI + 96 CONTINUE + RETURN +!----------------------------------------------------------------------- +! FORWARD RECUR FOR REMAINDER OF THE SEQUENCE +!----------------------------------------------------------------------- + 100 CONTINUE + S1R = CYR(1) + S1I = CYI(1) + S2R = CYR(2) + S2I = CYI(2) + C1R = CSRR(KFLAG) + ASCLE = BRY(KFLAG) + DO 120 I=IB,N + C2R = S2R + C2I = S2I + S2R = CKR*C2R - CKI*C2I + S1R + S2I = CKR*C2I + CKI*C2R + S1I + S1R = C2R + S1I = C2I + CKR = CKR + RZR + CKI = CKI + RZI + C2R = S2R*C1R + C2I = S2I*C1R + YR(I) = C2R + YI(I) = C2I + IF (KFLAG.GE.3) GO TO 120 + STR = DABS(C2R) + STI = DABS(C2I) + C2M = DMAX1(STR,STI) + IF (C2M.LE.ASCLE) GO TO 120 + KFLAG = KFLAG + 1 + ASCLE = BRY(KFLAG) + S1R = S1R*C1R + S1I = S1I*C1R + S2R = C2R + S2I = C2I + S1R = S1R*CSSR(KFLAG) + S1I = S1I*CSSR(KFLAG) + S2R = S2R*CSSR(KFLAG) + S2I = S2I*CSSR(KFLAG) + C1R = CSRR(KFLAG) + 120 CONTINUE + 160 CONTINUE + IF (MR.EQ.0) RETURN +!----------------------------------------------------------------------- +! ANALYTIC CONTINUATION FOR RE(Z).LT.0.0D0 +!----------------------------------------------------------------------- + NZ = 0 + FMR = DBLE(FLOAT(MR)) + SGN = -DSIGN(PI,FMR) +!----------------------------------------------------------------------- +! CSPN AND CSGN ARE COEFF OF K AND I FUNCTIONS RESP. +!----------------------------------------------------------------------- + CSGNI = SGN + INU = INT(SNGL(FNU)) + FNF = FNU - DBLE(FLOAT(INU)) + IFN = INU + N - 1 + ANG = FNF*SGN + CSPNR = DCOS(ANG) + CSPNI = DSIN(ANG) + IF (MOD(IFN,2).EQ.0) GO TO 170 + CSPNR = -CSPNR + CSPNI = -CSPNI + 170 CONTINUE + ASC = BRY(1) + IUF = 0 + KK = N + KDFLG = 1 + IB = IB - 1 + IC = IB - 1 + DO 270 K=1,N + FN = FNU + DBLE(FLOAT(KK-1)) +!----------------------------------------------------------------------- +! LOGIC TO SORT OUT CASES WHOSE PARAMETERS WERE SET FOR THE K +! FUNCTION ABOVE +!----------------------------------------------------------------------- + M=3 + IF (N.GT.2) GO TO 175 + 172 CONTINUE + INITD = INIT(J) + PHIDR = PHIR(J) + PHIDI = PHII(J) + ZET1DR = ZETA1R(J) + ZET1DI = ZETA1I(J) + ZET2DR = ZETA2R(J) + ZET2DI = ZETA2I(J) + SUMDR = SUMR(J) + SUMDI = SUMI(J) + M = J + J = 3 - J + GO TO 180 + 175 CONTINUE + IF ((KK.EQ.N).AND.(IB.LT.N)) GO TO 180 + IF ((KK.EQ.IB).OR.(KK.EQ.IC)) GO TO 172 + INITD = 0 + 180 CONTINUE + CALL ZUNIK(ZRR, ZRI, FN, 1, 0, TOL, INITD, PHIDR, PHIDI, & + ZET1DR, ZET1DI, ZET2DR, ZET2DI, SUMDR, SUMDI, & + CWRKR(1,M), CWRKI(1,M)) + IF (KODE.EQ.1) GO TO 200 + STR = ZRR + ZET2DR + STI = ZRI + ZET2DI + RAST = FN/ZABS(STR,STI) + STR = STR*RAST*RAST + STI = -STI*RAST*RAST + S1R = -ZET1DR + STR + S1I = -ZET1DI + STI + GO TO 210 + 200 CONTINUE + S1R = -ZET1DR + ZET2DR + S1I = -ZET1DI + ZET2DI + 210 CONTINUE +!----------------------------------------------------------------------- +! TEST FOR UNDERFLOW AND OVERFLOW +!----------------------------------------------------------------------- + RS1 = S1R + IF (DABS(RS1).GT.ELIM) GO TO 260 + IF (KDFLG.EQ.1) IFLAG = 2 + IF (DABS(RS1).LT.ALIM) GO TO 220 +!----------------------------------------------------------------------- +! REFINE TEST AND SCALE +!----------------------------------------------------------------------- + APHI = ZABS(PHIDR,PHIDI) + RS1 = RS1 + DLOG(APHI) + IF (DABS(RS1).GT.ELIM) GO TO 260 + IF (KDFLG.EQ.1) IFLAG = 1 + IF (RS1.LT.0.0D0) GO TO 220 + IF (KDFLG.EQ.1) IFLAG = 3 + 220 CONTINUE + STR = PHIDR*SUMDR - PHIDI*SUMDI + STI = PHIDR*SUMDI + PHIDI*SUMDR + S2R = -CSGNI*STI + S2I = CSGNI*STR + STR = DEXP(S1R)*CSSR(IFLAG) + S1R = STR*DCOS(S1I) + S1I = STR*DSIN(S1I) + STR = S2R*S1R - S2I*S1I + S2I = S2R*S1I + S2I*S1R + S2R = STR + IF (IFLAG.NE.1) GO TO 230 + CALL ZUCHK(S2R, S2I, NW, BRY(1), TOL) + IF (NW.EQ.0) GO TO 230 + S2R = ZEROR + S2I = ZEROI + 230 CONTINUE + CYR(KDFLG) = S2R + CYI(KDFLG) = S2I + C2R = S2R + C2I = S2I + S2R = S2R*CSRR(IFLAG) + S2I = S2I*CSRR(IFLAG) +!----------------------------------------------------------------------- +! ADD I AND K FUNCTIONS, K SEQUENCE IN Y(I), I=1,N +!----------------------------------------------------------------------- + S1R = YR(KK) + S1I = YI(KK) + IF (KODE.EQ.1) GO TO 250 + CALL ZS1S2(ZRR, ZRI, S1R, S1I, S2R, S2I, NW, ASC, ALIM, IUF) + NZ = NZ + NW + 250 CONTINUE + YR(KK) = S1R*CSPNR - S1I*CSPNI + S2R + YI(KK) = CSPNR*S1I + CSPNI*S1R + S2I + KK = KK - 1 + CSPNR = -CSPNR + CSPNI = -CSPNI + IF (C2R.NE.0.0D0 .OR. C2I.NE.0.0D0) GO TO 255 + KDFLG = 1 + GO TO 270 + 255 CONTINUE + IF (KDFLG.EQ.2) GO TO 275 + KDFLG = 2 + GO TO 270 + 260 CONTINUE + IF (RS1.GT.0.0D0) GO TO 300 + S2R = ZEROR + S2I = ZEROI + GO TO 230 + 270 CONTINUE + K = N + 275 CONTINUE + IL = N - K + IF (IL.EQ.0) RETURN +!----------------------------------------------------------------------- +! RECUR BACKWARD FOR REMAINDER OF I SEQUENCE AND ADD IN THE +! K FUNCTIONS, SCALING THE I SEQUENCE DURING RECURRENCE TO KEEP +! INTERMEDIATE ARITHMETIC ON SCALE NEAR EXPONENT EXTREMES. +!----------------------------------------------------------------------- + S1R = CYR(1) + S1I = CYI(1) + S2R = CYR(2) + S2I = CYI(2) + CSR = CSRR(IFLAG) + ASCLE = BRY(IFLAG) + FN = DBLE(FLOAT(INU+IL)) + DO 290 I=1,IL + C2R = S2R + C2I = S2I + S2R = S1R + (FN+FNF)*(RZR*C2R-RZI*C2I) + S2I = S1I + (FN+FNF)*(RZR*C2I+RZI*C2R) + S1R = C2R + S1I = C2I + FN = FN - 1.0D0 + C2R = S2R*CSR + C2I = S2I*CSR + CKR = C2R + CKI = C2I + C1R = YR(KK) + C1I = YI(KK) + IF (KODE.EQ.1) GO TO 280 + CALL ZS1S2(ZRR, ZRI, C1R, C1I, C2R, C2I, NW, ASC, ALIM, IUF) + NZ = NZ + NW + 280 CONTINUE + YR(KK) = C1R*CSPNR - C1I*CSPNI + C2R + YI(KK) = C1R*CSPNI + C1I*CSPNR + C2I + KK = KK - 1 + CSPNR = -CSPNR + CSPNI = -CSPNI + IF (IFLAG.GE.3) GO TO 290 + C2R = DABS(CKR) + C2I = DABS(CKI) + C2M = DMAX1(C2R,C2I) + IF (C2M.LE.ASCLE) GO TO 290 + IFLAG = IFLAG + 1 + ASCLE = BRY(IFLAG) + S1R = S1R*CSR + S1I = S1I*CSR + S2R = CKR + S2I = CKI + S1R = S1R*CSSR(IFLAG) + S1I = S1I*CSSR(IFLAG) + S2R = S2R*CSSR(IFLAG) + S2I = S2I*CSSR(IFLAG) + CSR = CSRR(IFLAG) + 290 CONTINUE + RETURN + 300 CONTINUE + NZ = -1 + RETURN +END + +SUBROUTINE ZUNK2(ZR, ZI, FNU, KODE, MR, N, YR, YI, NZ, TOL, ELIM, ALIM) +USE UTILIT +USE COMPLEX +!***BEGIN PROLOGUE ZUNK2 +!***REFER TO ZBESK +! +! ZUNK2 COMPUTES K(FNU,Z) AND ITS ANALYTIC CONTINUATION FROM THE +! RIGHT HALF PLANE TO THE LEFT HALF PLANE BY MEANS OF THE +! UNIFORM ASYMPTOTIC EXPANSIONS FOR H(KIND,FNU,ZN) AND J(FNU,ZN) +! WHERE ZN IS IN THE RIGHT HALF PLANE, KIND=(3-MR)/2, MR=+1 OR +! -1. HERE ZN=ZR*I OR -ZR*I WHERE ZR=Z IF Z IS IN THE RIGHT +! HALF PLANE OR ZR=-Z IF Z IS IN THE LEFT HALF PLANE. MR INDIC- +! ATES THE DIRECTION OF ROTATION FOR ANALYTIC CONTINUATION. +! NZ=-1 MEANS AN OVERFLOW WILL OCCUR +! +!***ROUTINES CALLED ZAIRY,ZKSCL,ZS1S2,ZUCHK,ZUNHJ,D1MACH,ZABS +!***END PROLOGUE ZUNK2 +! COMPLEX AI,ARG,ARGD,ASUM,ASUMD,BSUM,BSUMD,CFN,CI,CIP,CK,CONE,CRSC, +! *CR1,CR2,CS,CSCL,CSGN,CSPN,CSR,CSS,CY,CZERO,C1,C2,DAI,PHI,PHID,RZ, +! *S1,S2,Y,Z,ZB,ZETA1,ZETA1D,ZETA2,ZETA2D,ZN,ZR + DOUBLE PRECISION AARG, AIC, AII, AIR, ALIM, ANG, APHI, ARGDI, & + ARGDR, ARGI, ARGR, ASC, ASCLE, ASUMDI, ASUMDR, ASUMI, ASUMR, & + BRY, BSUMDI, BSUMDR, BSUMI, BSUMR, CAR, CIPI, CIPR, CKI, CKR, & + CONEI, CONER, CRSC, CR1I, CR1R, CR2I, CR2R, CSCL, CSGNI, CSI, & + CSPNI, CSPNR, CSR, CSRR, CSSR, CYI, CYR, C1I, C1R, C2I, C2M, & + C2R, DAII, DAIR, ELIM, FMR, FN, FNF, FNU, HPI, PHIDI, PHIDR, & + PHII, PHIR, PI, PTI, PTR, RAST, RAZR, RS1, RZI, RZR, SAR, SGN, & + STI, STR, S1I, S1R, S2I, S2R, TOL, YI, YR, YY, ZBI, ZBR, ZEROI, & + ZEROR, ZETA1I, ZETA1R, ZETA2I, ZETA2R, ZET1DI, ZET1DR, ZET2DI, & + ZET2DR, ZI, ZNI, ZNR, ZR, ZRI, ZRR + INTEGER I, IB, IFLAG, IFN, IL, IN, INU, IUF, K, KDFLG, KFLAG, KK, & + KODE, MR, N, NAI, NDAI, NW, NZ, IDUM, J, IPARD, IC + DIMENSION BRY(3), YR(1), YI(1), ASUMR(2), ASUMI(2), BSUMR(2), & + BSUMI(2), PHIR(2), PHII(2), ARGR(2), ARGI(2), ZETA1R(2), & + ZETA1I(2), ZETA2R(2), ZETA2I(2), CYR(2), CYI(2), CIPR(4), & + CIPI(4), CSSR(3), CSRR(3) + DATA ZEROR,ZEROI,CONER,CONEI,CR1R,CR1I,CR2R,CR2I / & + 0.0D0, 0.0D0, 1.0D0, 0.0D0, & + 1.0D0,1.73205080756887729D0 , -0.5D0,-8.66025403784438647D-01 / + DATA HPI, PI, AIC / & + 1.57079632679489662D+00, 3.14159265358979324D+00, & + 1.26551212348464539D+00/ + DATA CIPR(1),CIPI(1),CIPR(2),CIPI(2),CIPR(3),CIPI(3),CIPR(4), & + CIPI(4) / & + 1.0D0,0.0D0 , 0.0D0,-1.0D0 , -1.0D0,0.0D0 , 0.0D0,1.0D0 / + + KDFLG = 1 + NZ = 0 +!----------------------------------------------------------------------- +! EXP(-ALIM)=EXP(-ELIM)/TOL=APPROX. ONE PRECISION GREATER THAN +! THE UNDERFLOW LIMIT +!----------------------------------------------------------------------- + CSCL = 1.0D0/TOL + CRSC = TOL + CSSR(1) = CSCL + CSSR(2) = CONER + CSSR(3) = CRSC + CSRR(1) = CRSC + CSRR(2) = CONER + CSRR(3) = CSCL + BRY(1) = 1.0D+3*D1MACH(1)/TOL + BRY(2) = 1.0D0/BRY(1) + BRY(3) = D1MACH(2) + ZRR = ZR + ZRI = ZI + IF (ZR.GE.0.0D0) GO TO 10 + ZRR = -ZR + ZRI = -ZI + 10 CONTINUE + YY = ZRI + ZNR = ZRI + ZNI = -ZRR + ZBR = ZRR + ZBI = ZRI + INU = INT(SNGL(FNU)) + FNF = FNU - DBLE(FLOAT(INU)) + ANG = -HPI*FNF + CAR = DCOS(ANG) + SAR = DSIN(ANG) + C2R = HPI*SAR + C2I = -HPI*CAR + KK = MOD(INU,4) + 1 + STR = C2R*CIPR(KK) - C2I*CIPI(KK) + STI = C2R*CIPI(KK) + C2I*CIPR(KK) + CSR = CR1R*STR - CR1I*STI + CSI = CR1R*STI + CR1I*STR + IF (YY.GT.0.0D0) GO TO 20 + ZNR = -ZNR + ZBI = -ZBI + 20 CONTINUE +!----------------------------------------------------------------------- +! K(FNU,Z) IS COMPUTED FROM H(2,FNU,-I*Z) WHERE Z IS IN THE FIRST +! QUADRANT. FOURTH QUADRANT VALUES (YY.LE.0.0E0) ARE COMPUTED BY +! CONJUGATION SINCE THE K FUNCTION IS REAL ON THE POSITIVE REAL AXIS +!----------------------------------------------------------------------- + J = 2 + DO 80 I=1,N +!----------------------------------------------------------------------- +! J FLIP FLOPS BETWEEN 1 AND 2 IN J = 3 - J +!----------------------------------------------------------------------- + J = 3 - J + FN = FNU + DBLE(FLOAT(I-1)) + CALL ZUNHJ(ZNR, ZNI, FN, 0, TOL, PHIR(J), PHII(J), ARGR(J), & + ARGI(J), ZETA1R(J), ZETA1I(J), ZETA2R(J), ZETA2I(J), ASUMR(J), & + ASUMI(J), BSUMR(J), BSUMI(J)) + IF (KODE.EQ.1) GO TO 30 + STR = ZBR + ZETA2R(J) + STI = ZBI + ZETA2I(J) + RAST = FN/ZABS(STR,STI) + STR = STR*RAST*RAST + STI = -STI*RAST*RAST + S1R = ZETA1R(J) - STR + S1I = ZETA1I(J) - STI + GO TO 40 + 30 CONTINUE + S1R = ZETA1R(J) - ZETA2R(J) + S1I = ZETA1I(J) - ZETA2I(J) + 40 CONTINUE +!----------------------------------------------------------------------- +! TEST FOR UNDERFLOW AND OVERFLOW +!----------------------------------------------------------------------- + RS1 = S1R + IF (DABS(RS1).GT.ELIM) GO TO 70 + IF (KDFLG.EQ.1) KFLAG = 2 + IF (DABS(RS1).LT.ALIM) GO TO 50 +!----------------------------------------------------------------------- +! REFINE TEST AND SCALE +!----------------------------------------------------------------------- + APHI = ZABS(PHIR(J),PHII(J)) + AARG = ZABS(ARGR(J),ARGI(J)) + RS1 = RS1 + DLOG(APHI) - 0.25D0*DLOG(AARG) - AIC + IF (DABS(RS1).GT.ELIM) GO TO 70 + IF (KDFLG.EQ.1) KFLAG = 1 + IF (RS1.LT.0.0D0) GO TO 50 + IF (KDFLG.EQ.1) KFLAG = 3 + 50 CONTINUE +!----------------------------------------------------------------------- +! SCALE S1 TO KEEP INTERMEDIATE ARITHMETIC ON SCALE NEAR +! EXPONENT EXTREMES +!----------------------------------------------------------------------- + C2R = ARGR(J)*CR2R - ARGI(J)*CR2I + C2I = ARGR(J)*CR2I + ARGI(J)*CR2R + CALL ZAIRY(C2R, C2I, 0, 2, AIR, AII, NAI, IDUM) + CALL ZAIRY(C2R, C2I, 1, 2, DAIR, DAII, NDAI, IDUM) + STR = DAIR*BSUMR(J) - DAII*BSUMI(J) + STI = DAIR*BSUMI(J) + DAII*BSUMR(J) + PTR = STR*CR2R - STI*CR2I + PTI = STR*CR2I + STI*CR2R + STR = PTR + (AIR*ASUMR(J)-AII*ASUMI(J)) + STI = PTI + (AIR*ASUMI(J)+AII*ASUMR(J)) + PTR = STR*PHIR(J) - STI*PHII(J) + PTI = STR*PHII(J) + STI*PHIR(J) + S2R = PTR*CSR - PTI*CSI + S2I = PTR*CSI + PTI*CSR + STR = DEXP(S1R)*CSSR(KFLAG) + S1R = STR*DCOS(S1I) + S1I = STR*DSIN(S1I) + STR = S2R*S1R - S2I*S1I + S2I = S1R*S2I + S2R*S1I + S2R = STR + IF (KFLAG.NE.1) GO TO 60 + CALL ZUCHK(S2R, S2I, NW, BRY(1), TOL) + IF (NW.NE.0) GO TO 70 + 60 CONTINUE + IF (YY.LE.0.0D0) S2I = -S2I + CYR(KDFLG) = S2R + CYI(KDFLG) = S2I + YR(I) = S2R*CSRR(KFLAG) + YI(I) = S2I*CSRR(KFLAG) + STR = CSI + CSI = -CSR + CSR = STR + IF (KDFLG.EQ.2) GO TO 85 + KDFLG = 2 + GO TO 80 + 70 CONTINUE + IF (RS1.GT.0.0D0) GO TO 320 +!----------------------------------------------------------------------- +! FOR ZR.LT.0.0, THE I FUNCTION TO BE ADDED WILL OVERFLOW +!----------------------------------------------------------------------- + IF (ZR.LT.0.0D0) GO TO 320 + KDFLG = 1 + YR(I)=ZEROR + YI(I)=ZEROI + NZ=NZ+1 + STR = CSI + CSI =-CSR + CSR = STR + IF (I.EQ.1) GO TO 80 + IF ((YR(I-1).EQ.ZEROR).AND.(YI(I-1).EQ.ZEROI)) GO TO 80 + YR(I-1)=ZEROR + YI(I-1)=ZEROI + NZ=NZ+1 + 80 CONTINUE + I = N + 85 CONTINUE + RAZR = 1.0D0/ZABS(ZRR,ZRI) + STR = ZRR*RAZR + STI = -ZRI*RAZR + RZR = (STR+STR)*RAZR + RZI = (STI+STI)*RAZR + CKR = FN*RZR + CKI = FN*RZI + IB = I + 1 + IF (N.LT.IB) GO TO 180 +!----------------------------------------------------------------------- +! TEST LAST MEMBER FOR UNDERFLOW AND OVERFLOW. SET SEQUENCE TO ZERO +! ON UNDERFLOW. +!----------------------------------------------------------------------- + FN = FNU + DBLE(FLOAT(N-1)) + IPARD = 1 + IF (MR.NE.0) IPARD = 0 + CALL ZUNHJ(ZNR, ZNI, FN, IPARD, TOL, PHIDR, PHIDI, ARGDR, ARGDI, & + ZET1DR, ZET1DI, ZET2DR, ZET2DI, ASUMDR, ASUMDI, BSUMDR, BSUMDI) + IF (KODE.EQ.1) GO TO 90 + STR = ZBR + ZET2DR + STI = ZBI + ZET2DI + RAST = FN/ZABS(STR,STI) + STR = STR*RAST*RAST + STI = -STI*RAST*RAST + S1R = ZET1DR - STR + S1I = ZET1DI - STI + GO TO 100 + 90 CONTINUE + S1R = ZET1DR - ZET2DR + S1I = ZET1DI - ZET2DI + 100 CONTINUE + RS1 = S1R + IF (DABS(RS1).GT.ELIM) GO TO 105 + IF (DABS(RS1).LT.ALIM) GO TO 120 +!----------------------------------------------------------------------- +! REFINE ESTIMATE AND TEST +!----------------------------------------------------------------------- + APHI = ZABS(PHIDR,PHIDI) + RS1 = RS1+DLOG(APHI) + IF (DABS(RS1).LT.ELIM) GO TO 120 + 105 CONTINUE + IF (RS1.GT.0.0D0) GO TO 320 +!----------------------------------------------------------------------- +! FOR ZR.LT.0.0, THE I FUNCTION TO BE ADDED WILL OVERFLOW +!----------------------------------------------------------------------- + IF (ZR.LT.0.0D0) GO TO 320 + NZ = N + DO 106 I=1,N + YR(I) = ZEROR + YI(I) = ZEROI + 106 CONTINUE + RETURN + 120 CONTINUE + S1R = CYR(1) + S1I = CYI(1) + S2R = CYR(2) + S2I = CYI(2) + C1R = CSRR(KFLAG) + ASCLE = BRY(KFLAG) + DO 130 I=IB,N + C2R = S2R + C2I = S2I + S2R = CKR*C2R - CKI*C2I + S1R + S2I = CKR*C2I + CKI*C2R + S1I + S1R = C2R + S1I = C2I + CKR = CKR + RZR + CKI = CKI + RZI + C2R = S2R*C1R + C2I = S2I*C1R + YR(I) = C2R + YI(I) = C2I + IF (KFLAG.GE.3) GO TO 130 + STR = DABS(C2R) + STI = DABS(C2I) + C2M = DMAX1(STR,STI) + IF (C2M.LE.ASCLE) GO TO 130 + KFLAG = KFLAG + 1 + ASCLE = BRY(KFLAG) + S1R = S1R*C1R + S1I = S1I*C1R + S2R = C2R + S2I = C2I + S1R = S1R*CSSR(KFLAG) + S1I = S1I*CSSR(KFLAG) + S2R = S2R*CSSR(KFLAG) + S2I = S2I*CSSR(KFLAG) + C1R = CSRR(KFLAG) + 130 CONTINUE + 180 CONTINUE + IF (MR.EQ.0) RETURN +!----------------------------------------------------------------------- +! ANALYTIC CONTINUATION FOR RE(Z).LT.0.0D0 +!----------------------------------------------------------------------- + NZ = 0 + FMR = DBLE(FLOAT(MR)) + SGN = -DSIGN(PI,FMR) +!----------------------------------------------------------------------- +! CSPN AND CSGN ARE COEFF OF K AND I FUNCIONS RESP. +!----------------------------------------------------------------------- + CSGNI = SGN + IF (YY.LE.0.0D0) CSGNI = -CSGNI + IFN = INU + N - 1 + ANG = FNF*SGN + CSPNR = DCOS(ANG) + CSPNI = DSIN(ANG) + IF (MOD(IFN,2).EQ.0) GO TO 190 + CSPNR = -CSPNR + CSPNI = -CSPNI + 190 CONTINUE +!----------------------------------------------------------------------- +! CS=COEFF OF THE J FUNCTION TO GET THE I FUNCTION. I(FNU,Z) IS +! COMPUTED FROM EXP(I*FNU*HPI)*J(FNU,-I*Z) WHERE Z IS IN THE FIRST +! QUADRANT. FOURTH QUADRANT VALUES (YY.LE.0.0E0) ARE COMPUTED BY +! CONJUGATION SINCE THE I FUNCTION IS REAL ON THE POSITIVE REAL AXIS +!----------------------------------------------------------------------- + CSR = SAR*CSGNI + CSI = CAR*CSGNI + IN = MOD(IFN,4) + 1 + C2R = CIPR(IN) + C2I = CIPI(IN) + STR = CSR*C2R + CSI*C2I + CSI = -CSR*C2I + CSI*C2R + CSR = STR + ASC = BRY(1) + IUF = 0 + KK = N + KDFLG = 1 + IB = IB - 1 + IC = IB - 1 + DO 290 K=1,N + FN = FNU + DBLE(FLOAT(KK-1)) +!----------------------------------------------------------------------- +! LOGIC TO SORT OUT CASES WHOSE PARAMETERS WERE SET FOR THE K +! FUNCTION ABOVE +!----------------------------------------------------------------------- + IF (N.GT.2) GO TO 175 + 172 CONTINUE + PHIDR = PHIR(J) + PHIDI = PHII(J) + ARGDR = ARGR(J) + ARGDI = ARGI(J) + ZET1DR = ZETA1R(J) + ZET1DI = ZETA1I(J) + ZET2DR = ZETA2R(J) + ZET2DI = ZETA2I(J) + ASUMDR = ASUMR(J) + ASUMDI = ASUMI(J) + BSUMDR = BSUMR(J) + BSUMDI = BSUMI(J) + J = 3 - J + GO TO 210 + 175 CONTINUE + IF ((KK.EQ.N).AND.(IB.LT.N)) GO TO 210 + IF ((KK.EQ.IB).OR.(KK.EQ.IC)) GO TO 172 + CALL ZUNHJ(ZNR, ZNI, FN, 0, TOL, PHIDR, PHIDI, ARGDR, & + ARGDI, ZET1DR, ZET1DI, ZET2DR, ZET2DI, ASUMDR, & + ASUMDI, BSUMDR, BSUMDI) + 210 CONTINUE + IF (KODE.EQ.1) GO TO 220 + STR = ZBR + ZET2DR + STI = ZBI + ZET2DI + RAST = FN/ZABS(STR,STI) + STR = STR*RAST*RAST + STI = -STI*RAST*RAST + S1R = -ZET1DR + STR + S1I = -ZET1DI + STI + GO TO 230 + 220 CONTINUE + S1R = -ZET1DR + ZET2DR + S1I = -ZET1DI + ZET2DI + 230 CONTINUE +!----------------------------------------------------------------------- +! TEST FOR UNDERFLOW AND OVERFLOW +!----------------------------------------------------------------------- + RS1 = S1R + IF (DABS(RS1).GT.ELIM) GO TO 280 + IF (KDFLG.EQ.1) IFLAG = 2 + IF (DABS(RS1).LT.ALIM) GO TO 240 +!----------------------------------------------------------------------- +! REFINE TEST AND SCALE +!----------------------------------------------------------------------- + APHI = ZABS(PHIDR,PHIDI) + AARG = ZABS(ARGDR,ARGDI) + RS1 = RS1 + DLOG(APHI) - 0.25D0*DLOG(AARG) - AIC + IF (DABS(RS1).GT.ELIM) GO TO 280 + IF (KDFLG.EQ.1) IFLAG = 1 + IF (RS1.LT.0.0D0) GO TO 240 + IF (KDFLG.EQ.1) IFLAG = 3 + 240 CONTINUE + CALL ZAIRY(ARGDR, ARGDI, 0, 2, AIR, AII, NAI, IDUM) + CALL ZAIRY(ARGDR, ARGDI, 1, 2, DAIR, DAII, NDAI, IDUM) + STR = DAIR*BSUMDR - DAII*BSUMDI + STI = DAIR*BSUMDI + DAII*BSUMDR + STR = STR + (AIR*ASUMDR-AII*ASUMDI) + STI = STI + (AIR*ASUMDI+AII*ASUMDR) + PTR = STR*PHIDR - STI*PHIDI + PTI = STR*PHIDI + STI*PHIDR + S2R = PTR*CSR - PTI*CSI + S2I = PTR*CSI + PTI*CSR + STR = DEXP(S1R)*CSSR(IFLAG) + S1R = STR*DCOS(S1I) + S1I = STR*DSIN(S1I) + STR = S2R*S1R - S2I*S1I + S2I = S2R*S1I + S2I*S1R + S2R = STR + IF (IFLAG.NE.1) GO TO 250 + CALL ZUCHK(S2R, S2I, NW, BRY(1), TOL) + IF (NW.EQ.0) GO TO 250 + S2R = ZEROR + S2I = ZEROI + 250 CONTINUE + IF (YY.LE.0.0D0) S2I = -S2I + CYR(KDFLG) = S2R + CYI(KDFLG) = S2I + C2R = S2R + C2I = S2I + S2R = S2R*CSRR(IFLAG) + S2I = S2I*CSRR(IFLAG) +!----------------------------------------------------------------------- +! ADD I AND K FUNCTIONS, K SEQUENCE IN Y(I), I=1,N +!----------------------------------------------------------------------- + S1R = YR(KK) + S1I = YI(KK) + IF (KODE.EQ.1) GO TO 270 + CALL ZS1S2(ZRR, ZRI, S1R, S1I, S2R, S2I, NW, ASC, ALIM, IUF) + NZ = NZ + NW + 270 CONTINUE + YR(KK) = S1R*CSPNR - S1I*CSPNI + S2R + YI(KK) = S1R*CSPNI + S1I*CSPNR + S2I + KK = KK - 1 + CSPNR = -CSPNR + CSPNI = -CSPNI + STR = CSI + CSI = -CSR + CSR = STR + IF (C2R.NE.0.0D0 .OR. C2I.NE.0.0D0) GO TO 255 + KDFLG = 1 + GO TO 290 + 255 CONTINUE + IF (KDFLG.EQ.2) GO TO 295 + KDFLG = 2 + GO TO 290 + 280 CONTINUE + IF (RS1.GT.0.0D0) GO TO 320 + S2R = ZEROR + S2I = ZEROI + GO TO 250 + 290 CONTINUE + K = N + 295 CONTINUE + IL = N - K + IF (IL.EQ.0) RETURN +!----------------------------------------------------------------------- +! RECUR BACKWARD FOR REMAINDER OF I SEQUENCE AND ADD IN THE +! K FUNCTIONS, SCALING THE I SEQUENCE DURING RECURRENCE TO KEEP +! INTERMEDIATE ARITHMETIC ON SCALE NEAR EXPONENT EXTREMES. +!----------------------------------------------------------------------- + S1R = CYR(1) + S1I = CYI(1) + S2R = CYR(2) + S2I = CYI(2) + CSR = CSRR(IFLAG) + ASCLE = BRY(IFLAG) + FN = DBLE(FLOAT(INU+IL)) + DO 310 I=1,IL + C2R = S2R + C2I = S2I + S2R = S1R + (FN+FNF)*(RZR*C2R-RZI*C2I) + S2I = S1I + (FN+FNF)*(RZR*C2I+RZI*C2R) + S1R = C2R + S1I = C2I + FN = FN - 1.0D0 + C2R = S2R*CSR + C2I = S2I*CSR + CKR = C2R + CKI = C2I + C1R = YR(KK) + C1I = YI(KK) + IF (KODE.EQ.1) GO TO 300 + CALL ZS1S2(ZRR, ZRI, C1R, C1I, C2R, C2I, NW, ASC, ALIM, IUF) + NZ = NZ + NW + 300 CONTINUE + YR(KK) = C1R*CSPNR - C1I*CSPNI + C2R + YI(KK) = C1R*CSPNI + C1I*CSPNR + C2I + KK = KK - 1 + CSPNR = -CSPNR + CSPNI = -CSPNI + IF (IFLAG.GE.3) GO TO 310 + C2R = DABS(CKR) + C2I = DABS(CKI) + C2M = DMAX1(C2R,C2I) + IF (C2M.LE.ASCLE) GO TO 310 + IFLAG = IFLAG + 1 + ASCLE = BRY(IFLAG) + S1R = S1R*CSR + S1I = S1I*CSR + S2R = CKR + S2I = CKI + S1R = S1R*CSSR(IFLAG) + S1I = S1I*CSSR(IFLAG) + S2R = S2R*CSSR(IFLAG) + S2I = S2I*CSSR(IFLAG) + CSR = CSRR(IFLAG) + 310 CONTINUE + RETURN + 320 CONTINUE + NZ = -1 + RETURN +END + +SUBROUTINE ZUNHJ(ZR, ZI, FNU, IPMTR, TOL, PHIR, PHII, ARGR, ARGI, & + ZETA1R, ZETA1I, ZETA2R, ZETA2I, ASUMR, ASUMI, BSUMR, BSUMI) +USE COMPLEX +!***BEGIN PROLOGUE ZUNHJ +!***REFER TO ZBESI,ZBESK +! +! REFERENCES +! HANDBOOK OF MATHEMATICAL FUNCTIONS BY M. ABRAMOWITZ AND I.A. +! STEGUN, AMS55, NATIONAL BUREAU OF STANDARDS, 1965, CHAPTER 9. +! +! ASYMPTOTICS AND SPECIAL FUNCTIONS BY F.W.J. OLVER, ACADEMIC +! PRESS, N.Y., 1974, PAGE 420 +! +! ABSTRACT +! ZUNHJ COMPUTES PARAMETERS FOR BESSEL FUNCTIONS C(FNU,Z) = +! J(FNU,Z), Y(FNU,Z) OR H(I,FNU,Z) I=1,2 FOR LARGE ORDERS FNU +! BY MEANS OF THE UNIFORM ASYMPTOTIC EXPANSION +! +! C(FNU,Z)=C1*PHI*( ASUM*AIRY(ARG) + C2*BSUM*DAIRY(ARG) ) +! +! FOR PROPER CHOICES OF C1, C2, AIRY AND DAIRY WHERE AIRY IS +! AN AIRY FUNCTION AND DAIRY IS ITS DERIVATIVE. +! +! (2/3)*FNU*ZETA**1.5 = ZETA1-ZETA2, +! +! ZETA1=0.5*FNU*CLOG((1+W)/(1-W)), ZETA2=FNU*W FOR SCALING +! PURPOSES IN AIRY FUNCTIONS FROM CAIRY OR CBIRY. +! +! MCONJ=SIGN OF AIMAG(Z), BUT IS AMBIGUOUS WHEN Z IS REAL AND +! MUST BE SPECIFIED. IPMTR=0 RETURNS ALL PARAMETERS. IPMTR= +! 1 COMPUTES ALL EXCEPT ASUM AND BSUM. +! +!***ROUTINES CALLED ZABS,ZDIV,ZLOG,ZSQRT +!***END PROLOGUE ZUNHJ +! COMPLEX ARG,ASUM,BSUM,CFNU,CONE,CR,CZERO,DR,P,PHI,PRZTH,PTFN, +! *RFN13,RTZTA,RZTH,SUMA,SUMB,TFN,T2,UP,W,W2,Z,ZA,ZB,ZC,ZETA,ZETA1, +! *ZETA2,ZTH + DOUBLE PRECISION ALFA, ANG, AP, AR, ARGI, ARGR, ASUMI, ASUMR, & + ATOL, AW2, AZTH, BETA, BR, BSUMI, BSUMR, BTOL, C, CONEI, CONER, & + CRI, CRR, DRI, DRR, EX1, EX2, FNU, FN13, FN23, GAMA, GPI, HPI, & + PHII, PHIR, PI, PP, PR, PRZTHI, PRZTHR, PTFNI, PTFNR, RAW, RAW2, & + RAZTH, RFNU, RFNU2, RFN13, RTZTI, RTZTR, RZTHI, RZTHR, STI, STR, & + SUMAI, SUMAR, SUMBI, SUMBR, TEST, TFNI, TFNR, THPI, TOL, TZAI, & + TZAR, T2I, T2R, UPI, UPR, WI, WR, W2I, W2R, ZAI, ZAR, ZBI, ZBR, & + ZCI, ZCR, ZEROI, ZEROR, ZETAI, ZETAR, ZETA1I, ZETA1R, ZETA2I, & + ZETA2R, ZI, ZR, ZTHI, ZTHR + INTEGER IAS, IBS, IPMTR, IS, J, JR, JU, K, KMAX, KP1, KS, L, LR, & + LRP1, L1, L2, M, IDUM + DIMENSION AR(14), BR(14), C(105), ALFA(180), BETA(210), GAMA(30), & + AP(30), PR(30), PI(30), UPR(14), UPI(14), CRR(14), CRI(14), & + DRR(14), DRI(14) + DATA AR(1), AR(2), AR(3), AR(4), AR(5), AR(6), AR(7), AR(8), & + AR(9), AR(10), AR(11), AR(12), AR(13), AR(14)/ & + 1.00000000000000000D+00, 1.04166666666666667D-01, & + 8.35503472222222222D-02, 1.28226574556327160D-01, & + 2.91849026464140464D-01, 8.81627267443757652D-01, & + 3.32140828186276754D+00, 1.49957629868625547D+01, & + 7.89230130115865181D+01, 4.74451538868264323D+02, & + 3.20749009089066193D+03, 2.40865496408740049D+04, & + 1.98923119169509794D+05, 1.79190200777534383D+06/ + DATA BR(1), BR(2), BR(3), BR(4), BR(5), BR(6), BR(7), BR(8), & + BR(9), BR(10), BR(11), BR(12), BR(13), BR(14)/ & + 1.00000000000000000D+00, -1.45833333333333333D-01, & + -9.87413194444444444D-02, -1.43312053915895062D-01, & + -3.17227202678413548D-01, -9.42429147957120249D-01, & + -3.51120304082635426D+00, -1.57272636203680451D+01, & + -8.22814390971859444D+01, -4.92355370523670524D+02, & + -3.31621856854797251D+03, -2.48276742452085896D+04, & + -2.04526587315129788D+05, -1.83844491706820990D+06/ + DATA C(1), C(2), C(3), C(4), C(5), C(6), C(7), C(8), C(9), C(10), & + C(11), C(12), C(13), C(14), C(15), C(16), C(17), C(18), & + C(19), C(20), C(21), C(22), C(23), C(24)/ & + 1.00000000000000000D+00, -2.08333333333333333D-01, & + 1.25000000000000000D-01, 3.34201388888888889D-01, & + -4.01041666666666667D-01, 7.03125000000000000D-02, & + -1.02581259645061728D+00, 1.84646267361111111D+00, & + -8.91210937500000000D-01, 7.32421875000000000D-02, & + 4.66958442342624743D+00, -1.12070026162229938D+01, & + 8.78912353515625000D+00, -2.36408691406250000D+00, & + 1.12152099609375000D-01, -2.82120725582002449D+01, & + 8.46362176746007346D+01, -9.18182415432400174D+01, & + 4.25349987453884549D+01, -7.36879435947963170D+00, & + 2.27108001708984375D-01, 2.12570130039217123D+02, & + -7.65252468141181642D+02, 1.05999045252799988D+03/ + DATA C(25), C(26), C(27), C(28), C(29), C(30), C(31), C(32), & + C(33), C(34), C(35), C(36), C(37), C(38), C(39), C(40), & + C(41), C(42), C(43), C(44), C(45), C(46), C(47), C(48)/ & + -6.99579627376132541D+02, 2.18190511744211590D+02, & + -2.64914304869515555D+01, 5.72501420974731445D-01, & + -1.91945766231840700D+03, 8.06172218173730938D+03, & + -1.35865500064341374D+04, 1.16553933368645332D+04, & + -5.30564697861340311D+03, 1.20090291321635246D+03, & + -1.08090919788394656D+02, 1.72772750258445740D+00, & + 2.02042913309661486D+04, -9.69805983886375135D+04, & + 1.92547001232531532D+05, -2.03400177280415534D+05, & + 1.22200464983017460D+05, -4.11926549688975513D+04, & + 7.10951430248936372D+03, -4.93915304773088012D+02, & + 6.07404200127348304D+00, -2.42919187900551333D+05, & + 1.31176361466297720D+06, -2.99801591853810675D+06/ + DATA C(49), C(50), C(51), C(52), C(53), C(54), C(55), C(56), & + C(57), C(58), C(59), C(60), C(61), C(62), C(63), C(64), & + C(65), C(66), C(67), C(68), C(69), C(70), C(71), C(72)/ & + 3.76327129765640400D+06, -2.81356322658653411D+06, & + 1.26836527332162478D+06, -3.31645172484563578D+05, & + 4.52187689813627263D+04, -2.49983048181120962D+03, & + 2.43805296995560639D+01, 3.28446985307203782D+06, & + -1.97068191184322269D+07, 5.09526024926646422D+07, & + -7.41051482115326577D+07, 6.63445122747290267D+07, & + -3.75671766607633513D+07, 1.32887671664218183D+07, & + -2.78561812808645469D+06, 3.08186404612662398D+05, & + -1.38860897537170405D+04, 1.10017140269246738D+02, & + -4.93292536645099620D+07, 3.25573074185765749D+08, & + -9.39462359681578403D+08, 1.55359689957058006D+09, & + -1.62108055210833708D+09, 1.10684281682301447D+09/ + DATA C(73), C(74), C(75), C(76), C(77), C(78), C(79), C(80), & + C(81), C(82), C(83), C(84), C(85), C(86), C(87), C(88), & + C(89), C(90), C(91), C(92), C(93), C(94), C(95), C(96)/ & + -4.95889784275030309D+08, 1.42062907797533095D+08, & + -2.44740627257387285D+07, 2.24376817792244943D+06, & + -8.40054336030240853D+04, 5.51335896122020586D+02, & + 8.14789096118312115D+08, -5.86648149205184723D+09, & + 1.86882075092958249D+10, -3.46320433881587779D+10, & + 4.12801855797539740D+10, -3.30265997498007231D+10, & + 1.79542137311556001D+10, -6.56329379261928433D+09, & + 1.55927986487925751D+09, -2.25105661889415278D+08, & + 1.73951075539781645D+07, -5.49842327572288687D+05, & + 3.03809051092238427D+03, -1.46792612476956167D+10, & + 1.14498237732025810D+11, -3.99096175224466498D+11, & + 8.19218669548577329D+11, -1.09837515608122331D+12/ + DATA C(97), C(98), C(99), C(100), C(101), C(102), C(103), C(104), & + C(105)/ & + 1.00815810686538209D+12, -6.45364869245376503D+11, & + 2.87900649906150589D+11, -8.78670721780232657D+10, & + 1.76347306068349694D+10, -2.16716498322379509D+09, & + 1.43157876718888981D+08, -3.87183344257261262D+06, & + 1.82577554742931747D+04/ + DATA ALFA(1), ALFA(2), ALFA(3), ALFA(4), ALFA(5), ALFA(6), & + ALFA(7), ALFA(8), ALFA(9), ALFA(10), ALFA(11), ALFA(12), & + ALFA(13), ALFA(14), ALFA(15), ALFA(16), ALFA(17), ALFA(18), & + ALFA(19), ALFA(20), ALFA(21), ALFA(22)/ & + -4.44444444444444444D-03, -9.22077922077922078D-04, & + -8.84892884892884893D-05, 1.65927687832449737D-04, & + 2.46691372741792910D-04, 2.65995589346254780D-04, & + 2.61824297061500945D-04, 2.48730437344655609D-04, & + 2.32721040083232098D-04, 2.16362485712365082D-04, & + 2.00738858762752355D-04, 1.86267636637545172D-04, & + 1.73060775917876493D-04, 1.61091705929015752D-04, & + 1.50274774160908134D-04, 1.40503497391269794D-04, & + 1.31668816545922806D-04, 1.23667445598253261D-04, & + 1.16405271474737902D-04, 1.09798298372713369D-04, & + 1.03772410422992823D-04, 9.82626078369363448D-05/ + DATA ALFA(23), ALFA(24), ALFA(25), ALFA(26), ALFA(27), ALFA(28), & + ALFA(29), ALFA(30), ALFA(31), ALFA(32), ALFA(33), ALFA(34), & + ALFA(35), ALFA(36), ALFA(37), ALFA(38), ALFA(39), ALFA(40), & + ALFA(41), ALFA(42), ALFA(43), ALFA(44)/ & + 9.32120517249503256D-05, 8.85710852478711718D-05, & + 8.42963105715700223D-05, 8.03497548407791151D-05, & + 7.66981345359207388D-05, 7.33122157481777809D-05, & + 7.01662625163141333D-05, 6.72375633790160292D-05, & + 6.93735541354588974D-04, 2.32241745182921654D-04, & + -1.41986273556691197D-05, -1.16444931672048640D-04, & + -1.50803558053048762D-04, -1.55121924918096223D-04, & + -1.46809756646465549D-04, -1.33815503867491367D-04, & + -1.19744975684254051D-04, -1.06184319207974020D-04, & + -9.37699549891194492D-05, -8.26923045588193274D-05, & + -7.29374348155221211D-05, -6.44042357721016283D-05/ + DATA ALFA(45), ALFA(46), ALFA(47), ALFA(48), ALFA(49), ALFA(50), & + ALFA(51), ALFA(52), ALFA(53), ALFA(54), ALFA(55), ALFA(56), & + ALFA(57), ALFA(58), ALFA(59), ALFA(60), ALFA(61), ALFA(62), & + ALFA(63), ALFA(64), ALFA(65), ALFA(66)/ & + -5.69611566009369048D-05, -5.04731044303561628D-05, & + -4.48134868008882786D-05, -3.98688727717598864D-05, & + -3.55400532972042498D-05, -3.17414256609022480D-05, & + -2.83996793904174811D-05, -2.54522720634870566D-05, & + -2.28459297164724555D-05, -2.05352753106480604D-05, & + -1.84816217627666085D-05, -1.66519330021393806D-05, & + -1.50179412980119482D-05, -1.35554031379040526D-05, & + -1.22434746473858131D-05, -1.10641884811308169D-05, & + -3.54211971457743841D-04, -1.56161263945159416D-04, & + 3.04465503594936410D-05, 1.30198655773242693D-04, & + 1.67471106699712269D-04, 1.70222587683592569D-04/ + DATA ALFA(67), ALFA(68), ALFA(69), ALFA(70), ALFA(71), ALFA(72), & + ALFA(73), ALFA(74), ALFA(75), ALFA(76), ALFA(77), ALFA(78), & + ALFA(79), ALFA(80), ALFA(81), ALFA(82), ALFA(83), ALFA(84), & + ALFA(85), ALFA(86), ALFA(87), ALFA(88)/ & + 1.56501427608594704D-04, 1.36339170977445120D-04, & + 1.14886692029825128D-04, 9.45869093034688111D-05, & + 7.64498419250898258D-05, 6.07570334965197354D-05, & + 4.74394299290508799D-05, 3.62757512005344297D-05, & + 2.69939714979224901D-05, 1.93210938247939253D-05, & + 1.30056674793963203D-05, 7.82620866744496661D-06, & + 3.59257485819351583D-06, 1.44040049814251817D-07, & + -2.65396769697939116D-06, -4.91346867098485910D-06, & + -6.72739296091248287D-06, -8.17269379678657923D-06, & + -9.31304715093561232D-06, -1.02011418798016441D-05, & + -1.08805962510592880D-05, -1.13875481509603555D-05/ + DATA ALFA(89), ALFA(90), ALFA(91), ALFA(92), ALFA(93), ALFA(94), & + ALFA(95), ALFA(96), ALFA(97), ALFA(98), ALFA(99), ALFA(100), & + ALFA(101), ALFA(102), ALFA(103), ALFA(104), ALFA(105), & + ALFA(106), ALFA(107), ALFA(108), ALFA(109), ALFA(110)/ & + -1.17519675674556414D-05, -1.19987364870944141D-05, & + 3.78194199201772914D-04, 2.02471952761816167D-04, & + -6.37938506318862408D-05, -2.38598230603005903D-04, & + -3.10916256027361568D-04, -3.13680115247576316D-04, & + -2.78950273791323387D-04, -2.28564082619141374D-04, & + -1.75245280340846749D-04, -1.25544063060690348D-04, & + -8.22982872820208365D-05, -4.62860730588116458D-05, & + -1.72334302366962267D-05, 5.60690482304602267D-06, & + 2.31395443148286800D-05, 3.62642745856793957D-05, & + 4.58006124490188752D-05, 5.24595294959114050D-05, & + 5.68396208545815266D-05, 5.94349820393104052D-05/ + DATA ALFA(111), ALFA(112), ALFA(113), ALFA(114), ALFA(115), & + ALFA(116), ALFA(117), ALFA(118), ALFA(119), ALFA(120), & + ALFA(121), ALFA(122), ALFA(123), ALFA(124), ALFA(125), & + ALFA(126), ALFA(127), ALFA(128), ALFA(129), ALFA(130)/ & + 6.06478527578421742D-05, 6.08023907788436497D-05, & + 6.01577894539460388D-05, 5.89199657344698500D-05, & + 5.72515823777593053D-05, 5.52804375585852577D-05, & + 5.31063773802880170D-05, 5.08069302012325706D-05, & + 4.84418647620094842D-05, 4.60568581607475370D-05, & + -6.91141397288294174D-04, -4.29976633058871912D-04, & + 1.83067735980039018D-04, 6.60088147542014144D-04, & + 8.75964969951185931D-04, 8.77335235958235514D-04, & + 7.49369585378990637D-04, 5.63832329756980918D-04, & + 3.68059319971443156D-04, 1.88464535514455599D-04/ + DATA ALFA(131), ALFA(132), ALFA(133), ALFA(134), ALFA(135), & + ALFA(136), ALFA(137), ALFA(138), ALFA(139), ALFA(140), & + ALFA(141), ALFA(142), ALFA(143), ALFA(144), ALFA(145), & + ALFA(146), ALFA(147), ALFA(148), ALFA(149), ALFA(150)/ & + 3.70663057664904149D-05, -8.28520220232137023D-05, & + -1.72751952869172998D-04, -2.36314873605872983D-04, & + -2.77966150694906658D-04, -3.02079514155456919D-04, & + -3.12594712643820127D-04, -3.12872558758067163D-04, & + -3.05678038466324377D-04, -2.93226470614557331D-04, & + -2.77255655582934777D-04, -2.59103928467031709D-04, & + -2.39784014396480342D-04, -2.20048260045422848D-04, & + -2.00443911094971498D-04, -1.81358692210970687D-04, & + -1.63057674478657464D-04, -1.45712672175205844D-04, & + -1.29425421983924587D-04, -1.14245691942445952D-04/ + DATA ALFA(151), ALFA(152), ALFA(153), ALFA(154), ALFA(155), & + ALFA(156), ALFA(157), ALFA(158), ALFA(159), ALFA(160), & + ALFA(161), ALFA(162), ALFA(163), ALFA(164), ALFA(165), & + ALFA(166), ALFA(167), ALFA(168), ALFA(169), ALFA(170)/ & + 1.92821964248775885D-03, 1.35592576302022234D-03, & + -7.17858090421302995D-04, -2.58084802575270346D-03, & + -3.49271130826168475D-03, -3.46986299340960628D-03, & + -2.82285233351310182D-03, -1.88103076404891354D-03, & + -8.89531718383947600D-04, 3.87912102631035228D-06, & + 7.28688540119691412D-04, 1.26566373053457758D-03, & + 1.62518158372674427D-03, 1.83203153216373172D-03, & + 1.91588388990527909D-03, 1.90588846755546138D-03, & + 1.82798982421825727D-03, 1.70389506421121530D-03, & + 1.55097127171097686D-03, 1.38261421852276159D-03/ + DATA ALFA(171), ALFA(172), ALFA(173), ALFA(174), ALFA(175), & + ALFA(176), ALFA(177), ALFA(178), ALFA(179), ALFA(180)/ & + 1.20881424230064774D-03, 1.03676532638344962D-03, & + 8.71437918068619115D-04, 7.16080155297701002D-04, & + 5.72637002558129372D-04, 4.42089819465802277D-04, & + 3.24724948503090564D-04, 2.20342042730246599D-04, & + 1.28412898401353882D-04, 4.82005924552095464D-05/ + DATA BETA(1), BETA(2), BETA(3), BETA(4), BETA(5), BETA(6), & + BETA(7), BETA(8), BETA(9), BETA(10), BETA(11), BETA(12), & + BETA(13), BETA(14), BETA(15), BETA(16), BETA(17), BETA(18), & + BETA(19), BETA(20), BETA(21), BETA(22)/ & + 1.79988721413553309D-02, 5.59964911064388073D-03, & + 2.88501402231132779D-03, 1.80096606761053941D-03, & + 1.24753110589199202D-03, 9.22878876572938311D-04, & + 7.14430421727287357D-04, 5.71787281789704872D-04, & + 4.69431007606481533D-04, 3.93232835462916638D-04, & + 3.34818889318297664D-04, 2.88952148495751517D-04, & + 2.52211615549573284D-04, 2.22280580798883327D-04, & + 1.97541838033062524D-04, 1.76836855019718004D-04, & + 1.59316899661821081D-04, 1.44347930197333986D-04, & + 1.31448068119965379D-04, 1.20245444949302884D-04, & + 1.10449144504599392D-04, 1.01828770740567258D-04/ + DATA BETA(23), BETA(24), BETA(25), BETA(26), BETA(27), BETA(28), & + BETA(29), BETA(30), BETA(31), BETA(32), BETA(33), BETA(34), & + BETA(35), BETA(36), BETA(37), BETA(38), BETA(39), BETA(40), & + BETA(41), BETA(42), BETA(43), BETA(44)/ & + 9.41998224204237509D-05, 8.74130545753834437D-05, & + 8.13466262162801467D-05, 7.59002269646219339D-05, & + 7.09906300634153481D-05, 6.65482874842468183D-05, & + 6.25146958969275078D-05, 5.88403394426251749D-05, & + -1.49282953213429172D-03, -8.78204709546389328D-04, & + -5.02916549572034614D-04, -2.94822138512746025D-04, & + -1.75463996970782828D-04, -1.04008550460816434D-04, & + -5.96141953046457895D-05, -3.12038929076098340D-05, & + -1.26089735980230047D-05, -2.42892608575730389D-07, & + 8.05996165414273571D-06, 1.36507009262147391D-05, & + 1.73964125472926261D-05, 1.98672978842133780D-05/ + DATA BETA(45), BETA(46), BETA(47), BETA(48), BETA(49), BETA(50), & + BETA(51), BETA(52), BETA(53), BETA(54), BETA(55), BETA(56), & + BETA(57), BETA(58), BETA(59), BETA(60), BETA(61), BETA(62), & + BETA(63), BETA(64), BETA(65), BETA(66)/ & + 2.14463263790822639D-05, 2.23954659232456514D-05, & + 2.28967783814712629D-05, 2.30785389811177817D-05, & + 2.30321976080909144D-05, 2.28236073720348722D-05, & + 2.25005881105292418D-05, 2.20981015361991429D-05, & + 2.16418427448103905D-05, 2.11507649256220843D-05, & + 2.06388749782170737D-05, 2.01165241997081666D-05, & + 1.95913450141179244D-05, 1.90689367910436740D-05, & + 1.85533719641636667D-05, 1.80475722259674218D-05, & + 5.52213076721292790D-04, 4.47932581552384646D-04, & + 2.79520653992020589D-04, 1.52468156198446602D-04, & + 6.93271105657043598D-05, 1.76258683069991397D-05/ + DATA BETA(67), BETA(68), BETA(69), BETA(70), BETA(71), BETA(72), & + BETA(73), BETA(74), BETA(75), BETA(76), BETA(77), BETA(78), & + BETA(79), BETA(80), BETA(81), BETA(82), BETA(83), BETA(84), & + BETA(85), BETA(86), BETA(87), BETA(88)/ & + -1.35744996343269136D-05, -3.17972413350427135D-05, & + -4.18861861696693365D-05, -4.69004889379141029D-05, & + -4.87665447413787352D-05, -4.87010031186735069D-05, & + -4.74755620890086638D-05, -4.55813058138628452D-05, & + -4.33309644511266036D-05, -4.09230193157750364D-05, & + -3.84822638603221274D-05, -3.60857167535410501D-05, & + -3.37793306123367417D-05, -3.15888560772109621D-05, & + -2.95269561750807315D-05, -2.75978914828335759D-05, & + -2.58006174666883713D-05, -2.41308356761280200D-05, & + -2.25823509518346033D-05, -2.11479656768912971D-05, & + -1.98200638885294927D-05, -1.85909870801065077D-05/ + DATA BETA(89), BETA(90), BETA(91), BETA(92), BETA(93), BETA(94), & + BETA(95), BETA(96), BETA(97), BETA(98), BETA(99), BETA(100), & + BETA(101), BETA(102), BETA(103), BETA(104), BETA(105), & + BETA(106), BETA(107), BETA(108), BETA(109), BETA(110)/ & + -1.74532699844210224D-05, -1.63997823854497997D-05, & + -4.74617796559959808D-04, -4.77864567147321487D-04, & + -3.20390228067037603D-04, -1.61105016119962282D-04, & + -4.25778101285435204D-05, 3.44571294294967503D-05, & + 7.97092684075674924D-05, 1.03138236708272200D-04, & + 1.12466775262204158D-04, 1.13103642108481389D-04, & + 1.08651634848774268D-04, 1.01437951597661973D-04, & + 9.29298396593363896D-05, 8.40293133016089978D-05, & + 7.52727991349134062D-05, 6.69632521975730872D-05, & + 5.92564547323194704D-05, 5.22169308826975567D-05, & + 4.58539485165360646D-05, 4.01445513891486808D-05/ + DATA BETA(111), BETA(112), BETA(113), BETA(114), BETA(115), & + BETA(116), BETA(117), BETA(118), BETA(119), BETA(120), & + BETA(121), BETA(122), BETA(123), BETA(124), BETA(125), & + BETA(126), BETA(127), BETA(128), BETA(129), BETA(130)/ & + 3.50481730031328081D-05, 3.05157995034346659D-05, & + 2.64956119950516039D-05, 2.29363633690998152D-05, & + 1.97893056664021636D-05, 1.70091984636412623D-05, & + 1.45547428261524004D-05, 1.23886640995878413D-05, & + 1.04775876076583236D-05, 8.79179954978479373D-06, & + 7.36465810572578444D-04, 8.72790805146193976D-04, & + 6.22614862573135066D-04, 2.85998154194304147D-04, & + 3.84737672879366102D-06, -1.87906003636971558D-04, & + -2.97603646594554535D-04, -3.45998126832656348D-04, & + -3.53382470916037712D-04, -3.35715635775048757D-04/ + DATA BETA(131), BETA(132), BETA(133), BETA(134), BETA(135), & + BETA(136), BETA(137), BETA(138), BETA(139), BETA(140), & + BETA(141), BETA(142), BETA(143), BETA(144), BETA(145), & + BETA(146), BETA(147), BETA(148), BETA(149), BETA(150)/ & + -3.04321124789039809D-04, -2.66722723047612821D-04, & + -2.27654214122819527D-04, -1.89922611854562356D-04, & + -1.55058918599093870D-04, -1.23778240761873630D-04, & + -9.62926147717644187D-05, -7.25178327714425337D-05, & + -5.22070028895633801D-05, -3.50347750511900522D-05, & + -2.06489761035551757D-05, -8.70106096849767054D-06, & + 1.13698686675100290D-06, 9.16426474122778849D-06, & + 1.56477785428872620D-05, 2.08223629482466847D-05, & + 2.48923381004595156D-05, 2.80340509574146325D-05, & + 3.03987774629861915D-05, 3.21156731406700616D-05/ + DATA BETA(151), BETA(152), BETA(153), BETA(154), BETA(155), & + BETA(156), BETA(157), BETA(158), BETA(159), BETA(160), & + BETA(161), BETA(162), BETA(163), BETA(164), BETA(165), & + BETA(166), BETA(167), BETA(168), BETA(169), BETA(170)/ & + -1.80182191963885708D-03, -2.43402962938042533D-03, & + -1.83422663549856802D-03, -7.62204596354009765D-04, & + 2.39079475256927218D-04, 9.49266117176881141D-04, & + 1.34467449701540359D-03, 1.48457495259449178D-03, & + 1.44732339830617591D-03, 1.30268261285657186D-03, & + 1.10351597375642682D-03, 8.86047440419791759D-04, & + 6.73073208165665473D-04, 4.77603872856582378D-04, & + 3.05991926358789362D-04, 1.60315694594721630D-04, & + 4.00749555270613286D-05, -5.66607461635251611D-05, & + -1.32506186772982638D-04, -1.90296187989614057D-04/ + DATA BETA(171), BETA(172), BETA(173), BETA(174), BETA(175), & + BETA(176), BETA(177), BETA(178), BETA(179), BETA(180), & + BETA(181), BETA(182), BETA(183), BETA(184), BETA(185), & + BETA(186), BETA(187), BETA(188), BETA(189), BETA(190)/ & + -2.32811450376937408D-04, -2.62628811464668841D-04, & + -2.82050469867598672D-04, -2.93081563192861167D-04, & + -2.97435962176316616D-04, -2.96557334239348078D-04, & + -2.91647363312090861D-04, -2.83696203837734166D-04, & + -2.73512317095673346D-04, -2.61750155806768580D-04, & + 6.38585891212050914D-03, 9.62374215806377941D-03, & + 7.61878061207001043D-03, 2.83219055545628054D-03, & + -2.09841352012720090D-03, -5.73826764216626498D-03, & + -7.70804244495414620D-03, -8.21011692264844401D-03, & + -7.65824520346905413D-03, -6.47209729391045177D-03/ + DATA BETA(191), BETA(192), BETA(193), BETA(194), BETA(195), & + BETA(196), BETA(197), BETA(198), BETA(199), BETA(200), & + BETA(201), BETA(202), BETA(203), BETA(204), BETA(205), & + BETA(206), BETA(207), BETA(208), BETA(209), BETA(210)/ & + -4.99132412004966473D-03, -3.45612289713133280D-03, & + -2.01785580014170775D-03, -7.59430686781961401D-04, & + 2.84173631523859138D-04, 1.10891667586337403D-03, & + 1.72901493872728771D-03, 2.16812590802684701D-03, & + 2.45357710494539735D-03, 2.61281821058334862D-03, & + 2.67141039656276912D-03, 2.65203073395980430D-03, & + 2.57411652877287315D-03, 2.45389126236094427D-03, & + 2.30460058071795494D-03, 2.13684837686712662D-03, & + 1.95896528478870911D-03, 1.77737008679454412D-03, & + 1.59690280765839059D-03, 1.42111975664438546D-03/ + DATA GAMA(1), GAMA(2), GAMA(3), GAMA(4), GAMA(5), GAMA(6), & + GAMA(7), GAMA(8), GAMA(9), GAMA(10), GAMA(11), GAMA(12), & + GAMA(13), GAMA(14), GAMA(15), GAMA(16), GAMA(17), GAMA(18), & + GAMA(19), GAMA(20), GAMA(21), GAMA(22)/ & + 6.29960524947436582D-01, 2.51984209978974633D-01, & + 1.54790300415655846D-01, 1.10713062416159013D-01, & + 8.57309395527394825D-02, 6.97161316958684292D-02, & + 5.86085671893713576D-02, 5.04698873536310685D-02, & + 4.42600580689154809D-02, 3.93720661543509966D-02, & + 3.54283195924455368D-02, 3.21818857502098231D-02, & + 2.94646240791157679D-02, 2.71581677112934479D-02, & + 2.51768272973861779D-02, 2.34570755306078891D-02, & + 2.19508390134907203D-02, 2.06210828235646240D-02, & + 1.94388240897880846D-02, 1.83810633800683158D-02, & + 1.74293213231963172D-02, 1.65685837786612353D-02/ + DATA GAMA(23), GAMA(24), GAMA(25), GAMA(26), GAMA(27), GAMA(28), & + GAMA(29), GAMA(30)/ & + 1.57865285987918445D-02, 1.50729501494095594D-02, & + 1.44193250839954639D-02, 1.38184805735341786D-02, & + 1.32643378994276568D-02, 1.27517121970498651D-02, & + 1.22761545318762767D-02, 1.18338262398482403D-02/ + DATA EX1, EX2, HPI, GPI, THPI / & + 3.33333333333333333D-01, 6.66666666666666667D-01, & + 1.57079632679489662D+00, 3.14159265358979324D+00, & + 4.71238898038468986D+00/ + DATA ZEROR,ZEROI,CONER,CONEI / 0.0D0, 0.0D0, 1.0D0, 0.0D0 / + + RFNU = 1.0D0/FNU + ZBR = ZR*RFNU + ZBI = ZI*RFNU + RFNU2 = RFNU*RFNU +!----------------------------------------------------------------------- +! COMPUTE IN THE FOURTH QUADRANT +!----------------------------------------------------------------------- + FN13 = FNU**EX1 + FN23 = FN13*FN13 + RFN13 = 1.0D0/FN13 + W2R = CONER - ZBR*ZBR + ZBI*ZBI + W2I = CONEI - ZBR*ZBI - ZBR*ZBI + AW2 = ZABS(W2R,W2I) + IF (AW2.GT.0.25D0) GO TO 130 +!----------------------------------------------------------------------- +! POWER SERIES FOR CABS(W2).LE.0.25D0 +!----------------------------------------------------------------------- + K = 1 + PR(1) = CONER + PI(1) = CONEI + SUMAR = GAMA(1) + SUMAI = ZEROI + AP(1) = 1.0D0 + IF (AW2.LT.TOL) GO TO 20 + DO 10 K=2,30 + PR(K) = PR(K-1)*W2R - PI(K-1)*W2I + PI(K) = PR(K-1)*W2I + PI(K-1)*W2R + SUMAR = SUMAR + PR(K)*GAMA(K) + SUMAI = SUMAI + PI(K)*GAMA(K) + AP(K) = AP(K-1)*AW2 + IF (AP(K).LT.TOL) GO TO 20 + 10 CONTINUE + K = 30 + 20 CONTINUE + KMAX = K + ZETAR = W2R*SUMAR - W2I*SUMAI + ZETAI = W2R*SUMAI + W2I*SUMAR + ARGR = ZETAR*FN23 + ARGI = ZETAI*FN23 + CALL ZSQRT(SUMAR, SUMAI, ZAR, ZAI) + CALL ZSQRT(W2R, W2I, STR, STI) + ZETA2R = STR*FNU + ZETA2I = STI*FNU + STR = CONER + EX2*(ZETAR*ZAR-ZETAI*ZAI) + STI = CONEI + EX2*(ZETAR*ZAI+ZETAI*ZAR) + ZETA1R = STR*ZETA2R - STI*ZETA2I + ZETA1I = STR*ZETA2I + STI*ZETA2R + ZAR = ZAR + ZAR + ZAI = ZAI + ZAI + CALL ZSQRT(ZAR, ZAI, STR, STI) + PHIR = STR*RFN13 + PHII = STI*RFN13 + IF (IPMTR.EQ.1) GO TO 120 +!----------------------------------------------------------------------- +! SUM SERIES FOR ASUM AND BSUM +!----------------------------------------------------------------------- + SUMBR = ZEROR + SUMBI = ZEROI + DO 30 K=1,KMAX + SUMBR = SUMBR + PR(K)*BETA(K) + SUMBI = SUMBI + PI(K)*BETA(K) + 30 CONTINUE + ASUMR = ZEROR + ASUMI = ZEROI + BSUMR = SUMBR + BSUMI = SUMBI + L1 = 0 + L2 = 30 + BTOL = TOL*(DABS(BSUMR)+DABS(BSUMI)) + ATOL = TOL + PP = 1.0D0 + IAS = 0 + IBS = 0 + IF (RFNU2.LT.TOL) GO TO 110 + DO 100 IS=2,7 + ATOL = ATOL/RFNU2 + PP = PP*RFNU2 + IF (IAS.EQ.1) GO TO 60 + SUMAR = ZEROR + SUMAI = ZEROI + DO 40 K=1,KMAX + M = L1 + K + SUMAR = SUMAR + PR(K)*ALFA(M) + SUMAI = SUMAI + PI(K)*ALFA(M) + IF (AP(K).LT.ATOL) GO TO 50 + 40 CONTINUE + 50 CONTINUE + ASUMR = ASUMR + SUMAR*PP + ASUMI = ASUMI + SUMAI*PP + IF (PP.LT.TOL) IAS = 1 + 60 CONTINUE + IF (IBS.EQ.1) GO TO 90 + SUMBR = ZEROR + SUMBI = ZEROI + DO 70 K=1,KMAX + M = L2 + K + SUMBR = SUMBR + PR(K)*BETA(M) + SUMBI = SUMBI + PI(K)*BETA(M) + IF (AP(K).LT.ATOL) GO TO 80 + 70 CONTINUE + 80 CONTINUE + BSUMR = BSUMR + SUMBR*PP + BSUMI = BSUMI + SUMBI*PP + IF (PP.LT.BTOL) IBS = 1 + 90 CONTINUE + IF (IAS.EQ.1 .AND. IBS.EQ.1) GO TO 110 + L1 = L1 + 30 + L2 = L2 + 30 + 100 CONTINUE + 110 CONTINUE + ASUMR = ASUMR + CONER + PP = RFNU*RFN13 + BSUMR = BSUMR*PP + BSUMI = BSUMI*PP + 120 CONTINUE + RETURN +!----------------------------------------------------------------------- +! CABS(W2).GT.0.25D0 +!----------------------------------------------------------------------- + 130 CONTINUE + CALL ZSQRT(W2R, W2I, WR, WI) + IF (WR.LT.0.0D0) WR = 0.0D0 + IF (WI.LT.0.0D0) WI = 0.0D0 + STR = CONER + WR + STI = WI + CALL ZDIV(STR, STI, ZBR, ZBI, ZAR, ZAI) + CALL ZLOG(ZAR, ZAI, ZCR, ZCI, IDUM) + IF (ZCI.LT.0.0D0) ZCI = 0.0D0 + IF (ZCI.GT.HPI) ZCI = HPI + IF (ZCR.LT.0.0D0) ZCR = 0.0D0 + ZTHR = (ZCR-WR)*1.5D0 + ZTHI = (ZCI-WI)*1.5D0 + ZETA1R = ZCR*FNU + ZETA1I = ZCI*FNU + ZETA2R = WR*FNU + ZETA2I = WI*FNU + AZTH = ZABS(ZTHR,ZTHI) + ANG = THPI + IF (ZTHR.GE.0.0D0 .AND. ZTHI.LT.0.0D0) GO TO 140 + ANG = HPI + IF (ZTHR.EQ.0.0D0) GO TO 140 + ANG = DATAN(ZTHI/ZTHR) + IF (ZTHR.LT.0.0D0) ANG = ANG + GPI + 140 CONTINUE + PP = AZTH**EX2 + ANG = ANG*EX2 + ZETAR = PP*DCOS(ANG) + ZETAI = PP*DSIN(ANG) + IF (ZETAI.LT.0.0D0) ZETAI = 0.0D0 + ARGR = ZETAR*FN23 + ARGI = ZETAI*FN23 + CALL ZDIV(ZTHR, ZTHI, ZETAR, ZETAI, RTZTR, RTZTI) + CALL ZDIV(RTZTR, RTZTI, WR, WI, ZAR, ZAI) + TZAR = ZAR + ZAR + TZAI = ZAI + ZAI + CALL ZSQRT(TZAR, TZAI, STR, STI) + PHIR = STR*RFN13 + PHII = STI*RFN13 + IF (IPMTR.EQ.1) GO TO 120 + RAW = 1.0D0/DSQRT(AW2) + STR = WR*RAW + STI = -WI*RAW + TFNR = STR*RFNU*RAW + TFNI = STI*RFNU*RAW + RAZTH = 1.0D0/AZTH + STR = ZTHR*RAZTH + STI = -ZTHI*RAZTH + RZTHR = STR*RAZTH*RFNU + RZTHI = STI*RAZTH*RFNU + ZCR = RZTHR*AR(2) + ZCI = RZTHI*AR(2) + RAW2 = 1.0D0/AW2 + STR = W2R*RAW2 + STI = -W2I*RAW2 + T2R = STR*RAW2 + T2I = STI*RAW2 + STR = T2R*C(2) + C(3) + STI = T2I*C(2) + UPR(2) = STR*TFNR - STI*TFNI + UPI(2) = STR*TFNI + STI*TFNR + BSUMR = UPR(2) + ZCR + BSUMI = UPI(2) + ZCI + ASUMR = ZEROR + ASUMI = ZEROI + IF (RFNU.LT.TOL) GO TO 220 + PRZTHR = RZTHR + PRZTHI = RZTHI + PTFNR = TFNR + PTFNI = TFNI + UPR(1) = CONER + UPI(1) = CONEI + PP = 1.0D0 + BTOL = TOL*(DABS(BSUMR)+DABS(BSUMI)) + KS = 0 + KP1 = 2 + L = 3 + IAS = 0 + IBS = 0 + DO 210 LR=2,12,2 + LRP1 = LR + 1 +!----------------------------------------------------------------------- +! COMPUTE TWO ADDITIONAL CR, DR, AND UP FOR TWO MORE TERMS IN +! NEXT SUMA AND SUMB +!----------------------------------------------------------------------- + DO 160 K=LR,LRP1 + KS = KS + 1 + KP1 = KP1 + 1 + L = L + 1 + ZAR = C(L) + ZAI = ZEROI + DO 150 J=2,KP1 + L = L + 1 + STR = ZAR*T2R - T2I*ZAI + C(L) + ZAI = ZAR*T2I + ZAI*T2R + ZAR = STR + 150 CONTINUE + STR = PTFNR*TFNR - PTFNI*TFNI + PTFNI = PTFNR*TFNI + PTFNI*TFNR + PTFNR = STR + UPR(KP1) = PTFNR*ZAR - PTFNI*ZAI + UPI(KP1) = PTFNI*ZAR + PTFNR*ZAI + CRR(KS) = PRZTHR*BR(KS+1) + CRI(KS) = PRZTHI*BR(KS+1) + STR = PRZTHR*RZTHR - PRZTHI*RZTHI + PRZTHI = PRZTHR*RZTHI + PRZTHI*RZTHR + PRZTHR = STR + DRR(KS) = PRZTHR*AR(KS+2) + DRI(KS) = PRZTHI*AR(KS+2) + 160 CONTINUE + PP = PP*RFNU2 + IF (IAS.EQ.1) GO TO 180 + SUMAR = UPR(LRP1) + SUMAI = UPI(LRP1) + JU = LRP1 + DO 170 JR=1,LR + JU = JU - 1 + SUMAR = SUMAR + CRR(JR)*UPR(JU) - CRI(JR)*UPI(JU) + SUMAI = SUMAI + CRR(JR)*UPI(JU) + CRI(JR)*UPR(JU) + 170 CONTINUE + ASUMR = ASUMR + SUMAR + ASUMI = ASUMI + SUMAI + TEST = DABS(SUMAR) + DABS(SUMAI) + IF (PP.LT.TOL .AND. TEST.LT.TOL) IAS = 1 + 180 CONTINUE + IF (IBS.EQ.1) GO TO 200 + SUMBR = UPR(LR+2) + UPR(LRP1)*ZCR - UPI(LRP1)*ZCI + SUMBI = UPI(LR+2) + UPR(LRP1)*ZCI + UPI(LRP1)*ZCR + JU = LRP1 + DO 190 JR=1,LR + JU = JU - 1 + SUMBR = SUMBR + DRR(JR)*UPR(JU) - DRI(JR)*UPI(JU) + SUMBI = SUMBI + DRR(JR)*UPI(JU) + DRI(JR)*UPR(JU) + 190 CONTINUE + BSUMR = BSUMR + SUMBR + BSUMI = BSUMI + SUMBI + TEST = DABS(SUMBR) + DABS(SUMBI) + IF (PP.LT.BTOL .AND. TEST.LT.BTOL) IBS = 1 + 200 CONTINUE + IF (IAS.EQ.1 .AND. IBS.EQ.1) GO TO 220 + 210 CONTINUE + 220 CONTINUE + ASUMR = ASUMR + CONER + STR = -BSUMR*RFN13 + STI = -BSUMI*RFN13 + CALL ZDIV(STR, STI, RTZTR, RTZTI, BSUMR, BSUMI) + GO TO 120 +END + +SUBROUTINE ZUCHK(YR, YI, NZ, ASCLE, TOL) +!***BEGIN PROLOGUE ZUCHK +!***REFER TO ZSERI,ZUOIK,ZUNK1,ZUNK2,ZUNI1,ZUNI2,ZKSCL +! +! Y ENTERS AS A SCALED QUANTITY WHOSE MAGNITUDE IS GREATER THAN +! EXP(-ALIM)=ASCLE=1.0E+3*D1MACH(1)/TOL. THE TEST IS MADE TO SEE +! IF THE MAGNITUDE OF THE REAL OR IMAGINARY PART WOULD UNDERFLOW +! WHEN Y IS SCALED (BY TOL) TO ITS PROPER VALUE. Y IS ACCEPTED +! IF THE UNDERFLOW IS AT LEAST ONE PRECISION BELOW THE MAGNITUDE +! OF THE LARGEST COMPONENT; OTHERWISE THE PHASE ANGLE DOES NOT HAVE +! ABSOLUTE ACCURACY AND AN UNDERFLOW IS ASSUMED. +! +!***ROUTINES CALLED (NONE) +!***END PROLOGUE ZUCHK +! +! COMPLEX Y + DOUBLE PRECISION ASCLE, SS, ST, TOL, WR, WI, YR, YI + INTEGER NZ + NZ = 0 + WR = DABS(YR) + WI = DABS(YI) + ST = DMIN1(WR,WI) + IF (ST.GT.ASCLE) RETURN + SS = DMAX1(WR,WI) + ST = ST/TOL + IF (SS.LT.ST) NZ = 1 + RETURN +END + +SUBROUTINE ZBINU(ZR, ZI, FNU, KODE, N, CYR, CYI, NZ, RL, FNUL, TOL, ELIM, ALIM) +USE COMPLEX +!***BEGIN PROLOGUE ZBINU +!***REFER TO ZBESH,ZBESI,ZBESJ,ZBESK,ZAIRY,ZBIRY + +! ZBINU COMPUTES THE I FUNCTION IN THE RIGHT HALF Z PLANE + +!***ROUTINES CALLED ZABS,ZASYI,ZBUNI,ZMLRI,ZSERI,ZUOIK,ZWRSK +!***END PROLOGUE ZBINU + DOUBLE PRECISION ALIM, AZ, CWI, CWR, CYI, CYR, DFNU, ELIM, FNU, & + FNUL, RL, TOL, ZEROI, ZEROR, ZI, ZR + INTEGER I, INW, KODE, N, NLAST, NN, NUI, NW, NZ + DIMENSION CYR(1), CYI(1), CWR(2), CWI(2) + DATA ZEROR,ZEROI / 0.0D0, 0.0D0 / + + NZ = 0 + AZ = ZABS(ZR,ZI) + NN = N + DFNU = FNU + DBLE(FLOAT(N-1)) + IF (AZ.LE.2.0D0) GO TO 10 + IF (AZ*AZ*0.25D0.GT.DFNU+1.0D0) GO TO 20 + 10 CONTINUE +!----------------------------------------------------------------------- +! POWER SERIES +!----------------------------------------------------------------------- + CALL ZSERI(ZR, ZI, FNU, KODE, NN, CYR, CYI, NW, TOL, ELIM, ALIM) + INW = IABS(NW) + NZ = NZ + INW + NN = NN - INW + IF (NN.EQ.0) RETURN + IF (NW.GE.0) GO TO 120 + DFNU = FNU + DBLE(FLOAT(NN-1)) + 20 CONTINUE + IF (AZ.LT.RL) GO TO 40 + IF (DFNU.LE.1.0D0) GO TO 30 + IF (AZ+AZ.LT.DFNU*DFNU) GO TO 50 +!----------------------------------------------------------------------- +! ASYMPTOTIC EXPANSION FOR LARGE Z +!----------------------------------------------------------------------- + 30 CONTINUE + CALL ZASYI(ZR, ZI, FNU, KODE, NN, CYR, CYI, NW, RL, TOL, ELIM, ALIM) + IF (NW.LT.0) GO TO 130 + GO TO 120 + 40 CONTINUE + IF (DFNU.LE.1.0D0) GO TO 70 + 50 CONTINUE +!----------------------------------------------------------------------- +! OVERFLOW AND UNDERFLOW TEST ON I SEQUENCE FOR MILLER ALGORITHM +!----------------------------------------------------------------------- + CALL ZUOIK(ZR, ZI, FNU, KODE, 1, NN, CYR, CYI, NW, TOL, ELIM, ALIM) + IF (NW.LT.0) GO TO 130 + NZ = NZ + NW + NN = NN - NW + IF (NN.EQ.0) RETURN + DFNU = FNU+DBLE(FLOAT(NN-1)) + IF (DFNU.GT.FNUL) GO TO 110 + IF (AZ.GT.FNUL) GO TO 110 + 60 CONTINUE + IF (AZ.GT.RL) GO TO 80 + 70 CONTINUE +!----------------------------------------------------------------------- +! MILLER ALGORITHM NORMALIZED BY THE SERIES +!----------------------------------------------------------------------- + CALL ZMLRI(ZR, ZI, FNU, KODE, NN, CYR, CYI, NW, TOL) + IF(NW.LT.0) GO TO 130 + GO TO 120 + 80 CONTINUE +!----------------------------------------------------------------------- +! MILLER ALGORITHM NORMALIZED BY THE WRONSKIAN +!----------------------------------------------------------------------- +!----------------------------------------------------------------------- +! OVERFLOW TEST ON K FUNCTIONS USED IN WRONSKIAN +!----------------------------------------------------------------------- + CALL ZUOIK(ZR, ZI, FNU, KODE, 2, 2, CWR, CWI, NW, TOL, ELIM, ALIM) + IF (NW.GE.0) GO TO 100 + NZ = NN + DO 90 I=1,NN + CYR(I) = ZEROR + CYI(I) = ZEROI + 90 CONTINUE + RETURN + 100 CONTINUE + IF (NW.GT.0) GO TO 130 + CALL ZWRSK(ZR, ZI, FNU, KODE, NN, CYR, CYI, NW, CWR, CWI, TOL, ELIM, ALIM) + IF (NW.LT.0) GO TO 130 + GO TO 120 + 110 CONTINUE +!----------------------------------------------------------------------- +! INCREMENT FNU+NN-1 UP TO FNUL, COMPUTE AND RECUR BACKWARD +!----------------------------------------------------------------------- + NUI = INT(SNGL(FNUL-DFNU)) + 1 + NUI = MAX0(NUI,0) + CALL ZBUNI(ZR, ZI, FNU, KODE, NN, CYR, CYI, NW, NUI, NLAST, FNUL, & + TOL, ELIM, ALIM) + IF (NW.LT.0) GO TO 130 + NZ = NZ + NW + IF (NLAST.EQ.0) GO TO 120 + NN = NLAST + GO TO 60 + 120 CONTINUE + RETURN + 130 CONTINUE + NZ = -1 + IF(NW.EQ.(-2)) NZ=-2 + RETURN + END + +SUBROUTINE ZSHCH(ZR, ZI, CSHR, CSHI, CCHR, CCHI) +!***BEGIN PROLOGUE ZSHCH +!***REFER TO ZBESK,ZBESH +! +! ZSHCH COMPUTES THE COMPLEX HYPERBOLI! FUNCTIONS CSH=SINH(X+I*Y) +! AND CCH=COSH(X+I*Y), WHERE I**2=-1. +! +!***ROUTINES CALLED (NONE) +!***END PROLOGUE ZSHCH +! + DOUBLE PRECISION CCHI, CCHR, CH, CN, CSHI, CSHR, SH, SN, ZI, ZR, DCOSH, DSINH + SH = DSINH(ZR) + CH = DCOSH(ZR) + SN = DSIN(ZI) + CN = DCOS(ZI) + CSHR = SH*CN + CSHI = CH*SN + CCHR = CH*CN + CCHI = SH*SN + RETURN +END + +DOUBLE PRECISION FUNCTION DGAMLN(Z,IERR) +USE UTILIT +!***BEGIN PROLOGUE DGAMLN +!***DATE WRITTEN 830501 (YYMMDD) +!***REVISION DATE 830501 (YYMMDD) +!***CATEGORY NO. B5F +!***KEYWORDS GAMMA FUNCTION,LOGARITHM OF GAMMA FUNCTION +!***AUTHOR AMOS, DONALD E., SANDIA NATIONAL LABORATORIES +!***PURPOSE TO COMPUTE THE LOGARITHM OF THE GAMMA FUNCTION +!***DESCRIPTION +! +! **** A DOUBLE PRECISION ROUTINE **** +! DGAMLN COMPUTES THE NATURAL LOG OF THE GAMMA FUNCTION FOR +! Z.GT.0. THE ASYMPTOTIC EXPANSION IS USED TO GENERATE VALUES +! GREATER THAN ZMIN WHICH ARE ADJUSTED BY THE RECURSION +! G(Z+1)=Z*G(Z) FOR Z.LE.ZMIN. THE FUNCTION WAS MADE AS +! PORTABLE AS POSSIBLE BY COMPUTIMG ZMIN FROM THE NUMBER OF BASE +! 10 DIGITS IN A WORD, RLN=AMAX1(-ALOG10(R1MACH(4)),0.5E-18) +! LIMITED TO 18 DIGITS OF (RELATIVE) ACCURACY. +! +! SINCE INTEGER ARGUMENTS ARE COMMON, A TABLE LOOK UP ON 100 +! VALUES IS USED FOR SPEED OF EXECUTION. +! +! DESCRIPTION OF ARGUMENTS +! +! INPUT Z IS D0UBLE PRECISION +! Z - ARGUMENT, Z.GT.0.0D0 +! +! OUTPUT DGAMLN IS DOUBLE PRECISION +! DGAMLN - NATURAL LOG OF THE GAMMA FUNCTION AT Z.NE.0.0D0 +! IERR - ERROR FLAG +! IERR=0, NORMAL RETURN, COMPUTATION COMPLETED +! IERR=1, Z.LE.0.0D0, NO COMPUTATION +! +! +!***REFERENCES COMPUTATION OF BESSEL FUNCTIONS OF COMPLEX ARGUMENT +! BY D. E. AMOS, SAND83-0083, MAY, 1983. +!***ROUTINES CALLED I1MACH,D1MACH +!***END PROLOGUE DGAMLN + DOUBLE PRECISION CF, CON, FLN, FZ, GLN, RLN, S, TLG, TRM, TST, & + T1, WDTOL, Z, ZDMY, ZINC, ZM, ZMIN, ZP, ZSQ + INTEGER I, IERR, I1M, K, MZ, NZ + DIMENSION CF(22), GLN(100) +! LNGAMMA(N), N=1,100 + DATA GLN(1), GLN(2), GLN(3), GLN(4), GLN(5), GLN(6), GLN(7), & + GLN(8), GLN(9), GLN(10), GLN(11), GLN(12), GLN(13), GLN(14), & + GLN(15), GLN(16), GLN(17), GLN(18), GLN(19), GLN(20), & + GLN(21), GLN(22)/ & + 0.00000000000000000D+00, 0.00000000000000000D+00, & + 6.93147180559945309D-01, 1.79175946922805500D+00, & + 3.17805383034794562D+00, 4.78749174278204599D+00, & + 6.57925121201010100D+00, 8.52516136106541430D+00, & + 1.06046029027452502D+01, 1.28018274800814696D+01, & + 1.51044125730755153D+01, 1.75023078458738858D+01, & + 1.99872144956618861D+01, 2.25521638531234229D+01, & + 2.51912211827386815D+01, 2.78992713838408916D+01, & + 3.06718601060806728D+01, 3.35050734501368889D+01, & + 3.63954452080330536D+01, 3.93398841871994940D+01, & + 4.23356164607534850D+01, 4.53801388984769080D+01/ + DATA GLN(23), GLN(24), GLN(25), GLN(26), GLN(27), GLN(28), & + GLN(29), GLN(30), GLN(31), GLN(32), GLN(33), GLN(34), & + GLN(35), GLN(36), GLN(37), GLN(38), GLN(39), GLN(40), & + GLN(41), GLN(42), GLN(43), GLN(44)/ & + 4.84711813518352239D+01, 5.16066755677643736D+01, & + 5.47847293981123192D+01, 5.80036052229805199D+01, & + 6.12617017610020020D+01, 6.45575386270063311D+01, & + 6.78897431371815350D+01, 7.12570389671680090D+01, & + 7.46582363488301644D+01, 7.80922235533153106D+01, & + 8.15579594561150372D+01, 8.50544670175815174D+01, & + 8.85808275421976788D+01, 9.21361756036870925D+01, & + 9.57196945421432025D+01, 9.93306124547874269D+01, & + 1.02968198614513813D+02, 1.06631760260643459D+02, & + 1.10320639714757395D+02, 1.14034211781461703D+02, & + 1.17771881399745072D+02, 1.21533081515438634D+02/ + DATA GLN(45), GLN(46), GLN(47), GLN(48), GLN(49), GLN(50), & + GLN(51), GLN(52), GLN(53), GLN(54), GLN(55), GLN(56), & + GLN(57), GLN(58), GLN(59), GLN(60), GLN(61), GLN(62), & + GLN(63), GLN(64), GLN(65), GLN(66)/ & + 1.25317271149356895D+02, 1.29123933639127215D+02, & + 1.32952575035616310D+02, 1.36802722637326368D+02, & + 1.40673923648234259D+02, 1.44565743946344886D+02, & + 1.48477766951773032D+02, 1.52409592584497358D+02, & + 1.56360836303078785D+02, 1.60331128216630907D+02, & + 1.64320112263195181D+02, 1.68327445448427652D+02, & + 1.72352797139162802D+02, 1.76395848406997352D+02, & + 1.80456291417543771D+02, 1.84533828861449491D+02, & + 1.88628173423671591D+02, 1.92739047287844902D+02, & + 1.96866181672889994D+02, 2.01009316399281527D+02, & + 2.05168199482641199D+02, 2.09342586752536836D+02/ + DATA GLN(67), GLN(68), GLN(69), GLN(70), GLN(71), GLN(72), & + GLN(73), GLN(74), GLN(75), GLN(76), GLN(77), GLN(78), & + GLN(79), GLN(80), GLN(81), GLN(82), GLN(83), GLN(84), & + GLN(85), GLN(86), GLN(87), GLN(88)/ & + 2.13532241494563261D+02, 2.17736934113954227D+02, & + 2.21956441819130334D+02, 2.26190548323727593D+02, & + 2.30439043565776952D+02, 2.34701723442818268D+02, & + 2.38978389561834323D+02, 2.43268849002982714D+02, & + 2.47572914096186884D+02, 2.51890402209723194D+02, & + 2.56221135550009525D+02, 2.60564940971863209D+02, & + 2.64921649798552801D+02, 2.69291097651019823D+02, & + 2.73673124285693704D+02, 2.78067573440366143D+02, & + 2.82474292687630396D+02, 2.86893133295426994D+02, & + 2.91323950094270308D+02, 2.95766601350760624D+02, & + 3.00220948647014132D+02, 3.04686856765668715D+02/ + DATA GLN(89), GLN(90), GLN(91), GLN(92), GLN(93), GLN(94), & + GLN(95), GLN(96), GLN(97), GLN(98), GLN(99), GLN(100)/ & + 3.09164193580146922D+02, 3.13652829949879062D+02, & + 3.18152639620209327D+02, 3.22663499126726177D+02, & + 3.27185287703775217D+02, 3.31717887196928473D+02, & + 3.36261181979198477D+02, 3.40815058870799018D+02, & + 3.45379407062266854D+02, 3.49954118040770237D+02, & + 3.54539085519440809D+02, 3.59134205369575399D+02/ +! COEFFICIENTS OF ASYMPTOTIC EXPANSION + DATA CF(1), CF(2), CF(3), CF(4), CF(5), CF(6), CF(7), CF(8), & + CF(9), CF(10), CF(11), CF(12), CF(13), CF(14), CF(15), & + CF(16), CF(17), CF(18), CF(19), CF(20), CF(21), CF(22)/ & + 8.33333333333333333D-02, -2.77777777777777778D-03, & + 7.93650793650793651D-04, -5.95238095238095238D-04, & + 8.41750841750841751D-04, -1.91752691752691753D-03, & + 6.41025641025641026D-03, -2.95506535947712418D-02, & + 1.79644372368830573D-01, -1.39243221690590112D+00, & + 1.34028640441683920D+01, -1.56848284626002017D+02, & + 2.19310333333333333D+03, -3.61087712537249894D+04, & + 6.91472268851313067D+05, -1.52382215394074162D+07, & + 3.82900751391414141D+08, -1.08822660357843911D+10, & + 3.47320283765002252D+11, -1.23696021422692745D+13, & + 4.88788064793079335D+14, -2.13203339609193739D+16/ + +! LN(2*PI) + DATA CON / 1.83787706640934548D+00/ + +!***FIRST EXECUTABLE STATEMENT DGAMLN + IERR=0 + IF (Z.LE.0.0D0) GO TO 70 + IF (Z.GT.101.0D0) GO TO 10 + NZ = INT(SNGL(Z)) + FZ = Z - FLOAT(NZ) + IF (FZ.GT.0.0D0) GO TO 10 + IF (NZ.GT.100) GO TO 10 + DGAMLN = GLN(NZ) + RETURN + 10 CONTINUE + WDTOL = D1MACH(4) + WDTOL = DMAX1(WDTOL,0.5D-18) + I1M = I1MACH(14) + RLN = D1MACH(5)*FLOAT(I1M) + FLN = DMIN1(RLN,20.0D0) + FLN = DMAX1(FLN,3.0D0) + FLN = FLN - 3.0D0 + ZM = 1.8000D0 + 0.3875D0*FLN + MZ = INT(SNGL(ZM)) + 1 + ZMIN = FLOAT(MZ) + ZDMY = Z + ZINC = 0.0D0 + IF (Z.GE.ZMIN) GO TO 20 + ZINC = ZMIN - FLOAT(NZ) + ZDMY = Z + ZINC + 20 CONTINUE + ZP = 1.0D0/ZDMY + T1 = CF(1)*ZP + S = T1 + IF (ZP.LT.WDTOL) GO TO 40 + ZSQ = ZP*ZP + TST = T1*WDTOL + DO 30 K=2,22 + ZP = ZP*ZSQ + TRM = CF(K)*ZP + IF (DABS(TRM).LT.TST) GO TO 40 + S = S + TRM + 30 CONTINUE + 40 CONTINUE + IF (ZINC.NE.0.0D0) GO TO 50 + TLG = DLOG(Z) + DGAMLN = Z*(TLG-1.0D0) + 0.5D0*(CON-TLG) + S + RETURN + 50 CONTINUE + ZP = 1.0D0 + NZ = INT(SNGL(ZINC)) + DO 60 I=1,NZ + ZP = ZP*(Z+FLOAT(I-1)) + 60 CONTINUE + TLG = DLOG(ZDMY) + DGAMLN = ZDMY*(TLG-1.0D0) - DLOG(ZP) + 0.5D0*(CON-TLG) + S + RETURN + + 70 CONTINUE + IERR=1 + RETURN +END + +SUBROUTINE ZKSCL(ZRR,ZRI,FNU,N,YR,YI,NZ,RZR,RZI,ASCLE,TOL,ELIM) +USE COMPLEX +!***BEGIN PROLOGUE ZKSCL +!***REFER TO ZBESK +! +! SET K FUNCTIONS TO ZERO ON UNDERFLOW, CONTINUE RECURRENCE +! ON SCALED FUNCTIONS UNTIL TWO MEMBERS COME ON SCALE, THEN +! RETURN WITH MIN(NZ+2,N) VALUES SCALED BY 1/TOL. +! +!***ROUTINES CALLED ZUCHK,ZABS,ZLOG +!***END PROLOGUE ZKSCL +! COMPLEX CK,CS,CY,CZERO,RZ,S1,S2,Y,ZR,ZD,CELM + DOUBLE PRECISION ACS, AS, ASCLE, CKI, CKR, CSI, CSR, CYI, & + CYR, ELIM, FN, FNU, RZI, RZR, STR, S1I, S1R, S2I, S2R, & + TOL, YI, YR, ZEROI, ZEROR, ZRI, ZRR, ZDR, ZDI, CELMR, & + ELM, HELIM, ALAS + INTEGER I, IC, IDUM, KK, N, NN, NW, NZ + DIMENSION YR(1), YI(1), CYR(2), CYI(2) + DATA ZEROR,ZEROI / 0.0D0 , 0.0D0 / + + NZ = 0 + IC = 0 + NN = MIN0(2,N) + DO 10 I=1,NN + S1R = YR(I) + S1I = YI(I) + CYR(I) = S1R + CYI(I) = S1I + AS = ZABS(S1R,S1I) + ACS = -ZRR + DLOG(AS) + NZ = NZ + 1 + YR(I) = ZEROR + YI(I) = ZEROI + IF (ACS.LT.(-ELIM)) GO TO 10 + CALL ZLOG(S1R, S1I, CSR, CSI, IDUM) + CSR = CSR - ZRR + CSI = CSI - ZRI + STR = DEXP(CSR)/TOL + CSR = STR*DCOS(CSI) + CSI = STR*DSIN(CSI) + CALL ZUCHK(CSR, CSI, NW, ASCLE, TOL) + IF (NW.NE.0) GO TO 10 + YR(I) = CSR + YI(I) = CSI + IC = I + NZ = NZ - 1 + 10 CONTINUE + IF (N.EQ.1) RETURN + IF (IC.GT.1) GO TO 20 + YR(1) = ZEROR + YI(1) = ZEROI + NZ = 2 + 20 CONTINUE + IF (N.EQ.2) RETURN + IF (NZ.EQ.0) RETURN + FN = FNU + 1.0D0 + CKR = FN*RZR + CKI = FN*RZI + S1R = CYR(1) + S1I = CYI(1) + S2R = CYR(2) + S2I = CYI(2) + HELIM = 0.5D0*ELIM + ELM = DEXP(-ELIM) + CELMR = ELM + ZDR = ZRR + ZDI = ZRI + +! FIND TWO CONSECUTIVE Y VALUES ON SCALE. SCALE RECURRENCE IF +! S2 GETS LARGER THAN EXP(ELIM/2) + + DO 30 I=3,N + KK = I + CSR = S2R + CSI = S2I + S2R = CKR*CSR - CKI*CSI + S1R + S2I = CKI*CSR + CKR*CSI + S1I + S1R = CSR + S1I = CSI + CKR = CKR + RZR + CKI = CKI + RZI + AS = ZABS(S2R,S2I) + ALAS = DLOG(AS) + ACS = -ZDR + ALAS + NZ = NZ + 1 + YR(I) = ZEROR + YI(I) = ZEROI + IF (ACS.LT.(-ELIM)) GO TO 25 + CALL ZLOG(S2R, S2I, CSR, CSI, IDUM) + CSR = CSR - ZDR + CSI = CSI - ZDI + STR = DEXP(CSR)/TOL + CSR = STR*DCOS(CSI) + CSI = STR*DSIN(CSI) + CALL ZUCHK(CSR, CSI, NW, ASCLE, TOL) + IF (NW.NE.0) GO TO 25 + YR(I) = CSR + YI(I) = CSI + NZ = NZ - 1 + IF (IC.EQ.KK-1) GO TO 40 + IC = KK + GO TO 30 + 25 CONTINUE + IF(ALAS.LT.HELIM) GO TO 30 + ZDR = ZDR - ELIM + S1R = S1R*CELMR + S1I = S1I*CELMR + S2R = S2R*CELMR + S2I = S2I*CELMR + 30 CONTINUE + NZ = N + IF(IC.EQ.N) NZ=N-1 + GO TO 45 + 40 CONTINUE + NZ = KK - 2 + 45 CONTINUE + DO 50 I=1,NZ + YR(I) = ZEROR + YI(I) = ZEROI + 50 CONTINUE + RETURN +END + +SUBROUTINE ZACAI(ZR, ZI, FNU, KODE, MR, N, YR, YI, NZ, RL, TOL, ELIM, ALIM) +USE UTILIT +USE COMPLEX +!***BEGIN PROLOGUE ZACAI +!***REFER TO ZAIRY +! +! ZACAI APPLIES THE ANALYTIC CONTINUATION FORMULA +! +! K(FNU,ZN*EXP(MP))=K(FNU,ZN)*EXP(-MP*FNU) - MP*I(FNU,ZN) +! MP=PI*MR*CMPLX(0.0,1.0) +! +! TO CONTINUE THE K FUNCTION FROM THE RIGHT HALF TO THE LEFT +! HALF Z PLANE FOR USE WITH ZAIRY WHERE FNU=1/3 OR 2/3 AND N=1. +! ZACAI IS THE SAME AS ZACON WITH THE PARTS FOR LARGER ORDERS AND +! RECURRENCE REMOVED. A RECURSIVE CALL TO ZACON CAN RESULT IF ZACON +! IS CALLED FROM ZAIRY. +! +!***ROUTINES CALLED ZASYI,ZBKNU,ZMLRI,ZSERI,ZS1S2,D1MACH,ZABS +!***END PROLOGUE ZACAI +! COMPLEX CSGN,CSPN,C1,C2,Y,Z,ZN,CY + DOUBLE PRECISION ALIM, ARG, ASCLE, AZ, CSGNR, CSGNI, CSPNR, & + CSPNI, C1R, C1I, C2R, C2I, CYR, CYI, DFNU, ELIM, FMR, FNU, PI, & + RL, SGN, TOL, YY, YR, YI, ZR, ZI, ZNR, ZNI + INTEGER INU, IUF, KODE, MR, N, NN, NW, NZ + DIMENSION YR(1), YI(1), CYR(2), CYI(2) + DATA PI / 3.14159265358979324D0 / + NZ = 0 + ZNR = -ZR + ZNI = -ZI + AZ = ZABS(ZR,ZI) + NN = N + DFNU = FNU + DBLE(FLOAT(N-1)) + IF (AZ.LE.2.0D0) GO TO 10 + IF (AZ*AZ*0.25D0.GT.DFNU+1.0D0) GO TO 20 + 10 CONTINUE +!----------------------------------------------------------------------- +! POWER SERIES FOR THE I FUNCTION +!----------------------------------------------------------------------- + CALL ZSERI(ZNR, ZNI, FNU, KODE, NN, YR, YI, NW, TOL, ELIM, ALIM) + GO TO 40 + 20 CONTINUE + IF (AZ.LT.RL) GO TO 30 +!----------------------------------------------------------------------- +! ASYMPTOTIC EXPANSION FOR LARGE Z FOR THE I FUNCTION +!----------------------------------------------------------------------- + CALL ZASYI(ZNR, ZNI, FNU, KODE, NN, YR, YI, NW, RL, TOL, ELIM, ALIM) + IF (NW.LT.0) GO TO 80 + GO TO 40 + 30 CONTINUE +!----------------------------------------------------------------------- +! MILLER ALGORITHM NORMALIZED BY THE SERIES FOR THE I FUNCTION +!----------------------------------------------------------------------- + CALL ZMLRI(ZNR, ZNI, FNU, KODE, NN, YR, YI, NW, TOL) + IF(NW.LT.0) GO TO 80 + 40 CONTINUE +!----------------------------------------------------------------------- +! ANALYTIC CONTINUATION TO THE LEFT HALF PLANE FOR THE K FUNCTION +!----------------------------------------------------------------------- + CALL ZBKNU(ZNR, ZNI, FNU, KODE, 1, CYR, CYI, NW, TOL, ELIM, ALIM) + IF (NW.NE.0) GO TO 80 + FMR = DBLE(FLOAT(MR)) + SGN = -DSIGN(PI,FMR) + CSGNR = 0.0D0 + CSGNI = SGN + IF (KODE.EQ.1) GO TO 50 + YY = -ZNI + CSGNR = -CSGNI*DSIN(YY) + CSGNI = CSGNI*DCOS(YY) + 50 CONTINUE +!----------------------------------------------------------------------- +! CALCULATE CSPN=EXP(FNU*PI*I) TO MINIMIZE LOSSES OF SIGNIFICANCE +! WHEN FNU IS LARGE +!----------------------------------------------------------------------- + INU = INT(SNGL(FNU)) + ARG = (FNU-DBLE(FLOAT(INU)))*SGN + CSPNR = DCOS(ARG) + CSPNI = DSIN(ARG) + IF (MOD(INU,2).EQ.0) GO TO 60 + CSPNR = -CSPNR + CSPNI = -CSPNI + 60 CONTINUE + C1R = CYR(1) + C1I = CYI(1) + C2R = YR(1) + C2I = YI(1) + IF (KODE.EQ.1) GO TO 70 + IUF = 0 + ASCLE = 1.0D+3*D1MACH(1)/TOL + CALL ZS1S2(ZNR, ZNI, C1R, C1I, C2R, C2I, NW, ASCLE, ALIM, IUF) + NZ = NZ + NW + 70 CONTINUE + YR(1) = CSPNR*C1R - CSPNI*C1I + CSGNR*C2R - CSGNI*C2I + YI(1) = CSPNR*C1I + CSPNI*C1R + CSGNR*C2I + CSGNI*C2R + RETURN + 80 CONTINUE + NZ = -1 + IF(NW.EQ.(-2)) NZ=-2 + RETURN +END + +SUBROUTINE ZS1S2(ZRR, ZRI, S1R, S1I, S2R, S2I, NZ, ASCLE, ALIM, IUF) +USE COMPLEX +!***BEGIN PROLOGUE ZS1S2 +!***REFER TO ZBESK,ZAIRY +! +! ZS1S2 TESTS FOR A POSSIBLE UNDERFLOW RESULTING FROM THE +! ADDITION OF THE I AND K FUNCTIONS IN THE ANALYTIC CON- +! TINUATION FORMULA WHERE S1=K FUNCTION AND S2=I FUNCTION. +! ON KODE=1 THE I AND K FUNCTIONS ARE DIFFERENT ORDERS OF +! MAGNITUDE, BUT FOR KODE=2 THEY CAN BE OF THE SAME ORDER +! OF MAGNITUDE AND THE MAXIMUM MUST BE AT LEAST ONE +! PRECISION ABOVE THE UNDERFLOW LIMIT. +! +!***ROUTINES CALLED ZABS,ZEXP,ZLOG +!***END PROLOGUE ZS1S2 +! COMPLEX CZERO,C1,S1,S1D,S2,ZR + DOUBLE PRECISION AA, ALIM, ALN, ASCLE, AS1, AS2, C1I, C1R, S1DI, & + S1DR, S1I, S1R, S2I, S2R, ZEROI, ZEROR, ZRI, ZRR + INTEGER IUF, IDUM, NZ + DATA ZEROR,ZEROI / 0.0D0 , 0.0D0 / + NZ = 0 + AS1 = ZABS(S1R,S1I) + AS2 = ZABS(S2R,S2I) + IF (S1R.EQ.0.0D0 .AND. S1I.EQ.0.0D0) GO TO 10 + IF (AS1.EQ.0.0D0) GO TO 10 + ALN = -ZRR - ZRR + DLOG(AS1) + S1DR = S1R + S1DI = S1I + S1R = ZEROR + S1I = ZEROI + AS1 = ZEROR + IF (ALN.LT.(-ALIM)) GO TO 10 + CALL ZLOG(S1DR, S1DI, C1R, C1I, IDUM) + C1R = C1R - ZRR - ZRR + C1I = C1I - ZRI - ZRI + CALL ZEXP(C1R, C1I, S1R, S1I) + AS1 = ZABS(S1R,S1I) + IUF = IUF + 1 + 10 CONTINUE + AA = DMAX1(AS1,AS2) + IF (AA.GT.ASCLE) RETURN + S1R = ZEROR + S1I = ZEROI + S2R = ZEROR + S2I = ZEROI + NZ = 1 + IUF = 0 + RETURN +END + +SUBROUTINE ZRATI(ZR, ZI, FNU, N, CYR, CYI, TOL) +USE COMPLEX +!***BEGIN PROLOGUE ZRATI +!***REFER TO ZBESI,ZBESK,ZBESH +! +! ZRATI COMPUTES RATIOS OF I BESSEL FUNCTIONS BY BACKWARD +! RECURRENCE. THE STARTING INDEX IS DETERMINED BY FORWARD +! RECURRENCE AS DESCRIBED IN J. RES. OF NAT. BUR. OF STANDARDS-B, +! MATHEMATICAL SCIENCES, VOL 77B, P111-114, SEPTEMBER, 1973, +! BESSEL FUNCTIONS I AND J OF COMPLEX ARGUMENT AND INTEGER ORDER, +! BY D. J. SOOKNE. +! +!***ROUTINES CALLED ZABS,ZDIV +!***END PROLOGUE ZRATI +! COMPLEX Z,CY(1),CONE,CZERO,P1,P2,T1,RZ,PT,CDFNU + DOUBLE PRECISION AK, AMAGZ, AP1, AP2, ARG, AZ, CDFNUI, CDFNUR, & + CONEI, CONER, CYI, CYR, CZEROI, CZEROR, DFNU, FDNU, FLAM, FNU, & + FNUP, PTI, PTR, P1I, P1R, P2I, P2R, RAK, RAP1, RHO, RT2, RZI, & + RZR, TEST, TEST1, TOL, TTI, TTR, T1I, T1R, ZI, ZR + INTEGER I, ID, IDNU, INU, ITIME, K, KK, MAGZ, N + DIMENSION CYR(1), CYI(1) + DATA CZEROR,CZEROI,CONER,CONEI,RT2 & + /0.0D0, 0.0D0, 1.0D0, 0.0D0, 1.41421356237309505D0/ + AZ = ZABS(ZR,ZI) + INU = INT(SNGL(FNU)) + IDNU = INU + N - 1 + MAGZ = INT(SNGL(AZ)) + AMAGZ = DBLE(FLOAT(MAGZ+1)) + FDNU = DBLE(FLOAT(IDNU)) + FNUP = DMAX1(AMAGZ,FDNU) + ID = IDNU - MAGZ - 1 + ITIME = 1 + K = 1 + PTR = 1.0D0/AZ + RZR = PTR*(ZR+ZR)*PTR + RZI = -PTR*(ZI+ZI)*PTR + T1R = RZR*FNUP + T1I = RZI*FNUP + P2R = -T1R + P2I = -T1I + P1R = CONER + P1I = CONEI + T1R = T1R + RZR + T1I = T1I + RZI + IF (ID.GT.0) ID = 0 + AP2 = ZABS(P2R,P2I) + AP1 = ZABS(P1R,P1I) +!----------------------------------------------------------------------- +! THE OVERFLOW TEST ON K(FNU+I-1,Z) BEFORE THE CALL TO CBKNU +! GUARANTEES THAT P2 IS ON SCALE. SCALE TEST1 AND ALL SUBSEQUENT +! P2 VALUES BY AP1 TO ENSURE THAT AN OVERFLOW DOES NOT OCCUR +! PREMATURELY. +!----------------------------------------------------------------------- + ARG = (AP2+AP2)/(AP1*TOL) + TEST1 = DSQRT(ARG) + TEST = TEST1 + RAP1 = 1.0D0/AP1 + P1R = P1R*RAP1 + P1I = P1I*RAP1 + P2R = P2R*RAP1 + P2I = P2I*RAP1 + AP2 = AP2*RAP1 + 10 CONTINUE + K = K + 1 + AP1 = AP2 + PTR = P2R + PTI = P2I + P2R = P1R - (T1R*PTR-T1I*PTI) + P2I = P1I - (T1R*PTI+T1I*PTR) + P1R = PTR + P1I = PTI + T1R = T1R + RZR + T1I = T1I + RZI + AP2 = ZABS(P2R,P2I) + IF (AP1.LE.TEST) GO TO 10 + IF (ITIME.EQ.2) GO TO 20 + AK = ZABS(T1R,T1I)*0.5D0 + FLAM = AK + DSQRT(AK*AK-1.0D0) + RHO = DMIN1(AP2/AP1,FLAM) + TEST = TEST1*DSQRT(RHO/(RHO*RHO-1.0D0)) + ITIME = 2 + GO TO 10 + 20 CONTINUE + KK = K + 1 - ID + AK = DBLE(FLOAT(KK)) + T1R = AK + T1I = CZEROI + DFNU = FNU + DBLE(FLOAT(N-1)) + P1R = 1.0D0/AP2 + P1I = CZEROI + P2R = CZEROR + P2I = CZEROI + DO 30 I=1,KK + PTR = P1R + PTI = P1I + RAP1 = DFNU + T1R + TTR = RZR*RAP1 + TTI = RZI*RAP1 + P1R = (PTR*TTR-PTI*TTI) + P2R + P1I = (PTR*TTI+PTI*TTR) + P2I + P2R = PTR + P2I = PTI + T1R = T1R - CONER + 30 CONTINUE + IF (P1R.NE.CZEROR .OR. P1I.NE.CZEROI) GO TO 40 + P1R = TOL + P1I = TOL + 40 CONTINUE + CALL ZDIV(P2R, P2I, P1R, P1I, CYR(N), CYI(N)) + IF (N.EQ.1) RETURN + K = N - 1 + AK = DBLE(FLOAT(K)) + T1R = AK + T1I = CZEROI + CDFNUR = FNU*RZR + CDFNUI = FNU*RZI + DO 60 I=2,N + PTR = CDFNUR + (T1R*RZR-T1I*RZI) + CYR(K+1) + PTI = CDFNUI + (T1R*RZI+T1I*RZR) + CYI(K+1) + AK = ZABS(PTR,PTI) + IF (AK.NE.CZEROR) GO TO 50 + PTR = TOL + PTI = TOL + AK = TOL*RT2 + 50 CONTINUE + RAK = CONER/AK + CYR(K) = RAK*PTR*RAK + CYI(K) = -RAK*PTI*RAK + T1R = T1R - CONER + K = K - 1 + 60 CONTINUE + RETURN +END + +SUBROUTINE ZAIRY(ZR, ZI, ID, KODE, AIR, AII, NZ, IERR) +USE UTILIT +USE COMPLEX +!***BEGIN PROLOGUE ZAIRY +!***DATE WRITTEN 830501 (YYMMDD) +!***REVISION DATE 830501 (YYMMDD) +!***CATEGORY NO. B5K +!***KEYWORDS AIRY FUNCTION,BESSEL FUNCTIONS OF ORDER ONE THIRD +!***AUTHOR AMOS, DONALD E., SANDIA NATIONAL LABORATORIES +!***PURPOSE TO COMPUTE AIRY FUNCTIONS AI(Z) AND DAI(Z) FOR COMPLEX Z +!***DESCRIPTION +! +! ***A DOUBLE PRECISION ROUTINE*** +! ON KODE=1, ZAIRY COMPUTES THE COMPLEX AIRY FUNCTION AI(Z) OR +! ITS DERIVATIVE DAI(Z)/DZ ON ID=0 OR ID=1 RESPECTIVELY. ON +! KODE=2, A SCALING OPTION CEXP(ZTA)*AI(Z) OR CEXP(ZTA)* +! DAI(Z)/DZ IS PROVIDED TO REMOVE THE EXPONENTIAL DECAY IN +! -PI/3.LT.ARG(Z).LT.PI/3 AND THE EXPONENTIAL GROWTH IN +! PI/3.LT.ABS(ARG(Z)).LT.PI WHERE ZTA=(2/3)*Z*CSQRT(Z). +! +! WHILE THE AIRY FUNCTIONS AI(Z) AND DAI(Z)/DZ ARE ANALYTI! IN +! THE WHOLE Z PLANE, THE CORRESPONDING SCALED FUNCTIONS DEFINED +! FOR KODE=2 HAVE A CUT ALONG THE NEGATIVE REAL AXIS. +! DEFINTIONS AND NOTATION ARE FOUND IN THE NBS HANDBOOK OF +! MATHEMATICAL FUNCTIONS (REF. 1). +! +! INPUT ZR,ZI ARE DOUBLE PRECISION +! ZR,ZI - Z=CMPLX(ZR,ZI) +! ID - ORDER OF DERIVATIVE, ID=0 OR ID=1 +! KODE - A PARAMETER TO INDICATE THE SCALING OPTION +! KODE= 1 RETURNS +! AI=AI(Z) ON ID=0 OR +! AI=DAI(Z)/DZ ON ID=1 +! = 2 RETURNS +! AI=CEXP(ZTA)*AI(Z) ON ID=0 OR +! AI=CEXP(ZTA)*DAI(Z)/DZ ON ID=1 WHERE +! ZTA=(2/3)*Z*CSQRT(Z) +! +! OUTPUT AIR,AII ARE DOUBLE PRECISION +! AIR,AII- COMPLEX ANSWER DEPENDING ON THE CHOICES FOR ID AND +! KODE +! NZ - UNDERFLOW INDICATOR +! NZ= 0 , NORMAL RETURN +! NZ= 1 , AI=CMPLX(0.0D0,0.0D0) DUE TO UNDERFLOW IN +! -PI/3.LT.ARG(Z).LT.PI/3 ON KODE=1 +! IERR - ERROR FLAG +! IERR=0, NORMAL RETURN - COMPUTATION COMPLETED +! IERR=1, INPUT ERROR - NO COMPUTATION +! IERR=2, OVERFLOW - NO COMPUTATION, REAL(ZTA) +! TOO LARGE ON KODE=1 +! IERR=3, CABS(Z) LARGE - COMPUTATION COMPLETED +! LOSSES OF SIGNIFCANCE BY ARGUMENT REDUCTION +! PRODUCE LESS THAN HALF OF MACHINE ACCURACY +! IERR=4, CABS(Z) TOO LARGE - NO COMPUTATION +! COMPLETE LOSS OF ACCURACY BY ARGUMENT +! REDUCTION +! IERR=5, ERROR - NO COMPUTATION, +! ALGORITHM TERMINATION CONDITION NOT MET +! +!***LONG DESCRIPTION +! +! AI AND DAI ARE COMPUTED FOR CABS(Z).GT.1.0 FROM THE K BESSEL +! FUNCTIONS BY +! +! AI(Z)=C*SQRT(Z)*K(1/3,ZTA) , DAI(Z)=-C*Z*K(2/3,ZTA) +! C=1.0/(PI*SQRT(3.0)) +! ZTA=(2/3)*Z**(3/2) +! +! WITH THE POWER SERIES FOR CABS(Z).LE.1.0. +! +! IN MOST COMPLEX VARIABLE COMPUTATION, ONE MUST EVALUATE ELE- +! MENTARY FUNCTIONS. WHEN THE MAGNITUDE OF Z IS LARGE, LOSSES +! OF SIGNIFICANCE BY ARGUMENT REDUCTION OCCUR. CONSEQUENTLY, IF +! THE MAGNITUDE OF ZETA=(2/3)*Z**1.5 EXCEEDS U1=SQRT(0.5/UR), +! THEN LOSSES EXCEEDING HALF PRECISION ARE LIKELY AND AN ERROR +! FLAG IERR=3 IS TRIGGERED WHERE UR=DMAX1(D1MACH(4),1.0D-18) IS +! DOUBLE PRECISION UNIT ROUNDOFF LIMITED TO 18 DIGITS PRECISION. +! ALSO, IF THE MAGNITUDE OF ZETA IS LARGER THAN U2=0.5/UR, THEN +! ALL SIGNIFICANCE IS LOST AND IERR=4. IN ORDER TO USE THE INT +! FUNCTION, ZETA MUST BE FURTHER RESTRICTED NOT TO EXCEED THE +! LARGEST INTEGER, U3=I1MACH(9). THUS, THE MAGNITUDE OF ZETA +! MUST BE RESTRICTED BY MIN(U2,U3). ON 32 BIT MACHINES, U1,U2, +! AND U3 ARE APPROXIMATELY 2.0E+3, 4.2E+6, 2.1E+9 IN SINGLE +! PRECISION ARITHMETIC AND 1.3E+8, 1.8E+16, 2.1E+9 IN DOUBLE +! PRECISION ARITHMETIC RESPECTIVELY. THIS MAKES U2 AND U3 LIMIT- +! ING IN THEIR RESPECTIVE ARITHMETICS. THIS MEANS THAT THE MAG- +! NITUDE OF Z CANNOT EXCEED 3.1E+4 IN SINGLE AND 2.1E+6 IN +! DOUBLE PRECISION ARITHMETIC. THIS ALSO MEANS THAT ONE CAN +! EXPECT TO RETAIN, IN THE WORST CASES ON 32 BIT MACHINES, +! NO DIGITS IN SINGLE PRECISION AND ONLY 7 DIGITS IN DOUBLE +! PRECISION ARITHMETIC. SIMILAR CONSIDERATIONS HOLD FOR OTHER +! MACHINES. +! +! THE APPROXIMATE RELATIVE ERROR IN THE MAGNITUDE OF A COMPLEX +! BESSEL FUNCTION CAN BE EXPRESSED BY P*10**S WHERE P=MAX(UNIT +! ROUNDOFF,1.0E-18) IS THE NOMINAL PRECISION AND 10**S REPRE- +! SENTS THE INCREASE IN ERROR DUE TO ARGUMENT REDUCTION IN THE +! ELEMENTARY FUNCTIONS. HERE, S=MAX(1,ABS(LOG10(CABS(Z))), +! ABS(LOG10(FNU))) APPROXIMATELY (I.E. S=MAX(1,ABS(EXPONENT OF +! CABS(Z),ABS(EXPONENT OF FNU)) ). HOWEVER, THE PHASE ANGLE MAY +! HAVE ONLY ABSOLUTE ACCURACY. THIS IS MOST LIKELY TO OCCUR WHEN +! ONE COMPONENT (IN ABSOLUTE VALUE) IS LARGER THAN THE OTHER BY +! SEVERAL ORDERS OF MAGNITUDE. IF ONE COMPONENT IS 10**K LARGER +! THAN THE OTHER, THEN ONE CAN EXPECT ONLY MAX(ABS(LOG10(P))-K, +! 0) SIGNIFICANT DIGITS; OR, STATED ANOTHER WAY, WHEN K EXCEEDS +! THE EXPONENT OF P, NO SIGNIFICANT DIGITS REMAIN IN THE SMALLER +! COMPONENT. HOWEVER, THE PHASE ANGLE RETAINS ABSOLUTE ACCURACY +! BECAUSE, IN COMPLEX ARITHMETIC WITH PRECISION P, THE SMALLER +! COMPONENT WILL NOT (AS A RULE) DECREASE BELOW P TIMES THE +! MAGNITUDE OF THE LARGER COMPONENT. IN THESE EXTREME CASES, +! THE PRINCIPAL PHASE ANGLE IS ON THE ORDER OF +P, -P, PI/2-P, +! OR -PI/2+P. +! +!***REFERENCES HANDBOOK OF MATHEMATICAL FUNCTIONS BY M. ABRAMOWITZ +! AND I. A. STEGUN, NBS AMS SERIES 55, U.S. DEPT. OF +! COMMERCE, 1955. +! +! COMPUTATION OF BESSEL FUNCTIONS OF COMPLEX ARGUMENT +! AND LARGE ORDER BY D. E. AMOS, SAND83-0643, MAY, 1983 +! +! A SUBROUTINE PACKAGE FOR BESSEL FUNCTIONS OF A COMPLEX +! ARGUMENT AND NONNEGATIVE ORDER BY D. E. AMOS, SAND85- +! 1018, MAY, 1985 +! +! A PORTABLE PACKAGE FOR BESSEL FUNCTIONS OF A COMPLEX +! ARGUMENT AND NONNEGATIVE ORDER BY D. E. AMOS, TRANS. +! MATH. SOFTWARE, 1986 +! +!***ROUTINES CALLED ZACAI,ZBKNU,ZABS,ZEXP,ZSQRT,I1MACH,D1MACH +!***END PROLOGUE ZAIRY +! COMPLEX AI,CONE,CSQ,CY,S1,S2,TRM1,TRM2,Z,ZTA,Z3 + DOUBLE PRECISION AA, AD, AII, AIR, AK, ALIM, ATRM, AZ, AZ3, BK, & + CC, CK, COEF, CONEI, CONER, CSQI, CSQR, CYI, CYR, C1, C2, DIG, & + DK, D1, D2, ELIM, FID, FNU, PTR, RL, R1M5, SFAC, STI, STR, & + S1I, S1R, S2I, S2R, TOL, TRM1I, TRM1R, TRM2I, TRM2R, TTH, ZEROI, & + ZEROR, ZI, ZR, ZTAI, ZTAR, Z3I, Z3R, ALAZ, BB + INTEGER ID, IERR, IFLAG, K, KODE, K1, K2, MR, NN, NZ + DIMENSION CYR(1), CYI(1) + DATA TTH, C1, C2, COEF /6.66666666666666667D-01, & + 3.55028053887817240D-01,2.58819403792806799D-01, & + 1.83776298473930683D-01/ + DATA ZEROR, ZEROI, CONER, CONEI /0.0D0,0.0D0,1.0D0,0.0D0/ +!***FIRST EXECUTABLE STATEMENT ZAIRY + IERR = 0 + NZ=0 + IF (ID.LT.0 .OR. ID.GT.1) IERR=1 + IF (KODE.LT.1 .OR. KODE.GT.2) IERR=1 + IF (IERR.NE.0) RETURN + AZ = ZABS(ZR,ZI) + TOL = DMAX1(D1MACH(4),1.0D-18) + FID = DBLE(FLOAT(ID)) + IF (AZ.GT.1.0D0) GO TO 70 +!----------------------------------------------------------------------- +! POWER SERIES FOR CABS(Z).LE.1. +!----------------------------------------------------------------------- + S1R = CONER + S1I = CONEI + S2R = CONER + S2I = CONEI + IF (AZ.LT.TOL) GO TO 170 + AA = AZ*AZ + IF (AA.LT.TOL/AZ) GO TO 40 + TRM1R = CONER + TRM1I = CONEI + TRM2R = CONER + TRM2I = CONEI + ATRM = 1.0D0 + STR = ZR*ZR - ZI*ZI + STI = ZR*ZI + ZI*ZR + Z3R = STR*ZR - STI*ZI + Z3I = STR*ZI + STI*ZR + AZ3 = AZ*AA + AK = 2.0D0 + FID + BK = 3.0D0 - FID - FID + CK = 4.0D0 - FID + DK = 3.0D0 + FID + FID + D1 = AK*DK + D2 = BK*CK + AD = DMIN1(D1,D2) + AK = 24.0D0 + 9.0D0*FID + BK = 30.0D0 - 9.0D0*FID + DO 30 K=1,25 + STR = (TRM1R*Z3R-TRM1I*Z3I)/D1 + TRM1I = (TRM1R*Z3I+TRM1I*Z3R)/D1 + TRM1R = STR + S1R = S1R + TRM1R + S1I = S1I + TRM1I + STR = (TRM2R*Z3R-TRM2I*Z3I)/D2 + TRM2I = (TRM2R*Z3I+TRM2I*Z3R)/D2 + TRM2R = STR + S2R = S2R + TRM2R + S2I = S2I + TRM2I + ATRM = ATRM*AZ3/AD + D1 = D1 + AK + D2 = D2 + BK + AD = DMIN1(D1,D2) + IF (ATRM.LT.TOL*AD) GO TO 40 + AK = AK + 18.0D0 + BK = BK + 18.0D0 + 30 CONTINUE + 40 CONTINUE + IF (ID.EQ.1) GO TO 50 + AIR = S1R*C1 - C2*(ZR*S2R-ZI*S2I) + AII = S1I*C1 - C2*(ZR*S2I+ZI*S2R) + IF (KODE.EQ.1) RETURN + CALL ZSQRT(ZR, ZI, STR, STI) + ZTAR = TTH*(ZR*STR-ZI*STI) + ZTAI = TTH*(ZR*STI+ZI*STR) + CALL ZEXP(ZTAR, ZTAI, STR, STI) + PTR = AIR*STR - AII*STI + AII = AIR*STI + AII*STR + AIR = PTR + RETURN + 50 CONTINUE + AIR = -S2R*C2 + AII = -S2I*C2 + IF (AZ.LE.TOL) GO TO 60 + STR = ZR*S1R - ZI*S1I + STI = ZR*S1I + ZI*S1R + CC = C1/(1.0D0+FID) + AIR = AIR + CC*(STR*ZR-STI*ZI) + AII = AII + CC*(STR*ZI+STI*ZR) + 60 CONTINUE + IF (KODE.EQ.1) RETURN + CALL ZSQRT(ZR, ZI, STR, STI) + ZTAR = TTH*(ZR*STR-ZI*STI) + ZTAI = TTH*(ZR*STI+ZI*STR) + CALL ZEXP(ZTAR, ZTAI, STR, STI) + PTR = STR*AIR - STI*AII + AII = STR*AII + STI*AIR + AIR = PTR + RETURN +!----------------------------------------------------------------------- +! CASE FOR CABS(Z).GT.1.0 +!----------------------------------------------------------------------- + 70 CONTINUE + FNU = (1.0D0+FID)/3.0D0 +!----------------------------------------------------------------------- +! SET PARAMETERS RELATED TO MACHINE CONSTANTS. +! TOL IS THE APPROXIMATE UNIT ROUNDOFF LIMITED TO 1.0D-18. +! ELIM IS THE APPROXIMATE EXPONENTIAL OVER- AND UNDERFLOW LIMIT. +! EXP(-ELIM).LT.EXP(-ALIM)=EXP(-ELIM)/TOL AND +! EXP(ELIM).GT.EXP(ALIM)=EXP(ELIM)*TOL ARE INTERVALS NEAR +! UNDERFLOW AND OVERFLOW LIMITS WHERE SCALED ARITHMETIC IS DONE. +! RL IS THE LOWER BOUNDARY OF THE ASYMPTOTIC EXPANSION FOR LARGE Z. +! DIG = NUMBER OF BASE 10 DIGITS IN TOL = 10**(-DIG). +!----------------------------------------------------------------------- + K1 = I1MACH(15) + K2 = I1MACH(16) + R1M5 = D1MACH(5) + K = MIN0(IABS(K1),IABS(K2)) + ELIM = 2.303D0*(DBLE(FLOAT(K))*R1M5-3.0D0) + K1 = I1MACH(14) - 1 + AA = R1M5*DBLE(FLOAT(K1)) + DIG = DMIN1(AA,18.0D0) + AA = AA*2.303D0 + ALIM = ELIM + DMAX1(-AA,-41.45D0) + RL = 1.2D0*DIG + 3.0D0 + ALAZ = DLOG(AZ) +!----------------------------------------------------------------------- +! TEST FOR PROPER RANGE +!----------------------------------------------------------------------- + AA=0.5D0/TOL + BB=DBLE(FLOAT(I1MACH(9)))*0.5D0 + AA=DMIN1(AA,BB) + AA=AA**TTH + IF (AZ.GT.AA) GO TO 260 + AA=DSQRT(AA) + IF (AZ.GT.AA) IERR=3 + CALL ZSQRT(ZR, ZI, CSQR, CSQI) + ZTAR = TTH*(ZR*CSQR-ZI*CSQI) + ZTAI = TTH*(ZR*CSQI+ZI*CSQR) +!----------------------------------------------------------------------- +! RE(ZTA).LE.0 WHEN RE(Z).LT.0, ESPECIALLY WHEN IM(Z) IS SMALL +!----------------------------------------------------------------------- + IFLAG = 0 + SFAC = 1.0D0 + AK = ZTAI + IF (ZR.GE.0.0D0) GO TO 80 + BK = ZTAR + CK = -DABS(BK) + ZTAR = CK + ZTAI = AK + 80 CONTINUE + IF (ZI.NE.0.0D0) GO TO 90 + IF (ZR.GT.0.0D0) GO TO 90 + ZTAR = 0.0D0 + ZTAI = AK + 90 CONTINUE + AA = ZTAR + IF (AA.GE.0.0D0 .AND. ZR.GT.0.0D0) GO TO 110 + IF (KODE.EQ.2) GO TO 100 +!----------------------------------------------------------------------- +! OVERFLOW TEST +!----------------------------------------------------------------------- + IF (AA.GT.(-ALIM)) GO TO 100 + AA = -AA + 0.25D0*ALAZ + IFLAG = 1 + SFAC = TOL + IF (AA.GT.ELIM) GO TO 270 + 100 CONTINUE +!----------------------------------------------------------------------- +! CBKNU AND CACON RETURN EXP(ZTA)*K(FNU,ZTA) ON KODE=2 +!----------------------------------------------------------------------- + MR = 1 + IF (ZI.LT.0.0D0) MR = -1 + CALL ZACAI(ZTAR, ZTAI, FNU, KODE, MR, 1, CYR, CYI, NN, RL, TOL, & + ELIM, ALIM) + IF (NN.LT.0) GO TO 280 + NZ = NZ + NN + GO TO 130 + 110 CONTINUE + IF (KODE.EQ.2) GO TO 120 +!----------------------------------------------------------------------- +! UNDERFLOW TEST +!----------------------------------------------------------------------- + IF (AA.LT.ALIM) GO TO 120 + AA = -AA - 0.25D0*ALAZ + IFLAG = 2 + SFAC = 1.0D0/TOL + IF (AA.LT.(-ELIM)) GO TO 210 + 120 CONTINUE + CALL ZBKNU(ZTAR, ZTAI, FNU, KODE, 1, CYR, CYI, NZ, TOL, ELIM, ALIM) + 130 CONTINUE + S1R = CYR(1)*COEF + S1I = CYI(1)*COEF + IF (IFLAG.NE.0) GO TO 150 + IF (ID.EQ.1) GO TO 140 + AIR = CSQR*S1R - CSQI*S1I + AII = CSQR*S1I + CSQI*S1R + RETURN + 140 CONTINUE + AIR = -(ZR*S1R-ZI*S1I) + AII = -(ZR*S1I+ZI*S1R) + RETURN + 150 CONTINUE + S1R = S1R*SFAC + S1I = S1I*SFAC + IF (ID.EQ.1) GO TO 160 + STR = S1R*CSQR - S1I*CSQI + S1I = S1R*CSQI + S1I*CSQR + S1R = STR + AIR = S1R/SFAC + AII = S1I/SFAC + RETURN + 160 CONTINUE + STR = -(S1R*ZR-S1I*ZI) + S1I = -(S1R*ZI+S1I*ZR) + S1R = STR + AIR = S1R/SFAC + AII = S1I/SFAC + RETURN + 170 CONTINUE + AA = 1.0D+3*D1MACH(1) + S1R = ZEROR + S1I = ZEROI + IF (ID.EQ.1) GO TO 190 + IF (AZ.LE.AA) GO TO 180 + S1R = C2*ZR + S1I = C2*ZI + 180 CONTINUE + AIR = C1 - S1R + AII = -S1I + RETURN + 190 CONTINUE + AIR = -C2 + AII = 0.0D0 + AA = DSQRT(AA) + IF (AZ.LE.AA) GO TO 200 + S1R = 0.5D0*(ZR*ZR-ZI*ZI) + S1I = ZR*ZI + 200 CONTINUE + AIR = AIR + C1*S1R + AII = AII + C1*S1I + RETURN + 210 CONTINUE + NZ = 1 + AIR = ZEROR + AII = ZEROI + RETURN + 270 CONTINUE + NZ = 0 + IERR=2 + RETURN + 280 CONTINUE + IF(NN.EQ.(-1)) GO TO 270 + NZ=0 + IERR=5 + RETURN + 260 CONTINUE + IERR=4 + NZ=0 + RETURN +END + +SUBROUTINE ZSERI(ZR, ZI, FNU, KODE, N, YR, YI, NZ, TOL, ELIM, ALIM) +USE UTILIT +USE COMPLEX +!***BEGIN PROLOGUE ZSERI +!***REFER TO ZBESI,ZBESK +! +! ZSERI COMPUTES THE I BESSEL FUNCTION FOR REAL(Z).GE.0.0 BY +! MEANS OF THE POWER SERIES FOR LARGE CABS(Z) IN THE +! REGION CABS(Z).LE.2*SQRT(FNU+1). NZ=0 IS A NORMAL RETURN. +! NZ.GT.0 MEANS THAT THE LAST NZ COMPONENTS WERE SET TO ZERO +! DUE TO UNDERFLOW. NZ.LT.0 MEANS UNDERFLOW OCCURRED, BUT THE +! CONDITION CABS(Z).LE.2*SQRT(FNU+1) WAS VIOLATED AND THE +! COMPUTATION MUST BE COMPLETED IN ANOTHER ROUTINE WITH N=N-ABS(NZ). +! +!***ROUTINES CALLED DGAMLN,D1MACH,ZUCHK,ZABS,ZDIV,ZLOG,ZMLT +!***END PROLOGUE ZSERI +! COMPLEX AK1,CK,COEF,CONE,CRSC,CSCL,CZ,CZERO,HZ,RZ,S1,S2,Y,Z + DOUBLE PRECISION AA, ACZ, AK, AK1I, AK1R, ALIM, ARM, ASCLE, ATOL, & + AZ, CKI, CKR, COEFI, COEFR, CONEI, CONER, CRSCR, CZI, CZR, DFNU, & + ELIM, FNU, FNUP, HZI, HZR, RAZ, RS, RTR1, RZI, RZR, S, SS, STI, & + STR, S1I, S1R, S2I, S2R, TOL, YI, YR, WI, WR, ZEROI, ZEROR, ZI, & + ZR!, DGAMLN + INTEGER I, IB, IDUM, IFLAG, IL, K, KODE, L, M, N, NN, NZ, NW + DIMENSION YR(1), YI(1), WR(2), WI(2) + DATA ZEROR,ZEROI,CONER,CONEI / 0.0D0, 0.0D0, 1.0D0, 0.0D0 / + + NZ = 0 + AZ = ZABS(ZR,ZI) + IF (AZ.EQ.0.0D0) GO TO 160 + ARM = 1.0D+3*D1MACH(1) + RTR1 = DSQRT(ARM) + CRSCR = 1.0D0 + IFLAG = 0 + IF (AZ.LT.ARM) GO TO 150 + HZR = 0.5D0*ZR + HZI = 0.5D0*ZI + CZR = ZEROR + CZI = ZEROI + IF (AZ.LE.RTR1) GO TO 10 + CALL ZMLT(HZR, HZI, HZR, HZI, CZR, CZI) + 10 CONTINUE + ACZ = ZABS(CZR,CZI) + NN = N + CALL ZLOG(HZR, HZI, CKR, CKI, IDUM) + 20 CONTINUE + DFNU = FNU + DBLE(FLOAT(NN-1)) + FNUP = DFNU + 1.0D0 +!----------------------------------------------------------------------- +! UNDERFLOW TEST +!----------------------------------------------------------------------- + AK1R = CKR*DFNU + AK1I = CKI*DFNU + AK = DGAMLN(FNUP,IDUM) + AK1R = AK1R - AK + IF (KODE.EQ.2) AK1R = AK1R - ZR + IF (AK1R.GT.(-ELIM)) GO TO 40 + 30 CONTINUE + NZ = NZ + 1 + YR(NN) = ZEROR + YI(NN) = ZEROI + IF (ACZ.GT.DFNU) GO TO 190 + NN = NN - 1 + IF (NN.EQ.0) RETURN + GO TO 20 + 40 CONTINUE + IF (AK1R.GT.(-ALIM)) GO TO 50 + IFLAG = 1 + SS = 1.0D0/TOL + CRSCR = TOL + ASCLE = ARM*SS + 50 CONTINUE + AA = DEXP(AK1R) + IF (IFLAG.EQ.1) AA = AA*SS + COEFR = AA*DCOS(AK1I) + COEFI = AA*DSIN(AK1I) + ATOL = TOL*ACZ/FNUP + IL = MIN0(2,NN) + DO 90 I=1,IL + DFNU = FNU + DBLE(FLOAT(NN-I)) + FNUP = DFNU + 1.0D0 + S1R = CONER + S1I = CONEI + IF (ACZ.LT.TOL*FNUP) GO TO 70 + AK1R = CONER + AK1I = CONEI + AK = FNUP + 2.0D0 + S = FNUP + AA = 2.0D0 + 60 CONTINUE + RS = 1.0D0/S + STR = AK1R*CZR - AK1I*CZI + STI = AK1R*CZI + AK1I*CZR + AK1R = STR*RS + AK1I = STI*RS + S1R = S1R + AK1R + S1I = S1I + AK1I + S = S + AK + AK = AK + 2.0D0 + AA = AA*ACZ*RS + IF (AA.GT.ATOL) GO TO 60 + 70 CONTINUE + S2R = S1R*COEFR - S1I*COEFI + S2I = S1R*COEFI + S1I*COEFR + WR(I) = S2R + WI(I) = S2I + IF (IFLAG.EQ.0) GO TO 80 + CALL ZUCHK(S2R, S2I, NW, ASCLE, TOL) + IF (NW.NE.0) GO TO 30 + 80 CONTINUE + M = NN - I + 1 + YR(M) = S2R*CRSCR + YI(M) = S2I*CRSCR + IF (I.EQ.IL) GO TO 90 + CALL ZDIV(COEFR, COEFI, HZR, HZI, STR, STI) + COEFR = STR*DFNU + COEFI = STI*DFNU + 90 CONTINUE + IF (NN.LE.2) RETURN + K = NN - 2 + AK = DBLE(FLOAT(K)) + RAZ = 1.0D0/AZ + STR = ZR*RAZ + STI = -ZI*RAZ + RZR = (STR+STR)*RAZ + RZI = (STI+STI)*RAZ + IF (IFLAG.EQ.1) GO TO 120 + IB = 3 + 100 CONTINUE + DO 110 I=IB,NN + YR(K) = (AK+FNU)*(RZR*YR(K+1)-RZI*YI(K+1)) + YR(K+2) + YI(K) = (AK+FNU)*(RZR*YI(K+1)+RZI*YR(K+1)) + YI(K+2) + AK = AK - 1.0D0 + K = K - 1 + 110 CONTINUE + RETURN +!----------------------------------------------------------------------- +! RECUR BACKWARD WITH SCALED VALUES +!----------------------------------------------------------------------- + 120 CONTINUE +!----------------------------------------------------------------------- +! EXP(-ALIM)=EXP(-ELIM)/TOL=APPROX. ONE PRECISION ABOVE THE +! UNDERFLOW LIMIT = ASCLE = D1MACH(1)*SS*1.0D+3 +!----------------------------------------------------------------------- + S1R = WR(1) + S1I = WI(1) + S2R = WR(2) + S2I = WI(2) + DO 130 L=3,NN + CKR = S2R + CKI = S2I + S2R = S1R + (AK+FNU)*(RZR*CKR-RZI*CKI) + S2I = S1I + (AK+FNU)*(RZR*CKI+RZI*CKR) + S1R = CKR + S1I = CKI + CKR = S2R*CRSCR + CKI = S2I*CRSCR + YR(K) = CKR + YI(K) = CKI + AK = AK - 1.0D0 + K = K - 1 + IF (ZABS(CKR,CKI).GT.ASCLE) GO TO 140 + 130 CONTINUE + RETURN + 140 CONTINUE + IB = L + 1 + IF (IB.GT.NN) RETURN + GO TO 100 + 150 CONTINUE + NZ = N + IF (FNU.EQ.0.0D0) NZ = NZ - 1 + 160 CONTINUE + YR(1) = ZEROR + YI(1) = ZEROI + IF (FNU.NE.0.0D0) GO TO 170 + YR(1) = CONER + YI(1) = CONEI + 170 CONTINUE + IF (N.EQ.1) RETURN + DO 180 I=2,N + YR(I) = ZEROR + YI(I) = ZEROI + 180 CONTINUE + RETURN +!----------------------------------------------------------------------- +! RETURN WITH NZ.LT.0 IF CABS(Z*Z/4).GT.FNU+N-NZ-1 COMPLETE +! THE CALCULATION IN CBINU WITH N=N-IABS(NZ) +!----------------------------------------------------------------------- + 190 CONTINUE + NZ = -NZ + RETURN + END + +SUBROUTINE ZASYI(ZR, ZI, FNU, KODE, N, YR, YI, NZ, RL, TOL, ELIM, ALIM) +USE UTILIT +USE COMPLEX +!***BEGIN PROLOGUE ZASYI +!***REFER TO ZBESI,ZBESK + +! ZASYI COMPUTES THE I BESSEL FUNCTION FOR REAL(Z).GE.0.0 BY +! MEANS OF THE ASYMPTOTIC EXPANSION FOR LARGE CABS(Z) IN THE +! REGION CABS(Z).GT.MAX(RL,FNU*FNU/2). NZ=0 IS A NORMAL RETURN. +! NZ.LT.0 INDICATES AN OVERFLOW ON KODE=1. +! +!***ROUTINES CALLED D1MACH,ZABS,ZDIV,ZEXP,ZMLT,ZSQRT +!***END PROLOGUE ZASYI +! COMPLEX AK1,CK,CONE,CS1,CS2,CZ,CZERO,DK,EZ,P1,RZ,S2,Y,Z + DOUBLE PRECISION AA, AEZ, AK, AK1I, AK1R, ALIM, ARG, ARM, ATOL, & + AZ, BB, BK, CKI, CKR, CONEI, CONER, CS1I, CS1R, CS2I, CS2R, CZI, & + CZR, DFNU, DKI, DKR, DNU2, ELIM, EZI, EZR, FDN, FNU, PI, P1I, & + P1R, RAZ, RL, RTPI, RTR1, RZI, RZR, S, SGN, SQK, STI, STR, S2I, & + S2R, TOL, TZI, TZR, YI, YR, ZEROI, ZEROR, ZI, ZR + INTEGER I, IB, IL, INU, J, JL, K, KODE, KODED, M, N, NN, NZ + DIMENSION YR(1), YI(1) + DATA PI, RTPI /3.14159265358979324D0 , 0.159154943091895336D0 / + DATA ZEROR,ZEROI,CONER,CONEI / 0.0D0, 0.0D0, 1.0D0, 0.0D0 / + + NZ = 0 + AZ = ZABS(ZR,ZI) + ARM = 1.0D+3*D1MACH(1) + RTR1 = DSQRT(ARM) + IL = MIN0(2,N) + DFNU = FNU + DBLE(FLOAT(N-IL)) +!----------------------------------------------------------------------- +! OVERFLOW TEST +!----------------------------------------------------------------------- + RAZ = 1.0D0/AZ + STR = ZR*RAZ + STI = -ZI*RAZ + AK1R = RTPI*STR*RAZ + AK1I = RTPI*STI*RAZ + CALL ZSQRT(AK1R, AK1I, AK1R, AK1I) + CZR = ZR + CZI = ZI + IF (KODE.NE.2) GO TO 10 + CZR = ZEROR + CZI = ZI + 10 CONTINUE + IF (DABS(CZR).GT.ELIM) GO TO 100 + DNU2 = DFNU + DFNU + KODED = 1 + IF ((DABS(CZR).GT.ALIM) .AND. (N.GT.2)) GO TO 20 + KODED = 0 + CALL ZEXP(CZR, CZI, STR, STI) + CALL ZMLT(AK1R, AK1I, STR, STI, AK1R, AK1I) + 20 CONTINUE + FDN = 0.0D0 + IF (DNU2.GT.RTR1) FDN = DNU2*DNU2 + EZR = ZR*8.0D0 + EZI = ZI*8.0D0 +!----------------------------------------------------------------------- +! WHEN Z IS IMAGINARY, THE ERROR TEST MUST BE MADE RELATIVE TO THE +! FIRST RECIPROCAL POWER SINCE THIS IS THE LEADING TERM OF THE +! EXPANSION FOR THE IMAGINARY PART. +!----------------------------------------------------------------------- + AEZ = 8.0D0*AZ + S = TOL/AEZ + JL = INT(SNGL(RL+RL)) + 2 + P1R = ZEROR + P1I = ZEROI + IF (ZI.EQ.0.0D0) GO TO 30 +!----------------------------------------------------------------------- +! CALCULATE EXP(PI*(0.5+FNU+N-IL)*I) TO MINIMIZE LOSSES OF +! SIGNIFICANCE WHEN FNU OR N IS LARGE +!----------------------------------------------------------------------- + INU = INT(SNGL(FNU)) + ARG = (FNU-DBLE(FLOAT(INU)))*PI + INU = INU + N - IL + AK = -DSIN(ARG) + BK = DCOS(ARG) + IF (ZI.LT.0.0D0) BK = -BK + P1R = AK + P1I = BK + IF (MOD(INU,2).EQ.0) GO TO 30 + P1R = -P1R + P1I = -P1I + 30 CONTINUE + DO 70 K=1,IL + SQK = FDN - 1.0D0 + ATOL = S*DABS(SQK) + SGN = 1.0D0 + CS1R = CONER + CS1I = CONEI + CS2R = CONER + CS2I = CONEI + CKR = CONER + CKI = CONEI + AK = 0.0D0 + AA = 1.0D0 + BB = AEZ + DKR = EZR + DKI = EZI + DO 40 J=1,JL + CALL ZDIV(CKR, CKI, DKR, DKI, STR, STI) + CKR = STR*SQK + CKI = STI*SQK + CS2R = CS2R + CKR + CS2I = CS2I + CKI + SGN = -SGN + CS1R = CS1R + CKR*SGN + CS1I = CS1I + CKI*SGN + DKR = DKR + EZR + DKI = DKI + EZI + AA = AA*DABS(SQK)/BB + BB = BB + AEZ + AK = AK + 8.0D0 + SQK = SQK - AK + IF (AA.LE.ATOL) GO TO 50 + 40 CONTINUE + GO TO 110 + 50 CONTINUE + S2R = CS1R + S2I = CS1I + IF (ZR+ZR.GE.ELIM) GO TO 60 + TZR = ZR + ZR + TZI = ZI + ZI + CALL ZEXP(-TZR, -TZI, STR, STI) + CALL ZMLT(STR, STI, P1R, P1I, STR, STI) + CALL ZMLT(STR, STI, CS2R, CS2I, STR, STI) + S2R = S2R + STR + S2I = S2I + STI + 60 CONTINUE + FDN = FDN + 8.0D0*DFNU + 4.0D0 + P1R = -P1R + P1I = -P1I + M = N - IL + K + YR(M) = S2R*AK1R - S2I*AK1I + YI(M) = S2R*AK1I + S2I*AK1R + 70 CONTINUE + IF (N.LE.2) RETURN + NN = N + K = NN - 2 + AK = DBLE(FLOAT(K)) + STR = ZR*RAZ + STI = -ZI*RAZ + RZR = (STR+STR)*RAZ + RZI = (STI+STI)*RAZ + IB = 3 + DO 80 I=IB,NN + YR(K) = (AK+FNU)*(RZR*YR(K+1)-RZI*YI(K+1)) + YR(K+2) + YI(K) = (AK+FNU)*(RZR*YI(K+1)+RZI*YR(K+1)) + YI(K+2) + AK = AK - 1.0D0 + K = K - 1 + 80 CONTINUE + IF (KODED.EQ.0) RETURN + CALL ZEXP(CZR, CZI, CKR, CKI) + DO 90 I=1,NN + STR = YR(I)*CKR - YI(I)*CKI + YI(I) = YR(I)*CKI + YI(I)*CKR + YR(I) = STR + 90 CONTINUE + RETURN + 100 CONTINUE + NZ = -1 + RETURN + 110 CONTINUE + NZ=-2 + RETURN + END + +SUBROUTINE ZBUNI(ZR, ZI, FNU, KODE, N, YR, YI, NZ, NUI, NLAST, FNUL, TOL, ELIM, ALIM) +USE UTILIT +USE COMPLEX +!***BEGIN PROLOGUE ZBUNI +!***REFER TO ZBESI,ZBESK +! +! ZBUNI COMPUTES THE I BESSEL FUNCTION FOR LARGE CABS(Z).GT. +! FNUL AND FNU+N-1.LT.FNUL. THE ORDER IS INCREASED FROM +! FNU+N-1 GREATER THAN FNUL BY ADDING NUI AND COMPUTING +! ACCORDING TO THE UNIFORM ASYMPTOTIC EXPANSION FOR I(FNU,Z) +! ON IFORM=1 AND THE EXPANSION FOR J(FNU,Z) ON IFORM=2 +! +!***ROUTINES CALLED ZUNI1,ZUNI2,ZABS,D1MACH +!***END PROLOGUE ZBUNI +! COMPLEX CSCL,CSCR,CY,RZ,ST,S1,S2,Y,Z + DOUBLE PRECISION ALIM, AX, AY, CSCLR, CSCRR, CYI, CYR, DFNU, & + ELIM, FNU, FNUI, FNUL, GNU, RAZ, RZI, RZR, STI, STR, S1I, S1R, & + S2I, S2R, TOL, YI, YR, ZI, ZR, ASCLE, BRY, C1R, C1I, C1M + INTEGER I, IFLAG, IFORM, K, KODE, N, NL, NLAST, NUI, NW, NZ + DIMENSION YR(1), YI(1), CYR(2), CYI(2), BRY(3) + NZ = 0 + AX = DABS(ZR)*1.7321D0 + AY = DABS(ZI) + IFORM = 1 + IF (AY.GT.AX) IFORM = 2 + IF (NUI.EQ.0) GO TO 60 + FNUI = DBLE(FLOAT(NUI)) + DFNU = FNU + DBLE(FLOAT(N-1)) + GNU = DFNU + FNUI + IF (IFORM.EQ.2) GO TO 10 +!----------------------------------------------------------------------- +! ASYMPTOTIC EXPANSION FOR I(FNU,Z) FOR LARGE FNU APPLIED IN +! -PI/3.LE.ARG(Z).LE.PI/3 +!----------------------------------------------------------------------- + CALL ZUNI1(ZR, ZI, GNU, KODE, 2, CYR, CYI, NW, NLAST, FNUL, TOL, ELIM, ALIM) + GO TO 20 + 10 CONTINUE +!----------------------------------------------------------------------- +! ASYMPTOTIC EXPANSION FOR J(FNU,Z*EXP(M*HPI)) FOR LARGE FNU +! APPLIED IN PI/3.LT.ABS(ARG(Z)).LE.PI/2 WHERE M=+I OR -I +! AND HPI=PI/2 +!----------------------------------------------------------------------- + CALL ZUNI2(ZR, ZI, GNU, KODE, 2, CYR, CYI, NW, NLAST, FNUL, TOL, ELIM, ALIM) + 20 CONTINUE + IF (NW.LT.0) GO TO 50 + IF (NW.NE.0) GO TO 90 + STR = ZABS(CYR(1),CYI(1)) +!---------------------------------------------------------------------- +! SCALE BACKWARD RECURRENCE, BRY(3) IS DEFINED BUT NEVER USED +!---------------------------------------------------------------------- + BRY(1)=1.0D+3*D1MACH(1)/TOL + BRY(2) = 1.0D0/BRY(1) + BRY(3) = BRY(2) + IFLAG = 2 + ASCLE = BRY(2) + CSCLR = 1.0D0 + IF (STR.GT.BRY(1)) GO TO 21 + IFLAG = 1 + ASCLE = BRY(1) + CSCLR = 1.0D0/TOL + GO TO 25 + 21 CONTINUE + IF (STR.LT.BRY(2)) GO TO 25 + IFLAG = 3 + ASCLE=BRY(3) + CSCLR = TOL + 25 CONTINUE + CSCRR = 1.0D0/CSCLR + S1R = CYR(2)*CSCLR + S1I = CYI(2)*CSCLR + S2R = CYR(1)*CSCLR + S2I = CYI(1)*CSCLR + RAZ = 1.0D0/ZABS(ZR,ZI) + STR = ZR*RAZ + STI = -ZI*RAZ + RZR = (STR+STR)*RAZ + RZI = (STI+STI)*RAZ + DO 30 I=1,NUI + STR = S2R + STI = S2I + S2R = (DFNU+FNUI)*(RZR*STR-RZI*STI) + S1R + S2I = (DFNU+FNUI)*(RZR*STI+RZI*STR) + S1I + S1R = STR + S1I = STI + FNUI = FNUI - 1.0D0 + IF (IFLAG.GE.3) GO TO 30 + STR = S2R*CSCRR + STI = S2I*CSCRR + C1R = DABS(STR) + C1I = DABS(STI) + C1M = DMAX1(C1R,C1I) + IF (C1M.LE.ASCLE) GO TO 30 + IFLAG = IFLAG+1 + ASCLE = BRY(IFLAG) + S1R = S1R*CSCRR + S1I = S1I*CSCRR + S2R = STR + S2I = STI + CSCLR = CSCLR*TOL + CSCRR = 1.0D0/CSCLR + S1R = S1R*CSCLR + S1I = S1I*CSCLR + S2R = S2R*CSCLR + S2I = S2I*CSCLR + 30 CONTINUE + YR(N) = S2R*CSCRR + YI(N) = S2I*CSCRR + IF (N.EQ.1) RETURN + NL = N - 1 + FNUI = DBLE(FLOAT(NL)) + K = NL + DO 40 I=1,NL + STR = S2R + STI = S2I + S2R = (FNU+FNUI)*(RZR*STR-RZI*STI) + S1R + S2I = (FNU+FNUI)*(RZR*STI+RZI*STR) + S1I + S1R = STR + S1I = STI + STR = S2R*CSCRR + STI = S2I*CSCRR + YR(K) = STR + YI(K) = STI + FNUI = FNUI - 1.0D0 + K = K - 1 + IF (IFLAG.GE.3) GO TO 40 + C1R = DABS(STR) + C1I = DABS(STI) + C1M = DMAX1(C1R,C1I) + IF (C1M.LE.ASCLE) GO TO 40 + IFLAG = IFLAG+1 + ASCLE = BRY(IFLAG) + S1R = S1R*CSCRR + S1I = S1I*CSCRR + S2R = STR + S2I = STI + CSCLR = CSCLR*TOL + CSCRR = 1.0D0/CSCLR + S1R = S1R*CSCLR + S1I = S1I*CSCLR + S2R = S2R*CSCLR + S2I = S2I*CSCLR + 40 CONTINUE + RETURN + 50 CONTINUE + NZ = -1 + IF(NW.EQ.(-2)) NZ=-2 + RETURN + 60 CONTINUE + IF (IFORM.EQ.2) GO TO 70 +!----------------------------------------------------------------------- +! ASYMPTOTIC EXPANSION FOR I(FNU,Z) FOR LARGE FNU APPLIED IN +! -PI/3.LE.ARG(Z).LE.PI/3 +!----------------------------------------------------------------------- + CALL ZUNI1(ZR, ZI, FNU, KODE, N, YR, YI, NW, NLAST, FNUL, TOL, ELIM, ALIM) + GO TO 80 + 70 CONTINUE +!----------------------------------------------------------------------- +! ASYMPTOTIC EXPANSION FOR J(FNU,Z*EXP(M*HPI)) FOR LARGE FNU +! APPLIED IN PI/3.LT.ABS(ARG(Z)).LE.PI/2 WHERE M=+I OR -I +! AND HPI=PI/2 +!----------------------------------------------------------------------- + CALL ZUNI2(ZR, ZI, FNU, KODE, N, YR, YI, NW, NLAST, FNUL, TOL, ELIM, ALIM) + 80 CONTINUE + IF (NW.LT.0) GO TO 50 + NZ = NW + RETURN + 90 CONTINUE + NLAST = N + RETURN + END + +SUBROUTINE ZUNI1(ZR, ZI, FNU, KODE, N, YR, YI, NZ, NLAST, FNUL, TOL, ELIM, ALIM) +USE UTILIT +USE COMPLEX +!***BEGIN PROLOGUE ZUNI1 +!***REFER TO ZBESI,ZBESK +! +! ZUNI1 COMPUTES I(FNU,Z) BY MEANS OF THE UNIFORM ASYMPTOTIC +! EXPANSION FOR I(FNU,Z) IN -PI/3.LE.ARG Z.LE.PI/3. +! +! FNUL IS THE SMALLEST ORDER PERMITTED FOR THE ASYMPTOTIC +! EXPANSION. NLAST=0 MEANS ALL OF THE Y VALUES WERE SET. +! NLAST.NE.0 IS THE NUMBER LEFT TO BE COMPUTED BY ANOTHER +! FORMULA FOR ORDERS FNU TO FNU+NLAST-1 BECAUSE FNU+NLAST-1.LT.FNUL. +! Y(I)=CZERO FOR I=NLAST+1,N +! +!***ROUTINES CALLED ZUCHK,ZUNIK,ZUOIK,D1MACH,ZABS +!***END PROLOGUE ZUNI1 +! COMPLEX CFN,CONE,CRSC,CSCL,CSR,CSS,CWRK,CZERO,C1,C2,PHI,RZ,SUM,S1, +! *S2,Y,Z,ZETA1,ZETA2 + DOUBLE PRECISION ALIM, APHI, ASCLE, BRY, CONEI, CONER, CRSC, & + CSCL, CSRR, CSSR, CWRKI, CWRKR, C1R, C2I, C2M, C2R, ELIM, FN, & + FNU, FNUL, PHII, PHIR, RAST, RS1, RZI, RZR, STI, STR, SUMI, & + SUMR, S1I, S1R, S2I, S2R, TOL, YI, YR, ZEROI, ZEROR, ZETA1I, & + ZETA1R, ZETA2I, ZETA2R, ZI, ZR, CYR, CYI + INTEGER I, IFLAG, INIT, K, KODE, M, N, ND, NLAST, NN, NUF, NW, NZ + DIMENSION BRY(3), YR(1), YI(1), CWRKR(16), CWRKI(16), CSSR(3), & + CSRR(3), CYR(2), CYI(2) + DATA ZEROR,ZEROI,CONER,CONEI / 0.0D0, 0.0D0, 1.0D0, 0.0D0 / + + NZ = 0 + ND = N + NLAST = 0 +!----------------------------------------------------------------------- +! COMPUTED VALUES WITH EXPONENTS BETWEEN ALIM AND ELIM IN MAG- +! NITUDE ARE SCALED TO KEEP INTERMEDIATE ARITHMETIC ON SCALE, +! EXP(ALIM)=EXP(ELIM)*TOL +!----------------------------------------------------------------------- + CSCL = 1.0D0/TOL + CRSC = TOL + CSSR(1) = CSCL + CSSR(2) = CONER + CSSR(3) = CRSC + CSRR(1) = CRSC + CSRR(2) = CONER + CSRR(3) = CSCL + BRY(1) = 1.0D+3*D1MACH(1)/TOL +!----------------------------------------------------------------------- +! CHECK FOR UNDERFLOW AND OVERFLOW ON FIRST MEMBER +!----------------------------------------------------------------------- + FN = DMAX1(FNU,1.0D0) + INIT = 0 + CALL ZUNIK(ZR, ZI, FN, 1, 1, TOL, INIT, PHIR, PHII, ZETA1R, & + ZETA1I, ZETA2R, ZETA2I, SUMR, SUMI, CWRKR, CWRKI) + IF (KODE.EQ.1) GO TO 10 + STR = ZR + ZETA2R + STI = ZI + ZETA2I + RAST = FN/ZABS(STR,STI) + STR = STR*RAST*RAST + STI = -STI*RAST*RAST + S1R = -ZETA1R + STR + S1I = -ZETA1I + STI + GO TO 20 + 10 CONTINUE + S1R = -ZETA1R + ZETA2R + S1I = -ZETA1I + ZETA2I + 20 CONTINUE + RS1 = S1R + IF (DABS(RS1).GT.ELIM) GO TO 130 + 30 CONTINUE + NN = MIN0(2,ND) + DO 80 I=1,NN + FN = FNU + DBLE(FLOAT(ND-I)) + INIT = 0 + CALL ZUNIK(ZR, ZI, FN, 1, 0, TOL, INIT, PHIR, PHII, ZETA1R, & + ZETA1I, ZETA2R, ZETA2I, SUMR, SUMI, CWRKR, CWRKI) + IF (KODE.EQ.1) GO TO 40 + STR = ZR + ZETA2R + STI = ZI + ZETA2I + RAST = FN/ZABS(STR,STI) + STR = STR*RAST*RAST + STI = -STI*RAST*RAST + S1R = -ZETA1R + STR + S1I = -ZETA1I + STI + ZI + GO TO 50 + 40 CONTINUE + S1R = -ZETA1R + ZETA2R + S1I = -ZETA1I + ZETA2I + 50 CONTINUE +!----------------------------------------------------------------------- +! TEST FOR UNDERFLOW AND OVERFLOW +!----------------------------------------------------------------------- + RS1 = S1R + IF (DABS(RS1).GT.ELIM) GO TO 110 + IF (I.EQ.1) IFLAG = 2 + IF (DABS(RS1).LT.ALIM) GO TO 60 +!----------------------------------------------------------------------- +! REFINE TEST AND SCALE +!----------------------------------------------------------------------- + APHI = ZABS(PHIR,PHII) + RS1 = RS1 + DLOG(APHI) + IF (DABS(RS1).GT.ELIM) GO TO 110 + IF (I.EQ.1) IFLAG = 1 + IF (RS1.LT.0.0D0) GO TO 60 + IF (I.EQ.1) IFLAG = 3 + 60 CONTINUE +!----------------------------------------------------------------------- +! SCALE S1 IF CABS(S1).LT.ASCLE +!----------------------------------------------------------------------- + S2R = PHIR*SUMR - PHII*SUMI + S2I = PHIR*SUMI + PHII*SUMR + STR = DEXP(S1R)*CSSR(IFLAG) + S1R = STR*DCOS(S1I) + S1I = STR*DSIN(S1I) + STR = S2R*S1R - S2I*S1I + S2I = S2R*S1I + S2I*S1R + S2R = STR + IF (IFLAG.NE.1) GO TO 70 + CALL ZUCHK(S2R, S2I, NW, BRY(1), TOL) + IF (NW.NE.0) GO TO 110 + 70 CONTINUE + CYR(I) = S2R + CYI(I) = S2I + M = ND - I + 1 + YR(M) = S2R*CSRR(IFLAG) + YI(M) = S2I*CSRR(IFLAG) + 80 CONTINUE + IF (ND.LE.2) GO TO 100 + RAST = 1.0D0/ZABS(ZR,ZI) + STR = ZR*RAST + STI = -ZI*RAST + RZR = (STR+STR)*RAST + RZI = (STI+STI)*RAST + BRY(2) = 1.0D0/BRY(1) + BRY(3) = D1MACH(2) + S1R = CYR(1) + S1I = CYI(1) + S2R = CYR(2) + S2I = CYI(2) + C1R = CSRR(IFLAG) + ASCLE = BRY(IFLAG) + K = ND - 2 + FN = DBLE(FLOAT(K)) + DO 90 I=3,ND + C2R = S2R + C2I = S2I + S2R = S1R + (FNU+FN)*(RZR*C2R-RZI*C2I) + S2I = S1I + (FNU+FN)*(RZR*C2I+RZI*C2R) + S1R = C2R + S1I = C2I + C2R = S2R*C1R + C2I = S2I*C1R + YR(K) = C2R + YI(K) = C2I + K = K - 1 + FN = FN - 1.0D0 + IF (IFLAG.GE.3) GO TO 90 + STR = DABS(C2R) + STI = DABS(C2I) + C2M = DMAX1(STR,STI) + IF (C2M.LE.ASCLE) GO TO 90 + IFLAG = IFLAG + 1 + ASCLE = BRY(IFLAG) + S1R = S1R*C1R + S1I = S1I*C1R + S2R = C2R + S2I = C2I + S1R = S1R*CSSR(IFLAG) + S1I = S1I*CSSR(IFLAG) + S2R = S2R*CSSR(IFLAG) + S2I = S2I*CSSR(IFLAG) + C1R = CSRR(IFLAG) + 90 CONTINUE + 100 CONTINUE + RETURN +!----------------------------------------------------------------------- +! SET UNDERFLOW AND UPDATE PARAMETERS +!----------------------------------------------------------------------- + 110 CONTINUE + IF (RS1.GT.0.0D0) GO TO 120 + YR(ND) = ZEROR + YI(ND) = ZEROI + NZ = NZ + 1 + ND = ND - 1 + IF (ND.EQ.0) GO TO 100 + CALL ZUOIK(ZR, ZI, FNU, KODE, 1, ND, YR, YI, NUF, TOL, ELIM, ALIM) + IF (NUF.LT.0) GO TO 120 + ND = ND - NUF + NZ = NZ + NUF + IF (ND.EQ.0) GO TO 100 + FN = FNU + DBLE(FLOAT(ND-1)) + IF (FN.GE.FNUL) GO TO 30 + NLAST = ND + RETURN + 120 CONTINUE + NZ = -1 + RETURN + 130 CONTINUE + IF (RS1.GT.0.0D0) GO TO 120 + NZ = N + DO 140 I=1,N + YR(I) = ZEROR + YI(I) = ZEROI + 140 CONTINUE + RETURN + END + +SUBROUTINE ZUNI2(ZR, ZI, FNU, KODE, N, YR, YI, NZ, NLAST, FNUL, TOL, ELIM, ALIM) +USE UTILIT +USE COMPLEX +!***BEGIN PROLOGUE ZUNI2 +!***REFER TO ZBESI,ZBESK +! +! ZUNI2 COMPUTES I(FNU,Z) IN THE RIGHT HALF PLANE BY MEANS OF +! UNIFORM ASYMPTOTIC EXPANSION FOR J(FNU,ZN) WHERE ZN IS Z*I +! OR -Z*I AND ZN IS IN THE RIGHT HALF PLANE ALSO. +! +! FNUL IS THE SMALLEST ORDER PERMITTED FOR THE ASYMPTOTIC +! EXPANSION. NLAST=0 MEANS ALL OF THE Y VALUES WERE SET. +! NLAST.NE.0 IS THE NUMBER LEFT TO BE COMPUTED BY ANOTHER +! FORMULA FOR ORDERS FNU TO FNU+NLAST-1 BECAUSE FNU+NLAST-1.LT.FNUL. +! Y(I)=CZERO FOR I=NLAST+1,N +! +!***ROUTINES CALLED ZAIRY,ZUCHK,ZUNHJ,ZUOIK,D1MACH,ZABS +!***END PROLOGUE ZUNI2 +! COMPLEX AI,ARG,ASUM,BSUM,CFN,CI,CID,CIP,CONE,CRSC,CSCL,CSR,CSS, +! *CZERO,C1,C2,DAI,PHI,RZ,S1,S2,Y,Z,ZB,ZETA1,ZETA2,ZN + DOUBLE PRECISION AARG, AIC, AII, AIR, ALIM, ANG, APHI, ARGI, & + ARGR, ASCLE, ASUMI, ASUMR, BRY, BSUMI, BSUMR, CIDI, CIPI, CIPR, & + CONEI, CONER, CRSC, CSCL, CSRR, CSSR, C1R, C2I, C2M, C2R, DAII, & + DAIR, ELIM, FN, FNU, FNUL, HPI, PHII, PHIR, RAST, RAZ, RS1, RZI, & + RZR, STI, STR, S1I, S1R, S2I, S2R, TOL, YI, YR, ZBI, ZBR, ZEROI, & + ZEROR, ZETA1I, ZETA1R, ZETA2I, ZETA2R, ZI, ZNI, ZNR, ZR, CYR, CYI + INTEGER I, IFLAG, IN, INU, J, K, KODE, N, NAI, ND, NDAI, NLAST, & + NN, NUF, NW, NZ, IDUM + DIMENSION BRY(3), YR(1), YI(1), CIPR(4), CIPI(4), CSSR(3), & + CSRR(3), CYR(2), CYI(2) + DATA ZEROR,ZEROI,CONER,CONEI / 0.0D0, 0.0D0, 1.0D0, 0.0D0 / + DATA CIPR(1),CIPI(1),CIPR(2),CIPI(2),CIPR(3),CIPI(3),CIPR(4), & + CIPI(4)/ 1.0D0,0.0D0, 0.0D0,1.0D0, -1.0D0,0.0D0, 0.0D0,-1.0D0/ + DATA HPI, AIC /1.57079632679489662D+00, 1.265512123484645396D+00/ + + NZ = 0 + ND = N + NLAST = 0 +!----------------------------------------------------------------------- +! COMPUTED VALUES WITH EXPONENTS BETWEEN ALIM AND ELIM IN MAG- +! NITUDE ARE SCALED TO KEEP INTERMEDIATE ARITHMETIC ON SCALE, +! EXP(ALIM)=EXP(ELIM)*TOL +!----------------------------------------------------------------------- + CSCL = 1.0D0/TOL + CRSC = TOL + CSSR(1) = CSCL + CSSR(2) = CONER + CSSR(3) = CRSC + CSRR(1) = CRSC + CSRR(2) = CONER + CSRR(3) = CSCL + BRY(1) = 1.0D+3*D1MACH(1)/TOL +!----------------------------------------------------------------------- +! ZN IS IN THE RIGHT HALF PLANE AFTER ROTATION BY CI OR -CI +!----------------------------------------------------------------------- + ZNR = ZI + ZNI = -ZR + ZBR = ZR + ZBI = ZI + CIDI = -CONER + INU = INT(SNGL(FNU)) + ANG = HPI*(FNU-DBLE(FLOAT(INU))) + C2R = DCOS(ANG) + C2I = DSIN(ANG) + IN = INU + N - 1 + IN = MOD(IN,4) + 1 + STR = C2R*CIPR(IN) - C2I*CIPI(IN) + C2I = C2R*CIPI(IN) + C2I*CIPR(IN) + C2R = STR + IF (ZI.GT.0.0D0) GO TO 10 + ZNR = -ZNR + ZBI = -ZBI + CIDI = -CIDI + C2I = -C2I + 10 CONTINUE +!----------------------------------------------------------------------- +! CHECK FOR UNDERFLOW AND OVERFLOW ON FIRST MEMBER +!----------------------------------------------------------------------- + FN = DMAX1(FNU,1.0D0) + CALL ZUNHJ(ZNR, ZNI, FN, 1, TOL, PHIR, PHII, ARGR, ARGI, ZETA1R, & + ZETA1I, ZETA2R, ZETA2I, ASUMR, ASUMI, BSUMR, BSUMI) + IF (KODE.EQ.1) GO TO 20 + STR = ZBR + ZETA2R + STI = ZBI + ZETA2I + RAST = FN/ZABS(STR,STI) + STR = STR*RAST*RAST + STI = -STI*RAST*RAST + S1R = -ZETA1R + STR + S1I = -ZETA1I + STI + GO TO 30 + 20 CONTINUE + S1R = -ZETA1R + ZETA2R + S1I = -ZETA1I + ZETA2I + 30 CONTINUE + RS1 = S1R + IF (DABS(RS1).GT.ELIM) GO TO 150 + 40 CONTINUE + NN = MIN0(2,ND) + DO 90 I=1,NN + FN = FNU + DBLE(FLOAT(ND-I)) + CALL ZUNHJ(ZNR, ZNI, FN, 0, TOL, PHIR, PHII, ARGR, ARGI, & + ZETA1R, ZETA1I, ZETA2R, ZETA2I, ASUMR, ASUMI, BSUMR, BSUMI) + IF (KODE.EQ.1) GO TO 50 + STR = ZBR + ZETA2R + STI = ZBI + ZETA2I + RAST = FN/ZABS(STR,STI) + STR = STR*RAST*RAST + STI = -STI*RAST*RAST + S1R = -ZETA1R + STR + S1I = -ZETA1I + STI + DABS(ZI) + GO TO 60 + 50 CONTINUE + S1R = -ZETA1R + ZETA2R + S1I = -ZETA1I + ZETA2I + 60 CONTINUE +!----------------------------------------------------------------------- +! TEST FOR UNDERFLOW AND OVERFLOW +!----------------------------------------------------------------------- + RS1 = S1R + IF (DABS(RS1).GT.ELIM) GO TO 120 + IF (I.EQ.1) IFLAG = 2 + IF (DABS(RS1).LT.ALIM) GO TO 70 +!----------------------------------------------------------------------- +! REFINE TEST AND SCALE +!----------------------------------------------------------------------- + APHI = ZABS(PHIR,PHII) + AARG = ZABS(ARGR,ARGI) + RS1 = RS1 + DLOG(APHI) - 0.25D0*DLOG(AARG) - AIC + IF (DABS(RS1).GT.ELIM) GO TO 120 + IF (I.EQ.1) IFLAG = 1 + IF (RS1.LT.0.0D0) GO TO 70 + IF (I.EQ.1) IFLAG = 3 + 70 CONTINUE +!----------------------------------------------------------------------- +! SCALE S1 TO KEEP INTERMEDIATE ARITHMETIC ON SCALE NEAR +! EXPONENT EXTREMES +!----------------------------------------------------------------------- + CALL ZAIRY(ARGR, ARGI, 0, 2, AIR, AII, NAI, IDUM) + CALL ZAIRY(ARGR, ARGI, 1, 2, DAIR, DAII, NDAI, IDUM) + STR = DAIR*BSUMR - DAII*BSUMI + STI = DAIR*BSUMI + DAII*BSUMR + STR = STR + (AIR*ASUMR-AII*ASUMI) + STI = STI + (AIR*ASUMI+AII*ASUMR) + S2R = PHIR*STR - PHII*STI + S2I = PHIR*STI + PHII*STR + STR = DEXP(S1R)*CSSR(IFLAG) + S1R = STR*DCOS(S1I) + S1I = STR*DSIN(S1I) + STR = S2R*S1R - S2I*S1I + S2I = S2R*S1I + S2I*S1R + S2R = STR + IF (IFLAG.NE.1) GO TO 80 + CALL ZUCHK(S2R, S2I, NW, BRY(1), TOL) + IF (NW.NE.0) GO TO 120 + 80 CONTINUE + IF (ZI.LE.0.0D0) S2I = -S2I + STR = S2R*C2R - S2I*C2I + S2I = S2R*C2I + S2I*C2R + S2R = STR + CYR(I) = S2R + CYI(I) = S2I + J = ND - I + 1 + YR(J) = S2R*CSRR(IFLAG) + YI(J) = S2I*CSRR(IFLAG) + STR = -C2I*CIDI + C2I = C2R*CIDI + C2R = STR + 90 CONTINUE + IF (ND.LE.2) GO TO 110 + RAZ = 1.0D0/ZABS(ZR,ZI) + STR = ZR*RAZ + STI = -ZI*RAZ + RZR = (STR+STR)*RAZ + RZI = (STI+STI)*RAZ + BRY(2) = 1.0D0/BRY(1) + BRY(3) = D1MACH(2) + S1R = CYR(1) + S1I = CYI(1) + S2R = CYR(2) + S2I = CYI(2) + C1R = CSRR(IFLAG) + ASCLE = BRY(IFLAG) + K = ND - 2 + FN = DBLE(FLOAT(K)) + DO 100 I=3,ND + C2R = S2R + C2I = S2I + S2R = S1R + (FNU+FN)*(RZR*C2R-RZI*C2I) + S2I = S1I + (FNU+FN)*(RZR*C2I+RZI*C2R) + S1R = C2R + S1I = C2I + C2R = S2R*C1R + C2I = S2I*C1R + YR(K) = C2R + YI(K) = C2I + K = K - 1 + FN = FN - 1.0D0 + IF (IFLAG.GE.3) GO TO 100 + STR = DABS(C2R) + STI = DABS(C2I) + C2M = DMAX1(STR,STI) + IF (C2M.LE.ASCLE) GO TO 100 + IFLAG = IFLAG + 1 + ASCLE = BRY(IFLAG) + S1R = S1R*C1R + S1I = S1I*C1R + S2R = C2R + S2I = C2I + S1R = S1R*CSSR(IFLAG) + S1I = S1I*CSSR(IFLAG) + S2R = S2R*CSSR(IFLAG) + S2I = S2I*CSSR(IFLAG) + C1R = CSRR(IFLAG) + 100 CONTINUE + 110 CONTINUE + RETURN + 120 CONTINUE + IF (RS1.GT.0.0D0) GO TO 140 +!----------------------------------------------------------------------- +! SET UNDERFLOW AND UPDATE PARAMETERS +!----------------------------------------------------------------------- + YR(ND) = ZEROR + YI(ND) = ZEROI + NZ = NZ + 1 + ND = ND - 1 + IF (ND.EQ.0) GO TO 110 + CALL ZUOIK(ZR, ZI, FNU, KODE, 1, ND, YR, YI, NUF, TOL, ELIM, ALIM) + IF (NUF.LT.0) GO TO 140 + ND = ND - NUF + NZ = NZ + NUF + IF (ND.EQ.0) GO TO 110 + FN = FNU + DBLE(FLOAT(ND-1)) + IF (FN.LT.FNUL) GO TO 130 + FN = CIDI + J = NUF + 1 + K = MOD(J,4) + 1 + S1R = CIPR(K) + S1I = CIPI(K) + IF (FN.LT.0.0D0) S1I = -S1I + STR = C2R*S1R - C2I*S1I + C2I = C2R*S1I + C2I*S1R + C2R = STR + GO TO 40 + 130 CONTINUE + NLAST = ND + RETURN + 140 CONTINUE + NZ = -1 + RETURN + 150 CONTINUE + IF (RS1.GT.0.0D0) GO TO 140 + NZ = N + DO 160 I=1,N + YR(I) = ZEROR + YI(I) = ZEROI + 160 CONTINUE + RETURN + END + +SUBROUTINE ZWRSK(ZRR, ZRI, FNU, KODE, N, YR, YI, NZ, CWR, CWI, TOL, ELIM, ALIM) +USE UTILIT +USE COMPLEX +!***BEGIN PROLOGUE ZWRSK +!***REFER TO ZBESI,ZBESK +! +! ZWRSK COMPUTES THE I BESSEL FUNCTION FOR RE(Z).GE.0.0 BY +! NORMALIZING THE I FUNCTION RATIOS FROM ZRATI BY THE WRONSKIAN +! +!***ROUTINES CALLED D1MACH,ZBKNU,ZRATI,ZABS +!***END PROLOGUE ZWRSK +! COMPLEX CINU,CSCL,CT,CW,C1,C2,RCT,ST,Y,ZR + DOUBLE PRECISION ACT, ACW, ALIM, ASCLE, CINUI, CINUR, CSCLR, CTI, & + CTR, CWI, CWR, C1I, C1R, C2I, C2R, ELIM, FNU, PTI, PTR, RACT, & + STI, STR, TOL, YI, YR, ZRI, ZRR + INTEGER I, KODE, N, NW, NZ + DIMENSION YR(1), YI(1), CWR(2), CWI(2) +!----------------------------------------------------------------------- +! I(FNU+I-1,Z) BY BACKWARD RECURRENCE FOR RATIOS +! Y(I)=I(FNU+I,Z)/I(FNU+I-1,Z) FROM CRATI NORMALIZED BY THE +! WRONSKIAN WITH K(FNU,Z) AND K(FNU+1,Z) FROM CBKNU. +!----------------------------------------------------------------------- + NZ = 0 + CALL ZBKNU(ZRR, ZRI, FNU, KODE, 2, CWR, CWI, NW, TOL, ELIM, ALIM) + IF (NW.NE.0) GO TO 50 + CALL ZRATI(ZRR, ZRI, FNU, N, YR, YI, TOL) +!----------------------------------------------------------------------- +! RECUR FORWARD ON I(FNU+1,Z) = R(FNU,Z)*I(FNU,Z), +! R(FNU+J-1,Z)=Y(J), J=1,...,N +!----------------------------------------------------------------------- + CINUR = 1.0D0 + CINUI = 0.0D0 + IF (KODE.EQ.1) GO TO 10 + CINUR = DCOS(ZRI) + CINUI = DSIN(ZRI) + 10 CONTINUE +!----------------------------------------------------------------------- +! ON LOW EXPONENT MACHINES THE K FUNCTIONS CAN BE CLOSE TO BOTH +! THE UNDER AND OVERFLOW LIMITS AND THE NORMALIZATION MUST BE +! SCALED TO PREVENT OVER OR UNDERFLOW. CUOIK HAS DETERMINED THAT +! THE RESULT IS ON SCALE. +!----------------------------------------------------------------------- + ACW = ZABS(CWR(2),CWI(2)) + ASCLE = 1.0D+3*D1MACH(1)/TOL + CSCLR = 1.0D0 + IF (ACW.GT.ASCLE) GO TO 20 + CSCLR = 1.0D0/TOL + GO TO 30 + 20 CONTINUE + ASCLE = 1.0D0/ASCLE + IF (ACW.LT.ASCLE) GO TO 30 + CSCLR = TOL + 30 CONTINUE + C1R = CWR(1)*CSCLR + C1I = CWI(1)*CSCLR + C2R = CWR(2)*CSCLR + C2I = CWI(2)*CSCLR + STR = YR(1) + STI = YI(1) +!----------------------------------------------------------------------- +! CINU=CINU*(CONJG(CT)/CABS(CT))*(1.0D0/CABS(CT) PREVENTS +! UNDER- OR OVERFLOW PREMATURELY BY SQUARING CABS(CT) +!----------------------------------------------------------------------- + PTR = STR*C1R - STI*C1I + PTI = STR*C1I + STI*C1R + PTR = PTR + C2R + PTI = PTI + C2I + CTR = ZRR*PTR - ZRI*PTI + CTI = ZRR*PTI + ZRI*PTR + ACT = ZABS(CTR,CTI) + RACT = 1.0D0/ACT + CTR = CTR*RACT + CTI = -CTI*RACT + PTR = CINUR*RACT + PTI = CINUI*RACT + CINUR = PTR*CTR - PTI*CTI + CINUI = PTR*CTI + PTI*CTR + YR(1) = CINUR*CSCLR + YI(1) = CINUI*CSCLR + IF (N.EQ.1) RETURN + DO 40 I=2,N + PTR = STR*CINUR - STI*CINUI + CINUI = STR*CINUI + STI*CINUR + CINUR = PTR + STR = YR(I) + STI = YI(I) + YR(I) = CINUR*CSCLR + YI(I) = CINUI*CSCLR + 40 CONTINUE + RETURN + 50 CONTINUE + NZ = -1 + IF(NW.EQ.(-2)) NZ=-2 + RETURN +END + +SUBROUTINE ZMLRI(ZR, ZI, FNU, KODE, N, YR, YI, NZ, TOL) +USE UTILIT +USE COMPLEX +!***BEGIN PROLOGUE ZMLRI +!***REFER TO ZBESI,ZBESK +! +! ZMLRI COMPUTES THE I BESSEL FUNCTION FOR RE(Z).GE.0.0 BY THE +! MILLER ALGORITHM NORMALIZED BY A NEUMANN SERIES. +! +!***ROUTINES CALLED DGAMLN,D1MACH,ZABS,ZEXP,ZLOG,ZMLT +!***END PROLOGUE ZMLRI +! COMPLEX CK,CNORM,CONE,CTWO,CZERO,PT,P1,P2,RZ,SUM,Y,Z + DOUBLE PRECISION ACK, AK, AP, AT, AZ, BK, CKI, CKR, CNORMI, & + CNORMR, CONEI, CONER, FKAP, FKK, FLAM, FNF, FNU, PTI, PTR, P1I, & + P1R, P2I, P2R, RAZ, RHO, RHO2, RZI, RZR, SCLE, STI, STR, SUMI, & + SUMR, TFNF, TOL, TST, YI, YR, ZEROI, ZEROR, ZI, ZR!, DGAMLN + INTEGER I, IAZ, IDUM, IFNU, INU, ITIME, K, KK, KM, KODE, M, N, NZ + DIMENSION YR(1), YI(1) + DATA ZEROR,ZEROI,CONER,CONEI / 0.0D0, 0.0D0, 1.0D0, 0.0D0 / + SCLE = D1MACH(1)/TOL + NZ=0 + AZ = ZABS(ZR,ZI) + IAZ = INT(SNGL(AZ)) + IFNU = INT(SNGL(FNU)) + INU = IFNU + N - 1 + AT = DBLE(FLOAT(IAZ)) + 1.0D0 + RAZ = 1.0D0/AZ + STR = ZR*RAZ + STI = -ZI*RAZ + CKR = STR*AT*RAZ + CKI = STI*AT*RAZ + RZR = (STR+STR)*RAZ + RZI = (STI+STI)*RAZ + P1R = ZEROR + P1I = ZEROI + P2R = CONER + P2I = CONEI + ACK = (AT+1.0D0)*RAZ + RHO = ACK + DSQRT(ACK*ACK-1.0D0) + RHO2 = RHO*RHO + TST = (RHO2+RHO2)/((RHO2-1.0D0)*(RHO-1.0D0)) + TST = TST/TOL +!----------------------------------------------------------------------- +! COMPUTE RELATIVE TRUNCATION ERROR INDEX FOR SERIES +!----------------------------------------------------------------------- + AK = AT + DO 10 I=1,80 + PTR = P2R + PTI = P2I + P2R = P1R - (CKR*PTR-CKI*PTI) + P2I = P1I - (CKI*PTR+CKR*PTI) + P1R = PTR + P1I = PTI + CKR = CKR + RZR + CKI = CKI + RZI + AP = ZABS(P2R,P2I) + IF (AP.GT.TST*AK*AK) GO TO 20 + AK = AK + 1.0D0 + 10 CONTINUE + GO TO 110 + 20 CONTINUE + I = I + 1 + K = 0 + IF (INU.LT.IAZ) GO TO 40 +!----------------------------------------------------------------------- +! COMPUTE RELATIVE TRUNCATION ERROR FOR RATIOS +!----------------------------------------------------------------------- + P1R = ZEROR + P1I = ZEROI + P2R = CONER + P2I = CONEI + AT = DBLE(FLOAT(INU)) + 1.0D0 + STR = ZR*RAZ + STI = -ZI*RAZ + CKR = STR*AT*RAZ + CKI = STI*AT*RAZ + ACK = AT*RAZ + TST = DSQRT(ACK/TOL) + ITIME = 1 + DO 30 K=1,80 + PTR = P2R + PTI = P2I + P2R = P1R - (CKR*PTR-CKI*PTI) + P2I = P1I - (CKR*PTI+CKI*PTR) + P1R = PTR + P1I = PTI + CKR = CKR + RZR + CKI = CKI + RZI + AP = ZABS(P2R,P2I) + IF (AP.LT.TST) GO TO 30 + IF (ITIME.EQ.2) GO TO 40 + ACK = ZABS(CKR,CKI) + FLAM = ACK + DSQRT(ACK*ACK-1.0D0) + FKAP = AP/ZABS(P1R,P1I) + RHO = DMIN1(FLAM,FKAP) + TST = TST*DSQRT(RHO/(RHO*RHO-1.0D0)) + ITIME = 2 + 30 CONTINUE + GO TO 110 + 40 CONTINUE +!----------------------------------------------------------------------- +! BACKWARD RECURRENCE AND SUM NORMALIZING RELATION +!----------------------------------------------------------------------- + K = K + 1 + KK = MAX0(I+IAZ,K+INU) + FKK = DBLE(FLOAT(KK)) + P1R = ZEROR + P1I = ZEROI +!----------------------------------------------------------------------- +! SCALE P2 AND SUM BY SCLE +!----------------------------------------------------------------------- + P2R = SCLE + P2I = ZEROI + FNF = FNU - DBLE(FLOAT(IFNU)) + TFNF = FNF + FNF + BK = DGAMLN(FKK+TFNF+1.0D0,IDUM) - DGAMLN(FKK+1.0D0,IDUM) - & + DGAMLN(TFNF+1.0D0,IDUM) + BK = DEXP(BK) + SUMR = ZEROR + SUMI = ZEROI + KM = KK - INU + DO 50 I=1,KM + PTR = P2R + PTI = P2I + P2R = P1R + (FKK+FNF)*(RZR*PTR-RZI*PTI) + P2I = P1I + (FKK+FNF)*(RZI*PTR+RZR*PTI) + P1R = PTR + P1I = PTI + AK = 1.0D0 - TFNF/(FKK+TFNF) + ACK = BK*AK + SUMR = SUMR + (ACK+BK)*P1R + SUMI = SUMI + (ACK+BK)*P1I + BK = ACK + FKK = FKK - 1.0D0 + 50 CONTINUE + YR(N) = P2R + YI(N) = P2I + IF (N.EQ.1) GO TO 70 + DO 60 I=2,N + PTR = P2R + PTI = P2I + P2R = P1R + (FKK+FNF)*(RZR*PTR-RZI*PTI) + P2I = P1I + (FKK+FNF)*(RZI*PTR+RZR*PTI) + P1R = PTR + P1I = PTI + AK = 1.0D0 - TFNF/(FKK+TFNF) + ACK = BK*AK + SUMR = SUMR + (ACK+BK)*P1R + SUMI = SUMI + (ACK+BK)*P1I + BK = ACK + FKK = FKK - 1.0D0 + M = N - I + 1 + YR(M) = P2R + YI(M) = P2I + 60 CONTINUE + 70 CONTINUE + IF (IFNU.LE.0) GO TO 90 + DO 80 I=1,IFNU + PTR = P2R + PTI = P2I + P2R = P1R + (FKK+FNF)*(RZR*PTR-RZI*PTI) + P2I = P1I + (FKK+FNF)*(RZR*PTI+RZI*PTR) + P1R = PTR + P1I = PTI + AK = 1.0D0 - TFNF/(FKK+TFNF) + ACK = BK*AK + SUMR = SUMR + (ACK+BK)*P1R + SUMI = SUMI + (ACK+BK)*P1I + BK = ACK + FKK = FKK - 1.0D0 + 80 CONTINUE + 90 CONTINUE + PTR = ZR + PTI = ZI + IF (KODE.EQ.2) PTR = ZEROR + CALL ZLOG(RZR, RZI, STR, STI, IDUM) + P1R = -FNF*STR + PTR + P1I = -FNF*STI + PTI + AP = DGAMLN(1.0D0+FNF,IDUM) + PTR = P1R - AP + PTI = P1I +!----------------------------------------------------------------------- +! THE DIVISION CEXP(PT)/(SUM+P2) IS ALTERED TO AVOID OVERFLOW +! IN THE DENOMINATOR BY SQUARING LARGE QUANTITIES +!----------------------------------------------------------------------- + P2R = P2R + SUMR + P2I = P2I + SUMI + AP = ZABS(P2R,P2I) + P1R = 1.0D0/AP + CALL ZEXP(PTR, PTI, STR, STI) + CKR = STR*P1R + CKI = STI*P1R + PTR = P2R*P1R + PTI = -P2I*P1R + CALL ZMLT(CKR, CKI, PTR, PTI, CNORMR, CNORMI) + DO 100 I=1,N + STR = YR(I)*CNORMR - YI(I)*CNORMI + YI(I) = YR(I)*CNORMI + YI(I)*CNORMR + YR(I) = STR + 100 CONTINUE + RETURN + 110 CONTINUE + NZ=-2 + RETURN +END +end module bessely +!end of file tzbesy.f90 diff --git a/applications/PUfoam/MoDeNaModels/foamConductivity/src/src/complex.f90 b/applications/PUfoam/MoDeNaModels/foamConductivity/src/src/complex.f90 new file mode 100644 index 000000000..2950d8d44 --- /dev/null +++ b/applications/PUfoam/MoDeNaModels/foamConductivity/src/src/complex.f90 @@ -0,0 +1,183 @@ +! --------------------------------------------------------------------- +! Utility subroutines used by any program from Numath library +! with (not intrinsic) complex numbers z = (zr,zi). +! --------------------------------------------------------------------- +! Reference: From Numath Library By Tuan Dang Trong in Fortran 77 +! [BIBLI 18]. +! +! F90 Release 1.0 By J-P Moreau, Paris +! (www.jpmoreau.fr) +! --------------------------------------------------------------------- +MODULE COMPLEX + +CONTAINS + +SUBROUTINE ZSQRT(AR, AI, BR, BI) +!***BEGIN PROLOGUE ZSQRT +!***REFER TO ZBESH,ZBESI,ZBESJ,ZBESK,ZBESY,ZAIRY,ZBIRY +! +! DOUBLE PRECISION COMPLEX SQUARE ROOT, B=CSQRT(A) +! +!***ROUTINES CALLED ZABS +!***END PROLOGUE ZSQRT + DOUBLE PRECISION AR, AI, BR, BI, ZM, DTHETA, DPI, DRT + DATA DRT , DPI / 7.071067811865475244008443621D-1, & + 3.141592653589793238462643383D+0/ + ZM = ZABS(AR,AI) + ZM = DSQRT(ZM) + IF (AR.EQ.0.0D+0) GO TO 10 + IF (AI.EQ.0.0D+0) GO TO 20 + DTHETA = DATAN(AI/AR) + IF (DTHETA.LE.0.0D+0) GO TO 40 + IF (AR.LT.0.0D+0) DTHETA = DTHETA - DPI + GO TO 50 + 10 IF (AI.GT.0.0D+0) GO TO 60 + IF (AI.LT.0.0D+0) GO TO 70 + BR = 0.0D+0 + BI = 0.0D+0 + RETURN + 20 IF (AR.GT.0.0D+0) GO TO 30 + BR = 0.0D+0 + BI = DSQRT(DABS(AR)) + RETURN + 30 BR = DSQRT(AR) + BI = 0.0D+0 + RETURN + 40 IF (AR.LT.0.0D+0) DTHETA = DTHETA + DPI + 50 DTHETA = DTHETA*0.5D+0 + BR = ZM*DCOS(DTHETA) + BI = ZM*DSIN(DTHETA) + RETURN + 60 BR = ZM*DRT + BI = ZM*DRT + RETURN + 70 BR = ZM*DRT + BI = -ZM*DRT + RETURN +END SUBROUTINE ZSQRT + +SUBROUTINE ZEXP(AR, AI, BR, BI) +!***BEGIN PROLOGUE ZEXP +!***REFER TO ZBESH,ZBESI,ZBESJ,ZBESK,ZBESY,ZAIRY,ZBIRY +! +! DOUBLE PRECISION COMPLEX EXPONENTIAL FUNCTION B=EXP(A) +! +!***ROUTINES CALLED (NONE) +!***END PROLOGUE ZEXP + DOUBLE PRECISION AR, AI, BR, BI, ZM, CA, CB + ZM = DEXP(AR) + CA = ZM*DCOS(AI) + CB = ZM*DSIN(AI) + BR = CA + BI = CB +RETURN +END SUBROUTINE ZEXP + +SUBROUTINE ZMLT(AR, AI, BR, BI, CR, CI) +!***BEGIN PROLOGUE ZMLT +!***REFER TO ZBESH,ZBESI,ZBESJ,ZBESK,ZBESY,ZAIRY,ZBIRY +! +! DOUBLE PRECISION COMPLEX MULTIPLY, C=A*B. +! +!***ROUTINES CALLED (NONE) +!***END PROLOGUE ZMLT +DOUBLE PRECISION AR, AI, BR, BI, CR, CI, CA, CB + CA = AR*BR - AI*BI + CB = AR*BI + AI*BR + CR = CA + CI = CB +RETURN +END SUBROUTINE ZMLT + +SUBROUTINE ZDIV(AR, AI, BR, BI, CR, CI) +!***BEGIN PROLOGUE ZDIV +!***REFER TO ZBESH,ZBESI,ZBESJ,ZBESK,ZBESY,ZAIRY,ZBIRY +! +! DOUBLE PRECISION COMPLEX DIVIDE C=A/B. + +!***ROUTINES CALLED ZABS +!***END PROLOGUE ZDIV + DOUBLE PRECISION AR, AI, BR, BI, CR, CI, BM, CA, CB, CC, CD + BM = 1.0D0/ZABS(BR,BI) + CC = BR*BM + CD = BI*BM + CA = (AR*CC+AI*CD)*BM + CB = (AI*CC-AR*CD)*BM + CR = CA + CI = CB +RETURN +END SUBROUTINE ZDIV + +SUBROUTINE ZLOG(AR, AI, BR, BI, IERR) +!***BEGIN PROLOGUE ZLOG +!***REFER TO ZBESH,ZBESI,ZBESJ,ZBESK,ZBESY,ZAIRY,ZBIRY + +! DOUBLE PRECISION COMPLEX LOGARITHM B=CLOG(A) +! IERR=0,NORMAL RETURN IERR=1, Z=CMPLX(0.0,0.0) +!***ROUTINES CALLED ZABS +!***END PROLOGUE ZLOG + DOUBLE PRECISION AR, AI, BR, BI, ZM, DTHETA, DPI, DHPI + DATA DPI , DHPI / 3.141592653589793238462643383D+0, & + 1.570796326794896619231321696D+0/ + + IERR=0 + IF (AR.EQ.0.0D+0) GO TO 10 + IF (AI.EQ.0.0D+0) GO TO 20 + DTHETA = DATAN(AI/AR) + IF (DTHETA.LE.0.0D+0) GO TO 40 + IF (AR.LT.0.0D+0) DTHETA = DTHETA - DPI + GO TO 50 + 10 IF (AI.EQ.0.0D+0) GO TO 60 + BI = DHPI + BR = DLOG(DABS(AI)) + IF (AI.LT.0.0D+0) BI = -BI + RETURN + 20 IF (AR.GT.0.0D+0) GO TO 30 + BR = DLOG(DABS(AR)) + BI = DPI + RETURN + 30 BR = DLOG(AR) + BI = 0.0D+0 + RETURN + 40 IF (AR.LT.0.0D+0) DTHETA = DTHETA + DPI + 50 ZM = ZABS(AR,AI) + BR = DLOG(ZM) + BI = DTHETA + RETURN + 60 CONTINUE + IERR=1 +RETURN +END SUBROUTINE ZLOG + +DOUBLE PRECISION FUNCTION ZABS(ZR, ZI) +!***BEGIN PROLOGUE ZABS +!***REFER TO ZBESH,ZBESI,ZBESJ,ZBESK,ZBESY,ZAIRY,ZBIRY + +! ZABS COMPUTES THE ABSOLUTE VALUE OR MAGNITUDE OF A DOUBLE +! PRECISION COMPLEX VARIABLE CMPLX(ZR,ZI) + +!***ROUTINES CALLED (NONE) +!***END PROLOGUE ZABS + DOUBLE PRECISION ZR, ZI, U, V, Q, S + U = DABS(ZR) + V = DABS(ZI) + S = U + V +!----------------------------------------------------------------------- +! S*1.0D0 MAKES AN UNNORMALIZED UNDERFLOW ON CD! MACHINES INTO A +! TRUE FLOATING ZERO +!----------------------------------------------------------------------- + S = S*1.0D+0 + IF (S.EQ.0.0D+0) GO TO 20 + IF (U.GT.V) GO TO 10 + Q = U/V + ZABS = V*DSQRT(1.D+0+Q*Q) + RETURN + 10 Q = V/U + ZABS = U*DSQRT(1.D+0+Q*Q) + RETURN + 20 ZABS = 0.0D+0 + RETURN +END FUNCTION ZABS + +END MODULE COMPLEX +! end of file Complex.f90 diff --git a/applications/PUfoam/MoDeNaModels/foamConductivity/src/src/condrad.f90 b/applications/PUfoam/MoDeNaModels/foamConductivity/src/src/condrad.f90 new file mode 100644 index 000000000..d7be935a5 --- /dev/null +++ b/applications/PUfoam/MoDeNaModels/foamConductivity/src/src/condrad.f90 @@ -0,0 +1,218 @@ +!> @file +!! subroutines for calculation of equivalent conductivity of the foam +!! coupled conduction-radiation simulation +!! non-gray 1D P1-approximation +!! @author Pavel Ferkl +!! @ingroup foam_cond +module condrad + use constants + use ioutils + implicit none + private + public equcond,cond,alpha,sigma + !lapack variables + character :: trans='n' + character(len=30) :: fmt='(2x,A,1x,es9.3,1x,A)' + integer, parameter :: kl=1,ku=1,ldab=2*kl+ku+1,nrhs=1 + integer :: info + integer, dimension(:), allocatable :: tipiv,gipiv + real(dp), dimension(:), allocatable :: trhs,grhs + real(dp), dimension(:,:), allocatable :: tmatrix,gmatrix + !end of lapack variables + real(dp) :: dz + real(dp), dimension(:), allocatable :: tvec,qcon,qrad,qtot,gqrad,cond + real(dp), dimension(:,:), allocatable :: alpha,sigma +contains +!********************************BEGINNING************************************* +!> determines equivalent conductivity of the foam, main algorithm +subroutine equcond + integer :: i,maxiter=20,fi + real(dp) :: tol=1e-5_dp,res + write(*,*) 'Conduction-Radiation:' + write(mfi,*) 'Conduction-Radiation:' + dz=dfoam/nz + allocate(tmatrix(ldab,nz),gmatrix(ldab,nbox*nz),tipiv(nz),gipiv(nbox*nz),& + trhs(nz),grhs(nbox*nz),tvec(nz),qcon(nz),qrad(nz),qtot(nz),gqrad(nz)) + forall (i=1:nz) + tvec(i)=t1+(i-1)*(t2-t1)/(nz-1) !initial temperature profile + end forall + call make_tmatrix + call dgbtrf(nz,nz,kl,ku,tmatrix,ldab,tipiv,info) + call make_gmatrix + call dgbtrf(nbox*nz,nbox*nz,kl,ku,gmatrix,ldab,gipiv,info) + do i=1,maxiter + call make_trhs + call dgbtrs(trans,nz,kl,ku,nrhs,tmatrix,ldab,tipiv,trhs,nz,info) + res=abs(maxval(trhs-tvec)) + write(*,'(5x,A,1x,I2,A,1x,es9.3)') 'iteration:',i, ', residual:',res + write(mfi,'(5x,A,1x,I2,A,1x,es9.3)') 'iteration:',i, ', residual:',res + tvec=trhs + if (res creates matrix for calculation of incidence radiation +subroutine make_gmatrix + integer :: i,j,k,l + gmatrix=0 + gipiv=0 + l=0 + do k=1,nbox + l=l+1 + do i=2,nz-1 + l=l+1 + j=l + gmatrix(kl+ku+1+l-j,j)=2/((alpha(i,k)+sigma(i,k))*dz) + & + 3*alpha(i,k)*dz + j=l-1 + gmatrix(kl+ku+1+l-j,j)=-1/((alpha(i,k)+sigma(i,k))*dz) + j=l+1 + gmatrix(kl+ku+1+l-j,j)=-1/((alpha(i,k)+sigma(i,k))*dz) + enddo + l=l+1 + i=(k-1)*nz+1 + j=i + gmatrix(kl+ku+1+i-j,j)=1/((alpha(1,k)+sigma(1,k))*dz) + & + 3*alpha(1,k)*dz + & + 9*emi1/(2-emi1)*alpha(1,k)/4/(alpha(1,k)+sigma(1,k)) + j=i+1 + gmatrix(kl+ku+1+i-j,j)=-1/((alpha(1,k)+sigma(1,k))*dz) - & + 3*emi1/(2-emi1)*alpha(1,k)/4/(alpha(1,k)+sigma(1,k)) + i=nz*k + j=i-1 + gmatrix(kl+ku+1+i-j,j)=-1/((alpha(nz,k)+sigma(nz,k))*dz) - & + 3*emi2/(2-emi2)*alpha(nz,k)/4/(alpha(nz,k)+sigma(nz,k)) + j=i + gmatrix(kl+ku+1+i-j,j)=1/((alpha(nz,k)+sigma(nz,k))*dz) + & + 3*alpha(nz,k)*dz + & + 9*emi2/(2-emi2)*alpha(nz,k)/4/(alpha(nz,k)+sigma(nz,k)) + enddo +end subroutine make_gmatrix +!***********************************END**************************************** + + +!********************************BEGINNING************************************* +!> creates right hand side for calculation of incidence radiation +subroutine make_grhs + integer :: i,j,k + k=0 + do i=1,nbox + do j=1,nz + k=k+1 + grhs(k)=12*effn**2*sigmab*alpha(j,i)*tvec(j)**4*dz*fbepbox(i) + enddo + j=(i-1)*nz+1 + grhs(j)=grhs(j) + 6*emi1/(2-emi1)*alpha(1,i)*effn**2*sigmab*t1**4/& + (alpha(1,i)+sigma(1,i))*fbepbox(i) + j=nz*i + grhs(j)=grhs(j) + 6*emi2/(2-emi2)*alpha(nz,i)*effn**2*sigmab*t2**4/& + (alpha(nz,i)+sigma(nz,i))*fbepbox(i) + enddo +end subroutine make_grhs +!***********************************END**************************************** + + +!********************************BEGINNING************************************* +!> creates matrix for calculation of temperature +subroutine make_tmatrix + integer :: i,j + tmatrix=0 + tipiv=0 + i=1 + j=i + tmatrix(kl+ku+1+i-j,j)=(cond(i) + & + cond(i)*cond(i+1)/(cond(i)+cond(i+1)))*2/dz + j=i+1 + tmatrix(kl+ku+1+i-j,j)=-cond(i)*cond(i+1)/(cond(i)+cond(i+1))*2/dz + do i=2,nz-1 + j=i-1 + tmatrix(kl+ku+1+i-j,j)=-cond(i-1)*cond(i)/(cond(i-1)+cond(i))*2/dz + j=i + tmatrix(kl+ku+1+i-j,j)=(cond(i-1)*cond(i)/(cond(i-1)+cond(i)) + & + cond(i)*cond(i+1)/(cond(i)+cond(i+1)))*2/dz + j=i+1 + tmatrix(kl+ku+1+i-j,j)=-cond(i)*cond(i+1)/(cond(i)+cond(i+1))*2/dz + enddo + i=nz + j=i-1 + tmatrix(kl+ku+1+i-j,j)=-cond(i-1)*cond(i)/(cond(i-1)+cond(i))*2/dz + j=i + tmatrix(kl+ku+1+i-j,j)=(cond(i-1)*cond(i)/(cond(i-1)+cond(i)) + & + cond(i))*2/dz +end subroutine make_tmatrix +!***********************************END**************************************** + + +!********************************BEGINNING************************************* +!> creates right hand side for calculation of temperature +subroutine make_trhs + call make_gqrad + trhs=gqrad + trhs(1)=trhs(1)+2*cond(1)*t1/dz + trhs(nz)=trhs(nz)+2*cond(nz)*t2/dz +end subroutine make_trhs +!***********************************END**************************************** + + +!********************************BEGINNING************************************* +!> creates gradient of radiative heat flux (radiative source) +subroutine make_gqrad + integer :: i,j,k + call make_grhs + call dgbtrs(trans,nbox*nz,kl,ku,nrhs,gmatrix,ldab,gipiv,grhs,nbox*nz,info) + k=0 + gqrad=0 + do i=1,nbox + do j=1,nz + k=k+1 + gqrad(j)=gqrad(j) + alpha(j,i)*grhs(k)*dz - & + 4*effn**2*sigmab*alpha(j,i)*tvec(j)**4*dz*fbepbox(i) + enddo + enddo +end subroutine make_gqrad +!***********************************END**************************************** + + +!********************************BEGINNING************************************* +!> calculate heat flux +subroutine heatflux + integer :: i,j,k + qcon(1)=-2*cond(1)*cond(2)/(cond(1)+cond(2))*(tvec(2)-tvec(1))/dz + do i=2,nz + qcon(i)=-2*cond(i-1)*cond(i)/(cond(i-1)+cond(i))*(tvec(i)-tvec(i-1))/dz + enddo + qrad=0 + k=0 + do i=1,nbox + j=(i-1)*nz+1 + qrad(1)=qrad(1)-(grhs(j+1)-grhs(j))/(3*(alpha(1,i)+sigma(1,i))*dz) + k=k+1 + do j=2,nz + k=k+1 + qrad(j)=qrad(j)-(grhs(k)-grhs(k-1))/(3*(alpha(j,i)+sigma(j,i))*dz) + enddo + enddo + qtot=qcon+qrad +end subroutine heatflux +!***********************************END**************************************** +end module condrad diff --git a/applications/PUfoam/MoDeNaModels/foamConductivity/src/src/conduction.f90 b/applications/PUfoam/MoDeNaModels/foamConductivity/src/src/conduction.f90 new file mode 100644 index 000000000..10fc8807c --- /dev/null +++ b/applications/PUfoam/MoDeNaModels/foamConductivity/src/src/conduction.f90 @@ -0,0 +1,41 @@ +!> @file +!! subroutines for calculation of effective conductivity of the foam +!! (conduction-only) +!! @author Pavel Ferkl +!! @ingroup foam_cond +module conduction + use constants + implicit none + private + public effcond +contains +!********************************BEGINNING************************************* +!> determine effective conductivity of the foam +subroutine effcond + real(dp) :: xw,xs,f + character(len=30) :: fmt='(2x,A,1x,es9.3,1x,A)' + write(*,*) 'Conduction:' + write(mfi,*) 'Conduction:' + xw=2*(1+cond1/(2*cond2))/3 + xs=(1+4*cond1/(cond1+cond2))/3 + f=(1-fs)*xw+fs*xs + kgas=cond1*por/(por+(1-por)*f) + ksol=cond2*f*(1-por)/(por+(1-por)*f) + effc=kgas+ksol + eqc_ross=krad+effc + gcontr=kgas/eqc_ross + scontr=ksol/eqc_ross + rcontr=krad/eqc_ross + write(*,fmt) 'effective conductivity:',effc*1e3_dp,'mW/m/K' + write(*,fmt) 'equivalent conductivity:',eqc_ross*1e3_dp,'mW/m/K' + write(*,fmt) 'contribution of gas:',gcontr*1e2_dp,'%' + write(*,fmt) 'contribution of solid:',scontr*1e2_dp,'%' + write(*,fmt) 'contribution of radiation:',rcontr*1e2_dp,'%' + write(mfi,fmt) 'effective conductivity:',effc*1e3_dp,'mW/m/K' + write(mfi,fmt) 'equivalent conductivity:',eqc_ross*1e3_dp,'mW/m/K' + write(mfi,fmt) 'contribution of gas:',gcontr*1e2_dp,'%' + write(mfi,fmt) 'contribution of solid:',scontr*1e2_dp,'%' + write(mfi,fmt) 'contribution of radiation:',rcontr*1e2_dp,'%' +end subroutine effcond +!***********************************END**************************************** +end module conduction diff --git a/applications/PUfoam/MoDeNaModels/foamConductivity/src/src/constants.f90 b/applications/PUfoam/MoDeNaModels/foamConductivity/src/src/constants.f90 new file mode 100644 index 000000000..5cc4803b7 --- /dev/null +++ b/applications/PUfoam/MoDeNaModels/foamConductivity/src/src/constants.f90 @@ -0,0 +1,75 @@ +!> @file +!! stores parameters and commonly used variables as globals +!! @author Pavel Ferkl +!! @ingroup foam_cond +module constants + use,intrinsic :: iso_fortran_env, only: dp => real64 + implicit none + real(dp), parameter :: & + pi=3.1415926535897932384626433832795028841971693993751058209749445923& + &078164062862089986280348253421170679_dp,& !1-struttol + complex(dp), parameter :: iu=(0.0e0_dp,1.0e0_dp) ! @file +!! subroutines for evaluation of strut radiative properties +!! struts are modeled as cylinders +!! @author Pavel Ferkl +!! @ingroup foam_cond +module cylprop + use constants + use solidprop + use specfun + implicit none + private + public trextcoeffintstrut,extcoeffintstrut,scattcoeffintstrut,cylconst +contains +!********************************BEGINNING************************************* +!> determine efficiency factors of scattering, extinction and asymmetry factor +!!of infinitely long cylinder +!!according to Dombrovsky: Thermal Radiation in Disperse Systems: An Engineering +!!Approach (2010) +subroutine cylconst(lambda,theta,radius,Qs,Qt,gcyl) + real(dp), intent(in) :: & + lambda,& !wavelength + theta,& !incident angle + radius !radius of cylinder + real(dp), intent(out) :: & + Qs,& !efficiency factor of scattering + Qt,& !efficiency factor of extinction + gcyl !anisotropy factor + integer :: & + i,k,kmax,nwaw=1001 + real(dp) :: & + x,& !diffraction parameter + tol=1e-10_dp,& !tolerance for calculation of Bessel functions + phi,& !scattered angle + s1,s2,Qte,Qth,Qse,Qsh!,mue,muh + complex(dp) :: & + m,& !complex index of refraction + u,v,s,Dk,Rk,Ak1,Akm,Bk1,Bkm,Deltak + complex(dp) :: & + T1,T2,T3,T4 + real(dp), dimension(:), allocatable :: & + adsr !angular distribution of scattered radiation + complex(dp), dimension(:), allocatable :: & + ae,ah,be,bh,ju,dju,yu,dyu,jv,djv,yv,dyv,h1v,dh1v,h2v,dh2v + call optconst(lambda,n2,k2) +! n2=1.6_dp +! k2=0.01_dp + m=cmplx(n2,-k2,kind=dp) + x=2*pi*radius/lambda + u=x*sqrt(m**2-sin(theta)**2) + v=x*cos(theta) + s=1/u**2-1/v**2 + kmax=nint(x+4*x**(1/3.0_dp)+2)+2 !+2 for safety (also there is most likely + ! a mistake in Mackowski code on this place) + if (kmax>50) kmax=50 +! write(*,*) kmax + allocate(ae(0:kmax),ah(0:kmax),be(0:kmax),bh(0:kmax),ju(0:kmax),dju(0:kmax),& + yu(0:kmax),dyu(0:kmax),jv(0:kmax),djv(0:kmax),yv(0:kmax),dyv(0:kmax),& + h1v(0:kmax),dh1v(0:kmax),h2v(0:kmax),dh2v(0:kmax)) + call bessel(kmax,u,tol,ju,dju,yu,dyu) + call bessel(kmax,v,tol,jv,djv,yv,dyv) + call hankel(kmax,v,tol,h1v,dh1v,h2v,dh2v) + do k=0,kmax + Dk=k*s*sin(theta) + Rk=jv(k)/h2v(k) + Ak1=dh2v(k)/(v*h2v(k))-dju(k)/(u*ju(k)) + Akm=dh2v(k)/(v*h2v(k))-m**2*dju(k)/(u*ju(k)) + Bk1=djv(k)/(v*jv(k))-dju(k)/(u*ju(k)) + Bkm=djv(k)/(v*jv(k))-m**2*dju(k)/(u*ju(k)) + Deltak=Akm*Ak1-Dk**2 + ae(k)=iu*Dk*Rk*(Bk1-Ak1)/Deltak + ah(k)=Rk*(Akm*Bk1-Dk**2)/Deltak + be(k)=Rk*(Ak1*Bkm-Dk**2)/Deltak + bh(k)=-ae(k) + enddo + Qte=real(0.5_dp*be(0),kind=dp) + Qth=real(0.5_dp*ah(0),kind=dp) + Qse=real(0.5_dp*be(0)*conjg(be(0)),kind=dp) + Qsh=real(0.5_dp*ah(0)*conjg(ah(0)),kind=dp) + do k=1,kmax + Qte=Qte+real(be(k),kind=dp) + Qth=Qth+real(ah(k),kind=dp) + Qse=Qse+real(ae(k)*conjg(ae(k))+be(k)*conjg(be(k)),kind=dp) + Qsh=Qsh+real(ah(k)*conjg(ah(k))+bh(k)*conjg(bh(k)),kind=dp) + enddo + Qte=4/x*Qte + Qth=4/x*Qth + Qse=4/x*Qse + Qsh=4/x*Qsh + Qs=(Qse+Qsh)/2 + Qt=(Qte+Qth)/2 +! write(*,*) Qte,Qse,Qte-Qse +! write(*,*) Qth,Qsh,Qth-Qsh + !see Kaemmerlen, 2010: 10.1016/j.jqsrt.2009.11.018 +! Qs=Qs*(0.0015_dp*(lambda/(2*radius))**3-0.0219_dp*(lambda/(2*radius))**2+& + ! 0.0688_dp*(lambda/(2*radius))+0.7639_dp) +! Qt=Qt*(0.0015_dp*(lambda/(2*radius))**3-0.0219_dp*(lambda/(2*radius))**2+& + ! 0.0688_dp*(lambda/(2*radius))+0.7639_dp) + + ! asymmetry factor is not needed, we need gcyl according to Placido, + ! calculated as Dombrovsky +! mue=Qse*sin(theta)**2*x/(4*cos(theta)**2) +! muh=Qsh*sin(theta)**2*x/(4*cos(theta)**2) +! do k=0,kmax-1 +! mue=mue+real(ae(k)*conjg(ae(k+1))+be(k)*conjg(be(k+1)),kind=dp) +! muh=muh+real(ah(k)*conjg(ah(k+1))+bh(k)*conjg(bh(k+1)),kind=dp) +! enddo +! mue=mue*4*cos(theta)**2/x +! muh=muh*4*cos(theta)**2/x +! mu=(mue+muh)/(Qse+Qsh) !mue is actually mue*Qse + + allocate(adsr(nwaw)) + do i=1,nwaw + phi=(i-1)*pi/(nwaw) + T1=be(0) + T2=ah(0) + T3=0 + T4=0 + do k=1,kmax + T1=T1+2*be(k)*cos(k*phi) + T2=T2+2*ah(k)*cos(k*phi) + T3=T3-2*iu*ae(k)*sin(k*phi) + T4=-T3 + enddo + adsr(i)=(abs(T1)**2+abs(T2)**2)/(pi*x*Qs) + adsr(i)=(abs(T1)**2+abs(T2)**2+abs(T3)**2+abs(T4)**2)/2 + enddo + s1=adsr(1)*cos(0e0_dp)+adsr(nwaw)*cos(pi) + s2=adsr(1)+adsr(nwaw) + do i=2,nwaw-1 + phi=(i-1)*pi/(nwaw-1) + s1=s1+2*adsr(i)*cos(phi) + s2=s2+2*adsr(i) + enddo + s1=s1*pi/(2*(nwaw-1)) + s2=s2*pi/(2*(nwaw-1)) + gcyl=s1/s2 +! write(*,*) theta,s2*lambda/pi**2/radius,Qs +! write(*,*) s1/s2,mu +! phi=pi/2 +! T1=be(0) +! T2=ah(0) +! T3=0 +! T4=0 +! do k=1,kmax +! T1=T1+2*be(k)*cos(k*phi) +! T2=T2+2*ah(k)*cos(k*phi) +! T3=T3-2*iu*ae(k)*sin(k*phi) +! T4=-T3 +! enddo +! write(*,*) abs(T1)**2/Qs,abs(T2)**2/Qs,abs(T3)**2/Qs + +! Qs=abs(be(0))**2+abs(ah(0))**2 !according to Modest, doesn't work +! do i=1,kmax +! Qs=Qs+abs(be(i))**2+abs(ah(i))**2+abs(bh(i))**2+abs(ae(i))**2 +! enddo +! Qs=Qs/x +! write(*,*) Qs +! write(*,*) abs(T1)**2/Qs + deallocate(adsr) +end subroutine cylconst +!***********************************END**************************************** + + +!********************************BEGINNING************************************* +!> evaluates transport extinction coefficient of strut integrand +real(dp) function trextcoeffintstrut ( theta ) + real(dp), intent(in) :: theta + real(dp) :: Qs,Qt,gcyl + call cylconst(lambda,theta,dstrut/2,Qs,Qt,gcyl) + trextcoeffintstrut=(Qt-Qs*sin(theta)**2-gcyl*Qs*cos(theta)**2)*cos(theta) +end function trextcoeffintstrut +!***********************************END**************************************** + + +!********************************BEGINNING************************************* +!> evaluates extinction coefficient of strut integrand +real(dp) function extcoeffintstrut ( theta ) + real(dp), intent(in) :: theta + real(dp) :: Qs,Qt,gcyl + call cylconst(lambda,theta,dstrut/2,Qs,Qt,gcyl) + extcoeffintstrut=Qt*cos(theta) +end function extcoeffintstrut +!***********************************END**************************************** + + +!********************************BEGINNING************************************* +!> evaluates scattering coefficient of strut integrand +real(dp) function scattcoeffintstrut ( theta ) + real(dp), intent(in) :: theta + real(dp) :: Qs,Qt,gcyl + call cylconst(lambda,theta,dstrut/2,Qs,Qt,gcyl) + scattcoeffintstrut=Qs*cos(theta) +end function scattcoeffintstrut +!***********************************END**************************************** +end module cylprop diff --git a/applications/PUfoam/MoDeNaModels/foamConductivity/src/src/filmprop.f90 b/applications/PUfoam/MoDeNaModels/foamConductivity/src/src/filmprop.f90 new file mode 100644 index 000000000..c24ce06e0 --- /dev/null +++ b/applications/PUfoam/MoDeNaModels/foamConductivity/src/src/filmprop.f90 @@ -0,0 +1,263 @@ +!> @file +!! subroutines for evaluation of film radiative properties +!! @author Pavel Ferkl +!! @ingroup foam_cond +module filmprop + use constants + use solidprop + implicit none + private + public scattwall,trextwall,absorwall,scattcoeffintwall,& + trextcoeffintwall,abscoeffintwall,filmconst +contains +!********************************BEGINNING************************************* +!> determine film reflectance, transmittance and absorbance +subroutine filmconst(lambda,theta,h,Rwin,Twin,Awin) + real(dp), intent(in) :: & + lambda,& !wavelength + theta,& !incident angle + h !film thickness + real(dp), intent(out) :: & + Rwin,& !reflectance + Twin,& !transmittance + Awin !absorptance + integer :: & + method=1 !1 is recommended, 3 and 4 should work; 2 is for no interference; + ! 1,3,4 give similar results + real(dp) :: & + theta2,& !refracted agle + rho12,rho23,& !reflectivities + tau12,tau23,& !transmissivities + r12,r23,& !reflection coefficients + t12,t23,& !transmission coefficients + dzeta,& !interference parameter + p,q + complex(dp) :: & + cn,beta,rc,tc,rc2,tc2 + call optconst(lambda,n2,k2) + select case(method) + case(1) + !according to Modest + kappa2=4*pi*k2/lambda + ! theta2=asin(sin(theta)/n2) + ! rho12=(((cos(theta2)-n2*cos(theta))/(cos(theta2)+n2*cos(theta)))**2+& + ! ((cos(theta)-n2*cos(theta2))/(cos(theta)+n2*cos(theta2)))**2)/2 + ! rho23=(((n2*cos(theta)-cos(theta2))/(n2*cos(theta)+cos(theta2)))**2+& + ! ((n2*cos(theta2)-cos(theta))/(n2*cos(theta2)+cos(theta)))**2)/2 + ! write(*,*) rho23 + ! stop + p=sqrt((sqrt((n2**2-k2**2-n1**2*sin(theta)**2)**2+4*n2**2*k2**2)+& + (n2**2-k2**2-n1**2*sin(theta)**2))/2) + q=sqrt((sqrt((n2**2-k2**2-n1**2*sin(theta)**2)**2+4*n2**2*k2**2)-& + (n2**2-k2**2-n1**2*sin(theta)**2))/2) + theta2=atan(sin(theta)*n1/p) + rho12=((n1*cos(theta)-p)**2+q**2)/((n1*cos(theta)+p)**2+q**2) + rho12=rho12*(1+((p-n1*sin(theta)*tan(theta))**2+q**2)/& + ((p+n1*sin(theta)*tan(theta))**2+q**2))/2 + rho23=rho12 + ! write(*,*) rho12 + ! stop + r12=-sqrt(rho12) + r23=sqrt(rho23) + tau12=1-rho12 + tau23=1-rho23 + dzeta=4*pi*n2*h/lambda + Rwin=(r12**2+2*r12*r23*exp(-kappa2*h)*cos(dzeta)+r23**2*exp(-2*kappa2*h))/& + (1+2*r12*r23*exp(-kappa2*h)*cos(dzeta)+r12**2*r23**2*exp(-2*kappa2*h)) + Twin=(tau12*tau23*exp(-kappa2*h))/& + (1+2*r12*r23*exp(-kappa2*h)*cos(dzeta)+r12**2*r23**2*exp(-2*kappa2*h)) + Awin=1-Rwin-Twin + case(2) + !no interference + kappa2=4*pi*k2/lambda + theta2=asin(sin(theta)/n2) + rho12=(((cos(theta2)-n2*cos(theta))/(cos(theta2)+n2*cos(theta)))**2+& + ((cos(theta)-n2*cos(theta2))/(cos(theta)+n2*cos(theta2)))**2)/2 + rho23=(((n2*cos(theta)-cos(theta2))/(n2*cos(theta)+cos(theta2)))**2+& + ((n2*cos(theta2)-cos(theta))/(n2*cos(theta2)+cos(theta)))**2)/2 + tau12=exp(-kappa2*h) + Rwin=(rho12+(1-2*rho12)*rho23*tau12**2)/(1-rho12*rho23*tau12**2) + Twin=(1-rho12)*(1-rho23)*tau12/(1-rho12*rho23*tau12**2) + Awin=1-Rwin-Twin + case(3) + !Coquard (according to Ochsner), adapted + cn=cmplx(n2,-k2,kind=dp) + theta2=asin(sin(theta)/n2) + rho12=(((cos(theta2)-n2*cos(theta))/(cos(theta2)+n2*cos(theta)))**2+& + ((cos(theta)-n2*cos(theta2))/(cos(theta)+n2*cos(theta2)))**2)/2 + rho23=(((n2*cos(theta)-cos(theta2))/(n2*cos(theta)+cos(theta2)))**2+& + ((n2*cos(theta2)-cos(theta))/(n2*cos(theta2)+cos(theta)))**2)/2 + r12=-sqrt(rho12) + r23=sqrt(rho23) + tau12=1-r12**2 + tau23=1-r23**2 + t12=sqrt(tau12/n2) + t23=sqrt(tau23*n2) + beta=2*pi*cn*h*cos(theta2)/lambda + rc=(r12+r23*exp(-iu*2*beta))/(1+r12*r23*exp(-iu*2*beta)) + tc=(t12*t23*exp(-iu*beta))/(1+r12*r23*exp(-iu*2*beta)) + Rwin=abs(rc)**2 + Twin=abs(tc)**2 + Awin=1-Rwin-Twin + case(4) + !Coquard (according to Dombrovsky) + cn=cmplx(n2,-k2,kind=dp) + theta2=asin(sin(theta)/n2) + r12=(cos(theta2)-n2*cos(theta))/(cos(theta2)+n2*cos(theta)) + ! r12=(n2*cos(theta)-cos(theta2))/(n2*cos(theta)+cos(theta2)) !this gives + ! the same results + r23=-r12 + t12=1-r12**2 !actually this is t12*t23 + beta=2*pi*cn*h*cos(theta2)/lambda + rc=(r12+r23*exp(-iu*2*beta))/(1+r12*r23*exp(-iu*2*beta)) + tc=(t12*exp(-iu*beta))/(1+r12*r23*exp(-iu*2*beta)) + r12=(cos(theta)-n2*cos(theta2))/(cos(theta)+n2*cos(theta2)) + ! r12=(n2*cos(theta2)-cos(theta))/(n2*cos(theta2)+cos(theta)) + r23=-r12 + t12=1-r12**2 !actually this is t12*t23 + rc2=(r12+r23*exp(-iu*2*beta))/(1+r12*r23*exp(-iu*2*beta)) + tc2=(t12*exp(-iu*beta))/(1+r12*r23*exp(-iu*2*beta)) + Rwin=(abs(rc)**2+abs(rc2)**2)/2 + Twin=(abs(tc)**2+abs(tc2)**2)/2 + Awin=1-Rwin-Twin + case default + stop 'unknown method for calculation of slab reflectivity' + end select +end subroutine filmconst +!***********************************END**************************************** + + +!********************************BEGINNING************************************* +!> evaluates scattering coefficient as a function of wall thickness +real(dp) function scattwall ( dw ) + use quadpack + real(dp), intent(in) :: dw + real(dp) :: wtweight,dwold + !qags variables + real(dp) :: a !start point of integration + real(dp) :: abserr + real(dp) :: b !end point of integration + real(dp), parameter :: epsabs = 0.0e0_dp + real(dp), parameter :: epsrel = 1e-3_dp + integer :: ier + integer :: neval + real(dp) :: res + !end of qags variables + a=0 + b=pi/2 + wtweight=1/(sqrt(2*pi)*wsdev*dw)*exp(-(log(dw)-log(dwall))**2/(2*wsdev**2)) + dwold=dwall + dwall=dw + call qags(scattcoeffintwall, a, b, epsabs, epsrel, res, abserr, neval, ier) + if (ier /= 0) then + write(*,*) 'qags returned',ier + write(*,*) 'wall thickness',dw + write(*,*) 'scattering coefficient of walls not calculated' + stop + endif + scattwall=res*(1-por)/dwall*wtweight + dwall=dwold +end function scattwall +!***********************************END**************************************** + + +!********************************BEGINNING************************************* +!> evaluates scattering coefficient as a function of wall thickness +real(dp) function trextwall ( dw ) + use quadpack + real(dp), intent(in) :: dw + real(dp) :: wtweight,dwold + !qags variables + real(dp) :: a !start point of integration + real(dp) :: abserr + real(dp) :: b !end point of integration + real(dp), parameter :: epsabs = 0.0e0_dp + real(dp), parameter :: epsrel = 0.001e0_dp + integer :: ier + integer :: neval + real(dp) :: res + !end of qags variables + a=0 + b=pi/2 + wtweight=1/(sqrt(2*pi)*wsdev*dw)*exp(-(log(dw)-log(dwall))**2/(2*wsdev**2)) + dwold=dwall + dwall=dw + call qags(trextcoeffintwall, a, b, epsabs, epsrel, res, abserr, neval, ier) + if (ier /= 0) then + write(*,*) 'qags returned',ier + write(*,*) 'wall thickness',dw + write(*,*) 'transport extinction coefficient of walls not calculated' + stop + endif + trextwall=res*(1-por)/dwall*wtweight + dwall=dwold +end function trextwall +!***********************************END**************************************** + + +!********************************BEGINNING************************************* +!> evaluates absorption coefficient as a function of wall thickness +real(dp) function absorwall ( dw ) + use quadpack + real(dp), intent(in) :: dw + real(dp) :: wtweight,dwold + !qags variables + real(dp) :: a !start point of integration + real(dp) :: abserr + real(dp) :: b !end point of integration + real(dp), parameter :: epsabs = 0.0e0_dp + real(dp), parameter :: epsrel = 0.001e0_dp + integer :: ier + integer :: neval + real(dp) :: res + !end of qags variables + a=0 + b=pi/2 + wtweight=1/(sqrt(2*pi)*wsdev*dw)*exp(-(log(dw)-log(dwall))**2/(2*wsdev**2)) + dwold=dwall + dwall=dw + call qags ( abscoeffintwall, a, b, epsabs, epsrel, res, abserr, neval, ier ) + if (ier /= 0) then + write(*,*) 'qags returned',ier + write(*,*) 'wall thickness',dw + write(*,*) 'absorption coefficient of walls not calculated' + stop + endif + absorwall=res*(1-por)/dwall*wtweight + dwall=dwold +end function absorwall +!***********************************END**************************************** + + +!********************************BEGINNING************************************* +!> evaluates scattering coefficient of wall integrand +real(dp) function scattcoeffintwall ( theta ) + real(dp), intent(in) :: theta + real(dp) :: Rwin,Twin,Awin + call filmconst(lambda,theta,dwall,Rwin,Twin,Awin) + scattcoeffintwall=Rwin*sin(theta)*cos(theta) +end function scattcoeffintwall +!***********************************END**************************************** + + +!********************************BEGINNING************************************* +!> evaluates transport extinction coefficient of wall integrand +real(dp) function trextcoeffintwall ( theta ) + real(dp), intent(in) :: theta + real(dp) :: Rwin,Twin,Awin + call filmconst(lambda,theta,dwall,Rwin,Twin,Awin) + trextcoeffintwall=(1-Twin+Rwin*cos(2*theta))*sin(theta)*cos(theta) +end function trextcoeffintwall +!***********************************END**************************************** + + +!********************************BEGINNING************************************* +!> evaluates absorption coefficient of wall integrand +real(dp) function abscoeffintwall ( theta ) + real(dp), intent(in) :: theta + real(dp) :: Rwin,Twin,Awin + call filmconst(lambda,theta,dwall,Rwin,Twin,Awin) + abscoeffintwall=Awin*sin(theta)*cos(theta) +end function abscoeffintwall +!***********************************END**************************************** +end module filmprop diff --git a/applications/PUfoam/MoDeNaModels/foamConductivity/src/src/foamgeom.f90 b/applications/PUfoam/MoDeNaModels/foamConductivity/src/src/foamgeom.f90 new file mode 100644 index 000000000..3c14a6b39 --- /dev/null +++ b/applications/PUfoam/MoDeNaModels/foamConductivity/src/src/foamgeom.f90 @@ -0,0 +1,163 @@ +!> @file +!! subroutines for calculation of geometric properties of the foam +!! @author Pavel Ferkl +!! @ingroup foam_cond +module foamgeom + use constants + use Solve_NonLin + implicit none + private + public foam_morpholgy +contains +!********************************BEGINNING************************************* +!> determine all geometric parameters of the foam +subroutine foam_morpholgy + integer, parameter :: n=2 + integer :: info + real (dp) :: tol=1e-8_dp + real (dp), dimension(n) :: x,fvec,diag + write(*,*) 'Foam morphology:' + write(mfi,*) 'Foam morphology:' + select case(morph_input) + case(1) !dwall is input; fs and dstrut are calculated + x(1)=fs + x(2)=dstrut + call hbrd(fcn_dwall,n,x,fvec,epsilon(pi),tol,info,diag) + if (info /= 1) then + write(*,*) 'unable to determine foam morphology parameters, & + hbrd returned',info + write(mfi,*) 'unable to determine foam morphology parameters, & + hbrd returned',info + stop + endif + fs=x(1) + dstrut=x(2) + if (fs<0 .or. dstrut< 0) then + write(*,*) 'unable to determine foam morphology & + parameters, try different initial guess' + write(mfi,*) 'unable to determine foam morphology & + parameters, try different initial guess' + stop + endif + case(2) !fs is input; dwall and dstrut are calculated + if (fs residual function for fs and dstrut +subroutine fcn_dwall(n,x,fvec,iflag) + integer, intent(in) :: n + real (dp), intent(in) :: x(n) + real (dp), intent(out) :: fvec(n) + integer, intent(inout) :: iflag + real(dp) :: Vcell,Vstruts,Vwalls,fs,dstrut + fs=x(1) + dstrut=x(2) + Vcell=0.348_dp*dcell**3 + Vstruts=2.8_dp*dstrut**2*dcell-3.93_dp*dstrut**3 + Vwalls=(1.3143_dp*dcell**2-7.367_dp*dstrut*dcell+10.323_dp*dstrut**2)*dwall + fvec(1)=fs-Vstruts/(Vstruts+Vwalls) + fvec(2)=1-por-(Vstruts+Vwalls)/Vcell +end subroutine fcn_dwall +!***********************************END**************************************** + + +!********************************BEGINNING************************************* +!> residual function for dwall and dstrut +subroutine fcn_fs(n,x,fvec,iflag) + integer, intent(in) :: n + real (dp), intent(in) :: x(n) + real (dp), intent(out) :: fvec(n) + integer, intent(inout) :: iflag + real(dp) :: Vcell,Vstruts,Vwalls,dwall,dstrut + dwall=x(1) + dstrut=x(2) + Vcell=0.348_dp*dcell**3 + Vstruts=2.8_dp*dstrut**2*dcell-3.93_dp*dstrut**3 + Vwalls=(1.3143_dp*dcell**2-7.367_dp*dstrut*dcell+10.323_dp*dstrut**2)*dwall + fvec(1)=fs-Vstruts/(Vstruts+Vwalls) + fvec(2)=1-por-(Vstruts+Vwalls)/Vcell +end subroutine fcn_fs +!***********************************END**************************************** + + +!********************************BEGINNING************************************* +!> residual function for dwall and fs +subroutine fcn_dstrut(n,x,fvec,iflag) + integer, intent(in) :: n + real (dp), intent(in) :: x(n) + real (dp), intent(out) :: fvec(n) + integer, intent(inout) :: iflag + real(dp) :: Vcell,Vstruts,Vwalls,dwall,fs + dwall=x(1) + fs=x(2) + Vcell=0.348_dp*dcell**3 + Vstruts=2.8_dp*dstrut**2*dcell-3.93_dp*dstrut**3 + Vwalls=(1.3143_dp*dcell**2-7.367_dp*dstrut*dcell+10.323_dp*dstrut**2)*dwall + fvec(1)=fs-Vstruts/(Vstruts+Vwalls) + fvec(2)=1-por-(Vstruts+Vwalls)/Vcell +end subroutine fcn_dstrut +!***********************************END**************************************** +end module foamgeom diff --git a/applications/PUfoam/MoDeNaModels/foamConductivity/src/src/foamprop.f90 b/applications/PUfoam/MoDeNaModels/foamConductivity/src/src/foamprop.f90 new file mode 100644 index 000000000..411c931bc --- /dev/null +++ b/applications/PUfoam/MoDeNaModels/foamConductivity/src/src/foamprop.f90 @@ -0,0 +1,496 @@ +!> @file +!! subroutines for evaluation of effective radiative properties of foam +!! @author Pavel Ferkl +!! @ingroup foam_cond +module foamprop + use constants + use ioutils + use gasprop + use filmprop + use cylprop + implicit none + private + public effrad,fbep + real(dp) :: unin=1.57_dp + real(dp), dimension(:), allocatable :: & + lambdaf,& + !foam radiative properties - wall contribution + kappafwall,sigmafwall,betafwall,omegafwall,betatrfwall,& + !foam radiative properties - strut contribution + kappafstrut,sigmafstrut,betafstrut,omegafstrut,betatrfstrut,& + !foam radiative properties - gas contribution + kappafgas,& + !foam radiative properties - overall + kappaf,sigmaf,betaf,omegaf,betatrf +contains +!********************************BEGINNING************************************* +!> determine effective radiative properties of foam +subroutine effrad(spectra) + use quadpack + character(len=*), intent(in) :: spectra + integer :: i,j,fi,nwawel=100 +! real(dp) :: theta !incident angle +! real(dp) :: Rwin !reflectance +! real(dp) :: Twin !transmittance +! real(dp) :: Awin !absorptance +! real(dp) :: rn !random number +! real(dp) :: absp !absorption parameter +! real(dp) :: scap !scattering parameter +! real(dp) :: npart !number of particlesper unit volume + real(dp) :: dwmin,dwmax,lambdamin,lambdamax + !qags variables + real(dp) :: a !start point of integration + real(dp) :: abserr + real(dp) :: b !end point of integration + real(dp), parameter :: epsabs = 0.0e0_dp + real(dp) :: epsrel = 1e-3_dp + integer :: ier + integer :: neval + real(dp) :: res + !end of qags variables + write(*,*) 'Radiative properties of the foam:' + write(mfi,*) 'Radiative properties of the foam:' +! call cylconst(2*pi,pi/4,1.0e-1_dp,Qs,Qt,mu) +! stop + !monte carlo method, does not work properly +! swin=dcell**2 +! absp=0 +! scap=0 +! npart=3/dcell**3 +! lambda=10e-6 +! call srand(int(abs(sin(dble(time()))*1e6))) +! do i=1,nrays +! theta=acos(rand()) +!! theta=rand()*pi/2 +! call filmconst(lambda,theta,dwall,Rwin,Twin,Awin) +! absp=absp+Swin*Awin +! scap=scap+Swin*Rwin +!! absp=absp+cos(theta)*sin(theta)*Swin*Awin*pi/2 +!! scap=scap+cos(theta)*sin(theta)*Swin*Rwin*pi/2 +!! rn=rand() +!! if (rn>1-Awin) then +!! absp=absp+Swin +!! elseif(rnstruttol) then + a=0 + b=pi/2 + if (pi*dstrut/lambda>10) then + epsrel=1e-1_dp + elseif(pi*dstrut/lambda>1) then + epsrel=1e-2_dp + else + epsrel=1e-3_dp + endif + call qags ( trextcoeffintstrut, a, b, epsabs, epsrel, res, abserr, & + neval, ier ) + if (ier /= 0) then + write(*,*) 'qags returned',ier,neval + write(*,*) 'qags returned',res,abserr + write(*,*) 'wavelength',lambda + write(*,*) 'transport extinction coefficient of struts & + not calculated' + stop + endif + betatrfstrut(i)=res*4/pi/dstrut*(1-por) + call qags ( extcoeffintstrut, a, b, epsabs, epsrel, res, abserr, & + neval, ier ) + if (ier /= 0) then + write(*,*) 'qags returned',ier + write(*,*) 'wavelength',lambda + write(*,*) 'extinction coefficient of struts not calculated' + stop + endif + betafstrut(i)=res*4/pi/dstrut*(1-por) + call qags ( scattcoeffintstrut, a, b, epsabs, epsrel, res, abserr, & + neval, ier ) + if (ier /= 0) then + write(*,*) 'qags returned',ier + write(*,*) 'wavelength',lambda + write(*,*) 'scattering coefficient of struts not calculated' + stop + endif + sigmafstrut(i)=res*4/pi/dstrut*(1-por) + kappafstrut(i)=betafstrut(i)-sigmafstrut(i) + omegafstrut(i)=sigmafstrut(i)/betafstrut(i) + else + kappafstrut=0 + sigmafstrut=0 + betafstrut=0 + omegafstrut=0 + betatrfstrut=0 + endif + enddo + kappafwall=(1-fs)*kappafwall + sigmafwall=(1-fs)*sigmafwall + betafwall=(1-fs)*betafwall + betatrfwall=(1-fs)*betatrfwall + kappafstrut=fs*kappafstrut + sigmafstrut=fs*sigmafstrut + betafstrut=fs*betafstrut + betatrfstrut=fs*betatrfstrut + kappaf=kappafwall+kappafstrut + sigmaf=sigmafwall+sigmafstrut + betaf=betafwall+betafstrut + betatrf=betatrfwall+betatrfstrut +! kappaf=(1-fs)*kappafwall+fs*kappafstrut +! sigmaf=(1-fs)*sigmafwall+fs*sigmafstrut +! betaf=(1-fs)*betafwall+fs*betafstrut +! betatrf=(1-fs)*betatrfwall+fs*betatrfstrut + omegaf=sigmaf/betaf + open(newunit(fi),file=trim(adjustl(spectra))) + write(fi,'(1000A23)') '#wavelength','abs.coeff.wall','scatt.coeff.wall',& + 'ext.coeff.wall','albedo wall','tr.ext.coeff.wall','abs.coeff.strut',& + 'scatt.coeff.strut','ext.coeff.strut','albedo strut',& + 'tr.ext.coeff.strut','abs.coeff','scatt.coeff','ext.coeff','albedo ',& + 'tr.ext.coeff' + do i=1,nwawel + write(fi,'(1000es23.15)') lambdaf(i),kappafwall(i),sigmafwall(i),& + betafwall(i),omegafwall(i),betatrfwall(i),kappafstrut(i),& + sigmafstrut(i),betafstrut(i),omegafstrut(i),betatrfstrut(i),& + kappaf(i),sigmaf(i),betaf(i),omegaf(i),betatrf(i) + enddo + close(fi) + !calculate gray properties + a=lambdaf(1) + b=lambdaf(size(lambdaf)) + b=1e-4_dp !100 um is relatively enough (if you use lower value, you should + ! incorporate fraction of blackbody radiation function) + effn=por*n1+(1-por)*unin !this is not perfect, use of some average value + ! of n2 instead of unin would be better + call qags ( rosextc, a, b, epsabs, epsrel, res, abserr, neval, ier ) + if (ier /= 0) then + write(*,*) 'qags returned',ier + write(*,*) 'rosseland extinction coefficient not calculated' + stop + endif + rossextcoeff=(4*effn**2*sigmab*tmean**3)/res + call qags ( planckextc, a, b, epsabs, epsrel, res, abserr, neval, ier ) + if (ier /= 0) then + write(*,*) 'qags returned',ier + write(*,*) 'planck extinction coefficient not calculated' + stop + endif + planckextcoeff=res/(effn**2*sigmab*tmean**4) + call qags ( planckalbedo, a, b, epsabs, epsrel, res, abserr, neval, ier ) + if (ier /= 0) then + write(*,*) 'qags returned',ier + write(*,*) 'scattering albedo not calculated' + stop + endif + albedo=res/(effn**2*sigmab*tmean**4) + krad=16*sigmab*tmean**3/(3*rossextcoeff) + !calculate actual (usually non-gray) properties + if (nbox<1) then + stop 'choose number of gray boxes 1 for gray approximation, greater & + than 1 for non-gray simulation' + else + allocate(lambdabox(nbox+1),trextcoeffbox(nbox),albedobox(nbox),& + abscoeffbox(nbox),scattcoeffbox(nbox)) + if (.not. allocated(fbepbox)) allocate(fbepbox(nbox)) + lambdamin=2e-6_dp + lambdamax=25e-6_dp + lambdabox(nbox+1)=100e-6_dp + lambdabox(nbox)=lambdamax + lambdabox(1)=lambdamin !if nbox equals 1, then we have only one + ! box: 2-100 um + do i=2,nbox-1 + lambdabox(i)=lambdamin+(i-1)*(lambdamax-lambdamin)/(nbox-1._dp) + enddo + do i=1,nbox + fbepbox(i)=fbep(effn,lambdabox(i+1),tmean)-fbep(effn,lambdabox(i)& + ,tmean) + call qags(planckextc,lambdabox(i),lambdabox(i+1), epsabs, epsrel, & + res, abserr, neval, ier) + if (ier /= 0) then + write(*,*) 'qags returned',ier + write(*,*) 'gray box',i + write(*,*) 'planck extinction coefficient not calculated' + stop + endif + trextcoeffbox(i)=res/(effn**2*sigmab*tmean**4*fbepbox(i)) + call qags(planckalbedo,lambdabox(i),lambdabox(i+1), epsabs, & + epsrel, res, abserr, neval, ier) + if (ier /= 0) then + write(*,*) 'qags returned',ier + write(*,*) 'gray box',i + write(*,*) 'scattering albedo not calculated' + stop + endif + albedobox(i)=res/(effn**2*sigmab*tmean**4*fbepbox(i)) + enddo + scattcoeffbox=albedobox*trextcoeffbox + abscoeffbox=trextcoeffbox-scattcoeffbox + endif + write(*,'(2x,A,1x,es9.3)') 'effective index of refraction:',effn + write(*,'(2x,A,1x,es9.3,1x,A)') 'Planck mean extinction coefficient:',& + planckextcoeff,'m^-1' + write(*,'(2x,A,1x,es9.3,1x,A)') 'Rosseland extinction coefficient:',& + rossextcoeff,'m^-1' + write(*,'(2x,A,1x,es9.3,1x,A)') 'Rosseland extinction coefficient:',& + rossextcoeff/(1-por)/rho2,'kg/m^2' + write(*,'(2x,A,1x,es9.3,1x,A)') 'radiative conductivity:',& + krad*1e3_dp,'mW/m/K' + write(mfi,'(2x,A,1x,es9.3)') 'effective index of refraction:',effn + write(mfi,'(2x,A,1x,es9.3,1x,A)') 'Planck mean extinction coefficient:',& + planckextcoeff,'m^-1' + write(mfi,'(2x,A,1x,es9.3,1x,A)') 'Rosseland extinction coefficient:',& + rossextcoeff,'m^-1' + write(mfi,'(2x,A,1x,es9.3,1x,A)') 'Rosseland extinction coefficient:',& + rossextcoeff/(1-por)/rho2,'kg/m^2' + write(mfi,'(2x,A,1x,es9.3,1x,A)') 'radiative conductivity:',& + krad*1e3_dp,'mW/m/K' + deallocate(lambdaf) + deallocate(kappafwall,sigmafwall,betafwall,omegafwall,betatrfwall,& + kappafstrut,sigmafstrut,betafstrut,omegafstrut,betatrfstrut,& + kappaf,sigmaf,betaf,omegaf,betatrf,kappafgas,lambdabox,trextcoeffbox,& + albedobox) +end subroutine effrad +!***********************************END**************************************** + + + +!********************************BEGINNING************************************* +!> evaluate integrand for Rosseland extinction coefficient +real(dp) function rosextc(lambda) + use interpolation + real(dp), intent(in) :: lambda !wavelength + real(dp) :: beta + real(dp) :: n !refractive index + integer :: ni=1 !number of points, where we want to interpolate + real(dp) :: xi(1) !x-values of points, where we want to interpolate + real(dp) :: yi(1) !interpolated y-values +! call optconst(lambda,n,k) !could yield recursive call to qags + n=effn !used Planck law is valid only constant index of refraction + if (lambdalambdaf(size(lambdaf))) then +! write(*,*) 'No data for such high wavelength.' +! write(*,*) 'Maximum wavelength is',lambdaf(size(lambdaf)) +! stop + beta=betatrf(size(betatrf)) + else + xi(1)=lambda + call pwl_interp_1d ( size(lambdaf), lambdaf, betatrf, ni, xi, yi ) + beta=yi(1) + endif + rosextc=2*c0**3*exp(hPc*c0/(kb*n*tmean*lambda))*hPc**2*pi/& + ((exp(hPc*c0/(kb*n*tmean*lambda))-1)**2*kb*n**3*tmean**2*lambda**6)/beta +end function rosextc +!***********************************END**************************************** + + +!********************************BEGINNING************************************* +!> evaluate integrand for Planck mean extinction coefficient +real(dp) function planckextc(lambda) + use interpolation + real(dp), intent(in) :: lambda !wavelength + real(dp) :: beta + real(dp) :: n !refractive index + integer :: ni=1 !number of points, where we want to interpolate + real(dp) :: xi(1) !x-values of points, where we want to interpolate + real(dp) :: yi(1) !interpolated y-values +! call optconst(lambda,n,k) !could yield recursive call to qags + n=effn !used Planck law is valid only constant index of refraction + if (lambdalambdaf(size(lambdaf))) then +! write(*,*) 'No data for such high wavelength.' +! write(*,*) 'Maximum wavelength is',lambdaf(size(lambdaf)) +! stop + beta=betatrf(size(betatrf)) + else + xi(1)=lambda + call pwl_interp_1d ( size(lambdaf), lambdaf, betatrf, ni, xi, yi ) + beta=yi(1)+abscoeffgas(lambda) + endif + planckextc=2*pi*hPc*c0**2/& + (n**2*lambda**5*(Exp(hPc*c0/(n*lambda*kb*tmean))-1))*beta +end function planckextc +!***********************************END**************************************** + + +!********************************BEGINNING************************************* +!> evaluate integrand for scattering albedo - Planck style +real(dp) function planckalbedo(lambda) + use interpolation + real(dp), intent(in) :: lambda !wavelength + real(dp) :: omega + real(dp) :: n !refractive index + integer :: ni=1 !number of points, where we want to interpolate + real(dp) :: xi(1) !x-values of points, where we want to interpolate + real(dp) :: yi(1) !interpolated y-values +! call optconst(lambda,n,k) !could yield recursive call to qags + n=effn !used Planck law is valid only constant index of refraction + if (lambdalambdaf(size(lambdaf))) then +! write(*,*) 'No data for such high wavelength.' +! write(*,*) 'Maximum wavelength is',lambdaf(size(lambdaf)) +! stop + omega=omegaf(size(omegaf)) + else + xi(1)=lambda + call pwl_interp_1d ( size(lambdaf), lambdaf, omegaf, ni, xi, yi ) + omega=yi(1) + endif + planckalbedo=2*pi*hPc*c0**2/& + (n**2*lambda**5*(Exp(hPc*c0/(n*lambda*kb*tmean))-1))*omega +end function planckalbedo +!***********************************END**************************************** + + +!********************************BEGINNING************************************* +!> fraction of blackbody radiation according to eq. (1-33) in Siegel's and +!! Howell's 4th Thermal Radiation Heat Transfer +real(dp) function fbep(n,lambda,T) + integer :: i,maxit=100 + real(dp), intent(in) :: n,lambda,T !index of refraction,wavelength,temperature + real(dp) :: dzeta,old,res,tol=1e-12_dp + dzeta=C2/(n*lambda*T) + old=0 + do i=1,maxit + fbep=old+15/pi**4*(exp(-i*dzeta)/i*& + (dzeta**3+3*dzeta**2/i+6*dzeta/i**2+6e0_dp/i**3)) + res=abs(fbep-old) + if (res @file +!! subroutines for evaluation of radiative properties of gas phase +!! @author Pavel Ferkl +!! @ingroup foam_cond +module gasprop + use constants + implicit none + private + public abscoeffgas +contains +!********************************BEGINNING************************************* +!> evaluates gas absorption coefficient +real(dp) function abscoeffgas(lambda) + use interpolation + real(dp), intent(in) :: lambda !wavelength + integer :: ni=1 !number of points, where we want to interpolate + real(dp) :: xi(1) !x-values of points, where we want to interpolate + real(dp) :: yi(1) !interpolated y-values + xi(1)=lambda + call pwl_interp_1d ( size(lambdagas), lambdagas, acgas, ni, xi, yi ) + abscoeffgas=yi(1) +end function abscoeffgas +!***********************************END**************************************** +end module gasprop diff --git a/applications/PUfoam/MoDeNaModels/foamConductivity/src/src/hbrd.f90 b/applications/PUfoam/MoDeNaModels/foamConductivity/src/src/hbrd.f90 new file mode 100644 index 000000000..f754ee418 --- /dev/null +++ b/applications/PUfoam/MoDeNaModels/foamConductivity/src/src/hbrd.f90 @@ -0,0 +1,1644 @@ +!downloaded from http://jblevins.org/mirror/amiller/ +!(Code converted from the Naval Surface Warfare Center Math. Library) +MODULE Solve_NonLin +use constants, only:dp +! Corrections to FUNCTION Enorm - 28 November 2003 +IMPLICIT NONE +PRIVATE +PUBLIC :: hbrd, hybrd + + +CONTAINS + + +SUBROUTINE hbrd(fcn, n, x, fvec, epsfcn, tol, info, diag) + +! Code converted using TO_F90 by Alan Miller +! Date: 2003-07-15 Time: 13:27:42 + +INTEGER, INTENT(IN) :: n +REAL (dp), INTENT(IN OUT) :: x(n) +REAL (dp), INTENT(IN OUT) :: fvec(n) +REAL (dp), INTENT(IN) :: epsfcn +REAL (dp), INTENT(IN) :: tol +INTEGER, INTENT(OUT) :: info +REAL (dp), INTENT(OUT) :: diag(n) + +! EXTERNAL fcn +INTERFACE + SUBROUTINE FCN(N, X, FVEC, IFLAG) + use constants, only:dp + IMPLICIT NONE + INTEGER, INTENT(IN) :: n + REAL (dp), INTENT(IN) :: x(n) + REAL (dp), INTENT(OUT) :: fvec(n) + INTEGER, INTENT(IN OUT) :: iflag + END SUBROUTINE FCN +END INTERFACE + +! ********** + +! SUBROUTINE HBRD + +! THE PURPOSE OF HBRD IS TO FIND A ZERO OF A SYSTEM OF N NONLINEAR +! FUNCTIONS IN N VARIABLES BY A MODIFICATION OF THE POWELL HYBRID METHOD. +! THIS IS DONE BY USING THE MORE GENERAL NONLINEAR EQUATION SOLVER HYBRD. +! THE USER MUST PROVIDE A SUBROUTINE WHICH CALCULATES THE FUNCTIONS. +! THE JACOBIAN IS THEN CALCULATED BY A FORWARD-DIFFERENCE APPROXIMATION. + +! THE SUBROUTINE STATEMENT IS + +! SUBROUTINE HBRD(N, X, FVEC, EPSFCN, TOL, INFO, WA, LWA) + +! WHERE + +! FCN IS THE NAME OF THE USER-SUPPLIED SUBROUTINE WHICH CALCULATES +! THE FUNCTIONS. FCN MUST BE DECLARED IN AN EXTERNAL STATEMENT +! IN THE USER CALLING PROGRAM, AND SHOULD BE WRITTEN AS FOLLOWS. + +! SUBROUTINE FCN(N, X, FVEC, IFLAG) +! INTEGER N,IFLAG +! REAL X(N),FVEC(N) +! ---------- +! CALCULATE THE FUNCTIONS AT X AND RETURN THIS VECTOR IN FVEC. +! --------- +! RETURN +! END + +! THE VALUE OF IFLAG NOT BE CHANGED BY FCN UNLESS +! THE USER WANTS TO TERMINATE THE EXECUTION OF HBRD. +! IN THIS CASE SET IFLAG TO A NEGATIVE INTEGER. + +! N IS A POSITIVE INTEGER INPUT VARIABLE SET TO THE NUMBER +! OF FUNCTIONS AND VARIABLES. + +! X IS AN ARRAY OF LENGTH N. ON INPUT X MUST CONTAIN AN INITIAL +! ESTIMATE OF THE SOLUTION VECTOR. ON OUTPUT X CONTAINS THE +! FINAL ESTIMATE OF THE SOLUTION VECTOR. + +! FVEC IS AN OUTPUT ARRAY OF LENGTH N WHICH CONTAINS +! THE FUNCTIONS EVALUATED AT THE OUTPUT X. + +! EPSFCN IS AN INPUT VARIABLE USED IN DETERMINING A SUITABLE STEP LENGTH +! FOR THE FORWARD-DIFFERENCE APPROXIMATION. THIS APPROXIMATION ASSUMES +! THAT THE RELATIVE ERRORS IN THE FUNCTIONS ARE OF THE ORDER OF EPSFCN. +! IF EPSFCN IS LESS THAN THE MACHINE PRECISION, IT IS ASSUMED THAT THE +! RELATIVE ERRORS IN THE FUNCTIONS ARE OF THE ORDER OF THE MACHINE +! PRECISION. + +! TOL IS A NONNEGATIVE INPUT VARIABLE. TERMINATION OCCURS WHEN THE +! ALGORITHM ESTIMATES THAT THE RELATIVE ERROR BETWEEN X AND THE SOLUTION +! IS AT MOST TOL. + +! INFO IS AN INTEGER OUTPUT VARIABLE. IF THE USER HAS TERMINATED +! EXECUTION, INFO IS SET TO THE (NEGATIVE) VALUE OF IFLAG. +! SEE DESCRIPTION OF FCN. OTHERWISE, INFO IS SET AS FOLLOWS. + +! INFO = 0 IMPROPER INPUT PARAMETERS. + +! INFO = 1 ALGORITHM ESTIMATES THAT THE RELATIVE ERROR +! BETWEEN X AND THE SOLUTION IS AT MOST TOL. + +! INFO = 2 NUMBER OF CALLS TO FCN HAS REACHED OR EXCEEDED 200*(N+1). + +! INFO = 3 TOL IS TOO SMALL. NO FURTHER IMPROVEMENT IN +! THE APPROXIMATE SOLUTION X IS POSSIBLE. + +! INFO = 4 ITERATION IS NOT MAKING GOOD PROGRESS. + +! SUBPROGRAMS CALLED + +! USER-SUPPLIED ...... FCN + +! MINPACK-SUPPLIED ... HYBRD + +! ARGONNE NATIONAL LABORATORY. MINPACK PROJECT. MARCH 1980. +! BURTON S. GARBOW, KENNETH E. HILLSTROM, JORGE J. MORE + +! Reference: +! Powell, M.J.D. 'A hybrid method for nonlinear equations' in Numerical Methods +! for Nonlinear Algebraic Equations', P.Rabinowitz (editor), Gordon and +! Breach, London 1970. +! ********** +INTEGER :: maxfev, ml, mode, mu, nfev, nprint +REAL (dp) :: xtol +REAL (dp), PARAMETER :: factor = 100.0_dp, zero = 0.0_dp + +info = 0 + +! CHECK THE INPUT PARAMETERS FOR ERRORS. + + +IF (n <= 0 .OR. epsfcn < zero .OR. tol < zero) GO TO 20 + +! CALL HYBRD. + +maxfev = 200*(n + 1) +xtol = tol +ml = n - 1 +mu = n - 1 +mode = 2 +nprint = 0 +CALL hybrd(fcn, n, x, fvec, xtol, maxfev, ml, mu, epsfcn, diag, mode, & + factor, nprint, info, nfev) +IF (info == 5) info = 4 +20 RETURN + +! LAST CARD OF SUBROUTINE HBRD. + +END SUBROUTINE hbrd + + + +SUBROUTINE hybrd(fcn, n, x, fvec, xtol, maxfev, ml, mu, epsfcn, diag, mode, & + factor, nprint, info, nfev) + +INTEGER, INTENT(IN) :: n +REAL (dp), INTENT(IN OUT) :: x(n) +REAL (dp), INTENT(IN OUT) :: fvec(n) +REAL (dp), INTENT(IN) :: xtol +INTEGER, INTENT(IN OUT) :: maxfev +INTEGER, INTENT(IN OUT) :: ml +INTEGER, INTENT(IN) :: mu +REAL (dp), INTENT(IN) :: epsfcn +REAL (dp), INTENT(OUT) :: diag(n) +INTEGER, INTENT(IN) :: mode +REAL (dp), INTENT(IN) :: factor +INTEGER, INTENT(IN OUT) :: nprint +INTEGER, INTENT(OUT) :: info +INTEGER, INTENT(OUT) :: nfev + +! EXTERNAL fcn +INTERFACE + SUBROUTINE FCN(N, X, FVEC, IFLAG) + use constants, only:dp + IMPLICIT NONE + INTEGER, INTENT(IN) :: n + REAL (dp), INTENT(IN) :: x(n) + REAL (dp), INTENT(OUT) :: fvec(n) + INTEGER, INTENT(IN OUT) :: iflag + END SUBROUTINE FCN +END INTERFACE + +! ********** + +! SUBROUTINE HYBRD + +! THE PURPOSE OF HYBRD IS TO FIND A ZERO OF A SYSTEM OF N NONLINEAR +! FUNCTIONS IN N VARIABLES BY A MODIFICATION OF THE POWELL HYBRID METHOD. +! THE USER MUST PROVIDE A SUBROUTINE WHICH CALCULATES THE FUNCTIONS. +! THE JACOBIAN IS THEN CALCULATED BY A FORWARD-DIFFERENCE APPROXIMATION. + +! THE SUBROUTINE STATEMENT IS + +! SUBROUTINE HYBRD(FCN, N, X, FVEC, XTOL, MAXFEV, ML, MU, EPSFCN, +! DIAG, MODE, FACTOR, NPRINT, INFO, NFEV, FJAC, +! LDFJAC, R, LR, QTF, WA1, WA2, WA3, WA4) + +! WHERE + +! FCN IS THE NAME OF THE USER-SUPPLIED SUBROUTINE WHICH CALCULATES +! THE FUNCTIONS. FCN MUST BE DECLARED IN AN EXTERNAL STATEMENT IN +! THE USER CALLING PROGRAM, AND SHOULD BE WRITTEN AS FOLLOWS. + +! SUBROUTINE FCN(N, X, FVEC, IFLAG) +! INTEGER N, IFLAG +! REAL X(N), FVEC(N) +! ---------- +! CALCULATE THE FUNCTIONS AT X AND +! RETURN THIS VECTOR IN FVEC. +! --------- +! RETURN +! END + +! THE VALUE OF IFLAG SHOULD NOT BE CHANGED BY FCN UNLESS +! THE USER WANTS TO TERMINATE EXECUTION OF HYBRD. +! IN THIS CASE SET IFLAG TO A NEGATIVE INTEGER. + +! N IS A POSITIVE INTEGER INPUT VARIABLE SET TO THE NUMBER +! OF FUNCTIONS AND VARIABLES. + +! X IS AN ARRAY OF LENGTH N. ON INPUT X MUST CONTAIN AN INITIAL +! ESTIMATE OF THE SOLUTION VECTOR. ON OUTPUT X CONTAINS THE FINAL +! ESTIMATE OF THE SOLUTION VECTOR. + +! FVEC IS AN OUTPUT ARRAY OF LENGTH N WHICH CONTAINS +! THE FUNCTIONS EVALUATED AT THE OUTPUT X. + +! XTOL IS A NONNEGATIVE INPUT VARIABLE. TERMINATION OCCURS WHEN THE +! RELATIVE ERROR BETWEEN TWO CONSECUTIVE ITERATES IS AT MOST XTOL. + +! MAXFEV IS A POSITIVE INTEGER INPUT VARIABLE. TERMINATION OCCURS WHEN +! THE NUMBER OF CALLS TO FCN IS AT LEAST MAXFEV BY THE END OF AN +! ITERATION. + +! ML IS A NONNEGATIVE INTEGER INPUT VARIABLE WHICH SPECIFIES THE +! NUMBER OF SUBDIAGONALS WITHIN THE BAND OF THE JACOBIAN MATRIX. +! IF THE JACOBIAN IS NOT BANDED, SET ML TO AT LEAST N - 1. + +! MU IS A NONNEGATIVE INTEGER INPUT VARIABLE WHICH SPECIFIES THE NUMBER +! OF SUPERDIAGONALS WITHIN THE BAND OF THE JACOBIAN MATRIX. +! IF THE JACOBIAN IS NOT BANDED, SET MU TO AT LEAST N - 1. + +! EPSFCN IS AN INPUT VARIABLE USED IN DETERMINING A SUITABLE STEP LENGTH +! FOR THE FORWARD-DIFFERENCE APPROXIMATION. THIS APPROXIMATION +! ASSUMES THAT THE RELATIVE ERRORS IN THE FUNCTIONS ARE OF THE ORDER +! OF EPSFCN. IF EPSFCN IS LESS THAN THE MACHINE PRECISION, +! IT IS ASSUMED THAT THE RELATIVE ERRORS IN THE FUNCTIONS ARE OF THE +! ORDER OF THE MACHINE PRECISION. + +! DIAG IS AN ARRAY OF LENGTH N. IF MODE = 1 (SEE BELOW), +! DIAG IS INTERNALLY SET. IF MODE = 2, DIAG MUST CONTAIN POSITIVE +! ENTRIES THAT SERVE AS MULTIPLICATIVE SCALE FACTORS FOR THE +! VARIABLES. + +! MODE IS AN INTEGER INPUT VARIABLE. IF MODE = 1, THE VARIABLES WILL BE +! SCALED INTERNALLY. IF MODE = 2, THE SCALING IS SPECIFIED BY THE +! INPUT DIAG. OTHER VALUES OF MODE ARE EQUIVALENT TO MODE = 1. + +! FACTOR IS A POSITIVE INPUT VARIABLE USED IN DETERMINING THE +! INITIAL STEP BOUND. THIS BOUND IS SET TO THE PRODUCT OF +! FACTOR AND THE EUCLIDEAN NORM OF DIAG*X IF NONZERO, OR ELSE +! TO FACTOR ITSELF. IN MOST CASES FACTOR SHOULD LIE IN THE +! INTERVAL (.1,100.). 100. IS A GENERALLY RECOMMENDED VALUE. + +! NPRINT IS AN INTEGER INPUT VARIABLE THAT ENABLES CONTROLLED +! PRINTING OF ITERATES IF IT IS POSITIVE. IN THIS CASE, +! FCN IS CALLED WITH IFLAG = 0 AT THE BEGINNING OF THE FIRST +! ITERATION AND EVERY NPRINT ITERATIONS THEREAFTER AND +! IMMEDIATELY PRIOR TO RETURN, WITH X AND FVEC AVAILABLE +! FOR PRINTING. IF NPRINT IS NOT POSITIVE, NO SPECIAL CALLS +! OF FCN WITH IFLAG = 0 ARE MADE. + +! INFO IS AN INTEGER OUTPUT VARIABLE. IF THE USER HAS +! TERMINATED EXECUTION, INFO IS SET TO THE (NEGATIVE) +! VALUE OF IFLAG. SEE DESCRIPTION OF FCN. OTHERWISE, +! INFO IS SET AS FOLLOWS. + +! INFO = 0 IMPROPER INPUT PARAMETERS. + +! INFO = 1 RELATIVE ERROR BETWEEN TWO CONSECUTIVE ITERATES +! IS AT MOST XTOL. + +! INFO = 2 NUMBER OF CALLS TO FCN HAS REACHED OR EXCEEDED MAXFEV. + +! INFO = 3 XTOL IS TOO SMALL. NO FURTHER IMPROVEMENT IN +! THE APPROXIMATE SOLUTION X IS POSSIBLE. + +! INFO = 4 ITERATION IS NOT MAKING GOOD PROGRESS, AS +! MEASURED BY THE IMPROVEMENT FROM THE LAST +! FIVE JACOBIAN EVALUATIONS. + +! INFO = 5 ITERATION IS NOT MAKING GOOD PROGRESS, AS MEASURED BY +! THE IMPROVEMENT FROM THE LAST TEN ITERATIONS. + +! NFEV IS AN INTEGER OUTPUT VARIABLE SET TO THE NUMBER OF CALLS TO FCN. + +! FJAC IS AN OUTPUT N BY N ARRAY WHICH CONTAINS THE ORTHOGONAL MATRIX Q +! PRODUCED BY THE QR FACTORIZATION OF THE FINAL APPROXIMATE JACOBIAN. + +! LDFJAC IS A POSITIVE INTEGER INPUT VARIABLE NOT LESS THAN N +! WHICH SPECIFIES THE LEADING DIMENSION OF THE ARRAY FJAC. + +! R IS AN OUTPUT ARRAY OF LENGTH LR WHICH CONTAINS THE +! UPPER TRIANGULAR MATRIX PRODUCED BY THE QR FACTORIZATION +! OF THE FINAL APPROXIMATE JACOBIAN, STORED ROWWISE. + +! LR IS A POSITIVE INTEGER INPUT VARIABLE NOT LESS THAN (N*(N+1))/2. + +! QTF IS AN OUTPUT ARRAY OF LENGTH N WHICH CONTAINS +! THE VECTOR (Q TRANSPOSE)*FVEC. + +! WA1, WA2, WA3, AND WA4 ARE WORK ARRAYS OF LENGTH N. + +! SUBPROGRAMS CALLED + +! USER-SUPPLIED ...... FCN + +! MINPACK-SUPPLIED ... DOGLEG,SPMPAR,ENORM,FDJAC1, +! QFORM,QRFAC,R1MPYQ,R1UPDT + +! FORTRAN-SUPPLIED ... ABS,MAX,MIN,MIN,MOD + +! ARGONNE NATIONAL LABORATORY. MINPACK PROJECT. MARCH 1980. +! BURTON S. GARBOW, KENNETH E. HILLSTROM, JORGE J. MORE + +! ********** + +INTEGER :: i, iflag, iter, j, jm1, l, lr, msum, ncfail, ncsuc, nslow1, & + nslow2 +INTEGER :: iwa(1) +LOGICAL :: jeval, sing +REAL (dp) :: actred, delta, epsmch, fnorm, fnorm1, pnorm, prered, & + ratio, sum, temp, xnorm +REAL (dp), PARAMETER :: one = 1.0_dp, p1 = 0.1_dp, p5 = 0.5_dp, & + p001 = 0.001_dp, p0001 = 0.0001_dp, zero = 0.0_dp + +! The following were workspace arguments +REAL (dp) :: fjac(n,n), r(n*(n+1)/2), qtf(n), wa1(n), wa2(n), & + wa3(n), wa4(n) + +! EPSMCH IS THE MACHINE PRECISION. + +epsmch = EPSILON(1.0_dp) + +info = 0 +iflag = 0 +nfev = 0 +lr = n*(n+1)/2 + +! CHECK THE INPUT PARAMETERS FOR ERRORS. + +IF (n > 0 .AND. xtol >= zero .AND. maxfev > 0 .AND. ml >= 0 .AND. mu >= & + 0 .AND. factor > zero ) THEN +IF (mode == 2) THEN + diag(1:n) = one +END IF + +! EVALUATE THE FUNCTION AT THE STARTING POINT AND CALCULATE ITS NORM. + +iflag = 1 +CALL fcn(n, x, fvec, iflag) +nfev = 1 +IF (iflag >= 0) THEN + fnorm = enorm(n, fvec) + +! DETERMINE THE NUMBER OF CALLS TO FCN NEEDED TO COMPUTE THE JACOBIAN MATRIX. + + msum = MIN(ml+mu+1,n) + +! INITIALIZE ITERATION COUNTER AND MONITORS. + + iter = 1 + ncsuc = 0 + ncfail = 0 + nslow1 = 0 + nslow2 = 0 + +! BEGINNING OF THE OUTER LOOP. + + 20 jeval = .true. + +! CALCULATE THE JACOBIAN MATRIX. + + iflag = 2 + CALL fdjac1(fcn, n, x, fvec, fjac, n, iflag, ml, mu, epsfcn, wa1, wa2) + nfev = nfev + msum + IF (iflag >= 0) THEN + +! COMPUTE THE QR FACTORIZATION OF THE JACOBIAN. + + CALL qrfac(n, n, fjac, n, .false., iwa, 1, wa1, wa2, wa3) + +! ON THE FIRST ITERATION AND IF MODE IS 1, SCALE ACCORDING +! TO THE NORMS OF THE COLUMNS OF THE INITIAL JACOBIAN. + + IF (iter == 1) THEN + IF (mode /= 2) THEN + DO j = 1, n + diag(j) = wa2(j) + IF (wa2(j) == zero) diag(j) = one + END DO + END IF + +! ON THE FIRST ITERATION, CALCULATE THE NORM OF THE SCALED X +! AND INITIALIZE THE STEP BOUND DELTA. + + wa3(1:n) = diag(1:n) * x(1:n) + xnorm = enorm(n, wa3) + delta = factor * xnorm + IF (delta == zero) delta = factor + END IF + +! FORM (Q TRANSPOSE)*FVEC AND STORE IN QTF. + + qtf(1:n) = fvec(1:n) + DO j = 1, n + IF (fjac(j,j) /= zero) THEN + sum = zero + DO i = j, n + sum = sum + fjac(i,j) * qtf(i) + END DO + temp = -sum / fjac(j,j) + DO i = j, n + qtf(i) = qtf(i) + fjac(i,j) * temp + END DO + END IF + END DO + +! COPY THE TRIANGULAR FACTOR OF THE QR FACTORIZATION INTO R. + + sing = .false. + DO j = 1, n + l = j + jm1 = j - 1 + IF (jm1 >= 1) THEN + DO i = 1, jm1 + r(l) = fjac(i,j) + l = l + n - i + END DO + END IF + r(l) = wa1(j) + IF (wa1(j) == zero) sing = .true. + END DO + +! ACCUMULATE THE ORTHOGONAL FACTOR IN FJAC. + + CALL qform(n, n, fjac, n, wa1) + +! RESCALE IF NECESSARY. + + IF (mode /= 2) THEN + DO j = 1, n + diag(j) = MAX(diag(j), wa2(j)) + END DO + END IF + +! BEGINNING OF THE INNER LOOP. + +! IF REQUESTED, CALL FCN TO ENABLE PRINTING OF ITERATES. + + 120 IF (nprint > 0) THEN + iflag = 0 + IF (MOD(iter-1, nprint) == 0) CALL fcn(n, x, fvec, iflag) + IF (iflag < 0) GO TO 190 + END IF + +! DETERMINE THE DIRECTION P. + + CALL dogleg(n, r, lr, diag, qtf, delta, wa1, wa2, wa3) + +! STORE THE DIRECTION P AND X + P. CALCULATE THE NORM OF P. + + DO j = 1, n + wa1(j) = -wa1(j) + wa2(j) = x(j) + wa1(j) + wa3(j) = diag(j) * wa1(j) + END DO + pnorm = enorm(n, wa3) + +! ON THE FIRST ITERATION, ADJUST THE INITIAL STEP BOUND. + + IF (iter == 1) delta = MIN(delta, pnorm) + +! EVALUATE THE FUNCTION AT X + P AND CALCULATE ITS NORM. + + iflag = 1 + CALL fcn(n, wa2, wa4, iflag) + nfev = nfev + 1 + IF (iflag >= 0) THEN + fnorm1 = enorm(n, wa4) + +! COMPUTE THE SCALED ACTUAL REDUCTION. + + actred = -one + IF (fnorm1 < fnorm) actred = one - (fnorm1/fnorm) ** 2 + +! COMPUTE THE SCALED PREDICTED REDUCTION. + + l = 1 + DO i = 1, n + sum = zero + DO j = i, n + sum = sum + r(l) * wa1(j) + l = l + 1 + END DO + wa3(i) = qtf(i) + sum + END DO + temp = enorm(n, wa3) + prered = zero + IF (temp < fnorm) prered = one - (temp/fnorm) ** 2 + +! COMPUTE THE RATIO OF THE ACTUAL TO THE PREDICTED REDUCTION. + + ratio = zero + IF (prered > zero) ratio = actred / prered + +! UPDATE THE STEP BOUND. + + IF (ratio < p1) THEN + ncsuc = 0 + ncfail = ncfail + 1 + delta = p5 * delta + ELSE + ncfail = 0 + ncsuc = ncsuc + 1 + IF (ratio >= p5 .OR. ncsuc > 1) delta = MAX(delta,pnorm/p5) + IF (ABS(ratio-one) <= p1) delta = pnorm / p5 + END IF + +! TEST FOR SUCCESSFUL ITERATION. + + IF (ratio >= p0001) THEN + +! SUCCESSFUL ITERATION. UPDATE X, FVEC, AND THEIR NORMS. + + DO j = 1, n + x(j) = wa2(j) + wa2(j) = diag(j) * x(j) + fvec(j) = wa4(j) + END DO + xnorm = enorm(n, wa2) + fnorm = fnorm1 + iter = iter + 1 + END IF + +! DETERMINE THE PROGRESS OF THE ITERATION. + + nslow1 = nslow1 + 1 + IF (actred >= p001) nslow1 = 0 + IF (jeval) nslow2 = nslow2 + 1 + IF (actred >= p1) nslow2 = 0 + +! TEST FOR CONVERGENCE. + + IF (delta <= xtol*xnorm .OR. fnorm == zero) info = 1 + IF (info == 0) THEN + +! TESTS FOR TERMINATION AND STRINGENT TOLERANCES. + + IF (nfev >= maxfev) info = 2 + IF (p1*MAX(p1*delta, pnorm) <= epsmch*xnorm) info = 3 + IF (nslow2 == 5) info = 4 + IF (nslow1 == 10) info = 5 + IF (info == 0) THEN + +! CRITERION FOR RECALCULATING JACOBIAN APPROXIMATION +! BY FORWARD DIFFERENCES. + + IF (ncfail /= 2) THEN + +! CALCULATE THE RANK ONE MODIFICATION TO THE JACOBIAN +! AND UPDATE QTF IF NECESSARY. + + DO j = 1, n + sum = zero + DO i = 1, n + sum = sum + fjac(i,j) * wa4(i) + END DO + wa2(j) = (sum-wa3(j)) / pnorm + wa1(j) = diag(j) * ((diag(j)*wa1(j))/pnorm) + IF (ratio >= p0001) qtf(j) = sum + END DO + +! COMPUTE THE QR FACTORIZATION OF THE UPDATED JACOBIAN. + + CALL r1updt(n, n, r, lr, wa1, wa2, wa3, sing) + CALL r1mpyq(n, n, fjac, n, wa2, wa3) + CALL r1mpyq(1, n, qtf, 1, wa2, wa3) + +! END OF THE INNER LOOP. + + jeval = .false. + GO TO 120 + END IF + +! END OF THE OUTER LOOP. + + GO TO 20 + END IF + END IF + END IF + END IF +END IF +END IF + +! TERMINATION, EITHER NORMAL OR USER IMPOSED. + +190 IF (iflag < 0) info = iflag +iflag = 0 +IF (nprint > 0) CALL fcn(n, x, fvec, iflag) +RETURN + +! LAST CARD OF SUBROUTINE HYBRD. + +END SUBROUTINE hybrd + + + +SUBROUTINE dogleg(n, r, lr, diag, qtb, delta, x, wa1, wa2) + +INTEGER, INTENT(IN) :: n +INTEGER, INTENT(IN) :: lr +REAL (dp), INTENT(IN) :: r(lr) +REAL (dp), INTENT(IN) :: diag(n) +REAL (dp), INTENT(IN) :: qtb(n) +REAL (dp), INTENT(IN) :: delta +REAL (dp), INTENT(IN OUT) :: x(n) +REAL (dp), INTENT(OUT) :: wa1(n) +REAL (dp), INTENT(OUT) :: wa2(n) + + +! ********** + +! SUBROUTINE DOGLEG + +! GIVEN AN M BY N MATRIX A, AN N BY N NONSINGULAR DIAGONAL +! MATRIX D, AN M-VECTOR B, AND A POSITIVE NUMBER DELTA, THE +! PROBLEM IS TO DETERMINE THE CONVEX COMBINATION X OF THE +! GAUSS-NEWTON AND SCALED GRADIENT DIRECTIONS THAT MINIMIZES +! (A*X - B) IN THE LEAST SQUARES SENSE, SUBJECT TO THE +! RESTRICTION THAT THE EUCLIDEAN NORM OF D*X BE AT MOST DELTA. + +! THIS SUBROUTINE COMPLETES THE SOLUTION OF THE PROBLEM +! IF IT IS PROVIDED WITH THE NECESSARY INFORMATION FROM THE +! QR FACTORIZATION OF A. THAT IS, IF A = Q*R, WHERE Q HAS +! ORTHOGONAL COLUMNS AND R IS AN UPPER TRIANGULAR MATRIX, +! THEN DOGLEG EXPECTS THE FULL UPPER TRIANGLE OF R AND +! THE FIRST N COMPONENTS OF (Q TRANSPOSE)*B. + +! THE SUBROUTINE STATEMENT IS + +! SUBROUTINE DOGLEG(N,R,LR,DIAG,QTB,DELTA,X,WA1,WA2) + +! WHERE + +! N IS A POSITIVE INTEGER INPUT VARIABLE SET TO THE ORDER OF R. + +! R IS AN INPUT ARRAY OF LENGTH LR WHICH MUST CONTAIN THE UPPER +! TRIANGULAR MATRIX R STORED BY ROWS. + +! LR IS A POSITIVE INTEGER INPUT VARIABLE NOT LESS THAN +! (N*(N+1))/2. + +! DIAG IS AN INPUT ARRAY OF LENGTH N WHICH MUST CONTAIN THE +! DIAGONAL ELEMENTS OF THE MATRIX D. + +! QTB IS AN INPUT ARRAY OF LENGTH N WHICH MUST CONTAIN THE FIRST +! N ELEMENTS OF THE VECTOR (Q TRANSPOSE)*B. + +! DELTA IS A POSITIVE INPUT VARIABLE WHICH SPECIFIES AN UPPER +! BOUND ON THE EUCLIDEAN NORM OF D*X. + +! X IS AN OUTPUT ARRAY OF LENGTH N WHICH CONTAINS THE DESIRED +! CONVEX COMBINATION OF THE GAUSS-NEWTON DIRECTION AND THE +! SCALED GRADIENT DIRECTION. + +! WA1 AND WA2 ARE WORK ARRAYS OF LENGTH N. + +! SUBPROGRAMS CALLED + +! MINPACK-SUPPLIED ... SPMPAR,ENORM + +! FORTRAN-SUPPLIED ... ABS,MAX,MIN,SQRT + +! ARGONNE NATIONAL LABORATORY. MINPACK PROJECT. MARCH 1980. +! BURTON S. GARBOW, KENNETH E. HILLSTROM, JORGE J. MORE + +! ********** +INTEGER :: i, j, jj, jp1, k, l +REAL (dp) :: alpha, bnorm, epsmch, gnorm, qnorm, sgnorm, sum, temp + +! EPSMCH IS THE MACHINE PRECISION. + +epsmch = EPSILON(1.0_dp) + +! FIRST, CALCULATE THE GAUSS-NEWTON DIRECTION. + +jj = (n*(n+1)) / 2 + 1 +DO k = 1, n + j = n - k + 1 + jp1 = j + 1 + jj = jj - k + l = jj + 1 + sum = 0.0 + IF (n >= jp1) THEN + DO i = jp1, n + sum = sum + r(l) * x(i) + l = l + 1 + END DO + END IF + temp = r(jj) + IF (temp == 0.0_dp) THEN + l = j + DO i = 1, j + temp = MAX(temp,ABS(r(l))) + l = l + n - i + END DO + temp = epsmch * temp + IF (temp == 0.0_dp) temp = epsmch + END IF + x(j) = (qtb(j)-sum) / temp +END DO + +! TEST WHETHER THE GAUSS-NEWTON DIRECTION IS ACCEPTABLE. + +DO j = 1, n + wa1(j) = 0.0_dp + wa2(j) = diag(j) * x(j) +END DO +qnorm = enorm(n, wa2) +IF (qnorm > delta) THEN + +! THE GAUSS-NEWTON DIRECTION IS NOT ACCEPTABLE. +! NEXT, CALCULATE THE SCALED GRADIENT DIRECTION. + + l = 1 + DO j = 1, n + temp = qtb(j) + DO i = j, n + wa1(i) = wa1(i) + r(l) * temp + l = l + 1 + END DO + wa1(j) = wa1(j) / diag(j) + END DO + +! CALCULATE THE NORM OF THE SCALED GRADIENT AND TEST FOR +! THE SPECIAL CASE IN WHICH THE SCALED GRADIENT IS ZERO. + + gnorm = enorm(n, wa1) + sgnorm = 0.0_dp + alpha = delta / qnorm + IF (gnorm /= 0.0_dp) THEN + +! CALCULATE THE POINT ALONG THE SCALED GRADIENT +! AT WHICH THE QUADRATIC IS MINIMIZED. + + DO j = 1, n + wa1(j) = (wa1(j)/gnorm) / diag(j) + END DO + l = 1 + DO j = 1, n + sum = 0.0_dp + DO i = j, n + sum = sum + r(l) * wa1(i) + l = l + 1 + END DO + wa2(j) = sum + END DO + temp = enorm(n, wa2) + sgnorm = (gnorm/temp) / temp + +! TEST WHETHER THE SCALED GRADIENT DIRECTION IS ACCEPTABLE. + + alpha = 0.0_dp + IF (sgnorm < delta) THEN + +! THE SCALED GRADIENT DIRECTION IS NOT ACCEPTABLE. +! FINALLY, CALCULATE THE POINT ALONG THE DOGLEG +! AT WHICH THE QUADRATIC IS MINIMIZED. + + bnorm = enorm(n, qtb) + temp = (bnorm/gnorm) * (bnorm/qnorm) * (sgnorm/delta) + temp = temp - (delta/qnorm) * (sgnorm/delta) ** 2 + SQRT(( & + temp-(delta/qnorm))**2+(1.0_dp-(delta/qnorm)**2)*(1.0_dp-( sgnorm/delta)**2)) + alpha = ((delta/qnorm)*(1.0_dp-(sgnorm/delta)**2)) / temp + END IF + END IF + +! FORM APPROPRIATE CONVEX COMBINATION OF THE GAUSS-NEWTON +! DIRECTION AND THE SCALED GRADIENT DIRECTION. + + temp = (1.0_dp-alpha) * MIN(sgnorm,delta) + DO j = 1, n + x(j) = temp * wa1(j) + alpha * x(j) + END DO +END IF +RETURN +END SUBROUTINE dogleg + + +SUBROUTINE fdjac1(fcn, n, x, fvec, fjac, ldfjac, iflag, ml, mu, epsfcn, & + wa1, wa2) + +INTEGER, INTENT(IN) :: n +REAL (dp), INTENT(IN OUT) :: x(n) +REAL (dp), INTENT(IN) :: fvec(n) +INTEGER, INTENT(IN) :: ldfjac +REAL (dp), INTENT(OUT) :: fjac(ldfjac,n) +INTEGER, INTENT(IN OUT) :: iflag +INTEGER, INTENT(IN) :: ml +INTEGER, INTENT(IN) :: mu +REAL (dp), INTENT(IN) :: epsfcn +REAL (dp), INTENT(IN OUT) :: wa1(n) +REAL (dp), INTENT(OUT) :: wa2(n) + +! EXTERNAL fcn +INTERFACE + SUBROUTINE FCN(N, X, FVEC, IFLAG) + use constants, only:dp + IMPLICIT NONE + INTEGER, INTENT(IN) :: n + REAL (dp), INTENT(IN) :: x(n) + REAL (dp), INTENT(OUT) :: fvec(n) + INTEGER, INTENT(IN OUT) :: iflag + END SUBROUTINE FCN +END INTERFACE + +! ********** + +! SUBROUTINE FDJAC1 + +! THIS SUBROUTINE COMPUTES A FORWARD-DIFFERENCE APPROXIMATION TO THE N BY N +! JACOBIAN MATRIX ASSOCIATED WITH A SPECIFIED PROBLEM OF N FUNCTIONS IN N +! VARIABLES. IF THE JACOBIAN HAS A BANDED FORM, THEN FUNCTION EVALUATIONS +! ARE SAVED BY ONLY APPROXIMATING THE NONZERO TERMS. + +! THE SUBROUTINE STATEMENT IS + +! SUBROUTINE FDJAC1(FCN,N,X,FVEC,FJAC,LDFJAC,IFLAG,ML,MU,EPSFCN, +! WA1,WA2) + +! WHERE + +! FCN IS THE NAME OF THE USER-SUPPLIED SUBROUTINE WHICH CALCULATES +! THE FUNCTIONS. FCN MUST BE DECLARED IN AN EXTERNAL STATEMENT IN +! THE USER CALLING PROGRAM, AND SHOULD BE WRITTEN AS FOLLOWS. + +! SUBROUTINE FCN(N,X,FVEC,IFLAG) +! INTEGER N,IFLAG +! REAL X(N),FVEC(N) +! ---------- +! CALCULATE THE FUNCTIONS AT X AND +! RETURN THIS VECTOR IN FVEC. +! ---------- +! RETURN +! END + +! THE VALUE OF IFLAG SHOULD NOT BE CHANGED BY FCN UNLESS +! THE USER WANTS TO TERMINATE EXECUTION OF FDJAC1. +! IN THIS CASE SET IFLAG TO A NEGATIVE INTEGER. + +! N IS A POSITIVE INTEGER INPUT VARIABLE SET TO THE NUMBER +! OF FUNCTIONS AND VARIABLES. + +! X IS AN INPUT ARRAY OF LENGTH N. + +! FVEC IS AN INPUT ARRAY OF LENGTH N WHICH MUST CONTAIN THE +! FUNCTIONS EVALUATED AT X. + +! FJAC IS AN OUTPUT N BY N ARRAY WHICH CONTAINS THE +! APPROXIMATION TO THE JACOBIAN MATRIX EVALUATED AT X. + +! LDFJAC IS A POSITIVE INTEGER INPUT VARIABLE NOT LESS THAN N +! WHICH SPECIFIES THE LEADING DIMENSION OF THE ARRAY FJAC. + +! IFLAG IS AN INTEGER VARIABLE WHICH CAN BE USED TO TERMINATE +! THE EXECUTION OF FDJAC1. SEE DESCRIPTION OF FCN. + +! ML IS A NONNEGATIVE INTEGER INPUT VARIABLE WHICH SPECIFIES +! THE NUMBER OF SUBDIAGONALS WITHIN THE BAND OF THE +! JACOBIAN MATRIX. IF THE JACOBIAN IS NOT BANDED, SET +! ML TO AT LEAST N - 1. + +! EPSFCN IS AN INPUT VARIABLE USED IN DETERMINING A SUITABLE +! STEP LENGTH FOR THE FORWARD-DIFFERENCE APPROXIMATION. THIS +! APPROXIMATION ASSUMES THAT THE RELATIVE ERRORS IN THE +! FUNCTIONS ARE OF THE ORDER OF EPSFCN. IF EPSFCN IS LESS +! THAN THE MACHINE PRECISION, IT IS ASSUMED THAT THE RELATIVE +! ERRORS IN THE FUNCTIONS ARE OF THE ORDER OF THE MACHINE PRECISION. + +! MU IS A NONNEGATIVE INTEGER INPUT VARIABLE WHICH SPECIFIES +! THE NUMBER OF SUPERDIAGONALS WITHIN THE BAND OF THE +! JACOBIAN MATRIX. IF THE JACOBIAN IS NOT BANDED, SET +! MU TO AT LEAST N - 1. + +! WA1 AND WA2 ARE WORK ARRAYS OF LENGTH N. IF ML + MU + 1 IS AT +! LEAST N, THEN THE JACOBIAN IS CONSIDERED DENSE, AND WA2 IS +! NOT REFERENCED. + +! SUBPROGRAMS CALLED + +! MINPACK-SUPPLIED ... SPMPAR + +! FORTRAN-SUPPLIED ... ABS,MAX,SQRT + +! ARGONNE NATIONAL LABORATORY. MINPACK PROJECT. MARCH 1980. +! BURTON S. GARBOW, KENNETH E. HILLSTROM, JORGE J. MORE + +! ********** +INTEGER :: i, j, k, msum +REAL (dp) :: eps, epsmch, h, temp +REAL (dp), PARAMETER :: zero = 0.0_dp + +! EPSMCH IS THE MACHINE PRECISION. + +epsmch = EPSILON(1.0_dp) + +eps = SQRT(MAX(epsfcn, epsmch)) +msum = ml + mu + 1 +IF (msum >= n) THEN + +! COMPUTATION OF DENSE APPROXIMATE JACOBIAN. + + DO j = 1, n + temp = x(j) + h = eps * ABS(temp) + IF (h == zero) h = eps + x(j) = temp + h + CALL fcn(n, x, wa1, iflag) + IF (iflag < 0) EXIT + x(j) = temp + DO i = 1, n + fjac(i,j) = (wa1(i)-fvec(i)) / h + END DO + END DO +ELSE + +! COMPUTATION OF BANDED APPROXIMATE JACOBIAN. + + DO k = 1, msum + DO j = k, n, msum + wa2(j) = x(j) + h = eps * ABS(wa2(j)) + IF (h == zero) h = eps + x(j) = wa2(j) + h + END DO + CALL fcn(n, x, wa1, iflag) + IF (iflag < 0) EXIT + DO j = k, n, msum + x(j) = wa2(j) + h = eps * ABS(wa2(j)) + IF (h == zero) h = eps + DO i = 1, n + fjac(i,j) = zero + IF (i >= j-mu .AND. i <= j+ml) fjac(i,j) = (wa1(i)-fvec(i)) / h + END DO + END DO + END DO +END IF +RETURN + +! LAST CARD OF SUBROUTINE FDJAC1. + +END SUBROUTINE fdjac1 + + + +SUBROUTINE qform(m, n, q, ldq, wa) + +INTEGER, INTENT(IN) :: m +INTEGER, INTENT(IN) :: n +INTEGER, INTENT(IN) :: ldq +REAL (dp), INTENT(OUT) :: q(ldq,m) +REAL (dp), INTENT(OUT) :: wa(m) + + +! ********** + +! SUBROUTINE QFORM + +! THIS SUBROUTINE PROCEEDS FROM THE COMPUTED QR FACTORIZATION OF AN M BY N +! MATRIX A TO ACCUMULATE THE M BY M ORTHOGONAL MATRIX Q FROM ITS FACTORED FORM. + +! THE SUBROUTINE STATEMENT IS + +! SUBROUTINE QFORM(M,N,Q,LDQ,WA) + +! WHERE + +! M IS A POSITIVE INTEGER INPUT VARIABLE SET TO THE NUMBER +! OF ROWS OF A AND THE ORDER OF Q. + +! N IS A POSITIVE INTEGER INPUT VARIABLE SET TO THE NUMBER OF COLUMNS OF A. + +! Q IS AN M BY M ARRAY. ON INPUT THE FULL LOWER TRAPEZOID IN +! THE FIRST MIN(M,N) COLUMNS OF Q CONTAINS THE FACTORED FORM. +! ON OUTPUT Q HAS BEEN ACCUMULATED INTO A SQUARE MATRIX. + +! LDQ IS A POSITIVE INTEGER INPUT VARIABLE NOT LESS THAN M +! WHICH SPECIFIES THE LEADING DIMENSION OF THE ARRAY Q. + +! WA IS A WORK ARRAY OF LENGTH M. + +! SUBPROGRAMS CALLED + +! FORTRAN-SUPPLIED ... MIN + +! ARGONNE NATIONAL LABORATORY. MINPACK PROJECT. MARCH 1980. +! BURTON S. GARBOW, KENNETH E. HILLSTROM, JORGE J. MORE + +! ********** +INTEGER :: i, j, jm1, k, l, minmn, np1 +REAL (dp) :: sum, temp +REAL (dp), PARAMETER :: one = 1.0_dp, zero = 0.0_dp + +! ZERO OUT UPPER TRIANGLE OF Q IN THE FIRST MIN(M,N) COLUMNS. + +minmn = MIN(m,n) +IF (minmn >= 2) THEN + DO j = 2, minmn + jm1 = j - 1 + DO i = 1, jm1 + q(i,j) = zero + END DO + END DO +END IF + +! INITIALIZE REMAINING COLUMNS TO THOSE OF THE IDENTITY MATRIX. + +np1 = n + 1 +IF (m >= np1) THEN + DO j = np1, m + DO i = 1, m + q(i,j) = zero + END DO + q(j,j) = one + END DO +END IF + +! ACCUMULATE Q FROM ITS FACTORED FORM. + +DO l = 1, minmn + k = minmn - l + 1 + DO i = k, m + wa(i) = q(i,k) + q(i,k) = zero + END DO + q(k,k) = one + IF (wa(k) /= zero) THEN + DO j = k, m + sum = zero + DO i = k, m + sum = sum + q(i,j) * wa(i) + END DO + temp = sum / wa(k) + DO i = k, m + q(i,j) = q(i,j) - temp * wa(i) + END DO + END DO + END IF +END DO +RETURN + +! LAST CARD OF SUBROUTINE QFORM. + +END SUBROUTINE qform + + +SUBROUTINE qrfac(m, n, a, lda, pivot, ipvt, lipvt, rdiag, acnorm, wa) + +INTEGER, INTENT(IN) :: m +INTEGER, INTENT(IN) :: n +INTEGER, INTENT(IN) :: lda +REAL (dp), INTENT(IN OUT) :: a(lda,n) +LOGICAL, INTENT(IN) :: pivot +INTEGER, INTENT(IN) :: lipvt +INTEGER, INTENT(OUT) :: ipvt(lipvt) +REAL (dp), INTENT(OUT) :: rdiag(n) +REAL (dp), INTENT(OUT) :: acnorm(n) +REAL (dp), INTENT(OUT) :: wa(n) + + +! ********** + +! SUBROUTINE QRFAC + +! THIS SUBROUTINE USES HOUSEHOLDER TRANSFORMATIONS WITH COLUMN PIVOTING +! (OPTIONAL) TO COMPUTE A QR FACTORIZATION OF THE M BY N MATRIX A. +! THAT IS, QRFAC DETERMINES AN ORTHOGONAL MATRIX Q, A PERMUTATION MATRIX P, +! AND AN UPPER TRAPEZOIDAL MATRIX R WITH DIAGONAL ELEMENTS OF NONINCREASING +! MAGNITUDE, SUCH THAT A*P = Q*R. THE HOUSEHOLDER TRANSFORMATION FOR +! COLUMN K, K = 1,2,...,MIN(M,N), IS OF THE FORM + +! T +! I - (1/U(K))*U*U + +! WHERE U HAS ZEROS IN THE FIRST K-1 POSITIONS. THE FORM OF THIS +! TRANSFORMATION AND THE METHOD OF PIVOTING FIRST APPEARED IN THE +! CORRESPONDING LINPACK SUBROUTINE. + +! THE SUBROUTINE STATEMENT IS + +! SUBROUTINE QRFAC(M,N,A,LDA,PIVOT,IPVT,LIPVT,RDIAG,ACNORM,WA) + +! WHERE + +! M IS A POSITIVE INTEGER INPUT VARIABLE SET TO THE NUMBER OF ROWS OF A. + +! N IS A POSITIVE INTEGER INPUT VARIABLE SET TO THE NUMBER +! OF COLUMNS OF A. + +! A IS AN M BY N ARRAY. ON INPUT A CONTAINS THE MATRIX FOR WHICH THE +! QR FACTORIZATION IS TO BE COMPUTED. ON OUTPUT THE STRICT UPPER +! TRAPEZOIDAL PART OF A CONTAINS THE STRICT UPPER TRAPEZOIDAL PART OF R, +! AND THE LOWER TRAPEZOIDAL PART OF A CONTAINS A FACTORED FORM OF Q +! (THE NON-TRIVIAL ELEMENTS OF THE U VECTORS DESCRIBED ABOVE). + +! LDA IS A POSITIVE INTEGER INPUT VARIABLE NOT LESS THAN M +! WHICH SPECIFIES THE LEADING DIMENSION OF THE ARRAY A. + +! PIVOT IS A LOGICAL INPUT VARIABLE. IF PIVOT IS SET TRUE, +! THEN COLUMN PIVOTING IS ENFORCED. IF PIVOT IS SET FALSE, +! THEN NO COLUMN PIVOTING IS DONE. + +! IPVT IS AN INTEGER OUTPUT ARRAY OF LENGTH LIPVT. IPVT DEFINES THE +! PERMUTATION MATRIX P SUCH THAT A*P = Q*R. +! COLUMN J OF P IS COLUMN IPVT(J) OF THE IDENTITY MATRIX. +! IF PIVOT IS FALSE, IPVT IS NOT REFERENCED. + +! LIPVT IS A POSITIVE INTEGER INPUT VARIABLE. IF PIVOT IS FALSE, +! THEN LIPVT MAY BE AS SMALL AS 1. IF PIVOT IS TRUE, THEN +! LIPVT MUST BE AT LEAST N. + +! RDIAG IS AN OUTPUT ARRAY OF LENGTH N WHICH CONTAINS THE +! DIAGONAL ELEMENTS OF R. + +! ACNORM IS AN OUTPUT ARRAY OF LENGTH N WHICH CONTAINS THE NORMS OF +! THE CORRESPONDING COLUMNS OF THE INPUT MATRIX A. +! IF THIS INFORMATION IS NOT NEEDED, THEN ACNORM CAN COINCIDE WITH RDIAG. + +! WA IS A WORK ARRAY OF LENGTH N. IF PIVOT IS FALSE, THEN WA +! CAN COINCIDE WITH RDIAG. + +! SUBPROGRAMS CALLED + +! MINPACK-SUPPLIED ... SPMPAR,ENORM + +! FORTRAN-SUPPLIED ... MAX,SQRT,MIN + +! ARGONNE NATIONAL LABORATORY. MINPACK PROJECT. MARCH 1980. +! BURTON S. GARBOW, KENNETH E. HILLSTROM, JORGE J. MORE + +! ********** +INTEGER :: i, j, jp1, k, kmax, minmn +REAL (dp) :: ajnorm, epsmch, sum, temp +REAL (dp), PARAMETER :: one = 1.0_dp, p05 = 0.05_dp, zero = 0.0_dp + +! EPSMCH IS THE MACHINE PRECISION. + +epsmch = EPSILON(1.0_dp) + +! COMPUTE THE INITIAL COLUMN NORMS AND INITIALIZE SEVERAL ARRAYS. + +DO j = 1, n + acnorm(j) = enorm(m, a(1:,j)) + rdiag(j) = acnorm(j) + wa(j) = rdiag(j) + IF (pivot) ipvt(j) = j +END DO + +! REDUCE A TO R WITH HOUSEHOLDER TRANSFORMATIONS. + +minmn = MIN(m,n) +DO j = 1, minmn + IF (pivot) THEN + +! BRING THE COLUMN OF LARGEST NORM INTO THE PIVOT POSITION. + + kmax = j + DO k = j, n + IF (rdiag(k) > rdiag(kmax)) kmax = k + END DO + IF (kmax /= j) THEN + DO i = 1, m + temp = a(i,j) + a(i,j) = a(i,kmax) + a(i,kmax) = temp + END DO + rdiag(kmax) = rdiag(j) + wa(kmax) = wa(j) + k = ipvt(j) + ipvt(j) = ipvt(kmax) + ipvt(kmax) = k + END IF + END IF + +! COMPUTE THE HOUSEHOLDER TRANSFORMATION TO REDUCE THE +! J-TH COLUMN OF A TO A MULTIPLE OF THE J-TH UNIT VECTOR. + + ajnorm = enorm(m-j+1, a(j:,j)) + IF (ajnorm /= zero) THEN + IF (a(j,j) < zero) ajnorm = -ajnorm + DO i = j, m + a(i,j) = a(i,j) / ajnorm + END DO + a(j,j) = a(j,j) + one + +! APPLY THE TRANSFORMATION TO THE REMAINING COLUMNS AND UPDATE THE NORMS. + + jp1 = j + 1 + IF (n >= jp1) THEN + DO k = jp1, n + sum = zero + DO i = j, m + sum = sum + a(i,j) * a(i,k) + END DO + temp = sum / a(j,j) + DO i = j, m + a(i,k) = a(i,k) - temp * a(i,j) + END DO + IF (.NOT.(.NOT.pivot.OR.rdiag(k) == zero)) THEN + temp = a(j,k) / rdiag(k) + rdiag(k) = rdiag(k) * SQRT(MAX(zero,one-temp**2)) + IF (p05*(rdiag(k)/wa(k))**2 <= epsmch) THEN + rdiag(k) = enorm(m-j, a(jp1:,k)) + wa(k) = rdiag(k) + END IF + END IF + END DO + END IF + END IF + rdiag(j) = -ajnorm +END DO +RETURN + +! LAST CARD OF SUBROUTINE QRFAC. + +END SUBROUTINE qrfac + + + +SUBROUTINE r1mpyq(m, n, a, lda, v, w) + +INTEGER, INTENT(IN) :: m +INTEGER, INTENT(IN) :: n +INTEGER, INTENT(IN) :: lda +REAL (dp), INTENT(IN OUT) :: a(lda,n) +REAL (dp), INTENT(IN) :: v(n) +REAL (dp), INTENT(IN) :: w(n) + + +! ********** + +! SUBROUTINE R1MPYQ + +! GIVEN AN M BY N MATRIX A, THIS SUBROUTINE COMPUTES A*Q WHERE +! Q IS THE PRODUCT OF 2*(N - 1) TRANSFORMATIONS + +! GV(N-1)*...*GV(1)*GW(1)*...*GW(N-1) + +! AND GV(I), GW(I) ARE GIVENS ROTATIONS IN THE (I,N) PLANE WHICH +! ELIMINATE ELEMENTS IN THE I-TH AND N-TH PLANES, RESPECTIVELY. +! Q ITSELF IS NOT GIVEN, RATHER THE INFORMATION TO RECOVER THE +! GV, GW ROTATIONS IS SUPPLIED. + +! THE SUBROUTINE STATEMENT IS + +! SUBROUTINE R1MPYQ(M, N, A, LDA, V, W) + +! WHERE + +! M IS A POSITIVE INTEGER INPUT VARIABLE SET TO THE NUMBER OF ROWS OF A. + +! N IS A POSITIVE INTEGER INPUT VARIABLE SET TO THE NUMBER OF COLUMNS OF A. + +! A IS AN M BY N ARRAY. ON INPUT A MUST CONTAIN THE MATRIX TO BE +! POSTMULTIPLIED BY THE ORTHOGONAL MATRIX Q DESCRIBED ABOVE. +! ON OUTPUT A*Q HAS REPLACED A. + +! LDA IS A POSITIVE INTEGER INPUT VARIABLE NOT LESS THAN M +! WHICH SPECIFIES THE LEADING DIMENSION OF THE ARRAY A. + +! V IS AN INPUT ARRAY OF LENGTH N. V(I) MUST CONTAIN THE INFORMATION +! NECESSARY TO RECOVER THE GIVENS ROTATION GV(I) DESCRIBED ABOVE. + +! W IS AN INPUT ARRAY OF LENGTH N. W(I) MUST CONTAIN THE INFORMATION +! NECESSARY TO RECOVER THE GIVENS ROTATION GW(I) DESCRIBED ABOVE. + +! SUBROUTINES CALLED + +! FORTRAN-SUPPLIED ... ABS, SQRT + +! ARGONNE NATIONAL LABORATORY. MINPACK PROJECT. MARCH 1980. +! BURTON S. GARBOW, KENNETH E. HILLSTROM, JORGE J. MORE + +! ********** +INTEGER :: i, j, nmj, nm1 +REAL (dp) :: COS, SIN, temp +REAL (dp), PARAMETER :: one = 1.0_dp + +! APPLY THE FIRST SET OF GIVENS ROTATIONS TO A. + +nm1 = n - 1 +IF (nm1 >= 1) THEN + DO nmj = 1, nm1 + j = n - nmj + IF (ABS(v(j)) > one) COS = one / v(j) + IF (ABS(v(j)) > one) SIN = SQRT(one-COS**2) + IF (ABS(v(j)) <= one) SIN = v(j) + IF (ABS(v(j)) <= one) COS = SQRT(one-SIN**2) + DO i = 1, m + temp = COS * a(i,j) - SIN * a(i,n) + a(i,n) = SIN * a(i,j) + COS * a(i,n) + a(i,j) = temp + END DO + END DO + +! APPLY THE SECOND SET OF GIVENS ROTATIONS TO A. + + DO j = 1, nm1 + IF (ABS(w(j)) > one) COS = one / w(j) + IF (ABS(w(j)) > one) SIN = SQRT(one-COS**2) + IF (ABS(w(j)) <= one) SIN = w(j) + IF (ABS(w(j)) <= one) COS = SQRT(one-SIN**2) + DO i = 1, m + temp = COS * a(i,j) + SIN * a(i,n) + a(i,n) = -SIN * a(i,j) + COS * a(i,n) + a(i,j) = temp + END DO + END DO +END IF +RETURN + +! LAST CARD OF SUBROUTINE R1MPYQ. + +END SUBROUTINE r1mpyq + + + +SUBROUTINE r1updt(m, n, s, ls, u, v, w, sing) + +INTEGER, INTENT(IN) :: m +INTEGER, INTENT(IN) :: n +INTEGER, INTENT(IN) :: ls +REAL (dp), INTENT(IN OUT) :: s(ls) +REAL (dp), INTENT(IN) :: u(m) +REAL (dp), INTENT(IN OUT) :: v(n) +REAL (dp), INTENT(OUT) :: w(m) +LOGICAL, INTENT(OUT) :: sing + + +! ********** + +! SUBROUTINE R1UPDT + +! GIVEN AN M BY N LOWER TRAPEZOIDAL MATRIX S, AN M-VECTOR U, +! AND AN N-VECTOR V, THE PROBLEM IS TO DETERMINE AN +! ORTHOGONAL MATRIX Q SUCH THAT + +! T +! (S + U*V )*Q + +! IS AGAIN LOWER TRAPEZOIDAL. + +! THIS SUBROUTINE DETERMINES Q AS THE PRODUCT OF 2*(N - 1) TRANSFORMATIONS + +! GV(N-1)*...*GV(1)*GW(1)*...*GW(N-1) + +! WHERE GV(I), GW(I) ARE GIVENS ROTATIONS IN THE (I,N) PLANE +! WHICH ELIMINATE ELEMENTS IN THE I-TH AND N-TH PLANES, RESPECTIVELY. +! Q ITSELF IS NOT ACCUMULATED, RATHER THE INFORMATION TO RECOVER THE GV, +! GW ROTATIONS IS RETURNED. + +! THE SUBROUTINE STATEMENT IS + +! SUBROUTINE R1UPDT(M,N,S,LS,U,V,W,SING) + +! WHERE + +! M IS A POSITIVE INTEGER INPUT VARIABLE SET TO THE NUMBER OF ROWS OF S. + +! N IS A POSITIVE INTEGER INPUT VARIABLE SET TO THE NUMBER +! OF COLUMNS OF S. N MUST NOT EXCEED M. + +! S IS AN ARRAY OF LENGTH LS. ON INPUT S MUST CONTAIN THE LOWER +! TRAPEZOIDAL MATRIX S STORED BY COLUMNS. ON OUTPUT S CONTAINS +! THE LOWER TRAPEZOIDAL MATRIX PRODUCED AS DESCRIBED ABOVE. + +! LS IS A POSITIVE INTEGER INPUT VARIABLE NOT LESS THAN +! (N*(2*M-N+1))/2. + +! U IS AN INPUT ARRAY OF LENGTH M WHICH MUST CONTAIN THE VECTOR U. + +! V IS AN ARRAY OF LENGTH N. ON INPUT V MUST CONTAIN THE VECTOR V. +! ON OUTPUT V(I) CONTAINS THE INFORMATION NECESSARY TO +! RECOVER THE GIVENS ROTATION GV(I) DESCRIBED ABOVE. + +! W IS AN OUTPUT ARRAY OF LENGTH M. W(I) CONTAINS INFORMATION +! NECESSARY TO RECOVER THE GIVENS ROTATION GW(I) DESCRIBED ABOVE. + +! SING IS A LOGICAL OUTPUT VARIABLE. SING IS SET TRUE IF ANY OF THE +! DIAGONAL ELEMENTS OF THE OUTPUT S ARE ZERO. OTHERWISE SING IS +! SET FALSE. + +! SUBPROGRAMS CALLED + +! MINPACK-SUPPLIED ... SPMPAR + +! FORTRAN-SUPPLIED ... ABS,SQRT + +! ARGONNE NATIONAL LABORATORY. MINPACK PROJECT. MARCH 1980. +! BURTON S. GARBOW, KENNETH E. HILLSTROM, JORGE J. MORE, JOHN L. NAZARETH + +! ********** +INTEGER :: i, j, jj, l, nmj, nm1 +REAL (dp) :: COS, cotan, giant, SIN, TAN, tau, temp +REAL (dp), PARAMETER :: one = 1.0_dp, p5 = 0.5_dp, p25 = 0.25_dp, zero = 0.0_dp + +! GIANT IS THE LARGEST MAGNITUDE. + +giant = HUGE(1.0_dp) + +! INITIALIZE THE DIAGONAL ELEMENT POINTER. + +jj = (n*(2*m-n+1)) / 2 - (m-n) + +! MOVE THE NONTRIVIAL PART OF THE LAST COLUMN OF S INTO W. + +l = jj +DO i = n, m + w(i) = s(l) + l = l + 1 +END DO + +! ROTATE THE VECTOR V INTO A MULTIPLE OF THE N-TH UNIT VECTOR +! IN SUCH A WAY THAT A SPIKE IS INTRODUCED INTO W. + +nm1 = n - 1 +IF (nm1 >= 1) THEN + DO nmj = 1, nm1 + j = n - nmj + jj = jj - (m-j+1) + w(j) = zero + IF (v(j) /= zero) THEN + +! DETERMINE A GIVENS ROTATION WHICH ELIMINATES THE J-TH ELEMENT OF V. + + IF (ABS(v(n)) < ABS(v(j))) THEN + cotan = v(n) / v(j) + SIN = p5 / SQRT(p25+p25*cotan**2) + COS = SIN * cotan + tau = one + IF (ABS(COS)*giant > one) tau = one / COS + ELSE + TAN = v(j) / v(n) + COS = p5 / SQRT(p25+p25*TAN**2) + SIN = COS * TAN + tau = SIN + END IF + +! APPLY THE TRANSFORMATION TO V AND STORE THE INFORMATION +! NECESSARY TO RECOVER THE GIVENS ROTATION. + + v(n) = SIN * v(j) + COS * v(n) + v(j) = tau + +! APPLY THE TRANSFORMATION TO S AND EXTEND THE SPIKE IN W. + + l = jj + DO i = j, m + temp = COS * s(l) - SIN * w(i) + w(i) = SIN * s(l) + COS * w(i) + s(l) = temp + l = l + 1 + END DO + END IF + END DO +END IF + +! ADD THE SPIKE FROM THE RANK 1 UPDATE TO W. + +DO i = 1, m + w(i) = w(i) + v(n) * u(i) +END DO + +! ELIMINATE THE SPIKE. + +sing = .false. +IF (nm1 >= 1) THEN + DO j = 1, nm1 + IF (w(j) /= zero) THEN + +! DETERMINE A GIVENS ROTATION WHICH ELIMINATES THE +! J-TH ELEMENT OF THE SPIKE. + + IF (ABS(s(jj)) < ABS(w(j))) THEN + cotan = s(jj) / w(j) + SIN = p5 / SQRT(p25 + p25*cotan**2) + COS = SIN * cotan + tau = one + IF (ABS(COS)*giant > one) tau = one / COS + ELSE + TAN = w(j) / s(jj) + COS = p5 / SQRT(p25+p25*TAN**2) + SIN = COS * TAN + tau = SIN + END IF + +! APPLY THE TRANSFORMATION TO S AND REDUCE THE SPIKE IN W. + + l = jj + DO i = j, m + temp = COS * s(l) + SIN * w(i) + w(i) = -SIN * s(l) + COS * w(i) + s(l) = temp + l = l + 1 + END DO + +! STORE THE INFORMATION NECESSARY TO RECOVER THE GIVENS ROTATION. + + w(j) = tau + END IF + +! TEST FOR ZERO DIAGONAL ELEMENTS IN THE OUTPUT S. + + IF (s(jj) == zero) sing = .true. + jj = jj + (m-j+1) + END DO +END IF + +! MOVE W BACK INTO THE LAST COLUMN OF THE OUTPUT S. + +l = jj +DO i = n, m + s(l) = w(i) + l = l + 1 +END DO +IF (s(jj) == zero) sing = .true. +RETURN + +! LAST CARD OF SUBROUTINE R1UPDT. + +END SUBROUTINE r1updt + + +FUNCTION enorm(n, x) RESULT(fn_val) + +INTEGER, INTENT(IN) :: n +REAL (dp), INTENT(IN) :: x(n) +REAL (dp) :: fn_val + +! ********** + +! FUNCTION ENORM + +! GIVEN AN N-VECTOR X, THIS FUNCTION CALCULATES THE EUCLIDEAN NORM OF X. + +! THE EUCLIDEAN NORM IS COMPUTED BY ACCUMULATING THE SUM OF SQUARES IN THREE +! DIFFERENT SUMS. THE SUMS OF SQUARES FOR THE SMALL AND LARGE COMPONENTS +! ARE SCALED SO THAT NO OVERFLOWS OCCUR. NON-DESTRUCTIVE UNDERFLOWS ARE +! PERMITTED. UNDERFLOWS AND OVERFLOWS DO NOT OCCUR IN THE COMPUTATION OF THE UNSCALED +! SUM OF SQUARES FOR THE INTERMEDIATE COMPONENTS. +! THE DEFINITIONS OF SMALL, INTERMEDIATE AND LARGE COMPONENTS DEPEND ON +! TWO CONSTANTS, RDWARF AND RGIANT. THE MAIN RESTRICTIONS ON THESE CONSTANTS +! ARE THAT RDWARF**2 NOT UNDERFLOW AND RGIANT**2 NOT OVERFLOW. +! THE CONSTANTS GIVEN HERE ARE SUITABLE FOR EVERY KNOWN COMPUTER. + +! THE FUNCTION STATEMENT IS + +! REAL FUNCTION ENORM(N, X) + +! WHERE + +! N IS A POSITIVE INTEGER INPUT VARIABLE. + +! X IS AN INPUT ARRAY OF LENGTH N. + +! SUBPROGRAMS CALLED + +! FORTRAN-SUPPLIED ... ABS,SQRT + +! ARGONNE NATIONAL LABORATORY. MINPACK PROJECT. MARCH 1980. +! BURTON S. GARBOW, KENNETH E. HILLSTROM, JORGE J. MORE + +! ********** +INTEGER :: i +REAL (dp) :: agiant, floatn, s1, s2, s3, xabs, x1max, x3max +REAL (dp), PARAMETER :: rdwarf = 1.0D-100, rgiant = 1.0D+100 + +s1 = 0.0_dp +s2 = 0.0_dp +s3 = 0.0_dp +x1max = 0.0_dp +x3max = 0.0_dp +floatn = n +agiant = rgiant / floatn +DO i = 1, n + xabs = ABS(x(i)) + IF (xabs <= rdwarf .OR. xabs >= agiant) THEN + IF (xabs > rdwarf) THEN + +! SUM FOR LARGE COMPONENTS. + + IF (xabs > x1max) THEN + s1 = 1.0_dp + s1 * (x1max/xabs) ** 2 + x1max = xabs + ELSE + s1 = s1 + (xabs/x1max) ** 2 + END IF + ELSE + +! SUM FOR SMALL COMPONENTS. + + IF (xabs > x3max) THEN + s3 = 1.0_dp + s3 * (x3max/xabs) ** 2 + x3max = xabs + ELSE + IF (xabs /= 0.0_dp) s3 = s3 + (xabs/x3max) ** 2 + END IF + END IF + ELSE + +! SUM FOR INTERMEDIATE COMPONENTS. + + s2 = s2 + xabs ** 2 + END IF +END DO + +! CALCULATION OF NORM. + +IF (s1 /= 0.0_dp) THEN + fn_val = x1max * SQRT(s1 + (s2/x1max)/x1max) +ELSE + IF (s2 /= 0.0_dp) THEN + IF (s2 >= x3max) fn_val = SQRT(s2*(1.0_dp + (x3max/s2)*(x3max*s3))) + IF (s2 < x3max) fn_val = SQRT(x3max*((s2/x3max) + (x3max*s3))) + ELSE + fn_val = x3max * SQRT(s3) + END IF +END IF +RETURN +END FUNCTION enorm + +END MODULE Solve_NonLin diff --git a/applications/PUfoam/MoDeNaModels/foamConductivity/src/src/interpolation.f90 b/applications/PUfoam/MoDeNaModels/foamConductivity/src/src/interpolation.f90 new file mode 100644 index 000000000..bcf165a31 --- /dev/null +++ b/applications/PUfoam/MoDeNaModels/foamConductivity/src/src/interpolation.f90 @@ -0,0 +1,122 @@ +!Linear interpolation from +!http://people.sc.fsu.edu/~jburkardt/f_src/pwl_interp_1d/pwl_interp_1d.html +module interpolation + use constants, only: dp + implicit none + private + public pwl_interp_1d +contains +!!********************************BEGINNING************************************* +!!minimal working example (you have to supply xy values in "refl.dat" and change value of xi) +!subroutine test_pwl_interp_1d +! integer :: fi=154 !file index +! integer :: i !counter +! integer, parameter :: nd=101 !number of data points +! real(dp), dimension(nd) :: xd,yd !data for interpolation +! integer :: ni=1 !number of points, where we want to interpolate +! real(dp) :: xi(1) !x-values of points, where we want to interpolate +! real(dp) :: yi(1) !interpolated y-values +! open(fi,file="refl.dat") +! do i=1,nd +! read(fi,*) xd(i),yd(i) +! enddo +! close(fi) +! xi=2e-6_dp +! call pwl_interp_1d ( nd, xd, yd, ni, xi, yi ) +! write(*,*) xi,yi +!end subroutine test_pwl_interp_1d +!!***********************************END**************************************** + + +subroutine pwl_interp_1d ( nd, xd, yd, ni, xi, yi ) + +!*****************************************************************************80 +! +!! PWL_INTERP_1D evaluates the piecewise linear interpolant. +! +! Discussion: +! +! The piecewise linear interpolant L(ND,XD,YD)(X) is the piecewise +! linear function which interpolates the data (XD(I),YD(I)) for I = 1 +! to ND. +! +! Licensing: +! +! This code is distributed under the GNU LGPL license. +! +! Modified: +! +! 22 September 2012 +! +! Author: +! +! John Burkardt +! +! Parameters: +! +! Input, integer ( kind = 4 ) ND, the number of data points. +! ND must be at least 1. +! +! Input, real ( kind = 8 ) XD(ND), the data points. +! +! Input, real ( kind = 8 ) YD(ND), the data values. +! +! Input, integer ( kind = 4 ) NI, the number of interpolation points. +! +! Input, real ( kind = 8 ) XI(NI), the interpolation points. +! +! Output, real ( kind = 8 ) YI(NI), the interpolated values. +! + implicit none + + integer ( kind = 4 ) nd + integer ( kind = 4 ) ni + + integer ( kind = 4 ) i + integer ( kind = 4 ) k + real ( kind = dp ) t + real ( kind = dp ) xd(nd) + real ( kind = dp ) yd(nd) + real ( kind = dp ) xi(ni) + real ( kind = dp ) yi(ni) + + yi(1:ni) = 0.0e+00_dp + + if ( nd == 1 ) then + yi(1:ni) = yd(1) + return + end if + + do i = 1, ni + + if ( xi(i) <= xd(1) ) then + + t = ( xi(i) - xd(1) ) / ( xd(2) - xd(1) ) + yi(i) = ( 1.0e+00_dp - t ) * yd(1) + t * yd(2) + + else if ( xd(nd) <= xi(i) ) then + + t = ( xi(i) - xd(nd-1) ) / ( xd(nd) - xd(nd-1) ) + yi(i) = ( 1.0e+00_dp - t ) * yd(nd-1) + t * yd(nd) + + else + + do k = 2, nd + + if ( xd(k-1) <= xi(i) .and. xi(i) <= xd(k) ) then + + t = ( xi(i) - xd(k-1) ) / ( xd(k) - xd(k-1) ) + yi(i) = ( 1.0e+00_dp - t ) * yd(k-1) + t * yd(k) + exit + + end if + + end do + + end if + + end do + + return +end subroutine pwl_interp_1d +end module interpolation diff --git a/applications/PUfoam/MoDeNaModels/foamConductivity/src/src/ioutils.f90 b/applications/PUfoam/MoDeNaModels/foamConductivity/src/src/ioutils.f90 new file mode 100644 index 000000000..80a5bbb10 --- /dev/null +++ b/applications/PUfoam/MoDeNaModels/foamConductivity/src/src/ioutils.f90 @@ -0,0 +1,41 @@ +!> @file +!! i/o utilities +!! @author Pavel Ferkl +!! @ingroup foam_aging +module ioutils + implicit none + private + public newunit,str +contains +!********************************BEGINNING************************************* +!> returns lowest i/o unit number not in use +integer function newunit(unit) result(n) + integer, intent(out), optional :: unit + logical inuse + integer, parameter :: & + nmin=123,& ! avoid lower numbers which are sometimes reserved + nmax=999 ! may be system-dependent + do n = nmin, nmax + inquire(unit=n, opened=inuse) + if (.not. inuse) then + if (present(unit)) unit=n + return + end if + end do + write(*,*) "newunit ERROR: available unit not found." + stop +end function newunit +!***********************************END**************************************** + + + +!********************************BEGINNING************************************* +!> converts integer to string +function str(k) + character(len=20) :: str + integer, intent(in) :: k + write (str, *) k + str = adjustl(str) +end function str +!***********************************END**************************************** +end module ioutils diff --git a/applications/PUfoam/MoDeNaModels/foamConductivity/src/src/main.f90 b/applications/PUfoam/MoDeNaModels/foamConductivity/src/src/main.f90 new file mode 100644 index 000000000..4340f8c46 --- /dev/null +++ b/applications/PUfoam/MoDeNaModels/foamConductivity/src/src/main.f90 @@ -0,0 +1,21 @@ +!> @file +!! Main program. Homogenization approach to heat transfer in polymer foams +!! @author Pavel Ferkl +!! @ingroup foam_cond +program hahtf + use tests + use ioutils + use constants, only: mfi + implicit none + write(*,*) 'Welcome in hahtf' + open (newunit(mfi),file='hahtf.out') + write(mfi,*) 'Welcome in hahtf' + call loadParameters + call eqcond(1) +! call eqcond_por +! call eqcond_dcell +! call eqcond_strut + write(*,*) 'Program exited normally' + write(mfi,*) 'Program exited normally' + close(mfi) +end program diff --git a/applications/PUfoam/MoDeNaModels/foamConductivity/src/src/physicalProperties.f90 b/applications/PUfoam/MoDeNaModels/foamConductivity/src/src/physicalProperties.f90 new file mode 100644 index 000000000..29536defc --- /dev/null +++ b/applications/PUfoam/MoDeNaModels/foamConductivity/src/src/physicalProperties.f90 @@ -0,0 +1,44 @@ +!> @file +!! subroutines for calculation of physical properties of polymer and blowing +!! agents (using Modena calls) +!! @author Pavel Ferkl +!! @ingroup foam_cond +module physicalProperties + use constants + use fmodena + implicit none + private + public polymerConductivity +contains +!********************************BEGINNING************************************* +!> calculation of thermal conductivity of polymer +subroutine polymerConductivity(ksol,temp) + real(dp), intent(out) :: ksol + real(dp), intent(in) :: temp + !modena variables + integer(c_size_t) :: ksolTemppos + + integer(c_int) :: ret + + type(c_ptr) :: ksolModena = c_null_ptr + type(c_ptr) :: ksolInputs = c_null_ptr + type(c_ptr) :: ksolOutputs = c_null_ptr + ksolModena = modena_model_new (& + c_char_"polymer_thermal_conductivity"//c_null_char) + ksolInputs = modena_inputs_new (ksolModena) + ksolOutputs = modena_outputs_new (ksolModena) + ksolTemppos = modena_model_inputs_argPos(& + ksolModena, c_char_"T"//c_null_char) + call modena_model_argPos_check(ksolModena) + call modena_inputs_set(ksolInputs, ksolTemppos, temp) + ret = modena_model_call (ksolModena, ksolInputs, ksolOutputs) + if(ret /= 0) then + call exit(ret) + endif + ksol=modena_outputs_get(ksolOutputs, 0_c_size_t) + call modena_inputs_destroy (ksolInputs) + call modena_outputs_destroy (ksolOutputs) + call modena_model_destroy (ksolModena) +end subroutine polymerConductivity +!***********************************END**************************************** +end module physicalProperties diff --git a/applications/PUfoam/MoDeNaModels/foamConductivity/src/src/quadpack.f90 b/applications/PUfoam/MoDeNaModels/foamConductivity/src/src/quadpack.f90 new file mode 100644 index 000000000..211d55882 --- /dev/null +++ b/applications/PUfoam/MoDeNaModels/foamConductivity/src/src/quadpack.f90 @@ -0,0 +1,8484 @@ +!partially adatped to use higher precision, but I'm not sure if the results +!are more than single-precision (frequent use of numerical costants) +module quadpack + use constants, only:dp + implicit none + private + public qags,qag +contains +! +!****************************************************************************** +! +! 1. introduction +! +! quadpack is a fortran subroutine package for the numerical +! computation of definite one-dimensional integrals. it originated +! from a joint project of r. piessens and e. de doncker (appl. +! math. and progr. div.- k.u.leuven, belgium), c. ueberhuber (inst. +! fuer math.- techn.u.wien, austria), and d. kahaner (nation. bur. +! of standards- washington d.c., u.s.a.). +! +! 2. survey +! +! - qags : is an integrator based on globally adaptive interval +! subdivision in connection with extrapolation (de doncker, +! 1978) by the epsilon algorithm (wynn, 1956). +! +! - qagp : serves the same purposes as qags, but also allows +! for eventual user-supplied information, i.e. the +! abscissae of internal singularities, discontinuities +! and other difficulties of the integrand function. +! the algorithm is a modification of that in qags. +! +! - qagi : handles integration over infinite intervals. the +! infinite range is mapped onto a finite interval and +! then the same strategy as in qags is applied. +! +! - qawo : is a routine for the integration of cos(omega*x)*f(x) +! or sin(omega*x)*f(x) over a finite interval (a,b). +! omega is is specified by the user +! the rule evaluation component is based on the +! modified clenshaw-curtis technique. +! an adaptive subdivision scheme is used connected with +! an extrapolation procedure, which is a modification +! of that in qags and provides the possibility to deal +! even with singularities in f. +! +! - qawf : calculates the fourier cosine or fourier sine +! transform of f(x), for user-supplied interval (a, +! infinity), omega, and f. the procedure of qawo is +! used on successive finite intervals, and convergence +! acceleration by means of the epsilon algorithm (wynn, +! 1956) is applied to the series of the integral +! contributions. +! +! - qaws : integrates w(x)*f(x) over (a,b) with a < b finite, +! and w(x) = ((x-a)**alfa)*((b-x)**beta)*v(x) +! where v(x) = 1 or log(x-a) or log(b-x) +! or log(x-a)*log(b-x) +! and alfa > (-1), beta > (-1). +! the user specifies a, b, alfa, beta and the type of +! the function v. +! a globally adaptive subdivision strategy is applied, +! with modified clenshaw-curtis integration on the +! subintervals which contain a or b. +! +! - qawc : computes the cauchy principal value of f(x)/(x-c) +! over a finite interval (a,b) and for +! user-determined c. +! the strategy is globally adaptive, and modified +! clenshaw-curtis integration is used on the subranges +! which contain the point x = c. +! +! each of the routines above also has a "more detailed" version +! with a name ending in e, as qage. these provide more +! information and control than the easier versions. +! +! +! the preceeding routines are all automatic. that is, the user +! inputs his problem and an error tolerance. the routine +! attempts to perform the integration to within the requested +! absolute or relative error. +! there are, in addition, a number of non-automatic integrators. +! these are most useful when the problem is such that the +! user knows that a fixed rule will provide the accuracy +! required. typically they return an error estimate but make +! no attempt to satisfy any particular input error request. +! +! qk15 +! qk21 +! qk31 +! qk41 +! qk51 +! qk61 +! estimate the integral on [a,b] using 15, 21,..., 61 +! point rule and return an error estimate. +! qk15i 15 point rule for (semi)infinite interval. +! qk15w 15 point rule for special singular weight functions. +! qc25c 25 point rule for cauchy principal values +! qc25o 25 point rule for sin/cos integrand. +! qmomo integrates k-th degree chebychev polynomial times +! function with various explicit singularities. +! +! 3. guidelines for the use of quadpack +! +! here it is not our purpose to investigate the question when +! automatic quadrature should be used. we shall rather attempt +! to help the user who already made the decision to use quadpack, +! with selecting an appropriate routine or a combination of +! several routines for handling his problem. +! +! for both quadrature over finite and over infinite intervals, +! one of the first questions to be answered by the user is +! related to the amount of computer time he wants to spend, +! versus his -own- time which would be needed, for example, for +! manual subdivision of the interval or other analytic +! manipulations. +! +! (1) the user may not care about computer time, or not be +! willing to do any analysis of the problem. especially when +! only one or a few integrals must be calculated, this attitude +! can be perfectly reasonable. in this case it is clear that +! either the most sophisticated of the routines for finite +! intervals, qags, must be used, or its analogue for infinite +! intervals, qagi. these routines are able to cope with +! rather difficult, even with improper integrals. +! this way of proceeding may be expensive. but the integrator +! is supposed to give you an answer in return, with additional +! information in the case of a failure, through its error +! estimate and flag. yet it must be stressed that the programs +! cannot be totally reliable. +! +! (2) the user may want to examine the integrand function. +! if bad local difficulties occur, such as a discontinuity, a +! singularity, derivative singularity or high peak at one or +! more points within the interval, the first advice is to +! split up the interval at these points. the integrand must +! then be examinated over each of the subintervals separately, +! so that a suitable integrator can be selected for each of +! them. if this yields problems involving relative accuracies +! to be imposed on -finite- subintervals, one can make use of +! qagp, which must be provided with the positions of the local +! difficulties. however, if strong singularities are present +! and a high accuracy is requested, application of qags on the +! subintervals may yield a better result. +! +! for quadrature over finite intervals we thus dispose of qags +! and +! - qng for well-behaved integrands, +! - qag for functions with an oscillating behavior of a non +! specific type, +! - qawo for functions, eventually singular, containing a +! factor cos(omega*x) or sin(omega*x) where omega is known, +! - qaws for integrands with algebraico-logarithmic end point +! singularities of known type, +! - qawc for cauchy principal values. +! +! remark +! +! on return, the work arrays in the argument lists of the +! adaptive integrators contain information about the interval +! subdivision process and hence about the integrand behavior: +! the end points of the subintervals, the local integral +! contributions and error estimates, and eventually other +! characteristics. for this reason, and because of its simple +! globally adaptive nature, the routine qag in particular is +! well-suited for integrand examination. difficult spots can +! be located by investigating the error estimates on the +! subintervals. +! +! for infinite intervals we provide only one general-purpose +! routine, qagi. it is based on the qags algorithm applied +! after a transformation of the original interval into (0,1). +! yet it may eventuate that another type of transformation is +! more appropriate, or one might prefer to break up the +! original interval and use qagi only on the infinite part +! and so on. these kinds of actions suggest a combined use of +! different quadpack integrators. note that, when the only +! difficulty is an integrand singularity at the finite +! integration limit, it will in general not be necessary to +! break up the interval, as qagi deals with several types of +! singularity at the boundary point of the integration range. +! it also handles slowly convergent improper integrals, on +! the condition that the integrand does not oscillate over +! the entire infinite interval. if it does we would advise +! to sum succeeding positive and negative contributions to +! the integral -e.g. integrate between the zeros- with one +! or more of the finite-range integrators, and apply +! convergence acceleration eventually by means of quadpack +! subroutine qelg which implements the epsilon algorithm. +! such quadrature problems include the fourier transform as +! a special case. yet for the latter we have an automatic +! integrator available, qawf. +! +function pi ( ) +! +!******************************************************************************* +! +!! PI returns the value of pi. +! +! +! Modified: +! +! 04 December 1998 +! +! Author: +! +! John Burkardt +! +! Parameters: +! +! Output, real(dp) PI, the value of pi. +! + implicit none +! + real(dp) pi +! + pi = 3.14159265358979323846264338327950288419716939937510E+00_dp + + return +end function +subroutine qag ( f, a, b, epsabs, epsrel, key, result, abserr, neval, ier ) +! +!****************************************************************************** +! +!! QAG approximates an integral over a finite interval. +! +! +! Discussion: +! +! The routine calculates an approximation RESULT to a definite integral +! I = integral of F over (A,B), +! hopefully satisfying +! || I - RESULT || <= max ( EPSABS, EPSREL * ||I|| ). +! +! QAG is a simple globally adaptive integrator using the strategy of +! Aind (Piessens, 1973). It is possible to choose between 6 pairs of +! Gauss-Kronrod quadrature formulae for the rule evaluation component. +! The pairs of high degree of precision are suitable for handling +! integration difficulties due to a strongly oscillating integrand. +! +! Reference: +! +! R Piessens, E de Doncker-Kapenger, C W Ueberhuber, D K Kahaner, +! QUADPACK, a Subroutine Package for Automatic Integration, +! Springer Verlag, 1983 +! +! Parameters: +! +! Input, external real(dp) F, the name of the function routine, of the form +! function f ( x ) +! real(dp) f +! real(dp) x +! which evaluates the integrand function. +! +! Input, real(dp) A, B, the limits of integration. +! +! Input, real(dp) EPSABS, EPSREL, the absolute and relative accuracy requested. +! +! Input, integer KEY, chooses the order of the local integration rule: +! 1, 7 Gauss points, 15 Gauss-Kronrod points, +! 2, 10 Gauss points, 21 Gauss-Kronrod points, +! 3, 15 Gauss points, 31 Gauss-Kronrod points, +! 4, 20 Gauss points, 41 Gauss-Kronrod points, +! 5, 25 Gauss points, 51 Gauss-Kronrod points, +! 6, 30 Gauss points, 61 Gauss-Kronrod points. +! +! Output, real(dp) RESULT, the estimated value of the integral. +! +! Output, real(dp) ABSERR, an estimate of || I - RESULT ||. +! +! Output, integer NEVAL, the number of times the integral was evaluated. +! +! Output, integer IER, return code. +! 0, normal and reliable termination of the routine. It is assumed that the +! requested accuracy has been achieved. +! 1, maximum number of subdivisions allowed has been achieved. One can +! allow more subdivisions by increasing the value of LIMIT in QAG. +! However, if this yields no improvement it is advised to analyze the +! integrand to determine the integration difficulties. If the position +! of a local difficulty can be determined, such as a singularity or +! discontinuity within the interval) one will probably gain from +! splitting up the interval at this point and calling the integrator +! on the subranges. If possible, an appropriate special-purpose +! integrator should be used which is designed for handling the type +! of difficulty involved. +! 2, the occurrence of roundoff error is detected, which prevents the +! requested tolerance from being achieved. +! 3, extremely bad integrand behavior occurs at some points of the +! integration interval. +! 6, the input is invalid, because EPSABS < 0 and EPSREL < 0. +! +! Local parameters: +! +! LIMIT is the maximum number of subintervals allowed in +! the subdivision process of QAGE. +! + implicit none +! + integer, parameter :: limit = 500 +! + real(dp) a + real(dp) abserr + real(dp) alist(limit) + real(dp) b + real(dp) blist(limit) + real(dp) elist(limit) + real(dp) epsabs + real(dp) epsrel + real(dp), external :: f + integer ier + integer iord(limit) + integer key + integer last +! integer limit + integer neval + real(dp) result + real(dp) rlist(limit) +! + call qage ( f, a, b, epsabs, epsrel, key, limit, result, abserr, neval, & + ier, alist, blist, rlist, elist, iord, last ) + + return +end subroutine +subroutine qage ( f, a, b, epsabs, epsrel, key, limit, result, abserr, neval, & + ier, alist, blist, rlist, elist, iord, last ) +! +!****************************************************************************** +! +!! QAGE estimates a definite integral. +! +! +! Discussion: +! +! The routine calculates an approximation RESULT to a definite integral +! I = integral of F over (A,B), +! hopefully satisfying +! || I - RESULT || <= max ( EPSABS, EPSREL * ||I|| ). +! +! Reference: +! +! R Piessens, E de Doncker-Kapenger, C W Ueberhuber, D K Kahaner, +! QUADPACK, a Subroutine Package for Automatic Integration, +! Springer Verlag, 1983 +! +! Parameters: +! +! Input, external real(dp) F, the name of the function routine, of the form +! function f ( x ) +! real(dp) f +! real(dp) x +! which evaluates the integrand function. +! +! Input, real(dp) A, B, the limits of integration. +! +! Input, real(dp) EPSABS, EPSREL, the absolute and relative accuracy requested. +! +! Input, integer KEY, chooses the order of the local integration rule: +! 1, 7 Gauss points, 15 Gauss-Kronrod points, +! 2, 10 Gauss points, 21 Gauss-Kronrod points, +! 3, 15 Gauss points, 31 Gauss-Kronrod points, +! 4, 20 Gauss points, 41 Gauss-Kronrod points, +! 5, 25 Gauss points, 51 Gauss-Kronrod points, +! 6, 30 Gauss points, 61 Gauss-Kronrod points. +! +! Input, integer LIMIT, the maximum number of subintervals that +! can be used. +! +! Output, real(dp) RESULT, the estimated value of the integral. +! +! Output, real(dp) ABSERR, an estimate of || I - RESULT ||. +! +! Output, integer NEVAL, the number of times the integral was evaluated. +! +! Output, integer IER, return code. +! 0, normal and reliable termination of the routine. It is assumed that the +! requested accuracy has been achieved. +! 1, maximum number of subdivisions allowed has been achieved. One can +! allow more subdivisions by increasing the value of LIMIT in QAG. +! However, if this yields no improvement it is advised to analyze the +! integrand to determine the integration difficulties. If the position +! of a local difficulty can be determined, such as a singularity or +! discontinuity within the interval) one will probably gain from +! splitting up the interval at this point and calling the integrator +! on the subranges. If possible, an appropriate special-purpose +! integrator should be used which is designed for handling the type +! of difficulty involved. +! 2, the occurrence of roundoff error is detected, which prevents the +! requested tolerance from being achieved. +! 3, extremely bad integrand behavior occurs at some points of the +! integration interval. +! 6, the input is invalid, because EPSABS < 0 and EPSREL < 0. +! +! Workspace, real(dp) ALIST(LIMIT), BLIST(LIMIT), contains in entries 1 +! through LAST the left and right ends of the partition subintervals. +! +! Workspace, real(dp) RLIST(LIMIT), contains in entries 1 through LAST +! the integral approximations on the subintervals. +! +! Workspace, real(dp) ELIST(LIMIT), contains in entries 1 through LAST +! the absolute error estimates on the subintervals. +! +! Output, integer IORD(LIMIT), the first K elements of which are pointers +! to the error estimates over the subintervals, such that +! elist(iord(1)), ..., elist(iord(k)) form a decreasing sequence, with +! k = last if last <= (limit/2+2), and k = limit+1-last otherwise. +! +! Output, integer LAST, the number of subintervals actually produced +! in the subdivision process. +! +! Local parameters: +! +! alist - list of left end points of all subintervals +! considered up to now +! blist - list of right end points of all subintervals +! considered up to now +! elist(i) - error estimate applying to rlist(i) +! maxerr - pointer to the interval with largest error estimate +! errmax - elist(maxerr) +! area - sum of the integrals over the subintervals +! errsum - sum of the errors over the subintervals +! errbnd - requested accuracy max(epsabs,epsrel*abs(result)) +! *****1 - variable for the left subinterval +! *****2 - variable for the right subinterval +! last - index for subdivision +! + implicit none +! + integer limit +! + real(dp) a + real(dp) abserr + real(dp) alist(limit) + real(dp) area + real(dp) area1 + real(dp) area12 + real(dp) area2 + real(dp) a1 + real(dp) a2 + real(dp) b + real(dp) blist(limit) + real(dp) b1 + real(dp) b2 + real(dp) c + real(dp) defabs + real(dp) defab1 + real(dp) defab2 + real(dp) elist(limit) + real(dp) epsabs + real(dp) epsrel + real(dp) errbnd + real(dp) errmax + real(dp) error1 + real(dp) error2 + real(dp) erro12 + real(dp) errsum + real(dp), external :: f + integer ier + integer iord(limit) + integer iroff1 + integer iroff2 + integer k + integer key + integer keyf + integer last + integer maxerr + integer neval + integer nrmax + real(dp) resabs + real(dp) result + real(dp) rlist(limit) +! +! Test on validity of parameters. +! + ier = 0 + neval = 0 + last = 0 + result = 0.0e+00 + abserr = 0.0e+00 + alist(1) = a + blist(1) = b + rlist(1) = 0.0e+00 + elist(1) = 0.0e+00 + iord(1) = 0 + + if ( epsabs < 0.0e+00 .and. epsrel < 0.0e+00 ) then + ier = 6 + return + end if +! +! First approximation to the integral. +! + keyf = key + keyf = max ( keyf, 1 ) + keyf = min ( keyf, 6 ) + + c = keyf + neval = 0 + + if ( keyf == 1 ) then + call qk15 ( f, a, b, result, abserr, defabs, resabs ) + else if ( keyf == 2 ) then + call qk21 ( f, a, b, result, abserr, defabs, resabs ) + else if ( keyf == 3 ) then + call qk31 ( f, a, b, result, abserr, defabs, resabs ) + else if ( keyf == 4 ) then + call qk41 ( f, a, b, result, abserr, defabs, resabs ) + else if ( keyf == 5 ) then + call qk51 ( f, a, b, result, abserr, defabs, resabs ) + else if ( keyf == 6 ) then + call qk61 ( f, a, b, result, abserr, defabs, resabs ) + end if + + last = 1 + rlist(1) = result + elist(1) = abserr + iord(1) = 1 +! +! Test on accuracy. +! + errbnd = max ( epsabs, epsrel * abs ( result ) ) + + if ( abserr <= 5.0e+01 * epsilon ( defabs ) * defabs .and. & + abserr > errbnd ) then + ier = 2 + end if + + if ( limit == 1 ) then + ier = 1 + end if + + if ( ier /= 0 .or. & + ( abserr <= errbnd .and. abserr /= resabs ) .or. & + abserr == 0.0e+00 ) then + + if ( keyf /= 1 ) then + neval = (10*keyf+1) * (2*neval+1) + else + neval = 30 * neval + 15 + end if + + return + + end if +! +! Initialization. +! + errmax = abserr + maxerr = 1 + area = result + errsum = abserr + nrmax = 1 + iroff1 = 0 + iroff2 = 0 + + do last = 2, limit +! +! Bisect the subinterval with the largest error estimate. +! + a1 = alist(maxerr) + b1 = 0.5E+00 * ( alist(maxerr) + blist(maxerr) ) + a2 = b1 + b2 = blist(maxerr) + + if ( keyf == 1 ) then + call qk15 ( f, a1, b1, area1, error1, resabs, defab1 ) + else if ( keyf == 2 ) then + call qk21 ( f, a1, b1, area1, error1, resabs, defab1 ) + else if ( keyf == 3 ) then + call qk31 ( f, a1, b1, area1, error1, resabs, defab1 ) + else if ( keyf == 4 ) then + call qk41 ( f, a1, b1, area1, error1, resabs, defab1) + else if ( keyf == 5 ) then + call qk51 ( f, a1, b1, area1, error1, resabs, defab1 ) + else if ( keyf == 6 ) then + call qk61 ( f, a1, b1, area1, error1, resabs, defab1 ) + end if + + if ( keyf == 1 ) then + call qk15 ( f, a2, b2, area2, error2, resabs, defab2 ) + else if ( keyf == 2 ) then + call qk21 ( f, a2, b2, area2, error2, resabs, defab2 ) + else if ( keyf == 3 ) then + call qk31 ( f, a2, b2, area2, error2, resabs, defab2 ) + else if ( keyf == 4 ) then + call qk41 ( f, a2, b2, area2, error2, resabs, defab2 ) + else if ( keyf == 5 ) then + call qk51 ( f, a2, b2, area2, error2, resabs, defab2 ) + else if ( keyf == 6 ) then + call qk61 ( f, a2, b2, area2, error2, resabs, defab2 ) + end if +! +! Improve previous approximations to integral and error and +! test for accuracy. +! + neval = neval + 1 + area12 = area1 + area2 + erro12 = error1 + error2 + errsum = errsum + erro12 - errmax + area = area + area12 - rlist(maxerr) + + if ( defab1 /= error1 .and. defab2 /= error2 ) then + + if ( abs ( rlist(maxerr) - area12 ) <= 1.0e-05 * abs ( area12 ) & + .and. erro12 >= 9.9e-01 * errmax ) then + iroff1 = iroff1 + 1 + end if + + if ( last > 10 .and. erro12 > errmax ) then + iroff2 = iroff2 + 1 + end if + + end if + + rlist(maxerr) = area1 + rlist(last) = area2 + errbnd = max ( epsabs, epsrel * abs ( area ) ) +! +! Test for roundoff error and eventually set error flag. +! + if ( errsum > errbnd ) then + + if ( iroff1 >= 6 .or. iroff2 >= 20 ) then + ier = 2 + end if +! +! Set error flag in the case that the number of subintervals +! equals limit. +! + if ( last == limit ) then + ier = 1 + end if +! +! Set error flag in the case of bad integrand behavior +! at a point of the integration range. +! + if ( max ( abs ( a1 ), abs ( b2 ) ) <= ( 1.0e+00 + c * 1.0e+03 * & + epsilon ( a1 ) ) * ( abs ( a2 ) + 1.0e+04 * tiny ( a2 ) ) ) then + ier = 3 + end if + + end if +! +! Append the newly-created intervals to the list. +! + if ( error2 <= error1 ) then + alist(last) = a2 + blist(maxerr) = b1 + blist(last) = b2 + elist(maxerr) = error1 + elist(last) = error2 + else + alist(maxerr) = a2 + alist(last) = a1 + blist(last) = b1 + rlist(maxerr) = area2 + rlist(last) = area1 + elist(maxerr) = error2 + elist(last) = error1 + end if +! +! Call QSORT to maintain the descending ordering +! in the list of error estimates and select the subinterval +! with the largest error estimate (to be bisected next). +! + call qsort ( limit, last, maxerr, errmax, elist, iord, nrmax ) + + if ( ier /= 0 .or. errsum <= errbnd ) then + exit + end if + + end do +! +! Compute final result. +! + result = sum ( rlist(1:last) ) + + abserr = errsum + + if ( keyf /= 1 ) then + neval = ( 10 * keyf + 1 ) * ( 2 * neval + 1 ) + else + neval = 30 * neval + 15 + end if + + return +end subroutine +subroutine qagi ( f, bound, inf, epsabs, epsrel, result, abserr, neval, ier ) +! +!****************************************************************************** +! +!! QAGI estimates an integral over a semi-infinite or infinite interval. +! +! +! Discussion: +! +! The routine calculates an approximation RESULT to a definite integral +! I = integral of F over (A, +Infinity), +! or +! I = integral of F over (-Infinity,A) +! or +! I = integral of F over (-Infinity,+Infinity), +! hopefully satisfying +! || I - RESULT || <= max ( EPSABS, EPSREL * ||I|| ). +! +! Reference: +! +! R Piessens, E de Doncker-Kapenger, C W Ueberhuber, D K Kahaner, +! QUADPACK, a Subroutine Package for Automatic Integration, +! Springer Verlag, 1983 +! +! Parameters: +! +! Input, external real(dp) F, the name of the function routine, of the form +! function f ( x ) +! real(dp) f +! real(dp) x +! which evaluates the integrand function. +! +! Input, real(dp) BOUND, the value of the finite endpoint of the integration +! range, if any, that is, if INF is 1 or -1. +! +! Input, integer INF, indicates the type of integration range. +! 1: ( BOUND, +Infinity), +! -1: ( -Infinity, BOUND), +! 2: ( -Infinity, +Infinity). +! +! Input, real(dp) EPSABS, EPSREL, the absolute and relative accuracy requested. +! +! Output, real(dp) RESULT, the estimated value of the integral. +! +! Output, real(dp) ABSERR, an estimate of || I - RESULT ||. +! +! Output, integer NEVAL, the number of times the integral was evaluated. +! +! Output, integer IER, error indicator. +! 0, normal and reliable termination of the routine. It is assumed that +! the requested accuracy has been achieved. +! > 0, abnormal termination of the routine. The estimates for result +! and error are less reliable. It is assumed that the requested +! accuracy has not been achieved. +! 1, maximum number of subdivisions allowed has been achieved. One can +! allow more subdivisions by increasing the data value of LIMIT in QAGI +! (and taking the according dimension adjustments into account). +! However, if this yields no improvement it is advised to analyze the +! integrand in order to determine the integration difficulties. If the +! position of a local difficulty can be determined (e.g. singularity, +! discontinuity within the interval) one will probably gain from +! splitting up the interval at this point and calling the integrator +! on the subranges. If possible, an appropriate special-purpose +! integrator should be used, which is designed for handling the type +! of difficulty involved. +! 2, the occurrence of roundoff error is detected, which prevents the +! requested tolerance from being achieved. The error may be +! under-estimated. +! 3, extremely bad integrand behavior occurs at some points of the +! integration interval. +! 4, the algorithm does not converge. Roundoff error is detected in the +! extrapolation table. It is assumed that the requested tolerance +! cannot be achieved, and that the returned result is the best which +! can be obtained. +! 5, the integral is probably divergent, or slowly convergent. It must +! be noted that divergence can occur with any other value of IER. +! 6, the input is invalid, because INF /= 1 and INF /= -1 and INF /= 2, or +! epsabs < 0 and epsrel < 0. result, abserr, neval are set to zero. +! +! Local parameters: +! +! the dimension of rlist2 is determined by the value of +! limexp in QEXTR. +! +! alist - list of left end points of all subintervals +! considered up to now +! blist - list of right end points of all subintervals +! considered up to now +! rlist(i) - approximation to the integral over +! (alist(i),blist(i)) +! rlist2 - array of dimension at least (limexp+2), +! containing the part of the epsilon table +! which is still needed for further computations +! elist(i) - error estimate applying to rlist(i) +! maxerr - pointer to the interval with largest error +! estimate +! errmax - elist(maxerr) +! erlast - error on the interval currently subdivided +! (before that subdivision has taken place) +! area - sum of the integrals over the subintervals +! errsum - sum of the errors over the subintervals +! errbnd - requested accuracy max(epsabs,epsrel* +! abs(result)) +! *****1 - variable for the left subinterval +! *****2 - variable for the right subinterval +! last - index for subdivision +! nres - number of calls to the extrapolation routine +! numrl2 - number of elements currently in rlist2. if an +! appropriate approximation to the compounded +! integral has been obtained, it is put in +! rlist2(numrl2) after numrl2 has been increased +! by one. +! small - length of the smallest interval considered up +! to now, multiplied by 1.5 +! erlarg - sum of the errors over the intervals larger +! than the smallest interval considered up to now +! extrap - logical variable denoting that the routine +! is attempting to perform extrapolation. i.e. +! before subdividing the smallest interval we +! try to decrease the value of erlarg. +! noext - logical variable denoting that extrapolation +! is no longer allowed (true-value) +! + implicit none +! + integer, parameter :: limit = 500 +! + real(dp) abseps + real(dp) abserr + real(dp) alist(limit) + real(dp) area + real(dp) area1 + real(dp) area12 + real(dp) area2 + real(dp) a1 + real(dp) a2 + real(dp) blist(limit) + real(dp) boun + real(dp) bound + real(dp) b1 + real(dp) b2 + real(dp) correc + real(dp) defabs + real(dp) defab1 + real(dp) defab2 + real(dp) dres + real(dp) elist(limit) + real(dp) epsabs + real(dp) epsrel + real(dp) erlarg + real(dp) erlast + real(dp) errbnd + real(dp) errmax + real(dp) error1 + real(dp) error2 + real(dp) erro12 + real(dp) errsum + real(dp) ertest + logical extrap + real(dp), external :: f + integer id + integer ier + integer ierro + integer inf + integer iord(limit) + integer iroff1 + integer iroff2 + integer iroff3 + integer jupbnd + integer k + integer ksgn + integer ktmin + integer last + integer maxerr + integer neval + logical noext + integer nres + integer nrmax + integer numrl2 + real(dp) resabs + real(dp) reseps + real(dp) result + real(dp) res3la(3) + real(dp) rlist(limit) + real(dp) rlist2(52) + real(dp) small +! +! Test on validity of parameters. +! + ier = 0 + neval = 0 + last = 0 + result = 0.0e+00 + abserr = 0.0e+00 + alist(1) = 0.0e+00 + blist(1) = 1.0e+00 + rlist(1) = 0.0e+00 + elist(1) = 0.0e+00 + iord(1) = 0 + + if ( epsabs < 0.0e+00 .and. epsrel < 0.0e+00 ) then + ier = 6 + return + end if +! +! First approximation to the integral. +! +! Determine the interval to be mapped onto (0,1). +! If INF = 2 the integral is computed as i = i1+i2, where +! i1 = integral of f over (-infinity,0), +! i2 = integral of f over (0,+infinity). +! + if ( inf == 2 ) then + boun = 0.0e+00 + else + boun = bound + end if + + call qk15i ( f, boun, inf, 0.0e+00_dp, 1.0e+00_dp, result, abserr, defabs, resabs ) +! +! Test on accuracy. +! + last = 1 + rlist(1) = result + elist(1) = abserr + iord(1) = 1 + dres = abs ( result ) + errbnd = max ( epsabs, epsrel * dres ) + + if ( abserr <= 100.0E+00 * epsilon ( defabs ) * defabs .and. & + abserr > errbnd ) then + ier = 2 + end if + + if ( limit == 1 ) then + ier = 1 + end if + + if ( ier /= 0 .or. (abserr <= errbnd .and. abserr /= resabs ) .or. & + abserr == 0.0e+00 ) go to 130 +! +! Initialization. +! + rlist2(1) = result + errmax = abserr + maxerr = 1 + area = result + errsum = abserr + abserr = huge ( abserr ) + nrmax = 1 + nres = 0 + ktmin = 0 + numrl2 = 2 + extrap = .false. + noext = .false. + ierro = 0 + iroff1 = 0 + iroff2 = 0 + iroff3 = 0 + + if ( dres >= ( 1.0e+00 - 5.0e+01 * epsilon ( defabs ) ) * defabs ) then + ksgn = 1 + else + ksgn = -1 + end if + + do last = 2, limit +! +! Bisect the subinterval with nrmax-th largest error estimate. +! + a1 = alist(maxerr) + b1 = 5.0e-01 * ( alist(maxerr) + blist(maxerr) ) + a2 = b1 + b2 = blist(maxerr) + erlast = errmax + call qk15i ( f, boun, inf, a1, b1, area1, error1, resabs, defab1 ) + call qk15i ( f, boun, inf, a2, b2, area2, error2, resabs, defab2 ) +! +! Improve previous approximations to integral and error +! and test for accuracy. +! + area12 = area1 + area2 + erro12 = error1 + error2 + errsum = errsum + erro12 - errmax + area = area + area12 - rlist(maxerr) + + if ( defab1 /= error1 .and. defab2 /= error2 ) then + + if ( abs ( rlist(maxerr) - area12 ) <= 1.0e-05 * abs ( area12 ) & + .and. erro12 >= 9.9e-01 * errmax ) then + + if ( extrap ) then + iroff2 = iroff2 + 1 + end if + + if ( .not. extrap ) then + iroff1 = iroff1 + 1 + end if + + end if + + if ( last > 10 .and. erro12 > errmax ) then + iroff3 = iroff3 + 1 + end if + + end if + + rlist(maxerr) = area1 + rlist(last) = area2 + errbnd = max ( epsabs, epsrel * abs ( area ) ) +! +! Test for roundoff error and eventually set error flag. +! + if ( iroff1 + iroff2 >= 10 .or. iroff3 >= 20 ) then + ier = 2 + end if + + if ( iroff2 >= 5 ) then + ierro = 3 + end if +! +! Set error flag in the case that the number of subintervals equals LIMIT. +! + if ( last == limit ) then + ier = 1 + end if +! +! Set error flag in the case of bad integrand behavior +! at some points of the integration range. +! + if ( max ( abs(a1), abs(b2) ) <= (1.0e+00 + 1.0e+03 * epsilon ( a1 ) ) * & + ( abs(a2) + 1.0e+03 * tiny ( a2 ) )) then + ier = 4 + end if +! +! Append the newly-created intervals to the list. +! + if ( error2 <= error1 ) then + alist(last) = a2 + blist(maxerr) = b1 + blist(last) = b2 + elist(maxerr) = error1 + elist(last) = error2 + else + alist(maxerr) = a2 + alist(last) = a1 + blist(last) = b1 + rlist(maxerr) = area2 + rlist(last) = area1 + elist(maxerr) = error2 + elist(last) = error1 + end if +! +! Call QSORT to maintain the descending ordering +! in the list of error estimates and select the subinterval +! with NRMAX-th largest error estimate (to be bisected next). +! + call qsort ( limit, last, maxerr, errmax, elist, iord, nrmax ) + + if ( errsum <= errbnd ) go to 115 + + if ( ier /= 0 ) then + exit + end if + + if ( last == 2 ) then + small = 3.75e-01 + erlarg = errsum + ertest = errbnd + rlist2(2) = area + cycle + end if + + if ( noext ) then + cycle + end if + + erlarg = erlarg-erlast + + if ( abs(b1-a1) > small ) then + erlarg = erlarg+erro12 + end if +! +! Test whether the interval to be bisected next is the +! smallest interval. +! + if ( .not. extrap ) then + + if ( abs(blist(maxerr)-alist(maxerr)) > small ) then + cycle + end if + + extrap = .true. + nrmax = 2 + + end if + + if ( ierro == 3 .or. erlarg <= ertest ) go to 60 +! +! The smallest interval has the largest error. +! before bisecting decrease the sum of the errors over the +! larger intervals (erlarg) and perform extrapolation. +! + id = nrmax + jupbnd = last + + if ( last > (2+limit/2) ) then + jupbnd = limit + 3 - last + end if + + do k = id, jupbnd + maxerr = iord(nrmax) + errmax = elist(maxerr) + if ( abs ( blist(maxerr) - alist(maxerr) ) > small ) then + go to 90 + end if + nrmax = nrmax + 1 + end do +! +! Extrapolate. +! +60 continue + + numrl2 = numrl2 + 1 + rlist2(numrl2) = area + call qextr ( numrl2, rlist2, reseps, abseps, res3la, nres ) + ktmin = ktmin+1 + + if ( ktmin > 5.and.abserr < 1.0e-03*errsum ) then + ier = 5 + end if + + if ( abseps < abserr ) then + + ktmin = 0 + abserr = abseps + result = reseps + correc = erlarg + ertest = max ( epsabs, epsrel*abs(reseps) ) + + if ( abserr <= ertest ) then + exit + end if + + end if +! +! Prepare bisection of the smallest interval. +! + if ( numrl2 == 1 ) then + noext = .true. + end if + + if ( ier == 5 ) then + exit + end if + + maxerr = iord(1) + errmax = elist(maxerr) + nrmax = 1 + extrap = .false. + small = small*5.0e-01 + erlarg = errsum + +90 continue + + end do +! +! Set final result and error estimate. +! + if ( abserr == huge ( abserr ) ) go to 115 + + if ( (ier+ierro) == 0 ) go to 110 + + if ( ierro == 3 ) then + abserr = abserr+correc + end if + + if ( ier == 0 ) then + ier = 3 + end if + + if ( result /= 0.0e+00 .and. area /= 0.0e+00) go to 105 + if ( abserr > errsum)go to 115 + if ( area == 0.0e+00) go to 130 + + go to 110 + +105 continue + if ( abserr / abs(result) > errsum / abs(area) ) go to 115 +! +! Test on divergence +! +110 continue + + if ( ksgn == (-1) .and. & + max ( abs(result), abs(area) ) <= defabs * 1.0e-02) go to 130 + + if ( 1.0e-02 > (result/area) .or. & + (result/area) > 1.0e+02 .or. & + errsum > abs(area)) then + ier = 6 + end if + + go to 130 +! +! Compute global integral sum. +! + 115 continue + + result = sum ( rlist(1:last) ) + + abserr = errsum + 130 continue + + neval = 30*last-15 + if ( inf == 2 ) then + neval = 2*neval + end if + + if ( ier > 2 ) then + ier = ier - 1 + end if + + return +end subroutine +subroutine qagp ( f, a, b, npts2, points, epsabs, epsrel, result, abserr, & + neval, ier ) +! +!****************************************************************************** +! +!! QAGP computes a definite integral. +! +! +! Discussion: +! +! The routine calculates an approximation RESULT to a definite integral +! I = integral of F over (A,B), +! hopefully satisfying +! || I - RESULT || <= max ( EPSABS, EPSREL * ||I|| ). +! +! Interior break points of the integration interval, +! where local difficulties of the integrand may occur, such as +! singularities or discontinuities, are provided by the user. +! +! Reference: +! +! R Piessens, E de Doncker-Kapenger, C W Ueberhuber, D K Kahaner, +! QUADPACK, a Subroutine Package for Automatic Integration, +! Springer Verlag, 1983 +! +! Parameters: +! +! Input, external real(dp) F, the name of the function routine, of the form +! function f ( x ) +! real(dp) f +! real(dp) x +! which evaluates the integrand function. +! +! Input, real(dp) A, B, the limits of integration. +! +! Input, integer NPTS2, the number of user-supplied break points within +! the integration range, plus 2. NPTS2 must be at least 2. +! +! Input/output, real(dp) POINTS(NPTS2), contains the user provided interior +! breakpoints in entries 1 through NPTS2-2. If these points are not +! in ascending order on input, they will be sorted. +! +! Input, real(dp) EPSABS, EPSREL, the absolute and relative accuracy requested. +! +! Output, real(dp) RESULT, the estimated value of the integral. +! +! Output, real(dp) ABSERR, an estimate of || I - RESULT ||. +! +! Output, integer NEVAL, the number of times the integral was evaluated. +! +! ier - integer +! ier = 0 normal and reliable termination of the +! routine. it is assumed that the requested +! accuracy has been achieved. +! ier > 0 abnormal termination of the routine. +! the estimates for integral and error are +! less reliable. it is assumed that the +! requested accuracy has not been achieved. +! ier = 1 maximum number of subdivisions allowed +! has been achieved. one can allow more +! subdivisions by increasing the data value +! of limit in qagp(and taking the according +! dimension adjustments into account). +! however, if this yields no improvement +! it is advised to analyze the integrand +! in order to determine the integration +! difficulties. if the position of a local +! difficulty can be determined (i.e. +! singularity, discontinuity within the +! interval), it should be supplied to the +! routine as an element of the vector +! points. if necessary, an appropriate +! special-purpose integrator must be used, +! which is designed for handling the type +! of difficulty involved. +! = 2 the occurrence of roundoff error is +! detected, which prevents the requested +! tolerance from being achieved. +! the error may be under-estimated. +! = 3 extremely bad integrand behavior occurs +! at some points of the integration +! interval. +! = 4 the algorithm does not converge. roundoff +! error is detected in the extrapolation +! table. it is presumed that the requested +! tolerance cannot be achieved, and that +! the returned result is the best which +! can be obtained. +! = 5 the integral is probably divergent, or +! slowly convergent. it must be noted that +! divergence can occur with any other value +! of ier > 0. +! = 6 the input is invalid because +! npts2 < 2 or +! break points are specified outside +! the integration range or +! epsabs < 0 and epsrel < 0, +! or limit < npts2. +! result, abserr, neval are set to zero. +! +! Local parameters: +! +! the dimension of rlist2 is determined by the value of +! limexp in QEXTR (rlist2 should be of dimension +! (limexp+2) at least). +! +! alist - list of left end points of all subintervals +! considered up to now +! blist - list of right end points of all subintervals +! considered up to now +! rlist(i) - approximation to the integral over +! (alist(i),blist(i)) +! rlist2 - array of dimension at least limexp+2 +! containing the part of the epsilon table which +! is still needed for further computations +! elist(i) - error estimate applying to rlist(i) +! maxerr - pointer to the interval with largest error +! estimate +! errmax - elist(maxerr) +! erlast - error on the interval currently subdivided +! (before that subdivision has taken place) +! area - sum of the integrals over the subintervals +! errsum - sum of the errors over the subintervals +! errbnd - requested accuracy max(epsabs,epsrel* +! abs(result)) +! *****1 - variable for the left subinterval +! *****2 - variable for the right subinterval +! last - index for subdivision +! nres - number of calls to the extrapolation routine +! numrl2 - number of elements in rlist2. if an appropriate +! approximation to the compounded integral has +! obtained, it is put in rlist2(numrl2) after +! numrl2 has been increased by one. +! erlarg - sum of the errors over the intervals larger +! than the smallest interval considered up to now +! extrap - logical variable denoting that the routine +! is attempting to perform extrapolation. i.e. +! before subdividing the smallest interval we +! try to decrease the value of erlarg. +! noext - logical variable denoting that extrapolation is +! no longer allowed (true-value) +! + implicit none +! + integer, parameter :: limit = 500 +! + real(dp) a + real(dp) abseps + real(dp) abserr + real(dp) alist(limit) + real(dp) area + real(dp) area1 + real(dp) area12 + real(dp) area2 + real(dp) a1 + real(dp) a2 + real(dp) b + real(dp) blist(limit) + real(dp) b1 + real(dp) b2 + real(dp) correc + real(dp) defabs + real(dp) defab1 + real(dp) defab2 + real(dp) dres + real(dp) elist(limit) + real(dp) epsabs + real(dp) epsrel + real(dp) erlarg + real(dp) erlast + real(dp) errbnd + real(dp) errmax + real(dp) error1 + real(dp) erro12 + real(dp) error2 + real(dp) errsum + real(dp) ertest + logical extrap + real(dp), external :: f + integer i + integer id + integer ier + integer ierro + integer ind1 + integer ind2 + integer iord(limit) + integer ip1 + integer iroff1 + integer iroff2 + integer iroff3 + integer j + integer jlow + integer jupbnd + integer k + integer ksgn + integer ktmin + integer last + integer levcur + integer level(limit) + integer levmax + integer maxerr + integer ndin(40) + integer neval + integer nint + logical noext + integer npts + integer npts2 + integer nres + integer nrmax + integer numrl2 + real(dp) points(40) + real(dp) pts(40) + real(dp) resa + real(dp) resabs + real(dp) reseps + real(dp) result + real(dp) res3la(3) + real(dp) rlist(limit) + real(dp) rlist2(52) + real(dp) sign + real(dp) temp +! +! Test on validity of parameters. +! + ier = 0 + neval = 0 + last = 0 + result = 0.0e+00 + abserr = 0.0e+00 + alist(1) = a + blist(1) = b + rlist(1) = 0.0e+00 + elist(1) = 0.0e+00 + iord(1) = 0 + level(1) = 0 + npts = npts2-2 + + if ( npts2 < 2 ) then + ier = 6 + return + else if ( limit <= npts .or. (epsabs < 0.0e+00.and. & + epsrel < 0.0e+00) ) then + ier = 6 + return + end if +! +! If any break points are provided, sort them into an +! ascending sequence. +! + if ( a > b ) then + sign = -1.0e+00 + else + sign = +1.0E+00 + end if + + pts(1) = min ( a,b) + + do i = 1, npts + pts(i+1) = points(i) + end do + + pts(npts+2) = max ( a,b) + nint = npts+1 + a1 = pts(1) + + if ( npts /= 0 ) then + + do i = 1, nint + ip1 = i+1 + do j = ip1, nint+1 + if ( pts(i) > pts(j) ) then + call r_swap ( pts(i), pts(j) ) + end if + end do + end do + + if ( pts(1) /= min ( a, b ) .or. pts(nint+1) /= max ( a,b) ) then + ier = 6 + return + end if + + end if +! +! Compute first integral and error approximations. +! + resabs = 0.0e+00 + + do i = 1, nint + + b1 = pts(i+1) + call qk21 ( f, a1, b1, area1, error1, defabs, resa ) + abserr = abserr+error1 + result = result+area1 + ndin(i) = 0 + + if ( error1 == resa .and. error1 /= 0.0e+00 ) then + ndin(i) = 1 + end if + + resabs = resabs + defabs + level(i) = 0 + elist(i) = error1 + alist(i) = a1 + blist(i) = b1 + rlist(i) = area1 + iord(i) = i + a1 = b1 + + end do + + errsum = 0.0e+00 + + do i = 1, nint + if ( ndin(i) == 1 ) then + elist(i) = abserr + end if + errsum = errsum + elist(i) + end do +! +! Test on accuracy. +! + last = nint + neval = 21 * nint + dres = abs ( result ) + errbnd = max ( epsabs, epsrel * dres ) + + if ( abserr <= 1.0e+02 * epsilon ( resabs ) * resabs .and. & + abserr > errbnd ) then + ier = 2 + end if + + if ( nint /= 1 ) then + + do i = 1, npts + + jlow = i+1 + ind1 = iord(i) + + do j = jlow, nint + ind2 = iord(j) + if ( elist(ind1) <= elist(ind2) ) then + ind1 = ind2 + k = j + end if + end do + + if ( ind1 /= iord(i) ) then + iord(k) = iord(i) + iord(i) = ind1 + end if + + end do + + if ( limit < npts2 ) then + ier = 1 + end if + + end if + + if ( ier /= 0 .or. abserr <= errbnd ) then + return + end if +! +! Initialization +! + rlist2(1) = result + maxerr = iord(1) + errmax = elist(maxerr) + area = result + nrmax = 1 + nres = 0 + numrl2 = 1 + ktmin = 0 + extrap = .false. + noext = .false. + erlarg = errsum + ertest = errbnd + levmax = 1 + iroff1 = 0 + iroff2 = 0 + iroff3 = 0 + ierro = 0 + abserr = huge ( abserr ) + + if ( dres >= ( 1.0e+00 - 0.5E+00 * epsilon ( resabs ) ) * resabs ) then + ksgn = 1 + else + ksgn = -1 + end if + + do last = npts2, limit +! +! Bisect the subinterval with the nrmax-th largest error estimate. +! + levcur = level(maxerr)+1 + a1 = alist(maxerr) + b1 = 0.5E+00 * ( alist(maxerr) + blist(maxerr) ) + a2 = b1 + b2 = blist(maxerr) + erlast = errmax + call qk21 ( f, a1, b1, area1, error1, resa, defab1 ) + call qk21 ( f, a2, b2, area2, error2, resa, defab2 ) +! +! Improve previous approximations to integral and error +! and test for accuracy. +! + neval = neval+42 + area12 = area1+area2 + erro12 = error1+error2 + errsum = errsum+erro12-errmax + area = area+area12-rlist(maxerr) + + if ( defab1 /= error1 .and. defab2 /= error2 ) then + + if ( abs(rlist(maxerr)-area12) <= 1.0e-05*abs(area12) .and. & + erro12 >= 9.9e-01*errmax ) then + + if ( extrap ) then + iroff2 = iroff2+1 + else + iroff1 = iroff1+1 + end if + + end if + + if ( last > 10 .and. erro12 > errmax ) then + iroff3 = iroff3 + 1 + end if + + end if + + level(maxerr) = levcur + level(last) = levcur + rlist(maxerr) = area1 + rlist(last) = area2 + errbnd = max ( epsabs, epsrel * abs ( area ) ) +! +! Test for roundoff error and eventually set error flag. +! + if ( iroff1 + iroff2 >= 10 .or. iroff3 >= 20 ) then + ier = 2 + end if + + if ( iroff2 >= 5 ) then + ierro = 3 + end if +! +! Set error flag in the case that the number of subintervals +! equals limit. +! + if ( last == limit ) then + ier = 1 + end if +! +! Set error flag in the case of bad integrand behavior +! at a point of the integration range +! + if ( max ( abs(a1),abs(b2)) <= (1.0e+00+1.0e+03* epsilon ( a1 ) )* & + ( abs(a2) + 1.0e+03 * tiny ( a2 ) ) ) then + ier = 4 + end if +! +! Append the newly-created intervals to the list. +! + if ( error2 <= error1 ) then + alist(last) = a2 + blist(maxerr) = b1 + blist(last) = b2 + elist(maxerr) = error1 + elist(last) = error2 + else + alist(maxerr) = a2 + alist(last) = a1 + blist(last) = b1 + rlist(maxerr) = area2 + rlist(last) = area1 + elist(maxerr) = error2 + elist(last) = error1 + end if +! +! Call QSORT to maintain the descending ordering +! in the list of error estimates and select the subinterval +! with nrmax-th largest error estimate (to be bisected next). +! + call qsort ( limit, last, maxerr, errmax, elist, iord, nrmax ) + + if ( errsum <= errbnd ) go to 190 + + if ( ier /= 0 ) then + exit + end if + + if ( noext ) then + cycle + end if + + erlarg = erlarg - erlast + + if ( levcur+1 <= levmax ) then + erlarg = erlarg + erro12 + end if +! +! Test whether the interval to be bisected next is the +! smallest interval. +! + if ( .not. extrap ) then + + if ( level(maxerr)+1 <= levmax ) then + cycle + end if + + extrap = .true. + nrmax = 2 + + end if +! +! The smallest interval has the largest error. +! Before bisecting decrease the sum of the errors over the +! larger intervals (erlarg) and perform extrapolation. +! + if ( ierro /= 3 .and. erlarg > ertest ) then + + id = nrmax + jupbnd = last + if ( last > (2+limit/2) ) then + jupbnd = limit+3-last + end if + + do k = id, jupbnd + maxerr = iord(nrmax) + errmax = elist(maxerr) + if ( level(maxerr)+1 <= levmax ) go to 160 + nrmax = nrmax+1 + end do + + end if +! +! Perform extrapolation. +! + numrl2 = numrl2+1 + rlist2(numrl2) = area + if ( numrl2 <= 2 ) go to 155 + call qextr ( numrl2, rlist2, reseps, abseps, res3la, nres ) + ktmin = ktmin+1 + + if ( ktmin > 5 .and. abserr < 1.0e-03*errsum ) then + ier = 5 + end if + + if ( abseps < abserr ) then + + ktmin = 0 + abserr = abseps + result = reseps + correc = erlarg + ertest = max ( epsabs,epsrel*abs(reseps)) + + if ( abserr < ertest ) then + exit + end if + + end if +! +! Prepare bisection of the smallest interval. +! + if ( numrl2 == 1 ) then + noext = .true. + end if + + if ( ier >= 5 ) then + exit + end if + +155 continue + + maxerr = iord(1) + errmax = elist(maxerr) + nrmax = 1 + extrap = .false. + levmax = levmax+1 + erlarg = errsum + +160 continue + + end do +! +! Set the final result. +! + if ( abserr == huge ( abserr ) ) go to 190 + if ( (ier+ierro) == 0 ) go to 180 + + if ( ierro == 3 ) then + abserr = abserr+correc + end if + + if ( ier == 0 ) then + ier = 3 + end if + + if ( result /= 0.0e+00.and.area /= 0.0e+00 ) go to 175 + if ( abserr > errsum ) go to 190 + if ( area == 0.0e+00 ) go to 210 + go to 180 + +175 continue + + if ( abserr/abs(result) > errsum/abs(area) ) go to 190 +! +! Test on divergence. +! + 180 continue + + if ( ksgn == (-1) .and. max ( abs(result),abs(area)) <= & + resabs*1.0e-02 ) go to 210 + + if ( 1.0e-02 > (result/area) .or. (result/area) > 1.0e+02 .or. & + errsum > abs(area) ) then + ier = 6 + end if + + go to 210 +! +! Compute global integral sum. +! +190 continue + + result = sum ( rlist(1:last) ) + + abserr = errsum + +210 continue + + if ( ier > 2 ) then + ier = ier - 1 + end if + + result = result * sign + + return +end subroutine +subroutine qags ( f, a, b, epsabs, epsrel, result, abserr, neval, ier ) +! +!****************************************************************************** +! +!! QAGS estimates the integral of a function. +! +! +! Discussion: +! +! The routine calculates an approximation RESULT to a definite integral +! I = integral of F over (A,B), +! hopefully satisfying +! || I - RESULT || <= max ( EPSABS, EPSREL * ||I|| ). +! +! Reference: +! +! R Piessens, E de Doncker-Kapenger, C W Ueberhuber, D K Kahaner, +! QUADPACK, a Subroutine Package for Automatic Integration, +! Springer Verlag, 1983 +! +! Parameters: +! +! Input, external real(dp) F, the name of the function routine, of the form +! function f ( x ) +! real(dp) f +! real(dp) x +! which evaluates the integrand function. +! +! Input, real(dp) A, B, the limits of integration. +! +! Input, real(dp) EPSABS, EPSREL, the absolute and relative accuracy requested. +! +! Output, real(dp) RESULT, the estimated value of the integral. +! +! Output, real(dp) ABSERR, an estimate of || I - RESULT ||. +! +! Output, integer NEVAL, the number of times the integral was evaluated. +! +! Output, integer IER, error flag. +! ier = 0 normal and reliable termination of the +! routine. it is assumed that the requested +! accuracy has been achieved. +! ier > 0 abnormal termination of the routine +! the estimates for integral and error are +! less reliable. it is assumed that the +! requested accuracy has not been achieved. +! = 1 maximum number of subdivisions allowed +! has been achieved. one can allow more sub- +! divisions by increasing the data value of +! limit in qags (and taking the according +! dimension adjustments into account). +! however, if this yields no improvement +! it is advised to analyze the integrand +! in order to determine the integration +! difficulties. if the position of a +! local difficulty can be determined (e.g. +! singularity, discontinuity within the +! interval) one will probably gain from +! splitting up the interval at this point +! and calling the integrator on the sub- +! ranges. if possible, an appropriate +! special-purpose integrator should be used, +! which is designed for handling the type +! of difficulty involved. +! = 2 the occurrence of roundoff error is detec- +! ted, which prevents the requested +! tolerance from being achieved. +! the error may be under-estimated. +! = 3 extremely bad integrand behavior occurs +! at some points of the integration +! interval. +! = 4 the algorithm does not converge. roundoff +! error is detected in the extrapolation +! table. it is presumed that the requested +! tolerance cannot be achieved, and that the +! returned result is the best which can be +! obtained. +! = 5 the integral is probably divergent, or +! slowly convergent. it must be noted that +! divergence can occur with any other value +! of ier. +! = 6 the input is invalid, because +! epsabs < 0 and epsrel < 0, +! result, abserr and neval are set to zero. +! +! Local Parameters: +! +! alist - list of left end points of all subintervals +! considered up to now +! blist - list of right end points of all subintervals +! considered up to now +! rlist(i) - approximation to the integral over +! (alist(i),blist(i)) +! rlist2 - array of dimension at least limexp+2 containing +! the part of the epsilon table which is still +! needed for further computations +! elist(i) - error estimate applying to rlist(i) +! maxerr - pointer to the interval with largest error +! estimate +! errmax - elist(maxerr) +! erlast - error on the interval currently subdivided +! (before that subdivision has taken place) +! area - sum of the integrals over the subintervals +! errsum - sum of the errors over the subintervals +! errbnd - requested accuracy max(epsabs,epsrel* +! abs(result)) +! *****1 - variable for the left interval +! *****2 - variable for the right interval +! last - index for subdivision +! nres - number of calls to the extrapolation routine +! numrl2 - number of elements currently in rlist2. if an +! appropriate approximation to the compounded +! integral has been obtained it is put in +! rlist2(numrl2) after numrl2 has been increased +! by one. +! small - length of the smallest interval considered +! up to now, multiplied by 1.5 +! erlarg - sum of the errors over the intervals larger +! than the smallest interval considered up to now +! extrap - logical variable denoting that the routine is +! attempting to perform extrapolation i.e. before +! subdividing the smallest interval we try to +! decrease the value of erlarg. +! noext - logical variable denoting that extrapolation +! is no longer allowed (true value) +! + implicit none +! + integer, parameter :: limit = 500 +! + real(dp) a + real(dp) abseps + real(dp) abserr + real(dp) alist(limit) + real(dp) area + real(dp) area1 + real(dp) area12 + real(dp) area2 + real(dp) a1 + real(dp) a2 + real(dp) b + real(dp) blist(limit) + real(dp) b1 + real(dp) b2 + real(dp) correc + real(dp) defabs + real(dp) defab1 + real(dp) defab2 + real(dp) dres + real(dp) elist(limit) + real(dp) epsabs + real(dp) epsrel + real(dp) erlarg + real(dp) erlast + real(dp) errbnd + real(dp) errmax + real(dp) error1 + real(dp) error2 + real(dp) erro12 + real(dp) errsum + real(dp) ertest + logical extrap + real(dp), external :: f + integer id + integer ier + integer ierro + integer iord(limit) + integer iroff1 + integer iroff2 + integer iroff3 + integer jupbnd + integer k + integer ksgn + integer ktmin + integer last + logical noext + integer maxerr + integer neval + integer nres + integer nrmax + integer numrl2 + real(dp) resabs + real(dp) reseps + real(dp) result + real(dp) res3la(3) + real(dp) rlist(limit) + real(dp) rlist2(52) + real(dp) small +! +! The dimension of rlist2 is determined by the value of +! limexp in QEXTR (rlist2 should be of dimension +! (limexp+2) at least). +! +! Test on validity of parameters. +! + ier = 0 + neval = 0 + last = 0 + result = 0.0e+00 + abserr = 0.0e+00 + alist(1) = a + blist(1) = b + rlist(1) = 0.0e+00 + elist(1) = 0.0e+00 + + if ( epsabs < 0.0e+00 .and. epsrel < 0.0e+00 ) then + ier = 6 + return + end if +! +! First approximation to the integral. +! + ierro = 0 + call qk21 ( f, a, b, result, abserr, defabs, resabs ) +! +! Test on accuracy. +! + dres = abs ( result ) + errbnd = max ( epsabs, epsrel * dres ) + last = 1 + rlist(1) = result + elist(1) = abserr + iord(1) = 1 + + if ( abserr <= 1.0e+02 * epsilon ( defabs ) * defabs .and. & + abserr > errbnd ) then + ier = 2 + end if + + if ( limit == 1 ) then + ier = 1 + end if + + if ( ier /= 0 .or. (abserr <= errbnd .and. abserr /= resabs ) .or. & + abserr == 0.0e+00 ) go to 140 +! +! Initialization. +! + rlist2(1) = result + errmax = abserr + maxerr = 1 + area = result + errsum = abserr + abserr = huge ( abserr ) + nrmax = 1 + nres = 0 + numrl2 = 2 + ktmin = 0 + extrap = .false. + noext = .false. + iroff1 = 0 + iroff2 = 0 + iroff3 = 0 + + if ( dres >= (1.0e+00-5.0e+01* epsilon ( defabs ) )*defabs ) then + ksgn = 1 + else + ksgn = -1 + end if + + do last = 2, limit +! +! Bisect the subinterval with the nrmax-th largest error estimate. +! + a1 = alist(maxerr) + b1 = 5.0e-01*(alist(maxerr)+blist(maxerr)) + a2 = b1 + b2 = blist(maxerr) + erlast = errmax + call qk21 ( f, a1, b1, area1, error1, resabs, defab1 ) + call qk21 ( f, a2, b2, area2, error2, resabs, defab2 ) +! +! Improve previous approximations to integral and error +! and test for accuracy. +! + area12 = area1+area2 + erro12 = error1+error2 + errsum = errsum+erro12-errmax + area = area+area12-rlist(maxerr) + + if ( defab1 == error1 .or. defab2 == error2 ) go to 15 + + if ( abs ( rlist(maxerr) - area12) > 1.0e-05 * abs(area12) & + .or. erro12 < 9.9e-01 * errmax ) go to 10 + + if ( extrap ) then + iroff2 = iroff2+1 + else + iroff1 = iroff1+1 + end if + +10 continue + + if ( last > 10.and.erro12 > errmax ) iroff3 = iroff3+1 + +15 continue + + rlist(maxerr) = area1 + rlist(last) = area2 + errbnd = max ( epsabs,epsrel*abs(area)) +! +! Test for roundoff error and eventually set error flag. +! + if ( iroff1+iroff2 >= 10 .or. iroff3 >= 20 ) then + ier = 2 + end if + + if ( iroff2 >= 5 ) ierro = 3 +! +! Set error flag in the case that the number of subintervals +! equals limit. +! + if ( last == limit ) then + ier = 1 + end if +! +! Set error flag in the case of bad integrand behavior +! at a point of the integration range. +! + if ( max ( abs(a1),abs(b2)) <= (1.0e+00+1.0e+03* epsilon ( a1 ) )* & + (abs(a2)+1.0e+03* tiny ( a2 ) ) ) then + ier = 4 + end if +! +! Append the newly-created intervals to the list. +! + if ( error2 <= error1 ) then + alist(last) = a2 + blist(maxerr) = b1 + blist(last) = b2 + elist(maxerr) = error1 + elist(last) = error2 + else + alist(maxerr) = a2 + alist(last) = a1 + blist(last) = b1 + rlist(maxerr) = area2 + rlist(last) = area1 + elist(maxerr) = error2 + elist(last) = error1 + end if +! +! Call QSORT to maintain the descending ordering +! in the list of error estimates and select the subinterval +! with nrmax-th largest error estimate (to be bisected next). +! + call qsort ( limit, last, maxerr, errmax, elist, iord, nrmax ) + + if ( errsum <= errbnd ) go to 115 + + if ( ier /= 0 ) then + exit + end if + + if ( last == 2 ) go to 80 + if ( noext ) go to 90 + + erlarg = erlarg-erlast + + if ( abs(b1-a1) > small ) then + erlarg = erlarg+erro12 + end if + + if ( extrap ) go to 40 +! +! Test whether the interval to be bisected next is the +! smallest interval. +! + if ( abs(blist(maxerr)-alist(maxerr)) > small ) go to 90 + extrap = .true. + nrmax = 2 + +40 continue +! +! The smallest interval has the largest error. +! Before bisecting decrease the sum of the errors over the +! larger intervals (erlarg) and perform extrapolation. +! + if ( ierro /= 3 .and. erlarg > ertest ) then + + id = nrmax + jupbnd = last + + if ( last > (2+limit/2) ) then + jupbnd = limit+3-last + end if + + do k = id, jupbnd + maxerr = iord(nrmax) + errmax = elist(maxerr) + if ( abs(blist(maxerr)-alist(maxerr)) > small ) go to 90 + nrmax = nrmax+1 + end do + + end if +! +! Perform extrapolation. +! +60 continue + + numrl2 = numrl2+1 + rlist2(numrl2) = area + call qextr ( numrl2, rlist2, reseps, abseps, res3la, nres ) + ktmin = ktmin+1 + + if ( ktmin > 5 .and. abserr < 1.0e-03 * errsum ) then + ier = 5 + end if + + if ( abseps < abserr ) then + + ktmin = 0 + abserr = abseps + result = reseps + correc = erlarg + ertest = max ( epsabs,epsrel*abs(reseps)) + + if ( abserr <= ertest ) then + exit + end if + + end if +! +! Prepare bisection of the smallest interval. +! + if ( numrl2 == 1 ) then + noext = .true. + end if + + if ( ier == 5 ) then + exit + end if + + maxerr = iord(1) + errmax = elist(maxerr) + nrmax = 1 + extrap = .false. + small = small*5.0e-01 + erlarg = errsum + go to 90 + +80 continue + + small = abs(b-a)*3.75e-01 + erlarg = errsum + ertest = errbnd + rlist2(2) = area + +90 continue + + end do +! +! Set final result and error estimate. +! + if ( abserr == huge ( abserr ) ) go to 115 + if ( ier+ierro == 0 ) go to 110 + + if ( ierro == 3 ) then + abserr = abserr+correc + end if + + if ( ier == 0 ) ier = 3 + if ( result /= 0.0e+00.and.area /= 0.0e+00 ) go to 105 + if ( abserr > errsum ) go to 115 + if ( area == 0.0e+00 ) go to 130 + go to 110 + +105 continue + + if ( abserr/abs(result) > errsum/abs(area) ) go to 115 +! +! Test on divergence. +! +110 continue + + if ( ksgn == (-1).and.max ( abs(result),abs(area)) <= & + defabs*1.0e-02 ) go to 130 + + if ( 1.0e-02 > (result/area) .or. (result/area) > 1.0e+02 & + .or. errsum > abs(area) ) then + ier = 6 + end if + + go to 130 +! +! Compute global integral sum. +! +115 continue + + result = sum ( rlist(1:last) ) + + abserr = errsum + +130 continue + + if ( ier > 2 ) ier = ier-1 + +140 continue + + neval = 42*last-21 + + return +end subroutine +subroutine qawc ( f, a, b, c, epsabs, epsrel, result, abserr, neval, ier ) +! +!****************************************************************************** +! +!! QAWC computes a Cauchy principal value. +! +! +! Discussion: +! +! The routine calculates an approximation RESULT to a Cauchy principal +! value +! I = integral of F*W over (A,B), +! with +! W(X) = 1 / (X-C), +! with C distinct from A and B, hopefully satisfying +! || I - RESULT || <= max ( EPSABS, EPSREL * ||I|| ). +! +! Reference: +! +! R Piessens, E de Doncker-Kapenger, C W Ueberhuber, D K Kahaner, +! QUADPACK, a Subroutine Package for Automatic Integration, +! Springer Verlag, 1983 +! +! Parameters: +! +! Input, external real(dp) F, the name of the function routine, of the form +! function f ( x ) +! real(dp) f +! real(dp) x +! which evaluates the integrand function. +! +! Input, real(dp) A, B, the limits of integration. +! +! Input, real(dp) C, a parameter in the weight function, which must +! not be equal to A or B. +! +! Input, real(dp) EPSABS, EPSREL, the absolute and relative accuracy requested. +! +! Output, real(dp) RESULT, the estimated value of the integral. +! +! Output, real(dp) ABSERR, an estimate of || I - RESULT ||. +! +! Output, integer NEVAL, the number of times the integral was evaluated. +! +! ier - integer +! ier = 0 normal and reliable termination of the +! routine. it is assumed that the requested +! accuracy has been achieved. +! ier > 0 abnormal termination of the routine +! the estimates for integral and error are +! less reliable. it is assumed that the +! requested accuracy has not been achieved. +! ier = 1 maximum number of subdivisions allowed +! has been achieved. one can allow more sub- +! divisions by increasing the data value of +! limit in qawc (and taking the according +! dimension adjustments into account). +! however, if this yields no improvement it +! is advised to analyze the integrand in +! order to determine the integration +! difficulties. if the position of a local +! difficulty can be determined (e.g. +! singularity, discontinuity within the +! interval one will probably gain from +! splitting up the interval at this point +! and calling appropriate integrators on the +! subranges. +! = 2 the occurrence of roundoff error is detec- +! ted, which prevents the requested +! tolerance from being achieved. +! = 3 extremely bad integrand behavior occurs +! at some points of the integration +! interval. +! = 6 the input is invalid, because +! c = a or c = b or +! epsabs < 0 and epsrel < 0, +! result, abserr, neval are set to zero. +! +! Local parameters: +! +! LIMIT is the maximum number of subintervals allowed in the +! subdivision process of qawce. take care that limit >= 1. +! + implicit none +! + integer, parameter :: limit = 500 +! + real(dp) a + real(dp) abserr + real(dp) alist(limit) + real(dp) b + real(dp) blist(limit) + real(dp) elist(limit) + real(dp) c + real(dp) epsabs + real(dp) epsrel + real(dp), external :: f + integer ier + integer iord(limit) + integer last +! integer limit + integer neval + real(dp) result + real(dp) rlist(limit) +! + call qawce ( f, a, b, c, epsabs, epsrel, limit, result, abserr, neval, ier, & + alist, blist, rlist, elist, iord, last ) + + return +end subroutine +subroutine qawce ( f, a, b, c, epsabs, epsrel, limit, result, abserr, neval, & + ier, alist, blist, rlist, elist, iord, last ) +! +!****************************************************************************** +! +!! QAWCE computes a Cauchy principal value. +! +! +! Discussion: +! +! The routine calculates an approximation RESULT to a Cauchy principal +! value +! I = integral of F*W over (A,B), +! with +! W(X) = 1 / ( X - C ), +! with C distinct from A and B, hopefully satisfying +! | I - RESULT | <= max ( EPSABS, EPSREL * |I| ). +! +! Reference: +! +! R Piessens, E de Doncker-Kapenger, C W Ueberhuber, D K Kahaner, +! QUADPACK, a Subroutine Package for Automatic Integration, +! Springer Verlag, 1983 +! +! Parameters: +! +! Input, external real(dp) F, the name of the function routine, of the form +! function f ( x ) +! real(dp) f +! real(dp) x +! which evaluates the integrand function. +! +! Input, real(dp) A, B, the limits of integration. +! +! Input, real(dp) C, a parameter in the weight function, which cannot be +! equal to A or B. +! +! Input, real(dp) EPSABS, EPSREL, the absolute and relative accuracy requested. +! +! Input, integer LIMIT, the upper bound on the number of subintervals that +! will be used in the partition of [A,B]. LIMIT is typically 500. +! +! Output, real(dp) RESULT, the estimated value of the integral. +! +! Output, real(dp) ABSERR, an estimate of || I - RESULT ||. +! +! Output, integer NEVAL, the number of times the integral was evaluated. +! +! ier - integer +! ier = 0 normal and reliable termination of the +! routine. it is assumed that the requested +! accuracy has been achieved. +! ier > 0 abnormal termination of the routine +! the estimates for integral and error are +! less reliable. it is assumed that the +! requested accuracy has not been achieved. +! ier = 1 maximum number of subdivisions allowed +! has been achieved. one can allow more sub- +! divisions by increasing the value of +! limit. however, if this yields no +! improvement it is advised to analyze the +! integrand, in order to determine the +! integration difficulties. if the position +! of a local difficulty can be determined +! (e.g. singularity, discontinuity within +! the interval) one will probably gain +! from splitting up the interval at this +! point and calling appropriate integrators +! on the subranges. +! = 2 the occurrence of roundoff error is detec- +! ted, which prevents the requested +! tolerance from being achieved. +! = 3 extremely bad integrand behavior occurs +! at some interior points of the integration +! interval. +! = 6 the input is invalid, because +! c = a or c = b or +! epsabs < 0 and epsrel < 0, +! or limit < 1. +! result, abserr, neval, rlist(1), elist(1), +! iord(1) and last are set to zero. +! alist(1) and blist(1) are set to a and b +! respectively. +! +! Workspace, real(dp) ALIST(LIMIT), BLIST(LIMIT), contains in entries 1 +! through LAST the left and right ends of the partition subintervals. +! +! Workspace, real(dp) RLIST(LIMIT), contains in entries 1 through LAST +! the integral approximations on the subintervals. +! +! Workspace, real(dp) ELIST(LIMIT), contains in entries 1 through LAST +! the absolute error estimates on the subintervals. +! +! iord - integer +! vector of dimension at least limit, the first k +! elements of which are pointers to the error +! estimates over the subintervals, so that +! elist(iord(1)), ..., elist(iord(k)) with +! k = last if last <= (limit/2+2), and +! k = limit+1-last otherwise, form a decreasing +! sequence. +! +! last - integer +! number of subintervals actually produced in +! the subdivision process +! +! Local parameters: +! +! alist - list of left end points of all subintervals +! considered up to now +! blist - list of right end points of all subintervals +! considered up to now +! rlist(i) - approximation to the integral over +! (alist(i),blist(i)) +! elist(i) - error estimate applying to rlist(i) +! maxerr - pointer to the interval with largest error +! estimate +! errmax - elist(maxerr) +! area - sum of the integrals over the subintervals +! errsum - sum of the errors over the subintervals +! errbnd - requested accuracy max(epsabs,epsrel* +! abs(result)) +! *****1 - variable for the left subinterval +! *****2 - variable for the right subinterval +! last - index for subdivision +! + implicit none +! + integer limit +! + real(dp) a + real(dp) aa + real(dp) abserr + real(dp) alist(limit) + real(dp) area + real(dp) area1 + real(dp) area12 + real(dp) area2 + real(dp) a1 + real(dp) a2 + real(dp) b + real(dp) bb + real(dp) blist(limit) + real(dp) b1 + real(dp) b2 + real(dp) c + real(dp) elist(limit) + real(dp) epsabs + real(dp) epsrel + real(dp) errbnd + real(dp) errmax + real(dp) error1 + real(dp) error2 + real(dp) erro12 + real(dp) errsum + real(dp), external :: f + integer ier + integer iord(limit) + integer iroff1 + integer iroff2 + integer k + integer krule + integer last + integer maxerr + integer nev + integer neval + integer nrmax + real(dp) result + real(dp) rlist(limit) +! +! Test on validity of parameters. +! + ier = 0 + neval = 0 + last = 0 + alist(1) = a + blist(1) = b + rlist(1) = 0.0e+00 + elist(1) = 0.0e+00 + iord(1) = 0 + result = 0.0e+00 + abserr = 0.0e+00 + + if ( c == a ) then + ier = 6 + return + else if ( c == b ) then + ier = 6 + return + else if ( epsabs < 0.0e+00 .and. epsrel < 0.0e+00 ) then + ier = 6 + return + end if +! +! First approximation to the integral. +! + if ( a <= b ) then + aa = a + bb = b + else + aa = b + bb = a + end if + + krule = 1 + call qc25c ( f, aa, bb, c, result, abserr, krule, neval ) + last = 1 + rlist(1) = result + elist(1) = abserr + iord(1) = 1 + alist(1) = a + blist(1) = b +! +! Test on accuracy. +! + errbnd = max ( epsabs, epsrel*abs(result) ) + + if ( limit == 1 ) then + ier = 1 + go to 70 + end if + + if ( abserr < min ( 1.0e-02*abs(result),errbnd) ) then + go to 70 + end if +! +! Initialization +! + alist(1) = aa + blist(1) = bb + rlist(1) = result + errmax = abserr + maxerr = 1 + area = result + errsum = abserr + nrmax = 1 + iroff1 = 0 + iroff2 = 0 + + do last = 2, limit +! +! Bisect the subinterval with nrmax-th largest error estimate. +! + a1 = alist(maxerr) + b1 = 5.0e-01*(alist(maxerr)+blist(maxerr)) + b2 = blist(maxerr) + if ( c <= b1 .and. c > a1 ) b1 = 5.0e-01*(c+b2) + if ( c > b1 .and. c < b2 ) b1 = 5.0e-01*(a1+c) + a2 = b1 + krule = 2 + + call qc25c ( f, a1, b1, c, area1, error1, krule, nev ) + neval = neval+nev + + call qc25c ( f, a2, b2, c, area2, error2, krule, nev ) + neval = neval+nev +! +! Improve previous approximations to integral and error +! and test for accuracy. +! + area12 = area1+area2 + erro12 = error1+error2 + errsum = errsum+erro12-errmax + area = area+area12-rlist(maxerr) + + if ( abs(rlist(maxerr)-area12) < 1.0e-05*abs(area12) & + .and.erro12 >= 9.9e-01*errmax .and. krule == 0 ) & + iroff1 = iroff1+1 + + if ( last > 10.and.erro12 > errmax .and. krule == 0 ) then + iroff2 = iroff2+1 + end if + + rlist(maxerr) = area1 + rlist(last) = area2 + errbnd = max ( epsabs,epsrel*abs(area)) + + if ( errsum > errbnd ) then +! +! Test for roundoff error and eventually set error flag. +! + if ( iroff1 >= 6 .and. iroff2 > 20 ) then + ier = 2 + end if +! +! Set error flag in the case that number of interval +! bisections exceeds limit. +! + if ( last == limit ) then + ier = 1 + end if +! +! Set error flag in the case of bad integrand behavior at +! a point of the integration range. +! + if ( max ( abs(a1), abs(b2) ) <= ( 1.0e+00 + 1.0e+03 * epsilon ( a1 ) ) & + *(abs(a2)+1.0e+03* tiny ( a2 ) )) then + ier = 3 + end if + + end if +! +! Append the newly-created intervals to the list. +! + if ( error2 <= error1 ) then + alist(last) = a2 + blist(maxerr) = b1 + blist(last) = b2 + elist(maxerr) = error1 + elist(last) = error2 + else + alist(maxerr) = a2 + alist(last) = a1 + blist(last) = b1 + rlist(maxerr) = area2 + rlist(last) = area1 + elist(maxerr) = error2 + elist(last) = error1 + end if +! +! Call QSORT to maintain the descending ordering +! in the list of error estimates and select the subinterval +! with NRMAX-th largest error estimate (to be bisected next). +! + call qsort ( limit, last, maxerr, errmax, elist, iord, nrmax ) + + if ( ier /= 0 .or. errsum <= errbnd ) then + exit + end if + + end do +! +! Compute final result. +! + result = sum ( rlist(1:last) ) + + abserr = errsum + +70 continue + + if ( aa == b ) then + result = - result + end if + + return +end subroutine +subroutine qawf ( f, a, omega, integr, epsabs, result, abserr, neval, ier ) +! +!****************************************************************************** +! +!! QAWF computes Fourier integrals over the interval [ A, +Infinity ). +! +! +! Discussion: +! +! The routine calculates an approximation RESULT to a definite integral +! +! I = integral of F*COS(OMEGA*X) +! or +! I = integral of F*SIN(OMEGA*X) +! +! over the interval [A,+Infinity), hopefully satisfying +! +! || I - RESULT || <= EPSABS. +! +! If OMEGA = 0 and INTEGR = 1, the integral is calculated by means +! of QAGI, and IER has the meaning as described in the comments of QAGI. +! +! Reference: +! +! R Piessens, E de Doncker-Kapenger, C W Ueberhuber, D K Kahaner, +! QUADPACK, a Subroutine Package for Automatic Integration, +! Springer Verlag, 1983 +! +! Parameters: +! +! Input, external real(dp) F, the name of the function routine, of the form +! function f ( x ) +! real(dp) f +! real(dp) x +! which evaluates the integrand function. +! +! Input, real(dp) A, the lower limit of integration. +! +! Input, real(dp) OMEGA, the parameter in the weight function. +! +! Input, integer INTEGR, indicates which weight functions is used +! = 1, w(x) = cos(omega*x) +! = 2, w(x) = sin(omega*x) +! +! Input, real(dp) EPSABS, the absolute accuracy requested. +! +! Output, real(dp) RESULT, the estimated value of the integral. +! +! Output, real(dp) ABSERR, an estimate of || I - RESULT ||. +! +! Output, integer NEVAL, the number of times the integral was evaluated. +! +! ier - integer +! ier = 0 normal and reliable termination of the +! routine. it is assumed that the +! requested accuracy has been achieved. +! ier > 0 abnormal termination of the routine. +! the estimates for integral and error are +! less reliable. it is assumed that the +! requested accuracy has not been achieved. +! if omega /= 0 +! ier = 6 the input is invalid because +! (integr /= 1 and integr /= 2) or +! epsabs <= 0 +! result, abserr, neval, lst are set to +! zero. +! = 7 abnormal termination of the computation +! of one or more subintegrals +! = 8 maximum number of cycles allowed +! has been achieved, i.e. of subintervals +! (a+(k-1)c,a+kc) where +! c = (2*int(abs(omega))+1)*pi/abs(omega), +! for k = 1, 2, ... +! = 9 the extrapolation table constructed for +! convergence acceleration of the series +! formed by the integral contributions +! over the cycles, does not converge to +! within the requested accuracy. +! +! Local parameters: +! +! Integer LIMLST, gives an upper bound on the number of cycles, LIMLST >= 3. +! if limlst < 3, the routine will end with ier = 6. +! +! Integer MAXP1, an upper bound on the number of Chebyshev moments which +! can be stored, i.e. for the intervals of lengths abs(b-a)*2**(-l), +! l = 0,1, ..., maxp1-2, maxp1 >= 1. if maxp1 < 1, the routine will end +! with ier = 6. +! + implicit none +! + integer, parameter :: limit = 500 + integer, parameter :: limlst = 50 + integer, parameter :: maxp1 = 21 +! + real(dp) a + real(dp) abserr + real(dp) alist(limit) + real(dp) blist(limit) + real(dp) chebmo(maxp1,25) + real(dp) elist(limit) + real(dp) epsabs + real(dp) erlst(limlst) + real(dp), external :: f + integer ier + integer integr + integer iord(limit) + integer ierlst(limlst) + integer last +! integer limlst + integer lst + integer neval + integer nnlog(limit) + real(dp) omega + real(dp) result + real(dp) rlist(limit) + real(dp) rslst(limlst) +! + ier = 6 + neval = 0 + last = 0 + result = 0.0e+00 + abserr = 0.0e+00 + + if ( limlst < 3 .or. maxp1 < 1 ) then + return + end if + + call qawfe ( f, a, omega, integr, epsabs, limlst, limit, maxp1, result, & + abserr, neval, ier, rslst, erlst, ierlst, lst, alist, blist, rlist, & + elist, iord, nnlog, chebmo ) + + return +end subroutine +subroutine qawfe ( f, a, omega, integr, epsabs, limlst, limit, maxp1, & + result, abserr, neval, ier, rslst, erlst, ierlst, lst, alist, blist, & + rlist, elist, iord, nnlog, chebmo ) +! +!****************************************************************************** +! +!! QAWFE computes Fourier integrals. +! +! +! Discussion: +! +! The routine calculates an approximation RESULT to a definite integral +! I = integral of F*COS(OMEGA*X) or F*SIN(OMEGA*X) over (A,+Infinity), +! hopefully satisfying +! || I - RESULT || <= EPSABS. +! +! Reference: +! +! R Piessens, E de Doncker-Kapenger, C W Ueberhuber, D K Kahaner, +! QUADPACK, a Subroutine Package for Automatic Integration, +! Springer Verlag, 1983 +! +! Parameters: +! +! Input, external real(dp) F, the name of the function routine, of the form +! function f ( x ) +! real(dp) f +! real(dp) x +! which evaluates the integrand function. +! +! Input, real(dp) A, the lower limit of integration. +! +! Input, real(dp) OMEGA, the parameter in the weight function. +! +! Input, integer INTEGR, indicates which weight function is used +! = 1 w(x) = cos(omega*x) +! = 2 w(x) = sin(omega*x) +! +! Input, real(dp) EPSABS, the absolute accuracy requested. +! +! Input, integer LIMLST, an upper bound on the number of cycles. +! LIMLST must be at least 1. In fact, if LIMLST < 3, the routine +! will end with IER= 6. +! +! limit - integer +! gives an upper bound on the number of +! subintervals allowed in the partition of +! each cycle, limit >= 1. +! +! maxp1 - integer +! gives an upper bound on the number of +! Chebyshev moments which can be stored, i.e. +! for the intervals of lengths abs(b-a)*2**(-l), +! l=0,1, ..., maxp1-2, maxp1 >= 1 +! +! Output, real(dp) RESULT, the estimated value of the integral. +! +! Output, real(dp) ABSERR, an estimate of || I - RESULT ||. +! +! Output, integer NEVAL, the number of times the integral was evaluated. +! +! ier - ier = 0 normal and reliable termination of +! the routine. it is assumed that the +! requested accuracy has been achieved. +! ier > 0 abnormal termination of the routine +! the estimates for integral and error +! are less reliable. it is assumed that +! the requested accuracy has not been +! achieved. +! if omega /= 0 +! ier = 6 the input is invalid because +! (integr /= 1 and integr /= 2) or +! epsabs <= 0 or limlst < 3. +! result, abserr, neval, lst are set +! to zero. +! = 7 bad integrand behavior occurs within +! one or more of the cycles. location +! and type of the difficulty involved +! can be determined from the vector ierlst. +! here lst is the number of cycles actually +! needed (see below). +! ierlst(k) = 1 the maximum number of +! subdivisions (= limit) +! has been achieved on the +! k th cycle. +! = 2 occurence of roundoff +! error is detected and +! prevents the tolerance +! imposed on the k th cycle +! from being acheived. +! = 3 extremely bad integrand +! behavior occurs at some +! points of the k th cycle. +! = 4 the integration procedure +! over the k th cycle does +! not converge (to within the +! required accuracy) due to +! roundoff in the +! extrapolation procedure +! invoked on this cycle. it +! is assumed that the result +! on this interval is the +! best which can be obtained. +! = 5 the integral over the k th +! cycle is probably divergent +! or slowly convergent. it +! must be noted that +! divergence can occur with +! any other value of +! ierlst(k). +! = 8 maximum number of cycles allowed +! has been achieved, i.e. of subintervals +! (a+(k-1)c,a+kc) where +! c = (2*int(abs(omega))+1)*pi/abs(omega), +! for k = 1, 2, ..., lst. +! one can allow more cycles by increasing +! the value of limlst (and taking the +! according dimension adjustments into +! account). +! examine the array iwork which contains +! the error flags over the cycles, in order +! to eventual look for local integration +! difficulties. +! if the position of a local difficulty can +! be determined (e.g. singularity, +! discontinuity within the interval) +! one will probably gain from splitting +! up the interval at this point and +! calling appopriate integrators on the +! subranges. +! = 9 the extrapolation table constructed for +! convergence acceleration of the series +! formed by the integral contributions +! over the cycles, does not converge to +! within the required accuracy. +! as in the case of ier = 8, it is advised +! to examine the array iwork which contains +! the error flags on the cycles. +! if omega = 0 and integr = 1, +! the integral is calculated by means of qagi +! and ier = ierlst(1) (with meaning as described +! for ierlst(k), k = 1). +! +! rslst - real(dp) +! vector of dimension at least limlst +! rslst(k) contains the integral contribution +! over the interval (a+(k-1)c,a+kc) where +! c = (2*int(abs(omega))+1)*pi/abs(omega), +! k = 1, 2, ..., lst. +! note that, if omega = 0, rslst(1) contains +! the value of the integral over (a,infinity). +! +! erlst - real(dp) +! vector of dimension at least limlst +! erlst(k) contains the error estimate +! corresponding with rslst(k). +! +! ierlst - integer +! vector of dimension at least limlst +! ierlst(k) contains the error flag corresponding +! with rslst(k). for the meaning of the local error +! flags see description of output parameter ier. +! +! lst - integer +! number of subintervals needed for the integration +! if omega = 0 then lst is set to 1. +! +! alist, blist, rlist, elist - real(dp) +! vector of dimension at least limit, +! +! iord, nnlog - integer +! vector of dimension at least limit, providing +! space for the quantities needed in the +! subdivision process of each cycle +! +! chebmo - real(dp) +! array of dimension at least (maxp1,25), +! providing space for the Chebyshev moments +! needed within the cycles +! +! Local parameters: +! +! c1, c2 - end points of subinterval (of length +! cycle) +! cycle - (2*int(abs(omega))+1)*pi/abs(omega) +! psum - vector of dimension at least (limexp+2) +! (see routine qextr) +! psum contains the part of the epsilon table +! which is still needed for further computations. +! each element of psum is a partial sum of +! the series which should sum to the value of +! the integral. +! errsum - sum of error estimates over the +! subintervals, calculated cumulatively +! epsa - absolute tolerance requested over current +! subinterval +! chebmo - array containing the modified Chebyshev +! moments (see also routine qc25o) +! + implicit none +! + integer limit + integer limlst + integer maxp1 +! + real(dp) a + real(dp) abseps + real(dp) abserr + real(dp) alist(limit) + real(dp) blist(limit) + real(dp) chebmo(maxp1,25) + real(dp) correc + real(dp) cycle + real(dp) c1 + real(dp) c2 + real(dp) dl + real(dp) dla + real(dp) drl + real(dp) elist(limit) + real(dp) ep + real(dp) eps + real(dp) epsa + real(dp) epsabs + real(dp) erlst(limlst) + real(dp) errsum + real(dp), external :: f + real(dp) fact + integer ier + integer ierlst(limlst) + integer integr + integer iord(limit) + integer ktmin + integer l + integer ll + integer lst + integer momcom + integer nev + integer neval + integer nnlog(limit) + integer nres + integer numrl2 + real(dp) omega + real(dp), parameter :: p = 0.9E+00 + real(dp), parameter :: pi = 3.1415926535897932E+00 + real(dp) p1 + real(dp) psum(52) + real(dp) reseps + real(dp) result + real(dp) res3la(3) + real(dp) rlist(limit) + real(dp) rslst(limlst) +! +! The dimension of psum is determined by the value of +! limexp in QEXTR (psum must be +! of dimension (limexp+2) at least). +! +! Test on validity of parameters. +! + result = 0.0e+00 + abserr = 0.0e+00 + neval = 0 + lst = 0 + ier = 0 + + if ( (integr /= 1 .and. integr /= 2 ) .or. & + epsabs <= 0.0e+00 .or. & + limlst < 3 ) then + ier = 6 + return + end if + + if ( omega == 0.0e+00 ) then + + if ( integr == 1 ) then + call qagi ( f, 0.0e+00_dp, 1, epsabs, 0.0e+00_dp, result, abserr, neval, ier ) + else + result = 0.0E+00 + abserr = 0.0E+00 + neval = 0 + ier = 0 + end if + + rslst(1) = result + erlst(1) = abserr + ierlst(1) = ier + lst = 1 + + return + end if +! +! Initializations. +! + l = int(abs ( omega )) + dl = 2 * l + 1 + cycle = dl * pi / abs ( omega ) + ier = 0 + ktmin = 0 + neval = 0 + numrl2 = 0 + nres = 0 + c1 = a + c2 = cycle+a + p1 = 1.0e+00-p + eps = epsabs + + if ( epsabs > tiny ( epsabs ) / p1 ) then + eps = epsabs * p1 + end if + + ep = eps + fact = 1.0e+00 + correc = 0.0e+00 + abserr = 0.0e+00 + errsum = 0.0e+00 + + do lst = 1, limlst +! +! Integrate over current subinterval. +! + dla = lst + epsa = eps*fact + + call qfour ( f, c1, c2, omega, integr, epsa, 0.0e+00_dp, limit, lst, maxp1, & + rslst(lst), erlst(lst), nev, ierlst(lst), alist, blist, rlist, elist, & + iord, nnlog, momcom, chebmo ) + + neval = neval + nev + fact = fact * p + errsum = errsum + erlst(lst) + drl = 5.0e+01 * abs(rslst(lst)) +! +! Test on accuracy with partial sum. +! + if ((errsum+drl) <= epsabs.and.lst >= 6) go to 80 + + correc = max ( correc,erlst(lst)) + + if ( ierlst(lst) /= 0 ) then + eps = max ( ep,correc*p1) + ier = 7 + end if + + if ( ier == 7 .and. (errsum+drl) <= correc*1.0e+01.and. lst > 5) go to 80 + + numrl2 = numrl2+1 + + if ( lst <= 1 ) then + psum(1) = rslst(1) + go to 40 + end if + + psum(numrl2) = psum(ll)+rslst(lst) + + if ( lst == 2 ) then + go to 40 + end if +! +! Test on maximum number of subintervals +! + if ( lst == limlst ) then + ier = 8 + end if +! +! Perform new extrapolation +! + call qextr ( numrl2, psum, reseps, abseps, res3la, nres ) +! +! Test whether extrapolated result is influenced by roundoff +! + ktmin = ktmin+1 + + if ( ktmin >= 15 .and. abserr <= 1.0e-03 * (errsum+drl) ) then + ier = 9 + end if + + if ( abseps <= abserr .or. lst == 3 ) then + + abserr = abseps + result = reseps + ktmin = 0 +! +! If IER is not 0, check whether direct result (partial +! sum) or extrapolated result yields the best integral +! approximation +! + if ( ( abserr + 1.0e+01 * correc ) <= epsabs ) then + exit + end if + + if ( abserr <= epsabs .and. 1.0e+01 * correc >= epsabs ) then + exit + end if + + end if + + if ( ier /= 0 .and. ier /= 7 ) then + exit + end if + +40 continue + + ll = numrl2 + c1 = c2 + c2 = c2+cycle + + end do +! +! Set final result and error estimate. +! +60 continue + + abserr = abserr + 1.0e+01 * correc + + if ( ier == 0 ) then + return + end if + + if ( result /= 0.0e+00 .and. psum(numrl2) /= 0.0e+00) go to 70 + + if ( abserr > errsum ) go to 80 + + if ( psum(numrl2) == 0.0e+00 ) then + return + end if + +70 continue + + if ( abserr / abs(result) <= (errsum+drl)/abs(psum(numrl2)) ) then + + if ( ier >= 1 .and. ier /= 7 ) then + abserr = abserr + drl + end if + + return + + end if + +80 continue + + result = psum(numrl2) + abserr = errsum + drl + + return +end subroutine +subroutine qawo ( f, a, b, omega, integr, epsabs, epsrel, result, abserr, & + neval, ier ) +! +!****************************************************************************** +! +!! QAWO computes the integrals of oscillatory integrands. +! +! +! Discussion: +! +! The routine calculates an approximation RESULT to a given +! definite integral +! I = Integral ( A <= X <= B ) F(X) * cos ( OMEGA * X ) dx +! or +! I = Integral ( A <= X <= B ) F(X) * sin ( OMEGA * X ) dx +! hopefully satisfying following claim for accuracy +! | I - RESULT | <= max ( epsabs, epsrel * |I| ). +! +! Reference: +! +! R Piessens, E de Doncker-Kapenger, C W Ueberhuber, D K Kahaner, +! QUADPACK, a Subroutine Package for Automatic Integration, +! Springer Verlag, 1983 +! +! Parameters: +! +! Input, external real(dp) F, the name of the function routine, of the form +! function f ( x ) +! real(dp) f +! real(dp) x +! which evaluates the integrand function. +! +! Input, real(dp) A, B, the limits of integration. +! +! Input, real(dp) OMEGA, the parameter in the weight function. +! +! Input, integer INTEGR, specifies the weight function: +! 1, W(X) = cos ( OMEGA * X ) +! 2, W(X) = sin ( OMEGA * X ) +! +! Input, real(dp) EPSABS, EPSREL, the absolute and relative accuracy requested. +! +! Output, real(dp) RESULT, the estimated value of the integral. +! +! Output, real(dp) ABSERR, an estimate of || I - RESULT ||. +! +! Output, integer NEVAL, the number of times the integral was evaluated. +! +! ier - integer +! ier = 0 normal and reliable termination of the +! routine. it is assumed that the +! requested accuracy has been achieved. +! - ier > 0 abnormal termination of the routine. +! the estimates for integral and error are +! less reliable. it is assumed that the +! requested accuracy has not been achieved. +! ier = 1 maximum number of subdivisions allowed +! (= leniw/2) has been achieved. one can +! allow more subdivisions by increasing the +! value of leniw (and taking the according +! dimension adjustments into account). +! however, if this yields no improvement it +! is advised to analyze the integrand in +! order to determine the integration +! difficulties. if the position of a local +! difficulty can be determined (e.g. +! singularity, discontinuity within the +! interval) one will probably gain from +! splitting up the interval at this point +! and calling the integrator on the +! subranges. if possible, an appropriate +! special-purpose integrator should +! be used which is designed for handling +! the type of difficulty involved. +! = 2 the occurrence of roundoff error is +! detected, which prevents the requested +! tolerance from being achieved. +! the error may be under-estimated. +! = 3 extremely bad integrand behavior occurs +! at some interior points of the integration +! interval. +! = 4 the algorithm does not converge. roundoff +! error is detected in the extrapolation +! table. it is presumed that the requested +! tolerance cannot be achieved due to +! roundoff in the extrapolation table, +! and that the returned result is the best +! which can be obtained. +! = 5 the integral is probably divergent, or +! slowly convergent. it must be noted that +! divergence can occur with any other value +! of ier. +! = 6 the input is invalid, because +! epsabs < 0 and epsrel < 0, +! result, abserr, neval are set to zero. +! +! Local parameters: +! +! limit is the maximum number of subintervals allowed in the +! subdivision process of QFOUR. take care that limit >= 1. +! +! maxp1 gives an upper bound on the number of Chebyshev moments +! which can be stored, i.e. for the intervals of lengths +! abs(b-a)*2**(-l), l = 0, 1, ... , maxp1-2. take care that +! maxp1 >= 1. + + implicit none +! + integer, parameter :: limit = 500 + integer, parameter :: maxp1 = 21 +! + real(dp) a + real(dp) abserr + real(dp) alist(limit) + real(dp) b + real(dp) blist(limit) + real(dp) chebmo(maxp1,25) + real(dp) elist(limit) + real(dp) epsabs + real(dp) epsrel + real(dp), external :: f + integer ier + integer integr + integer iord(limit) +! integer limit +! integer maxp1 + integer momcom + integer neval + integer nnlog(limit) + real(dp) omega + real(dp) result + real(dp) rlist(limit) +! + call qfour ( f, a, b, omega, integr, epsabs, epsrel, limit, 1, maxp1, & + result, abserr, neval, ier, alist, blist, rlist, elist, iord, nnlog, & + momcom, chebmo ) + + return +end subroutine +subroutine qaws ( f, a, b, alfa, beta, integr, epsabs, epsrel, result, & + abserr, neval, ier ) +! +!****************************************************************************** +! +!! QAWS estimates integrals with algebraico-logarithmic endpoint singularities. +! +! +! Discussion: +! +! This routine calculates an approximation RESULT to a given +! definite integral +! I = integral of f*w over (a,b) +! where w shows a singular behavior at the end points, see parameter +! integr, hopefully satisfying following claim for accuracy +! abs(i-result) <= max(epsabs,epsrel*abs(i)). +! +! Reference: +! +! R Piessens, E de Doncker-Kapenger, C W Ueberhuber, D K Kahaner, +! QUADPACK, a Subroutine Package for Automatic Integration, +! Springer Verlag, 1983 +! +! Parameters: +! +! Input, external real(dp) F, the name of the function routine, of the form +! function f ( x ) +! real(dp) f +! real(dp) x +! which evaluates the integrand function. +! +! Input, real(dp) A, B, the limits of integration. +! +! Input, real(dp) ALFA, BETA, parameters used in the weight function. +! ALFA and BETA should be greater than -1. +! +! Input, integer INTEGR, indicates which weight function is to be used +! = 1 (x-a)**alfa*(b-x)**beta +! = 2 (x-a)**alfa*(b-x)**beta*log(x-a) +! = 3 (x-a)**alfa*(b-x)**beta*log(b-x) +! = 4 (x-a)**alfa*(b-x)**beta*log(x-a)*log(b-x) +! +! Input, real(dp) EPSABS, EPSREL, the absolute and relative accuracy requested. +! +! Output, real(dp) RESULT, the estimated value of the integral. +! +! Output, real(dp) ABSERR, an estimate of || I - RESULT ||. +! +! Output, integer NEVAL, the number of times the integral was evaluated. +! +! ier - integer +! ier = 0 normal and reliable termination of the +! routine. it is assumed that the requested +! accuracy has been achieved. +! ier > 0 abnormal termination of the routine +! the estimates for the integral and error +! are less reliable. it is assumed that the +! requested accuracy has not been achieved. +! ier = 1 maximum number of subdivisions allowed +! has been achieved. one can allow more +! subdivisions by increasing the data value +! of limit in qaws (and taking the according +! dimension adjustments into account). +! however, if this yields no improvement it +! is advised to analyze the integrand, in +! order to determine the integration +! difficulties which prevent the requested +! tolerance from being achieved. in case of +! a jump discontinuity or a local +! singularity of algebraico-logarithmic type +! at one or more interior points of the +! integration range, one should proceed by +! splitting up the interval at these points +! and calling the integrator on the +! subranges. +! = 2 the occurrence of roundoff error is +! detected, which prevents the requested +! tolerance from being achieved. +! = 3 extremely bad integrand behavior occurs +! at some points of the integration +! interval. +! = 6 the input is invalid, because +! b <= a or alfa <= (-1) or beta <= (-1) or +! integr < 1 or integr > 4 or +! epsabs < 0 and epsrel < 0, +! result, abserr, neval are set to zero. +! +! Local parameters: +! +! LIMIT is the maximum number of subintervals allowed in the +! subdivision process of qawse. take care that limit >= 2. +! + implicit none +! + integer, parameter :: limit = 500 +! + real(dp) a + real(dp) abserr + real(dp) alfa + real(dp) alist(limit) + real(dp) b + real(dp) blist(limit) + real(dp) beta + real(dp) elist(limit) + real(dp) epsabs + real(dp) epsrel + real(dp), external :: f + integer ier + integer integr + integer iord(limit) + integer last +! integer limit + integer neval + real(dp) result + real(dp) rlist(limit) +! + call qawse ( f, a, b, alfa, beta, integr, epsabs, epsrel, limit, result, & + abserr, neval, ier, alist, blist, rlist, elist, iord, last ) + + return +end subroutine +subroutine qawse ( f, a, b, alfa, beta, integr, epsabs, epsrel, limit, & + result, abserr, neval, ier, alist, blist, rlist, elist, iord, last ) +! +!****************************************************************************** +! +!! QAWSE estimates integrals with algebraico-logarithmic endpoint singularities. +! +! +! Discussion: +! +! This routine calculates an approximation RESULT to an integral +! I = integral of F(X) * W(X) over (a,b), +! where W(X) shows a singular behavior at the endpoints, hopefully +! satisfying: +! | I - RESULT | <= max ( epsabs, epsrel * |I| ). +! +! Reference: +! +! R Piessens, E de Doncker-Kapenger, C W Ueberhuber, D K Kahaner, +! QUADPACK, a Subroutine Package for Automatic Integration, +! Springer Verlag, 1983 +! +! Parameters: +! +! Input, external real(dp) F, the name of the function routine, of the form +! function f ( x ) +! real(dp) f +! real(dp) x +! which evaluates the integrand function. +! +! Input, real(dp) A, B, the limits of integration. +! +! Input, real(dp) ALFA, BETA, parameters used in the weight function. +! ALFA and BETA should be greater than -1. +! +! Input, integer INTEGR, indicates which weight function is used: +! = 1 (x-a)**alfa*(b-x)**beta +! = 2 (x-a)**alfa*(b-x)**beta*log(x-a) +! = 3 (x-a)**alfa*(b-x)**beta*log(b-x) +! = 4 (x-a)**alfa*(b-x)**beta*log(x-a)*log(b-x) +! +! Input, real(dp) EPSABS, EPSREL, the absolute and relative accuracy requested. +! +! Input, integer LIMIT, an upper bound on the number of subintervals +! in the partition of (A,B), LIMIT >= 2. If LIMIT < 2, the routine +! will end with IER = 6. +! +! Output, real(dp) RESULT, the estimated value of the integral. +! +! Output, real(dp) ABSERR, an estimate of || I - RESULT ||. +! +! Output, integer NEVAL, the number of times the integral was evaluated. +! +! ier - integer +! ier = 0 normal and reliable termination of the +! routine. it is assumed that the requested +! accuracy has been achieved. +! ier > 0 abnormal termination of the routine +! the estimates for the integral and error +! are less reliable. it is assumed that the +! requested accuracy has not been achieved. +! = 1 maximum number of subdivisions allowed +! has been achieved. one can allow more +! subdivisions by increasing the value of +! limit. however, if this yields no +! improvement it is advised to analyze the +! integrand, in order to determine the +! integration difficulties which prevent +! the requested tolerance from being +! achieved. in case of a jump discontinuity +! or a local singularity of algebraico- +! logarithmic type at one or more interior +! points of the integration range, one +! should proceed by splitting up the +! interval at these points and calling the +! integrator on the subranges. +! = 2 the occurrence of roundoff error is +! detected, which prevents the requested +! tolerance from being achieved. +! = 3 extremely bad integrand behavior occurs +! at some points of the integration +! interval. +! = 6 the input is invalid, because +! b <= a or alfa <= (-1) or beta <= (-1) or +! integr < 1 or integr > 4, or +! epsabs < 0 and epsrel < 0, +! or limit < 2. +! result, abserr, neval, rlist(1), elist(1), +! iord(1) and last are set to zero. +! alist(1) and blist(1) are set to a and b +! respectively. +! +! Workspace, real(dp) ALIST(LIMIT), BLIST(LIMIT), contains in entries 1 +! through LAST the left and right ends of the partition subintervals. +! +! Workspace, real(dp) RLIST(LIMIT), contains in entries 1 through LAST +! the integral approximations on the subintervals. +! +! Workspace, real(dp) ELIST(LIMIT), contains in entries 1 through LAST +! the absolute error estimates on the subintervals. +! +! iord - integer +! vector of dimension at least limit, the first k +! elements of which are pointers to the error +! estimates over the subintervals, so that +! elist(iord(1)), ..., elist(iord(k)) with k = last +! if last <= (limit/2+2), and k = limit+1-last +! otherwise, form a decreasing sequence. +! +! Output, integer LAST, the number of subintervals actually produced in +! the subdivision process. +! +! Local parameters: +! +! alist - list of left end points of all subintervals +! considered up to now +! blist - list of right end points of all subintervals +! considered up to now +! rlist(i) - approximation to the integral over +! (alist(i),blist(i)) +! elist(i) - error estimate applying to rlist(i) +! maxerr - pointer to the interval with largest error +! estimate +! errmax - elist(maxerr) +! area - sum of the integrals over the subintervals +! errsum - sum of the errors over the subintervals +! errbnd - requested accuracy max(epsabs,epsrel* +! abs(result)) +! *****1 - variable for the left subinterval +! *****2 - variable for the right subinterval +! last - index for subdivision +! + implicit none +! + integer limit +! + real(dp) a + real(dp) abserr + real(dp) alfa + real(dp) alist(limit) + real(dp) area + real(dp) area1 + real(dp) area12 + real(dp) area2 + real(dp) a1 + real(dp) a2 + real(dp) b + real(dp) beta + real(dp) blist(limit) + real(dp) b1 + real(dp) b2 + real(dp) centre + real(dp) elist(limit) + real(dp) epsabs + real(dp) epsrel + real(dp) errbnd + real(dp) errmax + real(dp) error1 + real(dp) erro12 + real(dp) error2 + real(dp) errsum + real(dp), external :: f + integer ier + integer integr + integer iord(limit) + integer iroff1 + integer iroff2 + integer k + integer last + integer maxerr + integer nev + integer neval + integer nrmax + real(dp) resas1 + real(dp) resas2 + real(dp) result + real(dp) rg(25) + real(dp) rh(25) + real(dp) ri(25) + real(dp) rj(25) + real(dp) rlist(limit) +! +! Test on validity of parameters. +! + ier = 0 + neval = 0 + last = 0 + rlist(1) = 0.0e+00 + elist(1) = 0.0e+00 + iord(1) = 0 + result = 0.0e+00 + abserr = 0.0e+00 + + if ( b <= a .or. & + (epsabs < 0.0e+00 .and. epsrel < 0.0e+00) .or. & + alfa <= (-1.0e+00) .or. & + beta <= (-1.0e+00) .or. & + integr < 1 .or. & + integr > 4 .or. & + limit < 2) then + ier = 6 + return + end if +! +! Compute the modified Chebyshev moments. +! + call qmomo ( alfa, beta, ri, rj, rg, rh, integr ) +! +! Integrate over the intervals (a,(a+b)/2) and ((a+b)/2,b). +! + centre = 5.0e-01 * ( b + a ) + + call qc25s ( f, a, b, a, centre, alfa, beta, ri, rj, rg, rh, area1, & + error1, resas1, integr, nev ) + + neval = nev + + call qc25s ( f, a, b, centre, b, alfa, beta, ri, rj, rg, rh, area2, & + error2, resas2, integr, nev ) + + last = 2 + neval = neval+nev + result = area1+area2 + abserr = error1+error2 +! +! Test on accuracy. +! + errbnd = max ( epsabs, epsrel * abs ( result ) ) +! +! Initialization. +! + if ( error2 <= error1 ) then + alist(1) = a + alist(2) = centre + blist(1) = centre + blist(2) = b + rlist(1) = area1 + rlist(2) = area2 + elist(1) = error1 + elist(2) = error2 + else + alist(1) = centre + alist(2) = a + blist(1) = b + blist(2) = centre + rlist(1) = area2 + rlist(2) = area1 + elist(1) = error2 + elist(2) = error1 + end if + + iord(1) = 1 + iord(2) = 2 + + if ( limit == 2 ) then + ier = 1 + return + end if + + if ( abserr <= errbnd ) then + return + end if + + errmax = elist(1) + maxerr = 1 + nrmax = 1 + area = result + errsum = abserr + iroff1 = 0 + iroff2 = 0 + + do last = 3, limit +! +! Bisect the subinterval with largest error estimate. +! + a1 = alist(maxerr) + b1 = 5.0e-01 * (alist(maxerr)+blist(maxerr)) + a2 = b1 + b2 = blist(maxerr) + + call qc25s ( f, a, b, a1, b1, alfa, beta, ri, rj, rg, rh, area1, & + error1, resas1, integr, nev ) + + neval = neval + nev + + call qc25s ( f, a, b, a2, b2, alfa, beta, ri, rj, rg, rh, area2, & + error2, resas2, integr, nev ) + + neval = neval + nev +! +! Improve previous approximations integral and error and +! test for accuracy. +! + area12 = area1+area2 + erro12 = error1+error2 + errsum = errsum+erro12-errmax + area = area+area12-rlist(maxerr) +! +! Test for roundoff error. +! + if ( a /= a1 .and. b /= b2 ) then + + if ( resas1 /= error1 .and. resas2 /= error2 ) then + + if ( abs(rlist(maxerr)-area12) < 1.0e-05*abs(area12) & + .and.erro12 >= 9.9e-01*errmax) then + iroff1 = iroff1+1 + end if + + if ( last > 10.and.erro12 > errmax ) then + iroff2 = iroff2+1 + end if + + end if + + end if + + rlist(maxerr) = area1 + rlist(last) = area2 +! +! Test on accuracy. +! + errbnd = max ( epsabs, epsrel * abs ( area ) ) + + if ( errsum > errbnd ) then +! +! Set error flag in the case that the number of interval +! bisections exceeds limit. +! + if ( last == limit ) then + ier = 1 + end if +! +! Set error flag in the case of roundoff error. +! + if ( iroff1 >= 6 .or. iroff2 >= 20 ) then + ier = 2 + end if +! +! Set error flag in the case of bad integrand behavior +! at interior points of integration range. +! + if ( max ( abs(a1),abs(b2)) <= (1.0e+00+1.0e+03* epsilon ( a1 ) )* & + (abs(a2)+1.0e+03* tiny ( a2) )) then + ier = 3 + end if + + end if +! +! Append the newly-created intervals to the list. +! + if ( error2 <= error1 ) then + alist(last) = a2 + blist(maxerr) = b1 + blist(last) = b2 + elist(maxerr) = error1 + elist(last) = error2 + else + alist(maxerr) = a2 + alist(last) = a1 + blist(last) = b1 + rlist(maxerr) = area2 + rlist(last) = area1 + elist(maxerr) = error2 + elist(last) = error1 + end if +! +! Call QSORT to maintain the descending ordering +! in the list of error estimates and select the subinterval +! with largest error estimate (to be bisected next). +! + call qsort ( limit, last, maxerr, errmax, elist, iord, nrmax ) + + if (ier /= 0 .or. errsum <= errbnd ) then + exit + end if + + end do +! +! Compute final result. +! + result = sum ( rlist(1:last) ) + + abserr = errsum + + return +end subroutine +subroutine qc25c ( f, a, b, c, result, abserr, krul, neval ) +! +!****************************************************************************** +! +!! QC25C returns integration rules for Cauchy Principal Value integrals. +! +! +! Discussion: +! +! This routine estimates +! I = integral of F(X) * W(X) over (a,b) +! with error estimate, where +! w(x) = 1/(x-c) +! +! Reference: +! +! R Piessens, E de Doncker-Kapenger, C W Ueberhuber, D K Kahaner, +! QUADPACK, a Subroutine Package for Automatic Integration, +! Springer Verlag, 1983 +! +! Parameters: +! +! Input, external real(dp) F, the name of the function routine, of the form +! function f ( x ) +! real(dp) f +! real(dp) x +! which evaluates the integrand function. +! +! Input, real(dp) A, B, the limits of integration. +! +! Input, real(dp) C, the parameter in the weight function. +! +! Output, real(dp) RESULT, the estimated value of the integral. +! RESULT is computed by using a generalized Clenshaw-Curtis method if +! C lies within ten percent of the integration interval. In the +! other case the 15-point Kronrod rule obtained by optimal addition +! of abscissae to the 7-point Gauss rule, is applied. +! +! Output, real(dp) ABSERR, an estimate of || I - RESULT ||. +! +! krul - integer +! key which is decreased by 1 if the 15-point +! Gauss-Kronrod scheme has been used +! +! Output, integer NEVAL, the number of times the integral was evaluated. +! +! Local parameters: +! +! fval - value of the function f at the points +! cos(k*pi/24), k = 0, ..., 24 +! cheb12 - Chebyshev series expansion coefficients, for the +! function f, of degree 12 +! cheb24 - Chebyshev series expansion coefficients, for the +! function f, of degree 24 +! res12 - approximation to the integral corresponding to the +! use of cheb12 +! res24 - approximation to the integral corresponding to the +! use of cheb24 +! qwgtc - external function subprogram defining the weight +! function +! hlgth - half-length of the interval +! centr - mid point of the interval +! + implicit none +! + real(dp) a + real(dp) abserr + real(dp) ak22 + real(dp) amom0 + real(dp) amom1 + real(dp) amom2 + real(dp) b + real(dp) c + real(dp) cc + real(dp) centr + real(dp) cheb12(13) + real(dp) cheb24(25) + real(dp), external :: f + real(dp) fval(25) + real(dp) hlgth + integer i + integer isym + integer k + integer kp + integer krul + integer neval + real(dp) p2 + real(dp) p3 + real(dp) p4 +! real(dp), external :: qwgtc + real(dp) resabs + real(dp) resasc + real(dp) result + real(dp) res12 + real(dp) res24 + real(dp) u + real(dp), parameter, dimension ( 11 ) :: x = (/ & + 9.914448613738104e-01, 9.659258262890683e-01, & + 9.238795325112868e-01, 8.660254037844386e-01, & + 7.933533402912352e-01, 7.071067811865475e-01, & + 6.087614290087206e-01, 5.000000000000000e-01, & + 3.826834323650898e-01, 2.588190451025208e-01, & + 1.305261922200516e-01 /) +! +! Check the position of C. +! + cc = ( 2.0e+00 * c - b - a ) / ( b - a ) +! +! Apply the 15-point Gauss-Kronrod scheme. +! + if ( abs ( cc ) >= 1.1e+00 ) then + krul = krul - 1 + call qk15w ( f, qwgtc, c, p2, p3, p4, kp, a, b, result, abserr, & + resabs, resasc ) + neval = 15 + if ( resasc == abserr ) then + krul = krul+1 + end if + return + end if +! +! Use the generalized Clenshaw-Curtis method. +! + hlgth = 5.0e-01 * ( b - a ) + centr = 5.0e-01 * ( b + a ) + neval = 25 + fval(1) = 5.0e-01 * f(hlgth+centr) + fval(13) = f(centr) + fval(25) = 5.0e-01 * f(centr-hlgth) + + do i = 2, 12 + u = hlgth * x(i-1) + isym = 26 - i + fval(i) = f(u+centr) + fval(isym) = f(centr-u) + end do +! +! Compute the Chebyshev series expansion. +! + call qcheb ( x, fval, cheb12, cheb24 ) +! +! The modified Chebyshev moments are computed by forward +! recursion, using AMOM0 and AMOM1 as starting values. +! + amom0 = log ( abs ( ( 1.0e+00 - cc ) / ( 1.0e+00 + cc ) ) ) + amom1 = 2.0e+00 + cc * amom0 + res12 = cheb12(1) * amom0 + cheb12(2) * amom1 + res24 = cheb24(1) * amom0 + cheb24(2) * amom1 + + do k = 3, 13 + amom2 = 2.0e+00 * cc * amom1 - amom0 + ak22 = ( k - 2 ) * ( k - 2 ) + if ( ( k / 2 ) * 2 == k ) then + amom2 = amom2 - 4.0e+00 / ( ak22 - 1.0e+00 ) + end if + res12 = res12 + cheb12(k) * amom2 + res24 = res24 + cheb24(k) * amom2 + amom0 = amom1 + amom1 = amom2 + end do + + do k = 14, 25 + amom2 = 2.0e+00 * cc * amom1 - amom0 + ak22 = ( k - 2 ) * ( k - 2 ) + if ( ( k / 2 ) * 2 == k ) then + amom2 = amom2 - 4.0e+00 / ( ak22 - 1.0e+00 ) + end if + res24 = res24 + cheb24(k) * amom2 + amom0 = amom1 + amom1 = amom2 + end do + + result = res24 + abserr = abs ( res24 - res12 ) + + return +end subroutine +subroutine qc25o ( f, a, b, omega, integr, nrmom, maxp1, ksave, result, & + abserr, neval, resabs, resasc, momcom, chebmo ) +! +!****************************************************************************** +! +!! QC25O returns integration rules for integrands with a COS or SIN factor. +! +! +! Discussion: +! +! This routine estimates the integral +! I = integral of f(x) * w(x) over (a,b) +! where +! w(x) = cos(omega*x) +! or +! w(x) = sin(omega*x), +! and estimates +! J = integral ( A <= X <= B ) |F(X)| dx. +! +! For small values of OMEGA or small intervals (a,b) the 15-point +! Gauss-Kronrod rule is used. In all other cases a generalized +! Clenshaw-Curtis method is used, that is, a truncated Chebyshev +! expansion of the function F is computed on (a,b), so that the +! integrand can be written as a sum of terms of the form W(X)*T(K,X), +! where T(K,X) is the Chebyshev polynomial of degree K. The Chebyshev +! moments are computed with use of a linear recurrence relation. +! +! Reference: +! +! R Piessens, E de Doncker-Kapenger, C W Ueberhuber, D K Kahaner, +! QUADPACK, a Subroutine Package for Automatic Integration, +! Springer Verlag, 1983 +! +! Parameters: +! +! Input, external real(dp) F, the name of the function routine, of the form +! function f ( x ) +! real(dp) f +! real(dp) x +! which evaluates the integrand function. +! +! Input, real(dp) A, B, the limits of integration. +! +! Input, real(dp) OMEGA, the parameter in the weight function. +! +! Input, integer INTEGR, indicates which weight function is to be used +! = 1, w(x) = cos(omega*x) +! = 2, w(x) = sin(omega*x) +! +! ?, integer NRMOM, the length of interval (a,b) is equal to the length +! of the original integration interval divided by +! 2**nrmom (we suppose that the routine is used in an +! adaptive integration process, otherwise set +! nrmom = 0). nrmom must be zero at the first call. +! +! maxp1 - integer +! gives an upper bound on the number of Chebyshev +! moments which can be stored, i.e. for the intervals +! of lengths abs(bb-aa)*2**(-l), l = 0,1,2, ..., +! maxp1-2. +! +! ksave - integer +! key which is one when the moments for the +! current interval have been computed +! +! Output, real(dp) RESULT, the estimated value of the integral. +! +! abserr - real(dp) +! estimate of the modulus of the absolute +! error, which should equal or exceed abs(i-result) +! +! Output, integer NEVAL, the number of times the integral was evaluated. +! +! Output, real(dp) RESABS, approximation to the integral J. +! +! Output, real(dp) RESASC, approximation to the integral of abs(F-I/(B-A)). +! +! on entry and return +! momcom - integer +! for each interval length we need to compute +! the Chebyshev moments. momcom counts the number +! of intervals for which these moments have already +! been computed. if nrmom < momcom or ksave = 1, +! the Chebyshev moments for the interval (a,b) +! have already been computed and stored, otherwise +! we compute them and we increase momcom. +! +! chebmo - real(dp) +! array of dimension at least (maxp1,25) containing +! the modified Chebyshev moments for the first momcom +! interval lengths +! +! Local parameters: +! +! maxp1 gives an upper bound +! on the number of Chebyshev moments which can be +! computed, i.e. for the interval (bb-aa), ..., +! (bb-aa)/2**(maxp1-2). +! should this number be altered, the first dimension of +! chebmo needs to be adapted. +! +! x contains the values cos(k*pi/24) +! k = 1, ...,11, to be used for the Chebyshev expansion of f +! +! centr - mid point of the integration interval +! hlgth - half length of the integration interval +! fval - value of the function f at the points +! (b-a)*0.5*cos(k*pi/12) + (b+a)*0.5 +! k = 0, ...,24 +! cheb12 - coefficients of the Chebyshev series expansion +! of degree 12, for the function f, in the +! interval (a,b) +! cheb24 - coefficients of the Chebyshev series expansion +! of degree 24, for the function f, in the +! interval (a,b) +! resc12 - approximation to the integral of +! cos(0.5*(b-a)*omega*x)*f(0.5*(b-a)*x+0.5*(b+a)) +! over (-1,+1), using the Chebyshev series +! expansion of degree 12 +! resc24 - approximation to the same integral, using the +! Chebyshev series expansion of degree 24 +! ress12 - the analogue of resc12 for the sine +! ress24 - the analogue of resc24 for the sine +! + implicit none +! + integer maxp1 +! + real(dp) a + real(dp) abserr + real(dp) ac + real(dp) an + real(dp) an2 + real(dp) as + real(dp) asap + real(dp) ass + real(dp) b + real(dp) centr + real(dp) chebmo(maxp1,25) + real(dp) cheb12(13) + real(dp) cheb24(25) + real(dp) conc + real(dp) cons + real(dp) cospar + real(dp) d(28) + real(dp) d1(28) + real(dp) d2(28) + real(dp) d3(28) + real(dp) estc + real(dp) ests + real(dp), external :: f + real(dp) fval(25) + real(dp) hlgth + integer i + integer integr + integer isym + integer j + integer k + integer ksave + integer m + integer momcom + integer neval + integer, parameter :: nmac = 28 + integer noeq1 + integer noequ + integer nrmom + real(dp) omega + real(dp) parint + real(dp) par2 + real(dp) par22 + real(dp) p2 + real(dp) p3 + real(dp) p4 +! real(dp), external :: qwgto + real(dp) resabs + real(dp) resasc + real(dp) resc12 + real(dp) resc24 + real(dp) ress12 + real(dp) ress24 + real(dp) result + real(dp) sinpar + real(dp) v(28) + real(dp), dimension ( 11 ) :: x = (/ & + 9.914448613738104e-01, 9.659258262890683e-01, & + 9.238795325112868e-01, 8.660254037844386e-01, & + 7.933533402912352e-01, 7.071067811865475e-01, & + 6.087614290087206e-01, 5.000000000000000e-01, & + 3.826834323650898e-01, 2.588190451025208e-01, & + 1.305261922200516e-01 /) +! + centr = 5.0e-01*(b+a) + hlgth = 5.0e-01*(b-a) + parint = omega * hlgth +! +! Compute the integral using the 15-point Gauss-Kronrod +! formula if the value of the parameter in the integrand +! is small or if the length of the integration interval +! is less than (bb-aa)/2**(maxp1-2), where (aa,bb) is the +! original integration interval. +! + if ( abs ( parint ) <= 2.0e+00 ) then + + call qk15w ( f, qwgto, omega, p2, p3, p4, integr, a, b, result, & + abserr, resabs, resasc ) + + neval = 15 + return + + end if +! +! Compute the integral using the generalized clenshaw-curtis method. +! + conc = hlgth * cos(centr*omega) + cons = hlgth * sin(centr*omega) + resasc = huge ( resasc ) + neval = 25 +! +! Check whether the Chebyshev moments for this interval +! have already been computed. +! + if ( nrmom < momcom .or. ksave == 1 ) go to 140 +! +! Compute a new set of Chebyshev moments. +! + m = momcom+1 + par2 = parint*parint + par22 = par2+2.0e+00 + sinpar = sin(parint) + cospar = cos(parint) +! +! Compute the Chebyshev moments with respect to cosine. +! + v(1) = 2.0e+00*sinpar/parint + v(2) = (8.0e+00*cospar+(par2+par2-8.0e+00)*sinpar/ parint)/par2 + v(3) = (3.2e+01*(par2-1.2e+01)*cospar+(2.0e+00* & + ((par2-8.0e+01)*par2+1.92e+02)*sinpar)/ & + parint)/(par2*par2) + ac = 8.0e+00*cospar + as = 2.4e+01*parint*sinpar + + if ( abs ( parint ) > 2.4e+01 ) then + go to 70 + end if +! +! Compute the Chebyshev moments as the solutions of a boundary value +! problem with one initial value (v(3)) and one end value computed +! using an asymptotic formula. +! + noequ = nmac-3 + noeq1 = noequ-1 + an = 6.0e+00 + + do k = 1, noeq1 + an2 = an*an + d(k) = -2.0e+00*(an2-4.0e+00)*(par22-an2-an2) + d2(k) = (an-1.0e+00)*(an-2.0e+00)*par2 + d1(k) = (an+3.0e+00)*(an+4.0e+00)*par2 + v(k+3) = as-(an2-4.0e+00)*ac + an = an+2.0e+00 + end do + + an2 = an*an + d(noequ) = -2.0e+00*(an2-4.0e+00)*(par22-an2-an2) + v(noequ+3) = as-(an2-4.0e+00)*ac + v(4) = v(4)-5.6e+01*par2*v(3) + ass = parint*sinpar + asap = (((((2.10e+02*par2-1.0e+00)*cospar-(1.05e+02*par2 & + -6.3e+01)*ass)/an2-(1.0e+00-1.5e+01*par2)*cospar & + +1.5e+01*ass)/an2-cospar+3.0e+00*ass)/an2-cospar)/an2 + v(noequ+3) = v(noequ+3)-2.0e+00*asap*par2*(an-1.0e+00)* & + (an-2.0e+00) +! +! Solve the tridiagonal system by means of Gaussian +! elimination with partial pivoting. +! + d3(1:noequ) = 0.0e+00 + + d2(noequ) = 0.0e+00 + + do i = 1, noeq1 + + if ( abs(d1(i)) > abs(d(i)) ) then + an = d1(i) + d1(i) = d(i) + d(i) = an + an = d2(i) + d2(i) = d(i+1) + d(i+1) = an + d3(i) = d2(i+1) + d2(i+1) = 0.0e+00 + an = v(i+4) + v(i+4) = v(i+3) + v(i+3) = an + end if + + d(i+1) = d(i+1)-d2(i)*d1(i)/d(i) + d2(i+1) = d2(i+1)-d3(i)*d1(i)/d(i) + v(i+4) = v(i+4)-v(i+3)*d1(i)/d(i) + + end do + + v(noequ+3) = v(noequ+3)/d(noequ) + v(noequ+2) = (v(noequ+2)-d2(noeq1)*v(noequ+3))/d(noeq1) + + do i = 2, noeq1 + k = noequ-i + v(k+3) = (v(k+3)-d3(k)*v(k+5)-d2(k)*v(k+4))/d(k) + end do + + go to 90 +! +! Compute the Chebyshev moments by means of forward recursion +! +70 continue + + an = 4.0e+00 + + do i = 4, 13 + an2 = an*an + v(i) = ((an2-4.0e+00)*(2.0e+00*(par22-an2-an2)*v(i-1)-ac) & + +as-par2*(an+1.0e+00)*(an+2.0e+00)*v(i-2))/ & + (par2*(an-1.0e+00)*(an-2.0e+00)) + an = an+2.0e+00 + end do + +90 continue + + do j = 1, 13 + chebmo(m,2*j-1) = v(j) + end do +! +! Compute the Chebyshev moments with respect to sine. +! + v(1) = 2.0e+00*(sinpar-parint*cospar)/par2 + v(2) = (1.8e+01-4.8e+01/par2)*sinpar/par2 & + +(-2.0e+00+4.8e+01/par2)*cospar/parint + ac = -2.4e+01*parint*cospar + as = -8.0e+00*sinpar + chebmo(m,2) = v(1) + chebmo(m,4) = v(2) + + if ( abs(parint) <= 2.4e+01 ) then + + do k = 3, 12 + an = k + chebmo(m,2*k) = -sinpar/(an*(2.0e+00*an-2.0e+00)) & + -2.5e-01*parint*(v(k+1)/an-v(k)/(an-1.0e+00)) + end do +! +! Compute the Chebyshev moments by means of forward recursion. +! + else + + an = 3.0e+00 + + do i = 3, 12 + an2 = an*an + v(i) = ((an2-4.0e+00)*(2.0e+00*(par22-an2-an2)*v(i-1)+as) & + +ac-par2*(an+1.0e+00)*(an+2.0e+00)*v(i-2)) & + /(par2*(an-1.0e+00)*(an-2.0e+00)) + an = an+2.0e+00 + chebmo(m,2*i) = v(i) + end do + + end if + +140 continue + + if ( nrmom < momcom ) then + m = nrmom + 1 + end if + + if ( momcom < maxp1 - 1 .and. nrmom >= momcom ) then + momcom = momcom + 1 + end if +! +! Compute the coefficients of the Chebyshev expansions +! of degrees 12 and 24 of the function F. +! + fval(1) = 5.0e-01*f(centr+hlgth) + fval(13) = f(centr) + fval(25) = 5.0e-01*f(centr-hlgth) + + do i = 2, 12 + isym = 26-i + fval(i) = f(hlgth*x(i-1)+centr) + fval(isym) = f(centr-hlgth*x(i-1)) + end do + + call qcheb ( x, fval, cheb12, cheb24 ) +! +! Compute the integral and error estimates. +! + resc12 = cheb12(13) * chebmo(m,13) + ress12 = 0.0e+00 + estc = abs ( cheb24(25)*chebmo(m,25))+abs((cheb12(13)- & + cheb24(13))*chebmo(m,13) ) + ests = 0.0e+00 + k = 11 + + do j = 1, 6 + resc12 = resc12+cheb12(k)*chebmo(m,k) + ress12 = ress12+cheb12(k+1)*chebmo(m,k+1) + estc = estc+abs((cheb12(k)-cheb24(k))*chebmo(m,k)) + ests = ests+abs((cheb12(k+1)-cheb24(k+1))*chebmo(m,k+1)) + k = k-2 + end do + + resc24 = cheb24(25)*chebmo(m,25) + ress24 = 0.0e+00 + resabs = abs(cheb24(25)) + k = 23 + + do j = 1, 12 + + resc24 = resc24+cheb24(k)*chebmo(m,k) + ress24 = ress24+cheb24(k+1)*chebmo(m,k+1) + resabs = resabs+abs(cheb24(k))+abs(cheb24(k+1)) + + if ( j <= 5 ) then + estc = estc+abs(cheb24(k)*chebmo(m,k)) + ests = ests+abs(cheb24(k+1)*chebmo(m,k+1)) + end if + + k = k-2 + + end do + + resabs = resabs * abs ( hlgth ) + + if ( integr == 1 ) then + result = conc * resc24-cons*ress24 + abserr = abs ( conc * estc ) + abs ( cons * ests ) + else + result = conc*ress24+cons*resc24 + abserr = abs(conc*ests)+abs(cons*estc) + end if + + return +end subroutine +subroutine qc25s ( f, a, b, bl, br, alfa, beta, ri, rj, rg, rh, result, & + abserr, resasc, integr, neval ) +! +!****************************************************************************** +! +!! QC25S returns rules for algebraico-logarithmic end point singularities. +! +! +! Discussion: +! +! This routine computes +! i = integral of F(X) * W(X) over (bl,br), +! with error estimate, where the weight function W(X) has a singular +! behavior of algebraico-logarithmic type at the points +! a and/or b. +! +! The interval (bl,br) is a subinterval of (a,b). +! +! Reference: +! +! R Piessens, E de Doncker-Kapenger, C W Ueberhuber, D K Kahaner, +! QUADPACK, a Subroutine Package for Automatic Integration, +! Springer Verlag, 1983 +! +! Parameters: +! +! Input, external real(dp) F, the name of the function routine, of the form +! function f ( x ) +! real(dp) f +! real(dp) x +! which evaluates the integrand function. +! +! Input, real(dp) A, B, the limits of integration. +! +! Input, real(dp) BL, BR, the lower and upper limits of integration. +! A <= BL < BR <= B. +! +! Input, real(dp) ALFA, BETA, parameters in the weight function. +! +! Input, real(dp) RI(25), RJ(25), RG(25), RH(25), modified Chebyshev moments +! for the application of the generalized Clenshaw-Curtis method, +! computed in QMOMO. +! +! Output, real(dp) RESULT, the estimated value of the integral, computed by +! using a generalized clenshaw-curtis method if b1 = a or br = b. +! In all other cases the 15-point Kronrod rule is applied, obtained by +! optimal addition of abscissae to the 7-point Gauss rule. +! +! Output, real(dp) ABSERR, an estimate of || I - RESULT ||. +! +! Output, real(dp) RESASC, approximation to the integral of abs(F*W-I/(B-A)). +! +! Input, integer INTEGR, determines the weight function +! 1, w(x) = (x-a)**alfa*(b-x)**beta +! 2, w(x) = (x-a)**alfa*(b-x)**beta*log(x-a) +! 3, w(x) = (x-a)**alfa*(b-x)**beta*log(b-x) +! 4, w(x) = (x-a)**alfa*(b-x)**beta*log(x-a)*log(b-x) +! +! Output, integer NEVAL, the number of times the integral was evaluated. +! +! Local Parameters: +! +! fval - value of the function f at the points +! (br-bl)*0.5*cos(k*pi/24)+(br+bl)*0.5 +! k = 0, ..., 24 +! cheb12 - coefficients of the Chebyshev series expansion +! of degree 12, for the function f, in the interval +! (bl,br) +! cheb24 - coefficients of the Chebyshev series expansion +! of degree 24, for the function f, in the interval +! (bl,br) +! res12 - approximation to the integral obtained from cheb12 +! res24 - approximation to the integral obtained from cheb24 +! qwgts - external function subprogram defining the four +! possible weight functions +! hlgth - half-length of the interval (bl,br) +! centr - mid point of the interval (bl,br) +! +! the vector x contains the values cos(k*pi/24) +! k = 1, ..., 11, to be used for the computation of the +! Chebyshev series expansion of f. +! + implicit none +! + real(dp) a + real(dp) abserr + real(dp) alfa + real(dp) b + real(dp) beta + real(dp) bl + real(dp) br + real(dp) centr + real(dp) cheb12(13) + real(dp) cheb24(25) + real(dp) dc + real(dp), external :: f + real(dp) factor + real(dp) fix + real(dp) fval(25) + real(dp) hlgth + integer i + integer integr + integer isym + integer neval +! real(dp), external :: qwgts + real(dp) resabs + real(dp) resasc + real(dp) result + real(dp) res12 + real(dp) res24 + real(dp) rg(25) + real(dp) rh(25) + real(dp) ri(25) + real(dp) rj(25) + real(dp) u + real(dp), dimension ( 11 ) :: x = (/ & + 9.914448613738104e-01, 9.659258262890683e-01, & + 9.238795325112868e-01, 8.660254037844386e-01, & + 7.933533402912352e-01, 7.071067811865475e-01, & + 6.087614290087206e-01, 5.000000000000000e-01, & + 3.826834323650898e-01, 2.588190451025208e-01, & + 1.305261922200516e-01 /) +! + neval = 25 + + if ( bl == a .and. (alfa /= 0.0e+00 .or. integr == 2 .or. integr == 4)) & + go to 10 + + if ( br == b .and. (beta /= 0.0e+00 .or. integr == 3 .or. integr == 4)) & + go to 140 +! +! If a > bl and b < br, apply the 15-point Gauss-Kronrod scheme. +! + call qk15w ( f, qwgts, a, b, alfa, beta, integr, bl, br, result, abserr, & + resabs, resasc ) + + neval = 15 + return +! +! This part of the program is executed only if a = bl. +! +! Compute the Chebyshev series expansion of the function +! f1 = (0.5*(b+b-br-a)-0.5*(br-a)*x)**beta*f(0.5*(br-a)*x+0.5*(br+a)) +! +10 continue + + hlgth = 5.0e-01*(br-bl) + centr = 5.0e-01*(br+bl) + fix = b-centr + fval(1) = 5.0e-01*f(hlgth+centr)*(fix-hlgth)**beta + fval(13) = f(centr)*(fix**beta) + fval(25) = 5.0e-01*f(centr-hlgth)*(fix+hlgth)**beta + + do i = 2, 12 + u = hlgth*x(i-1) + isym = 26-i + fval(i) = f(u+centr)*(fix-u)**beta + fval(isym) = f(centr-u)*(fix+u)**beta + end do + + factor = hlgth**(alfa+1.0e+00) + result = 0.0e+00 + abserr = 0.0e+00 + res12 = 0.0e+00 + res24 = 0.0e+00 + + if ( integr > 2 ) go to 70 + + call qcheb ( x, fval, cheb12, cheb24 ) +! +! integr = 1 (or 2) +! + do i = 1, 13 + res12 = res12+cheb12(i)*ri(i) + res24 = res24+cheb24(i)*ri(i) + end do + + do i = 14, 25 + res24 = res24 + cheb24(i) * ri(i) + end do + + if ( integr == 1 ) go to 130 +! +! integr = 2 +! + dc = log ( br - bl ) + result = res24 * dc + abserr = abs((res24-res12)*dc) + res12 = 0.0e+00 + res24 = 0.0e+00 + + do i = 1, 13 + res12 = res12+cheb12(i)*rg(i) + res24 = res24+cheb24(i)*rg(i) + end do + + do i = 14, 25 + res24 = res24+cheb24(i)*rg(i) + end do + + go to 130 +! +! Compute the Chebyshev series expansion of the function +! F4 = f1*log(0.5*(b+b-br-a)-0.5*(br-a)*x) +! +70 continue + + fval(1) = fval(1) * log ( fix - hlgth ) + fval(13) = fval(13) * log ( fix ) + fval(25) = fval(25) * log ( fix + hlgth ) + + do i = 2, 12 + u = hlgth*x(i-1) + isym = 26-i + fval(i) = fval(i) * log ( fix - u ) + fval(isym) = fval(isym) * log ( fix + u ) + end do + + call qcheb ( x, fval, cheb12, cheb24 ) +! +! integr = 3 (or 4) +! + do i = 1, 13 + res12 = res12+cheb12(i)*ri(i) + res24 = res24+cheb24(i)*ri(i) + end do + + do i = 14, 25 + res24 = res24+cheb24(i)*ri(i) + end do + + if ( integr == 3 ) go to 130 +! +! integr = 4 +! + dc = log ( br - bl ) + result = res24*dc + abserr = abs((res24-res12)*dc) + res12 = 0.0e+00 + res24 = 0.0e+00 + + do i = 1, 13 + res12 = res12+cheb12(i)*rg(i) + res24 = res24+cheb24(i)*rg(i) + end do + + do i = 14, 25 + res24 = res24+cheb24(i)*rg(i) + end do + +130 continue + + result = (result+res24)*factor + abserr = (abserr+abs(res24-res12))*factor + go to 270 +! +! This part of the program is executed only if b = br. +! +! Compute the Chebyshev series expansion of the function +! f2 = (0.5*(b+bl-a-a)+0.5*(b-bl)*x)**alfa*f(0.5*(b-bl)*x+0.5*(b+bl)) +! +140 continue + + hlgth = 5.0e-01*(br-bl) + centr = 5.0e-01*(br+bl) + fix = centr-a + fval(1) = 5.0e-01*f(hlgth+centr)*(fix+hlgth)**alfa + fval(13) = f(centr)*(fix**alfa) + fval(25) = 5.0e-01*f(centr-hlgth)*(fix-hlgth)**alfa + + do i = 2, 12 + u = hlgth*x(i-1) + isym = 26-i + fval(i) = f(u+centr)*(fix+u)**alfa + fval(isym) = f(centr-u)*(fix-u)**alfa + end do + + factor = hlgth**(beta+1.0e+00) + result = 0.0e+00 + abserr = 0.0e+00 + res12 = 0.0e+00 + res24 = 0.0e+00 + + if ( integr == 2 .or. integr == 4 ) go to 200 +! +! integr = 1 (or 3) +! + call qcheb ( x, fval, cheb12, cheb24 ) + + do i = 1, 13 + res12 = res12+cheb12(i)*rj(i) + res24 = res24+cheb24(i)*rj(i) + end do + + do i = 14, 25 + res24 = res24+cheb24(i)*rj(i) + end do + + if ( integr == 1 ) go to 260 +! +! integr = 3 +! + dc = log ( br - bl ) + result = res24*dc + abserr = abs((res24-res12)*dc) + res12 = 0.0e+00 + res24 = 0.0e+00 + + do i = 1, 13 + res12 = res12+cheb12(i)*rh(i) + res24 = res24+cheb24(i)*rh(i) + end do + + do i = 14, 25 + res24 = res24+cheb24(i)*rh(i) + end do + + go to 260 +! +! Compute the Chebyshev series expansion of the function +! f3 = f2*log(0.5*(b-bl)*x+0.5*(b+bl-a-a)) +! +200 continue + + fval(1) = fval(1) * log ( hlgth + fix ) + fval(13) = fval(13) * log ( fix ) + fval(25) = fval(25) * log ( fix - hlgth ) + + do i = 2, 12 + u = hlgth*x(i-1) + isym = 26-i + fval(i) = fval(i) * log(u+fix) + fval(isym) = fval(isym) * log(fix-u) + end do + + call qcheb ( x, fval, cheb12, cheb24 ) +! +! integr = 2 (or 4) +! + do i = 1, 13 + res12 = res12+cheb12(i)*rj(i) + res24 = res24+cheb24(i)*rj(i) + end do + + do i = 14, 25 + res24 = res24+cheb24(i)*rj(i) + end do + + if ( integr == 2 ) go to 260 + + dc = log(br-bl) + result = res24*dc + abserr = abs((res24-res12)*dc) + res12 = 0.0e+00 + res24 = 0.0e+00 +! +! integr = 4 +! + do i = 1, 13 + res12 = res12+cheb12(i)*rh(i) + res24 = res24+cheb24(i)*rh(i) + end do + + do i = 14, 25 + res24 = res24+cheb24(i)*rh(i) + end do + +260 continue + + result = (result+res24)*factor + abserr = (abserr+abs(res24-res12))*factor + +270 continue + + return +end subroutine +subroutine qcheb ( x, fval, cheb12, cheb24 ) +! +!****************************************************************************** +! +!! QCHEB computes the Chebyshev series expansion. +! +! +! Discussion: +! +! This routine computes the Chebyshev series expansion +! of degrees 12 and 24 of a function using a fast Fourier transform method +! +! f(x) = sum(k=1, ...,13) (cheb12(k)*t(k-1,x)), +! f(x) = sum(k=1, ...,25) (cheb24(k)*t(k-1,x)), +! +! where T(K,X) is the Chebyshev polynomial of degree K. +! +! Reference: +! +! R Piessens, E de Doncker-Kapenger, C W Ueberhuber, D K Kahaner, +! QUADPACK, a Subroutine Package for Automatic Integration, +! Springer Verlag, 1983 +! +! Parameters: +! +! Input, real(dp) X(11), contains the values of COS(K*PI/24), for K = 1 to 11. +! +! Input/output, real(dp) FVAL(25), the function values at the points +! (b+a+(b-a)*cos(k*pi/24))/2, k = 0, ...,24, where (a,b) is the +! approximation interval. FVAL(1) and FVAL(25) are divided by two +! These values are destroyed at output. +! +! on return +! cheb12 - real(dp) +! vector of dimension 13 containing the Chebyshev +! coefficients for degree 12 +! +! cheb24 - real(dp) +! vector of dimension 25 containing the Chebyshev +! coefficients for degree 24 +! + implicit none +! + real(dp) alam + real(dp) alam1 + real(dp) alam2 + real(dp) cheb12(13) + real(dp) cheb24(25) + real(dp) fval(25) + integer i + integer j + real(dp) part1 + real(dp) part2 + real(dp) part3 + real(dp) v(12) + real(dp) x(11) +! + do i = 1, 12 + j = 26-i + v(i) = fval(i)-fval(j) + fval(i) = fval(i)+fval(j) + end do + + alam1 = v(1)-v(9) + alam2 = x(6)*(v(3)-v(7)-v(11)) + cheb12(4) = alam1+alam2 + cheb12(10) = alam1-alam2 + alam1 = v(2)-v(8)-v(10) + alam2 = v(4)-v(6)-v(12) + alam = x(3)*alam1+x(9)*alam2 + cheb24(4) = cheb12(4)+alam + cheb24(22) = cheb12(4)-alam + alam = x(9)*alam1-x(3)*alam2 + cheb24(10) = cheb12(10)+alam + cheb24(16) = cheb12(10)-alam + part1 = x(4)*v(5) + part2 = x(8)*v(9) + part3 = x(6)*v(7) + alam1 = v(1)+part1+part2 + alam2 = x(2)*v(3)+part3+x(10)*v(11) + cheb12(2) = alam1+alam2 + cheb12(12) = alam1-alam2 + alam = x(1)*v(2)+x(3)*v(4)+x(5)*v(6)+x(7)*v(8) & + +x(9)*v(10)+x(11)*v(12) + cheb24(2) = cheb12(2)+alam + cheb24(24) = cheb12(2)-alam + alam = x(11)*v(2)-x(9)*v(4)+x(7)*v(6)-x(5)*v(8) & + +x(3)*v(10)-x(1)*v(12) + cheb24(12) = cheb12(12)+alam + cheb24(14) = cheb12(12)-alam + alam1 = v(1)-part1+part2 + alam2 = x(10)*v(3)-part3+x(2)*v(11) + cheb12(6) = alam1+alam2 + cheb12(8) = alam1-alam2 + alam = x(5)*v(2)-x(9)*v(4)-x(1)*v(6) & + -x(11)*v(8)+x(3)*v(10)+x(7)*v(12) + cheb24(6) = cheb12(6)+alam + cheb24(20) = cheb12(6)-alam + alam = x(7)*v(2)-x(3)*v(4)-x(11)*v(6)+x(1)*v(8) & + -x(9)*v(10)-x(5)*v(12) + cheb24(8) = cheb12(8)+alam + cheb24(18) = cheb12(8)-alam + + do i = 1, 6 + j = 14-i + v(i) = fval(i)-fval(j) + fval(i) = fval(i)+fval(j) + end do + + alam1 = v(1)+x(8)*v(5) + alam2 = x(4)*v(3) + cheb12(3) = alam1+alam2 + cheb12(11) = alam1-alam2 + cheb12(7) = v(1)-v(5) + alam = x(2)*v(2)+x(6)*v(4)+x(10)*v(6) + cheb24(3) = cheb12(3)+alam + cheb24(23) = cheb12(3)-alam + alam = x(6)*(v(2)-v(4)-v(6)) + cheb24(7) = cheb12(7)+alam + cheb24(19) = cheb12(7)-alam + alam = x(10)*v(2)-x(6)*v(4)+x(2)*v(6) + cheb24(11) = cheb12(11)+alam + cheb24(15) = cheb12(11)-alam + + do i = 1, 3 + j = 8-i + v(i) = fval(i)-fval(j) + fval(i) = fval(i)+fval(j) + end do + + cheb12(5) = v(1)+x(8)*v(3) + cheb12(9) = fval(1)-x(8)*fval(3) + alam = x(4)*v(2) + cheb24(5) = cheb12(5)+alam + cheb24(21) = cheb12(5)-alam + alam = x(8)*fval(2)-fval(4) + cheb24(9) = cheb12(9)+alam + cheb24(17) = cheb12(9)-alam + cheb12(1) = fval(1)+fval(3) + alam = fval(2)+fval(4) + cheb24(1) = cheb12(1)+alam + cheb24(25) = cheb12(1)-alam + cheb12(13) = v(1)-v(3) + cheb24(13) = cheb12(13) + alam = 1.0e+00/6.0e+00 + + do i = 2, 12 + cheb12(i) = cheb12(i)*alam + end do + + alam = 5.0e-01*alam + cheb12(1) = cheb12(1)*alam + cheb12(13) = cheb12(13)*alam + + do i = 2, 24 + cheb24(i) = cheb24(i)*alam + end do + + cheb24(1) = 0.5E+00 * alam*cheb24(1) + cheb24(25) = 0.5E+00 * alam*cheb24(25) + + return +end subroutine +subroutine qextr ( n, epstab, result, abserr, res3la, nres ) +! +!****************************************************************************** +! +!! QEXTR carries out the Epsilon extrapolation algorithm. +! +! +! Discussion: +! +! The routine determines the limit of a given sequence of approximations, +! by means of the epsilon algorithm of P. Wynn. An estimate of the +! absolute error is also given. The condensed epsilon table is computed. +! Only those elements needed for the computation of the next diagonal +! are preserved. +! +! Reference: +! +! R Piessens, E de Doncker-Kapenger, C W Ueberhuber, D K Kahaner, +! QUADPACK, a Subroutine Package for Automatic Integration, +! Springer Verlag, 1983 +! +! Parameters: +! +! Input, integer N, indicates the entry of EPSTAB which contains +! the new element in the first column of the epsilon table. +! +! Input/output, real(dp) EPSTAB(52), the two lower diagonals of the triangular +! epsilon table. The elements are numbered starting at the right-hand +! corner of the triangle. +! +! Output, real(dp) RESULT, the estimated value of the integral. +! +! Output, real(dp) ABSERR, estimate of the absolute error computed from +! RESULT and the 3 previous results. +! +! ?, real(dp) RES3LA(3), the last 3 results. +! +! Input/output, integer NRES, the number of calls to the routine. This +! should be zero on the first call, and is automatically updated +! before return. +! +! Local Parameters: +! +! e0 - the 4 elements on which the +! e1 computation of a new element in +! e2 the epsilon table is based +! e3 e0 +! e3 e1 new +! e2 +! newelm - number of elements to be computed in the new +! diagonal +! error - error = abs(e1-e0)+abs(e2-e1)+abs(new-e2) +! result - the element in the new diagonal with least value +! of error +! limexp is the maximum number of elements the epsilon table +! can contain. if this number is reached, the upper diagonal +! of the epsilon table is deleted. +! + implicit none +! + real(dp) abserr + real(dp) delta1 + real(dp) delta2 + real(dp) delta3 + real(dp) epsinf + real(dp) epstab(52) + real(dp) error + real(dp) err1 + real(dp) err2 + real(dp) err3 + real(dp) e0 + real(dp) e1 + real(dp) e1abs + real(dp) e2 + real(dp) e3 + integer i + integer ib + integer ib2 + integer ie + integer indx + integer k1 + integer k2 + integer k3 + integer limexp + integer n + integer newelm + integer nres + integer num + real(dp) res + real(dp) result + real(dp) res3la(3) + real(dp) ss + real(dp) tol1 + real(dp) tol2 + real(dp) tol3 +! + nres = nres+1 + abserr = huge ( abserr ) + result = epstab(n) + + if ( n < 3 ) go to 100 + limexp = 50 + epstab(n+2) = epstab(n) + newelm = (n-1)/2 + epstab(n) = huge ( epstab(n) ) + num = n + k1 = n + + do i = 1, newelm + + k2 = k1-1 + k3 = k1-2 + res = epstab(k1+2) + e0 = epstab(k3) + e1 = epstab(k2) + e2 = res + e1abs = abs(e1) + delta2 = e2-e1 + err2 = abs(delta2) + tol2 = max ( abs(e2),e1abs)* epsilon ( e2 ) + delta3 = e1-e0 + err3 = abs(delta3) + tol3 = max ( e1abs,abs(e0))* epsilon ( e0 ) +! +! If e0, e1 and e2 are equal to within machine accuracy, convergence +! is assumed. +! + if ( err2 <= tol2 .and. err3 <= tol3 ) then + result = res + abserr = err2+err3 + go to 100 + end if + + e3 = epstab(k1) + epstab(k1) = e1 + delta1 = e1-e3 + err1 = abs(delta1) + tol1 = max ( e1abs,abs(e3))* epsilon ( e3 ) +! +! If two elements are very close to each other, omit a part +! of the table by adjusting the value of N. +! + if ( err1 <= tol1 .or. err2 <= tol2 .or. err3 <= tol3 ) go to 20 + + ss = 1.0e+00/delta1+1.0e+00/delta2-1.0e+00/delta3 + epsinf = abs ( ss*e1 ) +! +! Test to detect irregular behavior in the table, and +! eventually omit a part of the table adjusting the value of N. +! + if ( epsinf > 1.0e-04 ) go to 30 + +20 continue + + n = i+i-1 + exit +! +! Compute a new element and eventually adjust the value of RESULT. +! +30 continue + + res = e1+1.0e+00/ss + epstab(k1) = res + k1 = k1-2 + error = err2+abs(res-e2)+err3 + + if ( error <= abserr ) then + abserr = error + result = res + end if + + end do +! +! Shift the table. +! + if ( n == limexp ) then + n = 2*(limexp/2)-1 + end if + + if ( (num/2)*2 == num ) then + ib = 2 + else + ib = 1 + end if + + ie = newelm+1 + + do i = 1, ie + ib2 = ib+2 + epstab(ib) = epstab(ib2) + ib = ib2 + end do + + if ( num /= n ) then + + indx = num-n+1 + + do i = 1, n + epstab(i)= epstab(indx) + indx = indx+1 + end do + + end if + + if ( nres < 4 ) then + res3la(nres) = result + abserr = huge ( abserr ) + else + abserr = abs(result-res3la(3))+abs(result-res3la(2)) & + +abs(result-res3la(1)) + res3la(1) = res3la(2) + res3la(2) = res3la(3) + res3la(3) = result + end if + +100 continue + + abserr = max ( abserr,0.5e+00* epsilon ( result ) *abs(result)) + + return +end subroutine +subroutine qfour ( f, a, b, omega, integr, epsabs, epsrel, limit, icall, & + maxp1, result, abserr, neval, ier, alist, blist, rlist, elist, iord, & + nnlog, momcom, chebmo ) +! +!****************************************************************************** +! +!! QFOUR estimates the integrals of oscillatory functions. +! +! +! Discussion: +! +! This routine calculates an approximation RESULT to a definite integral +! I = integral of F(X) * COS(OMEGA*X) +! or +! I = integral of F(X) * SIN(OMEGA*X) +! over (A,B), hopefully satisfying: +! | I - RESULT | <= max ( epsabs, epsrel * |I| ) ). +! +! QFOUR is called by QAWO and QAWF. It can also be called directly in +! a user-written program. In the latter case it is possible for the +! user to determine the first dimension of array CHEBMO(MAXP1,25). +! See also parameter description of MAXP1. Additionally see +! parameter description of ICALL for eventually re-using +! Chebyshev moments computed during former call on subinterval +! of equal length abs(B-A). +! +! Reference: +! +! R Piessens, E de Doncker-Kapenger, C W Ueberhuber, D K Kahaner, +! QUADPACK, a Subroutine Package for Automatic Integration, +! Springer Verlag, 1983 +! +! Parameters: +! +! Input, external real(dp) F, the name of the function routine, of the form +! function f ( x ) +! real(dp) f +! real(dp) x +! which evaluates the integrand function. +! +! Input, real(dp) A, B, the limits of integration. +! +! Input, real(dp) OMEGA, the multiplier of X in the weight function. +! +! Input, integer INTEGR, indicates the weight functions to be used. +! = 1, w(x) = cos(omega*x) +! = 2, w(x) = sin(omega*x) +! +! Input, real(dp) EPSABS, EPSREL, the absolute and relative accuracy requested. +! +! Input, integer LIMIT, the maximum number of subintervals of [A,B] +! that can be generated. +! +! icall - integer +! if qfour is to be used only once, ICALL must +! be set to 1. assume that during this call, the +! Chebyshev moments (for clenshaw-curtis integration +! of degree 24) have been computed for intervals of +! lenghts (abs(b-a))*2**(-l), l=0,1,2,...momcom-1. +! the Chebyshev moments already computed can be +! re-used in subsequent calls, if qfour must be +! called twice or more times on intervals of the +! same length abs(b-a). from the second call on, one +! has to put then ICALL > 1. +! if ICALL < 1, the routine will end with ier = 6. +! +! maxp1 - integer +! gives an upper bound on the number of +! Chebyshev moments which can be stored, i.e. +! for the intervals of lenghts abs(b-a)*2**(-l), +! l=0,1, ..., maxp1-2, maxp1 >= 1. +! if maxp1 < 1, the routine will end with ier = 6. +! increasing (decreasing) the value of maxp1 +! decreases (increases) the computational time but +! increases (decreases) the required memory space. +! +! Output, real(dp) RESULT, the estimated value of the integral. +! +! Output, real(dp) ABSERR, an estimate of || I - RESULT ||. +! +! Output, integer NEVAL, the number of times the integral was evaluated. +! +! ier - integer +! ier = 0 normal and reliable termination of the +! routine. it is assumed that the +! requested accuracy has been achieved. +! - ier > 0 abnormal termination of the routine. +! the estimates for integral and error are +! less reliable. it is assumed that the +! requested accuracy has not been achieved. +! ier = 1 maximum number of subdivisions allowed +! has been achieved. one can allow more +! subdivisions by increasing the value of +! limit (and taking according dimension +! adjustments into account). however, if +! this yields no improvement it is advised +! to analyze the integrand, in order to +! determine the integration difficulties. +! if the position of a local difficulty can +! be determined (e.g. singularity, +! discontinuity within the interval) one +! will probably gain from splitting up the +! interval at this point and calling the +! integrator on the subranges. if possible, +! an appropriate special-purpose integrator +! should be used which is designed for +! handling the type of difficulty involved. +! = 2 the occurrence of roundoff error is +! detected, which prevents the requested +! tolerance from being achieved. +! the error may be under-estimated. +! = 3 extremely bad integrand behavior occurs +! at some points of the integration +! interval. +! = 4 the algorithm does not converge. roundoff +! error is detected in the extrapolation +! table. it is presumed that the requested +! tolerance cannot be achieved due to +! roundoff in the extrapolation table, and +! that the returned result is the best which +! can be obtained. +! = 5 the integral is probably divergent, or +! slowly convergent. it must be noted that +! divergence can occur with any other value +! of ier > 0. +! = 6 the input is invalid, because +! epsabs < 0 and epsrel < 0, +! or (integr /= 1 and integr /= 2) or +! ICALL < 1 or maxp1 < 1. +! result, abserr, neval, last, rlist(1), +! elist(1), iord(1) and nnlog(1) are set to +! zero. alist(1) and blist(1) are set to a +! and b respectively. +! +! Workspace, real(dp) ALIST(LIMIT), BLIST(LIMIT), contains in entries 1 +! through LAST the left and right ends of the partition subintervals. +! +! Workspace, real(dp) RLIST(LIMIT), contains in entries 1 through LAST +! the integral approximations on the subintervals. +! +! Workspace, real(dp) ELIST(LIMIT), contains in entries 1 through LAST +! the absolute error estimates on the subintervals. +! +! iord - integer +! vector of dimension at least limit, the first k +! elements of which are pointers to the error +! estimates over the subintervals, such that +! elist(iord(1)), ..., elist(iord(k)), form +! a decreasing sequence, with k = last +! if last <= (limit/2+2), and +! k = limit+1-last otherwise. +! +! nnlog - integer +! vector of dimension at least limit, indicating the +! subdivision levels of the subintervals, i.e. +! iwork(i) = l means that the subinterval numbered +! i is of length abs(b-a)*2**(1-l) +! +! on entry and return +! momcom - integer +! indicating that the Chebyshev moments have been +! computed for intervals of lengths +! (abs(b-a))*2**(-l), l=0,1,2, ..., momcom-1, +! momcom < maxp1 +! +! chebmo - real(dp) +! array of dimension (maxp1,25) containing the +! Chebyshev moments +! +! Local Parameters: +! +! alist - list of left end points of all subintervals +! considered up to now +! blist - list of right end points of all subintervals +! considered up to now +! rlist(i) - approximation to the integral over +! (alist(i),blist(i)) +! rlist2 - array of dimension at least limexp+2 containing +! the part of the epsilon table which is still +! needed for further computations +! elist(i) - error estimate applying to rlist(i) +! maxerr - pointer to the interval with largest error +! estimate +! errmax - elist(maxerr) +! erlast - error on the interval currently subdivided +! area - sum of the integrals over the subintervals +! errsum - sum of the errors over the subintervals +! errbnd - requested accuracy max(epsabs,epsrel* +! abs(result)) +! *****1 - variable for the left subinterval +! *****2 - variable for the right subinterval +! last - index for subdivision +! nres - number of calls to the extrapolation routine +! numrl2 - number of elements in rlist2. if an appropriate +! approximation to the compounded integral has +! been obtained it is put in rlist2(numrl2) after +! numrl2 has been increased by one +! small - length of the smallest interval considered +! up to now, multiplied by 1.5 +! erlarg - sum of the errors over the intervals larger +! than the smallest interval considered up to now +! extrap - logical variable denoting that the routine is +! attempting to perform extrapolation, i.e. before +! subdividing the smallest interval we try to +! decrease the value of erlarg +! noext - logical variable denoting that extrapolation +! is no longer allowed (true value) +! + implicit none +! + integer limit + integer maxp1 +! + real(dp) a + real(dp) abseps + real(dp) abserr + real(dp) alist(limit) + real(dp) area + real(dp) area1 + real(dp) area12 + real(dp) area2 + real(dp) a1 + real(dp) a2 + real(dp) b + real(dp) blist(limit) + real(dp) b1 + real(dp) b2 + real(dp) chebmo(maxp1,25) + real(dp) correc + real(dp) defab1 + real(dp) defab2 + real(dp) defabs + real(dp) domega + real(dp) dres + real(dp) elist(limit) + real(dp) epsabs + real(dp) epsrel + real(dp) erlarg + real(dp) erlast + real(dp) errbnd + real(dp) errmax + real(dp) error1 + real(dp) erro12 + real(dp) error2 + real(dp) errsum + real(dp) ertest + logical extall + logical extrap + real(dp), external :: f + integer icall + integer id + integer ier + integer ierro + integer integr + integer iord(limit) + integer iroff1 + integer iroff2 + integer iroff3 + integer jupbnd + integer k + integer ksgn + integer ktmin + integer last + integer maxerr + integer momcom + integer nev + integer neval + integer nnlog(limit) + logical noext + integer nres + integer nrmax + integer nrmom + integer numrl2 + real(dp) omega + real(dp) resabs + real(dp) reseps + real(dp) result + real(dp) res3la(3) + real(dp) rlist(limit) + real(dp) rlist2(52) + real(dp) small + real(dp) width +! +! the dimension of rlist2 is determined by the value of +! limexp in QEXTR (rlist2 should be of dimension +! (limexp+2) at least). +! +! Test on validity of parameters. +! + ier = 0 + neval = 0 + last = 0 + result = 0.0e+00 + abserr = 0.0e+00 + alist(1) = a + blist(1) = b + rlist(1) = 0.0e+00 + elist(1) = 0.0e+00 + iord(1) = 0 + nnlog(1) = 0 + + if ( (integr /= 1.and.integr /= 2) .or. (epsabs < 0.0e+00.and. & + epsrel < 0.0e+00) .or. icall < 1 .or. maxp1 < 1 ) then + ier = 6 + return + end if +! +! First approximation to the integral. +! + domega = abs ( omega ) + nrmom = 0 + + if ( icall <= 1 ) then + momcom = 0 + end if + + call qc25o ( f, a, b, domega, integr, nrmom, maxp1, 0, result, abserr, & + neval, defabs, resabs, momcom, chebmo ) +! +! Test on accuracy. +! + dres = abs(result) + errbnd = max ( epsabs,epsrel*dres) + rlist(1) = result + elist(1) = abserr + iord(1) = 1 + if ( abserr <= 1.0e+02* epsilon ( defabs ) *defabs .and. & + abserr > errbnd ) ier = 2 + + if ( limit == 1 ) then + ier = 1 + end if + + if ( ier /= 0 .or. abserr <= errbnd ) go to 200 +! +! Initializations +! + errmax = abserr + maxerr = 1 + area = result + errsum = abserr + abserr = huge ( abserr ) + nrmax = 1 + extrap = .false. + noext = .false. + ierro = 0 + iroff1 = 0 + iroff2 = 0 + iroff3 = 0 + ktmin = 0 + small = abs(b-a)*7.5e-01 + nres = 0 + numrl2 = 0 + extall = .false. + + if ( 5.0e-01*abs(b-a)*domega <= 2.0e+00) then + numrl2 = 1 + extall = .true. + rlist2(1) = result + end if + + if ( 2.5e-01 * abs(b-a) * domega <= 2.0e+00 ) then + extall = .true. + end if + + if ( dres >= (1.0e+00-5.0e+01* epsilon ( defabs ) )*defabs ) then + ksgn = 1 + else + ksgn = -1 + end if +! +! main do-loop +! + do 140 last = 2, limit +! +! Bisect the subinterval with the nrmax-th largest error estimate. +! + nrmom = nnlog(maxerr)+1 + a1 = alist(maxerr) + b1 = 5.0e-01*(alist(maxerr)+blist(maxerr)) + a2 = b1 + b2 = blist(maxerr) + erlast = errmax + + call qc25o ( f, a1, b1, domega, integr, nrmom, maxp1, 0, area1, & + error1, nev, resabs, defab1, momcom, chebmo ) + + neval = neval+nev + + call qc25o ( f, a2, b2, domega, integr, nrmom, maxp1, 1, area2, & + error2, nev, resabs, defab2, momcom, chebmo ) + + neval = neval+nev +! +! Improve previous approximations to integral and error and +! test for accuracy. +! + area12 = area1+area2 + erro12 = error1+error2 + errsum = errsum+erro12-errmax + area = area+area12-rlist(maxerr) + if ( defab1 == error1 .or. defab2 == error2 ) go to 25 + if ( abs(rlist(maxerr)-area12) > 1.0e-05*abs(area12) & + .or. erro12 < 9.9e-01*errmax ) go to 20 + if ( extrap ) iroff2 = iroff2+1 + + if ( .not.extrap ) then + iroff1 = iroff1+1 + end if + +20 continue + + if ( last > 10.and.erro12 > errmax ) iroff3 = iroff3+1 + +25 continue + + rlist(maxerr) = area1 + rlist(last) = area2 + nnlog(maxerr) = nrmom + nnlog(last) = nrmom + errbnd = max ( epsabs,epsrel*abs(area)) +! +! Test for roundoff error and eventually set error flag +! + if ( iroff1+iroff2 >= 10 .or. iroff3 >= 20 ) ier = 2 + + if ( iroff2 >= 5) ierro = 3 +! +! Set error flag in the case that the number of subintervals +! equals limit. +! + if ( last == limit ) then + ier = 1 + end if +! +! Set error flag in the case of bad integrand behavior at +! a point of the integration range. +! + if ( max ( abs(a1),abs(b2)) <= (1.0e+00+1.0e+03* epsilon ( a1 ) ) & + *(abs(a2)+1.0e+03* tiny ( a2 ) )) then + ier = 4 + end if +! +! Append the newly-created intervals to the list. +! + if ( error2 <= error1 ) then + alist(last) = a2 + blist(maxerr) = b1 + blist(last) = b2 + elist(maxerr) = error1 + elist(last) = error2 + else + alist(maxerr) = a2 + alist(last) = a1 + blist(last) = b1 + rlist(maxerr) = area2 + rlist(last) = area1 + elist(maxerr) = error2 + elist(last) = error1 + end if +! +! Call QSORT to maintain the descending ordering +! in the list of error estimates and select the subinterval +! with nrmax-th largest error estimate (to be bisected next). +! +40 continue + + call qsort ( limit, last, maxerr, errmax, elist, iord, nrmax ) + + if ( errsum <= errbnd ) then + go to 170 + end if + + if ( ier /= 0 ) go to 150 + if ( last == 2 .and. extall ) go to 120 + if ( noext ) go to 140 + if ( .not. extall ) go to 50 + erlarg = erlarg-erlast + if ( abs(b1-a1) > small ) erlarg = erlarg+erro12 + if ( extrap ) go to 70 +! +! Test whether the interval to be bisected next is the +! smallest interval. +! +50 continue + + width = abs(blist(maxerr)-alist(maxerr)) + if ( width > small ) go to 140 + if ( extall ) go to 60 +! +! Test whether we can start with the extrapolation procedure +! (we do this if we integrate over the next interval with +! use of a Gauss-Kronrod rule - see QC25O). +! + small = small*5.0e-01 + if ( 2.5e-01*width*domega > 2.0e+00 ) go to 140 + extall = .true. + go to 130 + +60 continue + + extrap = .true. + nrmax = 2 + +70 continue + + if ( ierro == 3 .or. erlarg <= ertest ) go to 90 +! +! The smallest interval has the largest error. +! Before bisecting decrease the sum of the errors over the +! larger intervals (ERLARG) and perform extrapolation. +! + jupbnd = last + + if ( last > (limit/2+2) ) then + jupbnd = limit+3-last + end if + + id = nrmax + + do k = id, jupbnd + maxerr = iord(nrmax) + errmax = elist(maxerr) + if ( abs(blist(maxerr)-alist(maxerr)) > small ) go to 140 + nrmax = nrmax+1 + end do +! +! Perform extrapolation. +! +90 continue + + numrl2 = numrl2+1 + rlist2(numrl2) = area + if ( numrl2 < 3 ) go to 110 + call qextr ( numrl2, rlist2, reseps, abseps, res3la, nres ) + ktmin = ktmin+1 + + if ( ktmin > 5.and.abserr < 1.0e-03*errsum ) then + ier = 5 + end if + + if ( abseps >= abserr ) go to 100 + ktmin = 0 + abserr = abseps + result = reseps + correc = erlarg + ertest = max ( epsabs, epsrel*abs(reseps)) + if ( abserr <= ertest ) go to 150 +! +! Prepare bisection of the smallest interval. +! +100 continue + + if ( numrl2 == 1 ) noext = .true. + if ( ier == 5 ) go to 150 + +110 continue + + maxerr = iord(1) + errmax = elist(maxerr) + nrmax = 1 + extrap = .false. + small = small*5.0e-01 + erlarg = errsum + go to 140 + +120 continue + + small = small * 5.0e-01 + numrl2 = numrl2 + 1 + rlist2(numrl2) = area + +130 continue + + ertest = errbnd + erlarg = errsum + +140 continue +! +! set the final result. +! +150 continue + + if ( abserr == huge ( abserr ) .or. nres == 0 ) go to 170 + if ( ier+ierro == 0 ) go to 165 + if ( ierro == 3 ) abserr = abserr+correc + if ( ier == 0 ) ier = 3 + if ( result /= 0.0e+00.and.area /= 0.0e+00 ) go to 160 + if ( abserr > errsum ) go to 170 + if ( area == 0.0e+00 ) go to 190 + go to 165 + +160 continue + + if ( abserr/abs(result) > errsum/abs(area) ) go to 170 +! +! Test on divergence. +! + 165 continue + + if ( ksgn == (-1) .and. max ( abs(result),abs(area)) <= & + defabs*1.0e-02 ) go to 190 + + if ( 1.0e-02 > (result/area) .or. (result/area) > 1.0e+02 & + .or. errsum >= abs(area) ) ier = 6 + + go to 190 +! +! Compute global integral sum. +! +170 continue + + result = sum ( rlist(1:last) ) + + abserr = errsum + +190 continue + + if (ier > 2) ier=ier-1 + +200 continue + + if ( integr == 2 .and. omega < 0.0e+00 ) then + result = -result + end if + + return +end subroutine +subroutine qk15 ( f, a, b, result, abserr, resabs, resasc ) +! +!****************************************************************************** +! +!! QK15 carries out a 15 point Gauss-Kronrod quadrature rule. +! +! +! Discussion: +! +! This routine approximates +! I = integral ( A <= X <= B ) F(X) dx +! with an error estimate, and +! J = integral ( A <= X <= B ) | F(X) | dx +! +! Reference: +! +! R Piessens, E de Doncker-Kapenger, C W Ueberhuber, D K Kahaner, +! QUADPACK, a Subroutine Package for Automatic Integration, +! Springer Verlag, 1983 +! +! Parameters: +! +! Input, external real(dp) F, the name of the function routine, of the form +! function f ( x ) +! real(dp) f +! real(dp) x +! which evaluates the integrand function. +! +! Input, real(dp) A, B, the limits of integration. +! +! Output, real(dp) RESULT, the estimated value of the integral. +! RESULT is computed by applying the 15-point Kronrod rule (RESK) +! obtained by optimal addition of abscissae to the 7-point Gauss rule +! (RESG). +! +! Output, real(dp) ABSERR, an estimate of | I - RESULT |. +! +! Output, real(dp) RESABS, approximation to the integral of the absolute +! value of F. +! +! Output, real(dp) RESASC, approximation to the integral | F-I/(B-A) | +! over [A,B]. +! +! Local Parameters: +! +! the abscissae and weights are given for the interval (-1,1). +! because of symmetry only the positive abscissae and their +! corresponding weights are given. +! +! xgk - abscissae of the 15-point Kronrod rule +! xgk(2), xgk(4), ... abscissae of the 7-point +! Gauss rule +! xgk(1), xgk(3), ... abscissae which are optimally +! added to the 7-point Gauss rule +! +! wgk - weights of the 15-point Kronrod rule +! +! wg - weights of the 7-point Gauss rule +! +! centr - mid point of the interval +! hlgth - half-length of the interval +! absc - abscissa +! fval* - function value +! resg - result of the 7-point Gauss formula +! resk - result of the 15-point Kronrod formula +! reskh - approximation to the mean value of f over (a,b), +! i.e. to i/(b-a) +! + implicit none +! + real(dp) a + real(dp) absc + real(dp) abserr + real(dp) b + real(dp) centr + real(dp) dhlgth + real(dp), external :: f + real(dp) fc + real(dp) fsum + real(dp) fval1 + real(dp) fval2 + real(dp) fv1(7) + real(dp) fv2(7) + real(dp) hlgth + integer j + integer jtw + integer jtwm1 + real(dp) resabs + real(dp) resasc + real(dp) resg + real(dp) resk + real(dp) reskh + real(dp) result + real(dp) wg(4) + real(dp) wgk(8) + real(dp) xgk(8) +! + data xgk(1),xgk(2),xgk(3),xgk(4),xgk(5),xgk(6),xgk(7),xgk(8)/ & + 9.914553711208126e-01, 9.491079123427585e-01, & + 8.648644233597691e-01, 7.415311855993944e-01, & + 5.860872354676911e-01, 4.058451513773972e-01, & + 2.077849550078985e-01, 0.0e+00 / + data wgk(1),wgk(2),wgk(3),wgk(4),wgk(5),wgk(6),wgk(7),wgk(8)/ & + 2.293532201052922e-02, 6.309209262997855e-02, & + 1.047900103222502e-01, 1.406532597155259e-01, & + 1.690047266392679e-01, 1.903505780647854e-01, & + 2.044329400752989e-01, 2.094821410847278e-01/ + data wg(1),wg(2),wg(3),wg(4)/ & + 1.294849661688697e-01, 2.797053914892767e-01, & + 3.818300505051189e-01, 4.179591836734694e-01/ +! + centr = 5.0e-01*(a+b) + hlgth = 5.0e-01*(b-a) + dhlgth = abs(hlgth) +! +! Compute the 15-point Kronrod approximation to the integral, +! and estimate the absolute error. +! + fc = f(centr) + resg = fc*wg(4) + resk = fc*wgk(8) + resabs = abs(resk) + + do j = 1, 3 + jtw = j*2 + absc = hlgth*xgk(jtw) + fval1 = f(centr-absc) + fval2 = f(centr+absc) + fv1(jtw) = fval1 + fv2(jtw) = fval2 + fsum = fval1+fval2 + resg = resg+wg(j)*fsum + resk = resk+wgk(jtw)*fsum + resabs = resabs+wgk(jtw)*(abs(fval1)+abs(fval2)) + end do + + do j = 1, 4 + jtwm1 = j*2-1 + absc = hlgth*xgk(jtwm1) + fval1 = f(centr-absc) + fval2 = f(centr+absc) + fv1(jtwm1) = fval1 + fv2(jtwm1) = fval2 + fsum = fval1+fval2 + resk = resk+wgk(jtwm1)*fsum + resabs = resabs+wgk(jtwm1)*(abs(fval1)+abs(fval2)) + end do + + reskh = resk * 5.0e-01 + resasc = wgk(8)*abs(fc-reskh) + + do j = 1, 7 + resasc = resasc+wgk(j)*(abs(fv1(j)-reskh)+abs(fv2(j)-reskh)) + end do + + result = resk*hlgth + resabs = resabs*dhlgth + resasc = resasc*dhlgth + abserr = abs((resk-resg)*hlgth) + + if ( resasc /= 0.0e+00.and.abserr /= 0.0e+00 ) then + abserr = resasc*min ( 1.0e+00,(2.0e+02*abserr/resasc)**1.5e+00) + end if + + if ( resabs > tiny ( resabs ) / (5.0e+01* epsilon ( resabs ) ) ) then + abserr = max (( epsilon ( resabs ) *5.0e+01)*resabs,abserr) + end if + + return +end subroutine +subroutine qk15i ( f, boun, inf, a, b, result, abserr, resabs, resasc ) +! +!****************************************************************************** +! +!! QK15I applies a 15 point Gauss-Kronrod quadrature on an infinite interval. +! +! +! Discussion: +! +! The original infinite integration range is mapped onto the interval +! (0,1) and (a,b) is a part of (0,1). The routine then computes: +! +! i = integral of transformed integrand over (a,b), +! j = integral of abs(transformed integrand) over (a,b). +! +! Reference: +! +! R Piessens, E de Doncker-Kapenger, C W Ueberhuber, D K Kahaner, +! QUADPACK, a Subroutine Package for Automatic Integration, +! Springer Verlag, 1983 +! +! Parameters: +! +! Input, external real(dp) F, the name of the function routine, of the form +! function f ( x ) +! real(dp) f +! real(dp) x +! which evaluates the integrand function. +! +! Input, real(dp) BOUN, the finite bound of the original integration range, +! or zero if INF is 2. +! +! inf - integer +! if inf = -1, the original interval is +! (-infinity,BOUN), +! if inf = +1, the original interval is +! (BOUN,+infinity), +! if inf = +2, the original interval is +! (-infinity,+infinity) and +! The integral is computed as the sum of two +! integrals, one over (-infinity,0) and one +! over (0,+infinity). +! +! Input, real(dp) A, B, the limits of integration, over a subrange of [0,1]. +! +! Output, real(dp) RESULT, the estimated value of the integral. +! RESULT is computed by applying the 15-point Kronrod rule (RESK) obtained +! by optimal addition of abscissae to the 7-point Gauss rule (RESG). +! +! Output, real(dp) ABSERR, an estimate of | I - RESULT |. +! +! Output, real(dp) RESABS, approximation to the integral of the absolute +! value of F. +! +! Output, real(dp) RESASC, approximation to the integral of the +! transformated integrand | F-I/(B-A) | over [A,B]. +! +! Local Parameters: +! +! centr - mid point of the interval +! hlgth - half-length of the interval +! absc* - abscissa +! tabsc* - transformed abscissa +! fval* - function value +! resg - result of the 7-point Gauss formula +! resk - result of the 15-point Kronrod formula +! reskh - approximation to the mean value of the transformed +! integrand over (a,b), i.e. to i/(b-a) +! + implicit none +! + real(dp) a + real(dp) absc + real(dp) absc1 + real(dp) absc2 + real(dp) abserr + real(dp) b + real(dp) boun + real(dp) centr + real(dp) dinf + real(dp), external :: f + real(dp) fc + real(dp) fsum + real(dp) fval1 + real(dp) fval2 + real(dp) fv1(7) + real(dp) fv2(7) + real(dp) hlgth + integer inf + integer j + real(dp) resabs + real(dp) resasc + real(dp) resg + real(dp) resk + real(dp) reskh + real(dp) result + real(dp) tabsc1 + real(dp) tabsc2 + real(dp) wg(8) + real(dp) wgk(8) + real(dp) xgk(8) +! +! the abscissae and weights are supplied for the interval +! (-1,1). because of symmetry only the positive abscissae and +! their corresponding weights are given. +! +! xgk - abscissae of the 15-point Kronrod rule +! xgk(2), xgk(4), ... abscissae of the 7-point Gauss +! rule +! xgk(1), xgk(3), ... abscissae which are optimally +! added to the 7-point Gauss rule +! +! wgk - weights of the 15-point Kronrod rule +! +! wg - weights of the 7-point Gauss rule, corresponding +! to the abscissae xgk(2), xgk(4), ... +! wg(1), wg(3), ... are set to zero. +! + data xgk(1),xgk(2),xgk(3),xgk(4),xgk(5),xgk(6),xgk(7),xgk(8)/ & + 9.914553711208126e-01, 9.491079123427585e-01, & + 8.648644233597691e-01, 7.415311855993944e-01, & + 5.860872354676911e-01, 4.058451513773972e-01, & + 2.077849550078985e-01, 0.0000000000000000e+00/ +! + data wgk(1),wgk(2),wgk(3),wgk(4),wgk(5),wgk(6),wgk(7),wgk(8)/ & + 2.293532201052922e-02, 6.309209262997855e-02, & + 1.047900103222502e-01, 1.406532597155259e-01, & + 1.690047266392679e-01, 1.903505780647854e-01, & + 2.044329400752989e-01, 2.094821410847278e-01/ +! + data wg(1),wg(2),wg(3),wg(4),wg(5),wg(6),wg(7),wg(8)/ & + 0.0000000000000000e+00, 1.294849661688697e-01, & + 0.0000000000000000e+00, 2.797053914892767e-01, & + 0.0000000000000000e+00, 3.818300505051189e-01, & + 0.0000000000000000e+00, 4.179591836734694e-01/ +! + dinf = min ( 1, inf ) + + centr = 5.0e-01*(a+b) + hlgth = 5.0e-01*(b-a) + tabsc1 = boun+dinf*(1.0e+00-centr)/centr + fval1 = f(tabsc1) + if ( inf == 2 ) fval1 = fval1+f(-tabsc1) + fc = (fval1/centr)/centr +! +! Compute the 15-point Kronrod approximation to the integral, +! and estimate the error. +! + resg = wg(8)*fc + resk = wgk(8)*fc + resabs = abs(resk) + + do j = 1, 7 + + absc = hlgth*xgk(j) + absc1 = centr-absc + absc2 = centr+absc + tabsc1 = boun+dinf*(1.0e+00-absc1)/absc1 + tabsc2 = boun+dinf*(1.0e+00-absc2)/absc2 + fval1 = f(tabsc1) + fval2 = f(tabsc2) + + if ( inf == 2 ) then + fval1 = fval1+f(-tabsc1) + fval2 = fval2+f(-tabsc2) + end if + + fval1 = (fval1/absc1)/absc1 + fval2 = (fval2/absc2)/absc2 + fv1(j) = fval1 + fv2(j) = fval2 + fsum = fval1+fval2 + resg = resg+wg(j)*fsum + resk = resk+wgk(j)*fsum + resabs = resabs+wgk(j)*(abs(fval1)+abs(fval2)) + end do + + reskh = resk * 5.0e-01 + resasc = wgk(8) * abs(fc-reskh) + + do j = 1, 7 + resasc = resasc + wgk(j)*(abs(fv1(j)-reskh)+abs(fv2(j)-reskh)) + end do + + result = resk * hlgth + resasc = resasc * hlgth + resabs = resabs * hlgth + abserr = abs ( ( resk - resg ) * hlgth ) + + if ( resasc /= 0.0e+00.and.abserr /= 0.0e+00) then + abserr = resasc* min ( 1.0e+00,(2.0e+02*abserr/resasc)**1.5e+00) + end if + + if ( resabs > tiny ( resabs ) / ( 5.0e+01 * epsilon ( resabs ) ) ) then + abserr = max (( epsilon ( resabs ) *5.0e+01)*resabs,abserr) + end if + + return +end subroutine +subroutine qk15w ( f, w, p1, p2, p3, p4, kp, a, b, result, abserr, resabs, & + resasc ) +! +!****************************************************************************** +! +!! QK15W applies a 15 point Gauss-Kronrod rule for a weighted integrand. +! +! +! Discussion: +! +! This routine approximates +! i = integral of f*w over (a,b), +! with error estimate, and +! j = integral of abs(f*w) over (a,b) +! +! Reference: +! +! R Piessens, E de Doncker-Kapenger, C W Ueberhuber, D K Kahaner, +! QUADPACK, a Subroutine Package for Automatic Integration, +! Springer Verlag, 1983 +! +! Parameters: +! +! Input, external real(dp) F, the name of the function routine, of the form +! function f ( x ) +! real(dp) f +! real(dp) x +! which evaluates the integrand function. +! +! w - real(dp) +! function subprogram defining the integrand +! weight function w(x). the actual name for w +! needs to be declared e x t e r n a l in the +! calling program. +! +! ?, real(dp) P1, P2, P3, P4, parameters in the weight function +! +! kp - integer +! key for indicating the type of weight function +! +! Input, real(dp) A, B, the limits of integration. +! +! Output, real(dp) RESULT, the estimated value of the integral. +! RESULT is computed by applying the 15-point Kronrod rule (RESK) obtained by +! optimal addition of abscissae to the 7-point Gauss rule (RESG). +! +! Output, real(dp) ABSERR, an estimate of | I - RESULT |. +! +! Output, real(dp) RESABS, approximation to the integral of the absolute +! value of F. +! +! Output, real(dp) RESASC, approximation to the integral | F-I/(B-A) | +! over [A,B]. +! +! Local Parameters: +! +! centr - mid point of the interval +! hlgth - half-length of the interval +! absc* - abscissa +! fval* - function value +! resg - result of the 7-point Gauss formula +! resk - result of the 15-point Kronrod formula +! reskh - approximation to the mean value of f*w over (a,b), +! i.e. to i/(b-a) +! + implicit none +! + real(dp) a + real(dp) absc + real(dp) absc1 + real(dp) absc2 + real(dp) abserr + real(dp) b + real(dp) centr + real(dp) dhlgth + real(dp), external :: f + real(dp) fc + real(dp) fsum + real(dp) fval1 + real(dp) fval2 + real(dp) fv1(7) + real(dp) fv2(7) + real(dp) hlgth + integer j + integer jtw + integer jtwm1 + integer kp + real(dp) p1 + real(dp) p2 + real(dp) p3 + real(dp) p4 + real(dp) resabs + real(dp) resasc + real(dp) resg + real(dp) resk + real(dp) reskh + real(dp) result + real(dp), external :: w + real(dp), dimension ( 4 ) :: wg = (/ & + 1.294849661688697e-01, 2.797053914892767e-01, & + 3.818300505051889e-01, 4.179591836734694e-01 /) + real(dp) wgk(8) + real(dp) xgk(8) +! +! the abscissae and weights are given for the interval (-1,1). +! because of symmetry only the positive abscissae and their +! corresponding weights are given. +! +! xgk - abscissae of the 15-point Gauss-Kronrod rule +! xgk(2), xgk(4), ... abscissae of the 7-point Gauss +! rule +! xgk(1), xgk(3), ... abscissae which are optimally +! added to the 7-point Gauss rule +! +! wgk - weights of the 15-point Gauss-Kronrod rule +! +! wg - weights of the 7-point Gauss rule +! + data xgk(1),xgk(2),xgk(3),xgk(4),xgk(5),xgk(6),xgk(7),xgk(8)/ & + 9.914553711208126e-01, 9.491079123427585e-01, & + 8.648644233597691e-01, 7.415311855993944e-01, & + 5.860872354676911e-01, 4.058451513773972e-01, & + 2.077849550789850e-01, 0.000000000000000e+00/ +! + data wgk(1),wgk(2),wgk(3),wgk(4),wgk(5),wgk(6),wgk(7),wgk(8)/ & + 2.293532201052922e-02, 6.309209262997855e-02, & + 1.047900103222502e-01, 1.406532597155259e-01, & + 1.690047266392679e-01, 1.903505780647854e-01, & + 2.044329400752989e-01, 2.094821410847278e-01/ +! + centr = 5.0e-01*(a+b) + hlgth = 5.0e-01*(b-a) + dhlgth = abs(hlgth) +! +! Compute the 15-point Kronrod approximation to the integral, +! and estimate the error. +! + fc = f(centr)*w(centr,p1,p2,p3,p4,kp) + resg = wg(4)*fc + resk = wgk(8)*fc + resabs = abs(resk) + + do j = 1, 3 + jtw = j*2 + absc = hlgth*xgk(jtw) + absc1 = centr-absc + absc2 = centr+absc + fval1 = f(absc1)*w(absc1,p1,p2,p3,p4,kp) + fval2 = f(absc2)*w(absc2,p1,p2,p3,p4,kp) + fv1(jtw) = fval1 + fv2(jtw) = fval2 + fsum = fval1+fval2 + resg = resg+wg(j)*fsum + resk = resk+wgk(jtw)*fsum + resabs = resabs+wgk(jtw)*(abs(fval1)+abs(fval2)) + end do + + do j = 1, 4 + jtwm1 = j*2-1 + absc = hlgth*xgk(jtwm1) + absc1 = centr-absc + absc2 = centr+absc + fval1 = f(absc1)*w(absc1,p1,p2,p3,p4,kp) + fval2 = f(absc2)*w(absc2,p1,p2,p3,p4,kp) + fv1(jtwm1) = fval1 + fv2(jtwm1) = fval2 + fsum = fval1+fval2 + resk = resk+wgk(jtwm1)*fsum + resabs = resabs+wgk(jtwm1)*(abs(fval1)+abs(fval2)) + end do + + reskh = resk*5.0e-01 + resasc = wgk(8)*abs(fc-reskh) + + do j = 1, 7 + resasc = resasc+wgk(j)*(abs(fv1(j)-reskh)+abs(fv2(j)-reskh)) + end do + + result = resk*hlgth + resabs = resabs*dhlgth + resasc = resasc*dhlgth + abserr = abs((resk-resg)*hlgth) + + if ( resasc /= 0.0e+00.and.abserr /= 0.0e+00) then + abserr = resasc*min ( 1.0e+00,(2.0e+02*abserr/resasc)**1.5e+00) + end if + + if ( resabs > tiny ( resabs ) /(5.0e+01* epsilon ( resabs ) ) ) then + abserr = max ( ( epsilon ( resabs ) * 5.0e+01)*resabs,abserr) + end if + + return +end subroutine +subroutine qk21 ( f, a, b, result, abserr, resabs, resasc ) +! +!****************************************************************************** +! +!! QK21 carries out a 21 point Gauss-Kronrod quadrature rule. +! +! +! Discussion: +! +! This routine approximates +! I = integral ( A <= X <= B ) F(X) dx +! with an error estimate, and +! J = integral ( A <= X <= B ) | F(X) | dx +! +! Reference: +! +! R Piessens, E de Doncker-Kapenger, C W Ueberhuber, D K Kahaner, +! QUADPACK, a Subroutine Package for Automatic Integration, +! Springer Verlag, 1983 +! +! Parameters: +! +! Input, external real(dp) F, the name of the function routine, of the form +! function f ( x ) +! real(dp) f +! real(dp) x +! which evaluates the integrand function. +! +! Input, real(dp) A, B, the limits of integration. +! +! Output, real(dp) RESULT, the estimated value of the integral. +! result is computed by applying the 21-point +! Kronrod rule (resk) obtained by optimal addition +! of abscissae to the 10-point Gauss rule (resg). +! +! Output, real(dp) ABSERR, an estimate of | I - RESULT |. +! +! Output, real(dp) RESABS, approximation to the integral of the absolute +! value of F. +! +! Output, real(dp) RESASC, approximation to the integral | F-I/(B-A) | +! over [A,B]. +! + implicit none +! + real(dp) a + real(dp) absc + real(dp) abserr + real(dp) b + real(dp) centr + real(dp) dhlgth + real(dp), external :: f + real(dp) fc + real(dp) fsum + real(dp) fval1 + real(dp) fval2 + real(dp) fv1(10) + real(dp) fv2(10) + real(dp) hlgth + integer j + integer jtw + integer jtwm1 + real(dp) resabs + real(dp) resasc + real(dp) resg + real(dp) resk + real(dp) reskh + real(dp) result + real(dp) wg(5) + real(dp) wgk(11) + real(dp) xgk(11) +! +! the abscissae and weights are given for the interval (-1,1). +! because of symmetry only the positive abscissae and their +! corresponding weights are given. +! +! xgk - abscissae of the 21-point Kronrod rule +! xgk(2), xgk(4), ... abscissae of the 10-point +! Gauss rule +! xgk(1), xgk(3), ... abscissae which are optimally +! added to the 10-point Gauss rule +! +! wgk - weights of the 21-point Kronrod rule +! +! wg - weights of the 10-point Gauss rule +! + data xgk(1),xgk(2),xgk(3),xgk(4),xgk(5),xgk(6),xgk(7),xgk(8), & + xgk(9),xgk(10),xgk(11)/ & + 9.956571630258081e-01, 9.739065285171717e-01, & + 9.301574913557082e-01, 8.650633666889845e-01, & + 7.808177265864169e-01, 6.794095682990244e-01, & + 5.627571346686047e-01, 4.333953941292472e-01, & + 2.943928627014602e-01, 1.488743389816312e-01, & + 0.000000000000000e+00/ +! + data wgk(1),wgk(2),wgk(3),wgk(4),wgk(5),wgk(6),wgk(7),wgk(8), & + wgk(9),wgk(10),wgk(11)/ & + 1.169463886737187e-02, 3.255816230796473e-02, & + 5.475589657435200e-02, 7.503967481091995e-02, & + 9.312545458369761e-02, 1.093871588022976e-01, & + 1.234919762620659e-01, 1.347092173114733e-01, & + 1.427759385770601e-01, 1.477391049013385e-01, & + 1.494455540029169e-01/ +! + data wg(1),wg(2),wg(3),wg(4),wg(5)/ & + 6.667134430868814e-02, 1.494513491505806e-01, & + 2.190863625159820e-01, 2.692667193099964e-01, & + 2.955242247147529e-01/ +! +! +! list of major variables +! +! centr - mid point of the interval +! hlgth - half-length of the interval +! absc - abscissa +! fval* - function value +! resg - result of the 10-point Gauss formula +! resk - result of the 21-point Kronrod formula +! reskh - approximation to the mean value of f over (a,b), +! i.e. to i/(b-a) +! + centr = 5.0e-01*(a+b) + hlgth = 5.0e-01*(b-a) + dhlgth = abs(hlgth) +! +! Compute the 21-point Kronrod approximation to the +! integral, and estimate the absolute error. +! + resg = 0.0e+00 + fc = f(centr) + resk = wgk(11)*fc + resabs = abs(resk) + + do j = 1, 5 + jtw = 2*j + absc = hlgth*xgk(jtw) + fval1 = f(centr-absc) + fval2 = f(centr+absc) + fv1(jtw) = fval1 + fv2(jtw) = fval2 + fsum = fval1+fval2 + resg = resg+wg(j)*fsum + resk = resk+wgk(jtw)*fsum + resabs = resabs+wgk(jtw)*(abs(fval1)+abs(fval2)) + end do + + do j = 1, 5 + jtwm1 = 2*j-1 + absc = hlgth*xgk(jtwm1) + fval1 = f(centr-absc) + fval2 = f(centr+absc) + fv1(jtwm1) = fval1 + fv2(jtwm1) = fval2 + fsum = fval1+fval2 + resk = resk+wgk(jtwm1)*fsum + resabs = resabs+wgk(jtwm1)*(abs(fval1)+abs(fval2)) + end do + + reskh = resk*5.0e-01 + resasc = wgk(11)*abs(fc-reskh) + + do j = 1, 10 + resasc = resasc+wgk(j)*(abs(fv1(j)-reskh)+abs(fv2(j)-reskh)) + end do + + result = resk*hlgth + resabs = resabs*dhlgth + resasc = resasc*dhlgth + abserr = abs((resk-resg)*hlgth) + + if ( resasc /= 0.0e+00.and.abserr /= 0.0e+00) then + abserr = resasc*min ( 1.0e+00,(2.0e+02*abserr/resasc)**1.5e+00) + end if + + if ( resabs > tiny ( resabs ) /(5.0e+01* epsilon ( resabs ) )) then + abserr = max (( epsilon ( resabs ) *5.0e+01)*resabs,abserr) + end if + + return +end subroutine +subroutine qk31 ( f, a, b, result, abserr, resabs, resasc ) +! +!****************************************************************************** +! +!! QK31 carries out a 31 point Gauss-Kronrod quadrature rule. +! +! +! Discussion: +! +! This routine approximates +! I = integral ( A <= X <= B ) F(X) dx +! with an error estimate, and +! J = integral ( A <= X <= B ) | F(X) | dx +! +! Reference: +! +! R Piessens, E de Doncker-Kapenger, C W Ueberhuber, D K Kahaner, +! QUADPACK, a Subroutine Package for Automatic Integration, +! Springer Verlag, 1983 +! +! Parameters: +! +! Input, external real(dp) F, the name of the function routine, of the form +! function f ( x ) +! real(dp) f +! real(dp) x +! which evaluates the integrand function. +! +! Input, real(dp) A, B, the limits of integration. +! +! Output, real(dp) RESULT, the estimated value of the integral. +! result is computed by applying the 31-point +! Gauss-Kronrod rule (resk), obtained by optimal +! addition of abscissae to the 15-point Gauss +! rule (resg). +! +! Output, real(dp) ABSERR, an estimate of | I - RESULT |. +! +! Output, real(dp) RESABS, approximation to the integral of the absolute +! value of F. +! +! Output, real(dp) RESASC, approximation to the integral | F-I/(B-A) | +! over [A,B]. +! + implicit none +! + real(dp) a + real(dp) absc + real(dp) abserr + real(dp) b + real(dp) centr + real(dp) dhlgth + real(dp), external :: f + real(dp) fc + real(dp) fsum + real(dp) fval1 + real(dp) fval2 + real(dp) fv1(15) + real(dp) fv2(15) + real(dp) hlgth + integer j + integer jtw + integer jtwm1 + real(dp) resabs + real(dp) resasc + real(dp) resg + real(dp) resk + real(dp) reskh + real(dp) result + real(dp) wg(8) + real(dp) wgk(16) + real(dp) xgk(16) +! +! the abscissae and weights are given for the interval (-1,1). +! because of symmetry only the positive abscissae and their +! corresponding weights are given. +! +! xgk - abscissae of the 31-point Kronrod rule +! xgk(2), xgk(4), ... abscissae of the 15-point +! Gauss rule +! xgk(1), xgk(3), ... abscissae which are optimally +! added to the 15-point Gauss rule +! +! wgk - weights of the 31-point Kronrod rule +! +! wg - weights of the 15-point Gauss rule +! + data xgk(1),xgk(2),xgk(3),xgk(4),xgk(5),xgk(6),xgk(7),xgk(8), & + xgk(9),xgk(10),xgk(11),xgk(12),xgk(13),xgk(14),xgk(15),xgk(16)/ & + 9.980022986933971e-01, 9.879925180204854e-01, & + 9.677390756791391e-01, 9.372733924007059e-01, & + 8.972645323440819e-01, 8.482065834104272e-01, & + 7.904185014424659e-01, 7.244177313601700e-01, & + 6.509967412974170e-01, 5.709721726085388e-01, & + 4.850818636402397e-01, 3.941513470775634e-01, & + 2.991800071531688e-01, 2.011940939974345e-01, & + 1.011420669187175e-01, 0.0e+00 / + data wgk(1),wgk(2),wgk(3),wgk(4),wgk(5),wgk(6),wgk(7),wgk(8), & + wgk(9),wgk(10),wgk(11),wgk(12),wgk(13),wgk(14),wgk(15),wgk(16)/ & + 5.377479872923349e-03, 1.500794732931612e-02, & + 2.546084732671532e-02, 3.534636079137585e-02, & + 4.458975132476488e-02, 5.348152469092809e-02, & + 6.200956780067064e-02, 6.985412131872826e-02, & + 7.684968075772038e-02, 8.308050282313302e-02, & + 8.856444305621177e-02, 9.312659817082532e-02, & + 9.664272698362368e-02, 9.917359872179196e-02, & + 1.007698455238756e-01, 1.013300070147915e-01/ + data wg(1),wg(2),wg(3),wg(4),wg(5),wg(6),wg(7),wg(8)/ & + 3.075324199611727e-02, 7.036604748810812e-02, & + 1.071592204671719e-01, 1.395706779261543e-01, & + 1.662692058169939e-01, 1.861610000155622e-01, & + 1.984314853271116e-01, 2.025782419255613e-01/ +! +! +! list of major variables +! +! centr - mid point of the interval +! hlgth - half-length of the interval +! absc - abscissa +! fval* - function value +! resg - result of the 15-point Gauss formula +! resk - result of the 31-point Kronrod formula +! reskh - approximation to the mean value of f over (a,b), +! i.e. to i/(b-a) +! + centr = 5.0e-01*(a+b) + hlgth = 5.0e-01*(b-a) + dhlgth = abs(hlgth) +! +! Compute the 31-point Kronrod approximation to the integral, +! and estimate the absolute error. +! + fc = f(centr) + resg = wg(8)*fc + resk = wgk(16)*fc + resabs = abs(resk) + + do j = 1, 7 + jtw = j*2 + absc = hlgth*xgk(jtw) + fval1 = f(centr-absc) + fval2 = f(centr+absc) + fv1(jtw) = fval1 + fv2(jtw) = fval2 + fsum = fval1+fval2 + resg = resg+wg(j)*fsum + resk = resk+wgk(jtw)*fsum + resabs = resabs+wgk(jtw)*(abs(fval1)+abs(fval2)) + end do + + do j = 1, 8 + jtwm1 = j*2-1 + absc = hlgth*xgk(jtwm1) + fval1 = f(centr-absc) + fval2 = f(centr+absc) + fv1(jtwm1) = fval1 + fv2(jtwm1) = fval2 + fsum = fval1+fval2 + resk = resk+wgk(jtwm1)*fsum + resabs = resabs+wgk(jtwm1)*(abs(fval1)+abs(fval2)) + end do + + reskh = resk*5.0e-01 + resasc = wgk(16)*abs(fc-reskh) + + do j = 1, 15 + resasc = resasc+wgk(j)*(abs(fv1(j)-reskh)+abs(fv2(j)-reskh)) + end do + + result = resk*hlgth + resabs = resabs*dhlgth + resasc = resasc*dhlgth + abserr = abs((resk-resg)*hlgth) + + if ( resasc /= 0.0e+00.and.abserr /= 0.0e+00) & + abserr = resasc*min ( 1.0e+00,(2.0e+02*abserr/resasc)**1.5e+00) + + if ( resabs > tiny ( resabs ) /(5.0e+01* epsilon ( resabs ) )) then + abserr = max (( epsilon ( resabs ) *5.0e+01)*resabs,abserr) + end if + + return +end subroutine +subroutine qk41 ( f, a, b, result, abserr, resabs, resasc ) +! +!****************************************************************************** +! +!! QK41 carries out a 41 point Gauss-Kronrod quadrature rule. +! +! +! Discussion: +! +! This routine approximates +! I = integral ( A <= X <= B ) F(X) dx +! with an error estimate, and +! J = integral ( A <= X <= B ) | F(X) | dx +! +! Reference: +! +! R Piessens, E de Doncker-Kapenger, C W Ueberhuber, D K Kahaner, +! QUADPACK, a Subroutine Package for Automatic Integration, +! Springer Verlag, 1983 +! +! Parameters: +! +! Input, external real(dp) F, the name of the function routine, of the form +! function f ( x ) +! real(dp) f +! real(dp) x +! which evaluates the integrand function. +! +! Input, real(dp) A, B, the limits of integration. +! +! Output, real(dp) RESULT, the estimated value of the integral. +! result is computed by applying the 41-point +! Gauss-Kronrod rule (resk) obtained by optimal +! addition of abscissae to the 20-point Gauss +! rule (resg). +! +! Output, real(dp) ABSERR, an estimate of | I - RESULT |. +! +! Output, real(dp) RESABS, approximation to the integral of the absolute +! value of F. +! +! Output, real(dp) RESASC, approximation to the integral | F-I/(B-A) | +! over [A,B]. +! +! Local Parameters: +! +! centr - mid point of the interval +! hlgth - half-length of the interval +! absc - abscissa +! fval* - function value +! resg - result of the 20-point Gauss formula +! resk - result of the 41-point Kronrod formula +! reskh - approximation to mean value of f over (a,b), i.e. +! to i/(b-a) +! + implicit none +! + real(dp) a + real(dp) absc + real(dp) abserr + real(dp) b + real(dp) centr + real(dp) dhlgth + real(dp), external :: f + real(dp) fc + real(dp) fsum + real(dp) fval1 + real(dp) fval2 + real(dp) fv1(20) + real(dp) fv2(20) + real(dp) hlgth + integer j + integer jtw + integer jtwm1 + real(dp) resabs + real(dp) resasc + real(dp) resg + real(dp) resk + real(dp) reskh + real(dp) result + real(dp) wg(10) + real(dp) wgk(21) + real(dp) xgk(21) +! +! the abscissae and weights are given for the interval (-1,1). +! because of symmetry only the positive abscissae and their +! corresponding weights are given. +! +! xgk - abscissae of the 41-point Gauss-Kronrod rule +! xgk(2), xgk(4), ... abscissae of the 20-point +! Gauss rule +! xgk(1), xgk(3), ... abscissae which are optimally +! added to the 20-point Gauss rule +! +! wgk - weights of the 41-point Gauss-Kronrod rule +! +! wg - weights of the 20-point Gauss rule +! + data xgk(1),xgk(2),xgk(3),xgk(4),xgk(5),xgk(6),xgk(7),xgk(8), & + xgk(9),xgk(10),xgk(11),xgk(12),xgk(13),xgk(14),xgk(15),xgk(16), & + xgk(17),xgk(18),xgk(19),xgk(20),xgk(21)/ & + 9.988590315882777e-01, 9.931285991850949e-01, & + 9.815078774502503e-01, 9.639719272779138e-01, & + 9.408226338317548e-01, 9.122344282513259e-01, & + 8.782768112522820e-01, 8.391169718222188e-01, & + 7.950414288375512e-01, 7.463319064601508e-01, & + 6.932376563347514e-01, 6.360536807265150e-01, & + 5.751404468197103e-01, 5.108670019508271e-01, & + 4.435931752387251e-01, 3.737060887154196e-01, & + 3.016278681149130e-01, 2.277858511416451e-01, & + 1.526054652409227e-01, 7.652652113349733e-02, & + 0.0e+00 / + data wgk(1),wgk(2),wgk(3),wgk(4),wgk(5),wgk(6),wgk(7),wgk(8), & + wgk(9),wgk(10),wgk(11),wgk(12),wgk(13),wgk(14),wgk(15),wgk(16), & + wgk(17),wgk(18),wgk(19),wgk(20),wgk(21)/ & + 3.073583718520532e-03, 8.600269855642942e-03, & + 1.462616925697125e-02, 2.038837346126652e-02, & + 2.588213360495116e-02, 3.128730677703280e-02, & + 3.660016975820080e-02, 4.166887332797369e-02, & + 4.643482186749767e-02, 5.094457392372869e-02, & + 5.519510534828599e-02, 5.911140088063957e-02, & + 6.265323755478117e-02, 6.583459713361842e-02, & + 6.864867292852162e-02, 7.105442355344407e-02, & + 7.303069033278667e-02, 7.458287540049919e-02, & + 7.570449768455667e-02, 7.637786767208074e-02, & + 7.660071191799966e-02/ + data wg(1),wg(2),wg(3),wg(4),wg(5),wg(6),wg(7),wg(8),wg(9),wg(10)/ & + 1.761400713915212e-02, 4.060142980038694e-02, & + 6.267204833410906e-02, 8.327674157670475e-02, & + 1.019301198172404e-01, 1.181945319615184e-01, & + 1.316886384491766e-01, 1.420961093183821e-01, & + 1.491729864726037e-01, 1.527533871307259e-01/ +! + centr = 5.0e-01*(a+b) + hlgth = 5.0e-01*(b-a) + dhlgth = abs(hlgth) +! +! Compute 41-point Gauss-Kronrod approximation to the +! the integral, and estimate the absolute error. +! + resg = 0.0e+00 + fc = f(centr) + resk = wgk(21)*fc + resabs = abs(resk) + + do j = 1, 10 + jtw = j*2 + absc = hlgth*xgk(jtw) + fval1 = f(centr-absc) + fval2 = f(centr+absc) + fv1(jtw) = fval1 + fv2(jtw) = fval2 + fsum = fval1+fval2 + resg = resg+wg(j)*fsum + resk = resk+wgk(jtw)*fsum + resabs = resabs+wgk(jtw)*(abs(fval1)+abs(fval2)) + end do + + do j = 1, 10 + jtwm1 = j*2-1 + absc = hlgth*xgk(jtwm1) + fval1 = f(centr-absc) + fval2 = f(centr+absc) + fv1(jtwm1) = fval1 + fv2(jtwm1) = fval2 + fsum = fval1+fval2 + resk = resk+wgk(jtwm1)*fsum + resabs = resabs+wgk(jtwm1)*(abs(fval1)+abs(fval2)) + end do + + reskh = resk*5.0e-01 + resasc = wgk(21)*abs(fc-reskh) + + do j = 1, 20 + resasc = resasc+wgk(j)*(abs(fv1(j)-reskh)+abs(fv2(j)-reskh)) + end do + + result = resk*hlgth + resabs = resabs*dhlgth + resasc = resasc*dhlgth + abserr = abs((resk-resg)*hlgth) + + if ( resasc /= 0.0e+00.and.abserr /= 0.0e+00) & + abserr = resasc*min ( 1.0e+00,(2.0e+02*abserr/resasc)**1.5e+00) + + if ( resabs > tiny ( resabs ) /(5.0e+01* epsilon ( resabs ) )) then + abserr = max (( epsilon ( resabs ) *5.0e+01)*resabs,abserr) + end if + + return +end subroutine +subroutine qk51 ( f, a, b, result, abserr, resabs, resasc ) +! +!****************************************************************************** +! +!! QK51 carries out a 51 point Gauss-Kronrod quadrature rule. +! +! +! Discussion: +! +! This routine approximates +! I = integral ( A <= X <= B ) F(X) dx +! with an error estimate, and +! J = integral ( A <= X <= B ) | F(X) | dx +! +! Reference: +! +! R Piessens, E de Doncker-Kapenger, C W Ueberhuber, D K Kahaner, +! QUADPACK, a Subroutine Package for Automatic Integration, +! Springer Verlag, 1983 +! +! Parameters: +! +! Input, external real(dp) F, the name of the function routine, of the form +! function f ( x ) +! real(dp) f +! real(dp) x +! which evaluates the integrand function. +! +! Input, real(dp) A, B, the limits of integration. +! +! Output, real(dp) RESULT, the estimated value of the integral. +! result is computed by applying the 51-point +! Kronrod rule (resk) obtained by optimal addition +! of abscissae to the 25-point Gauss rule (resg). +! +! Output, real(dp) ABSERR, an estimate of | I - RESULT |. +! +! Output, real(dp) RESABS, approximation to the integral of the absolute +! value of F. +! +! Output, real(dp) RESASC, approximation to the integral | F-I/(B-A) | +! over [A,B]. +! +! Local Parameters: +! +! centr - mid point of the interval +! hlgth - half-length of the interval +! absc - abscissa +! fval* - function value +! resg - result of the 25-point Gauss formula +! resk - result of the 51-point Kronrod formula +! reskh - approximation to the mean value of f over (a,b), +! i.e. to i/(b-a) +! + implicit none +! + real(dp) a + real(dp) absc + real(dp) abserr + real(dp) b + real(dp) centr + real(dp) dhlgth + real(dp), external :: f + real(dp) fc + real(dp) fsum + real(dp) fval1 + real(dp) fval2 + real(dp) fv1(25) + real(dp) fv2(25) + real(dp) hlgth + integer j + integer jtw + integer jtwm1 + real(dp) resabs + real(dp) resasc + real(dp) resg + real(dp) resk + real(dp) reskh + real(dp) result + real(dp) wg(13) + real(dp) wgk(26) + real(dp) xgk(26) +! +! the abscissae and weights are given for the interval (-1,1). +! because of symmetry only the positive abscissae and their +! corresponding weights are given. +! +! xgk - abscissae of the 51-point Kronrod rule +! xgk(2), xgk(4), ... abscissae of the 25-point +! Gauss rule +! xgk(1), xgk(3), ... abscissae which are optimally +! added to the 25-point Gauss rule +! +! wgk - weights of the 51-point Kronrod rule +! +! wg - weights of the 25-point Gauss rule +! + data xgk(1),xgk(2),xgk(3),xgk(4),xgk(5),xgk(6),xgk(7),xgk(8), & + xgk(9),xgk(10),xgk(11),xgk(12),xgk(13),xgk(14)/ & + 9.992621049926098e-01, 9.955569697904981e-01, & + 9.880357945340772e-01, 9.766639214595175e-01, & + 9.616149864258425e-01, 9.429745712289743e-01, & + 9.207471152817016e-01, 8.949919978782754e-01, & + 8.658470652932756e-01, 8.334426287608340e-01, & + 7.978737979985001e-01, 7.592592630373576e-01, & + 7.177664068130844e-01, 6.735663684734684e-01/ + data xgk(15),xgk(16),xgk(17),xgk(18),xgk(19),xgk(20),xgk(21), & + xgk(22),xgk(23),xgk(24),xgk(25),xgk(26)/ & + 6.268100990103174e-01, 5.776629302412230e-01, & + 5.263252843347192e-01, 4.730027314457150e-01, & + 4.178853821930377e-01, 3.611723058093878e-01, & + 3.030895389311078e-01, 2.438668837209884e-01, & + 1.837189394210489e-01, 1.228646926107104e-01, & + 6.154448300568508e-02, 0.0e+00 / + data wgk(1),wgk(2),wgk(3),wgk(4),wgk(5),wgk(6),wgk(7),wgk(8), & + wgk(9),wgk(10),wgk(11),wgk(12),wgk(13),wgk(14)/ & + 1.987383892330316e-03, 5.561932135356714e-03, & + 9.473973386174152e-03, 1.323622919557167e-02, & + 1.684781770912830e-02, 2.043537114588284e-02, & + 2.400994560695322e-02, 2.747531758785174e-02, & + 3.079230016738749e-02, 3.400213027432934e-02, & + 3.711627148341554e-02, 4.008382550403238e-02, & + 4.287284502017005e-02, 4.550291304992179e-02/ + data wgk(15),wgk(16),wgk(17),wgk(18),wgk(19),wgk(20),wgk(21), & + wgk(22),wgk(23),wgk(24),wgk(25),wgk(26)/ & + 4.798253713883671e-02, 5.027767908071567e-02, & + 5.236288580640748e-02, 5.425112988854549e-02, & + 5.595081122041232e-02, 5.743711636156783e-02, & + 5.868968002239421e-02, 5.972034032417406e-02, & + 6.053945537604586e-02, 6.112850971705305e-02, & + 6.147118987142532e-02, 6.158081806783294e-02/ + data wg(1),wg(2),wg(3),wg(4),wg(5),wg(6),wg(7),wg(8),wg(9),wg(10), & + wg(11),wg(12),wg(13)/ & + 1.139379850102629e-02, 2.635498661503214e-02, & + 4.093915670130631e-02, 5.490469597583519e-02, & + 6.803833381235692e-02, 8.014070033500102e-02, & + 9.102826198296365e-02, 1.005359490670506e-01, & + 1.085196244742637e-01, 1.148582591457116e-01, & + 1.194557635357848e-01, 1.222424429903100e-01, & + 1.231760537267155e-01/ +! + centr = 5.0e-01*(a+b) + hlgth = 5.0e-01*(b-a) + dhlgth = abs(hlgth) +! +! Compute the 51-point Kronrod approximation to the integral, +! and estimate the absolute error. +! + fc = f(centr) + resg = wg(13)*fc + resk = wgk(26)*fc + resabs = abs(resk) + + do j = 1, 12 + jtw = j*2 + absc = hlgth*xgk(jtw) + fval1 = f(centr-absc) + fval2 = f(centr+absc) + fv1(jtw) = fval1 + fv2(jtw) = fval2 + fsum = fval1+fval2 + resg = resg+wg(j)*fsum + resk = resk+wgk(jtw)*fsum + resabs = resabs+wgk(jtw)*(abs(fval1)+abs(fval2)) + end do + + do j = 1, 13 + jtwm1 = j*2-1 + absc = hlgth*xgk(jtwm1) + fval1 = f(centr-absc) + fval2 = f(centr+absc) + fv1(jtwm1) = fval1 + fv2(jtwm1) = fval2 + fsum = fval1+fval2 + resk = resk+wgk(jtwm1)*fsum + resabs = resabs+wgk(jtwm1)*(abs(fval1)+abs(fval2)) + end do + + reskh = resk*5.0e-01 + resasc = wgk(26)*abs(fc-reskh) + + do j = 1, 25 + resasc = resasc+wgk(j)*(abs(fv1(j)-reskh)+abs(fv2(j)-reskh)) + end do + + result = resk*hlgth + resabs = resabs*dhlgth + resasc = resasc*dhlgth + abserr = abs((resk-resg)*hlgth) + + if ( resasc /= 0.0e+00.and.abserr /= 0.0e+00) then + abserr = resasc*min ( 1.0e+00,(2.0e+02*abserr/resasc)**1.5e+00) + end if + + if ( resabs > tiny ( resabs ) / (5.0e+01* epsilon ( resabs ) ) ) then + abserr = max (( epsilon ( resabs ) *5.0e+01)*resabs,abserr) + end if + + return +end subroutine +subroutine qk61 ( f, a, b, result, abserr, resabs, resasc ) +! +!****************************************************************************** +! +!! QK61 carries out a 61 point Gauss-Kronrod quadrature rule. +! +! +! Discussion: +! +! This routine approximates +! I = integral ( A <= X <= B ) F(X) dx +! with an error estimate, and +! J = integral ( A <= X <= B ) | F(X) | dx +! +! Reference: +! +! R Piessens, E de Doncker-Kapenger, C W Ueberhuber, D K Kahaner, +! QUADPACK, a Subroutine Package for Automatic Integration, +! Springer Verlag, 1983 +! +! Parameters: +! +! Input, external real(dp) F, the name of the function routine, of the form +! function f ( x ) +! real(dp) f +! real(dp) x +! which evaluates the integrand function. +! +! Input, real(dp) A, B, the limits of integration. +! +! Output, real(dp) RESULT, the estimated value of the integral. +! result is computed by applying the 61-point +! Kronrod rule (resk) obtained by optimal addition of +! abscissae to the 30-point Gauss rule (resg). +! +! Output, real(dp) ABSERR, an estimate of | I - RESULT |. +! +! Output, real(dp) RESABS, approximation to the integral of the absolute +! value of F. +! +! Output, real(dp) RESASC, approximation to the integral | F-I/(B-A) | +! over [A,B]. +! +! Local Parameters: +! +! centr - mid point of the interval +! hlgth - half-length of the interval +! absc - abscissa +! fval* - function value +! resg - result of the 30-point Gauss rule +! resk - result of the 61-point Kronrod rule +! reskh - approximation to the mean value of f +! over (a,b), i.e. to i/(b-a) +! + implicit none +! + real(dp) a + real(dp) absc + real(dp) abserr + real(dp) b + real(dp) centr + real(dp) dhlgth + real(dp), external :: f + real(dp) fc + real(dp) fsum + real(dp) fval1 + real(dp) fval2 + real(dp) fv1(30) + real(dp) fv2(30) + real(dp) hlgth + integer j + integer jtw + integer jtwm1 + real(dp) resabs + real(dp) resasc + real(dp) resg + real(dp) resk + real(dp) reskh + real(dp) result + real(dp) wg(15) + real(dp) wgk(31) + real(dp) xgk(31) +! +! the abscissae and weights are given for the +! interval (-1,1). because of symmetry only the positive +! abscissae and their corresponding weights are given. +! +! xgk - abscissae of the 61-point Kronrod rule +! xgk(2), xgk(4) ... abscissae of the 30-point +! Gauss rule +! xgk(1), xgk(3) ... optimally added abscissae +! to the 30-point Gauss rule +! +! wgk - weights of the 61-point Kronrod rule +! +! wg - weigths of the 30-point Gauss rule +! + data xgk(1),xgk(2),xgk(3),xgk(4),xgk(5),xgk(6),xgk(7),xgk(8), & + xgk(9),xgk(10)/ & + 9.994844100504906e-01, 9.968934840746495e-01, & + 9.916309968704046e-01, 9.836681232797472e-01, & + 9.731163225011263e-01, 9.600218649683075e-01, & + 9.443744447485600e-01, 9.262000474292743e-01, & + 9.055733076999078e-01, 8.825605357920527e-01/ + data xgk(11),xgk(12),xgk(13),xgk(14),xgk(15),xgk(16),xgk(17), & + xgk(18),xgk(19),xgk(20)/ & + 8.572052335460611e-01, 8.295657623827684e-01, & + 7.997278358218391e-01, 7.677774321048262e-01, & + 7.337900624532268e-01, 6.978504947933158e-01, & + 6.600610641266270e-01, 6.205261829892429e-01, & + 5.793452358263617e-01, 5.366241481420199e-01/ + data xgk(21),xgk(22),xgk(23),xgk(24),xgk(25),xgk(26),xgk(27), & + xgk(28),xgk(29),xgk(30),xgk(31)/ & + 4.924804678617786e-01, 4.470337695380892e-01, & + 4.004012548303944e-01, 3.527047255308781e-01, & + 3.040732022736251e-01, 2.546369261678898e-01, & + 2.045251166823099e-01, 1.538699136085835e-01, & + 1.028069379667370e-01, 5.147184255531770e-02, & + 0.0e+00 / + data wgk(1),wgk(2),wgk(3),wgk(4),wgk(5),wgk(6),wgk(7),wgk(8), & + wgk(9),wgk(10)/ & + 1.389013698677008e-03, 3.890461127099884e-03, & + 6.630703915931292e-03, 9.273279659517763e-03, & + 1.182301525349634e-02, 1.436972950704580e-02, & + 1.692088918905327e-02, 1.941414119394238e-02, & + 2.182803582160919e-02, 2.419116207808060e-02/ + data wgk(11),wgk(12),wgk(13),wgk(14),wgk(15),wgk(16),wgk(17), & + wgk(18),wgk(19),wgk(20)/ & + 2.650995488233310e-02, 2.875404876504129e-02, & + 3.090725756238776e-02, 3.298144705748373e-02, & + 3.497933802806002e-02, 3.688236465182123e-02, & + 3.867894562472759e-02, 4.037453895153596e-02, & + 4.196981021516425e-02, 4.345253970135607e-02/ + data wgk(21),wgk(22),wgk(23),wgk(24),wgk(25),wgk(26),wgk(27), & + wgk(28),wgk(29),wgk(30),wgk(31)/ & + 4.481480013316266e-02, 4.605923827100699e-02, & + 4.718554656929915e-02, 4.818586175708713e-02, & + 4.905543455502978e-02, 4.979568342707421e-02, & + 5.040592140278235e-02, 5.088179589874961e-02, & + 5.122154784925877e-02, 5.142612853745903e-02, & + 5.149472942945157e-02/ + data wg(1),wg(2),wg(3),wg(4),wg(5),wg(6),wg(7),wg(8)/ & + 7.968192496166606e-03, 1.846646831109096e-02, & + 2.878470788332337e-02, 3.879919256962705e-02, & + 4.840267283059405e-02, 5.749315621761907e-02, & + 6.597422988218050e-02, 7.375597473770521e-02/ + data wg(9),wg(10),wg(11),wg(12),wg(13),wg(14),wg(15)/ & + 8.075589522942022e-02, 8.689978720108298e-02, & + 9.212252223778613e-02, 9.636873717464426e-02, & + 9.959342058679527e-02, 1.017623897484055e-01, & + 1.028526528935588e-01/ +! + centr = 5.0e-01*(b+a) + hlgth = 5.0e-01*(b-a) + dhlgth = abs(hlgth) +! +! Compute the 61-point Kronrod approximation to the integral, +! and estimate the absolute error. +! + resg = 0.0e+00 + fc = f(centr) + resk = wgk(31)*fc + resabs = abs(resk) + + do j = 1, 15 + jtw = j*2 + absc = hlgth*xgk(jtw) + fval1 = f(centr-absc) + fval2 = f(centr+absc) + fv1(jtw) = fval1 + fv2(jtw) = fval2 + fsum = fval1+fval2 + resg = resg+wg(j)*fsum + resk = resk+wgk(jtw)*fsum + resabs = resabs+wgk(jtw)*(abs(fval1)+abs(fval2)) + end do + + do j = 1, 15 + jtwm1 = j*2-1 + absc = hlgth*xgk(jtwm1) + fval1 = f(centr-absc) + fval2 = f(centr+absc) + fv1(jtwm1) = fval1 + fv2(jtwm1) = fval2 + fsum = fval1+fval2 + resk = resk+wgk(jtwm1)*fsum + resabs = resabs+wgk(jtwm1)*(abs(fval1)+abs(fval2)) + end do + + reskh = resk * 5.0e-01 + resasc = wgk(31)*abs(fc-reskh) + + do j = 1, 30 + resasc = resasc+wgk(j)*(abs(fv1(j)-reskh)+abs(fv2(j)-reskh)) + end do + + result = resk*hlgth + resabs = resabs*dhlgth + resasc = resasc*dhlgth + abserr = abs((resk-resg)*hlgth) + + if ( resasc /= 0.0e+00 .and. abserr /= 0.0e+00) then + abserr = resasc*min ( 1.0e+00,(2.0e+02*abserr/resasc)**1.5e+00) + end if + + if ( resabs > tiny ( resabs ) / (5.0e+01* epsilon ( resabs ) )) then + abserr = max ( ( epsilon ( resabs ) *5.0e+01)*resabs, abserr ) + end if + + + return +end subroutine +subroutine qmomo ( alfa, beta, ri, rj, rg, rh, integr ) +! +!****************************************************************************** +! +!! QMOMO computes modified Chebyshev moments. +! +! +! Discussion: +! +! This routine computes modified Chebyshev moments. +! The K-th modified Chebyshev moment is defined as the +! integral over (-1,1) of W(X)*T(K,X), where T(K,X) is the +! Chebyshev polynomial of degree K. +! +! Reference: +! +! R Piessens, E de Doncker-Kapenger, C W Ueberhuber, D K Kahaner, +! QUADPACK, a Subroutine Package for Automatic Integration, +! Springer Verlag, 1983 +! +! Parameters: +! +! Input, real(dp) ALFA, a parameter in the weight function w(x), ALFA > -1. +! +! Input, real(dp) BETA, a parameter in the weight function w(x), BETA > -1. +! +! ri - real(dp) +! vector of dimension 25 +! ri(k) is the integral over (-1,1) of +! (1+x)**alfa*t(k-1,x), k = 1, ..., 25. +! +! rj - real(dp) +! vector of dimension 25 +! rj(k) is the integral over (-1,1) of +! (1-x)**beta*t(k-1,x), k = 1, ..., 25. +! +! rg - real(dp) +! vector of dimension 25 +! rg(k) is the integral over (-1,1) of +! (1+x)**alfa*log((1+x)/2)*t(k-1,x), k = 1, ...,25. +! +! rh - real(dp) +! vector of dimension 25 +! rh(k) is the integral over (-1,1) of +! (1-x)**beta*log((1-x)/2)*t(k-1,x), k = 1, ..., 25. +! +! integr - integer +! input parameter indicating the modified moments +! to be computed +! integr = 1 compute ri, rj +! = 2 compute ri, rj, rg +! = 3 compute ri, rj, rh +! = 4 compute ri, rj, rg, rh +! + implicit none +! + real(dp) alfa + real(dp) alfp1 + real(dp) alfp2 + real(dp) an + real(dp) anm1 + real(dp) beta + real(dp) betp1 + real(dp) betp2 + integer i + integer im1 + integer integr + real(dp) ralf + real(dp) rbet + real(dp) rg(25) + real(dp) rh(25) + real(dp) ri(25) + real(dp) rj(25) +! + alfp1 = alfa+1.0e+00 + betp1 = beta+1.0e+00 + alfp2 = alfa+2.0e+00 + betp2 = beta+2.0e+00 + ralf = 2.0e+00**alfp1 + rbet = 2.0e+00**betp1 +! +! Compute RI, RJ using a forward recurrence relation. +! + ri(1) = ralf/alfp1 + rj(1) = rbet/betp1 + ri(2) = ri(1)*alfa/alfp2 + rj(2) = rj(1)*beta/betp2 + an = 2.0e+00 + anm1 = 1.0e+00 + + do i = 3, 25 + ri(i) = -(ralf+an*(an-alfp2)*ri(i-1))/(anm1*(an+alfp1)) + rj(i) = -(rbet+an*(an-betp2)*rj(i-1))/(anm1*(an+betp1)) + anm1 = an + an = an+1.0e+00 + end do + + if ( integr == 1 ) go to 70 + if ( integr == 3 ) go to 40 +! +! Compute RG using a forward recurrence relation. +! + rg(1) = -ri(1)/alfp1 + rg(2) = -(ralf+ralf)/(alfp2*alfp2)-rg(1) + an = 2.0e+00 + anm1 = 1.0e+00 + im1 = 2 + + do i = 3, 25 + rg(i) = -(an*(an-alfp2)*rg(im1)-an*ri(im1)+anm1*ri(i))/ & + (anm1*(an+alfp1)) + anm1 = an + an = an+1.0e+00 + im1 = i + end do + + if ( integr == 2 ) go to 70 +! +! Compute RH using a forward recurrence relation. +! +40 continue + + rh(1) = -rj(1) / betp1 + rh(2) = -(rbet+rbet)/(betp2*betp2)-rh(1) + an = 2.0e+00 + anm1 = 1.0e+00 + im1 = 2 + + do i = 3, 25 + rh(i) = -(an*(an-betp2)*rh(im1)-an*rj(im1)+ & + anm1*rj(i))/(anm1*(an+betp1)) + anm1 = an + an = an+1.0e+00 + im1 = i + end do + + do i = 2, 25, 2 + rh(i) = -rh(i) + end do + + 70 continue + + do i = 2, 25, 2 + rj(i) = -rj(i) + end do + + 90 continue + + return +end subroutine +subroutine qng ( f, a, b, epsabs, epsrel, result, abserr, neval, ier ) +! +!****************************************************************************** +! +!! QNG estimates an integral, using non-adaptive integration. +! +! +! Discussion: +! +! The routine calculates an approximation RESULT to a definite integral +! I = integral of F over (A,B), +! hopefully satisfying +! || I - RESULT || <= max ( EPSABS, EPSREL * ||I|| ). +! +! The routine is a simple non-adaptive automatic integrator, based on +! a sequence of rules with increasing degree of algebraic +! precision (Patterson, 1968). +! +! Reference: +! +! R Piessens, E de Doncker-Kapenger, C W Ueberhuber, D K Kahaner, +! QUADPACK, a Subroutine Package for Automatic Integration, +! Springer Verlag, 1983 +! +! Parameters: +! +! Input, external real(dp) F, the name of the function routine, of the form +! function f ( x ) +! real(dp) f +! real(dp) x +! which evaluates the integrand function. +! +! Input, real(dp) A, B, the limits of integration. +! +! Input, real(dp) EPSABS, EPSREL, the absolute and relative accuracy requested. +! +! Output, real(dp) RESULT, the estimated value of the integral. +! RESULT is obtained by applying the 21-point Gauss-Kronrod rule (RES21) +! obtained by optimal addition of abscissae to the 10-point Gauss rule +! (RES10), or by applying the 43-point rule (RES43) obtained by optimal +! addition of abscissae to the 21-point Gauss-Kronrod rule, or by +! applying the 87-point rule (RES87) obtained by optimal addition of +! abscissae to the 43-point rule. +! +! Output, real(dp) ABSERR, an estimate of || I - RESULT ||. +! +! Output, integer NEVAL, the number of times the integral was evaluated. +! +! ier - ier = 0 normal and reliable termination of the +! routine. it is assumed that the requested +! accuracy has been achieved. +! ier > 0 abnormal termination of the routine. it is +! assumed that the requested accuracy has +! not been achieved. +! ier = 1 the maximum number of steps has been +! executed. the integral is probably too +! difficult to be calculated by qng. +! = 6 the input is invalid, because +! epsabs < 0 and epsrel < 0, +! result, abserr and neval are set to zero. +! +! Local Parameters: +! +! centr - mid point of the integration interval +! hlgth - half-length of the integration interval +! fcentr - function value at mid point +! absc - abscissa +! fval - function value +! savfun - array of function values which have already +! been computed +! res10 - 10-point Gauss result +! res21 - 21-point Kronrod result +! res43 - 43-point result +! res87 - 87-point result +! resabs - approximation to the integral of abs(f) +! resasc - approximation to the integral of abs(f-i/(b-a)) +! + implicit none +! + real(dp) a + real(dp) absc + real(dp) abserr + real(dp) b + real(dp) centr + real(dp) dhlgth + real(dp) epsabs + real(dp) epsrel + real(dp), external :: f + real(dp) fcentr + real(dp) fval + real(dp) fval1 + real(dp) fval2 + real(dp) fv1(5) + real(dp) fv2(5) + real(dp) fv3(5) + real(dp) fv4(5) + real(dp) hlgth + integer ier + integer ipx + integer k + integer l + integer neval + real(dp) result + real(dp) res10 + real(dp) res21 + real(dp) res43 + real(dp) res87 + real(dp) resabs + real(dp) resasc + real(dp) reskh + real(dp) savfun(21) + real(dp) w10(5) + real(dp) w21a(5) + real(dp) w21b(6) + real(dp) w43a(10) + real(dp) w43b(12) + real(dp) w87a(21) + real(dp) w87b(23) + real(dp) x1(5) + real(dp) x2(5) + real(dp) x3(11) + real(dp) x4(22) +! +! the following data statements contain the abscissae +! and weights of the integration rules used. +! +! x1 abscissae common to the 10-, 21-, 43- and 87-point +! rule +! x2 abscissae common to the 21-, 43- and 87-point rule +! x3 abscissae common to the 43- and 87-point rule +! x4 abscissae of the 87-point rule +! w10 weights of the 10-point formula +! w21a weights of the 21-point formula for abscissae x1 +! w21b weights of the 21-point formula for abscissae x2 +! w43a weights of the 43-point formula for absissae x1, x3 +! w43b weights of the 43-point formula for abscissae x3 +! w87a weights of the 87-point formula for abscissae x1, +! x2 and x3 +! w87b weights of the 87-point formula for abscissae x4 +! + data x1(1),x1(2),x1(3),x1(4),x1(5)/ & + 9.739065285171717e-01, 8.650633666889845e-01, & + 6.794095682990244e-01, 4.333953941292472e-01, & + 1.488743389816312e-01/ + data x2(1),x2(2),x2(3),x2(4),x2(5)/ & + 9.956571630258081e-01, 9.301574913557082e-01, & + 7.808177265864169e-01, 5.627571346686047e-01, & + 2.943928627014602e-01/ + data x3(1),x3(2),x3(3),x3(4),x3(5),x3(6),x3(7),x3(8),x3(9),x3(10), & + x3(11)/ & + 9.993333609019321e-01, 9.874334029080889e-01, & + 9.548079348142663e-01, 9.001486957483283e-01, & + 8.251983149831142e-01, 7.321483889893050e-01, & + 6.228479705377252e-01, 4.994795740710565e-01, & + 3.649016613465808e-01, 2.222549197766013e-01, & + 7.465061746138332e-02/ + data x4(1),x4(2),x4(3),x4(4),x4(5),x4(6),x4(7),x4(8),x4(9),x4(10), & + x4(11),x4(12),x4(13),x4(14),x4(15),x4(16),x4(17),x4(18),x4(19), & + x4(20),x4(21),x4(22)/ 9.999029772627292e-01, & + 9.979898959866787e-01, 9.921754978606872e-01, & + 9.813581635727128e-01, 9.650576238583846e-01, & + 9.431676131336706e-01, 9.158064146855072e-01, & + 8.832216577713165e-01, 8.457107484624157e-01, & + 8.035576580352310e-01, 7.570057306854956e-01, & + 7.062732097873218e-01, 6.515894665011779e-01, & + 5.932233740579611e-01, 5.314936059708319e-01, & + 4.667636230420228e-01, 3.994248478592188e-01, & + 3.298748771061883e-01, 2.585035592021616e-01, & + 1.856953965683467e-01, 1.118422131799075e-01, & + 3.735212339461987e-02/ + data w10(1),w10(2),w10(3),w10(4),w10(5)/ & + 6.667134430868814e-02, 1.494513491505806e-01, & + 2.190863625159820e-01, 2.692667193099964e-01, & + 2.955242247147529e-01/ + data w21a(1),w21a(2),w21a(3),w21a(4),w21a(5)/ & + 3.255816230796473e-02, 7.503967481091995e-02, & + 1.093871588022976e-01, 1.347092173114733e-01, & + 1.477391049013385e-01/ + data w21b(1),w21b(2),w21b(3),w21b(4),w21b(5),w21b(6)/ & + 1.169463886737187e-02, 5.475589657435200e-02, & + 9.312545458369761e-02, 1.234919762620659e-01, & + 1.427759385770601e-01, 1.494455540029169e-01/ + data w43a(1),w43a(2),w43a(3),w43a(4),w43a(5),w43a(6),w43a(7), & + w43a(8),w43a(9),w43a(10)/ 1.629673428966656e-02, & + 3.752287612086950e-02, 5.469490205825544e-02, & + 6.735541460947809e-02, 7.387019963239395e-02, & + 5.768556059769796e-03, 2.737189059324884e-02, & + 4.656082691042883e-02, 6.174499520144256e-02, & + 7.138726726869340e-02/ + data w43b(1),w43b(2),w43b(3),w43b(4),w43b(5),w43b(6),w43b(7), & + w43b(8),w43b(9),w43b(10),w43b(11),w43b(12)/ & + 1.844477640212414e-03, 1.079868958589165e-02, & + 2.189536386779543e-02, 3.259746397534569e-02, & + 4.216313793519181e-02, 5.074193960018458e-02, & + 5.837939554261925e-02, 6.474640495144589e-02, & + 6.956619791235648e-02, 7.282444147183321e-02, & + 7.450775101417512e-02, 7.472214751740301e-02/ + data w87a(1),w87a(2),w87a(3),w87a(4),w87a(5),w87a(6),w87a(7), & + w87a(8),w87a(9),w87a(10),w87a(11),w87a(12),w87a(13),w87a(14), & + w87a(15),w87a(16),w87a(17),w87a(18),w87a(19),w87a(20),w87a(21)/ & + 8.148377384149173e-03, 1.876143820156282e-02, & + 2.734745105005229e-02, 3.367770731163793e-02, & + 3.693509982042791e-02, 2.884872430211531e-03, & + 1.368594602271270e-02, 2.328041350288831e-02, & + 3.087249761171336e-02, 3.569363363941877e-02, & + 9.152833452022414e-04, 5.399280219300471e-03, & + 1.094767960111893e-02, 1.629873169678734e-02, & + 2.108156888920384e-02, 2.537096976925383e-02, & + 2.918969775647575e-02, 3.237320246720279e-02, & + 3.478309895036514e-02, 3.641222073135179e-02, & + 3.725387550304771e-02/ + data w87b(1),w87b(2),w87b(3),w87b(4),w87b(5),w87b(6),w87b(7), & + w87b(8),w87b(9),w87b(10),w87b(11),w87b(12),w87b(13),w87b(14), & + w87b(15),w87b(16),w87b(17),w87b(18),w87b(19),w87b(20),w87b(21), & + w87b(22),w87b(23)/ 2.741455637620724e-04, & + 1.807124155057943e-03, 4.096869282759165e-03, & + 6.758290051847379e-03, 9.549957672201647e-03, & + 1.232944765224485e-02, 1.501044734638895e-02, & + 1.754896798624319e-02, 1.993803778644089e-02, & + 2.219493596101229e-02, 2.433914712600081e-02, & + 2.637450541483921e-02, 2.828691078877120e-02, & + 3.005258112809270e-02, 3.164675137143993e-02, & + 3.305041341997850e-02, 3.425509970422606e-02, & + 3.526241266015668e-02, 3.607698962288870e-02, & + 3.669860449845609e-02, 3.712054926983258e-02, & + 3.733422875193504e-02, 3.736107376267902e-02/ +! +! Test on validity of parameters. +! + result = 0.0e+00 + abserr = 0.0e+00 + neval = 0 + + if ( epsabs < 0.0e+00 .and. epsrel < 0.0e+00 ) then + ier = 6 + return + end if + + hlgth = 5.0e-01*(b-a) + dhlgth = abs(hlgth) + centr = 5.0e-01*(b+a) + fcentr = f(centr) + neval = 21 + ier = 1 +! +! Compute the integral using the 10- and 21-point formula. +! + do l = 1, 3 + + if ( l == 1 ) then + + res10 = 0.0e+00 + res21 = w21b(6) * fcentr + resabs = w21b(6) * abs(fcentr) + + do k = 1, 5 + absc = hlgth*x1(k) + fval1 = f(centr+absc) + fval2 = f(centr-absc) + fval = fval1+fval2 + res10 = res10+w10(k)*fval + res21 = res21+w21a(k)*fval + resabs = resabs+w21a(k)*(abs(fval1)+abs(fval2)) + savfun(k) = fval + fv1(k) = fval1 + fv2(k) = fval2 + end do + + ipx = 5 + + do k = 1, 5 + ipx = ipx+1 + absc = hlgth*x2(k) + fval1 = f(centr+absc) + fval2 = f(centr-absc) + fval = fval1 + fval2 + res21 = res21 + w21b(k) * fval + resabs = resabs + w21b(k) * (abs(fval1)+abs(fval2)) + savfun(ipx) = fval + fv3(k) = fval1 + fv4(k) = fval2 + end do +! +! Test for convergence. +! + result = res21*hlgth + resabs = resabs*dhlgth + reskh = 5.0e-01*res21 + resasc = w21b(6)*abs(fcentr-reskh) + + do k = 1, 5 + resasc = resasc+w21a(k)*(abs(fv1(k)-reskh)+abs(fv2(k)-reskh)) & + +w21b(k)*(abs(fv3(k)-reskh)+abs(fv4(k)-reskh)) + end do + + abserr = abs((res21-res10)*hlgth) + resasc = resasc*dhlgth +! +! Compute the integral using the 43-point formula. +! + else if ( l == 2 ) then + + res43 = w43b(12)*fcentr + neval = 43 + + do k = 1, 10 + res43 = res43+savfun(k) * w43a(k) + end do + + do k = 1, 11 + ipx = ipx+1 + absc = hlgth*x3(k) + fval = f(absc+centr)+f(centr-absc) + res43 = res43+fval*w43b(k) + savfun(ipx) = fval + end do +! +! Test for convergence. +! + result = res43 * hlgth + abserr = abs((res43-res21)*hlgth) +! +! Compute the integral using the 87-point formula. +! + else if ( l == 3 ) then + + res87 = w87b(23) * fcentr + neval = 87 + + do k = 1, 21 + res87 = res87 + savfun(k) * w87a(k) + end do + + do k = 1, 22 + absc = hlgth * x4(k) + res87 = res87+w87b(k)*(f(absc+centr)+f(centr-absc)) + end do + + result = res87 * hlgth + abserr = abs ( ( res87-res43) * hlgth ) + + end if + + if ( resasc /= 0.0e+00.and.abserr /= 0.0e+00 ) then + abserr = resasc * min ( 1.0e+00,(2.0e+02*abserr/resasc)**1.5e+00) + end if + + if ( resabs > tiny ( resabs ) / ( 5.0e+01 * epsilon ( resabs ) ) ) then + abserr = max (( epsilon ( resabs ) *5.0e+01) * resabs, abserr ) + end if + + if ( abserr <= max ( epsabs, epsrel*abs(result))) then + ier = 0 + end if + + if ( ier == 0 ) then + exit + end if + + end do + + return +end subroutine +subroutine qsort ( limit, last, maxerr, ermax, elist, iord, nrmax ) +! +!****************************************************************************** +! +!! QSORT maintains the order of a list of local error estimates. +! +! +! Discussion: +! +! This routine maintains the descending ordering in the list of the +! local error estimates resulting from the interval subdivision process. +! At each call two error estimates are inserted using the sequential +! search top-down for the largest error estimate and bottom-up for the +! smallest error estimate. +! +! Reference: +! +! R Piessens, E de Doncker-Kapenger, C W Ueberhuber, D K Kahaner, +! QUADPACK, a Subroutine Package for Automatic Integration, +! Springer Verlag, 1983 +! +! Parameters: +! +! Input, integer LIMIT, the maximum number of error estimates the list can +! contain. +! +! Input, integer LAST, the current number of error estimates. +! +! Input/output, integer MAXERR, the index in the list of the NRMAX-th +! largest error. +! +! Output, real(dp) ERMAX, the NRMAX-th largest error = ELIST(MAXERR). +! +! Input, real(dp) ELIST(LIMIT), contains the error estimates. +! +! Input/output, integer IORD(LAST). The first K elements contain +! pointers to the error estimates such that ELIST(IORD(1)) through +! ELIST(IORD(K)) form a decreasing sequence, with +! K = LAST +! if +! LAST <= (LIMIT/2+2), +! and otherwise +! K = LIMIT+1-LAST. +! +! Input/output, integer NRMAX. +! + implicit none +! + integer last +! + real(dp) elist(last) + real(dp) ermax + real(dp) errmax + real(dp) errmin + integer i + integer ibeg + integer iord(last) + integer isucc + integer j + integer jbnd + integer jupbn + integer k + integer limit + integer maxerr + integer nrmax +! +! Check whether the list contains more than two error estimates. +! + if ( last <= 2 ) then + iord(1) = 1 + iord(2) = 2 + go to 90 + end if +! +! This part of the routine is only executed if, due to a +! difficult integrand, subdivision increased the error +! estimate. in the normal case the insert procedure should +! start after the nrmax-th largest error estimate. +! + errmax = elist(maxerr) + + do i = 1, nrmax-1 + + isucc = iord(nrmax-1) + + if ( errmax <= elist(isucc) ) then + exit + end if + + iord(nrmax) = isucc + nrmax = nrmax-1 + + end do +! +! Compute the number of elements in the list to be maintained +! in descending order. This number depends on the number of +! subdivisions still allowed. +! + jupbn = last + + if ( last > (limit/2+2) ) then + jupbn = limit+3-last + end if + + errmin = elist(last) +! +! Insert errmax by traversing the list top-down, starting +! comparison from the element elist(iord(nrmax+1)). +! + jbnd = jupbn-1 + ibeg = nrmax+1 + + do i = ibeg, jbnd + isucc = iord(i) + if ( errmax >= elist(isucc) ) go to 60 + iord(i-1) = isucc + end do + + iord(jbnd) = maxerr + iord(jupbn) = last + go to 90 +! +! Insert errmin by traversing the list bottom-up. +! +60 continue + + iord(i-1) = maxerr + k = jbnd + + do j = i, jbnd + isucc = iord(k) + if ( errmin < elist(isucc) ) go to 80 + iord(k+1) = isucc + k = k-1 + end do + + iord(i) = last + go to 90 + +80 continue + + iord(k+1) = last +! +! Set maxerr and ermax. +! +90 continue + + maxerr = iord(nrmax) + ermax = elist(maxerr) + + return +end subroutine +function qwgtc ( x, c, p2, p3, p4, kp ) +! +!****************************************************************************** +! +!! QWGTC defines the weight function used by QC25C. +! +! +! Discussion: +! +! The weight function has the form 1 / ( X - C ). +! +! Reference: +! +! R Piessens, E de Doncker-Kapenger, C W Ueberhuber, D K Kahaner, +! QUADPACK, a Subroutine Package for Automatic Integration, +! Springer Verlag, 1983 +! +! Parameters: +! +! Input, real(dp) X, the point at which the weight function is evaluated. +! +! Input, real(dp) C, the location of the singularity. +! +! Input, real(dp) P2, P3, P4, parameters that are not used. +! +! Input, integer KP, a parameter that is not used. +! +! Output, real(dp) QWGTC, the value of the weight function at X. +! + implicit none +! + real(dp) c + integer kp + real(dp) p2 + real(dp) p3 + real(dp) p4 + real(dp) qwgtc + real(dp) x +! + qwgtc = 1.0e+00 / ( x - c ) + + return +end function +function qwgto ( x, omega, p2, p3, p4, integr ) +! +!****************************************************************************** +! +!! QWGTO defines the weight functions used by QC25O. +! +! +! Reference: +! +! R Piessens, E de Doncker-Kapenger, C W Ueberhuber, D K Kahaner, +! QUADPACK, a Subroutine Package for Automatic Integration, +! Springer Verlag, 1983 +! +! Parameters: +! +! Input, real(dp) X, the point at which the weight function is evaluated. +! +! Input, real(dp) OMEGA, the factor multiplying X. +! +! Input, real(dp) P2, P3, P4, parameters that are not used. +! +! Input, integer INTEGR, specifies which weight function is used: +! 1. W(X) = cos ( OMEGA * X ) +! 2, W(X) = sin ( OMEGA * X ) +! +! Output, real(dp) QWGTO, the value of the weight function at X. +! + implicit none +! + integer integr + real(dp) omega + real(dp) p2 + real(dp) p3 + real(dp) p4 + real(dp) qwgto + real(dp) x +! + if ( integr == 1 ) then + qwgto = cos ( omega * x ) + else if ( integr == 2 ) then + qwgto = sin ( omega * x ) + end if + + return +end function +function qwgts ( x, a, b, alfa, beta, integr ) +! +!****************************************************************************** +! +!! QWGTS defines the weight functions used by QC25S. +! +! +! Reference: +! +! R Piessens, E de Doncker-Kapenger, C W Ueberhuber, D K Kahaner, +! QUADPACK, a Subroutine Package for Automatic Integration, +! Springer Verlag, 1983 +! +! Parameters: +! +! Input, real(dp) X, the point at which the weight function is evaluated. +! +! Input, real(dp) A, B, the endpoints of the integration interval. +! +! Input, real(dp) ALFA, BETA, exponents that occur in the weight function. +! +! Input, integer INTEGR, specifies which weight function is used: +! 1. W(X) = (X-A)**ALFA * (B-X)**BETA +! 2, W(X) = (X-A)**ALFA * (B-X)**BETA * log (X-A) +! 3, W(X) = (X-A)**ALFA * (B-X)**BETA * log (B-X) +! 4, W(X) = (X-A)**ALFA * (B-X)**BETA * log (X-A) * log(B-X) +! +! Output, real(dp) QWGTS, the value of the weight function at X. +! + implicit none +! + real(dp) a + real(dp) alfa + real(dp) b + real(dp) beta + integer integr + real(dp) qwgts + real(dp) x +! + if ( integr == 1 ) then + qwgts = ( x - a )**alfa * ( b - x )**beta + else if ( integr == 2 ) then + qwgts = ( x - a )**alfa * ( b - x )**beta * log ( x - a ) + else if ( integr == 3 ) then + qwgts = ( x - a )**alfa * ( b - x )**beta * log ( b - x ) + else if ( integr == 4 ) then + qwgts = ( x - a )**alfa * ( b - x )**beta * log ( x - a ) * log ( b - x ) + end if + + return +end function +subroutine r_swap ( x, y ) +! +!******************************************************************************* +! +!! R_SWAP swaps two real(dp) values. +! +! +! Modified: +! +! 01 May 2000 +! +! Author: +! +! John Burkardt +! +! Parameters: +! +! Input/output, real(dp) X, Y. On output, the values of X and +! Y have been interchanged. +! + implicit none +! + real(dp) x + real(dp) y + real(dp) z +! + z = x + x = y + y = z + + return +end subroutine +subroutine timestamp ( ) +! +!******************************************************************************* +! +!! TIMESTAMP prints the current YMDHMS date as a time stamp. +! +! +! Example: +! +! May 31 2001 9:45:54.872 AM +! +! Modified: +! +! 31 May 2001 +! +! Author: +! +! John Burkardt +! +! Parameters: +! +! None +! + implicit none +! + character ( len = 8 ) ampm + integer d + character ( len = 8 ) date + integer h + integer m + integer mm + character ( len = 9 ), parameter, dimension(12) :: month = (/ & + 'January ', 'February ', 'March ', 'April ', & + 'May ', 'June ', 'July ', 'August ', & + 'September', 'October ', 'November ', 'December ' /) + integer n + integer s + character ( len = 10 ) time + integer values(8) + integer y + character ( len = 5 ) zone +! + call date_and_time ( date, time, zone, values ) + + y = values(1) + m = values(2) + d = values(3) + h = values(5) + n = values(6) + s = values(7) + mm = values(8) + + if ( h < 12 ) then + ampm = 'AM' + else if ( h == 12 ) then + if ( n == 0 .and. s == 0 ) then + ampm = 'Noon' + else + ampm = 'PM' + end if + else + h = h - 12 + if ( h < 12 ) then + ampm = 'PM' + else if ( h == 12 ) then + if ( n == 0 .and. s == 0 ) then + ampm = 'Midnight' + else + ampm = 'AM' + end if + end if + end if + + write ( *, '(a,1x,i2,1x,i4,2x,i2,a1,i2.2,a1,i2.2,a1,i3.3,1x,a)' ) & + trim ( month(m) ), d, y, h, ':', n, ':', s, '.', mm, trim ( ampm ) + + return +end subroutine +end module quadpack diff --git a/applications/PUfoam/MoDeNaModels/foamConductivity/src/src/solidprop.f90 b/applications/PUfoam/MoDeNaModels/foamConductivity/src/src/solidprop.f90 new file mode 100644 index 000000000..89f29aeba --- /dev/null +++ b/applications/PUfoam/MoDeNaModels/foamConductivity/src/src/solidprop.f90 @@ -0,0 +1,132 @@ +!> @file +!! subroutines for evaluation of radiative properties of solid +!! @author Pavel Ferkl +!! @ingroup foam_cond +module solidprop + use constants + implicit none + private + public optconst +contains +!********************************BEGINNING************************************* +!> determine optical constants n,k for one wavelength +subroutine optconst(lambda,n,k) + use quadpack + use interpolation + real(dp), intent(in) :: lambda !wavelength + real(dp), intent(out) :: n,k !complex refractive index + !qags variables + real(dp) :: a !start point of integration + real(dp) :: abserr + real(dp) :: b !end point of integration + real(dp), parameter :: epsabs = 0.0e0_dp + real(dp), parameter :: epsrel = 0.001e0_dp + integer :: ier + integer :: neval + real(dp) :: res + !end of qags variables + integer :: ni=1 !number of points, where we want to interpolate + real(dp) :: xi(1) !x-values of points, where we want to interpolate + real(dp) :: yi(1) !interpolated y-values + a=lambdan(1) + b=lambdan(size(lambdan)) + if (lambdab) then + call qag ( nwew, a, b, epsabs, epsrel, 1, res, abserr, neval, ier ) + if (ier /= 0) then + write(*,*) 'qag returned',ier + write(*,*) 'wavelength',lambda + write(*,*) 'new real part of refractive index not calculated' + stop + endif + n=res + call qag ( kwew, a, b, epsabs, epsrel, 1, res, abserr, neval, ier ) + if (ier /= 0) then + write(*,*) 'qag returned',ier + write(*,*) 'wavelength',lambda + write(*,*) 'new imaginery part of refractive index not calculated' + stop + endif + k=res + call qag ( Planck2, a, b, epsabs, epsrel, 1, res, abserr, neval, ier ) + if (ier /= 0) then + write(*,*) 'qag returned',ier + write(*,*) 'wavelength',lambda + write(*,*) 'new refractive index not calculated' + stop + endif + n=n/res + k=k/res + else + xi(1)=lambda + call pwl_interp_1d ( size(lambdan), lambdan, nwl, ni, xi, yi ) + n=yi(1) + call pwl_interp_1d ( size(lambdak), lambdak, kwl, ni, xi, yi ) + k=yi(1) + endif +end subroutine optconst +!***********************************END**************************************** + + +!********************************BEGINNING************************************* +!> evaluates real part of index of refraction times emissive power +real(dp) function nwew ( lambda ) +!***************************DECLARATION****************************** + use interpolation + real(dp) :: lambda + integer :: ni=1 !number of points, where we want to interpolate + real(dp) :: xi(1) !x-values of points, where we want to interpolate + real(dp) :: yi(1) !interpolated y-values +!******************************BODY********************************** + xi(1)=lambda + call pwl_interp_1d ( size(lambdan), lambdan, nwl, ni, xi, yi ) + nwew=yi(1)*Planck(tmean,lambda) +end function nwew +!***********************************END**************************************** + + +!********************************BEGINNING************************************* +!> evaluates real part of index of refraction times emissive power +real(dp) function kwew ( lambda ) +!***************************DECLARATION****************************** + use interpolation + real(dp) :: lambda + integer :: ni=1 !number of points, where we want to interpolate + real(dp) :: xi(1) !x-values of points, where we want to interpolate + real(dp) :: yi(1) !interpolated y-values +!******************************BODY********************************** + xi(1)=lambda + call pwl_interp_1d ( size(lambdak), lambdak, kwl, ni, xi, yi ) + kwew=yi(1)*Planck(tmean,lambda) +end function kwew +!***********************************END**************************************** + + +!********************************BEGINNING************************************* +!> determines emissive power +real(dp) function Planck(temp,lambda) +!***************************DECLARATION****************************** + real(dp), intent(in) :: temp !temperature + real(dp), intent(in) :: lambda !wavelength + real(dp) :: n +!******************************BODY********************************** + n=1.57_dp !just guess, equation for emissive power is correct only + ! for constant n + Planck=2*pi*hPc*c0**2/(n**2*lambda**5*(exp(hPc*c0/(n*lambda*kb*temp))-1)) +end function Planck +!***********************************END**************************************** + + +!********************************BEGINNING************************************* +!> determines emissive power +real(dp) function Planck2(lambda) +!***************************DECLARATION****************************** + real(dp), intent(in) :: lambda !wavelength +!******************************BODY********************************** + Planck2=Planck(tmean,lambda) +end function Planck2 +!***********************************END**************************************** +end module solidprop diff --git a/applications/PUfoam/MoDeNaModels/foamConductivity/src/src/specfun.f90 b/applications/PUfoam/MoDeNaModels/foamConductivity/src/src/specfun.f90 new file mode 100644 index 000000000..05b2f43dc --- /dev/null +++ b/applications/PUfoam/MoDeNaModels/foamConductivity/src/src/specfun.f90 @@ -0,0 +1,218 @@ +!> @file +!! subroutines for special mathematical functions +!! @author Pavel Ferkl +!! @ingroup foam_cond +module specfun + use constants, only: dp,pi,iu,eulergamma + implicit none + private + public factorial,digamma,bessel,hankel +contains +!********************************BEGINNING************************************* +!> calculates Bessel functions of the first and second kind and +!! their derivatives for complex argument +subroutine bessel(n,x,tol,j,dj,y,dy) + use besselj, only: ZBESJ + use bessely, only: ZBESY + integer, intent(in) :: n !maximum order calculated + complex(dp), intent(in) :: x !argument + real(dp), intent(in) :: tol !relative tolerance, currently not used + complex(dp), dimension(0:n), intent(out) :: & + j,& !bessel function of the first kind + dj,& !derivative of bessel function of the first kind + y,& !bessel function of the second kind + dy !derivative of bessel function of the second kind + real(dp), dimension(n+1) :: cyr,cyi,cwr,cwi + integer :: i,m,nz,ierr + call ZBESJ(realpart(x),imagpart(x),0.e0_dp,1,n+1,cyr,cyi,nz,ierr) + if (nz>0) then + write(*,*) 'underflow encountered' + write(*,*) 'bessel function J not calculated',n,x + stop + endif + if (ierr /= 0) then + write(*,*) 'did not converge' + write(*,*) 'bessel function J not calculated',n,x + stop + endif + do i=0,n + j(i)=cmplx(cyr(i+1),cyi(i+1),kind=dp) + enddo +! write(*,*) x +! write(*,*) j + call ZBESY(realpart(x),imagpart(x),0.e0_dp,1,n+1,cyr,cyi,nz,cwr,cwi,ierr) + if (nz>0) then + write(*,*) 'underflow encountered' + write(*,*) 'bessel function Y not calculated',n,x + stop + endif + if (ierr /= 0) then + write(*,*) 'did not converge' + write(*,*) 'bessel function Y not calculated',n,x + stop + endif + do i=0,n + y(i)=cmplx(cyr(i+1),cyi(i+1),kind=dp) + enddo +! write(*,*) x +! write(*,*) y +! stop + !http://keisan.casio.com/exec/system/1180573474 + dj(0)=-j(1) + dy(0)=-y(1) + do m=1,n + dj(m)=j(m-1)-m/x*j(m) + dy(m)=y(m-1)-m/x*y(m) + enddo +end subroutine bessel +!***********************************END**************************************** + + +!********************************BEGINNING************************************* +!> calculates Hankel functions of the first and second kind and +!! their derivatives for complex argument +subroutine hankel(n,x,tol,h1,dh1,h2,dh2) + integer, intent(in) :: n !maximum order calculated + complex(dp), intent(in) :: x !argument + real(dp), intent(in) :: tol !relative tolerance + complex(dp), dimension(0:n), intent(out) :: & + h1,& !hankel function of the first kind + dh1,& !derivative of hankel function of the first kind + h2,& !hankel function of the second kind + dh2 !derivative of hankel function of the second kind + integer :: i + complex(dp), dimension(0:n) :: j,dj,y,dy + !http://keisan.casio.com/has10/SpecExec.cgi?id=system/2006/1222514923 + call bessel(n,x,tol,j,dj,y,dy) + h1=j+iu*y + h2=j-iu*y + dh1(0)=-h1(1) + dh2(0)=-h2(1) + do i=1,n + dh1(i)=h1(i-1)-i/x*h1(i) + dh2(i)=h2(i-1)-i/x*h2(i) + enddo +end subroutine hankel +!***********************************END**************************************** + + +!********************************BEGINNING************************************* +!> calculates factorial +recursive function factorial(n) result(fact) + integer, intent(in) :: n !argument + real(dp) :: fact + if (n<0) then + stop 'factorial defined only for nonnegative integers' + elseif (n==0) then + fact=1 + else + fact=n*factorial(n-1) + endif +end function factorial +!***********************************END**************************************** + + +!********************************BEGINNING************************************* +!> calculates digamma function +!! taken from http://mathworld.wolfram.com/DigammaFunction.html +real(dp) function digamma(n) + integer, intent(in) :: n !argument + integer :: i + digamma=-eulergamma + do i=1,n-1 + digamma=digamma+1.0_dp/i + enddo +end function digamma +!***********************************END**************************************** + + +!SUBROUTINE JNCOMP(Z,NS,JN) +! !taken from Daniel Mackowski code for scattering of radiation by long cylinders +! !it might be more effective, I did not test it thoroughly +! IMPLICIT none +! COMPLEX*16 JN(0:*),A,Z +! integer :: n,nd,ns +! +!! CALCULATES THE INTEGER-ORDER BESSEL FUNCTION JN(Z) +!! N=0,1,...NS, FOR COMPLEX ARGUMENT Z. REFER TO BOHREN & HUFFMAN +!! FOR DETAILS. CODED 9/20/90 +! +! ND=NINT((101+CDABS(Z))**.499+NS) +! ND=2*NINT(ND/2.) +! JN(ND)=0. +! JN(ND-1)=1.D-32 +! A=0. +! DO N=ND-1,3,-2 +! JN(N-1)=2.*N*JN(N)/Z-JN(N+1) +! JN(N-2)=2.*(N-1)*JN(N-1)/Z-JN(N) +! A=A+JN(N-1) +! enddo +! JN(0)=2.*JN(1)/Z-JN(2) +! A=JN(0)+2.*A +! DO N=0,NS +! JN(N)=JN(N)/A +! enddo +!RETURN +!END subroutine + + +!!********************************BEGINNING************************************* +!!calculates Bessel functions of the first and second kind and their derivatives for complex argument +!!doesn't work properly for high orders +!subroutine bessel(n,x,tol,j,dj,y,dy) +! integer, intent(in) :: n !maximum order calculated +! complex(dp), intent(in) :: x !argument +! real(dp), intent(in) :: tol !relative tolerance +! complex(dp), dimension(0:n), intent(out) :: j !bessel function of the first kind +! complex(dp), dimension(0:n), intent(out) :: dj !derivative of bessel function of the first kind +! complex(dp), dimension(0:n), intent(out) :: y !bessel function of the second kind +! complex(dp), dimension(0:n), intent(out) :: dy !derivative of bessel function of the second kind +! integer :: l,m,lmax=200 +! complex(dp) :: jold,yold +! jold=0;yold=0 +! j=0;dj=0;y=0;dy=0 +!! write(*,*) x +! do m=0,n +! do l=0,lmax +!! write(*,*) l,m,j(m) +!! j(m)=j(m)+(-1)**l/(2**(2*l+m)*factorial(l)*factorial(m+l)+0.0_dp)*x**(2*l+m) !http://mathworld.wolfram.com/BesselFunctionoftheFirstKind.html (it works just as well) +! j(m)=j(m)+(-1)**l/(factorial(l)*factorial(m+l)+0.0_dp)*(x/2)**(2*l+m) !http://keisan.casio.com/exec/system/1180573474 +! if (abs(j(m)-jold)/abs(j(m)) @file +!! subroutines for calculation of equivalent conductivity of foam, loading of +!! parameters and several parametric studies +!! @author Pavel Ferkl +!! @ingroup foam_cond +module tests + use constants + use ioutils + use foamprop, only: effrad + use foamgeom, only: foam_morpholgy + use conduction, only: effcond + use condrad, only: equcond,cond,alpha,sigma + implicit none + private + public loadParameters,eqcond,eqcond_por,eqcond_dcell,eqcond_strut + character(len=99) :: fileplacein_par='./' !modena + character(len=99) :: fileplacein_ref='../spectra/' !modena + character(len=99) :: fileplaceout='./' !modena + character(len=99) :: inputs='inputs.in',spectra='spectra.out' + character(len=99) :: nspec='spec_n.in' + character(len=99) :: kspec='spec_k.in' + character(len=99) :: gasspec='gasspec.in' +contains +!********************************BEGINNING************************************* +!> calculate equivalent conductivity for one specific foam +subroutine eqcond(regions) + integer, intent(in) :: regions + integer :: i,j + real(dp), dimension(:), allocatable :: regbound,regcond + real(dp), dimension(:,:), allocatable :: regalpha,regsigma + allocate(regbound(regions+1),regcond(regions),regalpha(regions,nbox),& + regsigma(regions,nbox),alpha(nz,nbox),sigma(nz,nbox),cond(nz)) + do i=1,regions+1 + regbound(i)=(i-1)*dfoam/regions + enddo + do i=1,regions + call foam_morpholgy + call effrad(spectra) + call effcond + regcond(i)=effc + regalpha(i,:)=abscoeffbox + regsigma(i,:)=scattcoeffbox + deallocate(abscoeffbox,scattcoeffbox) + enddo + do i=1,nz + do j=1,regions+1 + if ((i-0.5_dp)*dfoam/nz calculate dependance of equivalent conductivity on porosity +subroutine eqcond_por + integer :: fi,npoints,i + real(dp) :: pormin,pormax,dpor + pormin=0.90_dp + pormax=0.995_dp + npoints=20 + dpor=(pormax-pormin)/(npoints-1) + open(newunit(fi),file='eqcond_por.out') + write(fi,'(1000A23)') '#porosity','eq. conductivity','Ross. eq. cond.' + do i=1,npoints + por=pormin+(i-1)*dpor + call eqcond(1) + write(fi,'(1000es23.15)') por,eqc,eqc_ross + enddo + close(fi) +end subroutine eqcond_por +!***********************************END**************************************** + + +!********************************BEGINNING************************************* +!> calculate dependance of equivalent conductivity on cell size +subroutine eqcond_dcell + integer :: fi,npoints,i + real(dp) :: dcellmin,dcellmax,ddcell + dcellmin=1e-6_dp + dcellmax=1000e-6_dp + npoints=7 + ddcell=log10(dcellmax/dcellmin)/(npoints-1) + open(newunit(fi),file='eqcond_dcell.out') + write(fi,'(1000A23)') '#porosity','eq. conductivity' + do i=1,npoints + dcell=dcellmin*10**((i-1)*ddcell) + call eqcond(1) + write(fi,'(1000es23.15)') dcell,eqc + enddo + close(fi) +end subroutine eqcond_dcell +!***********************************END**************************************** + + +!********************************BEGINNING************************************* +!> calculate dependance of equivalent conductivity on strut content +subroutine eqcond_strut + integer :: fi,npoints,i + real(dp) :: strutmin,strutmax,dstrut + strutmin=0.0_dp + strutmax=0.9_dp + npoints=19 + dstrut=(strutmax-strutmin)/(npoints-1) + open(newunit(fi),file='eqcond_strut.out') + write(fi,'(1000A23)') '#strut content','eq. conductivity','Ross. eq. cond.' + do i=1,npoints + fs=strutmin+(i-1)*dstrut + call eqcond(1) + write(fi,'(1000es23.15)') fs,eqc,eqc_ross + enddo + close(fi) +end subroutine eqcond_strut +!***********************************END**************************************** + + +!********************************BEGINNING************************************* +!> loads parameters, usually from text file +subroutine loadParameters + use physicalProperties + integer :: fi,ios,i,j + logical :: file_exists + inputs=TRIM(ADJUSTL(fileplacein_par))//TRIM(ADJUSTL(inputs)) + spectra=TRIM(ADJUSTL(fileplaceout))//TRIM(ADJUSTL(spectra)) + inquire(file=inputs,exist=file_exists) + if (file_exists) then + open(newunit(fi),file=inputs) + else + open(newunit(fi),file='../'//inputs) + endif + read(fi,*) T1 !higher temperature + read(fi,*) T2 !lower temperature + read(fi,*) cond1 !gas conductivity +! read(fi,*) cond2 !solid conductivity + call polymerConductivity(cond2,(t1+t2)/2) + read(fi,*) emi1 !emittance 1 + read(fi,*) emi2 !emittance 2 + read(fi,*) rho1 !gas density + read(fi,*) rho2 !solid density + read(fi,*) por !porosity + read(fi,*) dcell !cell size + read(fi,*) morph_input !morphology input 1=wall thickness, + ! 2=strut content, 3=strut diameter (3 is recommended others can have + ! multiple solutions) + read(fi,*) dwall !wall thickness + read(fi,*) fs !strut content + read(fi,*) dstrut !strut diameter + read(fi,*) dfoam !foam thickness + read(fi,*) nz !spatial discretization + read(fi,*) nrays !number of testing rays + read(fi,*) wdist !use wall thickness distribution + read(fi,*) wsdev !wall thickness standard deviation + read(fi,*) nbox !number of gray boxes + close(fi) + tmean=(t1+t2)/2 + n1=1 + k1=0 + write(*,*) 'System information:' + write(*,'(2x,A,1x,es9.3,1x,A)') 'higher temperature:',T1,'K' + write(*,'(2x,A,1x,es9.3,1x,A)') 'lower temperature: ',T2,'K' + write(*,*) 'Phase properties:' + write(*,'(2x,A,1x,es9.3,1x,A)') 'gas conductivity: ',cond1*1e3_dp,'mW/m/K' + write(*,'(2x,A,1x,es9.3,1x,A)') 'solid conductivity:',cond2*1e3_dp,'mW/m/K' + write(mfi,*) 'System information:' + write(mfi,'(2x,A,1x,es9.3,1x,A)') 'higher temperature:',T1,'K' + write(mfi,'(2x,A,1x,es9.3,1x,A)') 'lower temperature: ',T2,'K' + write(mfi,*) 'Phase properties:' + write(mfi,'(2x,A,1x,es9.3,1x,A)') 'gas conductivity: ',cond1*1e3_dp,'mW/m/K' + write(mfi,'(2x,A,1x,es9.3,1x,A)') 'solid conductivity:',cond2*1e3_dp,'mW/m/K' + + j=0 + open(newunit(fi),file=TRIM(ADJUSTL(fileplacein_ref))//TRIM(ADJUSTL(nspec))) + do !find number of points + read(fi,*,iostat=ios) + if (ios/=0) exit + j=j+1 + enddo + rewind(fi) + allocate(lambdan(j),nwl(j)) + do i=1,j + read(fi,*) lambdan(i),nwl(i) + enddo + lambdan=lambdan*1e-6_dp + close(fi) + + j=0 + open(newunit(fi),file=TRIM(ADJUSTL(fileplacein_ref))//TRIM(ADJUSTL(kspec))) + do !find number of points + read(fi,*,iostat=ios) + if (ios/=0) exit + j=j+1 + enddo + rewind(fi) + allocate(lambdak(j),kwl(j)) + do i=1,j + read(fi,*) lambdak(i),kwl(i) + enddo + lambdak=lambdak*1e-6_dp + close(fi) + + j=0 + open(newunit(fi),file=TRIM(ADJUSTL(fileplacein_ref))//TRIM(ADJUSTL(gasspec))) + do !find number of points + read(fi,*,iostat=ios) + if (ios/=0) exit + j=j+1 + enddo + rewind(fi) + allocate(lambdagas(j),acgas(j)) + do i=1,j + read(fi,*) lambdagas(i),acgas(i) + enddo + lambdagas=lambdagas*1e-6_dp + close(fi) +end subroutine loadParameters +!***********************************END**************************************** +end module tests diff --git a/applications/PUfoam/MoDeNaModels/foamConductivity/src/src/utilit.f90 b/applications/PUfoam/MoDeNaModels/foamConductivity/src/src/utilit.f90 new file mode 100644 index 000000000..c8839ba54 --- /dev/null +++ b/applications/PUfoam/MoDeNaModels/foamConductivity/src/src/utilit.f90 @@ -0,0 +1,1675 @@ +! --------------------------------------------------------------------- +! Utility subroutines used by any program from Numath library +! --------------------------------------------------------------------- +! Reference: From Numath Library By Tuan Dang Trong in Fortran 77 +! [BIBLI 18]. +! +! F90 Release 1.0 By J-P Moreau, Paris +! (www.jpmoreau.fr) +! --------------------------------------------------------------------- +MODULE UTILIT + +CONTAINS + +!REAL*8 FUNCTION D1MACH(I) +!!***BEGIN PROLOGUE D1MACH +!!***DATE WRITTEN 750101 (YYMMDD) +!!***REVISION DATE 860501 (YYMMDD) +!!***CATEGORY NO. R1 +!!***KEYWORDS MACHINE CONSTANTS +!!***AUTHOR FOX, P. A., (BELL LABS) +!! HALL, A. D., (BELL LABS) +!! SCHRYER, N. L., (BELL LABS) +!!***PURPOSE RETURN DOUBLE PRECISION MACHINE DEPENDENT CONSTANTS. +!!***DESCRIPTION +! +!! D1MACH CAN BE USED TO OBTAIN MACHINE-DEPENDENT PARAMETERS +!! FOR THE LOCAL MACHINE ENVIRONMENT. IT IS A FUNCTION +!! SUBPROGRAM WITH ONE (INPUT) ARGUMENT, AND CAN BE CALLED +!! AS FOLLOWS, FOR EXAMPLE +! +!! D = D1MACH(I) +! +!! WHERE I=1,...,5. THE (OUTPUT) VALUE OF D ABOVE IS +!! DETERMINED BY THE (INPUT) VALUE OF I. THE RESULTS FOR +!! VARIOUS VALUES OF I ARE DISCUSSED BELOW. +! +!! DOUBLE-PRECISION MACHINE CONSTANTS +!! D1MACH( 1) = B**(EMIN-1), THE SMALLEST POSITIVE MAGNITUDE. +!! D1MACH( 2) = B**EMAX*(1 - B**(-T)), THE LARGEST MAGNITUDE. +!! D1MACH( 3) = B**(-T), THE SMALLEST RELATIVE SPACING. +!! D1MACH( 4) = B**(1-T), THE LARGEST RELATIVE SPACING. +!! D1MACH( 5) = LOG10(B) +!!***REFERENCES FOX P.A., HALL A.D., SCHRYER N.L.,*FRAMEWORK FOR A +!! PORTABLE LIBRARY*, ACM TRANSACTIONS ON MATHEMATICAL +!! SOFTWARE, VOL. 4, NO. 2, JUNE 1978, PP. 177-188. +!!***ROUTINES CALLED XERROR +!!***END PROLOGUE D1MACH +! +! INTEGER SMALL(4) +! INTEGER LARGE(4) +! INTEGER RIGHT(4) +! INTEGER DIVER(4) +! INTEGER LOG10(4) +! +! DOUBLE PRECISION DMACH(5) +! +! EQUIVALENCE (DMACH(1),SMALL(1)) +! EQUIVALENCE (DMACH(2),LARGE(1)) +! EQUIVALENCE (DMACH(3),RIGHT(1)) +! EQUIVALENCE (DMACH(4),DIVER(1)) +! EQUIVALENCE (DMACH(5),LOG10(1)) +! +!! MACHINE CONSTANTS FOR THE IBM 360/370 SERIES, +!! THE XEROX SIGMA 5/7/9, THE SEL SYSTEMS 85/86, AND +!! THE PERKIN ELMER (INTERDATA) 7/32. +! +! DATA SMALL(1), SMALL(2) / Z00100000, Z00000000 / +! DATA LARGE(1), LARGE(2) / Z7FFFFFFF, ZFFFFFFFF / +! DATA RIGHT(1), RIGHT(2) / Z33100000, Z00000000 / +! DATA DIVER(1), DIVER(2) / Z34100000, Z00000000 / +! DATA LOG10(1), LOG10(2) / Z41134413, Z509F79FF / + +! MACHINE CONSTANTS FOR THE APOLLO DNXXXX SERIES, + +! DATA DMACH(1) / 2.22559D-308/ +! DATA DMACH(2) / 1.79728D308/ +! DATA DMACH(3) / 1.11048D-16 / +! DATA DMACH(4) / 2.22096D-16 / +! DATA DMACH(5) / .301029995663981198D0 / + +! MACHINE CONSTANTS FOR THE BURROUGHS 1700 SYSTEM. + +! DATA SMALL(1) / ZC00800000 / +! DATA SMALL(2) / Z000000000 / + +! DATA LARGE(1) / ZDFFFFFFFF / +! DATA LARGE(2) / ZFFFFFFFFF / + +! DATA RIGHT(1) / ZCC5800000 / +! DATA RIGHT(2) / Z000000000 / + +! DATA DIVER(1) / ZCC6800000 / +! DATA DIVER(2) / Z000000000 / + +! DATA LOG10(1) / ZD00E730E7 / +! DATA LOG10(2) / ZC77800DC0 / + +! MACHINE CONSTANTS FOR THE BURROUGHS 5700 SYSTEM. + +! DATA SMALL(1) / O1771000000000000 / +! DATA SMALL(2) / O0000000000000000 / + +! DATA LARGE(1) / O0777777777777777 / +! DATA LARGE(2) / O0007777777777777 / + +! DATA RIGHT(1) / O1461000000000000 / +! DATA RIGHT(2) / O0000000000000000 / + +! DATA DIVER(1) / O1451000000000000 / +! DATA DIVER(2) / O0000000000000000 / + +! DATA LOG10(1) / O1157163034761674 / +! DATA LOG10(2) / O0006677466732724 / + +! MACHINE CONSTANTS FOR THE BURROUGHS 6700/7700 SYSTEMS. + +! DATA SMALL(1) / O1771000000000000 / +! DATA SMALL(2) / O7770000000000000 / + +! DATA LARGE(1) / O0777777777777777 / +! DATA LARGE(2) / O7777777777777777 / + +! DATA RIGHT(1) / O1461000000000000 / +! DATA RIGHT(2) / O0000000000000000 / + +! DATA DIVER(1) / O1451000000000000 / +! DATA DIVER(2) / O0000000000000000 / + +! DATA LOG10(1) / O1157163034761674 / +! DATA LOG10(2) / O0006677466732724 / + +! MACHINE CONSTANTS FOR THE CD! 6000/7000 SERIES. +! FOR FTN4 + +! DATA SMALL(1) / 00564000000000000000B / +! DATA SMALL(2) / 00000000000000000000B / + +! DATA LARGE(1) / 37757777777777777777B / +! DATA LARGE(2) / 37157777777777777777B / + +! DATA RIGHT(1) / 15624000000000000000B / +! DATA RIGHT(2) / 00000000000000000000B / + +! DATA DIVER(1) / 15634000000000000000B / +! DATA DIVER(2) / 00000000000000000000B / + +! DATA LOG10(1) / 17164642023241175717B / +! DATA LOG10(2) / 16367571421742254654B / + +! MACHINE CONSTANTS FOR THE CD! 6000/7000 SERIES. +! FOR FTN5 + +! DATA SMALL(1) / O"00564000000000000000" / +! DATA SMALL(2) / O"00000000000000000000" / + +! DATA LARGE(1) / O"37757777777777777777" / +! DATA LARGE(2) / O"37157777777777777777" / + +! DATA RIGHT(1) / O"15624000000000000000" / +! DATA RIGHT(2) / O"00000000000000000000" / + +! DATA DIVER(1) / O"15634000000000000000" / +! DATA DIVER(2) / O"00000000000000000000" / + +! DATA LOG10(1) / O"17164642023241175717" / +! DATA LOG10(2) / O"16367571421742254654" / + +! MACHINE CONSTANTS FOR THE CRAY 1 + +! DATA SMALL(1) / 201354000000000000000B / +! DATA SMALL(2) / 000000000000000000000B / + +! DATA LARGE(1) / 577767777777777777777B / +! DATA LARGE(2) / 000007777777777777774B / + +! DATA RIGHT(1) / 376434000000000000000B / +! DATA RIGHT(2) / 000000000000000000000B / + +! DATA DIVER(1) / 376444000000000000000B / +! DATA DIVER(2) / 000000000000000000000B / + +! DATA LOG10(1) / 377774642023241175717B / +! DATA LOG10(2) / 000007571421742254654B / + +! MACHINE CONSTANTS FOR THE DATA GENERAL ECLIPSE S/200 + +! NOTE - IT MAY BE APPROPRIATE TO INCLUDE THE FOLLOWING CARD - +! STATI! DMACH(5) + +! DATA SMALL/20K,3*0/,LARGE/77777K,3*177777K/ +! DATA RIGHT/31420K,3*0/,DIVER/32020K,3*0/ +! DATA LOG10/40423K,42023K,50237K,74776K/ + +! MACHINE CONSTANTS FOR THE HARRIS 220 + +! DATA SMALL(1), SMALL(2) / '20000000, '00000201 / +! DATA LARGE(1), LARGE(2) / '37777777, '37777577 / +! DATA RIGHT(1), RIGHT(2) / '20000000, '00000333 / +! DATA DIVER(1), DIVER(2) / '20000000, '00000334 / +! DATA LOG10(1), LOG10(2) / '23210115, '10237777 / + +! MACHINE CONSTANTS FOR THE HONEYWELL 600/6000 SERIES. + +! DATA SMALL(1), SMALL(2) / O402400000000, O000000000000 / +! DATA LARGE(1), LARGE(2) / O376777777777, O777777777777 / +! DATA RIGHT(1), RIGHT(2) / O604400000000, O000000000000 / +! DATA DIVER(1), DIVER(2) / O606400000000, O000000000000 / +! DATA LOG10(1), LOG10(2) / O776464202324, O117571775714 / + +! MACHINE CONSTANTS FOR THE HP 2100 +! THREE WORD DOUBLE PRECISION OPTION WITH FTN4 + +! DATA SMALL(1), SMALL(2), SMALL(3) / 40000B, 0, 1 / +! DATA LARGE(1), LARGE(2), LARGE(3) / 77777B, 177777B, 177776B / +! DATA RIGHT(1), RIGHT(2), RIGHT(3) / 40000B, 0, 265B / +! DATA DIVER(1), DIVER(2), DIVER(3) / 40000B, 0, 276B / +! DATA LOG10(1), LOG10(2), LOG10(3) / 46420B, 46502B, 77777B / + +! MACHINE CONSTANTS FOR THE HP 2100 +! FOUR WORD DOUBLE PRECISION OPTION WITH FTN4 + +! DATA SMALL(1), SMALL(2) / 40000B, 0 / +! DATA SMALL(3), SMALL(4) / 0, 1 / +! DATA LARGE(1), LARGE(2) / 77777B, 177777B / +! DATA LARGE(3), LARGE(4) / 177777B, 177776B / +! DATA RIGHT(1), RIGHT(2) / 40000B, 0 / +! DATA RIGHT(3), RIGHT(4) / 0, 225B / +! DATA DIVER(1), DIVER(2) / 40000B, 0 / +! DATA DIVER(3), DIVER(4) / 0, 227B / +! DATA LOG10(1), LOG10(2) / 46420B, 46502B / +! DATA LOG10(3), LOG10(4) / 76747B, 176377B / + +! MACHINE CONSTANTS FOR THE HP 9000 + +! D1MACH(1) = 2.8480954D-306 +! D1MACH(2) = 1.40444776D+306 +! D1MACH(3) = 2.22044605D-16 +! D1MACH(4) = 4.44089210D-16 +! D1MACH(5) = 3.01029996D-1 + +! DATA SMALL(1), SMALL(2) / 00040000000B, 00000000000B / +! DATA LARGE(1), LARGE(2) / 17737777777B, 37777777777B / +! DATA RIGHT(1), RIGHT(2) / 07454000000B, 00000000000B / +! DATA DIVER(1), DIVER(2) / 07460000000B, 00000000000B / +! DATA LOG10(1), LOG10(2) / 07764642023B, 12047674777B / + +! MACHINE CONSTANTS FOR THE PDP-10 (KA PROCESSOR). + +! DATA SMALL(1), SMALL(2) / "033400000000, "000000000000 / +! DATA LARGE(1), LARGE(2) / "377777777777, "344777777777 / +! DATA RIGHT(1), RIGHT(2) / "113400000000, "000000000000 / +! DATA DIVER(1), DIVER(2) / "114400000000, "000000000000 / +! DATA LOG10(1), LOG10(2) / "177464202324, "144117571776 / + +! MACHINE CONSTANTS FOR THE PDP-10 (KI PROCESSOR). + +! DATA SMALL(1), SMALL(2) / "000400000000, "000000000000 / +! DATA LARGE(1), LARGE(2) / "377777777777, "377777777777 / +! DATA RIGHT(1), RIGHT(2) / "103400000000, "000000000000 / +! DATA DIVER(1), DIVER(2) / "104400000000, "000000000000 / +! DATA LOG10(1), LOG10(2) / "177464202324, "476747767461 / + +! MACHINE CONSTANTS FOR PDP-11 FORTRAN SUPPORTING +! 32-BIT INTEGERS (EXPRESSED IN INTEGER AND OCTAL). + +! DATA SMALL(1), SMALL(2) / 8388608, 0 / +! DATA LARGE(1), LARGE(2) / 2147483647, -1 / +! DATA RIGHT(1), RIGHT(2) / 612368384, 0 / +! DATA DIVER(1), DIVER(2) / 620756992, 0 / +! DATA LOG10(1), LOG10(2) / 1067065498, -2063872008 / + +! DATA SMALL(1), SMALL(2) / O00040000000, O00000000000 / +! DATA LARGE(1), LARGE(2) / O17777777777, O37777777777 / +! DATA RIGHT(1), RIGHT(2) / O04440000000, O00000000000 / +! DATA DIVER(1), DIVER(2) / O04500000000, O00000000000 / +! DATA LOG10(1), LOG10(2) / O07746420232, O20476747770 / + +! MACHINE CONSTANTS FOR PDP-11 FORTRAN SUPPORTING +! 16-BIT INTEGERS (EXPRESSED IN INTEGER AND OCTAL). + +! DATA SMALL(1), SMALL(2) / 128, 0 / +! DATA SMALL(3), SMALL(4) / 0, 0 / + +! DATA LARGE(1), LARGE(2) / 32767, -1 / +! DATA LARGE(3), LARGE(4) / -1, -1 / + +! DATA RIGHT(1), RIGHT(2) / 9344, 0 / +! DATA RIGHT(3), RIGHT(4) / 0, 0 / + +! DATA DIVER(1), DIVER(2) / 9472, 0 / +! DATA DIVER(3), DIVER(4) / 0, 0 / + +! DATA LOG10(1), LOG10(2) / 16282, 8346 / +! DATA LOG10(3), LOG10(4) / -31493, -12296 / + +! DATA SMALL(1), SMALL(2) / O000200, O000000 / +! DATA SMALL(3), SMALL(4) / O000000, O000000 / + +! DATA LARGE(1), LARGE(2) / O077777, O177777 / +! DATA LARGE(3), LARGE(4) / O177777, O177777 / + +! DATA RIGHT(1), RIGHT(2) / O022200, O000000 / +! DATA RIGHT(3), RIGHT(4) / O000000, O000000 / + +! DATA DIVER(1), DIVER(2) / O022400, O000000 / +! DATA DIVER(3), DIVER(4) / O000000, O000000 / + +! DATA LOG10(1), LOG10(2) / O037632, O020232 / +! DATA LOG10(3), LOG10(4) / O102373, O147770 / + +! MACHINE CONSTANTS FOR THE UNIVA! 1100 SERIES. FTN COMPILER + +! DATA SMALL(1), SMALL(2) / O000040000000, O000000000000 / +! DATA LARGE(1), LARGE(2) / O377777777777, O777777777777 / +! DATA RIGHT(1), RIGHT(2) / O170540000000, O000000000000 / +! DATA DIVER(1), DIVER(2) / O170640000000, O000000000000 / +! DATA LOG10(1), LOG10(2) / O177746420232, O411757177572 / + +! MACHINE CONSTANTS FOR VAX 11/780 +! (EXPRESSED IN INTEGER AND HEXADECIMAL) +! ***THE HEX FORMAT BELOW MAY NOT BE SUITABLE FOR UNIX SYSYEMS*** +! *** THE INTEGER FORMAT SHOULD BE OK FOR UNIX SYSTEMS*** + +! DATA SMALL(1), SMALL(2) / 128, 0 / +! DATA LARGE(1), LARGE(2) / -32769, -1 / +! DATA RIGHT(1), RIGHT(2) / 9344, 0 / +! DATA DIVER(1), DIVER(2) / 9472, 0 / +! DATA LOG10(1), LOG10(2) / 546979738, -805796613 / + +! DATA SMALL(1), SMALL(2) / Z00000080, Z00000000 / +! DATA LARGE(1), LARGE(2) / ZFFFF7FFF, ZFFFFFFFF / +! DATA RIGHT(1), RIGHT(2) / Z00002480, Z00000000 / +! DATA DIVER(1), DIVER(2) / Z00002500, Z00000000 / +! DATA LOG10(1), LOG10(2) / Z209A3F9A, ZCFF884FB / + +! MACHINE CONSTANTS FOR VAX 11/780 (G-FLOATING) +! (EXPRESSED IN INTEGER AND HEXADECIMAL) +! ***THE HEX FORMAT BELOW MAY NOT BE SUITABLE FOR UNIX SYSYEMS*** +! *** THE INTEGER FORMAT SHOULD BE OK FOR UNIX SYSTEMS*** + +! DATA SMALL(1), SMALL(2) / 16, 0 / +! DATA LARGE(1), LARGE(2) / -32769, -1 / +! DATA RIGHT(1), RIGHT(2) / 15552, 0 / +! DATA DIVER(1), DIVER(2) / 15568, 0 / +! DATA LOG10(1), LOG10(2) / 1142112243, 2046775455 / + +! DATA SMALL(1), SMALL(2) / Z00000010, Z00000000 / +! DATA LARGE(1), LARGE(2) / ZFFFF7FFF, ZFFFFFFFF / +! DATA RIGHT(1), RIGHT(2) / Z00003CC0, Z00000000 / +! DATA DIVER(1), DIVER(2) / Z00003CD0, Z00000000 / +! DATA LOG10(1), LOG10(2) / Z44133FF3, Z79FF509F / + +! MACHINE CONSTANTS FOR THE ELXSI 6400 +! (ASSUMING REAL*8 IS THE DEFAULT DOUBLE PRECISION) + +! DATA SMALL(1), SMALL(2) / '00100000'X,'00000000'X / +! DATA LARGE(1), LARGE(2) / '7FEFFFFF'X,'FFFFFFFF'X / +! DATA RIGHT(1), RIGHT(2) / '3CB00000'X,'00000000'X / +! DATA DIVER(1), DIVER(2) / '3CC00000'X,'00000000'X / +! DATA LOG10(1), DIVER(2) / '3FD34413'X,'509F79FF'X / + +! MACHINE CONSTANTS FOR THE IBM PC - MICROSOFT FORTRAN + +! DATA SMALL(1), SMALL(2) / �00000000, �00100000 / +! DATA LARGE(1), LARGE(2) / �FFFFFFFF, �7FEFFFFF / +! DATA RIGHT(1), RIGHT(2) / �00000000, �3CA00000 / +! DATA DIVER(1), DIVER(2) / �00000000, �3CB00000 / +! DATA LOG10(1), LOG10(2) / �509F79FF, �3FD34413 / + +! MACHINE CONSTANTS FOR THE IBM PC - PROFESSIONAL FORTRAN +! AND LAHEY FORTRAN + +! DATA SMALL(1), SMALL(2) / Z'00000000', Z'00100000' / +! DATA LARGE(1), LARGE(2) / Z'FFFFFFFF', Z'7FEFFFFF' / +! DATA RIGHT(1), RIGHT(2) / Z'00000000', Z'3CA00000' / +! DATA DIVER(1), DIVER(2) / Z'00000000', Z'3CB00000' / +! DATA LOG10(1), LOG10(2) / Z'509F79FF', Z'3FD34413' / +! +!!***FIRST EXECUTABLE STATEMENT D1MACH +! IF (I .LT. 1 .OR. I .GT. 5) & +! CALL XERROR( 'D1MACH -- I OUT OF BOUNDS',25,1,2) +! +! D1MACH = DMACH(I) +! RETURN +! +!END FUNCTION D1MACH +!DECK D1MACH + DOUBLE PRECISION FUNCTION D1MACH (I) + IMPLICIT NONE + INTEGER :: I + DOUBLE PRECISION :: B, X +!***BEGIN PROLOGUE D1MACH +!***PURPOSE Return floating point machine dependent constants. +!***LIBRARY SLATEC +!***CATEGORY R1 +!***TYPE SINGLE PRECISION (D1MACH-S, D1MACH-D) +!***KEYWORDS MACHINE CONSTANTS +!***AUTHOR Fox, P. A., (Bell Labs) +! Hall, A. D., (Bell Labs) +! Schryer, N. L., (Bell Labs) +!***DESCRIPTION +! +! D1MACH can be used to obtain machine-dependent parameters for the +! local machine environment. It is a function subprogram with one +! (input) argument, and can be referenced as follows: +! +! A = D1MACH(I) +! +! where I=1,...,5. The (output) value of A above is determined by +! the (input) value of I. The results for various values of I are +! discussed below. +! +! D1MACH(1) = B**(EMIN-1), the smallest positive magnitude. +! D1MACH(2) = B**EMAX*(1 - B**(-T)), the largest magnitude. +! D1MACH(3) = B**(-T), the smallest relative spacing. +! D1MACH(4) = B**(1-T), the largest relative spacing. +! D1MACH(5) = LOG10(B) +! +! Assume single precision numbers are represented in the T-digit, +! base-B form +! +! sign (B**E)*( (X(1)/B) + ... + (X(T)/B**T) ) +! +! where 0 .LE. X(I) .LT. B for I=1,...,T, 0 .LT. X(1), and +! EMIN .LE. E .LE. EMAX. +! +! The values of B, T, EMIN and EMAX are provided in I1MACH as +! follows: +! I1MACH(10) = B, the base. +! I1MACH(11) = T, the number of base-B digits. +! I1MACH(12) = EMIN, the smallest exponent E. +! I1MACH(13) = EMAX, the largest exponent E. +! +! +!***REFERENCES P. A. Fox, A. D. Hall and N. L. Schryer, Framework for +! a portable library, ACM Transactions on Mathematical +! Software 4, 2 (June 1978), pp. 177-188. +!***ROUTINES CALLED XERMSG +!***REVISION HISTORY (YYMMDD) +! 790101 DATE WRITTEN +! 960329 Modified for Fortran 90 (BE after suggestions by EHG) +!***END PROLOGUE D1MACH +! + X = 1.0D0 + B = RADIX(X) + SELECT CASE (I) + CASE (1) + D1MACH = B**(MINEXPONENT(X)-1) ! the smallest positive magnitude. + CASE (2) + D1MACH = HUGE(X) ! the largest magnitude. + CASE (3) + D1MACH = B**(-DIGITS(X)) ! the smallest relative spacing. + CASE (4) + D1MACH = B**(1-DIGITS(X)) ! the largest relative spacing. + CASE (5) + D1MACH = LOG10(B) + CASE DEFAULT + WRITE (*, FMT = 9000) + 9000 FORMAT ('1ERROR 1 IN D1MACH - I OUT OF BOUNDS') + STOP + END SELECT + RETURN + END +! --------------------------------------------------------------------- +INTEGER FUNCTION I1MACH(I) +!***BEGIN PROLOGUE I1MACH +!***DATE WRITTEN 750101 (YYMMDD) +!***REVISION DATE 890313 (YYMMDD) +!***CATEGORY NO. R1 +!***KEYWORDS LIBRARY=SLATEC,TYPE=INTEGER(I1MACH-I),MACHINE CONSTANTS +!***AUTHOR FOX, P. A., (BELL LABS) +! HALL, A. D., (BELL LABS) +! SCHRYER, N. L., (BELL LABS) +!***PURPOSE Return integer machine dependent constants. +!***DESCRIPTION + +! I1MACH can be used to obtain machine-dependent parameters +! for the local machine environment. It is a function +! subroutine with one (input) argument, and can be called +! as follows, for example + +! K = I1MACH(I) + +! where I=1,...,16. The (output) value of K above is +! determined by the (input) value of I. The results for +! various values of I are discussed below. + +! I/O unit numbers. +! I1MACH( 1) = the standard input unit. +! I1MACH( 2) = the standard output unit. +! I1MACH( 3) = the standard punch unit. +! I1MACH( 4) = the standard error message unit. + +! Words. +! I1MACH( 5) = the number of bits per integer storage unit. +! I1MACH( 6) = the number of characters per integer storage unit. + +! Integers. +! assume integers are represented in the S-digit, base-A form + +! sign ( X(S-1)*A**(S-1) + ... + X(1)*A + X(0) ) + +! where 0 .LE. X(I) .LT. A for I=0,...,S-1. +! I1MACH( 7) = A, the base. +! I1MACH( 8) = S, the number of base-A digits. +! I1MACH( 9) = A**S - 1, the largest magnitude. + +! Floating-Point Numbers. +! Assume floating-point numbers are represented in the T-digit, +! base-B form +! sign (B**E)*( (X(1)/B) + ... + (X(T)/B**T) ) + +! where 0 .LE. X(I) .LT. B for I=1,...,T, +! 0 .LT. X(1), and EMIN .LE. E .LE. EMAX. +! I1MACH(10) = B, the base. + +! Single-Precision +! I1MACH(11) = T, the number of base-B digits. +! I1MACH(12) = EMIN, the smallest exponent E. +! I1MACH(13) = EMAX, the largest exponent E. + +! Double-Precision +! I1MACH(14) = T, the number of base-B digits. +! I1MACH(15) = EMIN, the smallest exponent E. +! I1MACH(16) = EMAX, the largest exponent E. + +! To alter this function for a particular environment, +! the desired set of DATA statements should be activated by +! removing the ! from column 1. Also, the values of +! I1MACH(1) - I1MACH(4) should be checked for consistency +! with the local operating system. + +!***REFERENCES FOX P.A., HALL A.D., SCHRYER N.L.,*FRAMEWORK FOR A +! PORTABLE LIBRARY*, ACM TRANSACTIONS ON MATHEMATICAL +! SOFTWARE, VOL. 4, NO. 2, JUNE 1978, PP. 177-188. +!***ROUTINES CALLED (NONE) +!***END PROLOGUE I1MACH + + INTEGER IMACH(16),OUTPUT + SAVE IMACH + EQUIVALENCE (IMACH(4),OUTPUT) + +! MACHINE CONSTANTS FOR THE AMIGA +! ABSOFT COMPILER + +! DATA IMACH(1) / 5 / +! DATA IMACH(2) / 6 / +! DATA IMACH(3) / 5 / +! DATA IMACH(4) / 6 / +! DATA IMACH(5) / 32 / +! DATA IMACH(6) / 4 / +! DATA IMACH(7) / 2 / +! DATA IMACH(8) / 31 / +! DATA IMACH(9) / 2147483647 / +! DATA IMACH(10)/ 2 / +! DATA IMACH(11)/ 24 / +! DATA IMACH(12)/ -126 / +! DATA IMACH(13)/ 127 / +! DATA IMACH(14)/ 53 / +! DATA IMACH(15)/ -1022 / +! DATA IMACH(16)/ 1023 / + +! MACHINE CONSTANTS FOR THE APOLLO + +! DATA IMACH(1) / 5 / +! DATA IMACH(2) / 6 / +! DATA IMACH(3) / 6 / +! DATA IMACH(4) / 6 / +! DATA IMACH(5) / 32 / +! DATA IMACH(6) / 4 / +! DATA IMACH(7) / 2 / +! DATA IMACH(8) / 31 / +! DATA IMACH(9) / 2147483647 / +! DATA IMACH(10)/ 2 / +! DATA IMACH(11)/ 24 / +! DATA IMACH(12)/ -125 / +! DATA IMACH(13)/ 129 / +! DATA IMACH(14)/ 53 / +! DATA IMACH(15)/ -1021 / +! DATA IMACH(16)/ 1025 / + +! MACHINE CONSTANTS FOR THE BURROUGHS 1700 SYSTEM + +! DATA IMACH( 1) / 7 / +! DATA IMACH( 2) / 2 / +! DATA IMACH( 3) / 2 / +! DATA IMACH( 4) / 2 / +! DATA IMACH( 5) / 36 / +! DATA IMACH( 6) / 4 / +! DATA IMACH( 7) / 2 / +! DATA IMACH( 8) / 33 / +! DATA IMACH( 9) / Z1FFFFFFFF / +! DATA IMACH(10) / 2 / +! DATA IMACH(11) / 24 / +! DATA IMACH(12) / -256 / +! DATA IMACH(13) / 255 / +! DATA IMACH(14) / 60 / +! DATA IMACH(15) / -256 / +! DATA IMACH(16) / 255 / + +! MACHINE CONSTANTS FOR THE BURROUGHS 5700 SYSTEM + +! DATA IMACH( 1) / 5 / +! DATA IMACH( 2) / 6 / +! DATA IMACH( 3) / 7 / +! DATA IMACH( 4) / 6 / +! DATA IMACH( 5) / 48 / +! DATA IMACH( 6) / 6 / +! DATA IMACH( 7) / 2 / +! DATA IMACH( 8) / 39 / +! DATA IMACH( 9) / O0007777777777777 / +! DATA IMACH(10) / 8 / +! DATA IMACH(11) / 13 / +! DATA IMACH(12) / -50 / +! DATA IMACH(13) / 76 / +! DATA IMACH(14) / 26 / +! DATA IMACH(15) / -50 / +! DATA IMACH(16) / 76 / + +! MACHINE CONSTANTS FOR THE BURROUGHS 6700/7700 SYSTEMS + +! DATA IMACH( 1) / 5 / +! DATA IMACH( 2) / 6 / +! DATA IMACH( 3) / 7 / +! DATA IMACH( 4) / 6 / +! DATA IMACH( 5) / 48 / +! DATA IMACH( 6) / 6 / +! DATA IMACH( 7) / 2 / +! DATA IMACH( 8) / 39 / +! DATA IMACH( 9) / O0007777777777777 / +! DATA IMACH(10) / 8 / +! DATA IMACH(11) / 13 / +! DATA IMACH(12) / -50 / +! DATA IMACH(13) / 76 / +! DATA IMACH(14) / 26 / +! DATA IMACH(15) / -32754 / +! DATA IMACH(16) / 32780 / + +! MACHINE CONSTANTS FOR THE CD! 170/180 SERIES USING NOS/VE + +! DATA IMACH( 1) / 5 / +! DATA IMACH( 2) / 6 / +! DATA IMACH( 3) / 7 / +! DATA IMACH( 4) / 6 / +! DATA IMACH( 5) / 64 / +! DATA IMACH( 6) / 8 / +! DATA IMACH( 7) / 2 / +! DATA IMACH( 8) / 63 / +! DATA IMACH( 9) / 9223372036854775807 / +! DATA IMACH(10) / 2 / +! DATA IMACH(11) / 47 / +! DATA IMACH(12) / -4095 / +! DATA IMACH(13) / 4094 / +! DATA IMACH(14) / 94 / +! DATA IMACH(15) / -4095 / +! DATA IMACH(16) / 4094 / + +! MACHINE CONSTANTS FOR THE CD! 6000/7000 SERIES + +! DATA IMACH( 1) / 5 / +! DATA IMACH( 2) / 6 / +! DATA IMACH( 3) / 7 / +! DATA IMACH( 4) /6LOUTPUT/ +! DATA IMACH( 5) / 60 / +! DATA IMACH( 6) / 10 / +! DATA IMACH( 7) / 2 / +! DATA IMACH( 8) / 48 / +! DATA IMACH( 9) / 00007777777777777777B / +! DATA IMACH(10) / 2 / +! DATA IMACH(11) / 47 / +! DATA IMACH(12) / -929 / +! DATA IMACH(13) / 1070 / +! DATA IMACH(14) / 94 / +! DATA IMACH(15) / -929 / +! DATA IMACH(16) / 1069 / + +! MACHINE CONSTANTS FOR THE CELERITY C1260 + +! DATA IMACH(1) / 5 / +! DATA IMACH(2) / 6 / +! DATA IMACH(3) / 6 / +! DATA IMACH(4) / 0 / +! DATA IMACH(5) / 32 / +! DATA IMACH(6) / 4 / +! DATA IMACH(7) / 2 / +! DATA IMACH(8) / 31 / +! DATA IMACH(9) / Z'7FFFFFFF' / +! DATA IMACH(10)/ 2 / +! DATA IMACH(11)/ 24 / +! DATA IMACH(12)/ -126 / +! DATA IMACH(13)/ 127 / +! DATA IMACH(14)/ 53 / +! DATA IMACH(15)/ -1022 / +! DATA IMACH(16)/ 1023 / + +! MACHINE CONSTANTS FOR THE CONVEX C-1 + +! DATA IMACH( 1) / 5/ +! DATA IMACH( 2) / 6/ +! DATA IMACH( 3) / 7/ +! DATA IMACH( 4) / 6/ +! DATA IMACH( 5) / 32/ +! DATA IMACH( 6) / 4/ +! DATA IMACH( 7) / 2/ +! DATA IMACH( 8) / 31/ +! DATA IMACH( 9) /2147483647/ +! DATA IMACH(10) / 2/ +! DATA IMACH(11) / 24/ +! DATA IMACH(12) / -128/ +! DATA IMACH(13) / 127/ +! DATA IMACH(14) / 53/ +! DATA IMACH(15) / -1024/ +! DATA IMACH(16) / 1023/ + +! MACHINE CONSTANTS FOR THE CRAY-1 +! USING THE 46 BIT INTEGER COMPILER OPTION + +! DATA IMACH( 1) / 100 / +! DATA IMACH( 2) / 101 / +! DATA IMACH( 3) / 102 / +! DATA IMACH( 4) / 101 / +! DATA IMACH( 5) / 64 / +! DATA IMACH( 6) / 8 / +! DATA IMACH( 7) / 2 / +! DATA IMACH( 8) / 46 / +! DATA IMACH( 9) / 1777777777777777B / +! DATA IMACH(10) / 2 / +! DATA IMACH(11) / 47 / +! DATA IMACH(12) / -8189 / +! DATA IMACH(13) / 8190 / +! DATA IMACH(14) / 94 / +! DATA IMACH(15) / -8099 / +! DATA IMACH(16) / 8190 / + +! MACHINE CONSTANTS FOR THE CRAY-1 +! USING THE 64 BIT INTEGER COMPILER OPTION + +! DATA IMACH( 1) / 100 / +! DATA IMACH( 2) / 101 / +! DATA IMACH( 3) / 102 / +! DATA IMACH( 4) / 101 / +! DATA IMACH( 5) / 64 / +! DATA IMACH( 6) / 8 / +! DATA IMACH( 7) / 2 / +! DATA IMACH( 8) / 63 / +! DATA IMACH( 9) / 777777777777777777777B / +! DATA IMACH(10) / 2 / +! DATA IMACH(11) / 47 / +! DATA IMACH(12) / -8189 / +! DATA IMACH(13) / 8190 / +! DATA IMACH(14) / 94 / +! DATA IMACH(15) / -8099 / +! DATA IMACH(16) / 8190 / + +! MACHINE CONSTANTS FOR THE DATA GENERAL ECLIPSE S/200 + +! DATA IMACH( 1) / 11 / +! DATA IMACH( 2) / 12 / +! DATA IMACH( 3) / 8 / +! DATA IMACH( 4) / 10 / +! DATA IMACH( 5) / 16 / +! DATA IMACH( 6) / 2 / +! DATA IMACH( 7) / 2 / +! DATA IMACH( 8) / 15 / +! DATA IMACH( 9) /32767 / +! DATA IMACH(10) / 16 / +! DATA IMACH(11) / 6 / +! DATA IMACH(12) / -64 / +! DATA IMACH(13) / 63 / +! DATA IMACH(14) / 14 / +! DATA IMACH(15) / -64 / +! DATA IMACH(16) / 63 / + +! MACHINE CONSTANTS FOR THE ELXSI 6400 + +! DATA IMACH( 1) / 5/ +! DATA IMACH( 2) / 6/ +! DATA IMACH( 3) / 6/ +! DATA IMACH( 4) / 6/ +! DATA IMACH( 5) / 32/ +! DATA IMACH( 6) / 4/ +! DATA IMACH( 7) / 2/ +! DATA IMACH( 8) / 32/ +! DATA IMACH( 9) /2147483647/ +! DATA IMACH(10) / 2/ +! DATA IMACH(11) / 24/ +! DATA IMACH(12) / -126/ +! DATA IMACH(13) / 127/ +! DATA IMACH(14) / 53/ +! DATA IMACH(15) / -1022/ +! DATA IMACH(16) / 1023/ + +! MACHINE CONSTANTS FOR THE HARRIS 220 + +! DATA IMACH( 1) / 5 / +! DATA IMACH( 2) / 6 / +! DATA IMACH( 3) / 0 / +! DATA IMACH( 4) / 6 / +! DATA IMACH( 5) / 24 / +! DATA IMACH( 6) / 3 / +! DATA IMACH( 7) / 2 / +! DATA IMACH( 8) / 23 / +! DATA IMACH( 9) / 8388607 / +! DATA IMACH(10) / 2 / +! DATA IMACH(11) / 23 / +! DATA IMACH(12) / -127 / +! DATA IMACH(13) / 127 / +! DATA IMACH(14) / 38 / +! DATA IMACH(15) / -127 / +! DATA IMACH(16) / 127 / + +! MACHINE CONSTANTS FOR THE HONEYWELL 600/6000 SERIES + +! DATA IMACH( 1) / 5 / +! DATA IMACH( 2) / 6 / +! DATA IMACH( 3) / 43 / +! DATA IMACH( 4) / 6 / +! DATA IMACH( 5) / 36 / +! DATA IMACH( 6) / 6 / +! DATA IMACH( 7) / 2 / +! DATA IMACH( 8) / 35 / +! DATA IMACH( 9) / O377777777777 / +! DATA IMACH(10) / 2 / +! DATA IMACH(11) / 27 / +! DATA IMACH(12) / -127 / +! DATA IMACH(13) / 127 / +! DATA IMACH(14) / 63 / +! DATA IMACH(15) / -127 / +! DATA IMACH(16) / 127 / + +! MACHINE CONSTANTS FOR THE HP 2100 +! 3 WORD DOUBLE PRECISION OPTION WITH FTN4 + +! DATA IMACH(1) / 5/ +! DATA IMACH(2) / 6 / +! DATA IMACH(3) / 4 / +! DATA IMACH(4) / 1 / +! DATA IMACH(5) / 16 / +! DATA IMACH(6) / 2 / +! DATA IMACH(7) / 2 / +! DATA IMACH(8) / 15 / +! DATA IMACH(9) / 32767 / +! DATA IMACH(10)/ 2 / +! DATA IMACH(11)/ 23 / +! DATA IMACH(12)/ -128 / +! DATA IMACH(13)/ 127 / +! DATA IMACH(14)/ 39 / +! DATA IMACH(15)/ -128 / +! DATA IMACH(16)/ 127 / + +! MACHINE CONSTANTS FOR THE HP 2100 +! 4 WORD DOUBLE PRECISION OPTION WITH FTN4 + +! DATA IMACH(1) / 5 / +! DATA IMACH(2) / 6 / +! DATA IMACH(3) / 4 / +! DATA IMACH(4) / 1 / +! DATA IMACH(5) / 16 / +! DATA IMACH(6) / 2 / +! DATA IMACH(7) / 2 / +! DATA IMACH(8) / 15 / +! DATA IMACH(9) / 32767 / +! DATA IMACH(10)/ 2 / +! DATA IMACH(11)/ 23 / +! DATA IMACH(12)/ -128 / +! DATA IMACH(13)/ 127 / +! DATA IMACH(14)/ 55 / +! DATA IMACH(15)/ -128 / +! DATA IMACH(16)/ 127 / + +! MACHINE CONSTANTS FOR THE HP 9000 + +! DATA IMACH(1) / 5 / +! DATA IMACH(2) / 6 / +! DATA IMACH(3) / 6 / +! DATA IMACH(3) / 7 / +! DATA IMACH(5) / 32 / +! DATA IMACH(6) / 4 / +! DATA IMACH(7) / 2 / +! DATA IMACH(8) / 32 / +! DATA IMACH(9) /2147483647 / +! DATA IMACH(10) / 2 / +! DATA IMACH(11) / 24 / +! DATA IMACH(12) / -126 / +! DATA IMACH(13) / 127 / +! DATA IMACH(14) / 53 / +! DATA IMACH(15) /-1015 / +! DATA IMACH(16) / 1017 / + +! MACHINE CONSTANTS FOR THE IBM 360/370 SERIES, +! THE XEROX SIGMA 5/7/9, THE SEL SYSTEMS 85/86, AND +! THE PERKIN ELMER (INTERDATA) 7/32. + +! DATA IMACH( 1) / 5 / +! DATA IMACH( 2) / 6 / +! DATA IMACH( 3) / 7 / +! DATA IMACH( 4) / 6 / +! DATA IMACH( 5) / 32 / +! DATA IMACH( 6) / 4 / +! DATA IMACH( 7) / 16 / +! DATA IMACH( 8) / 31 / +! DATA IMACH( 9) / Z7FFFFFFF / +! DATA IMACH(10) / 16 / +! DATA IMACH(11) / 6 / +! DATA IMACH(12) / -64 / +! DATA IMACH(13) / 63 / +! DATA IMACH(14) / 14 / +! DATA IMACH(15) / -64 / +! DATA IMACH(16) / 63 / + +! MACHINE CONSTANTS FOR THE IBM PC + + DATA IMACH( 1) / 5 / + DATA IMACH( 2) / 6 / + DATA IMACH( 3) / 0 / + DATA IMACH( 4) / 0 / + DATA IMACH( 5) / 32 / + DATA IMACH( 6) / 4 / + DATA IMACH( 7) / 2 / + DATA IMACH( 8) / 31 / + DATA IMACH( 9) / 2147483647 / + DATA IMACH(10) / 2 / + DATA IMACH(11) / 24 / + DATA IMACH(12) / -125 / + DATA IMACH(13) / 127 / + DATA IMACH(14) / 53 / + DATA IMACH(15) / -1021 / + DATA IMACH(16) / 1023 / + +! MACHINE CONSTANTS FOR THE PDP-10 (KA PROCESSOR) + +! DATA IMACH( 1) / 5 / +! DATA IMACH( 2) / 6 / +! DATA IMACH( 3) / 5 / +! DATA IMACH( 4) / 6 / +! DATA IMACH( 5) / 36 / +! DATA IMACH( 6) / 5 / +! DATA IMACH( 7) / 2 / +! DATA IMACH( 8) / 35 / +! DATA IMACH( 9) / "377777777777 / +! DATA IMACH(10) / 2 / +! DATA IMACH(11) / 27 / +! DATA IMACH(12) / -128 / +! DATA IMACH(13) / 127 / +! DATA IMACH(14) / 54 / +! DATA IMACH(15) / -101 / +! DATA IMACH(16) / 127 / + +! MACHINE CONSTANTS FOR THE PDP-10 (KI PROCESSOR) + +! DATA IMACH( 1) / 5 / +! DATA IMACH( 2) / 6 / +! DATA IMACH( 3) / 5 / +! DATA IMACH( 4) / 6 / +! DATA IMACH( 5) / 36 / +! DATA IMACH( 6) / 5 / +! DATA IMACH( 7) / 2 / +! DATA IMACH( 8) / 35 / +! DATA IMACH( 9) / "377777777777 / +! DATA IMACH(10) / 2 / +! DATA IMACH(11) / 27 / +! DATA IMACH(12) / -128 / +! DATA IMACH(13) / 127 / +! DATA IMACH(14) / 62 / +! DATA IMACH(15) / -128 / +! DATA IMACH(16) / 127 / + +! MACHINE CONSTANTS FOR PDP-11 FORTRAN SUPPORTING +! 32-BIT INTEGER ARITHMETIC. + +! DATA IMACH( 1) / 5 / +! DATA IMACH( 2) / 6 / +! DATA IMACH( 3) / 5 / +! DATA IMACH( 4) / 6 / +! DATA IMACH( 5) / 32 / +! DATA IMACH( 6) / 4 / +! DATA IMACH( 7) / 2 / +! DATA IMACH( 8) / 31 / +! DATA IMACH( 9) / 2147483647 / +! DATA IMACH(10) / 2 / +! DATA IMACH(11) / 24 / +! DATA IMACH(12) / -127 / +! DATA IMACH(13) / 127 / +! DATA IMACH(14) / 56 / +! DATA IMACH(15) / -127 / +! DATA IMACH(16) / 127 / + +! MACHINE CONSTANTS FOR PDP-11 FORTRAN SUPPORTING +! 16-BIT INTEGER ARITHMETIC. + +! DATA IMACH( 1) / 5 / +! DATA IMACH( 2) / 6 / +! DATA IMACH( 3) / 5 / +! DATA IMACH( 4) / 6 / +! DATA IMACH( 5) / 16 / +! DATA IMACH( 6) / 2 / +! DATA IMACH( 7) / 2 / +! DATA IMACH( 8) / 15 / +! DATA IMACH( 9) / 32767 / +! DATA IMACH(10) / 2 / +! DATA IMACH(11) / 24 / +! DATA IMACH(12) / -127 / +! DATA IMACH(13) / 127 / +! DATA IMACH(14) / 56 / +! DATA IMACH(15) / -127 / +! DATA IMACH(16) / 127 / + +! MACHINE CONSTANTS FOR THE SUN + +! DATA IMACH(1) / 5 / +! DATA IMACH(2) / 6 / +! DATA IMACH(3) / 6 / +! DATA IMACH(4) / 6 / +! DATA IMACH(5) / 32 / +! DATA IMACH(6) / 4 / +! DATA IMACH(7) / 2 / +! DATA IMACH(8) / 31 / +! DATA IMACH(9) /2147483647 / +! DATA IMACH(10)/ 2 / +! DATA IMACH(11)/ 24 / +! DATA IMACH(12)/ -125 / +! DATA IMACH(13)/ 128 / +! DATA IMACH(14)/ 53 / +! DATA IMACH(15)/ -1021 / +! DATA IMACH(16)/ 1024 / + +! MACHINE CONSTANTS FOR THE UNIVA! 1100 SERIES FTN COMPILER + +! DATA IMACH( 1) / 5 / +! DATA IMACH( 2) / 6 / +! DATA IMACH( 3) / 1 / +! DATA IMACH( 4) / 6 / +! DATA IMACH( 5) / 36 / +! DATA IMACH( 6) / 4 / +! DATA IMACH( 7) / 2 / +! DATA IMACH( 8) / 35 / +! DATA IMACH( 9) / O377777777777 / +! DATA IMACH(10) / 2 / +! DATA IMACH(11) / 27 / +! DATA IMACH(12) / -128 / +! DATA IMACH(13) / 127 / +! DATA IMACH(14) / 60 / +! DATA IMACH(15) /-1024 / +! DATA IMACH(16) / 1023 / + +! MACHINE CONSTANTS FOR THE VAX 11/780 + +! DATA IMACH(1) / 5 / +! DATA IMACH(2) / 6 / +! DATA IMACH(3) / 5 / +! DATA IMACH(4) / 6 / +! DATA IMACH(5) / 32 / +! DATA IMACH(6) / 4 / +! DATA IMACH(7) / 2 / +! DATA IMACH(8) / 31 / +! DATA IMACH(9) /2147483647 / +! DATA IMACH(10)/ 2 / +! DATA IMACH(11)/ 24 / +! DATA IMACH(12)/ -127 / +! DATA IMACH(13)/ 127 / +! DATA IMACH(14)/ 56 / +! DATA IMACH(15)/ -127 / +! DATA IMACH(16)/ 127 / + +! MACHINE CONSTANTS FOR THE Z80 MICROPROCESSOR + +! DATA IMACH( 1) / 1/ +! DATA IMACH( 2) / 1/ +! DATA IMACH( 3) / 0/ +! DATA IMACH( 4) / 1/ +! DATA IMACH( 5) / 16/ +! DATA IMACH( 6) / 2/ +! DATA IMACH( 7) / 2/ +! DATA IMACH( 8) / 15/ +! DATA IMACH( 9) / 32767/ +! DATA IMACH(10) / 2/ +! DATA IMACH(11) / 24/ +! DATA IMACH(12) / -127/ +! DATA IMACH(13) / 127/ +! DATA IMACH(14) / 56/ +! DATA IMACH(15) / -127/ +! DATA IMACH(16) / 127/ + +!***FIRST EXECUTABLE STATEMENT I1MACH + IF (I .LT. 1 .OR. I .GT. 16) GO TO 10 + + I1MACH = IMACH(I) + RETURN + + 10 CONTINUE + WRITE (UNIT = OUTPUT, FMT = 9000) + 9000 FORMAT ('1ERROR 1 IN I1MACH - I OUT OF BOUNDS') + +! CALL FDUMP + + STOP +END FUNCTION I1MACH +! --------------------------------------------------------------------- +SUBROUTINE XERROR(MESSG,NMESSG,NERR,LEVEL) +!***BEGIN PROLOGUE XERROR +!***DATE WRITTEN 790801 (YYMMDD) +!***REVISION DATE 861211 (YYMMDD) +!***CATEGORY NO. R3C +!***KEYWORDS LIBRARY=SLATEC(XERROR),TYPE=ALL(XERROR-A),ERROR +!***AUTHOR JONES, R. E., (SNLA) +!***PURPOSE Process an error (diagnostic) message. +!***DESCRIPTION + +! Abstract +! XERROR processes a diagnostic message, in a manner +! determined by the value of LEVEL and the current value +! of the library error control flag, KONTRL. +! (See subroutine XSETF for details.) + +! Description of Parameters +! --Input-- +! MESSG - the Hollerith message to be processed, containing +! no more than 72 characters. +! NMESSG- the actual number of characters in MESSG. +! NERR - the error number associated with this message. +! NERR must not be zero. +! LEVEL - error category. +! =2 means this is an unconditionally fatal error. +! =1 means this is a recoverable error. (I.e., it is +! non-fatal if XSETF has been appropriately called.) +! =0 means this is a warning message only. +! =-1 means this is a warning message which is to be +! printed at most once, regardless of how many +! times this call is executed. + +! Examples +! CALL XERROR('SMOOTH -- NUM WAS ZERO.',23,1,2) +! CALL XERROR('INTEG -- LESS THAN FULL ACCURACY ACHIEVED.', +! 1 43,2,1) +! CALL XERROR('ROOTER -- ACTUAL ZERO OF F FOUND BEFORE INTERVAL F +! 1ULLY COLLAPSED.',65,3,0) +! CALL XERROR('EXP -- UNDERFLOWS BEING SET TO ZERO.',39,1,-1) + +! Written by Ron Jones, with SLATEC Common Math Library Subcommittee +!***REFERENCES JONES R.E., KAHANER D.K., 'XERROR, THE SLATEC ERROR- +! HANDLING PACKAGE', SAND82-0800, SANDIA LABORATORIES, +! 1982. +!***ROUTINES CALLED XERRWV +!***END PROLOGUE XERROR + CHARACTER*(*) MESSG +!***FIRST EXECUTABLE STATEMENT XERROR + CALL XERRWV(MESSG,NMESSG,NERR,LEVEL,0,0,0,0,0.,0.) + RETURN +END SUBROUTINE XERROR +! --------------------------------------------------------------------- + SUBROUTINE XERRWV(MESSG,NMESSG,NERR,LEVEL,NI,I1,I2,NR,R1,R2) +!***BEGIN PROLOGUE XERRWV +!***DATE WRITTEN 800319 (YYMMDD) +!***REVISION DATE 890531 (YYMMDD) +!***CATEGORY NO. R3C +!***KEYWORDS LIBRARY=SLATEC(XERROR),TYPE=ALL(XERRWV-A),ERROR +!***AUTHOR JONES, R. E., (SNLA) +!***PURPOSE Process an error message allowing 2 integer and 2 real +! values to be included in the message. +!***DESCRIPTION + +! Abstract +! XERRWV processes a diagnostic message, in a manner +! determined by the value of LEVEL and the current value +! of the library error control flag, KONTRL. +! (See subroutine XSETF for details.) +! In addition, up to two integer values and two real +! values may be printed along with the message. + +! Description of Parameters +! --Input-- +! MESSG - the Hollerith message to be processed. +! NMESSG- the actual number of characters in MESSG. +! NERR - the error number associated with this message. +! NERR must not be zero. +! LEVEL - error category. +! =2 means this is an unconditionally fatal error. +! =1 means this is a recoverable error. (I.e., it is +! non-fatal if XSETF has been appropriately called.) +! =0 means this is a warning message only. +! =-1 means this is a warning message which is to be +! printed at most once, regardless of how many +! times this call is executed. +! NI - number of integer values to be printed. (0 to 2) +! I1 - first integer value. +! I2 - second integer value. +! NR - number of real values to be printed. (0 to 2) +! R1 - first real value. +! R2 - second real value. + +! Examples +! CALL XERRWV('SMOOTH -- NUM (=I1) WAS ZERO.',29,1,2, +! 1 1,NUM,0,0,0.,0.) +! CALL XERRWV('QUADXY -- REQUESTED ERROR (R1) LESS THAN MINIMUM ( +! 1R2).,54,77,1,0,0,0,2,ERRREQ,ERRMIN) + +! Latest revision --- 1 August 1985 +! Written by Ron Jones, with SLATEC Common Math Library Subcommittee +!***REFERENCES JONES R.E., KAHANER D.K., 'XERROR, THE SLATEC ERROR- +! HANDLING PACKAGE', SAND82-0800, SANDIA LABORATORIES, +! 1982. +!***ROUTINES CALLED FDUMP,I1MACH,J4SAVE,XERABT,XERCTL,XERPRT,XERSAV, +! XGETUA +!***END PROLOGUE XERRWV + +! ---------------------------------------------------------------------- + +! Change record: +! 89-05-31 Changed all specific intrinsics to generic. (WRB) + +! ---------------------------------------------------------------------- + + CHARACTER*(*) MESSG + CHARACTER*20 LFIRST + CHARACTER*37 FORM + DIMENSION LUN(5) +! GET FLAGS +!***FIRST EXECUTABLE STATEMENT XERRWV + LKNTRL = J4SAVE(2,0,.FALSE.) + MAXMES = J4SAVE(4,0,.FALSE.) +! CHECK FOR VALID INPUT + IF ((NMESSG.GT.0).AND.(NERR.NE.0).AND. & + (LEVEL.GE.(-1)).AND.(LEVEL.LE.2)) GO TO 10 + IF (LKNTRL.GT.0) CALL XERPRT('FATAL ERROR IN...',17) + CALL XERPRT('XERROR -- INVALID INPUT',23) + IF (LKNTRL.GT.0) CALL FDUMP + IF (LKNTRL.GT.0) CALL XERPRT('JOB ABORT DUE TO FATAL ERROR.', & + 29) + IF (LKNTRL.GT.0) CALL XERSAV(' ',0,0,0,KDUMMY) + CALL XERABT('XERROR -- INVALID INPUT',23) + RETURN + 10 CONTINUE +! RECORD MESSAGE + JUNK = J4SAVE(1,NERR,.TRUE.) + CALL XERSAV(MESSG,NMESSG,NERR,LEVEL,KOUNT) +! LET USER OVERRIDE + LFIRST = MESSG + LMESSG = NMESSG + LERR = NERR + LLEVEL = LEVEL + CALL XERCTL(LFIRST,LMESSG,LERR,LLEVEL,LKNTRL) +! RESET TO ORIGINAL VALUES + LMESSG = NMESSG + LERR = NERR + LLEVEL = LEVEL + LKNTRL = MAX(-2,MIN(2,LKNTRL)) + MKNTRL = ABS(LKNTRL) +! DECIDE WHETHER TO PRINT MESSAGE + IF ((LLEVEL.LT.2).AND.(LKNTRL.EQ.0)) GO TO 100 + IF (((LLEVEL.EQ.(-1)).AND.(KOUNT.GT.MIN(1,MAXMES))) & + .OR.((LLEVEL.EQ.0) .AND.(KOUNT.GT.MAXMES)) & + .OR.((LLEVEL.EQ.1) .AND.(KOUNT.GT.MAXMES).AND.(MKNTRL.EQ.1)) & + .OR.((LLEVEL.EQ.2) .AND.(KOUNT.GT.MAX(1,MAXMES)))) GO TO 100 + IF (LKNTRL.LE.0) GO TO 20 + CALL XERPRT(' ',1) +! INTRODUCTION + IF (LLEVEL.EQ.(-1)) CALL XERPRT & + ('WARNING MESSAGE...THIS MESSAGE WILL ONLY BE PRINTED ONCE.',57) + IF (LLEVEL.EQ.0) CALL XERPRT('WARNING IN...',13) + IF (LLEVEL.EQ.1) CALL XERPRT & + ('RECOVERABLE ERROR IN...',23) + IF (LLEVEL.EQ.2) CALL XERPRT('FATAL ERROR IN...',17) + 20 CONTINUE +! MESSAGE + CALL XERPRT(MESSG,LMESSG) + CALL XGETUA(LUN,NUNIT) + ISIZEI = LOG10(REAL(I1MACH(9))) + 1.0 + ISIZEF = LOG10(REAL(I1MACH(10))**I1MACH(11)) + 1.0 + DO 50 KUNIT=1,NUNIT + IUNIT = LUN(KUNIT) + IF (IUNIT.EQ.0) IUNIT = I1MACH(4) + DO 22 I=1,MIN(NI,2) + WRITE (FORM,21) I,ISIZEI + 21 FORMAT ('(11X,21HIN ABOVE MESSAGE, I',I1,'=,I',I2,') ') + IF (I.EQ.1) WRITE (IUNIT,FORM) I1 + IF (I.EQ.2) WRITE (IUNIT,FORM) I2 + 22 CONTINUE + DO 24 I=1,MIN(NR,2) + WRITE (FORM,23) I,ISIZEF+10,ISIZEF + 23 FORMAT ('(11X,21HIN ABOVE MESSAGE, R',I1,'=,E', & + I2,'.',I2,')') + IF (I.EQ.1) WRITE (IUNIT,FORM) R1 + IF (I.EQ.2) WRITE (IUNIT,FORM) R2 + 24 CONTINUE + IF (LKNTRL.LE.0) GO TO 40 +! ERROR NUMBER + WRITE (IUNIT,30) LERR + 30 FORMAT (15H ERROR NUMBER =,I10) + 40 CONTINUE + 50 CONTINUE +! TRACE-BACK + IF (LKNTRL.GT.0) CALL FDUMP + 100 CONTINUE + IFATAL = 0 + IF ((LLEVEL.EQ.2).OR.((LLEVEL.EQ.1).AND.(MKNTRL.EQ.2))) & + IFATAL = 1 +! QUIT HERE IF MESSAGE IS NOT FATAL + IF (IFATAL.LE.0) RETURN + IF ((LKNTRL.LE.0).OR.(KOUNT.GT.MAX(1,MAXMES))) GO TO 120 +! PRINT REASON FOR ABORT + IF (LLEVEL.EQ.1) CALL XERPRT & + ('JOB ABORT DUE TO UNRECOVERED ERROR.',35) + IF (LLEVEL.EQ.2) CALL XERPRT & + ('JOB ABORT DUE TO FATAL ERROR.',29) +! PRINT ERROR SUMMARY + CALL XERSAV(' ',-1,0,0,KDUMMY) + 120 CONTINUE +! ABORT + IF ((LLEVEL.EQ.2).AND.(KOUNT.GT.MAX(1,MAXMES))) LMESSG = 0 + CALL XERABT(MESSG,LMESSG) + RETURN +END SUBROUTINE XERRWV +! --------------------------------------------------------------------- +FUNCTION J4SAVE(IWHICH,IVALUE,ISET) +!***BEGIN PROLOGUE J4SAVE +!***REFER TO XERROR +!***ROUTINES CALLED (NONE) +!***DESCRIPTION + +! Abstract +! J4SAVE saves and recalls several global variables needed +! by the library error handling routines. + +! Description of Parameters +! --Input-- +! IWHICH - Index of item desired. +! = 1 Refers to current error number. +! = 2 Refers to current error control flag. +! = 3 Refers to current unit number to which error +! messages are to be sent. (0 means use standard.) +! = 4 Refers to the maximum number of times any +! message is to be printed (as set by XERMAX). +! = 5 Refers to the total number of units to which +! each error message is to be written. +! = 6 Refers to the 2nd unit for error messages +! = 7 Refers to the 3rd unit for error messages +! = 8 Refers to the 4th unit for error messages +! = 9 Refers to the 5th unit for error messages +! IVALUE - The value to be set for the IWHICH-th parameter, +! if ISET is .TRUE. . +! ISET - If ISET=.TRUE., the IWHICH-th parameter will BE +! given the value, IVALUE. If ISET=.FALSE., the +! IWHICH-th parameter will be unchanged, and IVALUE +! is a dummy parameter. +! --Output-- +! The (old) value of the IWHICH-th parameter will be returned +! in the function value, J4SAVE. + +! Written by Ron Jones, with SLATEC Common Math Library Subcommittee +! Adapted from Bell Laboratories PORT Library Error Handler +! Latest revision --- 1 August 1985 +!***REFERENCES JONES R.E., KAHANER D.K., 'XERROR, THE SLATEC ERROR- +! HANDLING PACKAGE', SAND82-0800, SANDIA LABORATORIES, +! 1982. +!***END PROLOGUE J4SAVE + LOGICAL ISET + INTEGER IPARAM(9) + SAVE IPARAM + DATA IPARAM(1),IPARAM(2),IPARAM(3),IPARAM(4)/0,2,0,10/ + DATA IPARAM(5)/1/ + DATA IPARAM(6),IPARAM(7),IPARAM(8),IPARAM(9)/0,0,0,0/ +!***FIRST EXECUTABLE STATEMENT J4SAVE + J4SAVE = IPARAM(IWHICH) + IF (ISET) IPARAM(IWHICH) = IVALUE + RETURN + END FUNCTION J4SAVE +! --------------------------------------------------------------------- + SUBROUTINE XERSAV(MESSG,NMESSG,NERR,LEVEL,ICOUNT) +!***BEGIN PROLOGUE XERSAV +!***DATE WRITTEN 800319 (YYMMDD) +!***REVISION DATE 861211 (YYMMDD) +!***CATEGORY NO. R3 +!***KEYWORDS LIBRARY=SLATEC(XERROR),TYPE=ALL(XERSAV-A),ERROR +!***AUTHOR JONES, R. E., (SNLA) +!***PURPOSE Record that an error has occurred. +!***DESCRIPTION + +! Abstract +! Record that this error occurred. + +! Description of Parameters +! --Input-- +! MESSG, NMESSG, NERR, LEVEL are as in XERROR, +! except that when NMESSG=0 the tables will be +! dumped and cleared, and when NMESSG is less than zero the +! tables will be dumped and not cleared. +! --Output-- +! ICOUNT will be the number of times this message has +! been seen, or zero if the table has overflowed and +! does not contain this message specifically. +! When NMESSG=0, ICOUNT will not be altered. + +! Written by Ron Jones, with SLATEC Common Math Library Subcommittee +! Latest revision --- 1 August 1985 +!***REFERENCES JONES R.E., KAHANER D.K., 'XERROR, THE SLATEC ERROR- +! HANDLING PACKAGE', SAND82-0800, SANDIA LABORATORIES, +! 1982. +!***ROUTINES CALLED I1MACH,XGETUA +!***END PROLOGUE XERSAV + INTEGER LUN(5) + CHARACTER*(*) MESSG + CHARACTER*20 MESTAB(10),MES + DIMENSION NERTAB(10),LEVTAB(10),KOUNT(10) + SAVE MESTAB,NERTAB,LEVTAB,KOUNT,KOUNTX +! NEXT TWO DATA STATEMENTS ARE NECESSARY TO PROVIDE A BLANK +! ERROR TABLE INITIALLY + DATA KOUNT(1),KOUNT(2),KOUNT(3),KOUNT(4),KOUNT(5), & + KOUNT(6),KOUNT(7),KOUNT(8),KOUNT(9),KOUNT(10) & + /0,0,0,0,0,0,0,0,0,0/ + DATA KOUNTX/0/ +!***FIRST EXECUTABLE STATEMENT XERSAV + IF (NMESSG.GT.0) GO TO 80 +! DUMP THE TABLE + IF (KOUNT(1).EQ.0) RETURN +! PRINT TO EACH UNIT + CALL XGETUA(LUN,NUNIT) + DO 60 KUNIT=1,NUNIT + IUNIT = LUN(KUNIT) + IF (IUNIT.EQ.0) IUNIT = I1MACH(4) +! PRINT TABLE HEADER + WRITE (IUNIT,10) + 10 FORMAT (32H0 ERROR MESSAGE SUMMARY/ & + 51H MESSAGE START NERR LEVEL COUNT) +! PRINT BODY OF TABLE + DO 20 I=1,10 + IF (KOUNT(I).EQ.0) GO TO 30 + WRITE (IUNIT,15) MESTAB(I),NERTAB(I),LEVTAB(I),KOUNT(I) + 15 FORMAT (1X,A20,3I10) + 20 CONTINUE + 30 CONTINUE +! PRINT NUMBER OF OTHER ERRORS + IF (KOUNTX.NE.0) WRITE (IUNIT,40) KOUNTX + 40 FORMAT (41H0OTHER ERRORS NOT INDIVIDUALLY TABULATED=,I10) + WRITE (IUNIT,50) + 50 FORMAT (1X) + 60 CONTINUE + IF (NMESSG.LT.0) RETURN +! CLEAR THE ERROR TABLES + DO 70 I=1,10 + 70 KOUNT(I) = 0 + KOUNTX = 0 + RETURN + 80 CONTINUE +! PROCESS A MESSAGE... +! SEARCH FOR THIS MESSG, OR ELSE AN EMPTY SLOT FOR THIS MESSG, +! OR ELSE DETERMINE THAT THE ERROR TABLE IS FULL. + MES = MESSG + DO 90 I=1,10 + II = I + IF (KOUNT(I).EQ.0) GO TO 110 + IF (MES.NE.MESTAB(I)) GO TO 90 + IF (NERR.NE.NERTAB(I)) GO TO 90 + IF (LEVEL.NE.LEVTAB(I)) GO TO 90 + GO TO 100 + 90 CONTINUE +! THREE POSSIBLE CASES... +! TABLE IS FULL + KOUNTX = KOUNTX+1 + ICOUNT = 1 + RETURN +! MESSAGE FOUND IN TABLE + 100 KOUNT(II) = KOUNT(II) + 1 + ICOUNT = KOUNT(II) + RETURN +! EMPTY SLOT FOUND FOR NEW MESSAGE + 110 MESTAB(II) = MES + NERTAB(II) = NERR + LEVTAB(II) = LEVEL + KOUNT(II) = 1 + ICOUNT = 1 + RETURN +END SUBROUTINE XERSAV +! --------------------------------------------------------------------- +SUBROUTINE XGETUA(IUNITA,N) +!***BEGIN PROLOGUE XGETUA +!***DATE WRITTEN 790801 (YYMMDD) +!***REVISION DATE 861211 (YYMMDD) +!***CATEGORY NO. R3C +!***KEYWORDS LIBRARY=SLATEC(XERROR),TYPE=ALL(XGETUA-A),ERROR +!***AUTHOR JONES, R. E., (SNLA) +!***PURPOSE Return unit number(s) to which error messages are being +! sent. +!***DESCRIPTION + +! Abstract +! XGETUA may be called to determine the unit number or numbers +! to which error messages are being sent. +! These unit numbers may have been set by a call to XSETUN, +! or a call to XSETUA, or may be a default value. + +! Description of Parameters +! --Output-- +! IUNIT - an array of one to five unit numbers, depending +! on the value of N. A value of zero refers to the +! default unit, as defined by the I1MACH machine +! constant routine. Only IUNIT(1),...,IUNIT(N) are +! defined by XGETUA. The values of IUNIT(N+1),..., +! IUNIT(5) are not defined (for N .LT. 5) or altered +! in any way by XGETUA. +! N - the number of units to which copies of the +! error messages are being sent. N will be in the +! range from 1 to 5. + +! Latest revision --- 19 MAR 1980 +! Written by Ron Jones, with SLATEC Common Math Library Subcommittee +!***REFERENCES JONES R.E., KAHANER D.K., 'XERROR, THE SLATEC ERROR- +! HANDLING PACKAGE', SAND82-0800, SANDIA LABORATORIES, +! 1982. +!***ROUTINES CALLED J4SAVE +!***END PROLOGUE XGETUA + DIMENSION IUNITA(5) +!***FIRST EXECUTABLE STATEMENT XGETUA + N = J4SAVE(5,0,.FALSE.) + DO 30 I=1,N + INDEX = I+4 + IF (I.EQ.1) INDEX = 3 + IUNITA(I) = J4SAVE(INDEX,0,.FALSE.) + 30 CONTINUE + RETURN +END SUBROUTINE XGETUA +! --------------------------------------------------------------------- +SUBROUTINE XERCTL(MESSG1,NMESSG,NERR,LEVEL,KONTRL) +!***BEGIN PROLOGUE XERCTL +!***DATE WRITTEN 790801 (YYMMDD) +!***REVISION DATE 861211 (YYMMDD) +!***CATEGORY NO. R3C +!***KEYWORDS LIBRARY=SLATEC(XERROR),TYPE=ALL(XERCTL-A),ERROR +!***AUTHOR JONES, R. E., (SNLA) +!***PURPOSE Allow user control over handling of errors. +!***DESCRIPTION + +! Abstract +! Allows user control over handling of individual errors. +! Just after each message is recorded, but before it is +! processed any further (i.e., before it is printed or +! a decision to abort is made), a call is made to XERCTL. +! If the user has provided his own version of XERCTL, he +! can then override the value of KONTROL used in processing +! this message by redefining its value. +! KONTRL may be set to any value from -2 to 2. +! The meanings for KONTRL are the same as in XSETF, except +! that the value of KONTRL changes only for this message. +! If KONTRL is set to a value outside the range from -2 to 2, +! it will be moved back into that range. + +! Description of Parameters + +! --Input-- +! MESSG1 - the first word (only) of the error message. +! NMESSG - same as in the call to XERROR or XERRWV. +! NERR - same as in the call to XERROR or XERRWV. +! LEVEL - same as in the call to XERROR or XERRWV. +! KONTRL - the current value of the control flag as set +! by a call to XSETF. + +! --Output-- +! KONTRL - the new value of KONTRL. If KONTRL is not +! defined, it will remain at its original value. +! This changed value of control affects only +! the current occurrence of the current message. +!***REFERENCES JONES R.E., KAHANER D.K., 'XERROR, THE SLATEC ERROR- +! HANDLING PACKAGE', SAND82-0800, SANDIA LABORATORIES, +! 1982. +!***ROUTINES CALLED (NONE) +!***END PROLOGUE XERCTL + CHARACTER*20 MESSG1 +!***FIRST EXECUTABLE STATEMENT XERCTL + RETURN + END SUBROUTINE XERCTL +! --------------------------------------------------------------------- + SUBROUTINE XERPRT(MESSG,NMESSG) +!***BEGIN PROLOGUE XERPRT +!***DATE WRITTEN 790801 (YYMMDD) +!***REVISION DATE 890531 (YYMMDD) +!***CATEGORY NO. R3 +!***KEYWORDS LIBRARY=SLATEC(XERROR),TYPE=ALL(XERPRT-A),ERROR +!***AUTHOR JONES, R. E., (SNLA) +!***PURPOSE Print error messages. +!***DESCRIPTION + +! Abstract +! Print the Hollerith message in MESSG, of length NMESSG, +! on each file indicated by XGETUA. +! Latest revision --- 1 August 1985 +!***REFERENCES JONES R.E., KAHANER D.K., 'XERROR, THE SLATEC ERROR- +! HANDLING PACKAGE', SAND82-0800, SANDIA LABORATORIES, +! 1982. +!***ROUTINES CALLED I1MACH,XGETUA +!***END PROLOGUE XERPRT + +! ---------------------------------------------------------------------- + +! Change record: +! 89-05-31 Changed all specific intrinsics to generic. (WRB) + +! ---------------------------------------------------------------------- + + INTEGER LUN(5) + CHARACTER*(*) MESSG +! OBTAIN UNIT NUMBERS AND WRITE LINE TO EACH UNIT +!***FIRST EXECUTABLE STATEMENT XERPRT + CALL XGETUA(LUN,NUNIT) + LENMES = LEN(MESSG) + DO 20 KUNIT=1,NUNIT + IUNIT = LUN(KUNIT) + IF (IUNIT.EQ.0) IUNIT = I1MACH(4) + DO 10 ICHAR=1,LENMES,72 + LAST = MIN(ICHAR+71 , LENMES) + WRITE (IUNIT,'(1X,A)') MESSG(ICHAR:LAST) + 10 CONTINUE + 20 CONTINUE + RETURN +END SUBROUTINE XERPRT +! --------------------------------------------------------------------- +SUBROUTINE FDUMP +!***BEGIN PROLOGUE FDUMP +!***DATE WRITTEN 790801 (YYMMDD) +!***REVISION DATE 861211 (YYMMDD) +!***CATEGORY NO. R3 +!***KEYWORDS LIBRARY=SLATEC(XERROR),TYPE=ALL(FDUMP-A),ERROR +!***AUTHOR JONES, R. E., (SNLA) +!***PURPOSE Symbolic dump (should be locally written). +!***DESCRIPTION + +! ***Note*** Machine Dependent Routine +! FDUMP is intended to be replaced by a locally written +! version which produces a symbolic dump. Failing this, +! it should be replaced by a version which prints the +! subprogram nesting list. Note that this dump must be +! printed on each of up to five files, as indicated by the +! XGETUA routine. See XSETUA and XGETUA for details. + +! Written by Ron Jones, with SLATEC Common Math Library Subcommittee +!***REFERENCES (NONE) +!***ROUTINES CALLED (NONE) +!***END PROLOGUE FDUMP +!***FIRST EXECUTABLE STATEMENT FDUMP + RETURN + END SUBROUTINE FDUMP +! --------------------------------------------------------------------- + SUBROUTINE XERABT(MESSG,NMESSG) +!***BEGIN PROLOGUE XERABT +!***DATE WRITTEN 790801 (YYMMDD) +!***REVISION DATE 861211 (YYMMDD) +!***CATEGORY NO. R3C +!***KEYWORDS LIBRARY=SLATEC(XERROR),TYPE=ALL(XERABT-A),ERROR +!***AUTHOR JONES, R. E., (SNLA) +!***PURPOSE Abort program execution and print error message. +!***DESCRIPTION + +! Abstract +! ***Note*** machine dependent routine +! XERABT aborts the execution of the program. +! The error message causing the abort is given in the calling +! sequence, in case one needs it for printing on a dayfile, +! for example. + +! Description of Parameters +! MESSG and NMESSG are as in XERROR, except that NMESSG may +! be zero, in which case no message is being supplied. + +! Written by Ron Jones, with SLATEC Common Math Library Subcommittee +! Latest revision --- 1 August 1982 +!***REFERENCES JONES R.E., KAHANER D.K., 'XERROR, THE SLATEC ERROR- +! HANDLING PACKAGE', SAND82-0800, SANDIA LABORATORIES, +! 1982. +!***ROUTINES CALLED (NONE) +!***END PROLOGUE XERABT + CHARACTER*(*) MESSG +!***FIRST EXECUTABLE STATEMENT XERABT + STOP +END SUBROUTINE XERABT +! --------------------------------------------------------------------- +END MODULE UTILIT +! end of file Utilit.f90 diff --git a/applications/PUfoam/MoDeNaModels/gasConductivity/__init__.py b/applications/PUfoam/MoDeNaModels/gasConductivity/__init__.py new file mode 100644 index 000000000..7e6156ce0 --- /dev/null +++ b/applications/PUfoam/MoDeNaModels/gasConductivity/__init__.py @@ -0,0 +1,44 @@ +''' + + ooo ooooo oooooooooo. ooooo ooo + `88. .888' `888' `Y8b `888b. `8' + 888b d'888 .ooooo. 888 888 .ooooo. 8 `88b. 8 .oooo. + 8 Y88. .P 888 d88' `88b 888 888 d88' `88b 8 `88b. 8 `P )88b + 8 `888' 888 888 888 888 888 888ooo888 8 `88b.8 .oP"888 + 8 Y 888 888 888 888 d88' 888 .o 8 `888 d8( 888 + o8o o888o `Y8bod8P' o888bood8P' `Y8bod8P' o8o `8 `Y888""8o + +Copyright + 2014-2015 MoDeNa Consortium, All rights reserved. + +License + This file is part of Modena. + + Modena is free software; you can redistribute it and/or modify it under + the terms of the GNU General Public License as published by the Free + Software Foundation, either version 3 of the License, or (at your option) + any later version. + + Modena is distributed in the hope that it will be useful, but WITHOUT ANY + WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS + FOR A PARTICULAR PURPOSE. See the GNU General Public License + for more details. + + You should have received a copy of the GNU General Public License along + with Modena. If not, see . + +Description + Python library of FireTasks + +Authors + Henrik Rusche + +Contributors +''' + +from gasConductivity import species +from gasConductivity import m_CyP_thermal_conductivity +from gasConductivity import m_Air_thermal_conductivity +from gasConductivity import m_CO2_thermal_conductivity +from gasConductivity import f_gas_thermal_conductivity + diff --git a/applications/PUfoam/MoDeNaModels/gasConductivity/gasConductivity.py b/applications/PUfoam/MoDeNaModels/gasConductivity/gasConductivity.py new file mode 100644 index 000000000..6a518ed9c --- /dev/null +++ b/applications/PUfoam/MoDeNaModels/gasConductivity/gasConductivity.py @@ -0,0 +1,128 @@ +'''@cond + + ooo ooooo oooooooooo. ooooo ooo + `88. .888' `888' `Y8b `888b. `8' + 888b d'888 .ooooo. 888 888 .ooooo. 8 `88b. 8 .oooo. + 8 Y88. .P 888 d88' `88b 888 888 d88' `88b 8 `88b. 8 `P )88b + 8 `888' 888 888 888 888 888 888ooo888 8 `88b.8 .oP"888 + 8 Y 888 888 888 888 d88' 888 .o 8 `888 d8( 888 + o8o o888o `Y8bod8P' o888bood8P' `Y8bod8P' o8o `8 `Y888""8o + +Copyright + 2014-2015 MoDeNa Consortium, All rights reserved. + +License + This file is part of Modena. + + Modena is free software; you can redistribute it and/or modify it under + the terms of the GNU General Public License as published by the Free + Software Foundation, either version 3 of the License, or (at your option) + any later version. + + Modena is distributed in the hope that it will be useful, but WITHOUT ANY + WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS + FOR A PARTICULAR PURPOSE. See the GNU General Public License + for more details. + + You should have received a copy of the GNU General Public License along + with Modena. If not, see . +@endcond''' + +""" +@file +Surrogate function and model definitions for thermal conductivity of blowing +agents. + +@author Erik Laurini +@author Pavel Ferkl +@copyright 2014-2015, MoDeNa Project. GNU Public License. +@ingroup app_aging +""" + +import os +import modena +from modena import CFunction, IndexSet, Workflow2, \ + ForwardMappingModel, BackwardMappingModel, SurrogateModel +import modena.Strategy as Strategy +from fireworks.user_objects.firetasks.script_task import FireTaskBase, ScriptTask +from fireworks import Firework, Workflow, FWAction +from fireworks.utilities.fw_utilities import explicit_serialize +from blessings import Terminal + +## Create terminal for colour output +term = Terminal() + +## List of components, for which surrogate model is provided +species = IndexSet( + name= 'gas_thermal_conductivity_species', + names= [ 'CO2', 'CyP', 'Air' ] +) + +## Surrogate function for thermal conductivity of blowing agents. +# +# Thermal conductivity of blowing agents is a function of temperature. +f_gas_thermal_conductivity = CFunction( + Ccode=''' +#include "modena.h" +#include "math.h" + +void gas_thermal_conductivity +( + const modena_model_t* model, + const double* inputs, + double *outputs +) +{ + {% block variables %}{% endblock %} + + const double a = parameters[0]; + const double b = parameters[1]; + + outputs[0] = (a*T)+b; +} +''', + # These are global bounds for the function + inputs={ + 'T': {'min': 273, 'max': 450}, + }, + outputs={ + 'gas_thermal_conductivity[A]': {'min': 0, 'max': +9e99, 'argPos': 0}, + }, + parameters={ + 'param0[A]': {'min': -9e99, 'max': +9e99, 'argPos': 0}, + 'param1[A]': {'min': -9e99, 'max': +9e99, 'argPos': 1}, + }, + indices={ + 'A': species, + }, +) + +## Surrogate model for thermal conductivity of blowing agent +# +# Forward mapping model is used. +m_CO2_thermal_conductivity = ForwardMappingModel( + _id='gas_thermal_conductivity[A=CO2]', + surrogateFunction=f_gas_thermal_conductivity, + substituteModels=[], + parameters=[0.0807e-3, -6.96e-3], +) + +## Surrogate model for thermal conductivity of blowing agent +# +# Forward mapping model is used. +m_Air_thermal_conductivity = ForwardMappingModel( + _id='gas_thermal_conductivity[A=Air]', + surrogateFunction=f_gas_thermal_conductivity, + substituteModels=[], + parameters=[0.0720e-3, 4.23e-3], +) + +## Surrogate model for thermal conductivity of blowing agent +# +# Forward mapping model is used. +m_CyP_thermal_conductivity = ForwardMappingModel( + _id='gas_thermal_conductivity[A=CyP]', + surrogateFunction=f_gas_thermal_conductivity, + substituteModels=[], + parameters=[0.0956e-3, -14.89e-3], +) diff --git a/applications/PUfoam/MoDeNaModels/gasMixtureConductivity/__init__.py b/applications/PUfoam/MoDeNaModels/gasMixtureConductivity/__init__.py new file mode 100644 index 000000000..5bb2edfa8 --- /dev/null +++ b/applications/PUfoam/MoDeNaModels/gasMixtureConductivity/__init__.py @@ -0,0 +1,40 @@ +''' + + ooo ooooo oooooooooo. ooooo ooo + `88. .888' `888' `Y8b `888b. `8' + 888b d'888 .ooooo. 888 888 .ooooo. 8 `88b. 8 .oooo. + 8 Y88. .P 888 d88' `88b 888 888 d88' `88b 8 `88b. 8 `P )88b + 8 `888' 888 888 888 888 888 888ooo888 8 `88b.8 .oP"888 + 8 Y 888 888 888 888 d88' 888 .o 8 `888 d8( 888 + o8o o888o `Y8bod8P' o888bood8P' `Y8bod8P' o8o `8 `Y888""8o + +Copyright + 2014-2015 MoDeNa Consortium, All rights reserved. + +License + This file is part of Modena. + + Modena is free software; you can redistribute it and/or modify it under + the terms of the GNU General Public License as published by the Free + Software Foundation, either version 3 of the License, or (at your option) + any later version. + + Modena is distributed in the hope that it will be useful, but WITHOUT ANY + WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS + FOR A PARTICULAR PURPOSE. See the GNU General Public License + for more details. + + You should have received a copy of the GNU General Public License along + with Modena. If not, see . + +Description + Python library of FireTasks + +Authors + Henrik Rusche + +Contributors +''' + +from gasMixtureConductivity import f_gasMixtureConductivity +from gasMixtureConductivity import m_gasMixtureConductivity diff --git a/applications/PUfoam/MoDeNaModels/gasMixtureConductivity/gasMixtureConductivity.py b/applications/PUfoam/MoDeNaModels/gasMixtureConductivity/gasMixtureConductivity.py new file mode 100644 index 000000000..dbd142658 --- /dev/null +++ b/applications/PUfoam/MoDeNaModels/gasMixtureConductivity/gasMixtureConductivity.py @@ -0,0 +1,120 @@ +'''@cond + + ooo ooooo oooooooooo. ooooo ooo + `88. .888' `888' `Y8b `888b. `8' + 888b d'888 .ooooo. 888 888 .ooooo. 8 `88b. 8 .oooo. + 8 Y88. .P 888 d88' `88b 888 888 d88' `88b 8 `88b. 8 `P )88b + 8 `888' 888 888 888 888 888 888ooo888 8 `88b.8 .oP"888 + 8 Y 888 888 888 888 d88' 888 .o 8 `888 d8( 888 + o8o o888o `Y8bod8P' o888bood8P' `Y8bod8P' o8o `8 `Y888""8o + +Copyright + 2014-2015 MoDeNa Consortium, All rights reserved. + +License + This file is part of Modena. + + Modena is free software; you can redistribute it and/or modify it under + the terms of the GNU General Public License as published by the Free + Software Foundation, either version 3 of the License, or (at your option) + any later version. + + Modena is distributed in the hope that it will be useful, but WITHOUT ANY + WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS + FOR A PARTICULAR PURPOSE. See the GNU General Public License + for more details. + + You should have received a copy of the GNU General Public License along + with Modena. If not, see . +@endcond''' + +""" +@file +Surrogate function and model definitions for thermal conductivity of mixture of +blowing agents. + +@author Pavel Ferkl +@copyright 2014-2015, MoDeNa Project. GNU Public License. +@ingroup app_aging +""" + +import os +import modena +from modena import CFunction, IndexSet, Workflow2, \ + ForwardMappingModel, BackwardMappingModel, SurrogateModel +import modena.Strategy as Strategy +from fireworks.user_objects.firetasks.script_task import FireTaskBase, ScriptTask +from fireworks import Firework, Workflow, FWAction +from fireworks.utilities.fw_utilities import explicit_serialize +from blessings import Terminal +import gasConductivity + +## Create terminal for colour output +term = Terminal() + +## Surrogate function for thermal conductivity of blowing agents. +# +# Thermal conductivity of blowing agents is a function of temperature. +f_gasMixtureConductivity = CFunction( + Ccode=r''' +#include "modena.h" +#include "math.h" +#include "stdio.h" + +void gasMixtureConductivity +( + const modena_model_t* model, + const double* inputs, + double *outputs +) +{ + {% block variables %}{% endblock %} + + double kgasmix=0; // gas mixture conductivity + int i; + + printf("temp = %g\\n", T); + printf("x = "); + for (i=0;i. + +Description + Python library of FireTasks + +Authors + Henrik Rusche + +Contributors +''' + +from polymerConductivity import m_polymer_thermal_conductivity, f_polymer_thermal_conductivity + diff --git a/applications/PUfoam/MoDeNaModels/polymerConductivity/polymerConductivity.py b/applications/PUfoam/MoDeNaModels/polymerConductivity/polymerConductivity.py new file mode 100644 index 000000000..505a17523 --- /dev/null +++ b/applications/PUfoam/MoDeNaModels/polymerConductivity/polymerConductivity.py @@ -0,0 +1,106 @@ +'''@cond + + ooo ooooo oooooooooo. ooooo ooo + `88. .888' `888' `Y8b `888b. `8' + 888b d'888 .ooooo. 888 888 .ooooo. 8 `88b. 8 .oooo. + 8 Y88. .P 888 d88' `88b 888 888 d88' `88b 8 `88b. 8 `P )88b + 8 `888' 888 888 888 888 888 888ooo888 8 `88b.8 .oP"888 + 8 Y 888 888 888 888 d88' 888 .o 8 `888 d8( 888 + o8o o888o `Y8bod8P' o888bood8P' `Y8bod8P' o8o `8 `Y888""8o + +Copyright + 2014-2015 MoDeNa Consortium, All rights reserved. + +License + This file is part of Modena. + + Modena is free software; you can redistribute it and/or modify it under + the terms of the GNU General Public License as published by the Free + Software Foundation, either version 3 of the License, or (at your option) + any later version. + + Modena is distributed in the hope that it will be useful, but WITHOUT ANY + WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS + FOR A PARTICULAR PURPOSE. See the GNU General Public License + for more details. + + You should have received a copy of the GNU General Public License along + with Modena. If not, see . +@endcond''' + +""" +@file +Surrogate function and model definitions for thermal conductivity of polyurethane + +@author Erik Laurini +@author Pavel Ferkl +@copyright 2014-2015, MoDeNa Project. GNU Public License. +@ingroup app_aging +""" + +import os +import modena +from modena import ForwardMappingModel, BackwardMappingModel, SurrogateModel, CFunction +import modena.Strategy as Strategy +from fireworks.user_objects.firetasks.script_task import FireTaskBase, ScriptTask +from fireworks import Firework, Workflow, FWAction +from fireworks.utilities.fw_utilities import explicit_serialize +from blessings import Terminal +from jinja2 import Template + +## Create terminal for colour output +term = Terminal() + +## Surrogate function for thermal conductivity of polyurethane. +# +# Thermal conductivity of polyurethane is a function of temperature. +f_polymer_thermal_conductivity = CFunction( + Ccode=''' +#include "modena.h" +#include "math.h" + +void thermal_conductivity +( + const modena_model_t* model, + const double* inputs, + double *outputs +) +{ + {% block variables %}{% endblock %} + + const double a = parameters[0]; + const double b = parameters[1]; + + outputs[0] = (a*T)+b; +} +''', + # These are global bounds for the function + inputs={ + 'T': {'min': 273, 'max': 450}, + }, + outputs={ + 'polymer_thermal_conductivity': { + 'min': 0, 'max': +9e99, 'argPos': 0 + }, + }, + parameters={ + 'param0': {'min': -9e99, 'max': +9e99, 'argPos': 0}, + 'param1': {'min': -9e99, 'max': +9e99, 'argPos': 1}, + }, +) + +## Surrogate model for thermal conductivity of polyurethane +# +# Forward mapping model is used. +m_polymer_thermal_conductivity = ForwardMappingModel( + _id='polymer_thermal_conductivity', + surrogateFunction=f_polymer_thermal_conductivity, + substituteModels=[], + parameters=[0.198e-3, 151.08e-3], + inputs={ + 'T': {'min': 273, 'max': 450}, + }, + outputs={ + 'polymer_thermal_conductivity': {'min': 0, 'max': +9e99}, + }, +) diff --git a/applications/PUfoam/MoDeNaModels/polymerViscosity/__init__.py b/applications/PUfoam/MoDeNaModels/polymerViscosity/__init__.py new file mode 100644 index 000000000..a1b817b80 --- /dev/null +++ b/applications/PUfoam/MoDeNaModels/polymerViscosity/__init__.py @@ -0,0 +1,43 @@ +#!/usr/bin/python +''' + + ooo ooooo oooooooooo. ooooo ooo + `88. .888' `888' `Y8b `888b. `8' + 888b d'888 .ooooo. 888 888 .ooooo. 8 `88b. 8 .oooo. + 8 Y88. .P 888 d88' `88b 888 888 d88' `88b 8 `88b. 8 `P )88b + 8 `888' 888 888 888 888 888 888ooo888 8 `88b.8 .oP"888 + 8 Y 888 888 888 888 d88' 888 .o 8 `888 d8( 888 + o8o o888o `Y8bod8P' o888bood8P' `Y8bod8P' o8o `8 `Y888""8o + +Copyright + 2014 MoDeNa Consortium, All rights reserved. + +License + This file is part of Modena. + + Modena is free software; you can redistribute it and/or modify it under + the terms of the GNU General Public License as published by the Free + Software Foundation, either version 3 of the License, or (at your option) + any later version. + + Modena is distributed in the hope that it will be useful, but WITHOUT ANY + WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS + FOR A PARTICULAR PURPOSE. See the GNU General Public License for more + details. + + You should have received a copy of the GNU General Public License along + with Modena. If not, see . + +Description + Initialisation script needed to run Bubble growth model. + +Authors + Henrik Rusche + Pavel Ferkl + +Contributors +''' + +from polymerViscosity import f_polymerViscosity +from polymerViscosity import m_polymerViscosity + diff --git a/applications/PUfoam/MoDeNaModels/polymerViscosity/polymerViscosity.py b/applications/PUfoam/MoDeNaModels/polymerViscosity/polymerViscosity.py new file mode 100644 index 000000000..3edbc33b5 --- /dev/null +++ b/applications/PUfoam/MoDeNaModels/polymerViscosity/polymerViscosity.py @@ -0,0 +1,130 @@ +'''@cond + + ooo ooooo oooooooooo. ooooo ooo + `88. .888' `888' `Y8b `888b. `8' + 888b d'888 .ooooo. 888 888 .ooooo. 8 `88b. 8 .oooo. + 8 Y88. .P 888 d88' `88b 888 888 d88' `88b 8 `88b. 8 `P )88b + 8 `888' 888 888 888 888 888 888ooo888 8 `88b.8 .oP"888 + 8 Y 888 888 888 888 d88' 888 .o 8 `888 d8( 888 + o8o o888o `Y8bod8P' o888bood8P' `Y8bod8P' o8o `8 `Y888""8o + +Copyright + 2014-2015 MoDeNa Consortium, All rights reserved. + +License + This file is part of Modena. + + Modena is free software; you can redistribute it and/or modify it under + the terms of the GNU General Public License as published by the Free + Software Foundation, either version 3 of the License, or (at your option) + any later version. + + Modena is distributed in the hope that it will be useful, but WITHOUT ANY + WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS + FOR A PARTICULAR PURPOSE. See the GNU General Public License + for more details. + + You should have received a copy of the GNU General Public License along + with Modena. If not, see . +@endcond''' + +""" +@file +Surrogate function and model definitions for polymer viscosity model. + +@author Pavel Ferkl +@copyright 2014-2015, MoDeNa Project. GNU Public License. +@ingroup app_foaming +""" + +import os +import modena +from modena import CFunction, IndexSet, Workflow2, \ + ForwardMappingModel, BackwardMappingModel, SurrogateModel +import modena.Strategy as Strategy +from fireworks.user_objects.firetasks.script_task import FireTaskBase, ScriptTask +from fireworks import Firework, Workflow, FWAction +from fireworks.utilities.fw_utilities import explicit_serialize +from blessings import Terminal +from jinja2 import Template + +## Create terminal for colour output +term = Terminal() + +## Surrogate function for polymer viscosity. +# +# Polymer viscosity is a function of temperature and conversion. +f_polymerViscosity = CFunction( + Ccode=''' +#include "modena.h" +#include "math.h" + +void viscosity_SM +( + const double* parameters, + const double* inherited_inputs, + const double* inputs, + double *outputs +) +{ + const double T = inputs[0]; + const double X = inputs[1]; + + const double Aeta = parameters[0]; + const double Eeta = parameters[1]; + const double AA = parameters[2]; + const double B = parameters[3]; + const double Xg = parameters[4]; + + const double Rg = 8.31446218; + + outputs[0] = Aeta*exp(Eeta/(Rg*T))*pow(Xg/(Xg-X),AA+B*X); +} +''', + # These are global bounds for the function + inputs={ + 'T': {'min': 200, 'max': 450, 'argPos': 0}, + 'X': {'min': 0, 'max': 1, 'argPos': 1}, + }, + outputs={ + 'mu': {'min': 0, 'max': +9e99, 'argPos': 0}, + }, + parameters={ + 'param1': {'min': -1e9, 'max': 1e9, 'argPos': 0}, + 'param2': {'min': -1e9, 'max': 1e9, 'argPos': 1}, + 'param3': {'min': -1e9, 'max': 1e9, 'argPos': 2}, + 'param4': {'min': -1e9, 'max': 1e9, 'argPos': 3}, + 'param5': {'min': -1e9, 'max': 1e9, 'argPos': 4}, + }, +) + +## [literature data](http://dx.doi.org/10.1002/aic.690280213) +par = [4.1e-8, 38.3e3, 4.0, -2.0, 0.85] + +## [literature data](http://dx.doi.org/10.1002/aic.690280213) +par2 = [10.3e-8, 41.3e3, 1.5, 1.0, 0.65] + +## [literature data][1] +## [1]: http://dx.doi.org/10.1002/(SICI)1097-4628(19961017)62:3<567::AID-APP14>3.0.CO;2-W +par3 = [3.32e-8, 42.9e3, 2.32, 1.4, 0.64] + +## based on [literature data](http://dx.doi.org/10.1002/aic.690280213), but +## gel point changed to 0.5 (Baser and Khakhar) +par4 = [4.1e-8, 38.3e3, 4.0, -2.0, 0.5] + +## Surrogate model for polymer viscosity +# +# Forward mapping model is used. +m_polymerViscosity = ForwardMappingModel( + _id='polymerViscosity', + surrogateFunction=f_polymerViscosity, + substituteModels=[], + parameters=par4, + inputs={ + 'T': {'min': 200, 'max': 450}, + 'X': {'min': 0, 'max': 1}, + }, + outputs={ + 'mu': {'min': 0, 'max': +9e99}, + }, +) diff --git a/examples/MoDeNaModels/flowRate/__init__.py b/examples/MoDeNaModels/flowRate/__init__.py new file mode 100644 index 000000000..65c066b3b --- /dev/null +++ b/examples/MoDeNaModels/flowRate/__init__.py @@ -0,0 +1,40 @@ +''' + + ooo ooooo oooooooooo. ooooo ooo + `88. .888' `888' `Y8b `888b. `8' + 888b d'888 .ooooo. 888 888 .ooooo. 8 `88b. 8 .oooo. + 8 Y88. .P 888 d88' `88b 888 888 d88' `88b 8 `88b. 8 `P )88b + 8 `888' 888 888 888 888 888 888ooo888 8 `88b.8 .oP"888 + 8 Y 888 888 888 888 d88' 888 .o 8 `888 d8( 888 + o8o o888o `Y8bod8P' o888bood8P' `Y8bod8P' o8o `8 `Y888""8o + +Copyright + 2014-2015 MoDeNa Consortium, All rights reserved. + +License + This file is part of Modena. + + Modena is free software; you can redistribute it and/or modify it under + the terms of the GNU General Public License as published by the Free + Software Foundation, either version 3 of the License, or (at your option) + any later version. + + Modena is distributed in the hope that it will be useful, but WITHOUT ANY + WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS + FOR A PARTICULAR PURPOSE. See the GNU General Public License + for more details. + + You should have received a copy of the GNU General Public License along + with Modena. If not, see . + +Description + Python library of FireTasks + +Authors + Henrik Rusche + +Contributors +''' + +from flowRate import f, m + diff --git a/examples/MoDeNaModels/flowRate/flowRate.py b/examples/MoDeNaModels/flowRate/flowRate.py new file mode 100644 index 000000000..1e2939f4b --- /dev/null +++ b/examples/MoDeNaModels/flowRate/flowRate.py @@ -0,0 +1,154 @@ +'''@cond + + ooo ooooo oooooooooo. ooooo ooo + `88. .888' `888' `Y8b `888b. `8' + 888b d'888 .ooooo. 888 888 .ooooo. 8 `88b. 8 .oooo. + 8 Y88. .P 888 d88' `88b 888 888 d88' `88b 8 `88b. 8 `P )88b + 8 `888' 888 888 888 888 888 888ooo888 8 `88b.8 .oP"888 + 8 Y 888 888 888 888 d88' 888 .o 8 `888 d8( 888 + o8o o888o `Y8bod8P' o888bood8P' `Y8bod8P' o8o `8 `Y888""8o + +Copyright + 2014-2015 MoDeNa Consortium, All rights reserved. + +License + This file is part of Modena. + + Modena is free software; you can redistribute it and/or modify it under + the terms of the GNU General Public License as published by the Free + Software Foundation, either version 3 of the License, or (at your option) + any later version. + + Modena is distributed in the hope that it will be useful, but WITHOUT ANY + WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS + FOR A PARTICULAR PURPOSE. See the GNU General Public License + for more details. + + You should have received a copy of the GNU General Public License along + with Modena. If not, see . +@endcond''' + +""" +@file +Python library of FireTasks + +@author Henrik Rusche +@copyright 2014-2015, MoDeNa Project. GNU Public License. +@ingroup twoTank +""" + +import os +import modena +from modena import ForwardMappingModel, BackwardMappingModel, SurrogateModel, CFunction, ModenaFireTask +import modena.Strategy as Strategy +from fireworks import Firework, Workflow, FWAction +from fireworks.utilities.fw_utilities import explicit_serialize +from blessings import Terminal +from jinja2 import Template + + +__author__ = 'Henrik Rusche' +__copyright__ = 'Copyright 2014, MoDeNa Project' +__version__ = '0.2' +__maintainer__ = 'Henrik Rusche' +__email__ = 'h.rusche@wikki.co.uk.' +__date__ = 'Sep 4, 2014' + +# ********************************* Class ********************************** # +@explicit_serialize +class FlowRateExactSim(ModenaFireTask): + """ + A FireTask that starts a microscopic code and updates the database. + """ + + def task(self, fw_spec): + # Write input + + # See http://jinja.pocoo.org/docs/dev/templates/ + Template(''' +{{ s['point']['D'] }} +{{ s['point']['rho0'] }} +{{ s['point']['p0'] }} +{{ s['point']['p1Byp0'] }} + '''.strip()).stream(s=self).dump('in.txt') + + # Execute the application + # In this simple example, this call stands for a complex microscopic + # code - such as full 3D CFD simulation. + # Source code in src/flowRateExact.C + ret = os.system(os.path.dirname(os.path.abspath(__file__))+'/src/flowRateExact') + + # This enables backward mapping capabilities (not needed in this example) + self.handleReturnCode(ret) + + # Analyse output + f = open('out.txt', 'r') + self['point']['flowRate'] = float(f.readline()) + f.close() + + +f = CFunction( + Ccode= ''' +#include "modena.h" +#include "math.h" + +void two_tank_flowRate +( + const modena_model_t* model, + const double* inputs, + double *outputs +) +{ + {% block variables %}{% endblock %} + + const double p1 = p0*inputs[3]; + + const double P0 = parameters[0]; + const double P1 = parameters[1]; + + outputs[0] = M_PI*pow(D, 2.0)*P1*sqrt(P0*rho0*p0); +} +''', + # These are global bounds for the function + inputs={ + 'D': { 'min': 0, 'max': 9e99 }, + 'rho0': { 'min': 0, 'max': 9e99 }, + 'p0': { 'min': 0, 'max': 9e99 }, + 'p1Byp0': { 'min': 0, 'max': 1.0 }, + }, + outputs={ + 'flowRate': { 'min': 9e99, 'max': -9e99, 'argPos': 0 }, + }, + parameters={ + 'param0': { 'min': 0.0, 'max': 10.0, 'argPos': 0 }, + 'param1': { 'min': 0.0, 'max': 10.0, 'argPos': 1 }, + }, +) + +m = BackwardMappingModel( + _id= 'flowRate', + surrogateFunction= f, + exactTask= FlowRateExactSim(), + substituteModels= [ ], + initialisationStrategy= Strategy.InitialPoints( + initialPoints= + { + 'D': [0.01, 0.01, 0.01, 0.01], + 'rho0': [3.4, 3.5, 3.4, 3.5], + 'p0': [2.8e5, 3.2e5, 2.8e5, 3.2e5], + 'p1Byp0': [0.03, 0.03, 0.04, 0.04], + }, + ), + outOfBoundsStrategy= Strategy.ExtendSpaceStochasticSampling( + nNewPoints= 4 + ), + parameterFittingStrategy= Strategy.NonLinFitWithErrorContol( + testDataPercentage= 0.2, + maxError= 0.05, + improveErrorStrategy= Strategy.StochasticSampling( + nNewPoints= 2 + ), + maxIterations= 5 # Currently not used + ), +) + diff --git a/examples/MoDeNaModels/flowRate/src/.gitignore b/examples/MoDeNaModels/flowRate/src/.gitignore new file mode 100644 index 000000000..7eedf35c4 --- /dev/null +++ b/examples/MoDeNaModels/flowRate/src/.gitignore @@ -0,0 +1,17 @@ +# Backups +*~ +*bak + +# Various intermediate files and directories generated CMAKE +CMakeFiles/ +build/ +Makefile +CMakeCache.txt +cmake_install.cmake + +# locate results (executables and libraries) +*.so* +*.l[ao] +*.mod + +flowRateExact diff --git a/examples/MoDeNaModels/flowRate/src/CMakeLists.txt b/examples/MoDeNaModels/flowRate/src/CMakeLists.txt new file mode 100644 index 000000000..ed838b608 --- /dev/null +++ b/examples/MoDeNaModels/flowRate/src/CMakeLists.txt @@ -0,0 +1,30 @@ +cmake_minimum_required (VERSION 2.8) +project (nozzleFlowRate C CXX) + +if( CMAKE_VERSION VERSION_GREATER "3.0" ) + cmake_policy(SET CMP0042 OLD) + cmake_policy(SET CMP0026 OLD) + cmake_policy(SET CMP0028 OLD) +endif() + +set(CMAKE_BUILD_TYPE Release) + +add_custom_target(debug + COMMAND ${CMAKE_COMMAND} -DCMAKE_BUILD_TYPE=Debug ${CMAKE_SOURCE_DIR} + COMMAND ${CMAKE_COMMAND} --build ${CMAKE_BINARY_DIR} --target all + COMMENT "Switch CMAKE_BUILD_TYPE to Debug" + ) + +add_custom_target(release + COMMAND ${CMAKE_COMMAND} -DCMAKE_BUILD_TYPE=Release ${CMAKE_SOURCE_DIR} + COMMAND ${CMAKE_COMMAND} --build ${CMAKE_BINARY_DIR} --target all + COMMENT "Switch CMAKE_BUILD_TYPE to Release" + ) + +find_package(MODENA REQUIRED) + +include(CheckCInline) +check_c_inline(C_INLINE) + +add_executable(flowRateExact flowRateExact.C) + diff --git a/examples/MoDeNaModels/flowRate/src/flowRateExact.C b/examples/MoDeNaModels/flowRate/src/flowRateExact.C new file mode 100644 index 000000000..a7d8fee0b --- /dev/null +++ b/examples/MoDeNaModels/flowRate/src/flowRateExact.C @@ -0,0 +1,125 @@ +/** +@cond + + ooo ooooo oooooooooo. ooooo ooo + `88. .888' `888' `Y8b `888b. `8' + 888b d'888 .ooooo. 888 888 .ooooo. 8 `88b. 8 .oooo. + 8 Y88. .P 888 d88' `88b 888 888 d88' `88b 8 `88b. 8 `P )88b + 8 `888' 888 888 888 888 888 888ooo888 8 `88b.8 .oP"888 + 8 Y 888 888 888 888 d88' 888 .o 8 `888 d8( 888 + o8o o888o `Y8bod8P' o888bood8P' `Y8bod8P' o8o `8 `Y888""8o + +Copyright + 2014-2015 MoDeNa Consortium, All rights reserved. + +License + This file is part of Modena. + + Modena is free software; you can redistribute it and/or modify it under + the terms of the GNU General Public License as published by the Free + Software Foundation, either version 3 of the License, or (at your option) + any later version. + + Modena is distributed in the hope that it will be useful, but WITHOUT ANY + WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS + FOR A PARTICULAR PURPOSE. See the GNU General Public License + for more details. + + You should have received a copy of the GNU General Public License along + with Modena. If not, see . + +@endcond +@file +This code calculates the flowRate through a nozzle as a function of the +diameter, density and pressure upstream and pressure downstream. It uses +expressions from VDI Waermeatlas Lbd 4 + +In the simple twoTank example, this piece of code stands for a complex +microscopic code - such as full 3D CFD simulation. + +@author Henrik Rusche +@copyright 2014-2015, MoDeNa Project. GNU Public License. +@ingroup twoTank +*/ + +#include +#include +#include +#include + +using namespace std; + + +double flowRate +( + const double D, + const double rho0, + const double p0, + const double p2Byp0 +) +{ + const double p2 = p0*p2Byp0; + const double kappa = 1.4; + + const double etac = pow(2.0/(kappa+1.0), kappa/(kappa-1.0)); + + double p1 = etac*p0; + if(p2 > p1) + { + p1 = p2; + } + + // for a nozzle + const double Cd0 = 0.84; + const double Cd1 = 0.66; + // Not 100% sure this is correct - eqn. (10) in Lbd 5 uses misleading + // nomenclature + const double Cdg = + Cd0 - Cd1*pow(p1/p0, 2.0) + (2*Cd1-Cd0)*pow(p1/p0, 3.0); + + const double Phi = + sqrt + ( + kappa/(kappa-1.0) + *(pow(p1/p0, 2.0/kappa) - pow(p1/p0, (kappa+1.0)/kappa)) + ); + + return M_PI*pow(D, 2.0)*Cdg*Phi*sqrt(2.0*rho0*p0); +} + + +int +main (int argc, char *argv[]) +{ + ifstream fi; + fi.open ("in.txt"); + if(!fi.is_open()) + { + cerr << "Could not open in.txt!" << endl; + return 1; + } + + double D, rho0, p0, p1Byp0; + fi >> D >> rho0 >> p0 >> p1Byp0; + + double mdot = flowRate(D, rho0, p0, p1Byp0); + + double p1 = p0*p1Byp0; + + cout << "D = " << D + << " rho0 = " << rho0 + << " p0 = " << p0 + << " p1/p0 = " << p1Byp0 + << " p1 = " << p1 + << " mdot = " << mdot + << endl; + + ofstream fo; + fo.open ("out.txt"); + + fo << mdot << endl; + + fi.close(); + fo.close(); +} + diff --git a/examples/MoDeNaModels/flowRate_idealGas/__init__.py b/examples/MoDeNaModels/flowRate_idealGas/__init__.py new file mode 100644 index 000000000..65c066b3b --- /dev/null +++ b/examples/MoDeNaModels/flowRate_idealGas/__init__.py @@ -0,0 +1,40 @@ +''' + + ooo ooooo oooooooooo. ooooo ooo + `88. .888' `888' `Y8b `888b. `8' + 888b d'888 .ooooo. 888 888 .ooooo. 8 `88b. 8 .oooo. + 8 Y88. .P 888 d88' `88b 888 888 d88' `88b 8 `88b. 8 `P )88b + 8 `888' 888 888 888 888 888 888ooo888 8 `88b.8 .oP"888 + 8 Y 888 888 888 888 d88' 888 .o 8 `888 d8( 888 + o8o o888o `Y8bod8P' o888bood8P' `Y8bod8P' o8o `8 `Y888""8o + +Copyright + 2014-2015 MoDeNa Consortium, All rights reserved. + +License + This file is part of Modena. + + Modena is free software; you can redistribute it and/or modify it under + the terms of the GNU General Public License as published by the Free + Software Foundation, either version 3 of the License, or (at your option) + any later version. + + Modena is distributed in the hope that it will be useful, but WITHOUT ANY + WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS + FOR A PARTICULAR PURPOSE. See the GNU General Public License + for more details. + + You should have received a copy of the GNU General Public License along + with Modena. If not, see . + +Description + Python library of FireTasks + +Authors + Henrik Rusche + +Contributors +''' + +from flowRate import f, m + diff --git a/examples/MoDeNaModels/flowRate_idealGas/flowRate.py b/examples/MoDeNaModels/flowRate_idealGas/flowRate.py new file mode 100644 index 000000000..476547802 --- /dev/null +++ b/examples/MoDeNaModels/flowRate_idealGas/flowRate.py @@ -0,0 +1,166 @@ +''' + + ooo ooooo oooooooooo. ooooo ooo + `88. .888' `888' `Y8b `888b. `8' + 888b d'888 .ooooo. 888 888 .ooooo. 8 `88b. 8 .oooo. + 8 Y88. .P 888 d88' `88b 888 888 d88' `88b 8 `88b. 8 `P )88b + 8 `888' 888 888 888 888 888 888ooo888 8 `88b.8 .oP"888 + 8 Y 888 888 888 888 d88' 888 .o 8 `888 d8( 888 + o8o o888o `Y8bod8P' o888bood8P' `Y8bod8P' o8o `8 `Y888""8o + +Copyright + 2014-2015 MoDeNa Consortium, All rights reserved. + +License + This file is part of Modena. + + Modena is free software; you can redistribute it and/or modify it under + the terms of the GNU General Public License as published by the Free + Software Foundation, either version 3 of the License, or (at your option) + any later version. + + Modena is distributed in the hope that it will be useful, but WITHOUT ANY + WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS + FOR A PARTICULAR PURPOSE. See the GNU General Public License + for more details. + + You should have received a copy of the GNU General Public License along + with Modena. If not, see . + +Description + Python library of FireTasks + +Authors + Henrik Rusche + +Contributors +''' + +import os +import modena +from modena import ForwardMappingModel, BackwardMappingModel, SurrogateModel, CFunction +import modena.Strategy as Strategy +from fireworks.user_objects.firetasks.script_task import FireTaskBase, ScriptTask +from fireworks import Firework, Workflow, FWAction +from fireworks.utilities.fw_utilities import explicit_serialize +from blessings import Terminal +from jinja2 import Template +import idealGas + +# Create terminal for colour output +term = Terminal() + + +__author__ = 'Henrik Rusche' +__copyright__ = 'Copyright 2014, MoDeNa Project' +__version__ = '0.2' +__maintainer__ = 'Henrik Rusche' +__email__ = 'h.rusche@wikki.co.uk.' +__date__ = 'Sep 4, 2014' + + +# ********************************* Class ********************************** # +@explicit_serialize +class FlowRateExactSim(FireTaskBase): + """ + A FireTask that starts a microscopic code and updates the database. + """ + + def run_task(self, fw_spec): + print( + term.yellow + + "Performing exact simulation (microscopic code recipe)" + + term.normal + ) + + # Write input + + # See http://jinja.pocoo.org/docs/dev/templates/ + Template(''' +{{ s['point']['D'] }} +{{ s['point']['rho0'] }} +{{ s['point']['p0'] }} +{{ s['point']['p1Byp0'] }} + '''.strip()).stream(s=self).dump('in.txt') + + # Execute the application + # In this simple example, this call stands for a complex microscopic + # code - such as full 3D CFD simulation. + # Source code in src/flowRateExact.C + os.system('../src/flowRateExact') + + # Analyse output + f = open('out.txt', 'r') + self['point']['flowRate'] = float(f.readline()) + f.close() + + return FWAction(mod_spec=[{'_push': self['point']}]) + + +f = CFunction( + Ccode= ''' +#include "modena.h" +#include "math.h" + +void two_tank_flowRate +( + const double* parameters, + const double* inherited_inputs, + const double* inputs, + double *outputs +) +{ + const double D = inputs[0]; + const double rho0 = inputs[1]; + const double p0 = inputs[2]; + const double p1 = p0*inputs[3]; + + const double P0 = parameters[0]; + const double P1 = parameters[1]; + + outputs[0] = M_PI*pow(D, 2.0)*P1*sqrt(P0*rho0*p0); +} +''', + # These are global bounds for the function + inputs={ + 'D': { 'min': 0, 'max': 9e99, 'argPos': 0 }, + 'T0': { 'min': 0, 'max': 9e99, 'argPos': 1 }, + 'p0': { 'min': 0, 'max': 9e99, 'argPos': 2 }, + 'p1Byp0': { 'min': 0, 'max': 1.0, 'argPos': 3}, + }, + outputs={ + 'flowRate': { 'min': 9e99, 'max': -9e99, 'argPos': 0 }, + }, + parameters={ + 'param0': { 'min': 0.0, 'max': 10.0, 'argPos': 0 }, + 'param1': { 'min': 0.0, 'max': 10.0, 'argPos': 1 }, + }, +) + +m = BackwardMappingModel( + _id= 'flowRate', + surrogateFunction= f, + exactTask= FlowRateExactSim(), + substituteModels= [ idealGas.m ], + initialisationStrategy= Strategy.InitialPoints( + initialPoints= + { + 'D': [0.01, 0.01, 0.01, 0.01], + 'T0': [300, 300, 300, 300], + 'p0': [2.8e5, 3.2e5, 2.8e5, 3.2e5], + 'p1Byp0': [0.03, 0.03, 0.04, 0.04], + }, + ), + outOfBoundsStrategy= Strategy.ExtendSpaceStochasticSampling( + nNewPoints= 4 + ), + parameterFittingStrategy= Strategy.NonLinFitWithErrorContol( + testDataPercentage= 0.2, + maxError= 0.05, + improveErrorStrategy= Strategy.StochasticSampling( + nNewPoints= 2 + ), + maxIterations= 5 # Currently not used + ), +) + diff --git a/examples/MoDeNaModels/flowRate_idealGas/src/.gitignore b/examples/MoDeNaModels/flowRate_idealGas/src/.gitignore new file mode 100644 index 000000000..7eedf35c4 --- /dev/null +++ b/examples/MoDeNaModels/flowRate_idealGas/src/.gitignore @@ -0,0 +1,17 @@ +# Backups +*~ +*bak + +# Various intermediate files and directories generated CMAKE +CMakeFiles/ +build/ +Makefile +CMakeCache.txt +cmake_install.cmake + +# locate results (executables and libraries) +*.so* +*.l[ao] +*.mod + +flowRateExact diff --git a/examples/MoDeNaModels/flowRate_idealGas/src/CMakeLists.txt b/examples/MoDeNaModels/flowRate_idealGas/src/CMakeLists.txt new file mode 100644 index 000000000..ed838b608 --- /dev/null +++ b/examples/MoDeNaModels/flowRate_idealGas/src/CMakeLists.txt @@ -0,0 +1,30 @@ +cmake_minimum_required (VERSION 2.8) +project (nozzleFlowRate C CXX) + +if( CMAKE_VERSION VERSION_GREATER "3.0" ) + cmake_policy(SET CMP0042 OLD) + cmake_policy(SET CMP0026 OLD) + cmake_policy(SET CMP0028 OLD) +endif() + +set(CMAKE_BUILD_TYPE Release) + +add_custom_target(debug + COMMAND ${CMAKE_COMMAND} -DCMAKE_BUILD_TYPE=Debug ${CMAKE_SOURCE_DIR} + COMMAND ${CMAKE_COMMAND} --build ${CMAKE_BINARY_DIR} --target all + COMMENT "Switch CMAKE_BUILD_TYPE to Debug" + ) + +add_custom_target(release + COMMAND ${CMAKE_COMMAND} -DCMAKE_BUILD_TYPE=Release ${CMAKE_SOURCE_DIR} + COMMAND ${CMAKE_COMMAND} --build ${CMAKE_BINARY_DIR} --target all + COMMENT "Switch CMAKE_BUILD_TYPE to Release" + ) + +find_package(MODENA REQUIRED) + +include(CheckCInline) +check_c_inline(C_INLINE) + +add_executable(flowRateExact flowRateExact.C) + diff --git a/examples/MoDeNaModels/flowRate_idealGas/src/flowRateExact.C b/examples/MoDeNaModels/flowRate_idealGas/src/flowRateExact.C new file mode 100644 index 000000000..79bf0f0f7 --- /dev/null +++ b/examples/MoDeNaModels/flowRate_idealGas/src/flowRateExact.C @@ -0,0 +1,124 @@ +/* + + ooo ooooo oooooooooo. ooooo ooo + `88. .888' `888' `Y8b `888b. `8' + 888b d'888 .ooooo. 888 888 .ooooo. 8 `88b. 8 .oooo. + 8 Y88. .P 888 d88' `88b 888 888 d88' `88b 8 `88b. 8 `P )88b + 8 `888' 888 888 888 888 888 888ooo888 8 `88b.8 .oP"888 + 8 Y 888 888 888 888 d88' 888 .o 8 `888 d8( 888 + o8o o888o `Y8bod8P' o888bood8P' `Y8bod8P' o8o `8 `Y888""8o + +Copyright + 2014-2015 MoDeNa Consortium, All rights reserved. + +License + This file is part of Modena. + + Modena is free software; you can redistribute it and/or modify it under + the terms of the GNU General Public License as published by the Free + Software Foundation, either version 3 of the License, or (at your option) + any later version. + + Modena is distributed in the hope that it will be useful, but WITHOUT ANY + WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS + FOR A PARTICULAR PURPOSE. See the GNU General Public License + for more details. + + You should have received a copy of the GNU General Public License along + with Modena. If not, see . + +Description + This code calculates the flowRate through a nozzle as a function of the + diameter, density and pressure upstream and pressure downstream. It uses + expressions from VDI Waermeatlas Lbd 4 + + In the simple twoTank example, this piece of code stands for a complex + microscopic code - such as full 3D CFD simulation. + +Authors + Henrik Rusche + +Contributors +*/ + +#include +#include +#include +#include + +using namespace std; + + +double flowRate +( + const double D, + const double rho0, + const double p0, + const double p2Byp0 +) +{ + const double p2 = p0*p2Byp0; + const double kappa = 1.4; + + const double etac = pow(2.0/(kappa+1.0), kappa/(kappa-1.0)); + + double p1 = etac*p0; + if(p2 > p1) + { + p1 = p2; + } + + // for a nozzle + const double Cd0 = 0.84; + const double Cd1 = 0.66; + // Not 100% sure this is correct - eqn. (10) in Lbd 5 uses misleading + // nomenclature + const double Cdg = + Cd0 - Cd1*pow(p1/p0, 2.0) + (2*Cd1-Cd0)*pow(p1/p0, 3.0); + + const double Phi = + sqrt + ( + kappa/(kappa-1.0) + *(pow(p1/p0, 2.0/kappa) - pow(p1/p0, (kappa+1.0)/kappa)) + ); + + return M_PI*pow(D, 2.0)*Cdg*Phi*sqrt(2.0*rho0*p0); +} + + +int +main (int argc, char *argv[]) +{ + ifstream fi; + fi.open ("in.txt"); + if(!fi.is_open()) + { + cerr << "Could not open in.txt!" << endl; + return 1; + } + + double D, rho0, p0, p1Byp0; + fi >> D >> rho0 >> p0 >> p1Byp0; + + double mdot = flowRate(D, rho0, p0, p1Byp0); + + double p1 = p0*p1Byp0; + + cout << "D = " << D + << " rho0 = " << rho0 + << " p0 = " << p0 + << " p1/p0 = " << p1Byp0 + << " p1 = " << p1 + << " mdot = " << mdot + << endl; + + ofstream fo; + fo.open ("out.txt"); + + fo << mdot << endl; + + fi.close(); + fo.close(); +} + diff --git a/examples/MoDeNaModels/fullerEtAlDiffusion/__init__.py b/examples/MoDeNaModels/fullerEtAlDiffusion/__init__.py new file mode 100644 index 000000000..3c0a815f3 --- /dev/null +++ b/examples/MoDeNaModels/fullerEtAlDiffusion/__init__.py @@ -0,0 +1,40 @@ +''' + + ooo ooooo oooooooooo. ooooo ooo + `88. .888' `888' `Y8b `888b. `8' + 888b d'888 .ooooo. 888 888 .ooooo. 8 `88b. 8 .oooo. + 8 Y88. .P 888 d88' `88b 888 888 d88' `88b 8 `88b. 8 `P )88b + 8 `888' 888 888 888 888 888 888ooo888 8 `88b.8 .oP"888 + 8 Y 888 888 888 888 d88' 888 .o 8 `888 d8( 888 + o8o o888o `Y8bod8P' o888bood8P' `Y8bod8P' o8o `8 `Y888""8o + +Copyright + 2014-2015 MoDeNa Consortium, All rights reserved. + +License + This file is part of Modena. + + Modena is free software; you can redistribute it and/or modify it under + the terms of the GNU General Public License as published by the Free + Software Foundation, either version 3 of the License, or (at your option) + any later version. + + Modena is distributed in the hope that it will be useful, but WITHOUT ANY + WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS + FOR A PARTICULAR PURPOSE. See the GNU General Public License + for more details. + + You should have received a copy of the GNU General Public License along + with Modena. If not, see . + +Description + Python library of FireTasks + +Authors + Henrik Rusche + +Contributors +''' + +from fullerEtAlDiffusion import f, m, species + diff --git a/examples/MoDeNaModels/fullerEtAlDiffusion/fullerEtAlDiffusion.py b/examples/MoDeNaModels/fullerEtAlDiffusion/fullerEtAlDiffusion.py new file mode 100755 index 000000000..2281e7bb4 --- /dev/null +++ b/examples/MoDeNaModels/fullerEtAlDiffusion/fullerEtAlDiffusion.py @@ -0,0 +1,98 @@ +'''@cond + + ooo ooooo oooooooooo. ooooo ooo + `88. .888' `888' `Y8b `888b. `8' + 888b d'888 .ooooo. 888 888 .ooooo. 8 `88b. 8 .oooo. + 8 Y88. .P 888 d88' `88b 888 888 d88' `88b 8 `88b. 8 `P )88b + 8 `888' 888 888 888 888 888 888ooo888 8 `88b.8 .oP"888 + 8 Y 888 888 888 888 d88' 888 .o 8 `888 d8( 888 + o8o o888o `Y8bod8P' o888bood8P' `Y8bod8P' o8o `8 `Y888""8o + +Copyright + 2014-2015 MoDeNa Consortium, All rights reserved. + +License + This file is part of Modena. + + Modena is free software; you can redistribute it and/or modify it under + the terms of the GNU General Public License as published by the Free + Software Foundation, either version 3 of the License, or (at your option) + any later version. + + Modena is distributed in the hope that it will be useful, but WITHOUT ANY + WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS + FOR A PARTICULAR PURPOSE. See the GNU General Public License + for more details. + + You should have received a copy of the GNU General Public License along + with Modena. If not, see . +@endcond''' + +""" +@file +Python library of FireTasks + +@author Henrik Rusche +@copyright 2014-2015, MoDeNa Project. GNU Public License. +@ingroup twoTank +""" + +from modena import CFunction, IndexSet, ForwardMappingModel +import modena.Strategy as Strategy + +species = IndexSet( + name= 'species', + names= [ 'H2O', 'N2', 'SO2' ] +) + + +f = CFunction( + inputs={ + 'T': { 'min': 0, 'max': 9e99 }, + 'p': { 'min': 0, 'max': 9e99 }, + }, + outputs={ + 'D[A]': { 'min': 0, 'max': 9e99, 'argPos': 0 }, + }, + parameters={ + 'W[A]': { 'min': 0, 'max': 9e99, 'argPos': 0 }, + 'V[A]': { 'min': 0, 'max': 9e99, 'argPos': 1 }, + 'W[B]': { 'min': 0, 'max': 9e99, 'argPos': 2 }, + 'V[B]': { 'min': 0, 'max': 9e99, 'argPos': 3 }, + }, + indices={ + 'A': species, + 'B': species, + }, + Ccode= ''' +#include "modena.h" +#include "math.h" + +void fullerEtAlDiffusion +( + const modena_model_t* model, + const double* inputs, + double *outputs +) +{ + {% block variables %}{% endblock %} + + const double WA = parameters[0]; + const double VA = parameters[1]; + const double WB = parameters[2]; + const double VB = parameters[3]; + + outputs[0] = 1.011e-4*pow(T, 1.75)*pow(1.0/WA + 1.0/WB, 1.0/2.0); + outputs[0] /= p*(pow(pow(VA, 1.0/3.0) + pow(VB, 1.0/3.0), 2.0)); +} +''', +) + +m = ForwardMappingModel( + _id= 'fullerEtAlDiffusion[A=H2O,B=N2]', + surrogateFunction= f, + substituteModels= [ ], + parameters= [ 16, 9.44, 14, 11.38 ], +) + + diff --git a/examples/MoDeNaModels/fullerEtAlDiffusion/src/.gitignore b/examples/MoDeNaModels/fullerEtAlDiffusion/src/.gitignore new file mode 100644 index 000000000..a434af21e --- /dev/null +++ b/examples/MoDeNaModels/fullerEtAlDiffusion/src/.gitignore @@ -0,0 +1,19 @@ +# Backups +*~ +*bak + +# Various intermediate files from automake +CMakeFiles/ +Makefile +libmodena.pc +CMakeCache.txt +cmake_install.cmake +install_manifest.txt + +# Intermediate files generated by SWIG +*_wrap.c + +# locate results (executables and libraries) +*.l[ao] + +fullerEtAlDiffusionTest diff --git a/examples/MoDeNaModels/idealGas/__init__.py b/examples/MoDeNaModels/idealGas/__init__.py new file mode 100644 index 000000000..a8c60a40c --- /dev/null +++ b/examples/MoDeNaModels/idealGas/__init__.py @@ -0,0 +1,40 @@ +''' + + ooo ooooo oooooooooo. ooooo ooo + `88. .888' `888' `Y8b `888b. `8' + 888b d'888 .ooooo. 888 888 .ooooo. 8 `88b. 8 .oooo. + 8 Y88. .P 888 d88' `88b 888 888 d88' `88b 8 `88b. 8 `P )88b + 8 `888' 888 888 888 888 888 888ooo888 8 `88b.8 .oP"888 + 8 Y 888 888 888 888 d88' 888 .o 8 `888 d8( 888 + o8o o888o `Y8bod8P' o888bood8P' `Y8bod8P' o8o `8 `Y888""8o + +Copyright + 2014-2015 MoDeNa Consortium, All rights reserved. + +License + This file is part of Modena. + + Modena is free software; you can redistribute it and/or modify it under + the terms of the GNU General Public License as published by the Free + Software Foundation, either version 3 of the License, or (at your option) + any later version. + + Modena is distributed in the hope that it will be useful, but WITHOUT ANY + WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS + FOR A PARTICULAR PURPOSE. See the GNU General Public License + for more details. + + You should have received a copy of the GNU General Public License along + with Modena. If not, see . + +Description + Python library of FireTasks + +Authors + Henrik Rusche + +Contributors +''' + +from idealGas import f, m + diff --git a/examples/MoDeNaModels/idealGas/idealGas.py b/examples/MoDeNaModels/idealGas/idealGas.py new file mode 100644 index 000000000..0b4ba05d1 --- /dev/null +++ b/examples/MoDeNaModels/idealGas/idealGas.py @@ -0,0 +1,103 @@ +'''@cond + + ooo ooooo oooooooooo. ooooo ooo + `88. .888' `888' `Y8b `888b. `8' + 888b d'888 .ooooo. 888 888 .ooooo. 8 `88b. 8 .oooo. + 8 Y88. .P 888 d88' `88b 888 888 d88' `88b 8 `88b. 8 `P )88b + 8 `888' 888 888 888 888 888 888ooo888 8 `88b.8 .oP"888 + 8 Y 888 888 888 888 d88' 888 .o 8 `888 d8( 888 + o8o o888o `Y8bod8P' o888bood8P' `Y8bod8P' o8o `8 `Y888""8o + +Copyright + 2014-2015 MoDeNa Consortium, All rights reserved. + +License + This file is part of Modena. + + Modena is free software; you can redistribute it and/or modify it under + the terms of the GNU General Public License as published by the Free + Software Foundation, either version 3 of the License, or (at your option) + any later version. + + Modena is distributed in the hope that it will be useful, but WITHOUT ANY + WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS + FOR A PARTICULAR PURPOSE. See the GNU General Public License + for more details. + + You should have received a copy of the GNU General Public License along + with Modena. If not, see . +@endcond''' + +""" +@file +Python library of FireTasks + +@author Henrik Rusche +@copyright 2014-2015, MoDeNa Project. GNU Public License. +@ingroup twoTank +""" + +import os +import modena +from modena import ForwardMappingModel, BackwardMappingModel, SurrogateModel, CFunction, ModenaFireTask +import modena.Strategy as Strategy +from fireworks import Firework, Workflow, FWAction +from fireworks.utilities.fw_utilities import explicit_serialize + + +__author__ = 'Henrik Rusche' +__copyright__ = 'Copyright 2014, MoDeNa Project' +__version__ = '0.2' +__maintainer__ = 'Henrik Rusche' +__email__ = 'h.rusche@wikki.co.uk.' +__date__ = 'Sep 4, 2014' + + +f = CFunction( + Ccode= ''' +#include "modena.h" +#include "math.h" + +void idealGas +( + const double* parameters, + const double* inherited_inputs, + const double* inputs, + double *outputs +) +{ + const double p0 = inputs[0]; + const double T0 = inputs[1]; + + const double R = parameters[0]; + + outputs[0] = p0/R/T0; +} +''', + # These are global bounds for the function + inputs={ + 'p0': { 'min': 0, 'max': 9e99, 'argPos': 0 }, + 'T0': { 'min': 0, 'max': 9e99, 'argPos': 1 }, + }, + outputs={ + 'rho0': { 'min': 9e99, 'max': -9e99, 'argPos': 0 }, + }, + parameters={ + 'R': { 'min': 0.0, 'max': 9e99, 'argPos': 0 } + }, +) + +m = ForwardMappingModel( + _id= 'idealGas', + surrogateFunction= f, + substituteModels= [ ], + parameters= [ 287.0 ], + inputs={ + 'p0': { 'min': 0, 'max': 9e99 }, + 'T0': { 'min': 0, 'max': 9e99 }, + }, + outputs={ + 'rho0': {'min': 0, 'max': 9e99 }, + }, +) + diff --git a/examples/MoDeNaModels/twoTank/__init__.py b/examples/MoDeNaModels/twoTank/__init__.py new file mode 100644 index 000000000..b439929d4 --- /dev/null +++ b/examples/MoDeNaModels/twoTank/__init__.py @@ -0,0 +1,40 @@ +''' + + ooo ooooo oooooooooo. ooooo ooo + `88. .888' `888' `Y8b `888b. `8' + 888b d'888 .ooooo. 888 888 .ooooo. 8 `88b. 8 .oooo. + 8 Y88. .P 888 d88' `88b 888 888 d88' `88b 8 `88b. 8 `P )88b + 8 `888' 888 888 888 888 888 888ooo888 8 `88b.8 .oP"888 + 8 Y 888 888 888 888 d88' 888 .o 8 `888 d8( 888 + o8o o888o `Y8bod8P' o888bood8P' `Y8bod8P' o8o `8 `Y888""8o + +Copyright + 2014-2015 MoDeNa Consortium, All rights reserved. + +License + This file is part of Modena. + + Modena is free software; you can redistribute it and/or modify it under + the terms of the GNU General Public License as published by the Free + Software Foundation, either version 3 of the License, or (at your option) + any later version. + + Modena is distributed in the hope that it will be useful, but WITHOUT ANY + WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS + FOR A PARTICULAR PURPOSE. See the GNU General Public License + for more details. + + You should have received a copy of the GNU General Public License along + with Modena. If not, see . + +Description + Python library of FireTasks + +Authors + Henrik Rusche + +Contributors +''' + +from twoTank import m + diff --git a/examples/MoDeNaModels/twoTank/src/.gitignore b/examples/MoDeNaModels/twoTank/src/.gitignore new file mode 100644 index 000000000..fcc90073c --- /dev/null +++ b/examples/MoDeNaModels/twoTank/src/.gitignore @@ -0,0 +1,17 @@ +# Backups +*~ +*bak + +# Various intermediate files and directories generated CMAKE +CMakeFiles/ +build/ +Makefile +CMakeCache.txt +cmake_install.cmake + +# locate results (executables and libraries) +*.so* +*.l[ao] +*.mod + +twoTanksMacroscopicProblem diff --git a/examples/MoDeNaModels/twoTank/src/CMakeLists.txt b/examples/MoDeNaModels/twoTank/src/CMakeLists.txt new file mode 100644 index 000000000..6f0a666b2 --- /dev/null +++ b/examples/MoDeNaModels/twoTank/src/CMakeLists.txt @@ -0,0 +1,31 @@ +cmake_minimum_required (VERSION 2.8) +project (twoTankMacroscopic C CXX) + +if( CMAKE_VERSION VERSION_GREATER "3.0" ) + cmake_policy(SET CMP0042 OLD) + cmake_policy(SET CMP0026 OLD) + cmake_policy(SET CMP0028 OLD) +endif() + +set(CMAKE_BUILD_TYPE Release) + +add_custom_target(debug + COMMAND ${CMAKE_COMMAND} -DCMAKE_BUILD_TYPE=Debug ${CMAKE_SOURCE_DIR} + COMMAND ${CMAKE_COMMAND} --build ${CMAKE_BINARY_DIR} --target all + COMMENT "Switch CMAKE_BUILD_TYPE to Debug" + ) + +add_custom_target(release + COMMAND ${CMAKE_COMMAND} -DCMAKE_BUILD_TYPE=Release ${CMAKE_SOURCE_DIR} + COMMAND ${CMAKE_COMMAND} --build ${CMAKE_BINARY_DIR} --target all + COMMENT "Switch CMAKE_BUILD_TYPE to Release" + ) + +find_package(MODENA REQUIRED) + +include(CheckCInline) +check_c_inline(C_INLINE) + +add_executable(twoTanksMacroscopicProblem twoTanksMacroscopicProblem.C) +target_link_libraries(twoTanksMacroscopicProblem MODENA::modena) + diff --git a/examples/MoDeNaModels/twoTank/src/twoTanksMacroscopicProblem.C b/examples/MoDeNaModels/twoTank/src/twoTanksMacroscopicProblem.C new file mode 100644 index 000000000..a95047333 --- /dev/null +++ b/examples/MoDeNaModels/twoTank/src/twoTanksMacroscopicProblem.C @@ -0,0 +1,160 @@ +/** +@cond + + ooo ooooo oooooooooo. ooooo ooo + `88. .888' `888' `Y8b `888b. `8' + 888b d'888 .ooooo. 888 888 .ooooo. 8 `88b. 8 .oooo. + 8 Y88. .P 888 d88' `88b 888 888 d88' `88b 8 `88b. 8 `P )88b + 8 `888' 888 888 888 888 888 888ooo888 8 `88b.8 .oP"888 + 8 Y 888 888 888 888 d88' 888 .o 8 `888 d8( 888 + o8o o888o `Y8bod8P' o888bood8P' `Y8bod8P' o8o `8 `Y888""8o + +Copyright + 2014-2015 MoDeNa Consortium, All rights reserved. + +License + This file is part of Modena. + + Modena is free software; you can redistribute it and/or modify it under + the terms of the GNU General Public License as published by the Free + Software Foundation, either version 3 of the License, or (at your option) + any later version. + + Modena is distributed in the hope that it will be useful, but WITHOUT ANY + WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS + FOR A PARTICULAR PURPOSE. See the GNU General Public License + for more details. + + You should have received a copy of the GNU General Public License along + with Modena. If not, see . + +@endcond +@file +Solving the two tank problem the MoDeNa way. +A prototypical macros-scopic code embeds a micro-scale model (flowRate) +through the MoDeNa interface library. +@author Henrik Rusche +@copyright 2014-2015, MoDeNa Project. GNU Public License. +@ingroup twoTank +*/ + +#include +#include +#include "modena.h" + +using namespace std; + +int +main(int argc, char *argv[]) +{ + const double D = 0.01; + + double p0 = 3e5; + double p1 = 10000; + double V0 = 0.1; + double V1 = 1; + double T = 300; + + double t = 0.0; + const double deltat = 1e-3; + const double tend = 5.5; + + double m0 = p0*V0/287.1/T; + double m1 = p1*V1/287.1/T; + + double rho0 = m0/V0; + double rho1 = m1/V1; + + + // Instantiate a model + modena_model_t *model = modena_model_new("flowRate"); + if(modena_error_occurred()) + { + return modena_error(); + } + + // Allocate memory and fetch arg positions + modena_inputs_t *inputs = modena_inputs_new(model); + modena_outputs_t *outputs = modena_outputs_new(model); + + size_t Dpos = modena_model_inputs_argPos(model, "D"); + size_t rho0Pos = modena_model_inputs_argPos(model, "rho0"); + size_t p0Pos = modena_model_inputs_argPos(model, "p0"); + size_t p1Byp0Pos = modena_model_inputs_argPos(model, "p1Byp0"); + + modena_model_argPos_check(model); + + while(t + deltat < tend + 1e-10) + { + t += deltat; + + if(p0 > p1) + { + // Set input vector + modena_inputs_set(inputs, Dpos, D); + modena_inputs_set(inputs, rho0Pos, rho0); + modena_inputs_set(inputs, p0Pos, p0); + modena_inputs_set(inputs, p1Byp0Pos, p1/p0); + + // Call the model + int ret = modena_model_call(model, inputs, outputs); + + // Terminate, if requested + if(modena_error_occurred()) + { + modena_inputs_destroy(inputs); + modena_outputs_destroy(outputs); + modena_model_destroy(model); + + return modena_error(); + } + + // Fetch result + double mdot = modena_outputs_get(outputs, 0); + + m0 -= mdot*deltat; + m1 += mdot*deltat; + } + else + { + // Set input vector + modena_inputs_set(inputs, Dpos, D); + modena_inputs_set(inputs, rho0Pos, rho1); + modena_inputs_set(inputs, p0Pos, p1); + modena_inputs_set(inputs, p1Byp0Pos, p0/p1); + + // Call the model + int ret = modena_model_call(model, inputs, outputs); + + // Terminate, if requested + if(modena_error_occurred()) + { + modena_inputs_destroy(inputs); + modena_outputs_destroy(outputs); + modena_model_destroy(model); + + return modena_error(); + } + + // Fetch result + double mdot = modena_outputs_get(outputs, 0); + + m0 += mdot*deltat; + m1 -= mdot*deltat; + } + + rho0 = m0/V0; + rho1 = m1/V1; + p0 = m0/V0*287.1*T; + p1 = m1/V1*287.1*T; + + cout << "t = " << t << " rho0 = " << rho0 << " p0 = " << p0 << " p1 = " << p1 << endl; + } + + modena_inputs_destroy(inputs); + modena_outputs_destroy(outputs); + modena_model_destroy(model); + + return 0; +} + diff --git a/examples/MoDeNaModels/twoTank/twoTank.py b/examples/MoDeNaModels/twoTank/twoTank.py new file mode 100644 index 000000000..eb181638e --- /dev/null +++ b/examples/MoDeNaModels/twoTank/twoTank.py @@ -0,0 +1,46 @@ +'''@cond + + ooo ooooo oooooooooo. ooooo ooo + `88. .888' `888' `Y8b `888b. `8' + 888b d'888 .ooooo. 888 888 .ooooo. 8 `88b. 8 .oooo. + 8 Y88. .P 888 d88' `88b 888 888 d88' `88b 8 `88b. 8 `P )88b + 8 `888' 888 888 888 888 888 888ooo888 8 `88b.8 .oP"888 + 8 Y 888 888 888 888 d88' 888 .o 8 `888 d8( 888 + o8o o888o `Y8bod8P' o888bood8P' `Y8bod8P' o8o `8 `Y888""8o + +Copyright + 2014-2015 MoDeNa Consortium, All rights reserved. + +License + This file is part of Modena. + + Modena is free software; you can redistribute it and/or modify it under + the terms of the GNU General Public License as published by the Free + Software Foundation, either version 3 of the License, or (at your option) + any later version. + + Modena is distributed in the hope that it will be useful, but WITHOUT ANY + WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS + FOR A PARTICULAR PURPOSE. See the GNU General Public License + for more details. + + You should have received a copy of the GNU General Public License along + with Modena. If not, see . +@endcond''' + +""" +@file +Python library of FireTasks + +@author Henrik Rusche +@copyright 2014-2015, MoDeNa Project. GNU Public License. +@ingroup twoTank +""" + +from modena.Strategy import BackwardMappingScriptTask +import os + +# Source code in src/twoTanksMacroscopicProblem.C +m = BackwardMappingScriptTask( + script=os.path.dirname(os.path.abspath(__file__))+'/src/twoTanksMacroscopicProblem' +) diff --git a/examples/MoDeNaModels/twoTankFortran/__init__.py b/examples/MoDeNaModels/twoTankFortran/__init__.py new file mode 100644 index 000000000..563c686df --- /dev/null +++ b/examples/MoDeNaModels/twoTankFortran/__init__.py @@ -0,0 +1,40 @@ +''' + + ooo ooooo oooooooooo. ooooo ooo + `88. .888' `888' `Y8b `888b. `8' + 888b d'888 .ooooo. 888 888 .ooooo. 8 `88b. 8 .oooo. + 8 Y88. .P 888 d88' `88b 888 888 d88' `88b 8 `88b. 8 `P )88b + 8 `888' 888 888 888 888 888 888ooo888 8 `88b.8 .oP"888 + 8 Y 888 888 888 888 d88' 888 .o 8 `888 d8( 888 + o8o o888o `Y8bod8P' o888bood8P' `Y8bod8P' o8o `8 `Y888""8o + +Copyright + 2014-2015 MoDeNa Consortium, All rights reserved. + +License + This file is part of Modena. + + Modena is free software; you can redistribute it and/or modify it under + the terms of the GNU General Public License as published by the Free + Software Foundation, either version 3 of the License, or (at your option) + any later version. + + Modena is distributed in the hope that it will be useful, but WITHOUT ANY + WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS + FOR A PARTICULAR PURPOSE. See the GNU General Public License + for more details. + + You should have received a copy of the GNU General Public License along + with Modena. If not, see . + +Description + Python library of FireTasks + +Authors + Henrik Rusche + +Contributors +''' + +from twoTankFortran import m + diff --git a/examples/MoDeNaModels/twoTankFortran/src/.gitignore b/examples/MoDeNaModels/twoTankFortran/src/.gitignore new file mode 100644 index 000000000..01fc8a952 --- /dev/null +++ b/examples/MoDeNaModels/twoTankFortran/src/.gitignore @@ -0,0 +1,17 @@ +# Backups +*~ +*bak + +# Various intermediate files and directories generated CMAKE +CMakeFiles/ +build/ +Makefile +CMakeCache.txt +cmake_install.cmake + +# locate results (executables and libraries) +*.so* +*.l[ao] +*.mod + +twoTanksMacroscopicProblemFortran diff --git a/examples/MoDeNaModels/twoTankFortran/src/CMakeLists.txt b/examples/MoDeNaModels/twoTankFortran/src/CMakeLists.txt new file mode 100644 index 000000000..7424f1376 --- /dev/null +++ b/examples/MoDeNaModels/twoTankFortran/src/CMakeLists.txt @@ -0,0 +1,26 @@ +cmake_minimum_required (VERSION 2.8) +project (tutorialModels C CXX Fortran) + +if( CMAKE_VERSION VERSION_GREATER "3.0" ) + cmake_policy(SET CMP0042 OLD) + cmake_policy(SET CMP0026 OLD) + cmake_policy(SET CMP0028 OLD) +endif() + +add_custom_target(debug + COMMAND ${CMAKE_COMMAND} -DCMAKE_BUILD_TYPE=Debug ${CMAKE_SOURCE_DIR} + COMMAND ${CMAKE_COMMAND} --build ${CMAKE_BINARY_DIR} --target all + COMMENT "Switch CMAKE_BUILD_TYPE to Debug" + ) + +add_custom_target(release + COMMAND ${CMAKE_COMMAND} -DCMAKE_BUILD_TYPE=Release ${CMAKE_SOURCE_DIR} + COMMAND ${CMAKE_COMMAND} --build ${CMAKE_BINARY_DIR} --target all + COMMENT "Switch CMAKE_BUILD_TYPE to Release" + ) + +find_package(MODENA REQUIRED) + +add_executable(twoTanksMacroscopicProblemFortran twoTanksMacroscopicProblemFortran.f90) +target_link_libraries(twoTanksMacroscopicProblemFortran MODENA::modena) + diff --git a/examples/MoDeNaModels/twoTankFortran/src/twoTanksMacroscopicProblemFortran.f90 b/examples/MoDeNaModels/twoTankFortran/src/twoTanksMacroscopicProblemFortran.f90 new file mode 100644 index 000000000..da779eec8 --- /dev/null +++ b/examples/MoDeNaModels/twoTankFortran/src/twoTanksMacroscopicProblemFortran.f90 @@ -0,0 +1,175 @@ +! +! +! ooo ooooo oooooooooo. ooooo ooo +! `88. .888' `888' `Y8b `888b. `8' +! 888b d'888 .ooooo. 888 888 .ooooo. 8 `88b. 8 .oooo. +! 8 Y88. .P 888 d88' `88b 888 888 d88' `88b 8 `88b. 8 `P )88b +! 8 `888' 888 888 888 888 888 888ooo888 8 `88b.8 .oP"888 +! 8 Y 888 888 888 888 d88' 888 .o 8 `888 d8( 888 +! o8o o888o `Y8bod8P' o888bood8P' `Y8bod8P' o8o `8 `Y888""8o +! +!Copyright +! 2014-2015 MoDeNa Consortium, All rights reserved. +! +!License +! This file is part of Modena. +! +! Modena is free software; you can redistribute it and/or modify it under +! the terms of the GNU General Public License as published by the Free +! Software Foundation, either version 3 of the License, or (at your option) +! any later version. +! +! Modena is distributed in the hope that it will be useful, but WITHOUT ANY +! WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS +! FOR A PARTICULAR PURPOSE. See the GNU General Public License +! for more details. +! +! You should have received a copy of the GNU General Public License along +! with Modena. If not, see . +! +!Description +! Solving the two tank problem the MoDeNa way. +! +! A prototypical macros-scopic code embeds a micro-scale model (flowRate) +! through the MoDeNa interface library. +! +! Re-programmed to Fortran +! +!Authors +! Henrik Rusche +! +!Contributors +! Pavel Ferkl +program twoTanksMacroscopicProblemFortran !command line arguments not implemented yet + use iso_c_binding + use fmodena + + implicit none + + integer, parameter ::dp=selected_real_kind(15) + + real(dp), parameter :: D = 0.01_dp; + + real(dp) :: p0 = 3e5; + real(dp) :: p1 = 10000; + real(dp) :: V0 = 0.1_dp; + real(dp) :: V1 = 1; + real(dp) :: temp = 300; + + real(dp) :: t = 0.0_dp; + real(dp), parameter :: deltat = 1e-3_dp; + real(dp), parameter :: tend = 5.5_dp; + + real(dp) :: m0 + real(dp) :: m1 + + real(dp) :: rho0 + real(dp) :: rho1 + + real(dp) :: mdot + + integer(c_int) :: ret + + type(c_ptr) :: client = c_null_ptr !mongoc_client_t + type(c_ptr) :: model = c_null_ptr !modena_model_t + type(c_ptr) :: inputs = c_null_ptr !modena_inputs_t + type(c_ptr) :: outputs = c_null_ptr !modena_outputs_t + + integer(c_size_t) :: Dpos + integer(c_size_t) :: rho0Pos + integer(c_size_t) :: p0Pos + integer(c_size_t) :: p1Byp0Pos + + m0 = p0*V0/287.1_dp/temp; + m1 = p1*V1/287.1_dp/temp; + rho0 = m0/V0; + rho1 = m1/V1; + +! //Instantiate a model + model = modena_model_new (c_char_"flowRate"//c_null_char); !modena_model_t + +! //Allocate memory and fetch arg positions + inputs = modena_inputs_new (model); !modena_inputs_t + outputs = modena_outputs_new (model); !modena_outputs_t + + Dpos = modena_model_inputs_argPos(model, c_char_"D"//c_null_char); + rho0Pos = modena_model_inputs_argPos(model, c_char_"rho0"//c_null_char); + p0Pos = modena_model_inputs_argPos(model, c_char_"p0"//c_null_char); + p1Byp0Pos = modena_model_inputs_argPos(model, c_char_"p1Byp0"//c_null_char); + +! //TODO: Add checking function that makes sure that the positions of all +! //arguments to the model are requested + call modena_model_argPos_check(model); + + do while(t + deltat < tend + 1e-10_dp) + + t = t + deltat; + + if(p0 > p1) then +! //Set input vector + call modena_inputs_set(inputs, Dpos, D); + call modena_inputs_set(inputs, rho0Pos, rho0); + call modena_inputs_set(inputs, p0Pos, p0); + call modena_inputs_set(inputs, p1Byp0Pos, p1/p0); + +! // Call the model + ret = modena_model_call (model, inputs, outputs); + +! // Terminate, if requested + if(ret /= 0) then + + call modena_inputs_destroy (inputs); + call modena_outputs_destroy (outputs); + call modena_model_destroy (model); + + call exit(ret) + endif + +! // Fetch result + mdot = modena_outputs_get(outputs, 0_c_size_t); + + m0 = m0 - mdot*deltat; + m1 = m1 + mdot*deltat; + + else + +! // Set input vector + call modena_inputs_set(inputs, Dpos, D); + call modena_inputs_set(inputs, rho0Pos, rho1); + call modena_inputs_set(inputs, p0Pos, p1); + call modena_inputs_set(inputs, p1Byp0Pos, p0/p1); + +! // Call the model + ret = modena_model_call (model, inputs, outputs); + +! // Terminate, if requested + if(ret /= 0) then + + call modena_inputs_destroy (inputs); + call modena_outputs_destroy (outputs); + call modena_model_destroy (model); + + call exit(ret) + endif + +! // Fetch result + mdot = modena_outputs_get(outputs, 0_c_size_t); + + m0 = m0 + mdot*deltat; + m1 = m1 - mdot*deltat; + endif + + rho0 = m0/V0; + rho1 = m1/V1; + p0 = m0/V0*287.1_dp*temp; + p1 = m1/V1*287.1_dp*temp; + + write(*,*) "t = ",t," rho0 = ",rho0," p0 = ",p0," p1 = ",p1 + enddo + + call modena_inputs_destroy (inputs); + call modena_outputs_destroy (outputs); + call modena_model_destroy (model); + + call exit(0) +end program twoTanksMacroscopicProblemFortran diff --git a/examples/MoDeNaModels/twoTankFortran/twoTankFortran.py b/examples/MoDeNaModels/twoTankFortran/twoTankFortran.py new file mode 100644 index 000000000..50ffce0fb --- /dev/null +++ b/examples/MoDeNaModels/twoTankFortran/twoTankFortran.py @@ -0,0 +1,46 @@ +'''@cond + + ooo ooooo oooooooooo. ooooo ooo + `88. .888' `888' `Y8b `888b. `8' + 888b d'888 .ooooo. 888 888 .ooooo. 8 `88b. 8 .oooo. + 8 Y88. .P 888 d88' `88b 888 888 d88' `88b 8 `88b. 8 `P )88b + 8 `888' 888 888 888 888 888 888ooo888 8 `88b.8 .oP"888 + 8 Y 888 888 888 888 d88' 888 .o 8 `888 d8( 888 + o8o o888o `Y8bod8P' o888bood8P' `Y8bod8P' o8o `8 `Y888""8o + +Copyright + 2014-2015 MoDeNa Consortium, All rights reserved. + +License + This file is part of Modena. + + Modena is free software; you can redistribute it and/or modify it under + the terms of the GNU General Public License as published by the Free + Software Foundation, either version 3 of the License, or (at your option) + any later version. + + Modena is distributed in the hope that it will be useful, but WITHOUT ANY + WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS + FOR A PARTICULAR PURPOSE. See the GNU General Public License + for more details. + + You should have received a copy of the GNU General Public License along + with Modena. If not, see . +@endcond''' + +""" +@file +Python library of FireTasks + +@author Henrik Rusche +@copyright 2014-2015, MoDeNa Project. GNU Public License. +@ingroup twoTank +""" + +from modena.Strategy import BackwardMappingScriptTask +import os + +# Source code in src/twoTanksMacroscopicProblem.C +m = BackwardMappingScriptTask( + script=os.path.dirname(os.path.abspath(__file__))+'/src/twoTanksMacroscopicProblemFortran' +) diff --git a/examples/multicomponentDiffusion/README.md b/examples/multicomponentDiffusion/README.md new file mode 100644 index 000000000..0354dfe64 --- /dev/null +++ b/examples/multicomponentDiffusion/README.md @@ -0,0 +1,31 @@ +MULTICOMPONENT DIFFUSION EXAMPLE: +================================= + +Binary diffusion by Fuller etal. is combined with Wilke multicomponent diffusion. + +This example only shows the use of index sets. No backward mapping! + + +How to run? +----------- + +# Make sure `PYTHONPATH` and `LD_LIBRARY_PATH` are set +# TODO: +# Make this easier to use + export PKG_CONFIG_PATH=${PKG_CONFIG_PATH:-}:${HOME}/lib/pkgconfig:/usr/local/lib/pkgconfig + export PYTHONPATH=${PYTHONPATH:-}:${HOME}/lib/python2.7/site-packages + export LD_LIBRARY_PATH=${LD_LIBRARY_PATH:-}:${HOME}/lib/python2.7/site-packages:${HOME}/lib:/usr/local/lib + +# Compile project specific sources, i.e. "models": + fuller="../models/fullerEtAlDiffusion/src" + cmake -H${fuller} -B${fuller} && make --directory=${fuller} + +# Initialise the model in the database + ./initModel + +# Start the workflow + ./workflow + +# Run again to see that no fitting is done on the second start + ./workflow + diff --git a/examples/twoTanks/README.md b/examples/twoTanks/README.md new file mode 100644 index 000000000..c3dbf9daa --- /dev/null +++ b/examples/twoTanks/README.md @@ -0,0 +1,44 @@ +TWO TANKS EXAMPLE: +================== + +The discharge of air from one tank into another through a nozzle. The +problem only makes sense, if you think of the flow through the nozzle as a +much more complex problem which you have to solve with - let's say 3D CFD. So +the two tanks are the macroscopic and the nozzle is the microscopic problem. +This is also a backward mapping problem if you assume that the range of +inputs is unknown a-priori. twoTanksMacroscopicProblem uses the MoDeNa +interface library to embed an even simpler model for the flow rate. While +twoTanksFullProblem implements it fully integrated. + +TODO: +The example specific sources should be moved into the example, but this requires +building (and finding) the execuables here. + + +How to run? +----------- + +# Make sure PYTHONPATH and LD_LIBRARY_PATH are set +# TODO: +# Make this easier to use + + + export PKG_CONFIG_PATH=${PKG_CONFIG_PATH:-}:${HOME}/lib/pkgconfig:/usr/local/lib/pkgconfig + export PYTHONPATH=${PYTHONPATH:-}:${HOME}/lib/python2.7/site-packages + export LD_LIBRARY_PATH=${LD_LIBRARY_PATH:-}:${HOME}/lib/python2.7/site-packages:${HOME}/lib:/usr/local/lib + +# Compile project specific sources, i.e. "models": + flowRate="../models/flowRate/src" + twoTank="../models/twoTank/src" + cmake -H${flowRate} -B${flowRate} && make --directory=${flowRate} + cmake -H${twoTank} -B${twoTank} && make --directory${twoTank} + +# Initialise the model in the database + ./initModel + +# Start the workflow + ./workflow + +# Run again to see that no fitting is done on the second start + ./workflow + diff --git a/examples/twoTanksAutoInit/README.md b/examples/twoTanksAutoInit/README.md new file mode 100644 index 000000000..51e31a546 --- /dev/null +++ b/examples/twoTanksAutoInit/README.md @@ -0,0 +1,45 @@ +TWO TANKS EXAMPLE: +================== + +The discharge of air from one tank into another through a nozzle. The +problem only makes sense, if you think of the flow through the nozzle as a +much more complex problem which you have to solve with - let's say 3D CFD. So +the two tanks are the macroscopic and the nozzle is the microscopic problem. +This is also a backward mapping problem if you assume that the range of +inputs is unknown a-priori. twoTanksMacroscopicProblem uses the MoDeNa +interface library to embed an even simpler model for the flow rate. While +twoTanksFullProblem implements it fully integrated. + +TODO: +The example specific sources should be moved into the example, but this requires +building (and finding) the execuables here. + + +How to run? +----------- + +# Make sure `PYTHONPATH` and `LD_LIBRARY_PATH` are set +# TODO: +# Make this easier to use + + export PKG_CONFIG_PATH=${PKG_CONFIG_PATH:-}:${HOME}/lib/pkgconfig:/usr/local/lib/pkgconfig + export PYTHONPATH=${PYTHONPATH:-}:${HOME}/lib/python2.7/site-packages + export LD_LIBRARY_PATH=${LD_LIBRARY_PATH:-}:${HOME}/lib/python2.7/site-packages:${HOME}/lib:/usr/local/lib + + +# Compile project specific sources, i.e. "models": + + flowRate="../models/flowRate/src" + twoTank="../models/twoTank/src" + cmake -H${flowRate} -B${flowRate} && make --directory=${flowRate} + cmake -H${twoTank} -B${twoTank} && make --directory${twoTank} + +# Initialise the model in the database + ./initModel + +# Start the workflow + ./workflow + +# Run again to see that no fitting is done on the second start + ./workflow + diff --git a/examples/twoTanksChained/README.md b/examples/twoTanksChained/README.md new file mode 100644 index 000000000..dfa75df37 --- /dev/null +++ b/examples/twoTanksChained/README.md @@ -0,0 +1,47 @@ +TWO TANKS EXAMPLE: +================== + +The discharge of air from one tank into another through a nozzle. The +problem only makes sense, if you think of the flow through the nozzle as a +much more complex problem which you have to solve with - let's say 3D CFD. So +the two tanks are the macroscopic and the nozzle is the microscopic problem. +This is also a backward mapping problem if you assume that the range of +inputs is unknown a-priori. twoTanksMacroscopicProblem uses the MoDeNa +interface library to embed an even simpler model for the flow rate. While +twoTanksFullProblem implements it fully integrated. + +TODO: +The example specific sources should be moved into the example, but this requires +building (and finding) the execuables here. + + +How to run? +----------- + +# Make sure `PYTHONPATH` and `LD_LIBRARY_PATH` are set +# TODO: +# Make this easier to use + + export PKG_CONFIG_PATH=${PKG_CONFIG_PATH:-}:${HOME}/lib/pkgconfig:/usr/local/lib/pkgconfig + export PYTHONPATH=${PYTHONPATH:-}:${HOME}/lib/python2.7/site-packages + export LD_LIBRARY_PATH=${LD_LIBRARY_PATH:-}:${HOME}/lib/python2.7/site-packages:${HOME}/lib:/usr/local/lib + +# Compile project specific sources, i.e. "models": + + flowRate="../models/flowRate_idealGas/src" + twoTank="../models/twoTank/src" + cmake -H${flowRate} -B${flowRate} && make --directory=${flowRate} + cmake -H${twoTank} -B${twoTank} && make --directory${twoTank} + +# Append path to the models directory to "PYTHONPATH": + export PYTHONPATH="${PYTHONPATH}:../models" + +# Initialise the model in the database + ./initModel + +# Start the workflow + ./workflow + +# Run again to see that no fitting is done on the second start + ./workflow + diff --git a/examples/twoTanksFortran/README.md b/examples/twoTanksFortran/README.md new file mode 100644 index 000000000..ac8367573 --- /dev/null +++ b/examples/twoTanksFortran/README.md @@ -0,0 +1,44 @@ +TWO TANKS EXAMPLE: +================== + +The discharge of air from one tank into another through a nozzle. The +problem only makes sense, if you think of the flow through the nozzle as a +much more complex problem which you have to solve with - let's say 3D CFD. So +the two tanks are the macroscopic and the nozzle is the microscopic problem. +This is also a backward mapping problem if you assume that the range of +inputs is unknown a-priori. twoTanksMacroscopicProblem uses the MoDeNa +interface library to embed an even simpler model for the flow rate. While +twoTanksFullProblem implements it fully integrated. + +TODO: +The example specific sources should be moved into the example, but this requires +building (and finding) the execuables here. + + +How to run? +----------- + +# Make sure `PYTHONPATH` and `LD_LIBRARY_PATH` are set +# TODO: +# Make this easier to use + + export PKG_CONFIG_PATH=${PKG_CONFIG_PATH:-}:${HOME}/lib/pkgconfig:/usr/local/lib/pkgconfig + export PYTHONPATH=${PYTHONPATH:-}:${HOME}/lib/python2.7/site-packages + export LD_LIBRARY_PATH=${LD_LIBRARY_PATH:-}:${HOME}/lib/python2.7/site-packages:${HOME}/lib:/usr/local/lib + + +# Compile project specific sources, i.e. "models": + flowRate="../models/flowRate/src" + twoTank="../models/twoTankFortran/src" + cmake -H${flowRate} -B${flowRate} && make --directory=${flowRate} + cmake -H${twoTank} -B${twoTank} && make --directory${twoTank} + +# Initialise the model in the database + ./initModel + +# Start the workflow + ./workflow + +# Run again to see that no fitting is done on the second start + ./workflow + From 2a9d34f0141a58327eb47c015fec3c6cb0a37ce6 Mon Sep 17 00:00:00 2001 From: Sigve Karolius Date: Wed, 9 Dec 2015 17:21:44 +0100 Subject: [PATCH 02/27] Adding files --- applications/PUfoam/0D_CFD/workflow | 55 +++++++++++++++++++++++++++++ 1 file changed, 55 insertions(+) create mode 100755 applications/PUfoam/0D_CFD/workflow diff --git a/applications/PUfoam/0D_CFD/workflow b/applications/PUfoam/0D_CFD/workflow new file mode 100755 index 000000000..d8c14de16 --- /dev/null +++ b/applications/PUfoam/0D_CFD/workflow @@ -0,0 +1,55 @@ +#!/usr/bin/python +''' + + ooo ooooo oooooooooo. ooooo ooo + `88. .888' `888' `Y8b `888b. `8' + 888b d'888 .ooooo. 888 888 .ooooo. 8 `88b. 8 .oooo. + 8 Y88. .P 888 d88' `88b 888 888 d88' `88b 8 `88b. 8 `P )88b + 8 `888' 888 888 888 888 888 888ooo888 8 `88b.8 .oP"888 + 8 Y 888 888 888 888 d88' 888 .o 8 `888 d8( 888 + o8o o888o `Y8bod8P' o888bood8P' `Y8bod8P' o8o `8 `Y888""8o + +Copyright + 2014 MoDeNa Consortium, All rights reserved. + +License + This file is part of Modena. + + Modena is free software; you can redistribute it and/or modify it under + the terms of the GNU General Public License as published by the Free + Software Foundation, either version 3 of the License, or (at your option) + any later version. + + Modena is distributed in the hope that it will be useful, but WITHOUT ANY + WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS + FOR A PARTICULAR PURPOSE. See the GNU General Public License for more + details. + + You should have received a copy of the GNU General Public License along + with Modena. If not, see . + +Description + A simple workflow + +Authors + Henrik Rusche + +Contributors +''' + +from fireworks import Firework, Workflow, LaunchPad +from fireworks.core.rocket_launcher import rapidfire +from CFD_tool_0D import m as SIMULATION +from modulefinder import ModuleFinder + + +# set up the LaunchPad and reset it +launchpad = LaunchPad() +launchpad.reset('', require_password=False) + +# create the individual FireWorks and Workflow +wf = Workflow([Firework(SIMULATION)], {}, name="simulation") + +# store workflow and launch it locally +launchpad.add_wf(wf) +rapidfire(launchpad) From 98fe4a209ebbe4baabac17cc5f67e8c34c69765e Mon Sep 17 00:00:00 2001 From: Sigve Karolius Date: Wed, 9 Dec 2015 17:27:15 +0100 Subject: [PATCH 03/27] Removed dir:'Content', saved locally if this was a mistake... --- Content/.DS_Store | Bin 6148 -> 0 bytes Content/Bibliography/bibliography.bib | 327 - .../Figures/Data_Flow-eps-converted-to.pdf | Bin 184088 -> 0 bytes Content/Figures/Data_Flow.eps | 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-@phdthesis{winkler_1993, - author = {Christian A. Winkler}, - title = {PhD thesis}, - school = {University of Stuttgart}, - year = 2009, -} - -@book{woods_1990, - title={Polyurethane Handbook: Chemistry, Raw Materials, Processing, Application, Properties}, - author={Woods, George}, - isbn={0471926582}, - lccn={90043732}, - year={1990}, - publisher={ICI Polyurethanes and Wiley in Chichester, New York . } -} - -@book{oertel_and_abele_1994, - title={Polyurethane Handbook: Chemistry, Raw Materials, Processing, Application, Properties}, - author={Oertel, G. and Abele, L.}, - isbn={9781569901571}, - lccn={93033469}, - year={1994}, - publisher={Hanser} -} - -@book{klempner_and_frisch_1991, - title={Handbook of Polymeric Foams and Foam Technology}, - author={Klempner, D. and Frisch, K.C.}, - isbn={9781569900499}, - url={http://books.google.no/books?id=QbcZHAAACAAJ}, - year={1991}, - publisher={Hanser Gardner Publications} -} - -@book{gibson_and_ashby_1999, - title={Cellular Solids: Structure and Properties}, - author={Gibson, L.J. and Ashby, M.F.}, - isbn={9780521499118}, - lccn={96031571}, - series={Cambridge Solid State Science Series}, - url={https://books.google.no/books?id=IySUr5sn4N8C}, - year={1999}, - publisher={Cambridge University Press} -} - -@article {niyogi_and_kumar_etal_2014, - author = {Niyogi, Debdarsan and Kumar, Rajinder and Gandhi, Kandukuri S.}, - title = {Modeling of bubble-size distribution in water and freon co-blown free rise polyurethane foams}, - journal = {Journal of Applied Polymer Science}, - volume = {131}, - number = {18}, - issn = {1097-4628}, - url = {http://dx.doi.org/10.1002/app.40745}, - doi = {10.1002/app.40745}, - pages = {n/a--n/a}, - keywords = {molding, morphology, polyurethanes, theory and modeling}, - year = {2014}, -} - -@article {beverte_2014, - author = {Beverte, Ilze}, - title = {Determination of highly porous plastic foam structural characteristics by processing light microscopy images data}, - journal = {Journal of Applied Polymer Science}, - volume = {131}, - number = {4}, - issn = {1097-4628}, - url = {http://dx.doi.org/10.1002/app.39477}, - doi = {10.1002/app.39477}, - pages = {n/a--n/a}, - keywords = {foams, microscopy, structure-property relations, mechanical properties, polyurethanes}, - year = {2014}, -} - -@article {shen_and_zaho_etal_2014, -author = {Shen, Lu and Zhao, Yusheng and Tekeei, Ali and Hsieh, Fu-Hung and Suppes, Galen J.}, -title = {Density modeling of polyurethane box foam}, -journal = {Polymer Engineering \& Science}, -volume = {54}, -number = {7}, -issn = {1548-2634}, -url = {http://dx.doi.org/10.1002/pen.23694}, -doi = {10.1002/pen.23694}, -pages = {1503--1511}, -year = {2014}, -} - -@article {zhao_and_gordon_etal_2013, - author = {Zhao, Yusheng and Gordon, Michael J. and Tekeei, Ali and Hsieh, Fu-Hung and Suppes, Galen J.}, - title = {Modeling reaction kinetics of rigid polyurethane foaming process}, - journal = {Journal of Applied Polymer Science}, - volume = {130}, - number = {2}, - issn = {1097-4628}, - url = {http://dx.doi.org/10.1002/app.39287}, - doi = {10.1002/app.39287}, - pages = {1131--1138}, - keywords = {polyurethane foams, kinetics, theory and modeling}, - year = {2013}, -} - -@article {mosanenzadeh_and_naguib_etal_2013, - author = {Mosanenzadeh, Shahrzad Ghaffari and Naguib, Hani E. and Park, Chul B. and Atalla, Noureddine}, - title = {Development, characterization, and modeling of environmentally friendly open-cell acoustic foams}, - journal = {Polymer Engineering \& Science}, - volume = {53}, - number = {9}, - publisher = {Wiley Subscription Services, Inc., A Wiley Company}, - issn = {1548-2634}, - url = {http://dx.doi.org/10.1002/pen.23443}, - doi = {10.1002/pen.23443}, - pages = {1979--1989}, - year = {2013}, -} - -@article {zhou_and_huang_etal_2006, - author = {Zhou, Hong and Li, Bo and Huang, Guangsu}, - title = {Sound absorption characteristics of polymer microparticles}, - journal = {Journal of Applied Polymer Science}, - volume = {101}, - number = {4}, - publisher = {Wiley Subscription Services, Inc., A Wiley Company}, - issn = {1097-4628}, - url = {http://dx.doi.org/10.1002/app.23911}, - doi = {10.1002/app.23911}, - pages = {2675--2679}, - keywords = {acoustic property, modeling, polymer microparticle, sound absorption material}, - year = {2006}, -} - -@article {tesser_and_deserio_etal_2004, - author = {Tesser, R. and Di Serio, M. and Sclafani, A. and Santacesaria, E.}, - title = {Modeling of polyurethane foam formation}, - journal = {Journal of Applied Polymer Science}, - volume = {92}, - number = {3}, - publisher = {Wiley Subscription Services, Inc., A Wiley Company}, - issn = {1097-4628}, - url = {http://dx.doi.org/10.1002/app.20170}, - doi = {10.1002/app.20170}, - pages = {1875--1886}, - keywords = {polyurethane foams, blowing agent, modeling, vapor-liquid equilibrium}, - year = {2004}, -} - -@article {lo_and_reible_etal_1994, - author = {Lo, Yu-Wen and Reible, Danny D. and Collier, John R. and Chen, Cheng-Ho}, - title = {Three-dimensional modeling of reaction injection molding. I}, - journal = {Polymer Engineering \& Science}, - volume = {34}, - number = {18}, - publisher = {Society of Plastics Engineers}, - issn = {1548-2634}, - url = {http://dx.doi.org/10.1002/pen.760341805}, - doi = {10.1002/pen.760341805}, - pages = {1393--1400}, - year = {1994}, -} - -@book{marchisio_and_fox_2013, - title={Computational Models for Polydisperse Particulate and Multiphase Systems}, - author={Marchisio, D.L. and Fox, R.O.}, - isbn={9781107328174}, - series={Cambridge Series in Chemical Engineering}, - year={2013}, - publisher={Cambridge University Press} -} - -@article {baser_and_khakhar_1994_a, - author = {Baser, S. A. and Khakhar, D. V.}, - title = {Modeling of the dynamics of R-11 blown polyurethane foam formation}, - journal = {Polymer Engineering \& Science}, - volume = {34}, - number = {8}, - publisher = {Society of Plastics Engineers}, - issn = {1548-2634}, - url = {http://dx.doi.org/10.1002/pen.760340804}, - doi = {10.1002/pen.760340804}, - pages = {632--641}, - year = {1994}, -} - -@article {baser_and_khakhar_1994_b, - author = {Baser, S. A. and Khakhar, D. 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- journal = "Chemical Engineering Science ", - volume = "63", - number = "19", - pages = "4846 - 4872", - year = "2008", - note = "Model-Based Experimental Analysis ", - issn = "0009-2509", - doi = "http://dx.doi.org/10.1016/j.ces.2007.11.034", - url = {http://www.sciencedirect.com/science/article/pii/S0009250907008871}, - author = "Gaia Franceschini and Sandro Macchietto", - keywords = "Mathematical modelling", - keywords = "Model-based experiment design", - keywords = "Model validation", - keywords = "Non-linear dynamics", - keywords = "Optimisation", - keywords = "Parameter identification", - keywords = "Process engineering ", -} - -@manual{RManual, - title = {R: A Language and Environment for Statistical Computing}, - author = {{R Core Team}}, - organization = {R Foundation for Statistical Computing}, - address = {Vienna, Austria}, - year = {2014}, - url = {http://www.R-project.org/}, -} - -@manual{MongoDBManual, - title = {MongoDB Documentation}, - author = {MongoDB Documentation 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:: ret + +! integer(c_size_t) :: surfaceTempPos +! integer(c_size_t) :: viscosityTempPos, viscosityConvPos +! type(c_ptr) :: surfaceModel, surfaceInputs, surfaceOutputs +! type(c_ptr) :: viscosityModel, viscosityInputs, viscosityOutputs + +! surfaceModel = modena_model_new (c_char_"SurfaceTension"//c_null_char); +! surfaceInputs = modena_inputs_new (surfaceModel); +! surfaceOutputs = modena_outputs_new (surfaceModel); +! surfaceTempPos = modena_model_inputs_argPos(surfaceModel, & +! c_char_"T"//c_null_char); +! +! viscosityModel = modena_model_new (c_char_"polymerViscosity"//c_null_char); +! viscosityInputs = modena_inputs_new (viscosityModel); +! viscosityOutputs = modena_outputs_new (viscosityModel); +! viscosityTempPos = modena_model_inputs_argPos(viscosityModel, & +! c_char_"T"//c_null_char); +! viscosityConvPos = modena_model_inputs_argPos(viscosityModel, & +! c_char_"X"//c_null_char); + +! call modena_model_argPos_check(surfaceModel) + +! call modena_model_argPos_check(viscosityModel) + + + open(14, file='RheologyExact.in') + read(14, * ) temp, shear, conv + close(14) + +! call modena_inputs_set( surfaceInputs, surfaceTempPos, temp ) + +! call modena_inputs_set( viscosityInputs, viscosityTempPos, temp ) +! call modena_inputs_set( viscosityInputs, viscosityConvPos, conv ) +! +! ret = modena_model_call(surfaceModel, surfaceInputs, surfaceOutputs) +! if ( ret /= 0 ) then +! call modena_inputs_destroy( surfaceInputs ) +! call modena_outputs_destroy( surfaceOutputs ) +! call modena_model_destroy( surfaceModel ) +! print*,ret +! call exit(ret) +! end if + +! ret = modena_model_call(viscosityModel, viscosityInputs, viscosityOutputs) +! if ( ret /= 0 ) then +! call modena_inputs_destroy( viscosityInputs ) +! call modena_outputs_destroy( viscosityOutputs ) +! call modena_model_destroy( viscosityModel ) +! print*,ret +! call exit(ret) +! end if + +! surfaceTension = modena_outputs_get(surfaceOutputs, 0_c_size_t); +! polymerViscosity = modena_outputs_get(viscosityOutputs, 0_c_size_t); + + + mu = 1.0 + open(15, file='RheologyExact.out') + write(15,*) mu + close(15) + + +end program rheologyexactdummy diff --git a/applications/PUfoam/MoDeNaModels/Rheology/src_dummy/CMakeLists.txt b/applications/PUfoam/MoDeNaModels/Rheology/src_dummy/CMakeLists.txt new file mode 100644 index 000000000..73ae27452 --- /dev/null +++ b/applications/PUfoam/MoDeNaModels/Rheology/src_dummy/CMakeLists.txt @@ -0,0 +1,20 @@ +cmake_minimum_required (VERSION 2.8) +project (workflowdummy C Fortran) + +if( CMAKE_VERSION VERSION_GREATER "3.0" ) + cmake_policy(SET CMP0042 OLD) + cmake_policy(SET CMP0026 OLD) +endif() + +find_package(MODENA REQUIRED) + +include_directories(${MODENA_INCLUDE_DIRS}) +link_directories(${MODENA_LIBRARY_DIRS}) + + +set (CMAKE_NO_SYSTEM_FROM_IMPORTED yes ) +set (CMAKE_Fortran_FLAGS "-ffree-line-length-none -O3") +set (CMAKE_Fortran_MODULE_DIRECTORY mod) +file (GLOB _sources RELATIVE ${CMAKE_CURRENT_SOURCE_DIR} *.f*) +add_executable(workflowdummy ${_sources}) +target_link_libraries(workflowdummy MODENA::modena) diff --git a/applications/PUfoam/MoDeNaModels/Rheology/src_dummy/workflowdummy.f90 b/applications/PUfoam/MoDeNaModels/Rheology/src_dummy/workflowdummy.f90 new file mode 100644 index 000000000..b7a447b7e --- /dev/null +++ b/applications/PUfoam/MoDeNaModels/Rheology/src_dummy/workflowdummy.f90 @@ -0,0 +1,79 @@ +program workflowdummy + use iso_c_binding + use fmodena +! use tfem_m + implicit none + real(8) :: temp, shear, conv + real(8) :: mu, surfaceTension, Viscosity + integer :: ret + + integer(c_size_t) :: TPos + integer(c_size_t) :: XPos + integer(c_size_t) :: shearPos + type(c_ptr) :: Model, Inputs, Outputs + + Model = modena_model_new (c_char_"Rheology"//c_null_char); + Inputs = modena_inputs_new (Model); + Outputs = modena_outputs_new (Model); + TPos = modena_model_inputs_argPos(Model, & + c_char_"T"//c_null_char); + shearPos = modena_model_inputs_argPos(Model, & + c_char_"shear"//c_null_char); + XPos = modena_model_inputs_argPos(Model, & + c_char_"X"//c_null_char); +! +! viscosityModel = modena_model_new (c_char_"polymerViscosity"//c_null_char); +! viscosityInputs = modena_inputs_new (viscosityModel); +! viscosityOutputs = modena_outputs_new (viscosityModel); +! viscosityTempPos = modena_model_inputs_argPos(viscosityModel, & +! c_char_"T"//c_null_char); +! viscosityConvPos = modena_model_inputs_argPos(viscosityModel, & +! c_char_"X"//c_null_char); + + call modena_model_argPos_check(Model) + +! call modena_model_argPos_check(viscosityModel) + + +! open(14, file='RheologyExact.in') +! read(14, * ) temp, shear, conv +! close(14) + shear =0.5 + temp = 320 + conv = 0.4 + call modena_inputs_set(Inputs, TPos, temp ) + call modena_inputs_set(Inputs, XPos, conv ) + call modena_inputs_set(Inputs, shearPos, shear ) + +! call modena_inputs_set( viscosityInputs, viscosityTempPos, temp ) +! call modena_inputs_set( viscosityInputs, viscosityConvPos, conv ) +! + ret = modena_model_call(Model, Inputs, Outputs) + if ( ret /= 0 ) then + call modena_inputs_destroy( Inputs ) + call modena_outputs_destroy( Outputs ) + call modena_model_destroy( Model ) + print*,ret + call exit(ret) + end if + +! ret = modena_model_call(viscosityModel, viscosityInputs, viscosityOutputs) +! if ( ret /= 0 ) then +! call modena_inputs_destroy( viscosityInputs ) +! call modena_outputs_destroy( viscosityOutputs ) +! call modena_model_destroy( viscosityModel ) +! print*,ret +! call exit(ret) +! end if + + viscosity = modena_outputs_get(Outputs, 0_c_size_t); +! polymerViscosity = modena_outputs_get(viscosityOutputs, 0_c_size_t); + + +! mu = 1.0 +! open(15, file='RheologyExact.out') +! write(15,*) mu +! close(15) + + +end program workflowdummy diff --git a/applications/PUfoam/MoDeNaModels/Rheology/workflow b/applications/PUfoam/MoDeNaModels/Rheology/workflow new file mode 100755 index 000000000..9c5438875 --- /dev/null +++ b/applications/PUfoam/MoDeNaModels/Rheology/workflow @@ -0,0 +1,57 @@ +#!/usr/bin/python +''' + + ooo ooooo oooooooooo. ooooo ooo + `88. .888' `888' `Y8b `888b. `8' + 888b d'888 .ooooo. 888 888 .ooooo. 8 `88b. 8 .oooo. + 8 Y88. .P 888 d88' `88b 888 888 d88' `88b 8 `88b. 8 `P )88b + 8 `888' 888 888 888 888 888 888ooo888 8 `88b.8 .oP"888 + 8 Y 888 888 888 888 d88' 888 .o 8 `888 d8( 888 + o8o o888o `Y8bod8P' o888bood8P' `Y8bod8P' o8o `8 `Y888""8o + +Copyright + 2014-2015 MoDeNa Consortium, All rights reserved. + +License + This file is part of Modena. + + Modena is free software; you can redistribute it and/or modify it under + the terms of the GNU General Public License as published by the Free + Software Foundation, either version 3 of the License, or (at your option) + any later version. + + Modena is distributed in the hope that it will be useful, but WITHOUT ANY + WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS + FOR A PARTICULAR PURPOSE. See the GNU General Public License for more + details. + + You should have received a copy of the GNU General Public License along + with Modena. If not, see . + +Description + A simple workflow + +Authors + Henrik Rusche + +Contributors +''' + +from fireworks import Firework, Workflow, LaunchPad +from fireworks.core.rocket_launcher import rapidfire +import WorkflowTest +from modulefinder import ModuleFinder + + +# set up the LaunchPad and reset it +launchpad = LaunchPad() +launchpad.reset('', require_password=False) + +# create the individual FireWorks and Workflow +# Source code in src/twoTanksMacroscopicProblem.C + +wf = Workflow([Firework(WorkflowTest.m)], {}, name="simulation") + +# store workflow and launch it locally +launchpad.add_wf(wf) +rapidfire(launchpad) diff --git a/applications/PUfoam/MoDeNaModels/Solubility/.gitignore b/applications/PUfoam/MoDeNaModels/Solubility/.gitignore new file mode 100644 index 000000000..d775b3f43 --- /dev/null +++ b/applications/PUfoam/MoDeNaModels/Solubility/.gitignore @@ -0,0 +1 @@ +PCSAFT_Henry diff --git a/applications/PUfoam/MoDeNaModels/Solubility/Description_Solubility.pdf 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